id	sid	tid	token	lemma	pos
ejpam-5758	1	1	european	european	PROPN
ejpam-5758	1	2	journal	journal	PROPN
ejpam-5758	1	3	of	of	ADP
ejpam-5758	1	4	pure	pure	ADJ
ejpam-5758	1	5	and	and	CCONJ
ejpam-5758	1	6	applied	applied	ADJ
ejpam-5758	1	7	mathematics	mathematic	NOUN
ejpam-5758	1	8	2025	2025	NUM
ejpam-5758	1	9	,	,	PUNCT
ejpam-5758	1	10	vol	vol	NOUN
ejpam-5758	1	11	.	.	PROPN
ejpam-5758	1	12	18	18	NUM
ejpam-5758	1	13	,	,	PUNCT
ejpam-5758	1	14	issue	issue	NOUN
ejpam-5758	1	15	1	1	NUM
ejpam-5758	1	16	,	,	PUNCT
ejpam-5758	1	17	article	article	NOUN
ejpam-5758	1	18	number	number	NOUN
ejpam-5758	1	19	5758	5758	NUM
ejpam-5758	1	20	issn	issn	VERB
ejpam-5758	1	21	1307	1307	NUM
ejpam-5758	1	22	-	-	SYM
ejpam-5758	1	23	5543	5543	NUM
ejpam-5758	1	24	–	–	PUNCT
ejpam-5758	1	25	ejpam.com	ejpam.com	X
ejpam-5758	1	26	published	publish	VERB
ejpam-5758	1	27	by	by	ADP
ejpam-5758	1	28	new	new	PROPN
ejpam-5758	1	29	york	york	PROPN
ejpam-5758	1	30	business	business	PROPN
ejpam-5758	1	31	global	global	PROPN
ejpam-5758	1	32	ulam	ulam	PROPN
ejpam-5758	1	33	stability	stability	NOUN
ejpam-5758	1	34	of	of	ADP
ejpam-5758	1	35	a	a	DET
ejpam-5758	1	36	pexiderized	pexiderize	VERB
ejpam-5758	1	37	additive	additive	ADJ
ejpam-5758	1	38	-	-	PUNCT
ejpam-5758	1	39	quadratic	quadratic	ADJ
ejpam-5758	1	40	equation	equation	NOUN
ejpam-5758	1	41	mehdi	mehdi	PROPN
ejpam-5758	1	42	dehghanian1,∗	dehghanian1,∗	PROPN
ejpam-5758	1	43	,	,	PUNCT
ejpam-5758	1	44	yamin	yamin	PROPN
ejpam-5758	1	45	sayyari1	sayyari1	PROPN
ejpam-5758	1	46	,	,	PUNCT
ejpam-5758	1	47	siriluk	siriluk	PROPN
ejpam-5758	1	48	donganont2,∗	donganont2,∗	PROPN
ejpam-5758	1	49	,	,	PUNCT
ejpam-5758	1	50	choonkil	choonkil	ADJ
ejpam-5758	1	51	park3	park3	PROPN
ejpam-5758	1	52	1	1	NUM
ejpam-5758	1	53	department	department	NOUN
ejpam-5758	1	54	of	of	ADP
ejpam-5758	1	55	mathematics	mathematic	NOUN
ejpam-5758	1	56	,	,	PUNCT
ejpam-5758	1	57	sirjan	sirjan	NOUN
ejpam-5758	1	58	university	university	PROPN
ejpam-5758	1	59	of	of	ADP
ejpam-5758	1	60	technology	technology	NOUN
ejpam-5758	1	61	,	,	PUNCT
ejpam-5758	1	62	sirjan	sirjan	NOUN
ejpam-5758	1	63	,	,	PUNCT
ejpam-5758	1	64	iran	iran	PROPN
ejpam-5758	1	65	2	2	NUM
ejpam-5758	1	66	school	school	NOUN
ejpam-5758	1	67	of	of	ADP
ejpam-5758	1	68	science	science	NOUN
ejpam-5758	1	69	,	,	PUNCT
ejpam-5758	1	70	university	university	NOUN
ejpam-5758	1	71	of	of	ADP
ejpam-5758	1	72	phayao	phayao	NOUN
ejpam-5758	1	73	,	,	PUNCT
ejpam-5758	1	74	phayao	phayao	NOUN
ejpam-5758	1	75	56000	56000	NUM
ejpam-5758	1	76	,	,	PUNCT
ejpam-5758	1	77	thailand	thailand	PROPN
ejpam-5758	1	78	3	3	NUM
ejpam-5758	1	79	department	department	NOUN
ejpam-5758	1	80	of	of	ADP
ejpam-5758	1	81	mathematics	mathematic	NOUN
ejpam-5758	1	82	,	,	PUNCT
ejpam-5758	1	83	research	research	NOUN
ejpam-5758	1	84	institute	institute	NOUN
ejpam-5758	1	85	for	for	ADP
ejpam-5758	1	86	convergence	convergence	NOUN
ejpam-5758	1	87	of	of	ADP
ejpam-5758	1	88	basic	basic	ADJ
ejpam-5758	1	89	science	science	NOUN
ejpam-5758	1	90	,	,	PUNCT
ejpam-5758	1	91	hanyang	hanyang	NOUN
ejpam-5758	1	92	university	university	PROPN
ejpam-5758	1	93	,	,	PUNCT
ejpam-5758	1	94	seoul	seoul	PROPN
ejpam-5758	1	95	04763	04763	NUM
ejpam-5758	1	96	,	,	PUNCT
ejpam-5758	1	97	korea	korea	PROPN
ejpam-5758	1	98	abstract	abstract	PROPN
ejpam-5758	1	99	.	.	PUNCT
ejpam-5758	2	1	suppose	suppose	VERB
ejpam-5758	2	2	that	that	SCONJ
ejpam-5758	2	3	e	e	PROPN
ejpam-5758	2	4	is	be	AUX
ejpam-5758	2	5	a	a	DET
ejpam-5758	2	6	normed	normed	ADJ
ejpam-5758	2	7	space	space	NOUN
ejpam-5758	2	8	.	.	PUNCT
ejpam-5758	3	1	in	in	ADP
ejpam-5758	3	2	this	this	DET
ejpam-5758	3	3	work	work	NOUN
ejpam-5758	3	4	,	,	PUNCT
ejpam-5758	3	5	using	use	VERB
ejpam-5758	3	6	brzdȩk	brzdȩk	NOUN
ejpam-5758	3	7	fixed	fix	VERB
ejpam-5758	3	8	point	point	NOUN
ejpam-5758	3	9	theorem	theorem	VERB
ejpam-5758	3	10	,	,	PUNCT
ejpam-5758	3	11	we	we	PRON
ejpam-5758	3	12	prove	prove	VERB
ejpam-5758	3	13	the	the	DET
ejpam-5758	3	14	hyers	hyers	PROPN
ejpam-5758	3	15	-	-	PUNCT
ejpam-5758	3	16	ulam	ulam	ADJ
ejpam-5758	3	17	stability	stability	NOUN
ejpam-5758	3	18	of	of	ADP
ejpam-5758	3	19	the	the	DET
ejpam-5758	3	20	pexiderized	pexiderize	VERB
ejpam-5758	3	21	additive	additive	ADJ
ejpam-5758	3	22	-	-	PUNCT
ejpam-5758	3	23	quadratic	quadratic	ADJ
ejpam-5758	3	24	functional	functional	ADJ
ejpam-5758	3	25	equation	equation	NOUN
ejpam-5758	3	26	f(x+	f(x+	NOUN
ejpam-5758	3	27	y	y	PROPN
ejpam-5758	3	28	)	)	PUNCT
ejpam-5758	4	1	+	+	CCONJ
ejpam-5758	4	2	f(x−	f(x−	PROPN
ejpam-5758	4	3	y	y	NOUN
ejpam-5758	4	4	)	)	PUNCT
ejpam-5758	5	1	+	+	CCONJ
ejpam-5758	5	2	h(x+	h(x+	ADV
ejpam-5758	5	3	y	y	X
ejpam-5758	5	4	)	)	PUNCT
ejpam-5758	5	5	=	=	SYM
ejpam-5758	5	6	2f(x	2f(x	PROPN
ejpam-5758	5	7	)	)	PUNCT
ejpam-5758	6	1	+	+	NUM
ejpam-5758	6	2	2f(y	2f(y	NUM
ejpam-5758	6	3	)	)	PUNCT
ejpam-5758	7	1	+	+	CCONJ
ejpam-5758	7	2	h(x	h(x	PROPN
ejpam-5758	7	3	)	)	PUNCT
ejpam-5758	8	1	+	+	NUM
ejpam-5758	8	2	h(y	h(y	ADV
ejpam-5758	8	3	)	)	PUNCT
ejpam-5758	8	4	for	for	ADP
ejpam-5758	8	5	all	all	DET
ejpam-5758	8	6	x	x	NOUN
ejpam-5758	8	7	,	,	PUNCT
ejpam-5758	8	8	y	y	PROPN
ejpam-5758	8	9	∈	∈	PROPN
ejpam-5758	8	10	e.	e.	PROPN
ejpam-5758	8	11	2020	2020	NUM
ejpam-5758	8	12	mathematics	mathematics	PROPN
ejpam-5758	8	13	subject	subject	NOUN
ejpam-5758	8	14	classifications	classification	NOUN
ejpam-5758	8	15	:	:	PUNCT
ejpam-5758	8	16	39b72	39b72	NUM
ejpam-5758	8	17	,	,	PUNCT
ejpam-5758	8	18	39b82	39b82	NUM
ejpam-5758	8	19	,	,	PUNCT
ejpam-5758	8	20	47h10	47h10	DET
ejpam-5758	8	21	key	key	ADJ
ejpam-5758	8	22	words	word	NOUN
ejpam-5758	8	23	and	and	CCONJ
ejpam-5758	8	24	phrases	phrase	NOUN
ejpam-5758	8	25	:	:	PUNCT
ejpam-5758	8	26	pexiderized	pexiderized	ADJ
ejpam-5758	8	27	additive	additive	ADJ
ejpam-5758	8	28	-	-	PUNCT
ejpam-5758	8	29	quadratic	quadratic	ADJ
ejpam-5758	8	30	functional	functional	ADJ
ejpam-5758	8	31	equation	equation	NOUN
ejpam-5758	8	32	,	,	PUNCT
ejpam-5758	8	33	hyers	hyers	PROPN
ejpam-5758	8	34	-	-	PUNCT
ejpam-5758	8	35	ulam	ulam	PROPN
ejpam-5758	8	36	stability	stability	NOUN
ejpam-5758	8	37	,	,	PUNCT
ejpam-5758	8	38	fixed	fix	VERB
ejpam-5758	8	39	point	point	NOUN
ejpam-5758	8	40	1	1	NUM
ejpam-5758	8	41	.	.	PUNCT
ejpam-5758	8	42	introduction	introduction	NOUN
ejpam-5758	8	43	and	and	CCONJ
ejpam-5758	8	44	preliminariess	preliminariess	NOUN
ejpam-5758	8	45	the	the	DET
ejpam-5758	8	46	concept	concept	NOUN
ejpam-5758	8	47	of	of	ADP
ejpam-5758	8	48	stability	stability	NOUN
ejpam-5758	8	49	of	of	ADP
ejpam-5758	8	50	functional	functional	ADJ
ejpam-5758	8	51	equations	equation	NOUN
ejpam-5758	8	52	originated	originate	VERB
ejpam-5758	8	53	from	from	ADP
ejpam-5758	8	54	a	a	DET
ejpam-5758	8	55	problem	problem	NOUN
ejpam-5758	8	56	of	of	ADP
ejpam-5758	8	57	ulam	ulam	PROPN
ejpam-5758	8	58	[	[	X
ejpam-5758	8	59	33	33	NUM
ejpam-5758	8	60	]	]	PUNCT
ejpam-5758	8	61	.	.	PUNCT
ejpam-5758	9	1	in	in	ADP
ejpam-5758	9	2	continue	continue	PROPN
ejpam-5758	9	3	,	,	PUNCT
ejpam-5758	9	4	hyers	hyer	NOUN
ejpam-5758	9	5	gave	give	VERB
ejpam-5758	9	6	a	a	DET
ejpam-5758	9	7	positive	positive	ADJ
ejpam-5758	9	8	answer	answer	NOUN
ejpam-5758	9	9	to	to	ADP
ejpam-5758	9	10	the	the	DET
ejpam-5758	9	11	question	question	NOUN
ejpam-5758	9	12	of	of	ADP
ejpam-5758	9	13	ulam	ulam	PROPN
ejpam-5758	9	14	in	in	ADP
ejpam-5758	9	15	the	the	DET
ejpam-5758	9	16	context	context	NOUN
ejpam-5758	9	17	of	of	ADP
ejpam-5758	9	18	banach	banach	NOUN
ejpam-5758	9	19	spaces	space	NOUN
ejpam-5758	9	20	in	in	ADP
ejpam-5758	9	21	the	the	DET
ejpam-5758	9	22	case	case	NOUN
ejpam-5758	9	23	of	of	ADP
ejpam-5758	9	24	additive	additive	ADJ
ejpam-5758	9	25	mappings	mapping	NOUN
ejpam-5758	9	26	,	,	PUNCT
ejpam-5758	9	27	that	that	PRON
ejpam-5758	9	28	was	be	AUX
ejpam-5758	9	29	the	the	DET
ejpam-5758	9	30	first	first	ADJ
ejpam-5758	9	31	notable	notable	ADJ
ejpam-5758	9	32	advance	advance	NOUN
ejpam-5758	9	33	and	and	CCONJ
ejpam-5758	9	34	a	a	DET
ejpam-5758	9	35	step	step	NOUN
ejpam-5758	9	36	toward	toward	ADP
ejpam-5758	9	37	more	more	ADJ
ejpam-5758	9	38	solutions	solution	NOUN
ejpam-5758	9	39	in	in	ADP
ejpam-5758	9	40	this	this	DET
ejpam-5758	9	41	field	field	NOUN
ejpam-5758	9	42	.	.	PUNCT
ejpam-5758	10	1	also	also	ADV
ejpam-5758	10	2	,	,	PUNCT
ejpam-5758	10	3	he	he	PRON
ejpam-5758	10	4	answered	answer	VERB
ejpam-5758	10	5	the	the	DET
ejpam-5758	10	6	question	question	NOUN
ejpam-5758	10	7	of	of	ADP
ejpam-5758	10	8	ulam	ulam	NOUN
ejpam-5758	10	9	for	for	ADP
ejpam-5758	10	10	the	the	DET
ejpam-5758	10	11	case	case	NOUN
ejpam-5758	10	12	of	of	ADP
ejpam-5758	10	13	approximate	approximate	ADJ
ejpam-5758	10	14	additive	additive	ADJ
ejpam-5758	10	15	mappings	mapping	NOUN
ejpam-5758	10	16	under	under	ADP
ejpam-5758	10	17	the	the	DET
ejpam-5758	10	18	assumption	assumption	NOUN
ejpam-5758	10	19	that	that	SCONJ
ejpam-5758	10	20	g1	g1	PROPN
ejpam-5758	10	21	and	and	CCONJ
ejpam-5758	10	22	g2	g2	PROPN
ejpam-5758	10	23	are	be	AUX
ejpam-5758	10	24	banach	banach	NOUN
ejpam-5758	10	25	spaces	space	NOUN
ejpam-5758	10	26	(	(	PUNCT
ejpam-5758	10	27	see	see	VERB
ejpam-5758	10	28	[	[	X
ejpam-5758	10	29	19	19	NUM
ejpam-5758	10	30	]	]	NUM
ejpam-5758	10	31	)	)	PUNCT
ejpam-5758	10	32	.	.	PUNCT
ejpam-5758	11	1	the	the	DET
ejpam-5758	11	2	method	method	NOUN
ejpam-5758	11	3	provided	provide	VERB
ejpam-5758	11	4	by	by	ADP
ejpam-5758	11	5	hyers	hyer	NOUN
ejpam-5758	11	6	[	[	X
ejpam-5758	11	7	19	19	NUM
ejpam-5758	11	8	]	]	PUNCT
ejpam-5758	11	9	which	which	PRON
ejpam-5758	11	10	produces	produce	VERB
ejpam-5758	11	11	the	the	DET
ejpam-5758	11	12	additive	additive	ADJ
ejpam-5758	11	13	function	function	NOUN
ejpam-5758	11	14	will	will	AUX
ejpam-5758	11	15	be	be	AUX
ejpam-5758	11	16	called	call	VERB
ejpam-5758	11	17	a	a	DET
ejpam-5758	11	18	direct	direct	ADJ
ejpam-5758	11	19	method	method	NOUN
ejpam-5758	11	20	.	.	PUNCT
ejpam-5758	12	1	this	this	DET
ejpam-5758	12	2	method	method	NOUN
ejpam-5758	12	3	is	be	AUX
ejpam-5758	12	4	the	the	DET
ejpam-5758	12	5	most	most	ADV
ejpam-5758	12	6	important	important	ADJ
ejpam-5758	12	7	and	and	CCONJ
ejpam-5758	12	8	powerful	powerful	ADJ
ejpam-5758	12	9	tool	tool	NOUN
ejpam-5758	12	10	to	to	ADP
ejpam-5758	12	11	concerning	concern	VERB
ejpam-5758	12	12	the	the	DET
ejpam-5758	12	13	stability	stability	NOUN
ejpam-5758	12	14	of	of	ADP
ejpam-5758	12	15	system	system	NOUN
ejpam-5758	12	16	of	of	ADP
ejpam-5758	12	17	different	different	ADJ
ejpam-5758	12	18	functional	functional	ADJ
ejpam-5758	12	19	equations	equation	NOUN
ejpam-5758	12	20	[	[	X
ejpam-5758	12	21	31	31	NUM
ejpam-5758	12	22	]	]	PUNCT
ejpam-5758	12	23	.	.	PUNCT
ejpam-5758	13	1	that	that	PRON
ejpam-5758	13	2	is	be	AUX
ejpam-5758	13	3	,	,	PUNCT
ejpam-5758	13	4	the	the	DET
ejpam-5758	13	5	exact	exact	ADJ
ejpam-5758	13	6	solution	solution	NOUN
ejpam-5758	13	7	of	of	ADP
ejpam-5758	13	8	the	the	DET
ejpam-5758	13	9	functional	functional	ADJ
ejpam-5758	13	10	equation	equation	NOUN
ejpam-5758	13	11	is	be	AUX
ejpam-5758	13	12	explicitly	explicitly	ADV
ejpam-5758	13	13	constructed	construct	VERB
ejpam-5758	13	14	as	as	ADP
ejpam-5758	13	15	a	a	DET
ejpam-5758	13	16	limit	limit	NOUN
ejpam-5758	13	17	of	of	ADP
ejpam-5758	13	18	a	a	DET
ejpam-5758	13	19	sequence	sequence	NOUN
ejpam-5758	13	20	,	,	PUNCT
ejpam-5758	13	21	starting	start	VERB
ejpam-5758	13	22	from	from	ADP
ejpam-5758	13	23	the	the	DET
ejpam-5758	13	24	∗corresponding	∗corresponding	NOUN
ejpam-5758	13	25	author	author	NOUN
ejpam-5758	13	26	.	.	PUNCT
ejpam-5758	14	1	∗corresponding	∗corresponde	VERB
ejpam-5758	14	2	author	author	NOUN
ejpam-5758	14	3	.	.	PUNCT
ejpam-5758	15	1	doi	doi	NOUN
ejpam-5758	15	2	:	:	PUNCT
ejpam-5758	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5758	https://doi.org/10.29020/nybg.ejpam.v18i1.5758	NOUN
ejpam-5758	15	4	email	email	NOUN
ejpam-5758	15	5	addresses	address	NOUN
ejpam-5758	15	6	:	:	PUNCT
ejpam-5758	15	7	mdehghanian@sirjantech.ac.ir	mdehghanian@sirjantech.ac.ir	NOUN
ejpam-5758	15	8	(	(	PUNCT
ejpam-5758	15	9	m.	m.	NOUN
ejpam-5758	15	10	dehghanian	dehghanian	PROPN
ejpam-5758	15	11	)	)	PUNCT
ejpam-5758	15	12	,	,	PUNCT
ejpam-5758	15	13	y.sayyari@sirjantech.ac.ir	y.sayyari@sirjantech.ac.ir	PROPN
ejpam-5758	15	14	(	(	PUNCT
ejpam-5758	15	15	y.	y.	PROPN
ejpam-5758	15	16	sayyari	sayyari	PROPN
ejpam-5758	15	17	)	)	PUNCT
ejpam-5758	15	18	,	,	PUNCT
ejpam-5758	15	19	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-5758	15	20	(	(	PUNCT
ejpam-5758	15	21	s.	s.	PROPN
ejpam-5758	15	22	donganont	donganont	PROPN
ejpam-5758	15	23	)	)	PUNCT
ejpam-5758	15	24	,	,	PUNCT
ejpam-5758	15	25	baak@hanyang.ac.kr	baak@hanyang.ac.kr	PROPN
ejpam-5758	15	26	(	(	PUNCT
ejpam-5758	15	27	c.	c.	PROPN
ejpam-5758	15	28	park	park	PROPN
ejpam-5758	15	29	)	)	PUNCT
ejpam-5758	15	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5758	16	1	1	1	NUM
ejpam-5758	16	2	copyright	copyright	NOUN
ejpam-5758	16	3	:	:	PUNCT
ejpam-5758	16	4	©	©	PROPN
ejpam-5758	16	5	2025	2025	NUM
ejpam-5758	16	6	the	the	DET
ejpam-5758	16	7	author(s	author(s	NOUN
ejpam-5758	16	8	)	)	PUNCT
ejpam-5758	16	9	.	.	PUNCT
ejpam-5758	17	1	(	(	PUNCT
ejpam-5758	17	2	cc	cc	NOUN
ejpam-5758	17	3	by	by	ADP
ejpam-5758	17	4	-	-	PUNCT
ejpam-5758	17	5	nc	nc	PROPN
ejpam-5758	17	6	4.0	4.0	NUM
ejpam-5758	17	7	)	)	PUNCT
ejpam-5758	17	8	m.	m.	NOUN
ejpam-5758	17	9	dehghanian	dehghanian	PROPN
ejpam-5758	17	10	et	et	PROPN
ejpam-5758	17	11	al	al	PROPN
ejpam-5758	17	12	.	.	PUNCT
ejpam-5758	17	13	/	/	SYM
ejpam-5758	17	14	eur	eur	PROPN
ejpam-5758	17	15	.	.	PUNCT
ejpam-5758	18	1	j.	j.	PROPN
ejpam-5758	18	2	pure	pure	PROPN
ejpam-5758	18	3	appl	appl	PROPN
ejpam-5758	18	4	.	.	PROPN
ejpam-5758	18	5	math	math	PROPN
ejpam-5758	18	6	,	,	PUNCT
ejpam-5758	18	7	18	18	NUM
ejpam-5758	18	8	(	(	PUNCT
ejpam-5758	18	9	1	1	NUM
ejpam-5758	18	10	)	)	PUNCT
ejpam-5758	18	11	(	(	PUNCT
ejpam-5758	18	12	2025	2025	NUM
ejpam-5758	18	13	)	)	PUNCT
ejpam-5758	18	14	,	,	PUNCT
ejpam-5758	18	15	5758	5758	NUM
ejpam-5758	18	16	2	2	NUM
ejpam-5758	18	17	of	of	ADP
ejpam-5758	18	18	13	13	NUM
ejpam-5758	18	19	given	give	VERB
ejpam-5758	18	20	approximate	approximate	ADJ
ejpam-5758	18	21	solution	solution	NOUN
ejpam-5758	18	22	(	(	PUNCT
ejpam-5758	18	23	see	see	VERB
ejpam-5758	18	24	[	[	X
ejpam-5758	18	25	14	14	NUM
ejpam-5758	18	26	,	,	PUNCT
ejpam-5758	18	27	23	23	NUM
ejpam-5758	18	28	,	,	PUNCT
ejpam-5758	18	29	32	32	NUM
ejpam-5758	18	30	]	]	PUNCT
ejpam-5758	18	31	)	)	PUNCT
ejpam-5758	18	32	.	.	PUNCT
ejpam-5758	19	1	the	the	DET
ejpam-5758	19	2	other	other	ADJ
ejpam-5758	19	3	method	method	NOUN
ejpam-5758	19	4	is	be	AUX
ejpam-5758	19	5	fixed	fix	VERB
ejpam-5758	19	6	point	point	NOUN
ejpam-5758	19	7	method	method	NOUN
ejpam-5758	19	8	,	,	PUNCT
ejpam-5758	19	9	that	that	ADV
ejpam-5758	19	10	is	is	ADV
ejpam-5758	19	11	,	,	PUNCT
ejpam-5758	19	12	the	the	DET
ejpam-5758	19	13	exact	exact	ADJ
ejpam-5758	19	14	solution	solution	NOUN
ejpam-5758	19	15	of	of	ADP
ejpam-5758	19	16	the	the	DET
ejpam-5758	19	17	functional	functional	ADJ
ejpam-5758	19	18	equation	equation	NOUN
ejpam-5758	19	19	is	be	AUX
ejpam-5758	19	20	explicitly	explicitly	ADV
ejpam-5758	19	21	constructed	construct	VERB
ejpam-5758	19	22	as	as	ADP
ejpam-5758	19	23	a	a	DET
ejpam-5758	19	24	fixed	fix	VERB
ejpam-5758	19	25	point	point	NOUN
ejpam-5758	19	26	of	of	ADP
ejpam-5758	19	27	some	some	DET
ejpam-5758	19	28	certain	certain	ADJ
ejpam-5758	19	29	map	map	NOUN
ejpam-5758	19	30	[	[	X
ejpam-5758	19	31	4	4	NUM
ejpam-5758	19	32	,	,	PUNCT
ejpam-5758	19	33	11–13	11–13	NUM
ejpam-5758	19	34	,	,	PUNCT
ejpam-5758	19	35	27	27	NUM
ejpam-5758	19	36	]	]	PUNCT
ejpam-5758	19	37	.	.	PUNCT
ejpam-5758	20	1	recently	recently	ADV
ejpam-5758	20	2	,	,	PUNCT
ejpam-5758	20	3	a	a	DET
ejpam-5758	20	4	number	number	NOUN
ejpam-5758	20	5	of	of	ADP
ejpam-5758	20	6	results	result	NOUN
ejpam-5758	20	7	concerning	concern	VERB
ejpam-5758	20	8	the	the	DET
ejpam-5758	20	9	stability	stability	NOUN
ejpam-5758	20	10	have	have	AUX
ejpam-5758	20	11	been	be	AUX
ejpam-5758	20	12	obtained	obtain	VERB
ejpam-5758	20	13	by	by	ADP
ejpam-5758	20	14	different	different	ADJ
ejpam-5758	20	15	ways	way	NOUN
ejpam-5758	20	16	and	and	CCONJ
ejpam-5758	20	17	been	be	AUX
ejpam-5758	20	18	applied	apply	VERB
ejpam-5758	20	19	to	to	ADP
ejpam-5758	20	20	a	a	DET
ejpam-5758	20	21	number	number	NOUN
ejpam-5758	20	22	of	of	ADP
ejpam-5758	20	23	functional	functional	ADJ
ejpam-5758	20	24	equations	equation	NOUN
ejpam-5758	20	25	,	,	PUNCT
ejpam-5758	20	26	functional	functional	ADJ
ejpam-5758	20	27	inequalities	inequality	NOUN
ejpam-5758	20	28	and	and	CCONJ
ejpam-5758	20	29	mappings	mapping	NOUN
ejpam-5758	20	30	(	(	PUNCT
ejpam-5758	20	31	see	see	VERB
ejpam-5758	20	32	[	[	X
ejpam-5758	20	33	6	6	NUM
ejpam-5758	20	34	,	,	PUNCT
ejpam-5758	20	35	7	7	NUM
ejpam-5758	20	36	,	,	PUNCT
ejpam-5758	20	37	22	22	NUM
ejpam-5758	20	38	,	,	PUNCT
ejpam-5758	20	39	29	29	NUM
ejpam-5758	20	40	,	,	PUNCT
ejpam-5758	20	41	30	30	NUM
ejpam-5758	20	42	]	]	PUNCT
ejpam-5758	20	43	)	)	PUNCT
ejpam-5758	20	44	.	.	PUNCT
ejpam-5758	21	1	also	also	ADV
ejpam-5758	21	2	,	,	PUNCT
ejpam-5758	21	3	many	many	ADJ
ejpam-5758	21	4	mathematicians	mathematician	NOUN
ejpam-5758	21	5	studied	study	VERB
ejpam-5758	21	6	the	the	DET
ejpam-5758	21	7	stabilities	stability	NOUN
ejpam-5758	21	8	additive	additive	ADJ
ejpam-5758	21	9	-	-	PUNCT
ejpam-5758	21	10	quadratic	quadratic	ADJ
ejpam-5758	21	11	equation	equation	NOUN
ejpam-5758	21	12	and	and	CCONJ
ejpam-5758	21	13	the	the	DET
ejpam-5758	21	14	drygas	drygas	NOUN
ejpam-5758	21	15	’	'	PUNCT
ejpam-5758	21	16	equation	equation	NOUN
ejpam-5758	21	17	(	(	PUNCT
ejpam-5758	21	18	see	see	VERB
ejpam-5758	21	19	[	[	X
ejpam-5758	21	20	12	12	NUM
ejpam-5758	21	21	,	,	PUNCT
ejpam-5758	21	22	18	18	NUM
ejpam-5758	21	23	,	,	PUNCT
ejpam-5758	21	24	21	21	NUM
ejpam-5758	21	25	]	]	PUNCT
ejpam-5758	21	26	)	)	PUNCT
ejpam-5758	21	27	.	.	PUNCT
ejpam-5758	22	1	a	a	DET
ejpam-5758	22	2	mapping	mapping	NOUN
ejpam-5758	22	3	f	f	NOUN
ejpam-5758	22	4	:	:	PUNCT
ejpam-5758	22	5	e	e	X
ejpam-5758	22	6	→	→	SYM
ejpam-5758	22	7	b	b	PROPN
ejpam-5758	22	8	is	be	AUX
ejpam-5758	22	9	said	say	VERB
ejpam-5758	22	10	to	to	PART
ejpam-5758	22	11	be	be	AUX
ejpam-5758	22	12	additive	additive	ADJ
ejpam-5758	22	13	if	if	SCONJ
ejpam-5758	22	14	it	it	PRON
ejpam-5758	22	15	satisfies	satisfy	VERB
ejpam-5758	22	16	f(x+	f(x+	VERB
ejpam-5758	22	17	y	y	NOUN
ejpam-5758	22	18	)	)	PUNCT
ejpam-5758	22	19	=	=	SYM
ejpam-5758	22	20	f(x	f(x	PROPN
ejpam-5758	22	21	)	)	PUNCT
ejpam-5758	23	1	+	+	SYM
ejpam-5758	23	2	f(y	f(y	NOUN
ejpam-5758	23	3	)	)	PUNCT
ejpam-5758	23	4	for	for	ADP
ejpam-5758	23	5	all	all	DET
ejpam-5758	23	6	x	x	NOUN
ejpam-5758	23	7	,	,	PUNCT
ejpam-5758	23	8	y	y	PROPN
ejpam-5758	23	9	∈	∈	PROPN
ejpam-5758	23	10	e.	e.	PROPN
ejpam-5758	24	1	a	a	DET
ejpam-5758	24	2	mapping	mapping	NOUN
ejpam-5758	24	3	f	f	X
ejpam-5758	24	4	:	:	PUNCT
ejpam-5758	24	5	e	e	X
ejpam-5758	24	6	→	→	SYM
ejpam-5758	24	7	b	b	PROPN
ejpam-5758	24	8	is	be	AUX
ejpam-5758	24	9	called	call	VERB
ejpam-5758	24	10	quadratic	quadratic	ADJ
ejpam-5758	24	11	if	if	SCONJ
ejpam-5758	24	12	f	f	PROPN
ejpam-5758	24	13	satisfies	satisfy	VERB
ejpam-5758	24	14	the	the	DET
ejpam-5758	24	15	functional	functional	ADJ
ejpam-5758	24	16	equation	equation	NOUN
ejpam-5758	24	17	f(x+	f(x+	NOUN
ejpam-5758	24	18	y	y	PROPN
ejpam-5758	24	19	)	)	PUNCT
ejpam-5758	25	1	+	+	CCONJ
ejpam-5758	25	2	f(x−	f(x−	PROPN
ejpam-5758	25	3	y	y	NOUN
ejpam-5758	25	4	)	)	PUNCT
ejpam-5758	25	5	=	=	SYM
ejpam-5758	25	6	2f(x	2f(x	PROPN
ejpam-5758	25	7	)	)	PUNCT
ejpam-5758	26	1	+	+	NUM
ejpam-5758	26	2	2f(y	2f(y	NUM
ejpam-5758	26	3	)	)	PUNCT
ejpam-5758	26	4	for	for	ADP
ejpam-5758	26	5	all	all	DET
ejpam-5758	26	6	x	x	NOUN
ejpam-5758	26	7	,	,	PUNCT
ejpam-5758	26	8	y	y	PROPN
ejpam-5758	26	9	∈	∈	PROPN
ejpam-5758	26	10	e.	e.	PROPN
ejpam-5758	26	11	in	in	ADP
ejpam-5758	26	12	[	[	X
ejpam-5758	26	13	1	1	NUM
ejpam-5758	26	14	]	]	PUNCT
ejpam-5758	26	15	,	,	PUNCT
ejpam-5758	26	16	aczél	aczél	NOUN
ejpam-5758	26	17	and	and	CCONJ
ejpam-5758	26	18	dhombres	dhombre	NOUN
ejpam-5758	26	19	showed	show	VERB
ejpam-5758	26	20	that	that	SCONJ
ejpam-5758	26	21	if	if	SCONJ
ejpam-5758	26	22	e	e	NOUN
ejpam-5758	26	23	is	be	AUX
ejpam-5758	26	24	a	a	DET
ejpam-5758	26	25	linear	linear	ADJ
ejpam-5758	26	26	space	space	NOUN
ejpam-5758	26	27	over	over	ADP
ejpam-5758	26	28	a	a	DET
ejpam-5758	26	29	field	field	NOUN
ejpam-5758	26	30	f	f	NOUN
ejpam-5758	26	31	of	of	ADP
ejpam-5758	26	32	characteristic	characteristic	ADJ
ejpam-5758	26	33	0	0	NUM
ejpam-5758	26	34	,	,	PUNCT
ejpam-5758	26	35	then	then	ADV
ejpam-5758	26	36	q	q	NOUN
ejpam-5758	26	37	:	:	PUNCT
ejpam-5758	26	38	e	e	X
ejpam-5758	26	39	→	→	SYM
ejpam-5758	26	40	f	f	PROPN
ejpam-5758	26	41	is	be	AUX
ejpam-5758	26	42	a	a	DET
ejpam-5758	26	43	solution	solution	NOUN
ejpam-5758	26	44	of	of	ADP
ejpam-5758	26	45	the	the	DET
ejpam-5758	26	46	quadratci	quadratci	ADJ
ejpam-5758	26	47	functional	functional	ADJ
ejpam-5758	26	48	equation	equation	NOUN
ejpam-5758	26	49	if	if	SCONJ
ejpam-5758	26	50	and	and	CCONJ
ejpam-5758	26	51	only	only	ADV
ejpam-5758	26	52	if	if	SCONJ
ejpam-5758	26	53	there	there	PRON
ejpam-5758	26	54	is	be	VERB
ejpam-5758	26	55	a	a	DET
ejpam-5758	26	56	unique	unique	ADJ
ejpam-5758	26	57	symmetric	symmetric	ADJ
ejpam-5758	26	58	biadditive	biadditive	ADJ
ejpam-5758	26	59	mapping	mapping	NOUN
ejpam-5758	26	60	l	l	NOUN
ejpam-5758	26	61	:	:	PUNCT
ejpam-5758	26	62	e2	e2	PROPN
ejpam-5758	26	63	→	→	SYM
ejpam-5758	26	64	f	f	PROPN
ejpam-5758	26	65	such	such	ADJ
ejpam-5758	26	66	that	that	SCONJ
ejpam-5758	26	67	q(x	q(x	PROPN
ejpam-5758	26	68	)	)	PUNCT
ejpam-5758	26	69	=	=	SYM
ejpam-5758	26	70	l(x	l(x	PROPN
ejpam-5758	26	71	,	,	PUNCT
ejpam-5758	26	72	x	x	NOUN
ejpam-5758	26	73	)	)	PUNCT
ejpam-5758	26	74	for	for	ADP
ejpam-5758	26	75	all	all	DET
ejpam-5758	26	76	x	x	SYM
ejpam-5758	26	77	∈	∈	PROPN
ejpam-5758	26	78	e.	e.	PROPN
ejpam-5758	26	79	various	various	ADJ
ejpam-5758	26	80	pexiderized	pexiderized	ADJ
ejpam-5758	26	81	versions	version	NOUN
ejpam-5758	26	82	of	of	ADP
ejpam-5758	26	83	the	the	DET
ejpam-5758	26	84	quadratic	quadratic	ADJ
ejpam-5758	26	85	functional	functional	ADJ
ejpam-5758	26	86	equation	equation	NOUN
ejpam-5758	26	87	have	have	AUX
ejpam-5758	26	88	been	be	AUX
ejpam-5758	26	89	studied	study	VERB
ejpam-5758	26	90	in	in	ADP
ejpam-5758	26	91	[	[	X
ejpam-5758	26	92	5	5	NUM
ejpam-5758	26	93	,	,	PUNCT
ejpam-5758	26	94	20	20	NUM
ejpam-5758	26	95	]	]	PUNCT
ejpam-5758	26	96	.	.	PUNCT
ejpam-5758	27	1	various	various	ADJ
ejpam-5758	27	2	works	work	NOUN
ejpam-5758	27	3	on	on	ADP
ejpam-5758	27	4	stability	stability	NOUN
ejpam-5758	27	5	of	of	ADP
ejpam-5758	27	6	the	the	DET
ejpam-5758	27	7	quadratic	quadratic	ADJ
ejpam-5758	27	8	functional	functional	ADJ
ejpam-5758	27	9	equation	equation	NOUN
ejpam-5758	27	10	can	can	AUX
ejpam-5758	27	11	be	be	AUX
ejpam-5758	27	12	found	find	VERB
ejpam-5758	27	13	in	in	ADP
ejpam-5758	27	14	[	[	X
ejpam-5758	27	15	9	9	NUM
ejpam-5758	27	16	,	,	PUNCT
ejpam-5758	27	17	16	16	NUM
ejpam-5758	27	18	,	,	PUNCT
ejpam-5758	27	19	28	28	NUM
ejpam-5758	27	20	]	]	PUNCT
ejpam-5758	27	21	.	.	PUNCT
ejpam-5758	28	1	in	in	ADP
ejpam-5758	28	2	2011	2011	NUM
ejpam-5758	28	3	,	,	PUNCT
ejpam-5758	28	4	brzdȩk	brzdȩk	PROPN
ejpam-5758	28	5	et	et	PROPN
ejpam-5758	28	6	al	al	PROPN
ejpam-5758	28	7	.	.	PUNCT
ejpam-5758	29	1	[	[	X
ejpam-5758	29	2	8	8	NUM
ejpam-5758	29	3	]	]	PUNCT
ejpam-5758	29	4	gave	give	VERB
ejpam-5758	29	5	a	a	DET
ejpam-5758	29	6	simple	simple	ADJ
ejpam-5758	29	7	fixed	fix	VERB
ejpam-5758	29	8	point	point	NOUN
ejpam-5758	29	9	theorem	theorem	VERB
ejpam-5758	29	10	.	.	PUNCT
ejpam-5758	30	1	before	before	ADP
ejpam-5758	30	2	stating	state	VERB
ejpam-5758	30	3	brzdȩk	brzdȩk	NOUN
ejpam-5758	30	4	fixed	fix	VERB
ejpam-5758	30	5	point	point	NOUN
ejpam-5758	30	6	theorem	theorem	ADJ
ejpam-5758	30	7	,	,	PUNCT
ejpam-5758	30	8	let	let	VERB
ejpam-5758	30	9	us	we	PRON
ejpam-5758	30	10	introduce	introduce	VERB
ejpam-5758	30	11	some	some	DET
ejpam-5758	30	12	hypothesis	hypothesis	NOUN
ejpam-5758	30	13	,	,	PUNCT
ejpam-5758	30	14	which	which	PRON
ejpam-5758	30	15	we	we	PRON
ejpam-5758	30	16	will	will	AUX
ejpam-5758	30	17	use	use	VERB
ejpam-5758	30	18	in	in	ADP
ejpam-5758	30	19	the	the	DET
ejpam-5758	30	20	sequel	sequel	NOUN
ejpam-5758	30	21	.	.	PUNCT
ejpam-5758	31	1	(	(	PUNCT
ejpam-5758	31	2	a1	a1	NOUN
ejpam-5758	31	3	)	)	PUNCT
ejpam-5758	31	4	e	e	NOUN
ejpam-5758	31	5	is	be	AUX
ejpam-5758	31	6	a	a	DET
ejpam-5758	31	7	nonempty	nonempty	ADV
ejpam-5758	31	8	set	set	VERB
ejpam-5758	31	9	and	and	CCONJ
ejpam-5758	31	10	b	b	NOUN
ejpam-5758	31	11	is	be	AUX
ejpam-5758	31	12	a	a	DET
ejpam-5758	31	13	banach	banach	NOUN
ejpam-5758	31	14	space	space	NOUN
ejpam-5758	31	15	.	.	PUNCT
ejpam-5758	32	1	(	(	PUNCT
ejpam-5758	32	2	a2	a2	PROPN
ejpam-5758	32	3	)	)	PUNCT
ejpam-5758	32	4	δ1	δ1	NOUN
ejpam-5758	32	5	,	,	PUNCT
ejpam-5758	32	6	.	.	PUNCT
ejpam-5758	32	7	.	.	PUNCT
ejpam-5758	33	1	.	.	PUNCT
ejpam-5758	34	1	,	,	PUNCT
ejpam-5758	34	2	δk	δk	X
ejpam-5758	34	3	:	:	PUNCT
ejpam-5758	34	4	e	e	X
ejpam-5758	34	5	→	→	SYM
ejpam-5758	34	6	e	e	X
ejpam-5758	34	7	and	and	CCONJ
ejpam-5758	34	8	λ1	λ1	PROPN
ejpam-5758	34	9	,	,	PUNCT
ejpam-5758	34	10	.	.	PUNCT
ejpam-5758	34	11	.	.	PUNCT
ejpam-5758	35	1	.	.	PUNCT
ejpam-5758	36	1	,	,	PUNCT
ejpam-5758	36	2	λk	λk	X
ejpam-5758	36	3	:	:	PUNCT
ejpam-5758	36	4	e	e	X
ejpam-5758	36	5	→	→	PUNCT
ejpam-5758	36	6	r+	r+	NOUN
ejpam-5758	36	7	are	be	AUX
ejpam-5758	36	8	given	give	VERB
ejpam-5758	36	9	maps	map	NOUN
ejpam-5758	36	10	.	.	PUNCT
ejpam-5758	37	1	(	(	PUNCT
ejpam-5758	37	2	a3	a3	NOUN
ejpam-5758	37	3	)	)	PUNCT
ejpam-5758	37	4	h	h	NOUN
ejpam-5758	37	5	:	:	PUNCT
ejpam-5758	37	6	be	be	AUX
ejpam-5758	37	7	→	→	PUNCT
ejpam-5758	37	8	be	be	AUX
ejpam-5758	37	9	is	be	AUX
ejpam-5758	37	10	an	an	DET
ejpam-5758	37	11	operator	operator	NOUN
ejpam-5758	37	12	satisfying	satisfy	VERB
ejpam-5758	37	13	the	the	DET
ejpam-5758	37	14	inequality	inequality	NOUN
ejpam-5758	37	15	∥hg(x)−hl(x)∥	∥hg(x)−hl(x)∥	NOUN
ejpam-5758	37	16	≤	≤	PROPN
ejpam-5758	37	17	k∑	k∑	VERB
ejpam-5758	37	18	i=1	i=1	PROPN
ejpam-5758	38	1	λi(x)∥g	λi(x)∥g	PROPN
ejpam-5758	38	2	(	(	PUNCT
ejpam-5758	38	3	δi(x))−	δi(x))−	NOUN
ejpam-5758	38	4	l	l	NOUN
ejpam-5758	38	5	(	(	PUNCT
ejpam-5758	38	6	δi(x	δi(x	NUM
ejpam-5758	38	7	)	)	PUNCT
ejpam-5758	38	8	)	)	PUNCT
ejpam-5758	39	1	∥	∥	NUM
ejpam-5758	39	2	for	for	ADP
ejpam-5758	39	3	all	all	DET
ejpam-5758	39	4	g	g	NOUN
ejpam-5758	39	5	,	,	PUNCT
ejpam-5758	39	6	h	h	NOUN
ejpam-5758	39	7	:	:	PUNCT
ejpam-5758	39	8	e	e	X
ejpam-5758	39	9	→	→	SYM
ejpam-5758	39	10	b	b	PROPN
ejpam-5758	39	11	and	and	CCONJ
ejpam-5758	39	12	x	x	PROPN
ejpam-5758	39	13	∈	∈	PROPN
ejpam-5758	39	14	e.	e.	PROPN
ejpam-5758	39	15	(	(	PUNCT
ejpam-5758	39	16	a4	a4	PROPN
ejpam-5758	39	17	)	)	PUNCT
ejpam-5758	39	18	λ	λ	NOUN
ejpam-5758	39	19	:	:	PUNCT
ejpam-5758	39	20	re	re	ADP
ejpam-5758	39	21	+	+	X
ejpam-5758	39	22	→	→	PUNCT
ejpam-5758	39	23	re	re	ADJ
ejpam-5758	39	24	+	+	X
ejpam-5758	39	25	is	be	AUX
ejpam-5758	39	26	a	a	DET
ejpam-5758	39	27	linear	linear	ADJ
ejpam-5758	39	28	operator	operator	NOUN
ejpam-5758	39	29	defined	define	VERB
ejpam-5758	39	30	by	by	ADP
ejpam-5758	39	31	λf(x	λf(x	NOUN
ejpam-5758	39	32	)	)	PUNCT
ejpam-5758	39	33	:	:	PUNCT
ejpam-5758	40	1	=	=	PUNCT
ejpam-5758	40	2	k∑	k∑	VERB
ejpam-5758	40	3	i=1	i=1	X
ejpam-5758	41	1	λi(x)f	λi(x)f	PUNCT
ejpam-5758	41	2	(	(	PUNCT
ejpam-5758	41	3	δi(x	δi(x	NUM
ejpam-5758	41	4	)	)	PUNCT
ejpam-5758	41	5	)	)	PUNCT
ejpam-5758	42	1	for	for	ADP
ejpam-5758	42	2	f	f	PROPN
ejpam-5758	42	3	:	:	PUNCT
ejpam-5758	42	4	e	e	X
ejpam-5758	42	5	→	→	PUNCT
ejpam-5758	42	6	r+	r+	NOUN
ejpam-5758	42	7	and	and	CCONJ
ejpam-5758	42	8	x	x	SYM
ejpam-5758	42	9	∈	∈	PROPN
ejpam-5758	42	10	e.	e.	PROPN
ejpam-5758	42	11	theorem	theorem	PROPN
ejpam-5758	42	12	1	1	NUM
ejpam-5758	42	13	.	.	PUNCT
ejpam-5758	43	1	[	[	X
ejpam-5758	43	2	8	8	NUM
ejpam-5758	43	3	]	]	PUNCT
ejpam-5758	43	4	suppose	suppose	VERB
ejpam-5758	43	5	that	that	SCONJ
ejpam-5758	43	6	the	the	DET
ejpam-5758	43	7	hypotheses	hypothesis	NOUN
ejpam-5758	43	8	(	(	PUNCT
ejpam-5758	43	9	a1)–(a4	a1)–(a4	INTJ
ejpam-5758	43	10	)	)	PUNCT
ejpam-5758	43	11	are	be	AUX
ejpam-5758	43	12	satisfied	satisfied	ADJ
ejpam-5758	43	13	.	.	PUNCT
ejpam-5758	44	1	assume	assume	VERB
ejpam-5758	44	2	that	that	SCONJ
ejpam-5758	44	3	there	there	PRON
ejpam-5758	44	4	are	be	VERB
ejpam-5758	44	5	functions	function	NOUN
ejpam-5758	44	6	µ	µ	X
ejpam-5758	44	7	:	:	PUNCT
ejpam-5758	44	8	e	e	X
ejpam-5758	44	9	→	→	PUNCT
ejpam-5758	44	10	r+	r+	X
ejpam-5758	44	11	and	and	CCONJ
ejpam-5758	44	12	φ	φ	NOUN
ejpam-5758	44	13	:	:	PUNCT
ejpam-5758	45	1	e	e	X
ejpam-5758	45	2	→	→	SYM
ejpam-5758	45	3	b	b	X
ejpam-5758	45	4	such	such	ADJ
ejpam-5758	45	5	that	that	PRON
ejpam-5758	45	6	,	,	PUNCT
ejpam-5758	45	7	for	for	ADP
ejpam-5758	45	8	all	all	DET
ejpam-5758	45	9	x	x	SYM
ejpam-5758	45	10	∈	∈	PROPN
ejpam-5758	45	11	e	e	NOUN
ejpam-5758	45	12	,	,	PUNCT
ejpam-5758	45	13	∥hφ(x)−	∥hφ(x)−	NOUN
ejpam-5758	45	14	φ(x)∥	φ(x)∥	AUX
ejpam-5758	45	15	≤	≤	ADJ
ejpam-5758	45	16	µ(x	µ(x	VERB
ejpam-5758	45	17	)	)	PUNCT
ejpam-5758	45	18	m.	m.	NOUN
ejpam-5758	45	19	dehghanian	dehghanian	PROPN
ejpam-5758	45	20	et	et	PROPN
ejpam-5758	45	21	al	al	PROPN
ejpam-5758	45	22	.	.	PUNCT
ejpam-5758	45	23	/	/	SYM
ejpam-5758	45	24	eur	eur	PROPN
ejpam-5758	45	25	.	.	PUNCT
ejpam-5758	46	1	j.	j.	PROPN
ejpam-5758	46	2	pure	pure	PROPN
ejpam-5758	46	3	appl	appl	PROPN
ejpam-5758	46	4	.	.	PROPN
ejpam-5758	46	5	math	math	PROPN
ejpam-5758	46	6	,	,	PUNCT
ejpam-5758	46	7	18	18	NUM
ejpam-5758	46	8	(	(	PUNCT
ejpam-5758	46	9	1	1	NUM
ejpam-5758	46	10	)	)	PUNCT
ejpam-5758	46	11	(	(	PUNCT
ejpam-5758	46	12	2025	2025	NUM
ejpam-5758	46	13	)	)	PUNCT
ejpam-5758	46	14	,	,	PUNCT
ejpam-5758	46	15	5758	5758	NUM
ejpam-5758	46	16	3	3	NUM
ejpam-5758	46	17	of	of	ADP
ejpam-5758	46	18	13	13	NUM
ejpam-5758	46	19	and	and	CCONJ
ejpam-5758	46	20	µ∗(x	µ∗(x	PROPN
ejpam-5758	46	21	)	)	PUNCT
ejpam-5758	46	22	:	:	PUNCT
ejpam-5758	47	1	=	=	NOUN
ejpam-5758	47	2	∞∑	∞∑	NUM
ejpam-5758	47	3	n=0	n=0	NUM
ejpam-5758	47	4	λnµ(x	λnµ(x	NOUN
ejpam-5758	47	5	)	)	PUNCT
ejpam-5758	47	6	<	<	X
ejpam-5758	47	7	∞	∞	NUM
ejpam-5758	47	8	hold	hold	NOUN
ejpam-5758	47	9	.	.	PUNCT
ejpam-5758	48	1	then	then	ADV
ejpam-5758	48	2	,	,	PUNCT
ejpam-5758	48	3	for	for	ADP
ejpam-5758	48	4	all	all	DET
ejpam-5758	48	5	x	x	SYM
ejpam-5758	48	6	∈	∈	NOUN
ejpam-5758	48	7	e	e	NOUN
ejpam-5758	48	8	the	the	DET
ejpam-5758	48	9	limit	limit	NOUN
ejpam-5758	48	10	t	t	X
ejpam-5758	48	11	(	(	PUNCT
ejpam-5758	48	12	x	x	NOUN
ejpam-5758	48	13	)	)	PUNCT
ejpam-5758	48	14	:	:	PUNCT
ejpam-5758	48	15	=	=	PUNCT
ejpam-5758	48	16	lim	lim	PROPN
ejpam-5758	48	17	n→∞	n→∞	NUM
ejpam-5758	48	18	hnφ(x	hnφ(x	PROPN
ejpam-5758	48	19	)	)	PUNCT
ejpam-5758	48	20	exists	exist	VERB
ejpam-5758	48	21	and	and	CCONJ
ejpam-5758	48	22	the	the	DET
ejpam-5758	48	23	mapping	mapping	NOUN
ejpam-5758	48	24	t	t	NOUN
ejpam-5758	48	25	:	:	PUNCT
ejpam-5758	48	26	e	e	X
ejpam-5758	48	27	→	→	SYM
ejpam-5758	48	28	b	b	PROPN
ejpam-5758	48	29	is	be	AUX
ejpam-5758	48	30	a	a	DET
ejpam-5758	48	31	unique	unique	ADJ
ejpam-5758	48	32	fixed	fix	VERB
ejpam-5758	48	33	point	point	NOUN
ejpam-5758	48	34	of	of	ADP
ejpam-5758	48	35	h	h	NOUN
ejpam-5758	48	36	with	with	ADP
ejpam-5758	48	37	∥φ(x)−	∥φ(x)−	PROPN
ejpam-5758	48	38	t	t	PROPN
ejpam-5758	48	39	(	(	PUNCT
ejpam-5758	48	40	x)∥	x)∥	PUNCT
ejpam-5758	48	41	≤	≤	NUM
ejpam-5758	48	42	µ∗(x	µ∗(x	PROPN
ejpam-5758	48	43	)	)	PUNCT
ejpam-5758	48	44	for	for	ADP
ejpam-5758	48	45	all	all	DET
ejpam-5758	48	46	x	x	SYM
ejpam-5758	48	47	∈	∈	PROPN
ejpam-5758	48	48	e.	e.	PROPN
ejpam-5758	48	49	theorem	theorem	PROPN
ejpam-5758	48	50	2	2	NUM
ejpam-5758	48	51	.	.	PUNCT
ejpam-5758	49	1	[	[	X
ejpam-5758	49	2	2	2	X
ejpam-5758	49	3	]	]	PUNCT
ejpam-5758	49	4	let	let	VERB
ejpam-5758	49	5	f	f	X
ejpam-5758	49	6	,	,	PUNCT
ejpam-5758	49	7	h	h	NOUN
ejpam-5758	49	8	:	:	PUNCT
ejpam-5758	50	1	e	e	X
ejpam-5758	50	2	→	→	SYM
ejpam-5758	50	3	b	b	X
ejpam-5758	50	4	be	be	AUX
ejpam-5758	50	5	mappings	mapping	NOUN
ejpam-5758	50	6	satisfying	satisfy	VERB
ejpam-5758	50	7	∥f(x+	∥f(x+	NOUN
ejpam-5758	50	8	y	y	NOUN
ejpam-5758	50	9	)	)	PUNCT
ejpam-5758	51	1	+	+	CCONJ
ejpam-5758	51	2	f(x−	f(x−	PROPN
ejpam-5758	51	3	y	y	NOUN
ejpam-5758	51	4	)	)	PUNCT
ejpam-5758	52	1	+	+	CCONJ
ejpam-5758	52	2	h(x+	h(x+	ADV
ejpam-5758	52	3	y)−	y)−	PROPN
ejpam-5758	52	4	2f(x)−	2f(x)−	NUM
ejpam-5758	52	5	2f(y)−	2f(y)−	NUM
ejpam-5758	52	6	h(x)−	h(x)−	PROPN
ejpam-5758	52	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	52	8	≤	≤	NOUN
ejpam-5758	52	9	ϵ	ϵ	X
ejpam-5758	52	10	for	for	ADP
ejpam-5758	52	11	some	some	DET
ejpam-5758	52	12	ϵ	ϵ	PROPN
ejpam-5758	52	13	>	>	X
ejpam-5758	52	14	0	0	PUNCT
ejpam-5758	52	15	and	and	CCONJ
ejpam-5758	52	16	for	for	ADP
ejpam-5758	52	17	all	all	DET
ejpam-5758	52	18	x	x	NOUN
ejpam-5758	52	19	,	,	PUNCT
ejpam-5758	52	20	y	y	PROPN
ejpam-5758	52	21	∈	∈	PROPN
ejpam-5758	52	22	e.	e.	PROPN
ejpam-5758	52	23	then	then	ADV
ejpam-5758	52	24	there	there	PRON
ejpam-5758	52	25	exist	exist	VERB
ejpam-5758	52	26	an	an	DET
ejpam-5758	52	27	additive	additive	ADJ
ejpam-5758	52	28	mapping	mapping	NOUN
ejpam-5758	52	29	a	a	DET
ejpam-5758	52	30	:	:	PUNCT
ejpam-5758	52	31	e	e	X
ejpam-5758	52	32	→	→	SYM
ejpam-5758	52	33	b	b	PROPN
ejpam-5758	52	34	and	and	CCONJ
ejpam-5758	52	35	a	a	DET
ejpam-5758	52	36	unique	unique	ADJ
ejpam-5758	52	37	quadratic	quadratic	ADJ
ejpam-5758	52	38	mapping	mapping	NOUN
ejpam-5758	52	39	q	q	NOUN
ejpam-5758	52	40	:	:	PUNCT
ejpam-5758	52	41	e	e	X
ejpam-5758	52	42	→	→	SYM
ejpam-5758	52	43	b	b	X
ejpam-5758	52	44	such	such	ADJ
ejpam-5758	52	45	that	that	PRON
ejpam-5758	52	46	∥h(x)−	∥h(x)−	PROPN
ejpam-5758	52	47	h(0)−a(x)∥	h(0)−a(x)∥	VERB
ejpam-5758	52	48	≤	≤	NOUN
ejpam-5758	52	49	13ϵ	13ϵ	NOUN
ejpam-5758	52	50	,	,	PUNCT
ejpam-5758	52	51	∥f(x)−	∥f(x)−	PROPN
ejpam-5758	52	52	f(0)−q(x)∥	f(0)−q(x)∥	PROPN
ejpam-5758	52	53	≤	≤	ADJ
ejpam-5758	52	54	24ϵ	24ϵ	NOUN
ejpam-5758	52	55	for	for	ADP
ejpam-5758	52	56	all	all	DET
ejpam-5758	52	57	x	x	SYM
ejpam-5758	52	58	∈	∈	PROPN
ejpam-5758	52	59	e.	e.	PROPN
ejpam-5758	52	60	motivated	motivate	VERB
ejpam-5758	52	61	by	by	ADP
ejpam-5758	52	62	the	the	DET
ejpam-5758	52	63	above	above	ADJ
ejpam-5758	52	64	results	result	NOUN
ejpam-5758	52	65	on	on	ADP
ejpam-5758	52	66	the	the	DET
ejpam-5758	52	67	hyers	hyers	PROPN
ejpam-5758	52	68	-	-	PUNCT
ejpam-5758	52	69	ulam	ulam	ADJ
ejpam-5758	52	70	stability	stability	NOUN
ejpam-5758	52	71	of	of	ADP
ejpam-5758	52	72	additive	additive	ADJ
ejpam-5758	52	73	functional	functional	ADJ
ejpam-5758	52	74	equations	equation	NOUN
ejpam-5758	52	75	,	,	PUNCT
ejpam-5758	52	76	quadratic	quadratic	ADJ
ejpam-5758	52	77	functional	functional	ADJ
ejpam-5758	52	78	equations	equation	NOUN
ejpam-5758	52	79	,	,	PUNCT
ejpam-5758	52	80	cubic	cubic	ADJ
ejpam-5758	52	81	functional	functional	ADJ
ejpam-5758	52	82	equations	equation	NOUN
ejpam-5758	52	83	and	and	CCONJ
ejpam-5758	52	84	quartic	quartic	ADJ
ejpam-5758	52	85	functional	functional	ADJ
ejpam-5758	52	86	equations	equation	NOUN
ejpam-5758	52	87	,	,	PUNCT
ejpam-5758	52	88	in	in	ADP
ejpam-5758	52	89	the	the	DET
ejpam-5758	52	90	current	current	ADJ
ejpam-5758	52	91	work	work	NOUN
ejpam-5758	52	92	,	,	PUNCT
ejpam-5758	52	93	we	we	PRON
ejpam-5758	52	94	try	try	VERB
ejpam-5758	52	95	to	to	PART
ejpam-5758	52	96	examine	examine	VERB
ejpam-5758	52	97	the	the	DET
ejpam-5758	52	98	hyers	hyers	PROPN
ejpam-5758	52	99	-	-	PUNCT
ejpam-5758	52	100	ulam	ulam	ADJ
ejpam-5758	52	101	stability	stability	NOUN
ejpam-5758	52	102	of	of	ADP
ejpam-5758	52	103	the	the	DET
ejpam-5758	52	104	following	follow	VERB
ejpam-5758	52	105	pexiderized	pexiderize	VERB
ejpam-5758	52	106	additive	additive	ADJ
ejpam-5758	52	107	-	-	PUNCT
ejpam-5758	52	108	quadratic	quadratic	ADJ
ejpam-5758	52	109	functional	functional	ADJ
ejpam-5758	52	110	equation	equation	NOUN
ejpam-5758	52	111	ϕ(u+	ϕ(u+	PROPN
ejpam-5758	53	1	3v)−	3v)−	NUM
ejpam-5758	53	2	5ϕ(u+	5ϕ(u+	NUM
ejpam-5758	53	3	2v)−	2v)−	NUM
ejpam-5758	53	4	ϕ(u−	ϕ(u−	NUM
ejpam-5758	53	5	2v	2v	NUM
ejpam-5758	53	6	)	)	PUNCT
ejpam-5758	54	1	+	+	CCONJ
ejpam-5758	54	2	10ϕ(u+	10ϕ(u+	NUM
ejpam-5758	54	3	v	v	NOUN
ejpam-5758	54	4	)	)	PUNCT
ejpam-5758	55	1	+	+	CCONJ
ejpam-5758	55	2	5ϕ(u−	5ϕ(u−	NUM
ejpam-5758	55	3	v)−	v)−	PROPN
ejpam-5758	55	4	10ϕ(u)−	10ϕ(u)−	NUM
ejpam-5758	55	5	120ϕ(v	120ϕ(v	NOUN
ejpam-5758	55	6	)	)	PUNCT
ejpam-5758	55	7	=	=	SYM
ejpam-5758	55	8	0	0	NUM
ejpam-5758	55	9	,	,	PUNCT
ejpam-5758	55	10	(	(	PUNCT
ejpam-5758	55	11	1	1	X
ejpam-5758	55	12	)	)	PUNCT
ejpam-5758	55	13	in	in	ADP
ejpam-5758	55	14	banach	banach	NOUN
ejpam-5758	55	15	spaces	space	NOUN
ejpam-5758	55	16	by	by	ADP
ejpam-5758	55	17	means	mean	NOUN
ejpam-5758	55	18	of	of	ADP
ejpam-5758	55	19	brzdȩk	brzdȩk	NOUN
ejpam-5758	55	20	’s	’s	PART
ejpam-5758	55	21	fixed	fix	VERB
ejpam-5758	55	22	point	point	NOUN
ejpam-5758	55	23	approach	approach	NOUN
ejpam-5758	55	24	.	.	PUNCT
ejpam-5758	56	1	a	a	DET
ejpam-5758	56	2	concept	concept	NOUN
ejpam-5758	56	3	employed	employ	VERB
ejpam-5758	56	4	by	by	ADP
ejpam-5758	56	5	brzdȩk	brzdȩk	PROPN
ejpam-5758	56	6	,	,	PUNCT
ejpam-5758	56	7	a	a	DET
ejpam-5758	56	8	lot	lot	NOUN
ejpam-5758	56	9	of	of	ADP
ejpam-5758	56	10	articles	article	NOUN
ejpam-5758	56	11	on	on	ADP
ejpam-5758	56	12	hyperstability	hyperstability	NOUN
ejpam-5758	56	13	have	have	AUX
ejpam-5758	56	14	been	be	AUX
ejpam-5758	56	15	written	write	VERB
ejpam-5758	56	16	on	on	ADP
ejpam-5758	56	17	this	this	DET
ejpam-5758	56	18	topic	topic	NOUN
ejpam-5758	56	19	and	and	CCONJ
ejpam-5758	56	20	we	we	PRON
ejpam-5758	56	21	refer	refer	VERB
ejpam-5758	56	22	to	to	ADP
ejpam-5758	56	23	[	[	X
ejpam-5758	56	24	24	24	NUM
ejpam-5758	56	25	,	,	PUNCT
ejpam-5758	56	26	25	25	NUM
ejpam-5758	56	27	]	]	PUNCT
ejpam-5758	56	28	.	.	PUNCT
ejpam-5758	57	1	throughout	throughout	ADP
ejpam-5758	57	2	the	the	DET
ejpam-5758	57	3	paper	paper	NOUN
ejpam-5758	57	4	n0	n0	PROPN
ejpam-5758	57	5	denotes	denote	VERB
ejpam-5758	57	6	the	the	DET
ejpam-5758	57	7	set	set	NOUN
ejpam-5758	57	8	of	of	ADP
ejpam-5758	57	9	all	all	DET
ejpam-5758	57	10	non	non	ADJ
ejpam-5758	57	11	-	-	ADJ
ejpam-5758	57	12	negative	negative	ADJ
ejpam-5758	57	13	integers	integer	NOUN
ejpam-5758	57	14	.	.	PUNCT
ejpam-5758	58	1	2	2	X
ejpam-5758	58	2	.	.	X
ejpam-5758	58	3	some	some	DET
ejpam-5758	58	4	auxiliary	auxiliary	ADJ
ejpam-5758	58	5	results	result	NOUN
ejpam-5758	58	6	in	in	ADP
ejpam-5758	58	7	this	this	DET
ejpam-5758	58	8	section	section	NOUN
ejpam-5758	58	9	,	,	PUNCT
ejpam-5758	58	10	we	we	PRON
ejpam-5758	58	11	establish	establish	VERB
ejpam-5758	58	12	lemmas	lemma	NOUN
ejpam-5758	58	13	for	for	ADP
ejpam-5758	58	14	the	the	DET
ejpam-5758	58	15	proof	proof	NOUN
ejpam-5758	58	16	of	of	ADP
ejpam-5758	58	17	hyers	hyers	PROPN
ejpam-5758	58	18	-	-	PUNCT
ejpam-5758	58	19	ulam	ulam	PROPN
ejpam-5758	58	20	stability	stability	NOUN
ejpam-5758	58	21	of	of	ADP
ejpam-5758	58	22	the	the	DET
ejpam-5758	58	23	functional	functional	ADJ
ejpam-5758	58	24	equation	equation	NOUN
ejpam-5758	58	25	(	(	PUNCT
ejpam-5758	58	26	1	1	NUM
ejpam-5758	58	27	)	)	PUNCT
ejpam-5758	58	28	.	.	PUNCT
ejpam-5758	59	1	the	the	DET
ejpam-5758	59	2	next	next	ADJ
ejpam-5758	59	3	theorem	theorem	NOUN
ejpam-5758	59	4	is	be	AUX
ejpam-5758	59	5	an	an	DET
ejpam-5758	59	6	example	example	NOUN
ejpam-5758	59	7	of	of	ADP
ejpam-5758	59	8	a	a	DET
ejpam-5758	59	9	very	very	ADV
ejpam-5758	59	10	classical	classical	ADJ
ejpam-5758	59	11	result	result	NOUN
ejpam-5758	59	12	in	in	ADP
ejpam-5758	59	13	hyers	hyer	NOUN
ejpam-5758	59	14	-	-	PUNCT
ejpam-5758	59	15	ulam	ulam	PROPN
ejpam-5758	59	16	stability	stability	NOUN
ejpam-5758	59	17	.	.	PUNCT
ejpam-5758	60	1	m.	m.	NOUN
ejpam-5758	60	2	dehghanian	dehghanian	PROPN
ejpam-5758	60	3	et	et	PROPN
ejpam-5758	60	4	al	al	PROPN
ejpam-5758	60	5	.	.	PUNCT
ejpam-5758	60	6	/	/	SYM
ejpam-5758	60	7	eur	eur	PROPN
ejpam-5758	60	8	.	.	PUNCT
ejpam-5758	61	1	j.	j.	PROPN
ejpam-5758	61	2	pure	pure	PROPN
ejpam-5758	61	3	appl	appl	PROPN
ejpam-5758	61	4	.	.	PROPN
ejpam-5758	61	5	math	math	PROPN
ejpam-5758	61	6	,	,	PUNCT
ejpam-5758	61	7	18	18	NUM
ejpam-5758	61	8	(	(	PUNCT
ejpam-5758	61	9	1	1	NUM
ejpam-5758	61	10	)	)	PUNCT
ejpam-5758	61	11	(	(	PUNCT
ejpam-5758	61	12	2025	2025	NUM
ejpam-5758	61	13	)	)	PUNCT
ejpam-5758	61	14	,	,	PUNCT
ejpam-5758	61	15	5758	5758	NUM
ejpam-5758	61	16	4	4	NUM
ejpam-5758	61	17	of	of	ADP
ejpam-5758	61	18	13	13	NUM
ejpam-5758	61	19	theorem	theorem	NOUN
ejpam-5758	61	20	3	3	NUM
ejpam-5758	61	21	.	.	PUNCT
ejpam-5758	62	1	[	[	X
ejpam-5758	62	2	17	17	NUM
ejpam-5758	62	3	]	]	PUNCT
ejpam-5758	62	4	let	let	VERB
ejpam-5758	62	5	h	h	NOUN
ejpam-5758	62	6	:	:	PUNCT
ejpam-5758	62	7	e	e	X
ejpam-5758	62	8	→	→	SYM
ejpam-5758	62	9	b	b	X
ejpam-5758	62	10	be	be	AUX
ejpam-5758	62	11	a	a	DET
ejpam-5758	62	12	mapping	mapping	NOUN
ejpam-5758	62	13	satisfying	satisfy	VERB
ejpam-5758	62	14	∥h(x+	∥h(x+	ADV
ejpam-5758	63	1	y)−	y)−	PROPN
ejpam-5758	63	2	h(x)−	h(x)−	PROPN
ejpam-5758	63	3	h(y)∥	h(y)∥	NOUN
ejpam-5758	63	4	≤	≤	PUNCT
ejpam-5758	63	5	η(∥x∥p	η(∥x∥p	PROPN
ejpam-5758	63	6	+	+	CCONJ
ejpam-5758	63	7	∥y∥p	∥y∥p	VERB
ejpam-5758	63	8	)	)	PUNCT
ejpam-5758	63	9	for	for	ADP
ejpam-5758	63	10	some	some	DET
ejpam-5758	63	11	η	η	PROPN
ejpam-5758	63	12	≥	≥	NOUN
ejpam-5758	63	13	0	0	NUM
ejpam-5758	63	14	,	,	PUNCT
ejpam-5758	63	15	p	p	X
ejpam-5758	63	16	>	>	X
ejpam-5758	63	17	0	0	NUM
ejpam-5758	63	18	,	,	PUNCT
ejpam-5758	63	19	p	p	PROPN
ejpam-5758	63	20	̸=	̸=	PROPN
ejpam-5758	63	21	1	1	NUM
ejpam-5758	63	22	and	and	CCONJ
ejpam-5758	63	23	for	for	ADP
ejpam-5758	63	24	all	all	DET
ejpam-5758	63	25	x	x	NOUN
ejpam-5758	63	26	,	,	PUNCT
ejpam-5758	63	27	y	y	PROPN
ejpam-5758	63	28	∈	∈	PROPN
ejpam-5758	63	29	e.	e.	PROPN
ejpam-5758	64	1	then	then	ADV
ejpam-5758	64	2	there	there	PRON
ejpam-5758	64	3	is	be	VERB
ejpam-5758	64	4	a	a	DET
ejpam-5758	64	5	unique	unique	ADJ
ejpam-5758	64	6	additive	additive	NOUN
ejpam-5758	64	7	mapping	mapping	NOUN
ejpam-5758	64	8	a	a	PRON
ejpam-5758	64	9	:	:	PUNCT
ejpam-5758	64	10	e	e	X
ejpam-5758	64	11	→	→	SYM
ejpam-5758	64	12	b	b	X
ejpam-5758	64	13	such	such	ADJ
ejpam-5758	64	14	that	that	DET
ejpam-5758	64	15	∥h(x)−a(x)∥	∥h(x)−a(x)∥	NOUN
ejpam-5758	64	16	≤	≤	PROPN
ejpam-5758	64	17	2η	2η	NUM
ejpam-5758	64	18	|2p	|2p	NUM
ejpam-5758	64	19	−	−	PROPN
ejpam-5758	64	20	2|	2|	NUM
ejpam-5758	64	21	∥x∥p	∥x∥p	NOUN
ejpam-5758	64	22	(	(	PUNCT
ejpam-5758	64	23	2	2	X
ejpam-5758	64	24	)	)	PUNCT
ejpam-5758	64	25	for	for	SCONJ
ejpam-5758	64	26	all	all	DET
ejpam-5758	64	27	x	x	SYM
ejpam-5758	64	28	∈	∈	PROPN
ejpam-5758	64	29	e.	e.	PROPN
ejpam-5758	64	30	researchers	researcher	NOUN
ejpam-5758	64	31	obtained	obtain	VERB
ejpam-5758	64	32	new	new	ADJ
ejpam-5758	64	33	results	result	NOUN
ejpam-5758	64	34	on	on	ADP
ejpam-5758	64	35	ulam	ulam	PROPN
ejpam-5758	64	36	stability	stability	NOUN
ejpam-5758	64	37	of	of	ADP
ejpam-5758	64	38	some	some	DET
ejpam-5758	64	39	functional	functional	ADJ
ejpam-5758	64	40	equations	equation	NOUN
ejpam-5758	64	41	using	use	VERB
ejpam-5758	64	42	the	the	DET
ejpam-5758	64	43	banach	banach	NOUN
ejpam-5758	64	44	limit	limit	NOUN
ejpam-5758	64	45	(	(	PUNCT
ejpam-5758	64	46	see	see	VERB
ejpam-5758	64	47	[	[	X
ejpam-5758	64	48	3	3	NUM
ejpam-5758	64	49	,	,	PUNCT
ejpam-5758	64	50	15	15	NUM
ejpam-5758	64	51	]	]	NUM
ejpam-5758	64	52	)	)	PUNCT
ejpam-5758	64	53	.	.	PUNCT
ejpam-5758	65	1	in	in	ADP
ejpam-5758	65	2	the	the	DET
ejpam-5758	65	3	continue	continue	NOUN
ejpam-5758	65	4	,	,	PUNCT
ejpam-5758	65	5	we	we	PRON
ejpam-5758	65	6	need	need	VERB
ejpam-5758	65	7	the	the	DET
ejpam-5758	65	8	following	follow	VERB
ejpam-5758	65	9	lemma	lemma	PROPN
ejpam-5758	65	10	,	,	PUNCT
ejpam-5758	65	11	whose	whose	DET
ejpam-5758	65	12	proof	proof	NOUN
ejpam-5758	65	13	is	be	AUX
ejpam-5758	65	14	similar	similar	ADJ
ejpam-5758	65	15	to	to	ADP
ejpam-5758	65	16	the	the	DET
ejpam-5758	65	17	proof	proof	NOUN
ejpam-5758	65	18	of	of	ADP
ejpam-5758	65	19	theorem	theorem	ADJ
ejpam-5758	65	20	3	3	NUM
ejpam-5758	65	21	,	,	PUNCT
ejpam-5758	65	22	and	and	CCONJ
ejpam-5758	65	23	so	so	ADV
ejpam-5758	65	24	we	we	PRON
ejpam-5758	65	25	will	will	AUX
ejpam-5758	65	26	omit	omit	VERB
ejpam-5758	65	27	it	it	PRON
ejpam-5758	65	28	.	.	PUNCT
ejpam-5758	66	1	lemma	lemma	PROPN
ejpam-5758	66	2	1	1	X
ejpam-5758	66	3	.	.	PUNCT
ejpam-5758	67	1	let	let	VERB
ejpam-5758	67	2	h	h	NOUN
ejpam-5758	67	3	:	:	PUNCT
ejpam-5758	67	4	e	e	X
ejpam-5758	67	5	→	→	SYM
ejpam-5758	67	6	b	b	X
ejpam-5758	67	7	be	be	AUX
ejpam-5758	67	8	a	a	DET
ejpam-5758	67	9	mapping	mapping	NOUN
ejpam-5758	67	10	satisfying	satisfy	VERB
ejpam-5758	67	11	∥h(x+	∥h(x+	ADV
ejpam-5758	68	1	y)−	y)−	PROPN
ejpam-5758	68	2	h(x)−	h(x)−	PROPN
ejpam-5758	68	3	h(y)∥	h(y)∥	NOUN
ejpam-5758	68	4	≤	≤	PUNCT
ejpam-5758	68	5	η(∥x∥p	η(∥x∥p	PROPN
ejpam-5758	68	6	+	+	CCONJ
ejpam-5758	68	7	∥y∥p	∥y∥p	PRON
ejpam-5758	68	8	)	)	PUNCT
ejpam-5758	69	1	+	+	CCONJ
ejpam-5758	69	2	θ∥x−	θ∥x−	NOUN
ejpam-5758	69	3	y∥p	y∥p	NOUN
ejpam-5758	69	4	for	for	ADP
ejpam-5758	69	5	some	some	DET
ejpam-5758	69	6	η	η	PROPN
ejpam-5758	69	7	,	,	PUNCT
ejpam-5758	69	8	θ	θ	PROPN
ejpam-5758	69	9	≥	≥	NOUN
ejpam-5758	69	10	0	0	NUM
ejpam-5758	69	11	,	,	PUNCT
ejpam-5758	69	12	p	p	X
ejpam-5758	69	13	>	>	X
ejpam-5758	69	14	0	0	NUM
ejpam-5758	69	15	,	,	PUNCT
ejpam-5758	69	16	p	p	PROPN
ejpam-5758	69	17	̸=	̸=	PROPN
ejpam-5758	69	18	1	1	NUM
ejpam-5758	69	19	and	and	CCONJ
ejpam-5758	69	20	for	for	ADP
ejpam-5758	69	21	all	all	DET
ejpam-5758	69	22	x	x	NOUN
ejpam-5758	69	23	,	,	PUNCT
ejpam-5758	69	24	y	y	PROPN
ejpam-5758	69	25	∈	∈	PROPN
ejpam-5758	69	26	e.	e.	PROPN
ejpam-5758	70	1	then	then	ADV
ejpam-5758	70	2	there	there	PRON
ejpam-5758	70	3	is	be	VERB
ejpam-5758	70	4	a	a	DET
ejpam-5758	70	5	unique	unique	ADJ
ejpam-5758	70	6	additive	additive	NOUN
ejpam-5758	70	7	mapping	mapping	NOUN
ejpam-5758	70	8	a	a	PRON
ejpam-5758	70	9	:	:	PUNCT
ejpam-5758	70	10	e	e	X
ejpam-5758	70	11	→	→	SYM
ejpam-5758	70	12	b	b	X
ejpam-5758	70	13	satisfying	satisfying	ADJ
ejpam-5758	70	14	(	(	PUNCT
ejpam-5758	70	15	2	2	NUM
ejpam-5758	70	16	)	)	PUNCT
ejpam-5758	70	17	.	.	PUNCT
ejpam-5758	71	1	lemma	lemma	PROPN
ejpam-5758	71	2	2	2	X
ejpam-5758	71	3	.	.	PUNCT
ejpam-5758	72	1	let	let	VERB
ejpam-5758	72	2	f	f	NOUN
ejpam-5758	72	3	:	:	PUNCT
ejpam-5758	72	4	e	e	X
ejpam-5758	72	5	→	→	SYM
ejpam-5758	72	6	b	b	X
ejpam-5758	72	7	be	be	AUX
ejpam-5758	72	8	a	a	DET
ejpam-5758	72	9	mapping	mapping	NOUN
ejpam-5758	72	10	satisfying	satisfy	VERB
ejpam-5758	72	11	∥f(x+	∥f(x+	NOUN
ejpam-5758	72	12	y	y	NOUN
ejpam-5758	72	13	)	)	PUNCT
ejpam-5758	73	1	+	+	CCONJ
ejpam-5758	73	2	f(x−	f(x−	ADP
ejpam-5758	73	3	y)−	y)−	PROPN
ejpam-5758	73	4	2f(x)−	2f(x)−	NUM
ejpam-5758	73	5	2f(y)∥	2f(y)∥	NUM
ejpam-5758	73	6	≤	≤	NOUN
ejpam-5758	73	7	η(∥x∥p	η(∥x∥p	NOUN
ejpam-5758	73	8	+	+	CCONJ
ejpam-5758	73	9	∥y∥p	∥y∥p	PRON
ejpam-5758	73	10	)	)	PUNCT
ejpam-5758	74	1	+	+	CCONJ
ejpam-5758	74	2	θ∥x−	θ∥x−	PROPN
ejpam-5758	74	3	y∥p	y∥p	NOUN
ejpam-5758	74	4	(	(	PUNCT
ejpam-5758	74	5	3	3	NUM
ejpam-5758	74	6	)	)	PUNCT
ejpam-5758	74	7	for	for	ADP
ejpam-5758	74	8	some	some	DET
ejpam-5758	74	9	η	η	PROPN
ejpam-5758	74	10	,	,	PUNCT
ejpam-5758	74	11	θ	θ	PROPN
ejpam-5758	74	12	≥	≥	NOUN
ejpam-5758	74	13	0	0	NUM
ejpam-5758	74	14	,	,	PUNCT
ejpam-5758	74	15	p	p	X
ejpam-5758	74	16	>	>	X
ejpam-5758	74	17	0	0	NUM
ejpam-5758	74	18	,	,	PUNCT
ejpam-5758	74	19	p	p	PROPN
ejpam-5758	74	20	̸=	̸=	PROPN
ejpam-5758	74	21	2	2	NUM
ejpam-5758	74	22	and	and	CCONJ
ejpam-5758	74	23	for	for	ADP
ejpam-5758	74	24	all	all	DET
ejpam-5758	74	25	x	x	NOUN
ejpam-5758	74	26	,	,	PUNCT
ejpam-5758	74	27	y	y	PROPN
ejpam-5758	74	28	∈	∈	PROPN
ejpam-5758	74	29	e.	e.	PROPN
ejpam-5758	75	1	then	then	ADV
ejpam-5758	75	2	there	there	PRON
ejpam-5758	75	3	exists	exist	VERB
ejpam-5758	75	4	a	a	DET
ejpam-5758	75	5	unique	unique	ADJ
ejpam-5758	75	6	quadratic	quadratic	ADJ
ejpam-5758	75	7	mapping	mapping	NOUN
ejpam-5758	75	8	q	q	NOUN
ejpam-5758	75	9	:	:	PUNCT
ejpam-5758	75	10	e	e	X
ejpam-5758	75	11	→	→	SYM
ejpam-5758	75	12	b	b	X
ejpam-5758	75	13	such	such	ADJ
ejpam-5758	75	14	that	that	DET
ejpam-5758	75	15	∥f(x)−q(x)∥	∥f(x)−q(x)∥	NOUN
ejpam-5758	75	16	≤	≤	PROPN
ejpam-5758	75	17	2η	2η	PROPN
ejpam-5758	75	18	|2p	|2p	NUM
ejpam-5758	75	19	−	−	NUM
ejpam-5758	75	20	4|	4|	NUM
ejpam-5758	75	21	∥x∥p	∥x∥p	NOUN
ejpam-5758	75	22	for	for	ADP
ejpam-5758	75	23	all	all	DET
ejpam-5758	75	24	x	x	SYM
ejpam-5758	75	25	∈	∈	PROPN
ejpam-5758	75	26	e.	e.	PROPN
ejpam-5758	75	27	proof	proof	PROPN
ejpam-5758	75	28	.	.	PUNCT
ejpam-5758	76	1	putting	put	VERB
ejpam-5758	76	2	x	x	PUNCT
ejpam-5758	76	3	=	=	PUNCT
ejpam-5758	76	4	y	y	PROPN
ejpam-5758	76	5	=	=	SYM
ejpam-5758	76	6	0	0	NUM
ejpam-5758	76	7	in	in	ADP
ejpam-5758	76	8	(	(	PUNCT
ejpam-5758	76	9	3	3	NUM
ejpam-5758	76	10	)	)	PUNCT
ejpam-5758	76	11	,	,	PUNCT
ejpam-5758	76	12	we	we	PRON
ejpam-5758	76	13	obtain	obtain	VERB
ejpam-5758	76	14	f(0	f(0	NOUN
ejpam-5758	76	15	)	)	PUNCT
ejpam-5758	76	16	=	=	SYM
ejpam-5758	77	1	0	0	X
ejpam-5758	77	2	.	.	X
ejpam-5758	77	3	setting	set	VERB
ejpam-5758	77	4	y	y	NOUN
ejpam-5758	77	5	=	=	PUNCT
ejpam-5758	77	6	x	x	PROPN
ejpam-5758	77	7	in	in	ADP
ejpam-5758	77	8	(	(	PUNCT
ejpam-5758	77	9	3	3	NUM
ejpam-5758	77	10	)	)	PUNCT
ejpam-5758	77	11	and	and	CCONJ
ejpam-5758	77	12	dividing	divide	VERB
ejpam-5758	77	13	by	by	ADP
ejpam-5758	77	14	4	4	NUM
ejpam-5758	77	15	,	,	PUNCT
ejpam-5758	77	16	we	we	PRON
ejpam-5758	77	17	obtain	obtain	VERB
ejpam-5758	77	18	∥f(x)−	∥f(x)−	PROPN
ejpam-5758	77	19	1	1	NUM
ejpam-5758	77	20	4	4	NUM
ejpam-5758	77	21	f(2x)∥	f(2x)∥	NOUN
ejpam-5758	77	22	≤	≤	NUM
ejpam-5758	77	23	η	η	PROPN
ejpam-5758	77	24	2	2	NUM
ejpam-5758	77	25	∥x∥p	∥x∥p	NOUN
ejpam-5758	77	26	(	(	PUNCT
ejpam-5758	77	27	4	4	NUM
ejpam-5758	77	28	)	)	PUNCT
ejpam-5758	77	29	for	for	ADP
ejpam-5758	77	30	all	all	PRON
ejpam-5758	77	31	x	x	SYM
ejpam-5758	77	32	∈	∈	PROPN
ejpam-5758	77	33	e.	e.	PROPN
ejpam-5758	77	34	let	let	VERB
ejpam-5758	77	35	h	h	NOUN
ejpam-5758	77	36	:	:	PUNCT
ejpam-5758	77	37	be	be	AUX
ejpam-5758	77	38	→	→	SYM
ejpam-5758	77	39	be	be	NOUN
ejpam-5758	77	40	and	and	CCONJ
ejpam-5758	77	41	µ	µ	X
ejpam-5758	77	42	:	:	PUNCT
ejpam-5758	77	43	e	e	X
ejpam-5758	77	44	→	→	PUNCT
ejpam-5758	77	45	r+	r+	NOUN
ejpam-5758	77	46	be	be	AUX
ejpam-5758	77	47	defined	define	VERB
ejpam-5758	77	48	by	by	ADP
ejpam-5758	77	49	hg(x	hg(x	PUNCT
ejpam-5758	77	50	)	)	PUNCT
ejpam-5758	77	51	=	=	SYM
ejpam-5758	78	1	1	1	NUM
ejpam-5758	78	2	4	4	NUM
ejpam-5758	78	3	g(2x	g(2x	VERB
ejpam-5758	78	4	)	)	PUNCT
ejpam-5758	78	5	,	,	PUNCT
ejpam-5758	78	6	g	g	PROPN
ejpam-5758	78	7	∈	∈	PROPN
ejpam-5758	78	8	be	be	VERB
ejpam-5758	78	9	and	and	CCONJ
ejpam-5758	78	10	µ(x	µ(x	ADJ
ejpam-5758	78	11	)	)	PUNCT
ejpam-5758	78	12	=	=	SYM
ejpam-5758	78	13	η	η	PROPN
ejpam-5758	78	14	2	2	NUM
ejpam-5758	78	15	∥x∥p	∥x∥p	NOUN
ejpam-5758	78	16	m.	m.	NOUN
ejpam-5758	78	17	dehghanian	dehghanian	PROPN
ejpam-5758	78	18	et	et	PROPN
ejpam-5758	78	19	al	al	PROPN
ejpam-5758	78	20	.	.	PUNCT
ejpam-5758	78	21	/	/	SYM
ejpam-5758	78	22	eur	eur	PROPN
ejpam-5758	78	23	.	.	PUNCT
ejpam-5758	79	1	j.	j.	PROPN
ejpam-5758	79	2	pure	pure	PROPN
ejpam-5758	79	3	appl	appl	PROPN
ejpam-5758	79	4	.	.	PROPN
ejpam-5758	79	5	math	math	PROPN
ejpam-5758	79	6	,	,	PUNCT
ejpam-5758	79	7	18	18	NUM
ejpam-5758	79	8	(	(	PUNCT
ejpam-5758	79	9	1	1	NUM
ejpam-5758	79	10	)	)	PUNCT
ejpam-5758	79	11	(	(	PUNCT
ejpam-5758	79	12	2025	2025	NUM
ejpam-5758	79	13	)	)	PUNCT
ejpam-5758	79	14	,	,	PUNCT
ejpam-5758	79	15	5758	5758	NUM
ejpam-5758	79	16	5	5	NUM
ejpam-5758	79	17	of	of	ADP
ejpam-5758	79	18	13	13	NUM
ejpam-5758	79	19	for	for	ADP
ejpam-5758	79	20	all	all	DET
ejpam-5758	79	21	x	x	SYM
ejpam-5758	79	22	∈	∈	PROPN
ejpam-5758	79	23	e.	e.	PROPN
ejpam-5758	79	24	then	then	ADV
ejpam-5758	79	25	∥hf(x)−	∥hf(x)−	PROPN
ejpam-5758	79	26	f(x)∥	f(x)∥	VERB
ejpam-5758	79	27	≤	≤	NOUN
ejpam-5758	79	28	µ(x	µ(x	NUM
ejpam-5758	79	29	)	)	PUNCT
ejpam-5758	79	30	for	for	ADP
ejpam-5758	79	31	all	all	PRON
ejpam-5758	79	32	x	x	SYM
ejpam-5758	79	33	∈	∈	PROPN
ejpam-5758	79	34	e.	e.	PROPN
ejpam-5758	79	35	hence	hence	ADV
ejpam-5758	79	36	∥hg(x)−hl(x)∥	∥hg(x)−hl(x)∥	ADV
ejpam-5758	79	37	≤	≤	ADV
ejpam-5758	79	38	1	1	NUM
ejpam-5758	79	39	4	4	NUM
ejpam-5758	79	40	∥g(2x)−	∥g(2x)−	PROPN
ejpam-5758	79	41	l(2x)∥	l(2x)∥	NOUN
ejpam-5758	79	42	for	for	ADP
ejpam-5758	79	43	all	all	DET
ejpam-5758	79	44	g	g	NOUN
ejpam-5758	79	45	,	,	PUNCT
ejpam-5758	79	46	h	h	NOUN
ejpam-5758	79	47	∈	∈	PROPN
ejpam-5758	79	48	be	be	VERB
ejpam-5758	79	49	and	and	CCONJ
ejpam-5758	79	50	x	x	SYM
ejpam-5758	79	51	∈	∈	PROPN
ejpam-5758	79	52	e	e	NOUN
ejpam-5758	79	53	,	,	PUNCT
ejpam-5758	79	54	h	h	NOUN
ejpam-5758	79	55	:	:	PUNCT
ejpam-5758	79	56	be	be	AUX
ejpam-5758	79	57	→	→	SYM
ejpam-5758	79	58	be	be	AUX
ejpam-5758	79	59	satisfies	satisfie	NOUN
ejpam-5758	79	60	the	the	DET
ejpam-5758	79	61	condition	condition	NOUN
ejpam-5758	79	62	(	(	PUNCT
ejpam-5758	79	63	a3	a3	NOUN
ejpam-5758	79	64	)	)	PUNCT
ejpam-5758	79	65	with	with	ADP
ejpam-5758	79	66	λ1(x	λ1(x	NOUN
ejpam-5758	79	67	)	)	PUNCT
ejpam-5758	79	68	=	=	SYM
ejpam-5758	79	69	1	1	NUM
ejpam-5758	79	70	4	4	NUM
ejpam-5758	79	71	and	and	CCONJ
ejpam-5758	79	72	δ1(x	δ1(x	NOUN
ejpam-5758	79	73	)	)	PUNCT
ejpam-5758	79	74	=	=	SYM
ejpam-5758	79	75	2x	2x	NUM
ejpam-5758	79	76	.	.	PUNCT
ejpam-5758	80	1	by	by	ADP
ejpam-5758	80	2	(	(	PUNCT
ejpam-5758	80	3	a4	a4	NOUN
ejpam-5758	80	4	)	)	PUNCT
ejpam-5758	80	5	,	,	PUNCT
ejpam-5758	80	6	the	the	DET
ejpam-5758	80	7	operator	operator	NOUN
ejpam-5758	80	8	λ	λ	NOUN
ejpam-5758	80	9	:	:	PUNCT
ejpam-5758	80	10	re	re	ADP
ejpam-5758	80	11	+	+	X
ejpam-5758	80	12	→	→	PUNCT
ejpam-5758	80	13	re	re	X
ejpam-5758	80	14	+	+	X
ejpam-5758	80	15	is	be	AUX
ejpam-5758	80	16	defined	define	VERB
ejpam-5758	80	17	by	by	ADP
ejpam-5758	80	18	:	:	PUNCT
ejpam-5758	80	19	λf(x	λf(x	NUM
ejpam-5758	80	20	)	)	PUNCT
ejpam-5758	80	21	=	=	SYM
ejpam-5758	81	1	1	1	NUM
ejpam-5758	81	2	4	4	NUM
ejpam-5758	81	3	f(2x	f(2x	NUM
ejpam-5758	81	4	)	)	PUNCT
ejpam-5758	81	5	,	,	PUNCT
ejpam-5758	81	6	f	f	PROPN
ejpam-5758	81	7	∈	∈	PROPN
ejpam-5758	81	8	re	re	PROPN
ejpam-5758	81	9	+	+	X
ejpam-5758	81	10	for	for	ADP
ejpam-5758	81	11	all	all	DET
ejpam-5758	81	12	x	x	SYM
ejpam-5758	81	13	∈	∈	PROPN
ejpam-5758	81	14	e.	e.	PROPN
ejpam-5758	81	15	hence	hence	ADV
ejpam-5758	81	16	λµ(x	λµ(x	PUNCT
ejpam-5758	81	17	)	)	PUNCT
ejpam-5758	81	18	=	=	SYM
ejpam-5758	81	19	1	1	NUM
ejpam-5758	81	20	4	4	NUM
ejpam-5758	81	21	µ(2x	µ(2x	NUM
ejpam-5758	81	22	)	)	PUNCT
ejpam-5758	81	23	=	=	SYM
ejpam-5758	81	24	2p−2µ(x	2p−2µ(x	NUM
ejpam-5758	81	25	)	)	PUNCT
ejpam-5758	81	26	,	,	PUNCT
ejpam-5758	81	27	µ	µ	X
ejpam-5758	81	28	∈	∈	NOUN
ejpam-5758	81	29	re	re	ADP
ejpam-5758	81	30	+	+	NOUN
ejpam-5758	81	31	for	for	ADP
ejpam-5758	81	32	all	all	DET
ejpam-5758	81	33	x	x	SYM
ejpam-5758	81	34	∈	∈	PROPN
ejpam-5758	81	35	e.	e.	PROPN
ejpam-5758	81	36	since	since	SCONJ
ejpam-5758	81	37	λ	λ	PROPN
ejpam-5758	81	38	is	be	AUX
ejpam-5758	81	39	linear	linear	ADJ
ejpam-5758	81	40	,	,	PUNCT
ejpam-5758	81	41	λnµ(x	λnµ(x	PROPN
ejpam-5758	81	42	)	)	PUNCT
ejpam-5758	81	43	=	=	PUNCT
ejpam-5758	81	44	2n(p−2)µ(x	2n(p−2)µ(x	NUM
ejpam-5758	81	45	)	)	PUNCT
ejpam-5758	81	46	,	,	PUNCT
ejpam-5758	81	47	n	n	PROPN
ejpam-5758	81	48	∈	∈	PROPN
ejpam-5758	81	49	n0	n0	NOUN
ejpam-5758	81	50	for	for	ADP
ejpam-5758	81	51	all	all	DET
ejpam-5758	81	52	x	x	SYM
ejpam-5758	81	53	∈	∈	PROPN
ejpam-5758	81	54	e.	e.	NOUN
ejpam-5758	82	1	if	if	SCONJ
ejpam-5758	82	2	p	p	X
ejpam-5758	82	3	<	<	X
ejpam-5758	82	4	2	2	NUM
ejpam-5758	82	5	,	,	PUNCT
ejpam-5758	82	6	then	then	ADV
ejpam-5758	82	7	the	the	DET
ejpam-5758	82	8	series	series	PROPN
ejpam-5758	82	9	∑∞	∑∞	PROPN
ejpam-5758	82	10	n=0	n=0	X
ejpam-5758	82	11	λ	λ	NOUN
ejpam-5758	82	12	nη(x	nη(x	NUM
ejpam-5758	82	13	)	)	PUNCT
ejpam-5758	82	14	is	be	AUX
ejpam-5758	82	15	convergent	convergent	ADJ
ejpam-5758	82	16	for	for	ADP
ejpam-5758	82	17	all	all	DET
ejpam-5758	82	18	x	x	SYM
ejpam-5758	82	19	∈	∈	PROPN
ejpam-5758	82	20	e	e	NOUN
ejpam-5758	82	21	and	and	CCONJ
ejpam-5758	82	22	µ∗(x	µ∗(x	PROPN
ejpam-5758	82	23	)	)	PUNCT
ejpam-5758	82	24	=	=	PUNCT
ejpam-5758	83	1	∞∑	∞∑	NUM
ejpam-5758	83	2	n=0	n=0	NUM
ejpam-5758	83	3	λnµ(x	λnµ(x	NOUN
ejpam-5758	83	4	)	)	PUNCT
ejpam-5758	83	5	=	=	SYM
ejpam-5758	84	1	∞∑	∞∑	PRON
ejpam-5758	84	2	n=0	n=0	NUM
ejpam-5758	84	3	2n(p−2)µ(x	2n(p−2)µ(x	NUM
ejpam-5758	84	4	)	)	PUNCT
ejpam-5758	84	5	=	=	SYM
ejpam-5758	84	6	2η	2η	NUM
ejpam-5758	84	7	4−	4−	NOUN
ejpam-5758	84	8	2p	2p	NOUN
ejpam-5758	84	9	∥x∥p	∥x∥p	NOUN
ejpam-5758	84	10	for	for	ADP
ejpam-5758	84	11	all	all	DET
ejpam-5758	84	12	x	x	SYM
ejpam-5758	84	13	∈	∈	PROPN
ejpam-5758	84	14	e.	e.	PROPN
ejpam-5758	84	15	by	by	ADP
ejpam-5758	84	16	theorem	theorem	NOUN
ejpam-5758	84	17	1	1	NUM
ejpam-5758	84	18	,	,	PUNCT
ejpam-5758	84	19	there	there	PRON
ejpam-5758	84	20	exists	exist	VERB
ejpam-5758	84	21	a	a	DET
ejpam-5758	84	22	mapping	mapping	NOUN
ejpam-5758	84	23	q	q	NOUN
ejpam-5758	84	24	:	:	PUNCT
ejpam-5758	84	25	e	e	X
ejpam-5758	84	26	→	→	SYM
ejpam-5758	84	27	b	b	X
ejpam-5758	84	28	such	such	ADJ
ejpam-5758	84	29	q(x	q(x	NOUN
ejpam-5758	84	30	)	)	PUNCT
ejpam-5758	84	31	=	=	VERB
ejpam-5758	84	32	lim	lim	PROPN
ejpam-5758	84	33	n→∞	n→∞	NUM
ejpam-5758	84	34	hnf(x	hnf(x	PROPN
ejpam-5758	84	35	)	)	PUNCT
ejpam-5758	84	36	,	,	PUNCT
ejpam-5758	84	37	q(x	q(x	PROPN
ejpam-5758	84	38	)	)	PUNCT
ejpam-5758	84	39	=	=	PUNCT
ejpam-5758	84	40	1	1	NUM
ejpam-5758	84	41	4	4	NUM
ejpam-5758	84	42	q(2x	q(2x	ADJ
ejpam-5758	84	43	)	)	PUNCT
ejpam-5758	84	44	and	and	CCONJ
ejpam-5758	84	45	∥f(x)−q(x)∥	∥f(x)−q(x)∥	VERB
ejpam-5758	84	46	≤	≤	PROPN
ejpam-5758	84	47	2η	2η	PROPN
ejpam-5758	84	48	4−	4−	NOUN
ejpam-5758	84	49	2p	2p	NOUN
ejpam-5758	84	50	∥x∥p	∥x∥p	NOUN
ejpam-5758	84	51	for	for	ADP
ejpam-5758	84	52	all	all	DET
ejpam-5758	84	53	x	x	SYM
ejpam-5758	84	54	∈	∈	PROPN
ejpam-5758	84	55	e.	e.	PROPN
ejpam-5758	84	56	next	next	ADV
ejpam-5758	84	57	,	,	PUNCT
ejpam-5758	84	58	by	by	ADP
ejpam-5758	84	59	induction	induction	NOUN
ejpam-5758	84	60	on	on	ADP
ejpam-5758	84	61	n	n	CCONJ
ejpam-5758	84	62	,	,	PUNCT
ejpam-5758	84	63	one	one	PRON
ejpam-5758	84	64	can	can	AUX
ejpam-5758	84	65	see	see	VERB
ejpam-5758	84	66	that	that	SCONJ
ejpam-5758	84	67	∥hnf(x+	∥hnf(x+	NUM
ejpam-5758	84	68	y	y	NOUN
ejpam-5758	84	69	)	)	PUNCT
ejpam-5758	85	1	+	+	ADP
ejpam-5758	85	2	hnf(x−	hnf(x−	X
ejpam-5758	85	3	y)−	y)−	PROPN
ejpam-5758	85	4	2hnf(x)−	2hnf(x)−	PROPN
ejpam-5758	85	5	2hnf(y)∥	2hnf(y)∥	NOUN
ejpam-5758	85	6	≤	≤	NOUN
ejpam-5758	85	7	2n(p−2	2n(p−2	NUM
ejpam-5758	85	8	)	)	PUNCT
ejpam-5758	86	1	[	[	X
ejpam-5758	86	2	η	η	X
ejpam-5758	86	3	(	(	PUNCT
ejpam-5758	86	4	∥x∥p	∥x∥p	ADJ
ejpam-5758	86	5	+	+	CCONJ
ejpam-5758	86	6	∥y∥p	∥y∥p	X
ejpam-5758	86	7	)	)	PUNCT
ejpam-5758	86	8	+	+	CCONJ
ejpam-5758	86	9	θ∥x−	θ∥x−	PROPN
ejpam-5758	86	10	y∥p	y∥p	PROPN
ejpam-5758	86	11	]	]	PUNCT
ejpam-5758	86	12	for	for	ADP
ejpam-5758	86	13	all	all	DET
ejpam-5758	86	14	x	x	NOUN
ejpam-5758	86	15	,	,	PUNCT
ejpam-5758	86	16	y	y	PROPN
ejpam-5758	86	17	∈	∈	PROPN
ejpam-5758	86	18	e	e	X
ejpam-5758	86	19	and	and	CCONJ
ejpam-5758	86	20	n	n	PRON
ejpam-5758	86	21	∈	∈	PROPN
ejpam-5758	86	22	n0	n0	PROPN
ejpam-5758	86	23	.	.	PUNCT
ejpam-5758	87	1	by	by	ADP
ejpam-5758	87	2	letting	let	VERB
ejpam-5758	87	3	n→	n→	PUNCT
ejpam-5758	87	4	∞	∞	NUM
ejpam-5758	87	5	we	we	PRON
ejpam-5758	87	6	conclude	conclude	VERB
ejpam-5758	87	7	that	that	PRON
ejpam-5758	87	8	q	q	VERB
ejpam-5758	87	9	is	be	AUX
ejpam-5758	87	10	a	a	DET
ejpam-5758	87	11	quadratic	quadratic	ADJ
ejpam-5758	87	12	mapping	mapping	NOUN
ejpam-5758	87	13	.	.	PUNCT
ejpam-5758	88	1	now	now	ADV
ejpam-5758	88	2	,	,	PUNCT
ejpam-5758	88	3	we	we	PRON
ejpam-5758	88	4	consider	consider	VERB
ejpam-5758	88	5	the	the	DET
ejpam-5758	88	6	case	case	NOUN
ejpam-5758	88	7	p	p	X
ejpam-5758	88	8	>	>	X
ejpam-5758	88	9	2	2	X
ejpam-5758	88	10	.	.	X
ejpam-5758	88	11	replacing	replace	VERB
ejpam-5758	88	12	x	x	PUNCT
ejpam-5758	88	13	and	and	CCONJ
ejpam-5758	88	14	y	y	PROPN
ejpam-5758	88	15	by	by	ADP
ejpam-5758	88	16	x	x	PROPN
ejpam-5758	88	17	2	2	NUM
ejpam-5758	88	18	in	in	ADP
ejpam-5758	88	19	(	(	PUNCT
ejpam-5758	88	20	3	3	NUM
ejpam-5758	88	21	)	)	PUNCT
ejpam-5758	88	22	,	,	PUNCT
ejpam-5758	88	23	we	we	PRON
ejpam-5758	88	24	have∥∥∥f(x)−	have∥∥∥f(x)−	VERB
ejpam-5758	88	25	4f	4f	NUM
ejpam-5758	88	26	(	(	PUNCT
ejpam-5758	88	27	x	x	SYM
ejpam-5758	88	28	2	2	NUM
ejpam-5758	88	29	)	)	PUNCT
ejpam-5758	88	30	∥∥∥	∥∥∥	PROPN
ejpam-5758	88	31	≤	≤	NUM
ejpam-5758	88	32	2η	2η	PROPN
ejpam-5758	88	33	2p	2p	NUM
ejpam-5758	88	34	∥x∥p	∥x∥p	ADJ
ejpam-5758	88	35	m.	m.	NOUN
ejpam-5758	88	36	dehghanian	dehghanian	PROPN
ejpam-5758	88	37	et	et	PROPN
ejpam-5758	88	38	al	al	PROPN
ejpam-5758	88	39	.	.	PUNCT
ejpam-5758	88	40	/	/	SYM
ejpam-5758	88	41	eur	eur	PROPN
ejpam-5758	88	42	.	.	PUNCT
ejpam-5758	89	1	j.	j.	PROPN
ejpam-5758	89	2	pure	pure	PROPN
ejpam-5758	89	3	appl	appl	PROPN
ejpam-5758	89	4	.	.	PROPN
ejpam-5758	89	5	math	math	PROPN
ejpam-5758	89	6	,	,	PUNCT
ejpam-5758	89	7	18	18	NUM
ejpam-5758	89	8	(	(	PUNCT
ejpam-5758	89	9	1	1	NUM
ejpam-5758	89	10	)	)	PUNCT
ejpam-5758	89	11	(	(	PUNCT
ejpam-5758	89	12	2025	2025	NUM
ejpam-5758	89	13	)	)	PUNCT
ejpam-5758	89	14	,	,	PUNCT
ejpam-5758	89	15	5758	5758	NUM
ejpam-5758	89	16	6	6	NUM
ejpam-5758	89	17	of	of	ADP
ejpam-5758	89	18	13	13	NUM
ejpam-5758	89	19	for	for	ADP
ejpam-5758	89	20	all	all	DET
ejpam-5758	89	21	x	x	SYM
ejpam-5758	89	22	∈	∈	PROPN
ejpam-5758	89	23	e.	e.	PROPN
ejpam-5758	89	24	consider	consider	VERB
ejpam-5758	89	25	hg(x	hg(x	PUNCT
ejpam-5758	89	26	)	)	PUNCT
ejpam-5758	89	27	=	=	SYM
ejpam-5758	89	28	4	4	NUM
ejpam-5758	89	29	g	g	NOUN
ejpam-5758	89	30	(	(	PUNCT
ejpam-5758	89	31	x	x	NOUN
ejpam-5758	89	32	2	2	NUM
ejpam-5758	89	33	)	)	PUNCT
ejpam-5758	89	34	,	,	PUNCT
ejpam-5758	89	35	g	g	PROPN
ejpam-5758	89	36	∈	∈	PROPN
ejpam-5758	89	37	be	be	VERB
ejpam-5758	89	38	,	,	PUNCT
ejpam-5758	89	39	λf(x	λf(x	PUNCT
ejpam-5758	89	40	)	)	PUNCT
ejpam-5758	89	41	=	=	SYM
ejpam-5758	90	1	4f	4f	NUM
ejpam-5758	90	2	(	(	PUNCT
ejpam-5758	90	3	x	x	SYM
ejpam-5758	90	4	2	2	NUM
ejpam-5758	90	5	)	)	PUNCT
ejpam-5758	90	6	,	,	PUNCT
ejpam-5758	90	7	f	f	PROPN
ejpam-5758	90	8	∈	∈	PROPN
ejpam-5758	90	9	re	re	X
ejpam-5758	90	10	+	+	NUM
ejpam-5758	90	11	and	and	CCONJ
ejpam-5758	90	12	µ(x	µ(x	NOUN
ejpam-5758	90	13	)	)	PUNCT
ejpam-5758	90	14	=	=	SYM
ejpam-5758	90	15	2η	2η	NUM
ejpam-5758	90	16	2p	2p	NUM
ejpam-5758	90	17	∥x∥	∥x∥	NOUN
ejpam-5758	90	18	p	p	NOUN
ejpam-5758	90	19	for	for	ADP
ejpam-5758	90	20	all	all	DET
ejpam-5758	90	21	x	x	SYM
ejpam-5758	90	22	∈	∈	PROPN
ejpam-5758	90	23	e.	e.	PROPN
ejpam-5758	90	24	also	also	ADV
ejpam-5758	90	25	,	,	PUNCT
ejpam-5758	90	26	λµ(x	λµ(x	PUNCT
ejpam-5758	90	27	)	)	PUNCT
ejpam-5758	90	28	=	=	SYM
ejpam-5758	90	29	22−pµ(x	22−pµ(x	NUM
ejpam-5758	90	30	)	)	PUNCT
ejpam-5758	90	31	for	for	ADP
ejpam-5758	90	32	all	all	DET
ejpam-5758	90	33	x	x	SYM
ejpam-5758	90	34	∈	∈	PROPN
ejpam-5758	90	35	e.	e.	PROPN
ejpam-5758	90	36	since	since	SCONJ
ejpam-5758	90	37	p	p	PROPN
ejpam-5758	90	38	>	>	X
ejpam-5758	90	39	2	2	NUM
ejpam-5758	90	40	,	,	PUNCT
ejpam-5758	90	41	the	the	DET
ejpam-5758	90	42	serie	serie	ADJ
ejpam-5758	90	43	∑∞	∑∞	NOUN
ejpam-5758	90	44	n=0	n=0	X
ejpam-5758	90	45	λ	λ	NOUN
ejpam-5758	90	46	nµ(x	nµ(x	NUM
ejpam-5758	90	47	)	)	PUNCT
ejpam-5758	90	48	is	be	AUX
ejpam-5758	90	49	convergent	convergent	ADJ
ejpam-5758	90	50	for	for	ADP
ejpam-5758	90	51	all	all	DET
ejpam-5758	90	52	x	x	SYM
ejpam-5758	90	53	∈	∈	PROPN
ejpam-5758	90	54	e	e	NOUN
ejpam-5758	90	55	and	and	CCONJ
ejpam-5758	90	56	µ∗(x	µ∗(x	PROPN
ejpam-5758	90	57	)	)	PUNCT
ejpam-5758	90	58	=	=	PUNCT
ejpam-5758	91	1	∞∑	∞∑	NUM
ejpam-5758	91	2	n=0	n=0	NUM
ejpam-5758	91	3	λnµ(x	λnµ(x	NOUN
ejpam-5758	91	4	)	)	PUNCT
ejpam-5758	91	5	=	=	SYM
ejpam-5758	91	6	2η	2η	NUM
ejpam-5758	91	7	2p	2p	NUM
ejpam-5758	91	8	−	−	PROPN
ejpam-5758	91	9	4	4	NUM
ejpam-5758	91	10	∥x∥p	∥x∥p	NOUN
ejpam-5758	91	11	for	for	ADP
ejpam-5758	91	12	all	all	DET
ejpam-5758	91	13	x	x	SYM
ejpam-5758	91	14	∈	∈	PROPN
ejpam-5758	91	15	e.	e.	PROPN
ejpam-5758	91	16	so	so	ADV
ejpam-5758	91	17	,	,	PUNCT
ejpam-5758	91	18	by	by	ADP
ejpam-5758	91	19	theorem	theorem	NOUN
ejpam-5758	91	20	1	1	NUM
ejpam-5758	91	21	there	there	PRON
ejpam-5758	91	22	is	be	VERB
ejpam-5758	91	23	q	q	NOUN
ejpam-5758	91	24	:	:	PUNCT
ejpam-5758	91	25	e	e	X
ejpam-5758	91	26	→	→	SYM
ejpam-5758	91	27	b	b	X
ejpam-5758	91	28	such	such	ADJ
ejpam-5758	91	29	that	that	SCONJ
ejpam-5758	91	30	q(x	q(x	PROPN
ejpam-5758	91	31	)	)	PUNCT
ejpam-5758	92	1	=	=	VERB
ejpam-5758	92	2	lim	lim	PROPN
ejpam-5758	92	3	n→∞	n→∞	NUM
ejpam-5758	92	4	hnf(x	hnf(x	PROPN
ejpam-5758	92	5	)	)	PUNCT
ejpam-5758	92	6	,	,	PUNCT
ejpam-5758	92	7	q(x	q(x	PROPN
ejpam-5758	92	8	)	)	PUNCT
ejpam-5758	93	1	=	=	SYM
ejpam-5758	93	2	4q	4q	NOUN
ejpam-5758	93	3	(	(	PUNCT
ejpam-5758	93	4	x	x	SYM
ejpam-5758	93	5	2	2	NUM
ejpam-5758	93	6	)	)	PUNCT
ejpam-5758	93	7	and	and	CCONJ
ejpam-5758	93	8	∥f(x)−q(x)∥	∥f(x)−q(x)∥	VERB
ejpam-5758	93	9	≤	≤	PROPN
ejpam-5758	93	10	2η	2η	NUM
ejpam-5758	93	11	2p	2p	NUM
ejpam-5758	93	12	−	−	PROPN
ejpam-5758	93	13	4	4	NUM
ejpam-5758	93	14	∥x∥p	∥x∥p	NOUN
ejpam-5758	93	15	for	for	ADP
ejpam-5758	93	16	all	all	DET
ejpam-5758	93	17	x	x	SYM
ejpam-5758	93	18	∈	∈	PROPN
ejpam-5758	93	19	e.	e.	PROPN
ejpam-5758	93	20	it	it	PRON
ejpam-5758	93	21	follows	follow	VERB
ejpam-5758	93	22	from	from	ADP
ejpam-5758	93	23	(	(	PUNCT
ejpam-5758	93	24	3	3	NUM
ejpam-5758	93	25	)	)	PUNCT
ejpam-5758	93	26	and	and	CCONJ
ejpam-5758	93	27	by	by	ADP
ejpam-5758	93	28	induction	induction	NOUN
ejpam-5758	93	29	n	n	CCONJ
ejpam-5758	93	30	∈	∈	PROPN
ejpam-5758	93	31	n0	n0	NOUN
ejpam-5758	93	32	that	that	SCONJ
ejpam-5758	93	33	∥hnf(x+	∥hnf(x+	NUM
ejpam-5758	93	34	y	y	NOUN
ejpam-5758	93	35	)	)	PUNCT
ejpam-5758	94	1	+	+	ADP
ejpam-5758	94	2	hnf(x−	hnf(x−	X
ejpam-5758	94	3	y)−	y)−	PROPN
ejpam-5758	94	4	2hnf(x)−	2hnf(x)−	PROPN
ejpam-5758	94	5	2hnf(y)∥	2hnf(y)∥	NOUN
ejpam-5758	94	6	≤	≤	ADJ
ejpam-5758	94	7	2n(2−p	2n(2−p	NOUN
ejpam-5758	94	8	)	)	PUNCT
ejpam-5758	95	1	[	[	X
ejpam-5758	95	2	η	η	X
ejpam-5758	95	3	(	(	PUNCT
ejpam-5758	95	4	∥x∥p	∥x∥p	ADJ
ejpam-5758	95	5	+	+	CCONJ
ejpam-5758	95	6	∥y∥p	∥y∥p	X
ejpam-5758	95	7	)	)	PUNCT
ejpam-5758	95	8	+	+	CCONJ
ejpam-5758	95	9	θ∥x−	θ∥x−	PROPN
ejpam-5758	95	10	y∥p	y∥p	PROPN
ejpam-5758	95	11	]	]	PUNCT
ejpam-5758	95	12	for	for	ADP
ejpam-5758	95	13	all	all	DET
ejpam-5758	95	14	x	x	NOUN
ejpam-5758	95	15	,	,	PUNCT
ejpam-5758	95	16	y	y	PROPN
ejpam-5758	95	17	∈	∈	PROPN
ejpam-5758	95	18	e.	e.	PROPN
ejpam-5758	95	19	therefore	therefore	ADV
ejpam-5758	95	20	,	,	PUNCT
ejpam-5758	95	21	q	q	PUNCT
ejpam-5758	95	22	satisfies	satisfy	VERB
ejpam-5758	95	23	the	the	DET
ejpam-5758	95	24	quadratic	quadratic	ADJ
ejpam-5758	95	25	functional	functional	ADJ
ejpam-5758	95	26	equation	equation	NOUN
ejpam-5758	95	27	.	.	PUNCT
ejpam-5758	96	1	to	to	PART
ejpam-5758	96	2	prove	prove	VERB
ejpam-5758	96	3	the	the	DET
ejpam-5758	96	4	uniqueness	uniqueness	NOUN
ejpam-5758	96	5	of	of	ADP
ejpam-5758	96	6	q	q	NOUN
ejpam-5758	96	7	for	for	ADP
ejpam-5758	96	8	the	the	DET
ejpam-5758	96	9	case	case	NOUN
ejpam-5758	96	10	p	p	X
ejpam-5758	96	11	<	<	X
ejpam-5758	96	12	2	2	NUM
ejpam-5758	96	13	,	,	PUNCT
ejpam-5758	96	14	assume	assume	VERB
ejpam-5758	96	15	that	that	SCONJ
ejpam-5758	96	16	q1	q1	PROPN
ejpam-5758	96	17	,	,	PUNCT
ejpam-5758	96	18	q2	q2	NOUN
ejpam-5758	96	19	:	:	PUNCT
ejpam-5758	96	20	e	e	X
ejpam-5758	96	21	→	→	SYM
ejpam-5758	96	22	b	b	X
ejpam-5758	96	23	satisfy	satisfy	VERB
ejpam-5758	96	24	the	the	DET
ejpam-5758	96	25	quadratic	quadratic	ADJ
ejpam-5758	96	26	functional	functional	ADJ
ejpam-5758	96	27	equation	equation	NOUN
ejpam-5758	96	28	on	on	ADP
ejpam-5758	96	29	e	e	NOUN
ejpam-5758	96	30	and	and	CCONJ
ejpam-5758	96	31	∥f(x)−q1(x)∥	∥f(x)−q1(x)∥	ADP
ejpam-5758	96	32	≤	≤	NUM
ejpam-5758	96	33	η1∥x∥p	η1∥x∥p	NOUN
ejpam-5758	96	34	,	,	PUNCT
ejpam-5758	96	35	∥f(x)−q2(x)∥	∥f(x)−q2(x)∥	PUNCT
ejpam-5758	96	36	≤	≤	X
ejpam-5758	96	37	η2∥x∥p	η2∥x∥p	NOUN
ejpam-5758	96	38	for	for	ADP
ejpam-5758	96	39	some	some	DET
ejpam-5758	96	40	η1	η1	NOUN
ejpam-5758	96	41	,	,	PUNCT
ejpam-5758	96	42	η2	η2	X
ejpam-5758	96	43	≥	≥	NOUN
ejpam-5758	96	44	0	0	NUM
ejpam-5758	96	45	and	and	CCONJ
ejpam-5758	96	46	for	for	ADP
ejpam-5758	96	47	all	all	DET
ejpam-5758	96	48	x	x	SYM
ejpam-5758	96	49	∈	∈	PROPN
ejpam-5758	96	50	e.	e.	PROPN
ejpam-5758	96	51	then	then	ADV
ejpam-5758	96	52	∥q1(x)−q2(x)∥	∥q1(x)−q2(x)∥	PUNCT
ejpam-5758	96	53	≤	≤	NOUN
ejpam-5758	96	54	(	(	PUNCT
ejpam-5758	96	55	η1	η1	NOUN
ejpam-5758	96	56	+	+	CCONJ
ejpam-5758	96	57	η2)∥x∥p	η2)∥x∥p	NOUN
ejpam-5758	96	58	for	for	ADP
ejpam-5758	96	59	all	all	DET
ejpam-5758	96	60	x	x	SYM
ejpam-5758	96	61	∈	∈	PROPN
ejpam-5758	96	62	e.	e.	NOUN
ejpam-5758	96	63	hence	hence	ADV
ejpam-5758	96	64	q1(x	q1(x	NOUN
ejpam-5758	96	65	)	)	PUNCT
ejpam-5758	96	66	=	=	SYM
ejpam-5758	96	67	1	1	NUM
ejpam-5758	96	68	4	4	NUM
ejpam-5758	96	69	q1(2x	q1(2x	ADJ
ejpam-5758	96	70	)	)	PUNCT
ejpam-5758	96	71	,	,	PUNCT
ejpam-5758	96	72	q2(x	q2(x	X
ejpam-5758	96	73	)	)	PUNCT
ejpam-5758	96	74	=	=	SYM
ejpam-5758	96	75	1	1	NUM
ejpam-5758	96	76	4	4	NUM
ejpam-5758	96	77	q2(2x	q2(2x	VERB
ejpam-5758	96	78	)	)	PUNCT
ejpam-5758	96	79	for	for	ADP
ejpam-5758	96	80	all	all	DET
ejpam-5758	96	81	x	x	SYM
ejpam-5758	96	82	∈	∈	PROPN
ejpam-5758	96	83	e.	e.	PROPN
ejpam-5758	96	84	thus	thus	ADV
ejpam-5758	96	85	∥q1(x)−q2(x)∥	∥q1(x)−q2(x)∥	X
ejpam-5758	96	86	≤	≤	NUM
ejpam-5758	96	87	1	1	NUM
ejpam-5758	96	88	4	4	NUM
ejpam-5758	96	89	∥q1(2x)−q2(2x)∥	∥q1(2x)−q2(2x)∥	NOUN
ejpam-5758	96	90	≤	≤	NUM
ejpam-5758	96	91	2p	2p	NUM
ejpam-5758	96	92	4	4	NUM
ejpam-5758	96	93	(	(	PUNCT
ejpam-5758	96	94	η1	η1	NOUN
ejpam-5758	96	95	+	+	CCONJ
ejpam-5758	96	96	η2)∥x∥p	η2)∥x∥p	PROPN
ejpam-5758	96	97	m.	m.	NOUN
ejpam-5758	96	98	dehghanian	dehghanian	PROPN
ejpam-5758	96	99	et	et	PROPN
ejpam-5758	96	100	al	al	PROPN
ejpam-5758	96	101	.	.	PUNCT
ejpam-5758	96	102	/	/	SYM
ejpam-5758	96	103	eur	eur	PROPN
ejpam-5758	96	104	.	.	PUNCT
ejpam-5758	97	1	j.	j.	PROPN
ejpam-5758	97	2	pure	pure	PROPN
ejpam-5758	97	3	appl	appl	PROPN
ejpam-5758	97	4	.	.	PROPN
ejpam-5758	97	5	math	math	PROPN
ejpam-5758	97	6	,	,	PUNCT
ejpam-5758	97	7	18	18	NUM
ejpam-5758	97	8	(	(	PUNCT
ejpam-5758	97	9	1	1	NUM
ejpam-5758	97	10	)	)	PUNCT
ejpam-5758	97	11	(	(	PUNCT
ejpam-5758	97	12	2025	2025	NUM
ejpam-5758	97	13	)	)	PUNCT
ejpam-5758	97	14	,	,	PUNCT
ejpam-5758	97	15	5758	5758	NUM
ejpam-5758	97	16	7	7	NUM
ejpam-5758	97	17	of	of	ADP
ejpam-5758	97	18	13	13	NUM
ejpam-5758	97	19	for	for	ADP
ejpam-5758	97	20	all	all	DET
ejpam-5758	97	21	x	x	SYM
ejpam-5758	97	22	∈	∈	PROPN
ejpam-5758	97	23	e.	e.	NOUN
ejpam-5758	97	24	by	by	ADP
ejpam-5758	97	25	induction	induction	NOUN
ejpam-5758	97	26	on	on	ADP
ejpam-5758	97	27	n	n	DET
ejpam-5758	97	28	∈	∈	PROPN
ejpam-5758	97	29	n0	n0	NOUN
ejpam-5758	97	30	we	we	PRON
ejpam-5758	97	31	see	see	VERB
ejpam-5758	97	32	that	that	DET
ejpam-5758	97	33	∥q1(x)−q2(x)∥	∥q1(x)−q2(x)∥	ADV
ejpam-5758	97	34	≤	≤	NUM
ejpam-5758	97	35	(	(	PUNCT
ejpam-5758	97	36	2p	2p	NUM
ejpam-5758	97	37	4	4	NUM
ejpam-5758	97	38	)	)	PUNCT
ejpam-5758	97	39	n	n	CCONJ
ejpam-5758	97	40	(	(	PUNCT
ejpam-5758	97	41	η1	η1	NOUN
ejpam-5758	97	42	+	+	CCONJ
ejpam-5758	97	43	η2)∥x∥p	η2)∥x∥p	NOUN
ejpam-5758	97	44	which	which	PRON
ejpam-5758	97	45	tends	tend	VERB
ejpam-5758	97	46	to	to	ADP
ejpam-5758	97	47	0	0	NUM
ejpam-5758	97	48	as	as	ADP
ejpam-5758	97	49	n→	n→	ADV
ejpam-5758	97	50	∞	∞	PROPN
ejpam-5758	97	51	for	for	ADP
ejpam-5758	97	52	all	all	DET
ejpam-5758	97	53	x	x	SYM
ejpam-5758	97	54	∈	∈	PROPN
ejpam-5758	97	55	e.	e.	PROPN
ejpam-5758	97	56	this	this	PRON
ejpam-5758	97	57	implies	imply	VERB
ejpam-5758	97	58	q1(x	q1(x	NOUN
ejpam-5758	97	59	)	)	PUNCT
ejpam-5758	97	60	=	=	SYM
ejpam-5758	97	61	q2(x	q2(x	X
ejpam-5758	97	62	)	)	PUNCT
ejpam-5758	97	63	for	for	ADP
ejpam-5758	97	64	all	all	DET
ejpam-5758	97	65	x	x	SYM
ejpam-5758	97	66	∈	∈	PROPN
ejpam-5758	97	67	e.	e.	NOUN
ejpam-5758	97	68	the	the	DET
ejpam-5758	97	69	proofs	proof	NOUN
ejpam-5758	97	70	of	of	ADP
ejpam-5758	97	71	the	the	DET
ejpam-5758	97	72	cases	case	NOUN
ejpam-5758	97	73	p	p	X
ejpam-5758	97	74	>	>	SYM
ejpam-5758	97	75	2	2	NUM
ejpam-5758	97	76	runs	run	NOUN
ejpam-5758	97	77	as	as	ADP
ejpam-5758	97	78	before	before	ADV
ejpam-5758	97	79	.	.	PUNCT
ejpam-5758	98	1	3	3	X
ejpam-5758	98	2	.	.	X
ejpam-5758	98	3	main	main	ADJ
ejpam-5758	98	4	results	result	NOUN
ejpam-5758	98	5	in	in	ADP
ejpam-5758	98	6	this	this	DET
ejpam-5758	98	7	section	section	NOUN
ejpam-5758	98	8	,	,	PUNCT
ejpam-5758	98	9	we	we	PRON
ejpam-5758	98	10	investigate	investigate	VERB
ejpam-5758	98	11	the	the	DET
ejpam-5758	98	12	hyers	hyers	PROPN
ejpam-5758	98	13	-	-	PUNCT
ejpam-5758	98	14	ulam	ulam	ADJ
ejpam-5758	98	15	stability	stability	NOUN
ejpam-5758	98	16	of	of	ADP
ejpam-5758	98	17	the	the	DET
ejpam-5758	98	18	pexiderized	pexiderize	VERB
ejpam-5758	98	19	additivequadratic	additivequadratic	ADJ
ejpam-5758	98	20	functional	functional	ADJ
ejpam-5758	98	21	equation	equation	NOUN
ejpam-5758	98	22	(	(	PUNCT
ejpam-5758	98	23	1	1	NUM
ejpam-5758	98	24	)	)	PUNCT
ejpam-5758	98	25	in	in	ADP
ejpam-5758	98	26	banach	banach	NOUN
ejpam-5758	98	27	spaces	space	NOUN
ejpam-5758	98	28	.	.	PUNCT
ejpam-5758	99	1	theorem	theorem	ADJ
ejpam-5758	99	2	4	4	NUM
ejpam-5758	99	3	.	.	PUNCT
ejpam-5758	100	1	let	let	VERB
ejpam-5758	100	2	f	f	X
ejpam-5758	100	3	,	,	PUNCT
ejpam-5758	100	4	h	h	NOUN
ejpam-5758	100	5	:	:	PUNCT
ejpam-5758	100	6	e	e	X
ejpam-5758	100	7	→	→	SYM
ejpam-5758	100	8	b	b	PROPN
ejpam-5758	100	9	be	be	AUX
ejpam-5758	100	10	mapings	maping	NOUN
ejpam-5758	100	11	satisfying	satisfy	VERB
ejpam-5758	100	12	∥f(x+	∥f(x+	NOUN
ejpam-5758	100	13	y	y	NOUN
ejpam-5758	100	14	)	)	PUNCT
ejpam-5758	101	1	+	+	CCONJ
ejpam-5758	101	2	f(x−	f(x−	PROPN
ejpam-5758	101	3	y	y	NOUN
ejpam-5758	101	4	)	)	PUNCT
ejpam-5758	102	1	+	+	CCONJ
ejpam-5758	102	2	h(x+	h(x+	ADV
ejpam-5758	102	3	y)−	y)−	PROPN
ejpam-5758	102	4	2f(x)−	2f(x)−	NUM
ejpam-5758	102	5	2f(y)−	2f(y)−	NUM
ejpam-5758	102	6	h(x)−	h(x)−	PROPN
ejpam-5758	102	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	102	8	≤	≤	PUNCT
ejpam-5758	102	9	ϵ	ϵ	X
ejpam-5758	102	10	(	(	PUNCT
ejpam-5758	102	11	∥x∥p	∥x∥p	X
ejpam-5758	102	12	+	+	CCONJ
ejpam-5758	102	13	∥y∥p	∥y∥p	NOUN
ejpam-5758	102	14	)	)	PUNCT
ejpam-5758	102	15	(	(	PUNCT
ejpam-5758	102	16	5	5	NUM
ejpam-5758	102	17	)	)	PUNCT
ejpam-5758	102	18	for	for	ADP
ejpam-5758	102	19	some	some	DET
ejpam-5758	102	20	ϵ	ϵ	PRON
ejpam-5758	102	21	≥	≥	NOUN
ejpam-5758	102	22	0	0	NUM
ejpam-5758	102	23	,	,	PUNCT
ejpam-5758	102	24	p	p	X
ejpam-5758	102	25	>	>	X
ejpam-5758	102	26	0	0	NUM
ejpam-5758	102	27	,	,	PUNCT
ejpam-5758	102	28	p	p	PROPN
ejpam-5758	102	29	̸=	̸=	PROPN
ejpam-5758	102	30	1	1	NUM
ejpam-5758	102	31	,	,	PUNCT
ejpam-5758	102	32	2	2	NUM
ejpam-5758	102	33	and	and	CCONJ
ejpam-5758	102	34	for	for	ADP
ejpam-5758	102	35	all	all	DET
ejpam-5758	102	36	x	x	NOUN
ejpam-5758	102	37	,	,	PUNCT
ejpam-5758	102	38	y	y	PROPN
ejpam-5758	102	39	∈	∈	PROPN
ejpam-5758	102	40	e.	e.	PROPN
ejpam-5758	102	41	then	then	ADV
ejpam-5758	102	42	there	there	PRON
ejpam-5758	102	43	exist	exist	VERB
ejpam-5758	102	44	an	an	DET
ejpam-5758	102	45	additive	additive	ADJ
ejpam-5758	102	46	mapping	mapping	NOUN
ejpam-5758	102	47	a	a	DET
ejpam-5758	102	48	:	:	PUNCT
ejpam-5758	102	49	e	e	X
ejpam-5758	102	50	→	→	SYM
ejpam-5758	102	51	b	b	PROPN
ejpam-5758	102	52	and	and	CCONJ
ejpam-5758	102	53	a	a	DET
ejpam-5758	102	54	unique	unique	ADJ
ejpam-5758	102	55	quadratic	quadratic	ADJ
ejpam-5758	102	56	mapping	mapping	NOUN
ejpam-5758	102	57	q	q	NOUN
ejpam-5758	102	58	:	:	PUNCT
ejpam-5758	102	59	e	e	X
ejpam-5758	102	60	→	→	SYM
ejpam-5758	102	61	b	b	X
ejpam-5758	102	62	such	such	ADJ
ejpam-5758	102	63	that	that	PRON
ejpam-5758	102	64	∥h(x)−	∥h(x)−	PROPN
ejpam-5758	102	65	h(0)−a(x)∥	h(0)−a(x)∥	VERB
ejpam-5758	102	66	≤	≤	NUM
ejpam-5758	102	67	8	8	NUM
ejpam-5758	102	68	+	+	CCONJ
ejpam-5758	102	69	24−p	24−p	NUM
ejpam-5758	102	70	|2p	|2p	NUM
ejpam-5758	102	71	−	−	PROPN
ejpam-5758	102	72	2|	2|	PRON
ejpam-5758	102	73	ϵ∥x∥p	ϵ∥x∥p	PROPN
ejpam-5758	102	74	,	,	PUNCT
ejpam-5758	102	75	∥f(x)−	∥f(x)−	PROPN
ejpam-5758	102	76	f(0)−q(x)∥	f(0)−q(x)∥	PROPN
ejpam-5758	102	77	≤	≤	ADV
ejpam-5758	102	78	10	10	NUM
ejpam-5758	102	79	+	+	NUM
ejpam-5758	102	80	24−p	24−p	NUM
ejpam-5758	102	81	|2p	|2p	NUM
ejpam-5758	102	82	−	−	NUM
ejpam-5758	102	83	4|	4|	NUM
ejpam-5758	102	84	ϵ∥x∥p	ϵ∥x∥p	VERB
ejpam-5758	102	85	for	for	ADP
ejpam-5758	102	86	all	all	DET
ejpam-5758	102	87	x	x	SYM
ejpam-5758	102	88	∈	∈	PROPN
ejpam-5758	102	89	e.	e.	PROPN
ejpam-5758	102	90	proof	proof	PROPN
ejpam-5758	102	91	.	.	PUNCT
ejpam-5758	103	1	interchanging	interchange	VERB
ejpam-5758	103	2	x	x	PUNCT
ejpam-5758	103	3	with	with	ADP
ejpam-5758	103	4	y	y	PROPN
ejpam-5758	103	5	in	in	ADP
ejpam-5758	103	6	(	(	PUNCT
ejpam-5758	103	7	5	5	NUM
ejpam-5758	103	8	)	)	PUNCT
ejpam-5758	103	9	,	,	PUNCT
ejpam-5758	103	10	we	we	PRON
ejpam-5758	103	11	obtain	obtain	VERB
ejpam-5758	103	12	∥f(x+	∥f(x+	NOUN
ejpam-5758	103	13	y	y	NOUN
ejpam-5758	103	14	)	)	PUNCT
ejpam-5758	104	1	+	+	CCONJ
ejpam-5758	104	2	f(y	f(y	ADJ
ejpam-5758	104	3	−	−	PROPN
ejpam-5758	104	4	x	x	NOUN
ejpam-5758	104	5	)	)	PUNCT
ejpam-5758	105	1	+	+	CCONJ
ejpam-5758	105	2	h(x+	h(x+	ADV
ejpam-5758	105	3	y)−	y)−	PROPN
ejpam-5758	105	4	2f(x)−	2f(x)−	NUM
ejpam-5758	105	5	2f(y)−	2f(y)−	NUM
ejpam-5758	105	6	h(x)−	h(x)−	PROPN
ejpam-5758	105	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	105	8	≤	≤	PUNCT
ejpam-5758	105	9	ϵ	ϵ	X
ejpam-5758	105	10	(	(	PUNCT
ejpam-5758	105	11	∥x∥p	∥x∥p	X
ejpam-5758	105	12	+	+	CCONJ
ejpam-5758	105	13	∥y∥p	∥y∥p	NOUN
ejpam-5758	105	14	)	)	PUNCT
ejpam-5758	105	15	(	(	PUNCT
ejpam-5758	105	16	6	6	NUM
ejpam-5758	105	17	)	)	PUNCT
ejpam-5758	105	18	for	for	ADP
ejpam-5758	105	19	all	all	DET
ejpam-5758	105	20	x	x	NOUN
ejpam-5758	105	21	,	,	PUNCT
ejpam-5758	105	22	y	y	PROPN
ejpam-5758	105	23	∈	∈	PROPN
ejpam-5758	105	24	e.	e.	PROPN
ejpam-5758	105	25	from	from	ADP
ejpam-5758	105	26	(	(	PUNCT
ejpam-5758	105	27	5	5	NUM
ejpam-5758	105	28	)	)	PUNCT
ejpam-5758	105	29	and	and	CCONJ
ejpam-5758	105	30	(	(	PUNCT
ejpam-5758	105	31	6	6	X
ejpam-5758	105	32	)	)	PUNCT
ejpam-5758	105	33	it	it	PRON
ejpam-5758	105	34	follows	follow	VERB
ejpam-5758	105	35	that	that	SCONJ
ejpam-5758	105	36	∥f(x−	∥f(x−	NUM
ejpam-5758	105	37	y)−	y)−	PROPN
ejpam-5758	105	38	f(y	f(y	NOUN
ejpam-5758	105	39	−	−	PROPN
ejpam-5758	105	40	x)∥	x)∥	PUNCT
ejpam-5758	105	41	≤	≤	NUM
ejpam-5758	105	42	2ϵ	2ϵ	NUM
ejpam-5758	105	43	(	(	PUNCT
ejpam-5758	105	44	∥x∥p	∥x∥p	X
ejpam-5758	105	45	+	+	CCONJ
ejpam-5758	105	46	∥y∥p	∥y∥p	X
ejpam-5758	105	47	)	)	PUNCT
ejpam-5758	105	48	for	for	ADP
ejpam-5758	105	49	all	all	DET
ejpam-5758	105	50	x	x	NOUN
ejpam-5758	105	51	,	,	PUNCT
ejpam-5758	105	52	y	y	PROPN
ejpam-5758	105	53	∈	∈	PROPN
ejpam-5758	105	54	e.	e.	NOUN
ejpam-5758	105	55	putting	put	VERB
ejpam-5758	105	56	y	y	PROPN
ejpam-5758	105	57	=	=	PUNCT
ejpam-5758	105	58	0	0	NUM
ejpam-5758	105	59	in	in	ADP
ejpam-5758	105	60	the	the	DET
ejpam-5758	105	61	above	above	ADJ
ejpam-5758	105	62	inequality	inequality	NOUN
ejpam-5758	105	63	,	,	PUNCT
ejpam-5758	105	64	we	we	PRON
ejpam-5758	105	65	get	get	VERB
ejpam-5758	105	66	∥f(x)−	∥f(x)−	PRON
ejpam-5758	105	67	f(−x)∥	f(−x)∥	ADP
ejpam-5758	105	68	≤	≤	ADJ
ejpam-5758	105	69	2ϵ∥x∥p	2ϵ∥x∥p	PROPN
ejpam-5758	105	70	(	(	PUNCT
ejpam-5758	105	71	7	7	NUM
ejpam-5758	105	72	)	)	PUNCT
ejpam-5758	105	73	for	for	ADP
ejpam-5758	105	74	all	all	PRON
ejpam-5758	105	75	x	x	SYM
ejpam-5758	105	76	∈	∈	PROPN
ejpam-5758	105	77	e.	e.	PROPN
ejpam-5758	105	78	substituting	substituting	NOUN
ejpam-5758	105	79	x	x	PROPN
ejpam-5758	105	80	and	and	CCONJ
ejpam-5758	105	81	then	then	ADV
ejpam-5758	105	82	−x	−x	VERB
ejpam-5758	105	83	in	in	ADP
ejpam-5758	105	84	the	the	DET
ejpam-5758	105	85	place	place	NOUN
ejpam-5758	105	86	of	of	ADP
ejpam-5758	105	87	y	y	PROPN
ejpam-5758	105	88	in	in	ADP
ejpam-5758	105	89	(	(	PUNCT
ejpam-5758	105	90	5	5	NUM
ejpam-5758	105	91	)	)	PUNCT
ejpam-5758	105	92	,	,	PUNCT
ejpam-5758	105	93	we	we	PRON
ejpam-5758	105	94	have	have	AUX
ejpam-5758	105	95	∥f(2x	∥f(2x	VERB
ejpam-5758	105	96	)	)	PUNCT
ejpam-5758	106	1	+	+	CCONJ
ejpam-5758	106	2	f(0	f(0	NOUN
ejpam-5758	106	3	)	)	PUNCT
ejpam-5758	107	1	+	+	CCONJ
ejpam-5758	108	1	h(2x)−	h(2x)−	PROPN
ejpam-5758	108	2	4f(x)−	4f(x)−	NUM
ejpam-5758	108	3	2h(x)∥	2h(x)∥	NUM
ejpam-5758	108	4	≤	≤	ADV
ejpam-5758	108	5	2ϵ∥x∥p	2ϵ∥x∥p	PROPN
ejpam-5758	108	6	,	,	PUNCT
ejpam-5758	108	7	(	(	PUNCT
ejpam-5758	108	8	8)	8)	NUM
ejpam-5758	108	9	∥f(0	∥f(0	NOUN
ejpam-5758	108	10	)	)	PUNCT
ejpam-5758	108	11	+	+	CCONJ
ejpam-5758	108	12	f(2x	f(2x	NUM
ejpam-5758	108	13	)	)	PUNCT
ejpam-5758	108	14	+	+	CCONJ
ejpam-5758	108	15	h(0)−	h(0)−	PROPN
ejpam-5758	108	16	2f(x)−	2f(x)−	NUM
ejpam-5758	108	17	2f(−x)−	2f(−x)−	NUM
ejpam-5758	109	1	h(x)−	h(x)−	PROPN
ejpam-5758	109	2	h(−x)∥	h(−x)∥	NOUN
ejpam-5758	109	3	≤	≤	ADJ
ejpam-5758	109	4	2ϵ∥x∥p	2ϵ∥x∥p	PROPN
ejpam-5758	109	5	(	(	PUNCT
ejpam-5758	109	6	9	9	NUM
ejpam-5758	109	7	)	)	PUNCT
ejpam-5758	109	8	m.	m.	NOUN
ejpam-5758	109	9	dehghanian	dehghanian	PROPN
ejpam-5758	109	10	et	et	PROPN
ejpam-5758	109	11	al	al	PROPN
ejpam-5758	109	12	.	.	PUNCT
ejpam-5758	109	13	/	/	SYM
ejpam-5758	109	14	eur	eur	PROPN
ejpam-5758	109	15	.	.	PUNCT
ejpam-5758	110	1	j.	j.	PROPN
ejpam-5758	110	2	pure	pure	PROPN
ejpam-5758	110	3	appl	appl	PROPN
ejpam-5758	110	4	.	.	PROPN
ejpam-5758	110	5	math	math	PROPN
ejpam-5758	110	6	,	,	PUNCT
ejpam-5758	110	7	18	18	NUM
ejpam-5758	110	8	(	(	PUNCT
ejpam-5758	110	9	1	1	NUM
ejpam-5758	110	10	)	)	PUNCT
ejpam-5758	110	11	(	(	PUNCT
ejpam-5758	110	12	2025	2025	NUM
ejpam-5758	110	13	)	)	PUNCT
ejpam-5758	110	14	,	,	PUNCT
ejpam-5758	110	15	5758	5758	NUM
ejpam-5758	110	16	8	8	NUM
ejpam-5758	110	17	of	of	ADP
ejpam-5758	110	18	13	13	NUM
ejpam-5758	110	19	for	for	ADP
ejpam-5758	110	20	all	all	DET
ejpam-5758	110	21	x	x	SYM
ejpam-5758	110	22	∈	∈	PROPN
ejpam-5758	110	23	e.	e.	PROPN
ejpam-5758	110	24	from	from	ADP
ejpam-5758	110	25	(	(	PUNCT
ejpam-5758	110	26	7	7	NUM
ejpam-5758	110	27	)	)	PUNCT
ejpam-5758	110	28	,	,	PUNCT
ejpam-5758	110	29	(	(	PUNCT
ejpam-5758	110	30	8)	8)	NUM
ejpam-5758	110	31	and	and	CCONJ
ejpam-5758	110	32	(	(	PUNCT
ejpam-5758	110	33	9	9	NUM
ejpam-5758	110	34	)	)	PUNCT
ejpam-5758	110	35	,	,	PUNCT
ejpam-5758	110	36	we	we	PRON
ejpam-5758	110	37	obtain	obtain	VERB
ejpam-5758	110	38	∥h(2x)−	∥h(2x)−	PROPN
ejpam-5758	110	39	h(x	h(x	PROPN
ejpam-5758	110	40	)	)	PUNCT
ejpam-5758	111	1	+	+	CCONJ
ejpam-5758	111	2	h(−x)−	h(−x)−	PROPN
ejpam-5758	111	3	h(0)∥	h(0)∥	PROPN
ejpam-5758	111	4	(	(	PUNCT
ejpam-5758	111	5	10	10	NUM
ejpam-5758	111	6	)	)	PUNCT
ejpam-5758	111	7	≤	≤	NOUN
ejpam-5758	111	8	∥f(2x	∥f(2x	VERB
ejpam-5758	111	9	)	)	PUNCT
ejpam-5758	112	1	+	+	CCONJ
ejpam-5758	112	2	f(0	f(0	NOUN
ejpam-5758	112	3	)	)	PUNCT
ejpam-5758	113	1	+	+	CCONJ
ejpam-5758	113	2	h(2x)−	h(2x)−	PROPN
ejpam-5758	113	3	4f(x)−	4f(x)−	NUM
ejpam-5758	113	4	2h(x)∥	2h(x)∥	NUM
ejpam-5758	113	5	+	+	NOUN
ejpam-5758	113	6	∥f(0	∥f(0	NOUN
ejpam-5758	113	7	)	)	PUNCT
ejpam-5758	113	8	+	+	NUM
ejpam-5758	113	9	f(2x	f(2x	NUM
ejpam-5758	113	10	)	)	PUNCT
ejpam-5758	113	11	+	+	CCONJ
ejpam-5758	113	12	h(0)−	h(0)−	PROPN
ejpam-5758	113	13	2f(x)−	2f(x)−	NUM
ejpam-5758	113	14	2f(−x)−	2f(−x)−	NUM
ejpam-5758	114	1	h(x)−	h(x)−	PROPN
ejpam-5758	114	2	h(−x)∥+	h(−x)∥+	PROPN
ejpam-5758	114	3	2∥f(x)−	2∥f(x)−	NUM
ejpam-5758	114	4	f(−x)∥	f(−x)∥	ADP
ejpam-5758	114	5	≤	≤	ADJ
ejpam-5758	114	6	2ϵ∥x∥p	2ϵ∥x∥p	PROPN
ejpam-5758	114	7	+	+	CCONJ
ejpam-5758	114	8	2ϵ∥x∥p	2ϵ∥x∥p	PROPN
ejpam-5758	114	9	+	+	CCONJ
ejpam-5758	114	10	4ϵ∥x∥p	4ϵ∥x∥p	VERB
ejpam-5758	114	11	=	=	SYM
ejpam-5758	114	12	8ϵ∥x∥p	8ϵ∥x∥p	NUM
ejpam-5758	114	13	for	for	ADP
ejpam-5758	114	14	all	all	DET
ejpam-5758	114	15	x	x	SYM
ejpam-5758	114	16	∈	∈	PROPN
ejpam-5758	114	17	e.	e.	NOUN
ejpam-5758	114	18	replacing	replace	VERB
ejpam-5758	114	19	x	x	PUNCT
ejpam-5758	114	20	by	by	ADP
ejpam-5758	114	21	−x	−x	NOUN
ejpam-5758	114	22	in	in	ADP
ejpam-5758	114	23	the	the	DET
ejpam-5758	114	24	last	last	ADJ
ejpam-5758	114	25	inequality	inequality	NOUN
ejpam-5758	114	26	,	,	PUNCT
ejpam-5758	114	27	we	we	PRON
ejpam-5758	114	28	obtain	obtain	VERB
ejpam-5758	114	29	∥h(−2x	∥h(−2x	NOUN
ejpam-5758	114	30	)	)	PUNCT
ejpam-5758	115	1	+	+	CCONJ
ejpam-5758	115	2	h(x)−	h(x)−	PROPN
ejpam-5758	115	3	h(−x)−	h(−x)−	PROPN
ejpam-5758	115	4	h(0)∥	h(0)∥	PROPN
ejpam-5758	115	5	≤	≤	ADV
ejpam-5758	115	6	8ϵ∥x∥p	8ϵ∥x∥p	PROPN
ejpam-5758	115	7	(	(	PUNCT
ejpam-5758	115	8	11	11	NUM
ejpam-5758	115	9	)	)	PUNCT
ejpam-5758	115	10	for	for	ADP
ejpam-5758	115	11	all	all	DET
ejpam-5758	115	12	x	x	SYM
ejpam-5758	115	13	∈	∈	PROPN
ejpam-5758	115	14	e.	e.	PROPN
ejpam-5758	115	15	it	it	PRON
ejpam-5758	115	16	follows	follow	VERB
ejpam-5758	115	17	from	from	ADP
ejpam-5758	115	18	(	(	PUNCT
ejpam-5758	115	19	10	10	NUM
ejpam-5758	115	20	)	)	PUNCT
ejpam-5758	115	21	and	and	CCONJ
ejpam-5758	115	22	(	(	PUNCT
ejpam-5758	115	23	11	11	NUM
ejpam-5758	115	24	)	)	PUNCT
ejpam-5758	115	25	that	that	PRON
ejpam-5758	115	26	∥h(2x	∥h(2x	VERB
ejpam-5758	115	27	)	)	PUNCT
ejpam-5758	116	1	+	+	CCONJ
ejpam-5758	116	2	h(−2x)−	h(−2x)−	PROPN
ejpam-5758	116	3	2h(0)∥	2h(0)∥	NUM
ejpam-5758	116	4	≤	≤	PROPN
ejpam-5758	116	5	16ϵ∥x∥p	16ϵ∥x∥p	PROPN
ejpam-5758	116	6	,	,	PUNCT
ejpam-5758	116	7	which	which	PRON
ejpam-5758	116	8	implies	imply	VERB
ejpam-5758	116	9	∥h(x	∥h(x	PROPN
ejpam-5758	116	10	)	)	PUNCT
ejpam-5758	117	1	+	+	CCONJ
ejpam-5758	117	2	h(−x)−	h(−x)−	PROPN
ejpam-5758	117	3	2h(0)∥	2h(0)∥	NUM
ejpam-5758	117	4	≤	≤	NUM
ejpam-5758	117	5	16	16	NUM
ejpam-5758	117	6	2p	2p	NUM
ejpam-5758	117	7	ϵ∥x∥p	ϵ∥x∥p	PROPN
ejpam-5758	117	8	(	(	PUNCT
ejpam-5758	117	9	12	12	NUM
ejpam-5758	117	10	)	)	PUNCT
ejpam-5758	117	11	for	for	ADP
ejpam-5758	117	12	all	all	DET
ejpam-5758	117	13	x	x	SYM
ejpam-5758	117	14	∈	∈	PROPN
ejpam-5758	117	15	e.	e.	NOUN
ejpam-5758	117	16	replacing	replace	VERB
ejpam-5758	117	17	y	y	PRON
ejpam-5758	117	18	by	by	ADP
ejpam-5758	117	19	−y	−y	VERB
ejpam-5758	117	20	in	in	ADP
ejpam-5758	117	21	(	(	PUNCT
ejpam-5758	117	22	5	5	NUM
ejpam-5758	117	23	)	)	PUNCT
ejpam-5758	117	24	,	,	PUNCT
ejpam-5758	117	25	we	we	PRON
ejpam-5758	117	26	have	have	AUX
ejpam-5758	117	27	∥f(x+	∥f(x+	VERB
ejpam-5758	117	28	y)+	y)+	NOUN
ejpam-5758	117	29	f(x−	f(x−	PROPN
ejpam-5758	117	30	y)+h(x−	y)+h(x−	NUM
ejpam-5758	117	31	y)−	y)−	PROPN
ejpam-5758	117	32	2f(x)−	2f(x)−	NUM
ejpam-5758	117	33	2f(−y)−h(x)−h(−y)∥	2f(−y)−h(x)−h(−y)∥	NOUN
ejpam-5758	117	34	≤	≤	NOUN
ejpam-5758	118	1	ϵ	ϵ	X
ejpam-5758	118	2	(	(	PUNCT
ejpam-5758	118	3	∥x∥p	∥x∥p	X
ejpam-5758	118	4	+	+	CCONJ
ejpam-5758	118	5	∥y∥p	∥y∥p	NOUN
ejpam-5758	118	6	)	)	PUNCT
ejpam-5758	118	7	(	(	PUNCT
ejpam-5758	118	8	13	13	NUM
ejpam-5758	118	9	)	)	PUNCT
ejpam-5758	118	10	for	for	ADP
ejpam-5758	118	11	all	all	DET
ejpam-5758	118	12	x	x	NOUN
ejpam-5758	118	13	,	,	PUNCT
ejpam-5758	118	14	y	y	PROPN
ejpam-5758	118	15	∈	∈	PROPN
ejpam-5758	118	16	e.	e.	PROPN
ejpam-5758	118	17	by	by	ADP
ejpam-5758	118	18	(	(	PUNCT
ejpam-5758	118	19	5	5	NUM
ejpam-5758	118	20	)	)	PUNCT
ejpam-5758	118	21	,	,	PUNCT
ejpam-5758	118	22	(	(	PUNCT
ejpam-5758	118	23	7	7	NUM
ejpam-5758	118	24	)	)	PUNCT
ejpam-5758	118	25	,	,	PUNCT
ejpam-5758	118	26	(	(	PUNCT
ejpam-5758	118	27	12	12	NUM
ejpam-5758	118	28	)	)	PUNCT
ejpam-5758	118	29	and	and	CCONJ
ejpam-5758	118	30	(	(	PUNCT
ejpam-5758	118	31	13	13	NUM
ejpam-5758	118	32	)	)	PUNCT
ejpam-5758	118	33	,	,	PUNCT
ejpam-5758	118	34	we	we	PRON
ejpam-5758	118	35	have	have	VERB
ejpam-5758	118	36	∥h(x+	∥h(x+	ADV
ejpam-5758	118	37	y)−	y)−	PROPN
ejpam-5758	118	38	h(x−	h(x−	ADP
ejpam-5758	118	39	y)−	y)−	PROPN
ejpam-5758	118	40	2h(y	2h(y	NUM
ejpam-5758	118	41	)	)	PUNCT
ejpam-5758	119	1	+	+	CCONJ
ejpam-5758	119	2	2h(0)∥	2h(0)∥	NUM
ejpam-5758	119	3	(	(	PUNCT
ejpam-5758	119	4	14	14	NUM
ejpam-5758	119	5	)	)	PUNCT
ejpam-5758	119	6	≤	≤	NOUN
ejpam-5758	119	7	∥f(x+	∥f(x+	VERB
ejpam-5758	119	8	y	y	NOUN
ejpam-5758	119	9	)	)	PUNCT
ejpam-5758	120	1	+	+	CCONJ
ejpam-5758	120	2	f(x−	f(x−	PROPN
ejpam-5758	120	3	y	y	NOUN
ejpam-5758	120	4	)	)	PUNCT
ejpam-5758	121	1	+	+	CCONJ
ejpam-5758	121	2	h(x+	h(x+	ADV
ejpam-5758	121	3	y)−	y)−	PROPN
ejpam-5758	121	4	2f(x)−	2f(x)−	NUM
ejpam-5758	121	5	2f(y)−	2f(y)−	NUM
ejpam-5758	121	6	h(x)−	h(x)−	PROPN
ejpam-5758	121	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	121	8	+	+	NOUN
ejpam-5758	121	9	∥f(x+	∥f(x+	VERB
ejpam-5758	121	10	y	y	NOUN
ejpam-5758	121	11	)	)	PUNCT
ejpam-5758	122	1	+	+	CCONJ
ejpam-5758	122	2	f(x−	f(x−	PROPN
ejpam-5758	122	3	y	y	NOUN
ejpam-5758	122	4	)	)	PUNCT
ejpam-5758	123	1	+	+	NUM
ejpam-5758	123	2	h(x−	h(x−	ADP
ejpam-5758	123	3	y)−	y)−	PROPN
ejpam-5758	123	4	2f(x)−	2f(x)−	NUM
ejpam-5758	123	5	2f(−y)−	2f(−y)−	PRON
ejpam-5758	124	1	h(x)−	h(x)−	PROPN
ejpam-5758	124	2	h(−y)∥	h(−y)∥	NOUN
ejpam-5758	124	3	+2∥f(y)−	+2∥f(y)−	NOUN
ejpam-5758	124	4	f(−y)∥+	f(−y)∥+	X
ejpam-5758	124	5	∥h(y	∥h(y	PROPN
ejpam-5758	124	6	)	)	PUNCT
ejpam-5758	125	1	+	+	CCONJ
ejpam-5758	125	2	h(−y)−	h(−y)−	PRON
ejpam-5758	125	3	2h(0)∥	2h(0)∥	NUM
ejpam-5758	125	4	≤	≤	NOUN
ejpam-5758	125	5	ϵ	ϵ	ADP
ejpam-5758	125	6	(	(	PUNCT
ejpam-5758	125	7	∥x∥p	∥x∥p	X
ejpam-5758	125	8	+	+	CCONJ
ejpam-5758	125	9	∥y∥p	∥y∥p	X
ejpam-5758	125	10	)	)	PUNCT
ejpam-5758	126	1	+	+	CCONJ
ejpam-5758	126	2	ϵ	ϵ	X
ejpam-5758	126	3	(	(	PUNCT
ejpam-5758	126	4	∥x∥p	∥x∥p	X
ejpam-5758	126	5	+	+	CCONJ
ejpam-5758	126	6	∥y∥p	∥y∥p	X
ejpam-5758	126	7	)	)	PUNCT
ejpam-5758	127	1	+	+	CCONJ
ejpam-5758	127	2	4ϵ∥y∥p	4ϵ∥y∥p	VERB
ejpam-5758	127	3	+	+	CCONJ
ejpam-5758	127	4	16	16	NUM
ejpam-5758	127	5	2p	2p	NUM
ejpam-5758	127	6	ϵ∥y∥p	ϵ∥y∥p	NOUN
ejpam-5758	127	7	=	=	SYM
ejpam-5758	127	8	ϵ	ϵ	X
ejpam-5758	127	9	(	(	PUNCT
ejpam-5758	127	10	2∥x∥p	2∥x∥p	NUM
ejpam-5758	127	11	+	+	CCONJ
ejpam-5758	127	12	(	(	PUNCT
ejpam-5758	127	13	6	6	NUM
ejpam-5758	127	14	+	+	NOUN
ejpam-5758	127	15	24−p	24−p	NUM
ejpam-5758	127	16	)	)	PUNCT
ejpam-5758	127	17	∥y∥p	∥y∥p	PROPN
ejpam-5758	127	18	)	)	PUNCT
ejpam-5758	127	19	for	for	ADP
ejpam-5758	127	20	all	all	DET
ejpam-5758	127	21	x	x	NOUN
ejpam-5758	127	22	,	,	PUNCT
ejpam-5758	127	23	y	y	PROPN
ejpam-5758	127	24	∈	∈	PROPN
ejpam-5758	127	25	e.	e.	PROPN
ejpam-5758	127	26	interchanging	interchanging	PROPN
ejpam-5758	127	27	x	x	PUNCT
ejpam-5758	127	28	with	with	ADP
ejpam-5758	127	29	y	y	PROPN
ejpam-5758	127	30	in	in	ADP
ejpam-5758	127	31	(	(	PUNCT
ejpam-5758	127	32	14	14	NUM
ejpam-5758	127	33	)	)	PUNCT
ejpam-5758	127	34	,	,	PUNCT
ejpam-5758	127	35	we	we	PRON
ejpam-5758	127	36	get	get	VERB
ejpam-5758	127	37	∥h(x+	∥h(x+	ADV
ejpam-5758	127	38	y)−	y)−	ADJ
ejpam-5758	127	39	h(y	h(y	ADV
ejpam-5758	127	40	−	−	PROPN
ejpam-5758	127	41	x)−	x)−	PROPN
ejpam-5758	127	42	2h(x	2h(x	NUM
ejpam-5758	127	43	)	)	PUNCT
ejpam-5758	128	1	+	+	CCONJ
ejpam-5758	128	2	2h(0)∥	2h(0)∥	NUM
ejpam-5758	128	3	≤	≤	NOUN
ejpam-5758	128	4	ϵ	ϵ	ADP
ejpam-5758	128	5	(	(	PUNCT
ejpam-5758	128	6	2∥y∥p	2∥y∥p	NUM
ejpam-5758	128	7	+	+	CCONJ
ejpam-5758	128	8	(	(	PUNCT
ejpam-5758	128	9	6	6	NUM
ejpam-5758	128	10	+	+	NUM
ejpam-5758	128	11	24−p	24−p	NUM
ejpam-5758	128	12	)	)	PUNCT
ejpam-5758	128	13	∥x∥p	∥x∥p	NOUN
ejpam-5758	128	14	)	)	PUNCT
ejpam-5758	128	15	(	(	PUNCT
ejpam-5758	128	16	15	15	NUM
ejpam-5758	128	17	)	)	PUNCT
ejpam-5758	128	18	for	for	ADP
ejpam-5758	128	19	all	all	DET
ejpam-5758	128	20	x	x	NOUN
ejpam-5758	128	21	,	,	PUNCT
ejpam-5758	128	22	y	y	PROPN
ejpam-5758	128	23	∈	∈	PROPN
ejpam-5758	128	24	e.	e.	PROPN
ejpam-5758	128	25	by	by	ADP
ejpam-5758	128	26	(	(	PUNCT
ejpam-5758	128	27	12	12	NUM
ejpam-5758	128	28	)	)	PUNCT
ejpam-5758	128	29	,	,	PUNCT
ejpam-5758	128	30	(	(	PUNCT
ejpam-5758	128	31	14	14	NUM
ejpam-5758	128	32	)	)	PUNCT
ejpam-5758	128	33	and	and	CCONJ
ejpam-5758	128	34	(	(	PUNCT
ejpam-5758	128	35	15	15	NUM
ejpam-5758	128	36	)	)	PUNCT
ejpam-5758	128	37	,	,	PUNCT
ejpam-5758	128	38	we	we	PRON
ejpam-5758	128	39	have	have	VERB
ejpam-5758	128	40	∥2h(x+	∥2h(x+	NUM
ejpam-5758	129	1	y)−	y)−	PROPN
ejpam-5758	129	2	2h(x)−	2h(x)−	NUM
ejpam-5758	129	3	2h(y	2h(y	NUM
ejpam-5758	129	4	)	)	PUNCT
ejpam-5758	130	1	+	+	CCONJ
ejpam-5758	130	2	2h(0)∥	2h(0)∥	NUM
ejpam-5758	130	3	≤	≤	NOUN
ejpam-5758	130	4	∥h(x+	∥h(x+	ADV
ejpam-5758	130	5	y)−	y)−	PROPN
ejpam-5758	130	6	h(x−	h(x−	ADP
ejpam-5758	130	7	y)−	y)−	PROPN
ejpam-5758	130	8	2h(y	2h(y	NUM
ejpam-5758	130	9	)	)	PUNCT
ejpam-5758	131	1	+	+	CCONJ
ejpam-5758	131	2	2h(0)∥+	2h(0)∥+	NUM
ejpam-5758	131	3	∥h(x+	∥h(x+	ADV
ejpam-5758	132	1	y)−	y)−	PROPN
ejpam-5758	132	2	h(y	h(y	ADV
ejpam-5758	132	3	−	−	PROPN
ejpam-5758	133	1	x)−	x)−	PROPN
ejpam-5758	133	2	2h(x	2h(x	NUM
ejpam-5758	133	3	)	)	PUNCT
ejpam-5758	134	1	+	+	CCONJ
ejpam-5758	134	2	2h(0)∥	2h(0)∥	NUM
ejpam-5758	134	3	+	+	SYM
ejpam-5758	134	4	∥h(x−	∥h(x−	X
ejpam-5758	134	5	y	y	NOUN
ejpam-5758	134	6	)	)	PUNCT
ejpam-5758	134	7	+	+	NUM
ejpam-5758	134	8	h(y	h(y	ADV
ejpam-5758	134	9	−	−	PROPN
ejpam-5758	134	10	x)−	x)−	PROPN
ejpam-5758	134	11	2h(0)∥	2h(0)∥	NUM
ejpam-5758	134	12	≤	≤	NOUN
ejpam-5758	134	13	(	(	PUNCT
ejpam-5758	134	14	8	8	NUM
ejpam-5758	134	15	+	+	NUM
ejpam-5758	134	16	24−p	24−p	NUM
ejpam-5758	134	17	)	)	PUNCT
ejpam-5758	135	1	ϵ	ϵ	X
ejpam-5758	135	2	(	(	PUNCT
ejpam-5758	135	3	∥x∥p	∥x∥p	X
ejpam-5758	135	4	+	+	CCONJ
ejpam-5758	135	5	∥y∥p	∥y∥p	X
ejpam-5758	135	6	)	)	PUNCT
ejpam-5758	136	1	+	+	CCONJ
ejpam-5758	136	2	24−pϵ∥x−	24−pϵ∥x−	NUM
ejpam-5758	136	3	y∥p	y∥p	NOUN
ejpam-5758	136	4	,	,	PUNCT
ejpam-5758	136	5	m.	m.	NOUN
ejpam-5758	136	6	dehghanian	dehghanian	PROPN
ejpam-5758	136	7	et	et	PROPN
ejpam-5758	136	8	al	al	PROPN
ejpam-5758	136	9	.	.	PUNCT
ejpam-5758	136	10	/	/	SYM
ejpam-5758	136	11	eur	eur	PROPN
ejpam-5758	136	12	.	.	PUNCT
ejpam-5758	137	1	j.	j.	PROPN
ejpam-5758	137	2	pure	pure	PROPN
ejpam-5758	137	3	appl	appl	PROPN
ejpam-5758	137	4	.	.	PROPN
ejpam-5758	137	5	math	math	PROPN
ejpam-5758	137	6	,	,	PUNCT
ejpam-5758	137	7	18	18	NUM
ejpam-5758	137	8	(	(	PUNCT
ejpam-5758	137	9	1	1	NUM
ejpam-5758	137	10	)	)	PUNCT
ejpam-5758	137	11	(	(	PUNCT
ejpam-5758	137	12	2025	2025	NUM
ejpam-5758	137	13	)	)	PUNCT
ejpam-5758	137	14	,	,	PUNCT
ejpam-5758	137	15	5758	5758	NUM
ejpam-5758	137	16	9	9	NUM
ejpam-5758	137	17	of	of	ADP
ejpam-5758	137	18	13	13	NUM
ejpam-5758	137	19	which	which	PRON
ejpam-5758	137	20	implies	imply	VERB
ejpam-5758	137	21	∥h(x+	∥h(x+	ADV
ejpam-5758	137	22	y)−	y)−	PROPN
ejpam-5758	137	23	h(x)−	h(x)−	PROPN
ejpam-5758	137	24	h(y	h(y	ADV
ejpam-5758	137	25	)	)	PUNCT
ejpam-5758	138	1	+	+	CCONJ
ejpam-5758	138	2	h(0)∥	h(0)∥	PROPN
ejpam-5758	138	3	≤	≤	NUM
ejpam-5758	138	4	(	(	PUNCT
ejpam-5758	138	5	4	4	NUM
ejpam-5758	138	6	+	+	NUM
ejpam-5758	138	7	23−p	23−p	NUM
ejpam-5758	138	8	)	)	PUNCT
ejpam-5758	138	9	ϵ	ϵ	X
ejpam-5758	138	10	(	(	PUNCT
ejpam-5758	138	11	∥x∥p	∥x∥p	X
ejpam-5758	138	12	+	+	CCONJ
ejpam-5758	138	13	∥y∥p	∥y∥p	X
ejpam-5758	138	14	)	)	PUNCT
ejpam-5758	138	15	+	+	CCONJ
ejpam-5758	138	16	23−pϵ∥x−	23−pϵ∥x−	NUM
ejpam-5758	138	17	y∥p	y∥p	NOUN
ejpam-5758	138	18	(	(	PUNCT
ejpam-5758	138	19	16	16	NUM
ejpam-5758	138	20	)	)	PUNCT
ejpam-5758	138	21	for	for	ADP
ejpam-5758	138	22	all	all	DET
ejpam-5758	138	23	x	x	NOUN
ejpam-5758	138	24	,	,	PUNCT
ejpam-5758	138	25	y	y	PROPN
ejpam-5758	138	26	∈	∈	PROPN
ejpam-5758	138	27	e.	e.	PROPN
ejpam-5758	138	28	define	define	VERB
ejpam-5758	138	29	ĥ	ĥ	X
ejpam-5758	138	30	:	:	PUNCT
ejpam-5758	138	31	e	e	X
ejpam-5758	138	32	→	→	SYM
ejpam-5758	138	33	b	b	PROPN
ejpam-5758	138	34	by	by	ADP
ejpam-5758	138	35	ĥ(x	ĥ(x	NOUN
ejpam-5758	138	36	)	)	PUNCT
ejpam-5758	138	37	:	:	PUNCT
ejpam-5758	138	38	=	=	SYM
ejpam-5758	138	39	h(x	h(x	PROPN
ejpam-5758	138	40	)	)	PUNCT
ejpam-5758	139	1	−	−	PROPN
ejpam-5758	139	2	h(0	h(0	PROPN
ejpam-5758	139	3	)	)	PUNCT
ejpam-5758	139	4	for	for	ADP
ejpam-5758	139	5	all	all	DET
ejpam-5758	139	6	x	x	SYM
ejpam-5758	139	7	∈	∈	PROPN
ejpam-5758	139	8	e.	e.	PROPN
ejpam-5758	139	9	then	then	ADV
ejpam-5758	139	10	we	we	PRON
ejpam-5758	139	11	can	can	AUX
ejpam-5758	139	12	rewrite	rewrite	VERB
ejpam-5758	139	13	the	the	DET
ejpam-5758	139	14	inequality	inequality	NOUN
ejpam-5758	139	15	(	(	PUNCT
ejpam-5758	139	16	16	16	NUM
ejpam-5758	139	17	)	)	PUNCT
ejpam-5758	139	18	in	in	ADP
ejpam-5758	139	19	the	the	DET
ejpam-5758	139	20	form	form	NOUN
ejpam-5758	139	21	∥ĥ(x+	∥ĥ(x+	ADP
ejpam-5758	139	22	y)−	y)−	PROPN
ejpam-5758	139	23	ĥ(x)−	ĥ(x)−	NOUN
ejpam-5758	139	24	ĥ(y)∥	ĥ(y)∥	PROPN
ejpam-5758	139	25	≤	≤	NOUN
ejpam-5758	139	26	(	(	PUNCT
ejpam-5758	139	27	4	4	NUM
ejpam-5758	139	28	+	+	NUM
ejpam-5758	139	29	23−p	23−p	NUM
ejpam-5758	139	30	)	)	PUNCT
ejpam-5758	140	1	ϵ	ϵ	X
ejpam-5758	140	2	(	(	PUNCT
ejpam-5758	140	3	∥x∥p	∥x∥p	X
ejpam-5758	140	4	+	+	CCONJ
ejpam-5758	140	5	∥y∥p	∥y∥p	X
ejpam-5758	140	6	)	)	PUNCT
ejpam-5758	141	1	+	+	CCONJ
ejpam-5758	141	2	23−pϵ∥x−	23−pϵ∥x−	NUM
ejpam-5758	141	3	y∥p	y∥p	NOUN
ejpam-5758	141	4	for	for	ADP
ejpam-5758	141	5	all	all	DET
ejpam-5758	141	6	x	x	NOUN
ejpam-5758	141	7	,	,	PUNCT
ejpam-5758	141	8	y	y	PROPN
ejpam-5758	141	9	∈	∈	PROPN
ejpam-5758	141	10	e.	e.	PROPN
ejpam-5758	141	11	applying	apply	VERB
ejpam-5758	141	12	lemma	lemma	PROPN
ejpam-5758	141	13	1	1	NUM
ejpam-5758	141	14	to	to	ADP
ejpam-5758	141	15	ĥ	ĥ	PROPN
ejpam-5758	141	16	,	,	PUNCT
ejpam-5758	141	17	we	we	PRON
ejpam-5758	141	18	get	get	VERB
ejpam-5758	141	19	a	a	DET
ejpam-5758	141	20	unique	unique	ADJ
ejpam-5758	141	21	additive	additive	ADJ
ejpam-5758	141	22	mapping	mapping	NOUN
ejpam-5758	141	23	a1	a1	NOUN
ejpam-5758	141	24	:	:	PUNCT
ejpam-5758	141	25	e	e	X
ejpam-5758	141	26	→	→	SYM
ejpam-5758	141	27	b	b	X
ejpam-5758	141	28	such	such	ADJ
ejpam-5758	141	29	that	that	DET
ejpam-5758	141	30	∥ĥ(x)−a1(x)∥	∥ĥ(x)−a1(x)∥	PROPN
ejpam-5758	141	31	≤	≤	NOUN
ejpam-5758	141	32	8	8	NUM
ejpam-5758	141	33	+	+	CCONJ
ejpam-5758	141	34	24−p	24−p	NUM
ejpam-5758	141	35	|2p	|2p	NUM
ejpam-5758	141	36	−	−	PROPN
ejpam-5758	141	37	2|	2|	PRON
ejpam-5758	141	38	ϵ∥x∥p	ϵ∥x∥p	PROPN
ejpam-5758	141	39	,	,	PUNCT
ejpam-5758	141	40	which	which	PRON
ejpam-5758	141	41	implies	imply	VERB
ejpam-5758	141	42	∥h(x)−	∥h(x)−	VERB
ejpam-5758	141	43	h(0)−a1(x)∥	h(0)−a1(x)∥	VERB
ejpam-5758	141	44	≤	≤	NUM
ejpam-5758	141	45	8	8	NUM
ejpam-5758	141	46	+	+	NUM
ejpam-5758	141	47	24−p	24−p	NUM
ejpam-5758	141	48	|2p	|2p	NUM
ejpam-5758	141	49	−	−	PROPN
ejpam-5758	141	50	2|	2|	PRON
ejpam-5758	141	51	ϵ∥x∥p	ϵ∥x∥p	VERB
ejpam-5758	141	52	for	for	ADP
ejpam-5758	141	53	all	all	DET
ejpam-5758	141	54	x	x	SYM
ejpam-5758	141	55	∈	∈	PROPN
ejpam-5758	141	56	e.	e.	NOUN
ejpam-5758	141	57	letting	let	VERB
ejpam-5758	141	58	x	x	PUNCT
ejpam-5758	142	1	=	=	PUNCT
ejpam-5758	142	2	y	y	PROPN
ejpam-5758	142	3	=	=	SYM
ejpam-5758	142	4	0	0	NUM
ejpam-5758	143	1	in	in	ADP
ejpam-5758	143	2	(	(	PUNCT
ejpam-5758	143	3	5	5	NUM
ejpam-5758	143	4	)	)	PUNCT
ejpam-5758	143	5	,	,	PUNCT
ejpam-5758	143	6	we	we	PRON
ejpam-5758	143	7	have	have	VERB
ejpam-5758	143	8	2f(0	2f(0	NUM
ejpam-5758	143	9	)	)	PUNCT
ejpam-5758	144	1	+	+	CCONJ
ejpam-5758	144	2	h(0	h(0	PROPN
ejpam-5758	144	3	)	)	PUNCT
ejpam-5758	144	4	=	=	SYM
ejpam-5758	144	5	0	0	X
ejpam-5758	144	6	.	.	PUNCT
ejpam-5758	144	7	(	(	PUNCT
ejpam-5758	144	8	17	17	NUM
ejpam-5758	144	9	)	)	PUNCT
ejpam-5758	144	10	next	next	ADV
ejpam-5758	144	11	,	,	PUNCT
ejpam-5758	144	12	using	use	VERB
ejpam-5758	144	13	(	(	PUNCT
ejpam-5758	144	14	5	5	NUM
ejpam-5758	144	15	)	)	PUNCT
ejpam-5758	144	16	,	,	PUNCT
ejpam-5758	144	17	(	(	PUNCT
ejpam-5758	144	18	16	16	NUM
ejpam-5758	144	19	)	)	PUNCT
ejpam-5758	144	20	and	and	CCONJ
ejpam-5758	144	21	(	(	PUNCT
ejpam-5758	144	22	17	17	NUM
ejpam-5758	144	23	)	)	PUNCT
ejpam-5758	144	24	,	,	PUNCT
ejpam-5758	144	25	we	we	PRON
ejpam-5758	144	26	get	get	VERB
ejpam-5758	144	27	∥f(x+	∥f(x+	NOUN
ejpam-5758	144	28	y	y	NOUN
ejpam-5758	144	29	)	)	PUNCT
ejpam-5758	144	30	+	+	CCONJ
ejpam-5758	144	31	f(x−	f(x−	ADP
ejpam-5758	144	32	y)−	y)−	PROPN
ejpam-5758	144	33	2f(x)−	2f(x)−	NUM
ejpam-5758	144	34	2f(y	2f(y	NUM
ejpam-5758	144	35	)	)	PUNCT
ejpam-5758	145	1	+	+	CCONJ
ejpam-5758	145	2	2f(0)∥	2f(0)∥	NUM
ejpam-5758	145	3	≤	≤	NOUN
ejpam-5758	145	4	∥f(x+	∥f(x+	NOUN
ejpam-5758	145	5	y	y	NOUN
ejpam-5758	145	6	)	)	PUNCT
ejpam-5758	146	1	+	+	CCONJ
ejpam-5758	146	2	f(x−	f(x−	PROPN
ejpam-5758	146	3	y	y	NOUN
ejpam-5758	146	4	)	)	PUNCT
ejpam-5758	147	1	+	+	CCONJ
ejpam-5758	147	2	h(x+	h(x+	ADV
ejpam-5758	147	3	y)−	y)−	PROPN
ejpam-5758	147	4	2f(x)−	2f(x)−	NUM
ejpam-5758	147	5	2f(y)−	2f(y)−	NUM
ejpam-5758	147	6	h(x)−	h(x)−	PROPN
ejpam-5758	147	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	147	8	+	+	NOUN
ejpam-5758	147	9	∥h(x+	∥h(x+	ADJ
ejpam-5758	147	10	y)−	y)−	PROPN
ejpam-5758	147	11	h(x)−	h(x)−	PROPN
ejpam-5758	147	12	h(y	h(y	ADV
ejpam-5758	147	13	)	)	PUNCT
ejpam-5758	148	1	+	+	CCONJ
ejpam-5758	148	2	h(0)∥	h(0)∥	NOUN
ejpam-5758	148	3	≤	≤	X
ejpam-5758	148	4	ϵ	ϵ	X
ejpam-5758	148	5	(	(	PUNCT
ejpam-5758	148	6	∥x∥p	∥x∥p	X
ejpam-5758	148	7	+	+	CCONJ
ejpam-5758	148	8	∥y∥p	∥y∥p	X
ejpam-5758	148	9	)	)	PUNCT
ejpam-5758	149	1	+	+	CCONJ
ejpam-5758	149	2	(	(	PUNCT
ejpam-5758	149	3	4	4	NUM
ejpam-5758	149	4	+	+	NUM
ejpam-5758	149	5	23−p	23−p	NUM
ejpam-5758	149	6	)	)	PUNCT
ejpam-5758	149	7	ϵ	ϵ	X
ejpam-5758	149	8	(	(	PUNCT
ejpam-5758	149	9	∥x∥p	∥x∥p	X
ejpam-5758	149	10	+	+	CCONJ
ejpam-5758	149	11	∥y∥p	∥y∥p	X
ejpam-5758	149	12	)	)	PUNCT
ejpam-5758	150	1	+	+	CCONJ
ejpam-5758	150	2	23−pϵ∥x−	23−pϵ∥x−	NUM
ejpam-5758	150	3	y∥p	y∥p	NOUN
ejpam-5758	150	4	=	=	PUNCT
ejpam-5758	150	5	(	(	PUNCT
ejpam-5758	150	6	5	5	NUM
ejpam-5758	150	7	+	+	NUM
ejpam-5758	150	8	23−p	23−p	NUM
ejpam-5758	150	9	)	)	PUNCT
ejpam-5758	150	10	ϵ	ϵ	X
ejpam-5758	150	11	(	(	PUNCT
ejpam-5758	150	12	∥x∥p	∥x∥p	X
ejpam-5758	150	13	+	+	CCONJ
ejpam-5758	150	14	∥y∥p	∥y∥p	X
ejpam-5758	150	15	)	)	PUNCT
ejpam-5758	151	1	+	+	CCONJ
ejpam-5758	151	2	23−pϵ∥x−	23−pϵ∥x−	NUM
ejpam-5758	151	3	y∥p	y∥p	NOUN
ejpam-5758	151	4	for	for	ADP
ejpam-5758	151	5	all	all	DET
ejpam-5758	151	6	x	x	NOUN
ejpam-5758	151	7	,	,	PUNCT
ejpam-5758	151	8	y	y	PROPN
ejpam-5758	151	9	∈	∈	PROPN
ejpam-5758	151	10	e.	e.	PROPN
ejpam-5758	151	11	similarly	similarly	ADV
ejpam-5758	151	12	,	,	PUNCT
ejpam-5758	151	13	we	we	PRON
ejpam-5758	151	14	define	define	VERB
ejpam-5758	151	15	f̂	f̂	NUM
ejpam-5758	151	16	:	:	PUNCT
ejpam-5758	151	17	e	e	X
ejpam-5758	151	18	→	→	SYM
ejpam-5758	151	19	b	b	PROPN
ejpam-5758	151	20	by	by	ADP
ejpam-5758	151	21	f̂(x	f̂(x	NOUN
ejpam-5758	151	22	)	)	PUNCT
ejpam-5758	151	23	:	:	PUNCT
ejpam-5758	151	24	=	=	PUNCT
ejpam-5758	151	25	f(x)−	f(x)−	PROPN
ejpam-5758	151	26	f(0	f(0	NOUN
ejpam-5758	151	27	)	)	PUNCT
ejpam-5758	151	28	for	for	ADP
ejpam-5758	151	29	all	all	DET
ejpam-5758	151	30	x	x	SYM
ejpam-5758	151	31	∈	∈	PROPN
ejpam-5758	151	32	e.	e.	PROPN
ejpam-5758	151	33	then	then	ADV
ejpam-5758	151	34	we	we	PRON
ejpam-5758	151	35	obtain	obtain	VERB
ejpam-5758	151	36	∥f̂(x+	∥f̂(x+	NOUN
ejpam-5758	151	37	y	y	X
ejpam-5758	151	38	)	)	PUNCT
ejpam-5758	152	1	+	+	CCONJ
ejpam-5758	152	2	f̂(x−	f̂(x−	X
ejpam-5758	152	3	y)−	y)−	PROPN
ejpam-5758	152	4	2f̂(x)−	2f̂(x)−	NUM
ejpam-5758	152	5	2f̂(y)∥	2f̂(y)∥	NUM
ejpam-5758	152	6	≤	≤	NOUN
ejpam-5758	152	7	(	(	PUNCT
ejpam-5758	152	8	5	5	NUM
ejpam-5758	152	9	+	+	NUM
ejpam-5758	152	10	23−p	23−p	NUM
ejpam-5758	152	11	)	)	PUNCT
ejpam-5758	152	12	ϵ	ϵ	X
ejpam-5758	152	13	(	(	PUNCT
ejpam-5758	152	14	∥x∥p	∥x∥p	X
ejpam-5758	152	15	+	+	CCONJ
ejpam-5758	152	16	∥y∥p	∥y∥p	X
ejpam-5758	152	17	)	)	PUNCT
ejpam-5758	153	1	+	+	CCONJ
ejpam-5758	153	2	23−pϵ∥x−	23−pϵ∥x−	NUM
ejpam-5758	153	3	y∥p	y∥p	NOUN
ejpam-5758	153	4	for	for	ADP
ejpam-5758	153	5	all	all	DET
ejpam-5758	153	6	x	x	NOUN
ejpam-5758	153	7	,	,	PUNCT
ejpam-5758	153	8	y	y	PROPN
ejpam-5758	153	9	∈	∈	PROPN
ejpam-5758	153	10	e.	e.	PROPN
ejpam-5758	153	11	by	by	ADP
ejpam-5758	153	12	lemma	lemma	PROPN
ejpam-5758	153	13	2	2	NUM
ejpam-5758	153	14	,	,	PUNCT
ejpam-5758	153	15	there	there	PRON
ejpam-5758	153	16	exists	exist	VERB
ejpam-5758	153	17	a	a	DET
ejpam-5758	153	18	unique	unique	ADJ
ejpam-5758	153	19	quadratic	quadratic	ADJ
ejpam-5758	153	20	mapping	mapping	NOUN
ejpam-5758	153	21	q	q	NOUN
ejpam-5758	153	22	:	:	PUNCT
ejpam-5758	153	23	e	e	X
ejpam-5758	153	24	→	→	SYM
ejpam-5758	153	25	b	b	X
ejpam-5758	153	26	such	such	ADJ
ejpam-5758	153	27	that	that	SCONJ
ejpam-5758	153	28	∥f̂(x)−q(x)∥	∥f̂(x)−q(x)∥	NOUN
ejpam-5758	153	29	≤	≤	ADV
ejpam-5758	153	30	10	10	NUM
ejpam-5758	153	31	+	+	NUM
ejpam-5758	153	32	24−p	24−p	NUM
ejpam-5758	153	33	|2p	|2p	NUM
ejpam-5758	153	34	−	−	NUM
ejpam-5758	153	35	4|	4|	NUM
ejpam-5758	153	36	ϵ∥x∥p	ϵ∥x∥p	PROPN
ejpam-5758	153	37	,	,	PUNCT
ejpam-5758	153	38	which	which	PRON
ejpam-5758	153	39	implies	imply	VERB
ejpam-5758	153	40	∥f(x)−	∥f(x)−	PROPN
ejpam-5758	153	41	f(0)−q(x)∥	f(0)−q(x)∥	PROPN
ejpam-5758	153	42	≤	≤	ADV
ejpam-5758	153	43	10	10	NUM
ejpam-5758	153	44	+	+	NUM
ejpam-5758	153	45	24−p	24−p	NUM
ejpam-5758	153	46	|2p	|2p	NUM
ejpam-5758	153	47	−	−	NUM
ejpam-5758	153	48	4|	4|	NUM
ejpam-5758	153	49	ϵ∥x∥p	ϵ∥x∥p	VERB
ejpam-5758	153	50	for	for	ADP
ejpam-5758	153	51	all	all	DET
ejpam-5758	153	52	x	x	SYM
ejpam-5758	153	53	∈	∈	PROPN
ejpam-5758	153	54	e	e	NOUN
ejpam-5758	153	55	,	,	PUNCT
ejpam-5758	153	56	which	which	PRON
ejpam-5758	153	57	ends	end	VERB
ejpam-5758	153	58	our	our	PRON
ejpam-5758	153	59	proof	proof	NOUN
ejpam-5758	153	60	.	.	PUNCT
ejpam-5758	154	1	the	the	DET
ejpam-5758	154	2	following	follow	VERB
ejpam-5758	154	3	example	example	NOUN
ejpam-5758	154	4	shows	show	VERB
ejpam-5758	154	5	that	that	SCONJ
ejpam-5758	154	6	for	for	ADP
ejpam-5758	154	7	p	p	NOUN
ejpam-5758	154	8	=	=	NOUN
ejpam-5758	154	9	1	1	NUM
ejpam-5758	154	10	the	the	DET
ejpam-5758	154	11	pexider	pexider	NOUN
ejpam-5758	154	12	additive	additive	ADJ
ejpam-5758	154	13	-	-	PUNCT
ejpam-5758	154	14	quadratic	quadratic	ADJ
ejpam-5758	154	15	functional	functional	ADJ
ejpam-5758	154	16	equation	equation	NOUN
ejpam-5758	154	17	(	(	PUNCT
ejpam-5758	154	18	1	1	X
ejpam-5758	154	19	)	)	PUNCT
ejpam-5758	154	20	is	be	AUX
ejpam-5758	154	21	not	not	PART
ejpam-5758	154	22	stable	stable	ADJ
ejpam-5758	154	23	(	(	PUNCT
ejpam-5758	154	24	see	see	VERB
ejpam-5758	154	25	[	[	X
ejpam-5758	154	26	26	26	NUM
ejpam-5758	154	27	]	]	NUM
ejpam-5758	154	28	)	)	PUNCT
ejpam-5758	154	29	.	.	PUNCT
ejpam-5758	155	1	m.	m.	NOUN
ejpam-5758	155	2	dehghanian	dehghanian	PROPN
ejpam-5758	155	3	et	et	PROPN
ejpam-5758	155	4	al	al	PROPN
ejpam-5758	155	5	.	.	PUNCT
ejpam-5758	155	6	/	/	SYM
ejpam-5758	155	7	eur	eur	PROPN
ejpam-5758	155	8	.	.	PUNCT
ejpam-5758	156	1	j.	j.	PROPN
ejpam-5758	156	2	pure	pure	PROPN
ejpam-5758	156	3	appl	appl	PROPN
ejpam-5758	156	4	.	.	PROPN
ejpam-5758	156	5	math	math	PROPN
ejpam-5758	156	6	,	,	PUNCT
ejpam-5758	156	7	18	18	NUM
ejpam-5758	156	8	(	(	PUNCT
ejpam-5758	156	9	1	1	NUM
ejpam-5758	156	10	)	)	PUNCT
ejpam-5758	156	11	(	(	PUNCT
ejpam-5758	156	12	2025	2025	NUM
ejpam-5758	156	13	)	)	PUNCT
ejpam-5758	156	14	,	,	PUNCT
ejpam-5758	156	15	5758	5758	NUM
ejpam-5758	156	16	10	10	NUM
ejpam-5758	156	17	of	of	ADP
ejpam-5758	156	18	13	13	NUM
ejpam-5758	156	19	example	example	NOUN
ejpam-5758	156	20	1	1	NUM
ejpam-5758	156	21	.	.	PUNCT
ejpam-5758	157	1	define	define	VERB
ejpam-5758	157	2	ψ	ψ	X
ejpam-5758	157	3	:	:	PUNCT
ejpam-5758	157	4	r	r	NOUN
ejpam-5758	157	5	→	→	SYM
ejpam-5758	157	6	r	r	NOUN
ejpam-5758	157	7	by	by	ADP
ejpam-5758	157	8	ψ(x	ψ(x	NOUN
ejpam-5758	157	9	)	)	PUNCT
ejpam-5758	158	1	=	=	PUNCT
ejpam-5758	159	1			PRON
ejpam-5758	159	2	−b	−b	VERB
ejpam-5758	159	3	x	x	PUNCT
ejpam-5758	159	4	≤	≤	NUM
ejpam-5758	159	5	−1	−1	NOUN
ejpam-5758	159	6	bx	bx	PROPN
ejpam-5758	159	7	−1	−1	NOUN
ejpam-5758	159	8	<	<	X
ejpam-5758	159	9	x	x	X
ejpam-5758	159	10	<	<	X
ejpam-5758	159	11	1	1	NUM
ejpam-5758	159	12	b	b	PROPN
ejpam-5758	159	13	x	x	X
ejpam-5758	159	14	≥	≥	NOUN
ejpam-5758	159	15	1	1	NUM
ejpam-5758	159	16	where	where	SCONJ
ejpam-5758	159	17	a	a	DET
ejpam-5758	159	18	,	,	PUNCT
ejpam-5758	159	19	b	b	X
ejpam-5758	159	20	>	>	X
ejpam-5758	159	21	0	0	PUNCT
ejpam-5758	159	22	and	and	CCONJ
ejpam-5758	159	23	assume	assume	VERB
ejpam-5758	159	24	that	that	SCONJ
ejpam-5758	159	25	f	f	X
ejpam-5758	159	26	,	,	PUNCT
ejpam-5758	159	27	h	h	NOUN
ejpam-5758	159	28	:	:	PUNCT
ejpam-5758	159	29	r	r	NOUN
ejpam-5758	159	30	→	→	SYM
ejpam-5758	159	31	r	r	NOUN
ejpam-5758	159	32	are	be	AUX
ejpam-5758	159	33	defined	define	VERB
ejpam-5758	159	34	by	by	ADP
ejpam-5758	159	35	f(x	f(x	PROPN
ejpam-5758	159	36	)	)	PUNCT
ejpam-5758	160	1	=	=	SYM
ejpam-5758	160	2	ax2	ax2	NOUN
ejpam-5758	160	3	and	and	CCONJ
ejpam-5758	160	4	h(x	h(x	PROPN
ejpam-5758	160	5	)	)	PUNCT
ejpam-5758	161	1	=	=	PUNCT
ejpam-5758	162	1	∞∑	∞∑	NUM
ejpam-5758	162	2	n=0	n=0	NUM
ejpam-5758	162	3	φ	φ	PROPN
ejpam-5758	162	4	(	(	PUNCT
ejpam-5758	162	5	2nx	2nx	NOUN
ejpam-5758	162	6	)	)	PUNCT
ejpam-5758	162	7	2n	2n	NUM
ejpam-5758	162	8	for	for	ADP
ejpam-5758	162	9	all	all	DET
ejpam-5758	162	10	x	x	PROPN
ejpam-5758	162	11	∈	∈	PROPN
ejpam-5758	162	12	r.	r.	NOUN
ejpam-5758	162	13	we	we	PRON
ejpam-5758	162	14	show	show	VERB
ejpam-5758	162	15	that	that	SCONJ
ejpam-5758	162	16	∥f(x+	∥f(x+	NOUN
ejpam-5758	162	17	y	y	NOUN
ejpam-5758	162	18	)	)	PUNCT
ejpam-5758	162	19	+	+	CCONJ
ejpam-5758	162	20	f(x−	f(x−	PROPN
ejpam-5758	162	21	y	y	NOUN
ejpam-5758	162	22	)	)	PUNCT
ejpam-5758	163	1	+	+	CCONJ
ejpam-5758	163	2	h(x+	h(x+	ADV
ejpam-5758	163	3	y)−	y)−	PROPN
ejpam-5758	163	4	2f(x)−	2f(x)−	NUM
ejpam-5758	163	5	2f(y)−	2f(y)−	NUM
ejpam-5758	163	6	h(x)−	h(x)−	PROPN
ejpam-5758	163	7	h(y)∥	h(y)∥	PROPN
ejpam-5758	163	8	≤	≤	PROPN
ejpam-5758	163	9	8b	8b	PROPN
ejpam-5758	163	10	(	(	PUNCT
ejpam-5758	163	11	|x|+	|x|+	NOUN
ejpam-5758	163	12	|y|	|y|	NOUN
ejpam-5758	163	13	)	)	PUNCT
ejpam-5758	163	14	for	for	ADP
ejpam-5758	163	15	all	all	DET
ejpam-5758	163	16	x	x	NOUN
ejpam-5758	163	17	,	,	PUNCT
ejpam-5758	163	18	y	y	PROPN
ejpam-5758	163	19	∈	∈	PROPN
ejpam-5758	163	20	r	r	NOUN
ejpam-5758	163	21	,	,	PUNCT
ejpam-5758	163	22	but	but	CCONJ
ejpam-5758	163	23	there	there	PRON
ejpam-5758	163	24	are	be	VERB
ejpam-5758	163	25	no	no	DET
ejpam-5758	163	26	constant	constant	ADJ
ejpam-5758	163	27	k	k	PROPN
ejpam-5758	163	28	≥	≥	NUM
ejpam-5758	163	29	0	0	NUM
ejpam-5758	164	1	and	and	CCONJ
ejpam-5758	164	2	no	no	DET
ejpam-5758	164	3	mapping	mapping	NOUN
ejpam-5758	164	4	a	a	DET
ejpam-5758	164	5	:	:	PUNCT
ejpam-5758	164	6	r	r	NOUN
ejpam-5758	164	7	→	→	SYM
ejpam-5758	164	8	r	r	NOUN
ejpam-5758	164	9	satisfying	satisfying	NOUN
ejpam-5758	164	10	(	(	PUNCT
ejpam-5758	164	11	1	1	NUM
ejpam-5758	164	12	)	)	PUNCT
ejpam-5758	164	13	and	and	CCONJ
ejpam-5758	164	14	|h(x)−	|h(x)−	NOUN
ejpam-5758	164	15	h(0)−a(x)|	h(0)−a(x)|	VERB
ejpam-5758	164	16	≤	≤	ADJ
ejpam-5758	164	17	k|x|	k|x|	NOUN
ejpam-5758	164	18	for	for	ADP
ejpam-5758	164	19	all	all	DET
ejpam-5758	164	20	x	x	PROPN
ejpam-5758	164	21	∈	∈	PROPN
ejpam-5758	164	22	r.	r.	NOUN
ejpam-5758	164	23	in	in	ADP
ejpam-5758	164	24	the	the	DET
ejpam-5758	164	25	following	following	NOUN
ejpam-5758	164	26	we	we	PRON
ejpam-5758	164	27	show	show	VERB
ejpam-5758	164	28	that	that	SCONJ
ejpam-5758	164	29	for	for	ADP
ejpam-5758	164	30	p	p	NOUN
ejpam-5758	164	31	=	=	SYM
ejpam-5758	164	32	2	2	NUM
ejpam-5758	164	33	the	the	DET
ejpam-5758	164	34	equation	equation	NOUN
ejpam-5758	164	35	(	(	PUNCT
ejpam-5758	164	36	1	1	X
ejpam-5758	164	37	)	)	PUNCT
ejpam-5758	164	38	is	be	AUX
ejpam-5758	164	39	not	not	PART
ejpam-5758	164	40	stable	stable	ADJ
ejpam-5758	164	41	(	(	PUNCT
ejpam-5758	164	42	see	see	VERB
ejpam-5758	164	43	[	[	X
ejpam-5758	164	44	10	10	NUM
ejpam-5758	164	45	]	]	NUM
ejpam-5758	164	46	)	)	PUNCT
ejpam-5758	164	47	.	.	PUNCT
ejpam-5758	165	1	example	example	NOUN
ejpam-5758	166	1	2	2	NUM
ejpam-5758	166	2	.	.	PUNCT
ejpam-5758	166	3	define	define	VERB
ejpam-5758	166	4	φ	φ	NOUN
ejpam-5758	166	5	:	:	PUNCT
ejpam-5758	166	6	r	r	NOUN
ejpam-5758	166	7	→	→	SYM
ejpam-5758	166	8	r	r	NOUN
ejpam-5758	166	9	by	by	ADP
ejpam-5758	166	10	φ(x	φ(x	NOUN
ejpam-5758	166	11	)	)	PUNCT
ejpam-5758	166	12	=	=	NOUN
ejpam-5758	166	13	{	{	PUNCT
ejpam-5758	166	14	ax2	ax2	NOUN
ejpam-5758	166	15	−1	−1	NOUN
ejpam-5758	166	16	<	<	X
ejpam-5758	166	17	x	x	X
ejpam-5758	166	18	<	<	X
ejpam-5758	166	19	1	1	NUM
ejpam-5758	166	20	a	a	DET
ejpam-5758	166	21	|x|	|x|	PROPN
ejpam-5758	166	22	≥	≥	NOUN
ejpam-5758	166	23	1	1	NUM
ejpam-5758	166	24	where	where	SCONJ
ejpam-5758	166	25	a	a	DET
ejpam-5758	166	26	,	,	PUNCT
ejpam-5758	166	27	b	b	X
ejpam-5758	166	28	>	>	X
ejpam-5758	166	29	0	0	PUNCT
ejpam-5758	166	30	and	and	CCONJ
ejpam-5758	166	31	assume	assume	VERB
ejpam-5758	166	32	that	that	SCONJ
ejpam-5758	166	33	f	f	X
ejpam-5758	166	34	,	,	PUNCT
ejpam-5758	166	35	h	h	NOUN
ejpam-5758	166	36	:	:	PUNCT
ejpam-5758	166	37	r	r	NOUN
ejpam-5758	166	38	→	→	SYM
ejpam-5758	166	39	r	r	NOUN
ejpam-5758	166	40	are	be	AUX
ejpam-5758	166	41	defined	define	VERB
ejpam-5758	166	42	by	by	ADP
ejpam-5758	166	43	f(x	f(x	PROPN
ejpam-5758	166	44	)	)	PUNCT
ejpam-5758	166	45	=	=	PUNCT
ejpam-5758	167	1	∞∑	∞∑	NUM
ejpam-5758	167	2	n=0	n=0	NUM
ejpam-5758	167	3	φ	φ	PROPN
ejpam-5758	167	4	(	(	PUNCT
ejpam-5758	167	5	2nx	2nx	NOUN
ejpam-5758	167	6	)	)	PUNCT
ejpam-5758	167	7	4n	4n	NOUN
ejpam-5758	167	8	and	and	CCONJ
ejpam-5758	167	9	h(x	h(x	PROPN
ejpam-5758	167	10	)	)	PUNCT
ejpam-5758	168	1	=	=	SYM
ejpam-5758	168	2	bx	bx	PROPN
ejpam-5758	168	3	for	for	ADP
ejpam-5758	168	4	all	all	DET
ejpam-5758	168	5	x	x	PROPN
ejpam-5758	168	6	∈	∈	PROPN
ejpam-5758	168	7	r.	r.	NOUN
ejpam-5758	168	8	we	we	PRON
ejpam-5758	168	9	show	show	VERB
ejpam-5758	168	10	that	that	SCONJ
ejpam-5758	168	11	∥f(x+	∥f(x+	NOUN
ejpam-5758	168	12	y	y	NOUN
ejpam-5758	168	13	)	)	PUNCT
ejpam-5758	169	1	+	+	CCONJ
ejpam-5758	169	2	f(x−	f(x−	PROPN
ejpam-5758	169	3	y	y	NOUN
ejpam-5758	169	4	)	)	PUNCT
ejpam-5758	170	1	+	+	CCONJ
ejpam-5758	170	2	h(x+	h(x+	ADV
ejpam-5758	170	3	y)−	y)−	PROPN
ejpam-5758	170	4	2f(x)−	2f(x)−	NUM
ejpam-5758	170	5	2f(y)−	2f(y)−	NUM
ejpam-5758	170	6	h(x)−	h(x)−	PROPN
ejpam-5758	170	7	h(y)∥	h(y)∥	NOUN
ejpam-5758	170	8	≤	≤	NOUN
ejpam-5758	170	9	32a	32a	NOUN
ejpam-5758	170	10	(	(	PUNCT
ejpam-5758	170	11	|x|2	|x|2	NOUN
ejpam-5758	170	12	+	+	CCONJ
ejpam-5758	170	13	|y|2	|y|2	ADJ
ejpam-5758	170	14	)	)	PUNCT
ejpam-5758	170	15	for	for	ADP
ejpam-5758	170	16	all	all	DET
ejpam-5758	170	17	x	x	NOUN
ejpam-5758	170	18	,	,	PUNCT
ejpam-5758	170	19	y	y	PROPN
ejpam-5758	170	20	∈	∈	PROPN
ejpam-5758	170	21	r	r	NOUN
ejpam-5758	170	22	,	,	PUNCT
ejpam-5758	170	23	but	but	CCONJ
ejpam-5758	170	24	there	there	PRON
ejpam-5758	170	25	are	be	VERB
ejpam-5758	170	26	no	no	DET
ejpam-5758	170	27	constant	constant	ADJ
ejpam-5758	170	28	k	k	PROPN
ejpam-5758	170	29	≥	≥	NUM
ejpam-5758	170	30	0	0	NUM
ejpam-5758	171	1	and	and	CCONJ
ejpam-5758	171	2	no	no	DET
ejpam-5758	171	3	mapping	mapping	NOUN
ejpam-5758	171	4	q	q	NOUN
ejpam-5758	171	5	:	:	PUNCT
ejpam-5758	171	6	r	r	NOUN
ejpam-5758	171	7	→	→	SYM
ejpam-5758	171	8	r	r	NOUN
ejpam-5758	171	9	satisfying	satisfying	NOUN
ejpam-5758	171	10	(	(	PUNCT
ejpam-5758	171	11	1	1	NUM
ejpam-5758	171	12	)	)	PUNCT
ejpam-5758	171	13	and	and	CCONJ
ejpam-5758	171	14	|f(x)−	|f(x)−	NOUN
ejpam-5758	171	15	f(0)−q(x)|	f(0)−q(x)|	VERB
ejpam-5758	171	16	≤	≤	ADJ
ejpam-5758	171	17	k|x|2	k|x|2	NOUN
ejpam-5758	171	18	for	for	ADP
ejpam-5758	171	19	all	all	DET
ejpam-5758	171	20	x	x	PROPN
ejpam-5758	171	21	∈	∈	PROPN
ejpam-5758	171	22	r.	r.	PROPN
ejpam-5758	171	23	m.	m.	PROPN
ejpam-5758	171	24	dehghanian	dehghanian	PROPN
ejpam-5758	171	25	et	et	PROPN
ejpam-5758	171	26	al	al	PROPN
ejpam-5758	171	27	.	.	PUNCT
ejpam-5758	171	28	/	/	SYM
ejpam-5758	171	29	eur	eur	PROPN
ejpam-5758	171	30	.	.	PUNCT
ejpam-5758	172	1	j.	j.	PROPN
ejpam-5758	172	2	pure	pure	PROPN
ejpam-5758	172	3	appl	appl	PROPN
ejpam-5758	172	4	.	.	PROPN
ejpam-5758	172	5	math	math	PROPN
ejpam-5758	172	6	,	,	PUNCT
ejpam-5758	172	7	18	18	NUM
ejpam-5758	172	8	(	(	PUNCT
ejpam-5758	172	9	1	1	NUM
ejpam-5758	172	10	)	)	PUNCT
ejpam-5758	172	11	(	(	PUNCT
ejpam-5758	172	12	2025	2025	NUM
ejpam-5758	172	13	)	)	PUNCT
ejpam-5758	172	14	,	,	PUNCT
ejpam-5758	172	15	5758	5758	NUM
ejpam-5758	172	16	11	11	NUM
ejpam-5758	172	17	of	of	ADP
ejpam-5758	172	18	13	13	NUM
ejpam-5758	172	19	4	4	NUM
ejpam-5758	172	20	.	.	PUNCT
ejpam-5758	172	21	conclusion	conclusion	NOUN
ejpam-5758	172	22	and	and	CCONJ
ejpam-5758	172	23	future	future	ADJ
ejpam-5758	172	24	works	work	NOUN
ejpam-5758	172	25	in	in	ADP
ejpam-5758	172	26	this	this	DET
ejpam-5758	172	27	work	work	NOUN
ejpam-5758	172	28	,	,	PUNCT
ejpam-5758	172	29	using	use	VERB
ejpam-5758	172	30	brzdȩk	brzdȩk	NOUN
ejpam-5758	172	31	fixed	fix	VERB
ejpam-5758	172	32	point	point	NOUN
ejpam-5758	172	33	theorem	theorem	VERB
ejpam-5758	172	34	,	,	PUNCT
ejpam-5758	172	35	we	we	PRON
ejpam-5758	172	36	proved	prove	VERB
ejpam-5758	172	37	the	the	DET
ejpam-5758	172	38	hyers	hyers	PROPN
ejpam-5758	172	39	-	-	PUNCT
ejpam-5758	172	40	ulam	ulam	ADJ
ejpam-5758	172	41	stability	stability	NOUN
ejpam-5758	172	42	of	of	ADP
ejpam-5758	172	43	the	the	DET
ejpam-5758	172	44	pexiderized	pexiderize	VERB
ejpam-5758	172	45	additive	additive	ADJ
ejpam-5758	172	46	-	-	PUNCT
ejpam-5758	172	47	quadratic	quadratic	ADJ
ejpam-5758	172	48	functional	functional	ADJ
ejpam-5758	172	49	equation	equation	NOUN
ejpam-5758	172	50	(	(	PUNCT
ejpam-5758	172	51	1	1	NUM
ejpam-5758	172	52	)	)	PUNCT
ejpam-5758	172	53	in	in	ADP
ejpam-5758	172	54	banach	banach	NOUN
ejpam-5758	172	55	spaces	space	NOUN
ejpam-5758	172	56	.	.	PUNCT
ejpam-5758	173	1	we	we	PRON
ejpam-5758	173	2	can	can	AUX
ejpam-5758	173	3	apply	apply	VERB
ejpam-5758	173	4	the	the	DET
ejpam-5758	173	5	method	method	NOUN
ejpam-5758	173	6	to	to	PART
ejpam-5758	173	7	study	study	VERB
ejpam-5758	173	8	the	the	DET
ejpam-5758	173	9	hyers	hyers	PROPN
ejpam-5758	173	10	-	-	PUNCT
ejpam-5758	173	11	ulam	ulam	ADJ
ejpam-5758	173	12	stability	stability	NOUN
ejpam-5758	173	13	problems	problem	NOUN
ejpam-5758	173	14	of	of	ADP
ejpam-5758	173	15	the	the	DET
ejpam-5758	173	16	pexiderized	pexiderize	VERB
ejpam-5758	173	17	additivequadratic	additivequadratic	ADJ
ejpam-5758	173	18	functional	functional	ADJ
ejpam-5758	173	19	equation	equation	NOUN
ejpam-5758	173	20	(	(	PUNCT
ejpam-5758	173	21	1	1	NUM
ejpam-5758	173	22	)	)	PUNCT
ejpam-5758	173	23	in	in	ADP
ejpam-5758	173	24	fuzzy	fuzzy	ADJ
ejpam-5758	173	25	banach	banach	NOUN
ejpam-5758	173	26	spaces	space	NOUN
ejpam-5758	173	27	,	,	PUNCT
ejpam-5758	173	28	matrix	matrix	NOUN
ejpam-5758	173	29	banach	banach	NOUN
ejpam-5758	173	30	spaces	space	VERB
ejpam-5758	173	31	,	,	PUNCT
ejpam-5758	173	32	hilbert	hilbert	PROPN
ejpam-5758	173	33	c∗-modules	c∗-modules	PROPN
ejpam-5758	173	34	and	and	CCONJ
ejpam-5758	173	35	fuzzy	fuzzy	ADJ
ejpam-5758	173	36	hilbert	hilbert	PROPN
ejpam-5758	173	37	c∗-modules	c∗-modules	PROPN
ejpam-5758	173	38	,	,	PUNCT
ejpam-5758	173	39	in	in	ADP
ejpam-5758	173	40	future	future	ADJ
ejpam-5758	173	41	work	work	NOUN
ejpam-5758	173	42	.	.	PUNCT
ejpam-5758	174	1	acknowledgements	acknowledgement	NOUN
ejpam-5758	174	2	the	the	DET
ejpam-5758	174	3	authors	author	NOUN
ejpam-5758	174	4	are	be	AUX
ejpam-5758	174	5	thankful	thankful	ADJ
ejpam-5758	174	6	to	to	ADP
ejpam-5758	174	7	the	the	DET
ejpam-5758	174	8	editors	editor	NOUN
ejpam-5758	174	9	and	and	CCONJ
ejpam-5758	174	10	the	the	DET
ejpam-5758	174	11	anonymous	anonymous	ADJ
ejpam-5758	174	12	reviewers	reviewer	NOUN
ejpam-5758	174	13	for	for	ADP
ejpam-5758	174	14	many	many	ADJ
ejpam-5758	174	15	valuable	valuable	ADJ
ejpam-5758	174	16	suggestions	suggestion	NOUN
ejpam-5758	174	17	to	to	PART
ejpam-5758	174	18	improve	improve	VERB
ejpam-5758	174	19	this	this	DET
ejpam-5758	174	20	paper	paper	NOUN
ejpam-5758	174	21	.	.	PUNCT
ejpam-5758	175	1	funding	funding	NOUN
ejpam-5758	175	2	s.	s.	PROPN
ejpam-5758	175	3	donganont	donganont	PROPN
ejpam-5758	175	4	was	be	AUX
ejpam-5758	175	5	supported	support	VERB
ejpam-5758	175	6	by	by	ADP
ejpam-5758	175	7	the	the	DET
ejpam-5758	175	8	university	university	NOUN
ejpam-5758	175	9	of	of	ADP
ejpam-5758	175	10	phayao	phayao	PROPN
ejpam-5758	175	11	and	and	CCONJ
ejpam-5758	175	12	thailand	thailand	PROPN
ejpam-5758	175	13	science	science	PROPN
ejpam-5758	175	14	research	research	PROPN
ejpam-5758	175	15	and	and	CCONJ
ejpam-5758	175	16	innovation	innovation	NOUN
ejpam-5758	175	17	fund	fund	NOUN
ejpam-5758	175	18	(	(	PUNCT
ejpam-5758	175	19	fundamental	fundamental	ADJ
ejpam-5758	175	20	fund	fund	NOUN
ejpam-5758	175	21	2025	2025	NUM
ejpam-5758	175	22	,	,	PUNCT
ejpam-5758	175	23	grant	grant	VERB
ejpam-5758	175	24	no	no	NOUN
ejpam-5758	175	25	.	.	PUNCT
ejpam-5758	176	1	5020/2567	5020/2567	NUM
ejpam-5758	176	2	)	)	PUNCT
ejpam-5758	176	3	.	.	PUNCT
ejpam-5758	177	1	conflict	conflict	NOUN
ejpam-5758	177	2	of	of	ADP
ejpam-5758	177	3	interest	interest	NOUN
ejpam-5758	177	4	the	the	DET
ejpam-5758	177	5	authors	author	NOUN
ejpam-5758	177	6	declare	declare	VERB
ejpam-5758	177	7	that	that	SCONJ
ejpam-5758	177	8	they	they	PRON
ejpam-5758	177	9	have	have	VERB
ejpam-5758	177	10	no	no	DET
ejpam-5758	177	11	competing	compete	VERB
ejpam-5758	177	12	interests	interest	NOUN
ejpam-5758	177	13	.	.	PUNCT
ejpam-5758	178	1	references	reference	NOUN
ejpam-5758	178	2	[	[	X
ejpam-5758	178	3	1	1	NUM
ejpam-5758	178	4	]	]	PUNCT
ejpam-5758	178	5	j	j	PROPN
ejpam-5758	178	6	aczél	aczél	PROPN
ejpam-5758	178	7	and	and	CCONJ
ejpam-5758	178	8	j	j	PROPN
ejpam-5758	178	9	dhombre	dhombre	PROPN
ejpam-5758	178	10	.	.	PUNCT
ejpam-5758	179	1	functional	functional	ADJ
ejpam-5758	179	2	equastions	equastion	NOUN
ejpam-5758	179	3	in	in	ADP
ejpam-5758	179	4	several	several	ADJ
ejpam-5758	179	5	variables	variable	NOUN
ejpam-5758	179	6	.	.	PUNCT
ejpam-5758	180	1	cambridge	cambridge	PROPN
ejpam-5758	180	2	university	university	PROPN
ejpam-5758	180	3	press	press	NOUN
ejpam-5758	180	4	.	.	PUNCT
ejpam-5758	180	5	,	,	PUNCT
ejpam-5758	180	6	cambridge	cambridge	PROPN
ejpam-5758	180	7	,	,	PUNCT
ejpam-5758	180	8	1989	1989	NUM
ejpam-5758	180	9	.	.	PUNCT
ejpam-5758	181	1	[	[	X
ejpam-5758	181	2	2	2	NUM
ejpam-5758	181	3	]	]	X
ejpam-5758	181	4	m	m	VERB
ejpam-5758	181	5	adam	adam	PROPN
ejpam-5758	181	6	.	.	PUNCT
ejpam-5758	182	1	alienation	alienation	NOUN
ejpam-5758	182	2	of	of	ADP
ejpam-5758	182	3	the	the	DET
ejpam-5758	182	4	quadratic	quadratic	ADJ
ejpam-5758	182	5	and	and	CCONJ
ejpam-5758	182	6	additive	additive	ADJ
ejpam-5758	182	7	functional	functional	ADJ
ejpam-5758	182	8	equations	equation	NOUN
ejpam-5758	182	9	.	.	PUNCT
ejpam-5758	183	1	anal	anal	PROPN
ejpam-5758	183	2	.	.	PUNCT
ejpam-5758	183	3	math	math	NOUN
ejpam-5758	183	4	.	.	PUNCT
ejpam-5758	183	5	,	,	PUNCT
ejpam-5758	184	1	45(3):449–460	45(3):449–460	PROPN
ejpam-5758	184	2	,	,	PUNCT
ejpam-5758	184	3	2019	2019	NUM
ejpam-5758	184	4	.	.	PUNCT
ejpam-5758	185	1	[	[	X
ejpam-5758	185	2	3	3	NUM
ejpam-5758	185	3	]	]	X
ejpam-5758	185	4	r	r	NOUN
ejpam-5758	185	5	badora	badora	PROPN
ejpam-5758	185	6	,	,	PUNCT
ejpam-5758	185	7	j	j	PROPN
ejpam-5758	185	8	brzdȩk	brzdȩk	PROPN
ejpam-5758	185	9	,	,	PUNCT
ejpam-5758	185	10	and	and	CCONJ
ejpam-5758	185	11	k	k	PROPN
ejpam-5758	185	12	ciepliński	ciepliński	PROPN
ejpam-5758	185	13	.	.	PUNCT
ejpam-5758	185	14	applications	application	NOUN
ejpam-5758	185	15	of	of	ADP
ejpam-5758	185	16	banach	banach	NOUN
ejpam-5758	185	17	limit	limit	NOUN
ejpam-5758	185	18	in	in	ADP
ejpam-5758	185	19	ulam	ulam	PROPN
ejpam-5758	185	20	stability	stability	PROPN
ejpam-5758	185	21	.	.	PUNCT
ejpam-5758	186	1	symmetry	symmetry	NOUN
ejpam-5758	186	2	,	,	PUNCT
ejpam-5758	186	3	13(5(841)):1–18	13(5(841)):1–18	NUM
ejpam-5758	186	4	,	,	PUNCT
ejpam-5758	186	5	2021	2021	NUM
ejpam-5758	186	6	.	.	PUNCT
ejpam-5758	187	1	[	[	X
ejpam-5758	187	2	4	4	X
ejpam-5758	187	3	]	]	X
ejpam-5758	187	4	a	a	DET
ejpam-5758	187	5	batool	batool	NOUN
ejpam-5758	187	6	,	,	PUNCT
ejpam-5758	187	7	s	s	VERB
ejpam-5758	187	8	nawaz	nawaz	NOUN
ejpam-5758	187	9	,	,	PUNCT
ejpam-5758	187	10	o	o	PROPN
ejpam-5758	187	11	ege	ege	PROPN
ejpam-5758	187	12	,	,	PUNCT
ejpam-5758	187	13	and	and	CCONJ
ejpam-5758	187	14	m	m	PROPN
ejpam-5758	187	15	de	de	X
ejpam-5758	187	16	cla	cla	PROPN
ejpam-5758	187	17	sen	sen	PROPN
ejpam-5758	187	18	.	.	PROPN
ejpam-5758	187	19	hyers	hyers	PROPN
ejpam-5758	187	20	-	-	PUNCT
ejpam-5758	187	21	ulam	ulam	PROPN
ejpam-5758	187	22	stability	stability	NOUN
ejpam-5758	187	23	of	of	ADP
ejpam-5758	187	24	functional	functional	ADJ
ejpam-5758	187	25	inequalities	inequality	NOUN
ejpam-5758	187	26	:	:	PUNCT
ejpam-5758	187	27	a	a	DET
ejpam-5758	187	28	fixed	fix	VERB
ejpam-5758	187	29	point	point	NOUN
ejpam-5758	187	30	approach	approach	NOUN
ejpam-5758	187	31	.	.	PUNCT
ejpam-5758	188	1	j.	j.	PROPN
ejpam-5758	188	2	inequal	inequal	PROPN
ejpam-5758	188	3	.	.	PUNCT
ejpam-5758	189	1	appl	appl	PROPN
ejpam-5758	189	2	.	.	PROPN
ejpam-5758	189	3	,	,	PUNCT
ejpam-5758	189	4	2020(1(251)):1–18	2020(1(251)):1–18	NUM
ejpam-5758	189	5	,	,	PUNCT
ejpam-5758	189	6	2020	2020	NUM
ejpam-5758	189	7	.	.	PUNCT
ejpam-5758	190	1	[	[	X
ejpam-5758	190	2	5	5	NUM
ejpam-5758	190	3	]	]	SYM
ejpam-5758	190	4	b	b	NOUN
ejpam-5758	190	5	bouikhalene	bouikhalene	NOUN
ejpam-5758	190	6	and	and	CCONJ
ejpam-5758	190	7	e	e	X
ejpam-5758	190	8	elqorachi	elqorachi	PROPN
ejpam-5758	190	9	.	.	PUNCT
ejpam-5758	191	1	ulam	ulam	PROPN
ejpam-5758	191	2	-	-	PUNCT
ejpam-5758	191	3	gǎvriţa	gǎvriţa	NOUN
ejpam-5758	191	4	-	-	PUNCT
ejpam-5758	191	5	rassias	rassias	NOUN
ejpam-5758	191	6	stability	stability	NOUN
ejpam-5758	191	7	of	of	ADP
ejpam-5758	191	8	the	the	DET
ejpam-5758	191	9	pexider	pexider	ADJ
ejpam-5758	191	10	functional	functional	ADJ
ejpam-5758	191	11	equation	equation	NOUN
ejpam-5758	191	12	.	.	PUNCT
ejpam-5758	192	1	int	int	NOUN
ejpam-5758	192	2	.	.	PUNCT
ejpam-5758	193	1	j.	j.	PROPN
ejpam-5758	193	2	appl	appl	PROPN
ejpam-5758	193	3	.	.	PROPN
ejpam-5758	193	4	math	math	PROPN
ejpam-5758	193	5	.	.	PUNCT
ejpam-5758	194	1	stat	stat	PROPN
ejpam-5758	194	2	.	.	PUNCT
ejpam-5758	194	3	,	,	PUNCT
ejpam-5758	194	4	7(fe07):27–39	7(fe07):27–39	NUM
ejpam-5758	194	5	,	,	PUNCT
ejpam-5758	194	6	2007	2007	NUM
ejpam-5758	194	7	.	.	PUNCT
ejpam-5758	195	1	[	[	X
ejpam-5758	195	2	6	6	NUM
ejpam-5758	195	3	]	]	PUNCT
ejpam-5758	195	4	s	s	PART
ejpam-5758	195	5	bowmiya	bowmiya	NOUN
ejpam-5758	195	6	,	,	PUNCT
ejpam-5758	195	7	g	g	PROPN
ejpam-5758	195	8	balasubramanian	balasubramanian	PROPN
ejpam-5758	195	9	,	,	PUNCT
ejpam-5758	195	10	v	v	ADJ
ejpam-5758	195	11	govindan	govindan	PROPN
ejpam-5758	195	12	,	,	PUNCT
ejpam-5758	195	13	m	m	VERB
ejpam-5758	195	14	donganont	donganont	NOUN
ejpam-5758	195	15	,	,	PUNCT
ejpam-5758	195	16	and	and	CCONJ
ejpam-5758	195	17	h	h	NOUN
ejpam-5758	195	18	byeon	byeon	NOUN
ejpam-5758	195	19	.	.	PUNCT
ejpam-5758	196	1	generalized	generalize	VERB
ejpam-5758	196	2	linear	linear	PROPN
ejpam-5758	196	3	differential	differential	NOUN
ejpam-5758	196	4	equation	equation	NOUN
ejpam-5758	196	5	using	use	VERB
ejpam-5758	196	6	hyers	hyers	PROPN
ejpam-5758	196	7	-	-	PUNCT
ejpam-5758	196	8	ulam	ulam	PROPN
ejpam-5758	196	9	stability	stability	PROPN
ejpam-5758	196	10	approach	approach	NOUN
ejpam-5758	196	11	.	.	PUNCT
ejpam-5758	197	1	eur	eur	PROPN
ejpam-5758	197	2	.	.	PUNCT
ejpam-5758	198	1	j.	j.	PROPN
ejpam-5758	198	2	pure	pure	PROPN
ejpam-5758	198	3	appl	appl	PROPN
ejpam-5758	198	4	.	.	PUNCT
ejpam-5758	198	5	math	math	PROPN
ejpam-5758	198	6	.	.	PUNCT
ejpam-5758	198	7	,	,	PUNCT
ejpam-5758	198	8	17(4):3415–3435	17(4):3415–3435	NUM
ejpam-5758	198	9	,	,	PUNCT
ejpam-5758	198	10	2024	2024	NUM
ejpam-5758	198	11	.	.	PUNCT
ejpam-5758	199	1	[	[	X
ejpam-5758	199	2	7	7	NUM
ejpam-5758	199	3	]	]	X
ejpam-5758	199	4	s	s	PART
ejpam-5758	199	5	bowmiya	bowmiya	NOUN
ejpam-5758	199	6	,	,	PUNCT
ejpam-5758	199	7	g	g	PROPN
ejpam-5758	199	8	balasubramanian	balasubramanian	PROPN
ejpam-5758	199	9	,	,	PUNCT
ejpam-5758	199	10	v	v	ADJ
ejpam-5758	199	11	govindan	govindan	PROPN
ejpam-5758	199	12	,	,	PUNCT
ejpam-5758	199	13	m	m	VERB
ejpam-5758	199	14	donganont	donganont	NOUN
ejpam-5758	199	15	,	,	PUNCT
ejpam-5758	199	16	and	and	CCONJ
ejpam-5758	199	17	h	h	NOUN
ejpam-5758	199	18	byeon	byeon	NOUN
ejpam-5758	199	19	.	.	PUNCT
ejpam-5758	200	1	hyersulam	hyersulam	PROPN
ejpam-5758	200	2	stability	stability	NOUN
ejpam-5758	200	3	of	of	ADP
ejpam-5758	200	4	fifth	fifth	ADJ
ejpam-5758	200	5	order	order	NOUN
ejpam-5758	200	6	linear	linear	PROPN
ejpam-5758	200	7	differential	differential	NOUN
ejpam-5758	200	8	equations	equation	NOUN
ejpam-5758	200	9	.	.	PUNCT
ejpam-5758	201	1	eur	eur	PROPN
ejpam-5758	201	2	.	.	PUNCT
ejpam-5758	202	1	j.	j.	PROPN
ejpam-5758	202	2	pure	pure	PROPN
ejpam-5758	202	3	appl	appl	PROPN
ejpam-5758	202	4	.	.	PUNCT
ejpam-5758	202	5	math	math	PROPN
ejpam-5758	202	6	.	.	PUNCT
ejpam-5758	202	7	,	,	PUNCT
ejpam-5758	202	8	17(4):3585–3609	17(4):3585–3609	NUM
ejpam-5758	202	9	,	,	PUNCT
ejpam-5758	202	10	2024	2024	NUM
ejpam-5758	202	11	.	.	PUNCT
ejpam-5758	203	1	[	[	X
ejpam-5758	203	2	8	8	NUM
ejpam-5758	203	3	]	]	X
ejpam-5758	203	4	j	j	PROPN
ejpam-5758	203	5	brzdȩk	brzdȩk	PROPN
ejpam-5758	203	6	,	,	PUNCT
ejpam-5758	203	7	j	j	PROPN
ejpam-5758	203	8	chudziak	chudziak	PROPN
ejpam-5758	203	9	,	,	PUNCT
ejpam-5758	203	10	and	and	CCONJ
ejpam-5758	203	11	z	z	NOUN
ejpam-5758	203	12	páles	pále	NOUN
ejpam-5758	203	13	.	.	PUNCT
ejpam-5758	204	1	a	a	DET
ejpam-5758	204	2	fixed	fix	VERB
ejpam-5758	204	3	point	point	NOUN
ejpam-5758	204	4	approach	approach	NOUN
ejpam-5758	204	5	to	to	ADP
ejpam-5758	204	6	stability	stability	NOUN
ejpam-5758	204	7	of	of	ADP
ejpam-5758	204	8	functional	functional	ADJ
ejpam-5758	204	9	equations	equation	NOUN
ejpam-5758	204	10	.	.	PUNCT
ejpam-5758	205	1	nonlinear	nonlinear	ADJ
ejpam-5758	205	2	anal	anal	PROPN
ejpam-5758	205	3	.	.	PUNCT
ejpam-5758	205	4	,	,	PUNCT
ejpam-5758	205	5	74:6728–6732	74:6728–6732	NUM
ejpam-5758	205	6	,	,	PUNCT
ejpam-5758	205	7	2011	2011	NUM
ejpam-5758	205	8	.	.	PUNCT
ejpam-5758	206	1	[	[	X
ejpam-5758	206	2	9	9	X
ejpam-5758	206	3	]	]	X
ejpam-5758	206	4	p	p	PROPN
ejpam-5758	206	5	w	w	PROPN
ejpam-5758	206	6	cholewa	cholewa	PROPN
ejpam-5758	206	7	.	.	PUNCT
ejpam-5758	207	1	remarks	remark	NOUN
ejpam-5758	207	2	on	on	ADP
ejpam-5758	207	3	the	the	DET
ejpam-5758	207	4	stability	stability	NOUN
ejpam-5758	207	5	of	of	ADP
ejpam-5758	207	6	functional	functional	ADJ
ejpam-5758	207	7	equations	equation	NOUN
ejpam-5758	207	8	.	.	PUNCT
ejpam-5758	208	1	aequationes	aequatione	NOUN
ejpam-5758	208	2	math	math	PROPN
ejpam-5758	208	3	.	.	PUNCT
ejpam-5758	208	4	,	,	PUNCT
ejpam-5758	209	1	27:76–86	27:76–86	NUM
ejpam-5758	209	2	,	,	PUNCT
ejpam-5758	209	3	1984	1984	NUM
ejpam-5758	209	4	.	.	PUNCT
ejpam-5758	210	1	m.	m.	NOUN
ejpam-5758	210	2	dehghanian	dehghanian	PROPN
ejpam-5758	210	3	et	et	PROPN
ejpam-5758	210	4	al	al	PROPN
ejpam-5758	210	5	.	.	PUNCT
ejpam-5758	210	6	/	/	SYM
ejpam-5758	210	7	eur	eur	PROPN
ejpam-5758	210	8	.	.	PUNCT
ejpam-5758	211	1	j.	j.	PROPN
ejpam-5758	211	2	pure	pure	PROPN
ejpam-5758	211	3	appl	appl	PROPN
ejpam-5758	211	4	.	.	PROPN
ejpam-5758	211	5	math	math	PROPN
ejpam-5758	211	6	,	,	PUNCT
ejpam-5758	211	7	18	18	NUM
ejpam-5758	211	8	(	(	PUNCT
ejpam-5758	211	9	1	1	NUM
ejpam-5758	211	10	)	)	PUNCT
ejpam-5758	211	11	(	(	PUNCT
ejpam-5758	211	12	2025	2025	NUM
ejpam-5758	211	13	)	)	PUNCT
ejpam-5758	211	14	,	,	PUNCT
ejpam-5758	211	15	5758	5758	NUM
ejpam-5758	211	16	12	12	NUM
ejpam-5758	211	17	of	of	ADP
ejpam-5758	211	18	13	13	NUM
ejpam-5758	212	1	[	[	SYM
ejpam-5758	212	2	10	10	NUM
ejpam-5758	212	3	]	]	PUNCT
ejpam-5758	212	4	s	s	PART
ejpam-5758	212	5	czerwik	czerwik	PROPN
ejpam-5758	212	6	.	.	PUNCT
ejpam-5758	213	1	on	on	ADP
ejpam-5758	213	2	the	the	DET
ejpam-5758	213	3	stability	stability	NOUN
ejpam-5758	213	4	of	of	ADP
ejpam-5758	213	5	the	the	DET
ejpam-5758	213	6	quadratic	quadratic	ADJ
ejpam-5758	213	7	mapping	mapping	NOUN
ejpam-5758	213	8	in	in	ADP
ejpam-5758	213	9	normed	normed	ADJ
ejpam-5758	213	10	spaces	space	NOUN
ejpam-5758	213	11	.	.	PUNCT
ejpam-5758	214	1	abh	abh	PROPN
ejpam-5758	214	2	.	.	PUNCT
ejpam-5758	214	3	math	math	PROPN
ejpam-5758	214	4	.	.	PUNCT
ejpam-5758	215	1	sem	sem	PROPN
ejpam-5758	215	2	.	.	PUNCT
ejpam-5758	216	1	univ	univ	PROPN
ejpam-5758	216	2	.	.	PUNCT
ejpam-5758	217	1	hamburg	hamburg	PROPN
ejpam-5758	217	2	,	,	PUNCT
ejpam-5758	217	3	62:59–64	62:59–64	PROPN
ejpam-5758	217	4	,	,	PUNCT
ejpam-5758	217	5	1992	1992	NUM
ejpam-5758	217	6	.	.	PUNCT
ejpam-5758	218	1	[	[	X
ejpam-5758	218	2	11	11	NUM
ejpam-5758	218	3	]	]	X
ejpam-5758	218	4	m	m	VERB
ejpam-5758	218	5	dehghanian	dehghanian	ADJ
ejpam-5758	218	6	,	,	PUNCT
ejpam-5758	218	7	c	c	NOUN
ejpam-5758	218	8	park	park	NOUN
ejpam-5758	218	9	,	,	PUNCT
ejpam-5758	218	10	and	and	CCONJ
ejpam-5758	218	11	y	y	PROPN
ejpam-5758	218	12	sayyari	sayyari	PROPN
ejpam-5758	218	13	.	.	PUNCT
ejpam-5758	219	1	stability	stability	NOUN
ejpam-5758	219	2	of	of	ADP
ejpam-5758	219	3	ternary	ternary	ADJ
ejpam-5758	219	4	antiderivation	antiderivation	NOUN
ejpam-5758	219	5	in	in	ADP
ejpam-5758	219	6	ternary	ternary	ADJ
ejpam-5758	219	7	banach	banach	NOUN
ejpam-5758	219	8	algebras	algebra	VERB
ejpam-5758	219	9	via	via	ADP
ejpam-5758	219	10	fixed	fix	VERB
ejpam-5758	219	11	point	point	NOUN
ejpam-5758	219	12	theorem	theorem	VERB
ejpam-5758	219	13	.	.	PUNCT
ejpam-5758	219	14	cubo	cubo	NOUN
ejpam-5758	219	15	,	,	PUNCT
ejpam-5758	219	16	25(2):273–288	25(2):273–288	NUM
ejpam-5758	219	17	,	,	PUNCT
ejpam-5758	219	18	2023	2023	NUM
ejpam-5758	219	19	.	.	PUNCT
ejpam-5758	220	1	[	[	X
ejpam-5758	220	2	12	12	NUM
ejpam-5758	220	3	]	]	X
ejpam-5758	220	4	m	m	VERB
ejpam-5758	220	5	dehghanian	dehghanian	ADJ
ejpam-5758	220	6	and	and	CCONJ
ejpam-5758	220	7	y	y	PROPN
ejpam-5758	220	8	sayyari	sayyari	PROPN
ejpam-5758	220	9	.	.	PUNCT
ejpam-5758	221	1	the	the	DET
ejpam-5758	221	2	application	application	NOUN
ejpam-5758	221	3	of	of	ADP
ejpam-5758	221	4	brzdȩk	brzdȩk	PROPN
ejpam-5758	221	5	’s	’s	PART
ejpam-5758	221	6	fixed	fix	VERB
ejpam-5758	221	7	point	point	NOUN
ejpam-5758	221	8	theorem	theorem	VERB
ejpam-5758	221	9	in	in	ADP
ejpam-5758	221	10	the	the	DET
ejpam-5758	221	11	stability	stability	NOUN
ejpam-5758	221	12	problem	problem	NOUN
ejpam-5758	221	13	of	of	ADP
ejpam-5758	221	14	the	the	DET
ejpam-5758	221	15	drygas	drygas	NOUN
ejpam-5758	221	16	functional	functional	ADJ
ejpam-5758	221	17	equation	equation	NOUN
ejpam-5758	221	18	.	.	PUNCT
ejpam-5758	222	1	turk	turk	PROPN
ejpam-5758	222	2	.	.	PUNCT
ejpam-5758	223	1	j.	j.	PROPN
ejpam-5758	223	2	math	math	PROPN
ejpam-5758	223	3	.	.	PUNCT
ejpam-5758	223	4	,	,	PUNCT
ejpam-5758	223	5	47(6):1778–1790	47(6):1778–1790	NOUN
ejpam-5758	223	6	,	,	PUNCT
ejpam-5758	223	7	2023	2023	NUM
ejpam-5758	223	8	.	.	PUNCT
ejpam-5758	224	1	[	[	X
ejpam-5758	224	2	13	13	NUM
ejpam-5758	224	3	]	]	SYM
ejpam-5758	224	4	m	m	VERB
ejpam-5758	224	5	dehghanian	dehghanian	ADJ
ejpam-5758	224	6	and	and	CCONJ
ejpam-5758	224	7	y	y	PROPN
ejpam-5758	224	8	sayyari	sayyari	PROPN
ejpam-5758	224	9	.	.	PUNCT
ejpam-5758	225	1	a	a	DET
ejpam-5758	225	2	fixed	fix	VERB
ejpam-5758	225	3	point	point	NOUN
ejpam-5758	225	4	technique	technique	NOUN
ejpam-5758	225	5	to	to	ADP
ejpam-5758	225	6	the	the	DET
ejpam-5758	225	7	stability	stability	NOUN
ejpam-5758	225	8	of	of	ADP
ejpam-5758	225	9	hadamard	hadamard	ADJ
ejpam-5758	225	10	d	d	PROPN
ejpam-5758	225	11	-	-	PUNCT
ejpam-5758	225	12	hom	hom	NOUN
ejpam-5758	225	13	-	-	PUNCT
ejpam-5758	225	14	der	der	NOUN
ejpam-5758	225	15	in	in	ADP
ejpam-5758	225	16	banach	banach	NOUN
ejpam-5758	225	17	algebras	algebra	NOUN
ejpam-5758	225	18	.	.	PUNCT
ejpam-5758	225	19	math	math	NOUN
ejpam-5758	225	20	.	.	PUNCT
ejpam-5758	226	1	slovaca	slovaca	PROPN
ejpam-5758	226	2	,	,	PUNCT
ejpam-5758	226	3	74(1):151–158	74(1):151–158	PROPN
ejpam-5758	226	4	,	,	PUNCT
ejpam-5758	226	5	2023	2023	NUM
ejpam-5758	226	6	.	.	PUNCT
ejpam-5758	227	1	[	[	X
ejpam-5758	227	2	14	14	NUM
ejpam-5758	227	3	]	]	X
ejpam-5758	227	4	m	m	VERB
ejpam-5758	227	5	dehghanian	dehghanian	ADJ
ejpam-5758	227	6	,	,	PUNCT
ejpam-5758	227	7	y	y	PROPN
ejpam-5758	227	8	sayyari	sayyari	PROPN
ejpam-5758	227	9	,	,	PUNCT
ejpam-5758	227	10	and	and	CCONJ
ejpam-5758	227	11	c	c	PROPN
ejpam-5758	227	12	park	park	NOUN
ejpam-5758	227	13	.	.	PUNCT
ejpam-5758	228	1	hadamard	hadamard	ADJ
ejpam-5758	228	2	homomorphisms	homomorphism	NOUN
ejpam-5758	228	3	and	and	CCONJ
ejpam-5758	228	4	hadamard	hadamard	ADJ
ejpam-5758	228	5	derivations	derivation	NOUN
ejpam-5758	228	6	on	on	ADP
ejpam-5758	228	7	banach	banach	NOUN
ejpam-5758	228	8	algebras	algebra	NOUN
ejpam-5758	228	9	.	.	PUNCT
ejpam-5758	229	1	misk	misk	PROPN
ejpam-5758	229	2	.	.	PUNCT
ejpam-5758	229	3	math	math	PROPN
ejpam-5758	229	4	.	.	PUNCT
ejpam-5758	230	1	notes	note	NOUN
ejpam-5758	230	2	,	,	PUNCT
ejpam-5758	230	3	24(1):129–137	24(1):129–137	NUM
ejpam-5758	230	4	,	,	PUNCT
ejpam-5758	230	5	2023	2023	NUM
ejpam-5758	230	6	.	.	PUNCT
ejpam-5758	231	1	[	[	X
ejpam-5758	231	2	15	15	NUM
ejpam-5758	231	3	]	]	X
ejpam-5758	231	4	e	e	PROPN
ejpam-5758	231	5	el	el	PROPN
ejpam-5758	231	6	-	-	PUNCT
ejpam-5758	231	7	hady	hady	PROPN
ejpam-5758	231	8	and	and	CCONJ
ejpam-5758	231	9	j	j	PROPN
ejpam-5758	231	10	brzdȩk	brzdȩk	PROPN
ejpam-5758	231	11	.	.	PUNCT
ejpam-5758	231	12	banach	banach	NOUN
ejpam-5758	231	13	limit	limit	NOUN
ejpam-5758	231	14	and	and	CCONJ
ejpam-5758	231	15	ulam	ulam	PROPN
ejpam-5758	231	16	stability	stability	NOUN
ejpam-5758	231	17	of	of	ADP
ejpam-5758	231	18	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5758	231	19	cauchy	cauchy	NOUN
ejpam-5758	231	20	equation	equation	NOUN
ejpam-5758	231	21	.	.	PUNCT
ejpam-5758	232	1	math	math	NOUN
ejpam-5758	232	2	.	.	PUNCT
ejpam-5758	232	3	,	,	PUNCT
ejpam-5758	232	4	10(1695):1–15	10(1695):1–15	NUM
ejpam-5758	232	5	,	,	PUNCT
ejpam-5758	232	6	2022	2022	NUM
ejpam-5758	232	7	.	.	PUNCT
ejpam-5758	233	1	[	[	X
ejpam-5758	233	2	16	16	NUM
ejpam-5758	233	3	]	]	X
ejpam-5758	233	4	e	e	PROPN
ejpam-5758	233	5	el	el	PROPN
ejpam-5758	233	6	-	-	PUNCT
ejpam-5758	233	7	hady	hady	PROPN
ejpam-5758	233	8	,	,	PUNCT
ejpam-5758	233	9	y	y	PROPN
ejpam-5758	233	10	sayyari	sayyari	PROPN
ejpam-5758	233	11	,	,	PUNCT
ejpam-5758	233	12	m	m	PROPN
ejpam-5758	233	13	dehghanian	dehghanian	ADJ
ejpam-5758	233	14	,	,	PUNCT
ejpam-5758	233	15	and	and	CCONJ
ejpam-5758	233	16	y	y	PROPN
ejpam-5758	233	17	alruwaily	alruwaily	ADV
ejpam-5758	233	18	.	.	PUNCT
ejpam-5758	234	1	stability	stability	NOUN
ejpam-5758	234	2	results	result	VERB
ejpam-5758	234	3	for	for	ADP
ejpam-5758	234	4	some	some	DET
ejpam-5758	234	5	classes	class	NOUN
ejpam-5758	234	6	of	of	ADP
ejpam-5758	234	7	cubic	cubic	ADJ
ejpam-5758	234	8	functional	functional	ADJ
ejpam-5758	234	9	equations	equation	NOUN
ejpam-5758	234	10	.	.	PUNCT
ejpam-5758	235	1	axioms	axiom	NOUN
ejpam-5758	235	2	,	,	PUNCT
ejpam-5758	235	3	13(7(480)):1–12	13(7(480)):1–12	NUM
ejpam-5758	235	4	,	,	PUNCT
ejpam-5758	235	5	2024	2024	NUM
ejpam-5758	235	6	.	.	PUNCT
ejpam-5758	236	1	[	[	X
ejpam-5758	236	2	17	17	NUM
ejpam-5758	236	3	]	]	X
ejpam-5758	236	4	z	z	NOUN
ejpam-5758	236	5	gajda	gajda	NOUN
ejpam-5758	236	6	.	.	PUNCT
ejpam-5758	237	1	on	on	ADP
ejpam-5758	237	2	stability	stability	NOUN
ejpam-5758	237	3	of	of	ADP
ejpam-5758	237	4	additive	additive	ADJ
ejpam-5758	237	5	mappings	mapping	NOUN
ejpam-5758	237	6	.	.	PUNCT
ejpam-5758	238	1	int	int	NOUN
ejpam-5758	238	2	.	.	PUNCT
ejpam-5758	239	1	j.	j.	PROPN
ejpam-5758	239	2	math	math	PROPN
ejpam-5758	239	3	.	.	PUNCT
ejpam-5758	240	1	math	math	NOUN
ejpam-5758	240	2	.	.	PUNCT
ejpam-5758	241	1	sci	sci	PROPN
ejpam-5758	241	2	.	.	PROPN
ejpam-5758	241	3	,	,	PUNCT
ejpam-5758	241	4	14:431–434	14:431–434	NUM
ejpam-5758	241	5	,	,	PUNCT
ejpam-5758	241	6	1991	1991	NUM
ejpam-5758	241	7	.	.	PUNCT
ejpam-5758	242	1	[	[	X
ejpam-5758	242	2	18	18	NUM
ejpam-5758	242	3	]	]	SYM
ejpam-5758	242	4	v	v	NOUN
ejpam-5758	242	5	govindan	govindan	PROPN
ejpam-5758	242	6	,	,	PUNCT
ejpam-5758	242	7	c	c	PROPN
ejpam-5758	242	8	park	park	PROPN
ejpam-5758	242	9	,	,	PUNCT
ejpam-5758	242	10	s	s	VERB
ejpam-5758	242	11	pinelas	pinela	NOUN
ejpam-5758	242	12	,	,	PUNCT
ejpam-5758	242	13	and	and	CCONJ
ejpam-5758	242	14	t	t	PROPN
ejpam-5758	242	15	m	m	NOUN
ejpam-5758	242	16	rassias	rassias	PROPN
ejpam-5758	242	17	.	.	PUNCT
ejpam-5758	243	1	hyers	hyer	NOUN
ejpam-5758	243	2	-	-	PUNCT
ejpam-5758	243	3	ulam	ulam	PROPN
ejpam-5758	243	4	stability	stability	NOUN
ejpam-5758	243	5	of	of	ADP
ejpam-5758	243	6	an	an	DET
ejpam-5758	243	7	additivequadratic	additivequadratic	ADJ
ejpam-5758	243	8	functional	functional	ADJ
ejpam-5758	243	9	equation	equation	NOUN
ejpam-5758	243	10	.	.	PUNCT
ejpam-5758	244	1	cubo	cubo	NOUN
ejpam-5758	244	2	,	,	PUNCT
ejpam-5758	244	3	22(2):233–255	22(2):233–255	PROPN
ejpam-5758	244	4	,	,	PUNCT
ejpam-5758	244	5	2020	2020	NUM
ejpam-5758	244	6	.	.	PUNCT
ejpam-5758	245	1	[	[	X
ejpam-5758	245	2	19	19	NUM
ejpam-5758	245	3	]	]	X
ejpam-5758	245	4	d	d	PROPN
ejpam-5758	245	5	h	h	PROPN
ejpam-5758	245	6	hyers	hyer	NOUN
ejpam-5758	245	7	.	.	PUNCT
ejpam-5758	246	1	on	on	ADP
ejpam-5758	246	2	the	the	DET
ejpam-5758	246	3	stability	stability	NOUN
ejpam-5758	246	4	of	of	ADP
ejpam-5758	246	5	the	the	DET
ejpam-5758	246	6	linear	linear	ADJ
ejpam-5758	246	7	functional	functional	ADJ
ejpam-5758	246	8	equation	equation	NOUN
ejpam-5758	246	9	.	.	PUNCT
ejpam-5758	247	1	proc	proc	PROPN
ejpam-5758	247	2	.	.	PUNCT
ejpam-5758	248	1	natl	natl	PROPN
ejpam-5758	248	2	.	.	PUNCT
ejpam-5758	249	1	acad	acad	PROPN
ejpam-5758	249	2	.	.	PUNCT
ejpam-5758	250	1	sci	sci	PROPN
ejpam-5758	250	2	.	.	PUNCT
ejpam-5758	250	3	u.s.a	u.s.a	PROPN
ejpam-5758	250	4	.	.	PROPN
ejpam-5758	250	5	,	,	PUNCT
ejpam-5758	250	6	27:222–224	27:222–224	NUM
ejpam-5758	250	7	,	,	PUNCT
ejpam-5758	250	8	1941	1941	NUM
ejpam-5758	250	9	.	.	PUNCT
ejpam-5758	251	1	[	[	X
ejpam-5758	251	2	20	20	NUM
ejpam-5758	251	3	]	]	SYM
ejpam-5758	251	4	s	s	PART
ejpam-5758	251	5	m	m	NOUN
ejpam-5758	251	6	jung	jung	NOUN
ejpam-5758	251	7	and	and	CCONJ
ejpam-5758	251	8	p	p	PROPN
ejpam-5758	251	9	k	k	PROPN
ejpam-5758	251	10	sahoo	sahoo	PROPN
ejpam-5758	251	11	.	.	PUNCT
ejpam-5758	252	1	hyers	hyers	PROPN
ejpam-5758	252	2	-	-	PUNCT
ejpam-5758	252	3	ulam	ulam	PROPN
ejpam-5758	252	4	stability	stability	NOUN
ejpam-5758	252	5	of	of	ADP
ejpam-5758	252	6	the	the	DET
ejpam-5758	252	7	quadratic	quadratic	ADJ
ejpam-5758	252	8	equation	equation	NOUN
ejpam-5758	252	9	of	of	ADP
ejpam-5758	252	10	pexider	pexider	NOUN
ejpam-5758	252	11	type	type	NOUN
ejpam-5758	252	12	.	.	PUNCT
ejpam-5758	253	1	j.	j.	PROPN
ejpam-5758	253	2	korean	korean	PROPN
ejpam-5758	253	3	math	math	PROPN
ejpam-5758	253	4	.	.	PUNCT
ejpam-5758	254	1	soc	soc	PROPN
ejpam-5758	254	2	.	.	PUNCT
ejpam-5758	254	3	,	,	PUNCT
ejpam-5758	254	4	38(3):645–656	38(3):645–656	NOUN
ejpam-5758	254	5	,	,	PUNCT
ejpam-5758	254	6	2001	2001	NUM
ejpam-5758	254	7	.	.	PUNCT
ejpam-5758	255	1	[	[	X
ejpam-5758	255	2	21	21	NUM
ejpam-5758	255	3	]	]	X
ejpam-5758	255	4	s	s	PART
ejpam-5758	255	5	m	m	NOUN
ejpam-5758	255	6	jung	jung	NOUN
ejpam-5758	255	7	and	and	CCONJ
ejpam-5758	255	8	p	p	PROPN
ejpam-5758	255	9	k	k	PROPN
ejpam-5758	255	10	sahoo	sahoo	PROPN
ejpam-5758	255	11	.	.	PUNCT
ejpam-5758	256	1	stability	stability	NOUN
ejpam-5758	256	2	of	of	ADP
ejpam-5758	256	3	a	a	DET
ejpam-5758	256	4	functional	functional	NOUN
ejpam-5758	256	5	of	of	ADP
ejpam-5758	256	6	drygas	dryga	NOUN
ejpam-5758	256	7	.	.	PUNCT
ejpam-5758	257	1	aequationes	aequatione	NOUN
ejpam-5758	257	2	math	math	PROPN
ejpam-5758	257	3	.	.	PUNCT
ejpam-5758	258	1	,	,	PUNCT
ejpam-5758	258	2	64:263–273	64:263–273	NUM
ejpam-5758	258	3	,	,	PUNCT
ejpam-5758	258	4	2002	2002	NUM
ejpam-5758	258	5	.	.	PUNCT
ejpam-5758	259	1	[	[	X
ejpam-5758	259	2	22	22	NUM
ejpam-5758	259	3	]	]	SYM
ejpam-5758	259	4	b	b	X
ejpam-5758	259	5	v	v	NUM
ejpam-5758	259	6	senthil	senthil	PROPN
ejpam-5758	259	7	kumar	kumar	PROPN
ejpam-5758	259	8	,	,	PUNCT
ejpam-5758	259	9	h	h	PROPN
ejpam-5758	259	10	dutta	dutta	PROPN
ejpam-5758	259	11	,	,	PUNCT
ejpam-5758	259	12	and	and	CCONJ
ejpam-5758	259	13	s	s	NOUN
ejpam-5758	259	14	sabarinathan	sabarinathan	NOUN
ejpam-5758	259	15	.	.	PUNCT
ejpam-5758	260	1	modular	modular	ADJ
ejpam-5758	260	2	stabilities	stability	NOUN
ejpam-5758	260	3	of	of	ADP
ejpam-5758	260	4	a	a	DET
ejpam-5758	260	5	reciprocal	reciprocal	ADJ
ejpam-5758	260	6	second	second	ADJ
ejpam-5758	260	7	power	power	NOUN
ejpam-5758	260	8	functional	functional	ADJ
ejpam-5758	260	9	equation	equation	NOUN
ejpam-5758	260	10	.	.	PUNCT
ejpam-5758	261	1	eur	eur	PROPN
ejpam-5758	261	2	.	.	PUNCT
ejpam-5758	262	1	j.	j.	PROPN
ejpam-5758	262	2	pure	pure	PROPN
ejpam-5758	262	3	appl	appl	PROPN
ejpam-5758	262	4	.	.	PUNCT
ejpam-5758	262	5	math	math	PROPN
ejpam-5758	262	6	.	.	PUNCT
ejpam-5758	262	7	,	,	PUNCT
ejpam-5758	263	1	13(5):1162–1175	13(5):1162–1175	NUM
ejpam-5758	263	2	,	,	PUNCT
ejpam-5758	263	3	2020	2020	NUM
ejpam-5758	263	4	.	.	PUNCT
ejpam-5758	264	1	[	[	X
ejpam-5758	264	2	23	23	NUM
ejpam-5758	264	3	]	]	X
ejpam-5758	264	4	s	s	VERB
ejpam-5758	264	5	paokanta	paokanta	NOUN
ejpam-5758	264	6	,	,	PUNCT
ejpam-5758	264	7	m	m	VERB
ejpam-5758	264	8	dehghanian	dehghanian	ADJ
ejpam-5758	264	9	,	,	PUNCT
ejpam-5758	264	10	c	c	NOUN
ejpam-5758	264	11	park	park	NOUN
ejpam-5758	264	12	,	,	PUNCT
ejpam-5758	264	13	and	and	CCONJ
ejpam-5758	264	14	y	y	PROPN
ejpam-5758	264	15	sayyari	sayyari	PROPN
ejpam-5758	264	16	.	.	PUNCT
ejpam-5758	265	1	a	a	DET
ejpam-5758	265	2	system	system	NOUN
ejpam-5758	265	3	of	of	ADP
ejpam-5758	265	4	additive	additive	ADJ
ejpam-5758	265	5	functional	functional	ADJ
ejpam-5758	265	6	equations	equation	NOUN
ejpam-5758	265	7	in	in	ADP
ejpam-5758	265	8	complex	complex	ADJ
ejpam-5758	265	9	banach	banach	NOUN
ejpam-5758	265	10	algebras	algebra	NOUN
ejpam-5758	265	11	.	.	PUNCT
ejpam-5758	266	1	demonstr	demonstr	PROPN
ejpam-5758	266	2	.	.	PUNCT
ejpam-5758	267	1	math	math	NOUN
ejpam-5758	267	2	.	.	PUNCT
ejpam-5758	267	3	,	,	PUNCT
ejpam-5758	268	1	56(1(20220165)):1–10	56(1(20220165)):1–10	NOUN
ejpam-5758	268	2	,	,	PUNCT
ejpam-5758	268	3	2023	2023	NUM
ejpam-5758	268	4	.	.	PUNCT
ejpam-5758	269	1	[	[	X
ejpam-5758	269	2	24	24	NUM
ejpam-5758	269	3	]	]	X
ejpam-5758	269	4	p	p	X
ejpam-5758	269	5	phochai	phochai	NOUN
ejpam-5758	269	6	and	and	CCONJ
ejpam-5758	269	7	s	s	PROPN
ejpam-5758	269	8	saejung	saejung	PROPN
ejpam-5758	269	9	.	.	PUNCT
ejpam-5758	270	1	the	the	DET
ejpam-5758	270	2	hyperstability	hyperstability	NOUN
ejpam-5758	270	3	of	of	ADP
ejpam-5758	270	4	general	general	ADJ
ejpam-5758	270	5	linear	linear	ADJ
ejpam-5758	270	6	equation	equation	NOUN
ejpam-5758	270	7	via	via	ADP
ejpam-5758	270	8	that	that	PRON
ejpam-5758	270	9	of	of	ADP
ejpam-5758	270	10	cauchy	cauchy	ADJ
ejpam-5758	270	11	equation	equation	NOUN
ejpam-5758	270	12	.	.	PUNCT
ejpam-5758	271	1	aequationes	aequatione	NOUN
ejpam-5758	271	2	math	math	PROPN
ejpam-5758	271	3	.	.	PUNCT
ejpam-5758	271	4	,	,	PUNCT
ejpam-5758	271	5	93(4):781–789	93(4):781–789	ADV
ejpam-5758	271	6	,	,	PUNCT
ejpam-5758	271	7	2019	2019	NUM
ejpam-5758	271	8	.	.	PUNCT
ejpam-5758	272	1	[	[	X
ejpam-5758	272	2	25	25	NUM
ejpam-5758	272	3	]	]	X
ejpam-5758	272	4	p	p	X
ejpam-5758	272	5	phochai	phochai	NOUN
ejpam-5758	272	6	and	and	CCONJ
ejpam-5758	272	7	s	s	PROPN
ejpam-5758	272	8	saejung	saejung	PROPN
ejpam-5758	272	9	.	.	PUNCT
ejpam-5758	273	1	hyperstability	hyperstability	NOUN
ejpam-5758	273	2	of	of	ADP
ejpam-5758	273	3	generalized	generalized	ADJ
ejpam-5758	273	4	linear	linear	ADJ
ejpam-5758	273	5	functional	functional	ADJ
ejpam-5758	273	6	equations	equation	NOUN
ejpam-5758	273	7	in	in	ADP
ejpam-5758	273	8	several	several	ADJ
ejpam-5758	273	9	variables	variable	NOUN
ejpam-5758	273	10	.	.	PUNCT
ejpam-5758	274	1	bull	bull	NOUN
ejpam-5758	274	2	.	.	PUNCT
ejpam-5758	275	1	aust	aust	PROPN
ejpam-5758	275	2	.	.	PUNCT
ejpam-5758	275	3	math	math	PROPN
ejpam-5758	275	4	.	.	PUNCT
ejpam-5758	276	1	soc	soc	PROPN
ejpam-5758	276	2	.	.	PROPN
ejpam-5758	276	3	,	,	PUNCT
ejpam-5758	276	4	102(2):293–302	102(2):293–302	NUM
ejpam-5758	276	5	,	,	PUNCT
ejpam-5758	276	6	2020	2020	NUM
ejpam-5758	276	7	.	.	PUNCT
ejpam-5758	277	1	[	[	X
ejpam-5758	277	2	26	26	NUM
ejpam-5758	277	3	]	]	X
ejpam-5758	277	4	m	m	VERB
ejpam-5758	277	5	piszczek	piszczek	NOUN
ejpam-5758	277	6	and	and	CCONJ
ejpam-5758	277	7	j	j	PROPN
ejpam-5758	277	8	szczawinska	szczawinska	NOUN
ejpam-5758	277	9	.	.	PUNCT
ejpam-5758	278	1	stability	stability	NOUN
ejpam-5758	278	2	of	of	ADP
ejpam-5758	278	3	the	the	DET
ejpam-5758	278	4	drygas	drygas	NOUN
ejpam-5758	278	5	functional	functional	ADJ
ejpam-5758	278	6	equation	equation	NOUN
ejpam-5758	278	7	on	on	ADP
ejpam-5758	278	8	restricted	restricted	ADJ
ejpam-5758	278	9	domain	domain	NOUN
ejpam-5758	278	10	.	.	PUNCT
ejpam-5758	279	1	results	result	VERB
ejpam-5758	279	2	math	math	NOUN
ejpam-5758	279	3	.	.	PUNCT
ejpam-5758	279	4	,	,	PUNCT
ejpam-5758	279	5	68:11–24	68:11–24	PROPN
ejpam-5758	279	6	,	,	PUNCT
ejpam-5758	279	7	2015	2015	NUM
ejpam-5758	279	8	.	.	PUNCT
ejpam-5758	280	1	[	[	X
ejpam-5758	280	2	27	27	NUM
ejpam-5758	280	3	]	]	PUNCT
ejpam-5758	280	4	a	a	DET
ejpam-5758	280	5	rani	rani	PROPN
ejpam-5758	280	6	,	,	PUNCT
ejpam-5758	280	7	s	s	NOUN
ejpam-5758	280	8	devi	devi	NOUN
ejpam-5758	280	9	,	,	PUNCT
ejpam-5758	280	10	and	and	CCONJ
ejpam-5758	280	11	m	m	PROPN
ejpam-5758	280	12	k	k	PROPN
ejpam-5758	280	13	antil	antil	PROPN
ejpam-5758	280	14	.	.	PUNCT
ejpam-5758	281	1	stability	stability	NOUN
ejpam-5758	281	2	results	result	NOUN
ejpam-5758	281	3	of	of	ADP
ejpam-5758	281	4	the	the	DET
ejpam-5758	281	5	additive	additive	ADJ
ejpam-5758	281	6	-	-	PUNCT
ejpam-5758	281	7	quadratic	quadratic	ADJ
ejpam-5758	281	8	functional	functional	ADJ
ejpam-5758	281	9	equations	equation	NOUN
ejpam-5758	281	10	in	in	ADP
ejpam-5758	281	11	random	random	ADJ
ejpam-5758	281	12	normed	norme	VERB
ejpam-5758	281	13	spaces	space	NOUN
ejpam-5758	281	14	by	by	ADP
ejpam-5758	281	15	using	use	VERB
ejpam-5758	281	16	direct	direct	ADJ
ejpam-5758	281	17	and	and	CCONJ
ejpam-5758	281	18	fixed	fix	VERB
ejpam-5758	281	19	-	-	PUNCT
ejpam-5758	281	20	point	point	NOUN
ejpam-5758	281	21	method	method	NOUN
ejpam-5758	281	22	.	.	PUNCT
ejpam-5758	282	1	commun	commun	PROPN
ejpam-5758	282	2	.	.	PUNCT
ejpam-5758	283	1	math	math	PROPN
ejpam-5758	283	2	.	.	PUNCT
ejpam-5758	284	1	appl	appl	PROPN
ejpam-5758	284	2	.	.	PROPN
ejpam-5758	284	3	,	,	PUNCT
ejpam-5758	284	4	14(2):827–843	14(2):827–843	PROPN
ejpam-5758	284	5	,	,	PUNCT
ejpam-5758	284	6	2023	2023	NUM
ejpam-5758	284	7	.	.	PUNCT
ejpam-5758	285	1	[	[	X
ejpam-5758	285	2	28	28	NUM
ejpam-5758	285	3	]	]	X
ejpam-5758	285	4	t	t	PROPN
ejpam-5758	285	5	m	m	NOUN
ejpam-5758	285	6	rassias	rassias	PROPN
ejpam-5758	285	7	.	.	PUNCT
ejpam-5758	286	1	on	on	ADP
ejpam-5758	286	2	the	the	DET
ejpam-5758	286	3	stability	stability	NOUN
ejpam-5758	286	4	of	of	ADP
ejpam-5758	286	5	the	the	DET
ejpam-5758	286	6	quadratic	quadratic	ADJ
ejpam-5758	286	7	functional	functional	ADJ
ejpam-5758	286	8	equation	equation	NOUN
ejpam-5758	286	9	and	and	CCONJ
ejpam-5758	286	10	its	its	PRON
ejpam-5758	286	11	applications	application	NOUN
ejpam-5758	286	12	.	.	PUNCT
ejpam-5758	287	1	studia	studia	PROPN
ejpam-5758	287	2	univ	univ	PROPN
ejpam-5758	287	3	.	.	PUNCT
ejpam-5758	288	1	babes	babe	NOUN
ejpam-5758	288	2	-	-	PUNCT
ejpam-5758	288	3	bolyai	bolyai	NOUN
ejpam-5758	288	4	math	math	NOUN
ejpam-5758	288	5	.	.	PUNCT
ejpam-5758	288	6	,	,	PUNCT
ejpam-5758	288	7	43(3):89–124	43(3):89–124	NUM
ejpam-5758	288	8	,	,	PUNCT
ejpam-5758	288	9	1998	1998	NUM
ejpam-5758	288	10	.	.	PUNCT
ejpam-5758	289	1	[	[	X
ejpam-5758	289	2	29	29	NUM
ejpam-5758	289	3	]	]	X
ejpam-5758	289	4	k	k	PROPN
ejpam-5758	289	5	ravi	ravi	PROPN
ejpam-5758	289	6	and	and	CCONJ
ejpam-5758	289	7	b	b	PROPN
ejpam-5758	289	8	v	v	PROPN
ejpam-5758	289	9	senthil	senthil	PROPN
ejpam-5758	289	10	kumar	kumar	PROPN
ejpam-5758	289	11	.	.	PROPN
ejpam-5758	290	1	generalized	generalized	PROPN
ejpam-5758	290	2	hyers	hyers	PROPN
ejpam-5758	290	3	-	-	PUNCT
ejpam-5758	290	4	ulam	ulam	ADJ
ejpam-5758	290	5	-	-	PUNCT
ejpam-5758	290	6	rassias	rassias	PROPN
ejpam-5758	290	7	stability	stability	NOUN
ejpam-5758	290	8	of	of	ADP
ejpam-5758	290	9	a	a	DET
ejpam-5758	290	10	system	system	NOUN
ejpam-5758	290	11	of	of	ADP
ejpam-5758	290	12	bi	bi	ADJ
ejpam-5758	290	13	-	-	ADJ
ejpam-5758	290	14	reciprocal	reciprocal	ADJ
ejpam-5758	290	15	functional	functional	ADJ
ejpam-5758	290	16	equations	equation	NOUN
ejpam-5758	290	17	.	.	PUNCT
ejpam-5758	291	1	eur	eur	PROPN
ejpam-5758	291	2	.	.	PUNCT
ejpam-5758	292	1	j.	j.	PROPN
ejpam-5758	292	2	pure	pure	PROPN
ejpam-5758	292	3	appl	appl	PROPN
ejpam-5758	292	4	.	.	PUNCT
ejpam-5758	292	5	math	math	PROPN
ejpam-5758	292	6	.	.	PUNCT
ejpam-5758	292	7	,	,	PUNCT
ejpam-5758	292	8	8(2):283–293	8(2):283–293	NUM
ejpam-5758	292	9	,	,	PUNCT
ejpam-5758	292	10	2015	2015	NUM
ejpam-5758	292	11	.	.	PUNCT
ejpam-5758	293	1	[	[	X
ejpam-5758	293	2	30	30	NUM
ejpam-5758	293	3	]	]	X
ejpam-5758	293	4	y	y	PROPN
ejpam-5758	293	5	sayyari	sayyari	PROPN
ejpam-5758	293	6	,	,	PUNCT
ejpam-5758	293	7	m	m	PROPN
ejpam-5758	293	8	dehghanian	dehghanian	ADJ
ejpam-5758	293	9	,	,	PUNCT
ejpam-5758	293	10	and	and	CCONJ
ejpam-5758	293	11	s	s	VERB
ejpam-5758	293	12	nasiri	nasiri	ADV
ejpam-5758	293	13	.	.	PUNCT
ejpam-5758	294	1	solution	solution	NOUN
ejpam-5758	294	2	of	of	ADP
ejpam-5758	294	3	some	some	DET
ejpam-5758	294	4	irregular	irregular	ADJ
ejpam-5758	294	5	functional	functional	ADJ
ejpam-5758	294	6	equam	equam	NOUN
ejpam-5758	294	7	.	.	PUNCT
ejpam-5758	295	1	dehghanian	dehghanian	PROPN
ejpam-5758	295	2	et	et	PROPN
ejpam-5758	295	3	al	al	PROPN
ejpam-5758	295	4	.	.	PUNCT
ejpam-5758	295	5	/	/	SYM
ejpam-5758	295	6	eur	eur	PROPN
ejpam-5758	295	7	.	.	PUNCT
ejpam-5758	296	1	j.	j.	PROPN
ejpam-5758	296	2	pure	pure	PROPN
ejpam-5758	296	3	appl	appl	PROPN
ejpam-5758	296	4	.	.	PROPN
ejpam-5758	296	5	math	math	PROPN
ejpam-5758	296	6	,	,	PUNCT
ejpam-5758	296	7	18	18	NUM
ejpam-5758	296	8	(	(	PUNCT
ejpam-5758	296	9	1	1	NUM
ejpam-5758	296	10	)	)	PUNCT
ejpam-5758	296	11	(	(	PUNCT
ejpam-5758	296	12	2025	2025	NUM
ejpam-5758	296	13	)	)	PUNCT
ejpam-5758	296	14	,	,	PUNCT
ejpam-5758	296	15	5758	5758	NUM
ejpam-5758	296	16	13	13	NUM
ejpam-5758	296	17	of	of	ADP
ejpam-5758	296	18	13	13	NUM
ejpam-5758	296	19	tions	tion	NOUN
ejpam-5758	296	20	and	and	CCONJ
ejpam-5758	296	21	their	their	PRON
ejpam-5758	296	22	stability	stability	NOUN
ejpam-5758	296	23	.	.	PUNCT
ejpam-5758	297	1	j.	j.	PROPN
ejpam-5758	297	2	linear	linear	PROPN
ejpam-5758	297	3	topol	topol	PROPN
ejpam-5758	297	4	.	.	PUNCT
ejpam-5758	298	1	algebra	algebra	PROPN
ejpam-5758	298	2	,	,	PUNCT
ejpam-5758	298	3	11(4):271–277	11(4):271–277	NOUN
ejpam-5758	298	4	,	,	PUNCT
ejpam-5758	298	5	2022	2022	NUM
ejpam-5758	298	6	.	.	PUNCT
ejpam-5758	299	1	[	[	X
ejpam-5758	299	2	31	31	NUM
ejpam-5758	299	3	]	]	X
ejpam-5758	299	4	y	y	PROPN
ejpam-5758	299	5	sayyari	sayyari	PROPN
ejpam-5758	299	6	,	,	PUNCT
ejpam-5758	299	7	m	m	PROPN
ejpam-5758	299	8	dehghanian	dehghanian	ADJ
ejpam-5758	299	9	,	,	PUNCT
ejpam-5758	299	10	and	and	CCONJ
ejpam-5758	299	11	c	c	PROPN
ejpam-5758	299	12	park	park	NOUN
ejpam-5758	299	13	.	.	PUNCT
ejpam-5758	300	1	some	some	DET
ejpam-5758	300	2	stabilities	stability	NOUN
ejpam-5758	300	3	of	of	ADP
ejpam-5758	300	4	system	system	NOUN
ejpam-5758	300	5	of	of	ADP
ejpam-5758	300	6	differential	differential	ADJ
ejpam-5758	300	7	equations	equation	NOUN
ejpam-5758	300	8	using	use	VERB
ejpam-5758	300	9	laplace	laplace	NOUN
ejpam-5758	300	10	transform	transform	NOUN
ejpam-5758	300	11	.	.	PUNCT
ejpam-5758	301	1	j.	j.	PROPN
ejpam-5758	301	2	appl	appl	PROPN
ejpam-5758	301	3	.	.	PROPN
ejpam-5758	301	4	math	math	PROPN
ejpam-5758	301	5	.	.	PUNCT
ejpam-5758	302	1	comput	comput	NOUN
ejpam-5758	302	2	.	.	PUNCT
ejpam-5758	302	3	,	,	PUNCT
ejpam-5758	303	1	69(4):3113–3129	69(4):3113–3129	NUM
ejpam-5758	303	2	,	,	PUNCT
ejpam-5758	303	3	2023	2023	NUM
ejpam-5758	303	4	.	.	PUNCT
ejpam-5758	304	1	[	[	X
ejpam-5758	304	2	32	32	NUM
ejpam-5758	304	3	]	]	X
ejpam-5758	304	4	y	y	PROPN
ejpam-5758	304	5	sayyari	sayyari	PROPN
ejpam-5758	304	6	,	,	PUNCT
ejpam-5758	304	7	m	m	PROPN
ejpam-5758	304	8	dehghanian	dehghanian	ADJ
ejpam-5758	304	9	,	,	PUNCT
ejpam-5758	304	10	and	and	CCONJ
ejpam-5758	304	11	c	c	PROPN
ejpam-5758	304	12	park	park	NOUN
ejpam-5758	304	13	.	.	PUNCT
ejpam-5758	305	1	a	a	DET
ejpam-5758	305	2	system	system	NOUN
ejpam-5758	305	3	of	of	ADP
ejpam-5758	305	4	biadditive	biadditive	ADJ
ejpam-5758	305	5	functional	functional	ADJ
ejpam-5758	305	6	equations	equation	NOUN
ejpam-5758	305	7	in	in	ADP
ejpam-5758	305	8	banach	banach	NOUN
ejpam-5758	305	9	algebras	algebra	NOUN
ejpam-5758	305	10	.	.	PUNCT
ejpam-5758	306	1	appl	appl	PROPN
ejpam-5758	306	2	.	.	PROPN
ejpam-5758	306	3	math	math	PROPN
ejpam-5758	306	4	.	.	PUNCT
ejpam-5758	307	1	sci	sci	PROPN
ejpam-5758	307	2	.	.	PUNCT
ejpam-5758	308	1	eng	eng	PROPN
ejpam-5758	308	2	.	.	PROPN
ejpam-5758	308	3	,	,	PUNCT
ejpam-5758	308	4	31(1(2176851)):1–11	31(1(2176851)):1–11	NOUN
ejpam-5758	308	5	,	,	PUNCT
ejpam-5758	308	6	2023	2023	NUM
ejpam-5758	308	7	.	.	PUNCT
ejpam-5758	309	1	[	[	X
ejpam-5758	309	2	33	33	NUM
ejpam-5758	309	3	]	]	SYM
ejpam-5758	309	4	s	s	NOUN
ejpam-5758	309	5	m	m	NOUN
ejpam-5758	309	6	ulam	ulam	PROPN
ejpam-5758	309	7	.	.	PUNCT
ejpam-5758	310	1	problems	problem	NOUN
ejpam-5758	310	2	in	in	ADP
ejpam-5758	310	3	modern	modern	ADJ
ejpam-5758	310	4	mathematics	mathematic	NOUN
ejpam-5758	310	5	.	.	PUNCT
ejpam-5758	311	1	john	john	PROPN
ejpam-5758	311	2	wiley	wiley	PROPN
ejpam-5758	311	3	&	&	CCONJ
ejpam-5758	311	4	sons	sons	PROPN
ejpam-5758	311	5	,	,	PUNCT
ejpam-5758	311	6	inc	inc	PROPN
ejpam-5758	311	7	.	.	PROPN
ejpam-5758	311	8	,	,	PUNCT
ejpam-5758	311	9	new	new	PROPN
ejpam-5758	311	10	york	york	PROPN
ejpam-5758	311	11	,	,	PUNCT
ejpam-5758	311	12	1964	1964	NUM
ejpam-5758	311	13	.	.	PUNCT