id	sid	tid	token	lemma	pos
cana-5422	1	1	stability	stability	NOUN
cana-5422	1	2	of	of	ADP
cana-5422	1	3	a	a	DET
cana-5422	1	4	affine	affine	ADJ
cana-5422	1	5	type	type	NOUN
cana-5422	1	6	aq	aq	NOUN
cana-5422	1	7	functional	functional	ADJ
cana-5422	1	8	equation	equation	NOUN
cana-5422	1	9	in	in	ADP
cana-5422	1	10	various	various	ADJ
cana-5422	1	11	banach	banach	NOUN
cana-5422	1	12	spaces	space	NOUN
cana-5422	1	13	s.	s.	PROPN
cana-5422	1	14	pinelas1	pinelas1	PROPN
cana-5422	1	15	,	,	PUNCT
cana-5422	1	16	m.	m.	NOUN
cana-5422	1	17	arunkumar2	arunkumar2	PROPN
cana-5422	1	18	,	,	PUNCT
cana-5422	1	19	e.	e.	PROPN
cana-5422	1	20	sathya3	sathya3	PROPN
cana-5422	1	21	,	,	PUNCT
cana-5422	1	22	v.	v.	PROPN
cana-5422	1	23	alexpandiyan4	alexpandiyan4	PROPN
cana-5422	1	24	,	,	PUNCT
cana-5422	1	25	v.	v.	PROPN
cana-5422	1	26	chandiran5	chandiran5	PROPN
cana-5422	1	27	,	,	PUNCT
cana-5422	1	28	t.	t.	NOUN
cana-5422	1	29	velmurugan6	velmurugan6	NOUN
cana-5422	1	30	1departamento	1departamento	NUM
cana-5422	1	31	de	de	X
cana-5422	1	32	ciencias	ciencias	PROPN
cana-5422	1	33	exatas	exatas	PROPN
cana-5422	1	34	e	e	PROPN
cana-5422	1	35	engenharia	engenharia	PROPN
cana-5422	1	36	,	,	PUNCT
cana-5422	1	37	academia	academia	NOUN
cana-5422	1	38	militar	militar	PROPN
cana-5422	1	39	,	,	PUNCT
cana-5422	1	40	av	av	PROPN
cana-5422	1	41	.	.	PUNCT
cana-5422	1	42	conde	conde	PROPN
cana-5422	1	43	castro	castro	PROPN
cana-5422	1	44	guimaraes	guimaraes	PROPN
cana-5422	1	45	,	,	PUNCT
cana-5422	1	46	2720	2720	NUM
cana-5422	1	47	-	-	SYM
cana-5422	1	48	113	113	NUM
cana-5422	1	49	amadora	amadora	PROPN
cana-5422	1	50	,	,	PUNCT
cana-5422	1	51	portugal	portugal	PROPN
cana-5422	1	52	center	center	NOUN
cana-5422	1	53	for	for	ADP
cana-5422	1	54	research	research	NOUN
cana-5422	1	55	and	and	CCONJ
cana-5422	1	56	development	development	NOUN
cana-5422	1	57	in	in	ADP
cana-5422	1	58	mathematics	mathematic	NOUN
cana-5422	1	59	and	and	CCONJ
cana-5422	1	60	applications	application	NOUN
cana-5422	1	61	(	(	PUNCT
cana-5422	1	62	cidma	cidma	NOUN
cana-5422	1	63	)	)	PUNCT
cana-5422	1	64	,	,	PUNCT
cana-5422	1	65	departamento	departamento	PROPN
cana-5422	1	66	de	de	PROPN
cana-5422	1	67	matemtica	matemtica	PROPN
cana-5422	1	68	,	,	PUNCT
cana-5422	1	69	universidade	universidade	PROPN
cana-5422	1	70	de	de	PROPN
cana-5422	1	71	aveiro	aveiro	PROPN
cana-5422	1	72	,	,	PUNCT
cana-5422	1	73	3810	3810	NUM
cana-5422	1	74	-	-	SYM
cana-5422	1	75	193	193	NUM
cana-5422	1	76	aveiro	aveiro	NOUN
cana-5422	1	77	.	.	PUNCT
cana-5422	2	1	e-mail:sandra.pinelas@gmail.com	e-mail:sandra.pinelas@gmail.com	X
cana-5422	2	2	;	;	PUNCT
cana-5422	2	3	2,3,4,5department	2,3,4,5department	NUM
cana-5422	2	4	of	of	ADP
cana-5422	2	5	mathematics	mathematic	NOUN
cana-5422	2	6	,	,	PUNCT
cana-5422	2	7	kalaignar	kalaignar	PROPN
cana-5422	2	8	karunanidhi	karunanidhi	PROPN
cana-5422	2	9	government	government	PROPN
cana-5422	2	10	arts	arts	PROPN
cana-5422	2	11	college	college	PROPN
cana-5422	2	12	,	,	PUNCT
cana-5422	2	13	(	(	PUNCT
cana-5422	2	14	affiliated	affiliate	VERB
cana-5422	2	15	to	to	PART
cana-5422	2	16	thiruvalluvar	thiruvalluvar	VERB
cana-5422	2	17	university	university	PROPN
cana-5422	2	18	)	)	PUNCT
cana-5422	2	19	,	,	PUNCT
cana-5422	2	20	tiruvannamalai	tiruvannamalai	PROPN
cana-5422	2	21	606	606	NUM
cana-5422	2	22	603	603	NUM
cana-5422	2	23	,	,	PUNCT
cana-5422	2	24	tamilnadu	tamilnadu	NOUN
cana-5422	2	25	,	,	PUNCT
cana-5422	2	26	india	india	PROPN
cana-5422	2	27	.	.	PUNCT
cana-5422	3	1	e	e	X
cana-5422	3	2	-	-	NOUN
cana-5422	3	3	mail	mail	NOUN
cana-5422	3	4	:	:	PUNCT
cana-5422	3	5	drarun4maths@gmail.com	drarun4maths@gmail.com	X
cana-5422	3	6	;	;	PUNCT
cana-5422	3	7	sathya24mathematics@gmail.com	sathya24mathematics@gmail.com	NUM
cana-5422	3	8	;	;	PUNCT
cana-5422	3	9	e	e	X
cana-5422	3	10	-	-	NOUN
cana-5422	3	11	mail	mail	NOUN
cana-5422	3	12	:	:	PUNCT
cana-5422	4	1	valexpandiyan98@gmail.com	valexpandiyan98@gmail.com	PROPN
cana-5422	4	2	;	;	PUNCT
cana-5422	4	3	chandhiranphd@gmail.com	chandhiranphd@gmail.com	NOUN
cana-5422	4	4	;	;	PUNCT
cana-5422	4	5	6department	6department	NUM
cana-5422	4	6	of	of	ADP
cana-5422	4	7	mathematics	mathematic	NOUN
cana-5422	4	8	,	,	PUNCT
cana-5422	4	9	mrk	mrk	PROPN
cana-5422	4	10	college	college	PROPN
cana-5422	4	11	of	of	ADP
cana-5422	4	12	arts	art	NOUN
cana-5422	4	13	and	and	CCONJ
cana-5422	4	14	science	science	NOUN
cana-5422	4	15	,	,	PUNCT
cana-5422	4	16	pazhanchanallur	pazhanchanallur	NOUN
cana-5422	4	17	,	,	PUNCT
cana-5422	4	18	kattumannarkoil	kattumannarkoil	NOUN
cana-5422	4	19	608	608	NUM
cana-5422	4	20	301,tamil	301,tamil	NUM
cana-5422	4	21	nadu	nadu	ADJ
cana-5422	4	22	,	,	PUNCT
cana-5422	4	23	india	india	PROPN
cana-5422	4	24	.	.	PUNCT
cana-5422	5	1	f-e-mail:smmuruganvel@gmail.com	f-e-mail:smmuruganvel@gmail.com	PROPN
cana-5422	5	2	1	1	NUM
cana-5422	5	3	.	.	PUNCT
cana-5422	6	1	introduction	introduction	NOUN
cana-5422	6	2	s.m	s.m	PROPN
cana-5422	6	3	.	.	PUNCT
cana-5422	6	4	ulam	ulam	PROPN
cana-5422	6	5	’s	’s	PART
cana-5422	6	6	question	question	NOUN
cana-5422	6	7	[	[	X
cana-5422	6	8	31	31	NUM
cana-5422	6	9	]	]	PUNCT
cana-5422	6	10	in	in	ADP
cana-5422	6	11	1940	1940	NUM
cana-5422	6	12	rewoke	rewoke	VERB
cana-5422	6	13	the	the	DET
cana-5422	6	14	journey	journey	NOUN
cana-5422	6	15	of	of	ADP
cana-5422	6	16	the	the	DET
cana-5422	6	17	research	research	NOUN
cana-5422	6	18	in	in	ADP
cana-5422	6	19	the	the	DET
cana-5422	6	20	stability	stability	NOUN
cana-5422	6	21	theory	theory	NOUN
cana-5422	6	22	of	of	ADP
cana-5422	6	23	functional	functional	ADJ
cana-5422	6	24	equations	equation	NOUN
cana-5422	6	25	.	.	PUNCT
cana-5422	7	1	many	many	ADJ
cana-5422	7	2	mathematicians	mathematician	NOUN
cana-5422	7	3	have	have	AUX
cana-5422	7	4	studied	study	VERB
cana-5422	7	5	and	and	CCONJ
cana-5422	7	6	published	publish	VERB
cana-5422	7	7	several	several	ADJ
cana-5422	7	8	novel	novel	ADJ
cana-5422	7	9	results	result	NOUN
cana-5422	7	10	in	in	ADP
cana-5422	7	11	the	the	DET
cana-5422	7	12	field	field	NOUN
cana-5422	7	13	of	of	ADP
cana-5422	7	14	stability	stability	NOUN
cana-5422	7	15	theory	theory	NOUN
cana-5422	7	16	,	,	PUNCT
cana-5422	7	17	such	such	ADJ
cana-5422	7	18	as	as	ADP
cana-5422	7	19	,	,	PUNCT
cana-5422	7	20	d.h	d.h	PROPN
cana-5422	7	21	.	.	PROPN
cana-5422	7	22	hyers	hyer	NOUN
cana-5422	7	23	(	(	PUNCT
cana-5422	7	24	1941	1941	NUM
cana-5422	7	25	)	)	PUNCT
cana-5422	8	1	[	[	X
cana-5422	8	2	14	14	NUM
cana-5422	8	3	]	]	PUNCT
cana-5422	8	4	,	,	PUNCT
cana-5422	8	5	t.	t.	PROPN
cana-5422	8	6	aoki	aoki	PROPN
cana-5422	8	7	(	(	PUNCT
cana-5422	8	8	1950	1950	NUM
cana-5422	8	9	)	)	PUNCT
cana-5422	9	1	[	[	X
cana-5422	9	2	2	2	NUM
cana-5422	9	3	]	]	PUNCT
cana-5422	9	4	,	,	PUNCT
cana-5422	9	5	th.m	th.m	PROPN
cana-5422	9	6	.	.	PUNCT
cana-5422	10	1	rassias	rassias	PROPN
cana-5422	10	2	(	(	PUNCT
cana-5422	10	3	1978	1978	NUM
cana-5422	10	4	)	)	PUNCT
cana-5422	11	1	[	[	X
cana-5422	11	2	24	24	NUM
cana-5422	11	3	]	]	PUNCT
cana-5422	11	4	,	,	PUNCT
cana-5422	11	5	j.m	j.m	PROPN
cana-5422	11	6	.	.	PROPN
cana-5422	11	7	rassias	rassias	PROPN
cana-5422	11	8	(	(	PUNCT
cana-5422	11	9	1982	1982	NUM
cana-5422	11	10	)	)	PUNCT
cana-5422	12	1	[	[	X
cana-5422	12	2	23	23	NUM
cana-5422	12	3	]	]	PUNCT
cana-5422	12	4	,	,	PUNCT
cana-5422	12	5	p.	p.	NOUN
cana-5422	12	6	gavruta	gavruta	PROPN
cana-5422	12	7	(	(	PUNCT
cana-5422	12	8	1994	1994	NUM
cana-5422	12	9	)	)	PUNCT
cana-5422	13	1	[	[	X
cana-5422	13	2	13	13	NUM
cana-5422	13	3	]	]	PUNCT
cana-5422	13	4	,	,	PUNCT
cana-5422	13	5	and	and	CCONJ
cana-5422	13	6	k.	k.	PROPN
cana-5422	13	7	ravi	ravi	PROPN
cana-5422	13	8	,	,	PUNCT
cana-5422	13	9	m.	m.	PROPN
cana-5422	13	10	arunkumar	arunkumar	PROPN
cana-5422	13	11	,	,	PUNCT
cana-5422	13	12	j.m	j.m	PROPN
cana-5422	13	13	.	.	PROPN
cana-5422	13	14	rassias	rassias	PROPN
cana-5422	13	15	(	(	PUNCT
cana-5422	13	16	2008	2008	NUM
cana-5422	13	17	)	)	PUNCT
cana-5422	14	1	[	[	X
cana-5422	14	2	26	26	NUM
cana-5422	14	3	]	]	PUNCT
cana-5422	14	4	.	.	PUNCT
cana-5422	15	1	famous	famous	ADJ
cana-5422	15	2	functional	functional	ADJ
cana-5422	15	3	equations	equation	NOUN
cana-5422	15	4	for	for	ADP
cana-5422	15	5	additive	additive	ADJ
cana-5422	15	6	and	and	CCONJ
cana-5422	15	7	quadratic	quadratic	ADJ
cana-5422	15	8	functions	function	NOUN
cana-5422	15	9	are	be	AUX
cana-5422	15	10	f	f	X
cana-5422	15	11	(	(	PUNCT
cana-5422	15	12	w1	w1	NOUN
cana-5422	15	13	+	+	SYM
cana-5422	15	14	w2	w2	NOUN
cana-5422	15	15	)	)	PUNCT
cana-5422	16	1	=	=	SYM
cana-5422	16	2	f	f	PROPN
cana-5422	16	3	(	(	PUNCT
cana-5422	16	4	w1	w1	NOUN
cana-5422	16	5	)	)	PUNCT
cana-5422	17	1	+	+	NOUN
cana-5422	17	2	f	f	X
cana-5422	17	3	(	(	PUNCT
cana-5422	17	4	w2	w2	NOUN
cana-5422	17	5	)	)	PUNCT
cana-5422	17	6	,	,	PUNCT
cana-5422	17	7	(	(	PUNCT
cana-5422	17	8	1.1	1.1	NUM
cana-5422	17	9	)	)	PUNCT
cana-5422	17	10	and	and	CCONJ
cana-5422	17	11	f	f	PROPN
cana-5422	17	12	(	(	PUNCT
cana-5422	17	13	w1	w1	NOUN
cana-5422	17	14	+	+	SYM
cana-5422	17	15	w2	w2	NOUN
cana-5422	17	16	)	)	PUNCT
cana-5422	18	1	+	+	NOUN
cana-5422	18	2	f	f	X
cana-5422	18	3	(	(	PUNCT
cana-5422	18	4	w1	w1	NOUN
cana-5422	18	5	−	−	PROPN
cana-5422	18	6	w2	w2	NOUN
cana-5422	18	7	)	)	PUNCT
cana-5422	18	8	=	=	SYM
cana-5422	18	9	2f	2f	NOUN
cana-5422	18	10	(	(	PUNCT
cana-5422	18	11	w1	w1	NOUN
cana-5422	18	12	)	)	PUNCT
cana-5422	18	13	+	+	CCONJ
cana-5422	18	14	2f	2f	NUM
cana-5422	18	15	(	(	PUNCT
cana-5422	18	16	w2	w2	NOUN
cana-5422	18	17	)	)	PUNCT
cana-5422	18	18	.	.	PUNCT
cana-5422	19	1	(	(	PUNCT
cana-5422	19	2	1.2	1.2	NUM
cana-5422	19	3	)	)	PUNCT
cana-5422	19	4	s.m	s.m	PROPN
cana-5422	19	5	.	.	PROPN
cana-5422	19	6	jung	jung	PROPN
cana-5422	20	1	[	[	X
cana-5422	20	2	15	15	NUM
cana-5422	20	3	]	]	PUNCT
cana-5422	20	4	,	,	PUNCT
cana-5422	20	5	pl	pl	PROPN
cana-5422	20	6	.	.	PROPN
cana-5422	20	7	kannappan	kannappan	PROPN
cana-5422	20	8	[	[	PUNCT
cana-5422	20	9	16	16	NUM
cana-5422	20	10	]	]	PUNCT
cana-5422	20	11	,	,	PUNCT
cana-5422	20	12	and	and	CCONJ
cana-5422	20	13	th.m	th.m	PROPN
cana-5422	20	14	.	.	PUNCT
cana-5422	21	1	rassias	rassias	PROPN
cana-5422	22	1	[	[	X
cana-5422	22	2	25	25	NUM
cana-5422	22	3	]	]	PUNCT
cana-5422	22	4	discussed	discuss	VERB
cana-5422	22	5	the	the	DET
cana-5422	22	6	general	general	ADJ
cana-5422	22	7	solution	solution	NOUN
cana-5422	22	8	and	and	CCONJ
cana-5422	22	9	generalized	generalize	VERB
cana-5422	22	10	ulam	ulam	PROPN
cana-5422	22	11	hyers	hyer	NOUN
cana-5422	22	12	stability	stability	NOUN
cana-5422	22	13	of	of	ADP
cana-5422	22	14	different	different	ADJ
cana-5422	22	15	forms	form	NOUN
cana-5422	22	16	of	of	ADP
cana-5422	22	17	functional	functional	ADJ
cana-5422	22	18	equations	equation	NOUN
cana-5422	22	19	in	in	ADP
cana-5422	22	20	various	various	ADJ
cana-5422	22	21	normed	normed	ADJ
cana-5422	22	22	spaces	space	NOUN
cana-5422	22	23	.	.	PUNCT
cana-5422	23	1	in	in	ADP
cana-5422	23	2	fact	fact	NOUN
cana-5422	23	3	,	,	PUNCT
cana-5422	23	4	m.	m.	NOUN
cana-5422	23	5	arunkumar	arunkumar	PROPN
cana-5422	23	6	et	et	PROPN
cana-5422	23	7	.	.	PUNCT
cana-5422	24	1	al	al	PROPN
cana-5422	24	2	.	.	PROPN
cana-5422	24	3	,	,	PUNCT
cana-5422	25	1	[	[	X
cana-5422	25	2	3	3	NUM
cana-5422	25	3	]	]	PUNCT
cana-5422	25	4	,	,	PUNCT
cana-5422	25	5	m.	m.	PROPN
cana-5422	25	6	arunkumar	arunkumar	PROPN
cana-5422	25	7	,	,	PUNCT
cana-5422	25	8	j.m	j.m	PROPN
cana-5422	25	9	.	.	PROPN
cana-5422	25	10	rassis	rassis	NOUN
cana-5422	26	1	[	[	X
cana-5422	26	2	4	4	NUM
cana-5422	26	3	]	]	PUNCT
cana-5422	26	4	,	,	PUNCT
cana-5422	26	5	m.	m.	NOUN
cana-5422	26	6	arunkumar	arunkumar	PROPN
cana-5422	26	7	et	et	PROPN
cana-5422	26	8	.	.	PUNCT
cana-5422	27	1	al	al	PROPN
cana-5422	27	2	.	.	PROPN
cana-5422	27	3	,	,	PUNCT
cana-5422	28	1	[	[	X
cana-5422	28	2	5	5	NUM
cana-5422	28	3	,	,	PUNCT
cana-5422	28	4	6	6	NUM
cana-5422	28	5	]	]	PUNCT
cana-5422	28	6	,	,	PUNCT
cana-5422	28	7	a.	a.	PROPN
cana-5422	28	8	bodaghi	bodaghi	PROPN
cana-5422	29	1	[	[	X
cana-5422	29	2	8	8	NUM
cana-5422	29	3	]	]	PUNCT
cana-5422	29	4	,	,	PUNCT
cana-5422	29	5	and	and	CCONJ
cana-5422	29	6	references	reference	NOUN
cana-5422	29	7	therein	therein	ADV
cana-5422	29	8	establish	establish	VERB
cana-5422	29	9	the	the	DET
cana-5422	29	10	general	general	ADJ
cana-5422	29	11	solution	solution	NOUN
cana-5422	29	12	and	and	CCONJ
cana-5422	29	13	generalized	generalized	ADJ
cana-5422	29	14	hyers	hyer	NOUN
cana-5422	29	15	-	-	PUNCT
cana-5422	29	16	ulam	ulam	PROPN
cana-5422	29	17	stability	stability	NOUN
cana-5422	29	18	of	of	ADP
cana-5422	29	19	the	the	DET
cana-5422	29	20	several	several	ADJ
cana-5422	29	21	aq	aq	ADJ
cana-5422	29	22	functional	functional	ADJ
cana-5422	29	23	equations	equation	NOUN
cana-5422	29	24	.	.	PUNCT
cana-5422	30	1	2010	2010	NUM
cana-5422	30	2	mathematics	mathematic	NOUN
cana-5422	30	3	subject	subject	NOUN
cana-5422	30	4	classification	classification	NOUN
cana-5422	30	5	.	.	PUNCT
cana-5422	31	1	:	:	PUNCT
cana-5422	31	2	39b52	39b52	NUM
cana-5422	31	3	,	,	PUNCT
cana-5422	31	4	32b72	32b72	NUM
cana-5422	31	5	,	,	PUNCT
cana-5422	31	6	32b82	32b82	NUM
cana-5422	31	7	.	.	PUNCT
cana-5422	32	1	key	key	ADJ
cana-5422	32	2	words	word	NOUN
cana-5422	32	3	and	and	CCONJ
cana-5422	32	4	phrases	phrase	NOUN
cana-5422	32	5	.	.	PUNCT
cana-5422	33	1	:	:	PUNCT
cana-5422	33	2	mixed	mixed	ADJ
cana-5422	33	3	functional	functional	ADJ
cana-5422	33	4	equations	equation	NOUN
cana-5422	33	5	,	,	PUNCT
cana-5422	33	6	generalized	generalize	VERB
cana-5422	33	7	ulam	ulam	PROPN
cana-5422	33	8	hyers	hyer	NOUN
cana-5422	33	9	stability	stability	NOUN
cana-5422	33	10	,	,	PUNCT
cana-5422	33	11	direct	direct	ADJ
cana-5422	33	12	method	method	NOUN
cana-5422	33	13	,	,	PUNCT
cana-5422	33	14	fixed	fix	VERB
cana-5422	33	15	method	method	NOUN
cana-5422	33	16	,	,	PUNCT
cana-5422	33	17	banach	banach	NOUN
cana-5422	33	18	space	space	NOUN
cana-5422	33	19	,	,	PUNCT
cana-5422	33	20	intuitionistic	intuitionistic	ADJ
cana-5422	33	21	fuzzy	fuzzy	ADJ
cana-5422	33	22	banach	banach	NOUN
cana-5422	33	23	space	space	NOUN
cana-5422	33	24	.	.	PUNCT
cana-5422	34	1	communications	communication	NOUN
cana-5422	34	2	on	on	ADP
cana-5422	34	3	applied	apply	VERB
cana-5422	34	4	nonlinear	nonlinear	ADJ
cana-5422	34	5	analysis	analysis	NOUN
cana-5422	34	6	issn	issn	NOUN
cana-5422	34	7	:	:	PUNCT
cana-5422	34	8	1074	1074	NUM
cana-5422	34	9	-	-	PUNCT
cana-5422	34	10	133x	133x	NUM
cana-5422	34	11	vol	vol	NOUN
cana-5422	34	12	32	32	NUM
cana-5422	34	13	no	no	NOUN
cana-5422	34	14	.	.	PUNCT
cana-5422	35	1	10s(2025	10s(2025	NUM
cana-5422	35	2	)	)	PUNCT
cana-5422	36	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	36	2	2186	2186	NUM
cana-5422	36	3	abstract	abstract	NOUN
cana-5422	36	4	.	.	PUNCT
cana-5422	37	1	in	in	ADP
cana-5422	37	2	this	this	DET
cana-5422	37	3	article	article	NOUN
cana-5422	37	4	,	,	PUNCT
cana-5422	37	5	a	a	DET
cana-5422	37	6	new	new	ADJ
cana-5422	37	7	affine	affine	NOUN
cana-5422	37	8	type	type	NOUN
cana-5422	37	9	aq	aq	ADP
cana-5422	37	10	functional	functional	ADJ
cana-5422	37	11	equations	equation	NOUN
cana-5422	37	12	is	be	AUX
cana-5422	37	13	proposed	propose	VERB
cana-5422	37	14	.	.	PUNCT
cana-5422	38	1	the	the	DET
cana-5422	38	2	generalized	generalize	VERB
cana-5422	38	3	ulam	ulam	NOUN
cana-5422	38	4	-	-	PUNCT
cana-5422	38	5	hyers	hyer	NOUN
cana-5422	38	6	stability	stability	NOUN
cana-5422	38	7	of	of	ADP
cana-5422	38	8	this	this	DET
cana-5422	38	9	equations	equation	NOUN
cana-5422	38	10	is	be	AUX
cana-5422	38	11	analyzed	analyze	VERB
cana-5422	38	12	using	use	VERB
cana-5422	38	13	the	the	DET
cana-5422	38	14	product	product	NOUN
cana-5422	38	15	,	,	PUNCT
cana-5422	38	16	sum	sum	NOUN
cana-5422	38	17	,	,	PUNCT
cana-5422	38	18	and	and	CCONJ
cana-5422	38	19	mixed	mixed	ADJ
cana-5422	38	20	product	product	NOUN
cana-5422	38	21	-	-	PUNCT
cana-5422	38	22	sum	sum	NOUN
cana-5422	38	23	of	of	ADP
cana-5422	38	24	powers	power	NOUN
cana-5422	38	25	of	of	ADP
cana-5422	38	26	norms	norm	NOUN
cana-5422	38	27	,	,	PUNCT
cana-5422	38	28	as	as	ADV
cana-5422	38	29	well	well	ADV
cana-5422	38	30	as	as	ADP
cana-5422	38	31	the	the	DET
cana-5422	38	32	general	general	ADJ
cana-5422	38	33	control	control	NOUN
cana-5422	38	34	function	function	NOUN
cana-5422	38	35	.	.	PUNCT
cana-5422	39	1	the	the	DET
cana-5422	39	2	stability	stability	NOUN
cana-5422	39	3	analysis	analysis	NOUN
cana-5422	39	4	is	be	AUX
cana-5422	39	5	carried	carry	VERB
cana-5422	39	6	out	out	ADP
cana-5422	39	7	in	in	ADP
cana-5422	39	8	banach	banach	NOUN
cana-5422	39	9	space	space	NOUN
cana-5422	39	10	and	and	CCONJ
cana-5422	39	11	intu	intu	NOUN
cana-5422	39	12	-	-	PUNCT
cana-5422	39	13	itionistic	itionistic	ADJ
cana-5422	39	14	fuzzy	fuzzy	ADJ
cana-5422	39	15	banach	banach	NOUN
cana-5422	39	16	spaces	space	NOUN
cana-5422	39	17	using	use	VERB
cana-5422	39	18	hyers	hyer	NOUN
cana-5422	39	19	direct	direct	ADJ
cana-5422	39	20	method	method	NOUN
cana-5422	39	21	.	.	PUNCT
cana-5422	40	1	also	also	ADV
cana-5422	40	2	,	,	PUNCT
cana-5422	40	3	we	we	PRON
cana-5422	40	4	examine	examine	VERB
cana-5422	40	5	the	the	DET
cana-5422	40	6	stability	stability	NOUN
cana-5422	40	7	of	of	ADP
cana-5422	40	8	same	same	ADJ
cana-5422	40	9	functional	functional	ADJ
cana-5422	40	10	equation	equation	NOUN
cana-5422	40	11	by	by	ADP
cana-5422	40	12	using	use	VERB
cana-5422	40	13	radus	radus	NOUN
cana-5422	40	14	fixed	fix	VERB
cana-5422	40	15	point	point	NOUN
cana-5422	40	16	method	method	NOUN
cana-5422	40	17	in	in	ADP
cana-5422	40	18	both	both	CCONJ
cana-5422	40	19	the	the	DET
cana-5422	40	20	spaces	space	NOUN
cana-5422	40	21	.	.	PUNCT
cana-5422	41	1	article	article	NOUN
cana-5422	41	2	history	history	NOUN
cana-5422	41	3	:	:	PUNCT
cana-5422	41	4	received	receive	VERB
cana-5422	41	5	:	:	PUNCT
cana-5422	41	6	14	14	NUM
cana-5422	41	7	-	-	SYM
cana-5422	41	8	01	01	NUM
cana-5422	41	9	-	-	PUNCT
cana-5422	41	10	2025	2025	NUM
cana-5422	41	11	revised	revise	VERB
cana-5422	41	12	:	:	PUNCT
cana-5422	41	13	16	16	NUM
cana-5422	41	14	-	-	PUNCT
cana-5422	41	15	02	02	NUM
cana-5422	41	16	-	-	PUNCT
cana-5422	41	17	2025	2025	NUM
cana-5422	41	18	accepted	accept	VERB
cana-5422	41	19	:	:	PUNCT
cana-5422	41	20	05	05	NUM
cana-5422	41	21	-	-	SYM
cana-5422	41	22	03	03	NUM
cana-5422	41	23	-	-	PUNCT
cana-5422	41	24	2025	2025	NUM
cana-5422	41	25	l.	l.	NOUN
cana-5422	41	26	lucht	lucht	PROPN
cana-5422	41	27	,	,	PUNCT
cana-5422	41	28	c.	c.	PROPN
cana-5422	41	29	methfessel	methfessel	NOUN
cana-5422	42	1	[	[	X
cana-5422	42	2	17	17	NUM
cana-5422	42	3	]	]	PUNCT
cana-5422	42	4	proposed	propose	VERB
cana-5422	42	5	affine	affine	ADJ
cana-5422	42	6	functional	functional	ADJ
cana-5422	42	7	equations	equation	NOUN
cana-5422	42	8	and	and	CCONJ
cana-5422	42	9	recurrent	recurrent	ADJ
cana-5422	42	10	sequences	sequence	NOUN
cana-5422	42	11	in	in	ADP
cana-5422	42	12	1993	1993	NUM
cana-5422	42	13	.	.	PUNCT
cana-5422	43	1	additionally	additionally	ADV
cana-5422	43	2	,	,	PUNCT
cana-5422	43	3	in	in	ADP
cana-5422	43	4	2013	2013	NUM
cana-5422	43	5	,	,	PUNCT
cana-5422	43	6	l.	l.	PROPN
cana-5422	43	7	cadariu	cadariu	PROPN
cana-5422	43	8	,	,	PUNCT
cana-5422	43	9	l.	l.	PROPN
cana-5422	43	10	gavruta	gavruta	PROPN
cana-5422	43	11	,	,	PUNCT
cana-5422	43	12	and	and	CCONJ
cana-5422	43	13	p.	p.	NOUN
cana-5422	43	14	gavruta	gavruta	NOUN
cana-5422	44	1	[	[	X
cana-5422	44	2	11	11	NUM
cana-5422	44	3	]	]	PUNCT
cana-5422	44	4	demonstrated	demonstrate	VERB
cana-5422	44	5	the	the	DET
cana-5422	44	6	generalized	generalized	ADJ
cana-5422	44	7	hyersulam	hyersulam	NOUN
cana-5422	44	8	stability	stability	NOUN
cana-5422	44	9	and	and	CCONJ
cana-5422	44	10	obtained	obtain	VERB
cana-5422	44	11	the	the	DET
cana-5422	44	12	general	general	ADJ
cana-5422	44	13	solution	solution	NOUN
cana-5422	44	14	for	for	ADP
cana-5422	44	15	an	an	DET
cana-5422	44	16	affine	affine	ADJ
cana-5422	44	17	functional	functional	ADJ
cana-5422	44	18	equation	equation	NOUN
cana-5422	44	19	of	of	ADP
cana-5422	44	20	the	the	DET
cana-5422	44	21	form	form	NOUN
cana-5422	44	22	f	f	PROPN
cana-5422	44	23	(	(	PUNCT
cana-5422	44	24	2x	2x	NUM
cana-5422	44	25	+	+	CCONJ
cana-5422	44	26	y	y	X
cana-5422	44	27	)	)	PUNCT
cana-5422	45	1	+	+	NOUN
cana-5422	45	2	f	f	X
cana-5422	45	3	(	(	PUNCT
cana-5422	45	4	x	x	X
cana-5422	45	5	+	+	PUNCT
cana-5422	45	6	2y	2y	NUM
cana-5422	45	7	)	)	PUNCT
cana-5422	46	1	+	+	CCONJ
cana-5422	46	2	f	f	X
cana-5422	46	3	(	(	PUNCT
cana-5422	46	4	x	x	X
cana-5422	46	5	)	)	PUNCT
cana-5422	47	1	+	+	NUM
cana-5422	47	2	f	f	X
cana-5422	47	3	(	(	PUNCT
cana-5422	47	4	y	y	NOUN
cana-5422	47	5	)	)	PUNCT
cana-5422	47	6	=	=	SYM
cana-5422	47	7	4	4	NUM
cana-5422	47	8	f	f	X
cana-5422	47	9	(	(	PUNCT
cana-5422	47	10	x	x	PROPN
cana-5422	47	11	+	+	NUM
cana-5422	47	12	y	y	PROPN
cana-5422	47	13	+	+	PROPN
cana-5422	47	14	z	z	NOUN
cana-5422	47	15	)	)	PUNCT
cana-5422	47	16	(	(	PUNCT
cana-5422	47	17	1.3	1.3	NUM
cana-5422	47	18	)	)	PUNCT
cana-5422	47	19	by	by	ADP
cana-5422	47	20	using	use	VERB
cana-5422	47	21	the	the	DET
cana-5422	47	22	direct	direct	ADJ
cana-5422	47	23	method	method	NOUN
cana-5422	47	24	as	as	ADV
cana-5422	47	25	well	well	ADV
cana-5422	47	26	as	as	ADP
cana-5422	47	27	the	the	DET
cana-5422	47	28	fixed	fix	VERB
cana-5422	47	29	point	point	NOUN
cana-5422	47	30	method	method	NOUN
cana-5422	47	31	.	.	PUNCT
cana-5422	48	1	infact	infact	PROPN
cana-5422	48	2	,	,	PUNCT
cana-5422	48	3	in	in	ADP
cana-5422	48	4	2014	2014	NUM
cana-5422	48	5	,	,	PUNCT
cana-5422	48	6	m.	m.	NOUN
cana-5422	48	7	mursaleen	mursaleen	PROPN
cana-5422	48	8	,	,	PUNCT
cana-5422	48	9	kj	kj	PROPN
cana-5422	48	10	.	.	PUNCT
cana-5422	48	11	ansari	ansari	PROPN
cana-5422	49	1	[	[	X
cana-5422	49	2	19	19	NUM
cana-5422	49	3	]	]	PUNCT
cana-5422	49	4	considered	consider	VERB
cana-5422	49	5	the	the	DET
cana-5422	49	6	following	follow	VERB
cana-5422	49	7	affine	affine	ADJ
cana-5422	49	8	functional	functional	ADJ
cana-5422	49	9	equation	equation	NOUN
cana-5422	49	10	f	f	PROPN
cana-5422	49	11	(	(	PUNCT
cana-5422	49	12	3x	3x	PROPN
cana-5422	49	13	+	+	CCONJ
cana-5422	49	14	y	y	PROPN
cana-5422	49	15	+	+	PROPN
cana-5422	49	16	z	z	NOUN
cana-5422	49	17	)	)	PUNCT
cana-5422	50	1	+	+	NOUN
cana-5422	50	2	f	f	X
cana-5422	50	3	(	(	PUNCT
cana-5422	50	4	x	x	SYM
cana-5422	50	5	+	+	NUM
cana-5422	50	6	3y	3y	NUM
cana-5422	50	7	+	+	X
cana-5422	50	8	z	z	X
cana-5422	50	9	)	)	PUNCT
cana-5422	51	1	+	+	NOUN
cana-5422	51	2	f	f	X
cana-5422	51	3	(	(	PUNCT
cana-5422	51	4	x	x	PROPN
cana-5422	51	5	+	+	NUM
cana-5422	51	6	y	y	PROPN
cana-5422	51	7	+	+	CCONJ
cana-5422	51	8	3z	3z	NUM
cana-5422	51	9	)	)	PUNCT
cana-5422	52	1	+	+	CCONJ
cana-5422	52	2	f	f	X
cana-5422	52	3	(	(	PUNCT
cana-5422	52	4	x	x	X
cana-5422	52	5	)	)	PUNCT
cana-5422	53	1	+	+	NUM
cana-5422	53	2	f	f	X
cana-5422	53	3	(	(	PUNCT
cana-5422	53	4	y	y	NOUN
cana-5422	53	5	)	)	PUNCT
cana-5422	54	1	+	+	NOUN
cana-5422	54	2	f	f	X
cana-5422	54	3	(	(	PUNCT
cana-5422	54	4	z	z	NOUN
cana-5422	54	5	)	)	PUNCT
cana-5422	54	6	=	=	PUNCT
cana-5422	54	7	6	6	NUM
cana-5422	54	8	f	f	X
cana-5422	54	9	(	(	PUNCT
cana-5422	54	10	x	x	PROPN
cana-5422	54	11	+	+	NUM
cana-5422	54	12	y	y	PROPN
cana-5422	54	13	+	+	PROPN
cana-5422	54	14	z	z	NOUN
cana-5422	54	15	)	)	PUNCT
cana-5422	54	16	(	(	PUNCT
cana-5422	54	17	1.4	1.4	NUM
cana-5422	54	18	)	)	PUNCT
cana-5422	54	19	and	and	CCONJ
cana-5422	54	20	find	find	VERB
cana-5422	54	21	its	its	PRON
cana-5422	54	22	general	general	ADJ
cana-5422	54	23	solution	solution	NOUN
cana-5422	54	24	and	and	CCONJ
cana-5422	54	25	proved	prove	VERB
cana-5422	54	26	some	some	DET
cana-5422	54	27	stability	stability	NOUN
cana-5422	54	28	results	result	NOUN
cana-5422	54	29	by	by	ADP
cana-5422	54	30	using	use	VERB
cana-5422	54	31	direct	direct	ADJ
cana-5422	54	32	method	method	NOUN
cana-5422	54	33	as	as	ADV
cana-5422	54	34	well	well	ADV
cana-5422	54	35	as	as	ADP
cana-5422	54	36	the	the	DET
cana-5422	54	37	fixed	fix	VERB
cana-5422	54	38	point	point	NOUN
cana-5422	54	39	method	method	NOUN
cana-5422	54	40	.	.	PUNCT
cana-5422	55	1	also	also	ADV
cana-5422	55	2	in	in	ADP
cana-5422	55	3	2015	2015	NUM
cana-5422	55	4	,	,	PUNCT
cana-5422	55	5	md	md	PROPN
cana-5422	55	6	.	.	PROPN
cana-5422	55	7	nasiruzzaman	nasiruzzaman	PROPN
cana-5422	56	1	[	[	X
cana-5422	56	2	21	21	NUM
cana-5422	56	3	]	]	PUNCT
cana-5422	56	4	provide	provide	VERB
cana-5422	56	5	the	the	DET
cana-5422	56	6	fuzzy	fuzzy	ADJ
cana-5422	56	7	version	version	NOUN
cana-5422	56	8	hyers	hyer	NOUN
cana-5422	56	9	-	-	PUNCT
cana-5422	56	10	ulamrassias	ulamrassias	ADJ
cana-5422	56	11	stability	stability	NOUN
cana-5422	56	12	of	of	ADP
cana-5422	56	13	(	(	PUNCT
cana-5422	56	14	1.4	1.4	NUM
cana-5422	56	15	)	)	PUNCT
cana-5422	56	16	.	.	PUNCT
cana-5422	57	1	further	far	ADV
cana-5422	57	2	,	,	PUNCT
cana-5422	57	3	in	in	ADP
cana-5422	57	4	2016	2016	NUM
cana-5422	57	5	m.	m.	NOUN
cana-5422	57	6	mursaleen	mursaleen	PROPN
cana-5422	57	7	,	,	PUNCT
cana-5422	57	8	kj	kj	PROPN
cana-5422	57	9	.	.	PUNCT
cana-5422	57	10	ansari[20	ansari[20	PROPN
cana-5422	57	11	]	]	PUNCT
cana-5422	57	12	prove	prove	VERB
cana-5422	57	13	the	the	DET
cana-5422	57	14	general	general	ADJ
cana-5422	57	15	solution	solution	NOUN
cana-5422	57	16	of	of	ADP
cana-5422	57	17	the	the	DET
cana-5422	57	18	following	follow	VERB
cana-5422	57	19	affine	affine	ADJ
cana-5422	57	20	functional	functional	ADJ
cana-5422	57	21	equation	equation	NOUN
cana-5422	57	22	f	f	PROPN
cana-5422	57	23	(	(	PUNCT
cana-5422	57	24	kx1	kx1	X
cana-5422	57	25	+	+	CCONJ
cana-5422	57	26	x2	x2	PROPN
cana-5422	58	1	+	+	CCONJ
cana-5422	59	1	·	·	PUNCT
cana-5422	59	2	·	·	PUNCT
cana-5422	59	3	·	·	PUNCT
cana-5422	59	4	+	+	NUM
cana-5422	59	5	xk	xk	NOUN
cana-5422	59	6	)	)	PUNCT
cana-5422	59	7	+	+	NUM
cana-5422	60	1	f	f	X
cana-5422	60	2	(	(	PUNCT
cana-5422	60	3	x1	x1	PROPN
cana-5422	60	4	+	+	NUM
cana-5422	60	5	kx2	kx2	X
cana-5422	60	6	+	+	X
cana-5422	60	7	·	·	PUNCT
cana-5422	60	8	·	·	PUNCT
cana-5422	60	9	·	·	PUNCT
cana-5422	60	10	+	+	NUM
cana-5422	60	11	xk	xk	NOUN
cana-5422	60	12	)	)	PUNCT
cana-5422	60	13	+	+	CCONJ
cana-5422	60	14	·	·	PUNCT
cana-5422	60	15	·	·	PUNCT
cana-5422	60	16	·	·	PUNCT
cana-5422	61	1	+	+	NUM
cana-5422	61	2	f	f	X
cana-5422	61	3	(	(	PUNCT
cana-5422	61	4	x1	x1	PROPN
cana-5422	61	5	+	+	NUM
cana-5422	61	6	x2	x2	PROPN
cana-5422	61	7	+	+	CCONJ
cana-5422	61	8	·	·	PUNCT
cana-5422	61	9	·	·	PUNCT
cana-5422	61	10	·	·	PUNCT
cana-5422	61	11	+	+	NUM
cana-5422	61	12	kxk	kxk	NOUN
cana-5422	61	13	)	)	PUNCT
cana-5422	62	1	+	+	NUM
cana-5422	62	2	f	f	X
cana-5422	62	3	(	(	PUNCT
cana-5422	62	4	x1	x1	PROPN
cana-5422	62	5	)	)	PUNCT
cana-5422	63	1	+	+	NUM
cana-5422	63	2	f	f	X
cana-5422	63	3	(	(	PUNCT
cana-5422	63	4	x2	x2	PROPN
cana-5422	63	5	)	)	PUNCT
cana-5422	63	6	+	+	CCONJ
cana-5422	63	7	·	·	PUNCT
cana-5422	63	8	·	·	PUNCT
cana-5422	63	9	·	·	PUNCT
cana-5422	64	1	+	+	NUM
cana-5422	64	2	f	f	X
cana-5422	64	3	(	(	PUNCT
cana-5422	64	4	xk	xk	PROPN
cana-5422	64	5	)	)	PUNCT
cana-5422	64	6	=	=	SYM
cana-5422	65	1	2k	2k	NUM
cana-5422	65	2	f	f	X
cana-5422	65	3	(	(	PUNCT
cana-5422	65	4	x1	x1	PROPN
cana-5422	65	5	+	+	NUM
cana-5422	65	6	x2	x2	PROPN
cana-5422	65	7	+	+	CCONJ
cana-5422	65	8	·	·	PUNCT
cana-5422	65	9	·	·	PUNCT
cana-5422	65	10	·	·	PUNCT
cana-5422	65	11	+	+	NUM
cana-5422	65	12	xk	xk	NOUN
cana-5422	65	13	)	)	PUNCT
cana-5422	65	14	,	,	PUNCT
cana-5422	65	15	k	k	PROPN
cana-5422	65	16	≥	≥	NUM
cana-5422	65	17	2	2	NUM
cana-5422	65	18	.	.	PUNCT
cana-5422	65	19	(	(	PUNCT
cana-5422	65	20	1.5	1.5	NUM
cana-5422	65	21	)	)	PUNCT
cana-5422	65	22	and	and	CCONJ
cana-5422	65	23	established	establish	VERB
cana-5422	65	24	the	the	DET
cana-5422	65	25	hyers	hyers	PROPN
cana-5422	65	26	-	-	PUNCT
cana-5422	65	27	ulam	ulam	ADJ
cana-5422	65	28	-	-	PUNCT
cana-5422	65	29	rassias	rassias	PROPN
cana-5422	65	30	stability	stability	NOUN
cana-5422	65	31	of	of	ADP
cana-5422	65	32	the	the	DET
cana-5422	65	33	above	above	ADJ
cana-5422	65	34	functional	functional	ADJ
cana-5422	65	35	equation	equation	NOUN
cana-5422	65	36	in	in	ADP
cana-5422	65	37	the	the	DET
cana-5422	65	38	fuzzy	fuzzy	ADJ
cana-5422	65	39	normed	norme	VERB
cana-5422	65	40	spaces	space	NOUN
cana-5422	65	41	which	which	PRON
cana-5422	65	42	as	as	ADP
cana-5422	65	43	an	an	DET
cana-5422	65	44	generalized	generalized	ADJ
cana-5422	65	45	version	version	NOUN
cana-5422	65	46	of	of	ADP
cana-5422	65	47	(	(	PUNCT
cana-5422	65	48	1.4	1.4	NUM
cana-5422	65	49	)	)	PUNCT
cana-5422	65	50	.	.	PUNCT
cana-5422	66	1	recently	recently	ADV
cana-5422	66	2	,	,	PUNCT
cana-5422	66	3	c.	c.	PROPN
cana-5422	66	4	benzarouala	benzarouala	PROPN
cana-5422	66	5	et.al	et.al	PROPN
cana-5422	66	6	.	.	PUNCT
cana-5422	66	7	,	,	PUNCT
cana-5422	67	1	[	[	X
cana-5422	67	2	9	9	NUM
cana-5422	67	3	,	,	PUNCT
cana-5422	67	4	10	10	NUM
cana-5422	67	5	]	]	PUNCT
cana-5422	67	6	proved	prove	VERB
cana-5422	67	7	the	the	DET
cana-5422	67	8	general	general	ADJ
cana-5422	67	9	ulam	ulam	PROPN
cana-5422	67	10	stability	stability	PROPN
cana-5422	67	11	result	result	VERB
cana-5422	67	12	for	for	ADP
cana-5422	67	13	the	the	DET
cana-5422	67	14	functional	functional	ADJ
cana-5422	67	15	equation	equation	NOUN
cana-5422	67	16	m	m	VERB
cana-5422	67	17	∑	∑	PROPN
cana-5422	67	18	i=1	i=1	PROPN
cana-5422	67	19	ai	ai	INTJ
cana-5422	67	20	f	f	PROPN
cana-5422	67	21	(	(	PUNCT
cana-5422	67	22	n	n	CCONJ
cana-5422	67	23	∑	∑	ADV
cana-5422	67	24	j=1	j=1	ADJ
cana-5422	67	25	aijxj	aijxj	NOUN
cana-5422	67	26	)	)	PUNCT
cana-5422	68	1	=	=	SYM
cana-5422	68	2	d(x1	d(x1	NOUN
cana-5422	68	3	,	,	PUNCT
cana-5422	68	4	·	·	PUNCT
cana-5422	68	5	·	·	PUNCT
cana-5422	68	6	·	·	PUNCT
cana-5422	68	7	,	,	PUNCT
cana-5422	68	8	xn	xn	PROPN
cana-5422	68	9	)	)	PUNCT
cana-5422	68	10	,	,	PUNCT
cana-5422	68	11	(	(	PUNCT
cana-5422	68	12	1.6	1.6	NUM
cana-5422	68	13	)	)	PUNCT
cana-5422	68	14	in	in	ADP
cana-5422	68	15	the	the	DET
cana-5422	68	16	class	class	NOUN
cana-5422	68	17	of	of	ADP
cana-5422	68	18	functions	function	NOUN
cana-5422	68	19	f	f	PROPN
cana-5422	68	20	mapping	map	VERB
cana-5422	68	21	a	a	DET
cana-5422	68	22	module	module	NOUN
cana-5422	68	23	x	x	NOUN
cana-5422	68	24	,	,	PUNCT
cana-5422	68	25	over	over	ADP
cana-5422	68	26	a	a	DET
cana-5422	68	27	commutative	commutative	ADJ
cana-5422	68	28	ring	ring	NOUN
cana-5422	68	29	k	k	PROPN
cana-5422	68	30	,	,	PUNCT
cana-5422	68	31	into	into	ADP
cana-5422	68	32	a	a	DET
cana-5422	68	33	banach	banach	NOUN
cana-5422	68	34	space	space	NOUN
cana-5422	68	35	y	y	NOUN
cana-5422	68	36	,	,	PUNCT
cana-5422	68	37	where	where	SCONJ
cana-5422	68	38	m	m	VERB
cana-5422	68	39	and	and	CCONJ
cana-5422	68	40	n	n	PRON
cana-5422	68	41	are	be	AUX
cana-5422	68	42	fixed	fix	VERB
cana-5422	68	43	positive	positive	ADJ
cana-5422	68	44	integers	integer	NOUN
cana-5422	68	45	,	,	PUNCT
cana-5422	68	46	aij	aij	PROPN
cana-5422	68	47	∈	∈	PROPN
cana-5422	68	48	k	k	PROPN
cana-5422	68	49	for	for	ADP
cana-5422	68	50	every	every	DET
cana-5422	68	51	i	i	PROPN
cana-5422	68	52	∈	∈	PROPN
cana-5422	68	53	{	{	PUNCT
cana-5422	68	54	1	1	NUM
cana-5422	68	55	,	,	PUNCT
cana-5422	68	56	·	·	PUNCT
cana-5422	68	57	·	·	PUNCT
cana-5422	68	58	·	·	PUNCT
cana-5422	68	59	,	,	PUNCT
cana-5422	68	60	m	m	VERB
cana-5422	68	61	}	}	PUNCT
cana-5422	68	62	and	and	CCONJ
cana-5422	68	63	j	j	PROPN
cana-5422	68	64	∈	∈	PROPN
cana-5422	68	65	{	{	PUNCT
cana-5422	68	66	1	1	NUM
cana-5422	68	67	,	,	PUNCT
cana-5422	68	68	·	·	PUNCT
cana-5422	68	69	·	·	PUNCT
cana-5422	68	70	·	·	PUNCT
cana-5422	68	71	n	n	CCONJ
cana-5422	68	72	}	}	PUNCT
cana-5422	68	73	,	,	PUNCT
cana-5422	68	74	a1	a1	PROPN
cana-5422	68	75	,	,	PUNCT
cana-5422	68	76	·	·	PUNCT
cana-5422	68	77	·	·	PUNCT
cana-5422	68	78	·	·	PUNCT
cana-5422	68	79	,	,	PUNCT
cana-5422	68	80	am	be	AUX
cana-5422	68	81	are	be	AUX
cana-5422	68	82	scalars	scalar	NOUN
cana-5422	68	83	,	,	PUNCT
cana-5422	68	84	and	and	CCONJ
cana-5422	68	85	the	the	DET
cana-5422	68	86	function	function	NOUN
cana-5422	68	87	d	d	NOUN
cana-5422	68	88	:	:	PUNCT
cana-5422	68	89	xn	xn	PROPN
cana-5422	68	90	→	→	SYM
cana-5422	68	91	y	y	PROPN
cana-5422	68	92	is	be	AUX
cana-5422	68	93	fixed	fix	VERB
cana-5422	68	94	.	.	PUNCT
cana-5422	69	1	numerous	numerous	ADJ
cana-5422	69	2	important	important	ADJ
cana-5422	69	3	functional	functional	ADJ
cana-5422	69	4	equations	equation	NOUN
cana-5422	69	5	are	be	AUX
cana-5422	69	6	particular	particular	ADJ
cana-5422	69	7	cases	case	NOUN
cana-5422	69	8	of	of	ADP
cana-5422	69	9	a′is	a′is	NOUN
cana-5422	69	10	the	the	DET
cana-5422	69	11	homogeneous	homogeneous	ADJ
cana-5422	69	12	version	version	NOUN
cana-5422	69	13	of	of	ADP
cana-5422	69	14	(	(	PUNCT
cana-5422	69	15	1.6	1.6	NUM
cana-5422	69	16	)	)	PUNCT
cana-5422	69	17	are	be	AUX
cana-5422	69	18	cauchy	cauchy	PROPN
cana-5422	69	19	,	,	PUNCT
cana-5422	69	20	jensen	jensen	PROPN
cana-5422	69	21	,	,	PUNCT
cana-5422	69	22	jordanvon	jordanvon	PROPN
cana-5422	69	23	neumann	neumann	PROPN
cana-5422	69	24	,	,	PUNCT
cana-5422	69	25	drygas	drygas	PROPN
cana-5422	69	26	,	,	PUNCT
cana-5422	69	27	frechet	frechet	NOUN
cana-5422	69	28	,	,	PUNCT
cana-5422	69	29	popoviciu	popoviciu	PROPN
cana-5422	69	30	,	,	PUNCT
cana-5422	69	31	wright	wright	PROPN
cana-5422	69	32	and	and	CCONJ
cana-5422	69	33	many	many	ADJ
cana-5422	69	34	others	other	NOUN
cana-5422	69	35	.	.	PUNCT
cana-5422	70	1	also	also	ADV
cana-5422	70	2	,	,	PUNCT
cana-5422	70	3	for	for	ADP
cana-5422	70	4	particular	particular	ADJ
cana-5422	70	5	cases	case	NOUN
cana-5422	70	6	of	of	ADP
cana-5422	70	7	a′is	a′is	NOUN
cana-5422	70	8	in	in	ADP
cana-5422	70	9	(	(	PUNCT
cana-5422	70	10	1.6	1.6	NUM
cana-5422	70	11	)	)	PUNCT
cana-5422	70	12	,	,	PUNCT
cana-5422	70	13	we	we	PRON
cana-5422	70	14	get	get	VERB
cana-5422	70	15	functional	functional	ADJ
cana-5422	70	16	equations	equation	NOUN
cana-5422	70	17	,	,	PUNCT
cana-5422	70	18	like	like	ADP
cana-5422	70	19	equation	equation	NOUN
cana-5422	70	20	in	in	ADP
cana-5422	70	21	a	a	DET
cana-5422	70	22	single	single	ADJ
cana-5422	70	23	variable	variable	NOUN
cana-5422	70	24	,	,	PUNCT
cana-5422	70	25	cohomological	cohomological	ADJ
cana-5422	70	26	equation	equation	NOUN
cana-5422	70	27	,	,	PUNCT
cana-5422	70	28	schroder	schroder	NOUN
cana-5422	70	29	equation	equation	NOUN
cana-5422	70	30	,	,	PUNCT
cana-5422	70	31	abel	abel	PROPN
cana-5422	70	32	equation	equation	NOUN
cana-5422	70	33	and	and	CCONJ
cana-5422	70	34	many	many	ADJ
cana-5422	70	35	others	other	NOUN
cana-5422	70	36	.	.	PUNCT
cana-5422	71	1	the	the	DET
cana-5422	71	2	stability	stability	NOUN
cana-5422	71	3	of	of	ADP
cana-5422	71	4	(	(	PUNCT
cana-5422	71	5	1.6	1.6	NUM
cana-5422	71	6	)	)	PUNCT
cana-5422	71	7	in	in	ADP
cana-5422	71	8	random	random	ADJ
cana-5422	71	9	normed	norme	VERB
cana-5422	71	10	spaces	space	NOUN
cana-5422	71	11	has	have	AUX
cana-5422	71	12	been	be	AUX
cana-5422	71	13	studied	study	VERB
cana-5422	71	14	by	by	ADP
cana-5422	71	15	c.	c.	PROPN
cana-5422	71	16	benzarouala	benzarouala	PROPN
cana-5422	71	17	et.al	et.al	PROPN
cana-5422	71	18	.	.	PUNCT
cana-5422	71	19	,	,	PUNCT
cana-5422	72	1	[	[	X
cana-5422	72	2	10	10	NUM
cana-5422	72	3	]	]	PUNCT
cana-5422	72	4	.	.	PUNCT
cana-5422	73	1	inspired	inspire	VERB
cana-5422	73	2	by	by	ADP
cana-5422	73	3	the	the	DET
cana-5422	73	4	aforementioned	aforementioned	ADJ
cana-5422	73	5	information	information	NOUN
cana-5422	73	6	and	and	CCONJ
cana-5422	73	7	study	study	NOUN
cana-5422	73	8	findings	finding	NOUN
cana-5422	73	9	,	,	PUNCT
cana-5422	73	10	in	in	ADP
cana-5422	73	11	this	this	DET
cana-5422	73	12	paper	paper	NOUN
cana-5422	73	13	we	we	PRON
cana-5422	73	14	present	present	VERB
cana-5422	73	15	a	a	DET
cana-5422	73	16	novel	novel	ADJ
cana-5422	73	17	affine	affine	NOUN
cana-5422	73	18	type	type	NOUN
cana-5422	73	19	additive	additive	ADJ
cana-5422	73	20	quadratic	quadratic	ADJ
cana-5422	73	21	mixed	mixed	ADJ
cana-5422	73	22	functional	functional	ADJ
cana-5422	73	23	equation	equation	NOUN
cana-5422	73	24	of	of	ADP
cana-5422	73	25	the	the	DET
cana-5422	73	26	form	form	NOUN
cana-5422	73	27	f	f	X
cana-5422	73	28	(	(	PUNCT
cana-5422	73	29	3w1	3w1	NUM
cana-5422	73	30	+	+	CCONJ
cana-5422	73	31	w2	w2	NOUN
cana-5422	73	32	+	+	CCONJ
cana-5422	73	33	w3	w3	PROPN
cana-5422	73	34	)	)	PUNCT
cana-5422	74	1	+	+	NOUN
cana-5422	74	2	f	f	X
cana-5422	74	3	(	(	PUNCT
cana-5422	74	4	w1	w1	NOUN
cana-5422	74	5	+	+	CCONJ
cana-5422	74	6	3w2	3w2	NUM
cana-5422	74	7	+	+	CCONJ
cana-5422	74	8	w3	w3	NOUN
cana-5422	74	9	)	)	PUNCT
cana-5422	75	1	+	+	NOUN
cana-5422	75	2	f	f	X
cana-5422	75	3	(	(	PUNCT
cana-5422	75	4	w1	w1	NOUN
cana-5422	75	5	+	+	NOUN
cana-5422	75	6	w2	w2	NOUN
cana-5422	75	7	+	+	CCONJ
cana-5422	75	8	3w3	3w3	NUM
cana-5422	75	9	)	)	PUNCT
cana-5422	76	1	=	=	SYM
cana-5422	76	2	6f	6f	NUM
cana-5422	76	3	(	(	PUNCT
cana-5422	76	4	3	3	NUM
cana-5422	76	5	∑	∑	PUNCT
cana-5422	76	6	ψ=1	ψ=1	PUNCT
cana-5422	76	7	wψ	wψ	ADP
cana-5422	76	8	)	)	PUNCT
cana-5422	77	1	+	+	CCONJ
cana-5422	77	2	1	1	NUM
cana-5422	77	3	2	2	NUM
cana-5422	77	4	{	{	PUNCT
cana-5422	77	5	f	f	PROPN
cana-5422	77	6	(	(	PUNCT
cana-5422	77	7	3	3	NUM
cana-5422	77	8	∑	∑	PUNCT
cana-5422	77	9	ψ=1	ψ=1	PUNCT
cana-5422	77	10	wψ	wψ	ADP
cana-5422	77	11	)	)	PUNCT
cana-5422	78	1	+	+	NOUN
cana-5422	78	2	f	f	X
cana-5422	78	3	(	(	PUNCT
cana-5422	78	4	−	−	PROPN
cana-5422	78	5	3	3	NUM
cana-5422	78	6	∑	∑	PUNCT
cana-5422	78	7	ψ=1	ψ=1	PUNCT
cana-5422	78	8	wψ	wψ	ADP
cana-5422	78	9	)	)	PUNCT
cana-5422	78	10	}	}	PUNCT
cana-5422	78	11	−	−	ADP
cana-5422	78	12	3	3	NUM
cana-5422	78	13	∑	∑	PUNCT
cana-5422	78	14	ψ=1	ψ=1	PUNCT
cana-5422	78	15	{	{	PUNCT
cana-5422	78	16	f	f	X
cana-5422	78	17	(	(	PUNCT
cana-5422	78	18	wψ)−	wψ)−	X
cana-5422	78	19	5	5	NUM
cana-5422	78	20	2	2	NUM
cana-5422	78	21	[	[	PUNCT
cana-5422	78	22	f	f	X
cana-5422	78	23	(	(	PUNCT
cana-5422	78	24	wψ	wψ	ADP
cana-5422	78	25	)	)	PUNCT
cana-5422	79	1	+	+	NOUN
cana-5422	79	2	f	f	X
cana-5422	79	3	(	(	PUNCT
cana-5422	79	4	−wψ	−wψ	NOUN
cana-5422	79	5	)	)	PUNCT
cana-5422	79	6	]	]	PUNCT
cana-5422	79	7	}	}	PUNCT
cana-5422	79	8	.	.	PUNCT
cana-5422	80	1	(	(	PUNCT
cana-5422	80	2	1.7	1.7	NUM
cana-5422	80	3	)	)	PUNCT
cana-5422	80	4	we	we	PRON
cana-5422	80	5	analyze	analyze	VERB
cana-5422	80	6	the	the	DET
cana-5422	80	7	stability	stability	NOUN
cana-5422	80	8	in	in	ADP
cana-5422	80	9	the	the	DET
cana-5422	80	10	sense	sense	NOUN
cana-5422	80	11	of	of	ADP
cana-5422	80	12	ulam	ulam	PROPN
cana-5422	80	13	,	,	PUNCT
cana-5422	80	14	hyers	hyer	NOUN
cana-5422	80	15	,	,	PUNCT
cana-5422	80	16	rassias	rassias	PROPN
cana-5422	80	17	’s	’s	PART
cana-5422	80	18	,	,	PUNCT
cana-5422	80	19	gavruta	gavruta	NOUN
cana-5422	80	20	and	and	CCONJ
cana-5422	80	21	radu	radu	PROPN
cana-5422	80	22	of	of	ADP
cana-5422	80	23	the	the	DET
cana-5422	80	24	above	above	ADJ
cana-5422	80	25	affine	affine	NOUN
cana-5422	80	26	type	type	NOUN
cana-5422	80	27	aq	aq	X
cana-5422	80	28	functional	functional	ADJ
cana-5422	80	29	equation	equation	NOUN
cana-5422	80	30	in	in	ADP
cana-5422	80	31	banach	banach	NOUN
cana-5422	80	32	space	space	NOUN
cana-5422	80	33	and	and	CCONJ
cana-5422	80	34	intuitionistic	intuitionistic	ADJ
cana-5422	80	35	fuzzy	fuzzy	ADJ
cana-5422	80	36	banach	banach	NOUN
cana-5422	80	37	space	space	NOUN
cana-5422	80	38	using	use	VERB
cana-5422	80	39	direct	direct	ADJ
cana-5422	80	40	and	and	CCONJ
cana-5422	80	41	fixed	fixed	ADJ
cana-5422	80	42	methods	method	NOUN
cana-5422	80	43	.	.	PUNCT
cana-5422	81	1	remark	remark	VERB
cana-5422	81	2	1.1	1.1	NUM
cana-5422	81	3	.	.	PUNCT
cana-5422	82	1	the	the	DET
cana-5422	82	2	homogeneous	homogeneous	ADJ
cana-5422	82	3	version	version	NOUN
cana-5422	82	4	of	of	ADP
cana-5422	82	5	(	(	PUNCT
cana-5422	82	6	1.6	1.6	NUM
cana-5422	82	7	)	)	PUNCT
cana-5422	82	8	for	for	ADP
cana-5422	82	9	m	m	PROPN
cana-5422	82	10	=	=	SYM
cana-5422	82	11	n	n	PROPN
cana-5422	82	12	=	=	SYM
cana-5422	82	13	3	3	NUM
cana-5422	82	14	,	,	PUNCT
cana-5422	82	15	a1	a1	NOUN
cana-5422	82	16	=	=	SYM
cana-5422	82	17	a2	a2	PROPN
cana-5422	82	18	=	=	PUNCT
cana-5422	82	19	a3	a3	NOUN
cana-5422	82	20	=	=	SYM
cana-5422	82	21	1	1	NUM
cana-5422	82	22	,	,	PUNCT
cana-5422	82	23	a11	a11	PROPN
cana-5422	82	24	=	=	SYM
cana-5422	82	25	a22	a22	PROPN
cana-5422	82	26	=	=	SYM
cana-5422	82	27	a33	a33	NOUN
cana-5422	82	28	=	=	SYM
cana-5422	82	29	3	3	NUM
cana-5422	82	30	and	and	CCONJ
cana-5422	82	31	a12	a12	NUM
cana-5422	82	32	=	=	SYM
cana-5422	82	33	a13	a13	PROPN
cana-5422	82	34	=	=	SYM
cana-5422	82	35	a21	a21	NOUN
cana-5422	82	36	=	=	SYM
cana-5422	82	37	a23	a23	PROPN
cana-5422	82	38	=	=	PROPN
cana-5422	82	39	a31	a31	NOUN
cana-5422	82	40	=	=	SYM
cana-5422	82	41	a32	a32	PROPN
cana-5422	82	42	=	=	SYM
cana-5422	82	43	1	1	NUM
cana-5422	82	44	is	be	AUX
cana-5422	82	45	f	f	PROPN
cana-5422	82	46	(	(	PUNCT
cana-5422	82	47	3x1	3x1	NUM
cana-5422	82	48	+	+	CCONJ
cana-5422	82	49	x2	x2	PROPN
cana-5422	83	1	+	+	CCONJ
cana-5422	83	2	x3	x3	ADJ
cana-5422	83	3	)	)	PUNCT
cana-5422	84	1	+	+	NUM
cana-5422	84	2	f	f	X
cana-5422	84	3	(	(	PUNCT
cana-5422	84	4	x1	x1	PROPN
cana-5422	84	5	+	+	NUM
cana-5422	84	6	3x2	3x2	NUM
cana-5422	84	7	+	+	CCONJ
cana-5422	84	8	x3	x3	ADJ
cana-5422	84	9	)	)	PUNCT
cana-5422	85	1	+	+	NUM
cana-5422	85	2	f	f	X
cana-5422	85	3	(	(	PUNCT
cana-5422	85	4	x1	x1	PROPN
cana-5422	85	5	+	+	NUM
cana-5422	85	6	x2	x2	PROPN
cana-5422	85	7	+	+	NUM
cana-5422	85	8	3x3	3x3	NUM
cana-5422	85	9	)	)	PUNCT
cana-5422	85	10	=	=	SYM
cana-5422	85	11	0	0	X
cana-5422	85	12	.	.	PUNCT
cana-5422	85	13	(	(	PUNCT
cana-5422	85	14	1.8	1.8	NUM
cana-5422	85	15	)	)	PUNCT
cana-5422	85	16	so	so	ADV
cana-5422	85	17	,	,	PUNCT
cana-5422	85	18	we	we	PRON
cana-5422	85	19	ca	can	AUX
cana-5422	85	20	nt	not	PART
cana-5422	85	21	get	get	VERB
cana-5422	85	22	our	our	PRON
cana-5422	85	23	functional	functional	ADJ
cana-5422	85	24	equation	equation	NOUN
cana-5422	85	25	(	(	PUNCT
cana-5422	85	26	1.7	1.7	NUM
cana-5422	85	27	)	)	PUNCT
cana-5422	85	28	from	from	ADP
cana-5422	85	29	(	(	PUNCT
cana-5422	85	30	1.6	1.6	NUM
cana-5422	85	31	)	)	PUNCT
cana-5422	85	32	.	.	PUNCT
cana-5422	86	1	communications	communication	NOUN
cana-5422	86	2	on	on	ADP
cana-5422	86	3	applied	apply	VERB
cana-5422	86	4	nonlinear	nonlinear	ADJ
cana-5422	86	5	analysis	analysis	NOUN
cana-5422	86	6	issn	issn	NOUN
cana-5422	86	7	:	:	PUNCT
cana-5422	86	8	1074	1074	NUM
cana-5422	86	9	-	-	PUNCT
cana-5422	86	10	133x	133x	NUM
cana-5422	86	11	vol	vol	NOUN
cana-5422	86	12	32	32	NUM
cana-5422	86	13	no	no	NOUN
cana-5422	86	14	.	.	PUNCT
cana-5422	87	1	10s(2025	10s(2025	NUM
cana-5422	87	2	)	)	PUNCT
cana-5422	87	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	87	4	2187	2187	NUM
cana-5422	87	5	remark	remark	VERB
cana-5422	87	6	1.2	1.2	NUM
cana-5422	87	7	.	.	PUNCT
cana-5422	88	1	in	in	ADP
cana-5422	88	2	the	the	DET
cana-5422	88	3	functional	functional	ADJ
cana-5422	88	4	equation	equation	NOUN
cana-5422	88	5	(	(	PUNCT
cana-5422	88	6	1.6	1.6	NUM
cana-5422	88	7	)	)	PUNCT
cana-5422	88	8	,	,	PUNCT
cana-5422	88	9	for	for	ADP
cana-5422	88	10	n	n	NOUN
cana-5422	88	11	=	=	SYM
cana-5422	88	12	3	3	NUM
cana-5422	88	13	,	,	PUNCT
cana-5422	88	14	m	m	VERB
cana-5422	88	15	=	=	NOUN
cana-5422	88	16	15	15	NUM
cana-5422	88	17	,	,	PUNCT
cana-5422	88	18	d	d	NOUN
cana-5422	88	19	=	=	SYM
cana-5422	88	20	0	0	NUM
cana-5422	88	21	,	,	PUNCT
cana-5422	88	22	a1	a1	NOUN
cana-5422	88	23	=	=	SYM
cana-5422	88	24	a2	a2	PROPN
cana-5422	88	25	=	=	PUNCT
cana-5422	88	26	a3	a3	NOUN
cana-5422	88	27	=	=	SYM
cana-5422	88	28	1	1	NUM
cana-5422	88	29	,	,	PUNCT
cana-5422	88	30	a11	a11	PROPN
cana-5422	88	31	=	=	SYM
cana-5422	88	32	a22	a22	PROPN
cana-5422	88	33	=	=	SYM
cana-5422	88	34	a33	a33	NOUN
cana-5422	88	35	=	=	SYM
cana-5422	88	36	3	3	NUM
cana-5422	88	37	,	,	PUNCT
cana-5422	88	38	a12	a12	NOUN
cana-5422	88	39	=	=	SYM
cana-5422	88	40	a13	a13	NOUN
cana-5422	88	41	=	=	SYM
cana-5422	88	42	a21	a21	NOUN
cana-5422	88	43	=	=	SYM
cana-5422	88	44	a23	a23	PROPN
cana-5422	88	45	=	=	PROPN
cana-5422	88	46	a31	a31	NOUN
cana-5422	88	47	=	=	SYM
cana-5422	88	48	a32	a32	PROPN
cana-5422	88	49	=	=	SYM
cana-5422	88	50	1	1	NUM
cana-5422	88	51	,	,	PUNCT
cana-5422	88	52	a4	a4	NOUN
cana-5422	88	53	=	=	SYM
cana-5422	88	54	−6	−6	NOUN
cana-5422	88	55	,	,	PUNCT
cana-5422	88	56	a41	a41	NOUN
cana-5422	88	57	=	=	PROPN
cana-5422	88	58	a42	a42	PROPN
cana-5422	88	59	=	=	SYM
cana-5422	88	60	a43	a43	PROPN
cana-5422	88	61	=	=	SYM
cana-5422	88	62	1	1	NUM
cana-5422	88	63	,	,	PUNCT
cana-5422	88	64	a5	a5	NOUN
cana-5422	88	65	=	=	SYM
cana-5422	88	66	a6	a6	NOUN
cana-5422	88	67	=	=	SYM
cana-5422	88	68	−1	−1	NOUN
cana-5422	88	69	2	2	NUM
cana-5422	88	70	,	,	PUNCT
cana-5422	88	71	a51	a51	PROPN
cana-5422	88	72	=	=	PROPN
cana-5422	88	73	a52	a52	PROPN
cana-5422	88	74	=	=	PROPN
cana-5422	88	75	a53	a53	PROPN
cana-5422	88	76	=	=	SYM
cana-5422	88	77	1	1	NUM
cana-5422	88	78	,	,	PUNCT
cana-5422	88	79	a61	a61	PROPN
cana-5422	88	80	=	=	SYM
cana-5422	89	1	a62	a62	NOUN
cana-5422	89	2	=	=	SYM
cana-5422	89	3	a63	a63	NOUN
cana-5422	89	4	=	=	SYM
cana-5422	89	5	−1	−1	NOUN
cana-5422	89	6	a7	a7	NOUN
cana-5422	89	7	=	=	SYM
cana-5422	89	8	a8	a8	PROPN
cana-5422	89	9	=	=	SYM
cana-5422	89	10	a9	a9	PROPN
cana-5422	89	11	=	=	SYM
cana-5422	89	12	1	1	NUM
cana-5422	89	13	,	,	PUNCT
cana-5422	89	14	a71	a71	PROPN
cana-5422	89	15	=	=	SYM
cana-5422	89	16	1	1	NUM
cana-5422	89	17	,	,	PUNCT
cana-5422	89	18	a72	a72	ADJ
cana-5422	89	19	=	=	SYM
cana-5422	89	20	a73	a73	PROPN
cana-5422	89	21	=	=	SYM
cana-5422	89	22	0	0	NUM
cana-5422	89	23	,	,	PUNCT
cana-5422	89	24	a81	a81	NOUN
cana-5422	89	25	=	=	SYM
cana-5422	89	26	a83	a83	NOUN
cana-5422	89	27	=	=	SYM
cana-5422	89	28	0	0	NUM
cana-5422	89	29	,	,	PUNCT
cana-5422	89	30	a82	a82	VERB
cana-5422	89	31	=	=	SYM
cana-5422	89	32	1	1	NUM
cana-5422	89	33	,	,	PUNCT
cana-5422	89	34	a91	a91	NOUN
cana-5422	89	35	=	=	PUNCT
cana-5422	89	36	a92	a92	NOUN
cana-5422	89	37	=	=	SYM
cana-5422	89	38	0	0	NUM
cana-5422	89	39	,	,	PUNCT
cana-5422	89	40	a93	a93	NOUN
cana-5422	89	41	=	=	SYM
cana-5422	89	42	1	1	NUM
cana-5422	89	43	,	,	PUNCT
cana-5422	89	44	a10	a10	NOUN
cana-5422	89	45	=	=	SYM
cana-5422	89	46	a11	a11	PROPN
cana-5422	89	47	=	=	SYM
cana-5422	90	1	a12	a12	NOUN
cana-5422	90	2	=	=	NOUN
cana-5422	90	3	a13	a13	PROPN
cana-5422	90	4	=	=	SYM
cana-5422	90	5	a14	a14	PROPN
cana-5422	90	6	=	=	SYM
cana-5422	90	7	a15	a15	NOUN
cana-5422	90	8	=	=	NOUN
cana-5422	90	9	−5	−5	NOUN
cana-5422	90	10	2	2	NUM
cana-5422	90	11	,	,	PUNCT
cana-5422	90	12	a10	a10	NOUN
cana-5422	90	13	1	1	NUM
cana-5422	90	14	=	=	SYM
cana-5422	90	15	1	1	NUM
cana-5422	90	16	,	,	PUNCT
cana-5422	90	17	a10	a10	NOUN
cana-5422	90	18	2	2	NUM
cana-5422	90	19	=	=	SYM
cana-5422	90	20	a10	a10	NOUN
cana-5422	90	21	3	3	NUM
cana-5422	90	22	=	=	SYM
cana-5422	90	23	0	0	NUM
cana-5422	90	24	,	,	PUNCT
cana-5422	90	25	a11	a11	PROPN
cana-5422	90	26	1	1	NUM
cana-5422	90	27	=	=	SYM
cana-5422	90	28	a11	a11	PROPN
cana-5422	90	29	3	3	NUM
cana-5422	90	30	=	=	SYM
cana-5422	90	31	0	0	PROPN
cana-5422	90	32	,	,	PUNCT
cana-5422	90	33	a11	a11	PROPN
cana-5422	90	34	2	2	NUM
cana-5422	90	35	=	=	SYM
cana-5422	90	36	1	1	NUM
cana-5422	90	37	,	,	PUNCT
cana-5422	90	38	a12	a12	NOUN
cana-5422	90	39	1	1	NUM
cana-5422	90	40	=	=	NOUN
cana-5422	90	41	a12	a12	NOUN
cana-5422	90	42	2	2	NUM
cana-5422	90	43	=	=	SYM
cana-5422	90	44	0	0	NUM
cana-5422	90	45	,	,	PUNCT
cana-5422	90	46	a12	a12	NOUN
cana-5422	90	47	3	3	NUM
cana-5422	90	48	=	=	SYM
cana-5422	90	49	1	1	NUM
cana-5422	90	50	,	,	PUNCT
cana-5422	90	51	a13	a13	VERB
cana-5422	90	52	1	1	NUM
cana-5422	90	53	=	=	SYM
cana-5422	90	54	−1	−1	NOUN
cana-5422	90	55	,	,	PUNCT
cana-5422	90	56	a13	a13	VERB
cana-5422	90	57	2	2	NUM
cana-5422	90	58	=	=	NOUN
cana-5422	90	59	a13	a13	VERB
cana-5422	90	60	3	3	NUM
cana-5422	90	61	=	=	SYM
cana-5422	90	62	0	0	NUM
cana-5422	90	63	,	,	PUNCT
cana-5422	90	64	a14	a14	PROPN
cana-5422	90	65	1	1	NUM
cana-5422	90	66	=	=	SYM
cana-5422	90	67	a14	a14	NOUN
cana-5422	90	68	3	3	NUM
cana-5422	90	69	=	=	SYM
cana-5422	90	70	0	0	NUM
cana-5422	90	71	,	,	PUNCT
cana-5422	90	72	a14	a14	PROPN
cana-5422	90	73	2	2	NUM
cana-5422	90	74	=	=	SYM
cana-5422	90	75	−1	−1	NOUN
cana-5422	90	76	,	,	PUNCT
cana-5422	90	77	a15	a15	NOUN
cana-5422	90	78	1	1	NUM
cana-5422	90	79	=	=	SYM
cana-5422	90	80	a15	a15	NOUN
cana-5422	90	81	2	2	NUM
cana-5422	90	82	=	=	SYM
cana-5422	90	83	0	0	NUM
cana-5422	90	84	,	,	PUNCT
cana-5422	90	85	a15	a15	NOUN
cana-5422	90	86	3	3	NUM
cana-5422	90	87	=	=	SYM
cana-5422	90	88	−1	−1	NOUN
cana-5422	90	89	.	.	PUNCT
cana-5422	91	1	so	so	ADV
cana-5422	91	2	,	,	PUNCT
cana-5422	91	3	after	after	ADP
cana-5422	91	4	giving	give	VERB
cana-5422	91	5	particular	particular	ADJ
cana-5422	91	6	values	value	NOUN
cana-5422	91	7	to	to	ADP
cana-5422	91	8	a′is	a′is	NOUN
cana-5422	91	9	and	and	CCONJ
cana-5422	91	10	a′is	a′is	PROPN
cana-5422	91	11	,	,	PUNCT
cana-5422	91	12	we	we	PRON
cana-5422	91	13	get	get	VERB
cana-5422	91	14	our	our	PRON
cana-5422	91	15	functional	functional	ADJ
cana-5422	91	16	equation	equation	NOUN
cana-5422	91	17	(	(	PUNCT
cana-5422	91	18	1.7	1.7	NUM
cana-5422	91	19	)	)	PUNCT
cana-5422	91	20	from	from	ADP
cana-5422	91	21	(	(	PUNCT
cana-5422	91	22	1.6	1.6	NUM
cana-5422	91	23	)	)	PUNCT
cana-5422	91	24	.	.	PUNCT
cana-5422	92	1	moreover	moreover	ADV
cana-5422	92	2	,	,	PUNCT
cana-5422	92	3	the	the	DET
cana-5422	92	4	results	result	NOUN
cana-5422	92	5	in	in	ADP
cana-5422	92	6	the	the	DET
cana-5422	92	7	manuscript	manuscript	NOUN
cana-5422	92	8	under	under	ADP
cana-5422	92	9	review	review	NOUN
cana-5422	92	10	complement	complement	NOUN
cana-5422	92	11	of	of	ADP
cana-5422	92	12	the	the	DET
cana-5422	92	13	results	result	NOUN
cana-5422	92	14	in	in	ADP
cana-5422	92	15	[	[	X
cana-5422	92	16	9	9	NUM
cana-5422	92	17	,	,	PUNCT
cana-5422	92	18	10	10	NUM
cana-5422	92	19	]	]	PUNCT
cana-5422	92	20	.	.	PUNCT
cana-5422	93	1	lemma	lemma	PROPN
cana-5422	93	2	1.3	1.3	NUM
cana-5422	93	3	.	.	PUNCT
cana-5422	94	1	[	[	X
cana-5422	94	2	21	21	NUM
cana-5422	94	3	]	]	PUNCT
cana-5422	94	4	let	let	VERB
cana-5422	94	5	a	a	PRON
cana-5422	94	6	and	and	CCONJ
cana-5422	94	7	b	b	NOUN
cana-5422	94	8	be	be	AUX
cana-5422	94	9	real	real	ADJ
cana-5422	94	10	vector	vector	NOUN
cana-5422	94	11	spaces	space	NOUN
cana-5422	94	12	.	.	PUNCT
cana-5422	95	1	suppose	suppose	VERB
cana-5422	95	2	f	f	X
cana-5422	95	3	:	:	PUNCT
cana-5422	95	4	a	a	DET
cana-5422	95	5	→	→	SYM
cana-5422	95	6	b	b	X
cana-5422	95	7	be	be	AUX
cana-5422	95	8	an	an	DET
cana-5422	95	9	odd	odd	ADJ
cana-5422	95	10	mapping	mapping	NOUN
cana-5422	95	11	satisfying	satisfy	VERB
cana-5422	95	12	(	(	PUNCT
cana-5422	95	13	1.7	1.7	NUM
cana-5422	95	14	)	)	PUNCT
cana-5422	95	15	.	.	PUNCT
cana-5422	96	1	then	then	ADV
cana-5422	96	2	f	f	PROPN
cana-5422	96	3	is	be	AUX
cana-5422	96	4	additive	additive	ADJ
cana-5422	96	5	.	.	PUNCT
cana-5422	97	1	lemma	lemma	PROPN
cana-5422	97	2	1.4	1.4	NUM
cana-5422	97	3	.	.	PUNCT
cana-5422	98	1	[	[	X
cana-5422	98	2	12	12	NUM
cana-5422	98	3	]	]	PUNCT
cana-5422	98	4	let	let	VERB
cana-5422	98	5	a	a	PRON
cana-5422	98	6	and	and	CCONJ
cana-5422	98	7	b	b	NOUN
cana-5422	98	8	be	be	AUX
cana-5422	98	9	real	real	ADJ
cana-5422	98	10	vector	vector	NOUN
cana-5422	98	11	spaces	space	NOUN
cana-5422	98	12	.	.	PUNCT
cana-5422	99	1	suppose	suppose	VERB
cana-5422	99	2	f	f	X
cana-5422	99	3	:	:	PUNCT
cana-5422	99	4	a	a	DET
cana-5422	99	5	→	→	SYM
cana-5422	99	6	b	b	X
cana-5422	99	7	be	be	AUX
cana-5422	99	8	an	an	DET
cana-5422	99	9	even	even	ADV
cana-5422	99	10	mapping	mapping	NOUN
cana-5422	99	11	satisfying	satisfy	VERB
cana-5422	99	12	(	(	PUNCT
cana-5422	99	13	1.7	1.7	NUM
cana-5422	99	14	)	)	PUNCT
cana-5422	99	15	.	.	PUNCT
cana-5422	100	1	then	then	ADV
cana-5422	100	2	f	f	PROPN
cana-5422	100	3	is	be	AUX
cana-5422	100	4	quadratic	quadratic	ADJ
cana-5422	100	5	.	.	PUNCT
cana-5422	101	1	now	now	ADV
cana-5422	101	2	,	,	PUNCT
cana-5422	101	3	we	we	PRON
cana-5422	101	4	present	present	VERB
cana-5422	101	5	the	the	DET
cana-5422	101	6	result	result	NOUN
cana-5422	101	7	due	due	ADP
cana-5422	101	8	to	to	ADP
cana-5422	101	9	margolis	margolis	PROPN
cana-5422	101	10	,	,	PUNCT
cana-5422	101	11	diaz	diaz	PROPN
cana-5422	102	1	[	[	X
cana-5422	102	2	18	18	NUM
cana-5422	102	3	]	]	PUNCT
cana-5422	102	4	and	and	CCONJ
cana-5422	102	5	radu	radu	VERB
cana-5422	102	6	[	[	X
cana-5422	102	7	22	22	NUM
cana-5422	102	8	]	]	PUNCT
cana-5422	102	9	for	for	ADP
cana-5422	102	10	fixed	fix	VERB
cana-5422	102	11	point	point	NOUN
cana-5422	102	12	theory	theory	NOUN
cana-5422	102	13	.	.	PUNCT
cana-5422	103	1	theorem	theorem	VERB
cana-5422	103	2	1.5	1.5	NUM
cana-5422	103	3	.	.	PUNCT
cana-5422	104	1	[	[	X
cana-5422	104	2	18	18	NUM
cana-5422	104	3	,	,	PUNCT
cana-5422	104	4	22	22	NUM
cana-5422	104	5	]	]	PUNCT
cana-5422	104	6	suppose	suppose	VERB
cana-5422	104	7	that	that	SCONJ
cana-5422	104	8	for	for	ADP
cana-5422	104	9	a	a	DET
cana-5422	104	10	complete	complete	ADJ
cana-5422	104	11	generalized	generalize	VERB
cana-5422	104	12	metric	metric	ADJ
cana-5422	104	13	space	space	NOUN
cana-5422	104	14	(	(	PUNCT
cana-5422	104	15	ω	ω	PROPN
cana-5422	104	16	,	,	PUNCT
cana-5422	104	17	δ	δ	PROPN
cana-5422	104	18	)	)	PUNCT
cana-5422	104	19	and	and	CCONJ
cana-5422	104	20	a	a	DET
cana-5422	104	21	strictly	strictly	ADV
cana-5422	104	22	contractive	contractive	ADJ
cana-5422	104	23	mapping	mapping	NOUN
cana-5422	104	24	t	t	NOUN
cana-5422	104	25	:	:	PUNCT
cana-5422	104	26	ω	ω	NUM
cana-5422	104	27	−→	−→	NOUN
cana-5422	104	28	ω	ω	PROPN
cana-5422	104	29	with	with	ADP
cana-5422	104	30	lipschitz	lipschitz	NOUN
cana-5422	104	31	constant	constant	ADJ
cana-5422	104	32	l.	l.	NOUN
cana-5422	104	33	then	then	ADV
cana-5422	104	34	,	,	PUNCT
cana-5422	104	35	for	for	ADP
cana-5422	104	36	each	each	DET
cana-5422	104	37	given	give	VERB
cana-5422	104	38	x	x	PUNCT
cana-5422	104	39	∈	∈	PROPN
cana-5422	104	40	ω	ω	NOUN
cana-5422	104	41	,	,	PUNCT
cana-5422	104	42	either	either	CCONJ
cana-5422	104	43	d(tnx	d(tnx	NOUN
cana-5422	104	44	,	,	PUNCT
cana-5422	104	45	tn+1x	tn+1x	ADV
cana-5422	104	46	)	)	PUNCT
cana-5422	105	1	=	=	SYM
cana-5422	106	1	∞	∞	NUM
cana-5422	106	2	∀	∀	X
cana-5422	106	3	n	n	PRON
cana-5422	106	4	≥	≥	NOUN
cana-5422	106	5	0	0	NUM
cana-5422	106	6	,	,	PUNCT
cana-5422	106	7	or	or	CCONJ
cana-5422	106	8	there	there	PRON
cana-5422	106	9	exists	exist	VERB
cana-5422	106	10	a	a	DET
cana-5422	106	11	natural	natural	ADJ
cana-5422	106	12	number	number	NOUN
cana-5422	106	13	n0	n0	NOUN
cana-5422	106	14	such	such	ADJ
cana-5422	106	15	that	that	SCONJ
cana-5422	106	16	(	(	PUNCT
cana-5422	106	17	fpc1	fpc1	PROPN
cana-5422	106	18	)	)	PUNCT
cana-5422	106	19	d(tnx	d(tnx	PROPN
cana-5422	106	20	,	,	PUNCT
cana-5422	106	21	tn+1x	tn+1x	ADV
cana-5422	106	22	)	)	PUNCT
cana-5422	106	23	<	<	X
cana-5422	106	24	∞	∞	PROPN
cana-5422	106	25	for	for	ADP
cana-5422	106	26	all	all	DET
cana-5422	106	27	n	n	PRON
cana-5422	106	28	≥	≥	NOUN
cana-5422	106	29	n0	n0	NUM
cana-5422	106	30	;	;	PUNCT
cana-5422	106	31	(	(	PUNCT
cana-5422	106	32	fpc2	fpc2	X
cana-5422	106	33	)	)	PUNCT
cana-5422	106	34	the	the	DET
cana-5422	106	35	sequence	sequence	NOUN
cana-5422	106	36	(	(	PUNCT
cana-5422	106	37	tnx	tnx	NOUN
cana-5422	106	38	)	)	PUNCT
cana-5422	106	39	is	be	AUX
cana-5422	106	40	convergent	convergent	ADJ
cana-5422	106	41	to	to	ADP
cana-5422	106	42	a	a	DET
cana-5422	106	43	fixed	fix	VERB
cana-5422	106	44	point	point	NOUN
cana-5422	106	45	y∗	y∗	ADV
cana-5422	106	46	of	of	ADP
cana-5422	106	47	t	t	PROPN
cana-5422	106	48	(	(	PUNCT
cana-5422	106	49	fpc3	fpc3	PROPN
cana-5422	106	50	)	)	PUNCT
cana-5422	106	51	y∗	y∗	ADV
cana-5422	106	52	is	be	AUX
cana-5422	106	53	the	the	DET
cana-5422	106	54	unique	unique	ADJ
cana-5422	106	55	fixed	fix	VERB
cana-5422	106	56	point	point	NOUN
cana-5422	106	57	of	of	ADP
cana-5422	106	58	t	t	PROPN
cana-5422	106	59	in	in	ADP
cana-5422	106	60	the	the	DET
cana-5422	106	61	set	set	NOUN
cana-5422	106	62	∆	∆	X
cana-5422	106	63	=	=	PRON
cana-5422	107	1	{	{	PUNCT
cana-5422	107	2	y	y	PROPN
cana-5422	107	3	∈	∈	PROPN
cana-5422	107	4	ω	ω	NOUN
cana-5422	107	5	:	:	PUNCT
cana-5422	107	6	d(tn0	d(tn0	PROPN
cana-5422	107	7	x	x	PROPN
cana-5422	107	8	,	,	PUNCT
cana-5422	107	9	y	y	PROPN
cana-5422	107	10	)	)	PUNCT
cana-5422	107	11	<	<	X
cana-5422	107	12	∞	∞	PROPN
cana-5422	107	13	}	}	PUNCT
cana-5422	107	14	;	;	PUNCT
cana-5422	107	15	(	(	PUNCT
cana-5422	107	16	fpc4	fpc4	PROPN
cana-5422	107	17	)	)	PUNCT
cana-5422	107	18	d(y∗	d(y∗	NOUN
cana-5422	107	19	,	,	PUNCT
cana-5422	107	20	y	y	NOUN
cana-5422	107	21	)	)	PUNCT
cana-5422	107	22	≤	≤	NUM
cana-5422	107	23	1	1	NUM
cana-5422	107	24	1−l	1−l	NUM
cana-5422	107	25	d(y	d(y	NOUN
cana-5422	107	26	,	,	PUNCT
cana-5422	107	27	ty	ty	INTJ
cana-5422	107	28	)	)	PUNCT
cana-5422	107	29	for	for	ADP
cana-5422	107	30	all	all	DET
cana-5422	107	31	y	y	PROPN
cana-5422	107	32	∈	∈	PROPN
cana-5422	108	1	∆.	∆.	ADJ
cana-5422	108	2	2	2	X
cana-5422	108	3	.	.	PUNCT
cana-5422	108	4	stability	stability	NOUN
cana-5422	108	5	of	of	ADP
cana-5422	108	6	(	(	PUNCT
cana-5422	108	7	1.7	1.7	NUM
cana-5422	108	8	)	)	PUNCT
cana-5422	108	9	in	in	ADP
cana-5422	108	10	banach	banach	NOUN
cana-5422	108	11	spaces	space	NOUN
cana-5422	108	12	in	in	ADP
cana-5422	108	13	this	this	DET
cana-5422	108	14	section	section	NOUN
cana-5422	108	15	,	,	PUNCT
cana-5422	108	16	we	we	PRON
cana-5422	108	17	explore	explore	VERB
cana-5422	108	18	the	the	DET
cana-5422	108	19	generalized	generalize	VERB
cana-5422	108	20	ulam	ulam	PROPN
cana-5422	108	21	hyers	hyer	NOUN
cana-5422	108	22	stability	stability	NOUN
cana-5422	108	23	of	of	ADP
cana-5422	108	24	the	the	DET
cana-5422	108	25	functional	functional	ADJ
cana-5422	108	26	equation	equation	NOUN
cana-5422	108	27	(	(	PUNCT
cana-5422	108	28	1.7	1.7	NUM
cana-5422	108	29	)	)	PUNCT
cana-5422	108	30	in	in	ADP
cana-5422	108	31	banach	banach	NOUN
cana-5422	108	32	space	space	NOUN
cana-5422	108	33	.	.	PUNCT
cana-5422	109	1	to	to	PART
cana-5422	109	2	prove	prove	VERB
cana-5422	109	3	the	the	DET
cana-5422	109	4	stability	stability	NOUN
cana-5422	109	5	results	result	NOUN
cana-5422	109	6	,	,	PUNCT
cana-5422	109	7	let	let	VERB
cana-5422	109	8	us	we	PRON
cana-5422	109	9	takew1	takew1	PROPN
cana-5422	109	10	be	be	AUX
cana-5422	109	11	a	a	DET
cana-5422	109	12	normed	normed	ADJ
cana-5422	109	13	space	space	NOUN
cana-5422	109	14	andw2	andw2	NOUN
cana-5422	109	15	be	be	AUX
cana-5422	109	16	a	a	DET
cana-5422	109	17	banach	banach	NOUN
cana-5422	109	18	space	space	NOUN
cana-5422	109	19	.	.	PUNCT
cana-5422	110	1	suppose	suppose	VERB
cana-5422	110	2	that	that	SCONJ
cana-5422	110	3	f	f	PROPN
cana-5422	110	4	:	:	PUNCT
cana-5422	110	5	w1	w1	PROPN
cana-5422	110	6	→w2	→w2	NOUN
cana-5422	110	7	and	and	CCONJ
cana-5422	110	8	ψ	ψ	X
cana-5422	110	9	:	:	PUNCT
cana-5422	110	10	w3	w3	NOUN
cana-5422	110	11	1	1	NUM
cana-5422	110	12	→	→	SYM
cana-5422	110	13	[	[	X
cana-5422	110	14	0	0	NUM
cana-5422	110	15	,	,	PUNCT
cana-5422	110	16	∞	∞	NUM
cana-5422	110	17	)	)	PUNCT
cana-5422	110	18	satisfying	satisfy	VERB
cana-5422	110	19	the	the	DET
cana-5422	110	20	following	follow	VERB
cana-5422	110	21	functional	functional	ADJ
cana-5422	110	22	inequalities	inequality	NOUN
cana-5422	110	23	∥∥∥f	∥∥∥f	NOUN
cana-5422	110	24	(	(	PUNCT
cana-5422	110	25	3w1	3w1	NUM
cana-5422	110	26	+	+	CCONJ
cana-5422	110	27	w2	w2	NOUN
cana-5422	110	28	+	+	CCONJ
cana-5422	110	29	w3	w3	PROPN
cana-5422	110	30	)	)	PUNCT
cana-5422	111	1	+	+	NOUN
cana-5422	111	2	f	f	X
cana-5422	111	3	(	(	PUNCT
cana-5422	111	4	w1	w1	NOUN
cana-5422	111	5	+	+	CCONJ
cana-5422	111	6	3w2	3w2	NUM
cana-5422	111	7	+	+	CCONJ
cana-5422	111	8	w3	w3	NOUN
cana-5422	111	9	)	)	PUNCT
cana-5422	112	1	+	+	NOUN
cana-5422	112	2	f	f	X
cana-5422	112	3	(	(	PUNCT
cana-5422	112	4	w1	w1	NOUN
cana-5422	112	5	+	+	NOUN
cana-5422	112	6	w2	w2	NOUN
cana-5422	112	7	+	+	CCONJ
cana-5422	112	8	3w3)−	3w3)−	PROPN
cana-5422	112	9	6f	6f	NOUN
cana-5422	112	10	(	(	PUNCT
cana-5422	112	11	3	3	NUM
cana-5422	112	12	∑	∑	PUNCT
cana-5422	112	13	ψ=1	ψ=1	PUNCT
cana-5422	112	14	wψ	wψ	ADP
cana-5422	112	15	)	)	PUNCT
cana-5422	112	16	−	−	PROPN
cana-5422	112	17	1	1	NUM
cana-5422	112	18	2	2	NUM
cana-5422	112	19	{	{	PUNCT
cana-5422	112	20	f	f	PROPN
cana-5422	112	21	(	(	PUNCT
cana-5422	112	22	3	3	NUM
cana-5422	112	23	∑	∑	PUNCT
cana-5422	112	24	ψ=1	ψ=1	PUNCT
cana-5422	112	25	wψ	wψ	ADP
cana-5422	112	26	)	)	PUNCT
cana-5422	113	1	+	+	NOUN
cana-5422	113	2	f	f	X
cana-5422	113	3	(	(	PUNCT
cana-5422	113	4	−	−	PROPN
cana-5422	113	5	3	3	NUM
cana-5422	113	6	∑	∑	PUNCT
cana-5422	113	7	ψ=1	ψ=1	PUNCT
cana-5422	113	8	wψ	wψ	ADP
cana-5422	113	9	)	)	PUNCT
cana-5422	113	10	}	}	PUNCT
cana-5422	113	11	+	+	CCONJ
cana-5422	113	12	3	3	NUM
cana-5422	113	13	∑	∑	NOUN
cana-5422	113	14	ψ=1	ψ=1	PUNCT
cana-5422	113	15	{	{	PUNCT
cana-5422	113	16	f	f	X
cana-5422	113	17	(	(	PUNCT
cana-5422	113	18	wψ)−	wψ)−	X
cana-5422	113	19	5	5	NUM
cana-5422	113	20	2	2	NUM
cana-5422	113	21	[	[	PUNCT
cana-5422	113	22	f	f	X
cana-5422	113	23	(	(	PUNCT
cana-5422	113	24	wψ	wψ	ADP
cana-5422	113	25	)	)	PUNCT
cana-5422	114	1	+	+	NOUN
cana-5422	114	2	f	f	X
cana-5422	114	3	(	(	PUNCT
cana-5422	114	4	−wψ	−wψ	NOUN
cana-5422	114	5	)	)	PUNCT
cana-5422	114	6	]	]	PUNCT
cana-5422	114	7	}	}	PUNCT
cana-5422	114	8	∥∥∥	∥∥∥	PROPN
cana-5422	114	9	≤	≤	NUM
cana-5422	114	10	ψ	ψ	X
cana-5422	114	11	(	(	PUNCT
cana-5422	114	12	w1	w1	NOUN
cana-5422	114	13	,	,	PUNCT
cana-5422	114	14	w2	w2	NOUN
cana-5422	114	15	,	,	PUNCT
cana-5422	114	16	w3	w3	PROPN
cana-5422	114	17	)	)	PUNCT
cana-5422	114	18	,	,	PUNCT
cana-5422	114	19	(	(	PUNCT
cana-5422	114	20	2.1	2.1	NUM
cana-5422	114	21	)	)	PUNCT
cana-5422	114	22	communications	communication	NOUN
cana-5422	114	23	on	on	ADP
cana-5422	114	24	applied	apply	VERB
cana-5422	114	25	nonlinear	nonlinear	ADJ
cana-5422	114	26	analysis	analysis	NOUN
cana-5422	114	27	issn	issn	NOUN
cana-5422	114	28	:	:	PUNCT
cana-5422	114	29	1074	1074	NUM
cana-5422	114	30	-	-	PUNCT
cana-5422	114	31	133x	133x	NUM
cana-5422	114	32	vol	vol	NOUN
cana-5422	114	33	32	32	NUM
cana-5422	114	34	no	no	NOUN
cana-5422	114	35	.	.	PUNCT
cana-5422	115	1	10s(2025	10s(2025	NUM
cana-5422	115	2	)	)	PUNCT
cana-5422	115	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	115	4	2188	2188	NUM
cana-5422	115	5	and	and	CCONJ
cana-5422	115	6	∥∥∥f	∥∥∥f	NOUN
cana-5422	115	7	(	(	PUNCT
cana-5422	115	8	3w1	3w1	NUM
cana-5422	115	9	+	+	CCONJ
cana-5422	115	10	w2	w2	NOUN
cana-5422	115	11	+	+	CCONJ
cana-5422	115	12	w3	w3	PROPN
cana-5422	115	13	)	)	PUNCT
cana-5422	116	1	+	+	NOUN
cana-5422	116	2	f	f	X
cana-5422	116	3	(	(	PUNCT
cana-5422	116	4	w1	w1	NOUN
cana-5422	116	5	+	+	CCONJ
cana-5422	116	6	3w2	3w2	NUM
cana-5422	116	7	+	+	CCONJ
cana-5422	116	8	w3	w3	NOUN
cana-5422	116	9	)	)	PUNCT
cana-5422	117	1	+	+	NOUN
cana-5422	117	2	f	f	X
cana-5422	117	3	(	(	PUNCT
cana-5422	117	4	w1	w1	NOUN
cana-5422	117	5	+	+	NOUN
cana-5422	117	6	w2	w2	NOUN
cana-5422	117	7	+	+	CCONJ
cana-5422	117	8	3w3)−	3w3)−	PROPN
cana-5422	117	9	6f	6f	NOUN
cana-5422	117	10	(	(	PUNCT
cana-5422	117	11	3	3	NUM
cana-5422	117	12	∑	∑	PUNCT
cana-5422	117	13	ψ=1	ψ=1	PUNCT
cana-5422	117	14	wψ	wψ	ADP
cana-5422	117	15	)	)	PUNCT
cana-5422	117	16	−	−	PROPN
cana-5422	117	17	1	1	NUM
cana-5422	117	18	2	2	NUM
cana-5422	117	19	{	{	PUNCT
cana-5422	117	20	f	f	PROPN
cana-5422	117	21	(	(	PUNCT
cana-5422	117	22	3	3	NUM
cana-5422	117	23	∑	∑	PUNCT
cana-5422	117	24	ψ=1	ψ=1	PUNCT
cana-5422	117	25	wψ	wψ	ADP
cana-5422	117	26	)	)	PUNCT
cana-5422	118	1	+	+	NOUN
cana-5422	118	2	f	f	X
cana-5422	118	3	(	(	PUNCT
cana-5422	118	4	−	−	PROPN
cana-5422	118	5	3	3	NUM
cana-5422	118	6	∑	∑	PUNCT
cana-5422	118	7	ψ=1	ψ=1	PUNCT
cana-5422	118	8	wψ	wψ	ADP
cana-5422	118	9	)	)	PUNCT
cana-5422	118	10	}	}	PUNCT
cana-5422	118	11	+	+	CCONJ
cana-5422	118	12	3	3	NUM
cana-5422	118	13	∑	∑	NOUN
cana-5422	118	14	ψ=1	ψ=1	PUNCT
cana-5422	118	15	{	{	PUNCT
cana-5422	118	16	f	f	X
cana-5422	118	17	(	(	PUNCT
cana-5422	118	18	wψ)−	wψ)−	X
cana-5422	118	19	5	5	NUM
cana-5422	118	20	2	2	NUM
cana-5422	118	21	[	[	PUNCT
cana-5422	118	22	f	f	X
cana-5422	118	23	(	(	PUNCT
cana-5422	118	24	wψ	wψ	ADP
cana-5422	118	25	)	)	PUNCT
cana-5422	118	26	+	+	NOUN
cana-5422	118	27	f	f	X
cana-5422	118	28	(	(	PUNCT
cana-5422	118	29	−wψ	−wψ	NOUN
cana-5422	118	30	)	)	PUNCT
cana-5422	118	31	]	]	PUNCT
cana-5422	118	32	}	}	PUNCT
cana-5422	118	33	∥∥∥	∥∥∥	PROPN
cana-5422	118	34	≤	≤	NUM
cana-5422	118	35			PROPN
cana-5422	118	36	δ	δ	PROPN
cana-5422	118	37	,	,	PUNCT
cana-5422	118	38	δ	δ	PROPN
cana-5422	118	39	3	3	NUM
cana-5422	118	40	∑	∑	PUNCT
cana-5422	118	41	ψ=1	ψ=1	PUNCT
cana-5422	118	42	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	43	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	118	44	,	,	PUNCT
cana-5422	118	45	δ	δ	PROPN
cana-5422	118	46	3	3	NUM
cana-5422	118	47	∑	∑	PUNCT
cana-5422	118	48	ψ=1	ψ=1	PUNCT
cana-5422	118	49	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	50	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	118	51	,	,	PUNCT
cana-5422	118	52	δ	δ	PROPN
cana-5422	118	53	3	3	NUM
cana-5422	118	54	∏	∏	PROPN
cana-5422	118	55	ψ=1	ψ=1	PUNCT
cana-5422	118	56	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	57	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	118	58	,	,	PUNCT
cana-5422	118	59	δ	δ	PROPN
cana-5422	118	60	3	3	NUM
cana-5422	118	61	∏	∏	PROPN
cana-5422	118	62	ψ=1	ψ=1	PUNCT
cana-5422	118	63	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	64	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	118	65	,	,	PUNCT
cana-5422	118	66	δ	δ	PROPN
cana-5422	118	67	{	{	PUNCT
cana-5422	118	68	3	3	NUM
cana-5422	118	69	∑	∑	PUNCT
cana-5422	118	70	ψ=1	ψ=1	X
cana-5422	118	71	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	72	∣∣3ϕ	∣∣3ϕ	ADJ
cana-5422	118	73	+	+	PROPN
cana-5422	118	74	3	3	NUM
cana-5422	118	75	∏	∏	NUM
cana-5422	118	76	ψ=1	ψ=1	PUNCT
cana-5422	118	77	∣∣wψ	∣∣wψ	PROPN
cana-5422	118	78	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	118	79	}	}	PUNCT
cana-5422	118	80	,	,	PUNCT
cana-5422	118	81	(	(	PUNCT
cana-5422	118	82	2.2	2.2	NUM
cana-5422	118	83	)	)	PUNCT
cana-5422	118	84	for	for	ADP
cana-5422	118	85	all	all	DET
cana-5422	118	86	w1	w1	NOUN
cana-5422	118	87	,	,	PUNCT
cana-5422	118	88	w2	w2	NOUN
cana-5422	118	89	,	,	PUNCT
cana-5422	118	90	w3	w3	PROPN
cana-5422	118	91	∈	∈	PROPN
cana-5422	118	92	w1	w1	NOUN
cana-5422	118	93	,	,	PUNCT
cana-5422	118	94	δ	δ	PROPN
cana-5422	118	95	be	be	VERB
cana-5422	118	96	a	a	DET
cana-5422	118	97	positive	positive	ADJ
cana-5422	118	98	constant	constant	NOUN
cana-5422	118	99	and	and	CCONJ
cana-5422	118	100	ϕ	ϕ	NOUN
cana-5422	118	101	be	be	AUX
cana-5422	118	102	any	any	DET
cana-5422	118	103	real	real	ADJ
cana-5422	118	104	number	number	NOUN
cana-5422	118	105	.	.	PUNCT
cana-5422	119	1	2.1	2.1	NUM
cana-5422	119	2	.	.	PUNCT
cana-5422	119	3	oddness	oddness	NOUN
cana-5422	119	4	of	of	ADP
cana-5422	119	5	f	f	NOUN
cana-5422	119	6	:	:	PUNCT
cana-5422	119	7	additive	additive	NOUN
cana-5422	119	8	case	case	NOUN
cana-5422	119	9	stability	stability	NOUN
cana-5422	119	10	results	result	VERB
cana-5422	119	11	:	:	PUNCT
cana-5422	119	12	direct	direct	ADJ
cana-5422	119	13	method	method	NOUN
cana-5422	119	14	.	.	PUNCT
cana-5422	120	1	theorem	theorem	VERB
cana-5422	120	2	2.1	2.1	NUM
cana-5422	120	3	.	.	PUNCT
cana-5422	121	1	suppose	suppose	VERB
cana-5422	121	2	that	that	SCONJ
cana-5422	121	3	an	an	DET
cana-5422	121	4	odd	odd	ADJ
cana-5422	121	5	function	function	NOUN
cana-5422	121	6	f	f	NOUN
cana-5422	121	7	:	:	PUNCT
cana-5422	121	8	w1	w1	PROPN
cana-5422	121	9	→	→	SYM
cana-5422	121	10	w2	w2	NOUN
cana-5422	121	11	satisfy	satisfy	VERB
cana-5422	121	12	the	the	DET
cana-5422	121	13	functional	functional	ADJ
cana-5422	121	14	inequality	inequality	NOUN
cana-5422	121	15	(	(	PUNCT
cana-5422	121	16	2.1	2.1	NUM
cana-5422	121	17	)	)	PUNCT
cana-5422	121	18	where	where	SCONJ
cana-5422	121	19	ψ	ψ	X
cana-5422	121	20	:	:	PUNCT
cana-5422	121	21	w3	w3	NOUN
cana-5422	121	22	1	1	NUM
cana-5422	121	23	→	→	SYM
cana-5422	122	1	[	[	X
cana-5422	122	2	0	0	NUM
cana-5422	122	3	,	,	PUNCT
cana-5422	122	4	∞	∞	PROPN
cana-5422	122	5	)	)	PUNCT
cana-5422	122	6	with	with	ADP
cana-5422	122	7	the	the	DET
cana-5422	122	8	condition	condition	NOUN
cana-5422	122	9	lim	lim	NOUN
cana-5422	122	10	`	`	PUNCT
cana-5422	122	11	→∞	→∞	PROPN
cana-5422	122	12	ψ	ψ	X
cana-5422	122	13	(	(	PUNCT
cana-5422	122	14	5`mw1	5`mw1	NUM
cana-5422	122	15	,	,	PUNCT
cana-5422	122	16	5`mw2	5`mw2	NUM
cana-5422	122	17	,	,	PUNCT
cana-5422	122	18	5`mw3	5`mw3	NOUN
cana-5422	122	19	)	)	PUNCT
cana-5422	122	20	5`m	5`m	NUM
cana-5422	122	21	=	=	SYM
cana-5422	122	22	0	0	NUM
cana-5422	122	23	;	;	PUNCT
cana-5422	122	24	µ	µ	X
cana-5422	122	25	=	=	SYM
cana-5422	122	26	±1	±1	VERB
cana-5422	122	27	,	,	PUNCT
cana-5422	122	28	(	(	PUNCT
cana-5422	122	29	2.3	2.3	NUM
cana-5422	122	30	)	)	PUNCT
cana-5422	122	31	for	for	ADP
cana-5422	122	32	all	all	DET
cana-5422	122	33	w1	w1	NOUN
cana-5422	122	34	,	,	PUNCT
cana-5422	122	35	w2	w2	NOUN
cana-5422	122	36	,	,	PUNCT
cana-5422	122	37	w3	w3	PROPN
cana-5422	122	38	∈	∈	PROPN
cana-5422	122	39	w1	w1	NOUN
cana-5422	122	40	.	.	PUNCT
cana-5422	123	1	then	then	ADV
cana-5422	123	2	there	there	PRON
cana-5422	123	3	exists	exist	VERB
cana-5422	123	4	a	a	DET
cana-5422	123	5	unique	unique	ADJ
cana-5422	123	6	additive	additive	ADJ
cana-5422	123	7	mapping	mapping	NOUN
cana-5422	123	8	a(w1	a(w1	NOUN
cana-5422	123	9	)	)	PUNCT
cana-5422	123	10	:	:	PUNCT
cana-5422	123	11	w1	w1	NOUN
cana-5422	123	12	→	→	SYM
cana-5422	123	13	w2	w2	NOUN
cana-5422	123	14	which	which	PRON
cana-5422	123	15	satisfies	satisfy	VERB
cana-5422	123	16	(	(	PUNCT
cana-5422	123	17	1.7	1.7	NUM
cana-5422	123	18	)	)	PUNCT
cana-5422	123	19	and	and	CCONJ
cana-5422	123	20	the	the	DET
cana-5422	123	21	functional	functional	ADJ
cana-5422	123	22	inequality	inequality	NOUN
cana-5422	123	23	‖f	‖f	PUNCT
cana-5422	123	24	(	(	PUNCT
cana-5422	123	25	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	123	26	≤	≤	NUM
cana-5422	123	27	1	1	NUM
cana-5422	123	28	5	5	NUM
cana-5422	123	29	∞	∞	NUM
cana-5422	123	30	∑	∑	PUNCT
cana-5422	123	31	η=	η=	ADJ
cana-5422	123	32	1−µ	1−µ	NOUN
cana-5422	123	33	2	2	NUM
cana-5422	123	34	1	1	NUM
cana-5422	123	35	5ηµ	5ηµ	NOUN
cana-5422	123	36	ψa	ψa	X
cana-5422	123	37	(	(	PUNCT
cana-5422	123	38	5ηµw1	5ηµw1	NOUN
cana-5422	123	39	)	)	PUNCT
cana-5422	123	40	(	(	PUNCT
cana-5422	123	41	2.4	2.4	NUM
cana-5422	123	42	)	)	PUNCT
cana-5422	123	43	=	=	SYM
cana-5422	124	1	1	1	NUM
cana-5422	124	2	5	5	NUM
cana-5422	124	3	∞	∞	NUM
cana-5422	124	4	∑	∑	PUNCT
cana-5422	124	5	η=	η=	ADJ
cana-5422	124	6	1−µ	1−µ	NOUN
cana-5422	124	7	2	2	NUM
cana-5422	124	8	1	1	NUM
cana-5422	124	9	5ηµ	5ηµ	NOUN
cana-5422	124	10	{	{	PUNCT
cana-5422	124	11	1	1	NUM
cana-5422	124	12	3	3	NUM
cana-5422	124	13	{	{	PUNCT
cana-5422	124	14	ψ	ψ	X
cana-5422	124	15	(	(	PUNCT
cana-5422	124	16	5ηµw1	5ηµw1	NUM
cana-5422	124	17	,	,	PUNCT
cana-5422	124	18	5ηµw1	5ηµw1	NUM
cana-5422	124	19	,	,	PUNCT
cana-5422	124	20	5ηµw1	5ηµw1	NUM
cana-5422	124	21	)	)	PUNCT
cana-5422	124	22	+	+	NUM
cana-5422	124	23	3ψ	3ψ	NUM
cana-5422	124	24	(	(	PUNCT
cana-5422	124	25	5ηµw1	5ηµw1	NUM
cana-5422	124	26	,	,	PUNCT
cana-5422	124	27	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	124	28	)	)	PUNCT
cana-5422	124	29	}	}	PUNCT
cana-5422	124	30	}	}	PUNCT
cana-5422	124	31	,	,	PUNCT
cana-5422	124	32	(	(	PUNCT
cana-5422	124	33	2.5	2.5	NUM
cana-5422	124	34	)	)	PUNCT
cana-5422	124	35	and	and	CCONJ
cana-5422	124	36	the	the	DET
cana-5422	124	37	mapping	mapping	NOUN
cana-5422	124	38	a(w1	a(w1	NOUN
cana-5422	124	39	)	)	PUNCT
cana-5422	124	40	is	be	AUX
cana-5422	124	41	obtained	obtain	VERB
cana-5422	124	42	by	by	ADP
cana-5422	124	43	a(w1	a(w1	NOUN
cana-5422	124	44	)	)	PUNCT
cana-5422	124	45	=	=	SYM
cana-5422	124	46	lim	lim	PROPN
cana-5422	124	47	`	`	PUNCT
cana-5422	124	48	→∞	→∞	PROPN
cana-5422	124	49	1	1	NUM
cana-5422	124	50	5`mf	5`mf	NUM
cana-5422	124	51	(	(	PUNCT
cana-5422	124	52	5`mw1	5`mw1	NUM
cana-5422	124	53	)	)	PUNCT
cana-5422	124	54	,	,	PUNCT
cana-5422	124	55	(	(	PUNCT
cana-5422	124	56	2.6	2.6	NUM
cana-5422	124	57	)	)	PUNCT
cana-5422	124	58	for	for	ADP
cana-5422	124	59	all	all	DET
cana-5422	124	60	w1	w1	NOUN
cana-5422	124	61	∈	∈	PROPN
cana-5422	124	62	w1	w1	NOUN
cana-5422	124	63	.	.	PUNCT
cana-5422	125	1	proof	proof	NOUN
cana-5422	125	2	.	.	PUNCT
cana-5422	126	1	using	use	VERB
cana-5422	126	2	oddness	oddness	NOUN
cana-5422	126	3	of	of	ADP
cana-5422	126	4	f	f	PROPN
cana-5422	126	5	in	in	ADP
cana-5422	126	6	(	(	PUNCT
cana-5422	126	7	2.1	2.1	NUM
cana-5422	126	8	)	)	PUNCT
cana-5422	126	9	,	,	PUNCT
cana-5422	126	10	we	we	PRON
cana-5422	126	11	get∥∥∥f	get∥∥∥f	VERB
cana-5422	126	12	(	(	PUNCT
cana-5422	126	13	3w1	3w1	NUM
cana-5422	126	14	+	+	CCONJ
cana-5422	126	15	w2	w2	NOUN
cana-5422	126	16	+	+	CCONJ
cana-5422	126	17	w3	w3	PROPN
cana-5422	126	18	)	)	PUNCT
cana-5422	127	1	+	+	NOUN
cana-5422	127	2	f	f	X
cana-5422	127	3	(	(	PUNCT
cana-5422	127	4	w1	w1	NOUN
cana-5422	127	5	+	+	CCONJ
cana-5422	127	6	3w2	3w2	NUM
cana-5422	127	7	+	+	CCONJ
cana-5422	127	8	w3	w3	NOUN
cana-5422	127	9	)	)	PUNCT
cana-5422	128	1	+	+	NOUN
cana-5422	128	2	f	f	X
cana-5422	128	3	(	(	PUNCT
cana-5422	128	4	w1	w1	NOUN
cana-5422	128	5	+	+	NOUN
cana-5422	128	6	w2	w2	NOUN
cana-5422	128	7	+	+	CCONJ
cana-5422	128	8	3w3)−	3w3)−	PROPN
cana-5422	128	9	6f	6f	NOUN
cana-5422	128	10	(	(	PUNCT
cana-5422	128	11	3	3	NUM
cana-5422	128	12	∑	∑	PUNCT
cana-5422	128	13	ψ=1	ψ=1	PUNCT
cana-5422	128	14	wψ	wψ	ADP
cana-5422	128	15	)	)	PUNCT
cana-5422	129	1	+	+	CCONJ
cana-5422	129	2	3	3	NUM
cana-5422	129	3	∑	∑	SYM
cana-5422	129	4	ψ=1	ψ=1	PUNCT
cana-5422	129	5	f	f	X
cana-5422	129	6	(	(	PUNCT
cana-5422	129	7	wψ	wψ	ADP
cana-5422	129	8	)	)	PUNCT
cana-5422	129	9	∥∥∥	∥∥∥	PROPN
cana-5422	129	10	≤	≤	NUM
cana-5422	129	11	ψ	ψ	X
cana-5422	129	12	(	(	PUNCT
cana-5422	129	13	w1	w1	NOUN
cana-5422	129	14	,	,	PUNCT
cana-5422	129	15	w2	w2	NOUN
cana-5422	129	16	,	,	PUNCT
cana-5422	129	17	w3	w3	PROPN
cana-5422	129	18	)	)	PUNCT
cana-5422	129	19	,	,	PUNCT
cana-5422	129	20	∀	∀	X
cana-5422	129	21	w1	w1	NOUN
cana-5422	129	22	,	,	PUNCT
cana-5422	129	23	w2	w2	NOUN
cana-5422	129	24	,	,	PUNCT
cana-5422	129	25	w3	w3	PROPN
cana-5422	129	26	∈	∈	PROPN
cana-5422	129	27	w1	w1	NOUN
cana-5422	129	28	.	.	PUNCT
cana-5422	130	1	(	(	PUNCT
cana-5422	130	2	2.7	2.7	NUM
cana-5422	130	3	)	)	PUNCT
cana-5422	130	4	interchanging	interchange	VERB
cana-5422	130	5	(	(	PUNCT
cana-5422	130	6	w1	w1	NOUN
cana-5422	130	7	,	,	PUNCT
cana-5422	130	8	w2	w2	NOUN
cana-5422	130	9	,	,	PUNCT
cana-5422	130	10	w3	w3	PROPN
cana-5422	130	11	)	)	PUNCT
cana-5422	130	12	by	by	ADP
cana-5422	130	13	(	(	PUNCT
cana-5422	130	14	w1	w1	NOUN
cana-5422	130	15	,	,	PUNCT
cana-5422	130	16	w1	w1	NOUN
cana-5422	130	17	,	,	PUNCT
cana-5422	130	18	w1	w1	NOUN
cana-5422	130	19	)	)	PUNCT
cana-5422	130	20	in	in	ADP
cana-5422	130	21	(	(	PUNCT
cana-5422	130	22	2.7	2.7	NUM
cana-5422	130	23	)	)	PUNCT
cana-5422	130	24	,	,	PUNCT
cana-5422	130	25	we	we	PRON
cana-5422	130	26	obtain∥∥∥3f	obtain∥∥∥3f	VERB
cana-5422	130	27	(	(	PUNCT
cana-5422	130	28	5w1)−	5w1)−	NOUN
cana-5422	130	29	6f	6f	PROPN
cana-5422	130	30	(	(	PUNCT
cana-5422	130	31	3w1	3w1	NUM
cana-5422	130	32	)	)	PUNCT
cana-5422	131	1	+	+	CCONJ
cana-5422	131	2	3f	3f	PROPN
cana-5422	131	3	(	(	PUNCT
cana-5422	131	4	w1	w1	NOUN
cana-5422	131	5	)	)	PUNCT
cana-5422	131	6	∥∥∥	∥∥∥	PROPN
cana-5422	131	7	≤	≤	NUM
cana-5422	131	8	ψ	ψ	X
cana-5422	131	9	(	(	PUNCT
cana-5422	131	10	w1	w1	NOUN
cana-5422	131	11	,	,	PUNCT
cana-5422	131	12	w1	w1	NOUN
cana-5422	131	13	,	,	PUNCT
cana-5422	131	14	w1	w1	NOUN
cana-5422	131	15	)	)	PUNCT
cana-5422	131	16	,	,	PUNCT
cana-5422	131	17	∀	∀	NOUN
cana-5422	131	18	w1	w1	NOUN
cana-5422	131	19	∈	∈	PROPN
cana-5422	131	20	w1	w1	NOUN
cana-5422	131	21	.	.	PUNCT
cana-5422	132	1	(	(	PUNCT
cana-5422	132	2	2.8	2.8	NUM
cana-5422	132	3	)	)	PUNCT
cana-5422	132	4	communications	communication	NOUN
cana-5422	132	5	on	on	ADP
cana-5422	132	6	applied	apply	VERB
cana-5422	132	7	nonlinear	nonlinear	ADJ
cana-5422	132	8	analysis	analysis	NOUN
cana-5422	132	9	issn	issn	NOUN
cana-5422	132	10	:	:	PUNCT
cana-5422	132	11	1074	1074	NUM
cana-5422	132	12	-	-	PUNCT
cana-5422	132	13	133x	133x	NUM
cana-5422	132	14	vol	vol	NOUN
cana-5422	132	15	32	32	NUM
cana-5422	132	16	no	no	NOUN
cana-5422	132	17	.	.	PUNCT
cana-5422	133	1	10s(2025	10s(2025	NUM
cana-5422	133	2	)	)	PUNCT
cana-5422	133	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	133	4	2189	2189	NUM
cana-5422	133	5	again	again	ADV
cana-5422	133	6	interchanging	interchange	VERB
cana-5422	133	7	(	(	PUNCT
cana-5422	133	8	w1	w1	NOUN
cana-5422	133	9	,	,	PUNCT
cana-5422	133	10	w2	w2	NOUN
cana-5422	133	11	,	,	PUNCT
cana-5422	133	12	w3	w3	PROPN
cana-5422	133	13	)	)	PUNCT
cana-5422	133	14	by	by	ADP
cana-5422	133	15	(	(	PUNCT
cana-5422	133	16	w1	w1	NOUN
cana-5422	133	17	,	,	PUNCT
cana-5422	133	18	w1,−w1	w1,−w1	NUM
cana-5422	133	19	)	)	PUNCT
cana-5422	133	20	in	in	ADP
cana-5422	133	21	(	(	PUNCT
cana-5422	133	22	2.7	2.7	NUM
cana-5422	133	23	)	)	PUNCT
cana-5422	133	24	,	,	PUNCT
cana-5422	133	25	we	we	PRON
cana-5422	133	26	have∥∥∥2f	have∥∥∥2f	VERB
cana-5422	133	27	(	(	PUNCT
cana-5422	133	28	3w1)−	3w1)−	NOUN
cana-5422	133	29	6f	6f	PROPN
cana-5422	133	30	(	(	PUNCT
cana-5422	133	31	w1	w1	NOUN
cana-5422	133	32	)	)	PUNCT
cana-5422	134	1	∥∥∥	∥∥∥	PROPN
cana-5422	134	2	≤	≤	NUM
cana-5422	135	1	ψ	ψ	X
cana-5422	135	2	(	(	PUNCT
cana-5422	135	3	w1	w1	NOUN
cana-5422	135	4	,	,	PUNCT
cana-5422	135	5	w1,−w1	w1,−w1	NUM
cana-5422	135	6	)	)	PUNCT
cana-5422	135	7	⇒	⇒	NOUN
cana-5422	135	8	∥∥∥6f	∥∥∥6f	PUNCT
cana-5422	135	9	(	(	PUNCT
cana-5422	135	10	3w1)−	3w1)−	PROPN
cana-5422	135	11	18f	18f	PROPN
cana-5422	135	12	(	(	PUNCT
cana-5422	135	13	w1	w1	NOUN
cana-5422	135	14	)	)	PUNCT
cana-5422	135	15	∥∥∥	∥∥∥	PROPN
cana-5422	135	16	≤	≤	ADJ
cana-5422	135	17	3ψ	3ψ	NUM
cana-5422	135	18	(	(	PUNCT
cana-5422	135	19	w1	w1	NOUN
cana-5422	135	20	,	,	PUNCT
cana-5422	135	21	w1,−w1	w1,−w1	NUM
cana-5422	135	22	)	)	PUNCT
cana-5422	135	23	,	,	PUNCT
cana-5422	135	24	∀	∀	NOUN
cana-5422	135	25	w1	w1	NOUN
cana-5422	135	26	∈	∈	PROPN
cana-5422	135	27	w1	w1	NOUN
cana-5422	135	28	.	.	PUNCT
cana-5422	136	1	(	(	PUNCT
cana-5422	136	2	2.9	2.9	NUM
cana-5422	136	3	)	)	PUNCT
cana-5422	136	4	combining	combine	VERB
cana-5422	136	5	(	(	PUNCT
cana-5422	136	6	2.8	2.8	NUM
cana-5422	136	7	)	)	PUNCT
cana-5422	136	8	and	and	CCONJ
cana-5422	136	9	(	(	PUNCT
cana-5422	136	10	2.9	2.9	NUM
cana-5422	136	11	)	)	PUNCT
cana-5422	136	12	,	,	PUNCT
cana-5422	136	13	we	we	PRON
cana-5422	136	14	arrive∥∥∥3f	arrive∥∥∥3f	VERB
cana-5422	136	15	(	(	PUNCT
cana-5422	136	16	5w1)−	5w1)−	PROPN
cana-5422	136	17	15f	15f	PROPN
cana-5422	136	18	(	(	PUNCT
cana-5422	136	19	w1	w1	NOUN
cana-5422	136	20	)	)	PUNCT
cana-5422	136	21	∥∥∥	∥∥∥	PROPN
cana-5422	136	22	≤	≤	NUM
cana-5422	136	23	∥∥∥3f	∥∥∥3f	PROPN
cana-5422	136	24	(	(	PUNCT
cana-5422	136	25	5w1)−	5w1)−	NOUN
cana-5422	136	26	6f	6f	PROPN
cana-5422	136	27	(	(	PUNCT
cana-5422	136	28	3w1	3w1	NUM
cana-5422	136	29	)	)	PUNCT
cana-5422	137	1	+	+	CCONJ
cana-5422	137	2	3f	3f	PROPN
cana-5422	137	3	(	(	PUNCT
cana-5422	137	4	w1	w1	NOUN
cana-5422	137	5	)	)	PUNCT
cana-5422	137	6	∥∥∥+	∥∥∥+	PROPN
cana-5422	137	7	∥∥∥6f	∥∥∥6f	PUNCT
cana-5422	137	8	(	(	PUNCT
cana-5422	137	9	3w1)−	3w1)−	PROPN
cana-5422	137	10	18f	18f	PROPN
cana-5422	137	11	(	(	PUNCT
cana-5422	137	12	w1	w1	NOUN
cana-5422	137	13	)	)	PUNCT
cana-5422	137	14	∥∥∥	∥∥∥	PROPN
cana-5422	137	15	≤	≤	NUM
cana-5422	137	16	ψ	ψ	X
cana-5422	137	17	(	(	PUNCT
cana-5422	137	18	w1	w1	NOUN
cana-5422	137	19	,	,	PUNCT
cana-5422	137	20	w1	w1	NOUN
cana-5422	137	21	,	,	PUNCT
cana-5422	137	22	w1	w1	NOUN
cana-5422	137	23	)	)	PUNCT
cana-5422	137	24	+	+	NUM
cana-5422	137	25	3ψ	3ψ	NUM
cana-5422	137	26	(	(	PUNCT
cana-5422	137	27	w1	w1	NOUN
cana-5422	137	28	,	,	PUNCT
cana-5422	137	29	w1,−w1	w1,−w1	NUM
cana-5422	137	30	)	)	PUNCT
cana-5422	137	31	,	,	PUNCT
cana-5422	137	32	∀	∀	NOUN
cana-5422	137	33	w1	w1	NOUN
cana-5422	137	34	∈	∈	PROPN
cana-5422	137	35	w1	w1	NOUN
cana-5422	137	36	.	.	PUNCT
cana-5422	138	1	(	(	PUNCT
cana-5422	138	2	2.10	2.10	NUM
cana-5422	138	3	)	)	PUNCT
cana-5422	138	4	one	one	NOUN
cana-5422	138	5	can	can	AUX
cana-5422	138	6	see	see	VERB
cana-5422	138	7	from	from	ADP
cana-5422	138	8	(	(	PUNCT
cana-5422	138	9	2.10	2.10	NUM
cana-5422	138	10	)	)	PUNCT
cana-5422	138	11	that∥∥∥f	that∥∥∥f	PROPN
cana-5422	138	12	(	(	PUNCT
cana-5422	138	13	5w1)−	5w1)−	PROPN
cana-5422	138	14	5f	5f	NOUN
cana-5422	138	15	(	(	PUNCT
cana-5422	138	16	w1	w1	NOUN
cana-5422	138	17	)	)	PUNCT
cana-5422	138	18	∥∥∥	∥∥∥	PROPN
cana-5422	138	19	≤	≤	NUM
cana-5422	138	20	1	1	NUM
cana-5422	138	21	3	3	NUM
cana-5422	138	22	{	{	PUNCT
cana-5422	138	23	ψ	ψ	X
cana-5422	138	24	(	(	PUNCT
cana-5422	138	25	w1	w1	NOUN
cana-5422	138	26	,	,	PUNCT
cana-5422	138	27	w1	w1	NOUN
cana-5422	138	28	,	,	PUNCT
cana-5422	138	29	w1	w1	NOUN
cana-5422	138	30	)	)	PUNCT
cana-5422	139	1	+	+	NUM
cana-5422	139	2	3ψ	3ψ	NUM
cana-5422	139	3	(	(	PUNCT
cana-5422	139	4	w1	w1	NOUN
cana-5422	139	5	,	,	PUNCT
cana-5422	139	6	w1,−w1	w1,−w1	NUM
cana-5422	139	7	)	)	PUNCT
cana-5422	139	8	}	}	PUNCT
cana-5422	139	9	=	=	PUNCT
cana-5422	139	10	ψa	ψa	X
cana-5422	139	11	(	(	PUNCT
cana-5422	139	12	w1	w1	NOUN
cana-5422	139	13	)	)	PUNCT
cana-5422	139	14	,	,	PUNCT
cana-5422	139	15	∀	∀	NOUN
cana-5422	139	16	w1	w1	NOUN
cana-5422	139	17	∈	∈	PROPN
cana-5422	139	18	w1	w1	NOUN
cana-5422	139	19	.	.	PUNCT
cana-5422	140	1	(	(	PUNCT
cana-5422	140	2	2.11	2.11	NUM
cana-5422	140	3	)	)	PUNCT
cana-5422	140	4	it	it	PRON
cana-5422	140	5	follows	follow	VERB
cana-5422	140	6	from	from	ADP
cana-5422	140	7	(	(	PUNCT
cana-5422	140	8	2.11	2.11	NUM
cana-5422	140	9	)	)	PUNCT
cana-5422	140	10	that	that	PRON
cana-5422	140	11	∥∥∥1	∥∥∥1	VERB
cana-5422	140	12	5	5	NUM
cana-5422	140	13	f	f	NOUN
cana-5422	140	14	(	(	PUNCT
cana-5422	140	15	5w1)−f	5w1)−f	PROPN
cana-5422	140	16	(	(	PUNCT
cana-5422	140	17	w1	w1	NOUN
cana-5422	140	18	)	)	PUNCT
cana-5422	140	19	∥∥∥	∥∥∥	PROPN
cana-5422	140	20	≤	≤	NUM
cana-5422	140	21	1	1	NUM
cana-5422	140	22	5	5	NUM
cana-5422	140	23	ψa	ψa	NOUN
cana-5422	140	24	(	(	PUNCT
cana-5422	140	25	w1	w1	NOUN
cana-5422	140	26	)	)	PUNCT
cana-5422	140	27	,	,	PUNCT
cana-5422	140	28	∀	∀	NOUN
cana-5422	140	29	w1	w1	NOUN
cana-5422	140	30	∈	∈	PROPN
cana-5422	140	31	w1	w1	NOUN
cana-5422	140	32	.	.	PUNCT
cana-5422	141	1	(	(	PUNCT
cana-5422	141	2	2.12	2.12	NUM
cana-5422	141	3	)	)	PUNCT
cana-5422	141	4	generalizing	generalize	VERB
cana-5422	141	5	for	for	ADP
cana-5422	141	6	a	a	DET
cana-5422	141	7	positive	positive	ADJ
cana-5422	141	8	integer	integer	NOUN
cana-5422	141	9	`	`	PUNCT
cana-5422	141	10	,	,	PUNCT
cana-5422	141	11	we	we	PRON
cana-5422	141	12	get∥∥∥	get∥∥∥	VERB
cana-5422	141	13	1	1	NUM
cana-5422	141	14	5	5	NUM
cana-5422	141	15	`	`	SYM
cana-5422	141	16	f	f	X
cana-5422	141	17	(	(	PUNCT
cana-5422	141	18	5`w1)−f	5`w1)−f	PROPN
cana-5422	141	19	(	(	PUNCT
cana-5422	141	20	w1	w1	NOUN
cana-5422	141	21	)	)	PUNCT
cana-5422	141	22	∥∥∥	∥∥∥	PROPN
cana-5422	141	23	≤	≤	NUM
cana-5422	141	24	1	1	NUM
cana-5422	141	25	5	5	NUM
cana-5422	141	26	`	`	PUNCT
cana-5422	141	27	∑	∑	PUNCT
cana-5422	141	28	η=0	η=0	PROPN
cana-5422	141	29	1	1	NUM
cana-5422	141	30	5η	5η	NUM
cana-5422	141	31	ψa	ψa	ADP
cana-5422	142	1	(	(	PUNCT
cana-5422	142	2	5ηw1	5ηw1	NUM
cana-5422	142	3	)	)	PUNCT
cana-5422	142	4	,	,	PUNCT
cana-5422	142	5	∀	∀	NOUN
cana-5422	142	6	w1	w1	NOUN
cana-5422	142	7	∈	∈	PROPN
cana-5422	142	8	w1	w1	NOUN
cana-5422	142	9	.	.	PUNCT
cana-5422	143	1	(	(	PUNCT
cana-5422	143	2	2.13	2.13	NUM
cana-5422	143	3	)	)	PUNCT
cana-5422	143	4	now	now	ADV
cana-5422	143	5	,	,	PUNCT
cana-5422	143	6	changing	change	VERB
cana-5422	143	7	w1	w1	NOUN
cana-5422	143	8	by	by	ADP
cana-5422	143	9	5`1	5`1	NUM
cana-5422	143	10	w1	w1	NOUN
cana-5422	143	11	in	in	ADP
cana-5422	143	12	(	(	PUNCT
cana-5422	143	13	2.13	2.13	NUM
cana-5422	143	14	)	)	PUNCT
cana-5422	143	15	,	,	PUNCT
cana-5422	143	16	we	we	PRON
cana-5422	143	17	obtain∥∥∥	obtain∥∥∥	VERB
cana-5422	143	18	1	1	NUM
cana-5422	143	19	5`+`1	5`+`1	NUM
cana-5422	143	20	f	f	NOUN
cana-5422	143	21	(	(	PUNCT
cana-5422	143	22	5`+`1	5`+`1	NUM
cana-5422	143	23	w1)−	w1)−	NOUN
cana-5422	143	24	1	1	NUM
cana-5422	143	25	5`1	5`1	NUM
cana-5422	143	26	f	f	X
cana-5422	143	27	(	(	PUNCT
cana-5422	143	28	5`1	5`1	NUM
cana-5422	143	29	w1	w1	NOUN
cana-5422	143	30	)	)	PUNCT
cana-5422	143	31	∥∥∥	∥∥∥	PROPN
cana-5422	144	1	=	=	SYM
cana-5422	145	1	1	1	NUM
cana-5422	145	2	5`1	5`1	NUM
cana-5422	145	3	∥∥∥	∥∥∥	NUM
cana-5422	145	4	1	1	NUM
cana-5422	145	5	5	5	NUM
cana-5422	145	6	`	`	SYM
cana-5422	145	7	f	f	X
cana-5422	145	8	(	(	PUNCT
cana-5422	145	9	5`+`1	5`+`1	NUM
cana-5422	145	10	w1)−f	w1)−f	PROPN
cana-5422	145	11	(	(	PUNCT
cana-5422	145	12	5`1	5`1	NUM
cana-5422	145	13	w1	w1	NOUN
cana-5422	145	14	)	)	PUNCT
cana-5422	145	15	∥∥∥	∥∥∥	PROPN
cana-5422	145	16	≤	≤	NUM
cana-5422	145	17	1	1	NUM
cana-5422	145	18	5	5	NUM
cana-5422	145	19	`	`	PUNCT
cana-5422	145	20	∑	∑	PUNCT
cana-5422	145	21	η=0	η=0	PROPN
cana-5422	145	22	1	1	NUM
cana-5422	145	23	5η+`1	5η+`1	NUM
cana-5422	145	24	ψa	ψa	NOUN
cana-5422	145	25	(	(	PUNCT
cana-5422	145	26	5η+`1	5η+`1	NUM
cana-5422	145	27	w1	w1	NOUN
cana-5422	145	28	)	)	PUNCT
cana-5422	145	29	→	→	SYM
cana-5422	145	30	0	0	PUNCT
cana-5422	145	31	as	as	ADP
cana-5422	145	32	`	`	PUNCT
cana-5422	145	33	1	1	NUM
cana-5422	145	34	→	→	SYM
cana-5422	145	35	∞	∞	PROPN
cana-5422	145	36	,	,	PUNCT
cana-5422	145	37	∀	∀	X
cana-5422	145	38	w1	w1	NOUN
cana-5422	145	39	∈	∈	PROPN
cana-5422	145	40	w1	w1	NOUN
cana-5422	145	41	.	.	PUNCT
cana-5422	146	1	(	(	PUNCT
cana-5422	146	2	2.14	2.14	NUM
cana-5422	146	3	)	)	PUNCT
cana-5422	146	4	therefore	therefore	ADV
cana-5422	146	5	,	,	PUNCT
cana-5422	146	6	the	the	DET
cana-5422	146	7	sequence	sequence	NOUN
cana-5422	146	8	{	{	PUNCT
cana-5422	146	9	1	1	NUM
cana-5422	146	10	5	5	NUM
cana-5422	146	11	`	`	PUNCT
cana-5422	146	12	f	f	X
cana-5422	146	13	(	(	PUNCT
cana-5422	146	14	5`w1	5`w1	NUM
cana-5422	146	15	)	)	PUNCT
cana-5422	146	16	}	}	PUNCT
cana-5422	146	17	,	,	PUNCT
cana-5422	146	18	is	be	AUX
cana-5422	146	19	a	a	DET
cana-5422	146	20	cauchy	cauchy	ADJ
cana-5422	146	21	sequence	sequence	NOUN
cana-5422	146	22	and	and	CCONJ
cana-5422	146	23	it	it	PRON
cana-5422	146	24	converges	converge	VERB
cana-5422	146	25	to	to	ADP
cana-5422	146	26	a(w1	a(w1	NOUN
cana-5422	146	27	)	)	PUNCT
cana-5422	146	28	inw2	inw2	PROPN
cana-5422	146	29	.	.	PUNCT
cana-5422	147	1	so	so	ADV
cana-5422	147	2	,	,	PUNCT
cana-5422	147	3	we	we	PRON
cana-5422	147	4	define	define	VERB
cana-5422	147	5	a(w1	a(w1	NOUN
cana-5422	147	6	)	)	PUNCT
cana-5422	147	7	=	=	SYM
cana-5422	147	8	lim	lim	PROPN
cana-5422	147	9	`	`	PUNCT
cana-5422	147	10	→∞	→∞	PROPN
cana-5422	147	11	1	1	NUM
cana-5422	147	12	5	5	NUM
cana-5422	147	13	`	`	SYM
cana-5422	147	14	f	f	X
cana-5422	147	15	(	(	PUNCT
cana-5422	147	16	5`w1	5`w1	NUM
cana-5422	147	17	)	)	PUNCT
cana-5422	147	18	,	,	PUNCT
cana-5422	147	19	∀	∀	NOUN
cana-5422	147	20	w1	w1	NOUN
cana-5422	147	21	∈	∈	PROPN
cana-5422	147	22	w1	w1	NOUN
cana-5422	147	23	.	.	PUNCT
cana-5422	148	1	(	(	PUNCT
cana-5422	148	2	2.15	2.15	NUM
cana-5422	148	3	)	)	PUNCT
cana-5422	148	4	taking	take	VERB
cana-5422	148	5	limit	limit	NOUN
cana-5422	148	6	`	`	PUNCT
cana-5422	148	7	→	→	SYM
cana-5422	148	8	∞	∞	NUM
cana-5422	148	9	in	in	ADP
cana-5422	148	10	(	(	PUNCT
cana-5422	148	11	2.13	2.13	NUM
cana-5422	148	12	)	)	PUNCT
cana-5422	148	13	,	,	PUNCT
cana-5422	148	14	we	we	PRON
cana-5422	148	15	have∥∥∥a(w1)−f	have∥∥∥a(w1)−f	PROPN
cana-5422	148	16	(	(	PUNCT
cana-5422	148	17	w1	w1	NOUN
cana-5422	148	18	)	)	PUNCT
cana-5422	148	19	∥∥∥	∥∥∥	PROPN
cana-5422	148	20	≤	≤	NUM
cana-5422	149	1	1	1	NUM
cana-5422	149	2	5	5	NUM
cana-5422	149	3	∞	∞	NUM
cana-5422	149	4	∑	∑	PUNCT
cana-5422	149	5	η=0	η=0	PROPN
cana-5422	149	6	1	1	NUM
cana-5422	149	7	5η	5η	NUM
cana-5422	149	8	ψa	ψa	ADP
cana-5422	149	9	(	(	PUNCT
cana-5422	149	10	5ηw1	5ηw1	NUM
cana-5422	149	11	)	)	PUNCT
cana-5422	149	12	,	,	PUNCT
cana-5422	149	13	∀	∀	NOUN
cana-5422	149	14	w1	w1	NOUN
cana-5422	149	15	∈	∈	PROPN
cana-5422	149	16	w1	w1	NOUN
cana-5422	149	17	.	.	PUNCT
cana-5422	150	1	(	(	PUNCT
cana-5422	150	2	2.16	2.16	NUM
cana-5422	150	3	)	)	PUNCT
cana-5422	150	4	thus	thus	ADV
cana-5422	150	5	,	,	PUNCT
cana-5422	150	6	(	(	PUNCT
cana-5422	150	7	2.4	2.4	NUM
cana-5422	150	8	)	)	PUNCT
cana-5422	150	9	and	and	CCONJ
cana-5422	150	10	(	(	PUNCT
cana-5422	150	11	2.5	2.5	NUM
cana-5422	150	12	)	)	PUNCT
cana-5422	150	13	holds	hold	VERB
cana-5422	150	14	for	for	ADP
cana-5422	150	15	µ	µ	NOUN
cana-5422	150	16	=	=	SYM
cana-5422	150	17	1	1	NUM
cana-5422	150	18	.	.	X
cana-5422	151	1	interchanging	interchanging	PROPN
cana-5422	151	2	(	(	PUNCT
cana-5422	151	3	w1	w1	NOUN
cana-5422	151	4	,	,	PUNCT
cana-5422	151	5	w2	w2	NOUN
cana-5422	151	6	,	,	PUNCT
cana-5422	151	7	w3	w3	PROPN
cana-5422	151	8	)	)	PUNCT
cana-5422	151	9	=	=	PRON
cana-5422	151	10	(	(	PUNCT
cana-5422	151	11	5`w1	5`w1	NUM
cana-5422	151	12	,	,	PUNCT
cana-5422	151	13	5`w2	5`w2	NUM
cana-5422	151	14	,	,	PUNCT
cana-5422	151	15	5`w3	5`w3	NUM
cana-5422	151	16	)	)	PUNCT
cana-5422	151	17	,	,	PUNCT
cana-5422	151	18	we	we	PRON
cana-5422	151	19	arrive	arrive	VERB
cana-5422	151	20	1	1	NUM
cana-5422	151	21	5	5	NUM
cana-5422	151	22	`	`	PUNCT
cana-5422	151	23	∥∥∥f	∥∥∥f	NOUN
cana-5422	151	24	(	(	PUNCT
cana-5422	151	25	5`(3w1	5`(3w1	NUM
cana-5422	151	26	+	+	CCONJ
cana-5422	151	27	w2	w2	NOUN
cana-5422	151	28	+	+	CCONJ
cana-5422	151	29	w3	w3	PROPN
cana-5422	151	30	)	)	PUNCT
cana-5422	151	31	)	)	PUNCT
cana-5422	152	1	+	+	NOUN
cana-5422	152	2	f	f	X
cana-5422	152	3	(	(	PUNCT
cana-5422	152	4	5`(w1	5`(w1	NUM
cana-5422	152	5	+	+	CCONJ
cana-5422	152	6	3w2	3w2	NUM
cana-5422	152	7	+	+	CCONJ
cana-5422	152	8	w3	w3	NOUN
cana-5422	152	9	)	)	PUNCT
cana-5422	152	10	)	)	PUNCT
cana-5422	153	1	+	+	NOUN
cana-5422	153	2	f	f	X
cana-5422	153	3	(	(	PUNCT
cana-5422	153	4	5`(w1	5`(w1	NOUN
cana-5422	153	5	+	+	NUM
cana-5422	153	6	w2	w2	NOUN
cana-5422	153	7	+	+	CCONJ
cana-5422	153	8	3w3))−	3w3))−	NUM
cana-5422	153	9	6f	6f	NUM
cana-5422	153	10	(	(	PUNCT
cana-5422	153	11	3	3	NUM
cana-5422	153	12	∑	∑	SYM
cana-5422	153	13	ψ=1	ψ=1	X
cana-5422	153	14	5`wψ	5`wψ	PROPN
cana-5422	153	15	)	)	PUNCT
cana-5422	153	16	−	−	NOUN
cana-5422	153	17	1	1	NUM
cana-5422	153	18	2	2	NUM
cana-5422	153	19	{	{	PUNCT
cana-5422	153	20	f	f	PROPN
cana-5422	153	21	(	(	PUNCT
cana-5422	153	22	3	3	NUM
cana-5422	153	23	∑	∑	SYM
cana-5422	153	24	ψ=1	ψ=1	X
cana-5422	153	25	5`wψ	5`wψ	PROPN
cana-5422	153	26	)	)	PUNCT
cana-5422	154	1	+	+	NOUN
cana-5422	154	2	f	f	X
cana-5422	154	3	(	(	PUNCT
cana-5422	154	4	−	−	PROPN
cana-5422	154	5	3	3	NUM
cana-5422	154	6	∑	∑	PUNCT
cana-5422	154	7	ψ=1	ψ=1	X
cana-5422	154	8	5`wψ	5`wψ	PROPN
cana-5422	154	9	)	)	PUNCT
cana-5422	154	10	}	}	PUNCT
cana-5422	155	1	+	+	CCONJ
cana-5422	155	2	3	3	NUM
cana-5422	155	3	∑	∑	NOUN
cana-5422	155	4	ψ=1	ψ=1	PUNCT
cana-5422	155	5	{	{	PUNCT
cana-5422	155	6	f	f	PROPN
cana-5422	155	7	(	(	PUNCT
cana-5422	155	8	5`wψ)−	5`wψ)−	NUM
cana-5422	155	9	5	5	NUM
cana-5422	155	10	2	2	NUM
cana-5422	155	11	[	[	PUNCT
cana-5422	155	12	f	f	X
cana-5422	155	13	(	(	PUNCT
cana-5422	155	14	5`wψ	5`wψ	PROPN
cana-5422	155	15	)	)	PUNCT
cana-5422	156	1	+	+	NOUN
cana-5422	156	2	f	f	X
cana-5422	156	3	(	(	PUNCT
cana-5422	156	4	−5`wψ	−5`wψ	NOUN
cana-5422	156	5	)	)	PUNCT
cana-5422	156	6	]	]	PUNCT
cana-5422	156	7	}	}	PUNCT
cana-5422	156	8	∥∥∥	∥∥∥	NUM
cana-5422	156	9	≤	≤	NUM
cana-5422	156	10	1	1	NUM
cana-5422	156	11	5	5	NUM
cana-5422	156	12	`	`	CCONJ
cana-5422	156	13	ψ	ψ	X
cana-5422	156	14	(	(	PUNCT
cana-5422	156	15	5`w1	5`w1	NUM
cana-5422	156	16	,	,	PUNCT
cana-5422	156	17	5`w2	5`w2	NUM
cana-5422	156	18	,	,	PUNCT
cana-5422	156	19	5`w3	5`w3	NUM
cana-5422	156	20	)	)	PUNCT
cana-5422	156	21	,	,	PUNCT
cana-5422	156	22	∀w1	∀w1	NOUN
cana-5422	156	23	,	,	PUNCT
cana-5422	156	24	w2	w2	NOUN
cana-5422	156	25	,	,	PUNCT
cana-5422	156	26	w3	w3	PROPN
cana-5422	156	27	∈	∈	PROPN
cana-5422	156	28	w1	w1	NOUN
cana-5422	156	29	.	.	PUNCT
cana-5422	157	1	(	(	PUNCT
cana-5422	157	2	2.17	2.17	NUM
cana-5422	157	3	)	)	PUNCT
cana-5422	157	4	communications	communication	NOUN
cana-5422	157	5	on	on	ADP
cana-5422	157	6	applied	apply	VERB
cana-5422	157	7	nonlinear	nonlinear	ADJ
cana-5422	157	8	analysis	analysis	NOUN
cana-5422	157	9	issn	issn	NOUN
cana-5422	157	10	:	:	PUNCT
cana-5422	157	11	1074	1074	NUM
cana-5422	157	12	-	-	PUNCT
cana-5422	157	13	133x	133x	NUM
cana-5422	157	14	vol	vol	NOUN
cana-5422	157	15	32	32	NUM
cana-5422	157	16	no	no	NOUN
cana-5422	157	17	.	.	PUNCT
cana-5422	158	1	10s(2025	10s(2025	NUM
cana-5422	158	2	)	)	PUNCT
cana-5422	158	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	158	4	2190	2190	NUM
cana-5422	158	5	taking	take	VERB
cana-5422	158	6	limit	limit	NOUN
cana-5422	158	7	`	`	PUNCT
cana-5422	158	8	→	→	SYM
cana-5422	158	9	∞	∞	NUM
cana-5422	158	10	in	in	ADP
cana-5422	158	11	(	(	PUNCT
cana-5422	158	12	2.17	2.17	NUM
cana-5422	158	13	)	)	PUNCT
cana-5422	158	14	,	,	PUNCT
cana-5422	158	15	using	use	VERB
cana-5422	158	16	(	(	PUNCT
cana-5422	158	17	2.15	2.15	NUM
cana-5422	158	18	)	)	PUNCT
cana-5422	158	19	and	and	CCONJ
cana-5422	158	20	(	(	PUNCT
cana-5422	158	21	2.3	2.3	NUM
cana-5422	158	22	)	)	PUNCT
cana-5422	158	23	,	,	PUNCT
cana-5422	158	24	we	we	PRON
cana-5422	158	25	get	get	VERB
cana-5422	158	26	a(3w1	a(3w1	NOUN
cana-5422	158	27	+	+	CCONJ
cana-5422	158	28	w2	w2	NOUN
cana-5422	158	29	+	+	CCONJ
cana-5422	158	30	w3	w3	PROPN
cana-5422	158	31	)	)	PUNCT
cana-5422	159	1	+	+	SYM
cana-5422	159	2	a(w1	a(w1	ADJ
cana-5422	159	3	+	+	NUM
cana-5422	159	4	3w2	3w2	NUM
cana-5422	159	5	+	+	CCONJ
cana-5422	159	6	w3	w3	NOUN
cana-5422	159	7	)	)	PUNCT
cana-5422	160	1	+	+	SYM
cana-5422	160	2	a(w1	a(w1	X
cana-5422	160	3	+	+	CCONJ
cana-5422	160	4	w2	w2	NOUN
cana-5422	160	5	+	+	CCONJ
cana-5422	160	6	3w3	3w3	NUM
cana-5422	160	7	)	)	PUNCT
cana-5422	160	8	=	=	SYM
cana-5422	160	9	6a	6a	NOUN
cana-5422	160	10	(	(	PUNCT
cana-5422	160	11	3	3	NUM
cana-5422	160	12	∑	∑	PUNCT
cana-5422	160	13	ψ=1	ψ=1	PUNCT
cana-5422	160	14	wψ	wψ	ADP
cana-5422	160	15	)	)	PUNCT
cana-5422	160	16	+	+	CCONJ
cana-5422	160	17	1	1	NUM
cana-5422	160	18	2	2	NUM
cana-5422	160	19	{	{	PUNCT
cana-5422	160	20	a	a	DET
cana-5422	160	21	(	(	PUNCT
cana-5422	160	22	3	3	NUM
cana-5422	160	23	∑	∑	PUNCT
cana-5422	160	24	ψ=1	ψ=1	PUNCT
cana-5422	160	25	wψ	wψ	ADP
cana-5422	160	26	)	)	PUNCT
cana-5422	161	1	+	+	ADP
cana-5422	161	2	a	a	PRON
cana-5422	161	3	(	(	PUNCT
cana-5422	161	4	−	−	PROPN
cana-5422	161	5	3	3	NUM
cana-5422	161	6	∑	∑	PUNCT
cana-5422	161	7	ψ=1	ψ=1	PUNCT
cana-5422	161	8	wψ	wψ	ADP
cana-5422	161	9	)	)	PUNCT
cana-5422	161	10	}	}	PUNCT
cana-5422	161	11	−	−	ADP
cana-5422	161	12	3	3	NUM
cana-5422	161	13	∑	∑	PUNCT
cana-5422	161	14	ψ=1	ψ=1	PUNCT
cana-5422	161	15	{	{	PUNCT
cana-5422	161	16	a(wψ)−	a(wψ)−	NOUN
cana-5422	161	17	5	5	NUM
cana-5422	161	18	2	2	NUM
cana-5422	161	19	[	[	PUNCT
cana-5422	161	20	a(wψ	a(wψ	PROPN
cana-5422	161	21	)	)	PUNCT
cana-5422	161	22	+	+	NOUN
cana-5422	161	23	a(−wψ	a(−wψ	NOUN
cana-5422	161	24	)	)	PUNCT
cana-5422	162	1	]	]	PUNCT
cana-5422	162	2	}	}	PUNCT
cana-5422	162	3	,	,	PUNCT
cana-5422	162	4	for	for	ADP
cana-5422	162	5	all	all	DET
cana-5422	162	6	w1	w1	NOUN
cana-5422	162	7	,	,	PUNCT
cana-5422	162	8	w2	w2	NOUN
cana-5422	162	9	,	,	PUNCT
cana-5422	162	10	w3	w3	PROPN
cana-5422	162	11	∈	∈	PROPN
cana-5422	162	12	w1	w1	NOUN
cana-5422	162	13	.	.	PUNCT
cana-5422	163	1	so	so	ADV
cana-5422	163	2	,	,	PUNCT
cana-5422	163	3	a(w1	a(w1	ADJ
cana-5422	163	4	)	)	PUNCT
cana-5422	163	5	satisfies	satisfie	NOUN
cana-5422	163	6	(	(	PUNCT
cana-5422	163	7	1.7	1.7	NUM
cana-5422	163	8	)	)	PUNCT
cana-5422	163	9	.	.	PUNCT
cana-5422	164	1	in	in	ADP
cana-5422	164	2	order	order	NOUN
cana-5422	164	3	to	to	PART
cana-5422	164	4	confirm	confirm	VERB
cana-5422	164	5	that	that	DET
cana-5422	164	6	a(w1	a(w1	NOUN
cana-5422	164	7	)	)	PUNCT
cana-5422	164	8	is	be	AUX
cana-5422	164	9	unique	unique	ADJ
cana-5422	164	10	,	,	PUNCT
cana-5422	164	11	suppose	suppose	VERB
cana-5422	164	12	b(w1	b(w1	NOUN
cana-5422	164	13	)	)	PUNCT
cana-5422	164	14	be	be	AUX
cana-5422	164	15	another	another	DET
cana-5422	164	16	mapping	mapping	NOUN
cana-5422	164	17	(	(	PUNCT
cana-5422	164	18	1.7	1.7	NUM
cana-5422	164	19	)	)	PUNCT
cana-5422	164	20	,	,	PUNCT
cana-5422	164	21	(	(	PUNCT
cana-5422	164	22	2.15	2.15	NUM
cana-5422	164	23	)	)	PUNCT
cana-5422	164	24	and	and	CCONJ
cana-5422	164	25	(	(	PUNCT
cana-5422	164	26	2.16	2.16	NUM
cana-5422	164	27	)	)	PUNCT
cana-5422	164	28	,	,	PUNCT
cana-5422	164	29	we	we	PRON
cana-5422	164	30	obtain∥∥∥a(w1)−b(w1	obtain∥∥∥a(w1)−b(w1	VERB
cana-5422	164	31	)	)	PUNCT
cana-5422	164	32	∥∥∥	∥∥∥	PROPN
cana-5422	165	1	=	=	SYM
cana-5422	165	2	∥∥∥	∥∥∥	PROPN
cana-5422	165	3	1	1	NUM
cana-5422	165	4	5	5	NUM
cana-5422	165	5	`	`	PUNCT
cana-5422	165	6	a	a	DET
cana-5422	165	7	(	(	PUNCT
cana-5422	165	8	5`w1	5`w1	NUM
cana-5422	165	9	)	)	PUNCT
cana-5422	165	10	−	−	ADP
cana-5422	166	1	1	1	NUM
cana-5422	166	2	5	5	NUM
cana-5422	166	3	`	`	SYM
cana-5422	166	4	b	b	PROPN
cana-5422	166	5	(	(	PUNCT
cana-5422	166	6	5`w1	5`w1	NUM
cana-5422	166	7	)	)	PUNCT
cana-5422	167	1	∥∥∥	∥∥∥	PROPN
cana-5422	167	2	≤	≤	NUM
cana-5422	167	3	1	1	NUM
cana-5422	167	4	5	5	NUM
cana-5422	167	5	`	`	PUNCT
cana-5422	167	6	∥∥∥a	∥∥∥a	NOUN
cana-5422	167	7	(	(	PUNCT
cana-5422	167	8	5`w1	5`w1	X
cana-5422	167	9	)	)	PUNCT
cana-5422	167	10	−f	−f	NOUN
cana-5422	167	11	(	(	PUNCT
cana-5422	167	12	5`w1	5`w1	NUM
cana-5422	167	13	)	)	PUNCT
cana-5422	167	14	∥∥∥+	∥∥∥+	VERB
cana-5422	167	15	1	1	NUM
cana-5422	167	16	5	5	NUM
cana-5422	167	17	`	`	PUNCT
cana-5422	167	18	∥∥∥f	∥∥∥f	NOUN
cana-5422	167	19	(	(	PUNCT
cana-5422	167	20	5`w1	5`w1	NUM
cana-5422	167	21	)	)	PUNCT
cana-5422	167	22	−b	−b	ADV
cana-5422	167	23	(	(	PUNCT
cana-5422	167	24	5`w1	5`w1	NUM
cana-5422	167	25	)	)	PUNCT
cana-5422	167	26	∥∥∥	∥∥∥	PROPN
cana-5422	167	27	≤	≤	NUM
cana-5422	168	1	2	2	NUM
cana-5422	168	2	5	5	NUM
cana-5422	168	3	∞	∞	NUM
cana-5422	168	4	∑	∑	PUNCT
cana-5422	168	5	η=0	η=0	PROPN
cana-5422	168	6	1	1	NUM
cana-5422	168	7	5η+	5η+	NUM
cana-5422	168	8	`	`	PUNCT
cana-5422	168	9	ψa	ψa	X
cana-5422	168	10	(	(	PUNCT
cana-5422	168	11	5η+`w1	5η+`w1	NOUN
cana-5422	168	12	)	)	PUNCT
cana-5422	168	13	→	→	SYM
cana-5422	168	14	0	0	NUM
cana-5422	168	15	as	as	ADP
cana-5422	168	16	`	`	PUNCT
cana-5422	168	17	1	1	NUM
cana-5422	168	18	→	→	SYM
cana-5422	168	19	∞	∞	PROPN
cana-5422	168	20	,	,	PUNCT
cana-5422	168	21	for	for	ADP
cana-5422	168	22	all	all	DET
cana-5422	168	23	w1	w1	NOUN
cana-5422	168	24	∈	∈	PROPN
cana-5422	168	25	w1	w1	NOUN
cana-5422	168	26	.	.	PUNCT
cana-5422	169	1	therefore	therefore	ADV
cana-5422	169	2	a(w1	a(w1	VERB
cana-5422	169	3	)	)	PUNCT
cana-5422	169	4	is	be	AUX
cana-5422	169	5	unique	unique	ADJ
cana-5422	169	6	.	.	PUNCT
cana-5422	170	1	so	so	ADV
cana-5422	170	2	,	,	PUNCT
cana-5422	170	3	the	the	DET
cana-5422	170	4	theorem	theorem	NOUN
cana-5422	170	5	holds	hold	VERB
cana-5422	170	6	for	for	ADP
cana-5422	170	7	µ	µ	NOUN
cana-5422	170	8	=	=	SYM
cana-5422	170	9	1	1	NUM
cana-5422	170	10	.	.	X
cana-5422	170	11	changing	change	VERB
cana-5422	170	12	w1	w1	NOUN
cana-5422	170	13	=	=	SYM
cana-5422	170	14	w1	w1	NOUN
cana-5422	170	15	5	5	NUM
cana-5422	170	16	in	in	ADP
cana-5422	170	17	(	(	PUNCT
cana-5422	170	18	2.11	2.11	NUM
cana-5422	170	19	)	)	PUNCT
cana-5422	170	20	,	,	PUNCT
cana-5422	170	21	we	we	PRON
cana-5422	170	22	have∥∥∥f	have∥∥∥f	VERB
cana-5422	170	23	(	(	PUNCT
cana-5422	170	24	w1)−	w1)−	PROPN
cana-5422	170	25	5f	5f	NOUN
cana-5422	170	26	(	(	PUNCT
cana-5422	170	27	w1	w1	NOUN
cana-5422	170	28	5	5	NUM
cana-5422	170	29	)	)	PUNCT
cana-5422	170	30	∥∥∥	∥∥∥	PROPN
cana-5422	170	31	≤	≤	PROPN
cana-5422	171	1	ψa	ψa	X
cana-5422	171	2	(	(	PUNCT
cana-5422	171	3	w1	w1	PROPN
cana-5422	171	4	5	5	NUM
cana-5422	171	5	)	)	PUNCT
cana-5422	171	6	,	,	PUNCT
cana-5422	171	7	∀	∀	X
cana-5422	171	8	w1	w1	NOUN
cana-5422	171	9	∈	∈	PROPN
cana-5422	171	10	w1	w1	NOUN
cana-5422	171	11	.	.	PUNCT
cana-5422	172	1	(	(	PUNCT
cana-5422	172	2	2.18	2.18	NUM
cana-5422	172	3	)	)	PUNCT
cana-5422	172	4	generalizing	generalize	VERB
cana-5422	172	5	for	for	ADP
cana-5422	172	6	a	a	DET
cana-5422	172	7	positive	positive	ADJ
cana-5422	172	8	integer	integer	NOUN
cana-5422	172	9	`	`	PUNCT
cana-5422	172	10	,	,	PUNCT
cana-5422	172	11	we	we	PRON
cana-5422	172	12	get∥∥∥f	get∥∥∥f	VERB
cana-5422	172	13	(	(	PUNCT
cana-5422	172	14	w1)−	w1)−	NOUN
cana-5422	172	15	5`f	5`f	PRON
cana-5422	172	16	(	(	PUNCT
cana-5422	172	17	w1	w1	NOUN
cana-5422	172	18	5η	5η	PROPN
cana-5422	172	19	)	)	PUNCT
cana-5422	173	1	∥∥∥	∥∥∥	PROPN
cana-5422	173	2	≤	≤	NUM
cana-5422	173	3	1	1	NUM
cana-5422	173	4	5	5	NUM
cana-5422	173	5	`	`	PUNCT
cana-5422	173	6	∑	∑	PUNCT
cana-5422	173	7	η=1	η=1	PROPN
cana-5422	173	8	5η	5η	PROPN
cana-5422	173	9	ψa	ψa	X
cana-5422	173	10	(	(	PUNCT
cana-5422	173	11	w1	w1	NOUN
cana-5422	173	12	5η	5η	PROPN
cana-5422	173	13	)	)	PUNCT
cana-5422	173	14	,	,	PUNCT
cana-5422	173	15	∀	∀	NOUN
cana-5422	173	16	w1	w1	NOUN
cana-5422	173	17	∈	∈	PROPN
cana-5422	173	18	w1	w1	NOUN
cana-5422	173	19	.	.	PUNCT
cana-5422	174	1	(	(	PUNCT
cana-5422	174	2	2.19	2.19	NUM
cana-5422	174	3	)	)	PUNCT
cana-5422	174	4	the	the	DET
cana-5422	174	5	rest	rest	NOUN
cana-5422	174	6	of	of	ADP
cana-5422	174	7	the	the	DET
cana-5422	174	8	proof	proof	NOUN
cana-5422	174	9	is	be	AUX
cana-5422	174	10	similar	similar	ADJ
cana-5422	174	11	to	to	ADP
cana-5422	174	12	that	that	PRON
cana-5422	174	13	of	of	ADP
cana-5422	174	14	above	above	ADP
cana-5422	174	15	case	case	NOUN
cana-5422	174	16	.	.	PUNCT
cana-5422	175	1	so	so	ADV
cana-5422	175	2	,	,	PUNCT
cana-5422	175	3	the	the	DET
cana-5422	175	4	theorem	theorem	NOUN
cana-5422	175	5	holds	hold	VERB
cana-5422	175	6	for	for	ADP
cana-5422	175	7	µ	µ	NOUN
cana-5422	175	8	=	=	SYM
cana-5422	175	9	−1	−1	NOUN
cana-5422	175	10	.	.	PUNCT
cana-5422	176	1	hence	hence	ADV
cana-5422	176	2	the	the	DET
cana-5422	176	3	proof	proof	NOUN
cana-5422	176	4	is	be	AUX
cana-5422	176	5	complete	complete	ADJ
cana-5422	176	6	�	�	PROPN
cana-5422	176	7	corollary	corollary	NOUN
cana-5422	176	8	2.2	2.2	NUM
cana-5422	176	9	.	.	PUNCT
cana-5422	177	1	suppose	suppose	VERB
cana-5422	177	2	that	that	SCONJ
cana-5422	177	3	an	an	DET
cana-5422	177	4	odd	odd	ADJ
cana-5422	177	5	function	function	NOUN
cana-5422	177	6	f	f	NOUN
cana-5422	177	7	:	:	PUNCT
cana-5422	177	8	w1	w1	PROPN
cana-5422	177	9	→	→	SYM
cana-5422	177	10	w2	w2	NOUN
cana-5422	177	11	satisfy	satisfy	VERB
cana-5422	177	12	the	the	DET
cana-5422	177	13	functional	functional	ADJ
cana-5422	177	14	inequality	inequality	NOUN
cana-5422	177	15	(	(	PUNCT
cana-5422	177	16	2.2	2.2	NUM
cana-5422	177	17	)	)	PUNCT
cana-5422	177	18	for	for	ADP
cana-5422	177	19	all	all	DET
cana-5422	177	20	w1	w1	NOUN
cana-5422	177	21	,	,	PUNCT
cana-5422	177	22	w2	w2	NOUN
cana-5422	177	23	,	,	PUNCT
cana-5422	177	24	w3	w3	PROPN
cana-5422	177	25	∈	∈	PROPN
cana-5422	177	26	w1	w1	NOUN
cana-5422	177	27	.	.	PUNCT
cana-5422	178	1	then	then	ADV
cana-5422	178	2	there	there	PRON
cana-5422	178	3	exists	exist	VERB
cana-5422	178	4	a	a	DET
cana-5422	178	5	unique	unique	ADJ
cana-5422	178	6	additive	additive	ADJ
cana-5422	178	7	mapping	mapping	NOUN
cana-5422	178	8	a(w1	a(w1	NOUN
cana-5422	178	9	)	)	PUNCT
cana-5422	178	10	:	:	PUNCT
cana-5422	178	11	w1	w1	PROPN
cana-5422	178	12	→w2	→w2	NOUN
cana-5422	178	13	which	which	PRON
cana-5422	178	14	satisfies	satisfy	VERB
cana-5422	178	15	(	(	PUNCT
cana-5422	178	16	1.7	1.7	NUM
cana-5422	178	17	)	)	PUNCT
cana-5422	178	18	and	and	CCONJ
cana-5422	178	19	the	the	DET
cana-5422	178	20	functional	functional	ADJ
cana-5422	178	21	inequality	inequality	NOUN
cana-5422	178	22	‖f	‖f	PRON
cana-5422	178	23	(	(	PUNCT
cana-5422	178	24	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	178	25	≤	≤	NUM
cana-5422	178	26			NOUN
cana-5422	178	27	δ	δ	PROPN
cana-5422	178	28	|3|	|3|	PROPN
cana-5422	178	29	,	,	PUNCT
cana-5422	178	30	4δ|w1|ϕ	4δ|w1|ϕ	NOUN
cana-5422	178	31	|5−5ϕ	|5−5ϕ	PROPN
cana-5422	178	32	|	|	ADV
cana-5422	178	33	;	;	PUNCT
cana-5422	178	34	ϕ	ϕ	PROPN
cana-5422	178	35	6=	6=	ADP
cana-5422	178	36	1	1	NUM
cana-5422	178	37	,	,	PUNCT
cana-5422	178	38	4δ	4δ	NOUN
cana-5422	178	39	3	3	NUM
cana-5422	178	40	3	3	NUM
cana-5422	178	41	∑	∑	PUNCT
cana-5422	178	42	ψ=1	ψ=1	PUNCT
cana-5422	178	43	|wψ	|wψ	PUNCT
cana-5422	178	44	|	|	ADV
cana-5422	178	45	ϕψ	ϕψ	ADV
cana-5422	178	46	|5−5	|5−5	NOUN
cana-5422	178	47	ϕψ	ϕψ	ADP
cana-5422	178	48	|	|	ADV
cana-5422	178	49	;	;	PUNCT
cana-5422	178	50	ϕ1	ϕ1	NOUN
cana-5422	178	51	,	,	PUNCT
cana-5422	178	52	ϕ2	ϕ2	ADV
cana-5422	178	53	,	,	PUNCT
cana-5422	178	54	ϕ3	ϕ3	PROPN
cana-5422	178	55	6=	6=	PROPN
cana-5422	178	56	1	1	NUM
cana-5422	178	57	,	,	PUNCT
cana-5422	178	58	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	179	1	3|5−53ϕ	3|5−53ϕ	NUM
cana-5422	180	1	|	|	ADV
cana-5422	180	2	;	;	PUNCT
cana-5422	180	3	3ϕ	3ϕ	NUM
cana-5422	180	4	6=	6=	SYM
cana-5422	180	5	1	1	NUM
cana-5422	180	6	,	,	PUNCT
cana-5422	180	7	4δ|wψ	4δ|wψ	PROPN
cana-5422	180	8	|	|	ADV
cana-5422	180	9	3	3	NUM
cana-5422	180	10	∑	∑	PUNCT
cana-5422	180	11	ψ=1	ψ=1	PUNCT
cana-5422	180	12	ϕψ	ϕψ	ADP
cana-5422	180	13	3	3	NUM
cana-5422	180	14	∣∣∣5−5	∣∣∣5−5	SYM
cana-5422	180	15	3	3	NUM
cana-5422	180	16	∑	∑	PUNCT
cana-5422	180	17	ψ=1	ψ=1	PUNCT
cana-5422	181	1	ϕψ	ϕψ	ADV
cana-5422	181	2	∣∣∣	∣∣∣	ADJ
cana-5422	181	3	;	;	PUNCT
cana-5422	181	4	3	3	NUM
cana-5422	181	5	∑	∑	PUNCT
cana-5422	181	6	ψ=1	ψ=1	PUNCT
cana-5422	181	7	ϕψ	ϕψ	ADP
cana-5422	181	8	6=	6=	PROPN
cana-5422	181	9	1	1	NUM
cana-5422	181	10	,	,	PUNCT
cana-5422	181	11	16δ|w1|3ϕ	16δ|w1|3ϕ	NOUN
cana-5422	182	1	3|5−53ϕ	3|5−53ϕ	NUM
cana-5422	183	1	|	|	ADV
cana-5422	183	2	;	;	PUNCT
cana-5422	183	3	3ϕ	3ϕ	NUM
cana-5422	183	4	6=	6=	SYM
cana-5422	183	5	1	1	NUM
cana-5422	183	6	,	,	PUNCT
cana-5422	183	7	(	(	PUNCT
cana-5422	183	8	2.20	2.20	NUM
cana-5422	183	9	)	)	PUNCT
cana-5422	183	10	for	for	ADP
cana-5422	183	11	all	all	DET
cana-5422	183	12	w1	w1	NOUN
cana-5422	183	13	∈	∈	PROPN
cana-5422	183	14	w1	w1	NOUN
cana-5422	183	15	.	.	PUNCT
cana-5422	184	1	2.2	2.2	NUM
cana-5422	184	2	.	.	PUNCT
cana-5422	184	3	evenness	evenness	NOUN
cana-5422	184	4	of	of	ADP
cana-5422	184	5	f	f	PROPN
cana-5422	184	6	:	:	PUNCT
cana-5422	184	7	quadratic	quadratic	ADJ
cana-5422	184	8	case	case	NOUN
cana-5422	184	9	stability	stability	NOUN
cana-5422	184	10	results	result	VERB
cana-5422	184	11	:	:	PUNCT
cana-5422	184	12	direct	direct	ADJ
cana-5422	184	13	method	method	NOUN
cana-5422	184	14	.	.	PUNCT
cana-5422	185	1	theorem	theorem	VERB
cana-5422	185	2	2.3	2.3	NUM
cana-5422	185	3	.	.	PUNCT
cana-5422	186	1	suppose	suppose	VERB
cana-5422	186	2	that	that	SCONJ
cana-5422	186	3	an	an	DET
cana-5422	186	4	even	even	ADV
cana-5422	186	5	function	function	NOUN
cana-5422	186	6	f	f	PROPN
cana-5422	186	7	:	:	PUNCT
cana-5422	186	8	w1	w1	PROPN
cana-5422	186	9	→	→	SYM
cana-5422	186	10	w2	w2	NOUN
cana-5422	186	11	satisfy	satisfy	VERB
cana-5422	186	12	the	the	DET
cana-5422	186	13	functional	functional	ADJ
cana-5422	186	14	inequality	inequality	NOUN
cana-5422	186	15	(	(	PUNCT
cana-5422	186	16	2.1	2.1	NUM
cana-5422	186	17	)	)	PUNCT
cana-5422	186	18	where	where	SCONJ
cana-5422	186	19	ψ	ψ	X
cana-5422	186	20	:	:	PUNCT
cana-5422	186	21	w3	w3	NOUN
cana-5422	186	22	1	1	NUM
cana-5422	186	23	→	→	SYM
cana-5422	187	1	[	[	X
cana-5422	187	2	0	0	NUM
cana-5422	187	3	,	,	PUNCT
cana-5422	187	4	∞	∞	PROPN
cana-5422	187	5	)	)	PUNCT
cana-5422	187	6	with	with	ADP
cana-5422	187	7	the	the	DET
cana-5422	187	8	condition	condition	NOUN
cana-5422	187	9	lim	lim	NOUN
cana-5422	187	10	`	`	PUNCT
cana-5422	187	11	→∞	→∞	PROPN
cana-5422	187	12	ψ	ψ	X
cana-5422	187	13	(	(	PUNCT
cana-5422	187	14	5`mw1	5`mw1	NUM
cana-5422	187	15	,	,	PUNCT
cana-5422	187	16	5`mw2	5`mw2	NUM
cana-5422	187	17	,	,	PUNCT
cana-5422	187	18	5`mw3	5`mw3	NUM
cana-5422	187	19	)	)	PUNCT
cana-5422	187	20	25`m	25`m	NUM
cana-5422	188	1	=	=	SYM
cana-5422	188	2	0	0	NUM
cana-5422	188	3	;	;	PUNCT
cana-5422	188	4	µ	µ	X
cana-5422	188	5	=	=	SYM
cana-5422	188	6	±1	±1	VERB
cana-5422	188	7	,	,	PUNCT
cana-5422	188	8	(	(	PUNCT
cana-5422	188	9	2.21	2.21	NUM
cana-5422	188	10	)	)	PUNCT
cana-5422	188	11	communications	communication	NOUN
cana-5422	188	12	on	on	ADP
cana-5422	188	13	applied	apply	VERB
cana-5422	188	14	nonlinear	nonlinear	ADJ
cana-5422	188	15	analysis	analysis	NOUN
cana-5422	188	16	issn	issn	NOUN
cana-5422	188	17	:	:	PUNCT
cana-5422	188	18	1074	1074	NUM
cana-5422	188	19	-	-	PUNCT
cana-5422	188	20	133x	133x	NUM
cana-5422	188	21	vol	vol	NOUN
cana-5422	188	22	32	32	NUM
cana-5422	188	23	no	no	NOUN
cana-5422	188	24	.	.	PUNCT
cana-5422	189	1	10s(2025	10s(2025	NUM
cana-5422	189	2	)	)	PUNCT
cana-5422	190	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	190	2	2191	2191	NUM
cana-5422	190	3	for	for	ADP
cana-5422	190	4	all	all	DET
cana-5422	190	5	w1	w1	NOUN
cana-5422	190	6	,	,	PUNCT
cana-5422	190	7	w2	w2	NOUN
cana-5422	190	8	,	,	PUNCT
cana-5422	190	9	w3	w3	PROPN
cana-5422	190	10	∈	∈	PROPN
cana-5422	190	11	w1	w1	NOUN
cana-5422	190	12	.	.	PUNCT
cana-5422	191	1	then	then	ADV
cana-5422	191	2	there	there	PRON
cana-5422	191	3	exists	exist	VERB
cana-5422	191	4	a	a	DET
cana-5422	191	5	unique	unique	ADJ
cana-5422	191	6	quadratic	quadratic	ADJ
cana-5422	191	7	mapping	mapping	NOUN
cana-5422	191	8	q(w1	q(w1	NOUN
cana-5422	191	9	)	)	PUNCT
cana-5422	191	10	:	:	PUNCT
cana-5422	191	11	w1	w1	PROPN
cana-5422	191	12	→w2	→w2	NOUN
cana-5422	191	13	which	which	PRON
cana-5422	191	14	satisfies	satisfy	VERB
cana-5422	191	15	(	(	PUNCT
cana-5422	191	16	1.7	1.7	NUM
cana-5422	191	17	)	)	PUNCT
cana-5422	191	18	and	and	CCONJ
cana-5422	191	19	the	the	DET
cana-5422	191	20	functional	functional	ADJ
cana-5422	191	21	inequality	inequality	NOUN
cana-5422	191	22	‖f	‖f	PRON
cana-5422	191	23	(	(	PUNCT
cana-5422	191	24	w1)−q(w1)‖	w1)−q(w1)‖	NOUN
cana-5422	191	25	≤	≤	NUM
cana-5422	191	26	1	1	NUM
cana-5422	191	27	25	25	NUM
cana-5422	191	28	∞	∞	NUM
cana-5422	191	29	∑	∑	PUNCT
cana-5422	191	30	η=	η=	ADJ
cana-5422	191	31	1−µ	1−µ	NOUN
cana-5422	191	32	2	2	NUM
cana-5422	191	33	1	1	NUM
cana-5422	191	34	25ηµ	25ηµ	NOUN
cana-5422	191	35	ψq	ψq	PART
cana-5422	191	36	(	(	PUNCT
cana-5422	191	37	5ηµw1	5ηµw1	NOUN
cana-5422	191	38	)	)	PUNCT
cana-5422	191	39	(	(	PUNCT
cana-5422	191	40	2.22	2.22	NUM
cana-5422	191	41	)	)	PUNCT
cana-5422	191	42	=	=	SYM
cana-5422	192	1	1	1	NUM
cana-5422	192	2	25	25	NUM
cana-5422	192	3	∞	∞	NUM
cana-5422	192	4	∑	∑	PUNCT
cana-5422	192	5	η=	η=	ADJ
cana-5422	192	6	1−µ	1−µ	NOUN
cana-5422	192	7	2	2	NUM
cana-5422	192	8	1	1	NUM
cana-5422	192	9	25ηµ	25ηµ	NOUN
cana-5422	192	10	{	{	PUNCT
cana-5422	192	11	1	1	NUM
cana-5422	192	12	3	3	NUM
cana-5422	192	13	{	{	PUNCT
cana-5422	192	14	ψ	ψ	X
cana-5422	192	15	(	(	PUNCT
cana-5422	192	16	5ηµw1	5ηµw1	NUM
cana-5422	192	17	,	,	PUNCT
cana-5422	192	18	5ηµw1	5ηµw1	NUM
cana-5422	192	19	,	,	PUNCT
cana-5422	192	20	5ηµw1	5ηµw1	NUM
cana-5422	192	21	)	)	PUNCT
cana-5422	192	22	+	+	CCONJ
cana-5422	192	23	7	7	NUM
cana-5422	192	24	2	2	NUM
cana-5422	192	25	ψ	ψ	X
cana-5422	192	26	(	(	PUNCT
cana-5422	192	27	5ηµw1	5ηµw1	NUM
cana-5422	192	28	,	,	PUNCT
cana-5422	192	29	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	192	30	)	)	PUNCT
cana-5422	192	31	}	}	PUNCT
cana-5422	192	32	}	}	PUNCT
cana-5422	192	33	,	,	PUNCT
cana-5422	192	34	(	(	PUNCT
cana-5422	192	35	2.23	2.23	NUM
cana-5422	192	36	)	)	PUNCT
cana-5422	192	37	and	and	CCONJ
cana-5422	192	38	the	the	DET
cana-5422	192	39	mapping	mapping	NOUN
cana-5422	192	40	q(w1	q(w1	NOUN
cana-5422	192	41	)	)	PUNCT
cana-5422	192	42	is	be	AUX
cana-5422	192	43	obtained	obtain	VERB
cana-5422	192	44	by	by	ADP
cana-5422	192	45	q(w1	q(w1	NOUN
cana-5422	192	46	)	)	PUNCT
cana-5422	193	1	=	=	SYM
cana-5422	193	2	lim	lim	PROPN
cana-5422	193	3	`	`	PUNCT
cana-5422	193	4	→∞	→∞	PROPN
cana-5422	193	5	1	1	NUM
cana-5422	193	6	25`mf	25`mf	NUM
cana-5422	193	7	(	(	PUNCT
cana-5422	193	8	5`mw1	5`mw1	NUM
cana-5422	193	9	)	)	PUNCT
cana-5422	193	10	,	,	PUNCT
cana-5422	193	11	(	(	PUNCT
cana-5422	193	12	2.24	2.24	NUM
cana-5422	193	13	)	)	PUNCT
cana-5422	193	14	for	for	ADP
cana-5422	193	15	all	all	DET
cana-5422	193	16	w1	w1	NOUN
cana-5422	193	17	∈	∈	PROPN
cana-5422	193	18	w1	w1	NOUN
cana-5422	193	19	.	.	PUNCT
cana-5422	194	1	proof	proof	NOUN
cana-5422	194	2	.	.	PUNCT
cana-5422	195	1	using	use	VERB
cana-5422	195	2	evenness	evenness	NOUN
cana-5422	195	3	of	of	ADP
cana-5422	195	4	f	f	PROPN
cana-5422	195	5	in	in	ADP
cana-5422	195	6	(	(	PUNCT
cana-5422	195	7	2.1	2.1	NUM
cana-5422	195	8	)	)	PUNCT
cana-5422	195	9	,	,	PUNCT
cana-5422	195	10	we	we	PRON
cana-5422	195	11	get	get	VERB
cana-5422	195	12	∥∥∥f	∥∥∥f	ADJ
cana-5422	195	13	(	(	PUNCT
cana-5422	195	14	3w1	3w1	NUM
cana-5422	195	15	+	+	CCONJ
cana-5422	195	16	w2	w2	NOUN
cana-5422	195	17	+	+	CCONJ
cana-5422	195	18	w3	w3	PROPN
cana-5422	195	19	)	)	PUNCT
cana-5422	196	1	+	+	NOUN
cana-5422	196	2	f	f	X
cana-5422	196	3	(	(	PUNCT
cana-5422	196	4	w1	w1	NOUN
cana-5422	196	5	+	+	CCONJ
cana-5422	196	6	3w2	3w2	NUM
cana-5422	196	7	+	+	CCONJ
cana-5422	196	8	w3	w3	NOUN
cana-5422	196	9	)	)	PUNCT
cana-5422	197	1	+	+	NOUN
cana-5422	197	2	f	f	X
cana-5422	197	3	(	(	PUNCT
cana-5422	197	4	w1	w1	NOUN
cana-5422	197	5	+	+	NOUN
cana-5422	197	6	w2	w2	NOUN
cana-5422	197	7	+	+	CCONJ
cana-5422	197	8	3w3)−	3w3)−	PROPN
cana-5422	197	9	7f	7f	NOUN
cana-5422	197	10	(	(	PUNCT
cana-5422	197	11	3	3	NUM
cana-5422	197	12	∑	∑	PUNCT
cana-5422	197	13	ψ=1	ψ=1	PUNCT
cana-5422	197	14	wψ	wψ	ADP
cana-5422	197	15	)	)	PUNCT
cana-5422	197	16	−	−	PROPN
cana-5422	197	17	4	4	NUM
cana-5422	197	18	3	3	NUM
cana-5422	197	19	∑	∑	PUNCT
cana-5422	197	20	ψ=1	ψ=1	PUNCT
cana-5422	197	21	f	f	X
cana-5422	197	22	(	(	PUNCT
cana-5422	197	23	wψ	wψ	ADP
cana-5422	197	24	)	)	PUNCT
cana-5422	197	25	∥∥∥	∥∥∥	PROPN
cana-5422	197	26	≤	≤	NUM
cana-5422	197	27	ψ	ψ	X
cana-5422	197	28	(	(	PUNCT
cana-5422	197	29	w1	w1	NOUN
cana-5422	197	30	,	,	PUNCT
cana-5422	197	31	w2	w2	NOUN
cana-5422	197	32	,	,	PUNCT
cana-5422	197	33	w3	w3	PROPN
cana-5422	197	34	)	)	PUNCT
cana-5422	197	35	,	,	PUNCT
cana-5422	197	36	∀	∀	X
cana-5422	197	37	w1	w1	NOUN
cana-5422	197	38	,	,	PUNCT
cana-5422	197	39	w2	w2	NOUN
cana-5422	197	40	,	,	PUNCT
cana-5422	197	41	w3	w3	PROPN
cana-5422	197	42	∈	∈	PROPN
cana-5422	197	43	w1	w1	NOUN
cana-5422	197	44	.	.	PUNCT
cana-5422	198	1	(	(	PUNCT
cana-5422	198	2	2.25	2.25	NUM
cana-5422	198	3	)	)	PUNCT
cana-5422	198	4	interchanging	interchange	VERB
cana-5422	198	5	(	(	PUNCT
cana-5422	198	6	w1	w1	NOUN
cana-5422	198	7	,	,	PUNCT
cana-5422	198	8	w2	w2	NOUN
cana-5422	198	9	,	,	PUNCT
cana-5422	198	10	w3	w3	PROPN
cana-5422	198	11	)	)	PUNCT
cana-5422	198	12	by	by	ADP
cana-5422	198	13	(	(	PUNCT
cana-5422	198	14	w1	w1	NOUN
cana-5422	198	15	,	,	PUNCT
cana-5422	198	16	w1	w1	NOUN
cana-5422	198	17	,	,	PUNCT
cana-5422	198	18	w1	w1	NOUN
cana-5422	198	19	)	)	PUNCT
cana-5422	198	20	in	in	ADP
cana-5422	198	21	(	(	PUNCT
cana-5422	198	22	2.25	2.25	NUM
cana-5422	198	23	)	)	PUNCT
cana-5422	198	24	,	,	PUNCT
cana-5422	198	25	we	we	PRON
cana-5422	198	26	obtain∥∥∥3f	obtain∥∥∥3f	VERB
cana-5422	198	27	(	(	PUNCT
cana-5422	198	28	5w1)−	5w1)−	PROPN
cana-5422	198	29	7f	7f	X
cana-5422	198	30	(	(	PUNCT
cana-5422	198	31	3w1)−	3w1)−	NOUN
cana-5422	198	32	12f	12f	NUM
cana-5422	198	33	(	(	PUNCT
cana-5422	198	34	w1	w1	NOUN
cana-5422	198	35	)	)	PUNCT
cana-5422	198	36	∥∥∥	∥∥∥	PROPN
cana-5422	198	37	≤	≤	NUM
cana-5422	199	1	ψ	ψ	X
cana-5422	199	2	(	(	PUNCT
cana-5422	199	3	w1	w1	NOUN
cana-5422	199	4	,	,	PUNCT
cana-5422	199	5	w1	w1	NOUN
cana-5422	199	6	,	,	PUNCT
cana-5422	199	7	w1	w1	NOUN
cana-5422	199	8	)	)	PUNCT
cana-5422	199	9	,	,	PUNCT
cana-5422	199	10	∀	∀	NOUN
cana-5422	199	11	w1	w1	NOUN
cana-5422	199	12	∈	∈	PROPN
cana-5422	199	13	w1	w1	NOUN
cana-5422	199	14	.	.	PUNCT
cana-5422	200	1	(	(	PUNCT
cana-5422	200	2	2.26	2.26	NUM
cana-5422	200	3	)	)	PUNCT
cana-5422	200	4	again	again	ADV
cana-5422	200	5	interchanging	interchange	VERB
cana-5422	200	6	(	(	PUNCT
cana-5422	200	7	w1	w1	NOUN
cana-5422	200	8	,	,	PUNCT
cana-5422	200	9	w2	w2	NOUN
cana-5422	200	10	,	,	PUNCT
cana-5422	200	11	w3	w3	PROPN
cana-5422	200	12	)	)	PUNCT
cana-5422	200	13	by	by	ADP
cana-5422	200	14	(	(	PUNCT
cana-5422	200	15	w1	w1	NOUN
cana-5422	200	16	,	,	PUNCT
cana-5422	200	17	w1,−w1	w1,−w1	NUM
cana-5422	200	18	)	)	PUNCT
cana-5422	200	19	in	in	ADP
cana-5422	200	20	(	(	PUNCT
cana-5422	200	21	2.25	2.25	NUM
cana-5422	200	22	)	)	PUNCT
cana-5422	200	23	,	,	PUNCT
cana-5422	200	24	we	we	PRON
cana-5422	200	25	have∥∥∥2f	have∥∥∥2f	VERB
cana-5422	200	26	(	(	PUNCT
cana-5422	200	27	3w1)−	3w1)−	PROPN
cana-5422	200	28	18f	18f	PROPN
cana-5422	200	29	(	(	PUNCT
cana-5422	200	30	w1	w1	NOUN
cana-5422	200	31	)	)	PUNCT
cana-5422	201	1	∥∥∥	∥∥∥	PROPN
cana-5422	201	2	≤	≤	NUM
cana-5422	202	1	ψ	ψ	X
cana-5422	202	2	(	(	PUNCT
cana-5422	202	3	w1	w1	NOUN
cana-5422	202	4	,	,	PUNCT
cana-5422	202	5	w1,−w1	w1,−w1	NUM
cana-5422	202	6	)	)	PUNCT
cana-5422	202	7	⇒	⇒	NOUN
cana-5422	202	8	∥∥∥7f	∥∥∥7f	PUNCT
cana-5422	203	1	(	(	PUNCT
cana-5422	203	2	3w1)−	3w1)−	NUM
cana-5422	203	3	63f	63f	X
cana-5422	203	4	(	(	PUNCT
cana-5422	203	5	w1	w1	NOUN
cana-5422	203	6	)	)	PUNCT
cana-5422	203	7	∥∥∥	∥∥∥	PROPN
cana-5422	203	8	≤	≤	NUM
cana-5422	203	9	7	7	NUM
cana-5422	203	10	2	2	NUM
cana-5422	203	11	ψ	ψ	X
cana-5422	203	12	(	(	PUNCT
cana-5422	203	13	w1	w1	NOUN
cana-5422	203	14	,	,	PUNCT
cana-5422	203	15	w1,−w1	w1,−w1	NUM
cana-5422	203	16	)	)	PUNCT
cana-5422	203	17	,	,	PUNCT
cana-5422	203	18	∀	∀	NOUN
cana-5422	203	19	w1	w1	NOUN
cana-5422	203	20	∈	∈	PROPN
cana-5422	203	21	w1	w1	NOUN
cana-5422	203	22	.	.	PUNCT
cana-5422	204	1	(	(	PUNCT
cana-5422	204	2	2.27	2.27	NUM
cana-5422	204	3	)	)	PUNCT
cana-5422	204	4	combining	combine	VERB
cana-5422	204	5	(	(	PUNCT
cana-5422	204	6	2.26	2.26	NUM
cana-5422	204	7	)	)	PUNCT
cana-5422	204	8	and	and	CCONJ
cana-5422	204	9	(	(	PUNCT
cana-5422	204	10	2.27	2.27	NUM
cana-5422	204	11	)	)	PUNCT
cana-5422	204	12	,	,	PUNCT
cana-5422	204	13	we	we	PRON
cana-5422	204	14	arrive∥∥∥3f	arrive∥∥∥3f	VERB
cana-5422	204	15	(	(	PUNCT
cana-5422	204	16	5w1)−	5w1)−	NOUN
cana-5422	204	17	75f	75f	NOUN
cana-5422	204	18	(	(	PUNCT
cana-5422	204	19	w1	w1	NOUN
cana-5422	204	20	)	)	PUNCT
cana-5422	204	21	∥∥∥	∥∥∥	PROPN
cana-5422	204	22	≤	≤	NUM
cana-5422	204	23	∥∥∥3f	∥∥∥3f	PROPN
cana-5422	205	1	(	(	PUNCT
cana-5422	205	2	5w1)−	5w1)−	PROPN
cana-5422	205	3	7f	7f	X
cana-5422	205	4	(	(	PUNCT
cana-5422	205	5	3w1)−	3w1)−	NOUN
cana-5422	205	6	12f	12f	NUM
cana-5422	205	7	(	(	PUNCT
cana-5422	205	8	w1	w1	NOUN
cana-5422	205	9	)	)	PUNCT
cana-5422	205	10	∥∥∥+	∥∥∥+	PROPN
cana-5422	205	11	∥∥∥7f	∥∥∥7f	PUNCT
cana-5422	206	1	(	(	PUNCT
cana-5422	206	2	3w1)−	3w1)−	NUM
cana-5422	206	3	63f	63f	X
cana-5422	206	4	(	(	PUNCT
cana-5422	206	5	w1	w1	NOUN
cana-5422	206	6	)	)	PUNCT
cana-5422	206	7	∥∥∥	∥∥∥	PROPN
cana-5422	206	8	≤	≤	NUM
cana-5422	207	1	ψ	ψ	X
cana-5422	207	2	(	(	PUNCT
cana-5422	207	3	w1	w1	NOUN
cana-5422	207	4	,	,	PUNCT
cana-5422	207	5	w1	w1	NOUN
cana-5422	207	6	,	,	PUNCT
cana-5422	207	7	w1	w1	NOUN
cana-5422	207	8	)	)	PUNCT
cana-5422	207	9	+	+	CCONJ
cana-5422	207	10	7	7	NUM
cana-5422	207	11	2	2	NUM
cana-5422	207	12	ψ	ψ	NOUN
cana-5422	207	13	(	(	PUNCT
cana-5422	207	14	w1	w1	NOUN
cana-5422	207	15	,	,	PUNCT
cana-5422	207	16	w1,−w1	w1,−w1	NUM
cana-5422	207	17	)	)	PUNCT
cana-5422	207	18	,	,	PUNCT
cana-5422	207	19	∀	∀	NOUN
cana-5422	207	20	w1	w1	NOUN
cana-5422	207	21	∈	∈	PROPN
cana-5422	207	22	w1	w1	NOUN
cana-5422	207	23	.	.	PUNCT
cana-5422	208	1	(	(	PUNCT
cana-5422	208	2	2.28	2.28	NUM
cana-5422	208	3	)	)	PUNCT
cana-5422	208	4	one	one	PRON
cana-5422	208	5	can	can	AUX
cana-5422	208	6	see	see	VERB
cana-5422	208	7	from	from	ADP
cana-5422	208	8	(	(	PUNCT
cana-5422	208	9	2.28	2.28	NUM
cana-5422	208	10	)	)	PUNCT
cana-5422	208	11	that∥∥∥f	that∥∥∥f	PROPN
cana-5422	208	12	(	(	PUNCT
cana-5422	208	13	5w1)−	5w1)−	PROPN
cana-5422	208	14	25f	25f	X
cana-5422	208	15	(	(	PUNCT
cana-5422	208	16	w1	w1	NOUN
cana-5422	208	17	)	)	PUNCT
cana-5422	208	18	∥∥∥	∥∥∥	PROPN
cana-5422	208	19	≤	≤	NUM
cana-5422	208	20	1	1	NUM
cana-5422	208	21	3	3	NUM
cana-5422	208	22	{	{	PUNCT
cana-5422	208	23	ψ	ψ	X
cana-5422	208	24	(	(	PUNCT
cana-5422	208	25	w1	w1	NOUN
cana-5422	208	26	,	,	PUNCT
cana-5422	208	27	w1	w1	NOUN
cana-5422	208	28	,	,	PUNCT
cana-5422	208	29	w1	w1	NOUN
cana-5422	208	30	)	)	PUNCT
cana-5422	209	1	+	+	CCONJ
cana-5422	209	2	7	7	NUM
cana-5422	209	3	2	2	NUM
cana-5422	209	4	ψ	ψ	NOUN
cana-5422	209	5	(	(	PUNCT
cana-5422	209	6	w1	w1	NOUN
cana-5422	209	7	,	,	PUNCT
cana-5422	209	8	w1,−w1	w1,−w1	NUM
cana-5422	209	9	)	)	PUNCT
cana-5422	209	10	}	}	PUNCT
cana-5422	210	1	=	=	PUNCT
cana-5422	210	2	ψq	ψq	PROPN
cana-5422	210	3	(	(	PUNCT
cana-5422	210	4	w1	w1	NOUN
cana-5422	210	5	)	)	PUNCT
cana-5422	210	6	,	,	PUNCT
cana-5422	210	7	∀	∀	NOUN
cana-5422	210	8	w1	w1	NOUN
cana-5422	210	9	∈	∈	PROPN
cana-5422	210	10	w1	w1	NOUN
cana-5422	210	11	.	.	PUNCT
cana-5422	211	1	(	(	PUNCT
cana-5422	211	2	2.29	2.29	NUM
cana-5422	211	3	)	)	PUNCT
cana-5422	211	4	it	it	PRON
cana-5422	211	5	follows	follow	VERB
cana-5422	211	6	from	from	ADP
cana-5422	211	7	(	(	PUNCT
cana-5422	211	8	2.29	2.29	NUM
cana-5422	211	9	)	)	PUNCT
cana-5422	211	10	that	that	DET
cana-5422	211	11	∥∥∥	∥∥∥	PROPN
cana-5422	211	12	1	1	NUM
cana-5422	211	13	25	25	NUM
cana-5422	211	14	f	f	NOUN
cana-5422	211	15	(	(	PUNCT
cana-5422	211	16	5w1)−f	5w1)−f	PROPN
cana-5422	211	17	(	(	PUNCT
cana-5422	211	18	w1	w1	NOUN
cana-5422	211	19	)	)	PUNCT
cana-5422	211	20	∥∥∥	∥∥∥	PROPN
cana-5422	211	21	≤	≤	NUM
cana-5422	211	22	1	1	NUM
cana-5422	211	23	25	25	NUM
cana-5422	211	24	ψq	ψq	PROPN
cana-5422	211	25	(	(	PUNCT
cana-5422	211	26	w1	w1	NOUN
cana-5422	211	27	)	)	PUNCT
cana-5422	211	28	,	,	PUNCT
cana-5422	211	29	∀	∀	NOUN
cana-5422	211	30	w1	w1	NOUN
cana-5422	211	31	∈	∈	PROPN
cana-5422	211	32	w1	w1	NOUN
cana-5422	211	33	.	.	PUNCT
cana-5422	212	1	(	(	PUNCT
cana-5422	212	2	2.30	2.30	NUM
cana-5422	212	3	)	)	PUNCT
cana-5422	212	4	the	the	DET
cana-5422	212	5	rest	rest	NOUN
cana-5422	212	6	of	of	ADP
cana-5422	212	7	the	the	DET
cana-5422	212	8	proof	proof	NOUN
cana-5422	212	9	is	be	AUX
cana-5422	212	10	similar	similar	ADJ
cana-5422	212	11	to	to	ADP
cana-5422	212	12	that	that	PRON
cana-5422	212	13	of	of	ADP
cana-5422	212	14	theorem	theorem	ADJ
cana-5422	212	15	2.1	2.1	NUM
cana-5422	212	16	.	.	PUNCT
cana-5422	213	1	hence	hence	ADV
cana-5422	213	2	the	the	DET
cana-5422	213	3	proof	proof	NOUN
cana-5422	213	4	is	be	AUX
cana-5422	213	5	complete	complete	ADJ
cana-5422	213	6	.	.	PUNCT
cana-5422	214	1	�	�	PROPN
cana-5422	214	2	corollary	corollary	ADJ
cana-5422	214	3	2.4	2.4	NUM
cana-5422	214	4	.	.	PUNCT
cana-5422	215	1	suppose	suppose	VERB
cana-5422	215	2	that	that	SCONJ
cana-5422	215	3	an	an	DET
cana-5422	215	4	even	even	ADV
cana-5422	215	5	function	function	NOUN
cana-5422	215	6	f	f	PROPN
cana-5422	215	7	:	:	PUNCT
cana-5422	215	8	w1	w1	PROPN
cana-5422	215	9	→	→	SYM
cana-5422	215	10	w2	w2	NOUN
cana-5422	215	11	satisfy	satisfy	VERB
cana-5422	215	12	the	the	DET
cana-5422	215	13	functional	functional	ADJ
cana-5422	215	14	inequality	inequality	NOUN
cana-5422	215	15	(	(	PUNCT
cana-5422	215	16	2.2	2.2	NUM
cana-5422	215	17	)	)	PUNCT
cana-5422	215	18	for	for	ADP
cana-5422	215	19	all	all	DET
cana-5422	215	20	w1	w1	NOUN
cana-5422	215	21	,	,	PUNCT
cana-5422	215	22	w2	w2	NOUN
cana-5422	215	23	,	,	PUNCT
cana-5422	215	24	w3	w3	PROPN
cana-5422	215	25	∈	∈	PROPN
cana-5422	215	26	w1	w1	NOUN
cana-5422	215	27	.	.	PUNCT
cana-5422	216	1	then	then	ADV
cana-5422	216	2	there	there	PRON
cana-5422	216	3	exists	exist	VERB
cana-5422	216	4	a	a	DET
cana-5422	216	5	unique	unique	ADJ
cana-5422	216	6	quadratic	quadratic	ADJ
cana-5422	216	7	mapping	mapping	NOUN
cana-5422	216	8	q(w1	q(w1	NOUN
cana-5422	216	9	)	)	PUNCT
cana-5422	216	10	:	:	PUNCT
cana-5422	216	11	w1	w1	NOUN
cana-5422	216	12	→	→	SYM
cana-5422	216	13	w2	w2	NOUN
cana-5422	216	14	which	which	PRON
cana-5422	216	15	satisfies	satisfy	VERB
cana-5422	216	16	(	(	PUNCT
cana-5422	216	17	1.7	1.7	NUM
cana-5422	216	18	)	)	PUNCT
cana-5422	216	19	and	and	CCONJ
cana-5422	216	20	communications	communication	NOUN
cana-5422	216	21	on	on	ADP
cana-5422	216	22	applied	apply	VERB
cana-5422	216	23	nonlinear	nonlinear	ADJ
cana-5422	216	24	analysis	analysis	NOUN
cana-5422	216	25	issn	issn	NOUN
cana-5422	216	26	:	:	PUNCT
cana-5422	216	27	1074	1074	NUM
cana-5422	216	28	-	-	PUNCT
cana-5422	216	29	133x	133x	NUM
cana-5422	216	30	vol	vol	NOUN
cana-5422	216	31	32	32	NUM
cana-5422	216	32	no	no	NOUN
cana-5422	216	33	.	.	PUNCT
cana-5422	217	1	10s(2025	10s(2025	NUM
cana-5422	217	2	)	)	PUNCT
cana-5422	218	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	218	2	2192	2192	NUM
cana-5422	218	3	the	the	DET
cana-5422	218	4	functional	functional	ADJ
cana-5422	218	5	inequality	inequality	NOUN
cana-5422	218	6	‖f	‖f	PRON
cana-5422	218	7	(	(	PUNCT
cana-5422	218	8	w1)−q(w1)‖	w1)−q(w1)‖	NOUN
cana-5422	218	9	≤	≤	NUM
cana-5422	218	10			NOUN
cana-5422	218	11	3δ	3δ	PROPN
cana-5422	218	12	2|24|	2|24|	PROPN
cana-5422	218	13	,	,	PUNCT
cana-5422	218	14	27δ|w1|ϕ	27δ|w1|ϕ	NUM
cana-5422	218	15	6|25−5ϕ	6|25−5ϕ	PROPN
cana-5422	218	16	|	|	NOUN
cana-5422	218	17	;	;	PUNCT
cana-5422	218	18	ϕ	ϕ	PROPN
cana-5422	218	19	6=	6=	ADP
cana-5422	218	20	2	2	NUM
cana-5422	218	21	,	,	PUNCT
cana-5422	218	22	9δ	9δ	NUM
cana-5422	218	23	6	6	NUM
cana-5422	218	24	3	3	NUM
cana-5422	218	25	∑	∑	PUNCT
cana-5422	218	26	ψ=1	ψ=1	PUNCT
cana-5422	218	27	|wψ	|wψ	PUNCT
cana-5422	218	28	|	|	ADV
cana-5422	218	29	ϕψ	ϕψ	ADV
cana-5422	218	30	|25−5	|25−5	PROPN
cana-5422	219	1	ϕψ	ϕψ	ADP
cana-5422	219	2	|	|	ADV
cana-5422	219	3	;	;	PUNCT
cana-5422	220	1	ϕ1	ϕ1	NOUN
cana-5422	220	2	,	,	PUNCT
cana-5422	220	3	ϕ2	ϕ2	ADV
cana-5422	220	4	,	,	PUNCT
cana-5422	220	5	ϕ3	ϕ3	PROPN
cana-5422	220	6	6=	6=	PROPN
cana-5422	220	7	2	2	NUM
cana-5422	220	8	,	,	PUNCT
cana-5422	220	9	9δ|w1|3ϕ	9δ|w1|3ϕ	NUM
cana-5422	220	10	6|25−53ϕ	6|25−53ϕ	NUM
cana-5422	220	11	|	|	NOUN
cana-5422	220	12	;	;	PUNCT
cana-5422	220	13	3ϕ	3ϕ	NUM
cana-5422	220	14	6=	6=	SYM
cana-5422	220	15	2	2	NUM
cana-5422	220	16	,	,	PUNCT
cana-5422	220	17	9δ|wψ	9δ|wψ	NUM
cana-5422	220	18	|	|	NOUN
cana-5422	220	19	3	3	NUM
cana-5422	220	20	∑	∑	PUNCT
cana-5422	220	21	ψ=1	ψ=1	PUNCT
cana-5422	220	22	ϕψ	ϕψ	ADP
cana-5422	220	23	6	6	NUM
cana-5422	220	24	∣∣∣25−5	∣∣∣25−5	NOUN
cana-5422	220	25	3	3	NUM
cana-5422	220	26	∑	∑	PUNCT
cana-5422	220	27	ψ=1	ψ=1	PUNCT
cana-5422	220	28	ϕψ	ϕψ	ADV
cana-5422	220	29	∣∣∣	∣∣∣	ADJ
cana-5422	220	30	;	;	PUNCT
cana-5422	220	31	3	3	NUM
cana-5422	220	32	∑	∑	PUNCT
cana-5422	220	33	ψ=1	ψ=1	PUNCT
cana-5422	220	34	ϕψ	ϕψ	ADP
cana-5422	220	35	6=	6=	PROPN
cana-5422	220	36	2	2	NUM
cana-5422	220	37	,	,	PUNCT
cana-5422	220	38	36δ|w1|3ϕ	36δ|w1|3ϕ	NUM
cana-5422	220	39	6|25−	6|25−	NUM
cana-5422	220	40	53ϕ|	53ϕ|	NUM
cana-5422	220	41	;	;	PUNCT
cana-5422	220	42	3ϕ	3ϕ	NUM
cana-5422	220	43	6=	6=	SYM
cana-5422	220	44	2	2	NUM
cana-5422	220	45	,	,	PUNCT
cana-5422	220	46	(	(	PUNCT
cana-5422	220	47	2.31	2.31	NUM
cana-5422	220	48	)	)	PUNCT
cana-5422	220	49	for	for	ADP
cana-5422	220	50	all	all	DET
cana-5422	220	51	w1	w1	NOUN
cana-5422	220	52	∈	∈	PROPN
cana-5422	220	53	w1	w1	NOUN
cana-5422	220	54	.	.	PUNCT
cana-5422	221	1	2.3	2.3	NUM
cana-5422	221	2	.	.	PUNCT
cana-5422	221	3	oddness	oddness	ADJ
cana-5422	221	4	and	and	CCONJ
cana-5422	221	5	evenness	evenness	NOUN
cana-5422	221	6	of	of	ADP
cana-5422	221	7	f	f	NOUN
cana-5422	221	8	:	:	PUNCT
cana-5422	221	9	additive	additive	ADJ
cana-5422	221	10	quadratic	quadratic	ADJ
cana-5422	221	11	case	case	NOUN
cana-5422	221	12	stability	stability	NOUN
cana-5422	221	13	results	result	VERB
cana-5422	221	14	:	:	PUNCT
cana-5422	221	15	direct	direct	ADJ
cana-5422	221	16	method	method	NOUN
cana-5422	221	17	.	.	PUNCT
cana-5422	222	1	theorem	theorem	VERB
cana-5422	222	2	2.5	2.5	NUM
cana-5422	222	3	.	.	PUNCT
cana-5422	223	1	suppose	suppose	VERB
cana-5422	223	2	that	that	SCONJ
cana-5422	223	3	a	a	DET
cana-5422	223	4	function	function	NOUN
cana-5422	223	5	f	f	NOUN
cana-5422	223	6	:	:	PUNCT
cana-5422	223	7	w1	w1	PROPN
cana-5422	223	8	→	→	SYM
cana-5422	223	9	w2	w2	NOUN
cana-5422	223	10	satisfy	satisfy	VERB
cana-5422	223	11	the	the	DET
cana-5422	223	12	functional	functional	ADJ
cana-5422	223	13	inequality	inequality	NOUN
cana-5422	223	14	(	(	PUNCT
cana-5422	223	15	2.1	2.1	NUM
cana-5422	223	16	)	)	PUNCT
cana-5422	223	17	where	where	SCONJ
cana-5422	223	18	ψ	ψ	X
cana-5422	223	19	:	:	PUNCT
cana-5422	223	20	w3	w3	NOUN
cana-5422	223	21	1	1	NUM
cana-5422	223	22	→	→	SYM
cana-5422	224	1	[	[	X
cana-5422	224	2	0	0	NUM
cana-5422	224	3	,	,	PUNCT
cana-5422	224	4	∞	∞	PROPN
cana-5422	224	5	)	)	PUNCT
cana-5422	224	6	with	with	ADP
cana-5422	224	7	the	the	DET
cana-5422	224	8	conditions	condition	NOUN
cana-5422	224	9	(	(	PUNCT
cana-5422	224	10	2.3	2.3	NUM
cana-5422	224	11	)	)	PUNCT
cana-5422	224	12	and	and	CCONJ
cana-5422	224	13	(	(	PUNCT
cana-5422	224	14	2.21	2.21	NUM
cana-5422	224	15	)	)	PUNCT
cana-5422	224	16	for	for	ADP
cana-5422	224	17	all	all	DET
cana-5422	224	18	w1	w1	NOUN
cana-5422	224	19	,	,	PUNCT
cana-5422	224	20	w2	w2	NOUN
cana-5422	224	21	,	,	PUNCT
cana-5422	224	22	w3	w3	PROPN
cana-5422	224	23	∈	∈	PROPN
cana-5422	224	24	w1	w1	NOUN
cana-5422	224	25	.	.	PUNCT
cana-5422	225	1	then	then	ADV
cana-5422	225	2	there	there	PRON
cana-5422	225	3	exists	exist	VERB
cana-5422	225	4	a	a	DET
cana-5422	225	5	unique	unique	ADJ
cana-5422	225	6	additive	additive	ADJ
cana-5422	225	7	mapping	mapping	NOUN
cana-5422	225	8	a(w1	a(w1	NOUN
cana-5422	225	9	)	)	PUNCT
cana-5422	225	10	:	:	PUNCT
cana-5422	225	11	w1	w1	NOUN
cana-5422	225	12	→w2	→w2	NOUN
cana-5422	225	13	and	and	CCONJ
cana-5422	225	14	a	a	DET
cana-5422	225	15	unique	unique	ADJ
cana-5422	225	16	quadratic	quadratic	ADJ
cana-5422	225	17	mappingq(w1	mappingq(w1	NOUN
cana-5422	225	18	)	)	PUNCT
cana-5422	225	19	:	:	PUNCT
cana-5422	225	20	w1	w1	PROPN
cana-5422	225	21	→w2	→w2	NOUN
cana-5422	225	22	which	which	PRON
cana-5422	225	23	satisfies	satisfy	VERB
cana-5422	225	24	(	(	PUNCT
cana-5422	225	25	1.7	1.7	NUM
cana-5422	225	26	)	)	PUNCT
cana-5422	225	27	and	and	CCONJ
cana-5422	225	28	the	the	DET
cana-5422	225	29	functional	functional	ADJ
cana-5422	225	30	inequality	inequality	NOUN
cana-5422	225	31	‖f	‖f	ADP
cana-5422	225	32	(	(	PUNCT
cana-5422	225	33	w1)−a(w1)−q(w1)‖	w1)−a(w1)−q(w1)‖	PROPN
cana-5422	225	34	≤	≤	ADJ
cana-5422	225	35	1	1	NUM
cana-5422	225	36	2	2	NUM
cana-5422	225	37	1	1	NUM
cana-5422	225	38	5	5	NUM
cana-5422	225	39	∞	∞	NUM
cana-5422	225	40	∑	∑	PUNCT
cana-5422	225	41	η=	η=	ADJ
cana-5422	225	42	1−µ	1−µ	NOUN
cana-5422	225	43	2	2	NUM
cana-5422	225	44	1	1	NUM
cana-5422	225	45	5ηµ	5ηµ	NOUN
cana-5422	225	46	{	{	PUNCT
cana-5422	225	47	ψa	ψa	X
cana-5422	225	48	(	(	PUNCT
cana-5422	225	49	5ηµw1	5ηµw1	NOUN
cana-5422	225	50	)	)	PUNCT
cana-5422	225	51	+	+	CCONJ
cana-5422	225	52	ψa	ψa	ADJ
cana-5422	225	53	(	(	PUNCT
cana-5422	225	54	−5ηµw1	−5ηµw1	ADV
cana-5422	225	55	)	)	PUNCT
cana-5422	225	56	}	}	PUNCT
cana-5422	226	1	+	+	CCONJ
cana-5422	226	2	1	1	NUM
cana-5422	226	3	25	25	NUM
cana-5422	226	4	∞	∞	NUM
cana-5422	226	5	∑	∑	PUNCT
cana-5422	226	6	η=	η=	ADJ
cana-5422	226	7	1−µ	1−µ	NOUN
cana-5422	226	8	2	2	NUM
cana-5422	226	9	1	1	NUM
cana-5422	226	10	25ηµ	25ηµ	NOUN
cana-5422	226	11	{	{	PUNCT
cana-5422	226	12	ψq	ψq	PROPN
cana-5422	226	13	(	(	PUNCT
cana-5422	226	14	5ηµw1	5ηµw1	NOUN
cana-5422	226	15	)	)	PUNCT
cana-5422	226	16	+	+	CCONJ
cana-5422	226	17	ψq	ψq	PROPN
cana-5422	226	18	(	(	PUNCT
cana-5422	226	19	−5ηµw1	−5ηµw1	NOUN
cana-5422	226	20	)	)	PUNCT
cana-5422	226	21	}	}	PUNCT
cana-5422	226	22			ADP
cana-5422	226	23	≤	≤	NUM
cana-5422	226	24	1	1	NUM
cana-5422	226	25	2	2	NUM
cana-5422	226	26	1	1	NUM
cana-5422	226	27	5	5	NUM
cana-5422	226	28	∞	∞	NUM
cana-5422	226	29	∑	∑	PUNCT
cana-5422	226	30	η=	η=	ADJ
cana-5422	226	31	1−µ	1−µ	NOUN
cana-5422	226	32	2	2	NUM
cana-5422	226	33	1	1	NUM
cana-5422	226	34	5ηµ	5ηµ	NOUN
cana-5422	226	35	{	{	PUNCT
cana-5422	226	36	1	1	NUM
cana-5422	226	37	3	3	NUM
cana-5422	226	38	{	{	PUNCT
cana-5422	226	39	ψ	ψ	X
cana-5422	226	40	(	(	PUNCT
cana-5422	226	41	5ηµw1	5ηµw1	NUM
cana-5422	226	42	,	,	PUNCT
cana-5422	226	43	5ηµw1	5ηµw1	NUM
cana-5422	226	44	,	,	PUNCT
cana-5422	226	45	5ηµw1	5ηµw1	NUM
cana-5422	226	46	)	)	PUNCT
cana-5422	227	1	+	+	NUM
cana-5422	227	2	3ψ	3ψ	NUM
cana-5422	227	3	(	(	PUNCT
cana-5422	227	4	5ηµw1	5ηµw1	NUM
cana-5422	227	5	,	,	PUNCT
cana-5422	227	6	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	227	7	)	)	PUNCT
cana-5422	227	8	}	}	PUNCT
cana-5422	228	1	+	+	CCONJ
cana-5422	228	2	1	1	NUM
cana-5422	228	3	3	3	NUM
cana-5422	228	4	{	{	PUNCT
cana-5422	228	5	ψ	ψ	X
cana-5422	228	6	(	(	PUNCT
cana-5422	228	7	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	228	8	)	)	PUNCT
cana-5422	228	9	+	+	NUM
cana-5422	228	10	3ψ	3ψ	NUM
cana-5422	228	11	(	(	PUNCT
cana-5422	228	12	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	228	13	,	,	PUNCT
cana-5422	228	14	5ηµw1	5ηµw1	NUM
cana-5422	228	15	)	)	PUNCT
cana-5422	228	16	}	}	PUNCT
cana-5422	228	17	}	}	PUNCT
cana-5422	229	1	+	+	CCONJ
cana-5422	229	2	1	1	NUM
cana-5422	229	3	25	25	NUM
cana-5422	229	4	∞	∞	NUM
cana-5422	229	5	∑	∑	PUNCT
cana-5422	229	6	η=	η=	ADJ
cana-5422	229	7	1−µ	1−µ	NOUN
cana-5422	229	8	2	2	NUM
cana-5422	229	9	1	1	NUM
cana-5422	229	10	25ηµ	25ηµ	NOUN
cana-5422	229	11	{	{	PUNCT
cana-5422	229	12	1	1	NUM
cana-5422	229	13	3	3	NUM
cana-5422	229	14	{	{	PUNCT
cana-5422	229	15	ψ	ψ	X
cana-5422	229	16	(	(	PUNCT
cana-5422	229	17	5ηµw1	5ηµw1	NUM
cana-5422	229	18	,	,	PUNCT
cana-5422	229	19	5ηµw1	5ηµw1	NUM
cana-5422	229	20	,	,	PUNCT
cana-5422	229	21	5ηµw1	5ηµw1	NUM
cana-5422	229	22	)	)	PUNCT
cana-5422	229	23	+	+	CCONJ
cana-5422	229	24	7	7	NUM
cana-5422	229	25	2	2	NUM
cana-5422	229	26	ψ	ψ	X
cana-5422	229	27	(	(	PUNCT
cana-5422	229	28	5ηµw1	5ηµw1	NUM
cana-5422	229	29	,	,	PUNCT
cana-5422	229	30	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	229	31	)	)	PUNCT
cana-5422	229	32	}	}	PUNCT
cana-5422	229	33	+	+	CCONJ
cana-5422	229	34	1	1	NUM
cana-5422	229	35	3	3	NUM
cana-5422	229	36	{	{	PUNCT
cana-5422	229	37	ψ	ψ	X
cana-5422	229	38	(	(	PUNCT
cana-5422	229	39	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	229	40	)	)	PUNCT
cana-5422	229	41	+	+	CCONJ
cana-5422	229	42	7	7	NUM
cana-5422	229	43	2	2	NUM
cana-5422	229	44	ψ	ψ	X
cana-5422	229	45	(	(	PUNCT
cana-5422	229	46	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	229	47	,	,	PUNCT
cana-5422	229	48	5ηµw1	5ηµw1	NUM
cana-5422	229	49	)	)	PUNCT
cana-5422	229	50	}	}	PUNCT
cana-5422	229	51	}	}	PUNCT
cana-5422	229	52	}	}	PUNCT
cana-5422	229	53	,	,	PUNCT
cana-5422	229	54	(	(	PUNCT
cana-5422	229	55	2.32	2.32	NUM
cana-5422	229	56	)	)	PUNCT
cana-5422	229	57	and	and	CCONJ
cana-5422	229	58	the	the	DET
cana-5422	229	59	mapping	mapping	NOUN
cana-5422	229	60	a(w1	a(w1	NOUN
cana-5422	229	61	)	)	PUNCT
cana-5422	229	62	and	and	CCONJ
cana-5422	229	63	q(w1	q(w1	NOUN
cana-5422	229	64	)	)	PUNCT
cana-5422	229	65	are	be	AUX
cana-5422	229	66	given	give	VERB
cana-5422	229	67	in	in	ADP
cana-5422	229	68	(	(	PUNCT
cana-5422	229	69	2.6	2.6	NUM
cana-5422	229	70	)	)	PUNCT
cana-5422	229	71	and	and	CCONJ
cana-5422	229	72	(	(	PUNCT
cana-5422	229	73	2.24	2.24	NUM
cana-5422	229	74	)	)	PUNCT
cana-5422	229	75	for	for	ADP
cana-5422	229	76	all	all	DET
cana-5422	229	77	w1	w1	NOUN
cana-5422	229	78	∈	∈	PROPN
cana-5422	229	79	w1	w1	NOUN
cana-5422	229	80	.	.	PUNCT
cana-5422	230	1	proof	proof	NOUN
cana-5422	230	2	.	.	PUNCT
cana-5422	231	1	consider	consider	VERB
cana-5422	231	2	a	a	DET
cana-5422	231	3	function	function	NOUN
cana-5422	231	4	fodd(w1	fodd(w1	NOUN
cana-5422	231	5	)	)	PUNCT
cana-5422	231	6	by	by	ADP
cana-5422	231	7	fodd(w1	fodd(w1	NOUN
cana-5422	231	8	)	)	PUNCT
cana-5422	231	9	=	=	SYM
cana-5422	231	10	1	1	NUM
cana-5422	231	11	2	2	NUM
cana-5422	231	12	{	{	PUNCT
cana-5422	231	13	f	f	PROPN
cana-5422	231	14	(	(	PUNCT
cana-5422	231	15	w1)−f	w1)−f	X
cana-5422	231	16	(	(	PUNCT
cana-5422	231	17	−w1	−w1	PROPN
cana-5422	231	18	)	)	PUNCT
cana-5422	231	19	}	}	PUNCT
cana-5422	231	20	,	,	PUNCT
cana-5422	231	21	∀	∀	NOUN
cana-5422	231	22	w1	w1	NOUN
cana-5422	231	23	∈	∈	PROPN
cana-5422	231	24	w1	w1	NOUN
cana-5422	231	25	,	,	PUNCT
cana-5422	231	26	(	(	PUNCT
cana-5422	231	27	2.33	2.33	NUM
cana-5422	231	28	)	)	PUNCT
cana-5422	231	29	which	which	PRON
cana-5422	231	30	gives	give	VERB
cana-5422	231	31	fodd(0	fodd(0	PRON
cana-5422	231	32	)	)	PUNCT
cana-5422	231	33	=	=	SYM
cana-5422	231	34	0	0	NUM
cana-5422	231	35	;	;	PUNCT
cana-5422	232	1	fodd(−w1	fodd(−w1	ADJ
cana-5422	232	2	)	)	PUNCT
cana-5422	232	3	=	=	SYM
cana-5422	232	4	−fodd(w1	−fodd(w1	PROPN
cana-5422	232	5	)	)	PUNCT
cana-5422	232	6	,	,	PUNCT
cana-5422	232	7	∀	∀	X
cana-5422	232	8	w1	w1	NOUN
cana-5422	232	9	∈	∈	PROPN
cana-5422	232	10	w1	w1	NOUN
cana-5422	232	11	.	.	PUNCT
cana-5422	233	1	(	(	PUNCT
cana-5422	233	2	2.34	2.34	NUM
cana-5422	233	3	)	)	PUNCT
cana-5422	233	4	communications	communication	NOUN
cana-5422	233	5	on	on	ADP
cana-5422	233	6	applied	apply	VERB
cana-5422	233	7	nonlinear	nonlinear	ADJ
cana-5422	233	8	analysis	analysis	NOUN
cana-5422	233	9	issn	issn	NOUN
cana-5422	233	10	:	:	PUNCT
cana-5422	233	11	1074	1074	NUM
cana-5422	233	12	-	-	PUNCT
cana-5422	233	13	133x	133x	NUM
cana-5422	233	14	vol	vol	NOUN
cana-5422	233	15	32	32	NUM
cana-5422	233	16	no	no	NOUN
cana-5422	233	17	.	.	PUNCT
cana-5422	234	1	10s(2025	10s(2025	NUM
cana-5422	234	2	)	)	PUNCT
cana-5422	234	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	234	4	2193	2193	NUM
cana-5422	234	5	by	by	ADP
cana-5422	234	6	theorem	theorem	NOUN
cana-5422	234	7	2.1	2.1	NUM
cana-5422	234	8	,	,	PUNCT
cana-5422	234	9	it	it	PRON
cana-5422	234	10	follows	follow	VERB
cana-5422	234	11	from	from	ADP
cana-5422	234	12	(	(	PUNCT
cana-5422	234	13	2.33	2.33	NUM
cana-5422	234	14	)	)	PUNCT
cana-5422	234	15	,	,	PUNCT
cana-5422	234	16	(	(	PUNCT
cana-5422	234	17	2.1	2.1	NUM
cana-5422	234	18	)	)	PUNCT
cana-5422	234	19	,	,	PUNCT
cana-5422	234	20	(	(	PUNCT
cana-5422	234	21	2.5	2.5	NUM
cana-5422	234	22	)	)	PUNCT
cana-5422	234	23	and	and	CCONJ
cana-5422	234	24	(	(	PUNCT
cana-5422	234	25	2.6	2.6	NUM
cana-5422	234	26	)	)	PUNCT
cana-5422	234	27	,	,	PUNCT
cana-5422	234	28	we	we	PRON
cana-5422	234	29	arrive	arrive	VERB
cana-5422	234	30	‖fodd(w1)−a(w1)‖	‖fodd(w1)−a(w1)‖	PROPN
cana-5422	234	31	≤	≤	NUM
cana-5422	234	32	1	1	NUM
cana-5422	234	33	2	2	NUM
cana-5422	234	34	·	·	SYM
cana-5422	234	35	1	1	NUM
cana-5422	234	36	5	5	NUM
cana-5422	234	37	∞	∞	NUM
cana-5422	234	38	∑	∑	PUNCT
cana-5422	234	39	η=	η=	ADJ
cana-5422	234	40	1−µ	1−µ	NOUN
cana-5422	234	41	2	2	NUM
cana-5422	234	42	1	1	NUM
cana-5422	234	43	5ηµ	5ηµ	NOUN
cana-5422	234	44	{	{	PUNCT
cana-5422	234	45	ψa	ψa	X
cana-5422	234	46	(	(	PUNCT
cana-5422	234	47	5ηµw1	5ηµw1	NOUN
cana-5422	234	48	)	)	PUNCT
cana-5422	234	49	+	+	CCONJ
cana-5422	234	50	ψa	ψa	ADJ
cana-5422	234	51	(	(	PUNCT
cana-5422	234	52	−5ηµw1	−5ηµw1	NOUN
cana-5422	234	53	)	)	PUNCT
cana-5422	234	54	}	}	PUNCT
cana-5422	234	55	(	(	PUNCT
cana-5422	234	56	2.35	2.35	NUM
cana-5422	234	57	)	)	PUNCT
cana-5422	234	58	=	=	SYM
cana-5422	234	59	1	1	NUM
cana-5422	234	60	2	2	NUM
cana-5422	234	61	·	·	SYM
cana-5422	234	62	1	1	NUM
cana-5422	234	63	5	5	NUM
cana-5422	234	64	∞	∞	NUM
cana-5422	234	65	∑	∑	PUNCT
cana-5422	234	66	η=	η=	ADJ
cana-5422	234	67	1−µ	1−µ	NOUN
cana-5422	234	68	2	2	NUM
cana-5422	234	69	1	1	NUM
cana-5422	234	70	5ηµ	5ηµ	NOUN
cana-5422	234	71	{	{	PUNCT
cana-5422	234	72	1	1	NUM
cana-5422	234	73	3	3	NUM
cana-5422	234	74	{	{	PUNCT
cana-5422	234	75	ψ	ψ	X
cana-5422	234	76	(	(	PUNCT
cana-5422	234	77	5ηµw1	5ηµw1	NUM
cana-5422	234	78	,	,	PUNCT
cana-5422	234	79	5ηµw1	5ηµw1	NUM
cana-5422	234	80	,	,	PUNCT
cana-5422	234	81	5ηµw1	5ηµw1	NUM
cana-5422	234	82	)	)	PUNCT
cana-5422	235	1	+	+	NUM
cana-5422	235	2	3ψ	3ψ	NUM
cana-5422	235	3	(	(	PUNCT
cana-5422	235	4	5ηµw1	5ηµw1	NUM
cana-5422	235	5	,	,	PUNCT
cana-5422	235	6	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	235	7	)	)	PUNCT
cana-5422	235	8	}	}	PUNCT
cana-5422	236	1	+	+	CCONJ
cana-5422	236	2	1	1	NUM
cana-5422	236	3	3	3	NUM
cana-5422	236	4	{	{	PUNCT
cana-5422	236	5	ψ	ψ	X
cana-5422	236	6	(	(	PUNCT
cana-5422	236	7	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	236	8	)	)	PUNCT
cana-5422	236	9	+	+	NUM
cana-5422	236	10	3ψ	3ψ	NUM
cana-5422	236	11	(	(	PUNCT
cana-5422	236	12	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	236	13	,	,	PUNCT
cana-5422	236	14	5ηµw1	5ηµw1	NUM
cana-5422	236	15	)	)	PUNCT
cana-5422	236	16	}	}	PUNCT
cana-5422	236	17	}	}	PUNCT
cana-5422	236	18	,	,	PUNCT
cana-5422	236	19	(	(	PUNCT
cana-5422	236	20	2.36	2.36	NUM
cana-5422	236	21	)	)	PUNCT
cana-5422	236	22	for	for	ADP
cana-5422	236	23	all	all	DET
cana-5422	236	24	w1	w1	NOUN
cana-5422	236	25	∈	∈	PROPN
cana-5422	236	26	w1	w1	NOUN
cana-5422	236	27	.	.	PUNCT
cana-5422	237	1	consider	consider	VERB
cana-5422	237	2	a	a	DET
cana-5422	237	3	function	function	NOUN
cana-5422	237	4	feven(w1	feven(w1	NOUN
cana-5422	237	5	)	)	PUNCT
cana-5422	237	6	by	by	ADP
cana-5422	237	7	feven(w1	feven(w1	NOUN
cana-5422	237	8	)	)	PUNCT
cana-5422	237	9	=	=	SYM
cana-5422	237	10	1	1	NUM
cana-5422	237	11	2	2	NUM
cana-5422	237	12	{	{	PUNCT
cana-5422	237	13	f	f	PROPN
cana-5422	237	14	(	(	PUNCT
cana-5422	237	15	w1	w1	NOUN
cana-5422	237	16	)	)	PUNCT
cana-5422	238	1	+	+	NOUN
cana-5422	238	2	f	f	X
cana-5422	238	3	(	(	PUNCT
cana-5422	238	4	−w1	−w1	PROPN
cana-5422	238	5	)	)	PUNCT
cana-5422	238	6	}	}	PUNCT
cana-5422	238	7	,	,	PUNCT
cana-5422	238	8	∀	∀	NOUN
cana-5422	238	9	w1	w1	NOUN
cana-5422	238	10	∈	∈	PROPN
cana-5422	238	11	w1	w1	NOUN
cana-5422	238	12	,	,	PUNCT
cana-5422	238	13	(	(	PUNCT
cana-5422	238	14	2.37	2.37	NUM
cana-5422	238	15	)	)	PUNCT
cana-5422	238	16	which	which	PRON
cana-5422	238	17	gives	give	VERB
cana-5422	238	18	feven(0	feven(0	NOUN
cana-5422	238	19	)	)	PUNCT
cana-5422	238	20	=	=	SYM
cana-5422	238	21	0	0	NUM
cana-5422	238	22	;	;	PUNCT
cana-5422	238	23	feven(−w1	feven(−w1	ADJ
cana-5422	238	24	)	)	PUNCT
cana-5422	238	25	=	=	SYM
cana-5422	238	26	feven(w1	feven(w1	NOUN
cana-5422	238	27	)	)	PUNCT
cana-5422	238	28	,	,	PUNCT
cana-5422	238	29	∀	∀	X
cana-5422	238	30	w1	w1	NOUN
cana-5422	238	31	∈	∈	PROPN
cana-5422	238	32	w1	w1	NOUN
cana-5422	238	33	.	.	PUNCT
cana-5422	239	1	(	(	PUNCT
cana-5422	239	2	2.38	2.38	NUM
cana-5422	239	3	)	)	PUNCT
cana-5422	239	4	by	by	ADP
cana-5422	239	5	theorem	theorem	ADJ
cana-5422	239	6	2.3	2.3	NUM
cana-5422	239	7	,	,	PUNCT
cana-5422	239	8	it	it	PRON
cana-5422	239	9	follows	follow	VERB
cana-5422	239	10	from	from	ADP
cana-5422	239	11	(	(	PUNCT
cana-5422	239	12	2.37	2.37	NUM
cana-5422	239	13	)	)	PUNCT
cana-5422	239	14	,	,	PUNCT
cana-5422	239	15	(	(	PUNCT
cana-5422	239	16	2.1	2.1	NUM
cana-5422	239	17	)	)	PUNCT
cana-5422	239	18	,	,	PUNCT
cana-5422	239	19	(	(	PUNCT
cana-5422	239	20	2.22	2.22	NUM
cana-5422	239	21	)	)	PUNCT
cana-5422	239	22	and	and	CCONJ
cana-5422	239	23	(	(	PUNCT
cana-5422	239	24	2.23	2.23	NUM
cana-5422	239	25	)	)	PUNCT
cana-5422	239	26	,	,	PUNCT
cana-5422	239	27	we	we	PRON
cana-5422	239	28	see	see	VERB
cana-5422	239	29	‖feven(w1)−q(w1)‖	‖feven(w1)−q(w1)‖	PROPN
cana-5422	239	30	≤	≤	NUM
cana-5422	240	1	1	1	NUM
cana-5422	240	2	2	2	NUM
cana-5422	240	3	·	·	SYM
cana-5422	240	4	1	1	NUM
cana-5422	240	5	25	25	NUM
cana-5422	240	6	∞	∞	NUM
cana-5422	240	7	∑	∑	PUNCT
cana-5422	240	8	η=	η=	ADJ
cana-5422	240	9	1−µ	1−µ	NOUN
cana-5422	240	10	2	2	NUM
cana-5422	240	11	1	1	NUM
cana-5422	240	12	25ηµ	25ηµ	NOUN
cana-5422	240	13	{	{	PUNCT
cana-5422	240	14	ψq	ψq	PROPN
cana-5422	240	15	(	(	PUNCT
cana-5422	240	16	5ηµw1	5ηµw1	NOUN
cana-5422	240	17	)	)	PUNCT
cana-5422	240	18	+	+	CCONJ
cana-5422	240	19	ψq	ψq	PROPN
cana-5422	240	20	(	(	PUNCT
cana-5422	240	21	−5ηµw1	−5ηµw1	NOUN
cana-5422	240	22	)	)	PUNCT
cana-5422	240	23	}	}	PUNCT
cana-5422	240	24	(	(	PUNCT
cana-5422	240	25	2.39	2.39	NUM
cana-5422	240	26	)	)	PUNCT
cana-5422	240	27	=	=	SYM
cana-5422	241	1	1	1	NUM
cana-5422	241	2	2	2	NUM
cana-5422	241	3	·	·	SYM
cana-5422	241	4	1	1	NUM
cana-5422	241	5	25	25	NUM
cana-5422	241	6	∞	∞	NUM
cana-5422	241	7	∑	∑	PUNCT
cana-5422	241	8	η=	η=	ADJ
cana-5422	241	9	1−µ	1−µ	NOUN
cana-5422	241	10	2	2	NUM
cana-5422	241	11	1	1	NUM
cana-5422	241	12	25ηµ	25ηµ	NOUN
cana-5422	241	13	{	{	PUNCT
cana-5422	241	14	1	1	NUM
cana-5422	241	15	3	3	NUM
cana-5422	241	16	{	{	PUNCT
cana-5422	241	17	ψ	ψ	X
cana-5422	241	18	(	(	PUNCT
cana-5422	241	19	5ηµw1	5ηµw1	NUM
cana-5422	241	20	,	,	PUNCT
cana-5422	241	21	5ηµw1	5ηµw1	NUM
cana-5422	241	22	,	,	PUNCT
cana-5422	241	23	5ηµw1	5ηµw1	NUM
cana-5422	241	24	)	)	PUNCT
cana-5422	241	25	+	+	CCONJ
cana-5422	241	26	7	7	NUM
cana-5422	241	27	2	2	NUM
cana-5422	241	28	ψ	ψ	X
cana-5422	241	29	(	(	PUNCT
cana-5422	241	30	5ηµw1	5ηµw1	NUM
cana-5422	241	31	,	,	PUNCT
cana-5422	241	32	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	241	33	)	)	PUNCT
cana-5422	241	34	}	}	PUNCT
cana-5422	241	35	+	+	CCONJ
cana-5422	241	36	1	1	NUM
cana-5422	241	37	3	3	NUM
cana-5422	241	38	{	{	PUNCT
cana-5422	241	39	ψ	ψ	X
cana-5422	241	40	(	(	PUNCT
cana-5422	241	41	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	241	42	)	)	PUNCT
cana-5422	241	43	+	+	CCONJ
cana-5422	241	44	7	7	NUM
cana-5422	241	45	2	2	NUM
cana-5422	241	46	ψ	ψ	X
cana-5422	241	47	(	(	PUNCT
cana-5422	241	48	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	241	49	,	,	PUNCT
cana-5422	241	50	5ηµw1	5ηµw1	NUM
cana-5422	241	51	)	)	PUNCT
cana-5422	241	52	}	}	PUNCT
cana-5422	241	53	}	}	PUNCT
cana-5422	241	54	,	,	PUNCT
cana-5422	241	55	(	(	PUNCT
cana-5422	241	56	2.40	2.40	NUM
cana-5422	241	57	)	)	PUNCT
cana-5422	241	58	for	for	ADP
cana-5422	241	59	all	all	DET
cana-5422	241	60	w1	w1	NOUN
cana-5422	241	61	∈	∈	PROPN
cana-5422	241	62	w1	w1	NOUN
cana-5422	241	63	.	.	PUNCT
cana-5422	242	1	assume	assume	VERB
cana-5422	242	2	a	a	DET
cana-5422	242	3	function	function	NOUN
cana-5422	242	4	f	f	X
cana-5422	242	5	(	(	PUNCT
cana-5422	242	6	w1	w1	NOUN
cana-5422	242	7	)	)	PUNCT
cana-5422	242	8	by	by	ADP
cana-5422	242	9	f	f	PROPN
cana-5422	242	10	(	(	PUNCT
cana-5422	242	11	w1	w1	NOUN
cana-5422	242	12	)	)	PUNCT
cana-5422	242	13	=	=	SYM
cana-5422	242	14	fodd(w1	fodd(w1	NOUN
cana-5422	242	15	)	)	PUNCT
cana-5422	242	16	+	+	ADJ
cana-5422	242	17	feven(w1	feven(w1	NOUN
cana-5422	242	18	)	)	PUNCT
cana-5422	242	19	,	,	PUNCT
cana-5422	242	20	∀	∀	X
cana-5422	242	21	w1	w1	NOUN
cana-5422	242	22	∈	∈	PROPN
cana-5422	242	23	w1	w1	NOUN
cana-5422	242	24	.	.	PUNCT
cana-5422	243	1	(	(	PUNCT
cana-5422	243	2	2.41	2.41	NUM
cana-5422	243	3	)	)	PUNCT
cana-5422	243	4	now	now	ADV
cana-5422	243	5	,	,	PUNCT
cana-5422	243	6	it	it	PRON
cana-5422	243	7	follows	follow	VERB
cana-5422	243	8	from	from	ADP
cana-5422	243	9	(	(	PUNCT
cana-5422	243	10	2.35	2.35	NUM
cana-5422	243	11	)	)	PUNCT
cana-5422	243	12	,	,	PUNCT
cana-5422	243	13	(	(	PUNCT
cana-5422	243	14	2.36	2.36	NUM
cana-5422	243	15	)	)	PUNCT
cana-5422	243	16	,	,	PUNCT
cana-5422	243	17	(	(	PUNCT
cana-5422	243	18	2.39	2.39	NUM
cana-5422	243	19	)	)	PUNCT
cana-5422	243	20	,	,	PUNCT
cana-5422	243	21	(	(	PUNCT
cana-5422	243	22	2.40	2.40	NUM
cana-5422	243	23	)	)	PUNCT
cana-5422	243	24	and	and	CCONJ
cana-5422	243	25	(	(	PUNCT
cana-5422	243	26	2.41	2.41	NUM
cana-5422	243	27	)	)	PUNCT
cana-5422	243	28	,	,	PUNCT
cana-5422	243	29	we	we	PRON
cana-5422	243	30	have	have	VERB
cana-5422	243	31	‖f	‖f	PRON
cana-5422	243	32	(	(	PUNCT
cana-5422	243	33	w1)−a(w1)−q(w1)‖	w1)−a(w1)−q(w1)‖	X
cana-5422	243	34	≤	≤	PRON
cana-5422	243	35	‖fodd(w1)−a(w1)‖+	‖fodd(w1)−a(w1)‖+	PROPN
cana-5422	244	1	‖feven(w1)−q(w1)‖	‖feven(w1)−q(w1)‖	PROPN
cana-5422	244	2	≤	≤	NUM
cana-5422	244	3	1	1	NUM
cana-5422	244	4	2	2	NUM
cana-5422	244	5	1	1	NUM
cana-5422	244	6	5	5	NUM
cana-5422	244	7	∞	∞	NUM
cana-5422	244	8	∑	∑	PUNCT
cana-5422	244	9	η=	η=	ADJ
cana-5422	244	10	1−µ	1−µ	NOUN
cana-5422	244	11	2	2	NUM
cana-5422	244	12	1	1	NUM
cana-5422	244	13	5ηµ	5ηµ	NOUN
cana-5422	244	14	{	{	PUNCT
cana-5422	244	15	ψa	ψa	X
cana-5422	244	16	(	(	PUNCT
cana-5422	244	17	5ηµw1	5ηµw1	NOUN
cana-5422	244	18	)	)	PUNCT
cana-5422	244	19	+	+	CCONJ
cana-5422	244	20	ψa	ψa	ADJ
cana-5422	244	21	(	(	PUNCT
cana-5422	244	22	−5ηµw1	−5ηµw1	ADV
cana-5422	244	23	)	)	PUNCT
cana-5422	244	24	}	}	PUNCT
cana-5422	245	1	+	+	CCONJ
cana-5422	245	2	1	1	NUM
cana-5422	245	3	25	25	NUM
cana-5422	245	4	∞	∞	NUM
cana-5422	245	5	∑	∑	PUNCT
cana-5422	245	6	η=	η=	ADJ
cana-5422	245	7	1−µ	1−µ	NOUN
cana-5422	245	8	2	2	NUM
cana-5422	245	9	1	1	NUM
cana-5422	245	10	25ηµ	25ηµ	NOUN
cana-5422	245	11	{	{	PUNCT
cana-5422	245	12	ψq	ψq	PROPN
cana-5422	245	13	(	(	PUNCT
cana-5422	245	14	5ηµw1	5ηµw1	NOUN
cana-5422	245	15	)	)	PUNCT
cana-5422	245	16	+	+	CCONJ
cana-5422	245	17	ψq	ψq	PROPN
cana-5422	245	18	(	(	PUNCT
cana-5422	245	19	−5ηµw1	−5ηµw1	NOUN
cana-5422	245	20	)	)	PUNCT
cana-5422	245	21	}	}	PUNCT
cana-5422	245	22			ADP
cana-5422	245	23	≤	≤	NUM
cana-5422	245	24	1	1	NUM
cana-5422	245	25	2	2	NUM
cana-5422	245	26	1	1	NUM
cana-5422	245	27	5	5	NUM
cana-5422	245	28	∞	∞	NUM
cana-5422	245	29	∑	∑	PUNCT
cana-5422	245	30	η=	η=	ADJ
cana-5422	245	31	1−µ	1−µ	NOUN
cana-5422	245	32	2	2	NUM
cana-5422	245	33	1	1	NUM
cana-5422	245	34	5ηµ	5ηµ	NOUN
cana-5422	245	35	{	{	PUNCT
cana-5422	245	36	1	1	NUM
cana-5422	245	37	3	3	NUM
cana-5422	245	38	{	{	PUNCT
cana-5422	245	39	ψ	ψ	X
cana-5422	245	40	(	(	PUNCT
cana-5422	245	41	5ηµw1	5ηµw1	NUM
cana-5422	245	42	,	,	PUNCT
cana-5422	245	43	5ηµw1	5ηµw1	NUM
cana-5422	245	44	,	,	PUNCT
cana-5422	245	45	5ηµw1	5ηµw1	NUM
cana-5422	245	46	)	)	PUNCT
cana-5422	246	1	+	+	NUM
cana-5422	246	2	3ψ	3ψ	NUM
cana-5422	246	3	(	(	PUNCT
cana-5422	246	4	5ηµw1	5ηµw1	NUM
cana-5422	246	5	,	,	PUNCT
cana-5422	246	6	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	246	7	)	)	PUNCT
cana-5422	246	8	}	}	PUNCT
cana-5422	247	1	+	+	CCONJ
cana-5422	247	2	1	1	NUM
cana-5422	247	3	3	3	NUM
cana-5422	247	4	{	{	PUNCT
cana-5422	247	5	ψ	ψ	X
cana-5422	247	6	(	(	PUNCT
cana-5422	247	7	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	247	8	)	)	PUNCT
cana-5422	247	9	+	+	NUM
cana-5422	247	10	3ψ	3ψ	NUM
cana-5422	247	11	(	(	PUNCT
cana-5422	247	12	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	247	13	,	,	PUNCT
cana-5422	247	14	5ηµw1	5ηµw1	NUM
cana-5422	247	15	)	)	PUNCT
cana-5422	247	16	}	}	PUNCT
cana-5422	247	17	}	}	PUNCT
cana-5422	248	1	+	+	CCONJ
cana-5422	248	2	1	1	NUM
cana-5422	248	3	25	25	NUM
cana-5422	248	4	∞	∞	NUM
cana-5422	248	5	∑	∑	PUNCT
cana-5422	248	6	η=	η=	ADJ
cana-5422	248	7	1−µ	1−µ	NOUN
cana-5422	248	8	2	2	NUM
cana-5422	248	9	1	1	NUM
cana-5422	248	10	25ηµ	25ηµ	NOUN
cana-5422	248	11	{	{	PUNCT
cana-5422	248	12	1	1	NUM
cana-5422	248	13	3	3	NUM
cana-5422	248	14	{	{	PUNCT
cana-5422	248	15	ψ	ψ	X
cana-5422	248	16	(	(	PUNCT
cana-5422	248	17	5ηµw1	5ηµw1	NUM
cana-5422	248	18	,	,	PUNCT
cana-5422	248	19	5ηµw1	5ηµw1	NUM
cana-5422	248	20	,	,	PUNCT
cana-5422	248	21	5ηµw1	5ηµw1	NUM
cana-5422	248	22	)	)	PUNCT
cana-5422	248	23	+	+	CCONJ
cana-5422	248	24	7	7	NUM
cana-5422	248	25	2	2	NUM
cana-5422	248	26	ψ	ψ	X
cana-5422	248	27	(	(	PUNCT
cana-5422	248	28	5ηµw1	5ηµw1	NUM
cana-5422	248	29	,	,	PUNCT
cana-5422	248	30	5ηµw1,−5ηµw1	5ηµw1,−5ηµw1	NUM
cana-5422	248	31	)	)	PUNCT
cana-5422	248	32	}	}	PUNCT
cana-5422	248	33	+	+	CCONJ
cana-5422	248	34	1	1	NUM
cana-5422	248	35	3	3	NUM
cana-5422	248	36	{	{	PUNCT
cana-5422	248	37	ψ	ψ	X
cana-5422	248	38	(	(	PUNCT
cana-5422	248	39	−5ηµw1,−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1,−5ηµw1	NOUN
cana-5422	248	40	)	)	PUNCT
cana-5422	248	41	+	+	CCONJ
cana-5422	248	42	7	7	NUM
cana-5422	248	43	2	2	NUM
cana-5422	248	44	ψ	ψ	X
cana-5422	248	45	(	(	PUNCT
cana-5422	248	46	−5ηµw1,−5ηµw1	−5ηµw1,−5ηµw1	PROPN
cana-5422	248	47	,	,	PUNCT
cana-5422	248	48	5ηµw1	5ηµw1	NUM
cana-5422	248	49	)	)	PUNCT
cana-5422	248	50	}	}	PUNCT
cana-5422	248	51	}	}	PUNCT
cana-5422	248	52	}	}	PUNCT
cana-5422	248	53	,	,	PUNCT
cana-5422	248	54	for	for	ADP
cana-5422	248	55	all	all	DET
cana-5422	248	56	w1	w1	NOUN
cana-5422	248	57	,	,	PUNCT
cana-5422	248	58	w2	w2	NOUN
cana-5422	248	59	,	,	PUNCT
cana-5422	248	60	w3	w3	PROPN
cana-5422	248	61	∈	∈	PROPN
cana-5422	248	62	w1	w1	PROPN
cana-5422	248	63	.	.	PUNCT
cana-5422	249	1	�	�	PROPN
cana-5422	249	2	communications	communication	NOUN
cana-5422	249	3	on	on	ADP
cana-5422	249	4	applied	apply	VERB
cana-5422	249	5	nonlinear	nonlinear	ADJ
cana-5422	249	6	analysis	analysis	NOUN
cana-5422	249	7	issn	issn	NOUN
cana-5422	249	8	:	:	PUNCT
cana-5422	249	9	1074	1074	NUM
cana-5422	249	10	-	-	PUNCT
cana-5422	249	11	133x	133x	NUM
cana-5422	249	12	vol	vol	NOUN
cana-5422	249	13	32	32	NUM
cana-5422	249	14	no	no	NOUN
cana-5422	249	15	.	.	PUNCT
cana-5422	250	1	10s(2025	10s(2025	NUM
cana-5422	250	2	)	)	PUNCT
cana-5422	250	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	250	4	2194	2194	NUM
cana-5422	250	5	corollary	corollary	NOUN
cana-5422	250	6	2.6	2.6	NUM
cana-5422	250	7	.	.	PUNCT
cana-5422	251	1	suppose	suppose	VERB
cana-5422	251	2	that	that	SCONJ
cana-5422	251	3	a	a	DET
cana-5422	251	4	functionf	functionf	NOUN
cana-5422	251	5	:	:	PUNCT
cana-5422	251	6	w1	w1	PROPN
cana-5422	251	7	→w2	→w2	NOUN
cana-5422	251	8	satisfy	satisfy	VERB
cana-5422	251	9	the	the	DET
cana-5422	251	10	functional	functional	ADJ
cana-5422	251	11	inequality	inequality	NOUN
cana-5422	251	12	(	(	PUNCT
cana-5422	251	13	2.2	2.2	NUM
cana-5422	251	14	)	)	PUNCT
cana-5422	251	15	for	for	ADP
cana-5422	251	16	all	all	DET
cana-5422	251	17	w1	w1	NOUN
cana-5422	251	18	,	,	PUNCT
cana-5422	251	19	w2	w2	NOUN
cana-5422	251	20	,	,	PUNCT
cana-5422	251	21	w3	w3	PROPN
cana-5422	251	22	∈	∈	PROPN
cana-5422	251	23	w1	w1	NOUN
cana-5422	251	24	.	.	PUNCT
cana-5422	252	1	then	then	ADV
cana-5422	252	2	there	there	PRON
cana-5422	252	3	exists	exist	VERB
cana-5422	252	4	a	a	DET
cana-5422	252	5	unique	unique	ADJ
cana-5422	252	6	additive	additive	ADJ
cana-5422	252	7	mapping	mapping	NOUN
cana-5422	252	8	a(w1	a(w1	NOUN
cana-5422	252	9	)	)	PUNCT
cana-5422	252	10	:	:	PUNCT
cana-5422	252	11	w1	w1	NOUN
cana-5422	252	12	→w2	→w2	NOUN
cana-5422	252	13	and	and	CCONJ
cana-5422	252	14	a	a	DET
cana-5422	252	15	unique	unique	ADJ
cana-5422	252	16	quadratic	quadratic	ADJ
cana-5422	252	17	mapping	mapping	NOUN
cana-5422	252	18	q(w1	q(w1	NOUN
cana-5422	252	19	)	)	PUNCT
cana-5422	252	20	:	:	PUNCT
cana-5422	252	21	w1	w1	PROPN
cana-5422	252	22	→w2	→w2	PROPN
cana-5422	252	23	which	which	PRON
cana-5422	252	24	satisfies	satisfy	VERB
cana-5422	252	25	(	(	PUNCT
cana-5422	252	26	1.7	1.7	NUM
cana-5422	252	27	)	)	PUNCT
cana-5422	252	28	and	and	CCONJ
cana-5422	252	29	the	the	DET
cana-5422	252	30	functional	functional	ADJ
cana-5422	252	31	inequality	inequality	NOUN
cana-5422	252	32	‖f	‖f	ADP
cana-5422	252	33	(	(	PUNCT
cana-5422	252	34	w1)−a(w1)−q(w1)‖	w1)−a(w1)−q(w1)‖	PROPN
cana-5422	252	35	≤	≤	ADV
cana-5422	252	36			NOUN
cana-5422	252	37	δ	δ	PROPN
cana-5422	252	38	|3|	|3|	PUNCT
cana-5422	253	1	+	+	NUM
cana-5422	253	2	3δ	3δ	PROPN
cana-5422	253	3	2|24|	2|24|	PROPN
cana-5422	253	4	,	,	PUNCT
cana-5422	253	5	4δ|w1|ϕ	4δ|w1|ϕ	NOUN
cana-5422	253	6	|5−5ϕ	|5−5ϕ	PROPN
cana-5422	253	7	|	|	ADV
cana-5422	253	8	+	+	CCONJ
cana-5422	253	9	27δ|w1|ϕ	27δ|w1|ϕ	NUM
cana-5422	253	10	6|25−5ϕ	6|25−5ϕ	NUM
cana-5422	253	11	|	|	NOUN
cana-5422	253	12	;	;	PUNCT
cana-5422	253	13	ϕ	ϕ	PROPN
cana-5422	253	14	6=	6=	ADP
cana-5422	253	15	1	1	NUM
cana-5422	253	16	,	,	PUNCT
cana-5422	253	17	2	2	NUM
cana-5422	253	18	,	,	PUNCT
cana-5422	253	19	4δ	4δ	NOUN
cana-5422	253	20	3	3	NUM
cana-5422	253	21	3	3	NUM
cana-5422	253	22	∑	∑	PUNCT
cana-5422	253	23	ψ=1	ψ=1	PUNCT
cana-5422	253	24	|wψ	|wψ	PUNCT
cana-5422	253	25	|	|	ADV
cana-5422	253	26	ϕψ	ϕψ	ADV
cana-5422	253	27	|5−5	|5−5	NOUN
cana-5422	254	1	ϕψ	ϕψ	ADP
cana-5422	254	2	|	|	ADV
cana-5422	255	1	+	+	NUM
cana-5422	255	2	9δ	9δ	NUM
cana-5422	255	3	6	6	NUM
cana-5422	255	4	3	3	NUM
cana-5422	255	5	∑	∑	PUNCT
cana-5422	255	6	ψ=1	ψ=1	PUNCT
cana-5422	255	7	|wψ	|wψ	PUNCT
cana-5422	255	8	|	|	ADV
cana-5422	255	9	ϕψ	ϕψ	ADV
cana-5422	255	10	|25−5	|25−5	PROPN
cana-5422	256	1	ϕψ	ϕψ	ADP
cana-5422	256	2	|	|	ADV
cana-5422	256	3	;	;	PUNCT
cana-5422	257	1	ϕ1	ϕ1	NOUN
cana-5422	257	2	,	,	PUNCT
cana-5422	257	3	ϕ2	ϕ2	ADV
cana-5422	257	4	,	,	PUNCT
cana-5422	257	5	ϕ3	ϕ3	PROPN
cana-5422	257	6	6=	6=	PROPN
cana-5422	257	7	1	1	NUM
cana-5422	257	8	,	,	PUNCT
cana-5422	257	9	2	2	NUM
cana-5422	257	10	,	,	PUNCT
cana-5422	257	11	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	258	1	3|5−53ϕ	3|5−53ϕ	NUM
cana-5422	259	1	|	|	ADV
cana-5422	260	1	+	+	CCONJ
cana-5422	260	2	9δ|w1|3ϕ	9δ|w1|3ϕ	NUM
cana-5422	260	3	6|25−53ϕ	6|25−53ϕ	NUM
cana-5422	260	4	|	|	NOUN
cana-5422	260	5	;	;	PUNCT
cana-5422	260	6	3ϕ	3ϕ	NUM
cana-5422	260	7	6=	6=	SYM
cana-5422	260	8	1	1	NUM
cana-5422	260	9	,	,	PUNCT
cana-5422	260	10	2	2	NUM
cana-5422	260	11	,	,	PUNCT
cana-5422	260	12	4δ|wψ	4δ|wψ	PROPN
cana-5422	260	13	|	|	ADV
cana-5422	260	14	3	3	NUM
cana-5422	260	15	∑	∑	PUNCT
cana-5422	260	16	ψ=1	ψ=1	PUNCT
cana-5422	260	17	ϕψ	ϕψ	ADP
cana-5422	260	18	3	3	NUM
cana-5422	260	19	∣∣∣5−5	∣∣∣5−5	SYM
cana-5422	260	20	3	3	NUM
cana-5422	260	21	∑	∑	PUNCT
cana-5422	260	22	ψ=1	ψ=1	PUNCT
cana-5422	260	23	ϕψ	ϕψ	ADV
cana-5422	260	24	∣∣∣	∣∣∣	NOUN
cana-5422	261	1	+	+	CCONJ
cana-5422	261	2	9δ|wψ	9δ|wψ	NUM
cana-5422	261	3	|	|	NOUN
cana-5422	261	4	3	3	NUM
cana-5422	261	5	∑	∑	PUNCT
cana-5422	261	6	ψ=1	ψ=1	PUNCT
cana-5422	261	7	ϕψ	ϕψ	ADP
cana-5422	261	8	6	6	NUM
cana-5422	261	9	∣∣∣25−5	∣∣∣25−5	NOUN
cana-5422	261	10	3	3	NUM
cana-5422	261	11	∑	∑	PUNCT
cana-5422	261	12	ψ=1	ψ=1	PUNCT
cana-5422	261	13	ϕψ	ϕψ	ADV
cana-5422	261	14	∣∣∣	∣∣∣	ADJ
cana-5422	261	15	;	;	PUNCT
cana-5422	261	16	3	3	NUM
cana-5422	261	17	∑	∑	PUNCT
cana-5422	261	18	ψ=1	ψ=1	PUNCT
cana-5422	261	19	ϕψ	ϕψ	ADP
cana-5422	261	20	6=	6=	PROPN
cana-5422	261	21	1	1	NUM
cana-5422	261	22	,	,	PUNCT
cana-5422	261	23	2	2	NUM
cana-5422	261	24	,	,	PUNCT
cana-5422	261	25	16δ|w1|3ϕ	16δ|w1|3ϕ	NOUN
cana-5422	261	26	3|5−53ϕ	3|5−53ϕ	NUM
cana-5422	262	1	|	|	ADV
cana-5422	263	1	+	+	CCONJ
cana-5422	263	2	36δ|w1|3ϕ	36δ|w1|3ϕ	NUM
cana-5422	264	1	6|25−53ϕ	6|25−53ϕ	NUM
cana-5422	264	2	|	|	NOUN
cana-5422	264	3	;	;	PUNCT
cana-5422	264	4	3ϕ	3ϕ	NUM
cana-5422	264	5	6=	6=	SYM
cana-5422	264	6	1	1	NUM
cana-5422	264	7	,	,	PUNCT
cana-5422	264	8	2	2	NUM
cana-5422	264	9	,	,	PUNCT
cana-5422	264	10	(	(	PUNCT
cana-5422	264	11	2.42	2.42	NUM
cana-5422	264	12	)	)	PUNCT
cana-5422	264	13	for	for	ADP
cana-5422	264	14	all	all	DET
cana-5422	264	15	w1	w1	NOUN
cana-5422	264	16	∈	∈	PROPN
cana-5422	264	17	w1	w1	NOUN
cana-5422	264	18	.	.	PUNCT
cana-5422	265	1	2.4	2.4	NUM
cana-5422	265	2	.	.	PUNCT
cana-5422	266	1	oddness	oddness	NOUN
cana-5422	266	2	of	of	ADP
cana-5422	266	3	f	f	NOUN
cana-5422	266	4	:	:	PUNCT
cana-5422	266	5	additive	additive	NOUN
cana-5422	266	6	case	case	NOUN
cana-5422	266	7	stability	stability	NOUN
cana-5422	266	8	results	result	VERB
cana-5422	266	9	:	:	PUNCT
cana-5422	266	10	fixed	fixed	ADJ
cana-5422	266	11	point	point	NOUN
cana-5422	266	12	method	method	NOUN
cana-5422	266	13	.	.	PUNCT
cana-5422	267	1	theorem	theorem	ADJ
cana-5422	267	2	2.7	2.7	NUM
cana-5422	267	3	.	.	PUNCT
cana-5422	268	1	suppose	suppose	VERB
cana-5422	268	2	that	that	SCONJ
cana-5422	268	3	an	an	DET
cana-5422	268	4	odd	odd	ADJ
cana-5422	268	5	function	function	NOUN
cana-5422	268	6	f	f	NOUN
cana-5422	268	7	:	:	PUNCT
cana-5422	268	8	w1	w1	PROPN
cana-5422	268	9	→	→	SYM
cana-5422	268	10	w2	w2	NOUN
cana-5422	268	11	satisfy	satisfy	VERB
cana-5422	268	12	the	the	DET
cana-5422	268	13	functional	functional	ADJ
cana-5422	268	14	inequality	inequality	NOUN
cana-5422	268	15	(	(	PUNCT
cana-5422	268	16	2.1	2.1	NUM
cana-5422	268	17	)	)	PUNCT
cana-5422	268	18	where	where	SCONJ
cana-5422	268	19	ψ	ψ	X
cana-5422	268	20	:	:	PUNCT
cana-5422	268	21	w3	w3	NOUN
cana-5422	268	22	1	1	NUM
cana-5422	268	23	→	→	SYM
cana-5422	269	1	[	[	X
cana-5422	269	2	0	0	NUM
cana-5422	269	3	,	,	PUNCT
cana-5422	269	4	∞	∞	PROPN
cana-5422	269	5	)	)	PUNCT
cana-5422	269	6	with	with	ADP
cana-5422	269	7	the	the	DET
cana-5422	269	8	condition	condition	NOUN
cana-5422	269	9	lim	lim	NOUN
cana-5422	269	10	`	`	PUNCT
cana-5422	269	11	→∞	→∞	PROPN
cana-5422	269	12	ψ	ψ	PROPN
cana-5422	269	13	(	(	PUNCT
cana-5422	269	14	τ	τ	PROPN
cana-5422	269	15	`	`	PUNCT
cana-5422	269	16	v	v	PROPN
cana-5422	269	17	w1	w1	NOUN
cana-5422	269	18	,	,	PUNCT
cana-5422	269	19	τ	τ	PROPN
cana-5422	269	20	`	`	PUNCT
cana-5422	269	21	v	v	PROPN
cana-5422	269	22	w2	w2	NOUN
cana-5422	269	23	,	,	PUNCT
cana-5422	269	24	τ	τ	PROPN
cana-5422	269	25	`	`	PROPN
cana-5422	269	26	v	v	PROPN
cana-5422	269	27	w3	w3	PROPN
cana-5422	269	28	)	)	PUNCT
cana-5422	269	29	τ	τ	PROPN
cana-5422	269	30	`	`	PUNCT
cana-5422	269	31	v	v	X
cana-5422	269	32	=	=	SYM
cana-5422	269	33	0	0	NUM
cana-5422	269	34	;	;	PUNCT
cana-5422	269	35	τv	τv	X
cana-5422	269	36	=	=	PRON
cana-5422	269	37	{	{	PUNCT
cana-5422	269	38	5	5	NUM
cana-5422	269	39	;	;	PUNCT
cana-5422	269	40	ν	ν	X
cana-5422	269	41	=	=	SYM
cana-5422	269	42	0	0	NUM
cana-5422	269	43	1	1	NUM
cana-5422	269	44	5	5	NUM
cana-5422	269	45	;	;	PUNCT
cana-5422	269	46	ν	ν	X
cana-5422	269	47	=	=	SYM
cana-5422	269	48	1	1	NUM
cana-5422	269	49	,	,	PUNCT
cana-5422	269	50	∀	∀	X
cana-5422	269	51	w1	w1	NOUN
cana-5422	269	52	,	,	PUNCT
cana-5422	269	53	w2	w2	NOUN
cana-5422	269	54	,	,	PUNCT
cana-5422	269	55	w3	w3	PROPN
cana-5422	269	56	∈	∈	PROPN
cana-5422	269	57	w1	w1	NOUN
cana-5422	269	58	.	.	PUNCT
cana-5422	270	1	(	(	PUNCT
cana-5422	270	2	2.43	2.43	NUM
cana-5422	270	3	)	)	PUNCT
cana-5422	270	4	if	if	SCONJ
cana-5422	270	5	there	there	PRON
cana-5422	270	6	exists	exist	VERB
cana-5422	270	7	l	l	NOUN
cana-5422	270	8	=	=	SYM
cana-5422	270	9	l(ν	l(ν	PROPN
cana-5422	270	10	)	)	PUNCT
cana-5422	270	11	be	be	VERB
cana-5422	270	12	a	a	DET
cana-5422	270	13	function	function	NOUN
cana-5422	270	14	have	have	VERB
cana-5422	270	15	the	the	DET
cana-5422	270	16	property	property	NOUN
cana-5422	270	17	ψa(w1	ψa(w1	NOUN
cana-5422	270	18	)	)	PUNCT
cana-5422	271	1	=	=	SYM
cana-5422	271	2	ψa	ψa	X
cana-5422	271	3	(	(	PUNCT
cana-5422	271	4	w1	w1	NOUN
cana-5422	271	5	5	5	NUM
cana-5422	271	6	)	)	PUNCT
cana-5422	271	7	and	and	CCONJ
cana-5422	271	8	1	1	NUM
cana-5422	271	9	τv	τv	ADV
cana-5422	271	10	ψa	ψa	PROPN
cana-5422	271	11	(	(	PUNCT
cana-5422	271	12	τvw1	τvw1	PROPN
cana-5422	271	13	)	)	PUNCT
cana-5422	271	14	=	=	SYM
cana-5422	272	1	l	l	NOUN
cana-5422	272	2	ψa(w1	ψa(w1	NOUN
cana-5422	272	3	)	)	PUNCT
cana-5422	272	4	,	,	PUNCT
cana-5422	272	5	∀	∀	X
cana-5422	272	6	w1	w1	NOUN
cana-5422	272	7	∈	∈	PROPN
cana-5422	272	8	w1	w1	NOUN
cana-5422	272	9	.	.	PUNCT
cana-5422	273	1	(	(	PUNCT
cana-5422	273	2	2.44	2.44	NUM
cana-5422	273	3	)	)	PUNCT
cana-5422	273	4	then	then	ADV
cana-5422	273	5	there	there	PRON
cana-5422	273	6	exists	exist	VERB
cana-5422	273	7	a	a	DET
cana-5422	273	8	unique	unique	ADJ
cana-5422	273	9	additive	additive	ADJ
cana-5422	273	10	mappinga(w1	mappinga(w1	NOUN
cana-5422	273	11	)	)	PUNCT
cana-5422	273	12	:	:	PUNCT
cana-5422	273	13	w1	w1	PROPN
cana-5422	273	14	→w2	→w2	NOUN
cana-5422	273	15	which	which	PRON
cana-5422	273	16	satisfies	satisfy	VERB
cana-5422	273	17	(	(	PUNCT
cana-5422	273	18	1.7	1.7	NUM
cana-5422	273	19	)	)	PUNCT
cana-5422	273	20	and	and	CCONJ
cana-5422	273	21	the	the	DET
cana-5422	273	22	functional	functional	ADJ
cana-5422	273	23	inequality	inequality	NOUN
cana-5422	273	24	‖f	‖f	PUNCT
cana-5422	273	25	(	(	PUNCT
cana-5422	273	26	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	273	27	≤	≤	VERB
cana-5422	274	1	l1−ν	l1−ν	PROPN
cana-5422	274	2	1−	1−	NUM
cana-5422	274	3	l	l	NOUN
cana-5422	274	4	ψa	ψa	PROPN
cana-5422	274	5	(	(	PUNCT
cana-5422	274	6	w1	w1	NOUN
cana-5422	274	7	)	)	PUNCT
cana-5422	274	8	(	(	PUNCT
cana-5422	274	9	2.45	2.45	NUM
cana-5422	274	10	)	)	PUNCT
cana-5422	274	11	=	=	SYM
cana-5422	275	1	l1−ν	l1−ν	PROPN
cana-5422	275	2	1−	1−	NUM
cana-5422	275	3	l	l	NOUN
cana-5422	275	4	{	{	PUNCT
cana-5422	275	5	1	1	NUM
cana-5422	275	6	3	3	NUM
cana-5422	275	7	{	{	PUNCT
cana-5422	275	8	ψ	ψ	X
cana-5422	275	9	(	(	PUNCT
cana-5422	275	10	w1	w1	NOUN
cana-5422	275	11	,	,	PUNCT
cana-5422	275	12	w1	w1	NOUN
cana-5422	275	13	,	,	PUNCT
cana-5422	275	14	w1	w1	NOUN
cana-5422	275	15	)	)	PUNCT
cana-5422	276	1	+	+	NUM
cana-5422	276	2	3ψ	3ψ	NUM
cana-5422	276	3	(	(	PUNCT
cana-5422	276	4	w1	w1	NOUN
cana-5422	276	5	,	,	PUNCT
cana-5422	276	6	w1,−w1	w1,−w1	NUM
cana-5422	276	7	)	)	PUNCT
cana-5422	276	8	}	}	PUNCT
cana-5422	276	9	}	}	PUNCT
cana-5422	276	10	,	,	PUNCT
cana-5422	276	11	(	(	PUNCT
cana-5422	276	12	2.46	2.46	NUM
cana-5422	276	13	)	)	PUNCT
cana-5422	276	14	and	and	CCONJ
cana-5422	276	15	the	the	DET
cana-5422	276	16	mapping	mapping	NOUN
cana-5422	276	17	a(w1	a(w1	NOUN
cana-5422	276	18	)	)	PUNCT
cana-5422	276	19	is	be	AUX
cana-5422	276	20	obtained	obtain	VERB
cana-5422	276	21	by	by	ADP
cana-5422	276	22	a(w1	a(w1	NOUN
cana-5422	276	23	)	)	PUNCT
cana-5422	276	24	=	=	SYM
cana-5422	276	25	lim	lim	PROPN
cana-5422	276	26	`	`	PUNCT
cana-5422	276	27	→∞	→∞	PROPN
cana-5422	276	28	1	1	NUM
cana-5422	276	29	τ	τ	NOUN
cana-5422	276	30	`	`	PROPN
cana-5422	276	31	v	v	PROPN
cana-5422	276	32	f	f	PROPN
cana-5422	276	33	(	(	PUNCT
cana-5422	276	34	τ	τ	PROPN
cana-5422	276	35	`	`	PROPN
cana-5422	276	36	v	v	PROPN
cana-5422	276	37	w1	w1	NOUN
cana-5422	276	38	)	)	PUNCT
cana-5422	276	39	,	,	PUNCT
cana-5422	276	40	(	(	PUNCT
cana-5422	276	41	2.47	2.47	NUM
cana-5422	276	42	)	)	PUNCT
cana-5422	276	43	for	for	ADP
cana-5422	276	44	all	all	DET
cana-5422	276	45	w1	w1	NOUN
cana-5422	276	46	∈	∈	PROPN
cana-5422	276	47	w1	w1	NOUN
cana-5422	276	48	.	.	PUNCT
cana-5422	277	1	proof	proof	NOUN
cana-5422	277	2	.	.	PUNCT
cana-5422	278	1	assume	assume	VERB
cana-5422	278	2	a	a	DET
cana-5422	278	3	set	set	NOUN
cana-5422	278	4	g	g	NOUN
cana-5422	278	5	=	=	SYM
cana-5422	278	6	{	{	PUNCT
cana-5422	278	7	f	f	X
cana-5422	278	8	/	/	SYM
cana-5422	278	9	f	f	PROPN
cana-5422	278	10	:	:	PUNCT
cana-5422	278	11	w1	w1	PROPN
cana-5422	278	12	→w2	→w2	PROPN
cana-5422	278	13	,	,	PUNCT
cana-5422	278	14	f	f	PROPN
cana-5422	278	15	(	(	PUNCT
cana-5422	278	16	0	0	NUM
cana-5422	278	17	)	)	PUNCT
cana-5422	278	18	=	=	SYM
cana-5422	278	19	0	0	NUM
cana-5422	278	20	}	}	PUNCT
cana-5422	278	21	,	,	PUNCT
cana-5422	278	22	(	(	PUNCT
cana-5422	278	23	2.48	2.48	NUM
cana-5422	278	24	)	)	PUNCT
cana-5422	278	25	and	and	CCONJ
cana-5422	278	26	introduce	introduce	VERB
cana-5422	278	27	the	the	DET
cana-5422	278	28	generalized	generalize	VERB
cana-5422	278	29	metric	metric	NOUN
cana-5422	278	30	on	on	ADP
cana-5422	278	31	the	the	DET
cana-5422	278	32	above	above	ADJ
cana-5422	278	33	set	set	VERB
cana-5422	278	34	g	g	NOUN
cana-5422	278	35	as	as	ADP
cana-5422	278	36	d(f	d(f	NOUN
cana-5422	278	37	,	,	PUNCT
cana-5422	278	38	f1	f1	NOUN
cana-5422	278	39	)	)	PUNCT
cana-5422	278	40	=	=	SYM
cana-5422	279	1	inf{k	inf{k	NUM
cana-5422	279	2	∈	∈	PROPN
cana-5422	279	3	(	(	PUNCT
cana-5422	279	4	0	0	NUM
cana-5422	279	5	,	,	PUNCT
cana-5422	279	6	∞	∞	PROPN
cana-5422	279	7	)	)	PUNCT
cana-5422	279	8	:	:	PUNCT
cana-5422	280	1	‖f	‖f	ADP
cana-5422	280	2	(	(	PUNCT
cana-5422	280	3	w1)−f1(w1)‖	w1)−f1(w1)‖	PROPN
cana-5422	280	4	≤	≤	PROPN
cana-5422	280	5	k	k	PROPN
cana-5422	280	6	ψ(w1	ψ(w1	PROPN
cana-5422	280	7	,	,	PUNCT
cana-5422	280	8	w1	w1	NOUN
cana-5422	280	9	,	,	PUNCT
cana-5422	280	10	w1	w1	NOUN
cana-5422	280	11	)	)	PUNCT
cana-5422	280	12	,	,	PUNCT
cana-5422	280	13	w1	w1	PROPN
cana-5422	280	14	∈	∈	PROPN
cana-5422	280	15	w1	w1	NOUN
cana-5422	280	16	}	}	PUNCT
cana-5422	280	17	.	.	PUNCT
cana-5422	281	1	(	(	PUNCT
cana-5422	281	2	2.49	2.49	NUM
cana-5422	281	3	)	)	PUNCT
cana-5422	281	4	it	it	PRON
cana-5422	281	5	is	be	AUX
cana-5422	281	6	easy	easy	ADJ
cana-5422	281	7	to	to	PART
cana-5422	281	8	see	see	VERB
cana-5422	281	9	that	that	PRON
cana-5422	281	10	(	(	PUNCT
cana-5422	281	11	g	g	NOUN
cana-5422	281	12	,	,	PUNCT
cana-5422	281	13	d	d	NOUN
cana-5422	281	14	)	)	PUNCT
cana-5422	281	15	is	be	AUX
cana-5422	281	16	complete	complete	ADJ
cana-5422	281	17	.	.	PUNCT
cana-5422	282	1	define	define	VERB
cana-5422	282	2	a	a	DET
cana-5422	282	3	functionh	functionh	NOUN
cana-5422	282	4	:	:	PUNCT
cana-5422	282	5	g	g	NOUN
cana-5422	282	6	→	→	SYM
cana-5422	282	7	g	g	NOUN
cana-5422	282	8	by	by	ADP
cana-5422	282	9	hf	hf	PROPN
cana-5422	282	10	(	(	PUNCT
cana-5422	282	11	w1	w1	NOUN
cana-5422	282	12	)	)	PUNCT
cana-5422	282	13	=	=	SYM
cana-5422	283	1	1	1	NUM
cana-5422	283	2	τv	τv	X
cana-5422	283	3	f	f	PROPN
cana-5422	283	4	(	(	PUNCT
cana-5422	283	5	τv	τv	ADP
cana-5422	283	6	w1	w1	NOUN
cana-5422	283	7	)	)	PUNCT
cana-5422	283	8	,	,	PUNCT
cana-5422	283	9	f	f	PROPN
cana-5422	283	10	or	or	CCONJ
cana-5422	283	11	all	all	DET
cana-5422	283	12	w1	w1	NOUN
cana-5422	283	13	∈	∈	PROPN
cana-5422	283	14	w1	w1	NOUN
cana-5422	283	15	.	.	PUNCT
cana-5422	284	1	(	(	PUNCT
cana-5422	284	2	2.50	2.50	NUM
cana-5422	284	3	)	)	PUNCT
cana-5422	284	4	communications	communication	NOUN
cana-5422	284	5	on	on	ADP
cana-5422	284	6	applied	apply	VERB
cana-5422	284	7	nonlinear	nonlinear	ADJ
cana-5422	284	8	analysis	analysis	NOUN
cana-5422	284	9	issn	issn	NOUN
cana-5422	284	10	:	:	PUNCT
cana-5422	284	11	1074	1074	NUM
cana-5422	284	12	-	-	PUNCT
cana-5422	284	13	133x	133x	NUM
cana-5422	284	14	vol	vol	NOUN
cana-5422	284	15	32	32	NUM
cana-5422	284	16	no	no	NOUN
cana-5422	284	17	.	.	PUNCT
cana-5422	285	1	10s(2025	10s(2025	NUM
cana-5422	285	2	)	)	PUNCT
cana-5422	286	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	286	2	2195	2195	NUM
cana-5422	286	3	now	now	ADV
cana-5422	286	4	f	f	X
cana-5422	286	5	,	,	PUNCT
cana-5422	286	6	f1	f1	PROPN
cana-5422	286	7	∈	∈	PROPN
cana-5422	286	8	g	g	NOUN
cana-5422	286	9	and	and	CCONJ
cana-5422	286	10	w1	w1	PROPN
cana-5422	286	11	∈	∈	PROPN
cana-5422	286	12	w1	w1	NOUN
cana-5422	286	13	,	,	PUNCT
cana-5422	286	14	we	we	PRON
cana-5422	286	15	see	see	VERB
cana-5422	286	16	d(f	d(f	NOUN
cana-5422	286	17	,	,	PUNCT
cana-5422	286	18	f1	f1	NOUN
cana-5422	286	19	)	)	PUNCT
cana-5422	286	20	≤	≤	PUNCT
cana-5422	287	1	k	k	PROPN
cana-5422	287	2	⇒	⇒	PROPN
cana-5422	287	3	‖	‖	PROPN
cana-5422	287	4	f	f	PROPN
cana-5422	287	5	(	(	PUNCT
cana-5422	287	6	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	287	7	)	)	PUNCT
cana-5422	287	8	‖≤	‖≤	PROPN
cana-5422	287	9	k	k	PROPN
cana-5422	287	10	ψ(w1	ψ(w1	PROPN
cana-5422	287	11	,	,	PUNCT
cana-5422	287	12	w1	w1	NOUN
cana-5422	287	13	,	,	PUNCT
cana-5422	287	14	w1	w1	NOUN
cana-5422	287	15	)	)	PUNCT
cana-5422	287	16	,	,	PUNCT
cana-5422	287	17	⇒	⇒	NOUN
cana-5422	287	18	∥∥∥∥	∥∥∥∥	NUM
cana-5422	287	19	1	1	NUM
cana-5422	287	20	τv	τv	ADP
cana-5422	287	21	f	f	PROPN
cana-5422	287	22	(	(	PUNCT
cana-5422	287	23	τvw1)−	τvw1)−	NOUN
cana-5422	287	24	1	1	NUM
cana-5422	287	25	τv	τv	ADP
cana-5422	287	26	f1(τvw1	f1(τvw1	NOUN
cana-5422	287	27	)	)	PUNCT
cana-5422	287	28	∥∥∥∥	∥∥∥∥	NUM
cana-5422	287	29	≤	≤	NUM
cana-5422	287	30	1	1	NUM
cana-5422	287	31	τv	τv	ADP
cana-5422	287	32	k	k	PROPN
cana-5422	287	33	ψ(τvw1	ψ(τvw1	NOUN
cana-5422	287	34	,	,	PUNCT
cana-5422	287	35	τvw1	τvw1	NOUN
cana-5422	287	36	,	,	PUNCT
cana-5422	287	37	τvw1	τvw1	PROPN
cana-5422	287	38	)	)	PUNCT
cana-5422	287	39	,	,	PUNCT
cana-5422	287	40	⇒	⇒	NOUN
cana-5422	287	41	‖	‖	PROPN
cana-5422	287	42	hf	hf	X
cana-5422	287	43	(	(	PUNCT
cana-5422	287	44	w1)−hf1	w1)−hf1	PROPN
cana-5422	287	45	(	(	PUNCT
cana-5422	287	46	w1	w1	NOUN
cana-5422	287	47	)	)	PUNCT
cana-5422	287	48	‖≤	‖≤	PROPN
cana-5422	288	1	l	l	NOUN
cana-5422	288	2	k	k	X
cana-5422	288	3	ψ(w1	ψ(w1	PROPN
cana-5422	288	4	,	,	PUNCT
cana-5422	288	5	w1	w1	NOUN
cana-5422	288	6	,	,	PUNCT
cana-5422	288	7	w1	w1	NOUN
cana-5422	288	8	)	)	PUNCT
cana-5422	288	9	,	,	PUNCT
cana-5422	288	10	⇒d(hf	⇒d(hf	NOUN
cana-5422	288	11	,	,	PUNCT
cana-5422	288	12	hf1	hf1	NOUN
cana-5422	288	13	)	)	PUNCT
cana-5422	288	14	≤	≤	NUM
cana-5422	289	1	l	l	NOUN
cana-5422	290	1	k	k	NOUN
cana-5422	290	2	,	,	PUNCT
cana-5422	290	3	i.e.	i.e.	X
cana-5422	290	4	,h	,h	PUNCT
cana-5422	290	5	is	be	AUX
cana-5422	290	6	a	a	DET
cana-5422	290	7	strictly	strictly	ADV
cana-5422	290	8	contractive	contractive	ADJ
cana-5422	290	9	mapping	mapping	NOUN
cana-5422	290	10	on	on	ADP
cana-5422	290	11	g	g	NOUN
cana-5422	290	12	with	with	ADP
cana-5422	290	13	lipschitz	lipschitz	NOUN
cana-5422	290	14	constant	constant	ADJ
cana-5422	290	15	l	l	NOUN
cana-5422	290	16	(	(	PUNCT
cana-5422	290	17	see	see	VERB
cana-5422	290	18	[	[	X
cana-5422	290	19	18	18	NUM
cana-5422	290	20	]	]	NUM
cana-5422	290	21	)	)	PUNCT
cana-5422	290	22	.	.	PUNCT
cana-5422	291	1	for	for	ADP
cana-5422	291	2	the	the	DET
cana-5422	291	3	case	case	NOUN
cana-5422	291	4	ν	ν	X
cana-5422	291	5	=	=	SYM
cana-5422	291	6	0	0	NUM
cana-5422	291	7	,	,	PUNCT
cana-5422	291	8	it	it	PRON
cana-5422	291	9	follows	follow	VERB
cana-5422	291	10	from	from	ADP
cana-5422	291	11	(	(	PUNCT
cana-5422	291	12	2.12	2.12	NUM
cana-5422	291	13	)	)	PUNCT
cana-5422	291	14	and	and	CCONJ
cana-5422	291	15	with	with	ADP
cana-5422	291	16	the	the	DET
cana-5422	291	17	help	help	NOUN
cana-5422	291	18	of	of	ADP
cana-5422	291	19	(	(	PUNCT
cana-5422	291	20	2.44	2.44	NUM
cana-5422	291	21	)	)	PUNCT
cana-5422	291	22	,	,	PUNCT
cana-5422	291	23	(	(	PUNCT
cana-5422	291	24	2.50	2.50	NUM
cana-5422	291	25	)	)	PUNCT
cana-5422	291	26	,	,	PUNCT
cana-5422	291	27	(	(	PUNCT
cana-5422	291	28	2.49	2.49	NUM
cana-5422	291	29	)	)	PUNCT
cana-5422	291	30	,	,	PUNCT
cana-5422	291	31	we	we	PRON
cana-5422	291	32	get∥∥∥1	get∥∥∥1	VERB
cana-5422	291	33	5	5	NUM
cana-5422	291	34	f	f	PROPN
cana-5422	291	35	(	(	PUNCT
cana-5422	291	36	5w1)−f	5w1)−f	PROPN
cana-5422	291	37	(	(	PUNCT
cana-5422	291	38	w1	w1	NOUN
cana-5422	291	39	)	)	PUNCT
cana-5422	291	40	∥∥∥	∥∥∥	PROPN
cana-5422	291	41	≤	≤	NUM
cana-5422	291	42	1	1	NUM
cana-5422	291	43	5	5	NUM
cana-5422	291	44	ψa	ψa	NOUN
cana-5422	291	45	(	(	PUNCT
cana-5422	291	46	w1	w1	NOUN
cana-5422	291	47	)	)	PUNCT
cana-5422	291	48	,	,	PUNCT
cana-5422	291	49	⇒	⇒	VERB
cana-5422	291	50	d(hf	d(hf	PROPN
cana-5422	291	51	,	,	PUNCT
cana-5422	291	52	f	f	PROPN
cana-5422	291	53	)	)	PUNCT
cana-5422	291	54	≤	≤	NUM
cana-5422	292	1	l	l	NOUN
cana-5422	292	2	=	=	PUNCT
cana-5422	292	3	l1−ν	l1−ν	PROPN
cana-5422	292	4	,	,	PUNCT
cana-5422	292	5	∀	∀	NOUN
cana-5422	292	6	w1	w1	NOUN
cana-5422	292	7	∈	∈	PROPN
cana-5422	292	8	w1	w1	NOUN
cana-5422	292	9	.	.	PUNCT
cana-5422	293	1	(	(	PUNCT
cana-5422	293	2	2.51	2.51	NUM
cana-5422	293	3	)	)	PUNCT
cana-5422	293	4	for	for	ADP
cana-5422	293	5	the	the	DET
cana-5422	293	6	case	case	NOUN
cana-5422	293	7	ν	ν	X
cana-5422	293	8	=	=	SYM
cana-5422	293	9	1	1	NUM
cana-5422	293	10	,	,	PUNCT
cana-5422	293	11	it	it	PRON
cana-5422	293	12	follows	follow	VERB
cana-5422	293	13	from	from	ADP
cana-5422	293	14	(	(	PUNCT
cana-5422	293	15	2.18	2.18	NUM
cana-5422	293	16	)	)	PUNCT
cana-5422	293	17	and	and	CCONJ
cana-5422	293	18	with	with	ADP
cana-5422	293	19	the	the	DET
cana-5422	293	20	help	help	NOUN
cana-5422	293	21	of	of	ADP
cana-5422	293	22	(	(	PUNCT
cana-5422	293	23	2.44	2.44	NUM
cana-5422	293	24	)	)	PUNCT
cana-5422	293	25	,	,	PUNCT
cana-5422	293	26	(	(	PUNCT
cana-5422	293	27	2.50	2.50	NUM
cana-5422	293	28	)	)	PUNCT
cana-5422	293	29	,	,	PUNCT
cana-5422	293	30	(	(	PUNCT
cana-5422	293	31	2.49	2.49	NUM
cana-5422	293	32	)	)	PUNCT
cana-5422	293	33	,	,	PUNCT
cana-5422	293	34	we	we	PRON
cana-5422	293	35	obtain∥∥∥f	obtain∥∥∥f	VERB
cana-5422	293	36	(	(	PUNCT
cana-5422	293	37	w1)−	w1)−	PROPN
cana-5422	293	38	5f	5f	NOUN
cana-5422	293	39	(	(	PUNCT
cana-5422	293	40	w1	w1	NOUN
cana-5422	293	41	5	5	NUM
cana-5422	293	42	)	)	PUNCT
cana-5422	293	43	∥∥∥	∥∥∥	PROPN
cana-5422	293	44	≤	≤	PROPN
cana-5422	294	1	ψa	ψa	X
cana-5422	294	2	(	(	PUNCT
cana-5422	294	3	w1	w1	PROPN
cana-5422	294	4	5	5	NUM
cana-5422	294	5	)	)	PUNCT
cana-5422	294	6	,	,	PUNCT
cana-5422	294	7	⇒	⇒	NOUN
cana-5422	294	8	d(f	d(f	PROPN
cana-5422	294	9	,	,	PUNCT
cana-5422	294	10	hf	hf	INTJ
cana-5422	294	11	)	)	PUNCT
cana-5422	294	12	≤	≤	NOUN
cana-5422	294	13	1	1	NUM
cana-5422	294	14	=	=	SYM
cana-5422	294	15	l1−ν	l1−ν	PROPN
cana-5422	294	16	,	,	PUNCT
cana-5422	294	17	∀	∀	NOUN
cana-5422	294	18	w1	w1	NOUN
cana-5422	294	19	∈	∈	PROPN
cana-5422	294	20	w1	w1	NOUN
cana-5422	294	21	.	.	PUNCT
cana-5422	295	1	(	(	PUNCT
cana-5422	295	2	2.52	2.52	NUM
cana-5422	295	3	)	)	PUNCT
cana-5422	295	4	combining	combine	VERB
cana-5422	295	5	(	(	PUNCT
cana-5422	295	6	2.51	2.51	NUM
cana-5422	295	7	)	)	PUNCT
cana-5422	295	8	and	and	CCONJ
cana-5422	295	9	(	(	PUNCT
cana-5422	295	10	2.52	2.52	NUM
cana-5422	295	11	)	)	PUNCT
cana-5422	295	12	,	,	PUNCT
cana-5422	295	13	we	we	PRON
cana-5422	295	14	have	have	VERB
cana-5422	295	15	d(f	d(f	NOUN
cana-5422	295	16	,	,	PUNCT
cana-5422	295	17	hf	hf	INTJ
cana-5422	295	18	)	)	PUNCT
cana-5422	295	19	≤	≤	NOUN
cana-5422	295	20	1	1	NUM
cana-5422	295	21	=	=	SYM
cana-5422	295	22	l1−ν	l1−ν	PROPN
cana-5422	295	23	.	.	PUNCT
cana-5422	296	1	(	(	PUNCT
cana-5422	296	2	2.53	2.53	NUM
cana-5422	296	3	)	)	PUNCT
cana-5422	296	4	therefore	therefore	ADV
cana-5422	296	5	(	(	PUNCT
cana-5422	296	6	fpc1	fpc1	PROPN
cana-5422	296	7	)	)	PUNCT
cana-5422	296	8	of	of	ADP
cana-5422	296	9	theorem	theorem	ADJ
cana-5422	296	10	1.5	1.5	NUM
cana-5422	296	11	holds	hold	NOUN
cana-5422	296	12	.	.	PUNCT
cana-5422	297	1	the	the	DET
cana-5422	297	2	rest	rest	NOUN
cana-5422	297	3	of	of	ADP
cana-5422	297	4	the	the	DET
cana-5422	297	5	proof	proof	NOUN
cana-5422	297	6	follows	follow	VERB
cana-5422	297	7	by	by	ADP
cana-5422	297	8	theorem	theorem	ADJ
cana-5422	297	9	1.5	1.5	NUM
cana-5422	297	10	.	.	PUNCT
cana-5422	298	1	hence	hence	ADV
cana-5422	298	2	the	the	DET
cana-5422	298	3	proof	proof	NOUN
cana-5422	298	4	is	be	AUX
cana-5422	298	5	complete	complete	ADJ
cana-5422	298	6	.	.	PUNCT
cana-5422	299	1	�	�	PROPN
cana-5422	299	2	corollary	corollary	ADJ
cana-5422	299	3	2.8	2.8	NUM
cana-5422	299	4	.	.	PUNCT
cana-5422	300	1	suppose	suppose	VERB
cana-5422	300	2	that	that	SCONJ
cana-5422	300	3	an	an	DET
cana-5422	300	4	odd	odd	ADJ
cana-5422	300	5	function	function	NOUN
cana-5422	300	6	f	f	NOUN
cana-5422	300	7	:	:	PUNCT
cana-5422	300	8	w1	w1	PROPN
cana-5422	300	9	→	→	SYM
cana-5422	300	10	w2	w2	NOUN
cana-5422	300	11	satisfy	satisfy	VERB
cana-5422	300	12	the	the	DET
cana-5422	300	13	functional	functional	ADJ
cana-5422	300	14	inequality	inequality	NOUN
cana-5422	300	15	(	(	PUNCT
cana-5422	300	16	2.2	2.2	NUM
cana-5422	300	17	)	)	PUNCT
cana-5422	300	18	for	for	ADP
cana-5422	300	19	all	all	DET
cana-5422	300	20	w1	w1	NOUN
cana-5422	300	21	,	,	PUNCT
cana-5422	300	22	w2	w2	NOUN
cana-5422	300	23	,	,	PUNCT
cana-5422	300	24	w3	w3	PROPN
cana-5422	300	25	∈	∈	PROPN
cana-5422	300	26	w1	w1	NOUN
cana-5422	300	27	.	.	PUNCT
cana-5422	301	1	then	then	ADV
cana-5422	301	2	there	there	PRON
cana-5422	301	3	exists	exist	VERB
cana-5422	301	4	a	a	DET
cana-5422	301	5	unique	unique	ADJ
cana-5422	301	6	additive	additive	ADJ
cana-5422	301	7	mapping	mapping	NOUN
cana-5422	301	8	a(w1	a(w1	NOUN
cana-5422	301	9	)	)	PUNCT
cana-5422	301	10	:	:	PUNCT
cana-5422	301	11	w1	w1	PROPN
cana-5422	301	12	→w2	→w2	NOUN
cana-5422	301	13	which	which	PRON
cana-5422	301	14	satisfies	satisfy	VERB
cana-5422	301	15	(	(	PUNCT
cana-5422	301	16	1.7	1.7	NUM
cana-5422	301	17	)	)	PUNCT
cana-5422	301	18	and	and	CCONJ
cana-5422	301	19	the	the	DET
cana-5422	301	20	functional	functional	ADJ
cana-5422	301	21	inequality	inequality	NOUN
cana-5422	301	22	(	(	PUNCT
cana-5422	301	23	2.20	2.20	NUM
cana-5422	301	24	)	)	PUNCT
cana-5422	301	25	for	for	ADP
cana-5422	301	26	all	all	DET
cana-5422	301	27	w1	w1	NOUN
cana-5422	301	28	∈	∈	PROPN
cana-5422	301	29	w1	w1	NOUN
cana-5422	301	30	.	.	PUNCT
cana-5422	302	1	proof	proof	NOUN
cana-5422	302	2	.	.	PUNCT
cana-5422	303	1	if	if	SCONJ
cana-5422	303	2	we	we	PRON
cana-5422	303	3	take	take	VERB
cana-5422	303	4	ψ	ψ	X
cana-5422	303	5	(	(	PUNCT
cana-5422	303	6	w1	w1	NOUN
cana-5422	303	7	,	,	PUNCT
cana-5422	303	8	w2	w2	NOUN
cana-5422	303	9	,	,	PUNCT
cana-5422	303	10	w3	w3	PROPN
cana-5422	303	11	)	)	PUNCT
cana-5422	303	12	=	=	SYM
cana-5422	303	13			NUM
cana-5422	303	14	δ	δ	PROPN
cana-5422	303	15	,	,	PUNCT
cana-5422	303	16	δ	δ	PROPN
cana-5422	303	17	∑3	∑3	PROPN
cana-5422	303	18	ψ=1	ψ=1	PUNCT
cana-5422	303	19	∣∣wψ	∣∣wψ	PROPN
cana-5422	303	20	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	303	21	,	,	PUNCT
cana-5422	303	22	δ	δ	PROPN
cana-5422	303	23	∑3	∑3	PROPN
cana-5422	303	24	ψ=1	ψ=1	X
cana-5422	303	25	∣∣wψ	∣∣wψ	PROPN
cana-5422	303	26	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	303	27	,	,	PUNCT
cana-5422	303	28	δ	δ	PROPN
cana-5422	303	29	∏3	∏3	NOUN
cana-5422	303	30	ψ=1	ψ=1	PUNCT
cana-5422	303	31	∣∣wψ	∣∣wψ	PROPN
cana-5422	303	32	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	303	33	,	,	PUNCT
cana-5422	303	34	δ	δ	PROPN
cana-5422	303	35	∏3	∏3	NOUN
cana-5422	303	36	ψ=1	ψ=1	PUNCT
cana-5422	303	37	∣∣wψ	∣∣wψ	PROPN
cana-5422	303	38	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	303	39	,	,	PUNCT
cana-5422	303	40	δ	δ	PROPN
cana-5422	303	41	{	{	PUNCT
cana-5422	303	42	∑3	∑3	PROPN
cana-5422	303	43	ψ=1	ψ=1	PUNCT
cana-5422	303	44	∣∣wψ	∣∣wψ	PROPN
cana-5422	303	45	∣∣3ϕ	∣∣3ϕ	ADJ
cana-5422	303	46	+	+	PROPN
cana-5422	303	47	∏3	∏3	NOUN
cana-5422	303	48	ψ=1	ψ=1	PUNCT
cana-5422	303	49	∣∣wψ	∣∣wψ	ADJ
cana-5422	303	50	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	303	51	}	}	PUNCT
cana-5422	303	52	,	,	PUNCT
cana-5422	303	53	(	(	PUNCT
cana-5422	303	54	2.54	2.54	NUM
cana-5422	303	55	)	)	PUNCT
cana-5422	303	56	in	in	ADP
cana-5422	303	57	theorem	theorem	ADJ
cana-5422	303	58	2.7	2.7	NUM
cana-5422	303	59	and	and	CCONJ
cana-5422	303	60	changing	change	VERB
cana-5422	303	61	(	(	PUNCT
cana-5422	303	62	w1	w1	NOUN
cana-5422	303	63	,	,	PUNCT
cana-5422	303	64	w2	w2	NOUN
cana-5422	303	65	,	,	PUNCT
cana-5422	303	66	w3	w3	PROPN
cana-5422	303	67	)	)	PUNCT
cana-5422	303	68	by	by	ADP
cana-5422	303	69	(	(	PUNCT
cana-5422	303	70	τ	τ	PROPN
cana-5422	303	71	`	`	PROPN
cana-5422	303	72	v	v	PROPN
cana-5422	303	73	w1	w1	NOUN
cana-5422	303	74	,	,	PUNCT
cana-5422	303	75	τ	τ	PROPN
cana-5422	303	76	`	`	PUNCT
cana-5422	303	77	v	v	PROPN
cana-5422	303	78	w2	w2	NOUN
cana-5422	303	79	,	,	PUNCT
cana-5422	303	80	τ	τ	PROPN
cana-5422	303	81	`	`	PROPN
cana-5422	303	82	v	v	PROPN
cana-5422	303	83	w3	w3	PROPN
cana-5422	303	84	)	)	PUNCT
cana-5422	303	85	and	and	CCONJ
cana-5422	303	86	dividing	divide	VERB
cana-5422	303	87	by	by	ADP
cana-5422	303	88	τ	τ	PROPN
cana-5422	303	89	`	`	PUNCT
cana-5422	303	90	v	v	NOUN
cana-5422	303	91	in	in	ADP
cana-5422	303	92	(	(	PUNCT
cana-5422	303	93	2.54	2.54	NUM
cana-5422	303	94	)	)	PUNCT
cana-5422	303	95	,	,	PUNCT
cana-5422	303	96	one	one	PRON
cana-5422	303	97	can	can	AUX
cana-5422	303	98	see	see	VERB
cana-5422	303	99	1	1	NUM
cana-5422	303	100	τ	τ	PROPN
cana-5422	303	101	`	`	PUNCT
cana-5422	303	102	v	v	PROPN
cana-5422	303	103	ψ	ψ	X
cana-5422	303	104	(	(	PUNCT
cana-5422	303	105	τ	τ	PROPN
cana-5422	303	106	`	`	PROPN
cana-5422	303	107	v	v	PROPN
cana-5422	303	108	w1	w1	NOUN
cana-5422	303	109	,	,	PUNCT
cana-5422	303	110	τvw	τvw	PROPN
cana-5422	303	111	`	`	PUNCT
cana-5422	303	112	2	2	NUM
cana-5422	303	113	,	,	PUNCT
cana-5422	303	114	τ	τ	PROPN
cana-5422	303	115	`	`	PUNCT
cana-5422	303	116	v	v	PROPN
cana-5422	303	117	w3	w3	PROPN
cana-5422	303	118	)	)	PUNCT
cana-5422	304	1	=	=	PUNCT
cana-5422	304	2			VERB
cana-5422	304	3	δ	δ	X
cana-5422	304	4	τ`v	τ`v	ADV
cana-5422	304	5	→	→	SYM
cana-5422	304	6	0	0	PUNCT
cana-5422	304	7	as	as	ADP
cana-5422	304	8	`	`	PUNCT
cana-5422	304	9	to	to	ADP
cana-5422	304	10	∞	∞	PROPN
cana-5422	304	11	,	,	PUNCT
cana-5422	304	12	δ	δ	X
cana-5422	304	13	τ`v	τ`v	NOUN
cana-5422	304	14	∑3	∑3	PUNCT
cana-5422	304	15	ψ=1	ψ=1	PUNCT
cana-5422	304	16	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	17	`	`	PUNCT
cana-5422	304	18	v	v	NOUN
cana-5422	304	19	wψ	wψ	ADP
cana-5422	304	20	∣∣∣ϕ	∣∣∣ϕ	NOUN
cana-5422	304	21	,	,	PUNCT
cana-5422	304	22	→	→	SYM
cana-5422	304	23	0	0	PUNCT
cana-5422	304	24	as	as	ADP
cana-5422	304	25	`	`	PUNCT
cana-5422	304	26	to	to	ADP
cana-5422	304	27	∞	∞	PROPN
cana-5422	304	28	,	,	PUNCT
cana-5422	304	29	δ	δ	X
cana-5422	304	30	τ`v	τ`v	NOUN
cana-5422	304	31	∑3	∑3	PUNCT
cana-5422	304	32	ψ=1	ψ=1	PUNCT
cana-5422	304	33	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	34	`	`	PUNCT
cana-5422	304	35	v	v	NOUN
cana-5422	304	36	wψ	wψ	ADP
cana-5422	304	37	∣∣∣ϕψ	∣∣∣ϕψ	PROPN
cana-5422	304	38	,	,	PUNCT
cana-5422	304	39	→	→	SYM
cana-5422	304	40	0	0	PUNCT
cana-5422	304	41	as	as	ADP
cana-5422	304	42	`	`	PUNCT
cana-5422	304	43	to	to	ADP
cana-5422	304	44	∞	∞	PROPN
cana-5422	304	45	,	,	PUNCT
cana-5422	304	46	δ	δ	PROPN
cana-5422	304	47	τ`v	τ`v	NOUN
cana-5422	304	48	∏3	∏3	NOUN
cana-5422	304	49	ψ=1	ψ=1	PUNCT
cana-5422	304	50	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	51	`	`	PUNCT
cana-5422	304	52	v	v	NOUN
cana-5422	304	53	wψ	wψ	ADP
cana-5422	304	54	∣∣∣ϕ	∣∣∣ϕ	NOUN
cana-5422	304	55	,	,	PUNCT
cana-5422	304	56	→	→	SYM
cana-5422	304	57	0	0	PUNCT
cana-5422	304	58	as	as	ADP
cana-5422	304	59	`	`	PUNCT
cana-5422	304	60	to	to	ADP
cana-5422	304	61	∞	∞	PROPN
cana-5422	304	62	,	,	PUNCT
cana-5422	304	63	δ	δ	PROPN
cana-5422	304	64	τ`v	τ`v	NOUN
cana-5422	304	65	∏3	∏3	NOUN
cana-5422	304	66	ψ=1	ψ=1	PUNCT
cana-5422	304	67	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	68	`	`	PUNCT
cana-5422	304	69	v	v	NOUN
cana-5422	304	70	wψ	wψ	ADP
cana-5422	304	71	∣∣∣ϕψ	∣∣∣ϕψ	PROPN
cana-5422	304	72	,	,	PUNCT
cana-5422	304	73	→	→	SYM
cana-5422	304	74	0	0	PUNCT
cana-5422	304	75	as	as	ADP
cana-5422	304	76	`	`	PUNCT
cana-5422	304	77	to	to	ADP
cana-5422	304	78	∞	∞	PROPN
cana-5422	304	79	,	,	PUNCT
cana-5422	304	80	δ	δ	PROPN
cana-5422	304	81	τ`v	τ`v	NOUN
cana-5422	304	82	{	{	PUNCT
cana-5422	304	83	∑3	∑3	PROPN
cana-5422	304	84	ψ=1	ψ=1	PUNCT
cana-5422	304	85	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	86	`	`	PUNCT
cana-5422	304	87	v	v	NOUN
cana-5422	304	88	wψ	wψ	ADP
cana-5422	304	89	∣∣∣3ϕ	∣∣∣3ϕ	PROPN
cana-5422	304	90	+	+	CCONJ
cana-5422	304	91	∏3	∏3	NOUN
cana-5422	304	92	ψ=1	ψ=1	PUNCT
cana-5422	304	93	∣∣∣τ	∣∣∣τ	NOUN
cana-5422	304	94	`	`	PUNCT
cana-5422	304	95	v	v	NOUN
cana-5422	304	96	wψ	wψ	ADP
cana-5422	304	97	∣∣∣ϕ	∣∣∣ϕ	NOUN
cana-5422	304	98	}	}	PUNCT
cana-5422	304	99	,	,	PUNCT
cana-5422	304	100	→	→	SYM
cana-5422	304	101	0	0	PUNCT
cana-5422	304	102	as	as	SCONJ
cana-5422	304	103	`	`	PUNCT
cana-5422	304	104	to	to	ADP
cana-5422	304	105	∞.	∞.	PROPN
cana-5422	304	106	communications	communication	NOUN
cana-5422	304	107	on	on	ADP
cana-5422	304	108	applied	apply	VERB
cana-5422	304	109	nonlinear	nonlinear	ADJ
cana-5422	304	110	analysis	analysis	NOUN
cana-5422	304	111	issn	issn	NOUN
cana-5422	304	112	:	:	PUNCT
cana-5422	304	113	1074	1074	NUM
cana-5422	304	114	-	-	PUNCT
cana-5422	304	115	133x	133x	NUM
cana-5422	304	116	vol	vol	NOUN
cana-5422	304	117	32	32	NUM
cana-5422	304	118	no	no	NOUN
cana-5422	304	119	.	.	PUNCT
cana-5422	304	120	10s(2025	10s(2025	NUM
cana-5422	304	121	)	)	PUNCT
cana-5422	304	122	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	304	123	2196	2196	NUM
cana-5422	304	124	therefore	therefore	ADV
cana-5422	304	125	(	(	PUNCT
cana-5422	304	126	2.43	2.43	NUM
cana-5422	304	127	)	)	PUNCT
cana-5422	304	128	holds	hold	VERB
cana-5422	304	129	for	for	ADP
cana-5422	304	130	all	all	DET
cana-5422	304	131	w1	w1	NOUN
cana-5422	304	132	,	,	PUNCT
cana-5422	304	133	w2	w2	NOUN
cana-5422	304	134	,	,	PUNCT
cana-5422	304	135	w3	w3	PROPN
cana-5422	304	136	∈	∈	PROPN
cana-5422	304	137	w1	w1	NOUN
cana-5422	304	138	.	.	PUNCT
cana-5422	305	1	now	now	ADV
cana-5422	305	2	,	,	PUNCT
cana-5422	305	3	from	from	ADP
cana-5422	305	4	(	(	PUNCT
cana-5422	305	5	2.44	2.44	NUM
cana-5422	305	6	)	)	PUNCT
cana-5422	305	7	,	,	PUNCT
cana-5422	305	8	we	we	PRON
cana-5422	305	9	have	have	AUX
cana-5422	305	10	ψa(w1	ψa(w1	VERB
cana-5422	305	11	)	)	PUNCT
cana-5422	306	1	=	=	SYM
cana-5422	306	2	ψa	ψa	X
cana-5422	306	3	(	(	PUNCT
cana-5422	306	4	w1	w1	NOUN
cana-5422	306	5	5	5	NUM
cana-5422	306	6	)	)	PUNCT
cana-5422	306	7	=	=	SYM
cana-5422	306	8	1	1	NUM
cana-5422	306	9	3	3	NUM
cana-5422	306	10	{	{	PUNCT
cana-5422	306	11	ψ	ψ	X
cana-5422	306	12	(	(	PUNCT
cana-5422	306	13	w1	w1	NOUN
cana-5422	306	14	5	5	NUM
cana-5422	306	15	,	,	PUNCT
cana-5422	306	16	w1	w1	NOUN
cana-5422	306	17	5	5	NUM
cana-5422	306	18	,	,	PUNCT
cana-5422	306	19	w1	w1	NOUN
cana-5422	306	20	5	5	NUM
cana-5422	306	21	)	)	PUNCT
cana-5422	307	1	+	+	NUM
cana-5422	307	2	3ψ	3ψ	NUM
cana-5422	307	3	(	(	PUNCT
cana-5422	307	4	w1	w1	NOUN
cana-5422	307	5	5	5	NUM
cana-5422	307	6	,	,	PUNCT
cana-5422	307	7	w1	w1	NOUN
cana-5422	307	8	5	5	NUM
cana-5422	307	9	,	,	PUNCT
cana-5422	307	10	−w1	−w1	NOUN
cana-5422	307	11	5	5	NUM
cana-5422	307	12	)	)	PUNCT
cana-5422	307	13	}	}	PUNCT
cana-5422	307	14	=	=	PUNCT
cana-5422	308	1			NUM
cana-5422	308	2	4δ	4δ	NOUN
cana-5422	308	3	3	3	NUM
cana-5422	308	4	,	,	PUNCT
cana-5422	308	5	12|	12|	NUM
cana-5422	308	6	w1	w1	NOUN
cana-5422	308	7	5	5	NUM
cana-5422	308	8	|	|	ADV
cana-5422	308	9	ϕ	ϕ	NOUN
cana-5422	308	10	3	3	NUM
cana-5422	308	11	,	,	PUNCT
cana-5422	308	12	4δ	4δ	NOUN
cana-5422	308	13	3	3	NUM
cana-5422	308	14	∑3	∑3	PROPN
cana-5422	308	15	ψ=1	ψ=1	PUNCT
cana-5422	308	16	∣∣w1	∣∣w1	VERB
cana-5422	308	17	5	5	NUM
cana-5422	308	18	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	308	19	,	,	PUNCT
cana-5422	308	20	4δ|	4δ|	NUM
cana-5422	308	21	w1	w1	NOUN
cana-5422	308	22	5	5	NUM
cana-5422	309	1	|	|	ADV
cana-5422	309	2	3ϕ	3ϕ	NUM
cana-5422	309	3	3	3	NUM
cana-5422	309	4	,	,	PUNCT
cana-5422	309	5	4δ|	4δ|	NUM
cana-5422	309	6	w1	w1	NOUN
cana-5422	309	7	5	5	NUM
cana-5422	309	8	|	|	CCONJ
cana-5422	309	9	3	3	NUM
cana-5422	309	10	∑	∑	PUNCT
cana-5422	309	11	ψ=1	ψ=1	PUNCT
cana-5422	309	12	ϕψ	ϕψ	ADP
cana-5422	309	13	3	3	NUM
cana-5422	309	14	,	,	PUNCT
cana-5422	309	15	16δ|	16δ|	NUM
cana-5422	309	16	w1	w1	NOUN
cana-5422	309	17	5	5	NUM
cana-5422	310	1	|	|	ADV
cana-5422	310	2	3ϕ	3ϕ	NUM
cana-5422	310	3	3	3	NUM
cana-5422	310	4	,	,	PUNCT
cana-5422	310	5	(	(	PUNCT
cana-5422	310	6	2.55	2.55	NUM
cana-5422	310	7	)	)	PUNCT
cana-5422	310	8	1	1	NUM
cana-5422	310	9	τv	τv	ADP
cana-5422	310	10	ψa	ψa	PROPN
cana-5422	310	11	(	(	PUNCT
cana-5422	310	12	τvw1	τvw1	PROPN
cana-5422	310	13	)	)	PUNCT
cana-5422	310	14	=	=	SYM
cana-5422	311	1	1	1	NUM
cana-5422	311	2	τv	τv	ADP
cana-5422	311	3	1	1	NUM
cana-5422	311	4	3	3	NUM
cana-5422	311	5	{	{	PUNCT
cana-5422	311	6	ψ	ψ	X
cana-5422	311	7	(	(	PUNCT
cana-5422	311	8	τvw1	τvw1	PROPN
cana-5422	311	9	,	,	PUNCT
cana-5422	311	10	τvw1	τvw1	PROPN
cana-5422	311	11	,	,	PUNCT
cana-5422	311	12	τvw1	τvw1	PROPN
cana-5422	311	13	)	)	PUNCT
cana-5422	312	1	+	+	CCONJ
cana-5422	312	2	3ψ	3ψ	NUM
cana-5422	312	3	(	(	PUNCT
cana-5422	312	4	τvw1	τvw1	NOUN
cana-5422	312	5	,	,	PUNCT
cana-5422	312	6	τvw1,−τvw1	τvw1,−τvw1	NOUN
cana-5422	312	7	)	)	PUNCT
cana-5422	312	8	}	}	PUNCT
cana-5422	312	9	=	=	PUNCT
cana-5422	312	10			NUM
cana-5422	312	11	4δ	4δ	NOUN
cana-5422	312	12	τv	τv	ADP
cana-5422	312	13	·	·	SYM
cana-5422	312	14	3	3	NUM
cana-5422	312	15	,	,	PUNCT
cana-5422	312	16	12δ|τvw1|ϕ	12δ|τvw1|ϕ	NUM
cana-5422	312	17	τv	τv	NOUN
cana-5422	312	18	·	·	SYM
cana-5422	312	19	3	3	NUM
cana-5422	312	20	,	,	PUNCT
cana-5422	312	21	4δ	4δ	NOUN
cana-5422	312	22	τv	τv	NOUN
cana-5422	312	23	·	·	SYM
cana-5422	312	24	3	3	NUM
cana-5422	312	25	∑3	∑3	PROPN
cana-5422	312	26	ψ=1	ψ=1	X
cana-5422	312	27	∣∣τvwψ	∣∣τvwψ	ADV
cana-5422	312	28	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	312	29	,	,	PUNCT
cana-5422	312	30	4δ|τvw1|3ϕ	4δ|τvw1|3ϕ	PROPN
cana-5422	312	31	τv	τv	NOUN
cana-5422	312	32	·	·	SYM
cana-5422	312	33	3	3	NUM
cana-5422	312	34	,	,	PUNCT
cana-5422	312	35	4δ|τvw1|	4δ|τvw1|	NUM
cana-5422	312	36	∑3	∑3	SYM
cana-5422	312	37	ψ=1	ψ=1	PUNCT
cana-5422	312	38	ϕψ	ϕψ	ADP
cana-5422	312	39	τv	τv	ADP
cana-5422	312	40	·	·	SYM
cana-5422	312	41	3	3	NUM
cana-5422	312	42	,	,	PUNCT
cana-5422	312	43	16δ|τvw1|3ϕ	16δ|τvw1|3ϕ	NUM
cana-5422	312	44	τv	τv	ADP
cana-5422	312	45	·	·	SYM
cana-5422	312	46	3	3	NUM
cana-5422	312	47	,	,	PUNCT
cana-5422	312	48	=	=	SYM
cana-5422	312	49			NUM
cana-5422	312	50	τ−1	τ−1	PROPN
cana-5422	312	51	v	v	NUM
cana-5422	312	52	ψa(w1	ψa(w1	NOUN
cana-5422	312	53	)	)	PUNCT
cana-5422	312	54	,	,	PUNCT
cana-5422	312	55	τ	τ	PROPN
cana-5422	312	56	ϕ−1	ϕ−1	PROPN
cana-5422	312	57	v	v	PROPN
cana-5422	312	58	ψa(w1	ψa(w1	NOUN
cana-5422	312	59	)	)	PUNCT
cana-5422	312	60	,	,	PUNCT
cana-5422	312	61	∑3	∑3	PROPN
cana-5422	312	62	ψ=1	ψ=1	PUNCT
cana-5422	312	63	τ	τ	PROPN
cana-5422	312	64	ϕψ−1	ϕψ−1	PROPN
cana-5422	312	65	v	v	PROPN
cana-5422	312	66	ψa(w1	ψa(w1	NOUN
cana-5422	312	67	)	)	PUNCT
cana-5422	312	68	,	,	PUNCT
cana-5422	312	69	τ	τ	PROPN
cana-5422	312	70	3ϕ−1	3ϕ−1	NUM
cana-5422	312	71	v	v	NOUN
cana-5422	312	72	ψa(w1	ψa(w1	NOUN
cana-5422	312	73	)	)	PUNCT
cana-5422	312	74	,	,	PUNCT
cana-5422	312	75	τ	τ	PROPN
cana-5422	312	76	∑3	∑3	PROPN
cana-5422	312	77	ψ=1	ψ=1	PUNCT
cana-5422	312	78	ϕψ−1	ϕψ−1	PROPN
cana-5422	312	79	v	v	PROPN
cana-5422	312	80	ψa(w1	ψa(w1	VERB
cana-5422	312	81	)	)	PUNCT
cana-5422	312	82	,	,	PUNCT
cana-5422	312	83	τ	τ	PROPN
cana-5422	312	84	3ϕ−1	3ϕ−1	NUM
cana-5422	312	85	v	v	NOUN
cana-5422	312	86	ψa(w1	ψa(w1	NOUN
cana-5422	312	87	)	)	PUNCT
cana-5422	312	88	,	,	PUNCT
cana-5422	312	89	=	=	PUNCT
cana-5422	312	90			X
cana-5422	312	91	l	l	NOUN
cana-5422	312	92	ψa(w1	ψa(w1	NOUN
cana-5422	312	93	)	)	PUNCT
cana-5422	312	94	,	,	PUNCT
cana-5422	312	95	l	l	NOUN
cana-5422	312	96	ψa(w1	ψa(w1	NOUN
cana-5422	312	97	)	)	PUNCT
cana-5422	312	98	,	,	PUNCT
cana-5422	312	99	l	l	NOUN
cana-5422	312	100	ψa(w1	ψa(w1	NOUN
cana-5422	312	101	)	)	PUNCT
cana-5422	312	102	,	,	PUNCT
cana-5422	312	103	l	l	NOUN
cana-5422	312	104	ψa(w1	ψa(w1	NOUN
cana-5422	312	105	)	)	PUNCT
cana-5422	312	106	,	,	PUNCT
cana-5422	312	107	l	l	NOUN
cana-5422	312	108	ψa(w1	ψa(w1	NOUN
cana-5422	312	109	)	)	PUNCT
cana-5422	312	110	,	,	PUNCT
cana-5422	312	111	l	l	NOUN
cana-5422	312	112	ψa(w1	ψa(w1	NOUN
cana-5422	312	113	)	)	PUNCT
cana-5422	312	114	,	,	PUNCT
cana-5422	312	115	(	(	PUNCT
cana-5422	312	116	2.56	2.56	NUM
cana-5422	312	117	)	)	PUNCT
cana-5422	312	118	for	for	ADP
cana-5422	312	119	all	all	DET
cana-5422	312	120	w1	w1	NOUN
cana-5422	312	121	∈	∈	PROPN
cana-5422	312	122	w1	w1	NOUN
cana-5422	312	123	.	.	PUNCT
cana-5422	313	1	for	for	ADP
cana-5422	313	2	the	the	DET
cana-5422	313	3	case	case	NOUN
cana-5422	313	4	ν	ν	X
cana-5422	313	5	=	=	SYM
cana-5422	313	6	0	0	NUM
cana-5422	313	7	,	,	PUNCT
cana-5422	313	8	we	we	PRON
cana-5422	313	9	have	have	VERB
cana-5422	313	10	l	l	NOUN
cana-5422	313	11	=	=	SYM
cana-5422	313	12	τ−1	τ−1	PROPN
cana-5422	313	13	0	0	PUNCT
cana-5422	313	14	=	=	NUM
cana-5422	313	15	5−1	5−1	NUM
cana-5422	313	16	and	and	CCONJ
cana-5422	313	17	from	from	ADP
cana-5422	313	18	(	(	PUNCT
cana-5422	313	19	2.46	2.46	NUM
cana-5422	313	20	)	)	PUNCT
cana-5422	313	21	,	,	PUNCT
cana-5422	313	22	we	we	PRON
cana-5422	313	23	arrive	arrive	VERB
cana-5422	313	24	‖f	‖f	PRON
cana-5422	313	25	(	(	PUNCT
cana-5422	313	26	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	313	27	≤	≤	VERB
cana-5422	314	1	l1−ν	l1−ν	PROPN
cana-5422	314	2	1−	1−	NUM
cana-5422	314	3	l	l	NOUN
cana-5422	314	4	ψa	ψa	PROPN
cana-5422	314	5	(	(	PUNCT
cana-5422	314	6	w1	w1	NOUN
cana-5422	314	7	)	)	PUNCT
cana-5422	314	8	=	=	SYM
cana-5422	315	1	l1−ν	l1−ν	PROPN
cana-5422	315	2	1−	1−	NUM
cana-5422	315	3	l	l	NOUN
cana-5422	315	4	{	{	PUNCT
cana-5422	315	5	1	1	NUM
cana-5422	315	6	3	3	NUM
cana-5422	315	7	{	{	PUNCT
cana-5422	315	8	ψ	ψ	X
cana-5422	315	9	(	(	PUNCT
cana-5422	315	10	w1	w1	NOUN
cana-5422	315	11	,	,	PUNCT
cana-5422	315	12	w1	w1	NOUN
cana-5422	315	13	,	,	PUNCT
cana-5422	315	14	w1	w1	NOUN
cana-5422	315	15	)	)	PUNCT
cana-5422	316	1	+	+	NUM
cana-5422	316	2	3ψ	3ψ	NUM
cana-5422	316	3	(	(	PUNCT
cana-5422	316	4	w1	w1	NOUN
cana-5422	316	5	,	,	PUNCT
cana-5422	316	6	w1,−w1	w1,−w1	NUM
cana-5422	316	7	)	)	PUNCT
cana-5422	316	8	}	}	PUNCT
cana-5422	316	9	}	}	PUNCT
cana-5422	316	10	=	=	SYM
cana-5422	316	11	(	(	PUNCT
cana-5422	316	12	5−1)1−0	5−1)1−0	NUM
cana-5422	316	13	1−	1−	NUM
cana-5422	316	14	5−1	5−1	NUM
cana-5422	316	15	{	{	PUNCT
cana-5422	316	16	4δ	4δ	NOUN
cana-5422	316	17	3	3	X
cana-5422	316	18	}	}	PUNCT
cana-5422	316	19	=	=	PUNCT
cana-5422	316	20	δ	δ	PROPN
cana-5422	316	21	3	3	NUM
cana-5422	316	22	.	.	PUNCT
cana-5422	317	1	for	for	ADP
cana-5422	317	2	the	the	DET
cana-5422	317	3	case	case	NOUN
cana-5422	317	4	ν	ν	X
cana-5422	317	5	=	=	SYM
cana-5422	317	6	1	1	NUM
cana-5422	317	7	,	,	PUNCT
cana-5422	317	8	we	we	PRON
cana-5422	317	9	have	have	VERB
cana-5422	317	10	l	l	NOUN
cana-5422	317	11	=	=	SYM
cana-5422	317	12	τ−1	τ−1	PROPN
cana-5422	317	13	1	1	NUM
cana-5422	317	14	=	=	SYM
cana-5422	317	15	(	(	PUNCT
cana-5422	317	16	1	1	NUM
cana-5422	317	17	5	5	NUM
cana-5422	317	18	)	)	PUNCT
cana-5422	317	19	−1	−1	NOUN
cana-5422	317	20	=	=	SYM
cana-5422	317	21	5	5	NUM
cana-5422	317	22	and	and	CCONJ
cana-5422	317	23	from	from	ADP
cana-5422	317	24	(	(	PUNCT
cana-5422	317	25	2.46	2.46	NUM
cana-5422	317	26	)	)	PUNCT
cana-5422	317	27	,	,	PUNCT
cana-5422	317	28	we	we	PRON
cana-5422	317	29	obtain	obtain	VERB
cana-5422	317	30	‖f	‖f	PRON
cana-5422	317	31	(	(	PUNCT
cana-5422	317	32	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	317	33	≤	≤	VERB
cana-5422	318	1	l1−ν	l1−ν	PROPN
cana-5422	318	2	1−	1−	NUM
cana-5422	318	3	l	l	NOUN
cana-5422	318	4	ψa	ψa	PROPN
cana-5422	318	5	(	(	PUNCT
cana-5422	318	6	w1	w1	NOUN
cana-5422	318	7	)	)	PUNCT
cana-5422	318	8	=	=	SYM
cana-5422	319	1	l1−ν	l1−ν	PROPN
cana-5422	319	2	1−	1−	NUM
cana-5422	319	3	l	l	NOUN
cana-5422	319	4	{	{	PUNCT
cana-5422	319	5	1	1	NUM
cana-5422	319	6	3	3	NUM
cana-5422	319	7	{	{	PUNCT
cana-5422	319	8	ψ	ψ	X
cana-5422	319	9	(	(	PUNCT
cana-5422	319	10	w1	w1	NOUN
cana-5422	319	11	,	,	PUNCT
cana-5422	319	12	w1	w1	NOUN
cana-5422	319	13	,	,	PUNCT
cana-5422	319	14	w1	w1	NOUN
cana-5422	319	15	)	)	PUNCT
cana-5422	320	1	+	+	NUM
cana-5422	320	2	3ψ	3ψ	NUM
cana-5422	320	3	(	(	PUNCT
cana-5422	320	4	w1	w1	NOUN
cana-5422	320	5	,	,	PUNCT
cana-5422	320	6	w1,−w1	w1,−w1	NUM
cana-5422	320	7	)	)	PUNCT
cana-5422	320	8	}	}	PUNCT
cana-5422	320	9	}	}	PUNCT
cana-5422	320	10	=	=	SYM
cana-5422	320	11	(	(	PUNCT
cana-5422	320	12	5)1−1	5)1−1	NUM
cana-5422	320	13	1−	1−	NUM
cana-5422	320	14	5	5	NUM
cana-5422	320	15	{	{	PUNCT
cana-5422	320	16	4δ	4δ	NOUN
cana-5422	320	17	3	3	X
cana-5422	320	18	}	}	PUNCT
cana-5422	320	19	=	=	PUNCT
cana-5422	320	20	δ	δ	PROPN
cana-5422	320	21	−3	−3	PROPN
cana-5422	320	22	.	.	PUNCT
cana-5422	321	1	for	for	ADP
cana-5422	321	2	the	the	DET
cana-5422	321	3	case	case	NOUN
cana-5422	321	4	ν	ν	X
cana-5422	321	5	=	=	SYM
cana-5422	321	6	0	0	NUM
cana-5422	321	7	,	,	PUNCT
cana-5422	321	8	we	we	PRON
cana-5422	321	9	have	have	VERB
cana-5422	321	10	l	l	NOUN
cana-5422	322	1	=	=	SYM
cana-5422	322	2	τ	τ	X
cana-5422	322	3	ϕ−1	ϕ−1	ADP
cana-5422	322	4	0	0	NUM
cana-5422	322	5	=	=	SYM
cana-5422	322	6	5ϕ−1	5ϕ−1	NUM
cana-5422	322	7	and	and	CCONJ
cana-5422	322	8	from	from	ADP
cana-5422	322	9	(	(	PUNCT
cana-5422	322	10	2.46	2.46	NUM
cana-5422	322	11	)	)	PUNCT
cana-5422	322	12	,	,	PUNCT
cana-5422	322	13	we	we	PRON
cana-5422	322	14	arrive	arrive	VERB
cana-5422	322	15	‖f	‖f	PRON
cana-5422	322	16	(	(	PUNCT
cana-5422	322	17	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	322	18	≤	≤	VERB
cana-5422	323	1	l1−ν	l1−ν	PROPN
cana-5422	323	2	1−	1−	NUM
cana-5422	323	3	l	l	NOUN
cana-5422	323	4	ψa	ψa	PROPN
cana-5422	323	5	(	(	PUNCT
cana-5422	323	6	w1	w1	NOUN
cana-5422	323	7	)	)	PUNCT
cana-5422	323	8	=	=	SYM
cana-5422	324	1	l1−ν	l1−ν	PROPN
cana-5422	324	2	1−	1−	NUM
cana-5422	324	3	l	l	NOUN
cana-5422	324	4	{	{	PUNCT
cana-5422	324	5	1	1	NUM
cana-5422	324	6	3	3	NUM
cana-5422	324	7	{	{	PUNCT
cana-5422	324	8	ψ	ψ	X
cana-5422	324	9	(	(	PUNCT
cana-5422	324	10	w1	w1	NOUN
cana-5422	324	11	,	,	PUNCT
cana-5422	324	12	w1	w1	NOUN
cana-5422	324	13	,	,	PUNCT
cana-5422	324	14	w1	w1	NOUN
cana-5422	324	15	)	)	PUNCT
cana-5422	325	1	+	+	NUM
cana-5422	325	2	3ψ	3ψ	NUM
cana-5422	325	3	(	(	PUNCT
cana-5422	325	4	w1	w1	NOUN
cana-5422	325	5	,	,	PUNCT
cana-5422	325	6	w1,−w1	w1,−w1	NUM
cana-5422	325	7	)	)	PUNCT
cana-5422	325	8	}	}	PUNCT
cana-5422	325	9	}	}	PUNCT
cana-5422	326	1	=	=	SYM
cana-5422	326	2	(	(	PUNCT
cana-5422	326	3	5ϕ−1)1−0	5ϕ−1)1−0	NUM
cana-5422	326	4	1−	1−	NUM
cana-5422	326	5	5ϕ−1	5ϕ−1	NUM
cana-5422	326	6	{	{	PUNCT
cana-5422	326	7	12δ|w1	12δ|w1	NUM
cana-5422	326	8	5	5	NUM
cana-5422	326	9	|ϕ	|ϕ	NOUN
cana-5422	326	10	3	3	NUM
cana-5422	326	11	}	}	PUNCT
cana-5422	326	12	=	=	NOUN
cana-5422	326	13	4δ	4δ	NOUN
cana-5422	326	14	5−	5−	NUM
cana-5422	326	15	5ϕ	5ϕ	NOUN
cana-5422	326	16	.	.	PUNCT
cana-5422	327	1	for	for	ADP
cana-5422	327	2	the	the	DET
cana-5422	327	3	case	case	NOUN
cana-5422	327	4	ν	ν	X
cana-5422	327	5	=	=	SYM
cana-5422	327	6	1	1	NUM
cana-5422	327	7	,	,	PUNCT
cana-5422	327	8	we	we	PRON
cana-5422	327	9	have	have	VERB
cana-5422	327	10	l	l	NOUN
cana-5422	328	1	=	=	SYM
cana-5422	328	2	τ	τ	X
cana-5422	328	3	ϕ−1	ϕ−1	ADP
cana-5422	328	4	1	1	NUM
cana-5422	328	5	=	=	SYM
cana-5422	328	6	(	(	PUNCT
cana-5422	328	7	1	1	NUM
cana-5422	328	8	5	5	NUM
cana-5422	328	9	)	)	PUNCT
cana-5422	328	10	ϕ−1	ϕ−1	PROPN
cana-5422	329	1	=	=	SYM
cana-5422	329	2	51−ϕ	51−ϕ	NUM
cana-5422	329	3	and	and	CCONJ
cana-5422	329	4	from	from	ADP
cana-5422	329	5	(	(	PUNCT
cana-5422	329	6	2.46	2.46	NUM
cana-5422	329	7	)	)	PUNCT
cana-5422	329	8	,	,	PUNCT
cana-5422	329	9	we	we	PRON
cana-5422	329	10	get	get	VERB
cana-5422	329	11	‖f	‖f	PRON
cana-5422	330	1	(	(	PUNCT
cana-5422	330	2	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	330	3	≤	≤	VERB
cana-5422	331	1	l1−ν	l1−ν	PROPN
cana-5422	331	2	1−	1−	NUM
cana-5422	331	3	l	l	NOUN
cana-5422	331	4	ψa	ψa	PROPN
cana-5422	331	5	(	(	PUNCT
cana-5422	331	6	w1	w1	NOUN
cana-5422	331	7	)	)	PUNCT
cana-5422	331	8	=	=	SYM
cana-5422	332	1	l1−ν	l1−ν	PROPN
cana-5422	332	2	1−	1−	NUM
cana-5422	332	3	l	l	NOUN
cana-5422	332	4	{	{	PUNCT
cana-5422	332	5	1	1	NUM
cana-5422	332	6	3	3	NUM
cana-5422	332	7	{	{	PUNCT
cana-5422	332	8	ψ	ψ	X
cana-5422	332	9	(	(	PUNCT
cana-5422	332	10	w1	w1	NOUN
cana-5422	332	11	,	,	PUNCT
cana-5422	332	12	w1	w1	NOUN
cana-5422	332	13	,	,	PUNCT
cana-5422	332	14	w1	w1	NOUN
cana-5422	332	15	)	)	PUNCT
cana-5422	333	1	+	+	NUM
cana-5422	333	2	3ψ	3ψ	NUM
cana-5422	333	3	(	(	PUNCT
cana-5422	333	4	w1	w1	NOUN
cana-5422	333	5	,	,	PUNCT
cana-5422	333	6	w1,−w1	w1,−w1	NUM
cana-5422	333	7	)	)	PUNCT
cana-5422	333	8	}	}	PUNCT
cana-5422	333	9	}	}	PUNCT
cana-5422	333	10	=	=	SYM
cana-5422	333	11	(	(	PUNCT
cana-5422	333	12	51−ϕ)1−1	51−ϕ)1−1	NUM
cana-5422	333	13	1−	1−	NUM
cana-5422	333	14	51−ϕ	51−ϕ	NUM
cana-5422	333	15	{	{	PUNCT
cana-5422	333	16	12δ|w1	12δ|w1	NUM
cana-5422	333	17	5	5	NUM
cana-5422	333	18	|ϕ	|ϕ	NOUN
cana-5422	333	19	3	3	NUM
cana-5422	333	20	}	}	PUNCT
cana-5422	333	21	=	=	NOUN
cana-5422	333	22	4δ	4δ	NUM
cana-5422	333	23	5ϕ	5ϕ	NOUN
cana-5422	333	24	−	−	PROPN
cana-5422	333	25	5	5	NUM
cana-5422	333	26	.	.	PUNCT
cana-5422	334	1	communications	communication	NOUN
cana-5422	334	2	on	on	ADP
cana-5422	334	3	applied	apply	VERB
cana-5422	334	4	nonlinear	nonlinear	ADJ
cana-5422	334	5	analysis	analysis	NOUN
cana-5422	334	6	issn	issn	NOUN
cana-5422	334	7	:	:	PUNCT
cana-5422	334	8	1074	1074	NUM
cana-5422	334	9	-	-	PUNCT
cana-5422	334	10	133x	133x	NUM
cana-5422	334	11	vol	vol	NOUN
cana-5422	334	12	32	32	NUM
cana-5422	334	13	no	no	NOUN
cana-5422	334	14	.	.	PUNCT
cana-5422	335	1	10s(2025	10s(2025	NUM
cana-5422	335	2	)	)	PUNCT
cana-5422	336	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	336	2	2197	2197	NUM
cana-5422	336	3	for	for	ADP
cana-5422	336	4	the	the	DET
cana-5422	336	5	case	case	NOUN
cana-5422	336	6	ν	ν	X
cana-5422	336	7	=	=	SYM
cana-5422	336	8	0	0	NUM
cana-5422	336	9	,	,	PUNCT
cana-5422	336	10	we	we	PRON
cana-5422	336	11	have	have	VERB
cana-5422	336	12	l	l	NOUN
cana-5422	336	13	=	=	SYM
cana-5422	336	14	τ	τ	X
cana-5422	336	15	3ϕ−1	3ϕ−1	NUM
cana-5422	336	16	0	0	NUM
cana-5422	336	17	=	=	SYM
cana-5422	336	18	53ϕ−1	53ϕ−1	NUM
cana-5422	336	19	and	and	CCONJ
cana-5422	336	20	from	from	ADP
cana-5422	336	21	(	(	PUNCT
cana-5422	336	22	2.46	2.46	NUM
cana-5422	336	23	)	)	PUNCT
cana-5422	336	24	,	,	PUNCT
cana-5422	336	25	we	we	PRON
cana-5422	336	26	arrive	arrive	VERB
cana-5422	336	27	‖f	‖f	PRON
cana-5422	336	28	(	(	PUNCT
cana-5422	336	29	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	336	30	≤	≤	VERB
cana-5422	337	1	l1−ν	l1−ν	PROPN
cana-5422	337	2	1−	1−	NUM
cana-5422	337	3	l	l	NOUN
cana-5422	337	4	ψa	ψa	PROPN
cana-5422	337	5	(	(	PUNCT
cana-5422	337	6	w1	w1	NOUN
cana-5422	337	7	)	)	PUNCT
cana-5422	337	8	=	=	SYM
cana-5422	338	1	l1−ν	l1−ν	PROPN
cana-5422	338	2	1−	1−	NUM
cana-5422	338	3	l	l	NOUN
cana-5422	338	4	{	{	PUNCT
cana-5422	338	5	1	1	NUM
cana-5422	338	6	3	3	NUM
cana-5422	338	7	{	{	PUNCT
cana-5422	338	8	ψ	ψ	X
cana-5422	338	9	(	(	PUNCT
cana-5422	338	10	w1	w1	NOUN
cana-5422	338	11	,	,	PUNCT
cana-5422	338	12	w1	w1	NOUN
cana-5422	338	13	,	,	PUNCT
cana-5422	338	14	w1	w1	NOUN
cana-5422	338	15	)	)	PUNCT
cana-5422	339	1	+	+	NUM
cana-5422	339	2	3ψ	3ψ	NUM
cana-5422	339	3	(	(	PUNCT
cana-5422	339	4	w1	w1	NOUN
cana-5422	339	5	,	,	PUNCT
cana-5422	339	6	w1,−w1	w1,−w1	NUM
cana-5422	339	7	)	)	PUNCT
cana-5422	339	8	}	}	PUNCT
cana-5422	340	1	}	}	PUNCT
cana-5422	340	2	=	=	SYM
cana-5422	340	3	(	(	PUNCT
cana-5422	340	4	53ϕ−1)1−0	53ϕ−1)1−0	NUM
cana-5422	340	5	1−	1−	NUM
cana-5422	340	6	53ϕ−1	53ϕ−1	NUM
cana-5422	340	7	{	{	PUNCT
cana-5422	340	8	4δ|w1	4δ|w1	PROPN
cana-5422	340	9	5	5	NUM
cana-5422	340	10	|3ϕ	|3ϕ	PRON
cana-5422	340	11	3	3	NUM
cana-5422	340	12	}	}	PUNCT
cana-5422	340	13	=	=	SYM
cana-5422	340	14	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	340	15	3(5−	3(5−	NUM
cana-5422	340	16	53ϕ	53ϕ	NUM
cana-5422	340	17	)	)	PUNCT
cana-5422	340	18	.	.	PUNCT
cana-5422	341	1	for	for	ADP
cana-5422	341	2	the	the	DET
cana-5422	341	3	case	case	NOUN
cana-5422	341	4	ν	ν	X
cana-5422	341	5	=	=	SYM
cana-5422	341	6	1	1	NUM
cana-5422	341	7	,	,	PUNCT
cana-5422	341	8	we	we	PRON
cana-5422	341	9	have	have	VERB
cana-5422	341	10	l	l	NOUN
cana-5422	342	1	=	=	SYM
cana-5422	342	2	τ	τ	X
cana-5422	342	3	3ϕ−1	3ϕ−1	NUM
cana-5422	342	4	1	1	NUM
cana-5422	342	5	=	=	SYM
cana-5422	342	6	(	(	PUNCT
cana-5422	342	7	1	1	NUM
cana-5422	342	8	5	5	NUM
cana-5422	342	9	)	)	PUNCT
cana-5422	342	10	3ϕ−1	3ϕ−1	NUM
cana-5422	342	11	=	=	SYM
cana-5422	342	12	51−3ϕ	51−3ϕ	NUM
cana-5422	342	13	and	and	CCONJ
cana-5422	342	14	from	from	ADP
cana-5422	342	15	(	(	PUNCT
cana-5422	342	16	2.46	2.46	NUM
cana-5422	342	17	)	)	PUNCT
cana-5422	342	18	,	,	PUNCT
cana-5422	342	19	we	we	PRON
cana-5422	342	20	obtain	obtain	VERB
cana-5422	342	21	‖f	‖f	PRON
cana-5422	342	22	(	(	PUNCT
cana-5422	342	23	w1)−a(w1)‖	w1)−a(w1)‖	VERB
cana-5422	342	24	≤	≤	VERB
cana-5422	343	1	l1−ν	l1−ν	PROPN
cana-5422	343	2	1−	1−	NUM
cana-5422	343	3	l	l	NOUN
cana-5422	343	4	ψa	ψa	PROPN
cana-5422	343	5	(	(	PUNCT
cana-5422	343	6	w1	w1	NOUN
cana-5422	343	7	)	)	PUNCT
cana-5422	343	8	=	=	SYM
cana-5422	344	1	l1−ν	l1−ν	PROPN
cana-5422	344	2	1−	1−	NUM
cana-5422	344	3	l	l	NOUN
cana-5422	344	4	{	{	PUNCT
cana-5422	344	5	1	1	NUM
cana-5422	344	6	3	3	NUM
cana-5422	344	7	{	{	PUNCT
cana-5422	344	8	ψ	ψ	X
cana-5422	344	9	(	(	PUNCT
cana-5422	344	10	w1	w1	NOUN
cana-5422	344	11	,	,	PUNCT
cana-5422	344	12	w1	w1	NOUN
cana-5422	344	13	,	,	PUNCT
cana-5422	344	14	w1	w1	NOUN
cana-5422	344	15	)	)	PUNCT
cana-5422	345	1	+	+	NUM
cana-5422	345	2	3ψ	3ψ	NUM
cana-5422	345	3	(	(	PUNCT
cana-5422	345	4	w1	w1	NOUN
cana-5422	345	5	,	,	PUNCT
cana-5422	345	6	w1,−w1	w1,−w1	NUM
cana-5422	345	7	)	)	PUNCT
cana-5422	345	8	}	}	PUNCT
cana-5422	345	9	}	}	PUNCT
cana-5422	346	1	=	=	SYM
cana-5422	346	2	(	(	PUNCT
cana-5422	346	3	51−3ϕ)1−1	51−3ϕ)1−1	NUM
cana-5422	346	4	1−	1−	NUM
cana-5422	346	5	51−3ϕ	51−3ϕ	NUM
cana-5422	346	6	{	{	PUNCT
cana-5422	346	7	4δ|w1	4δ|w1	PROPN
cana-5422	346	8	5	5	NUM
cana-5422	346	9	|3ϕ	|3ϕ	PRON
cana-5422	346	10	3	3	NUM
cana-5422	346	11	}	}	PUNCT
cana-5422	346	12	=	=	SYM
cana-5422	346	13	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	347	1	3(53ϕ	3(53ϕ	NUM
cana-5422	347	2	−	−	NOUN
cana-5422	347	3	5	5	NUM
cana-5422	347	4	)	)	PUNCT
cana-5422	347	5	.	.	PUNCT
cana-5422	348	1	similarly	similarly	ADV
cana-5422	348	2	,	,	PUNCT
cana-5422	348	3	we	we	PRON
cana-5422	348	4	can	can	AUX
cana-5422	348	5	prove	prove	VERB
cana-5422	348	6	the	the	DET
cana-5422	348	7	rest	rest	NOUN
cana-5422	348	8	cases	case	NOUN
cana-5422	348	9	.	.	PUNCT
cana-5422	349	1	�	�	PROPN
cana-5422	349	2	2.5	2.5	NUM
cana-5422	349	3	.	.	PUNCT
cana-5422	350	1	evenness	evenness	NOUN
cana-5422	350	2	of	of	ADP
cana-5422	350	3	f	f	PROPN
cana-5422	350	4	:	:	PUNCT
cana-5422	350	5	quadratic	quadratic	ADJ
cana-5422	350	6	case	case	NOUN
cana-5422	350	7	stability	stability	NOUN
cana-5422	350	8	results	result	VERB
cana-5422	350	9	:	:	PUNCT
cana-5422	350	10	fixed	fixed	ADJ
cana-5422	350	11	point	point	NOUN
cana-5422	350	12	method	method	NOUN
cana-5422	350	13	.	.	PUNCT
cana-5422	351	1	theorem	theorem	VERB
cana-5422	351	2	2.9	2.9	NUM
cana-5422	351	3	.	.	PUNCT
cana-5422	352	1	suppose	suppose	VERB
cana-5422	352	2	that	that	SCONJ
cana-5422	352	3	an	an	DET
cana-5422	352	4	even	even	ADV
cana-5422	352	5	function	function	NOUN
cana-5422	352	6	f	f	PROPN
cana-5422	352	7	:	:	PUNCT
cana-5422	352	8	w1	w1	PROPN
cana-5422	352	9	→	→	SYM
cana-5422	352	10	w2	w2	NOUN
cana-5422	352	11	satisfy	satisfy	VERB
cana-5422	352	12	the	the	DET
cana-5422	352	13	functional	functional	ADJ
cana-5422	352	14	inequality	inequality	NOUN
cana-5422	352	15	(	(	PUNCT
cana-5422	352	16	2.1	2.1	NUM
cana-5422	352	17	)	)	PUNCT
cana-5422	352	18	where	where	SCONJ
cana-5422	352	19	ψ	ψ	X
cana-5422	352	20	:	:	PUNCT
cana-5422	352	21	w3	w3	NOUN
cana-5422	352	22	1	1	NUM
cana-5422	352	23	→	→	SYM
cana-5422	353	1	[	[	X
cana-5422	353	2	0	0	NUM
cana-5422	353	3	,	,	PUNCT
cana-5422	353	4	∞	∞	PROPN
cana-5422	353	5	)	)	PUNCT
cana-5422	353	6	with	with	ADP
cana-5422	353	7	the	the	DET
cana-5422	353	8	condition	condition	NOUN
cana-5422	353	9	lim	lim	NOUN
cana-5422	353	10	`	`	PUNCT
cana-5422	353	11	→∞	→∞	PROPN
cana-5422	353	12	ψ	ψ	PROPN
cana-5422	353	13	(	(	PUNCT
cana-5422	353	14	τ	τ	PROPN
cana-5422	353	15	`	`	PUNCT
cana-5422	353	16	v	v	PROPN
cana-5422	353	17	w1	w1	NOUN
cana-5422	353	18	,	,	PUNCT
cana-5422	353	19	τ	τ	PROPN
cana-5422	353	20	`	`	PUNCT
cana-5422	353	21	v	v	PROPN
cana-5422	353	22	w2	w2	NOUN
cana-5422	353	23	,	,	PUNCT
cana-5422	353	24	τ	τ	PROPN
cana-5422	353	25	`	`	PROPN
cana-5422	353	26	v	v	PROPN
cana-5422	353	27	w3	w3	PROPN
cana-5422	353	28	)	)	PUNCT
cana-5422	353	29	τ2	τ2	PROPN
cana-5422	353	30	`	`	PUNCT
cana-5422	353	31	v	v	NOUN
cana-5422	353	32	=	=	SYM
cana-5422	353	33	0	0	NUM
cana-5422	353	34	;	;	PUNCT
cana-5422	353	35	τv	τv	X
cana-5422	353	36	=	=	PRON
cana-5422	353	37	{	{	PUNCT
cana-5422	353	38	5	5	NUM
cana-5422	353	39	;	;	PUNCT
cana-5422	353	40	ν	ν	X
cana-5422	353	41	=	=	SYM
cana-5422	353	42	0	0	NUM
cana-5422	353	43	1	1	NUM
cana-5422	353	44	5	5	NUM
cana-5422	353	45	;	;	PUNCT
cana-5422	353	46	ν	ν	X
cana-5422	353	47	=	=	SYM
cana-5422	353	48	1	1	NUM
cana-5422	353	49	,	,	PUNCT
cana-5422	353	50	∀	∀	X
cana-5422	353	51	w1	w1	NOUN
cana-5422	353	52	,	,	PUNCT
cana-5422	353	53	w2	w2	NOUN
cana-5422	353	54	,	,	PUNCT
cana-5422	353	55	w3	w3	PROPN
cana-5422	353	56	∈	∈	PROPN
cana-5422	353	57	w1	w1	NOUN
cana-5422	353	58	.	.	PUNCT
cana-5422	354	1	(	(	PUNCT
cana-5422	354	2	2.57	2.57	NUM
cana-5422	354	3	)	)	PUNCT
cana-5422	354	4	if	if	SCONJ
cana-5422	354	5	there	there	PRON
cana-5422	354	6	exists	exist	VERB
cana-5422	354	7	l	l	NOUN
cana-5422	354	8	=	=	SYM
cana-5422	354	9	l(ν	l(ν	PROPN
cana-5422	354	10	)	)	PUNCT
cana-5422	354	11	be	be	VERB
cana-5422	354	12	a	a	DET
cana-5422	354	13	function	function	NOUN
cana-5422	354	14	have	have	AUX
cana-5422	354	15	the	the	DET
cana-5422	354	16	property	property	NOUN
cana-5422	354	17	ψq(w1	ψq(w1	NOUN
cana-5422	354	18	)	)	PUNCT
cana-5422	355	1	=	=	SYM
cana-5422	355	2	ψq	ψq	PROPN
cana-5422	355	3	(	(	PUNCT
cana-5422	355	4	w1	w1	PROPN
cana-5422	355	5	5	5	NUM
cana-5422	355	6	)	)	PUNCT
cana-5422	355	7	and	and	CCONJ
cana-5422	355	8	1	1	NUM
cana-5422	355	9	τ2	τ2	NOUN
cana-5422	355	10	v	v	NOUN
cana-5422	355	11	ψq	ψq	PROPN
cana-5422	355	12	(	(	PUNCT
cana-5422	355	13	τvw1	τvw1	NOUN
cana-5422	355	14	)	)	PUNCT
cana-5422	355	15	=	=	SYM
cana-5422	356	1	l	l	NOUN
cana-5422	356	2	ψq(w1	ψq(w1	NOUN
cana-5422	356	3	)	)	PUNCT
cana-5422	356	4	,	,	PUNCT
cana-5422	356	5	∀	∀	X
cana-5422	356	6	w1	w1	NOUN
cana-5422	356	7	∈	∈	PROPN
cana-5422	356	8	w1	w1	NOUN
cana-5422	356	9	.	.	PUNCT
cana-5422	357	1	(	(	PUNCT
cana-5422	357	2	2.58	2.58	NUM
cana-5422	357	3	)	)	PUNCT
cana-5422	357	4	for	for	ADP
cana-5422	357	5	all	all	DET
cana-5422	357	6	w1	w1	NOUN
cana-5422	357	7	,	,	PUNCT
cana-5422	357	8	w2	w2	NOUN
cana-5422	357	9	,	,	PUNCT
cana-5422	357	10	w3	w3	PROPN
cana-5422	357	11	∈	∈	PROPN
cana-5422	357	12	w1	w1	NOUN
cana-5422	357	13	.	.	PUNCT
cana-5422	358	1	then	then	ADV
cana-5422	358	2	there	there	PRON
cana-5422	358	3	exists	exist	VERB
cana-5422	358	4	a	a	DET
cana-5422	358	5	unique	unique	ADJ
cana-5422	358	6	quadratic	quadratic	ADJ
cana-5422	358	7	mapping	mapping	NOUN
cana-5422	358	8	q(w1	q(w1	NOUN
cana-5422	358	9	)	)	PUNCT
cana-5422	358	10	:	:	PUNCT
cana-5422	358	11	w1	w1	PROPN
cana-5422	358	12	→w2	→w2	NOUN
cana-5422	358	13	which	which	PRON
cana-5422	358	14	satisfies	satisfy	VERB
cana-5422	358	15	(	(	PUNCT
cana-5422	358	16	1.7	1.7	NUM
cana-5422	358	17	)	)	PUNCT
cana-5422	358	18	and	and	CCONJ
cana-5422	358	19	the	the	DET
cana-5422	358	20	functional	functional	ADJ
cana-5422	358	21	inequality	inequality	NOUN
cana-5422	358	22	‖f	‖f	PRON
cana-5422	358	23	(	(	PUNCT
cana-5422	358	24	w1)−q(w1)‖	w1)−q(w1)‖	NOUN
cana-5422	358	25	≤	≤	X
cana-5422	359	1	l1−ν	l1−ν	PROPN
cana-5422	359	2	1−	1−	NUM
cana-5422	359	3	l	l	NOUN
cana-5422	359	4	ψq	ψq	PROPN
cana-5422	359	5	(	(	PUNCT
cana-5422	359	6	w1	w1	NOUN
cana-5422	359	7	)	)	PUNCT
cana-5422	359	8	(	(	PUNCT
cana-5422	359	9	2.59	2.59	NUM
cana-5422	359	10	)	)	PUNCT
cana-5422	359	11	=	=	SYM
cana-5422	360	1	l1−ν	l1−ν	PROPN
cana-5422	360	2	1−	1−	NUM
cana-5422	360	3	l	l	NOUN
cana-5422	360	4	{	{	PUNCT
cana-5422	360	5	1	1	NUM
cana-5422	360	6	3	3	NUM
cana-5422	360	7	{	{	PUNCT
cana-5422	360	8	ψ	ψ	X
cana-5422	360	9	(	(	PUNCT
cana-5422	360	10	w1	w1	NOUN
cana-5422	360	11	,	,	PUNCT
cana-5422	360	12	w1	w1	NOUN
cana-5422	360	13	,	,	PUNCT
cana-5422	360	14	w1	w1	NOUN
cana-5422	360	15	)	)	PUNCT
cana-5422	361	1	+	+	CCONJ
cana-5422	361	2	7	7	NUM
cana-5422	361	3	2	2	NUM
cana-5422	361	4	ψ	ψ	NOUN
cana-5422	361	5	(	(	PUNCT
cana-5422	361	6	w1	w1	NOUN
cana-5422	361	7	,	,	PUNCT
cana-5422	361	8	w1,−w1	w1,−w1	NUM
cana-5422	361	9	)	)	PUNCT
cana-5422	361	10	}	}	PUNCT
cana-5422	361	11	}	}	PUNCT
cana-5422	361	12	,	,	PUNCT
cana-5422	361	13	(	(	PUNCT
cana-5422	361	14	2.60	2.60	NUM
cana-5422	361	15	)	)	PUNCT
cana-5422	361	16	and	and	CCONJ
cana-5422	361	17	the	the	DET
cana-5422	361	18	mapping	mapping	NOUN
cana-5422	361	19	q(w1	q(w1	NOUN
cana-5422	361	20	)	)	PUNCT
cana-5422	361	21	is	be	AUX
cana-5422	361	22	obtained	obtain	VERB
cana-5422	361	23	by	by	ADP
cana-5422	361	24	q(w1	q(w1	NOUN
cana-5422	361	25	)	)	PUNCT
cana-5422	362	1	=	=	SYM
cana-5422	362	2	lim	lim	PROPN
cana-5422	362	3	`	`	PUNCT
cana-5422	362	4	→∞	→∞	PROPN
cana-5422	362	5	1	1	NUM
cana-5422	362	6	τ2	τ2	PROPN
cana-5422	362	7	`	`	PUNCT
cana-5422	362	8	v	v	NOUN
cana-5422	362	9	f	f	PROPN
cana-5422	362	10	(	(	PUNCT
cana-5422	362	11	τ	τ	PROPN
cana-5422	362	12	`	`	PROPN
cana-5422	362	13	v	v	PROPN
cana-5422	362	14	w1	w1	NOUN
cana-5422	362	15	)	)	PUNCT
cana-5422	362	16	,	,	PUNCT
cana-5422	362	17	(	(	PUNCT
cana-5422	362	18	2.61	2.61	NUM
cana-5422	362	19	)	)	PUNCT
cana-5422	362	20	for	for	ADP
cana-5422	362	21	all	all	DET
cana-5422	362	22	w1	w1	NOUN
cana-5422	362	23	∈	∈	PROPN
cana-5422	362	24	w1	w1	NOUN
cana-5422	362	25	.	.	PUNCT
cana-5422	363	1	proof	proof	NOUN
cana-5422	363	2	.	.	PUNCT
cana-5422	364	1	by	by	ADP
cana-5422	364	2	theorem	theorem	NOUN
cana-5422	364	3	2.7	2.7	NUM
cana-5422	364	4	,	,	PUNCT
cana-5422	364	5	define	define	VERB
cana-5422	364	6	a	a	DET
cana-5422	364	7	functionh	functionh	NOUN
cana-5422	364	8	:	:	PUNCT
cana-5422	364	9	g	g	NOUN
cana-5422	364	10	→	→	SYM
cana-5422	364	11	g	g	NOUN
cana-5422	364	12	by	by	ADP
cana-5422	364	13	hf	hf	PROPN
cana-5422	364	14	(	(	PUNCT
cana-5422	364	15	w1	w1	NOUN
cana-5422	364	16	)	)	PUNCT
cana-5422	364	17	=	=	SYM
cana-5422	365	1	1	1	NUM
cana-5422	365	2	τ2	τ2	NOUN
cana-5422	365	3	v	v	NOUN
cana-5422	365	4	f	f	X
cana-5422	365	5	(	(	PUNCT
cana-5422	365	6	τv	τv	ADP
cana-5422	365	7	w1	w1	NOUN
cana-5422	365	8	)	)	PUNCT
cana-5422	365	9	,	,	PUNCT
cana-5422	365	10	f	f	PROPN
cana-5422	365	11	or	or	CCONJ
cana-5422	365	12	all	all	DET
cana-5422	365	13	w1	w1	NOUN
cana-5422	365	14	∈	∈	PROPN
cana-5422	365	15	w1	w1	NOUN
cana-5422	365	16	.	.	PUNCT
cana-5422	366	1	(	(	PUNCT
cana-5422	366	2	2.62	2.62	NUM
cana-5422	366	3	)	)	PUNCT
cana-5422	366	4	now	now	ADV
cana-5422	366	5	f	f	X
cana-5422	366	6	,	,	PUNCT
cana-5422	366	7	f1	f1	PROPN
cana-5422	366	8	∈	∈	PROPN
cana-5422	366	9	g	g	NOUN
cana-5422	366	10	and	and	CCONJ
cana-5422	366	11	w1	w1	PROPN
cana-5422	366	12	∈	∈	PROPN
cana-5422	366	13	w1	w1	NOUN
cana-5422	366	14	,	,	PUNCT
cana-5422	366	15	we	we	PRON
cana-5422	366	16	see	see	VERB
cana-5422	366	17	d(f	d(f	NOUN
cana-5422	366	18	,	,	PUNCT
cana-5422	366	19	f1	f1	NOUN
cana-5422	366	20	)	)	PUNCT
cana-5422	366	21	≤	≤	PUNCT
cana-5422	367	1	k	k	PROPN
cana-5422	367	2	⇒	⇒	PROPN
cana-5422	367	3	‖	‖	PROPN
cana-5422	367	4	f	f	PROPN
cana-5422	367	5	(	(	PUNCT
cana-5422	367	6	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	367	7	)	)	PUNCT
cana-5422	367	8	‖≤	‖≤	PROPN
cana-5422	367	9	k	k	PROPN
cana-5422	367	10	ψ(w1	ψ(w1	PROPN
cana-5422	367	11	,	,	PUNCT
cana-5422	367	12	w1	w1	NOUN
cana-5422	367	13	,	,	PUNCT
cana-5422	367	14	w1	w1	NOUN
cana-5422	367	15	)	)	PUNCT
cana-5422	367	16	,	,	PUNCT
cana-5422	367	17	⇒	⇒	NOUN
cana-5422	367	18	∥∥∥∥	∥∥∥∥	NUM
cana-5422	367	19	1	1	NUM
cana-5422	367	20	τ2	τ2	PROPN
cana-5422	367	21	v	v	NOUN
cana-5422	367	22	f	f	NOUN
cana-5422	367	23	(	(	PUNCT
cana-5422	367	24	τvw1)−	τvw1)−	PROPN
cana-5422	367	25	1	1	NUM
cana-5422	367	26	τ2	τ2	PROPN
cana-5422	367	27	v	v	ADP
cana-5422	367	28	f1(τvw1	f1(τvw1	NOUN
cana-5422	367	29	)	)	PUNCT
cana-5422	367	30	∥∥∥∥	∥∥∥∥	PUNCT
cana-5422	367	31	≤	≤	NUM
cana-5422	367	32	1	1	NUM
cana-5422	367	33	τ2	τ2	NOUN
cana-5422	367	34	v	v	NOUN
cana-5422	367	35	k	k	PROPN
cana-5422	367	36	ψ(τvw1	ψ(τvw1	NOUN
cana-5422	367	37	,	,	PUNCT
cana-5422	367	38	τvw1	τvw1	NOUN
cana-5422	367	39	,	,	PUNCT
cana-5422	367	40	τvw1	τvw1	PROPN
cana-5422	367	41	)	)	PUNCT
cana-5422	367	42	,	,	PUNCT
cana-5422	367	43	⇒	⇒	NOUN
cana-5422	367	44	‖	‖	PROPN
cana-5422	367	45	hf	hf	X
cana-5422	367	46	(	(	PUNCT
cana-5422	367	47	w1)−hf1	w1)−hf1	PROPN
cana-5422	367	48	(	(	PUNCT
cana-5422	367	49	w1	w1	NOUN
cana-5422	367	50	)	)	PUNCT
cana-5422	367	51	‖≤	‖≤	PROPN
cana-5422	368	1	l	l	NOUN
cana-5422	368	2	k	k	X
cana-5422	368	3	ψ(w1	ψ(w1	PROPN
cana-5422	368	4	,	,	PUNCT
cana-5422	368	5	w1	w1	NOUN
cana-5422	368	6	,	,	PUNCT
cana-5422	368	7	w1	w1	NOUN
cana-5422	368	8	)	)	PUNCT
cana-5422	368	9	,	,	PUNCT
cana-5422	368	10	⇒d(hf	⇒d(hf	NOUN
cana-5422	368	11	,	,	PUNCT
cana-5422	368	12	hf1	hf1	NOUN
cana-5422	368	13	)	)	PUNCT
cana-5422	368	14	≤	≤	NUM
cana-5422	369	1	l	l	NOUN
cana-5422	370	1	k	k	NOUN
cana-5422	370	2	,	,	PUNCT
cana-5422	370	3	i.e.	i.e.	X
cana-5422	370	4	,h	,h	PUNCT
cana-5422	370	5	is	be	AUX
cana-5422	370	6	a	a	DET
cana-5422	370	7	strictly	strictly	ADV
cana-5422	370	8	contractive	contractive	ADJ
cana-5422	370	9	mapping	mapping	NOUN
cana-5422	370	10	on	on	ADP
cana-5422	370	11	g	g	NOUN
cana-5422	370	12	with	with	ADP
cana-5422	370	13	lipschitz	lipschitz	NOUN
cana-5422	370	14	constant	constant	ADJ
cana-5422	370	15	l	l	NOUN
cana-5422	370	16	(	(	PUNCT
cana-5422	370	17	see	see	VERB
cana-5422	370	18	[	[	X
cana-5422	370	19	18	18	NUM
cana-5422	370	20	]	]	NUM
cana-5422	370	21	)	)	PUNCT
cana-5422	370	22	.	.	PUNCT
cana-5422	371	1	the	the	DET
cana-5422	371	2	rest	rest	NOUN
cana-5422	371	3	of	of	ADP
cana-5422	371	4	the	the	DET
cana-5422	371	5	proof	proof	NOUN
cana-5422	371	6	is	be	AUX
cana-5422	371	7	similar	similar	ADJ
cana-5422	371	8	to	to	ADP
cana-5422	371	9	that	that	PRON
cana-5422	371	10	of	of	ADP
cana-5422	371	11	theorem	theorem	ADJ
cana-5422	371	12	2.7	2.7	NUM
cana-5422	371	13	.	.	PUNCT
cana-5422	372	1	hence	hence	ADV
cana-5422	372	2	the	the	DET
cana-5422	372	3	proof	proof	NOUN
cana-5422	372	4	is	be	AUX
cana-5422	372	5	complete	complete	ADJ
cana-5422	372	6	.	.	PUNCT
cana-5422	373	1	�	�	PROPN
cana-5422	373	2	communications	communication	NOUN
cana-5422	373	3	on	on	ADP
cana-5422	373	4	applied	apply	VERB
cana-5422	373	5	nonlinear	nonlinear	ADJ
cana-5422	373	6	analysis	analysis	NOUN
cana-5422	373	7	issn	issn	NOUN
cana-5422	373	8	:	:	PUNCT
cana-5422	373	9	1074	1074	NUM
cana-5422	373	10	-	-	PUNCT
cana-5422	373	11	133x	133x	NUM
cana-5422	373	12	vol	vol	NOUN
cana-5422	373	13	32	32	NUM
cana-5422	373	14	no	no	NOUN
cana-5422	373	15	.	.	PUNCT
cana-5422	374	1	10s(2025	10s(2025	NUM
cana-5422	374	2	)	)	PUNCT
cana-5422	374	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	374	4	2198	2198	NUM
cana-5422	374	5	corollary	corollary	ADJ
cana-5422	374	6	2.10	2.10	NUM
cana-5422	374	7	.	.	PUNCT
cana-5422	374	8	suppose	suppose	VERB
cana-5422	374	9	that	that	SCONJ
cana-5422	374	10	an	an	DET
cana-5422	374	11	even	even	ADV
cana-5422	374	12	function	function	NOUN
cana-5422	374	13	f	f	PROPN
cana-5422	374	14	:	:	PUNCT
cana-5422	374	15	w1	w1	PROPN
cana-5422	374	16	→	→	SYM
cana-5422	374	17	w2	w2	NOUN
cana-5422	374	18	satisfy	satisfy	VERB
cana-5422	374	19	the	the	DET
cana-5422	374	20	functional	functional	ADJ
cana-5422	374	21	inequality	inequality	NOUN
cana-5422	374	22	(	(	PUNCT
cana-5422	374	23	2.2	2.2	NUM
cana-5422	374	24	)	)	PUNCT
cana-5422	374	25	for	for	ADP
cana-5422	374	26	all	all	DET
cana-5422	374	27	w1	w1	NOUN
cana-5422	374	28	,	,	PUNCT
cana-5422	374	29	w2	w2	NOUN
cana-5422	374	30	,	,	PUNCT
cana-5422	374	31	w3	w3	PROPN
cana-5422	374	32	∈	∈	PROPN
cana-5422	374	33	w1	w1	NOUN
cana-5422	374	34	.	.	PUNCT
cana-5422	375	1	then	then	ADV
cana-5422	375	2	there	there	PRON
cana-5422	375	3	exists	exist	VERB
cana-5422	375	4	a	a	DET
cana-5422	375	5	unique	unique	ADJ
cana-5422	375	6	quadratic	quadratic	ADJ
cana-5422	375	7	mapping	mapping	NOUN
cana-5422	375	8	q(w1	q(w1	NOUN
cana-5422	375	9	)	)	PUNCT
cana-5422	375	10	:	:	PUNCT
cana-5422	375	11	w1	w1	NOUN
cana-5422	375	12	→	→	SYM
cana-5422	375	13	w2	w2	NOUN
cana-5422	375	14	which	which	PRON
cana-5422	375	15	satisfies	satisfy	VERB
cana-5422	375	16	(	(	PUNCT
cana-5422	375	17	1.7	1.7	NUM
cana-5422	375	18	)	)	PUNCT
cana-5422	375	19	and	and	CCONJ
cana-5422	375	20	the	the	DET
cana-5422	375	21	functional	functional	ADJ
cana-5422	375	22	inequality	inequality	NOUN
cana-5422	375	23	(	(	PUNCT
cana-5422	375	24	2.31	2.31	NUM
cana-5422	375	25	)	)	PUNCT
cana-5422	375	26	for	for	ADP
cana-5422	375	27	all	all	DET
cana-5422	375	28	w1	w1	NOUN
cana-5422	375	29	∈	∈	PROPN
cana-5422	375	30	w1	w1	NOUN
cana-5422	375	31	.	.	PUNCT
cana-5422	376	1	2.6	2.6	NUM
cana-5422	376	2	.	.	PUNCT
cana-5422	376	3	oddness	oddness	ADJ
cana-5422	376	4	and	and	CCONJ
cana-5422	376	5	evenness	evenness	NOUN
cana-5422	376	6	of	of	ADP
cana-5422	376	7	f	f	NOUN
cana-5422	376	8	:	:	PUNCT
cana-5422	376	9	additive	additive	ADJ
cana-5422	376	10	quadratic	quadratic	ADJ
cana-5422	376	11	case	case	NOUN
cana-5422	376	12	stability	stability	NOUN
cana-5422	376	13	results	result	VERB
cana-5422	376	14	:	:	PUNCT
cana-5422	376	15	fixed	fixed	ADJ
cana-5422	376	16	point	point	NOUN
cana-5422	376	17	method	method	NOUN
cana-5422	376	18	.	.	PUNCT
cana-5422	377	1	theorem	theorem	VERB
cana-5422	377	2	2.11	2.11	NUM
cana-5422	377	3	.	.	PUNCT
cana-5422	378	1	suppose	suppose	VERB
cana-5422	378	2	that	that	SCONJ
cana-5422	378	3	a	a	DET
cana-5422	378	4	function	function	NOUN
cana-5422	378	5	f	f	NOUN
cana-5422	378	6	:	:	PUNCT
cana-5422	378	7	w1	w1	PROPN
cana-5422	378	8	→w2	→w2	NOUN
cana-5422	378	9	satisfy	satisfy	VERB
cana-5422	378	10	the	the	DET
cana-5422	378	11	functional	functional	ADJ
cana-5422	378	12	inequality	inequality	NOUN
cana-5422	378	13	(	(	PUNCT
cana-5422	378	14	2.1	2.1	NUM
cana-5422	378	15	)	)	PUNCT
cana-5422	378	16	where	where	SCONJ
cana-5422	378	17	ψ	ψ	X
cana-5422	378	18	:	:	PUNCT
cana-5422	378	19	w3	w3	NOUN
cana-5422	378	20	1	1	NUM
cana-5422	378	21	→	→	SYM
cana-5422	379	1	[	[	X
cana-5422	379	2	0	0	NUM
cana-5422	379	3	,	,	PUNCT
cana-5422	379	4	∞	∞	PROPN
cana-5422	379	5	)	)	PUNCT
cana-5422	379	6	with	with	ADP
cana-5422	379	7	the	the	DET
cana-5422	379	8	conditions	condition	NOUN
cana-5422	379	9	(	(	PUNCT
cana-5422	379	10	2.43	2.43	NUM
cana-5422	379	11	)	)	PUNCT
cana-5422	379	12	and	and	CCONJ
cana-5422	379	13	(	(	PUNCT
cana-5422	379	14	2.57	2.57	NUM
cana-5422	379	15	)	)	PUNCT
cana-5422	379	16	for	for	ADP
cana-5422	379	17	all	all	DET
cana-5422	379	18	w1	w1	NOUN
cana-5422	379	19	,	,	PUNCT
cana-5422	379	20	w2	w2	NOUN
cana-5422	379	21	,	,	PUNCT
cana-5422	379	22	w3	w3	PROPN
cana-5422	379	23	∈	∈	PROPN
cana-5422	379	24	w1	w1	NOUN
cana-5422	379	25	.	.	PUNCT
cana-5422	380	1	if	if	SCONJ
cana-5422	380	2	there	there	PRON
cana-5422	380	3	exists	exist	VERB
cana-5422	380	4	l	l	NOUN
cana-5422	380	5	=	=	SYM
cana-5422	380	6	l(ν	l(ν	PROPN
cana-5422	380	7	)	)	PUNCT
cana-5422	380	8	be	be	VERB
cana-5422	380	9	function	function	NOUN
cana-5422	380	10	have	have	VERB
cana-5422	380	11	the	the	DET
cana-5422	380	12	properties	property	NOUN
cana-5422	380	13	(	(	PUNCT
cana-5422	380	14	2.44	2.44	NUM
cana-5422	380	15	)	)	PUNCT
cana-5422	380	16	and	and	CCONJ
cana-5422	380	17	(	(	PUNCT
cana-5422	380	18	2.58	2.58	NUM
cana-5422	380	19	)	)	PUNCT
cana-5422	380	20	then	then	ADV
cana-5422	380	21	there	there	PRON
cana-5422	380	22	exists	exist	VERB
cana-5422	380	23	a	a	DET
cana-5422	380	24	unique	unique	ADJ
cana-5422	380	25	additive	additive	ADJ
cana-5422	380	26	mapping	mapping	NOUN
cana-5422	380	27	a(w1	a(w1	NOUN
cana-5422	380	28	)	)	PUNCT
cana-5422	380	29	:	:	PUNCT
cana-5422	380	30	w1	w1	NOUN
cana-5422	380	31	→	→	SYM
cana-5422	380	32	w2	w2	NOUN
cana-5422	380	33	and	and	CCONJ
cana-5422	380	34	a	a	DET
cana-5422	380	35	unique	unique	ADJ
cana-5422	380	36	quadratic	quadratic	ADJ
cana-5422	380	37	mapping	mapping	NOUN
cana-5422	380	38	q(w1	q(w1	NOUN
cana-5422	380	39	)	)	PUNCT
cana-5422	380	40	:	:	PUNCT
cana-5422	380	41	w1	w1	PROPN
cana-5422	380	42	→w2	→w2	NOUN
cana-5422	380	43	which	which	PRON
cana-5422	380	44	satisfies	satisfy	VERB
cana-5422	380	45	(	(	PUNCT
cana-5422	380	46	1.7	1.7	NUM
cana-5422	380	47	)	)	PUNCT
cana-5422	380	48	and	and	CCONJ
cana-5422	380	49	the	the	DET
cana-5422	380	50	functional	functional	ADJ
cana-5422	380	51	inequality	inequality	NOUN
cana-5422	380	52	‖f	‖f	ADP
cana-5422	380	53	(	(	PUNCT
cana-5422	380	54	w1)−a(w1)−q(w1)‖	w1)−a(w1)−q(w1)‖	X
cana-5422	380	55	≤	≤	NOUN
cana-5422	380	56	1	1	NUM
cana-5422	380	57	2	2	NUM
cana-5422	380	58	·	·	PUNCT
cana-5422	380	59	l1−ν	l1−ν	NOUN
cana-5422	380	60	1−	1−	NUM
cana-5422	380	61	l	l	NOUN
cana-5422	380	62	{	{	PUNCT
cana-5422	380	63	ψa	ψa	X
cana-5422	380	64	(	(	PUNCT
cana-5422	380	65	w1	w1	NOUN
cana-5422	380	66	)	)	PUNCT
cana-5422	381	1	+	+	CCONJ
cana-5422	381	2	ψa	ψa	X
cana-5422	381	3	(	(	PUNCT
cana-5422	381	4	−w1	−w1	PROPN
cana-5422	381	5	)	)	PUNCT
cana-5422	381	6	+	+	CCONJ
cana-5422	381	7	ψq	ψq	PROPN
cana-5422	381	8	(	(	PUNCT
cana-5422	381	9	w1	w1	NOUN
cana-5422	381	10	)	)	PUNCT
cana-5422	381	11	+	+	CCONJ
cana-5422	381	12	ψq	ψq	PROPN
cana-5422	381	13	(	(	PUNCT
cana-5422	381	14	−w1	−w1	PROPN
cana-5422	381	15	)	)	PUNCT
cana-5422	381	16	}	}	PUNCT
cana-5422	381	17	(	(	PUNCT
cana-5422	381	18	2.63	2.63	NUM
cana-5422	381	19	)	)	PUNCT
cana-5422	381	20	=	=	SYM
cana-5422	381	21	1	1	NUM
cana-5422	381	22	2	2	NUM
cana-5422	381	23	·	·	PUNCT
cana-5422	381	24	l1−ν	l1−ν	NOUN
cana-5422	381	25	1−	1−	NUM
cana-5422	381	26	l	l	NOUN
cana-5422	381	27	{	{	PUNCT
cana-5422	381	28	1	1	NUM
cana-5422	381	29	3	3	NUM
cana-5422	381	30	{	{	PUNCT
cana-5422	381	31	ψ	ψ	X
cana-5422	381	32	(	(	PUNCT
cana-5422	381	33	w1	w1	NOUN
cana-5422	381	34	,	,	PUNCT
cana-5422	381	35	w1	w1	NOUN
cana-5422	381	36	,	,	PUNCT
cana-5422	381	37	w1	w1	NOUN
cana-5422	381	38	)	)	PUNCT
cana-5422	382	1	+	+	NUM
cana-5422	382	2	3ψ	3ψ	NUM
cana-5422	382	3	(	(	PUNCT
cana-5422	382	4	w1	w1	NOUN
cana-5422	382	5	,	,	PUNCT
cana-5422	382	6	w1,−w1	w1,−w1	NUM
cana-5422	382	7	)	)	PUNCT
cana-5422	383	1	+	+	NUM
cana-5422	383	2	ψ	ψ	X
cana-5422	383	3	(	(	PUNCT
cana-5422	383	4	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	383	5	)	)	PUNCT
cana-5422	384	1	+	+	NUM
cana-5422	384	2	3ψ	3ψ	NUM
cana-5422	384	3	(	(	PUNCT
cana-5422	384	4	−w1,−w1	−w1,−w1	NUM
cana-5422	384	5	,	,	PUNCT
cana-5422	384	6	w1	w1	NOUN
cana-5422	384	7	)	)	PUNCT
cana-5422	384	8	+	+	NOUN
cana-5422	384	9	ψ	ψ	X
cana-5422	384	10	(	(	PUNCT
cana-5422	384	11	w1	w1	NOUN
cana-5422	384	12	,	,	PUNCT
cana-5422	384	13	w1	w1	NOUN
cana-5422	384	14	,	,	PUNCT
cana-5422	384	15	w1	w1	NOUN
cana-5422	384	16	)	)	PUNCT
cana-5422	384	17	+	+	CCONJ
cana-5422	384	18	7	7	NUM
cana-5422	384	19	2	2	NUM
cana-5422	384	20	ψ	ψ	NOUN
cana-5422	384	21	(	(	PUNCT
cana-5422	384	22	w1	w1	NOUN
cana-5422	384	23	,	,	PUNCT
cana-5422	384	24	w1,−w1	w1,−w1	NUM
cana-5422	384	25	)	)	PUNCT
cana-5422	385	1	+	+	NUM
cana-5422	385	2	ψ	ψ	X
cana-5422	385	3	(	(	PUNCT
cana-5422	385	4	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	385	5	)	)	PUNCT
cana-5422	386	1	+	+	CCONJ
cana-5422	386	2	7	7	NUM
cana-5422	386	3	2	2	NUM
cana-5422	386	4	ψ	ψ	NOUN
cana-5422	386	5	(	(	PUNCT
cana-5422	386	6	−w1,−w1	−w1,−w1	PROPN
cana-5422	386	7	,	,	PUNCT
cana-5422	386	8	w1	w1	NOUN
cana-5422	386	9	)	)	PUNCT
cana-5422	386	10	}	}	PUNCT
cana-5422	386	11	}	}	PUNCT
cana-5422	386	12	,	,	PUNCT
cana-5422	386	13	(	(	PUNCT
cana-5422	386	14	2.64	2.64	NUM
cana-5422	386	15	)	)	PUNCT
cana-5422	386	16	and	and	CCONJ
cana-5422	386	17	the	the	DET
cana-5422	386	18	mapping	mapping	NOUN
cana-5422	386	19	a(w1	a(w1	NOUN
cana-5422	386	20	)	)	PUNCT
cana-5422	386	21	and	and	CCONJ
cana-5422	386	22	q(w1	q(w1	NOUN
cana-5422	386	23	)	)	PUNCT
cana-5422	386	24	are	be	AUX
cana-5422	386	25	given	give	VERB
cana-5422	386	26	in	in	ADP
cana-5422	386	27	(	(	PUNCT
cana-5422	386	28	2.47	2.47	NUM
cana-5422	386	29	)	)	PUNCT
cana-5422	386	30	and	and	CCONJ
cana-5422	386	31	(	(	PUNCT
cana-5422	386	32	2.61	2.61	NUM
cana-5422	386	33	)	)	PUNCT
cana-5422	386	34	for	for	ADP
cana-5422	386	35	all	all	DET
cana-5422	386	36	w1	w1	NOUN
cana-5422	386	37	∈	∈	PROPN
cana-5422	386	38	w1	w1	NOUN
cana-5422	386	39	.	.	PUNCT
cana-5422	387	1	proof	proof	NOUN
cana-5422	387	2	.	.	PUNCT
cana-5422	388	1	the	the	DET
cana-5422	388	2	proof	proof	NOUN
cana-5422	388	3	is	be	AUX
cana-5422	388	4	similar	similar	ADJ
cana-5422	388	5	ideas	idea	NOUN
cana-5422	388	6	to	to	ADP
cana-5422	388	7	that	that	PRON
cana-5422	388	8	of	of	ADP
cana-5422	388	9	theorem	theorem	ADJ
cana-5422	388	10	2.5	2.5	NUM
cana-5422	388	11	.	.	PUNCT
cana-5422	389	1	�	�	PROPN
cana-5422	389	2	corollary	corollary	PROPN
cana-5422	389	3	2.12	2.12	PROPN
cana-5422	389	4	.	.	PUNCT
cana-5422	389	5	suppose	suppose	VERB
cana-5422	389	6	that	that	SCONJ
cana-5422	389	7	a	a	DET
cana-5422	389	8	functionf	functionf	NOUN
cana-5422	389	9	:	:	PUNCT
cana-5422	389	10	w1	w1	PROPN
cana-5422	389	11	→w2	→w2	NOUN
cana-5422	389	12	satisfy	satisfy	VERB
cana-5422	389	13	the	the	DET
cana-5422	389	14	functional	functional	ADJ
cana-5422	389	15	inequality	inequality	NOUN
cana-5422	389	16	(	(	PUNCT
cana-5422	389	17	2.2	2.2	NUM
cana-5422	389	18	)	)	PUNCT
cana-5422	389	19	for	for	ADP
cana-5422	389	20	all	all	DET
cana-5422	389	21	w1	w1	NOUN
cana-5422	389	22	,	,	PUNCT
cana-5422	389	23	w2	w2	NOUN
cana-5422	389	24	,	,	PUNCT
cana-5422	389	25	w3	w3	PROPN
cana-5422	389	26	∈	∈	PROPN
cana-5422	389	27	w1	w1	NOUN
cana-5422	389	28	.	.	PUNCT
cana-5422	390	1	then	then	ADV
cana-5422	390	2	there	there	PRON
cana-5422	390	3	exists	exist	VERB
cana-5422	390	4	a	a	DET
cana-5422	390	5	unique	unique	ADJ
cana-5422	390	6	additive	additive	ADJ
cana-5422	390	7	mapping	mapping	NOUN
cana-5422	390	8	a(w1	a(w1	NOUN
cana-5422	390	9	)	)	PUNCT
cana-5422	390	10	:	:	PUNCT
cana-5422	390	11	w1	w1	NOUN
cana-5422	390	12	→	→	SYM
cana-5422	390	13	w2	w2	NOUN
cana-5422	390	14	and	and	CCONJ
cana-5422	390	15	a	a	DET
cana-5422	390	16	unique	unique	ADJ
cana-5422	390	17	quadratic	quadratic	ADJ
cana-5422	390	18	mapping	mapping	NOUN
cana-5422	390	19	q(w1	q(w1	NOUN
cana-5422	390	20	)	)	PUNCT
cana-5422	390	21	:	:	PUNCT
cana-5422	390	22	w1	w1	PROPN
cana-5422	390	23	→w2	→w2	NOUN
cana-5422	390	24	which	which	PRON
cana-5422	390	25	satisfies	satisfy	VERB
cana-5422	390	26	(	(	PUNCT
cana-5422	390	27	1.7	1.7	NUM
cana-5422	390	28	)	)	PUNCT
cana-5422	390	29	and	and	CCONJ
cana-5422	390	30	the	the	DET
cana-5422	390	31	functional	functional	ADJ
cana-5422	390	32	inequality	inequality	NOUN
cana-5422	390	33	(	(	PUNCT
cana-5422	390	34	2.42	2.42	NUM
cana-5422	390	35	)	)	PUNCT
cana-5422	390	36	for	for	ADP
cana-5422	390	37	all	all	DET
cana-5422	390	38	w1	w1	NOUN
cana-5422	390	39	∈	∈	PROPN
cana-5422	390	40	w1	w1	NOUN
cana-5422	390	41	.	.	PUNCT
cana-5422	391	1	3	3	X
cana-5422	391	2	.	.	X
cana-5422	391	3	stability	stability	NOUN
cana-5422	391	4	in	in	ADP
cana-5422	391	5	intuitionistic	intuitionistic	ADJ
cana-5422	391	6	fuzzy	fuzzy	ADJ
cana-5422	391	7	banach	banach	NOUN
cana-5422	391	8	space	space	NOUN
cana-5422	391	9	of	of	ADP
cana-5422	391	10	(	(	PUNCT
cana-5422	391	11	1.7	1.7	NUM
cana-5422	391	12	)	)	PUNCT
cana-5422	391	13	in	in	ADP
cana-5422	391	14	this	this	DET
cana-5422	391	15	section	section	NOUN
cana-5422	391	16	,	,	PUNCT
cana-5422	391	17	we	we	PRON
cana-5422	391	18	explore	explore	VERB
cana-5422	391	19	the	the	DET
cana-5422	391	20	generalized	generalize	VERB
cana-5422	391	21	ulam	ulam	PROPN
cana-5422	391	22	hyers	hyer	NOUN
cana-5422	391	23	stability	stability	NOUN
cana-5422	391	24	of	of	ADP
cana-5422	391	25	the	the	DET
cana-5422	391	26	functional	functional	ADJ
cana-5422	391	27	equation	equation	NOUN
cana-5422	391	28	(	(	PUNCT
cana-5422	391	29	1.7	1.7	NUM
cana-5422	391	30	)	)	PUNCT
cana-5422	391	31	in	in	ADP
cana-5422	391	32	intuitionistic	intuitionistic	ADJ
cana-5422	391	33	fuzzy	fuzzy	ADJ
cana-5422	391	34	banach	banach	NOUN
cana-5422	391	35	space	space	NOUN
cana-5422	391	36	.	.	PUNCT
cana-5422	392	1	in	in	ADP
cana-5422	392	2	order	order	NOUN
cana-5422	392	3	to	to	PART
cana-5422	392	4	prove	prove	VERB
cana-5422	392	5	stability	stability	NOUN
cana-5422	392	6	results	result	NOUN
cana-5422	392	7	,	,	PUNCT
cana-5422	392	8	assume	assume	VERB
cana-5422	392	9	(	(	PUNCT
cana-5422	392	10	w1	w1	NOUN
cana-5422	392	11	,	,	PUNCT
cana-5422	392	12	µ	µ	NOUN
cana-5422	392	13	,	,	PUNCT
cana-5422	392	14	ν	ν	NOUN
cana-5422	392	15	)	)	PUNCT
cana-5422	392	16	and	and	CCONJ
cana-5422	392	17	(	(	PUNCT
cana-5422	392	18	w2	w2	NOUN
cana-5422	392	19	,	,	PUNCT
cana-5422	392	20	µ′	µ′	NUM
cana-5422	392	21	,	,	PUNCT
cana-5422	392	22	ν′	ν′	NOUN
cana-5422	392	23	)	)	PUNCT
cana-5422	392	24	are	be	AUX
cana-5422	392	25	intuitionistic	intuitionistic	ADJ
cana-5422	392	26	fuzzy	fuzzy	ADJ
cana-5422	392	27	normed	normed	ADJ
cana-5422	392	28	space	space	NOUN
cana-5422	392	29	and	and	CCONJ
cana-5422	392	30	intuitionistic	intuitionistic	ADJ
cana-5422	392	31	fuzzy	fuzzy	ADJ
cana-5422	392	32	banach	banach	NOUN
cana-5422	392	33	space	space	NOUN
cana-5422	392	34	respectively	respectively	ADV
cana-5422	392	35	.	.	PUNCT
cana-5422	392	36	suppose	suppose	VERB
cana-5422	392	37	that	that	SCONJ
cana-5422	392	38	f	f	PROPN
cana-5422	392	39	:	:	PUNCT
cana-5422	392	40	w1	w1	NOUN
cana-5422	392	41	→	→	SYM
cana-5422	392	42	w2	w2	NOUN
cana-5422	392	43	and	and	CCONJ
cana-5422	392	44	ψ	ψ	PROPN
cana-5422	392	45	:	:	PUNCT
cana-5422	392	46	w3	w3	NOUN
cana-5422	392	47	1	1	NUM
cana-5422	392	48	→	→	SYM
cana-5422	392	49	[	[	X
cana-5422	392	50	0	0	NUM
cana-5422	392	51	,	,	PUNCT
cana-5422	392	52	∞	∞	NUM
cana-5422	392	53	)	)	PUNCT
cana-5422	392	54	satisfy	satisfy	VERB
cana-5422	392	55	the	the	DET
cana-5422	392	56	following	follow	VERB
cana-5422	392	57	functional	functional	ADJ
cana-5422	392	58	inequalities	inequality	NOUN
cana-5422	392	59	µ	µ	X
cana-5422	392	60	(	(	PUNCT
cana-5422	392	61	f	f	X
cana-5422	392	62	(	(	PUNCT
cana-5422	392	63	3w1	3w1	NUM
cana-5422	392	64	+	+	CCONJ
cana-5422	392	65	w2	w2	NOUN
cana-5422	392	66	+	+	CCONJ
cana-5422	392	67	w3	w3	PROPN
cana-5422	392	68	)	)	PUNCT
cana-5422	393	1	+	+	NOUN
cana-5422	393	2	f	f	X
cana-5422	393	3	(	(	PUNCT
cana-5422	393	4	w1	w1	NOUN
cana-5422	393	5	+	+	CCONJ
cana-5422	393	6	3w2	3w2	NUM
cana-5422	393	7	+	+	CCONJ
cana-5422	393	8	w3	w3	NOUN
cana-5422	393	9	)	)	PUNCT
cana-5422	394	1	+	+	NOUN
cana-5422	394	2	f	f	X
cana-5422	394	3	(	(	PUNCT
cana-5422	394	4	w1	w1	NOUN
cana-5422	394	5	+	+	NOUN
cana-5422	394	6	w2	w2	NOUN
cana-5422	394	7	+	+	CCONJ
cana-5422	394	8	3w3)−	3w3)−	PROPN
cana-5422	394	9	6f	6f	NOUN
cana-5422	394	10	(	(	PUNCT
cana-5422	394	11	∑3	∑3	PROPN
cana-5422	394	12	ψ=1	ψ=1	PRON
cana-5422	394	13	wψ	wψ	ADP
cana-5422	394	14	)	)	PUNCT
cana-5422	394	15	−	−	PROPN
cana-5422	394	16	1	1	NUM
cana-5422	394	17	2	2	NUM
cana-5422	394	18	{	{	PUNCT
cana-5422	394	19	f	f	PROPN
cana-5422	394	20	(	(	PUNCT
cana-5422	394	21	∑3	∑3	PROPN
cana-5422	394	22	ψ=1	ψ=1	PUNCT
cana-5422	394	23	wψ	wψ	ADP
cana-5422	394	24	)	)	PUNCT
cana-5422	395	1	+	+	NOUN
cana-5422	395	2	f	f	X
cana-5422	395	3	(	(	PUNCT
cana-5422	395	4	−∑3	−∑3	PROPN
cana-5422	395	5	ψ=1	ψ=1	PUNCT
cana-5422	395	6	wψ	wψ	ADP
cana-5422	395	7	)	)	PUNCT
cana-5422	395	8	}	}	PUNCT
cana-5422	395	9	+	+	CCONJ
cana-5422	395	10	∑3	∑3	SYM
cana-5422	395	11	ψ=1	ψ=1	X
cana-5422	395	12	{	{	PUNCT
cana-5422	395	13	f	f	X
cana-5422	395	14	(	(	PUNCT
cana-5422	395	15	wψ)−	wψ)−	X
cana-5422	395	16	5	5	NUM
cana-5422	395	17	2	2	NUM
cana-5422	395	18	[	[	PUNCT
cana-5422	395	19	f	f	X
cana-5422	395	20	(	(	PUNCT
cana-5422	395	21	wψ	wψ	ADP
cana-5422	395	22	)	)	PUNCT
cana-5422	396	1	+	+	NOUN
cana-5422	396	2	f	f	X
cana-5422	396	3	(	(	PUNCT
cana-5422	396	4	−wψ	−wψ	NOUN
cana-5422	396	5	)	)	PUNCT
cana-5422	396	6	]	]	PUNCT
cana-5422	396	7	}	}	PUNCT
cana-5422	396	8	,	,	PUNCT
cana-5422	396	9	λ	λ	PROPN
cana-5422	396	10	)	)	PUNCT
cana-5422	396	11	≥	≥	NOUN
cana-5422	396	12	µ′	µ′	PUNCT
cana-5422	396	13	(	(	PUNCT
cana-5422	396	14	ψ	ψ	X
cana-5422	396	15	(	(	PUNCT
cana-5422	396	16	w1	w1	NOUN
cana-5422	396	17	,	,	PUNCT
cana-5422	396	18	w2	w2	NOUN
cana-5422	396	19	,	,	PUNCT
cana-5422	396	20	w3	w3	PROPN
cana-5422	396	21	)	)	PUNCT
cana-5422	396	22	,	,	PUNCT
cana-5422	396	23	λ	λ	X
cana-5422	396	24	)	)	PUNCT
cana-5422	396	25	ν	ν	NOUN
cana-5422	396	26	(	(	PUNCT
cana-5422	396	27	f	f	X
cana-5422	396	28	(	(	PUNCT
cana-5422	396	29	3w1	3w1	NUM
cana-5422	396	30	+	+	CCONJ
cana-5422	396	31	w2	w2	NOUN
cana-5422	396	32	+	+	CCONJ
cana-5422	396	33	w3	w3	PROPN
cana-5422	396	34	)	)	PUNCT
cana-5422	397	1	+	+	NOUN
cana-5422	397	2	f	f	X
cana-5422	397	3	(	(	PUNCT
cana-5422	397	4	w1	w1	NOUN
cana-5422	397	5	+	+	CCONJ
cana-5422	397	6	3w2	3w2	NUM
cana-5422	397	7	+	+	CCONJ
cana-5422	397	8	w3	w3	NOUN
cana-5422	397	9	)	)	PUNCT
cana-5422	398	1	+	+	NOUN
cana-5422	398	2	f	f	X
cana-5422	398	3	(	(	PUNCT
cana-5422	398	4	w1	w1	NOUN
cana-5422	398	5	+	+	NOUN
cana-5422	398	6	w2	w2	NOUN
cana-5422	398	7	+	+	CCONJ
cana-5422	398	8	3w3)−	3w3)−	PROPN
cana-5422	398	9	6f	6f	NOUN
cana-5422	398	10	(	(	PUNCT
cana-5422	398	11	∑3	∑3	PROPN
cana-5422	398	12	ψ=1	ψ=1	PRON
cana-5422	398	13	wψ	wψ	ADP
cana-5422	398	14	)	)	PUNCT
cana-5422	398	15	−	−	PROPN
cana-5422	398	16	1	1	NUM
cana-5422	398	17	2	2	NUM
cana-5422	398	18	{	{	PUNCT
cana-5422	398	19	f	f	PROPN
cana-5422	398	20	(	(	PUNCT
cana-5422	398	21	∑3	∑3	PROPN
cana-5422	398	22	ψ=1	ψ=1	PUNCT
cana-5422	398	23	wψ	wψ	ADP
cana-5422	398	24	)	)	PUNCT
cana-5422	399	1	+	+	NOUN
cana-5422	399	2	f	f	X
cana-5422	399	3	(	(	PUNCT
cana-5422	399	4	−∑3	−∑3	PROPN
cana-5422	399	5	ψ=1	ψ=1	PUNCT
cana-5422	399	6	wψ	wψ	ADP
cana-5422	399	7	)	)	PUNCT
cana-5422	399	8	}	}	PUNCT
cana-5422	399	9	+	+	CCONJ
cana-5422	399	10	∑3	∑3	SYM
cana-5422	399	11	ψ=1	ψ=1	X
cana-5422	399	12	{	{	PUNCT
cana-5422	399	13	f	f	X
cana-5422	399	14	(	(	PUNCT
cana-5422	399	15	wψ)−	wψ)−	X
cana-5422	399	16	5	5	NUM
cana-5422	399	17	2	2	NUM
cana-5422	399	18	[	[	PUNCT
cana-5422	399	19	f	f	X
cana-5422	399	20	(	(	PUNCT
cana-5422	399	21	wψ	wψ	ADP
cana-5422	399	22	)	)	PUNCT
cana-5422	400	1	+	+	NOUN
cana-5422	400	2	f	f	X
cana-5422	400	3	(	(	PUNCT
cana-5422	400	4	−wψ	−wψ	NOUN
cana-5422	400	5	)	)	PUNCT
cana-5422	400	6	]	]	PUNCT
cana-5422	400	7	}	}	PUNCT
cana-5422	400	8	,	,	PUNCT
cana-5422	400	9	λ	λ	PROPN
cana-5422	400	10	)	)	PUNCT
cana-5422	400	11	≤	≤	NUM
cana-5422	400	12	ν′	ν′	NOUN
cana-5422	400	13	(	(	PUNCT
cana-5422	400	14	ψ	ψ	X
cana-5422	400	15	(	(	PUNCT
cana-5422	400	16	w1	w1	NOUN
cana-5422	400	17	,	,	PUNCT
cana-5422	400	18	w2	w2	NOUN
cana-5422	400	19	,	,	PUNCT
cana-5422	400	20	w3	w3	PROPN
cana-5422	400	21	)	)	PUNCT
cana-5422	400	22	,	,	PUNCT
cana-5422	400	23	λ	λ	X
cana-5422	400	24	)	)	PUNCT
cana-5422	400	25			NOUN
cana-5422	400	26	(	(	PUNCT
cana-5422	400	27	3.1	3.1	NUM
cana-5422	400	28	)	)	PUNCT
cana-5422	400	29	µ	µ	X
cana-5422	400	30	(	(	PUNCT
cana-5422	400	31	f	f	X
cana-5422	400	32	(	(	PUNCT
cana-5422	400	33	3w1	3w1	NUM
cana-5422	400	34	+	+	CCONJ
cana-5422	400	35	w2	w2	NOUN
cana-5422	400	36	+	+	CCONJ
cana-5422	400	37	w3	w3	PROPN
cana-5422	400	38	)	)	PUNCT
cana-5422	401	1	+	+	NOUN
cana-5422	401	2	f	f	X
cana-5422	401	3	(	(	PUNCT
cana-5422	401	4	w1	w1	NOUN
cana-5422	401	5	+	+	CCONJ
cana-5422	401	6	3w2	3w2	NUM
cana-5422	401	7	+	+	CCONJ
cana-5422	401	8	w3	w3	NOUN
cana-5422	401	9	)	)	PUNCT
cana-5422	402	1	+	+	NOUN
cana-5422	402	2	f	f	X
cana-5422	402	3	(	(	PUNCT
cana-5422	402	4	w1	w1	NOUN
cana-5422	402	5	+	+	NOUN
cana-5422	402	6	w2	w2	NOUN
cana-5422	402	7	+	+	CCONJ
cana-5422	402	8	3w3)−	3w3)−	PROPN
cana-5422	402	9	6f	6f	NOUN
cana-5422	402	10	(	(	PUNCT
cana-5422	402	11	∑3	∑3	PROPN
cana-5422	402	12	ψ=1	ψ=1	PRON
cana-5422	402	13	wψ	wψ	ADP
cana-5422	402	14	)	)	PUNCT
cana-5422	402	15	−	−	PROPN
cana-5422	402	16	1	1	NUM
cana-5422	402	17	2	2	NUM
cana-5422	402	18	{	{	PUNCT
cana-5422	402	19	f	f	PROPN
cana-5422	402	20	(	(	PUNCT
cana-5422	402	21	∑3	∑3	PROPN
cana-5422	402	22	ψ=1	ψ=1	PUNCT
cana-5422	402	23	wψ	wψ	ADP
cana-5422	402	24	)	)	PUNCT
cana-5422	403	1	+	+	NOUN
cana-5422	403	2	f	f	X
cana-5422	403	3	(	(	PUNCT
cana-5422	403	4	−∑3	−∑3	PROPN
cana-5422	403	5	ψ=1	ψ=1	PUNCT
cana-5422	403	6	wψ	wψ	ADP
cana-5422	403	7	)	)	PUNCT
cana-5422	403	8	}	}	PUNCT
cana-5422	403	9	+	+	CCONJ
cana-5422	403	10	∑3	∑3	SYM
cana-5422	403	11	ψ=1	ψ=1	X
cana-5422	403	12	{	{	PUNCT
cana-5422	403	13	f	f	X
cana-5422	403	14	(	(	PUNCT
cana-5422	403	15	wψ)−	wψ)−	X
cana-5422	403	16	5	5	NUM
cana-5422	403	17	2	2	NUM
cana-5422	403	18	[	[	PUNCT
cana-5422	403	19	f	f	X
cana-5422	403	20	(	(	PUNCT
cana-5422	403	21	wψ	wψ	ADP
cana-5422	403	22	)	)	PUNCT
cana-5422	404	1	+	+	NOUN
cana-5422	404	2	f	f	X
cana-5422	404	3	(	(	PUNCT
cana-5422	404	4	−wψ	−wψ	NOUN
cana-5422	404	5	)	)	PUNCT
cana-5422	404	6	]	]	PUNCT
cana-5422	404	7	}	}	PUNCT
cana-5422	404	8	,	,	PUNCT
cana-5422	404	9	λ	λ	PROPN
cana-5422	404	10	)	)	PUNCT
cana-5422	404	11	≥	≥	NOUN
cana-5422	404	12	µ′	µ′	PUNCT
cana-5422	404	13	(	(	PUNCT
cana-5422	404	14	δ	δ	PROPN
cana-5422	404	15	,	,	PUNCT
cana-5422	404	16	λ	λ	PROPN
cana-5422	404	17	)	)	PUNCT
cana-5422	404	18	,	,	PUNCT
cana-5422	404	19	ν	ν	X
cana-5422	404	20	(	(	PUNCT
cana-5422	404	21	f	f	X
cana-5422	404	22	(	(	PUNCT
cana-5422	404	23	3w1	3w1	NUM
cana-5422	404	24	+	+	CCONJ
cana-5422	404	25	w2	w2	NOUN
cana-5422	404	26	+	+	CCONJ
cana-5422	404	27	w3	w3	PROPN
cana-5422	404	28	)	)	PUNCT
cana-5422	405	1	+	+	NOUN
cana-5422	405	2	f	f	X
cana-5422	405	3	(	(	PUNCT
cana-5422	405	4	w1	w1	NOUN
cana-5422	405	5	+	+	CCONJ
cana-5422	405	6	3w2	3w2	NUM
cana-5422	405	7	+	+	CCONJ
cana-5422	405	8	w3	w3	NOUN
cana-5422	405	9	)	)	PUNCT
cana-5422	406	1	+	+	NOUN
cana-5422	406	2	f	f	X
cana-5422	406	3	(	(	PUNCT
cana-5422	406	4	w1	w1	NOUN
cana-5422	406	5	+	+	NOUN
cana-5422	406	6	w2	w2	NOUN
cana-5422	406	7	+	+	CCONJ
cana-5422	406	8	3w3)−	3w3)−	PROPN
cana-5422	406	9	6f	6f	NOUN
cana-5422	406	10	(	(	PUNCT
cana-5422	406	11	∑3	∑3	PROPN
cana-5422	406	12	ψ=1	ψ=1	PRON
cana-5422	406	13	wψ	wψ	ADP
cana-5422	406	14	)	)	PUNCT
cana-5422	406	15	−	−	PROPN
cana-5422	406	16	1	1	NUM
cana-5422	406	17	2	2	NUM
cana-5422	406	18	{	{	PUNCT
cana-5422	406	19	f	f	PROPN
cana-5422	406	20	(	(	PUNCT
cana-5422	406	21	∑3	∑3	PROPN
cana-5422	406	22	ψ=1	ψ=1	PUNCT
cana-5422	406	23	wψ	wψ	ADP
cana-5422	406	24	)	)	PUNCT
cana-5422	407	1	+	+	NOUN
cana-5422	407	2	f	f	X
cana-5422	407	3	(	(	PUNCT
cana-5422	407	4	−∑3	−∑3	PROPN
cana-5422	407	5	ψ=1	ψ=1	PUNCT
cana-5422	407	6	wψ	wψ	ADP
cana-5422	407	7	)	)	PUNCT
cana-5422	407	8	}	}	PUNCT
cana-5422	407	9	+	+	CCONJ
cana-5422	407	10	∑3	∑3	SYM
cana-5422	407	11	ψ=1	ψ=1	X
cana-5422	407	12	{	{	PUNCT
cana-5422	407	13	f	f	X
cana-5422	407	14	(	(	PUNCT
cana-5422	407	15	wψ)−	wψ)−	X
cana-5422	407	16	5	5	NUM
cana-5422	407	17	2	2	NUM
cana-5422	407	18	[	[	PUNCT
cana-5422	407	19	f	f	X
cana-5422	407	20	(	(	PUNCT
cana-5422	407	21	wψ	wψ	ADP
cana-5422	407	22	)	)	PUNCT
cana-5422	407	23	+	+	NOUN
cana-5422	407	24	f	f	X
cana-5422	407	25	(	(	PUNCT
cana-5422	407	26	−wψ	−wψ	NOUN
cana-5422	407	27	)	)	PUNCT
cana-5422	407	28	]	]	PUNCT
cana-5422	407	29	}	}	PUNCT
cana-5422	407	30	,	,	PUNCT
cana-5422	407	31	λ	λ	PROPN
cana-5422	407	32	)	)	PUNCT
cana-5422	407	33	≤	≤	NUM
cana-5422	407	34	ν′	ν′	NOUN
cana-5422	407	35	(	(	PUNCT
cana-5422	407	36	δ	δ	PROPN
cana-5422	407	37	,	,	PUNCT
cana-5422	407	38	λ	λ	PROPN
cana-5422	407	39	)	)	PUNCT
cana-5422	407	40	,	,	PUNCT
cana-5422	407	41			NOUN
cana-5422	407	42	(	(	PUNCT
cana-5422	407	43	3.2	3.2	NUM
cana-5422	407	44	)	)	PUNCT
cana-5422	407	45	communications	communication	NOUN
cana-5422	407	46	on	on	ADP
cana-5422	407	47	applied	apply	VERB
cana-5422	407	48	nonlinear	nonlinear	ADJ
cana-5422	407	49	analysis	analysis	NOUN
cana-5422	407	50	issn	issn	NOUN
cana-5422	407	51	:	:	PUNCT
cana-5422	407	52	1074	1074	NUM
cana-5422	407	53	-	-	PUNCT
cana-5422	407	54	133x	133x	NUM
cana-5422	407	55	vol	vol	NOUN
cana-5422	407	56	32	32	NUM
cana-5422	407	57	no	no	NOUN
cana-5422	407	58	.	.	PUNCT
cana-5422	408	1	10s(2025	10s(2025	NUM
cana-5422	408	2	)	)	PUNCT
cana-5422	409	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	409	2	2199	2199	NUM
cana-5422	409	3	µ	µ	X
cana-5422	409	4	(	(	PUNCT
cana-5422	409	5	f	f	X
cana-5422	409	6	(	(	PUNCT
cana-5422	409	7	3w1	3w1	NUM
cana-5422	409	8	+	+	CCONJ
cana-5422	409	9	w2	w2	NOUN
cana-5422	409	10	+	+	CCONJ
cana-5422	409	11	w3	w3	PROPN
cana-5422	409	12	)	)	PUNCT
cana-5422	410	1	+	+	NOUN
cana-5422	410	2	f	f	X
cana-5422	410	3	(	(	PUNCT
cana-5422	410	4	w1	w1	NOUN
cana-5422	410	5	+	+	CCONJ
cana-5422	410	6	3w2	3w2	NUM
cana-5422	410	7	+	+	CCONJ
cana-5422	410	8	w3	w3	NOUN
cana-5422	410	9	)	)	PUNCT
cana-5422	411	1	+	+	NOUN
cana-5422	411	2	f	f	X
cana-5422	411	3	(	(	PUNCT
cana-5422	411	4	w1	w1	NOUN
cana-5422	411	5	+	+	NOUN
cana-5422	411	6	w2	w2	NOUN
cana-5422	411	7	+	+	CCONJ
cana-5422	411	8	3w3)−	3w3)−	PROPN
cana-5422	411	9	6f	6f	NOUN
cana-5422	411	10	(	(	PUNCT
cana-5422	411	11	∑3	∑3	PROPN
cana-5422	411	12	ψ=1	ψ=1	PRON
cana-5422	411	13	wψ	wψ	ADP
cana-5422	411	14	)	)	PUNCT
cana-5422	411	15	−	−	PROPN
cana-5422	411	16	1	1	NUM
cana-5422	411	17	2	2	NUM
cana-5422	411	18	{	{	PUNCT
cana-5422	411	19	f	f	PROPN
cana-5422	411	20	(	(	PUNCT
cana-5422	411	21	∑3	∑3	PROPN
cana-5422	411	22	ψ=1	ψ=1	PUNCT
cana-5422	411	23	wψ	wψ	ADP
cana-5422	411	24	)	)	PUNCT
cana-5422	412	1	+	+	NOUN
cana-5422	412	2	f	f	X
cana-5422	412	3	(	(	PUNCT
cana-5422	412	4	−∑3	−∑3	PROPN
cana-5422	412	5	ψ=1	ψ=1	PUNCT
cana-5422	412	6	wψ	wψ	ADP
cana-5422	412	7	)	)	PUNCT
cana-5422	412	8	}	}	PUNCT
cana-5422	412	9	+	+	CCONJ
cana-5422	412	10	∑3	∑3	SYM
cana-5422	412	11	ψ=1	ψ=1	X
cana-5422	412	12	{	{	PUNCT
cana-5422	412	13	f	f	X
cana-5422	412	14	(	(	PUNCT
cana-5422	412	15	wψ)−	wψ)−	X
cana-5422	412	16	5	5	NUM
cana-5422	412	17	2	2	NUM
cana-5422	412	18	[	[	PUNCT
cana-5422	412	19	f	f	X
cana-5422	412	20	(	(	PUNCT
cana-5422	412	21	wψ	wψ	ADP
cana-5422	412	22	)	)	PUNCT
cana-5422	412	23	+	+	NOUN
cana-5422	412	24	f	f	X
cana-5422	412	25	(	(	PUNCT
cana-5422	412	26	−wψ	−wψ	NOUN
cana-5422	412	27	)	)	PUNCT
cana-5422	412	28	]	]	PUNCT
cana-5422	412	29	}	}	PUNCT
cana-5422	412	30	,	,	PUNCT
cana-5422	412	31	λ	λ	PROPN
cana-5422	412	32	)	)	PUNCT
cana-5422	412	33	≥	≥	NOUN
cana-5422	412	34	µ′	µ′	PUNCT
cana-5422	412	35	(	(	PUNCT
cana-5422	412	36	δ	δ	PROPN
cana-5422	412	37	∑3	∑3	PROPN
cana-5422	412	38	ψ=1	ψ=1	PUNCT
cana-5422	412	39	∣∣wψ	∣∣wψ	PROPN
cana-5422	412	40	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	412	41	,	,	PUNCT
cana-5422	412	42	λ	λ	PROPN
cana-5422	412	43	)	)	PUNCT
cana-5422	412	44	,	,	PUNCT
cana-5422	412	45	ν	ν	X
cana-5422	412	46	(	(	PUNCT
cana-5422	412	47	f	f	X
cana-5422	412	48	(	(	PUNCT
cana-5422	412	49	3w1	3w1	NUM
cana-5422	412	50	+	+	CCONJ
cana-5422	412	51	w2	w2	NOUN
cana-5422	412	52	+	+	CCONJ
cana-5422	412	53	w3	w3	PROPN
cana-5422	412	54	)	)	PUNCT
cana-5422	413	1	+	+	NOUN
cana-5422	413	2	f	f	X
cana-5422	413	3	(	(	PUNCT
cana-5422	413	4	w1	w1	NOUN
cana-5422	413	5	+	+	CCONJ
cana-5422	413	6	3w2	3w2	NUM
cana-5422	413	7	+	+	CCONJ
cana-5422	413	8	w3	w3	NOUN
cana-5422	413	9	)	)	PUNCT
cana-5422	414	1	+	+	NOUN
cana-5422	414	2	f	f	X
cana-5422	414	3	(	(	PUNCT
cana-5422	414	4	w1	w1	NOUN
cana-5422	414	5	+	+	NOUN
cana-5422	414	6	w2	w2	NOUN
cana-5422	414	7	+	+	CCONJ
cana-5422	414	8	3w3)−	3w3)−	PROPN
cana-5422	414	9	6f	6f	NOUN
cana-5422	414	10	(	(	PUNCT
cana-5422	414	11	∑3	∑3	PROPN
cana-5422	414	12	ψ=1	ψ=1	PRON
cana-5422	414	13	wψ	wψ	ADP
cana-5422	414	14	)	)	PUNCT
cana-5422	414	15	−	−	PROPN
cana-5422	414	16	1	1	NUM
cana-5422	414	17	2	2	NUM
cana-5422	414	18	{	{	PUNCT
cana-5422	414	19	f	f	PROPN
cana-5422	414	20	(	(	PUNCT
cana-5422	414	21	∑3	∑3	PROPN
cana-5422	414	22	ψ=1	ψ=1	PUNCT
cana-5422	414	23	wψ	wψ	ADP
cana-5422	414	24	)	)	PUNCT
cana-5422	415	1	+	+	NOUN
cana-5422	415	2	f	f	X
cana-5422	415	3	(	(	PUNCT
cana-5422	415	4	−∑3	−∑3	PROPN
cana-5422	415	5	ψ=1	ψ=1	PUNCT
cana-5422	415	6	wψ	wψ	ADP
cana-5422	415	7	)	)	PUNCT
cana-5422	415	8	}	}	PUNCT
cana-5422	415	9	+	+	CCONJ
cana-5422	415	10	∑3	∑3	SYM
cana-5422	415	11	ψ=1	ψ=1	X
cana-5422	415	12	{	{	PUNCT
cana-5422	415	13	f	f	X
cana-5422	415	14	(	(	PUNCT
cana-5422	415	15	wψ)−	wψ)−	X
cana-5422	415	16	5	5	NUM
cana-5422	415	17	2	2	NUM
cana-5422	415	18	[	[	PUNCT
cana-5422	415	19	f	f	X
cana-5422	415	20	(	(	PUNCT
cana-5422	415	21	wψ	wψ	ADP
cana-5422	415	22	)	)	PUNCT
cana-5422	415	23	+	+	NOUN
cana-5422	415	24	f	f	X
cana-5422	415	25	(	(	PUNCT
cana-5422	415	26	−wψ	−wψ	NOUN
cana-5422	415	27	)	)	PUNCT
cana-5422	415	28	]	]	PUNCT
cana-5422	415	29	}	}	PUNCT
cana-5422	415	30	,	,	PUNCT
cana-5422	415	31	λ	λ	PROPN
cana-5422	415	32	)	)	PUNCT
cana-5422	415	33	≤	≤	NUM
cana-5422	415	34	ν′	ν′	NOUN
cana-5422	415	35	(	(	PUNCT
cana-5422	415	36	δ	δ	NOUN
cana-5422	415	37	∑3	∑3	PROPN
cana-5422	415	38	ψ=1	ψ=1	PUNCT
cana-5422	415	39	∣∣wψ	∣∣wψ	PROPN
cana-5422	415	40	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	415	41	,	,	PUNCT
cana-5422	415	42	λ	λ	PROPN
cana-5422	415	43	)	)	PUNCT
cana-5422	415	44	,	,	PUNCT
cana-5422	415	45			ADJ
cana-5422	415	46	(	(	PUNCT
cana-5422	415	47	3.3	3.3	NUM
cana-5422	415	48	)	)	PUNCT
cana-5422	415	49	µ	µ	X
cana-5422	415	50	(	(	PUNCT
cana-5422	415	51	f	f	X
cana-5422	415	52	(	(	PUNCT
cana-5422	415	53	3w1	3w1	NUM
cana-5422	415	54	+	+	CCONJ
cana-5422	415	55	w2	w2	NOUN
cana-5422	415	56	+	+	CCONJ
cana-5422	415	57	w3	w3	PROPN
cana-5422	415	58	)	)	PUNCT
cana-5422	416	1	+	+	NOUN
cana-5422	416	2	f	f	X
cana-5422	416	3	(	(	PUNCT
cana-5422	416	4	w1	w1	NOUN
cana-5422	416	5	+	+	CCONJ
cana-5422	416	6	3w2	3w2	NUM
cana-5422	416	7	+	+	CCONJ
cana-5422	416	8	w3	w3	NOUN
cana-5422	416	9	)	)	PUNCT
cana-5422	417	1	+	+	NOUN
cana-5422	417	2	f	f	X
cana-5422	417	3	(	(	PUNCT
cana-5422	417	4	w1	w1	NOUN
cana-5422	417	5	+	+	NOUN
cana-5422	417	6	w2	w2	NOUN
cana-5422	417	7	+	+	CCONJ
cana-5422	417	8	3w3)−	3w3)−	PROPN
cana-5422	417	9	6f	6f	NOUN
cana-5422	417	10	(	(	PUNCT
cana-5422	417	11	∑3	∑3	PROPN
cana-5422	417	12	ψ=1	ψ=1	PRON
cana-5422	417	13	wψ	wψ	ADP
cana-5422	417	14	)	)	PUNCT
cana-5422	417	15	−	−	PROPN
cana-5422	417	16	1	1	NUM
cana-5422	417	17	2	2	NUM
cana-5422	417	18	{	{	PUNCT
cana-5422	417	19	f	f	PROPN
cana-5422	417	20	(	(	PUNCT
cana-5422	417	21	∑3	∑3	PROPN
cana-5422	417	22	ψ=1	ψ=1	PUNCT
cana-5422	417	23	wψ	wψ	ADP
cana-5422	417	24	)	)	PUNCT
cana-5422	418	1	+	+	NOUN
cana-5422	418	2	f	f	X
cana-5422	418	3	(	(	PUNCT
cana-5422	418	4	−∑3	−∑3	PROPN
cana-5422	418	5	ψ=1	ψ=1	PUNCT
cana-5422	418	6	wψ	wψ	ADP
cana-5422	418	7	)	)	PUNCT
cana-5422	418	8	}	}	PUNCT
cana-5422	418	9	+	+	CCONJ
cana-5422	418	10	∑3	∑3	SYM
cana-5422	418	11	ψ=1	ψ=1	X
cana-5422	418	12	{	{	PUNCT
cana-5422	418	13	f	f	X
cana-5422	418	14	(	(	PUNCT
cana-5422	418	15	wψ)−	wψ)−	X
cana-5422	418	16	5	5	NUM
cana-5422	418	17	2	2	NUM
cana-5422	418	18	[	[	PUNCT
cana-5422	418	19	f	f	X
cana-5422	418	20	(	(	PUNCT
cana-5422	418	21	wψ	wψ	ADP
cana-5422	418	22	)	)	PUNCT
cana-5422	418	23	+	+	NOUN
cana-5422	418	24	f	f	X
cana-5422	418	25	(	(	PUNCT
cana-5422	418	26	−wψ	−wψ	NOUN
cana-5422	418	27	)	)	PUNCT
cana-5422	418	28	]	]	PUNCT
cana-5422	418	29	}	}	PUNCT
cana-5422	418	30	,	,	PUNCT
cana-5422	418	31	λ	λ	PROPN
cana-5422	418	32	)	)	PUNCT
cana-5422	418	33	≥	≥	NOUN
cana-5422	418	34	µ′	µ′	PUNCT
cana-5422	418	35	(	(	PUNCT
cana-5422	418	36	δ	δ	PROPN
cana-5422	418	37	∑3	∑3	PROPN
cana-5422	418	38	ψ=1	ψ=1	X
cana-5422	418	39	∣∣wψ	∣∣wψ	PROPN
cana-5422	418	40	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	418	41	,	,	PUNCT
cana-5422	418	42	λ	λ	PROPN
cana-5422	418	43	)	)	PUNCT
cana-5422	418	44	,	,	PUNCT
cana-5422	418	45	ν	ν	X
cana-5422	418	46	(	(	PUNCT
cana-5422	418	47	f	f	X
cana-5422	418	48	(	(	PUNCT
cana-5422	418	49	3w1	3w1	NUM
cana-5422	418	50	+	+	CCONJ
cana-5422	418	51	w2	w2	NOUN
cana-5422	418	52	+	+	CCONJ
cana-5422	418	53	w3	w3	PROPN
cana-5422	418	54	)	)	PUNCT
cana-5422	419	1	+	+	NOUN
cana-5422	419	2	f	f	X
cana-5422	419	3	(	(	PUNCT
cana-5422	419	4	w1	w1	NOUN
cana-5422	419	5	+	+	CCONJ
cana-5422	419	6	3w2	3w2	NUM
cana-5422	419	7	+	+	CCONJ
cana-5422	419	8	w3	w3	NOUN
cana-5422	419	9	)	)	PUNCT
cana-5422	420	1	+	+	NOUN
cana-5422	420	2	f	f	X
cana-5422	420	3	(	(	PUNCT
cana-5422	420	4	w1	w1	NOUN
cana-5422	420	5	+	+	NOUN
cana-5422	420	6	w2	w2	NOUN
cana-5422	420	7	+	+	CCONJ
cana-5422	420	8	3w3)−	3w3)−	PROPN
cana-5422	420	9	6f	6f	NOUN
cana-5422	420	10	(	(	PUNCT
cana-5422	420	11	∑3	∑3	PROPN
cana-5422	420	12	ψ=1	ψ=1	PRON
cana-5422	420	13	wψ	wψ	ADP
cana-5422	420	14	)	)	PUNCT
cana-5422	420	15	−	−	PROPN
cana-5422	420	16	1	1	NUM
cana-5422	420	17	2	2	NUM
cana-5422	420	18	{	{	PUNCT
cana-5422	420	19	f	f	PROPN
cana-5422	420	20	(	(	PUNCT
cana-5422	420	21	∑3	∑3	PROPN
cana-5422	420	22	ψ=1	ψ=1	PUNCT
cana-5422	420	23	wψ	wψ	ADP
cana-5422	420	24	)	)	PUNCT
cana-5422	421	1	+	+	NOUN
cana-5422	421	2	f	f	X
cana-5422	421	3	(	(	PUNCT
cana-5422	421	4	−∑3	−∑3	PROPN
cana-5422	421	5	ψ=1	ψ=1	PUNCT
cana-5422	421	6	wψ	wψ	ADP
cana-5422	421	7	)	)	PUNCT
cana-5422	421	8	}	}	PUNCT
cana-5422	421	9	+	+	CCONJ
cana-5422	421	10	∑3	∑3	SYM
cana-5422	421	11	ψ=1	ψ=1	X
cana-5422	421	12	{	{	PUNCT
cana-5422	421	13	f	f	X
cana-5422	421	14	(	(	PUNCT
cana-5422	421	15	wψ)−	wψ)−	X
cana-5422	421	16	5	5	NUM
cana-5422	421	17	2	2	NUM
cana-5422	421	18	[	[	PUNCT
cana-5422	421	19	f	f	X
cana-5422	421	20	(	(	PUNCT
cana-5422	421	21	wψ	wψ	ADP
cana-5422	421	22	)	)	PUNCT
cana-5422	421	23	+	+	NOUN
cana-5422	421	24	f	f	X
cana-5422	421	25	(	(	PUNCT
cana-5422	421	26	−wψ	−wψ	NOUN
cana-5422	421	27	)	)	PUNCT
cana-5422	421	28	]	]	PUNCT
cana-5422	421	29	}	}	PUNCT
cana-5422	421	30	,	,	PUNCT
cana-5422	421	31	λ	λ	PROPN
cana-5422	421	32	)	)	PUNCT
cana-5422	421	33	≤	≤	NUM
cana-5422	421	34	ν′	ν′	NOUN
cana-5422	421	35	(	(	PUNCT
cana-5422	421	36	δ	δ	NOUN
cana-5422	421	37	∑3	∑3	PROPN
cana-5422	421	38	ψ=1	ψ=1	X
cana-5422	421	39	∣∣wψ	∣∣wψ	PROPN
cana-5422	421	40	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	421	41	,	,	PUNCT
cana-5422	421	42	λ	λ	PROPN
cana-5422	421	43	)	)	PUNCT
cana-5422	421	44	,	,	PUNCT
cana-5422	421	45			ADJ
cana-5422	421	46	(	(	PUNCT
cana-5422	421	47	3.4	3.4	NUM
cana-5422	421	48	)	)	PUNCT
cana-5422	421	49	µ	µ	X
cana-5422	421	50	(	(	PUNCT
cana-5422	421	51	f	f	X
cana-5422	421	52	(	(	PUNCT
cana-5422	421	53	3w1	3w1	NUM
cana-5422	421	54	+	+	CCONJ
cana-5422	421	55	w2	w2	NOUN
cana-5422	421	56	+	+	CCONJ
cana-5422	421	57	w3	w3	PROPN
cana-5422	421	58	)	)	PUNCT
cana-5422	422	1	+	+	NOUN
cana-5422	422	2	f	f	X
cana-5422	422	3	(	(	PUNCT
cana-5422	422	4	w1	w1	NOUN
cana-5422	422	5	+	+	CCONJ
cana-5422	422	6	3w2	3w2	NUM
cana-5422	422	7	+	+	CCONJ
cana-5422	422	8	w3	w3	NOUN
cana-5422	422	9	)	)	PUNCT
cana-5422	423	1	+	+	NOUN
cana-5422	423	2	f	f	X
cana-5422	423	3	(	(	PUNCT
cana-5422	423	4	w1	w1	NOUN
cana-5422	423	5	+	+	NOUN
cana-5422	423	6	w2	w2	NOUN
cana-5422	423	7	+	+	CCONJ
cana-5422	423	8	3w3)−	3w3)−	PROPN
cana-5422	423	9	6f	6f	NOUN
cana-5422	423	10	(	(	PUNCT
cana-5422	423	11	∑3	∑3	PROPN
cana-5422	423	12	ψ=1	ψ=1	PRON
cana-5422	423	13	wψ	wψ	ADP
cana-5422	423	14	)	)	PUNCT
cana-5422	423	15	−	−	PROPN
cana-5422	423	16	1	1	NUM
cana-5422	423	17	2	2	NUM
cana-5422	423	18	{	{	PUNCT
cana-5422	423	19	f	f	PROPN
cana-5422	423	20	(	(	PUNCT
cana-5422	423	21	∑3	∑3	PROPN
cana-5422	423	22	ψ=1	ψ=1	PUNCT
cana-5422	423	23	wψ	wψ	ADP
cana-5422	423	24	)	)	PUNCT
cana-5422	424	1	+	+	NOUN
cana-5422	424	2	f	f	X
cana-5422	424	3	(	(	PUNCT
cana-5422	424	4	−∑3	−∑3	PROPN
cana-5422	424	5	ψ=1	ψ=1	PUNCT
cana-5422	424	6	wψ	wψ	ADP
cana-5422	424	7	)	)	PUNCT
cana-5422	424	8	}	}	PUNCT
cana-5422	424	9	+	+	CCONJ
cana-5422	424	10	∑3	∑3	SYM
cana-5422	424	11	ψ=1	ψ=1	X
cana-5422	424	12	{	{	PUNCT
cana-5422	424	13	f	f	X
cana-5422	424	14	(	(	PUNCT
cana-5422	424	15	wψ)−	wψ)−	X
cana-5422	424	16	5	5	NUM
cana-5422	424	17	2	2	NUM
cana-5422	424	18	[	[	PUNCT
cana-5422	424	19	f	f	X
cana-5422	424	20	(	(	PUNCT
cana-5422	424	21	wψ	wψ	ADP
cana-5422	424	22	)	)	PUNCT
cana-5422	425	1	+	+	NOUN
cana-5422	425	2	f	f	X
cana-5422	425	3	(	(	PUNCT
cana-5422	425	4	−wψ	−wψ	NOUN
cana-5422	425	5	)	)	PUNCT
cana-5422	425	6	]	]	PUNCT
cana-5422	425	7	}	}	PUNCT
cana-5422	425	8	,	,	PUNCT
cana-5422	425	9	λ	λ	PROPN
cana-5422	425	10	)	)	PUNCT
cana-5422	425	11	≥	≥	NOUN
cana-5422	425	12	µ′	µ′	PUNCT
cana-5422	425	13	(	(	PUNCT
cana-5422	425	14	δ	δ	PROPN
cana-5422	425	15	∏3	∏3	NOUN
cana-5422	425	16	ψ=1	ψ=1	PUNCT
cana-5422	426	1	∣∣wψ	∣∣wψ	PROPN
cana-5422	426	2	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	426	3	,	,	PUNCT
cana-5422	426	4	λ	λ	PROPN
cana-5422	426	5	)	)	PUNCT
cana-5422	426	6	,	,	PUNCT
cana-5422	426	7	ν	ν	X
cana-5422	426	8	(	(	PUNCT
cana-5422	426	9	f	f	X
cana-5422	426	10	(	(	PUNCT
cana-5422	426	11	3w1	3w1	NUM
cana-5422	426	12	+	+	CCONJ
cana-5422	426	13	w2	w2	NOUN
cana-5422	426	14	+	+	CCONJ
cana-5422	426	15	w3	w3	PROPN
cana-5422	426	16	)	)	PUNCT
cana-5422	427	1	+	+	NOUN
cana-5422	427	2	f	f	X
cana-5422	427	3	(	(	PUNCT
cana-5422	427	4	w1	w1	NOUN
cana-5422	427	5	+	+	CCONJ
cana-5422	427	6	3w2	3w2	NUM
cana-5422	427	7	+	+	CCONJ
cana-5422	427	8	w3	w3	NOUN
cana-5422	427	9	)	)	PUNCT
cana-5422	428	1	+	+	NOUN
cana-5422	428	2	f	f	X
cana-5422	428	3	(	(	PUNCT
cana-5422	428	4	w1	w1	NOUN
cana-5422	428	5	+	+	NOUN
cana-5422	428	6	w2	w2	NOUN
cana-5422	428	7	+	+	CCONJ
cana-5422	428	8	3w3)−	3w3)−	PROPN
cana-5422	428	9	6f	6f	NOUN
cana-5422	428	10	(	(	PUNCT
cana-5422	428	11	∑3	∑3	PROPN
cana-5422	428	12	ψ=1	ψ=1	PRON
cana-5422	428	13	wψ	wψ	ADP
cana-5422	428	14	)	)	PUNCT
cana-5422	428	15	−	−	PROPN
cana-5422	428	16	1	1	NUM
cana-5422	428	17	2	2	NUM
cana-5422	428	18	{	{	PUNCT
cana-5422	428	19	f	f	PROPN
cana-5422	428	20	(	(	PUNCT
cana-5422	428	21	∑3	∑3	PROPN
cana-5422	428	22	ψ=1	ψ=1	PUNCT
cana-5422	428	23	wψ	wψ	ADP
cana-5422	428	24	)	)	PUNCT
cana-5422	429	1	+	+	NOUN
cana-5422	429	2	f	f	X
cana-5422	429	3	(	(	PUNCT
cana-5422	429	4	−∑3	−∑3	PROPN
cana-5422	429	5	ψ=1	ψ=1	PUNCT
cana-5422	429	6	wψ	wψ	ADP
cana-5422	429	7	)	)	PUNCT
cana-5422	429	8	}	}	PUNCT
cana-5422	429	9	+	+	CCONJ
cana-5422	429	10	∑3	∑3	SYM
cana-5422	429	11	ψ=1	ψ=1	X
cana-5422	429	12	{	{	PUNCT
cana-5422	429	13	f	f	X
cana-5422	429	14	(	(	PUNCT
cana-5422	429	15	wψ)−	wψ)−	X
cana-5422	429	16	5	5	NUM
cana-5422	429	17	2	2	NUM
cana-5422	429	18	[	[	PUNCT
cana-5422	429	19	f	f	X
cana-5422	429	20	(	(	PUNCT
cana-5422	429	21	wψ	wψ	ADP
cana-5422	429	22	)	)	PUNCT
cana-5422	429	23	+	+	NOUN
cana-5422	429	24	f	f	X
cana-5422	429	25	(	(	PUNCT
cana-5422	429	26	−wψ	−wψ	NOUN
cana-5422	429	27	)	)	PUNCT
cana-5422	429	28	]	]	PUNCT
cana-5422	429	29	}	}	PUNCT
cana-5422	429	30	,	,	PUNCT
cana-5422	429	31	λ	λ	PROPN
cana-5422	429	32	)	)	PUNCT
cana-5422	429	33	≤	≤	NUM
cana-5422	429	34	ν′	ν′	NOUN
cana-5422	429	35	(	(	PUNCT
cana-5422	429	36	δ	δ	PROPN
cana-5422	429	37	∏3	∏3	NOUN
cana-5422	429	38	ψ=1	ψ=1	PUNCT
cana-5422	430	1	∣∣wψ	∣∣wψ	PROPN
cana-5422	430	2	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	430	3	,	,	PUNCT
cana-5422	430	4	λ	λ	PROPN
cana-5422	430	5	)	)	PUNCT
cana-5422	430	6	,	,	PUNCT
cana-5422	430	7			ADJ
cana-5422	430	8	(	(	PUNCT
cana-5422	430	9	3.5	3.5	NUM
cana-5422	430	10	)	)	PUNCT
cana-5422	430	11	µ	µ	X
cana-5422	430	12	(	(	PUNCT
cana-5422	430	13	f	f	X
cana-5422	430	14	(	(	PUNCT
cana-5422	430	15	3w1	3w1	NUM
cana-5422	430	16	+	+	CCONJ
cana-5422	430	17	w2	w2	NOUN
cana-5422	430	18	+	+	CCONJ
cana-5422	430	19	w3	w3	PROPN
cana-5422	430	20	)	)	PUNCT
cana-5422	431	1	+	+	NOUN
cana-5422	431	2	f	f	X
cana-5422	431	3	(	(	PUNCT
cana-5422	431	4	w1	w1	NOUN
cana-5422	431	5	+	+	CCONJ
cana-5422	431	6	3w2	3w2	NUM
cana-5422	431	7	+	+	CCONJ
cana-5422	431	8	w3	w3	NOUN
cana-5422	431	9	)	)	PUNCT
cana-5422	432	1	+	+	NOUN
cana-5422	432	2	f	f	X
cana-5422	432	3	(	(	PUNCT
cana-5422	432	4	w1	w1	NOUN
cana-5422	432	5	+	+	NOUN
cana-5422	432	6	w2	w2	NOUN
cana-5422	432	7	+	+	CCONJ
cana-5422	432	8	3w3)−	3w3)−	PROPN
cana-5422	432	9	6f	6f	NOUN
cana-5422	432	10	(	(	PUNCT
cana-5422	432	11	∑3	∑3	PROPN
cana-5422	432	12	ψ=1	ψ=1	PRON
cana-5422	432	13	wψ	wψ	ADP
cana-5422	432	14	)	)	PUNCT
cana-5422	432	15	−	−	PROPN
cana-5422	432	16	1	1	NUM
cana-5422	432	17	2	2	NUM
cana-5422	432	18	{	{	PUNCT
cana-5422	432	19	f	f	PROPN
cana-5422	432	20	(	(	PUNCT
cana-5422	432	21	∑3	∑3	PROPN
cana-5422	432	22	ψ=1	ψ=1	PUNCT
cana-5422	432	23	wψ	wψ	ADP
cana-5422	432	24	)	)	PUNCT
cana-5422	433	1	+	+	NOUN
cana-5422	433	2	f	f	X
cana-5422	433	3	(	(	PUNCT
cana-5422	433	4	−∑3	−∑3	PROPN
cana-5422	433	5	ψ=1	ψ=1	PUNCT
cana-5422	433	6	wψ	wψ	ADP
cana-5422	433	7	)	)	PUNCT
cana-5422	433	8	}	}	PUNCT
cana-5422	433	9	+	+	CCONJ
cana-5422	433	10	∑3	∑3	SYM
cana-5422	433	11	ψ=1	ψ=1	X
cana-5422	433	12	{	{	PUNCT
cana-5422	433	13	f	f	X
cana-5422	433	14	(	(	PUNCT
cana-5422	433	15	wψ)−	wψ)−	X
cana-5422	433	16	5	5	NUM
cana-5422	433	17	2	2	NUM
cana-5422	433	18	[	[	PUNCT
cana-5422	433	19	f	f	X
cana-5422	433	20	(	(	PUNCT
cana-5422	433	21	wψ	wψ	ADP
cana-5422	433	22	)	)	PUNCT
cana-5422	433	23	+	+	NOUN
cana-5422	433	24	f	f	X
cana-5422	433	25	(	(	PUNCT
cana-5422	433	26	−wψ	−wψ	NOUN
cana-5422	433	27	)	)	PUNCT
cana-5422	433	28	]	]	PUNCT
cana-5422	433	29	}	}	PUNCT
cana-5422	433	30	,	,	PUNCT
cana-5422	433	31	λ	λ	PROPN
cana-5422	433	32	)	)	PUNCT
cana-5422	433	33	≥	≥	NOUN
cana-5422	433	34	µ′	µ′	PUNCT
cana-5422	433	35	(	(	PUNCT
cana-5422	433	36	δ	δ	PROPN
cana-5422	433	37	3	3	NUM
cana-5422	433	38	∏	∏	PROPN
cana-5422	433	39	ψ=1	ψ=1	PUNCT
cana-5422	433	40	∣∣wψ	∣∣wψ	PROPN
cana-5422	433	41	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	433	42	,	,	PUNCT
cana-5422	433	43	λ	λ	PROPN
cana-5422	433	44	)	)	PUNCT
cana-5422	433	45	,	,	PUNCT
cana-5422	433	46	ν	ν	X
cana-5422	433	47	(	(	PUNCT
cana-5422	433	48	f	f	X
cana-5422	433	49	(	(	PUNCT
cana-5422	433	50	3w1	3w1	NUM
cana-5422	433	51	+	+	CCONJ
cana-5422	433	52	w2	w2	NOUN
cana-5422	433	53	+	+	CCONJ
cana-5422	433	54	w3	w3	PROPN
cana-5422	433	55	)	)	PUNCT
cana-5422	434	1	+	+	NOUN
cana-5422	434	2	f	f	X
cana-5422	434	3	(	(	PUNCT
cana-5422	434	4	w1	w1	NOUN
cana-5422	434	5	+	+	CCONJ
cana-5422	434	6	3w2	3w2	NUM
cana-5422	434	7	+	+	CCONJ
cana-5422	434	8	w3	w3	NOUN
cana-5422	434	9	)	)	PUNCT
cana-5422	435	1	+	+	NOUN
cana-5422	435	2	f	f	X
cana-5422	435	3	(	(	PUNCT
cana-5422	435	4	w1	w1	NOUN
cana-5422	435	5	+	+	NOUN
cana-5422	435	6	w2	w2	NOUN
cana-5422	435	7	+	+	CCONJ
cana-5422	435	8	3w3)−	3w3)−	PROPN
cana-5422	435	9	6f	6f	NOUN
cana-5422	435	10	(	(	PUNCT
cana-5422	435	11	∑3	∑3	PROPN
cana-5422	435	12	ψ=1	ψ=1	PRON
cana-5422	435	13	wψ	wψ	ADP
cana-5422	435	14	)	)	PUNCT
cana-5422	435	15	−	−	PROPN
cana-5422	435	16	1	1	NUM
cana-5422	435	17	2	2	NUM
cana-5422	435	18	{	{	PUNCT
cana-5422	435	19	f	f	PROPN
cana-5422	435	20	(	(	PUNCT
cana-5422	435	21	∑3	∑3	PROPN
cana-5422	435	22	ψ=1	ψ=1	PUNCT
cana-5422	435	23	wψ	wψ	ADP
cana-5422	435	24	)	)	PUNCT
cana-5422	436	1	+	+	NOUN
cana-5422	436	2	f	f	X
cana-5422	436	3	(	(	PUNCT
cana-5422	436	4	−∑3	−∑3	PROPN
cana-5422	436	5	ψ=1	ψ=1	PUNCT
cana-5422	436	6	wψ	wψ	ADP
cana-5422	436	7	)	)	PUNCT
cana-5422	436	8	}	}	PUNCT
cana-5422	436	9	+	+	CCONJ
cana-5422	436	10	∑3	∑3	SYM
cana-5422	436	11	ψ=1	ψ=1	X
cana-5422	436	12	{	{	PUNCT
cana-5422	436	13	f	f	X
cana-5422	436	14	(	(	PUNCT
cana-5422	436	15	wψ)−	wψ)−	X
cana-5422	436	16	5	5	NUM
cana-5422	436	17	2	2	NUM
cana-5422	436	18	[	[	PUNCT
cana-5422	436	19	f	f	X
cana-5422	436	20	(	(	PUNCT
cana-5422	436	21	wψ	wψ	ADP
cana-5422	436	22	)	)	PUNCT
cana-5422	436	23	+	+	NOUN
cana-5422	436	24	f	f	X
cana-5422	436	25	(	(	PUNCT
cana-5422	436	26	−wψ	−wψ	NOUN
cana-5422	436	27	)	)	PUNCT
cana-5422	436	28	]	]	PUNCT
cana-5422	436	29	}	}	PUNCT
cana-5422	436	30	,	,	PUNCT
cana-5422	436	31	λ	λ	PROPN
cana-5422	436	32	)	)	PUNCT
cana-5422	436	33	≤	≤	NUM
cana-5422	436	34	ν′	ν′	NOUN
cana-5422	436	35	(	(	PUNCT
cana-5422	436	36	δ	δ	PROPN
cana-5422	436	37	3	3	NUM
cana-5422	436	38	∏	∏	PROPN
cana-5422	436	39	ψ=1	ψ=1	PUNCT
cana-5422	436	40	∣∣wψ	∣∣wψ	PROPN
cana-5422	436	41	∣∣ϕψ	∣∣ϕψ	PROPN
cana-5422	436	42	,	,	PUNCT
cana-5422	436	43	λ	λ	PROPN
cana-5422	436	44	)	)	PUNCT
cana-5422	436	45	,	,	PUNCT
cana-5422	436	46			NOUN
cana-5422	436	47	(	(	PUNCT
cana-5422	436	48	3.6	3.6	NUM
cana-5422	436	49	)	)	PUNCT
cana-5422	436	50	µ	µ	X
cana-5422	436	51	(	(	PUNCT
cana-5422	436	52	f	f	X
cana-5422	436	53	(	(	PUNCT
cana-5422	436	54	3w1	3w1	NUM
cana-5422	436	55	+	+	CCONJ
cana-5422	436	56	w2	w2	NOUN
cana-5422	436	57	+	+	CCONJ
cana-5422	436	58	w3	w3	PROPN
cana-5422	436	59	)	)	PUNCT
cana-5422	437	1	+	+	NOUN
cana-5422	437	2	f	f	X
cana-5422	437	3	(	(	PUNCT
cana-5422	437	4	w1	w1	NOUN
cana-5422	437	5	+	+	CCONJ
cana-5422	437	6	3w2	3w2	NUM
cana-5422	437	7	+	+	CCONJ
cana-5422	437	8	w3	w3	NOUN
cana-5422	437	9	)	)	PUNCT
cana-5422	438	1	+	+	NOUN
cana-5422	438	2	f	f	X
cana-5422	438	3	(	(	PUNCT
cana-5422	438	4	w1	w1	NOUN
cana-5422	438	5	+	+	NOUN
cana-5422	438	6	w2	w2	NOUN
cana-5422	438	7	+	+	CCONJ
cana-5422	438	8	3w3)−	3w3)−	PROPN
cana-5422	438	9	6f	6f	NOUN
cana-5422	438	10	(	(	PUNCT
cana-5422	438	11	∑3	∑3	PROPN
cana-5422	438	12	ψ=1	ψ=1	PRON
cana-5422	438	13	wψ	wψ	ADP
cana-5422	438	14	)	)	PUNCT
cana-5422	438	15	−	−	PROPN
cana-5422	438	16	1	1	NUM
cana-5422	438	17	2	2	NUM
cana-5422	438	18	{	{	PUNCT
cana-5422	438	19	f	f	PROPN
cana-5422	438	20	(	(	PUNCT
cana-5422	438	21	∑3	∑3	PROPN
cana-5422	438	22	ψ=1	ψ=1	PUNCT
cana-5422	438	23	wψ	wψ	ADP
cana-5422	438	24	)	)	PUNCT
cana-5422	439	1	+	+	NOUN
cana-5422	439	2	f	f	X
cana-5422	439	3	(	(	PUNCT
cana-5422	439	4	−∑3	−∑3	PROPN
cana-5422	439	5	ψ=1	ψ=1	PUNCT
cana-5422	439	6	wψ	wψ	ADP
cana-5422	439	7	)	)	PUNCT
cana-5422	439	8	}	}	PUNCT
cana-5422	439	9	+	+	CCONJ
cana-5422	439	10	∑3	∑3	SYM
cana-5422	439	11	ψ=1	ψ=1	X
cana-5422	439	12	{	{	PUNCT
cana-5422	439	13	f	f	X
cana-5422	439	14	(	(	PUNCT
cana-5422	439	15	wψ)−	wψ)−	X
cana-5422	439	16	5	5	NUM
cana-5422	439	17	2	2	NUM
cana-5422	439	18	[	[	PUNCT
cana-5422	439	19	f	f	X
cana-5422	439	20	(	(	PUNCT
cana-5422	439	21	wψ	wψ	ADP
cana-5422	439	22	)	)	PUNCT
cana-5422	439	23	+	+	NOUN
cana-5422	439	24	f	f	X
cana-5422	439	25	(	(	PUNCT
cana-5422	439	26	−wψ	−wψ	NOUN
cana-5422	439	27	)	)	PUNCT
cana-5422	439	28	]	]	PUNCT
cana-5422	439	29	}	}	PUNCT
cana-5422	439	30	,	,	PUNCT
cana-5422	439	31	λ	λ	PROPN
cana-5422	439	32	)	)	PUNCT
cana-5422	439	33	≥	≥	NOUN
cana-5422	439	34	µ′	µ′	PUNCT
cana-5422	439	35	(	(	PUNCT
cana-5422	439	36	δ	δ	PROPN
cana-5422	439	37	{	{	PUNCT
cana-5422	439	38	∑3	∑3	PROPN
cana-5422	439	39	ψ=1	ψ=1	PUNCT
cana-5422	439	40	∣∣wψ	∣∣wψ	PROPN
cana-5422	439	41	∣∣3ϕ	∣∣3ϕ	ADJ
cana-5422	439	42	+	+	PROPN
cana-5422	439	43	∏3	∏3	NOUN
cana-5422	439	44	ψ=1	ψ=1	PUNCT
cana-5422	439	45	∣∣wψ	∣∣wψ	ADJ
cana-5422	439	46	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	439	47	}	}	PUNCT
cana-5422	439	48	,	,	PUNCT
cana-5422	439	49	λ	λ	PROPN
cana-5422	439	50	)	)	PUNCT
cana-5422	439	51	,	,	PUNCT
cana-5422	439	52	ν	ν	X
cana-5422	439	53	(	(	PUNCT
cana-5422	439	54	f	f	X
cana-5422	439	55	(	(	PUNCT
cana-5422	439	56	3w1	3w1	NUM
cana-5422	439	57	+	+	CCONJ
cana-5422	439	58	w2	w2	NOUN
cana-5422	439	59	+	+	CCONJ
cana-5422	439	60	w3	w3	PROPN
cana-5422	439	61	)	)	PUNCT
cana-5422	440	1	+	+	NOUN
cana-5422	440	2	f	f	X
cana-5422	440	3	(	(	PUNCT
cana-5422	440	4	w1	w1	NOUN
cana-5422	440	5	+	+	CCONJ
cana-5422	440	6	3w2	3w2	NUM
cana-5422	440	7	+	+	CCONJ
cana-5422	440	8	w3	w3	NOUN
cana-5422	440	9	)	)	PUNCT
cana-5422	441	1	+	+	NOUN
cana-5422	441	2	f	f	X
cana-5422	441	3	(	(	PUNCT
cana-5422	441	4	w1	w1	NOUN
cana-5422	441	5	+	+	NOUN
cana-5422	441	6	w2	w2	NOUN
cana-5422	441	7	+	+	CCONJ
cana-5422	441	8	3w3)−	3w3)−	PROPN
cana-5422	441	9	6f	6f	NOUN
cana-5422	441	10	(	(	PUNCT
cana-5422	441	11	∑3	∑3	PROPN
cana-5422	441	12	ψ=1	ψ=1	PRON
cana-5422	441	13	wψ	wψ	ADP
cana-5422	441	14	)	)	PUNCT
cana-5422	441	15	−	−	PROPN
cana-5422	441	16	1	1	NUM
cana-5422	441	17	2	2	NUM
cana-5422	441	18	{	{	PUNCT
cana-5422	441	19	f	f	PROPN
cana-5422	441	20	(	(	PUNCT
cana-5422	441	21	∑3	∑3	PROPN
cana-5422	441	22	ψ=1	ψ=1	PUNCT
cana-5422	441	23	wψ	wψ	ADP
cana-5422	441	24	)	)	PUNCT
cana-5422	442	1	+	+	NOUN
cana-5422	442	2	f	f	X
cana-5422	442	3	(	(	PUNCT
cana-5422	442	4	−∑3	−∑3	PROPN
cana-5422	442	5	ψ=1	ψ=1	PUNCT
cana-5422	442	6	wψ	wψ	ADP
cana-5422	442	7	)	)	PUNCT
cana-5422	442	8	}	}	PUNCT
cana-5422	442	9	+	+	CCONJ
cana-5422	442	10	∑3	∑3	SYM
cana-5422	442	11	ψ=1	ψ=1	X
cana-5422	442	12	{	{	PUNCT
cana-5422	442	13	f	f	X
cana-5422	442	14	(	(	PUNCT
cana-5422	442	15	wψ)−	wψ)−	X
cana-5422	442	16	5	5	NUM
cana-5422	442	17	2	2	NUM
cana-5422	442	18	[	[	PUNCT
cana-5422	442	19	f	f	X
cana-5422	442	20	(	(	PUNCT
cana-5422	442	21	wψ	wψ	ADP
cana-5422	442	22	)	)	PUNCT
cana-5422	442	23	+	+	NOUN
cana-5422	442	24	f	f	X
cana-5422	442	25	(	(	PUNCT
cana-5422	442	26	−wψ	−wψ	NOUN
cana-5422	442	27	)	)	PUNCT
cana-5422	442	28	]	]	PUNCT
cana-5422	442	29	}	}	PUNCT
cana-5422	442	30	,	,	PUNCT
cana-5422	442	31	λ	λ	PROPN
cana-5422	442	32	)	)	PUNCT
cana-5422	442	33	≤	≤	NUM
cana-5422	442	34	ν′	ν′	NOUN
cana-5422	442	35	(	(	PUNCT
cana-5422	442	36	δ	δ	PROPN
cana-5422	442	37	{	{	PUNCT
cana-5422	442	38	∑3	∑3	PROPN
cana-5422	442	39	ψ=1	ψ=1	PUNCT
cana-5422	442	40	∣∣wψ	∣∣wψ	PROPN
cana-5422	442	41	∣∣3ϕ	∣∣3ϕ	ADJ
cana-5422	442	42	+	+	PROPN
cana-5422	442	43	∏3	∏3	NOUN
cana-5422	442	44	ψ=1	ψ=1	PUNCT
cana-5422	442	45	∣∣wψ	∣∣wψ	ADJ
cana-5422	442	46	∣∣ϕ	∣∣ϕ	NOUN
cana-5422	442	47	}	}	PUNCT
cana-5422	442	48	,	,	PUNCT
cana-5422	442	49	λ	λ	PROPN
cana-5422	442	50	)	)	PUNCT
cana-5422	442	51	,	,	PUNCT
cana-5422	442	52			NOUN
cana-5422	442	53	(	(	PUNCT
cana-5422	442	54	3.7	3.7	NUM
cana-5422	442	55	)	)	PUNCT
cana-5422	442	56	for	for	ADP
cana-5422	442	57	all	all	DET
cana-5422	442	58	w1	w1	NOUN
cana-5422	442	59	,	,	PUNCT
cana-5422	442	60	w2	w2	NOUN
cana-5422	442	61	,	,	PUNCT
cana-5422	442	62	w3	w3	PROPN
cana-5422	442	63	∈	∈	PROPN
cana-5422	442	64	w1	w1	NOUN
cana-5422	442	65	and	and	CCONJ
cana-5422	442	66	all	all	DET
cana-5422	442	67	λ	λ	X
cana-5422	442	68	>	>	X
cana-5422	442	69	0	0	PUNCT
cana-5422	442	70	with	with	SCONJ
cana-5422	442	71	δ	δ	PROPN
cana-5422	442	72	be	be	AUX
cana-5422	442	73	a	a	DET
cana-5422	442	74	positive	positive	ADJ
cana-5422	442	75	constant	constant	NOUN
cana-5422	442	76	and	and	CCONJ
cana-5422	442	77	ϕ	ϕ	NOUN
cana-5422	442	78	be	be	AUX
cana-5422	442	79	any	any	DET
cana-5422	442	80	real	real	ADJ
cana-5422	442	81	number	number	NOUN
cana-5422	442	82	.	.	PUNCT
cana-5422	443	1	communications	communication	NOUN
cana-5422	443	2	on	on	ADP
cana-5422	443	3	applied	apply	VERB
cana-5422	443	4	nonlinear	nonlinear	ADJ
cana-5422	443	5	analysis	analysis	NOUN
cana-5422	443	6	issn	issn	NOUN
cana-5422	443	7	:	:	PUNCT
cana-5422	443	8	1074	1074	NUM
cana-5422	443	9	-	-	PUNCT
cana-5422	443	10	133x	133x	NUM
cana-5422	443	11	vol	vol	NOUN
cana-5422	443	12	32	32	NUM
cana-5422	443	13	no	no	NOUN
cana-5422	443	14	.	.	PUNCT
cana-5422	444	1	10s(2025	10s(2025	NUM
cana-5422	444	2	)	)	PUNCT
cana-5422	445	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	445	2	2200	2200	NUM
cana-5422	445	3	3.1	3.1	NUM
cana-5422	445	4	.	.	PUNCT
cana-5422	446	1	definitions	definition	NOUN
cana-5422	446	2	and	and	CCONJ
cana-5422	446	3	notations	notation	NOUN
cana-5422	446	4	of	of	ADP
cana-5422	446	5	intuitionistic	intuitionistic	ADJ
cana-5422	446	6	fuzzy	fuzzy	ADJ
cana-5422	446	7	banach	banach	NOUN
cana-5422	446	8	space	space	NOUN
cana-5422	446	9	.	.	PUNCT
cana-5422	447	1	now	now	ADV
cana-5422	447	2	,	,	PUNCT
cana-5422	447	3	we	we	PRON
cana-5422	447	4	recall	recall	VERB
cana-5422	447	5	the	the	DET
cana-5422	447	6	basic	basic	ADJ
cana-5422	447	7	definitions	definition	NOUN
cana-5422	447	8	and	and	CCONJ
cana-5422	447	9	notations	notation	NOUN
cana-5422	447	10	in	in	ADP
cana-5422	447	11	the	the	DET
cana-5422	447	12	setting	setting	NOUN
cana-5422	447	13	of	of	ADP
cana-5422	447	14	intuitionistic	intuitionistic	ADJ
cana-5422	447	15	fuzzy	fuzzy	ADJ
cana-5422	447	16	normed	normed	ADJ
cana-5422	447	17	space	space	NOUN
cana-5422	447	18	given	give	VERB
cana-5422	447	19	in	in	ADP
cana-5422	447	20	[	[	X
cana-5422	447	21	27	27	NUM
cana-5422	447	22	]	]	PUNCT
cana-5422	447	23	.	.	PUNCT
cana-5422	448	1	definition	definition	NOUN
cana-5422	448	2	3.1	3.1	NUM
cana-5422	448	3	.	.	PUNCT
cana-5422	449	1	[	[	X
cana-5422	449	2	27	27	NUM
cana-5422	449	3	]	]	PUNCT
cana-5422	449	4	a	a	DET
cana-5422	449	5	binary	binary	ADJ
cana-5422	449	6	operation	operation	NOUN
cana-5422	449	7	∗	∗	NOUN
cana-5422	449	8	:	:	PUNCT
cana-5422	450	1	[	[	X
cana-5422	450	2	0	0	NUM
cana-5422	450	3	,	,	PUNCT
cana-5422	450	4	1]×	1]×	NUM
cana-5422	450	5	[	[	X
cana-5422	450	6	0	0	NUM
cana-5422	450	7	,	,	PUNCT
cana-5422	450	8	1	1	NUM
cana-5422	450	9	]	]	X
cana-5422	450	10	−→	−→	NOUN
cana-5422	450	11	[	[	X
cana-5422	450	12	0	0	NUM
cana-5422	450	13	,	,	PUNCT
cana-5422	450	14	1	1	NUM
cana-5422	450	15	]	]	PUNCT
cana-5422	450	16	is	be	AUX
cana-5422	450	17	said	say	VERB
cana-5422	450	18	to	to	PART
cana-5422	450	19	be	be	AUX
cana-5422	450	20	continuous	continuous	ADJ
cana-5422	450	21	t	t	NOUN
cana-5422	450	22	-	-	PUNCT
cana-5422	450	23	norm	norm	NOUN
cana-5422	450	24	if	if	SCONJ
cana-5422	450	25	∗	∗	NOUN
cana-5422	450	26	satisfies	satisfy	VERB
cana-5422	450	27	the	the	DET
cana-5422	450	28	following	follow	VERB
cana-5422	450	29	conditions	condition	NOUN
cana-5422	450	30	:	:	PUNCT
cana-5422	450	31	(	(	PUNCT
cana-5422	450	32	∗1	∗1	X
cana-5422	450	33	)	)	PUNCT
cana-5422	450	34	∗	∗	NOUN
cana-5422	450	35	is	be	AUX
cana-5422	450	36	commutative	commutative	ADJ
cana-5422	450	37	and	and	CCONJ
cana-5422	450	38	associative	associative	ADJ
cana-5422	450	39	;	;	PUNCT
cana-5422	450	40	(	(	PUNCT
cana-5422	450	41	∗2	∗2	NOUN
cana-5422	450	42	)	)	PUNCT
cana-5422	450	43	∗	∗	NOUN
cana-5422	450	44	is	be	AUX
cana-5422	450	45	continuous	continuous	ADJ
cana-5422	450	46	;	;	PUNCT
cana-5422	450	47	(	(	PUNCT
cana-5422	450	48	∗3	∗3	X
cana-5422	450	49	)	)	PUNCT
cana-5422	450	50	a	a	DET
cana-5422	450	51	∗	∗	NOUN
cana-5422	450	52	1	1	NUM
cana-5422	450	53	=	=	NOUN
cana-5422	450	54	a	a	PRON
cana-5422	450	55	for	for	ADP
cana-5422	450	56	all	all	DET
cana-5422	450	57	a	a	DET
cana-5422	450	58	∈	∈	NOUN
cana-5422	451	1	[	[	X
cana-5422	451	2	0	0	NUM
cana-5422	451	3	,	,	PUNCT
cana-5422	451	4	1	1	NUM
cana-5422	451	5	]	]	PUNCT
cana-5422	451	6	;	;	PUNCT
cana-5422	451	7	(	(	PUNCT
cana-5422	451	8	∗4	∗4	NOUN
cana-5422	451	9	)	)	PUNCT
cana-5422	451	10	a	a	DET
cana-5422	451	11	∗	∗	NOUN
cana-5422	451	12	b	b	NOUN
cana-5422	451	13	≤	≤	NOUN
cana-5422	451	14	c	c	NOUN
cana-5422	451	15	∗	∗	NOUN
cana-5422	451	16	d	d	NOUN
cana-5422	451	17	whenever	whenever	SCONJ
cana-5422	451	18	a	a	DET
cana-5422	451	19	≤	≤	PROPN
cana-5422	451	20	c	c	NOUN
cana-5422	451	21	and	and	CCONJ
cana-5422	451	22	b	b	NOUN
cana-5422	451	23	≤	≤	NUM
cana-5422	451	24	d	d	NOUN
cana-5422	451	25	for	for	ADP
cana-5422	451	26	all	all	DET
cana-5422	451	27	a	a	DET
cana-5422	451	28	,	,	PUNCT
cana-5422	451	29	b	b	NOUN
cana-5422	451	30	,	,	PUNCT
cana-5422	451	31	c	c	NOUN
cana-5422	451	32	,	,	PUNCT
cana-5422	451	33	d	d	PROPN
cana-5422	451	34	∈	∈	PROPN
cana-5422	452	1	[	[	X
cana-5422	452	2	0	0	NUM
cana-5422	452	3	,	,	PUNCT
cana-5422	452	4	1	1	NUM
cana-5422	452	5	]	]	PUNCT
cana-5422	452	6	.	.	PUNCT
cana-5422	453	1	definition	definition	NOUN
cana-5422	453	2	3.2	3.2	NUM
cana-5422	453	3	.	.	PUNCT
cana-5422	454	1	[	[	X
cana-5422	454	2	27	27	NUM
cana-5422	454	3	]	]	PUNCT
cana-5422	454	4	a	a	DET
cana-5422	454	5	binary	binary	ADJ
cana-5422	454	6	operation	operation	NOUN
cana-5422	454	7	�	�	PROPN
cana-5422	454	8	:	:	PUNCT
cana-5422	455	1	[	[	X
cana-5422	455	2	0	0	NUM
cana-5422	455	3	,	,	PUNCT
cana-5422	455	4	1	1	NUM
cana-5422	455	5	]	]	SYM
cana-5422	455	6	×	×	NOUN
cana-5422	456	1	[	[	X
cana-5422	456	2	0	0	NUM
cana-5422	456	3	,	,	PUNCT
cana-5422	456	4	1	1	NUM
cana-5422	456	5	]	]	X
cana-5422	456	6	−→	−→	NOUN
cana-5422	456	7	[	[	X
cana-5422	456	8	0	0	NUM
cana-5422	456	9	,	,	PUNCT
cana-5422	456	10	1	1	NUM
cana-5422	456	11	]	]	PUNCT
cana-5422	456	12	is	be	AUX
cana-5422	456	13	said	say	VERB
cana-5422	456	14	to	to	PART
cana-5422	456	15	be	be	AUX
cana-5422	456	16	continuous	continuous	ADJ
cana-5422	456	17	t	t	NOUN
cana-5422	456	18	-	-	PUNCT
cana-5422	456	19	conorm	conorm	NOUN
cana-5422	456	20	if	if	SCONJ
cana-5422	456	21	�	�	PROPN
cana-5422	456	22	satisfies	satisfy	VERB
cana-5422	456	23	the	the	DET
cana-5422	456	24	following	follow	VERB
cana-5422	456	25	conditions	condition	NOUN
cana-5422	456	26	:	:	PUNCT
cana-5422	456	27	(	(	PUNCT
cana-5422	456	28	�	�	NOUN
cana-5422	456	29	1	1	NUM
cana-5422	456	30	)	)	PUNCT
cana-5422	456	31	�	�	PROPN
cana-5422	456	32	is	be	AUX
cana-5422	456	33	commutative	commutative	ADJ
cana-5422	456	34	and	and	CCONJ
cana-5422	456	35	associative	associative	ADJ
cana-5422	456	36	;	;	PUNCT
cana-5422	456	37	(	(	PUNCT
cana-5422	456	38	�	�	NOUN
cana-5422	456	39	2	2	NUM
cana-5422	456	40	)	)	PUNCT
cana-5422	456	41	�	�	PROPN
cana-5422	456	42	is	be	AUX
cana-5422	456	43	continuous	continuous	ADJ
cana-5422	456	44	;	;	PUNCT
cana-5422	456	45	(	(	PUNCT
cana-5422	456	46	�	�	NOUN
cana-5422	456	47	3	3	NUM
cana-5422	456	48	)	)	PUNCT
cana-5422	456	49	a	a	DET
cana-5422	456	50	�	�	PROPN
cana-5422	456	51	0	0	NUM
cana-5422	456	52	=	=	NOUN
cana-5422	456	53	a	a	PRON
cana-5422	456	54	for	for	ADP
cana-5422	456	55	all	all	DET
cana-5422	456	56	a	a	DET
cana-5422	456	57	∈	∈	NOUN
cana-5422	457	1	[	[	X
cana-5422	457	2	0	0	NUM
cana-5422	457	3	,	,	PUNCT
cana-5422	457	4	1	1	NUM
cana-5422	457	5	]	]	PUNCT
cana-5422	457	6	;	;	PUNCT
cana-5422	457	7	(	(	PUNCT
cana-5422	457	8	�	�	NOUN
cana-5422	457	9	4	4	NUM
cana-5422	457	10	)	)	PUNCT
cana-5422	457	11	a	a	DET
cana-5422	457	12	�	�	PROPN
cana-5422	457	13	b	b	PROPN
cana-5422	457	14	≤	≤	PROPN
cana-5422	457	15	c	c	NOUN
cana-5422	457	16	�	�	PROPN
cana-5422	457	17	d	d	PROPN
cana-5422	457	18	whenever	whenever	SCONJ
cana-5422	457	19	a	a	DET
cana-5422	457	20	≤	≤	PROPN
cana-5422	457	21	c	c	NOUN
cana-5422	457	22	and	and	CCONJ
cana-5422	457	23	b	b	NOUN
cana-5422	457	24	≤	≤	NUM
cana-5422	457	25	d	d	NOUN
cana-5422	457	26	for	for	ADP
cana-5422	457	27	all	all	DET
cana-5422	457	28	a	a	DET
cana-5422	457	29	,	,	PUNCT
cana-5422	457	30	b	b	NOUN
cana-5422	457	31	,	,	PUNCT
cana-5422	457	32	c	c	NOUN
cana-5422	457	33	,	,	PUNCT
cana-5422	457	34	d	d	PROPN
cana-5422	457	35	∈	∈	PROPN
cana-5422	458	1	[	[	X
cana-5422	458	2	0	0	NUM
cana-5422	458	3	,	,	PUNCT
cana-5422	458	4	1	1	NUM
cana-5422	458	5	]	]	PUNCT
cana-5422	458	6	.	.	PUNCT
cana-5422	459	1	definition	definition	NOUN
cana-5422	459	2	3.3	3.3	NUM
cana-5422	459	3	.	.	PUNCT
cana-5422	460	1	[	[	X
cana-5422	460	2	27	27	NUM
cana-5422	460	3	]	]	PUNCT
cana-5422	460	4	the	the	DET
cana-5422	460	5	five	five	NUM
cana-5422	460	6	-	-	PUNCT
cana-5422	460	7	tuple	tuple	NOUN
cana-5422	460	8	(	(	PUNCT
cana-5422	460	9	x	x	X
cana-5422	460	10	,	,	PUNCT
cana-5422	460	11	µ	µ	NOUN
cana-5422	460	12	,	,	PUNCT
cana-5422	460	13	ν	ν	NOUN
cana-5422	460	14	,	,	PUNCT
cana-5422	460	15	∗	∗	NOUN
cana-5422	460	16	,	,	PUNCT
cana-5422	460	17	�	�	PROPN
cana-5422	460	18	)	)	PUNCT
cana-5422	460	19	is	be	AUX
cana-5422	460	20	said	say	VERB
cana-5422	460	21	to	to	PART
cana-5422	460	22	be	be	AUX
cana-5422	460	23	an	an	DET
cana-5422	460	24	intuitionistic	intuitionistic	ADJ
cana-5422	460	25	fuzzy	fuzzy	ADJ
cana-5422	460	26	normed	normed	ADJ
cana-5422	460	27	space	space	NOUN
cana-5422	460	28	(	(	PUNCT
cana-5422	460	29	for	for	ADP
cana-5422	460	30	short	short	ADJ
cana-5422	460	31	,	,	PUNCT
cana-5422	460	32	ifns	ifns	NOUN
cana-5422	460	33	)	)	PUNCT
cana-5422	460	34	if	if	SCONJ
cana-5422	460	35	x	x	PRON
cana-5422	460	36	is	be	AUX
cana-5422	460	37	a	a	DET
cana-5422	460	38	vector	vector	NOUN
cana-5422	460	39	space	space	NOUN
cana-5422	460	40	,	,	PUNCT
cana-5422	460	41	∗	∗	PROPN
cana-5422	460	42	is	be	AUX
cana-5422	460	43	a	a	DET
cana-5422	460	44	continuous	continuous	ADJ
cana-5422	460	45	t	t	NOUN
cana-5422	460	46	-	-	PUNCT
cana-5422	460	47	norm	norm	NOUN
cana-5422	460	48	,	,	PUNCT
cana-5422	460	49	�	�	PROPN
cana-5422	460	50	is	be	AUX
cana-5422	460	51	a	a	DET
cana-5422	460	52	continuous	continuous	ADJ
cana-5422	460	53	t−	t−	ADJ
cana-5422	460	54	conorm	conorm	NOUN
cana-5422	460	55	,	,	PUNCT
cana-5422	460	56	and	and	CCONJ
cana-5422	460	57	µ	µ	NOUN
cana-5422	460	58	,	,	PUNCT
cana-5422	460	59	ν	ν	NOUN
cana-5422	460	60	are	be	AUX
cana-5422	460	61	fuzzy	fuzzy	ADJ
cana-5422	460	62	sets	set	NOUN
cana-5422	460	63	on	on	ADP
cana-5422	460	64	x×	x×	PROPN
cana-5422	460	65	(	(	PUNCT
cana-5422	460	66	0	0	NUM
cana-5422	460	67	,	,	PUNCT
cana-5422	460	68	∞	∞	NUM
cana-5422	460	69	)	)	PUNCT
cana-5422	460	70	satisfy	satisfy	VERB
cana-5422	460	71	the	the	DET
cana-5422	460	72	following	follow	VERB
cana-5422	460	73	conditions	condition	NOUN
cana-5422	460	74	.	.	PUNCT
cana-5422	461	1	for	for	ADP
cana-5422	461	2	every	every	DET
cana-5422	461	3	x	x	NOUN
cana-5422	461	4	,	,	PUNCT
cana-5422	461	5	y	y	PROPN
cana-5422	461	6	∈	∈	PROPN
cana-5422	461	7	x	x	X
cana-5422	461	8	and	and	CCONJ
cana-5422	461	9	s	s	PROPN
cana-5422	461	10	,	,	PUNCT
cana-5422	461	11	t	t	X
cana-5422	461	12	>	>	X
cana-5422	461	13	0	0	PUNCT
cana-5422	462	1	(	(	PUNCT
cana-5422	462	2	ifn1	ifn1	PROPN
cana-5422	462	3	)	)	PUNCT
cana-5422	462	4	µ(x	µ(x	PROPN
cana-5422	462	5	,	,	PUNCT
cana-5422	462	6	t	t	PROPN
cana-5422	462	7	)	)	PUNCT
cana-5422	462	8	+	+	CCONJ
cana-5422	463	1	ν(x	ν(x	PROPN
cana-5422	463	2	,	,	PUNCT
cana-5422	463	3	t	t	PROPN
cana-5422	463	4	)	)	PUNCT
cana-5422	463	5	≤	≤	NOUN
cana-5422	463	6	1	1	NUM
cana-5422	463	7	;	;	PUNCT
cana-5422	463	8	(	(	PUNCT
cana-5422	463	9	ifn2	ifn2	NOUN
cana-5422	463	10	)	)	PUNCT
cana-5422	463	11	µ(x	µ(x	PROPN
cana-5422	463	12	,	,	PUNCT
cana-5422	463	13	t	t	PROPN
cana-5422	463	14	)	)	PUNCT
cana-5422	463	15	>	>	X
cana-5422	463	16	0	0	NUM
cana-5422	463	17	;	;	PUNCT
cana-5422	463	18	(	(	PUNCT
cana-5422	463	19	ifn3	ifn3	NOUN
cana-5422	463	20	)	)	PUNCT
cana-5422	463	21	µ(x	µ(x	PROPN
cana-5422	463	22	,	,	PUNCT
cana-5422	463	23	t	t	NOUN
cana-5422	463	24	)	)	PUNCT
cana-5422	463	25	=	=	SYM
cana-5422	463	26	1	1	X
cana-5422	463	27	,	,	PUNCT
cana-5422	463	28	if	if	SCONJ
cana-5422	463	29	and	and	CCONJ
cana-5422	463	30	only	only	ADV
cana-5422	463	31	if	if	SCONJ
cana-5422	463	32	x	x	SYM
cana-5422	463	33	=	=	SYM
cana-5422	463	34	0	0	NUM
cana-5422	463	35	;	;	PUNCT
cana-5422	463	36	(	(	PUNCT
cana-5422	463	37	ifn4	ifn4	NOUN
cana-5422	463	38	)	)	PUNCT
cana-5422	463	39	µ(dx	µ(dx	NOUN
cana-5422	463	40	,	,	PUNCT
cana-5422	463	41	t	t	PROPN
cana-5422	463	42	)	)	PUNCT
cana-5422	463	43	=	=	SYM
cana-5422	463	44	µ	µ	X
cana-5422	463	45	(	(	PUNCT
cana-5422	463	46	x	x	PROPN
cana-5422	463	47	,	,	PUNCT
cana-5422	463	48	t	t	PROPN
cana-5422	463	49	d	d	PROPN
cana-5422	463	50	)	)	PUNCT
cana-5422	463	51	for	for	ADP
cana-5422	463	52	each	each	DET
cana-5422	463	53	d	d	PROPN
cana-5422	463	54	6=	6=	PROPN
cana-5422	463	55	0	0	NUM
cana-5422	463	56	;	;	PUNCT
cana-5422	463	57	(	(	PUNCT
cana-5422	463	58	ifn5	ifn5	NOUN
cana-5422	463	59	)	)	PUNCT
cana-5422	463	60	µ(x	µ(x	PROPN
cana-5422	463	61	,	,	PUNCT
cana-5422	463	62	t	t	NOUN
cana-5422	463	63	)	)	PUNCT
cana-5422	463	64	∗	∗	PROPN
cana-5422	463	65	µ(y	µ(y	PROPN
cana-5422	463	66	,	,	PUNCT
cana-5422	463	67	s	s	NOUN
cana-5422	463	68	)	)	PUNCT
cana-5422	463	69	≤	≤	NOUN
cana-5422	463	70	µ(x	µ(x	ADJ
cana-5422	463	71	+	+	NUM
cana-5422	463	72	y	y	PROPN
cana-5422	463	73	,	,	PUNCT
cana-5422	463	74	t	t	PROPN
cana-5422	463	75	+	+	NUM
cana-5422	463	76	s	s	NOUN
cana-5422	463	77	)	)	PUNCT
cana-5422	463	78	;	;	PUNCT
cana-5422	463	79	(	(	PUNCT
cana-5422	463	80	ifn6	ifn6	PROPN
cana-5422	463	81	)	)	PUNCT
cana-5422	463	82	µ(x	µ(x	PROPN
cana-5422	463	83	,	,	PUNCT
cana-5422	463	84	·	·	PUNCT
cana-5422	463	85	)	)	PUNCT
cana-5422	463	86	:	:	PUNCT
cana-5422	463	87	(	(	PUNCT
cana-5422	463	88	0	0	NUM
cana-5422	463	89	,	,	PUNCT
cana-5422	463	90	∞)→	∞)→	PROPN
cana-5422	463	91	[	[	X
cana-5422	463	92	0	0	NUM
cana-5422	463	93	,	,	PUNCT
cana-5422	463	94	1	1	NUM
cana-5422	463	95	]	]	PUNCT
cana-5422	463	96	is	be	AUX
cana-5422	463	97	continuous	continuous	ADJ
cana-5422	463	98	;	;	PUNCT
cana-5422	463	99	(	(	PUNCT
cana-5422	463	100	ifn7	ifn7	PROPN
cana-5422	463	101	)	)	PUNCT
cana-5422	463	102	lim	lim	PROPN
cana-5422	463	103	t→∞	t→∞	PRON
cana-5422	463	104	µ(x	µ(x	PROPN
cana-5422	463	105	,	,	PUNCT
cana-5422	463	106	t	t	NOUN
cana-5422	463	107	)	)	PUNCT
cana-5422	463	108	=	=	SYM
cana-5422	463	109	1	1	NUM
cana-5422	463	110	and	and	CCONJ
cana-5422	463	111	lim	lim	PROPN
cana-5422	463	112	t→0	t→0	PUNCT
cana-5422	463	113	µ(x	µ(x	PROPN
cana-5422	463	114	,	,	PUNCT
cana-5422	463	115	t	t	PROPN
cana-5422	463	116	)	)	PUNCT
cana-5422	463	117	=	=	SYM
cana-5422	463	118	0	0	NUM
cana-5422	463	119	;	;	PUNCT
cana-5422	464	1	(	(	PUNCT
cana-5422	464	2	ifn8	ifn8	PROPN
cana-5422	464	3	)	)	PUNCT
cana-5422	464	4	ν(x	ν(x	PROPN
cana-5422	464	5	,	,	PUNCT
cana-5422	464	6	t	t	PROPN
cana-5422	464	7	)	)	PUNCT
cana-5422	464	8	<	<	X
cana-5422	464	9	1	1	NUM
cana-5422	464	10	;	;	PUNCT
cana-5422	464	11	(	(	PUNCT
cana-5422	464	12	ifn9	ifn9	PROPN
cana-5422	464	13	)	)	PUNCT
cana-5422	464	14	ν(x	ν(x	PROPN
cana-5422	464	15	,	,	PUNCT
cana-5422	464	16	t	t	NOUN
cana-5422	464	17	)	)	PUNCT
cana-5422	464	18	=	=	SYM
cana-5422	465	1	0	0	NUM
cana-5422	465	2	,	,	PUNCT
cana-5422	465	3	if	if	SCONJ
cana-5422	465	4	and	and	CCONJ
cana-5422	465	5	only	only	ADV
cana-5422	465	6	if	if	SCONJ
cana-5422	465	7	x	x	SYM
cana-5422	465	8	=	=	SYM
cana-5422	465	9	0	0	NUM
cana-5422	465	10	;	;	PUNCT
cana-5422	465	11	(	(	PUNCT
cana-5422	465	12	ifn10	ifn10	PROPN
cana-5422	465	13	)	)	PUNCT
cana-5422	465	14	ν(dx	ν(dx	PROPN
cana-5422	465	15	,	,	PUNCT
cana-5422	465	16	t	t	PROPN
cana-5422	465	17	)	)	PUNCT
cana-5422	465	18	=	=	SYM
cana-5422	466	1	ν	ν	NOUN
cana-5422	466	2	(	(	PUNCT
cana-5422	466	3	x	x	PROPN
cana-5422	466	4	,	,	PUNCT
cana-5422	466	5	t	t	PROPN
cana-5422	466	6	d	d	PROPN
cana-5422	466	7	)	)	PUNCT
cana-5422	466	8	for	for	ADP
cana-5422	466	9	each	each	DET
cana-5422	466	10	d	d	PROPN
cana-5422	466	11	6=	6=	PROPN
cana-5422	466	12	0	0	NUM
cana-5422	466	13	;	;	PUNCT
cana-5422	466	14	(	(	PUNCT
cana-5422	466	15	ifn11	ifn11	INTJ
cana-5422	466	16	)	)	PUNCT
cana-5422	466	17	ν(x	ν(x	PROPN
cana-5422	466	18	,	,	PUNCT
cana-5422	466	19	t	t	PROPN
cana-5422	466	20	)	)	PUNCT
cana-5422	466	21	�	�	PROPN
cana-5422	466	22	ν(y	ν(y	PROPN
cana-5422	466	23	,	,	PUNCT
cana-5422	466	24	s	s	NOUN
cana-5422	466	25	)	)	PUNCT
cana-5422	466	26	≥	≥	NOUN
cana-5422	467	1	ν(x	ν(x	PROPN
cana-5422	467	2	+	+	CCONJ
cana-5422	467	3	y	y	PROPN
cana-5422	467	4	,	,	PUNCT
cana-5422	467	5	t	t	PROPN
cana-5422	467	6	+	+	NUM
cana-5422	467	7	s	s	NOUN
cana-5422	467	8	)	)	PUNCT
cana-5422	467	9	;	;	PUNCT
cana-5422	467	10	(	(	PUNCT
cana-5422	467	11	ifn12	ifn12	NOUN
cana-5422	467	12	)	)	PUNCT
cana-5422	467	13	ν(x	ν(x	PROPN
cana-5422	467	14	,	,	PUNCT
cana-5422	467	15	·	·	PUNCT
cana-5422	467	16	)	)	PUNCT
cana-5422	467	17	:	:	PUNCT
cana-5422	467	18	(	(	PUNCT
cana-5422	467	19	0	0	NUM
cana-5422	467	20	,	,	PUNCT
cana-5422	467	21	∞)→	∞)→	PROPN
cana-5422	468	1	[	[	X
cana-5422	468	2	0	0	NUM
cana-5422	468	3	,	,	PUNCT
cana-5422	468	4	1	1	NUM
cana-5422	468	5	]	]	PUNCT
cana-5422	468	6	is	be	AUX
cana-5422	468	7	continuous	continuous	ADJ
cana-5422	468	8	;	;	PUNCT
cana-5422	468	9	(	(	PUNCT
cana-5422	468	10	ifn13	ifn13	PROPN
cana-5422	468	11	)	)	PUNCT
cana-5422	468	12	lim	lim	PROPN
cana-5422	468	13	t→∞	t→∞	NUM
cana-5422	468	14	ν(x	ν(x	PROPN
cana-5422	468	15	,	,	PUNCT
cana-5422	468	16	t	t	PROPN
cana-5422	468	17	)	)	PUNCT
cana-5422	468	18	=	=	SYM
cana-5422	468	19	0	0	NUM
cana-5422	469	1	and	and	CCONJ
cana-5422	469	2	lim	lim	PROPN
cana-5422	469	3	t→0	t→0	PUNCT
cana-5422	469	4	ν(x	ν(x	PROPN
cana-5422	469	5	,	,	PUNCT
cana-5422	469	6	t	t	PROPN
cana-5422	469	7	)	)	PUNCT
cana-5422	469	8	=	=	SYM
cana-5422	470	1	1	1	X
cana-5422	470	2	.	.	PUNCT
cana-5422	470	3	in	in	ADP
cana-5422	470	4	this	this	DET
cana-5422	470	5	case	case	NOUN
cana-5422	470	6	,	,	PUNCT
cana-5422	470	7	(	(	PUNCT
cana-5422	470	8	µ	µ	X
cana-5422	470	9	,	,	PUNCT
cana-5422	470	10	ν	ν	NOUN
cana-5422	470	11	)	)	PUNCT
cana-5422	470	12	is	be	AUX
cana-5422	470	13	called	call	VERB
cana-5422	470	14	an	an	DET
cana-5422	470	15	intuitionistic	intuitionistic	ADJ
cana-5422	470	16	fuzzy	fuzzy	ADJ
cana-5422	470	17	norm	norm	NOUN
cana-5422	470	18	.	.	PUNCT
cana-5422	470	19	example	example	NOUN
cana-5422	470	20	3.4	3.4	NUM
cana-5422	470	21	.	.	PUNCT
cana-5422	471	1	[	[	X
cana-5422	471	2	27	27	NUM
cana-5422	471	3	]	]	X
cana-5422	471	4	let	let	VERB
cana-5422	471	5	(	(	PUNCT
cana-5422	471	6	x	x	NOUN
cana-5422	471	7	,	,	PUNCT
cana-5422	471	8	‖·‖	‖·‖	NUM
cana-5422	471	9	)	)	PUNCT
cana-5422	471	10	be	be	AUX
cana-5422	471	11	a	a	DET
cana-5422	471	12	normed	normed	ADJ
cana-5422	471	13	space	space	NOUN
cana-5422	471	14	.	.	PUNCT
cana-5422	472	1	let	let	VERB
cana-5422	472	2	a	a	DET
cana-5422	472	3	∗	∗	NOUN
cana-5422	472	4	b	b	NOUN
cana-5422	472	5	=	=	SYM
cana-5422	472	6	ab	ab	PROPN
cana-5422	472	7	and	and	CCONJ
cana-5422	472	8	a	a	DET
cana-5422	472	9	�	�	PROPN
cana-5422	472	10	d	d	NOUN
cana-5422	472	11	=	=	SYM
cana-5422	472	12	min	min	PROPN
cana-5422	472	13	{	{	PUNCT
cana-5422	472	14	a	a	DET
cana-5422	472	15	+	+	NOUN
cana-5422	472	16	b	b	NOUN
cana-5422	472	17	,	,	PUNCT
cana-5422	472	18	1	1	NUM
cana-5422	472	19	}	}	PUNCT
cana-5422	472	20	for	for	ADP
cana-5422	472	21	all	all	DET
cana-5422	472	22	a	a	PRON
cana-5422	472	23	,	,	PUNCT
cana-5422	472	24	b	b	X
cana-5422	472	25	∈	∈	PROPN
cana-5422	473	1	[	[	X
cana-5422	473	2	0	0	NUM
cana-5422	473	3	,	,	PUNCT
cana-5422	473	4	1	1	NUM
cana-5422	473	5	]	]	PUNCT
cana-5422	473	6	.	.	PUNCT
cana-5422	474	1	for	for	ADP
cana-5422	474	2	all	all	DET
cana-5422	474	3	x	x	SYM
cana-5422	474	4	∈	∈	ADV
cana-5422	474	5	x	x	X
cana-5422	474	6	and	and	CCONJ
cana-5422	474	7	every	every	DET
cana-5422	474	8	t	t	NOUN
cana-5422	474	9	>	>	X
cana-5422	474	10	0	0	NUM
cana-5422	474	11	,	,	PUNCT
cana-5422	474	12	consider	consider	VERB
cana-5422	474	13	µ(x	µ(x	NOUN
cana-5422	474	14	,	,	PUNCT
cana-5422	474	15	t	t	NOUN
cana-5422	474	16	)	)	PUNCT
cana-5422	474	17	=	=	PRON
cana-5422	474	18	{	{	PUNCT
cana-5422	474	19	t	t	NOUN
cana-5422	474	20	t+‖x‖	t+‖x‖	NUM
cana-5422	475	1	i	i	PRON
cana-5422	475	2	f	f	PROPN
cana-5422	475	3	t	t	PROPN
cana-5422	475	4	>	>	X
cana-5422	475	5	0	0	NUM
cana-5422	475	6	;	;	PUNCT
cana-5422	475	7	0	0	NUM
cana-5422	476	1	i	i	PRON
cana-5422	476	2	f	f	PROPN
cana-5422	476	3	t	t	VERB
cana-5422	476	4	≤	≤	NUM
cana-5422	476	5	0	0	NUM
cana-5422	476	6	;	;	PUNCT
cana-5422	476	7	and	and	CCONJ
cana-5422	476	8	ν(x	ν(x	PROPN
cana-5422	476	9	,	,	PUNCT
cana-5422	476	10	t	t	PROPN
cana-5422	476	11	)	)	PUNCT
cana-5422	476	12	=	=	PRON
cana-5422	476	13	{	{	PUNCT
cana-5422	476	14	‖x‖	‖x‖	PROPN
cana-5422	476	15	t+‖x‖	t+‖x‖	PROPN
cana-5422	477	1	i	i	PRON
cana-5422	477	2	f	f	PROPN
cana-5422	477	3	t	t	PROPN
cana-5422	477	4	>	>	X
cana-5422	477	5	0	0	NUM
cana-5422	477	6	;	;	PUNCT
cana-5422	477	7	0	0	NUM
cana-5422	478	1	i	i	PRON
cana-5422	478	2	f	f	PROPN
cana-5422	478	3	t	t	PROPN
cana-5422	478	4	≤	≤	NUM
cana-5422	478	5	0	0	NUM
cana-5422	478	6	.	.	PUNCT
cana-5422	479	1	then	then	ADV
cana-5422	479	2	(	(	PUNCT
cana-5422	479	3	x	x	X
cana-5422	479	4	,	,	PUNCT
cana-5422	479	5	µ	µ	NOUN
cana-5422	479	6	,	,	PUNCT
cana-5422	479	7	ν	ν	NOUN
cana-5422	479	8	,	,	PUNCT
cana-5422	479	9	∗	∗	NOUN
cana-5422	479	10	,	,	PUNCT
cana-5422	479	11	�	�	PROPN
cana-5422	479	12	)	)	PUNCT
cana-5422	479	13	is	be	AUX
cana-5422	479	14	an	an	DET
cana-5422	479	15	ifn	ifn	NOUN
cana-5422	479	16	-	-	PUNCT
cana-5422	479	17	space	space	NOUN
cana-5422	479	18	.	.	PUNCT
cana-5422	480	1	definition	definition	NOUN
cana-5422	480	2	3.5	3.5	NUM
cana-5422	480	3	.	.	PUNCT
cana-5422	481	1	[	[	X
cana-5422	481	2	27	27	NUM
cana-5422	481	3	]	]	X
cana-5422	481	4	let	let	VERB
cana-5422	481	5	(	(	PUNCT
cana-5422	481	6	x	x	X
cana-5422	481	7	,	,	PUNCT
cana-5422	481	8	µ	µ	NOUN
cana-5422	481	9	,	,	PUNCT
cana-5422	481	10	ν	ν	NOUN
cana-5422	481	11	,	,	PUNCT
cana-5422	481	12	∗	∗	NOUN
cana-5422	481	13	,	,	PUNCT
cana-5422	481	14	�	�	PROPN
cana-5422	481	15	)	)	PUNCT
cana-5422	481	16	be	be	VERB
cana-5422	481	17	an	an	DET
cana-5422	481	18	ifns	ifns	NOUN
cana-5422	481	19	.	.	PUNCT
cana-5422	482	1	then	then	ADV
cana-5422	482	2	,	,	PUNCT
cana-5422	482	3	a	a	DET
cana-5422	482	4	sequence	sequence	NOUN
cana-5422	482	5	x	x	PUNCT
cana-5422	482	6	=	=	SYM
cana-5422	482	7	{	{	PUNCT
cana-5422	482	8	xk	xk	NOUN
cana-5422	482	9	}	}	PUNCT
cana-5422	482	10	is	be	AUX
cana-5422	482	11	said	say	VERB
cana-5422	482	12	to	to	PART
cana-5422	482	13	be	be	AUX
cana-5422	482	14	intuitionistic	intuitionistic	ADJ
cana-5422	482	15	fuzzy	fuzzy	ADJ
cana-5422	482	16	convergent	convergent	NOUN
cana-5422	482	17	to	to	ADP
cana-5422	482	18	a	a	DET
cana-5422	482	19	point	point	NOUN
cana-5422	482	20	l	l	NOUN
cana-5422	482	21	∈	∈	PROPN
cana-5422	482	22	x	x	INTJ
cana-5422	483	1	if	if	SCONJ
cana-5422	483	2	lim	lim	PROPN
cana-5422	483	3	µ(xk	µ(xk	X
cana-5422	483	4	−	−	PROPN
cana-5422	483	5	l	l	PROPN
cana-5422	483	6	,	,	PUNCT
cana-5422	483	7	t	t	PROPN
cana-5422	483	8	)	)	PUNCT
cana-5422	483	9	=	=	SYM
cana-5422	483	10	1	1	NUM
cana-5422	483	11	and	and	CCONJ
cana-5422	483	12	lim	lim	PROPN
cana-5422	483	13	ν(xk	ν(xk	PROPN
cana-5422	483	14	−	−	PROPN
cana-5422	483	15	l	l	PROPN
cana-5422	483	16	,	,	PUNCT
cana-5422	483	17	t	t	PROPN
cana-5422	483	18	)	)	PUNCT
cana-5422	483	19	=	=	SYM
cana-5422	483	20	0	0	NUM
cana-5422	483	21	,	,	PUNCT
cana-5422	483	22	for	for	ADP
cana-5422	483	23	all	all	DET
cana-5422	483	24	ρ	ρ	NOUN
cana-5422	483	25	>	>	X
cana-5422	483	26	0	0	NUM
cana-5422	483	27	.	.	PUNCT
cana-5422	484	1	in	in	ADP
cana-5422	484	2	this	this	DET
cana-5422	484	3	case	case	NOUN
cana-5422	484	4	,	,	PUNCT
cana-5422	484	5	we	we	PRON
cana-5422	484	6	write	write	VERB
cana-5422	484	7	xk	xk	PROPN
cana-5422	484	8	if−→	if−→	PROPN
cana-5422	484	9	l	l	PROPN
cana-5422	484	10	as	as	ADP
cana-5422	484	11	k→	k→	PROPN
cana-5422	484	12	∞.	∞.	PROPN
cana-5422	484	13	definition	definition	NOUN
cana-5422	484	14	3.6	3.6	NUM
cana-5422	484	15	.	.	PUNCT
cana-5422	485	1	[	[	X
cana-5422	485	2	27	27	NUM
cana-5422	485	3	]	]	X
cana-5422	485	4	let	let	VERB
cana-5422	485	5	(	(	PUNCT
cana-5422	485	6	x	x	X
cana-5422	485	7	,	,	PUNCT
cana-5422	485	8	µ	µ	NOUN
cana-5422	485	9	,	,	PUNCT
cana-5422	485	10	ν	ν	NOUN
cana-5422	485	11	,	,	PUNCT
cana-5422	485	12	∗	∗	NOUN
cana-5422	485	13	,	,	PUNCT
cana-5422	485	14	�	�	PROPN
cana-5422	485	15	)	)	PUNCT
cana-5422	485	16	be	be	VERB
cana-5422	485	17	an	an	DET
cana-5422	485	18	ifn	ifn	NOUN
cana-5422	485	19	-	-	PUNCT
cana-5422	485	20	space	space	NOUN
cana-5422	485	21	.	.	PUNCT
cana-5422	486	1	then	then	ADV
cana-5422	486	2	,	,	PUNCT
cana-5422	486	3	x	x	SYM
cana-5422	486	4	=	=	PRON
cana-5422	486	5	{	{	PUNCT
cana-5422	486	6	xk	xk	NOUN
cana-5422	486	7	}	}	PUNCT
cana-5422	486	8	is	be	AUX
cana-5422	486	9	said	say	VERB
cana-5422	486	10	to	to	PART
cana-5422	486	11	be	be	AUX
cana-5422	486	12	intuitionistic	intuitionistic	ADJ
cana-5422	486	13	fuzzy	fuzzy	ADJ
cana-5422	486	14	cauchy	cauchy	ADJ
cana-5422	486	15	sequence	sequence	NOUN
cana-5422	486	16	if	if	SCONJ
cana-5422	486	17	µ	µ	X
cana-5422	486	18	(	(	PUNCT
cana-5422	486	19	xk+p	xk+p	PROPN
cana-5422	486	20	−	−	PROPN
cana-5422	486	21	xk	xk	PROPN
cana-5422	486	22	,	,	PUNCT
cana-5422	486	23	t	t	PROPN
cana-5422	486	24	)	)	PUNCT
cana-5422	486	25	=	=	SYM
cana-5422	486	26	1	1	NUM
cana-5422	486	27	and	and	CCONJ
cana-5422	486	28	ν	ν	X
cana-5422	486	29	(	(	PUNCT
cana-5422	486	30	xk+p	xk+p	PROPN
cana-5422	486	31	−	−	PROPN
cana-5422	486	32	xk	xk	PROPN
cana-5422	486	33	,	,	PUNCT
cana-5422	486	34	t	t	PROPN
cana-5422	486	35	)	)	PUNCT
cana-5422	486	36	=	=	SYM
cana-5422	487	1	0	0	NUM
cana-5422	487	2	,	,	PUNCT
cana-5422	487	3	for	for	ADP
cana-5422	487	4	all	all	DET
cana-5422	487	5	ρ	ρ	PROPN
cana-5422	487	6	>	>	X
cana-5422	487	7	0	0	NUM
cana-5422	487	8	,	,	PUNCT
cana-5422	487	9	and	and	CCONJ
cana-5422	487	10	p	p	X
cana-5422	487	11	=	=	SYM
cana-5422	487	12	1	1	NUM
cana-5422	487	13	,	,	PUNCT
cana-5422	487	14	2	2	NUM
cana-5422	487	15	·	·	PUNCT
cana-5422	487	16	·	·	PUNCT
cana-5422	487	17	·	·	PUNCT
cana-5422	487	18	.	.	PUNCT
cana-5422	488	1	communications	communication	NOUN
cana-5422	488	2	on	on	ADP
cana-5422	488	3	applied	apply	VERB
cana-5422	488	4	nonlinear	nonlinear	ADJ
cana-5422	488	5	analysis	analysis	NOUN
cana-5422	488	6	issn	issn	NOUN
cana-5422	488	7	:	:	PUNCT
cana-5422	488	8	1074	1074	NUM
cana-5422	488	9	-	-	PUNCT
cana-5422	488	10	133x	133x	NUM
cana-5422	488	11	vol	vol	NOUN
cana-5422	488	12	32	32	NUM
cana-5422	488	13	no	no	NOUN
cana-5422	488	14	.	.	PUNCT
cana-5422	489	1	10s(2025	10s(2025	NUM
cana-5422	489	2	)	)	PUNCT
cana-5422	489	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	489	4	2201	2201	NUM
cana-5422	489	5	definition	definition	NOUN
cana-5422	489	6	3.7	3.7	NUM
cana-5422	489	7	.	.	PUNCT
cana-5422	490	1	[	[	X
cana-5422	490	2	27	27	NUM
cana-5422	490	3	]	]	X
cana-5422	490	4	let	let	VERB
cana-5422	490	5	(	(	PUNCT
cana-5422	490	6	x	x	X
cana-5422	490	7	,	,	PUNCT
cana-5422	490	8	µ	µ	NOUN
cana-5422	490	9	,	,	PUNCT
cana-5422	490	10	ν	ν	NOUN
cana-5422	490	11	,	,	PUNCT
cana-5422	490	12	∗	∗	NOUN
cana-5422	490	13	,	,	PUNCT
cana-5422	490	14	�	�	PROPN
cana-5422	490	15	)	)	PUNCT
cana-5422	490	16	be	be	VERB
cana-5422	490	17	an	an	DET
cana-5422	490	18	ifn	ifn	NOUN
cana-5422	490	19	-	-	PUNCT
cana-5422	490	20	space	space	NOUN
cana-5422	490	21	.	.	PUNCT
cana-5422	491	1	then	then	ADV
cana-5422	491	2	(	(	PUNCT
cana-5422	491	3	x	x	X
cana-5422	491	4	,	,	PUNCT
cana-5422	491	5	µ	µ	NOUN
cana-5422	491	6	,	,	PUNCT
cana-5422	491	7	ν	ν	NOUN
cana-5422	491	8	,	,	PUNCT
cana-5422	491	9	∗	∗	NOUN
cana-5422	491	10	,	,	PUNCT
cana-5422	491	11	�	�	PROPN
cana-5422	491	12	)	)	PUNCT
cana-5422	491	13	is	be	AUX
cana-5422	491	14	said	say	VERB
cana-5422	491	15	to	to	PART
cana-5422	491	16	be	be	AUX
cana-5422	491	17	complete	complete	ADJ
cana-5422	491	18	if	if	SCONJ
cana-5422	491	19	every	every	DET
cana-5422	491	20	intuitionistic	intuitionistic	ADJ
cana-5422	491	21	fuzzy	fuzzy	ADJ
cana-5422	491	22	cauchy	cauchy	ADJ
cana-5422	491	23	sequence	sequence	NOUN
cana-5422	491	24	in	in	ADP
cana-5422	491	25	(	(	PUNCT
cana-5422	491	26	x	x	X
cana-5422	491	27	,	,	PUNCT
cana-5422	491	28	µ	µ	NOUN
cana-5422	491	29	,	,	PUNCT
cana-5422	491	30	ν	ν	NOUN
cana-5422	491	31	,	,	PUNCT
cana-5422	491	32	∗	∗	NOUN
cana-5422	491	33	,	,	PUNCT
cana-5422	491	34	�	�	PROPN
cana-5422	491	35	)	)	PUNCT
cana-5422	491	36	is	be	AUX
cana-5422	491	37	intuitionistic	intuitionistic	ADJ
cana-5422	491	38	fuzzy	fuzzy	ADJ
cana-5422	491	39	convergent	convergent	NOUN
cana-5422	491	40	(	(	PUNCT
cana-5422	491	41	x	x	X
cana-5422	491	42	,	,	PUNCT
cana-5422	491	43	µ	µ	NOUN
cana-5422	491	44	,	,	PUNCT
cana-5422	491	45	ν	ν	NOUN
cana-5422	491	46	,	,	PUNCT
cana-5422	491	47	∗	∗	NOUN
cana-5422	491	48	,	,	PUNCT
cana-5422	491	49	�	�	PROPN
cana-5422	491	50	)	)	PUNCT
cana-5422	491	51	.	.	PUNCT
cana-5422	492	1	3.2	3.2	NUM
cana-5422	492	2	.	.	PUNCT
cana-5422	493	1	oddness	oddness	NOUN
cana-5422	493	2	of	of	ADP
cana-5422	493	3	f	f	NOUN
cana-5422	493	4	:	:	PUNCT
cana-5422	493	5	additive	additive	NOUN
cana-5422	493	6	case	case	NOUN
cana-5422	493	7	stability	stability	NOUN
cana-5422	493	8	results	result	VERB
cana-5422	493	9	:	:	PUNCT
cana-5422	493	10	direct	direct	ADJ
cana-5422	493	11	method	method	NOUN
cana-5422	493	12	.	.	PUNCT
cana-5422	494	1	theorem	theorem	VERB
cana-5422	494	2	3.8	3.8	NUM
cana-5422	494	3	.	.	PUNCT
cana-5422	495	1	suppose	suppose	VERB
cana-5422	495	2	that	that	SCONJ
cana-5422	495	3	an	an	DET
cana-5422	495	4	odd	odd	ADJ
cana-5422	495	5	function	function	NOUN
cana-5422	495	6	f	f	NOUN
cana-5422	495	7	:	:	PUNCT
cana-5422	495	8	w1	w1	PROPN
cana-5422	495	9	→	→	SYM
cana-5422	495	10	w2	w2	NOUN
cana-5422	495	11	satisfy	satisfy	VERB
cana-5422	495	12	the	the	DET
cana-5422	495	13	functional	functional	ADJ
cana-5422	495	14	inequality	inequality	NOUN
cana-5422	495	15	(	(	PUNCT
cana-5422	495	16	3.1	3.1	NUM
cana-5422	495	17	)	)	PUNCT
cana-5422	495	18	where	where	SCONJ
cana-5422	495	19	ψ	ψ	X
cana-5422	495	20	:	:	PUNCT
cana-5422	495	21	w3	w3	NOUN
cana-5422	495	22	1	1	NUM
cana-5422	495	23	→	→	SYM
cana-5422	496	1	[	[	X
cana-5422	496	2	0	0	NUM
cana-5422	496	3	,	,	PUNCT
cana-5422	496	4	∞	∞	PROPN
cana-5422	496	5	)	)	PUNCT
cana-5422	496	6	with	with	ADP
cana-5422	496	7	the	the	DET
cana-5422	496	8	conditions	condition	NOUN
cana-5422	496	9	µ′	µ′	PUNCT
cana-5422	496	10	(	(	PUNCT
cana-5422	496	11	ψ	ψ	X
cana-5422	496	12	(	(	PUNCT
cana-5422	496	13	5`mw1	5`mw1	NUM
cana-5422	496	14	,	,	PUNCT
cana-5422	496	15	5`mw2	5`mw2	NUM
cana-5422	496	16	,	,	PUNCT
cana-5422	496	17	5`mw3	5`mw3	NUM
cana-5422	496	18	)	)	PUNCT
cana-5422	496	19	,	,	PUNCT
cana-5422	496	20	λ	λ	PROPN
cana-5422	496	21	)	)	PUNCT
cana-5422	496	22	≥	≥	NOUN
cana-5422	496	23	µ′	µ′	PUNCT
cana-5422	496	24	(	(	PUNCT
cana-5422	496	25	i`mψ	i`mψ	PROPN
cana-5422	496	26	(	(	PUNCT
cana-5422	496	27	w1	w1	NOUN
cana-5422	496	28	,	,	PUNCT
cana-5422	496	29	w2	w2	NOUN
cana-5422	496	30	,	,	PUNCT
cana-5422	496	31	w3	w3	PROPN
cana-5422	496	32	)	)	PUNCT
cana-5422	496	33	,	,	PUNCT
cana-5422	496	34	λ	λ	NOUN
cana-5422	496	35	)	)	PUNCT
cana-5422	496	36	ν′	ν′	NOUN
cana-5422	496	37	(	(	PUNCT
cana-5422	496	38	ψ	ψ	X
cana-5422	496	39	(	(	PUNCT
cana-5422	496	40	5`mw1	5`mw1	NUM
cana-5422	496	41	,	,	PUNCT
cana-5422	496	42	5`mw2	5`mw2	NUM
cana-5422	496	43	,	,	PUNCT
cana-5422	496	44	5`mw3	5`mw3	NUM
cana-5422	496	45	)	)	PUNCT
cana-5422	496	46	,	,	PUNCT
cana-5422	496	47	λ	λ	NOUN
cana-5422	496	48	)	)	PUNCT
cana-5422	496	49	≤	≤	NUM
cana-5422	496	50	ν′	ν′	NOUN
cana-5422	496	51	(	(	PUNCT
cana-5422	496	52	i`mψ	i`mψ	PROPN
cana-5422	496	53	(	(	PUNCT
cana-5422	496	54	w1	w1	NOUN
cana-5422	496	55	,	,	PUNCT
cana-5422	496	56	w2	w2	NOUN
cana-5422	496	57	,	,	PUNCT
cana-5422	496	58	w3	w3	PROPN
cana-5422	496	59	)	)	PUNCT
cana-5422	496	60	,	,	PUNCT
cana-5422	496	61	λ	λ	INTJ
cana-5422	496	62	)	)	PUNCT
cana-5422	496	63			NOUN
cana-5422	496	64	(	(	PUNCT
cana-5422	496	65	3.8	3.8	NUM
cana-5422	496	66	)	)	PUNCT
cana-5422	496	67	and	and	CCONJ
cana-5422	496	68	lim	lim	PROPN
cana-5422	496	69	`	`	PUNCT
cana-5422	496	70	→∞	→∞	X
cana-5422	496	71	µ′	µ′	PUNCT
cana-5422	496	72	(	(	PUNCT
cana-5422	496	73	ψ	ψ	X
cana-5422	496	74	(	(	PUNCT
cana-5422	496	75	5`mw1	5`mw1	NUM
cana-5422	496	76	,	,	PUNCT
cana-5422	496	77	5`mw2	5`mw2	NUM
cana-5422	496	78	,	,	PUNCT
cana-5422	496	79	5`mw3	5`mw3	NUM
cana-5422	496	80	)	)	PUNCT
cana-5422	496	81	,	,	PUNCT
cana-5422	496	82	5`mλ	5`mλ	NUM
cana-5422	496	83	)	)	PUNCT
cana-5422	496	84	=	=	SYM
cana-5422	497	1	1	1	NUM
cana-5422	497	2	lim	lim	NOUN
cana-5422	497	3	`	`	PUNCT
cana-5422	497	4	→∞	→∞	X
cana-5422	497	5	ν′	ν′	NOUN
cana-5422	497	6	(	(	PUNCT
cana-5422	497	7	ψ	ψ	X
cana-5422	497	8	(	(	PUNCT
cana-5422	497	9	5`mw1	5`mw1	NUM
cana-5422	497	10	,	,	PUNCT
cana-5422	497	11	5`mw2	5`mw2	NUM
cana-5422	497	12	,	,	PUNCT
cana-5422	497	13	5`mw3	5`mw3	NUM
cana-5422	497	14	)	)	PUNCT
cana-5422	497	15	,	,	PUNCT
cana-5422	497	16	5`mλ	5`mλ	NUM
cana-5422	497	17	)	)	PUNCT
cana-5422	497	18	=	=	SYM
cana-5422	497	19	0	0	NUM
cana-5422	498	1			NOUN
cana-5422	498	2	(	(	PUNCT
cana-5422	498	3	3.9	3.9	NUM
cana-5422	498	4	)	)	PUNCT
cana-5422	498	5	for	for	ADP
cana-5422	498	6	all	all	DET
cana-5422	498	7	w1	w1	NOUN
cana-5422	498	8	,	,	PUNCT
cana-5422	498	9	w2	w2	NOUN
cana-5422	498	10	,	,	PUNCT
cana-5422	498	11	w3	w3	PROPN
cana-5422	498	12	∈	∈	PROPN
cana-5422	498	13	w1	w1	NOUN
cana-5422	498	14	and	and	CCONJ
cana-5422	498	15	all	all	DET
cana-5422	498	16	λ	λ	X
cana-5422	498	17	>	>	X
cana-5422	498	18	0	0	PUNCT
cana-5422	498	19	with	with	ADP
cana-5422	498	20	m	m	NOUN
cana-5422	498	21	=	=	SYM
cana-5422	498	22	±1	±1	ADJ
cana-5422	498	23	and	and	CCONJ
cana-5422	498	24	0	0	NUM
cana-5422	498	25	<	<	X
cana-5422	499	1	(	(	PUNCT
cana-5422	499	2	i	i	NOUN
cana-5422	499	3	5	5	NUM
cana-5422	499	4	)	)	PUNCT
cana-5422	499	5	µ	µ	X
cana-5422	499	6	<	<	X
cana-5422	499	7	1	1	NUM
cana-5422	499	8	.	.	PUNCT
cana-5422	500	1	then	then	ADV
cana-5422	500	2	there	there	PRON
cana-5422	500	3	exists	exist	VERB
cana-5422	500	4	a	a	DET
cana-5422	500	5	unique	unique	ADJ
cana-5422	500	6	additive	additive	ADJ
cana-5422	500	7	mapping	mapping	NOUN
cana-5422	500	8	a(w1	a(w1	NOUN
cana-5422	500	9	)	)	PUNCT
cana-5422	500	10	:	:	PUNCT
cana-5422	500	11	w1	w1	PROPN
cana-5422	500	12	→w2	→w2	NOUN
cana-5422	500	13	which	which	PRON
cana-5422	500	14	satisfies	satisfy	VERB
cana-5422	500	15	(	(	PUNCT
cana-5422	500	16	1.7	1.7	NUM
cana-5422	500	17	)	)	PUNCT
cana-5422	500	18	and	and	CCONJ
cana-5422	500	19	the	the	DET
cana-5422	500	20	functional	functional	ADJ
cana-5422	500	21	inequality	inequality	NOUN
cana-5422	500	22	µ	µ	X
cana-5422	500	23	(	(	PUNCT
cana-5422	500	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	500	25	(	(	PUNCT
cana-5422	500	26	w1	w1	NOUN
cana-5422	500	27	)	)	PUNCT
cana-5422	500	28	,	,	PUNCT
cana-5422	500	29	λ	λ	X
cana-5422	500	30	)	)	PUNCT
cana-5422	500	31	≥	≥	NOUN
cana-5422	500	32	µ′	µ′	PUNCT
cana-5422	500	33	(	(	PUNCT
cana-5422	500	34	ψa	ψa	X
cana-5422	500	35	(	(	PUNCT
cana-5422	500	36	w1	w1	NOUN
cana-5422	500	37	)	)	PUNCT
cana-5422	500	38	,	,	PUNCT
cana-5422	500	39	3λ	3λ	NUM
cana-5422	500	40	4	4	NUM
cana-5422	500	41	|5−	|5−	PROPN
cana-5422	500	42	i|	i|	PROPN
cana-5422	500	43	)	)	PUNCT
cana-5422	501	1	=	=	PUNCT
cana-5422	501	2	µ′	µ′	NOUN
cana-5422	501	3	(	(	PUNCT
cana-5422	501	4	ψ	ψ	X
cana-5422	501	5	(	(	PUNCT
cana-5422	501	6	w1	w1	NOUN
cana-5422	501	7	,	,	PUNCT
cana-5422	501	8	w1	w1	NOUN
cana-5422	501	9	,	,	PUNCT
cana-5422	501	10	w1	w1	NOUN
cana-5422	501	11	)	)	PUNCT
cana-5422	501	12	,	,	PUNCT
cana-5422	501	13	3λ	3λ	NUM
cana-5422	501	14	4	4	NUM
cana-5422	501	15	|5−	|5−	PROPN
cana-5422	501	16	i|	i|	PROPN
cana-5422	501	17	)	)	PUNCT
cana-5422	501	18	∗	∗	NOUN
cana-5422	501	19	µ′	µ′	PUNCT
cana-5422	501	20	(	(	PUNCT
cana-5422	501	21	ψ	ψ	X
cana-5422	501	22	(	(	PUNCT
cana-5422	501	23	w1	w1	NOUN
cana-5422	501	24	,	,	PUNCT
cana-5422	501	25	w1,−w1	w1,−w1	NUM
cana-5422	501	26	)	)	PUNCT
cana-5422	501	27	,	,	PUNCT
cana-5422	501	28	3λ	3λ	NUM
cana-5422	501	29	4	4	NUM
cana-5422	501	30	|5−	|5−	PROPN
cana-5422	501	31	i|	i|	PROPN
cana-5422	501	32	)	)	PUNCT
cana-5422	501	33	ν	ν	NOUN
cana-5422	501	34	(	(	PUNCT
cana-5422	501	35	a(w1)−f	a(w1)−f	PROPN
cana-5422	501	36	(	(	PUNCT
cana-5422	501	37	w1	w1	NOUN
cana-5422	501	38	)	)	PUNCT
cana-5422	501	39	,	,	PUNCT
cana-5422	501	40	λ	λ	NOUN
cana-5422	501	41	)	)	PUNCT
cana-5422	501	42	≤	≤	NUM
cana-5422	501	43	ν′	ν′	NOUN
cana-5422	501	44	(	(	PUNCT
cana-5422	501	45	ψa	ψa	X
cana-5422	501	46	(	(	PUNCT
cana-5422	501	47	w1	w1	NOUN
cana-5422	501	48	)	)	PUNCT
cana-5422	501	49	,	,	PUNCT
cana-5422	501	50	3λ	3λ	NUM
cana-5422	501	51	4	4	NUM
cana-5422	501	52	(	(	PUNCT
cana-5422	501	53	5−	5−	NUM
cana-5422	501	54	i	i	NOUN
cana-5422	501	55	)	)	PUNCT
cana-5422	501	56	)	)	PUNCT
cana-5422	502	1	=	=	SYM
cana-5422	502	2	ν′	ν′	NOUN
cana-5422	502	3	(	(	PUNCT
cana-5422	502	4	ψ	ψ	X
cana-5422	502	5	(	(	PUNCT
cana-5422	502	6	w1	w1	NOUN
cana-5422	502	7	,	,	PUNCT
cana-5422	502	8	w1	w1	NOUN
cana-5422	502	9	,	,	PUNCT
cana-5422	502	10	w1	w1	NOUN
cana-5422	502	11	)	)	PUNCT
cana-5422	502	12	,	,	PUNCT
cana-5422	502	13	3λ	3λ	NUM
cana-5422	502	14	4	4	NUM
cana-5422	502	15	(	(	PUNCT
cana-5422	502	16	5−	5−	NUM
cana-5422	502	17	i	i	NOUN
cana-5422	502	18	)	)	PUNCT
cana-5422	502	19	)	)	PUNCT
cana-5422	502	20	�	�	PROPN
cana-5422	502	21	ν′	ν′	NOUN
cana-5422	502	22	(	(	PUNCT
cana-5422	502	23	ψ	ψ	X
cana-5422	502	24	(	(	PUNCT
cana-5422	502	25	w1	w1	NOUN
cana-5422	502	26	,	,	PUNCT
cana-5422	502	27	w1,−w1	w1,−w1	NUM
cana-5422	502	28	)	)	PUNCT
cana-5422	502	29	,	,	PUNCT
cana-5422	502	30	3λ	3λ	NUM
cana-5422	502	31	4	4	NUM
cana-5422	502	32	(	(	PUNCT
cana-5422	502	33	5−	5−	NUM
cana-5422	502	34	i	i	NOUN
cana-5422	502	35	)	)	PUNCT
cana-5422	502	36	)	)	PUNCT
cana-5422	502	37			NOUN
cana-5422	502	38	(	(	PUNCT
cana-5422	502	39	3.10	3.10	NUM
cana-5422	502	40	)	)	PUNCT
cana-5422	502	41	and	and	CCONJ
cana-5422	502	42	the	the	DET
cana-5422	502	43	mapping	mapping	NOUN
cana-5422	502	44	a(w1	a(w1	NOUN
cana-5422	502	45	)	)	PUNCT
cana-5422	502	46	is	be	AUX
cana-5422	502	47	obtained	obtain	VERB
cana-5422	502	48	by	by	ADP
cana-5422	502	49	lim	lim	PROPN
cana-5422	502	50	`	`	PUNCT
cana-5422	502	51	→∞	→∞	PROPN
cana-5422	502	52	µ	µ	X
cana-5422	502	53	(	(	PUNCT
cana-5422	502	54	1	1	NUM
cana-5422	502	55	5`mf	5`mf	NUM
cana-5422	502	56	(	(	PUNCT
cana-5422	502	57	5`mw1	5`mw1	NUM
cana-5422	502	58	)	)	PUNCT
cana-5422	502	59	−a(w1	−a(w1	PROPN
cana-5422	502	60	)	)	PUNCT
cana-5422	502	61	,	,	PUNCT
cana-5422	502	62	λ	λ	NOUN
cana-5422	502	63	)	)	PUNCT
cana-5422	502	64	=	=	SYM
cana-5422	502	65	1	1	NUM
cana-5422	502	66	lim	lim	NOUN
cana-5422	502	67	`	`	PUNCT
cana-5422	502	68	→∞	→∞	PROPN
cana-5422	502	69	ν	ν	X
cana-5422	502	70	(	(	PUNCT
cana-5422	502	71	1	1	NUM
cana-5422	502	72	5`mf	5`mf	NUM
cana-5422	502	73	(	(	PUNCT
cana-5422	502	74	5`mw1	5`mw1	NUM
cana-5422	502	75	)	)	PUNCT
cana-5422	502	76	−a(w1	−a(w1	PROPN
cana-5422	502	77	)	)	PUNCT
cana-5422	502	78	,	,	PUNCT
cana-5422	502	79	λ	λ	NOUN
cana-5422	502	80	)	)	PUNCT
cana-5422	503	1	=	=	SYM
cana-5422	503	2	0	0	X
cana-5422	504	1			PROPN
cana-5422	504	2	(	(	PUNCT
cana-5422	504	3	3.11	3.11	NUM
cana-5422	504	4	)	)	PUNCT
cana-5422	504	5	for	for	ADP
cana-5422	504	6	all	all	DET
cana-5422	504	7	w1	w1	NOUN
cana-5422	504	8	∈	∈	PROPN
cana-5422	504	9	w1	w1	NOUN
cana-5422	504	10	and	and	CCONJ
cana-5422	504	11	all	all	DET
cana-5422	504	12	λ	λ	PROPN
cana-5422	504	13	>	>	X
cana-5422	504	14	0	0	X
cana-5422	504	15	.	.	PUNCT
cana-5422	505	1	proof	proof	NOUN
cana-5422	505	2	.	.	PUNCT
cana-5422	506	1	using	use	VERB
cana-5422	506	2	oddness	oddness	NOUN
cana-5422	506	3	of	of	ADP
cana-5422	506	4	f	f	PROPN
cana-5422	506	5	in	in	ADP
cana-5422	506	6	(	(	PUNCT
cana-5422	506	7	2.1	2.1	NUM
cana-5422	506	8	)	)	PUNCT
cana-5422	506	9	,	,	PUNCT
cana-5422	506	10	we	we	PRON
cana-5422	506	11	get	get	VERB
cana-5422	506	12	µ	µ	X
cana-5422	506	13	(	(	PUNCT
cana-5422	506	14	f	f	X
cana-5422	506	15	(	(	PUNCT
cana-5422	506	16	3w1	3w1	NUM
cana-5422	506	17	+	+	CCONJ
cana-5422	506	18	w2	w2	NOUN
cana-5422	506	19	+	+	CCONJ
cana-5422	506	20	w3	w3	PROPN
cana-5422	506	21	)	)	PUNCT
cana-5422	507	1	+	+	NOUN
cana-5422	507	2	f	f	X
cana-5422	507	3	(	(	PUNCT
cana-5422	507	4	w1	w1	NOUN
cana-5422	507	5	+	+	CCONJ
cana-5422	507	6	3w2	3w2	NUM
cana-5422	507	7	+	+	CCONJ
cana-5422	507	8	w3	w3	NOUN
cana-5422	507	9	)	)	PUNCT
cana-5422	508	1	+	+	NOUN
cana-5422	508	2	f	f	X
cana-5422	508	3	(	(	PUNCT
cana-5422	508	4	w1	w1	NOUN
cana-5422	508	5	+	+	NOUN
cana-5422	508	6	w2	w2	NOUN
cana-5422	508	7	+	+	CCONJ
cana-5422	508	8	3w3)−	3w3)−	PROPN
cana-5422	508	9	6f	6f	NOUN
cana-5422	508	10	(	(	PUNCT
cana-5422	508	11	∑3	∑3	PROPN
cana-5422	508	12	ψ=1	ψ=1	PUNCT
cana-5422	508	13	wψ	wψ	ADP
cana-5422	508	14	)	)	PUNCT
cana-5422	509	1	+	+	CCONJ
cana-5422	509	2	∑3	∑3	PROPN
cana-5422	509	3	ψ=1	ψ=1	PUNCT
cana-5422	509	4	f	f	X
cana-5422	509	5	(	(	PUNCT
cana-5422	509	6	wψ	wψ	ADP
cana-5422	509	7	)	)	PUNCT
cana-5422	509	8	,	,	PUNCT
cana-5422	509	9	λ	λ	PROPN
cana-5422	509	10	)	)	PUNCT
cana-5422	509	11	≥	≥	NOUN
cana-5422	509	12	µ′	µ′	PUNCT
cana-5422	509	13	(	(	PUNCT
cana-5422	509	14	ψ	ψ	X
cana-5422	509	15	(	(	PUNCT
cana-5422	509	16	w1	w1	NOUN
cana-5422	509	17	,	,	PUNCT
cana-5422	509	18	w2	w2	NOUN
cana-5422	509	19	,	,	PUNCT
cana-5422	509	20	w3	w3	PROPN
cana-5422	509	21	)	)	PUNCT
cana-5422	509	22	,	,	PUNCT
cana-5422	509	23	λ	λ	X
cana-5422	509	24	)	)	PUNCT
cana-5422	509	25	ν	ν	NOUN
cana-5422	509	26	(	(	PUNCT
cana-5422	509	27	f	f	X
cana-5422	509	28	(	(	PUNCT
cana-5422	509	29	3w1	3w1	NUM
cana-5422	509	30	+	+	CCONJ
cana-5422	509	31	w2	w2	NOUN
cana-5422	509	32	+	+	CCONJ
cana-5422	509	33	w3	w3	PROPN
cana-5422	509	34	)	)	PUNCT
cana-5422	510	1	+	+	NOUN
cana-5422	510	2	f	f	X
cana-5422	510	3	(	(	PUNCT
cana-5422	510	4	w1	w1	NOUN
cana-5422	510	5	+	+	CCONJ
cana-5422	510	6	3w2	3w2	NUM
cana-5422	510	7	+	+	CCONJ
cana-5422	510	8	w3	w3	NOUN
cana-5422	510	9	)	)	PUNCT
cana-5422	511	1	+	+	NOUN
cana-5422	511	2	f	f	X
cana-5422	511	3	(	(	PUNCT
cana-5422	511	4	w1	w1	NOUN
cana-5422	511	5	+	+	NOUN
cana-5422	511	6	w2	w2	NOUN
cana-5422	511	7	+	+	CCONJ
cana-5422	511	8	3w3)−	3w3)−	PROPN
cana-5422	511	9	6f	6f	NOUN
cana-5422	511	10	(	(	PUNCT
cana-5422	511	11	∑3	∑3	PROPN
cana-5422	511	12	ψ=1	ψ=1	PUNCT
cana-5422	511	13	wψ	wψ	ADP
cana-5422	511	14	)	)	PUNCT
cana-5422	512	1	+	+	CCONJ
cana-5422	512	2	∑3	∑3	PROPN
cana-5422	512	3	ψ=1	ψ=1	PUNCT
cana-5422	512	4	f	f	X
cana-5422	512	5	(	(	PUNCT
cana-5422	512	6	wψ	wψ	ADP
cana-5422	512	7	)	)	PUNCT
cana-5422	512	8	,	,	PUNCT
cana-5422	512	9	λ	λ	PROPN
cana-5422	512	10	)	)	PUNCT
cana-5422	512	11	≤	≤	NUM
cana-5422	512	12	ν′	ν′	NOUN
cana-5422	512	13	(	(	PUNCT
cana-5422	512	14	ψ	ψ	X
cana-5422	512	15	(	(	PUNCT
cana-5422	512	16	w1	w1	NOUN
cana-5422	512	17	,	,	PUNCT
cana-5422	512	18	w2	w2	NOUN
cana-5422	512	19	,	,	PUNCT
cana-5422	512	20	w3	w3	PROPN
cana-5422	512	21	)	)	PUNCT
cana-5422	512	22	,	,	PUNCT
cana-5422	512	23	λ	λ	NOUN
cana-5422	512	24	)	)	PUNCT
cana-5422	512	25			ADJ
cana-5422	512	26	(	(	PUNCT
cana-5422	512	27	3.12	3.12	NUM
cana-5422	512	28	)	)	PUNCT
cana-5422	512	29	for	for	ADP
cana-5422	512	30	all	all	DET
cana-5422	512	31	w1	w1	NOUN
cana-5422	512	32	,	,	PUNCT
cana-5422	512	33	w2	w2	NOUN
cana-5422	512	34	,	,	PUNCT
cana-5422	512	35	w3	w3	PROPN
cana-5422	512	36	∈	∈	PROPN
cana-5422	512	37	w1	w1	NOUN
cana-5422	512	38	and	and	CCONJ
cana-5422	512	39	all	all	DET
cana-5422	512	40	λ	λ	X
cana-5422	512	41	>	>	X
cana-5422	512	42	0	0	PUNCT
cana-5422	512	43	.	.	PUNCT
cana-5422	513	1	interchanging	interchanging	PROPN
cana-5422	513	2	(	(	PUNCT
cana-5422	513	3	w1	w1	NOUN
cana-5422	513	4	,	,	PUNCT
cana-5422	513	5	w2	w2	NOUN
cana-5422	513	6	,	,	PUNCT
cana-5422	513	7	w3	w3	PROPN
cana-5422	513	8	)	)	PUNCT
cana-5422	513	9	by	by	ADP
cana-5422	513	10	(	(	PUNCT
cana-5422	513	11	w1	w1	NOUN
cana-5422	513	12	,	,	PUNCT
cana-5422	513	13	w1	w1	NOUN
cana-5422	513	14	,	,	PUNCT
cana-5422	513	15	w1	w1	NOUN
cana-5422	513	16	)	)	PUNCT
cana-5422	513	17	in	in	ADP
cana-5422	513	18	(	(	PUNCT
cana-5422	513	19	3.12	3.12	NUM
cana-5422	513	20	)	)	PUNCT
cana-5422	513	21	,	,	PUNCT
cana-5422	513	22	we	we	PRON
cana-5422	513	23	obtain	obtain	VERB
cana-5422	513	24	µ	µ	X
cana-5422	513	25	(	(	PUNCT
cana-5422	513	26	3f	3f	X
cana-5422	513	27	(	(	PUNCT
cana-5422	513	28	5w1)−	5w1)−	NOUN
cana-5422	513	29	6f	6f	PROPN
cana-5422	513	30	(	(	PUNCT
cana-5422	513	31	3w1	3w1	NUM
cana-5422	513	32	)	)	PUNCT
cana-5422	514	1	+	+	CCONJ
cana-5422	514	2	3f	3f	PROPN
cana-5422	514	3	(	(	PUNCT
cana-5422	514	4	w1	w1	NOUN
cana-5422	514	5	)	)	PUNCT
cana-5422	514	6	,	,	PUNCT
cana-5422	514	7	λ	λ	X
cana-5422	514	8	)	)	PUNCT
cana-5422	514	9	≥	≥	NOUN
cana-5422	514	10	µ′	µ′	PUNCT
cana-5422	514	11	(	(	PUNCT
cana-5422	514	12	ψ	ψ	X
cana-5422	514	13	(	(	PUNCT
cana-5422	514	14	w1	w1	NOUN
cana-5422	514	15	,	,	PUNCT
cana-5422	514	16	w1	w1	NOUN
cana-5422	514	17	,	,	PUNCT
cana-5422	514	18	w1	w1	NOUN
cana-5422	514	19	)	)	PUNCT
cana-5422	514	20	,	,	PUNCT
cana-5422	514	21	λ	λ	X
cana-5422	514	22	)	)	PUNCT
cana-5422	514	23	ν	ν	NOUN
cana-5422	514	24	(	(	PUNCT
cana-5422	514	25	3f	3f	PROPN
cana-5422	514	26	(	(	PUNCT
cana-5422	514	27	5w1)−	5w1)−	NOUN
cana-5422	514	28	6f	6f	PROPN
cana-5422	514	29	(	(	PUNCT
cana-5422	514	30	3w1	3w1	NUM
cana-5422	514	31	)	)	PUNCT
cana-5422	515	1	+	+	CCONJ
cana-5422	515	2	3f	3f	PROPN
cana-5422	515	3	(	(	PUNCT
cana-5422	515	4	w1	w1	NOUN
cana-5422	515	5	)	)	PUNCT
cana-5422	515	6	,	,	PUNCT
cana-5422	515	7	λ	λ	NOUN
cana-5422	515	8	)	)	PUNCT
cana-5422	515	9	≤	≤	NUM
cana-5422	515	10	ν′	ν′	NOUN
cana-5422	515	11	(	(	PUNCT
cana-5422	515	12	ψ	ψ	X
cana-5422	515	13	(	(	PUNCT
cana-5422	515	14	w1	w1	NOUN
cana-5422	515	15	,	,	PUNCT
cana-5422	515	16	w1	w1	NOUN
cana-5422	515	17	,	,	PUNCT
cana-5422	515	18	w1	w1	NOUN
cana-5422	515	19	)	)	PUNCT
cana-5422	515	20	,	,	PUNCT
cana-5422	515	21	λ	λ	NOUN
cana-5422	515	22	)	)	PUNCT
cana-5422	515	23	}	}	PUNCT
cana-5422	515	24	(	(	PUNCT
cana-5422	515	25	3.13	3.13	NUM
cana-5422	515	26	)	)	PUNCT
cana-5422	515	27	for	for	ADP
cana-5422	515	28	all	all	DET
cana-5422	515	29	w1	w1	NOUN
cana-5422	515	30	∈	∈	PROPN
cana-5422	515	31	w1	w1	NOUN
cana-5422	515	32	and	and	CCONJ
cana-5422	515	33	all	all	DET
cana-5422	515	34	λ	λ	X
cana-5422	515	35	>	>	X
cana-5422	515	36	0	0	PUNCT
cana-5422	515	37	.	.	PUNCT
cana-5422	516	1	again	again	ADV
cana-5422	516	2	interchanging	interchange	VERB
cana-5422	516	3	(	(	PUNCT
cana-5422	516	4	w1	w1	NOUN
cana-5422	516	5	,	,	PUNCT
cana-5422	516	6	w2	w2	NOUN
cana-5422	516	7	,	,	PUNCT
cana-5422	516	8	w3	w3	PROPN
cana-5422	516	9	)	)	PUNCT
cana-5422	516	10	by	by	ADP
cana-5422	516	11	(	(	PUNCT
cana-5422	516	12	w1	w1	NOUN
cana-5422	516	13	,	,	PUNCT
cana-5422	516	14	w1,−w1	w1,−w1	NUM
cana-5422	516	15	)	)	PUNCT
cana-5422	516	16	in	in	ADP
cana-5422	516	17	(	(	PUNCT
cana-5422	516	18	3.12	3.12	NUM
cana-5422	516	19	)	)	PUNCT
cana-5422	516	20	and	and	CCONJ
cana-5422	516	21	using	use	VERB
cana-5422	516	22	(	(	PUNCT
cana-5422	516	23	ifn4	ifn4	PROPN
cana-5422	516	24	)	)	PUNCT
cana-5422	516	25	,	,	PUNCT
cana-5422	516	26	(	(	PUNCT
cana-5422	516	27	ifn10	ifn10	PROPN
cana-5422	516	28	)	)	PUNCT
cana-5422	516	29	,	,	PUNCT
cana-5422	516	30	we	we	PRON
cana-5422	516	31	have	have	VERB
cana-5422	516	32	µ	µ	X
cana-5422	516	33	(	(	PUNCT
cana-5422	516	34	2f	2f	NUM
cana-5422	516	35	(	(	PUNCT
cana-5422	516	36	3w1)−	3w1)−	ADJ
cana-5422	516	37	6f	6f	NOUN
cana-5422	516	38	(	(	PUNCT
cana-5422	516	39	w1	w1	NOUN
cana-5422	516	40	)	)	PUNCT
cana-5422	516	41	,	,	PUNCT
cana-5422	516	42	λ	λ	X
cana-5422	516	43	)	)	PUNCT
cana-5422	516	44	≥	≥	NOUN
cana-5422	516	45	µ′	µ′	PUNCT
cana-5422	516	46	(	(	PUNCT
cana-5422	516	47	ψ	ψ	X
cana-5422	516	48	(	(	PUNCT
cana-5422	516	49	w1	w1	NOUN
cana-5422	516	50	,	,	PUNCT
cana-5422	516	51	w1,−w1	w1,−w1	NUM
cana-5422	516	52	)	)	PUNCT
cana-5422	516	53	,	,	PUNCT
cana-5422	516	54	λ	λ	X
cana-5422	516	55	)	)	PUNCT
cana-5422	516	56	ν	ν	NOUN
cana-5422	516	57	(	(	PUNCT
cana-5422	516	58	2f	2f	NUM
cana-5422	516	59	(	(	PUNCT
cana-5422	516	60	3w1)−	3w1)−	NUM
cana-5422	516	61	6f	6f	NOUN
cana-5422	516	62	(	(	PUNCT
cana-5422	516	63	w1	w1	NOUN
cana-5422	516	64	)	)	PUNCT
cana-5422	516	65	,	,	PUNCT
cana-5422	516	66	λ	λ	NOUN
cana-5422	516	67	)	)	PUNCT
cana-5422	516	68	≤	≤	NUM
cana-5422	516	69	ν′	ν′	NOUN
cana-5422	516	70	(	(	PUNCT
cana-5422	516	71	ψ	ψ	X
cana-5422	516	72	(	(	PUNCT
cana-5422	516	73	w1	w1	NOUN
cana-5422	516	74	,	,	PUNCT
cana-5422	516	75	w1,−w1	w1,−w1	NUM
cana-5422	516	76	)	)	PUNCT
cana-5422	516	77	,	,	PUNCT
cana-5422	516	78	λ	λ	NOUN
cana-5422	516	79	)	)	PUNCT
cana-5422	516	80	}	}	PUNCT
cana-5422	516	81	⇒	⇒	VERB
cana-5422	516	82	µ	µ	X
cana-5422	516	83	(	(	PUNCT
cana-5422	516	84	6f	6f	X
cana-5422	516	85	(	(	PUNCT
cana-5422	516	86	3w1)−	3w1)−	PROPN
cana-5422	516	87	18f	18f	PROPN
cana-5422	516	88	(	(	PUNCT
cana-5422	516	89	w1	w1	NOUN
cana-5422	516	90	)	)	PUNCT
cana-5422	516	91	,	,	PUNCT
cana-5422	516	92	3λ	3λ	NUM
cana-5422	516	93	)	)	PUNCT
cana-5422	516	94	≥	≥	NOUN
cana-5422	516	95	µ′	µ′	PUNCT
cana-5422	516	96	(	(	PUNCT
cana-5422	516	97	ψ	ψ	X
cana-5422	516	98	(	(	PUNCT
cana-5422	516	99	w1	w1	NOUN
cana-5422	516	100	,	,	PUNCT
cana-5422	516	101	w1,−w1	w1,−w1	NUM
cana-5422	516	102	)	)	PUNCT
cana-5422	516	103	,	,	PUNCT
cana-5422	516	104	λ	λ	X
cana-5422	516	105	)	)	PUNCT
cana-5422	516	106	ν	ν	NOUN
cana-5422	516	107	(	(	PUNCT
cana-5422	516	108	6f	6f	X
cana-5422	516	109	(	(	PUNCT
cana-5422	516	110	3w1)−	3w1)−	PROPN
cana-5422	516	111	18f	18f	PROPN
cana-5422	516	112	(	(	PUNCT
cana-5422	516	113	w1	w1	NOUN
cana-5422	516	114	)	)	PUNCT
cana-5422	516	115	,	,	PUNCT
cana-5422	516	116	3λ	3λ	NUM
cana-5422	516	117	)	)	PUNCT
cana-5422	516	118	≤	≤	NUM
cana-5422	516	119	ν′	ν′	NOUN
cana-5422	516	120	(	(	PUNCT
cana-5422	516	121	ψ	ψ	X
cana-5422	516	122	(	(	PUNCT
cana-5422	516	123	w1	w1	NOUN
cana-5422	516	124	,	,	PUNCT
cana-5422	516	125	w1,−w1	w1,−w1	NUM
cana-5422	516	126	)	)	PUNCT
cana-5422	516	127	,	,	PUNCT
cana-5422	516	128	λ	λ	NOUN
cana-5422	516	129	)	)	PUNCT
cana-5422	516	130	}	}	PUNCT
cana-5422	516	131	(	(	PUNCT
cana-5422	516	132	3.14	3.14	NUM
cana-5422	516	133	)	)	PUNCT
cana-5422	516	134	communications	communication	NOUN
cana-5422	516	135	on	on	ADP
cana-5422	516	136	applied	apply	VERB
cana-5422	516	137	nonlinear	nonlinear	ADJ
cana-5422	516	138	analysis	analysis	NOUN
cana-5422	516	139	issn	issn	NOUN
cana-5422	516	140	:	:	PUNCT
cana-5422	516	141	1074	1074	NUM
cana-5422	516	142	-	-	PUNCT
cana-5422	516	143	133x	133x	NUM
cana-5422	516	144	vol	vol	NOUN
cana-5422	516	145	32	32	NUM
cana-5422	516	146	no	no	NOUN
cana-5422	516	147	.	.	PUNCT
cana-5422	517	1	10s(2025	10s(2025	NUM
cana-5422	517	2	)	)	PUNCT
cana-5422	518	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	518	2	2202	2202	NUM
cana-5422	518	3	for	for	ADP
cana-5422	518	4	all	all	DET
cana-5422	518	5	w1	w1	NOUN
cana-5422	518	6	∈	∈	PROPN
cana-5422	518	7	w1	w1	NOUN
cana-5422	518	8	and	and	CCONJ
cana-5422	518	9	all	all	DET
cana-5422	518	10	λ	λ	PROPN
cana-5422	518	11	>	>	X
cana-5422	518	12	0	0	X
cana-5422	518	13	.	.	PUNCT
cana-5422	519	1	combining	combine	VERB
cana-5422	519	2	(	(	PUNCT
cana-5422	519	3	3.13	3.13	NUM
cana-5422	519	4	)	)	PUNCT
cana-5422	519	5	and	and	CCONJ
cana-5422	519	6	(	(	PUNCT
cana-5422	519	7	3.14	3.14	NUM
cana-5422	519	8	)	)	PUNCT
cana-5422	519	9	using	use	VERB
cana-5422	519	10	(	(	PUNCT
cana-5422	519	11	ifn5	ifn5	PROPN
cana-5422	519	12	)	)	PUNCT
cana-5422	519	13	,	,	PUNCT
cana-5422	519	14	(	(	PUNCT
cana-5422	519	15	ifn11	ifn11	INTJ
cana-5422	519	16	)	)	PUNCT
cana-5422	519	17	,	,	PUNCT
cana-5422	519	18	we	we	PRON
cana-5422	519	19	arrive	arrive	VERB
cana-5422	519	20	µ	µ	X
cana-5422	519	21	(	(	PUNCT
cana-5422	519	22	3f	3f	PROPN
cana-5422	519	23	(	(	PUNCT
cana-5422	519	24	5w1)−	5w1)−	PROPN
cana-5422	519	25	15f	15f	PROPN
cana-5422	519	26	(	(	PUNCT
cana-5422	519	27	w1	w1	PROPN
cana-5422	519	28	)	)	PUNCT
cana-5422	519	29	,	,	PUNCT
cana-5422	519	30	4λ	4λ	PROPN
cana-5422	519	31	)	)	PUNCT
cana-5422	519	32	≥	≥	PROPN
cana-5422	519	33	µ	µ	X
cana-5422	519	34	(	(	PUNCT
cana-5422	519	35	3f	3f	PROPN
cana-5422	519	36	(	(	PUNCT
cana-5422	519	37	5w1)−	5w1)−	NOUN
cana-5422	519	38	6f	6f	PROPN
cana-5422	519	39	(	(	PUNCT
cana-5422	519	40	3w1	3w1	NUM
cana-5422	519	41	)	)	PUNCT
cana-5422	520	1	+	+	CCONJ
cana-5422	520	2	3f	3f	PROPN
cana-5422	520	3	(	(	PUNCT
cana-5422	520	4	w1	w1	NOUN
cana-5422	520	5	)	)	PUNCT
cana-5422	520	6	,	,	PUNCT
cana-5422	520	7	λ	λ	X
cana-5422	520	8	)	)	PUNCT
cana-5422	520	9	∗	∗	NOUN
cana-5422	520	10	µ	µ	X
cana-5422	520	11	(	(	PUNCT
cana-5422	520	12	6f	6f	X
cana-5422	520	13	(	(	PUNCT
cana-5422	520	14	3w1)−	3w1)−	PROPN
cana-5422	520	15	18f	18f	PROPN
cana-5422	520	16	(	(	PUNCT
cana-5422	520	17	w1	w1	NOUN
cana-5422	520	18	)	)	PUNCT
cana-5422	520	19	,	,	PUNCT
cana-5422	520	20	3λ	3λ	NUM
cana-5422	520	21	)	)	PUNCT
cana-5422	520	22	≥	≥	NOUN
cana-5422	520	23	µ′	µ′	PUNCT
cana-5422	520	24	(	(	PUNCT
cana-5422	520	25	ψ	ψ	X
cana-5422	520	26	(	(	PUNCT
cana-5422	520	27	w1	w1	NOUN
cana-5422	520	28	,	,	PUNCT
cana-5422	520	29	w1	w1	NOUN
cana-5422	520	30	,	,	PUNCT
cana-5422	520	31	w1	w1	NOUN
cana-5422	520	32	)	)	PUNCT
cana-5422	520	33	,	,	PUNCT
cana-5422	520	34	λ	λ	X
cana-5422	520	35	)	)	PUNCT
cana-5422	520	36	∗	∗	NOUN
cana-5422	520	37	µ′	µ′	PUNCT
cana-5422	520	38	(	(	PUNCT
cana-5422	520	39	ψ	ψ	X
cana-5422	520	40	(	(	PUNCT
cana-5422	520	41	w1	w1	NOUN
cana-5422	520	42	,	,	PUNCT
cana-5422	520	43	w1,−w1	w1,−w1	NUM
cana-5422	520	44	)	)	PUNCT
cana-5422	520	45	,	,	PUNCT
cana-5422	520	46	λ	λ	X
cana-5422	520	47	)	)	PUNCT
cana-5422	520	48	=	=	SYM
cana-5422	520	49	µ′	µ′	PUNCT
cana-5422	520	50	(	(	PUNCT
cana-5422	520	51	ψa	ψa	X
cana-5422	520	52	(	(	PUNCT
cana-5422	520	53	w1	w1	NOUN
cana-5422	520	54	)	)	PUNCT
cana-5422	520	55	,	,	PUNCT
cana-5422	520	56	λ	λ	X
cana-5422	520	57	)	)	PUNCT
cana-5422	520	58	ν	ν	NOUN
cana-5422	520	59	(	(	PUNCT
cana-5422	520	60	3f	3f	PROPN
cana-5422	520	61	(	(	PUNCT
cana-5422	520	62	5w1)−	5w1)−	PROPN
cana-5422	520	63	15f	15f	PROPN
cana-5422	520	64	(	(	PUNCT
cana-5422	520	65	w1	w1	PROPN
cana-5422	520	66	)	)	PUNCT
cana-5422	520	67	,	,	PUNCT
cana-5422	520	68	4λ	4λ	NOUN
cana-5422	520	69	)	)	PUNCT
cana-5422	520	70	≤	≤	NUM
cana-5422	520	71	ν	ν	NOUN
cana-5422	520	72	(	(	PUNCT
cana-5422	520	73	3f	3f	PROPN
cana-5422	520	74	(	(	PUNCT
cana-5422	520	75	5w1)−	5w1)−	NOUN
cana-5422	520	76	6f	6f	PROPN
cana-5422	520	77	(	(	PUNCT
cana-5422	520	78	3w1	3w1	NUM
cana-5422	520	79	)	)	PUNCT
cana-5422	521	1	+	+	CCONJ
cana-5422	521	2	3f	3f	PROPN
cana-5422	521	3	(	(	PUNCT
cana-5422	521	4	w1	w1	NOUN
cana-5422	521	5	)	)	PUNCT
cana-5422	521	6	,	,	PUNCT
cana-5422	521	7	λ	λ	X
cana-5422	521	8	)	)	PUNCT
cana-5422	521	9	�	�	PROPN
cana-5422	521	10	ν	ν	NOUN
cana-5422	521	11	(	(	PUNCT
cana-5422	521	12	6f	6f	X
cana-5422	521	13	(	(	PUNCT
cana-5422	521	14	3w1)−	3w1)−	PROPN
cana-5422	521	15	18f	18f	PROPN
cana-5422	521	16	(	(	PUNCT
cana-5422	521	17	w1	w1	NOUN
cana-5422	521	18	)	)	PUNCT
cana-5422	521	19	,	,	PUNCT
cana-5422	521	20	3λ	3λ	NUM
cana-5422	521	21	)	)	PUNCT
cana-5422	522	1	≤	≤	NUM
cana-5422	522	2	ν′	ν′	NOUN
cana-5422	522	3	(	(	PUNCT
cana-5422	522	4	ψ	ψ	X
cana-5422	522	5	(	(	PUNCT
cana-5422	522	6	w1	w1	NOUN
cana-5422	522	7	,	,	PUNCT
cana-5422	522	8	w1	w1	NOUN
cana-5422	522	9	,	,	PUNCT
cana-5422	522	10	w1	w1	NOUN
cana-5422	522	11	)	)	PUNCT
cana-5422	522	12	,	,	PUNCT
cana-5422	522	13	λ	λ	X
cana-5422	522	14	)	)	PUNCT
cana-5422	522	15	�	�	PROPN
cana-5422	522	16	ν′	ν′	NOUN
cana-5422	522	17	(	(	PUNCT
cana-5422	522	18	ψ	ψ	X
cana-5422	522	19	(	(	PUNCT
cana-5422	522	20	w1	w1	NOUN
cana-5422	522	21	,	,	PUNCT
cana-5422	522	22	w1,−w1	w1,−w1	NUM
cana-5422	522	23	)	)	PUNCT
cana-5422	522	24	,	,	PUNCT
cana-5422	522	25	λ	λ	X
cana-5422	522	26	)	)	PUNCT
cana-5422	522	27	=	=	SYM
cana-5422	522	28	ν′	ν′	NOUN
cana-5422	522	29	(	(	PUNCT
cana-5422	522	30	ψa	ψa	X
cana-5422	522	31	(	(	PUNCT
cana-5422	522	32	w1	w1	NOUN
cana-5422	522	33	)	)	PUNCT
cana-5422	522	34	,	,	PUNCT
cana-5422	522	35	λ	λ	X
cana-5422	522	36	)	)	PUNCT
cana-5422	522	37			PROPN
cana-5422	522	38	(	(	PUNCT
cana-5422	522	39	3.15	3.15	NUM
cana-5422	522	40	)	)	PUNCT
cana-5422	522	41	for	for	ADP
cana-5422	522	42	all	all	DET
cana-5422	522	43	w1	w1	NOUN
cana-5422	522	44	∈	∈	PROPN
cana-5422	522	45	w1	w1	NOUN
cana-5422	522	46	and	and	CCONJ
cana-5422	522	47	all	all	DET
cana-5422	522	48	λ	λ	PROPN
cana-5422	522	49	>	>	X
cana-5422	522	50	0	0	X
cana-5422	522	51	.	.	PUNCT
cana-5422	523	1	using	use	VERB
cana-5422	523	2	(	(	PUNCT
cana-5422	523	3	ifn4	ifn4	PROPN
cana-5422	523	4	)	)	PUNCT
cana-5422	523	5	,	,	PUNCT
cana-5422	523	6	(	(	PUNCT
cana-5422	523	7	ifn10	ifn10	PROPN
cana-5422	523	8	)	)	PUNCT
cana-5422	523	9	,	,	PUNCT
cana-5422	523	10	one	one	PRON
cana-5422	523	11	can	can	AUX
cana-5422	523	12	see	see	VERB
cana-5422	523	13	from	from	ADP
cana-5422	523	14	(	(	PUNCT
cana-5422	523	15	3.15	3.15	NUM
cana-5422	523	16	)	)	PUNCT
cana-5422	524	1	that	that	PRON
cana-5422	524	2	µ	µ	X
cana-5422	524	3	(	(	PUNCT
cana-5422	524	4	1	1	NUM
cana-5422	524	5	5	5	NUM
cana-5422	524	6	f	f	NOUN
cana-5422	524	7	(	(	PUNCT
cana-5422	524	8	5w1)−f	5w1)−f	PROPN
cana-5422	524	9	(	(	PUNCT
cana-5422	524	10	w1	w1	NOUN
cana-5422	524	11	)	)	PUNCT
cana-5422	524	12	,	,	PUNCT
cana-5422	524	13	4	4	NUM
cana-5422	524	14	3	3	NUM
cana-5422	524	15	·	·	SYM
cana-5422	524	16	1	1	NUM
cana-5422	524	17	5	5	NUM
cana-5422	524	18	λ	λ	PROPN
cana-5422	524	19	)	)	PUNCT
cana-5422	524	20	≥	≥	NOUN
cana-5422	524	21	µ′	µ′	PUNCT
cana-5422	524	22	(	(	PUNCT
cana-5422	524	23	ψa	ψa	X
cana-5422	524	24	(	(	PUNCT
cana-5422	524	25	w1	w1	NOUN
cana-5422	524	26	)	)	PUNCT
cana-5422	524	27	,	,	PUNCT
cana-5422	524	28	λ	λ	X
cana-5422	524	29	)	)	PUNCT
cana-5422	524	30	ν	ν	NOUN
cana-5422	524	31	(	(	PUNCT
cana-5422	524	32	1	1	NUM
cana-5422	524	33	5	5	NUM
cana-5422	524	34	f	f	NOUN
cana-5422	524	35	(	(	PUNCT
cana-5422	524	36	5w1)−f	5w1)−f	PROPN
cana-5422	524	37	(	(	PUNCT
cana-5422	524	38	w1	w1	NOUN
cana-5422	524	39	)	)	PUNCT
cana-5422	524	40	,	,	PUNCT
cana-5422	524	41	4	4	NUM
cana-5422	524	42	3	3	NUM
cana-5422	524	43	·	·	SYM
cana-5422	524	44	1	1	NUM
cana-5422	524	45	5	5	NUM
cana-5422	524	46	λ	λ	NOUN
cana-5422	524	47	)	)	PUNCT
cana-5422	524	48	≤	≤	NUM
cana-5422	524	49	ν′	ν′	NOUN
cana-5422	524	50	(	(	PUNCT
cana-5422	524	51	ψa	ψa	X
cana-5422	524	52	(	(	PUNCT
cana-5422	524	53	w1	w1	NOUN
cana-5422	524	54	)	)	PUNCT
cana-5422	524	55	,	,	PUNCT
cana-5422	524	56	λ	λ	X
cana-5422	524	57	)	)	PUNCT
cana-5422	524	58			PROPN
cana-5422	524	59	(	(	PUNCT
cana-5422	524	60	3.16	3.16	NUM
cana-5422	524	61	)	)	PUNCT
cana-5422	524	62	for	for	ADP
cana-5422	524	63	all	all	DET
cana-5422	524	64	w1	w1	NOUN
cana-5422	524	65	∈	∈	PROPN
cana-5422	524	66	w1	w1	NOUN
cana-5422	524	67	and	and	CCONJ
cana-5422	524	68	all	all	DET
cana-5422	524	69	λ	λ	PROPN
cana-5422	524	70	>	>	X
cana-5422	524	71	0	0	X
cana-5422	524	72	.	.	PUNCT
cana-5422	524	73	changing	change	VERB
cana-5422	524	74	w1	w1	NOUN
cana-5422	524	75	by	by	ADP
cana-5422	524	76	5`w1	5`w1	NUM
cana-5422	524	77	in	in	ADP
cana-5422	524	78	(	(	PUNCT
cana-5422	524	79	3.16	3.16	NUM
cana-5422	524	80	)	)	PUNCT
cana-5422	524	81	,	,	PUNCT
cana-5422	524	82	and	and	CCONJ
cana-5422	524	83	using	use	VERB
cana-5422	524	84	(	(	PUNCT
cana-5422	524	85	ifn4	ifn4	PROPN
cana-5422	524	86	)	)	PUNCT
cana-5422	524	87	,	,	PUNCT
cana-5422	524	88	(	(	PUNCT
cana-5422	524	89	ifn10	ifn10	PROPN
cana-5422	524	90	)	)	PUNCT
cana-5422	524	91	,	,	PUNCT
cana-5422	524	92	(	(	PUNCT
cana-5422	524	93	3.8	3.8	NUM
cana-5422	524	94	)	)	PUNCT
cana-5422	524	95	,	,	PUNCT
cana-5422	524	96	we	we	PRON
cana-5422	524	97	get	get	VERB
cana-5422	524	98	µ	µ	X
cana-5422	524	99	(	(	PUNCT
cana-5422	524	100	1	1	NUM
cana-5422	524	101	5`+1f	5`+1f	NUM
cana-5422	524	102	(	(	PUNCT
cana-5422	524	103	5	5	NUM
cana-5422	524	104	`	`	PUNCT
cana-5422	524	105	+1w1)−	+1w1)−	PROPN
cana-5422	524	106	1	1	NUM
cana-5422	524	107	5	5	NUM
cana-5422	524	108	`	`	SYM
cana-5422	524	109	f	f	X
cana-5422	524	110	(	(	PUNCT
cana-5422	524	111	5`w1	5`w1	NUM
cana-5422	524	112	)	)	PUNCT
cana-5422	524	113	,	,	PUNCT
cana-5422	524	114	4	4	NUM
cana-5422	524	115	3	3	NUM
cana-5422	524	116	·	·	SYM
cana-5422	524	117	5	5	NUM
cana-5422	524	118	·	·	SYM
cana-5422	524	119	1	1	NUM
cana-5422	524	120	5	5	NUM
cana-5422	524	121	`	`	PART
cana-5422	524	122	λ	λ	PROPN
cana-5422	524	123	)	)	PUNCT
cana-5422	524	124	≥	≥	NOUN
cana-5422	524	125	µ′	µ′	PUNCT
cana-5422	524	126	(	(	PUNCT
cana-5422	524	127	ψa	ψa	X
cana-5422	524	128	(	(	PUNCT
cana-5422	524	129	5`w1	5`w1	NUM
cana-5422	524	130	)	)	PUNCT
cana-5422	524	131	,	,	PUNCT
cana-5422	524	132	λ	λ	PROPN
cana-5422	524	133	)	)	PUNCT
cana-5422	524	134	≥	≥	NOUN
cana-5422	524	135	µ′	µ′	PUNCT
cana-5422	524	136	(	(	PUNCT
cana-5422	524	137	i`ψa	i`ψa	PROPN
cana-5422	524	138	(	(	PUNCT
cana-5422	524	139	w1	w1	NOUN
cana-5422	524	140	)	)	PUNCT
cana-5422	524	141	,	,	PUNCT
cana-5422	524	142	λ	λ	NOUN
cana-5422	524	143	)	)	PUNCT
cana-5422	524	144	=	=	PUNCT
cana-5422	524	145	µ′	µ′	PUNCT
cana-5422	524	146	(	(	PUNCT
cana-5422	524	147	ψa	ψa	X
cana-5422	524	148	(	(	PUNCT
cana-5422	524	149	w1	w1	NOUN
cana-5422	524	150	)	)	PUNCT
cana-5422	524	151	,	,	PUNCT
cana-5422	525	1	1	1	NUM
cana-5422	525	2	i	i	PRON
cana-5422	525	3	`	`	PUNCT
cana-5422	525	4	λ	λ	PROPN
cana-5422	525	5	)	)	PUNCT
cana-5422	525	6	ν	ν	NOUN
cana-5422	525	7	(	(	PUNCT
cana-5422	525	8	1	1	NUM
cana-5422	525	9	5`+1f	5`+1f	NUM
cana-5422	525	10	(	(	PUNCT
cana-5422	525	11	5	5	NUM
cana-5422	525	12	`	`	PUNCT
cana-5422	525	13	+1w1)−	+1w1)−	PROPN
cana-5422	525	14	1	1	NUM
cana-5422	525	15	5	5	NUM
cana-5422	525	16	`	`	SYM
cana-5422	525	17	f	f	X
cana-5422	525	18	(	(	PUNCT
cana-5422	525	19	5`w1	5`w1	NUM
cana-5422	525	20	)	)	PUNCT
cana-5422	525	21	,	,	PUNCT
cana-5422	525	22	4	4	NUM
cana-5422	525	23	3	3	NUM
cana-5422	525	24	·	·	SYM
cana-5422	525	25	5	5	NUM
cana-5422	525	26	·	·	SYM
cana-5422	525	27	1	1	NUM
cana-5422	525	28	5	5	NUM
cana-5422	525	29	`	`	PART
cana-5422	525	30	λ	λ	PROPN
cana-5422	525	31	)	)	PUNCT
cana-5422	525	32	≤	≤	NUM
cana-5422	525	33	ν′	ν′	NOUN
cana-5422	525	34	(	(	PUNCT
cana-5422	525	35	ψa	ψa	X
cana-5422	525	36	(	(	PUNCT
cana-5422	525	37	5`w1	5`w1	NUM
cana-5422	525	38	)	)	PUNCT
cana-5422	525	39	,	,	PUNCT
cana-5422	525	40	λ	λ	INTJ
cana-5422	525	41	)	)	PUNCT
cana-5422	525	42	≤	≤	NUM
cana-5422	525	43	ν′	ν′	NOUN
cana-5422	525	44	(	(	PUNCT
cana-5422	525	45	i`ψa	i`ψa	PROPN
cana-5422	525	46	(	(	PUNCT
cana-5422	525	47	w1	w1	NOUN
cana-5422	525	48	)	)	PUNCT
cana-5422	525	49	,	,	PUNCT
cana-5422	525	50	λ	λ	NOUN
cana-5422	525	51	)	)	PUNCT
cana-5422	526	1	=	=	SYM
cana-5422	526	2	ν′	ν′	NOUN
cana-5422	526	3	(	(	PUNCT
cana-5422	526	4	ψa	ψa	X
cana-5422	526	5	(	(	PUNCT
cana-5422	526	6	w1	w1	NOUN
cana-5422	526	7	)	)	PUNCT
cana-5422	526	8	,	,	PUNCT
cana-5422	526	9	1	1	NUM
cana-5422	526	10	i	i	PRON
cana-5422	526	11	`	`	PUNCT
cana-5422	526	12	λ	λ	PROPN
cana-5422	526	13	)	)	PUNCT
cana-5422	526	14			NOUN
cana-5422	526	15	(	(	PUNCT
cana-5422	526	16	3.17	3.17	NUM
cana-5422	526	17	)	)	PUNCT
cana-5422	526	18	for	for	ADP
cana-5422	526	19	all	all	DET
cana-5422	526	20	w1	w1	NOUN
cana-5422	526	21	∈	∈	PROPN
cana-5422	526	22	w1	w1	NOUN
cana-5422	526	23	and	and	CCONJ
cana-5422	526	24	all	all	DET
cana-5422	526	25	λ	λ	PROPN
cana-5422	526	26	>	>	X
cana-5422	526	27	0	0	PUNCT
cana-5422	526	28	also	also	ADV
cana-5422	526	29	`	`	PUNCT
cana-5422	526	30	>	>	X
cana-5422	526	31	0	0	X
cana-5422	526	32	.	.	PUNCT
cana-5422	526	33	changing	change	VERB
cana-5422	526	34	λ	λ	PROPN
cana-5422	526	35	by	by	ADP
cana-5422	526	36	i`λ	i`λ	NOUN
cana-5422	526	37	in	in	ADP
cana-5422	526	38	(	(	PUNCT
cana-5422	526	39	3.17	3.17	NUM
cana-5422	526	40	)	)	PUNCT
cana-5422	526	41	,	,	PUNCT
cana-5422	526	42	we	we	PRON
cana-5422	526	43	see	see	VERB
cana-5422	526	44	µ	µ	X
cana-5422	526	45	(	(	PUNCT
cana-5422	526	46	1	1	NUM
cana-5422	526	47	5`+1f	5`+1f	NUM
cana-5422	526	48	(	(	PUNCT
cana-5422	526	49	5	5	NUM
cana-5422	526	50	`	`	PUNCT
cana-5422	526	51	+1w1)−	+1w1)−	PROPN
cana-5422	526	52	1	1	NUM
cana-5422	526	53	5	5	NUM
cana-5422	526	54	`	`	SYM
cana-5422	526	55	f	f	X
cana-5422	526	56	(	(	PUNCT
cana-5422	526	57	5`w1	5`w1	NUM
cana-5422	526	58	)	)	PUNCT
cana-5422	526	59	,	,	PUNCT
cana-5422	526	60	4	4	NUM
cana-5422	526	61	3	3	NUM
cana-5422	526	62	·	·	SYM
cana-5422	526	63	5	5	NUM
cana-5422	526	64	·	·	PUNCT
cana-5422	526	65	(	(	PUNCT
cana-5422	526	66	i	i	NOUN
cana-5422	526	67	5	5	NUM
cana-5422	526	68	)	)	PUNCT
cana-5422	526	69	`	`	PUNCT
cana-5422	526	70	λ	λ	PROPN
cana-5422	526	71	)	)	PUNCT
cana-5422	526	72	≥	≥	NOUN
cana-5422	526	73	µ′	µ′	PUNCT
cana-5422	526	74	(	(	PUNCT
cana-5422	526	75	ψa	ψa	X
cana-5422	526	76	(	(	PUNCT
cana-5422	526	77	w1	w1	NOUN
cana-5422	526	78	)	)	PUNCT
cana-5422	526	79	,	,	PUNCT
cana-5422	526	80	λ	λ	X
cana-5422	526	81	)	)	PUNCT
cana-5422	526	82	ν	ν	NOUN
cana-5422	526	83	(	(	PUNCT
cana-5422	526	84	1	1	NUM
cana-5422	526	85	5`+1f	5`+1f	NUM
cana-5422	526	86	(	(	PUNCT
cana-5422	526	87	5	5	NUM
cana-5422	526	88	`	`	PUNCT
cana-5422	526	89	+1w1)−	+1w1)−	PROPN
cana-5422	526	90	1	1	NUM
cana-5422	526	91	5	5	NUM
cana-5422	526	92	`	`	SYM
cana-5422	526	93	f	f	X
cana-5422	526	94	(	(	PUNCT
cana-5422	526	95	5`w1	5`w1	NUM
cana-5422	526	96	)	)	PUNCT
cana-5422	526	97	,	,	PUNCT
cana-5422	526	98	4	4	NUM
cana-5422	526	99	3	3	NUM
cana-5422	526	100	·	·	SYM
cana-5422	526	101	5	5	NUM
cana-5422	526	102	·	·	PUNCT
cana-5422	526	103	(	(	PUNCT
cana-5422	526	104	i	i	NOUN
cana-5422	526	105	5	5	NUM
cana-5422	526	106	)	)	PUNCT
cana-5422	526	107	`	`	PUNCT
cana-5422	526	108	λ	λ	PROPN
cana-5422	526	109	)	)	PUNCT
cana-5422	526	110	≤	≤	NUM
cana-5422	526	111	ν′	ν′	NOUN
cana-5422	526	112	(	(	PUNCT
cana-5422	526	113	ψa	ψa	X
cana-5422	526	114	(	(	PUNCT
cana-5422	526	115	w1	w1	NOUN
cana-5422	526	116	)	)	PUNCT
cana-5422	526	117	,	,	PUNCT
cana-5422	526	118	λ	λ	X
cana-5422	526	119	)	)	PUNCT
cana-5422	526	120			PROPN
cana-5422	526	121	(	(	PUNCT
cana-5422	526	122	3.18	3.18	NUM
cana-5422	526	123	)	)	PUNCT
cana-5422	526	124	for	for	ADP
cana-5422	526	125	all	all	DET
cana-5422	526	126	w1	w1	NOUN
cana-5422	526	127	∈	∈	PROPN
cana-5422	526	128	w1	w1	NOUN
cana-5422	526	129	and	and	CCONJ
cana-5422	526	130	all	all	DET
cana-5422	526	131	λ	λ	X
cana-5422	526	132	>	>	X
cana-5422	526	133	0	0	X
cana-5422	526	134	.	.	PUNCT
cana-5422	527	1	it	it	PRON
cana-5422	527	2	is	be	AUX
cana-5422	527	3	easy	easy	ADJ
cana-5422	527	4	to	to	PART
cana-5422	527	5	check	check	VERB
cana-5422	527	6	that	that	PRON
cana-5422	527	7	1	1	NUM
cana-5422	527	8	5	5	NUM
cana-5422	527	9	`	`	SYM
cana-5422	527	10	f	f	X
cana-5422	527	11	(	(	PUNCT
cana-5422	527	12	5`w1)−f	5`w1)−f	PROPN
cana-5422	527	13	(	(	PUNCT
cana-5422	527	14	w1	w1	NOUN
cana-5422	527	15	)	)	PUNCT
cana-5422	527	16	=	=	PUNCT
cana-5422	527	17	`	`	PUNCT
cana-5422	527	18	−1	−1	NOUN
cana-5422	527	19	∑	∑	PUNCT
cana-5422	527	20	η=0	η=0	PROPN
cana-5422	527	21	1	1	NUM
cana-5422	527	22	5η+1f	5η+1f	NUM
cana-5422	527	23	(	(	PUNCT
cana-5422	527	24	5	5	NUM
cana-5422	527	25	η+1w1)−	η+1w1)−	NOUN
cana-5422	527	26	1	1	NUM
cana-5422	527	27	5ηf	5ηf	NOUN
cana-5422	527	28	(	(	PUNCT
cana-5422	527	29	5	5	NUM
cana-5422	527	30	ηw1	ηw1	NOUN
cana-5422	527	31	)	)	PUNCT
cana-5422	527	32	(	(	PUNCT
cana-5422	527	33	3.19	3.19	NUM
cana-5422	527	34	)	)	PUNCT
cana-5422	527	35	for	for	ADP
cana-5422	527	36	all	all	DET
cana-5422	527	37	w1	w1	NOUN
cana-5422	527	38	∈	∈	PROPN
cana-5422	527	39	w1	w1	NOUN
cana-5422	527	40	.	.	PUNCT
cana-5422	528	1	using	use	VERB
cana-5422	528	2	(	(	PUNCT
cana-5422	528	3	ifn5	ifn5	PROPN
cana-5422	528	4	)	)	PUNCT
cana-5422	528	5	,	,	PUNCT
cana-5422	528	6	(	(	PUNCT
cana-5422	528	7	ifn11	ifn11	INTJ
cana-5422	528	8	)	)	PUNCT
cana-5422	528	9	,	,	PUNCT
cana-5422	528	10	it	it	PRON
cana-5422	528	11	follows	follow	VERB
cana-5422	528	12	from	from	ADP
cana-5422	528	13	(	(	PUNCT
cana-5422	528	14	3.18	3.18	NUM
cana-5422	528	15	)	)	PUNCT
cana-5422	528	16	and	and	CCONJ
cana-5422	528	17	(	(	PUNCT
cana-5422	528	18	3.19	3.19	NUM
cana-5422	528	19	)	)	PUNCT
cana-5422	528	20	,	,	PUNCT
cana-5422	528	21	we	we	PRON
cana-5422	528	22	obtain	obtain	VERB
cana-5422	528	23	µ	µ	X
cana-5422	528	24	(	(	PUNCT
cana-5422	528	25	1	1	NUM
cana-5422	528	26	5	5	NUM
cana-5422	528	27	`	`	SYM
cana-5422	528	28	f	f	X
cana-5422	528	29	(	(	PUNCT
cana-5422	528	30	5`w1)−f	5`w1)−f	PROPN
cana-5422	528	31	(	(	PUNCT
cana-5422	528	32	w1	w1	NOUN
cana-5422	528	33	)	)	PUNCT
cana-5422	528	34	,	,	PUNCT
cana-5422	528	35	`	`	PUNCT
cana-5422	528	36	−1	−1	VERB
cana-5422	528	37	∑	∑	PUNCT
cana-5422	528	38	η=0	η=0	PROPN
cana-5422	528	39	4	4	NUM
cana-5422	528	40	3	3	NUM
cana-5422	528	41	·	·	SYM
cana-5422	528	42	5	5	NUM
cana-5422	528	43	·	·	PUNCT
cana-5422	528	44	(	(	PUNCT
cana-5422	528	45	i	i	PRON
cana-5422	528	46	5	5	NUM
cana-5422	528	47	)	)	PUNCT
cana-5422	528	48	η	η	PROPN
cana-5422	528	49	λ	λ	PROPN
cana-5422	528	50	)	)	PUNCT
cana-5422	528	51	=	=	SYM
cana-5422	528	52	µ	µ	X
cana-5422	528	53	(	(	PUNCT
cana-5422	528	54	`	`	PUNCT
cana-5422	528	55	−1	−1	VERB
cana-5422	528	56	∑	∑	PUNCT
cana-5422	528	57	η=0	η=0	PROPN
cana-5422	528	58	1	1	NUM
cana-5422	528	59	5η+1f	5η+1f	NUM
cana-5422	528	60	(	(	PUNCT
cana-5422	528	61	5	5	NUM
cana-5422	528	62	η+1w1)−	η+1w1)−	NOUN
cana-5422	528	63	1	1	NUM
cana-5422	528	64	5ηf	5ηf	NOUN
cana-5422	528	65	(	(	PUNCT
cana-5422	528	66	5	5	NUM
cana-5422	528	67	ηw1	ηw1	NOUN
cana-5422	528	68	)	)	PUNCT
cana-5422	528	69	,	,	PUNCT
cana-5422	528	70	`	`	PUNCT
cana-5422	528	71	−1	−1	VERB
cana-5422	528	72	∑	∑	PUNCT
cana-5422	528	73	η=0	η=0	PROPN
cana-5422	528	74	4	4	NUM
cana-5422	528	75	3	3	NUM
cana-5422	528	76	·	·	SYM
cana-5422	528	77	5	5	NUM
cana-5422	528	78	·	·	PUNCT
cana-5422	528	79	(	(	PUNCT
cana-5422	528	80	i	i	PRON
cana-5422	528	81	5	5	NUM
cana-5422	528	82	)	)	PUNCT
cana-5422	528	83	η	η	PROPN
cana-5422	528	84	λ	λ	PROPN
cana-5422	528	85	)	)	PUNCT
cana-5422	528	86	≥	≥	NOUN
cana-5422	528	87	`	`	PUNCT
cana-5422	528	88	−1	−1	NOUN
cana-5422	528	89	∏	∏	PROPN
cana-5422	528	90	η=0	η=0	PROPN
cana-5422	528	91	µ	µ	X
cana-5422	528	92	(	(	PUNCT
cana-5422	528	93	1	1	NUM
cana-5422	528	94	5η+1f	5η+1f	NUM
cana-5422	528	95	(	(	PUNCT
cana-5422	528	96	5	5	NUM
cana-5422	528	97	η+1w1)−	η+1w1)−	NOUN
cana-5422	528	98	1	1	NUM
cana-5422	528	99	5ηf	5ηf	NOUN
cana-5422	528	100	(	(	PUNCT
cana-5422	528	101	5	5	NUM
cana-5422	528	102	ηw1	ηw1	NOUN
cana-5422	528	103	)	)	PUNCT
cana-5422	528	104	,	,	PUNCT
cana-5422	528	105	4	4	NUM
cana-5422	528	106	3	3	NUM
cana-5422	528	107	·	·	SYM
cana-5422	528	108	5	5	NUM
cana-5422	528	109	·	·	PUNCT
cana-5422	528	110	(	(	PUNCT
cana-5422	528	111	i	i	PRON
cana-5422	528	112	5	5	NUM
cana-5422	528	113	)	)	PUNCT
cana-5422	528	114	η	η	PROPN
cana-5422	528	115	λ	λ	PROPN
cana-5422	528	116	)	)	PUNCT
cana-5422	528	117	≥	≥	NOUN
cana-5422	528	118	∏`−1	∏`−1	PROPN
cana-5422	528	119	η=0	η=0	PROPN
cana-5422	528	120	µ′	µ′	PUNCT
cana-5422	528	121	(	(	PUNCT
cana-5422	528	122	ψa	ψa	X
cana-5422	528	123	(	(	PUNCT
cana-5422	528	124	w1	w1	NOUN
cana-5422	528	125	)	)	PUNCT
cana-5422	528	126	,	,	PUNCT
cana-5422	528	127	λ	λ	X
cana-5422	528	128	)	)	PUNCT
cana-5422	528	129	=	=	SYM
cana-5422	528	130	µ′	µ′	PUNCT
cana-5422	528	131	(	(	PUNCT
cana-5422	528	132	ψa	ψa	X
cana-5422	528	133	(	(	PUNCT
cana-5422	528	134	w1	w1	NOUN
cana-5422	528	135	)	)	PUNCT
cana-5422	528	136	,	,	PUNCT
cana-5422	528	137	λ	λ	X
cana-5422	528	138	)	)	PUNCT
cana-5422	528	139	ν	ν	NOUN
cana-5422	528	140	(	(	PUNCT
cana-5422	528	141	1	1	NUM
cana-5422	528	142	5	5	NUM
cana-5422	528	143	`	`	SYM
cana-5422	528	144	f	f	X
cana-5422	528	145	(	(	PUNCT
cana-5422	528	146	5`w1)−f	5`w1)−f	PROPN
cana-5422	528	147	(	(	PUNCT
cana-5422	528	148	w1	w1	NOUN
cana-5422	528	149	)	)	PUNCT
cana-5422	528	150	,	,	PUNCT
cana-5422	528	151	`	`	PUNCT
cana-5422	528	152	−1	−1	VERB
cana-5422	528	153	∑	∑	PUNCT
cana-5422	528	154	η=0	η=0	PROPN
cana-5422	528	155	4	4	NUM
cana-5422	528	156	3	3	NUM
cana-5422	528	157	·	·	SYM
cana-5422	528	158	5	5	NUM
cana-5422	528	159	·	·	PUNCT
cana-5422	528	160	(	(	PUNCT
cana-5422	528	161	i	i	PRON
cana-5422	528	162	5	5	NUM
cana-5422	528	163	)	)	PUNCT
cana-5422	528	164	η	η	PROPN
cana-5422	528	165	λ	λ	PROPN
cana-5422	528	166	)	)	PUNCT
cana-5422	529	1	=	=	PUNCT
cana-5422	529	2	ν	ν	NOUN
cana-5422	529	3	(	(	PUNCT
cana-5422	529	4	`	`	PUNCT
cana-5422	529	5	−1	−1	VERB
cana-5422	529	6	∑	∑	PUNCT
cana-5422	529	7	η=0	η=0	PROPN
cana-5422	529	8	1	1	NUM
cana-5422	529	9	5η+1f	5η+1f	NUM
cana-5422	529	10	(	(	PUNCT
cana-5422	529	11	5	5	NUM
cana-5422	529	12	η+1w1)−	η+1w1)−	NOUN
cana-5422	529	13	1	1	NUM
cana-5422	529	14	5ηf	5ηf	NOUN
cana-5422	529	15	(	(	PUNCT
cana-5422	529	16	5	5	NUM
cana-5422	529	17	ηw1	ηw1	NOUN
cana-5422	529	18	)	)	PUNCT
cana-5422	529	19	,	,	PUNCT
cana-5422	529	20	`	`	PUNCT
cana-5422	529	21	−1	−1	VERB
cana-5422	529	22	∑	∑	PUNCT
cana-5422	529	23	η=0	η=0	PROPN
cana-5422	529	24	4	4	NUM
cana-5422	529	25	3	3	NUM
cana-5422	529	26	·	·	SYM
cana-5422	529	27	5	5	NUM
cana-5422	529	28	·	·	PUNCT
cana-5422	529	29	(	(	PUNCT
cana-5422	529	30	i	i	PRON
cana-5422	529	31	5	5	NUM
cana-5422	529	32	)	)	PUNCT
cana-5422	529	33	η	η	PROPN
cana-5422	529	34	λ	λ	PROPN
cana-5422	529	35	)	)	PUNCT
cana-5422	529	36	≤	≤	NUM
cana-5422	529	37	`	`	PUNCT
cana-5422	529	38	−1	−1	NOUN
cana-5422	529	39	ä	ä	VERB
cana-5422	529	40	η=0	η=0	PROPN
cana-5422	529	41	ν	ν	X
cana-5422	529	42	(	(	PUNCT
cana-5422	529	43	1	1	NUM
cana-5422	529	44	5η+1f	5η+1f	NUM
cana-5422	529	45	(	(	PUNCT
cana-5422	529	46	5	5	NUM
cana-5422	529	47	η+1w1)−	η+1w1)−	NOUN
cana-5422	529	48	1	1	NUM
cana-5422	529	49	5ηf	5ηf	NOUN
cana-5422	529	50	(	(	PUNCT
cana-5422	529	51	5	5	NUM
cana-5422	529	52	ηw1	ηw1	NOUN
cana-5422	529	53	)	)	PUNCT
cana-5422	529	54	,	,	PUNCT
cana-5422	529	55	4	4	NUM
cana-5422	529	56	3	3	NUM
cana-5422	529	57	·	·	SYM
cana-5422	529	58	5	5	NUM
cana-5422	529	59	·	·	PUNCT
cana-5422	530	1	(	(	PUNCT
cana-5422	530	2	i	i	PRON
cana-5422	530	3	5	5	NUM
cana-5422	530	4	)	)	PUNCT
cana-5422	530	5	η	η	PROPN
cana-5422	530	6	λ	λ	PROPN
cana-5422	530	7	)	)	PUNCT
cana-5422	530	8	≤	≤	NUM
cana-5422	530	9	ä`−1	ä`−1	NUM
cana-5422	530	10	η=0	η=0	PRON
cana-5422	530	11	ν′	ν′	NOUN
cana-5422	530	12	(	(	PUNCT
cana-5422	530	13	ψa	ψa	X
cana-5422	530	14	(	(	PUNCT
cana-5422	530	15	w1	w1	NOUN
cana-5422	530	16	)	)	PUNCT
cana-5422	530	17	,	,	PUNCT
cana-5422	530	18	λ	λ	X
cana-5422	530	19	)	)	PUNCT
cana-5422	530	20	=	=	SYM
cana-5422	530	21	ν′	ν′	NOUN
cana-5422	530	22	(	(	PUNCT
cana-5422	530	23	ψa	ψa	X
cana-5422	530	24	(	(	PUNCT
cana-5422	530	25	w1	w1	NOUN
cana-5422	530	26	)	)	PUNCT
cana-5422	530	27	,	,	PUNCT
cana-5422	530	28	λ	λ	X
cana-5422	530	29	)	)	PUNCT
cana-5422	530	30			NOUN
cana-5422	530	31	(	(	PUNCT
cana-5422	530	32	3.20	3.20	NUM
cana-5422	530	33	)	)	PUNCT
cana-5422	530	34	communications	communication	NOUN
cana-5422	530	35	on	on	ADP
cana-5422	530	36	applied	apply	VERB
cana-5422	530	37	nonlinear	nonlinear	ADJ
cana-5422	530	38	analysis	analysis	NOUN
cana-5422	530	39	issn	issn	NOUN
cana-5422	530	40	:	:	PUNCT
cana-5422	530	41	1074	1074	NUM
cana-5422	530	42	-	-	PUNCT
cana-5422	530	43	133x	133x	NUM
cana-5422	530	44	vol	vol	NOUN
cana-5422	530	45	32	32	NUM
cana-5422	530	46	no	no	NOUN
cana-5422	530	47	.	.	PUNCT
cana-5422	531	1	10s(2025	10s(2025	NUM
cana-5422	531	2	)	)	PUNCT
cana-5422	532	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	532	2	2203	2203	NUM
cana-5422	532	3	where	where	SCONJ
cana-5422	532	4	`	`	PUNCT
cana-5422	532	5	−1	−1	NOUN
cana-5422	532	6	∏	∏	VERB
cana-5422	532	7	η=0	η=0	PROPN
cana-5422	532	8	µ	µ	PROPN
cana-5422	532	9	=	=	SYM
cana-5422	532	10	µ	µ	X
cana-5422	532	11	∗	∗	X
cana-5422	532	12	µ	µ	X
cana-5422	532	13	∗	∗	X
cana-5422	532	14	µ	µ	NOUN
cana-5422	532	15	∗	∗	NOUN
cana-5422	532	16	...	...	PUNCT
cana-5422	532	17	and	and	CCONJ
cana-5422	532	18	`	`	PUNCT
cana-5422	532	19	−1	−1	NOUN
cana-5422	532	20	ä	ä	VERB
cana-5422	532	21	η=0	η=0	NOUN
cana-5422	532	22	ν	ν	NOUN
cana-5422	532	23	=	=	PUNCT
cana-5422	532	24	ν	ν	X
cana-5422	532	25	�	�	PROPN
cana-5422	532	26	ν	ν	ADP
cana-5422	532	27	�	�	PROPN
cana-5422	532	28	ν	ν	X
cana-5422	532	29	�	�	PROPN
cana-5422	532	30	...	...	PUNCT
cana-5422	532	31	for	for	ADP
cana-5422	532	32	all	all	DET
cana-5422	532	33	w1	w1	NOUN
cana-5422	532	34	∈	∈	PROPN
cana-5422	532	35	w1	w1	NOUN
cana-5422	532	36	and	and	CCONJ
cana-5422	532	37	all	all	DET
cana-5422	532	38	λ	λ	X
cana-5422	532	39	>	>	X
cana-5422	532	40	0	0	X
cana-5422	532	41	.	.	PUNCT
cana-5422	533	1	again	again	ADV
cana-5422	533	2	changing	change	VERB
cana-5422	533	3	w1	w1	NOUN
cana-5422	533	4	by	by	ADP
cana-5422	533	5	5`1	5`1	NUM
cana-5422	533	6	w1	w1	NOUN
cana-5422	533	7	in	in	ADP
cana-5422	533	8	(	(	PUNCT
cana-5422	533	9	3.20	3.20	NUM
cana-5422	533	10	)	)	PUNCT
cana-5422	533	11	,	,	PUNCT
cana-5422	533	12	and	and	CCONJ
cana-5422	533	13	using	use	VERB
cana-5422	533	14	(	(	PUNCT
cana-5422	533	15	ifn4	ifn4	PROPN
cana-5422	533	16	)	)	PUNCT
cana-5422	533	17	,	,	PUNCT
cana-5422	533	18	(	(	PUNCT
cana-5422	533	19	ifn10	ifn10	PROPN
cana-5422	533	20	)	)	PUNCT
cana-5422	533	21	,	,	PUNCT
cana-5422	533	22	(	(	PUNCT
cana-5422	533	23	3.8	3.8	NUM
cana-5422	533	24	)	)	PUNCT
cana-5422	533	25	in	in	ADP
cana-5422	533	26	that	that	DET
cana-5422	533	27	changing	change	VERB
cana-5422	533	28	λ	λ	NOUN
cana-5422	533	29	by	by	ADP
cana-5422	533	30	i`1	i`1	PROPN
cana-5422	533	31	λ	λ	PROPN
cana-5422	533	32	,	,	PUNCT
cana-5422	533	33	we	we	PRON
cana-5422	533	34	have	have	VERB
cana-5422	533	35	µ	µ	X
cana-5422	533	36	(	(	PUNCT
cana-5422	533	37	1	1	NUM
cana-5422	533	38	5`+`1	5`+`1	NUM
cana-5422	533	39	f	f	NOUN
cana-5422	533	40	(	(	PUNCT
cana-5422	533	41	5`+`1	5`+`1	NUM
cana-5422	533	42	w1)−	w1)−	NOUN
cana-5422	533	43	1	1	NUM
cana-5422	533	44	5`1	5`1	NUM
cana-5422	533	45	f	f	X
cana-5422	533	46	(	(	PUNCT
cana-5422	533	47	`	`	PUNCT
cana-5422	533	48	1w1	1w1	NUM
cana-5422	533	49	)	)	PUNCT
cana-5422	533	50	,	,	PUNCT
cana-5422	533	51	`	`	PUNCT
cana-5422	533	52	−1	−1	VERB
cana-5422	533	53	∑	∑	PUNCT
cana-5422	533	54	η=0	η=0	PROPN
cana-5422	533	55	4	4	NUM
cana-5422	533	56	3	3	NUM
cana-5422	533	57	·	·	SYM
cana-5422	533	58	5	5	NUM
cana-5422	533	59	·	·	PUNCT
cana-5422	533	60	(	(	PUNCT
cana-5422	533	61	i	i	PRON
cana-5422	533	62	5	5	NUM
cana-5422	533	63	)	)	PUNCT
cana-5422	533	64	η+`1	η+`1	NOUN
cana-5422	533	65	λ	λ	PROPN
cana-5422	533	66	)	)	PUNCT
cana-5422	533	67	≥	≥	NOUN
cana-5422	533	68	µ′	µ′	PUNCT
cana-5422	533	69	(	(	PUNCT
cana-5422	533	70	ψa	ψa	X
cana-5422	533	71	(	(	PUNCT
cana-5422	533	72	w1	w1	NOUN
cana-5422	533	73	)	)	PUNCT
cana-5422	533	74	,	,	PUNCT
cana-5422	533	75	λ	λ	X
cana-5422	533	76	)	)	PUNCT
cana-5422	533	77	ν	ν	NOUN
cana-5422	533	78	(	(	PUNCT
cana-5422	533	79	1	1	NUM
cana-5422	533	80	5`+`1	5`+`1	NUM
cana-5422	533	81	f	f	NOUN
cana-5422	533	82	(	(	PUNCT
cana-5422	533	83	5`+`1	5`+`1	NUM
cana-5422	533	84	w1)−	w1)−	NOUN
cana-5422	533	85	1	1	NUM
cana-5422	533	86	5`1	5`1	NUM
cana-5422	533	87	f	f	X
cana-5422	533	88	(	(	PUNCT
cana-5422	533	89	`	`	PUNCT
cana-5422	533	90	1w1	1w1	NUM
cana-5422	533	91	)	)	PUNCT
cana-5422	533	92	,	,	PUNCT
cana-5422	533	93	`	`	PUNCT
cana-5422	533	94	−1	−1	VERB
cana-5422	533	95	∑	∑	PUNCT
cana-5422	533	96	η=0	η=0	PROPN
cana-5422	533	97	4	4	NUM
cana-5422	533	98	3	3	NUM
cana-5422	533	99	·	·	SYM
cana-5422	533	100	5	5	NUM
cana-5422	533	101	·	·	PUNCT
cana-5422	533	102	(	(	PUNCT
cana-5422	533	103	i	i	PRON
cana-5422	533	104	5	5	NUM
cana-5422	533	105	)	)	PUNCT
cana-5422	533	106	η+`1	η+`1	NOUN
cana-5422	533	107	λ	λ	PROPN
cana-5422	533	108	)	)	PUNCT
cana-5422	533	109	≤	≤	NUM
cana-5422	533	110	ν′	ν′	NOUN
cana-5422	533	111	(	(	PUNCT
cana-5422	533	112	ψa	ψa	X
cana-5422	533	113	(	(	PUNCT
cana-5422	533	114	w1	w1	NOUN
cana-5422	533	115	)	)	PUNCT
cana-5422	533	116	,	,	PUNCT
cana-5422	533	117	λ	λ	NOUN
cana-5422	533	118	)	)	PUNCT
cana-5422	533	119			ADJ
cana-5422	533	120	(	(	PUNCT
cana-5422	533	121	3.21	3.21	NUM
cana-5422	533	122	)	)	PUNCT
cana-5422	533	123	for	for	ADP
cana-5422	533	124	all	all	DET
cana-5422	533	125	w1	w1	NOUN
cana-5422	533	126	∈	∈	PROPN
cana-5422	533	127	w1	w1	NOUN
cana-5422	533	128	and	and	CCONJ
cana-5422	533	129	all	all	DET
cana-5422	533	130	λ	λ	PROPN
cana-5422	533	131	>	>	X
cana-5422	533	132	0	0	PUNCT
cana-5422	534	1	also	also	ADV
cana-5422	534	2	`	`	PUNCT
cana-5422	534	3	,	,	PUNCT
cana-5422	534	4	`	`	PUNCT
cana-5422	534	5	1	1	X
cana-5422	534	6	>	>	SYM
cana-5422	534	7	0	0	X
cana-5422	534	8	.	.	PUNCT
cana-5422	535	1	it	it	PRON
cana-5422	535	2	follows	follow	VERB
cana-5422	535	3	from	from	ADP
cana-5422	535	4	(	(	PUNCT
cana-5422	535	5	3.21	3.21	NUM
cana-5422	535	6	)	)	PUNCT
cana-5422	535	7	that	that	PRON
cana-5422	535	8	µ	µ	X
cana-5422	535	9	(	(	PUNCT
cana-5422	535	10	1	1	NUM
cana-5422	535	11	5`+`1	5`+`1	NUM
cana-5422	535	12	f	f	NOUN
cana-5422	535	13	(	(	PUNCT
cana-5422	535	14	5`+`1	5`+`1	NUM
cana-5422	535	15	w1)−	w1)−	NOUN
cana-5422	535	16	1	1	NUM
cana-5422	535	17	5`1	5`1	NUM
cana-5422	535	18	f	f	X
cana-5422	535	19	(	(	PUNCT
cana-5422	535	20	`	`	PUNCT
cana-5422	535	21	1w1	1w1	NUM
cana-5422	535	22	)	)	PUNCT
cana-5422	535	23	,	,	PUNCT
cana-5422	535	24	λ	λ	PROPN
cana-5422	535	25	)	)	PUNCT
cana-5422	535	26	≥	≥	NOUN
cana-5422	535	27	µ′	µ′	NOUN
cana-5422	535	28	ψa	ψa	PROPN
cana-5422	535	29	(	(	PUNCT
cana-5422	535	30	w1	w1	NOUN
cana-5422	535	31	)	)	PUNCT
cana-5422	535	32	,	,	PUNCT
cana-5422	536	1	λ	λ	X
cana-5422	536	2	∑`−1	∑`−1	PROPN
cana-5422	536	3	η=0	η=0	PROPN
cana-5422	536	4	4	4	NUM
cana-5422	536	5	3·5	3·5	NUM
cana-5422	536	6	·	·	PUNCT
cana-5422	537	1	(	(	PUNCT
cana-5422	537	2	i	i	PRON
cana-5422	537	3	5	5	NUM
cana-5422	537	4	)	)	PUNCT
cana-5422	537	5	η+`1	η+`1	NOUN
cana-5422	537	6			PROPN
cana-5422	537	7	ν	ν	X
cana-5422	537	8	(	(	PUNCT
cana-5422	537	9	1	1	NUM
cana-5422	537	10	5`+`1	5`+`1	NUM
cana-5422	537	11	f	f	NOUN
cana-5422	537	12	(	(	PUNCT
cana-5422	537	13	5`+`1	5`+`1	NUM
cana-5422	537	14	w1)−	w1)−	NOUN
cana-5422	537	15	1	1	NUM
cana-5422	537	16	5`1	5`1	NUM
cana-5422	537	17	f	f	X
cana-5422	537	18	(	(	PUNCT
cana-5422	537	19	`	`	PUNCT
cana-5422	537	20	1w1	1w1	NUM
cana-5422	537	21	)	)	PUNCT
cana-5422	537	22	,	,	PUNCT
cana-5422	537	23	λ	λ	PROPN
cana-5422	537	24	)	)	PUNCT
cana-5422	537	25	≤	≤	NUM
cana-5422	537	26	ν′	ν′	NOUN
cana-5422	537	27	ψa	ψa	NOUN
cana-5422	537	28	(	(	PUNCT
cana-5422	537	29	w1	w1	NOUN
cana-5422	537	30	)	)	PUNCT
cana-5422	537	31	,	,	PUNCT
cana-5422	537	32	λ	λ	X
cana-5422	537	33	∑`−1	∑`−1	PROPN
cana-5422	537	34	η=0	η=0	PROPN
cana-5422	537	35	4	4	NUM
cana-5422	537	36	3·5	3·5	NUM
cana-5422	537	37	·	·	PUNCT
cana-5422	537	38	(	(	PUNCT
cana-5422	537	39	i	i	PRON
cana-5422	537	40	5	5	NUM
cana-5422	537	41	)	)	PUNCT
cana-5422	537	42	η+`1	η+`1	NOUN
cana-5422	537	43			PROPN
cana-5422	537	44			NOUN
cana-5422	537	45	(	(	PUNCT
cana-5422	537	46	3.22	3.22	NUM
cana-5422	537	47	)	)	PUNCT
cana-5422	537	48	for	for	ADP
cana-5422	537	49	all	all	DET
cana-5422	537	50	w1	w1	NOUN
cana-5422	537	51	∈	∈	PROPN
cana-5422	537	52	w1	w1	NOUN
cana-5422	537	53	and	and	CCONJ
cana-5422	537	54	all	all	DET
cana-5422	537	55	λ	λ	PROPN
cana-5422	537	56	>	>	X
cana-5422	537	57	0	0	NUM
cana-5422	537	58	.	.	PUNCT
cana-5422	538	1	by	by	ADP
cana-5422	538	2	data	datum	NOUN
cana-5422	538	3	,	,	PUNCT
cana-5422	538	4	the	the	DET
cana-5422	538	5	cauchy	cauchy	ADJ
cana-5422	538	6	criterion	criterion	NOUN
cana-5422	538	7	for	for	ADP
cana-5422	538	8	convergence	convergence	NOUN
cana-5422	538	9	in	in	ADP
cana-5422	538	10	intuitionistic	intuitionistic	ADJ
cana-5422	538	11	fuzzy	fuzzy	ADJ
cana-5422	538	12	normed	normed	ADJ
cana-5422	538	13	space	space	NOUN
cana-5422	538	14	gives	give	VERB
cana-5422	538	15	that	that	SCONJ
cana-5422	538	16	the	the	DET
cana-5422	538	17	sequence	sequence	NOUN
cana-5422	538	18	{	{	PUNCT
cana-5422	538	19	1	1	NUM
cana-5422	538	20	5	5	NUM
cana-5422	538	21	`	`	PUNCT
cana-5422	538	22	f	f	X
cana-5422	538	23	(	(	PUNCT
cana-5422	538	24	5`w1	5`w1	NUM
cana-5422	538	25	)	)	PUNCT
cana-5422	538	26	}	}	PUNCT
cana-5422	538	27	,	,	PUNCT
cana-5422	538	28	is	be	AUX
cana-5422	538	29	cauchy	cauchy	ADJ
cana-5422	538	30	in	in	ADP
cana-5422	538	31	(	(	PUNCT
cana-5422	538	32	w2	w2	NOUN
cana-5422	538	33	,	,	PUNCT
cana-5422	538	34	µ′	µ′	NUM
cana-5422	538	35	,	,	PUNCT
cana-5422	538	36	ν′	ν′	NOUN
cana-5422	538	37	)	)	PUNCT
cana-5422	538	38	and	and	CCONJ
cana-5422	538	39	it	it	PRON
cana-5422	538	40	is	be	AUX
cana-5422	538	41	a	a	DET
cana-5422	538	42	complete	complete	ADJ
cana-5422	538	43	intuitionistic	intuitionistic	ADJ
cana-5422	538	44	fuzzy	fuzzy	ADJ
cana-5422	538	45	normed	normed	ADJ
cana-5422	538	46	space	space	NOUN
cana-5422	538	47	,	,	PUNCT
cana-5422	538	48	this	this	DET
cana-5422	538	49	sequence	sequence	NOUN
cana-5422	538	50	converges	converge	VERB
cana-5422	538	51	to	to	ADP
cana-5422	538	52	some	some	DET
cana-5422	538	53	point	point	NOUN
cana-5422	538	54	a(w1	a(w1	NOUN
cana-5422	538	55	)	)	PUNCT
cana-5422	538	56	in	in	ADP
cana-5422	538	57	(	(	PUNCT
cana-5422	538	58	w2	w2	NOUN
cana-5422	538	59	,	,	PUNCT
cana-5422	538	60	µ′	µ′	NUM
cana-5422	538	61	,	,	PUNCT
cana-5422	538	62	ν′	ν′	NOUN
cana-5422	538	63	)	)	PUNCT
cana-5422	538	64	for	for	ADP
cana-5422	538	65	all	all	DET
cana-5422	538	66	w1	w1	NOUN
cana-5422	538	67	∈	∈	PROPN
cana-5422	538	68	w1	w1	NOUN
cana-5422	538	69	.	.	PUNCT
cana-5422	539	1	so	so	ADV
cana-5422	539	2	,	,	PUNCT
cana-5422	539	3	by	by	ADP
cana-5422	539	4	notation	notation	NOUN
cana-5422	539	5	,	,	PUNCT
cana-5422	539	6	we	we	PRON
cana-5422	539	7	write	write	VERB
cana-5422	539	8	lim	lim	PROPN
cana-5422	539	9	`	`	PUNCT
cana-5422	539	10	→∞	→∞	PROPN
cana-5422	539	11	µ	µ	X
cana-5422	539	12	(	(	PUNCT
cana-5422	539	13	1	1	NUM
cana-5422	539	14	5	5	NUM
cana-5422	539	15	`	`	PUNCT
cana-5422	539	16	f	f	X
cana-5422	539	17	(	(	PUNCT
cana-5422	539	18	5`w1	5`w1	NUM
cana-5422	539	19	)	)	PUNCT
cana-5422	539	20	−a(w1	−a(w1	PROPN
cana-5422	539	21	)	)	PUNCT
cana-5422	539	22	,	,	PUNCT
cana-5422	539	23	λ	λ	NOUN
cana-5422	539	24	)	)	PUNCT
cana-5422	539	25	=	=	SYM
cana-5422	540	1	1	1	NUM
cana-5422	540	2	;	;	PUNCT
cana-5422	540	3	lim	lim	PROPN
cana-5422	540	4	`	`	PUNCT
cana-5422	540	5	→∞	→∞	PROPN
cana-5422	540	6	ν	ν	X
cana-5422	540	7	(	(	PUNCT
cana-5422	540	8	1	1	NUM
cana-5422	540	9	5	5	NUM
cana-5422	540	10	`	`	PUNCT
cana-5422	540	11	f	f	X
cana-5422	540	12	(	(	PUNCT
cana-5422	540	13	5`w1	5`w1	NUM
cana-5422	540	14	)	)	PUNCT
cana-5422	540	15	−a(w1	−a(w1	PROPN
cana-5422	540	16	)	)	PUNCT
cana-5422	540	17	,	,	PUNCT
cana-5422	540	18	λ	λ	NOUN
cana-5422	540	19	)	)	PUNCT
cana-5422	540	20	=	=	SYM
cana-5422	541	1	0	0	NUM
cana-5422	541	2	;	;	PUNCT
cana-5422	541	3			PROPN
cana-5422	541	4	(	(	PUNCT
cana-5422	541	5	3.23	3.23	NUM
cana-5422	541	6	)	)	PUNCT
cana-5422	541	7	for	for	ADP
cana-5422	541	8	all	all	DET
cana-5422	541	9	w1	w1	NOUN
cana-5422	541	10	∈	∈	PROPN
cana-5422	541	11	w1	w1	NOUN
cana-5422	541	12	and	and	CCONJ
cana-5422	541	13	all	all	DET
cana-5422	541	14	λ	λ	PROPN
cana-5422	541	15	>	>	X
cana-5422	541	16	0	0	X
cana-5422	541	17	.	.	PUNCT
cana-5422	542	1	letting	let	VERB
cana-5422	542	2	`	`	PUNCT
cana-5422	542	3	1	1	NUM
cana-5422	542	4	=	=	SYM
cana-5422	542	5	0	0	NUM
cana-5422	542	6	and	and	CCONJ
cana-5422	542	7	`	`	PUNCT
cana-5422	542	8	→	→	SYM
cana-5422	542	9	∞	∞	NUM
cana-5422	542	10	in	in	ADP
cana-5422	542	11	(	(	PUNCT
cana-5422	542	12	3.22	3.22	NUM
cana-5422	542	13	)	)	PUNCT
cana-5422	542	14	and	and	CCONJ
cana-5422	542	15	using	use	VERB
cana-5422	542	16	(	(	PUNCT
cana-5422	542	17	3.23	3.23	NUM
cana-5422	542	18	)	)	PUNCT
cana-5422	542	19	,	,	PUNCT
cana-5422	542	20	we	we	PRON
cana-5422	542	21	arrive	arrive	VERB
cana-5422	542	22	µ	µ	X
cana-5422	542	23	(	(	PUNCT
cana-5422	542	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	542	25	(	(	PUNCT
cana-5422	542	26	w1	w1	NOUN
cana-5422	542	27	)	)	PUNCT
cana-5422	542	28	,	,	PUNCT
cana-5422	542	29	λ	λ	X
cana-5422	542	30	)	)	PUNCT
cana-5422	542	31	≥	≥	NOUN
cana-5422	542	32	µ′	µ′	PUNCT
cana-5422	542	33	(	(	PUNCT
cana-5422	542	34	ψa	ψa	X
cana-5422	542	35	(	(	PUNCT
cana-5422	542	36	w1	w1	NOUN
cana-5422	542	37	)	)	PUNCT
cana-5422	542	38	,	,	PUNCT
cana-5422	542	39	3λ	3λ	NUM
cana-5422	542	40	4	4	NUM
cana-5422	542	41	(	(	PUNCT
cana-5422	542	42	5−	5−	NUM
cana-5422	542	43	i	i	NOUN
cana-5422	542	44	)	)	PUNCT
cana-5422	542	45	)	)	PUNCT
cana-5422	543	1	=	=	PUNCT
cana-5422	543	2	µ′	µ′	NOUN
cana-5422	543	3	(	(	PUNCT
cana-5422	543	4	ψ	ψ	X
cana-5422	543	5	(	(	PUNCT
cana-5422	543	6	w1	w1	NOUN
cana-5422	543	7	,	,	PUNCT
cana-5422	543	8	w1	w1	NOUN
cana-5422	543	9	,	,	PUNCT
cana-5422	543	10	w1	w1	NOUN
cana-5422	543	11	)	)	PUNCT
cana-5422	543	12	,	,	PUNCT
cana-5422	543	13	3λ	3λ	NUM
cana-5422	543	14	4	4	NUM
cana-5422	543	15	(	(	PUNCT
cana-5422	543	16	5−	5−	NUM
cana-5422	543	17	i	i	NOUN
cana-5422	543	18	)	)	PUNCT
cana-5422	543	19	)	)	PUNCT
cana-5422	543	20	∗	∗	NOUN
cana-5422	543	21	µ′	µ′	PUNCT
cana-5422	543	22	(	(	PUNCT
cana-5422	543	23	ψ	ψ	X
cana-5422	543	24	(	(	PUNCT
cana-5422	543	25	w1	w1	NOUN
cana-5422	543	26	,	,	PUNCT
cana-5422	543	27	w1,−w1	w1,−w1	NUM
cana-5422	543	28	)	)	PUNCT
cana-5422	543	29	,	,	PUNCT
cana-5422	543	30	3λ	3λ	NUM
cana-5422	543	31	4	4	NUM
cana-5422	543	32	(	(	PUNCT
cana-5422	543	33	5−	5−	NUM
cana-5422	543	34	i	i	NOUN
cana-5422	543	35	)	)	PUNCT
cana-5422	543	36	)	)	PUNCT
cana-5422	544	1	ν	ν	NOUN
cana-5422	544	2	(	(	PUNCT
cana-5422	544	3	a(w1)−f	a(w1)−f	PROPN
cana-5422	544	4	(	(	PUNCT
cana-5422	544	5	w1	w1	NOUN
cana-5422	544	6	)	)	PUNCT
cana-5422	544	7	,	,	PUNCT
cana-5422	544	8	λ	λ	NOUN
cana-5422	544	9	)	)	PUNCT
cana-5422	544	10	≤	≤	NUM
cana-5422	544	11	ν′	ν′	NOUN
cana-5422	544	12	(	(	PUNCT
cana-5422	544	13	ψa	ψa	X
cana-5422	544	14	(	(	PUNCT
cana-5422	544	15	w1	w1	NOUN
cana-5422	544	16	)	)	PUNCT
cana-5422	544	17	,	,	PUNCT
cana-5422	544	18	3λ	3λ	NUM
cana-5422	544	19	4	4	NUM
cana-5422	544	20	(	(	PUNCT
cana-5422	544	21	5−	5−	NUM
cana-5422	544	22	i	i	NOUN
cana-5422	544	23	)	)	PUNCT
cana-5422	544	24	)	)	PUNCT
cana-5422	545	1	=	=	SYM
cana-5422	545	2	ν′	ν′	NOUN
cana-5422	545	3	(	(	PUNCT
cana-5422	545	4	ψ	ψ	X
cana-5422	545	5	(	(	PUNCT
cana-5422	545	6	w1	w1	NOUN
cana-5422	545	7	,	,	PUNCT
cana-5422	545	8	w1	w1	NOUN
cana-5422	545	9	,	,	PUNCT
cana-5422	545	10	w1	w1	NOUN
cana-5422	545	11	)	)	PUNCT
cana-5422	545	12	,	,	PUNCT
cana-5422	545	13	3λ	3λ	NUM
cana-5422	545	14	4	4	NUM
cana-5422	545	15	(	(	PUNCT
cana-5422	545	16	5−	5−	NUM
cana-5422	545	17	i	i	NOUN
cana-5422	545	18	)	)	PUNCT
cana-5422	545	19	)	)	PUNCT
cana-5422	545	20	�	�	PROPN
cana-5422	545	21	ν′	ν′	NOUN
cana-5422	545	22	(	(	PUNCT
cana-5422	545	23	ψ	ψ	X
cana-5422	545	24	(	(	PUNCT
cana-5422	545	25	w1	w1	NOUN
cana-5422	545	26	,	,	PUNCT
cana-5422	545	27	w1,−w1	w1,−w1	NUM
cana-5422	545	28	)	)	PUNCT
cana-5422	545	29	,	,	PUNCT
cana-5422	545	30	3λ	3λ	NUM
cana-5422	545	31	4	4	NUM
cana-5422	545	32	(	(	PUNCT
cana-5422	545	33	5−	5−	NUM
cana-5422	545	34	i	i	NOUN
cana-5422	545	35	)	)	PUNCT
cana-5422	545	36	)	)	PUNCT
cana-5422	545	37			NOUN
cana-5422	545	38	(	(	PUNCT
cana-5422	545	39	3.24	3.24	NUM
cana-5422	545	40	)	)	PUNCT
cana-5422	545	41	for	for	ADP
cana-5422	545	42	all	all	DET
cana-5422	545	43	w1	w1	NOUN
cana-5422	545	44	∈	∈	PROPN
cana-5422	545	45	w1	w1	NOUN
cana-5422	545	46	and	and	CCONJ
cana-5422	545	47	all	all	DET
cana-5422	545	48	λ	λ	PROPN
cana-5422	545	49	>	>	X
cana-5422	545	50	0	0	NUM
cana-5422	545	51	.	.	PUNCT
cana-5422	546	1	thus	thus	ADV
cana-5422	546	2	,	,	PUNCT
cana-5422	546	3	(	(	PUNCT
cana-5422	546	4	3.10	3.10	NUM
cana-5422	546	5	)	)	PUNCT
cana-5422	546	6	and	and	CCONJ
cana-5422	546	7	(	(	PUNCT
cana-5422	546	8	3.11	3.11	NUM
cana-5422	546	9	)	)	PUNCT
cana-5422	546	10	holds	hold	VERB
cana-5422	546	11	for	for	ADP
cana-5422	546	12	µ	µ	NOUN
cana-5422	546	13	=	=	SYM
cana-5422	546	14	1	1	NUM
cana-5422	546	15	.	.	X
cana-5422	546	16	interchanging	interchanging	PROPN
cana-5422	546	17	(	(	PUNCT
cana-5422	546	18	w1	w1	NOUN
cana-5422	546	19	,	,	PUNCT
cana-5422	546	20	w2	w2	NOUN
cana-5422	546	21	,	,	PUNCT
cana-5422	546	22	w3	w3	PROPN
cana-5422	546	23	)	)	PUNCT
cana-5422	546	24	=	=	PRON
cana-5422	546	25	(	(	PUNCT
cana-5422	546	26	5`w1	5`w1	NUM
cana-5422	546	27	,	,	PUNCT
cana-5422	546	28	5`w2	5`w2	NUM
cana-5422	546	29	,	,	PUNCT
cana-5422	546	30	5`w3	5`w3	NUM
cana-5422	546	31	)	)	PUNCT
cana-5422	546	32	,	,	PUNCT
cana-5422	546	33	in	in	ADP
cana-5422	546	34	(	(	PUNCT
cana-5422	546	35	3.1	3.1	NUM
cana-5422	546	36	)	)	PUNCT
cana-5422	546	37	and	and	CCONJ
cana-5422	546	38	using	use	VERB
cana-5422	546	39	(	(	PUNCT
cana-5422	546	40	ifn4	ifn4	PROPN
cana-5422	546	41	)	)	PUNCT
cana-5422	546	42	,	,	PUNCT
cana-5422	546	43	(	(	PUNCT
cana-5422	546	44	ifn10	ifn10	PROPN
cana-5422	546	45	)	)	PUNCT
cana-5422	546	46	,	,	PUNCT
cana-5422	546	47	we	we	PRON
cana-5422	546	48	have	have	VERB
cana-5422	546	49	µ	µ	X
cana-5422	546	50	(	(	PUNCT
cana-5422	546	51	1	1	NUM
cana-5422	546	52	5	5	NUM
cana-5422	546	53	`	`	PUNCT
cana-5422	546	54	{	{	PUNCT
cana-5422	546	55	f	f	X
cana-5422	546	56	(	(	PUNCT
cana-5422	546	57	5`(3w1	5`(3w1	NUM
cana-5422	546	58	+	+	CCONJ
cana-5422	546	59	w2	w2	NOUN
cana-5422	546	60	+	+	CCONJ
cana-5422	546	61	w3	w3	PROPN
cana-5422	546	62	)	)	PUNCT
cana-5422	546	63	)	)	PUNCT
cana-5422	547	1	+	+	NOUN
cana-5422	547	2	f	f	X
cana-5422	547	3	(	(	PUNCT
cana-5422	547	4	5`(w1	5`(w1	NUM
cana-5422	547	5	+	+	CCONJ
cana-5422	547	6	3w2	3w2	NUM
cana-5422	547	7	+	+	CCONJ
cana-5422	547	8	w3	w3	NOUN
cana-5422	547	9	)	)	PUNCT
cana-5422	547	10	)	)	PUNCT
cana-5422	548	1	+	+	NOUN
cana-5422	548	2	f	f	X
cana-5422	548	3	(	(	PUNCT
cana-5422	548	4	5`(w1	5`(w1	NOUN
cana-5422	548	5	+	+	NUM
cana-5422	548	6	w2	w2	NOUN
cana-5422	548	7	+	+	CCONJ
cana-5422	548	8	3w3))−	3w3))−	NUM
cana-5422	548	9	6f	6f	NOUN
cana-5422	548	10	(	(	PUNCT
cana-5422	548	11	∑3	∑3	PROPN
cana-5422	548	12	ψ=1	ψ=1	PUNCT
cana-5422	548	13	5`wψ	5`wψ	PROPN
cana-5422	548	14	)	)	PUNCT
cana-5422	548	15	−	−	NOUN
cana-5422	549	1	1	1	NUM
cana-5422	549	2	2	2	NUM
cana-5422	549	3	{	{	PUNCT
cana-5422	549	4	f	f	PROPN
cana-5422	549	5	(	(	PUNCT
cana-5422	549	6	∑3	∑3	PROPN
cana-5422	549	7	ψ=1	ψ=1	X
cana-5422	549	8	5`wψ	5`wψ	PROPN
cana-5422	549	9	)	)	PUNCT
cana-5422	550	1	+	+	NOUN
cana-5422	550	2	f	f	X
cana-5422	550	3	(	(	PUNCT
cana-5422	550	4	−∑3	−∑3	PROPN
cana-5422	550	5	ψ=1	ψ=1	SYM
cana-5422	550	6	5`wψ	5`wψ	PROPN
cana-5422	550	7	)	)	PUNCT
cana-5422	550	8	}	}	PUNCT
cana-5422	550	9	+	+	CCONJ
cana-5422	550	10	∑3	∑3	SYM
cana-5422	550	11	ψ=1	ψ=1	X
cana-5422	550	12	{	{	PUNCT
cana-5422	550	13	f	f	PROPN
cana-5422	550	14	(	(	PUNCT
cana-5422	550	15	5`wψ)−	5`wψ)−	NUM
cana-5422	550	16	5	5	NUM
cana-5422	550	17	2	2	NUM
cana-5422	550	18	[	[	PUNCT
cana-5422	550	19	f	f	X
cana-5422	550	20	(	(	PUNCT
cana-5422	550	21	5`wψ	5`wψ	PROPN
cana-5422	550	22	)	)	PUNCT
cana-5422	551	1	+	+	NOUN
cana-5422	551	2	f	f	X
cana-5422	551	3	(	(	PUNCT
cana-5422	551	4	−5`wψ	−5`wψ	NOUN
cana-5422	551	5	)	)	PUNCT
cana-5422	551	6	]	]	PUNCT
cana-5422	551	7	}	}	PUNCT
cana-5422	551	8	}	}	PUNCT
cana-5422	551	9	,	,	PUNCT
cana-5422	551	10	λ	λ	PROPN
cana-5422	551	11	)	)	PUNCT
cana-5422	551	12	≥	≥	NOUN
cana-5422	551	13	µ′	µ′	PUNCT
cana-5422	551	14	(	(	PUNCT
cana-5422	551	15	ψ	ψ	X
cana-5422	551	16	(	(	PUNCT
cana-5422	551	17	5`w1	5`w1	NUM
cana-5422	551	18	,	,	PUNCT
cana-5422	551	19	5`w2	5`w2	NUM
cana-5422	551	20	,	,	PUNCT
cana-5422	551	21	5`w3	5`w3	NUM
cana-5422	551	22	)	)	PUNCT
cana-5422	551	23	,	,	PUNCT
cana-5422	551	24	5	5	NUM
cana-5422	551	25	`	`	PUNCT
cana-5422	551	26	λ	λ	PROPN
cana-5422	551	27	)	)	PUNCT
cana-5422	551	28	ν	ν	NOUN
cana-5422	551	29	(	(	PUNCT
cana-5422	551	30	1	1	NUM
cana-5422	551	31	5	5	NUM
cana-5422	551	32	`	`	PUNCT
cana-5422	551	33	{	{	PUNCT
cana-5422	551	34	f	f	X
cana-5422	551	35	(	(	PUNCT
cana-5422	551	36	5`(3w1	5`(3w1	NUM
cana-5422	551	37	+	+	CCONJ
cana-5422	551	38	w2	w2	NOUN
cana-5422	551	39	+	+	CCONJ
cana-5422	551	40	w3	w3	PROPN
cana-5422	551	41	)	)	PUNCT
cana-5422	551	42	)	)	PUNCT
cana-5422	552	1	+	+	NOUN
cana-5422	552	2	f	f	X
cana-5422	552	3	(	(	PUNCT
cana-5422	552	4	5`(w1	5`(w1	NUM
cana-5422	552	5	+	+	CCONJ
cana-5422	552	6	3w2	3w2	NUM
cana-5422	552	7	+	+	CCONJ
cana-5422	552	8	w3	w3	NOUN
cana-5422	552	9	)	)	PUNCT
cana-5422	552	10	)	)	PUNCT
cana-5422	553	1	+	+	NOUN
cana-5422	553	2	f	f	X
cana-5422	553	3	(	(	PUNCT
cana-5422	553	4	5`(w1	5`(w1	NOUN
cana-5422	553	5	+	+	NUM
cana-5422	553	6	w2	w2	NOUN
cana-5422	553	7	+	+	CCONJ
cana-5422	553	8	3w3))−	3w3))−	NUM
cana-5422	553	9	6f	6f	NOUN
cana-5422	553	10	(	(	PUNCT
cana-5422	553	11	∑3	∑3	PROPN
cana-5422	553	12	ψ=1	ψ=1	PUNCT
cana-5422	553	13	5`wψ	5`wψ	PROPN
cana-5422	553	14	)	)	PUNCT
cana-5422	553	15	−	−	NOUN
cana-5422	554	1	1	1	NUM
cana-5422	554	2	2	2	NUM
cana-5422	554	3	{	{	PUNCT
cana-5422	554	4	f	f	PROPN
cana-5422	554	5	(	(	PUNCT
cana-5422	554	6	∑3	∑3	PROPN
cana-5422	554	7	ψ=1	ψ=1	X
cana-5422	554	8	5`wψ	5`wψ	PROPN
cana-5422	554	9	)	)	PUNCT
cana-5422	555	1	+	+	NOUN
cana-5422	555	2	f	f	X
cana-5422	555	3	(	(	PUNCT
cana-5422	555	4	−∑3	−∑3	PROPN
cana-5422	555	5	ψ=1	ψ=1	SYM
cana-5422	555	6	5`wψ	5`wψ	PROPN
cana-5422	555	7	)	)	PUNCT
cana-5422	555	8	}	}	PUNCT
cana-5422	555	9	+	+	CCONJ
cana-5422	555	10	∑3	∑3	SYM
cana-5422	555	11	ψ=1	ψ=1	X
cana-5422	555	12	{	{	PUNCT
cana-5422	555	13	f	f	PROPN
cana-5422	555	14	(	(	PUNCT
cana-5422	555	15	5`wψ)−	5`wψ)−	NUM
cana-5422	555	16	5	5	NUM
cana-5422	555	17	2	2	NUM
cana-5422	555	18	[	[	PUNCT
cana-5422	555	19	f	f	X
cana-5422	555	20	(	(	PUNCT
cana-5422	555	21	5`wψ	5`wψ	PROPN
cana-5422	555	22	)	)	PUNCT
cana-5422	556	1	+	+	NOUN
cana-5422	556	2	f	f	X
cana-5422	556	3	(	(	PUNCT
cana-5422	556	4	−5`wψ	−5`wψ	NOUN
cana-5422	556	5	)	)	PUNCT
cana-5422	556	6	]	]	PUNCT
cana-5422	556	7	}	}	PUNCT
cana-5422	556	8	}	}	PUNCT
cana-5422	556	9	,	,	PUNCT
cana-5422	556	10	λ	λ	PROPN
cana-5422	556	11	)	)	PUNCT
cana-5422	556	12	≤	≤	NUM
cana-5422	556	13	ν′	ν′	NOUN
cana-5422	556	14	(	(	PUNCT
cana-5422	556	15	ψ	ψ	X
cana-5422	556	16	(	(	PUNCT
cana-5422	556	17	5`w1	5`w1	NUM
cana-5422	556	18	,	,	PUNCT
cana-5422	556	19	5`w2	5`w2	NUM
cana-5422	556	20	,	,	PUNCT
cana-5422	556	21	5`w3	5`w3	NUM
cana-5422	556	22	)	)	PUNCT
cana-5422	556	23	,	,	PUNCT
cana-5422	556	24	5	5	NUM
cana-5422	556	25	`	`	PART
cana-5422	556	26	λ	λ	PROPN
cana-5422	556	27	)	)	PUNCT
cana-5422	556	28			ADJ
cana-5422	556	29	(	(	PUNCT
cana-5422	556	30	3.25	3.25	NUM
cana-5422	556	31	)	)	PUNCT
cana-5422	556	32	communications	communication	NOUN
cana-5422	556	33	on	on	ADP
cana-5422	556	34	applied	apply	VERB
cana-5422	556	35	nonlinear	nonlinear	ADJ
cana-5422	556	36	analysis	analysis	NOUN
cana-5422	556	37	issn	issn	NOUN
cana-5422	556	38	:	:	PUNCT
cana-5422	556	39	1074	1074	NUM
cana-5422	556	40	-	-	PUNCT
cana-5422	556	41	133x	133x	NUM
cana-5422	556	42	vol	vol	NOUN
cana-5422	556	43	32	32	NUM
cana-5422	556	44	no	no	NOUN
cana-5422	556	45	.	.	PUNCT
cana-5422	557	1	10s(2025	10s(2025	NUM
cana-5422	557	2	)	)	PUNCT
cana-5422	558	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	558	2	2204	2204	NUM
cana-5422	558	3	for	for	ADP
cana-5422	558	4	all	all	DET
cana-5422	558	5	w1	w1	NOUN
cana-5422	558	6	,	,	PUNCT
cana-5422	558	7	w2	w2	NOUN
cana-5422	558	8	,	,	PUNCT
cana-5422	558	9	w3	w3	PROPN
cana-5422	558	10	∈	∈	PROPN
cana-5422	558	11	w1	w1	NOUN
cana-5422	558	12	and	and	CCONJ
cana-5422	558	13	all	all	DET
cana-5422	558	14	λ	λ	X
cana-5422	558	15	>	>	X
cana-5422	558	16	0	0	X
cana-5422	558	17	.	.	PUNCT
cana-5422	559	1	now	now	ADV
cana-5422	559	2	,	,	PUNCT
cana-5422	559	3	µ	µ	X
cana-5422	559	4	(	(	PUNCT
cana-5422	559	5	a(3w1	a(3w1	VERB
cana-5422	559	6	+	+	CCONJ
cana-5422	559	7	w2	w2	NOUN
cana-5422	559	8	+	+	CCONJ
cana-5422	559	9	w3	w3	PROPN
cana-5422	559	10	)	)	PUNCT
cana-5422	560	1	+	+	SYM
cana-5422	560	2	a(w1	a(w1	ADJ
cana-5422	560	3	+	+	NUM
cana-5422	560	4	3w2	3w2	NUM
cana-5422	560	5	+	+	CCONJ
cana-5422	560	6	w3	w3	NOUN
cana-5422	560	7	)	)	PUNCT
cana-5422	561	1	+	+	SYM
cana-5422	561	2	a(w1	a(w1	X
cana-5422	561	3	+	+	CCONJ
cana-5422	561	4	w2	w2	NOUN
cana-5422	561	5	+	+	CCONJ
cana-5422	561	6	3w3)−	3w3)−	NUM
cana-5422	561	7	6a	6a	NOUN
cana-5422	561	8	(	(	PUNCT
cana-5422	561	9	∑3	∑3	PROPN
cana-5422	561	10	ψ=1	ψ=1	PRON
cana-5422	561	11	wψ	wψ	ADP
cana-5422	561	12	)	)	PUNCT
cana-5422	562	1	−	−	PROPN
cana-5422	562	2	1	1	NUM
cana-5422	562	3	2	2	NUM
cana-5422	562	4	{	{	PUNCT
cana-5422	562	5	a	a	PRON
cana-5422	562	6	(	(	PUNCT
cana-5422	562	7	∑3	∑3	PROPN
cana-5422	562	8	ψ=1	ψ=1	PRON
cana-5422	562	9	wψ	wψ	ADP
cana-5422	562	10	)	)	PUNCT
cana-5422	562	11	−a	−a	NOUN
cana-5422	562	12	(	(	PUNCT
cana-5422	562	13	−∑3	−∑3	PROPN
cana-5422	562	14	ψ=1	ψ=1	PUNCT
cana-5422	562	15	wψ	wψ	ADP
cana-5422	562	16	)	)	PUNCT
cana-5422	562	17	}	}	PUNCT
cana-5422	563	1	+	+	CCONJ
cana-5422	563	2	∑3	∑3	SYM
cana-5422	563	3	ψ=1	ψ=1	X
cana-5422	563	4	{	{	PUNCT
cana-5422	563	5	a(wψ)−	a(wψ)−	NOUN
cana-5422	563	6	5	5	NUM
cana-5422	563	7	2	2	NUM
cana-5422	563	8	[	[	PUNCT
cana-5422	563	9	a(wψ	a(wψ	PROPN
cana-5422	563	10	)	)	PUNCT
cana-5422	563	11	+	+	NOUN
cana-5422	563	12	a(−wψ	a(−wψ	NOUN
cana-5422	563	13	)	)	PUNCT
cana-5422	563	14	]	]	PUNCT
cana-5422	563	15	}	}	PUNCT
cana-5422	563	16	,	,	PUNCT
cana-5422	563	17	λ	λ	PROPN
cana-5422	563	18	)	)	PUNCT
cana-5422	563	19	≥	≥	PROPN
cana-5422	563	20	µ	µ	X
cana-5422	563	21	(	(	PUNCT
cana-5422	563	22	a(3w1	a(3w1	VERB
cana-5422	563	23	+	+	NUM
cana-5422	563	24	w2	w2	NOUN
cana-5422	563	25	+	+	CCONJ
cana-5422	563	26	w3)−	w3)−	PROPN
cana-5422	563	27	1	1	NUM
cana-5422	563	28	5	5	NUM
cana-5422	563	29	`	`	SYM
cana-5422	563	30	f	f	X
cana-5422	563	31	(	(	PUNCT
cana-5422	563	32	5`(3w1	5`(3w1	NUM
cana-5422	563	33	+	+	CCONJ
cana-5422	563	34	w2	w2	NOUN
cana-5422	563	35	+	+	CCONJ
cana-5422	563	36	w3	w3	PROPN
cana-5422	563	37	)	)	PUNCT
cana-5422	563	38	)	)	PUNCT
cana-5422	563	39	,	,	PUNCT
cana-5422	563	40	λ	λ	PROPN
cana-5422	563	41	7	7	NUM
cana-5422	563	42	)	)	PUNCT
cana-5422	563	43	∗	∗	NOUN
cana-5422	563	44	µ	µ	X
cana-5422	563	45	(	(	PUNCT
cana-5422	563	46	a(w1	a(w1	X
cana-5422	563	47	+	+	X
cana-5422	563	48	3w2	3w2	NUM
cana-5422	563	49	+	+	CCONJ
cana-5422	563	50	w3)−	w3)−	PROPN
cana-5422	563	51	1	1	NUM
cana-5422	563	52	5	5	NUM
cana-5422	563	53	`	`	SYM
cana-5422	563	54	f	f	X
cana-5422	563	55	(	(	PUNCT
cana-5422	563	56	5`(w1	5`(w1	NUM
cana-5422	563	57	+	+	CCONJ
cana-5422	563	58	3w2	3w2	NUM
cana-5422	563	59	+	+	CCONJ
cana-5422	563	60	w3	w3	NOUN
cana-5422	563	61	)	)	PUNCT
cana-5422	563	62	)	)	PUNCT
cana-5422	563	63	,	,	PUNCT
cana-5422	563	64	λ	λ	PROPN
cana-5422	563	65	7	7	NUM
cana-5422	563	66	)	)	PUNCT
cana-5422	563	67	∗	∗	NOUN
cana-5422	563	68	µ	µ	X
cana-5422	563	69	(	(	PUNCT
cana-5422	563	70	a(w1	a(w1	X
cana-5422	563	71	+	+	NUM
cana-5422	563	72	w2	w2	NOUN
cana-5422	563	73	+	+	CCONJ
cana-5422	563	74	3w3)−	3w3)−	NOUN
cana-5422	563	75	1	1	NUM
cana-5422	563	76	5	5	NUM
cana-5422	563	77	`	`	SYM
cana-5422	563	78	f	f	X
cana-5422	563	79	(	(	PUNCT
cana-5422	563	80	5`(w1	5`(w1	NOUN
cana-5422	563	81	+	+	NUM
cana-5422	563	82	w2	w2	NOUN
cana-5422	563	83	+	+	CCONJ
cana-5422	563	84	3w3	3w3	NUM
cana-5422	563	85	)	)	PUNCT
cana-5422	563	86	)	)	PUNCT
cana-5422	563	87	,	,	PUNCT
cana-5422	563	88	λ	λ	PROPN
cana-5422	563	89	7	7	NUM
cana-5422	563	90	)	)	PUNCT
cana-5422	563	91	∗	∗	NOUN
cana-5422	563	92	µ	µ	X
cana-5422	563	93	(	(	PUNCT
cana-5422	563	94	−6a	−6a	PROPN
cana-5422	563	95	(	(	PUNCT
cana-5422	563	96	∑3	∑3	PROPN
cana-5422	563	97	ψ=1	ψ=1	PUNCT
cana-5422	563	98	wψ	wψ	ADP
cana-5422	563	99	)	)	PUNCT
cana-5422	564	1	+	+	CCONJ
cana-5422	564	2	1	1	NUM
cana-5422	564	3	5	5	NUM
cana-5422	564	4	`	`	NUM
cana-5422	564	5	6f	6f	NUM
cana-5422	564	6	(	(	PUNCT
cana-5422	564	7	∑3	∑3	PROPN
cana-5422	564	8	ψ=1	ψ=1	PROPN
cana-5422	564	9	5`wψ	5`wψ	PROPN
cana-5422	564	10	,	,	PUNCT
cana-5422	564	11	λ	λ	PROPN
cana-5422	564	12	7	7	NUM
cana-5422	564	13	)	)	PUNCT
cana-5422	564	14	)	)	PUNCT
cana-5422	564	15	∗	∗	NOUN
cana-5422	564	16	µ	µ	X
cana-5422	564	17	(	(	PUNCT
cana-5422	564	18	1	1	NUM
cana-5422	564	19	2	2	NUM
cana-5422	564	20	{	{	PUNCT
cana-5422	564	21	a	a	PRON
cana-5422	564	22	(	(	PUNCT
cana-5422	564	23	∑3	∑3	PROPN
cana-5422	564	24	ψ=1	ψ=1	PRON
cana-5422	564	25	wψ	wψ	ADP
cana-5422	564	26	)	)	PUNCT
cana-5422	565	1	+	+	ADP
cana-5422	565	2	a	a	DET
cana-5422	565	3	(	(	PUNCT
cana-5422	565	4	−∑3	−∑3	NOUN
cana-5422	565	5	ψ=1	ψ=1	PUNCT
cana-5422	565	6	wψ	wψ	ADP
cana-5422	565	7	)	)	PUNCT
cana-5422	565	8	}	}	PUNCT
cana-5422	565	9	−	−	NUM
cana-5422	566	1	1	1	NUM
cana-5422	566	2	5	5	NUM
cana-5422	566	3	`	`	SYM
cana-5422	566	4	1	1	NUM
cana-5422	566	5	2	2	NUM
cana-5422	566	6	{	{	PUNCT
cana-5422	566	7	f	f	PROPN
cana-5422	566	8	(	(	PUNCT
cana-5422	566	9	∑3	∑3	PROPN
cana-5422	566	10	ψ=1	ψ=1	X
cana-5422	566	11	5`wψ	5`wψ	PROPN
cana-5422	566	12	)	)	PUNCT
cana-5422	567	1	+	+	NOUN
cana-5422	567	2	f	f	X
cana-5422	567	3	(	(	PUNCT
cana-5422	567	4	−∑3	−∑3	PROPN
cana-5422	567	5	ψ=1	ψ=1	SYM
cana-5422	567	6	5`wψ	5`wψ	PROPN
cana-5422	567	7	)	)	PUNCT
cana-5422	567	8	}	}	PUNCT
cana-5422	567	9	,	,	PUNCT
cana-5422	567	10	λ	λ	PROPN
cana-5422	567	11	7	7	NUM
cana-5422	567	12	)	)	PUNCT
cana-5422	567	13	∗	∗	NOUN
cana-5422	567	14	µ	µ	X
cana-5422	567	15	(	(	PUNCT
cana-5422	567	16	∑3	∑3	PROPN
cana-5422	567	17	ψ=1	ψ=1	X
cana-5422	567	18	{	{	PUNCT
cana-5422	567	19	a(wψ)−	a(wψ)−	NOUN
cana-5422	567	20	5	5	NUM
cana-5422	567	21	2	2	NUM
cana-5422	567	22	[	[	PUNCT
cana-5422	567	23	a(wψ	a(wψ	PROPN
cana-5422	567	24	)	)	PUNCT
cana-5422	567	25	+	+	NOUN
cana-5422	567	26	a(−wψ	a(−wψ	NOUN
cana-5422	567	27	)	)	PUNCT
cana-5422	567	28	]	]	PUNCT
cana-5422	567	29	}	}	PUNCT
cana-5422	567	30	−	−	NUM
cana-5422	567	31	1	1	NUM
cana-5422	567	32	5	5	NUM
cana-5422	567	33	`	`	NUM
cana-5422	567	34	∑3	∑3	PROPN
cana-5422	567	35	ψ=1	ψ=1	X
cana-5422	567	36	{	{	PUNCT
cana-5422	567	37	f	f	PROPN
cana-5422	567	38	(	(	PUNCT
cana-5422	567	39	5`wψ)−	5`wψ)−	NUM
cana-5422	567	40	5	5	NUM
cana-5422	567	41	2	2	NUM
cana-5422	567	42	[	[	PUNCT
cana-5422	567	43	f	f	X
cana-5422	567	44	(	(	PUNCT
cana-5422	567	45	5`wψ	5`wψ	PROPN
cana-5422	567	46	)	)	PUNCT
cana-5422	568	1	+	+	NOUN
cana-5422	568	2	f	f	X
cana-5422	568	3	(	(	PUNCT
cana-5422	568	4	−5`wψ	−5`wψ	NOUN
cana-5422	568	5	)	)	PUNCT
cana-5422	568	6	]	]	PUNCT
cana-5422	568	7	}	}	PUNCT
cana-5422	568	8	,	,	PUNCT
cana-5422	568	9	λ	λ	PROPN
cana-5422	568	10	7	7	NUM
cana-5422	568	11	)	)	PUNCT
cana-5422	568	12	∗	∗	NOUN
cana-5422	568	13	µ	µ	X
cana-5422	568	14	(	(	PUNCT
cana-5422	568	15	1	1	NUM
cana-5422	568	16	5	5	NUM
cana-5422	568	17	`	`	PUNCT
cana-5422	568	18	{	{	PUNCT
cana-5422	568	19	f	f	X
cana-5422	568	20	(	(	PUNCT
cana-5422	568	21	5`(3w1	5`(3w1	NUM
cana-5422	568	22	+	+	CCONJ
cana-5422	568	23	w2	w2	NOUN
cana-5422	568	24	+	+	CCONJ
cana-5422	568	25	w3	w3	PROPN
cana-5422	568	26	)	)	PUNCT
cana-5422	568	27	)	)	PUNCT
cana-5422	569	1	+	+	NOUN
cana-5422	569	2	f	f	X
cana-5422	569	3	(	(	PUNCT
cana-5422	569	4	5`(w1	5`(w1	NUM
cana-5422	569	5	+	+	CCONJ
cana-5422	569	6	3w2	3w2	NUM
cana-5422	569	7	+	+	CCONJ
cana-5422	569	8	w3	w3	NOUN
cana-5422	569	9	)	)	PUNCT
cana-5422	569	10	)	)	PUNCT
cana-5422	570	1	+	+	NOUN
cana-5422	570	2	f	f	X
cana-5422	570	3	(	(	PUNCT
cana-5422	570	4	5`(w1	5`(w1	NOUN
cana-5422	570	5	+	+	NUM
cana-5422	570	6	w2	w2	NOUN
cana-5422	570	7	+	+	CCONJ
cana-5422	570	8	3w3	3w3	NUM
cana-5422	570	9	)	)	PUNCT
cana-5422	570	10	)	)	PUNCT
cana-5422	570	11	−6f	−6f	PROPN
cana-5422	570	12	(	(	PUNCT
cana-5422	570	13	∑3	∑3	PROPN
cana-5422	570	14	ψ=1	ψ=1	PUNCT
cana-5422	570	15	5`wψ	5`wψ	PROPN
cana-5422	570	16	)	)	PUNCT
cana-5422	571	1	−	−	NOUN
cana-5422	571	2	1	1	NUM
cana-5422	571	3	2	2	NUM
cana-5422	571	4	{	{	PUNCT
cana-5422	571	5	f	f	PROPN
cana-5422	571	6	(	(	PUNCT
cana-5422	571	7	∑3	∑3	PROPN
cana-5422	571	8	ψ=1	ψ=1	X
cana-5422	571	9	5`wψ	5`wψ	PROPN
cana-5422	571	10	)	)	PUNCT
cana-5422	572	1	+	+	NOUN
cana-5422	572	2	f	f	X
cana-5422	572	3	(	(	PUNCT
cana-5422	572	4	−∑3	−∑3	PROPN
cana-5422	572	5	ψ=1	ψ=1	SYM
cana-5422	572	6	5`wψ	5`wψ	PROPN
cana-5422	572	7	)	)	PUNCT
cana-5422	572	8	}	}	PUNCT
cana-5422	573	1	+	+	NUM
cana-5422	573	2	∑3	∑3	X
cana-5422	573	3	ψ=1	ψ=1	X
cana-5422	573	4	{	{	PUNCT
cana-5422	573	5	f	f	PROPN
cana-5422	573	6	(	(	PUNCT
cana-5422	573	7	5`wψ)−	5`wψ)−	NUM
cana-5422	573	8	5	5	NUM
cana-5422	573	9	2	2	NUM
cana-5422	573	10	[	[	PUNCT
cana-5422	573	11	f	f	X
cana-5422	573	12	(	(	PUNCT
cana-5422	573	13	5`wψ	5`wψ	PROPN
cana-5422	573	14	)	)	PUNCT
cana-5422	573	15	+	+	NOUN
cana-5422	573	16	f	f	X
cana-5422	573	17	(	(	PUNCT
cana-5422	573	18	−5`wψ	−5`wψ	NOUN
cana-5422	573	19	)	)	PUNCT
cana-5422	573	20	]	]	PUNCT
cana-5422	573	21	}	}	PUNCT
cana-5422	573	22	}	}	PUNCT
cana-5422	573	23	,	,	PUNCT
cana-5422	573	24	λ	λ	PROPN
cana-5422	573	25	7	7	NUM
cana-5422	573	26	)	)	PUNCT
cana-5422	573	27	ν	ν	NOUN
cana-5422	573	28	(	(	PUNCT
cana-5422	573	29	a(3w1	a(3w1	VERB
cana-5422	573	30	+	+	CCONJ
cana-5422	573	31	w2	w2	NOUN
cana-5422	573	32	+	+	CCONJ
cana-5422	573	33	w3	w3	PROPN
cana-5422	573	34	)	)	PUNCT
cana-5422	573	35	+	+	SYM
cana-5422	573	36	a(w1	a(w1	ADJ
cana-5422	573	37	+	+	NUM
cana-5422	573	38	3w2	3w2	NUM
cana-5422	573	39	+	+	CCONJ
cana-5422	573	40	w3	w3	NOUN
cana-5422	573	41	)	)	PUNCT
cana-5422	573	42	+	+	SYM
cana-5422	573	43	a(w1	a(w1	X
cana-5422	573	44	+	+	CCONJ
cana-5422	573	45	w2	w2	NOUN
cana-5422	573	46	+	+	CCONJ
cana-5422	573	47	3w3)−	3w3)−	NUM
cana-5422	573	48	6a	6a	NOUN
cana-5422	573	49	(	(	PUNCT
cana-5422	573	50	∑3	∑3	PROPN
cana-5422	573	51	ψ=1	ψ=1	PRON
cana-5422	573	52	wψ	wψ	ADP
cana-5422	573	53	)	)	PUNCT
cana-5422	573	54	−	−	PROPN
cana-5422	574	1	1	1	NUM
cana-5422	574	2	2	2	NUM
cana-5422	574	3	{	{	PUNCT
cana-5422	574	4	a	a	PRON
cana-5422	574	5	(	(	PUNCT
cana-5422	574	6	∑3	∑3	PROPN
cana-5422	574	7	ψ=1	ψ=1	PRON
cana-5422	574	8	wψ	wψ	ADP
cana-5422	574	9	)	)	PUNCT
cana-5422	574	10	−a	−a	NOUN
cana-5422	574	11	(	(	PUNCT
cana-5422	574	12	−∑3	−∑3	PROPN
cana-5422	574	13	ψ=1	ψ=1	PUNCT
cana-5422	574	14	wψ	wψ	ADP
cana-5422	574	15	)	)	PUNCT
cana-5422	574	16	}	}	PUNCT
cana-5422	575	1	+	+	CCONJ
cana-5422	575	2	∑3	∑3	SYM
cana-5422	575	3	ψ=1	ψ=1	X
cana-5422	575	4	{	{	PUNCT
cana-5422	575	5	a(wψ)−	a(wψ)−	NOUN
cana-5422	575	6	5	5	NUM
cana-5422	575	7	2	2	NUM
cana-5422	575	8	[	[	PUNCT
cana-5422	575	9	a(wψ	a(wψ	PROPN
cana-5422	575	10	)	)	PUNCT
cana-5422	575	11	+	+	NOUN
cana-5422	575	12	a(−wψ	a(−wψ	NOUN
cana-5422	575	13	)	)	PUNCT
cana-5422	575	14	]	]	PUNCT
cana-5422	575	15	}	}	PUNCT
cana-5422	575	16	,	,	PUNCT
cana-5422	575	17	λ	λ	PROPN
cana-5422	575	18	)	)	PUNCT
cana-5422	575	19	≤	≤	NUM
cana-5422	575	20	ν	ν	NOUN
cana-5422	575	21	(	(	PUNCT
cana-5422	575	22	a(3w1	a(3w1	VERB
cana-5422	575	23	+	+	NUM
cana-5422	575	24	w2	w2	NOUN
cana-5422	575	25	+	+	CCONJ
cana-5422	575	26	w3)−	w3)−	PROPN
cana-5422	575	27	1	1	NUM
cana-5422	575	28	5	5	NUM
cana-5422	575	29	`	`	SYM
cana-5422	575	30	f	f	X
cana-5422	575	31	(	(	PUNCT
cana-5422	575	32	5`(3w1	5`(3w1	NUM
cana-5422	575	33	+	+	CCONJ
cana-5422	575	34	w2	w2	NOUN
cana-5422	575	35	+	+	CCONJ
cana-5422	575	36	w3	w3	PROPN
cana-5422	575	37	)	)	PUNCT
cana-5422	575	38	)	)	PUNCT
cana-5422	575	39	,	,	PUNCT
cana-5422	575	40	λ	λ	PROPN
cana-5422	575	41	7	7	NUM
cana-5422	575	42	)	)	PUNCT
cana-5422	575	43	�	�	PROPN
cana-5422	575	44	ν	ν	NOUN
cana-5422	575	45	(	(	PUNCT
cana-5422	575	46	a(w1	a(w1	X
cana-5422	575	47	+	+	X
cana-5422	575	48	3w2	3w2	NUM
cana-5422	575	49	+	+	CCONJ
cana-5422	575	50	w3)−	w3)−	PROPN
cana-5422	575	51	1	1	NUM
cana-5422	575	52	5	5	NUM
cana-5422	575	53	`	`	SYM
cana-5422	575	54	f	f	X
cana-5422	575	55	(	(	PUNCT
cana-5422	575	56	5`(w1	5`(w1	NUM
cana-5422	575	57	+	+	CCONJ
cana-5422	575	58	3w2	3w2	NUM
cana-5422	575	59	+	+	CCONJ
cana-5422	575	60	w3	w3	NOUN
cana-5422	575	61	)	)	PUNCT
cana-5422	575	62	)	)	PUNCT
cana-5422	575	63	,	,	PUNCT
cana-5422	575	64	λ	λ	PROPN
cana-5422	575	65	7	7	NUM
cana-5422	575	66	)	)	PUNCT
cana-5422	575	67	�	�	PROPN
cana-5422	575	68	ν	ν	NOUN
cana-5422	575	69	(	(	PUNCT
cana-5422	575	70	a(w1	a(w1	X
cana-5422	575	71	+	+	NUM
cana-5422	575	72	w2	w2	NOUN
cana-5422	575	73	+	+	CCONJ
cana-5422	575	74	3w3)−	3w3)−	NOUN
cana-5422	575	75	1	1	NUM
cana-5422	575	76	5	5	NUM
cana-5422	575	77	`	`	SYM
cana-5422	575	78	f	f	X
cana-5422	575	79	(	(	PUNCT
cana-5422	575	80	5`(w1	5`(w1	NOUN
cana-5422	575	81	+	+	NUM
cana-5422	575	82	w2	w2	NOUN
cana-5422	575	83	+	+	CCONJ
cana-5422	575	84	3w3	3w3	NUM
cana-5422	575	85	)	)	PUNCT
cana-5422	575	86	)	)	PUNCT
cana-5422	575	87	,	,	PUNCT
cana-5422	575	88	λ	λ	PROPN
cana-5422	575	89	7	7	NUM
cana-5422	575	90	)	)	PUNCT
cana-5422	575	91	�	�	PROPN
cana-5422	575	92	ν	ν	NOUN
cana-5422	575	93	(	(	PUNCT
cana-5422	575	94	−6a	−6a	PROPN
cana-5422	575	95	(	(	PUNCT
cana-5422	575	96	∑3	∑3	PROPN
cana-5422	575	97	ψ=1	ψ=1	PUNCT
cana-5422	575	98	wψ	wψ	ADP
cana-5422	575	99	)	)	PUNCT
cana-5422	576	1	+	+	CCONJ
cana-5422	576	2	1	1	NUM
cana-5422	576	3	5	5	NUM
cana-5422	576	4	`	`	NUM
cana-5422	576	5	6f	6f	NUM
cana-5422	576	6	(	(	PUNCT
cana-5422	576	7	∑3	∑3	PROPN
cana-5422	576	8	ψ=1	ψ=1	PROPN
cana-5422	576	9	5`wψ	5`wψ	PROPN
cana-5422	576	10	,	,	PUNCT
cana-5422	576	11	λ	λ	PROPN
cana-5422	576	12	7	7	NUM
cana-5422	576	13	)	)	PUNCT
cana-5422	576	14	)	)	PUNCT
cana-5422	577	1	�	�	PROPN
cana-5422	577	2	ν	ν	NOUN
cana-5422	577	3	(	(	PUNCT
cana-5422	577	4	1	1	NUM
cana-5422	577	5	2	2	NUM
cana-5422	577	6	{	{	PUNCT
cana-5422	577	7	a	a	PRON
cana-5422	577	8	(	(	PUNCT
cana-5422	577	9	∑3	∑3	PROPN
cana-5422	577	10	ψ=1	ψ=1	PRON
cana-5422	577	11	wψ	wψ	ADP
cana-5422	577	12	)	)	PUNCT
cana-5422	578	1	+	+	ADP
cana-5422	578	2	a	a	DET
cana-5422	578	3	(	(	PUNCT
cana-5422	578	4	−∑3	−∑3	NOUN
cana-5422	578	5	ψ=1	ψ=1	PUNCT
cana-5422	578	6	wψ	wψ	ADP
cana-5422	578	7	)	)	PUNCT
cana-5422	578	8	}	}	PUNCT
cana-5422	578	9	−	−	NUM
cana-5422	579	1	1	1	NUM
cana-5422	579	2	5	5	NUM
cana-5422	579	3	`	`	SYM
cana-5422	579	4	1	1	NUM
cana-5422	579	5	2	2	NUM
cana-5422	579	6	{	{	PUNCT
cana-5422	579	7	f	f	PROPN
cana-5422	579	8	(	(	PUNCT
cana-5422	579	9	∑3	∑3	PROPN
cana-5422	579	10	ψ=1	ψ=1	X
cana-5422	579	11	5`wψ	5`wψ	PROPN
cana-5422	579	12	)	)	PUNCT
cana-5422	580	1	+	+	NOUN
cana-5422	580	2	f	f	X
cana-5422	580	3	(	(	PUNCT
cana-5422	580	4	−∑3	−∑3	PROPN
cana-5422	580	5	ψ=1	ψ=1	SYM
cana-5422	580	6	5`wψ	5`wψ	PROPN
cana-5422	580	7	)	)	PUNCT
cana-5422	580	8	}	}	PUNCT
cana-5422	580	9	,	,	PUNCT
cana-5422	580	10	λ	λ	PROPN
cana-5422	580	11	7	7	NUM
cana-5422	580	12	)	)	PUNCT
cana-5422	580	13	�	�	PROPN
cana-5422	580	14	ν	ν	NOUN
cana-5422	580	15	(	(	PUNCT
cana-5422	580	16	∑3	∑3	PROPN
cana-5422	580	17	ψ=1	ψ=1	X
cana-5422	580	18	{	{	PUNCT
cana-5422	580	19	a(wψ)−	a(wψ)−	NOUN
cana-5422	580	20	5	5	NUM
cana-5422	580	21	2	2	NUM
cana-5422	580	22	[	[	PUNCT
cana-5422	580	23	a(wψ	a(wψ	PROPN
cana-5422	580	24	)	)	PUNCT
cana-5422	580	25	+	+	NOUN
cana-5422	580	26	a(−wψ	a(−wψ	NOUN
cana-5422	580	27	)	)	PUNCT
cana-5422	580	28	]	]	PUNCT
cana-5422	580	29	}	}	PUNCT
cana-5422	580	30	−	−	NUM
cana-5422	580	31	1	1	NUM
cana-5422	580	32	5	5	NUM
cana-5422	580	33	`	`	NUM
cana-5422	580	34	∑3	∑3	PROPN
cana-5422	580	35	ψ=1	ψ=1	X
cana-5422	580	36	{	{	PUNCT
cana-5422	580	37	f	f	PROPN
cana-5422	580	38	(	(	PUNCT
cana-5422	580	39	5`wψ)−	5`wψ)−	NUM
cana-5422	580	40	5	5	NUM
cana-5422	580	41	2	2	NUM
cana-5422	580	42	[	[	PUNCT
cana-5422	580	43	f	f	X
cana-5422	580	44	(	(	PUNCT
cana-5422	580	45	5`wψ	5`wψ	PROPN
cana-5422	580	46	)	)	PUNCT
cana-5422	581	1	+	+	NOUN
cana-5422	581	2	f	f	X
cana-5422	581	3	(	(	PUNCT
cana-5422	581	4	−5`wψ	−5`wψ	NOUN
cana-5422	581	5	)	)	PUNCT
cana-5422	581	6	]	]	PUNCT
cana-5422	581	7	}	}	PUNCT
cana-5422	581	8	,	,	PUNCT
cana-5422	581	9	λ	λ	PROPN
cana-5422	581	10	7	7	NUM
cana-5422	581	11	)	)	PUNCT
cana-5422	581	12	�	�	PROPN
cana-5422	581	13	ν	ν	NOUN
cana-5422	581	14	(	(	PUNCT
cana-5422	581	15	1	1	NUM
cana-5422	581	16	5	5	NUM
cana-5422	581	17	`	`	PUNCT
cana-5422	581	18	{	{	PUNCT
cana-5422	581	19	f	f	X
cana-5422	581	20	(	(	PUNCT
cana-5422	581	21	5`(3w1	5`(3w1	NUM
cana-5422	581	22	+	+	CCONJ
cana-5422	581	23	w2	w2	NOUN
cana-5422	581	24	+	+	CCONJ
cana-5422	581	25	w3	w3	PROPN
cana-5422	581	26	)	)	PUNCT
cana-5422	581	27	)	)	PUNCT
cana-5422	582	1	+	+	NOUN
cana-5422	582	2	f	f	X
cana-5422	582	3	(	(	PUNCT
cana-5422	582	4	5`(w1	5`(w1	NUM
cana-5422	582	5	+	+	CCONJ
cana-5422	582	6	3w2	3w2	NUM
cana-5422	582	7	+	+	CCONJ
cana-5422	582	8	w3	w3	NOUN
cana-5422	582	9	)	)	PUNCT
cana-5422	582	10	)	)	PUNCT
cana-5422	583	1	+	+	NOUN
cana-5422	583	2	f	f	X
cana-5422	583	3	(	(	PUNCT
cana-5422	583	4	5`(w1	5`(w1	NOUN
cana-5422	583	5	+	+	NUM
cana-5422	583	6	w2	w2	NOUN
cana-5422	583	7	+	+	CCONJ
cana-5422	583	8	3w3	3w3	NUM
cana-5422	583	9	)	)	PUNCT
cana-5422	583	10	)	)	PUNCT
cana-5422	583	11	−6f	−6f	PROPN
cana-5422	583	12	(	(	PUNCT
cana-5422	583	13	∑3	∑3	PROPN
cana-5422	583	14	ψ=1	ψ=1	PUNCT
cana-5422	583	15	5`wψ	5`wψ	PROPN
cana-5422	583	16	)	)	PUNCT
cana-5422	584	1	−	−	NOUN
cana-5422	584	2	1	1	NUM
cana-5422	584	3	2	2	NUM
cana-5422	584	4	{	{	PUNCT
cana-5422	584	5	f	f	PROPN
cana-5422	584	6	(	(	PUNCT
cana-5422	584	7	∑3	∑3	PROPN
cana-5422	584	8	ψ=1	ψ=1	X
cana-5422	584	9	5`wψ	5`wψ	PROPN
cana-5422	584	10	)	)	PUNCT
cana-5422	585	1	+	+	NOUN
cana-5422	585	2	f	f	X
cana-5422	585	3	(	(	PUNCT
cana-5422	585	4	−∑3	−∑3	PROPN
cana-5422	585	5	ψ=1	ψ=1	SYM
cana-5422	585	6	5`wψ	5`wψ	PROPN
cana-5422	585	7	)	)	PUNCT
cana-5422	585	8	}	}	PUNCT
cana-5422	586	1	+	+	NUM
cana-5422	586	2	∑3	∑3	X
cana-5422	586	3	ψ=1	ψ=1	X
cana-5422	586	4	{	{	PUNCT
cana-5422	586	5	f	f	PROPN
cana-5422	586	6	(	(	PUNCT
cana-5422	586	7	5`wψ)−	5`wψ)−	NUM
cana-5422	586	8	5	5	NUM
cana-5422	586	9	2	2	NUM
cana-5422	586	10	[	[	PUNCT
cana-5422	586	11	f	f	X
cana-5422	586	12	(	(	PUNCT
cana-5422	586	13	5`wψ	5`wψ	PROPN
cana-5422	586	14	)	)	PUNCT
cana-5422	587	1	+	+	NOUN
cana-5422	587	2	f	f	X
cana-5422	587	3	(	(	PUNCT
cana-5422	587	4	−5`wψ	−5`wψ	NOUN
cana-5422	587	5	)	)	PUNCT
cana-5422	587	6	]	]	PUNCT
cana-5422	587	7	}	}	PUNCT
cana-5422	587	8	}	}	PUNCT
cana-5422	587	9	,	,	PUNCT
cana-5422	587	10	λ	λ	PROPN
cana-5422	587	11	7	7	NUM
cana-5422	587	12	)	)	PUNCT
cana-5422	587	13			NOUN
cana-5422	587	14	(	(	PUNCT
cana-5422	587	15	3.26	3.26	NUM
cana-5422	587	16	)	)	PUNCT
cana-5422	587	17	for	for	ADP
cana-5422	587	18	all	all	DET
cana-5422	587	19	w1	w1	NOUN
cana-5422	587	20	,	,	PUNCT
cana-5422	587	21	w2	w2	NOUN
cana-5422	587	22	,	,	PUNCT
cana-5422	587	23	w3	w3	PROPN
cana-5422	587	24	∈	∈	PROPN
cana-5422	587	25	w1	w1	NOUN
cana-5422	587	26	and	and	CCONJ
cana-5422	587	27	all	all	DET
cana-5422	587	28	λ	λ	PROPN
cana-5422	587	29	>	>	X
cana-5422	587	30	0	0	X
cana-5422	587	31	.	.	PUNCT
cana-5422	588	1	taking	take	VERB
cana-5422	588	2	limit	limit	NOUN
cana-5422	588	3	`	`	PUNCT
cana-5422	588	4	→	→	SYM
cana-5422	588	5	∞	∞	NUM
cana-5422	588	6	in	in	ADP
cana-5422	588	7	(	(	PUNCT
cana-5422	588	8	3.26	3.26	NUM
cana-5422	588	9	)	)	PUNCT
cana-5422	588	10	,	,	PUNCT
cana-5422	588	11	using	use	VERB
cana-5422	588	12	(	(	PUNCT
cana-5422	588	13	3.23	3.23	NUM
cana-5422	588	14	)	)	PUNCT
cana-5422	588	15	and	and	CCONJ
cana-5422	588	16	(	(	PUNCT
cana-5422	588	17	3.25	3.25	NUM
cana-5422	588	18	)	)	PUNCT
cana-5422	588	19	,	,	PUNCT
cana-5422	588	20	we	we	PRON
cana-5422	588	21	get	get	VERB
cana-5422	588	22	µ	µ	X
cana-5422	588	23	(	(	PUNCT
cana-5422	588	24	a(3w1	a(3w1	PUNCT
cana-5422	588	25	+	+	CCONJ
cana-5422	588	26	w2	w2	NOUN
cana-5422	588	27	+	+	CCONJ
cana-5422	588	28	w3	w3	PROPN
cana-5422	588	29	)	)	PUNCT
cana-5422	589	1	+	+	SYM
cana-5422	589	2	a(w1	a(w1	ADJ
cana-5422	589	3	+	+	NUM
cana-5422	589	4	3w2	3w2	NUM
cana-5422	589	5	+	+	CCONJ
cana-5422	589	6	w3	w3	NOUN
cana-5422	589	7	)	)	PUNCT
cana-5422	590	1	+	+	SYM
cana-5422	590	2	a(w1	a(w1	X
cana-5422	590	3	+	+	CCONJ
cana-5422	590	4	w2	w2	NOUN
cana-5422	590	5	+	+	CCONJ
cana-5422	590	6	3w3)−	3w3)−	NUM
cana-5422	590	7	6a	6a	NOUN
cana-5422	590	8	(	(	PUNCT
cana-5422	590	9	∑3	∑3	PROPN
cana-5422	590	10	ψ=1	ψ=1	PRON
cana-5422	590	11	wψ	wψ	ADP
cana-5422	590	12	)	)	PUNCT
cana-5422	591	1	−	−	PROPN
cana-5422	591	2	1	1	NUM
cana-5422	591	3	2	2	NUM
cana-5422	591	4	{	{	PUNCT
cana-5422	591	5	a	a	PRON
cana-5422	591	6	(	(	PUNCT
cana-5422	591	7	∑3	∑3	PROPN
cana-5422	591	8	ψ=1	ψ=1	PRON
cana-5422	591	9	wψ	wψ	ADP
cana-5422	591	10	)	)	PUNCT
cana-5422	592	1	+	+	ADP
cana-5422	592	2	a	a	DET
cana-5422	592	3	(	(	PUNCT
cana-5422	592	4	−∑3	−∑3	NOUN
cana-5422	592	5	ψ=1	ψ=1	PUNCT
cana-5422	592	6	wψ	wψ	ADP
cana-5422	592	7	)	)	PUNCT
cana-5422	592	8	}	}	PUNCT
cana-5422	593	1	+	+	CCONJ
cana-5422	593	2	∑3	∑3	SYM
cana-5422	593	3	ψ=1	ψ=1	X
cana-5422	593	4	{	{	PUNCT
cana-5422	593	5	a(wψ)−	a(wψ)−	NOUN
cana-5422	593	6	5	5	NUM
cana-5422	593	7	2	2	NUM
cana-5422	593	8	[	[	PUNCT
cana-5422	593	9	a(wψ	a(wψ	PROPN
cana-5422	593	10	)	)	PUNCT
cana-5422	593	11	+	+	NOUN
cana-5422	593	12	a(−wψ	a(−wψ	NOUN
cana-5422	593	13	)	)	PUNCT
cana-5422	593	14	]	]	PUNCT
cana-5422	593	15	}	}	PUNCT
cana-5422	593	16	,	,	PUNCT
cana-5422	593	17	λ	λ	INTJ
cana-5422	593	18	)	)	PUNCT
cana-5422	593	19	=	=	SYM
cana-5422	593	20	1	1	NUM
cana-5422	593	21	ν	ν	NOUN
cana-5422	593	22	(	(	PUNCT
cana-5422	593	23	a(3w1	a(3w1	VERB
cana-5422	593	24	+	+	CCONJ
cana-5422	593	25	w2	w2	NOUN
cana-5422	593	26	+	+	CCONJ
cana-5422	593	27	w3	w3	PROPN
cana-5422	593	28	)	)	PUNCT
cana-5422	593	29	+	+	SYM
cana-5422	593	30	a(w1	a(w1	ADJ
cana-5422	593	31	+	+	NUM
cana-5422	593	32	3w2	3w2	NUM
cana-5422	593	33	+	+	CCONJ
cana-5422	593	34	w3	w3	NOUN
cana-5422	593	35	)	)	PUNCT
cana-5422	593	36	+	+	SYM
cana-5422	593	37	a(w1	a(w1	X
cana-5422	593	38	+	+	CCONJ
cana-5422	593	39	w2	w2	NOUN
cana-5422	593	40	+	+	CCONJ
cana-5422	593	41	3w3)−	3w3)−	NUM
cana-5422	593	42	6a	6a	NOUN
cana-5422	593	43	(	(	PUNCT
cana-5422	593	44	∑3	∑3	PROPN
cana-5422	593	45	ψ=1	ψ=1	PRON
cana-5422	593	46	wψ	wψ	ADP
cana-5422	593	47	)	)	PUNCT
cana-5422	593	48	−	−	PROPN
cana-5422	593	49	1	1	NUM
cana-5422	593	50	2	2	NUM
cana-5422	593	51	{	{	PUNCT
cana-5422	593	52	a	a	PRON
cana-5422	593	53	(	(	PUNCT
cana-5422	593	54	∑3	∑3	PROPN
cana-5422	593	55	ψ=1	ψ=1	PRON
cana-5422	593	56	wψ	wψ	ADP
cana-5422	593	57	)	)	PUNCT
cana-5422	593	58	+	+	ADP
cana-5422	593	59	a	a	DET
cana-5422	593	60	(	(	PUNCT
cana-5422	593	61	−∑3	−∑3	NOUN
cana-5422	593	62	ψ=1	ψ=1	PUNCT
cana-5422	593	63	wψ	wψ	ADP
cana-5422	593	64	)	)	PUNCT
cana-5422	593	65	}	}	PUNCT
cana-5422	593	66	+	+	CCONJ
cana-5422	593	67	∑3	∑3	SYM
cana-5422	593	68	ψ=1	ψ=1	X
cana-5422	593	69	{	{	PUNCT
cana-5422	593	70	a(wψ)−	a(wψ)−	NOUN
cana-5422	593	71	5	5	NUM
cana-5422	593	72	2	2	NUM
cana-5422	593	73	[	[	PUNCT
cana-5422	593	74	a(wψ	a(wψ	PROPN
cana-5422	593	75	)	)	PUNCT
cana-5422	593	76	+	+	NOUN
cana-5422	593	77	a(−wψ	a(−wψ	NOUN
cana-5422	593	78	)	)	PUNCT
cana-5422	593	79	]	]	PUNCT
cana-5422	593	80	}	}	PUNCT
cana-5422	593	81	,	,	PUNCT
cana-5422	593	82	λ	λ	INTJ
cana-5422	593	83	)	)	PUNCT
cana-5422	593	84	=	=	SYM
cana-5422	593	85	0	0	NUM
cana-5422	593	86			VERB
cana-5422	593	87	(	(	PUNCT
cana-5422	593	88	3.27	3.27	NUM
cana-5422	593	89	)	)	PUNCT
cana-5422	593	90	for	for	ADP
cana-5422	593	91	all	all	DET
cana-5422	593	92	w1	w1	NOUN
cana-5422	593	93	,	,	PUNCT
cana-5422	593	94	w2	w2	NOUN
cana-5422	593	95	,	,	PUNCT
cana-5422	593	96	w3	w3	PROPN
cana-5422	593	97	∈	∈	PROPN
cana-5422	593	98	w1	w1	NOUN
cana-5422	593	99	and	and	CCONJ
cana-5422	593	100	all	all	DET
cana-5422	593	101	λ	λ	PROPN
cana-5422	593	102	>	>	X
cana-5422	593	103	0	0	X
cana-5422	593	104	.	.	PUNCT
cana-5422	593	105	using	use	VERB
cana-5422	593	106	(	(	PUNCT
cana-5422	593	107	ifn3	ifn3	PROPN
cana-5422	593	108	)	)	PUNCT
cana-5422	593	109	,	,	PUNCT
cana-5422	593	110	(	(	PUNCT
cana-5422	593	111	ifn9	ifn9	PROPN
cana-5422	593	112	)	)	PUNCT
cana-5422	593	113	in	in	ADP
cana-5422	593	114	(	(	PUNCT
cana-5422	593	115	3.27	3.27	NUM
cana-5422	593	116	)	)	PUNCT
cana-5422	593	117	,	,	PUNCT
cana-5422	593	118	we	we	PRON
cana-5422	593	119	see	see	VERB
cana-5422	593	120	,	,	PUNCT
cana-5422	593	121	a(w1	a(w1	ADJ
cana-5422	593	122	)	)	PUNCT
cana-5422	593	123	satisfies	satisfie	NOUN
cana-5422	593	124	(	(	PUNCT
cana-5422	593	125	1.7	1.7	NUM
cana-5422	593	126	)	)	PUNCT
cana-5422	593	127	.	.	PUNCT
cana-5422	594	1	in	in	ADP
cana-5422	594	2	order	order	NOUN
cana-5422	594	3	to	to	PART
cana-5422	594	4	confirm	confirm	VERB
cana-5422	594	5	that	that	DET
cana-5422	594	6	a(w1	a(w1	NOUN
cana-5422	594	7	)	)	PUNCT
cana-5422	594	8	is	be	AUX
cana-5422	594	9	unique	unique	ADJ
cana-5422	594	10	,	,	PUNCT
cana-5422	594	11	suppose	suppose	VERB
cana-5422	594	12	b(w1	b(w1	NOUN
cana-5422	594	13	)	)	PUNCT
cana-5422	594	14	be	be	AUX
cana-5422	594	15	another	another	DET
cana-5422	594	16	mapping	mapping	NOUN
cana-5422	594	17	(	(	PUNCT
cana-5422	594	18	1.7	1.7	NUM
cana-5422	594	19	)	)	PUNCT
cana-5422	594	20	,	,	PUNCT
cana-5422	594	21	(	(	PUNCT
cana-5422	594	22	3.23	3.23	NUM
cana-5422	594	23	)	)	PUNCT
cana-5422	594	24	and	and	CCONJ
cana-5422	594	25	(	(	PUNCT
cana-5422	594	26	3.24	3.24	NUM
cana-5422	594	27	)	)	PUNCT
cana-5422	594	28	,	,	PUNCT
cana-5422	594	29	we	we	PRON
cana-5422	594	30	communications	communication	VERB
cana-5422	594	31	on	on	ADP
cana-5422	594	32	applied	apply	VERB
cana-5422	594	33	nonlinear	nonlinear	ADJ
cana-5422	594	34	analysis	analysis	NOUN
cana-5422	594	35	issn	issn	NOUN
cana-5422	594	36	:	:	PUNCT
cana-5422	594	37	1074	1074	NUM
cana-5422	594	38	-	-	PUNCT
cana-5422	594	39	133x	133x	NUM
cana-5422	594	40	vol	vol	NOUN
cana-5422	594	41	32	32	NUM
cana-5422	594	42	no	no	NOUN
cana-5422	594	43	.	.	PUNCT
cana-5422	595	1	10s(2025	10s(2025	NUM
cana-5422	595	2	)	)	PUNCT
cana-5422	595	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	595	4	2205	2205	NUM
cana-5422	595	5	obtain	obtain	VERB
cana-5422	595	6	µ	µ	X
cana-5422	595	7	(	(	PUNCT
cana-5422	595	8	a(w1)−b(w1	a(w1)−b(w1	PROPN
cana-5422	595	9	)	)	PUNCT
cana-5422	595	10	,	,	PUNCT
cana-5422	595	11	2λ	2λ	NUM
cana-5422	595	12	)	)	PUNCT
cana-5422	596	1	=	=	SYM
cana-5422	596	2	µ	µ	X
cana-5422	596	3	(	(	PUNCT
cana-5422	596	4	a	a	PRON
cana-5422	596	5	(	(	PUNCT
cana-5422	596	6	5`w1	5`w1	NUM
cana-5422	596	7	)	)	PUNCT
cana-5422	596	8	−b	−b	ADV
cana-5422	596	9	(	(	PUNCT
cana-5422	596	10	5`w1	5`w1	NUM
cana-5422	596	11	)	)	PUNCT
cana-5422	596	12	,	,	PUNCT
cana-5422	596	13	5	5	NUM
cana-5422	596	14	`	`	NUM
cana-5422	596	15	2λ	2λ	NUM
cana-5422	596	16	)	)	PUNCT
cana-5422	596	17	≥	≥	PROPN
cana-5422	596	18	µ	µ	X
cana-5422	596	19	(	(	PUNCT
cana-5422	596	20	a	a	PRON
cana-5422	596	21	(	(	PUNCT
cana-5422	596	22	5`w1	5`w1	NUM
cana-5422	596	23	)	)	PUNCT
cana-5422	597	1	−f	−f	NOUN
cana-5422	597	2	(	(	PUNCT
cana-5422	597	3	5`w1	5`w1	NUM
cana-5422	597	4	)	)	PUNCT
cana-5422	597	5	,	,	PUNCT
cana-5422	597	6	5`λ	5`λ	NUM
cana-5422	597	7	)	)	PUNCT
cana-5422	597	8	∗	∗	NOUN
cana-5422	597	9	µ	µ	X
cana-5422	597	10	(	(	PUNCT
cana-5422	597	11	f	f	X
cana-5422	597	12	(	(	PUNCT
cana-5422	597	13	5`w1	5`w1	X
cana-5422	597	14	)	)	PUNCT
cana-5422	597	15	−b	−b	ADV
cana-5422	597	16	(	(	PUNCT
cana-5422	597	17	5`w1	5`w1	NUM
cana-5422	597	18	)	)	PUNCT
cana-5422	597	19	,	,	PUNCT
cana-5422	597	20	5`λ	5`λ	NUM
cana-5422	597	21	)	)	PUNCT
cana-5422	597	22	≥	≥	NOUN
cana-5422	597	23	µ′	µ′	PUNCT
cana-5422	597	24	(	(	PUNCT
cana-5422	597	25	ψa	ψa	X
cana-5422	597	26	(	(	PUNCT
cana-5422	597	27	5`w1	5`w1	NUM
cana-5422	597	28	)	)	PUNCT
cana-5422	597	29	,	,	PUNCT
cana-5422	597	30	3λ	3λ	NUM
cana-5422	597	31	4	4	NUM
cana-5422	597	32	5`(5−	5`(5−	NUM
cana-5422	597	33	i	i	NOUN
cana-5422	597	34	)	)	PUNCT
cana-5422	597	35	)	)	PUNCT
cana-5422	597	36	∗	∗	NOUN
cana-5422	597	37	µ′	µ′	PUNCT
cana-5422	597	38	(	(	PUNCT
cana-5422	597	39	ψa	ψa	X
cana-5422	597	40	(	(	PUNCT
cana-5422	597	41	5`w1	5`w1	NUM
cana-5422	597	42	)	)	PUNCT
cana-5422	597	43	,	,	PUNCT
cana-5422	597	44	3λ	3λ	NUM
cana-5422	597	45	4	4	NUM
cana-5422	597	46	5`(5−	5`(5−	NUM
cana-5422	597	47	i	i	NOUN
cana-5422	597	48	)	)	PUNCT
cana-5422	597	49	)	)	PUNCT
cana-5422	597	50	≥	≥	NOUN
cana-5422	597	51	µ′	µ′	PUNCT
cana-5422	597	52	(	(	PUNCT
cana-5422	597	53	ψa	ψa	X
cana-5422	597	54	(	(	PUNCT
cana-5422	597	55	w1	w1	NOUN
cana-5422	597	56	)	)	PUNCT
cana-5422	597	57	,	,	PUNCT
cana-5422	597	58	3λ	3λ	NUM
cana-5422	597	59	4	4	NUM
cana-5422	597	60	5	5	NUM
cana-5422	597	61	`	`	PUNCT
cana-5422	597	62	i	i	PRON
cana-5422	597	63	`	`	PUNCT
cana-5422	597	64	(	(	PUNCT
cana-5422	597	65	5−	5−	NUM
cana-5422	597	66	i	i	NOUN
cana-5422	597	67	)	)	PUNCT
cana-5422	597	68	)	)	PUNCT
cana-5422	598	1	ν	ν	NOUN
cana-5422	598	2	(	(	PUNCT
cana-5422	598	3	a(w1)−b(w1	a(w1)−b(w1	PROPN
cana-5422	598	4	)	)	PUNCT
cana-5422	598	5	,	,	PUNCT
cana-5422	598	6	2λ	2λ	NUM
cana-5422	598	7	)	)	PUNCT
cana-5422	599	1	=	=	PUNCT
cana-5422	599	2	ν	ν	NOUN
cana-5422	599	3	(	(	PUNCT
cana-5422	599	4	a	a	DET
cana-5422	599	5	(	(	PUNCT
cana-5422	599	6	5`w1	5`w1	NUM
cana-5422	599	7	)	)	PUNCT
cana-5422	599	8	−b	−b	ADV
cana-5422	599	9	(	(	PUNCT
cana-5422	599	10	5`w1	5`w1	NUM
cana-5422	599	11	)	)	PUNCT
cana-5422	599	12	,	,	PUNCT
cana-5422	599	13	5	5	NUM
cana-5422	599	14	`	`	NUM
cana-5422	599	15	2λ	2λ	NUM
cana-5422	599	16	)	)	PUNCT
cana-5422	599	17	≤	≤	NUM
cana-5422	600	1	ν	ν	NOUN
cana-5422	600	2	(	(	PUNCT
cana-5422	600	3	a	a	PRON
cana-5422	600	4	(	(	PUNCT
cana-5422	600	5	5`w1	5`w1	NUM
cana-5422	600	6	)	)	PUNCT
cana-5422	600	7	−f	−f	NOUN
cana-5422	600	8	(	(	PUNCT
cana-5422	600	9	5`w1	5`w1	NUM
cana-5422	600	10	)	)	PUNCT
cana-5422	600	11	,	,	PUNCT
cana-5422	600	12	5`λ	5`λ	NUM
cana-5422	600	13	)	)	PUNCT
cana-5422	600	14	�	�	PROPN
cana-5422	600	15	ν	ν	PROPN
cana-5422	600	16	(	(	PUNCT
cana-5422	600	17	f	f	X
cana-5422	600	18	(	(	PUNCT
cana-5422	600	19	5`w1	5`w1	X
cana-5422	600	20	)	)	PUNCT
cana-5422	600	21	−b	−b	ADV
cana-5422	600	22	(	(	PUNCT
cana-5422	600	23	5`w1	5`w1	NUM
cana-5422	600	24	)	)	PUNCT
cana-5422	600	25	,	,	PUNCT
cana-5422	600	26	5`λ	5`λ	NUM
cana-5422	600	27	)	)	PUNCT
cana-5422	600	28	≤	≤	NUM
cana-5422	600	29	ν′	ν′	NOUN
cana-5422	600	30	(	(	PUNCT
cana-5422	600	31	ψa	ψa	X
cana-5422	600	32	(	(	PUNCT
cana-5422	600	33	5`w1	5`w1	NUM
cana-5422	600	34	)	)	PUNCT
cana-5422	600	35	,	,	PUNCT
cana-5422	600	36	3λ	3λ	NUM
cana-5422	600	37	4	4	NUM
cana-5422	600	38	5`(5−	5`(5−	NUM
cana-5422	600	39	i	i	NOUN
cana-5422	600	40	)	)	PUNCT
cana-5422	600	41	)	)	PUNCT
cana-5422	601	1	�	�	PROPN
cana-5422	601	2	ν′	ν′	NOUN
cana-5422	601	3	(	(	PUNCT
cana-5422	601	4	ψa	ψa	X
cana-5422	601	5	(	(	PUNCT
cana-5422	601	6	5`w1	5`w1	NUM
cana-5422	601	7	)	)	PUNCT
cana-5422	601	8	,	,	PUNCT
cana-5422	601	9	3λ	3λ	NUM
cana-5422	601	10	4	4	NUM
cana-5422	601	11	5`(5−	5`(5−	NUM
cana-5422	601	12	i	i	NOUN
cana-5422	601	13	)	)	PUNCT
cana-5422	601	14	)	)	PUNCT
cana-5422	601	15	≤	≤	NUM
cana-5422	601	16	ν′	ν′	NOUN
cana-5422	601	17	(	(	PUNCT
cana-5422	601	18	ψa	ψa	X
cana-5422	601	19	(	(	PUNCT
cana-5422	601	20	w1	w1	NOUN
cana-5422	601	21	)	)	PUNCT
cana-5422	601	22	,	,	PUNCT
cana-5422	601	23	3λ	3λ	NUM
cana-5422	602	1	4	4	NUM
cana-5422	602	2	5	5	NUM
cana-5422	602	3	`	`	PUNCT
cana-5422	602	4	i	i	PRON
cana-5422	602	5	`	`	PUNCT
cana-5422	602	6	(	(	PUNCT
cana-5422	602	7	5−	5−	NUM
cana-5422	602	8	i	i	NOUN
cana-5422	602	9	)	)	PUNCT
cana-5422	602	10	)	)	PUNCT
cana-5422	602	11			NOUN
cana-5422	602	12	(	(	PUNCT
cana-5422	602	13	3.28	3.28	NUM
cana-5422	602	14	)	)	PUNCT
cana-5422	602	15	for	for	ADP
cana-5422	602	16	all	all	DET
cana-5422	602	17	w1	w1	NOUN
cana-5422	602	18	∈	∈	PROPN
cana-5422	602	19	w1	w1	NOUN
cana-5422	602	20	and	and	CCONJ
cana-5422	602	21	all	all	DET
cana-5422	602	22	λ	λ	PROPN
cana-5422	602	23	>	>	X
cana-5422	602	24	0	0	X
cana-5422	602	25	.	.	PUNCT
cana-5422	602	26	taking	take	VERB
cana-5422	602	27	limit	limit	NOUN
cana-5422	602	28	`	`	PUNCT
cana-5422	602	29	→	→	SYM
cana-5422	602	30	∞	∞	NUM
cana-5422	602	31	in	in	ADP
cana-5422	602	32	(	(	PUNCT
cana-5422	602	33	3.28	3.28	NUM
cana-5422	602	34	)	)	PUNCT
cana-5422	602	35	,	,	PUNCT
cana-5422	602	36	and	and	CCONJ
cana-5422	602	37	using	use	VERB
cana-5422	602	38	(	(	PUNCT
cana-5422	602	39	ifn7	ifn7	PROPN
cana-5422	602	40	)	)	PUNCT
cana-5422	602	41	,	,	PUNCT
cana-5422	602	42	(	(	PUNCT
cana-5422	602	43	ifn13	ifn13	ADJ
cana-5422	602	44	)	)	PUNCT
cana-5422	602	45	,	,	PUNCT
cana-5422	602	46	we	we	PRON
cana-5422	602	47	arrive	arrive	VERB
cana-5422	602	48	µ	µ	X
cana-5422	602	49	(	(	PUNCT
cana-5422	602	50	a(w1)−b(w1	a(w1)−b(w1	PROPN
cana-5422	602	51	)	)	PUNCT
cana-5422	602	52	,	,	PUNCT
cana-5422	602	53	2λ	2λ	NUM
cana-5422	602	54	)	)	PUNCT
cana-5422	603	1	=	=	SYM
cana-5422	603	2	1	1	NUM
cana-5422	603	3	ν	ν	NOUN
cana-5422	603	4	(	(	PUNCT
cana-5422	603	5	a(w1)−b(w1	a(w1)−b(w1	PROPN
cana-5422	603	6	)	)	PUNCT
cana-5422	603	7	,	,	PUNCT
cana-5422	603	8	2λ	2λ	NUM
cana-5422	603	9	)	)	PUNCT
cana-5422	604	1	=	=	SYM
cana-5422	604	2	0	0	X
cana-5422	604	3	}	}	PUNCT
cana-5422	604	4	(	(	PUNCT
cana-5422	604	5	3.29	3.29	NUM
cana-5422	604	6	)	)	PUNCT
cana-5422	604	7	for	for	ADP
cana-5422	604	8	all	all	DET
cana-5422	604	9	w1	w1	NOUN
cana-5422	604	10	∈	∈	PROPN
cana-5422	604	11	w1	w1	NOUN
cana-5422	604	12	and	and	CCONJ
cana-5422	604	13	all	all	DET
cana-5422	604	14	λ	λ	PROPN
cana-5422	604	15	>	>	X
cana-5422	604	16	0	0	NUM
cana-5422	604	17	.	.	PUNCT
cana-5422	605	1	by	by	ADP
cana-5422	605	2	(	(	PUNCT
cana-5422	605	3	ifn4	ifn4	PROPN
cana-5422	605	4	)	)	PUNCT
cana-5422	605	5	and	and	CCONJ
cana-5422	605	6	(	(	PUNCT
cana-5422	605	7	ifn10	ifn10	PROPN
cana-5422	605	8	)	)	PUNCT
cana-5422	605	9	,	,	PUNCT
cana-5422	605	10	we	we	PRON
cana-5422	605	11	get	get	VERB
cana-5422	605	12	a(w1	a(w1	NOUN
cana-5422	605	13	)	)	PUNCT
cana-5422	605	14	is	be	AUX
cana-5422	605	15	unique	unique	ADJ
cana-5422	605	16	.	.	PUNCT
cana-5422	606	1	so	so	ADV
cana-5422	606	2	,	,	PUNCT
cana-5422	606	3	the	the	DET
cana-5422	606	4	theorem	theorem	NOUN
cana-5422	606	5	holds	hold	VERB
cana-5422	606	6	for	for	ADP
cana-5422	606	7	m	m	NOUN
cana-5422	606	8	=	=	SYM
cana-5422	606	9	1	1	NUM
cana-5422	606	10	.	.	X
cana-5422	606	11	changing	change	VERB
cana-5422	606	12	w1	w1	NOUN
cana-5422	606	13	=	=	SYM
cana-5422	606	14	w1	w1	NOUN
cana-5422	606	15	5	5	NUM
cana-5422	606	16	in	in	ADP
cana-5422	606	17	(	(	PUNCT
cana-5422	606	18	3.15	3.15	NUM
cana-5422	606	19	)	)	PUNCT
cana-5422	606	20	and	and	CCONJ
cana-5422	606	21	using	use	VERB
cana-5422	606	22	(	(	PUNCT
cana-5422	606	23	ifn4	ifn4	PROPN
cana-5422	606	24	)	)	PUNCT
cana-5422	606	25	,	,	PUNCT
cana-5422	606	26	(	(	PUNCT
cana-5422	606	27	ifn10	ifn10	PROPN
cana-5422	606	28	)	)	PUNCT
cana-5422	606	29	,	,	PUNCT
cana-5422	606	30	(	(	PUNCT
cana-5422	606	31	3.8	3.8	NUM
cana-5422	606	32	)	)	PUNCT
cana-5422	606	33	,	,	PUNCT
cana-5422	606	34	in	in	ADP
cana-5422	606	35	that	that	DET
cana-5422	606	36	changing	change	VERB
cana-5422	606	37	λ	λ	NOUN
cana-5422	606	38	by	by	ADP
cana-5422	606	39	λ	λ	PROPN
cana-5422	606	40	i	i	PRON
cana-5422	606	41	,	,	PUNCT
cana-5422	606	42	we	we	PRON
cana-5422	606	43	have	have	VERB
cana-5422	606	44	µ	µ	X
cana-5422	606	45	(	(	PUNCT
cana-5422	606	46	f	f	X
cana-5422	606	47	(	(	PUNCT
cana-5422	606	48	w1)−	w1)−	PROPN
cana-5422	606	49	5f	5f	NOUN
cana-5422	606	50	(	(	PUNCT
cana-5422	606	51	w1	w1	NOUN
cana-5422	606	52	5	5	NUM
cana-5422	606	53	)	)	PUNCT
cana-5422	606	54	,	,	PUNCT
cana-5422	606	55	4	4	NUM
cana-5422	606	56	3	3	NUM
cana-5422	606	57	·	·	PUNCT
cana-5422	606	58	i	i	PRON
cana-5422	606	59	λ	λ	PROPN
cana-5422	606	60	)	)	PUNCT
cana-5422	606	61	≥	≥	NOUN
cana-5422	606	62	µ′	µ′	PUNCT
cana-5422	606	63	(	(	PUNCT
cana-5422	606	64	ψa	ψa	X
cana-5422	606	65	(	(	PUNCT
cana-5422	606	66	w1	w1	NOUN
cana-5422	606	67	)	)	PUNCT
cana-5422	606	68	,	,	PUNCT
cana-5422	606	69	λ	λ	X
cana-5422	606	70	)	)	PUNCT
cana-5422	606	71	ν	ν	NOUN
cana-5422	606	72	(	(	PUNCT
cana-5422	606	73	f	f	X
cana-5422	606	74	(	(	PUNCT
cana-5422	606	75	w1)−	w1)−	PROPN
cana-5422	606	76	5f	5f	NOUN
cana-5422	606	77	(	(	PUNCT
cana-5422	606	78	w1	w1	NOUN
cana-5422	606	79	5	5	NUM
cana-5422	606	80	)	)	PUNCT
cana-5422	606	81	,	,	PUNCT
cana-5422	606	82	4	4	NUM
cana-5422	606	83	3	3	NUM
cana-5422	606	84	·	·	PUNCT
cana-5422	606	85	i	i	PRON
cana-5422	606	86	λ	λ	PROPN
cana-5422	606	87	)	)	PUNCT
cana-5422	606	88	≤	≤	NUM
cana-5422	606	89	ν′	ν′	NOUN
cana-5422	606	90	(	(	PUNCT
cana-5422	606	91	ψa	ψa	X
cana-5422	606	92	(	(	PUNCT
cana-5422	606	93	w1	w1	NOUN
cana-5422	606	94	)	)	PUNCT
cana-5422	606	95	,	,	PUNCT
cana-5422	606	96	λ	λ	X
cana-5422	606	97	)	)	PUNCT
cana-5422	606	98			PROPN
cana-5422	606	99	(	(	PUNCT
cana-5422	606	100	3.30	3.30	NUM
cana-5422	606	101	)	)	PUNCT
cana-5422	606	102	for	for	ADP
cana-5422	606	103	all	all	DET
cana-5422	606	104	w1	w1	NOUN
cana-5422	606	105	∈	∈	PROPN
cana-5422	606	106	w1	w1	NOUN
cana-5422	606	107	and	and	CCONJ
cana-5422	606	108	all	all	DET
cana-5422	606	109	λ	λ	PROPN
cana-5422	606	110	>	>	X
cana-5422	606	111	0	0	X
cana-5422	606	112	.	.	PUNCT
cana-5422	606	113	changing	change	VERB
cana-5422	606	114	w1	w1	NOUN
cana-5422	606	115	by	by	ADP
cana-5422	606	116	w1	w1	PROPN
cana-5422	606	117	5	5	NUM
cana-5422	606	118	`	`	PUNCT
cana-5422	606	119	in	in	ADP
cana-5422	606	120	(	(	PUNCT
cana-5422	606	121	3.30	3.30	NUM
cana-5422	606	122	)	)	PUNCT
cana-5422	606	123	,	,	PUNCT
cana-5422	606	124	and	and	CCONJ
cana-5422	606	125	using	use	VERB
cana-5422	606	126	(	(	PUNCT
cana-5422	606	127	ifn4	ifn4	PROPN
cana-5422	606	128	)	)	PUNCT
cana-5422	606	129	,	,	PUNCT
cana-5422	606	130	(	(	PUNCT
cana-5422	606	131	ifn10	ifn10	PROPN
cana-5422	606	132	)	)	PUNCT
cana-5422	606	133	,	,	PUNCT
cana-5422	606	134	(	(	PUNCT
cana-5422	606	135	3.8	3.8	NUM
cana-5422	606	136	)	)	PUNCT
cana-5422	606	137	in	in	ADP
cana-5422	606	138	that	that	DET
cana-5422	606	139	changing	change	VERB
cana-5422	606	140	λ	λ	PROPN
cana-5422	606	141	by	by	ADP
cana-5422	606	142	λ	λ	PROPN
cana-5422	606	143	i	i	PRON
cana-5422	606	144	`	`	PUNCT
cana-5422	606	145	,	,	PUNCT
cana-5422	606	146	we	we	PRON
cana-5422	606	147	get	get	VERB
cana-5422	606	148	µ	µ	X
cana-5422	606	149	(	(	PUNCT
cana-5422	606	150	5`f	5`f	NUM
cana-5422	606	151	(	(	PUNCT
cana-5422	606	152	w1	w1	NOUN
cana-5422	606	153	5	5	NUM
cana-5422	606	154	`	`	PUNCT
cana-5422	606	155	)	)	PUNCT
cana-5422	607	1	−	−	PROPN
cana-5422	607	2	5`+1f	5`+1f	NUM
cana-5422	607	3	(	(	PUNCT
cana-5422	607	4	w1	w1	NOUN
cana-5422	607	5	5`+1	5`+1	PROPN
cana-5422	607	6	)	)	PUNCT
cana-5422	607	7	,	,	PUNCT
cana-5422	607	8	4	4	NUM
cana-5422	607	9	3	3	NUM
cana-5422	607	10	·	·	PUNCT
cana-5422	607	11	i	i	PRON
cana-5422	607	12	(	(	PUNCT
cana-5422	607	13	5	5	NUM
cana-5422	607	14	i	i	NOUN
cana-5422	607	15	)	)	PUNCT
cana-5422	607	16	`	`	PUNCT
cana-5422	607	17	λ	λ	X
cana-5422	607	18	)	)	PUNCT
cana-5422	607	19	≤	≤	NOUN
cana-5422	607	20	µ′	µ′	PUNCT
cana-5422	607	21	(	(	PUNCT
cana-5422	607	22	ψa	ψa	X
cana-5422	607	23	(	(	PUNCT
cana-5422	607	24	w1	w1	NOUN
cana-5422	607	25	)	)	PUNCT
cana-5422	607	26	,	,	PUNCT
cana-5422	607	27	λ	λ	X
cana-5422	607	28	)	)	PUNCT
cana-5422	607	29	ν	ν	NOUN
cana-5422	607	30	(	(	PUNCT
cana-5422	607	31	5`f	5`f	NUM
cana-5422	607	32	(	(	PUNCT
cana-5422	607	33	w1	w1	NOUN
cana-5422	607	34	5	5	NUM
cana-5422	607	35	`	`	PUNCT
cana-5422	607	36	)	)	PUNCT
cana-5422	607	37	−	−	PROPN
cana-5422	608	1	5`+1f	5`+1f	NUM
cana-5422	608	2	(	(	PUNCT
cana-5422	608	3	w1	w1	NOUN
cana-5422	608	4	5`+1	5`+1	PROPN
cana-5422	608	5	)	)	PUNCT
cana-5422	608	6	,	,	PUNCT
cana-5422	608	7	4	4	NUM
cana-5422	608	8	3	3	NUM
cana-5422	608	9	·	·	PUNCT
cana-5422	608	10	i	i	PRON
cana-5422	608	11	(	(	PUNCT
cana-5422	608	12	5	5	NUM
cana-5422	608	13	i	i	NOUN
cana-5422	608	14	)	)	PUNCT
cana-5422	608	15	`	`	PUNCT
cana-5422	608	16	λ	λ	X
cana-5422	608	17	)	)	PUNCT
cana-5422	608	18	≤	≤	NUM
cana-5422	608	19	ν′	ν′	NOUN
cana-5422	608	20	(	(	PUNCT
cana-5422	608	21	ψa	ψa	X
cana-5422	608	22	(	(	PUNCT
cana-5422	608	23	w1	w1	NOUN
cana-5422	608	24	)	)	PUNCT
cana-5422	608	25	,	,	PUNCT
cana-5422	608	26	λ	λ	X
cana-5422	608	27	)	)	PUNCT
cana-5422	608	28			PROPN
cana-5422	608	29	(	(	PUNCT
cana-5422	608	30	3.31	3.31	NUM
cana-5422	608	31	)	)	PUNCT
cana-5422	608	32	for	for	ADP
cana-5422	608	33	all	all	DET
cana-5422	608	34	w1	w1	NOUN
cana-5422	608	35	∈	∈	PROPN
cana-5422	608	36	w1	w1	NOUN
cana-5422	608	37	and	and	CCONJ
cana-5422	609	1	all	all	DET
cana-5422	609	2	λ	λ	PROPN
cana-5422	609	3	>	>	X
cana-5422	609	4	0	0	PUNCT
cana-5422	610	1	also	also	ADV
cana-5422	610	2	`	`	PUNCT
cana-5422	610	3	>	>	X
cana-5422	610	4	0	0	X
cana-5422	610	5	.	.	PUNCT
cana-5422	611	1	it	it	PRON
cana-5422	611	2	is	be	AUX
cana-5422	611	3	easy	easy	ADJ
cana-5422	611	4	to	to	PART
cana-5422	611	5	check	check	VERB
cana-5422	611	6	that	that	DET
cana-5422	611	7	f	f	PROPN
cana-5422	611	8	(	(	PUNCT
cana-5422	611	9	w1)−	w1)−	NOUN
cana-5422	611	10	5`f	5`f	PRON
cana-5422	611	11	(	(	PUNCT
cana-5422	611	12	w1	w1	NOUN
cana-5422	611	13	5	5	NUM
cana-5422	611	14	`	`	PUNCT
cana-5422	611	15	)	)	PUNCT
cana-5422	611	16	=	=	PUNCT
cana-5422	611	17	`	`	PUNCT
cana-5422	611	18	∑	∑	PUNCT
cana-5422	611	19	η=1	η=1	PROPN
cana-5422	611	20	5η−1f	5η−1f	PROPN
cana-5422	611	21	(	(	PUNCT
cana-5422	611	22	w1	w1	NOUN
cana-5422	611	23	5η−1	5η−1	NUM
cana-5422	611	24	)	)	PUNCT
cana-5422	611	25	−	−	PROPN
cana-5422	611	26	5ηf	5ηf	NOUN
cana-5422	611	27	(	(	PUNCT
cana-5422	611	28	w1	w1	NOUN
cana-5422	611	29	5η	5η	PROPN
cana-5422	611	30	)	)	PUNCT
cana-5422	611	31	(	(	PUNCT
cana-5422	611	32	3.32	3.32	NUM
cana-5422	611	33	)	)	PUNCT
cana-5422	611	34	for	for	ADP
cana-5422	611	35	all	all	DET
cana-5422	611	36	w1	w1	NOUN
cana-5422	611	37	∈	∈	PROPN
cana-5422	611	38	w1	w1	NOUN
cana-5422	611	39	.	.	PUNCT
cana-5422	612	1	the	the	DET
cana-5422	612	2	rest	rest	NOUN
cana-5422	612	3	of	of	ADP
cana-5422	612	4	the	the	DET
cana-5422	612	5	proof	proof	NOUN
cana-5422	612	6	is	be	AUX
cana-5422	612	7	similar	similar	ADJ
cana-5422	612	8	to	to	ADP
cana-5422	612	9	that	that	PRON
cana-5422	612	10	of	of	ADP
cana-5422	612	11	above	above	ADP
cana-5422	612	12	case	case	NOUN
cana-5422	612	13	.	.	PUNCT
cana-5422	613	1	so	so	ADV
cana-5422	613	2	,	,	PUNCT
cana-5422	613	3	the	the	DET
cana-5422	613	4	theorem	theorem	NOUN
cana-5422	613	5	holds	hold	VERB
cana-5422	613	6	for	for	ADP
cana-5422	613	7	m	m	PROPN
cana-5422	613	8	=	=	SYM
cana-5422	613	9	−1	−1	NOUN
cana-5422	613	10	.	.	PUNCT
cana-5422	614	1	hence	hence	ADV
cana-5422	614	2	the	the	DET
cana-5422	614	3	proof	proof	NOUN
cana-5422	614	4	is	be	AUX
cana-5422	614	5	complete	complete	ADJ
cana-5422	614	6	.	.	PUNCT
cana-5422	615	1	�	�	PROPN
cana-5422	615	2	corollary	corollary	ADJ
cana-5422	615	3	3.9	3.9	NUM
cana-5422	615	4	.	.	PUNCT
cana-5422	616	1	suppose	suppose	VERB
cana-5422	616	2	that	that	SCONJ
cana-5422	616	3	an	an	DET
cana-5422	616	4	odd	odd	ADJ
cana-5422	616	5	function	function	NOUN
cana-5422	616	6	f	f	NOUN
cana-5422	616	7	:	:	PUNCT
cana-5422	616	8	w1	w1	PROPN
cana-5422	616	9	→	→	SYM
cana-5422	616	10	w2	w2	NOUN
cana-5422	616	11	satisfy	satisfy	VERB
cana-5422	616	12	the	the	DET
cana-5422	616	13	functional	functional	ADJ
cana-5422	616	14	inequality	inequality	NOUN
cana-5422	616	15	(	(	PUNCT
cana-5422	616	16	3.2	3.2	NUM
cana-5422	616	17	)	)	PUNCT
cana-5422	616	18	for	for	ADP
cana-5422	616	19	all	all	DET
cana-5422	616	20	w1	w1	NOUN
cana-5422	616	21	,	,	PUNCT
cana-5422	616	22	w2	w2	NOUN
cana-5422	616	23	,	,	PUNCT
cana-5422	616	24	w3	w3	PROPN
cana-5422	616	25	∈	∈	PROPN
cana-5422	616	26	w1	w1	NOUN
cana-5422	616	27	and	and	CCONJ
cana-5422	616	28	all	all	DET
cana-5422	616	29	λ	λ	X
cana-5422	616	30	>	>	X
cana-5422	616	31	0	0	PUNCT
cana-5422	616	32	with	with	SCONJ
cana-5422	616	33	δ	δ	PROPN
cana-5422	616	34	be	be	AUX
cana-5422	616	35	a	a	DET
cana-5422	616	36	positive	positive	ADJ
cana-5422	616	37	constant	constant	NOUN
cana-5422	616	38	and	and	CCONJ
cana-5422	616	39	ϕ	ϕ	NOUN
cana-5422	616	40	be	be	AUX
cana-5422	616	41	any	any	DET
cana-5422	616	42	real	real	ADJ
cana-5422	616	43	number	number	NOUN
cana-5422	616	44	.	.	PUNCT
cana-5422	617	1	then	then	ADV
cana-5422	617	2	there	there	PRON
cana-5422	617	3	exists	exist	VERB
cana-5422	617	4	a	a	DET
cana-5422	617	5	unique	unique	ADJ
cana-5422	617	6	additive	additive	ADJ
cana-5422	617	7	mapping	mapping	NOUN
cana-5422	617	8	a(w1	a(w1	NOUN
cana-5422	617	9	)	)	PUNCT
cana-5422	617	10	:	:	PUNCT
cana-5422	617	11	w1	w1	PROPN
cana-5422	617	12	→w2	→w2	NOUN
cana-5422	617	13	which	which	PRON
cana-5422	617	14	satisfies	satisfy	VERB
cana-5422	617	15	(	(	PUNCT
cana-5422	617	16	1.7	1.7	NUM
cana-5422	617	17	)	)	PUNCT
cana-5422	617	18	and	and	CCONJ
cana-5422	617	19	the	the	DET
cana-5422	617	20	functional	functional	ADJ
cana-5422	617	21	inequality	inequality	NOUN
cana-5422	617	22	µ	µ	X
cana-5422	617	23	(	(	PUNCT
cana-5422	617	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	617	25	(	(	PUNCT
cana-5422	617	26	w1	w1	NOUN
cana-5422	617	27	)	)	PUNCT
cana-5422	617	28	,	,	PUNCT
cana-5422	617	29	λ	λ	X
cana-5422	617	30	)	)	PUNCT
cana-5422	617	31	≥	≥	NOUN
cana-5422	617	32	µ′	µ′	PUNCT
cana-5422	617	33	(	(	PUNCT
cana-5422	617	34	δ	δ	PROPN
cana-5422	617	35	,	,	PUNCT
cana-5422	617	36	|3|	|3|	PROPN
cana-5422	617	37	λ	λ	NOUN
cana-5422	617	38	)	)	PUNCT
cana-5422	617	39	,	,	PUNCT
cana-5422	617	40	ν	ν	X
cana-5422	617	41	(	(	PUNCT
cana-5422	617	42	a(w1)−f	a(w1)−f	PROPN
cana-5422	617	43	(	(	PUNCT
cana-5422	617	44	w1	w1	NOUN
cana-5422	617	45	)	)	PUNCT
cana-5422	617	46	,	,	PUNCT
cana-5422	617	47	λ	λ	NOUN
cana-5422	617	48	)	)	PUNCT
cana-5422	617	49	≤	≤	NUM
cana-5422	617	50	ν′	ν′	NOUN
cana-5422	617	51	(	(	PUNCT
cana-5422	617	52	δ	δ	PROPN
cana-5422	617	53	,	,	PUNCT
cana-5422	617	54	|3|	|3|	PROPN
cana-5422	617	55	λ	λ	NOUN
cana-5422	617	56	)	)	PUNCT
cana-5422	617	57	,	,	PUNCT
cana-5422	617	58	}	}	PUNCT
cana-5422	617	59	(	(	PUNCT
cana-5422	617	60	3.33	3.33	NUM
cana-5422	617	61	)	)	PUNCT
cana-5422	617	62	for	for	ADP
cana-5422	617	63	all	all	DET
cana-5422	617	64	w1	w1	NOUN
cana-5422	617	65	∈	∈	PROPN
cana-5422	617	66	w1	w1	NOUN
cana-5422	617	67	.	.	PUNCT
cana-5422	618	1	corollary	corollary	ADJ
cana-5422	618	2	3.10	3.10	NUM
cana-5422	618	3	.	.	PUNCT
cana-5422	618	4	suppose	suppose	VERB
cana-5422	618	5	that	that	SCONJ
cana-5422	618	6	an	an	DET
cana-5422	618	7	odd	odd	ADJ
cana-5422	618	8	function	function	NOUN
cana-5422	618	9	f	f	NOUN
cana-5422	618	10	:	:	PUNCT
cana-5422	618	11	w1	w1	PROPN
cana-5422	618	12	→	→	SYM
cana-5422	618	13	w2	w2	NOUN
cana-5422	618	14	satisfy	satisfy	VERB
cana-5422	618	15	the	the	DET
cana-5422	618	16	functional	functional	ADJ
cana-5422	618	17	inequality	inequality	NOUN
cana-5422	618	18	(	(	PUNCT
cana-5422	618	19	3.3	3.3	NUM
cana-5422	618	20	)	)	PUNCT
cana-5422	618	21	for	for	ADP
cana-5422	618	22	all	all	DET
cana-5422	618	23	w1	w1	NOUN
cana-5422	618	24	,	,	PUNCT
cana-5422	618	25	w2	w2	NOUN
cana-5422	618	26	,	,	PUNCT
cana-5422	618	27	w3	w3	PROPN
cana-5422	618	28	∈	∈	PROPN
cana-5422	618	29	w1	w1	NOUN
cana-5422	618	30	and	and	CCONJ
cana-5422	618	31	all	all	DET
cana-5422	618	32	λ	λ	X
cana-5422	618	33	>	>	X
cana-5422	618	34	0	0	PUNCT
cana-5422	618	35	with	with	SCONJ
cana-5422	618	36	δ	δ	PROPN
cana-5422	618	37	be	be	AUX
cana-5422	618	38	a	a	DET
cana-5422	618	39	positive	positive	ADJ
cana-5422	618	40	constant	constant	NOUN
cana-5422	618	41	and	and	CCONJ
cana-5422	618	42	ϕ	ϕ	NOUN
cana-5422	618	43	be	be	AUX
cana-5422	618	44	any	any	DET
cana-5422	618	45	real	real	ADJ
cana-5422	618	46	number	number	NOUN
cana-5422	618	47	.	.	PUNCT
cana-5422	619	1	then	then	ADV
cana-5422	619	2	there	there	PRON
cana-5422	619	3	exists	exist	VERB
cana-5422	619	4	a	a	DET
cana-5422	619	5	communications	communication	NOUN
cana-5422	619	6	on	on	ADP
cana-5422	619	7	applied	apply	VERB
cana-5422	619	8	nonlinear	nonlinear	ADJ
cana-5422	619	9	analysis	analysis	NOUN
cana-5422	619	10	issn	issn	NOUN
cana-5422	619	11	:	:	PUNCT
cana-5422	619	12	1074	1074	NUM
cana-5422	619	13	-	-	PUNCT
cana-5422	619	14	133x	133x	NUM
cana-5422	619	15	vol	vol	NOUN
cana-5422	619	16	32	32	NUM
cana-5422	619	17	no	no	NOUN
cana-5422	619	18	.	.	PUNCT
cana-5422	620	1	10s(2025	10s(2025	NUM
cana-5422	620	2	)	)	PUNCT
cana-5422	620	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	620	4	2206	2206	NUM
cana-5422	620	5	unique	unique	ADJ
cana-5422	620	6	additive	additive	ADJ
cana-5422	620	7	mapping	mapping	NOUN
cana-5422	620	8	a(w1	a(w1	NOUN
cana-5422	620	9	)	)	PUNCT
cana-5422	620	10	:	:	PUNCT
cana-5422	620	11	w1	w1	PROPN
cana-5422	620	12	→w2	→w2	NOUN
cana-5422	620	13	which	which	PRON
cana-5422	620	14	satisfies	satisfy	VERB
cana-5422	620	15	(	(	PUNCT
cana-5422	620	16	1.7	1.7	NUM
cana-5422	620	17	)	)	PUNCT
cana-5422	620	18	and	and	CCONJ
cana-5422	620	19	the	the	DET
cana-5422	620	20	functional	functional	ADJ
cana-5422	620	21	inequality	inequality	NOUN
cana-5422	620	22	µ	µ	X
cana-5422	620	23	(	(	PUNCT
cana-5422	620	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	620	25	(	(	PUNCT
cana-5422	620	26	w1	w1	NOUN
cana-5422	620	27	)	)	PUNCT
cana-5422	620	28	,	,	PUNCT
cana-5422	620	29	λ	λ	X
cana-5422	620	30	)	)	PUNCT
cana-5422	620	31	≥	≥	NOUN
cana-5422	620	32	µ′	µ′	PUNCT
cana-5422	620	33	(	(	PUNCT
cana-5422	620	34	δ|w1|ϕ	δ|w1|ϕ	NOUN
cana-5422	620	35	,	,	PUNCT
cana-5422	620	36	λ	λ	PROPN
cana-5422	620	37	4	4	NUM
cana-5422	620	38	|5−	|5−	NOUN
cana-5422	620	39	5ϕ|	5ϕ|	NUM
cana-5422	620	40	)	)	PUNCT
cana-5422	620	41	,	,	PUNCT
cana-5422	620	42	ϕ	ϕ	PROPN
cana-5422	620	43	6=	6=	ADP
cana-5422	620	44	1	1	NUM
cana-5422	620	45	,	,	PUNCT
cana-5422	620	46	ν	ν	X
cana-5422	620	47	(	(	PUNCT
cana-5422	620	48	a(w1)−f	a(w1)−f	PROPN
cana-5422	620	49	(	(	PUNCT
cana-5422	620	50	w1	w1	NOUN
cana-5422	620	51	)	)	PUNCT
cana-5422	620	52	,	,	PUNCT
cana-5422	620	53	λ	λ	NOUN
cana-5422	620	54	)	)	PUNCT
cana-5422	620	55	≤	≤	NUM
cana-5422	620	56	ν′	ν′	NOUN
cana-5422	620	57	(	(	PUNCT
cana-5422	620	58	δ|w1|ϕ	δ|w1|ϕ	NOUN
cana-5422	620	59	,	,	PUNCT
cana-5422	620	60	λ	λ	PROPN
cana-5422	620	61	4	4	NUM
cana-5422	620	62	|5−	|5−	NOUN
cana-5422	620	63	5ϕ|	5ϕ|	NUM
cana-5422	620	64	)	)	PUNCT
cana-5422	620	65	,	,	PUNCT
cana-5422	620	66	ϕ	ϕ	PROPN
cana-5422	620	67	6=	6=	ADP
cana-5422	620	68	1	1	NUM
cana-5422	620	69	,	,	PUNCT
cana-5422	620	70			PROPN
cana-5422	620	71	(	(	PUNCT
cana-5422	620	72	3.34	3.34	NUM
cana-5422	620	73	)	)	PUNCT
cana-5422	620	74	for	for	ADP
cana-5422	620	75	all	all	DET
cana-5422	620	76	w1	w1	NOUN
cana-5422	620	77	∈	∈	PROPN
cana-5422	620	78	w1	w1	NOUN
cana-5422	620	79	.	.	PUNCT
cana-5422	621	1	corollary	corollary	NOUN
cana-5422	621	2	3.11	3.11	NUM
cana-5422	621	3	.	.	PUNCT
cana-5422	621	4	suppose	suppose	VERB
cana-5422	621	5	that	that	SCONJ
cana-5422	621	6	an	an	DET
cana-5422	621	7	odd	odd	ADJ
cana-5422	621	8	function	function	NOUN
cana-5422	621	9	f	f	NOUN
cana-5422	621	10	:	:	PUNCT
cana-5422	621	11	w1	w1	PROPN
cana-5422	621	12	→	→	SYM
cana-5422	621	13	w2	w2	NOUN
cana-5422	621	14	satisfy	satisfy	VERB
cana-5422	621	15	the	the	DET
cana-5422	621	16	functional	functional	ADJ
cana-5422	621	17	inequality	inequality	NOUN
cana-5422	621	18	(	(	PUNCT
cana-5422	621	19	3.4	3.4	NUM
cana-5422	621	20	)	)	PUNCT
cana-5422	621	21	for	for	ADP
cana-5422	621	22	all	all	DET
cana-5422	621	23	w1	w1	NOUN
cana-5422	621	24	,	,	PUNCT
cana-5422	621	25	w2	w2	NOUN
cana-5422	621	26	,	,	PUNCT
cana-5422	621	27	w3	w3	PROPN
cana-5422	621	28	∈	∈	PROPN
cana-5422	621	29	w1	w1	NOUN
cana-5422	621	30	and	and	CCONJ
cana-5422	621	31	all	all	DET
cana-5422	621	32	λ	λ	X
cana-5422	621	33	>	>	X
cana-5422	621	34	0	0	PUNCT
cana-5422	621	35	with	with	SCONJ
cana-5422	621	36	δ	δ	PROPN
cana-5422	621	37	be	be	AUX
cana-5422	621	38	a	a	DET
cana-5422	621	39	positive	positive	ADJ
cana-5422	621	40	constant	constant	NOUN
cana-5422	621	41	and	and	CCONJ
cana-5422	621	42	ϕ	ϕ	NOUN
cana-5422	621	43	be	be	AUX
cana-5422	621	44	any	any	DET
cana-5422	621	45	real	real	ADJ
cana-5422	621	46	number	number	NOUN
cana-5422	621	47	.	.	PUNCT
cana-5422	622	1	then	then	ADV
cana-5422	622	2	there	there	PRON
cana-5422	622	3	exists	exist	VERB
cana-5422	622	4	a	a	DET
cana-5422	622	5	unique	unique	ADJ
cana-5422	622	6	additive	additive	ADJ
cana-5422	622	7	mapping	mapping	NOUN
cana-5422	622	8	a(w1	a(w1	NOUN
cana-5422	622	9	)	)	PUNCT
cana-5422	622	10	:	:	PUNCT
cana-5422	622	11	w1	w1	PROPN
cana-5422	622	12	→w2	→w2	NOUN
cana-5422	622	13	which	which	PRON
cana-5422	622	14	satisfies	satisfy	VERB
cana-5422	622	15	(	(	PUNCT
cana-5422	622	16	1.7	1.7	NUM
cana-5422	622	17	)	)	PUNCT
cana-5422	622	18	and	and	CCONJ
cana-5422	622	19	the	the	DET
cana-5422	622	20	functional	functional	ADJ
cana-5422	622	21	inequality	inequality	NOUN
cana-5422	622	22	µ	µ	X
cana-5422	622	23	(	(	PUNCT
cana-5422	622	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	622	25	(	(	PUNCT
cana-5422	622	26	w1	w1	NOUN
cana-5422	622	27	)	)	PUNCT
cana-5422	622	28	,	,	PUNCT
cana-5422	622	29	λ	λ	X
cana-5422	622	30	)	)	PUNCT
cana-5422	622	31	≥	≥	NOUN
cana-5422	622	32	µ′	µ′	PUNCT
cana-5422	622	33	(	(	PUNCT
cana-5422	622	34	δ	δ	PROPN
cana-5422	622	35	∑3	∑3	PROPN
cana-5422	622	36	ψ=1	ψ=1	PUNCT
cana-5422	622	37	|w1|	|w1|	NOUN
cana-5422	622	38	ϕψ	ϕψ	ADV
cana-5422	622	39	,	,	PUNCT
cana-5422	622	40	3λ	3λ	NUM
cana-5422	622	41	4	4	NUM
cana-5422	622	42	∑3	∑3	PROPN
cana-5422	622	43	ψ=1	ψ=1	PUNCT
cana-5422	622	44	|5−	|5−	PROPN
cana-5422	622	45	5ϕψ	5ϕψ	NOUN
cana-5422	622	46	|	|	CCONJ
cana-5422	622	47	)	)	PUNCT
cana-5422	622	48	,	,	PUNCT
cana-5422	622	49	ϕ1	ϕ1	NOUN
cana-5422	622	50	,	,	PUNCT
cana-5422	622	51	ϕ2	ϕ2	ADV
cana-5422	622	52	,	,	PUNCT
cana-5422	622	53	ϕ3	ϕ3	PROPN
cana-5422	622	54	6=	6=	PROPN
cana-5422	622	55	1	1	NUM
cana-5422	622	56	,	,	PUNCT
cana-5422	622	57	ν	ν	X
cana-5422	622	58	(	(	PUNCT
cana-5422	622	59	a(w1)−f	a(w1)−f	PROPN
cana-5422	622	60	(	(	PUNCT
cana-5422	622	61	w1	w1	NOUN
cana-5422	622	62	)	)	PUNCT
cana-5422	622	63	,	,	PUNCT
cana-5422	622	64	λ	λ	NOUN
cana-5422	622	65	)	)	PUNCT
cana-5422	622	66	≤	≤	NUM
cana-5422	622	67	ν′	ν′	NOUN
cana-5422	622	68	(	(	PUNCT
cana-5422	622	69	δ	δ	NOUN
cana-5422	622	70	∑3	∑3	PROPN
cana-5422	622	71	ψ=1	ψ=1	PUNCT
cana-5422	622	72	|w1|	|w1|	NOUN
cana-5422	622	73	ϕψ	ϕψ	ADV
cana-5422	622	74	,	,	PUNCT
cana-5422	622	75	3λ	3λ	NUM
cana-5422	622	76	4	4	NUM
cana-5422	622	77	∑3	∑3	PROPN
cana-5422	622	78	ψ=1	ψ=1	PUNCT
cana-5422	622	79	|5−	|5−	PROPN
cana-5422	622	80	5ϕψ	5ϕψ	NOUN
cana-5422	622	81	|	|	CCONJ
cana-5422	622	82	)	)	PUNCT
cana-5422	622	83	,	,	PUNCT
cana-5422	622	84	ϕ1	ϕ1	NOUN
cana-5422	622	85	,	,	PUNCT
cana-5422	622	86	ϕ2	ϕ2	ADV
cana-5422	622	87	,	,	PUNCT
cana-5422	622	88	ϕ3	ϕ3	PROPN
cana-5422	622	89	6=	6=	PROPN
cana-5422	622	90	1	1	NUM
cana-5422	622	91	,	,	PUNCT
cana-5422	622	92			PROPN
cana-5422	622	93	(	(	PUNCT
cana-5422	622	94	3.35	3.35	NUM
cana-5422	622	95	)	)	PUNCT
cana-5422	622	96	for	for	ADP
cana-5422	622	97	all	all	DET
cana-5422	622	98	w1	w1	NOUN
cana-5422	622	99	∈	∈	PROPN
cana-5422	622	100	w1	w1	NOUN
cana-5422	622	101	.	.	PUNCT
cana-5422	623	1	corollary	corollary	ADJ
cana-5422	623	2	3.12	3.12	NUM
cana-5422	623	3	.	.	PUNCT
cana-5422	623	4	suppose	suppose	VERB
cana-5422	623	5	that	that	SCONJ
cana-5422	623	6	an	an	DET
cana-5422	623	7	odd	odd	ADJ
cana-5422	623	8	function	function	NOUN
cana-5422	623	9	f	f	NOUN
cana-5422	623	10	:	:	PUNCT
cana-5422	623	11	w1	w1	PROPN
cana-5422	623	12	→	→	SYM
cana-5422	623	13	w2	w2	NOUN
cana-5422	623	14	satisfy	satisfy	VERB
cana-5422	623	15	the	the	DET
cana-5422	623	16	functional	functional	ADJ
cana-5422	623	17	inequality	inequality	NOUN
cana-5422	623	18	(	(	PUNCT
cana-5422	623	19	3.5	3.5	NUM
cana-5422	623	20	)	)	PUNCT
cana-5422	623	21	for	for	ADP
cana-5422	623	22	all	all	DET
cana-5422	623	23	w1	w1	NOUN
cana-5422	623	24	,	,	PUNCT
cana-5422	623	25	w2	w2	NOUN
cana-5422	623	26	,	,	PUNCT
cana-5422	623	27	w3	w3	PROPN
cana-5422	623	28	∈	∈	PROPN
cana-5422	623	29	w1	w1	NOUN
cana-5422	623	30	and	and	CCONJ
cana-5422	623	31	all	all	DET
cana-5422	623	32	λ	λ	X
cana-5422	623	33	>	>	X
cana-5422	623	34	0	0	PUNCT
cana-5422	623	35	with	with	SCONJ
cana-5422	623	36	δ	δ	PROPN
cana-5422	623	37	be	be	AUX
cana-5422	623	38	a	a	DET
cana-5422	623	39	positive	positive	ADJ
cana-5422	623	40	constant	constant	NOUN
cana-5422	623	41	and	and	CCONJ
cana-5422	623	42	ϕ	ϕ	NOUN
cana-5422	623	43	be	be	AUX
cana-5422	623	44	any	any	DET
cana-5422	623	45	real	real	ADJ
cana-5422	623	46	number	number	NOUN
cana-5422	623	47	.	.	PUNCT
cana-5422	624	1	then	then	ADV
cana-5422	624	2	there	there	PRON
cana-5422	624	3	exists	exist	VERB
cana-5422	624	4	a	a	DET
cana-5422	624	5	unique	unique	ADJ
cana-5422	624	6	additive	additive	ADJ
cana-5422	624	7	mapping	mapping	NOUN
cana-5422	624	8	a(w1	a(w1	NOUN
cana-5422	624	9	)	)	PUNCT
cana-5422	624	10	:	:	PUNCT
cana-5422	624	11	w1	w1	PROPN
cana-5422	624	12	→w2	→w2	NOUN
cana-5422	624	13	which	which	PRON
cana-5422	624	14	satisfies	satisfy	VERB
cana-5422	624	15	(	(	PUNCT
cana-5422	624	16	1.7	1.7	NUM
cana-5422	624	17	)	)	PUNCT
cana-5422	624	18	and	and	CCONJ
cana-5422	624	19	the	the	DET
cana-5422	624	20	functional	functional	ADJ
cana-5422	624	21	inequality	inequality	NOUN
cana-5422	624	22	µ	µ	X
cana-5422	624	23	(	(	PUNCT
cana-5422	624	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	624	25	(	(	PUNCT
cana-5422	624	26	w1	w1	NOUN
cana-5422	624	27	)	)	PUNCT
cana-5422	624	28	,	,	PUNCT
cana-5422	624	29	λ	λ	X
cana-5422	624	30	)	)	PUNCT
cana-5422	624	31	≥	≥	NOUN
cana-5422	624	32	µ′	µ′	PUNCT
cana-5422	624	33	(	(	PUNCT
cana-5422	624	34	δ|w1|3ϕ	δ|w1|3ϕ	ADV
cana-5422	624	35	,	,	PUNCT
cana-5422	624	36	3λ	3λ	NUM
cana-5422	624	37	4	4	NUM
cana-5422	624	38	|5−	|5−	PROPN
cana-5422	624	39	53ϕ|	53ϕ|	NUM
cana-5422	624	40	)	)	PUNCT
cana-5422	624	41	,	,	PUNCT
cana-5422	624	42	3ϕ	3ϕ	NUM
cana-5422	624	43	6=	6=	NUM
cana-5422	624	44	1	1	NUM
cana-5422	624	45	,	,	PUNCT
cana-5422	624	46	ν	ν	X
cana-5422	624	47	(	(	PUNCT
cana-5422	624	48	a(w1)−f	a(w1)−f	PROPN
cana-5422	624	49	(	(	PUNCT
cana-5422	624	50	w1	w1	NOUN
cana-5422	624	51	)	)	PUNCT
cana-5422	624	52	,	,	PUNCT
cana-5422	624	53	λ	λ	NOUN
cana-5422	624	54	)	)	PUNCT
cana-5422	624	55	≤	≤	NUM
cana-5422	624	56	ν′	ν′	NOUN
cana-5422	624	57	(	(	PUNCT
cana-5422	624	58	δ|w1|3ϕ	δ|w1|3ϕ	ADV
cana-5422	624	59	,	,	PUNCT
cana-5422	624	60	3λ	3λ	NUM
cana-5422	624	61	4	4	NUM
cana-5422	624	62	|5−	|5−	PROPN
cana-5422	624	63	53ϕ|	53ϕ|	NUM
cana-5422	624	64	)	)	PUNCT
cana-5422	624	65	,	,	PUNCT
cana-5422	624	66	3ϕ	3ϕ	NUM
cana-5422	624	67	6=	6=	NUM
cana-5422	624	68	1	1	NUM
cana-5422	624	69	,	,	PUNCT
cana-5422	624	70			PROPN
cana-5422	624	71	(	(	PUNCT
cana-5422	624	72	3.36	3.36	NUM
cana-5422	624	73	)	)	PUNCT
cana-5422	624	74	for	for	ADP
cana-5422	624	75	all	all	DET
cana-5422	624	76	w1	w1	NOUN
cana-5422	624	77	∈	∈	PROPN
cana-5422	624	78	w1	w1	NOUN
cana-5422	624	79	.	.	PUNCT
cana-5422	625	1	corollary	corollary	NOUN
cana-5422	625	2	3.13	3.13	NUM
cana-5422	625	3	.	.	PUNCT
cana-5422	625	4	suppose	suppose	VERB
cana-5422	625	5	that	that	SCONJ
cana-5422	625	6	an	an	DET
cana-5422	625	7	odd	odd	ADJ
cana-5422	625	8	function	function	NOUN
cana-5422	625	9	f	f	NOUN
cana-5422	625	10	:	:	PUNCT
cana-5422	625	11	w1	w1	PROPN
cana-5422	625	12	→	→	SYM
cana-5422	625	13	w2	w2	NOUN
cana-5422	625	14	satisfy	satisfy	VERB
cana-5422	625	15	the	the	DET
cana-5422	625	16	functional	functional	ADJ
cana-5422	625	17	inequality	inequality	NOUN
cana-5422	625	18	(	(	PUNCT
cana-5422	625	19	3.6	3.6	NUM
cana-5422	625	20	)	)	PUNCT
cana-5422	625	21	for	for	ADP
cana-5422	625	22	all	all	DET
cana-5422	625	23	w1	w1	NOUN
cana-5422	625	24	,	,	PUNCT
cana-5422	625	25	w2	w2	NOUN
cana-5422	625	26	,	,	PUNCT
cana-5422	625	27	w3	w3	PROPN
cana-5422	625	28	∈	∈	PROPN
cana-5422	625	29	w1	w1	NOUN
cana-5422	625	30	and	and	CCONJ
cana-5422	625	31	all	all	DET
cana-5422	625	32	λ	λ	X
cana-5422	625	33	>	>	X
cana-5422	625	34	0	0	PUNCT
cana-5422	625	35	with	with	SCONJ
cana-5422	625	36	δ	δ	PROPN
cana-5422	625	37	be	be	AUX
cana-5422	625	38	a	a	DET
cana-5422	625	39	positive	positive	ADJ
cana-5422	625	40	constant	constant	NOUN
cana-5422	625	41	and	and	CCONJ
cana-5422	625	42	ϕ	ϕ	NOUN
cana-5422	625	43	be	be	AUX
cana-5422	625	44	any	any	DET
cana-5422	625	45	real	real	ADJ
cana-5422	625	46	number	number	NOUN
cana-5422	625	47	.	.	PUNCT
cana-5422	626	1	then	then	ADV
cana-5422	626	2	there	there	PRON
cana-5422	626	3	exists	exist	VERB
cana-5422	626	4	a	a	DET
cana-5422	626	5	unique	unique	ADJ
cana-5422	626	6	additive	additive	ADJ
cana-5422	626	7	mapping	mapping	NOUN
cana-5422	626	8	a(w1	a(w1	NOUN
cana-5422	626	9	)	)	PUNCT
cana-5422	626	10	:	:	PUNCT
cana-5422	626	11	w1	w1	PROPN
cana-5422	626	12	→w2	→w2	NOUN
cana-5422	626	13	which	which	PRON
cana-5422	626	14	satisfies	satisfy	VERB
cana-5422	626	15	(	(	PUNCT
cana-5422	626	16	1.7	1.7	NUM
cana-5422	626	17	)	)	PUNCT
cana-5422	626	18	and	and	CCONJ
cana-5422	626	19	the	the	DET
cana-5422	626	20	functional	functional	ADJ
cana-5422	626	21	inequality	inequality	NOUN
cana-5422	626	22	µ	µ	X
cana-5422	626	23	(	(	PUNCT
cana-5422	626	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	626	25	(	(	PUNCT
cana-5422	626	26	w1	w1	NOUN
cana-5422	626	27	)	)	PUNCT
cana-5422	626	28	,	,	PUNCT
cana-5422	626	29	λ	λ	X
cana-5422	626	30	)	)	PUNCT
cana-5422	626	31	≥	≥	NOUN
cana-5422	626	32	µ′	µ′	PUNCT
cana-5422	626	33	(	(	PUNCT
cana-5422	626	34	δ|wψ|∑	δ|wψ|∑	PROPN
cana-5422	626	35	3	3	NUM
cana-5422	626	36	ψ=1	ψ=1	PUNCT
cana-5422	626	37	ϕψ	ϕψ	NOUN
cana-5422	626	38	,	,	PUNCT
cana-5422	626	39	3λ	3λ	NUM
cana-5422	626	40	4	4	NUM
cana-5422	626	41	∣∣∣5−	∣∣∣5−	NOUN
cana-5422	626	42	5∑3	5∑3	NUM
cana-5422	626	43	ψ=1	ψ=1	PUNCT
cana-5422	626	44	ϕψ	ϕψ	ADV
cana-5422	626	45	∣∣∣	∣∣∣	ADJ
cana-5422	626	46	)	)	PUNCT
cana-5422	626	47	,	,	PUNCT
cana-5422	626	48	∑3	∑3	PROPN
cana-5422	626	49	ψ=1	ψ=1	PUNCT
cana-5422	626	50	ϕψ	ϕψ	ADP
cana-5422	626	51	6=	6=	PROPN
cana-5422	626	52	1	1	NUM
cana-5422	626	53	,	,	PUNCT
cana-5422	626	54	ν	ν	X
cana-5422	626	55	(	(	PUNCT
cana-5422	626	56	a(w1)−f	a(w1)−f	PROPN
cana-5422	626	57	(	(	PUNCT
cana-5422	626	58	w1	w1	NOUN
cana-5422	626	59	)	)	PUNCT
cana-5422	626	60	,	,	PUNCT
cana-5422	626	61	λ	λ	NOUN
cana-5422	626	62	)	)	PUNCT
cana-5422	626	63	≤	≤	NUM
cana-5422	626	64	ν′	ν′	NOUN
cana-5422	626	65	(	(	PUNCT
cana-5422	626	66	δ|wψ|∑	δ|wψ|∑	PUNCT
cana-5422	626	67	ψ=13	ψ=13	VERB
cana-5422	626	68	ϕψ	ϕψ	ADV
cana-5422	626	69	,	,	PUNCT
cana-5422	626	70	3λ	3λ	NUM
cana-5422	626	71	4	4	NUM
cana-5422	626	72	∣∣∣5−	∣∣∣5−	NOUN
cana-5422	626	73	5∑3	5∑3	NUM
cana-5422	626	74	ψ=1	ψ=1	PUNCT
cana-5422	626	75	ϕψ	ϕψ	ADV
cana-5422	626	76	∣∣∣	∣∣∣	ADJ
cana-5422	626	77	)	)	PUNCT
cana-5422	626	78	,	,	PUNCT
cana-5422	626	79	∑3	∑3	PROPN
cana-5422	626	80	ψ=1	ψ=1	PUNCT
cana-5422	626	81	ϕψ	ϕψ	ADP
cana-5422	626	82	6=	6=	PROPN
cana-5422	626	83	1	1	NUM
cana-5422	626	84	,	,	PUNCT
cana-5422	626	85			PROPN
cana-5422	626	86	(	(	PUNCT
cana-5422	626	87	3.37	3.37	NUM
cana-5422	626	88	)	)	PUNCT
cana-5422	626	89	for	for	ADP
cana-5422	626	90	all	all	DET
cana-5422	626	91	w1	w1	NOUN
cana-5422	626	92	∈	∈	PROPN
cana-5422	626	93	w1	w1	NOUN
cana-5422	626	94	.	.	PUNCT
cana-5422	627	1	corollary	corollary	ADJ
cana-5422	627	2	3.14	3.14	NUM
cana-5422	627	3	.	.	PUNCT
cana-5422	627	4	suppose	suppose	VERB
cana-5422	627	5	that	that	SCONJ
cana-5422	627	6	an	an	DET
cana-5422	627	7	odd	odd	ADJ
cana-5422	627	8	function	function	NOUN
cana-5422	627	9	f	f	NOUN
cana-5422	627	10	:	:	PUNCT
cana-5422	627	11	w1	w1	PROPN
cana-5422	627	12	→	→	SYM
cana-5422	627	13	w2	w2	NOUN
cana-5422	627	14	satisfy	satisfy	VERB
cana-5422	627	15	the	the	DET
cana-5422	627	16	functional	functional	ADJ
cana-5422	627	17	inequality	inequality	NOUN
cana-5422	627	18	(	(	PUNCT
cana-5422	627	19	3.7	3.7	NUM
cana-5422	627	20	)	)	PUNCT
cana-5422	627	21	for	for	ADP
cana-5422	627	22	all	all	DET
cana-5422	627	23	w1	w1	NOUN
cana-5422	627	24	,	,	PUNCT
cana-5422	627	25	w2	w2	NOUN
cana-5422	627	26	,	,	PUNCT
cana-5422	627	27	w3	w3	PROPN
cana-5422	627	28	∈	∈	PROPN
cana-5422	627	29	w1	w1	NOUN
cana-5422	627	30	and	and	CCONJ
cana-5422	627	31	all	all	DET
cana-5422	627	32	λ	λ	X
cana-5422	627	33	>	>	X
cana-5422	627	34	0	0	PUNCT
cana-5422	627	35	with	with	SCONJ
cana-5422	627	36	δ	δ	PROPN
cana-5422	627	37	be	be	AUX
cana-5422	627	38	a	a	DET
cana-5422	627	39	positive	positive	ADJ
cana-5422	627	40	constant	constant	NOUN
cana-5422	627	41	and	and	CCONJ
cana-5422	627	42	ϕ	ϕ	NOUN
cana-5422	627	43	be	be	AUX
cana-5422	627	44	any	any	DET
cana-5422	627	45	real	real	ADJ
cana-5422	627	46	number	number	NOUN
cana-5422	627	47	.	.	PUNCT
cana-5422	628	1	then	then	ADV
cana-5422	628	2	there	there	PRON
cana-5422	628	3	exists	exist	VERB
cana-5422	628	4	a	a	DET
cana-5422	628	5	unique	unique	ADJ
cana-5422	628	6	additive	additive	ADJ
cana-5422	628	7	mapping	mapping	NOUN
cana-5422	628	8	a(w1	a(w1	NOUN
cana-5422	628	9	)	)	PUNCT
cana-5422	628	10	:	:	PUNCT
cana-5422	628	11	w1	w1	PROPN
cana-5422	628	12	→w2	→w2	NOUN
cana-5422	628	13	which	which	PRON
cana-5422	628	14	satisfies	satisfy	VERB
cana-5422	628	15	(	(	PUNCT
cana-5422	628	16	1.7	1.7	NUM
cana-5422	628	17	)	)	PUNCT
cana-5422	628	18	and	and	CCONJ
cana-5422	628	19	the	the	DET
cana-5422	628	20	functional	functional	ADJ
cana-5422	628	21	inequality	inequality	NOUN
cana-5422	628	22	µ	µ	X
cana-5422	628	23	(	(	PUNCT
cana-5422	628	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	628	25	(	(	PUNCT
cana-5422	628	26	w1	w1	NOUN
cana-5422	628	27	)	)	PUNCT
cana-5422	628	28	,	,	PUNCT
cana-5422	628	29	λ	λ	X
cana-5422	628	30	)	)	PUNCT
cana-5422	628	31	≥	≥	NOUN
cana-5422	628	32	µ′	µ′	PUNCT
cana-5422	628	33	(	(	PUNCT
cana-5422	628	34	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	628	35	,	,	PUNCT
cana-5422	628	36	3λ	3λ	NUM
cana-5422	628	37	4	4	NUM
cana-5422	628	38	|5−	|5−	PROPN
cana-5422	628	39	53ϕ|	53ϕ|	NUM
cana-5422	628	40	)	)	PUNCT
cana-5422	628	41	,	,	PUNCT
cana-5422	628	42	3ϕ	3ϕ	NUM
cana-5422	628	43	6=	6=	NUM
cana-5422	628	44	1	1	NUM
cana-5422	628	45	,	,	PUNCT
cana-5422	628	46	ν	ν	X
cana-5422	628	47	(	(	PUNCT
cana-5422	628	48	a(w1)−f	a(w1)−f	PROPN
cana-5422	628	49	(	(	PUNCT
cana-5422	628	50	w1	w1	NOUN
cana-5422	628	51	)	)	PUNCT
cana-5422	628	52	,	,	PUNCT
cana-5422	628	53	λ	λ	NOUN
cana-5422	628	54	)	)	PUNCT
cana-5422	628	55	≤	≤	NUM
cana-5422	628	56	ν′	ν′	NOUN
cana-5422	628	57	(	(	PUNCT
cana-5422	628	58	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	628	59	,	,	PUNCT
cana-5422	628	60	3λ	3λ	NUM
cana-5422	628	61	4	4	NUM
cana-5422	628	62	|5−	|5−	PROPN
cana-5422	628	63	53ϕ|	53ϕ|	NUM
cana-5422	628	64	)	)	PUNCT
cana-5422	628	65	,	,	PUNCT
cana-5422	628	66	3ϕ	3ϕ	NUM
cana-5422	628	67	6=	6=	NUM
cana-5422	628	68	1	1	NUM
cana-5422	628	69	,	,	PUNCT
cana-5422	628	70			PROPN
cana-5422	628	71	(	(	PUNCT
cana-5422	628	72	3.38	3.38	NUM
cana-5422	628	73	)	)	PUNCT
cana-5422	628	74	for	for	ADP
cana-5422	628	75	all	all	DET
cana-5422	628	76	w1	w1	NOUN
cana-5422	628	77	∈	∈	PROPN
cana-5422	628	78	w1	w1	NOUN
cana-5422	628	79	.	.	PUNCT
cana-5422	629	1	3.3	3.3	NUM
cana-5422	629	2	.	.	PUNCT
cana-5422	630	1	evenness	evenness	NOUN
cana-5422	630	2	of	of	ADP
cana-5422	630	3	f	f	PROPN
cana-5422	630	4	:	:	PUNCT
cana-5422	630	5	quadratic	quadratic	ADJ
cana-5422	630	6	case	case	NOUN
cana-5422	630	7	stability	stability	NOUN
cana-5422	630	8	results	result	VERB
cana-5422	630	9	:	:	PUNCT
cana-5422	630	10	direct	direct	ADJ
cana-5422	630	11	method	method	NOUN
cana-5422	630	12	.	.	PUNCT
cana-5422	631	1	theorem	theorem	VERB
cana-5422	631	2	3.15	3.15	NUM
cana-5422	631	3	.	.	PUNCT
cana-5422	632	1	suppose	suppose	VERB
cana-5422	632	2	that	that	SCONJ
cana-5422	632	3	an	an	DET
cana-5422	632	4	even	even	ADV
cana-5422	632	5	function	function	NOUN
cana-5422	632	6	f	f	PROPN
cana-5422	632	7	:	:	PUNCT
cana-5422	632	8	w1	w1	PROPN
cana-5422	632	9	→	→	SYM
cana-5422	632	10	w2	w2	NOUN
cana-5422	632	11	satisfy	satisfy	VERB
cana-5422	632	12	the	the	DET
cana-5422	632	13	functional	functional	ADJ
cana-5422	632	14	inequality	inequality	NOUN
cana-5422	632	15	(	(	PUNCT
cana-5422	632	16	3.1	3.1	NUM
cana-5422	632	17	)	)	PUNCT
cana-5422	632	18	where	where	SCONJ
cana-5422	632	19	ψ	ψ	X
cana-5422	632	20	:	:	PUNCT
cana-5422	632	21	w3	w3	NOUN
cana-5422	632	22	1	1	NUM
cana-5422	632	23	→	→	SYM
cana-5422	633	1	[	[	X
cana-5422	633	2	0	0	NUM
cana-5422	633	3	,	,	PUNCT
cana-5422	633	4	∞	∞	PROPN
cana-5422	633	5	)	)	PUNCT
cana-5422	633	6	with	with	ADP
cana-5422	633	7	the	the	DET
cana-5422	633	8	conditions	condition	NOUN
cana-5422	633	9	(	(	PUNCT
cana-5422	633	10	3.8	3.8	NUM
cana-5422	633	11	)	)	PUNCT
cana-5422	633	12	and	and	CCONJ
cana-5422	633	13	lim	lim	PROPN
cana-5422	633	14	`	`	PUNCT
cana-5422	633	15	→∞	→∞	X
cana-5422	633	16	µ′	µ′	PUNCT
cana-5422	633	17	(	(	PUNCT
cana-5422	633	18	ψ	ψ	X
cana-5422	633	19	(	(	PUNCT
cana-5422	633	20	5`mw1	5`mw1	NUM
cana-5422	633	21	,	,	PUNCT
cana-5422	633	22	5`mw2	5`mw2	NUM
cana-5422	633	23	,	,	PUNCT
cana-5422	633	24	5`mw3	5`mw3	NUM
cana-5422	633	25	)	)	PUNCT
cana-5422	633	26	,	,	PUNCT
cana-5422	633	27	25`mλ	25`mλ	NOUN
cana-5422	633	28	)	)	PUNCT
cana-5422	633	29	=	=	SYM
cana-5422	633	30	1	1	NUM
cana-5422	633	31	lim	lim	NOUN
cana-5422	633	32	`	`	PUNCT
cana-5422	633	33	→∞	→∞	X
cana-5422	633	34	ν′	ν′	NOUN
cana-5422	633	35	(	(	PUNCT
cana-5422	633	36	ψ	ψ	X
cana-5422	633	37	(	(	PUNCT
cana-5422	633	38	5`mw1	5`mw1	NUM
cana-5422	633	39	,	,	PUNCT
cana-5422	633	40	5`mw2	5`mw2	NUM
cana-5422	633	41	,	,	PUNCT
cana-5422	633	42	5`mw3	5`mw3	NUM
cana-5422	633	43	)	)	PUNCT
cana-5422	633	44	,	,	PUNCT
cana-5422	633	45	25`mλ	25`mλ	NOUN
cana-5422	633	46	)	)	PUNCT
cana-5422	633	47	=	=	SYM
cana-5422	633	48	0	0	NUM
cana-5422	634	1			NOUN
cana-5422	634	2	(	(	PUNCT
cana-5422	634	3	3.39	3.39	NUM
cana-5422	634	4	)	)	PUNCT
cana-5422	634	5	communications	communication	NOUN
cana-5422	634	6	on	on	ADP
cana-5422	634	7	applied	apply	VERB
cana-5422	634	8	nonlinear	nonlinear	ADJ
cana-5422	634	9	analysis	analysis	NOUN
cana-5422	634	10	issn	issn	NOUN
cana-5422	634	11	:	:	PUNCT
cana-5422	634	12	1074	1074	NUM
cana-5422	634	13	-	-	PUNCT
cana-5422	634	14	133x	133x	NUM
cana-5422	634	15	vol	vol	NOUN
cana-5422	634	16	32	32	NUM
cana-5422	634	17	no	no	NOUN
cana-5422	634	18	.	.	PUNCT
cana-5422	635	1	10s(2025	10s(2025	NUM
cana-5422	635	2	)	)	PUNCT
cana-5422	636	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	636	2	2207	2207	NUM
cana-5422	636	3	for	for	ADP
cana-5422	636	4	all	all	DET
cana-5422	636	5	w1	w1	NOUN
cana-5422	636	6	,	,	PUNCT
cana-5422	636	7	w2	w2	NOUN
cana-5422	636	8	,	,	PUNCT
cana-5422	636	9	w3	w3	PROPN
cana-5422	636	10	∈	∈	PROPN
cana-5422	636	11	w1	w1	NOUN
cana-5422	636	12	and	and	CCONJ
cana-5422	636	13	all	all	DET
cana-5422	636	14	λ	λ	X
cana-5422	636	15	>	>	X
cana-5422	636	16	0	0	PUNCT
cana-5422	636	17	with	with	ADP
cana-5422	636	18	m	m	NOUN
cana-5422	636	19	=	=	SYM
cana-5422	636	20	±1	±1	ADJ
cana-5422	636	21	and	and	CCONJ
cana-5422	636	22	0	0	NUM
cana-5422	636	23	<	<	X
cana-5422	636	24	(	(	PUNCT
cana-5422	636	25	i	i	NOUN
cana-5422	636	26	25	25	NUM
cana-5422	636	27	)	)	PUNCT
cana-5422	636	28	µ	µ	X
cana-5422	636	29	<	<	X
cana-5422	636	30	1	1	NUM
cana-5422	636	31	.	.	PUNCT
cana-5422	637	1	then	then	ADV
cana-5422	637	2	there	there	PRON
cana-5422	637	3	exists	exist	VERB
cana-5422	637	4	a	a	DET
cana-5422	637	5	unique	unique	ADJ
cana-5422	637	6	quadratic	quadratic	ADJ
cana-5422	637	7	mapping	mapping	NOUN
cana-5422	637	8	q(w1	q(w1	NOUN
cana-5422	637	9	)	)	PUNCT
cana-5422	637	10	:	:	PUNCT
cana-5422	637	11	w1	w1	PROPN
cana-5422	637	12	→w2	→w2	NOUN
cana-5422	637	13	which	which	PRON
cana-5422	637	14	satisfies	satisfy	VERB
cana-5422	637	15	(	(	PUNCT
cana-5422	637	16	1.7	1.7	NUM
cana-5422	637	17	)	)	PUNCT
cana-5422	637	18	and	and	CCONJ
cana-5422	637	19	the	the	DET
cana-5422	637	20	functional	functional	ADJ
cana-5422	637	21	inequality	inequality	NOUN
cana-5422	637	22	µ	µ	X
cana-5422	637	23	(	(	PUNCT
cana-5422	637	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	637	25	(	(	PUNCT
cana-5422	637	26	w1	w1	NOUN
cana-5422	637	27	)	)	PUNCT
cana-5422	637	28	,	,	PUNCT
cana-5422	637	29	λ	λ	X
cana-5422	637	30	)	)	PUNCT
cana-5422	637	31	≥	≥	NOUN
cana-5422	637	32	µ′	µ′	PUNCT
cana-5422	637	33	(	(	PUNCT
cana-5422	637	34	ψq	ψq	PROPN
cana-5422	637	35	(	(	PUNCT
cana-5422	637	36	w1	w1	NOUN
cana-5422	637	37	)	)	PUNCT
cana-5422	637	38	,	,	PUNCT
cana-5422	637	39	7λ	7λ	NUM
cana-5422	637	40	3	3	NUM
cana-5422	637	41	|25−	|25−	PROPN
cana-5422	637	42	i|	i|	PROPN
cana-5422	637	43	)	)	PUNCT
cana-5422	637	44	=	=	PUNCT
cana-5422	637	45	µ′	µ′	NOUN
cana-5422	637	46	(	(	PUNCT
cana-5422	637	47	ψ	ψ	X
cana-5422	637	48	(	(	PUNCT
cana-5422	637	49	w1	w1	NOUN
cana-5422	637	50	,	,	PUNCT
cana-5422	637	51	w1	w1	NOUN
cana-5422	637	52	,	,	PUNCT
cana-5422	637	53	w1	w1	NOUN
cana-5422	637	54	)	)	PUNCT
cana-5422	637	55	,	,	PUNCT
cana-5422	637	56	7λ	7λ	NUM
cana-5422	637	57	3	3	NUM
cana-5422	637	58	|25−	|25−	PROPN
cana-5422	637	59	i|	i|	PROPN
cana-5422	637	60	)	)	PUNCT
cana-5422	637	61	∗	∗	NOUN
cana-5422	637	62	µ′	µ′	PUNCT
cana-5422	637	63	(	(	PUNCT
cana-5422	637	64	ψ	ψ	X
cana-5422	637	65	(	(	PUNCT
cana-5422	637	66	w1	w1	NOUN
cana-5422	637	67	,	,	PUNCT
cana-5422	637	68	w1,−w1	w1,−w1	NUM
cana-5422	637	69	)	)	PUNCT
cana-5422	637	70	,	,	PUNCT
cana-5422	637	71	7λ	7λ	NUM
cana-5422	637	72	3	3	NUM
cana-5422	637	73	|25−	|25−	PROPN
cana-5422	637	74	i|	i|	PROPN
cana-5422	637	75	)	)	PUNCT
cana-5422	637	76	ν	ν	NOUN
cana-5422	637	77	(	(	PUNCT
cana-5422	637	78	q(w1)−f	q(w1)−f	PROPN
cana-5422	637	79	(	(	PUNCT
cana-5422	637	80	w1	w1	NOUN
cana-5422	637	81	)	)	PUNCT
cana-5422	637	82	,	,	PUNCT
cana-5422	637	83	λ	λ	NOUN
cana-5422	637	84	)	)	PUNCT
cana-5422	637	85	≤	≤	NUM
cana-5422	637	86	ν′	ν′	NOUN
cana-5422	637	87	(	(	PUNCT
cana-5422	637	88	ψq	ψq	PROPN
cana-5422	637	89	(	(	PUNCT
cana-5422	637	90	w1	w1	NOUN
cana-5422	637	91	)	)	PUNCT
cana-5422	637	92	,	,	PUNCT
cana-5422	637	93	7λ	7λ	NUM
cana-5422	637	94	3	3	NUM
cana-5422	637	95	(	(	PUNCT
cana-5422	637	96	25−	25−	NUM
cana-5422	637	97	i	i	NOUN
cana-5422	637	98	)	)	PUNCT
cana-5422	637	99	)	)	PUNCT
cana-5422	638	1	=	=	SYM
cana-5422	638	2	ν′	ν′	NOUN
cana-5422	638	3	(	(	PUNCT
cana-5422	638	4	ψ	ψ	X
cana-5422	638	5	(	(	PUNCT
cana-5422	638	6	w1	w1	NOUN
cana-5422	638	7	,	,	PUNCT
cana-5422	638	8	w1	w1	NOUN
cana-5422	638	9	,	,	PUNCT
cana-5422	638	10	w1	w1	NOUN
cana-5422	638	11	)	)	PUNCT
cana-5422	638	12	,	,	PUNCT
cana-5422	638	13	7λ	7λ	NUM
cana-5422	638	14	3	3	NUM
cana-5422	638	15	(	(	PUNCT
cana-5422	638	16	25−	25−	NUM
cana-5422	638	17	i	i	NOUN
cana-5422	638	18	)	)	PUNCT
cana-5422	638	19	)	)	PUNCT
cana-5422	638	20	�	�	PROPN
cana-5422	638	21	ν′	ν′	NOUN
cana-5422	638	22	(	(	PUNCT
cana-5422	638	23	ψ	ψ	X
cana-5422	638	24	(	(	PUNCT
cana-5422	638	25	w1	w1	NOUN
cana-5422	638	26	,	,	PUNCT
cana-5422	638	27	w1,−w1	w1,−w1	NUM
cana-5422	638	28	)	)	PUNCT
cana-5422	638	29	,	,	PUNCT
cana-5422	638	30	7λ	7λ	NUM
cana-5422	638	31	3	3	NUM
cana-5422	638	32	(	(	PUNCT
cana-5422	638	33	25−	25−	NUM
cana-5422	638	34	i	i	NOUN
cana-5422	638	35	)	)	PUNCT
cana-5422	638	36	)	)	PUNCT
cana-5422	638	37			NOUN
cana-5422	638	38	(	(	PUNCT
cana-5422	638	39	3.40	3.40	NUM
cana-5422	638	40	)	)	PUNCT
cana-5422	638	41	and	and	CCONJ
cana-5422	638	42	the	the	DET
cana-5422	638	43	mapping	mapping	NOUN
cana-5422	638	44	q(w1	q(w1	NOUN
cana-5422	638	45	)	)	PUNCT
cana-5422	638	46	is	be	AUX
cana-5422	638	47	obtained	obtain	VERB
cana-5422	638	48	by	by	ADP
cana-5422	638	49	lim	lim	PROPN
cana-5422	638	50	`	`	PUNCT
cana-5422	638	51	→∞	→∞	PROPN
cana-5422	638	52	µ	µ	X
cana-5422	638	53	(	(	PUNCT
cana-5422	638	54	1	1	NUM
cana-5422	638	55	25`mf	25`mf	NUM
cana-5422	638	56	(	(	PUNCT
cana-5422	638	57	5`mw1	5`mw1	NUM
cana-5422	638	58	)	)	PUNCT
cana-5422	638	59	−q(w1	−q(w1	PROPN
cana-5422	638	60	)	)	PUNCT
cana-5422	638	61	,	,	PUNCT
cana-5422	638	62	λ	λ	NOUN
cana-5422	638	63	)	)	PUNCT
cana-5422	638	64	=	=	SYM
cana-5422	639	1	1	1	NUM
cana-5422	639	2	lim	lim	NOUN
cana-5422	639	3	`	`	PUNCT
cana-5422	639	4	→∞	→∞	PROPN
cana-5422	639	5	ν	ν	X
cana-5422	639	6	(	(	PUNCT
cana-5422	639	7	1	1	NUM
cana-5422	639	8	25`mf	25`mf	NUM
cana-5422	639	9	(	(	PUNCT
cana-5422	639	10	5`mw1	5`mw1	NUM
cana-5422	639	11	)	)	PUNCT
cana-5422	639	12	−q(w1	−q(w1	PROPN
cana-5422	639	13	)	)	PUNCT
cana-5422	639	14	,	,	PUNCT
cana-5422	639	15	λ	λ	NOUN
cana-5422	639	16	)	)	PUNCT
cana-5422	639	17	=	=	SYM
cana-5422	639	18	0	0	X
cana-5422	639	19			PROPN
cana-5422	639	20	(	(	PUNCT
cana-5422	639	21	3.41	3.41	NUM
cana-5422	639	22	)	)	PUNCT
cana-5422	639	23	for	for	ADP
cana-5422	639	24	all	all	DET
cana-5422	639	25	w1	w1	NOUN
cana-5422	639	26	∈	∈	PROPN
cana-5422	639	27	w1	w1	NOUN
cana-5422	639	28	and	and	CCONJ
cana-5422	639	29	all	all	DET
cana-5422	639	30	λ	λ	PROPN
cana-5422	639	31	>	>	X
cana-5422	639	32	0	0	X
cana-5422	639	33	.	.	PUNCT
cana-5422	640	1	proof	proof	NOUN
cana-5422	640	2	.	.	PUNCT
cana-5422	641	1	using	use	VERB
cana-5422	641	2	evenness	evenness	NOUN
cana-5422	641	3	of	of	ADP
cana-5422	641	4	f	f	PROPN
cana-5422	641	5	in	in	ADP
cana-5422	641	6	(	(	PUNCT
cana-5422	641	7	2.1	2.1	NUM
cana-5422	641	8	)	)	PUNCT
cana-5422	641	9	,	,	PUNCT
cana-5422	641	10	we	we	PRON
cana-5422	641	11	get	get	VERB
cana-5422	641	12	µ	µ	X
cana-5422	641	13	(	(	PUNCT
cana-5422	641	14	f	f	X
cana-5422	641	15	(	(	PUNCT
cana-5422	641	16	3w1	3w1	NUM
cana-5422	641	17	+	+	CCONJ
cana-5422	641	18	w2	w2	NOUN
cana-5422	641	19	+	+	CCONJ
cana-5422	641	20	w3	w3	PROPN
cana-5422	641	21	)	)	PUNCT
cana-5422	642	1	+	+	NOUN
cana-5422	642	2	f	f	X
cana-5422	642	3	(	(	PUNCT
cana-5422	642	4	w1	w1	NOUN
cana-5422	642	5	+	+	CCONJ
cana-5422	642	6	3w2	3w2	NUM
cana-5422	642	7	+	+	CCONJ
cana-5422	642	8	w3	w3	NOUN
cana-5422	642	9	)	)	PUNCT
cana-5422	643	1	+	+	NOUN
cana-5422	643	2	f	f	X
cana-5422	643	3	(	(	PUNCT
cana-5422	643	4	w1	w1	NOUN
cana-5422	643	5	+	+	NOUN
cana-5422	643	6	w2	w2	NOUN
cana-5422	643	7	+	+	CCONJ
cana-5422	643	8	3w3)−	3w3)−	PROPN
cana-5422	643	9	7f	7f	NOUN
cana-5422	643	10	(	(	PUNCT
cana-5422	643	11	3	3	NUM
cana-5422	643	12	∑	∑	PUNCT
cana-5422	643	13	ψ=1	ψ=1	PUNCT
cana-5422	643	14	wψ	wψ	ADP
cana-5422	643	15	)	)	PUNCT
cana-5422	643	16	−	−	PROPN
cana-5422	643	17	4	4	NUM
cana-5422	643	18	3	3	NUM
cana-5422	643	19	∑	∑	PUNCT
cana-5422	643	20	ψ=1	ψ=1	PUNCT
cana-5422	643	21	f	f	X
cana-5422	643	22	(	(	PUNCT
cana-5422	643	23	wψ	wψ	ADP
cana-5422	643	24	)	)	PUNCT
cana-5422	643	25	,	,	PUNCT
cana-5422	643	26	λ	λ	PROPN
cana-5422	643	27	)	)	PUNCT
cana-5422	643	28	≥	≥	NOUN
cana-5422	643	29	µ′	µ′	PUNCT
cana-5422	643	30	(	(	PUNCT
cana-5422	643	31	ψ	ψ	X
cana-5422	643	32	(	(	PUNCT
cana-5422	643	33	w1	w1	NOUN
cana-5422	643	34	,	,	PUNCT
cana-5422	643	35	w2	w2	NOUN
cana-5422	643	36	,	,	PUNCT
cana-5422	643	37	w3	w3	PROPN
cana-5422	643	38	)	)	PUNCT
cana-5422	643	39	,	,	PUNCT
cana-5422	643	40	λ	λ	X
cana-5422	643	41	)	)	PUNCT
cana-5422	643	42	ν	ν	NOUN
cana-5422	643	43	(	(	PUNCT
cana-5422	643	44	f	f	X
cana-5422	643	45	(	(	PUNCT
cana-5422	643	46	3w1	3w1	NUM
cana-5422	643	47	+	+	CCONJ
cana-5422	643	48	w2	w2	NOUN
cana-5422	643	49	+	+	CCONJ
cana-5422	643	50	w3	w3	PROPN
cana-5422	643	51	)	)	PUNCT
cana-5422	644	1	+	+	NOUN
cana-5422	644	2	f	f	X
cana-5422	644	3	(	(	PUNCT
cana-5422	644	4	w1	w1	NOUN
cana-5422	644	5	+	+	CCONJ
cana-5422	644	6	3w2	3w2	NUM
cana-5422	644	7	+	+	CCONJ
cana-5422	644	8	w3	w3	NOUN
cana-5422	644	9	)	)	PUNCT
cana-5422	645	1	+	+	NOUN
cana-5422	645	2	f	f	X
cana-5422	645	3	(	(	PUNCT
cana-5422	645	4	w1	w1	NOUN
cana-5422	645	5	+	+	NOUN
cana-5422	645	6	w2	w2	NOUN
cana-5422	645	7	+	+	CCONJ
cana-5422	645	8	3w3)−	3w3)−	PROPN
cana-5422	645	9	7f	7f	NOUN
cana-5422	645	10	(	(	PUNCT
cana-5422	645	11	3	3	NUM
cana-5422	645	12	∑	∑	PUNCT
cana-5422	645	13	ψ=1	ψ=1	PUNCT
cana-5422	645	14	wψ	wψ	ADP
cana-5422	645	15	)	)	PUNCT
cana-5422	645	16	−	−	PROPN
cana-5422	645	17	4	4	NUM
cana-5422	645	18	3	3	NUM
cana-5422	645	19	∑	∑	PUNCT
cana-5422	645	20	ψ=1	ψ=1	PUNCT
cana-5422	645	21	f	f	X
cana-5422	645	22	(	(	PUNCT
cana-5422	645	23	wψ	wψ	ADP
cana-5422	645	24	)	)	PUNCT
cana-5422	645	25	,	,	PUNCT
cana-5422	645	26	λ	λ	PROPN
cana-5422	645	27	)	)	PUNCT
cana-5422	645	28	≤	≤	NUM
cana-5422	645	29	ν′	ν′	NOUN
cana-5422	645	30	(	(	PUNCT
cana-5422	645	31	ψ	ψ	X
cana-5422	645	32	(	(	PUNCT
cana-5422	645	33	w1	w1	NOUN
cana-5422	645	34	,	,	PUNCT
cana-5422	645	35	w2	w2	NOUN
cana-5422	645	36	,	,	PUNCT
cana-5422	645	37	w3	w3	PROPN
cana-5422	645	38	)	)	PUNCT
cana-5422	645	39	,	,	PUNCT
cana-5422	645	40	λ	λ	NOUN
cana-5422	645	41	)	)	PUNCT
cana-5422	645	42			NOUN
cana-5422	645	43	(	(	PUNCT
cana-5422	645	44	3.42	3.42	NUM
cana-5422	645	45	)	)	PUNCT
cana-5422	645	46	for	for	ADP
cana-5422	645	47	all	all	DET
cana-5422	645	48	w1	w1	NOUN
cana-5422	645	49	,	,	PUNCT
cana-5422	645	50	w2	w2	NOUN
cana-5422	645	51	,	,	PUNCT
cana-5422	645	52	w3	w3	PROPN
cana-5422	645	53	∈	∈	PROPN
cana-5422	645	54	w1	w1	NOUN
cana-5422	645	55	and	and	CCONJ
cana-5422	645	56	all	all	DET
cana-5422	645	57	λ	λ	X
cana-5422	645	58	>	>	X
cana-5422	645	59	0	0	PUNCT
cana-5422	645	60	.	.	PUNCT
cana-5422	646	1	interchanging	interchanging	PROPN
cana-5422	646	2	(	(	PUNCT
cana-5422	646	3	w1	w1	NOUN
cana-5422	646	4	,	,	PUNCT
cana-5422	646	5	w2	w2	NOUN
cana-5422	646	6	,	,	PUNCT
cana-5422	646	7	w3	w3	PROPN
cana-5422	646	8	)	)	PUNCT
cana-5422	646	9	by	by	ADP
cana-5422	646	10	(	(	PUNCT
cana-5422	646	11	w1	w1	NOUN
cana-5422	646	12	,	,	PUNCT
cana-5422	646	13	w1	w1	NOUN
cana-5422	646	14	,	,	PUNCT
cana-5422	646	15	w1	w1	NOUN
cana-5422	646	16	)	)	PUNCT
cana-5422	646	17	in	in	ADP
cana-5422	646	18	(	(	PUNCT
cana-5422	646	19	3.42	3.42	NUM
cana-5422	646	20	)	)	PUNCT
cana-5422	646	21	,	,	PUNCT
cana-5422	646	22	we	we	PRON
cana-5422	646	23	obtain	obtain	VERB
cana-5422	646	24	µ	µ	X
cana-5422	646	25	(	(	PUNCT
cana-5422	646	26	3f	3f	PROPN
cana-5422	646	27	(	(	PUNCT
cana-5422	646	28	5w1)−	5w1)−	PROPN
cana-5422	646	29	7f	7f	X
cana-5422	646	30	(	(	PUNCT
cana-5422	646	31	3w1)−	3w1)−	NOUN
cana-5422	646	32	12f	12f	NUM
cana-5422	646	33	(	(	PUNCT
cana-5422	646	34	w1	w1	NOUN
cana-5422	646	35	)	)	PUNCT
cana-5422	646	36	,	,	PUNCT
cana-5422	646	37	λ	λ	X
cana-5422	646	38	)	)	PUNCT
cana-5422	646	39	≥	≥	NOUN
cana-5422	646	40	µ′	µ′	PUNCT
cana-5422	646	41	(	(	PUNCT
cana-5422	646	42	ψ	ψ	X
cana-5422	646	43	(	(	PUNCT
cana-5422	646	44	w1	w1	NOUN
cana-5422	646	45	,	,	PUNCT
cana-5422	646	46	w1	w1	NOUN
cana-5422	646	47	,	,	PUNCT
cana-5422	646	48	w1	w1	NOUN
cana-5422	646	49	)	)	PUNCT
cana-5422	646	50	,	,	PUNCT
cana-5422	646	51	λ	λ	X
cana-5422	646	52	)	)	PUNCT
cana-5422	646	53	ν	ν	NOUN
cana-5422	646	54	(	(	PUNCT
cana-5422	646	55	3f	3f	PROPN
cana-5422	646	56	(	(	PUNCT
cana-5422	646	57	5w1)−	5w1)−	PROPN
cana-5422	646	58	7f	7f	X
cana-5422	646	59	(	(	PUNCT
cana-5422	646	60	3w1)−	3w1)−	NOUN
cana-5422	646	61	12f	12f	NUM
cana-5422	646	62	(	(	PUNCT
cana-5422	646	63	w1	w1	NOUN
cana-5422	646	64	)	)	PUNCT
cana-5422	646	65	,	,	PUNCT
cana-5422	646	66	λ	λ	NOUN
cana-5422	646	67	)	)	PUNCT
cana-5422	646	68	≤	≤	NUM
cana-5422	646	69	ν′	ν′	NOUN
cana-5422	646	70	(	(	PUNCT
cana-5422	646	71	ψ	ψ	X
cana-5422	646	72	(	(	PUNCT
cana-5422	646	73	w1	w1	NOUN
cana-5422	646	74	,	,	PUNCT
cana-5422	646	75	w1	w1	NOUN
cana-5422	646	76	,	,	PUNCT
cana-5422	646	77	w1	w1	NOUN
cana-5422	646	78	)	)	PUNCT
cana-5422	646	79	,	,	PUNCT
cana-5422	646	80	λ	λ	NOUN
cana-5422	646	81	)	)	PUNCT
cana-5422	646	82	}	}	PUNCT
cana-5422	646	83	(	(	PUNCT
cana-5422	646	84	3.43	3.43	NUM
cana-5422	646	85	)	)	PUNCT
cana-5422	646	86	for	for	ADP
cana-5422	646	87	all	all	DET
cana-5422	646	88	w1	w1	NOUN
cana-5422	646	89	∈	∈	PROPN
cana-5422	646	90	w1	w1	NOUN
cana-5422	646	91	and	and	CCONJ
cana-5422	646	92	all	all	DET
cana-5422	646	93	λ	λ	X
cana-5422	646	94	>	>	X
cana-5422	646	95	0	0	PUNCT
cana-5422	646	96	.	.	PUNCT
cana-5422	647	1	again	again	ADV
cana-5422	647	2	interchanging	interchange	VERB
cana-5422	647	3	(	(	PUNCT
cana-5422	647	4	w1	w1	NOUN
cana-5422	647	5	,	,	PUNCT
cana-5422	647	6	w2	w2	NOUN
cana-5422	647	7	,	,	PUNCT
cana-5422	647	8	w3	w3	PROPN
cana-5422	647	9	)	)	PUNCT
cana-5422	647	10	by	by	ADP
cana-5422	647	11	(	(	PUNCT
cana-5422	647	12	w1	w1	NOUN
cana-5422	647	13	,	,	PUNCT
cana-5422	647	14	w1,−w1	w1,−w1	NUM
cana-5422	647	15	)	)	PUNCT
cana-5422	647	16	in	in	ADP
cana-5422	647	17	(	(	PUNCT
cana-5422	647	18	3.42	3.42	NUM
cana-5422	647	19	)	)	PUNCT
cana-5422	647	20	and	and	CCONJ
cana-5422	647	21	using	use	VERB
cana-5422	647	22	(	(	PUNCT
cana-5422	647	23	ifn4	ifn4	PROPN
cana-5422	647	24	)	)	PUNCT
cana-5422	647	25	,	,	PUNCT
cana-5422	647	26	(	(	PUNCT
cana-5422	647	27	ifn10	ifn10	PROPN
cana-5422	647	28	)	)	PUNCT
cana-5422	647	29	,	,	PUNCT
cana-5422	647	30	we	we	PRON
cana-5422	647	31	have	have	VERB
cana-5422	647	32	µ	µ	X
cana-5422	647	33	(	(	PUNCT
cana-5422	647	34	2f	2f	NUM
cana-5422	647	35	(	(	PUNCT
cana-5422	647	36	3w1)−	3w1)−	PROPN
cana-5422	647	37	18f	18f	PROPN
cana-5422	647	38	(	(	PUNCT
cana-5422	647	39	w1	w1	NOUN
cana-5422	647	40	)	)	PUNCT
cana-5422	647	41	,	,	PUNCT
cana-5422	647	42	λ	λ	X
cana-5422	647	43	)	)	PUNCT
cana-5422	647	44	≥	≥	NOUN
cana-5422	647	45	µ′	µ′	PUNCT
cana-5422	647	46	(	(	PUNCT
cana-5422	647	47	ψ	ψ	X
cana-5422	647	48	(	(	PUNCT
cana-5422	647	49	w1	w1	NOUN
cana-5422	647	50	,	,	PUNCT
cana-5422	647	51	w1,−w1	w1,−w1	NUM
cana-5422	647	52	)	)	PUNCT
cana-5422	647	53	,	,	PUNCT
cana-5422	647	54	λ	λ	X
cana-5422	647	55	)	)	PUNCT
cana-5422	647	56	ν	ν	NOUN
cana-5422	647	57	(	(	PUNCT
cana-5422	647	58	2f	2f	NUM
cana-5422	647	59	(	(	PUNCT
cana-5422	647	60	3w1)−	3w1)−	PROPN
cana-5422	647	61	18f	18f	PROPN
cana-5422	647	62	(	(	PUNCT
cana-5422	647	63	w1	w1	NOUN
cana-5422	647	64	)	)	PUNCT
cana-5422	647	65	,	,	PUNCT
cana-5422	647	66	λ	λ	NOUN
cana-5422	647	67	)	)	PUNCT
cana-5422	647	68	≤	≤	NUM
cana-5422	647	69	ν′	ν′	NOUN
cana-5422	647	70	(	(	PUNCT
cana-5422	647	71	ψ	ψ	X
cana-5422	647	72	(	(	PUNCT
cana-5422	647	73	w1	w1	NOUN
cana-5422	647	74	,	,	PUNCT
cana-5422	647	75	w1,−w1	w1,−w1	NUM
cana-5422	647	76	)	)	PUNCT
cana-5422	647	77	,	,	PUNCT
cana-5422	647	78	λ	λ	NOUN
cana-5422	647	79	)	)	PUNCT
cana-5422	647	80	}	}	PUNCT
cana-5422	647	81	⇒	⇒	VERB
cana-5422	647	82	µ	µ	X
cana-5422	647	83	(	(	PUNCT
cana-5422	647	84	7f	7f	X
cana-5422	647	85	(	(	PUNCT
cana-5422	647	86	3w1)−	3w1)−	PROPN
cana-5422	647	87	63f	63f	PROPN
cana-5422	647	88	(	(	PUNCT
cana-5422	647	89	w1	w1	NOUN
cana-5422	647	90	)	)	PUNCT
cana-5422	647	91	,	,	PUNCT
cana-5422	647	92	2	2	NUM
cana-5422	647	93	7	7	NUM
cana-5422	647	94	λ	λ	NOUN
cana-5422	647	95	)	)	PUNCT
cana-5422	647	96	≥	≥	NOUN
cana-5422	647	97	µ′	µ′	PUNCT
cana-5422	647	98	(	(	PUNCT
cana-5422	647	99	ψ	ψ	X
cana-5422	647	100	(	(	PUNCT
cana-5422	647	101	w1	w1	NOUN
cana-5422	647	102	,	,	PUNCT
cana-5422	647	103	w1,−w1	w1,−w1	NUM
cana-5422	647	104	)	)	PUNCT
cana-5422	647	105	,	,	PUNCT
cana-5422	647	106	λ	λ	X
cana-5422	647	107	)	)	PUNCT
cana-5422	647	108	ν	ν	NOUN
cana-5422	647	109	(	(	PUNCT
cana-5422	647	110	7f	7f	X
cana-5422	647	111	(	(	PUNCT
cana-5422	647	112	3w1)−	3w1)−	PROPN
cana-5422	647	113	63f	63f	PROPN
cana-5422	647	114	(	(	PUNCT
cana-5422	647	115	w1	w1	NOUN
cana-5422	647	116	)	)	PUNCT
cana-5422	647	117	,	,	PUNCT
cana-5422	647	118	2	2	NUM
cana-5422	647	119	7	7	NUM
cana-5422	647	120	λ	λ	NOUN
cana-5422	647	121	)	)	PUNCT
cana-5422	647	122	≤	≤	NUM
cana-5422	647	123	ν′	ν′	NOUN
cana-5422	647	124	(	(	PUNCT
cana-5422	647	125	ψ	ψ	X
cana-5422	647	126	(	(	PUNCT
cana-5422	647	127	w1	w1	NOUN
cana-5422	647	128	,	,	PUNCT
cana-5422	647	129	w1,−w1	w1,−w1	NUM
cana-5422	647	130	)	)	PUNCT
cana-5422	647	131	,	,	PUNCT
cana-5422	647	132	λ	λ	NOUN
cana-5422	647	133	)	)	PUNCT
cana-5422	647	134	}	}	PUNCT
cana-5422	647	135	(	(	PUNCT
cana-5422	647	136	3.44	3.44	NUM
cana-5422	647	137	)	)	PUNCT
cana-5422	647	138	for	for	ADP
cana-5422	647	139	all	all	DET
cana-5422	647	140	w1	w1	NOUN
cana-5422	647	141	∈	∈	PROPN
cana-5422	647	142	w1	w1	NOUN
cana-5422	647	143	and	and	CCONJ
cana-5422	647	144	all	all	DET
cana-5422	647	145	λ	λ	PROPN
cana-5422	647	146	>	>	X
cana-5422	647	147	0	0	X
cana-5422	647	148	.	.	PUNCT
cana-5422	648	1	combining	combine	VERB
cana-5422	648	2	(	(	PUNCT
cana-5422	648	3	3.43	3.43	NUM
cana-5422	648	4	)	)	PUNCT
cana-5422	648	5	and	and	CCONJ
cana-5422	648	6	(	(	PUNCT
cana-5422	648	7	3.44	3.44	NUM
cana-5422	648	8	)	)	PUNCT
cana-5422	648	9	using	use	VERB
cana-5422	648	10	(	(	PUNCT
cana-5422	648	11	ifn5	ifn5	PROPN
cana-5422	648	12	)	)	PUNCT
cana-5422	648	13	,	,	PUNCT
cana-5422	648	14	(	(	PUNCT
cana-5422	648	15	ifn11	ifn11	INTJ
cana-5422	648	16	)	)	PUNCT
cana-5422	648	17	,	,	PUNCT
cana-5422	648	18	we	we	PRON
cana-5422	648	19	arrive	arrive	VERB
cana-5422	648	20	µ	µ	X
cana-5422	648	21	(	(	PUNCT
cana-5422	648	22	3f	3f	PROPN
cana-5422	648	23	(	(	PUNCT
cana-5422	648	24	5w1)−	5w1)−	PROPN
cana-5422	648	25	75f	75f	NOUN
cana-5422	648	26	(	(	PUNCT
cana-5422	648	27	w1	w1	NOUN
cana-5422	648	28	)	)	PUNCT
cana-5422	648	29	,	,	PUNCT
cana-5422	648	30	9	9	NUM
cana-5422	648	31	7	7	NUM
cana-5422	648	32	λ	λ	NOUN
cana-5422	648	33	)	)	PUNCT
cana-5422	648	34	≥	≥	PROPN
cana-5422	648	35	µ	µ	X
cana-5422	648	36	(	(	PUNCT
cana-5422	648	37	3f	3f	PROPN
cana-5422	648	38	(	(	PUNCT
cana-5422	648	39	5w1)−	5w1)−	PROPN
cana-5422	648	40	7f	7f	X
cana-5422	648	41	(	(	PUNCT
cana-5422	648	42	3w1)−	3w1)−	NOUN
cana-5422	648	43	12f	12f	NUM
cana-5422	648	44	(	(	PUNCT
cana-5422	648	45	w1	w1	NOUN
cana-5422	648	46	)	)	PUNCT
cana-5422	648	47	,	,	PUNCT
cana-5422	648	48	λ	λ	X
cana-5422	648	49	)	)	PUNCT
cana-5422	648	50	∗	∗	NOUN
cana-5422	648	51	µ	µ	X
cana-5422	648	52	(	(	PUNCT
cana-5422	648	53	7f	7f	X
cana-5422	648	54	(	(	PUNCT
cana-5422	648	55	3w1)−	3w1)−	PROPN
cana-5422	648	56	63f	63f	PROPN
cana-5422	648	57	(	(	PUNCT
cana-5422	648	58	w1	w1	NOUN
cana-5422	648	59	)	)	PUNCT
cana-5422	648	60	,	,	PUNCT
cana-5422	648	61	2	2	NUM
cana-5422	648	62	7	7	NUM
cana-5422	648	63	λ	λ	NOUN
cana-5422	648	64	)	)	PUNCT
cana-5422	648	65	≥	≥	NOUN
cana-5422	648	66	µ′	µ′	PUNCT
cana-5422	648	67	(	(	PUNCT
cana-5422	648	68	ψ	ψ	X
cana-5422	648	69	(	(	PUNCT
cana-5422	648	70	w1	w1	NOUN
cana-5422	648	71	,	,	PUNCT
cana-5422	648	72	w1	w1	NOUN
cana-5422	648	73	,	,	PUNCT
cana-5422	648	74	w1	w1	NOUN
cana-5422	648	75	)	)	PUNCT
cana-5422	648	76	,	,	PUNCT
cana-5422	648	77	λ	λ	X
cana-5422	648	78	)	)	PUNCT
cana-5422	648	79	∗	∗	NOUN
cana-5422	648	80	µ′	µ′	PUNCT
cana-5422	648	81	(	(	PUNCT
cana-5422	648	82	ψ	ψ	X
cana-5422	648	83	(	(	PUNCT
cana-5422	648	84	w1	w1	NOUN
cana-5422	648	85	,	,	PUNCT
cana-5422	648	86	w1,−w1	w1,−w1	NUM
cana-5422	648	87	)	)	PUNCT
cana-5422	648	88	,	,	PUNCT
cana-5422	648	89	λ	λ	X
cana-5422	648	90	)	)	PUNCT
cana-5422	648	91	=	=	SYM
cana-5422	648	92	µ′	µ′	PUNCT
cana-5422	649	1	(	(	PUNCT
cana-5422	649	2	ψq	ψq	PROPN
cana-5422	649	3	(	(	PUNCT
cana-5422	649	4	w1	w1	NOUN
cana-5422	649	5	)	)	PUNCT
cana-5422	649	6	,	,	PUNCT
cana-5422	649	7	λ	λ	NOUN
cana-5422	649	8	)	)	PUNCT
cana-5422	649	9	ν	ν	PROPN
cana-5422	649	10	(	(	PUNCT
cana-5422	649	11	3f	3f	PROPN
cana-5422	649	12	(	(	PUNCT
cana-5422	649	13	5w1)−	5w1)−	PROPN
cana-5422	649	14	15f	15f	PROPN
cana-5422	649	15	(	(	PUNCT
cana-5422	649	16	w1	w1	PROPN
cana-5422	649	17	)	)	PUNCT
cana-5422	649	18	,	,	PUNCT
cana-5422	649	19	9	9	NUM
cana-5422	649	20	7	7	NUM
cana-5422	649	21	λ	λ	NOUN
cana-5422	649	22	)	)	PUNCT
cana-5422	649	23	≤	≤	NUM
cana-5422	649	24	ν	ν	NOUN
cana-5422	649	25	(	(	PUNCT
cana-5422	649	26	3f	3f	PROPN
cana-5422	649	27	(	(	PUNCT
cana-5422	649	28	5w1)−	5w1)−	PROPN
cana-5422	649	29	7f	7f	X
cana-5422	649	30	(	(	PUNCT
cana-5422	649	31	3w1)−	3w1)−	NOUN
cana-5422	649	32	12f	12f	NUM
cana-5422	649	33	(	(	PUNCT
cana-5422	649	34	w1	w1	NOUN
cana-5422	649	35	)	)	PUNCT
cana-5422	649	36	,	,	PUNCT
cana-5422	649	37	λ	λ	X
cana-5422	649	38	)	)	PUNCT
cana-5422	649	39	�	�	PROPN
cana-5422	649	40	ν	ν	PROPN
cana-5422	649	41	(	(	PUNCT
cana-5422	649	42	7f	7f	X
cana-5422	649	43	(	(	PUNCT
cana-5422	649	44	3w1)−	3w1)−	PROPN
cana-5422	649	45	63f	63f	PROPN
cana-5422	649	46	(	(	PUNCT
cana-5422	649	47	w1	w1	NOUN
cana-5422	649	48	)	)	PUNCT
cana-5422	649	49	,	,	PUNCT
cana-5422	649	50	2	2	NUM
cana-5422	649	51	7	7	NUM
cana-5422	649	52	λ	λ	NOUN
cana-5422	649	53	)	)	PUNCT
cana-5422	649	54	≤	≤	NUM
cana-5422	649	55	ν′	ν′	NOUN
cana-5422	649	56	(	(	PUNCT
cana-5422	649	57	ψ	ψ	X
cana-5422	649	58	(	(	PUNCT
cana-5422	649	59	w1	w1	NOUN
cana-5422	649	60	,	,	PUNCT
cana-5422	649	61	w1	w1	NOUN
cana-5422	649	62	,	,	PUNCT
cana-5422	649	63	w1	w1	NOUN
cana-5422	649	64	)	)	PUNCT
cana-5422	649	65	,	,	PUNCT
cana-5422	649	66	λ	λ	X
cana-5422	649	67	)	)	PUNCT
cana-5422	649	68	�	�	PROPN
cana-5422	649	69	ν′	ν′	NOUN
cana-5422	649	70	(	(	PUNCT
cana-5422	649	71	ψ	ψ	X
cana-5422	649	72	(	(	PUNCT
cana-5422	649	73	w1	w1	NOUN
cana-5422	649	74	,	,	PUNCT
cana-5422	649	75	w1,−w1	w1,−w1	NUM
cana-5422	649	76	)	)	PUNCT
cana-5422	649	77	,	,	PUNCT
cana-5422	649	78	λ	λ	X
cana-5422	649	79	)	)	PUNCT
cana-5422	649	80	=	=	SYM
cana-5422	649	81	ν′	ν′	NOUN
cana-5422	649	82	(	(	PUNCT
cana-5422	649	83	ψq	ψq	PROPN
cana-5422	649	84	(	(	PUNCT
cana-5422	649	85	w1	w1	NOUN
cana-5422	649	86	)	)	PUNCT
cana-5422	649	87	,	,	PUNCT
cana-5422	649	88	λ	λ	X
cana-5422	649	89	)	)	PUNCT
cana-5422	649	90			PROPN
cana-5422	649	91	(	(	PUNCT
cana-5422	649	92	3.45	3.45	NUM
cana-5422	649	93	)	)	PUNCT
cana-5422	649	94	for	for	ADP
cana-5422	649	95	all	all	DET
cana-5422	649	96	w1	w1	NOUN
cana-5422	649	97	∈	∈	PROPN
cana-5422	649	98	w1	w1	NOUN
cana-5422	649	99	and	and	CCONJ
cana-5422	649	100	all	all	DET
cana-5422	649	101	λ	λ	PROPN
cana-5422	649	102	>	>	X
cana-5422	649	103	0	0	X
cana-5422	649	104	.	.	PUNCT
cana-5422	650	1	using	use	VERB
cana-5422	650	2	(	(	PUNCT
cana-5422	650	3	ifn4	ifn4	PROPN
cana-5422	650	4	)	)	PUNCT
cana-5422	650	5	,	,	PUNCT
cana-5422	650	6	(	(	PUNCT
cana-5422	650	7	ifn10	ifn10	PROPN
cana-5422	650	8	)	)	PUNCT
cana-5422	650	9	,	,	PUNCT
cana-5422	650	10	one	one	PRON
cana-5422	650	11	can	can	AUX
cana-5422	650	12	see	see	VERB
cana-5422	650	13	from	from	ADP
cana-5422	650	14	(	(	PUNCT
cana-5422	650	15	3.45	3.45	NUM
cana-5422	650	16	)	)	PUNCT
cana-5422	651	1	that	that	PRON
cana-5422	651	2	µ	µ	X
cana-5422	651	3	(	(	PUNCT
cana-5422	651	4	1	1	NUM
cana-5422	651	5	25	25	NUM
cana-5422	651	6	f	f	NOUN
cana-5422	651	7	(	(	PUNCT
cana-5422	651	8	5w1)−f	5w1)−f	PROPN
cana-5422	651	9	(	(	PUNCT
cana-5422	651	10	w1	w1	NOUN
cana-5422	651	11	)	)	PUNCT
cana-5422	651	12	,	,	PUNCT
cana-5422	651	13	9	9	NUM
cana-5422	651	14	7	7	NUM
cana-5422	651	15	·	·	SYM
cana-5422	651	16	3	3	NUM
cana-5422	651	17	·	·	SYM
cana-5422	651	18	1	1	NUM
cana-5422	651	19	25	25	NUM
cana-5422	651	20	λ	λ	PROPN
cana-5422	651	21	)	)	PUNCT
cana-5422	651	22	≥	≥	NOUN
cana-5422	651	23	µ′	µ′	PUNCT
cana-5422	651	24	(	(	PUNCT
cana-5422	651	25	ψq	ψq	PROPN
cana-5422	651	26	(	(	PUNCT
cana-5422	651	27	w1	w1	NOUN
cana-5422	651	28	)	)	PUNCT
cana-5422	651	29	,	,	PUNCT
cana-5422	651	30	λ	λ	NOUN
cana-5422	651	31	)	)	PUNCT
cana-5422	651	32	ν	ν	NOUN
cana-5422	651	33	(	(	PUNCT
cana-5422	651	34	1	1	NUM
cana-5422	651	35	25	25	NUM
cana-5422	651	36	f	f	NOUN
cana-5422	651	37	(	(	PUNCT
cana-5422	651	38	5w1)−f	5w1)−f	PROPN
cana-5422	651	39	(	(	PUNCT
cana-5422	651	40	w1	w1	NOUN
cana-5422	651	41	)	)	PUNCT
cana-5422	651	42	,	,	PUNCT
cana-5422	651	43	9	9	NUM
cana-5422	651	44	7	7	NUM
cana-5422	651	45	·	·	SYM
cana-5422	651	46	3	3	NUM
cana-5422	651	47	·	·	SYM
cana-5422	651	48	1	1	NUM
cana-5422	651	49	25	25	NUM
cana-5422	651	50	λ	λ	NOUN
cana-5422	651	51	)	)	PUNCT
cana-5422	651	52	≤	≤	NUM
cana-5422	651	53	ν′	ν′	NOUN
cana-5422	651	54	(	(	PUNCT
cana-5422	651	55	ψq	ψq	PROPN
cana-5422	651	56	(	(	PUNCT
cana-5422	651	57	w1	w1	NOUN
cana-5422	651	58	)	)	PUNCT
cana-5422	651	59	,	,	PUNCT
cana-5422	651	60	λ	λ	X
cana-5422	651	61	)	)	PUNCT
cana-5422	651	62			PROPN
cana-5422	651	63	(	(	PUNCT
cana-5422	651	64	3.46	3.46	NUM
cana-5422	651	65	)	)	PUNCT
cana-5422	651	66	communications	communication	NOUN
cana-5422	651	67	on	on	ADP
cana-5422	651	68	applied	apply	VERB
cana-5422	651	69	nonlinear	nonlinear	ADJ
cana-5422	651	70	analysis	analysis	NOUN
cana-5422	651	71	issn	issn	NOUN
cana-5422	651	72	:	:	PUNCT
cana-5422	651	73	1074	1074	NUM
cana-5422	651	74	-	-	PUNCT
cana-5422	651	75	133x	133x	NUM
cana-5422	651	76	vol	vol	NOUN
cana-5422	651	77	32	32	NUM
cana-5422	651	78	no	no	NOUN
cana-5422	651	79	.	.	PUNCT
cana-5422	652	1	10s(2025	10s(2025	NUM
cana-5422	652	2	)	)	PUNCT
cana-5422	653	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	653	2	2208	2208	NUM
cana-5422	653	3	for	for	ADP
cana-5422	653	4	all	all	DET
cana-5422	653	5	w1	w1	NOUN
cana-5422	653	6	∈	∈	PROPN
cana-5422	653	7	w1	w1	NOUN
cana-5422	653	8	and	and	CCONJ
cana-5422	653	9	all	all	DET
cana-5422	653	10	λ	λ	PROPN
cana-5422	653	11	>	>	X
cana-5422	653	12	0	0	NUM
cana-5422	653	13	.	.	PUNCT
cana-5422	654	1	the	the	DET
cana-5422	654	2	rest	rest	NOUN
cana-5422	654	3	of	of	ADP
cana-5422	654	4	the	the	DET
cana-5422	654	5	proof	proof	NOUN
cana-5422	654	6	is	be	AUX
cana-5422	654	7	similar	similar	ADJ
cana-5422	654	8	to	to	ADP
cana-5422	654	9	that	that	PRON
cana-5422	654	10	of	of	ADP
cana-5422	654	11	theorem	theorem	ADJ
cana-5422	654	12	3.8	3.8	NUM
cana-5422	654	13	.	.	PUNCT
cana-5422	655	1	hence	hence	ADV
cana-5422	655	2	the	the	DET
cana-5422	655	3	proof	proof	NOUN
cana-5422	655	4	is	be	AUX
cana-5422	655	5	complete	complete	ADJ
cana-5422	655	6	.	.	PUNCT
cana-5422	656	1	�	�	PROPN
cana-5422	656	2	corollary	corollary	PROPN
cana-5422	656	3	3.16	3.16	NUM
cana-5422	656	4	.	.	PUNCT
cana-5422	657	1	suppose	suppose	VERB
cana-5422	657	2	that	that	SCONJ
cana-5422	657	3	an	an	DET
cana-5422	657	4	even	even	ADV
cana-5422	657	5	function	function	NOUN
cana-5422	657	6	f	f	PROPN
cana-5422	657	7	:	:	PUNCT
cana-5422	657	8	w1	w1	PROPN
cana-5422	657	9	→	→	SYM
cana-5422	657	10	w2	w2	NOUN
cana-5422	657	11	satisfy	satisfy	VERB
cana-5422	657	12	the	the	DET
cana-5422	657	13	functional	functional	ADJ
cana-5422	657	14	inequality	inequality	NOUN
cana-5422	657	15	(	(	PUNCT
cana-5422	657	16	3.2	3.2	NUM
cana-5422	657	17	)	)	PUNCT
cana-5422	657	18	for	for	ADP
cana-5422	657	19	all	all	DET
cana-5422	657	20	w1	w1	NOUN
cana-5422	657	21	,	,	PUNCT
cana-5422	657	22	w2	w2	NOUN
cana-5422	657	23	,	,	PUNCT
cana-5422	657	24	w3	w3	PROPN
cana-5422	657	25	∈	∈	PROPN
cana-5422	657	26	w1	w1	NOUN
cana-5422	657	27	and	and	CCONJ
cana-5422	657	28	all	all	DET
cana-5422	657	29	λ	λ	X
cana-5422	657	30	>	>	X
cana-5422	657	31	0	0	PUNCT
cana-5422	657	32	with	with	SCONJ
cana-5422	657	33	δ	δ	PROPN
cana-5422	657	34	be	be	AUX
cana-5422	657	35	a	a	DET
cana-5422	657	36	positive	positive	ADJ
cana-5422	657	37	constant	constant	NOUN
cana-5422	657	38	and	and	CCONJ
cana-5422	657	39	ϕ	ϕ	NOUN
cana-5422	657	40	be	be	AUX
cana-5422	657	41	any	any	DET
cana-5422	657	42	real	real	ADJ
cana-5422	657	43	number	number	NOUN
cana-5422	657	44	.	.	PUNCT
cana-5422	658	1	then	then	ADV
cana-5422	658	2	there	there	PRON
cana-5422	658	3	exists	exist	VERB
cana-5422	658	4	a	a	DET
cana-5422	658	5	unique	unique	ADJ
cana-5422	658	6	quadratic	quadratic	ADJ
cana-5422	658	7	mapping	mapping	NOUN
cana-5422	658	8	q(w1	q(w1	NOUN
cana-5422	658	9	)	)	PUNCT
cana-5422	658	10	:	:	PUNCT
cana-5422	658	11	w1	w1	PROPN
cana-5422	658	12	→w2	→w2	NOUN
cana-5422	658	13	which	which	PRON
cana-5422	658	14	satisfies	satisfy	VERB
cana-5422	658	15	(	(	PUNCT
cana-5422	658	16	1.7	1.7	NUM
cana-5422	658	17	)	)	PUNCT
cana-5422	658	18	and	and	CCONJ
cana-5422	658	19	the	the	DET
cana-5422	658	20	functional	functional	ADJ
cana-5422	658	21	inequality	inequality	NOUN
cana-5422	658	22	µ	µ	X
cana-5422	658	23	(	(	PUNCT
cana-5422	658	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	658	25	(	(	PUNCT
cana-5422	658	26	w1	w1	NOUN
cana-5422	658	27	)	)	PUNCT
cana-5422	658	28	,	,	PUNCT
cana-5422	658	29	λ	λ	X
cana-5422	658	30	)	)	PUNCT
cana-5422	658	31	≥	≥	NOUN
cana-5422	658	32	µ′	µ′	PUNCT
cana-5422	658	33	(	(	PUNCT
cana-5422	658	34	δ	δ	PROPN
cana-5422	658	35	,	,	PUNCT
cana-5422	658	36	|8|	|8|	PROPN
cana-5422	658	37	7λ	7λ	NUM
cana-5422	658	38	)	)	PUNCT
cana-5422	658	39	,	,	PUNCT
cana-5422	658	40	ν	ν	X
cana-5422	658	41	(	(	PUNCT
cana-5422	658	42	q(w1)−f	q(w1)−f	PROPN
cana-5422	658	43	(	(	PUNCT
cana-5422	658	44	w1	w1	NOUN
cana-5422	658	45	)	)	PUNCT
cana-5422	658	46	,	,	PUNCT
cana-5422	658	47	λ	λ	NOUN
cana-5422	658	48	)	)	PUNCT
cana-5422	658	49	≤	≤	NUM
cana-5422	658	50	ν′	ν′	NOUN
cana-5422	658	51	(	(	PUNCT
cana-5422	658	52	δ	δ	PROPN
cana-5422	658	53	,	,	PUNCT
cana-5422	658	54	|8|	|8|	PROPN
cana-5422	658	55	7λ	7λ	NUM
cana-5422	658	56	)	)	PUNCT
cana-5422	658	57	,	,	PUNCT
cana-5422	658	58	}	}	PUNCT
cana-5422	658	59	(	(	PUNCT
cana-5422	658	60	3.47	3.47	NUM
cana-5422	658	61	)	)	PUNCT
cana-5422	658	62	for	for	ADP
cana-5422	658	63	all	all	DET
cana-5422	658	64	w1	w1	NOUN
cana-5422	658	65	∈	∈	PROPN
cana-5422	658	66	w1	w1	NOUN
cana-5422	658	67	and	and	CCONJ
cana-5422	658	68	all	all	DET
cana-5422	658	69	λ	λ	PROPN
cana-5422	658	70	>	>	X
cana-5422	658	71	0	0	X
cana-5422	658	72	.	.	PUNCT
cana-5422	659	1	corollary	corollary	ADJ
cana-5422	659	2	3.17	3.17	NUM
cana-5422	659	3	.	.	PUNCT
cana-5422	659	4	suppose	suppose	VERB
cana-5422	659	5	that	that	SCONJ
cana-5422	659	6	an	an	DET
cana-5422	659	7	even	even	ADV
cana-5422	659	8	function	function	NOUN
cana-5422	659	9	f	f	PROPN
cana-5422	659	10	:	:	PUNCT
cana-5422	659	11	w1	w1	PROPN
cana-5422	659	12	→	→	SYM
cana-5422	659	13	w2	w2	NOUN
cana-5422	659	14	satisfy	satisfy	VERB
cana-5422	659	15	the	the	DET
cana-5422	659	16	functional	functional	ADJ
cana-5422	659	17	inequality	inequality	NOUN
cana-5422	659	18	(	(	PUNCT
cana-5422	659	19	3.3	3.3	NUM
cana-5422	659	20	)	)	PUNCT
cana-5422	659	21	for	for	ADP
cana-5422	659	22	all	all	DET
cana-5422	659	23	w1	w1	NOUN
cana-5422	659	24	,	,	PUNCT
cana-5422	659	25	w2	w2	NOUN
cana-5422	659	26	,	,	PUNCT
cana-5422	659	27	w3	w3	PROPN
cana-5422	659	28	∈	∈	PROPN
cana-5422	659	29	w1	w1	NOUN
cana-5422	659	30	and	and	CCONJ
cana-5422	659	31	all	all	DET
cana-5422	659	32	λ	λ	X
cana-5422	659	33	>	>	X
cana-5422	659	34	0	0	PUNCT
cana-5422	659	35	with	with	SCONJ
cana-5422	659	36	δ	δ	PROPN
cana-5422	659	37	be	be	AUX
cana-5422	659	38	a	a	DET
cana-5422	659	39	positive	positive	ADJ
cana-5422	659	40	constant	constant	NOUN
cana-5422	659	41	and	and	CCONJ
cana-5422	659	42	ϕ	ϕ	NOUN
cana-5422	659	43	be	be	AUX
cana-5422	659	44	any	any	DET
cana-5422	659	45	real	real	ADJ
cana-5422	659	46	number	number	NOUN
cana-5422	659	47	.	.	PUNCT
cana-5422	660	1	then	then	ADV
cana-5422	660	2	there	there	PRON
cana-5422	660	3	exists	exist	VERB
cana-5422	660	4	a	a	DET
cana-5422	660	5	unique	unique	ADJ
cana-5422	660	6	quadratic	quadratic	ADJ
cana-5422	660	7	mapping	mapping	NOUN
cana-5422	660	8	q(w1	q(w1	NOUN
cana-5422	660	9	)	)	PUNCT
cana-5422	660	10	:	:	PUNCT
cana-5422	660	11	w1	w1	PROPN
cana-5422	660	12	→w2	→w2	NOUN
cana-5422	660	13	which	which	PRON
cana-5422	660	14	satisfies	satisfy	VERB
cana-5422	660	15	(	(	PUNCT
cana-5422	660	16	1.7	1.7	NUM
cana-5422	660	17	)	)	PUNCT
cana-5422	660	18	and	and	CCONJ
cana-5422	660	19	the	the	DET
cana-5422	660	20	functional	functional	ADJ
cana-5422	660	21	inequality	inequality	NOUN
cana-5422	660	22	µ	µ	X
cana-5422	660	23	(	(	PUNCT
cana-5422	660	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	660	25	(	(	PUNCT
cana-5422	660	26	w1	w1	NOUN
cana-5422	660	27	)	)	PUNCT
cana-5422	660	28	,	,	PUNCT
cana-5422	660	29	λ	λ	X
cana-5422	660	30	)	)	PUNCT
cana-5422	660	31	≥	≥	NOUN
cana-5422	660	32	µ′	µ′	PUNCT
cana-5422	660	33	(	(	PUNCT
cana-5422	660	34	δ|w1|ϕ	δ|w1|ϕ	NOUN
cana-5422	660	35	,	,	PUNCT
cana-5422	660	36	7λ	7λ	NUM
cana-5422	660	37	9	9	NUM
cana-5422	660	38	|25−	|25−	NOUN
cana-5422	660	39	5ϕ|	5ϕ|	NUM
cana-5422	660	40	)	)	PUNCT
cana-5422	660	41	,	,	PUNCT
cana-5422	660	42	ϕ	ϕ	PROPN
cana-5422	660	43	6=	6=	ADP
cana-5422	660	44	2	2	NUM
cana-5422	660	45	,	,	PUNCT
cana-5422	660	46	ν	ν	X
cana-5422	660	47	(	(	PUNCT
cana-5422	660	48	q(w1)−f	q(w1)−f	PROPN
cana-5422	660	49	(	(	PUNCT
cana-5422	660	50	w1	w1	NOUN
cana-5422	660	51	)	)	PUNCT
cana-5422	660	52	,	,	PUNCT
cana-5422	660	53	λ	λ	NOUN
cana-5422	660	54	)	)	PUNCT
cana-5422	660	55	≤	≤	NUM
cana-5422	660	56	ν′	ν′	NOUN
cana-5422	660	57	(	(	PUNCT
cana-5422	660	58	δ|w1|ϕ	δ|w1|ϕ	NOUN
cana-5422	660	59	,	,	PUNCT
cana-5422	660	60	7λ	7λ	NUM
cana-5422	660	61	9	9	NUM
cana-5422	660	62	|25−	|25−	NOUN
cana-5422	660	63	5ϕ|	5ϕ|	NUM
cana-5422	660	64	)	)	PUNCT
cana-5422	660	65	,	,	PUNCT
cana-5422	660	66	ϕ	ϕ	PROPN
cana-5422	660	67	6=	6=	ADP
cana-5422	660	68	2	2	NUM
cana-5422	660	69	,	,	PUNCT
cana-5422	660	70			PROPN
cana-5422	660	71	(	(	PUNCT
cana-5422	660	72	3.48	3.48	NUM
cana-5422	660	73	)	)	PUNCT
cana-5422	660	74	for	for	ADP
cana-5422	660	75	all	all	DET
cana-5422	660	76	w1	w1	NOUN
cana-5422	660	77	∈	∈	PROPN
cana-5422	660	78	w1	w1	NOUN
cana-5422	660	79	and	and	CCONJ
cana-5422	660	80	all	all	DET
cana-5422	660	81	λ	λ	PROPN
cana-5422	660	82	>	>	X
cana-5422	660	83	0	0	X
cana-5422	660	84	.	.	PUNCT
cana-5422	660	85	corollary	corollary	ADJ
cana-5422	660	86	3.18	3.18	NUM
cana-5422	660	87	.	.	PUNCT
cana-5422	660	88	suppose	suppose	VERB
cana-5422	660	89	that	that	SCONJ
cana-5422	660	90	an	an	DET
cana-5422	660	91	even	even	ADV
cana-5422	660	92	function	function	NOUN
cana-5422	660	93	f	f	PROPN
cana-5422	660	94	:	:	PUNCT
cana-5422	660	95	w1	w1	PROPN
cana-5422	660	96	→	→	SYM
cana-5422	660	97	w2	w2	NOUN
cana-5422	660	98	satisfy	satisfy	VERB
cana-5422	660	99	the	the	DET
cana-5422	660	100	functional	functional	ADJ
cana-5422	660	101	inequality	inequality	NOUN
cana-5422	660	102	(	(	PUNCT
cana-5422	660	103	3.4	3.4	NUM
cana-5422	660	104	)	)	PUNCT
cana-5422	660	105	for	for	ADP
cana-5422	660	106	all	all	DET
cana-5422	660	107	w1	w1	NOUN
cana-5422	660	108	,	,	PUNCT
cana-5422	660	109	w2	w2	NOUN
cana-5422	660	110	,	,	PUNCT
cana-5422	660	111	w3	w3	PROPN
cana-5422	660	112	∈	∈	PROPN
cana-5422	660	113	w1	w1	NOUN
cana-5422	660	114	and	and	CCONJ
cana-5422	660	115	all	all	DET
cana-5422	660	116	λ	λ	X
cana-5422	660	117	>	>	X
cana-5422	660	118	0	0	PUNCT
cana-5422	660	119	with	with	SCONJ
cana-5422	660	120	δ	δ	PROPN
cana-5422	660	121	be	be	AUX
cana-5422	660	122	a	a	DET
cana-5422	660	123	positive	positive	ADJ
cana-5422	660	124	constant	constant	NOUN
cana-5422	660	125	and	and	CCONJ
cana-5422	660	126	ϕ	ϕ	NOUN
cana-5422	660	127	be	be	AUX
cana-5422	660	128	any	any	DET
cana-5422	660	129	real	real	ADJ
cana-5422	660	130	number	number	NOUN
cana-5422	660	131	.	.	PUNCT
cana-5422	661	1	then	then	ADV
cana-5422	661	2	there	there	PRON
cana-5422	661	3	exists	exist	VERB
cana-5422	661	4	a	a	DET
cana-5422	661	5	unique	unique	ADJ
cana-5422	661	6	quadratic	quadratic	ADJ
cana-5422	661	7	mapping	mapping	NOUN
cana-5422	661	8	q(w1	q(w1	NOUN
cana-5422	661	9	)	)	PUNCT
cana-5422	661	10	:	:	PUNCT
cana-5422	661	11	w1	w1	PROPN
cana-5422	661	12	→w2	→w2	NOUN
cana-5422	661	13	which	which	PRON
cana-5422	661	14	satisfies	satisfy	VERB
cana-5422	661	15	(	(	PUNCT
cana-5422	661	16	1.7	1.7	NUM
cana-5422	661	17	)	)	PUNCT
cana-5422	661	18	and	and	CCONJ
cana-5422	661	19	the	the	DET
cana-5422	661	20	functional	functional	ADJ
cana-5422	661	21	inequality	inequality	NOUN
cana-5422	661	22	µ	µ	X
cana-5422	661	23	(	(	PUNCT
cana-5422	661	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	661	25	(	(	PUNCT
cana-5422	661	26	w1	w1	NOUN
cana-5422	661	27	)	)	PUNCT
cana-5422	661	28	,	,	PUNCT
cana-5422	661	29	λ	λ	X
cana-5422	661	30	)	)	PUNCT
cana-5422	661	31	≥	≥	NOUN
cana-5422	661	32	µ′	µ′	PUNCT
cana-5422	661	33	(	(	PUNCT
cana-5422	661	34	δ	δ	PROPN
cana-5422	661	35	∑3	∑3	PROPN
cana-5422	661	36	ψ=1	ψ=1	PUNCT
cana-5422	661	37	|w1|	|w1|	NOUN
cana-5422	661	38	ϕψ	ϕψ	ADV
cana-5422	661	39	,	,	PUNCT
cana-5422	661	40	7λ	7λ	NUM
cana-5422	661	41	3	3	NUM
cana-5422	661	42	∑3	∑3	ADP
cana-5422	661	43	ψ=1	ψ=1	PUNCT
cana-5422	661	44	|25−	|25−	VERB
cana-5422	661	45	5ϕψ	5ϕψ	PROPN
cana-5422	661	46	|	|	NOUN
cana-5422	661	47	)	)	PUNCT
cana-5422	661	48	,	,	PUNCT
cana-5422	661	49	ϕ1	ϕ1	NOUN
cana-5422	661	50	,	,	PUNCT
cana-5422	661	51	ϕ2	ϕ2	ADV
cana-5422	661	52	,	,	PUNCT
cana-5422	661	53	ϕ3	ϕ3	PROPN
cana-5422	661	54	6=	6=	PROPN
cana-5422	661	55	2	2	NUM
cana-5422	661	56	,	,	PUNCT
cana-5422	661	57	ν	ν	X
cana-5422	661	58	(	(	PUNCT
cana-5422	661	59	q(w1)−f	q(w1)−f	PROPN
cana-5422	661	60	(	(	PUNCT
cana-5422	661	61	w1	w1	NOUN
cana-5422	661	62	)	)	PUNCT
cana-5422	661	63	,	,	PUNCT
cana-5422	661	64	λ	λ	NOUN
cana-5422	661	65	)	)	PUNCT
cana-5422	661	66	≤	≤	NUM
cana-5422	661	67	ν′	ν′	NOUN
cana-5422	661	68	(	(	PUNCT
cana-5422	661	69	δ	δ	NOUN
cana-5422	661	70	∑3	∑3	PROPN
cana-5422	661	71	ψ=1	ψ=1	PUNCT
cana-5422	661	72	|w1|	|w1|	NOUN
cana-5422	661	73	ϕψ	ϕψ	ADV
cana-5422	661	74	,	,	PUNCT
cana-5422	661	75	7λ	7λ	NUM
cana-5422	661	76	3	3	NUM
cana-5422	661	77	∑3	∑3	ADP
cana-5422	661	78	ψ=1	ψ=1	PUNCT
cana-5422	661	79	|25−	|25−	VERB
cana-5422	661	80	5ϕψ	5ϕψ	PROPN
cana-5422	661	81	|	|	NOUN
cana-5422	661	82	)	)	PUNCT
cana-5422	661	83	,	,	PUNCT
cana-5422	661	84	ϕ1	ϕ1	NOUN
cana-5422	661	85	,	,	PUNCT
cana-5422	661	86	ϕ2	ϕ2	ADV
cana-5422	661	87	,	,	PUNCT
cana-5422	661	88	ϕ3	ϕ3	PROPN
cana-5422	661	89	6=	6=	ADP
cana-5422	661	90	2	2	NUM
cana-5422	661	91	,	,	PUNCT
cana-5422	661	92			PROPN
cana-5422	661	93	(	(	PUNCT
cana-5422	661	94	3.49	3.49	NUM
cana-5422	661	95	)	)	PUNCT
cana-5422	661	96	for	for	ADP
cana-5422	661	97	all	all	DET
cana-5422	661	98	w1	w1	NOUN
cana-5422	661	99	∈	∈	PROPN
cana-5422	661	100	w1	w1	NOUN
cana-5422	661	101	and	and	CCONJ
cana-5422	661	102	all	all	DET
cana-5422	661	103	λ	λ	PROPN
cana-5422	661	104	>	>	X
cana-5422	661	105	0	0	X
cana-5422	661	106	.	.	PUNCT
cana-5422	662	1	corollary	corollary	ADJ
cana-5422	662	2	3.19	3.19	NUM
cana-5422	662	3	.	.	PUNCT
cana-5422	662	4	suppose	suppose	VERB
cana-5422	662	5	that	that	SCONJ
cana-5422	662	6	an	an	DET
cana-5422	662	7	even	even	ADV
cana-5422	662	8	function	function	NOUN
cana-5422	662	9	f	f	PROPN
cana-5422	662	10	:	:	PUNCT
cana-5422	662	11	w1	w1	PROPN
cana-5422	662	12	→	→	SYM
cana-5422	662	13	w2	w2	NOUN
cana-5422	662	14	satisfy	satisfy	VERB
cana-5422	662	15	the	the	DET
cana-5422	662	16	functional	functional	ADJ
cana-5422	662	17	inequality	inequality	NOUN
cana-5422	662	18	(	(	PUNCT
cana-5422	662	19	3.5	3.5	NUM
cana-5422	662	20	)	)	PUNCT
cana-5422	662	21	for	for	ADP
cana-5422	662	22	all	all	DET
cana-5422	662	23	w1	w1	NOUN
cana-5422	662	24	,	,	PUNCT
cana-5422	662	25	w2	w2	NOUN
cana-5422	662	26	,	,	PUNCT
cana-5422	662	27	w3	w3	PROPN
cana-5422	662	28	∈	∈	PROPN
cana-5422	662	29	w1	w1	NOUN
cana-5422	662	30	and	and	CCONJ
cana-5422	662	31	all	all	DET
cana-5422	662	32	λ	λ	X
cana-5422	662	33	>	>	X
cana-5422	662	34	0	0	PUNCT
cana-5422	662	35	with	with	SCONJ
cana-5422	662	36	δ	δ	PROPN
cana-5422	662	37	be	be	AUX
cana-5422	662	38	a	a	DET
cana-5422	662	39	positive	positive	ADJ
cana-5422	662	40	constant	constant	NOUN
cana-5422	662	41	and	and	CCONJ
cana-5422	662	42	ϕ	ϕ	NOUN
cana-5422	662	43	be	be	AUX
cana-5422	662	44	any	any	DET
cana-5422	662	45	real	real	ADJ
cana-5422	662	46	number	number	NOUN
cana-5422	662	47	.	.	PUNCT
cana-5422	663	1	then	then	ADV
cana-5422	663	2	there	there	PRON
cana-5422	663	3	exists	exist	VERB
cana-5422	663	4	a	a	DET
cana-5422	663	5	unique	unique	ADJ
cana-5422	663	6	quadratic	quadratic	ADJ
cana-5422	663	7	mapping	mapping	NOUN
cana-5422	663	8	q(w1	q(w1	NOUN
cana-5422	663	9	)	)	PUNCT
cana-5422	663	10	:	:	PUNCT
cana-5422	663	11	w1	w1	PROPN
cana-5422	663	12	→w2	→w2	NOUN
cana-5422	663	13	which	which	PRON
cana-5422	663	14	satisfies	satisfy	VERB
cana-5422	663	15	(	(	PUNCT
cana-5422	663	16	1.7	1.7	NUM
cana-5422	663	17	)	)	PUNCT
cana-5422	663	18	and	and	CCONJ
cana-5422	663	19	the	the	DET
cana-5422	663	20	functional	functional	ADJ
cana-5422	663	21	inequality	inequality	NOUN
cana-5422	663	22	µ	µ	X
cana-5422	663	23	(	(	PUNCT
cana-5422	663	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	663	25	(	(	PUNCT
cana-5422	663	26	w1	w1	NOUN
cana-5422	663	27	)	)	PUNCT
cana-5422	663	28	,	,	PUNCT
cana-5422	663	29	λ	λ	X
cana-5422	663	30	)	)	PUNCT
cana-5422	663	31	≥	≥	NOUN
cana-5422	663	32	µ′	µ′	PUNCT
cana-5422	663	33	(	(	PUNCT
cana-5422	663	34	δ|w1|3ϕ	δ|w1|3ϕ	ADV
cana-5422	663	35	,	,	PUNCT
cana-5422	663	36	7λ	7λ	NUM
cana-5422	663	37	3	3	NUM
cana-5422	663	38	|25−	|25−	PROPN
cana-5422	663	39	53ϕ|	53ϕ|	NUM
cana-5422	663	40	)	)	PUNCT
cana-5422	663	41	,	,	PUNCT
cana-5422	663	42	3ϕ	3ϕ	NUM
cana-5422	663	43	6=	6=	NUM
cana-5422	663	44	2	2	NUM
cana-5422	663	45	,	,	PUNCT
cana-5422	663	46	ν	ν	X
cana-5422	663	47	(	(	PUNCT
cana-5422	663	48	q(w1)−f	q(w1)−f	PROPN
cana-5422	663	49	(	(	PUNCT
cana-5422	663	50	w1	w1	NOUN
cana-5422	663	51	)	)	PUNCT
cana-5422	663	52	,	,	PUNCT
cana-5422	663	53	λ	λ	NOUN
cana-5422	663	54	)	)	PUNCT
cana-5422	663	55	≤	≤	NUM
cana-5422	663	56	ν′	ν′	NOUN
cana-5422	663	57	(	(	PUNCT
cana-5422	663	58	δ|w1|3ϕ	δ|w1|3ϕ	ADV
cana-5422	663	59	,	,	PUNCT
cana-5422	663	60	7λ	7λ	NUM
cana-5422	663	61	3	3	NUM
cana-5422	663	62	|25−	|25−	PROPN
cana-5422	663	63	53ϕ|	53ϕ|	NUM
cana-5422	663	64	)	)	PUNCT
cana-5422	663	65	,	,	PUNCT
cana-5422	663	66	3ϕ	3ϕ	NUM
cana-5422	663	67	6=	6=	SYM
cana-5422	663	68	2	2	NUM
cana-5422	663	69	,	,	PUNCT
cana-5422	663	70			PROPN
cana-5422	663	71	(	(	PUNCT
cana-5422	663	72	3.50	3.50	NUM
cana-5422	663	73	)	)	PUNCT
cana-5422	663	74	for	for	ADP
cana-5422	663	75	all	all	DET
cana-5422	663	76	w1	w1	NOUN
cana-5422	663	77	∈	∈	PROPN
cana-5422	663	78	w1	w1	NOUN
cana-5422	663	79	and	and	CCONJ
cana-5422	663	80	all	all	DET
cana-5422	663	81	λ	λ	PROPN
cana-5422	663	82	>	>	X
cana-5422	663	83	0	0	X
cana-5422	663	84	.	.	PUNCT
cana-5422	664	1	corollary	corollary	ADJ
cana-5422	664	2	3.20	3.20	NUM
cana-5422	664	3	.	.	PUNCT
cana-5422	664	4	suppose	suppose	VERB
cana-5422	664	5	that	that	SCONJ
cana-5422	664	6	an	an	DET
cana-5422	664	7	even	even	ADV
cana-5422	664	8	function	function	NOUN
cana-5422	664	9	f	f	PROPN
cana-5422	664	10	:	:	PUNCT
cana-5422	664	11	w1	w1	PROPN
cana-5422	664	12	→	→	SYM
cana-5422	664	13	w2	w2	NOUN
cana-5422	664	14	satisfy	satisfy	VERB
cana-5422	664	15	the	the	DET
cana-5422	664	16	functional	functional	ADJ
cana-5422	664	17	inequality	inequality	NOUN
cana-5422	664	18	(	(	PUNCT
cana-5422	664	19	3.6	3.6	NUM
cana-5422	664	20	)	)	PUNCT
cana-5422	664	21	for	for	ADP
cana-5422	664	22	all	all	DET
cana-5422	664	23	w1	w1	NOUN
cana-5422	664	24	,	,	PUNCT
cana-5422	664	25	w2	w2	NOUN
cana-5422	664	26	,	,	PUNCT
cana-5422	664	27	w3	w3	PROPN
cana-5422	664	28	∈	∈	PROPN
cana-5422	664	29	w1	w1	NOUN
cana-5422	664	30	and	and	CCONJ
cana-5422	664	31	all	all	DET
cana-5422	664	32	λ	λ	X
cana-5422	664	33	>	>	X
cana-5422	664	34	0	0	PUNCT
cana-5422	664	35	with	with	SCONJ
cana-5422	664	36	δ	δ	PROPN
cana-5422	664	37	be	be	AUX
cana-5422	664	38	a	a	DET
cana-5422	664	39	positive	positive	ADJ
cana-5422	664	40	constant	constant	NOUN
cana-5422	664	41	and	and	CCONJ
cana-5422	664	42	ϕ	ϕ	NOUN
cana-5422	664	43	be	be	AUX
cana-5422	664	44	any	any	DET
cana-5422	664	45	real	real	ADJ
cana-5422	664	46	number	number	NOUN
cana-5422	664	47	.	.	PUNCT
cana-5422	665	1	then	then	ADV
cana-5422	665	2	there	there	PRON
cana-5422	665	3	exists	exist	VERB
cana-5422	665	4	a	a	DET
cana-5422	665	5	unique	unique	ADJ
cana-5422	665	6	quadratic	quadratic	ADJ
cana-5422	665	7	mapping	mapping	NOUN
cana-5422	665	8	q(w1	q(w1	NOUN
cana-5422	665	9	)	)	PUNCT
cana-5422	665	10	:	:	PUNCT
cana-5422	665	11	w1	w1	PROPN
cana-5422	665	12	→w2	→w2	NOUN
cana-5422	665	13	which	which	PRON
cana-5422	665	14	satisfies	satisfy	VERB
cana-5422	665	15	(	(	PUNCT
cana-5422	665	16	1.7	1.7	NUM
cana-5422	665	17	)	)	PUNCT
cana-5422	665	18	and	and	CCONJ
cana-5422	665	19	the	the	DET
cana-5422	665	20	functional	functional	ADJ
cana-5422	665	21	inequality	inequality	NOUN
cana-5422	665	22	µ	µ	X
cana-5422	665	23	(	(	PUNCT
cana-5422	665	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	665	25	(	(	PUNCT
cana-5422	665	26	w1	w1	NOUN
cana-5422	665	27	)	)	PUNCT
cana-5422	665	28	,	,	PUNCT
cana-5422	665	29	λ	λ	X
cana-5422	665	30	)	)	PUNCT
cana-5422	665	31	≥	≥	NOUN
cana-5422	665	32	µ′	µ′	PUNCT
cana-5422	665	33	(	(	PUNCT
cana-5422	665	34	δ|wψ|∑	δ|wψ|∑	PROPN
cana-5422	665	35	3	3	NUM
cana-5422	665	36	ψ=1	ψ=1	PUNCT
cana-5422	665	37	ϕψ	ϕψ	NOUN
cana-5422	665	38	,	,	PUNCT
cana-5422	665	39	7λ	7λ	NUM
cana-5422	665	40	3	3	NUM
cana-5422	665	41	∣∣∣25−	∣∣∣25−	NOUN
cana-5422	665	42	5∑3	5∑3	NUM
cana-5422	665	43	ψ=1	ψ=1	PUNCT
cana-5422	665	44	ϕψ	ϕψ	ADV
cana-5422	665	45	∣∣∣	∣∣∣	ADJ
cana-5422	665	46	)	)	PUNCT
cana-5422	665	47	,	,	PUNCT
cana-5422	665	48	∑3	∑3	PROPN
cana-5422	665	49	ψ=1	ψ=1	PUNCT
cana-5422	665	50	ϕψ	ϕψ	ADP
cana-5422	665	51	6=	6=	PROPN
cana-5422	665	52	2	2	NUM
cana-5422	665	53	,	,	PUNCT
cana-5422	665	54	ν	ν	X
cana-5422	665	55	(	(	PUNCT
cana-5422	665	56	q(w1)−f	q(w1)−f	PROPN
cana-5422	665	57	(	(	PUNCT
cana-5422	665	58	w1	w1	NOUN
cana-5422	665	59	)	)	PUNCT
cana-5422	665	60	,	,	PUNCT
cana-5422	665	61	λ	λ	NOUN
cana-5422	665	62	)	)	PUNCT
cana-5422	665	63	≤	≤	NUM
cana-5422	665	64	ν′	ν′	NOUN
cana-5422	665	65	(	(	PUNCT
cana-5422	665	66	δ|wψ|∑	δ|wψ|∑	PROPN
cana-5422	665	67	3	3	NUM
cana-5422	665	68	ψ=1	ψ=1	PUNCT
cana-5422	665	69	ϕψ	ϕψ	NOUN
cana-5422	665	70	,	,	PUNCT
cana-5422	665	71	7λ	7λ	NUM
cana-5422	665	72	3	3	NUM
cana-5422	665	73	∣∣∣25−	∣∣∣25−	NOUN
cana-5422	665	74	5∑3	5∑3	NUM
cana-5422	665	75	ψ=1	ψ=1	PUNCT
cana-5422	665	76	ϕψ	ϕψ	ADV
cana-5422	665	77	∣∣∣	∣∣∣	ADJ
cana-5422	665	78	)	)	PUNCT
cana-5422	665	79	,	,	PUNCT
cana-5422	665	80	∑3	∑3	PROPN
cana-5422	665	81	ψ=1	ψ=1	PUNCT
cana-5422	665	82	ϕψ	ϕψ	ADP
cana-5422	665	83	6=	6=	PROPN
cana-5422	665	84	2	2	NUM
cana-5422	665	85	,	,	PUNCT
cana-5422	665	86			PROPN
cana-5422	665	87	(	(	PUNCT
cana-5422	665	88	3.51	3.51	NUM
cana-5422	665	89	)	)	PUNCT
cana-5422	665	90	for	for	ADP
cana-5422	665	91	all	all	DET
cana-5422	665	92	w1	w1	NOUN
cana-5422	665	93	∈	∈	PROPN
cana-5422	665	94	w1	w1	NOUN
cana-5422	665	95	and	and	CCONJ
cana-5422	665	96	all	all	DET
cana-5422	665	97	λ	λ	PROPN
cana-5422	665	98	>	>	X
cana-5422	665	99	0	0	X
cana-5422	665	100	.	.	PUNCT
cana-5422	665	101	corollary	corollary	ADJ
cana-5422	665	102	3.21	3.21	NUM
cana-5422	665	103	.	.	PUNCT
cana-5422	665	104	suppose	suppose	VERB
cana-5422	665	105	that	that	SCONJ
cana-5422	665	106	an	an	DET
cana-5422	665	107	even	even	ADV
cana-5422	665	108	function	function	NOUN
cana-5422	665	109	f	f	PROPN
cana-5422	665	110	:	:	PUNCT
cana-5422	665	111	w1	w1	PROPN
cana-5422	665	112	→	→	SYM
cana-5422	665	113	w2	w2	NOUN
cana-5422	665	114	satisfy	satisfy	VERB
cana-5422	665	115	the	the	DET
cana-5422	665	116	functional	functional	ADJ
cana-5422	665	117	inequality	inequality	NOUN
cana-5422	665	118	(	(	PUNCT
cana-5422	665	119	3.7	3.7	NUM
cana-5422	665	120	)	)	PUNCT
cana-5422	665	121	for	for	ADP
cana-5422	665	122	all	all	DET
cana-5422	665	123	w1	w1	NOUN
cana-5422	665	124	,	,	PUNCT
cana-5422	665	125	w2	w2	NOUN
cana-5422	665	126	,	,	PUNCT
cana-5422	665	127	w3	w3	PROPN
cana-5422	665	128	∈	∈	PROPN
cana-5422	665	129	w1	w1	NOUN
cana-5422	665	130	and	and	CCONJ
cana-5422	665	131	all	all	DET
cana-5422	665	132	λ	λ	X
cana-5422	665	133	>	>	X
cana-5422	665	134	0	0	PUNCT
cana-5422	665	135	with	with	SCONJ
cana-5422	665	136	δ	δ	PROPN
cana-5422	665	137	be	be	AUX
cana-5422	665	138	a	a	DET
cana-5422	665	139	positive	positive	ADJ
cana-5422	665	140	constant	constant	NOUN
cana-5422	665	141	and	and	CCONJ
cana-5422	665	142	ϕ	ϕ	NOUN
cana-5422	665	143	be	be	AUX
cana-5422	665	144	any	any	DET
cana-5422	665	145	real	real	ADJ
cana-5422	665	146	number	number	NOUN
cana-5422	665	147	.	.	PUNCT
cana-5422	666	1	then	then	ADV
cana-5422	666	2	there	there	PRON
cana-5422	666	3	exists	exist	VERB
cana-5422	666	4	a	a	DET
cana-5422	666	5	unique	unique	ADJ
cana-5422	666	6	quadratic	quadratic	ADJ
cana-5422	666	7	mapping	mapping	NOUN
cana-5422	666	8	q(w1	q(w1	NOUN
cana-5422	666	9	)	)	PUNCT
cana-5422	666	10	:	:	PUNCT
cana-5422	666	11	w1	w1	PROPN
cana-5422	666	12	→w2	→w2	NOUN
cana-5422	666	13	which	which	PRON
cana-5422	666	14	satisfies	satisfy	VERB
cana-5422	666	15	(	(	PUNCT
cana-5422	666	16	1.7	1.7	NUM
cana-5422	666	17	)	)	PUNCT
cana-5422	666	18	and	and	CCONJ
cana-5422	666	19	the	the	DET
cana-5422	666	20	functional	functional	ADJ
cana-5422	666	21	inequality	inequality	NOUN
cana-5422	666	22	µ	µ	X
cana-5422	666	23	(	(	PUNCT
cana-5422	666	24	q(w1)−f	q(w1)−f	PROPN
cana-5422	666	25	(	(	PUNCT
cana-5422	666	26	w1	w1	NOUN
cana-5422	666	27	)	)	PUNCT
cana-5422	666	28	,	,	PUNCT
cana-5422	666	29	λ	λ	X
cana-5422	666	30	)	)	PUNCT
cana-5422	666	31	≥	≥	NOUN
cana-5422	666	32	µ′	µ′	PUNCT
cana-5422	666	33	(	(	PUNCT
cana-5422	666	34	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	666	35	,	,	PUNCT
cana-5422	666	36	7λ	7λ	NUM
cana-5422	666	37	3	3	NUM
cana-5422	666	38	|25−	|25−	PROPN
cana-5422	666	39	53ϕ|	53ϕ|	NUM
cana-5422	666	40	)	)	PUNCT
cana-5422	666	41	,	,	PUNCT
cana-5422	666	42	3ϕ	3ϕ	NUM
cana-5422	666	43	6=	6=	NUM
cana-5422	666	44	2	2	NUM
cana-5422	666	45	,	,	PUNCT
cana-5422	666	46	ν	ν	X
cana-5422	666	47	(	(	PUNCT
cana-5422	666	48	q(w1)−f	q(w1)−f	PROPN
cana-5422	666	49	(	(	PUNCT
cana-5422	666	50	w1	w1	NOUN
cana-5422	666	51	)	)	PUNCT
cana-5422	666	52	,	,	PUNCT
cana-5422	666	53	λ	λ	NOUN
cana-5422	666	54	)	)	PUNCT
cana-5422	666	55	≤	≤	NUM
cana-5422	666	56	ν′	ν′	NOUN
cana-5422	666	57	(	(	PUNCT
cana-5422	666	58	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	666	59	,	,	PUNCT
cana-5422	666	60	7λ	7λ	NUM
cana-5422	666	61	3	3	NUM
cana-5422	666	62	|25−	|25−	PROPN
cana-5422	666	63	53ϕ|	53ϕ|	NUM
cana-5422	666	64	)	)	PUNCT
cana-5422	666	65	,	,	PUNCT
cana-5422	666	66	3ϕ	3ϕ	NUM
cana-5422	666	67	6=	6=	SYM
cana-5422	666	68	2	2	NUM
cana-5422	666	69	,	,	PUNCT
cana-5422	666	70			PROPN
cana-5422	666	71	(	(	PUNCT
cana-5422	666	72	3.52	3.52	NUM
cana-5422	666	73	)	)	PUNCT
cana-5422	666	74	for	for	ADP
cana-5422	666	75	all	all	DET
cana-5422	666	76	w1	w1	NOUN
cana-5422	666	77	∈	∈	PROPN
cana-5422	666	78	w1	w1	NOUN
cana-5422	666	79	and	and	CCONJ
cana-5422	666	80	all	all	DET
cana-5422	666	81	λ	λ	PROPN
cana-5422	666	82	>	>	X
cana-5422	666	83	0	0	X
cana-5422	666	84	.	.	PUNCT
cana-5422	666	85	communications	communication	NOUN
cana-5422	666	86	on	on	ADP
cana-5422	666	87	applied	apply	VERB
cana-5422	666	88	nonlinear	nonlinear	ADJ
cana-5422	666	89	analysis	analysis	NOUN
cana-5422	666	90	issn	issn	NOUN
cana-5422	666	91	:	:	PUNCT
cana-5422	666	92	1074	1074	NUM
cana-5422	666	93	-	-	PUNCT
cana-5422	666	94	133x	133x	NUM
cana-5422	666	95	vol	vol	NOUN
cana-5422	666	96	32	32	NUM
cana-5422	666	97	no	no	NOUN
cana-5422	666	98	.	.	PUNCT
cana-5422	667	1	10s(2025	10s(2025	NUM
cana-5422	667	2	)	)	PUNCT
cana-5422	668	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	668	2	2209	2209	NUM
cana-5422	668	3	3.4	3.4	NUM
cana-5422	668	4	.	.	PUNCT
cana-5422	669	1	oddness	oddness	ADJ
cana-5422	669	2	and	and	CCONJ
cana-5422	669	3	evenness	evenness	NOUN
cana-5422	669	4	of	of	ADP
cana-5422	669	5	f	f	NOUN
cana-5422	669	6	:	:	PUNCT
cana-5422	669	7	additive	additive	ADJ
cana-5422	669	8	quadratic	quadratic	ADJ
cana-5422	669	9	case	case	NOUN
cana-5422	669	10	stability	stability	NOUN
cana-5422	669	11	results	result	VERB
cana-5422	669	12	:	:	PUNCT
cana-5422	669	13	direct	direct	ADJ
cana-5422	669	14	method	method	NOUN
cana-5422	669	15	.	.	PUNCT
cana-5422	670	1	theorem	theorem	VERB
cana-5422	670	2	3.22	3.22	NUM
cana-5422	670	3	.	.	PUNCT
cana-5422	671	1	suppose	suppose	VERB
cana-5422	671	2	that	that	SCONJ
cana-5422	671	3	a	a	DET
cana-5422	671	4	function	function	NOUN
cana-5422	671	5	f	f	NOUN
cana-5422	671	6	:	:	PUNCT
cana-5422	671	7	w1	w1	PROPN
cana-5422	671	8	→w2	→w2	NOUN
cana-5422	671	9	satisfy	satisfy	VERB
cana-5422	671	10	the	the	DET
cana-5422	671	11	functional	functional	ADJ
cana-5422	671	12	inequality	inequality	NOUN
cana-5422	671	13	(	(	PUNCT
cana-5422	671	14	3.1	3.1	NUM
cana-5422	671	15	)	)	PUNCT
cana-5422	671	16	where	where	SCONJ
cana-5422	671	17	ψ	ψ	X
cana-5422	671	18	:	:	PUNCT
cana-5422	671	19	w3	w3	NOUN
cana-5422	671	20	1	1	NUM
cana-5422	671	21	→	→	SYM
cana-5422	671	22	[	[	X
cana-5422	671	23	0	0	NUM
cana-5422	671	24	,	,	PUNCT
cana-5422	671	25	∞	∞	PROPN
cana-5422	671	26	)	)	PUNCT
cana-5422	671	27	with	with	ADP
cana-5422	671	28	the	the	DET
cana-5422	671	29	conditions	condition	NOUN
cana-5422	671	30	(	(	PUNCT
cana-5422	671	31	3.8	3.8	NUM
cana-5422	671	32	)	)	PUNCT
cana-5422	671	33	,	,	PUNCT
cana-5422	671	34	(	(	PUNCT
cana-5422	671	35	3.9	3.9	NUM
cana-5422	671	36	)	)	PUNCT
cana-5422	671	37	,	,	PUNCT
cana-5422	671	38	and	and	CCONJ
cana-5422	671	39	(	(	PUNCT
cana-5422	671	40	3.39	3.39	NUM
cana-5422	671	41	)	)	PUNCT
cana-5422	671	42	for	for	ADP
cana-5422	671	43	all	all	DET
cana-5422	671	44	w1	w1	NOUN
cana-5422	671	45	,	,	PUNCT
cana-5422	671	46	w2	w2	NOUN
cana-5422	671	47	,	,	PUNCT
cana-5422	671	48	w3	w3	PROPN
cana-5422	671	49	∈	∈	PROPN
cana-5422	671	50	w1	w1	NOUN
cana-5422	671	51	and	and	CCONJ
cana-5422	671	52	all	all	DET
cana-5422	671	53	λ	λ	X
cana-5422	671	54	>	>	X
cana-5422	671	55	0	0	PUNCT
cana-5422	671	56	with	with	ADP
cana-5422	671	57	m	m	NOUN
cana-5422	671	58	=	=	SYM
cana-5422	671	59	±1	±1	ADJ
cana-5422	671	60	and	and	CCONJ
cana-5422	671	61	0	0	NUM
cana-5422	671	62	<	<	X
cana-5422	671	63	(	(	PUNCT
cana-5422	671	64	i	i	NOUN
cana-5422	671	65	5	5	NUM
cana-5422	671	66	)	)	PUNCT
cana-5422	671	67	µ	µ	X
cana-5422	671	68	<	<	X
cana-5422	671	69	1	1	NUM
cana-5422	671	70	,	,	PUNCT
cana-5422	671	71	0	0	NUM
cana-5422	671	72	<	<	X
cana-5422	671	73	(	(	PUNCT
cana-5422	671	74	i	i	NOUN
cana-5422	671	75	25	25	NUM
cana-5422	671	76	)	)	PUNCT
cana-5422	671	77	µ	µ	X
cana-5422	671	78	<	<	X
cana-5422	671	79	1	1	NUM
cana-5422	671	80	.	.	PUNCT
cana-5422	672	1	then	then	ADV
cana-5422	672	2	there	there	PRON
cana-5422	672	3	exists	exist	VERB
cana-5422	672	4	a	a	DET
cana-5422	672	5	unique	unique	ADJ
cana-5422	672	6	additive	additive	ADJ
cana-5422	672	7	mappinga(w1	mappinga(w1	NOUN
cana-5422	672	8	)	)	PUNCT
cana-5422	672	9	:	:	PUNCT
cana-5422	672	10	w1	w1	NOUN
cana-5422	672	11	→w2	→w2	NOUN
cana-5422	672	12	and	and	CCONJ
cana-5422	672	13	a	a	DET
cana-5422	672	14	unique	unique	ADJ
cana-5422	672	15	quadratic	quadratic	ADJ
cana-5422	672	16	mapping	mapping	NOUN
cana-5422	672	17	q(w1	q(w1	NOUN
cana-5422	672	18	)	)	PUNCT
cana-5422	672	19	:	:	PUNCT
cana-5422	672	20	w1	w1	PROPN
cana-5422	672	21	→w2	→w2	NOUN
cana-5422	672	22	which	which	PRON
cana-5422	672	23	satisfies	satisfy	VERB
cana-5422	672	24	(	(	PUNCT
cana-5422	672	25	1.7	1.7	NUM
cana-5422	672	26	)	)	PUNCT
cana-5422	672	27	and	and	CCONJ
cana-5422	672	28	the	the	DET
cana-5422	672	29	functional	functional	ADJ
cana-5422	672	30	inequality	inequality	NOUN
cana-5422	672	31	µ	µ	X
cana-5422	672	32	(	(	PUNCT
cana-5422	672	33	f	f	PROPN
cana-5422	672	34	(	(	PUNCT
cana-5422	672	35	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	672	36	)	)	PUNCT
cana-5422	672	37	,	,	PUNCT
cana-5422	672	38	4λ	4λ	PROPN
cana-5422	672	39	)	)	PUNCT
cana-5422	672	40	≥	≥	NOUN
cana-5422	672	41	µ′	µ′	PUNCT
cana-5422	672	42	(	(	PUNCT
cana-5422	672	43	ψa	ψa	X
cana-5422	672	44	(	(	PUNCT
cana-5422	672	45	w1	w1	NOUN
cana-5422	672	46	)	)	PUNCT
cana-5422	672	47	,	,	PUNCT
cana-5422	672	48	3λ	3λ	NUM
cana-5422	672	49	4	4	NUM
cana-5422	672	50	|5−	|5−	PROPN
cana-5422	672	51	i|	i|	PROPN
cana-5422	672	52	)	)	PUNCT
cana-5422	672	53	∗	∗	NOUN
cana-5422	672	54	µ′	µ′	PUNCT
cana-5422	672	55	(	(	PUNCT
cana-5422	672	56	ψa	ψa	X
cana-5422	672	57	(	(	PUNCT
cana-5422	672	58	−w1	−w1	PROPN
cana-5422	672	59	)	)	PUNCT
cana-5422	672	60	,	,	PUNCT
cana-5422	672	61	3λ	3λ	NUM
cana-5422	672	62	4	4	NUM
cana-5422	672	63	|5−	|5−	PROPN
cana-5422	672	64	i|	i|	PROPN
cana-5422	672	65	)	)	PUNCT
cana-5422	672	66	∗	∗	NOUN
cana-5422	672	67	µ′	µ′	PUNCT
cana-5422	672	68	(	(	PUNCT
cana-5422	672	69	ψq	ψq	PROPN
cana-5422	672	70	(	(	PUNCT
cana-5422	672	71	w1	w1	NOUN
cana-5422	672	72	)	)	PUNCT
cana-5422	672	73	,	,	PUNCT
cana-5422	672	74	7λ	7λ	NUM
cana-5422	672	75	3	3	NUM
cana-5422	672	76	|25−	|25−	PROPN
cana-5422	672	77	i|	i|	PROPN
cana-5422	672	78	)	)	PUNCT
cana-5422	672	79	∗	∗	NOUN
cana-5422	672	80	µ′	µ′	PUNCT
cana-5422	672	81	(	(	PUNCT
cana-5422	672	82	ψq	ψq	PROPN
cana-5422	672	83	(	(	PUNCT
cana-5422	672	84	−w1	−w1	PROPN
cana-5422	672	85	)	)	PUNCT
cana-5422	672	86	,	,	PUNCT
cana-5422	672	87	7λ	7λ	NUM
cana-5422	672	88	3	3	NUM
cana-5422	672	89	|25−	|25−	PROPN
cana-5422	672	90	i|	i|	PROPN
cana-5422	672	91	)	)	PUNCT
cana-5422	672	92	=	=	PUNCT
cana-5422	673	1	µ′	µ′	NOUN
cana-5422	673	2	(	(	PUNCT
cana-5422	673	3	ψ	ψ	X
cana-5422	673	4	(	(	PUNCT
cana-5422	673	5	w1	w1	NOUN
cana-5422	673	6	,	,	PUNCT
cana-5422	673	7	w1	w1	NOUN
cana-5422	673	8	,	,	PUNCT
cana-5422	673	9	w1	w1	NOUN
cana-5422	673	10	)	)	PUNCT
cana-5422	673	11	,	,	PUNCT
cana-5422	673	12	3λ	3λ	NUM
cana-5422	673	13	4	4	NUM
cana-5422	673	14	|5−	|5−	PROPN
cana-5422	673	15	i|	i|	PROPN
cana-5422	673	16	)	)	PUNCT
cana-5422	673	17	∗	∗	NOUN
cana-5422	673	18	µ′	µ′	PUNCT
cana-5422	673	19	(	(	PUNCT
cana-5422	673	20	ψ	ψ	X
cana-5422	673	21	(	(	PUNCT
cana-5422	673	22	w1	w1	NOUN
cana-5422	673	23	,	,	PUNCT
cana-5422	673	24	w1,−w1	w1,−w1	NUM
cana-5422	673	25	)	)	PUNCT
cana-5422	673	26	,	,	PUNCT
cana-5422	673	27	3λ	3λ	NUM
cana-5422	673	28	4	4	NUM
cana-5422	673	29	|5−	|5−	PROPN
cana-5422	673	30	i|	i|	PROPN
cana-5422	673	31	)	)	PUNCT
cana-5422	673	32	∗	∗	NOUN
cana-5422	673	33	µ′	µ′	PUNCT
cana-5422	673	34	(	(	PUNCT
cana-5422	673	35	ψ	ψ	X
cana-5422	673	36	(	(	PUNCT
cana-5422	673	37	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	673	38	)	)	PUNCT
cana-5422	673	39	,	,	PUNCT
cana-5422	673	40	3λ	3λ	NUM
cana-5422	673	41	4	4	NUM
cana-5422	673	42	|5−	|5−	PROPN
cana-5422	673	43	i|	i|	PROPN
cana-5422	673	44	)	)	PUNCT
cana-5422	673	45	∗	∗	NOUN
cana-5422	673	46	µ′	µ′	PUNCT
cana-5422	673	47	(	(	PUNCT
cana-5422	673	48	ψ	ψ	X
cana-5422	673	49	(	(	PUNCT
cana-5422	673	50	−w1,−w1	−w1,−w1	ADJ
cana-5422	673	51	,	,	PUNCT
cana-5422	673	52	w1	w1	NOUN
cana-5422	673	53	)	)	PUNCT
cana-5422	673	54	,	,	PUNCT
cana-5422	673	55	3λ	3λ	NUM
cana-5422	673	56	4	4	NUM
cana-5422	673	57	|5−	|5−	PROPN
cana-5422	673	58	i|	i|	PROPN
cana-5422	673	59	)	)	PUNCT
cana-5422	673	60	∗	∗	NOUN
cana-5422	673	61	µ′	µ′	PUNCT
cana-5422	673	62	(	(	PUNCT
cana-5422	673	63	ψ	ψ	X
cana-5422	673	64	(	(	PUNCT
cana-5422	673	65	w1	w1	NOUN
cana-5422	673	66	,	,	PUNCT
cana-5422	673	67	w1	w1	NOUN
cana-5422	673	68	,	,	PUNCT
cana-5422	673	69	w1	w1	NOUN
cana-5422	673	70	)	)	PUNCT
cana-5422	673	71	,	,	PUNCT
cana-5422	673	72	7λ	7λ	NUM
cana-5422	673	73	3	3	NUM
cana-5422	673	74	|5−	|5−	PROPN
cana-5422	673	75	i|	i|	PROPN
cana-5422	673	76	)	)	PUNCT
cana-5422	673	77	∗	∗	NOUN
cana-5422	673	78	µ′	µ′	PUNCT
cana-5422	673	79	(	(	PUNCT
cana-5422	673	80	ψ	ψ	X
cana-5422	673	81	(	(	PUNCT
cana-5422	673	82	w1	w1	NOUN
cana-5422	673	83	,	,	PUNCT
cana-5422	673	84	w1,−w1	w1,−w1	NUM
cana-5422	673	85	)	)	PUNCT
cana-5422	673	86	,	,	PUNCT
cana-5422	673	87	7λ	7λ	NUM
cana-5422	673	88	3	3	NUM
cana-5422	673	89	|5−	|5−	PROPN
cana-5422	673	90	i|	i|	PROPN
cana-5422	673	91	)	)	PUNCT
cana-5422	673	92	∗	∗	NOUN
cana-5422	673	93	µ′	µ′	PUNCT
cana-5422	673	94	(	(	PUNCT
cana-5422	673	95	ψ	ψ	X
cana-5422	673	96	(	(	PUNCT
cana-5422	673	97	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	673	98	)	)	PUNCT
cana-5422	673	99	,	,	PUNCT
cana-5422	673	100	7λ	7λ	NUM
cana-5422	673	101	3	3	NUM
cana-5422	673	102	|5−	|5−	PROPN
cana-5422	673	103	i|	i|	PROPN
cana-5422	673	104	)	)	PUNCT
cana-5422	673	105	∗	∗	NOUN
cana-5422	673	106	µ′	µ′	PUNCT
cana-5422	673	107	(	(	PUNCT
cana-5422	673	108	ψ	ψ	X
cana-5422	673	109	(	(	PUNCT
cana-5422	673	110	−w1,−w1	−w1,−w1	ADJ
cana-5422	673	111	,	,	PUNCT
cana-5422	673	112	w1	w1	NOUN
cana-5422	673	113	)	)	PUNCT
cana-5422	673	114	,	,	PUNCT
cana-5422	673	115	7λ	7λ	NUM
cana-5422	673	116	3	3	NUM
cana-5422	673	117	|5−	|5−	PROPN
cana-5422	673	118	i|	i|	PROPN
cana-5422	673	119	)	)	PUNCT
cana-5422	673	120	ν	ν	PROPN
cana-5422	673	121	(	(	PUNCT
cana-5422	673	122	f	f	PROPN
cana-5422	673	123	(	(	PUNCT
cana-5422	673	124	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	673	125	)	)	PUNCT
cana-5422	673	126	,	,	PUNCT
cana-5422	673	127	4λ	4λ	NOUN
cana-5422	673	128	)	)	PUNCT
cana-5422	673	129	≤	≤	NUM
cana-5422	673	130	ν′	ν′	NOUN
cana-5422	673	131	(	(	PUNCT
cana-5422	673	132	ψa	ψa	X
cana-5422	673	133	(	(	PUNCT
cana-5422	673	134	w1	w1	NOUN
cana-5422	673	135	)	)	PUNCT
cana-5422	673	136	,	,	PUNCT
cana-5422	674	1	3λ	3λ	NUM
cana-5422	674	2	4	4	NUM
cana-5422	674	3	|5−	|5−	PROPN
cana-5422	674	4	i|	i|	PROPN
cana-5422	674	5	)	)	PUNCT
cana-5422	674	6	�	�	PROPN
cana-5422	674	7	ν′	ν′	NOUN
cana-5422	674	8	(	(	PUNCT
cana-5422	674	9	ψa	ψa	X
cana-5422	674	10	(	(	PUNCT
cana-5422	674	11	−w1	−w1	PROPN
cana-5422	674	12	)	)	PUNCT
cana-5422	674	13	,	,	PUNCT
cana-5422	674	14	3λ	3λ	NUM
cana-5422	674	15	4	4	NUM
cana-5422	674	16	|5−	|5−	PROPN
cana-5422	674	17	i|	i|	PROPN
cana-5422	674	18	)	)	PUNCT
cana-5422	674	19	�	�	PROPN
cana-5422	674	20	ν′	ν′	NOUN
cana-5422	674	21	(	(	PUNCT
cana-5422	674	22	ψq	ψq	PROPN
cana-5422	674	23	(	(	PUNCT
cana-5422	674	24	w1	w1	NOUN
cana-5422	674	25	)	)	PUNCT
cana-5422	674	26	,	,	PUNCT
cana-5422	674	27	7λ	7λ	NUM
cana-5422	674	28	3	3	NUM
cana-5422	674	29	|25−	|25−	PROPN
cana-5422	674	30	i|	i|	PROPN
cana-5422	674	31	)	)	PUNCT
cana-5422	674	32	�	�	PROPN
cana-5422	674	33	ν′	ν′	NOUN
cana-5422	674	34	(	(	PUNCT
cana-5422	674	35	ψq	ψq	PROPN
cana-5422	674	36	(	(	PUNCT
cana-5422	674	37	−w1	−w1	PROPN
cana-5422	674	38	)	)	PUNCT
cana-5422	674	39	,	,	PUNCT
cana-5422	674	40	7λ	7λ	NUM
cana-5422	674	41	3	3	NUM
cana-5422	674	42	|25−	|25−	PROPN
cana-5422	674	43	i|	i|	PROPN
cana-5422	674	44	)	)	PUNCT
cana-5422	675	1	=	=	SYM
cana-5422	675	2	ν′	ν′	NOUN
cana-5422	675	3	(	(	PUNCT
cana-5422	675	4	ψ	ψ	X
cana-5422	675	5	(	(	PUNCT
cana-5422	675	6	w1	w1	NOUN
cana-5422	675	7	,	,	PUNCT
cana-5422	675	8	w1	w1	NOUN
cana-5422	675	9	,	,	PUNCT
cana-5422	675	10	w1	w1	NOUN
cana-5422	675	11	)	)	PUNCT
cana-5422	675	12	,	,	PUNCT
cana-5422	675	13	3λ	3λ	NUM
cana-5422	675	14	4	4	NUM
cana-5422	675	15	|5−	|5−	PROPN
cana-5422	675	16	i|	i|	PROPN
cana-5422	675	17	)	)	PUNCT
cana-5422	675	18	�	�	PROPN
cana-5422	675	19	ν′	ν′	NOUN
cana-5422	675	20	(	(	PUNCT
cana-5422	675	21	ψ	ψ	X
cana-5422	675	22	(	(	PUNCT
cana-5422	675	23	w1	w1	NOUN
cana-5422	675	24	,	,	PUNCT
cana-5422	675	25	w1,−w1	w1,−w1	NUM
cana-5422	675	26	)	)	PUNCT
cana-5422	675	27	,	,	PUNCT
cana-5422	675	28	3λ	3λ	NUM
cana-5422	675	29	4	4	NUM
cana-5422	675	30	|5−	|5−	PROPN
cana-5422	675	31	i|	i|	PROPN
cana-5422	675	32	)	)	PUNCT
cana-5422	675	33	�	�	PROPN
cana-5422	675	34	ν′	ν′	NOUN
cana-5422	675	35	(	(	PUNCT
cana-5422	675	36	ψ	ψ	X
cana-5422	675	37	(	(	PUNCT
cana-5422	675	38	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	675	39	)	)	PUNCT
cana-5422	675	40	,	,	PUNCT
cana-5422	675	41	3λ	3λ	NUM
cana-5422	675	42	4	4	NUM
cana-5422	675	43	|5−	|5−	PROPN
cana-5422	675	44	i|	i|	PROPN
cana-5422	675	45	)	)	PUNCT
cana-5422	675	46	�	�	PROPN
cana-5422	675	47	ν′	ν′	NOUN
cana-5422	675	48	(	(	PUNCT
cana-5422	675	49	ψ	ψ	X
cana-5422	675	50	(	(	PUNCT
cana-5422	675	51	−w1,−w1	−w1,−w1	ADJ
cana-5422	675	52	,	,	PUNCT
cana-5422	675	53	w1	w1	NOUN
cana-5422	675	54	)	)	PUNCT
cana-5422	675	55	,	,	PUNCT
cana-5422	675	56	3λ	3λ	NUM
cana-5422	675	57	4	4	NUM
cana-5422	675	58	|5−	|5−	PROPN
cana-5422	675	59	i|	i|	PROPN
cana-5422	675	60	)	)	PUNCT
cana-5422	675	61	�	�	PROPN
cana-5422	675	62	ν′	ν′	NOUN
cana-5422	675	63	(	(	PUNCT
cana-5422	675	64	ψ	ψ	X
cana-5422	675	65	(	(	PUNCT
cana-5422	675	66	w1	w1	NOUN
cana-5422	675	67	,	,	PUNCT
cana-5422	675	68	w1	w1	NOUN
cana-5422	675	69	,	,	PUNCT
cana-5422	675	70	w1	w1	NOUN
cana-5422	675	71	)	)	PUNCT
cana-5422	675	72	,	,	PUNCT
cana-5422	675	73	7λ	7λ	NUM
cana-5422	675	74	3	3	NUM
cana-5422	675	75	|5−	|5−	PROPN
cana-5422	675	76	i|	i|	PROPN
cana-5422	675	77	)	)	PUNCT
cana-5422	675	78	�	�	PROPN
cana-5422	675	79	ν′	ν′	NOUN
cana-5422	675	80	(	(	PUNCT
cana-5422	675	81	ψ	ψ	X
cana-5422	675	82	(	(	PUNCT
cana-5422	675	83	w1	w1	NOUN
cana-5422	675	84	,	,	PUNCT
cana-5422	675	85	w1,−w1	w1,−w1	NUM
cana-5422	675	86	)	)	PUNCT
cana-5422	675	87	,	,	PUNCT
cana-5422	675	88	7λ	7λ	NUM
cana-5422	675	89	3	3	NUM
cana-5422	675	90	|5−	|5−	PROPN
cana-5422	675	91	i|	i|	PROPN
cana-5422	675	92	)	)	PUNCT
cana-5422	675	93	�	�	PROPN
cana-5422	675	94	ν′	ν′	NOUN
cana-5422	675	95	(	(	PUNCT
cana-5422	675	96	ψ	ψ	X
cana-5422	675	97	(	(	PUNCT
cana-5422	675	98	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	675	99	)	)	PUNCT
cana-5422	675	100	,	,	PUNCT
cana-5422	675	101	7λ	7λ	NUM
cana-5422	675	102	3	3	NUM
cana-5422	675	103	|5−	|5−	PROPN
cana-5422	675	104	i|	i|	PROPN
cana-5422	675	105	)	)	PUNCT
cana-5422	675	106	�	�	PROPN
cana-5422	675	107	ν′	ν′	NOUN
cana-5422	675	108	(	(	PUNCT
cana-5422	675	109	ψ	ψ	X
cana-5422	675	110	(	(	PUNCT
cana-5422	675	111	−w1,−w1	−w1,−w1	ADJ
cana-5422	675	112	,	,	PUNCT
cana-5422	675	113	w1	w1	NOUN
cana-5422	675	114	)	)	PUNCT
cana-5422	675	115	,	,	PUNCT
cana-5422	675	116	7λ	7λ	NUM
cana-5422	675	117	3	3	NUM
cana-5422	675	118	|5−	|5−	PROPN
cana-5422	675	119	i|	i|	PROPN
cana-5422	675	120	)	)	PUNCT
cana-5422	675	121			NOUN
cana-5422	675	122	(	(	PUNCT
cana-5422	675	123	3.53	3.53	NUM
cana-5422	675	124	)	)	PUNCT
cana-5422	675	125	and	and	CCONJ
cana-5422	675	126	the	the	DET
cana-5422	675	127	mapping	mapping	NOUN
cana-5422	675	128	a(w1	a(w1	NOUN
cana-5422	675	129	)	)	PUNCT
cana-5422	675	130	and	and	CCONJ
cana-5422	675	131	q(w1	q(w1	NOUN
cana-5422	675	132	)	)	PUNCT
cana-5422	675	133	are	be	AUX
cana-5422	675	134	given	give	VERB
cana-5422	675	135	in	in	ADP
cana-5422	675	136	(	(	PUNCT
cana-5422	675	137	3.11	3.11	NUM
cana-5422	675	138	)	)	PUNCT
cana-5422	675	139	and	and	CCONJ
cana-5422	675	140	(	(	PUNCT
cana-5422	675	141	3.41	3.41	NUM
cana-5422	675	142	)	)	PUNCT
cana-5422	675	143	for	for	ADP
cana-5422	675	144	all	all	DET
cana-5422	675	145	w1	w1	NOUN
cana-5422	675	146	∈	∈	PROPN
cana-5422	675	147	w1	w1	NOUN
cana-5422	675	148	.	.	PUNCT
cana-5422	676	1	proof	proof	NOUN
cana-5422	676	2	.	.	PUNCT
cana-5422	677	1	by	by	ADP
cana-5422	677	2	theorem	theorem	NOUN
cana-5422	677	3	3.8	3.8	NUM
cana-5422	677	4	,	,	PUNCT
cana-5422	677	5	it	it	PRON
cana-5422	677	6	follows	follow	VERB
cana-5422	677	7	from	from	ADP
cana-5422	677	8	(	(	PUNCT
cana-5422	677	9	2.33	2.33	NUM
cana-5422	677	10	)	)	PUNCT
cana-5422	677	11	,	,	PUNCT
cana-5422	677	12	(	(	PUNCT
cana-5422	677	13	3.1	3.1	NUM
cana-5422	677	14	)	)	PUNCT
cana-5422	677	15	and	and	CCONJ
cana-5422	677	16	(	(	PUNCT
cana-5422	677	17	3.10	3.10	NUM
cana-5422	677	18	)	)	PUNCT
cana-5422	677	19	,	,	PUNCT
cana-5422	677	20	we	we	PRON
cana-5422	677	21	arrive	arrive	VERB
cana-5422	677	22	µ	µ	PROPN
cana-5422	677	23	(	(	PUNCT
cana-5422	677	24	a(w1)−fodd(w1	a(w1)−fodd(w1	PROPN
cana-5422	677	25	)	)	PUNCT
cana-5422	677	26	,	,	PUNCT
cana-5422	677	27	2λ	2λ	NUM
cana-5422	677	28	)	)	PUNCT
cana-5422	677	29	≥	≥	NOUN
cana-5422	677	30	µ′	µ′	PUNCT
cana-5422	677	31	(	(	PUNCT
cana-5422	677	32	ψa	ψa	X
cana-5422	677	33	(	(	PUNCT
cana-5422	677	34	w1	w1	NOUN
cana-5422	677	35	)	)	PUNCT
cana-5422	677	36	,	,	PUNCT
cana-5422	677	37	3λ	3λ	NUM
cana-5422	677	38	4	4	NUM
cana-5422	677	39	|5−	|5−	PROPN
cana-5422	677	40	i|	i|	PROPN
cana-5422	677	41	)	)	PUNCT
cana-5422	677	42	∗	∗	NOUN
cana-5422	677	43	µ′	µ′	PUNCT
cana-5422	677	44	(	(	PUNCT
cana-5422	677	45	ψa	ψa	X
cana-5422	677	46	(	(	PUNCT
cana-5422	677	47	−w1	−w1	PROPN
cana-5422	677	48	)	)	PUNCT
cana-5422	677	49	,	,	PUNCT
cana-5422	677	50	3λ	3λ	NUM
cana-5422	677	51	4	4	NUM
cana-5422	677	52	|5−	|5−	PROPN
cana-5422	677	53	i|	i|	PROPN
cana-5422	677	54	)	)	PUNCT
cana-5422	678	1	ν	ν	PROPN
cana-5422	678	2	(	(	PUNCT
cana-5422	678	3	a(w1)−fodd(w1	a(w1)−fodd(w1	PROPN
cana-5422	678	4	)	)	PUNCT
cana-5422	678	5	,	,	PUNCT
cana-5422	678	6	2λ	2λ	NOUN
cana-5422	678	7	)	)	PUNCT
cana-5422	678	8	≤	≤	NUM
cana-5422	678	9	ν′	ν′	NOUN
cana-5422	678	10	(	(	PUNCT
cana-5422	678	11	ψa	ψa	X
cana-5422	678	12	(	(	PUNCT
cana-5422	678	13	w1	w1	NOUN
cana-5422	678	14	)	)	PUNCT
cana-5422	678	15	,	,	PUNCT
cana-5422	678	16	3λ	3λ	NUM
cana-5422	678	17	4	4	NUM
cana-5422	678	18	|5−	|5−	PROPN
cana-5422	678	19	i|	i|	PROPN
cana-5422	678	20	)	)	PUNCT
cana-5422	678	21	�	�	PROPN
cana-5422	678	22	ν′	ν′	NOUN
cana-5422	678	23	(	(	PUNCT
cana-5422	678	24	ψa	ψa	X
cana-5422	678	25	(	(	PUNCT
cana-5422	678	26	−w1	−w1	PROPN
cana-5422	678	27	)	)	PUNCT
cana-5422	678	28	,	,	PUNCT
cana-5422	678	29	3λ	3λ	NUM
cana-5422	678	30	4	4	NUM
cana-5422	678	31	|5−	|5−	PROPN
cana-5422	678	32	i|	i|	PROPN
cana-5422	678	33	)	)	PUNCT
cana-5422	678	34			PROPN
cana-5422	678	35	(	(	PUNCT
cana-5422	678	36	3.54	3.54	NUM
cana-5422	678	37	)	)	PUNCT
cana-5422	678	38	for	for	ADP
cana-5422	678	39	all	all	DET
cana-5422	678	40	w1	w1	NOUN
cana-5422	678	41	∈	∈	PROPN
cana-5422	678	42	w1	w1	NOUN
cana-5422	678	43	and	and	CCONJ
cana-5422	678	44	all	all	DET
cana-5422	678	45	λ	λ	PROPN
cana-5422	678	46	>	>	X
cana-5422	678	47	0	0	NUM
cana-5422	678	48	.	.	PUNCT
cana-5422	679	1	by	by	ADP
cana-5422	679	2	theorem	theorem	NOUN
cana-5422	679	3	3.15	3.15	NUM
cana-5422	679	4	,	,	PUNCT
cana-5422	679	5	it	it	PRON
cana-5422	679	6	follows	follow	VERB
cana-5422	679	7	from	from	ADP
cana-5422	679	8	(	(	PUNCT
cana-5422	679	9	2.37	2.37	NUM
cana-5422	679	10	)	)	PUNCT
cana-5422	679	11	,	,	PUNCT
cana-5422	679	12	(	(	PUNCT
cana-5422	679	13	3.1	3.1	NUM
cana-5422	679	14	)	)	PUNCT
cana-5422	679	15	,	,	PUNCT
cana-5422	679	16	and	and	CCONJ
cana-5422	679	17	(	(	PUNCT
cana-5422	679	18	3.40	3.40	NUM
cana-5422	679	19	)	)	PUNCT
cana-5422	679	20	,	,	PUNCT
cana-5422	679	21	we	we	PRON
cana-5422	679	22	see	see	VERB
cana-5422	679	23	µ	µ	X
cana-5422	679	24	(	(	PUNCT
cana-5422	679	25	q(w1)−feven(w1	q(w1)−feven(w1	PROPN
cana-5422	679	26	)	)	PUNCT
cana-5422	679	27	,	,	PUNCT
cana-5422	679	28	2λ	2λ	NUM
cana-5422	679	29	)	)	PUNCT
cana-5422	679	30	≥	≥	NOUN
cana-5422	679	31	µ′	µ′	PUNCT
cana-5422	679	32	(	(	PUNCT
cana-5422	679	33	ψq	ψq	PROPN
cana-5422	679	34	(	(	PUNCT
cana-5422	679	35	w1	w1	NOUN
cana-5422	679	36	)	)	PUNCT
cana-5422	679	37	,	,	PUNCT
cana-5422	679	38	7λ	7λ	NUM
cana-5422	679	39	3	3	NUM
cana-5422	679	40	|25−	|25−	PROPN
cana-5422	679	41	i|	i|	PROPN
cana-5422	679	42	)	)	PUNCT
cana-5422	679	43	∗	∗	NOUN
cana-5422	679	44	µ′	µ′	PUNCT
cana-5422	679	45	(	(	PUNCT
cana-5422	679	46	ψq	ψq	PROPN
cana-5422	679	47	(	(	PUNCT
cana-5422	679	48	−w1	−w1	PROPN
cana-5422	679	49	)	)	PUNCT
cana-5422	679	50	,	,	PUNCT
cana-5422	679	51	7λ	7λ	NUM
cana-5422	679	52	3	3	NUM
cana-5422	679	53	|25−	|25−	PROPN
cana-5422	679	54	i|	i|	PROPN
cana-5422	679	55	)	)	PUNCT
cana-5422	679	56	ν	ν	NOUN
cana-5422	679	57	(	(	PUNCT
cana-5422	679	58	q(w1)−feven(w1	q(w1)−feven(w1	PROPN
cana-5422	679	59	)	)	PUNCT
cana-5422	679	60	,	,	PUNCT
cana-5422	679	61	2λ	2λ	NOUN
cana-5422	679	62	)	)	PUNCT
cana-5422	679	63	≤	≤	NUM
cana-5422	679	64	ν′	ν′	NOUN
cana-5422	679	65	(	(	PUNCT
cana-5422	679	66	ψq	ψq	PROPN
cana-5422	679	67	(	(	PUNCT
cana-5422	679	68	w1	w1	NOUN
cana-5422	679	69	)	)	PUNCT
cana-5422	679	70	,	,	PUNCT
cana-5422	679	71	7λ	7λ	NUM
cana-5422	679	72	3	3	NUM
cana-5422	679	73	|25−	|25−	PROPN
cana-5422	679	74	i|	i|	PROPN
cana-5422	679	75	)	)	PUNCT
cana-5422	679	76	�	�	PROPN
cana-5422	679	77	ν′	ν′	NOUN
cana-5422	679	78	(	(	PUNCT
cana-5422	679	79	ψq	ψq	PROPN
cana-5422	679	80	(	(	PUNCT
cana-5422	679	81	−w1	−w1	PROPN
cana-5422	679	82	)	)	PUNCT
cana-5422	679	83	,	,	PUNCT
cana-5422	679	84	7λ	7λ	NUM
cana-5422	679	85	3	3	NUM
cana-5422	679	86	|25−	|25−	PROPN
cana-5422	679	87	i|	i|	PROPN
cana-5422	679	88	)	)	PUNCT
cana-5422	679	89			PROPN
cana-5422	679	90	(	(	PUNCT
cana-5422	679	91	3.55	3.55	NUM
cana-5422	679	92	)	)	PUNCT
cana-5422	679	93	for	for	ADP
cana-5422	679	94	all	all	DET
cana-5422	679	95	w1	w1	NOUN
cana-5422	679	96	∈	∈	PROPN
cana-5422	679	97	w1	w1	NOUN
cana-5422	679	98	and	and	CCONJ
cana-5422	679	99	all	all	DET
cana-5422	679	100	λ	λ	X
cana-5422	679	101	>	>	X
cana-5422	679	102	0	0	X
cana-5422	679	103	.	.	PUNCT
cana-5422	680	1	now	now	ADV
cana-5422	680	2	,	,	PUNCT
cana-5422	680	3	it	it	PRON
cana-5422	680	4	follows	follow	VERB
cana-5422	680	5	from	from	ADP
cana-5422	680	6	(	(	PUNCT
cana-5422	680	7	3.54	3.54	NUM
cana-5422	680	8	)	)	PUNCT
cana-5422	680	9	,	,	PUNCT
cana-5422	680	10	(	(	PUNCT
cana-5422	680	11	3.55	3.55	NUM
cana-5422	680	12	)	)	PUNCT
cana-5422	680	13	and	and	CCONJ
cana-5422	680	14	(	(	PUNCT
cana-5422	680	15	2.40	2.40	NUM
cana-5422	680	16	)	)	PUNCT
cana-5422	680	17	,	,	PUNCT
cana-5422	680	18	we	we	PRON
cana-5422	680	19	have	have	VERB
cana-5422	680	20	µ	µ	X
cana-5422	680	21	(	(	PUNCT
cana-5422	680	22	f	f	X
cana-5422	680	23	(	(	PUNCT
cana-5422	680	24	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	680	25	)	)	PUNCT
cana-5422	680	26	,	,	PUNCT
cana-5422	680	27	4λ	4λ	PROPN
cana-5422	680	28	)	)	PUNCT
cana-5422	680	29	≥	≥	PROPN
cana-5422	680	30	µ	µ	X
cana-5422	680	31	(	(	PUNCT
cana-5422	680	32	a(w1)−fodd(w1	a(w1)−fodd(w1	PROPN
cana-5422	680	33	)	)	PUNCT
cana-5422	680	34	,	,	PUNCT
cana-5422	680	35	2λ	2λ	NUM
cana-5422	680	36	)	)	PUNCT
cana-5422	680	37	∗	∗	PROPN
cana-5422	680	38	µ	µ	X
cana-5422	680	39	(	(	PUNCT
cana-5422	680	40	q(w1)−feven(w1	q(w1)−feven(w1	PROPN
cana-5422	680	41	)	)	PUNCT
cana-5422	680	42	,	,	PUNCT
cana-5422	680	43	2λ	2λ	NUM
cana-5422	680	44	)	)	PUNCT
cana-5422	680	45	≥	≥	NOUN
cana-5422	680	46	µ′	µ′	PUNCT
cana-5422	680	47	(	(	PUNCT
cana-5422	680	48	ψa	ψa	X
cana-5422	680	49	(	(	PUNCT
cana-5422	680	50	w1	w1	NOUN
cana-5422	680	51	)	)	PUNCT
cana-5422	680	52	,	,	PUNCT
cana-5422	681	1	3λ	3λ	NUM
cana-5422	681	2	4	4	NUM
cana-5422	681	3	|5−	|5−	PROPN
cana-5422	681	4	i|	i|	PROPN
cana-5422	681	5	)	)	PUNCT
cana-5422	681	6	∗	∗	NOUN
cana-5422	681	7	µ′	µ′	PUNCT
cana-5422	681	8	(	(	PUNCT
cana-5422	681	9	ψa	ψa	X
cana-5422	681	10	(	(	PUNCT
cana-5422	681	11	−w1	−w1	PROPN
cana-5422	681	12	)	)	PUNCT
cana-5422	681	13	,	,	PUNCT
cana-5422	681	14	3λ	3λ	NUM
cana-5422	681	15	4	4	NUM
cana-5422	681	16	|5−	|5−	PROPN
cana-5422	681	17	i|	i|	PROPN
cana-5422	681	18	)	)	PUNCT
cana-5422	681	19	∗	∗	NOUN
cana-5422	681	20	µ′	µ′	PUNCT
cana-5422	681	21	(	(	PUNCT
cana-5422	681	22	ψq	ψq	PROPN
cana-5422	681	23	(	(	PUNCT
cana-5422	681	24	w1	w1	NOUN
cana-5422	681	25	)	)	PUNCT
cana-5422	681	26	,	,	PUNCT
cana-5422	681	27	7λ	7λ	NUM
cana-5422	681	28	3	3	NUM
cana-5422	681	29	|25−	|25−	PROPN
cana-5422	681	30	i|	i|	PROPN
cana-5422	681	31	)	)	PUNCT
cana-5422	681	32	∗	∗	NOUN
cana-5422	681	33	µ′	µ′	PUNCT
cana-5422	681	34	(	(	PUNCT
cana-5422	681	35	ψq	ψq	PROPN
cana-5422	681	36	(	(	PUNCT
cana-5422	681	37	−w1	−w1	PROPN
cana-5422	681	38	)	)	PUNCT
cana-5422	681	39	,	,	PUNCT
cana-5422	681	40	7λ	7λ	NUM
cana-5422	681	41	3	3	NUM
cana-5422	681	42	|25−	|25−	PROPN
cana-5422	681	43	i|	i|	PROPN
cana-5422	681	44	)	)	PUNCT
cana-5422	681	45	ν	ν	NOUN
cana-5422	681	46	(	(	PUNCT
cana-5422	681	47	f	f	PROPN
cana-5422	681	48	(	(	PUNCT
cana-5422	681	49	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	681	50	)	)	PUNCT
cana-5422	681	51	,	,	PUNCT
cana-5422	681	52	4λ	4λ	NOUN
cana-5422	681	53	)	)	PUNCT
cana-5422	681	54	≤	≤	NUM
cana-5422	681	55	ν	ν	NOUN
cana-5422	681	56	(	(	PUNCT
cana-5422	681	57	a(w1)−fodd(w1	a(w1)−fodd(w1	PROPN
cana-5422	681	58	)	)	PUNCT
cana-5422	681	59	,	,	PUNCT
cana-5422	681	60	2λ	2λ	NUM
cana-5422	681	61	)	)	PUNCT
cana-5422	681	62	�	�	PROPN
cana-5422	681	63	ν	ν	X
cana-5422	681	64	(	(	PUNCT
cana-5422	681	65	q(w1)−feven(w1	q(w1)−feven(w1	PROPN
cana-5422	681	66	)	)	PUNCT
cana-5422	681	67	,	,	PUNCT
cana-5422	681	68	2λ	2λ	NOUN
cana-5422	681	69	)	)	PUNCT
cana-5422	681	70	≤	≤	NUM
cana-5422	681	71	ν′	ν′	NOUN
cana-5422	681	72	(	(	PUNCT
cana-5422	681	73	ψa	ψa	X
cana-5422	681	74	(	(	PUNCT
cana-5422	681	75	w1	w1	NOUN
cana-5422	681	76	)	)	PUNCT
cana-5422	681	77	,	,	PUNCT
cana-5422	681	78	3λ	3λ	NUM
cana-5422	681	79	4	4	NUM
cana-5422	681	80	|5−	|5−	PROPN
cana-5422	681	81	i|	i|	PROPN
cana-5422	681	82	)	)	PUNCT
cana-5422	681	83	�	�	PROPN
cana-5422	681	84	ν′	ν′	NOUN
cana-5422	681	85	(	(	PUNCT
cana-5422	681	86	ψa	ψa	X
cana-5422	681	87	(	(	PUNCT
cana-5422	681	88	−w1	−w1	PROPN
cana-5422	681	89	)	)	PUNCT
cana-5422	681	90	,	,	PUNCT
cana-5422	681	91	3λ	3λ	NUM
cana-5422	681	92	4	4	NUM
cana-5422	681	93	|5−	|5−	PROPN
cana-5422	681	94	i|	i|	PROPN
cana-5422	681	95	)	)	PUNCT
cana-5422	681	96	�	�	PROPN
cana-5422	681	97	ν′	ν′	NOUN
cana-5422	681	98	(	(	PUNCT
cana-5422	681	99	ψq	ψq	PROPN
cana-5422	681	100	(	(	PUNCT
cana-5422	681	101	w1	w1	NOUN
cana-5422	681	102	)	)	PUNCT
cana-5422	681	103	,	,	PUNCT
cana-5422	681	104	7λ	7λ	NUM
cana-5422	681	105	3	3	NUM
cana-5422	681	106	|25−	|25−	PROPN
cana-5422	681	107	i|	i|	PROPN
cana-5422	681	108	)	)	PUNCT
cana-5422	681	109	�	�	PROPN
cana-5422	681	110	ν′	ν′	NOUN
cana-5422	681	111	(	(	PUNCT
cana-5422	681	112	ψq	ψq	PROPN
cana-5422	681	113	(	(	PUNCT
cana-5422	681	114	−w1	−w1	PROPN
cana-5422	681	115	)	)	PUNCT
cana-5422	681	116	,	,	PUNCT
cana-5422	681	117	7λ	7λ	NUM
cana-5422	681	118	3	3	NUM
cana-5422	681	119	|25−	|25−	PROPN
cana-5422	681	120	i|	i|	PROPN
cana-5422	681	121	)	)	PUNCT
cana-5422	681	122			NOUN
cana-5422	681	123	(	(	PUNCT
cana-5422	681	124	3.56	3.56	NUM
cana-5422	681	125	)	)	PUNCT
cana-5422	681	126	communications	communication	NOUN
cana-5422	681	127	on	on	ADP
cana-5422	681	128	applied	apply	VERB
cana-5422	681	129	nonlinear	nonlinear	ADJ
cana-5422	681	130	analysis	analysis	NOUN
cana-5422	681	131	issn	issn	NOUN
cana-5422	681	132	:	:	PUNCT
cana-5422	681	133	1074	1074	NUM
cana-5422	681	134	-	-	PUNCT
cana-5422	681	135	133x	133x	NUM
cana-5422	681	136	vol	vol	NOUN
cana-5422	681	137	32	32	NUM
cana-5422	681	138	no	no	NOUN
cana-5422	681	139	.	.	PUNCT
cana-5422	682	1	10s(2025	10s(2025	NUM
cana-5422	682	2	)	)	PUNCT
cana-5422	683	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	683	2	2210	2210	NUM
cana-5422	683	3	for	for	ADP
cana-5422	683	4	all	all	DET
cana-5422	683	5	w1	w1	NOUN
cana-5422	683	6	∈	∈	PROPN
cana-5422	683	7	w1	w1	NOUN
cana-5422	683	8	and	and	CCONJ
cana-5422	683	9	all	all	DET
cana-5422	683	10	λ	λ	PROPN
cana-5422	683	11	>	>	X
cana-5422	683	12	0	0	X
cana-5422	683	13	.	.	PUNCT
cana-5422	683	14	�	�	PROPN
cana-5422	683	15	corollary	corollary	PROPN
cana-5422	683	16	3.23	3.23	NUM
cana-5422	683	17	.	.	PUNCT
cana-5422	684	1	suppose	suppose	VERB
cana-5422	684	2	that	that	SCONJ
cana-5422	684	3	a	a	DET
cana-5422	684	4	functionf	functionf	NOUN
cana-5422	684	5	:	:	PUNCT
cana-5422	684	6	w1	w1	PROPN
cana-5422	684	7	→w2	→w2	NOUN
cana-5422	684	8	satisfy	satisfy	VERB
cana-5422	684	9	the	the	DET
cana-5422	684	10	functional	functional	ADJ
cana-5422	684	11	inequality	inequality	NOUN
cana-5422	684	12	(	(	PUNCT
cana-5422	684	13	3.2	3.2	NUM
cana-5422	684	14	)	)	PUNCT
cana-5422	684	15	for	for	ADP
cana-5422	684	16	all	all	DET
cana-5422	684	17	w1	w1	NOUN
cana-5422	684	18	,	,	PUNCT
cana-5422	684	19	w2	w2	NOUN
cana-5422	684	20	,	,	PUNCT
cana-5422	684	21	w3	w3	PROPN
cana-5422	684	22	∈	∈	PROPN
cana-5422	684	23	w1	w1	NOUN
cana-5422	684	24	and	and	CCONJ
cana-5422	684	25	all	all	DET
cana-5422	684	26	λ	λ	X
cana-5422	684	27	>	>	X
cana-5422	684	28	0	0	PUNCT
cana-5422	684	29	with	with	SCONJ
cana-5422	684	30	δ	δ	PROPN
cana-5422	684	31	be	be	AUX
cana-5422	684	32	a	a	DET
cana-5422	684	33	positive	positive	ADJ
cana-5422	684	34	constant	constant	NOUN
cana-5422	684	35	and	and	CCONJ
cana-5422	684	36	ϕ	ϕ	NOUN
cana-5422	684	37	be	be	AUX
cana-5422	684	38	any	any	DET
cana-5422	684	39	real	real	ADJ
cana-5422	684	40	number	number	NOUN
cana-5422	684	41	.	.	PUNCT
cana-5422	685	1	then	then	ADV
cana-5422	685	2	there	there	PRON
cana-5422	685	3	exists	exist	VERB
cana-5422	685	4	a	a	DET
cana-5422	685	5	unique	unique	ADJ
cana-5422	685	6	additive	additive	ADJ
cana-5422	685	7	mapping	mapping	NOUN
cana-5422	685	8	a(w1	a(w1	NOUN
cana-5422	685	9	)	)	PUNCT
cana-5422	685	10	:	:	PUNCT
cana-5422	685	11	w1	w1	NOUN
cana-5422	685	12	→w2	→w2	NOUN
cana-5422	685	13	and	and	CCONJ
cana-5422	685	14	a	a	DET
cana-5422	685	15	unique	unique	ADJ
cana-5422	685	16	quadratic	quadratic	ADJ
cana-5422	685	17	mapping	mapping	NOUN
cana-5422	685	18	q(w1	q(w1	NOUN
cana-5422	685	19	)	)	PUNCT
cana-5422	685	20	:	:	PUNCT
cana-5422	685	21	w1	w1	PROPN
cana-5422	685	22	→w2	→w2	NOUN
cana-5422	685	23	which	which	PRON
cana-5422	685	24	satisfies	satisfy	VERB
cana-5422	685	25	(	(	PUNCT
cana-5422	685	26	1.7	1.7	NUM
cana-5422	685	27	)	)	PUNCT
cana-5422	685	28	and	and	CCONJ
cana-5422	685	29	the	the	DET
cana-5422	685	30	functional	functional	ADJ
cana-5422	685	31	inequality	inequality	NOUN
cana-5422	685	32	µ	µ	X
cana-5422	685	33	(	(	PUNCT
cana-5422	685	34	f	f	PROPN
cana-5422	685	35	(	(	PUNCT
cana-5422	685	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	685	37	)	)	PUNCT
cana-5422	685	38	,	,	PUNCT
cana-5422	685	39	4λ	4λ	PROPN
cana-5422	685	40	)	)	PUNCT
cana-5422	685	41	≥	≥	NOUN
cana-5422	685	42	µ′	µ′	PUNCT
cana-5422	685	43	(	(	PUNCT
cana-5422	685	44	2δ	2δ	NOUN
cana-5422	685	45	,	,	PUNCT
cana-5422	685	46	(	(	PUNCT
cana-5422	685	47	|3|+	|3|+	PROPN
cana-5422	685	48	7	7	NUM
cana-5422	685	49	|8|)λ	|8|)λ	NOUN
cana-5422	685	50	)	)	PUNCT
cana-5422	685	51	ν	ν	NOUN
cana-5422	685	52	(	(	PUNCT
cana-5422	685	53	f	f	PROPN
cana-5422	685	54	(	(	PUNCT
cana-5422	685	55	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	685	56	)	)	PUNCT
cana-5422	685	57	,	,	PUNCT
cana-5422	685	58	4λ	4λ	NOUN
cana-5422	685	59	)	)	PUNCT
cana-5422	685	60	≤	≤	NUM
cana-5422	685	61	ν′	ν′	NOUN
cana-5422	685	62	(	(	PUNCT
cana-5422	685	63	2δ	2δ	NOUN
cana-5422	685	64	,	,	PUNCT
cana-5422	685	65	(	(	PUNCT
cana-5422	685	66	|3|+	|3|+	PROPN
cana-5422	685	67	7	7	NUM
cana-5422	685	68	|8|)λ	|8|)λ	NOUN
cana-5422	685	69	)	)	PUNCT
cana-5422	685	70	}	}	PUNCT
cana-5422	685	71	(	(	PUNCT
cana-5422	685	72	3.57	3.57	NUM
cana-5422	685	73	)	)	PUNCT
cana-5422	685	74	for	for	ADP
cana-5422	685	75	all	all	DET
cana-5422	685	76	w1	w1	NOUN
cana-5422	685	77	∈	∈	PROPN
cana-5422	685	78	w1	w1	NOUN
cana-5422	685	79	.	.	PUNCT
cana-5422	686	1	corollary	corollary	ADJ
cana-5422	686	2	3.24	3.24	NUM
cana-5422	686	3	.	.	PUNCT
cana-5422	686	4	suppose	suppose	VERB
cana-5422	686	5	that	that	SCONJ
cana-5422	686	6	a	a	DET
cana-5422	686	7	functionf	functionf	NOUN
cana-5422	686	8	:	:	PUNCT
cana-5422	686	9	w1	w1	PROPN
cana-5422	686	10	→w2	→w2	NOUN
cana-5422	686	11	satisfy	satisfy	VERB
cana-5422	686	12	the	the	DET
cana-5422	686	13	functional	functional	ADJ
cana-5422	686	14	inequality	inequality	NOUN
cana-5422	686	15	(	(	PUNCT
cana-5422	686	16	3.3	3.3	NUM
cana-5422	686	17	)	)	PUNCT
cana-5422	686	18	for	for	ADP
cana-5422	686	19	all	all	DET
cana-5422	686	20	w1	w1	NOUN
cana-5422	686	21	,	,	PUNCT
cana-5422	686	22	w2	w2	NOUN
cana-5422	686	23	,	,	PUNCT
cana-5422	686	24	w3	w3	PROPN
cana-5422	686	25	∈	∈	PROPN
cana-5422	686	26	w1	w1	NOUN
cana-5422	686	27	and	and	CCONJ
cana-5422	686	28	all	all	DET
cana-5422	686	29	λ	λ	X
cana-5422	686	30	>	>	X
cana-5422	686	31	0	0	PUNCT
cana-5422	686	32	with	with	SCONJ
cana-5422	686	33	δ	δ	PROPN
cana-5422	686	34	be	be	AUX
cana-5422	686	35	a	a	DET
cana-5422	686	36	positive	positive	ADJ
cana-5422	686	37	constant	constant	NOUN
cana-5422	686	38	and	and	CCONJ
cana-5422	686	39	ϕ	ϕ	NOUN
cana-5422	686	40	be	be	AUX
cana-5422	686	41	any	any	DET
cana-5422	686	42	real	real	ADJ
cana-5422	686	43	number	number	NOUN
cana-5422	686	44	.	.	PUNCT
cana-5422	687	1	then	then	ADV
cana-5422	687	2	there	there	PRON
cana-5422	687	3	exists	exist	VERB
cana-5422	687	4	a	a	DET
cana-5422	687	5	unique	unique	ADJ
cana-5422	687	6	additive	additive	ADJ
cana-5422	687	7	mapping	mapping	NOUN
cana-5422	687	8	a(w1	a(w1	NOUN
cana-5422	687	9	)	)	PUNCT
cana-5422	687	10	:	:	PUNCT
cana-5422	687	11	w1	w1	NOUN
cana-5422	687	12	→w2	→w2	NOUN
cana-5422	687	13	and	and	CCONJ
cana-5422	687	14	a	a	DET
cana-5422	687	15	unique	unique	ADJ
cana-5422	687	16	quadratic	quadratic	ADJ
cana-5422	687	17	mapping	mapping	NOUN
cana-5422	687	18	q(w1	q(w1	NOUN
cana-5422	687	19	)	)	PUNCT
cana-5422	687	20	:	:	PUNCT
cana-5422	687	21	w1	w1	PROPN
cana-5422	687	22	→w2	→w2	NOUN
cana-5422	687	23	which	which	PRON
cana-5422	687	24	satisfies	satisfy	VERB
cana-5422	687	25	(	(	PUNCT
cana-5422	687	26	1.7	1.7	NUM
cana-5422	687	27	)	)	PUNCT
cana-5422	687	28	and	and	CCONJ
cana-5422	687	29	the	the	DET
cana-5422	687	30	functional	functional	ADJ
cana-5422	687	31	inequality	inequality	NOUN
cana-5422	687	32	µ	µ	X
cana-5422	687	33	(	(	PUNCT
cana-5422	687	34	f	f	PROPN
cana-5422	687	35	(	(	PUNCT
cana-5422	687	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	687	37	)	)	PUNCT
cana-5422	687	38	,	,	PUNCT
cana-5422	687	39	4λ	4λ	PROPN
cana-5422	687	40	)	)	PUNCT
cana-5422	687	41	≥	≥	NOUN
cana-5422	687	42	µ′	µ′	PUNCT
cana-5422	687	43	(	(	PUNCT
cana-5422	687	44	2δ|w1|ϕ	2δ|w1|ϕ	NUM
cana-5422	687	45	,	,	PUNCT
cana-5422	687	46	λ	λ	X
cana-5422	687	47	{	{	PUNCT
cana-5422	687	48	1	1	NUM
cana-5422	687	49	4	4	NUM
cana-5422	687	50	|5−	|5−	NOUN
cana-5422	687	51	5ϕ|+	5ϕ|+	NUM
cana-5422	687	52	7	7	NUM
cana-5422	687	53	9	9	NUM
cana-5422	687	54	|25−	|25−	NOUN
cana-5422	687	55	5ϕ|	5ϕ|	NUM
cana-5422	687	56	}	}	PUNCT
cana-5422	687	57	)	)	PUNCT
cana-5422	687	58	,	,	PUNCT
cana-5422	687	59	ϕ	ϕ	PROPN
cana-5422	687	60	6=	6=	ADP
cana-5422	687	61	1	1	NUM
cana-5422	687	62	,	,	PUNCT
cana-5422	687	63	2	2	NUM
cana-5422	687	64	,	,	PUNCT
cana-5422	687	65	ν	ν	X
cana-5422	687	66	(	(	PUNCT
cana-5422	687	67	f	f	X
cana-5422	687	68	(	(	PUNCT
cana-5422	687	69	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	687	70	)	)	PUNCT
cana-5422	687	71	,	,	PUNCT
cana-5422	687	72	4λ	4λ	NOUN
cana-5422	687	73	)	)	PUNCT
cana-5422	687	74	≤	≤	NUM
cana-5422	687	75	ν′	ν′	NOUN
cana-5422	687	76	(	(	PUNCT
cana-5422	687	77	2δ|w1|ϕ	2δ|w1|ϕ	NUM
cana-5422	687	78	,	,	PUNCT
cana-5422	687	79	λ	λ	X
cana-5422	687	80	{	{	PUNCT
cana-5422	687	81	1	1	NUM
cana-5422	687	82	4	4	NUM
cana-5422	687	83	|5−	|5−	NOUN
cana-5422	687	84	5ϕ|+	5ϕ|+	NUM
cana-5422	687	85	7	7	NUM
cana-5422	687	86	9	9	NUM
cana-5422	687	87	|25−	|25−	NOUN
cana-5422	687	88	5ϕ|	5ϕ|	NUM
cana-5422	687	89	}	}	PUNCT
cana-5422	687	90	)	)	PUNCT
cana-5422	687	91	,	,	PUNCT
cana-5422	687	92	ϕ	ϕ	PROPN
cana-5422	687	93	6=	6=	ADP
cana-5422	687	94	1	1	NUM
cana-5422	687	95	,	,	PUNCT
cana-5422	687	96	2	2	NUM
cana-5422	687	97	,	,	PUNCT
cana-5422	687	98			PROPN
cana-5422	687	99	(	(	PUNCT
cana-5422	687	100	3.58	3.58	NUM
cana-5422	687	101	)	)	PUNCT
cana-5422	687	102	for	for	ADP
cana-5422	687	103	all	all	DET
cana-5422	687	104	w1	w1	NOUN
cana-5422	687	105	∈	∈	PROPN
cana-5422	687	106	w1	w1	NOUN
cana-5422	687	107	.	.	PUNCT
cana-5422	688	1	corollary	corollary	ADJ
cana-5422	688	2	3.25	3.25	NUM
cana-5422	688	3	.	.	PUNCT
cana-5422	688	4	suppose	suppose	VERB
cana-5422	688	5	that	that	SCONJ
cana-5422	688	6	a	a	DET
cana-5422	688	7	functionf	functionf	NOUN
cana-5422	688	8	:	:	PUNCT
cana-5422	688	9	w1	w1	PROPN
cana-5422	688	10	→w2	→w2	NOUN
cana-5422	688	11	satisfy	satisfy	VERB
cana-5422	688	12	the	the	DET
cana-5422	688	13	functional	functional	ADJ
cana-5422	688	14	inequality	inequality	NOUN
cana-5422	688	15	(	(	PUNCT
cana-5422	688	16	3.4	3.4	NUM
cana-5422	688	17	)	)	PUNCT
cana-5422	688	18	for	for	ADP
cana-5422	688	19	all	all	DET
cana-5422	688	20	w1	w1	NOUN
cana-5422	688	21	,	,	PUNCT
cana-5422	688	22	w2	w2	NOUN
cana-5422	688	23	,	,	PUNCT
cana-5422	688	24	w3	w3	PROPN
cana-5422	688	25	∈	∈	PROPN
cana-5422	688	26	w1	w1	NOUN
cana-5422	688	27	and	and	CCONJ
cana-5422	688	28	all	all	DET
cana-5422	688	29	λ	λ	X
cana-5422	688	30	>	>	X
cana-5422	688	31	0	0	PUNCT
cana-5422	688	32	with	with	SCONJ
cana-5422	688	33	δ	δ	PROPN
cana-5422	688	34	be	be	AUX
cana-5422	688	35	a	a	DET
cana-5422	688	36	positive	positive	ADJ
cana-5422	688	37	constant	constant	NOUN
cana-5422	688	38	and	and	CCONJ
cana-5422	688	39	ϕ	ϕ	NOUN
cana-5422	688	40	be	be	AUX
cana-5422	688	41	any	any	DET
cana-5422	688	42	real	real	ADJ
cana-5422	688	43	number	number	NOUN
cana-5422	688	44	.	.	PUNCT
cana-5422	689	1	then	then	ADV
cana-5422	689	2	there	there	PRON
cana-5422	689	3	exists	exist	VERB
cana-5422	689	4	a	a	DET
cana-5422	689	5	unique	unique	ADJ
cana-5422	689	6	additive	additive	ADJ
cana-5422	689	7	mapping	mapping	NOUN
cana-5422	689	8	a(w1	a(w1	NOUN
cana-5422	689	9	)	)	PUNCT
cana-5422	689	10	:	:	PUNCT
cana-5422	689	11	w1	w1	NOUN
cana-5422	689	12	→w2	→w2	NOUN
cana-5422	689	13	and	and	CCONJ
cana-5422	689	14	a	a	DET
cana-5422	689	15	unique	unique	ADJ
cana-5422	689	16	quadratic	quadratic	ADJ
cana-5422	689	17	mapping	mapping	NOUN
cana-5422	689	18	q(w1	q(w1	NOUN
cana-5422	689	19	)	)	PUNCT
cana-5422	689	20	:	:	PUNCT
cana-5422	689	21	w1	w1	PROPN
cana-5422	689	22	→w2	→w2	NOUN
cana-5422	689	23	which	which	PRON
cana-5422	689	24	satisfies	satisfy	VERB
cana-5422	689	25	(	(	PUNCT
cana-5422	689	26	1.7	1.7	NUM
cana-5422	689	27	)	)	PUNCT
cana-5422	689	28	and	and	CCONJ
cana-5422	689	29	the	the	DET
cana-5422	689	30	functional	functional	ADJ
cana-5422	689	31	inequality	inequality	NOUN
cana-5422	689	32	µ	µ	X
cana-5422	689	33	(	(	PUNCT
cana-5422	689	34	f	f	PROPN
cana-5422	689	35	(	(	PUNCT
cana-5422	689	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	689	37	)	)	PUNCT
cana-5422	689	38	,	,	PUNCT
cana-5422	689	39	4λ	4λ	PROPN
cana-5422	689	40	)	)	PUNCT
cana-5422	689	41	≥	≥	NOUN
cana-5422	689	42	µ′	µ′	PUNCT
cana-5422	689	43	(	(	PUNCT
cana-5422	689	44	2δ	2δ	NUM
cana-5422	689	45	∑3	∑3	PROPN
cana-5422	689	46	ψ=1	ψ=1	PUNCT
cana-5422	689	47	|wψ|	|wψ|	NOUN
cana-5422	689	48	ϕψ	ϕψ	ADV
cana-5422	689	49	,	,	PUNCT
cana-5422	689	50	{	{	PUNCT
cana-5422	689	51	3	3	NUM
cana-5422	689	52	4	4	NUM
cana-5422	689	53	∑3	∑3	PROPN
cana-5422	689	54	ψ=1	ψ=1	PUNCT
cana-5422	689	55	|5−	|5−	PROPN
cana-5422	689	56	5ϕψ	5ϕψ	NOUN
cana-5422	689	57	|+	|+	NOUN
cana-5422	689	58	7	7	NUM
cana-5422	689	59	3	3	NUM
cana-5422	689	60	∑3	∑3	PROPN
cana-5422	689	61	ψ=1	ψ=1	PUNCT
cana-5422	689	62	|25−	|25−	VERB
cana-5422	689	63	5ϕψ	5ϕψ	NOUN
cana-5422	689	64	|	|	CCONJ
cana-5422	689	65	}	}	PUNCT
cana-5422	689	66	)	)	PUNCT
cana-5422	689	67	,	,	PUNCT
cana-5422	689	68	ϕ1	ϕ1	NOUN
cana-5422	689	69	,	,	PUNCT
cana-5422	689	70	ϕ2	ϕ2	ADV
cana-5422	689	71	,	,	PUNCT
cana-5422	689	72	ϕ3	ϕ3	PROPN
cana-5422	689	73	6=	6=	PROPN
cana-5422	689	74	1	1	NUM
cana-5422	689	75	,	,	PUNCT
cana-5422	689	76	2	2	NUM
cana-5422	689	77	,	,	PUNCT
cana-5422	689	78	ν	ν	X
cana-5422	689	79	(	(	PUNCT
cana-5422	689	80	f	f	X
cana-5422	689	81	(	(	PUNCT
cana-5422	689	82	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	689	83	)	)	PUNCT
cana-5422	689	84	,	,	PUNCT
cana-5422	689	85	4λ	4λ	NOUN
cana-5422	689	86	)	)	PUNCT
cana-5422	689	87	≤	≤	NUM
cana-5422	689	88	ν′	ν′	NOUN
cana-5422	689	89	(	(	PUNCT
cana-5422	689	90	2δ	2δ	NUM
cana-5422	689	91	∑3	∑3	PROPN
cana-5422	689	92	ψ=1	ψ=1	PUNCT
cana-5422	689	93	|wψ|	|wψ|	NOUN
cana-5422	689	94	ϕψ	ϕψ	ADV
cana-5422	689	95	,	,	PUNCT
cana-5422	689	96	{	{	PUNCT
cana-5422	689	97	3	3	NUM
cana-5422	689	98	4	4	NUM
cana-5422	689	99	∑3	∑3	PROPN
cana-5422	689	100	ψ=1	ψ=1	PUNCT
cana-5422	689	101	|5−	|5−	PROPN
cana-5422	689	102	5ϕψ	5ϕψ	NOUN
cana-5422	689	103	|+	|+	NOUN
cana-5422	689	104	7	7	NUM
cana-5422	689	105	3	3	NUM
cana-5422	689	106	∑3	∑3	PROPN
cana-5422	689	107	ψ=1	ψ=1	PUNCT
cana-5422	689	108	|25−	|25−	VERB
cana-5422	689	109	5ϕψ	5ϕψ	NOUN
cana-5422	689	110	|	|	CCONJ
cana-5422	689	111	}	}	PUNCT
cana-5422	689	112	)	)	PUNCT
cana-5422	689	113	,	,	PUNCT
cana-5422	689	114	ϕ1	ϕ1	NOUN
cana-5422	689	115	,	,	PUNCT
cana-5422	689	116	ϕ2	ϕ2	ADV
cana-5422	689	117	,	,	PUNCT
cana-5422	689	118	ϕ3	ϕ3	PROPN
cana-5422	689	119	6=	6=	PROPN
cana-5422	689	120	1	1	NUM
cana-5422	689	121	,	,	PUNCT
cana-5422	689	122	2	2	NUM
cana-5422	689	123	,	,	PUNCT
cana-5422	689	124			ADJ
cana-5422	689	125	(	(	PUNCT
cana-5422	689	126	3.59	3.59	NUM
cana-5422	689	127	)	)	PUNCT
cana-5422	689	128	for	for	ADP
cana-5422	689	129	all	all	DET
cana-5422	689	130	w1	w1	NOUN
cana-5422	689	131	∈	∈	PROPN
cana-5422	689	132	w1	w1	NOUN
cana-5422	689	133	.	.	PUNCT
cana-5422	690	1	corollary	corollary	ADJ
cana-5422	690	2	3.26	3.26	NUM
cana-5422	690	3	.	.	PUNCT
cana-5422	690	4	suppose	suppose	VERB
cana-5422	690	5	that	that	SCONJ
cana-5422	690	6	a	a	DET
cana-5422	690	7	functionf	functionf	NOUN
cana-5422	690	8	:	:	PUNCT
cana-5422	690	9	w1	w1	PROPN
cana-5422	690	10	→w2	→w2	NOUN
cana-5422	690	11	satisfy	satisfy	VERB
cana-5422	690	12	the	the	DET
cana-5422	690	13	functional	functional	ADJ
cana-5422	690	14	inequality	inequality	NOUN
cana-5422	690	15	(	(	PUNCT
cana-5422	690	16	3.5	3.5	NUM
cana-5422	690	17	)	)	PUNCT
cana-5422	690	18	for	for	ADP
cana-5422	690	19	all	all	DET
cana-5422	690	20	w1	w1	NOUN
cana-5422	690	21	,	,	PUNCT
cana-5422	690	22	w2	w2	NOUN
cana-5422	690	23	,	,	PUNCT
cana-5422	690	24	w3	w3	PROPN
cana-5422	690	25	∈	∈	PROPN
cana-5422	690	26	w1	w1	NOUN
cana-5422	690	27	and	and	CCONJ
cana-5422	690	28	all	all	DET
cana-5422	690	29	λ	λ	X
cana-5422	690	30	>	>	X
cana-5422	690	31	0	0	PUNCT
cana-5422	690	32	with	with	SCONJ
cana-5422	690	33	δ	δ	PROPN
cana-5422	690	34	be	be	AUX
cana-5422	690	35	a	a	DET
cana-5422	690	36	positive	positive	ADJ
cana-5422	690	37	constant	constant	NOUN
cana-5422	690	38	and	and	CCONJ
cana-5422	690	39	ϕ	ϕ	NOUN
cana-5422	690	40	be	be	AUX
cana-5422	690	41	any	any	DET
cana-5422	690	42	real	real	ADJ
cana-5422	690	43	number	number	NOUN
cana-5422	690	44	.	.	PUNCT
cana-5422	691	1	then	then	ADV
cana-5422	691	2	there	there	PRON
cana-5422	691	3	exists	exist	VERB
cana-5422	691	4	a	a	DET
cana-5422	691	5	unique	unique	ADJ
cana-5422	691	6	additive	additive	ADJ
cana-5422	691	7	mapping	mapping	NOUN
cana-5422	691	8	a(w1	a(w1	NOUN
cana-5422	691	9	)	)	PUNCT
cana-5422	691	10	:	:	PUNCT
cana-5422	691	11	w1	w1	NOUN
cana-5422	691	12	→w2	→w2	NOUN
cana-5422	691	13	and	and	CCONJ
cana-5422	691	14	a	a	DET
cana-5422	691	15	unique	unique	ADJ
cana-5422	691	16	quadratic	quadratic	ADJ
cana-5422	691	17	mapping	mapping	NOUN
cana-5422	691	18	q(w1	q(w1	NOUN
cana-5422	691	19	)	)	PUNCT
cana-5422	691	20	:	:	PUNCT
cana-5422	691	21	w1	w1	PROPN
cana-5422	691	22	→w2	→w2	NOUN
cana-5422	691	23	which	which	PRON
cana-5422	691	24	satisfies	satisfy	VERB
cana-5422	691	25	(	(	PUNCT
cana-5422	691	26	1.7	1.7	NUM
cana-5422	691	27	)	)	PUNCT
cana-5422	691	28	and	and	CCONJ
cana-5422	691	29	the	the	DET
cana-5422	691	30	functional	functional	ADJ
cana-5422	691	31	inequality	inequality	NOUN
cana-5422	691	32	µ	µ	X
cana-5422	691	33	(	(	PUNCT
cana-5422	691	34	f	f	PROPN
cana-5422	691	35	(	(	PUNCT
cana-5422	691	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	691	37	)	)	PUNCT
cana-5422	691	38	,	,	PUNCT
cana-5422	691	39	4λ	4λ	PROPN
cana-5422	691	40	)	)	PUNCT
cana-5422	691	41	≥	≥	NOUN
cana-5422	691	42	µ′	µ′	PUNCT
cana-5422	691	43	(	(	PUNCT
cana-5422	691	44	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	691	45	,	,	PUNCT
cana-5422	691	46	λ	λ	NOUN
cana-5422	691	47	{	{	PUNCT
cana-5422	691	48	3	3	NUM
cana-5422	691	49	4	4	NUM
cana-5422	691	50	|5−	|5−	PROPN
cana-5422	691	51	53ϕ|+	53ϕ|+	PROPN
cana-5422	691	52	7	7	NUM
cana-5422	691	53	3	3	NUM
cana-5422	691	54	|25−	|25−	PROPN
cana-5422	691	55	53ϕ|	53ϕ|	NUM
cana-5422	691	56	}	}	PUNCT
cana-5422	691	57	)	)	PUNCT
cana-5422	691	58	,	,	PUNCT
cana-5422	691	59	3ϕ	3ϕ	NUM
cana-5422	691	60	6=	6=	NUM
cana-5422	691	61	1	1	NUM
cana-5422	691	62	,	,	PUNCT
cana-5422	691	63	2	2	NUM
cana-5422	691	64	,	,	PUNCT
cana-5422	691	65	ν	ν	X
cana-5422	691	66	(	(	PUNCT
cana-5422	691	67	f	f	X
cana-5422	691	68	(	(	PUNCT
cana-5422	691	69	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	691	70	)	)	PUNCT
cana-5422	691	71	,	,	PUNCT
cana-5422	691	72	4λ	4λ	NOUN
cana-5422	691	73	)	)	PUNCT
cana-5422	691	74	≤	≤	NUM
cana-5422	691	75	ν′	ν′	NOUN
cana-5422	691	76	(	(	PUNCT
cana-5422	691	77	2δ|w1|3ϕ	2δ|w1|3ϕ	NUM
cana-5422	691	78	,	,	PUNCT
cana-5422	691	79	λ	λ	NOUN
cana-5422	691	80	{	{	PUNCT
cana-5422	691	81	3	3	NUM
cana-5422	691	82	4	4	NUM
cana-5422	691	83	|5−	|5−	PROPN
cana-5422	691	84	53ϕ|+	53ϕ|+	PROPN
cana-5422	691	85	7	7	NUM
cana-5422	691	86	3	3	NUM
cana-5422	691	87	|25−	|25−	PROPN
cana-5422	691	88	53ϕ|	53ϕ|	NUM
cana-5422	691	89	}	}	PUNCT
cana-5422	691	90	)	)	PUNCT
cana-5422	691	91	,	,	PUNCT
cana-5422	691	92	3ϕ	3ϕ	NUM
cana-5422	691	93	6=	6=	NUM
cana-5422	691	94	1	1	NUM
cana-5422	691	95	,	,	PUNCT
cana-5422	691	96	2	2	NUM
cana-5422	691	97	,	,	PUNCT
cana-5422	691	98	}	}	PUNCT
cana-5422	691	99	(	(	PUNCT
cana-5422	691	100	3.60	3.60	NUM
cana-5422	691	101	)	)	PUNCT
cana-5422	691	102	for	for	ADP
cana-5422	691	103	all	all	DET
cana-5422	691	104	w1	w1	NOUN
cana-5422	691	105	∈	∈	PROPN
cana-5422	691	106	w1	w1	NOUN
cana-5422	691	107	.	.	PUNCT
cana-5422	692	1	corollary	corollary	ADJ
cana-5422	692	2	3.27	3.27	NUM
cana-5422	692	3	.	.	PUNCT
cana-5422	692	4	suppose	suppose	VERB
cana-5422	692	5	that	that	SCONJ
cana-5422	692	6	a	a	DET
cana-5422	692	7	functionf	functionf	NOUN
cana-5422	692	8	:	:	PUNCT
cana-5422	692	9	w1	w1	PROPN
cana-5422	692	10	→w2	→w2	NOUN
cana-5422	692	11	satisfy	satisfy	VERB
cana-5422	692	12	the	the	DET
cana-5422	692	13	functional	functional	ADJ
cana-5422	692	14	inequality	inequality	NOUN
cana-5422	692	15	(	(	PUNCT
cana-5422	692	16	3.6	3.6	NUM
cana-5422	692	17	)	)	PUNCT
cana-5422	692	18	for	for	ADP
cana-5422	692	19	all	all	DET
cana-5422	692	20	w1	w1	NOUN
cana-5422	692	21	,	,	PUNCT
cana-5422	692	22	w2	w2	NOUN
cana-5422	692	23	,	,	PUNCT
cana-5422	692	24	w3	w3	PROPN
cana-5422	692	25	∈	∈	PROPN
cana-5422	692	26	w1	w1	NOUN
cana-5422	692	27	and	and	CCONJ
cana-5422	692	28	all	all	DET
cana-5422	692	29	λ	λ	X
cana-5422	692	30	>	>	X
cana-5422	692	31	0	0	PUNCT
cana-5422	692	32	with	with	SCONJ
cana-5422	692	33	δ	δ	PROPN
cana-5422	692	34	be	be	AUX
cana-5422	692	35	a	a	DET
cana-5422	692	36	positive	positive	ADJ
cana-5422	692	37	constant	constant	NOUN
cana-5422	692	38	and	and	CCONJ
cana-5422	692	39	ϕ	ϕ	NOUN
cana-5422	692	40	be	be	AUX
cana-5422	692	41	any	any	DET
cana-5422	692	42	real	real	ADJ
cana-5422	692	43	number	number	NOUN
cana-5422	692	44	.	.	PUNCT
cana-5422	693	1	then	then	ADV
cana-5422	693	2	there	there	PRON
cana-5422	693	3	exists	exist	VERB
cana-5422	693	4	a	a	DET
cana-5422	693	5	unique	unique	ADJ
cana-5422	693	6	additive	additive	ADJ
cana-5422	693	7	mapping	mapping	NOUN
cana-5422	693	8	a(w1	a(w1	NOUN
cana-5422	693	9	)	)	PUNCT
cana-5422	693	10	:	:	PUNCT
cana-5422	693	11	w1	w1	NOUN
cana-5422	693	12	→w2	→w2	NOUN
cana-5422	693	13	and	and	CCONJ
cana-5422	693	14	a	a	DET
cana-5422	693	15	unique	unique	ADJ
cana-5422	693	16	quadratic	quadratic	ADJ
cana-5422	693	17	mapping	mapping	NOUN
cana-5422	693	18	q(w1	q(w1	NOUN
cana-5422	693	19	)	)	PUNCT
cana-5422	693	20	:	:	PUNCT
cana-5422	693	21	w1	w1	PROPN
cana-5422	693	22	→w2	→w2	NOUN
cana-5422	693	23	which	which	PRON
cana-5422	693	24	satisfies	satisfy	VERB
cana-5422	693	25	(	(	PUNCT
cana-5422	693	26	1.7	1.7	NUM
cana-5422	693	27	)	)	PUNCT
cana-5422	693	28	and	and	CCONJ
cana-5422	693	29	the	the	DET
cana-5422	693	30	functional	functional	ADJ
cana-5422	693	31	inequality	inequality	NOUN
cana-5422	693	32	µ	µ	X
cana-5422	693	33	(	(	PUNCT
cana-5422	693	34	f	f	PROPN
cana-5422	693	35	(	(	PUNCT
cana-5422	693	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	693	37	)	)	PUNCT
cana-5422	693	38	,	,	PUNCT
cana-5422	693	39	4λ	4λ	PROPN
cana-5422	693	40	)	)	PUNCT
cana-5422	693	41	≥	≥	NOUN
cana-5422	693	42	µ′	µ′	PUNCT
cana-5422	693	43	(	(	PUNCT
cana-5422	693	44	4δ|wψ|∑	4δ|wψ|∑	NOUN
cana-5422	693	45	3	3	X
cana-5422	693	46	ψ=1	ψ=1	PUNCT
cana-5422	693	47	ϕψ	ϕψ	ADV
cana-5422	693	48	,	,	PUNCT
cana-5422	693	49	2λ	2λ	X
cana-5422	693	50	{	{	PUNCT
cana-5422	693	51	3	3	NUM
cana-5422	693	52	4	4	NUM
cana-5422	693	53	∣∣∣5−	∣∣∣5−	NOUN
cana-5422	693	54	5∑3	5∑3	NUM
cana-5422	693	55	ψ=1	ψ=1	PUNCT
cana-5422	693	56	ϕψ	ϕψ	ADP
cana-5422	693	57	∣∣∣+	∣∣∣+	PROPN
cana-5422	693	58	7	7	NUM
cana-5422	693	59	3	3	NUM
cana-5422	693	60	∣∣∣25−	∣∣∣25−	NOUN
cana-5422	693	61	5∑3	5∑3	NUM
cana-5422	693	62	ψ=1	ψ=1	PUNCT
cana-5422	693	63	ϕψ	ϕψ	ADV
cana-5422	693	64	∣∣∣	∣∣∣	ADJ
cana-5422	693	65	}	}	PUNCT
cana-5422	693	66	)	)	PUNCT
cana-5422	693	67	,	,	PUNCT
cana-5422	693	68	∑3	∑3	PROPN
cana-5422	693	69	ψ=1	ψ=1	PUNCT
cana-5422	693	70	ϕψ	ϕψ	ADP
cana-5422	693	71	6=	6=	PROPN
cana-5422	693	72	1	1	NUM
cana-5422	693	73	,	,	PUNCT
cana-5422	693	74	2	2	NUM
cana-5422	693	75	,	,	PUNCT
cana-5422	693	76	ν	ν	X
cana-5422	693	77	(	(	PUNCT
cana-5422	693	78	f	f	X
cana-5422	693	79	(	(	PUNCT
cana-5422	693	80	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	693	81	)	)	PUNCT
cana-5422	693	82	,	,	PUNCT
cana-5422	693	83	4λ	4λ	NOUN
cana-5422	693	84	)	)	PUNCT
cana-5422	693	85	≤	≤	NUM
cana-5422	693	86	ν′	ν′	NOUN
cana-5422	693	87	(	(	PUNCT
cana-5422	693	88	4δ|wψ|∑	4δ|wψ|∑	NOUN
cana-5422	693	89	3	3	X
cana-5422	693	90	ψ=1	ψ=1	PUNCT
cana-5422	693	91	ϕψ	ϕψ	ADV
cana-5422	693	92	,	,	PUNCT
cana-5422	693	93	2λ	2λ	X
cana-5422	693	94	{	{	PUNCT
cana-5422	693	95	3	3	NUM
cana-5422	693	96	4	4	NUM
cana-5422	693	97	∣∣∣5−	∣∣∣5−	NOUN
cana-5422	693	98	5∑3	5∑3	NUM
cana-5422	693	99	ψ=1	ψ=1	PUNCT
cana-5422	693	100	ϕψ	ϕψ	ADP
cana-5422	693	101	∣∣∣+	∣∣∣+	PROPN
cana-5422	693	102	7	7	NUM
cana-5422	693	103	3	3	NUM
cana-5422	693	104	∣∣∣25−	∣∣∣25−	NOUN
cana-5422	693	105	5∑3	5∑3	NUM
cana-5422	693	106	ψ=1	ψ=1	PUNCT
cana-5422	693	107	ϕψ	ϕψ	ADV
cana-5422	693	108	∣∣∣	∣∣∣	ADJ
cana-5422	693	109	}	}	PUNCT
cana-5422	693	110	)	)	PUNCT
cana-5422	693	111	,	,	PUNCT
cana-5422	693	112	∑3	∑3	PROPN
cana-5422	693	113	ψ=1	ψ=1	PUNCT
cana-5422	693	114	ϕψ	ϕψ	ADP
cana-5422	693	115	6=	6=	PROPN
cana-5422	693	116	1	1	NUM
cana-5422	693	117	,	,	PUNCT
cana-5422	693	118	2	2	NUM
cana-5422	693	119	,	,	PUNCT
cana-5422	693	120			NOUN
cana-5422	693	121	(	(	PUNCT
cana-5422	693	122	3.61	3.61	NUM
cana-5422	693	123	)	)	PUNCT
cana-5422	693	124	for	for	ADP
cana-5422	693	125	all	all	DET
cana-5422	693	126	w1	w1	NOUN
cana-5422	693	127	∈	∈	PROPN
cana-5422	693	128	w1	w1	NOUN
cana-5422	693	129	.	.	PUNCT
cana-5422	694	1	communications	communication	NOUN
cana-5422	694	2	on	on	ADP
cana-5422	694	3	applied	apply	VERB
cana-5422	694	4	nonlinear	nonlinear	ADJ
cana-5422	694	5	analysis	analysis	NOUN
cana-5422	694	6	issn	issn	NOUN
cana-5422	694	7	:	:	PUNCT
cana-5422	694	8	1074	1074	NUM
cana-5422	694	9	-	-	PUNCT
cana-5422	694	10	133x	133x	NUM
cana-5422	694	11	vol	vol	NOUN
cana-5422	694	12	32	32	NUM
cana-5422	694	13	no	no	NOUN
cana-5422	694	14	.	.	PUNCT
cana-5422	695	1	10s(2025	10s(2025	NUM
cana-5422	695	2	)	)	PUNCT
cana-5422	695	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	695	4	2211	2211	NUM
cana-5422	695	5	corollary	corollary	ADJ
cana-5422	695	6	3.28	3.28	NUM
cana-5422	695	7	.	.	PUNCT
cana-5422	695	8	suppose	suppose	VERB
cana-5422	695	9	that	that	SCONJ
cana-5422	695	10	a	a	DET
cana-5422	695	11	functionf	functionf	NOUN
cana-5422	695	12	:	:	PUNCT
cana-5422	695	13	w1	w1	PROPN
cana-5422	695	14	→w2	→w2	NOUN
cana-5422	695	15	satisfy	satisfy	VERB
cana-5422	695	16	the	the	DET
cana-5422	695	17	functional	functional	ADJ
cana-5422	695	18	inequality	inequality	NOUN
cana-5422	695	19	(	(	PUNCT
cana-5422	695	20	3.7	3.7	NUM
cana-5422	695	21	)	)	PUNCT
cana-5422	695	22	for	for	ADP
cana-5422	695	23	all	all	DET
cana-5422	695	24	w1	w1	NOUN
cana-5422	695	25	,	,	PUNCT
cana-5422	695	26	w2	w2	NOUN
cana-5422	695	27	,	,	PUNCT
cana-5422	695	28	w3	w3	PROPN
cana-5422	695	29	∈	∈	PROPN
cana-5422	695	30	w1	w1	NOUN
cana-5422	695	31	and	and	CCONJ
cana-5422	695	32	all	all	DET
cana-5422	695	33	λ	λ	X
cana-5422	695	34	>	>	X
cana-5422	695	35	0	0	PUNCT
cana-5422	695	36	with	with	SCONJ
cana-5422	695	37	δ	δ	PROPN
cana-5422	695	38	be	be	AUX
cana-5422	695	39	a	a	DET
cana-5422	695	40	positive	positive	ADJ
cana-5422	695	41	constant	constant	NOUN
cana-5422	695	42	and	and	CCONJ
cana-5422	695	43	ϕ	ϕ	NOUN
cana-5422	695	44	be	be	AUX
cana-5422	695	45	any	any	DET
cana-5422	695	46	real	real	ADJ
cana-5422	695	47	number	number	NOUN
cana-5422	695	48	.	.	PUNCT
cana-5422	696	1	then	then	ADV
cana-5422	696	2	there	there	PRON
cana-5422	696	3	exists	exist	VERB
cana-5422	696	4	a	a	DET
cana-5422	696	5	unique	unique	ADJ
cana-5422	696	6	additive	additive	ADJ
cana-5422	696	7	mapping	mapping	NOUN
cana-5422	696	8	a(w1	a(w1	NOUN
cana-5422	696	9	)	)	PUNCT
cana-5422	696	10	:	:	PUNCT
cana-5422	696	11	w1	w1	NOUN
cana-5422	696	12	→w2	→w2	NOUN
cana-5422	696	13	and	and	CCONJ
cana-5422	696	14	a	a	DET
cana-5422	696	15	unique	unique	ADJ
cana-5422	696	16	quadratic	quadratic	ADJ
cana-5422	696	17	mapping	mapping	NOUN
cana-5422	696	18	q(w1	q(w1	NOUN
cana-5422	696	19	)	)	PUNCT
cana-5422	696	20	:	:	PUNCT
cana-5422	696	21	w1	w1	PROPN
cana-5422	696	22	→w2	→w2	NOUN
cana-5422	696	23	which	which	PRON
cana-5422	696	24	satisfies	satisfy	VERB
cana-5422	696	25	(	(	PUNCT
cana-5422	696	26	1.7	1.7	NUM
cana-5422	696	27	)	)	PUNCT
cana-5422	696	28	and	and	CCONJ
cana-5422	696	29	the	the	DET
cana-5422	696	30	functional	functional	ADJ
cana-5422	696	31	inequality	inequality	NOUN
cana-5422	696	32	µ	µ	X
cana-5422	696	33	(	(	PUNCT
cana-5422	696	34	f	f	PROPN
cana-5422	696	35	(	(	PUNCT
cana-5422	696	36	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	696	37	)	)	PUNCT
cana-5422	696	38	,	,	PUNCT
cana-5422	696	39	4λ	4λ	PROPN
cana-5422	696	40	)	)	PUNCT
cana-5422	696	41	≥	≥	NOUN
cana-5422	696	42	µ′	µ′	PUNCT
cana-5422	696	43	(	(	PUNCT
cana-5422	696	44	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	696	45	,	,	PUNCT
cana-5422	696	46	λ	λ	X
cana-5422	696	47	{	{	PUNCT
cana-5422	696	48	3	3	NUM
cana-5422	696	49	4	4	NUM
cana-5422	696	50	|5−	|5−	PROPN
cana-5422	696	51	53ϕ|+	53ϕ|+	PROPN
cana-5422	696	52	7	7	NUM
cana-5422	696	53	3	3	NUM
cana-5422	696	54	|25−	|25−	PROPN
cana-5422	696	55	53ϕ|	53ϕ|	NUM
cana-5422	696	56	}	}	PUNCT
cana-5422	696	57	)	)	PUNCT
cana-5422	696	58	,	,	PUNCT
cana-5422	696	59	3ϕ	3ϕ	NUM
cana-5422	696	60	6=	6=	NUM
cana-5422	696	61	1	1	NUM
cana-5422	696	62	,	,	PUNCT
cana-5422	696	63	2	2	NUM
cana-5422	696	64	,	,	PUNCT
cana-5422	696	65	ν	ν	X
cana-5422	696	66	(	(	PUNCT
cana-5422	696	67	f	f	X
cana-5422	696	68	(	(	PUNCT
cana-5422	696	69	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	696	70	)	)	PUNCT
cana-5422	696	71	,	,	PUNCT
cana-5422	696	72	4λ	4λ	NOUN
cana-5422	696	73	)	)	PUNCT
cana-5422	696	74	≤	≤	NUM
cana-5422	696	75	ν′	ν′	NOUN
cana-5422	696	76	(	(	PUNCT
cana-5422	696	77	4δ|w1|3ϕ	4δ|w1|3ϕ	NUM
cana-5422	696	78	,	,	PUNCT
cana-5422	696	79	λ	λ	X
cana-5422	696	80	{	{	PUNCT
cana-5422	696	81	3	3	NUM
cana-5422	696	82	4	4	NUM
cana-5422	696	83	|5−	|5−	PROPN
cana-5422	696	84	53ϕ|+	53ϕ|+	PROPN
cana-5422	696	85	7	7	NUM
cana-5422	696	86	3	3	NUM
cana-5422	696	87	|25−	|25−	PROPN
cana-5422	696	88	53ϕ|	53ϕ|	NUM
cana-5422	696	89	}	}	PUNCT
cana-5422	696	90	)	)	PUNCT
cana-5422	696	91	,	,	PUNCT
cana-5422	696	92	3ϕ	3ϕ	NUM
cana-5422	696	93	6=	6=	NUM
cana-5422	696	94	1	1	NUM
cana-5422	696	95	,	,	PUNCT
cana-5422	696	96	2	2	NUM
cana-5422	696	97	,	,	PUNCT
cana-5422	696	98	}	}	PUNCT
cana-5422	696	99	(	(	PUNCT
cana-5422	696	100	3.62	3.62	NUM
cana-5422	696	101	)	)	PUNCT
cana-5422	696	102	for	for	ADP
cana-5422	696	103	all	all	DET
cana-5422	696	104	w1	w1	NOUN
cana-5422	696	105	∈	∈	PROPN
cana-5422	696	106	w1	w1	NOUN
cana-5422	696	107	.	.	PUNCT
cana-5422	697	1	3.5	3.5	NUM
cana-5422	697	2	.	.	PUNCT
cana-5422	698	1	oddness	oddness	NOUN
cana-5422	698	2	of	of	ADP
cana-5422	698	3	f	f	NOUN
cana-5422	698	4	:	:	PUNCT
cana-5422	698	5	additive	additive	NOUN
cana-5422	698	6	case	case	NOUN
cana-5422	698	7	stability	stability	NOUN
cana-5422	698	8	results	result	VERB
cana-5422	698	9	:	:	PUNCT
cana-5422	698	10	fixed	fixed	ADJ
cana-5422	698	11	point	point	NOUN
cana-5422	698	12	method	method	NOUN
cana-5422	698	13	.	.	PUNCT
cana-5422	699	1	theorem	theorem	VERB
cana-5422	699	2	3.29	3.29	NUM
cana-5422	699	3	.	.	PUNCT
cana-5422	700	1	suppose	suppose	VERB
cana-5422	700	2	that	that	SCONJ
cana-5422	700	3	an	an	DET
cana-5422	700	4	odd	odd	ADJ
cana-5422	700	5	function	function	NOUN
cana-5422	700	6	f	f	NOUN
cana-5422	700	7	:	:	PUNCT
cana-5422	700	8	w1	w1	PROPN
cana-5422	700	9	→	→	SYM
cana-5422	700	10	w2	w2	NOUN
cana-5422	700	11	satisfy	satisfy	VERB
cana-5422	700	12	the	the	DET
cana-5422	700	13	functional	functional	ADJ
cana-5422	700	14	inequality	inequality	NOUN
cana-5422	700	15	(	(	PUNCT
cana-5422	700	16	3.1	3.1	NUM
cana-5422	700	17	)	)	PUNCT
cana-5422	700	18	where	where	SCONJ
cana-5422	700	19	ψ	ψ	X
cana-5422	700	20	:	:	PUNCT
cana-5422	700	21	w3	w3	NOUN
cana-5422	700	22	1	1	NUM
cana-5422	700	23	→	→	SYM
cana-5422	701	1	[	[	X
cana-5422	701	2	0	0	NUM
cana-5422	701	3	,	,	PUNCT
cana-5422	701	4	∞	∞	PROPN
cana-5422	701	5	)	)	PUNCT
cana-5422	701	6	with	with	ADP
cana-5422	701	7	the	the	DET
cana-5422	701	8	condition	condition	NOUN
cana-5422	701	9	lim	lim	NOUN
cana-5422	701	10	`	`	PUNCT
cana-5422	701	11	→∞	→∞	X
cana-5422	701	12	µ′	µ′	PUNCT
cana-5422	701	13	(	(	PUNCT
cana-5422	701	14	ψ	ψ	X
cana-5422	701	15	(	(	PUNCT
cana-5422	701	16	τ	τ	PROPN
cana-5422	701	17	`	`	PUNCT
cana-5422	701	18	v	v	PROPN
cana-5422	701	19	w1	w1	NOUN
cana-5422	701	20	,	,	PUNCT
cana-5422	701	21	τ	τ	PROPN
cana-5422	701	22	`	`	PUNCT
cana-5422	701	23	v	v	PROPN
cana-5422	701	24	w2	w2	NOUN
cana-5422	701	25	,	,	PUNCT
cana-5422	701	26	τ	τ	PROPN
cana-5422	701	27	`	`	PROPN
cana-5422	701	28	v	v	PROPN
cana-5422	701	29	w3	w3	PROPN
cana-5422	701	30	)	)	PUNCT
cana-5422	701	31	,	,	PUNCT
cana-5422	701	32	τ	τ	PROPN
cana-5422	701	33	`	`	PUNCT
cana-5422	701	34	v	v	PROPN
cana-5422	701	35	λ	λ	PROPN
cana-5422	701	36	)	)	PUNCT
cana-5422	701	37	=	=	SYM
cana-5422	701	38	1	1	NUM
cana-5422	701	39	lim	lim	NOUN
cana-5422	701	40	`	`	PUNCT
cana-5422	701	41	→∞	→∞	X
cana-5422	701	42	ν′	ν′	NOUN
cana-5422	701	43	(	(	PUNCT
cana-5422	701	44	ψ	ψ	X
cana-5422	701	45	(	(	PUNCT
cana-5422	701	46	τ	τ	PROPN
cana-5422	701	47	`	`	PUNCT
cana-5422	701	48	v	v	PROPN
cana-5422	701	49	w1	w1	NOUN
cana-5422	701	50	,	,	PUNCT
cana-5422	701	51	τ	τ	PROPN
cana-5422	701	52	`	`	PUNCT
cana-5422	701	53	v	v	PROPN
cana-5422	701	54	w2	w2	NOUN
cana-5422	701	55	,	,	PUNCT
cana-5422	701	56	τ	τ	PROPN
cana-5422	701	57	`	`	PROPN
cana-5422	701	58	v	v	PROPN
cana-5422	701	59	w3	w3	PROPN
cana-5422	701	60	)	)	PUNCT
cana-5422	701	61	,	,	PUNCT
cana-5422	701	62	τ	τ	PROPN
cana-5422	701	63	`	`	PUNCT
cana-5422	701	64	v	v	PROPN
cana-5422	701	65	λ	λ	PROPN
cana-5422	701	66	)	)	PUNCT
cana-5422	701	67	=	=	SYM
cana-5422	701	68	0	0	NUM
cana-5422	702	1			NOUN
cana-5422	702	2	;	;	PUNCT
cana-5422	702	3	τv	τv	X
cana-5422	702	4	=	=	PRON
cana-5422	702	5	{	{	PUNCT
cana-5422	702	6	5	5	NUM
cana-5422	702	7	;	;	PUNCT
cana-5422	702	8	v	v	NOUN
cana-5422	702	9	=	=	SYM
cana-5422	702	10	0	0	NUM
cana-5422	702	11	;	;	PUNCT
cana-5422	702	12	1	1	NUM
cana-5422	702	13	5	5	NUM
cana-5422	702	14	;	;	PUNCT
cana-5422	702	15	v	v	NOUN
cana-5422	702	16	=	=	SYM
cana-5422	702	17	1	1	NUM
cana-5422	702	18	;	;	PUNCT
cana-5422	702	19	(	(	PUNCT
cana-5422	702	20	3.63	3.63	NUM
cana-5422	702	21	)	)	PUNCT
cana-5422	702	22	for	for	ADP
cana-5422	702	23	all	all	DET
cana-5422	702	24	w1	w1	NOUN
cana-5422	702	25	,	,	PUNCT
cana-5422	702	26	w2	w2	NOUN
cana-5422	702	27	,	,	PUNCT
cana-5422	702	28	w3	w3	PROPN
cana-5422	702	29	∈	∈	PROPN
cana-5422	702	30	w1	w1	NOUN
cana-5422	702	31	and	and	CCONJ
cana-5422	702	32	all	all	DET
cana-5422	702	33	λ	λ	X
cana-5422	702	34	>	>	X
cana-5422	702	35	0	0	PUNCT
cana-5422	703	1	if	if	SCONJ
cana-5422	703	2	there	there	PRON
cana-5422	703	3	exists	exist	VERB
cana-5422	703	4	l	l	NOUN
cana-5422	703	5	=	=	SYM
cana-5422	703	6	l(ν	l(ν	PROPN
cana-5422	703	7	)	)	PUNCT
cana-5422	703	8	be	be	VERB
cana-5422	703	9	a	a	DET
cana-5422	703	10	function	function	NOUN
cana-5422	703	11	have	have	AUX
cana-5422	703	12	the	the	DET
cana-5422	703	13	property	property	NOUN
cana-5422	703	14	µ	µ	X
cana-5422	703	15	(	(	PUNCT
cana-5422	703	16	ψa(w1	ψa(w1	NOUN
cana-5422	703	17	)	)	PUNCT
cana-5422	703	18	,	,	PUNCT
cana-5422	703	19	λ	λ	X
cana-5422	703	20	)	)	PUNCT
cana-5422	704	1	=	=	SYM
cana-5422	704	2	µ	µ	X
cana-5422	704	3	(	(	PUNCT
cana-5422	704	4	ψa	ψa	X
cana-5422	704	5	(	(	PUNCT
cana-5422	704	6	w1	w1	NOUN
cana-5422	704	7	5	5	NUM
cana-5422	704	8	)	)	PUNCT
cana-5422	704	9	,	,	PUNCT
cana-5422	704	10	λ	λ	NOUN
cana-5422	704	11	)	)	PUNCT
cana-5422	704	12	ν	ν	NOUN
cana-5422	704	13	(	(	PUNCT
cana-5422	704	14	ψa(w1	ψa(w1	NOUN
cana-5422	704	15	)	)	PUNCT
cana-5422	704	16	,	,	PUNCT
cana-5422	704	17	λ	λ	X
cana-5422	704	18	)	)	PUNCT
cana-5422	704	19	=	=	SYM
cana-5422	705	1	ν	ν	NOUN
cana-5422	705	2	(	(	PUNCT
cana-5422	705	3	ψa	ψa	X
cana-5422	705	4	(	(	PUNCT
cana-5422	705	5	w1	w1	NOUN
cana-5422	705	6	5	5	NUM
cana-5422	705	7	)	)	PUNCT
cana-5422	705	8	,	,	PUNCT
cana-5422	705	9	λ	λ	PROPN
cana-5422	705	10	)	)	PUNCT
cana-5422	705	11	}	}	PUNCT
cana-5422	705	12	and	and	CCONJ
cana-5422	705	13	µ	µ	X
cana-5422	705	14	(	(	PUNCT
cana-5422	705	15	1	1	NUM
cana-5422	705	16	τv	τv	ADP
cana-5422	705	17	ψa	ψa	PROPN
cana-5422	705	18	(	(	PUNCT
cana-5422	705	19	τvw1	τvw1	PROPN
cana-5422	705	20	)	)	PUNCT
cana-5422	705	21	,	,	PUNCT
cana-5422	705	22	λ	λ	INTJ
cana-5422	705	23	)	)	PUNCT
cana-5422	705	24	=	=	SYM
cana-5422	705	25	µ	µ	X
cana-5422	705	26	(	(	PUNCT
cana-5422	705	27	l	l	NOUN
cana-5422	705	28	ψa(w1	ψa(w1	NOUN
cana-5422	705	29	)	)	PUNCT
cana-5422	705	30	,	,	PUNCT
cana-5422	705	31	λ	λ	X
cana-5422	705	32	)	)	PUNCT
cana-5422	705	33	ν	ν	NOUN
cana-5422	705	34	(	(	PUNCT
cana-5422	705	35	1	1	NUM
cana-5422	705	36	τv	τv	ADP
cana-5422	705	37	ψa	ψa	PROPN
cana-5422	705	38	(	(	PUNCT
cana-5422	705	39	τvw1	τvw1	PROPN
cana-5422	705	40	)	)	PUNCT
cana-5422	705	41	,	,	PUNCT
cana-5422	705	42	λ	λ	NOUN
cana-5422	705	43	)	)	PUNCT
cana-5422	705	44	=	=	PUNCT
cana-5422	706	1	ν	ν	X
cana-5422	706	2	(	(	PUNCT
cana-5422	706	3	l	l	NOUN
cana-5422	706	4	ψa(w1	ψa(w1	NOUN
cana-5422	706	5	)	)	PUNCT
cana-5422	706	6	,	,	PUNCT
cana-5422	706	7	λ	λ	NOUN
cana-5422	706	8	)	)	PUNCT
cana-5422	706	9			NOUN
cana-5422	706	10	,	,	PUNCT
cana-5422	706	11	(	(	PUNCT
cana-5422	706	12	3.64	3.64	NUM
cana-5422	706	13	)	)	PUNCT
cana-5422	706	14	for	for	ADP
cana-5422	706	15	all	all	DET
cana-5422	706	16	w1	w1	NOUN
cana-5422	706	17	∈	∈	PROPN
cana-5422	706	18	w1	w1	NOUN
cana-5422	706	19	and	and	CCONJ
cana-5422	706	20	all	all	DET
cana-5422	706	21	λ	λ	X
cana-5422	706	22	>	>	X
cana-5422	706	23	0	0	NUM
cana-5422	706	24	.	.	PUNCT
cana-5422	707	1	then	then	ADV
cana-5422	707	2	there	there	PRON
cana-5422	707	3	exists	exist	VERB
cana-5422	707	4	a	a	DET
cana-5422	707	5	unique	unique	ADJ
cana-5422	707	6	additive	additive	ADJ
cana-5422	707	7	mapping	mapping	NOUN
cana-5422	707	8	a(w1	a(w1	NOUN
cana-5422	707	9	)	)	PUNCT
cana-5422	707	10	:	:	PUNCT
cana-5422	707	11	w1	w1	PROPN
cana-5422	707	12	→w2	→w2	NOUN
cana-5422	707	13	which	which	PRON
cana-5422	707	14	satisfies	satisfy	VERB
cana-5422	707	15	(	(	PUNCT
cana-5422	707	16	1.7	1.7	NUM
cana-5422	707	17	)	)	PUNCT
cana-5422	707	18	and	and	CCONJ
cana-5422	707	19	the	the	DET
cana-5422	707	20	functional	functional	ADJ
cana-5422	707	21	inequality	inequality	NOUN
cana-5422	707	22	µ	µ	X
cana-5422	707	23	(	(	PUNCT
cana-5422	707	24	a(w1)−f	a(w1)−f	PROPN
cana-5422	707	25	(	(	PUNCT
cana-5422	707	26	w1	w1	NOUN
cana-5422	707	27	)	)	PUNCT
cana-5422	707	28	,	,	PUNCT
cana-5422	707	29	λ	λ	X
cana-5422	707	30	)	)	PUNCT
cana-5422	707	31	≥	≥	NOUN
cana-5422	707	32	µ′	µ′	PUNCT
cana-5422	707	33	(	(	PUNCT
cana-5422	707	34	l1−v	l1−v	PROPN
cana-5422	707	35	1−	1−	NUM
cana-5422	707	36	l	l	NOUN
cana-5422	707	37	ψa	ψa	PROPN
cana-5422	707	38	(	(	PUNCT
cana-5422	707	39	w1	w1	NOUN
cana-5422	707	40	)	)	PUNCT
cana-5422	707	41	,	,	PUNCT
cana-5422	707	42	3λ	3λ	NUM
cana-5422	707	43	4	4	NUM
cana-5422	707	44	)	)	PUNCT
cana-5422	707	45	=	=	SYM
cana-5422	707	46	µ′	µ′	NOUN
cana-5422	708	1	(	(	PUNCT
cana-5422	708	2	l1−v	l1−v	PROPN
cana-5422	708	3	1−	1−	NUM
cana-5422	708	4	l	l	NOUN
cana-5422	708	5	ψ	ψ	X
cana-5422	708	6	(	(	PUNCT
cana-5422	708	7	w1	w1	NOUN
cana-5422	708	8	,	,	PUNCT
cana-5422	708	9	w1	w1	NOUN
cana-5422	708	10	,	,	PUNCT
cana-5422	708	11	w1	w1	NOUN
cana-5422	708	12	)	)	PUNCT
cana-5422	708	13	,	,	PUNCT
cana-5422	708	14	3λ	3λ	NUM
cana-5422	708	15	4	4	NUM
cana-5422	708	16	)	)	PUNCT
cana-5422	708	17	∗	∗	NOUN
cana-5422	708	18	µ′	µ′	PUNCT
cana-5422	708	19	(	(	PUNCT
cana-5422	708	20	l1−v	l1−v	PROPN
cana-5422	708	21	1−	1−	NUM
cana-5422	708	22	l	l	NOUN
cana-5422	708	23	ψ	ψ	X
cana-5422	708	24	(	(	PUNCT
cana-5422	708	25	w1	w1	NOUN
cana-5422	708	26	,	,	PUNCT
cana-5422	708	27	w1,−w1	w1,−w1	NUM
cana-5422	708	28	)	)	PUNCT
cana-5422	708	29	,	,	PUNCT
cana-5422	708	30	3λ	3λ	NUM
cana-5422	708	31	4	4	NUM
cana-5422	708	32	)	)	PUNCT
cana-5422	708	33	ν	ν	NOUN
cana-5422	708	34	(	(	PUNCT
cana-5422	708	35	a(w1)−f	a(w1)−f	PROPN
cana-5422	708	36	(	(	PUNCT
cana-5422	708	37	w1	w1	NOUN
cana-5422	708	38	)	)	PUNCT
cana-5422	708	39	,	,	PUNCT
cana-5422	708	40	λ	λ	NOUN
cana-5422	708	41	)	)	PUNCT
cana-5422	708	42	≤	≤	NUM
cana-5422	708	43	ν′	ν′	NOUN
cana-5422	708	44	(	(	PUNCT
cana-5422	708	45	l1−v	l1−v	PROPN
cana-5422	708	46	1−	1−	NUM
cana-5422	708	47	l	l	NOUN
cana-5422	708	48	ψa	ψa	PROPN
cana-5422	708	49	(	(	PUNCT
cana-5422	708	50	w1	w1	NOUN
cana-5422	708	51	)	)	PUNCT
cana-5422	708	52	,	,	PUNCT
cana-5422	708	53	3λ	3λ	NUM
cana-5422	708	54	4	4	NUM
cana-5422	708	55	)	)	PUNCT
cana-5422	708	56	=	=	SYM
cana-5422	708	57	ν′	ν′	NOUN
cana-5422	708	58	(	(	PUNCT
cana-5422	708	59	l1−v	l1−v	PROPN
cana-5422	708	60	1−	1−	NUM
cana-5422	708	61	l	l	NOUN
cana-5422	708	62	ψ	ψ	X
cana-5422	708	63	(	(	PUNCT
cana-5422	708	64	w1	w1	NOUN
cana-5422	708	65	,	,	PUNCT
cana-5422	708	66	w1	w1	NOUN
cana-5422	708	67	,	,	PUNCT
cana-5422	708	68	w1	w1	NOUN
cana-5422	708	69	)	)	PUNCT
cana-5422	708	70	,	,	PUNCT
cana-5422	708	71	3λ	3λ	NUM
cana-5422	708	72	4	4	X
cana-5422	708	73	)	)	PUNCT
cana-5422	708	74	�	�	PROPN
cana-5422	708	75	ν′	ν′	NOUN
cana-5422	708	76	(	(	PUNCT
cana-5422	708	77	l1−v	l1−v	PROPN
cana-5422	708	78	1−	1−	NUM
cana-5422	708	79	l	l	NOUN
cana-5422	708	80	ψ	ψ	X
cana-5422	708	81	(	(	PUNCT
cana-5422	708	82	w1	w1	NOUN
cana-5422	708	83	,	,	PUNCT
cana-5422	708	84	w1,−w1	w1,−w1	NUM
cana-5422	708	85	)	)	PUNCT
cana-5422	708	86	,	,	PUNCT
cana-5422	708	87	3λ	3λ	NUM
cana-5422	708	88	4	4	X
cana-5422	708	89	)	)	PUNCT
cana-5422	708	90			NOUN
cana-5422	708	91	(	(	PUNCT
cana-5422	708	92	3.65	3.65	NUM
cana-5422	708	93	)	)	PUNCT
cana-5422	708	94	and	and	CCONJ
cana-5422	708	95	the	the	DET
cana-5422	708	96	mapping	mapping	NOUN
cana-5422	708	97	a(w1	a(w1	NOUN
cana-5422	708	98	)	)	PUNCT
cana-5422	708	99	is	be	AUX
cana-5422	708	100	obtained	obtain	VERB
cana-5422	708	101	by	by	ADP
cana-5422	708	102	lim	lim	PROPN
cana-5422	708	103	`	`	PUNCT
cana-5422	708	104	→∞	→∞	PROPN
cana-5422	708	105	µ	µ	X
cana-5422	708	106	(	(	PUNCT
cana-5422	708	107	1	1	NUM
cana-5422	708	108	τ	τ	PROPN
cana-5422	708	109	`	`	PROPN
cana-5422	708	110	v	v	NOUN
cana-5422	708	111	f	f	PROPN
cana-5422	708	112	(	(	PUNCT
cana-5422	708	113	τ	τ	PROPN
cana-5422	708	114	`	`	PROPN
cana-5422	708	115	v	v	PROPN
cana-5422	708	116	w1	w1	NOUN
cana-5422	708	117	)	)	PUNCT
cana-5422	708	118	−a(w1	−a(w1	PROPN
cana-5422	708	119	)	)	PUNCT
cana-5422	708	120	,	,	PUNCT
cana-5422	708	121	λ	λ	NOUN
cana-5422	708	122	)	)	PUNCT
cana-5422	708	123	=	=	SYM
cana-5422	708	124	1	1	NUM
cana-5422	708	125	lim	lim	NOUN
cana-5422	708	126	`	`	PUNCT
cana-5422	708	127	→∞	→∞	PROPN
cana-5422	708	128	ν	ν	X
cana-5422	708	129	(	(	PUNCT
cana-5422	708	130	1	1	NUM
cana-5422	708	131	τ	τ	PROPN
cana-5422	708	132	`	`	PROPN
cana-5422	708	133	v	v	NOUN
cana-5422	708	134	f	f	PROPN
cana-5422	708	135	(	(	PUNCT
cana-5422	708	136	τ	τ	PROPN
cana-5422	708	137	`	`	PROPN
cana-5422	708	138	v	v	PROPN
cana-5422	708	139	w1	w1	NOUN
cana-5422	708	140	)	)	PUNCT
cana-5422	708	141	−a(w1	−a(w1	PROPN
cana-5422	708	142	)	)	PUNCT
cana-5422	708	143	,	,	PUNCT
cana-5422	708	144	λ	λ	NOUN
cana-5422	708	145	)	)	PUNCT
cana-5422	708	146	=	=	SYM
cana-5422	708	147	0	0	X
cana-5422	709	1			PROPN
cana-5422	709	2	(	(	PUNCT
cana-5422	709	3	3.66	3.66	NUM
cana-5422	709	4	)	)	PUNCT
cana-5422	709	5	for	for	ADP
cana-5422	709	6	all	all	DET
cana-5422	709	7	w1	w1	NOUN
cana-5422	709	8	∈	∈	PROPN
cana-5422	709	9	w1	w1	NOUN
cana-5422	709	10	and	and	CCONJ
cana-5422	709	11	all	all	DET
cana-5422	709	12	λ	λ	PROPN
cana-5422	709	13	>	>	X
cana-5422	709	14	0	0	X
cana-5422	709	15	.	.	PUNCT
cana-5422	709	16	proof	proof	NOUN
cana-5422	709	17	.	.	PUNCT
cana-5422	710	1	assume	assume	VERB
cana-5422	710	2	a	a	DET
cana-5422	710	3	set	set	NOUN
cana-5422	710	4	g	g	NOUN
cana-5422	710	5	as	as	ADP
cana-5422	710	6	in	in	ADP
cana-5422	710	7	theorem	theorem	ADJ
cana-5422	710	8	2.7	2.7	NUM
cana-5422	710	9	of	of	ADP
cana-5422	710	10	(	(	PUNCT
cana-5422	710	11	2.48	2.48	NUM
cana-5422	710	12	)	)	PUNCT
cana-5422	710	13	and	and	CCONJ
cana-5422	710	14	introduce	introduce	VERB
cana-5422	710	15	the	the	DET
cana-5422	710	16	generalized	generalize	VERB
cana-5422	710	17	metric	metric	NOUN
cana-5422	710	18	on	on	ADP
cana-5422	710	19	the	the	DET
cana-5422	710	20	above	above	ADJ
cana-5422	710	21	set	set	VERB
cana-5422	710	22	g	g	NOUN
cana-5422	710	23	as	as	ADP
cana-5422	710	24	d(f	d(f	NOUN
cana-5422	710	25	,	,	PUNCT
cana-5422	710	26	f1	f1	NOUN
cana-5422	710	27	)	)	PUNCT
cana-5422	710	28	=	=	SYM
cana-5422	710	29	inf	inf	NOUN
cana-5422	710	30	{	{	PUNCT
cana-5422	710	31	k	k	PROPN
cana-5422	710	32	∈	∈	PROPN
cana-5422	710	33	(	(	PUNCT
cana-5422	710	34	0	0	NUM
cana-5422	710	35	,	,	PUNCT
cana-5422	710	36	∞	∞	PROPN
cana-5422	710	37	)	)	PUNCT
cana-5422	710	38	:	:	PUNCT
cana-5422	710	39	{	{	PUNCT
cana-5422	710	40	µ	µ	X
cana-5422	710	41	(	(	PUNCT
cana-5422	710	42	f	f	X
cana-5422	710	43	(	(	PUNCT
cana-5422	710	44	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	710	45	)	)	PUNCT
cana-5422	710	46	,	,	PUNCT
cana-5422	710	47	λ	λ	PROPN
cana-5422	710	48	)	)	PUNCT
cana-5422	710	49	≥	≥	PROPN
cana-5422	710	50	µ	µ	X
cana-5422	710	51	(	(	PUNCT
cana-5422	710	52	k	k	PROPN
cana-5422	710	53	ψ(w1	ψ(w1	PROPN
cana-5422	710	54	,	,	PUNCT
cana-5422	710	55	w1	w1	NOUN
cana-5422	710	56	,	,	PUNCT
cana-5422	710	57	w1	w1	NOUN
cana-5422	710	58	)	)	PUNCT
cana-5422	710	59	,	,	PUNCT
cana-5422	710	60	λ	λ	X
cana-5422	710	61	)	)	PUNCT
cana-5422	710	62	ν	ν	NOUN
cana-5422	710	63	(	(	PUNCT
cana-5422	710	64	f	f	X
cana-5422	710	65	(	(	PUNCT
cana-5422	710	66	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	710	67	)	)	PUNCT
cana-5422	710	68	,	,	PUNCT
cana-5422	710	69	λ	λ	NOUN
cana-5422	710	70	)	)	PUNCT
cana-5422	710	71	≤	≤	NUM
cana-5422	710	72	ν	ν	NOUN
cana-5422	710	73	(	(	PUNCT
cana-5422	710	74	k	k	PROPN
cana-5422	710	75	ψ(w1	ψ(w1	PROPN
cana-5422	710	76	,	,	PUNCT
cana-5422	710	77	w1	w1	NOUN
cana-5422	710	78	,	,	PUNCT
cana-5422	710	79	w1	w1	NOUN
cana-5422	710	80	)	)	PUNCT
cana-5422	710	81	,	,	PUNCT
cana-5422	710	82	λ	λ	NOUN
cana-5422	710	83	)	)	PUNCT
cana-5422	710	84	}	}	PUNCT
cana-5422	710	85	}	}	PUNCT
cana-5422	710	86	.	.	PUNCT
cana-5422	711	1	(	(	PUNCT
cana-5422	711	2	3.67	3.67	NUM
cana-5422	711	3	)	)	PUNCT
cana-5422	711	4	communications	communication	NOUN
cana-5422	711	5	on	on	ADP
cana-5422	711	6	applied	apply	VERB
cana-5422	711	7	nonlinear	nonlinear	ADJ
cana-5422	711	8	analysis	analysis	NOUN
cana-5422	711	9	issn	issn	NOUN
cana-5422	711	10	:	:	PUNCT
cana-5422	711	11	1074	1074	NUM
cana-5422	711	12	-	-	PUNCT
cana-5422	711	13	133x	133x	NUM
cana-5422	711	14	vol	vol	NOUN
cana-5422	711	15	32	32	NUM
cana-5422	711	16	no	no	NOUN
cana-5422	711	17	.	.	PUNCT
cana-5422	712	1	10s(2025	10s(2025	NUM
cana-5422	712	2	)	)	PUNCT
cana-5422	713	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	713	2	2212	2212	NUM
cana-5422	713	3	for	for	ADP
cana-5422	713	4	all	all	DET
cana-5422	713	5	w1	w1	NOUN
cana-5422	713	6	∈	∈	PROPN
cana-5422	713	7	w1	w1	NOUN
cana-5422	713	8	and	and	CCONJ
cana-5422	713	9	all	all	DET
cana-5422	713	10	λ	λ	X
cana-5422	713	11	>	>	X
cana-5422	713	12	0	0	X
cana-5422	713	13	.	.	PUNCT
cana-5422	714	1	it	it	PRON
cana-5422	714	2	is	be	AUX
cana-5422	714	3	easy	easy	ADJ
cana-5422	714	4	to	to	PART
cana-5422	714	5	see	see	VERB
cana-5422	714	6	that	that	PRON
cana-5422	714	7	(	(	PUNCT
cana-5422	714	8	g	g	NOUN
cana-5422	714	9	,	,	PUNCT
cana-5422	714	10	d	d	NOUN
cana-5422	714	11	)	)	PUNCT
cana-5422	714	12	is	be	AUX
cana-5422	714	13	complete	complete	ADJ
cana-5422	714	14	.	.	PUNCT
cana-5422	715	1	define	define	VERB
cana-5422	715	2	a	a	DET
cana-5422	715	3	function	function	NOUN
cana-5422	715	4	h	h	NOUN
cana-5422	715	5	:	:	PUNCT
cana-5422	715	6	g	g	NOUN
cana-5422	715	7	→	→	SYM
cana-5422	715	8	g	g	PROPN
cana-5422	715	9	as	as	ADP
cana-5422	715	10	by	by	ADP
cana-5422	715	11	theorem	theorem	ADJ
cana-5422	715	12	2.7	2.7	NUM
cana-5422	715	13	of	of	ADP
cana-5422	715	14	(	(	PUNCT
cana-5422	715	15	2.50	2.50	NUM
cana-5422	715	16	)	)	PUNCT
cana-5422	715	17	and	and	CCONJ
cana-5422	715	18	for	for	ADP
cana-5422	715	19	f	f	PROPN
cana-5422	715	20	,	,	PUNCT
cana-5422	715	21	f1	f1	PROPN
cana-5422	715	22	∈	∈	PROPN
cana-5422	715	23	g	g	NOUN
cana-5422	715	24	and	and	CCONJ
cana-5422	715	25	w1	w1	NOUN
cana-5422	715	26	∈	∈	PROPN
cana-5422	715	27	w1	w1	NOUN
cana-5422	715	28	and	and	CCONJ
cana-5422	715	29	all	all	DET
cana-5422	715	30	λ	λ	PROPN
cana-5422	715	31	>	>	X
cana-5422	715	32	0	0	NUM
cana-5422	715	33	,	,	PUNCT
cana-5422	715	34	we	we	PRON
cana-5422	715	35	see	see	VERB
cana-5422	715	36	d(f	d(f	NOUN
cana-5422	715	37	,	,	PUNCT
cana-5422	715	38	f1	f1	NOUN
cana-5422	715	39	)	)	PUNCT
cana-5422	715	40	≤	≤	PUNCT
cana-5422	716	1	k	k	PROPN
cana-5422	716	2	⇒	⇒	PROPN
cana-5422	716	3	{	{	PUNCT
cana-5422	716	4	µ	µ	X
cana-5422	716	5	(	(	PUNCT
cana-5422	716	6	f	f	X
cana-5422	716	7	(	(	PUNCT
cana-5422	716	8	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	716	9	)	)	PUNCT
cana-5422	716	10	,	,	PUNCT
cana-5422	716	11	λ	λ	PROPN
cana-5422	716	12	)	)	PUNCT
cana-5422	716	13	≥	≥	PROPN
cana-5422	716	14	µ	µ	X
cana-5422	716	15	(	(	PUNCT
cana-5422	716	16	k	k	PROPN
cana-5422	716	17	ψ(w1	ψ(w1	PROPN
cana-5422	716	18	,	,	PUNCT
cana-5422	716	19	w1	w1	NOUN
cana-5422	716	20	,	,	PUNCT
cana-5422	716	21	w1	w1	NOUN
cana-5422	716	22	)	)	PUNCT
cana-5422	716	23	,	,	PUNCT
cana-5422	716	24	λ	λ	X
cana-5422	716	25	)	)	PUNCT
cana-5422	716	26	ν	ν	NOUN
cana-5422	716	27	(	(	PUNCT
cana-5422	716	28	f	f	X
cana-5422	716	29	(	(	PUNCT
cana-5422	716	30	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	716	31	)	)	PUNCT
cana-5422	716	32	,	,	PUNCT
cana-5422	716	33	λ	λ	NOUN
cana-5422	716	34	)	)	PUNCT
cana-5422	716	35	≤	≤	NUM
cana-5422	716	36	ν	ν	NOUN
cana-5422	716	37	(	(	PUNCT
cana-5422	716	38	k	k	PROPN
cana-5422	716	39	ψ(w1	ψ(w1	PROPN
cana-5422	716	40	,	,	PUNCT
cana-5422	716	41	w1	w1	NOUN
cana-5422	716	42	,	,	PUNCT
cana-5422	716	43	w1	w1	NOUN
cana-5422	716	44	)	)	PUNCT
cana-5422	716	45	,	,	PUNCT
cana-5422	716	46	λ	λ	NOUN
cana-5422	716	47	)	)	PUNCT
cana-5422	716	48	}	}	PUNCT
cana-5422	716	49	⇒	⇒	NOUN
cana-5422	716	50			PUNCT
cana-5422	716	51	µ	µ	X
cana-5422	716	52	(	(	PUNCT
cana-5422	716	53	∥∥∥	∥∥∥	PROPN
cana-5422	716	54	1	1	NUM
cana-5422	716	55	τv	τv	ADP
cana-5422	716	56	f	f	PROPN
cana-5422	716	57	(	(	PUNCT
cana-5422	716	58	τvw1)−	τvw1)−	NOUN
cana-5422	716	59	1	1	NUM
cana-5422	716	60	τv	τv	ADP
cana-5422	716	61	f1(τvw1	f1(τvw1	PROPN
cana-5422	716	62	)	)	PUNCT
cana-5422	716	63	∥∥∥	∥∥∥	NOUN
cana-5422	716	64	,	,	PUNCT
cana-5422	716	65	λ	λ	PROPN
cana-5422	716	66	)	)	PUNCT
cana-5422	716	67	≥	≥	PROPN
cana-5422	716	68	µ	µ	X
cana-5422	716	69	(	(	PUNCT
cana-5422	716	70	τvk	τvk	NOUN
cana-5422	716	71	ψ	ψ	X
cana-5422	716	72	(	(	PUNCT
cana-5422	716	73	1	1	NUM
cana-5422	716	74	τv	τv	NOUN
cana-5422	716	75	w1	w1	NOUN
cana-5422	716	76	,	,	PUNCT
cana-5422	716	77	τvw1	τvw1	NOUN
cana-5422	716	78	,	,	PUNCT
cana-5422	716	79	τvw1	τvw1	PROPN
cana-5422	716	80	)	)	PUNCT
cana-5422	716	81	,	,	PUNCT
cana-5422	716	82	λ	λ	X
cana-5422	716	83	)	)	PUNCT
cana-5422	716	84	ν	ν	NOUN
cana-5422	716	85	(	(	PUNCT
cana-5422	716	86	∥∥∥	∥∥∥	PROPN
cana-5422	716	87	1	1	NUM
cana-5422	716	88	τv	τv	ADP
cana-5422	716	89	f	f	PROPN
cana-5422	716	90	(	(	PUNCT
cana-5422	716	91	τvw1)−	τvw1)−	NOUN
cana-5422	716	92	1	1	NUM
cana-5422	716	93	τv	τv	ADP
cana-5422	716	94	f1(τvw1	f1(τvw1	PROPN
cana-5422	716	95	)	)	PUNCT
cana-5422	716	96	∥∥∥	∥∥∥	NOUN
cana-5422	716	97	,	,	PUNCT
cana-5422	716	98	λ	λ	PROPN
cana-5422	716	99	)	)	PUNCT
cana-5422	716	100	≤	≤	NUM
cana-5422	716	101	ν	ν	NOUN
cana-5422	716	102	(	(	PUNCT
cana-5422	716	103	τvk	τvk	NOUN
cana-5422	716	104	ψ	ψ	X
cana-5422	716	105	(	(	PUNCT
cana-5422	716	106	1	1	NUM
cana-5422	716	107	τv	τv	NOUN
cana-5422	716	108	w1	w1	NOUN
cana-5422	716	109	,	,	PUNCT
cana-5422	716	110	τvw1	τvw1	NOUN
cana-5422	716	111	,	,	PUNCT
cana-5422	716	112	τvw1	τvw1	PROPN
cana-5422	716	113	)	)	PUNCT
cana-5422	716	114	,	,	PUNCT
cana-5422	716	115	λ	λ	INTJ
cana-5422	716	116	)	)	PUNCT
cana-5422	717	1			NOUN
cana-5422	717	2	⇒	⇒	NOUN
cana-5422	717	3	{	{	PUNCT
cana-5422	717	4	µ	µ	X
cana-5422	717	5	(	(	PUNCT
cana-5422	717	6	hf	hf	INTJ
cana-5422	717	7	(	(	PUNCT
cana-5422	717	8	w1)−hf1(w1	w1)−hf1(w1	NOUN
cana-5422	717	9	)	)	PUNCT
cana-5422	717	10	,	,	PUNCT
cana-5422	717	11	λ	λ	X
cana-5422	717	12	)	)	PUNCT
cana-5422	717	13	≥	≥	PROPN
cana-5422	717	14	µ	µ	X
cana-5422	717	15	(	(	PUNCT
cana-5422	717	16	l	l	NOUN
cana-5422	717	17	k	k	X
cana-5422	717	18	ψ(w1	ψ(w1	PROPN
cana-5422	717	19	,	,	PUNCT
cana-5422	717	20	w1	w1	NOUN
cana-5422	717	21	,	,	PUNCT
cana-5422	717	22	w1	w1	NOUN
cana-5422	717	23	)	)	PUNCT
cana-5422	717	24	,	,	PUNCT
cana-5422	717	25	λ	λ	X
cana-5422	717	26	)	)	PUNCT
cana-5422	717	27	ν	ν	NOUN
cana-5422	717	28	(	(	PUNCT
cana-5422	717	29	hf	hf	INTJ
cana-5422	717	30	(	(	PUNCT
cana-5422	717	31	w1)−hf1(w1	w1)−hf1(w1	NOUN
cana-5422	717	32	)	)	PUNCT
cana-5422	717	33	,	,	PUNCT
cana-5422	717	34	λ	λ	NOUN
cana-5422	717	35	)	)	PUNCT
cana-5422	717	36	≤	≤	NUM
cana-5422	717	37	ν	ν	NOUN
cana-5422	717	38	(	(	PUNCT
cana-5422	717	39	l	l	X
cana-5422	717	40	k	k	X
cana-5422	717	41	ψ(w1	ψ(w1	PROPN
cana-5422	717	42	,	,	PUNCT
cana-5422	717	43	w1	w1	NOUN
cana-5422	717	44	,	,	PUNCT
cana-5422	717	45	w1	w1	NOUN
cana-5422	717	46	)	)	PUNCT
cana-5422	717	47	,	,	PUNCT
cana-5422	717	48	λ	λ	NOUN
cana-5422	717	49	)	)	PUNCT
cana-5422	717	50	}	}	PUNCT
cana-5422	717	51	⇒d(hf	⇒d(hf	NOUN
cana-5422	717	52	,	,	PUNCT
cana-5422	717	53	hf1	hf1	NOUN
cana-5422	717	54	)	)	PUNCT
cana-5422	717	55	≤	≤	NUM
cana-5422	718	1	l	l	NOUN
cana-5422	719	1	k	k	NOUN
cana-5422	719	2	,	,	PUNCT
cana-5422	719	3	i.e.	i.e.	X
cana-5422	719	4	,h	,h	PUNCT
cana-5422	719	5	is	be	AUX
cana-5422	719	6	a	a	DET
cana-5422	719	7	strictly	strictly	ADV
cana-5422	719	8	contractive	contractive	ADJ
cana-5422	719	9	mapping	mapping	NOUN
cana-5422	719	10	on	on	ADP
cana-5422	719	11	g	g	NOUN
cana-5422	719	12	with	with	ADP
cana-5422	719	13	lipschitz	lipschitz	NOUN
cana-5422	719	14	constant	constant	ADJ
cana-5422	719	15	l	l	NOUN
cana-5422	719	16	(	(	PUNCT
cana-5422	719	17	see	see	VERB
cana-5422	719	18	[	[	X
cana-5422	719	19	18	18	NUM
cana-5422	719	20	]	]	NUM
cana-5422	719	21	)	)	PUNCT
cana-5422	719	22	.	.	PUNCT
cana-5422	720	1	for	for	ADP
cana-5422	720	2	the	the	DET
cana-5422	720	3	case	case	NOUN
cana-5422	720	4	ν	ν	X
cana-5422	720	5	=	=	SYM
cana-5422	720	6	0	0	NUM
cana-5422	720	7	,	,	PUNCT
cana-5422	720	8	it	it	PRON
cana-5422	720	9	follows	follow	VERB
cana-5422	720	10	from	from	ADP
cana-5422	720	11	(	(	PUNCT
cana-5422	720	12	3.16	3.16	NUM
cana-5422	720	13	)	)	PUNCT
cana-5422	720	14	and	and	CCONJ
cana-5422	720	15	with	with	ADP
cana-5422	720	16	the	the	DET
cana-5422	720	17	help	help	NOUN
cana-5422	720	18	of	of	ADP
cana-5422	720	19	(	(	PUNCT
cana-5422	720	20	3.64	3.64	NUM
cana-5422	720	21	)	)	PUNCT
cana-5422	720	22	,	,	PUNCT
cana-5422	720	23	(	(	PUNCT
cana-5422	720	24	2.50	2.50	NUM
cana-5422	720	25	)	)	PUNCT
cana-5422	720	26	,	,	PUNCT
cana-5422	720	27	(	(	PUNCT
cana-5422	720	28	3.67	3.67	NUM
cana-5422	720	29	)	)	PUNCT
cana-5422	720	30	,	,	PUNCT
cana-5422	720	31	we	we	PRON
cana-5422	720	32	get	get	VERB
cana-5422	720	33	µ	µ	X
cana-5422	720	34	(	(	PUNCT
cana-5422	720	35	1	1	NUM
cana-5422	720	36	5	5	NUM
cana-5422	720	37	f	f	NOUN
cana-5422	720	38	(	(	PUNCT
cana-5422	720	39	5w1)−f	5w1)−f	PROPN
cana-5422	720	40	(	(	PUNCT
cana-5422	720	41	w1	w1	NOUN
cana-5422	720	42	)	)	PUNCT
cana-5422	720	43	,	,	PUNCT
cana-5422	720	44	4	4	NUM
cana-5422	720	45	3	3	NUM
cana-5422	720	46	λ	λ	NOUN
cana-5422	720	47	)	)	PUNCT
cana-5422	720	48	≥	≥	NOUN
cana-5422	720	49	µ′	µ′	PUNCT
cana-5422	720	50	(	(	PUNCT
cana-5422	720	51	1	1	NUM
cana-5422	720	52	5	5	NUM
cana-5422	720	53	ψa	ψa	NOUN
cana-5422	720	54	(	(	PUNCT
cana-5422	720	55	w1	w1	NOUN
cana-5422	720	56	)	)	PUNCT
cana-5422	720	57	,	,	PUNCT
cana-5422	720	58	λ	λ	NOUN
cana-5422	720	59	)	)	PUNCT
cana-5422	720	60	ν	ν	NOUN
cana-5422	720	61	(	(	PUNCT
cana-5422	720	62	1	1	NUM
cana-5422	720	63	5	5	NUM
cana-5422	720	64	f	f	NOUN
cana-5422	720	65	(	(	PUNCT
cana-5422	720	66	5w1)−f	5w1)−f	PROPN
cana-5422	720	67	(	(	PUNCT
cana-5422	720	68	w1	w1	NOUN
cana-5422	720	69	)	)	PUNCT
cana-5422	720	70	,	,	PUNCT
cana-5422	720	71	4	4	NUM
cana-5422	720	72	3	3	NUM
cana-5422	720	73	λ	λ	NOUN
cana-5422	720	74	)	)	PUNCT
cana-5422	720	75	≤	≤	NUM
cana-5422	720	76	ν′	ν′	NOUN
cana-5422	720	77	(	(	PUNCT
cana-5422	720	78	1	1	NUM
cana-5422	720	79	5	5	NUM
cana-5422	720	80	ψa	ψa	NOUN
cana-5422	720	81	(	(	PUNCT
cana-5422	720	82	w1	w1	NOUN
cana-5422	720	83	)	)	PUNCT
cana-5422	720	84	,	,	PUNCT
cana-5422	720	85	λ	λ	NOUN
cana-5422	720	86	)	)	PUNCT
cana-5422	720	87	⇒	⇒	NOUN
cana-5422	720	88	d(hf	d(hf	PROPN
cana-5422	720	89	,	,	PUNCT
cana-5422	720	90	f	f	PROPN
cana-5422	720	91	)	)	PUNCT
cana-5422	720	92	≤	≤	NUM
cana-5422	721	1	l	l	NOUN
cana-5422	722	1	=	=	SYM
cana-5422	723	1	l1−v	l1−v	PROPN
cana-5422	723	2	,	,	PUNCT
cana-5422	723	3	(	(	PUNCT
cana-5422	723	4	3.68	3.68	NUM
cana-5422	723	5	)	)	PUNCT
cana-5422	723	6	for	for	ADP
cana-5422	723	7	all	all	DET
cana-5422	723	8	w1	w1	NOUN
cana-5422	723	9	∈	∈	PROPN
cana-5422	723	10	w1	w1	NOUN
cana-5422	723	11	and	and	CCONJ
cana-5422	723	12	all	all	DET
cana-5422	723	13	λ	λ	PROPN
cana-5422	723	14	>	>	X
cana-5422	723	15	0	0	NUM
cana-5422	723	16	.	.	PUNCT
cana-5422	724	1	for	for	ADP
cana-5422	724	2	the	the	DET
cana-5422	724	3	case	case	NOUN
cana-5422	724	4	ν	ν	X
cana-5422	724	5	=	=	SYM
cana-5422	724	6	1	1	NUM
cana-5422	724	7	,	,	PUNCT
cana-5422	724	8	it	it	PRON
cana-5422	724	9	follows	follow	VERB
cana-5422	724	10	from	from	ADP
cana-5422	724	11	(	(	PUNCT
cana-5422	724	12	3.22	3.22	NUM
cana-5422	724	13	)	)	PUNCT
cana-5422	724	14	and	and	CCONJ
cana-5422	724	15	with	with	ADP
cana-5422	724	16	the	the	DET
cana-5422	724	17	help	help	NOUN
cana-5422	724	18	of	of	ADP
cana-5422	724	19	(	(	PUNCT
cana-5422	724	20	3.64	3.64	NUM
cana-5422	724	21	)	)	PUNCT
cana-5422	724	22	,	,	PUNCT
cana-5422	724	23	(	(	PUNCT
cana-5422	724	24	2.50	2.50	NUM
cana-5422	724	25	)	)	PUNCT
cana-5422	724	26	,	,	PUNCT
cana-5422	724	27	(	(	PUNCT
cana-5422	724	28	3.67	3.67	NUM
cana-5422	724	29	)	)	PUNCT
cana-5422	724	30	,	,	PUNCT
cana-5422	724	31	we	we	PRON
cana-5422	724	32	obtain	obtain	VERB
cana-5422	724	33	µ	µ	X
cana-5422	724	34	(	(	PUNCT
cana-5422	724	35	f	f	X
cana-5422	724	36	(	(	PUNCT
cana-5422	724	37	w1)−	w1)−	PROPN
cana-5422	724	38	5f	5f	NOUN
cana-5422	724	39	(	(	PUNCT
cana-5422	724	40	w1	w1	NOUN
cana-5422	724	41	5	5	NUM
cana-5422	724	42	)	)	PUNCT
cana-5422	724	43	,	,	PUNCT
cana-5422	725	1	4	4	NUM
cana-5422	725	2	3	3	NUM
cana-5422	725	3	·	·	PUNCT
cana-5422	725	4	i	i	PRON
cana-5422	725	5	λ	λ	PROPN
cana-5422	725	6	)	)	PUNCT
cana-5422	725	7	≥	≥	NOUN
cana-5422	725	8	µ′	µ′	PUNCT
cana-5422	725	9	(	(	PUNCT
cana-5422	725	10	ψa	ψa	X
cana-5422	725	11	(	(	PUNCT
cana-5422	725	12	w1	w1	NOUN
cana-5422	725	13	5	5	NUM
cana-5422	725	14	)	)	PUNCT
cana-5422	725	15	,	,	PUNCT
cana-5422	725	16	λ	λ	NOUN
cana-5422	725	17	)	)	PUNCT
cana-5422	725	18	ν	ν	PROPN
cana-5422	725	19	(	(	PUNCT
cana-5422	725	20	f	f	X
cana-5422	725	21	(	(	PUNCT
cana-5422	725	22	w1)−	w1)−	PROPN
cana-5422	725	23	5f	5f	NOUN
cana-5422	725	24	(	(	PUNCT
cana-5422	725	25	w1	w1	NOUN
cana-5422	725	26	5	5	NUM
cana-5422	725	27	)	)	PUNCT
cana-5422	725	28	,	,	PUNCT
cana-5422	725	29	4	4	NUM
cana-5422	725	30	3	3	NUM
cana-5422	725	31	·	·	PUNCT
cana-5422	725	32	i	i	PRON
cana-5422	725	33	λ	λ	PROPN
cana-5422	725	34	)	)	PUNCT
cana-5422	725	35	≤	≤	NUM
cana-5422	725	36	ν′	ν′	NOUN
cana-5422	725	37	(	(	PUNCT
cana-5422	725	38	ψa	ψa	X
cana-5422	725	39	(	(	PUNCT
cana-5422	725	40	w1	w1	NOUN
cana-5422	725	41	5	5	NUM
cana-5422	725	42	)	)	PUNCT
cana-5422	725	43	,	,	PUNCT
cana-5422	725	44	λ	λ	NOUN
cana-5422	725	45	)	)	PUNCT
cana-5422	725	46	⇒	⇒	NOUN
cana-5422	725	47	d(f	d(f	NOUN
cana-5422	725	48	,	,	PUNCT
cana-5422	725	49	hf	hf	INTJ
cana-5422	725	50	)	)	PUNCT
cana-5422	725	51	≤	≤	NOUN
cana-5422	725	52	1	1	NUM
cana-5422	725	53	=	=	SYM
cana-5422	725	54	l1−v	l1−v	PROPN
cana-5422	725	55	,	,	PUNCT
cana-5422	725	56	(	(	PUNCT
cana-5422	725	57	3.69	3.69	NUM
cana-5422	725	58	)	)	PUNCT
cana-5422	725	59	for	for	ADP
cana-5422	725	60	all	all	DET
cana-5422	725	61	w1	w1	NOUN
cana-5422	725	62	∈	∈	PROPN
cana-5422	725	63	w1	w1	NOUN
cana-5422	725	64	and	and	CCONJ
cana-5422	725	65	all	all	DET
cana-5422	725	66	λ	λ	PROPN
cana-5422	725	67	>	>	X
cana-5422	725	68	0	0	X
cana-5422	725	69	.	.	PUNCT
cana-5422	726	1	combining	combine	VERB
cana-5422	726	2	(	(	PUNCT
cana-5422	726	3	3.68	3.68	NUM
cana-5422	726	4	)	)	PUNCT
cana-5422	726	5	and	and	CCONJ
cana-5422	726	6	(	(	PUNCT
cana-5422	726	7	3.69	3.69	NUM
cana-5422	726	8	)	)	PUNCT
cana-5422	726	9	,	,	PUNCT
cana-5422	726	10	we	we	PRON
cana-5422	726	11	have	have	VERB
cana-5422	726	12	d(f	d(f	NOUN
cana-5422	726	13	,	,	PUNCT
cana-5422	726	14	hf	hf	INTJ
cana-5422	726	15	)	)	PUNCT
cana-5422	726	16	≤	≤	NOUN
cana-5422	726	17	1	1	NUM
cana-5422	726	18	=	=	SYM
cana-5422	726	19	l1−v	l1−v	PROPN
cana-5422	726	20	.	.	PUNCT
cana-5422	727	1	(	(	PUNCT
cana-5422	727	2	3.70	3.70	NUM
cana-5422	727	3	)	)	PUNCT
cana-5422	727	4	therefore	therefore	ADV
cana-5422	727	5	(	(	PUNCT
cana-5422	727	6	fpc1	fpc1	PROPN
cana-5422	727	7	)	)	PUNCT
cana-5422	727	8	of	of	ADP
cana-5422	727	9	theorem	theorem	ADJ
cana-5422	727	10	1.5	1.5	NUM
cana-5422	727	11	holds	hold	NOUN
cana-5422	727	12	.	.	PUNCT
cana-5422	728	1	the	the	DET
cana-5422	728	2	rest	rest	NOUN
cana-5422	728	3	of	of	ADP
cana-5422	728	4	the	the	DET
cana-5422	728	5	proof	proof	NOUN
cana-5422	728	6	follows	follow	VERB
cana-5422	728	7	by	by	ADP
cana-5422	728	8	theorem	theorem	ADJ
cana-5422	728	9	1.5	1.5	NUM
cana-5422	728	10	.	.	PUNCT
cana-5422	729	1	hence	hence	ADV
cana-5422	729	2	the	the	DET
cana-5422	729	3	proof	proof	NOUN
cana-5422	729	4	is	be	AUX
cana-5422	729	5	complete	complete	ADJ
cana-5422	729	6	.	.	PUNCT
cana-5422	730	1	�	�	PROPN
cana-5422	730	2	corollary	corollary	ADJ
cana-5422	730	3	3.30	3.30	NUM
cana-5422	730	4	.	.	PUNCT
cana-5422	731	1	suppose	suppose	VERB
cana-5422	731	2	that	that	SCONJ
cana-5422	731	3	an	an	DET
cana-5422	731	4	odd	odd	ADJ
cana-5422	731	5	function	function	NOUN
cana-5422	731	6	f	f	NOUN
cana-5422	731	7	:	:	PUNCT
cana-5422	731	8	w1	w1	PROPN
cana-5422	731	9	→	→	SYM
cana-5422	731	10	w2	w2	NOUN
cana-5422	731	11	satisfy	satisfy	VERB
cana-5422	731	12	the	the	DET
cana-5422	731	13	functional	functional	ADJ
cana-5422	731	14	inequalities	inequality	NOUN
cana-5422	731	15	(	(	PUNCT
cana-5422	731	16	3.2	3.2	NUM
cana-5422	731	17	)	)	PUNCT
cana-5422	731	18	,	,	PUNCT
cana-5422	731	19	(	(	PUNCT
cana-5422	731	20	3.3	3.3	NUM
cana-5422	731	21	)	)	PUNCT
cana-5422	731	22	,	,	PUNCT
cana-5422	731	23	(	(	PUNCT
cana-5422	731	24	3.4	3.4	NUM
cana-5422	731	25	)	)	PUNCT
cana-5422	731	26	,	,	PUNCT
cana-5422	731	27	(	(	PUNCT
cana-5422	731	28	3.5	3.5	NUM
cana-5422	731	29	)	)	PUNCT
cana-5422	731	30	,	,	PUNCT
cana-5422	731	31	(	(	PUNCT
cana-5422	731	32	3.6	3.6	NUM
cana-5422	731	33	)	)	PUNCT
cana-5422	731	34	,	,	PUNCT
cana-5422	731	35	(	(	PUNCT
cana-5422	731	36	3.7	3.7	NUM
cana-5422	731	37	)	)	PUNCT
cana-5422	731	38	for	for	ADP
cana-5422	731	39	all	all	DET
cana-5422	731	40	w1	w1	NOUN
cana-5422	731	41	,	,	PUNCT
cana-5422	731	42	w2	w2	NOUN
cana-5422	731	43	,	,	PUNCT
cana-5422	731	44	w3	w3	PROPN
cana-5422	731	45	∈	∈	PROPN
cana-5422	731	46	w1	w1	PROPN
cana-5422	731	47	with	with	SCONJ
cana-5422	731	48	δ	δ	PROPN
cana-5422	731	49	be	be	AUX
cana-5422	731	50	a	a	DET
cana-5422	731	51	positive	positive	ADJ
cana-5422	731	52	constant	constant	NOUN
cana-5422	731	53	and	and	CCONJ
cana-5422	731	54	ϕ	ϕ	NOUN
cana-5422	731	55	be	be	AUX
cana-5422	731	56	any	any	DET
cana-5422	731	57	real	real	ADJ
cana-5422	731	58	number	number	NOUN
cana-5422	731	59	.	.	PUNCT
cana-5422	732	1	then	then	ADV
cana-5422	732	2	there	there	PRON
cana-5422	732	3	exists	exist	VERB
cana-5422	732	4	a	a	DET
cana-5422	732	5	a	a	DET
cana-5422	732	6	unique	unique	ADJ
cana-5422	732	7	additive	additive	ADJ
cana-5422	732	8	mapping	mapping	NOUN
cana-5422	732	9	a(w1	a(w1	NOUN
cana-5422	732	10	)	)	PUNCT
cana-5422	732	11	:	:	PUNCT
cana-5422	732	12	w1	w1	PROPN
cana-5422	732	13	→w2	→w2	NOUN
cana-5422	732	14	which	which	PRON
cana-5422	732	15	satisfies	satisfy	VERB
cana-5422	732	16	(	(	PUNCT
cana-5422	732	17	1.7	1.7	NUM
cana-5422	732	18	)	)	PUNCT
cana-5422	732	19	and	and	CCONJ
cana-5422	732	20	the	the	DET
cana-5422	732	21	functional	functional	ADJ
cana-5422	732	22	inequalities	inequality	NOUN
cana-5422	732	23	(	(	PUNCT
cana-5422	732	24	3.33	3.33	NUM
cana-5422	732	25	)	)	PUNCT
cana-5422	732	26	,	,	PUNCT
cana-5422	732	27	(	(	PUNCT
cana-5422	732	28	3.34	3.34	NUM
cana-5422	732	29	)	)	PUNCT
cana-5422	732	30	,	,	PUNCT
cana-5422	732	31	(	(	PUNCT
cana-5422	732	32	3.35	3.35	NUM
cana-5422	732	33	)	)	PUNCT
cana-5422	732	34	,	,	PUNCT
cana-5422	732	35	(	(	PUNCT
cana-5422	732	36	3.36	3.36	NUM
cana-5422	732	37	)	)	PUNCT
cana-5422	732	38	,	,	PUNCT
cana-5422	732	39	(	(	PUNCT
cana-5422	732	40	3.37	3.37	NUM
cana-5422	732	41	)	)	PUNCT
cana-5422	732	42	,	,	PUNCT
cana-5422	732	43	(	(	PUNCT
cana-5422	732	44	3.38	3.38	NUM
cana-5422	732	45	)	)	PUNCT
cana-5422	732	46	,	,	PUNCT
cana-5422	732	47	respectively	respectively	ADV
cana-5422	732	48	for	for	ADP
cana-5422	732	49	all	all	DET
cana-5422	732	50	w1	w1	NOUN
cana-5422	732	51	∈	∈	PROPN
cana-5422	732	52	w1	w1	NOUN
cana-5422	732	53	.	.	PUNCT
cana-5422	733	1	3.6	3.6	NUM
cana-5422	733	2	.	.	PUNCT
cana-5422	733	3	evenness	evenness	NOUN
cana-5422	733	4	of	of	ADP
cana-5422	733	5	f	f	PROPN
cana-5422	733	6	:	:	PUNCT
cana-5422	733	7	quadratic	quadratic	ADJ
cana-5422	733	8	case	case	NOUN
cana-5422	733	9	stability	stability	NOUN
cana-5422	733	10	results	result	VERB
cana-5422	733	11	:	:	PUNCT
cana-5422	733	12	fixed	fixed	ADJ
cana-5422	733	13	point	point	NOUN
cana-5422	733	14	method	method	NOUN
cana-5422	733	15	.	.	PUNCT
cana-5422	734	1	theorem	theorem	VERB
cana-5422	734	2	3.31	3.31	NUM
cana-5422	734	3	.	.	PUNCT
cana-5422	735	1	suppose	suppose	VERB
cana-5422	735	2	that	that	SCONJ
cana-5422	735	3	an	an	DET
cana-5422	735	4	even	even	ADV
cana-5422	735	5	function	function	NOUN
cana-5422	735	6	f	f	PROPN
cana-5422	735	7	:	:	PUNCT
cana-5422	735	8	w1	w1	PROPN
cana-5422	735	9	→	→	SYM
cana-5422	735	10	w2	w2	NOUN
cana-5422	735	11	satisfy	satisfy	VERB
cana-5422	735	12	the	the	DET
cana-5422	735	13	functional	functional	ADJ
cana-5422	735	14	inequality	inequality	NOUN
cana-5422	735	15	(	(	PUNCT
cana-5422	735	16	3.1	3.1	NUM
cana-5422	735	17	)	)	PUNCT
cana-5422	735	18	where	where	SCONJ
cana-5422	735	19	ψ	ψ	X
cana-5422	735	20	:	:	PUNCT
cana-5422	735	21	w3	w3	NOUN
cana-5422	735	22	1	1	NUM
cana-5422	735	23	→	→	SYM
cana-5422	736	1	[	[	X
cana-5422	736	2	0	0	NUM
cana-5422	736	3	,	,	PUNCT
cana-5422	736	4	∞	∞	PROPN
cana-5422	736	5	)	)	PUNCT
cana-5422	736	6	with	with	ADP
cana-5422	736	7	the	the	DET
cana-5422	736	8	condition	condition	NOUN
cana-5422	736	9	lim	lim	NOUN
cana-5422	736	10	`	`	PUNCT
cana-5422	736	11	→∞	→∞	X
cana-5422	736	12	µ′	µ′	PUNCT
cana-5422	736	13	(	(	PUNCT
cana-5422	736	14	ψ	ψ	X
cana-5422	736	15	(	(	PUNCT
cana-5422	736	16	τ	τ	PROPN
cana-5422	736	17	`	`	PUNCT
cana-5422	736	18	v	v	PROPN
cana-5422	736	19	w1	w1	NOUN
cana-5422	736	20	,	,	PUNCT
cana-5422	736	21	τ	τ	PROPN
cana-5422	736	22	`	`	PUNCT
cana-5422	736	23	v	v	PROPN
cana-5422	736	24	w2	w2	NOUN
cana-5422	736	25	,	,	PUNCT
cana-5422	736	26	τ	τ	PROPN
cana-5422	736	27	`	`	PROPN
cana-5422	736	28	v	v	PROPN
cana-5422	736	29	w3	w3	PROPN
cana-5422	736	30	)	)	PUNCT
cana-5422	736	31	,	,	PUNCT
cana-5422	736	32	τ2	τ2	PROPN
cana-5422	736	33	`	`	PUNCT
cana-5422	736	34	v	v	NUM
cana-5422	736	35	λ	λ	NOUN
cana-5422	736	36	)	)	PUNCT
cana-5422	736	37	=	=	SYM
cana-5422	736	38	1	1	NUM
cana-5422	736	39	lim	lim	NOUN
cana-5422	736	40	`	`	PUNCT
cana-5422	736	41	→∞	→∞	X
cana-5422	736	42	ν′	ν′	NOUN
cana-5422	736	43	(	(	PUNCT
cana-5422	736	44	ψ	ψ	X
cana-5422	736	45	(	(	PUNCT
cana-5422	736	46	τ	τ	PROPN
cana-5422	736	47	`	`	PUNCT
cana-5422	736	48	v	v	PROPN
cana-5422	736	49	w1	w1	NOUN
cana-5422	736	50	,	,	PUNCT
cana-5422	736	51	τ	τ	PROPN
cana-5422	736	52	`	`	PUNCT
cana-5422	736	53	v	v	PROPN
cana-5422	736	54	w2	w2	NOUN
cana-5422	736	55	,	,	PUNCT
cana-5422	736	56	τ	τ	PROPN
cana-5422	736	57	`	`	PROPN
cana-5422	736	58	v	v	PROPN
cana-5422	736	59	w3	w3	PROPN
cana-5422	736	60	)	)	PUNCT
cana-5422	736	61	,	,	PUNCT
cana-5422	736	62	τ2	τ2	PROPN
cana-5422	736	63	`	`	PUNCT
cana-5422	736	64	v	v	NUM
cana-5422	736	65	λ	λ	NOUN
cana-5422	736	66	)	)	PUNCT
cana-5422	736	67	=	=	SYM
cana-5422	736	68	0	0	NUM
cana-5422	737	1			NOUN
cana-5422	737	2	;	;	PUNCT
cana-5422	737	3	τv	τv	X
cana-5422	737	4	=	=	PRON
cana-5422	737	5	{	{	PUNCT
cana-5422	737	6	5	5	NUM
cana-5422	737	7	;	;	PUNCT
cana-5422	737	8	v	v	NOUN
cana-5422	737	9	=	=	SYM
cana-5422	737	10	0	0	NUM
cana-5422	737	11	;	;	PUNCT
cana-5422	737	12	1	1	NUM
cana-5422	737	13	5	5	NUM
cana-5422	737	14	;	;	PUNCT
cana-5422	737	15	v	v	NOUN
cana-5422	737	16	=	=	SYM
cana-5422	737	17	1	1	NUM
cana-5422	737	18	;	;	PUNCT
cana-5422	737	19	(	(	PUNCT
cana-5422	737	20	3.71	3.71	NUM
cana-5422	737	21	)	)	PUNCT
cana-5422	737	22	for	for	ADP
cana-5422	737	23	all	all	DET
cana-5422	737	24	w1	w1	NOUN
cana-5422	737	25	,	,	PUNCT
cana-5422	737	26	w2	w2	NOUN
cana-5422	737	27	,	,	PUNCT
cana-5422	737	28	w3	w3	PROPN
cana-5422	737	29	∈	∈	PROPN
cana-5422	737	30	w1	w1	NOUN
cana-5422	737	31	and	and	CCONJ
cana-5422	737	32	all	all	DET
cana-5422	737	33	λ	λ	X
cana-5422	737	34	>	>	X
cana-5422	737	35	0	0	X
cana-5422	737	36	.	.	PUNCT
cana-5422	738	1	if	if	SCONJ
cana-5422	738	2	there	there	PRON
cana-5422	738	3	exists	exist	VERB
cana-5422	738	4	l	l	NOUN
cana-5422	738	5	=	=	SYM
cana-5422	738	6	l(ν	l(ν	PROPN
cana-5422	738	7	)	)	PUNCT
cana-5422	738	8	be	be	VERB
cana-5422	738	9	function	function	NOUN
cana-5422	738	10	have	have	VERB
cana-5422	738	11	the	the	DET
cana-5422	738	12	property	property	NOUN
cana-5422	738	13	µ	µ	X
cana-5422	738	14	(	(	PUNCT
cana-5422	738	15	ψq(w1	ψq(w1	NOUN
cana-5422	738	16	)	)	PUNCT
cana-5422	738	17	,	,	PUNCT
cana-5422	738	18	λ	λ	NOUN
cana-5422	738	19	)	)	PUNCT
cana-5422	738	20	=	=	SYM
cana-5422	738	21	µ	µ	X
cana-5422	738	22	(	(	PUNCT
cana-5422	738	23	ψq	ψq	PROPN
cana-5422	738	24	(	(	PUNCT
cana-5422	738	25	w1	w1	NOUN
cana-5422	738	26	5	5	NUM
cana-5422	738	27	)	)	PUNCT
cana-5422	738	28	,	,	PUNCT
cana-5422	738	29	λ	λ	NOUN
cana-5422	738	30	)	)	PUNCT
cana-5422	738	31	ν	ν	NOUN
cana-5422	738	32	(	(	PUNCT
cana-5422	738	33	ψq(w1	ψq(w1	NOUN
cana-5422	738	34	)	)	PUNCT
cana-5422	738	35	,	,	PUNCT
cana-5422	738	36	λ	λ	NOUN
cana-5422	738	37	)	)	PUNCT
cana-5422	739	1	=	=	PUNCT
cana-5422	739	2	ν	ν	NOUN
cana-5422	739	3	(	(	PUNCT
cana-5422	739	4	ψq	ψq	PROPN
cana-5422	739	5	(	(	PUNCT
cana-5422	739	6	w1	w1	NOUN
cana-5422	739	7	5	5	NUM
cana-5422	739	8	)	)	PUNCT
cana-5422	739	9	,	,	PUNCT
cana-5422	739	10	λ	λ	PROPN
cana-5422	739	11	)	)	PUNCT
cana-5422	739	12	}	}	PUNCT
cana-5422	739	13	and	and	CCONJ
cana-5422	739	14	µ	µ	X
cana-5422	739	15	(	(	PUNCT
cana-5422	739	16	1	1	NUM
cana-5422	739	17	τ2	τ2	NOUN
cana-5422	739	18	v	v	NOUN
cana-5422	739	19	ψq	ψq	PROPN
cana-5422	739	20	(	(	PUNCT
cana-5422	739	21	τvw1	τvw1	PROPN
cana-5422	739	22	)	)	PUNCT
cana-5422	739	23	,	,	PUNCT
cana-5422	739	24	λ	λ	INTJ
cana-5422	739	25	)	)	PUNCT
cana-5422	739	26	=	=	SYM
cana-5422	740	1	µ	µ	X
cana-5422	740	2	(	(	PUNCT
cana-5422	740	3	l	l	NOUN
cana-5422	740	4	ψq(w1	ψq(w1	NOUN
cana-5422	740	5	)	)	PUNCT
cana-5422	740	6	,	,	PUNCT
cana-5422	740	7	λ	λ	NOUN
cana-5422	740	8	)	)	PUNCT
cana-5422	740	9	ν	ν	NOUN
cana-5422	740	10	(	(	PUNCT
cana-5422	740	11	1	1	NUM
cana-5422	740	12	τ2	τ2	NOUN
cana-5422	740	13	v	v	NOUN
cana-5422	740	14	ψq	ψq	PROPN
cana-5422	740	15	(	(	PUNCT
cana-5422	740	16	τvw1	τvw1	PROPN
cana-5422	740	17	)	)	PUNCT
cana-5422	740	18	,	,	PUNCT
cana-5422	740	19	λ	λ	NOUN
cana-5422	740	20	)	)	PUNCT
cana-5422	740	21	=	=	PUNCT
cana-5422	741	1	ν	ν	NOUN
cana-5422	741	2	(	(	PUNCT
cana-5422	741	3	l	l	NOUN
cana-5422	741	4	ψq(w1	ψq(w1	NOUN
cana-5422	741	5	)	)	PUNCT
cana-5422	741	6	,	,	PUNCT
cana-5422	741	7	λ	λ	INTJ
cana-5422	741	8	)	)	PUNCT
cana-5422	741	9			NOUN
cana-5422	741	10	,	,	PUNCT
cana-5422	741	11	(	(	PUNCT
cana-5422	741	12	3.72	3.72	NUM
cana-5422	741	13	)	)	PUNCT
cana-5422	741	14	communications	communication	NOUN
cana-5422	741	15	on	on	ADP
cana-5422	741	16	applied	apply	VERB
cana-5422	741	17	nonlinear	nonlinear	ADJ
cana-5422	741	18	analysis	analysis	NOUN
cana-5422	741	19	issn	issn	NOUN
cana-5422	741	20	:	:	PUNCT
cana-5422	741	21	1074	1074	NUM
cana-5422	741	22	-	-	PUNCT
cana-5422	741	23	133x	133x	NUM
cana-5422	741	24	vol	vol	NOUN
cana-5422	741	25	32	32	NUM
cana-5422	741	26	no	no	NOUN
cana-5422	741	27	.	.	PUNCT
cana-5422	742	1	10s(2025	10s(2025	NUM
cana-5422	742	2	)	)	PUNCT
cana-5422	743	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	743	2	2213	2213	NUM
cana-5422	743	3	for	for	ADP
cana-5422	743	4	all	all	DET
cana-5422	743	5	w1	w1	NOUN
cana-5422	743	6	∈	∈	PROPN
cana-5422	743	7	w1	w1	NOUN
cana-5422	743	8	and	and	CCONJ
cana-5422	743	9	all	all	DET
cana-5422	743	10	λ	λ	X
cana-5422	743	11	>	>	X
cana-5422	743	12	0	0	NUM
cana-5422	743	13	.	.	PUNCT
cana-5422	744	1	then	then	ADV
cana-5422	744	2	there	there	PRON
cana-5422	744	3	exists	exist	VERB
cana-5422	744	4	a	a	DET
cana-5422	744	5	unique	unique	ADJ
cana-5422	744	6	quadratic	quadratic	ADJ
cana-5422	744	7	mapping	mapping	NOUN
cana-5422	744	8	q(w1	q(w1	NOUN
cana-5422	744	9	)	)	PUNCT
cana-5422	744	10	:	:	PUNCT
cana-5422	744	11	w1	w1	NOUN
cana-5422	744	12	→	→	SYM
cana-5422	744	13	w2	w2	NOUN
cana-5422	744	14	which	which	PRON
cana-5422	744	15	satisfies	satisfy	VERB
cana-5422	744	16	(	(	PUNCT
cana-5422	744	17	1.7	1.7	NUM
cana-5422	744	18	)	)	PUNCT
cana-5422	744	19	and	and	CCONJ
cana-5422	744	20	the	the	DET
cana-5422	744	21	functional	functional	ADJ
cana-5422	744	22	inequality	inequality	NOUN
cana-5422	744	23	µ	µ	X
cana-5422	744	24	(	(	PUNCT
cana-5422	744	25	q(w1)−f	q(w1)−f	PROPN
cana-5422	744	26	(	(	PUNCT
cana-5422	744	27	w1	w1	NOUN
cana-5422	744	28	)	)	PUNCT
cana-5422	744	29	,	,	PUNCT
cana-5422	744	30	λ	λ	X
cana-5422	744	31	)	)	PUNCT
cana-5422	744	32	≥	≥	NOUN
cana-5422	744	33	µ′	µ′	PUNCT
cana-5422	745	1	(	(	PUNCT
cana-5422	745	2	l1−v	l1−v	PROPN
cana-5422	745	3	1−	1−	NUM
cana-5422	745	4	l	l	NOUN
cana-5422	745	5	ψq	ψq	PROPN
cana-5422	745	6	(	(	PUNCT
cana-5422	745	7	w1	w1	NOUN
cana-5422	745	8	)	)	PUNCT
cana-5422	745	9	,	,	PUNCT
cana-5422	745	10	7λ	7λ	NUM
cana-5422	745	11	3	3	NUM
cana-5422	745	12	)	)	PUNCT
cana-5422	745	13	=	=	SYM
cana-5422	745	14	µ′	µ′	NOUN
cana-5422	745	15	(	(	PUNCT
cana-5422	745	16	l1−v	l1−v	PROPN
cana-5422	745	17	1−	1−	NUM
cana-5422	745	18	l	l	NOUN
cana-5422	745	19	ψ	ψ	X
cana-5422	745	20	(	(	PUNCT
cana-5422	745	21	w1	w1	NOUN
cana-5422	745	22	,	,	PUNCT
cana-5422	745	23	w1	w1	NOUN
cana-5422	745	24	,	,	PUNCT
cana-5422	745	25	w1	w1	NOUN
cana-5422	745	26	)	)	PUNCT
cana-5422	745	27	,	,	PUNCT
cana-5422	745	28	7λ	7λ	NUM
cana-5422	745	29	3	3	NUM
cana-5422	745	30	)	)	PUNCT
cana-5422	745	31	∗	∗	NOUN
cana-5422	745	32	µ′	µ′	PUNCT
cana-5422	745	33	(	(	PUNCT
cana-5422	745	34	l1−v	l1−v	PROPN
cana-5422	745	35	1−	1−	NUM
cana-5422	745	36	l	l	NOUN
cana-5422	745	37	ψ	ψ	X
cana-5422	745	38	(	(	PUNCT
cana-5422	745	39	w1	w1	NOUN
cana-5422	745	40	,	,	PUNCT
cana-5422	745	41	w1,−w1	w1,−w1	NUM
cana-5422	745	42	)	)	PUNCT
cana-5422	745	43	,	,	PUNCT
cana-5422	745	44	7λ	7λ	NUM
cana-5422	745	45	3	3	X
cana-5422	745	46	)	)	PUNCT
cana-5422	745	47	ν	ν	NOUN
cana-5422	745	48	(	(	PUNCT
cana-5422	745	49	q(w1)−f	q(w1)−f	PROPN
cana-5422	745	50	(	(	PUNCT
cana-5422	745	51	w1	w1	NOUN
cana-5422	745	52	)	)	PUNCT
cana-5422	745	53	,	,	PUNCT
cana-5422	745	54	λ	λ	NOUN
cana-5422	745	55	)	)	PUNCT
cana-5422	745	56	≤	≤	NUM
cana-5422	745	57	ν′	ν′	NOUN
cana-5422	745	58	(	(	PUNCT
cana-5422	745	59	l1−v	l1−v	PROPN
cana-5422	745	60	1−	1−	NUM
cana-5422	745	61	l	l	NOUN
cana-5422	745	62	ψq	ψq	PROPN
cana-5422	745	63	(	(	PUNCT
cana-5422	745	64	w1	w1	NOUN
cana-5422	745	65	)	)	PUNCT
cana-5422	745	66	,	,	PUNCT
cana-5422	745	67	7λ	7λ	NUM
cana-5422	745	68	3	3	X
cana-5422	745	69	)	)	PUNCT
cana-5422	745	70	=	=	SYM
cana-5422	745	71	ν′	ν′	NOUN
cana-5422	745	72	(	(	PUNCT
cana-5422	745	73	l1−v	l1−v	PROPN
cana-5422	745	74	1−	1−	NUM
cana-5422	745	75	l	l	NOUN
cana-5422	745	76	ψ	ψ	X
cana-5422	745	77	(	(	PUNCT
cana-5422	745	78	w1	w1	NOUN
cana-5422	745	79	,	,	PUNCT
cana-5422	745	80	w1	w1	NOUN
cana-5422	745	81	,	,	PUNCT
cana-5422	745	82	w1	w1	NOUN
cana-5422	745	83	)	)	PUNCT
cana-5422	745	84	,	,	PUNCT
cana-5422	745	85	7λ	7λ	NUM
cana-5422	745	86	3	3	X
cana-5422	745	87	)	)	PUNCT
cana-5422	745	88	�	�	PROPN
cana-5422	745	89	ν′	ν′	NOUN
cana-5422	745	90	(	(	PUNCT
cana-5422	745	91	l1−v	l1−v	PROPN
cana-5422	745	92	1−	1−	NUM
cana-5422	745	93	l	l	NOUN
cana-5422	745	94	ψ	ψ	X
cana-5422	745	95	(	(	PUNCT
cana-5422	745	96	w1	w1	NOUN
cana-5422	745	97	,	,	PUNCT
cana-5422	745	98	w1,−w1	w1,−w1	NUM
cana-5422	745	99	)	)	PUNCT
cana-5422	745	100	,	,	PUNCT
cana-5422	745	101	7λ	7λ	NUM
cana-5422	745	102	3	3	X
cana-5422	745	103	)	)	PUNCT
cana-5422	745	104			NOUN
cana-5422	745	105	(	(	PUNCT
cana-5422	745	106	3.73	3.73	NUM
cana-5422	745	107	)	)	PUNCT
cana-5422	745	108	and	and	CCONJ
cana-5422	745	109	the	the	DET
cana-5422	745	110	mapping	mapping	NOUN
cana-5422	745	111	q(w1	q(w1	NOUN
cana-5422	745	112	)	)	PUNCT
cana-5422	745	113	is	be	AUX
cana-5422	745	114	obtained	obtain	VERB
cana-5422	745	115	by	by	ADP
cana-5422	745	116	lim	lim	PROPN
cana-5422	745	117	`	`	PUNCT
cana-5422	745	118	→∞	→∞	PROPN
cana-5422	745	119	µ	µ	X
cana-5422	745	120	(	(	PUNCT
cana-5422	745	121	1	1	NUM
cana-5422	745	122	τ2	τ2	PROPN
cana-5422	745	123	`	`	PUNCT
cana-5422	745	124	v	v	NOUN
cana-5422	745	125	f	f	PROPN
cana-5422	745	126	(	(	PUNCT
cana-5422	745	127	τ	τ	PROPN
cana-5422	745	128	`	`	PROPN
cana-5422	745	129	v	v	PROPN
cana-5422	745	130	w1	w1	NOUN
cana-5422	745	131	)	)	PUNCT
cana-5422	745	132	−q(w1	−q(w1	PROPN
cana-5422	745	133	)	)	PUNCT
cana-5422	745	134	,	,	PUNCT
cana-5422	745	135	λ	λ	NOUN
cana-5422	745	136	)	)	PUNCT
cana-5422	745	137	=	=	SYM
cana-5422	745	138	1	1	NUM
cana-5422	745	139	lim	lim	NOUN
cana-5422	745	140	`	`	PUNCT
cana-5422	745	141	→∞	→∞	PROPN
cana-5422	745	142	ν	ν	X
cana-5422	745	143	(	(	PUNCT
cana-5422	745	144	1	1	NUM
cana-5422	745	145	τ2	τ2	PROPN
cana-5422	745	146	`	`	PUNCT
cana-5422	745	147	v	v	NOUN
cana-5422	745	148	f	f	PROPN
cana-5422	745	149	(	(	PUNCT
cana-5422	745	150	τ	τ	PROPN
cana-5422	745	151	`	`	PROPN
cana-5422	745	152	v	v	PROPN
cana-5422	745	153	w1	w1	NOUN
cana-5422	745	154	)	)	PUNCT
cana-5422	745	155	−q(w1	−q(w1	PROPN
cana-5422	745	156	)	)	PUNCT
cana-5422	745	157	,	,	PUNCT
cana-5422	745	158	λ	λ	NOUN
cana-5422	745	159	)	)	PUNCT
cana-5422	746	1	=	=	SYM
cana-5422	746	2	0	0	X
cana-5422	747	1			PROPN
cana-5422	747	2	(	(	PUNCT
cana-5422	747	3	3.74	3.74	NUM
cana-5422	747	4	)	)	PUNCT
cana-5422	747	5	for	for	ADP
cana-5422	747	6	all	all	DET
cana-5422	747	7	w1	w1	NOUN
cana-5422	747	8	∈	∈	PROPN
cana-5422	747	9	w1	w1	NOUN
cana-5422	747	10	and	and	CCONJ
cana-5422	747	11	all	all	DET
cana-5422	747	12	λ	λ	PROPN
cana-5422	747	13	>	>	X
cana-5422	747	14	0	0	X
cana-5422	747	15	.	.	PUNCT
cana-5422	748	1	proof	proof	NOUN
cana-5422	748	2	.	.	PUNCT
cana-5422	749	1	define	define	VERB
cana-5422	749	2	a	a	DET
cana-5422	749	3	function	function	NOUN
cana-5422	749	4	h	h	NOUN
cana-5422	749	5	:	:	PUNCT
cana-5422	749	6	g	g	NOUN
cana-5422	749	7	→	→	SYM
cana-5422	749	8	g	g	PROPN
cana-5422	749	9	as	as	ADP
cana-5422	749	10	by	by	ADP
cana-5422	749	11	theorem	theorem	ADJ
cana-5422	749	12	2.9	2.9	NUM
cana-5422	749	13	of	of	ADP
cana-5422	749	14	(	(	PUNCT
cana-5422	749	15	2.62	2.62	NUM
cana-5422	749	16	)	)	PUNCT
cana-5422	749	17	and	and	CCONJ
cana-5422	749	18	for	for	ADP
cana-5422	749	19	f	f	PROPN
cana-5422	749	20	,	,	PUNCT
cana-5422	749	21	f1	f1	PROPN
cana-5422	749	22	∈	∈	PROPN
cana-5422	749	23	g	g	NOUN
cana-5422	749	24	and	and	CCONJ
cana-5422	749	25	w1	w1	NOUN
cana-5422	749	26	∈	∈	PROPN
cana-5422	749	27	w1	w1	NOUN
cana-5422	749	28	and	and	CCONJ
cana-5422	749	29	all	all	DET
cana-5422	749	30	λ	λ	PROPN
cana-5422	749	31	>	>	X
cana-5422	749	32	0	0	NUM
cana-5422	749	33	,	,	PUNCT
cana-5422	749	34	we	we	PRON
cana-5422	749	35	see	see	VERB
cana-5422	749	36	d(f	d(f	NOUN
cana-5422	749	37	,	,	PUNCT
cana-5422	749	38	f1	f1	NOUN
cana-5422	749	39	)	)	PUNCT
cana-5422	749	40	≤	≤	PUNCT
cana-5422	750	1	k	k	PROPN
cana-5422	750	2	⇒	⇒	PROPN
cana-5422	750	3	{	{	PUNCT
cana-5422	750	4	µ	µ	X
cana-5422	750	5	(	(	PUNCT
cana-5422	750	6	f	f	X
cana-5422	750	7	(	(	PUNCT
cana-5422	750	8	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	750	9	)	)	PUNCT
cana-5422	750	10	,	,	PUNCT
cana-5422	750	11	λ	λ	PROPN
cana-5422	750	12	)	)	PUNCT
cana-5422	750	13	≥	≥	PROPN
cana-5422	750	14	µ	µ	X
cana-5422	750	15	(	(	PUNCT
cana-5422	750	16	k	k	PROPN
cana-5422	750	17	ψ(w1	ψ(w1	PROPN
cana-5422	750	18	,	,	PUNCT
cana-5422	750	19	w1	w1	NOUN
cana-5422	750	20	,	,	PUNCT
cana-5422	750	21	w1	w1	NOUN
cana-5422	750	22	)	)	PUNCT
cana-5422	750	23	,	,	PUNCT
cana-5422	750	24	λ	λ	X
cana-5422	750	25	)	)	PUNCT
cana-5422	750	26	ν	ν	NOUN
cana-5422	750	27	(	(	PUNCT
cana-5422	750	28	f	f	X
cana-5422	750	29	(	(	PUNCT
cana-5422	750	30	w1)−f1(w1	w1)−f1(w1	PROPN
cana-5422	750	31	)	)	PUNCT
cana-5422	750	32	,	,	PUNCT
cana-5422	750	33	λ	λ	NOUN
cana-5422	750	34	)	)	PUNCT
cana-5422	750	35	≤	≤	NUM
cana-5422	750	36	ν	ν	NOUN
cana-5422	750	37	(	(	PUNCT
cana-5422	750	38	k	k	PROPN
cana-5422	750	39	ψ(w1	ψ(w1	PROPN
cana-5422	750	40	,	,	PUNCT
cana-5422	750	41	w1	w1	NOUN
cana-5422	750	42	,	,	PUNCT
cana-5422	750	43	w1	w1	NOUN
cana-5422	750	44	)	)	PUNCT
cana-5422	750	45	,	,	PUNCT
cana-5422	750	46	λ	λ	NOUN
cana-5422	750	47	)	)	PUNCT
cana-5422	750	48	}	}	PUNCT
cana-5422	750	49	⇒	⇒	NOUN
cana-5422	750	50			PUNCT
cana-5422	750	51	µ	µ	X
cana-5422	750	52	(	(	PUNCT
cana-5422	750	53	∥∥∥	∥∥∥	PROPN
cana-5422	750	54	1	1	NUM
cana-5422	750	55	τ2	τ2	PROPN
cana-5422	750	56	v	v	NOUN
cana-5422	750	57	f	f	NOUN
cana-5422	750	58	(	(	PUNCT
cana-5422	750	59	τvw1)−	τvw1)−	PROPN
cana-5422	750	60	1	1	NUM
cana-5422	750	61	τ2	τ2	PROPN
cana-5422	750	62	v	v	ADP
cana-5422	750	63	f1(τvw1	f1(τvw1	NOUN
cana-5422	750	64	)	)	PUNCT
cana-5422	750	65	∥∥∥	∥∥∥	NOUN
cana-5422	750	66	,	,	PUNCT
cana-5422	750	67	λ	λ	PROPN
cana-5422	750	68	)	)	PUNCT
cana-5422	750	69	≥	≥	PROPN
cana-5422	750	70	µ	µ	X
cana-5422	750	71	(	(	PUNCT
cana-5422	750	72	τvk	τvk	X
cana-5422	750	73	ψ(τvw1	ψ(τvw1	NOUN
cana-5422	750	74	,	,	PUNCT
cana-5422	750	75	τvw1	τvw1	NOUN
cana-5422	750	76	,	,	PUNCT
cana-5422	750	77	τvw1	τvw1	PROPN
cana-5422	750	78	)	)	PUNCT
cana-5422	750	79	,	,	PUNCT
cana-5422	750	80	λ	λ	X
cana-5422	750	81	)	)	PUNCT
cana-5422	750	82	ν	ν	NOUN
cana-5422	750	83	(	(	PUNCT
cana-5422	750	84	∥∥∥	∥∥∥	PROPN
cana-5422	750	85	1	1	NUM
cana-5422	750	86	τ2	τ2	PROPN
cana-5422	750	87	v	v	NOUN
cana-5422	750	88	f	f	NOUN
cana-5422	750	89	(	(	PUNCT
cana-5422	750	90	τvw1)−	τvw1)−	PROPN
cana-5422	750	91	1	1	NUM
cana-5422	750	92	τ2	τ2	PROPN
cana-5422	750	93	v	v	ADP
cana-5422	750	94	f1(τvw1	f1(τvw1	NOUN
cana-5422	750	95	)	)	PUNCT
cana-5422	750	96	∥∥∥	∥∥∥	NOUN
cana-5422	750	97	,	,	PUNCT
cana-5422	750	98	λ	λ	PROPN
cana-5422	750	99	)	)	PUNCT
cana-5422	750	100	≤	≤	NUM
cana-5422	750	101	ν	ν	NOUN
cana-5422	750	102	(	(	PUNCT
cana-5422	750	103	τ2	τ2	PROPN
cana-5422	750	104	v	v	PROPN
cana-5422	750	105	k	k	PROPN
cana-5422	750	106	ψ(τvw1	ψ(τvw1	NOUN
cana-5422	750	107	,	,	PUNCT
cana-5422	750	108	τvw1	τvw1	NOUN
cana-5422	750	109	,	,	PUNCT
cana-5422	750	110	τvw1	τvw1	PROPN
cana-5422	750	111	)	)	PUNCT
cana-5422	750	112	,	,	PUNCT
cana-5422	750	113	λ	λ	INTJ
cana-5422	750	114	)	)	PUNCT
cana-5422	751	1			NOUN
cana-5422	751	2	⇒	⇒	NOUN
cana-5422	751	3	{	{	PUNCT
cana-5422	751	4	µ	µ	X
cana-5422	751	5	(	(	PUNCT
cana-5422	751	6	hf	hf	INTJ
cana-5422	751	7	(	(	PUNCT
cana-5422	751	8	w1)−hf1(w1	w1)−hf1(w1	NOUN
cana-5422	751	9	)	)	PUNCT
cana-5422	751	10	,	,	PUNCT
cana-5422	751	11	λ	λ	X
cana-5422	751	12	)	)	PUNCT
cana-5422	751	13	≥	≥	PROPN
cana-5422	751	14	µ	µ	X
cana-5422	751	15	(	(	PUNCT
cana-5422	751	16	l	l	NOUN
cana-5422	751	17	k	k	X
cana-5422	751	18	ψ(w1	ψ(w1	PROPN
cana-5422	751	19	,	,	PUNCT
cana-5422	751	20	w1	w1	NOUN
cana-5422	751	21	,	,	PUNCT
cana-5422	751	22	w1	w1	NOUN
cana-5422	751	23	)	)	PUNCT
cana-5422	751	24	,	,	PUNCT
cana-5422	751	25	λ	λ	X
cana-5422	751	26	)	)	PUNCT
cana-5422	751	27	ν	ν	NOUN
cana-5422	751	28	(	(	PUNCT
cana-5422	751	29	hf	hf	INTJ
cana-5422	751	30	(	(	PUNCT
cana-5422	751	31	w1)−hf1(w1	w1)−hf1(w1	NOUN
cana-5422	751	32	)	)	PUNCT
cana-5422	751	33	,	,	PUNCT
cana-5422	751	34	λ	λ	NOUN
cana-5422	751	35	)	)	PUNCT
cana-5422	751	36	≤	≤	NUM
cana-5422	751	37	ν	ν	NOUN
cana-5422	751	38	(	(	PUNCT
cana-5422	751	39	l	l	X
cana-5422	751	40	k	k	X
cana-5422	751	41	ψ(w1	ψ(w1	PROPN
cana-5422	751	42	,	,	PUNCT
cana-5422	751	43	w1	w1	NOUN
cana-5422	751	44	,	,	PUNCT
cana-5422	751	45	w1	w1	NOUN
cana-5422	751	46	)	)	PUNCT
cana-5422	751	47	,	,	PUNCT
cana-5422	751	48	λ	λ	NOUN
cana-5422	751	49	)	)	PUNCT
cana-5422	751	50	}	}	PUNCT
cana-5422	751	51	⇒d(hf	⇒d(hf	NOUN
cana-5422	751	52	,	,	PUNCT
cana-5422	751	53	hf1	hf1	NOUN
cana-5422	751	54	)	)	PUNCT
cana-5422	751	55	≤	≤	NUM
cana-5422	752	1	l	l	NOUN
cana-5422	753	1	k	k	NOUN
cana-5422	753	2	,	,	PUNCT
cana-5422	753	3	i.e.	i.e.	X
cana-5422	753	4	,h	,h	PUNCT
cana-5422	753	5	is	be	AUX
cana-5422	753	6	a	a	DET
cana-5422	753	7	strictly	strictly	ADV
cana-5422	753	8	contractive	contractive	ADJ
cana-5422	753	9	mapping	mapping	NOUN
cana-5422	753	10	on	on	ADP
cana-5422	753	11	g	g	NOUN
cana-5422	753	12	with	with	ADP
cana-5422	753	13	lipschitz	lipschitz	NOUN
cana-5422	753	14	constant	constant	ADJ
cana-5422	753	15	l	l	NOUN
cana-5422	753	16	(	(	PUNCT
cana-5422	753	17	see	see	VERB
cana-5422	753	18	[	[	X
cana-5422	753	19	18	18	NUM
cana-5422	753	20	]	]	NUM
cana-5422	753	21	)	)	PUNCT
cana-5422	753	22	.	.	PUNCT
cana-5422	754	1	the	the	DET
cana-5422	754	2	rest	rest	NOUN
cana-5422	754	3	of	of	ADP
cana-5422	754	4	the	the	DET
cana-5422	754	5	proof	proof	NOUN
cana-5422	754	6	is	be	AUX
cana-5422	754	7	similar	similar	ADJ
cana-5422	754	8	to	to	ADP
cana-5422	754	9	that	that	PRON
cana-5422	754	10	of	of	ADP
cana-5422	754	11	theorem	theorem	ADJ
cana-5422	754	12	3.29	3.29	NUM
cana-5422	754	13	.	.	PUNCT
cana-5422	755	1	hence	hence	ADV
cana-5422	755	2	the	the	DET
cana-5422	755	3	proof	proof	NOUN
cana-5422	755	4	is	be	AUX
cana-5422	755	5	complete	complete	ADJ
cana-5422	755	6	.	.	PUNCT
cana-5422	756	1	�	�	PROPN
cana-5422	756	2	corollary	corollary	PROPN
cana-5422	756	3	3.32	3.32	NUM
cana-5422	756	4	.	.	PUNCT
cana-5422	756	5	suppose	suppose	VERB
cana-5422	756	6	that	that	SCONJ
cana-5422	756	7	an	an	DET
cana-5422	756	8	even	even	ADV
cana-5422	756	9	function	function	NOUN
cana-5422	756	10	f	f	PROPN
cana-5422	756	11	:	:	PUNCT
cana-5422	756	12	w1	w1	PROPN
cana-5422	756	13	→	→	SYM
cana-5422	756	14	w2	w2	NOUN
cana-5422	756	15	satisfy	satisfy	VERB
cana-5422	756	16	the	the	DET
cana-5422	756	17	functional	functional	ADJ
cana-5422	756	18	iinequalities	iinequalitie	NOUN
cana-5422	756	19	(	(	PUNCT
cana-5422	756	20	3.2	3.2	NUM
cana-5422	756	21	)	)	PUNCT
cana-5422	756	22	,	,	PUNCT
cana-5422	756	23	(	(	PUNCT
cana-5422	756	24	3.3	3.3	NUM
cana-5422	756	25	)	)	PUNCT
cana-5422	756	26	,	,	PUNCT
cana-5422	756	27	(	(	PUNCT
cana-5422	756	28	3.4	3.4	NUM
cana-5422	756	29	)	)	PUNCT
cana-5422	756	30	,	,	PUNCT
cana-5422	756	31	(	(	PUNCT
cana-5422	756	32	3.5	3.5	NUM
cana-5422	756	33	)	)	PUNCT
cana-5422	756	34	,	,	PUNCT
cana-5422	756	35	(	(	PUNCT
cana-5422	756	36	3.6	3.6	NUM
cana-5422	756	37	)	)	PUNCT
cana-5422	756	38	,	,	PUNCT
cana-5422	756	39	(	(	PUNCT
cana-5422	756	40	3.7	3.7	NUM
cana-5422	756	41	)	)	PUNCT
cana-5422	756	42	for	for	ADP
cana-5422	756	43	all	all	DET
cana-5422	756	44	w1	w1	NOUN
cana-5422	756	45	,	,	PUNCT
cana-5422	756	46	w2	w2	NOUN
cana-5422	756	47	,	,	PUNCT
cana-5422	756	48	w3	w3	PROPN
cana-5422	756	49	∈	∈	PROPN
cana-5422	756	50	w1	w1	PROPN
cana-5422	756	51	with	with	SCONJ
cana-5422	756	52	δ	δ	PROPN
cana-5422	756	53	be	be	AUX
cana-5422	756	54	a	a	DET
cana-5422	756	55	positive	positive	ADJ
cana-5422	756	56	constant	constant	NOUN
cana-5422	756	57	and	and	CCONJ
cana-5422	756	58	ϕ	ϕ	NOUN
cana-5422	756	59	be	be	AUX
cana-5422	756	60	any	any	DET
cana-5422	756	61	real	real	ADJ
cana-5422	756	62	number	number	NOUN
cana-5422	756	63	.	.	PUNCT
cana-5422	757	1	then	then	ADV
cana-5422	757	2	there	there	PRON
cana-5422	757	3	exists	exist	VERB
cana-5422	757	4	a	a	DET
cana-5422	757	5	unique	unique	ADJ
cana-5422	757	6	quadratic	quadratic	ADJ
cana-5422	757	7	mapping	mapping	NOUN
cana-5422	757	8	q(w1	q(w1	NOUN
cana-5422	757	9	)	)	PUNCT
cana-5422	757	10	:	:	PUNCT
cana-5422	757	11	w1	w1	NOUN
cana-5422	757	12	→	→	SYM
cana-5422	757	13	w2	w2	NOUN
cana-5422	757	14	which	which	PRON
cana-5422	757	15	satisfies	satisfy	VERB
cana-5422	757	16	(	(	PUNCT
cana-5422	757	17	1.7	1.7	NUM
cana-5422	757	18	)	)	PUNCT
cana-5422	757	19	and	and	CCONJ
cana-5422	757	20	the	the	DET
cana-5422	757	21	functional	functional	ADJ
cana-5422	757	22	inequalities	inequality	NOUN
cana-5422	757	23	(	(	PUNCT
cana-5422	757	24	3.47	3.47	NUM
cana-5422	757	25	)	)	PUNCT
cana-5422	757	26	,	,	PUNCT
cana-5422	757	27	(	(	PUNCT
cana-5422	757	28	3.48	3.48	NUM
cana-5422	757	29	)	)	PUNCT
cana-5422	757	30	,	,	PUNCT
cana-5422	757	31	(	(	PUNCT
cana-5422	757	32	3.49	3.49	NUM
cana-5422	757	33	)	)	PUNCT
cana-5422	757	34	,	,	PUNCT
cana-5422	757	35	(	(	PUNCT
cana-5422	757	36	3.50	3.50	NUM
cana-5422	757	37	)	)	PUNCT
cana-5422	757	38	,	,	PUNCT
cana-5422	757	39	(	(	PUNCT
cana-5422	757	40	3.51	3.51	NUM
cana-5422	757	41	)	)	PUNCT
cana-5422	757	42	,	,	PUNCT
cana-5422	757	43	(	(	PUNCT
cana-5422	757	44	3.52	3.52	NUM
cana-5422	757	45	)	)	PUNCT
cana-5422	757	46	,	,	PUNCT
cana-5422	757	47	for	for	ADP
cana-5422	757	48	all	all	DET
cana-5422	757	49	w1	w1	NOUN
cana-5422	757	50	∈	∈	PROPN
cana-5422	757	51	w1	w1	NOUN
cana-5422	757	52	.	.	PUNCT
cana-5422	758	1	3.7	3.7	NUM
cana-5422	758	2	.	.	PUNCT
cana-5422	758	3	oddness	oddness	ADJ
cana-5422	758	4	and	and	CCONJ
cana-5422	758	5	evenness	evenness	NOUN
cana-5422	758	6	of	of	ADP
cana-5422	758	7	f	f	NOUN
cana-5422	758	8	:	:	PUNCT
cana-5422	758	9	additive	additive	ADJ
cana-5422	758	10	quadratic	quadratic	ADJ
cana-5422	758	11	case	case	NOUN
cana-5422	758	12	stability	stability	NOUN
cana-5422	758	13	results	result	VERB
cana-5422	758	14	:	:	PUNCT
cana-5422	758	15	fixed	fixed	ADJ
cana-5422	758	16	point	point	NOUN
cana-5422	758	17	method	method	NOUN
cana-5422	758	18	.	.	PUNCT
cana-5422	759	1	theorem	theorem	VERB
cana-5422	759	2	3.33	3.33	NUM
cana-5422	759	3	.	.	PUNCT
cana-5422	760	1	suppose	suppose	VERB
cana-5422	760	2	that	that	SCONJ
cana-5422	760	3	a	a	DET
cana-5422	760	4	function	function	NOUN
cana-5422	760	5	f	f	NOUN
cana-5422	760	6	:	:	PUNCT
cana-5422	760	7	w1	w1	PROPN
cana-5422	760	8	→w2	→w2	NOUN
cana-5422	760	9	satisfy	satisfy	VERB
cana-5422	760	10	the	the	DET
cana-5422	760	11	functional	functional	ADJ
cana-5422	760	12	inequality	inequality	NOUN
cana-5422	760	13	(	(	PUNCT
cana-5422	760	14	3.1	3.1	NUM
cana-5422	760	15	)	)	PUNCT
cana-5422	760	16	where	where	SCONJ
cana-5422	760	17	ψ	ψ	X
cana-5422	760	18	:	:	PUNCT
cana-5422	760	19	w3	w3	NOUN
cana-5422	760	20	1	1	NUM
cana-5422	760	21	→	→	SYM
cana-5422	760	22	[	[	X
cana-5422	760	23	0	0	NUM
cana-5422	760	24	,	,	PUNCT
cana-5422	760	25	∞	∞	PROPN
cana-5422	760	26	)	)	PUNCT
cana-5422	760	27	with	with	ADP
cana-5422	760	28	the	the	DET
cana-5422	760	29	conditions	condition	NOUN
cana-5422	760	30	(	(	PUNCT
cana-5422	760	31	3.63	3.63	NUM
cana-5422	760	32	)	)	PUNCT
cana-5422	760	33	and	and	CCONJ
cana-5422	760	34	(	(	PUNCT
cana-5422	760	35	3.71	3.71	NUM
cana-5422	760	36	)	)	PUNCT
cana-5422	760	37	for	for	ADP
cana-5422	760	38	all	all	DET
cana-5422	760	39	w1	w1	NOUN
cana-5422	760	40	,	,	PUNCT
cana-5422	760	41	w2	w2	NOUN
cana-5422	760	42	,	,	PUNCT
cana-5422	760	43	w3	w3	PROPN
cana-5422	760	44	∈	∈	PROPN
cana-5422	760	45	w1	w1	NOUN
cana-5422	760	46	and	and	CCONJ
cana-5422	760	47	all	all	DET
cana-5422	760	48	λ	λ	X
cana-5422	760	49	>	>	X
cana-5422	760	50	0	0	X
cana-5422	760	51	.	.	PUNCT
cana-5422	761	1	if	if	SCONJ
cana-5422	761	2	there	there	PRON
cana-5422	761	3	exists	exist	VERB
cana-5422	761	4	l	l	NOUN
cana-5422	761	5	=	=	SYM
cana-5422	761	6	l(ν	l(ν	PROPN
cana-5422	761	7	)	)	PUNCT
cana-5422	761	8	be	be	VERB
cana-5422	761	9	function	function	NOUN
cana-5422	761	10	have	have	VERB
cana-5422	761	11	the	the	DET
cana-5422	761	12	properties	property	NOUN
cana-5422	761	13	(	(	PUNCT
cana-5422	761	14	3.64	3.64	NUM
cana-5422	761	15	)	)	PUNCT
cana-5422	761	16	and	and	CCONJ
cana-5422	761	17	(	(	PUNCT
cana-5422	761	18	3.72	3.72	NUM
cana-5422	761	19	)	)	PUNCT
cana-5422	761	20	for	for	ADP
cana-5422	761	21	all	all	DET
cana-5422	761	22	w1	w1	NOUN
cana-5422	761	23	∈	∈	PROPN
cana-5422	761	24	w1	w1	NOUN
cana-5422	761	25	and	and	CCONJ
cana-5422	761	26	all	all	DET
cana-5422	761	27	λ	λ	X
cana-5422	761	28	>	>	X
cana-5422	761	29	0	0	NUM
cana-5422	761	30	.	.	PUNCT
cana-5422	762	1	then	then	ADV
cana-5422	762	2	there	there	PRON
cana-5422	762	3	exists	exist	VERB
cana-5422	762	4	a	a	DET
cana-5422	762	5	unique	unique	ADJ
cana-5422	762	6	additive	additive	ADJ
cana-5422	762	7	mapping	mapping	NOUN
cana-5422	762	8	a(w1	a(w1	NOUN
cana-5422	762	9	)	)	PUNCT
cana-5422	762	10	:	:	PUNCT
cana-5422	762	11	w1	w1	NOUN
cana-5422	762	12	→w2	→w2	NOUN
cana-5422	762	13	and	and	CCONJ
cana-5422	762	14	a	a	DET
cana-5422	762	15	unique	unique	ADJ
cana-5422	762	16	quadratic	quadratic	ADJ
cana-5422	762	17	mapping	mapping	NOUN
cana-5422	762	18	q(w1	q(w1	NOUN
cana-5422	762	19	)	)	PUNCT
cana-5422	762	20	:	:	PUNCT
cana-5422	762	21	w1	w1	PROPN
cana-5422	762	22	→w2	→w2	NOUN
cana-5422	762	23	which	which	PRON
cana-5422	762	24	satisfies	satisfy	VERB
cana-5422	762	25	(	(	PUNCT
cana-5422	762	26	1.7	1.7	NUM
cana-5422	762	27	)	)	PUNCT
cana-5422	762	28	and	and	CCONJ
cana-5422	762	29	the	the	DET
cana-5422	762	30	communications	communication	NOUN
cana-5422	762	31	on	on	ADP
cana-5422	762	32	applied	apply	VERB
cana-5422	762	33	nonlinear	nonlinear	ADJ
cana-5422	762	34	analysis	analysis	NOUN
cana-5422	762	35	issn	issn	NOUN
cana-5422	762	36	:	:	PUNCT
cana-5422	762	37	1074	1074	NUM
cana-5422	762	38	-	-	PUNCT
cana-5422	762	39	133x	133x	NUM
cana-5422	762	40	vol	vol	NOUN
cana-5422	762	41	32	32	NUM
cana-5422	762	42	no	no	NOUN
cana-5422	762	43	.	.	PUNCT
cana-5422	763	1	10s(2025	10s(2025	NUM
cana-5422	763	2	)	)	PUNCT
cana-5422	763	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	763	4	2214	2214	NUM
cana-5422	763	5	functional	functional	ADJ
cana-5422	763	6	inequality	inequality	NOUN
cana-5422	763	7	µ	µ	X
cana-5422	763	8	(	(	PUNCT
cana-5422	763	9	f	f	PROPN
cana-5422	763	10	(	(	PUNCT
cana-5422	763	11	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	763	12	)	)	PUNCT
cana-5422	763	13	,	,	PUNCT
cana-5422	763	14	4λ	4λ	PROPN
cana-5422	763	15	)	)	PUNCT
cana-5422	763	16	≥	≥	NOUN
cana-5422	763	17	µ′	µ′	PUNCT
cana-5422	763	18	(	(	PUNCT
cana-5422	763	19	l1−v	l1−v	PROPN
cana-5422	763	20	1−l	1−l	NUM
cana-5422	763	21	ψa	ψa	NOUN
cana-5422	763	22	(	(	PUNCT
cana-5422	763	23	w1	w1	NOUN
cana-5422	763	24	)	)	PUNCT
cana-5422	763	25	,	,	PUNCT
cana-5422	763	26	3λ	3λ	NUM
cana-5422	763	27	4	4	NUM
cana-5422	763	28	)	)	PUNCT
cana-5422	763	29	∗	∗	NOUN
cana-5422	763	30	µ′	µ′	PUNCT
cana-5422	763	31	(	(	PUNCT
cana-5422	763	32	l1−v	l1−v	PROPN
cana-5422	763	33	1−l	1−l	NUM
cana-5422	763	34	ψa	ψa	NOUN
cana-5422	763	35	(	(	PUNCT
cana-5422	763	36	−w1	−w1	PROPN
cana-5422	763	37	)	)	PUNCT
cana-5422	763	38	,	,	PUNCT
cana-5422	763	39	3λ	3λ	NUM
cana-5422	763	40	4	4	NUM
cana-5422	763	41	)	)	PUNCT
cana-5422	763	42	∗	∗	NOUN
cana-5422	763	43	µ′	µ′	PUNCT
cana-5422	763	44	(	(	PUNCT
cana-5422	763	45	l1−v	l1−v	PROPN
cana-5422	763	46	1−l	1−l	NUM
cana-5422	763	47	ψq	ψq	PROPN
cana-5422	763	48	(	(	PUNCT
cana-5422	763	49	w1	w1	NOUN
cana-5422	763	50	)	)	PUNCT
cana-5422	763	51	,	,	PUNCT
cana-5422	763	52	7λ	7λ	NUM
cana-5422	763	53	3	3	NUM
cana-5422	763	54	)	)	PUNCT
cana-5422	763	55	∗	∗	NOUN
cana-5422	763	56	µ′	µ′	PUNCT
cana-5422	763	57	(	(	PUNCT
cana-5422	763	58	l1−v	l1−v	PROPN
cana-5422	763	59	1−l	1−l	NUM
cana-5422	763	60	ψq	ψq	PROPN
cana-5422	763	61	(	(	PUNCT
cana-5422	763	62	−w1	−w1	PROPN
cana-5422	763	63	)	)	PUNCT
cana-5422	763	64	,	,	PUNCT
cana-5422	763	65	7λ	7λ	NUM
cana-5422	763	66	3	3	NUM
cana-5422	763	67	)	)	PUNCT
cana-5422	763	68	=	=	SYM
cana-5422	763	69	µ′	µ′	NOUN
cana-5422	763	70	(	(	PUNCT
cana-5422	763	71	l1−v	l1−v	PROPN
cana-5422	763	72	1−l	1−l	NUM
cana-5422	763	73	ψ	ψ	NOUN
cana-5422	763	74	(	(	PUNCT
cana-5422	763	75	w1	w1	NOUN
cana-5422	763	76	,	,	PUNCT
cana-5422	763	77	w1	w1	NOUN
cana-5422	763	78	,	,	PUNCT
cana-5422	763	79	w1	w1	NOUN
cana-5422	763	80	)	)	PUNCT
cana-5422	763	81	,	,	PUNCT
cana-5422	763	82	3λ	3λ	NUM
cana-5422	763	83	4	4	NUM
cana-5422	763	84	)	)	PUNCT
cana-5422	763	85	∗	∗	NOUN
cana-5422	763	86	µ′	µ′	PUNCT
cana-5422	763	87	(	(	PUNCT
cana-5422	763	88	l1−v	l1−v	PROPN
cana-5422	763	89	1−l	1−l	NUM
cana-5422	763	90	ψ	ψ	NOUN
cana-5422	763	91	(	(	PUNCT
cana-5422	763	92	w1	w1	NOUN
cana-5422	763	93	,	,	PUNCT
cana-5422	763	94	w1,−w1	w1,−w1	NUM
cana-5422	763	95	)	)	PUNCT
cana-5422	763	96	,	,	PUNCT
cana-5422	764	1	3λ	3λ	NUM
cana-5422	764	2	4	4	NUM
cana-5422	764	3	)	)	PUNCT
cana-5422	764	4	∗	∗	NOUN
cana-5422	764	5	µ′	µ′	PUNCT
cana-5422	764	6	(	(	PUNCT
cana-5422	764	7	l1−v	l1−v	PROPN
cana-5422	764	8	1−l	1−l	NUM
cana-5422	764	9	ψ	ψ	X
cana-5422	764	10	(	(	PUNCT
cana-5422	764	11	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	764	12	)	)	PUNCT
cana-5422	764	13	,	,	PUNCT
cana-5422	764	14	3λ	3λ	NUM
cana-5422	764	15	4	4	NUM
cana-5422	764	16	)	)	PUNCT
cana-5422	764	17	∗	∗	NOUN
cana-5422	764	18	µ′	µ′	PUNCT
cana-5422	764	19	(	(	PUNCT
cana-5422	764	20	l1−v	l1−v	PROPN
cana-5422	764	21	1−l	1−l	NUM
cana-5422	764	22	ψ	ψ	NOUN
cana-5422	764	23	(	(	PUNCT
cana-5422	764	24	−w1,−w1	−w1,−w1	PROPN
cana-5422	764	25	,	,	PUNCT
cana-5422	764	26	w1	w1	NOUN
cana-5422	764	27	)	)	PUNCT
cana-5422	764	28	,	,	PUNCT
cana-5422	764	29	3λ	3λ	NUM
cana-5422	764	30	4	4	NUM
cana-5422	764	31	)	)	PUNCT
cana-5422	764	32	∗	∗	NOUN
cana-5422	764	33	µ′	µ′	PUNCT
cana-5422	764	34	(	(	PUNCT
cana-5422	764	35	l1−v	l1−v	PROPN
cana-5422	764	36	1−l	1−l	NUM
cana-5422	764	37	ψ	ψ	NOUN
cana-5422	764	38	(	(	PUNCT
cana-5422	764	39	w1	w1	NOUN
cana-5422	764	40	,	,	PUNCT
cana-5422	764	41	w1	w1	NOUN
cana-5422	764	42	,	,	PUNCT
cana-5422	764	43	w1	w1	NOUN
cana-5422	764	44	)	)	PUNCT
cana-5422	764	45	,	,	PUNCT
cana-5422	764	46	7λ	7λ	NUM
cana-5422	764	47	3	3	NUM
cana-5422	764	48	)	)	PUNCT
cana-5422	764	49	∗	∗	NOUN
cana-5422	764	50	µ′	µ′	PUNCT
cana-5422	764	51	(	(	PUNCT
cana-5422	764	52	l1−v	l1−v	PROPN
cana-5422	764	53	1−l	1−l	NUM
cana-5422	764	54	ψ	ψ	NOUN
cana-5422	764	55	(	(	PUNCT
cana-5422	764	56	w1	w1	NOUN
cana-5422	764	57	,	,	PUNCT
cana-5422	764	58	w1,−w1	w1,−w1	NUM
cana-5422	764	59	)	)	PUNCT
cana-5422	764	60	,	,	PUNCT
cana-5422	764	61	7λ	7λ	NUM
cana-5422	764	62	3	3	NUM
cana-5422	764	63	)	)	PUNCT
cana-5422	764	64	∗	∗	NOUN
cana-5422	764	65	µ′	µ′	PUNCT
cana-5422	764	66	(	(	PUNCT
cana-5422	764	67	l1−v	l1−v	PROPN
cana-5422	764	68	1−l	1−l	NUM
cana-5422	764	69	ψ	ψ	X
cana-5422	764	70	(	(	PUNCT
cana-5422	764	71	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	764	72	)	)	PUNCT
cana-5422	764	73	,	,	PUNCT
cana-5422	764	74	7λ	7λ	NUM
cana-5422	764	75	3	3	NUM
cana-5422	764	76	)	)	PUNCT
cana-5422	764	77	∗	∗	NOUN
cana-5422	764	78	µ′	µ′	PUNCT
cana-5422	764	79	(	(	PUNCT
cana-5422	764	80	l1−v	l1−v	PROPN
cana-5422	764	81	1−l	1−l	NUM
cana-5422	764	82	ψ	ψ	NOUN
cana-5422	764	83	(	(	PUNCT
cana-5422	764	84	−w1,−w1	−w1,−w1	PROPN
cana-5422	764	85	,	,	PUNCT
cana-5422	764	86	w1	w1	NOUN
cana-5422	764	87	)	)	PUNCT
cana-5422	764	88	,	,	PUNCT
cana-5422	764	89	7λ	7λ	NUM
cana-5422	764	90	3	3	X
cana-5422	764	91	)	)	PUNCT
cana-5422	764	92	ν	ν	NOUN
cana-5422	764	93	(	(	PUNCT
cana-5422	764	94	f	f	PROPN
cana-5422	764	95	(	(	PUNCT
cana-5422	764	96	w1)−a(w1)−q(w1	w1)−a(w1)−q(w1	PROPN
cana-5422	764	97	)	)	PUNCT
cana-5422	764	98	,	,	PUNCT
cana-5422	764	99	4λ	4λ	NOUN
cana-5422	764	100	)	)	PUNCT
cana-5422	764	101	≤	≤	NUM
cana-5422	764	102	ν′	ν′	NOUN
cana-5422	764	103	(	(	PUNCT
cana-5422	764	104	l1−v	l1−v	PROPN
cana-5422	764	105	1−l	1−l	NUM
cana-5422	764	106	ψa	ψa	NOUN
cana-5422	764	107	(	(	PUNCT
cana-5422	764	108	w1	w1	NOUN
cana-5422	764	109	)	)	PUNCT
cana-5422	764	110	,	,	PUNCT
cana-5422	764	111	3λ	3λ	NUM
cana-5422	764	112	4	4	X
cana-5422	764	113	)	)	PUNCT
cana-5422	764	114	�	�	PROPN
cana-5422	764	115	ν′	ν′	NOUN
cana-5422	764	116	(	(	PUNCT
cana-5422	764	117	l1−v	l1−v	PROPN
cana-5422	764	118	1−l	1−l	NUM
cana-5422	764	119	ψa	ψa	NOUN
cana-5422	764	120	(	(	PUNCT
cana-5422	764	121	−w1	−w1	PROPN
cana-5422	764	122	)	)	PUNCT
cana-5422	764	123	,	,	PUNCT
cana-5422	764	124	3λ	3λ	NUM
cana-5422	764	125	4	4	X
cana-5422	764	126	)	)	PUNCT
cana-5422	764	127	�	�	PROPN
cana-5422	764	128	ν′	ν′	NOUN
cana-5422	764	129	(	(	PUNCT
cana-5422	764	130	l1−v	l1−v	PROPN
cana-5422	764	131	1−l	1−l	NUM
cana-5422	764	132	ψq	ψq	PROPN
cana-5422	764	133	(	(	PUNCT
cana-5422	764	134	w1	w1	NOUN
cana-5422	764	135	)	)	PUNCT
cana-5422	764	136	,	,	PUNCT
cana-5422	764	137	7λ	7λ	NUM
cana-5422	764	138	3	3	X
cana-5422	764	139	)	)	PUNCT
cana-5422	764	140	�	�	PROPN
cana-5422	764	141	ν′	ν′	NOUN
cana-5422	764	142	(	(	PUNCT
cana-5422	764	143	l1−v	l1−v	PROPN
cana-5422	764	144	1−l	1−l	NUM
cana-5422	764	145	ψq	ψq	PROPN
cana-5422	764	146	(	(	PUNCT
cana-5422	764	147	−w1	−w1	PROPN
cana-5422	764	148	)	)	PUNCT
cana-5422	764	149	,	,	PUNCT
cana-5422	764	150	7λ	7λ	NUM
cana-5422	764	151	3	3	X
cana-5422	764	152	)	)	PUNCT
cana-5422	764	153	=	=	SYM
cana-5422	764	154	ν′	ν′	NOUN
cana-5422	764	155	(	(	PUNCT
cana-5422	764	156	l1−v	l1−v	PROPN
cana-5422	764	157	1−l	1−l	NUM
cana-5422	764	158	ψ	ψ	NOUN
cana-5422	764	159	(	(	PUNCT
cana-5422	764	160	w1	w1	NOUN
cana-5422	764	161	,	,	PUNCT
cana-5422	764	162	w1	w1	NOUN
cana-5422	764	163	,	,	PUNCT
cana-5422	764	164	w1	w1	NOUN
cana-5422	764	165	)	)	PUNCT
cana-5422	764	166	,	,	PUNCT
cana-5422	764	167	3λ	3λ	NUM
cana-5422	764	168	4	4	X
cana-5422	764	169	)	)	PUNCT
cana-5422	764	170	�	�	PROPN
cana-5422	764	171	ν′	ν′	NOUN
cana-5422	764	172	(	(	PUNCT
cana-5422	764	173	l1−v	l1−v	PROPN
cana-5422	764	174	1−l	1−l	NUM
cana-5422	764	175	ψ	ψ	NOUN
cana-5422	764	176	(	(	PUNCT
cana-5422	764	177	w1	w1	NOUN
cana-5422	764	178	,	,	PUNCT
cana-5422	764	179	w1,−w1	w1,−w1	NUM
cana-5422	764	180	)	)	PUNCT
cana-5422	764	181	,	,	PUNCT
cana-5422	764	182	3λ	3λ	NUM
cana-5422	764	183	4	4	X
cana-5422	764	184	)	)	PUNCT
cana-5422	764	185	�	�	PROPN
cana-5422	764	186	ν′	ν′	NOUN
cana-5422	764	187	(	(	PUNCT
cana-5422	764	188	l1−v	l1−v	PROPN
cana-5422	764	189	1−l	1−l	NUM
cana-5422	764	190	ψ	ψ	X
cana-5422	764	191	(	(	PUNCT
cana-5422	764	192	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	764	193	)	)	PUNCT
cana-5422	764	194	,	,	PUNCT
cana-5422	764	195	3λ	3λ	NUM
cana-5422	764	196	4	4	X
cana-5422	764	197	)	)	PUNCT
cana-5422	764	198	�	�	PROPN
cana-5422	764	199	ν′	ν′	NOUN
cana-5422	764	200	(	(	PUNCT
cana-5422	764	201	l1−v	l1−v	PROPN
cana-5422	764	202	1−l	1−l	NUM
cana-5422	764	203	ψ	ψ	NOUN
cana-5422	764	204	(	(	PUNCT
cana-5422	764	205	−w1,−w1	−w1,−w1	PROPN
cana-5422	764	206	,	,	PUNCT
cana-5422	764	207	w1	w1	NOUN
cana-5422	764	208	)	)	PUNCT
cana-5422	764	209	,	,	PUNCT
cana-5422	764	210	3λ	3λ	NUM
cana-5422	764	211	4	4	X
cana-5422	764	212	)	)	PUNCT
cana-5422	764	213	�	�	PROPN
cana-5422	764	214	ν′	ν′	NOUN
cana-5422	764	215	(	(	PUNCT
cana-5422	764	216	l1−v	l1−v	PROPN
cana-5422	764	217	1−l	1−l	NUM
cana-5422	764	218	ψ	ψ	NOUN
cana-5422	764	219	(	(	PUNCT
cana-5422	764	220	w1	w1	NOUN
cana-5422	764	221	,	,	PUNCT
cana-5422	764	222	w1	w1	NOUN
cana-5422	764	223	,	,	PUNCT
cana-5422	764	224	w1	w1	NOUN
cana-5422	764	225	)	)	PUNCT
cana-5422	764	226	,	,	PUNCT
cana-5422	764	227	7λ	7λ	NUM
cana-5422	764	228	3	3	X
cana-5422	764	229	)	)	PUNCT
cana-5422	764	230	�	�	PROPN
cana-5422	764	231	ν′	ν′	NOUN
cana-5422	764	232	(	(	PUNCT
cana-5422	764	233	l1−v	l1−v	PROPN
cana-5422	764	234	1−l	1−l	NUM
cana-5422	764	235	ψ	ψ	NOUN
cana-5422	764	236	(	(	PUNCT
cana-5422	764	237	w1	w1	NOUN
cana-5422	764	238	,	,	PUNCT
cana-5422	764	239	w1,−w1	w1,−w1	NUM
cana-5422	764	240	)	)	PUNCT
cana-5422	764	241	,	,	PUNCT
cana-5422	764	242	7λ	7λ	NUM
cana-5422	764	243	3	3	X
cana-5422	764	244	)	)	PUNCT
cana-5422	764	245	�	�	PROPN
cana-5422	764	246	ν′	ν′	NOUN
cana-5422	764	247	(	(	PUNCT
cana-5422	764	248	l1−v	l1−v	PROPN
cana-5422	764	249	1−l	1−l	NUM
cana-5422	764	250	ψ	ψ	X
cana-5422	764	251	(	(	PUNCT
cana-5422	764	252	−w1,−w1,−w1	−w1,−w1,−w1	PROPN
cana-5422	764	253	)	)	PUNCT
cana-5422	764	254	,	,	PUNCT
cana-5422	764	255	7λ	7λ	NUM
cana-5422	764	256	3	3	X
cana-5422	764	257	)	)	PUNCT
cana-5422	764	258	�	�	PROPN
cana-5422	764	259	ν′	ν′	NOUN
cana-5422	764	260	(	(	PUNCT
cana-5422	764	261	l1−v	l1−v	PROPN
cana-5422	764	262	1−l	1−l	NUM
cana-5422	764	263	ψ	ψ	NOUN
cana-5422	764	264	(	(	PUNCT
cana-5422	764	265	−w1,−w1	−w1,−w1	PROPN
cana-5422	764	266	,	,	PUNCT
cana-5422	764	267	w1	w1	NOUN
cana-5422	764	268	)	)	PUNCT
cana-5422	764	269	,	,	PUNCT
cana-5422	764	270	7λ	7λ	NUM
cana-5422	764	271	3	3	X
cana-5422	764	272	)	)	PUNCT
cana-5422	764	273			NOUN
cana-5422	764	274	(	(	PUNCT
cana-5422	764	275	3.75	3.75	NUM
cana-5422	764	276	)	)	PUNCT
cana-5422	764	277	and	and	CCONJ
cana-5422	764	278	the	the	DET
cana-5422	764	279	mapping	mapping	NOUN
cana-5422	764	280	a(w1	a(w1	NOUN
cana-5422	764	281	)	)	PUNCT
cana-5422	764	282	and	and	CCONJ
cana-5422	764	283	q(w1	q(w1	NOUN
cana-5422	764	284	)	)	PUNCT
cana-5422	764	285	are	be	AUX
cana-5422	764	286	given	give	VERB
cana-5422	764	287	in	in	ADP
cana-5422	764	288	(	(	PUNCT
cana-5422	764	289	3.65	3.65	NUM
cana-5422	764	290	)	)	PUNCT
cana-5422	764	291	and	and	CCONJ
cana-5422	764	292	(	(	PUNCT
cana-5422	764	293	3.74	3.74	NUM
cana-5422	764	294	)	)	PUNCT
cana-5422	764	295	for	for	ADP
cana-5422	764	296	all	all	DET
cana-5422	764	297	w1	w1	NOUN
cana-5422	764	298	∈	∈	PROPN
cana-5422	764	299	w1	w1	NOUN
cana-5422	764	300	and	and	CCONJ
cana-5422	764	301	all	all	DET
cana-5422	764	302	λ	λ	PROPN
cana-5422	764	303	>	>	X
cana-5422	764	304	0	0	X
cana-5422	764	305	.	.	PUNCT
cana-5422	765	1	proof	proof	NOUN
cana-5422	765	2	.	.	PUNCT
cana-5422	766	1	the	the	DET
cana-5422	766	2	proof	proof	NOUN
cana-5422	766	3	is	be	AUX
cana-5422	766	4	similar	similar	ADJ
cana-5422	766	5	ideas	idea	NOUN
cana-5422	766	6	to	to	ADP
cana-5422	766	7	that	that	PRON
cana-5422	766	8	of	of	ADP
cana-5422	766	9	theorem	theorem	NOUN
cana-5422	766	10	3.22	3.22	NUM
cana-5422	766	11	.	.	PUNCT
cana-5422	766	12	�	�	PROPN
cana-5422	766	13	corollary	corollary	PROPN
cana-5422	766	14	3.34	3.34	NUM
cana-5422	766	15	.	.	PUNCT
cana-5422	767	1	suppose	suppose	VERB
cana-5422	767	2	that	that	SCONJ
cana-5422	767	3	a	a	DET
cana-5422	767	4	function	function	NOUN
cana-5422	767	5	f	f	NOUN
cana-5422	767	6	:	:	PUNCT
cana-5422	767	7	w1	w1	PROPN
cana-5422	767	8	→	→	SYM
cana-5422	767	9	w2	w2	NOUN
cana-5422	767	10	satisfy	satisfy	VERB
cana-5422	767	11	the	the	DET
cana-5422	767	12	functional	functional	ADJ
cana-5422	767	13	inequalities	inequality	NOUN
cana-5422	767	14	(	(	PUNCT
cana-5422	767	15	3.2	3.2	NUM
cana-5422	767	16	)	)	PUNCT
cana-5422	767	17	,	,	PUNCT
cana-5422	767	18	(	(	PUNCT
cana-5422	767	19	3.3	3.3	NUM
cana-5422	767	20	)	)	PUNCT
cana-5422	767	21	,	,	PUNCT
cana-5422	767	22	(	(	PUNCT
cana-5422	767	23	3.4	3.4	NUM
cana-5422	767	24	)	)	PUNCT
cana-5422	767	25	,	,	PUNCT
cana-5422	767	26	(	(	PUNCT
cana-5422	767	27	3.5	3.5	NUM
cana-5422	767	28	)	)	PUNCT
cana-5422	767	29	,	,	PUNCT
cana-5422	767	30	(	(	PUNCT
cana-5422	767	31	3.6	3.6	NUM
cana-5422	767	32	)	)	PUNCT
cana-5422	767	33	,	,	PUNCT
cana-5422	767	34	(	(	PUNCT
cana-5422	767	35	3.7	3.7	NUM
cana-5422	767	36	)	)	PUNCT
cana-5422	767	37	for	for	ADP
cana-5422	767	38	all	all	DET
cana-5422	767	39	w1	w1	NOUN
cana-5422	767	40	,	,	PUNCT
cana-5422	767	41	w2	w2	NOUN
cana-5422	767	42	,	,	PUNCT
cana-5422	767	43	w3	w3	PROPN
cana-5422	767	44	∈	∈	PROPN
cana-5422	767	45	w1	w1	NOUN
cana-5422	767	46	and	and	CCONJ
cana-5422	767	47	all	all	DET
cana-5422	767	48	λ	λ	X
cana-5422	767	49	>	>	X
cana-5422	767	50	0	0	PUNCT
cana-5422	767	51	with	with	SCONJ
cana-5422	767	52	δ	δ	PROPN
cana-5422	767	53	be	be	AUX
cana-5422	767	54	a	a	DET
cana-5422	767	55	positive	positive	ADJ
cana-5422	767	56	constant	constant	NOUN
cana-5422	767	57	and	and	CCONJ
cana-5422	767	58	ϕ	ϕ	NOUN
cana-5422	767	59	be	be	AUX
cana-5422	767	60	any	any	DET
cana-5422	767	61	real	real	ADJ
cana-5422	767	62	number	number	NOUN
cana-5422	767	63	.	.	PUNCT
cana-5422	768	1	then	then	ADV
cana-5422	768	2	there	there	PRON
cana-5422	768	3	exists	exist	VERB
cana-5422	768	4	a	a	DET
cana-5422	768	5	unique	unique	ADJ
cana-5422	768	6	additive	additive	ADJ
cana-5422	768	7	mapping	mapping	NOUN
cana-5422	768	8	a(w1	a(w1	NOUN
cana-5422	768	9	)	)	PUNCT
cana-5422	768	10	:	:	PUNCT
cana-5422	768	11	w1	w1	NOUN
cana-5422	768	12	→	→	SYM
cana-5422	768	13	w2	w2	NOUN
cana-5422	768	14	and	and	CCONJ
cana-5422	768	15	a	a	DET
cana-5422	768	16	unique	unique	ADJ
cana-5422	768	17	quadratic	quadratic	ADJ
cana-5422	768	18	mapping	mapping	NOUN
cana-5422	768	19	q(w1	q(w1	NOUN
cana-5422	768	20	)	)	PUNCT
cana-5422	768	21	:	:	PUNCT
cana-5422	768	22	w1	w1	NOUN
cana-5422	768	23	→	→	SYM
cana-5422	768	24	w2	w2	NOUN
cana-5422	768	25	which	which	PRON
cana-5422	768	26	satisfies	satisfy	VERB
cana-5422	768	27	(	(	PUNCT
cana-5422	768	28	1.7	1.7	NUM
cana-5422	768	29	)	)	PUNCT
cana-5422	768	30	and	and	CCONJ
cana-5422	768	31	the	the	DET
cana-5422	768	32	functional	functional	ADJ
cana-5422	768	33	inequalities	inequality	NOUN
cana-5422	768	34	(	(	PUNCT
cana-5422	768	35	3.57	3.57	NUM
cana-5422	768	36	)	)	PUNCT
cana-5422	768	37	,	,	PUNCT
cana-5422	768	38	(	(	PUNCT
cana-5422	768	39	3.58	3.58	NUM
cana-5422	768	40	)	)	PUNCT
cana-5422	768	41	,	,	PUNCT
cana-5422	768	42	(	(	PUNCT
cana-5422	768	43	3.59	3.59	NUM
cana-5422	768	44	)	)	PUNCT
cana-5422	768	45	,	,	PUNCT
cana-5422	768	46	(	(	PUNCT
cana-5422	768	47	3.60	3.60	NUM
cana-5422	768	48	)	)	PUNCT
cana-5422	768	49	,	,	PUNCT
cana-5422	768	50	(	(	PUNCT
cana-5422	768	51	3.61	3.61	NUM
cana-5422	768	52	)	)	PUNCT
cana-5422	768	53	,	,	PUNCT
cana-5422	768	54	(	(	PUNCT
cana-5422	768	55	3.62	3.62	NUM
cana-5422	768	56	)	)	PUNCT
cana-5422	768	57	for	for	ADP
cana-5422	768	58	all	all	DET
cana-5422	768	59	w1	w1	NOUN
cana-5422	768	60	∈	∈	PROPN
cana-5422	768	61	w1	w1	NOUN
cana-5422	768	62	.	.	PUNCT
cana-5422	769	1	conclusion	conclusion	NOUN
cana-5422	769	2	in	in	ADP
cana-5422	769	3	this	this	DET
cana-5422	769	4	paper	paper	NOUN
cana-5422	769	5	,	,	PUNCT
cana-5422	769	6	we	we	PRON
cana-5422	769	7	analyze	analyze	VERB
cana-5422	769	8	the	the	DET
cana-5422	769	9	generalized	generalize	VERB
cana-5422	769	10	ulam	ulam	NOUN
cana-5422	769	11	-	-	PUNCT
cana-5422	769	12	hyers	hyer	NOUN
cana-5422	769	13	stability	stability	NOUN
cana-5422	769	14	of	of	ADP
cana-5422	769	15	a	a	DET
cana-5422	769	16	affine	affine	ADJ
cana-5422	769	17	type	type	NOUN
cana-5422	769	18	aq	aq	NOUN
cana-5422	769	19	functional	functional	ADJ
cana-5422	769	20	equation	equation	NOUN
cana-5422	769	21	in	in	ADP
cana-5422	769	22	banach	banach	NOUN
cana-5422	769	23	space	space	NOUN
cana-5422	769	24	and	and	CCONJ
cana-5422	769	25	intuitionistic	intuitionistic	ADJ
cana-5422	769	26	fuzzy	fuzzy	ADJ
cana-5422	769	27	banach	banach	NOUN
cana-5422	769	28	space	space	NOUN
cana-5422	769	29	with	with	ADP
cana-5422	769	30	the	the	DET
cana-5422	769	31	help	help	NOUN
cana-5422	769	32	of	of	ADP
cana-5422	769	33	classical	classical	ADJ
cana-5422	769	34	hyers	hyer	NOUN
cana-5422	769	35	direct	direct	ADJ
cana-5422	769	36	and	and	CCONJ
cana-5422	769	37	radus	radus	VERB
cana-5422	769	38	fixed	fix	VERB
cana-5422	769	39	methods	method	NOUN
cana-5422	769	40	.	.	PUNCT
cana-5422	770	1	the	the	DET
cana-5422	770	2	results	result	NOUN
cana-5422	770	3	are	be	AUX
cana-5422	770	4	new	new	ADJ
cana-5422	770	5	,	,	PUNCT
cana-5422	770	6	since	since	SCONJ
cana-5422	770	7	we	we	PRON
cana-5422	770	8	are	be	AUX
cana-5422	770	9	getting	get	VERB
cana-5422	770	10	better	well	ADJ
cana-5422	770	11	possible	possible	ADJ
cana-5422	770	12	upper	upper	ADJ
cana-5422	770	13	bound	bind	VERB
cana-5422	770	14	than	than	ADP
cana-5422	770	15	previous	previous	ADJ
cana-5422	770	16	stability	stability	NOUN
cana-5422	770	17	analysis	analysis	NOUN
cana-5422	770	18	(	(	PUNCT
cana-5422	770	19	see	see	VERB
cana-5422	770	20	[	[	X
cana-5422	770	21	6	6	NUM
cana-5422	770	22	]	]	NUM
cana-5422	770	23	)	)	PUNCT
cana-5422	770	24	.	.	PUNCT
cana-5422	771	1	acknowledgment	acknowledgment	NOUN
cana-5422	771	2	supported	support	VERB
cana-5422	771	3	by	by	ADP
cana-5422	771	4	the	the	DET
cana-5422	771	5	center	center	NOUN
cana-5422	771	6	for	for	ADP
cana-5422	771	7	research	research	NOUN
cana-5422	771	8	and	and	CCONJ
cana-5422	771	9	development	development	NOUN
cana-5422	771	10	in	in	ADP
cana-5422	771	11	mathematics	mathematic	NOUN
cana-5422	771	12	and	and	CCONJ
cana-5422	771	13	applications	application	NOUN
cana-5422	771	14	(	(	PUNCT
cana-5422	771	15	cidma	cidma	NOUN
cana-5422	771	16	)	)	PUNCT
cana-5422	771	17	through	through	ADP
cana-5422	771	18	the	the	DET
cana-5422	771	19	portuguese	portuguese	ADJ
cana-5422	771	20	foundation	foundation	NOUN
cana-5422	771	21	for	for	ADP
cana-5422	771	22	science	science	NOUN
cana-5422	771	23	and	and	CCONJ
cana-5422	771	24	technology	technology	NOUN
cana-5422	771	25	(	(	PUNCT
cana-5422	771	26	fct	fct	PROPN
cana-5422	771	27	fundao	fundao	AUX
cana-5422	771	28	para	para	VERB
cana-5422	771	29	a	a	DET
cana-5422	771	30	ciłncia	ciłncia	NOUN
cana-5422	771	31	e	e	X
cana-5422	771	32	a	a	DET
cana-5422	771	33	tecnologia	tecnologia	NOUN
cana-5422	771	34	)	)	PUNCT
cana-5422	771	35	,	,	PUNCT
cana-5422	771	36	references	reference	NOUN
cana-5422	771	37	uidb/04106/2020	uidb/04106/2020	NOUN
cana-5422	771	38	and	and	CCONJ
cana-5422	771	39	uidp/04106/2020	uidp/04106/2020	NOUN
cana-5422	771	40	.	.	PUNCT
cana-5422	772	1	https://doi.org/10.54499/uidb/04106/2020	https://doi.org/10.54499/uidb/04106/2020	PROPN
cana-5422	772	2	and	and	CCONJ
cana-5422	772	3	https://doi.org/10.54499/uidp/04106/2020	https://doi.org/10.54499/uidp/04106/2020	NOUN
cana-5422	772	4	.	.	PUNCT
cana-5422	773	1	conflict	conflict	NOUN
cana-5422	773	2	of	of	ADP
cana-5422	773	3	interest	interest	NOUN
cana-5422	773	4	all	all	DET
cana-5422	773	5	authors	author	NOUN
cana-5422	773	6	declare	declare	VERB
cana-5422	773	7	that	that	SCONJ
cana-5422	773	8	they	they	PRON
cana-5422	773	9	have	have	VERB
cana-5422	773	10	no	no	DET
cana-5422	773	11	conflicts	conflict	NOUN
cana-5422	773	12	of	of	ADP
cana-5422	773	13	interest	interest	NOUN
cana-5422	773	14	.	.	PUNCT
cana-5422	774	1	communications	communication	NOUN
cana-5422	774	2	on	on	ADP
cana-5422	774	3	applied	apply	VERB
cana-5422	774	4	nonlinear	nonlinear	ADJ
cana-5422	774	5	analysis	analysis	NOUN
cana-5422	774	6	issn	issn	NOUN
cana-5422	774	7	:	:	PUNCT
cana-5422	774	8	1074	1074	NUM
cana-5422	774	9	-	-	PUNCT
cana-5422	774	10	133x	133x	NUM
cana-5422	774	11	vol	vol	NOUN
cana-5422	774	12	32	32	NUM
cana-5422	774	13	no	no	NOUN
cana-5422	774	14	.	.	PUNCT
cana-5422	775	1	10s(2025	10s(2025	NUM
cana-5422	775	2	)	)	PUNCT
cana-5422	775	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	775	4	2215	2215	NUM
cana-5422	775	5	references	reference	NOUN
cana-5422	775	6	[	[	X
cana-5422	775	7	1	1	NUM
cana-5422	775	8	]	]	PUNCT
cana-5422	775	9	j.	j.	PROPN
cana-5422	775	10	aczel	aczel	PROPN
cana-5422	775	11	lectures	lecture	NOUN
cana-5422	775	12	on	on	ADP
cana-5422	775	13	functional	functional	ADJ
cana-5422	775	14	equations	equation	NOUN
cana-5422	775	15	and	and	CCONJ
cana-5422	775	16	their	their	PRON
cana-5422	775	17	applications	application	NOUN
cana-5422	775	18	,	,	PUNCT
cana-5422	775	19	academic	academic	ADJ
cana-5422	775	20	press	press	NOUN
cana-5422	775	21	,	,	PUNCT
cana-5422	775	22	new	new	PROPN
cana-5422	775	23	york	york	PROPN
cana-5422	775	24	(	(	PUNCT
cana-5422	775	25	1966	1966	NUM
cana-5422	775	26	)	)	PUNCT
cana-5422	775	27	.	.	PUNCT
cana-5422	776	1	mr:348020	mr:348020	PROPN
cana-5422	776	2	(	(	PUNCT
cana-5422	776	3	1967	1967	NUM
cana-5422	776	4	)	)	PUNCT
cana-5422	776	5	.	.	PUNCT
cana-5422	777	1	[	[	X
cana-5422	777	2	2	2	X
cana-5422	777	3	]	]	PUNCT
cana-5422	777	4	t.	t.	PROPN
cana-5422	777	5	aoki	aoki	PROPN
cana-5422	777	6	,	,	PUNCT
cana-5422	777	7	on	on	ADP
cana-5422	777	8	the	the	DET
cana-5422	777	9	stability	stability	NOUN
cana-5422	777	10	of	of	ADP
cana-5422	777	11	the	the	DET
cana-5422	777	12	linear	linear	ADJ
cana-5422	777	13	transformation	transformation	NOUN
cana-5422	777	14	in	in	ADP
cana-5422	777	15	banach	banach	NOUN
cana-5422	777	16	spaces	space	NOUN
cana-5422	777	17	,	,	PUNCT
cana-5422	777	18	j.	j.	PROPN
cana-5422	777	19	math	math	PROPN
cana-5422	777	20	.	.	PUNCT
cana-5422	777	21	soc	soc	PROPN
cana-5422	777	22	.	.	PUNCT
cana-5422	778	1	japan	japan	PROPN
cana-5422	778	2	,	,	PUNCT
cana-5422	778	3	2	2	NUM
cana-5422	778	4	(	(	PUNCT
cana-5422	778	5	1950	1950	NUM
cana-5422	778	6	)	)	PUNCT
cana-5422	778	7	,	,	PUNCT
cana-5422	778	8	64–66	64–66	NUM
cana-5422	778	9	.	.	PUNCT
cana-5422	779	1	[	[	X
cana-5422	779	2	3	3	NUM
cana-5422	779	3	]	]	X
cana-5422	779	4	m.	m.	NOUN
cana-5422	779	5	arunkumar	arunkumar	PROPN
cana-5422	779	6	,	,	PUNCT
cana-5422	779	7	c.	c.	PROPN
cana-5422	779	8	devi	devi	PROPN
cana-5422	779	9	shyamala	shyamala	PROPN
cana-5422	779	10	mary	mary	PROPN
cana-5422	779	11	,	,	PUNCT
cana-5422	779	12	g.	g.	PROPN
cana-5422	779	13	shobana	shobana	PROPN
cana-5422	779	14	,	,	PUNCT
cana-5422	779	15	simple	simple	ADJ
cana-5422	779	16	aq	aq	NOUN
cana-5422	779	17	and	and	CCONJ
cana-5422	779	18	simple	simple	ADJ
cana-5422	779	19	cq	cq	PROPN
cana-5422	779	20	functional	functional	ADJ
cana-5422	779	21	equations	equation	NOUN
cana-5422	779	22	,	,	PUNCT
cana-5422	779	23	journal	journal	NOUN
cana-5422	779	24	of	of	ADP
cana-5422	779	25	concrete	concrete	ADJ
cana-5422	779	26	and	and	CCONJ
cana-5422	779	27	applicable	applicable	ADJ
cana-5422	779	28	mathematics	mathematic	NOUN
cana-5422	779	29	(	(	PUNCT
cana-5422	779	30	jcaam	jcaam	NOUN
cana-5422	779	31	)	)	PUNCT
cana-5422	779	32	,	,	PUNCT
cana-5422	779	33	13	13	NUM
cana-5422	779	34	,	,	PUNCT
cana-5422	779	35	issue	issue	NOUN
cana-5422	779	36	1/2	1/2	NUM
cana-5422	779	37	,	,	PUNCT
cana-5422	779	38	jan	jan	PROPN
cana-5422	779	39	apr	apr	PROPN
cana-5422	779	40	2015	2015	NUM
cana-5422	779	41	,	,	PUNCT
cana-5422	779	42	120	120	NUM
cana-5422	779	43	151	151	NUM
cana-5422	779	44	.	.	PUNCT
cana-5422	780	1	[	[	X
cana-5422	780	2	4	4	NUM
cana-5422	780	3	]	]	PUNCT
cana-5422	780	4	m.	m.	NOUN
cana-5422	780	5	arunkumar	arunkumar	PROPN
cana-5422	780	6	,	,	PUNCT
cana-5422	780	7	john	john	PROPN
cana-5422	780	8	m.	m.	PROPN
cana-5422	780	9	rassias	rassias	PROPN
cana-5422	780	10	,	,	PUNCT
cana-5422	780	11	on	on	ADP
cana-5422	780	12	the	the	DET
cana-5422	780	13	generalized	generalize	VERB
cana-5422	780	14	ulam	ulam	NOUN
cana-5422	780	15	-	-	PUNCT
cana-5422	780	16	hyers	hyer	NOUN
cana-5422	780	17	stability	stability	NOUN
cana-5422	780	18	of	of	ADP
cana-5422	780	19	an	an	DET
cana-5422	780	20	aq	aq	ADJ
cana-5422	780	21	-	-	PUNCT
cana-5422	780	22	mixed	mixed	ADJ
cana-5422	780	23	type	type	NOUN
cana-5422	780	24	functional	functional	ADJ
cana-5422	780	25	equation	equation	NOUN
cana-5422	780	26	with	with	ADP
cana-5422	780	27	counter	counter	ADJ
cana-5422	780	28	examples	example	NOUN
cana-5422	780	29	,	,	PUNCT
cana-5422	780	30	far	far	PROPN
cana-5422	780	31	east	east	NOUN
cana-5422	780	32	journal	journal	NOUN
cana-5422	780	33	of	of	ADP
cana-5422	780	34	applied	apply	VERB
cana-5422	780	35	mathematics	mathematic	NOUN
cana-5422	780	36	,	,	PUNCT
cana-5422	780	37	71	71	NUM
cana-5422	780	38	,	,	PUNCT
cana-5422	780	39	no	no	INTJ
cana-5422	780	40	.	.	NOUN
cana-5422	780	41	2	2	NUM
cana-5422	780	42	,	,	PUNCT
cana-5422	780	43	(	(	PUNCT
cana-5422	780	44	2012	2012	NUM
cana-5422	780	45	)	)	PUNCT
cana-5422	780	46	,	,	PUNCT
cana-5422	780	47	279	279	NUM
cana-5422	780	48	-	-	SYM
cana-5422	780	49	305	305	NUM
cana-5422	780	50	.	.	PUNCT
cana-5422	781	1	[	[	X
cana-5422	781	2	5	5	NUM
cana-5422	781	3	]	]	PUNCT
cana-5422	781	4	m.	m.	NOUN
cana-5422	781	5	arunkumar	arunkumar	PROPN
cana-5422	781	6	,	,	PUNCT
cana-5422	781	7	g.	g.	PROPN
cana-5422	781	8	ganapathy	ganapathy	PROPN
cana-5422	781	9	,	,	PUNCT
cana-5422	781	10	s.	s.	PROPN
cana-5422	781	11	murthy	murthy	PROPN
cana-5422	781	12	,	,	PUNCT
cana-5422	781	13	s.	s.	PROPN
cana-5422	781	14	karthikeyan	karthikeyan	PROPN
cana-5422	781	15	,	,	PUNCT
cana-5422	781	16	stability	stability	NOUN
cana-5422	781	17	of	of	ADP
cana-5422	781	18	the	the	DET
cana-5422	781	19	generalized	generalize	VERB
cana-5422	781	20	arun	arun	ADJ
cana-5422	781	21	-	-	PUNCT
cana-5422	781	22	additive	additive	ADJ
cana-5422	781	23	functional	functional	ADJ
cana-5422	781	24	equation	equation	NOUN
cana-5422	781	25	in	in	ADP
cana-5422	781	26	instutionistic	instutionistic	ADJ
cana-5422	781	27	fuzzy	fuzzy	ADJ
cana-5422	781	28	normed	normed	ADJ
cana-5422	781	29	spaces	space	NOUN
cana-5422	781	30	,	,	PUNCT
cana-5422	781	31	international	international	ADJ
cana-5422	781	32	journal	journal	PROPN
cana-5422	781	33	mathematical	mathematical	PROPN
cana-5422	781	34	sciences	sciences	PROPN
cana-5422	781	35	and	and	CCONJ
cana-5422	781	36	engineering	engineering	NOUN
cana-5422	781	37	applications	application	NOUN
cana-5422	781	38	,	,	PUNCT
cana-5422	781	39	4	4	NUM
cana-5422	781	40	,	,	PUNCT
cana-5422	781	41	no	no	INTJ
cana-5422	781	42	.	.	NOUN
cana-5422	781	43	v	v	NOUN
cana-5422	781	44	,	,	PUNCT
cana-5422	781	45	december	december	PROPN
cana-5422	781	46	2010	2010	NUM
cana-5422	781	47	,	,	PUNCT
cana-5422	781	48	135	135	NUM
cana-5422	781	49	-	-	SYM
cana-5422	781	50	146	146	NUM
cana-5422	781	51	.	.	PUNCT
cana-5422	782	1	[	[	X
cana-5422	782	2	6	6	NUM
cana-5422	782	3	]	]	PUNCT
cana-5422	782	4	m.arunkumar	m.arunkumar	NOUN
cana-5422	782	5	,	,	PUNCT
cana-5422	782	6	e.	e.	PROPN
cana-5422	782	7	sathya	sathya	PROPN
cana-5422	782	8	,	,	PUNCT
cana-5422	782	9	t.	t.	PROPN
cana-5422	782	10	namachivayam	namachivayam	PROPN
cana-5422	782	11	,	,	PUNCT
cana-5422	782	12	ulam	ulam	PROPN
cana-5422	782	13	stability	stability	NOUN
cana-5422	782	14	of	of	ADP
cana-5422	782	15	a	a	DET
cana-5422	782	16	alternate	alternate	ADJ
cana-5422	782	17	additive	additive	ADJ
cana-5422	782	18	quadratic	quadratic	ADJ
cana-5422	782	19	functional	functional	ADJ
cana-5422	782	20	equation	equation	NOUN
cana-5422	782	21	in	in	ADP
cana-5422	782	22	ifb	ifb	PROPN
cana-5422	782	23	space	space	NOUN
cana-5422	782	24	,	,	PUNCT
cana-5422	782	25	malaya	malaya	PROPN
cana-5422	782	26	journal	journal	PROPN
cana-5422	782	27	of	of	ADP
cana-5422	782	28	matematik	matematik	PROPN
cana-5422	782	29	,	,	PUNCT
cana-5422	782	30	s	s	PART
cana-5422	782	31	,	,	PUNCT
cana-5422	782	32	issue	issue	NOUN
cana-5422	782	33	1	1	NUM
cana-5422	782	34	(	(	PUNCT
cana-5422	782	35	2019	2019	NUM
cana-5422	782	36	)	)	PUNCT
cana-5422	782	37	,	,	PUNCT
cana-5422	782	38	171	171	NUM
cana-5422	782	39	-	-	SYM
cana-5422	782	40	187	187	NUM
cana-5422	782	41	.	.	PUNCT
cana-5422	783	1	[	[	X
cana-5422	783	2	7	7	X
cana-5422	783	3	]	]	X
cana-5422	783	4	k.t	k.t	PROPN
cana-5422	783	5	.	.	PROPN
cana-5422	783	6	atanassov	atanassov	PROPN
cana-5422	783	7	,	,	PUNCT
cana-5422	783	8	intuitionistic	intuitionistic	ADJ
cana-5422	783	9	fuzzy	fuzzy	ADJ
cana-5422	783	10	sets	set	NOUN
cana-5422	783	11	,	,	PUNCT
cana-5422	783	12	fuzzy	fuzzy	ADJ
cana-5422	783	13	sets	set	NOUN
cana-5422	783	14	and	and	CCONJ
cana-5422	783	15	systems	system	NOUN
cana-5422	783	16	,	,	PUNCT
cana-5422	783	17	20	20	NUM
cana-5422	783	18	(	(	PUNCT
cana-5422	783	19	1986	1986	NUM
cana-5422	783	20	)	)	PUNCT
cana-5422	783	21	,	,	PUNCT
cana-5422	783	22	87	87	NUM
cana-5422	783	23	-	-	SYM
cana-5422	783	24	96	96	NUM
cana-5422	783	25	.	.	PUNCT
cana-5422	784	1	[	[	X
cana-5422	784	2	8	8	NUM
cana-5422	784	3	]	]	PUNCT
cana-5422	784	4	a.	a.	NOUN
cana-5422	784	5	bodaghi	bodaghi	PROPN
cana-5422	784	6	,	,	PUNCT
cana-5422	784	7	m.	m.	PROPN
cana-5422	784	8	arunkumar	arunkumar	PROPN
cana-5422	784	9	,	,	PUNCT
cana-5422	784	10	e.sathya	e.sathya	NOUN
cana-5422	784	11	,	,	PUNCT
cana-5422	784	12	t.	t.	PROPN
cana-5422	784	13	namachivayam	namachivayam	PROPN
cana-5422	784	14	,	,	PUNCT
cana-5422	784	15	a	a	DET
cana-5422	784	16	new	new	ADJ
cana-5422	784	17	type	type	NOUN
cana-5422	784	18	of	of	ADP
cana-5422	784	19	the	the	DET
cana-5422	784	20	additive	additive	ADJ
cana-5422	784	21	functional	functional	ADJ
cana-5422	784	22	equations	equation	NOUN
cana-5422	784	23	on	on	ADP
cana-5422	784	24	intuitionistic	intuitionistic	ADJ
cana-5422	784	25	fuzzy	fuzzy	ADJ
cana-5422	784	26	normed	normed	ADJ
cana-5422	784	27	spaces	space	NOUN
cana-5422	784	28	,	,	PUNCT
cana-5422	784	29	commun	commun	PROPN
cana-5422	784	30	.	.	PUNCT
cana-5422	785	1	korean	korean	ADJ
cana-5422	785	2	math	math	PROPN
cana-5422	785	3	.	.	PUNCT
cana-5422	786	1	soc	soc	PROPN
cana-5422	786	2	.	.	PUNCT
cana-5422	786	3	,	,	PUNCT
cana-5422	786	4	32	32	NUM
cana-5422	786	5	(	(	PUNCT
cana-5422	786	6	2017	2017	NUM
cana-5422	786	7	)	)	PUNCT
cana-5422	786	8	,	,	PUNCT
cana-5422	786	9	no	no	INTJ
cana-5422	786	10	.	.	NOUN
cana-5422	786	11	4	4	NUM
cana-5422	786	12	,	,	PUNCT
cana-5422	786	13	pp	pp	ADJ
cana-5422	786	14	.	.	PUNCT
cana-5422	787	1	915	915	NUM
cana-5422	787	2	932	932	NUM
cana-5422	787	3	.	.	PUNCT
cana-5422	788	1	[	[	X
cana-5422	788	2	9	9	NUM
cana-5422	788	3	]	]	PUNCT
cana-5422	788	4	c.	c.	NOUN
cana-5422	788	5	benzarouala	benzarouala	PROPN
cana-5422	788	6	,	,	PUNCT
cana-5422	788	7	j.	j.	PROPN
cana-5422	788	8	brzdek	brzdek	PROPN
cana-5422	788	9	,	,	PUNCT
cana-5422	788	10	els	els	PROPN
cana-5422	788	11	.	.	PROPN
cana-5422	788	12	hady	hady	PROPN
cana-5422	788	13	,	,	PUNCT
cana-5422	788	14	l.	l.	PROPN
cana-5422	788	15	oubbi	oubbi	PROPN
cana-5422	788	16	,	,	PUNCT
cana-5422	788	17	on	on	ADP
cana-5422	788	18	ulam	ulam	PROPN
cana-5422	788	19	stability	stability	NOUN
cana-5422	788	20	of	of	ADP
cana-5422	788	21	the	the	DET
cana-5422	788	22	inhomogeneous	inhomogeneous	ADJ
cana-5422	788	23	version	version	NOUN
cana-5422	788	24	of	of	ADP
cana-5422	788	25	the	the	DET
cana-5422	788	26	general	general	ADJ
cana-5422	788	27	linear	linear	ADJ
cana-5422	788	28	functional	functional	ADJ
cana-5422	788	29	equation	equation	NOUN
cana-5422	788	30	,	,	PUNCT
cana-5422	788	31	results	result	VERB
cana-5422	788	32	math	math	NOUN
cana-5422	788	33	(	(	PUNCT
cana-5422	788	34	2023	2023	NUM
cana-5422	788	35	)	)	PUNCT
cana-5422	788	36	,	,	PUNCT
cana-5422	788	37	78:76	78:76	NUM
cana-5422	788	38	.	.	PUNCT
cana-5422	789	1	https://doi.org/10.1007/s00025-023-01840-7	https://doi.org/10.1007/s00025-023-01840-7	NOUN
cana-5422	789	2	.	.	PUNCT
cana-5422	790	1	[	[	X
cana-5422	790	2	10	10	NUM
cana-5422	790	3	]	]	X
cana-5422	790	4	c.	c.	PROPN
cana-5422	790	5	benzarouala	benzarouala	PROPN
cana-5422	790	6	,	,	PUNCT
cana-5422	790	7	j.	j.	PROPN
cana-5422	790	8	brzdek	brzdek	PROPN
cana-5422	790	9	,	,	PUNCT
cana-5422	790	10	l.	l.	PROPN
cana-5422	790	11	oubbi	oubbi	PROPN
cana-5422	790	12	,	,	PUNCT
cana-5422	790	13	a	a	DET
cana-5422	790	14	fixed	fix	VERB
cana-5422	790	15	point	point	NOUN
cana-5422	790	16	theorem	theorem	NOUN
cana-5422	790	17	and	and	CCONJ
cana-5422	790	18	ulam	ulam	PROPN
cana-5422	790	19	stability	stability	NOUN
cana-5422	790	20	of	of	ADP
cana-5422	790	21	a	a	DET
cana-5422	790	22	general	general	ADJ
cana-5422	790	23	linear	linear	ADJ
cana-5422	790	24	functional	functional	ADJ
cana-5422	790	25	equation	equation	NOUN
cana-5422	790	26	in	in	ADP
cana-5422	790	27	random	random	ADJ
cana-5422	790	28	normed	normed	ADJ
cana-5422	790	29	spaces	space	NOUN
cana-5422	790	30	,	,	PUNCT
cana-5422	790	31	j.	j.	PROPN
cana-5422	790	32	fixed	fix	VERB
cana-5422	790	33	point	point	PROPN
cana-5422	790	34	theory	theory	NOUN
cana-5422	790	35	appl	appl	PROPN
cana-5422	790	36	.	.	PROPN
cana-5422	790	37	,	,	PUNCT
cana-5422	790	38	(	(	PUNCT
cana-5422	790	39	2023	2023	NUM
cana-5422	790	40	)	)	PUNCT
cana-5422	790	41	25:33	25:33	NUM
cana-5422	790	42	.	.	PUNCT
cana-5422	791	1	https://doi.org/10.1007/s11784-022-01034-8	https://doi.org/10.1007/s11784-022-01034-8	NOUN
cana-5422	791	2	.	.	PUNCT
cana-5422	792	1	[	[	X
cana-5422	792	2	11	11	NUM
cana-5422	792	3	]	]	PUNCT
cana-5422	792	4	l.	l.	PROPN
cana-5422	792	5	cadariu	cadariu	PROPN
cana-5422	792	6	,	,	PUNCT
cana-5422	792	7	l.	l.	PROPN
cana-5422	792	8	gavruta	gavruta	PROPN
cana-5422	792	9	,	,	PUNCT
cana-5422	792	10	p.	p.	NOUN
cana-5422	792	11	gavruta	gavruta	NOUN
cana-5422	792	12	,	,	PUNCT
cana-5422	792	13	on	on	ADP
cana-5422	792	14	the	the	DET
cana-5422	792	15	stability	stability	NOUN
cana-5422	792	16	of	of	ADP
cana-5422	792	17	an	an	DET
cana-5422	792	18	affine	affine	ADJ
cana-5422	792	19	functional	functional	ADJ
cana-5422	792	20	equation	equation	NOUN
cana-5422	792	21	,	,	PUNCT
cana-5422	792	22	j.	j.	PROPN
cana-5422	792	23	nonlinear	nonlinear	PROPN
cana-5422	792	24	sci	sci	PROPN
cana-5422	792	25	.	.	PUNCT
cana-5422	792	26	appl	appl	PROPN
cana-5422	792	27	.	.	PROPN
cana-5422	792	28	,	,	PUNCT
cana-5422	792	29	6	6	NUM
cana-5422	792	30	(	(	PUNCT
cana-5422	792	31	2013	2013	NUM
cana-5422	792	32	)	)	PUNCT
cana-5422	792	33	,	,	PUNCT
cana-5422	792	34	60	60	NUM
cana-5422	792	35	-	-	SYM
cana-5422	792	36	67	67	NUM
cana-5422	792	37	.	.	PUNCT
cana-5422	793	1	[	[	X
cana-5422	793	2	12	12	NUM
cana-5422	793	3	]	]	X
cana-5422	793	4	i.s	i.s	PROPN
cana-5422	793	5	.	.	PROPN
cana-5422	793	6	chang	chang	PROPN
cana-5422	793	7	,	,	PUNCT
cana-5422	793	8	and	and	CCONJ
cana-5422	793	9	h.m	h.m	PROPN
cana-5422	793	10	.	.	PROPN
cana-5422	793	11	kim	kim	PROPN
cana-5422	793	12	,	,	PUNCT
cana-5422	793	13	on	on	ADP
cana-5422	793	14	the	the	DET
cana-5422	793	15	hyers	hyers	PROPN
cana-5422	793	16	-	-	PUNCT
cana-5422	793	17	ulam	ulam	ADJ
cana-5422	793	18	stability	stability	NOUN
cana-5422	793	19	of	of	ADP
cana-5422	793	20	quadratic	quadratic	ADJ
cana-5422	793	21	functional	functional	ADJ
cana-5422	793	22	equations	equation	NOUN
cana-5422	793	23	,	,	PUNCT
cana-5422	793	24	journal	journal	NOUN
cana-5422	793	25	of	of	ADP
cana-5422	793	26	inequalities	inequality	NOUN
cana-5422	793	27	in	in	ADP
cana-5422	793	28	pure	pure	ADJ
cana-5422	793	29	and	and	CCONJ
cana-5422	793	30	applied	applied	ADJ
cana-5422	793	31	mathematics	mathematic	NOUN
cana-5422	793	32	,	,	PUNCT
cana-5422	793	33	volume	volume	NOUN
cana-5422	793	34	3	3	NUM
cana-5422	793	35	,	,	PUNCT
cana-5422	793	36	issue	issue	NOUN
cana-5422	793	37	3	3	NUM
cana-5422	793	38	,	,	PUNCT
cana-5422	793	39	article	article	NOUN
cana-5422	793	40	33	33	NUM
cana-5422	793	41	,	,	PUNCT
cana-5422	793	42	2002	2002	NUM
cana-5422	793	43	.	.	PUNCT
cana-5422	794	1	[	[	X
cana-5422	794	2	13	13	NUM
cana-5422	794	3	]	]	PUNCT
cana-5422	794	4	p.	p.	NOUN
cana-5422	794	5	gǎvrutǎ	gǎvrutǎ	PROPN
cana-5422	794	6	,	,	PUNCT
cana-5422	794	7	a	a	DET
cana-5422	794	8	generalization	generalization	NOUN
cana-5422	794	9	of	of	ADP
cana-5422	794	10	the	the	DET
cana-5422	794	11	hyers	hyers	PROPN
cana-5422	794	12	-	-	PUNCT
cana-5422	794	13	ulam	ulam	ADJ
cana-5422	794	14	-	-	PUNCT
cana-5422	794	15	rassias	rassias	PROPN
cana-5422	794	16	stability	stability	NOUN
cana-5422	794	17	of	of	ADP
cana-5422	794	18	approximately	approximately	ADV
cana-5422	794	19	additive	additive	ADJ
cana-5422	794	20	mappings	mapping	NOUN
cana-5422	794	21	,	,	PUNCT
cana-5422	794	22	j.	j.	PROPN
cana-5422	794	23	math	math	PROPN
cana-5422	794	24	.	.	PUNCT
cana-5422	795	1	anal	anal	PROPN
cana-5422	795	2	.	.	PUNCT
cana-5422	795	3	appl	appl	PROPN
cana-5422	795	4	.	.	PROPN
cana-5422	796	1	,	,	PUNCT
cana-5422	796	2	184	184	NUM
cana-5422	796	3	(	(	PUNCT
cana-5422	796	4	1994	1994	NUM
cana-5422	796	5	)	)	PUNCT
cana-5422	796	6	,	,	PUNCT
cana-5422	796	7	no	no	INTJ
cana-5422	796	8	.	.	NOUN
cana-5422	796	9	3	3	NUM
cana-5422	796	10	,	,	PUNCT
cana-5422	796	11	431–436	431–436	NUM
cana-5422	796	12	.	.	PUNCT
cana-5422	797	1	[	[	X
cana-5422	797	2	14	14	NUM
cana-5422	797	3	]	]	X
cana-5422	797	4	d.	d.	PROPN
cana-5422	797	5	h.	h.	PROPN
cana-5422	797	6	hyers	hyers	PROPN
cana-5422	797	7	,	,	PUNCT
cana-5422	797	8	on	on	ADP
cana-5422	797	9	the	the	DET
cana-5422	797	10	stability	stability	NOUN
cana-5422	797	11	of	of	ADP
cana-5422	797	12	the	the	DET
cana-5422	797	13	linear	linear	ADJ
cana-5422	797	14	functional	functional	ADJ
cana-5422	797	15	equation	equation	NOUN
cana-5422	797	16	,	,	PUNCT
cana-5422	797	17	proc	proc	NOUN
cana-5422	797	18	.	.	PUNCT
cana-5422	798	1	nat	nat	PROPN
cana-5422	798	2	.	.	PUNCT
cana-5422	799	1	acad	acad	PROPN
cana-5422	799	2	.	.	PUNCT
cana-5422	800	1	sci	sci	PROPN
cana-5422	800	2	.	.	PROPN
cana-5422	800	3	,	,	PUNCT
cana-5422	800	4	u.	u.	PROPN
cana-5422	800	5	s.	s.	PROPN
cana-5422	800	6	a.	a.	PROPN
cana-5422	800	7	27	27	NUM
cana-5422	800	8	(	(	PUNCT
cana-5422	800	9	1941	1941	NUM
cana-5422	800	10	)	)	PUNCT
cana-5422	800	11	,	,	PUNCT
cana-5422	800	12	222–224	222–224	NUM
cana-5422	800	13	.	.	PUNCT
cana-5422	801	1	[	[	X
cana-5422	801	2	15	15	NUM
cana-5422	801	3	]	]	X
cana-5422	801	4	s.m	s.m	PROPN
cana-5422	801	5	.	.	PROPN
cana-5422	801	6	jung	jung	PROPN
cana-5422	801	7	,	,	PUNCT
cana-5422	801	8	hyers	hyers	PROPN
cana-5422	801	9	-	-	PUNCT
cana-5422	801	10	ulam	ulam	ADJ
cana-5422	801	11	-	-	PUNCT
cana-5422	801	12	rassias	rassias	PROPN
cana-5422	801	13	stability	stability	NOUN
cana-5422	801	14	of	of	ADP
cana-5422	801	15	functional	functional	ADJ
cana-5422	801	16	equations	equation	NOUN
cana-5422	801	17	in	in	ADP
cana-5422	801	18	mathematical	mathematical	ADJ
cana-5422	801	19	analysis	analysis	NOUN
cana-5422	801	20	,	,	PUNCT
cana-5422	801	21	hadronic	hadronic	ADJ
cana-5422	801	22	press	press	NOUN
cana-5422	801	23	,	,	PUNCT
cana-5422	801	24	palm	palm	NOUN
cana-5422	801	25	harbor	harbor	NOUN
cana-5422	801	26	,	,	PUNCT
cana-5422	801	27	2001	2001	NUM
cana-5422	801	28	.	.	PUNCT
cana-5422	802	1	[	[	X
cana-5422	802	2	16	16	NUM
cana-5422	802	3	]	]	X
cana-5422	802	4	pl	pl	PROPN
cana-5422	802	5	.	.	PROPN
cana-5422	802	6	kannappan	kannappan	PROPN
cana-5422	802	7	,	,	PUNCT
cana-5422	802	8	functional	functional	ADJ
cana-5422	802	9	equations	equation	NOUN
cana-5422	802	10	and	and	CCONJ
cana-5422	802	11	inequalities	inequality	NOUN
cana-5422	802	12	with	with	ADP
cana-5422	802	13	applications	application	NOUN
cana-5422	802	14	,	,	PUNCT
cana-5422	802	15	springer	springer	NOUN
cana-5422	802	16	monographs	monograph	NOUN
cana-5422	802	17	in	in	ADP
cana-5422	802	18	mathematics	mathematic	NOUN
cana-5422	802	19	,	,	PUNCT
cana-5422	802	20	2009	2009	NUM
cana-5422	802	21	.	.	PUNCT
cana-5422	803	1	[	[	X
cana-5422	803	2	17	17	NUM
cana-5422	803	3	]	]	X
cana-5422	803	4	l.	l.	PROPN
cana-5422	803	5	lucht	lucht	PROPN
cana-5422	803	6	,	,	PUNCT
cana-5422	803	7	c.	c.	PROPN
cana-5422	803	8	methfessel	methfessel	NOUN
cana-5422	803	9	,	,	PUNCT
cana-5422	803	10	recurrent	recurrent	ADJ
cana-5422	803	11	sequences	sequence	NOUN
cana-5422	803	12	and	and	CCONJ
cana-5422	803	13	affine	affine	ADJ
cana-5422	803	14	functional	functional	ADJ
cana-5422	803	15	equations	equation	NOUN
cana-5422	803	16	,	,	PUNCT
cana-5422	803	17	journal	journal	NOUN
cana-5422	803	18	of	of	ADP
cana-5422	803	19	number	number	NOUN
cana-5422	803	20	theory	theory	NOUN
cana-5422	803	21	57	57	NUM
cana-5422	803	22	,	,	PUNCT
cana-5422	803	23	(	(	PUNCT
cana-5422	803	24	1996	1996	NUM
cana-5422	803	25	)	)	PUNCT
cana-5422	803	26	,	,	PUNCT
cana-5422	803	27	105	105	NUM
cana-5422	803	28	-	-	SYM
cana-5422	803	29	113	113	NUM
cana-5422	803	30	.	.	PUNCT
cana-5422	803	31	,	,	PUNCT
cana-5422	803	32	autumn	autumn	NOUN
cana-5422	803	33	2008	2008	NUM
cana-5422	803	34	3	3	NUM
cana-5422	803	35	,	,	PUNCT
cana-5422	803	36	no	no	INTJ
cana-5422	803	37	.	.	NOUN
cana-5422	803	38	08	08	NUM
cana-5422	803	39	,	,	PUNCT
cana-5422	803	40	36	36	NUM
cana-5422	803	41	-	-	SYM
cana-5422	803	42	47	47	NUM
cana-5422	803	43	.	.	PUNCT
cana-5422	804	1	[	[	X
cana-5422	804	2	18	18	NUM
cana-5422	804	3	]	]	X
cana-5422	804	4	b.	b.	PROPN
cana-5422	804	5	margolis	margolis	PROPN
cana-5422	804	6	,	,	PUNCT
cana-5422	804	7	j.	j.	PROPN
cana-5422	804	8	b.	b.	PROPN
cana-5422	804	9	diaz	diaz	PROPN
cana-5422	804	10	,	,	PUNCT
cana-5422	804	11	a	a	DET
cana-5422	804	12	fixed	fix	VERB
cana-5422	804	13	point	point	NOUN
cana-5422	804	14	theorem	theorem	NOUN
cana-5422	804	15	of	of	ADP
cana-5422	804	16	the	the	DET
cana-5422	804	17	alternative	alternative	NOUN
cana-5422	804	18	for	for	ADP
cana-5422	804	19	contractions	contraction	NOUN
cana-5422	804	20	on	on	ADP
cana-5422	804	21	a	a	DET
cana-5422	804	22	generalized	generalized	ADJ
cana-5422	804	23	complete	complete	ADJ
cana-5422	804	24	metric	metric	ADJ
cana-5422	804	25	space	space	NOUN
cana-5422	804	26	,	,	PUNCT
cana-5422	804	27	bull	bull	NOUN
cana-5422	804	28	.	.	PUNCT
cana-5422	805	1	amer	amer	PROPN
cana-5422	805	2	.	.	PUNCT
cana-5422	805	3	math	math	PROPN
cana-5422	805	4	.	.	PUNCT
cana-5422	806	1	soc	soc	PROPN
cana-5422	806	2	.	.	PUNCT
cana-5422	807	1	126	126	NUM
cana-5422	807	2	,	,	PUNCT
cana-5422	807	3	no.74	no.74	NOUN
cana-5422	807	4	(	(	PUNCT
cana-5422	807	5	1968	1968	NUM
cana-5422	807	6	)	)	PUNCT
cana-5422	807	7	,	,	PUNCT
cana-5422	807	8	305	305	NUM
cana-5422	807	9	-	-	SYM
cana-5422	807	10	309	309	NUM
cana-5422	807	11	.	.	PUNCT
cana-5422	808	1	[	[	X
cana-5422	808	2	19	19	NUM
cana-5422	808	3	]	]	PUNCT
cana-5422	808	4	m.	m.	NOUN
cana-5422	808	5	mursaleen	mursaleen	PROPN
cana-5422	808	6	and	and	CCONJ
cana-5422	808	7	kj	kj	PROPN
cana-5422	808	8	.	.	PUNCT
cana-5422	808	9	ansari	ansari	PROPN
cana-5422	808	10	,	,	PUNCT
cana-5422	808	11	the	the	DET
cana-5422	808	12	stability	stability	NOUN
cana-5422	808	13	of	of	ADP
cana-5422	808	14	an	an	DET
cana-5422	808	15	affine	affine	ADJ
cana-5422	808	16	type	type	NOUN
cana-5422	808	17	functional	functional	ADJ
cana-5422	808	18	equation	equation	NOUN
cana-5422	808	19	with	with	ADP
cana-5422	808	20	the	the	DET
cana-5422	808	21	fixed	fix	VERB
cana-5422	808	22	point	point	NOUN
cana-5422	808	23	alternative	alternative	NOUN
cana-5422	808	24	,	,	PUNCT
cana-5422	808	25	in	in	ADP
cana-5422	808	26	:	:	PUNCT
cana-5422	808	27	t.	t.	PROPN
cana-5422	808	28	rassias	rassias	PROPN
cana-5422	808	29	and	and	CCONJ
cana-5422	808	30	l.	l.	PROPN
cana-5422	808	31	toth	toth	PROPN
cana-5422	808	32	(	(	PUNCT
cana-5422	808	33	eds	eds	PROPN
cana-5422	808	34	.	.	PUNCT
cana-5422	808	35	)	)	PUNCT
cana-5422	808	36	,	,	PUNCT
cana-5422	808	37	topics	topic	NOUN
cana-5422	808	38	in	in	ADP
cana-5422	808	39	mathematical	mathematical	ADJ
cana-5422	808	40	analysis	analysis	NOUN
cana-5422	808	41	and	and	CCONJ
cana-5422	808	42	applications	application	NOUN
cana-5422	808	43	,	,	PUNCT
cana-5422	808	44	springer	springer	NOUN
cana-5422	808	45	,	,	PUNCT
cana-5422	808	46	switzerland	switzerland	PROPN
cana-5422	808	47	,	,	PUNCT
cana-5422	808	48	(	(	PUNCT
cana-5422	808	49	2014	2014	NUM
cana-5422	808	50	)	)	PUNCT
cana-5422	808	51	,	,	PUNCT
cana-5422	808	52	557571	557571	NUM
cana-5422	808	53	.	.	PUNCT
cana-5422	809	1	[	[	X
cana-5422	809	2	20	20	NUM
cana-5422	809	3	]	]	PUNCT
cana-5422	809	4	m.	m.	NOUN
cana-5422	809	5	mursaleen	mursaleen	PROPN
cana-5422	809	6	and	and	CCONJ
cana-5422	809	7	kj	kj	PROPN
cana-5422	809	8	.	.	PUNCT
cana-5422	809	9	ansari	ansari	PROPN
cana-5422	809	10	,	,	PUNCT
cana-5422	809	11	the	the	DET
cana-5422	809	12	stability	stability	NOUN
cana-5422	809	13	of	of	ADP
cana-5422	809	14	a	a	DET
cana-5422	809	15	generalized	generalize	VERB
cana-5422	809	16	affine	affine	ADJ
cana-5422	809	17	functional	functional	ADJ
cana-5422	809	18	equation	equation	NOUN
cana-5422	809	19	in	in	ADP
cana-5422	809	20	fuzzy	fuzzy	ADJ
cana-5422	809	21	normed	normed	ADJ
cana-5422	809	22	spaces	space	NOUN
cana-5422	809	23	,	,	PUNCT
cana-5422	809	24	publications	publication	NOUN
cana-5422	809	25	de	de	X
cana-5422	809	26	linstitut	linstitut	PROPN
cana-5422	809	27	mathmatique	mathmatique	NOUN
cana-5422	809	28	,	,	PUNCT
cana-5422	809	29	nouvelle	nouvelle	PROPN
cana-5422	809	30	srie	srie	NOUN
cana-5422	809	31	,	,	PUNCT
cana-5422	809	32	tome	tome	NOUN
cana-5422	809	33	,	,	PUNCT
cana-5422	809	34	100	100	NUM
cana-5422	809	35	(	(	PUNCT
cana-5422	809	36	114	114	NUM
cana-5422	809	37	)	)	PUNCT
cana-5422	809	38	(	(	PUNCT
cana-5422	809	39	2016	2016	NUM
cana-5422	809	40	)	)	PUNCT
cana-5422	809	41	,	,	PUNCT
cana-5422	809	42	163	163	NUM
cana-5422	809	43	-	-	SYM
cana-5422	809	44	181	181	NUM
cana-5422	809	45	.	.	PUNCT
cana-5422	809	46	doi	doi	NOUN
cana-5422	809	47	:	:	PUNCT
cana-5422	809	48	10.2298	10.2298	NUM
cana-5422	809	49	/	/	SYM
cana-5422	809	50	pim1614163	pim1614163	NOUN
cana-5422	809	51	m.	m.	NOUN
cana-5422	810	1	[	[	X
cana-5422	810	2	21	21	NUM
cana-5422	810	3	]	]	X
cana-5422	810	4	md	md	PROPN
cana-5422	810	5	.	.	PROPN
cana-5422	810	6	nasiruzzaman	nasiruzzaman	PROPN
cana-5422	810	7	,	,	PUNCT
cana-5422	810	8	on	on	ADP
cana-5422	810	9	the	the	DET
cana-5422	810	10	fuzzy	fuzzy	ADJ
cana-5422	810	11	stability	stability	NOUN
cana-5422	810	12	of	of	ADP
cana-5422	810	13	an	an	DET
cana-5422	810	14	affine	affine	ADJ
cana-5422	810	15	functional	functional	ADJ
cana-5422	810	16	equation	equation	NOUN
cana-5422	810	17	,	,	PUNCT
cana-5422	810	18	http://arxiv.org/abs/1506.02488v1	http://arxiv.org/abs/1506.02488v1	X
cana-5422	810	19	.	.	PUNCT
cana-5422	811	1	[	[	X
cana-5422	811	2	math.ca	math.ca	X
cana-5422	811	3	]	]	X
cana-5422	811	4	24	24	NUM
cana-5422	811	5	may	may	PROPN
cana-5422	811	6	2015	2015	NUM
cana-5422	811	7	.	.	PUNCT
cana-5422	812	1	[	[	X
cana-5422	812	2	22	22	NUM
cana-5422	812	3	]	]	X
cana-5422	812	4	v.	v.	X
cana-5422	812	5	radu	radu	PROPN
cana-5422	812	6	,	,	PUNCT
cana-5422	812	7	the	the	DET
cana-5422	812	8	fixed	fix	VERB
cana-5422	812	9	point	point	NOUN
cana-5422	812	10	alternative	alternative	NOUN
cana-5422	812	11	and	and	CCONJ
cana-5422	812	12	the	the	DET
cana-5422	812	13	stability	stability	NOUN
cana-5422	812	14	of	of	ADP
cana-5422	812	15	functional	functional	ADJ
cana-5422	812	16	equations	equation	NOUN
cana-5422	812	17	,	,	PUNCT
cana-5422	812	18	fixed	fix	VERB
cana-5422	812	19	point	point	NOUN
cana-5422	812	20	theory	theory	NOUN
cana-5422	812	21	,	,	PUNCT
cana-5422	812	22	4	4	NUM
cana-5422	812	23	,	,	PUNCT
cana-5422	812	24	no	no	INTJ
cana-5422	812	25	.	.	NOUN
cana-5422	812	26	1	1	NUM
cana-5422	812	27	,	,	PUNCT
cana-5422	812	28	pp	pp	ADJ
cana-5422	812	29	.	.	PUNCT
cana-5422	812	30	91	91	NUM
cana-5422	812	31	-	-	SYM
cana-5422	812	32	96	96	NUM
cana-5422	812	33	,	,	PUNCT
cana-5422	812	34	2003	2003	NUM
cana-5422	812	35	.	.	PUNCT
cana-5422	813	1	[	[	X
cana-5422	813	2	23	23	NUM
cana-5422	813	3	]	]	PUNCT
cana-5422	813	4	j.	j.	PROPN
cana-5422	813	5	m.	m.	PROPN
cana-5422	813	6	rassias	rassias	PROPN
cana-5422	813	7	,	,	PUNCT
cana-5422	813	8	on	on	ADP
cana-5422	813	9	approximation	approximation	NOUN
cana-5422	813	10	of	of	ADP
cana-5422	813	11	approximately	approximately	ADV
cana-5422	813	12	linear	linear	ADJ
cana-5422	813	13	mappings	mapping	NOUN
cana-5422	813	14	by	by	ADP
cana-5422	813	15	linear	linear	PROPN
cana-5422	813	16	mappings	mapping	NOUN
cana-5422	813	17	,	,	PUNCT
cana-5422	813	18	j.	j.	PROPN
cana-5422	813	19	funct	funct	PROPN
cana-5422	813	20	.	.	PUNCT
cana-5422	814	1	anal	anal	PROPN
cana-5422	814	2	.	.	PROPN
cana-5422	814	3	,	,	PUNCT
cana-5422	814	4	46	46	NUM
cana-5422	814	5	(	(	PUNCT
cana-5422	814	6	1982	1982	NUM
cana-5422	814	7	)	)	PUNCT
cana-5422	814	8	,	,	PUNCT
cana-5422	815	1	no	no	INTJ
cana-5422	815	2	.	.	NOUN
cana-5422	815	3	1	1	NUM
cana-5422	815	4	,	,	PUNCT
cana-5422	815	5	126–130	126–130	NUM
cana-5422	815	6	.	.	PUNCT
cana-5422	816	1	[	[	X
cana-5422	816	2	24	24	NUM
cana-5422	816	3	]	]	SYM
cana-5422	816	4	th	th	X
cana-5422	816	5	.	.	PUNCT
cana-5422	816	6	m.	m.	NOUN
cana-5422	816	7	rassias	rassias	PROPN
cana-5422	816	8	,	,	PUNCT
cana-5422	816	9	on	on	ADP
cana-5422	816	10	the	the	DET
cana-5422	816	11	stability	stability	NOUN
cana-5422	816	12	of	of	ADP
cana-5422	816	13	the	the	DET
cana-5422	816	14	linear	linear	ADJ
cana-5422	816	15	mapping	mapping	NOUN
cana-5422	816	16	in	in	ADP
cana-5422	816	17	banach	banach	NOUN
cana-5422	816	18	spaces	space	NOUN
cana-5422	816	19	,	,	PUNCT
cana-5422	816	20	proc	proc	NOUN
cana-5422	816	21	.	.	PUNCT
cana-5422	817	1	amer	amer	PROPN
cana-5422	817	2	.	.	PUNCT
cana-5422	817	3	math	math	PROPN
cana-5422	817	4	.	.	PUNCT
cana-5422	818	1	soc	soc	PROPN
cana-5422	818	2	.	.	PUNCT
cana-5422	818	3	,	,	PUNCT
cana-5422	818	4	72	72	NUM
cana-5422	818	5	(	(	PUNCT
cana-5422	818	6	1978	1978	NUM
cana-5422	818	7	)	)	PUNCT
cana-5422	818	8	,	,	PUNCT
cana-5422	818	9	no	no	INTJ
cana-5422	818	10	.	.	NOUN
cana-5422	818	11	2	2	NUM
cana-5422	818	12	,	,	PUNCT
cana-5422	818	13	297–300	297–300	NUM
cana-5422	818	14	.	.	PUNCT
cana-5422	819	1	[	[	X
cana-5422	819	2	25	25	NUM
cana-5422	819	3	]	]	PUNCT
cana-5422	819	4	th.m	th.m	PROPN
cana-5422	819	5	.	.	PUNCT
cana-5422	820	1	rassias	rassias	PROPN
cana-5422	820	2	,	,	PUNCT
cana-5422	820	3	functional	functional	ADJ
cana-5422	820	4	equations	equation	NOUN
cana-5422	820	5	,	,	PUNCT
cana-5422	820	6	inequalities	inequality	NOUN
cana-5422	820	7	and	and	CCONJ
cana-5422	820	8	applications	application	NOUN
cana-5422	820	9	,	,	PUNCT
cana-5422	820	10	kluwer	kluwer	NOUN
cana-5422	820	11	acedamic	acedamic	ADJ
cana-5422	820	12	publishers	publisher	NOUN
cana-5422	820	13	,	,	PUNCT
cana-5422	820	14	dordrecht	dordrecht	PROPN
cana-5422	820	15	,	,	PUNCT
cana-5422	820	16	bostan	bostan	PROPN
cana-5422	820	17	london	london	PROPN
cana-5422	820	18	,	,	PUNCT
cana-5422	820	19	2003	2003	NUM
cana-5422	820	20	.	.	PUNCT
cana-5422	821	1	[	[	X
cana-5422	821	2	26	26	NUM
cana-5422	821	3	]	]	PUNCT
cana-5422	821	4	k.	k.	PROPN
cana-5422	821	5	ravi	ravi	PROPN
cana-5422	821	6	,	,	PUNCT
cana-5422	821	7	m.	m.	NOUN
cana-5422	821	8	arunkumar	arunkumar	PROPN
cana-5422	821	9	and	and	CCONJ
cana-5422	821	10	j.m	j.m	PROPN
cana-5422	821	11	.	.	PROPN
cana-5422	821	12	rassias	rassias	PROPN
cana-5422	821	13	,	,	PUNCT
cana-5422	821	14	on	on	ADP
cana-5422	821	15	the	the	DET
cana-5422	821	16	ulam	ulam	PROPN
cana-5422	821	17	stability	stability	NOUN
cana-5422	821	18	for	for	ADP
cana-5422	821	19	the	the	DET
cana-5422	821	20	orthogonally	orthogonally	ADV
cana-5422	821	21	general	general	ADJ
cana-5422	821	22	euler	euler	PROPN
cana-5422	821	23	-	-	PUNCT
cana-5422	821	24	lagrange	lagrange	NOUN
cana-5422	821	25	type	type	NOUN
cana-5422	821	26	functional	functional	ADJ
cana-5422	821	27	equation	equation	NOUN
cana-5422	821	28	,	,	PUNCT
cana-5422	821	29	international	international	ADJ
cana-5422	821	30	journal	journal	NOUN
cana-5422	821	31	of	of	ADP
cana-5422	821	32	mathematical	mathematical	ADJ
cana-5422	821	33	sciences	sciences	PROPN
cana-5422	821	34	,	,	PUNCT
cana-5422	821	35	autumn	autumn	NOUN
cana-5422	821	36	2008	2008	NUM
cana-5422	821	37	3	3	NUM
cana-5422	821	38	,	,	PUNCT
cana-5422	821	39	no	no	INTJ
cana-5422	821	40	.	.	NOUN
cana-5422	821	41	08	08	NUM
cana-5422	821	42	,	,	PUNCT
cana-5422	821	43	36	36	NUM
cana-5422	821	44	-	-	SYM
cana-5422	821	45	47	47	NUM
cana-5422	821	46	.	.	PUNCT
cana-5422	822	1	[	[	X
cana-5422	822	2	27	27	NUM
cana-5422	822	3	]	]	X
cana-5422	822	4	r.	r.	PROPN
cana-5422	822	5	saadati	saadati	PROPN
cana-5422	822	6	,	,	PUNCT
cana-5422	822	7	j.	j.	PROPN
cana-5422	822	8	h.	h.	PROPN
cana-5422	822	9	park	park	PROPN
cana-5422	822	10	,	,	PUNCT
cana-5422	822	11	on	on	ADP
cana-5422	822	12	the	the	DET
cana-5422	822	13	intuitionistic	intuitionistic	ADJ
cana-5422	822	14	fuzzy	fuzzy	ADJ
cana-5422	822	15	topological	topological	ADJ
cana-5422	822	16	spaces	space	NOUN
cana-5422	822	17	,	,	PUNCT
cana-5422	822	18	chaos	chaos	NOUN
cana-5422	822	19	,	,	PUNCT
cana-5422	822	20	solitons	soliton	NOUN
cana-5422	822	21	and	and	CCONJ
cana-5422	822	22	fractals	fractal	NOUN
cana-5422	822	23	.	.	PUNCT
cana-5422	823	1	27	27	NUM
cana-5422	823	2	(	(	PUNCT
cana-5422	823	3	2006	2006	NUM
cana-5422	823	4	)	)	PUNCT
cana-5422	823	5	,	,	PUNCT
cana-5422	823	6	331–344	331–344	NUM
cana-5422	823	7	.	.	PUNCT
cana-5422	824	1	[	[	X
cana-5422	824	2	28	28	NUM
cana-5422	824	3	]	]	X
cana-5422	824	4	r.	r.	PROPN
cana-5422	824	5	saadati	saadati	PROPN
cana-5422	824	6	,	,	PUNCT
cana-5422	824	7	j.	j.	PROPN
cana-5422	824	8	h.	h.	PROPN
cana-5422	824	9	park	park	PROPN
cana-5422	824	10	,	,	PUNCT
cana-5422	824	11	intuitionstic	intuitionstic	ADJ
cana-5422	824	12	fuzzy	fuzzy	ADJ
cana-5422	824	13	euclidean	euclidean	ADJ
cana-5422	824	14	normed	normed	PROPN
cana-5422	824	15	spaces	space	NOUN
cana-5422	824	16	,	,	PUNCT
cana-5422	824	17	commun	commun	PROPN
cana-5422	824	18	.	.	PUNCT
cana-5422	824	19	math	math	PROPN
cana-5422	824	20	.	.	PUNCT
cana-5422	825	1	anal	anal	PROPN
cana-5422	825	2	.	.	PROPN
cana-5422	825	3	,	,	PUNCT
cana-5422	825	4	1	1	NUM
cana-5422	825	5	(	(	PUNCT
cana-5422	825	6	2006	2006	NUM
cana-5422	825	7	)	)	PUNCT
cana-5422	825	8	,	,	PUNCT
cana-5422	825	9	85–90	85–90	NUM
cana-5422	825	10	.	.	PUNCT
cana-5422	826	1	[	[	X
cana-5422	826	2	29	29	NUM
cana-5422	826	3	]	]	X
cana-5422	826	4	r.	r.	PROPN
cana-5422	826	5	saadati	saadati	PROPN
cana-5422	826	6	,	,	PUNCT
cana-5422	826	7	s.	s.	PROPN
cana-5422	826	8	sedghi	sedghi	PROPN
cana-5422	826	9	and	and	CCONJ
cana-5422	826	10	n.	n.	PROPN
cana-5422	826	11	shobe	shobe	PROPN
cana-5422	826	12	,	,	PUNCT
cana-5422	826	13	modified	modify	VERB
cana-5422	826	14	intuitionistic	intuitionistic	ADJ
cana-5422	826	15	fuzzy	fuzzy	ADJ
cana-5422	826	16	metric	metric	ADJ
cana-5422	826	17	spaces	space	NOUN
cana-5422	826	18	and	and	CCONJ
cana-5422	826	19	some	some	DET
cana-5422	826	20	fixed	fix	VERB
cana-5422	826	21	point	point	NOUN
cana-5422	826	22	theorems	theorem	NOUN
cana-5422	826	23	,	,	PUNCT
cana-5422	826	24	chaos	chaos	NOUN
cana-5422	826	25	,	,	PUNCT
cana-5422	826	26	solitons	soliton	NOUN
cana-5422	826	27	and	and	CCONJ
cana-5422	826	28	fractals	fractal	NOUN
cana-5422	826	29	,	,	PUNCT
cana-5422	826	30	38	38	NUM
cana-5422	826	31	(	(	PUNCT
cana-5422	826	32	2008	2008	NUM
cana-5422	826	33	)	)	PUNCT
cana-5422	826	34	,	,	PUNCT
cana-5422	826	35	36–47	36–47	NUM
cana-5422	826	36	.	.	PUNCT
cana-5422	827	1	[	[	X
cana-5422	827	2	30	30	NUM
cana-5422	827	3	]	]	PUNCT
cana-5422	828	1	p.	p.	PROPN
cana-5422	828	2	k.	k.	PROPN
cana-5422	829	1	sahoo	sahoo	PROPN
cana-5422	829	2	,	,	PUNCT
cana-5422	829	3	pl	pl	PROPN
cana-5422	829	4	.	.	PROPN
cana-5422	829	5	kannappan	kannappan	PROPN
cana-5422	829	6	,	,	PUNCT
cana-5422	829	7	introduction	introduction	NOUN
cana-5422	829	8	to	to	ADP
cana-5422	829	9	functional	functional	ADJ
cana-5422	829	10	equations	equation	NOUN
cana-5422	829	11	,	,	PUNCT
cana-5422	829	12	chapman	chapman	NOUN
cana-5422	829	13	and	and	CCONJ
cana-5422	829	14	hall	hall	PROPN
cana-5422	829	15	/	/	SYM
cana-5422	829	16	crc	crc	PROPN
cana-5422	829	17	taylor	taylor	PROPN
cana-5422	829	18	and	and	CCONJ
cana-5422	829	19	francis	francis	PROPN
cana-5422	829	20	group	group	PROPN
cana-5422	829	21	,	,	PUNCT
cana-5422	829	22	2011	2011	NUM
cana-5422	829	23	.	.	PUNCT
cana-5422	830	1	[	[	X
cana-5422	830	2	31	31	NUM
cana-5422	830	3	]	]	PUNCT
cana-5422	830	4	s.	s.	PROPN
cana-5422	830	5	m.	m.	PROPN
cana-5422	830	6	ulam	ulam	PROPN
cana-5422	830	7	,	,	PUNCT
cana-5422	830	8	problems	problem	NOUN
cana-5422	830	9	in	in	ADP
cana-5422	830	10	modern	modern	ADJ
cana-5422	830	11	mathematics	mathematic	NOUN
cana-5422	830	12	,	,	PUNCT
cana-5422	830	13	science	science	NOUN
cana-5422	830	14	editions	edition	NOUN
cana-5422	830	15	john	john	PROPN
cana-5422	830	16	wiley	wiley	PROPN
cana-5422	830	17	&	&	CCONJ
cana-5422	830	18	sons	sons	PROPN
cana-5422	830	19	,	,	PUNCT
cana-5422	830	20	inc	inc	PROPN
cana-5422	830	21	.	.	PROPN
cana-5422	830	22	,	,	PUNCT
cana-5422	830	23	new	new	PROPN
cana-5422	830	24	york	york	PROPN
cana-5422	830	25	,	,	PUNCT
cana-5422	830	26	1964	1964	NUM
cana-5422	830	27	.	.	PUNCT
cana-5422	831	1	communications	communication	NOUN
cana-5422	831	2	on	on	ADP
cana-5422	831	3	applied	apply	VERB
cana-5422	831	4	nonlinear	nonlinear	ADJ
cana-5422	831	5	analysis	analysis	NOUN
cana-5422	831	6	issn	issn	NOUN
cana-5422	831	7	:	:	PUNCT
cana-5422	831	8	1074	1074	NUM
cana-5422	831	9	-	-	PUNCT
cana-5422	831	10	133x	133x	NUM
cana-5422	831	11	vol	vol	NOUN
cana-5422	831	12	32	32	NUM
cana-5422	831	13	no	no	NOUN
cana-5422	831	14	.	.	PUNCT
cana-5422	832	1	10s(2025	10s(2025	NUM
cana-5422	832	2	)	)	PUNCT
cana-5422	833	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5422	833	2	2216	2216	NUM
cana-5422	833	3	1	1	NUM
cana-5422	833	4	.	.	PUNCT
cana-5422	833	5	introduction	introduction	NOUN
cana-5422	833	6	2	2	NUM
cana-5422	833	7	.	.	PUNCT
cana-5422	833	8	stability	stability	NOUN
cana-5422	833	9	of	of	ADP
cana-5422	833	10	(	(	PUNCT
cana-5422	833	11	1.7	1.7	NUM
cana-5422	833	12	)	)	PUNCT
cana-5422	833	13	in	in	ADP
cana-5422	833	14	banach	banach	NOUN
cana-5422	833	15	spaces	space	VERB
cana-5422	833	16	2.1	2.1	NUM
cana-5422	833	17	.	.	PUNCT
cana-5422	834	1	oddness	oddness	NOUN
cana-5422	834	2	of	of	ADP
cana-5422	834	3	f	f	NOUN
cana-5422	834	4	:	:	PUNCT
cana-5422	834	5	additive	additive	ADJ
cana-5422	834	6	case	case	NOUN
cana-5422	834	7	stability	stability	NOUN
cana-5422	834	8	results	result	VERB
cana-5422	834	9	:	:	PUNCT
cana-5422	834	10	direct	direct	ADJ
cana-5422	834	11	method	method	NOUN
cana-5422	834	12	2.2	2.2	NUM
cana-5422	834	13	.	.	PUNCT
cana-5422	835	1	evenness	evenness	NOUN
cana-5422	835	2	of	of	ADP
cana-5422	835	3	f	f	NOUN
cana-5422	835	4	:	:	PUNCT
cana-5422	835	5	quadratic	quadratic	ADJ
cana-5422	835	6	case	case	NOUN
cana-5422	835	7	stability	stability	NOUN
cana-5422	835	8	results	result	VERB
cana-5422	835	9	:	:	PUNCT
cana-5422	835	10	direct	direct	ADJ
cana-5422	835	11	method	method	NOUN
cana-5422	835	12	2.3	2.3	NUM
cana-5422	835	13	.	.	PUNCT
cana-5422	836	1	oddness	oddness	ADJ
cana-5422	836	2	and	and	CCONJ
cana-5422	836	3	evenness	evenness	NOUN
cana-5422	836	4	of	of	ADP
cana-5422	836	5	f	f	NOUN
cana-5422	836	6	:	:	PUNCT
cana-5422	836	7	additive	additive	ADJ
cana-5422	836	8	quadratic	quadratic	ADJ
cana-5422	836	9	case	case	NOUN
cana-5422	836	10	stability	stability	NOUN
cana-5422	836	11	results	result	VERB
cana-5422	836	12	:	:	PUNCT
cana-5422	836	13	direct	direct	ADJ
cana-5422	836	14	method	method	NOUN
cana-5422	836	15	2.4	2.4	NUM
cana-5422	836	16	.	.	PUNCT
cana-5422	837	1	oddness	oddness	NOUN
cana-5422	837	2	of	of	ADP
cana-5422	837	3	f	f	NOUN
cana-5422	837	4	:	:	PUNCT
cana-5422	837	5	additive	additive	ADJ
cana-5422	837	6	case	case	NOUN
cana-5422	837	7	stability	stability	NOUN
cana-5422	837	8	results	result	VERB
cana-5422	837	9	:	:	PUNCT
cana-5422	837	10	fixed	fix	VERB
cana-5422	837	11	point	point	NOUN
cana-5422	837	12	method	method	NOUN
cana-5422	837	13	2.5	2.5	NUM
cana-5422	837	14	.	.	PUNCT
cana-5422	838	1	evenness	evenness	NOUN
cana-5422	838	2	of	of	ADP
cana-5422	838	3	f	f	NOUN
cana-5422	838	4	:	:	PUNCT
cana-5422	838	5	quadratic	quadratic	ADJ
cana-5422	838	6	case	case	NOUN
cana-5422	838	7	stability	stability	NOUN
cana-5422	838	8	results	result	VERB
cana-5422	838	9	:	:	PUNCT
cana-5422	838	10	fixed	fix	VERB
cana-5422	838	11	point	point	NOUN
cana-5422	838	12	method	method	NOUN
cana-5422	838	13	2.6	2.6	NUM
cana-5422	838	14	.	.	PUNCT
cana-5422	839	1	oddness	oddness	ADJ
cana-5422	839	2	and	and	CCONJ
cana-5422	839	3	evenness	evenness	NOUN
cana-5422	839	4	of	of	ADP
cana-5422	839	5	f	f	NOUN
cana-5422	839	6	:	:	PUNCT
cana-5422	839	7	additive	additive	ADJ
cana-5422	839	8	quadratic	quadratic	ADJ
cana-5422	839	9	case	case	NOUN
cana-5422	839	10	stability	stability	NOUN
cana-5422	839	11	results	result	VERB
cana-5422	839	12	:	:	PUNCT
cana-5422	839	13	fixed	fixed	ADJ
cana-5422	839	14	point	point	NOUN
cana-5422	839	15	method	method	NOUN
cana-5422	839	16	3	3	NUM
cana-5422	839	17	.	.	PUNCT
cana-5422	839	18	stability	stability	NOUN
cana-5422	839	19	in	in	ADP
cana-5422	839	20	intuitionistic	intuitionistic	ADJ
cana-5422	839	21	fuzzy	fuzzy	ADJ
cana-5422	839	22	banach	banach	NOUN
cana-5422	839	23	space	space	NOUN
cana-5422	839	24	of	of	ADP
cana-5422	839	25	(	(	PUNCT
cana-5422	839	26	1.7	1.7	NUM
cana-5422	839	27	)	)	PUNCT
cana-5422	839	28	3.1	3.1	NUM
cana-5422	839	29	.	.	PUNCT
cana-5422	840	1	definitions	definition	NOUN
cana-5422	840	2	and	and	CCONJ
cana-5422	840	3	notations	notation	NOUN
cana-5422	840	4	of	of	ADP
cana-5422	840	5	intuitionistic	intuitionistic	ADJ
cana-5422	840	6	fuzzy	fuzzy	ADJ
cana-5422	840	7	banach	banach	NOUN
cana-5422	840	8	space	space	NOUN
cana-5422	840	9	3.2	3.2	NUM
cana-5422	840	10	.	.	PUNCT
cana-5422	841	1	oddness	oddness	ADJ
cana-5422	841	2	of	of	ADP
cana-5422	841	3	f	f	NOUN
cana-5422	841	4	:	:	PUNCT
cana-5422	841	5	additive	additive	ADJ
cana-5422	841	6	case	case	NOUN
cana-5422	841	7	stability	stability	NOUN
cana-5422	841	8	results	result	VERB
cana-5422	841	9	:	:	PUNCT
cana-5422	841	10	direct	direct	ADJ
cana-5422	841	11	method	method	NOUN
cana-5422	841	12	3.3	3.3	NUM
cana-5422	841	13	.	.	PUNCT
cana-5422	842	1	evenness	evenness	NOUN
cana-5422	842	2	of	of	ADP
cana-5422	842	3	f	f	NOUN
cana-5422	842	4	:	:	PUNCT
cana-5422	842	5	quadratic	quadratic	ADJ
cana-5422	842	6	case	case	NOUN
cana-5422	842	7	stability	stability	NOUN
cana-5422	842	8	results	result	VERB
cana-5422	842	9	:	:	PUNCT
cana-5422	842	10	direct	direct	ADJ
cana-5422	842	11	method	method	NOUN
cana-5422	842	12	3.4	3.4	NUM
cana-5422	842	13	.	.	PUNCT
cana-5422	842	14	oddness	oddness	ADJ
cana-5422	842	15	and	and	CCONJ
cana-5422	842	16	evenness	evenness	NOUN
cana-5422	842	17	of	of	ADP
cana-5422	842	18	f	f	NOUN
cana-5422	842	19	:	:	PUNCT
cana-5422	842	20	additive	additive	ADJ
cana-5422	842	21	quadratic	quadratic	ADJ
cana-5422	842	22	case	case	NOUN
cana-5422	842	23	stability	stability	NOUN
cana-5422	842	24	results	result	VERB
cana-5422	842	25	:	:	PUNCT
cana-5422	842	26	direct	direct	ADJ
cana-5422	842	27	method	method	NOUN
cana-5422	842	28	3.5	3.5	NUM
cana-5422	842	29	.	.	PUNCT
cana-5422	843	1	oddness	oddness	NOUN
cana-5422	843	2	of	of	ADP
cana-5422	843	3	f	f	NOUN
cana-5422	843	4	:	:	PUNCT
cana-5422	843	5	additive	additive	ADJ
cana-5422	843	6	case	case	NOUN
cana-5422	843	7	stability	stability	NOUN
cana-5422	843	8	results	result	VERB
cana-5422	843	9	:	:	PUNCT
cana-5422	843	10	fixed	fixed	ADJ
cana-5422	843	11	point	point	NOUN
cana-5422	843	12	method	method	NOUN
cana-5422	843	13	3.6	3.6	NUM
cana-5422	843	14	.	.	PUNCT
cana-5422	844	1	evenness	evenness	NOUN
cana-5422	844	2	of	of	ADP
cana-5422	844	3	f	f	NOUN
cana-5422	844	4	:	:	PUNCT
cana-5422	844	5	quadratic	quadratic	ADJ
cana-5422	844	6	case	case	NOUN
cana-5422	844	7	stability	stability	NOUN
cana-5422	844	8	results	result	VERB
cana-5422	844	9	:	:	PUNCT
cana-5422	844	10	fixed	fix	VERB
cana-5422	844	11	point	point	NOUN
cana-5422	844	12	method	method	NOUN
cana-5422	844	13	3.7	3.7	NUM
cana-5422	844	14	.	.	PUNCT
cana-5422	845	1	oddness	oddness	ADJ
cana-5422	845	2	and	and	CCONJ
cana-5422	845	3	evenness	evenness	NOUN
cana-5422	845	4	of	of	ADP
cana-5422	845	5	f	f	NOUN
cana-5422	845	6	:	:	PUNCT
cana-5422	845	7	additive	additive	ADJ
cana-5422	845	8	quadratic	quadratic	ADJ
cana-5422	845	9	case	case	NOUN
cana-5422	845	10	stability	stability	NOUN
cana-5422	845	11	results	result	VERB
cana-5422	845	12	:	:	PUNCT
cana-5422	845	13	fixed	fix	VERB
cana-5422	845	14	point	point	NOUN
cana-5422	845	15	method	method	NOUN
cana-5422	845	16	conclusion	conclusion	NOUN
cana-5422	845	17	acknowledgment	acknowledgment	NOUN
cana-5422	845	18	conflict	conflict	NOUN
cana-5422	845	19	of	of	ADP
cana-5422	845	20	interest	interest	NOUN
cana-5422	845	21	references	reference	NOUN