id	sid	tid	token	lemma	pos
cana-3294	1	1	communications	communication	NOUN
cana-3294	1	2	on	on	ADP
cana-3294	1	3	applied	apply	VERB
cana-3294	1	4	nonlinear	nonlinear	ADJ
cana-3294	1	5	analysis	analysis	NOUN
cana-3294	1	6	issn	issn	NOUN
cana-3294	1	7	:	:	PUNCT
cana-3294	1	8	1074	1074	NUM
cana-3294	1	9	-	-	PUNCT
cana-3294	1	10	133x	133x	NUM
cana-3294	1	11	vol	vol	NOUN
cana-3294	1	12	32	32	NUM
cana-3294	1	13	no	no	NOUN
cana-3294	1	14	.	.	PUNCT
cana-3294	2	1	6s	6s	NUM
cana-3294	2	2	(	(	PUNCT
cana-3294	2	3	2025	2025	NUM
cana-3294	2	4	)	)	PUNCT
cana-3294	2	5	275	275	NUM
cana-3294	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3294	2	7	fixed	fix	VERB
cana-3294	2	8	point	point	NOUN
cana-3294	2	9	results	result	NOUN
cana-3294	2	10	in	in	ADP
cana-3294	2	11	g	g	PROPN
cana-3294	2	12	metric	metric	ADJ
cana-3294	2	13	space	space	NOUN
cana-3294	2	14	via	via	ADP
cana-3294	2	15	α	α	NOUN
cana-3294	2	16	-	-	PUNCT
cana-3294	2	17	series	series	NOUN
cana-3294	2	18	k.	k.	PROPN
cana-3294	2	19	varalakshmi	varalakshmi	PROPN
cana-3294	2	20	1	1	NUM
cana-3294	2	21	,	,	PUNCT
cana-3294	2	22	*	*	PUNCT
cana-3294	2	23	,	,	PUNCT
cana-3294	2	24	g.upender	g.upender	NOUN
cana-3294	2	25	reddy2	reddy2	NOUN
cana-3294	2	26	1	1	NUM
cana-3294	2	27	research	research	NOUN
cana-3294	2	28	scholar	scholar	NOUN
cana-3294	2	29	,	,	PUNCT
cana-3294	2	30	department	department	NOUN
cana-3294	2	31	of	of	ADP
cana-3294	2	32	mathematics	mathematics	PROPN
cana-3294	2	33	,	,	PUNCT
cana-3294	2	34	osmania	osmania	PROPN
cana-3294	2	35	university	university	PROPN
cana-3294	2	36	,	,	PUNCT
cana-3294	2	37	telangana	telangana	PROPN
cana-3294	2	38	,	,	PUNCT
cana-3294	2	39	india	india	PROPN
cana-3294	2	40	.	.	PUNCT
cana-3294	3	1	e	e	X
cana-3294	3	2	-	-	NOUN
cana-3294	3	3	mail	mail	NOUN
cana-3294	3	4	:	:	PUNCT
cana-3294	4	1	varak2121@gmail.com	varak2121@gmail.com	X
cana-3294	4	2	.	.	PROPN
cana-3294	5	1	2	2	NUM
cana-3294	5	2	associate	associate	NOUN
cana-3294	5	3	professor	professor	NOUN
cana-3294	5	4	of	of	ADP
cana-3294	5	5	mathematics	mathematic	NOUN
cana-3294	5	6	,	,	PUNCT
cana-3294	5	7	nizam	nizam	PROPN
cana-3294	5	8	college	college	PROPN
cana-3294	5	9	(	(	PUNCT
cana-3294	5	10	a	a	NOUN
cana-3294	5	11	)	)	PUNCT
cana-3294	5	12	,	,	PUNCT
cana-3294	5	13	osmania	osmania	PROPN
cana-3294	5	14	university	university	PROPN
cana-3294	5	15	,	,	PUNCT
cana-3294	5	16	telangana	telangana	PROPN
cana-3294	5	17	,	,	PUNCT
cana-3294	5	18	india	india	PROPN
cana-3294	5	19	.	.	PUNCT
cana-3294	6	1	e	e	X
cana-3294	6	2	-	-	NOUN
cana-3294	6	3	mail	mail	NOUN
cana-3294	6	4	:	:	PUNCT
cana-3294	7	1	yuviganga@gmail.com	yuviganga@gmail.com	X
cana-3294	7	2	.	.	PUNCT
cana-3294	8	1	article	article	PROPN
cana-3294	8	2	history	history	NOUN
cana-3294	8	3	:	:	PUNCT
cana-3294	8	4	received	receive	VERB
cana-3294	8	5	:	:	PUNCT
cana-3294	8	6	19	19	NUM
cana-3294	8	7	-	-	SYM
cana-3294	8	8	10	10	NUM
cana-3294	8	9	-	-	PUNCT
cana-3294	8	10	2024	2024	NUM
cana-3294	8	11	revised	revise	VERB
cana-3294	8	12	:	:	PUNCT
cana-3294	8	13	03	03	NUM
cana-3294	8	14	-	-	SYM
cana-3294	8	15	12	12	NUM
cana-3294	8	16	-	-	PUNCT
cana-3294	8	17	2024	2024	NUM
cana-3294	8	18	accepted	accept	VERB
cana-3294	8	19	:	:	PUNCT
cana-3294	8	20	11	11	NUM
cana-3294	8	21	-	-	SYM
cana-3294	8	22	12	12	NUM
cana-3294	8	23	-	-	PUNCT
cana-3294	8	24	2024	2024	NUM
cana-3294	8	25	abstract	abstract	NOUN
cana-3294	8	26	:	:	PUNCT
cana-3294	8	27	introduction	introduction	NOUN
cana-3294	8	28	:	:	PUNCT
cana-3294	8	29	mustafa	mustafa	NOUN
cana-3294	8	30	and	and	CCONJ
cana-3294	8	31	sims	sim	NOUN
cana-3294	8	32	[	[	X
cana-3294	8	33	1	1	X
cana-3294	8	34	]	]	PUNCT
cana-3294	8	35	introduced	introduce	VERB
cana-3294	8	36	the	the	DET
cana-3294	8	37	concept	concept	NOUN
cana-3294	8	38	of	of	ADP
cana-3294	8	39	g	g	NOUN
cana-3294	8	40	-	-	PUNCT
cana-3294	8	41	metric	metric	ADJ
cana-3294	8	42	space	space	NOUN
cana-3294	8	43	in	in	ADP
cana-3294	8	44	2005	2005	NUM
cana-3294	8	45	.	.	PUNCT
cana-3294	9	1	afterwards	afterwards	ADV
cana-3294	9	2	,	,	PUNCT
cana-3294	9	3	mustafa	mustafa	PROPN
cana-3294	9	4	et	et	PROPN
cana-3294	9	5	al	al	PROPN
cana-3294	9	6	and	and	CCONJ
cana-3294	9	7	many	many	ADJ
cana-3294	9	8	authors	author	NOUN
cana-3294	10	1	[	[	X
cana-3294	10	2	3]-[19	3]-[19	NUM
cana-3294	10	3	]	]	PUNCT
cana-3294	10	4	obtained	obtain	VERB
cana-3294	10	5	some	some	DET
cana-3294	10	6	common	common	ADJ
cana-3294	10	7	fixed	fix	VERB
cana-3294	10	8	-	-	PUNCT
cana-3294	10	9	point	point	NOUN
cana-3294	10	10	theorems	theorem	NOUN
cana-3294	10	11	,	,	PUNCT
cana-3294	10	12	coupled	couple	VERB
cana-3294	10	13	and	and	CCONJ
cana-3294	10	14	tripled	triple	VERB
cana-3294	10	15	fixed	fix	VERB
cana-3294	10	16	point	point	NOUN
cana-3294	10	17	results	result	NOUN
cana-3294	10	18	for	for	ADP
cana-3294	10	19	mappings	mapping	NOUN
cana-3294	10	20	satisfying	satisfy	VERB
cana-3294	10	21	different	different	ADJ
cana-3294	10	22	contractive	contractive	ADJ
cana-3294	10	23	conditions	condition	NOUN
cana-3294	10	24	in	in	ADP
cana-3294	10	25	g	g	PROPN
cana-3294	10	26	metric	metric	ADJ
cana-3294	10	27	space	space	NOUN
cana-3294	10	28	.	.	PUNCT
cana-3294	11	1	in	in	ADP
cana-3294	11	2	this	this	DET
cana-3294	11	3	study	study	NOUN
cana-3294	11	4	we	we	PRON
cana-3294	11	5	prove	prove	VERB
cana-3294	11	6	fixed	fixed	ADJ
cana-3294	11	7	point	point	NOUN
cana-3294	11	8	results	result	NOUN
cana-3294	11	9	in	in	ADP
cana-3294	11	10	g	g	PROPN
cana-3294	11	11	metric	metric	ADJ
cana-3294	11	12	space	space	NOUN
cana-3294	11	13	via	via	ADP
cana-3294	11	14	α	α	NOUN
cana-3294	11	15	-	-	PUNCT
cana-3294	11	16	series	series	NOUN
cana-3294	11	17	by	by	ADP
cana-3294	11	18	using	use	VERB
cana-3294	11	19	some	some	DET
cana-3294	11	20	conditions	condition	NOUN
cana-3294	11	21	that	that	PRON
cana-3294	11	22	are	be	AUX
cana-3294	11	23	a	a	DET
cana-3294	11	24	sequence	sequence	NOUN
cana-3294	11	25	of	of	ADP
cana-3294	11	26	a	a	DET
cana-3294	11	27	mappings	mapping	NOUN
cana-3294	11	28	and	and	CCONJ
cana-3294	11	29	a	a	DET
cana-3294	11	30	self	self	NOUN
cana-3294	11	31	-	-	PUNCT
cana-3294	11	32	mapping	mapping	NOUN
cana-3294	11	33	.	.	PUNCT
cana-3294	12	1	objectives	objective	NOUN
cana-3294	12	2	:	:	PUNCT
cana-3294	12	3	to	to	PART
cana-3294	12	4	show	show	VERB
cana-3294	12	5	tripled	triple	VERB
cana-3294	12	6	fixed	fix	VERB
cana-3294	12	7	-	-	PUNCT
cana-3294	12	8	point	point	NOUN
cana-3294	12	9	theorems	theorem	NOUN
cana-3294	12	10	and	and	CCONJ
cana-3294	12	11	common	common	ADJ
cana-3294	12	12	fixed	fix	VERB
cana-3294	12	13	point	point	NOUN
cana-3294	12	14	theorems	theorem	NOUN
cana-3294	12	15	by	by	ADP
cana-3294	12	16	using	use	VERB
cana-3294	12	17	sequence	sequence	NOUN
cana-3294	12	18	of	of	ADP
cana-3294	12	19	mappings	mapping	NOUN
cana-3294	12	20	and	and	CCONJ
cana-3294	12	21	self	self	NOUN
cana-3294	12	22	a	a	DET
cana-3294	12	23	self	self	NOUN
cana-3294	12	24	-	-	PUNCT
cana-3294	12	25	mapping	mapping	NOUN
cana-3294	12	26	via	via	ADP
cana-3294	12	27	α	α	NOUN
cana-3294	12	28	-	-	PUNCT
cana-3294	12	29	series	series	NOUN
cana-3294	12	30	and	and	CCONJ
cana-3294	12	31	shown	show	VERB
cana-3294	12	32	an	an	DET
cana-3294	12	33	example	example	NOUN
cana-3294	12	34	which	which	PRON
cana-3294	12	35	supports	support	VERB
cana-3294	12	36	the	the	DET
cana-3294	12	37	main	main	ADJ
cana-3294	12	38	result	result	NOUN
cana-3294	12	39	.	.	PUNCT
cana-3294	13	1	methods	method	NOUN
cana-3294	13	2	:	:	PUNCT
cana-3294	13	3	in	in	ADP
cana-3294	13	4	recent	recent	ADJ
cana-3294	13	5	study	study	NOUN
cana-3294	13	6	the	the	DET
cana-3294	13	7	authors	author	NOUN
cana-3294	13	8	worked	work	VERB
cana-3294	13	9	on	on	ADP
cana-3294	13	10	fixed	fix	VERB
cana-3294	13	11	point	point	NOUN
cana-3294	13	12	results	result	NOUN
cana-3294	13	13	by	by	ADP
cana-3294	13	14	using	use	VERB
cana-3294	13	15	different	different	ADJ
cana-3294	13	16	contractions	contraction	NOUN
cana-3294	13	17	such	such	ADJ
cana-3294	13	18	as	as	ADP
cana-3294	13	19	suzuki	suzuki	NOUN
cana-3294	13	20	type	type	NOUN
cana-3294	13	21	contraction	contraction	NOUN
cana-3294	13	22	,	,	PUNCT
cana-3294	13	23	rational	rational	ADJ
cana-3294	13	24	type	type	NOUN
cana-3294	13	25	contraction	contraction	NOUN
cana-3294	13	26	,	,	PUNCT
cana-3294	13	27	cyclic	cyclic	ADJ
cana-3294	13	28	contraction	contraction	NOUN
cana-3294	13	29	,	,	PUNCT
cana-3294	13	30	f	f	X
cana-3294	13	31	-	-	PUNCT
cana-3294	13	32	contraction	contraction	NOUN
cana-3294	13	33	,	,	PUNCT
cana-3294	13	34	mier	mier	PROPN
cana-3294	13	35	keeler	keeler	PROPN
cana-3294	13	36	contraction	contraction	PROPN
cana-3294	13	37	,	,	PUNCT
cana-3294	13	38	(	(	PUNCT
cana-3294	13	39	ψ	ψ	X
cana-3294	13	40	,	,	PUNCT
cana-3294	13	41	ϕ)-weakly	ϕ)-weakly	PUNCT
cana-3294	13	42	contractive	contractive	ADJ
cana-3294	13	43	mappings	mapping	NOUN
cana-3294	13	44	and	and	CCONJ
cana-3294	13	45	integral	integral	ADJ
cana-3294	13	46	type	type	NOUN
cana-3294	13	47	contractions	contraction	NOUN
cana-3294	13	48	etc	etc	X
cana-3294	13	49	.	.	X
cana-3294	14	1	in	in	ADP
cana-3294	14	2	g	g	NOUN
cana-3294	14	3	-	-	PUNCT
cana-3294	14	4	metric	metric	ADJ
cana-3294	14	5	spaces	space	NOUN
cana-3294	14	6	.	.	PUNCT
cana-3294	15	1	in	in	ADP
cana-3294	15	2	this	this	DET
cana-3294	15	3	study	study	NOUN
cana-3294	15	4	we	we	PRON
cana-3294	15	5	proved	prove	VERB
cana-3294	15	6	fixed	fix	VERB
cana-3294	15	7	point	point	NOUN
cana-3294	15	8	results	result	NOUN
cana-3294	15	9	in	in	ADP
cana-3294	15	10	g	g	PROPN
cana-3294	15	11	metric	metric	ADJ
cana-3294	15	12	space	space	NOUN
cana-3294	15	13	via	via	ADP
cana-3294	15	14	α	α	NOUN
cana-3294	15	15	-	-	PUNCT
cana-3294	15	16	series	series	NOUN
cana-3294	15	17	by	by	ADP
cana-3294	15	18	using	use	VERB
cana-3294	15	19	sequence	sequence	NOUN
cana-3294	15	20	of	of	ADP
cana-3294	15	21	mappings	mapping	NOUN
cana-3294	15	22	.	.	PUNCT
cana-3294	16	1	results	result	NOUN
cana-3294	16	2	:	:	PUNCT
cana-3294	16	3	obtained	obtain	VERB
cana-3294	16	4	unique	unique	ADJ
cana-3294	16	5	common	common	ADJ
cana-3294	16	6	fixed	fix	VERB
cana-3294	16	7	point	point	NOUN
cana-3294	16	8	and	and	CCONJ
cana-3294	16	9	tripled	triple	VERB
cana-3294	16	10	fixed	fix	VERB
cana-3294	16	11	point	point	NOUN
cana-3294	16	12	results	result	NOUN
cana-3294	16	13	in	in	ADP
cana-3294	16	14	g	g	PROPN
cana-3294	16	15	metric	metric	ADJ
cana-3294	16	16	spcace	spcace	NOUN
cana-3294	16	17	via	via	ADP
cana-3294	16	18	α	α	NOUN
cana-3294	16	19	-	-	PUNCT
cana-3294	16	20	series	series	NOUN
cana-3294	16	21	.	.	PUNCT
cana-3294	17	1	conclusion	conclusion	NOUN
cana-3294	17	2	:	:	PUNCT
cana-3294	17	3	in	in	ADP
cana-3294	17	4	this	this	DET
cana-3294	17	5	study	study	NOUN
cana-3294	17	6	we	we	PRON
cana-3294	17	7	present	present	VERB
cana-3294	17	8	unique	unique	ADJ
cana-3294	17	9	tripled	triple	VERB
cana-3294	17	10	fixed	fix	VERB
cana-3294	17	11	-	-	PUNCT
cana-3294	17	12	point	point	NOUN
cana-3294	17	13	and	and	CCONJ
cana-3294	17	14	common	common	ADJ
cana-3294	17	15	fixed	fix	VERB
cana-3294	17	16	-	-	PUNCT
cana-3294	17	17	point	point	NOUN
cana-3294	17	18	results	result	NOUN
cana-3294	17	19	for	for	ADP
cana-3294	17	20	a	a	DET
cana-3294	17	21	sequence	sequence	NOUN
cana-3294	17	22	of	of	ADP
cana-3294	17	23	mappings	mapping	NOUN
cana-3294	17	24	and	and	CCONJ
cana-3294	17	25	a	a	DET
cana-3294	17	26	self	self	NOUN
cana-3294	17	27	-	-	PUNCT
cana-3294	17	28	mapping	mapping	NOUN
cana-3294	17	29	in	in	ADP
cana-3294	17	30	g	g	PROPN
cana-3294	17	31	metric	metric	ADJ
cana-3294	17	32	space	space	NOUN
cana-3294	17	33	via	via	ADP
cana-3294	17	34	α	α	NOUN
cana-3294	17	35	-	-	PUNCT
cana-3294	17	36	series	series	NOUN
cana-3294	17	37	and	and	CCONJ
cana-3294	17	38	discussed	discuss	VERB
cana-3294	17	39	corollary	corollary	NOUN
cana-3294	17	40	with	with	ADP
cana-3294	17	41	supporting	support	VERB
cana-3294	17	42	example	example	NOUN
cana-3294	17	43	.	.	PUNCT
cana-3294	18	1	keywords	keyword	NOUN
cana-3294	18	2	:	:	PUNCT
cana-3294	18	3	g	g	NOUN
cana-3294	18	4	-	-	PUNCT
cana-3294	18	5	metric	metric	ADJ
cana-3294	18	6	space	space	NOUN
cana-3294	18	7	,	,	PUNCT
cana-3294	18	8	tripled	triple	VERB
cana-3294	18	9	fixed	fix	VERB
cana-3294	18	10	point	point	NOUN
cana-3294	18	11	,	,	PUNCT
cana-3294	18	12	α	α	NOUN
cana-3294	18	13	-	-	PUNCT
cana-3294	18	14	series	series	NOUN
cana-3294	18	15	,	,	PUNCT
cana-3294	18	16	compatible	compatible	ADJ
cana-3294	18	17	mapping	mapping	NOUN
cana-3294	18	18	,	,	PUNCT
cana-3294	18	19	weakly	weakly	ADV
cana-3294	18	20	reciprocally	reciprocally	ADV
cana-3294	18	21	continuous	continuous	ADJ
cana-3294	18	22	mappings	mapping	NOUN
cana-3294	18	23	.	.	PUNCT
cana-3294	19	1	1.introduction	1.introduction	NUM
cana-3294	19	2	:	:	PUNCT
cana-3294	19	3	mustafa	mustafa	NOUN
cana-3294	19	4	and	and	CCONJ
cana-3294	19	5	sims	sim	NOUN
cana-3294	20	1	[	[	X
cana-3294	20	2	1	1	X
cana-3294	20	3	]	]	PUNCT
cana-3294	20	4	introduced	introduce	VERB
cana-3294	20	5	the	the	DET
cana-3294	20	6	concept	concept	NOUN
cana-3294	20	7	of	of	ADP
cana-3294	20	8	g	g	NOUN
cana-3294	20	9	-	-	PUNCT
cana-3294	20	10	metric	metric	ADJ
cana-3294	20	11	space	space	NOUN
cana-3294	20	12	in	in	ADP
cana-3294	20	13	2005	2005	NUM
cana-3294	20	14	.	.	PUNCT
cana-3294	21	1	afterwards	afterwards	ADV
cana-3294	21	2	,	,	PUNCT
cana-3294	21	3	mustafa	mustafa	PROPN
cana-3294	21	4	et	et	PROPN
cana-3294	21	5	al	al	PROPN
cana-3294	21	6	and	and	CCONJ
cana-3294	21	7	many	many	ADJ
cana-3294	21	8	authors	author	NOUN
cana-3294	22	1	[	[	X
cana-3294	22	2	3]-[19	3]-[19	NUM
cana-3294	22	3	]	]	PUNCT
cana-3294	22	4	obtained	obtain	VERB
cana-3294	22	5	some	some	DET
cana-3294	22	6	common	common	ADJ
cana-3294	22	7	fixed	fix	VERB
cana-3294	22	8	-	-	PUNCT
cana-3294	22	9	point	point	NOUN
cana-3294	22	10	theorems	theorem	NOUN
cana-3294	22	11	,	,	PUNCT
cana-3294	22	12	coupled	couple	VERB
cana-3294	22	13	and	and	CCONJ
cana-3294	22	14	tripled	triple	VERB
cana-3294	22	15	fixed	fix	VERB
cana-3294	22	16	point	point	NOUN
cana-3294	22	17	results	result	NOUN
cana-3294	22	18	for	for	ADP
cana-3294	22	19	mappings	mapping	NOUN
cana-3294	22	20	satisfying	satisfy	VERB
cana-3294	22	21	different	different	ADJ
cana-3294	22	22	contractive	contractive	ADJ
cana-3294	22	23	conditions	condition	NOUN
cana-3294	22	24	in	in	ADP
cana-3294	22	25	g	g	PROPN
cana-3294	22	26	metric	metric	ADJ
cana-3294	22	27	space	space	NOUN
cana-3294	22	28	.	.	PUNCT
cana-3294	23	1	in	in	ADP
cana-3294	23	2	2014	2014	NUM
cana-3294	23	3	,	,	PUNCT
cana-3294	23	4	sihag	sihag	NOUN
cana-3294	23	5	et	et	NOUN
cana-3294	23	6	al	al	PROPN
cana-3294	23	7	[	[	X
cana-3294	23	8	21	21	NUM
cana-3294	23	9	]	]	PUNCT
cana-3294	23	10	proposed	propose	VERB
cana-3294	23	11	an	an	DET
cana-3294	23	12	α	α	NOUN
cana-3294	23	13	-	-	PUNCT
cana-3294	23	14	series	series	NOUN
cana-3294	23	15	to	to	PART
cana-3294	23	16	find	find	VERB
cana-3294	23	17	a	a	DET
cana-3294	23	18	common	common	ADJ
cana-3294	23	19	fixed	fix	VERB
cana-3294	23	20	point	point	NOUN
cana-3294	23	21	by	by	ADP
cana-3294	23	22	utilizing	utilize	VERB
cana-3294	23	23	the	the	DET
cana-3294	23	24	sequence	sequence	NOUN
cana-3294	23	25	of	of	ADP
cana-3294	23	26	mappings	mapping	NOUN
cana-3294	23	27	and	and	CCONJ
cana-3294	23	28	selfmappings	selfmapping	NOUN
cana-3294	23	29	.	.	PUNCT
cana-3294	24	1	chang	chang	PROPN
cana-3294	24	2	and	and	CCONJ
cana-3294	24	3	ma	ma	PROPN
cana-3294	25	1	[	[	X
cana-3294	25	2	22	22	NUM
cana-3294	25	3	]	]	PUNCT
cana-3294	25	4	presented	present	VERB
cana-3294	25	5	coupled	couple	VERB
cana-3294	25	6	fixed	fix	VERB
cana-3294	25	7	point	point	NOUN
cana-3294	25	8	in	in	ADP
cana-3294	25	9	1991.later	1991.later	NOUN
cana-3294	25	10	this	this	DET
cana-3294	25	11	concept	concept	NOUN
cana-3294	25	12	has	have	AUX
cana-3294	25	13	attracted	attract	VERB
cana-3294	25	14	numerous	numerous	ADJ
cana-3294	25	15	researchers	researcher	NOUN
cana-3294	25	16	[	[	X
cana-3294	25	17	23]-[28	23]-[28	X
cana-3294	25	18	]	]	X
cana-3294	25	19	across	across	ADP
cana-3294	25	20	various	various	ADJ
cana-3294	25	21	fields	field	NOUN
cana-3294	25	22	.	.	PUNCT
cana-3294	26	1	the	the	DET
cana-3294	26	2	notation	notation	NOUN
cana-3294	26	3	of	of	ADP
cana-3294	26	4	tripled	triple	VERB
cana-3294	26	5	fixed	fix	VERB
cana-3294	26	6	point	point	NOUN
cana-3294	26	7	was	be	AUX
cana-3294	26	8	initiated	initiate	VERB
cana-3294	26	9	by	by	ADP
cana-3294	26	10	berinde	berinde	NOUN
cana-3294	26	11	and	and	CCONJ
cana-3294	26	12	borcut	borcut	VERB
cana-3294	26	13	[	[	X
cana-3294	26	14	32],[33	32],[33	X
cana-3294	26	15	]	]	X
cana-3294	26	16	in	in	ADP
cana-3294	26	17	partially	partially	ADV
cana-3294	26	18	ordered	order	VERB
cana-3294	26	19	metric	metric	ADJ
cana-3294	26	20	spaces	space	NOUN
cana-3294	26	21	and	and	CCONJ
cana-3294	26	22	also	also	ADV
cana-3294	26	23	presented	present	VERB
cana-3294	26	24	the	the	DET
cana-3294	26	25	concept	concept	NOUN
cana-3294	26	26	of	of	ADP
cana-3294	26	27	tripled	triple	VERB
cana-3294	26	28	coincidence	coincidence	NOUN
cana-3294	26	29	point	point	NOUN
cana-3294	26	30	and	and	CCONJ
cana-3294	26	31	obtained	obtain	VERB
cana-3294	26	32	tripled	triple	VERB
cana-3294	26	33	coincidence	coincidence	NOUN
cana-3294	26	34	point	point	NOUN
cana-3294	26	35	outcomes	outcome	NOUN
cana-3294	26	36	.	.	PUNCT
cana-3294	27	1	later	later	ADV
cana-3294	27	2	many	many	ADJ
cana-3294	27	3	authors	author	NOUN
cana-3294	27	4	obtained	obtain	VERB
cana-3294	27	5	common	common	ADJ
cana-3294	27	6	tripled	triple	VERB
cana-3294	27	7	fixed	fix	VERB
cana-3294	27	8	-	-	PUNCT
cana-3294	27	9	point	point	NOUN
cana-3294	27	10	results	result	NOUN
cana-3294	27	11	by	by	ADP
cana-3294	27	12	using	use	VERB
cana-3294	27	13	different	different	ADJ
cana-3294	27	14	contraction	contraction	NOUN
cana-3294	27	15	conditions	condition	NOUN
cana-3294	27	16	in	in	ADP
cana-3294	27	17	different	different	ADJ
cana-3294	27	18	communications	communication	NOUN
cana-3294	27	19	on	on	ADP
cana-3294	27	20	applied	apply	VERB
cana-3294	27	21	nonlinear	nonlinear	ADJ
cana-3294	27	22	analysis	analysis	NOUN
cana-3294	27	23	issn	issn	NOUN
cana-3294	27	24	:	:	PUNCT
cana-3294	27	25	1074	1074	NUM
cana-3294	27	26	-	-	PUNCT
cana-3294	27	27	133x	133x	NUM
cana-3294	27	28	vol	vol	NOUN
cana-3294	27	29	32	32	NUM
cana-3294	27	30	no	no	NOUN
cana-3294	27	31	.	.	PUNCT
cana-3294	28	1	6s	6s	NUM
cana-3294	28	2	(	(	PUNCT
cana-3294	28	3	2025	2025	NUM
cana-3294	28	4	)	)	PUNCT
cana-3294	28	5	276	276	NUM
cana-3294	29	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	29	2	metric	metric	ADJ
cana-3294	29	3	spaces	space	NOUN
cana-3294	29	4	.	.	PUNCT
cana-3294	30	1	in	in	ADP
cana-3294	30	2	this	this	DET
cana-3294	30	3	paper	paper	NOUN
cana-3294	30	4	we	we	PRON
cana-3294	30	5	prove	prove	VERB
cana-3294	30	6	tripled	triple	VERB
cana-3294	30	7	fixed	fix	VERB
cana-3294	30	8	-	-	PUNCT
cana-3294	30	9	point	point	NOUN
cana-3294	30	10	results	result	NOUN
cana-3294	30	11	in	in	ADP
cana-3294	30	12	g	g	PROPN
cana-3294	30	13	metric	metric	ADJ
cana-3294	30	14	space	space	NOUN
cana-3294	30	15	by	by	ADP
cana-3294	30	16	utilizing	utilize	VERB
cana-3294	30	17	the	the	DET
cana-3294	30	18	sequence	sequence	NOUN
cana-3294	30	19	of	of	ADP
cana-3294	30	20	mappings	mapping	NOUN
cana-3294	30	21	via	via	ADP
cana-3294	30	22	αseries	αserie	NOUN
cana-3294	30	23	and	and	CCONJ
cana-3294	30	24	we	we	PRON
cana-3294	30	25	provided	provide	VERB
cana-3294	30	26	illustrations	illustration	NOUN
cana-3294	30	27	to	to	PART
cana-3294	30	28	support	support	VERB
cana-3294	30	29	our	our	PRON
cana-3294	30	30	results	result	NOUN
cana-3294	30	31	.	.	PUNCT
cana-3294	31	1	2.objectives	2.objectives	NUM
cana-3294	31	2	:	:	PUNCT
cana-3294	31	3	to	to	PART
cana-3294	31	4	show	show	VERB
cana-3294	31	5	tripled	triple	VERB
cana-3294	31	6	fixed	fix	VERB
cana-3294	31	7	-	-	PUNCT
cana-3294	31	8	point	point	NOUN
cana-3294	31	9	theorems	theorem	NOUN
cana-3294	31	10	and	and	CCONJ
cana-3294	31	11	common	common	ADJ
cana-3294	31	12	fixed	fix	VERB
cana-3294	31	13	point	point	NOUN
cana-3294	31	14	theorems	theorem	NOUN
cana-3294	31	15	by	by	ADP
cana-3294	31	16	using	use	VERB
cana-3294	31	17	sequence	sequence	NOUN
cana-3294	31	18	of	of	ADP
cana-3294	31	19	mappings	mapping	NOUN
cana-3294	31	20	and	and	CCONJ
cana-3294	31	21	self	self	NOUN
cana-3294	31	22	a	a	DET
cana-3294	31	23	self	self	NOUN
cana-3294	31	24	-	-	PUNCT
cana-3294	31	25	mapping	mapping	NOUN
cana-3294	31	26	via	via	ADP
cana-3294	31	27	α	α	NOUN
cana-3294	31	28	-	-	PUNCT
cana-3294	31	29	series	series	NOUN
cana-3294	31	30	and	and	CCONJ
cana-3294	31	31	shown	show	VERB
cana-3294	31	32	an	an	DET
cana-3294	31	33	example	example	NOUN
cana-3294	31	34	which	which	PRON
cana-3294	31	35	supports	support	VERB
cana-3294	31	36	the	the	DET
cana-3294	31	37	main	main	ADJ
cana-3294	31	38	result	result	NOUN
cana-3294	31	39	3.methodology	3.methodology	NUM
cana-3294	31	40	:	:	PUNCT
cana-3294	31	41	defnition	defnition	NOUN
cana-3294	31	42	3.1	3.1	NUM
cana-3294	31	43	[	[	X
cana-3294	31	44	1	1	NUM
cana-3294	31	45	]	]	PUNCT
cana-3294	31	46	consider	consider	VERB
cana-3294	31	47	ɱ	ɱ	PROPN
cana-3294	31	48	be	be	AUX
cana-3294	31	49	a	a	DET
cana-3294	31	50	non	non	ADJ
cana-3294	31	51	-	-	ADJ
cana-3294	31	52	void	void	ADJ
cana-3294	31	53	set	set	NOUN
cana-3294	31	54	and	and	CCONJ
cana-3294	31	55	g	g	NOUN
cana-3294	31	56	:	:	PUNCT
cana-3294	31	57	ɱ	ɱ	PROPN
cana-3294	31	58	3	3	NUM
cana-3294	31	59	→	→	SYM
cana-3294	31	60	[	[	X
cana-3294	31	61	0,∞	0,∞	NUM
cana-3294	31	62	)	)	PUNCT
cana-3294	31	63	is	be	AUX
cana-3294	31	64	a	a	DET
cana-3294	31	65	mapping	mapping	NOUN
cana-3294	32	1	such	such	ADJ
cana-3294	32	2	that	that	SCONJ
cana-3294	32	3	(	(	PUNCT
cana-3294	32	4	g1	g1	PROPN
cana-3294	32	5	)	)	PUNCT
cana-3294	32	6	g	g	NOUN
cana-3294	32	7	(	(	PUNCT
cana-3294	32	8	ꝕ	ꝕ	PROPN
cana-3294	32	9	,	,	PUNCT
cana-3294	32	10	ꝙ	ꝙ	NOUN
cana-3294	32	11	,	,	PUNCT
cana-3294	32	12	𝟉	𝟉	X
cana-3294	32	13	)	)	PUNCT
cana-3294	32	14	=	=	SYM
cana-3294	32	15	0	0	PUNCT
cana-3294	32	16	if	if	SCONJ
cana-3294	32	17	ꝕ	ꝕ	NOUN
cana-3294	32	18	=	=	SYM
cana-3294	32	19	ꝙ	ꝙ	X
cana-3294	32	20	=	=	SYM
cana-3294	32	21	𝟉	𝟉	PROPN
cana-3294	32	22	for	for	ADP
cana-3294	32	23	all	all	DET
cana-3294	32	24	ꝕ	ꝕ	ADJ
cana-3294	32	25	,	,	PUNCT
cana-3294	32	26	ꝙ	ꝙ	NOUN
cana-3294	32	27	,	,	PUNCT
cana-3294	32	28	𝟉	𝟉	PROPN
cana-3294	32	29	𝜖	𝜖	X
cana-3294	32	30	ɱ	ɱ	PROPN
cana-3294	32	31	(	(	PUNCT
cana-3294	32	32	g2	g2	PROPN
cana-3294	32	33	)	)	PUNCT
cana-3294	32	34	g	g	PROPN
cana-3294	32	35	(	(	PUNCT
cana-3294	32	36	ꝕ	ꝕ	PROPN
cana-3294	32	37	,	,	PUNCT
cana-3294	32	38	ꝕ	ꝕ	NOUN
cana-3294	32	39	,	,	PUNCT
cana-3294	32	40	ꝙ	ꝙ	NOUN
cana-3294	32	41	)	)	PUNCT
cana-3294	32	42	>	>	X
cana-3294	32	43	0	0	PUNCT
cana-3294	32	44	for	for	ADP
cana-3294	32	45	ꝕ	ꝕ	NOUN
cana-3294	32	46	,	,	PUNCT
cana-3294	32	47	ꝙ	ꝙ	X
cana-3294	32	48	𝜖	𝜖	X
cana-3294	32	49	ɱ	ɱ	PROPN
cana-3294	32	50	with	with	ADP
cana-3294	32	51	ꝕ≠ꝙ	ꝕ≠ꝙ	PROPN
cana-3294	32	52	(	(	PUNCT
cana-3294	32	53	g3	g3	PROPN
cana-3294	32	54	)	)	PUNCT
cana-3294	32	55	g	g	NOUN
cana-3294	32	56	(	(	PUNCT
cana-3294	32	57	ꝕ	ꝕ	PROPN
cana-3294	32	58	,	,	PUNCT
cana-3294	32	59	ꝕ	ꝕ	NOUN
cana-3294	32	60	,	,	PUNCT
cana-3294	32	61	ꝙ	ꝙ	NOUN
cana-3294	32	62	)	)	PUNCT
cana-3294	32	63	≤	≤	NOUN
cana-3294	32	64	g	g	PROPN
cana-3294	32	65	(	(	PUNCT
cana-3294	32	66	ꝕ	ꝕ	PROPN
cana-3294	32	67	,	,	PUNCT
cana-3294	32	68	ꝙ	ꝙ	NOUN
cana-3294	32	69	,	,	PUNCT
cana-3294	32	70	𝟉	𝟉	NOUN
cana-3294	32	71	)	)	PUNCT
cana-3294	32	72	for	for	ADP
cana-3294	32	73	all	all	DET
cana-3294	32	74	ꝕ	ꝕ	PROPN
cana-3294	32	75	,	,	PUNCT
cana-3294	32	76	ꝙ	ꝙ	NOUN
cana-3294	32	77	,	,	PUNCT
cana-3294	32	78	𝟉	𝟉	PROPN
cana-3294	32	79	𝜖	𝜖	X
cana-3294	32	80	ɱ	ɱ	PROPN
cana-3294	32	81	with	with	ADP
cana-3294	32	82	ꝙ	ꝙ	PROPN
cana-3294	32	83	≠	≠	PROPN
cana-3294	32	84	𝟉	𝟉	X
cana-3294	32	85	(	(	PUNCT
cana-3294	32	86	g4	g4	NOUN
cana-3294	32	87	)	)	PUNCT
cana-3294	32	88	g	g	NOUN
cana-3294	32	89	(	(	PUNCT
cana-3294	32	90	ꝕ	ꝕ	PROPN
cana-3294	32	91	,	,	PUNCT
cana-3294	32	92	ꝙ	ꝙ	NOUN
cana-3294	32	93	,	,	PUNCT
cana-3294	32	94	𝟉	𝟉	NOUN
cana-3294	32	95	)	)	PUNCT
cana-3294	32	96	=	=	SYM
cana-3294	32	97	g	g	PROPN
cana-3294	32	98	(	(	PUNCT
cana-3294	32	99	ꝙ	ꝙ	NUM
cana-3294	32	100	,	,	PUNCT
cana-3294	32	101	𝟉	𝟉	PROPN
cana-3294	32	102	,	,	PUNCT
cana-3294	32	103	ꝕ	ꝕ	NOUN
cana-3294	32	104	)	)	PUNCT
cana-3294	32	105	=	=	SYM
cana-3294	32	106	g	g	PROPN
cana-3294	32	107	(	(	PUNCT
cana-3294	32	108	𝟉	𝟉	PROPN
cana-3294	32	109	,	,	PUNCT
cana-3294	32	110	ꝙ	ꝙ	NOUN
cana-3294	32	111	,	,	PUNCT
cana-3294	32	112	ꝕ	ꝕ	NOUN
cana-3294	32	113	)	)	PUNCT
cana-3294	32	114	=	=	NOUN
cana-3294	32	115	_	_	PUNCT
cana-3294	32	116	_	_	PUNCT
cana-3294	33	1	_	_	PUNCT
cana-3294	34	1	_	_	PUNCT
cana-3294	35	1	_	_	PUNCT
cana-3294	35	2	(	(	PUNCT
cana-3294	35	3	symmetry	symmetry	NOUN
cana-3294	35	4	)	)	PUNCT
cana-3294	35	5	(	(	PUNCT
cana-3294	35	6	g5	g5	NOUN
cana-3294	35	7	)	)	PUNCT
cana-3294	35	8	g	g	PROPN
cana-3294	35	9	(	(	PUNCT
cana-3294	35	10	ꝕ	ꝕ	PROPN
cana-3294	35	11	,	,	PUNCT
cana-3294	35	12	ꝙ	ꝙ	NOUN
cana-3294	35	13	,	,	PUNCT
cana-3294	35	14	𝟉	𝟉	NOUN
cana-3294	35	15	)	)	PUNCT
cana-3294	35	16	≤	≤	NOUN
cana-3294	35	17	g	g	PROPN
cana-3294	35	18	(	(	PUNCT
cana-3294	35	19	ꝕ	ꝕ	PROPN
cana-3294	35	20	,	,	PUNCT
cana-3294	35	21	𝝏	𝝏	NOUN
cana-3294	35	22	,	,	PUNCT
cana-3294	35	23	𝝏	𝝏	NOUN
cana-3294	35	24	)	)	PUNCT
cana-3294	36	1	+	+	CCONJ
cana-3294	36	2	g	g	PROPN
cana-3294	36	3	(	(	PUNCT
cana-3294	36	4	𝝏	𝝏	PROPN
cana-3294	36	5	,	,	PUNCT
cana-3294	36	6	ꝙ	ꝙ	NOUN
cana-3294	36	7	,	,	PUNCT
cana-3294	36	8	𝟉	𝟉	NOUN
cana-3294	36	9	)	)	PUNCT
cana-3294	36	10	for	for	ADP
cana-3294	36	11	all	all	DET
cana-3294	36	12	𝝏	𝝏	PROPN
cana-3294	36	13	,	,	PUNCT
cana-3294	36	14	ꝕ	ꝕ	X
cana-3294	36	15	,	,	PUNCT
cana-3294	36	16	ꝙ	ꝙ	NOUN
cana-3294	36	17	,	,	PUNCT
cana-3294	36	18	𝟉	𝟉	PROPN
cana-3294	36	19	ϵ	ϵ	X
cana-3294	36	20	ɱ	ɱ	PROPN
cana-3294	36	21	.	.	PUNCT
cana-3294	37	1	then	then	ADV
cana-3294	37	2	the	the	DET
cana-3294	37	3	function	function	NOUN
cana-3294	37	4	g	g	NOUN
cana-3294	37	5	is	be	AUX
cana-3294	37	6	termed	term	VERB
cana-3294	37	7	as	as	ADP
cana-3294	37	8	g	g	PROPN
cana-3294	37	9	–	–	PUNCT
cana-3294	37	10	metric	metric	ADJ
cana-3294	37	11	on	on	ADP
cana-3294	37	12	ɱ	ɱ	PROPN
cana-3294	37	13	and	and	CCONJ
cana-3294	37	14	(	(	PUNCT
cana-3294	37	15	ɱ	ɱ	PROPN
cana-3294	37	16	,	,	PUNCT
cana-3294	37	17	g	g	NOUN
cana-3294	37	18	)	)	PUNCT
cana-3294	37	19	is	be	AUX
cana-3294	37	20	a	a	DET
cana-3294	37	21	g	g	NOUN
cana-3294	37	22	-	-	PUNCT
cana-3294	37	23	metric	metric	ADJ
cana-3294	37	24	space	space	NOUN
cana-3294	37	25	.	.	PUNCT
cana-3294	38	1	definiton	definiton	PROPN
cana-3294	38	2	3.2	3.2	NUM
cana-3294	39	1	[	[	X
cana-3294	39	2	22	22	NUM
cana-3294	39	3	]	]	PUNCT
cana-3294	39	4	:	:	PUNCT
cana-3294	39	5	assume	assume	VERB
cana-3294	39	6	ɱ	ɱ	PROPN
cana-3294	39	7	≠∅	≠∅	NOUN
cana-3294	39	8	and	and	CCONJ
cana-3294	39	9	a	a	DET
cana-3294	39	10	mapping	mapping	NOUN
cana-3294	39	11	e	e	NOUN
cana-3294	39	12	:	:	PUNCT
cana-3294	39	13	ɱ	ɱ	PROPN
cana-3294	39	14	2	2	NUM
cana-3294	39	15	→	→	SYM
cana-3294	39	16	ɱ	ɱ	PROPN
cana-3294	39	17	.	.	PUNCT
cana-3294	40	1	an	an	DET
cana-3294	40	2	element	element	NOUN
cana-3294	40	3	(	(	PUNCT
cana-3294	40	4	λ	λ	PROPN
cana-3294	40	5	,	,	PUNCT
cana-3294	40	6	μ	μ	NOUN
cana-3294	40	7	)	)	PUNCT
cana-3294	40	8	ϵ	ϵ	PROPN
cana-3294	40	9	ɱ	ɱ	ADJ
cana-3294	40	10	2	2	NUM
cana-3294	40	11	is	be	AUX
cana-3294	40	12	a	a	DET
cana-3294	40	13	coupled	couple	VERB
cana-3294	40	14	fixed	fix	VERB
cana-3294	40	15	point	point	NOUN
cana-3294	40	16	of	of	ADP
cana-3294	40	17	e	e	PROPN
cana-3294	40	18	if	if	SCONJ
cana-3294	40	19	ɱ	ɱ	PROPN
cana-3294	40	20	(	(	PUNCT
cana-3294	40	21	λ	λ	PROPN
cana-3294	40	22	,	,	PUNCT
cana-3294	40	23	μ	μ	NOUN
cana-3294	40	24	)	)	PUNCT
cana-3294	40	25	=	=	SYM
cana-3294	40	26	λ	λ	PROPN
cana-3294	40	27	&	&	CCONJ
cana-3294	40	28	ɱ	ɱ	PROPN
cana-3294	40	29	(	(	PUNCT
cana-3294	40	30	μ	μ	PROPN
cana-3294	40	31	,	,	PUNCT
cana-3294	40	32	λ)=	λ)=	PROPN
cana-3294	40	33	μ	μ	PROPN
cana-3294	40	34	.	.	PUNCT
cana-3294	41	1	definition	definition	NOUN
cana-3294	41	2	3.3[32	3.3[32	NUM
cana-3294	41	3	]	]	PUNCT
cana-3294	41	4	:	:	PUNCT
cana-3294	41	5	an	an	DET
cana-3294	41	6	element	element	NOUN
cana-3294	41	7	(	(	PUNCT
cana-3294	41	8	ꝕ	ꝕ	PROPN
cana-3294	41	9	,	,	PUNCT
cana-3294	41	10	ꝙ	ꝙ	NOUN
cana-3294	41	11	,	,	PUNCT
cana-3294	41	12	ν	ν	NOUN
cana-3294	41	13	)	)	PUNCT
cana-3294	41	14	ϵ	ϵ	PROPN
cana-3294	41	15	ɱ3	ɱ3	PROPN
cana-3294	41	16	be	be	AUX
cana-3294	41	17	a	a	DET
cana-3294	41	18	tripled	triple	VERB
cana-3294	41	19	fixed	fix	VERB
cana-3294	41	20	point	point	NOUN
cana-3294	41	21	of	of	ADP
cana-3294	41	22	mapping	map	VERB
cana-3294	41	23	𝛄	𝛄	X
cana-3294	41	24	:	:	PUNCT
cana-3294	41	25	ɱ3→ɱ	ɱ3→ɱ	X
cana-3294	41	26	if	if	SCONJ
cana-3294	41	27	𝛄	𝛄	PROPN
cana-3294	41	28	(	(	PUNCT
cana-3294	41	29	ꝕ	ꝕ	PROPN
cana-3294	41	30	,	,	PUNCT
cana-3294	41	31	ꝙ	ꝙ	NOUN
cana-3294	41	32	,	,	PUNCT
cana-3294	41	33	ν	ν	NOUN
cana-3294	41	34	)	)	PUNCT
cana-3294	42	1	=	=	SYM
cana-3294	42	2	ꝕ	ꝕ	PROPN
cana-3294	42	3	,	,	PUNCT
cana-3294	42	4	𝛄	𝛄	PROPN
cana-3294	42	5	(	(	PUNCT
cana-3294	42	6	ꝙ	ꝙ	NOUN
cana-3294	42	7	,	,	PUNCT
cana-3294	42	8	ꝕ	ꝕ	NOUN
cana-3294	42	9	,	,	PUNCT
cana-3294	42	10	ꝙ	ꝙ	NOUN
cana-3294	42	11	)	)	PUNCT
cana-3294	42	12	=	=	SYM
cana-3294	42	13	ꝙ	ꝙ	PROPN
cana-3294	42	14	and	and	CCONJ
cana-3294	42	15	𝛄	𝛄	PROPN
cana-3294	42	16	(	(	PUNCT
cana-3294	42	17	ν	ν	PROPN
cana-3294	42	18	,	,	PUNCT
cana-3294	42	19	ꝙ	ꝙ	NOUN
cana-3294	42	20	,	,	PUNCT
cana-3294	42	21	ꝕ	ꝕ	NOUN
cana-3294	42	22	)	)	PUNCT
cana-3294	42	23	=	=	SYM
cana-3294	42	24	ν	ν	X
cana-3294	42	25	.	.	PUNCT
cana-3294	42	26	definition	definition	NOUN
cana-3294	42	27	3.4	3.4	NUM
cana-3294	43	1	[	[	SYM
cana-3294	43	2	33	33	NUM
cana-3294	43	3	]	]	X
cana-3294	43	4	:	:	PUNCT
cana-3294	43	5	a	a	DET
cana-3294	43	6	trio	trio	NOUN
cana-3294	43	7	(	(	PUNCT
cana-3294	43	8	𝞎	𝞎	X
cana-3294	43	9	,	,	PUNCT
cana-3294	43	10	ꝙ	ꝙ	NUM
cana-3294	43	11	,	,	PUNCT
cana-3294	43	12	ꝛ	ꝛ	NOUN
cana-3294	43	13	)	)	PUNCT
cana-3294	43	14	ϵ	ϵ	NOUN
cana-3294	43	15	ℱ3	ℱ3	NOUN
cana-3294	43	16	is	be	AUX
cana-3294	43	17	a	a	DET
cana-3294	43	18	tripled	triple	VERB
cana-3294	43	19	coincidence	coincidence	NOUN
cana-3294	43	20	point	point	NOUN
cana-3294	43	21	of	of	ADP
cana-3294	43	22	the	the	DET
cana-3294	43	23	mappings	mapping	NOUN
cana-3294	43	24	𝕲	𝕲	NOUN
cana-3294	43	25	:	:	PUNCT
cana-3294	43	26	ℱ3	ℱ3	NOUN
cana-3294	43	27	→	→	SYM
cana-3294	43	28	ℱ	ℱ	PROPN
cana-3294	43	29	and	and	CCONJ
cana-3294	43	30	𝒻	𝒻	ADJ
cana-3294	43	31	:	:	PUNCT
cana-3294	43	32	𝓕→𝓕	𝓕→𝓕	NOUN
cana-3294	43	33	if	if	SCONJ
cana-3294	43	34	𝒻(𝞎)=𝓕	𝒻(𝞎)=𝓕	PROPN
cana-3294	43	35	(	(	PUNCT
cana-3294	43	36	𝞎	𝞎	SYM
cana-3294	43	37	,	,	PUNCT
cana-3294	43	38	ꝙ	ꝙ	NUM
cana-3294	43	39	,	,	PUNCT
cana-3294	43	40	ꝛ	ꝛ	NOUN
cana-3294	43	41	)	)	PUNCT
cana-3294	43	42	,	,	PUNCT
cana-3294	43	43	𝒻(ꝙ)=𝓕	𝒻(ꝙ)=𝓕	PROPN
cana-3294	43	44	(	(	PUNCT
cana-3294	43	45	ꝙ	ꝙ	NOUN
cana-3294	43	46	,	,	PUNCT
cana-3294	43	47	𝞎	𝞎	X
cana-3294	43	48	,	,	PUNCT
cana-3294	43	49	ꝙ	ꝙ	NUM
cana-3294	43	50	)	)	PUNCT
cana-3294	43	51	and	and	CCONJ
cana-3294	43	52	𝒻(ꝛ)=𝓕	𝒻(ꝛ)=𝓕	NOUN
cana-3294	43	53	(	(	PUNCT
cana-3294	43	54	ꝛ	ꝛ	NOUN
cana-3294	43	55	,	,	PUNCT
cana-3294	43	56	ꝙ	ꝙ	NUM
cana-3294	43	57	,	,	PUNCT
cana-3294	43	58	𝞎	𝞎	NOUN
cana-3294	43	59	)	)	PUNCT
cana-3294	43	60	.	.	PUNCT
cana-3294	44	1	definition	definition	NOUN
cana-3294	44	2	3.5[34	3.5[34	NUM
cana-3294	44	3	]	]	X
cana-3294	44	4	:	:	PUNCT
cana-3294	45	1	let	let	VERB
cana-3294	45	2	(	(	PUNCT
cana-3294	45	3	k	k	X
cana-3294	45	4	,	,	PUNCT
cana-3294	45	5	≤	≤	NUM
cana-3294	45	6	)	)	PUNCT
cana-3294	45	7	be	be	VERB
cana-3294	45	8	a	a	DET
cana-3294	45	9	poset	poset	NOUN
cana-3294	45	10	and	and	CCONJ
cana-3294	45	11	𝕻	𝕻	NOUN
cana-3294	45	12	:	:	PUNCT
cana-3294	45	13	k3→k	k3→k	INTJ
cana-3294	45	14	.	.	PUNCT
cana-3294	46	1	if	if	SCONJ
cana-3294	46	2	𝕻	𝕻	PROPN
cana-3294	46	3	(	(	PUNCT
cana-3294	46	4	λ	λ	PROPN
cana-3294	46	5	,	,	PUNCT
cana-3294	46	6	μ	μ	PROPN
cana-3294	46	7	,	,	PUNCT
cana-3294	46	8	ν	ν	X
cana-3294	46	9	)	)	PUNCT
cana-3294	46	10	is	be	AUX
cana-3294	46	11	monotone	monotone	ADJ
cana-3294	46	12	-	-	PUNCT
cana-3294	46	13	non	non	NOUN
cana-3294	46	14	increasing	increase	VERB
cana-3294	46	15	in	in	ADP
cana-3294	46	16	μ	μ	NOUN
cana-3294	46	17	and	and	CCONJ
cana-3294	46	18	monotone	monotone	ADJ
cana-3294	46	19	non	non	ADJ
cana-3294	46	20	-	-	ADJ
cana-3294	46	21	decreasing	decrease	VERB
cana-3294	46	22	in	in	ADP
cana-3294	46	23	λ	λ	PROPN
cana-3294	46	24	&	&	CCONJ
cana-3294	46	25	ν	ν	PROPN
cana-3294	46	26	then	then	ADV
cana-3294	46	27	𝕻	𝕻	PRON
cana-3294	46	28	has	have	AUX
cana-3294	46	29	mixed	mix	VERB
cana-3294	46	30	monotone	monotone	ADJ
cana-3294	46	31	property	property	NOUN
cana-3294	46	32	.	.	PUNCT
cana-3294	47	1	i.e	i.e	X
cana-3294	47	2	,	,	PUNCT
cana-3294	47	3	for	for	ADP
cana-3294	47	4	any	any	DET
cana-3294	47	5	λ	λ	PROPN
cana-3294	47	6	,	,	PUNCT
cana-3294	47	7	μ	μ	PROPN
cana-3294	47	8	,	,	PUNCT
cana-3294	47	9	ν	ν	PROPN
cana-3294	47	10	ϵ	ϵ	PROPN
cana-3294	47	11	k.	k.	PROPN
cana-3294	47	12	λ1	λ1	PROPN
cana-3294	47	13	,	,	PUNCT
cana-3294	47	14	λ2	λ2	PROPN
cana-3294	47	15	,	,	PUNCT
cana-3294	47	16	ϵ	ϵ	X
cana-3294	47	17	k	k	PROPN
cana-3294	47	18	,	,	PUNCT
cana-3294	47	19	λ1	λ1	ADJ
cana-3294	47	20	≤	≤	NUM
cana-3294	47	21	λ2	λ2	NOUN
cana-3294	47	22	⟹	⟹	NUM
cana-3294	47	23	𝕻	𝕻	PROPN
cana-3294	47	24	(	(	PUNCT
cana-3294	47	25	λ1	λ1	PROPN
cana-3294	47	26	,	,	PUNCT
cana-3294	47	27	μ	μ	PROPN
cana-3294	47	28	,	,	PUNCT
cana-3294	47	29	ν	ν	NOUN
cana-3294	47	30	)	)	PUNCT
cana-3294	47	31	≤	≤	NOUN
cana-3294	47	32	𝕻	𝕻	PROPN
cana-3294	47	33	(	(	PUNCT
cana-3294	47	34	λ2	λ2	PROPN
cana-3294	47	35	,	,	PUNCT
cana-3294	47	36	μ	μ	PROPN
cana-3294	47	37	,	,	PUNCT
cana-3294	47	38	ν	ν	NOUN
cana-3294	47	39	)	)	PUNCT
cana-3294	47	40	μ1	μ1	PROPN
cana-3294	47	41	,	,	PUNCT
cana-3294	47	42	μ2	μ2	NOUN
cana-3294	47	43	ϵ	ϵ	X
cana-3294	47	44	k	k	PROPN
cana-3294	47	45	,	,	PUNCT
cana-3294	47	46	μ1	μ1	PROPN
cana-3294	47	47	≤	≤	NUM
cana-3294	47	48	μ2	μ2	NOUN
cana-3294	47	49	⟹	⟹	NUM
cana-3294	47	50	𝕻	𝕻	PROPN
cana-3294	47	51	(	(	PUNCT
cana-3294	47	52	λ	λ	PROPN
cana-3294	47	53	,	,	PUNCT
cana-3294	47	54	μ1	μ1	NOUN
cana-3294	47	55	,	,	PUNCT
cana-3294	47	56	ν	ν	NOUN
cana-3294	47	57	)	)	PUNCT
cana-3294	47	58	≥	≥	NOUN
cana-3294	47	59	𝕻	𝕻	PROPN
cana-3294	47	60	(	(	PUNCT
cana-3294	47	61	λ	λ	PROPN
cana-3294	47	62	,	,	PUNCT
cana-3294	47	63	μ2	μ2	NOUN
cana-3294	47	64	,	,	PUNCT
cana-3294	47	65	ν	ν	NOUN
cana-3294	47	66	)	)	PUNCT
cana-3294	47	67	ν1	ν1	NOUN
cana-3294	47	68	,	,	PUNCT
cana-3294	47	69	ν2	ν2	NOUN
cana-3294	47	70	ϵ	ϵ	PROPN
cana-3294	47	71	k	k	PROPN
cana-3294	47	72	,	,	PUNCT
cana-3294	47	73	ν1	ν1	NOUN
cana-3294	47	74	≤	≤	PUNCT
cana-3294	47	75	ν2	ν2	ADP
cana-3294	47	76	⟹	⟹	NUM
cana-3294	47	77	𝕻	𝕻	PROPN
cana-3294	47	78	(	(	PUNCT
cana-3294	47	79	λ	λ	PROPN
cana-3294	47	80	,	,	PUNCT
cana-3294	47	81	μ	μ	PROPN
cana-3294	47	82	,	,	PUNCT
cana-3294	47	83	ν1	ν1	NOUN
cana-3294	47	84	)	)	PUNCT
cana-3294	47	85	≤	≤	PROPN
cana-3294	47	86	𝕻(λ	𝕻(λ	PROPN
cana-3294	47	87	,	,	PUNCT
cana-3294	47	88	μ	μ	NOUN
cana-3294	47	89	,	,	PUNCT
cana-3294	47	90	ν2	ν2	NOUN
cana-3294	47	91	)	)	PUNCT
cana-3294	47	92	definition	definition	NOUN
cana-3294	47	93	3.6[34	3.6[34	NUM
cana-3294	47	94	]	]	X
cana-3294	47	95	:	:	PUNCT
cana-3294	47	96	let	let	VERB
cana-3294	47	97	(	(	PUNCT
cana-3294	47	98	e	e	NOUN
cana-3294	47	99	,	,	PUNCT
cana-3294	47	100	≤	≤	NUM
cana-3294	47	101	)	)	PUNCT
cana-3294	47	102	be	be	VERB
cana-3294	47	103	a	a	DET
cana-3294	47	104	partially	partially	ADV
cana-3294	47	105	ordered	order	VERB
cana-3294	47	106	set	set	NOUN
cana-3294	47	107	and	and	CCONJ
cana-3294	47	108	ϔ	ϔ	NOUN
cana-3294	47	109	:	:	PUNCT
cana-3294	47	110	e3→e	e3→e	NOUN
cana-3294	47	111	and	and	CCONJ
cana-3294	47	112	g	g	NOUN
cana-3294	47	113	:	:	PUNCT
cana-3294	47	114	e→e	e→e	NOUN
cana-3294	47	115	be	be	AUX
cana-3294	47	116	two	two	NUM
cana-3294	47	117	maps	map	NOUN
cana-3294	47	118	.	.	PUNCT
cana-3294	48	1	if	if	SCONJ
cana-3294	48	2	ϔ	ϔ	NOUN
cana-3294	48	3	(	(	PUNCT
cana-3294	48	4	λ	λ	PROPN
cana-3294	48	5	,	,	PUNCT
cana-3294	48	6	μ	μ	PROPN
cana-3294	48	7	,	,	PUNCT
cana-3294	48	8	ν	ν	X
cana-3294	48	9	)	)	PUNCT
cana-3294	48	10	is	be	AUX
cana-3294	48	11	monotone	monotone	ADJ
cana-3294	48	12	non	non	ADJ
cana-3294	48	13	increasing	increase	VERB
cana-3294	48	14	in	in	ADP
cana-3294	48	15	μ	μ	PROPN
cana-3294	48	16	and	and	CCONJ
cana-3294	48	17	ϔ	ϔ	PROPN
cana-3294	48	18	(	(	PUNCT
cana-3294	48	19	λ	λ	PROPN
cana-3294	48	20	,	,	PUNCT
cana-3294	48	21	μ	μ	PROPN
cana-3294	48	22	,	,	PUNCT
cana-3294	48	23	ν	ν	X
cana-3294	48	24	)	)	PUNCT
cana-3294	48	25	is	be	AUX
cana-3294	48	26	monotone	monotone	ADJ
cana-3294	48	27	non	non	NOUN
cana-3294	48	28	decreasing	decrease	VERB
cana-3294	48	29	in	in	ADP
cana-3294	48	30	λ	λ	PROPN
cana-3294	48	31	and	and	CCONJ
cana-3294	48	32	ν	ν	NOUN
cana-3294	48	33	then	then	ADV
cana-3294	48	34	ϔ	ϔ	PROPN
cana-3294	48	35	has	have	VERB
cana-3294	48	36	g	g	NOUN
cana-3294	48	37	-	-	PUNCT
cana-3294	48	38	mixed	mixed	ADJ
cana-3294	48	39	monotone	monotone	ADJ
cana-3294	48	40	property	property	NOUN
cana-3294	48	41	.	.	PUNCT
cana-3294	49	1	i.e	i.e	X
cana-3294	49	2	,	,	PUNCT
cana-3294	49	3	for	for	ADP
cana-3294	49	4	any	any	DET
cana-3294	49	5	λ	λ	PROPN
cana-3294	49	6	,	,	PUNCT
cana-3294	49	7	μ	μ	PROPN
cana-3294	49	8	,	,	PUNCT
cana-3294	49	9	ν	ν	PROPN
cana-3294	49	10	ϵ	ϵ	PROPN
cana-3294	49	11	e.	e.	PROPN
cana-3294	49	12	λ1	λ1	PROPN
cana-3294	49	13	,	,	PUNCT
cana-3294	49	14	λ2	λ2	PROPN
cana-3294	49	15	,	,	PUNCT
cana-3294	49	16	ϵ	ϵ	X
cana-3294	49	17	e	e	PROPN
cana-3294	49	18	,	,	PUNCT
cana-3294	49	19	g(λ1	g(λ1	NOUN
cana-3294	49	20	)	)	PUNCT
cana-3294	49	21	≤	≤	NOUN
cana-3294	50	1	g	g	PROPN
cana-3294	50	2	(	(	PUNCT
cana-3294	50	3	λ2	λ2	PROPN
cana-3294	50	4	)	)	PUNCT
cana-3294	50	5	⟹	⟹	PROPN
cana-3294	50	6	ϔ	ϔ	NOUN
cana-3294	50	7	(	(	PUNCT
cana-3294	50	8	λ1	λ1	PROPN
cana-3294	50	9	,	,	PUNCT
cana-3294	50	10	μ	μ	PROPN
cana-3294	50	11	,	,	PUNCT
cana-3294	50	12	ν	ν	NOUN
cana-3294	50	13	)	)	PUNCT
cana-3294	50	14	≤	≤	NOUN
cana-3294	50	15	ϔ	ϔ	NOUN
cana-3294	50	16	(	(	PUNCT
cana-3294	50	17	λ2	λ2	PROPN
cana-3294	50	18	,	,	PUNCT
cana-3294	50	19	μ	μ	PROPN
cana-3294	50	20	,	,	PUNCT
cana-3294	50	21	ν	ν	NOUN
cana-3294	50	22	)	)	PUNCT
cana-3294	50	23	μ1	μ1	PROPN
cana-3294	50	24	,	,	PUNCT
cana-3294	50	25	μ2	μ2	NOUN
cana-3294	50	26	ϵ	ϵ	X
cana-3294	50	27	e	e	NOUN
cana-3294	50	28	,	,	PUNCT
cana-3294	50	29	g(μ1	g(μ1	NOUN
cana-3294	50	30	)	)	PUNCT
cana-3294	50	31	≤	≤	NUM
cana-3294	50	32	g(μ2	g(μ2	NOUN
cana-3294	50	33	)	)	PUNCT
cana-3294	50	34	⟹	⟹	PROPN
cana-3294	51	1	ϔ	ϔ	NOUN
cana-3294	51	2	(	(	PUNCT
cana-3294	51	3	λ	λ	PROPN
cana-3294	51	4	,	,	PUNCT
cana-3294	51	5	μ1	μ1	NOUN
cana-3294	51	6	,	,	PUNCT
cana-3294	51	7	ν	ν	NOUN
cana-3294	51	8	)	)	PUNCT
cana-3294	51	9	≥	≥	NOUN
cana-3294	51	10	ϔ	ϔ	NOUN
cana-3294	51	11	(	(	PUNCT
cana-3294	51	12	λ	λ	PROPN
cana-3294	51	13	,	,	PUNCT
cana-3294	51	14	μ2	μ2	NOUN
cana-3294	51	15	,	,	PUNCT
cana-3294	51	16	ν	ν	NOUN
cana-3294	51	17	)	)	PUNCT
cana-3294	51	18	ν1	ν1	NOUN
cana-3294	51	19	,	,	PUNCT
cana-3294	51	20	ν2	ν2	NOUN
cana-3294	51	21	ϵ	ϵ	PROPN
cana-3294	51	22	e	e	NOUN
cana-3294	51	23	,	,	PUNCT
cana-3294	51	24	g(ν1	g(ν1	NOUN
cana-3294	51	25	)	)	PUNCT
cana-3294	51	26	≤	≤	NUM
cana-3294	51	27	g(ν2	g(ν2	NOUN
cana-3294	51	28	)	)	PUNCT
cana-3294	51	29	⟹	⟹	PUNCT
cana-3294	52	1	ϔ(λ	ϔ(λ	PROPN
cana-3294	52	2	,	,	PUNCT
cana-3294	52	3	μ	μ	PROPN
cana-3294	52	4	,	,	PUNCT
cana-3294	52	5	ν1	ν1	NOUN
cana-3294	52	6	)	)	PUNCT
cana-3294	52	7	≤	≤	NOUN
cana-3294	52	8	ϔ(λ	ϔ(λ	PRON
cana-3294	52	9	,	,	PUNCT
cana-3294	52	10	μ	μ	NOUN
cana-3294	52	11	,	,	PUNCT
cana-3294	52	12	ν2	ν2	NOUN
cana-3294	52	13	)	)	PUNCT
cana-3294	52	14	definition	definition	NOUN
cana-3294	52	15	3.7[24	3.7[24	NUM
cana-3294	52	16	]	]	PUNCT
cana-3294	52	17	:	:	PUNCT
cana-3294	52	18	let	let	VERB
cana-3294	52	19	(	(	PUNCT
cana-3294	52	20	u	u	NOUN
cana-3294	52	21	,	,	PUNCT
cana-3294	52	22	d	d	PROPN
cana-3294	52	23	)	)	PUNCT
cana-3294	52	24	be	be	AUX
cana-3294	52	25	a	a	DET
cana-3294	52	26	metric	metric	ADJ
cana-3294	52	27	space	space	NOUN
cana-3294	52	28	and	and	CCONJ
cana-3294	52	29	mappings	mapping	NOUN
cana-3294	52	30	e	e	NOUN
cana-3294	52	31	and	and	CCONJ
cana-3294	52	32	g	g	PROPN
cana-3294	52	33	where	where	SCONJ
cana-3294	52	34	e	e	NOUN
cana-3294	52	35	:	:	PUNCT
cana-3294	52	36	u3→u	u3→u	NOUN
cana-3294	52	37	and	and	CCONJ
cana-3294	52	38	g	g	NOUN
cana-3294	52	39	:	:	PUNCT
cana-3294	52	40	u→u	u→u	X
cana-3294	52	41	are	be	AUX
cana-3294	52	42	compatible	compatible	ADJ
cana-3294	52	43	if	if	SCONJ
cana-3294	52	44	lim	lim	PROPN
cana-3294	52	45	𝑛→∞	𝑛→∞	NUM
cana-3294	52	46	𝑑	𝑑	PROPN
cana-3294	52	47	(	(	PUNCT
cana-3294	52	48	𝑔(𝐸(𝜆𝑛	𝑔(𝐸(𝜆𝑛	PROPN
cana-3294	52	49	,	,	PUNCT
cana-3294	52	50	𝜇𝑛	𝜇𝑛	INTJ
cana-3294	52	51	,	,	PUNCT
cana-3294	52	52	𝜈𝑛	𝜈𝑛	ADP
cana-3294	52	53	)	)	PUNCT
cana-3294	52	54	)	)	PUNCT
cana-3294	52	55	,	,	PUNCT
cana-3294	52	56	𝐸(𝑔𝜆𝑛	𝐸(𝑔𝜆𝑛	PROPN
cana-3294	52	57	,	,	PUNCT
cana-3294	52	58	𝑔𝜇𝑛	𝑔𝜇𝑛	NOUN
cana-3294	52	59	,	,	PUNCT
cana-3294	52	60	𝑔𝜈𝑛	𝑔𝜈𝑛	NOUN
cana-3294	52	61	)	)	PUNCT
cana-3294	52	62	)	)	PUNCT
cana-3294	53	1	=	=	SYM
cana-3294	53	2	0	0	NUM
cana-3294	53	3	communications	communication	NOUN
cana-3294	53	4	on	on	ADP
cana-3294	53	5	applied	apply	VERB
cana-3294	53	6	nonlinear	nonlinear	ADJ
cana-3294	53	7	analysis	analysis	NOUN
cana-3294	53	8	issn	issn	NOUN
cana-3294	53	9	:	:	PUNCT
cana-3294	53	10	1074	1074	NUM
cana-3294	53	11	-	-	PUNCT
cana-3294	53	12	133x	133x	NUM
cana-3294	53	13	vol	vol	NOUN
cana-3294	53	14	32	32	NUM
cana-3294	53	15	no	no	NOUN
cana-3294	53	16	.	.	PUNCT
cana-3294	54	1	6s	6s	NUM
cana-3294	54	2	(	(	PUNCT
cana-3294	54	3	2025	2025	NUM
cana-3294	54	4	)	)	PUNCT
cana-3294	54	5	277	277	NUM
cana-3294	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	54	7	lim	lim	NOUN
cana-3294	54	8	𝑛→∞	𝑛→∞	NUM
cana-3294	54	9	𝑑	𝑑	PROPN
cana-3294	54	10	(	(	PUNCT
cana-3294	54	11	𝑔(𝐸(𝜇𝑛	𝑔(𝐸(𝜇𝑛	PROPN
cana-3294	54	12	,	,	PUNCT
cana-3294	54	13	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	54	14	,	,	PUNCT
cana-3294	54	15	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	54	16	)	)	PUNCT
cana-3294	54	17	)	)	PUNCT
cana-3294	54	18	,	,	PUNCT
cana-3294	54	19	𝐸(𝑔𝜇𝑛	𝐸(𝑔𝜇𝑛	PROPN
cana-3294	54	20	,	,	PUNCT
cana-3294	54	21	𝑔𝜆𝑛	𝑔𝜆𝑛	PROPN
cana-3294	54	22	,	,	PUNCT
cana-3294	54	23	𝑔𝜇𝑛	𝑔𝜇𝑛	NOUN
cana-3294	54	24	)	)	PUNCT
cana-3294	54	25	)	)	PUNCT
cana-3294	55	1	=	=	SYM
cana-3294	55	2	0	0	NUM
cana-3294	56	1	lim	lim	PROPN
cana-3294	56	2	𝑛→∞	𝑛→∞	NUM
cana-3294	56	3	𝑑(𝑔(𝐸(𝜈𝑛	𝑑(𝑔(𝐸(𝜈𝑛	PROPN
cana-3294	56	4	,	,	PUNCT
cana-3294	56	5	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	56	6	,	,	PUNCT
cana-3294	56	7	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	56	8	)	)	PUNCT
cana-3294	56	9	,	,	PUNCT
cana-3294	56	10	𝐸(𝑔𝜈𝑛	𝐸(𝑔𝜈𝑛	PROPN
cana-3294	56	11	,	,	PUNCT
cana-3294	56	12	𝑔𝜇𝑛	𝑔𝜇𝑛	NOUN
cana-3294	56	13	,	,	PUNCT
cana-3294	56	14	𝑔𝜈𝑛	𝑔𝜈𝑛	NOUN
cana-3294	56	15	)	)	PUNCT
cana-3294	56	16	)	)	PUNCT
cana-3294	57	1	=	=	PUNCT
cana-3294	57	2	0	0	PUNCT
cana-3294	58	1	whenever	whenever	SCONJ
cana-3294	58	2	{	{	PUNCT
cana-3294	58	3	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	58	4	}	}	PUNCT
cana-3294	58	5	,	,	PUNCT
cana-3294	58	6	{	{	PUNCT
cana-3294	58	7	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	58	8	}	}	PUNCT
cana-3294	58	9	,	,	PUNCT
cana-3294	58	10	{	{	PUNCT
cana-3294	58	11	𝜈𝑛}𝑎𝑟𝑒	𝜈𝑛}𝑎𝑟𝑒	PROPN
cana-3294	58	12	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	NOUN
cana-3294	58	13	𝑖𝑛	𝑖𝑛	NOUN
cana-3294	58	14	𝑋	𝑋	PROPN
cana-3294	58	15	,	,	PUNCT
cana-3294	58	16	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
cana-3294	58	17	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
cana-3294	58	18	lim	lim	PROPN
cana-3294	58	19	𝑛→∞	𝑛→∞	NUM
cana-3294	58	20	𝐸(𝜆𝑛	𝐸(𝜆𝑛	PROPN
cana-3294	58	21	,	,	PUNCT
cana-3294	58	22	𝜇𝑛,𝑣𝑛	𝜇𝑛,𝑣𝑛	NOUN
cana-3294	58	23	)	)	PUNCT
cana-3294	59	1	=	=	VERB
cana-3294	59	2	lim	lim	PROPN
cana-3294	59	3	𝑛→∞	𝑛→∞	NUM
cana-3294	59	4	𝑔(𝜆𝑛	𝑔(𝜆𝑛	PROPN
cana-3294	59	5	)	)	PUNCT
cana-3294	60	1	=	=	SYM
cana-3294	60	2	𝜆	𝜆	X
cana-3294	60	3	,	,	PUNCT
cana-3294	60	4	lim	lim	NOUN
cana-3294	60	5	𝑛→∞	𝑛→∞	NUM
cana-3294	60	6	e	e	X
cana-3294	60	7	(	(	PUNCT
cana-3294	60	8	𝜇𝑛	𝜇𝑛	INTJ
cana-3294	60	9	,	,	PUNCT
cana-3294	60	10	𝜆n	𝜆n	NOUN
cana-3294	60	11	,	,	PUNCT
cana-3294	60	12	μn	μn	NOUN
cana-3294	60	13	)	)	PUNCT
cana-3294	60	14	=	=	SYM
cana-3294	60	15	lim	lim	NOUN
cana-3294	60	16	𝑛→∞	𝑛→∞	NUM
cana-3294	60	17	𝑔(𝜇n	𝑔(𝜇n	NOUN
cana-3294	60	18	)	)	PUNCT
cana-3294	60	19	=	=	SYM
cana-3294	60	20	μ	μ	PROPN
cana-3294	60	21	lim	lim	PROPN
cana-3294	60	22	𝑛→∞	𝑛→∞	NUM
cana-3294	60	23	𝐸(𝑣𝑛	𝐸(𝑣𝑛	PROPN
cana-3294	60	24	,	,	PUNCT
cana-3294	60	25	𝜇𝑛,𝜆𝑛	𝜇𝑛,𝜆𝑛	NOUN
cana-3294	60	26	)	)	PUNCT
cana-3294	61	1	=	=	SYM
cana-3294	61	2	lim	lim	PROPN
cana-3294	61	3	𝑛→∞	𝑛→∞	NUM
cana-3294	61	4	𝑔(𝑣𝑛	𝑔(𝑣𝑛	PROPN
cana-3294	61	5	)	)	PUNCT
cana-3294	61	6	=	=	SYM
cana-3294	61	7	𝑣	𝑣	PROPN
cana-3294	61	8	for	for	ADP
cana-3294	61	9	all	all	PRON
cana-3294	61	10	𝜆	𝜆	NOUN
cana-3294	61	11	,	,	PUNCT
cana-3294	61	12	𝜇	𝜇	ADP
cana-3294	61	13	,	,	PUNCT
cana-3294	61	14	𝑣	𝑣	X
cana-3294	61	15	,	,	PUNCT
cana-3294	61	16	𝜖𝑈	𝜖𝑈	ADP
cana-3294	61	17	definition	definition	NOUN
cana-3294	61	18	3.8[24	3.8[24	NUM
cana-3294	61	19	]	]	PUNCT
cana-3294	61	20	:	:	PUNCT
cana-3294	61	21	the	the	DET
cana-3294	61	22	mapping	mapping	NOUN
cana-3294	61	23	e	e	NOUN
cana-3294	61	24	:	:	PUNCT
cana-3294	61	25	ɱ3→ɱ	ɱ3→ɱ	X
cana-3294	61	26	and	and	CCONJ
cana-3294	61	27	𝕻	𝕻	NOUN
cana-3294	61	28	:	:	PUNCT
cana-3294	61	29	ɱ→ɱ	ɱ→ɱ	NUM
cana-3294	61	30	are	be	AUX
cana-3294	61	31	(	(	PUNCT
cana-3294	61	32	i	i	NOUN
cana-3294	61	33	)	)	PUNCT
cana-3294	61	34	reciprocally	reciprocally	ADV
cana-3294	61	35	continuous	continuous	ADJ
cana-3294	61	36	if	if	SCONJ
cana-3294	61	37	lim	lim	PROPN
cana-3294	61	38	𝑛→∞	𝑛→∞	PUNCT
cana-3294	61	39	𝔓	𝔓	PROPN
cana-3294	61	40	(	(	PUNCT
cana-3294	61	41	𝐸(𝜆𝑛,𝜇𝑛,𝑣𝑛	𝐸(𝜆𝑛,𝜇𝑛,𝑣𝑛	NUM
cana-3294	61	42	)	)	PUNCT
cana-3294	61	43	)	)	PUNCT
cana-3294	61	44	=	=	SYM
cana-3294	61	45	𝔓(𝜆	𝔓(𝜆	NUM
cana-3294	61	46	)	)	PUNCT
cana-3294	61	47	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3294	61	48	lim	lim	PROPN
cana-3294	61	49	𝑛→∞	𝑛→∞	NUM
cana-3294	61	50	𝐸(𝔓(𝜆𝑛	𝐸(𝔓(𝜆𝑛	PROPN
cana-3294	61	51	)	)	PUNCT
cana-3294	61	52	,	,	PUNCT
cana-3294	61	53	𝔓(𝜇𝑛	𝔓(𝜇𝑛	X
cana-3294	61	54	)	)	PUNCT
cana-3294	61	55	,	,	PUNCT
cana-3294	61	56	𝔓(𝑣𝑛	𝔓(𝑣𝑛	NOUN
cana-3294	61	57	)	)	PUNCT
cana-3294	61	58	)	)	PUNCT
cana-3294	61	59	=	=	SYM
cana-3294	62	1	𝐸(𝜆	𝐸(𝜆	X
cana-3294	62	2	,	,	PUNCT
cana-3294	62	3	𝜇	𝜇	ADP
cana-3294	62	4	,	,	PUNCT
cana-3294	62	5	𝑣	𝑣	NOUN
cana-3294	62	6	)	)	PUNCT
cana-3294	62	7	lim	lim	NOUN
cana-3294	62	8	𝑛→∞	𝑛→∞	NUM
cana-3294	62	9	𝔓	𝔓	PROPN
cana-3294	62	10	(	(	PUNCT
cana-3294	62	11	𝐸(𝜇𝑛,𝜆𝑛,𝜇𝑛	𝐸(𝜇𝑛,𝜆𝑛,𝜇𝑛	NOUN
cana-3294	62	12	)	)	PUNCT
cana-3294	62	13	)	)	PUNCT
cana-3294	62	14	=	=	SYM
cana-3294	63	1	𝔓(𝜇	𝔓(𝜇	NUM
cana-3294	63	2	)	)	PUNCT
cana-3294	63	3	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3294	63	4	lim	lim	PROPN
cana-3294	63	5	𝑛→∞	𝑛→∞	NUM
cana-3294	63	6	𝐸(𝔓	𝐸(𝔓	NOUN
cana-3294	63	7	(	(	PUNCT
cana-3294	63	8	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	63	9	)	)	PUNCT
cana-3294	63	10	,	,	PUNCT
cana-3294	63	11	𝔓(𝜆𝑛	𝔓(𝜆𝑛	PROPN
cana-3294	63	12	)	)	PUNCT
cana-3294	63	13	,	,	PUNCT
cana-3294	63	14	𝔓(𝜇𝑛	𝔓(𝜇𝑛	X
cana-3294	63	15	)	)	PUNCT
cana-3294	63	16	)	)	PUNCT
cana-3294	64	1	=	=	SYM
cana-3294	64	2	e	e	X
cana-3294	64	3	(	(	PUNCT
cana-3294	64	4	μ	μ	PROPN
cana-3294	64	5	,	,	PUNCT
cana-3294	64	6	λ	λ	PROPN
cana-3294	64	7	,	,	PUNCT
cana-3294	64	8	μ	μ	NOUN
cana-3294	64	9	)	)	PUNCT
cana-3294	64	10	and	and	CCONJ
cana-3294	64	11	lim	lim	PROPN
cana-3294	64	12	𝑛→∞	𝑛→∞	NUM
cana-3294	64	13	𝔓	𝔓	PROPN
cana-3294	64	14	(	(	PUNCT
cana-3294	64	15	𝐸(𝑣𝑛	𝐸(𝑣𝑛	PROPN
cana-3294	64	16	,	,	PUNCT
cana-3294	64	17	𝜇𝑛,𝜆𝑛	𝜇𝑛,𝜆𝑛	NOUN
cana-3294	64	18	,	,	PUNCT
cana-3294	64	19	)	)	PUNCT
cana-3294	64	20	)	)	PUNCT
cana-3294	64	21	=	=	SYM
cana-3294	65	1	𝔓(𝜈	𝔓(𝜈	X
cana-3294	65	2	)	)	PUNCT
cana-3294	65	3	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3294	65	4	lim	lim	PROPN
cana-3294	65	5	𝑛→∞	𝑛→∞	NUM
cana-3294	65	6	𝐸(𝔓(𝑣𝑛	𝐸(𝔓(𝑣𝑛	PROPN
cana-3294	65	7	)	)	PUNCT
cana-3294	65	8	,	,	PUNCT
cana-3294	65	9	𝔓(𝜇𝑛),𝔓(𝜆𝑛	𝔓(𝜇𝑛),𝔓(𝜆𝑛	PROPN
cana-3294	65	10	,	,	PUNCT
cana-3294	65	11	)	)	PUNCT
cana-3294	65	12	)	)	PUNCT
cana-3294	66	1	=	=	SYM
cana-3294	66	2	e(ν	e(ν	PROPN
cana-3294	66	3	,	,	PUNCT
cana-3294	66	4	μ	μ	PROPN
cana-3294	66	5	,	,	PUNCT
cana-3294	66	6	λ	λ	NOUN
cana-3294	66	7	)	)	PUNCT
cana-3294	66	8	whenever	whenever	SCONJ
cana-3294	66	9	{	{	PUNCT
cana-3294	66	10	𝜆𝑛,},{𝜇𝑛},{𝑣𝑛}are	𝜆𝑛,},{𝜇𝑛},{𝑣𝑛}are	VERB
cana-3294	66	11	sequences	sequence	NOUN
cana-3294	66	12	in	in	ADP
cana-3294	66	13	ɱ	ɱ	PROPN
cana-3294	66	14	such	such	ADJ
cana-3294	66	15	that	that	SCONJ
cana-3294	66	16	lim	lim	PROPN
cana-3294	66	17	𝑛→∞	𝑛→∞	NUM
cana-3294	66	18	𝐸(𝜆𝑛,𝜇𝑛,𝑣𝑛)=	𝐸(𝜆𝑛,𝜇𝑛,𝑣𝑛)=	X
cana-3294	66	19	lim	lim	NOUN
cana-3294	66	20	𝑛→∞	𝑛→∞	NUM
cana-3294	66	21	𝔓(𝜆𝑛	𝔓(𝜆𝑛	PROPN
cana-3294	66	22	)	)	PUNCT
cana-3294	67	1	=	=	SYM
cana-3294	67	2	𝜆	𝜆	DET
cana-3294	67	3	lim	lim	PROPN
cana-3294	67	4	𝑛→∞	𝑛→∞	NUM
cana-3294	67	5	𝐸(𝜇𝑛,𝜆𝑛,𝜇𝑛,)=	𝐸(𝜇𝑛,𝜆𝑛,𝜇𝑛,)=	PROPN
cana-3294	67	6	lim	lim	NOUN
cana-3294	67	7	𝑛→∞	𝑛→∞	NUM
cana-3294	67	8	𝔓(𝜇𝑛	𝔓(𝜇𝑛	X
cana-3294	67	9	)	)	PUNCT
cana-3294	67	10	=	=	PUNCT
cana-3294	67	11	𝜇	𝜇	ADP
cana-3294	67	12	lim	lim	PROPN
cana-3294	67	13	𝑛→∞	𝑛→∞	NUM
cana-3294	67	14	𝐸	𝐸	PROPN
cana-3294	67	15	(	(	PUNCT
cana-3294	67	16	𝐸(𝑣𝑛	𝐸(𝑣𝑛	PROPN
cana-3294	67	17	,	,	PUNCT
cana-3294	67	18	𝜇𝑛,𝜆𝑛,))=	𝜇𝑛,𝜆𝑛,))=	PROPN
cana-3294	67	19	lim	lim	PROPN
cana-3294	67	20	𝑛→∞	𝑛→∞	NUM
cana-3294	67	21	𝔓(𝑣𝑛	𝔓(𝑣𝑛	NOUN
cana-3294	67	22	)	)	PUNCT
cana-3294	67	23	=	=	NOUN
cana-3294	67	24	ν	ν	X
cana-3294	67	25	(	(	PUNCT
cana-3294	67	26	ii	ii	NOUN
cana-3294	67	27	)	)	PUNCT
cana-3294	67	28	weakly	weakly	ADV
cana-3294	67	29	reciprocally	reciprocally	ADV
cana-3294	67	30	continuous	continuous	ADJ
cana-3294	67	31	if	if	SCONJ
cana-3294	67	32	lim	lim	PROPN
cana-3294	67	33	𝑛→∞	𝑛→∞	NUM
cana-3294	67	34	𝔓(𝐸	𝔓(𝐸	PROPN
cana-3294	67	35	(	(	PUNCT
cana-3294	67	36	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	67	37	,	,	PUNCT
cana-3294	67	38	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	67	39	,	,	PUNCT
cana-3294	67	40	𝜈𝑛	𝜈𝑛	ADP
cana-3294	67	41	)	)	PUNCT
cana-3294	67	42	=	=	SYM
cana-3294	67	43	𝔓(𝜆𝑛	𝔓(𝜆𝑛	NOUN
cana-3294	67	44	)	)	PUNCT
cana-3294	67	45	or	or	CCONJ
cana-3294	67	46	lim	lim	PROPN
cana-3294	67	47	𝑛→∞	𝑛→∞	NUM
cana-3294	67	48	𝐸(𝔓	𝐸(𝔓	NOUN
cana-3294	67	49	(	(	PUNCT
cana-3294	67	50	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	67	51	)	)	PUNCT
cana-3294	67	52	,	,	PUNCT
cana-3294	67	53	𝔓	𝔓	PROPN
cana-3294	67	54	(	(	PUNCT
cana-3294	67	55	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	67	56	)	)	PUNCT
cana-3294	67	57	,	,	PUNCT
cana-3294	67	58	𝔓	𝔓	PROPN
cana-3294	67	59	(	(	PUNCT
cana-3294	67	60	𝜈𝑛	𝜈𝑛	ADP
cana-3294	67	61	)	)	PUNCT
cana-3294	67	62	)	)	PUNCT
cana-3294	68	1	=	=	SYM
cana-3294	68	2	e(𝜆	e(𝜆	NOUN
cana-3294	68	3	,	,	PUNCT
cana-3294	68	4	μ	μ	NOUN
cana-3294	68	5	,	,	PUNCT
cana-3294	68	6	ν	ν	NOUN
cana-3294	68	7	)	)	PUNCT
cana-3294	68	8	lim	lim	NOUN
cana-3294	68	9	𝑛→∞	𝑛→∞	NUM
cana-3294	68	10	𝔓(𝐸(𝜇𝑛	𝔓(𝐸(𝜇𝑛	PROPN
cana-3294	68	11	,	,	PUNCT
cana-3294	68	12	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	68	13	,	,	PUNCT
cana-3294	68	14	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	68	15	)	)	PUNCT
cana-3294	68	16	=	=	SYM
cana-3294	68	17	𝕻(μ	𝕻(μ	X
cana-3294	68	18	)	)	PUNCT
cana-3294	68	19	or	or	CCONJ
cana-3294	68	20	lim	lim	PROPN
cana-3294	68	21	𝑛→∞	𝑛→∞	NUM
cana-3294	68	22	𝐸(𝔓	𝐸(𝔓	NOUN
cana-3294	68	23	(	(	PUNCT
cana-3294	68	24	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	68	25	)	)	PUNCT
cana-3294	68	26	,	,	PUNCT
cana-3294	68	27	𝔓(𝜆𝑛	𝔓(𝜆𝑛	PROPN
cana-3294	68	28	)	)	PUNCT
cana-3294	68	29	,	,	PUNCT
cana-3294	68	30	𝔓(𝜈𝑛	𝔓(𝜈𝑛	PROPN
cana-3294	68	31	)	)	PUNCT
cana-3294	68	32	)	)	PUNCT
cana-3294	69	1	=	=	SYM
cana-3294	69	2	e	e	X
cana-3294	69	3	(	(	PUNCT
cana-3294	69	4	μ	μ	PROPN
cana-3294	69	5	,	,	PUNCT
cana-3294	69	6	λ	λ	PROPN
cana-3294	69	7	,	,	PUNCT
cana-3294	69	8	μ	μ	NOUN
cana-3294	69	9	)	)	PUNCT
cana-3294	69	10	lim	lim	NOUN
cana-3294	69	11	𝑛→∞	𝑛→∞	NUM
cana-3294	69	12	𝔓(𝐸(𝜈𝑛	𝔓(𝐸(𝜈𝑛	PROPN
cana-3294	69	13	,	,	PUNCT
cana-3294	69	14	𝜇𝑛	𝜇𝑛	INTJ
cana-3294	69	15	,	,	PUNCT
cana-3294	69	16	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	69	17	)	)	PUNCT
cana-3294	69	18	=	=	SYM
cana-3294	69	19	𝔓(ν	𝔓(ν	NUM
cana-3294	69	20	)	)	PUNCT
cana-3294	69	21	or	or	CCONJ
cana-3294	69	22	lim	lim	PROPN
cana-3294	69	23	𝑛→∞	𝑛→∞	NUM
cana-3294	69	24	𝐸(𝔓(𝜈𝑛	𝐸(𝔓(𝜈𝑛	NOUN
cana-3294	69	25	)	)	PUNCT
cana-3294	69	26	,	,	PUNCT
cana-3294	69	27	𝔓	𝔓	PROPN
cana-3294	69	28	(	(	PUNCT
cana-3294	69	29	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	69	30	)	)	PUNCT
cana-3294	69	31	,	,	PUNCT
cana-3294	69	32	𝔓(𝜆𝑛	𝔓(𝜆𝑛	PROPN
cana-3294	69	33	)	)	PUNCT
cana-3294	69	34	)	)	PUNCT
cana-3294	70	1	=	=	PUNCT
cana-3294	70	2	e	e	X
cana-3294	70	3	(	(	PUNCT
cana-3294	70	4	ν	ν	PROPN
cana-3294	70	5	,	,	PUNCT
cana-3294	70	6	μ	μ	PROPN
cana-3294	70	7	,	,	PUNCT
cana-3294	70	8	λ	λ	NOUN
cana-3294	70	9	)	)	PUNCT
cana-3294	70	10	whenever	whenever	SCONJ
cana-3294	70	11	{	{	PUNCT
cana-3294	70	12	λn	λn	NOUN
cana-3294	70	13	}	}	PUNCT
cana-3294	70	14	,	,	PUNCT
cana-3294	70	15	{	{	PUNCT
cana-3294	70	16	μn	μn	NOUN
cana-3294	70	17	}	}	PUNCT
cana-3294	70	18	,	,	PUNCT
cana-3294	70	19	{	{	PUNCT
cana-3294	70	20	νn	νn	AUX
cana-3294	70	21	}	}	PUNCT
cana-3294	70	22	are	be	AUX
cana-3294	70	23	sequences	sequence	NOUN
cana-3294	70	24	in	in	ADP
cana-3294	70	25	ɱ	ɱ	PROPN
cana-3294	70	26	such	such	ADJ
cana-3294	70	27	that	that	SCONJ
cana-3294	70	28	lim	lim	PROPN
cana-3294	70	29	𝑛→∞	𝑛→∞	NUM
cana-3294	70	30	𝐸	𝐸	PROPN
cana-3294	70	31	(	(	PUNCT
cana-3294	70	32	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	70	33	,	,	PUNCT
cana-3294	70	34	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	70	35	,	,	PUNCT
cana-3294	70	36	𝜈𝑛	𝜈𝑛	ADJ
cana-3294	70	37	)	)	PUNCT
cana-3294	70	38	=	=	SYM
cana-3294	70	39	lim	lim	NOUN
cana-3294	70	40	𝑛→∞	𝑛→∞	NUM
cana-3294	70	41	𝔓	𝔓	PROPN
cana-3294	70	42	(	(	PUNCT
cana-3294	70	43	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	70	44	)	)	PUNCT
cana-3294	70	45	=	=	PUNCT
cana-3294	71	1	λ	λ	PROPN
cana-3294	71	2	lim	lim	PROPN
cana-3294	71	3	𝑛→∞	𝑛→∞	NUM
cana-3294	71	4	𝐸	𝐸	PROPN
cana-3294	71	5	(	(	PUNCT
cana-3294	71	6	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	71	7	,	,	PUNCT
cana-3294	71	8	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	71	9	,	,	PUNCT
cana-3294	71	10	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	71	11	)	)	PUNCT
cana-3294	72	1	=	=	SYM
cana-3294	72	2	lim	lim	NOUN
cana-3294	72	3	𝑛→∞	𝑛→∞	NUM
cana-3294	72	4	𝔓	𝔓	PROPN
cana-3294	72	5	(	(	PUNCT
cana-3294	72	6	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	72	7	)	)	PUNCT
cana-3294	72	8	=	=	SYM
cana-3294	73	1	μ	μ	PROPN
cana-3294	73	2	lim	lim	PROPN
cana-3294	73	3	𝑛→∞	𝑛→∞	NUM
cana-3294	73	4	𝐸	𝐸	PROPN
cana-3294	73	5	(	(	PUNCT
cana-3294	73	6	𝜈𝑛	𝜈𝑛	ADP
cana-3294	73	7	,	,	PUNCT
cana-3294	73	8	𝜇𝑛	𝜇𝑛	NOUN
cana-3294	73	9	,	,	PUNCT
cana-3294	73	10	𝜆𝑛	𝜆𝑛	NOUN
cana-3294	73	11	)	)	PUNCT
cana-3294	74	1	=	=	SYM
cana-3294	74	2	lim	lim	NOUN
cana-3294	74	3	𝑛→∞	𝑛→∞	NUM
cana-3294	74	4	𝔓	𝔓	PROPN
cana-3294	74	5	(	(	PUNCT
cana-3294	74	6	𝜈𝑛	𝜈𝑛	ADP
cana-3294	74	7	)	)	PUNCT
cana-3294	74	8	=	=	SYM
cana-3294	74	9	ν	ν	NOUN
cana-3294	74	10	for	for	ADP
cana-3294	74	11	some	some	DET
cana-3294	74	12	λ	λ	PROPN
cana-3294	74	13	,	,	PUNCT
cana-3294	74	14	μ	μ	PROPN
cana-3294	74	15	,	,	PUNCT
cana-3294	74	16	ν	ν	PROPN
cana-3294	74	17	∈	∈	PROPN
cana-3294	74	18	ɱ	ɱ	PROPN
cana-3294	74	19	.	.	PUNCT
cana-3294	75	1	definition	definition	NOUN
cana-3294	75	2	3.9[21	3.9[21	PROPN
cana-3294	75	3	]	]	PUNCT
cana-3294	75	4	:	:	PUNCT
cana-3294	75	5	assume	assume	VERB
cana-3294	75	6	〈	〈	PROPN
cana-3294	75	7	𝑎𝑛	𝑎𝑛	PRON
cana-3294	75	8	〉	〉	NOUN
cana-3294	75	9	be	be	VERB
cana-3294	75	10	a	a	DET
cana-3294	75	11	sequence	sequence	NOUN
cana-3294	75	12	of	of	ADP
cana-3294	75	13	non	non	ADJ
cana-3294	75	14	-	-	ADJ
cana-3294	75	15	negative	negative	ADJ
cana-3294	75	16	real	real	ADJ
cana-3294	75	17	numbers	number	NOUN
cana-3294	75	18	.	.	PUNCT
cana-3294	76	1	if	if	SCONJ
cana-3294	76	2	there	there	PRON
cana-3294	76	3	exist	exist	VERB
cana-3294	76	4	0	0	NUM
cana-3294	76	5	<	<	X
cana-3294	76	6	α	α	X
cana-3294	76	7	<	<	X
cana-3294	76	8	1	1	NUM
cana-3294	76	9	and	and	CCONJ
cana-3294	76	10	nα	nα	ADP
cana-3294	76	11	∈	∈	NOUN
cana-3294	76	12	n	n	PRON
cana-3294	76	13	such	such	ADJ
cana-3294	76	14	that	that	SCONJ
cana-3294	76	15	∑	∑	PROPN
cana-3294	76	16	𝑎𝑖	𝑎𝑖	ADP
cana-3294	76	17	𝑘	𝑘	DET
cana-3294	76	18	𝑖=1	𝑖=1	PROPN
cana-3294	76	19	≤	≤	ADJ
cana-3294	76	20	αk	αk	NOUN
cana-3294	76	21	for	for	ADP
cana-3294	76	22	each	each	DET
cana-3294	76	23	k	k	PROPN
cana-3294	76	24	≥	≥	X
cana-3294	77	1	nα	nα	VERB
cana-3294	78	1	then	then	ADV
cana-3294	78	2	the	the	DET
cana-3294	78	3	series	series	NOUN
cana-3294	78	4	∑	∑	PROPN
cana-3294	78	5	𝑎𝑛	𝑎𝑛	PROPN
cana-3294	78	6	∞	∞	PROPN
cana-3294	78	7	𝑛=1	𝑛=1	NOUN
cana-3294	78	8	is	be	AUX
cana-3294	78	9	called	call	VERB
cana-3294	78	10	an	an	DET
cana-3294	78	11	α	α	NOUN
cana-3294	78	12	-	-	PUNCT
cana-3294	78	13	series	series	NOUN
cana-3294	78	14	.	.	PUNCT
cana-3294	79	1	communications	communication	NOUN
cana-3294	79	2	on	on	ADP
cana-3294	79	3	applied	apply	VERB
cana-3294	79	4	nonlinear	nonlinear	ADJ
cana-3294	79	5	analysis	analysis	NOUN
cana-3294	79	6	issn	issn	NOUN
cana-3294	79	7	:	:	PUNCT
cana-3294	79	8	1074	1074	NUM
cana-3294	79	9	-	-	PUNCT
cana-3294	79	10	133x	133x	NUM
cana-3294	79	11	vol	vol	NOUN
cana-3294	79	12	32	32	NUM
cana-3294	79	13	no	no	NOUN
cana-3294	79	14	.	.	PUNCT
cana-3294	80	1	6s	6s	NUM
cana-3294	80	2	(	(	PUNCT
cana-3294	80	3	2025	2025	NUM
cana-3294	80	4	)	)	PUNCT
cana-3294	80	5	278	278	NUM
cana-3294	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	80	7	lemma	lemma	PROPN
cana-3294	80	8	3.10	3.10	NUM
cana-3294	80	9	[	[	X
cana-3294	80	10	34	34	NUM
cana-3294	80	11	]	]	PUNCT
cana-3294	80	12	let	let	NOUN
cana-3294	80	13	(	(	PUNCT
cana-3294	80	14	k	k	NOUN
cana-3294	80	15	,	,	PUNCT
cana-3294	80	16	≤	≤	NUM
cana-3294	80	17	)	)	PUNCT
cana-3294	80	18	be	be	VERB
cana-3294	80	19	a	a	DET
cana-3294	80	20	poset	poset	NOUN
cana-3294	80	21	and	and	CCONJ
cana-3294	80	22	g	g	NOUN
cana-3294	80	23	:	:	PUNCT
cana-3294	81	1	k→k	k→k	PROPN
cana-3294	81	2	and	and	CCONJ
cana-3294	81	3	{	{	PUNCT
cana-3294	81	4	tn}nϵn	tn}nϵn	NOUN
cana-3294	81	5	:	:	PUNCT
cana-3294	81	6	k3	k3	PROPN
cana-3294	81	7	→	→	SYM
cana-3294	81	8	k	k	X
cana-3294	81	9	be	be	AUX
cana-3294	81	10	a	a	DET
cana-3294	81	11	sequence	sequence	NOUN
cana-3294	81	12	of	of	ADP
cana-3294	81	13	mappings	mapping	NOUN
cana-3294	81	14	such	such	ADJ
cana-3294	81	15	that	that	SCONJ
cana-3294	81	16	tn(k	tn(k	NOUN
cana-3294	81	17	3	3	X
cana-3294	81	18	)	)	PUNCT
cana-3294	81	19	⊆	⊆	NUM
cana-3294	81	20	g(k	g(k	NOUN
cana-3294	81	21	)	)	PUNCT
cana-3294	81	22	then	then	ADV
cana-3294	81	23	tn	tn	PROPN
cana-3294	81	24	has	have	VERB
cana-3294	81	25	g	g	NOUN
cana-3294	81	26	-	-	PUNCT
cana-3294	81	27	mixed	mix	VERB
cana-3294	81	28	monotone	monotone	ADJ
cana-3294	81	29	property	property	NOUN
cana-3294	81	30	if	if	SCONJ
cana-3294	81	31	g(λ	g(λ	PROPN
cana-3294	81	32	)	)	PUNCT
cana-3294	81	33	≤	≤	NUM
cana-3294	81	34	g(ꝕ	g(ꝕ	PROPN
cana-3294	81	35	)	)	PUNCT
cana-3294	81	36	,	,	PUNCT
cana-3294	81	37	g(ꝙ	g(ꝙ	PROPN
cana-3294	81	38	)	)	PUNCT
cana-3294	81	39	≤	≤	NUM
cana-3294	81	40	g(μ	g(μ	PROPN
cana-3294	81	41	)	)	PUNCT
cana-3294	81	42	and	and	CCONJ
cana-3294	81	43	g(ν	g(ν	PROPN
cana-3294	81	44	)	)	PUNCT
cana-3294	81	45	≤	≤	NUM
cana-3294	81	46	g(𝝏	g(𝝏	NOUN
cana-3294	81	47	)	)	PUNCT
cana-3294	81	48	for	for	ADP
cana-3294	81	49	any	any	DET
cana-3294	81	50	λ	λ	PROPN
cana-3294	81	51	,	,	PUNCT
cana-3294	81	52	μ	μ	PROPN
cana-3294	81	53	,	,	PUNCT
cana-3294	81	54	ν	ν	PROPN
cana-3294	81	55	,	,	PUNCT
cana-3294	81	56	ꝕ	ꝕ	NOUN
cana-3294	81	57	,	,	PUNCT
cana-3294	81	58	ꝙ,𝝏	ꝙ,𝝏	PROPN
cana-3294	81	59	∈	∈	PROPN
cana-3294	82	1	k	k	NOUN
cana-3294	82	2	imply	imply	VERB
cana-3294	82	3	tn(λ	tn(λ	PUNCT
cana-3294	82	4	,	,	PUNCT
cana-3294	82	5	μ	μ	PROPN
cana-3294	82	6	,	,	PUNCT
cana-3294	82	7	ν	ν	NOUN
cana-3294	82	8	)	)	PUNCT
cana-3294	82	9	≤	≤	NOUN
cana-3294	82	10	tn+1(ꝕ	tn+1(ꝕ	NOUN
cana-3294	82	11	,	,	PUNCT
cana-3294	82	12	ꝙ	ꝙ	NOUN
cana-3294	82	13	,	,	PUNCT
cana-3294	82	14	𝝏	𝝏	NOUN
cana-3294	82	15	)	)	PUNCT
cana-3294	82	16	tn+1(ꝙ	tn+1(ꝙ	ADP
cana-3294	82	17	,	,	PUNCT
cana-3294	82	18	ꝕ	ꝕ	NOUN
cana-3294	82	19	,	,	PUNCT
cana-3294	82	20	ꝙ	ꝙ	NOUN
cana-3294	82	21	)	)	PUNCT
cana-3294	82	22	≤	≤	NOUN
cana-3294	82	23	tn(μ	tn(μ	NUM
cana-3294	82	24	,	,	PUNCT
cana-3294	82	25	λ	λ	PROPN
cana-3294	82	26	,	,	PUNCT
cana-3294	82	27	μ	μ	NOUN
cana-3294	82	28	)	)	PUNCT
cana-3294	82	29	(	(	PUNCT
cana-3294	82	30	1	1	NUM
cana-3294	82	31	)	)	PUNCT
cana-3294	82	32	tn(ν	tn(ν	PUNCT
cana-3294	82	33	,	,	PUNCT
cana-3294	82	34	μ	μ	NOUN
cana-3294	82	35	,	,	PUNCT
cana-3294	82	36	λ	λ	NOUN
cana-3294	82	37	)	)	PUNCT
cana-3294	82	38	≤	≤	NOUN
cana-3294	82	39	tn+1(𝝏	tn+1(𝝏	PUNCT
cana-3294	82	40	,	,	PUNCT
cana-3294	82	41	ꝙ	ꝙ	NUM
cana-3294	82	42	,	,	PUNCT
cana-3294	82	43	ꝕ	ꝕ	NOUN
cana-3294	82	44	)	)	PUNCT
cana-3294	82	45	in	in	ADP
cana-3294	82	46	our	our	PRON
cana-3294	82	47	main	main	ADJ
cana-3294	82	48	proof	proof	NOUN
cana-3294	82	49	we	we	PRON
cana-3294	82	50	construct	construct	VERB
cana-3294	82	51	the	the	DET
cana-3294	82	52	sequence	sequence	NOUN
cana-3294	82	53	as	as	SCONJ
cana-3294	82	54	follows	follow	VERB
cana-3294	82	55	assume	assume	VERB
cana-3294	82	56	λ0	λ0	NOUN
cana-3294	82	57	,	,	PUNCT
cana-3294	82	58	µ0	µ0	NOUN
cana-3294	82	59	,	,	PUNCT
cana-3294	82	60	ν0	ν0	PROPN
cana-3294	82	61	∈	∈	PROPN
cana-3294	83	1	k	k	PROPN
cana-3294	84	1	such	such	ADJ
cana-3294	84	2	that	that	DET
cana-3294	84	3	g(λ0	g(λ0	NOUN
cana-3294	84	4	)	)	PUNCT
cana-3294	84	5	≤	≤	NOUN
cana-3294	85	1	t0(λ0	t0(λ0	ADJ
cana-3294	85	2	,	,	PUNCT
cana-3294	85	3	μ0	μ0	PROPN
cana-3294	85	4	,	,	PUNCT
cana-3294	85	5	ν0	ν0	PROPN
cana-3294	85	6	)	)	PUNCT
cana-3294	85	7	,	,	PUNCT
cana-3294	85	8	g(μ0	g(μ0	NOUN
cana-3294	85	9	)	)	PUNCT
cana-3294	85	10	≥t0(μ0	≥t0(μ0	NOUN
cana-3294	85	11	,	,	PUNCT
cana-3294	85	12	λ0	λ0	NOUN
cana-3294	85	13	,	,	PUNCT
cana-3294	85	14	μ0	μ0	PROPN
cana-3294	85	15	)	)	PUNCT
cana-3294	85	16	,	,	PUNCT
cana-3294	85	17	g(ν0	g(ν0	PROPN
cana-3294	85	18	)	)	PUNCT
cana-3294	85	19	≤	≤	PROPN
cana-3294	86	1	t0(ν0	t0(ν0	PROPN
cana-3294	86	2	,	,	PUNCT
cana-3294	86	3	μ0	μ0	PROPN
cana-3294	86	4	,	,	PUNCT
cana-3294	86	5	λ0	λ0	NOUN
cana-3294	86	6	)	)	PUNCT
cana-3294	86	7	(	(	PUNCT
cana-3294	86	8	2	2	X
cana-3294	86	9	)	)	PUNCT
cana-3294	86	10	since	since	SCONJ
cana-3294	86	11	t0(k	t0(k	X
cana-3294	86	12	3	3	NUM
cana-3294	86	13	)	)	PUNCT
cana-3294	86	14	⊆	⊆	NUM
cana-3294	86	15	g(k	g(k	NOUN
cana-3294	86	16	)	)	PUNCT
cana-3294	86	17	we	we	PRON
cana-3294	86	18	choose	choose	VERB
cana-3294	86	19	λ1	λ1	ADJ
cana-3294	86	20	,	,	PUNCT
cana-3294	86	21	μ1	μ1	NOUN
cana-3294	86	22	,	,	PUNCT
cana-3294	86	23	ν1∈	ν1∈	PROPN
cana-3294	86	24	k	k	NOUN
cana-3294	86	25	such	such	ADJ
cana-3294	86	26	that	that	DET
cana-3294	86	27	g(λ1	g(λ1	NOUN
cana-3294	86	28	)	)	PUNCT
cana-3294	87	1	=	=	SYM
cana-3294	87	2	t0(λ0	t0(λ0	PROPN
cana-3294	87	3	,	,	PUNCT
cana-3294	87	4	μ0	μ0	PROPN
cana-3294	87	5	,	,	PUNCT
cana-3294	87	6	ν0	ν0	PROPN
cana-3294	87	7	)	)	PUNCT
cana-3294	87	8	,	,	PUNCT
cana-3294	87	9	g(μ1	g(μ1	NOUN
cana-3294	87	10	)	)	PUNCT
cana-3294	88	1	=	=	SYM
cana-3294	88	2	t0(μ0	t0(μ0	ADJ
cana-3294	88	3	,	,	PUNCT
cana-3294	88	4	λ0	λ0	NOUN
cana-3294	88	5	,	,	PUNCT
cana-3294	88	6	ν0	ν0	PROPN
cana-3294	88	7	)	)	PUNCT
cana-3294	88	8	,	,	PUNCT
cana-3294	88	9	g(ν1	g(ν1	NOUN
cana-3294	88	10	)	)	PUNCT
cana-3294	89	1	=	=	SYM
cana-3294	89	2	t0(ν0	t0(ν0	PROPN
cana-3294	89	3	,	,	PUNCT
cana-3294	89	4	μ0	μ0	PROPN
cana-3294	89	5	,	,	PUNCT
cana-3294	89	6	λ0	λ0	NOUN
cana-3294	89	7	)	)	PUNCT
cana-3294	89	8	again	again	ADV
cana-3294	89	9	,	,	PUNCT
cana-3294	89	10	we	we	PRON
cana-3294	89	11	choose	choose	VERB
cana-3294	89	12	λ2	λ2	NOUN
cana-3294	89	13	,	,	PUNCT
cana-3294	89	14	μ2	μ2	NOUN
cana-3294	89	15	,	,	PUNCT
cana-3294	89	16	ν2	ν2	NOUN
cana-3294	89	17	∈	∈	PROPN
cana-3294	89	18	k	k	NOUN
cana-3294	89	19	such	such	ADJ
cana-3294	89	20	that	that	DET
cana-3294	89	21	g(λ2	g(λ2	NOUN
cana-3294	89	22	)	)	PUNCT
cana-3294	89	23	=	=	PUNCT
cana-3294	90	1	t1(λ1	t1(λ1	NOUN
cana-3294	90	2	,	,	PUNCT
cana-3294	90	3	μ1	μ1	NOUN
cana-3294	90	4	,	,	PUNCT
cana-3294	90	5	ν1	ν1	NOUN
cana-3294	90	6	)	)	PUNCT
cana-3294	90	7	,	,	PUNCT
cana-3294	90	8	g(μ2	g(μ2	NOUN
cana-3294	90	9	)	)	PUNCT
cana-3294	90	10	=	=	PUNCT
cana-3294	90	11	t1(μ1	t1(μ1	X
cana-3294	90	12	,	,	PUNCT
cana-3294	90	13	λ1	λ1	ADJ
cana-3294	90	14	,	,	PUNCT
cana-3294	90	15	μ1	μ1	NOUN
cana-3294	90	16	)	)	PUNCT
cana-3294	90	17	,	,	PUNCT
cana-3294	90	18	g(ν2	g(ν2	NOUN
cana-3294	90	19	)	)	PUNCT
cana-3294	90	20	=	=	SYM
cana-3294	90	21	t1(ν1	t1(ν1	NOUN
cana-3294	90	22	,	,	PUNCT
cana-3294	90	23	μ1	μ1	NOUN
cana-3294	90	24	,	,	PUNCT
cana-3294	90	25	λ1	λ1	PROPN
cana-3294	90	26	)	)	PUNCT
cana-3294	90	27	continuing	continue	VERB
cana-3294	90	28	this	this	DET
cana-3294	90	29	process	process	NOUN
cana-3294	90	30	,	,	PUNCT
cana-3294	90	31	we	we	PRON
cana-3294	90	32	construct	construct	VERB
cana-3294	90	33	three	three	NUM
cana-3294	90	34	sequences	sequence	NOUN
cana-3294	90	35	{	{	PUNCT
cana-3294	90	36	λm	λm	NOUN
cana-3294	90	37	}	}	PUNCT
cana-3294	90	38	,	,	PUNCT
cana-3294	90	39	{	{	PUNCT
cana-3294	90	40	μm	μm	NUM
cana-3294	90	41	}	}	PUNCT
cana-3294	90	42	,	,	PUNCT
cana-3294	90	43	{	{	PUNCT
cana-3294	90	44	νm	νm	INTJ
cana-3294	90	45	}	}	PUNCT
cana-3294	90	46	such	such	ADJ
cana-3294	90	47	that	that	SCONJ
cana-3294	90	48	g(λm+1	g(λm+1	NOUN
cana-3294	90	49	)	)	PUNCT
cana-3294	91	1	=	=	SYM
cana-3294	91	2	tm(λm	tm(λm	PROPN
cana-3294	91	3	,	,	PUNCT
cana-3294	91	4	μm	μm	INTJ
cana-3294	91	5	,	,	PUNCT
cana-3294	91	6	νm	νm	NOUN
cana-3294	91	7	)	)	PUNCT
cana-3294	91	8	,	,	PUNCT
cana-3294	91	9	g(μm+1	g(μm+1	PROPN
cana-3294	91	10	)	)	PUNCT
cana-3294	91	11	=	=	SYM
cana-3294	91	12	tm(μm	tm(μm	PROPN
cana-3294	91	13	,	,	PUNCT
cana-3294	91	14	λm	λm	ADP
cana-3294	91	15	,	,	PUNCT
cana-3294	91	16	μm	μm	NUM
cana-3294	91	17	)	)	PUNCT
cana-3294	91	18	,	,	PUNCT
cana-3294	91	19	g(νm+1	g(νm+1	ADJ
cana-3294	91	20	)	)	PUNCT
cana-3294	91	21	=	=	SYM
cana-3294	91	22	tm	tm	PROPN
cana-3294	91	23	(	(	PUNCT
cana-3294	91	24	νm	νm	PROPN
cana-3294	91	25	,	,	PUNCT
cana-3294	91	26	μm	μm	INTJ
cana-3294	91	27	,	,	PUNCT
cana-3294	91	28	λm	λm	NOUN
cana-3294	91	29	)	)	PUNCT
cana-3294	91	30	for	for	ADP
cana-3294	91	31	all	all	DET
cana-3294	91	32	m	m	PROPN
cana-3294	91	33	≥	≥	NOUN
cana-3294	91	34	0	0	NUM
cana-3294	91	35	(	(	PUNCT
cana-3294	91	36	3	3	NUM
cana-3294	91	37	)	)	PUNCT
cana-3294	91	38	by	by	ADP
cana-3294	91	39	mathematical	mathematical	ADJ
cana-3294	91	40	induction	induction	NOUN
cana-3294	91	41	,	,	PUNCT
cana-3294	91	42	we	we	PRON
cana-3294	91	43	prove	prove	VERB
cana-3294	91	44	that	that	SCONJ
cana-3294	91	45	g(λm	g(λm	NOUN
cana-3294	91	46	)	)	PUNCT
cana-3294	91	47	≤	≤	NOUN
cana-3294	91	48	g(λm+1	g(λm+1	ADJ
cana-3294	91	49	)	)	PUNCT
cana-3294	91	50	,	,	PUNCT
cana-3294	91	51	g(μm	g(μm	PROPN
cana-3294	91	52	)	)	PUNCT
cana-3294	91	53	≥	≥	NOUN
cana-3294	91	54	g(μm+1	g(μm+1	NOUN
cana-3294	91	55	)	)	PUNCT
cana-3294	91	56	and	and	CCONJ
cana-3294	91	57	g(νm	g(νm	PROPN
cana-3294	91	58	)	)	PUNCT
cana-3294	91	59	≤	≤	NOUN
cana-3294	91	60	g(νm+1	g(νm+1	VERB
cana-3294	91	61	)	)	PUNCT
cana-3294	91	62	for	for	ADP
cana-3294	91	63	all	all	DET
cana-3294	91	64	m	m	PROPN
cana-3294	91	65	≥	≥	NOUN
cana-3294	91	66	0	0	NUM
cana-3294	91	67	.	.	PUNCT
cana-3294	92	1	(	(	PUNCT
cana-3294	92	2	4	4	NUM
cana-3294	92	3	)	)	PUNCT
cana-3294	92	4	since	since	SCONJ
cana-3294	92	5	condition	condition	NOUN
cana-3294	92	6	2	2	NUM
cana-3294	92	7	holds	hold	NOUN
cana-3294	92	8	,	,	PUNCT
cana-3294	92	9	in	in	ADP
cana-3294	92	10	view	view	NOUN
cana-3294	92	11	of	of	ADP
cana-3294	92	12	g(λ1	g(λ1	NOUN
cana-3294	92	13	)	)	PUNCT
cana-3294	93	1	=	=	SYM
cana-3294	93	2	t0(λ0	t0(λ0	ADJ
cana-3294	93	3	,	,	PUNCT
cana-3294	93	4	μ0	μ0	PROPN
cana-3294	93	5	,	,	PUNCT
cana-3294	93	6	ν0	ν0	PROPN
cana-3294	93	7	)	)	PUNCT
cana-3294	93	8	,	,	PUNCT
cana-3294	93	9	g	g	PROPN
cana-3294	93	10	(	(	PUNCT
cana-3294	93	11	μ	μ	PROPN
cana-3294	93	12	1	1	NUM
cana-3294	93	13	)	)	PUNCT
cana-3294	93	14	=	=	SYM
cana-3294	93	15	t0(μ0	t0(μ0	ADJ
cana-3294	93	16	,	,	PUNCT
cana-3294	93	17	λ0	λ0	NOUN
cana-3294	93	18	,	,	PUNCT
cana-3294	93	19	μ	μ	NOUN
cana-3294	93	20	0	0	NUM
cana-3294	93	21	)	)	PUNCT
cana-3294	93	22	,	,	PUNCT
cana-3294	93	23	g(ν1	g(ν1	NOUN
cana-3294	93	24	)	)	PUNCT
cana-3294	94	1	=	=	SYM
cana-3294	94	2	t0(ν0	t0(ν0	PROPN
cana-3294	94	3	,	,	PUNCT
cana-3294	94	4	μ0	μ0	PROPN
cana-3294	94	5	,	,	PUNCT
cana-3294	94	6	λ0	λ0	NOUN
cana-3294	94	7	)	)	PUNCT
cana-3294	94	8	we	we	PRON
cana-3294	94	9	obtain	obtain	VERB
cana-3294	94	10	g(λ0	g(λ0	NOUN
cana-3294	94	11	)	)	PUNCT
cana-3294	94	12	≤	≤	NUM
cana-3294	94	13	g(λ1	g(λ1	NOUN
cana-3294	94	14	)	)	PUNCT
cana-3294	94	15	,	,	PUNCT
cana-3294	94	16	g(μ0	g(μ0	PROPN
cana-3294	94	17	)	)	PUNCT
cana-3294	94	18	≥	≥	NOUN
cana-3294	94	19	g(μ1	g(μ1	NOUN
cana-3294	94	20	)	)	PUNCT
cana-3294	94	21	,	,	PUNCT
cana-3294	94	22	g(ν0	g(ν0	PROPN
cana-3294	94	23	)	)	PUNCT
cana-3294	94	24	≤	≤	NOUN
cana-3294	94	25	g(ν1	g(ν1	NOUN
cana-3294	94	26	)	)	PUNCT
cana-3294	94	27	.	.	PUNCT
cana-3294	95	1	that	that	PRON
cana-3294	95	2	is	be	AUX
cana-3294	95	3	condition	condition	NOUN
cana-3294	95	4	…	…	PUNCT
cana-3294	95	5	4	4	NUM
cana-3294	95	6	is	be	AUX
cana-3294	95	7	true	true	ADJ
cana-3294	95	8	for	for	ADP
cana-3294	95	9	m=0	m=0	PROPN
cana-3294	95	10	.	.	PUNCT
cana-3294	96	1	now	now	ADV
cana-3294	96	2	we	we	PRON
cana-3294	96	3	consider	consider	VERB
cana-3294	96	4	condition	condition	NOUN
cana-3294	96	5	4	4	NUM
cana-3294	96	6	is	be	AUX
cana-3294	96	7	true	true	ADJ
cana-3294	96	8	for	for	ADP
cana-3294	96	9	some	some	DET
cana-3294	96	10	m>0	m>0	NOUN
cana-3294	96	11	from	from	ADP
cana-3294	96	12	(	(	PUNCT
cana-3294	96	13	3	3	NUM
cana-3294	96	14	)	)	PUNCT
cana-3294	96	15	and	and	CCONJ
cana-3294	96	16	(	(	PUNCT
cana-3294	96	17	4	4	X
cana-3294	96	18	)	)	PUNCT
cana-3294	96	19	we	we	PRON
cana-3294	96	20	deduce	deduce	VERB
cana-3294	96	21	g(λm+1	g(λm+1	PUNCT
cana-3294	96	22	)	)	PUNCT
cana-3294	97	1	=	=	NUM
cana-3294	97	2	tm	tm	NOUN
cana-3294	97	3	(	(	PUNCT
cana-3294	97	4	λm	λm	ADP
cana-3294	97	5	,	,	PUNCT
cana-3294	97	6	μm	μm	INTJ
cana-3294	97	7	,	,	PUNCT
cana-3294	97	8	νm	νm	NOUN
cana-3294	97	9	)	)	PUNCT
cana-3294	97	10	≤	≤	NOUN
cana-3294	97	11	tm+1(λm+1	tm+1(λm+1	PROPN
cana-3294	97	12	,	,	PUNCT
cana-3294	97	13	μm+1	μm+1	NUM
cana-3294	97	14	,	,	PUNCT
cana-3294	97	15	νm+1	νm+1	X
cana-3294	97	16	)	)	PUNCT
cana-3294	97	17	=	=	SYM
cana-3294	97	18	g(λm+2	g(λm+2	NOUN
cana-3294	97	19	)	)	PUNCT
cana-3294	97	20	g(μm+2	g(μm+2	NOUN
cana-3294	97	21	)	)	PUNCT
cana-3294	97	22	=	=	SYM
cana-3294	98	1	tm+1(μm+1	tm+1(μm+1	NOUN
cana-3294	98	2	,	,	PUNCT
cana-3294	98	3	λm+1	λm+1	X
cana-3294	98	4	,	,	PUNCT
cana-3294	98	5	μm+1	μm+1	NUM
cana-3294	98	6	)	)	PUNCT
cana-3294	98	7	≤	≤	NOUN
cana-3294	98	8	tm	tm	PROPN
cana-3294	98	9	(	(	PUNCT
cana-3294	98	10	μm	μm	INTJ
cana-3294	98	11	,	,	PUNCT
cana-3294	98	12	λm	λm	ADP
cana-3294	98	13	,	,	PUNCT
cana-3294	98	14	μm	μm	NUM
cana-3294	98	15	)	)	PUNCT
cana-3294	98	16	=	=	SYM
cana-3294	98	17	g(μm+1	g(μm+1	NOUN
cana-3294	98	18	)	)	PUNCT
cana-3294	98	19	g(νm+1	g(νm+1	ADJ
cana-3294	98	20	)	)	PUNCT
cana-3294	99	1	=	=	PRON
cana-3294	99	2	tm(μm	tm(μm	PROPN
cana-3294	99	3	,	,	PUNCT
cana-3294	99	4	λm	λm	X
cana-3294	99	5	,	,	PUNCT
cana-3294	99	6	νm	νm	NOUN
cana-3294	99	7	)	)	PUNCT
cana-3294	99	8	≤	≤	NOUN
cana-3294	99	9	tm+1(νm+1	tm+1(νm+1	PROPN
cana-3294	99	10	,	,	PUNCT
cana-3294	99	11	μm+1	μm+1	NUM
cana-3294	99	12	,	,	PUNCT
cana-3294	99	13	λm+1	λm+1	X
cana-3294	99	14	)	)	PUNCT
cana-3294	99	15	=	=	SYM
cana-3294	99	16	g(νm+2	g(νm+2	NOUN
cana-3294	99	17	)	)	PUNCT
cana-3294	99	18	we	we	PRON
cana-3294	99	19	conclude	conclude	VERB
cana-3294	99	20	that	that	SCONJ
cana-3294	99	21	4	4	NUM
cana-3294	99	22	holds	hold	VERB
cana-3294	99	23	for	for	ADP
cana-3294	99	24	all	all	DET
cana-3294	99	25	m	m	PROPN
cana-3294	99	26	≥	≥	NOUN
cana-3294	99	27	0	0	NUM
cana-3294	99	28	by	by	ADP
cana-3294	99	29	the	the	DET
cana-3294	99	30	mathematical	mathematical	ADJ
cana-3294	99	31	induction	induction	NOUN
cana-3294	99	32	∴	∴	PROPN
cana-3294	99	33	we	we	PRON
cana-3294	99	34	have	have	VERB
cana-3294	99	35	g(λ0	g(λ0	NOUN
cana-3294	99	36	)	)	PUNCT
cana-3294	99	37	≤	≤	NUM
cana-3294	99	38	g(λ1	g(λ1	NOUN
cana-3294	99	39	)	)	PUNCT
cana-3294	99	40	≤	≤	NUM
cana-3294	99	41	g(λ2	g(λ2	NOUN
cana-3294	99	42	)	)	PUNCT
cana-3294	99	43	≤.	≤.	NOUN
cana-3294	99	44	.	.	PUNCT
cana-3294	99	45	..	..	PUNCT
cana-3294	100	1	g(λm+1	g(λm+1	ADJ
cana-3294	100	2	)	)	PUNCT
cana-3294	100	3	≤	≤	NOUN
cana-3294	100	4	.	.	PUNCT
cana-3294	100	5	.	.	PUNCT
cana-3294	100	6	.	.	PUNCT
cana-3294	100	7	.	.	PUNCT
cana-3294	100	8	.	.	PUNCT
cana-3294	101	1	..	..	PUNCT
cana-3294	101	2	g(μ0	g(μ0	NOUN
cana-3294	101	3	)	)	PUNCT
cana-3294	101	4	≥	≥	NOUN
cana-3294	101	5	g(μ1	g(μ1	NOUN
cana-3294	101	6	)	)	PUNCT
cana-3294	101	7	≥	≥	NOUN
cana-3294	101	8	g(μ2	g(μ2	NOUN
cana-3294	101	9	)	)	PUNCT
cana-3294	101	10	≥	≥	PROPN
cana-3294	101	11	.	.	PUNCT
cana-3294	101	12	.	.	PUNCT
cana-3294	101	13	.	.	PUNCT
cana-3294	101	14	.	.	PUNCT
cana-3294	101	15	.	.	PUNCT
cana-3294	101	16	.	.	PUNCT
cana-3294	102	1	g(μm+1	g(μm+1	ADJ
cana-3294	102	2	)	)	PUNCT
cana-3294	102	3	≥	≥	NOUN
cana-3294	102	4	.	.	PUNCT
cana-3294	102	5	.	.	PUNCT
cana-3294	102	6	.	.	PUNCT
cana-3294	102	7	.	.	PUNCT
cana-3294	102	8	.	.	PUNCT
cana-3294	102	9	.	.	PUNCT
cana-3294	103	1	g(ν0	g(ν0	PROPN
cana-3294	103	2	)	)	PUNCT
cana-3294	104	1	≤	≤	NOUN
cana-3294	104	2	g(ν1	g(ν1	VERB
cana-3294	104	3	)	)	PUNCT
cana-3294	104	4	≤	≤	NUM
cana-3294	104	5	g(ν2	g(ν2	NOUN
cana-3294	104	6	)	)	PUNCT
cana-3294	104	7	≤	≤	NOUN
cana-3294	104	8	.	.	PUNCT
cana-3294	104	9	..	..	PUNCT
cana-3294	104	10	.	.	PUNCT
cana-3294	104	11	..	..	PUNCT
cana-3294	104	12	.	.	PUNCT
cana-3294	105	1	g(νm+1	g(νm+1	ADJ
cana-3294	105	2	)	)	PUNCT
cana-3294	105	3	≤	≤	NOUN
cana-3294	105	4	.	.	PUNCT
cana-3294	105	5	.	.	PUNCT
cana-3294	105	6	.	.	PUNCT
cana-3294	105	7	.	.	PUNCT
cana-3294	105	8	.	.	PUNCT
cana-3294	105	9	.	.	PUNCT
cana-3294	106	1	definitions	definition	NOUN
cana-3294	106	2	2.7	2.7	NUM
cana-3294	106	3	and	and	CCONJ
cana-3294	106	4	2.8	2.8	NUM
cana-3294	106	5	are	be	AUX
cana-3294	106	6	revised	revise	VERB
cana-3294	106	7	in	in	ADP
cana-3294	106	8	main	main	ADJ
cana-3294	106	9	results	result	NOUN
cana-3294	106	10	as	as	SCONJ
cana-3294	106	11	follows	follow	VERB
cana-3294	106	12	by	by	ADP
cana-3294	106	13	using	use	VERB
cana-3294	106	14	above	above	ADP
cana-3294	106	15	considerations	consideration	NOUN
cana-3294	106	16	.	.	PUNCT
cana-3294	107	1	communications	communication	NOUN
cana-3294	107	2	on	on	ADP
cana-3294	107	3	applied	apply	VERB
cana-3294	107	4	nonlinear	nonlinear	ADJ
cana-3294	107	5	analysis	analysis	NOUN
cana-3294	107	6	issn	issn	NOUN
cana-3294	107	7	:	:	PUNCT
cana-3294	107	8	1074	1074	NUM
cana-3294	107	9	-	-	PUNCT
cana-3294	107	10	133x	133x	NUM
cana-3294	107	11	vol	vol	NOUN
cana-3294	107	12	32	32	NUM
cana-3294	107	13	no	no	NOUN
cana-3294	107	14	.	.	PUNCT
cana-3294	108	1	6s	6s	NUM
cana-3294	108	2	(	(	PUNCT
cana-3294	108	3	2025	2025	NUM
cana-3294	108	4	)	)	PUNCT
cana-3294	108	5	279	279	NUM
cana-3294	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	108	7	4.results	4.results	NUM
cana-3294	108	8	and	and	CCONJ
cana-3294	108	9	discussion	discussion	NOUN
cana-3294	108	10	definition	definition	NOUN
cana-3294	108	11	4.1	4.1	NUM
cana-3294	108	12	:	:	PUNCT
cana-3294	108	13	consider	consider	VERB
cana-3294	108	14	(	(	PUNCT
cana-3294	108	15	𝓜	𝓜	PROPN
cana-3294	108	16	,	,	PUNCT
cana-3294	108	17	g	g	NOUN
cana-3294	108	18	)	)	PUNCT
cana-3294	108	19	be	be	AUX
cana-3294	108	20	a	a	DET
cana-3294	108	21	generalized	generalized	ADJ
cana-3294	108	22	metric	metric	ADJ
cana-3294	108	23	space	space	NOUN
cana-3294	108	24	,	,	PUNCT
cana-3294	108	25	{	{	PUNCT
cana-3294	108	26	tm}m∈	tm}m∈	NOUN
cana-3294	108	27	n	n	CCONJ
cana-3294	108	28	:	:	PUNCT
cana-3294	108	29	𝓜3	𝓜3	PROPN
cana-3294	108	30	→𝓜	→𝓜	NOUN
cana-3294	108	31	be	be	VERB
cana-3294	108	32	a	a	DET
cana-3294	108	33	sequence	sequence	NOUN
cana-3294	108	34	of	of	ADP
cana-3294	108	35	mappings	mapping	NOUN
cana-3294	108	36	and	and	CCONJ
cana-3294	108	37	a	a	DET
cana-3294	108	38	self	self	NOUN
cana-3294	108	39	-	-	PUNCT
cana-3294	108	40	mapping	mapping	NOUN
cana-3294	108	41	g	g	NOUN
cana-3294	108	42	:	:	PUNCT
cana-3294	108	43	𝓜→𝓜	𝓜→𝓜	NOUN
cana-3294	108	44	are	be	AUX
cana-3294	108	45	compatible	compatible	ADJ
cana-3294	108	46	if	if	SCONJ
cana-3294	108	47	lim	lim	PROPN
cana-3294	108	48	𝑚→∞	𝑚→∞	PRON
cana-3294	108	49	𝐺(g(tm	𝐺(g(tm	X
cana-3294	108	50	(	(	PUNCT
cana-3294	108	51	λm	λm	ADP
cana-3294	108	52	,	,	PUNCT
cana-3294	108	53	μm	μm	INTJ
cana-3294	108	54	,	,	PUNCT
cana-3294	108	55	νm	νm	NOUN
cana-3294	108	56	)	)	PUNCT
cana-3294	108	57	)	)	PUNCT
cana-3294	108	58	,	,	PUNCT
cana-3294	108	59	tm	tm	PROPN
cana-3294	108	60	(	(	PUNCT
cana-3294	108	61	gλm	gλm	PROPN
cana-3294	108	62	,	,	PUNCT
cana-3294	108	63	gμm	gμm	PROPN
cana-3294	108	64	,	,	PUNCT
cana-3294	108	65	gνm	gνm	PROPN
cana-3294	108	66	)	)	PUNCT
cana-3294	108	67	,	,	PUNCT
cana-3294	108	68	tm	tm	PROPN
cana-3294	108	69	(	(	PUNCT
cana-3294	108	70	gλm	gλm	PROPN
cana-3294	108	71	,	,	PUNCT
cana-3294	108	72	gμm	gμm	PROPN
cana-3294	108	73	,	,	PUNCT
cana-3294	108	74	gνm	gνm	NOUN
cana-3294	108	75	)	)	PUNCT
cana-3294	108	76	)	)	PUNCT
cana-3294	109	1	=	=	SYM
cana-3294	109	2	0	0	NUM
cana-3294	110	1	lim	lim	PROPN
cana-3294	110	2	𝑚→∞	𝑚→∞	X
cana-3294	110	3	𝐺(g(tm	𝐺(g(tm	PROPN
cana-3294	110	4	(	(	PUNCT
cana-3294	110	5	μm	μm	INTJ
cana-3294	110	6	,	,	PUNCT
cana-3294	110	7	λm	λm	ADP
cana-3294	110	8	,	,	PUNCT
cana-3294	110	9	μm	μm	NOUN
cana-3294	110	10	)	)	PUNCT
cana-3294	110	11	)	)	PUNCT
cana-3294	110	12	,	,	PUNCT
cana-3294	110	13	tm	tm	PROPN
cana-3294	110	14	(	(	PUNCT
cana-3294	110	15	gμm	gμm	PROPN
cana-3294	110	16	,	,	PUNCT
cana-3294	110	17	gλm	gλm	NOUN
cana-3294	110	18	,	,	PUNCT
cana-3294	110	19	gμm	gμm	PROPN
cana-3294	110	20	)	)	PUNCT
cana-3294	110	21	,	,	PUNCT
cana-3294	110	22	tm	tm	PROPN
cana-3294	110	23	(	(	PUNCT
cana-3294	110	24	gμm	gμm	PROPN
cana-3294	110	25	,	,	PUNCT
cana-3294	110	26	gλm	gλm	NOUN
cana-3294	110	27	,	,	PUNCT
cana-3294	110	28	gμm	gμm	NOUN
cana-3294	110	29	)	)	PUNCT
cana-3294	110	30	)	)	PUNCT
cana-3294	111	1	=	=	SYM
cana-3294	111	2	0	0	NUM
cana-3294	112	1	lim	lim	PROPN
cana-3294	112	2	𝑚→∞	𝑚→∞	PROPN
cana-3294	112	3	𝐺	𝐺	PROPN
cana-3294	112	4	(	(	PUNCT
cana-3294	112	5	g(tm	g(tm	NOUN
cana-3294	112	6	(	(	PUNCT
cana-3294	112	7	νm	νm	ADJ
cana-3294	112	8	,	,	PUNCT
cana-3294	112	9	μm	μm	INTJ
cana-3294	112	10	,	,	PUNCT
cana-3294	112	11	λm	λm	NOUN
cana-3294	112	12	)	)	PUNCT
cana-3294	112	13	)	)	PUNCT
cana-3294	112	14	,	,	PUNCT
cana-3294	112	15	tm(gνm	tm(gνm	PROPN
cana-3294	112	16	,	,	PUNCT
cana-3294	112	17	gμm	gμm	ADJ
cana-3294	112	18	,	,	PUNCT
cana-3294	112	19	gλm	gλm	NOUN
cana-3294	112	20	)	)	PUNCT
cana-3294	112	21	,	,	PUNCT
cana-3294	112	22	tm	tm	PROPN
cana-3294	112	23	(	(	PUNCT
cana-3294	112	24	gνm	gνm	PROPN
cana-3294	112	25	,	,	PUNCT
cana-3294	112	26	gμm	gμm	PROPN
cana-3294	112	27	,	,	PUNCT
cana-3294	112	28	gλm	gλm	NOUN
cana-3294	112	29	)	)	PUNCT
cana-3294	112	30	)	)	PUNCT
cana-3294	113	1	=	=	SYM
cana-3294	113	2	0	0	PUNCT
cana-3294	114	1	whenever	whenever	SCONJ
cana-3294	114	2	{	{	PUNCT
cana-3294	114	3	λm	λm	NOUN
cana-3294	114	4	}	}	PUNCT
cana-3294	114	5	,	,	PUNCT
cana-3294	114	6	{	{	PUNCT
cana-3294	114	7	μm	μm	INTJ
cana-3294	114	8	,	,	PUNCT
cana-3294	114	9	{	{	PUNCT
cana-3294	114	10	νm	νm	PRON
cana-3294	114	11	}	}	PUNCT
cana-3294	114	12	are	be	AUX
cana-3294	114	13	sequences	sequence	NOUN
cana-3294	114	14	in	in	ADP
cana-3294	114	15	𝓜	𝓜	PROPN
cana-3294	114	16	such	such	ADJ
cana-3294	114	17	that	that	SCONJ
cana-3294	114	18	lim	lim	PROPN
cana-3294	114	19	m→∞	m→∞	NUM
cana-3294	114	20	tm	tm	PROPN
cana-3294	114	21	(	(	PUNCT
cana-3294	114	22	λm	λm	ADP
cana-3294	114	23	,	,	PUNCT
cana-3294	114	24	μm	μm	INTJ
cana-3294	114	25	,	,	PUNCT
cana-3294	114	26	νm	νm	NOUN
cana-3294	114	27	)	)	PUNCT
cana-3294	114	28	=	=	SYM
cana-3294	115	1	lim	lim	PROPN
cana-3294	115	2	m→∞	m→∞	NUM
cana-3294	115	3	g(λm+1	g(λm+1	NOUN
cana-3294	115	4	)	)	PUNCT
cana-3294	115	5	=	=	SYM
cana-3294	115	6	λ	λ	PROPN
cana-3294	115	7	lim	lim	PROPN
cana-3294	115	8	m→∞	m→∞	NUM
cana-3294	115	9	tm	tm	NOUN
cana-3294	115	10	(	(	PUNCT
cana-3294	115	11	μm	μm	INTJ
cana-3294	115	12	,	,	PUNCT
cana-3294	115	13	λm	λm	ADP
cana-3294	115	14	,	,	PUNCT
cana-3294	115	15	μm	μm	NOUN
cana-3294	115	16	)	)	PUNCT
cana-3294	115	17	=	=	SYM
cana-3294	115	18	lim	lim	PROPN
cana-3294	115	19	m→∞	m→∞	NUM
cana-3294	115	20	g(μm+1	g(μm+1	NOUN
cana-3294	115	21	)	)	PUNCT
cana-3294	115	22	=	=	SYM
cana-3294	115	23	μ	μ	PROPN
cana-3294	115	24	lim	lim	PROPN
cana-3294	115	25	m→∞	m→∞	NUM
cana-3294	115	26	tm	tm	PROPN
cana-3294	115	27	(	(	PUNCT
cana-3294	115	28	νm	νm	PROPN
cana-3294	115	29	,	,	PUNCT
cana-3294	115	30	μm	μm	INTJ
cana-3294	115	31	,	,	PUNCT
cana-3294	115	32	λm	λm	NOUN
cana-3294	115	33	)	)	PUNCT
cana-3294	115	34	=	=	SYM
cana-3294	115	35	lim	lim	PROPN
cana-3294	115	36	m→∞	m→∞	NOUN
cana-3294	115	37	g(νm+1	g(νm+1	NOUN
cana-3294	115	38	)	)	PUNCT
cana-3294	116	1	=	=	NOUN
cana-3294	116	2	ν	ν	NOUN
cana-3294	116	3	for	for	ADP
cana-3294	116	4	some	some	DET
cana-3294	116	5	λ	λ	PROPN
cana-3294	116	6	,	,	PUNCT
cana-3294	116	7	μ	μ	PROPN
cana-3294	116	8	,	,	PUNCT
cana-3294	116	9	ν	ν	PROPN
cana-3294	116	10	∈	∈	NOUN
cana-3294	116	11	𝓜.	𝓜.	PROPN
cana-3294	116	12	definition	definition	NOUN
cana-3294	116	13	4.2	4.2	NUM
cana-3294	116	14	:	:	PUNCT
cana-3294	116	15	assume	assume	VERB
cana-3294	116	16	(	(	PUNCT
cana-3294	116	17	𝓠	𝓠	NOUN
cana-3294	116	18	,	,	PUNCT
cana-3294	116	19	g	g	NOUN
cana-3294	116	20	)	)	PUNCT
cana-3294	116	21	be	be	AUX
cana-3294	116	22	a	a	DET
cana-3294	116	23	gmetric	gmetric	ADJ
cana-3294	116	24	space	space	NOUN
cana-3294	116	25	,	,	PUNCT
cana-3294	116	26	the	the	DET
cana-3294	116	27	mappings	mapping	NOUN
cana-3294	116	28	{	{	PUNCT
cana-3294	116	29	tm}m∈	tm}m∈	PROPN
cana-3294	116	30	n	n	CCONJ
cana-3294	116	31	:	:	PUNCT
cana-3294	116	32	𝓠3	𝓠3	PROPN
cana-3294	116	33	→𝓠	→𝓠	X
cana-3294	116	34	and	and	CCONJ
cana-3294	116	35	g	g	NOUN
cana-3294	116	36	:	:	PUNCT
cana-3294	116	37	𝓠→𝓠	𝓠→𝓠	X
cana-3294	116	38	are	be	AUX
cana-3294	116	39	weakly	weakly	ADV
cana-3294	116	40	reciprocally	reciprocally	ADV
cana-3294	116	41	continuous	continuous	ADJ
cana-3294	116	42	if	if	SCONJ
cana-3294	116	43	lim	lim	PROPN
cana-3294	116	44	𝑚→∞	𝑚→∞	NUM
cana-3294	116	45	g(𝑇𝑚(𝜉𝑚	g(𝑇𝑚(𝜉𝑚	NOUN
cana-3294	116	46	,	,	PUNCT
cana-3294	116	47	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	116	48	,	,	PUNCT
cana-3294	116	49	𝜃𝑚	𝜃𝑚	NOUN
cana-3294	116	50	)	)	PUNCT
cana-3294	116	51	)	)	PUNCT
cana-3294	117	1	=	=	SYM
cana-3294	117	2	g(𝜉	g(𝜉	NOUN
cana-3294	117	3	)	)	PUNCT
cana-3294	117	4	lim	lim	PROPN
cana-3294	117	5	𝑚→∞	𝑚→∞	NUM
cana-3294	117	6	g(𝑇𝑚(𝜂𝑚	g(𝑇𝑚(𝜂𝑚	PROPN
cana-3294	117	7	,	,	PUNCT
cana-3294	117	8	𝜉𝑚	𝜉𝑚	NOUN
cana-3294	117	9	,	,	PUNCT
cana-3294	117	10	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	117	11	)	)	PUNCT
cana-3294	117	12	)	)	PUNCT
cana-3294	117	13	=	=	PUNCT
cana-3294	117	14	g(𝜂	g(𝜂	PROPN
cana-3294	117	15	)	)	PUNCT
cana-3294	117	16	lim	lim	PROPN
cana-3294	117	17	𝑚→∞	𝑚→∞	PUNCT
cana-3294	117	18	g(𝑇𝑚(𝜃𝑚	g(𝑇𝑚(𝜃𝑚	PROPN
cana-3294	117	19	,	,	PUNCT
cana-3294	117	20	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	117	21	,	,	PUNCT
cana-3294	117	22	𝜉𝑚	𝜉𝑚	NOUN
cana-3294	117	23	)	)	PUNCT
cana-3294	117	24	)	)	PUNCT
cana-3294	118	1	=	=	SYM
cana-3294	118	2	g(𝜃	g(𝜃	NOUN
cana-3294	118	3	)	)	PUNCT
cana-3294	118	4	whenever	whenever	SCONJ
cana-3294	118	5	{	{	PUNCT
cana-3294	118	6	𝜉𝑚	𝜉𝑚	NOUN
cana-3294	118	7	}	}	PUNCT
cana-3294	118	8	,	,	PUNCT
cana-3294	118	9	{	{	PUNCT
cana-3294	118	10	𝜂𝑚	𝜂𝑚	PART
cana-3294	118	11	}	}	PUNCT
cana-3294	118	12	,	,	PUNCT
cana-3294	118	13	{	{	PUNCT
cana-3294	118	14	𝜃𝑚	𝜃𝑚	ADV
cana-3294	118	15	}	}	PUNCT
cana-3294	118	16	are	be	AUX
cana-3294	118	17	sequences	sequence	NOUN
cana-3294	118	18	in	in	ADP
cana-3294	118	19	𝓠	𝓠	PRON
cana-3294	118	20	such	such	ADJ
cana-3294	118	21	that	that	SCONJ
cana-3294	118	22	lim	lim	PROPN
cana-3294	118	23	𝑚→∞	𝑚→∞	NUM
cana-3294	118	24	𝑇𝑚(𝜉𝑚	𝑇𝑚(𝜉𝑚	PROPN
cana-3294	118	25	,	,	PUNCT
cana-3294	118	26	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	118	27	,	,	PUNCT
cana-3294	118	28	𝜃𝑚	𝜃𝑚	NOUN
cana-3294	118	29	)	)	PUNCT
cana-3294	118	30	)	)	PUNCT
cana-3294	119	1	=	=	SYM
cana-3294	119	2	lim	lim	PROPN
cana-3294	119	3	𝑚→∞	𝑚→∞	NUM
cana-3294	119	4	g(𝜉𝑚+1	g(𝜉𝑚+1	PUNCT
cana-3294	119	5	)	)	PUNCT
cana-3294	120	1	=	=	SYM
cana-3294	120	2	𝜉	𝜉	PROPN
cana-3294	120	3	lim	lim	PROPN
cana-3294	120	4	𝑚→∞	𝑚→∞	PUNCT
cana-3294	120	5	𝑇𝑚	𝑇𝑚	PROPN
cana-3294	120	6	(	(	PUNCT
cana-3294	120	7	𝜂𝑚	𝜂𝑚	PROPN
cana-3294	120	8	,	,	PUNCT
cana-3294	120	9	𝜉𝑚	𝜉𝑚	NOUN
cana-3294	120	10	,	,	PUNCT
cana-3294	120	11	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	120	12	)	)	PUNCT
cana-3294	120	13	=	=	SYM
cana-3294	120	14	lim	lim	PROPN
cana-3294	120	15	𝑚→∞	𝑚→∞	NUM
cana-3294	120	16	g(𝜂𝑚+1	g(𝜂𝑚+1	PROPN
cana-3294	120	17	)	)	PUNCT
cana-3294	121	1	=	=	SYM
cana-3294	121	2	𝜂	𝜂	PROPN
cana-3294	121	3	lim	lim	PROPN
cana-3294	121	4	𝑚→∞	𝑚→∞	PUNCT
cana-3294	121	5	𝑇𝑚	𝑇𝑚	PROPN
cana-3294	121	6	(	(	PUNCT
cana-3294	121	7	𝜃𝑚	𝜃𝑚	NOUN
cana-3294	121	8	,	,	PUNCT
cana-3294	121	9	𝜂𝑚	𝜂𝑚	NOUN
cana-3294	121	10	,	,	PUNCT
cana-3294	121	11	𝜉𝑚	𝜉𝑚	NOUN
cana-3294	121	12	)	)	PUNCT
cana-3294	122	1	=	=	VERB
cana-3294	122	2	lim	lim	PROPN
cana-3294	122	3	𝑚→∞	𝑚→∞	NUM
cana-3294	122	4	g(𝜃𝑚+1	g(𝜃𝑚+1	PROPN
cana-3294	122	5	)	)	PUNCT
cana-3294	122	6	=	=	SYM
cana-3294	123	1	𝜃	𝜃	PROPN
cana-3294	123	2	for	for	ADP
cana-3294	123	3	some	some	DET
cana-3294	123	4	𝜉	𝜉	NOUN
cana-3294	123	5	,	,	PUNCT
cana-3294	123	6	𝜂	𝜂	PROPN
cana-3294	123	7	,	,	PUNCT
cana-3294	123	8	𝜃	𝜃	NOUN
cana-3294	123	9	ϵ	ϵ	PRON
cana-3294	123	10	𝓠.	𝓠.	PROPN
cana-3294	123	11	theorem	theorem	VERB
cana-3294	123	12	4.3	4.3	NUM
cana-3294	123	13	:	:	PUNCT
cana-3294	123	14	assume	assume	VERB
cana-3294	123	15	(	(	PUNCT
cana-3294	123	16	℧	℧	PROPN
cana-3294	123	17	,	,	PUNCT
cana-3294	123	18	g	g	NOUN
cana-3294	123	19	)	)	PUNCT
cana-3294	123	20	be	be	VERB
cana-3294	123	21	a	a	DET
cana-3294	123	22	partially	partially	ADV
cana-3294	123	23	ordered	order	VERB
cana-3294	123	24	complete	complete	ADJ
cana-3294	123	25	g	g	NOUN
cana-3294	123	26	-	-	PUNCT
cana-3294	123	27	metric	metric	ADJ
cana-3294	123	28	space	space	NOUN
cana-3294	123	29	.	.	PUNCT
cana-3294	124	1	let	let	VERB
cana-3294	124	2	a	a	DET
cana-3294	124	3	sequence	sequence	NOUN
cana-3294	124	4	of	of	ADP
cana-3294	124	5	mappings	mapping	NOUN
cana-3294	124	6	tn	tn	NUM
cana-3294	124	7	:	:	PUNCT
cana-3294	124	8	℧	℧	PROPN
cana-3294	124	9	3→	3→	NUM
cana-3294	124	10	℧	℧	PROPN
cana-3294	124	11	and	and	CCONJ
cana-3294	124	12	a	a	DET
cana-3294	124	13	self	self	NOUN
cana-3294	124	14	-	-	PUNCT
cana-3294	124	15	mapping	mapping	NOUN
cana-3294	124	16	g	g	NOUN
cana-3294	124	17	:	:	PUNCT
cana-3294	124	18	℧	℧	PROPN
cana-3294	124	19	→	→	SYM
cana-3294	124	20	℧	℧	PROPN
cana-3294	124	21	such	such	ADJ
cana-3294	124	22	that	that	DET
cana-3294	124	23	tn	tn	PROPN
cana-3294	124	24	(	(	PUNCT
cana-3294	124	25	℧	℧	PROPN
cana-3294	124	26	3	3	NUM
cana-3294	124	27	)	)	PUNCT
cana-3294	125	1	⊆	⊆	NUM
cana-3294	125	2	g	g	NOUN
cana-3294	125	3	(	(	PUNCT
cana-3294	125	4	℧	℧	NOUN
cana-3294	125	5	)	)	PUNCT
cana-3294	125	6	and	and	CCONJ
cana-3294	125	7	g	g	PROPN
cana-3294	125	8	(	(	PUNCT
cana-3294	125	9	℧	℧	NOUN
cana-3294	125	10	)	)	PUNCT
cana-3294	125	11	is	be	AUX
cana-3294	125	12	closed	closed	ADJ
cana-3294	125	13	.	.	PUNCT
cana-3294	126	1	{	{	PUNCT
cana-3294	126	2	tn}nϵn	tn}nϵn	PROPN
cana-3294	126	3	&	&	CCONJ
cana-3294	126	4	g	g	PROPN
cana-3294	126	5	has	have	VERB
cana-3294	126	6	g	g	ADV
cana-3294	126	7	-	-	PUNCT
cana-3294	126	8	mixed	mix	VERB
cana-3294	126	9	monotone	monotone	ADJ
cana-3294	126	10	property	property	NOUN
cana-3294	126	11	and	and	CCONJ
cana-3294	126	12	both	both	PRON
cana-3294	126	13	are	be	AUX
cana-3294	126	14	continuous	continuous	ADJ
cana-3294	126	15	,	,	PUNCT
cana-3294	126	16	compatible	compatible	ADJ
cana-3294	126	17	,	,	PUNCT
cana-3294	126	18	weakly	weakly	ADV
cana-3294	126	19	reciprocally	reciprocally	ADV
cana-3294	126	20	continuous	continuous	ADJ
cana-3294	126	21	and	and	CCONJ
cana-3294	126	22	satisfying	satisfy	VERB
cana-3294	126	23	the	the	DET
cana-3294	126	24	below	below	ADJ
cana-3294	126	25	conditions	condition	NOUN
cana-3294	126	26	.	.	PUNCT
cana-3294	127	1	1	1	X
cana-3294	127	2	.	.	X
cana-3294	127	3	there	there	PRON
cana-3294	127	4	exists	exist	VERB
cana-3294	127	5	𝜆0	𝜆0	PROPN
cana-3294	127	6	,	,	PUNCT
cana-3294	127	7	𝜇0	𝜇0	PROPN
cana-3294	127	8	,	,	PUNCT
cana-3294	127	9	𝜈0	𝜈0	PROPN
cana-3294	127	10	ϵ	ϵ	X
cana-3294	127	11	x	x	NOUN
cana-3294	128	1	such	such	ADJ
cana-3294	128	2	that	that	DET
cana-3294	128	3	g(λ0	g(λ0	NOUN
cana-3294	128	4	)	)	PUNCT
cana-3294	128	5	≤	≤	NOUN
cana-3294	128	6	t0(λ0	t0(λ0	ADJ
cana-3294	128	7	,	,	PUNCT
cana-3294	128	8	μ0	μ0	PROPN
cana-3294	128	9	,	,	PUNCT
cana-3294	128	10	ν0	ν0	PROPN
cana-3294	128	11	)	)	PUNCT
cana-3294	128	12	,	,	PUNCT
cana-3294	128	13	g(μ0	g(μ0	NOUN
cana-3294	128	14	)	)	PUNCT
cana-3294	128	15	≥t0(μ0	≥t0(μ0	NOUN
cana-3294	128	16	,	,	PUNCT
cana-3294	128	17	λ0	λ0	NOUN
cana-3294	128	18	,	,	PUNCT
cana-3294	128	19	μ0	μ0	PROPN
cana-3294	128	20	)	)	PUNCT
cana-3294	128	21	,	,	PUNCT
cana-3294	128	22	g(ν0	g(ν0	PROPN
cana-3294	128	23	)	)	PUNCT
cana-3294	128	24	≤	≤	PROPN
cana-3294	129	1	t0(ν0	t0(ν0	PROPN
cana-3294	129	2	,	,	PUNCT
cana-3294	129	3	μ0	μ0	PROPN
cana-3294	129	4	,	,	PUNCT
cana-3294	129	5	λ0	λ0	NOUN
cana-3294	129	6	)	)	PUNCT
cana-3294	129	7	holds	hold	NOUN
cana-3294	129	8	.	.	PUNCT
cana-3294	130	1	2	2	X
cana-3294	130	2	.	.	PUNCT
cana-3294	130	3	{	{	PUNCT
cana-3294	130	4	tn}nϵn	tn}nϵn	PUNCT
cana-3294	130	5	and	and	CCONJ
cana-3294	130	6	g	g	PROPN
cana-3294	130	7	satisfies	satisfy	VERB
cana-3294	130	8	the	the	DET
cana-3294	130	9	condition	condition	NOUN
cana-3294	130	10	g(tn(λ	g(tn(λ	PROPN
cana-3294	130	11	,	,	PUNCT
cana-3294	130	12	μ	μ	PROPN
cana-3294	130	13	,	,	PUNCT
cana-3294	130	14	ν),tj(𝜻,𝜼,𝝒),tj(𝝆,𝝈,𝝉	ν),tj(𝜻,𝜼,𝝒),tj(𝝆,𝝈,𝝉	NUM
cana-3294	130	15	)	)	PUNCT
cana-3294	130	16	)	)	PUNCT
cana-3294	131	1	≤	≤	NUM
cana-3294	131	2	γn	γn	ADP
cana-3294	131	3	,	,	PUNCT
cana-3294	131	4	j[g(gλ	j[g(gλ	PROPN
cana-3294	131	5	,	,	PUNCT
cana-3294	131	6	tn(λ	tn(λ	NOUN
cana-3294	131	7	,	,	PUNCT
cana-3294	131	8	μ	μ	PROPN
cana-3294	131	9	,	,	PUNCT
cana-3294	131	10	ν	ν	NOUN
cana-3294	131	11	)	)	PUNCT
cana-3294	131	12	,	,	PUNCT
cana-3294	131	13	tn(λ	tn(λ	NUM
cana-3294	131	14	,	,	PUNCT
cana-3294	131	15	μ	μ	PROPN
cana-3294	131	16	,	,	PUNCT
cana-3294	131	17	ν	ν	NOUN
cana-3294	131	18	)	)	PUNCT
cana-3294	131	19	)	)	PUNCT
cana-3294	132	1	+	+	PUNCT
cana-3294	132	2	g(g𝜻,tj(𝜻,𝜼,𝝒),tj(𝝆,𝝈,𝝉	g(g𝜻,tj(𝜻,𝜼,𝝒),tj(𝝆,𝝈,𝝉	X
cana-3294	132	3	)	)	PUNCT
cana-3294	132	4	]	]	PUNCT
cana-3294	133	1	+	+	CCONJ
cana-3294	133	2	δn	δn	PROPN
cana-3294	133	3	,	,	PUNCT
cana-3294	133	4	j	j	PROPN
cana-3294	133	5	g(gλ	g(gλ	PROPN
cana-3294	133	6	,	,	PUNCT
cana-3294	133	7	g𝜻	g𝜻	INTJ
cana-3294	133	8	,	,	PUNCT
cana-3294	133	9	g𝝆	g𝝆	PROPN
cana-3294	133	10	)	)	PUNCT
cana-3294	133	11	(	(	PUNCT
cana-3294	133	12	5	5	X
cana-3294	133	13	)	)	PUNCT
cana-3294	133	14	communications	communication	NOUN
cana-3294	133	15	on	on	ADP
cana-3294	133	16	applied	apply	VERB
cana-3294	133	17	nonlinear	nonlinear	ADJ
cana-3294	133	18	analysis	analysis	NOUN
cana-3294	133	19	issn	issn	NOUN
cana-3294	133	20	:	:	PUNCT
cana-3294	133	21	1074	1074	NUM
cana-3294	133	22	-	-	PUNCT
cana-3294	133	23	133x	133x	NUM
cana-3294	133	24	vol	vol	NOUN
cana-3294	133	25	32	32	NUM
cana-3294	133	26	no	no	NOUN
cana-3294	133	27	.	.	PUNCT
cana-3294	134	1	6s	6s	NUM
cana-3294	134	2	(	(	PUNCT
cana-3294	134	3	2025	2025	NUM
cana-3294	134	4	)	)	PUNCT
cana-3294	134	5	280	280	NUM
cana-3294	134	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	134	7	for	for	ADP
cana-3294	134	8	λ	λ	PROPN
cana-3294	134	9	,	,	PUNCT
cana-3294	134	10	μ	μ	PROPN
cana-3294	134	11	,	,	PUNCT
cana-3294	134	12	ν	ν	PROPN
cana-3294	134	13	,	,	PUNCT
cana-3294	134	14	𝜻	𝜻	PROPN
cana-3294	134	15	,	,	PUNCT
cana-3294	134	16	𝜼	𝜼	PROPN
cana-3294	134	17	,	,	PUNCT
cana-3294	134	18	𝝒	𝝒	NOUN
cana-3294	134	19	,	,	PUNCT
cana-3294	134	20	𝝆	𝝆	PRON
cana-3294	134	21	,	,	PUNCT
cana-3294	134	22	𝝈	𝝈	NOUN
cana-3294	134	23	,	,	PUNCT
cana-3294	134	24	𝝉	𝝉	NOUN
cana-3294	134	25	ϵ	ϵ	X
cana-3294	134	26	℧	℧	PROPN
cana-3294	134	27	and	and	CCONJ
cana-3294	134	28	0	0	NUM
cana-3294	134	29	≤	≤	NUM
cana-3294	134	30	γ	γ	PROPN
cana-3294	134	31	n	n	X
cana-3294	134	32	,	,	PUNCT
cana-3294	134	33	j	j	PROPN
cana-3294	134	34	,	,	PUNCT
cana-3294	134	35	δ	δ	PROPN
cana-3294	134	36	n	n	PRON
cana-3294	134	37	,	,	PUNCT
cana-3294	134	38	j	j	PROPN
cana-3294	134	39	<	<	X
cana-3294	134	40	1	1	NUM
cana-3294	134	41	,	,	PUNCT
cana-3294	134	42	n≠j=1,2	n≠j=1,2	ADJ
cana-3294	134	43	,	,	PUNCT
cana-3294	134	44	…	…	PUNCT
cana-3294	134	45	..	..	PUNCT
cana-3294	135	1	i.e	i.e	PROPN
cana-3294	135	2	n	n	X
cana-3294	135	3	,	,	PUNCT
cana-3294	135	4	j	j	PROPN
cana-3294	136	1	ϵn	ϵn	INTJ
cana-3294	136	2	if	if	SCONJ
cana-3294	136	3	∑	∑	PROPN
cana-3294	136	4	(	(	PUNCT
cana-3294	136	5	𝛾𝑛,𝑛+1	𝛾𝑛,𝑛+1	PROPN
cana-3294	136	6	+	+	X
cana-3294	136	7	𝛿𝑛,𝑛+1	𝛿𝑛,𝑛+1	NOUN
cana-3294	136	8	1−𝛾𝑛,𝑛+1	1−𝛾𝑛,𝑛+1	NUM
cana-3294	136	9	∞	∞	NUM
cana-3294	136	10	𝑛=1	𝑛=1	NOUN
cana-3294	136	11	)	)	PUNCT
cana-3294	136	12	is	be	AUX
cana-3294	136	13	an	an	DET
cana-3294	136	14	α	α	NOUN
cana-3294	136	15	-	-	PUNCT
cana-3294	136	16	series	series	NOUN
cana-3294	136	17	then	then	ADV
cana-3294	136	18	g	g	PROPN
cana-3294	136	19	and	and	CCONJ
cana-3294	136	20	{	{	PUNCT
cana-3294	136	21	tn}nϵn	tn}nϵn	AUX
cana-3294	136	22	have	have	AUX
cana-3294	136	23	a	a	DET
cana-3294	136	24	tripled	triple	VERB
cana-3294	136	25	coincidence	coincidence	NOUN
cana-3294	136	26	point	point	NOUN
cana-3294	136	27	.	.	PUNCT
cana-3294	137	1	3	3	X
cana-3294	137	2	.	.	X
cana-3294	137	3	if{tn}nϵn	if{tn}nϵn	PROPN
cana-3294	137	4	and	and	CCONJ
cana-3294	137	5	g	g	PROPN
cana-3294	137	6	have	have	AUX
cana-3294	137	7	tripled	triple	VERB
cana-3294	137	8	coincidence	coincidence	NOUN
cana-3294	137	9	point	point	NOUN
cana-3294	137	10	comparable	comparable	ADJ
cana-3294	137	11	with	with	ADP
cana-3294	137	12	respect	respect	NOUN
cana-3294	137	13	to	to	ADP
cana-3294	137	14	g	g	NOUN
cana-3294	137	15	then	then	ADV
cana-3294	137	16	{	{	PUNCT
cana-3294	137	17	tn}nϵn	tn}nϵn	X
cana-3294	137	18	and	and	CCONJ
cana-3294	137	19	g	g	PROPN
cana-3294	137	20	have	have	VERB
cana-3294	137	21	a	a	DET
cana-3294	137	22	unique	unique	ADJ
cana-3294	137	23	tripled	triple	VERB
cana-3294	137	24	fixed	fix	VERB
cana-3294	137	25	point	point	NOUN
cana-3294	137	26	.	.	PUNCT
cana-3294	138	1	proof	proof	NOUN
cana-3294	138	2	:	:	PUNCT
cana-3294	138	3	for	for	ADP
cana-3294	138	4	any	any	DET
cana-3294	138	5	λ0	λ0	NOUN
cana-3294	138	6	,	,	PUNCT
cana-3294	138	7	μ0	μ0	PROPN
cana-3294	138	8	,	,	PUNCT
cana-3294	138	9	ν0	ν0	PROPN
cana-3294	138	10	ϵ	ϵ	X
cana-3294	138	11	℧	℧	PROPN
cana-3294	138	12	.	.	PUNCT
cana-3294	139	1	we	we	PRON
cana-3294	139	2	consider	consider	VERB
cana-3294	139	3	three	three	NUM
cana-3294	139	4	sequences	sequence	NOUN
cana-3294	139	5	{	{	PUNCT
cana-3294	139	6	𝜆𝑚},{𝜇𝑚	𝜆𝑚},{𝜇𝑚	NUM
cana-3294	139	7	}	}	PUNCT
cana-3294	139	8	,	,	PUNCT
cana-3294	139	9	{	{	PUNCT
cana-3294	139	10	𝜈𝑚	𝜈𝑚	ADP
cana-3294	139	11	}	}	PUNCT
cana-3294	139	12	constructed	construct	VERB
cana-3294	139	13	above	above	ADV
cana-3294	139	14	by	by	ADP
cana-3294	139	15	taking	take	VERB
cana-3294	139	16	gλm+1	gλm+1	NOUN
cana-3294	139	17	=	=	ADJ
cana-3294	139	18	tm	tm	NOUN
cana-3294	139	19	(	(	PUNCT
cana-3294	139	20	λm	λm	ADP
cana-3294	139	21	,	,	PUNCT
cana-3294	139	22	μm	μm	INTJ
cana-3294	139	23	,	,	PUNCT
cana-3294	139	24	νm	νm	NOUN
cana-3294	139	25	)	)	PUNCT
cana-3294	139	26	,	,	PUNCT
cana-3294	139	27	gμm+1	gμm+1	PROPN
cana-3294	139	28	=	=	SYM
cana-3294	139	29	tm	tm	NOUN
cana-3294	139	30	(	(	PUNCT
cana-3294	139	31	μm	μm	INTJ
cana-3294	139	32	,	,	PUNCT
cana-3294	139	33	λm	λm	ADP
cana-3294	139	34	,	,	PUNCT
cana-3294	139	35	𝝁m	𝝁m	NOUN
cana-3294	139	36	)	)	PUNCT
cana-3294	139	37	,	,	PUNCT
cana-3294	139	38	gνm+1	gνm+1	NOUN
cana-3294	139	39	=	=	SYM
cana-3294	139	40	tm	tm	NOUN
cana-3294	139	41	(	(	PUNCT
cana-3294	139	42	νm	νm	PROPN
cana-3294	139	43	,	,	PUNCT
cana-3294	139	44	μm	μm	INTJ
cana-3294	139	45	,	,	PUNCT
cana-3294	139	46	λm	λm	NOUN
cana-3294	139	47	)	)	PUNCT
cana-3294	139	48	by	by	ADP
cana-3294	139	49	condition	condition	NOUN
cana-3294	139	50	(	(	PUNCT
cana-3294	139	51	5	5	NUM
cana-3294	139	52	)	)	PUNCT
cana-3294	139	53	g	g	NOUN
cana-3294	139	54	(	(	PUNCT
cana-3294	139	55	gλ1	gλ1	PROPN
cana-3294	139	56	,	,	PUNCT
cana-3294	139	57	gλ2	gλ2	PROPN
cana-3294	139	58	,	,	PUNCT
cana-3294	139	59	gλ2	gλ2	PROPN
cana-3294	139	60	)	)	PUNCT
cana-3294	139	61	=	=	SYM
cana-3294	139	62	g	g	PROPN
cana-3294	139	63	(	(	PUNCT
cana-3294	139	64	t0(λ0	t0(λ0	PROPN
cana-3294	139	65	,	,	PUNCT
cana-3294	139	66	μ0	μ0	PROPN
cana-3294	139	67	,	,	PUNCT
cana-3294	139	68	ν0	ν0	PROPN
cana-3294	139	69	)	)	PUNCT
cana-3294	139	70	,	,	PUNCT
cana-3294	139	71	t1(λ1	t1(λ1	NOUN
cana-3294	139	72	,	,	PUNCT
cana-3294	139	73	μ1	μ1	NOUN
cana-3294	139	74	,	,	PUNCT
cana-3294	139	75	ν1	ν1	NOUN
cana-3294	139	76	)	)	PUNCT
cana-3294	139	77	,	,	PUNCT
cana-3294	139	78	t1(λ1	t1(λ1	NOUN
cana-3294	139	79	,	,	PUNCT
cana-3294	139	80	μ1	μ1	NOUN
cana-3294	139	81	,	,	PUNCT
cana-3294	139	82	ν1	ν1	NOUN
cana-3294	139	83	)	)	PUNCT
cana-3294	139	84	)	)	PUNCT
cana-3294	140	1	≤	≤	NUM
cana-3294	140	2	γ0,1[g	γ0,1[g	NOUN
cana-3294	140	3	(	(	PUNCT
cana-3294	140	4	gλ0	gλ0	NOUN
cana-3294	140	5	,	,	PUNCT
cana-3294	140	6	t0(λ0	t0(λ0	ADJ
cana-3294	140	7	,	,	PUNCT
cana-3294	140	8	μ0	μ0	PROPN
cana-3294	140	9	,	,	PUNCT
cana-3294	140	10	ν0	ν0	PROPN
cana-3294	140	11	)	)	PUNCT
cana-3294	140	12	,	,	PUNCT
cana-3294	140	13	t0(λ0	t0(λ0	NOUN
cana-3294	140	14	,	,	PUNCT
cana-3294	140	15	μ0	μ0	PROPN
cana-3294	140	16	,	,	PUNCT
cana-3294	140	17	ν0	ν0	PROPN
cana-3294	140	18	)	)	PUNCT
cana-3294	140	19	)	)	PUNCT
cana-3294	141	1	+	+	CCONJ
cana-3294	141	2	g	g	NOUN
cana-3294	141	3	(	(	PUNCT
cana-3294	141	4	(	(	PUNCT
cana-3294	141	5	gλ1	gλ1	X
cana-3294	141	6	,	,	PUNCT
cana-3294	141	7	t1(λ1	t1(λ1	NOUN
cana-3294	141	8	,	,	PUNCT
cana-3294	141	9	μ1	μ1	NOUN
cana-3294	141	10	,	,	PUNCT
cana-3294	141	11	ν1	ν1	NOUN
cana-3294	141	12	)	)	PUNCT
cana-3294	141	13	,	,	PUNCT
cana-3294	141	14	t1(λ1	t1(λ1	NOUN
cana-3294	141	15	,	,	PUNCT
cana-3294	141	16	μ1	μ1	NOUN
cana-3294	141	17	,	,	PUNCT
cana-3294	141	18	ν1	ν1	NOUN
cana-3294	141	19	)	)	PUNCT
cana-3294	141	20	)	)	PUNCT
cana-3294	141	21	]	]	PUNCT
cana-3294	142	1	+	+	CCONJ
cana-3294	142	2	δ0,1	δ0,1	NOUN
cana-3294	142	3	g	g	NOUN
cana-3294	142	4	(	(	PUNCT
cana-3294	142	5	gλ0	gλ0	NOUN
cana-3294	142	6	,	,	PUNCT
cana-3294	142	7	gλ1	gλ1	PROPN
cana-3294	142	8	,	,	PUNCT
cana-3294	142	9	gλ1	gλ1	PROPN
cana-3294	142	10	)	)	PUNCT
cana-3294	142	11	⟹g	⟹g	X
cana-3294	142	12	(	(	PUNCT
cana-3294	142	13	gλ1	gλ1	PROPN
cana-3294	142	14	,	,	PUNCT
cana-3294	142	15	gλ2	gλ2	PROPN
cana-3294	142	16	,	,	PUNCT
cana-3294	142	17	gλ2	gλ2	PROPN
cana-3294	142	18	)	)	PUNCT
cana-3294	142	19	≤	≤	NUM
cana-3294	142	20	γ0,1[g	γ0,1[g	NOUN
cana-3294	142	21	(	(	PUNCT
cana-3294	142	22	gλ0	gλ0	NOUN
cana-3294	142	23	,	,	PUNCT
cana-3294	142	24	gλ1	gλ1	PROPN
cana-3294	142	25	,	,	PUNCT
cana-3294	142	26	gλ1	gλ1	PROPN
cana-3294	142	27	)	)	PUNCT
cana-3294	143	1	+	+	CCONJ
cana-3294	143	2	g	g	PROPN
cana-3294	143	3	(	(	PUNCT
cana-3294	143	4	gλ1	gλ1	PROPN
cana-3294	143	5	,	,	PUNCT
cana-3294	143	6	gλ2	gλ2	PROPN
cana-3294	143	7	,	,	PUNCT
cana-3294	143	8	gλ2	gλ2	PROPN
cana-3294	143	9	)	)	PUNCT
cana-3294	143	10	]	]	PUNCT
cana-3294	144	1	+	+	PROPN
cana-3294	144	2	δ0,1	δ0,1	PROPN
cana-3294	144	3	g	g	PROPN
cana-3294	144	4	(	(	PUNCT
cana-3294	144	5	gλ0	gλ0	NOUN
cana-3294	144	6	,	,	PUNCT
cana-3294	144	7	gλ1	gλ1	PROPN
cana-3294	144	8	,	,	PUNCT
cana-3294	144	9	gλ1	gλ1	PROPN
cana-3294	144	10	)	)	PUNCT
cana-3294	144	11	≤	≤	NOUN
cana-3294	144	12	(	(	PUNCT
cana-3294	144	13	γ	γ	NOUN
cana-3294	144	14	0,1	0,1	NUM
cana-3294	144	15	+	+	CCONJ
cana-3294	144	16	δ0,1	δ0,1	NOUN
cana-3294	144	17	)	)	PUNCT
cana-3294	144	18	(	(	PUNCT
cana-3294	144	19	1−γ	1−γ	NUM
cana-3294	144	20	0,1	0,1	NUM
cana-3294	144	21	)	)	PUNCT
cana-3294	144	22	g	g	NOUN
cana-3294	144	23	(	(	PUNCT
cana-3294	144	24	gλ0	gλ0	NOUN
cana-3294	144	25	,	,	PUNCT
cana-3294	144	26	gλ1	gλ1	PROPN
cana-3294	144	27	,	,	PUNCT
cana-3294	144	28	gλ1	gλ1	PROPN
cana-3294	144	29	)	)	PUNCT
cana-3294	144	30	similarly	similarly	ADV
cana-3294	144	31	g(gλ2	g(gλ2	NOUN
cana-3294	144	32	,	,	PUNCT
cana-3294	144	33	gλ3	gλ3	PROPN
cana-3294	144	34	,	,	PUNCT
cana-3294	144	35	gλ3	gλ3	PROPN
cana-3294	144	36	)	)	PUNCT
cana-3294	144	37	≤	≤	NOUN
cana-3294	144	38	(	(	PUNCT
cana-3294	144	39	γ	γ	NOUN
cana-3294	144	40	1,2	1,2	NUM
cana-3294	144	41	+	+	CCONJ
cana-3294	144	42	δ1,2	δ1,2	ADJ
cana-3294	144	43	)	)	PUNCT
cana-3294	144	44	(	(	PUNCT
cana-3294	144	45	1−γ	1−γ	NUM
cana-3294	144	46	1,2	1,2	NUM
cana-3294	144	47	)	)	PUNCT
cana-3294	144	48	g(gλ1,gλ2	g(gλ1,gλ2	PROPN
cana-3294	144	49	,	,	PUNCT
cana-3294	144	50	gλ2	gλ2	PROPN
cana-3294	144	51	)	)	PUNCT
cana-3294	144	52	≤	≤	NOUN
cana-3294	144	53	(	(	PUNCT
cana-3294	144	54	γ	γ	PROPN
cana-3294	144	55	1,2+δ1,2	1,2+δ1,2	NUM
cana-3294	144	56	1−γ	1−γ	NUM
cana-3294	144	57	1,2	1,2	NUM
cana-3294	144	58	)	)	PUNCT
cana-3294	144	59	(	(	PUNCT
cana-3294	144	60	γ	γ	X
cana-3294	144	61	0,1+δ0,1	0,1+δ0,1	NOUN
cana-3294	144	62	1−γ	1−γ	NUM
cana-3294	144	63	0,1	0,1	NUM
cana-3294	144	64	)	)	PUNCT
cana-3294	144	65	g	g	NOUN
cana-3294	144	66	(	(	PUNCT
cana-3294	144	67	gλ0	gλ0	NOUN
cana-3294	144	68	,	,	PUNCT
cana-3294	144	69	gλ1	gλ1	PROPN
cana-3294	144	70	,	,	PUNCT
cana-3294	144	71	gλ1	gλ1	PROPN
cana-3294	144	72	)	)	PUNCT
cana-3294	144	73	repeating	repeat	VERB
cana-3294	144	74	the	the	DET
cana-3294	144	75	above	above	NOUN
cana-3294	144	76	,	,	PUNCT
cana-3294	144	77	we	we	PRON
cana-3294	144	78	obtain	obtain	VERB
cana-3294	144	79	g	g	NOUN
cana-3294	144	80	(	(	PUNCT
cana-3294	144	81	gλm	gλm	NOUN
cana-3294	144	82	,	,	PUNCT
cana-3294	144	83	gλm+1	gλm+1	X
cana-3294	144	84	,	,	PUNCT
cana-3294	144	85	gλm+1	gλm+1	PROPN
cana-3294	144	86	)	)	PUNCT
cana-3294	144	87	≤	≤	NOUN
cana-3294	144	88	∏	∏	PROPN
cana-3294	144	89	(	(	PUNCT
cana-3294	144	90	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	X
cana-3294	144	91	𝟏−𝜸𝒏,𝒏+𝟏	𝟏−𝜸𝒏,𝒏+𝟏	PROPN
cana-3294	144	92	m−1	m−1	PROPN
cana-3294	144	93	n=0	n=0	X
cana-3294	144	94	)	)	PUNCT
cana-3294	144	95	g	g	NOUN
cana-3294	144	96	(	(	PUNCT
cana-3294	144	97	gλ0	gλ0	NOUN
cana-3294	144	98	,	,	PUNCT
cana-3294	144	99	gλ1	gλ1	PROPN
cana-3294	144	100	,	,	PUNCT
cana-3294	144	101	gλ1	gλ1	PROPN
cana-3294	144	102	)	)	PUNCT
cana-3294	145	1	---------(6	---------(6	CCONJ
cana-3294	145	2	)	)	PUNCT
cana-3294	145	3	using	use	VERB
cana-3294	145	4	similar	similar	ADJ
cana-3294	145	5	procedure	procedure	NOUN
cana-3294	145	6	,	,	PUNCT
cana-3294	145	7	we	we	PRON
cana-3294	145	8	can	can	AUX
cana-3294	145	9	also	also	ADV
cana-3294	145	10	prove	prove	VERB
cana-3294	145	11	that	that	SCONJ
cana-3294	145	12	g	g	PROPN
cana-3294	145	13	(	(	PUNCT
cana-3294	145	14	gμm	gμm	PROPN
cana-3294	145	15	,	,	PUNCT
cana-3294	145	16	gμm+1	gμm+1	PROPN
cana-3294	145	17	,	,	PUNCT
cana-3294	145	18	gμm+1	gμm+1	PROPN
cana-3294	145	19	)	)	PUNCT
cana-3294	145	20	≤	≤	NOUN
cana-3294	145	21	∏	∏	PROPN
cana-3294	145	22	(	(	PUNCT
cana-3294	145	23	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	X
cana-3294	145	24	𝟏−𝜸𝒏,𝒏+𝟏	𝟏−𝜸𝒏,𝒏+𝟏	PROPN
cana-3294	145	25	m−1	m−1	PROPN
cana-3294	145	26	n=0	n=0	X
cana-3294	145	27	)	)	PUNCT
cana-3294	145	28	g	g	PROPN
cana-3294	145	29	(	(	PUNCT
cana-3294	145	30	gμ0	gμ0	PROPN
cana-3294	145	31	,	,	PUNCT
cana-3294	145	32	gμ1	gμ1	NOUN
cana-3294	145	33	,	,	PUNCT
cana-3294	145	34	gμ1	gμ1	NOUN
cana-3294	145	35	)	)	PUNCT
cana-3294	145	36	------(7	------(7	NOUN
cana-3294	145	37	)	)	PUNCT
cana-3294	145	38	and	and	CCONJ
cana-3294	145	39	g	g	PROPN
cana-3294	145	40	(	(	PUNCT
cana-3294	145	41	νm	νm	PROPN
cana-3294	145	42	,	,	PUNCT
cana-3294	145	43	νm+1	νm+1	PROPN
cana-3294	145	44	,	,	PUNCT
cana-3294	145	45	νm+1	νm+1	PROPN
cana-3294	145	46	)	)	PUNCT
cana-3294	145	47	≤	≤	NOUN
cana-3294	145	48	∏	∏	PROPN
cana-3294	145	49	(	(	PUNCT
cana-3294	145	50	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	𝜸𝒏,𝒏+𝟏+𝜹𝒏,𝒏+𝟏	PROPN
cana-3294	145	51	𝟏−𝜸𝒏,𝒏+𝟏	𝟏−𝜸𝒏,𝒏+𝟏	PROPN
cana-3294	145	52	)	)	PUNCT
cana-3294	146	1	m−1	m−1	PROPN
cana-3294	146	2	n=0	n=0	PUNCT
cana-3294	146	3	g	g	NOUN
cana-3294	146	4	(	(	PUNCT
cana-3294	146	5	gν0	gν0	NOUN
cana-3294	146	6	,	,	PUNCT
cana-3294	146	7	gν1	gν1	NOUN
cana-3294	146	8	,	,	PUNCT
cana-3294	146	9	gν1	gν1	NOUN
cana-3294	146	10	)	)	PUNCT
cana-3294	146	11	-------(8	-------(8	NOUN
cana-3294	146	12	)	)	PUNCT
cana-3294	146	13	adding	add	VERB
cana-3294	146	14	(	(	PUNCT
cana-3294	146	15	6	6	NUM
cana-3294	146	16	)	)	PUNCT
cana-3294	146	17	,	,	PUNCT
cana-3294	146	18	(	(	PUNCT
cana-3294	146	19	7	7	NUM
cana-3294	146	20	)	)	PUNCT
cana-3294	146	21	,	,	PUNCT
cana-3294	146	22	(	(	PUNCT
cana-3294	146	23	8)	8)	NUM
cana-3294	146	24	we	we	PRON
cana-3294	146	25	get	get	VERB
cana-3294	146	26	g	g	NOUN
cana-3294	146	27	(	(	PUNCT
cana-3294	146	28	gλm	gλm	NOUN
cana-3294	146	29	,	,	PUNCT
cana-3294	146	30	gλm+1	gλm+1	X
cana-3294	146	31	,	,	PUNCT
cana-3294	146	32	gλm+1	gλm+1	PROPN
cana-3294	146	33	)	)	PUNCT
cana-3294	147	1	+	+	CCONJ
cana-3294	147	2	g	g	PROPN
cana-3294	147	3	(	(	PUNCT
cana-3294	147	4	gμm	gμm	PROPN
cana-3294	147	5	,	,	PUNCT
cana-3294	147	6	gμm+1	gμm+1	PROPN
cana-3294	147	7	,	,	PUNCT
cana-3294	147	8	gμm+1	gμm+1	PROPN
cana-3294	147	9	)	)	PUNCT
cana-3294	147	10	+	+	CCONJ
cana-3294	147	11	g	g	PROPN
cana-3294	147	12	(	(	PUNCT
cana-3294	147	13	νm	νm	PROPN
cana-3294	147	14	,	,	PUNCT
cana-3294	147	15	νm+1	νm+1	PROPN
cana-3294	147	16	,	,	PUNCT
cana-3294	147	17	νm+1	νm+1	PROPN
cana-3294	147	18	)	)	PUNCT
cana-3294	147	19	≤	≤	NOUN
cana-3294	147	20	∏	∏	PROPN
cana-3294	147	21	(	(	PUNCT
cana-3294	147	22	γ	γ	PROPN
cana-3294	147	23	n	n	CCONJ
cana-3294	147	24	,	,	PUNCT
cana-3294	147	25	n+1	n+1	PROPN
cana-3294	147	26	+	+	NOUN
cana-3294	147	27	δn	δn	ADJ
cana-3294	147	28	,	,	PUNCT
cana-3294	147	29	n+1	n+1	PROPN
cana-3294	147	30	1−γ	1−γ	NUM
cana-3294	147	31	n	n	CCONJ
cana-3294	147	32	,	,	PUNCT
cana-3294	147	33	n+1	n+1	PROPN
cana-3294	147	34	𝒎−1	𝒎−1	PROPN
cana-3294	147	35	n=0	n=0	NUM
cana-3294	147	36	)	)	PUNCT
cana-3294	148	1	[	[	X
cana-3294	148	2	g	g	X
cana-3294	148	3	(	(	PUNCT
cana-3294	148	4	gλ0	gλ0	NOUN
cana-3294	148	5	,	,	PUNCT
cana-3294	148	6	gλ1	gλ1	PROPN
cana-3294	148	7	,	,	PUNCT
cana-3294	148	8	gλ1	gλ1	PROPN
cana-3294	148	9	)	)	PUNCT
cana-3294	149	1	+	+	CCONJ
cana-3294	149	2	g	g	PROPN
cana-3294	149	3	(	(	PUNCT
cana-3294	149	4	gμ0	gμ0	PROPN
cana-3294	149	5	,	,	PUNCT
cana-3294	149	6	gμ1	gμ1	NOUN
cana-3294	149	7	,	,	PUNCT
cana-3294	149	8	gμ1	gμ1	NOUN
cana-3294	149	9	)	)	PUNCT
cana-3294	150	1	+	+	CCONJ
cana-3294	150	2	g	g	PROPN
cana-3294	150	3	(	(	PUNCT
cana-3294	150	4	gν0	gν0	NOUN
cana-3294	150	5	,	,	PUNCT
cana-3294	150	6	gν1	gν1	NOUN
cana-3294	150	7	,	,	PUNCT
cana-3294	150	8	gν1	gν1	PROPN
cana-3294	150	9	)	)	PUNCT
cana-3294	150	10	]	]	PUNCT
cana-3294	151	1	let	let	VERB
cana-3294	151	2	βm	βm	VERB
cana-3294	151	3	≤	≤	ADJ
cana-3294	151	4	∏	∏	PROPN
cana-3294	151	5	(	(	PUNCT
cana-3294	151	6	γ	γ	PROPN
cana-3294	151	7	n	n	CCONJ
cana-3294	151	8	,	,	PUNCT
cana-3294	151	9	n+1	n+1	PROPN
cana-3294	151	10	+	+	NOUN
cana-3294	151	11	δn	δn	ADJ
cana-3294	151	12	,	,	PUNCT
cana-3294	151	13	n+1	n+1	PROPN
cana-3294	151	14	1−γ	1−γ	NUM
cana-3294	151	15	n	n	CCONJ
cana-3294	151	16	,	,	PUNCT
cana-3294	151	17	n+1	n+1	PROPN
cana-3294	151	18	)	)	PUNCT
cana-3294	151	19	m−1	m−1	PROPN
cana-3294	151	20	n=0	n=0	PUNCT
cana-3294	152	1	β0	β0	NOUN
cana-3294	152	2	where	where	SCONJ
cana-3294	152	3	βm	βm	ADP
cana-3294	152	4	=	=	SYM
cana-3294	152	5	g	g	PROPN
cana-3294	152	6	(	(	PUNCT
cana-3294	152	7	gλm	gλm	NOUN
cana-3294	152	8	,	,	PUNCT
cana-3294	152	9	gλm+1	gλm+1	X
cana-3294	152	10	,	,	PUNCT
cana-3294	152	11	gλm+1	gλm+1	PROPN
cana-3294	152	12	)	)	PUNCT
cana-3294	153	1	+	+	CCONJ
cana-3294	153	2	g	g	PROPN
cana-3294	153	3	(	(	PUNCT
cana-3294	153	4	gμm	gμm	PROPN
cana-3294	153	5	,	,	PUNCT
cana-3294	153	6	gμm+1	gμm+1	PROPN
cana-3294	153	7	,	,	PUNCT
cana-3294	153	8	gμm+1	gμm+1	PROPN
cana-3294	153	9	)	)	PUNCT
cana-3294	153	10	+	+	CCONJ
cana-3294	153	11	g(νm	g(νm	X
cana-3294	153	12	,	,	PUNCT
cana-3294	153	13	νm+1,νm+1	νm+1,νm+1	X
cana-3294	153	14	)	)	PUNCT
cana-3294	153	15	.	.	PUNCT
cana-3294	154	1	for	for	ADP
cana-3294	154	2	p	p	PROPN
cana-3294	154	3	>	>	X
cana-3294	154	4	0	0	PUNCT
cana-3294	154	5	and	and	CCONJ
cana-3294	154	6	by	by	ADP
cana-3294	154	7	using	use	VERB
cana-3294	154	8	(	(	PUNCT
cana-3294	154	9	g5	g5	NOUN
cana-3294	154	10	)	)	PUNCT
cana-3294	154	11	,	,	PUNCT
cana-3294	154	12	we	we	PRON
cana-3294	154	13	have	have	VERB
cana-3294	154	14	communications	communication	NOUN
cana-3294	154	15	on	on	ADP
cana-3294	154	16	applied	apply	VERB
cana-3294	154	17	nonlinear	nonlinear	ADJ
cana-3294	154	18	analysis	analysis	NOUN
cana-3294	154	19	issn	issn	NOUN
cana-3294	154	20	:	:	PUNCT
cana-3294	154	21	1074	1074	NUM
cana-3294	154	22	-	-	PUNCT
cana-3294	154	23	133x	133x	NUM
cana-3294	154	24	vol	vol	NOUN
cana-3294	154	25	32	32	NUM
cana-3294	154	26	no	no	NOUN
cana-3294	154	27	.	.	PUNCT
cana-3294	155	1	6s	6s	NUM
cana-3294	155	2	(	(	PUNCT
cana-3294	155	3	2025	2025	NUM
cana-3294	155	4	)	)	PUNCT
cana-3294	155	5	281	281	NUM
cana-3294	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	155	7	g(gλm	g(gλm	PROPN
cana-3294	155	8	,	,	PUNCT
cana-3294	155	9	gλm+p	gλm+p	PROPN
cana-3294	155	10	,	,	PUNCT
cana-3294	155	11	gλm+p)+	gλm+p)+	PROPN
cana-3294	155	12	g(gμm	g(gμm	PROPN
cana-3294	155	13	,	,	PUNCT
cana-3294	155	14	gμm+p	gμm+p	PROPN
cana-3294	155	15	,	,	PUNCT
cana-3294	155	16	gμm+p)+	gμm+p)+	PROPN
cana-3294	155	17	g(νm	g(νm	PROPN
cana-3294	155	18	,	,	PUNCT
cana-3294	155	19	νm+p	νm+p	NOUN
cana-3294	155	20	,	,	PUNCT
cana-3294	155	21	νm+p	νm+p	NOUN
cana-3294	155	22	)	)	PUNCT
cana-3294	155	23	≤	≤	NOUN
cana-3294	155	24	g(gλm	g(gλm	PROPN
cana-3294	155	25	,	,	PUNCT
cana-3294	155	26	gλm+1	gλm+1	PROPN
cana-3294	155	27	,	,	PUNCT
cana-3294	155	28	gλm+1)+	gλm+1)+	PROPN
cana-3294	155	29	g(gμm	g(gμm	PROPN
cana-3294	155	30	,	,	PUNCT
cana-3294	155	31	gμm+1,gμm+1)+	gμm+1,gμm+1)+	VERB
cana-3294	155	32	g(νm	g(νm	NOUN
cana-3294	155	33	,	,	PUNCT
cana-3294	155	34	νm+1,νm+1)+	νm+1,νm+1)+	PROPN
cana-3294	155	35	g(gλm+1,gλm+2	g(gλm+1,gλm+2	PROPN
cana-3294	155	36	,	,	PUNCT
cana-3294	155	37	gλm+2)+	gλm+2)+	PROPN
cana-3294	155	38	g(gμm+1,gμm+2,gμm+2)+	g(gμm+1,gμm+2,gμm+2)+	NOUN
cana-3294	155	39	g(νm+1,νm+2,νm+2)+----+	g(νm+1,νm+2,νm+2)+----+	PROPN
cana-3294	155	40	g(gλm+p-1	g(gλm+p-1	NOUN
cana-3294	155	41	,	,	PUNCT
cana-3294	155	42	gλm+p	gλm+p	PROPN
cana-3294	155	43	,	,	PUNCT
cana-3294	155	44	gλm+p)+	gλm+p)+	PROPN
cana-3294	155	45	g(gμm+p-1,gμm+p	g(gμm+p-1,gμm+p	PROPN
cana-3294	155	46	,	,	PUNCT
cana-3294	155	47	gμm+p)+	gμm+p)+	PROPN
cana-3294	155	48	g(νm+p-1,νm+p	g(νm+p-1,νm+p	NOUN
cana-3294	155	49	,	,	PUNCT
cana-3294	155	50	νm+p	νm+p	NOUN
cana-3294	155	51	)	)	PUNCT
cana-3294	155	52	≤∏	≤∏	NOUN
cana-3294	155	53	(	(	PUNCT
cana-3294	155	54	γ	γ	PROPN
cana-3294	155	55	n	n	CCONJ
cana-3294	155	56	,	,	PUNCT
cana-3294	155	57	n+1	n+1	PROPN
cana-3294	155	58	+	+	NOUN
cana-3294	155	59	δn	δn	ADJ
cana-3294	155	60	,	,	PUNCT
cana-3294	155	61	n+1	n+1	PROPN
cana-3294	155	62	1−γ	1−γ	NUM
cana-3294	155	63	n	n	CCONJ
cana-3294	155	64	,	,	PUNCT
cana-3294	155	65	n+1	n+1	PART
cana-3294	155	66	)	)	PUNCT
cana-3294	155	67	β	β	X
cana-3294	155	68	0	0	PUNCT
cana-3294	156	1	𝒎−1	𝒎−1	ADJ
cana-3294	156	2	n=0	n=0	PROPN
cana-3294	156	3	+	+	NUM
cana-3294	156	4	∏	∏	PROPN
cana-3294	156	5	(	(	PUNCT
cana-3294	156	6	γ	γ	PROPN
cana-3294	156	7	n	n	CCONJ
cana-3294	156	8	,	,	PUNCT
cana-3294	156	9	n+1	n+1	PROPN
cana-3294	156	10	+	+	NOUN
cana-3294	156	11	δn	δn	ADJ
cana-3294	156	12	,	,	PUNCT
cana-3294	156	13	n+1	n+1	PROPN
cana-3294	156	14	1−γ	1−γ	NUM
cana-3294	156	15	n	n	CCONJ
cana-3294	156	16	,	,	PUNCT
cana-3294	156	17	n+1	n+1	PART
cana-3294	156	18	)	)	PUNCT
cana-3294	156	19	β	β	NOUN
cana-3294	156	20	0	0	NUM
cana-3294	156	21	𝒎	𝒎	PROPN
cana-3294	156	22	n=0	n=0	PROPN
cana-3294	156	23	+	+	NUM
cana-3294	156	24	---+∏	---+∏	PROPN
cana-3294	156	25	(	(	PUNCT
cana-3294	156	26	γ	γ	X
cana-3294	156	27	n	n	CCONJ
cana-3294	156	28	,	,	PUNCT
cana-3294	156	29	n+1	n+1	PROPN
cana-3294	156	30	+	+	NOUN
cana-3294	156	31	δn	δn	ADJ
cana-3294	156	32	,	,	PUNCT
cana-3294	156	33	n+1	n+1	PROPN
cana-3294	156	34	1−γ	1−γ	NUM
cana-3294	156	35	n	n	CCONJ
cana-3294	156	36	,	,	PUNCT
cana-3294	156	37	n+1	n+1	NUM
cana-3294	156	38	)	)	PUNCT
cana-3294	156	39	𝒎+𝒎−2	𝒎+𝒎−2	X
cana-3294	156	40	n=0	n=0	PUNCT
cana-3294	156	41	β	β	NOUN
cana-3294	156	42	0	0	NUM
cana-3294	156	43	≤∑	≤∑	PROPN
cana-3294	156	44	∏	∏	PROPN
cana-3294	156	45	(	(	PUNCT
cana-3294	156	46	γ	γ	PROPN
cana-3294	156	47	n	n	CCONJ
cana-3294	156	48	,	,	PUNCT
cana-3294	156	49	n+1	n+1	PROPN
cana-3294	156	50	+	+	NOUN
cana-3294	156	51	δn	δn	ADJ
cana-3294	156	52	,	,	PUNCT
cana-3294	156	53	n+1	n+1	PROPN
cana-3294	156	54	1−γ	1−γ	NUM
cana-3294	156	55	n	n	CCONJ
cana-3294	156	56	,	,	PUNCT
cana-3294	156	57	n+1	n+1	X
cana-3294	156	58	)	)	PUNCT
cana-3294	156	59	𝑚+𝑚−1	𝑚+𝑚−1	PROPN
cana-3294	156	60	𝑚=0	𝑚=0	SYM
cana-3294	156	61	𝑚−1	𝑚−1	PROPN
cana-3294	156	62	𝑚=0	𝑚=0	PUNCT
cana-3294	156	63	β0	β0	NOUN
cana-3294	156	64	≤∑	≤∑	PROPN
cana-3294	156	65	∏	∏	PROPN
cana-3294	156	66	(	(	PUNCT
cana-3294	156	67	γ	γ	PROPN
cana-3294	156	68	n	n	CCONJ
cana-3294	156	69	,	,	PUNCT
cana-3294	156	70	n+1	n+1	PROPN
cana-3294	156	71	+	+	NOUN
cana-3294	156	72	δn	δn	ADJ
cana-3294	156	73	,	,	PUNCT
cana-3294	156	74	n+1	n+1	PROPN
cana-3294	156	75	1−γ	1−γ	NUM
cana-3294	156	76	n	n	CCONJ
cana-3294	156	77	,	,	PUNCT
cana-3294	156	78	n+1	n+1	NUM
cana-3294	156	79	)	)	PUNCT
cana-3294	156	80	𝑚−1	𝑚−1	PROPN
cana-3294	156	81	𝑚=0	𝑚=0	SYM
cana-3294	156	82	𝑚+𝑚−1	𝑚+𝑚−1	PROPN
cana-3294	156	83	𝑚=𝑚	𝑚=𝑚	PROPN
cana-3294	156	84	β0	β0	PROPN
cana-3294	156	85	g(gλm	g(gλm	PROPN
cana-3294	156	86	,	,	PUNCT
cana-3294	156	87	gλm+p	gλm+p	PROPN
cana-3294	156	88	,	,	PUNCT
cana-3294	156	89	gλm+p)+	gλm+p)+	PROPN
cana-3294	156	90	g(gμm	g(gμm	PROPN
cana-3294	156	91	,	,	PUNCT
cana-3294	156	92	gμm+p	gμm+p	PROPN
cana-3294	156	93	,	,	PUNCT
cana-3294	156	94	gμm+p)+	gμm+p)+	PROPN
cana-3294	156	95	g(νm	g(νm	PROPN
cana-3294	156	96	,	,	PUNCT
cana-3294	156	97	νm+p	νm+p	NOUN
cana-3294	156	98	,	,	PUNCT
cana-3294	156	99	νm+p	νm+p	NOUN
cana-3294	156	100	)	)	PUNCT
cana-3294	156	101	≤∑	≤∑	PROPN
cana-3294	156	102	∏	∏	PROPN
cana-3294	156	103	(	(	PUNCT
cana-3294	156	104	γn	γn	NUM
cana-3294	156	105	,	,	PUNCT
cana-3294	156	106	n+1+δn	n+1+δn	PROPN
cana-3294	156	107	,	,	PUNCT
cana-3294	156	108	n+1	n+1	PROPN
cana-3294	156	109	1−γn	1−γn	NUM
cana-3294	156	110	,	,	PUNCT
cana-3294	156	111	n+1	n+1	NUM
cana-3294	156	112	)	)	PUNCT
cana-3294	156	113	𝑘−1	𝑘−1	PROPN
cana-3294	157	1	𝑛=0	𝑛=0	PROPN
cana-3294	157	2	𝑚+𝑝−1	𝑚+𝑝−1	PROPN
cana-3294	157	3	𝑘=𝑚	𝑘=𝑚	PROPN
cana-3294	157	4	β0	β0	NOUN
cana-3294	157	5	…	…	PUNCT
cana-3294	157	6	…	…	PUNCT
cana-3294	157	7	(	(	PUNCT
cana-3294	157	8	9	9	NUM
cana-3294	157	9	)	)	PUNCT
cana-3294	157	10	by	by	ADP
cana-3294	157	11	the	the	DET
cana-3294	157	12	fact	fact	NOUN
cana-3294	157	13	that	that	SCONJ
cana-3294	157	14	the	the	DET
cana-3294	157	15	arithmetic	arithmetic	ADJ
cana-3294	157	16	mean	mean	NOUN
cana-3294	157	17	is	be	AUX
cana-3294	157	18	greater	great	ADJ
cana-3294	157	19	than	than	ADP
cana-3294	157	20	or	or	CCONJ
cana-3294	157	21	equal	equal	ADJ
cana-3294	157	22	to	to	ADP
cana-3294	157	23	geometric	geometric	ADJ
cana-3294	157	24	mean	mean	NOUN
cana-3294	157	25	for	for	ADP
cana-3294	157	26	non	non	ADJ
cana-3294	157	27	-	-	ADJ
cana-3294	157	28	negative	negative	ADJ
cana-3294	157	29	real	real	ADJ
cana-3294	157	30	numbers	number	NOUN
cana-3294	157	31	and	and	CCONJ
cana-3294	157	32	α	α	NOUN
cana-3294	157	33	,	,	PUNCT
cana-3294	157	34	nα	nα	PRON
cana-3294	157	35	are	be	AUX
cana-3294	157	36	like	like	ADP
cana-3294	157	37	in	in	ADP
cana-3294	157	38	definition	definition	NOUN
cana-3294	157	39	2.9	2.9	NUM
cana-3294	157	40	for	for	ADP
cana-3294	157	41	m≥	m≥	PROPN
cana-3294	157	42	nα	nα	NOUN
cana-3294	157	43	follows	follow	VERB
cana-3294	157	44	as	as	ADP
cana-3294	157	45	below	below	ADP
cana-3294	157	46	∑	∑	PROPN
cana-3294	157	47	∏	∏	PROPN
cana-3294	157	48	(	(	PUNCT
cana-3294	157	49	γ	γ	PROPN
cana-3294	157	50	n	n	CCONJ
cana-3294	157	51	,	,	PUNCT
cana-3294	157	52	n+1	n+1	PROPN
cana-3294	158	1	+	+	NOUN
cana-3294	158	2	δn	δn	ADJ
cana-3294	158	3	,	,	PUNCT
cana-3294	158	4	n+1	n+1	PROPN
cana-3294	158	5	1−γ	1−γ	NUM
cana-3294	158	6	n	n	CCONJ
cana-3294	158	7	,	,	PUNCT
cana-3294	158	8	n+1	n+1	NUM
cana-3294	158	9	)	)	PUNCT
cana-3294	158	10	𝑘−1	𝑘−1	PROPN
cana-3294	158	11	𝑛=0	𝑛=0	PROPN
cana-3294	159	1	𝑚+𝑝−1	𝑚+𝑝−1	PROPN
cana-3294	159	2	𝑘=𝑚	𝑘=𝑚	ADJ
cana-3294	159	3	≤	≤	NOUN
cana-3294	159	4	∑	∑	PUNCT
cana-3294	159	5	[	[	PUNCT
cana-3294	159	6	1	1	NUM
cana-3294	159	7	𝑘	𝑘	X
cana-3294	159	8	∑	∑	PROPN
cana-3294	159	9	(	(	PUNCT
cana-3294	159	10	γ	γ	PROPN
cana-3294	159	11	n	n	CCONJ
cana-3294	159	12	,	,	PUNCT
cana-3294	159	13	n+1	n+1	PROPN
cana-3294	159	14	+	+	NOUN
cana-3294	159	15	δn	δn	ADJ
cana-3294	159	16	,	,	PUNCT
cana-3294	159	17	n+1	n+1	PROPN
cana-3294	159	18	1−γ	1−γ	NUM
cana-3294	159	19	n	n	CCONJ
cana-3294	159	20	,	,	PUNCT
cana-3294	159	21	n+1	n+1	NUM
cana-3294	159	22	)	)	PUNCT
cana-3294	159	23	𝑘−1	𝑘−1	PROPN
cana-3294	160	1	𝑛=0	𝑛=0	PROPN
cana-3294	160	2	𝑚+𝑝−1	𝑚+𝑝−1	PROPN
cana-3294	161	1	𝑘=𝑚	𝑘=𝑚	PROPN
cana-3294	161	2	]	]	X
cana-3294	161	3	k	k	X
cana-3294	161	4	…	…	PUNCT
cana-3294	161	5	…	…	PUNCT
cana-3294	161	6	…	…	PUNCT
cana-3294	161	7	…	…	PUNCT
cana-3294	161	8	……	……	NOUN
cana-3294	161	9	……	……	NOUN
cana-3294	161	10	……	……	NOUN
cana-3294	161	11	(	(	PUNCT
cana-3294	161	12	10	10	NUM
cana-3294	161	13	)	)	PUNCT
cana-3294	161	14	from	from	ADP
cana-3294	161	15	(	(	PUNCT
cana-3294	161	16	9	9	NUM
cana-3294	161	17	)	)	PUNCT
cana-3294	161	18	and	and	CCONJ
cana-3294	161	19	(	(	PUNCT
cana-3294	161	20	10	10	NUM
cana-3294	161	21	)	)	PUNCT
cana-3294	161	22	∴	∴	PROPN
cana-3294	161	23	g(gλm	g(gλm	PROPN
cana-3294	161	24	,	,	PUNCT
cana-3294	161	25	gλm+p	gλm+p	PROPN
cana-3294	161	26	,	,	PUNCT
cana-3294	161	27	gλm+p)+	gλm+p)+	PROPN
cana-3294	161	28	g(gμm	g(gμm	PROPN
cana-3294	161	29	,	,	PUNCT
cana-3294	161	30	gμm+p	gμm+p	PROPN
cana-3294	161	31	,	,	PUNCT
cana-3294	161	32	gμm+p)+	gμm+p)+	PROPN
cana-3294	161	33	g(νm	g(νm	PROPN
cana-3294	161	34	,	,	PUNCT
cana-3294	161	35	νm+p	νm+p	NOUN
cana-3294	161	36	,	,	PUNCT
cana-3294	161	37	νm+p	νm+p	NOUN
cana-3294	161	38	)	)	PUNCT
cana-3294	161	39	≤	≤	NOUN
cana-3294	161	40	∑	∑	PUNCT
cana-3294	161	41	[	[	PUNCT
cana-3294	161	42	1	1	NUM
cana-3294	161	43	𝑘	𝑘	X
cana-3294	161	44	∑	∑	PROPN
cana-3294	161	45	(	(	PUNCT
cana-3294	161	46	γ	γ	PROPN
cana-3294	161	47	n	n	CCONJ
cana-3294	161	48	,	,	PUNCT
cana-3294	161	49	n+1	n+1	PROPN
cana-3294	161	50	+	+	NOUN
cana-3294	161	51	δn	δn	ADJ
cana-3294	161	52	,	,	PUNCT
cana-3294	161	53	n+1	n+1	PROPN
cana-3294	161	54	1−γ	1−γ	NUM
cana-3294	161	55	n	n	CCONJ
cana-3294	161	56	,	,	PUNCT
cana-3294	161	57	n+1	n+1	NUM
cana-3294	161	58	)	)	PUNCT
cana-3294	161	59	𝑘−1	𝑘−1	PROPN
cana-3294	162	1	𝑛=0	𝑛=0	PROPN
cana-3294	162	2	𝑚+𝑝−1	𝑚+𝑝−1	PROPN
cana-3294	163	1	𝑘=𝑚	𝑘=𝑚	PROPN
cana-3294	163	2	]	]	X
cana-3294	163	3	k	k	PROPN
cana-3294	163	4	β0	β0	PROPN
cana-3294	163	5	≤	≤	PROPN
cana-3294	163	6	(	(	PUNCT
cana-3294	163	7	∑	∑	PUNCT
cana-3294	163	8	αkm+p−1	αkm+p−1	NOUN
cana-3294	163	9	k	k	NOUN
cana-3294	163	10	=	=	NOUN
cana-3294	163	11	m	m	NOUN
cana-3294	163	12	)	)	PUNCT
cana-3294	164	1	β	β	X
cana-3294	164	2	where	where	SCONJ
cana-3294	164	3	α	α	NOUN
cana-3294	164	4	=	=	NOUN
cana-3294	164	5	1	1	NUM
cana-3294	164	6	𝑘	𝑘	NOUN
cana-3294	164	7	∑	∑	PROPN
cana-3294	164	8	(	(	PUNCT
cana-3294	164	9	γ	γ	PROPN
cana-3294	164	10	n	n	CCONJ
cana-3294	164	11	,	,	PUNCT
cana-3294	164	12	n+1	n+1	PROPN
cana-3294	164	13	+	+	NOUN
cana-3294	164	14	δn	δn	ADJ
cana-3294	164	15	,	,	PUNCT
cana-3294	164	16	n+1	n+1	PROPN
cana-3294	164	17	1−γ	1−γ	NUM
cana-3294	164	18	n	n	CCONJ
cana-3294	164	19	,	,	PUNCT
cana-3294	164	20	n+1	n+1	NUM
cana-3294	164	21	)	)	PUNCT
cana-3294	164	22	𝑘−1	𝑘−1	PROPN
cana-3294	164	23	𝑛=0	𝑛=0	PROPN
cana-3294	164	24	≤	≤	NUM
cana-3294	164	25	(	(	PUNCT
cana-3294	164	26	αm	αm	NOUN
cana-3294	164	27	+	+	CCONJ
cana-3294	164	28	αm+1	αm+1	NUM
cana-3294	164	29	+	+	SYM
cana-3294	164	30	αm+2	αm+2	NOUN
cana-3294	164	31	+	+	NOUN
cana-3294	164	32	-----+αm+p−1	-----+αm+p−1	ADJ
cana-3294	164	33	)	)	PUNCT
cana-3294	164	34	β0	β0	ADJ
cana-3294	164	35	≤	≤	NOUN
cana-3294	164	36	αm(1+α1+α2	αm(1+α1+α2	PUNCT
cana-3294	164	37	+	+	PROPN
cana-3294	164	38	------+αp−1	------+αp−1	ADJ
cana-3294	164	39	)	)	PUNCT
cana-3294	164	40	β0	β0	ADJ
cana-3294	164	41	≤	≤	NOUN
cana-3294	164	42	(	(	PUNCT
cana-3294	164	43	αm	αm	NOUN
cana-3294	164	44	1−α	1−α	NUM
cana-3294	164	45	)	)	PUNCT
cana-3294	164	46	β0	β0	NOUN
cana-3294	164	47	g	g	PROPN
cana-3294	164	48	(	(	PUNCT
cana-3294	164	49	gλm	gλm	NOUN
cana-3294	164	50	,	,	PUNCT
cana-3294	164	51	gλm+p	gλm+p	PROPN
cana-3294	164	52	,	,	PUNCT
cana-3294	164	53	gλm+p	gλm+p	NOUN
cana-3294	164	54	)	)	PUNCT
cana-3294	165	1	+	+	CCONJ
cana-3294	165	2	g	g	PROPN
cana-3294	165	3	(	(	PUNCT
cana-3294	165	4	gμm	gμm	PROPN
cana-3294	165	5	,	,	PUNCT
cana-3294	165	6	gμm+p	gμm+p	NOUN
cana-3294	165	7	,	,	PUNCT
cana-3294	165	8	gμm+p	gμm+p	NOUN
cana-3294	165	9	)	)	PUNCT
cana-3294	166	1	+	+	CCONJ
cana-3294	166	2	g	g	PROPN
cana-3294	166	3	(	(	PUNCT
cana-3294	166	4	gνm	gνm	NOUN
cana-3294	166	5	,	,	PUNCT
cana-3294	166	6	gνm+p	gνm+p	PROPN
cana-3294	166	7	,	,	PUNCT
cana-3294	166	8	gνm+p	gνm+p	NUM
cana-3294	166	9	)	)	PUNCT
cana-3294	167	1	+	+	CCONJ
cana-3294	167	2	g	g	PROPN
cana-3294	167	3	(	(	PUNCT
cana-3294	167	4	gνm	gνm	NOUN
cana-3294	167	5	,	,	PUNCT
cana-3294	167	6	gνm+p	gνm+p	PROPN
cana-3294	167	7	,	,	PUNCT
cana-3294	167	8	gνm+p	gνm+p	NOUN
cana-3294	167	9	)	)	PUNCT
cana-3294	167	10	≤	≤	NOUN
cana-3294	167	11	(	(	PUNCT
cana-3294	167	12	αm	αm	NOUN
cana-3294	167	13	1−α	1−α	NUM
cana-3294	167	14	)	)	PUNCT
cana-3294	167	15	β0	β0	ADV
cana-3294	167	16	now	now	ADV
cana-3294	167	17	letting	let	VERB
cana-3294	167	18	the	the	DET
cana-3294	167	19	limit	limit	NOUN
cana-3294	167	20	as	as	ADP
cana-3294	167	21	m	m	PROPN
cana-3294	167	22	,	,	PUNCT
cana-3294	167	23	𝑝	𝑝	PROPN
cana-3294	167	24	→	→	SYM
cana-3294	167	25	∞	∞	PROPN
cana-3294	167	26	,	,	PUNCT
cana-3294	167	27	we	we	PRON
cana-3294	167	28	obtain	obtain	VERB
cana-3294	167	29	lim	lim	PROPN
cana-3294	167	30	𝑚→∞	𝑚→∞	PUNCT
cana-3294	167	31	g	g	PROPN
cana-3294	167	32	(	(	PUNCT
cana-3294	167	33	gλm	gλm	NOUN
cana-3294	167	34	,	,	PUNCT
cana-3294	167	35	gλm+p	gλm+p	PROPN
cana-3294	167	36	,	,	PUNCT
cana-3294	167	37	gλm+p	gλm+p	NOUN
cana-3294	167	38	)	)	PUNCT
cana-3294	168	1	+	+	CCONJ
cana-3294	168	2	g	g	PROPN
cana-3294	168	3	(	(	PUNCT
cana-3294	168	4	(	(	PUNCT
cana-3294	168	5	gμm	gμm	X
cana-3294	168	6	,	,	PUNCT
cana-3294	168	7	gμm+p	gμm+p	NOUN
cana-3294	168	8	,	,	PUNCT
cana-3294	168	9	gμm+p	gμm+p	NOUN
cana-3294	168	10	)	)	PUNCT
cana-3294	169	1	+	+	CCONJ
cana-3294	169	2	g	g	PROPN
cana-3294	169	3	(	(	PUNCT
cana-3294	169	4	gνm	gνm	NOUN
cana-3294	169	5	,	,	PUNCT
cana-3294	169	6	gνm+p	gνm+p	PROPN
cana-3294	169	7	,	,	PUNCT
cana-3294	169	8	gνm+p	gνm+p	NOUN
cana-3294	169	9	)	)	PUNCT
cana-3294	169	10	=	=	SYM
cana-3294	169	11	0	0	PUNCT
cana-3294	170	1	since	since	SCONJ
cana-3294	170	2	0	0	NUM
cana-3294	170	3	<	<	X
cana-3294	170	4	α	α	X
cana-3294	170	5	<	<	X
cana-3294	170	6	1	1	NUM
cana-3294	170	7	further	far	ADV
cana-3294	170	8	which	which	PRON
cana-3294	170	9	implies	imply	VERB
cana-3294	170	10	that	that	SCONJ
cana-3294	170	11	lim	lim	PROPN
cana-3294	170	12	𝑚→∞	𝑚→∞	NUM
cana-3294	170	13	g(gλm	g(gλm	PROPN
cana-3294	170	14	,	,	PUNCT
cana-3294	170	15	gλm+p	gλm+p	PROPN
cana-3294	170	16	,	,	PUNCT
cana-3294	170	17	gλm+p	gλm+p	NOUN
cana-3294	170	18	)	)	PUNCT
cana-3294	170	19	=	=	SYM
cana-3294	170	20	0	0	NUM
cana-3294	170	21	lim	lim	PROPN
cana-3294	170	22	𝑚→∞	𝑚→∞	PUNCT
cana-3294	170	23	g	g	PROPN
cana-3294	170	24	(	(	PUNCT
cana-3294	170	25	g𝜇𝑚	g𝜇𝑚	ADJ
cana-3294	170	26	,	,	PUNCT
cana-3294	170	27	g𝜇𝑚+𝑝	g𝜇𝑚+𝑝	PROPN
cana-3294	170	28	,	,	PUNCT
cana-3294	170	29	g𝜇𝑚+𝑝	g𝜇𝑚+𝑝	NUM
cana-3294	170	30	)	)	PUNCT
cana-3294	170	31	=	=	SYM
cana-3294	170	32	0	0	PUNCT
cana-3294	171	1	(	(	PUNCT
cana-3294	171	2	11	11	NUM
cana-3294	171	3	)	)	PUNCT
cana-3294	171	4	lim	lim	NOUN
cana-3294	171	5	𝑚→∞	𝑚→∞	NUM
cana-3294	171	6	𝐺(gν𝑚	𝐺(gν𝑚	NUM
cana-3294	171	7	,	,	PUNCT
cana-3294	171	8	gν𝑚+𝑝	gν𝑚+𝑝	PROPN
cana-3294	171	9	,	,	PUNCT
cana-3294	171	10	gν	gν	ADJ
cana-3294	171	11	𝑚+𝑝	𝑚+𝑝	PROPN
cana-3294	171	12	)	)	PUNCT
cana-3294	171	13	)	)	PUNCT
cana-3294	172	1	=	=	SYM
cana-3294	172	2	0	0	NUM
cana-3294	172	3	communications	communication	NOUN
cana-3294	172	4	on	on	ADP
cana-3294	172	5	applied	apply	VERB
cana-3294	172	6	nonlinear	nonlinear	ADJ
cana-3294	172	7	analysis	analysis	NOUN
cana-3294	172	8	issn	issn	NOUN
cana-3294	172	9	:	:	PUNCT
cana-3294	172	10	1074	1074	NUM
cana-3294	172	11	-	-	PUNCT
cana-3294	172	12	133x	133x	NUM
cana-3294	172	13	vol	vol	NOUN
cana-3294	172	14	32	32	NUM
cana-3294	172	15	no	no	NOUN
cana-3294	172	16	.	.	PUNCT
cana-3294	173	1	6s	6s	NUM
cana-3294	173	2	(	(	PUNCT
cana-3294	173	3	2025	2025	NUM
cana-3294	173	4	)	)	PUNCT
cana-3294	173	5	282	282	NUM
cana-3294	173	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	173	7	thus	thus	ADV
cana-3294	173	8	,	,	PUNCT
cana-3294	173	9	{	{	PUNCT
cana-3294	173	10	g𝜆𝑚	g𝜆𝑚	PROPN
cana-3294	173	11	}	}	PUNCT
cana-3294	173	12	,	,	PUNCT
cana-3294	173	13	{	{	PUNCT
cana-3294	173	14	gμm	gμm	PROPN
cana-3294	173	15	}	}	PUNCT
cana-3294	173	16	,	,	PUNCT
cana-3294	173	17	{	{	PUNCT
cana-3294	173	18	gνm	gνm	AUX
cana-3294	173	19	}	}	PUNCT
cana-3294	173	20	are	be	AUX
cana-3294	173	21	cauchey	cauchey	PROPN
cana-3294	173	22	sequences	sequence	NOUN
cana-3294	173	23	in	in	ADP
cana-3294	173	24	℧	℧	PROPN
cana-3294	173	25	.	.	PUNCT
cana-3294	174	1	since	since	SCONJ
cana-3294	174	2	g	g	PROPN
cana-3294	174	3	(	(	PUNCT
cana-3294	174	4	℧	℧	NOUN
cana-3294	174	5	)	)	PUNCT
cana-3294	174	6	is	be	AUX
cana-3294	174	7	closed	close	VERB
cana-3294	174	8	and	and	CCONJ
cana-3294	174	9	by	by	ADP
cana-3294	174	10	the	the	DET
cana-3294	174	11	completeness	completeness	NOUN
cana-3294	174	12	of	of	ADP
cana-3294	174	13	℧	℧	PROPN
cana-3294	174	14	there	there	PRON
cana-3294	174	15	exists	exist	VERB
cana-3294	174	16	(	(	PUNCT
cana-3294	174	17	r	r	NOUN
cana-3294	174	18	,	,	PUNCT
cana-3294	174	19	s	s	PROPN
cana-3294	174	20	,	,	PUNCT
cana-3294	174	21	t	t	PROPN
cana-3294	174	22	)	)	PUNCT
cana-3294	174	23	ϵ	ϵ	ADP
cana-3294	174	24	℧	℧	NOUN
cana-3294	174	25	3	3	NUM
cana-3294	174	26	with	with	ADP
cana-3294	174	27	lim	lim	PROPN
cana-3294	174	28	m→∞	m→∞	NUM
cana-3294	174	29	{	{	PUNCT
cana-3294	174	30	gλm}=g(r)=λ	gλm}=g(r)=λ	NOUN
cana-3294	174	31	,	,	PUNCT
cana-3294	174	32	lim	lim	PROPN
cana-3294	174	33	𝑚→∞	𝑚→∞	NUM
cana-3294	174	34	{	{	PUNCT
cana-3294	174	35	g𝜇𝑚}=g(s)=μ	g𝜇𝑚}=g(s)=μ	PROPN
cana-3294	174	36	,	,	PUNCT
cana-3294	174	37	lim	lim	PROPN
cana-3294	174	38	n→∞	n→∞	X
cana-3294	174	39	{	{	PUNCT
cana-3294	174	40	gνm}=g(t)=ν	gνm}=g(t)=ν	NOUN
cana-3294	174	41	by	by	ADP
cana-3294	174	42	construction	construction	NOUN
cana-3294	174	43	lim	lim	PROPN
cana-3294	174	44	m→∞	m→∞	NUM
cana-3294	174	45	g(λm+1	g(λm+1	NOUN
cana-3294	174	46	)	)	PUNCT
cana-3294	175	1	=	=	SYM
cana-3294	175	2	lim	lim	PROPN
cana-3294	175	3	m→∞	m→∞	NOUN
cana-3294	175	4	tm(𝜆𝑚	tm(𝜆𝑚	PROPN
cana-3294	175	5	,	,	PUNCT
cana-3294	175	6	𝜇𝑚	𝜇𝑚	NOUN
cana-3294	175	7	,	,	PUNCT
cana-3294	175	8	𝜈𝑚)=λ	𝜈𝑚)=λ	NOUN
cana-3294	175	9	lim	lim	NOUN
cana-3294	175	10	m→∞	m→∞	NOUN
cana-3294	175	11	g(μ	g(μ	VERB
cana-3294	175	12	m+1	m+1	NUM
cana-3294	175	13	)	)	PUNCT
cana-3294	176	1	=	=	SYM
cana-3294	176	2	lim	lim	PROPN
cana-3294	176	3	m→∞	m→∞	NOUN
cana-3294	176	4	tm(𝜇𝑚	tm(𝜇𝑚	PROPN
cana-3294	176	5	,	,	PUNCT
cana-3294	176	6	𝜆𝑚	𝜆𝑚	NOUN
cana-3294	176	7	,	,	PUNCT
cana-3294	176	8	𝜇𝑚)=μ	𝜇𝑚)=μ	PROPN
cana-3294	176	9	and	and	CCONJ
cana-3294	176	10	lim	lim	PROPN
cana-3294	176	11	m→∞	m→∞	NOUN
cana-3294	176	12	g(νm+1	g(νm+1	PROPN
cana-3294	176	13	)	)	PUNCT
cana-3294	176	14	=	=	SYM
cana-3294	176	15	lim	lim	PROPN
cana-3294	176	16	m→∞	m→∞	NOUN
cana-3294	176	17	tm(𝜈𝑚	tm(𝜈𝑚	ADV
cana-3294	176	18	,	,	PUNCT
cana-3294	176	19	𝜇𝑚	𝜇𝑚	NOUN
cana-3294	176	20	,	,	PUNCT
cana-3294	176	21	𝜆𝑚)=ν	𝜆𝑚)=ν	PUNCT
cana-3294	176	22	.	.	PUNCT
cana-3294	177	1	now	now	ADV
cana-3294	177	2	by	by	ADP
cana-3294	177	3	compatibility	compatibility	NOUN
cana-3294	177	4	and	and	CCONJ
cana-3294	177	5	weakly	weakly	ADV
cana-3294	177	6	reciprocally	reciprocally	ADV
cana-3294	177	7	continuous	continuous	ADJ
cana-3294	177	8	of	of	ADP
cana-3294	177	9	g	g	PROPN
cana-3294	177	10	and	and	CCONJ
cana-3294	177	11	{	{	PUNCT
cana-3294	177	12	tn}nϵn	tn}nϵn	X
cana-3294	177	13	we	we	PRON
cana-3294	177	14	have	have	VERB
cana-3294	177	15	lim	lim	PROPN
cana-3294	177	16	m→∞	m→∞	NUM
cana-3294	177	17	tm(g𝜆𝑚	tm(g𝜆𝑚	PROPN
cana-3294	177	18	,	,	PUNCT
cana-3294	177	19	g𝜇𝑚	g𝜇𝑚	ADJ
cana-3294	177	20	,	,	PUNCT
cana-3294	177	21	g𝜈𝑚	g𝜈𝑚	NOUN
cana-3294	177	22	)	)	PUNCT
cana-3294	177	23	=	=	SYM
cana-3294	177	24	g(λ	g(λ	PROPN
cana-3294	177	25	)	)	PUNCT
cana-3294	178	1	lim	lim	PROPN
cana-3294	178	2	m→∞	m→∞	NUM
cana-3294	178	3	tm(g𝜇𝑚	tm(g𝜇𝑚	NOUN
cana-3294	178	4	,	,	PUNCT
cana-3294	178	5	g𝜆𝑚	g𝜆𝑚	PROPN
cana-3294	178	6	,	,	PUNCT
cana-3294	178	7	g𝜇𝑚	g𝜇𝑚	NOUN
cana-3294	178	8	)	)	PUNCT
cana-3294	178	9	=	=	SYM
cana-3294	178	10	g(μ	g(μ	PROPN
cana-3294	178	11	)	)	PUNCT
cana-3294	178	12	(	(	PUNCT
cana-3294	178	13	12	12	NUM
cana-3294	178	14	)	)	PUNCT
cana-3294	178	15	lim	lim	PROPN
cana-3294	178	16	m→∞	m→∞	NUM
cana-3294	178	17	tm(g𝜈𝑚	tm(g𝜈𝑚	PROPN
cana-3294	178	18	,	,	PUNCT
cana-3294	178	19	g𝜇𝑚	g𝜇𝑚	NOUN
cana-3294	178	20	,	,	PUNCT
cana-3294	178	21	g𝜆𝑚	g𝜆𝑚	PROPN
cana-3294	178	22	)	)	PUNCT
cana-3294	178	23	=	=	SYM
cana-3294	178	24	g(ν	g(ν	PROPN
cana-3294	178	25	)	)	PUNCT
cana-3294	178	26	.	.	PUNCT
cana-3294	179	1	suppose	suppose	VERB
cana-3294	179	2	{	{	PUNCT
cana-3294	179	3	tn}nϵn	tn}nϵn	X
cana-3294	179	4	is	be	AUX
cana-3294	179	5	continuous	continuous	ADJ
cana-3294	179	6	&	&	CCONJ
cana-3294	179	7	using	use	VERB
cana-3294	179	8	g(5	g(5	PROPN
cana-3294	179	9	)	)	PUNCT
cana-3294	179	10	,	,	PUNCT
cana-3294	179	11	we	we	PRON
cana-3294	179	12	have	have	VERB
cana-3294	179	13	g	g	PROPN
cana-3294	179	14	(	(	PUNCT
cana-3294	179	15	tn	tn	PROPN
cana-3294	179	16	(	(	PUNCT
cana-3294	179	17	λ	λ	PROPN
cana-3294	179	18	,	,	PUNCT
cana-3294	179	19	μ	μ	PROPN
cana-3294	179	20	,	,	PUNCT
cana-3294	179	21	ν	ν	NOUN
cana-3294	179	22	)	)	PUNCT
cana-3294	179	23	,	,	PUNCT
cana-3294	179	24	tm	tm	PROPN
cana-3294	179	25	(	(	PUNCT
cana-3294	179	26	gλm	gλm	PROPN
cana-3294	179	27	,	,	PUNCT
cana-3294	179	28	gμm	gμm	PROPN
cana-3294	179	29	,	,	PUNCT
cana-3294	179	30	gνm	gνm	PROPN
cana-3294	179	31	)	)	PUNCT
cana-3294	179	32	,	,	PUNCT
cana-3294	179	33	tm	tm	PROPN
cana-3294	179	34	(	(	PUNCT
cana-3294	179	35	gλm	gλm	PROPN
cana-3294	179	36	,	,	PUNCT
cana-3294	179	37	gμm	gμm	PROPN
cana-3294	179	38	,	,	PUNCT
cana-3294	179	39	gνm	gνm	NOUN
cana-3294	179	40	)	)	PUNCT
cana-3294	179	41	)	)	PUNCT
cana-3294	179	42	≤	≤	NOUN
cana-3294	180	1	g	g	PROPN
cana-3294	180	2	(	(	PUNCT
cana-3294	180	3	tn	tn	PROPN
cana-3294	180	4	(	(	PUNCT
cana-3294	180	5	λ	λ	PROPN
cana-3294	180	6	,	,	PUNCT
cana-3294	180	7	μ	μ	PROPN
cana-3294	180	8	,	,	PUNCT
cana-3294	180	9	ν	ν	NOUN
cana-3294	180	10	)	)	PUNCT
cana-3294	180	11	,	,	PUNCT
cana-3294	180	12	g	g	PROPN
cana-3294	180	13	(	(	PUNCT
cana-3294	180	14	tm	tm	PROPN
cana-3294	180	15	(	(	PUNCT
cana-3294	180	16	λm	λm	ADP
cana-3294	180	17	,	,	PUNCT
cana-3294	180	18	μm	μm	INTJ
cana-3294	180	19	,	,	PUNCT
cana-3294	180	20	νm	νm	NOUN
cana-3294	180	21	)	)	PUNCT
cana-3294	180	22	)	)	PUNCT
cana-3294	180	23	,	,	PUNCT
cana-3294	180	24	g	g	PROPN
cana-3294	180	25	(	(	PUNCT
cana-3294	180	26	tm	tm	PROPN
cana-3294	180	27	(	(	PUNCT
cana-3294	180	28	λm	λm	ADP
cana-3294	180	29	,	,	PUNCT
cana-3294	180	30	μm	μm	INTJ
cana-3294	180	31	,	,	PUNCT
cana-3294	180	32	νm	νm	NOUN
cana-3294	180	33	)	)	PUNCT
cana-3294	180	34	)	)	PUNCT
cana-3294	180	35	)	)	PUNCT
cana-3294	181	1	+	+	CCONJ
cana-3294	181	2	g	g	NOUN
cana-3294	181	3	(	(	PUNCT
cana-3294	181	4	g	g	PROPN
cana-3294	181	5	(	(	PUNCT
cana-3294	181	6	tm	tm	PROPN
cana-3294	181	7	(	(	PUNCT
cana-3294	181	8	λm	λm	ADP
cana-3294	181	9	,	,	PUNCT
cana-3294	181	10	μm	μm	INTJ
cana-3294	181	11	,	,	PUNCT
cana-3294	181	12	νm	νm	NOUN
cana-3294	181	13	)	)	PUNCT
cana-3294	181	14	)	)	PUNCT
cana-3294	181	15	,	,	PUNCT
cana-3294	181	16	tm	tm	PROPN
cana-3294	181	17	(	(	PUNCT
cana-3294	181	18	gλm	gλm	PROPN
cana-3294	181	19	,	,	PUNCT
cana-3294	181	20	gμm	gμm	PROPN
cana-3294	181	21	,	,	PUNCT
cana-3294	181	22	gνm	gνm	PROPN
cana-3294	181	23	)	)	PUNCT
cana-3294	181	24	,	,	PUNCT
cana-3294	181	25	tm	tm	PROPN
cana-3294	181	26	(	(	PUNCT
cana-3294	181	27	gλm	gλm	PROPN
cana-3294	181	28	,	,	PUNCT
cana-3294	181	29	gμm	gμm	PROPN
cana-3294	181	30	,	,	PUNCT
cana-3294	181	31	gνm	gνm	NOUN
cana-3294	181	32	)	)	PUNCT
cana-3294	181	33	)	)	PUNCT
cana-3294	181	34	similarly	similarly	ADV
cana-3294	181	35	g	g	PROPN
cana-3294	181	36	(	(	PUNCT
cana-3294	181	37	tn	tn	PROPN
cana-3294	181	38	(	(	PUNCT
cana-3294	181	39	μ	μ	PROPN
cana-3294	181	40	,	,	PUNCT
cana-3294	181	41	λ	λ	PROPN
cana-3294	181	42	,	,	PUNCT
cana-3294	181	43	μ	μ	NOUN
cana-3294	181	44	)	)	PUNCT
cana-3294	181	45	,	,	PUNCT
cana-3294	181	46	tm	tm	PROPN
cana-3294	181	47	(	(	PUNCT
cana-3294	181	48	gμm	gμm	PROPN
cana-3294	181	49	,	,	PUNCT
cana-3294	181	50	gλm	gλm	NOUN
cana-3294	181	51	,	,	PUNCT
cana-3294	181	52	gμm	gμm	PROPN
cana-3294	181	53	)	)	PUNCT
cana-3294	181	54	,	,	PUNCT
cana-3294	181	55	tm	tm	PROPN
cana-3294	181	56	(	(	PUNCT
cana-3294	181	57	gμm	gμm	PROPN
cana-3294	181	58	,	,	PUNCT
cana-3294	181	59	gλm	gλm	NOUN
cana-3294	181	60	,	,	PUNCT
cana-3294	181	61	gμm	gμm	NOUN
cana-3294	181	62	)	)	PUNCT
cana-3294	181	63	)	)	PUNCT
cana-3294	181	64	≤	≤	NOUN
cana-3294	181	65	g	g	PROPN
cana-3294	181	66	(	(	PUNCT
cana-3294	181	67	tn	tn	PROPN
cana-3294	181	68	(	(	PUNCT
cana-3294	181	69	μ	μ	PROPN
cana-3294	181	70	,	,	PUNCT
cana-3294	181	71	λ	λ	PROPN
cana-3294	181	72	,	,	PUNCT
cana-3294	181	73	μ	μ	NOUN
cana-3294	181	74	)	)	PUNCT
cana-3294	181	75	,	,	PUNCT
cana-3294	181	76	g	g	PROPN
cana-3294	181	77	(	(	PUNCT
cana-3294	181	78	tm	tm	PROPN
cana-3294	181	79	(	(	PUNCT
cana-3294	181	80	μm	μm	INTJ
cana-3294	181	81	,	,	PUNCT
cana-3294	181	82	λm	λm	ADP
cana-3294	181	83	,	,	PUNCT
cana-3294	181	84	μm	μm	NOUN
cana-3294	181	85	)	)	PUNCT
cana-3294	181	86	)	)	PUNCT
cana-3294	181	87	,	,	PUNCT
cana-3294	181	88	g	g	PROPN
cana-3294	181	89	(	(	PUNCT
cana-3294	181	90	tm	tm	PROPN
cana-3294	181	91	(	(	PUNCT
cana-3294	181	92	μm	μm	INTJ
cana-3294	181	93	,	,	PUNCT
cana-3294	181	94	λm	λm	ADP
cana-3294	181	95	,	,	PUNCT
cana-3294	181	96	μm	μm	NOUN
cana-3294	181	97	)	)	PUNCT
cana-3294	181	98	)	)	PUNCT
cana-3294	181	99	)	)	PUNCT
cana-3294	182	1	+	+	CCONJ
cana-3294	182	2	g	g	NOUN
cana-3294	182	3	(	(	PUNCT
cana-3294	182	4	g	g	PROPN
cana-3294	182	5	(	(	PUNCT
cana-3294	182	6	tm	tm	PROPN
cana-3294	182	7	(	(	PUNCT
cana-3294	182	8	μm	μm	INTJ
cana-3294	182	9	,	,	PUNCT
cana-3294	182	10	λm	λm	ADP
cana-3294	182	11	,	,	PUNCT
cana-3294	182	12	μm	μm	NOUN
cana-3294	182	13	)	)	PUNCT
cana-3294	182	14	)	)	PUNCT
cana-3294	182	15	,	,	PUNCT
cana-3294	182	16	tm	tm	PROPN
cana-3294	182	17	(	(	PUNCT
cana-3294	182	18	gμm	gμm	PROPN
cana-3294	182	19	,	,	PUNCT
cana-3294	182	20	gλm	gλm	NOUN
cana-3294	182	21	,	,	PUNCT
cana-3294	182	22	gμm	gμm	PROPN
cana-3294	182	23	)	)	PUNCT
cana-3294	182	24	,	,	PUNCT
cana-3294	182	25	tm(gμm	tm(gμm	NOUN
cana-3294	182	26	,	,	PUNCT
cana-3294	182	27	gλm	gλm	NOUN
cana-3294	182	28	,	,	PUNCT
cana-3294	182	29	gμm	gμm	PROPN
cana-3294	182	30	)	)	PUNCT
cana-3294	182	31	)	)	PUNCT
cana-3294	182	32	and	and	CCONJ
cana-3294	182	33	g	g	PROPN
cana-3294	182	34	(	(	PUNCT
cana-3294	182	35	tn	tn	PROPN
cana-3294	182	36	(	(	PUNCT
cana-3294	182	37	ν	ν	PROPN
cana-3294	182	38	,	,	PUNCT
cana-3294	182	39	μ	μ	PROPN
cana-3294	182	40	,	,	PUNCT
cana-3294	182	41	λ	λ	PROPN
cana-3294	182	42	)	)	PUNCT
cana-3294	182	43	,	,	PUNCT
cana-3294	182	44	tm	tm	PROPN
cana-3294	182	45	(	(	PUNCT
cana-3294	182	46	gνm	gνm	PROPN
cana-3294	182	47	,	,	PUNCT
cana-3294	182	48	gμm	gμm	PROPN
cana-3294	182	49	,	,	PUNCT
cana-3294	182	50	gλm	gλm	NOUN
cana-3294	182	51	)	)	PUNCT
cana-3294	182	52	,	,	PUNCT
cana-3294	182	53	tm	tm	PROPN
cana-3294	182	54	(	(	PUNCT
cana-3294	182	55	gνm	gνm	PROPN
cana-3294	182	56	,	,	PUNCT
cana-3294	182	57	gμm	gμm	PROPN
cana-3294	182	58	,	,	PUNCT
cana-3294	182	59	gλm	gλm	NOUN
cana-3294	182	60	)	)	PUNCT
cana-3294	182	61	)	)	PUNCT
cana-3294	182	62	≤	≤	NOUN
cana-3294	182	63	g	g	PROPN
cana-3294	182	64	(	(	PUNCT
cana-3294	182	65	tn	tn	PROPN
cana-3294	182	66	(	(	PUNCT
cana-3294	182	67	ν	ν	PROPN
cana-3294	182	68	,	,	PUNCT
cana-3294	182	69	μ	μ	PROPN
cana-3294	182	70	,	,	PUNCT
cana-3294	182	71	λ	λ	PROPN
cana-3294	182	72	)	)	PUNCT
cana-3294	182	73	,	,	PUNCT
cana-3294	182	74	g	g	PROPN
cana-3294	182	75	(	(	PUNCT
cana-3294	182	76	tm	tm	PROPN
cana-3294	182	77	(	(	PUNCT
cana-3294	182	78	νm	νm	PROPN
cana-3294	182	79	,	,	PUNCT
cana-3294	182	80	μm	μm	INTJ
cana-3294	182	81	,	,	PUNCT
cana-3294	182	82	λm	λm	NOUN
cana-3294	182	83	)	)	PUNCT
cana-3294	182	84	)	)	PUNCT
cana-3294	182	85	,	,	PUNCT
cana-3294	182	86	g	g	PROPN
cana-3294	182	87	(	(	PUNCT
cana-3294	182	88	tm	tm	PROPN
cana-3294	182	89	(	(	PUNCT
cana-3294	182	90	νm	νm	PROPN
cana-3294	182	91	,	,	PUNCT
cana-3294	182	92	μm	μm	INTJ
cana-3294	182	93	,	,	PUNCT
cana-3294	182	94	λm	λm	NOUN
cana-3294	182	95	)	)	PUNCT
cana-3294	182	96	)	)	PUNCT
cana-3294	182	97	)	)	PUNCT
cana-3294	183	1	+	+	CCONJ
cana-3294	183	2	g	g	NOUN
cana-3294	183	3	(	(	PUNCT
cana-3294	183	4	g	g	PROPN
cana-3294	183	5	(	(	PUNCT
cana-3294	183	6	tm	tm	PROPN
cana-3294	183	7	(	(	PUNCT
cana-3294	183	8	νm	νm	PROPN
cana-3294	183	9	,	,	PUNCT
cana-3294	183	10	μm	μm	INTJ
cana-3294	183	11	,	,	PUNCT
cana-3294	183	12	λm	λm	NOUN
cana-3294	183	13	)	)	PUNCT
cana-3294	183	14	)	)	PUNCT
cana-3294	183	15	,	,	PUNCT
cana-3294	183	16	tm	tm	PROPN
cana-3294	183	17	(	(	PUNCT
cana-3294	183	18	gνm	gνm	PROPN
cana-3294	183	19	,	,	PUNCT
cana-3294	183	20	gμm	gμm	PROPN
cana-3294	183	21	,	,	PUNCT
cana-3294	183	22	gλm	gλm	NOUN
cana-3294	183	23	)	)	PUNCT
cana-3294	183	24	,	,	PUNCT
cana-3294	183	25	tm	tm	PROPN
cana-3294	183	26	(	(	PUNCT
cana-3294	183	27	gνm	gνm	PROPN
cana-3294	183	28	,	,	PUNCT
cana-3294	183	29	gμm	gμm	PROPN
cana-3294	183	30	,	,	PUNCT
cana-3294	183	31	gλm	gλm	NOUN
cana-3294	183	32	)	)	PUNCT
cana-3294	183	33	)	)	PUNCT
cana-3294	183	34	taking	take	VERB
cana-3294	183	35	limit	limit	NOUN
cana-3294	183	36	as	as	ADP
cana-3294	183	37	m→∞	m→∞	NOUN
cana-3294	183	38	,	,	PUNCT
cana-3294	183	39	and	and	CCONJ
cana-3294	183	40	weakly	weakly	ADV
cana-3294	183	41	reciprocally	reciprocally	ADV
cana-3294	183	42	continues	continue	VERB
cana-3294	183	43	we	we	PRON
cana-3294	183	44	get	get	VERB
cana-3294	183	45	g	g	NOUN
cana-3294	183	46	(	(	PUNCT
cana-3294	183	47	tn	tn	PROPN
cana-3294	183	48	(	(	PUNCT
cana-3294	183	49	λ	λ	PROPN
cana-3294	183	50	,	,	PUNCT
cana-3294	183	51	μ	μ	PROPN
cana-3294	183	52	,	,	PUNCT
cana-3294	183	53	ν	ν	NOUN
cana-3294	183	54	)	)	PUNCT
cana-3294	183	55	,	,	PUNCT
cana-3294	183	56	gλ	gλ	NOUN
cana-3294	183	57	,	,	PUNCT
cana-3294	183	58	gλ	gλ	NOUN
cana-3294	183	59	)	)	PUNCT
cana-3294	183	60	≤	≤	NOUN
cana-3294	183	61	g	g	PROPN
cana-3294	183	62	(	(	PUNCT
cana-3294	183	63	tn	tn	PROPN
cana-3294	183	64	(	(	PUNCT
cana-3294	183	65	λ	λ	PROPN
cana-3294	183	66	,	,	PUNCT
cana-3294	183	67	μ	μ	PROPN
cana-3294	183	68	,	,	PUNCT
cana-3294	183	69	ν	ν	NOUN
cana-3294	183	70	)	)	PUNCT
cana-3294	183	71	,	,	PUNCT
cana-3294	183	72	gλ	gλ	NOUN
cana-3294	183	73	,	,	PUNCT
cana-3294	183	74	gλ	gλ	NOUN
cana-3294	183	75	)	)	PUNCT
cana-3294	183	76	+	+	CCONJ
cana-3294	183	77	g	g	PROPN
cana-3294	183	78	(	(	PUNCT
cana-3294	183	79	gλ	gλ	NOUN
cana-3294	183	80	,	,	PUNCT
cana-3294	183	81	gλ	gλ	NOUN
cana-3294	183	82	,	,	PUNCT
cana-3294	183	83	gλ	gλ	NOUN
cana-3294	183	84	)	)	PUNCT
cana-3294	183	85	g	g	PROPN
cana-3294	183	86	(	(	PUNCT
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cana-3294	183	88	(	(	PUNCT
cana-3294	183	89	λ	λ	PROPN
cana-3294	183	90	,	,	PUNCT
cana-3294	183	91	μ	μ	PROPN
cana-3294	183	92	,	,	PUNCT
cana-3294	183	93	ν	ν	NOUN
cana-3294	183	94	)	)	PUNCT
cana-3294	183	95	,	,	PUNCT
cana-3294	183	96	gλ	gλ	NOUN
cana-3294	183	97	,	,	PUNCT
cana-3294	183	98	gλ	gλ	NOUN
cana-3294	183	99	)	)	PUNCT
cana-3294	183	100	)	)	PUNCT
cana-3294	184	1	=	=	PUNCT
cana-3294	184	2	0	0	X
cana-3294	184	3	.	.	PUNCT
cana-3294	184	4	similarly	similarly	ADV
cana-3294	184	5	,	,	PUNCT
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cana-3294	184	7	(	(	PUNCT
cana-3294	184	8	tn	tn	PROPN
cana-3294	184	9	(	(	PUNCT
cana-3294	184	10	μ	μ	PROPN
cana-3294	184	11	,	,	PUNCT
cana-3294	184	12	λ	λ	PROPN
cana-3294	184	13	,	,	PUNCT
cana-3294	184	14	μ	μ	NOUN
cana-3294	184	15	)	)	PUNCT
cana-3294	184	16	,	,	PUNCT
cana-3294	184	17	gμ	gμ	PROPN
cana-3294	184	18	,	,	PUNCT
cana-3294	184	19	gμ	gμ	NOUN
cana-3294	184	20	)	)	PUNCT
cana-3294	184	21	=	=	SYM
cana-3294	184	22	0	0	NUM
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cana-3294	184	24	g	g	PROPN
cana-3294	184	25	(	(	PUNCT
cana-3294	184	26	tn	tn	PROPN
cana-3294	184	27	(	(	PUNCT
cana-3294	184	28	ν	ν	PROPN
cana-3294	184	29	,	,	PUNCT
cana-3294	184	30	μ	μ	PROPN
cana-3294	184	31	,	,	PUNCT
cana-3294	184	32	λ	λ	PROPN
cana-3294	184	33	)	)	PUNCT
cana-3294	184	34	,	,	PUNCT
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cana-3294	184	36	,	,	PUNCT
cana-3294	184	37	gν	gν	ADJ
cana-3294	184	38	)	)	PUNCT
cana-3294	184	39	=	=	SYM
cana-3294	184	40	0	0	PUNCT
cana-3294	185	1	i.e.	i.e.	X
cana-3294	185	2	,	,	PUNCT
cana-3294	185	3	tn	tn	PROPN
cana-3294	185	4	(	(	PUNCT
cana-3294	185	5	λ	λ	PROPN
cana-3294	185	6	,	,	PUNCT
cana-3294	185	7	μ	μ	PROPN
cana-3294	185	8	,	,	PUNCT
cana-3294	185	9	ν	ν	NOUN
cana-3294	185	10	)	)	PUNCT
cana-3294	185	11	=	=	SYM
cana-3294	185	12	gλ	gλ	PROPN
cana-3294	185	13	tn	tn	PROPN
cana-3294	185	14	(	(	PUNCT
cana-3294	185	15	μ	μ	PROPN
cana-3294	185	16	,	,	PUNCT
cana-3294	185	17	λ	λ	PROPN
cana-3294	185	18	,	,	PUNCT
cana-3294	185	19	μ	μ	NOUN
cana-3294	185	20	)	)	PUNCT
cana-3294	185	21	=	=	PRON
cana-3294	185	22	gμ	gμ	PROPN
cana-3294	185	23	tn	tn	PROPN
cana-3294	185	24	(	(	PUNCT
cana-3294	185	25	ν	ν	PROPN
cana-3294	185	26	,	,	PUNCT
cana-3294	185	27	μ	μ	PROPN
cana-3294	185	28	,	,	PUNCT
cana-3294	185	29	λ	λ	X
cana-3294	185	30	)	)	PUNCT
cana-3294	185	31	=	=	VERB
cana-3294	185	32	gν	gν	VERB
cana-3294	185	33	thus	thus	ADV
cana-3294	185	34	(	(	PUNCT
cana-3294	185	35	λ	λ	PROPN
cana-3294	185	36	,	,	PUNCT
cana-3294	185	37	μ	μ	PROPN
cana-3294	185	38	,	,	PUNCT
cana-3294	185	39	ν	ν	NOUN
cana-3294	185	40	)	)	PUNCT
cana-3294	185	41	is	be	AUX
cana-3294	185	42	tripled	triple	VERB
cana-3294	185	43	coincidence	coincidence	NOUN
cana-3294	185	44	point	point	NOUN
cana-3294	185	45	of	of	ADP
cana-3294	185	46	{	{	PUNCT
cana-3294	185	47	tn	tn	NOUN
cana-3294	185	48	}	}	PUNCT
cana-3294	185	49	and	and	CCONJ
cana-3294	185	50	g.	g.	PROPN
cana-3294	186	1	now	now	ADV
cana-3294	186	2	we	we	PRON
cana-3294	186	3	prove	prove	VERB
cana-3294	186	4	it	it	PRON
cana-3294	186	5	is	be	AUX
cana-3294	186	6	unique	unique	ADJ
cana-3294	186	7	.	.	PUNCT
cana-3294	187	1	assume	assume	VERB
cana-3294	187	2	(	(	PUNCT
cana-3294	187	3	ꝕ	ꝕ	NOUN
cana-3294	187	4	,	,	PUNCT
cana-3294	187	5	ꝙ	ꝙ	NOUN
cana-3294	187	6	,	,	PUNCT
cana-3294	187	7	r	r	NOUN
cana-3294	187	8	)	)	PUNCT
cana-3294	187	9	is	be	AUX
cana-3294	187	10	another	another	DET
cana-3294	187	11	tripled	triple	VERB
cana-3294	187	12	coincidence	coincidence	NOUN
cana-3294	187	13	points	point	NOUN
cana-3294	187	14	.	.	PUNCT
cana-3294	188	1	communications	communication	NOUN
cana-3294	188	2	on	on	ADP
cana-3294	188	3	applied	apply	VERB
cana-3294	188	4	nonlinear	nonlinear	ADJ
cana-3294	188	5	analysis	analysis	NOUN
cana-3294	188	6	issn	issn	NOUN
cana-3294	188	7	:	:	PUNCT
cana-3294	188	8	1074	1074	NUM
cana-3294	188	9	-	-	PUNCT
cana-3294	188	10	133x	133x	NUM
cana-3294	188	11	vol	vol	NOUN
cana-3294	188	12	32	32	NUM
cana-3294	188	13	no	no	NOUN
cana-3294	188	14	.	.	PUNCT
cana-3294	189	1	6s	6s	NUM
cana-3294	189	2	(	(	PUNCT
cana-3294	189	3	2025	2025	NUM
cana-3294	189	4	)	)	PUNCT
cana-3294	189	5	283	283	NUM
cana-3294	189	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	189	7	i.e	i.e	PROPN
cana-3294	189	8	,	,	PUNCT
cana-3294	189	9	g(ꝕ)=tn(ꝕ	g(ꝕ)=tn(ꝕ	NOUN
cana-3294	189	10	,	,	PUNCT
cana-3294	189	11	ꝙ	ꝙ	NUM
cana-3294	189	12	,	,	PUNCT
cana-3294	189	13	r	r	NOUN
cana-3294	189	14	)	)	PUNCT
cana-3294	189	15	,	,	PUNCT
cana-3294	189	16	g(ꝙ)=tn(ꝙ	g(ꝙ)=tn(ꝙ	ADV
cana-3294	189	17	,	,	PUNCT
cana-3294	189	18	ꝕ	ꝕ	NOUN
cana-3294	189	19	,	,	PUNCT
cana-3294	189	20	ꝙ	ꝙ	NOUN
cana-3294	189	21	)	)	PUNCT
cana-3294	189	22	and	and	CCONJ
cana-3294	189	23	g(r)=tn(r	g(r)=tn(r	NUM
cana-3294	189	24	,	,	PUNCT
cana-3294	189	25	ꝙ	ꝙ	NOUN
cana-3294	189	26	,	,	PUNCT
cana-3294	189	27	ꝕ	ꝕ	NOUN
cana-3294	189	28	)	)	PUNCT
cana-3294	189	29	then	then	ADV
cana-3294	189	30	we	we	PRON
cana-3294	189	31	prove	prove	VERB
cana-3294	189	32	that	that	PRON
cana-3294	189	33	g(λ)=	g(λ)=	NOUN
cana-3294	189	34	g(ꝕ	g(ꝕ	PROPN
cana-3294	189	35	)	)	PUNCT
cana-3294	189	36	,	,	PUNCT
cana-3294	189	37	g(μ)=g(ꝙ	g(μ)=g(ꝙ	PROPN
cana-3294	189	38	)	)	PUNCT
cana-3294	189	39	and	and	CCONJ
cana-3294	189	40	g(v)=g(r	g(v)=g(r	PROPN
cana-3294	189	41	)	)	PUNCT
cana-3294	189	42	since	since	SCONJ
cana-3294	189	43	the	the	DET
cana-3294	189	44	set	set	NOUN
cana-3294	189	45	of	of	ADP
cana-3294	189	46	tripled	triple	VERB
cana-3294	189	47	coincidence	coincidence	NOUN
cana-3294	189	48	points	point	NOUN
cana-3294	189	49	are	be	AUX
cana-3294	189	50	comparable	comparable	ADJ
cana-3294	189	51	,	,	PUNCT
cana-3294	189	52	applying	apply	VERB
cana-3294	189	53	condition	condition	NOUN
cana-3294	189	54	(	(	PUNCT
cana-3294	189	55	5	5	NUM
cana-3294	189	56	)	)	PUNCT
cana-3294	189	57	,	,	PUNCT
cana-3294	189	58	we	we	PRON
cana-3294	189	59	obtain	obtain	VERB
cana-3294	189	60	g(gλ	g(gλ	NOUN
cana-3294	189	61	,	,	PUNCT
cana-3294	189	62	gꝕ	gꝕ	INTJ
cana-3294	189	63	,	,	PUNCT
cana-3294	189	64	gꝕ	gꝕ	NOUN
cana-3294	189	65	)	)	PUNCT
cana-3294	189	66	=	=	SYM
cana-3294	189	67	g(tn(λ	g(tn(λ	PROPN
cana-3294	189	68	,	,	PUNCT
cana-3294	189	69	μ	μ	PROPN
cana-3294	189	70	,	,	PUNCT
cana-3294	189	71	ν),tm(ꝕ	ν),tm(ꝕ	PROPN
cana-3294	189	72	,	,	PUNCT
cana-3294	189	73	ꝙ	ꝙ	NOUN
cana-3294	189	74	,	,	PUNCT
cana-3294	189	75	r	r	NOUN
cana-3294	189	76	)	)	PUNCT
cana-3294	189	77	,	,	PUNCT
cana-3294	189	78	tm(ꝕ	tm(ꝕ	NOUN
cana-3294	189	79	,	,	PUNCT
cana-3294	189	80	ꝙ	ꝙ	NOUN
cana-3294	189	81	,	,	PUNCT
cana-3294	189	82	r	r	NOUN
cana-3294	189	83	)	)	PUNCT
cana-3294	189	84	)	)	PUNCT
cana-3294	189	85	≤	≤	NUM
cana-3294	190	1	γn	γn	ADP
cana-3294	190	2	,	,	PUNCT
cana-3294	190	3	m[g(gλ	m[g(gλ	NOUN
cana-3294	190	4	,	,	PUNCT
cana-3294	190	5	tn(λ	tn(λ	NOUN
cana-3294	190	6	,	,	PUNCT
cana-3294	190	7	μ	μ	NOUN
cana-3294	190	8	,	,	PUNCT
cana-3294	190	9	ν),tn(λ	ν),tn(λ	PROPN
cana-3294	190	10	,	,	PUNCT
cana-3294	190	11	μ	μ	NOUN
cana-3294	190	12	,	,	PUNCT
cana-3294	190	13	ν))+g(gp	ν))+g(gp	PROPN
cana-3294	190	14	,	,	PUNCT
cana-3294	190	15	tm(p	tm(p	NUM
cana-3294	190	16	,	,	PUNCT
cana-3294	190	17	q	q	NOUN
cana-3294	190	18	,	,	PUNCT
cana-3294	190	19	r),tm(p	r),tm(p	PROPN
cana-3294	190	20	,	,	PUNCT
cana-3294	190	21	q	q	NOUN
cana-3294	190	22	,	,	PUNCT
cana-3294	190	23	r))]+δn	r))]+δn	ADJ
cana-3294	190	24	,	,	PUNCT
cana-3294	190	25	mg(gλ	mg(gλ	ADJ
cana-3294	190	26	,	,	PUNCT
cana-3294	190	27	gp	gp	NOUN
cana-3294	190	28	,	,	PUNCT
cana-3294	190	29	gp	gp	NOUN
cana-3294	190	30	)	)	PUNCT
cana-3294	190	31	g(gλ	g(gλ	NOUN
cana-3294	190	32	,	,	PUNCT
cana-3294	190	33	gp	gp	NOUN
cana-3294	190	34	,	,	PUNCT
cana-3294	190	35	gp	gp	NOUN
cana-3294	190	36	)	)	PUNCT
cana-3294	190	37	≤	≤	NOUN
cana-3294	190	38	γn	γn	ADP
cana-3294	190	39	,	,	PUNCT
cana-3294	190	40	m[g(gλ	m[g(gλ	NOUN
cana-3294	190	41	,	,	PUNCT
cana-3294	190	42	gλ	gλ	NOUN
cana-3294	190	43	,	,	PUNCT
cana-3294	190	44	gλ)+g(gp	gλ)+g(gp	NOUN
cana-3294	190	45	,	,	PUNCT
cana-3294	190	46	gp	gp	NOUN
cana-3294	190	47	,	,	PUNCT
cana-3294	190	48	gp)]+δn	gp)]+δn	NOUN
cana-3294	190	49	,	,	PUNCT
cana-3294	190	50	m(gλ	m(gλ	NOUN
cana-3294	190	51	,	,	PUNCT
cana-3294	190	52	gp	gp	NOUN
cana-3294	190	53	,	,	PUNCT
cana-3294	190	54	gp	gp	NOUN
cana-3294	190	55	)	)	PUNCT
cana-3294	190	56	g(gλ	g(gλ	NOUN
cana-3294	190	57	,	,	PUNCT
cana-3294	190	58	gp	gp	NOUN
cana-3294	190	59	,	,	PUNCT
cana-3294	190	60	gp	gp	NOUN
cana-3294	190	61	)	)	PUNCT
cana-3294	190	62	=	=	SYM
cana-3294	190	63	0	0	PUNCT
cana-3294	190	64	as	as	ADP
cana-3294	190	65	δn	δn	NOUN
cana-3294	190	66	,	,	PUNCT
cana-3294	190	67	m	m	VERB
cana-3294	190	68	<	<	X
cana-3294	190	69	1	1	NUM
cana-3294	190	70	∴	∴	NOUN
cana-3294	190	71	gλ	gλ	NOUN
cana-3294	190	72	=	=	NOUN
cana-3294	190	73	gp	gp	NOUN
cana-3294	190	74	in	in	ADP
cana-3294	190	75	the	the	DET
cana-3294	190	76	same	same	ADJ
cana-3294	190	77	way	way	NOUN
cana-3294	190	78	we	we	PRON
cana-3294	190	79	can	can	AUX
cana-3294	190	80	prove	prove	VERB
cana-3294	190	81	g(μ)=g(q	g(μ)=g(q	NOUN
cana-3294	190	82	)	)	PUNCT
cana-3294	190	83	and	and	CCONJ
cana-3294	190	84	g(v	g(v	PROPN
cana-3294	190	85	)	)	PUNCT
cana-3294	190	86	=	=	SYM
cana-3294	190	87	g(r	g(r	NOUN
cana-3294	190	88	)	)	PUNCT
cana-3294	190	89	hence	hence	ADV
cana-3294	190	90	g	g	PROPN
cana-3294	190	91	and	and	CCONJ
cana-3294	190	92	{	{	PUNCT
cana-3294	190	93	tn}nϵn	tn}nϵn	AUX
cana-3294	190	94	have	have	VERB
cana-3294	190	95	a	a	DET
cana-3294	190	96	unique	unique	ADJ
cana-3294	190	97	tripled	triple	VERB
cana-3294	190	98	point	point	NOUN
cana-3294	190	99	of	of	ADP
cana-3294	190	100	coincidence	coincidence	NOUN
cana-3294	190	101	.	.	PUNCT
cana-3294	191	1	i.e	i.e	PRON
cana-3294	191	2	,	,	PUNCT
cana-3294	191	3	(	(	PUNCT
cana-3294	191	4	gλ	gλ	NOUN
cana-3294	191	5	,	,	PUNCT
cana-3294	191	6	gμ	gμ	PROPN
cana-3294	191	7	,	,	PUNCT
cana-3294	191	8	gν	gν	NOUN
cana-3294	191	9	)	)	PUNCT
cana-3294	191	10	.	.	PUNCT
cana-3294	192	1	{	{	PUNCT
cana-3294	192	2	tn}nϵn	tn}nϵn	X
cana-3294	192	3	and	and	CCONJ
cana-3294	192	4	g	g	PROPN
cana-3294	192	5	are	be	AUX
cana-3294	192	6	weakly	weakly	ADV
cana-3294	192	7	compatible	compatible	ADJ
cana-3294	192	8	since	since	SCONJ
cana-3294	192	9	they	they	PRON
cana-3294	192	10	are	be	AUX
cana-3294	192	11	compatible	compatible	ADJ
cana-3294	192	12	,	,	PUNCT
cana-3294	192	13	i.e	i.e	PRON
cana-3294	192	14	,	,	PUNCT
cana-3294	192	15	they	they	PRON
cana-3294	192	16	commute	commute	VERB
cana-3294	192	17	at	at	ADP
cana-3294	192	18	their	their	PRON
cana-3294	192	19	coincidence	coincidence	NOUN
cana-3294	192	20	points	point	NOUN
cana-3294	192	21	,	,	PUNCT
cana-3294	192	22	i.e	i.e	PRON
cana-3294	192	23	,	,	PUNCT
cana-3294	192	24	λ	λ	X
cana-3294	192	25	=	=	NOUN
cana-3294	192	26	gλ	gλ	NOUN
cana-3294	192	27	=	=	SYM
cana-3294	192	28	tn(λ	tn(λ	NOUN
cana-3294	192	29	,	,	PUNCT
cana-3294	192	30	μ	μ	PROPN
cana-3294	192	31	,	,	PUNCT
cana-3294	192	32	ν	ν	NOUN
cana-3294	192	33	)	)	PUNCT
cana-3294	192	34	,	,	PUNCT
cana-3294	192	35	μ	μ	NOUN
cana-3294	192	36	=	=	NOUN
cana-3294	192	37	gμ	gμ	NOUN
cana-3294	192	38	=	=	PUNCT
cana-3294	192	39	tn(μ	tn(μ	NUM
cana-3294	192	40	,	,	PUNCT
cana-3294	192	41	λ	λ	PROPN
cana-3294	192	42	,	,	PUNCT
cana-3294	192	43	μ	μ	NOUN
cana-3294	192	44	)	)	PUNCT
cana-3294	192	45	,	,	PUNCT
cana-3294	192	46	ν	ν	X
cana-3294	192	47	=	=	VERB
cana-3294	192	48	gν	gν	NOUN
cana-3294	192	49	=	=	NOUN
cana-3294	192	50	tn(ν	tn(ν	PROPN
cana-3294	192	51	,	,	PUNCT
cana-3294	192	52	μ	μ	NOUN
cana-3294	192	53	,	,	PUNCT
cana-3294	192	54	λ	λ	PROPN
cana-3294	192	55	)	)	PUNCT
cana-3294	192	56	.	.	PUNCT
cana-3294	193	1	thus	thus	ADV
cana-3294	193	2	,	,	PUNCT
cana-3294	193	3	{	{	PUNCT
cana-3294	193	4	tn}nϵn	tn}nϵn	X
cana-3294	193	5	and	and	CCONJ
cana-3294	193	6	g	g	PROPN
cana-3294	193	7	have	have	AUX
cana-3294	193	8	unique	unique	ADJ
cana-3294	193	9	tripled	triple	VERB
cana-3294	193	10	common	common	ADJ
cana-3294	193	11	fixed	fix	VERB
cana-3294	193	12	point	point	NOUN
cana-3294	193	13	whenever	whenever	SCONJ
cana-3294	193	14	they	they	PRON
cana-3294	193	15	are	be	AUX
cana-3294	193	16	weakly	weakly	ADV
cana-3294	193	17	compatible	compatible	ADJ
cana-3294	193	18	.	.	PUNCT
cana-3294	194	1	corollary	corollary	NOUN
cana-3294	194	2	4.4	4.4	NUM
cana-3294	195	1	:	:	PUNCT
cana-3294	195	2	assume	assume	VERB
cana-3294	195	3	(	(	PUNCT
cana-3294	195	4	ℬ	ℬ	NOUN
cana-3294	195	5	,	,	PUNCT
cana-3294	195	6	g	g	NOUN
cana-3294	195	7	,	,	PUNCT
cana-3294	195	8	≤	≤	NUM
cana-3294	195	9	)	)	PUNCT
cana-3294	195	10	is	be	AUX
cana-3294	195	11	a	a	DET
cana-3294	195	12	complete	complete	ADJ
cana-3294	195	13	partially	partially	ADV
cana-3294	195	14	ordered	order	VERB
cana-3294	195	15	g	g	PROPN
cana-3294	195	16	–	–	PUNCT
cana-3294	195	17	metric	metric	ADJ
cana-3294	195	18	space	space	NOUN
cana-3294	195	19	.	.	PUNCT
cana-3294	196	1	let	let	VERB
cana-3294	196	2	{	{	PUNCT
cana-3294	196	3	tn}nϵn	tn}nϵn	NUM
cana-3294	196	4	:	:	PUNCT
cana-3294	196	5	ℬ3	ℬ3	PROPN
cana-3294	196	6	→ℬ	→ℬ	PROPN
cana-3294	196	7	be	be	AUX
cana-3294	196	8	a	a	DET
cana-3294	196	9	sequence	sequence	NOUN
cana-3294	196	10	of	of	ADP
cana-3294	196	11	mappings	mapping	NOUN
cana-3294	196	12	and	and	CCONJ
cana-3294	196	13	g	g	NOUN
cana-3294	196	14	is	be	AUX
cana-3294	196	15	an	an	DET
cana-3294	196	16	identity	identity	NOUN
cana-3294	196	17	mapping	mapping	NOUN
cana-3294	196	18	for	for	ADP
cana-3294	196	19	𝜌	𝜌	ADP
cana-3294	196	20	,	,	PUNCT
cana-3294	196	21	𝝈	𝝈	NOUN
cana-3294	196	22	,	,	PUNCT
cana-3294	196	23	𝝉,𝝒,𝜼,𝜻	𝝉,𝝒,𝜼,𝜻	ADP
cana-3294	196	24	∈	∈	PROPN
cana-3294	196	25	ℬ	ℬ	NOUN
cana-3294	196	26	,	,	PUNCT
cana-3294	196	27	{	{	PUNCT
cana-3294	196	28	tn}nϵn	tn}nϵn	X
cana-3294	196	29	with	with	ADP
cana-3294	196	30	𝝆	𝝆	PROPN
cana-3294	196	31	≤	≤	NUM
cana-3294	196	32	𝝒	𝝒	NOUN
cana-3294	196	33	,	,	PUNCT
cana-3294	196	34	𝜼	𝜼	PROPN
cana-3294	196	35	≤	≤	NUM
cana-3294	196	36	𝝈	𝝈	NOUN
cana-3294	196	37	,	,	PUNCT
cana-3294	196	38	𝝉	𝝉	PROPN
cana-3294	196	39	≤	≤	PROPN
cana-3294	196	40	𝜻	𝜻	NOUN
cana-3294	196	41	or	or	CCONJ
cana-3294	196	42	𝝒	𝝒	NOUN
cana-3294	196	43	≤	≤	NOUN
cana-3294	196	44	𝝆,𝝈	𝝆,𝝈	X
cana-3294	196	45	≤	≤	NUM
cana-3294	196	46	𝜼	𝜼	PROPN
cana-3294	196	47	,	,	PUNCT
cana-3294	196	48	𝜻	𝜻	NOUN
cana-3294	196	49	≤	≤	NUM
cana-3294	196	50	𝝉	𝝉	NOUN
cana-3294	196	51	,	,	PUNCT
cana-3294	196	52	satifies	satifie	VERB
cana-3294	196	53	the	the	DET
cana-3294	196	54	following	following	ADJ
cana-3294	196	55	conditions	condition	NOUN
cana-3294	196	56	.	.	PUNCT
cana-3294	197	1	(	(	PUNCT
cana-3294	197	2	i	i	NOUN
cana-3294	197	3	)	)	PUNCT
cana-3294	197	4	tm(𝝆,𝝈,𝝉	tm(𝝆,𝝈,𝝉	PROPN
cana-3294	197	5	)	)	PUNCT
cana-3294	197	6	≤	≤	NOUN
cana-3294	198	1	tm+1(𝝒,𝜼	tm+1(𝝒,𝜼	PROPN
cana-3294	198	2	,	,	PUNCT
cana-3294	198	3	𝜻	𝜻	NOUN
cana-3294	198	4	)	)	PUNCT
cana-3294	198	5	(	(	PUNCT
cana-3294	198	6	ii	ii	NOUN
cana-3294	198	7	)	)	PUNCT
cana-3294	198	8	g(tn(𝝆,𝝈,𝝉	g(tn(𝝆,𝝈,𝝉	PROPN
cana-3294	198	9	)	)	PUNCT
cana-3294	198	10	,	,	PUNCT
cana-3294	198	11	tm(𝝒,𝜼	tm(𝝒,𝜼	ADJ
cana-3294	198	12	,	,	PUNCT
cana-3294	198	13	𝜻),tm(𝞁,𝝰,𝝏	𝜻),tm(𝞁,𝝰,𝝏	PROPN
cana-3294	198	14	)	)	PUNCT
cana-3294	198	15	)	)	PUNCT
cana-3294	199	1	≤	≤	NUM
cana-3294	199	2	γn	γn	ADP
cana-3294	199	3	,	,	PUNCT
cana-3294	199	4	m	m	VERB
cana-3294	199	5	[	[	X
cana-3294	199	6	(	(	PUNCT
cana-3294	199	7	ρ	ρ	PROPN
cana-3294	199	8	,	,	PUNCT
cana-3294	199	9	tn(𝝆,𝝈,𝝉),tn(𝝆,𝝈,𝝉))+g(𝝒,tm(𝝒,𝜼	tn(𝝆,𝝈,𝝉),tn(𝝆,𝝈,𝝉))+g(𝝒,tm(𝝒,𝜼	NOUN
cana-3294	199	10	,	,	PUNCT
cana-3294	199	11	𝜻	𝜻	NOUN
cana-3294	199	12	)	)	PUNCT
cana-3294	199	13	,	,	PUNCT
cana-3294	199	14	tm(𝞁,𝝰,𝝏))]+δn	tm(𝞁,𝝰,𝝏))]+δn	PROPN
cana-3294	199	15	,	,	PUNCT
cana-3294	199	16	m	m	PRON
cana-3294	199	17	g(𝝆,𝝒,𝞁	g(𝝆,𝝒,𝞁	NOUN
cana-3294	199	18	)	)	PUNCT
cana-3294	199	19	with	with	ADP
cana-3294	199	20	0	0	NUM
cana-3294	199	21	≤	≤	NUM
cana-3294	199	22	γn	γn	ADP
cana-3294	199	23	,	,	PUNCT
cana-3294	199	24	m	m	NOUN
cana-3294	199	25	,	,	PUNCT
cana-3294	199	26	δn	δn	VERB
cana-3294	199	27	,	,	PUNCT
cana-3294	199	28	m	m	VERB
cana-3294	199	29	<	<	X
cana-3294	199	30	1	1	NUM
cana-3294	199	31	and	and	CCONJ
cana-3294	199	32	n	n	CCONJ
cana-3294	199	33	,	,	PUNCT
cana-3294	199	34	m	m	AUX
cana-3294	199	35	∈n	∈n	ADJ
cana-3294	199	36	if	if	SCONJ
cana-3294	199	37	∑	∑	PROPN
cana-3294	199	38	(	(	PUNCT
cana-3294	199	39	𝛾𝑛,𝑛+1	𝛾𝑛,𝑛+1	PROPN
cana-3294	199	40	+	+	X
cana-3294	199	41	𝛿𝑛,𝑛+1	𝛿𝑛,𝑛+1	NOUN
cana-3294	199	42	1−𝛾𝑛,𝑛+1	1−𝛾𝑛,𝑛+1	NUM
cana-3294	199	43	∞	∞	NUM
cana-3294	199	44	𝑛=1	𝑛=1	NOUN
cana-3294	199	45	)	)	PUNCT
cana-3294	199	46	is	be	AUX
cana-3294	199	47	an	an	DET
cana-3294	199	48	αseries	αserie	NOUN
cana-3294	199	49	and	and	CCONJ
cana-3294	199	50	ℬ	ℬ	NOUN
cana-3294	199	51	is	be	AUX
cana-3294	199	52	regular	regular	ADJ
cana-3294	199	53	,	,	PUNCT
cana-3294	199	54	then	then	ADV
cana-3294	199	55	there	there	PRON
cana-3294	199	56	exists	exist	VERB
cana-3294	199	57	a	a	DET
cana-3294	199	58	tripled	triple	VERB
cana-3294	199	59	fixed	fix	VERB
cana-3294	199	60	point	point	NOUN
cana-3294	199	61	of	of	ADP
cana-3294	199	62	{	{	PUNCT
cana-3294	199	63	tn}n∈n	tn}n∈n	PROPN
cana-3294	199	64	.	.	PUNCT
cana-3294	200	1	i.e	i.e	PROPN
cana-3294	200	2	,	,	PUNCT
cana-3294	200	3	∃	∃	PROPN
cana-3294	200	4	(	(	PUNCT
cana-3294	200	5	𝝆,𝝈,𝝉	𝝆,𝝈,𝝉	PROPN
cana-3294	200	6	)	)	PUNCT
cana-3294	200	7	∈ℬ3	∈ℬ3	NOUN
cana-3294	200	8	such	such	ADJ
cana-3294	200	9	that	that	DET
cana-3294	200	10	𝝆=tn(𝝆,𝝈,𝝉	𝝆=tn(𝝆,𝝈,𝝉	NOUN
cana-3294	200	11	)	)	PUNCT
cana-3294	200	12	,	,	PUNCT
cana-3294	200	13	𝝈=	𝝈=	VERB
cana-3294	200	14	tn(𝝈,𝝆,𝝈),𝝉=tn(𝝉,𝝈,𝝆	tn(𝝈,𝝆,𝝈),𝝉=tn(𝝉,𝝈,𝝆	NOUN
cana-3294	200	15	)	)	PUNCT
cana-3294	200	16	for	for	ADP
cana-3294	200	17	n∈n	n∈n	NOUN
cana-3294	200	18	.	.	PUNCT
cana-3294	201	1	theorem	theorem	VERB
cana-3294	201	2	4.5	4.5	NUM
cana-3294	201	3	:	:	PUNCT
cana-3294	201	4	consider	consider	VERB
cana-3294	201	5	(	(	PUNCT
cana-3294	201	6	ℬ	ℬ	NOUN
cana-3294	201	7	,	,	PUNCT
cana-3294	201	8	g	g	NOUN
cana-3294	201	9	,	,	PUNCT
cana-3294	201	10	≤	≤	NUM
cana-3294	201	11	)	)	PUNCT
cana-3294	201	12	be	be	VERB
cana-3294	201	13	a	a	DET
cana-3294	201	14	partially	partially	ADV
cana-3294	201	15	ordered	order	VERB
cana-3294	201	16	complete	complete	ADJ
cana-3294	201	17	g	g	NOUN
cana-3294	201	18	-	-	PUNCT
cana-3294	201	19	metric	metric	ADJ
cana-3294	201	20	space	space	NOUN
cana-3294	201	21	and	and	CCONJ
cana-3294	201	22	is	be	AUX
cana-3294	201	23	regular.let	regular.let	X
cana-3294	201	24	g	g	NOUN
cana-3294	201	25	and	and	CCONJ
cana-3294	201	26	{	{	PUNCT
cana-3294	201	27	tm}m∈n	tm}m∈n	INTJ
cana-3294	201	28	is	be	AUX
cana-3294	201	29	same	same	ADJ
cana-3294	201	30	as	as	ADP
cana-3294	201	31	in	in	ADP
cana-3294	201	32	theorem	theorem	ADJ
cana-3294	201	33	3.3	3.3	NUM
cana-3294	201	34	and	and	CCONJ
cana-3294	201	35	lim	lim	PROPN
cana-3294	201	36	𝑛⟶∞	𝑛⟶∞	PROPN
cana-3294	201	37	sup	sup	NOUN
cana-3294	201	38	𝛽𝑚,𝑛	𝛽𝑚,𝑛	PUNCT
cana-3294	201	39	<	<	X
cana-3294	201	40	1	1	NUM
cana-3294	201	41	,	,	PUNCT
cana-3294	201	42	0	0	NUM
cana-3294	201	43	≤	≤	NUM
cana-3294	201	44	𝛽𝑖,𝑗	𝛽𝑖,𝑗	PUNCT
cana-3294	201	45	,	,	PUNCT
cana-3294	201	46	𝛾𝑖,𝑗	𝛾𝑖,𝑗	PUNCT
cana-3294	201	47	<	<	X
cana-3294	201	48	1𝑎𝑛𝑑	1𝑎𝑛𝑑	NUM
cana-3294	201	49	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
cana-3294	201	50	𝑔	𝑔	PROPN
cana-3294	201	51	𝑎𝑛𝑑	𝑎𝑛𝑑	X
cana-3294	201	52	{	{	PUNCT
cana-3294	201	53	𝑇𝑚	𝑇𝑚	NOUN
cana-3294	201	54	}	}	PUNCT
cana-3294	201	55	𝑠𝑎𝑡𝑖𝑓𝑖𝑒𝑠	𝑠𝑎𝑡𝑖𝑓𝑖𝑒𝑠	NOUN
cana-3294	201	56	𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠	𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠	NOUN
cana-3294	201	57	(	(	PUNCT
cana-3294	201	58	2	2	NUM
cana-3294	201	59	)	)	PUNCT
cana-3294	201	60	,	,	PUNCT
cana-3294	201	61	(	(	PUNCT
cana-3294	201	62	3	3	X
cana-3294	201	63	)	)	PUNCT
cana-3294	201	64	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
cana-3294	201	65	(	(	PUNCT
cana-3294	201	66	5	5	NUM
cana-3294	201	67	)	)	PUNCT
cana-3294	201	68	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-3294	201	69	𝑔	𝑔	PROPN
cana-3294	201	70	𝑎𝑛𝑑	𝑎𝑛𝑑	X
cana-3294	201	71	{	{	PUNCT
cana-3294	201	72	tm}m∈n	tm}m∈n	X
cana-3294	201	73	have	have	AUX
cana-3294	201	74	tripled	triple	VERB
cana-3294	201	75	coincidence	coincidence	NOUN
cana-3294	201	76	point	point	NOUN
cana-3294	201	77	.	.	PUNCT
cana-3294	202	1	proof	proof	NOUN
cana-3294	202	2	:	:	PUNCT
cana-3294	202	3	from	from	ADP
cana-3294	202	4	the	the	DET
cana-3294	202	5	theorem	theorem	NOUN
cana-3294	202	6	,	,	PUNCT
cana-3294	202	7	sequences	sequence	NOUN
cana-3294	202	8	{	{	PUNCT
cana-3294	202	9	𝑔𝜆𝑚	𝑔𝜆𝑚	ADV
cana-3294	202	10	}	}	PUNCT
cana-3294	202	11	,	,	PUNCT
cana-3294	202	12	{	{	PUNCT
cana-3294	202	13	𝑔𝜇𝑚	𝑔𝜇𝑚	ADJ
cana-3294	202	14	}	}	PUNCT
cana-3294	202	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-3294	202	16	{	{	PUNCT
cana-3294	202	17	𝑔𝜐𝑚	𝑔𝜐𝑚	NOUN
cana-3294	202	18	}	}	PUNCT
cana-3294	202	19	𝑎𝑟𝑒	𝑎𝑟𝑒	NOUN
cana-3294	202	20	𝑐𝑎𝑢𝑐ℎ𝑦	𝑐𝑎𝑢𝑐ℎ𝑦	NOUN
cana-3294	202	21	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	PROPN
cana-3294	202	22	𝑖𝑛	𝑖𝑛	PROPN
cana-3294	202	23	𝐺(ℬ).since	𝐺(ℬ).since	PROPN
cana-3294	202	24	{	{	PUNCT
cana-3294	202	25	𝑔𝜆𝑚	𝑔𝜆𝑚	ADJ
cana-3294	202	26	}	}	PUNCT
cana-3294	202	27	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-3294	202	28	{	{	PUNCT
cana-3294	202	29	𝑔𝜐𝑚	𝑔𝜐𝑚	NOUN
cana-3294	202	30	}	}	PUNCT
cana-3294	202	31	𝑎𝑟𝑒	𝑎𝑟𝑒	NOUN
cana-3294	202	32	𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	ADV
cana-3294	202	33	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	NOUN
cana-3294	202	34	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-3294	202	35	{	{	PUNCT
cana-3294	202	36	𝑔𝜇𝑚	𝑔𝜇𝑚	NOUN
cana-3294	202	37	}	}	PUNCT
cana-3294	202	38	𝑖𝑠	𝑖𝑠	NOUN
cana-3294	203	1	𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	NOUN
cana-3294	203	2	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠	PROPN
cana-3294	203	3	𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦	𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦	NOUN
cana-3294	203	4	:	:	PUNCT
cana-3294	203	5	𝑏𝑦	𝑏𝑦	PROPN
cana-3294	203	6	𝑢𝑠𝑖𝑛𝑔	𝑢𝑠𝑖𝑛𝑔	PROPN
cana-3294	203	7	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-3294	203	8	𝑟𝑒𝑔𝑢𝑙𝑎𝑟𝑖𝑡𝑦	𝑟𝑒𝑔𝑢𝑙𝑎𝑟𝑖𝑡𝑦	NOUN
cana-3294	203	9	𝑜𝑓	𝑜𝑓	ADP
cana-3294	203	10	(	(	PUNCT
cana-3294	203	11	ℬ	ℬ	PROPN
cana-3294	203	12	,	,	PUNCT
cana-3294	203	13	g	g	NOUN
cana-3294	203	14	,	,	PUNCT
cana-3294	203	15	≤	≤	NUM
cana-3294	203	16	)	)	PUNCT
cana-3294	203	17	,	,	PUNCT
cana-3294	203	18	we	we	PRON
cana-3294	203	19	have	have	AUX
cana-3294	203	20	𝑔𝛼𝑚	𝑔𝛼𝑚	NOUN
cana-3294	203	21	≤	≤	PROPN
cana-3294	203	22	𝞪	𝞪	PROPN
cana-3294	203	23	,	,	PUNCT
cana-3294	203	24	ρ	ρ	PROPN
cana-3294	203	25	≤	≤	NUM
cana-3294	203	26	𝑔𝜌𝑚	𝑔𝜌𝑚	NOUN
cana-3294	203	27	,	,	PUNCT
cana-3294	203	28	𝑔𝜎𝑚	𝑔𝜎𝑚	VERB
cana-3294	203	29	≤	≤	NOUN
cana-3294	203	30	𝝈	𝝈	NOUN
cana-3294	203	31	for	for	ADP
cana-3294	203	32	all	all	DET
cana-3294	203	33	m	m	PROPN
cana-3294	203	34	≥	≥	NOUN
cana-3294	203	35	0	0	NUM
cana-3294	203	36	then	then	ADV
cana-3294	203	37	by	by	ADP
cana-3294	203	38	(	(	PUNCT
cana-3294	203	39	5	5	NUM
cana-3294	203	40	)	)	PUNCT
cana-3294	203	41	,	,	PUNCT
cana-3294	203	42	we	we	PRON
cana-3294	203	43	obtain	obtain	VERB
cana-3294	203	44	g(𝑇𝑚(𝑔𝛼𝑚	g(𝑇𝑚(𝑔𝛼𝑚	PROPN
cana-3294	203	45	,	,	PUNCT
cana-3294	203	46	𝑔𝜌𝑚	𝑔𝜌𝑚	NOUN
cana-3294	203	47	,	,	PUNCT
cana-3294	203	48	𝑔𝜎𝑚	𝑔𝜎𝑚	PROPN
cana-3294	203	49	)	)	PUNCT
cana-3294	203	50	,	,	PUNCT
cana-3294	204	1	𝑇𝑛(𝛼	𝑇𝑛(𝛼	NOUN
cana-3294	204	2	,	,	PUNCT
cana-3294	204	3	𝜌	𝜌	X
cana-3294	204	4	,	,	PUNCT
cana-3294	204	5	𝜎	𝜎	NOUN
cana-3294	204	6	)	)	PUNCT
cana-3294	204	7	,	,	PUNCT
cana-3294	204	8	𝑇𝑛(𝛼	𝑇𝑛(𝛼	NOUN
cana-3294	204	9	,	,	PUNCT
cana-3294	204	10	𝜌	𝜌	X
cana-3294	204	11	,	,	PUNCT
cana-3294	204	12	𝜎	𝜎	NOUN
cana-3294	204	13	)	)	PUNCT
cana-3294	204	14	)	)	PUNCT
cana-3294	204	15	≤	≤	NUM
cana-3294	204	16	communications	communication	NOUN
cana-3294	204	17	on	on	ADP
cana-3294	204	18	applied	apply	VERB
cana-3294	204	19	nonlinear	nonlinear	ADJ
cana-3294	204	20	analysis	analysis	NOUN
cana-3294	204	21	issn	issn	NOUN
cana-3294	204	22	:	:	PUNCT
cana-3294	204	23	1074	1074	NUM
cana-3294	204	24	-	-	PUNCT
cana-3294	204	25	133x	133x	NUM
cana-3294	204	26	vol	vol	NOUN
cana-3294	204	27	32	32	NUM
cana-3294	204	28	no	no	NOUN
cana-3294	204	29	.	.	PUNCT
cana-3294	205	1	6s	6s	NUM
cana-3294	205	2	(	(	PUNCT
cana-3294	205	3	2025	2025	NUM
cana-3294	205	4	)	)	PUNCT
cana-3294	205	5	284	284	NUM
cana-3294	205	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	205	7	𝛽𝑚,𝑛[𝐺(𝑔(𝑔𝛼𝑚	𝛽𝑚,𝑛[𝐺(𝑔(𝑔𝛼𝑚	PROPN
cana-3294	205	8	)	)	PUNCT
cana-3294	205	9	,	,	PUNCT
cana-3294	205	10	𝑇𝑚(𝑔𝛼𝑚	𝑇𝑚(𝑔𝛼𝑚	PROPN
cana-3294	205	11	,	,	PUNCT
cana-3294	205	12	𝑔𝜌𝑚	𝑔𝜌𝑚	PROPN
cana-3294	205	13	,	,	PUNCT
cana-3294	205	14	𝑔𝜎𝑚	𝑔𝜎𝑚	PROPN
cana-3294	205	15	)	)	PUNCT
cana-3294	205	16	,	,	PUNCT
cana-3294	205	17	𝑇𝑚(𝑔𝛼𝑚	𝑇𝑚(𝑔𝛼𝑚	PROPN
cana-3294	205	18	,	,	PUNCT
cana-3294	205	19	𝑔𝜌𝑚	𝑔𝜌𝑚	PROPN
cana-3294	205	20	,	,	PUNCT
cana-3294	205	21	𝑔𝜎𝑚	𝑔𝜎𝑚	NOUN
cana-3294	205	22	)	)	PUNCT
cana-3294	205	23	)	)	PUNCT
cana-3294	206	1	+	+	CCONJ
cana-3294	206	2	𝐺(𝑔𝛼	𝐺(𝑔𝛼	X
cana-3294	206	3	,	,	PUNCT
cana-3294	206	4	𝑇𝑛(𝛼	𝑇𝑛(𝛼	NOUN
cana-3294	206	5	,	,	PUNCT
cana-3294	206	6	𝜌	𝜌	X
cana-3294	206	7	,	,	PUNCT
cana-3294	206	8	𝜎	𝜎	NOUN
cana-3294	206	9	)	)	PUNCT
cana-3294	206	10	,	,	PUNCT
cana-3294	206	11	𝑇𝑛(𝛼	𝑇𝑛(𝛼	NOUN
cana-3294	206	12	,	,	PUNCT
cana-3294	206	13	𝜌	𝜌	X
cana-3294	206	14	,	,	PUNCT
cana-3294	206	15	𝜎	𝜎	NOUN
cana-3294	206	16	)	)	PUNCT
cana-3294	206	17	)	)	PUNCT
cana-3294	207	1	+	+	CCONJ
cana-3294	207	2	𝛾𝑚,𝑛(𝐺(𝑔(𝑔𝛼𝑚	𝛾𝑚,𝑛(𝐺(𝑔(𝑔𝛼𝑚	PROPN
cana-3294	207	3	)	)	PUNCT
cana-3294	207	4	,	,	PUNCT
cana-3294	207	5	𝑔𝛼	𝑔𝛼	PROPN
cana-3294	207	6	,	,	PUNCT
cana-3294	207	7	𝑔𝛼	𝑔𝛼	NOUN
cana-3294	207	8	)	)	PUNCT
cana-3294	207	9	taking	take	VERB
cana-3294	207	10	as	as	ADP
cana-3294	207	11	m→∞	m→∞	NOUN
cana-3294	207	12	,	,	PUNCT
cana-3294	207	13	we	we	PRON
cana-3294	207	14	obtain	obtain	VERB
cana-3294	207	15	𝑇𝑚(𝛼	𝑇𝑚(𝛼	ADV
cana-3294	207	16	,	,	PUNCT
cana-3294	207	17	𝜌	𝜌	X
cana-3294	207	18	,	,	PUNCT
cana-3294	207	19	𝜎	𝜎	X
cana-3294	207	20	)	)	PUNCT
cana-3294	207	21	=	=	PRON
cana-3294	207	22	𝑔𝛼	𝑔𝛼	VERB
cana-3294	207	23	𝑎𝑠	𝑎𝑠	NOUN
cana-3294	207	24	𝛽𝑚,𝑛	𝛽𝑚,𝑛	X
cana-3294	207	25	<	<	X
cana-3294	207	26	1	1	NUM
cana-3294	207	27	,	,	PUNCT
cana-3294	207	28	similarly	similarly	ADV
cana-3294	207	29	we	we	PRON
cana-3294	207	30	can	can	AUX
cana-3294	207	31	prove	prove	VERB
cana-3294	207	32	𝑇𝑚(𝜌	𝑇𝑚(𝜌	PROPN
cana-3294	207	33	,	,	PUNCT
cana-3294	207	34	𝛼	𝛼	NOUN
cana-3294	207	35	,	,	PUNCT
cana-3294	207	36	𝜌	𝜌	ADP
cana-3294	207	37	)	)	PUNCT
cana-3294	207	38	=	=	SYM
cana-3294	207	39	𝑔𝝆	𝑔𝝆	NOUN
cana-3294	207	40	and	and	CCONJ
cana-3294	207	41	𝑇𝑚(𝜎	𝑇𝑚(𝜎	PROPN
cana-3294	207	42	,	,	PUNCT
cana-3294	207	43	𝜌	𝜌	X
cana-3294	207	44	,	,	PUNCT
cana-3294	207	45	𝛼	𝛼	NOUN
cana-3294	207	46	)	)	PUNCT
cana-3294	207	47	=	=	VERB
cana-3294	207	48	𝑔𝝈	𝑔𝝈	ADJ
cana-3294	207	49	thus	thus	ADV
cana-3294	207	50	(	(	PUNCT
cana-3294	207	51	𝛼	𝛼	X
cana-3294	207	52	,	,	PUNCT
cana-3294	207	53	𝜌	𝜌	X
cana-3294	207	54	,	,	PUNCT
cana-3294	207	55	𝜎	𝜎	X
cana-3294	207	56	)	)	PUNCT
cana-3294	207	57	𝑖𝑠	𝑖𝑠	NOUN
cana-3294	207	58	𝑡𝑟𝑖𝑝𝑙𝑒𝑑	𝑡𝑟𝑖𝑝𝑙𝑒𝑑	NOUN
cana-3294	207	59	𝑐𝑜𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒	𝑐𝑜𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒	PROPN
cana-3294	207	60	𝑝𝑜𝑖𝑛𝑡	𝑝𝑜𝑖𝑛𝑡	PROPN
cana-3294	207	61	𝑜𝑓	𝑜𝑓	ADP
cana-3294	207	62	{	{	PUNCT
cana-3294	207	63	𝑇𝑚}𝑚∈𝑁	𝑇𝑚}𝑚∈𝑁	PROPN
cana-3294	207	64	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3294	207	65	𝑔	𝑔	PROPN
cana-3294	207	66	example	example	NOUN
cana-3294	207	67	4.6	4.6	NUM
cana-3294	207	68	:	:	PUNCT
cana-3294	207	69	consider	consider	VERB
cana-3294	207	70	e	e	NOUN
cana-3294	207	71	=	=	PUNCT
cana-3294	208	1	[	[	X
cana-3294	208	2	0,1	0,1	NUM
cana-3294	208	3	]	]	PUNCT
cana-3294	208	4	and	and	CCONJ
cana-3294	208	5	g(𝛼	g(𝛼	PROPN
cana-3294	208	6	,	,	PUNCT
cana-3294	208	7	𝜌	𝜌	X
cana-3294	208	8	,	,	PUNCT
cana-3294	208	9	𝜎	𝜎	X
cana-3294	208	10	)	)	PUNCT
cana-3294	208	11	=	=	SYM
cana-3294	208	12	max{|𝛼	max{|𝛼	PROPN
cana-3294	208	13	−	−	PROPN
cana-3294	208	14	𝜌|	𝜌|	PROPN
cana-3294	208	15	,	,	PUNCT
cana-3294	208	16	|𝜌	|𝜌	NOUN
cana-3294	208	17	−	−	PROPN
cana-3294	208	18	𝜎|	𝜎|	PROPN
cana-3294	208	19	,	,	PUNCT
cana-3294	208	20	|𝜎	|𝜎	X
cana-3294	208	21	−	−	PROPN
cana-3294	208	22	𝛼|	𝛼|	PROPN
cana-3294	208	23	}	}	PUNCT
cana-3294	208	24	.	.	PUNCT
cana-3294	209	1	clearly	clearly	ADV
cana-3294	209	2	(	(	PUNCT
cana-3294	209	3	e	e	NOUN
cana-3294	209	4	,	,	PUNCT
cana-3294	209	5	g	g	NOUN
cana-3294	209	6	)	)	PUNCT
cana-3294	209	7	is	be	AUX
cana-3294	209	8	complete	complete	ADJ
cana-3294	209	9	g	g	ADP
cana-3294	209	10	metric	metric	ADJ
cana-3294	209	11	space	space	NOUN
cana-3294	209	12	define	define	VERB
cana-3294	209	13	𝛾𝑖,𝑗	𝛾𝑖,𝑗	PUNCT
cana-3294	209	14	=	=	SYM
cana-3294	209	15	1	1	NUM
cana-3294	209	16	42𝑖+1	42𝑖+1	NUM
cana-3294	209	17	,	,	PUNCT
cana-3294	209	18	𝛿𝑖,𝑗	𝛿𝑖,𝑗	PUNCT
cana-3294	210	1	=	=	SYM
cana-3294	210	2	1	1	NUM
cana-3294	210	3	4𝑖	4𝑖	NOUN
cana-3294	210	4	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-3294	210	5	𝑎𝑙𝑙	𝑎𝑙𝑙	X
cana-3294	210	6	𝑖	𝑖	SYM
cana-3294	210	7	,	,	PUNCT
cana-3294	210	8	𝑗	𝑗	NOUN
cana-3294	210	9	=	=	SYM
cana-3294	210	10	1,2	1,2	NUM
cana-3294	210	11	,	,	PUNCT
cana-3294	210	12	…	…	PUNCT
cana-3294	210	13	…	…	PUNCT
cana-3294	210	14	…	…	PUNCT
cana-3294	210	15	..	..	PUNCT
cana-3294	210	16	consider	consider	VERB
cana-3294	210	17	the	the	DET
cana-3294	210	18	mapping	mapping	NOUN
cana-3294	210	19	tn	tn	NOUN
cana-3294	210	20	:	:	PUNCT
cana-3294	211	1	e	e	NOUN
cana-3294	211	2	3→e	3→e	NUM
cana-3294	211	3	and	and	CCONJ
cana-3294	211	4	g	g	NOUN
cana-3294	211	5	:	:	PUNCT
cana-3294	211	6	e→e	e→e	NUM
cana-3294	211	7	by	by	ADP
cana-3294	211	8	ti	ti	PROPN
cana-3294	211	9	(	(	PUNCT
cana-3294	211	10	𝝰	𝝰	X
cana-3294	211	11	,	,	PUNCT
cana-3294	211	12	𝝆	𝝆	X
cana-3294	211	13	,	,	PUNCT
cana-3294	211	14	𝝈	𝝈	NOUN
cana-3294	211	15	)	)	PUNCT
cana-3294	211	16	=	=	VERB
cana-3294	211	17	α+ρ+σ	α+ρ+σ	VERB
cana-3294	211	18	3i	3i	NOUN
cana-3294	211	19	,	,	PUNCT
cana-3294	211	20	g(𝝰)=2𝝰	g(𝝰)=2𝝰	ADJ
cana-3294	211	21	for	for	ADP
cana-3294	211	22	all	all	DET
cana-3294	211	23	𝝰	𝝰	NOUN
cana-3294	211	24	,	,	PUNCT
cana-3294	211	25	𝝆	𝝆	AUX
cana-3294	211	26	,	,	PUNCT
cana-3294	211	27	𝝈	𝝈	X
cana-3294	211	28	ϵ	ϵ	X
cana-3294	211	29	e	e	NOUN
cana-3294	211	30	,	,	PUNCT
cana-3294	211	31	n=1,2,3	n=1,2,3	NUM
cana-3294	211	32	-	-	PUNCT
cana-3294	211	33	----	----	PUNCT
cana-3294	211	34	assume	assume	VERB
cana-3294	211	35	i	i	PRON
cana-3294	211	36	<	<	X
cana-3294	211	37	j	j	PROPN
cana-3294	211	38	and	and	CCONJ
cana-3294	211	39	for	for	ADP
cana-3294	211	40	all	all	DET
cana-3294	211	41	α	α	PROPN
cana-3294	211	42	,	,	PUNCT
cana-3294	211	43	ρ	ρ	PROPN
cana-3294	211	44	,	,	PUNCT
cana-3294	211	45	σ	σ	PROPN
cana-3294	211	46	,	,	PUNCT
cana-3294	211	47	𝔪	𝔪	NOUN
cana-3294	211	48	,	,	PUNCT
cana-3294	211	49	𝔫	𝔫	PROPN
cana-3294	211	50	,	,	PUNCT
cana-3294	211	51	𝔬	𝔬	PROPN
cana-3294	211	52	,	,	PUNCT
cana-3294	211	53	𝒻	𝒻	PROPN
cana-3294	211	54	,	,	PUNCT
cana-3294	211	55	ℊ	ℊ	PROPN
cana-3294	211	56	,	,	PUNCT
cana-3294	211	57	𝒽ϵ	𝒽ϵ	ADP
cana-3294	211	58	e	e	PROPN
cana-3294	211	59	with	with	ADP
cana-3294	211	60	α	α	PROPN
cana-3294	211	61	>	>	X
cana-3294	211	62	𝔪	𝔪	X
cana-3294	211	63	≥	≥	NOUN
cana-3294	211	64	𝒻	𝒻	PROPN
cana-3294	211	65	,	,	PUNCT
cana-3294	211	66	ρ	ρ	PROPN
cana-3294	211	67	<	<	X
cana-3294	211	68	𝔫	𝔫	X
cana-3294	211	69	≤	≤	PROPN
cana-3294	211	70	ℊ	ℊ	PROPN
cana-3294	211	71	,	,	PUNCT
cana-3294	211	72	σ	σ	PROPN
cana-3294	211	73	>	>	X
cana-3294	211	74	𝔬	𝔬	PROPN
cana-3294	211	75	≥	≥	X
cana-3294	211	76	𝒽	𝒽	SYM
cana-3294	211	77	g(ti(𝝰	g(ti(𝝰	PROPN
cana-3294	211	78	,	,	PUNCT
cana-3294	211	79	𝝆,𝝈),tj(𝔪,𝔫,𝔬),tj(𝒻	𝝆,𝝈),tj(𝔪,𝔫,𝔬),tj(𝒻	PROPN
cana-3294	211	80	,	,	PUNCT
cana-3294	211	81	𝓰	𝓰	PROPN
cana-3294	211	82	,	,	PUNCT
cana-3294	211	83	𝓱))=	𝓱))=	PROPN
cana-3294	211	84	|	|	ADV
cana-3294	211	85	𝛼+𝜌+𝜎	𝛼+𝜌+𝜎	NOUN
cana-3294	211	86	3𝑖	3𝑖	NUM
cana-3294	211	87	−	−	PROPN
cana-3294	211	88	𝒻+ℊ+𝒽	𝒻+ℊ+𝒽	PROPN
cana-3294	211	89	3𝑗	3𝑗	NOUN
cana-3294	211	90	|	|	ADV
cana-3294	211	91	and	and	CCONJ
cana-3294	211	92	g(gα	g(gα	NUM
cana-3294	211	93	,	,	PUNCT
cana-3294	211	94	ti(α	ti(α	NUM
cana-3294	211	95	,	,	PUNCT
cana-3294	211	96	ρ	ρ	PROPN
cana-3294	211	97	,	,	PUNCT
cana-3294	211	98	σ	σ	PROPN
cana-3294	211	99	)	)	PUNCT
cana-3294	211	100	,	,	PUNCT
cana-3294	211	101	ti(α	ti(α	PROPN
cana-3294	211	102	,	,	PUNCT
cana-3294	211	103	ρ	ρ	PROPN
cana-3294	211	104	,	,	PUNCT
cana-3294	211	105	σ	σ	PROPN
cana-3294	211	106	)	)	PUNCT
cana-3294	211	107	)	)	PUNCT
cana-3294	212	1	+	+	CCONJ
cana-3294	212	2	g(g𝔪	g(g𝔪	ADJ
cana-3294	212	3	,	,	PUNCT
cana-3294	212	4	tj(𝔪	tj(𝔪	ADV
cana-3294	212	5	,	,	PUNCT
cana-3294	212	6	𝔫	𝔫	NOUN
cana-3294	212	7	,	,	PUNCT
cana-3294	212	8	𝔬	𝔬	NOUN
cana-3294	212	9	)	)	PUNCT
cana-3294	212	10	,	,	PUNCT
cana-3294	212	11	tj(𝒻	tj(𝒻	NOUN
cana-3294	212	12	,	,	PUNCT
cana-3294	212	13	ℊ	ℊ	NOUN
cana-3294	212	14	,	,	PUNCT
cana-3294	212	15	𝒽)=|2𝛼	𝒽)=|2𝛼	NOUN
cana-3294	212	16	−	−	PROPN
cana-3294	212	17	α+ρ+σ	α+ρ+σ	VERB
cana-3294	212	18	3i	3i	NOUN
cana-3294	212	19	|+|2𝔪	|+|2𝔪	NOUN
cana-3294	212	20	−	−	NOUN
cana-3294	212	21	𝒻+ℊ+𝑐	𝒻+ℊ+𝑐	NOUN
cana-3294	212	22	3𝑗	3𝑗	NOUN
cana-3294	212	23	|	|	ADV
cana-3294	212	24	𝐺(𝑔𝞪	𝐺(𝑔𝞪	PROPN
cana-3294	212	25	,	,	PUNCT
cana-3294	212	26	𝒈𝖒	𝒈𝖒	ADV
cana-3294	212	27	,	,	PUNCT
cana-3294	212	28	𝒈𝓯	𝒈𝓯	NOUN
cana-3294	212	29	)	)	PUNCT
cana-3294	212	30	=	=	NOUN
cana-3294	212	31	|𝟔𝞪	|𝟔𝞪	NUM
cana-3294	212	32	−	−	PROPN
cana-3294	212	33	𝟔𝓯|	𝟔𝓯|	PUNCT
cana-3294	212	34	since	since	SCONJ
cana-3294	212	35	𝛾𝑖,𝑗	𝛾𝑖,𝑗	NOUN
cana-3294	212	36	,	,	PUNCT
cana-3294	212	37	𝛿𝑖,𝑗	𝛿𝑖,𝑗	X
cana-3294	212	38	<	<	X
cana-3294	212	39	1	1	NUM
cana-3294	212	40	,	,	PUNCT
cana-3294	212	41	condition	condition	NOUN
cana-3294	212	42	(	(	PUNCT
cana-3294	212	43	5	5	NUM
cana-3294	212	44	)	)	PUNCT
cana-3294	212	45	satisfied	satisfied	ADJ
cana-3294	212	46	for	for	ADP
cana-3294	212	47	all	all	DET
cana-3294	212	48	α	α	PROPN
cana-3294	212	49	,	,	PUNCT
cana-3294	212	50	ρ	ρ	PROPN
cana-3294	212	51	,	,	PUNCT
cana-3294	212	52	σ	σ	PROPN
cana-3294	212	53	,	,	PUNCT
cana-3294	212	54	𝔪	𝔪	NOUN
cana-3294	212	55	,	,	PUNCT
cana-3294	212	56	𝔫	𝔫	PROPN
cana-3294	212	57	,	,	PUNCT
cana-3294	212	58	𝔬	𝔬	PROPN
cana-3294	212	59	,	,	PUNCT
cana-3294	212	60	𝒻	𝒻	PROPN
cana-3294	212	61	,	,	PUNCT
cana-3294	212	62	ℊ	ℊ	PROPN
cana-3294	212	63	,	,	PUNCT
cana-3294	212	64	𝒽	𝒽	PRON
cana-3294	212	65	ϵ	ϵ	X
cana-3294	212	66	e	e	NOUN
cana-3294	212	67	with	with	ADP
cana-3294	212	68	α	α	PROPN
cana-3294	212	69	>	>	X
cana-3294	212	70	𝔪	𝔪	X
cana-3294	212	71	≥	≥	NOUN
cana-3294	212	72	𝒻	𝒻	PROPN
cana-3294	212	73	,	,	PUNCT
cana-3294	212	74	ρ	ρ	PROPN
cana-3294	212	75	<	<	X
cana-3294	212	76	𝔫	𝔫	X
cana-3294	212	77	≤	≤	PROPN
cana-3294	212	78	ℊ	ℊ	PROPN
cana-3294	212	79	,	,	PUNCT
cana-3294	212	80	σ	σ	PROPN
cana-3294	212	81	>	>	X
cana-3294	212	82	𝔬	𝔬	PROPN
cana-3294	212	83	≥	≥	PUNCT
cana-3294	212	84	𝒽	𝒽	X
cana-3294	212	85	moreover	moreover	ADV
cana-3294	212	86	,	,	PUNCT
cana-3294	212	87	the	the	DET
cana-3294	212	88	series	series	NOUN
cana-3294	212	89	∑	∑	PROPN
cana-3294	212	90	(	(	PUNCT
cana-3294	212	91	γ	γ	X
cana-3294	212	92	i	i	PRON
cana-3294	212	93	,	,	PUNCT
cana-3294	212	94	i+1	i+1	X
cana-3294	212	95	+	+	ADJ
cana-3294	212	96	δi	δi	ADJ
cana-3294	212	97	,	,	PUNCT
cana-3294	212	98	i+1	i+1	NUM
cana-3294	212	99	1−γ	1−γ	NUM
cana-3294	212	100	i	i	NOUN
cana-3294	212	101	,	,	PUNCT
cana-3294	212	102	i+1	i+1	NUM
cana-3294	212	103	)	)	PUNCT
cana-3294	212	104	∞	∞	NUM
cana-3294	212	105	𝑖=1	𝑖=1	PUNCT
cana-3294	213	1	=	=	PRON
cana-3294	213	2	∑	∑	PROPN
cana-3294	213	3	1	1	NUM
cana-3294	213	4	42𝑖+1	42𝑖+1	NUM
cana-3294	213	5	+	+	SYM
cana-3294	213	6	1	1	NUM
cana-3294	213	7	4𝑖	4𝑖	NOUN
cana-3294	213	8	1−4	1−4	NUM
cana-3294	213	9	1	1	NUM
cana-3294	213	10	2𝑖+1	2𝑖+1	NUM
cana-3294	213	11	∞	∞	NUM
cana-3294	213	12	𝑖=1	𝑖=1	PUNCT
cana-3294	213	13	=	=	PRON
cana-3294	213	14	∑	∑	PROPN
cana-3294	213	15	4𝑖+1	4𝑖+1	PROPN
cana-3294	213	16	+	+	PROPN
cana-3294	213	17	1	1	NUM
cana-3294	213	18	42𝑖+1−1	42𝑖+1−1	NUM
cana-3294	213	19	∞	∞	NUM
cana-3294	213	20	𝑖=1	𝑖=1	PROPN
cana-3294	213	21	is	be	AUX
cana-3294	213	22	an	an	DET
cana-3294	213	23	α	α	NOUN
cana-3294	213	24	-	-	PUNCT
cana-3294	213	25	series	series	NOUN
cana-3294	213	26	with	with	ADP
cana-3294	213	27	α	α	PROPN
cana-3294	213	28	=	=	SYM
cana-3294	213	29	1	1	NUM
cana-3294	213	30	4	4	NUM
cana-3294	213	31	.	.	PUNCT
cana-3294	214	1	unique	unique	ADJ
cana-3294	214	2	common	common	ADJ
cana-3294	214	3	tripled	triple	VERB
cana-3294	214	4	fixed	fix	VERB
cana-3294	214	5	point	point	NOUN
cana-3294	214	6	for	for	ADP
cana-3294	214	7	g	g	PROPN
cana-3294	214	8	and	and	CCONJ
cana-3294	214	9	tn	tn	NOUN
cana-3294	214	10	is	be	AUX
cana-3294	214	11	(	(	PUNCT
cana-3294	214	12	0,0,0	0,0,0	NOUN
cana-3294	214	13	)	)	PUNCT
cana-3294	214	14	theorem	theorem	VERB
cana-3294	214	15	4.7	4.7	NUM
cana-3294	214	16	:	:	PUNCT
cana-3294	214	17	let	let	VERB
cana-3294	214	18	(	(	PUNCT
cana-3294	214	19	ℋ	ℋ	PROPN
cana-3294	214	20	,	,	PUNCT
cana-3294	214	21	g	g	NOUN
cana-3294	214	22	)	)	PUNCT
cana-3294	214	23	be	be	AUX
cana-3294	214	24	complete	complete	ADJ
cana-3294	214	25	g	g	ADP
cana-3294	214	26	metric	metric	ADJ
cana-3294	214	27	space	space	NOUN
cana-3294	214	28	and	and	CCONJ
cana-3294	214	29	{	{	PUNCT
cana-3294	214	30	tn	tn	NOUN
cana-3294	214	31	}	}	PUNCT
cana-3294	214	32	:	:	PUNCT
cana-3294	214	33	ℋ	ℋ	PROPN
cana-3294	214	34	→	→	SYM
cana-3294	214	35	ℋ	ℋ	PROPN
cana-3294	214	36	be	be	AUX
cana-3294	214	37	a	a	DET
cana-3294	214	38	sequence	sequence	NOUN
cana-3294	214	39	of	of	ADP
cana-3294	214	40	self	self	NOUN
cana-3294	214	41	-	-	PUNCT
cana-3294	214	42	mappings	mapping	NOUN
cana-3294	214	43	such	such	ADJ
cana-3294	214	44	that	that	PRON
cana-3294	214	45	g(tj(ꝕ),tk(ꝙ),tk(υ	g(tj(ꝕ),tk(ꝙ),tk(υ	PROPN
cana-3294	214	46	)	)	PUNCT
cana-3294	214	47	)	)	PUNCT
cana-3294	215	1	≤	≤	NUM
cana-3294	215	2	βj	βj	ADP
cana-3294	215	3	,	,	PUNCT
cana-3294	215	4	k	k	PROPN
cana-3294	216	1	[	[	X
cana-3294	216	2	g(ꝕ	g(ꝕ	PROPN
cana-3294	216	3	,	,	PUNCT
cana-3294	216	4	tj(ꝕ),tj(ꝕ))+g(ꝙ	tj(ꝕ),tj(ꝕ))+g(ꝙ	ADJ
cana-3294	216	5	,	,	PUNCT
cana-3294	216	6	tk(ꝙ),tk(ꝙ))+g(υ	tk(ꝙ),tk(ꝙ))+g(υ	ADJ
cana-3294	216	7	,	,	PUNCT
cana-3294	216	8	tk(υ),tk(υ	tk(υ),tk(υ	NOUN
cana-3294	216	9	)	)	PUNCT
cana-3294	216	10	)	)	PUNCT
cana-3294	216	11	]	]	PUNCT
cana-3294	217	1	+	+	ADP
cana-3294	217	2	γj	γj	ADP
cana-3294	217	3	k	k	PROPN
cana-3294	217	4	g(ꝕ	g(ꝕ	PROPN
cana-3294	217	5	,	,	PUNCT
cana-3294	217	6	ꝙ	ꝙ	NOUN
cana-3294	217	7	,	,	PUNCT
cana-3294	217	8	υ	υ	NOUN
cana-3294	217	9	)	)	PUNCT
cana-3294	217	10	(	(	PUNCT
cana-3294	217	11	a	a	NOUN
cana-3294	217	12	)	)	PUNCT
cana-3294	217	13	for	for	ADP
cana-3294	217	14	ꝕ	ꝕ	NOUN
cana-3294	217	15	,	,	PUNCT
cana-3294	217	16	ꝙ	ꝙ	NOUN
cana-3294	217	17	,	,	PUNCT
cana-3294	217	18	υ	υ	PROPN
cana-3294	217	19	∈	∈	PROPN
cana-3294	217	20	ℋ	ℋ	PROPN
cana-3294	217	21	with	with	ADP
cana-3294	217	22	ꝕ	ꝕ	DET
cana-3294	217	23	≠	≠	PROPN
cana-3294	217	24	ꝙ	ꝙ	NUM
cana-3294	217	25	,	,	PUNCT
cana-3294	217	26	0	0	NUM
cana-3294	217	27	≤	≤	NUM
cana-3294	217	28	βj	βj	NOUN
cana-3294	217	29	,	,	PUNCT
cana-3294	217	30	k	k	NOUN
cana-3294	217	31	,	,	PUNCT
cana-3294	217	32	,	,	PUNCT
cana-3294	217	33	γj	γj	PROPN
cana-3294	217	34	,	,	PUNCT
cana-3294	217	35	k	k	X
cana-3294	217	36	<	<	X
cana-3294	217	37	1	1	NUM
cana-3294	217	38	2	2	NUM
cana-3294	217	39	,	,	PUNCT
cana-3294	217	40	j	j	PROPN
cana-3294	217	41	,	,	PUNCT
cana-3294	217	42	k=1,2,---	k=1,2,---	PROPN
cana-3294	217	43	if	if	SCONJ
cana-3294	217	44	∑	∑	ADP
cana-3294	217	45	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	217	46	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	ADJ
cana-3294	217	47	∞	∞	PROPN
cana-3294	217	48	𝑗=1	𝑗=1	PROPN
cana-3294	217	49	is	be	AUX
cana-3294	217	50	an	an	DET
cana-3294	217	51	α	α	NOUN
cana-3294	217	52	-	-	PUNCT
cana-3294	217	53	series	series	NOUN
cana-3294	217	54	then	then	ADV
cana-3294	217	55	{	{	PUNCT
cana-3294	217	56	tn	tn	NOUN
cana-3294	217	57	}	}	PUNCT
cana-3294	217	58	has	have	AUX
cana-3294	217	59	unique	unique	ADJ
cana-3294	217	60	common	common	ADJ
cana-3294	217	61	fixed	fix	VERB
cana-3294	217	62	point	point	NOUN
cana-3294	217	63	in	in	ADP
cana-3294	217	64	ℋ.	ℋ.	PROPN
cana-3294	217	65	communications	communication	NOUN
cana-3294	217	66	on	on	ADP
cana-3294	217	67	applied	apply	VERB
cana-3294	217	68	nonlinear	nonlinear	ADJ
cana-3294	217	69	analysis	analysis	NOUN
cana-3294	217	70	issn	issn	NOUN
cana-3294	217	71	:	:	PUNCT
cana-3294	217	72	1074	1074	NUM
cana-3294	217	73	-	-	PUNCT
cana-3294	217	74	133x	133x	NUM
cana-3294	217	75	vol	vol	NOUN
cana-3294	217	76	32	32	NUM
cana-3294	217	77	no	no	NOUN
cana-3294	217	78	.	.	PUNCT
cana-3294	218	1	6s	6s	NUM
cana-3294	218	2	(	(	PUNCT
cana-3294	218	3	2025	2025	NUM
cana-3294	218	4	)	)	PUNCT
cana-3294	218	5	285	285	NUM
cana-3294	219	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	219	2	proof	proof	NOUN
cana-3294	219	3	:	:	PUNCT
cana-3294	219	4	for	for	ADP
cana-3294	219	5	any	any	DET
cana-3294	219	6	ꝕ0∈ℋ	ꝕ0∈ℋ	NOUN
cana-3294	219	7	,	,	PUNCT
cana-3294	219	8	we	we	PRON
cana-3294	219	9	can	can	AUX
cana-3294	219	10	consider	consider	VERB
cana-3294	219	11	the	the	DET
cana-3294	219	12	sequence	sequence	NOUN
cana-3294	219	13	ꝕn=	ꝕn=	PROPN
cana-3294	219	14	tn(ꝕn-1	tn(ꝕn-1	NOUN
cana-3294	219	15	)	)	PUNCT
cana-3294	219	16	,	,	PUNCT
cana-3294	219	17	n=1,2	n=1,2	NOUN
cana-3294	219	18	-	-	PUNCT
cana-3294	219	19	--	--	PUNCT
cana-3294	219	20	from	from	ADP
cana-3294	219	21	(	(	PUNCT
cana-3294	219	22	a	a	X
cana-3294	219	23	)	)	PUNCT
cana-3294	219	24	we	we	PRON
cana-3294	219	25	have	have	AUX
cana-3294	219	26	g(ꝕ1,ꝕ2,ꝕ2)=	g(ꝕ1,ꝕ2,ꝕ2)=	PROPN
cana-3294	219	27	g(t1ꝕ0	g(t1ꝕ0	PROPN
cana-3294	219	28	,	,	PUNCT
cana-3294	219	29	t2ꝕ1	t2ꝕ1	PROPN
cana-3294	219	30	,	,	PUNCT
cana-3294	219	31	t2ꝕ1	t2ꝕ1	NOUN
cana-3294	219	32	)	)	PUNCT
cana-3294	219	33	≤	≤	NOUN
cana-3294	219	34	β1,2[g(ꝕ0	β1,2[g(ꝕ0	PROPN
cana-3294	219	35	,	,	PUNCT
cana-3294	219	36	t1ꝕ0	t1ꝕ0	NOUN
cana-3294	219	37	,	,	PUNCT
cana-3294	219	38	t1ꝕ0)+	t1ꝕ0)+	PROPN
cana-3294	219	39	g(ꝕ1	g(ꝕ1	NOUN
cana-3294	219	40	,	,	PUNCT
cana-3294	219	41	t2ꝕ1	t2ꝕ1	PROPN
cana-3294	219	42	,	,	PUNCT
cana-3294	219	43	t1ꝕ1)+g(ꝕ1,t2ꝕ1	t1ꝕ1)+g(ꝕ1,t2ꝕ1	NUM
cana-3294	219	44	,	,	PUNCT
cana-3294	219	45	t2ꝕ1)]+	t2ꝕ1)]+	NUM
cana-3294	219	46	γ1,2g(ꝕ0	γ1,2g(ꝕ0	ADJ
cana-3294	219	47	,	,	PUNCT
cana-3294	219	48	ꝕ1	ꝕ1	NOUN
cana-3294	219	49	,	,	PUNCT
cana-3294	219	50	ꝕ1	ꝕ1	PROPN
cana-3294	219	51	)	)	PUNCT
cana-3294	219	52	≤	≤	PUNCT
cana-3294	219	53	β1,2[g(ꝕ0	β1,2[g(ꝕ0	PROPN
cana-3294	219	54	,	,	PUNCT
cana-3294	219	55	ꝕ1	ꝕ1	NOUN
cana-3294	219	56	,	,	PUNCT
cana-3294	219	57	ꝕ1)+g(ꝕ1	ꝕ1)+g(ꝕ1	NOUN
cana-3294	219	58	,	,	PUNCT
cana-3294	219	59	ꝕ2	ꝕ2	NOUN
cana-3294	219	60	,	,	PUNCT
cana-3294	219	61	ꝕ2)+g(ꝕ1	ꝕ2)+g(ꝕ1	NOUN
cana-3294	219	62	,	,	PUNCT
cana-3294	219	63	ꝕ2	ꝕ2	NOUN
cana-3294	219	64	,	,	PUNCT
cana-3294	219	65	ꝕ2)]+	ꝕ2)]+	PROPN
cana-3294	219	66	γ1,2g(ꝕ0	γ1,2g(ꝕ0	ADJ
cana-3294	219	67	,	,	PUNCT
cana-3294	219	68	ꝕ1	ꝕ1	NOUN
cana-3294	219	69	,	,	PUNCT
cana-3294	219	70	ꝕ1	ꝕ1	PROPN
cana-3294	219	71	)	)	PUNCT
cana-3294	219	72	≤	≤	PUNCT
cana-3294	220	1	β1,2[g(ꝕ0	β1,2[g(ꝕ0	PROPN
cana-3294	220	2	,	,	PUNCT
cana-3294	220	3	ꝕ1	ꝕ1	NOUN
cana-3294	220	4	,	,	PUNCT
cana-3294	220	5	ꝕ1)+2g(ꝕ1	ꝕ1)+2g(ꝕ1	PROPN
cana-3294	220	6	,	,	PUNCT
cana-3294	220	7	ꝕ2	ꝕ2	PROPN
cana-3294	220	8	,	,	PUNCT
cana-3294	220	9	ꝕ2)]+	ꝕ2)]+	PROPN
cana-3294	220	10	γ1,2g(ꝕ0	γ1,2g(ꝕ0	ADJ
cana-3294	220	11	,	,	PUNCT
cana-3294	220	12	ꝕ1	ꝕ1	PROPN
cana-3294	220	13	,	,	PUNCT
cana-3294	220	14	ꝕ1	ꝕ1	NOUN
cana-3294	220	15	)	)	PUNCT
cana-3294	220	16	g(ꝕ1,ꝕ2	g(ꝕ1,ꝕ2	PROPN
cana-3294	220	17	,	,	PUNCT
cana-3294	220	18	ꝕ2	ꝕ2	NOUN
cana-3294	220	19	)	)	PUNCT
cana-3294	220	20	≤	≤	NOUN
cana-3294	220	21	(	(	PUNCT
cana-3294	220	22	𝛽1,2+𝛾1,2	𝛽1,2+𝛾1,2	NOUN
cana-3294	220	23	1−2𝛽1,2	1−2𝛽1,2	NUM
cana-3294	220	24	)	)	PUNCT
cana-3294	220	25	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	220	26	,	,	PUNCT
cana-3294	220	27	ꝕ1	ꝕ1	NOUN
cana-3294	220	28	,	,	PUNCT
cana-3294	220	29	ꝕ1	ꝕ1	PROPN
cana-3294	220	30	)	)	PUNCT
cana-3294	220	31	.	.	PUNCT
cana-3294	221	1	also	also	ADV
cana-3294	221	2	we	we	PRON
cana-3294	221	3	get	get	VERB
cana-3294	221	4	g(ꝕ2	g(ꝕ2	NOUN
cana-3294	221	5	,	,	PUNCT
cana-3294	221	6	ꝕ3	ꝕ3	PROPN
cana-3294	221	7	,	,	PUNCT
cana-3294	221	8	ꝕ3	ꝕ3	PROPN
cana-3294	221	9	)	)	PUNCT
cana-3294	221	10	]	]	PUNCT
cana-3294	222	1	=	=	PUNCT
cana-3294	222	2	g(t2ꝕ1	g(t2ꝕ1	PROPN
cana-3294	222	3	,	,	PUNCT
cana-3294	222	4	t3ꝕ2	t3ꝕ2	ADP
cana-3294	222	5	,	,	PUNCT
cana-3294	222	6	t3ꝕ2	t3ꝕ2	ADP
cana-3294	222	7	)	)	PUNCT
cana-3294	222	8	≤	≤	NOUN
cana-3294	222	9	(	(	PUNCT
cana-3294	222	10	𝛽2,3+𝛾2,3	𝛽2,3+𝛾2,3	PROPN
cana-3294	222	11	1−2𝛽2,3	1−2𝛽2,3	NUM
cana-3294	222	12	)	)	PUNCT
cana-3294	222	13	g(ꝕ1	g(ꝕ1	NOUN
cana-3294	222	14	,	,	PUNCT
cana-3294	222	15	ꝕ2	ꝕ2	NOUN
cana-3294	222	16	,	,	PUNCT
cana-3294	222	17	ꝕ2	ꝕ2	NOUN
cana-3294	222	18	)	)	PUNCT
cana-3294	222	19	≤	≤	NUM
cana-3294	222	20	(	(	PUNCT
cana-3294	222	21	𝛽2,3+𝛾2,3	𝛽2,3+𝛾2,3	PROPN
cana-3294	222	22	1−2𝛽2,3	1−2𝛽2,3	NUM
cana-3294	222	23	)	)	PUNCT
cana-3294	222	24	(	(	PUNCT
cana-3294	222	25	𝛽1,2+𝛾1,2	𝛽1,2+𝛾1,2	NOUN
cana-3294	222	26	1−2𝛽1,2	1−2𝛽1,2	NUM
cana-3294	222	27	)	)	PUNCT
cana-3294	222	28	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	222	29	,	,	PUNCT
cana-3294	222	30	ꝕ1	ꝕ1	NOUN
cana-3294	222	31	,	,	PUNCT
cana-3294	222	32	ꝕ1	ꝕ1	PROPN
cana-3294	222	33	)	)	PUNCT
cana-3294	222	34	.	.	PUNCT
cana-3294	223	1	repeating	repeat	VERB
cana-3294	223	2	the	the	DET
cana-3294	223	3	above	above	ADJ
cana-3294	223	4	reasoning	reason	VERB
cana-3294	223	5	we	we	PRON
cana-3294	223	6	obtain	obtain	VERB
cana-3294	223	7	g(ꝕn	g(ꝕn	NOUN
cana-3294	223	8	,	,	PUNCT
cana-3294	223	9	ꝕn+1,ꝕn+1	ꝕn+1,ꝕn+1	NOUN
cana-3294	223	10	)	)	PUNCT
cana-3294	223	11	≤	≤	NOUN
cana-3294	223	12	∏	∏	PROPN
cana-3294	223	13	(	(	PUNCT
cana-3294	223	14	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	223	15	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	223	16	)	)	PUNCT
cana-3294	223	17	𝑛	𝑛	PRON
cana-3294	223	18	𝑗=1	𝑗=1	PROPN
cana-3294	223	19	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	223	20	,	,	PUNCT
cana-3294	223	21	ꝕ1	ꝕ1	NOUN
cana-3294	223	22	,	,	PUNCT
cana-3294	223	23	ꝕ1	ꝕ1	PROPN
cana-3294	223	24	)	)	PUNCT
cana-3294	223	25	.	.	PUNCT
cana-3294	224	1	for	for	ADP
cana-3294	224	2	p>0	p>0	ADV
cana-3294	224	3	and	and	CCONJ
cana-3294	224	4	by	by	ADP
cana-3294	224	5	g5	g5	PROPN
cana-3294	224	6	g(ꝕn	g(ꝕn	PROPN
cana-3294	224	7	,	,	PUNCT
cana-3294	224	8	ꝕn+p	ꝕn+p	PROPN
cana-3294	224	9	,	,	PUNCT
cana-3294	224	10	ꝕn+p	ꝕn+p	NOUN
cana-3294	224	11	)	)	PUNCT
cana-3294	224	12	≤	≤	NUM
cana-3294	224	13	g(ꝕn	g(ꝕn	NOUN
cana-3294	224	14	,	,	PUNCT
cana-3294	224	15	ꝕn+1,ꝕn+1)+	ꝕn+1,ꝕn+1)+	PROPN
cana-3294	224	16	g(ꝕn+1	g(ꝕn+1	PROPN
cana-3294	224	17	,	,	PUNCT
cana-3294	224	18	ꝕn+2,ꝕn+2)+	ꝕn+2,ꝕn+2)+	ADJ
cana-3294	224	19	g(ꝕn+2	g(ꝕn+2	NOUN
cana-3294	224	20	,	,	PUNCT
cana-3294	224	21	ꝕn+3,ꝕn+3)+--	ꝕn+3,ꝕn+3)+--	PROPN
cana-3294	224	22	+	+	CCONJ
cana-3294	224	23	g(ꝕn+p-1	g(ꝕn+p-1	PROPN
cana-3294	224	24	,	,	PUNCT
cana-3294	224	25	ꝕn+p	ꝕn+p	NOUN
cana-3294	224	26	,	,	PUNCT
cana-3294	224	27	ꝕn+p	ꝕn+p	NOUN
cana-3294	224	28	)	)	PUNCT
cana-3294	224	29	≤	≤	NOUN
cana-3294	224	30	∏	∏	PROPN
cana-3294	224	31	(	(	PUNCT
cana-3294	224	32	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	224	33	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	224	34	)	)	PUNCT
cana-3294	224	35	𝑛	𝑛	DET
cana-3294	224	36	𝑗=1	𝑗=1	PROPN
cana-3294	224	37	+	+	NOUN
cana-3294	224	38	∏	∏	PROPN
cana-3294	224	39	(	(	PUNCT
cana-3294	224	40	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	224	41	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	224	42	)	)	PUNCT
cana-3294	224	43	𝑛+1	𝑛+1	PROPN
cana-3294	224	44	𝑗=1	𝑗=1	SYM
cana-3294	224	45	+	+	PROPN
cana-3294	224	46	---	---	PUNCT
cana-3294	224	47	+	+	ADJ
cana-3294	224	48	∏	∏	NOUN
cana-3294	224	49	(	(	PUNCT
cana-3294	224	50	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	224	51	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	224	52	)	)	PUNCT
cana-3294	224	53	𝑛+𝑝−1	𝑛+𝑝−1	PROPN
cana-3294	224	54	𝑗=1	𝑗=1	PROPN
cana-3294	224	55	]	]	PUNCT
cana-3294	224	56	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	224	57	,	,	PUNCT
cana-3294	224	58	ꝕ1	ꝕ1	NOUN
cana-3294	224	59	,	,	PUNCT
cana-3294	224	60	ꝕ1	ꝕ1	PROPN
cana-3294	224	61	)	)	PUNCT
cana-3294	224	62	)	)	PUNCT
cana-3294	224	63	.	.	PUNCT
cana-3294	225	1	≤	≤	NUM
cana-3294	225	2	∑	∑	PUNCT
cana-3294	225	3	∏	∏	PROPN
cana-3294	225	4	(	(	PUNCT
cana-3294	225	5	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	225	6	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NUM
cana-3294	225	7	)	)	PUNCT
cana-3294	225	8	𝑛+𝑘	𝑛+𝑘	PROPN
cana-3294	225	9	𝑗=1	𝑗=1	X
cana-3294	226	1	𝑝−1	𝑝−1	PROPN
cana-3294	226	2	𝑘=0	𝑘=0	PROPN
cana-3294	226	3	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	226	4	,	,	PUNCT
cana-3294	226	5	ꝕ1	ꝕ1	NOUN
cana-3294	226	6	,	,	PUNCT
cana-3294	226	7	ꝕ1	ꝕ1	PROPN
cana-3294	226	8	)	)	PUNCT
cana-3294	226	9	.	.	PUNCT
cana-3294	227	1	≤	≤	NUM
cana-3294	227	2	∑	∑	PUNCT
cana-3294	227	3	∏	∏	PROPN
cana-3294	227	4	(	(	PUNCT
cana-3294	227	5	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	227	6	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	227	7	)	)	PUNCT
cana-3294	228	1	𝑘	𝑘	X
cana-3294	228	2	𝑗=1	𝑗=1	PROPN
cana-3294	228	3	𝑛+𝑝−1	𝑛+𝑝−1	ADJ
cana-3294	228	4	𝑘=𝑛	𝑘=𝑛	PROPN
cana-3294	228	5	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	228	6	,	,	PUNCT
cana-3294	228	7	ꝕ1	ꝕ1	NOUN
cana-3294	228	8	,	,	PUNCT
cana-3294	228	9	ꝕ1	ꝕ1	PROPN
cana-3294	228	10	)	)	PUNCT
cana-3294	228	11	by	by	ADP
cana-3294	228	12	using	use	VERB
cana-3294	228	13	the	the	DET
cana-3294	228	14	fact	fact	NOUN
cana-3294	228	15	that	that	SCONJ
cana-3294	228	16	the	the	DET
cana-3294	228	17	geometric	geometric	ADJ
cana-3294	228	18	mean	mean	NOUN
cana-3294	228	19	is	be	AUX
cana-3294	228	20	less	less	ADJ
cana-3294	228	21	than	than	ADP
cana-3294	228	22	or	or	CCONJ
cana-3294	228	23	equal	equal	ADJ
cana-3294	228	24	to	to	ADP
cana-3294	228	25	arithmetic	arithmetic	ADJ
cana-3294	228	26	mean	mean	NOUN
cana-3294	228	27	for	for	ADP
cana-3294	228	28	non	non	ADJ
cana-3294	228	29	-	-	ADJ
cana-3294	228	30	negative	negative	ADJ
cana-3294	228	31	real	real	ADJ
cana-3294	228	32	numbers	number	NOUN
cana-3294	228	33	and	and	CCONJ
cana-3294	228	34	let	let	VERB
cana-3294	228	35	α	α	PRON
cana-3294	228	36	and	and	CCONJ
cana-3294	228	37	nα	nα	VERB
cana-3294	228	38	for	for	ADP
cana-3294	228	39	m≥	m≥	PROPN
cana-3294	228	40	nα	nα	PROPN
cana-3294	228	41	as	as	ADV
cana-3294	228	42	in	in	ADP
cana-3294	228	43	definition	definition	NOUN
cana-3294	228	44	2.9	2.9	NUM
cana-3294	228	45	follows	follow	VERB
cana-3294	228	46	as	as	ADP
cana-3294	228	47	below	below	ADP
cana-3294	228	48	≤	≤	NUM
cana-3294	228	49	∑	∑	PUNCT
cana-3294	228	50	[	[	PUNCT
cana-3294	228	51	1	1	NUM
cana-3294	228	52	𝑘	𝑘	X
cana-3294	228	53	∑	∑	PUNCT
cana-3294	228	54	(	(	PUNCT
cana-3294	228	55	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	228	56	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	228	57	)	)	PUNCT
cana-3294	229	1	𝑘	𝑘	X
cana-3294	229	2	𝑗=1	𝑗=1	NOUN
cana-3294	230	1	]	]	PUNCT
cana-3294	230	2	𝑛+𝑝−1	𝑛+𝑝−1	PROPN
cana-3294	230	3	𝑘=𝑛	𝑘=𝑛	PROPN
cana-3294	230	4	𝑘	𝑘	PRON
cana-3294	230	5	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	230	6	,	,	PUNCT
cana-3294	230	7	ꝕ1	ꝕ1	NOUN
cana-3294	230	8	,	,	PUNCT
cana-3294	230	9	ꝕ1	ꝕ1	PROPN
cana-3294	230	10	)	)	PUNCT
cana-3294	230	11	.	.	PUNCT
cana-3294	231	1	∴	∴	PROPN
cana-3294	231	2	g(ꝕn	g(ꝕn	PROPN
cana-3294	231	3	,	,	PUNCT
cana-3294	231	4	ꝕn+p	ꝕn+p	PROPN
cana-3294	231	5	,	,	PUNCT
cana-3294	231	6	ꝕn+p)≤	ꝕn+p)≤	PROPN
cana-3294	231	7	∑	∑	PROPN
cana-3294	231	8	[	[	PUNCT
cana-3294	231	9	1	1	NUM
cana-3294	231	10	𝑘	𝑘	X
cana-3294	231	11	∑	∑	PUNCT
cana-3294	231	12	(	(	PUNCT
cana-3294	231	13	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	231	14	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	231	15	)	)	PUNCT
cana-3294	231	16	𝑘	𝑘	X
cana-3294	232	1	𝑗=1	𝑗=1	NOUN
cana-3294	232	2	]	]	PUNCT
cana-3294	232	3	𝑛+𝑝−1	𝑛+𝑝−1	PROPN
cana-3294	232	4	𝑘=𝑛	𝑘=𝑛	PROPN
cana-3294	232	5	𝑘	𝑘	PRON
cana-3294	232	6	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	232	7	,	,	PUNCT
cana-3294	232	8	ꝕ1	ꝕ1	NOUN
cana-3294	232	9	,	,	PUNCT
cana-3294	232	10	ꝕ1	ꝕ1	PROPN
cana-3294	232	11	)	)	PUNCT
cana-3294	232	12	.	.	PUNCT
cana-3294	233	1	≤	≤	NUM
cana-3294	233	2	(	(	PUNCT
cana-3294	233	3	∑	∑	PART
cana-3294	233	4	𝛼𝑘𝑛+𝑝−1	𝛼𝑘𝑛+𝑝−1	PROPN
cana-3294	233	5	𝑘=𝑛	𝑘=𝑛	PROPN
cana-3294	233	6	)	)	PUNCT
cana-3294	233	7	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	233	8	,	,	PUNCT
cana-3294	233	9	ꝕ1	ꝕ1	NOUN
cana-3294	233	10	,	,	PUNCT
cana-3294	233	11	ꝕ1	ꝕ1	PROPN
cana-3294	233	12	)	)	PUNCT
cana-3294	233	13	.	.	PUNCT
cana-3294	234	1	≤	≤	NUM
cana-3294	234	2	(	(	PUNCT
cana-3294	234	3	𝛼𝑛	𝛼𝑛	ADP
cana-3294	234	4	+	+	CCONJ
cana-3294	234	5	𝛼𝑛+1	𝛼𝑛+1	NUM
cana-3294	234	6	+	+	CCONJ
cana-3294	234	7	𝛼𝑛+2	𝛼𝑛+2	NUM
cana-3294	234	8	+	+	ADJ
cana-3294	234	9	---+𝛼𝑛+𝑝−1)g(ꝕ0	---+𝛼𝑛+𝑝−1)g(ꝕ0	ADJ
cana-3294	234	10	,	,	PUNCT
cana-3294	234	11	ꝕ1	ꝕ1	NOUN
cana-3294	234	12	,	,	PUNCT
cana-3294	234	13	ꝕ1	ꝕ1	PROPN
cana-3294	234	14	)	)	PUNCT
cana-3294	234	15	.	.	PUNCT
cana-3294	235	1	communications	communication	NOUN
cana-3294	235	2	on	on	ADP
cana-3294	235	3	applied	apply	VERB
cana-3294	235	4	nonlinear	nonlinear	ADJ
cana-3294	235	5	analysis	analysis	NOUN
cana-3294	235	6	issn	issn	NOUN
cana-3294	235	7	:	:	PUNCT
cana-3294	235	8	1074	1074	NUM
cana-3294	235	9	-	-	PUNCT
cana-3294	235	10	133x	133x	NUM
cana-3294	235	11	vol	vol	NOUN
cana-3294	235	12	32	32	NUM
cana-3294	235	13	no	no	NOUN
cana-3294	235	14	.	.	PUNCT
cana-3294	236	1	6s	6s	NUM
cana-3294	236	2	(	(	PUNCT
cana-3294	236	3	2025	2025	NUM
cana-3294	236	4	)	)	PUNCT
cana-3294	236	5	286	286	NUM
cana-3294	236	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	236	7	≤	≤	NUM
cana-3294	236	8	𝛼𝑛(1+α+𝛼2+𝛼3	𝛼𝑛(1+α+𝛼2+𝛼3	NOUN
cana-3294	236	9	+	+	NOUN
cana-3294	236	10	------+𝛼𝑝−1	------+𝛼𝑝−1	NOUN
cana-3294	236	11	)	)	PUNCT
cana-3294	236	12	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	236	13	,	,	PUNCT
cana-3294	236	14	ꝕ1	ꝕ1	NOUN
cana-3294	236	15	,	,	PUNCT
cana-3294	236	16	ꝕ1	ꝕ1	PROPN
cana-3294	236	17	)	)	PUNCT
cana-3294	236	18	.	.	PUNCT
cana-3294	237	1	≤	≤	NUM
cana-3294	237	2	𝛼𝑛	𝛼𝑛	PROPN
cana-3294	237	3	1−𝛼	1−𝛼	NUM
cana-3294	237	4	g(ꝕ0	g(ꝕ0	NOUN
cana-3294	237	5	,	,	PUNCT
cana-3294	237	6	ꝕ1	ꝕ1	NOUN
cana-3294	237	7	,	,	PUNCT
cana-3294	237	8	ꝕ1	ꝕ1	PROPN
cana-3294	237	9	)	)	PUNCT
cana-3294	237	10	.	.	PUNCT
cana-3294	238	1	let	let	VERB
cana-3294	238	2	n	n	PRON
cana-3294	238	3	,	,	PUNCT
cana-3294	238	4	p	p	PROPN
cana-3294	238	5	→∞	→∞	X
cana-3294	238	6	,	,	PUNCT
cana-3294	238	7	g(ꝕn	g(ꝕn	PROPN
cana-3294	238	8	,	,	PUNCT
cana-3294	238	9	ꝕn+p	ꝕn+p	NOUN
cana-3294	238	10	,	,	PUNCT
cana-3294	238	11	ꝕn+p)→0	ꝕn+p)→0	NUM
cana-3294	238	12	since	since	SCONJ
cana-3294	238	13	0	0	NUM
cana-3294	238	14	<	<	X
cana-3294	238	15	α	α	X
cana-3294	238	16	<	<	X
cana-3294	238	17	1	1	NUM
cana-3294	238	18	.	.	PUNCT
cana-3294	239	1	thus	thus	ADV
cana-3294	239	2	,	,	PUNCT
cana-3294	239	3	{	{	PUNCT
cana-3294	239	4	ꝕn	ꝕn	X
cana-3294	239	5	}	}	PUNCT
cana-3294	239	6	is	be	AUX
cana-3294	239	7	a	a	DET
cana-3294	239	8	cauchy	cauchy	ADJ
cana-3294	239	9	sequence	sequence	NOUN
cana-3294	239	10	in	in	ADP
cana-3294	239	11	ℋ	ℋ	PROPN
cana-3294	239	12	.due	.due	NOUN
cana-3294	239	13	to	to	ADP
cana-3294	239	14	completeness	completeness	NOUN
cana-3294	239	15	of	of	ADP
cana-3294	239	16	ℋ	ℋ	PROPN
cana-3294	239	17	it	it	PRON
cana-3294	239	18	converges	converge	VERB
cana-3294	239	19	to	to	ADP
cana-3294	239	20	ς	ς	PROPN
cana-3294	239	21	in	in	ADP
cana-3294	239	22	ℋ	ℋ	PROPN
cana-3294	239	23	.	.	PUNCT
cana-3294	240	1	for	for	ADP
cana-3294	240	2	m>0	m>0	PROPN
cana-3294	240	3	,	,	PUNCT
cana-3294	240	4	we	we	PRON
cana-3294	240	5	have	have	VERB
cana-3294	240	6	g(ꝕn	g(ꝕn	NOUN
cana-3294	240	7	,	,	PUNCT
cana-3294	240	8	tm(ς),tm(ς	tm(ς),tm(ς	NUM
cana-3294	240	9	)	)	PUNCT
cana-3294	240	10	)	)	PUNCT
cana-3294	241	1	=	=	SYM
cana-3294	241	2	g(tn(ꝕn-1),tm(ς	g(tn(ꝕn-1),tm(ς	PROPN
cana-3294	241	3	)	)	PUNCT
cana-3294	241	4	,	,	PUNCT
cana-3294	241	5	tm(ς	tm(ς	NUM
cana-3294	241	6	)	)	PUNCT
cana-3294	241	7	)	)	PUNCT
cana-3294	242	1	≤	≤	NUM
cana-3294	242	2	𝛽𝑛,𝑚[g(ꝕn-1	𝛽𝑛,𝑚[g(ꝕn-1	NOUN
cana-3294	242	3	,	,	PUNCT
cana-3294	242	4	ꝕn	ꝕn	CCONJ
cana-3294	242	5	,	,	PUNCT
cana-3294	242	6	ꝕn)+	ꝕn)+	NOUN
cana-3294	242	7	g(ς	g(ς	PROPN
cana-3294	242	8	,	,	PUNCT
cana-3294	242	9	tmς	tmς	NOUN
cana-3294	242	10	,	,	PUNCT
cana-3294	242	11	tmς	tmς	NOUN
cana-3294	242	12	)	)	PUNCT
cana-3294	242	13	+	+	CCONJ
cana-3294	242	14	g(ς	g(ς	PROPN
cana-3294	242	15	,	,	PUNCT
cana-3294	242	16	tmς	tmς	NOUN
cana-3294	242	17	,	,	PUNCT
cana-3294	242	18	tmς)]+	tmς)]+	NUM
cana-3294	242	19	γn	γn	NUM
cana-3294	242	20	,	,	PUNCT
cana-3294	242	21	m	m	VERB
cana-3294	242	22	(	(	PUNCT
cana-3294	242	23	ꝕn-1	ꝕn-1	NOUN
cana-3294	242	24	,	,	PUNCT
cana-3294	242	25	ς	ς	PROPN
cana-3294	242	26	,	,	PUNCT
cana-3294	242	27	ς	ς	NOUN
cana-3294	242	28	)	)	PUNCT
cana-3294	242	29	letting	let	VERB
cana-3294	242	30	n→∞	n→∞	NUM
cana-3294	242	31	,	,	PUNCT
cana-3294	242	32	as	as	ADP
cana-3294	242	33	ꝕn→ς	ꝕn→ς	PROPN
cana-3294	242	34	we	we	PRON
cana-3294	242	35	obtain	obtain	VERB
cana-3294	242	36	g(ς	g(ς	PROPN
cana-3294	242	37	,	,	PUNCT
cana-3294	242	38	tmς	tmς	NOUN
cana-3294	242	39	,	,	PUNCT
cana-3294	242	40	tmς	tmς	NOUN
cana-3294	242	41	)	)	PUNCT
cana-3294	242	42	≤	≤	PROPN
cana-3294	243	1	𝛽𝑛,𝑚[g(ς	𝛽𝑛,𝑚[g(ς	PROPN
cana-3294	243	2	,	,	PUNCT
cana-3294	243	3	ς	ς	PROPN
cana-3294	243	4	,	,	PUNCT
cana-3294	243	5	ς)+2g(ς	ς)+2g(ς	PROPN
cana-3294	243	6	,	,	PUNCT
cana-3294	243	7	tmς	tmς	NOUN
cana-3294	243	8	,	,	PUNCT
cana-3294	243	9	tmς)+γn	tmς)+γn	NOUN
cana-3294	243	10	,	,	PUNCT
cana-3294	243	11	mg(ς	mg(ς	PROPN
cana-3294	243	12	,	,	PUNCT
cana-3294	243	13	ς	ς	PROPN
cana-3294	243	14	,	,	PUNCT
cana-3294	243	15	ς	ς	NOUN
cana-3294	243	16	)	)	PUNCT
cana-3294	243	17	g(ς	g(ς	PROPN
cana-3294	243	18	,	,	PUNCT
cana-3294	243	19	tmς	tmς	NOUN
cana-3294	243	20	,	,	PUNCT
cana-3294	243	21	tmς	tmς	NOUN
cana-3294	243	22	)	)	PUNCT
cana-3294	243	23	≤2𝛽𝑛,𝑚	≤2𝛽𝑛,𝑚	PROPN
cana-3294	243	24	g(ς	g(ς	PROPN
cana-3294	243	25	,	,	PUNCT
cana-3294	243	26	tmς	tmς	NOUN
cana-3294	243	27	,	,	PUNCT
cana-3294	243	28	tmς	tmς	NOUN
cana-3294	243	29	)	)	PUNCT
cana-3294	243	30	since	since	SCONJ
cana-3294	243	31	𝛽𝑛,𝑚	𝛽𝑛,𝑚	NOUN
cana-3294	243	32	<	<	X
cana-3294	243	33	1	1	NUM
cana-3294	243	34	2	2	NUM
cana-3294	243	35	,	,	PUNCT
cana-3294	243	36	g(ς	g(ς	PROPN
cana-3294	243	37	,	,	PUNCT
cana-3294	243	38	tmς	tmς	NOUN
cana-3294	243	39	,	,	PUNCT
cana-3294	243	40	tmς	tmς	NOUN
cana-3294	243	41	)	)	PUNCT
cana-3294	243	42	=	=	SYM
cana-3294	243	43	0	0	NUM
cana-3294	243	44	∴	∴	NOUN
cana-3294	243	45	tmς	tmς	NOUN
cana-3294	244	1	=	=	SYM
cana-3294	244	2	ς	ς	PROPN
cana-3294	244	3	ς	ς	PROPN
cana-3294	244	4	is	be	AUX
cana-3294	244	5	fixed	fix	VERB
cana-3294	244	6	point	point	NOUN
cana-3294	244	7	of	of	ADP
cana-3294	244	8	{	{	PUNCT
cana-3294	244	9	tm	tm	NOUN
cana-3294	244	10	}	}	PUNCT
cana-3294	244	11	.	.	PUNCT
cana-3294	245	1	assume	assume	VERB
cana-3294	245	2	ϑ	ϑ	X
cana-3294	245	3	is	be	AUX
cana-3294	245	4	another	another	DET
cana-3294	245	5	fixed	fix	VERB
cana-3294	245	6	point	point	NOUN
cana-3294	245	7	of	of	ADP
cana-3294	245	8	{	{	PUNCT
cana-3294	245	9	tm	tm	NOUN
cana-3294	245	10	}	}	PUNCT
cana-3294	245	11	,	,	PUNCT
cana-3294	245	12	i.e.	i.e.	X
cana-3294	245	13	,	,	PUNCT
cana-3294	245	14	tm(ϑ)=ϑ.	tm(ϑ)=ϑ.	PROPN
cana-3294	245	15	such	such	ADJ
cana-3294	245	16	that	that	DET
cana-3294	245	17	ς≠ϑ.	ς≠ϑ.	PROPN
cana-3294	245	18	g(ς	g(ς	PROPN
cana-3294	245	19	,	,	PUNCT
cana-3294	245	20	ϑ	ϑ	X
cana-3294	245	21	,	,	PUNCT
cana-3294	245	22	ϑ	ϑ	NOUN
cana-3294	245	23	)	)	PUNCT
cana-3294	245	24	=	=	SYM
cana-3294	245	25	g(tmς	g(tmς	PROPN
cana-3294	245	26	,	,	PUNCT
cana-3294	245	27	tmϑ	tmϑ	PRON
cana-3294	245	28	,	,	PUNCT
cana-3294	245	29	tmϑ	tmϑ	ADJ
cana-3294	245	30	)	)	PUNCT
cana-3294	245	31	≤	≤	PROPN
cana-3294	246	1	𝛽𝑛,𝑚[g(ς	𝛽𝑛,𝑚[g(ς	PROPN
cana-3294	246	2	,	,	PUNCT
cana-3294	246	3	tmς	tmς	NOUN
cana-3294	246	4	,	,	PUNCT
cana-3294	246	5	tmς)+	tmς)+	PROPN
cana-3294	246	6	g(ϑ	g(ϑ	PROPN
cana-3294	246	7	,	,	PUNCT
cana-3294	246	8	tmϑ	tmϑ	PRON
cana-3294	246	9	,	,	PUNCT
cana-3294	246	10	tmϑ)+	tmϑ)+	PROPN
cana-3294	246	11	g(ϑ	g(ϑ	PROPN
cana-3294	246	12	,	,	PUNCT
cana-3294	246	13	tmϑ	tmϑ	PRON
cana-3294	246	14	,	,	PUNCT
cana-3294	246	15	tmϑ)]+	tmϑ)]+	NOUN
cana-3294	246	16	γn	γn	NUM
cana-3294	246	17	,	,	PUNCT
cana-3294	246	18	mg(ς	mg(ς	PROPN
cana-3294	246	19	,	,	PUNCT
cana-3294	246	20	ϑ	ϑ	X
cana-3294	246	21	,	,	PUNCT
cana-3294	246	22	ϑ	ϑ	NOUN
cana-3294	246	23	)	)	PUNCT
cana-3294	246	24	g(ς	g(ς	PROPN
cana-3294	246	25	,	,	PUNCT
cana-3294	246	26	ϑ	ϑ	X
cana-3294	246	27	,	,	PUNCT
cana-3294	246	28	ϑ	ϑ	NOUN
cana-3294	246	29	)	)	PUNCT
cana-3294	246	30	≤	≤	PROPN
cana-3294	246	31	𝛽𝑛,𝑚[g(ς	𝛽𝑛,𝑚[g(ς	PROPN
cana-3294	246	32	,	,	PUNCT
cana-3294	246	33	ς	ς	PROPN
cana-3294	246	34	,	,	PUNCT
cana-3294	246	35	ς)+g(ϑ	ς)+g(ϑ	PROPN
cana-3294	246	36	,	,	PUNCT
cana-3294	246	37	ϑ	ϑ	NOUN
cana-3294	246	38	,	,	PUNCT
cana-3294	246	39	ϑ)+	ϑ)+	PROPN
cana-3294	246	40	g(ϑ	g(ϑ	PROPN
cana-3294	246	41	,	,	PUNCT
cana-3294	246	42	ϑ	ϑ	NOUN
cana-3294	246	43	,	,	PUNCT
cana-3294	246	44	ϑ)]+	ϑ)]+	NOUN
cana-3294	246	45	γn	γn	NUM
cana-3294	246	46	,	,	PUNCT
cana-3294	246	47	mg(ς	mg(ς	PROPN
cana-3294	246	48	,	,	PUNCT
cana-3294	246	49	ϑ	ϑ	X
cana-3294	246	50	,	,	PUNCT
cana-3294	246	51	ϑ	ϑ	NOUN
cana-3294	246	52	)	)	PUNCT
cana-3294	246	53	.	.	PUNCT
cana-3294	247	1	g(u,ϑ,ϑ	g(u,ϑ,ϑ	PUNCT
cana-3294	247	2	)	)	PUNCT
cana-3294	248	1	≤	≤	NOUN
cana-3294	248	2	γn	γn	ADP
cana-3294	248	3	,	,	PUNCT
cana-3294	248	4	mg(u	mg(u	NOUN
cana-3294	248	5	,	,	PUNCT
cana-3294	248	6	ϑ	ϑ	NOUN
cana-3294	248	7	,	,	PUNCT
cana-3294	248	8	ϑ	ϑ	NOUN
cana-3294	248	9	)	)	PUNCT
cana-3294	248	10	.	.	PUNCT
cana-3294	249	1	,	,	PUNCT
cana-3294	249	2	which	which	PRON
cana-3294	249	3	is	be	AUX
cana-3294	249	4	a	a	DET
cana-3294	249	5	contradiction	contradiction	NOUN
cana-3294	249	6	since	since	SCONJ
cana-3294	249	7	γn	γn	NUM
cana-3294	249	8	,	,	PUNCT
cana-3294	249	9	m	m	VERB
cana-3294	249	10	<	<	X
cana-3294	249	11	1	1	NUM
cana-3294	249	12	2	2	NUM
cana-3294	249	13	∴	∴	NOUN
cana-3294	249	14	ς	ς	PROPN
cana-3294	249	15	=	=	NOUN
cana-3294	249	16	ϑ	ϑ	PROPN
cana-3294	249	17	∴	∴	PROPN
cana-3294	249	18	ς	ς	PROPN
cana-3294	249	19	is	be	AUX
cana-3294	249	20	a	a	DET
cana-3294	249	21	unique	unique	ADJ
cana-3294	249	22	fixed	fix	VERB
cana-3294	249	23	point	point	NOUN
cana-3294	249	24	of	of	ADP
cana-3294	249	25	{	{	PUNCT
cana-3294	249	26	tm	tm	NOUN
cana-3294	249	27	}	}	PUNCT
cana-3294	249	28	.	.	PUNCT
cana-3294	250	1	corollary	corollary	ADJ
cana-3294	250	2	4.8	4.8	NUM
cana-3294	251	1	:	:	PUNCT
cana-3294	251	2	consider	consider	VERB
cana-3294	251	3	a	a	DET
cana-3294	251	4	sequence	sequence	NOUN
cana-3294	251	5	of	of	ADP
cana-3294	251	6	self	self	NOUN
cana-3294	251	7	mappings	mapping	NOUN
cana-3294	251	8	be	be	AUX
cana-3294	251	9	{	{	PUNCT
cana-3294	251	10	tn	tn	NOUN
cana-3294	251	11	}	}	PUNCT
cana-3294	251	12	and	and	CCONJ
cana-3294	251	13	(	(	PUNCT
cana-3294	251	14	ℋ	ℋ	PROPN
cana-3294	251	15	,	,	PUNCT
cana-3294	251	16	g	g	NOUN
cana-3294	251	17	)	)	PUNCT
cana-3294	251	18	be	be	AUX
cana-3294	251	19	a	a	DET
cana-3294	251	20	complete	complete	ADJ
cana-3294	251	21	gmetric	gmetric	ADJ
cana-3294	251	22	space	space	NOUN
cana-3294	251	23	satisfies	satisfy	VERB
cana-3294	251	24	the	the	DET
cana-3294	251	25	following	follow	VERB
cana-3294	251	26	contraction	contraction	NOUN
cana-3294	251	27	such	such	ADJ
cana-3294	251	28	that	that	DET
cana-3294	251	29	g(tjꝕ	g(tjꝕ	NOUN
cana-3294	251	30	,	,	PUNCT
cana-3294	251	31	tkꝙ	tkꝙ	NOUN
cana-3294	251	32	,	,	PUNCT
cana-3294	251	33	tkυ	tkυ	NOUN
cana-3294	251	34	)	)	PUNCT
cana-3294	251	35	≤	≤	NOUN
cana-3294	251	36	𝛽𝑗,𝑘[g(ꝕ	𝛽𝑗,𝑘[g(ꝕ	PROPN
cana-3294	251	37	,	,	PUNCT
cana-3294	251	38	tjꝕ	tjꝕ	ADJ
cana-3294	251	39	,	,	PUNCT
cana-3294	251	40	tjꝕ)+g(ꝙ	tjꝕ)+g(ꝙ	ADJ
cana-3294	251	41	,	,	PUNCT
cana-3294	251	42	tkꝙ	tkꝙ	NOUN
cana-3294	251	43	,	,	PUNCT
cana-3294	251	44	tkꝙ)+	tkꝙ)+	NOUN
cana-3294	251	45	g(υ	g(υ	VERB
cana-3294	251	46	,	,	PUNCT
cana-3294	251	47	tkυ	tkυ	NOUN
cana-3294	251	48	,	,	PUNCT
cana-3294	251	49	tkυ	tkυ	NOUN
cana-3294	251	50	)	)	PUNCT
cana-3294	251	51	(	(	PUNCT
cana-3294	251	52	b	b	X
cana-3294	251	53	)	)	PUNCT
cana-3294	251	54	for	for	ADP
cana-3294	251	55	ꝕ	ꝕ	NOUN
cana-3294	251	56	,	,	PUNCT
cana-3294	251	57	ꝙ	ꝙ	NOUN
cana-3294	251	58	,	,	PUNCT
cana-3294	251	59	υ	υ	PROPN
cana-3294	251	60	∈	∈	PROPN
cana-3294	251	61	ℋ	ℋ	PROPN
cana-3294	251	62	with	with	ADP
cana-3294	251	63	ꝕ	ꝕ	DET
cana-3294	251	64	≠	≠	PROPN
cana-3294	251	65	ꝙ	ꝙ	NUM
cana-3294	251	66	,	,	PUNCT
cana-3294	251	67	0≤𝛽𝑗,𝑘	0≤𝛽𝑗,𝑘	PROPN
cana-3294	251	68	<	<	X
cana-3294	251	69	1	1	NUM
cana-3294	251	70	2	2	NUM
cana-3294	251	71	j	j	PROPN
cana-3294	251	72	,	,	PUNCT
cana-3294	251	73	k=1,2,3	k=1,2,3	PROPN
cana-3294	251	74	-	-	PUNCT
cana-3294	251	75	--	--	PUNCT
cana-3294	251	76	then	then	ADV
cana-3294	251	77	{	{	PUNCT
cana-3294	251	78	tn	tn	NOUN
cana-3294	251	79	}	}	PUNCT
cana-3294	251	80	has	have	VERB
cana-3294	251	81	a	a	DET
cana-3294	251	82	unique	unique	ADJ
cana-3294	251	83	fixed	fix	VERB
cana-3294	251	84	point	point	NOUN
cana-3294	251	85	in	in	ADP
cana-3294	251	86	ℋ	ℋ	PROPN
cana-3294	251	87	if	if	SCONJ
cana-3294	251	88	∑	∑	PROPN
cana-3294	251	89	(	(	PUNCT
cana-3294	251	90	𝛽𝑗,𝑗+1	𝛽𝑗,𝑗+1	NOUN
cana-3294	251	91	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NUM
cana-3294	251	92	)	)	PUNCT
cana-3294	252	1	∞	∞	PROPN
cana-3294	252	2	𝑗=1	𝑗=1	PROPN
cana-3294	252	3	is	be	AUX
cana-3294	252	4	an	an	DET
cana-3294	252	5	α	α	NOUN
cana-3294	252	6	-	-	PUNCT
cana-3294	252	7	series	series	NOUN
cana-3294	252	8	example	example	NOUN
cana-3294	252	9	4.9	4.9	NUM
cana-3294	252	10	.	.	PUNCT
cana-3294	253	1	let	let	VERB
cana-3294	253	2	ℋ=	ℋ=	VERB
cana-3294	253	3	[	[	NOUN
cana-3294	253	4	0,1	0,1	NUM
cana-3294	253	5	]	]	PUNCT
cana-3294	253	6	and	and	CCONJ
cana-3294	253	7	g(ꝕ	g(ꝕ	PROPN
cana-3294	253	8	,	,	PUNCT
cana-3294	253	9	ꝙ	ꝙ	NOUN
cana-3294	253	10	,	,	PUNCT
cana-3294	253	11	υ	υ	NOUN
cana-3294	253	12	)	)	PUNCT
cana-3294	254	1	=	=	SYM
cana-3294	254	2	𝑚𝑎𝑥{|ꝕ−	𝑚𝑎𝑥{|ꝕ−	NUM
cana-3294	254	3	ꝙ|	ꝙ|	NOUN
cana-3294	254	4	,	,	PUNCT
cana-3294	254	5	|ꝙ−	|ꝙ−	NOUN
cana-3294	254	6	𝜐|	𝜐|	PROPN
cana-3294	254	7	,	,	PUNCT
cana-3294	254	8	|𝜐	|𝜐	X
cana-3294	254	9	−ꝕ|	−ꝕ|	PROPN
cana-3294	254	10	}	}	PUNCT
cana-3294	254	11	.	.	PUNCT
cana-3294	255	1	communications	communication	NOUN
cana-3294	255	2	on	on	ADP
cana-3294	255	3	applied	apply	VERB
cana-3294	255	4	nonlinear	nonlinear	ADJ
cana-3294	255	5	analysis	analysis	NOUN
cana-3294	255	6	issn	issn	NOUN
cana-3294	255	7	:	:	PUNCT
cana-3294	255	8	1074	1074	NUM
cana-3294	255	9	-	-	PUNCT
cana-3294	255	10	133x	133x	NUM
cana-3294	255	11	vol	vol	NOUN
cana-3294	255	12	32	32	NUM
cana-3294	255	13	no	no	NOUN
cana-3294	255	14	.	.	PUNCT
cana-3294	256	1	6s	6s	NUM
cana-3294	256	2	(	(	PUNCT
cana-3294	256	3	2025	2025	NUM
cana-3294	256	4	)	)	PUNCT
cana-3294	256	5	287	287	NUM
cana-3294	256	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	256	7	clearly	clearly	ADV
cana-3294	256	8	(	(	PUNCT
cana-3294	256	9	ℋ	ℋ	PROPN
cana-3294	256	10	,	,	PUNCT
cana-3294	256	11	g	g	NOUN
cana-3294	256	12	)	)	PUNCT
cana-3294	256	13	is	be	AUX
cana-3294	256	14	a	a	DET
cana-3294	256	15	complete	complete	ADJ
cana-3294	256	16	generalized	generalize	VERB
cana-3294	256	17	metric	metric	ADJ
cana-3294	256	18	space	space	NOUN
cana-3294	256	19	.	.	PUNCT
cana-3294	257	1	define	define	VERB
cana-3294	257	2	βj	βj	PRON
cana-3294	257	3	,	,	PUNCT
cana-3294	257	4	k=	k=	X
cana-3294	257	5	1	1	NUM
cana-3294	257	6	2	2	NUM
cana-3294	257	7	+	+	NOUN
cana-3294	257	8	3𝑘	3𝑘	NOUN
cana-3294	257	9	for	for	ADP
cana-3294	257	10	all	all	DET
cana-3294	257	11	j	j	PROPN
cana-3294	257	12	,	,	PUNCT
cana-3294	257	13	k	k	PROPN
cana-3294	257	14	=	=	NOUN
cana-3294	257	15	1,2,3	1,2,3	NUM
cana-3294	257	16	,	,	PUNCT
cana-3294	257	17	…	…	PUNCT
cana-3294	257	18	.	.	PUNCT
cana-3294	257	19	and	and	CCONJ
cana-3294	257	20	tj(ꝕ	tj(ꝕ	NOUN
cana-3294	257	21	)	)	PUNCT
cana-3294	257	22	=	=	SYM
cana-3294	258	1	ꝕ	ꝕ	PRON
cana-3294	258	2	3𝑗	3𝑗	NOUN
cana-3294	258	3	for	for	ADP
cana-3294	258	4	all	all	PRON
cana-3294	258	5	ꝕϵ	ꝕϵ	VERB
cana-3294	258	6	ℋ	ℋ	PROPN
cana-3294	258	7	and	and	CCONJ
cana-3294	258	8	j	j	NOUN
cana-3294	258	9	=	=	SYM
cana-3294	258	10	1,2	1,2	NUM
cana-3294	258	11	,	,	PUNCT
cana-3294	258	12	…	…	PUNCT
cana-3294	258	13	.	.	PUNCT
cana-3294	259	1	assume	assume	VERB
cana-3294	259	2	j	j	PROPN
cana-3294	259	3	<	<	X
cana-3294	259	4	k	k	PROPN
cana-3294	259	5	and	and	CCONJ
cana-3294	259	6	ꝕ	ꝕ	X
cana-3294	259	7	>	>	X
cana-3294	259	8	ꝙ	ꝙ	NUM
cana-3294	259	9	≥	≥	NOUN
cana-3294	259	10	υ	υ	NOUN
cana-3294	260	1	so	so	ADV
cana-3294	260	2	we	we	PRON
cana-3294	260	3	have	have	VERB
cana-3294	260	4	g(tjꝕ	g(tjꝕ	PROPN
cana-3294	260	5	,	,	PUNCT
cana-3294	260	6	tkꝙ	tkꝙ	NOUN
cana-3294	260	7	,	,	PUNCT
cana-3294	260	8	tkυ	tkυ	NOUN
cana-3294	260	9	)	)	PUNCT
cana-3294	260	10	=	=	PUNCT
cana-3294	260	11	𝑚𝑎𝑥{|	𝑚𝑎𝑥{|	NOUN
cana-3294	260	12	ꝕ	ꝕ	PRON
cana-3294	260	13	3𝑗	3𝑗	NOUN
cana-3294	261	1	−	−	NOUN
cana-3294	261	2	ꝙ	ꝙ	NUM
cana-3294	261	3	3𝑘	3𝑘	NOUN
cana-3294	261	4	|,|	|,|	NUM
cana-3294	261	5	ꝙ	ꝙ	NUM
cana-3294	261	6	3𝑘	3𝑘	NOUN
cana-3294	261	7	−	−	NOUN
cana-3294	262	1	𝜐	𝜐	X
cana-3294	262	2	3𝑘	3𝑘	NUM
cana-3294	262	3	|,|	|,|	NUM
cana-3294	262	4	𝜐	𝜐	NOUN
cana-3294	262	5	3𝑘	3𝑘	ADJ
cana-3294	262	6	−	−	NOUN
cana-3294	263	1	ꝕ	ꝕ	DET
cana-3294	263	2	3𝑗	3𝑗	NOUN
cana-3294	263	3	|	|	NOUN
cana-3294	263	4	}	}	PUNCT
cana-3294	263	5	=	=	PUNCT
cana-3294	263	6	|	|	ADV
cana-3294	263	7	ꝕ	ꝕ	PRON
cana-3294	263	8	3𝑗	3𝑗	NOUN
cana-3294	263	9	−	−	NOUN
cana-3294	263	10	ꝙ	ꝙ	NUM
cana-3294	263	11	3𝑘	3𝑘	NOUN
cana-3294	263	12	|	|	INTJ
cana-3294	263	13	g(ꝕ	g(ꝕ	PROPN
cana-3294	263	14	,	,	PUNCT
cana-3294	263	15	tjꝕ	tjꝕ	ADJ
cana-3294	263	16	,	,	PUNCT
cana-3294	263	17	tjꝕ)+g(ꝙ	tjꝕ)+g(ꝙ	ADJ
cana-3294	263	18	,	,	PUNCT
cana-3294	263	19	tkꝙ	tkꝙ	NOUN
cana-3294	263	20	,	,	PUNCT
cana-3294	263	21	tkꝙ)+	tkꝙ)+	NOUN
cana-3294	263	22	g(υ	g(υ	VERB
cana-3294	263	23	,	,	PUNCT
cana-3294	263	24	tkυ	tkυ	NOUN
cana-3294	263	25	,	,	PUNCT
cana-3294	263	26	tkυ	tkυ	NOUN
cana-3294	263	27	)	)	PUNCT
cana-3294	263	28	=	=	PUNCT
cana-3294	263	29	|ꝕ	|ꝕ	NOUN
cana-3294	263	30	−	−	PROPN
cana-3294	264	1	ꝕ	ꝕ	DET
cana-3294	264	2	3𝑗	3𝑗	NOUN
cana-3294	264	3	|	|	NOUN
cana-3294	264	4	+	+	NOUN
cana-3294	264	5	|ꝙ−	|ꝙ−	NOUN
cana-3294	264	6	ꝙ	ꝙ	NUM
cana-3294	264	7	3𝑘	3𝑘	NOUN
cana-3294	265	1	|	|	NOUN
cana-3294	265	2	+	+	NOUN
cana-3294	265	3	|𝜐	|𝜐	X
cana-3294	265	4	−	−	NOUN
cana-3294	265	5	𝜐	𝜐	NUM
cana-3294	265	6	3𝑘	3𝑘	NOUN
cana-3294	266	1	|	|	ADV
cana-3294	266	2	clearly	clearly	ADV
cana-3294	266	3	g(tjꝕ	g(tjꝕ	ADJ
cana-3294	266	4	,	,	PUNCT
cana-3294	266	5	tkꝙ	tkꝙ	NOUN
cana-3294	266	6	,	,	PUNCT
cana-3294	266	7	tkυ	tkυ	NOUN
cana-3294	266	8	)	)	PUNCT
cana-3294	266	9	≤	≤	NOUN
cana-3294	266	10	g(ꝕ	g(ꝕ	PROPN
cana-3294	266	11	,	,	PUNCT
cana-3294	266	12	tjꝕ	tjꝕ	ADJ
cana-3294	266	13	,	,	PUNCT
cana-3294	266	14	tjꝕ)+g(ꝙ	tjꝕ)+g(ꝙ	ADJ
cana-3294	266	15	,	,	PUNCT
cana-3294	266	16	tkꝙ	tkꝙ	NOUN
cana-3294	266	17	,	,	PUNCT
cana-3294	266	18	tkꝙ)+	tkꝙ)+	NOUN
cana-3294	266	19	g(υ	g(υ	VERB
cana-3294	266	20	,	,	PUNCT
cana-3294	266	21	tkυ	tkυ	NOUN
cana-3294	266	22	,	,	PUNCT
cana-3294	266	23	tkυ	tkυ	NOUN
cana-3294	266	24	)	)	PUNCT
cana-3294	266	25	.	.	PUNCT
cana-3294	267	1	∴	∴	NOUN
cana-3294	267	2	condition	condition	NOUN
cana-3294	267	3	(	(	PUNCT
cana-3294	267	4	b	b	NOUN
cana-3294	267	5	)	)	PUNCT
cana-3294	267	6	satisfied	satisfied	ADJ
cana-3294	267	7	for	for	ADP
cana-3294	267	8	all	all	DET
cana-3294	267	9	ꝕ	ꝕ	ADJ
cana-3294	267	10	,	,	PUNCT
cana-3294	267	11	ꝙ	ꝙ	NOUN
cana-3294	267	12	,	,	PUNCT
cana-3294	267	13	υ	υ	PROPN
cana-3294	267	14	∈	∈	PROPN
cana-3294	267	15	ℋ	ℋ	PROPN
cana-3294	267	16	with	with	ADP
cana-3294	267	17	ꝕ≠ꝙ	ꝕ≠ꝙ	PROPN
cana-3294	267	18	∑	∑	PUNCT
cana-3294	267	19	(	(	PUNCT
cana-3294	267	20	𝛽𝑗,𝑗+1	𝛽𝑗,𝑗+1	NOUN
cana-3294	267	21	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NUM
cana-3294	267	22	)	)	PUNCT
cana-3294	267	23	∞	∞	NUM
cana-3294	267	24	𝑗=1	𝑗=1	PUNCT
cana-3294	268	1	=	=	PUNCT
cana-3294	268	2	∑	∑	PROPN
cana-3294	268	3	1	1	NUM
cana-3294	268	4	2	2	NUM
cana-3294	268	5	+	+	NUM
cana-3294	268	6	3𝑗	3𝑗	NOUN
cana-3294	268	7	1−2	1−2	NUM
cana-3294	268	8	1	1	NUM
cana-3294	268	9	2	2	NUM
cana-3294	268	10	+	+	NUM
cana-3294	268	11	3𝑗	3𝑗	NOUN
cana-3294	268	12	∞	∞	NUM
cana-3294	268	13	𝑗=1	𝑗=1	PUNCT
cana-3294	269	1	=	=	PUNCT
cana-3294	269	2	∑	∑	PROPN
cana-3294	269	3	1	1	NUM
cana-3294	269	4	2	2	NUM
cana-3294	269	5	+	+	NUM
cana-3294	269	6	3𝑗	3𝑗	NOUN
cana-3294	269	7	2	2	NUM
cana-3294	269	8	+	+	NOUN
cana-3294	269	9	3𝑗−2	3𝑗−2	NUM
cana-3294	269	10	2	2	NUM
cana-3294	269	11	+	+	NOUN
cana-3294	269	12	3𝑗	3𝑗	NOUN
cana-3294	269	13	∞	∞	NUM
cana-3294	269	14	𝑗=1	𝑗=1	PUNCT
cana-3294	270	1	=	=	PUNCT
cana-3294	270	2	∑	∑	PUNCT
cana-3294	270	3	1	1	NUM
cana-3294	270	4	3𝑗	3𝑗	NUM
cana-3294	270	5	∞	∞	NUM
cana-3294	270	6	𝑗=1	𝑗=1	PROPN
cana-3294	270	7	is	be	AUX
cana-3294	270	8	an	an	DET
cana-3294	270	9	α	α	NOUN
cana-3294	270	10	series	series	NOUN
cana-3294	270	11	with	with	ADP
cana-3294	270	12	α	α	PROPN
cana-3294	270	13	=	=	SYM
cana-3294	270	14	1	1	NUM
cana-3294	270	15	3	3	NUM
cana-3294	270	16	.	.	PUNCT
cana-3294	271	1	by	by	ADP
cana-3294	271	2	corollary	corollary	ADJ
cana-3294	271	3	3.8	3.8	NUM
cana-3294	271	4	,	,	PUNCT
cana-3294	271	5	{	{	PUNCT
cana-3294	271	6	tn	tn	NOUN
cana-3294	271	7	}	}	PUNCT
cana-3294	271	8	has	have	VERB
cana-3294	271	9	a	a	DET
cana-3294	271	10	unique	unique	ADJ
cana-3294	271	11	fixed	fix	VERB
cana-3294	271	12	point	point	NOUN
cana-3294	271	13	0	0	NUM
cana-3294	271	14	∈	∈	PROPN
cana-3294	271	15	ℋ.	ℋ.	PROPN
cana-3294	271	16	theorem	theorem	VERB
cana-3294	271	17	4.10	4.10	NUM
cana-3294	271	18	:	:	PUNCT
cana-3294	271	19	assume	assume	VERB
cana-3294	271	20	(	(	PUNCT
cana-3294	271	21	ℋ,g	ℋ,g	NUM
cana-3294	271	22	)	)	PUNCT
cana-3294	271	23	be	be	AUX
cana-3294	271	24	a	a	DET
cana-3294	271	25	complete	complete	ADJ
cana-3294	271	26	g	g	NOUN
cana-3294	271	27	metric	metric	ADJ
cana-3294	272	1	space.{tn	space.{tn	PROPN
cana-3294	272	2	}	}	PUNCT
cana-3294	272	3	be	be	AUX
cana-3294	272	4	a	a	DET
cana-3294	272	5	sequence	sequence	NOUN
cana-3294	272	6	of	of	ADP
cana-3294	272	7	self	self	NOUN
cana-3294	272	8	mappings	mapping	NOUN
cana-3294	272	9	on	on	ADP
cana-3294	272	10	ℋ	ℋ	PROPN
cana-3294	272	11	such	such	ADJ
cana-3294	272	12	that	that	DET
cana-3294	272	13	g(𝑇𝑗	g(𝑇𝑗	NOUN
cana-3294	272	14	𝑝(ꝕ	𝑝(ꝕ	PROPN
cana-3294	272	15	)	)	PUNCT
cana-3294	272	16	,	,	PUNCT
cana-3294	272	17	𝑇𝑘	𝑇𝑘	PROPN
cana-3294	272	18	𝑝(ꝙ	𝑝(ꝙ	NOUN
cana-3294	272	19	)	)	PUNCT
cana-3294	272	20	,	,	PUNCT
cana-3294	273	1	𝑇𝑘	𝑇𝑘	PROPN
cana-3294	273	2	𝑝(𝜐	𝑝(𝜐	PROPN
cana-3294	273	3	)	)	PUNCT
cana-3294	273	4	)	)	PUNCT
cana-3294	274	1	≤	≤	PROPN
cana-3294	274	2	𝛽𝑗,𝑘[g(ꝕ	𝛽𝑗,𝑘[g(ꝕ	PROPN
cana-3294	274	3	,	,	PUNCT
cana-3294	274	4	𝑇𝑗	𝑇𝑗	PROPN
cana-3294	274	5	𝑝(ꝕ	𝑝(ꝕ	PROPN
cana-3294	274	6	)	)	PUNCT
cana-3294	274	7	,	,	PUNCT
cana-3294	274	8	𝑇𝑗	𝑇𝑗	PROPN
cana-3294	274	9	𝑝(ꝕ))+g(ꝙ	𝑝(ꝕ))+g(ꝙ	PRON
cana-3294	274	10	,	,	PUNCT
cana-3294	274	11	𝑇𝑘	𝑇𝑘	PROPN
cana-3294	274	12	𝑝(ꝙ	𝑝(ꝙ	NOUN
cana-3294	274	13	)	)	PUNCT
cana-3294	274	14	,	,	PUNCT
cana-3294	274	15	𝑇𝑘	𝑇𝑘	VERB
cana-3294	274	16	𝑝(ꝙ))+	𝑝(ꝙ))+	NOUN
cana-3294	274	17	g(υ	g(υ	VERB
cana-3294	274	18	,	,	PUNCT
cana-3294	274	19	𝑇𝑘	𝑇𝑘	PROPN
cana-3294	274	20	𝑝(𝜐	𝑝(𝜐	PROPN
cana-3294	274	21	)	)	PUNCT
cana-3294	274	22	,	,	PUNCT
cana-3294	274	23	𝑇𝑘	𝑇𝑘	PROPN
cana-3294	274	24	𝑝(𝜐))+	𝑝(𝜐))+	ADJ
cana-3294	274	25	γj	γj	PROPN
cana-3294	274	26	,	,	PUNCT
cana-3294	274	27	kg(ꝕ	kg(ꝕ	PROPN
cana-3294	274	28	,	,	PUNCT
cana-3294	274	29	ꝙ	ꝙ	NOUN
cana-3294	274	30	,	,	PUNCT
cana-3294	274	31	υ	υ	NOUN
cana-3294	274	32	)	)	PUNCT
cana-3294	274	33	.	.	PUNCT
cana-3294	275	1	for	for	ADP
cana-3294	275	2	ꝕ	ꝕ	PROPN
cana-3294	275	3	,	,	PUNCT
cana-3294	275	4	ꝙ	ꝙ	NOUN
cana-3294	275	5	,	,	PUNCT
cana-3294	275	6	υ	υ	PROPN
cana-3294	275	7	∈	∈	PROPN
cana-3294	275	8	ℋ	ℋ	PROPN
cana-3294	275	9	,	,	PUNCT
cana-3294	275	10	ꝕ≠ꝙ	ꝕ≠ꝙ	PROPN
cana-3294	275	11	,	,	PUNCT
cana-3294	275	12	0≤𝛽𝑗,𝑘	0≤𝛽𝑗,𝑘	PROPN
cana-3294	275	13	,	,	PUNCT
cana-3294	275	14	γj	γj	PROPN
cana-3294	275	15	,	,	PUNCT
cana-3294	275	16	k	k	X
cana-3294	275	17	<	<	X
cana-3294	275	18	1	1	NUM
cana-3294	275	19	2	2	NUM
cana-3294	275	20	j	j	PROPN
cana-3294	275	21	,	,	PUNCT
cana-3294	275	22	k=1,2,3	k=1,2,3	PROPN
cana-3294	275	23	-	-	PUNCT
cana-3294	275	24	---	---	PUNCT
cana-3294	275	25	if	if	SCONJ
cana-3294	275	26	∑	∑	PROPN
cana-3294	275	27	(	(	PUNCT
cana-3294	275	28	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	𝛽𝑗,𝑗+1+𝛾𝑗,𝑗+1	NOUN
cana-3294	275	29	1−2𝛽𝑗,𝑗+1	1−2𝛽𝑗,𝑗+1	NOUN
cana-3294	275	30	)	)	PUNCT
cana-3294	275	31	∞	∞	PROPN
cana-3294	275	32	𝑗=1	𝑗=1	PROPN
cana-3294	275	33	is	be	AUX
cana-3294	275	34	an	an	DET
cana-3294	275	35	α	α	NOUN
cana-3294	275	36	-	-	PUNCT
cana-3294	275	37	series	series	NOUN
cana-3294	275	38	,	,	PUNCT
cana-3294	275	39	then	then	ADV
cana-3294	275	40	{	{	PUNCT
cana-3294	275	41	tn	tn	NOUN
cana-3294	275	42	}	}	PUNCT
cana-3294	275	43	has	have	VERB
cana-3294	275	44	unique	unique	ADJ
cana-3294	275	45	common	common	ADJ
cana-3294	275	46	fixed	fix	VERB
cana-3294	275	47	point	point	NOUN
cana-3294	275	48	in	in	ADP
cana-3294	275	49	ℋ.	ℋ.	PROPN
cana-3294	275	50	5.conclusion	5.conclusion	NUM
cana-3294	275	51	in	in	ADP
cana-3294	275	52	this	this	DET
cana-3294	275	53	study	study	NOUN
cana-3294	275	54	we	we	PRON
cana-3294	275	55	present	present	VERB
cana-3294	275	56	unique	unique	ADJ
cana-3294	275	57	tripled	triple	VERB
cana-3294	275	58	fixed	fix	VERB
cana-3294	275	59	-	-	PUNCT
cana-3294	275	60	point	point	NOUN
cana-3294	275	61	and	and	CCONJ
cana-3294	275	62	common	common	ADJ
cana-3294	275	63	fixed	fix	VERB
cana-3294	275	64	-	-	PUNCT
cana-3294	275	65	point	point	NOUN
cana-3294	275	66	results	result	NOUN
cana-3294	275	67	for	for	ADP
cana-3294	275	68	a	a	DET
cana-3294	275	69	sequence	sequence	NOUN
cana-3294	275	70	of	of	ADP
cana-3294	275	71	mappings	mapping	NOUN
cana-3294	275	72	and	and	CCONJ
cana-3294	275	73	a	a	DET
cana-3294	275	74	self	self	NOUN
cana-3294	275	75	-	-	PUNCT
cana-3294	275	76	mapping	mapping	NOUN
cana-3294	275	77	in	in	ADP
cana-3294	275	78	g	g	PROPN
cana-3294	275	79	metric	metric	ADJ
cana-3294	275	80	space	space	NOUN
cana-3294	275	81	via	via	ADP
cana-3294	275	82	α	α	NOUN
cana-3294	275	83	-	-	PUNCT
cana-3294	275	84	series	series	NOUN
cana-3294	275	85	with	with	ADP
cana-3294	275	86	supporting	support	VERB
cana-3294	275	87	examples	example	NOUN
cana-3294	275	88	.	.	PUNCT
cana-3294	276	1	references	reference	NOUN
cana-3294	276	2	[	[	X
cana-3294	276	3	1	1	NUM
cana-3294	276	4	]	]	PUNCT
cana-3294	276	5	z.	z.	PROPN
cana-3294	276	6	mustafa	mustafa	PROPN
cana-3294	276	7	;	;	PUNCT
cana-3294	276	8	a	a	DET
cana-3294	276	9	new	new	ADJ
cana-3294	276	10	structure	structure	NOUN
cana-3294	276	11	for	for	ADP
cana-3294	276	12	generalized	generalized	ADJ
cana-3294	276	13	metric	metric	ADJ
cana-3294	276	14	spaces	space	NOUN
cana-3294	276	15	with	with	ADP
cana-3294	276	16	applications	application	NOUN
cana-3294	276	17	to	to	ADP
cana-3294	276	18	fixed	fix	VERB
cana-3294	276	19	point	point	NOUN
cana-3294	276	20	theory	theory	NOUN
cana-3294	276	21	,	,	PUNCT
cana-3294	276	22	ph	ph	PROPN
cana-3294	276	23	.	.	PUNCT
cana-3294	277	1	d	d	X
cana-3294	277	2	thesis	thesis	NOUN
cana-3294	277	3	,	,	PUNCT
cana-3294	277	4	the	the	DET
cana-3294	277	5	university	university	PROPN
cana-3294	277	6	of	of	ADP
cana-3294	277	7	newcastle	newcastle	PROPN
cana-3294	277	8	,	,	PUNCT
cana-3294	277	9	callaghan	callaghan	PROPN
cana-3294	277	10	,	,	PUNCT
cana-3294	277	11	australia	australia	PROPN
cana-3294	277	12	(	(	PUNCT
cana-3294	277	13	2005	2005	NUM
cana-3294	277	14	)	)	PUNCT
cana-3294	277	15	.	.	PUNCT
cana-3294	278	1	[	[	X
cana-3294	278	2	2	2	NUM
cana-3294	278	3	]	]	PUNCT
cana-3294	278	4	z.mastafa	z.mastafa	NOUN
cana-3294	278	5	,	,	PUNCT
cana-3294	278	6	b.sims	b.sim	NOUN
cana-3294	278	7	,	,	PUNCT
cana-3294	278	8	a	a	DET
cana-3294	278	9	new	new	ADJ
cana-3294	278	10	approach	approach	NOUN
cana-3294	278	11	to	to	ADP
cana-3294	278	12	generalized	generalize	VERB
cana-3294	278	13	metric	metric	ADJ
cana-3294	278	14	spaces	space	NOUN
cana-3294	278	15	,	,	PUNCT
cana-3294	278	16	j.nonlinear	j.nonlinear	ADJ
cana-3294	278	17	convex	convex	PROPN
cana-3294	278	18	anal	anal	NOUN
cana-3294	278	19	;	;	PUNCT
cana-3294	278	20	7	7	NUM
cana-3294	278	21	(	(	PUNCT
cana-3294	278	22	2	2	NUM
cana-3294	278	23	)	)	PUNCT
cana-3294	278	24	,	,	PUNCT
cana-3294	278	25	289	289	NUM
cana-3294	278	26	–	–	SYM
cana-3294	278	27	297	297	NUM
cana-3294	278	28	(	(	PUNCT
cana-3294	278	29	2006	2006	NUM
cana-3294	278	30	)	)	PUNCT
cana-3294	278	31	.	.	PUNCT
cana-3294	279	1	[	[	X
cana-3294	279	2	3	3	NUM
cana-3294	279	3	]	]	X
cana-3294	279	4	mustafa	mustafa	PROPN
cana-3294	279	5	,	,	PUNCT
cana-3294	279	6	z	z	PROPN
cana-3294	279	7	,	,	PUNCT
cana-3294	279	8	obiedat	obiedat	NOUN
cana-3294	279	9	,	,	PUNCT
cana-3294	279	10	h	h	NOUN
cana-3294	279	11	,	,	PUNCT
cana-3294	279	12	awawdeh	awawdeh	NOUN
cana-3294	279	13	,	,	PUNCT
cana-3294	279	14	f	f	X
cana-3294	279	15	:	:	PUNCT
cana-3294	279	16	some	some	DET
cana-3294	279	17	fixed	fix	VERB
cana-3294	279	18	-	-	PUNCT
cana-3294	279	19	point	point	NOUN
cana-3294	279	20	theorem	theorem	NOUN
cana-3294	279	21	for	for	ADP
cana-3294	279	22	mapping	mapping	NOUN
cana-3294	279	23	on	on	ADP
cana-3294	279	24	complete	complete	ADJ
cana-3294	279	25	g	g	NOUN
cana-3294	279	26	-	-	PUNCT
cana-3294	279	27	metric	metric	ADJ
cana-3294	279	28	spaces	space	NOUN
cana-3294	279	29	.	.	PUNCT
cana-3294	280	1	fixed	fix	VERB
cana-3294	280	2	point	point	NOUN
cana-3294	280	3	theory	theory	NOUN
cana-3294	280	4	appl	appl	PROPN
cana-3294	280	5	2008	2008	NUM
cana-3294	280	6	,	,	PUNCT
cana-3294	280	7	12	12	NUM
cana-3294	280	8	(	(	PUNCT
cana-3294	280	9	2008	2008	NUM
cana-3294	280	10	)	)	PUNCT
cana-3294	280	11	.	.	PUNCT
cana-3294	281	1	i	i	PRON
cana-3294	281	2	d	d	PROPN
cana-3294	281	3	189870	189870	NUM
cana-3294	281	4	.	.	PUNCT
cana-3294	282	1	communications	communication	NOUN
cana-3294	282	2	on	on	ADP
cana-3294	282	3	applied	apply	VERB
cana-3294	282	4	nonlinear	nonlinear	ADJ
cana-3294	282	5	analysis	analysis	NOUN
cana-3294	282	6	issn	issn	NOUN
cana-3294	282	7	:	:	PUNCT
cana-3294	282	8	1074	1074	NUM
cana-3294	282	9	-	-	PUNCT
cana-3294	282	10	133x	133x	NUM
cana-3294	282	11	vol	vol	NOUN
cana-3294	282	12	32	32	NUM
cana-3294	282	13	no	no	NOUN
cana-3294	282	14	.	.	PUNCT
cana-3294	283	1	6s	6s	NUM
cana-3294	283	2	(	(	PUNCT
cana-3294	283	3	2025	2025	NUM
cana-3294	283	4	)	)	PUNCT
cana-3294	283	5	288	288	NUM
cana-3294	283	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3294	284	1	[	[	X
cana-3294	284	2	4	4	NUM
cana-3294	284	3	]	]	X
cana-3294	284	4	mustafa	mustafa	PROPN
cana-3294	284	5	,	,	PUNCT
cana-3294	284	6	z	z	PROPN
cana-3294	284	7	,	,	PUNCT
cana-3294	284	8	sims	sim	NOUN
cana-3294	284	9	,	,	PUNCT
cana-3294	284	10	b	b	NOUN
cana-3294	284	11	:	:	PUNCT
cana-3294	284	12	fixed	fix	VERB
cana-3294	284	13	point	point	NOUN
cana-3294	284	14	theorems	theorem	NOUN
cana-3294	284	15	for	for	ADP
cana-3294	284	16	contractive	contractive	ADJ
cana-3294	284	17	mappings	mapping	NOUN
cana-3294	284	18	in	in	ADP
cana-3294	284	19	complete	complete	ADJ
cana-3294	284	20	g	g	NOUN
cana-3294	284	21	-	-	PUNCT
cana-3294	284	22	metric	metric	ADJ
cana-3294	284	23	spaces	space	NOUN
cana-3294	284	24	.	.	PUNCT
cana-3294	285	1	fixed	fix	VERB
cana-3294	285	2	point	point	NOUN
cana-3294	285	3	theory	theory	NOUN
cana-3294	285	4	appl	appl	PROPN
cana-3294	285	5	2009	2009	NUM
cana-3294	285	6	,	,	PUNCT
cana-3294	285	7	10	10	NUM
cana-3294	285	8	(	(	PUNCT
cana-3294	285	9	2009	2009	NUM
cana-3294	285	10	)	)	PUNCT
cana-3294	285	11	.	.	PUNCT
cana-3294	286	1	i	i	PRON
cana-3294	286	2	d	d	PROPN
cana-3294	286	3	917175	917175	NUM
cana-3294	286	4	.	.	PUNCT
cana-3294	287	1	[	[	X
cana-3294	287	2	5	5	NUM
cana-3294	287	3	]	]	X
cana-3294	287	4	mustafa	mustafa	PROPN
cana-3294	287	5	,	,	PUNCT
cana-3294	287	6	z	z	PROPN
cana-3294	287	7	,	,	PUNCT
cana-3294	287	8	shatanawi	shatanawi	ADJ
cana-3294	287	9	,	,	PUNCT
cana-3294	287	10	w	w	PROPN
cana-3294	287	11	,	,	PUNCT
cana-3294	287	12	bataineh	bataineh	PROPN
cana-3294	287	13	,	,	PUNCT
cana-3294	287	14	m	m	PRON
cana-3294	287	15	:	:	PUNCT
cana-3294	287	16	existence	existence	NOUN
cana-3294	287	17	of	of	ADP
cana-3294	287	18	fixed	fix	VERB
cana-3294	287	19	point	point	NOUN
cana-3294	287	20	results	result	NOUN
cana-3294	287	21	in	in	ADP
cana-3294	287	22	g	g	NOUN
cana-3294	287	23	-	-	PUNCT
cana-3294	287	24	metric	metric	ADJ
cana-3294	287	25	spaces	space	NOUN
cana-3294	287	26	.	.	PUNCT
cana-3294	288	1	int	int	PROPN
cana-3294	288	2	j	j	PROPN
cana-3294	288	3	math	math	PROPN
cana-3294	288	4	math	math	PROPN
cana-3294	288	5	sci	sci	PROPN
cana-3294	288	6	2009	2009	NUM
cana-3294	288	7	,	,	PUNCT
cana-3294	288	8	10	10	NUM
cana-3294	288	9	(	(	PUNCT
cana-3294	288	10	2009	2009	NUM
cana-3294	288	11	)	)	PUNCT
cana-3294	288	12	.	.	PUNCT
cana-3294	289	1	i	i	PRON
cana-3294	289	2	d	d	PROPN
cana-3294	289	3	283028	283028	NUM
cana-3294	289	4	.	.	PUNCT
cana-3294	290	1	[	[	X
cana-3294	290	2	6	6	NUM
cana-3294	290	3	]	]	X
cana-3294	290	4	mustafa	mustafa	PROPN
cana-3294	290	5	,	,	PUNCT
cana-3294	290	6	z	z	PROPN
cana-3294	290	7	,	,	PUNCT
cana-3294	290	8	awawdeh	awawdeh	PROPN
cana-3294	290	9	,	,	PUNCT
cana-3294	290	10	f	f	X
cana-3294	290	11	,	,	PUNCT
cana-3294	290	12	shatanawi	shatanawi	ADJ
cana-3294	290	13	,	,	PUNCT
cana-3294	290	14	w	w	PROPN
cana-3294	290	15	:	:	PUNCT
cana-3294	290	16	fixed	fixed	ADJ
cana-3294	290	17	point	point	NOUN
cana-3294	290	18	theorem	theorem	VERB
cana-3294	290	19	for	for	ADP
cana-3294	290	20	expansive	expansive	ADJ
cana-3294	290	21	mappings	mapping	NOUN
cana-3294	290	22	in	in	ADP
cana-3294	290	23	g	g	NOUN
cana-3294	290	24	-	-	PUNCT
cana-3294	290	25	metric	metric	ADJ
cana-3294	290	26	spaces	space	NOUN
cana-3294	290	27	.	.	PUNCT
cana-3294	291	1	int	int	NOUN
cana-3294	291	2	.	.	PUNCT
cana-3294	292	1	j.	j.	PROPN
cana-3294	292	2	contemp	contemp	PROPN
cana-3294	292	3	.	.	PUNCT
cana-3294	293	1	math	math	NOUN
cana-3294	293	2	.	.	PUNCT
cana-3294	294	1	sci	sci	PROPN
cana-3294	294	2	.	.	PROPN
cana-3294	294	3	5	5	NUM
cana-3294	294	4	,	,	PUNCT
cana-3294	294	5	49	49	NUM
cana-3294	294	6	-	-	SYM
cana-3294	294	7	52	52	NUM
cana-3294	294	8	(	(	PUNCT
cana-3294	294	9	2010	2010	NUM
cana-3294	294	10	)	)	PUNCT
cana-3294	294	11	.	.	PUNCT
cana-3294	295	1	[	[	X
cana-3294	295	2	7	7	NUM
cana-3294	295	3	]	]	X
cana-3294	295	4	mustafa	mustafa	PROPN
cana-3294	295	5	,	,	PUNCT
cana-3294	295	6	z	z	PROPN
cana-3294	295	7	,	,	PUNCT
cana-3294	295	8	khandaqji	khandaqji	ADJ
cana-3294	295	9	,	,	PUNCT
cana-3294	295	10	m	m	PROPN
cana-3294	295	11	,	,	PUNCT
cana-3294	295	12	shatanawi	shatanawi	ADJ
cana-3294	295	13	,	,	PUNCT
cana-3294	295	14	w	w	PROPN
cana-3294	295	15	:	:	PUNCT
cana-3294	295	16	fixed	fix	VERB
cana-3294	295	17	point	point	NOUN
cana-3294	295	18	results	result	NOUN
cana-3294	295	19	on	on	ADP
cana-3294	295	20	complete	complete	ADJ
cana-3294	295	21	g	g	NOUN
cana-3294	295	22	-	-	PUNCT
cana-3294	295	23	metric	metric	ADJ
cana-3294	295	24	spaces	space	NOUN
cana-3294	295	25	.	.	PUNCT
cana-3294	296	1	studia	studia	PROPN
cana-3294	296	2	scientiarum	scientiarum	PROPN
cana-3294	296	3	mathematicarum	mathematicarum	PROPN
cana-3294	296	4	hungarica	hungarica	PROPN
cana-3294	296	5	.	.	PUNCT
cana-3294	297	1	48	48	NUM
cana-3294	297	2	,	,	PUNCT
cana-3294	297	3	304–319	304–319	NUM
cana-3294	297	4	(	(	PUNCT
cana-3294	297	5	2011	2011	NUM
cana-3294	297	6	)	)	PUNCT
cana-3294	297	7	.	.	PUNCT
cana-3294	298	1	doi:10.1556	doi:10.1556	NOUN
cana-3294	298	2	/	/	SYM
cana-3294	298	3	sscmath.48.2011.3.1170	sscmath.48.2011.3.1170	X
cana-3294	299	1	[	[	X
cana-3294	299	2	8	8	NUM
cana-3294	299	3	]	]	X
cana-3294	299	4	mustafa	mustafa	PROPN
cana-3294	299	5	,	,	PUNCT
cana-3294	299	6	z	z	NOUN
cana-3294	299	7	:	:	PUNCT
cana-3294	299	8	common	common	ADJ
cana-3294	299	9	fixed	fix	VERB
cana-3294	299	10	points	point	NOUN
cana-3294	299	11	of	of	ADP
cana-3294	299	12	weakly	weakly	ADJ
cana-3294	299	13	compatible	compatible	ADJ
cana-3294	299	14	mappings	mapping	NOUN
cana-3294	299	15	in	in	ADP
cana-3294	299	16	g	g	NOUN
cana-3294	299	17	-	-	PUNCT
cana-3294	299	18	metric	metric	ADJ
cana-3294	299	19	spaces	space	NOUN
cana-3294	299	20	.	.	PUNCT
cana-3294	300	1	appl	appl	PROPN
cana-3294	300	2	.	.	PROPN
cana-3294	300	3	math	math	PROPN
cana-3294	300	4	.	.	PUNCT
cana-3294	301	1	sci	sci	PROPN
cana-3294	301	2	.	.	PUNCT
cana-3294	301	3	6(92	6(92	NUM
cana-3294	301	4	)	)	PUNCT
cana-3294	301	5	,	,	PUNCT
cana-3294	301	6	45894600	45894600	NUM
cana-3294	301	7	(	(	PUNCT
cana-3294	301	8	2012	2012	NUM
cana-3294	301	9	)	)	PUNCT
cana-3294	302	1	[	[	X
cana-3294	302	2	9	9	NUM
cana-3294	302	3	]	]	X
cana-3294	302	4	mustafa	mustafa	PROPN
cana-3294	302	5	,	,	PUNCT
cana-3294	302	6	z	z	PROPN
cana-3294	302	7	:	:	PUNCT
cana-3294	302	8	some	some	DET
cana-3294	302	9	new	new	ADJ
cana-3294	302	10	common	common	ADJ
cana-3294	302	11	fixed	fix	VERB
cana-3294	302	12	point	point	NOUN
cana-3294	302	13	theorems	theorem	NOUN
cana-3294	302	14	under	under	ADP
cana-3294	302	15	strict	strict	ADJ
cana-3294	302	16	contractive	contractive	ADJ
cana-3294	302	17	conditions	condition	NOUN
cana-3294	302	18	in	in	ADP
cana-3294	302	19	g	g	NOUN
cana-3294	302	20	-	-	PUNCT
cana-3294	302	21	metric	metric	ADJ
cana-3294	302	22	spaces	space	NOUN
cana-3294	302	23	.	.	PUNCT
cana-3294	303	1	j.	j.	PROPN
cana-3294	303	2	appl	appl	PROPN
cana-3294	303	3	.	.	PROPN
cana-3294	303	4	math	math	PROPN
cana-3294	303	5	.	.	PUNCT
cana-3294	304	1	2012	2012	NUM
cana-3294	304	2	,	,	PUNCT
cana-3294	304	3	article	article	NOUN
cana-3294	304	4	i	i	PROPN
cana-3294	304	5	d	d	PROPN
cana-3294	304	6	248937	248937	NUM
cana-3294	304	7	(	(	PUNCT
cana-3294	304	8	2012	2012	NUM
cana-3294	304	9	)	)	PUNCT
cana-3294	304	10	.	.	PUNCT
cana-3294	305	1	doi:10.1155/2012/248937	doi:10.1155/2012/248937	PROPN
cana-3294	306	1	[	[	X
cana-3294	306	2	10	10	NUM
cana-3294	306	3	]	]	X
cana-3294	306	4	mustafa	mustafa	PROPN
cana-3294	306	5	,	,	PUNCT
cana-3294	306	6	z	z	PROPN
cana-3294	306	7	,	,	PUNCT
cana-3294	306	8	aydi	aydi	ADJ
cana-3294	306	9	,	,	PUNCT
cana-3294	306	10	h	h	NOUN
cana-3294	306	11	,	,	PUNCT
cana-3294	306	12	karapınar	karapınar	NOUN
cana-3294	306	13	,	,	PUNCT
cana-3294	306	14	e	e	NOUN
cana-3294	306	15	:	:	PUNCT
cana-3294	306	16	on	on	ADP
cana-3294	306	17	common	common	ADJ
cana-3294	306	18	fixed	fix	VERB
cana-3294	306	19	points	point	NOUN
cana-3294	306	20	in	in	ADP
cana-3294	306	21	g	g	NOUN
cana-3294	306	22	-	-	PUNCT
cana-3294	306	23	metric	metric	ADJ
cana-3294	306	24	spaces	space	NOUN
cana-3294	306	25	using	use	VERB
cana-3294	306	26	(	(	PUNCT
cana-3294	306	27	e.a	e.a	PROPN
cana-3294	306	28	)	)	PUNCT
cana-3294	306	29	property	property	NOUN
cana-3294	306	30	.	.	PUNCT
cana-3294	307	1	comput	comput	NOUN
cana-3294	307	2	.	.	PUNCT
cana-3294	308	1	math	math	NOUN
cana-3294	308	2	.	.	PUNCT
cana-3294	309	1	appl	appl	PROPN
cana-3294	309	2	.	.	PROPN
cana-3294	310	1	64	64	NUM
cana-3294	310	2	,	,	PUNCT
cana-3294	310	3	1944	1944	NUM
cana-3294	310	4	-	-	SYM
cana-3294	310	5	1956	1956	NUM
cana-3294	310	6	(	(	PUNCT
cana-3294	310	7	2012	2012	NUM
cana-3294	310	8	)	)	PUNCT
cana-3294	310	9	.	.	PUNCT
cana-3294	311	1	doi:10.1016	doi:10.1016	PROPN
cana-3294	311	2	/	/	SYM
cana-3294	311	3	j.camwa.2012.03.051	j.camwa.2012.03.051	PROPN
cana-3294	312	1	[	[	X
cana-3294	312	2	11	11	NUM
cana-3294	312	3	]	]	PUNCT
cana-3294	312	4	aydi	aydi	ADJ
cana-3294	312	5	,	,	PUNCT
cana-3294	312	6	h	h	NOUN
cana-3294	312	7	,	,	PUNCT
cana-3294	312	8	shatanawi	shatanawi	ADJ
cana-3294	312	9	,	,	PUNCT
cana-3294	312	10	w	w	NOUN
cana-3294	312	11	,	,	PUNCT
cana-3294	312	12	vetro	vetro	NOUN
cana-3294	312	13	,	,	PUNCT
cana-3294	312	14	c	c	X
cana-3294	312	15	:	:	PUNCT
cana-3294	312	16	on	on	ADP
cana-3294	312	17	generalized	generalized	ADJ
cana-3294	312	18	weakly	weakly	ADJ
cana-3294	312	19	g	g	NOUN
cana-3294	312	20	-	-	PUNCT
cana-3294	312	21	contraction	contraction	NOUN
cana-3294	312	22	mapping	mapping	NOUN
cana-3294	312	23	in	in	ADP
cana-3294	312	24	g	g	NOUN
cana-3294	312	25	-	-	PUNCT
cana-3294	312	26	metric	metric	ADJ
cana-3294	312	27	spaces	space	NOUN
cana-3294	312	28	.	.	PUNCT
cana-3294	313	1	comput	comput	NOUN
cana-3294	313	2	.	.	PUNCT
cana-3294	314	1	math	math	NOUN
cana-3294	314	2	.	.	PUNCT
cana-3294	315	1	appl	appl	PROPN
cana-3294	315	2	.	.	PROPN
cana-3294	316	1	62	62	NUM
cana-3294	316	2	,	,	PUNCT
cana-3294	316	3	4222	4222	NUM
cana-3294	316	4	-	-	SYM
cana-3294	316	5	4229	4229	NUM
cana-3294	316	6	(	(	PUNCT
cana-3294	316	7	2011	2011	NUM
cana-3294	316	8	)	)	PUNCT
cana-3294	317	1	[	[	X
cana-3294	317	2	12	12	NUM
cana-3294	317	3	]	]	X
cana-3294	317	4	shatanawi	shatanawi	ADJ
cana-3294	317	5	,	,	PUNCT
cana-3294	317	6	w	w	PROPN
cana-3294	317	7	,	,	PUNCT
cana-3294	317	8	postolache	postolache	NOUN
cana-3294	317	9	,	,	PUNCT
cana-3294	317	10	m	m	PRON
cana-3294	317	11	:	:	PUNCT
cana-3294	317	12	some	some	DET
cana-3294	317	13	fixed	fix	VERB
cana-3294	317	14	-	-	PUNCT
cana-3294	317	15	point	point	NOUN
cana-3294	317	16	results	result	NOUN
cana-3294	317	17	for	for	ADP
cana-3294	317	18	a	a	DET
cana-3294	317	19	g	g	NOUN
cana-3294	317	20	-	-	PUNCT
cana-3294	317	21	weak	weak	ADJ
cana-3294	317	22	contraction	contraction	NOUN
cana-3294	317	23	in	in	ADP
cana-3294	317	24	g	g	NOUN
cana-3294	317	25	-	-	PUNCT
cana-3294	317	26	metric	metric	ADJ
cana-3294	317	27	spaces	space	NOUN
cana-3294	317	28	.	.	PUNCT
cana-3294	318	1	abstr	abstr	PROPN
cana-3294	318	2	.	.	PUNCT
cana-3294	318	3	appl	appl	PROPN
cana-3294	318	4	.	.	PUNCT
cana-3294	319	1	anal	anal	PROPN
cana-3294	319	2	.	.	PUNCT
cana-3294	320	1	2012	2012	NUM
cana-3294	320	2	,	,	PUNCT
cana-3294	320	3	article	article	NOUN
cana-3294	320	4	i	i	PROPN
cana-3294	320	5	d	d	PROPN
cana-3294	320	6	815870	815870	NUM
cana-3294	320	7	(	(	PUNCT
cana-3294	320	8	2012	2012	NUM
cana-3294	320	9	)	)	PUNCT
cana-3294	321	1	[	[	X
cana-3294	321	2	13	13	NUM
cana-3294	321	3	]	]	SYM
cana-3294	321	4	sepet	sepet	NOUN
cana-3294	321	5	,	,	PUNCT
cana-3294	321	6	s.	s.	PROPN
cana-3294	321	7	s.	s.	PROPN
cana-3294	321	8	and	and	CCONJ
cana-3294	321	9	aydin	aydin	PROPN
cana-3294	321	10	,	,	PUNCT
cana-3294	321	11	c.	c.	PROPN
cana-3294	321	12	common	common	ADJ
cana-3294	321	13	fixed	fix	VERB
cana-3294	321	14	point	point	NOUN
cana-3294	321	15	theorems	theorem	NOUN
cana-3294	321	16	for	for	ADP
cana-3294	321	17	f	f	NOUN
cana-3294	321	18	-	-	PUNCT
cana-3294	321	19	contractions	contraction	NOUN
cana-3294	321	20	in	in	ADP
cana-3294	321	21	g	g	NOUN
cana-3294	321	22	-	-	PUNCT
cana-3294	321	23	metric	metric	ADJ
cana-3294	321	24	spaces	space	NOUN
cana-3294	321	25	using	use	VERB
cana-3294	321	26	compatible	compatible	ADJ
cana-3294	321	27	mappings	mapping	NOUN
cana-3294	321	28	.	.	PUNCT
cana-3294	322	1	konuralp	konuralp	PROPN
cana-3294	322	2	journal	journal	PROPN
cana-3294	322	3	of	of	ADP
cana-3294	322	4	mathematics	mathematic	NOUN
cana-3294	322	5	,	,	PUNCT
cana-3294	322	6	6(1	6(1	NUM
cana-3294	322	7	)	)	PUNCT
cana-3294	322	8	,	,	PUNCT
cana-3294	322	9	92	92	NUM
cana-3294	322	10	-	-	SYM
cana-3294	322	11	97	97	NUM
cana-3294	322	12	.	.	PUNCT
cana-3294	323	1	(	(	PUNCT
cana-3294	323	2	2018	2018	NUM
cana-3294	323	3	)	)	PUNCT
cana-3294	324	1	[	[	X
cana-3294	324	2	14	14	NUM
cana-3294	324	3	]	]	X
cana-3294	324	4	kumar	kumar	PROPN
cana-3294	324	5	,	,	PUNCT
cana-3294	324	6	m.	m.	NOUN
cana-3294	324	7	and	and	CCONJ
cana-3294	324	8	sharma	sharma	PROPN
cana-3294	324	9	,	,	PUNCT
cana-3294	324	10	r.a	r.a	PROPN
cana-3294	324	11	new	new	ADJ
cana-3294	324	12	approach	approach	NOUN
cana-3294	324	13	to	to	ADP
cana-3294	324	14	the	the	DET
cana-3294	324	15	study	study	NOUN
cana-3294	324	16	of	of	ADP
cana-3294	324	17	fixed	fix	VERB
cana-3294	324	18	point	point	NOUN
cana-3294	324	19	theorems	theorem	NOUN
cana-3294	324	20	for	for	ADP
cana-3294	324	21	simulation	simulation	NOUN
cana-3294	324	22	functions	function	NOUN
cana-3294	324	23	in	in	ADP
cana-3294	324	24	g	g	NOUN
cana-3294	324	25	-	-	PUNCT
cana-3294	324	26	metric	metric	ADJ
cana-3294	324	27	spaces	space	NOUN
cana-3294	324	28	.	.	PUNCT
cana-3294	325	1	boletim	boletim	PROPN
cana-3294	325	2	da	da	PROPN
cana-3294	325	3	sociedade	sociedade	PROPN
cana-3294	325	4	paranaense	paranaense	PROPN
cana-3294	325	5	de	de	PROPN
cana-3294	325	6	matematica	matematica	PROPN
cana-3294	325	7	,	,	PUNCT
cana-3294	325	8	37(2	37(2	PROPN
cana-3294	325	9	)	)	PUNCT
cana-3294	325	10	,	,	PUNCT
cana-3294	325	11	115–121	115–121	NUM
cana-3294	325	12	.	.	PUNCT
cana-3294	325	13	(	(	PUNCT
cana-3294	325	14	2019	2019	NUM
cana-3294	325	15	)	)	PUNCT
cana-3294	325	16	.	.	PUNCT
cana-3294	326	1	[	[	X
cana-3294	326	2	15	15	NUM
cana-3294	326	3	]	]	X
cana-3294	326	4	kumar	kumar	PROPN
cana-3294	326	5	,	,	PUNCT
cana-3294	326	6	m.	m.	NOUN
cana-3294	326	7	,	,	PUNCT
cana-3294	326	8	arora	arora	PROPN
cana-3294	326	9	,	,	PUNCT
cana-3294	326	10	s.	s.	PROPN
cana-3294	326	11	,	,	PUNCT
cana-3294	326	12	imdad	imdad	PROPN
cana-3294	326	13	,	,	PUNCT
cana-3294	326	14	m.	m.	NOUN
cana-3294	326	15	and	and	CCONJ
cana-3294	326	16	alfaqih	alfaqih	VERB
cana-3294	326	17	,	,	PUNCT
cana-3294	326	18	w.	w.	PROPN
cana-3294	326	19	m.	m.	PROPN
cana-3294	326	20	coincidence	coincidence	NOUN
cana-3294	326	21	and	and	CCONJ
cana-3294	326	22	common	common	ADJ
cana-3294	326	23	fixed	fix	VERB
cana-3294	326	24	point	point	NOUN
cana-3294	326	25	results	result	NOUN
cana-3294	326	26	via	via	ADP
cana-3294	326	27	simulation	simulation	NOUN
cana-3294	326	28	functions	function	NOUN
cana-3294	326	29	in	in	ADP
cana-3294	326	30	g	g	NOUN
cana-3294	326	31	-	-	PUNCT
cana-3294	326	32	metric	metric	ADJ
cana-3294	326	33	spaces	space	NOUN
cana-3294	326	34	.	.	PUNCT
cana-3294	327	1	journal	journal	NOUN
cana-3294	327	2	of	of	ADP
cana-3294	327	3	mathematics	mathematic	NOUN
cana-3294	327	4	and	and	CCONJ
cana-3294	327	5	computer	computer	NOUN
cana-3294	327	6	science	science	NOUN
cana-3294	327	7	,	,	PUNCT
cana-3294	327	8	19	19	NUM
cana-3294	327	9	,	,	PUNCT
cana-3294	327	10	288–300	288–300	NUM
cana-3294	327	11	.	.	PUNCT
cana-3294	328	1	(	(	PUNCT
cana-3294	328	2	2019	2019	NUM
cana-3294	328	3	)	)	PUNCT
cana-3294	328	4	.	.	PUNCT
cana-3294	329	1	[	[	X
cana-3294	329	2	16	16	NUM
cana-3294	329	3	]	]	X
cana-3294	329	4	kumar	kumar	PROPN
cana-3294	329	5	,	,	PUNCT
cana-3294	329	6	m.	m.	NOUN
cana-3294	329	7	,	,	PUNCT
cana-3294	329	8	arora	arora	PROPN
cana-3294	329	9	,	,	PUNCT
cana-3294	329	10	s.	s.	PROPN
cana-3294	329	11	and	and	CCONJ
cana-3294	329	12	mishra	mishra	PROPN
cana-3294	329	13	,	,	PUNCT
cana-3294	329	14	s.	s.	PROPN
cana-3294	329	15	on	on	ADP
cana-3294	329	16	the	the	DET
cana-3294	329	17	power	power	NOUN
cana-3294	329	18	of	of	ADP
cana-3294	329	19	simulation	simulation	NOUN
cana-3294	329	20	map	map	NOUN
cana-3294	329	21	for	for	ADP
cana-3294	329	22	almost	almost	ADV
cana-3294	329	23	z	z	NOUN
cana-3294	329	24	-	-	NOUN
cana-3294	329	25	contraction	contraction	NOUN
cana-3294	329	26	in	in	ADP
cana-3294	329	27	g	g	NOUN
cana-3294	329	28	-	-	PUNCT
cana-3294	329	29	metric	metric	ADJ
cana-3294	329	30	space	space	NOUN
cana-3294	329	31	with	with	ADP
cana-3294	329	32	applications	application	NOUN
cana-3294	329	33	to	to	ADP
cana-3294	329	34	the	the	DET
cana-3294	329	35	solution	solution	NOUN
cana-3294	329	36	of	of	ADP
cana-3294	329	37	the	the	DET
cana-3294	329	38	integral	integral	ADJ
cana-3294	329	39	equation	equation	NOUN
cana-3294	329	40	.	.	PUNCT
cana-3294	330	1	italian	italian	ADJ
cana-3294	330	2	journal	journal	NOUN
cana-3294	330	3	of	of	ADP
cana-3294	330	4	pure	pure	ADJ
cana-3294	330	5	and	and	CCONJ
cana-3294	330	6	applied	applied	ADJ
cana-3294	330	7	mathematics	mathematic	NOUN
cana-3294	330	8	,	,	PUNCT
cana-3294	330	9	44	44	NUM
cana-3294	330	10	,	,	PUNCT
cana-3294	330	11	639648	639648	NUM
cana-3294	330	12	.	.	PUNCT
cana-3294	331	1	(	(	PUNCT
cana-3294	331	2	2020	2020	NUM
cana-3294	331	3	)	)	PUNCT
cana-3294	331	4	.	.	PUNCT
cana-3294	332	1	[	[	X
cana-3294	332	2	17	17	NUM
cana-3294	332	3	]	]	X
cana-3294	332	4	chen	chen	PROPN
cana-3294	332	5	,	,	PUNCT
cana-3294	332	6	j.	j.	PROPN
cana-3294	332	7	,	,	PUNCT
cana-3294	332	8	zhu	zhu	PROPN
cana-3294	332	9	,	,	PUNCT
cana-3294	332	10	c.	c.	PROPN
cana-3294	332	11	and	and	CCONJ
cana-3294	332	12	zhu	zhu	PROPN
cana-3294	332	13	,	,	PUNCT
cana-3294	332	14	l.	l.	PROPN
cana-3294	332	15	a	a	DET
cana-3294	332	16	note	note	NOUN
cana-3294	332	17	on	on	ADP
cana-3294	332	18	some	some	DET
cana-3294	332	19	fixed	fix	VERB
cana-3294	332	20	point	point	NOUN
cana-3294	332	21	theorems	theorem	NOUN
cana-3294	332	22	on	on	ADP
cana-3294	332	23	g	g	NOUN
cana-3294	332	24	-	-	PUNCT
cana-3294	332	25	metric	metric	ADJ
cana-3294	332	26	spaces	space	NOUN
cana-3294	332	27	.	.	PUNCT
cana-3294	333	1	journal	journal	NOUN
cana-3294	333	2	of	of	ADP
cana-3294	333	3	applied	apply	VERB
cana-3294	333	4	analysis	analysis	NOUN
cana-3294	333	5	and	and	CCONJ
cana-3294	333	6	computation	computation	NOUN
cana-3294	333	7	,	,	PUNCT
cana-3294	333	8	11(1	11(1	NUM
cana-3294	333	9	)	)	PUNCT
cana-3294	333	10	,	,	PUNCT
cana-3294	333	11	101	101	NUM
cana-3294	333	12	-	-	SYM
cana-3294	333	13	112	112	NUM
cana-3294	333	14	.	.	PUNCT
cana-3294	334	1	(	(	PUNCT
cana-3294	334	2	2021	2021	NUM
cana-3294	334	3	)	)	PUNCT
cana-3294	334	4	.	.	PUNCT
cana-3294	335	1	[	[	X
cana-3294	335	2	18	18	NUM
cana-3294	335	3	]	]	PUNCT
cana-3294	335	4	priyobarta	priyobarta	NOUN
cana-3294	335	5	,	,	PUNCT
cana-3294	335	6	n.	n.	NOUN
cana-3294	335	7	,	,	PUNCT
cana-3294	335	8	khomdram	khomdram	PROPN
cana-3294	335	9	,	,	PUNCT
cana-3294	335	10	b.	b.	PROPN
cana-3294	335	11	,	,	PUNCT
cana-3294	335	12	rohen	rohen	NOUN
cana-3294	335	13	,	,	PUNCT
cana-3294	335	14	y.	y.	PROPN
cana-3294	335	15	and	and	CCONJ
cana-3294	335	16	saleem	saleem	PROPN
cana-3294	335	17	,	,	PUNCT
cana-3294	335	18	n.	n.	NOUN
cana-3294	335	19	on	on	ADP
cana-3294	335	20	generalized	generalized	ADJ
cana-3294	335	21	rational	rational	ADJ
cana-3294	335	22	α	α	PROPN
cana-3294	335	23	-	-	PUNCT
cana-3294	335	24	geraghty	geraghty	VERB
cana-3294	335	25	contraction	contraction	NOUN
cana-3294	335	26	mappings	mapping	NOUN
cana-3294	335	27	in	in	ADP
cana-3294	335	28	g	g	NOUN
cana-3294	335	29	-	-	PUNCT
cana-3294	335	30	metric	metric	ADJ
cana-3294	335	31	spaces	space	NOUN
cana-3294	335	32	.	.	PUNCT
cana-3294	336	1	journal	journal	NOUN
cana-3294	336	2	of	of	ADP
cana-3294	336	3	mathematics	mathematic	NOUN
cana-3294	336	4	,	,	PUNCT
cana-3294	336	5	volume	volume	NOUN
cana-3294	336	6	2021	2021	NUM
cana-3294	336	7	,	,	PUNCT
cana-3294	336	8	article	article	NOUN
cana-3294	336	9	i	i	PROPN
cana-3294	336	10	d	d	PROPN
cana-3294	336	11	6661045	6661045	NUM
cana-3294	336	12	,	,	PUNCT
cana-3294	336	13	12	12	NUM
cana-3294	336	14	pages	page	NOUN
cana-3294	336	15	,	,	PUNCT
cana-3294	336	16	doi:10.1155/2021/6661045	doi:10.1155/2021/6661045	ADJ
cana-3294	336	17	.	.	PUNCT
cana-3294	336	18	(	(	PUNCT
cana-3294	336	19	2021	2021	NUM
cana-3294	336	20	)	)	PUNCT
cana-3294	336	21	.	.	PUNCT
cana-3294	337	1	[	[	X
cana-3294	337	2	19	19	NUM
cana-3294	337	3	]	]	X
cana-3294	337	4	kumar	kumar	PROPN
cana-3294	337	5	,	,	PUNCT
cana-3294	337	6	m.	m.	NOUN
cana-3294	337	7	and	and	CCONJ
cana-3294	337	8	arora	arora	PROPN
cana-3294	337	9	,	,	PUNCT
cana-3294	337	10	s.	s.	PROPN
cana-3294	337	11	fixed	fix	VERB
cana-3294	337	12	point	point	NOUN
cana-3294	337	13	theorems	theorem	NOUN
cana-3294	337	14	for	for	ADP
cana-3294	337	15	modified	modified	ADJ
cana-3294	337	16	generalized	generalize	VERB
cana-3294	337	17	f	f	NOUN
cana-3294	337	18	-	-	PUNCT
cana-3294	337	19	contraction	contraction	NOUN
cana-3294	337	20	in	in	ADP
cana-3294	337	21	g	g	NOUN
cana-3294	337	22	-	-	PUNCT
cana-3294	337	23	metric	metric	ADJ
cana-3294	337	24	spaces	space	NOUN
cana-3294	337	25	.	.	PUNCT
cana-3294	338	1	boletim	boletim	PROPN
cana-3294	338	2	da	da	PROPN
cana-3294	338	3	sociedade	sociedade	PROPN
cana-3294	338	4	paranaense	paranaense	PROPN
cana-3294	338	5	de	de	PROPN
cana-3294	338	6	matematica	matematica	PROPN
cana-3294	338	7	,	,	PUNCT
cana-3294	338	8	40	40	NUM
cana-3294	338	9	,	,	PUNCT
cana-3294	338	10	1	1	NUM
cana-3294	338	11	-	-	SYM
cana-3294	338	12	8	8	NUM
cana-3294	338	13	.	.	PUNCT
cana-3294	338	14	(	(	PUNCT
cana-3294	338	15	2022	2022	NUM
cana-3294	338	16	)	)	PUNCT
cana-3294	338	17	.	.	PUNCT
cana-3294	339	1	´	´	VERB
cana-3294	340	1	[	[	X
cana-3294	340	2	20	20	NUM
cana-3294	340	3	]	]	PUNCT
cana-3294	340	4	jiddah	jiddah	NOUN
cana-3294	340	5	,	,	PUNCT
cana-3294	340	6	j.	j.	PROPN
cana-3294	340	7	a.	a.	PROPN
cana-3294	340	8	,	,	PUNCT
cana-3294	340	9	alansari	alansari	PROPN
cana-3294	340	10	,	,	PUNCT
cana-3294	340	11	m.	m.	NOUN
cana-3294	340	12	,	,	PUNCT
cana-3294	340	13	mohamed	mohamed	PROPN
cana-3294	340	14	,	,	PUNCT
cana-3294	340	15	o.	o.	PROPN
cana-3294	340	16	,	,	PUNCT
cana-3294	340	17	shagari	shagari	PROPN
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cana-3294	340	20	s.	s.	PROPN
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cana-3294	340	30	jaggi	jaggi	NOUN
cana-3294	340	31	-	-	PUNCT
cana-3294	340	32	type	type	NOUN
cana-3294	340	33	hybrid	hybrid	ADJ
cana-3294	340	34	contraction	contraction	NOUN
cana-3294	340	35	in	in	ADP
cana-3294	340	36	generalized	generalized	ADJ
cana-3294	340	37	metric	metric	ADJ
cana-3294	340	38	space	space	NOUN
cana-3294	340	39	.	.	PUNCT
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cana-3294	341	2	of	of	ADP
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cana-3294	341	5	,	,	PUNCT
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cana-3294	341	9	,	,	PUNCT
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cana-3294	342	3	)	)	PUNCT
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cana-3294	343	2	21	21	NUM
cana-3294	343	3	]	]	PUNCT
cana-3294	343	4	v.sihag	v.sihag	NOUN
cana-3294	343	5	,	,	PUNCT
cana-3294	343	6	c.vetro	c.vetro	NOUN
cana-3294	343	7	,	,	PUNCT
cana-3294	343	8	rk.vats	rk.vat	VERB
cana-3294	343	9	:	:	PUNCT
cana-3294	343	10	a	a	DET
cana-3294	343	11	fixed	fix	VERB
cana-3294	343	12	point	point	NOUN
cana-3294	343	13	theorems	theorem	NOUN
cana-3294	343	14	in	in	ADP
cana-3294	343	15	gmetric	gmetric	ADJ
cana-3294	343	16	spaces	space	VERB
cana-3294	343	17	.	.	PUNCT
cana-3294	344	1	via	via	ADP
cana-3294	344	2	α	α	NOUN
cana-3294	344	3	-	-	PUNCT
cana-3294	344	4	series	series	NOUN
cana-3294	344	5	,	,	PUNCT
cana-3294	344	6	quaest.math;37,1	quaest.math;37,1	PROPN
cana-3294	344	7	6	6	NUM
cana-3294	344	8	(	(	PUNCT
cana-3294	344	9	2014	2014	NUM
cana-3294	344	10	)	)	PUNCT
cana-3294	344	11	.	.	PUNCT
cana-3294	345	1	[	[	X
cana-3294	345	2	22	22	NUM
cana-3294	345	3	]	]	X
cana-3294	345	4	chang	chang	PROPN
cana-3294	345	5	,	,	PUNCT
cana-3294	345	6	ss	ss	PROPN
cana-3294	345	7	.	.	PROPN
cana-3294	345	8	ma	ma	PROPN
cana-3294	345	9	,	,	PUNCT
cana-3294	345	10	yh	yh	PROPN
cana-3294	345	11	:	:	PUNCT
cana-3294	345	12	coupled	couple	VERB
cana-3294	345	13	fixed	fix	VERB
cana-3294	345	14	point	point	NOUN
cana-3294	345	15	for	for	ADP
cana-3294	345	16	mixed	mixed	ADJ
cana-3294	345	17	monotone	monotone	ADJ
cana-3294	345	18	condensing	condense	VERB
cana-3294	345	19	operators	operator	NOUN
cana-3294	345	20	and	and	CCONJ
cana-3294	345	21	an	an	DET
cana-3294	345	22	existence	existence	NOUN
cana-3294	345	23	theorem	theorem	NOUN
cana-3294	345	24	of	of	ADP
cana-3294	345	25	the	the	DET
cana-3294	345	26	solutions	solution	NOUN
cana-3294	345	27	for	for	ADP
cana-3294	345	28	a	a	DET
cana-3294	345	29	class	class	NOUN
cana-3294	345	30	of	of	ADP
cana-3294	345	31	functional	functional	ADJ
cana-3294	345	32	equations	equation	NOUN
cana-3294	345	33	arising	arise	VERB
cana-3294	345	34	in	in	ADP
cana-3294	345	35	dynamic	dynamic	ADJ
cana-3294	345	36	programming	programming	NOUN
cana-3294	345	37	.	.	PUNCT
cana-3294	346	1	j.	j.	PROPN
cana-3294	346	2	math	math	PROPN
cana-3294	346	3	.	.	PUNCT
cana-3294	347	1	anal	anal	PROPN
cana-3294	347	2	.	.	PUNCT
cana-3294	347	3	appl	appl	PROPN
cana-3294	347	4	.	.	PUNCT
cana-3294	348	1	160	160	NUM
cana-3294	348	2	,	,	PUNCT
cana-3294	348	3	468	468	NUM
cana-3294	348	4	-	-	SYM
cana-3294	348	5	479	479	NUM
cana-3294	348	6	(	(	PUNCT
cana-3294	348	7	1991	1991	NUM
cana-3294	348	8	)	)	PUNCT
cana-3294	348	9	.	.	PUNCT
cana-3294	349	1	[	[	X
cana-3294	349	2	23	23	NUM
cana-3294	349	3	]	]	PUNCT
cana-3294	349	4	berinde	berinde	NOUN
cana-3294	349	5	v	v	NOUN
cana-3294	349	6	:	:	PUNCT
cana-3294	349	7	generalized	generalized	ADJ
cana-3294	349	8	coupled	couple	VERB
cana-3294	349	9	fixed	fix	VERB
cana-3294	349	10	point	point	NOUN
cana-3294	349	11	theorems	theorem	NOUN
cana-3294	349	12	for	for	ADP
cana-3294	349	13	mixed	mixed	ADJ
cana-3294	349	14	monotone	monotone	ADJ
cana-3294	349	15	mappings	mapping	NOUN
cana-3294	349	16	in	in	ADP
cana-3294	349	17	partially	partially	ADV
cana-3294	349	18	ordered	order	VERB
cana-3294	349	19	metric	metric	ADJ
cana-3294	349	20	spaces	space	NOUN
cana-3294	349	21	.	.	PUNCT
cana-3294	350	1	nonlinear	nonlinear	ADJ
cana-3294	350	2	anal.72,4508	anal.72,4508	NOUN
cana-3294	350	3	–	–	PUNCT
cana-3294	350	4	4517	4517	NUM
cana-3294	350	5	(	(	PUNCT
cana-3294	350	6	2010	2010	NUM
cana-3294	350	7	)	)	PUNCT
cana-3294	350	8	.	.	PUNCT
cana-3294	351	1	[	[	X
cana-3294	351	2	24	24	NUM
cana-3294	351	3	]	]	SYM
cana-3294	351	4	b.s	b.s	PROPN
cana-3294	351	5	.	.	PROPN
cana-3294	351	6	choudary	choudary	PROPN
cana-3294	351	7	,	,	PUNCT
cana-3294	351	8	a.	a.	NOUN
cana-3294	351	9	kundu	kundu	NOUN
cana-3294	351	10	:	:	PUNCT
cana-3294	351	11	a	a	DET
cana-3294	351	12	coupled	couple	VERB
cana-3294	351	13	coincidence	coincidence	NOUN
cana-3294	351	14	point	point	NOUN
cana-3294	351	15	result	result	NOUN
cana-3294	351	16	in	in	ADP
cana-3294	351	17	partially	partially	ADV
cana-3294	351	18	ordered	order	VERB
cana-3294	351	19	metric	metric	ADJ
cana-3294	351	20	spaces	space	NOUN
cana-3294	351	21	for	for	ADP
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cana-3294	351	23	mappings	mapping	NOUN
cana-3294	351	24	,	,	PUNCT
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cana-3294	351	27	–	–	PUNCT
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cana-3294	351	29	(	(	PUNCT
cana-3294	351	30	2010	2010	NUM
cana-3294	351	31	)	)	PUNCT
cana-3294	351	32	.	.	PUNCT
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cana-3294	352	3	]	]	X
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cana-3294	352	9	,	,	PUNCT
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cana-3294	352	11	:	:	PUNCT
cana-3294	352	12	coupled	couple	VERB
cana-3294	352	13	fixed	fix	VERB
cana-3294	352	14	point	point	NOUN
cana-3294	352	15	theorems	theorem	NOUN
cana-3294	352	16	for	for	ADP
cana-3294	352	17	nonlinear	nonlinear	ADJ
cana-3294	352	18	contractions	contraction	NOUN
cana-3294	352	19	in	in	ADP
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cana-3294	352	21	ordered	order	VERB
cana-3294	352	22	metric	metric	ADJ
cana-3294	352	23	spaces	space	NOUN
cana-3294	352	24	.	.	PUNCT
cana-3294	353	1	nonlinear	nonlinear	PROPN
cana-3294	353	2	anal.70	anal.70	PROPN
cana-3294	353	3	,	,	PUNCT
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cana-3294	353	5	–	–	PUNCT
cana-3294	353	6	4349	4349	NUM
cana-3294	353	7	(	(	PUNCT
cana-3294	353	8	2009	2009	NUM
cana-3294	353	9	)	)	PUNCT
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cana-3294	354	5	,	,	PUNCT
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cana-3294	354	7	:	:	PUNCT
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cana-3294	354	12	in	in	ADP
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cana-3294	354	14	metric	metric	ADJ
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cana-3294	354	16	.	.	PUNCT
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cana-3294	357	2	.	.	PUNCT
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cana-3294	358	2	,	,	PUNCT
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cana-3294	358	4	-	-	SYM
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cana-3294	358	8	)	)	PUNCT
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cana-3294	359	9	,	,	PUNCT
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cana-3294	361	4	-	-	SYM
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cana-3294	362	3	]	]	PUNCT
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cana-3294	362	5	,	,	PUNCT
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cana-3294	363	5	,	,	PUNCT
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cana-3294	365	2	,	,	PUNCT
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cana-3294	365	4	-	-	SYM
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cana-3294	365	7	2011	2011	NUM
cana-3294	365	8	)	)	PUNCT
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cana-3294	365	10	on	on	ADP
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cana-3294	365	12	nonlinear	nonlinear	ADJ
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cana-3294	365	14	issn	issn	NOUN
cana-3294	365	15	:	:	PUNCT
cana-3294	365	16	1074	1074	NUM
cana-3294	365	17	-	-	PUNCT
cana-3294	365	18	133x	133x	NUM
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cana-3294	366	4	)	)	PUNCT
cana-3294	366	5	289	289	NUM
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cana-3294	367	1	[	[	X
cana-3294	367	2	29	29	NUM
cana-3294	367	3	]	]	PUNCT
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cana-3294	367	6	,	,	PUNCT
cana-3294	367	7	r.	r.	PROPN
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cana-3294	367	9	,	,	PUNCT
cana-3294	367	10	a.	a.	PROPN
cana-3294	367	11	bagheria	bagheria	PROPN
cana-3294	367	12	vakilabad	vakilabad	PROPN
cana-3294	367	13	,	,	PUNCT
cana-3294	367	14	h.hosseinzadeh	h.hosseinzadeh	ADV
cana-3294	367	15	:	:	PUNCT
cana-3294	367	16	coupled	couple	VERB
cana-3294	367	17	fixed	fix	VERB
cana-3294	367	18	point	point	NOUN
cana-3294	367	19	theorems	theorem	NOUN
cana-3294	367	20	on	on	ADP
cana-3294	367	21	gmetric	gmetric	PROPN
cana-3294	367	22	spaces	space	NOUN
cana-3294	367	23	via	via	ADP
cana-3294	367	24	α	α	NOUN
cana-3294	367	25	-	-	PUNCT
cana-3294	367	26	series	series	NOUN
cana-3294	367	27	.	.	PUNCT
cana-3294	368	1	global	global	ADJ
cana-3294	368	2	anal	anal	PROPN
cana-3294	368	3	:	:	PUNCT
cana-3294	368	4	and	and	CCONJ
cana-3294	368	5	discrete	discrete	ADJ
cana-3294	368	6	mathematics	mathematic	NOUN
cana-3294	368	7	6(1	6(1	NUM
cana-3294	368	8	)	)	PUNCT
cana-3294	368	9	1	1	NUM
cana-3294	368	10	-	-	SYM
cana-3294	368	11	12	12	NUM
cana-3294	368	12	pp	pp	PROPN
cana-3294	368	13	,	,	PUNCT
cana-3294	368	14	issn	issn	PROPN
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cana-3294	368	16	–	–	PUNCT
cana-3294	368	17	5341(2021	5341(2021	NUM
cana-3294	368	18	)	)	PUNCT
cana-3294	369	1	[	[	X
cana-3294	369	2	30	30	NUM
cana-3294	369	3	]	]	X
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cana-3294	369	5	,	,	PUNCT
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cana-3294	369	7	:	:	PUNCT
cana-3294	369	8	borcut	borcut	VERB
cana-3294	369	9	,	,	PUNCT
cana-3294	369	10	m	m	VERB
cana-3294	369	11	:	:	PUNCT
cana-3294	369	12	tripled	triple	VERB
cana-3294	369	13	fixed	fix	VERB
cana-3294	369	14	point	point	NOUN
cana-3294	369	15	theorems	theorem	NOUN
cana-3294	369	16	for	for	ADP
cana-3294	369	17	contractive	contractive	ADJ
cana-3294	369	18	type	type	NOUN
cana-3294	369	19	mappings	mapping	NOUN
cana-3294	369	20	in	in	ADP
cana-3294	369	21	partially	partially	ADV
cana-3294	369	22	ordered	order	VERB
cana-3294	369	23	metric	metric	ADJ
cana-3294	369	24	spaces	space	NOUN
cana-3294	369	25	.	.	PUNCT
cana-3294	370	1	nonlinear	nonlinear	ADJ
cana-3294	370	2	anal.74(15	anal.74(15	NOUN
cana-3294	370	3	)	)	PUNCT
cana-3294	370	4	4889	4889	NUM
cana-3294	370	5	–	–	PUNCT
cana-3294	370	6	4897(2011	4897(2011	NUM
cana-3294	370	7	)	)	PUNCT
cana-3294	370	8	.	.	PUNCT
cana-3294	371	1	[	[	X
cana-3294	371	2	31	31	NUM
cana-3294	371	3	]	]	PUNCT
cana-3294	371	4	borcut	borcut	VERB
cana-3294	371	5	,	,	PUNCT
cana-3294	371	6	m	m	NOUN
cana-3294	371	7	,	,	PUNCT
cana-3294	371	8	berinde	berinde	NOUN
cana-3294	371	9	,	,	PUNCT
cana-3294	371	10	v	v	NOUN
cana-3294	371	11	:	:	PUNCT
cana-3294	371	12	tripled	triple	VERB
cana-3294	371	13	coincidence	coincidence	NOUN
cana-3294	371	14	theorems	theorem	NOUN
cana-3294	371	15	for	for	ADP
cana-3294	371	16	contractive	contractive	ADJ
cana-3294	371	17	type	type	NOUN
cana-3294	371	18	mappings	mapping	NOUN
cana-3294	371	19	in	in	ADP
cana-3294	371	20	partially	partially	ADV
cana-3294	371	21	ordered	order	VERB
cana-3294	371	22	metric	metric	ADJ
cana-3294	371	23	spaces	space	NOUN
cana-3294	371	24	.	.	PUNCT
cana-3294	372	1	apple.math.comput.218	apple.math.comput.218	PROPN
cana-3294	373	1	(	(	PUNCT
cana-3294	373	2	10	10	NUM
cana-3294	373	3	)	)	PUNCT
cana-3294	373	4	,	,	PUNCT
cana-3294	373	5	5929	5929	NUM
cana-3294	373	6	–	–	PUNCT
cana-3294	373	7	5936	5936	NUM
cana-3294	373	8	(	(	PUNCT
cana-3294	373	9	2012	2012	NUM
cana-3294	373	10	)	)	PUNCT
cana-3294	373	11	.	.	PUNCT
cana-3294	374	1	[	[	X
cana-3294	374	2	32	32	NUM
cana-3294	374	3	]	]	PUNCT
cana-3294	374	4	rk.vats	rk.vat	NOUN
cana-3294	374	5	,	,	PUNCT
cana-3294	374	6	k.tal	k.tal	NOUN
cana-3294	374	7	,	,	PUNCT
cana-3294	374	8	v.sihag	v.sihag	NOUN
cana-3294	374	9	and	and	CCONJ
cana-3294	374	10	a	a	DET
cana-3294	374	11	,	,	PUNCT
cana-3294	374	12	kumar	kumar	PROPN
cana-3294	374	13	:	:	PUNCT
cana-3294	374	14	tripled	triple	VERB
cana-3294	374	15	fixed	fix	VERB
cana-3294	374	16	point	point	NOUN
cana-3294	374	17	theorems	theorem	NOUN
cana-3294	374	18	via	via	ADP
cana-3294	374	19	α	α	NOUN
cana-3294	374	20	-	-	PUNCT
cana-3294	374	21	series	series	NOUN
cana-3294	374	22	in	in	ADP
cana-3294	374	23	partially	partially	ADV
cana-3294	374	24	ordered	order	VERB
cana-3294	374	25	metric	metric	ADJ
cana-3294	374	26	spaces	space	NOUN
cana-3294	374	27	,	,	PUNCT
cana-3294	374	28	j.inequal.appl.1	j.inequal.appl.1	ADV
cana-3294	374	29	–	–	PUNCT
cana-3294	374	30	12	12	NUM
cana-3294	374	31	(	(	PUNCT
cana-3294	374	32	2014	2014	NUM
cana-3294	374	33	)	)	PUNCT
cana-3294	374	34	.	.	PUNCT
cana-3294	375	1	[	[	X
cana-3294	375	2	33	33	NUM
cana-3294	375	3	]	]	PUNCT
cana-3294	375	4	t.g.bhaskar	t.g.bhaskar	NOUN
cana-3294	375	5	,	,	PUNCT
cana-3294	375	6	v.	v.	ADP
cana-3294	375	7	lakshmikantham	lakshmikantham	ADJ
cana-3294	375	8	:	:	PUNCT
cana-3294	375	9	fixed	fix	VERB
cana-3294	375	10	point	point	NOUN
cana-3294	375	11	theorems	theorem	NOUN
cana-3294	375	12	in	in	ADP
cana-3294	375	13	partially	partially	ADV
cana-3294	375	14	ordered	order	VERB
cana-3294	375	15	metric	metric	ADJ
cana-3294	375	16	spaces	space	NOUN
cana-3294	375	17	and	and	CCONJ
cana-3294	375	18	applications	application	NOUN
cana-3294	375	19	,	,	PUNCT
cana-3294	375	20	nonlinear	nonlinear	ADJ
cana-3294	375	21	anal;65,1379	anal;65,1379	PROPN
cana-3294	375	22	–	–	PUNCT
cana-3294	375	23	1393	1393	NUM
cana-3294	375	24	(	(	PUNCT
cana-3294	375	25	2006	2006	NUM
cana-3294	375	26	)	)	PUNCT
cana-3294	375	27	.	.	PUNCT