id	sid	tid	token	lemma	pos
ejpam-5719	1	1	european	european	PROPN
ejpam-5719	1	2	journal	journal	PROPN
ejpam-5719	1	3	of	of	ADP
ejpam-5719	1	4	pure	pure	ADJ
ejpam-5719	1	5	and	and	CCONJ
ejpam-5719	1	6	applied	applied	ADJ
ejpam-5719	1	7	mathematics	mathematic	NOUN
ejpam-5719	1	8	2025	2025	NUM
ejpam-5719	1	9	,	,	PUNCT
ejpam-5719	1	10	vol	vol	NOUN
ejpam-5719	1	11	.	.	PROPN
ejpam-5719	1	12	18	18	NUM
ejpam-5719	1	13	,	,	PUNCT
ejpam-5719	1	14	issue	issue	NOUN
ejpam-5719	1	15	1	1	NUM
ejpam-5719	1	16	,	,	PUNCT
ejpam-5719	1	17	article	article	NOUN
ejpam-5719	1	18	number	number	NOUN
ejpam-5719	1	19	5719	5719	NUM
ejpam-5719	1	20	issn	issn	VERB
ejpam-5719	1	21	1307	1307	NUM
ejpam-5719	1	22	-	-	SYM
ejpam-5719	1	23	5543	5543	NUM
ejpam-5719	1	24	–	–	PUNCT
ejpam-5719	1	25	ejpam.com	ejpam.com	X
ejpam-5719	1	26	published	publish	VERB
ejpam-5719	1	27	by	by	ADP
ejpam-5719	1	28	new	new	PROPN
ejpam-5719	1	29	york	york	PROPN
ejpam-5719	1	30	business	business	PROPN
ejpam-5719	1	31	global	global	ADJ
ejpam-5719	1	32	quadratic	quadratic	ADJ
ejpam-5719	1	33	f	f	PROPN
ejpam-5719	1	34	-	-	PUNCT
ejpam-5719	1	35	hom	hom	NOUN
ejpam-5719	1	36	-	-	PUNCT
ejpam-5719	1	37	ders	der	NOUN
ejpam-5719	1	38	in	in	ADP
ejpam-5719	1	39	banach	banach	NOUN
ejpam-5719	1	40	algebra	algebra	NOUN
ejpam-5719	1	41	related	relate	VERB
ejpam-5719	1	42	to	to	ADP
ejpam-5719	1	43	system	system	NOUN
ejpam-5719	1	44	of	of	ADP
ejpam-5719	1	45	quadratic	quadratic	ADJ
ejpam-5719	1	46	functional	functional	ADJ
ejpam-5719	1	47	equations	equation	NOUN
ejpam-5719	1	48	choonkil	choonkil	NOUN
ejpam-5719	1	49	park1	park1	PROPN
ejpam-5719	1	50	,	,	PUNCT
ejpam-5719	1	51	siriluk	siriluk	PROPN
ejpam-5719	1	52	donganont2,∗	donganont2,∗	PROPN
ejpam-5719	1	53	,	,	PUNCT
ejpam-5719	1	54	se	se	X
ejpam-5719	1	55	won	win	VERB
ejpam-5719	1	56	min3,∗	min3,∗	PROPN
ejpam-5719	1	57	1	1	NUM
ejpam-5719	1	58	research	research	NOUN
ejpam-5719	1	59	institute	institute	NOUN
ejpam-5719	1	60	for	for	ADP
ejpam-5719	1	61	convergence	convergence	NOUN
ejpam-5719	1	62	of	of	ADP
ejpam-5719	1	63	basic	basic	ADJ
ejpam-5719	1	64	sciences	science	NOUN
ejpam-5719	1	65	,	,	PUNCT
ejpam-5719	1	66	hanyang	hanyang	NOUN
ejpam-5719	1	67	university	university	PROPN
ejpam-5719	1	68	,	,	PUNCT
ejpam-5719	1	69	seoul	seoul	PROPN
ejpam-5719	1	70	04763	04763	NUM
ejpam-5719	1	71	,	,	PUNCT
ejpam-5719	1	72	korea	korea	PROPN
ejpam-5719	1	73	2	2	NUM
ejpam-5719	1	74	school	school	NOUN
ejpam-5719	1	75	of	of	ADP
ejpam-5719	1	76	science	science	NOUN
ejpam-5719	1	77	,	,	PUNCT
ejpam-5719	1	78	university	university	NOUN
ejpam-5719	1	79	of	of	ADP
ejpam-5719	1	80	phayao	phayao	NOUN
ejpam-5719	1	81	,	,	PUNCT
ejpam-5719	1	82	phayao	phayao	NOUN
ejpam-5719	1	83	56000	56000	NUM
ejpam-5719	1	84	,	,	PUNCT
ejpam-5719	1	85	thailand	thailand	PROPN
ejpam-5719	1	86	3	3	NUM
ejpam-5719	1	87	department	department	PROPN
ejpam-5719	1	88	of	of	ADP
ejpam-5719	1	89	mathematics	mathematics	PROPN
ejpam-5719	1	90	,	,	PUNCT
ejpam-5719	1	91	hanyang	hanyang	PROPN
ejpam-5719	1	92	university	university	PROPN
ejpam-5719	1	93	,	,	PUNCT
ejpam-5719	1	94	seoul	seoul	PROPN
ejpam-5719	1	95	04763	04763	NUM
ejpam-5719	1	96	,	,	PUNCT
ejpam-5719	1	97	korea	korea	PROPN
ejpam-5719	1	98	abstract	abstract	NOUN
ejpam-5719	1	99	.	.	PUNCT
ejpam-5719	2	1	mirzavaziri	mirzavaziri	PROPN
ejpam-5719	2	2	and	and	CCONJ
ejpam-5719	2	3	moslehian	moslehian	ADJ
ejpam-5719	3	1	[	[	X
ejpam-5719	3	2	13	13	NUM
ejpam-5719	3	3	]	]	PUNCT
ejpam-5719	3	4	introduced	introduce	VERB
ejpam-5719	3	5	the	the	DET
ejpam-5719	3	6	concept	concept	NOUN
ejpam-5719	3	7	of	of	ADP
ejpam-5719	3	8	f	f	PROPN
ejpam-5719	3	9	-derivations	-derivation	NOUN
ejpam-5719	3	10	and	and	CCONJ
ejpam-5719	3	11	sripattanet	sripattanet	NOUN
ejpam-5719	3	12	et	et	PROPN
ejpam-5719	3	13	al	al	PROPN
ejpam-5719	3	14	.	.	PUNCT
ejpam-5719	4	1	[	[	X
ejpam-5719	4	2	18	18	NUM
ejpam-5719	4	3	]	]	PUNCT
ejpam-5719	4	4	introduced	introduce	VERB
ejpam-5719	4	5	a	a	DET
ejpam-5719	4	6	quadratic	quadratic	ADJ
ejpam-5719	4	7	hom	hom	NOUN
ejpam-5719	4	8	-	-	PUNCT
ejpam-5719	4	9	der	der	NOUN
ejpam-5719	4	10	in	in	ADP
ejpam-5719	4	11	banach	banach	NOUN
ejpam-5719	4	12	algebras	algebra	NOUN
ejpam-5719	4	13	.	.	PUNCT
ejpam-5719	5	1	in	in	ADP
ejpam-5719	5	2	this	this	DET
ejpam-5719	5	3	paper	paper	NOUN
ejpam-5719	5	4	,	,	PUNCT
ejpam-5719	5	5	we	we	PRON
ejpam-5719	5	6	solve	solve	VERB
ejpam-5719	5	7	the	the	DET
ejpam-5719	5	8	system	system	NOUN
ejpam-5719	5	9	of	of	ADP
ejpam-5719	5	10	quadratic	quadratic	ADJ
ejpam-5719	5	11	functional	functional	ADJ
ejpam-5719	5	12	equations	equation	NOUN
ejpam-5719	5	13	{	{	PUNCT
ejpam-5719	5	14	f(x+	f(x+	NOUN
ejpam-5719	5	15	y	y	NUM
ejpam-5719	5	16	)	)	PUNCT
ejpam-5719	6	1	+	+	CCONJ
ejpam-5719	6	2	f(x−	f(x−	PROPN
ejpam-5719	6	3	y	y	NOUN
ejpam-5719	6	4	)	)	PUNCT
ejpam-5719	6	5	=	=	SYM
ejpam-5719	6	6	g(x	g(x	NOUN
ejpam-5719	6	7	)	)	PUNCT
ejpam-5719	7	1	+	+	CCONJ
ejpam-5719	8	1	g(y	g(y	NOUN
ejpam-5719	8	2	)	)	PUNCT
ejpam-5719	8	3	,	,	PUNCT
ejpam-5719	8	4	g	g	PROPN
ejpam-5719	8	5	(	(	PUNCT
ejpam-5719	8	6	x+y	x+y	PROPN
ejpam-5719	8	7	2	2	NUM
ejpam-5719	8	8	)	)	PUNCT
ejpam-5719	9	1	+	+	CCONJ
ejpam-5719	9	2	g	g	PROPN
ejpam-5719	9	3	(	(	PUNCT
ejpam-5719	9	4	x−y	x−y	PROPN
ejpam-5719	9	5	2	2	NUM
ejpam-5719	9	6	)	)	PUNCT
ejpam-5719	9	7	=	=	SYM
ejpam-5719	9	8	f(x	f(x	PROPN
ejpam-5719	9	9	)	)	PUNCT
ejpam-5719	9	10	+	+	SYM
ejpam-5719	9	11	f(y	f(y	NOUN
ejpam-5719	9	12	)	)	PUNCT
ejpam-5719	9	13	.	.	PUNCT
ejpam-5719	10	1	using	use	VERB
ejpam-5719	10	2	mirzavaziri	mirzavaziri	ADV
ejpam-5719	10	3	and	and	CCONJ
ejpam-5719	10	4	moslehian	moslehian	PROPN
ejpam-5719	10	5	’s	’s	PART
ejpam-5719	10	6	idea	idea	NOUN
ejpam-5719	10	7	and	and	CCONJ
ejpam-5719	10	8	sripattanet	sripattanet	NOUN
ejpam-5719	10	9	et	et	PROPN
ejpam-5719	10	10	al	al	PROPN
ejpam-5719	10	11	.	.	PROPN
ejpam-5719	10	12	’s	’s	PART
ejpam-5719	10	13	idea	idea	NOUN
ejpam-5719	10	14	,	,	PUNCT
ejpam-5719	10	15	we	we	PRON
ejpam-5719	10	16	define	define	VERB
ejpam-5719	10	17	a	a	DET
ejpam-5719	10	18	quadratic	quadratic	ADJ
ejpam-5719	10	19	f	f	NOUN
ejpam-5719	10	20	-homder	-homder	NOUN
ejpam-5719	10	21	in	in	ADP
ejpam-5719	10	22	banach	banach	NOUN
ejpam-5719	10	23	algebras	algebra	NOUN
ejpam-5719	10	24	,	,	PUNCT
ejpam-5719	10	25	and	and	CCONJ
ejpam-5719	10	26	we	we	PRON
ejpam-5719	10	27	investigate	investigate	VERB
ejpam-5719	10	28	the	the	DET
ejpam-5719	10	29	hyers	hyers	PROPN
ejpam-5719	10	30	-	-	PUNCT
ejpam-5719	10	31	ulam	ulam	ADJ
ejpam-5719	10	32	stability	stability	NOUN
ejpam-5719	10	33	of	of	ADP
ejpam-5719	10	34	quadratic	quadratic	ADJ
ejpam-5719	10	35	f	f	PROPN
ejpam-5719	10	36	-hom	-hom	X
ejpam-5719	10	37	-	-	PUNCT
ejpam-5719	10	38	ders	der	NOUN
ejpam-5719	10	39	in	in	ADP
ejpam-5719	10	40	banach	banach	NOUN
ejpam-5719	10	41	algebras	algebra	NOUN
ejpam-5719	10	42	.	.	PUNCT
ejpam-5719	11	1	2020	2020	NUM
ejpam-5719	11	2	mathematics	mathematics	PROPN
ejpam-5719	11	3	subject	subject	NOUN
ejpam-5719	11	4	classifications	classification	NOUN
ejpam-5719	11	5	:	:	PUNCT
ejpam-5719	11	6	47h10	47h10	NUM
ejpam-5719	11	7	,	,	PUNCT
ejpam-5719	11	8	47b47	47b47	NOUN
ejpam-5719	11	9	,	,	PUNCT
ejpam-5719	11	10	17b40	17b40	NUM
ejpam-5719	11	11	,	,	PUNCT
ejpam-5719	11	12	39b72	39b72	NUM
ejpam-5719	11	13	,	,	PUNCT
ejpam-5719	11	14	39b52	39b52	NUM
ejpam-5719	11	15	key	key	ADJ
ejpam-5719	11	16	words	word	NOUN
ejpam-5719	11	17	and	and	CCONJ
ejpam-5719	11	18	phrases	phrase	NOUN
ejpam-5719	11	19	:	:	PUNCT
ejpam-5719	11	20	quadratic	quadratic	ADJ
ejpam-5719	11	21	f	f	NOUN
ejpam-5719	11	22	-hom	-hom	X
ejpam-5719	11	23	-	-	PUNCT
ejpam-5719	11	24	der	der	NOUN
ejpam-5719	11	25	;	;	PUNCT
ejpam-5719	11	26	fixed	fix	VERB
ejpam-5719	11	27	point	point	NOUN
ejpam-5719	11	28	method	method	NOUN
ejpam-5719	11	29	;	;	PUNCT
ejpam-5719	11	30	hyers	hyers	PROPN
ejpam-5719	11	31	-	-	PUNCT
ejpam-5719	11	32	ulam	ulam	PROPN
ejpam-5719	11	33	stability	stability	NOUN
ejpam-5719	11	34	;	;	PUNCT
ejpam-5719	11	35	system	system	NOUN
ejpam-5719	11	36	of	of	ADP
ejpam-5719	11	37	quadratic	quadratic	ADJ
ejpam-5719	11	38	functional	functional	ADJ
ejpam-5719	11	39	equations	equation	NOUN
ejpam-5719	11	40	1	1	NUM
ejpam-5719	11	41	.	.	PUNCT
ejpam-5719	12	1	introduction	introduction	NOUN
ejpam-5719	12	2	let	let	VERB
ejpam-5719	12	3	b	b	X
ejpam-5719	12	4	be	be	AUX
ejpam-5719	12	5	a	a	DET
ejpam-5719	12	6	complex	complex	ADJ
ejpam-5719	12	7	banach	banach	NOUN
ejpam-5719	12	8	algebra	algebra	NOUN
ejpam-5719	12	9	and	and	CCONJ
ejpam-5719	12	10	f	f	NOUN
ejpam-5719	12	11	:	:	PUNCT
ejpam-5719	12	12	b	b	X
ejpam-5719	12	13	→	→	SYM
ejpam-5719	12	14	b	b	X
ejpam-5719	12	15	be	be	AUX
ejpam-5719	12	16	a	a	DET
ejpam-5719	12	17	c	c	NOUN
ejpam-5719	12	18	-	-	PUNCT
ejpam-5719	12	19	linear	linear	ADJ
ejpam-5719	12	20	mapping	mapping	NOUN
ejpam-5719	12	21	.	.	PUNCT
ejpam-5719	13	1	mirzavaziri	mirzavaziri	PROPN
ejpam-5719	13	2	and	and	CCONJ
ejpam-5719	13	3	moslehian	moslehian	ADJ
ejpam-5719	14	1	[	[	X
ejpam-5719	14	2	13	13	NUM
ejpam-5719	14	3	]	]	PUNCT
ejpam-5719	14	4	introduced	introduce	VERB
ejpam-5719	14	5	the	the	DET
ejpam-5719	14	6	concept	concept	NOUN
ejpam-5719	14	7	of	of	ADP
ejpam-5719	14	8	f	f	PROPN
ejpam-5719	14	9	-derivation	-derivation	PROPN
ejpam-5719	14	10	g	g	PROPN
ejpam-5719	14	11	:	:	PUNCT
ejpam-5719	14	12	b	b	X
ejpam-5719	14	13	→	→	SYM
ejpam-5719	14	14	b	b	PROPN
ejpam-5719	14	15	as	as	SCONJ
ejpam-5719	14	16	follows	follow	VERB
ejpam-5719	14	17	:	:	PUNCT
ejpam-5719	14	18	g(xy	g(xy	NOUN
ejpam-5719	14	19	)	)	PUNCT
ejpam-5719	14	20	=	=	SYM
ejpam-5719	14	21	f(x)g(y	f(x)g(y	NOUN
ejpam-5719	14	22	)	)	PUNCT
ejpam-5719	14	23	+	+	NUM
ejpam-5719	14	24	g(x)f(y	g(x)f(y	NOUN
ejpam-5719	14	25	)	)	PUNCT
ejpam-5719	14	26	(	(	PUNCT
ejpam-5719	14	27	1	1	X
ejpam-5719	14	28	)	)	PUNCT
ejpam-5719	14	29	for	for	ADP
ejpam-5719	14	30	all	all	DET
ejpam-5719	14	31	x	x	NOUN
ejpam-5719	14	32	,	,	PUNCT
ejpam-5719	14	33	y	y	PROPN
ejpam-5719	14	34	∈	∈	PROPN
ejpam-5719	14	35	b.	b.	PROPN
ejpam-5719	14	36	∗corresponding	∗corresponde	VERB
ejpam-5719	14	37	author	author	NOUN
ejpam-5719	14	38	.	.	PUNCT
ejpam-5719	15	1	∗corresponding	∗corresponde	VERB
ejpam-5719	15	2	author	author	NOUN
ejpam-5719	15	3	.	.	PUNCT
ejpam-5719	16	1	doi	doi	NOUN
ejpam-5719	16	2	:	:	PUNCT
ejpam-5719	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5719	https://doi.org/10.29020/nybg.ejpam.v18i1.5719	PROPN
ejpam-5719	16	4	email	email	NOUN
ejpam-5719	16	5	addresses	address	VERB
ejpam-5719	16	6	:	:	PUNCT
ejpam-5719	16	7	baak@hanyang.ac.kr	baak@hanyang.ac.kr	PROPN
ejpam-5719	16	8	(	(	PUNCT
ejpam-5719	16	9	c.	c.	PROPN
ejpam-5719	16	10	park	park	PROPN
ejpam-5719	16	11	)	)	PUNCT
ejpam-5719	16	12	,	,	PUNCT
ejpam-5719	16	13	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-5719	16	14	(	(	PUNCT
ejpam-5719	16	15	s.	s.	PROPN
ejpam-5719	16	16	donganont	donganont	PROPN
ejpam-5719	16	17	)	)	PUNCT
ejpam-5719	16	18	,	,	PUNCT
ejpam-5719	16	19	blavely526@hanyang.ac.kr	blavely526@hanyang.ac.kr	PROPN
ejpam-5719	16	20	(	(	PUNCT
ejpam-5719	16	21	s.	s.	PROPN
ejpam-5719	16	22	w.	w.	PROPN
ejpam-5719	16	23	min	min	PROPN
ejpam-5719	16	24	)	)	PUNCT
ejpam-5719	16	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5719	16	26	1	1	NUM
ejpam-5719	16	27	copyright	copyright	NOUN
ejpam-5719	16	28	:	:	PUNCT
ejpam-5719	17	1	©	©	PROPN
ejpam-5719	17	2	2025	2025	NUM
ejpam-5719	17	3	the	the	DET
ejpam-5719	17	4	author(s	author(s	NOUN
ejpam-5719	17	5	)	)	PUNCT
ejpam-5719	17	6	.	.	PUNCT
ejpam-5719	18	1	(	(	PUNCT
ejpam-5719	18	2	cc	cc	NOUN
ejpam-5719	18	3	by	by	ADP
ejpam-5719	18	4	-	-	PUNCT
ejpam-5719	18	5	nc	nc	PROPN
ejpam-5719	18	6	4.0	4.0	NUM
ejpam-5719	18	7	)	)	PUNCT
ejpam-5719	18	8	c.	c.	NOUN
ejpam-5719	18	9	park	park	PROPN
ejpam-5719	18	10	,	,	PUNCT
ejpam-5719	18	11	s.	s.	PROPN
ejpam-5719	18	12	donganont	donganont	PROPN
ejpam-5719	18	13	,	,	PUNCT
ejpam-5719	18	14	s.	s.	PROPN
ejpam-5719	18	15	w.	w.	PROPN
ejpam-5719	18	16	min	min	PROPN
ejpam-5719	18	17	/	/	SYM
ejpam-5719	18	18	eur	eur	PROPN
ejpam-5719	18	19	.	.	PUNCT
ejpam-5719	19	1	j.	j.	PROPN
ejpam-5719	19	2	pure	pure	PROPN
ejpam-5719	19	3	appl	appl	PROPN
ejpam-5719	19	4	.	.	PROPN
ejpam-5719	19	5	math	math	PROPN
ejpam-5719	19	6	,	,	PUNCT
ejpam-5719	19	7	18	18	NUM
ejpam-5719	19	8	(	(	PUNCT
ejpam-5719	19	9	1	1	NUM
ejpam-5719	19	10	)	)	PUNCT
ejpam-5719	19	11	(	(	PUNCT
ejpam-5719	19	12	2025	2025	NUM
ejpam-5719	19	13	)	)	PUNCT
ejpam-5719	19	14	,	,	PUNCT
ejpam-5719	19	15	5719	5719	NUM
ejpam-5719	19	16	2	2	NUM
ejpam-5719	19	17	of	of	ADP
ejpam-5719	19	18	10	10	NUM
ejpam-5719	19	19	park	park	NOUN
ejpam-5719	19	20	et	et	PROPN
ejpam-5719	19	21	al	al	PROPN
ejpam-5719	19	22	.	.	PUNCT
ejpam-5719	20	1	[	[	X
ejpam-5719	20	2	16	16	NUM
ejpam-5719	20	3	]	]	PUNCT
ejpam-5719	20	4	introduced	introduce	VERB
ejpam-5719	20	5	the	the	DET
ejpam-5719	20	6	concept	concept	NOUN
ejpam-5719	20	7	of	of	ADP
ejpam-5719	20	8	hom	hom	NOUN
ejpam-5719	20	9	-	-	PUNCT
ejpam-5719	20	10	derivation	derivation	NOUN
ejpam-5719	20	11	on	on	ADP
ejpam-5719	20	12	b	b	NOUN
ejpam-5719	20	13	,	,	PUNCT
ejpam-5719	20	14	i.e.	i.e.	X
ejpam-5719	20	15	,	,	PUNCT
ejpam-5719	20	16	g	g	NOUN
ejpam-5719	20	17	:	:	PUNCT
ejpam-5719	20	18	b	b	X
ejpam-5719	20	19	→	→	SYM
ejpam-5719	20	20	b	b	PROPN
ejpam-5719	20	21	is	be	AUX
ejpam-5719	20	22	a	a	DET
ejpam-5719	20	23	homomorphism	homomorphism	NOUN
ejpam-5719	20	24	and	and	CCONJ
ejpam-5719	20	25	f	f	NOUN
ejpam-5719	20	26	satisfies	satisfie	NOUN
ejpam-5719	20	27	(	(	PUNCT
ejpam-5719	20	28	1	1	NUM
ejpam-5719	20	29	)	)	PUNCT
ejpam-5719	20	30	for	for	ADP
ejpam-5719	20	31	all	all	DET
ejpam-5719	20	32	x	x	NOUN
ejpam-5719	20	33	,	,	PUNCT
ejpam-5719	20	34	y	y	PROPN
ejpam-5719	20	35	∈	∈	PROPN
ejpam-5719	20	36	b.	b.	PROPN
ejpam-5719	20	37	dehghanian	dehghanian	PROPN
ejpam-5719	20	38	et	et	PROPN
ejpam-5719	20	39	al	al	PROPN
ejpam-5719	20	40	.	.	PROPN
ejpam-5719	20	41	introduced	introduce	VERB
ejpam-5719	20	42	the	the	DET
ejpam-5719	20	43	concept	concept	NOUN
ejpam-5719	20	44	of	of	ADP
ejpam-5719	20	45	hom	hom	NOUN
ejpam-5719	20	46	-	-	PUNCT
ejpam-5719	20	47	der	der	NOUN
ejpam-5719	20	48	g	g	PROPN
ejpam-5719	20	49	:	:	PUNCT
ejpam-5719	20	50	b	b	X
ejpam-5719	20	51	→	→	SYM
ejpam-5719	20	52	b	b	PROPN
ejpam-5719	20	53	as	as	SCONJ
ejpam-5719	20	54	follows	follow	VERB
ejpam-5719	20	55	:	:	PUNCT
ejpam-5719	20	56	g(x)g(y	g(x)g(y	X
ejpam-5719	20	57	)	)	PUNCT
ejpam-5719	20	58	=	=	SYM
ejpam-5719	20	59	xg(y	xg(y	X
ejpam-5719	20	60	)	)	PUNCT
ejpam-5719	21	1	+	+	CCONJ
ejpam-5719	21	2	g(x)y	g(x)y	PROPN
ejpam-5719	21	3	for	for	ADP
ejpam-5719	21	4	all	all	DET
ejpam-5719	21	5	x	x	NOUN
ejpam-5719	21	6	,	,	PUNCT
ejpam-5719	21	7	y	y	PROPN
ejpam-5719	21	8	∈	∈	PROPN
ejpam-5719	21	9	b.	b.	PROPN
ejpam-5719	21	10	dehghanian	dehghanian	PROPN
ejpam-5719	21	11	et	et	PROPN
ejpam-5719	21	12	al	al	PROPN
ejpam-5719	21	13	.	.	PUNCT
ejpam-5719	22	1	[	[	X
ejpam-5719	22	2	6	6	NUM
ejpam-5719	22	3	]	]	PUNCT
ejpam-5719	22	4	introduced	introduce	VERB
ejpam-5719	22	5	and	and	CCONJ
ejpam-5719	22	6	investigated	investigate	VERB
ejpam-5719	22	7	ternary	ternary	ADJ
ejpam-5719	22	8	hom	hom	NOUN
ejpam-5719	22	9	-	-	PUNCT
ejpam-5719	22	10	ders	der	NOUN
ejpam-5719	22	11	in	in	ADP
ejpam-5719	22	12	ternary	ternary	ADJ
ejpam-5719	22	13	banach	banach	NOUN
ejpam-5719	22	14	algebras	algebra	NOUN
ejpam-5719	22	15	and	and	CCONJ
ejpam-5719	22	16	kheawborisuk	kheawborisuk	NOUN
ejpam-5719	22	17	et	et	PROPN
ejpam-5719	22	18	al	al	PROPN
ejpam-5719	22	19	.	.	PUNCT
ejpam-5719	23	1	[	[	X
ejpam-5719	23	2	10	10	NUM
ejpam-5719	23	3	]	]	PUNCT
ejpam-5719	23	4	defined	define	VERB
ejpam-5719	23	5	and	and	CCONJ
ejpam-5719	23	6	studied	study	VERB
ejpam-5719	23	7	hom	hom	NOUN
ejpam-5719	23	8	-	-	PUNCT
ejpam-5719	23	9	ders	der	NOUN
ejpam-5719	23	10	in	in	ADP
ejpam-5719	23	11	fuzzy	fuzzy	ADJ
ejpam-5719	23	12	banach	banach	NOUN
ejpam-5719	23	13	algebras	algebra	VERB
ejpam-5719	23	14	.	.	PUNCT
ejpam-5719	24	1	recently	recently	ADV
ejpam-5719	24	2	,	,	PUNCT
ejpam-5719	24	3	sripattanet	sripattanet	PROPN
ejpam-5719	24	4	et	et	PROPN
ejpam-5719	24	5	al	al	PROPN
ejpam-5719	24	6	.	.	PUNCT
ejpam-5719	25	1	[	[	X
ejpam-5719	25	2	18	18	NUM
ejpam-5719	25	3	]	]	PUNCT
ejpam-5719	25	4	introduced	introduce	VERB
ejpam-5719	25	5	a	a	DET
ejpam-5719	25	6	quadratic	quadratic	ADJ
ejpam-5719	25	7	hom	hom	NOUN
ejpam-5719	25	8	-	-	PUNCT
ejpam-5719	25	9	der	der	NOUN
ejpam-5719	25	10	in	in	ADP
ejpam-5719	25	11	banach	banach	NOUN
ejpam-5719	25	12	algebras	algebras	PROPN
ejpam-5719	25	13	b	b	PROPN
ejpam-5719	25	14	as	as	SCONJ
ejpam-5719	25	15	follows	follow	VERB
ejpam-5719	25	16	:	:	PUNCT
ejpam-5719	25	17	a	a	DET
ejpam-5719	25	18	quadratic	quadratic	ADJ
ejpam-5719	25	19	mapping	mapping	NOUN
ejpam-5719	26	1	d	d	NOUN
ejpam-5719	26	2	:	:	PUNCT
ejpam-5719	26	3	b	b	X
ejpam-5719	26	4	→	→	SYM
ejpam-5719	26	5	b	b	PROPN
ejpam-5719	26	6	is	be	AUX
ejpam-5719	26	7	said	say	VERB
ejpam-5719	26	8	to	to	PART
ejpam-5719	26	9	be	be	AUX
ejpam-5719	26	10	a	a	DET
ejpam-5719	26	11	quadratic	quadratic	ADJ
ejpam-5719	26	12	hom	hom	NOUN
ejpam-5719	26	13	-	-	PUNCT
ejpam-5719	26	14	der	der	NOUN
ejpam-5719	26	15	if	if	SCONJ
ejpam-5719	26	16	it	it	PRON
ejpam-5719	26	17	satisfies	satisfy	VERB
ejpam-5719	26	18	d(x)d(y	d(x)d(y	NUM
ejpam-5719	26	19	)	)	PUNCT
ejpam-5719	26	20	=	=	SYM
ejpam-5719	27	1	x2d(y	x2d(y	PROPN
ejpam-5719	27	2	)	)	PUNCT
ejpam-5719	28	1	+	+	VERB
ejpam-5719	28	2	d(x)y2	d(x)y2	NOUN
ejpam-5719	28	3	for	for	ADP
ejpam-5719	28	4	all	all	DET
ejpam-5719	28	5	x	x	NOUN
ejpam-5719	28	6	,	,	PUNCT
ejpam-5719	28	7	y	y	PROPN
ejpam-5719	28	8	∈	∈	PROPN
ejpam-5719	28	9	b.	b.	PROPN
ejpam-5719	28	10	in	in	ADP
ejpam-5719	28	11	this	this	DET
ejpam-5719	28	12	papere	papere	NOUN
ejpam-5719	28	13	,	,	PUNCT
ejpam-5719	28	14	we	we	PRON
ejpam-5719	28	15	introduce	introduce	VERB
ejpam-5719	28	16	the	the	DET
ejpam-5719	28	17	concept	concept	NOUN
ejpam-5719	28	18	of	of	ADP
ejpam-5719	28	19	quadartic	quadartic	ADJ
ejpam-5719	28	20	hom	hom	NOUN
ejpam-5719	28	21	-	-	PUNCT
ejpam-5719	28	22	der	der	NOUN
ejpam-5719	28	23	in	in	ADP
ejpam-5719	28	24	banach	banach	NOUN
ejpam-5719	28	25	algebras	algebra	NOUN
ejpam-5719	28	26	.	.	PUNCT
ejpam-5719	29	1	definition	definition	NOUN
ejpam-5719	29	2	1	1	NUM
ejpam-5719	29	3	.	.	PUNCT
ejpam-5719	30	1	let	let	VERB
ejpam-5719	30	2	b	b	X
ejpam-5719	30	3	be	be	AUX
ejpam-5719	30	4	a	a	DET
ejpam-5719	30	5	complex	complex	ADJ
ejpam-5719	30	6	banach	banach	NOUN
ejpam-5719	30	7	algebra	algebra	NOUN
ejpam-5719	30	8	and	and	CCONJ
ejpam-5719	30	9	f	f	NOUN
ejpam-5719	30	10	:	:	PUNCT
ejpam-5719	30	11	b	b	X
ejpam-5719	30	12	→	→	SYM
ejpam-5719	30	13	b	b	X
ejpam-5719	30	14	be	be	AUX
ejpam-5719	30	15	a	a	DET
ejpam-5719	30	16	quadratic	quadratic	ADJ
ejpam-5719	30	17	mapping	mapping	NOUN
ejpam-5719	30	18	.	.	PUNCT
ejpam-5719	31	1	a	a	DET
ejpam-5719	31	2	quadratic	quadratic	ADJ
ejpam-5719	31	3	mapping	mapping	NOUN
ejpam-5719	31	4	g	g	NOUN
ejpam-5719	31	5	:	:	PUNCT
ejpam-5719	31	6	b	b	X
ejpam-5719	31	7	→	→	SYM
ejpam-5719	31	8	b	b	PROPN
ejpam-5719	31	9	is	be	AUX
ejpam-5719	31	10	called	call	VERB
ejpam-5719	31	11	a	a	DET
ejpam-5719	31	12	quadratic	quadratic	ADJ
ejpam-5719	31	13	f	f	NOUN
ejpam-5719	31	14	-hom	-hom	X
ejpam-5719	31	15	-	-	PUNCT
ejpam-5719	31	16	der	der	NOUN
ejpam-5719	31	17	if	if	SCONJ
ejpam-5719	31	18	it	it	PRON
ejpam-5719	31	19	satisfies	satisfy	VERB
ejpam-5719	31	20	g(x)g(y	g(x)g(y	NOUN
ejpam-5719	31	21	)	)	PUNCT
ejpam-5719	31	22	=	=	SYM
ejpam-5719	31	23	f(x)g(y	f(x)g(y	NOUN
ejpam-5719	31	24	)	)	PUNCT
ejpam-5719	31	25	+	+	NUM
ejpam-5719	31	26	g(x)f(y	g(x)f(y	NOUN
ejpam-5719	31	27	)	)	PUNCT
ejpam-5719	31	28	for	for	ADP
ejpam-5719	31	29	all	all	DET
ejpam-5719	31	30	x	x	NOUN
ejpam-5719	31	31	,	,	PUNCT
ejpam-5719	31	32	y	y	PROPN
ejpam-5719	31	33	∈	∈	PROPN
ejpam-5719	31	34	b.	b.	PROPN
ejpam-5719	31	35	example	example	NOUN
ejpam-5719	32	1	1	1	X
ejpam-5719	32	2	.	.	PUNCT
ejpam-5719	33	1	let	let	AUX
ejpam-5719	33	2	c0(x	c0(x	NOUN
ejpam-5719	33	3	)	)	PUNCT
ejpam-5719	33	4	be	be	AUX
ejpam-5719	33	5	the	the	DET
ejpam-5719	33	6	complex	complex	ADJ
ejpam-5719	33	7	banach	banach	NOUN
ejpam-5719	33	8	algebra	algebra	NOUN
ejpam-5719	33	9	of	of	ADP
ejpam-5719	33	10	complex	complex	ADJ
ejpam-5719	33	11	valued	value	VERB
ejpam-5719	33	12	continuous	continuous	ADJ
ejpam-5719	33	13	functions	function	NOUN
ejpam-5719	33	14	on	on	ADP
ejpam-5719	33	15	a	a	DET
ejpam-5719	33	16	locally	locally	ADV
ejpam-5719	33	17	compact	compact	ADJ
ejpam-5719	33	18	hausdorff	hausdorff	NOUN
ejpam-5719	33	19	space	space	NOUN
ejpam-5719	33	20	x	x	PUNCT
ejpam-5719	33	21	and	and	CCONJ
ejpam-5719	33	22	g	g	NOUN
ejpam-5719	33	23	:	:	PUNCT
ejpam-5719	33	24	c0(x	c0(x	NOUN
ejpam-5719	33	25	)	)	PUNCT
ejpam-5719	33	26	→	→	SYM
ejpam-5719	33	27	c0(x	c0(x	NOUN
ejpam-5719	33	28	)	)	PUNCT
ejpam-5719	33	29	be	be	AUX
ejpam-5719	33	30	defined	define	VERB
ejpam-5719	33	31	by	by	ADP
ejpam-5719	33	32	g(m	g(m	NOUN
ejpam-5719	33	33	)	)	PUNCT
ejpam-5719	33	34	=	=	SYM
ejpam-5719	33	35	2m2	2m2	NUM
ejpam-5719	33	36	and	and	CCONJ
ejpam-5719	33	37	f	f	NOUN
ejpam-5719	33	38	:	:	PUNCT
ejpam-5719	33	39	c0(x	c0(x	NOUN
ejpam-5719	33	40	)	)	PUNCT
ejpam-5719	33	41	→	→	SYM
ejpam-5719	33	42	c0(x	c0(x	NOUN
ejpam-5719	33	43	)	)	PUNCT
ejpam-5719	33	44	be	be	AUX
ejpam-5719	33	45	defined	define	VERB
ejpam-5719	33	46	by	by	ADP
ejpam-5719	33	47	f(m	f(m	PROPN
ejpam-5719	33	48	)	)	PUNCT
ejpam-5719	34	1	=	=	SYM
ejpam-5719	34	2	m2	m2	PROPN
ejpam-5719	34	3	.	.	PUNCT
ejpam-5719	35	1	then	then	ADV
ejpam-5719	35	2	f	f	PROPN
ejpam-5719	35	3	is	be	AUX
ejpam-5719	35	4	a	a	DET
ejpam-5719	35	5	quadratic	quadratic	ADJ
ejpam-5719	35	6	mapping	mapping	NOUN
ejpam-5719	35	7	and	and	CCONJ
ejpam-5719	35	8	g	g	NOUN
ejpam-5719	35	9	is	be	AUX
ejpam-5719	35	10	a	a	DET
ejpam-5719	35	11	quadratic	quadratic	ADJ
ejpam-5719	35	12	f	f	NOUN
ejpam-5719	35	13	-hom	-hom	X
ejpam-5719	35	14	-	-	PUNCT
ejpam-5719	35	15	der	der	NOUN
ejpam-5719	35	16	.	.	PUNCT
ejpam-5719	36	1	we	we	PRON
ejpam-5719	36	2	say	say	VERB
ejpam-5719	36	3	that	that	SCONJ
ejpam-5719	36	4	an	an	DET
ejpam-5719	36	5	equation	equation	NOUN
ejpam-5719	36	6	is	be	AUX
ejpam-5719	36	7	stable	stable	ADJ
ejpam-5719	36	8	if	if	SCONJ
ejpam-5719	36	9	any	any	DET
ejpam-5719	36	10	function	function	NOUN
ejpam-5719	36	11	satisfying	satisfy	VERB
ejpam-5719	36	12	the	the	DET
ejpam-5719	36	13	equation	equation	NOUN
ejpam-5719	36	14	approximately	approximately	ADV
ejpam-5719	36	15	is	be	AUX
ejpam-5719	36	16	near	near	ADJ
ejpam-5719	36	17	to	to	ADP
ejpam-5719	36	18	an	an	DET
ejpam-5719	36	19	exact	exact	ADJ
ejpam-5719	36	20	solution	solution	NOUN
ejpam-5719	36	21	of	of	ADP
ejpam-5719	36	22	the	the	DET
ejpam-5719	36	23	equation	equation	NOUN
ejpam-5719	36	24	.	.	PUNCT
ejpam-5719	37	1	the	the	DET
ejpam-5719	37	2	stability	stability	NOUN
ejpam-5719	37	3	analysis	analysis	NOUN
ejpam-5719	37	4	of	of	ADP
ejpam-5719	37	5	functional	functional	ADJ
ejpam-5719	37	6	equations	equation	NOUN
ejpam-5719	37	7	emanated	emanate	VERB
ejpam-5719	37	8	from	from	ADP
ejpam-5719	37	9	a	a	DET
ejpam-5719	37	10	question	question	NOUN
ejpam-5719	37	11	of	of	ADP
ejpam-5719	37	12	ulam	ulam	PROPN
ejpam-5719	37	13	[	[	X
ejpam-5719	37	14	19	19	NUM
ejpam-5719	37	15	]	]	PUNCT
ejpam-5719	37	16	,	,	PUNCT
ejpam-5719	37	17	was	be	AUX
ejpam-5719	37	18	raised	raise	VERB
ejpam-5719	37	19	in	in	ADP
ejpam-5719	37	20	1940	1940	NUM
ejpam-5719	37	21	,	,	PUNCT
ejpam-5719	37	22	about	about	ADP
ejpam-5719	37	23	the	the	DET
ejpam-5719	37	24	stability	stability	NOUN
ejpam-5719	37	25	of	of	ADP
ejpam-5719	37	26	group	group	NOUN
ejpam-5719	37	27	homomorphisms	homomorphism	NOUN
ejpam-5719	37	28	and	and	CCONJ
ejpam-5719	37	29	then	then	ADV
ejpam-5719	37	30	was	be	AUX
ejpam-5719	37	31	extended	extend	VERB
ejpam-5719	37	32	by	by	ADP
ejpam-5719	37	33	hyers	hyer	NOUN
ejpam-5719	38	1	[	[	X
ejpam-5719	38	2	9	9	NUM
ejpam-5719	38	3	]	]	PUNCT
ejpam-5719	38	4	.	.	PUNCT
ejpam-5719	39	1	recently	recently	ADV
ejpam-5719	39	2	,	,	PUNCT
ejpam-5719	39	3	results	result	VERB
ejpam-5719	39	4	on	on	ADP
ejpam-5719	39	5	the	the	DET
ejpam-5719	39	6	so	so	ADV
ejpam-5719	39	7	-	-	PUNCT
ejpam-5719	39	8	called	call	VERB
ejpam-5719	39	9	hyers	hyers	PROPN
ejpam-5719	39	10	-	-	PUNCT
ejpam-5719	39	11	ulam	ulam	PROPN
ejpam-5719	39	12	stability	stability	NOUN
ejpam-5719	39	13	have	have	AUX
ejpam-5719	39	14	comfortabled	comfortable	VERB
ejpam-5719	39	15	the	the	DET
ejpam-5719	39	16	stability	stability	NOUN
ejpam-5719	39	17	conditions	condition	NOUN
ejpam-5719	39	18	.	.	PUNCT
ejpam-5719	40	1	dehghanian	dehghanian	ADJ
ejpam-5719	40	2	and	and	CCONJ
ejpam-5719	40	3	modarres	modarre	NOUN
ejpam-5719	40	4	[	[	X
ejpam-5719	40	5	3	3	NUM
ejpam-5719	40	6	]	]	PUNCT
ejpam-5719	40	7	studied	study	VERB
ejpam-5719	40	8	ternary	ternary	ADJ
ejpam-5719	40	9	γ	γ	X
ejpam-5719	40	10	-	-	PUNCT
ejpam-5719	40	11	homomorphisms	homomorphism	NOUN
ejpam-5719	40	12	and	and	CCONJ
ejpam-5719	40	13	ternary	ternary	ADJ
ejpam-5719	40	14	γ	γ	NOUN
ejpam-5719	40	15	-	-	NOUN
ejpam-5719	40	16	derivations	derivation	NOUN
ejpam-5719	40	17	on	on	ADP
ejpam-5719	40	18	ternary	ternary	ADJ
ejpam-5719	40	19	semigroups	semigroup	NOUN
ejpam-5719	40	20	,	,	PUNCT
ejpam-5719	40	21	dehghanian	dehghanian	ADJ
ejpam-5719	40	22	et	et	PROPN
ejpam-5719	40	23	al	al	PROPN
ejpam-5719	40	24	.	.	PUNCT
ejpam-5719	41	1	[	[	X
ejpam-5719	41	2	4	4	X
ejpam-5719	41	3	]	]	PUNCT
ejpam-5719	41	4	studied	study	VERB
ejpam-5719	41	5	ternary	ternary	ADJ
ejpam-5719	41	6	3	3	NUM
ejpam-5719	41	7	-	-	PUNCT
ejpam-5719	41	8	derivations	derivation	NOUN
ejpam-5719	41	9	on	on	ADP
ejpam-5719	41	10	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	41	11	algebras	algebra	NOUN
ejpam-5719	41	12	and	and	CCONJ
ejpam-5719	41	13	dehghanian	dehghanian	ADJ
ejpam-5719	41	14	and	and	CCONJ
ejpam-5719	41	15	park	park	NOUN
ejpam-5719	41	16	[	[	X
ejpam-5719	41	17	5	5	NUM
ejpam-5719	41	18	]	]	PUNCT
ejpam-5719	41	19	studied	study	VERB
ejpam-5719	41	20	c∗-ternary	c∗-ternary	PROPN
ejpam-5719	41	21	3homomorphisms	3homomorphisms	NUM
ejpam-5719	41	22	on	on	ADP
ejpam-5719	41	23	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	41	24	algebras	algebra	NOUN
ejpam-5719	41	25	.	.	PUNCT
ejpam-5719	42	1	moreover	moreover	ADV
ejpam-5719	42	2	,	,	PUNCT
ejpam-5719	42	3	senthil	senthil	PROPN
ejpam-5719	42	4	kumar	kumar	PROPN
ejpam-5719	42	5	et	et	PROPN
ejpam-5719	42	6	al	al	PROPN
ejpam-5719	42	7	.	.	PUNCT
ejpam-5719	43	1	[	[	X
ejpam-5719	43	2	11	11	NUM
ejpam-5719	43	3	]	]	PUNCT
ejpam-5719	43	4	investigated	investigate	VERB
ejpam-5719	43	5	modular	modular	ADJ
ejpam-5719	43	6	stabilities	stability	NOUN
ejpam-5719	43	7	of	of	ADP
ejpam-5719	43	8	a	a	DET
ejpam-5719	43	9	reciprocal	reciprocal	ADJ
ejpam-5719	43	10	second	second	ADJ
ejpam-5719	43	11	power	power	NOUN
ejpam-5719	43	12	functional	functional	ADJ
ejpam-5719	43	13	equation	equation	NOUN
ejpam-5719	43	14	and	and	CCONJ
ejpam-5719	43	15	bowniya	bowniya	NOUN
ejpam-5719	43	16	et	et	PROPN
ejpam-5719	43	17	al	al	PROPN
ejpam-5719	43	18	.	.	PUNCT
ejpam-5719	44	1	[	[	X
ejpam-5719	44	2	1	1	NUM
ejpam-5719	44	3	,	,	PUNCT
ejpam-5719	44	4	2	2	NUM
ejpam-5719	44	5	]	]	PUNCT
ejpam-5719	44	6	obtained	obtain	VERB
ejpam-5719	44	7	the	the	DET
ejpam-5719	44	8	hyers	hyers	PROPN
ejpam-5719	44	9	-	-	PUNCT
ejpam-5719	44	10	ulam	ulam	PROPN
ejpam-5719	44	11	stability	stability	PROPN
ejpam-5719	44	12	results	result	NOUN
ejpam-5719	44	13	of	of	ADP
ejpam-5719	44	14	linear	linear	PROPN
ejpam-5719	44	15	differential	differential	ADJ
ejpam-5719	44	16	equations	equation	NOUN
ejpam-5719	44	17	.	.	PUNCT
ejpam-5719	45	1	the	the	DET
ejpam-5719	45	2	method	method	NOUN
ejpam-5719	45	3	provided	provide	VERB
ejpam-5719	45	4	by	by	ADP
ejpam-5719	45	5	hyers	hyer	NOUN
ejpam-5719	45	6	[	[	X
ejpam-5719	45	7	9	9	X
ejpam-5719	45	8	]	]	PUNCT
ejpam-5719	45	9	which	which	PRON
ejpam-5719	45	10	produces	produce	VERB
ejpam-5719	45	11	the	the	DET
ejpam-5719	45	12	additive	additive	ADJ
ejpam-5719	45	13	function	function	NOUN
ejpam-5719	45	14	will	will	AUX
ejpam-5719	45	15	be	be	AUX
ejpam-5719	45	16	called	call	VERB
ejpam-5719	45	17	a	a	DET
ejpam-5719	45	18	direct	direct	ADJ
ejpam-5719	45	19	method	method	NOUN
ejpam-5719	45	20	.	.	PUNCT
ejpam-5719	46	1	this	this	DET
ejpam-5719	46	2	method	method	NOUN
ejpam-5719	46	3	is	be	AUX
ejpam-5719	46	4	the	the	DET
ejpam-5719	46	5	most	most	ADV
ejpam-5719	46	6	significant	significant	ADJ
ejpam-5719	46	7	and	and	CCONJ
ejpam-5719	46	8	strong	strong	ADJ
ejpam-5719	46	9	tool	tool	NOUN
ejpam-5719	46	10	to	to	ADP
ejpam-5719	46	11	concerning	concern	VERB
ejpam-5719	46	12	the	the	DET
ejpam-5719	46	13	stability	stability	NOUN
ejpam-5719	46	14	of	of	ADP
ejpam-5719	46	15	different	different	ADJ
ejpam-5719	46	16	functional	functional	ADJ
ejpam-5719	46	17	equations	equation	NOUN
ejpam-5719	46	18	.	.	PUNCT
ejpam-5719	47	1	that	that	PRON
ejpam-5719	47	2	is	be	AUX
ejpam-5719	47	3	,	,	PUNCT
ejpam-5719	47	4	the	the	DET
ejpam-5719	47	5	exact	exact	ADJ
ejpam-5719	47	6	solution	solution	NOUN
ejpam-5719	47	7	of	of	ADP
ejpam-5719	47	8	the	the	DET
ejpam-5719	47	9	functional	functional	ADJ
ejpam-5719	47	10	equation	equation	NOUN
ejpam-5719	47	11	is	be	AUX
ejpam-5719	47	12	explicitly	explicitly	ADV
ejpam-5719	47	13	constructed	construct	VERB
ejpam-5719	47	14	as	as	ADP
ejpam-5719	47	15	a	a	DET
ejpam-5719	47	16	limit	limit	NOUN
ejpam-5719	47	17	of	of	ADP
ejpam-5719	47	18	a	a	DET
ejpam-5719	47	19	sequence	sequence	NOUN
ejpam-5719	47	20	,	,	PUNCT
ejpam-5719	47	21	starting	start	VERB
ejpam-5719	47	22	from	from	ADP
ejpam-5719	47	23	the	the	DET
ejpam-5719	47	24	given	give	VERB
ejpam-5719	47	25	approximate	approximate	ADJ
ejpam-5719	47	26	solution	solution	NOUN
ejpam-5719	47	27	[	[	X
ejpam-5719	47	28	17	17	NUM
ejpam-5719	47	29	]	]	PUNCT
ejpam-5719	47	30	.	.	PUNCT
ejpam-5719	48	1	the	the	DET
ejpam-5719	48	2	other	other	ADJ
ejpam-5719	48	3	significant	significant	ADJ
ejpam-5719	48	4	method	method	NOUN
ejpam-5719	48	5	is	be	AUX
ejpam-5719	48	6	fixed	fix	VERB
ejpam-5719	48	7	point	point	NOUN
ejpam-5719	48	8	theorem	theorem	VERB
ejpam-5719	48	9	,	,	PUNCT
ejpam-5719	48	10	that	that	ADV
ejpam-5719	48	11	is	is	ADV
ejpam-5719	48	12	,	,	PUNCT
ejpam-5719	48	13	the	the	DET
ejpam-5719	48	14	exact	exact	ADJ
ejpam-5719	48	15	solution	solution	NOUN
ejpam-5719	48	16	of	of	ADP
ejpam-5719	48	17	the	the	DET
ejpam-5719	48	18	functional	functional	ADJ
ejpam-5719	48	19	equation	equation	NOUN
ejpam-5719	48	20	is	be	AUX
ejpam-5719	48	21	explicitly	explicitly	ADV
ejpam-5719	48	22	created	create	VERB
ejpam-5719	48	23	as	as	ADP
ejpam-5719	48	24	a	a	DET
ejpam-5719	48	25	fixed	fix	VERB
ejpam-5719	48	26	point	point	NOUN
ejpam-5719	48	27	of	of	ADP
ejpam-5719	48	28	some	some	DET
ejpam-5719	48	29	certain	certain	ADJ
ejpam-5719	48	30	mapping	mapping	NOUN
ejpam-5719	49	1	[	[	X
ejpam-5719	49	2	8	8	NUM
ejpam-5719	49	3	,	,	PUNCT
ejpam-5719	49	4	14	14	NUM
ejpam-5719	49	5	,	,	PUNCT
ejpam-5719	49	6	15	15	NUM
ejpam-5719	49	7	]	]	PUNCT
ejpam-5719	49	8	.	.	PUNCT
ejpam-5719	50	1	we	we	PRON
ejpam-5719	50	2	remember	remember	VERB
ejpam-5719	50	3	a	a	DET
ejpam-5719	50	4	fixed	fix	VERB
ejpam-5719	50	5	point	point	NOUN
ejpam-5719	50	6	alternative	alternative	NOUN
ejpam-5719	50	7	theorem	theorem	VERB
ejpam-5719	50	8	.	.	PUNCT
ejpam-5719	51	1	c.	c.	PROPN
ejpam-5719	51	2	park	park	PROPN
ejpam-5719	51	3	,	,	PUNCT
ejpam-5719	51	4	s.	s.	PROPN
ejpam-5719	51	5	donganont	donganont	PROPN
ejpam-5719	51	6	,	,	PUNCT
ejpam-5719	51	7	s.	s.	PROPN
ejpam-5719	51	8	w.	w.	PROPN
ejpam-5719	51	9	min	min	PROPN
ejpam-5719	51	10	/	/	SYM
ejpam-5719	51	11	eur	eur	PROPN
ejpam-5719	51	12	.	.	PUNCT
ejpam-5719	52	1	j.	j.	PROPN
ejpam-5719	52	2	pure	pure	PROPN
ejpam-5719	52	3	appl	appl	PROPN
ejpam-5719	52	4	.	.	PROPN
ejpam-5719	52	5	math	math	PROPN
ejpam-5719	52	6	,	,	PUNCT
ejpam-5719	52	7	18	18	NUM
ejpam-5719	52	8	(	(	PUNCT
ejpam-5719	52	9	1	1	NUM
ejpam-5719	52	10	)	)	PUNCT
ejpam-5719	52	11	(	(	PUNCT
ejpam-5719	52	12	2025	2025	NUM
ejpam-5719	52	13	)	)	PUNCT
ejpam-5719	52	14	,	,	PUNCT
ejpam-5719	52	15	5719	5719	NUM
ejpam-5719	52	16	3	3	NUM
ejpam-5719	52	17	of	of	ADP
ejpam-5719	52	18	10	10	NUM
ejpam-5719	52	19	theorem	theorem	NOUN
ejpam-5719	52	20	1	1	NUM
ejpam-5719	52	21	.	.	PUNCT
ejpam-5719	53	1	[	[	X
ejpam-5719	53	2	7	7	X
ejpam-5719	53	3	]	]	X
ejpam-5719	53	4	if	if	SCONJ
ejpam-5719	53	5	(	(	PUNCT
ejpam-5719	53	6	b	b	NOUN
ejpam-5719	53	7	,	,	PUNCT
ejpam-5719	53	8	d	d	NOUN
ejpam-5719	53	9	)	)	PUNCT
ejpam-5719	53	10	is	be	AUX
ejpam-5719	53	11	a	a	DET
ejpam-5719	53	12	complete	complete	ADJ
ejpam-5719	53	13	generalized	generalize	VERB
ejpam-5719	53	14	metric	metric	ADJ
ejpam-5719	53	15	space	space	NOUN
ejpam-5719	53	16	and	and	CCONJ
ejpam-5719	53	17	i	i	PRON
ejpam-5719	53	18	:	:	PUNCT
ejpam-5719	53	19	b	b	X
ejpam-5719	53	20	→	→	SYM
ejpam-5719	53	21	b	b	X
ejpam-5719	53	22	a	a	DET
ejpam-5719	53	23	strictly	strictly	ADV
ejpam-5719	53	24	contractive	contractive	ADJ
ejpam-5719	53	25	mapping	mapping	NOUN
ejpam-5719	53	26	,	,	PUNCT
ejpam-5719	53	27	that	that	ADV
ejpam-5719	53	28	is	be	AUX
ejpam-5719	53	29	,	,	PUNCT
ejpam-5719	53	30	d(iu	d(iu	PROPN
ejpam-5719	53	31	,	,	PUNCT
ejpam-5719	53	32	iv	iv	NUM
ejpam-5719	53	33	)	)	PUNCT
ejpam-5719	53	34	≤	≤	NOUN
ejpam-5719	53	35	ld(u	ld(u	X
ejpam-5719	53	36	,	,	PUNCT
ejpam-5719	53	37	v	v	NOUN
ejpam-5719	53	38	)	)	PUNCT
ejpam-5719	53	39	for	for	ADP
ejpam-5719	53	40	all	all	DET
ejpam-5719	53	41	u	u	NOUN
ejpam-5719	53	42	,	,	PUNCT
ejpam-5719	53	43	v	v	PROPN
ejpam-5719	53	44	∈	∈	PROPN
ejpam-5719	53	45	b	b	NOUN
ejpam-5719	53	46	and	and	CCONJ
ejpam-5719	53	47	a	a	DET
ejpam-5719	53	48	lipschitz	lipschitz	NOUN
ejpam-5719	53	49	constant	constant	ADJ
ejpam-5719	53	50	l	l	NOUN
ejpam-5719	53	51	<	<	X
ejpam-5719	53	52	1	1	X
ejpam-5719	53	53	.	.	PUNCT
ejpam-5719	54	1	then	then	ADV
ejpam-5719	54	2	for	for	SCONJ
ejpam-5719	54	3	each	each	DET
ejpam-5719	54	4	given	give	VERB
ejpam-5719	54	5	element	element	NOUN
ejpam-5719	54	6	u	u	NOUN
ejpam-5719	54	7	∈	∈	PROPN
ejpam-5719	54	8	b	b	PROPN
ejpam-5719	54	9	,	,	PUNCT
ejpam-5719	54	10	either	either	DET
ejpam-5719	54	11	d(inu	d(inu	NOUN
ejpam-5719	54	12	,	,	PUNCT
ejpam-5719	54	13	in+1u	in+1u	ADV
ejpam-5719	54	14	)	)	PUNCT
ejpam-5719	55	1	=	=	PUNCT
ejpam-5719	56	1	+	+	NUM
ejpam-5719	56	2	∞	∞	PROPN
ejpam-5719	56	3	,	,	PUNCT
ejpam-5719	56	4	∀n	∀n	NUM
ejpam-5719	56	5	≥	≥	NOUN
ejpam-5719	56	6	0	0	NUM
ejpam-5719	56	7	,	,	PUNCT
ejpam-5719	56	8	or	or	CCONJ
ejpam-5719	56	9	d(inu	d(inu	NOUN
ejpam-5719	56	10	,	,	PUNCT
ejpam-5719	56	11	in+1u	in+1u	PROPN
ejpam-5719	56	12	)	)	PUNCT
ejpam-5719	57	1	<	<	X
ejpam-5719	58	1	+	+	PROPN
ejpam-5719	58	2	∞	∞	PROPN
ejpam-5719	58	3	,	,	PUNCT
ejpam-5719	58	4	∀n	∀n	NUM
ejpam-5719	58	5	≥	≥	NOUN
ejpam-5719	58	6	n0	n0	NUM
ejpam-5719	58	7	,	,	PUNCT
ejpam-5719	58	8	for	for	ADP
ejpam-5719	58	9	some	some	DET
ejpam-5719	58	10	positive	positive	ADJ
ejpam-5719	58	11	integer	integer	NOUN
ejpam-5719	58	12	n0	n0	PROPN
ejpam-5719	58	13	.	.	PUNCT
ejpam-5719	59	1	furthermore	furthermore	ADV
ejpam-5719	59	2	,	,	PUNCT
ejpam-5719	59	3	if	if	SCONJ
ejpam-5719	59	4	the	the	DET
ejpam-5719	59	5	second	second	ADJ
ejpam-5719	59	6	alternative	alternative	NOUN
ejpam-5719	59	7	holds	hold	VERB
ejpam-5719	59	8	,	,	PUNCT
ejpam-5719	59	9	then	then	ADV
ejpam-5719	59	10	(	(	PUNCT
ejpam-5719	59	11	i	i	NOUN
ejpam-5719	59	12	)	)	PUNCT
ejpam-5719	59	13	the	the	DET
ejpam-5719	59	14	sequence	sequence	NOUN
ejpam-5719	59	15	(	(	PUNCT
ejpam-5719	59	16	inu	inu	NOUN
ejpam-5719	59	17	)	)	PUNCT
ejpam-5719	59	18	is	be	AUX
ejpam-5719	59	19	convergent	convergent	ADJ
ejpam-5719	59	20	to	to	ADP
ejpam-5719	59	21	a	a	DET
ejpam-5719	59	22	fixed	fixed	ADJ
ejpam-5719	59	23	point	point	NOUN
ejpam-5719	59	24	v∗	v∗	PROPN
ejpam-5719	59	25	of	of	ADP
ejpam-5719	59	26	i	i	PRON
ejpam-5719	59	27	;	;	PUNCT
ejpam-5719	59	28	(	(	PUNCT
ejpam-5719	59	29	ii	ii	NOUN
ejpam-5719	59	30	)	)	PUNCT
ejpam-5719	59	31	v∗	v∗	PROPN
ejpam-5719	59	32	is	be	AUX
ejpam-5719	59	33	the	the	DET
ejpam-5719	59	34	unique	unique	ADJ
ejpam-5719	59	35	fixed	fix	VERB
ejpam-5719	59	36	point	point	NOUN
ejpam-5719	59	37	of	of	ADP
ejpam-5719	59	38	i	i	PRON
ejpam-5719	59	39	in	in	ADP
ejpam-5719	59	40	the	the	DET
ejpam-5719	59	41	set	set	NOUN
ejpam-5719	59	42	v	v	NOUN
ejpam-5719	59	43	:	:	PUNCT
ejpam-5719	59	44	=	=	SYM
ejpam-5719	59	45	{	{	PUNCT
ejpam-5719	59	46	v	v	NUM
ejpam-5719	59	47	∈	∈	PROPN
ejpam-5719	59	48	b	b	NOUN
ejpam-5719	59	49	,	,	PUNCT
ejpam-5719	59	50	d(in0u	d(in0u	PROPN
ejpam-5719	59	51	,	,	PUNCT
ejpam-5719	59	52	v	v	NOUN
ejpam-5719	59	53	)	)	PUNCT
ejpam-5719	59	54	<	<	X
ejpam-5719	60	1	+	+	NOUN
ejpam-5719	60	2	∞	∞	NOUN
ejpam-5719	60	3	}	}	PUNCT
ejpam-5719	60	4	;	;	PUNCT
ejpam-5719	60	5	(	(	PUNCT
ejpam-5719	60	6	iii	iii	X
ejpam-5719	60	7	)	)	PUNCT
ejpam-5719	60	8	d(v	d(v	PROPN
ejpam-5719	60	9	,	,	PUNCT
ejpam-5719	60	10	v∗	v∗	NOUN
ejpam-5719	60	11	)	)	PUNCT
ejpam-5719	60	12	≤	≤	NUM
ejpam-5719	60	13	1	1	NUM
ejpam-5719	60	14	1−ld(v	1−ld(v	NUM
ejpam-5719	60	15	,	,	PUNCT
ejpam-5719	60	16	iv	iv	X
ejpam-5719	60	17	)	)	PUNCT
ejpam-5719	60	18	for	for	ADP
ejpam-5719	60	19	all	all	DET
ejpam-5719	60	20	u	u	NOUN
ejpam-5719	60	21	,	,	PUNCT
ejpam-5719	60	22	v	v	NOUN
ejpam-5719	60	23	∈	∈	PROPN
ejpam-5719	60	24	v	v	NOUN
ejpam-5719	60	25	.	.	PUNCT
ejpam-5719	61	1	in	in	ADP
ejpam-5719	61	2	this	this	DET
ejpam-5719	61	3	paper	paper	NOUN
ejpam-5719	61	4	,	,	PUNCT
ejpam-5719	61	5	we	we	PRON
ejpam-5719	61	6	consider	consider	VERB
ejpam-5719	61	7	the	the	DET
ejpam-5719	61	8	following	follow	VERB
ejpam-5719	61	9	system	system	NOUN
ejpam-5719	61	10	of	of	ADP
ejpam-5719	61	11	additive	additive	ADJ
ejpam-5719	61	12	functional	functional	ADJ
ejpam-5719	61	13	equations	equation	NOUN
ejpam-5719	61	14	{	{	PUNCT
ejpam-5719	61	15	f(x+	f(x+	NOUN
ejpam-5719	61	16	y	y	NUM
ejpam-5719	61	17	)	)	PUNCT
ejpam-5719	62	1	+	+	CCONJ
ejpam-5719	62	2	f(x−	f(x−	PROPN
ejpam-5719	62	3	y	y	NOUN
ejpam-5719	62	4	)	)	PUNCT
ejpam-5719	62	5	=	=	SYM
ejpam-5719	62	6	g(x	g(x	NOUN
ejpam-5719	62	7	)	)	PUNCT
ejpam-5719	63	1	+	+	CCONJ
ejpam-5719	64	1	g(y	g(y	NOUN
ejpam-5719	64	2	)	)	PUNCT
ejpam-5719	64	3	,	,	PUNCT
ejpam-5719	64	4	g	g	PROPN
ejpam-5719	64	5	(	(	PUNCT
ejpam-5719	64	6	x+y	x+y	PROPN
ejpam-5719	64	7	2	2	NUM
ejpam-5719	64	8	)	)	PUNCT
ejpam-5719	65	1	+	+	CCONJ
ejpam-5719	65	2	g	g	PROPN
ejpam-5719	65	3	(	(	PUNCT
ejpam-5719	65	4	x−y	x−y	PROPN
ejpam-5719	65	5	2	2	NUM
ejpam-5719	65	6	)	)	PUNCT
ejpam-5719	65	7	=	=	SYM
ejpam-5719	65	8	f(x	f(x	PROPN
ejpam-5719	65	9	)	)	PUNCT
ejpam-5719	65	10	+	+	SYM
ejpam-5719	66	1	f(y	f(y	NOUN
ejpam-5719	66	2	)	)	PUNCT
ejpam-5719	66	3	(	(	PUNCT
ejpam-5719	66	4	2	2	X
ejpam-5719	66	5	)	)	PUNCT
ejpam-5719	66	6	for	for	ADP
ejpam-5719	66	7	all	all	DET
ejpam-5719	66	8	x	x	NOUN
ejpam-5719	66	9	,	,	PUNCT
ejpam-5719	66	10	y	y	PROPN
ejpam-5719	66	11	∈	∈	PROPN
ejpam-5719	66	12	b.	b.	PROPN
ejpam-5719	67	1	the	the	DET
ejpam-5719	67	2	aim	aim	NOUN
ejpam-5719	67	3	of	of	ADP
ejpam-5719	67	4	the	the	DET
ejpam-5719	67	5	present	present	ADJ
ejpam-5719	67	6	paper	paper	NOUN
ejpam-5719	67	7	is	be	AUX
ejpam-5719	67	8	to	to	PART
ejpam-5719	67	9	solve	solve	VERB
ejpam-5719	67	10	the	the	DET
ejpam-5719	67	11	system	system	NOUN
ejpam-5719	67	12	of	of	ADP
ejpam-5719	67	13	quadratic	quadratic	ADJ
ejpam-5719	67	14	functional	functional	ADJ
ejpam-5719	67	15	equations	equation	NOUN
ejpam-5719	67	16	and	and	CCONJ
ejpam-5719	67	17	prove	prove	VERB
ejpam-5719	67	18	the	the	DET
ejpam-5719	67	19	hyers	hyers	PROPN
ejpam-5719	67	20	-	-	PUNCT
ejpam-5719	67	21	ulam	ulam	ADJ
ejpam-5719	67	22	stability	stability	NOUN
ejpam-5719	67	23	of	of	ADP
ejpam-5719	67	24	quadratic	quadratic	ADJ
ejpam-5719	67	25	f	f	PROPN
ejpam-5719	67	26	-hom	-hom	X
ejpam-5719	67	27	-	-	PUNCT
ejpam-5719	67	28	ders	der	NOUN
ejpam-5719	67	29	in	in	ADP
ejpam-5719	67	30	complex	complex	ADJ
ejpam-5719	67	31	banach	banach	NOUN
ejpam-5719	67	32	algebras	algebra	VERB
ejpam-5719	67	33	by	by	ADP
ejpam-5719	67	34	using	use	VERB
ejpam-5719	67	35	the	the	DET
ejpam-5719	67	36	fixed	fix	VERB
ejpam-5719	67	37	point	point	NOUN
ejpam-5719	67	38	method	method	NOUN
ejpam-5719	67	39	.	.	PUNCT
ejpam-5719	68	1	throughout	throughout	ADP
ejpam-5719	68	2	this	this	DET
ejpam-5719	68	3	paper	paper	NOUN
ejpam-5719	68	4	,	,	PUNCT
ejpam-5719	68	5	assume	assume	VERB
ejpam-5719	68	6	that	that	SCONJ
ejpam-5719	68	7	b	b	PROPN
ejpam-5719	68	8	is	be	AUX
ejpam-5719	68	9	a	a	DET
ejpam-5719	68	10	complex	complex	ADJ
ejpam-5719	68	11	banach	banach	NOUN
ejpam-5719	68	12	algebra	algebra	NOUN
ejpam-5719	68	13	.	.	PUNCT
ejpam-5719	69	1	2	2	X
ejpam-5719	69	2	.	.	X
ejpam-5719	69	3	stability	stability	NOUN
ejpam-5719	69	4	of	of	ADP
ejpam-5719	69	5	system	system	NOUN
ejpam-5719	69	6	of	of	ADP
ejpam-5719	69	7	quadratic	quadratic	ADJ
ejpam-5719	69	8	functional	functional	ADJ
ejpam-5719	69	9	equations	equation	NOUN
ejpam-5719	69	10	we	we	PRON
ejpam-5719	69	11	solve	solve	VERB
ejpam-5719	69	12	and	and	CCONJ
ejpam-5719	69	13	investigate	investigate	VERB
ejpam-5719	69	14	the	the	DET
ejpam-5719	69	15	system	system	NOUN
ejpam-5719	69	16	of	of	ADP
ejpam-5719	69	17	quadratic	quadratic	ADJ
ejpam-5719	69	18	functional	functional	ADJ
ejpam-5719	69	19	equations	equation	NOUN
ejpam-5719	69	20	(	(	PUNCT
ejpam-5719	69	21	2	2	NUM
ejpam-5719	69	22	)	)	PUNCT
ejpam-5719	69	23	in	in	ADP
ejpam-5719	69	24	complex	complex	ADJ
ejpam-5719	69	25	banach	banach	NOUN
ejpam-5719	69	26	algebras	algebra	NOUN
ejpam-5719	69	27	.	.	PUNCT
ejpam-5719	70	1	lemma	lemma	PROPN
ejpam-5719	70	2	1	1	X
ejpam-5719	70	3	.	.	PUNCT
ejpam-5719	71	1	let	let	VERB
ejpam-5719	71	2	f	f	X
ejpam-5719	71	3	,	,	PUNCT
ejpam-5719	71	4	g	g	NOUN
ejpam-5719	71	5	:	:	PUNCT
ejpam-5719	71	6	b	b	X
ejpam-5719	71	7	→	→	SYM
ejpam-5719	71	8	b	b	X
ejpam-5719	71	9	be	be	AUX
ejpam-5719	71	10	mappings	mapping	NOUN
ejpam-5719	71	11	satisfying	satisfy	VERB
ejpam-5719	71	12	g(0	g(0	NOUN
ejpam-5719	71	13	)	)	PUNCT
ejpam-5719	71	14	=	=	SYM
ejpam-5719	71	15	0	0	NUM
ejpam-5719	72	1	and	and	CCONJ
ejpam-5719	72	2	(	(	PUNCT
ejpam-5719	72	3	2	2	NUM
ejpam-5719	72	4	)	)	PUNCT
ejpam-5719	72	5	for	for	ADP
ejpam-5719	72	6	all	all	DET
ejpam-5719	72	7	x	x	NOUN
ejpam-5719	72	8	,	,	PUNCT
ejpam-5719	72	9	y	y	PROPN
ejpam-5719	72	10	∈	∈	PROPN
ejpam-5719	72	11	b.	b.	PROPN
ejpam-5719	73	1	then	then	ADV
ejpam-5719	73	2	the	the	DET
ejpam-5719	73	3	mappings	mapping	NOUN
ejpam-5719	73	4	f	f	X
ejpam-5719	73	5	,	,	PUNCT
ejpam-5719	73	6	g	g	NOUN
ejpam-5719	73	7	:	:	PUNCT
ejpam-5719	73	8	b	b	X
ejpam-5719	73	9	→	→	SYM
ejpam-5719	73	10	b	b	NOUN
ejpam-5719	73	11	are	be	AUX
ejpam-5719	73	12	quadratic	quadratic	ADJ
ejpam-5719	73	13	.	.	PUNCT
ejpam-5719	74	1	proof	proof	NOUN
ejpam-5719	74	2	.	.	PUNCT
ejpam-5719	75	1	letting	let	VERB
ejpam-5719	75	2	x	x	PUNCT
ejpam-5719	75	3	=	=	PUNCT
ejpam-5719	75	4	y	y	PROPN
ejpam-5719	75	5	=	=	SYM
ejpam-5719	75	6	0	0	NUM
ejpam-5719	75	7	in	in	ADP
ejpam-5719	75	8	(	(	PUNCT
ejpam-5719	75	9	2	2	NUM
ejpam-5719	75	10	)	)	PUNCT
ejpam-5719	75	11	,	,	PUNCT
ejpam-5719	75	12	we	we	PRON
ejpam-5719	75	13	get	get	VERB
ejpam-5719	75	14	f(0	f(0	NOUN
ejpam-5719	75	15	)	)	PUNCT
ejpam-5719	76	1	=	=	SYM
ejpam-5719	76	2	g(0	g(0	PROPN
ejpam-5719	76	3	)	)	PUNCT
ejpam-5719	76	4	=	=	SYM
ejpam-5719	77	1	0	0	X
ejpam-5719	77	2	.	.	PUNCT
ejpam-5719	77	3	putting	put	VERB
ejpam-5719	77	4	y	y	NOUN
ejpam-5719	77	5	=	=	PUNCT
ejpam-5719	77	6	0	0	NUM
ejpam-5719	77	7	in	in	ADP
ejpam-5719	77	8	(	(	PUNCT
ejpam-5719	77	9	2	2	NUM
ejpam-5719	77	10	)	)	PUNCT
ejpam-5719	77	11	,	,	PUNCT
ejpam-5719	77	12	we	we	PRON
ejpam-5719	77	13	have	have	VERB
ejpam-5719	77	14	2f(x	2f(x	NUM
ejpam-5719	77	15	)	)	PUNCT
ejpam-5719	78	1	=	=	PUNCT
ejpam-5719	78	2	g(x	g(x	NOUN
ejpam-5719	78	3	)	)	PUNCT
ejpam-5719	78	4	,	,	PUNCT
ejpam-5719	78	5	2	2	NUM
ejpam-5719	78	6	g	g	NOUN
ejpam-5719	78	7	(	(	PUNCT
ejpam-5719	78	8	x	x	NOUN
ejpam-5719	78	9	2	2	X
ejpam-5719	78	10	)	)	PUNCT
ejpam-5719	78	11	=	=	SYM
ejpam-5719	78	12	f(x	f(x	PROPN
ejpam-5719	78	13	)	)	PUNCT
ejpam-5719	78	14	=	=	SYM
ejpam-5719	78	15	1	1	NUM
ejpam-5719	78	16	2	2	NUM
ejpam-5719	78	17	g(x	g(x	NOUN
ejpam-5719	78	18	)	)	PUNCT
ejpam-5719	78	19	(	(	PUNCT
ejpam-5719	78	20	3	3	X
ejpam-5719	78	21	)	)	PUNCT
ejpam-5719	78	22	c.	c.	NOUN
ejpam-5719	78	23	park	park	PROPN
ejpam-5719	78	24	,	,	PUNCT
ejpam-5719	78	25	s.	s.	PROPN
ejpam-5719	78	26	donganont	donganont	PROPN
ejpam-5719	78	27	,	,	PUNCT
ejpam-5719	78	28	s.	s.	PROPN
ejpam-5719	78	29	w.	w.	PROPN
ejpam-5719	78	30	min	min	PROPN
ejpam-5719	78	31	/	/	SYM
ejpam-5719	78	32	eur	eur	PROPN
ejpam-5719	78	33	.	.	PUNCT
ejpam-5719	79	1	j.	j.	PROPN
ejpam-5719	79	2	pure	pure	PROPN
ejpam-5719	79	3	appl	appl	PROPN
ejpam-5719	79	4	.	.	PROPN
ejpam-5719	79	5	math	math	PROPN
ejpam-5719	79	6	,	,	PUNCT
ejpam-5719	79	7	18	18	NUM
ejpam-5719	79	8	(	(	PUNCT
ejpam-5719	79	9	1	1	NUM
ejpam-5719	79	10	)	)	PUNCT
ejpam-5719	79	11	(	(	PUNCT
ejpam-5719	79	12	2025	2025	NUM
ejpam-5719	79	13	)	)	PUNCT
ejpam-5719	79	14	,	,	PUNCT
ejpam-5719	79	15	5719	5719	NUM
ejpam-5719	79	16	4	4	NUM
ejpam-5719	79	17	of	of	ADP
ejpam-5719	79	18	10	10	NUM
ejpam-5719	79	19	for	for	ADP
ejpam-5719	79	20	all	all	DET
ejpam-5719	79	21	x	x	SYM
ejpam-5719	79	22	∈	∈	PROPN
ejpam-5719	79	23	b.	b.	NOUN
ejpam-5719	80	1	so	so	ADV
ejpam-5719	80	2	f(x+	f(x+	ADV
ejpam-5719	80	3	y	y	NUM
ejpam-5719	80	4	)	)	PUNCT
ejpam-5719	81	1	+	+	CCONJ
ejpam-5719	81	2	f(x−	f(x−	PROPN
ejpam-5719	81	3	y	y	NOUN
ejpam-5719	81	4	)	)	PUNCT
ejpam-5719	81	5	=	=	SYM
ejpam-5719	81	6	2f(x	2f(x	PROPN
ejpam-5719	81	7	)	)	PUNCT
ejpam-5719	82	1	+	+	NUM
ejpam-5719	82	2	2f(y	2f(y	NUM
ejpam-5719	82	3	)	)	PUNCT
ejpam-5719	82	4	for	for	ADP
ejpam-5719	82	5	all	all	DET
ejpam-5719	82	6	x	x	NOUN
ejpam-5719	82	7	,	,	PUNCT
ejpam-5719	82	8	y	y	PROPN
ejpam-5719	82	9	∈	∈	PROPN
ejpam-5719	82	10	b.	b.	PROPN
ejpam-5719	83	1	hence	hence	ADV
ejpam-5719	83	2	the	the	DET
ejpam-5719	83	3	mapping	mapping	NOUN
ejpam-5719	83	4	f	f	NOUN
ejpam-5719	83	5	:	:	PUNCT
ejpam-5719	83	6	b	b	X
ejpam-5719	83	7	→	→	SYM
ejpam-5719	83	8	b	b	PROPN
ejpam-5719	83	9	is	be	AUX
ejpam-5719	83	10	quadratic	quadratic	ADJ
ejpam-5719	83	11	.	.	PUNCT
ejpam-5719	84	1	moreover	moreover	ADV
ejpam-5719	84	2	,	,	PUNCT
ejpam-5719	84	3	by	by	ADP
ejpam-5719	84	4	(	(	PUNCT
ejpam-5719	84	5	3	3	NUM
ejpam-5719	84	6	)	)	PUNCT
ejpam-5719	84	7	,	,	PUNCT
ejpam-5719	84	8	g	g	PROPN
ejpam-5719	84	9	(	(	PUNCT
ejpam-5719	84	10	x	x	PROPN
ejpam-5719	84	11	2	2	X
ejpam-5719	84	12	)	)	PUNCT
ejpam-5719	84	13	=	=	SYM
ejpam-5719	84	14	1	1	NUM
ejpam-5719	84	15	4	4	NUM
ejpam-5719	84	16	g(x	g(x	NUM
ejpam-5719	84	17	)	)	PUNCT
ejpam-5719	84	18	and	and	CCONJ
ejpam-5719	84	19	so	so	ADV
ejpam-5719	84	20	1	1	NUM
ejpam-5719	84	21	4	4	NUM
ejpam-5719	84	22	g(x+	g(x+	ADV
ejpam-5719	84	23	y	y	NOUN
ejpam-5719	84	24	)	)	PUNCT
ejpam-5719	84	25	+	+	CCONJ
ejpam-5719	84	26	1	1	NUM
ejpam-5719	84	27	4	4	NUM
ejpam-5719	84	28	g(x−	g(x−	NOUN
ejpam-5719	84	29	y	y	NOUN
ejpam-5719	84	30	)	)	PUNCT
ejpam-5719	84	31	=	=	SYM
ejpam-5719	85	1	g	g	PROPN
ejpam-5719	85	2	(	(	PUNCT
ejpam-5719	85	3	x+	x+	PROPN
ejpam-5719	85	4	y	y	PROPN
ejpam-5719	85	5	2	2	NUM
ejpam-5719	85	6	)	)	PUNCT
ejpam-5719	86	1	+	+	CCONJ
ejpam-5719	86	2	g	g	PROPN
ejpam-5719	86	3	(	(	PUNCT
ejpam-5719	86	4	x−	x−	PROPN
ejpam-5719	86	5	y	y	PROPN
ejpam-5719	86	6	2	2	NUM
ejpam-5719	86	7	)	)	PUNCT
ejpam-5719	86	8	=	=	SYM
ejpam-5719	86	9	f(x	f(x	PROPN
ejpam-5719	86	10	)	)	PUNCT
ejpam-5719	86	11	+	+	SYM
ejpam-5719	86	12	f(y	f(y	NOUN
ejpam-5719	86	13	)	)	PUNCT
ejpam-5719	86	14	=	=	SYM
ejpam-5719	86	15	1	1	NUM
ejpam-5719	86	16	2	2	NUM
ejpam-5719	86	17	g(x	g(x	NOUN
ejpam-5719	86	18	)	)	PUNCT
ejpam-5719	87	1	+	+	CCONJ
ejpam-5719	87	2	1	1	NUM
ejpam-5719	87	3	2	2	NUM
ejpam-5719	87	4	g(y	g(y	NOUN
ejpam-5719	87	5	)	)	PUNCT
ejpam-5719	87	6	for	for	ADP
ejpam-5719	87	7	all	all	DET
ejpam-5719	87	8	x	x	NOUN
ejpam-5719	87	9	,	,	PUNCT
ejpam-5719	87	10	y	y	PROPN
ejpam-5719	87	11	∈	∈	PROPN
ejpam-5719	87	12	b.	b.	PROPN
ejpam-5719	88	1	thus	thus	ADV
ejpam-5719	88	2	g(x+	g(x+	ADV
ejpam-5719	88	3	y	y	X
ejpam-5719	88	4	)	)	PUNCT
ejpam-5719	88	5	+	+	CCONJ
ejpam-5719	88	6	g(x−	g(x−	PROPN
ejpam-5719	88	7	y	y	NOUN
ejpam-5719	88	8	)	)	PUNCT
ejpam-5719	88	9	=	=	SYM
ejpam-5719	88	10	2g(x	2g(x	NUM
ejpam-5719	88	11	)	)	PUNCT
ejpam-5719	89	1	+	+	CCONJ
ejpam-5719	90	1	2g(y	2g(y	NUM
ejpam-5719	90	2	)	)	PUNCT
ejpam-5719	91	1	for	for	ADP
ejpam-5719	91	2	all	all	DET
ejpam-5719	91	3	x	x	NOUN
ejpam-5719	91	4	,	,	PUNCT
ejpam-5719	91	5	y	y	PROPN
ejpam-5719	91	6	∈	∈	PROPN
ejpam-5719	91	7	b	b	PROPN
ejpam-5719	91	8	and	and	CCONJ
ejpam-5719	91	9	so	so	ADV
ejpam-5719	91	10	the	the	DET
ejpam-5719	91	11	mapping	mapping	NOUN
ejpam-5719	91	12	g	g	NOUN
ejpam-5719	91	13	:	:	PUNCT
ejpam-5719	91	14	b	b	X
ejpam-5719	91	15	→	→	SYM
ejpam-5719	91	16	b	b	PROPN
ejpam-5719	91	17	is	be	AUX
ejpam-5719	91	18	quadratic	quadratic	ADJ
ejpam-5719	91	19	.	.	PUNCT
ejpam-5719	92	1	using	use	VERB
ejpam-5719	92	2	the	the	DET
ejpam-5719	92	3	fixed	fix	VERB
ejpam-5719	92	4	point	point	NOUN
ejpam-5719	92	5	technique	technique	NOUN
ejpam-5719	92	6	,	,	PUNCT
ejpam-5719	92	7	we	we	PRON
ejpam-5719	92	8	prove	prove	VERB
ejpam-5719	92	9	the	the	DET
ejpam-5719	92	10	hyers	hyers	PROPN
ejpam-5719	92	11	-	-	PUNCT
ejpam-5719	92	12	ulam	ulam	ADJ
ejpam-5719	92	13	stability	stability	NOUN
ejpam-5719	92	14	of	of	ADP
ejpam-5719	92	15	the	the	DET
ejpam-5719	92	16	system	system	NOUN
ejpam-5719	92	17	of	of	ADP
ejpam-5719	92	18	quadratic	quadratic	ADJ
ejpam-5719	92	19	functional	functional	ADJ
ejpam-5719	92	20	equations	equation	NOUN
ejpam-5719	92	21	(	(	PUNCT
ejpam-5719	92	22	2	2	NUM
ejpam-5719	92	23	)	)	PUNCT
ejpam-5719	92	24	in	in	ADP
ejpam-5719	92	25	complex	complex	ADJ
ejpam-5719	92	26	banach	banach	NOUN
ejpam-5719	92	27	algebras	algebra	NOUN
ejpam-5719	92	28	.	.	PUNCT
ejpam-5719	93	1	theorem	theorem	NOUN
ejpam-5719	93	2	2	2	NUM
ejpam-5719	93	3	.	.	PUNCT
ejpam-5719	93	4	suppose	suppose	VERB
ejpam-5719	93	5	that	that	SCONJ
ejpam-5719	93	6	∆	∆	PROPN
ejpam-5719	93	7	:	:	PUNCT
ejpam-5719	93	8	b2	b2	NOUN
ejpam-5719	93	9	→	→	SYM
ejpam-5719	93	10	[	[	X
ejpam-5719	93	11	0,∞	0,∞	NUM
ejpam-5719	93	12	)	)	PUNCT
ejpam-5719	93	13	is	be	AUX
ejpam-5719	93	14	a	a	DET
ejpam-5719	93	15	function	function	NOUN
ejpam-5719	93	16	such	such	ADJ
ejpam-5719	93	17	that	that	SCONJ
ejpam-5719	93	18	there	there	PRON
ejpam-5719	93	19	exists	exist	VERB
ejpam-5719	93	20	an	an	DET
ejpam-5719	93	21	l	l	NOUN
ejpam-5719	93	22	<	<	X
ejpam-5719	93	23	1	1	NUM
ejpam-5719	93	24	with	with	ADP
ejpam-5719	93	25	∆	∆	PROPN
ejpam-5719	93	26	(	(	PUNCT
ejpam-5719	93	27	x	x	SYM
ejpam-5719	93	28	2	2	NUM
ejpam-5719	93	29	,	,	PUNCT
ejpam-5719	93	30	y	y	PROPN
ejpam-5719	93	31	2	2	NUM
ejpam-5719	93	32	)	)	PUNCT
ejpam-5719	93	33	≤	≤	NUM
ejpam-5719	93	34	l	l	NOUN
ejpam-5719	93	35	4	4	NUM
ejpam-5719	93	36	∆(x	∆(x	NOUN
ejpam-5719	93	37	,	,	PUNCT
ejpam-5719	93	38	y	y	NOUN
ejpam-5719	93	39	)	)	PUNCT
ejpam-5719	93	40	(	(	PUNCT
ejpam-5719	93	41	4	4	X
ejpam-5719	93	42	)	)	PUNCT
ejpam-5719	93	43	for	for	ADP
ejpam-5719	93	44	all	all	DET
ejpam-5719	93	45	x	x	NOUN
ejpam-5719	93	46	,	,	PUNCT
ejpam-5719	93	47	y	y	PROPN
ejpam-5719	93	48	∈	∈	PROPN
ejpam-5719	93	49	b.	b.	PROPN
ejpam-5719	93	50	let	let	VERB
ejpam-5719	93	51	f	f	X
ejpam-5719	93	52	,	,	PUNCT
ejpam-5719	93	53	g	g	NOUN
ejpam-5719	93	54	:	:	PUNCT
ejpam-5719	93	55	b	b	X
ejpam-5719	93	56	→	→	SYM
ejpam-5719	93	57	b	b	X
ejpam-5719	93	58	be	be	AUX
ejpam-5719	93	59	mappings	mapping	NOUN
ejpam-5719	93	60	satisfying	satisfy	VERB
ejpam-5719	93	61	g(0	g(0	NOUN
ejpam-5719	93	62	)	)	PUNCT
ejpam-5719	93	63	=	=	SYM
ejpam-5719	93	64	0	0	PUNCT
ejpam-5719	94	1	and	and	CCONJ
ejpam-5719	94	2	{	{	PUNCT
ejpam-5719	94	3	∥f(x+	∥f(x+	VERB
ejpam-5719	94	4	y	y	NOUN
ejpam-5719	94	5	)	)	PUNCT
ejpam-5719	95	1	+	+	CCONJ
ejpam-5719	95	2	f(x−	f(x−	ADP
ejpam-5719	95	3	y)−	y)−	PROPN
ejpam-5719	95	4	g(x)−	g(x)−	PROPN
ejpam-5719	95	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	95	6	≤	≤	PUNCT
ejpam-5719	95	7	∆(x	∆(x	PROPN
ejpam-5719	95	8	,	,	PUNCT
ejpam-5719	95	9	y	y	NOUN
ejpam-5719	95	10	)	)	PUNCT
ejpam-5719	95	11	,	,	PUNCT
ejpam-5719	95	12	∥g	∥g	PROPN
ejpam-5719	95	13	(	(	PUNCT
ejpam-5719	95	14	x+y	x+y	NUM
ejpam-5719	95	15	2	2	NUM
ejpam-5719	95	16	)	)	PUNCT
ejpam-5719	96	1	+	+	CCONJ
ejpam-5719	96	2	g	g	PROPN
ejpam-5719	96	3	(	(	PUNCT
ejpam-5719	96	4	x−y	x−y	PROPN
ejpam-5719	96	5	2	2	NUM
ejpam-5719	96	6	)	)	PUNCT
ejpam-5719	96	7	−	−	PROPN
ejpam-5719	97	1	f(x)−	f(x)−	PROPN
ejpam-5719	97	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	97	3	≤	≤	PUNCT
ejpam-5719	97	4	∆(x	∆(x	PROPN
ejpam-5719	97	5	,	,	PUNCT
ejpam-5719	97	6	y	y	NOUN
ejpam-5719	97	7	)	)	PUNCT
ejpam-5719	97	8	(	(	PUNCT
ejpam-5719	97	9	5	5	NUM
ejpam-5719	97	10	)	)	PUNCT
ejpam-5719	97	11	for	for	ADP
ejpam-5719	97	12	all	all	DET
ejpam-5719	97	13	x	x	NOUN
ejpam-5719	97	14	,	,	PUNCT
ejpam-5719	97	15	y	y	PROPN
ejpam-5719	97	16	∈	∈	PROPN
ejpam-5719	97	17	b.	b.	PROPN
ejpam-5719	98	1	then	then	ADV
ejpam-5719	98	2	there	there	PRON
ejpam-5719	98	3	exist	exist	VERB
ejpam-5719	98	4	unique	unique	ADJ
ejpam-5719	98	5	quadratic	quadratic	ADJ
ejpam-5719	98	6	mappings	mapping	NOUN
ejpam-5719	98	7	f	f	X
ejpam-5719	98	8	,	,	PUNCT
ejpam-5719	98	9	g	g	NOUN
ejpam-5719	98	10	:	:	PUNCT
ejpam-5719	98	11	b	b	X
ejpam-5719	98	12	→	→	SYM
ejpam-5719	98	13	b	b	X
ejpam-5719	98	14	such	such	ADJ
ejpam-5719	98	15	that	that	SCONJ
ejpam-5719	98	16	∥f	∥f	PROPN
ejpam-5719	98	17	(	(	PUNCT
ejpam-5719	98	18	x)−	x)−	PROPN
ejpam-5719	98	19	f(x)∥	f(x)∥	VERB
ejpam-5719	98	20	≤	≤	NUM
ejpam-5719	98	21	2	2	NUM
ejpam-5719	98	22	+	+	NUM
ejpam-5719	98	23	l	l	NOUN
ejpam-5719	98	24	4(1−	4(1−	NUM
ejpam-5719	98	25	l	l	NOUN
ejpam-5719	98	26	)	)	PUNCT
ejpam-5719	98	27	∆(x	∆(x	PROPN
ejpam-5719	98	28	,	,	PUNCT
ejpam-5719	98	29	x	x	NOUN
ejpam-5719	98	30	)	)	PUNCT
ejpam-5719	98	31	,	,	PUNCT
ejpam-5719	98	32	(	(	PUNCT
ejpam-5719	98	33	6	6	X
ejpam-5719	98	34	)	)	PUNCT
ejpam-5719	98	35	∥g(x)−	∥g(x)−	X
ejpam-5719	98	36	g(x)∥	g(x)∥	VERB
ejpam-5719	98	37	≤	≤	NUM
ejpam-5719	98	38	2	2	NUM
ejpam-5719	98	39	+	+	NUM
ejpam-5719	98	40	l	l	NOUN
ejpam-5719	98	41	2(1−	2(1−	NUM
ejpam-5719	98	42	l	l	NOUN
ejpam-5719	98	43	)	)	PUNCT
ejpam-5719	98	44	∆(x	∆(x	PROPN
ejpam-5719	98	45	,	,	PUNCT
ejpam-5719	98	46	x	x	PRON
ejpam-5719	98	47	)	)	PUNCT
ejpam-5719	98	48	(	(	PUNCT
ejpam-5719	98	49	7	7	X
ejpam-5719	98	50	)	)	PUNCT
ejpam-5719	98	51	for	for	ADP
ejpam-5719	98	52	all	all	DET
ejpam-5719	98	53	x	x	SYM
ejpam-5719	98	54	∈	∈	PROPN
ejpam-5719	98	55	b.	b.	NOUN
ejpam-5719	98	56	proof	proof	NOUN
ejpam-5719	98	57	.	.	PUNCT
ejpam-5719	99	1	putting	put	VERB
ejpam-5719	99	2	x	x	PUNCT
ejpam-5719	99	3	=	=	PUNCT
ejpam-5719	99	4	y	y	PROPN
ejpam-5719	99	5	=	=	SYM
ejpam-5719	99	6	0	0	NUM
ejpam-5719	99	7	in	in	ADP
ejpam-5719	99	8	(	(	PUNCT
ejpam-5719	99	9	5	5	NUM
ejpam-5719	99	10	)	)	PUNCT
ejpam-5719	99	11	,	,	PUNCT
ejpam-5719	99	12	we	we	PRON
ejpam-5719	99	13	get	get	VERB
ejpam-5719	99	14	{	{	PUNCT
ejpam-5719	99	15	∥2f(0)−	∥2f(0)−	NOUN
ejpam-5719	99	16	2g(0)∥	2g(0)∥	NUM
ejpam-5719	99	17	≤	≤	NUM
ejpam-5719	99	18	∆(0	∆(0	NOUN
ejpam-5719	99	19	,	,	PUNCT
ejpam-5719	99	20	0	0	NUM
ejpam-5719	99	21	)	)	PUNCT
ejpam-5719	99	22	=	=	SYM
ejpam-5719	99	23	0	0	NUM
ejpam-5719	99	24	,	,	PUNCT
ejpam-5719	99	25	∥2g(0)−	∥2g(0)−	NOUN
ejpam-5719	99	26	2f(0)∥	2f(0)∥	NUM
ejpam-5719	99	27	≤	≤	NUM
ejpam-5719	99	28	∆(0	∆(0	NOUN
ejpam-5719	99	29	,	,	PUNCT
ejpam-5719	99	30	0	0	NUM
ejpam-5719	99	31	)	)	PUNCT
ejpam-5719	99	32	=	=	SYM
ejpam-5719	99	33	0	0	NUM
ejpam-5719	99	34	and	and	CCONJ
ejpam-5719	99	35	so	so	ADV
ejpam-5719	99	36	f(0	f(0	NOUN
ejpam-5719	99	37	)	)	PUNCT
ejpam-5719	100	1	=	=	SYM
ejpam-5719	100	2	g(0	g(0	PROPN
ejpam-5719	100	3	)	)	PUNCT
ejpam-5719	100	4	=	=	SYM
ejpam-5719	100	5	0	0	X
ejpam-5719	100	6	.	.	PUNCT
ejpam-5719	100	7	c.	c.	PROPN
ejpam-5719	100	8	park	park	PROPN
ejpam-5719	100	9	,	,	PUNCT
ejpam-5719	100	10	s.	s.	PROPN
ejpam-5719	100	11	donganont	donganont	PROPN
ejpam-5719	100	12	,	,	PUNCT
ejpam-5719	100	13	s.	s.	PROPN
ejpam-5719	100	14	w.	w.	PROPN
ejpam-5719	100	15	min	min	PROPN
ejpam-5719	100	16	/	/	SYM
ejpam-5719	100	17	eur	eur	PROPN
ejpam-5719	100	18	.	.	PUNCT
ejpam-5719	101	1	j.	j.	PROPN
ejpam-5719	101	2	pure	pure	PROPN
ejpam-5719	101	3	appl	appl	PROPN
ejpam-5719	101	4	.	.	PROPN
ejpam-5719	101	5	math	math	PROPN
ejpam-5719	101	6	,	,	PUNCT
ejpam-5719	101	7	18	18	NUM
ejpam-5719	101	8	(	(	PUNCT
ejpam-5719	101	9	1	1	NUM
ejpam-5719	101	10	)	)	PUNCT
ejpam-5719	101	11	(	(	PUNCT
ejpam-5719	101	12	2025	2025	NUM
ejpam-5719	101	13	)	)	PUNCT
ejpam-5719	101	14	,	,	PUNCT
ejpam-5719	101	15	5719	5719	NUM
ejpam-5719	101	16	5	5	NUM
ejpam-5719	101	17	of	of	ADP
ejpam-5719	101	18	10	10	NUM
ejpam-5719	101	19	letting	let	VERB
ejpam-5719	101	20	y	y	NOUN
ejpam-5719	101	21	=	=	PUNCT
ejpam-5719	102	1	x	x	X
ejpam-5719	102	2	in	in	ADP
ejpam-5719	102	3	(	(	PUNCT
ejpam-5719	102	4	5	5	NUM
ejpam-5719	102	5	)	)	PUNCT
ejpam-5719	102	6	,	,	PUNCT
ejpam-5719	102	7	we	we	PRON
ejpam-5719	102	8	obtain	obtain	VERB
ejpam-5719	102	9	{	{	PUNCT
ejpam-5719	102	10	∥f(2x)−	∥f(2x)−	PROPN
ejpam-5719	102	11	2g(x)∥	2g(x)∥	NUM
ejpam-5719	102	12	≤	≤	ADJ
ejpam-5719	102	13	∆(x	∆(x	NOUN
ejpam-5719	102	14	,	,	PUNCT
ejpam-5719	102	15	x	x	NOUN
ejpam-5719	102	16	)	)	PUNCT
ejpam-5719	102	17	,	,	PUNCT
ejpam-5719	102	18	∥g(x)−	∥g(x)−	PROPN
ejpam-5719	102	19	2f(x)∥	2f(x)∥	NUM
ejpam-5719	102	20	≤	≤	NUM
ejpam-5719	102	21	∆(x	∆(x	PROPN
ejpam-5719	102	22	,	,	PUNCT
ejpam-5719	102	23	x	x	PRON
ejpam-5719	102	24	)	)	PUNCT
ejpam-5719	102	25	and	and	CCONJ
ejpam-5719	102	26	so	so	ADV
ejpam-5719	102	27	{	{	PUNCT
ejpam-5719	102	28	∥∥g(x)−	∥∥g(x)−	NOUN
ejpam-5719	102	29	4	4	NUM
ejpam-5719	102	30	g	g	NOUN
ejpam-5719	102	31	(	(	PUNCT
ejpam-5719	102	32	x	x	SYM
ejpam-5719	102	33	2	2	X
ejpam-5719	102	34	)	)	PUNCT
ejpam-5719	102	35	∥∥	∥∥	PROPN
ejpam-5719	103	1	≤	≤	NUM
ejpam-5719	103	2	2∆	2∆	NUM
ejpam-5719	103	3	(	(	PUNCT
ejpam-5719	103	4	x	x	SYM
ejpam-5719	103	5	2	2	NUM
ejpam-5719	103	6	,	,	PUNCT
ejpam-5719	103	7	x	x	NOUN
ejpam-5719	103	8	2	2	X
ejpam-5719	103	9	)	)	PUNCT
ejpam-5719	104	1	+	+	NOUN
ejpam-5719	104	2	∆(x	∆(x	PROPN
ejpam-5719	104	3	,	,	PUNCT
ejpam-5719	104	4	x	x	NOUN
ejpam-5719	104	5	)	)	PUNCT
ejpam-5719	104	6	≤	≤	NOUN
ejpam-5719	104	7	2+l	2+l	NUM
ejpam-5719	104	8	2	2	NUM
ejpam-5719	104	9	∆(x	∆(x	NOUN
ejpam-5719	104	10	,	,	PUNCT
ejpam-5719	104	11	x),∥∥f(x)−	x),∥∥f(x)−	PROPN
ejpam-5719	104	12	4f	4f	NUM
ejpam-5719	104	13	(	(	PUNCT
ejpam-5719	104	14	x	x	SYM
ejpam-5719	104	15	2	2	X
ejpam-5719	104	16	)	)	PUNCT
ejpam-5719	104	17	∥∥	∥∥	PROPN
ejpam-5719	104	18	≤	≤	NUM
ejpam-5719	104	19	∆	∆	X
ejpam-5719	104	20	(	(	PUNCT
ejpam-5719	104	21	x	x	SYM
ejpam-5719	104	22	2	2	NUM
ejpam-5719	104	23	,	,	PUNCT
ejpam-5719	104	24	x	x	NOUN
ejpam-5719	104	25	2	2	X
ejpam-5719	104	26	)	)	PUNCT
ejpam-5719	105	1	+	+	CCONJ
ejpam-5719	105	2	1	1	NUM
ejpam-5719	105	3	2∆(x	2∆(x	NUM
ejpam-5719	105	4	,	,	PUNCT
ejpam-5719	105	5	x	x	NOUN
ejpam-5719	105	6	)	)	PUNCT
ejpam-5719	105	7	≤	≤	NOUN
ejpam-5719	105	8	2+l	2+l	NUM
ejpam-5719	105	9	4	4	NUM
ejpam-5719	105	10	∆(x	∆(x	NOUN
ejpam-5719	105	11	,	,	PUNCT
ejpam-5719	105	12	x	x	PRON
ejpam-5719	105	13	)	)	PUNCT
ejpam-5719	105	14	(	(	PUNCT
ejpam-5719	105	15	8)	8)	NUM
ejpam-5719	105	16	for	for	ADP
ejpam-5719	105	17	all	all	DET
ejpam-5719	105	18	x	x	SYM
ejpam-5719	105	19	∈	∈	PROPN
ejpam-5719	105	20	b.	b.	PROPN
ejpam-5719	105	21	let	let	VERB
ejpam-5719	105	22	γ	γ	X
ejpam-5719	105	23	=	=	PRON
ejpam-5719	105	24	{	{	PUNCT
ejpam-5719	105	25	γ	γ	X
ejpam-5719	105	26	:	:	PUNCT
ejpam-5719	105	27	b	b	PROPN
ejpam-5719	105	28	→	→	SYM
ejpam-5719	105	29	b	b	PROPN
ejpam-5719	105	30	:	:	PUNCT
ejpam-5719	105	31	γ(0	γ(0	PROPN
ejpam-5719	105	32	)	)	PUNCT
ejpam-5719	105	33	=	=	PUNCT
ejpam-5719	106	1	0	0	NUM
ejpam-5719	106	2	}	}	PUNCT
ejpam-5719	106	3	.	.	PUNCT
ejpam-5719	107	1	we	we	PRON
ejpam-5719	107	2	define	define	VERB
ejpam-5719	107	3	a	a	DET
ejpam-5719	107	4	generalized	generalized	ADJ
ejpam-5719	107	5	metric	metric	NOUN
ejpam-5719	107	6	on	on	ADP
ejpam-5719	107	7	γ	γ	NOUN
ejpam-5719	107	8	as	as	SCONJ
ejpam-5719	107	9	follows	follow	VERB
ejpam-5719	107	10	:	:	PUNCT
ejpam-5719	107	11	d	d	NOUN
ejpam-5719	107	12	:	:	PUNCT
ejpam-5719	107	13	γ×	γ×	PUNCT
ejpam-5719	107	14	γ	γ	X
ejpam-5719	107	15	−→	−→	NOUN
ejpam-5719	107	16	[	[	X
ejpam-5719	107	17	0,∞	0,∞	X
ejpam-5719	107	18	]	]	PUNCT
ejpam-5719	107	19	by	by	ADP
ejpam-5719	107	20	d(δ	d(δ	PROPN
ejpam-5719	107	21	,	,	PUNCT
ejpam-5719	107	22	γ	γ	NOUN
ejpam-5719	107	23	)	)	PUNCT
ejpam-5719	107	24	=	=	SYM
ejpam-5719	107	25	inf	inf	NOUN
ejpam-5719	107	26	{	{	PUNCT
ejpam-5719	107	27	µ	µ	X
ejpam-5719	107	28	∈	∈	NOUN
ejpam-5719	107	29	r+	r+	NOUN
ejpam-5719	107	30	:	:	PUNCT
ejpam-5719	107	31	∥δ(x)−	∥δ(x)−	PROPN
ejpam-5719	107	32	γ(x)∥	γ(x)∥	X
ejpam-5719	107	33	≤	≤	ADV
ejpam-5719	107	34	µ∆(x	µ∆(x	ADV
ejpam-5719	107	35	,	,	PUNCT
ejpam-5719	107	36	x),∀x	x),∀x	PROPN
ejpam-5719	107	37	∈	∈	PROPN
ejpam-5719	107	38	b	b	X
ejpam-5719	107	39	}	}	PUNCT
ejpam-5719	107	40	,	,	PUNCT
ejpam-5719	107	41	and	and	CCONJ
ejpam-5719	107	42	we	we	PRON
ejpam-5719	107	43	consider	consider	VERB
ejpam-5719	107	44	inf	inf	NOUN
ejpam-5719	107	45	∅	∅	NOUN
ejpam-5719	107	46	=	=	PUNCT
ejpam-5719	108	1	+	+	NUM
ejpam-5719	108	2	∞.	∞.	PROPN
ejpam-5719	108	3	then	then	ADV
ejpam-5719	108	4	d	d	PROPN
ejpam-5719	108	5	is	be	AUX
ejpam-5719	108	6	a	a	DET
ejpam-5719	108	7	complete	complete	ADJ
ejpam-5719	108	8	generalized	generalize	VERB
ejpam-5719	108	9	metric	metric	NOUN
ejpam-5719	108	10	on	on	ADP
ejpam-5719	108	11	γ	γ	X
ejpam-5719	108	12	(	(	PUNCT
ejpam-5719	108	13	see	see	VERB
ejpam-5719	108	14	[	[	X
ejpam-5719	108	15	12	12	NUM
ejpam-5719	108	16	]	]	PUNCT
ejpam-5719	108	17	)	)	PUNCT
ejpam-5719	108	18	.	.	PUNCT
ejpam-5719	109	1	now	now	ADV
ejpam-5719	109	2	,	,	PUNCT
ejpam-5719	109	3	we	we	PRON
ejpam-5719	109	4	define	define	VERB
ejpam-5719	109	5	the	the	DET
ejpam-5719	109	6	mapping	mapping	NOUN
ejpam-5719	109	7	j	j	NOUN
ejpam-5719	109	8	:	:	PUNCT
ejpam-5719	109	9	(	(	PUNCT
ejpam-5719	109	10	γ	γ	X
ejpam-5719	109	11	,	,	PUNCT
ejpam-5719	109	12	d	d	NOUN
ejpam-5719	109	13	)	)	PUNCT
ejpam-5719	109	14	→	→	SYM
ejpam-5719	109	15	(	(	PUNCT
ejpam-5719	109	16	γ	γ	X
ejpam-5719	109	17	,	,	PUNCT
ejpam-5719	109	18	d	d	NOUN
ejpam-5719	109	19	)	)	PUNCT
ejpam-5719	109	20	such	such	ADJ
ejpam-5719	109	21	that	that	SCONJ
ejpam-5719	109	22	j	j	PROPN
ejpam-5719	109	23	δ(x	δ(x	PROPN
ejpam-5719	109	24	)	)	PUNCT
ejpam-5719	109	25	:	:	PUNCT
ejpam-5719	110	1	=	=	SYM
ejpam-5719	110	2	4δ	4δ	NOUN
ejpam-5719	110	3	(	(	PUNCT
ejpam-5719	110	4	x	x	SYM
ejpam-5719	110	5	2	2	NUM
ejpam-5719	110	6	)	)	PUNCT
ejpam-5719	110	7	for	for	ADP
ejpam-5719	110	8	all	all	DET
ejpam-5719	110	9	x	x	PROPN
ejpam-5719	110	10	∈	∈	PROPN
ejpam-5719	110	11	b.	b.	PROPN
ejpam-5719	110	12	actually	actually	ADV
ejpam-5719	110	13	,	,	PUNCT
ejpam-5719	110	14	let	let	VERB
ejpam-5719	110	15	δ	δ	PROPN
ejpam-5719	110	16	,	,	PUNCT
ejpam-5719	110	17	γ	γ	PROPN
ejpam-5719	110	18	∈	∈	PROPN
ejpam-5719	110	19	(	(	PUNCT
ejpam-5719	110	20	γ	γ	X
ejpam-5719	110	21	,	,	PUNCT
ejpam-5719	110	22	d	d	NOUN
ejpam-5719	110	23	)	)	PUNCT
ejpam-5719	110	24	be	be	AUX
ejpam-5719	110	25	given	give	VERB
ejpam-5719	110	26	such	such	ADJ
ejpam-5719	110	27	that	that	DET
ejpam-5719	110	28	d(δ	d(δ	PROPN
ejpam-5719	110	29	,	,	PUNCT
ejpam-5719	110	30	γ	γ	NOUN
ejpam-5719	110	31	)	)	PUNCT
ejpam-5719	111	1	=	=	SYM
ejpam-5719	111	2	µ.	µ.	NOUN
ejpam-5719	111	3	then	then	ADV
ejpam-5719	111	4	∥δ(x)−	∥δ(x)−	PROPN
ejpam-5719	111	5	γ(x)∥	γ(x)∥	ADV
ejpam-5719	111	6	≤	≤	ADV
ejpam-5719	111	7	µ∆(x	µ∆(x	NUM
ejpam-5719	111	8	,	,	PUNCT
ejpam-5719	111	9	x	x	NOUN
ejpam-5719	111	10	)	)	PUNCT
ejpam-5719	111	11	for	for	ADP
ejpam-5719	111	12	all	all	DET
ejpam-5719	111	13	x	x	SYM
ejpam-5719	111	14	∈	∈	PROPN
ejpam-5719	111	15	b.	b.	NOUN
ejpam-5719	112	1	hence	hence	ADV
ejpam-5719	112	2	∥j	∥j	ADV
ejpam-5719	112	3	δ(x)−	δ(x)−	PROPN
ejpam-5719	112	4	j	j	NOUN
ejpam-5719	112	5	γ(x)∥	γ(x)∥	ADV
ejpam-5719	113	1	=	=	SYM
ejpam-5719	114	1	∥∥∥4δ	∥∥∥4δ	NUM
ejpam-5719	115	1	(	(	PUNCT
ejpam-5719	115	2	x	x	NOUN
ejpam-5719	115	3	2	2	X
ejpam-5719	115	4	)	)	PUNCT
ejpam-5719	115	5	−	−	PROPN
ejpam-5719	115	6	4γ	4γ	NOUN
ejpam-5719	115	7	(	(	PUNCT
ejpam-5719	115	8	x	x	SYM
ejpam-5719	115	9	2	2	NUM
ejpam-5719	115	10	)	)	PUNCT
ejpam-5719	115	11	∥∥∥	∥∥∥	PROPN
ejpam-5719	115	12	≤	≤	NOUN
ejpam-5719	115	13	4µ∆	4µ∆	NUM
ejpam-5719	115	14	(	(	PUNCT
ejpam-5719	115	15	x	x	SYM
ejpam-5719	115	16	2	2	NUM
ejpam-5719	115	17	,	,	PUNCT
ejpam-5719	115	18	x	x	NOUN
ejpam-5719	115	19	2	2	X
ejpam-5719	115	20	)	)	PUNCT
ejpam-5719	115	21	≤	≤	NOUN
ejpam-5719	115	22	lµ∆(x	lµ∆(x	PROPN
ejpam-5719	115	23	,	,	PUNCT
ejpam-5719	115	24	x	x	NOUN
ejpam-5719	115	25	)	)	PUNCT
ejpam-5719	115	26	for	for	ADP
ejpam-5719	115	27	all	all	DET
ejpam-5719	115	28	x	x	SYM
ejpam-5719	115	29	∈	∈	PROPN
ejpam-5719	115	30	b.	b.	NOUN
ejpam-5719	115	31	it	it	PRON
ejpam-5719	115	32	follows	follow	VERB
ejpam-5719	115	33	that	that	SCONJ
ejpam-5719	115	34	d(j	d(j	PRON
ejpam-5719	115	35	δ(x),j	δ(x),j	VERB
ejpam-5719	115	36	γ(x	γ(x	NOUN
ejpam-5719	115	37	)	)	PUNCT
ejpam-5719	115	38	)	)	PUNCT
ejpam-5719	116	1	≤	≤	NUM
ejpam-5719	116	2	lµ.	lµ.	NOUN
ejpam-5719	116	3	so	so	SCONJ
ejpam-5719	116	4	d(j	d(j	PROPN
ejpam-5719	116	5	δ(x),j	δ(x),j	VERB
ejpam-5719	116	6	γ(x	γ(x	NOUN
ejpam-5719	116	7	)	)	PUNCT
ejpam-5719	116	8	)	)	PUNCT
ejpam-5719	116	9	≤	≤	PROPN
ejpam-5719	116	10	ld(δ	ld(δ	NOUN
ejpam-5719	116	11	,	,	PUNCT
ejpam-5719	116	12	γ	γ	NOUN
ejpam-5719	116	13	)	)	PUNCT
ejpam-5719	116	14	for	for	ADP
ejpam-5719	116	15	all	all	DET
ejpam-5719	116	16	x	x	SYM
ejpam-5719	116	17	∈	∈	PROPN
ejpam-5719	116	18	b	b	PROPN
ejpam-5719	116	19	and	and	CCONJ
ejpam-5719	116	20	all	all	DET
ejpam-5719	116	21	δ	δ	PROPN
ejpam-5719	116	22	,	,	PUNCT
ejpam-5719	116	23	γ	γ	PROPN
ejpam-5719	116	24	∈	∈	PROPN
ejpam-5719	116	25	γ	γ	X
ejpam-5719	116	26	.	.	PUNCT
ejpam-5719	117	1	it	it	PRON
ejpam-5719	117	2	follows	follow	VERB
ejpam-5719	117	3	from	from	ADP
ejpam-5719	117	4	(	(	PUNCT
ejpam-5719	117	5	8)	8)	NUM
ejpam-5719	117	6	that	that	DET
ejpam-5719	117	7	d(f	d(f	NOUN
ejpam-5719	117	8	,	,	PUNCT
ejpam-5719	117	9	j	j	PROPN
ejpam-5719	117	10	f	f	X
ejpam-5719	117	11	)	)	PUNCT
ejpam-5719	117	12	≤	≤	NOUN
ejpam-5719	118	1	2+l	2+l	NUM
ejpam-5719	118	2	4	4	NUM
ejpam-5719	118	3	and	and	CCONJ
ejpam-5719	118	4	d(g	d(g	PROPN
ejpam-5719	118	5	,	,	PUNCT
ejpam-5719	118	6	j	j	PROPN
ejpam-5719	118	7	g	g	NOUN
ejpam-5719	118	8	)	)	PUNCT
ejpam-5719	118	9	≤	≤	NOUN
ejpam-5719	118	10	2+l	2+l	NUM
ejpam-5719	118	11	2	2	NUM
ejpam-5719	118	12	.	.	PUNCT
ejpam-5719	119	1	using	use	VERB
ejpam-5719	119	2	the	the	DET
ejpam-5719	119	3	fixed	fix	VERB
ejpam-5719	119	4	point	point	NOUN
ejpam-5719	119	5	alternative	alternative	NOUN
ejpam-5719	119	6	we	we	PRON
ejpam-5719	119	7	deduce	deduce	VERB
ejpam-5719	119	8	the	the	DET
ejpam-5719	119	9	existence	existence	NOUN
ejpam-5719	119	10	of	of	ADP
ejpam-5719	119	11	a	a	DET
ejpam-5719	119	12	unique	unique	ADJ
ejpam-5719	119	13	fixed	fix	VERB
ejpam-5719	119	14	point	point	NOUN
ejpam-5719	119	15	of	of	ADP
ejpam-5719	119	16	j	j	PROPN
ejpam-5719	119	17	and	and	CCONJ
ejpam-5719	119	18	a	a	DET
ejpam-5719	119	19	unique	unique	ADJ
ejpam-5719	119	20	fixed	fix	VERB
ejpam-5719	119	21	point	point	NOUN
ejpam-5719	119	22	of	of	ADP
ejpam-5719	119	23	j	j	PROPN
ejpam-5719	119	24	,	,	PUNCT
ejpam-5719	119	25	that	that	ADV
ejpam-5719	119	26	is	is	ADV
ejpam-5719	119	27	,	,	PUNCT
ejpam-5719	119	28	the	the	DET
ejpam-5719	119	29	existence	existence	NOUN
ejpam-5719	119	30	of	of	ADP
ejpam-5719	119	31	mappings	mapping	NOUN
ejpam-5719	120	1	f	f	X
ejpam-5719	120	2	,	,	PUNCT
ejpam-5719	120	3	g	g	NOUN
ejpam-5719	120	4	:	:	PUNCT
ejpam-5719	120	5	b	b	PROPN
ejpam-5719	120	6	→	→	SYM
ejpam-5719	120	7	b	b	PROPN
ejpam-5719	120	8	,	,	PUNCT
ejpam-5719	120	9	respectively	respectively	ADV
ejpam-5719	120	10	,	,	PUNCT
ejpam-5719	120	11	such	such	ADJ
ejpam-5719	120	12	that	that	SCONJ
ejpam-5719	120	13	f	f	PROPN
ejpam-5719	120	14	(	(	PUNCT
ejpam-5719	120	15	x	x	X
ejpam-5719	120	16	)	)	PUNCT
ejpam-5719	120	17	=	=	SYM
ejpam-5719	120	18	4f	4f	NUM
ejpam-5719	120	19	(	(	PUNCT
ejpam-5719	120	20	x	x	SYM
ejpam-5719	120	21	2	2	NUM
ejpam-5719	120	22	)	)	PUNCT
ejpam-5719	120	23	,	,	PUNCT
ejpam-5719	120	24	g(x	g(x	NOUN
ejpam-5719	120	25	)	)	PUNCT
ejpam-5719	120	26	=	=	SYM
ejpam-5719	121	1	4	4	NUM
ejpam-5719	121	2	g	g	NOUN
ejpam-5719	121	3	(	(	PUNCT
ejpam-5719	121	4	x	x	NOUN
ejpam-5719	121	5	2	2	NUM
ejpam-5719	121	6	)	)	PUNCT
ejpam-5719	121	7	with	with	ADP
ejpam-5719	121	8	the	the	DET
ejpam-5719	121	9	following	follow	VERB
ejpam-5719	121	10	property	property	NOUN
ejpam-5719	121	11	:	:	PUNCT
ejpam-5719	121	12	there	there	PRON
ejpam-5719	121	13	exist	exist	VERB
ejpam-5719	121	14	µ	µ	NUM
ejpam-5719	121	15	,	,	PUNCT
ejpam-5719	121	16	η	η	PROPN
ejpam-5719	121	17	∈	∈	PROPN
ejpam-5719	121	18	(	(	PUNCT
ejpam-5719	121	19	0,∞	0,∞	NOUN
ejpam-5719	121	20	)	)	PUNCT
ejpam-5719	121	21	satisfying	satisfy	VERB
ejpam-5719	121	22	∥f(x)−	∥f(x)−	PROPN
ejpam-5719	121	23	f	f	PROPN
ejpam-5719	121	24	(	(	PUNCT
ejpam-5719	121	25	x)∥	x)∥	PUNCT
ejpam-5719	121	26	≤	≤	PROPN
ejpam-5719	121	27	µ∆(x	µ∆(x	NUM
ejpam-5719	121	28	,	,	PUNCT
ejpam-5719	121	29	x	x	NOUN
ejpam-5719	121	30	)	)	PUNCT
ejpam-5719	121	31	,	,	PUNCT
ejpam-5719	121	32	∥g(x)−g(x)∥	∥g(x)−g(x)∥	VERB
ejpam-5719	121	33	≤	≤	NUM
ejpam-5719	121	34	η∆(x	η∆(x	PROPN
ejpam-5719	121	35	,	,	PUNCT
ejpam-5719	121	36	x	x	NOUN
ejpam-5719	121	37	)	)	PUNCT
ejpam-5719	121	38	for	for	ADP
ejpam-5719	121	39	all	all	DET
ejpam-5719	121	40	x	x	SYM
ejpam-5719	121	41	∈	∈	PROPN
ejpam-5719	121	42	b.	b.	PROPN
ejpam-5719	121	43	c.	c.	PROPN
ejpam-5719	121	44	park	park	PROPN
ejpam-5719	121	45	,	,	PUNCT
ejpam-5719	121	46	s.	s.	PROPN
ejpam-5719	121	47	donganont	donganont	PROPN
ejpam-5719	121	48	,	,	PUNCT
ejpam-5719	121	49	s.	s.	PROPN
ejpam-5719	121	50	w.	w.	PROPN
ejpam-5719	121	51	min	min	PROPN
ejpam-5719	121	52	/	/	SYM
ejpam-5719	121	53	eur	eur	PROPN
ejpam-5719	121	54	.	.	PUNCT
ejpam-5719	122	1	j.	j.	PROPN
ejpam-5719	122	2	pure	pure	PROPN
ejpam-5719	122	3	appl	appl	PROPN
ejpam-5719	122	4	.	.	PROPN
ejpam-5719	122	5	math	math	PROPN
ejpam-5719	122	6	,	,	PUNCT
ejpam-5719	122	7	18	18	NUM
ejpam-5719	122	8	(	(	PUNCT
ejpam-5719	122	9	1	1	NUM
ejpam-5719	122	10	)	)	PUNCT
ejpam-5719	122	11	(	(	PUNCT
ejpam-5719	122	12	2025	2025	NUM
ejpam-5719	122	13	)	)	PUNCT
ejpam-5719	122	14	,	,	PUNCT
ejpam-5719	122	15	5719	5719	NUM
ejpam-5719	122	16	6	6	NUM
ejpam-5719	122	17	of	of	ADP
ejpam-5719	122	18	10	10	NUM
ejpam-5719	122	19	since	since	ADV
ejpam-5719	122	20	limn→+∞	limn→+∞	ADP
ejpam-5719	122	21	d(j	d(j	PROPN
ejpam-5719	122	22	nf	nf	PROPN
ejpam-5719	122	23	,	,	PUNCT
ejpam-5719	122	24	f	f	PROPN
ejpam-5719	122	25	)	)	PUNCT
ejpam-5719	123	1	=	=	SYM
ejpam-5719	123	2	0	0	NUM
ejpam-5719	123	3	and	and	CCONJ
ejpam-5719	123	4	limn→+∞	limn→+∞	VERB
ejpam-5719	123	5	d(j	d(j	PROPN
ejpam-5719	123	6	ng	ng	PROPN
ejpam-5719	123	7	,	,	PUNCT
ejpam-5719	123	8	g	g	NOUN
ejpam-5719	123	9	)	)	PUNCT
ejpam-5719	123	10	=	=	SYM
ejpam-5719	123	11	0	0	PROPN
ejpam-5719	123	12	,	,	PUNCT
ejpam-5719	123	13	lim	lim	PROPN
ejpam-5719	123	14	n→+∞	n→+∞	VERB
ejpam-5719	123	15	4nf	4nf	NOUN
ejpam-5719	123	16	(	(	PUNCT
ejpam-5719	123	17	x	x	X
ejpam-5719	123	18	2n	2n	NUM
ejpam-5719	123	19	)	)	PUNCT
ejpam-5719	124	1	=	=	SYM
ejpam-5719	124	2	f	f	X
ejpam-5719	124	3	(	(	PUNCT
ejpam-5719	124	4	x	x	X
ejpam-5719	124	5	)	)	PUNCT
ejpam-5719	124	6	,	,	PUNCT
ejpam-5719	124	7	lim	lim	PROPN
ejpam-5719	124	8	n→+∞	n→+∞	VERB
ejpam-5719	124	9	4ng	4ng	NOUN
ejpam-5719	124	10	(	(	PUNCT
ejpam-5719	124	11	x	x	X
ejpam-5719	124	12	2n	2n	NUM
ejpam-5719	124	13	)	)	PUNCT
ejpam-5719	124	14	=	=	SYM
ejpam-5719	124	15	g(x	g(x	NOUN
ejpam-5719	124	16	)	)	PUNCT
ejpam-5719	124	17	for	for	ADP
ejpam-5719	124	18	all	all	DET
ejpam-5719	124	19	x	x	PROPN
ejpam-5719	124	20	∈	∈	PROPN
ejpam-5719	124	21	b.	b.	NOUN
ejpam-5719	124	22	next	next	ADV
ejpam-5719	124	23	,	,	PUNCT
ejpam-5719	124	24	d(f	d(f	PROPN
ejpam-5719	124	25	,	,	PUNCT
ejpam-5719	124	26	f	f	PROPN
ejpam-5719	124	27	)	)	PUNCT
ejpam-5719	124	28	≤	≤	NOUN
ejpam-5719	124	29	1	1	NUM
ejpam-5719	124	30	1−ld(f	1−ld(f	NUM
ejpam-5719	124	31	,	,	PUNCT
ejpam-5719	124	32	j	j	PROPN
ejpam-5719	124	33	f	f	X
ejpam-5719	124	34	)	)	PUNCT
ejpam-5719	124	35	and	and	CCONJ
ejpam-5719	124	36	d(g	d(g	PROPN
ejpam-5719	124	37	,	,	PUNCT
ejpam-5719	124	38	g	g	NOUN
ejpam-5719	124	39	)	)	PUNCT
ejpam-5719	124	40	≤	≤	NUM
ejpam-5719	124	41	1	1	NUM
ejpam-5719	124	42	1−ld(g	1−ld(g	NUM
ejpam-5719	124	43	,	,	PUNCT
ejpam-5719	124	44	j	j	PROPN
ejpam-5719	124	45	g	g	PROPN
ejpam-5719	124	46	)	)	PUNCT
ejpam-5719	124	47	which	which	PRON
ejpam-5719	124	48	imply	imply	VERB
ejpam-5719	124	49	∥f(x)−	∥f(x)−	PROPN
ejpam-5719	124	50	f	f	PROPN
ejpam-5719	124	51	(	(	PUNCT
ejpam-5719	124	52	x)∥	x)∥	SYM
ejpam-5719	124	53	≤	≤	NUM
ejpam-5719	124	54	2	2	NUM
ejpam-5719	125	1	+	+	NUM
ejpam-5719	125	2	l	l	NOUN
ejpam-5719	125	3	4(1−	4(1−	NUM
ejpam-5719	125	4	l	l	NOUN
ejpam-5719	125	5	)	)	PUNCT
ejpam-5719	125	6	∆(x	∆(x	PROPN
ejpam-5719	125	7	,	,	PUNCT
ejpam-5719	125	8	x	x	NOUN
ejpam-5719	125	9	)	)	PUNCT
ejpam-5719	125	10	,	,	PUNCT
ejpam-5719	125	11	∥g(x)−g(x)∥	∥g(x)−g(x)∥	VERB
ejpam-5719	125	12	≤	≤	NUM
ejpam-5719	125	13	2	2	NUM
ejpam-5719	125	14	+	+	NUM
ejpam-5719	125	15	l	l	NOUN
ejpam-5719	125	16	2(1−	2(1−	NUM
ejpam-5719	125	17	l	l	NOUN
ejpam-5719	125	18	)	)	PUNCT
ejpam-5719	125	19	∆(x	∆(x	PROPN
ejpam-5719	125	20	,	,	PUNCT
ejpam-5719	125	21	x	x	NOUN
ejpam-5719	125	22	)	)	PUNCT
ejpam-5719	125	23	for	for	ADP
ejpam-5719	125	24	all	all	DET
ejpam-5719	125	25	x	x	SYM
ejpam-5719	125	26	∈	∈	PROPN
ejpam-5719	125	27	b.	b.	NOUN
ejpam-5719	125	28	using	use	VERB
ejpam-5719	125	29	(	(	PUNCT
ejpam-5719	125	30	4	4	NUM
ejpam-5719	125	31	)	)	PUNCT
ejpam-5719	125	32	and	and	CCONJ
ejpam-5719	125	33	(	(	PUNCT
ejpam-5719	125	34	5	5	NUM
ejpam-5719	125	35	)	)	PUNCT
ejpam-5719	125	36	,	,	PUNCT
ejpam-5719	125	37	we	we	PRON
ejpam-5719	125	38	conclude	conclude	VERB
ejpam-5719	125	39	that	that	SCONJ
ejpam-5719	126	1	∥f	∥f	PROPN
ejpam-5719	126	2	(	(	PUNCT
ejpam-5719	126	3	x+	x+	PROPN
ejpam-5719	126	4	y	y	NOUN
ejpam-5719	126	5	)	)	PUNCT
ejpam-5719	127	1	+	+	CCONJ
ejpam-5719	127	2	f	f	X
ejpam-5719	127	3	(	(	PUNCT
ejpam-5719	127	4	x−	x−	PROPN
ejpam-5719	127	5	y)−g(x)−g(y)∥	y)−g(x)−g(y)∥	NOUN
ejpam-5719	127	6	=	=	PROPN
ejpam-5719	127	7	lim	lim	PROPN
ejpam-5719	127	8	n→+∞	n→+∞	VERB
ejpam-5719	127	9	4n	4n	PROPN
ejpam-5719	127	10	∥∥∥∥f	∥∥∥∥f	PUNCT
ejpam-5719	128	1	(	(	PUNCT
ejpam-5719	128	2	x+	x+	PROPN
ejpam-5719	128	3	y	y	PROPN
ejpam-5719	128	4	2n	2n	NUM
ejpam-5719	128	5	)	)	PUNCT
ejpam-5719	129	1	+	+	CCONJ
ejpam-5719	129	2	f	f	X
ejpam-5719	129	3	(	(	PUNCT
ejpam-5719	129	4	x−	x−	PROPN
ejpam-5719	129	5	y	y	PROPN
ejpam-5719	129	6	2n	2n	NUM
ejpam-5719	129	7	)	)	PUNCT
ejpam-5719	130	1	−	−	PROPN
ejpam-5719	130	2	g	g	PROPN
ejpam-5719	130	3	(	(	PUNCT
ejpam-5719	130	4	x	x	X
ejpam-5719	130	5	2n	2n	NUM
ejpam-5719	130	6	)	)	PUNCT
ejpam-5719	130	7	−	−	PROPN
ejpam-5719	130	8	g	g	PROPN
ejpam-5719	130	9	(	(	PUNCT
ejpam-5719	130	10	y	y	PROPN
ejpam-5719	130	11	2n	2n	NUM
ejpam-5719	130	12	)	)	PUNCT
ejpam-5719	130	13	∥∥∥∥	∥∥∥∥	NUM
ejpam-5719	130	14	≤	≤	NUM
ejpam-5719	130	15	lim	lim	PROPN
ejpam-5719	130	16	n→+∞	n→+∞	PROPN
ejpam-5719	130	17	4n∆	4n∆	PROPN
ejpam-5719	130	18	(	(	PUNCT
ejpam-5719	130	19	x	x	SYM
ejpam-5719	130	20	2n	2n	NUM
ejpam-5719	130	21	,	,	PUNCT
ejpam-5719	130	22	y	y	PROPN
ejpam-5719	130	23	2n	2n	NUM
ejpam-5719	130	24	)	)	PUNCT
ejpam-5719	130	25	≤	≤	PROPN
ejpam-5719	130	26	lim	lim	PROPN
ejpam-5719	130	27	n→+∞	n→+∞	PROPN
ejpam-5719	130	28	ln∆(x	ln∆(x	PROPN
ejpam-5719	130	29	,	,	PUNCT
ejpam-5719	130	30	y	y	NOUN
ejpam-5719	130	31	)	)	PUNCT
ejpam-5719	130	32	=	=	SYM
ejpam-5719	130	33	0	0	NUM
ejpam-5719	130	34	and	and	CCONJ
ejpam-5719	130	35	∥g	∥g	PROPN
ejpam-5719	130	36	(	(	PUNCT
ejpam-5719	130	37	x+	x+	PROPN
ejpam-5719	130	38	y	y	PROPN
ejpam-5719	130	39	2	2	NUM
ejpam-5719	130	40	)	)	PUNCT
ejpam-5719	131	1	+	+	ADP
ejpam-5719	131	2	g	g	PROPN
ejpam-5719	131	3	(	(	PUNCT
ejpam-5719	131	4	x−	x−	PROPN
ejpam-5719	131	5	y	y	PROPN
ejpam-5719	131	6	2	2	NUM
ejpam-5719	131	7	)	)	PUNCT
ejpam-5719	131	8	−	−	PROPN
ejpam-5719	131	9	f	f	X
ejpam-5719	131	10	(	(	PUNCT
ejpam-5719	131	11	x)−	x)−	PROPN
ejpam-5719	131	12	f	f	PROPN
ejpam-5719	131	13	(	(	PUNCT
ejpam-5719	131	14	y)∥	y)∥	X
ejpam-5719	131	15	=	=	SYM
ejpam-5719	131	16	lim	lim	PROPN
ejpam-5719	131	17	n→+∞	n→+∞	VERB
ejpam-5719	131	18	4n	4n	NOUN
ejpam-5719	131	19	∥∥∥∥g(x+	∥∥∥∥g(x+	VERB
ejpam-5719	131	20	y	y	PROPN
ejpam-5719	131	21	2	2	NUM
ejpam-5719	131	22	·	·	SYM
ejpam-5719	131	23	2n	2n	NUM
ejpam-5719	131	24	)	)	PUNCT
ejpam-5719	132	1	+	+	CCONJ
ejpam-5719	132	2	g	g	PROPN
ejpam-5719	132	3	(	(	PUNCT
ejpam-5719	132	4	x−	x−	PROPN
ejpam-5719	132	5	y	y	PROPN
ejpam-5719	132	6	2	2	NUM
ejpam-5719	132	7	·	·	SYM
ejpam-5719	132	8	2n	2n	NUM
ejpam-5719	132	9	)	)	PUNCT
ejpam-5719	133	1	−	−	PROPN
ejpam-5719	133	2	f	f	X
ejpam-5719	133	3	(	(	PUNCT
ejpam-5719	133	4	x	x	X
ejpam-5719	133	5	2n	2n	NUM
ejpam-5719	133	6	)	)	PUNCT
ejpam-5719	133	7	−	−	PROPN
ejpam-5719	134	1	f	f	X
ejpam-5719	134	2	(	(	PUNCT
ejpam-5719	134	3	y	y	PROPN
ejpam-5719	134	4	2n	2n	NUM
ejpam-5719	134	5	)	)	PUNCT
ejpam-5719	134	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-5719	134	7	≤	≤	NUM
ejpam-5719	135	1	lim	lim	PROPN
ejpam-5719	135	2	n→+∞	n→+∞	PROPN
ejpam-5719	135	3	4n∆	4n∆	PROPN
ejpam-5719	135	4	(	(	PUNCT
ejpam-5719	135	5	x	x	SYM
ejpam-5719	135	6	2n	2n	NUM
ejpam-5719	135	7	,	,	PUNCT
ejpam-5719	135	8	y	y	PROPN
ejpam-5719	135	9	2n	2n	NUM
ejpam-5719	135	10	)	)	PUNCT
ejpam-5719	135	11	≤	≤	PROPN
ejpam-5719	135	12	lim	lim	PROPN
ejpam-5719	135	13	n→+∞	n→+∞	PROPN
ejpam-5719	135	14	ln∆(x	ln∆(x	PROPN
ejpam-5719	135	15	,	,	PUNCT
ejpam-5719	135	16	y	y	NOUN
ejpam-5719	135	17	)	)	PUNCT
ejpam-5719	135	18	=	=	SYM
ejpam-5719	135	19	0	0	NUM
ejpam-5719	135	20	for	for	ADP
ejpam-5719	135	21	all	all	DET
ejpam-5719	135	22	x	x	NOUN
ejpam-5719	135	23	,	,	PUNCT
ejpam-5719	135	24	y	y	PROPN
ejpam-5719	135	25	∈	∈	PROPN
ejpam-5719	135	26	b	b	PROPN
ejpam-5719	135	27	,	,	PUNCT
ejpam-5719	135	28	since	since	SCONJ
ejpam-5719	135	29	l	l	NOUN
ejpam-5719	135	30	<	<	X
ejpam-5719	135	31	1	1	X
ejpam-5719	135	32	.	.	PUNCT
ejpam-5719	136	1	hence	hence	ADV
ejpam-5719	136	2	{	{	PUNCT
ejpam-5719	136	3	f	f	PROPN
ejpam-5719	136	4	(	(	PUNCT
ejpam-5719	136	5	x+	x+	PROPN
ejpam-5719	136	6	y	y	NOUN
ejpam-5719	136	7	)	)	PUNCT
ejpam-5719	137	1	+	+	CCONJ
ejpam-5719	137	2	f	f	X
ejpam-5719	137	3	(	(	PUNCT
ejpam-5719	137	4	x−	x−	PROPN
ejpam-5719	137	5	y	y	PROPN
ejpam-5719	137	6	)	)	PUNCT
ejpam-5719	137	7	=	=	SYM
ejpam-5719	137	8	g(x	g(x	NOUN
ejpam-5719	137	9	)	)	PUNCT
ejpam-5719	138	1	+	+	NOUN
ejpam-5719	138	2	g(y	g(y	X
ejpam-5719	138	3	)	)	PUNCT
ejpam-5719	138	4	,	,	PUNCT
ejpam-5719	138	5	g	g	PROPN
ejpam-5719	138	6	(	(	PUNCT
ejpam-5719	138	7	x+y	x+y	PROPN
ejpam-5719	138	8	2	2	NUM
ejpam-5719	138	9	)	)	PUNCT
ejpam-5719	138	10	+	+	ADP
ejpam-5719	138	11	g	g	NOUN
ejpam-5719	138	12	(	(	PUNCT
ejpam-5719	138	13	x−y	x−y	NOUN
ejpam-5719	138	14	2	2	NUM
ejpam-5719	138	15	)	)	PUNCT
ejpam-5719	138	16	=	=	SYM
ejpam-5719	139	1	f	f	X
ejpam-5719	139	2	(	(	PUNCT
ejpam-5719	139	3	x	x	X
ejpam-5719	139	4	)	)	PUNCT
ejpam-5719	140	1	+	+	NUM
ejpam-5719	140	2	f	f	X
ejpam-5719	140	3	(	(	PUNCT
ejpam-5719	140	4	y	y	NOUN
ejpam-5719	140	5	)	)	PUNCT
ejpam-5719	140	6	for	for	ADP
ejpam-5719	140	7	all	all	DET
ejpam-5719	140	8	x	x	NOUN
ejpam-5719	140	9	,	,	PUNCT
ejpam-5719	140	10	y	y	PROPN
ejpam-5719	140	11	∈	∈	PROPN
ejpam-5719	140	12	b.	b.	PROPN
ejpam-5719	140	13	therefore	therefore	ADV
ejpam-5719	140	14	by	by	ADP
ejpam-5719	140	15	lemma	lemma	PROPN
ejpam-5719	140	16	1	1	NUM
ejpam-5719	140	17	,	,	PUNCT
ejpam-5719	140	18	the	the	DET
ejpam-5719	140	19	mappings	mapping	NOUN
ejpam-5719	140	20	f	f	X
ejpam-5719	140	21	,	,	PUNCT
ejpam-5719	140	22	g	g	NOUN
ejpam-5719	140	23	:	:	PUNCT
ejpam-5719	140	24	b	b	X
ejpam-5719	140	25	→	→	SYM
ejpam-5719	140	26	b	b	NOUN
ejpam-5719	140	27	are	be	AUX
ejpam-5719	140	28	quadratic	quadratic	ADJ
ejpam-5719	140	29	.	.	PUNCT
ejpam-5719	141	1	corollary	corollary	ADJ
ejpam-5719	141	2	1	1	NUM
ejpam-5719	141	3	.	.	PUNCT
ejpam-5719	142	1	let	let	VERB
ejpam-5719	142	2	p	p	NOUN
ejpam-5719	142	3	and	and	CCONJ
ejpam-5719	142	4	q	q	NOUN
ejpam-5719	142	5	be	be	AUX
ejpam-5719	142	6	nonnegative	nonnegative	ADJ
ejpam-5719	142	7	real	real	ADJ
ejpam-5719	142	8	numbers	number	NOUN
ejpam-5719	142	9	with	with	ADP
ejpam-5719	142	10	p	p	NOUN
ejpam-5719	143	1	+	+	NOUN
ejpam-5719	143	2	q	q	ADJ
ejpam-5719	143	3	>	>	X
ejpam-5719	143	4	4	4	NUM
ejpam-5719	143	5	and	and	CCONJ
ejpam-5719	143	6	f	f	NOUN
ejpam-5719	143	7	,	,	PUNCT
ejpam-5719	143	8	g	g	NOUN
ejpam-5719	143	9	:	:	PUNCT
ejpam-5719	143	10	b	b	X
ejpam-5719	143	11	→	→	SYM
ejpam-5719	143	12	b	b	X
ejpam-5719	143	13	be	be	AUX
ejpam-5719	143	14	mappings	mapping	NOUN
ejpam-5719	143	15	satisfying	satisfy	VERB
ejpam-5719	143	16	g(0	g(0	NOUN
ejpam-5719	143	17	)	)	PUNCT
ejpam-5719	143	18	=	=	SYM
ejpam-5719	144	1	0	0	NUM
ejpam-5719	144	2	and	and	NOUN
ejpam-5719	144	3	∥f(x+	∥f(x+	PROPN
ejpam-5719	144	4	y	y	PROPN
ejpam-5719	144	5	)	)	PUNCT
ejpam-5719	145	1	+	+	CCONJ
ejpam-5719	145	2	f(x−	f(x−	ADP
ejpam-5719	145	3	y)−	y)−	PROPN
ejpam-5719	145	4	g(x)−	g(x)−	PROPN
ejpam-5719	145	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	145	6	≤	≤	PUNCT
ejpam-5719	145	7	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	145	8	,	,	PUNCT
ejpam-5719	145	9	∥g	∥g	PROPN
ejpam-5719	145	10	(	(	PUNCT
ejpam-5719	145	11	x+y	x+y	NUM
ejpam-5719	145	12	2	2	NUM
ejpam-5719	145	13	)	)	PUNCT
ejpam-5719	146	1	+	+	CCONJ
ejpam-5719	146	2	g	g	PROPN
ejpam-5719	146	3	(	(	PUNCT
ejpam-5719	146	4	x−y	x−y	PROPN
ejpam-5719	146	5	2	2	NUM
ejpam-5719	146	6	)	)	PUNCT
ejpam-5719	146	7	−	−	PROPN
ejpam-5719	147	1	f(x)−	f(x)−	PROPN
ejpam-5719	147	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	147	3	≤	≤	NOUN
ejpam-5719	147	4	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	147	5	for	for	ADP
ejpam-5719	147	6	all	all	DET
ejpam-5719	147	7	x	x	NOUN
ejpam-5719	147	8	,	,	PUNCT
ejpam-5719	147	9	y	y	PROPN
ejpam-5719	147	10	∈	∈	PROPN
ejpam-5719	147	11	b.	b.	PROPN
ejpam-5719	147	12	then	then	ADV
ejpam-5719	147	13	there	there	PRON
ejpam-5719	147	14	exist	exist	VERB
ejpam-5719	147	15	unique	unique	ADJ
ejpam-5719	147	16	quadratic	quadratic	ADJ
ejpam-5719	147	17	mappings	mapping	NOUN
ejpam-5719	147	18	f	f	X
ejpam-5719	147	19	,	,	PUNCT
ejpam-5719	147	20	g	g	NOUN
ejpam-5719	147	21	:	:	PUNCT
ejpam-5719	147	22	b	b	X
ejpam-5719	147	23	→	→	SYM
ejpam-5719	147	24	b	b	X
ejpam-5719	147	25	such	such	ADJ
ejpam-5719	147	26	that	that	SCONJ
ejpam-5719	147	27	∥f	∥f	PROPN
ejpam-5719	147	28	(	(	PUNCT
ejpam-5719	147	29	x)−	x)−	PROPN
ejpam-5719	147	30	f(x)∥	f(x)∥	VERB
ejpam-5719	147	31	≤	≤	NOUN
ejpam-5719	147	32	2p+q	2p+q	NUM
ejpam-5719	148	1	+	+	CCONJ
ejpam-5719	148	2	8	8	NUM
ejpam-5719	148	3	2(2p+q	2(2p+q	NUM
ejpam-5719	148	4	−	−	NOUN
ejpam-5719	148	5	16	16	NUM
ejpam-5719	148	6	)	)	PUNCT
ejpam-5719	148	7	∥x∥p+q	∥x∥p+q	PROPN
ejpam-5719	148	8	,	,	PUNCT
ejpam-5719	148	9	∥g(x)−	∥g(x)−	X
ejpam-5719	148	10	g(x)∥	g(x)∥	VERB
ejpam-5719	148	11	≤	≤	NOUN
ejpam-5719	148	12	2p+q	2p+q	NUM
ejpam-5719	149	1	+	+	CCONJ
ejpam-5719	149	2	8	8	NUM
ejpam-5719	149	3	2p+q	2p+q	NUM
ejpam-5719	149	4	−	−	NOUN
ejpam-5719	149	5	16	16	NUM
ejpam-5719	149	6	∥x∥p+q	∥x∥p+q	NOUN
ejpam-5719	149	7	for	for	ADP
ejpam-5719	149	8	all	all	DET
ejpam-5719	149	9	x	x	SYM
ejpam-5719	149	10	∈	∈	PROPN
ejpam-5719	149	11	b.	b.	PROPN
ejpam-5719	149	12	c.	c.	PROPN
ejpam-5719	149	13	park	park	PROPN
ejpam-5719	149	14	,	,	PUNCT
ejpam-5719	149	15	s.	s.	PROPN
ejpam-5719	149	16	donganont	donganont	PROPN
ejpam-5719	149	17	,	,	PUNCT
ejpam-5719	149	18	s.	s.	PROPN
ejpam-5719	149	19	w.	w.	PROPN
ejpam-5719	149	20	min	min	PROPN
ejpam-5719	149	21	/	/	SYM
ejpam-5719	149	22	eur	eur	PROPN
ejpam-5719	149	23	.	.	PUNCT
ejpam-5719	150	1	j.	j.	PROPN
ejpam-5719	150	2	pure	pure	PROPN
ejpam-5719	150	3	appl	appl	PROPN
ejpam-5719	150	4	.	.	PROPN
ejpam-5719	150	5	math	math	PROPN
ejpam-5719	150	6	,	,	PUNCT
ejpam-5719	150	7	18	18	NUM
ejpam-5719	150	8	(	(	PUNCT
ejpam-5719	150	9	1	1	NUM
ejpam-5719	150	10	)	)	PUNCT
ejpam-5719	150	11	(	(	PUNCT
ejpam-5719	150	12	2025	2025	NUM
ejpam-5719	150	13	)	)	PUNCT
ejpam-5719	150	14	,	,	PUNCT
ejpam-5719	150	15	5719	5719	NUM
ejpam-5719	150	16	7	7	NUM
ejpam-5719	150	17	of	of	ADP
ejpam-5719	150	18	10	10	NUM
ejpam-5719	150	19	proof	proof	NOUN
ejpam-5719	150	20	.	.	PUNCT
ejpam-5719	151	1	the	the	DET
ejpam-5719	151	2	proof	proof	NOUN
ejpam-5719	151	3	follows	follow	VERB
ejpam-5719	151	4	from	from	ADP
ejpam-5719	151	5	theorem	theorem	NOUN
ejpam-5719	151	6	2	2	NUM
ejpam-5719	151	7	by	by	ADP
ejpam-5719	151	8	taking	take	VERB
ejpam-5719	151	9	l	l	NOUN
ejpam-5719	151	10	=	=	NUM
ejpam-5719	151	11	24	24	NUM
ejpam-5719	151	12	2p+q	2p+q	NUM
ejpam-5719	151	13	and	and	CCONJ
ejpam-5719	151	14	∆(x	∆(x	PROPN
ejpam-5719	151	15	,	,	PUNCT
ejpam-5719	151	16	y	y	NOUN
ejpam-5719	151	17	)	)	PUNCT
ejpam-5719	151	18	=	=	PUNCT
ejpam-5719	152	1	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	152	2	for	for	ADP
ejpam-5719	152	3	all	all	DET
ejpam-5719	152	4	x	x	NOUN
ejpam-5719	152	5	,	,	PUNCT
ejpam-5719	152	6	y	y	PROPN
ejpam-5719	152	7	∈	∈	PROPN
ejpam-5719	152	8	b.	b.	PROPN
ejpam-5719	152	9	corollary	corollary	NOUN
ejpam-5719	152	10	2	2	X
ejpam-5719	152	11	.	.	PUNCT
ejpam-5719	153	1	let	let	VERB
ejpam-5719	153	2	p	p	NOUN
ejpam-5719	153	3	and	and	CCONJ
ejpam-5719	153	4	θ	θ	PROPN
ejpam-5719	153	5	be	be	AUX
ejpam-5719	153	6	nonnegative	nonnegative	ADJ
ejpam-5719	153	7	real	real	ADJ
ejpam-5719	153	8	numbers	number	NOUN
ejpam-5719	153	9	with	with	ADP
ejpam-5719	153	10	p	p	PROPN
ejpam-5719	153	11	>	>	X
ejpam-5719	153	12	4	4	NUM
ejpam-5719	153	13	and	and	CCONJ
ejpam-5719	153	14	f	f	NOUN
ejpam-5719	153	15	,	,	PUNCT
ejpam-5719	153	16	g	g	NOUN
ejpam-5719	153	17	:	:	PUNCT
ejpam-5719	153	18	b	b	X
ejpam-5719	153	19	→	→	SYM
ejpam-5719	153	20	b	b	X
ejpam-5719	153	21	be	be	AUX
ejpam-5719	153	22	mappings	mapping	NOUN
ejpam-5719	153	23	satisfying	satisfy	VERB
ejpam-5719	153	24	g(0	g(0	NOUN
ejpam-5719	153	25	)	)	PUNCT
ejpam-5719	153	26	=	=	SYM
ejpam-5719	154	1	0	0	NUM
ejpam-5719	154	2	and	and	NOUN
ejpam-5719	154	3	∥f(x+	∥f(x+	PROPN
ejpam-5719	154	4	y	y	PROPN
ejpam-5719	154	5	)	)	PUNCT
ejpam-5719	155	1	+	+	CCONJ
ejpam-5719	155	2	f(x−	f(x−	AUX
ejpam-5719	155	3	y)−	y)−	PROPN
ejpam-5719	155	4	g(x)−	g(x)−	NOUN
ejpam-5719	155	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	155	6	≤	≤	PUNCT
ejpam-5719	155	7	θ(∥x∥p	θ(∥x∥p	VERB
ejpam-5719	155	8	+	+	CCONJ
ejpam-5719	155	9	∥y∥p	∥y∥p	NOUN
ejpam-5719	155	10	)	)	PUNCT
ejpam-5719	155	11	,	,	PUNCT
ejpam-5719	155	12	∥g	∥g	PROPN
ejpam-5719	155	13	(	(	PUNCT
ejpam-5719	155	14	x+y	x+y	NUM
ejpam-5719	155	15	2	2	NUM
ejpam-5719	155	16	)	)	PUNCT
ejpam-5719	156	1	+	+	CCONJ
ejpam-5719	156	2	g	g	PROPN
ejpam-5719	156	3	(	(	PUNCT
ejpam-5719	156	4	x−y	x−y	PROPN
ejpam-5719	156	5	2	2	NUM
ejpam-5719	156	6	)	)	PUNCT
ejpam-5719	156	7	−	−	PROPN
ejpam-5719	157	1	f(x)−	f(x)−	PROPN
ejpam-5719	157	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	157	3	≤	≤	PUNCT
ejpam-5719	157	4	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	157	5	+	+	CCONJ
ejpam-5719	157	6	∥y∥p	∥y∥p	NOUN
ejpam-5719	157	7	)	)	PUNCT
ejpam-5719	157	8	for	for	ADP
ejpam-5719	157	9	all	all	DET
ejpam-5719	157	10	x	x	NOUN
ejpam-5719	157	11	,	,	PUNCT
ejpam-5719	157	12	y	y	PROPN
ejpam-5719	157	13	∈	∈	PROPN
ejpam-5719	157	14	b.	b.	PROPN
ejpam-5719	158	1	then	then	ADV
ejpam-5719	158	2	there	there	PRON
ejpam-5719	158	3	exist	exist	VERB
ejpam-5719	158	4	unique	unique	ADJ
ejpam-5719	158	5	quadratic	quadratic	ADJ
ejpam-5719	158	6	mappings	mapping	NOUN
ejpam-5719	158	7	f	f	X
ejpam-5719	158	8	,	,	PUNCT
ejpam-5719	158	9	g	g	NOUN
ejpam-5719	158	10	:	:	PUNCT
ejpam-5719	158	11	b	b	X
ejpam-5719	158	12	→	→	SYM
ejpam-5719	158	13	b	b	X
ejpam-5719	158	14	such	such	ADJ
ejpam-5719	158	15	that	that	SCONJ
ejpam-5719	158	16	∥f	∥f	PROPN
ejpam-5719	158	17	(	(	PUNCT
ejpam-5719	158	18	x)−	x)−	PROPN
ejpam-5719	158	19	f(x)∥	f(x)∥	VERB
ejpam-5719	158	20	≤	≤	NUM
ejpam-5719	158	21	2p	2p	NUM
ejpam-5719	158	22	+	+	CCONJ
ejpam-5719	158	23	2	2	NUM
ejpam-5719	158	24	2p	2p	NUM
ejpam-5719	158	25	−	−	NOUN
ejpam-5719	158	26	4	4	NUM
ejpam-5719	158	27	θ∥x∥p	θ∥x∥p	NOUN
ejpam-5719	158	28	,	,	PUNCT
ejpam-5719	158	29	∥g(x)−	∥g(x)−	X
ejpam-5719	158	30	g(x)∥	g(x)∥	VERB
ejpam-5719	158	31	≤	≤	NUM
ejpam-5719	158	32	2(2p	2(2p	NUM
ejpam-5719	158	33	+	+	CCONJ
ejpam-5719	158	34	2	2	NUM
ejpam-5719	158	35	)	)	PUNCT
ejpam-5719	158	36	2p	2p	NUM
ejpam-5719	158	37	−	−	NOUN
ejpam-5719	158	38	4	4	NUM
ejpam-5719	158	39	θ∥x∥p	θ∥x∥p	NOUN
ejpam-5719	158	40	for	for	ADP
ejpam-5719	158	41	all	all	DET
ejpam-5719	158	42	x	x	SYM
ejpam-5719	158	43	∈	∈	PROPN
ejpam-5719	158	44	b.	b.	NOUN
ejpam-5719	158	45	proof	proof	NOUN
ejpam-5719	158	46	.	.	PUNCT
ejpam-5719	159	1	the	the	DET
ejpam-5719	159	2	proof	proof	NOUN
ejpam-5719	159	3	follows	follow	VERB
ejpam-5719	159	4	from	from	ADP
ejpam-5719	159	5	theorem	theorem	NOUN
ejpam-5719	159	6	2	2	NUM
ejpam-5719	159	7	by	by	ADP
ejpam-5719	159	8	taking	take	VERB
ejpam-5719	159	9	l	l	NOUN
ejpam-5719	159	10	=	=	NUM
ejpam-5719	159	11	4	4	NUM
ejpam-5719	159	12	2p	2p	NUM
ejpam-5719	159	13	and	and	CCONJ
ejpam-5719	159	14	∆(x	∆(x	PROPN
ejpam-5719	159	15	,	,	PUNCT
ejpam-5719	159	16	y	y	NOUN
ejpam-5719	159	17	)	)	PUNCT
ejpam-5719	159	18	=	=	VERB
ejpam-5719	160	1	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	160	2	+	+	CCONJ
ejpam-5719	160	3	∥y∥p	∥y∥p	NOUN
ejpam-5719	160	4	)	)	PUNCT
ejpam-5719	160	5	for	for	ADP
ejpam-5719	160	6	all	all	DET
ejpam-5719	160	7	x	x	NOUN
ejpam-5719	160	8	,	,	PUNCT
ejpam-5719	160	9	y	y	PROPN
ejpam-5719	160	10	∈	∈	PROPN
ejpam-5719	160	11	b.	b.	PROPN
ejpam-5719	161	1	3	3	X
ejpam-5719	161	2	.	.	PUNCT
ejpam-5719	161	3	stability	stability	NOUN
ejpam-5719	161	4	of	of	ADP
ejpam-5719	161	5	quadratic	quadratic	ADJ
ejpam-5719	161	6	f	f	PROPN
ejpam-5719	161	7	-hom	-hom	X
ejpam-5719	161	8	-	-	PUNCT
ejpam-5719	161	9	ders	der	NOUN
ejpam-5719	161	10	in	in	ADP
ejpam-5719	161	11	banach	banach	NOUN
ejpam-5719	161	12	algebras	algebra	NOUN
ejpam-5719	161	13	in	in	ADP
ejpam-5719	161	14	this	this	DET
ejpam-5719	161	15	section	section	NOUN
ejpam-5719	161	16	,	,	PUNCT
ejpam-5719	161	17	by	by	ADP
ejpam-5719	161	18	using	use	VERB
ejpam-5719	161	19	the	the	DET
ejpam-5719	161	20	fixed	fix	VERB
ejpam-5719	161	21	point	point	NOUN
ejpam-5719	161	22	technique	technique	NOUN
ejpam-5719	161	23	,	,	PUNCT
ejpam-5719	161	24	we	we	PRON
ejpam-5719	161	25	prove	prove	VERB
ejpam-5719	161	26	the	the	DET
ejpam-5719	161	27	hyers	hyers	PROPN
ejpam-5719	161	28	-	-	PUNCT
ejpam-5719	161	29	ulam	ulam	ADJ
ejpam-5719	161	30	stability	stability	NOUN
ejpam-5719	161	31	of	of	ADP
ejpam-5719	161	32	quadratic	quadratic	ADJ
ejpam-5719	161	33	f	f	PROPN
ejpam-5719	161	34	-hom	-hom	X
ejpam-5719	161	35	-	-	PUNCT
ejpam-5719	161	36	ders	der	NOUN
ejpam-5719	161	37	in	in	ADP
ejpam-5719	161	38	complex	complex	ADJ
ejpam-5719	161	39	banach	banach	NOUN
ejpam-5719	161	40	algebras	algebra	NOUN
ejpam-5719	161	41	.	.	PUNCT
ejpam-5719	162	1	theorem	theorem	NOUN
ejpam-5719	162	2	3	3	X
ejpam-5719	162	3	.	.	PUNCT
ejpam-5719	162	4	suppose	suppose	VERB
ejpam-5719	162	5	that	that	SCONJ
ejpam-5719	162	6	∆	∆	PROPN
ejpam-5719	162	7	:	:	PUNCT
ejpam-5719	162	8	b2	b2	NOUN
ejpam-5719	162	9	→	→	SYM
ejpam-5719	162	10	[	[	X
ejpam-5719	162	11	0,∞	0,∞	NUM
ejpam-5719	162	12	)	)	PUNCT
ejpam-5719	162	13	is	be	AUX
ejpam-5719	162	14	a	a	DET
ejpam-5719	162	15	function	function	NOUN
ejpam-5719	162	16	such	such	ADJ
ejpam-5719	162	17	that	that	SCONJ
ejpam-5719	162	18	there	there	PRON
ejpam-5719	162	19	exists	exist	VERB
ejpam-5719	162	20	an	an	DET
ejpam-5719	162	21	l	l	NOUN
ejpam-5719	162	22	<	<	X
ejpam-5719	162	23	1	1	NUM
ejpam-5719	162	24	with	with	ADP
ejpam-5719	162	25	∆(x	∆(x	PROPN
ejpam-5719	162	26	,	,	PUNCT
ejpam-5719	162	27	y	y	NOUN
ejpam-5719	162	28	)	)	PUNCT
ejpam-5719	162	29	≤	≤	NUM
ejpam-5719	162	30	l	l	NOUN
ejpam-5719	162	31	16	16	NUM
ejpam-5719	162	32	∆(2x	∆(2x	NUM
ejpam-5719	162	33	,	,	PUNCT
ejpam-5719	162	34	2y	2y	NUM
ejpam-5719	162	35	)	)	PUNCT
ejpam-5719	162	36	(	(	PUNCT
ejpam-5719	162	37	9	9	X
ejpam-5719	162	38	)	)	PUNCT
ejpam-5719	162	39	for	for	ADP
ejpam-5719	162	40	all	all	DET
ejpam-5719	162	41	x	x	NOUN
ejpam-5719	162	42	,	,	PUNCT
ejpam-5719	162	43	y	y	PROPN
ejpam-5719	162	44	∈	∈	PROPN
ejpam-5719	162	45	b.	b.	PROPN
ejpam-5719	162	46	let	let	VERB
ejpam-5719	162	47	f	f	X
ejpam-5719	162	48	,	,	PUNCT
ejpam-5719	162	49	g	g	NOUN
ejpam-5719	162	50	:	:	PUNCT
ejpam-5719	162	51	b	b	X
ejpam-5719	162	52	→	→	SYM
ejpam-5719	162	53	b	b	X
ejpam-5719	162	54	be	be	AUX
ejpam-5719	162	55	mappings	mapping	NOUN
ejpam-5719	162	56	satisfying	satisfy	VERB
ejpam-5719	162	57	g(0	g(0	NOUN
ejpam-5719	162	58	)	)	PUNCT
ejpam-5719	162	59	=	=	SYM
ejpam-5719	162	60	0	0	PUNCT
ejpam-5719	163	1	and	and	CCONJ
ejpam-5719	163	2	{	{	PUNCT
ejpam-5719	163	3	∥f(x+	∥f(x+	VERB
ejpam-5719	163	4	y	y	NOUN
ejpam-5719	163	5	)	)	PUNCT
ejpam-5719	164	1	+	+	CCONJ
ejpam-5719	164	2	f(x−	f(x−	ADP
ejpam-5719	164	3	y)−	y)−	PROPN
ejpam-5719	164	4	g(x)−	g(x)−	PROPN
ejpam-5719	164	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	164	6	≤	≤	PUNCT
ejpam-5719	164	7	∆(x	∆(x	PROPN
ejpam-5719	164	8	,	,	PUNCT
ejpam-5719	164	9	y	y	NOUN
ejpam-5719	164	10	)	)	PUNCT
ejpam-5719	164	11	,	,	PUNCT
ejpam-5719	164	12	∥g	∥g	PROPN
ejpam-5719	164	13	(	(	PUNCT
ejpam-5719	164	14	x+y	x+y	NUM
ejpam-5719	164	15	2	2	NUM
ejpam-5719	164	16	)	)	PUNCT
ejpam-5719	165	1	+	+	CCONJ
ejpam-5719	165	2	g	g	PROPN
ejpam-5719	165	3	(	(	PUNCT
ejpam-5719	165	4	x−y	x−y	PROPN
ejpam-5719	165	5	2	2	NUM
ejpam-5719	165	6	)	)	PUNCT
ejpam-5719	165	7	−	−	PROPN
ejpam-5719	166	1	f(x)−	f(x)−	PROPN
ejpam-5719	166	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	166	3	≤	≤	PUNCT
ejpam-5719	166	4	∆(x	∆(x	PROPN
ejpam-5719	166	5	,	,	PUNCT
ejpam-5719	166	6	y	y	NOUN
ejpam-5719	166	7	)	)	PUNCT
ejpam-5719	166	8	(	(	PUNCT
ejpam-5719	166	9	10	10	NUM
ejpam-5719	166	10	)	)	PUNCT
ejpam-5719	166	11	and	and	CCONJ
ejpam-5719	166	12	∥g(x)g(y)−	∥g(x)g(y)−	ADV
ejpam-5719	166	13	f(x)g(y)−	f(x)g(y)−	VERB
ejpam-5719	166	14	g(x)f(y)∥	g(x)f(y)∥	PROPN
ejpam-5719	166	15	≤	≤	PROPN
ejpam-5719	166	16	∆(x	∆(x	PROPN
ejpam-5719	166	17	,	,	PUNCT
ejpam-5719	166	18	y	y	NOUN
ejpam-5719	166	19	)	)	PUNCT
ejpam-5719	166	20	(	(	PUNCT
ejpam-5719	166	21	11	11	NUM
ejpam-5719	166	22	)	)	PUNCT
ejpam-5719	166	23	for	for	ADP
ejpam-5719	166	24	all	all	DET
ejpam-5719	166	25	x	x	NOUN
ejpam-5719	166	26	,	,	PUNCT
ejpam-5719	166	27	y	y	PROPN
ejpam-5719	166	28	∈	∈	PROPN
ejpam-5719	166	29	b.	b.	PROPN
ejpam-5719	166	30	then	then	ADV
ejpam-5719	166	31	there	there	PRON
ejpam-5719	166	32	exist	exist	VERB
ejpam-5719	166	33	unique	unique	ADJ
ejpam-5719	166	34	quadratic	quadratic	ADJ
ejpam-5719	166	35	mappings	mapping	NOUN
ejpam-5719	167	1	f	f	X
ejpam-5719	167	2	,	,	PUNCT
ejpam-5719	167	3	g	g	NOUN
ejpam-5719	167	4	:	:	PUNCT
ejpam-5719	167	5	b	b	X
ejpam-5719	167	6	→	→	SYM
ejpam-5719	167	7	b	b	X
ejpam-5719	167	8	satisfying	satisfying	ADJ
ejpam-5719	167	9	(	(	PUNCT
ejpam-5719	167	10	6	6	NUM
ejpam-5719	167	11	)	)	PUNCT
ejpam-5719	167	12	and	and	CCONJ
ejpam-5719	167	13	(	(	PUNCT
ejpam-5719	167	14	7	7	X
ejpam-5719	167	15	)	)	PUNCT
ejpam-5719	167	16	and	and	CCONJ
ejpam-5719	167	17	g	g	PROPN
ejpam-5719	167	18	is	be	AUX
ejpam-5719	167	19	a	a	DET
ejpam-5719	167	20	quadratic	quadratic	ADJ
ejpam-5719	167	21	f	f	NOUN
ejpam-5719	167	22	-hom	-hom	X
ejpam-5719	167	23	-	-	PUNCT
ejpam-5719	167	24	der	der	NOUN
ejpam-5719	167	25	.	.	PUNCT
ejpam-5719	168	1	c.	c.	PROPN
ejpam-5719	168	2	park	park	PROPN
ejpam-5719	168	3	,	,	PUNCT
ejpam-5719	168	4	s.	s.	PROPN
ejpam-5719	168	5	donganont	donganont	PROPN
ejpam-5719	168	6	,	,	PUNCT
ejpam-5719	168	7	s.	s.	PROPN
ejpam-5719	168	8	w.	w.	PROPN
ejpam-5719	168	9	min	min	PROPN
ejpam-5719	168	10	/	/	SYM
ejpam-5719	168	11	eur	eur	PROPN
ejpam-5719	168	12	.	.	PUNCT
ejpam-5719	169	1	j.	j.	PROPN
ejpam-5719	169	2	pure	pure	PROPN
ejpam-5719	169	3	appl	appl	PROPN
ejpam-5719	169	4	.	.	PROPN
ejpam-5719	169	5	math	math	PROPN
ejpam-5719	169	6	,	,	PUNCT
ejpam-5719	169	7	18	18	NUM
ejpam-5719	169	8	(	(	PUNCT
ejpam-5719	169	9	1	1	NUM
ejpam-5719	169	10	)	)	PUNCT
ejpam-5719	169	11	(	(	PUNCT
ejpam-5719	169	12	2025	2025	NUM
ejpam-5719	169	13	)	)	PUNCT
ejpam-5719	169	14	,	,	PUNCT
ejpam-5719	169	15	5719	5719	NUM
ejpam-5719	169	16	8	8	NUM
ejpam-5719	169	17	of	of	ADP
ejpam-5719	169	18	10	10	NUM
ejpam-5719	169	19	proof	proof	NOUN
ejpam-5719	169	20	.	.	PUNCT
ejpam-5719	170	1	since	since	SCONJ
ejpam-5719	170	2	∆(x	∆(x	PROPN
ejpam-5719	170	3	,	,	PUNCT
ejpam-5719	170	4	y	y	NOUN
ejpam-5719	170	5	)	)	PUNCT
ejpam-5719	170	6	≤	≤	NUM
ejpam-5719	170	7	l	l	NOUN
ejpam-5719	170	8	16	16	NUM
ejpam-5719	170	9	∆(2x	∆(2x	NUM
ejpam-5719	170	10	,	,	PUNCT
ejpam-5719	170	11	2y	2y	NUM
ejpam-5719	170	12	)	)	PUNCT
ejpam-5719	170	13	≤	≤	NUM
ejpam-5719	170	14	l	l	NOUN
ejpam-5719	170	15	4	4	NUM
ejpam-5719	170	16	∆(2x	∆(2x	NUM
ejpam-5719	170	17	,	,	PUNCT
ejpam-5719	170	18	2y	2y	NUM
ejpam-5719	170	19	)	)	PUNCT
ejpam-5719	170	20	for	for	ADP
ejpam-5719	170	21	all	all	DET
ejpam-5719	170	22	x	x	NOUN
ejpam-5719	170	23	,	,	PUNCT
ejpam-5719	170	24	y	y	PROPN
ejpam-5719	170	25	∈	∈	PROPN
ejpam-5719	170	26	b	b	PROPN
ejpam-5719	170	27	,	,	PUNCT
ejpam-5719	170	28	by	by	ADP
ejpam-5719	170	29	theorem	theorem	NOUN
ejpam-5719	170	30	2	2	NUM
ejpam-5719	170	31	,	,	PUNCT
ejpam-5719	170	32	there	there	PRON
ejpam-5719	170	33	exist	exist	VERB
ejpam-5719	170	34	unique	unique	ADJ
ejpam-5719	170	35	mappings	mapping	NOUN
ejpam-5719	171	1	f	f	NOUN
ejpam-5719	171	2	,	,	PUNCT
ejpam-5719	171	3	g	g	NOUN
ejpam-5719	171	4	:	:	PUNCT
ejpam-5719	171	5	b	b	X
ejpam-5719	171	6	→	→	SYM
ejpam-5719	171	7	b	b	X
ejpam-5719	171	8	satisfying	satisfying	ADJ
ejpam-5719	171	9	(	(	PUNCT
ejpam-5719	171	10	6	6	NUM
ejpam-5719	171	11	)	)	PUNCT
ejpam-5719	171	12	and	and	CCONJ
ejpam-5719	171	13	(	(	PUNCT
ejpam-5719	171	14	7	7	X
ejpam-5719	171	15	)	)	PUNCT
ejpam-5719	171	16	which	which	PRON
ejpam-5719	171	17	are	be	AUX
ejpam-5719	171	18	given	give	VERB
ejpam-5719	171	19	by	by	ADP
ejpam-5719	171	20	lim	lim	PROPN
ejpam-5719	171	21	n→+∞	n→+∞	PROPN
ejpam-5719	171	22	4nf	4nf	NOUN
ejpam-5719	171	23	(	(	PUNCT
ejpam-5719	171	24	x	x	X
ejpam-5719	171	25	2n	2n	NUM
ejpam-5719	171	26	)	)	PUNCT
ejpam-5719	172	1	=	=	SYM
ejpam-5719	172	2	f	f	X
ejpam-5719	172	3	(	(	PUNCT
ejpam-5719	172	4	x	x	X
ejpam-5719	172	5	)	)	PUNCT
ejpam-5719	172	6	,	,	PUNCT
ejpam-5719	172	7	lim	lim	PROPN
ejpam-5719	172	8	n→+∞	n→+∞	VERB
ejpam-5719	172	9	4ng	4ng	NOUN
ejpam-5719	172	10	(	(	PUNCT
ejpam-5719	172	11	x	x	X
ejpam-5719	172	12	2n	2n	NUM
ejpam-5719	172	13	)	)	PUNCT
ejpam-5719	172	14	=	=	SYM
ejpam-5719	172	15	g(x	g(x	NOUN
ejpam-5719	172	16	)	)	PUNCT
ejpam-5719	172	17	for	for	ADP
ejpam-5719	172	18	all	all	DET
ejpam-5719	172	19	x	x	SYM
ejpam-5719	172	20	∈	∈	PROPN
ejpam-5719	172	21	b.	b.	NOUN
ejpam-5719	172	22	it	it	PRON
ejpam-5719	172	23	follows	follow	VERB
ejpam-5719	172	24	from	from	ADP
ejpam-5719	172	25	(	(	PUNCT
ejpam-5719	172	26	11	11	NUM
ejpam-5719	172	27	)	)	PUNCT
ejpam-5719	173	1	that	that	SCONJ
ejpam-5719	173	2	∥g(x)g(y)−	∥g(x)g(y)−	ADV
ejpam-5719	173	3	f	f	X
ejpam-5719	173	4	(	(	PUNCT
ejpam-5719	173	5	x)g(y)−g(x)f	x)g(y)−g(x)f	X
ejpam-5719	173	6	(	(	PUNCT
ejpam-5719	173	7	y)∥	y)∥	X
ejpam-5719	173	8	=	=	SYM
ejpam-5719	173	9	lim	lim	PROPN
ejpam-5719	173	10	n→+∞	n→+∞	PROPN
ejpam-5719	173	11	16n	16n	NUM
ejpam-5719	173	12	∥∥∥g	∥∥∥g	PROPN
ejpam-5719	173	13	(	(	PUNCT
ejpam-5719	173	14	x	x	X
ejpam-5719	173	15	2n	2n	NUM
ejpam-5719	173	16	)	)	PUNCT
ejpam-5719	173	17	g	g	PROPN
ejpam-5719	173	18	(	(	PUNCT
ejpam-5719	173	19	y	y	PROPN
ejpam-5719	173	20	2n	2n	NUM
ejpam-5719	173	21	)	)	PUNCT
ejpam-5719	174	1	−	−	PROPN
ejpam-5719	174	2	f	f	X
ejpam-5719	174	3	(	(	PUNCT
ejpam-5719	174	4	x	x	X
ejpam-5719	174	5	2n	2n	NUM
ejpam-5719	174	6	)	)	PUNCT
ejpam-5719	174	7	g	g	PROPN
ejpam-5719	174	8	(	(	PUNCT
ejpam-5719	174	9	y	y	PROPN
ejpam-5719	174	10	2n	2n	NUM
ejpam-5719	174	11	)	)	PUNCT
ejpam-5719	175	1	−	−	PROPN
ejpam-5719	175	2	g	g	PROPN
ejpam-5719	175	3	(	(	PUNCT
ejpam-5719	175	4	x	x	X
ejpam-5719	175	5	2n	2n	NUM
ejpam-5719	175	6	)	)	PUNCT
ejpam-5719	175	7	f	f	PROPN
ejpam-5719	175	8	(	(	PUNCT
ejpam-5719	175	9	y	y	PROPN
ejpam-5719	175	10	2n	2n	NUM
ejpam-5719	175	11	)	)	PUNCT
ejpam-5719	175	12	∥∥∥	∥∥∥	PROPN
ejpam-5719	175	13	≤	≤	PROPN
ejpam-5719	175	14	lim	lim	PROPN
ejpam-5719	175	15	n→+∞	n→+∞	VERB
ejpam-5719	175	16	16n∆	16n∆	NUM
ejpam-5719	175	17	(	(	PUNCT
ejpam-5719	175	18	x	x	X
ejpam-5719	175	19	2n	2n	NUM
ejpam-5719	175	20	,	,	PUNCT
ejpam-5719	175	21	y	y	PROPN
ejpam-5719	175	22	2n	2n	NUM
ejpam-5719	175	23	)	)	PUNCT
ejpam-5719	175	24	≤	≤	PROPN
ejpam-5719	175	25	lim	lim	PROPN
ejpam-5719	175	26	n→+∞	n→+∞	PROPN
ejpam-5719	175	27	ln∆(x	ln∆(x	PROPN
ejpam-5719	175	28	,	,	PUNCT
ejpam-5719	175	29	y	y	NOUN
ejpam-5719	175	30	)	)	PUNCT
ejpam-5719	175	31	=	=	SYM
ejpam-5719	175	32	0	0	NUM
ejpam-5719	175	33	for	for	ADP
ejpam-5719	175	34	all	all	DET
ejpam-5719	175	35	x	x	NOUN
ejpam-5719	175	36	,	,	PUNCT
ejpam-5719	175	37	y	y	PROPN
ejpam-5719	175	38	∈	∈	PROPN
ejpam-5719	175	39	b.	b.	PROPN
ejpam-5719	176	1	so	so	ADV
ejpam-5719	176	2	g(x)g(y	g(x)g(y	PROPN
ejpam-5719	176	3	)	)	PUNCT
ejpam-5719	177	1	=	=	SYM
ejpam-5719	177	2	f	f	PROPN
ejpam-5719	177	3	(	(	PUNCT
ejpam-5719	177	4	x)g(y	x)g(y	PROPN
ejpam-5719	177	5	)	)	PUNCT
ejpam-5719	178	1	+	+	ADV
ejpam-5719	178	2	g(x)f	g(x)f	PROPN
ejpam-5719	178	3	(	(	PUNCT
ejpam-5719	178	4	y	y	NOUN
ejpam-5719	178	5	)	)	PUNCT
ejpam-5719	178	6	for	for	ADP
ejpam-5719	178	7	all	all	DET
ejpam-5719	178	8	x	x	NOUN
ejpam-5719	178	9	,	,	PUNCT
ejpam-5719	178	10	y	y	PROPN
ejpam-5719	178	11	∈	∈	PROPN
ejpam-5719	178	12	b.	b.	PROPN
ejpam-5719	179	1	thus	thus	ADV
ejpam-5719	179	2	the	the	DET
ejpam-5719	179	3	quadratic	quadratic	ADJ
ejpam-5719	179	4	mapping	mapping	NOUN
ejpam-5719	179	5	g	g	NOUN
ejpam-5719	179	6	is	be	AUX
ejpam-5719	179	7	a	a	DET
ejpam-5719	179	8	quadratic	quadratic	ADJ
ejpam-5719	179	9	f	f	NOUN
ejpam-5719	179	10	-hom	-hom	X
ejpam-5719	179	11	-	-	PUNCT
ejpam-5719	179	12	der	der	NOUN
ejpam-5719	179	13	.	.	PUNCT
ejpam-5719	180	1	corollary	corollary	ADJ
ejpam-5719	180	2	3	3	X
ejpam-5719	180	3	.	.	PUNCT
ejpam-5719	181	1	let	let	VERB
ejpam-5719	181	2	p	p	NOUN
ejpam-5719	181	3	and	and	CCONJ
ejpam-5719	181	4	q	q	NOUN
ejpam-5719	181	5	be	be	AUX
ejpam-5719	181	6	nonnegative	nonnegative	ADJ
ejpam-5719	181	7	real	real	ADJ
ejpam-5719	181	8	numbers	number	NOUN
ejpam-5719	181	9	with	with	ADP
ejpam-5719	181	10	p	p	NOUN
ejpam-5719	182	1	+	+	NOUN
ejpam-5719	182	2	q	q	ADJ
ejpam-5719	182	3	>	>	X
ejpam-5719	182	4	4	4	NUM
ejpam-5719	182	5	and	and	CCONJ
ejpam-5719	182	6	f	f	NOUN
ejpam-5719	182	7	,	,	PUNCT
ejpam-5719	182	8	g	g	NOUN
ejpam-5719	182	9	:	:	PUNCT
ejpam-5719	182	10	b	b	X
ejpam-5719	182	11	→	→	SYM
ejpam-5719	182	12	b	b	X
ejpam-5719	182	13	be	be	AUX
ejpam-5719	182	14	mappings	mapping	NOUN
ejpam-5719	182	15	satisfying	satisfy	VERB
ejpam-5719	182	16	g(0	g(0	NOUN
ejpam-5719	182	17	)	)	PUNCT
ejpam-5719	182	18	=	=	SYM
ejpam-5719	182	19	0	0	PUNCT
ejpam-5719	182	20	and	and	CCONJ
ejpam-5719	182	21	{	{	PUNCT
ejpam-5719	182	22	∥f(x+	∥f(x+	VERB
ejpam-5719	182	23	y	y	NOUN
ejpam-5719	182	24	)	)	PUNCT
ejpam-5719	183	1	+	+	CCONJ
ejpam-5719	183	2	f(x−	f(x−	ADP
ejpam-5719	183	3	y)−	y)−	PROPN
ejpam-5719	183	4	g(x)−	g(x)−	PROPN
ejpam-5719	183	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	183	6	≤	≤	PUNCT
ejpam-5719	183	7	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	183	8	,	,	PUNCT
ejpam-5719	183	9	∥g	∥g	PROPN
ejpam-5719	183	10	(	(	PUNCT
ejpam-5719	183	11	x+y	x+y	NUM
ejpam-5719	183	12	2	2	NUM
ejpam-5719	183	13	)	)	PUNCT
ejpam-5719	184	1	+	+	CCONJ
ejpam-5719	184	2	g	g	PROPN
ejpam-5719	184	3	(	(	PUNCT
ejpam-5719	184	4	x−y	x−y	PROPN
ejpam-5719	184	5	2	2	NUM
ejpam-5719	184	6	)	)	PUNCT
ejpam-5719	184	7	−	−	PROPN
ejpam-5719	185	1	f(x)−	f(x)−	PROPN
ejpam-5719	185	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	185	3	≤	≤	PUNCT
ejpam-5719	185	4	∥x∥p∥y∥q	∥x∥p∥y∥q	PROPN
ejpam-5719	185	5	and	and	CCONJ
ejpam-5719	185	6	∥g(xy)−	∥g(xy)−	PROPN
ejpam-5719	185	7	f(x)g(y)−	f(x)g(y)−	NOUN
ejpam-5719	185	8	g(x)f(y)∥	g(x)f(y)∥	X
ejpam-5719	186	1	≤	≤	ADJ
ejpam-5719	186	2	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	186	3	for	for	ADP
ejpam-5719	186	4	all	all	DET
ejpam-5719	186	5	x	x	NOUN
ejpam-5719	186	6	,	,	PUNCT
ejpam-5719	186	7	y	y	PROPN
ejpam-5719	186	8	∈	∈	PROPN
ejpam-5719	186	9	b.	b.	PROPN
ejpam-5719	187	1	then	then	ADV
ejpam-5719	187	2	there	there	PRON
ejpam-5719	187	3	exist	exist	VERB
ejpam-5719	187	4	unique	unique	ADJ
ejpam-5719	187	5	quadratic	quadratic	ADJ
ejpam-5719	187	6	mappings	mapping	NOUN
ejpam-5719	187	7	f	f	X
ejpam-5719	187	8	,	,	PUNCT
ejpam-5719	187	9	g	g	NOUN
ejpam-5719	187	10	:	:	PUNCT
ejpam-5719	187	11	b	b	X
ejpam-5719	187	12	→	→	SYM
ejpam-5719	187	13	b	b	X
ejpam-5719	187	14	such	such	ADJ
ejpam-5719	187	15	that	that	SCONJ
ejpam-5719	187	16	g	g	PROPN
ejpam-5719	187	17	is	be	AUX
ejpam-5719	187	18	a	a	DET
ejpam-5719	187	19	quadratic	quadratic	ADJ
ejpam-5719	187	20	f	f	NOUN
ejpam-5719	187	21	-hom	-hom	X
ejpam-5719	187	22	-	-	PUNCT
ejpam-5719	187	23	der	der	NOUN
ejpam-5719	187	24	and	and	CCONJ
ejpam-5719	187	25	∥f	∥f	PROPN
ejpam-5719	187	26	(	(	PUNCT
ejpam-5719	187	27	x)−	x)−	PROPN
ejpam-5719	187	28	f(x)∥	f(x)∥	VERB
ejpam-5719	187	29	≤	≤	NOUN
ejpam-5719	187	30	2p+q	2p+q	NUM
ejpam-5719	188	1	+	+	CCONJ
ejpam-5719	188	2	8	8	NUM
ejpam-5719	188	3	2(2p+q	2(2p+q	NUM
ejpam-5719	188	4	−	−	NOUN
ejpam-5719	188	5	16	16	NUM
ejpam-5719	188	6	)	)	PUNCT
ejpam-5719	188	7	∥x∥p+q	∥x∥p+q	PROPN
ejpam-5719	188	8	,	,	PUNCT
ejpam-5719	188	9	∥g(x)−	∥g(x)−	X
ejpam-5719	188	10	g(x)∥	g(x)∥	VERB
ejpam-5719	188	11	≤	≤	NOUN
ejpam-5719	188	12	2p+q	2p+q	NUM
ejpam-5719	189	1	+	+	CCONJ
ejpam-5719	189	2	8	8	NUM
ejpam-5719	189	3	2p+q	2p+q	NUM
ejpam-5719	189	4	−	−	NOUN
ejpam-5719	189	5	16	16	NUM
ejpam-5719	189	6	∥x∥p+q	∥x∥p+q	NOUN
ejpam-5719	189	7	for	for	ADP
ejpam-5719	189	8	all	all	DET
ejpam-5719	189	9	x	x	SYM
ejpam-5719	189	10	∈	∈	PROPN
ejpam-5719	189	11	b.	b.	PROPN
ejpam-5719	189	12	c.	c.	PROPN
ejpam-5719	189	13	park	park	PROPN
ejpam-5719	189	14	,	,	PUNCT
ejpam-5719	189	15	s.	s.	PROPN
ejpam-5719	189	16	donganont	donganont	PROPN
ejpam-5719	189	17	,	,	PUNCT
ejpam-5719	189	18	s.	s.	PROPN
ejpam-5719	189	19	w.	w.	PROPN
ejpam-5719	189	20	min	min	PROPN
ejpam-5719	189	21	/	/	SYM
ejpam-5719	189	22	eur	eur	PROPN
ejpam-5719	189	23	.	.	PUNCT
ejpam-5719	190	1	j.	j.	PROPN
ejpam-5719	190	2	pure	pure	PROPN
ejpam-5719	190	3	appl	appl	PROPN
ejpam-5719	190	4	.	.	PROPN
ejpam-5719	190	5	math	math	PROPN
ejpam-5719	190	6	,	,	PUNCT
ejpam-5719	190	7	18	18	NUM
ejpam-5719	190	8	(	(	PUNCT
ejpam-5719	190	9	1	1	NUM
ejpam-5719	190	10	)	)	PUNCT
ejpam-5719	190	11	(	(	PUNCT
ejpam-5719	190	12	2025	2025	NUM
ejpam-5719	190	13	)	)	PUNCT
ejpam-5719	190	14	,	,	PUNCT
ejpam-5719	190	15	5719	5719	NUM
ejpam-5719	190	16	9	9	NUM
ejpam-5719	190	17	of	of	ADP
ejpam-5719	190	18	10	10	NUM
ejpam-5719	190	19	proof	proof	NOUN
ejpam-5719	190	20	.	.	PUNCT
ejpam-5719	191	1	the	the	DET
ejpam-5719	191	2	proof	proof	NOUN
ejpam-5719	191	3	follows	follow	VERB
ejpam-5719	191	4	from	from	ADP
ejpam-5719	191	5	theorem	theorem	NOUN
ejpam-5719	191	6	3	3	NUM
ejpam-5719	191	7	by	by	ADP
ejpam-5719	191	8	taking	take	VERB
ejpam-5719	191	9	∆(x	∆(x	PROPN
ejpam-5719	191	10	,	,	PUNCT
ejpam-5719	191	11	y	y	NOUN
ejpam-5719	191	12	)	)	PUNCT
ejpam-5719	191	13	=	=	PUNCT
ejpam-5719	192	1	∥x∥p∥y∥q	∥x∥p∥y∥q	NOUN
ejpam-5719	192	2	for	for	ADP
ejpam-5719	192	3	all	all	DET
ejpam-5719	192	4	x	x	NOUN
ejpam-5719	192	5	,	,	PUNCT
ejpam-5719	192	6	y	y	PROPN
ejpam-5719	192	7	∈	∈	PROPN
ejpam-5719	192	8	b.	b.	PROPN
ejpam-5719	192	9	choosing	choose	VERB
ejpam-5719	192	10	l	l	PROPN
ejpam-5719	192	11	=	=	SYM
ejpam-5719	193	1	24−p−q	24−p−q	NUM
ejpam-5719	193	2	,	,	PUNCT
ejpam-5719	193	3	we	we	PRON
ejpam-5719	193	4	obtain	obtain	VERB
ejpam-5719	193	5	the	the	DET
ejpam-5719	193	6	desired	desire	VERB
ejpam-5719	193	7	result	result	NOUN
ejpam-5719	193	8	.	.	PUNCT
ejpam-5719	194	1	corollary	corollary	ADJ
ejpam-5719	194	2	4	4	NUM
ejpam-5719	194	3	.	.	PUNCT
ejpam-5719	195	1	let	let	VERB
ejpam-5719	195	2	p	p	NOUN
ejpam-5719	195	3	and	and	CCONJ
ejpam-5719	195	4	θ	θ	PROPN
ejpam-5719	195	5	be	be	AUX
ejpam-5719	195	6	nonnegative	nonnegative	ADJ
ejpam-5719	195	7	real	real	ADJ
ejpam-5719	195	8	numbers	number	NOUN
ejpam-5719	195	9	with	with	ADP
ejpam-5719	195	10	p	p	PROPN
ejpam-5719	195	11	>	>	X
ejpam-5719	195	12	4	4	NUM
ejpam-5719	195	13	and	and	CCONJ
ejpam-5719	195	14	f	f	NOUN
ejpam-5719	195	15	,	,	PUNCT
ejpam-5719	195	16	g	g	NOUN
ejpam-5719	195	17	:	:	PUNCT
ejpam-5719	195	18	b	b	X
ejpam-5719	195	19	→	→	SYM
ejpam-5719	195	20	b	b	X
ejpam-5719	195	21	be	be	AUX
ejpam-5719	195	22	mappings	mapping	NOUN
ejpam-5719	195	23	satisfying	satisfy	VERB
ejpam-5719	195	24	g(0	g(0	NOUN
ejpam-5719	195	25	)	)	PUNCT
ejpam-5719	195	26	=	=	SYM
ejpam-5719	195	27	0	0	PUNCT
ejpam-5719	196	1	and	and	CCONJ
ejpam-5719	196	2	{	{	PUNCT
ejpam-5719	196	3	∥f(x+	∥f(x+	VERB
ejpam-5719	196	4	y	y	NOUN
ejpam-5719	196	5	)	)	PUNCT
ejpam-5719	197	1	+	+	CCONJ
ejpam-5719	197	2	f(x−	f(x−	ADP
ejpam-5719	197	3	y)−	y)−	PROPN
ejpam-5719	197	4	g(x)−	g(x)−	NOUN
ejpam-5719	197	5	g(y)∥	g(y)∥	NOUN
ejpam-5719	197	6	≤	≤	PUNCT
ejpam-5719	197	7	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	197	8	+	+	CCONJ
ejpam-5719	197	9	∥y∥q	∥y∥q	NOUN
ejpam-5719	197	10	)	)	PUNCT
ejpam-5719	197	11	,	,	PUNCT
ejpam-5719	197	12	∥g	∥g	PROPN
ejpam-5719	197	13	(	(	PUNCT
ejpam-5719	197	14	x+y	x+y	NUM
ejpam-5719	197	15	2	2	NUM
ejpam-5719	197	16	)	)	PUNCT
ejpam-5719	198	1	+	+	CCONJ
ejpam-5719	198	2	g	g	PROPN
ejpam-5719	198	3	(	(	PUNCT
ejpam-5719	198	4	x−y	x−y	PROPN
ejpam-5719	198	5	2	2	NUM
ejpam-5719	198	6	)	)	PUNCT
ejpam-5719	198	7	−	−	PROPN
ejpam-5719	199	1	f(x)−	f(x)−	PROPN
ejpam-5719	199	2	f(y)∥	f(y)∥	NOUN
ejpam-5719	199	3	≤	≤	PUNCT
ejpam-5719	199	4	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	199	5	+	+	CCONJ
ejpam-5719	199	6	∥y∥q	∥y∥q	NOUN
ejpam-5719	199	7	)	)	PUNCT
ejpam-5719	199	8	and	and	CCONJ
ejpam-5719	199	9	∥g(xy)−	∥g(xy)−	PROPN
ejpam-5719	199	10	f(x)g(y)−	f(x)g(y)−	NOUN
ejpam-5719	199	11	g(x)f(y)∥	g(x)f(y)∥	X
ejpam-5719	199	12	≤	≤	PUNCT
ejpam-5719	199	13	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	199	14	+	+	CCONJ
ejpam-5719	199	15	∥y∥q	∥y∥q	NOUN
ejpam-5719	199	16	)	)	PUNCT
ejpam-5719	199	17	for	for	ADP
ejpam-5719	199	18	all	all	DET
ejpam-5719	199	19	x	x	NOUN
ejpam-5719	199	20	,	,	PUNCT
ejpam-5719	199	21	y	y	PROPN
ejpam-5719	199	22	∈	∈	PROPN
ejpam-5719	199	23	b.	b.	PROPN
ejpam-5719	200	1	then	then	ADV
ejpam-5719	200	2	there	there	PRON
ejpam-5719	200	3	exist	exist	VERB
ejpam-5719	200	4	unique	unique	ADJ
ejpam-5719	200	5	quadratic	quadratic	ADJ
ejpam-5719	200	6	mappings	mapping	NOUN
ejpam-5719	200	7	f	f	X
ejpam-5719	200	8	,	,	PUNCT
ejpam-5719	200	9	g	g	NOUN
ejpam-5719	200	10	:	:	PUNCT
ejpam-5719	200	11	b	b	X
ejpam-5719	200	12	→	→	SYM
ejpam-5719	200	13	b	b	X
ejpam-5719	200	14	such	such	ADJ
ejpam-5719	200	15	that	that	SCONJ
ejpam-5719	200	16	g	g	PROPN
ejpam-5719	200	17	is	be	AUX
ejpam-5719	200	18	a	a	DET
ejpam-5719	200	19	quadratic	quadratic	ADJ
ejpam-5719	200	20	f	f	NOUN
ejpam-5719	200	21	-hom	-hom	X
ejpam-5719	200	22	-	-	PUNCT
ejpam-5719	200	23	der	der	NOUN
ejpam-5719	200	24	and	and	CCONJ
ejpam-5719	200	25	∥f	∥f	PROPN
ejpam-5719	200	26	(	(	PUNCT
ejpam-5719	200	27	x)−	x)−	PROPN
ejpam-5719	200	28	f(x)∥	f(x)∥	VERB
ejpam-5719	200	29	≤	≤	NUM
ejpam-5719	200	30	2p	2p	NUM
ejpam-5719	200	31	+	+	CCONJ
ejpam-5719	200	32	2	2	NUM
ejpam-5719	200	33	2p	2p	NUM
ejpam-5719	200	34	−	−	NOUN
ejpam-5719	200	35	4	4	NUM
ejpam-5719	200	36	θ∥x∥p	θ∥x∥p	NOUN
ejpam-5719	200	37	,	,	PUNCT
ejpam-5719	200	38	∥g(x)−	∥g(x)−	X
ejpam-5719	200	39	g(x)∥	g(x)∥	VERB
ejpam-5719	200	40	≤	≤	NUM
ejpam-5719	200	41	2(2p	2(2p	NUM
ejpam-5719	200	42	+	+	CCONJ
ejpam-5719	200	43	2	2	NUM
ejpam-5719	200	44	)	)	PUNCT
ejpam-5719	200	45	2p	2p	NUM
ejpam-5719	200	46	−	−	NOUN
ejpam-5719	200	47	4	4	NUM
ejpam-5719	200	48	θ∥x∥p	θ∥x∥p	NOUN
ejpam-5719	200	49	for	for	ADP
ejpam-5719	200	50	all	all	DET
ejpam-5719	200	51	x	x	SYM
ejpam-5719	200	52	∈	∈	PROPN
ejpam-5719	200	53	b.	b.	NOUN
ejpam-5719	200	54	proof	proof	NOUN
ejpam-5719	200	55	.	.	PUNCT
ejpam-5719	201	1	the	the	DET
ejpam-5719	201	2	proof	proof	NOUN
ejpam-5719	201	3	follows	follow	VERB
ejpam-5719	201	4	from	from	ADP
ejpam-5719	201	5	theorem	theorem	NOUN
ejpam-5719	201	6	3	3	NUM
ejpam-5719	201	7	by	by	ADP
ejpam-5719	201	8	taking	take	VERB
ejpam-5719	201	9	∆(x	∆(x	PROPN
ejpam-5719	201	10	,	,	PUNCT
ejpam-5719	201	11	y	y	NOUN
ejpam-5719	201	12	)	)	PUNCT
ejpam-5719	201	13	=	=	VERB
ejpam-5719	202	1	θ(∥x∥p	θ(∥x∥p	PROPN
ejpam-5719	202	2	+	+	CCONJ
ejpam-5719	202	3	∥y∥q	∥y∥q	NOUN
ejpam-5719	202	4	)	)	PUNCT
ejpam-5719	202	5	for	for	ADP
ejpam-5719	202	6	all	all	DET
ejpam-5719	202	7	x	x	NOUN
ejpam-5719	202	8	,	,	PUNCT
ejpam-5719	202	9	y	y	PROPN
ejpam-5719	202	10	∈	∈	PROPN
ejpam-5719	202	11	b.	b.	PROPN
ejpam-5719	203	1	choosing	choose	VERB
ejpam-5719	203	2	l	l	PROPN
ejpam-5719	203	3	=	=	PRON
ejpam-5719	203	4	24−p	24−p	NUM
ejpam-5719	203	5	,	,	PUNCT
ejpam-5719	203	6	we	we	PRON
ejpam-5719	203	7	obtain	obtain	VERB
ejpam-5719	203	8	the	the	DET
ejpam-5719	203	9	desired	desire	VERB
ejpam-5719	203	10	result	result	NOUN
ejpam-5719	203	11	.	.	PUNCT
ejpam-5719	204	1	4	4	X
ejpam-5719	204	2	.	.	X
ejpam-5719	204	3	conclusion	conclusion	NOUN
ejpam-5719	204	4	and	and	CCONJ
ejpam-5719	204	5	future	future	ADJ
ejpam-5719	204	6	work	work	NOUN
ejpam-5719	204	7	we	we	PRON
ejpam-5719	204	8	solved	solve	VERB
ejpam-5719	204	9	the	the	DET
ejpam-5719	204	10	system	system	NOUN
ejpam-5719	204	11	of	of	ADP
ejpam-5719	204	12	quadratic	quadratic	ADJ
ejpam-5719	204	13	functional	functional	ADJ
ejpam-5719	204	14	equations	equation	NOUN
ejpam-5719	204	15	(	(	PUNCT
ejpam-5719	204	16	2	2	NUM
ejpam-5719	204	17	)	)	PUNCT
ejpam-5719	204	18	and	and	CCONJ
ejpam-5719	204	19	we	we	PRON
ejpam-5719	204	20	defined	define	VERB
ejpam-5719	204	21	quadratic	quadratic	ADJ
ejpam-5719	204	22	f	f	NOUN
ejpam-5719	204	23	-hom	-hom	X
ejpam-5719	204	24	-	-	PUNCT
ejpam-5719	204	25	ders	der	NOUN
ejpam-5719	204	26	in	in	ADP
ejpam-5719	204	27	banach	banach	NOUN
ejpam-5719	204	28	algebras	algebra	NOUN
ejpam-5719	204	29	and	and	CCONJ
ejpam-5719	204	30	investigated	investigate	VERB
ejpam-5719	204	31	the	the	DET
ejpam-5719	204	32	hyers	hyers	PROPN
ejpam-5719	204	33	-	-	PUNCT
ejpam-5719	204	34	ulam	ulam	ADJ
ejpam-5719	204	35	stability	stability	NOUN
ejpam-5719	204	36	of	of	ADP
ejpam-5719	204	37	quadratic	quadratic	ADJ
ejpam-5719	204	38	f	f	PROPN
ejpam-5719	204	39	-hom	-hom	X
ejpam-5719	204	40	-	-	PUNCT
ejpam-5719	204	41	ders	der	NOUN
ejpam-5719	204	42	in	in	ADP
ejpam-5719	204	43	banach	banach	NOUN
ejpam-5719	204	44	algebras	algebra	NOUN
ejpam-5719	204	45	.	.	PUNCT
ejpam-5719	205	1	we	we	PRON
ejpam-5719	205	2	will	will	AUX
ejpam-5719	205	3	define	define	VERB
ejpam-5719	205	4	cubic	cubic	ADJ
ejpam-5719	205	5	f	f	PROPN
ejpam-5719	205	6	-hom	-hom	X
ejpam-5719	205	7	-	-	PUNCT
ejpam-5719	205	8	ders	der	NOUN
ejpam-5719	205	9	and	and	CCONJ
ejpam-5719	205	10	quartic	quartic	ADJ
ejpam-5719	205	11	f	f	PROPN
ejpam-5719	205	12	-hom	-hom	X
ejpam-5719	205	13	-	-	PUNCT
ejpam-5719	205	14	ders	der	NOUN
ejpam-5719	205	15	in	in	ADP
ejpam-5719	205	16	banach	banach	NOUN
ejpam-5719	205	17	algebras	algebra	NOUN
ejpam-5719	205	18	,	,	PUNCT
ejpam-5719	205	19	fuzzy	fuzzy	ADJ
ejpam-5719	205	20	banach	banach	NOUN
ejpam-5719	205	21	algebras	algebra	NOUN
ejpam-5719	205	22	and	and	CCONJ
ejpam-5719	205	23	non	non	ADJ
ejpam-5719	205	24	-	-	ADJ
ejpam-5719	205	25	archimedean	archimedean	ADJ
ejpam-5719	205	26	banach	banach	NOUN
ejpam-5719	205	27	algebras	algebra	VERB
ejpam-5719	205	28	and	and	CCONJ
ejpam-5719	205	29	investigate	investigate	VERB
ejpam-5719	205	30	the	the	DET
ejpam-5719	205	31	hyers	hyers	PROPN
ejpam-5719	205	32	-	-	PUNCT
ejpam-5719	205	33	ulam	ulam	ADJ
ejpam-5719	205	34	stability	stability	NOUN
ejpam-5719	205	35	of	of	ADP
ejpam-5719	205	36	them	they	PRON
ejpam-5719	205	37	.	.	PUNCT
ejpam-5719	206	1	acknowledgements	acknowledgement	NOUN
ejpam-5719	206	2	this	this	DET
ejpam-5719	206	3	research	research	NOUN
ejpam-5719	206	4	was	be	AUX
ejpam-5719	206	5	supported	support	VERB
ejpam-5719	206	6	by	by	ADP
ejpam-5719	206	7	university	university	NOUN
ejpam-5719	206	8	of	of	ADP
ejpam-5719	206	9	phayao	phayao	NOUN
ejpam-5719	206	10	and	and	CCONJ
ejpam-5719	206	11	thailand	thailand	PROPN
ejpam-5719	206	12	science	science	PROPN
ejpam-5719	206	13	research	research	PROPN
ejpam-5719	206	14	and	and	CCONJ
ejpam-5719	206	15	innovation	innovation	NOUN
ejpam-5719	206	16	fund	fund	NOUN
ejpam-5719	206	17	(	(	PUNCT
ejpam-5719	206	18	fundamental	fundamental	ADJ
ejpam-5719	206	19	fund	fund	NOUN
ejpam-5719	206	20	2025	2025	NUM
ejpam-5719	206	21	,	,	PUNCT
ejpam-5719	206	22	grant	grant	VERB
ejpam-5719	206	23	no	no	NOUN
ejpam-5719	206	24	.	.	PUNCT
ejpam-5719	207	1	5020/2567	5020/2567	NUM
ejpam-5719	207	2	)	)	PUNCT
ejpam-5719	207	3	.	.	PUNCT
ejpam-5719	208	1	references	reference	NOUN
ejpam-5719	208	2	[	[	X
ejpam-5719	208	3	1	1	X
ejpam-5719	208	4	]	]	PUNCT
ejpam-5719	208	5	s.	s.	PROPN
ejpam-5719	208	6	bowmiya	bowmiya	PROPN
ejpam-5719	208	7	,	,	PUNCT
ejpam-5719	208	8	g.	g.	PROPN
ejpam-5719	208	9	balasubramanian	balasubramanian	PROPN
ejpam-5719	208	10	,	,	PUNCT
ejpam-5719	208	11	v.	v.	ADP
ejpam-5719	208	12	govindan	govindan	PROPN
ejpam-5719	208	13	,	,	PUNCT
ejpam-5719	208	14	m.	m.	NOUN
ejpam-5719	208	15	donganont	donganont	PROPN
ejpam-5719	208	16	,	,	PUNCT
ejpam-5719	208	17	and	and	CCONJ
ejpam-5719	208	18	h.	h.	PROPN
ejpam-5719	208	19	byeon	byeon	PROPN
ejpam-5719	208	20	.	.	PUNCT
ejpam-5719	209	1	generalized	generalize	VERB
ejpam-5719	209	2	linear	linear	PROPN
ejpam-5719	209	3	differential	differential	NOUN
ejpam-5719	209	4	equation	equation	NOUN
ejpam-5719	209	5	using	use	VERB
ejpam-5719	209	6	hyers	hyers	PROPN
ejpam-5719	209	7	-	-	PUNCT
ejpam-5719	209	8	ulam	ulam	PROPN
ejpam-5719	209	9	stability	stability	PROPN
ejpam-5719	209	10	approach	approach	NOUN
ejpam-5719	209	11	.	.	PUNCT
ejpam-5719	210	1	european	european	PROPN
ejpam-5719	210	2	journal	journal	PROPN
ejpam-5719	210	3	of	of	ADP
ejpam-5719	210	4	pure	pure	ADJ
ejpam-5719	210	5	and	and	CCONJ
ejpam-5719	210	6	applied	applied	ADJ
ejpam-5719	210	7	mathematics	mathematic	NOUN
ejpam-5719	210	8	,	,	PUNCT
ejpam-5719	210	9	17:3415–3435	17:3415–3435	NUM
ejpam-5719	210	10	,	,	PUNCT
ejpam-5719	210	11	2024	2024	NUM
ejpam-5719	210	12	.	.	PUNCT
ejpam-5719	211	1	c.	c.	PROPN
ejpam-5719	211	2	park	park	PROPN
ejpam-5719	211	3	,	,	PUNCT
ejpam-5719	211	4	s.	s.	PROPN
ejpam-5719	211	5	donganont	donganont	PROPN
ejpam-5719	211	6	,	,	PUNCT
ejpam-5719	211	7	s.	s.	PROPN
ejpam-5719	211	8	w.	w.	PROPN
ejpam-5719	211	9	min	min	PROPN
ejpam-5719	211	10	/	/	SYM
ejpam-5719	211	11	eur	eur	PROPN
ejpam-5719	211	12	.	.	PUNCT
ejpam-5719	212	1	j.	j.	PROPN
ejpam-5719	212	2	pure	pure	PROPN
ejpam-5719	212	3	appl	appl	PROPN
ejpam-5719	212	4	.	.	PROPN
ejpam-5719	212	5	math	math	PROPN
ejpam-5719	212	6	,	,	PUNCT
ejpam-5719	212	7	18	18	NUM
ejpam-5719	212	8	(	(	PUNCT
ejpam-5719	212	9	1	1	NUM
ejpam-5719	212	10	)	)	PUNCT
ejpam-5719	212	11	(	(	PUNCT
ejpam-5719	212	12	2025	2025	NUM
ejpam-5719	212	13	)	)	PUNCT
ejpam-5719	212	14	,	,	PUNCT
ejpam-5719	212	15	5719	5719	NUM
ejpam-5719	212	16	10	10	NUM
ejpam-5719	212	17	of	of	ADP
ejpam-5719	212	18	10	10	NUM
ejpam-5719	212	19	[	[	SYM
ejpam-5719	212	20	2	2	NUM
ejpam-5719	212	21	]	]	PUNCT
ejpam-5719	212	22	s.	s.	PROPN
ejpam-5719	212	23	bowmiya	bowmiya	PROPN
ejpam-5719	212	24	,	,	PUNCT
ejpam-5719	212	25	g.	g.	PROPN
ejpam-5719	212	26	balasubramanian	balasubramanian	PROPN
ejpam-5719	212	27	,	,	PUNCT
ejpam-5719	212	28	v.	v.	ADP
ejpam-5719	212	29	govindan	govindan	PROPN
ejpam-5719	212	30	,	,	PUNCT
ejpam-5719	212	31	m.	m.	NOUN
ejpam-5719	212	32	donganont	donganont	PROPN
ejpam-5719	212	33	,	,	PUNCT
ejpam-5719	212	34	and	and	CCONJ
ejpam-5719	212	35	h.	h.	PROPN
ejpam-5719	212	36	byeon	byeon	PROPN
ejpam-5719	212	37	.	.	PUNCT
ejpam-5719	213	1	hyersulam	hyersulam	PROPN
ejpam-5719	213	2	stability	stability	NOUN
ejpam-5719	213	3	of	of	ADP
ejpam-5719	213	4	fifth	fifth	ADJ
ejpam-5719	213	5	order	order	NOUN
ejpam-5719	213	6	linear	linear	PROPN
ejpam-5719	213	7	differential	differential	NOUN
ejpam-5719	213	8	equations	equation	NOUN
ejpam-5719	213	9	.	.	PUNCT
ejpam-5719	214	1	european	european	PROPN
ejpam-5719	214	2	journal	journal	PROPN
ejpam-5719	214	3	of	of	ADP
ejpam-5719	214	4	pure	pure	ADJ
ejpam-5719	214	5	and	and	CCONJ
ejpam-5719	214	6	applied	applied	ADJ
ejpam-5719	214	7	mathematics	mathematic	NOUN
ejpam-5719	214	8	,	,	PUNCT
ejpam-5719	214	9	17:3585–3609	17:3585–3609	NUM
ejpam-5719	214	10	,	,	PUNCT
ejpam-5719	214	11	2024	2024	NUM
ejpam-5719	214	12	.	.	PUNCT
ejpam-5719	215	1	[	[	X
ejpam-5719	215	2	3	3	X
ejpam-5719	215	3	]	]	PUNCT
ejpam-5719	215	4	m.	m.	NOUN
ejpam-5719	215	5	dehghanian	dehghanian	PROPN
ejpam-5719	215	6	and	and	CCONJ
ejpam-5719	215	7	s.	s.	PROPN
ejpam-5719	215	8	m.	m.	PROPN
ejpam-5719	215	9	s.	s.	PROPN
ejpam-5719	215	10	modarres	modarres	PROPN
ejpam-5719	215	11	.	.	PUNCT
ejpam-5719	216	1	ternary	ternary	ADJ
ejpam-5719	216	2	γ	γ	PROPN
ejpam-5719	216	3	-	-	PUNCT
ejpam-5719	216	4	homomorphisms	homomorphism	NOUN
ejpam-5719	216	5	and	and	CCONJ
ejpam-5719	216	6	ternary	ternary	ADJ
ejpam-5719	216	7	γderivations	γderivation	NOUN
ejpam-5719	216	8	on	on	ADP
ejpam-5719	216	9	ternary	ternary	ADJ
ejpam-5719	216	10	semigroups	semigroup	NOUN
ejpam-5719	216	11	.	.	PUNCT
ejpam-5719	217	1	journal	journal	PROPN
ejpam-5719	217	2	of	of	ADP
ejpam-5719	217	3	inequalities	inequality	NOUN
ejpam-5719	217	4	and	and	CCONJ
ejpam-5719	217	5	applications	application	NOUN
ejpam-5719	217	6	,	,	PUNCT
ejpam-5719	217	7	34	34	NUM
ejpam-5719	217	8	,	,	PUNCT
ejpam-5719	217	9	2012	2012	NUM
ejpam-5719	217	10	.	.	PUNCT
ejpam-5719	218	1	[	[	X
ejpam-5719	218	2	4	4	NUM
ejpam-5719	218	3	]	]	X
ejpam-5719	218	4	m.	m.	NOUN
ejpam-5719	218	5	dehghanian	dehghanian	PROPN
ejpam-5719	218	6	,	,	PUNCT
ejpam-5719	218	7	s.	s.	PROPN
ejpam-5719	218	8	m.	m.	PROPN
ejpam-5719	218	9	s.	s.	PROPN
ejpam-5719	218	10	modarres	modarres	PROPN
ejpam-5719	218	11	,	,	PUNCT
ejpam-5719	218	12	c.	c.	PROPN
ejpam-5719	218	13	park	park	NOUN
ejpam-5719	218	14	,	,	PUNCT
ejpam-5719	218	15	and	and	CCONJ
ejpam-5719	218	16	d.	d.	PROPN
ejpam-5719	218	17	shin	shin	PROPN
ejpam-5719	218	18	.	.	PUNCT
ejpam-5719	219	1	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	219	2	3	3	NUM
ejpam-5719	219	3	-	-	PUNCT
ejpam-5719	219	4	derivations	derivation	NOUN
ejpam-5719	219	5	on	on	ADP
ejpam-5719	219	6	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	219	7	algebras	algebras	X
ejpam-5719	219	8	.	.	PUNCT
ejpam-5719	220	1	journal	journal	PROPN
ejpam-5719	220	2	of	of	ADP
ejpam-5719	220	3	inequalities	inequality	NOUN
ejpam-5719	220	4	and	and	CCONJ
ejpam-5719	220	5	applications	application	NOUN
ejpam-5719	220	6	,	,	PUNCT
ejpam-5719	220	7	124	124	NUM
ejpam-5719	220	8	,	,	PUNCT
ejpam-5719	220	9	2013	2013	NUM
ejpam-5719	220	10	.	.	PUNCT
ejpam-5719	221	1	[	[	X
ejpam-5719	221	2	5	5	X
ejpam-5719	221	3	]	]	PUNCT
ejpam-5719	221	4	m.	m.	NOUN
ejpam-5719	221	5	dehghanian	dehghanian	ADJ
ejpam-5719	221	6	and	and	CCONJ
ejpam-5719	221	7	c.	c.	PROPN
ejpam-5719	221	8	park	park	PROPN
ejpam-5719	221	9	.	.	PUNCT
ejpam-5719	222	1	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	222	2	3	3	NUM
ejpam-5719	222	3	-	-	PUNCT
ejpam-5719	222	4	homomorphisms	homomorphism	NOUN
ejpam-5719	222	5	on	on	ADP
ejpam-5719	222	6	c∗-ternary	c∗-ternary	ADJ
ejpam-5719	222	7	algebras	algebra	NOUN
ejpam-5719	222	8	.	.	PUNCT
ejpam-5719	223	1	results	result	NOUN
ejpam-5719	223	2	in	in	ADP
ejpam-5719	223	3	mathematics	mathematic	NOUN
ejpam-5719	223	4	,	,	PUNCT
ejpam-5719	223	5	3:385–404	3:385–404	NUM
ejpam-5719	223	6	,	,	PUNCT
ejpam-5719	223	7	2014	2014	NUM
ejpam-5719	223	8	.	.	PUNCT
ejpam-5719	224	1	[	[	X
ejpam-5719	224	2	6	6	NUM
ejpam-5719	224	3	]	]	PUNCT
ejpam-5719	224	4	m.	m.	NOUN
ejpam-5719	224	5	dehghanian	dehghanian	PROPN
ejpam-5719	224	6	,	,	PUNCT
ejpam-5719	224	7	c.	c.	PROPN
ejpam-5719	224	8	park	park	PROPN
ejpam-5719	224	9	,	,	PUNCT
ejpam-5719	224	10	and	and	CCONJ
ejpam-5719	224	11	y.	y.	PROPN
ejpam-5719	224	12	sayyari	sayyari	PROPN
ejpam-5719	224	13	.	.	PUNCT
ejpam-5719	225	1	ternary	ternary	PROPN
ejpam-5719	225	2	hom	hom	NOUN
ejpam-5719	225	3	-	-	PUNCT
ejpam-5719	225	4	ders	der	NOUN
ejpam-5719	225	5	in	in	ADP
ejpam-5719	225	6	ternary	ternary	ADJ
ejpam-5719	225	7	banach	banach	NOUN
ejpam-5719	225	8	algebras	algebra	VERB
ejpam-5719	225	9	.	.	PUNCT
ejpam-5719	226	1	rendiconti	rendiconti	PROPN
ejpam-5719	226	2	del	del	PROPN
ejpam-5719	226	3	circolo	circolo	PROPN
ejpam-5719	226	4	matematico	matematico	NOUN
ejpam-5719	226	5	di	di	PROPN
ejpam-5719	226	6	palermo	palermo	PROPN
ejpam-5719	226	7	series	series	PROPN
ejpam-5719	226	8	2	2	NUM
ejpam-5719	226	9	,	,	PUNCT
ejpam-5719	226	10	2:747–756	2:747–756	NUM
ejpam-5719	226	11	,	,	PUNCT
ejpam-5719	226	12	2024	2024	NUM
ejpam-5719	226	13	.	.	PUNCT
ejpam-5719	227	1	[	[	X
ejpam-5719	227	2	7	7	X
ejpam-5719	227	3	]	]	X
ejpam-5719	227	4	j.	j.	PROPN
ejpam-5719	227	5	b.	b.	PROPN
ejpam-5719	227	6	diaz	diaz	PROPN
ejpam-5719	227	7	and	and	CCONJ
ejpam-5719	227	8	b.	b.	PROPN
ejpam-5719	227	9	margolis	margolis	PROPN
ejpam-5719	227	10	.	.	PUNCT
ejpam-5719	228	1	a	a	DET
ejpam-5719	228	2	fixed	fix	VERB
ejpam-5719	228	3	point	point	NOUN
ejpam-5719	228	4	theorem	theorem	NOUN
ejpam-5719	228	5	of	of	ADP
ejpam-5719	228	6	the	the	DET
ejpam-5719	228	7	alternative	alternative	NOUN
ejpam-5719	228	8	,	,	PUNCT
ejpam-5719	228	9	for	for	ADP
ejpam-5719	228	10	contractions	contraction	NOUN
ejpam-5719	228	11	on	on	ADP
ejpam-5719	228	12	a	a	DET
ejpam-5719	228	13	generalized	generalized	ADJ
ejpam-5719	228	14	complete	complete	ADJ
ejpam-5719	228	15	metric	metric	ADJ
ejpam-5719	228	16	space	space	NOUN
ejpam-5719	228	17	.	.	PUNCT
ejpam-5719	229	1	bulletin	bulletin	NOUN
ejpam-5719	229	2	of	of	ADP
ejpam-5719	229	3	the	the	DET
ejpam-5719	229	4	american	american	PROPN
ejpam-5719	229	5	mathematical	mathematical	PROPN
ejpam-5719	229	6	society	society	NOUN
ejpam-5719	229	7	,	,	PUNCT
ejpam-5719	229	8	74(2):305–309	74(2):305–309	PROPN
ejpam-5719	229	9	,	,	PUNCT
ejpam-5719	229	10	1968	1968	NUM
ejpam-5719	229	11	.	.	PUNCT
ejpam-5719	230	1	[	[	X
ejpam-5719	230	2	8	8	NUM
ejpam-5719	230	3	]	]	X
ejpam-5719	230	4	i.	i.	PROPN
ejpam-5719	230	5	hwang	hwang	PROPN
ejpam-5719	230	6	and	and	CCONJ
ejpam-5719	230	7	c.	c.	PROPN
ejpam-5719	230	8	park	park	PROPN
ejpam-5719	230	9	.	.	PUNCT
ejpam-5719	231	1	bihom	bihom	ADJ
ejpam-5719	231	2	derivations	derivation	NOUN
ejpam-5719	231	3	in	in	ADP
ejpam-5719	231	4	banach	banach	NOUN
ejpam-5719	231	5	algebras	algebra	NOUN
ejpam-5719	231	6	.	.	PUNCT
ejpam-5719	232	1	journal	journal	PROPN
ejpam-5719	232	2	of	of	ADP
ejpam-5719	232	3	fixed	fix	VERB
ejpam-5719	232	4	point	point	NOUN
ejpam-5719	232	5	theory	theory	NOUN
ejpam-5719	232	6	and	and	CCONJ
ejpam-5719	232	7	applications	application	NOUN
ejpam-5719	232	8	,	,	PUNCT
ejpam-5719	232	9	21:81	21:81	NUM
ejpam-5719	232	10	,	,	PUNCT
ejpam-5719	232	11	2019	2019	NUM
ejpam-5719	232	12	.	.	PUNCT
ejpam-5719	233	1	[	[	X
ejpam-5719	233	2	9	9	NUM
ejpam-5719	233	3	]	]	X
ejpam-5719	233	4	d.	d.	PROPN
ejpam-5719	233	5	h.	h.	PROPN
ejpam-5719	233	6	hyers	hyers	PROPN
ejpam-5719	233	7	.	.	PUNCT
ejpam-5719	234	1	on	on	ADP
ejpam-5719	234	2	the	the	DET
ejpam-5719	234	3	stability	stability	NOUN
ejpam-5719	234	4	of	of	ADP
ejpam-5719	234	5	the	the	DET
ejpam-5719	234	6	linear	linear	ADJ
ejpam-5719	234	7	functional	functional	ADJ
ejpam-5719	234	8	equation	equation	NOUN
ejpam-5719	234	9	.	.	PUNCT
ejpam-5719	235	1	proceedings	proceeding	NOUN
ejpam-5719	235	2	of	of	ADP
ejpam-5719	235	3	the	the	DET
ejpam-5719	235	4	national	national	PROPN
ejpam-5719	235	5	academy	academy	PROPN
ejpam-5719	235	6	of	of	ADP
ejpam-5719	235	7	sciences	sciences	PROPN
ejpam-5719	235	8	of	of	ADP
ejpam-5719	235	9	the	the	DET
ejpam-5719	235	10	united	united	PROPN
ejpam-5719	235	11	states	states	PROPN
ejpam-5719	235	12	of	of	ADP
ejpam-5719	235	13	america	america	PROPN
ejpam-5719	235	14	,	,	PUNCT
ejpam-5719	235	15	27(4):222–224	27(4):222–224	PROPN
ejpam-5719	235	16	,	,	PUNCT
ejpam-5719	235	17	1941	1941	NUM
ejpam-5719	235	18	.	.	PUNCT
ejpam-5719	236	1	[	[	X
ejpam-5719	236	2	10	10	NUM
ejpam-5719	236	3	]	]	PUNCT
ejpam-5719	236	4	a.	a.	NOUN
ejpam-5719	236	5	kheawborisut	kheawborisut	PROPN
ejpam-5719	236	6	,	,	PUNCT
ejpam-5719	236	7	s.	s.	PROPN
ejpam-5719	236	8	paokanta	paokanta	PROPN
ejpam-5719	236	9	,	,	PUNCT
ejpam-5719	236	10	j.	j.	PROPN
ejpam-5719	236	11	senasukh	senasukh	PROPN
ejpam-5719	236	12	,	,	PUNCT
ejpam-5719	236	13	and	and	CCONJ
ejpam-5719	236	14	c.	c.	PROPN
ejpam-5719	236	15	park	park	PROPN
ejpam-5719	236	16	.	.	PUNCT
ejpam-5719	237	1	ulam	ulam	PROPN
ejpam-5719	237	2	stability	stability	NOUN
ejpam-5719	237	3	of	of	ADP
ejpam-5719	237	4	hom	hom	NOUN
ejpam-5719	237	5	-	-	PUNCT
ejpam-5719	237	6	ders	der	NOUN
ejpam-5719	237	7	in	in	ADP
ejpam-5719	237	8	fuzzy	fuzzy	ADJ
ejpam-5719	237	9	banach	banach	NOUN
ejpam-5719	237	10	algebras	algebra	NOUN
ejpam-5719	237	11	.	.	PUNCT
ejpam-5719	238	1	aims	aim	VERB
ejpam-5719	238	2	mathematics	mathematic	NOUN
ejpam-5719	238	3	,	,	PUNCT
ejpam-5719	238	4	7(9):16556–16568	7(9):16556–16568	NOUN
ejpam-5719	238	5	,	,	PUNCT
ejpam-5719	238	6	2022	2022	NUM
ejpam-5719	238	7	.	.	PUNCT
ejpam-5719	239	1	[	[	X
ejpam-5719	239	2	11	11	NUM
ejpam-5719	239	3	]	]	X
ejpam-5719	239	4	b.	b.	PROPN
ejpam-5719	239	5	v.	v.	PROPN
ejpam-5719	239	6	senthil	senthil	PROPN
ejpam-5719	239	7	kumar	kumar	PROPN
ejpam-5719	239	8	,	,	PUNCT
ejpam-5719	239	9	h.	h.	PROPN
ejpam-5719	239	10	dutta	dutta	PROPN
ejpam-5719	239	11	,	,	PUNCT
ejpam-5719	239	12	and	and	CCONJ
ejpam-5719	239	13	s.	s.	PROPN
ejpam-5719	239	14	sabarinathan	sabarinathan	PROPN
ejpam-5719	239	15	.	.	PUNCT
ejpam-5719	240	1	modular	modular	ADJ
ejpam-5719	240	2	stabilities	stability	NOUN
ejpam-5719	240	3	of	of	ADP
ejpam-5719	240	4	a	a	DET
ejpam-5719	240	5	reciprocal	reciprocal	ADJ
ejpam-5719	240	6	second	second	ADJ
ejpam-5719	240	7	power	power	NOUN
ejpam-5719	240	8	functional	functional	ADJ
ejpam-5719	240	9	equation	equation	NOUN
ejpam-5719	240	10	.	.	PUNCT
ejpam-5719	241	1	european	european	ADJ
ejpam-5719	241	2	journal	journal	PROPN
ejpam-5719	241	3	of	of	ADP
ejpam-5719	241	4	pure	pure	ADJ
ejpam-5719	241	5	and	and	CCONJ
ejpam-5719	241	6	applied	applied	ADJ
ejpam-5719	241	7	mathematics	mathematic	NOUN
ejpam-5719	241	8	,	,	PUNCT
ejpam-5719	241	9	13:1162–1175	13:1162–1175	NUM
ejpam-5719	241	10	,	,	PUNCT
ejpam-5719	241	11	2020	2020	NUM
ejpam-5719	241	12	.	.	PUNCT
ejpam-5719	242	1	[	[	X
ejpam-5719	242	2	12	12	NUM
ejpam-5719	242	3	]	]	X
ejpam-5719	242	4	d.	d.	PROPN
ejpam-5719	242	5	miheţ	miheţ	PROPN
ejpam-5719	242	6	and	and	CCONJ
ejpam-5719	242	7	r.	r.	PROPN
ejpam-5719	242	8	saadati	saadati	PROPN
ejpam-5719	242	9	.	.	PUNCT
ejpam-5719	243	1	on	on	ADP
ejpam-5719	243	2	the	the	DET
ejpam-5719	243	3	stability	stability	NOUN
ejpam-5719	243	4	of	of	ADP
ejpam-5719	243	5	the	the	DET
ejpam-5719	243	6	additive	additive	ADJ
ejpam-5719	243	7	cauchy	cauchy	ADJ
ejpam-5719	243	8	functional	functional	ADJ
ejpam-5719	243	9	equation	equation	NOUN
ejpam-5719	243	10	in	in	ADP
ejpam-5719	243	11	random	random	ADJ
ejpam-5719	243	12	normed	normed	ADJ
ejpam-5719	243	13	spaces	space	NOUN
ejpam-5719	243	14	.	.	PUNCT
ejpam-5719	244	1	applied	apply	VERB
ejpam-5719	244	2	mathematics	mathematics	NOUN
ejpam-5719	244	3	letters	letter	NOUN
ejpam-5719	244	4	,	,	PUNCT
ejpam-5719	244	5	24(12):2005–2009	24(12):2005–2009	NUM
ejpam-5719	244	6	,	,	PUNCT
ejpam-5719	244	7	2011	2011	NUM
ejpam-5719	244	8	.	.	PUNCT
ejpam-5719	245	1	[	[	X
ejpam-5719	245	2	13	13	NUM
ejpam-5719	245	3	]	]	PUNCT
ejpam-5719	245	4	m.	m.	NOUN
ejpam-5719	245	5	mirzavaziri	mirzavaziri	PROPN
ejpam-5719	245	6	and	and	CCONJ
ejpam-5719	245	7	m.	m.	PROPN
ejpam-5719	245	8	s.	s.	PROPN
ejpam-5719	245	9	moslehian	moslehian	PROPN
ejpam-5719	245	10	.	.	PUNCT
ejpam-5719	246	1	automatic	automatic	ADJ
ejpam-5719	246	2	continuity	continuity	NOUN
ejpam-5719	246	3	of	of	ADP
ejpam-5719	246	4	σ	σ	NOUN
ejpam-5719	246	5	-	-	PUNCT
ejpam-5719	246	6	derivations	derivation	NOUN
ejpam-5719	246	7	on	on	ADP
ejpam-5719	246	8	c∗algebras	c∗algebra	NOUN
ejpam-5719	246	9	.	.	PUNCT
ejpam-5719	247	1	proceedings	proceeding	NOUN
ejpam-5719	247	2	of	of	ADP
ejpam-5719	247	3	the	the	DET
ejpam-5719	247	4	american	american	PROPN
ejpam-5719	247	5	mathematical	mathematical	PROPN
ejpam-5719	247	6	society	society	NOUN
ejpam-5719	247	7	,	,	PUNCT
ejpam-5719	247	8	134(11):3319–3327	134(11):3319–3327	NUM
ejpam-5719	247	9	,	,	PUNCT
ejpam-5719	247	10	2006	2006	NUM
ejpam-5719	247	11	.	.	PUNCT
ejpam-5719	248	1	[	[	X
ejpam-5719	248	2	14	14	NUM
ejpam-5719	248	3	]	]	X
ejpam-5719	248	4	c.	c.	PROPN
ejpam-5719	248	5	park	park	PROPN
ejpam-5719	248	6	.	.	PUNCT
ejpam-5719	249	1	an	an	DET
ejpam-5719	249	2	additive	additive	ADJ
ejpam-5719	249	3	(	(	PUNCT
ejpam-5719	249	4	α	α	NOUN
ejpam-5719	249	5	,	,	PUNCT
ejpam-5719	249	6	β)-functional	β)-functional	ADJ
ejpam-5719	249	7	equation	equation	NOUN
ejpam-5719	249	8	and	and	CCONJ
ejpam-5719	249	9	linear	linear	ADJ
ejpam-5719	249	10	mappings	mapping	NOUN
ejpam-5719	249	11	in	in	ADP
ejpam-5719	249	12	banach	banach	NOUN
ejpam-5719	249	13	spaces	space	NOUN
ejpam-5719	249	14	.	.	PUNCT
ejpam-5719	250	1	journal	journal	NOUN
ejpam-5719	250	2	of	of	ADP
ejpam-5719	250	3	fixed	fix	VERB
ejpam-5719	250	4	point	point	NOUN
ejpam-5719	250	5	theory	theory	NOUN
ejpam-5719	250	6	and	and	CCONJ
ejpam-5719	250	7	applications	application	NOUN
ejpam-5719	250	8	,	,	PUNCT
ejpam-5719	250	9	18:495–504	18:495–504	NUM
ejpam-5719	250	10	,	,	PUNCT
ejpam-5719	250	11	2016	2016	NUM
ejpam-5719	250	12	.	.	PUNCT
ejpam-5719	251	1	[	[	X
ejpam-5719	251	2	15	15	NUM
ejpam-5719	251	3	]	]	X
ejpam-5719	251	4	c	c	NOUN
ejpam-5719	251	5	park	park	NOUN
ejpam-5719	251	6	.	.	PUNCT
ejpam-5719	252	1	the	the	DET
ejpam-5719	252	2	stability	stability	NOUN
ejpam-5719	252	3	of	of	ADP
ejpam-5719	252	4	an	an	DET
ejpam-5719	252	5	additive	additive	ADJ
ejpam-5719	252	6	(	(	PUNCT
ejpam-5719	252	7	ρ1	ρ1	NOUN
ejpam-5719	252	8	,	,	PUNCT
ejpam-5719	252	9	ρ2)-functional	ρ2)-functional	ADJ
ejpam-5719	252	10	inequality	inequality	NOUN
ejpam-5719	252	11	in	in	ADP
ejpam-5719	252	12	banach	banach	NOUN
ejpam-5719	252	13	spaces	space	NOUN
ejpam-5719	252	14	.	.	PUNCT
ejpam-5719	253	1	journal	journal	NOUN
ejpam-5719	253	2	of	of	ADP
ejpam-5719	253	3	mathematical	mathematical	ADJ
ejpam-5719	253	4	inequalities	inequality	NOUN
ejpam-5719	253	5	,	,	PUNCT
ejpam-5719	253	6	13:95–104	13:95–104	NUM
ejpam-5719	253	7	,	,	PUNCT
ejpam-5719	253	8	2019	2019	NUM
ejpam-5719	253	9	.	.	PUNCT
ejpam-5719	254	1	[	[	X
ejpam-5719	254	2	16	16	NUM
ejpam-5719	254	3	]	]	X
ejpam-5719	254	4	c.	c.	PROPN
ejpam-5719	254	5	park	park	PROPN
ejpam-5719	254	6	,	,	PUNCT
ejpam-5719	254	7	j.	j.	PROPN
ejpam-5719	254	8	r.	r.	PROPN
ejpam-5719	254	9	lee	lee	PROPN
ejpam-5719	254	10	,	,	PUNCT
ejpam-5719	254	11	and	and	CCONJ
ejpam-5719	254	12	x.	x.	NOUN
ejpam-5719	254	13	zhang	zhang	PROPN
ejpam-5719	254	14	.	.	PUNCT
ejpam-5719	255	1	additive	additive	PROPN
ejpam-5719	255	2	s	s	ADJ
ejpam-5719	255	3	-	-	ADJ
ejpam-5719	255	4	functional	functional	ADJ
ejpam-5719	255	5	inequality	inequality	NOUN
ejpam-5719	255	6	and	and	CCONJ
ejpam-5719	255	7	homderivations	homderivation	NOUN
ejpam-5719	255	8	in	in	ADP
ejpam-5719	255	9	banach	banach	NOUN
ejpam-5719	255	10	algebras	algebras	PROPN
ejpam-5719	255	11	.	.	PUNCT
ejpam-5719	256	1	journal	journal	PROPN
ejpam-5719	256	2	of	of	ADP
ejpam-5719	256	3	fixed	fix	VERB
ejpam-5719	256	4	point	point	NOUN
ejpam-5719	256	5	theory	theory	NOUN
ejpam-5719	256	6	and	and	CCONJ
ejpam-5719	256	7	applications	application	NOUN
ejpam-5719	256	8	,	,	PUNCT
ejpam-5719	256	9	21:1–14	21:1–14	NUM
ejpam-5719	256	10	,	,	PUNCT
ejpam-5719	256	11	2019	2019	NUM
ejpam-5719	256	12	.	.	PUNCT
ejpam-5719	257	1	[	[	X
ejpam-5719	257	2	17	17	NUM
ejpam-5719	257	3	]	]	X
ejpam-5719	257	4	y.	y.	PROPN
ejpam-5719	257	5	sayyari	sayyari	PROPN
ejpam-5719	257	6	,	,	PUNCT
ejpam-5719	257	7	m.	m.	PROPN
ejpam-5719	257	8	dehghanian	dehghanian	PROPN
ejpam-5719	257	9	,	,	PUNCT
ejpam-5719	257	10	c.	c.	PROPN
ejpam-5719	257	11	park	park	PROPN
ejpam-5719	257	12	,	,	PUNCT
ejpam-5719	257	13	and	and	CCONJ
ejpam-5719	257	14	j.	j.	PROPN
ejpam-5719	257	15	r.	r.	PROPN
ejpam-5719	257	16	lee	lee	PROPN
ejpam-5719	257	17	.	.	PROPN
ejpam-5719	258	1	stability	stability	NOUN
ejpam-5719	258	2	of	of	ADP
ejpam-5719	258	3	hyper	hyper	ADJ
ejpam-5719	258	4	homomorphisms	homomorphism	NOUN
ejpam-5719	258	5	and	and	CCONJ
ejpam-5719	258	6	hyper	hyper	ADJ
ejpam-5719	258	7	derivations	derivation	NOUN
ejpam-5719	258	8	in	in	ADP
ejpam-5719	258	9	complex	complex	ADJ
ejpam-5719	258	10	banach	banach	NOUN
ejpam-5719	258	11	algebras	algebra	NOUN
ejpam-5719	258	12	.	.	PUNCT
ejpam-5719	259	1	aims	aim	VERB
ejpam-5719	259	2	mathematics	mathematic	NOUN
ejpam-5719	259	3	,	,	PUNCT
ejpam-5719	259	4	7(6):10700	7(6):10700	NUM
ejpam-5719	259	5	–	–	PUNCT
ejpam-5719	259	6	10710	10710	NUM
ejpam-5719	259	7	,	,	PUNCT
ejpam-5719	259	8	2022	2022	NUM
ejpam-5719	259	9	.	.	PUNCT
ejpam-5719	260	1	[	[	X
ejpam-5719	260	2	18	18	NUM
ejpam-5719	260	3	]	]	X
ejpam-5719	260	4	j.	j.	PROPN
ejpam-5719	260	5	senasukh	senasukh	PROPN
ejpam-5719	260	6	,	,	PUNCT
ejpam-5719	260	7	s.	s.	PROPN
ejpam-5719	260	8	paokanta	paokanta	PROPN
ejpam-5719	260	9	,	,	PUNCT
ejpam-5719	260	10	and	and	CCONJ
ejpam-5719	260	11	c.	c.	PROPN
ejpam-5719	260	12	park	park	PROPN
ejpam-5719	260	13	.	.	PUNCT
ejpam-5719	261	1	on	on	ADP
ejpam-5719	261	2	stability	stability	NOUN
ejpam-5719	261	3	of	of	ADP
ejpam-5719	261	4	quadratic	quadratic	ADJ
ejpam-5719	261	5	lie	lie	NOUN
ejpam-5719	261	6	hom	hom	NOUN
ejpam-5719	261	7	-	-	PUNCT
ejpam-5719	261	8	ders	der	NOUN
ejpam-5719	261	9	in	in	ADP
ejpam-5719	261	10	lie	lie	NOUN
ejpam-5719	261	11	banach	banach	NOUN
ejpam-5719	261	12	algebras	algebra	VERB
ejpam-5719	261	13	.	.	PUNCT
ejpam-5719	262	1	rocky	rocky	ADJ
ejpam-5719	262	2	mountain	mountain	PROPN
ejpam-5719	262	3	journal	journal	NOUN
ejpam-5719	262	4	of	of	ADP
ejpam-5719	262	5	mathematics	mathematic	NOUN
ejpam-5719	262	6	,	,	PUNCT
ejpam-5719	262	7	53(6):1983–1996	53(6):1983–1996	NUM
ejpam-5719	262	8	,	,	PUNCT
ejpam-5719	262	9	2023	2023	NUM
ejpam-5719	262	10	.	.	PUNCT
ejpam-5719	263	1	[	[	X
ejpam-5719	263	2	19	19	NUM
ejpam-5719	263	3	]	]	X
ejpam-5719	263	4	s.	s.	PROPN
ejpam-5719	263	5	m.	m.	PROPN
ejpam-5719	263	6	ulam	ulam	PROPN
ejpam-5719	263	7	.	.	PUNCT
ejpam-5719	264	1	a	a	DET
ejpam-5719	264	2	collection	collection	NOUN
ejpam-5719	264	3	of	of	ADP
ejpam-5719	264	4	mathematical	mathematical	ADJ
ejpam-5719	264	5	problems	problem	NOUN
ejpam-5719	264	6	.	.	PUNCT
ejpam-5719	265	1	interscience	interscience	NOUN
ejpam-5719	265	2	tracts	tract	NOUN
ejpam-5719	265	3	in	in	ADP
ejpam-5719	265	4	pure	pure	ADJ
ejpam-5719	265	5	and	and	CCONJ
ejpam-5719	265	6	applied	applied	ADJ
ejpam-5719	265	7	mathematics	mathematic	NOUN
ejpam-5719	265	8	.	.	PUNCT
ejpam-5719	266	1	interscience	interscience	NOUN
ejpam-5719	266	2	publishers	publisher	NOUN
ejpam-5719	266	3	,	,	PUNCT
ejpam-5719	266	4	1960	1960	NUM
ejpam-5719	266	5	.	.	PUNCT