id	sid	tid	token	lemma	pos
ejpam-3407	1	1	compile	compile	NOUN
ejpam-3407	1	2	/	/	SYM
ejpam-3407	1	3	output.dvi	output.dvi	NOUN
ejpam-3407	1	4	european	european	ADJ
ejpam-3407	1	5	journal	journal	NOUN
ejpam-3407	1	6	of	of	ADP
ejpam-3407	1	7	pure	pure	ADJ
ejpam-3407	1	8	and	and	CCONJ
ejpam-3407	1	9	applied	apply	VERB
ejpam-3407	1	10	mathematics	mathematic	NOUN
ejpam-3407	1	11	vol	vol	NOUN
ejpam-3407	1	12	.	.	PROPN
ejpam-3407	2	1	12	12	NUM
ejpam-3407	2	2	,	,	PUNCT
ejpam-3407	2	3	no	no	INTJ
ejpam-3407	2	4	.	.	NOUN
ejpam-3407	2	5	2	2	NUM
ejpam-3407	2	6	,	,	PUNCT
ejpam-3407	2	7	2019	2019	NUM
ejpam-3407	2	8	,	,	PUNCT
ejpam-3407	2	9	432	432	NUM
ejpam-3407	2	10	-	-	SYM
ejpam-3407	2	11	447	447	NUM
ejpam-3407	2	12	issn	issn	PROPN
ejpam-3407	2	13	1307	1307	NUM
ejpam-3407	2	14	-	-	SYM
ejpam-3407	2	15	5543	5543	NUM
ejpam-3407	2	16	–	–	PUNCT
ejpam-3407	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3407	3	2	published	publish	VERB
ejpam-3407	3	3	by	by	ADP
ejpam-3407	3	4	new	new	PROPN
ejpam-3407	3	5	york	york	PROPN
ejpam-3407	3	6	business	business	PROPN
ejpam-3407	3	7	global	global	ADJ
ejpam-3407	3	8	monotone	monotone	ADJ
ejpam-3407	3	9	iterative	iterative	NOUN
ejpam-3407	3	10	technique	technique	NOUN
ejpam-3407	3	11	and	and	CCONJ
ejpam-3407	3	12	ulam	ulam	NOUN
ejpam-3407	3	13	-	-	PUNCT
ejpam-3407	3	14	hyers	hyer	NOUN
ejpam-3407	3	15	stability	stability	NOUN
ejpam-3407	3	16	analysis	analysis	NOUN
ejpam-3407	3	17	for	for	ADP
ejpam-3407	3	18	nonlinear	nonlinear	ADJ
ejpam-3407	3	19	fractional	fractional	ADJ
ejpam-3407	3	20	order	order	NOUN
ejpam-3407	3	21	differential	differential	ADJ
ejpam-3407	3	22	equations	equation	NOUN
ejpam-3407	3	23	with	with	ADP
ejpam-3407	3	24	integral	integral	ADJ
ejpam-3407	3	25	boundary	boundary	ADJ
ejpam-3407	3	26	value	value	NOUN
ejpam-3407	3	27	conditions	condition	NOUN
ejpam-3407	3	28	sajjad	sajjad	PROPN
ejpam-3407	3	29	ali1	ali1	PROPN
ejpam-3407	3	30	,	,	PUNCT
ejpam-3407	3	31	kamal	kamal	PROPN
ejpam-3407	3	32	shah2,∗	shah2,∗	PROPN
ejpam-3407	3	33	,	,	PUNCT
ejpam-3407	3	34	hassan	hassan	PROPN
ejpam-3407	3	35	khan1	khan1	PROPN
ejpam-3407	3	36	,	,	PUNCT
ejpam-3407	3	37	muhammad	muhammad	PROPN
ejpam-3407	3	38	arif1	arif1	PROPN
ejpam-3407	3	39	,	,	PUNCT
ejpam-3407	3	40	shahid	shahid	PROPN
ejpam-3407	3	41	mahmood3	mahmood3	PROPN
ejpam-3407	3	42	3	3	NUM
ejpam-3407	3	43	sarhad	sarhad	PROPN
ejpam-3407	3	44	university	university	NOUN
ejpam-3407	3	45	of	of	ADP
ejpam-3407	3	46	science	science	NOUN
ejpam-3407	3	47	and	and	CCONJ
ejpam-3407	3	48	it	it	PRON
ejpam-3407	3	49	,	,	PUNCT
ejpam-3407	3	50	peshawar	peshawar	PROPN
ejpam-3407	3	51	,	,	PUNCT
ejpam-3407	3	52	khyber	khyber	PROPN
ejpam-3407	3	53	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-3407	3	54	,	,	PUNCT
ejpam-3407	3	55	pakistan	pakistan	PROPN
ejpam-3407	3	56	1	1	NUM
ejpam-3407	3	57	abdul	abdul	PROPN
ejpam-3407	3	58	wali	wali	PROPN
ejpam-3407	3	59	khan	khan	PROPN
ejpam-3407	3	60	university	university	PROPN
ejpam-3407	3	61	mardan	mardan	PROPN
ejpam-3407	3	62	,	,	PUNCT
ejpam-3407	3	63	khyber	khyber	PROPN
ejpam-3407	3	64	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-3407	3	65	,	,	PUNCT
ejpam-3407	3	66	pakistan	pakistan	PROPN
ejpam-3407	3	67	2	2	NUM
ejpam-3407	3	68	university	university	NOUN
ejpam-3407	3	69	of	of	ADP
ejpam-3407	3	70	malakand	malakand	PROPN
ejpam-3407	3	71	,	,	PUNCT
ejpam-3407	3	72	dir(l	dir(l	PROPN
ejpam-3407	3	73	)	)	PUNCT
ejpam-3407	3	74	,	,	PUNCT
ejpam-3407	3	75	khyber	khyber	PROPN
ejpam-3407	3	76	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-3407	3	77	,	,	PUNCT
ejpam-3407	3	78	pakistan	pakistan	PROPN
ejpam-3407	3	79	abstract	abstract	NOUN
ejpam-3407	3	80	.	.	PUNCT
ejpam-3407	4	1	in	in	ADP
ejpam-3407	4	2	this	this	DET
ejpam-3407	4	3	manuscript	manuscript	NOUN
ejpam-3407	4	4	,	,	PUNCT
ejpam-3407	4	5	the	the	DET
ejpam-3407	4	6	monotone	monotone	ADJ
ejpam-3407	4	7	iterative	iterative	NOUN
ejpam-3407	4	8	scheme	scheme	NOUN
ejpam-3407	4	9	has	have	AUX
ejpam-3407	4	10	been	be	AUX
ejpam-3407	4	11	extended	extend	VERB
ejpam-3407	4	12	to	to	ADP
ejpam-3407	4	13	the	the	DET
ejpam-3407	4	14	nature	nature	NOUN
ejpam-3407	4	15	of	of	ADP
ejpam-3407	4	16	solution	solution	NOUN
ejpam-3407	4	17	to	to	ADP
ejpam-3407	4	18	boundary	boundary	ADJ
ejpam-3407	4	19	value	value	NOUN
ejpam-3407	4	20	problem	problem	NOUN
ejpam-3407	4	21	of	of	ADP
ejpam-3407	4	22	fractional	fractional	ADJ
ejpam-3407	4	23	differential	differential	ADJ
ejpam-3407	4	24	equation	equation	NOUN
ejpam-3407	4	25	that	that	PRON
ejpam-3407	4	26	consist	consist	VERB
ejpam-3407	4	27	integral	integral	ADJ
ejpam-3407	4	28	boundary	boundary	ADJ
ejpam-3407	4	29	conditions	condition	NOUN
ejpam-3407	4	30	.	.	PUNCT
ejpam-3407	5	1	in	in	ADP
ejpam-3407	5	2	this	this	DET
ejpam-3407	5	3	concern	concern	NOUN
ejpam-3407	5	4	,	,	PUNCT
ejpam-3407	5	5	some	some	DET
ejpam-3407	5	6	sufficient	sufficient	ADJ
ejpam-3407	5	7	conditions	condition	NOUN
ejpam-3407	5	8	are	be	AUX
ejpam-3407	5	9	developed	develop	VERB
ejpam-3407	5	10	in	in	ADP
ejpam-3407	5	11	this	this	DET
ejpam-3407	5	12	manuscript	manuscript	NOUN
ejpam-3407	5	13	.	.	PUNCT
ejpam-3407	6	1	on	on	ADP
ejpam-3407	6	2	the	the	DET
ejpam-3407	6	3	base	base	NOUN
ejpam-3407	6	4	of	of	ADP
ejpam-3407	6	5	sufficient	sufficient	ADJ
ejpam-3407	6	6	conditions	condition	NOUN
ejpam-3407	6	7	,	,	PUNCT
ejpam-3407	6	8	the	the	DET
ejpam-3407	6	9	monotone	monotone	ADJ
ejpam-3407	6	10	iterative	iterative	NOUN
ejpam-3407	6	11	scheme	scheme	NOUN
ejpam-3407	6	12	combined	combine	VERB
ejpam-3407	6	13	with	with	ADP
ejpam-3407	6	14	lower	low	ADJ
ejpam-3407	6	15	and	and	CCONJ
ejpam-3407	6	16	upper	upper	ADJ
ejpam-3407	6	17	solution	solution	NOUN
ejpam-3407	6	18	method	method	NOUN
ejpam-3407	6	19	for	for	ADP
ejpam-3407	6	20	the	the	DET
ejpam-3407	6	21	existence	existence	NOUN
ejpam-3407	6	22	,	,	PUNCT
ejpam-3407	6	23	uniqueness	uniqueness	NOUN
ejpam-3407	6	24	,	,	PUNCT
ejpam-3407	6	25	error	error	NOUN
ejpam-3407	6	26	estimates	estimate	NOUN
ejpam-3407	6	27	and	and	CCONJ
ejpam-3407	6	28	various	various	ADJ
ejpam-3407	6	29	view	view	NOUN
ejpam-3407	6	30	plots	plot	NOUN
ejpam-3407	6	31	of	of	ADP
ejpam-3407	6	32	the	the	DET
ejpam-3407	6	33	extremal	extremal	ADJ
ejpam-3407	6	34	solutions	solution	NOUN
ejpam-3407	6	35	to	to	ADP
ejpam-3407	6	36	boundary	boundary	ADJ
ejpam-3407	6	37	value	value	NOUN
ejpam-3407	6	38	problem	problem	NOUN
ejpam-3407	6	39	of	of	ADP
ejpam-3407	6	40	nonlinear	nonlinear	ADJ
ejpam-3407	6	41	fractional	fractional	ADJ
ejpam-3407	6	42	differential	differential	ADJ
ejpam-3407	6	43	equations	equation	NOUN
ejpam-3407	6	44	have	have	AUX
ejpam-3407	6	45	been	be	AUX
ejpam-3407	6	46	studied	study	VERB
ejpam-3407	6	47	.	.	PUNCT
ejpam-3407	7	1	the	the	DET
ejpam-3407	7	2	obtain	obtain	NOUN
ejpam-3407	7	3	results	result	NOUN
ejpam-3407	7	4	have	have	AUX
ejpam-3407	7	5	clarified	clarify	VERB
ejpam-3407	7	6	the	the	DET
ejpam-3407	7	7	nature	nature	NOUN
ejpam-3407	7	8	of	of	ADP
ejpam-3407	7	9	the	the	DET
ejpam-3407	7	10	extremal	extremal	ADJ
ejpam-3407	7	11	solutions	solution	NOUN
ejpam-3407	7	12	.	.	PUNCT
ejpam-3407	8	1	further	far	ADV
ejpam-3407	8	2	,	,	PUNCT
ejpam-3407	8	3	the	the	DET
ejpam-3407	8	4	ulam	ulam	X
ejpam-3407	8	5	–	–	PUNCT
ejpam-3407	8	6	hyers	hyer	NOUN
ejpam-3407	8	7	and	and	CCONJ
ejpam-3407	8	8	ulam	ulam	NOUN
ejpam-3407	8	9	–	–	PUNCT
ejpam-3407	8	10	hyers	hyer	NOUN
ejpam-3407	8	11	–	–	PUNCT
ejpam-3407	8	12	rassias	rassias	PROPN
ejpam-3407	8	13	stability	stability	NOUN
ejpam-3407	8	14	have	have	AUX
ejpam-3407	8	15	been	be	AUX
ejpam-3407	8	16	investigated	investigate	VERB
ejpam-3407	8	17	for	for	ADP
ejpam-3407	8	18	the	the	DET
ejpam-3407	8	19	considered	consider	VERB
ejpam-3407	8	20	problem	problem	NOUN
ejpam-3407	8	21	.	.	PUNCT
ejpam-3407	9	1	two	two	NUM
ejpam-3407	9	2	illustrative	illustrative	ADJ
ejpam-3407	9	3	examples	example	NOUN
ejpam-3407	9	4	of	of	ADP
ejpam-3407	9	5	the	the	DET
ejpam-3407	9	6	bvp	bvp	NOUN
ejpam-3407	9	7	of	of	ADP
ejpam-3407	9	8	the	the	DET
ejpam-3407	9	9	nonlinear	nonlinear	ADJ
ejpam-3407	9	10	fractional	fractional	ADJ
ejpam-3407	9	11	differential	differential	NOUN
ejpam-3407	9	12	equations	equation	NOUN
ejpam-3407	9	13	have	have	AUX
ejpam-3407	9	14	been	be	AUX
ejpam-3407	9	15	provided	provide	VERB
ejpam-3407	9	16	to	to	PART
ejpam-3407	9	17	justify	justify	VERB
ejpam-3407	9	18	our	our	PRON
ejpam-3407	9	19	contribution	contribution	NOUN
ejpam-3407	9	20	.	.	PUNCT
ejpam-3407	10	1	2010	2010	NUM
ejpam-3407	10	2	mathematics	mathematic	NOUN
ejpam-3407	10	3	subject	subject	NOUN
ejpam-3407	10	4	classifications	classification	NOUN
ejpam-3407	10	5	:	:	PUNCT
ejpam-3407	10	6	26a33	26a33	NUM
ejpam-3407	10	7	,	,	PUNCT
ejpam-3407	10	8	34a08	34a08	NUM
ejpam-3407	10	9	,	,	PUNCT
ejpam-3407	10	10	34a45	34a45	NUM
ejpam-3407	10	11	key	key	ADJ
ejpam-3407	10	12	words	word	NOUN
ejpam-3407	10	13	and	and	CCONJ
ejpam-3407	10	14	phrases	phrase	NOUN
ejpam-3407	10	15	:	:	PUNCT
ejpam-3407	10	16	nonlinear	nonlinear	ADJ
ejpam-3407	10	17	fractional	fractional	ADJ
ejpam-3407	10	18	differential	differential	NOUN
ejpam-3407	10	19	equations	equation	NOUN
ejpam-3407	10	20	,	,	PUNCT
ejpam-3407	10	21	iterative	iterative	NOUN
ejpam-3407	10	22	technique	technique	NOUN
ejpam-3407	10	23	,	,	PUNCT
ejpam-3407	10	24	maximal	maximal	ADJ
ejpam-3407	10	25	and	and	CCONJ
ejpam-3407	10	26	minimal	minimal	ADJ
ejpam-3407	10	27	solutions	solution	NOUN
ejpam-3407	10	28	,	,	PUNCT
ejpam-3407	10	29	uniqueness	uniqueness	NOUN
ejpam-3407	10	30	and	and	CCONJ
ejpam-3407	10	31	existence	existence	NOUN
ejpam-3407	10	32	1	1	NUM
ejpam-3407	10	33	.	.	PUNCT
ejpam-3407	11	1	introduction	introduction	NOUN
ejpam-3407	11	2	in	in	ADP
ejpam-3407	11	3	the	the	DET
ejpam-3407	11	4	last	last	ADJ
ejpam-3407	11	5	few	few	ADJ
ejpam-3407	11	6	decades	decade	NOUN
ejpam-3407	11	7	,	,	PUNCT
ejpam-3407	11	8	the	the	DET
ejpam-3407	11	9	class	class	NOUN
ejpam-3407	11	10	of	of	ADP
ejpam-3407	11	11	nonlinear	nonlinear	ADJ
ejpam-3407	11	12	fractional	fractional	ADJ
ejpam-3407	11	13	differential	differential	ADJ
ejpam-3407	11	14	equations	equation	NOUN
ejpam-3407	11	15	(	(	PUNCT
ejpam-3407	11	16	nfdes	nfde	NOUN
ejpam-3407	11	17	)	)	PUNCT
ejpam-3407	11	18	has	have	AUX
ejpam-3407	11	19	been	be	AUX
ejpam-3407	11	20	attracted	attract	VERB
ejpam-3407	11	21	the	the	DET
ejpam-3407	11	22	attentions	attention	NOUN
ejpam-3407	11	23	of	of	ADP
ejpam-3407	11	24	researchers	researcher	NOUN
ejpam-3407	11	25	very	very	ADV
ejpam-3407	11	26	well	well	ADV
ejpam-3407	11	27	.	.	PUNCT
ejpam-3407	12	1	the	the	DET
ejpam-3407	12	2	area	area	NOUN
ejpam-3407	12	3	devoted	devote	VERB
ejpam-3407	12	4	to	to	PART
ejpam-3407	12	5	study	study	VERB
ejpam-3407	12	6	nfdes	nfde	NOUN
ejpam-3407	12	7	has	have	AUX
ejpam-3407	12	8	attracted	attract	VERB
ejpam-3407	12	9	many	many	ADJ
ejpam-3407	12	10	researcher	researcher	NOUN
ejpam-3407	12	11	in	in	ADP
ejpam-3407	12	12	almost	almost	ADV
ejpam-3407	12	13	every	every	PRON
ejpam-3407	12	14	field	field	NOUN
ejpam-3407	12	15	of	of	ADP
ejpam-3407	12	16	science	science	NOUN
ejpam-3407	12	17	.	.	PUNCT
ejpam-3407	13	1	we	we	PRON
ejpam-3407	13	2	refer	refer	VERB
ejpam-3407	13	3	some	some	DET
ejpam-3407	13	4	papers	paper	NOUN
ejpam-3407	13	5	in	in	ADP
ejpam-3407	13	6	[	[	X
ejpam-3407	13	7	1–8	1–8	X
ejpam-3407	13	8	]	]	X
ejpam-3407	13	9	about	about	ADP
ejpam-3407	13	10	the	the	DET
ejpam-3407	13	11	applications	application	NOUN
ejpam-3407	13	12	.	.	PUNCT
ejpam-3407	14	1	various	various	ADJ
ejpam-3407	14	2	aspects	aspect	NOUN
ejpam-3407	14	3	like	like	ADP
ejpam-3407	14	4	existence	existence	NOUN
ejpam-3407	14	5	theory	theory	NOUN
ejpam-3407	14	6	for	for	ADP
ejpam-3407	14	7	the	the	DET
ejpam-3407	14	8	aforesaid	aforesaid	ADJ
ejpam-3407	14	9	equations	equation	NOUN
ejpam-3407	14	10	has	have	AUX
ejpam-3407	14	11	been	be	AUX
ejpam-3407	14	12	considered	consider	VERB
ejpam-3407	14	13	in	in	ADP
ejpam-3407	14	14	plenty	plenty	NOUN
ejpam-3407	14	15	of	of	ADP
ejpam-3407	14	16	research	research	NOUN
ejpam-3407	14	17	papers	paper	NOUN
ejpam-3407	14	18	,	,	PUNCT
ejpam-3407	14	19	see	see	VERB
ejpam-3407	14	20	[	[	X
ejpam-3407	14	21	9–12	9–12	NOUN
ejpam-3407	14	22	,	,	PUNCT
ejpam-3407	14	23	17	17	NUM
ejpam-3407	14	24	,	,	PUNCT
ejpam-3407	14	25	18	18	NUM
ejpam-3407	14	26	]	]	PUNCT
ejpam-3407	14	27	for	for	ADP
ejpam-3407	14	28	existence	existence	NOUN
ejpam-3407	14	29	and	and	CCONJ
ejpam-3407	14	30	uniqueness	uniqueness	NOUN
ejpam-3407	14	31	of	of	ADP
ejpam-3407	14	32	solutions	solution	NOUN
ejpam-3407	14	33	to	to	ADP
ejpam-3407	14	34	nfdes	nfde	NOUN
ejpam-3407	14	35	.	.	PUNCT
ejpam-3407	15	1	∗corresponding	∗corresponde	VERB
ejpam-3407	15	2	author	author	NOUN
ejpam-3407	15	3	.	.	PUNCT
ejpam-3407	16	1	doi	doi	NOUN
ejpam-3407	16	2	:	:	PUNCT
ejpam-3407	16	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3407	https://doi.org/10.29020/nybg.ejpam.v12i2.3407	PROPN
ejpam-3407	16	4	email	email	NOUN
ejpam-3407	16	5	addresses	address	NOUN
ejpam-3407	16	6	:	:	PUNCT
ejpam-3407	16	7	sajjad	sajjad	PROPN
ejpam-3407	16	8	ali@sbbu.edu.pk	ali@sbbu.edu.pk	PROPN
ejpam-3407	16	9	(	(	PUNCT
ejpam-3407	16	10	s.	s.	PROPN
ejpam-3407	16	11	ali	ali	PROPN
ejpam-3407	16	12	)	)	PUNCT
ejpam-3407	16	13	,	,	PUNCT
ejpam-3407	16	14	kamalshah408@gmail.com	kamalshah408@gmail.com	X
ejpam-3407	16	15	(	(	PUNCT
ejpam-3407	16	16	k.	k.	NOUN
ejpam-3407	16	17	shah	shah	PROPN
ejpam-3407	16	18	)	)	PUNCT
ejpam-3407	16	19	,	,	PUNCT
ejpam-3407	16	20	hassanmath@awkum.edu.pk	hassanmath@awkum.edu.pk	NOUN
ejpam-3407	16	21	(	(	PUNCT
ejpam-3407	16	22	h.	h.	PROPN
ejpam-3407	16	23	khan	khan	PROPN
ejpam-3407	16	24	)	)	PUNCT
ejpam-3407	16	25	,	,	PUNCT
ejpam-3407	16	26	marifmaths@awkum.edu.pk	marifmaths@awkum.edu.pk	PROPN
ejpam-3407	16	27	(	(	PUNCT
ejpam-3407	16	28	m.	m.	PROPN
ejpam-3407	16	29	arif	arif	PROPN
ejpam-3407	16	30	)	)	PUNCT
ejpam-3407	16	31	,	,	PUNCT
ejpam-3407	16	32	shahidmahmood757@gmail.com	shahidmahmood757@gmail.com	X
ejpam-3407	16	33	(	(	PUNCT
ejpam-3407	16	34	s.	s.	PROPN
ejpam-3407	16	35	mahmood	mahmood	PROPN
ejpam-3407	16	36	)	)	PUNCT
ejpam-3407	16	37	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3407	17	1	432	432	NUM
ejpam-3407	17	2	c	c	X
ejpam-3407	17	3	©	©	NOUN
ejpam-3407	17	4	2019	2019	NUM
ejpam-3407	17	5	ejpam	ejpam	NOUN
ejpam-3407	17	6	all	all	DET
ejpam-3407	17	7	rights	right	NOUN
ejpam-3407	17	8	reserved	reserve	VERB
ejpam-3407	17	9	.	.	PUNCT
ejpam-3407	18	1	k.	k.	PROPN
ejpam-3407	18	2	shah	shah	PROPN
ejpam-3407	18	3	et	et	PROPN
ejpam-3407	18	4	al	al	PROPN
ejpam-3407	18	5	.	.	PUNCT
ejpam-3407	18	6	/	/	SYM
ejpam-3407	18	7	eur	eur	PROPN
ejpam-3407	18	8	.	.	PUNCT
ejpam-3407	19	1	j.	j.	PROPN
ejpam-3407	19	2	pure	pure	PROPN
ejpam-3407	19	3	appl	appl	PROPN
ejpam-3407	19	4	.	.	PROPN
ejpam-3407	19	5	math	math	PROPN
ejpam-3407	19	6	,	,	PUNCT
ejpam-3407	19	7	12	12	NUM
ejpam-3407	19	8	(	(	PUNCT
ejpam-3407	19	9	2	2	NUM
ejpam-3407	19	10	)	)	PUNCT
ejpam-3407	19	11	(	(	PUNCT
ejpam-3407	19	12	2019	2019	NUM
ejpam-3407	19	13	)	)	PUNCT
ejpam-3407	19	14	,	,	PUNCT
ejpam-3407	19	15	432	432	NUM
ejpam-3407	19	16	-	-	SYM
ejpam-3407	19	17	447	447	NUM
ejpam-3407	19	18	433	433	NUM
ejpam-3407	19	19	the	the	DET
ejpam-3407	19	20	iterative	iterative	NOUN
ejpam-3407	19	21	technique	technique	NOUN
ejpam-3407	19	22	with	with	ADP
ejpam-3407	19	23	the	the	DET
ejpam-3407	19	24	method	method	NOUN
ejpam-3407	19	25	of	of	ADP
ejpam-3407	19	26	upper	upper	ADJ
ejpam-3407	19	27	and	and	CCONJ
ejpam-3407	19	28	lower	low	ADJ
ejpam-3407	19	29	solutions	solution	NOUN
ejpam-3407	19	30	has	have	AUX
ejpam-3407	19	31	gained	gain	VERB
ejpam-3407	19	32	much	much	ADJ
ejpam-3407	19	33	attention	attention	NOUN
ejpam-3407	19	34	of	of	ADP
ejpam-3407	19	35	most	most	ADJ
ejpam-3407	19	36	of	of	ADP
ejpam-3407	19	37	the	the	DET
ejpam-3407	19	38	researcher	researcher	NOUN
ejpam-3407	19	39	in	in	ADP
ejpam-3407	19	40	last	last	ADJ
ejpam-3407	19	41	few	few	ADJ
ejpam-3407	19	42	decades	decade	NOUN
ejpam-3407	19	43	.	.	PUNCT
ejpam-3407	20	1	it	it	PRON
ejpam-3407	20	2	is	be	AUX
ejpam-3407	20	3	very	very	ADV
ejpam-3407	20	4	useful	useful	ADJ
ejpam-3407	20	5	tools	tool	NOUN
ejpam-3407	20	6	for	for	ADP
ejpam-3407	20	7	the	the	DET
ejpam-3407	20	8	existence	existence	NOUN
ejpam-3407	20	9	and	and	CCONJ
ejpam-3407	20	10	approximation	approximation	NOUN
ejpam-3407	20	11	of	of	ADP
ejpam-3407	20	12	solutions	solution	NOUN
ejpam-3407	20	13	to	to	ADP
ejpam-3407	20	14	the	the	DET
ejpam-3407	20	15	initial	initial	ADJ
ejpam-3407	20	16	and	and	CCONJ
ejpam-3407	20	17	boundary	boundary	ADJ
ejpam-3407	20	18	value	value	NOUN
ejpam-3407	20	19	problems	problem	NOUN
ejpam-3407	20	20	.	.	PUNCT
ejpam-3407	21	1	this	this	DET
ejpam-3407	21	2	scheme	scheme	NOUN
ejpam-3407	21	3	is	be	AUX
ejpam-3407	21	4	well	well	ADV
ejpam-3407	21	5	studied	study	VERB
ejpam-3407	21	6	for	for	ADP
ejpam-3407	21	7	the	the	DET
ejpam-3407	21	8	intial	intial	ADJ
ejpam-3407	21	9	value	value	NOUN
ejpam-3407	21	10	problems	problem	NOUN
ejpam-3407	21	11	,	,	PUNCT
ejpam-3407	21	12	we	we	PRON
ejpam-3407	21	13	refer	refer	VERB
ejpam-3407	21	14	to	to	PART
ejpam-3407	21	15	see	see	VERB
ejpam-3407	21	16	the	the	DET
ejpam-3407	21	17	work	work	NOUN
ejpam-3407	21	18	in	in	ADP
ejpam-3407	21	19	[	[	X
ejpam-3407	21	20	13–16	13–16	NUM
ejpam-3407	21	21	,	,	PUNCT
ejpam-3407	21	22	19–24	19–24	NUM
ejpam-3407	21	23	]	]	PUNCT
ejpam-3407	21	24	.	.	PUNCT
ejpam-3407	22	1	however	however	ADV
ejpam-3407	22	2	,	,	PUNCT
ejpam-3407	22	3	the	the	DET
ejpam-3407	22	4	study	study	NOUN
ejpam-3407	22	5	of	of	ADP
ejpam-3407	22	6	the	the	DET
ejpam-3407	22	7	scheme	scheme	NOUN
ejpam-3407	22	8	is	be	AUX
ejpam-3407	22	9	on	on	ADP
ejpam-3407	22	10	intial	intial	ADJ
ejpam-3407	22	11	stage	stage	NOUN
ejpam-3407	22	12	for	for	ADP
ejpam-3407	22	13	integral	integral	ADJ
ejpam-3407	22	14	boundary	boundary	ADJ
ejpam-3407	22	15	value	value	NOUN
ejpam-3407	22	16	problem	problem	NOUN
ejpam-3407	22	17	.	.	PUNCT
ejpam-3407	23	1	a	a	DET
ejpam-3407	23	2	few	few	ADJ
ejpam-3407	23	3	authors	author	NOUN
ejpam-3407	23	4	have	have	VERB
ejpam-3407	23	5	its	its	PRON
ejpam-3407	23	6	study	study	NOUN
ejpam-3407	23	7	for	for	ADP
ejpam-3407	23	8	nfdes	nfde	NOUN
ejpam-3407	23	9	with	with	ADP
ejpam-3407	23	10	boundary	boundary	ADJ
ejpam-3407	23	11	conditions	condition	NOUN
ejpam-3407	23	12	.	.	PUNCT
ejpam-3407	24	1	for	for	ADP
ejpam-3407	24	2	instance	instance	NOUN
ejpam-3407	24	3	,	,	PUNCT
ejpam-3407	24	4	khan	khan	PROPN
ejpam-3407	24	5	[	[	X
ejpam-3407	24	6	25	25	NUM
ejpam-3407	24	7	]	]	PUNCT
ejpam-3407	24	8	have	have	AUX
ejpam-3407	24	9	considered	consider	VERB
ejpam-3407	24	10	it	it	PRON
ejpam-3407	24	11	for	for	ADP
ejpam-3407	24	12	the	the	DET
ejpam-3407	24	13	following	follow	VERB
ejpam-3407	24	14	class	class	NOUN
ejpam-3407	24	15	of	of	ADP
ejpam-3407	24	16	fdes	fde	NOUN
ejpam-3407	24	17	{	{	PUNCT
ejpam-3407	24	18	cdpz(t	cdpz(t	PROPN
ejpam-3407	24	19	)	)	PUNCT
ejpam-3407	24	20	+	+	CCONJ
ejpam-3407	24	21	h(t	h(t	PROPN
ejpam-3407	24	22	,	,	PUNCT
ejpam-3407	24	23	z(t	z(t	NOUN
ejpam-3407	24	24	)	)	PUNCT
ejpam-3407	24	25	)	)	PUNCT
ejpam-3407	25	1	=	=	SYM
ejpam-3407	25	2	0	0	NUM
ejpam-3407	25	3	,	,	PUNCT
ejpam-3407	25	4	1	1	NUM
ejpam-3407	25	5	<	<	X
ejpam-3407	25	6	p	p	X
ejpam-3407	25	7	<	<	X
ejpam-3407	25	8	2	2	NUM
ejpam-3407	25	9	,	,	PUNCT
ejpam-3407	25	10	z′(t)|t=0	z′(t)|t=0	NUM
ejpam-3407	25	11	=	=	SYM
ejpam-3407	25	12	0	0	NUM
ejpam-3407	25	13	,	,	PUNCT
ejpam-3407	25	14	z(1	z(1	PROPN
ejpam-3407	25	15	)	)	PUNCT
ejpam-3407	25	16	=	=	SYM
ejpam-3407	25	17	δz(t	δz(t	X
ejpam-3407	25	18	)	)	PUNCT
ejpam-3407	25	19	,	,	PUNCT
ejpam-3407	25	20	4	4	NUM
ejpam-3407	25	21	where	where	SCONJ
ejpam-3407	25	22	δ	δ	PROPN
ejpam-3407	25	23	,	,	PUNCT
ejpam-3407	25	24	t	t	PROPN
ejpam-3407	25	25	∈	∈	PROPN
ejpam-3407	25	26	(	(	PUNCT
ejpam-3407	25	27	0	0	NUM
ejpam-3407	25	28	,	,	PUNCT
ejpam-3407	25	29	1	1	NUM
ejpam-3407	25	30	)	)	PUNCT
ejpam-3407	25	31	.	.	PUNCT
ejpam-3407	26	1	the	the	DET
ejpam-3407	26	2	aforementioned	aforementioned	ADJ
ejpam-3407	26	3	method	method	NOUN
ejpam-3407	26	4	has	have	AUX
ejpam-3407	26	5	also	also	ADV
ejpam-3407	26	6	been	be	AUX
ejpam-3407	26	7	applied	apply	VERB
ejpam-3407	26	8	to	to	ADP
ejpam-3407	26	9	the	the	DET
ejpam-3407	26	10	study	study	NOUN
ejpam-3407	26	11	of	of	ADP
ejpam-3407	26	12	a	a	DET
ejpam-3407	26	13	coupled	couple	VERB
ejpam-3407	26	14	system	system	NOUN
ejpam-3407	26	15	of	of	ADP
ejpam-3407	26	16	the	the	DET
ejpam-3407	26	17	nfdes	nfde	NOUN
ejpam-3407	26	18	with	with	ADP
ejpam-3407	26	19	three	three	NUM
ejpam-3407	26	20	point	point	NOUN
ejpam-3407	26	21	boundary	boundary	ADJ
ejpam-3407	26	22	conditions	condition	NOUN
ejpam-3407	26	23	by	by	ADP
ejpam-3407	26	24	kamal[26	kamal[26	NOUN
ejpam-3407	26	25	]	]	PUNCT
ejpam-3407	26	26	and	and	CCONJ
ejpam-3407	26	27	his	his	PRON
ejpam-3407	26	28	co	co	NOUN
ejpam-3407	26	29	-	-	NOUN
ejpam-3407	26	30	author	author	NOUN
ejpam-3407	26	31	.	.	PUNCT
ejpam-3407	27	1	recently	recently	ADV
ejpam-3407	27	2	,	,	PUNCT
ejpam-3407	27	3	the	the	DET
ejpam-3407	27	4	investigation	investigation	NOUN
ejpam-3407	27	5	of	of	ADP
ejpam-3407	27	6	stability	stability	NOUN
ejpam-3407	27	7	is	be	AUX
ejpam-3407	27	8	also	also	ADV
ejpam-3407	27	9	a	a	DET
ejpam-3407	27	10	key	key	ADJ
ejpam-3407	27	11	research	research	NOUN
ejpam-3407	27	12	area	area	NOUN
ejpam-3407	27	13	for	for	ADP
ejpam-3407	27	14	the	the	DET
ejpam-3407	27	15	the	the	DET
ejpam-3407	27	16	development	development	NOUN
ejpam-3407	27	17	of	of	ADP
ejpam-3407	27	18	the	the	DET
ejpam-3407	27	19	fractional	fractional	ADJ
ejpam-3407	27	20	calculus	calculus	NOUN
ejpam-3407	27	21	.	.	PUNCT
ejpam-3407	28	1	it	it	PRON
ejpam-3407	28	2	an	an	DET
ejpam-3407	28	3	important	important	ADJ
ejpam-3407	28	4	field	field	NOUN
ejpam-3407	28	5	of	of	ADP
ejpam-3407	28	6	fractional	fractional	ADJ
ejpam-3407	28	7	calculus	calculus	NOUN
ejpam-3407	28	8	.	.	PUNCT
ejpam-3407	29	1	in	in	ADP
ejpam-3407	29	2	this	this	DET
ejpam-3407	29	3	concern	concern	NOUN
ejpam-3407	29	4	many	many	ADJ
ejpam-3407	29	5	researchers	researcher	NOUN
ejpam-3407	29	6	have	have	AUX
ejpam-3407	29	7	introduced	introduce	VERB
ejpam-3407	29	8	numerous	numerous	ADJ
ejpam-3407	29	9	type	type	NOUN
ejpam-3407	29	10	of	of	ADP
ejpam-3407	29	11	stability	stability	NOUN
ejpam-3407	29	12	including	include	VERB
ejpam-3407	29	13	exponential	exponential	ADJ
ejpam-3407	29	14	stability	stability	NOUN
ejpam-3407	29	15	,	,	PUNCT
ejpam-3407	29	16	lyapunov	lyapunov	NOUN
ejpam-3407	29	17	stability	stability	NOUN
ejpam-3407	29	18	,	,	PUNCT
ejpam-3407	29	19	ulam	ulam	PROPN
ejpam-3407	29	20	type	type	NOUN
ejpam-3407	29	21	stability	stability	NOUN
ejpam-3407	29	22	analysis	analysis	NOUN
ejpam-3407	29	23	etc	etc	X
ejpam-3407	29	24	.	.	X
ejpam-3407	29	25	among	among	ADP
ejpam-3407	29	26	them	they	PRON
ejpam-3407	29	27	,	,	PUNCT
ejpam-3407	29	28	the	the	DET
ejpam-3407	29	29	ulam	ulam	PROPN
ejpam-3407	29	30	type	type	NOUN
ejpam-3407	29	31	stability	stability	NOUN
ejpam-3407	29	32	has	have	AUX
ejpam-3407	29	33	attracted	attract	VERB
ejpam-3407	29	34	the	the	DET
ejpam-3407	29	35	attention	attention	NOUN
ejpam-3407	29	36	of	of	ADP
ejpam-3407	29	37	most	most	ADJ
ejpam-3407	29	38	of	of	ADP
ejpam-3407	29	39	the	the	DET
ejpam-3407	29	40	authors	author	NOUN
ejpam-3407	29	41	.	.	PUNCT
ejpam-3407	30	1	the	the	DET
ejpam-3407	30	2	ulam	ulam	PROPN
ejpam-3407	30	3	type	type	NOUN
ejpam-3407	30	4	stability	stability	NOUN
ejpam-3407	30	5	has	have	AUX
ejpam-3407	30	6	been	be	AUX
ejpam-3407	30	7	well	well	ADV
ejpam-3407	30	8	investigated	investigate	VERB
ejpam-3407	30	9	for	for	ADP
ejpam-3407	30	10	classical	classical	ADJ
ejpam-3407	30	11	differential	differential	ADJ
ejpam-3407	30	12	equations	equation	NOUN
ejpam-3407	30	13	.	.	PUNCT
ejpam-3407	31	1	in	in	ADP
ejpam-3407	31	2	last	last	ADJ
ejpam-3407	31	3	few	few	ADJ
ejpam-3407	31	4	years	year	NOUN
ejpam-3407	31	5	,	,	PUNCT
ejpam-3407	31	6	for	for	ADP
ejpam-3407	31	7	initial	initial	ADJ
ejpam-3407	31	8	value	value	NOUN
ejpam-3407	31	9	problems	problem	NOUN
ejpam-3407	31	10	of	of	ADP
ejpam-3407	31	11	fdes	fde	NOUN
ejpam-3407	31	12	,	,	PUNCT
ejpam-3407	31	13	the	the	DET
ejpam-3407	31	14	ulam	ulam	PROPN
ejpam-3407	31	15	type	type	NOUN
ejpam-3407	31	16	stability	stability	NOUN
ejpam-3407	31	17	has	have	AUX
ejpam-3407	31	18	been	be	AUX
ejpam-3407	31	19	well	well	ADV
ejpam-3407	31	20	investigated	investigate	VERB
ejpam-3407	31	21	in	in	ADP
ejpam-3407	31	22	many	many	ADJ
ejpam-3407	31	23	articles	article	NOUN
ejpam-3407	31	24	for	for	ADP
ejpam-3407	31	25	detail	detail	NOUN
ejpam-3407	31	26	see	see	VERB
ejpam-3407	31	27	[	[	X
ejpam-3407	31	28	27–31	27–31	PROPN
ejpam-3407	31	29	]	]	PUNCT
ejpam-3407	31	30	.	.	PUNCT
ejpam-3407	32	1	but	but	CCONJ
ejpam-3407	32	2	,	,	PUNCT
ejpam-3407	32	3	as	as	ADV
ejpam-3407	32	4	far	far	ADV
ejpam-3407	32	5	we	we	PRON
ejpam-3407	32	6	know	know	VERB
ejpam-3407	32	7	,	,	PUNCT
ejpam-3407	32	8	its	its	PRON
ejpam-3407	32	9	study	study	NOUN
ejpam-3407	32	10	is	be	AUX
ejpam-3407	32	11	very	very	ADV
ejpam-3407	32	12	limited	limited	ADJ
ejpam-3407	32	13	for	for	ADP
ejpam-3407	32	14	bvps	bvps	NOUN
ejpam-3407	32	15	of	of	ADP
ejpam-3407	32	16	fdes	fde	NOUN
ejpam-3407	32	17	.	.	PUNCT
ejpam-3407	33	1	therefore	therefore	ADV
ejpam-3407	33	2	inspired	inspire	VERB
ejpam-3407	33	3	from	from	ADP
ejpam-3407	33	4	the	the	DET
ejpam-3407	33	5	aforesaid	aforesaid	ADJ
ejpam-3407	33	6	work	work	NOUN
ejpam-3407	33	7	,	,	PUNCT
ejpam-3407	33	8	we	we	PRON
ejpam-3407	33	9	study	study	VERB
ejpam-3407	33	10	the	the	DET
ejpam-3407	33	11	following	follow	VERB
ejpam-3407	33	12	nfdes	nfde	NOUN
ejpam-3407	33	13	with	with	ADP
ejpam-3407	33	14	integral	integral	ADJ
ejpam-3407	33	15	boundary	boundary	ADJ
ejpam-3407	33	16	value	value	NOUN
ejpam-3407	33	17	conditions	condition	NOUN
ejpam-3407	33	18	as	as	ADP
ejpam-3407	33	19	cdpz(s	cdpz(s	NOUN
ejpam-3407	33	20	)	)	PUNCT
ejpam-3407	34	1	+	+	NOUN
ejpam-3407	34	2	q(s	q(s	ADJ
ejpam-3407	34	3	,	,	PUNCT
ejpam-3407	34	4	z(s	z(s	PROPN
ejpam-3407	34	5	)	)	PUNCT
ejpam-3407	34	6	)	)	PUNCT
ejpam-3407	35	1	=	=	PUNCT
ejpam-3407	35	2	0	0	NUM
ejpam-3407	35	3	,	,	PUNCT
ejpam-3407	35	4	s	s	VERB
ejpam-3407	35	5	∈	∈	PROPN
ejpam-3407	36	1	[	[	X
ejpam-3407	36	2	0	0	NUM
ejpam-3407	36	3	,	,	PUNCT
ejpam-3407	36	4	1	1	NUM
ejpam-3407	36	5	]	]	PUNCT
ejpam-3407	36	6	,	,	PUNCT
ejpam-3407	36	7	2	2	NUM
ejpam-3407	36	8	<	<	X
ejpam-3407	36	9	p	p	X
ejpam-3407	36	10	≤	≤	NOUN
ejpam-3407	36	11	3	3	NUM
ejpam-3407	36	12	,	,	PUNCT
ejpam-3407	36	13	z(0	z(0	X
ejpam-3407	36	14	)	)	PUNCT
ejpam-3407	36	15	=	=	PUNCT
ejpam-3407	36	16	z′′(s)|s=0	z′′(s)|s=0	X
ejpam-3407	36	17	=	=	SYM
ejpam-3407	36	18	0	0	NUM
ejpam-3407	36	19	,	,	PUNCT
ejpam-3407	36	20	z(1	z(1	PROPN
ejpam-3407	36	21	)	)	PUNCT
ejpam-3407	36	22	=	=	PUNCT
ejpam-3407	37	1	δ	δ	X
ejpam-3407	37	2	∫	∫	PROPN
ejpam-3407	37	3	1	1	NUM
ejpam-3407	37	4	0	0	NUM
ejpam-3407	37	5	z(s)ds	z(s)d	NOUN
ejpam-3407	37	6	,	,	PUNCT
ejpam-3407	37	7	(	(	PUNCT
ejpam-3407	37	8	1	1	X
ejpam-3407	37	9	)	)	PUNCT
ejpam-3407	37	10	where	where	SCONJ
ejpam-3407	37	11	cdp	cdp	PROPN
ejpam-3407	37	12	denotes	denote	VERB
ejpam-3407	37	13	caputo	caputo	PROPN
ejpam-3407	37	14	derivative	derivative	PROPN
ejpam-3407	37	15	,	,	PUNCT
ejpam-3407	37	16	q	q	X
ejpam-3407	37	17	:	:	PUNCT
ejpam-3407	37	18	i	i	PRON
ejpam-3407	37	19	×	×	VERB
ejpam-3407	37	20	r	r	NOUN
ejpam-3407	37	21	→	→	SYM
ejpam-3407	37	22	r	r	NOUN
ejpam-3407	37	23	,	,	PUNCT
ejpam-3407	37	24	2	2	NUM
ejpam-3407	37	25	<	<	X
ejpam-3407	37	26	p	p	X
ejpam-3407	37	27	≤	≤	NOUN
ejpam-3407	37	28	3	3	NUM
ejpam-3407	37	29	and	and	CCONJ
ejpam-3407	37	30	0	0	NUM
ejpam-3407	37	31	<	<	X
ejpam-3407	37	32	δ	δ	X
ejpam-3407	37	33	<	<	X
ejpam-3407	37	34	2	2	NUM
ejpam-3407	37	35	,	,	PUNCT
ejpam-3407	37	36	z	z	NOUN
ejpam-3407	37	37	∈	∈	PROPN
ejpam-3407	37	38	ac2[0	ac2[0	ADJ
ejpam-3407	37	39	,	,	PUNCT
ejpam-3407	37	40	1	1	NUM
ejpam-3407	37	41	]	]	PUNCT
ejpam-3407	37	42	.	.	PUNCT
ejpam-3407	38	1	in	in	ADP
ejpam-3407	38	2	comparison	comparison	NOUN
ejpam-3407	38	3	to	to	ADP
ejpam-3407	38	4	the	the	DET
ejpam-3407	38	5	work	work	NOUN
ejpam-3407	38	6	[	[	X
ejpam-3407	38	7	10	10	NUM
ejpam-3407	38	8	,	,	PUNCT
ejpam-3407	38	9	11	11	NUM
ejpam-3407	38	10	,	,	PUNCT
ejpam-3407	38	11	25	25	NUM
ejpam-3407	38	12	,	,	PUNCT
ejpam-3407	38	13	26	26	NUM
ejpam-3407	38	14	]	]	PUNCT
ejpam-3407	38	15	,	,	PUNCT
ejpam-3407	38	16	we	we	PRON
ejpam-3407	38	17	contribute	contribute	VERB
ejpam-3407	38	18	the	the	DET
ejpam-3407	38	19	improvement	improvement	NOUN
ejpam-3407	38	20	of	of	ADP
ejpam-3407	38	21	iterative	iterative	ADJ
ejpam-3407	38	22	scheme	scheme	NOUN
ejpam-3407	38	23	together	together	ADV
ejpam-3407	38	24	with	with	ADP
ejpam-3407	38	25	upper	upper	ADJ
ejpam-3407	38	26	and	and	CCONJ
ejpam-3407	38	27	lower	low	ADJ
ejpam-3407	38	28	solution	solution	NOUN
ejpam-3407	38	29	to	to	PART
ejpam-3407	38	30	study	study	VERB
ejpam-3407	38	31	existence	existence	NOUN
ejpam-3407	38	32	,	,	PUNCT
ejpam-3407	38	33	uniqueness	uniqueness	NOUN
ejpam-3407	38	34	,	,	PUNCT
ejpam-3407	38	35	error	error	NOUN
ejpam-3407	38	36	estimates	estimate	NOUN
ejpam-3407	38	37	and	and	CCONJ
ejpam-3407	38	38	plotting	plotting	NOUN
ejpam-3407	38	39	of	of	ADP
ejpam-3407	38	40	the	the	DET
ejpam-3407	38	41	iterative	iterative	NOUN
ejpam-3407	38	42	extremal	extremal	ADJ
ejpam-3407	38	43	solutions	solution	NOUN
ejpam-3407	38	44	of	of	ADP
ejpam-3407	38	45	nonlinear	nonlinear	ADJ
ejpam-3407	38	46	fractional	fractional	ADJ
ejpam-3407	38	47	differential	differential	ADJ
ejpam-3407	38	48	equations	equation	NOUN
ejpam-3407	38	49	with	with	ADP
ejpam-3407	38	50	integral	integral	ADJ
ejpam-3407	38	51	boundary	boundary	ADJ
ejpam-3407	38	52	conditions	condition	NOUN
ejpam-3407	38	53	(	(	PUNCT
ejpam-3407	38	54	1	1	NUM
ejpam-3407	38	55	)	)	PUNCT
ejpam-3407	38	56	.	.	PUNCT
ejpam-3407	39	1	in	in	ADP
ejpam-3407	39	2	addition	addition	NOUN
ejpam-3407	39	3	,	,	PUNCT
ejpam-3407	39	4	we	we	PRON
ejpam-3407	39	5	investigate	investigate	VERB
ejpam-3407	39	6	stability	stability	NOUN
ejpam-3407	39	7	analysis	analysis	NOUN
ejpam-3407	39	8	for	for	ADP
ejpam-3407	39	9	the	the	DET
ejpam-3407	39	10	solution	solution	NOUN
ejpam-3407	39	11	of	of	ADP
ejpam-3407	39	12	nonlinear	nonlinear	ADJ
ejpam-3407	39	13	fractional	fractional	ADJ
ejpam-3407	39	14	differential	differential	ADJ
ejpam-3407	39	15	equations	equation	NOUN
ejpam-3407	39	16	which	which	PRON
ejpam-3407	39	17	not	not	PART
ejpam-3407	39	18	established	establish	VERB
ejpam-3407	39	19	in	in	ADP
ejpam-3407	39	20	the	the	DET
ejpam-3407	39	21	work	work	NOUN
ejpam-3407	39	22	of	of	ADP
ejpam-3407	39	23	[	[	X
ejpam-3407	39	24	10	10	NUM
ejpam-3407	39	25	,	,	PUNCT
ejpam-3407	39	26	11	11	NUM
ejpam-3407	39	27	,	,	PUNCT
ejpam-3407	39	28	25	25	NUM
ejpam-3407	39	29	,	,	PUNCT
ejpam-3407	39	30	26	26	NUM
ejpam-3407	39	31	]	]	PUNCT
ejpam-3407	39	32	.	.	PUNCT
ejpam-3407	40	1	two	two	NUM
ejpam-3407	40	2	illustrative	illustrative	ADJ
ejpam-3407	40	3	examples	example	NOUN
ejpam-3407	40	4	of	of	ADP
ejpam-3407	40	5	problem	problem	NOUN
ejpam-3407	40	6	(	(	PUNCT
ejpam-3407	40	7	1	1	X
ejpam-3407	40	8	)	)	PUNCT
ejpam-3407	40	9	have	have	AUX
ejpam-3407	40	10	been	be	AUX
ejpam-3407	40	11	considered	consider	VERB
ejpam-3407	40	12	to	to	PART
ejpam-3407	40	13	demonstrate	demonstrate	VERB
ejpam-3407	40	14	our	our	PRON
ejpam-3407	40	15	existence	existence	NOUN
ejpam-3407	40	16	theory	theory	NOUN
ejpam-3407	40	17	.	.	PUNCT
ejpam-3407	41	1	behavior	behavior	NOUN
ejpam-3407	41	2	of	of	ADP
ejpam-3407	41	3	the	the	DET
ejpam-3407	41	4	upper	upper	ADJ
ejpam-3407	41	5	and	and	CCONJ
ejpam-3407	41	6	lower	low	ADJ
ejpam-3407	41	7	solutions	solution	NOUN
ejpam-3407	41	8	of	of	ADP
ejpam-3407	41	9	proposed	propose	VERB
ejpam-3407	41	10	examples	example	NOUN
ejpam-3407	41	11	are	be	AUX
ejpam-3407	41	12	plotted	plot	VERB
ejpam-3407	41	13	as	as	ADP
ejpam-3407	41	14	figure	figure	NOUN
ejpam-3407	41	15	1	1	NUM
ejpam-3407	41	16	and	and	CCONJ
ejpam-3407	41	17	2	2	NUM
ejpam-3407	41	18	via	via	ADP
ejpam-3407	41	19	using	use	VERB
ejpam-3407	41	20	matlab	matlab	PROPN
ejpam-3407	41	21	which	which	PRON
ejpam-3407	41	22	have	have	AUX
ejpam-3407	41	23	not	not	PART
ejpam-3407	41	24	been	be	AUX
ejpam-3407	41	25	done	do	VERB
ejpam-3407	41	26	in	in	ADP
ejpam-3407	41	27	the	the	DET
ejpam-3407	41	28	work	work	NOUN
ejpam-3407	41	29	of	of	ADP
ejpam-3407	41	30	cited	cite	VERB
ejpam-3407	41	31	above	above	ADV
ejpam-3407	41	32	.	.	PUNCT
ejpam-3407	42	1	2	2	X
ejpam-3407	42	2	.	.	X
ejpam-3407	42	3	preliminaries	preliminary	NOUN
ejpam-3407	42	4	we	we	PRON
ejpam-3407	42	5	provide	provide	VERB
ejpam-3407	42	6	the	the	DET
ejpam-3407	42	7	following	follow	VERB
ejpam-3407	42	8	few	few	ADJ
ejpam-3407	42	9	preliminary	preliminary	ADJ
ejpam-3407	42	10	results	result	NOUN
ejpam-3407	42	11	,	,	PUNCT
ejpam-3407	42	12	we	we	PRON
ejpam-3407	42	13	refer	refer	VERB
ejpam-3407	42	14	to	to	PART
ejpam-3407	42	15	see	see	VERB
ejpam-3407	42	16	[	[	X
ejpam-3407	42	17	2–5	2–5	NOUN
ejpam-3407	42	18	,	,	PUNCT
ejpam-3407	42	19	17–19	17–19	NUM
ejpam-3407	42	20	]	]	PUNCT
ejpam-3407	42	21	.	.	PUNCT
ejpam-3407	43	1	k.	k.	PROPN
ejpam-3407	43	2	shah	shah	PROPN
ejpam-3407	43	3	et	et	PROPN
ejpam-3407	43	4	al	al	PROPN
ejpam-3407	43	5	.	.	PUNCT
ejpam-3407	43	6	/	/	SYM
ejpam-3407	43	7	eur	eur	PROPN
ejpam-3407	43	8	.	.	PUNCT
ejpam-3407	44	1	j.	j.	PROPN
ejpam-3407	44	2	pure	pure	PROPN
ejpam-3407	44	3	appl	appl	PROPN
ejpam-3407	44	4	.	.	PROPN
ejpam-3407	44	5	math	math	PROPN
ejpam-3407	44	6	,	,	PUNCT
ejpam-3407	44	7	12	12	NUM
ejpam-3407	44	8	(	(	PUNCT
ejpam-3407	44	9	2	2	NUM
ejpam-3407	44	10	)	)	PUNCT
ejpam-3407	44	11	(	(	PUNCT
ejpam-3407	44	12	2019	2019	NUM
ejpam-3407	44	13	)	)	PUNCT
ejpam-3407	44	14	,	,	PUNCT
ejpam-3407	44	15	432	432	NUM
ejpam-3407	44	16	-	-	SYM
ejpam-3407	44	17	447	447	NUM
ejpam-3407	44	18	434	434	NUM
ejpam-3407	44	19	definition	definition	NOUN
ejpam-3407	44	20	1	1	NUM
ejpam-3407	44	21	.	.	PUNCT
ejpam-3407	45	1	the	the	DET
ejpam-3407	45	2	riemann	riemann	PROPN
ejpam-3407	45	3	-	-	PUNCT
ejpam-3407	45	4	liouville	liouville	VERB
ejpam-3407	45	5	integral	integral	ADJ
ejpam-3407	45	6	of	of	ADP
ejpam-3407	45	7	fractional	fractional	ADJ
ejpam-3407	45	8	order	order	NOUN
ejpam-3407	45	9	δ	δ	PROPN
ejpam-3407	45	10	∈	∈	PROPN
ejpam-3407	45	11	r+	r+	NOUN
ejpam-3407	45	12	of	of	ADP
ejpam-3407	45	13	a	a	DET
ejpam-3407	45	14	function	function	NOUN
ejpam-3407	45	15	φ	φ	PROPN
ejpam-3407	45	16	is	be	AUX
ejpam-3407	45	17	defined	define	VERB
ejpam-3407	45	18	by	by	ADP
ejpam-3407	45	19	ipφ(s	ipφ(s	PROPN
ejpam-3407	45	20	)	)	PUNCT
ejpam-3407	46	1	=	=	SYM
ejpam-3407	46	2	1	1	NUM
ejpam-3407	46	3	γ(p	γ(p	ADJ
ejpam-3407	46	4	)	)	PUNCT
ejpam-3407	46	5	∫	∫	PROPN
ejpam-3407	46	6	s	s	PART
ejpam-3407	46	7	0	0	NUM
ejpam-3407	46	8	(	(	PUNCT
ejpam-3407	46	9	s−	s−	PROPN
ejpam-3407	46	10	γ)p−1φ(γ)dγ	γ)p−1φ(γ)dγ	NOUN
ejpam-3407	46	11	,	,	PUNCT
ejpam-3407	46	12	provided	provide	VERB
ejpam-3407	46	13	the	the	DET
ejpam-3407	46	14	right	right	ADJ
ejpam-3407	46	15	side	side	NOUN
ejpam-3407	46	16	exits	exit	NOUN
ejpam-3407	46	17	.	.	PUNCT
ejpam-3407	47	1	definition	definition	NOUN
ejpam-3407	47	2	2	2	NUM
ejpam-3407	47	3	.	.	PUNCT
ejpam-3407	48	1	[	[	X
ejpam-3407	48	2	3	3	X
ejpam-3407	48	3	]	]	PUNCT
ejpam-3407	48	4	the	the	DET
ejpam-3407	48	5	caputo	caputo	PROPN
ejpam-3407	48	6	fractional	fractional	PROPN
ejpam-3407	48	7	order	order	NOUN
ejpam-3407	48	8	derivative	derivative	NOUN
ejpam-3407	48	9	of	of	ADP
ejpam-3407	48	10	order	order	NOUN
ejpam-3407	48	11	p	p	NOUN
ejpam-3407	48	12	of	of	ADP
ejpam-3407	48	13	function	function	NOUN
ejpam-3407	48	14	φ	φ	PROPN
ejpam-3407	48	15	is	be	AUX
ejpam-3407	48	16	defined	define	VERB
ejpam-3407	48	17	by	by	ADP
ejpam-3407	48	18	cdpφ(s	cdpφ(s	NOUN
ejpam-3407	48	19	)	)	PUNCT
ejpam-3407	48	20	=	=	PUNCT
ejpam-3407	48	21	1	1	NUM
ejpam-3407	48	22	γ(n−	γ(n−	PROPN
ejpam-3407	48	23	p	p	PROPN
ejpam-3407	48	24	)	)	PUNCT
ejpam-3407	48	25	∫	∫	PROPN
ejpam-3407	48	26	s	s	PART
ejpam-3407	48	27	0	0	NUM
ejpam-3407	48	28	(	(	PUNCT
ejpam-3407	48	29	s−	s−	PROPN
ejpam-3407	48	30	γ)n−p−1φ(n)(γ)dγ	γ)n−p−1φ(n)(γ)dγ	PROPN
ejpam-3407	48	31	,	,	PUNCT
ejpam-3407	48	32	provided	provide	VERB
ejpam-3407	48	33	that	that	PRON
ejpam-3407	48	34	integral	integral	ADJ
ejpam-3407	48	35	on	on	ADP
ejpam-3407	48	36	the	the	DET
ejpam-3407	48	37	right	right	NOUN
ejpam-3407	48	38	is	be	AUX
ejpam-3407	48	39	pointwise	pointwise	ADV
ejpam-3407	48	40	defined	define	VERB
ejpam-3407	48	41	on	on	ADP
ejpam-3407	48	42	(	(	PUNCT
ejpam-3407	48	43	0,∞	0,∞	NOUN
ejpam-3407	48	44	)	)	PUNCT
ejpam-3407	48	45	,	,	PUNCT
ejpam-3407	48	46	where	where	SCONJ
ejpam-3407	48	47	n	n	PROPN
ejpam-3407	48	48	=	=	SYM
ejpam-3407	48	49	⌊p⌋+1	⌊p⌋+1	PROPN
ejpam-3407	48	50	and	and	CCONJ
ejpam-3407	48	51	⌊p⌋	⌊p⌋	NOUN
ejpam-3407	48	52	denotes	denote	NOUN
ejpam-3407	48	53	the	the	DET
ejpam-3407	48	54	greatest	great	ADJ
ejpam-3407	48	55	integer	integer	NOUN
ejpam-3407	48	56	which	which	PRON
ejpam-3407	48	57	is	be	AUX
ejpam-3407	48	58	less	less	ADJ
ejpam-3407	48	59	than	than	ADP
ejpam-3407	48	60	or	or	CCONJ
ejpam-3407	48	61	equal	equal	ADJ
ejpam-3407	48	62	to	to	ADP
ejpam-3407	48	63	the	the	DET
ejpam-3407	48	64	real	real	ADJ
ejpam-3407	48	65	number	number	NOUN
ejpam-3407	48	66	p.	p.	NOUN
ejpam-3407	48	67	definition	definition	NOUN
ejpam-3407	49	1	3	3	X
ejpam-3407	49	2	.	.	PUNCT
ejpam-3407	50	1	[	[	X
ejpam-3407	50	2	33	33	NUM
ejpam-3407	50	3	]	]	PUNCT
ejpam-3407	50	4	let	let	VERB
ejpam-3407	50	5	v	v	NOUN
ejpam-3407	50	6	=	=	SYM
ejpam-3407	50	7	c[0	c[0	PROPN
ejpam-3407	50	8	,	,	PUNCT
ejpam-3407	50	9	1	1	NUM
ejpam-3407	50	10	]	]	PUNCT
ejpam-3407	50	11	be	be	AUX
ejpam-3407	50	12	the	the	DET
ejpam-3407	50	13	banach	banach	NOUN
ejpam-3407	50	14	space	space	NOUN
ejpam-3407	50	15	endowed	endow	VERB
ejpam-3407	50	16	with	with	ADP
ejpam-3407	50	17	‖z‖	‖z‖	PROPN
ejpam-3407	50	18	=	=	SYM
ejpam-3407	51	1	maxs∈[0,1	maxs∈[0,1	PROPN
ejpam-3407	51	2	]	]	X
ejpam-3407	51	3	|z(s)|	|z(s)|	NUM
ejpam-3407	51	4	which	which	PRON
ejpam-3407	51	5	satisfies	satisfy	VERB
ejpam-3407	51	6	the	the	DET
ejpam-3407	51	7	partially	partially	ADV
ejpam-3407	51	8	ordering	ordering	NOUN
ejpam-3407	51	9	and	and	CCONJ
ejpam-3407	51	10	let	let	VERB
ejpam-3407	51	11	u	u	PRON
ejpam-3407	51	12	=	=	PUNCT
ejpam-3407	51	13	[	[	X
ejpam-3407	51	14	z1	z1	PROPN
ejpam-3407	51	15	,	,	PUNCT
ejpam-3407	51	16	z2	z2	PROPN
ejpam-3407	51	17	]	]	PUNCT
ejpam-3407	51	18	with	with	ADP
ejpam-3407	51	19	z1	z1	ADJ
ejpam-3407	51	20	≤	≤	PROPN
ejpam-3407	51	21	z2	z2	PROPN
ejpam-3407	51	22	be	be	AUX
ejpam-3407	51	23	a	a	DET
ejpam-3407	51	24	set	set	NOUN
ejpam-3407	51	25	such	such	ADJ
ejpam-3407	51	26	that	that	SCONJ
ejpam-3407	51	27	u	u	PROPN
ejpam-3407	51	28	⊂	⊂	PROPN
ejpam-3407	51	29	v	v	PROPN
ejpam-3407	51	30	,	,	PUNCT
ejpam-3407	51	31	then	then	ADV
ejpam-3407	52	1	the	the	DET
ejpam-3407	52	2	operator	operator	NOUN
ejpam-3407	52	3	t	t	NOUN
ejpam-3407	52	4	:	:	PUNCT
ejpam-3407	52	5	u	u	NOUN
ejpam-3407	52	6	→	→	SYM
ejpam-3407	52	7	v	v	PROPN
ejpam-3407	52	8	is	be	AUX
ejpam-3407	52	9	known	know	VERB
ejpam-3407	52	10	as	as	ADP
ejpam-3407	52	11	increasing	increase	VERB
ejpam-3407	52	12	function	function	NOUN
ejpam-3407	52	13	if	if	SCONJ
ejpam-3407	52	14	for	for	ADP
ejpam-3407	52	15	each	each	DET
ejpam-3407	52	16	z1	z1	VERB
ejpam-3407	52	17	,	,	PUNCT
ejpam-3407	52	18	z2	z2	PROPN
ejpam-3407	52	19	∈	∈	PROPN
ejpam-3407	52	20	u	u	NOUN
ejpam-3407	52	21	and	and	CCONJ
ejpam-3407	52	22	z1	z1	ADJ
ejpam-3407	52	23	≤	≤	PROPN
ejpam-3407	52	24	z2	z2	PROPN
ejpam-3407	52	25	gives	give	VERB
ejpam-3407	52	26	tz1	tz1	ADJ
ejpam-3407	52	27	≤	≤	ADJ
ejpam-3407	52	28	tz2	tz2	NOUN
ejpam-3407	52	29	.	.	PUNCT
ejpam-3407	53	1	the	the	DET
ejpam-3407	53	2	operator	operator	NOUN
ejpam-3407	53	3	t	t	PROPN
ejpam-3407	53	4	is	be	AUX
ejpam-3407	53	5	known	know	VERB
ejpam-3407	53	6	as	as	ADP
ejpam-3407	53	7	decreasing	decrease	VERB
ejpam-3407	53	8	function	function	NOUN
ejpam-3407	53	9	if	if	SCONJ
ejpam-3407	53	10	for	for	ADP
ejpam-3407	53	11	each	each	DET
ejpam-3407	53	12	z1	z1	VERB
ejpam-3407	53	13	,	,	PUNCT
ejpam-3407	53	14	z2	z2	PROPN
ejpam-3407	53	15	∈	∈	PROPN
ejpam-3407	53	16	u	u	NOUN
ejpam-3407	53	17	and	and	CCONJ
ejpam-3407	53	18	z1	z1	ADJ
ejpam-3407	53	19	≤	≤	PROPN
ejpam-3407	53	20	z2	z2	PROPN
ejpam-3407	53	21	gives	give	VERB
ejpam-3407	53	22	tz1	tz1	PROPN
ejpam-3407	53	23	≥	≥	NOUN
ejpam-3407	53	24	tz2	tz2	NOUN
ejpam-3407	53	25	.	.	PUNCT
ejpam-3407	54	1	definition	definition	NOUN
ejpam-3407	54	2	4	4	NUM
ejpam-3407	54	3	.	.	PUNCT
ejpam-3407	55	1	[	[	X
ejpam-3407	55	2	33	33	NUM
ejpam-3407	55	3	]	]	PUNCT
ejpam-3407	55	4	let	let	NOUN
ejpam-3407	55	5	(	(	PUNCT
ejpam-3407	55	6	i	i	PRON
ejpam-3407	55	7	−	−	PROPN
ejpam-3407	55	8	t	t	NOUN
ejpam-3407	55	9	)	)	PUNCT
ejpam-3407	55	10	z1	z1	PROPN
ejpam-3407	55	11	≤	≤	NOUN
ejpam-3407	55	12	0	0	NUM
ejpam-3407	55	13	,	,	PUNCT
ejpam-3407	55	14	then	then	ADV
ejpam-3407	55	15	z1	z1	PROPN
ejpam-3407	55	16	∈	∈	PROPN
ejpam-3407	55	17	u	u	NOUN
ejpam-3407	55	18	is	be	AUX
ejpam-3407	55	19	known	know	VERB
ejpam-3407	55	20	as	as	ADP
ejpam-3407	55	21	a	a	DET
ejpam-3407	55	22	lower	low	ADJ
ejpam-3407	55	23	solution	solution	NOUN
ejpam-3407	55	24	of	of	ADP
ejpam-3407	55	25	(	(	PUNCT
ejpam-3407	55	26	i−t	i−t	NOUN
ejpam-3407	55	27	)	)	PUNCT
ejpam-3407	55	28	z	z	NOUN
ejpam-3407	55	29	=	=	SYM
ejpam-3407	55	30	0	0	NUM
ejpam-3407	56	1	and	and	CCONJ
ejpam-3407	56	2	(	(	PUNCT
ejpam-3407	56	3	i−t	i−t	NOUN
ejpam-3407	56	4	)	)	PUNCT
ejpam-3407	56	5	z2	z2	PROPN
ejpam-3407	56	6	≥	≥	NUM
ejpam-3407	56	7	0	0	NUM
ejpam-3407	56	8	,	,	PUNCT
ejpam-3407	56	9	then	then	ADV
ejpam-3407	56	10	z2	z2	PROPN
ejpam-3407	56	11	∈	∈	PROPN
ejpam-3407	56	12	u	u	NOUN
ejpam-3407	56	13	is	be	AUX
ejpam-3407	56	14	known	know	VERB
ejpam-3407	56	15	as	as	ADP
ejpam-3407	56	16	an	an	DET
ejpam-3407	56	17	upper	upper	ADJ
ejpam-3407	56	18	solution	solution	NOUN
ejpam-3407	56	19	of	of	ADP
ejpam-3407	56	20	(	(	PUNCT
ejpam-3407	56	21	i−t	i−t	NOUN
ejpam-3407	56	22	)	)	PUNCT
ejpam-3407	56	23	z	z	NOUN
ejpam-3407	56	24	=	=	SYM
ejpam-3407	57	1	0	0	X
ejpam-3407	57	2	.	.	PUNCT
ejpam-3407	58	1	lemma	lemma	PROPN
ejpam-3407	58	2	1	1	NUM
ejpam-3407	58	3	.	.	PUNCT
ejpam-3407	59	1	[	[	X
ejpam-3407	59	2	18	18	NUM
ejpam-3407	59	3	]	]	PUNCT
ejpam-3407	59	4	let	let	VERB
ejpam-3407	59	5	w	w	NOUN
ejpam-3407	59	6	be	be	AUX
ejpam-3407	59	7	banach	banach	NOUN
ejpam-3407	59	8	space	space	NOUN
ejpam-3407	59	9	with	with	ADP
ejpam-3407	59	10	satisfying	satisfy	VERB
ejpam-3407	59	11	partially	partially	ADV
ejpam-3407	59	12	order	order	NOUN
ejpam-3407	59	13	and	and	CCONJ
ejpam-3407	59	14	zn	zn	NUM
ejpam-3407	59	15	,	,	PUNCT
ejpam-3407	59	16	yn	yn	PROPN
ejpam-3407	59	17	∈	∈	PROPN
ejpam-3407	59	18	u	u	NOUN
ejpam-3407	59	19	so	so	SCONJ
ejpam-3407	59	20	that	that	SCONJ
ejpam-3407	59	21	zn	zn	PROPN
ejpam-3407	59	22	≤	≤	PROPN
ejpam-3407	59	23	yn	yn	PROPN
ejpam-3407	59	24	,	,	PUNCT
ejpam-3407	59	25	n	n	PROPN
ejpam-3407	59	26	∈	∈	PROPN
ejpam-3407	59	27	z+	z+	PUNCT
ejpam-3407	59	28	.	.	PUNCT
ejpam-3407	60	1	if	if	SCONJ
ejpam-3407	60	2	zn	zn	PROPN
ejpam-3407	60	3	→	→	SYM
ejpam-3407	60	4	z	z	PROPN
ejpam-3407	60	5	and	and	CCONJ
ejpam-3407	60	6	yn	yn	PROPN
ejpam-3407	60	7	→	→	SYM
ejpam-3407	60	8	y	y	PROPN
ejpam-3407	60	9	,	,	PUNCT
ejpam-3407	60	10	then	then	ADV
ejpam-3407	60	11	z	z	NOUN
ejpam-3407	60	12	≤	≤	PROPN
ejpam-3407	60	13	y.	y.	PROPN
ejpam-3407	60	14	assume	assume	VERB
ejpam-3407	60	15	that	that	SCONJ
ejpam-3407	60	16	(	(	PUNCT
ejpam-3407	60	17	c1	c1	NOUN
ejpam-3407	60	18	)	)	PUNCT
ejpam-3407	60	19	q	q	NOUN
ejpam-3407	61	1	:	:	PUNCT
ejpam-3407	61	2	[	[	X
ejpam-3407	61	3	0	0	NUM
ejpam-3407	61	4	,	,	PUNCT
ejpam-3407	61	5	1]×	1]×	NUM
ejpam-3407	61	6	r	r	NOUN
ejpam-3407	61	7	→	→	SYM
ejpam-3407	61	8	r	r	NOUN
ejpam-3407	61	9	satisfies	satisfie	NOUN
ejpam-3407	61	10	caratheodory	caratheodory	ADJ
ejpam-3407	61	11	conditions	condition	NOUN
ejpam-3407	61	12	;	;	PUNCT
ejpam-3407	61	13	(	(	PUNCT
ejpam-3407	61	14	c2	c2	PROPN
ejpam-3407	61	15	)	)	PUNCT
ejpam-3407	61	16	q(s	q(s	PROPN
ejpam-3407	61	17	,	,	PUNCT
ejpam-3407	61	18	z	z	NOUN
ejpam-3407	61	19	)	)	PUNCT
ejpam-3407	61	20	is	be	AUX
ejpam-3407	61	21	increasing	increase	VERB
ejpam-3407	61	22	with	with	ADP
ejpam-3407	61	23	respect	respect	NOUN
ejpam-3407	61	24	to	to	ADP
ejpam-3407	61	25	z	z	NOUN
ejpam-3407	61	26	for	for	ADP
ejpam-3407	61	27	each	each	DET
ejpam-3407	61	28	s	s	X
ejpam-3407	61	29	∈	∈	PROPN
ejpam-3407	62	1	[	[	X
ejpam-3407	62	2	0	0	NUM
ejpam-3407	62	3	,	,	PUNCT
ejpam-3407	62	4	1	1	NUM
ejpam-3407	62	5	]	]	PUNCT
ejpam-3407	62	6	;	;	PUNCT
ejpam-3407	62	7	(	(	PUNCT
ejpam-3407	62	8	c3	c3	NOUN
ejpam-3407	62	9	)	)	PUNCT
ejpam-3407	62	10	there	there	PRON
ejpam-3407	62	11	is	be	VERB
ejpam-3407	62	12	a	a	DET
ejpam-3407	62	13	constant	constant	ADJ
ejpam-3407	62	14	b	b	NOUN
ejpam-3407	62	15	>	>	X
ejpam-3407	62	16	0	0	PUNCT
ejpam-3407	63	1	so	so	SCONJ
ejpam-3407	63	2	that	that	SCONJ
ejpam-3407	63	3	0	0	NUM
ejpam-3407	63	4	≤	≤	NUM
ejpam-3407	63	5	q(s	q(s	NOUN
ejpam-3407	63	6	,	,	PUNCT
ejpam-3407	63	7	z1(s))−q(s	z1(s))−q(s	NUM
ejpam-3407	63	8	,	,	PUNCT
ejpam-3407	63	9	z2(s	z2(s	NOUN
ejpam-3407	63	10	)	)	PUNCT
ejpam-3407	63	11	≤	≤	NUM
ejpam-3407	63	12	b(z1	b(z1	NOUN
ejpam-3407	63	13	−	−	PROPN
ejpam-3407	63	14	z2	z2	PROPN
ejpam-3407	63	15	)	)	PUNCT
ejpam-3407	63	16	.	.	PUNCT
ejpam-3407	64	1	lemma	lemma	PROPN
ejpam-3407	64	2	2	2	NUM
ejpam-3407	64	3	.	.	PUNCT
ejpam-3407	65	1	[	[	X
ejpam-3407	65	2	32	32	NUM
ejpam-3407	65	3	]	]	PUNCT
ejpam-3407	65	4	let	let	VERB
ejpam-3407	65	5	p	p	PRON
ejpam-3407	65	6	>	>	X
ejpam-3407	65	7	0	0	PROPN
ejpam-3407	65	8	,	,	PUNCT
ejpam-3407	65	9	then	then	ADV
ejpam-3407	65	10	z	z	PROPN
ejpam-3407	65	11	(	(	PUNCT
ejpam-3407	65	12	s	s	X
ejpam-3407	65	13	)	)	PUNCT
ejpam-3407	65	14	=	=	PUNCT
ejpam-3407	65	15	⌊p⌋	⌊p⌋	PUNCT
ejpam-3407	65	16	∑	∑	PUNCT
ejpam-3407	65	17	i=0	i=0	PROPN
ejpam-3407	65	18	zi	zi	X
ejpam-3407	65	19	(	(	PUNCT
ejpam-3407	65	20	0	0	X
ejpam-3407	65	21	)	)	PUNCT
ejpam-3407	65	22	i	i	PRON
ejpam-3407	65	23	!	!	PUNCT
ejpam-3407	66	1	si	si	X
ejpam-3407	66	2	(	(	PUNCT
ejpam-3407	66	3	2	2	NUM
ejpam-3407	66	4	)	)	PUNCT
ejpam-3407	66	5	is	be	AUX
ejpam-3407	66	6	the	the	DET
ejpam-3407	66	7	solution	solution	NOUN
ejpam-3407	66	8	of	of	ADP
ejpam-3407	66	9	fractional	fractional	ADJ
ejpam-3407	66	10	differential	differential	NOUN
ejpam-3407	66	11	equation	equation	NOUN
ejpam-3407	66	12	cdpz	cdpz	NOUN
ejpam-3407	66	13	(	(	PUNCT
ejpam-3407	66	14	s	s	X
ejpam-3407	66	15	)	)	PUNCT
ejpam-3407	66	16	=	=	SYM
ejpam-3407	66	17	0	0	X
ejpam-3407	66	18	.	.	PUNCT
ejpam-3407	67	1	(	(	PUNCT
ejpam-3407	67	2	3	3	X
ejpam-3407	67	3	)	)	PUNCT
ejpam-3407	67	4	lemma	lemma	PROPN
ejpam-3407	67	5	3	3	NUM
ejpam-3407	67	6	.	.	PUNCT
ejpam-3407	68	1	[	[	X
ejpam-3407	68	2	32	32	NUM
ejpam-3407	68	3	]	]	PUNCT
ejpam-3407	68	4	let	let	VERB
ejpam-3407	68	5	p	p	PRON
ejpam-3407	68	6	>	>	X
ejpam-3407	68	7	0	0	NUM
ejpam-3407	68	8	,	,	PUNCT
ejpam-3407	68	9	then	then	ADV
ejpam-3407	68	10	in	in	ADP
ejpam-3407	68	11	view	view	NOUN
ejpam-3407	68	12	of	of	ADP
ejpam-3407	68	13	definition	definition	NOUN
ejpam-3407	68	14	24	24	NUM
ejpam-3407	68	15	and	and	CCONJ
ejpam-3407	68	16	lemma	lemma	PROPN
ejpam-3407	68	17	2	2	NUM
ejpam-3407	68	18	,	,	PUNCT
ejpam-3407	68	19	the	the	DET
ejpam-3407	68	20	solution	solution	NOUN
ejpam-3407	68	21	of	of	ADP
ejpam-3407	68	22	the	the	DET
ejpam-3407	68	23	solution	solution	NOUN
ejpam-3407	68	24	of	of	ADP
ejpam-3407	68	25	fractional	fractional	ADJ
ejpam-3407	68	26	differential	differential	NOUN
ejpam-3407	68	27	equation	equation	NOUN
ejpam-3407	68	28	cdpz	cdpz	NOUN
ejpam-3407	68	29	(	(	PUNCT
ejpam-3407	68	30	s	s	NOUN
ejpam-3407	68	31	)	)	PUNCT
ejpam-3407	68	32	=	=	SYM
ejpam-3407	68	33	y(s	y(s	PROPN
ejpam-3407	68	34	)	)	PUNCT
ejpam-3407	68	35	(	(	PUNCT
ejpam-3407	68	36	4	4	X
ejpam-3407	68	37	)	)	PUNCT
ejpam-3407	68	38	is	be	AUX
ejpam-3407	68	39	given	give	VERB
ejpam-3407	68	40	by	by	ADP
ejpam-3407	68	41	z	z	PROPN
ejpam-3407	68	42	(	(	PUNCT
ejpam-3407	68	43	s	s	NOUN
ejpam-3407	68	44	)	)	PUNCT
ejpam-3407	68	45	=	=	SYM
ejpam-3407	68	46	ipy(s	ipy(s	PROPN
ejpam-3407	68	47	)	)	PUNCT
ejpam-3407	68	48	+	+	NUM
ejpam-3407	68	49	⌊p⌋	⌊p⌋	NOUN
ejpam-3407	68	50	∑	∑	ADP
ejpam-3407	68	51	i=0	i=0	PROPN
ejpam-3407	68	52	zi	zi	X
ejpam-3407	68	53	(	(	PUNCT
ejpam-3407	68	54	0	0	X
ejpam-3407	68	55	)	)	PUNCT
ejpam-3407	68	56	i	i	PRON
ejpam-3407	68	57	!	!	PUNCT
ejpam-3407	69	1	si	si	AUX
ejpam-3407	69	2	.	.	PROPN
ejpam-3407	69	3	(	(	PUNCT
ejpam-3407	69	4	5	5	NUM
ejpam-3407	69	5	)	)	PUNCT
ejpam-3407	69	6	k.	k.	NOUN
ejpam-3407	69	7	shah	shah	PROPN
ejpam-3407	69	8	et	et	PROPN
ejpam-3407	69	9	al	al	PROPN
ejpam-3407	69	10	.	.	PUNCT
ejpam-3407	69	11	/	/	SYM
ejpam-3407	69	12	eur	eur	PROPN
ejpam-3407	69	13	.	.	PUNCT
ejpam-3407	70	1	j.	j.	PROPN
ejpam-3407	70	2	pure	pure	PROPN
ejpam-3407	70	3	appl	appl	PROPN
ejpam-3407	70	4	.	.	PROPN
ejpam-3407	70	5	math	math	PROPN
ejpam-3407	70	6	,	,	PUNCT
ejpam-3407	70	7	12	12	NUM
ejpam-3407	70	8	(	(	PUNCT
ejpam-3407	70	9	2	2	NUM
ejpam-3407	70	10	)	)	PUNCT
ejpam-3407	70	11	(	(	PUNCT
ejpam-3407	70	12	2019	2019	NUM
ejpam-3407	70	13	)	)	PUNCT
ejpam-3407	70	14	,	,	PUNCT
ejpam-3407	70	15	432	432	NUM
ejpam-3407	70	16	-	-	SYM
ejpam-3407	70	17	447	447	NUM
ejpam-3407	70	18	435	435	NUM
ejpam-3407	70	19	3	3	NUM
ejpam-3407	70	20	.	.	PUNCT
ejpam-3407	70	21	iterative	iterative	NOUN
ejpam-3407	70	22	solutions	solution	NOUN
ejpam-3407	70	23	this	this	DET
ejpam-3407	70	24	portion	portion	NOUN
ejpam-3407	70	25	of	of	ADP
ejpam-3407	70	26	the	the	DET
ejpam-3407	70	27	manuscript	manuscript	NOUN
ejpam-3407	70	28	is	be	AUX
ejpam-3407	70	29	devoted	devote	VERB
ejpam-3407	70	30	to	to	ADP
ejpam-3407	70	31	existence	existence	NOUN
ejpam-3407	70	32	and	and	CCONJ
ejpam-3407	70	33	uniqueness	uniqueness	NOUN
ejpam-3407	70	34	of	of	ADP
ejpam-3407	70	35	extremal	extremal	ADJ
ejpam-3407	70	36	solutions	solution	NOUN
ejpam-3407	70	37	to	to	ADP
ejpam-3407	70	38	the	the	DET
ejpam-3407	70	39	considered	consider	VERB
ejpam-3407	70	40	bvp	bvp	NOUN
ejpam-3407	70	41	of	of	ADP
ejpam-3407	70	42	the	the	DET
ejpam-3407	70	43	nonlinear	nonlinear	ADJ
ejpam-3407	70	44	fde	fde	PROPN
ejpam-3407	70	45	(	(	PUNCT
ejpam-3407	70	46	1	1	NUM
ejpam-3407	70	47	)	)	PUNCT
ejpam-3407	70	48	.	.	PUNCT
ejpam-3407	71	1	further	far	ADV
ejpam-3407	71	2	,	,	PUNCT
ejpam-3407	71	3	we	we	PRON
ejpam-3407	71	4	study	study	VERB
ejpam-3407	71	5	the	the	DET
ejpam-3407	71	6	iterative	iterative	NOUN
ejpam-3407	71	7	technique	technique	NOUN
ejpam-3407	71	8	coupled	couple	VERB
ejpam-3407	71	9	with	with	ADP
ejpam-3407	71	10	method	method	NOUN
ejpam-3407	71	11	of	of	ADP
ejpam-3407	71	12	the	the	DET
ejpam-3407	71	13	lower	low	ADJ
ejpam-3407	71	14	and	and	CCONJ
ejpam-3407	71	15	upper	upper	ADJ
ejpam-3407	71	16	solutions	solution	NOUN
ejpam-3407	71	17	for	for	ADP
ejpam-3407	71	18	the	the	DET
ejpam-3407	71	19	approximation	approximation	NOUN
ejpam-3407	71	20	and	and	CCONJ
ejpam-3407	71	21	error	error	NOUN
ejpam-3407	71	22	estimates	estimate	NOUN
ejpam-3407	71	23	to	to	ADP
ejpam-3407	71	24	the	the	DET
ejpam-3407	71	25	extremal	extremal	ADJ
ejpam-3407	71	26	solution	solution	NOUN
ejpam-3407	71	27	of	of	ADP
ejpam-3407	71	28	(	(	PUNCT
ejpam-3407	71	29	1	1	NUM
ejpam-3407	71	30	)	)	PUNCT
ejpam-3407	71	31	.	.	PUNCT
ejpam-3407	72	1	we	we	PRON
ejpam-3407	72	2	also	also	ADV
ejpam-3407	72	3	investigate	investigate	VERB
ejpam-3407	72	4	the	the	DET
ejpam-3407	72	5	various	various	ADJ
ejpam-3407	72	6	type	type	NOUN
ejpam-3407	72	7	stabilities	stability	NOUN
ejpam-3407	72	8	like	like	ADP
ejpam-3407	72	9	ulam	ulam	X
ejpam-3407	72	10	-	-	PUNCT
ejpam-3407	72	11	hyers	hyer	NOUN
ejpam-3407	72	12	stability	stability	NOUN
ejpam-3407	72	13	,	,	PUNCT
ejpam-3407	72	14	generalized	generalize	VERB
ejpam-3407	72	15	ulam	ulam	PROPN
ejpam-3407	72	16	-	-	PUNCT
ejpam-3407	72	17	hyers	hyer	NOUN
ejpam-3407	72	18	stability	stability	NOUN
ejpam-3407	72	19	,	,	PUNCT
ejpam-3407	72	20	ulam	ulam	PROPN
ejpam-3407	72	21	-	-	PUNCT
ejpam-3407	72	22	hyers	hyer	NOUN
ejpam-3407	72	23	-	-	PUNCT
ejpam-3407	72	24	rassias	rassias	PROPN
ejpam-3407	72	25	stability	stability	NOUN
ejpam-3407	72	26	and	and	CCONJ
ejpam-3407	72	27	generalized	generalize	VERB
ejpam-3407	72	28	ulam	ulam	PROPN
ejpam-3407	72	29	-	-	PUNCT
ejpam-3407	72	30	hyers	hyer	NOUN
ejpam-3407	72	31	-	-	PUNCT
ejpam-3407	72	32	rassias	rassias	PROPN
ejpam-3407	72	33	stability	stability	NOUN
ejpam-3407	72	34	for	for	ADP
ejpam-3407	72	35	the	the	DET
ejpam-3407	72	36	considered	consider	VERB
ejpam-3407	72	37	bvp	bvp	NOUN
ejpam-3407	72	38	.	.	PUNCT
ejpam-3407	73	1	first	first	ADV
ejpam-3407	73	2	,	,	PUNCT
ejpam-3407	73	3	we	we	PRON
ejpam-3407	73	4	convert	convert	VERB
ejpam-3407	73	5	our	our	PRON
ejpam-3407	73	6	considered	consider	VERB
ejpam-3407	73	7	problem	problem	NOUN
ejpam-3407	73	8	into	into	ADP
ejpam-3407	73	9	the	the	DET
ejpam-3407	73	10	integral	integral	ADJ
ejpam-3407	73	11	equation	equation	NOUN
ejpam-3407	73	12	.	.	PUNCT
ejpam-3407	74	1	lemma	lemma	PROPN
ejpam-3407	74	2	4	4	X
ejpam-3407	74	3	.	.	PUNCT
ejpam-3407	75	1	if	if	SCONJ
ejpam-3407	75	2	q	q	PROPN
ejpam-3407	75	3	∈	∈	PROPN
ejpam-3407	75	4	c[0	c[0	PROPN
ejpam-3407	75	5	,	,	PUNCT
ejpam-3407	75	6	1	1	NUM
ejpam-3407	75	7	]	]	PUNCT
ejpam-3407	75	8	,	,	PUNCT
ejpam-3407	75	9	then	then	ADV
ejpam-3407	75	10	the	the	DET
ejpam-3407	75	11	linear	linear	ADJ
ejpam-3407	75	12	problem	problem	NOUN
ejpam-3407	75	13	cdpz(s	cdpz(s	NOUN
ejpam-3407	75	14	)	)	PUNCT
ejpam-3407	76	1	+	+	NOUN
ejpam-3407	76	2	q(s	q(s	X
ejpam-3407	76	3	)	)	PUNCT
ejpam-3407	76	4	=	=	SYM
ejpam-3407	76	5	0	0	NUM
ejpam-3407	76	6	,	,	PUNCT
ejpam-3407	76	7	s	s	VERB
ejpam-3407	76	8	∈	∈	PROPN
ejpam-3407	77	1	[	[	X
ejpam-3407	77	2	0	0	NUM
ejpam-3407	77	3	,	,	PUNCT
ejpam-3407	77	4	1	1	NUM
ejpam-3407	77	5	]	]	PUNCT
ejpam-3407	77	6	,	,	PUNCT
ejpam-3407	77	7	2	2	NUM
ejpam-3407	77	8	<	<	X
ejpam-3407	77	9	p	p	X
ejpam-3407	77	10	≤	≤	NOUN
ejpam-3407	77	11	3	3	NUM
ejpam-3407	77	12	,	,	PUNCT
ejpam-3407	77	13	z(0	z(0	X
ejpam-3407	77	14	)	)	PUNCT
ejpam-3407	77	15	=	=	PUNCT
ejpam-3407	77	16	z′′(s)|s=0	z′′(s)|s=0	X
ejpam-3407	77	17	=	=	SYM
ejpam-3407	77	18	0	0	NUM
ejpam-3407	77	19	,	,	PUNCT
ejpam-3407	77	20	z(1	z(1	PROPN
ejpam-3407	77	21	)	)	PUNCT
ejpam-3407	77	22	=	=	PUNCT
ejpam-3407	77	23	δ	δ	X
ejpam-3407	77	24	∫	∫	PROPN
ejpam-3407	77	25	1	1	NUM
ejpam-3407	77	26	0	0	NUM
ejpam-3407	77	27	z(s)ds	z(s)ds	NOUN
ejpam-3407	77	28	.	.	PUNCT
ejpam-3407	78	1	(	(	PUNCT
ejpam-3407	78	2	6	6	NUM
ejpam-3407	78	3	)	)	PUNCT
ejpam-3407	78	4	has	have	VERB
ejpam-3407	78	5	a	a	DET
ejpam-3407	78	6	solution	solution	NOUN
ejpam-3407	78	7	defined	define	VERB
ejpam-3407	78	8	by	by	ADP
ejpam-3407	78	9	z(s	z(s	PROPN
ejpam-3407	78	10	)	)	PUNCT
ejpam-3407	79	1	=	=	PUNCT
ejpam-3407	79	2	∫	∫	PROPN
ejpam-3407	79	3	1	1	NUM
ejpam-3407	79	4	0	0	NUM
ejpam-3407	79	5	r(t	r(t	NOUN
ejpam-3407	79	6	,	,	PUNCT
ejpam-3407	79	7	γ)q(γ)dγ	γ)q(γ)dγ	NOUN
ejpam-3407	79	8	,	,	PUNCT
ejpam-3407	79	9	(	(	PUNCT
ejpam-3407	79	10	7	7	X
ejpam-3407	79	11	)	)	PUNCT
ejpam-3407	79	12	where	where	SCONJ
ejpam-3407	79	13	r(s	r(s	PROPN
ejpam-3407	79	14	,	,	PUNCT
ejpam-3407	79	15	γ	γ	NOUN
ejpam-3407	79	16	)	)	PUNCT
ejpam-3407	79	17	is	be	AUX
ejpam-3407	79	18	defined	define	VERB
ejpam-3407	79	19	by	by	ADP
ejpam-3407	79	20	r	r	NOUN
ejpam-3407	79	21	(	(	PUNCT
ejpam-3407	79	22	s	s	PROPN
ejpam-3407	79	23	,	,	PUNCT
ejpam-3407	79	24	γ	γ	NOUN
ejpam-3407	79	25	)	)	PUNCT
ejpam-3407	79	26	=	=	SYM
ejpam-3407	79	27	1	1	NUM
ejpam-3407	79	28	(	(	PUNCT
ejpam-3407	79	29	2−	2−	NUM
ejpam-3407	79	30	δ	δ	NOUN
ejpam-3407	79	31	)	)	PUNCT
ejpam-3407	79	32	γ	γ	PROPN
ejpam-3407	79	33	(	(	PUNCT
ejpam-3407	79	34	p+	p+	NOUN
ejpam-3407	79	35	1	1	NUM
ejpam-3407	79	36	)	)	PUNCT
ejpam-3407	79	37	{	{	PUNCT
ejpam-3407	79	38	2s(1−	2s(1−	NUM
ejpam-3407	79	39	γ)p−1	γ)p−1	NOUN
ejpam-3407	79	40	(	(	PUNCT
ejpam-3407	79	41	p−	p−	NOUN
ejpam-3407	79	42	δ	δ	NOUN
ejpam-3407	79	43	+	+	X
ejpam-3407	79	44	δγ)−	δγ)−	X
ejpam-3407	79	45	(	(	PUNCT
ejpam-3407	79	46	2−	2−	NUM
ejpam-3407	79	47	δ	δ	NOUN
ejpam-3407	79	48	)	)	PUNCT
ejpam-3407	79	49	p(s−	p(s−	PROPN
ejpam-3407	79	50	γ)p−1	γ)p−1	NOUN
ejpam-3407	79	51	,	,	PUNCT
ejpam-3407	79	52	0	0	NUM
ejpam-3407	79	53	≤	≤	NUM
ejpam-3407	79	54	γ	γ	X
ejpam-3407	79	55	≤	≤	PROPN
ejpam-3407	79	56	s	s	PART
ejpam-3407	79	57	≤	≤	NUM
ejpam-3407	79	58	1	1	NUM
ejpam-3407	79	59	,	,	PUNCT
ejpam-3407	79	60	2s(1−	2s(1−	NUM
ejpam-3407	79	61	γ)p−1	γ)p−1	NOUN
ejpam-3407	79	62	(	(	PUNCT
ejpam-3407	79	63	p−	p−	NOUN
ejpam-3407	79	64	δ	δ	NOUN
ejpam-3407	79	65	+	+	CCONJ
ejpam-3407	79	66	δγ	δγ	PROPN
ejpam-3407	79	67	)	)	PUNCT
ejpam-3407	79	68	,	,	PUNCT
ejpam-3407	79	69	0	0	NUM
ejpam-3407	80	1	≤	≤	NUM
ejpam-3407	80	2	s	s	PART
ejpam-3407	80	3	≤	≤	NUM
ejpam-3407	80	4	γ	γ	X
ejpam-3407	80	5	≤	≤	NOUN
ejpam-3407	80	6	1	1	NUM
ejpam-3407	80	7	.	.	PUNCT
ejpam-3407	81	1	(	(	PUNCT
ejpam-3407	81	2	8)	8)	NUM
ejpam-3407	81	3	proof	proof	NOUN
ejpam-3407	81	4	.	.	PUNCT
ejpam-3407	82	1	we	we	PRON
ejpam-3407	82	2	may	may	AUX
ejpam-3407	82	3	apply	apply	VERB
ejpam-3407	82	4	a	a	DET
ejpam-3407	82	5	well	well	ADV
ejpam-3407	82	6	known	know	VERB
ejpam-3407	82	7	lemma	lemma	PROPN
ejpam-3407	82	8	3	3	NUM
ejpam-3407	82	9	to	to	PART
ejpam-3407	82	10	reduce	reduce	VERB
ejpam-3407	82	11	the	the	DET
ejpam-3407	82	12	equation	equation	NOUN
ejpam-3407	82	13	(	(	PUNCT
ejpam-3407	82	14	6	6	NUM
ejpam-3407	82	15	)	)	PUNCT
ejpam-3407	82	16	to	to	PART
ejpam-3407	82	17	equivalent	equivalent	ADJ
ejpam-3407	82	18	integral	integral	ADJ
ejpam-3407	82	19	form	form	NOUN
ejpam-3407	82	20	z	z	NOUN
ejpam-3407	82	21	(	(	PUNCT
ejpam-3407	82	22	s	s	NOUN
ejpam-3407	82	23	)	)	PUNCT
ejpam-3407	82	24	=	=	SYM
ejpam-3407	82	25	−ipq	−ipq	NOUN
ejpam-3407	82	26	(	(	PUNCT
ejpam-3407	82	27	s	s	X
ejpam-3407	82	28	)	)	PUNCT
ejpam-3407	82	29	+	+	CCONJ
ejpam-3407	82	30	2	2	NUM
ejpam-3407	82	31	∑	∑	NOUN
ejpam-3407	82	32	i=0	i=0	PROPN
ejpam-3407	82	33	z(i	z(i	PROPN
ejpam-3407	82	34	)	)	PUNCT
ejpam-3407	82	35	(	(	PUNCT
ejpam-3407	82	36	0	0	X
ejpam-3407	82	37	)	)	PUNCT
ejpam-3407	82	38	i	i	PRON
ejpam-3407	82	39	!	!	PUNCT
ejpam-3407	83	1	si	si	X
ejpam-3407	83	2	=	=	PUNCT
ejpam-3407	83	3	−	−	PROPN
ejpam-3407	83	4	s	s	PART
ejpam-3407	83	5	∫	∫	PROPN
ejpam-3407	83	6	0	0	PUNCT
ejpam-3407	84	1	(	(	PUNCT
ejpam-3407	84	2	s−	s−	PROPN
ejpam-3407	84	3	γ)p−1	γ)p−1	ADP
ejpam-3407	84	4	γ	γ	X
ejpam-3407	84	5	(	(	PUNCT
ejpam-3407	84	6	p	p	NOUN
ejpam-3407	84	7	)	)	PUNCT
ejpam-3407	84	8	q	q	NOUN
ejpam-3407	84	9	(	(	PUNCT
ejpam-3407	84	10	γ	γ	NOUN
ejpam-3407	84	11	)	)	PUNCT
ejpam-3407	84	12	dγ	dγ	ADP
ejpam-3407	84	13	+	+	NOUN
ejpam-3407	84	14	2	2	NUM
ejpam-3407	84	15	∑	∑	NOUN
ejpam-3407	84	16	i=0	i=0	PROPN
ejpam-3407	84	17	z(i	z(i	PROPN
ejpam-3407	84	18	)	)	PUNCT
ejpam-3407	84	19	(	(	PUNCT
ejpam-3407	84	20	0	0	X
ejpam-3407	84	21	)	)	PUNCT
ejpam-3407	84	22	i	i	PRON
ejpam-3407	84	23	!	!	PUNCT
ejpam-3407	85	1	si	si	AUX
ejpam-3407	85	2	.	.	PROPN
ejpam-3407	85	3	(	(	PUNCT
ejpam-3407	85	4	9	9	NUM
ejpam-3407	85	5	)	)	PUNCT
ejpam-3407	85	6	by	by	ADP
ejpam-3407	85	7	considering	consider	VERB
ejpam-3407	85	8	the	the	DET
ejpam-3407	85	9	given	give	VERB
ejpam-3407	85	10	conditions	condition	NOUN
ejpam-3407	85	11	z(0	z(0	NOUN
ejpam-3407	85	12	)	)	PUNCT
ejpam-3407	85	13	=	=	SYM
ejpam-3407	85	14	z	z	PROPN
ejpam-3407	85	15	′′	′′	PROPN
ejpam-3407	85	16	(	(	PUNCT
ejpam-3407	85	17	0	0	NUM
ejpam-3407	85	18	)	)	PUNCT
ejpam-3407	85	19	=	=	SYM
ejpam-3407	85	20	0	0	NUM
ejpam-3407	85	21	,	,	PUNCT
ejpam-3407	85	22	z	z	NOUN
ejpam-3407	85	23	(	(	PUNCT
ejpam-3407	85	24	1	1	NUM
ejpam-3407	85	25	)	)	PUNCT
ejpam-3407	85	26	=	=	SYM
ejpam-3407	85	27	δ	δ	PROPN
ejpam-3407	85	28	1	1	NUM
ejpam-3407	85	29	∫	∫	NOUN
ejpam-3407	85	30	0	0	PUNCT
ejpam-3407	85	31	z	z	NOUN
ejpam-3407	85	32	(	(	PUNCT
ejpam-3407	85	33	s	s	X
ejpam-3407	85	34	)	)	PUNCT
ejpam-3407	85	35	ds	ds	NOUN
ejpam-3407	85	36	,	,	PUNCT
ejpam-3407	85	37	we	we	PRON
ejpam-3407	85	38	can	can	AUX
ejpam-3407	85	39	obtain	obtain	VERB
ejpam-3407	85	40	that	that	DET
ejpam-3407	85	41	z	z	NOUN
ejpam-3407	85	42	(	(	PUNCT
ejpam-3407	85	43	s	s	X
ejpam-3407	85	44	)	)	PUNCT
ejpam-3407	85	45	=	=	SYM
ejpam-3407	86	1	−	−	PROPN
ejpam-3407	86	2	s	s	PART
ejpam-3407	86	3	∫	∫	PROPN
ejpam-3407	86	4	0	0	PUNCT
ejpam-3407	87	1	(	(	PUNCT
ejpam-3407	87	2	s−	s−	PROPN
ejpam-3407	87	3	γ)p−1	γ)p−1	ADP
ejpam-3407	87	4	γ	γ	X
ejpam-3407	87	5	(	(	PUNCT
ejpam-3407	87	6	p	p	NOUN
ejpam-3407	87	7	)	)	PUNCT
ejpam-3407	87	8	q	q	NOUN
ejpam-3407	87	9	(	(	PUNCT
ejpam-3407	87	10	γ	γ	NOUN
ejpam-3407	87	11	)	)	PUNCT
ejpam-3407	87	12	dγ	dγ	ADP
ejpam-3407	88	1	+	+	SYM
ejpam-3407	88	2	s	s	PART
ejpam-3407	88	3	1	1	NUM
ejpam-3407	88	4	∫	∫	NOUN
ejpam-3407	88	5	0	0	NUM
ejpam-3407	89	1	(	(	PUNCT
ejpam-3407	89	2	1−	1−	NUM
ejpam-3407	89	3	γ)p−1	γ)p−1	PROPN
ejpam-3407	89	4	γ	γ	X
ejpam-3407	89	5	(	(	PUNCT
ejpam-3407	89	6	p	p	NOUN
ejpam-3407	89	7	)	)	PUNCT
ejpam-3407	89	8	q	q	NOUN
ejpam-3407	89	9	(	(	PUNCT
ejpam-3407	89	10	γ	γ	NOUN
ejpam-3407	89	11	)	)	PUNCT
ejpam-3407	89	12	dγ	dγ	ADP
ejpam-3407	90	1	+	+	CCONJ
ejpam-3407	90	2	tδ	tδ	PROPN
ejpam-3407	90	3	1	1	NUM
ejpam-3407	90	4	∫	∫	NOUN
ejpam-3407	90	5	0	0	PUNCT
ejpam-3407	91	1	z	z	NOUN
ejpam-3407	91	2	(	(	PUNCT
ejpam-3407	91	3	s)ds	s)ds	PROPN
ejpam-3407	91	4	.	.	PUNCT
ejpam-3407	92	1	(	(	PUNCT
ejpam-3407	92	2	10	10	NUM
ejpam-3407	92	3	)	)	PUNCT
ejpam-3407	92	4	k.	k.	NOUN
ejpam-3407	92	5	shah	shah	PROPN
ejpam-3407	92	6	et	et	PROPN
ejpam-3407	92	7	al	al	PROPN
ejpam-3407	92	8	.	.	PUNCT
ejpam-3407	92	9	/	/	SYM
ejpam-3407	92	10	eur	eur	PROPN
ejpam-3407	92	11	.	.	PUNCT
ejpam-3407	93	1	j.	j.	PROPN
ejpam-3407	93	2	pure	pure	PROPN
ejpam-3407	93	3	appl	appl	PROPN
ejpam-3407	93	4	.	.	PROPN
ejpam-3407	93	5	math	math	PROPN
ejpam-3407	93	6	,	,	PUNCT
ejpam-3407	93	7	12	12	NUM
ejpam-3407	93	8	(	(	PUNCT
ejpam-3407	93	9	2	2	NUM
ejpam-3407	93	10	)	)	PUNCT
ejpam-3407	93	11	(	(	PUNCT
ejpam-3407	93	12	2019	2019	NUM
ejpam-3407	93	13	)	)	PUNCT
ejpam-3407	93	14	,	,	PUNCT
ejpam-3407	93	15	432	432	NUM
ejpam-3407	93	16	-	-	SYM
ejpam-3407	93	17	447	447	NUM
ejpam-3407	93	18	436	436	NUM
ejpam-3407	93	19	let	let	AUX
ejpam-3407	93	20	say	say	VERB
ejpam-3407	93	21	a	a	DET
ejpam-3407	93	22	=	=	SYM
ejpam-3407	93	23	1	1	NUM
ejpam-3407	93	24	∫	∫	NOUN
ejpam-3407	93	25	0	0	PUNCT
ejpam-3407	93	26	z	z	NOUN
ejpam-3407	93	27	(	(	PUNCT
ejpam-3407	93	28	s)ds	s)ds	PROPN
ejpam-3407	93	29	a	a	X
ejpam-3407	93	30	=	=	SYM
ejpam-3407	93	31	−	−	PROPN
ejpam-3407	93	32	1	1	NUM
ejpam-3407	93	33	∫	∫	NOUN
ejpam-3407	93	34	0	0	NUM
ejpam-3407	93	35	s	s	PART
ejpam-3407	93	36	∫	∫	PROPN
ejpam-3407	93	37	0	0	PUNCT
ejpam-3407	94	1	(	(	PUNCT
ejpam-3407	94	2	s−	s−	PROPN
ejpam-3407	94	3	γ)p−1	γ)p−1	ADP
ejpam-3407	94	4	γ	γ	X
ejpam-3407	94	5	(	(	PUNCT
ejpam-3407	94	6	p	p	NOUN
ejpam-3407	94	7	)	)	PUNCT
ejpam-3407	94	8	q	q	NOUN
ejpam-3407	94	9	(	(	PUNCT
ejpam-3407	94	10	γ	γ	NOUN
ejpam-3407	94	11	)	)	PUNCT
ejpam-3407	94	12	dγds+	dγds+	X
ejpam-3407	94	13	1	1	NUM
ejpam-3407	94	14	∫	∫	NOUN
ejpam-3407	94	15	0	0	NUM
ejpam-3407	94	16	1	1	NUM
ejpam-3407	94	17	∫	∫	NOUN
ejpam-3407	94	18	0	0	NUM
ejpam-3407	94	19	s	s	PROPN
ejpam-3407	94	20	(	(	PUNCT
ejpam-3407	94	21	1−	1−	NUM
ejpam-3407	94	22	γ)p−1	γ)p−1	PROPN
ejpam-3407	94	23	γ	γ	X
ejpam-3407	94	24	(	(	PUNCT
ejpam-3407	94	25	p	p	NOUN
ejpam-3407	94	26	)	)	PUNCT
ejpam-3407	94	27	q	q	NOUN
ejpam-3407	94	28	(	(	PUNCT
ejpam-3407	94	29	γ	γ	X
ejpam-3407	94	30	)	)	PUNCT
ejpam-3407	94	31	dγds+	dγds+	X
ejpam-3407	94	32	δa	δa	PROPN
ejpam-3407	94	33	1	1	NUM
ejpam-3407	94	34	∫	∫	NOUN
ejpam-3407	94	35	0	0	PROPN
ejpam-3407	95	1	sds	sds	PROPN
ejpam-3407	95	2	a	a	X
ejpam-3407	95	3	=	=	SYM
ejpam-3407	95	4	−	−	PROPN
ejpam-3407	95	5	2	2	NUM
ejpam-3407	95	6	(	(	PUNCT
ejpam-3407	95	7	2−	2−	NUM
ejpam-3407	95	8	δ	δ	NOUN
ejpam-3407	95	9	)	)	PUNCT
ejpam-3407	95	10	1	1	NUM
ejpam-3407	95	11	∫	∫	NOUN
ejpam-3407	95	12	0	0	NUM
ejpam-3407	96	1	(	(	PUNCT
ejpam-3407	96	2	1−	1−	NUM
ejpam-3407	96	3	γ)p	γ)p	NOUN
ejpam-3407	96	4	pγ	pγ	PROPN
ejpam-3407	96	5	(	(	PUNCT
ejpam-3407	96	6	p	p	NOUN
ejpam-3407	96	7	)	)	PUNCT
ejpam-3407	96	8	q	q	NOUN
ejpam-3407	96	9	(	(	PUNCT
ejpam-3407	96	10	γ	γ	NOUN
ejpam-3407	96	11	)	)	PUNCT
ejpam-3407	96	12	dγ	dγ	ADP
ejpam-3407	96	13	+	+	NOUN
ejpam-3407	96	14	1	1	NUM
ejpam-3407	96	15	(	(	PUNCT
ejpam-3407	96	16	2−	2−	NUM
ejpam-3407	96	17	δ	δ	NOUN
ejpam-3407	96	18	)	)	PUNCT
ejpam-3407	96	19	1	1	NUM
ejpam-3407	96	20	∫	∫	NOUN
ejpam-3407	96	21	0	0	NUM
ejpam-3407	97	1	(	(	PUNCT
ejpam-3407	97	2	1−	1−	NUM
ejpam-3407	97	3	γ)p−1	γ)p−1	PROPN
ejpam-3407	97	4	γ	γ	X
ejpam-3407	97	5	(	(	PUNCT
ejpam-3407	97	6	p	p	NOUN
ejpam-3407	97	7	)	)	PUNCT
ejpam-3407	97	8	q	q	NOUN
ejpam-3407	97	9	(	(	PUNCT
ejpam-3407	97	10	γ	γ	NOUN
ejpam-3407	97	11	)	)	PUNCT
ejpam-3407	97	12	dγ	dγ	PROPN
ejpam-3407	97	13	.	.	PUNCT
ejpam-3407	98	1	then	then	ADV
ejpam-3407	98	2	equation	equation	NOUN
ejpam-3407	98	3	(	(	PUNCT
ejpam-3407	98	4	3.5	3.5	NUM
ejpam-3407	98	5	)	)	PUNCT
ejpam-3407	98	6	implies	imply	VERB
ejpam-3407	98	7	z	z	NOUN
ejpam-3407	98	8	(	(	PUNCT
ejpam-3407	98	9	s	s	X
ejpam-3407	98	10	)	)	PUNCT
ejpam-3407	98	11	=	=	SYM
ejpam-3407	99	1	−	−	PROPN
ejpam-3407	99	2	s	s	PART
ejpam-3407	99	3	∫	∫	PROPN
ejpam-3407	99	4	0	0	PUNCT
ejpam-3407	100	1	(	(	PUNCT
ejpam-3407	100	2	s−γ)p−1	s−γ)p−1	PROPN
ejpam-3407	100	3	γ(p	γ(p	PROPN
ejpam-3407	100	4	)	)	PUNCT
ejpam-3407	100	5	q	q	NOUN
ejpam-3407	100	6	(	(	PUNCT
ejpam-3407	100	7	γ	γ	NOUN
ejpam-3407	100	8	)	)	PUNCT
ejpam-3407	100	9	dγ	dγ	ADP
ejpam-3407	101	1	+	+	NOUN
ejpam-3407	101	2	1	1	NUM
ejpam-3407	101	3	∫	∫	NOUN
ejpam-3407	101	4	0	0	NUM
ejpam-3407	101	5	s(1−γ)p−1	s(1−γ)p−1	PROPN
ejpam-3407	101	6	γ(p	γ(p	PROPN
ejpam-3407	101	7	)	)	PUNCT
ejpam-3407	101	8	q	q	NOUN
ejpam-3407	101	9	(	(	PUNCT
ejpam-3407	101	10	γ	γ	NOUN
ejpam-3407	101	11	)	)	PUNCT
ejpam-3407	101	12	dγ	dγ	ADP
ejpam-3407	101	13	−	−	PROPN
ejpam-3407	101	14	2δ	2δ	NUM
ejpam-3407	101	15	(	(	PUNCT
ejpam-3407	101	16	2−δ	2−δ	NUM
ejpam-3407	101	17	)	)	PUNCT
ejpam-3407	101	18	1	1	NUM
ejpam-3407	101	19	∫	∫	NOUN
ejpam-3407	101	20	0	0	NUM
ejpam-3407	102	1	s(1−γ)p	s(1−γ)p	DET
ejpam-3407	102	2	pγ(p	pγ(p	PROPN
ejpam-3407	102	3	)	)	PUNCT
ejpam-3407	102	4	q	q	NOUN
ejpam-3407	102	5	(	(	PUNCT
ejpam-3407	102	6	γ	γ	NOUN
ejpam-3407	102	7	)	)	PUNCT
ejpam-3407	102	8	dγ	dγ	ADP
ejpam-3407	102	9	+	+	PROPN
ejpam-3407	102	10	δ	δ	PROPN
ejpam-3407	102	11	(	(	PUNCT
ejpam-3407	102	12	2−δ	2−δ	NUM
ejpam-3407	102	13	)	)	PUNCT
ejpam-3407	102	14	1	1	NUM
ejpam-3407	102	15	∫	∫	NOUN
ejpam-3407	102	16	0	0	SYM
ejpam-3407	102	17	t	t	PROPN
ejpam-3407	102	18	(	(	PUNCT
ejpam-3407	102	19	1−γ)p−1	1−γ)p−1	PROPN
ejpam-3407	102	20	γ(p	γ(p	NOUN
ejpam-3407	102	21	)	)	PUNCT
ejpam-3407	102	22	q	q	NOUN
ejpam-3407	102	23	(	(	PUNCT
ejpam-3407	102	24	γ	γ	NOUN
ejpam-3407	102	25	)	)	PUNCT
ejpam-3407	102	26	dγ	dγ	NOUN
ejpam-3407	102	27	.	.	PUNCT
ejpam-3407	103	1	z	z	NOUN
ejpam-3407	103	2	(	(	PUNCT
ejpam-3407	103	3	s	s	X
ejpam-3407	103	4	)	)	PUNCT
ejpam-3407	103	5	=	=	SYM
ejpam-3407	103	6	1	1	NUM
ejpam-3407	103	7	∫	∫	NOUN
ejpam-3407	103	8	0	0	NUM
ejpam-3407	104	1	k	k	X
ejpam-3407	104	2	(	(	PUNCT
ejpam-3407	104	3	s	s	PROPN
ejpam-3407	104	4	,	,	PUNCT
ejpam-3407	104	5	γ)q	γ)q	X
ejpam-3407	104	6	(	(	PUNCT
ejpam-3407	104	7	γ	γ	X
ejpam-3407	104	8	)	)	PUNCT
ejpam-3407	104	9	dγ	dγ	PROPN
ejpam-3407	104	10	.	.	PUNCT
ejpam-3407	105	1	clearly	clearly	ADV
ejpam-3407	105	2	,	,	PUNCT
ejpam-3407	105	3	for	for	ADP
ejpam-3407	105	4	all	all	DET
ejpam-3407	105	5	s	s	PROPN
ejpam-3407	105	6	,	,	PUNCT
ejpam-3407	105	7	γ	γ	X
ejpam-3407	105	8	∈	∈	PROPN
ejpam-3407	106	1	[	[	X
ejpam-3407	106	2	0	0	NUM
ejpam-3407	106	3	,	,	PUNCT
ejpam-3407	106	4	1	1	NUM
ejpam-3407	106	5	]	]	PUNCT
ejpam-3407	106	6	,	,	PUNCT
ejpam-3407	106	7	we	we	PRON
ejpam-3407	106	8	have	have	VERB
ejpam-3407	106	9	r(s	r(s	PROPN
ejpam-3407	106	10	,	,	PUNCT
ejpam-3407	106	11	γ	γ	NOUN
ejpam-3407	106	12	)	)	PUNCT
ejpam-3407	106	13	≥	≥	NOUN
ejpam-3407	106	14	0	0	NUM
ejpam-3407	106	15	.	.	PUNCT
ejpam-3407	107	1	lemma	lemma	PROPN
ejpam-3407	107	2	5	5	NUM
ejpam-3407	107	3	.	.	PUNCT
ejpam-3407	108	1	if	if	SCONJ
ejpam-3407	108	2	we	we	PRON
ejpam-3407	108	3	consider	consider	VERB
ejpam-3407	108	4	the	the	DET
ejpam-3407	108	5	lemma	lemma	PROPN
ejpam-3407	108	6	4	4	NUM
ejpam-3407	108	7	and	and	CCONJ
ejpam-3407	108	8	condition	condition	NOUN
ejpam-3407	108	9	(	(	PUNCT
ejpam-3407	108	10	c1	c1	PROPN
ejpam-3407	108	11	)	)	PUNCT
ejpam-3407	108	12	with	with	ADP
ejpam-3407	108	13	q	q	PROPN
ejpam-3407	108	14	∈	∈	PROPN
ejpam-3407	108	15	c([0	c([0	NOUN
ejpam-3407	108	16	,	,	PUNCT
ejpam-3407	108	17	1],r	1],r	NUM
ejpam-3407	108	18	)	)	PUNCT
ejpam-3407	108	19	,	,	PUNCT
ejpam-3407	108	20	then	then	ADV
ejpam-3407	108	21	we	we	PRON
ejpam-3407	108	22	see	see	VERB
ejpam-3407	108	23	that	that	SCONJ
ejpam-3407	108	24	the	the	DET
ejpam-3407	108	25	integral	integral	ADJ
ejpam-3407	108	26	equation	equation	NOUN
ejpam-3407	108	27	z(s	z(s	NOUN
ejpam-3407	108	28	)	)	PUNCT
ejpam-3407	108	29	=	=	PUNCT
ejpam-3407	109	1	∫	∫	PROPN
ejpam-3407	109	2	1	1	NUM
ejpam-3407	109	3	0	0	NUM
ejpam-3407	109	4	r(s	r(s	PROPN
ejpam-3407	109	5	,	,	PUNCT
ejpam-3407	109	6	γ)q(γ)dγ	γ)q(γ)dγ	NOUN
ejpam-3407	109	7	,	,	PUNCT
ejpam-3407	109	8	(	(	PUNCT
ejpam-3407	109	9	11	11	NUM
ejpam-3407	109	10	)	)	PUNCT
ejpam-3407	109	11	is	be	AUX
ejpam-3407	109	12	the	the	DET
ejpam-3407	109	13	solution	solution	NOUN
ejpam-3407	109	14	of	of	ADP
ejpam-3407	109	15	problem	problem	NOUN
ejpam-3407	109	16	(	(	PUNCT
ejpam-3407	109	17	1	1	NUM
ejpam-3407	109	18	)	)	PUNCT
ejpam-3407	109	19	,	,	PUNCT
ejpam-3407	109	20	where	where	SCONJ
ejpam-3407	109	21	r(s	r(s	PROPN
ejpam-3407	109	22	,	,	PUNCT
ejpam-3407	109	23	γ	γ	NOUN
ejpam-3407	109	24	)	)	PUNCT
ejpam-3407	109	25	is	be	AUX
ejpam-3407	109	26	provided	provide	VERB
ejpam-3407	109	27	in	in	ADP
ejpam-3407	109	28	the	the	DET
ejpam-3407	109	29	equation	equation	NOUN
ejpam-3407	109	30	(	(	PUNCT
ejpam-3407	109	31	8)	8)	NUM
ejpam-3407	109	32	.	.	PUNCT
ejpam-3407	110	1	lemma	lemma	PROPN
ejpam-3407	110	2	6	6	NUM
ejpam-3407	110	3	.	.	PUNCT
ejpam-3407	111	1	for	for	ADP
ejpam-3407	111	2	green	green	PROPN
ejpam-3407	111	3	’s	’s	PART
ejpam-3407	111	4	function	function	PROPN
ejpam-3407	111	5	r(s	r(s	PROPN
ejpam-3407	111	6	,	,	PUNCT
ejpam-3407	111	7	γ	γ	NOUN
ejpam-3407	111	8	)	)	PUNCT
ejpam-3407	111	9	,	,	PUNCT
ejpam-3407	111	10	we	we	PRON
ejpam-3407	111	11	have	have	VERB
ejpam-3407	111	12	that	that	DET
ejpam-3407	111	13	max	max	PROPN
ejpam-3407	111	14	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	111	15	]	]	PUNCT
ejpam-3407	111	16	∫	∫	PROPN
ejpam-3407	112	1	1	1	NUM
ejpam-3407	112	2	0	0	NUM
ejpam-3407	112	3	r(s	r(s	PROPN
ejpam-3407	112	4	,	,	PUNCT
ejpam-3407	112	5	γ)dγ	γ)dγ	PROPN
ejpam-3407	112	6	≤	≤	NOUN
ejpam-3407	112	7	2	2	NUM
ejpam-3407	112	8	(	(	PUNCT
ejpam-3407	112	9	2−	2−	NUM
ejpam-3407	112	10	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	112	11	)	)	PUNCT
ejpam-3407	112	12	,	,	PUNCT
ejpam-3407	112	13	s	s	VERB
ejpam-3407	112	14	∈	∈	PROPN
ejpam-3407	113	1	[	[	X
ejpam-3407	113	2	0	0	NUM
ejpam-3407	113	3	,	,	PUNCT
ejpam-3407	113	4	1	1	NUM
ejpam-3407	113	5	]	]	PUNCT
ejpam-3407	113	6	.	.	PUNCT
ejpam-3407	114	1	proof	proof	NOUN
ejpam-3407	114	2	.	.	PUNCT
ejpam-3407	115	1	since	since	SCONJ
ejpam-3407	115	2	r(s	r(s	PROPN
ejpam-3407	115	3	,	,	PUNCT
ejpam-3407	115	4	γ	γ	NOUN
ejpam-3407	115	5	)	)	PUNCT
ejpam-3407	115	6	≤	≤	NUM
ejpam-3407	115	7	2t(1−γ)p−1(p−δ+δγ	2t(1−γ)p−1(p−δ+δγ	NUM
ejpam-3407	115	8	)	)	PUNCT
ejpam-3407	115	9	(	(	PUNCT
ejpam-3407	115	10	2−δ)γ(p+1	2−δ)γ(p+1	X
ejpam-3407	115	11	)	)	PUNCT
ejpam-3407	115	12	,	,	PUNCT
ejpam-3407	115	13	it	it	PRON
ejpam-3407	115	14	follows	follow	VERB
ejpam-3407	115	15	that	that	SCONJ
ejpam-3407	115	16	max	max	PROPN
ejpam-3407	115	17	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	115	18	]	]	PUNCT
ejpam-3407	115	19	∫	∫	PROPN
ejpam-3407	116	1	1	1	NUM
ejpam-3407	116	2	0	0	NUM
ejpam-3407	116	3	r(s	r(s	PROPN
ejpam-3407	116	4	,	,	PUNCT
ejpam-3407	116	5	γ)dγ	γ)dγ	PROPN
ejpam-3407	116	6	≤	≤	NOUN
ejpam-3407	116	7	2	2	NUM
ejpam-3407	116	8	(	(	PUNCT
ejpam-3407	116	9	2−	2−	NUM
ejpam-3407	116	10	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	116	11	)	)	PUNCT
ejpam-3407	116	12	.	.	PUNCT
ejpam-3407	117	1	we	we	PRON
ejpam-3407	117	2	define	define	VERB
ejpam-3407	117	3	the	the	DET
ejpam-3407	117	4	operator	operator	NOUN
ejpam-3407	117	5	t	t	NOUN
ejpam-3407	117	6	:	:	PUNCT
ejpam-3407	117	7	u	u	PROPN
ejpam-3407	117	8	→	→	SYM
ejpam-3407	117	9	u	u	NOUN
ejpam-3407	117	10	by	by	ADP
ejpam-3407	117	11	tz(s	tz(s	PUNCT
ejpam-3407	117	12	)	)	PUNCT
ejpam-3407	117	13	=	=	SYM
ejpam-3407	118	1	∫	∫	PROPN
ejpam-3407	118	2	1	1	NUM
ejpam-3407	118	3	0	0	NUM
ejpam-3407	118	4	r(s	r(s	PROPN
ejpam-3407	118	5	,	,	PUNCT
ejpam-3407	118	6	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	118	7	,	,	PUNCT
ejpam-3407	118	8	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	118	9	.	.	PUNCT
ejpam-3407	119	1	(	(	PUNCT
ejpam-3407	119	2	12	12	NUM
ejpam-3407	119	3	)	)	PUNCT
ejpam-3407	119	4	k.	k.	NOUN
ejpam-3407	119	5	shah	shah	PROPN
ejpam-3407	119	6	et	et	PROPN
ejpam-3407	119	7	al	al	PROPN
ejpam-3407	119	8	.	.	PUNCT
ejpam-3407	119	9	/	/	SYM
ejpam-3407	119	10	eur	eur	PROPN
ejpam-3407	119	11	.	.	PUNCT
ejpam-3407	120	1	j.	j.	PROPN
ejpam-3407	120	2	pure	pure	PROPN
ejpam-3407	120	3	appl	appl	PROPN
ejpam-3407	120	4	.	.	PROPN
ejpam-3407	120	5	math	math	PROPN
ejpam-3407	120	6	,	,	PUNCT
ejpam-3407	120	7	12	12	NUM
ejpam-3407	120	8	(	(	PUNCT
ejpam-3407	120	9	2	2	NUM
ejpam-3407	120	10	)	)	PUNCT
ejpam-3407	120	11	(	(	PUNCT
ejpam-3407	120	12	2019	2019	NUM
ejpam-3407	120	13	)	)	PUNCT
ejpam-3407	120	14	,	,	PUNCT
ejpam-3407	120	15	432	432	NUM
ejpam-3407	120	16	-	-	SYM
ejpam-3407	120	17	447	447	NUM
ejpam-3407	120	18	437	437	NUM
ejpam-3407	120	19	then	then	ADV
ejpam-3407	120	20	,	,	PUNCT
ejpam-3407	120	21	in	in	ADP
ejpam-3407	120	22	view	view	NOUN
ejpam-3407	120	23	of	of	ADP
ejpam-3407	120	24	(	(	PUNCT
ejpam-3407	120	25	11	11	NUM
ejpam-3407	120	26	)	)	PUNCT
ejpam-3407	120	27	and	and	CCONJ
ejpam-3407	120	28	(	(	PUNCT
ejpam-3407	120	29	12	12	NUM
ejpam-3407	120	30	)	)	PUNCT
ejpam-3407	120	31	,	,	PUNCT
ejpam-3407	120	32	we	we	PRON
ejpam-3407	120	33	obtain	obtain	VERB
ejpam-3407	120	34	the	the	DET
ejpam-3407	120	35	operator	operator	NOUN
ejpam-3407	120	36	equation	equation	NOUN
ejpam-3407	120	37	(	(	PUNCT
ejpam-3407	120	38	iz	iz	INTJ
ejpam-3407	120	39	−	−	PROPN
ejpam-3407	120	40	tz)(s	tz)(s	NOUN
ejpam-3407	120	41	)	)	PUNCT
ejpam-3407	121	1	=	=	SYM
ejpam-3407	121	2	0	0	NUM
ejpam-3407	121	3	,	,	PUNCT
ejpam-3407	121	4	s	s	VERB
ejpam-3407	121	5	∈	∈	PROPN
ejpam-3407	122	1	[	[	X
ejpam-3407	122	2	0	0	NUM
ejpam-3407	122	3	,	,	PUNCT
ejpam-3407	122	4	1	1	NUM
ejpam-3407	122	5	]	]	PUNCT
ejpam-3407	122	6	.	.	PUNCT
ejpam-3407	123	1	(	(	PUNCT
ejpam-3407	123	2	13	13	NUM
ejpam-3407	123	3	)	)	PUNCT
ejpam-3407	123	4	let	let	AUX
ejpam-3407	123	5	consider	consider	VERB
ejpam-3407	123	6	the	the	DET
ejpam-3407	123	7	condition	condition	NOUN
ejpam-3407	123	8	(	(	PUNCT
ejpam-3407	123	9	c2	c2	PROPN
ejpam-3407	123	10	)	)	PUNCT
ejpam-3407	123	11	,	,	PUNCT
ejpam-3407	123	12	then	then	ADV
ejpam-3407	123	13	for	for	ADP
ejpam-3407	123	14	z1	z1	PROPN
ejpam-3407	123	15	,	,	PUNCT
ejpam-3407	123	16	z2	z2	PROPN
ejpam-3407	123	17	∈	∈	PROPN
ejpam-3407	123	18	u	u	NOUN
ejpam-3407	123	19	with	with	ADP
ejpam-3407	123	20	z1	z1	ADJ
ejpam-3407	123	21	≤	≤	PROPN
ejpam-3407	123	22	z2	z2	NOUN
ejpam-3407	123	23	,	,	PUNCT
ejpam-3407	123	24	we	we	PRON
ejpam-3407	123	25	obtain	obtain	VERB
ejpam-3407	123	26	tz1(s	tz1(	NOUN
ejpam-3407	123	27	)	)	PUNCT
ejpam-3407	123	28	=	=	SYM
ejpam-3407	124	1	∫	∫	PROPN
ejpam-3407	124	2	1	1	NUM
ejpam-3407	124	3	0	0	NUM
ejpam-3407	124	4	r(s	r(s	PROPN
ejpam-3407	124	5	,	,	PUNCT
ejpam-3407	124	6	γ)q	γ)q	PUNCT
ejpam-3407	124	7	(	(	PUNCT
ejpam-3407	124	8	γ	γ	X
ejpam-3407	124	9	,	,	PUNCT
ejpam-3407	124	10	z1(γ	z1(γ	NUM
ejpam-3407	124	11	)	)	PUNCT
ejpam-3407	124	12	)	)	PUNCT
ejpam-3407	125	1	dγ	dγ	ADP
ejpam-3407	125	2	≤	≤	NUM
ejpam-3407	125	3	∫	∫	PROPN
ejpam-3407	125	4	1	1	NUM
ejpam-3407	125	5	0	0	NUM
ejpam-3407	125	6	r(s	r(s	PROPN
ejpam-3407	125	7	,	,	PUNCT
ejpam-3407	125	8	γ)q	γ)q	PUNCT
ejpam-3407	125	9	(	(	PUNCT
ejpam-3407	125	10	γ	γ	X
ejpam-3407	125	11	,	,	PUNCT
ejpam-3407	125	12	z2(γ	z2(γ	NOUN
ejpam-3407	125	13	)	)	PUNCT
ejpam-3407	125	14	)	)	PUNCT
ejpam-3407	126	1	dγ	dγ	ADP
ejpam-3407	126	2	=	=	SYM
ejpam-3407	126	3	tz2(s	tz2(s	PROPN
ejpam-3407	126	4	)	)	PUNCT
ejpam-3407	126	5	(	(	PUNCT
ejpam-3407	126	6	14	14	NUM
ejpam-3407	126	7	)	)	PUNCT
ejpam-3407	126	8	that	that	PRON
ejpam-3407	126	9	is	be	AUX
ejpam-3407	126	10	,	,	PUNCT
ejpam-3407	126	11	t	t	PROPN
ejpam-3407	126	12	is	be	AUX
ejpam-3407	126	13	nondecreasing	nondecrease	VERB
ejpam-3407	126	14	.	.	PUNCT
ejpam-3407	127	1	we	we	PRON
ejpam-3407	127	2	can	can	AUX
ejpam-3407	127	3	assume	assume	VERB
ejpam-3407	127	4	another	another	DET
ejpam-3407	127	5	condition	condition	NOUN
ejpam-3407	127	6	which	which	PRON
ejpam-3407	127	7	is	be	AUX
ejpam-3407	127	8	(	(	PUNCT
ejpam-3407	127	9	c4	c4	NOUN
ejpam-3407	127	10	)	)	PUNCT
ejpam-3407	127	11	for	for	ADP
ejpam-3407	127	12	minimal	minimal	ADJ
ejpam-3407	127	13	and	and	CCONJ
ejpam-3407	127	14	maximal	maximal	ADJ
ejpam-3407	127	15	solutions	solution	NOUN
ejpam-3407	127	16	α	α	NOUN
ejpam-3407	127	17	,	,	PUNCT
ejpam-3407	127	18	β	β	X
ejpam-3407	127	19	∈	∈	NOUN
ejpam-3407	127	20	u	u	NOUN
ejpam-3407	127	21	of	of	ADP
ejpam-3407	127	22	the	the	DET
ejpam-3407	127	23	equation	equation	NOUN
ejpam-3407	127	24	(	(	PUNCT
ejpam-3407	127	25	13	13	NUM
ejpam-3407	127	26	)	)	PUNCT
ejpam-3407	127	27	,	,	PUNCT
ejpam-3407	127	28	the	the	DET
ejpam-3407	127	29	inequality	inequality	NOUN
ejpam-3407	127	30	α	α	NOUN
ejpam-3407	127	31	≤	≤	NOUN
ejpam-3407	127	32	β	β	X
ejpam-3407	127	33	on	on	ADP
ejpam-3407	127	34	[	[	X
ejpam-3407	127	35	0	0	NUM
ejpam-3407	127	36	,	,	PUNCT
ejpam-3407	127	37	1	1	NUM
ejpam-3407	127	38	]	]	PUNCT
ejpam-3407	127	39	is	be	AUX
ejpam-3407	127	40	obvious	obvious	ADJ
ejpam-3407	127	41	.	.	PUNCT
ejpam-3407	128	1	lemma	lemma	PROPN
ejpam-3407	128	2	7	7	NUM
ejpam-3407	128	3	.	.	PUNCT
ejpam-3407	129	1	under	under	ADP
ejpam-3407	129	2	the	the	DET
ejpam-3407	129	3	conditions	condition	NOUN
ejpam-3407	129	4	(	(	PUNCT
ejpam-3407	129	5	c1)−	c1)−	NOUN
ejpam-3407	129	6	(	(	PUNCT
ejpam-3407	129	7	c4	c4	NOUN
ejpam-3407	129	8	)	)	PUNCT
ejpam-3407	129	9	the	the	DET
ejpam-3407	129	10	iterative	iterative	NOUN
ejpam-3407	129	11	solutions	solution	NOUN
ejpam-3407	129	12	of	of	ADP
ejpam-3407	129	13	operator	operator	NOUN
ejpam-3407	129	14	equation	equation	NOUN
ejpam-3407	129	15	(	(	PUNCT
ejpam-3407	129	16	13	13	NUM
ejpam-3407	129	17	)	)	PUNCT
ejpam-3407	129	18	is	be	AUX
ejpam-3407	129	19	the	the	DET
ejpam-3407	129	20	monotonic	monotonic	ADJ
ejpam-3407	129	21	sequence	sequence	NOUN
ejpam-3407	129	22	which	which	PRON
ejpam-3407	129	23	converges	converge	VERB
ejpam-3407	129	24	to	to	ADP
ejpam-3407	129	25	the	the	DET
ejpam-3407	129	26	solution	solution	NOUN
ejpam-3407	129	27	of	of	ADP
ejpam-3407	129	28	equation	equation	NOUN
ejpam-3407	129	29	(	(	PUNCT
ejpam-3407	129	30	11	11	NUM
ejpam-3407	129	31	)	)	PUNCT
ejpam-3407	129	32	.	.	PUNCT
ejpam-3407	130	1	proof	proof	NOUN
ejpam-3407	130	2	.	.	PUNCT
ejpam-3407	131	1	we	we	PRON
ejpam-3407	131	2	consider	consider	VERB
ejpam-3407	131	3	that	that	SCONJ
ejpam-3407	131	4	the	the	DET
ejpam-3407	131	5	conditions	condition	NOUN
ejpam-3407	131	6	(	(	PUNCT
ejpam-3407	131	7	c1	c1	NOUN
ejpam-3407	131	8	)	)	PUNCT
ejpam-3407	131	9	−	−	PROPN
ejpam-3407	131	10	(	(	PUNCT
ejpam-3407	131	11	c4	c4	NOUN
ejpam-3407	131	12	)	)	PUNCT
ejpam-3407	131	13	hold	hold	NOUN
ejpam-3407	131	14	,	,	PUNCT
ejpam-3407	131	15	then	then	ADV
ejpam-3407	131	16	we	we	PRON
ejpam-3407	131	17	show	show	VERB
ejpam-3407	131	18	that	that	SCONJ
ejpam-3407	131	19	t	t	PROPN
ejpam-3407	131	20	is	be	AUX
ejpam-3407	131	21	continuous	continuous	ADJ
ejpam-3407	131	22	.	.	PUNCT
ejpam-3407	132	1	for	for	ADP
ejpam-3407	132	2	this	this	PRON
ejpam-3407	132	3	,	,	PUNCT
ejpam-3407	132	4	let	let	VERB
ejpam-3407	132	5	z1	z1	ADJ
ejpam-3407	132	6	,	,	PUNCT
ejpam-3407	132	7	z2	z2	PROPN
ejpam-3407	132	8	∈	∈	PROPN
ejpam-3407	132	9	u	u	NOUN
ejpam-3407	132	10	,	,	PUNCT
ejpam-3407	132	11	then	then	ADV
ejpam-3407	132	12	|tz1(s)−	|tz1(s)−	PROPN
ejpam-3407	132	13	tz2(s)|	tz2(s)|	NOUN
ejpam-3407	132	14	=	=	SYM
ejpam-3407	132	15	∣	∣	ADJ
ejpam-3407	132	16	∣	∣	ADJ
ejpam-3407	132	17	∣	∣	ADJ
ejpam-3407	132	18	∣	∣	ADJ
ejpam-3407	132	19	∫	∫	PROPN
ejpam-3407	132	20	1	1	NUM
ejpam-3407	132	21	0	0	NUM
ejpam-3407	132	22	r(s	r(s	PROPN
ejpam-3407	132	23	,	,	PUNCT
ejpam-3407	132	24	γ)q	γ)q	PUNCT
ejpam-3407	132	25	(	(	PUNCT
ejpam-3407	132	26	γ	γ	X
ejpam-3407	132	27	,	,	PUNCT
ejpam-3407	132	28	z1(γ	z1(γ	NUM
ejpam-3407	132	29	)	)	PUNCT
ejpam-3407	132	30	)	)	PUNCT
ejpam-3407	133	1	dγ	dγ	ADP
ejpam-3407	133	2	−	−	PROPN
ejpam-3407	133	3	∫	∫	PROPN
ejpam-3407	133	4	1	1	NUM
ejpam-3407	133	5	0	0	NUM
ejpam-3407	133	6	r(s	r(s	PROPN
ejpam-3407	133	7	,	,	PUNCT
ejpam-3407	133	8	γ)q	γ)q	PUNCT
ejpam-3407	133	9	(	(	PUNCT
ejpam-3407	133	10	γ	γ	X
ejpam-3407	133	11	,	,	PUNCT
ejpam-3407	133	12	z2(γ	z2(γ	NOUN
ejpam-3407	133	13	)	)	PUNCT
ejpam-3407	133	14	)	)	PUNCT
ejpam-3407	134	1	dγ	dγ	ADP
ejpam-3407	134	2	∣	∣	ADJ
ejpam-3407	134	3	∣	∣	ADJ
ejpam-3407	134	4	∣	∣	ADJ
ejpam-3407	134	5	∣	∣	ADJ
ejpam-3407	134	6	=	=	PUNCT
ejpam-3407	134	7	∣	∣	ADJ
ejpam-3407	134	8	∣	∣	ADJ
ejpam-3407	134	9	∣	∣	ADJ
ejpam-3407	134	10	∣	∣	ADJ
ejpam-3407	134	11	∫	∫	PROPN
ejpam-3407	134	12	1	1	NUM
ejpam-3407	134	13	0	0	NUM
ejpam-3407	134	14	[	[	PUNCT
ejpam-3407	134	15	r(s	r(s	PROPN
ejpam-3407	134	16	,	,	PUNCT
ejpam-3407	134	17	γ)q	γ)q	X
ejpam-3407	134	18	(	(	PUNCT
ejpam-3407	134	19	γ	γ	X
ejpam-3407	134	20	,	,	PUNCT
ejpam-3407	134	21	x1(γ	x1(γ	PROPN
ejpam-3407	134	22	)	)	PUNCT
ejpam-3407	134	23	)	)	PUNCT
ejpam-3407	134	24	−r(s	−r(s	NOUN
ejpam-3407	134	25	,	,	PUNCT
ejpam-3407	134	26	γ)q	γ)q	PUNCT
ejpam-3407	134	27	(	(	PUNCT
ejpam-3407	134	28	γ	γ	X
ejpam-3407	134	29	,	,	PUNCT
ejpam-3407	134	30	z2(γ	z2(γ	NOUN
ejpam-3407	134	31	)	)	PUNCT
ejpam-3407	134	32	)	)	PUNCT
ejpam-3407	134	33	]	]	PUNCT
ejpam-3407	135	1	dγ	dγ	ADP
ejpam-3407	135	2	∣	∣	ADJ
ejpam-3407	135	3	∣	∣	ADJ
ejpam-3407	135	4	∣	∣	ADJ
ejpam-3407	135	5	∣	∣	ADJ
ejpam-3407	135	6	≤	≤	NUM
ejpam-3407	135	7	∫	∫	NOUN
ejpam-3407	136	1	1	1	NUM
ejpam-3407	136	2	0	0	NUM
ejpam-3407	136	3	r(s	r(s	PROPN
ejpam-3407	136	4	,	,	PUNCT
ejpam-3407	136	5	γ	γ	NOUN
ejpam-3407	136	6	)	)	PUNCT
ejpam-3407	136	7	∣	∣	ADJ
ejpam-3407	136	8	∣	∣	ADJ
ejpam-3407	136	9	∣	∣	ADJ
ejpam-3407	136	10	∣	∣	ADJ
ejpam-3407	136	11	q	q	NOUN
ejpam-3407	136	12	(	(	PUNCT
ejpam-3407	136	13	γ	γ	X
ejpam-3407	136	14	,	,	PUNCT
ejpam-3407	136	15	z1(γ	z1(γ	NUM
ejpam-3407	136	16	)	)	PUNCT
ejpam-3407	136	17	−q	−q	NOUN
ejpam-3407	136	18	(	(	PUNCT
ejpam-3407	136	19	γ	γ	X
ejpam-3407	136	20	,	,	PUNCT
ejpam-3407	136	21	z2(γ	z2(γ	NOUN
ejpam-3407	136	22	)	)	PUNCT
ejpam-3407	136	23	)	)	PUNCT
ejpam-3407	136	24	∣	∣	PROPN
ejpam-3407	136	25	∣	∣	ADJ
ejpam-3407	136	26	∣	∣	ADJ
ejpam-3407	136	27	∣	∣	ADJ
ejpam-3407	136	28	dγ	dγ	ADP
ejpam-3407	136	29	≤	≤	ADJ
ejpam-3407	136	30	2b	2b	NUM
ejpam-3407	136	31	(	(	PUNCT
ejpam-3407	136	32	2−	2−	NUM
ejpam-3407	136	33	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	136	34	)	)	PUNCT
ejpam-3407	136	35	‖z1	‖z1	NOUN
ejpam-3407	137	1	−	−	PROPN
ejpam-3407	137	2	z2‖.	z2‖.	PROPN
ejpam-3407	137	3	thus	thus	ADV
ejpam-3407	137	4	t	t	PROPN
ejpam-3407	137	5	is	be	AUX
ejpam-3407	137	6	continuous	continuous	ADJ
ejpam-3407	137	7	.	.	PUNCT
ejpam-3407	138	1	it	it	PRON
ejpam-3407	138	2	is	be	AUX
ejpam-3407	138	3	easy	easy	ADJ
ejpam-3407	138	4	to	to	PART
ejpam-3407	138	5	prove	prove	VERB
ejpam-3407	138	6	that	that	SCONJ
ejpam-3407	138	7	t	t	PROPN
ejpam-3407	138	8	is	be	AUX
ejpam-3407	138	9	also	also	ADV
ejpam-3407	138	10	uniformly	uniformly	ADV
ejpam-3407	138	11	bounded	bound	VERB
ejpam-3407	138	12	and	and	CCONJ
ejpam-3407	138	13	equicontinuous	equicontinuous	ADJ
ejpam-3407	138	14	.	.	PUNCT
ejpam-3407	139	1	thank	thank	VERB
ejpam-3407	139	2	to	to	ADP
ejpam-3407	139	3	the	the	DET
ejpam-3407	139	4	arzela	arzela	PROPN
ejpam-3407	139	5	ascoli	ascoli	PROPN
ejpam-3407	139	6	theorem	theorem	PROPN
ejpam-3407	139	7	’s	’s	PART
ejpam-3407	139	8	statement	statement	NOUN
ejpam-3407	139	9	:	:	PUNCT
ejpam-3407	139	10	“	"	PUNCT
ejpam-3407	139	11	if	if	SCONJ
ejpam-3407	139	12	m	m	NOUN
ejpam-3407	139	13	be	be	VERB
ejpam-3407	139	14	a	a	DET
ejpam-3407	139	15	family	family	NOUN
ejpam-3407	139	16	(	(	PUNCT
ejpam-3407	139	17	finite	finite	NOUN
ejpam-3407	139	18	or	or	CCONJ
ejpam-3407	139	19	infinite	infinite	NOUN
ejpam-3407	139	20	)	)	PUNCT
ejpam-3407	139	21	of	of	ADP
ejpam-3407	139	22	an	an	DET
ejpam-3407	139	23	equi	equi	NOUN
ejpam-3407	139	24	-	-	PUNCT
ejpam-3407	139	25	continuous	continuous	ADJ
ejpam-3407	139	26	,	,	PUNCT
ejpam-3407	139	27	uniformly	uniformly	ADV
ejpam-3407	139	28	bounded	bound	VERB
ejpam-3407	139	29	real	real	ADJ
ejpam-3407	139	30	valued	value	VERB
ejpam-3407	139	31	functions	function	NOUN
ejpam-3407	139	32	z	z	NOUN
ejpam-3407	139	33	on	on	ADP
ejpam-3407	139	34	an	an	DET
ejpam-3407	139	35	interval	interval	NOUN
ejpam-3407	139	36	[	[	X
ejpam-3407	139	37	0	0	NUM
ejpam-3407	139	38	,	,	PUNCT
ejpam-3407	139	39	1	1	NUM
ejpam-3407	139	40	]	]	PUNCT
ejpam-3407	139	41	.	.	PUNCT
ejpam-3407	140	1	then	then	ADV
ejpam-3407	140	2	m	m	PROPN
ejpam-3407	140	3	contains	contain	VERB
ejpam-3407	140	4	a	a	DET
ejpam-3407	140	5	uniformly	uniformly	ADV
ejpam-3407	140	6	convergent	convergent	ADJ
ejpam-3407	140	7	sequence	sequence	NOUN
ejpam-3407	140	8	of	of	ADP
ejpam-3407	140	9	functions	function	NOUN
ejpam-3407	140	10	zn	zn	X
ejpam-3407	140	11	,	,	PUNCT
ejpam-3407	140	12	converging	converge	VERB
ejpam-3407	140	13	to	to	ADP
ejpam-3407	140	14	a	a	DET
ejpam-3407	140	15	function	function	NOUN
ejpam-3407	140	16	z	z	NOUN
ejpam-3407	140	17	in	in	ADP
ejpam-3407	140	18	u	u	NOUN
ejpam-3407	140	19	as	as	ADP
ejpam-3407	140	20	n	n	PROPN
ejpam-3407	140	21	→	→	SYM
ejpam-3407	140	22	∞	∞	PROPN
ejpam-3407	140	23	,	,	PUNCT
ejpam-3407	140	24	where	where	SCONJ
ejpam-3407	140	25	u	u	PRON
ejpam-3407	140	26	denotes	denote	VERB
ejpam-3407	140	27	the	the	DET
ejpam-3407	140	28	space	space	NOUN
ejpam-3407	140	29	of	of	ADP
ejpam-3407	140	30	all	all	DET
ejpam-3407	140	31	continuous	continuous	ADJ
ejpam-3407	140	32	bounded	bounded	ADJ
ejpam-3407	140	33	functions	function	NOUN
ejpam-3407	140	34	on	on	ADP
ejpam-3407	140	35	[	[	X
ejpam-3407	140	36	0	0	NUM
ejpam-3407	140	37	,	,	PUNCT
ejpam-3407	140	38	1	1	NUM
ejpam-3407	140	39	]	]	PUNCT
ejpam-3407	140	40	.	.	PUNCT
ejpam-3407	141	1	thus	thus	ADV
ejpam-3407	141	2	any	any	DET
ejpam-3407	141	3	sequence	sequence	NOUN
ejpam-3407	141	4	in	in	ADP
ejpam-3407	141	5	m	m	PROPN
ejpam-3407	141	6	contains	contain	VERB
ejpam-3407	141	7	a	a	DET
ejpam-3407	141	8	uniformly	uniformly	ADV
ejpam-3407	141	9	bounded	bound	VERB
ejpam-3407	141	10	convergent	convergent	NOUN
ejpam-3407	141	11	subsequence	subsequence	NOUN
ejpam-3407	141	12	on	on	ADP
ejpam-3407	141	13	[	[	X
ejpam-3407	141	14	0	0	NUM
ejpam-3407	141	15	,	,	PUNCT
ejpam-3407	141	16	1	1	NUM
ejpam-3407	141	17	]	]	PUNCT
ejpam-3407	141	18	and	and	CCONJ
ejpam-3407	141	19	consequently	consequently	ADV
ejpam-3407	141	20	m	m	VERB
ejpam-3407	141	21	has	have	VERB
ejpam-3407	141	22	a	a	DET
ejpam-3407	141	23	compact	compact	ADJ
ejpam-3407	141	24	closure	closure	NOUN
ejpam-3407	141	25	in	in	ADP
ejpam-3407	141	26	u	u	NOUN
ejpam-3407	141	27	”	"	PUNCT
ejpam-3407	141	28	.	.	PUNCT
ejpam-3407	142	1	we	we	PRON
ejpam-3407	142	2	obtain	obtain	VERB
ejpam-3407	142	3	t	t	PROPN
ejpam-3407	142	4	is	be	AUX
ejpam-3407	142	5	compact	compact	ADJ
ejpam-3407	142	6	.	.	PUNCT
ejpam-3407	143	1	further	far	ADV
ejpam-3407	143	2	,	,	PUNCT
ejpam-3407	143	3	we	we	PRON
ejpam-3407	143	4	may	may	AUX
ejpam-3407	143	5	choose	choose	VERB
ejpam-3407	143	6	z0	z0	PROPN
ejpam-3407	143	7	=	=	SYM
ejpam-3407	143	8	α	α	PROPN
ejpam-3407	143	9	.	.	PUNCT
ejpam-3407	144	1	then	then	ADV
ejpam-3407	144	2	,	,	PUNCT
ejpam-3407	144	3	in	in	ADP
ejpam-3407	144	4	the	the	DET
ejpam-3407	144	5	view	view	NOUN
ejpam-3407	144	6	of	of	ADP
ejpam-3407	144	7	c4	c4	NOUN
ejpam-3407	144	8	,	,	PUNCT
ejpam-3407	144	9	we	we	PRON
ejpam-3407	144	10	obtain	obtain	VERB
ejpam-3407	144	11	α	α	NOUN
ejpam-3407	144	12	≤	≤	NOUN
ejpam-3407	144	13	β	β	X
ejpam-3407	144	14	z0	z0	PROPN
ejpam-3407	144	15	≤	≤	PROPN
ejpam-3407	144	16	β	β	X
ejpam-3407	144	17	k.	k.	PROPN
ejpam-3407	144	18	shah	shah	PROPN
ejpam-3407	144	19	et	et	PROPN
ejpam-3407	144	20	al	al	PROPN
ejpam-3407	144	21	.	.	PUNCT
ejpam-3407	144	22	/	/	SYM
ejpam-3407	144	23	eur	eur	PROPN
ejpam-3407	144	24	.	.	PUNCT
ejpam-3407	145	1	j.	j.	PROPN
ejpam-3407	145	2	pure	pure	PROPN
ejpam-3407	145	3	appl	appl	PROPN
ejpam-3407	145	4	.	.	PROPN
ejpam-3407	145	5	math	math	PROPN
ejpam-3407	145	6	,	,	PUNCT
ejpam-3407	145	7	12	12	NUM
ejpam-3407	145	8	(	(	PUNCT
ejpam-3407	145	9	2	2	NUM
ejpam-3407	145	10	)	)	PUNCT
ejpam-3407	145	11	(	(	PUNCT
ejpam-3407	145	12	2019	2019	NUM
ejpam-3407	145	13	)	)	PUNCT
ejpam-3407	145	14	,	,	PUNCT
ejpam-3407	145	15	432	432	NUM
ejpam-3407	145	16	-	-	SYM
ejpam-3407	145	17	447	447	NUM
ejpam-3407	145	18	438	438	NUM
ejpam-3407	145	19	z0	z0	PROPN
ejpam-3407	145	20	≤	≤	NUM
ejpam-3407	145	21	tz0	tz0	PROPN
ejpam-3407	145	22	≤	≤	NUM
ejpam-3407	145	23	tβ	tβ	NOUN
ejpam-3407	145	24	≤	≤	NUM
ejpam-3407	145	25	β	β	NOUN
ejpam-3407	145	26	,	,	PUNCT
ejpam-3407	145	27	t	t	PROPN
ejpam-3407	145	28	is	be	AUX
ejpam-3407	145	29	increasing	increase	VERB
ejpam-3407	145	30	z0	z0	PROPN
ejpam-3407	145	31	≤	≤	ADJ
ejpam-3407	145	32	z1	z1	NOUN
ejpam-3407	145	33	≤	≤	X
ejpam-3407	145	34	β	β	NOUN
ejpam-3407	145	35	on	on	ADP
ejpam-3407	145	36	[	[	X
ejpam-3407	145	37	0	0	NUM
ejpam-3407	145	38	,	,	PUNCT
ejpam-3407	145	39	1	1	NUM
ejpam-3407	145	40	]	]	PUNCT
ejpam-3407	145	41	,	,	PUNCT
ejpam-3407	145	42	where	where	SCONJ
ejpam-3407	145	43	z1	z1	PROPN
ejpam-3407	145	44	=	=	SYM
ejpam-3407	145	45	tz0	tz0	PROPN
ejpam-3407	145	46	.	.	PUNCT
ejpam-3407	146	1	similarly	similarly	ADV
ejpam-3407	146	2	,	,	PUNCT
ejpam-3407	146	3	tz0	tz0	PROPN
ejpam-3407	146	4	≤	≤	NUM
ejpam-3407	146	5	tz1	tz1	VERB
ejpam-3407	146	6	≤	≤	NUM
ejpam-3407	146	7	tβ	tβ	NOUN
ejpam-3407	147	1	≤	≤	NUM
ejpam-3407	147	2	β	β	NOUN
ejpam-3407	147	3	,	,	PUNCT
ejpam-3407	147	4	that	that	ADV
ejpam-3407	147	5	is	is	ADV
ejpam-3407	147	6	,	,	PUNCT
ejpam-3407	147	7	z1	z1	ADJ
ejpam-3407	147	8	≤	≤	PROPN
ejpam-3407	147	9	z2	z2	PROPN
ejpam-3407	147	10	≤	≤	NOUN
ejpam-3407	147	11	β	β	NOUN
ejpam-3407	147	12	on	on	ADP
ejpam-3407	147	13	[	[	X
ejpam-3407	147	14	0	0	NUM
ejpam-3407	147	15	,	,	PUNCT
ejpam-3407	147	16	1	1	NUM
ejpam-3407	147	17	]	]	PUNCT
ejpam-3407	147	18	,	,	PUNCT
ejpam-3407	147	19	where	where	SCONJ
ejpam-3407	147	20	z2	z2	PROPN
ejpam-3407	147	21	=	=	SYM
ejpam-3407	147	22	tz1	tz1	PROPN
ejpam-3407	147	23	.	.	PUNCT
ejpam-3407	148	1	in	in	ADP
ejpam-3407	148	2	same	same	ADJ
ejpam-3407	148	3	way	way	NOUN
ejpam-3407	148	4	,	,	PUNCT
ejpam-3407	148	5	we	we	PRON
ejpam-3407	148	6	obtain	obtain	VERB
ejpam-3407	148	7	the	the	DET
ejpam-3407	148	8	bounded	bounded	ADJ
ejpam-3407	148	9	monotone	monotone	ADJ
ejpam-3407	148	10	sequence	sequence	NOUN
ejpam-3407	148	11	{	{	PUNCT
ejpam-3407	148	12	zn	zn	NOUN
ejpam-3407	148	13	}	}	PUNCT
ejpam-3407	148	14	,	,	PUNCT
ejpam-3407	148	15	that	that	PRON
ejpam-3407	148	16	is	is	ADV
ejpam-3407	148	17	z0	z0	PROPN
ejpam-3407	148	18	≤	≤	PROPN
ejpam-3407	148	19	z1	z1	VERB
ejpam-3407	148	20	≤	≤	PROPN
ejpam-3407	148	21	z2	z2	PROPN
ejpam-3407	148	22	≤	≤	NOUN
ejpam-3407	148	23	...	...	PUNCT
ejpam-3407	148	24	zn−1	zn−1	ADJ
ejpam-3407	148	25	≤	≤	NUM
ejpam-3407	148	26	zn	zn	NOUN
ejpam-3407	148	27	≤	≤	NOUN
ejpam-3407	148	28	β	β	X
ejpam-3407	148	29	on	on	ADP
ejpam-3407	148	30	[	[	X
ejpam-3407	148	31	0	0	NUM
ejpam-3407	148	32	,	,	PUNCT
ejpam-3407	148	33	1	1	NUM
ejpam-3407	148	34	]	]	PUNCT
ejpam-3407	148	35	,	,	PUNCT
ejpam-3407	148	36	(	(	PUNCT
ejpam-3407	148	37	15	15	NUM
ejpam-3407	148	38	)	)	PUNCT
ejpam-3407	148	39	where	where	SCONJ
ejpam-3407	148	40	zn	zn	X
ejpam-3407	148	41	=	=	PUNCT
ejpam-3407	149	1	tzn−1	tzn−1	PROPN
ejpam-3407	149	2	.	.	PUNCT
ejpam-3407	150	1	then	then	ADV
ejpam-3407	150	2	,	,	PUNCT
ejpam-3407	150	3	there	there	PRON
ejpam-3407	150	4	will	will	AUX
ejpam-3407	150	5	be	be	AUX
ejpam-3407	150	6	z	z	PROPN
ejpam-3407	150	7	∈	∈	PROPN
ejpam-3407	150	8	u	u	NOUN
ejpam-3407	150	9	such	such	ADJ
ejpam-3407	150	10	that	that	SCONJ
ejpam-3407	150	11	zn	zn	PROPN
ejpam-3407	150	12	→	→	SYM
ejpam-3407	150	13	z	z	PROPN
ejpam-3407	150	14	as	as	ADP
ejpam-3407	150	15	n	n	PROPN
ejpam-3407	150	16	→	→	SYM
ejpam-3407	150	17	∞.	∞.	PROPN
ejpam-3407	150	18	hence	hence	ADV
ejpam-3407	150	19	,	,	PUNCT
ejpam-3407	150	20	we	we	PRON
ejpam-3407	150	21	obtain	obtain	VERB
ejpam-3407	150	22	that	that	DET
ejpam-3407	150	23	z	z	NOUN
ejpam-3407	150	24	=	=	SYM
ejpam-3407	150	25	tz	tz	PROPN
ejpam-3407	150	26	.	.	PUNCT
ejpam-3407	151	1	but	but	CCONJ
ejpam-3407	151	2	z	z	NOUN
ejpam-3407	151	3	is	be	AUX
ejpam-3407	151	4	solution	solution	NOUN
ejpam-3407	151	5	of	of	ADP
ejpam-3407	151	6	the	the	DET
ejpam-3407	151	7	equation	equation	NOUN
ejpam-3407	151	8	(	(	PUNCT
ejpam-3407	151	9	11	11	NUM
ejpam-3407	151	10	)	)	PUNCT
ejpam-3407	151	11	given	give	VERB
ejpam-3407	151	12	by	by	ADP
ejpam-3407	151	13	z(s	z(s	PROPN
ejpam-3407	151	14	)	)	PUNCT
ejpam-3407	152	1	=	=	PUNCT
ejpam-3407	152	2	∫	∫	PROPN
ejpam-3407	152	3	1	1	NUM
ejpam-3407	152	4	0	0	NUM
ejpam-3407	152	5	r(s	r(s	PROPN
ejpam-3407	152	6	,	,	PUNCT
ejpam-3407	152	7	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	152	8	,	,	PUNCT
ejpam-3407	152	9	z(γ))dγ	z(γ))dγ	NUM
ejpam-3407	152	10	,	,	PUNCT
ejpam-3407	152	11	s	s	PART
ejpam-3407	152	12	∈	∈	PROPN
ejpam-3407	153	1	[	[	X
ejpam-3407	153	2	0	0	NUM
ejpam-3407	153	3	,	,	PUNCT
ejpam-3407	153	4	1	1	NUM
ejpam-3407	153	5	]	]	PUNCT
ejpam-3407	153	6	.	.	PUNCT
ejpam-3407	154	1	let	let	AUX
ejpam-3407	154	2	consider	consider	VERB
ejpam-3407	154	3	the	the	DET
ejpam-3407	154	4	condition	condition	NOUN
ejpam-3407	154	5	(	(	PUNCT
ejpam-3407	154	6	c3	c3	PROPN
ejpam-3407	154	7	)	)	PUNCT
ejpam-3407	154	8	,	,	PUNCT
ejpam-3407	154	9	then	then	ADV
ejpam-3407	154	10	for	for	ADP
ejpam-3407	154	11	z	z	PROPN
ejpam-3407	154	12	,	,	PUNCT
ejpam-3407	154	13	y	y	PROPN
ejpam-3407	154	14	∈	∈	PROPN
ejpam-3407	154	15	u	u	NOUN
ejpam-3407	154	16	with	with	ADP
ejpam-3407	154	17	z	z	PROPN
ejpam-3407	154	18	≤	≤	PROPN
ejpam-3407	154	19	y	y	PROPN
ejpam-3407	154	20	,	,	PUNCT
ejpam-3407	154	21	we	we	PRON
ejpam-3407	154	22	have	have	VERB
ejpam-3407	154	23	the	the	DET
ejpam-3407	154	24	inequality	inequality	NOUN
ejpam-3407	154	25	‖ty	‖ty	NUM
ejpam-3407	154	26	−	−	NOUN
ejpam-3407	154	27	tz‖	tz‖	PROPN
ejpam-3407	154	28	≤	≤	NUM
ejpam-3407	154	29	∆‖y	∆‖y	NOUN
ejpam-3407	154	30	−	−	PROPN
ejpam-3407	154	31	z‖,where	z‖,where	PROPN
ejpam-3407	155	1	∆	∆	PUNCT
ejpam-3407	156	1	=	=	SYM
ejpam-3407	156	2	2b	2b	NOUN
ejpam-3407	156	3	(	(	PUNCT
ejpam-3407	156	4	2−	2−	NUM
ejpam-3407	156	5	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	156	6	)	)	PUNCT
ejpam-3407	156	7	.	.	PUNCT
ejpam-3407	157	1	(	(	PUNCT
ejpam-3407	157	2	16	16	NUM
ejpam-3407	157	3	)	)	PUNCT
ejpam-3407	157	4	hence	hence	ADV
ejpam-3407	157	5	in	in	ADP
ejpam-3407	157	6	view	view	NOUN
ejpam-3407	157	7	of	of	ADP
ejpam-3407	157	8	(	(	PUNCT
ejpam-3407	157	9	15	15	NUM
ejpam-3407	157	10	)	)	PUNCT
ejpam-3407	157	11	and	and	CCONJ
ejpam-3407	157	12	(	(	PUNCT
ejpam-3407	157	13	16	16	NUM
ejpam-3407	157	14	)	)	PUNCT
ejpam-3407	157	15	,	,	PUNCT
ejpam-3407	157	16	we	we	PRON
ejpam-3407	157	17	get	get	VERB
ejpam-3407	157	18	‖z2	‖z2	NOUN
ejpam-3407	157	19	−	−	PROPN
ejpam-3407	157	20	z1‖	z1‖	NOUN
ejpam-3407	157	21	=	=	SYM
ejpam-3407	158	1	‖tz	‖tz	NUM
ejpam-3407	158	2	−	−	NOUN
ejpam-3407	158	3	tz0‖	tz0‖	NOUN
ejpam-3407	158	4	≤	≤	PROPN
ejpam-3407	158	5	∆e1	∆e1	NOUN
ejpam-3407	158	6	,	,	PUNCT
ejpam-3407	159	1	‖z3	‖z3	ADJ
ejpam-3407	159	2	−	−	PROPN
ejpam-3407	159	3	z2‖	z2‖	PROPN
ejpam-3407	159	4	=	=	SYM
ejpam-3407	159	5	‖tz2	‖tz2	PROPN
ejpam-3407	159	6	−	−	PROPN
ejpam-3407	159	7	tz0‖	tz0‖	PROPN
ejpam-3407	159	8	≤	≤	ADJ
ejpam-3407	159	9	∆2e1	∆2e1	NOUN
ejpam-3407	159	10	,	,	PUNCT
ejpam-3407	159	11	‖z4	‖z4	PROPN
ejpam-3407	160	1	−	−	PROPN
ejpam-3407	160	2	z3‖	z3‖	PROPN
ejpam-3407	160	3	=	=	SYM
ejpam-3407	161	1	‖tz3	‖tz3	PROPN
ejpam-3407	161	2	−	−	PROPN
ejpam-3407	161	3	tz2‖	tz2‖	NUM
ejpam-3407	161	4	≤	≤	NOUN
ejpam-3407	161	5	∆3e1	∆3e1	PROPN
ejpam-3407	161	6	,	,	PUNCT
ejpam-3407	161	7	...	...	PUNCT
ejpam-3407	161	8	‖zn+1	‖zn+1	PUNCT
ejpam-3407	162	1	−	−	NOUN
ejpam-3407	162	2	zn‖	zn‖	PROPN
ejpam-3407	162	3	=	=	SYM
ejpam-3407	162	4	‖tzn	‖tzn	ADJ
ejpam-3407	162	5	−	−	NOUN
ejpam-3407	162	6	tz0‖	tz0‖	PROPN
ejpam-3407	162	7	≤	≤	ADV
ejpam-3407	162	8	∆ne1	∆ne1	PROPN
ejpam-3407	162	9	.	.	PUNCT
ejpam-3407	163	1	therfore	therfore	ADV
ejpam-3407	163	2	,	,	PUNCT
ejpam-3407	163	3	we	we	PRON
ejpam-3407	163	4	can	can	AUX
ejpam-3407	163	5	obtain	obtain	VERB
ejpam-3407	163	6	‖zm+n−zn‖	‖zm+n−zn‖	ADJ
ejpam-3407	163	7	≤	≤	ADJ
ejpam-3407	163	8	‖zn+p−zn+p−1‖	‖zn+p−zn+p−1‖	PROPN
ejpam-3407	164	1	+	+	CCONJ
ejpam-3407	164	2	‖zn+m−1−zn+m−2‖	‖zn+m−1−zn+m−2‖	PROPN
ejpam-3407	164	3	+	+	PROPN
ejpam-3407	164	4	.	.	PUNCT
ejpam-3407	164	5	.	.	PUNCT
ejpam-3407	164	6	.	.	PUNCT
ejpam-3407	165	1	‖zn+1−zn‖	‖zn+1−zn‖	X
ejpam-3407	165	2	≤	≤	NUM
ejpam-3407	166	1	∆n	∆n	PROPN
ejpam-3407	166	2	1−∆m	1−∆m	NUM
ejpam-3407	166	3	1−∆	1−∆	NUM
ejpam-3407	166	4	e1	e1	NOUN
ejpam-3407	166	5	.	.	PUNCT
ejpam-3407	167	1	(	(	PUNCT
ejpam-3407	167	2	17	17	NUM
ejpam-3407	167	3	)	)	PUNCT
ejpam-3407	167	4	where	where	SCONJ
ejpam-3407	167	5	m	m	PROPN
ejpam-3407	167	6	,	,	PUNCT
ejpam-3407	167	7	n	n	PRON
ejpam-3407	167	8	are	be	AUX
ejpam-3407	167	9	positive	positive	ADJ
ejpam-3407	167	10	integers	integer	NOUN
ejpam-3407	167	11	and	and	CCONJ
ejpam-3407	167	12	∆	∆	X
ejpam-3407	167	13	<	<	X
ejpam-3407	168	1	1	1	X
ejpam-3407	168	2	.	.	PUNCT
ejpam-3407	168	3	now	now	ADV
ejpam-3407	168	4	if	if	SCONJ
ejpam-3407	168	5	n→	n→	PROPN
ejpam-3407	168	6	∞	∞	PROPN
ejpam-3407	168	7	,	,	PUNCT
ejpam-3407	168	8	then	then	ADV
ejpam-3407	168	9	we	we	PRON
ejpam-3407	168	10	obtain	obtain	VERB
ejpam-3407	168	11	that	that	DET
ejpam-3407	168	12	‖zm+n	‖zm+n	PROPN
ejpam-3407	168	13	−	−	PROPN
ejpam-3407	168	14	zn‖	zn‖	PROPN
ejpam-3407	168	15	→	→	SYM
ejpam-3407	168	16	0	0	NUM
ejpam-3407	168	17	.	.	PUNCT
ejpam-3407	169	1	hence	hence	ADV
ejpam-3407	169	2	{	{	PUNCT
ejpam-3407	169	3	zn	zn	X
ejpam-3407	169	4	}	}	PUNCT
ejpam-3407	169	5	is	be	AUX
ejpam-3407	169	6	cauchy	cauchy	ADJ
ejpam-3407	169	7	sequence	sequence	NOUN
ejpam-3407	169	8	in	in	ADP
ejpam-3407	169	9	u	u	PROPN
ejpam-3407	169	10	.	.	PUNCT
ejpam-3407	170	1	thus	thus	ADV
ejpam-3407	170	2	z∗(s	z∗(s	X
ejpam-3407	170	3	)	)	PUNCT
ejpam-3407	170	4	=	=	SYM
ejpam-3407	170	5	limn→∞	limn→∞	PRON
ejpam-3407	170	6	zn(s	zn(s	NUM
ejpam-3407	170	7	)	)	PUNCT
ejpam-3407	170	8	.	.	PUNCT
ejpam-3407	171	1	therefore	therefore	ADV
ejpam-3407	171	2	,	,	PUNCT
ejpam-3407	171	3	we	we	PRON
ejpam-3407	171	4	obtain	obtain	VERB
ejpam-3407	171	5	that	that	PRON
ejpam-3407	171	6	tz∗	tz∗	PROPN
ejpam-3407	171	7	=	=	NOUN
ejpam-3407	171	8	z∗.	z∗.	PROPN
ejpam-3407	171	9	let	let	VERB
ejpam-3407	171	10	m→	m→	NOUN
ejpam-3407	171	11	∞	∞	PROPN
ejpam-3407	171	12	in	in	ADP
ejpam-3407	171	13	the	the	DET
ejpam-3407	171	14	equation	equation	NOUN
ejpam-3407	171	15	(	(	PUNCT
ejpam-3407	171	16	17	17	NUM
ejpam-3407	171	17	)	)	PUNCT
ejpam-3407	171	18	,	,	PUNCT
ejpam-3407	171	19	then	then	ADV
ejpam-3407	171	20	estimate	estimate	VERB
ejpam-3407	171	21	of	of	ADP
ejpam-3407	171	22	error	error	NOUN
ejpam-3407	171	23	for	for	ADP
ejpam-3407	171	24	the	the	DET
ejpam-3407	171	25	minimal	minimal	ADJ
ejpam-3407	171	26	solution	solution	NOUN
ejpam-3407	171	27	is	be	AUX
ejpam-3407	171	28	provided	provide	VERB
ejpam-3407	171	29	by	by	ADP
ejpam-3407	171	30	en	en	X
ejpam-3407	171	31	=	=	SYM
ejpam-3407	171	32	‖z∗	‖z∗	PROPN
ejpam-3407	172	1	−	−	PROPN
ejpam-3407	172	2	zn‖	zn‖	PROPN
ejpam-3407	172	3	≤	≤	PROPN
ejpam-3407	172	4	∆n	∆n	PROPN
ejpam-3407	172	5	1−∆	1−∆	PROPN
ejpam-3407	172	6	e1,where	e1,where	AUX
ejpam-3407	172	7	e1	e1	PROPN
ejpam-3407	172	8	=	=	SYM
ejpam-3407	172	9	‖z1	‖z1	PROPN
ejpam-3407	172	10	−	−	PROPN
ejpam-3407	172	11	z0‖.	z0‖.	PROPN
ejpam-3407	172	12	remark	remark	NOUN
ejpam-3407	172	13	.	.	PUNCT
ejpam-3407	173	1	if	if	SCONJ
ejpam-3407	173	2	we	we	PRON
ejpam-3407	173	3	consider	consider	VERB
ejpam-3407	173	4	that	that	DET
ejpam-3407	173	5	z0	z0	PROPN
ejpam-3407	173	6	=	=	SYM
ejpam-3407	173	7	β	β	NOUN
ejpam-3407	173	8	,	,	PUNCT
ejpam-3407	173	9	then	then	ADV
ejpam-3407	173	10	we	we	PRON
ejpam-3407	173	11	have	have	VERB
ejpam-3407	173	12	that	that	SCONJ
ejpam-3407	173	13	{	{	PUNCT
ejpam-3407	173	14	zn	zn	X
ejpam-3407	173	15	}	}	PUNCT
ejpam-3407	173	16	is	be	AUX
ejpam-3407	173	17	cauchy	cauchy	ADJ
ejpam-3407	173	18	sequence	sequence	NOUN
ejpam-3407	173	19	such	such	ADJ
ejpam-3407	173	20	that	that	SCONJ
ejpam-3407	173	21	z0	z0	PROPN
ejpam-3407	173	22	≥	≥	PRON
ejpam-3407	173	23	z1	z1	PROPN
ejpam-3407	173	24	≥	≥	PROPN
ejpam-3407	173	25	z2	z2	PROPN
ejpam-3407	173	26	≥	≥	NUM
ejpam-3407	173	27	...	...	PUNCT
ejpam-3407	174	1	zn−1	zn−1	PROPN
ejpam-3407	174	2	≥	≥	NUM
ejpam-3407	174	3	zn	zn	PROPN
ejpam-3407	174	4	≥	≥	NUM
ejpam-3407	174	5	α	α	NOUN
ejpam-3407	174	6	on	on	ADP
ejpam-3407	174	7	[	[	X
ejpam-3407	174	8	0	0	NUM
ejpam-3407	174	9	,	,	PUNCT
ejpam-3407	174	10	1	1	NUM
ejpam-3407	174	11	]	]	PUNCT
ejpam-3407	174	12	,	,	PUNCT
ejpam-3407	174	13	k.	k.	PROPN
ejpam-3407	174	14	shah	shah	PROPN
ejpam-3407	174	15	et	et	PROPN
ejpam-3407	174	16	al	al	PROPN
ejpam-3407	174	17	.	.	PUNCT
ejpam-3407	174	18	/	/	SYM
ejpam-3407	174	19	eur	eur	PROPN
ejpam-3407	174	20	.	.	PUNCT
ejpam-3407	175	1	j.	j.	PROPN
ejpam-3407	175	2	pure	pure	PROPN
ejpam-3407	175	3	appl	appl	PROPN
ejpam-3407	175	4	.	.	PROPN
ejpam-3407	175	5	math	math	PROPN
ejpam-3407	175	6	,	,	PUNCT
ejpam-3407	175	7	12	12	NUM
ejpam-3407	175	8	(	(	PUNCT
ejpam-3407	175	9	2	2	NUM
ejpam-3407	175	10	)	)	PUNCT
ejpam-3407	175	11	(	(	PUNCT
ejpam-3407	175	12	2019	2019	NUM
ejpam-3407	175	13	)	)	PUNCT
ejpam-3407	175	14	,	,	PUNCT
ejpam-3407	175	15	432	432	NUM
ejpam-3407	175	16	-	-	SYM
ejpam-3407	175	17	447	447	NUM
ejpam-3407	175	18	439	439	NUM
ejpam-3407	175	19	which	which	PRON
ejpam-3407	175	20	converges	converge	VERB
ejpam-3407	175	21	to	to	ADP
ejpam-3407	175	22	the	the	DET
ejpam-3407	175	23	solution	solution	NOUN
ejpam-3407	175	24	of	of	ADP
ejpam-3407	175	25	the	the	DET
ejpam-3407	175	26	equation	equation	NOUN
ejpam-3407	175	27	(	(	PUNCT
ejpam-3407	175	28	11	11	NUM
ejpam-3407	175	29	)	)	PUNCT
ejpam-3407	175	30	.	.	PUNCT
ejpam-3407	176	1	hence	hence	ADV
ejpam-3407	176	2	,	,	PUNCT
ejpam-3407	176	3	we	we	PRON
ejpam-3407	176	4	obtain	obtain	VERB
ejpam-3407	176	5	corresponding	corresponding	ADJ
ejpam-3407	176	6	estimate	estimate	NOUN
ejpam-3407	176	7	of	of	ADP
ejpam-3407	176	8	error	error	NOUN
ejpam-3407	176	9	for	for	ADP
ejpam-3407	176	10	the	the	DET
ejpam-3407	176	11	maximal	maximal	ADJ
ejpam-3407	176	12	solutions	solution	NOUN
ejpam-3407	176	13	which	which	PRON
ejpam-3407	176	14	is	be	AUX
ejpam-3407	176	15	provided	provide	VERB
ejpam-3407	176	16	by	by	ADP
ejpam-3407	176	17	e∗n	e∗n	PROPN
ejpam-3407	176	18	=	=	SYM
ejpam-3407	176	19	‖z∗n	‖z∗n	NOUN
ejpam-3407	176	20	−	−	PROPN
ejpam-3407	176	21	z̄∗‖	z̄∗‖	PROPN
ejpam-3407	176	22	≤	≤	PROPN
ejpam-3407	176	23	∆n	∆n	PROPN
ejpam-3407	176	24	1−∆e	1−∆e	NUM
ejpam-3407	176	25	∗	∗	NOUN
ejpam-3407	176	26	1,where	1,where	NUM
ejpam-3407	177	1	e	e	NOUN
ejpam-3407	177	2	∗	∗	NOUN
ejpam-3407	177	3	1	1	NUM
ejpam-3407	177	4	=	=	SYM
ejpam-3407	177	5	‖z∗0	‖z∗0	NOUN
ejpam-3407	177	6	−	−	PROPN
ejpam-3407	177	7	z	z	NOUN
ejpam-3407	177	8	∗	∗	NOUN
ejpam-3407	177	9	1‖.	1‖.	NUM
ejpam-3407	177	10	in	in	ADP
ejpam-3407	177	11	the	the	DET
ejpam-3407	177	12	view	view	NOUN
ejpam-3407	177	13	of	of	ADP
ejpam-3407	177	14	lemma	lemma	PROPN
ejpam-3407	177	15	7	7	NUM
ejpam-3407	177	16	,	,	PUNCT
ejpam-3407	177	17	we	we	PRON
ejpam-3407	177	18	can	can	AUX
ejpam-3407	177	19	fix	fix	VERB
ejpam-3407	177	20	the	the	DET
ejpam-3407	177	21	iterative	iterative	NOUN
ejpam-3407	177	22	schemes	scheme	NOUN
ejpam-3407	177	23	for	for	ADP
ejpam-3407	177	24	nfde	nfde	NOUN
ejpam-3407	177	25	(	(	PUNCT
ejpam-3407	177	26	1	1	NUM
ejpam-3407	177	27	)	)	PUNCT
ejpam-3407	177	28	as	as	ADP
ejpam-3407	177	29	zm(s	zm(s	NUM
ejpam-3407	177	30	)	)	PUNCT
ejpam-3407	178	1	=	=	SYM
ejpam-3407	178	2	∫	∫	PROPN
ejpam-3407	178	3	1	1	NUM
ejpam-3407	178	4	0	0	NUM
ejpam-3407	178	5	r(s	r(s	PROPN
ejpam-3407	178	6	,	,	PUNCT
ejpam-3407	178	7	γ)q	γ)q	X
ejpam-3407	178	8	(	(	PUNCT
ejpam-3407	178	9	γ	γ	X
ejpam-3407	178	10	,	,	PUNCT
ejpam-3407	178	11	zm−1	zm−1	NOUN
ejpam-3407	178	12	)	)	PUNCT
ejpam-3407	178	13	dγ	dγ	PROPN
ejpam-3407	178	14	,	,	PUNCT
ejpam-3407	178	15	m	m	VERB
ejpam-3407	178	16	≥	≥	NOUN
ejpam-3407	178	17	1	1	NUM
ejpam-3407	178	18	,	,	PUNCT
ejpam-3407	178	19	z∗m(s	z∗m(s	NUM
ejpam-3407	178	20	)	)	PUNCT
ejpam-3407	179	1	=	=	SYM
ejpam-3407	179	2	∫	∫	PROPN
ejpam-3407	179	3	1	1	NUM
ejpam-3407	179	4	0	0	NUM
ejpam-3407	179	5	r(s	r(s	PROPN
ejpam-3407	179	6	,	,	PUNCT
ejpam-3407	179	7	γ)q	γ)q	PUNCT
ejpam-3407	179	8	(	(	PUNCT
ejpam-3407	179	9	γ	γ	X
ejpam-3407	179	10	,	,	PUNCT
ejpam-3407	179	11	z∗m−1	z∗m−1	PROPN
ejpam-3407	179	12	)	)	PUNCT
ejpam-3407	179	13	dγ	dγ	PROPN
ejpam-3407	179	14	,	,	PUNCT
ejpam-3407	179	15	m	m	VERB
ejpam-3407	179	16	≥	≥	NOUN
ejpam-3407	179	17	1	1	NUM
ejpam-3407	179	18	,	,	PUNCT
ejpam-3407	179	19	from	from	ADP
ejpam-3407	179	20	which	which	PRON
ejpam-3407	179	21	,	,	PUNCT
ejpam-3407	179	22	we	we	PRON
ejpam-3407	179	23	obtain	obtain	VERB
ejpam-3407	179	24	z∗(s	z∗(s	NUM
ejpam-3407	179	25	)	)	PUNCT
ejpam-3407	180	1	=	=	SYM
ejpam-3407	180	2	lim	lim	PROPN
ejpam-3407	180	3	m→∞	m→∞	NUM
ejpam-3407	180	4	zm(s	zm(s	NUM
ejpam-3407	180	5	)	)	PUNCT
ejpam-3407	180	6	z̄∗(s	z̄∗(s	NOUN
ejpam-3407	180	7	)	)	PUNCT
ejpam-3407	181	1	=	=	SYM
ejpam-3407	181	2	lim	lim	PROPN
ejpam-3407	181	3	m→∞	m→∞	NUM
ejpam-3407	181	4	z∗m(s	z∗m(s	NUM
ejpam-3407	181	5	)	)	PUNCT
ejpam-3407	181	6	.	.	PUNCT
ejpam-3407	182	1	theorem	theorem	NOUN
ejpam-3407	182	2	1	1	NUM
ejpam-3407	182	3	.	.	PUNCT
ejpam-3407	183	1	under	under	ADP
ejpam-3407	183	2	the	the	DET
ejpam-3407	183	3	assumptions	assumption	NOUN
ejpam-3407	183	4	(	(	PUNCT
ejpam-3407	183	5	c1	c1	NOUN
ejpam-3407	183	6	)	)	PUNCT
ejpam-3407	183	7	,	,	PUNCT
ejpam-3407	183	8	(	(	PUNCT
ejpam-3407	183	9	c2	c2	PROPN
ejpam-3407	183	10	)	)	PUNCT
ejpam-3407	183	11	and	and	CCONJ
ejpam-3407	183	12	(	(	PUNCT
ejpam-3407	183	13	c3	c3	PROPN
ejpam-3407	183	14	)	)	PUNCT
ejpam-3407	183	15	with	with	ADP
ejpam-3407	183	16	∆	∆	PROPN
ejpam-3407	183	17	<	<	X
ejpam-3407	183	18	1	1	X
ejpam-3407	183	19	,	,	PUNCT
ejpam-3407	183	20	there	there	PRON
ejpam-3407	183	21	exist	exist	VERB
ejpam-3407	183	22	unique	unique	ADJ
ejpam-3407	183	23	lower	low	ADJ
ejpam-3407	183	24	and	and	CCONJ
ejpam-3407	183	25	upper	upper	ADJ
ejpam-3407	183	26	solutions	solution	NOUN
ejpam-3407	183	27	to	to	ADP
ejpam-3407	183	28	the	the	DET
ejpam-3407	183	29	problem	problem	NOUN
ejpam-3407	183	30	(	(	PUNCT
ejpam-3407	183	31	1	1	NUM
ejpam-3407	183	32	)	)	PUNCT
ejpam-3407	183	33	.	.	PUNCT
ejpam-3407	184	1	proof	proof	NOUN
ejpam-3407	184	2	.	.	PUNCT
ejpam-3407	185	1	proof	proof	NOUN
ejpam-3407	185	2	is	be	AUX
ejpam-3407	185	3	similar	similar	ADJ
ejpam-3407	185	4	as	as	SCONJ
ejpam-3407	185	5	given	give	VERB
ejpam-3407	185	6	in	in	ADP
ejpam-3407	185	7	[	[	X
ejpam-3407	185	8	33	33	NUM
ejpam-3407	185	9	]	]	PUNCT
ejpam-3407	185	10	.	.	PUNCT
ejpam-3407	186	1	4	4	X
ejpam-3407	186	2	.	.	X
ejpam-3407	186	3	ulam	ulam	PROPN
ejpam-3407	186	4	type	type	NOUN
ejpam-3407	186	5	stability	stability	NOUN
ejpam-3407	186	6	in	in	ADP
ejpam-3407	186	7	this	this	DET
ejpam-3407	186	8	section	section	NOUN
ejpam-3407	186	9	,	,	PUNCT
ejpam-3407	186	10	we	we	PRON
ejpam-3407	186	11	develop	develop	VERB
ejpam-3407	186	12	sufficient	sufficient	ADJ
ejpam-3407	186	13	conditions	condition	NOUN
ejpam-3407	186	14	for	for	ADP
ejpam-3407	186	15	the	the	DET
ejpam-3407	186	16	ulam	ulam	PROPN
ejpam-3407	186	17	stability	stability	PROPN
ejpam-3407	186	18	analysis	analysis	NOUN
ejpam-3407	186	19	of	of	ADP
ejpam-3407	186	20	the	the	DET
ejpam-3407	186	21	solutions	solution	NOUN
ejpam-3407	186	22	to	to	ADP
ejpam-3407	186	23	the	the	DET
ejpam-3407	186	24	considered	consider	VERB
ejpam-3407	186	25	bvp	bvp	NOUN
ejpam-3407	186	26	of	of	ADP
ejpam-3407	186	27	fdes	fde	NOUN
ejpam-3407	186	28	(	(	PUNCT
ejpam-3407	186	29	1	1	NUM
ejpam-3407	186	30	)	)	PUNCT
ejpam-3407	186	31	.	.	PUNCT
ejpam-3407	187	1	the	the	DET
ejpam-3407	187	2	required	required	ADJ
ejpam-3407	187	3	definitions	definition	NOUN
ejpam-3407	187	4	and	and	CCONJ
ejpam-3407	187	5	lemmas	lemma	NOUN
ejpam-3407	187	6	can	can	AUX
ejpam-3407	187	7	be	be	AUX
ejpam-3407	187	8	found	find	VERB
ejpam-3407	187	9	in	in	ADP
ejpam-3407	187	10	[	[	X
ejpam-3407	187	11	27–31	27–31	PROPN
ejpam-3407	187	12	,	,	PUNCT
ejpam-3407	187	13	34–36	34–36	NUM
ejpam-3407	187	14	]	]	PUNCT
ejpam-3407	187	15	.	.	PUNCT
ejpam-3407	188	1	definition	definition	NOUN
ejpam-3407	188	2	5	5	NUM
ejpam-3407	188	3	.	.	PUNCT
ejpam-3407	189	1	if	if	SCONJ
ejpam-3407	189	2	,	,	PUNCT
ejpam-3407	189	3	we	we	PRON
ejpam-3407	189	4	have	have	VERB
ejpam-3407	189	5	ck	ck	PROPN
ejpam-3407	189	6	∈	∈	PROPN
ejpam-3407	189	7	r	r	NOUN
ejpam-3407	189	8	+	+	NOUN
ejpam-3407	189	9	and	and	CCONJ
ejpam-3407	189	10	for	for	ADP
ejpam-3407	189	11	every	every	DET
ejpam-3407	189	12	ε	ε	PROPN
ejpam-3407	189	13	>	>	X
ejpam-3407	189	14	0	0	NUM
ejpam-3407	189	15	such	such	ADJ
ejpam-3407	189	16	that	that	PRON
ejpam-3407	189	17	for	for	ADP
ejpam-3407	189	18	any	any	DET
ejpam-3407	189	19	solution	solution	NOUN
ejpam-3407	189	20	z	z	PROPN
ejpam-3407	189	21	∈	∈	PROPN
ejpam-3407	189	22	ac2[0	ac2[0	ADJ
ejpam-3407	189	23	,	,	PUNCT
ejpam-3407	189	24	1	1	NUM
ejpam-3407	189	25	]	]	PUNCT
ejpam-3407	189	26	of	of	ADP
ejpam-3407	189	27	|cdpz(s	|cdpz(s	PROPN
ejpam-3407	189	28	)	)	PUNCT
ejpam-3407	190	1	+	+	NOUN
ejpam-3407	190	2	q(s	q(s	PROPN
ejpam-3407	190	3	,	,	PUNCT
ejpam-3407	190	4	z(s))|	z(s))|	PROPN
ejpam-3407	190	5	≤	≤	X
ejpam-3407	190	6	ε	ε	PROPN
ejpam-3407	190	7	,	,	PUNCT
ejpam-3407	190	8	s	s	PART
ejpam-3407	190	9	∈	∈	PROPN
ejpam-3407	191	1	[	[	X
ejpam-3407	191	2	0	0	NUM
ejpam-3407	191	3	,	,	PUNCT
ejpam-3407	191	4	1	1	NUM
ejpam-3407	191	5	]	]	PUNCT
ejpam-3407	191	6	,	,	PUNCT
ejpam-3407	191	7	(	(	PUNCT
ejpam-3407	191	8	18	18	NUM
ejpam-3407	191	9	)	)	PUNCT
ejpam-3407	191	10	there	there	PRON
ejpam-3407	191	11	exists	exist	VERB
ejpam-3407	191	12	v	v	ADP
ejpam-3407	191	13	∈	∈	PROPN
ejpam-3407	191	14	ac2[0	ac2[0	NOUN
ejpam-3407	191	15	,	,	PUNCT
ejpam-3407	191	16	1	1	NUM
ejpam-3407	191	17	]	]	PUNCT
ejpam-3407	191	18	is	be	AUX
ejpam-3407	191	19	a	a	DET
ejpam-3407	191	20	unique	unique	ADJ
ejpam-3407	191	21	solution	solution	NOUN
ejpam-3407	191	22	of	of	ADP
ejpam-3407	191	23	equation	equation	NOUN
ejpam-3407	191	24	(	(	PUNCT
ejpam-3407	191	25	1	1	X
ejpam-3407	191	26	)	)	PUNCT
ejpam-3407	191	27	such	such	ADJ
ejpam-3407	191	28	that	that	SCONJ
ejpam-3407	191	29	|z(s)−	|z(s)−	NOUN
ejpam-3407	191	30	v(s)|	v(s)|	NOUN
ejpam-3407	191	31	≤	≤	NUM
ejpam-3407	191	32	ckε	ckε	NOUN
ejpam-3407	191	33	,	,	PUNCT
ejpam-3407	191	34	s	s	VERB
ejpam-3407	191	35	∈	∈	PROPN
ejpam-3407	192	1	[	[	X
ejpam-3407	192	2	0	0	NUM
ejpam-3407	192	3	,	,	PUNCT
ejpam-3407	192	4	1	1	NUM
ejpam-3407	192	5	]	]	PUNCT
ejpam-3407	192	6	.	.	PUNCT
ejpam-3407	193	1	then	then	ADV
ejpam-3407	193	2	bvp	bvp	PROPN
ejpam-3407	193	3	(	(	PUNCT
ejpam-3407	193	4	1	1	X
ejpam-3407	193	5	)	)	PUNCT
ejpam-3407	193	6	is	be	AUX
ejpam-3407	193	7	said	say	VERB
ejpam-3407	193	8	to	to	PART
ejpam-3407	193	9	be	be	AUX
ejpam-3407	193	10	ulam	ulam	NOUN
ejpam-3407	193	11	–	–	PUNCT
ejpam-3407	193	12	hyers	hyer	NOUN
ejpam-3407	193	13	stable	stable	ADJ
ejpam-3407	193	14	.	.	PUNCT
ejpam-3407	194	1	definition	definition	NOUN
ejpam-3407	194	2	6	6	NUM
ejpam-3407	194	3	.	.	PUNCT
ejpam-3407	195	1	if	if	SCONJ
ejpam-3407	195	2	,	,	PUNCT
ejpam-3407	195	3	we	we	PRON
ejpam-3407	195	4	have	have	VERB
ejpam-3407	195	5	ϕ	ϕ	PROPN
ejpam-3407	195	6	∈	∈	PROPN
ejpam-3407	195	7	c(r+,r+	c(r+,r+	PROPN
ejpam-3407	195	8	)	)	PUNCT
ejpam-3407	195	9	,	,	PUNCT
ejpam-3407	195	10	ϕ(0	ϕ(0	PROPN
ejpam-3407	195	11	)	)	PUNCT
ejpam-3407	196	1	=	=	SYM
ejpam-3407	196	2	0	0	NUM
ejpam-3407	197	1	and	and	CCONJ
ejpam-3407	197	2	for	for	ADP
ejpam-3407	197	3	every	every	DET
ejpam-3407	197	4	ε	ε	PROPN
ejpam-3407	197	5	>	>	X
ejpam-3407	197	6	0	0	PUNCT
ejpam-3407	198	1	so	so	SCONJ
ejpam-3407	198	2	that	that	SCONJ
ejpam-3407	198	3	for	for	ADP
ejpam-3407	198	4	any	any	DET
ejpam-3407	198	5	solution	solution	NOUN
ejpam-3407	198	6	z	z	PROPN
ejpam-3407	198	7	∈	∈	PROPN
ejpam-3407	198	8	ac2[0	ac2[0	ADJ
ejpam-3407	198	9	,	,	PUNCT
ejpam-3407	198	10	1	1	NUM
ejpam-3407	198	11	]	]	PUNCT
ejpam-3407	198	12	of	of	ADP
ejpam-3407	198	13	|cdpz(s	|cdpz(s	PROPN
ejpam-3407	198	14	)	)	PUNCT
ejpam-3407	199	1	+	+	NOUN
ejpam-3407	199	2	q(s	q(s	PROPN
ejpam-3407	199	3	,	,	PUNCT
ejpam-3407	199	4	z(s))|	z(s))|	PROPN
ejpam-3407	199	5	≤	≤	X
ejpam-3407	199	6	ε	ε	PROPN
ejpam-3407	199	7	,	,	PUNCT
ejpam-3407	199	8	s	s	PART
ejpam-3407	199	9	∈	∈	PROPN
ejpam-3407	200	1	[	[	X
ejpam-3407	200	2	0	0	NUM
ejpam-3407	200	3	,	,	PUNCT
ejpam-3407	200	4	1	1	NUM
ejpam-3407	200	5	]	]	PUNCT
ejpam-3407	200	6	,	,	PUNCT
ejpam-3407	200	7	(	(	PUNCT
ejpam-3407	200	8	19	19	NUM
ejpam-3407	200	9	)	)	PUNCT
ejpam-3407	200	10	there	there	PRON
ejpam-3407	200	11	exists	exist	VERB
ejpam-3407	200	12	v	v	ADP
ejpam-3407	200	13	∈	∈	PROPN
ejpam-3407	200	14	ac2[0	ac2[0	NOUN
ejpam-3407	200	15	,	,	PUNCT
ejpam-3407	200	16	1	1	NUM
ejpam-3407	200	17	]	]	PUNCT
ejpam-3407	200	18	is	be	AUX
ejpam-3407	200	19	a	a	DET
ejpam-3407	200	20	unique	unique	ADJ
ejpam-3407	200	21	solution	solution	NOUN
ejpam-3407	200	22	of	of	ADP
ejpam-3407	200	23	the	the	DET
ejpam-3407	200	24	considered	consider	VERB
ejpam-3407	200	25	problem	problem	NOUN
ejpam-3407	200	26	(	(	PUNCT
ejpam-3407	200	27	1	1	X
ejpam-3407	200	28	)	)	PUNCT
ejpam-3407	201	1	such	such	ADJ
ejpam-3407	201	2	that	that	SCONJ
ejpam-3407	201	3	|z(s)−	|z(s)−	NOUN
ejpam-3407	201	4	v(s)|	v(s)|	X
ejpam-3407	201	5	≤	≤	ADJ
ejpam-3407	201	6	φ(s)ε	φ(s)ε	PROPN
ejpam-3407	201	7	,	,	PUNCT
ejpam-3407	201	8	s	s	NOUN
ejpam-3407	201	9	∈	∈	PROPN
ejpam-3407	202	1	[	[	X
ejpam-3407	202	2	0	0	NUM
ejpam-3407	202	3	,	,	PUNCT
ejpam-3407	202	4	1	1	NUM
ejpam-3407	202	5	]	]	PUNCT
ejpam-3407	202	6	.	.	PUNCT
ejpam-3407	203	1	then	then	ADV
ejpam-3407	203	2	bvp	bvp	PROPN
ejpam-3407	203	3	of	of	ADP
ejpam-3407	203	4	fdes	fde	NOUN
ejpam-3407	203	5	(	(	PUNCT
ejpam-3407	203	6	1	1	NUM
ejpam-3407	203	7	)	)	PUNCT
ejpam-3407	203	8	is	be	AUX
ejpam-3407	203	9	said	say	VERB
ejpam-3407	203	10	to	to	PART
ejpam-3407	203	11	be	be	AUX
ejpam-3407	203	12	generalized	generalize	VERB
ejpam-3407	203	13	ulam	ulam	NOUN
ejpam-3407	203	14	–	–	PUNCT
ejpam-3407	203	15	hyers	hyer	NOUN
ejpam-3407	203	16	stable	stable	ADJ
ejpam-3407	203	17	.	.	PUNCT
ejpam-3407	204	1	k.	k.	PROPN
ejpam-3407	204	2	shah	shah	PROPN
ejpam-3407	204	3	et	et	PROPN
ejpam-3407	204	4	al	al	PROPN
ejpam-3407	204	5	.	.	PUNCT
ejpam-3407	204	6	/	/	SYM
ejpam-3407	204	7	eur	eur	PROPN
ejpam-3407	204	8	.	.	PUNCT
ejpam-3407	205	1	j.	j.	PROPN
ejpam-3407	205	2	pure	pure	PROPN
ejpam-3407	205	3	appl	appl	PROPN
ejpam-3407	205	4	.	.	PROPN
ejpam-3407	205	5	math	math	PROPN
ejpam-3407	205	6	,	,	PUNCT
ejpam-3407	205	7	12	12	NUM
ejpam-3407	205	8	(	(	PUNCT
ejpam-3407	205	9	2	2	NUM
ejpam-3407	205	10	)	)	PUNCT
ejpam-3407	205	11	(	(	PUNCT
ejpam-3407	205	12	2019	2019	NUM
ejpam-3407	205	13	)	)	PUNCT
ejpam-3407	205	14	,	,	PUNCT
ejpam-3407	205	15	432	432	NUM
ejpam-3407	205	16	-	-	SYM
ejpam-3407	205	17	447	447	NUM
ejpam-3407	205	18	440	440	NUM
ejpam-3407	205	19	definition	definition	NOUN
ejpam-3407	205	20	7	7	NUM
ejpam-3407	205	21	.	.	PUNCT
ejpam-3407	206	1	if	if	SCONJ
ejpam-3407	206	2	,	,	PUNCT
ejpam-3407	206	3	we	we	PRON
ejpam-3407	206	4	have	have	VERB
ejpam-3407	206	5	φ	φ	PROPN
ejpam-3407	206	6	∈	∈	PROPN
ejpam-3407	206	7	c([0	c([0	NOUN
ejpam-3407	206	8	,	,	PUNCT
ejpam-3407	206	9	1],r+	1],r+	NUM
ejpam-3407	206	10	)	)	PUNCT
ejpam-3407	206	11	,	,	PUNCT
ejpam-3407	206	12	ck	ck	PROPN
ejpam-3407	206	13	>	>	X
ejpam-3407	206	14	0	0	PUNCT
ejpam-3407	206	15	and	and	CCONJ
ejpam-3407	206	16	for	for	ADP
ejpam-3407	206	17	every	every	DET
ejpam-3407	206	18	ε	ε	PROPN
ejpam-3407	206	19	>	>	X
ejpam-3407	206	20	0	0	NUM
ejpam-3407	206	21	such	such	ADJ
ejpam-3407	206	22	that	that	PRON
ejpam-3407	206	23	for	for	ADP
ejpam-3407	206	24	any	any	DET
ejpam-3407	206	25	solution	solution	NOUN
ejpam-3407	206	26	z	z	PROPN
ejpam-3407	206	27	∈	∈	PROPN
ejpam-3407	206	28	ac2[0	ac2[0	ADJ
ejpam-3407	206	29	,	,	PUNCT
ejpam-3407	206	30	1	1	NUM
ejpam-3407	206	31	]	]	PUNCT
ejpam-3407	206	32	of	of	ADP
ejpam-3407	206	33	inequality	inequality	NOUN
ejpam-3407	206	34	|cdpz(s	|cdpz(s	PROPN
ejpam-3407	206	35	)	)	PUNCT
ejpam-3407	207	1	+	+	NOUN
ejpam-3407	207	2	q(s	q(s	PROPN
ejpam-3407	207	3	,	,	PUNCT
ejpam-3407	207	4	z(s))|	z(s))|	PROPN
ejpam-3407	207	5	≤	≤	X
ejpam-3407	207	6	εφ(s	εφ(s	NOUN
ejpam-3407	207	7	)	)	PUNCT
ejpam-3407	207	8	,	,	PUNCT
ejpam-3407	207	9	s	s	VERB
ejpam-3407	207	10	∈	∈	PROPN
ejpam-3407	208	1	[	[	X
ejpam-3407	208	2	0	0	NUM
ejpam-3407	208	3	,	,	PUNCT
ejpam-3407	208	4	1	1	NUM
ejpam-3407	208	5	]	]	PUNCT
ejpam-3407	208	6	,	,	PUNCT
ejpam-3407	208	7	(	(	PUNCT
ejpam-3407	208	8	20	20	NUM
ejpam-3407	208	9	)	)	PUNCT
ejpam-3407	208	10	there	there	PRON
ejpam-3407	208	11	exists	exist	VERB
ejpam-3407	208	12	v	v	ADP
ejpam-3407	208	13	∈	∈	PROPN
ejpam-3407	208	14	ac2[0	ac2[0	NOUN
ejpam-3407	208	15	,	,	PUNCT
ejpam-3407	208	16	1	1	NUM
ejpam-3407	208	17	]	]	PUNCT
ejpam-3407	208	18	is	be	AUX
ejpam-3407	208	19	a	a	DET
ejpam-3407	208	20	unique	unique	ADJ
ejpam-3407	208	21	solution	solution	NOUN
ejpam-3407	208	22	of	of	ADP
ejpam-3407	208	23	considered	consider	VERB
ejpam-3407	208	24	problem	problem	NOUN
ejpam-3407	208	25	(	(	PUNCT
ejpam-3407	208	26	1	1	X
ejpam-3407	208	27	)	)	PUNCT
ejpam-3407	208	28	such	such	ADJ
ejpam-3407	208	29	that	that	SCONJ
ejpam-3407	208	30	|z(s)−	|z(s)−	NOUN
ejpam-3407	208	31	v(s)|	v(s)|	X
ejpam-3407	208	32	≤	≤	NUM
ejpam-3407	208	33	ckεφ(s	ckεφ(s	PROPN
ejpam-3407	208	34	)	)	PUNCT
ejpam-3407	208	35	,	,	PUNCT
ejpam-3407	208	36	s	s	VERB
ejpam-3407	208	37	∈	∈	PROPN
ejpam-3407	209	1	[	[	X
ejpam-3407	209	2	0	0	NUM
ejpam-3407	209	3	,	,	PUNCT
ejpam-3407	209	4	1	1	NUM
ejpam-3407	209	5	]	]	PUNCT
ejpam-3407	209	6	.	.	PUNCT
ejpam-3407	210	1	then	then	ADV
ejpam-3407	210	2	bvp(1)is	bvp(1)is	PROPN
ejpam-3407	210	3	said	say	VERB
ejpam-3407	210	4	to	to	PART
ejpam-3407	210	5	be	be	AUX
ejpam-3407	210	6	the	the	DET
ejpam-3407	210	7	ulam	ulam	X
ejpam-3407	210	8	–	–	PUNCT
ejpam-3407	210	9	hyers	hyer	NOUN
ejpam-3407	210	10	–	–	PUNCT
ejpam-3407	210	11	rassias	rassia	NOUN
ejpam-3407	210	12	stable	stable	ADJ
ejpam-3407	210	13	with	with	ADP
ejpam-3407	210	14	respect	respect	NOUN
ejpam-3407	210	15	to	to	ADP
ejpam-3407	210	16	φ	φ	PROPN
ejpam-3407	210	17	∈	∈	PROPN
ejpam-3407	210	18	c([0	c([0	NOUN
ejpam-3407	210	19	,	,	PUNCT
ejpam-3407	210	20	1],r+	1],r+	NUM
ejpam-3407	210	21	)	)	PUNCT
ejpam-3407	210	22	.	.	PUNCT
ejpam-3407	211	1	definition	definition	NOUN
ejpam-3407	211	2	8	8	NUM
ejpam-3407	211	3	.	.	PUNCT
ejpam-3407	212	1	if	if	SCONJ
ejpam-3407	212	2	,	,	PUNCT
ejpam-3407	212	3	we	we	PRON
ejpam-3407	212	4	have	have	VERB
ejpam-3407	212	5	φ	φ	PROPN
ejpam-3407	212	6	∈	∈	PROPN
ejpam-3407	212	7	c([0	c([0	NOUN
ejpam-3407	212	8	,	,	PUNCT
ejpam-3407	212	9	1],r	1],r	NUM
ejpam-3407	212	10	)	)	PUNCT
ejpam-3407	212	11	and	and	CCONJ
ejpam-3407	212	12	cφ	cφ	ADP
ejpam-3407	212	13	∈	∈	NOUN
ejpam-3407	212	14	r	r	NOUN
ejpam-3407	213	1	+	+	CCONJ
ejpam-3407	213	2	so	so	SCONJ
ejpam-3407	213	3	that	that	SCONJ
ejpam-3407	213	4	for	for	ADP
ejpam-3407	213	5	any	any	DET
ejpam-3407	213	6	solution	solution	NOUN
ejpam-3407	213	7	z	z	PROPN
ejpam-3407	213	8	∈	∈	PROPN
ejpam-3407	213	9	ac2[0	ac2[0	ADJ
ejpam-3407	213	10	,	,	PUNCT
ejpam-3407	213	11	1	1	NUM
ejpam-3407	213	12	]	]	PUNCT
ejpam-3407	213	13	of	of	ADP
ejpam-3407	213	14	inequality	inequality	NOUN
ejpam-3407	213	15	|cdpz(s	|cdpz(s	PROPN
ejpam-3407	213	16	)	)	PUNCT
ejpam-3407	214	1	+	+	NOUN
ejpam-3407	214	2	q(s	q(s	ADJ
ejpam-3407	214	3	,	,	PUNCT
ejpam-3407	214	4	z(s))|	z(s))|	NOUN
ejpam-3407	214	5	≤	≤	NUM
ejpam-3407	214	6	φ(s	φ(s	NOUN
ejpam-3407	214	7	)	)	PUNCT
ejpam-3407	214	8	,	,	PUNCT
ejpam-3407	214	9	s	s	VERB
ejpam-3407	214	10	∈	∈	PROPN
ejpam-3407	215	1	[	[	X
ejpam-3407	215	2	0	0	NUM
ejpam-3407	215	3	,	,	PUNCT
ejpam-3407	215	4	1	1	NUM
ejpam-3407	215	5	]	]	PUNCT
ejpam-3407	215	6	,	,	PUNCT
ejpam-3407	215	7	(	(	PUNCT
ejpam-3407	215	8	21	21	NUM
ejpam-3407	215	9	)	)	PUNCT
ejpam-3407	215	10	there	there	PRON
ejpam-3407	215	11	exists	exist	VERB
ejpam-3407	215	12	v	v	ADP
ejpam-3407	215	13	∈	∈	PROPN
ejpam-3407	215	14	ac2[0	ac2[0	NOUN
ejpam-3407	215	15	,	,	PUNCT
ejpam-3407	215	16	1	1	NUM
ejpam-3407	215	17	]	]	PUNCT
ejpam-3407	215	18	is	be	AUX
ejpam-3407	215	19	a	a	DET
ejpam-3407	215	20	unique	unique	ADJ
ejpam-3407	215	21	solution	solution	NOUN
ejpam-3407	215	22	of	of	ADP
ejpam-3407	215	23	considered	consider	VERB
ejpam-3407	215	24	problem	problem	NOUN
ejpam-3407	215	25	(	(	PUNCT
ejpam-3407	215	26	1	1	NUM
ejpam-3407	215	27	)	)	PUNCT
ejpam-3407	215	28	so	so	SCONJ
ejpam-3407	215	29	that	that	SCONJ
ejpam-3407	215	30	|z(s)−	|z(s)−	NOUN
ejpam-3407	215	31	v(s)|	v(s)|	VERB
ejpam-3407	215	32	≤	≤	NUM
ejpam-3407	215	33	cφφ(s	cφφ(s	PROPN
ejpam-3407	215	34	)	)	PUNCT
ejpam-3407	215	35	,	,	PUNCT
ejpam-3407	215	36	s	s	VERB
ejpam-3407	215	37	∈	∈	PROPN
ejpam-3407	216	1	[	[	X
ejpam-3407	216	2	0	0	NUM
ejpam-3407	216	3	,	,	PUNCT
ejpam-3407	216	4	1	1	NUM
ejpam-3407	216	5	]	]	PUNCT
ejpam-3407	216	6	.	.	PUNCT
ejpam-3407	217	1	then	then	ADV
ejpam-3407	217	2	bvp(1	bvp(1	NOUN
ejpam-3407	217	3	)	)	PUNCT
ejpam-3407	217	4	is	be	AUX
ejpam-3407	217	5	said	say	VERB
ejpam-3407	217	6	to	to	PART
ejpam-3407	217	7	be	be	AUX
ejpam-3407	217	8	generalized	generalize	VERB
ejpam-3407	217	9	ulam	ulam	NOUN
ejpam-3407	217	10	–	–	PUNCT
ejpam-3407	217	11	hyers	hyer	NOUN
ejpam-3407	217	12	–	–	PUNCT
ejpam-3407	217	13	rassias	rassia	NOUN
ejpam-3407	217	14	stable	stable	ADJ
ejpam-3407	217	15	with	with	ADP
ejpam-3407	217	16	respect	respect	NOUN
ejpam-3407	217	17	to	to	ADP
ejpam-3407	217	18	φ	φ	PROPN
ejpam-3407	217	19	∈	∈	PROPN
ejpam-3407	217	20	c([0	c([0	NOUN
ejpam-3407	217	21	,	,	PUNCT
ejpam-3407	217	22	1],r	1],r	NUM
ejpam-3407	217	23	)	)	PUNCT
ejpam-3407	217	24	.	.	PUNCT
ejpam-3407	218	1	remark	remark	PROPN
ejpam-3407	218	2	1	1	NUM
ejpam-3407	218	3	.	.	PUNCT
ejpam-3407	219	1	let	let	VERB
ejpam-3407	219	2	z	z	NOUN
ejpam-3407	219	3	∈	∈	PROPN
ejpam-3407	219	4	ac2[0	ac2[0	ADJ
ejpam-3407	219	5	,	,	PUNCT
ejpam-3407	219	6	1	1	NUM
ejpam-3407	219	7	]	]	PUNCT
ejpam-3407	219	8	is	be	AUX
ejpam-3407	219	9	the	the	DET
ejpam-3407	219	10	solution	solution	NOUN
ejpam-3407	219	11	of	of	ADP
ejpam-3407	219	12	inequality	inequality	NOUN
ejpam-3407	219	13	(	(	PUNCT
ejpam-3407	219	14	19	19	NUM
ejpam-3407	219	15	)	)	PUNCT
ejpam-3407	219	16	whenever	whenever	SCONJ
ejpam-3407	219	17	,	,	PUNCT
ejpam-3407	219	18	there	there	PRON
ejpam-3407	219	19	exists	exist	VERB
ejpam-3407	219	20	the	the	DET
ejpam-3407	219	21	function	function	NOUN
ejpam-3407	219	22	ψ	ψ	ADP
ejpam-3407	219	23	∈	∈	PROPN
ejpam-3407	219	24	c([0	c([0	NOUN
ejpam-3407	219	25	,	,	PUNCT
ejpam-3407	219	26	1],r	1],r	NUM
ejpam-3407	219	27	)	)	PUNCT
ejpam-3407	219	28	(	(	PUNCT
ejpam-3407	219	29	dependent	dependent	ADJ
ejpam-3407	219	30	on	on	ADP
ejpam-3407	219	31	z	z	PROPN
ejpam-3407	219	32	)	)	PUNCT
ejpam-3407	219	33	,	,	PUNCT
ejpam-3407	219	34	so	so	SCONJ
ejpam-3407	219	35	that	that	SCONJ
ejpam-3407	219	36	(	(	PUNCT
ejpam-3407	219	37	i	i	NOUN
ejpam-3407	219	38	)	)	PUNCT
ejpam-3407	219	39	cdpz(s	cdpz(s	NOUN
ejpam-3407	219	40	)	)	PUNCT
ejpam-3407	220	1	+	+	NOUN
ejpam-3407	220	2	q(s	q(s	ADJ
ejpam-3407	220	3	,	,	PUNCT
ejpam-3407	220	4	z(s	z(s	PROPN
ejpam-3407	220	5	)	)	PUNCT
ejpam-3407	220	6	)	)	PUNCT
ejpam-3407	221	1	=	=	SYM
ejpam-3407	221	2	ψ(s	ψ(s	PROPN
ejpam-3407	221	3	)	)	PUNCT
ejpam-3407	221	4	,	,	PUNCT
ejpam-3407	221	5	s	s	VERB
ejpam-3407	221	6	∈	∈	PROPN
ejpam-3407	222	1	[	[	X
ejpam-3407	222	2	0	0	NUM
ejpam-3407	222	3	,	,	PUNCT
ejpam-3407	222	4	1	1	NUM
ejpam-3407	222	5	]	]	PUNCT
ejpam-3407	222	6	;	;	PUNCT
ejpam-3407	222	7	(	(	PUNCT
ejpam-3407	222	8	ii	ii	X
ejpam-3407	222	9	)	)	PUNCT
ejpam-3407	222	10	|ψ(s)|	|ψ(s)|	PROPN
ejpam-3407	222	11	≤	≤	PROPN
ejpam-3407	222	12	ε	ε	PROPN
ejpam-3407	222	13	,	,	PUNCT
ejpam-3407	222	14	for	for	ADP
ejpam-3407	222	15	all	all	DET
ejpam-3407	222	16	s	s	PART
ejpam-3407	222	17	∈	∈	NOUN
ejpam-3407	223	1	[	[	X
ejpam-3407	223	2	0	0	NUM
ejpam-3407	223	3	,	,	PUNCT
ejpam-3407	223	4	1	1	NUM
ejpam-3407	223	5	]	]	PUNCT
ejpam-3407	223	6	.	.	PUNCT
ejpam-3407	224	1	theorem	theorem	NOUN
ejpam-3407	224	2	2	2	NUM
ejpam-3407	224	3	.	.	PUNCT
ejpam-3407	225	1	if	if	SCONJ
ejpam-3407	225	2	consider	consider	VERB
ejpam-3407	225	3	the	the	DET
ejpam-3407	225	4	conditions	condition	NOUN
ejpam-3407	225	5	(	(	PUNCT
ejpam-3407	225	6	c2	c2	PROPN
ejpam-3407	225	7	)	)	PUNCT
ejpam-3407	225	8	,	,	PUNCT
ejpam-3407	225	9	(	(	PUNCT
ejpam-3407	225	10	c3	c3	PROPN
ejpam-3407	225	11	)	)	PUNCT
ejpam-3407	225	12	coupled	couple	VERB
ejpam-3407	225	13	with	with	ADP
ejpam-3407	225	14	δ	δ	PROPN
ejpam-3407	225	15	<	<	X
ejpam-3407	225	16	1	1	NUM
ejpam-3407	225	17	,	,	PUNCT
ejpam-3407	225	18	then	then	ADV
ejpam-3407	225	19	the	the	DET
ejpam-3407	225	20	ulamhyers	ulamhyer	NOUN
ejpam-3407	225	21	stability	stability	NOUN
ejpam-3407	225	22	results	result	VERB
ejpam-3407	225	23	for	for	ADP
ejpam-3407	225	24	the	the	DET
ejpam-3407	225	25	solutions	solution	NOUN
ejpam-3407	225	26	of	of	ADP
ejpam-3407	225	27	bvp	bvp	NOUN
ejpam-3407	225	28	(	(	PUNCT
ejpam-3407	225	29	1	1	X
ejpam-3407	225	30	)	)	PUNCT
ejpam-3407	225	31	are	be	AUX
ejpam-3407	225	32	obtained	obtain	VERB
ejpam-3407	225	33	which	which	PRON
ejpam-3407	225	34	further	far	ADV
ejpam-3407	225	35	implies	imply	VERB
ejpam-3407	225	36	that	that	SCONJ
ejpam-3407	225	37	the	the	DET
ejpam-3407	225	38	solutions	solution	NOUN
ejpam-3407	225	39	of	of	ADP
ejpam-3407	225	40	bvp	bvp	NOUN
ejpam-3407	225	41	(	(	PUNCT
ejpam-3407	225	42	1	1	X
ejpam-3407	225	43	)	)	PUNCT
ejpam-3407	225	44	are	be	AUX
ejpam-3407	225	45	generalized	generalize	VERB
ejpam-3407	225	46	ulam	ulam	NOUN
ejpam-3407	225	47	-	-	PUNCT
ejpam-3407	225	48	hyers	hyer	NOUN
ejpam-3407	225	49	stable	stable	ADJ
ejpam-3407	225	50	.	.	PUNCT
ejpam-3407	226	1	proof	proof	NOUN
ejpam-3407	226	2	.	.	PUNCT
ejpam-3407	227	1	let	let	AUX
ejpam-3407	227	2	consider	consider	VERB
ejpam-3407	227	3	the	the	DET
ejpam-3407	227	4	conditions	condition	NOUN
ejpam-3407	227	5	(	(	PUNCT
ejpam-3407	227	6	c2),(c3	c2),(c3	NOUN
ejpam-3407	227	7	)	)	PUNCT
ejpam-3407	227	8	coupled	couple	VERB
ejpam-3407	227	9	with	with	ADP
ejpam-3407	227	10	δ	δ	PROPN
ejpam-3407	227	11	<	<	X
ejpam-3407	227	12	1	1	X
ejpam-3407	227	13	.	.	PUNCT
ejpam-3407	228	1	let	let	VERB
ejpam-3407	228	2	z	z	NOUN
ejpam-3407	228	3	∈	∈	PROPN
ejpam-3407	228	4	ac2[0	ac2[0	ADJ
ejpam-3407	228	5	,	,	PUNCT
ejpam-3407	228	6	1	1	NUM
ejpam-3407	228	7	]	]	PUNCT
ejpam-3407	228	8	be	be	AUX
ejpam-3407	228	9	any	any	DET
ejpam-3407	228	10	solution	solution	NOUN
ejpam-3407	228	11	of	of	ADP
ejpam-3407	228	12	bvp	bvp	PROPN
ejpam-3407	228	13	(	(	PUNCT
ejpam-3407	228	14	1	1	NUM
ejpam-3407	228	15	)	)	PUNCT
ejpam-3407	228	16	.	.	PUNCT
ejpam-3407	229	1	then	then	ADV
ejpam-3407	229	2	using	use	VERB
ejpam-3407	229	3	the	the	DET
ejpam-3407	229	4	condition	condition	NOUN
ejpam-3407	229	5	(	(	PUNCT
ejpam-3407	229	6	i	i	NOUN
ejpam-3407	229	7	)	)	PUNCT
ejpam-3407	229	8	of	of	ADP
ejpam-3407	229	9	the	the	DET
ejpam-3407	229	10	remark	remark	NOUN
ejpam-3407	229	11	1	1	NUM
ejpam-3407	229	12	for	for	ADP
ejpam-3407	229	13	z	z	PROPN
ejpam-3407	229	14	∈	∈	PROPN
ejpam-3407	229	15	ac2[0	ac2[0	ADJ
ejpam-3407	229	16	,	,	PUNCT
ejpam-3407	229	17	1	1	NUM
ejpam-3407	229	18	]	]	PUNCT
ejpam-3407	229	19	,	,	PUNCT
ejpam-3407	229	20	which	which	PRON
ejpam-3407	229	21	is	be	AUX
ejpam-3407	229	22	cdpz(s	cdpz(	VERB
ejpam-3407	229	23	)	)	PUNCT
ejpam-3407	230	1	+	+	VERB
ejpam-3407	230	2	q(s	q(s	ADJ
ejpam-3407	230	3	,	,	PUNCT
ejpam-3407	230	4	z(s	z(s	PROPN
ejpam-3407	230	5	)	)	PUNCT
ejpam-3407	230	6	)	)	PUNCT
ejpam-3407	231	1	=	=	SYM
ejpam-3407	231	2	ψ(s	ψ(s	PROPN
ejpam-3407	231	3	)	)	PUNCT
ejpam-3407	231	4	,	,	PUNCT
ejpam-3407	231	5	for	for	ADP
ejpam-3407	231	6	all	all	DET
ejpam-3407	231	7	s	s	PART
ejpam-3407	231	8	∈	∈	NOUN
ejpam-3407	232	1	[	[	X
ejpam-3407	232	2	0	0	NUM
ejpam-3407	232	3	,	,	PUNCT
ejpam-3407	232	4	1	1	NUM
ejpam-3407	232	5	]	]	PUNCT
ejpam-3407	232	6	,	,	PUNCT
ejpam-3407	232	7	2	2	NUM
ejpam-3407	232	8	<	<	X
ejpam-3407	232	9	p	p	X
ejpam-3407	232	10	≤	≤	NOUN
ejpam-3407	232	11	3	3	NUM
ejpam-3407	232	12	.	.	PUNCT
ejpam-3407	232	13	thank	thank	VERB
ejpam-3407	232	14	to	to	PART
ejpam-3407	232	15	lemma	lemma	PROPN
ejpam-3407	232	16	4	4	NUM
ejpam-3407	232	17	,	,	PUNCT
ejpam-3407	232	18	we	we	PRON
ejpam-3407	232	19	obtain	obtain	VERB
ejpam-3407	232	20	z(s	z(s	NUM
ejpam-3407	232	21	)	)	PUNCT
ejpam-3407	233	1	=	=	PUNCT
ejpam-3407	233	2	∫	∫	PROPN
ejpam-3407	233	3	1	1	NUM
ejpam-3407	234	1	0	0	NUM
ejpam-3407	234	2	r(s	r(s	PROPN
ejpam-3407	234	3	,	,	PUNCT
ejpam-3407	234	4	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	234	5	,	,	PUNCT
ejpam-3407	234	6	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	234	7	+	+	CCONJ
ejpam-3407	234	8	∫	∫	PROPN
ejpam-3407	234	9	1	1	NUM
ejpam-3407	234	10	0	0	NUM
ejpam-3407	234	11	r(s	r(s	PROPN
ejpam-3407	234	12	,	,	PUNCT
ejpam-3407	234	13	γ)ψ(γ)dγ	γ)ψ(γ)dγ	NOUN
ejpam-3407	234	14	,	,	PUNCT
ejpam-3407	234	15	where	where	SCONJ
ejpam-3407	234	16	ψ	ψ	ADP
ejpam-3407	234	17	∈	∈	PROPN
ejpam-3407	234	18	c([0	c([0	NOUN
ejpam-3407	234	19	,	,	PUNCT
ejpam-3407	234	20	1],r	1],r	NUM
ejpam-3407	234	21	)	)	PUNCT
ejpam-3407	234	22	.	.	PUNCT
ejpam-3407	235	1	which	which	PRON
ejpam-3407	235	2	yields	yield	VERB
ejpam-3407	235	3	|z(s)−	|z(s)−	PUNCT
ejpam-3407	235	4	∫	∫	PROPN
ejpam-3407	235	5	1	1	NUM
ejpam-3407	235	6	0	0	NUM
ejpam-3407	235	7	r(s	r(s	PROPN
ejpam-3407	235	8	,	,	PUNCT
ejpam-3407	235	9	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	235	10	,	,	PUNCT
ejpam-3407	235	11	z(γ))dγ|	z(γ))dγ|	NOUN
ejpam-3407	235	12	≤	≤	NUM
ejpam-3407	235	13	2ε	2ε	NOUN
ejpam-3407	235	14	(	(	PUNCT
ejpam-3407	235	15	2−	2−	NUM
ejpam-3407	235	16	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	235	17	)	)	PUNCT
ejpam-3407	235	18	,	,	PUNCT
ejpam-3407	235	19	s	s	VERB
ejpam-3407	235	20	∈	∈	PROPN
ejpam-3407	236	1	[	[	X
ejpam-3407	236	2	0	0	NUM
ejpam-3407	236	3	,	,	PUNCT
ejpam-3407	236	4	1	1	NUM
ejpam-3407	236	5	]	]	PUNCT
ejpam-3407	236	6	.	.	PUNCT
ejpam-3407	237	1	(	(	PUNCT
ejpam-3407	237	2	22	22	NUM
ejpam-3407	237	3	)	)	PUNCT
ejpam-3407	237	4	k.	k.	NOUN
ejpam-3407	237	5	shah	shah	PROPN
ejpam-3407	237	6	et	et	PROPN
ejpam-3407	237	7	al	al	PROPN
ejpam-3407	237	8	.	.	PUNCT
ejpam-3407	237	9	/	/	SYM
ejpam-3407	237	10	eur	eur	PROPN
ejpam-3407	237	11	.	.	PUNCT
ejpam-3407	238	1	j.	j.	PROPN
ejpam-3407	238	2	pure	pure	PROPN
ejpam-3407	238	3	appl	appl	PROPN
ejpam-3407	238	4	.	.	PROPN
ejpam-3407	238	5	math	math	PROPN
ejpam-3407	238	6	,	,	PUNCT
ejpam-3407	238	7	12	12	NUM
ejpam-3407	238	8	(	(	PUNCT
ejpam-3407	238	9	2	2	NUM
ejpam-3407	238	10	)	)	PUNCT
ejpam-3407	238	11	(	(	PUNCT
ejpam-3407	238	12	2019	2019	NUM
ejpam-3407	238	13	)	)	PUNCT
ejpam-3407	238	14	,	,	PUNCT
ejpam-3407	238	15	432	432	NUM
ejpam-3407	238	16	-	-	SYM
ejpam-3407	238	17	447	447	NUM
ejpam-3407	238	18	441	441	NUM
ejpam-3407	238	19	let	let	VERB
ejpam-3407	238	20	v	v	NUM
ejpam-3407	238	21	∈	∈	PROPN
ejpam-3407	238	22	ac2[0	ac2[0	NOUN
ejpam-3407	238	23	,	,	PUNCT
ejpam-3407	238	24	1	1	NUM
ejpam-3407	238	25	]	]	PUNCT
ejpam-3407	238	26	be	be	AUX
ejpam-3407	238	27	a	a	DET
ejpam-3407	238	28	unique	unique	ADJ
ejpam-3407	238	29	solution	solution	NOUN
ejpam-3407	238	30	of	of	ADP
ejpam-3407	238	31	bvp	bvp	PROPN
ejpam-3407	238	32	(	(	PUNCT
ejpam-3407	238	33	1).then	1).then	X
ejpam-3407	238	34	|z(s)−	|z(s)−	NUM
ejpam-3407	239	1	v(s)|	v(s)|	NOUN
ejpam-3407	240	1	=	=	SYM
ejpam-3407	241	1	∣	∣	PROPN
ejpam-3407	241	2	∣	∣	ADJ
ejpam-3407	241	3	∣	∣	ADJ
ejpam-3407	241	4	∣	∣	ADJ
ejpam-3407	241	5	z(s)−	z(s)−	PROPN
ejpam-3407	241	6	∫	∫	PROPN
ejpam-3407	241	7	1	1	NUM
ejpam-3407	241	8	0	0	NUM
ejpam-3407	241	9	r(s	r(s	PROPN
ejpam-3407	241	10	,	,	PUNCT
ejpam-3407	241	11	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	241	12	,	,	PUNCT
ejpam-3407	241	13	v(γ))dγ	v(γ))dγ	VERB
ejpam-3407	241	14	∣	∣	PROPN
ejpam-3407	241	15	∣	∣	ADJ
ejpam-3407	241	16	∣	∣	ADJ
ejpam-3407	241	17	∣	∣	ADJ
ejpam-3407	241	18	=	=	PUNCT
ejpam-3407	241	19	∣	∣	ADJ
ejpam-3407	241	20	∣	∣	ADJ
ejpam-3407	241	21	∣	∣	ADJ
ejpam-3407	241	22	∣	∣	ADJ
ejpam-3407	241	23	z(s)−	z(s)−	PROPN
ejpam-3407	241	24	∫	∫	PROPN
ejpam-3407	241	25	1	1	NUM
ejpam-3407	242	1	0	0	NUM
ejpam-3407	242	2	r(s	r(s	PROPN
ejpam-3407	242	3	,	,	PUNCT
ejpam-3407	242	4	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	242	5	,	,	PUNCT
ejpam-3407	242	6	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	242	7	+	+	CCONJ
ejpam-3407	242	8	∫	∫	PROPN
ejpam-3407	242	9	1	1	NUM
ejpam-3407	242	10	0	0	NUM
ejpam-3407	242	11	r(s	r(s	PROPN
ejpam-3407	242	12	,	,	PUNCT
ejpam-3407	242	13	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	242	14	,	,	PUNCT
ejpam-3407	242	15	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	243	1	−	−	PROPN
ejpam-3407	243	2	∫	∫	PROPN
ejpam-3407	243	3	1	1	NUM
ejpam-3407	243	4	0	0	NUM
ejpam-3407	243	5	r(s	r(s	PROPN
ejpam-3407	243	6	,	,	PUNCT
ejpam-3407	243	7	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	243	8	,	,	PUNCT
ejpam-3407	243	9	v(γ))dγ	v(γ))dγ	VERB
ejpam-3407	243	10	∣	∣	PROPN
ejpam-3407	243	11	∣	∣	ADJ
ejpam-3407	243	12	∣	∣	ADJ
ejpam-3407	243	13	∣	∣	ADJ
ejpam-3407	243	14	≤	≤	NUM
ejpam-3407	243	15	∣	∣	ADJ
ejpam-3407	243	16	∣	∣	ADJ
ejpam-3407	243	17	∣	∣	ADJ
ejpam-3407	243	18	∣	∣	ADJ
ejpam-3407	243	19	z(s)−	z(s)−	PROPN
ejpam-3407	243	20	∫	∫	PROPN
ejpam-3407	243	21	1	1	NUM
ejpam-3407	243	22	0	0	NUM
ejpam-3407	243	23	r(s	r(s	PROPN
ejpam-3407	243	24	,	,	PUNCT
ejpam-3407	243	25	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	243	26	,	,	PUNCT
ejpam-3407	243	27	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	243	28	∣	∣	PROPN
ejpam-3407	243	29	∣	∣	ADJ
ejpam-3407	243	30	∣	∣	ADJ
ejpam-3407	243	31	∣	∣	ADJ
ejpam-3407	243	32	+	+	CCONJ
ejpam-3407	243	33	∫	∫	PROPN
ejpam-3407	243	34	1	1	NUM
ejpam-3407	243	35	0	0	X
ejpam-3407	244	1	|r(s	|r(s	NOUN
ejpam-3407	244	2	,	,	PUNCT
ejpam-3407	244	3	γ)|q(γ	γ)|q(γ	NOUN
ejpam-3407	244	4	,	,	PUNCT
ejpam-3407	244	5	z(γ))−q(γ	z(γ))−q(γ	NUM
ejpam-3407	244	6	,	,	PUNCT
ejpam-3407	244	7	v(γ))|dγ	v(γ))|dγ	X
ejpam-3407	244	8	.	.	PUNCT
ejpam-3407	245	1	by	by	ADP
ejpam-3407	245	2	using	use	VERB
ejpam-3407	245	3	the	the	DET
ejpam-3407	245	4	inequality	inequality	NOUN
ejpam-3407	245	5	(	(	PUNCT
ejpam-3407	245	6	22	22	NUM
ejpam-3407	245	7	)	)	PUNCT
ejpam-3407	245	8	,	,	PUNCT
ejpam-3407	245	9	we	we	PRON
ejpam-3407	245	10	obtain	obtain	VERB
ejpam-3407	245	11	that	that	DET
ejpam-3407	245	12	‖z	‖z	NOUN
ejpam-3407	245	13	−	−	NOUN
ejpam-3407	245	14	v‖	v‖	NOUN
ejpam-3407	245	15	≤	≤	NUM
ejpam-3407	245	16	2ε	2ε	NOUN
ejpam-3407	245	17	(	(	PUNCT
ejpam-3407	245	18	2−	2−	NUM
ejpam-3407	245	19	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	245	20	)	)	PUNCT
ejpam-3407	246	1	+	+	NUM
ejpam-3407	246	2	2b	2b	NUM
ejpam-3407	246	3	(	(	PUNCT
ejpam-3407	246	4	2−	2−	NUM
ejpam-3407	246	5	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	246	6	)	)	PUNCT
ejpam-3407	246	7	‖z	‖z	NOUN
ejpam-3407	246	8	−	−	PROPN
ejpam-3407	246	9	v‖	v‖	NOUN
ejpam-3407	246	10	,	,	PUNCT
ejpam-3407	246	11	hence	hence	ADV
ejpam-3407	246	12	we	we	PRON
ejpam-3407	246	13	have	have	VERB
ejpam-3407	246	14	‖z	‖z	NOUN
ejpam-3407	246	15	−	−	NOUN
ejpam-3407	246	16	v‖	v‖	NOUN
ejpam-3407	246	17	≤	≤	NUM
ejpam-3407	246	18	ckε	ckε	NOUN
ejpam-3407	246	19	,	,	PUNCT
ejpam-3407	246	20	where	where	SCONJ
ejpam-3407	246	21	ck	ck	NOUN
ejpam-3407	246	22	=	=	SYM
ejpam-3407	246	23	2	2	NUM
ejpam-3407	246	24	(	(	PUNCT
ejpam-3407	246	25	2−	2−	NUM
ejpam-3407	246	26	δ)γ(p)−	δ)γ(p)−	NOUN
ejpam-3407	246	27	2b	2b	NOUN
ejpam-3407	246	28	>	>	X
ejpam-3407	246	29	0	0	X
ejpam-3407	246	30	.	.	PUNCT
ejpam-3407	247	1	hence	hence	ADV
ejpam-3407	247	2	the	the	DET
ejpam-3407	247	3	solutions	solution	NOUN
ejpam-3407	247	4	of	of	ADP
ejpam-3407	247	5	bvp	bvp	NOUN
ejpam-3407	247	6	(	(	PUNCT
ejpam-3407	247	7	1	1	X
ejpam-3407	247	8	)	)	PUNCT
ejpam-3407	247	9	are	be	AUX
ejpam-3407	247	10	ulam	ulam	NOUN
ejpam-3407	247	11	-	-	PUNCT
ejpam-3407	247	12	hyers	hyer	NOUN
ejpam-3407	247	13	stable	stable	ADJ
ejpam-3407	247	14	.	.	PUNCT
ejpam-3407	248	1	when	when	SCONJ
ejpam-3407	248	2	,	,	PUNCT
ejpam-3407	248	3	we	we	PRON
ejpam-3407	248	4	substitute	substitute	VERB
ejpam-3407	248	5	φ(ε	φ(ε	ADV
ejpam-3407	248	6	)	)	PUNCT
ejpam-3407	248	7	=	=	SYM
ejpam-3407	248	8	ckε	ckε	NOUN
ejpam-3407	248	9	,	,	PUNCT
ejpam-3407	248	10	φ(0	φ(0	ADJ
ejpam-3407	248	11	)	)	PUNCT
ejpam-3407	248	12	=	=	SYM
ejpam-3407	249	1	0	0	X
ejpam-3407	249	2	.	.	PUNCT
ejpam-3407	250	1	then	then	ADV
ejpam-3407	250	2	consequently	consequently	ADV
ejpam-3407	250	3	generalized	generalize	VERB
ejpam-3407	250	4	ulam	ulam	NOUN
ejpam-3407	250	5	-	-	PUNCT
ejpam-3407	250	6	hyers	hyer	NOUN
ejpam-3407	250	7	stability	stability	NOUN
ejpam-3407	250	8	for	for	ADP
ejpam-3407	250	9	the	the	DET
ejpam-3407	250	10	solutions	solution	NOUN
ejpam-3407	250	11	of	of	ADP
ejpam-3407	250	12	bvp	bvp	NOUN
ejpam-3407	250	13	(	(	PUNCT
ejpam-3407	250	14	1	1	X
ejpam-3407	250	15	)	)	PUNCT
ejpam-3407	250	16	are	be	AUX
ejpam-3407	250	17	obtained	obtain	VERB
ejpam-3407	250	18	.	.	PUNCT
ejpam-3407	251	1	remark	remark	PROPN
ejpam-3407	251	2	2	2	NUM
ejpam-3407	251	3	.	.	PUNCT
ejpam-3407	252	1	let	let	VERB
ejpam-3407	252	2	z	z	NOUN
ejpam-3407	252	3	∈	∈	PROPN
ejpam-3407	252	4	ac2[0	ac2[0	ADJ
ejpam-3407	252	5	,	,	PUNCT
ejpam-3407	252	6	1	1	NUM
ejpam-3407	252	7	]	]	PUNCT
ejpam-3407	252	8	is	be	AUX
ejpam-3407	252	9	the	the	DET
ejpam-3407	252	10	solution	solution	NOUN
ejpam-3407	252	11	of	of	ADP
ejpam-3407	252	12	inequality	inequality	NOUN
ejpam-3407	252	13	(	(	PUNCT
ejpam-3407	252	14	20	20	NUM
ejpam-3407	252	15	)	)	PUNCT
ejpam-3407	252	16	whenever	whenever	SCONJ
ejpam-3407	252	17	there	there	PRON
ejpam-3407	252	18	exists	exist	VERB
ejpam-3407	252	19	the	the	DET
ejpam-3407	252	20	function	function	NOUN
ejpam-3407	252	21	ψ	ψ	ADP
ejpam-3407	252	22	∈	∈	PROPN
ejpam-3407	252	23	c([0	c([0	NOUN
ejpam-3407	252	24	,	,	PUNCT
ejpam-3407	252	25	1],r	1],r	NUM
ejpam-3407	252	26	)	)	PUNCT
ejpam-3407	252	27	(	(	PUNCT
ejpam-3407	252	28	dependent	dependent	ADJ
ejpam-3407	252	29	on	on	ADP
ejpam-3407	252	30	z	z	PROPN
ejpam-3407	252	31	)	)	PUNCT
ejpam-3407	252	32	so	so	SCONJ
ejpam-3407	252	33	that	that	SCONJ
ejpam-3407	252	34	(	(	PUNCT
ejpam-3407	252	35	i	i	NOUN
ejpam-3407	252	36	)	)	PUNCT
ejpam-3407	252	37	cdpz(s	cdpz(s	NOUN
ejpam-3407	252	38	)	)	PUNCT
ejpam-3407	253	1	+	+	NOUN
ejpam-3407	253	2	q(s	q(s	ADJ
ejpam-3407	253	3	,	,	PUNCT
ejpam-3407	253	4	z(s	z(s	PROPN
ejpam-3407	253	5	)	)	PUNCT
ejpam-3407	253	6	)	)	PUNCT
ejpam-3407	254	1	=	=	SYM
ejpam-3407	254	2	ψ(s	ψ(s	PROPN
ejpam-3407	254	3	)	)	PUNCT
ejpam-3407	254	4	,	,	PUNCT
ejpam-3407	254	5	s	s	VERB
ejpam-3407	254	6	∈	∈	PROPN
ejpam-3407	255	1	[	[	X
ejpam-3407	255	2	0	0	NUM
ejpam-3407	255	3	,	,	PUNCT
ejpam-3407	255	4	1	1	NUM
ejpam-3407	255	5	]	]	PUNCT
ejpam-3407	255	6	;	;	PUNCT
ejpam-3407	255	7	(	(	PUNCT
ejpam-3407	255	8	ii	ii	X
ejpam-3407	255	9	)	)	PUNCT
ejpam-3407	255	10	|ψ(s)|	|ψ(s)|	PROPN
ejpam-3407	255	11	≤	≤	PROPN
ejpam-3407	255	12	εφ(s	εφ(s	NOUN
ejpam-3407	255	13	)	)	PUNCT
ejpam-3407	255	14	,	,	PUNCT
ejpam-3407	255	15	for	for	ADP
ejpam-3407	255	16	all	all	DET
ejpam-3407	255	17	s	s	PART
ejpam-3407	255	18	∈	∈	NOUN
ejpam-3407	256	1	[	[	X
ejpam-3407	256	2	0	0	NUM
ejpam-3407	256	3	,	,	PUNCT
ejpam-3407	256	4	1	1	NUM
ejpam-3407	256	5	]	]	PUNCT
ejpam-3407	256	6	,	,	PUNCT
ejpam-3407	256	7	where	where	SCONJ
ejpam-3407	256	8	φ	φ	PROPN
ejpam-3407	256	9	∈	∈	PROPN
ejpam-3407	256	10	c([0	c([0	NOUN
ejpam-3407	256	11	,	,	PUNCT
ejpam-3407	256	12	1],r	1],r	NUM
ejpam-3407	256	13	)	)	PUNCT
ejpam-3407	256	14	.	.	PUNCT
ejpam-3407	257	1	by	by	ADP
ejpam-3407	257	2	using	use	VERB
ejpam-3407	257	3	the	the	DET
ejpam-3407	257	4	remark	remark	NOUN
ejpam-3407	257	5	2	2	NUM
ejpam-3407	257	6	,	,	PUNCT
ejpam-3407	257	7	let	let	VERB
ejpam-3407	257	8	z	z	NOUN
ejpam-3407	257	9	∈	∈	PROPN
ejpam-3407	257	10	ac2[0	ac2[0	ADJ
ejpam-3407	257	11	,	,	PUNCT
ejpam-3407	257	12	1	1	NUM
ejpam-3407	257	13	]	]	PUNCT
ejpam-3407	257	14	be	be	AUX
ejpam-3407	257	15	any	any	DET
ejpam-3407	257	16	solution	solution	NOUN
ejpam-3407	257	17	of	of	ADP
ejpam-3407	257	18	bvp	bvp	PROPN
ejpam-3407	257	19	(	(	PUNCT
ejpam-3407	257	20	1	1	X
ejpam-3407	257	21	)	)	PUNCT
ejpam-3407	257	22	such	such	ADJ
ejpam-3407	257	23	that	that	DET
ejpam-3407	257	24	cdpz(s	cdpz(s	NOUN
ejpam-3407	257	25	)	)	PUNCT
ejpam-3407	258	1	+	+	NOUN
ejpam-3407	258	2	q(s	q(s	ADJ
ejpam-3407	258	3	,	,	PUNCT
ejpam-3407	258	4	z(s	z(s	PROPN
ejpam-3407	258	5	)	)	PUNCT
ejpam-3407	258	6	)	)	PUNCT
ejpam-3407	259	1	=	=	SYM
ejpam-3407	259	2	ψ(s	ψ(s	PROPN
ejpam-3407	259	3	)	)	PUNCT
ejpam-3407	259	4	,	,	PUNCT
ejpam-3407	259	5	s	s	VERB
ejpam-3407	259	6	∈	∈	PROPN
ejpam-3407	260	1	[	[	X
ejpam-3407	260	2	0	0	NUM
ejpam-3407	260	3	,	,	PUNCT
ejpam-3407	260	4	1	1	NUM
ejpam-3407	260	5	]	]	PUNCT
ejpam-3407	260	6	.	.	PUNCT
ejpam-3407	261	1	(	(	PUNCT
ejpam-3407	261	2	23	23	NUM
ejpam-3407	261	3	)	)	PUNCT
ejpam-3407	261	4	then	then	ADV
ejpam-3407	261	5	,	,	PUNCT
ejpam-3407	261	6	thank	thank	VERB
ejpam-3407	261	7	to	to	PART
ejpam-3407	261	8	lemma	lemma	PROPN
ejpam-3407	261	9	4	4	NUM
ejpam-3407	261	10	,	,	PUNCT
ejpam-3407	261	11	we	we	PRON
ejpam-3407	261	12	have	have	VERB
ejpam-3407	261	13	z(s	z(s	NUM
ejpam-3407	261	14	)	)	PUNCT
ejpam-3407	262	1	=	=	PUNCT
ejpam-3407	262	2	∫	∫	PROPN
ejpam-3407	262	3	1	1	NUM
ejpam-3407	263	1	0	0	NUM
ejpam-3407	263	2	r(s	r(s	PROPN
ejpam-3407	263	3	,	,	PUNCT
ejpam-3407	263	4	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	263	5	,	,	PUNCT
ejpam-3407	263	6	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	263	7	+	+	CCONJ
ejpam-3407	263	8	∫	∫	PROPN
ejpam-3407	263	9	1	1	NUM
ejpam-3407	263	10	0	0	NUM
ejpam-3407	263	11	r(s	r(s	PROPN
ejpam-3407	263	12	,	,	PUNCT
ejpam-3407	263	13	γ)ψ(γ)dγ	γ)ψ(γ)dγ	NOUN
ejpam-3407	263	14	,	,	PUNCT
ejpam-3407	263	15	where	where	SCONJ
ejpam-3407	263	16	ψ	ψ	ADP
ejpam-3407	263	17	∈	∈	PROPN
ejpam-3407	263	18	c([0	c([0	NOUN
ejpam-3407	263	19	,	,	PUNCT
ejpam-3407	263	20	1],r	1],r	NUM
ejpam-3407	263	21	)	)	PUNCT
ejpam-3407	263	22	which	which	PRON
ejpam-3407	263	23	yields	yield	VERB
ejpam-3407	263	24	|z(s)−	|z(s)−	PUNCT
ejpam-3407	263	25	∫	∫	PROPN
ejpam-3407	263	26	1	1	NUM
ejpam-3407	263	27	0	0	NUM
ejpam-3407	263	28	r(s	r(s	PROPN
ejpam-3407	263	29	,	,	PUNCT
ejpam-3407	263	30	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	263	31	,	,	PUNCT
ejpam-3407	263	32	z(γ))dγ|	z(γ))dγ|	NOUN
ejpam-3407	263	33	≤	≤	NUM
ejpam-3407	263	34	2ε	2ε	NOUN
ejpam-3407	263	35	(	(	PUNCT
ejpam-3407	263	36	2−	2−	NUM
ejpam-3407	263	37	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	263	38	)	)	PUNCT
ejpam-3407	263	39	φ(s	φ(s	NOUN
ejpam-3407	263	40	)	)	PUNCT
ejpam-3407	263	41	,	,	PUNCT
ejpam-3407	263	42	s	s	VERB
ejpam-3407	263	43	∈	∈	PROPN
ejpam-3407	264	1	[	[	X
ejpam-3407	264	2	0	0	NUM
ejpam-3407	264	3	,	,	PUNCT
ejpam-3407	264	4	1	1	NUM
ejpam-3407	264	5	]	]	PUNCT
ejpam-3407	264	6	.	.	PUNCT
ejpam-3407	265	1	(	(	PUNCT
ejpam-3407	265	2	24	24	NUM
ejpam-3407	265	3	)	)	PUNCT
ejpam-3407	265	4	theorem	theorem	NOUN
ejpam-3407	265	5	3	3	NUM
ejpam-3407	265	6	.	.	PUNCT
ejpam-3407	266	1	if	if	SCONJ
ejpam-3407	266	2	consider	consider	VERB
ejpam-3407	266	3	the	the	DET
ejpam-3407	266	4	conditions	condition	NOUN
ejpam-3407	266	5	(	(	PUNCT
ejpam-3407	266	6	c2	c2	PROPN
ejpam-3407	266	7	)	)	PUNCT
ejpam-3407	266	8	,	,	PUNCT
ejpam-3407	266	9	(	(	PUNCT
ejpam-3407	266	10	c3	c3	PROPN
ejpam-3407	266	11	)	)	PUNCT
ejpam-3407	266	12	coupled	couple	VERB
ejpam-3407	266	13	with	with	ADP
ejpam-3407	266	14	δ	δ	PROPN
ejpam-3407	266	15	<	<	X
ejpam-3407	266	16	1	1	NUM
ejpam-3407	266	17	,	,	PUNCT
ejpam-3407	266	18	then	then	ADV
ejpam-3407	266	19	the	the	DET
ejpam-3407	266	20	ulamhyers	ulamhyer	NOUN
ejpam-3407	266	21	-	-	PUNCT
ejpam-3407	266	22	rassias	rassias	PROPN
ejpam-3407	266	23	stability	stability	NOUN
ejpam-3407	266	24	results	result	NOUN
ejpam-3407	266	25	for	for	ADP
ejpam-3407	266	26	the	the	DET
ejpam-3407	266	27	solutions	solution	NOUN
ejpam-3407	266	28	of	of	ADP
ejpam-3407	266	29	bvp	bvp	NOUN
ejpam-3407	266	30	(	(	PUNCT
ejpam-3407	266	31	1	1	X
ejpam-3407	266	32	)	)	PUNCT
ejpam-3407	266	33	are	be	AUX
ejpam-3407	266	34	obtained	obtain	VERB
ejpam-3407	266	35	which	which	PRON
ejpam-3407	266	36	further	far	ADV
ejpam-3407	266	37	implies	imply	VERB
ejpam-3407	266	38	that	that	SCONJ
ejpam-3407	266	39	the	the	DET
ejpam-3407	266	40	solutions	solution	NOUN
ejpam-3407	266	41	of	of	ADP
ejpam-3407	266	42	bvp	bvp	NOUN
ejpam-3407	266	43	(	(	PUNCT
ejpam-3407	266	44	1	1	X
ejpam-3407	266	45	)	)	PUNCT
ejpam-3407	266	46	are	be	AUX
ejpam-3407	266	47	generalized	generalize	VERB
ejpam-3407	266	48	ulam	ulam	NOUN
ejpam-3407	266	49	-	-	PUNCT
ejpam-3407	266	50	hyers	hyer	NOUN
ejpam-3407	266	51	-	-	PUNCT
ejpam-3407	266	52	rassias	rassia	NOUN
ejpam-3407	266	53	stable	stable	ADJ
ejpam-3407	266	54	.	.	PUNCT
ejpam-3407	267	1	k.	k.	PROPN
ejpam-3407	267	2	shah	shah	PROPN
ejpam-3407	267	3	et	et	PROPN
ejpam-3407	267	4	al	al	PROPN
ejpam-3407	267	5	.	.	PUNCT
ejpam-3407	267	6	/	/	SYM
ejpam-3407	267	7	eur	eur	PROPN
ejpam-3407	267	8	.	.	PUNCT
ejpam-3407	268	1	j.	j.	PROPN
ejpam-3407	268	2	pure	pure	PROPN
ejpam-3407	268	3	appl	appl	PROPN
ejpam-3407	268	4	.	.	PROPN
ejpam-3407	268	5	math	math	PROPN
ejpam-3407	268	6	,	,	PUNCT
ejpam-3407	268	7	12	12	NUM
ejpam-3407	268	8	(	(	PUNCT
ejpam-3407	268	9	2	2	NUM
ejpam-3407	268	10	)	)	PUNCT
ejpam-3407	268	11	(	(	PUNCT
ejpam-3407	268	12	2019	2019	NUM
ejpam-3407	268	13	)	)	PUNCT
ejpam-3407	268	14	,	,	PUNCT
ejpam-3407	268	15	432	432	NUM
ejpam-3407	268	16	-	-	SYM
ejpam-3407	268	17	447	447	NUM
ejpam-3407	268	18	442	442	NUM
ejpam-3407	268	19	proof	proof	NOUN
ejpam-3407	268	20	.	.	PUNCT
ejpam-3407	269	1	let	let	AUX
ejpam-3407	269	2	consider	consider	VERB
ejpam-3407	269	3	the	the	DET
ejpam-3407	269	4	conditions	condition	NOUN
ejpam-3407	269	5	(	(	PUNCT
ejpam-3407	269	6	c2),(c3	c2),(c3	NOUN
ejpam-3407	269	7	)	)	PUNCT
ejpam-3407	269	8	coupled	couple	VERB
ejpam-3407	269	9	with	with	ADP
ejpam-3407	269	10	δ	δ	PROPN
ejpam-3407	269	11	<	<	X
ejpam-3407	269	12	1	1	NUM
ejpam-3407	269	13	.	.	PUNCT
ejpam-3407	270	1	if	if	SCONJ
ejpam-3407	270	2	v	v	NUM
ejpam-3407	270	3	∈	∈	PROPN
ejpam-3407	270	4	ac2[0	ac2[0	NOUN
ejpam-3407	270	5	,	,	PUNCT
ejpam-3407	270	6	1	1	NUM
ejpam-3407	270	7	]	]	PUNCT
ejpam-3407	270	8	is	be	AUX
ejpam-3407	270	9	the	the	DET
ejpam-3407	270	10	unique	unique	ADJ
ejpam-3407	270	11	solution	solution	NOUN
ejpam-3407	270	12	of	of	ADP
ejpam-3407	270	13	bvp	bvp	PROPN
ejpam-3407	270	14	(	(	PUNCT
ejpam-3407	270	15	1	1	NUM
ejpam-3407	270	16	)	)	PUNCT
ejpam-3407	270	17	and	and	CCONJ
ejpam-3407	270	18	z	z	NOUN
ejpam-3407	270	19	∈	∈	PROPN
ejpam-3407	270	20	ac2[0	ac2[0	ADJ
ejpam-3407	270	21	,	,	PUNCT
ejpam-3407	270	22	1	1	NUM
ejpam-3407	270	23	]	]	PUNCT
ejpam-3407	270	24	be	be	AUX
ejpam-3407	270	25	any	any	DET
ejpam-3407	270	26	solution	solution	NOUN
ejpam-3407	270	27	of	of	ADP
ejpam-3407	270	28	bvp	bvp	PROPN
ejpam-3407	270	29	(	(	PUNCT
ejpam-3407	270	30	1	1	X
ejpam-3407	270	31	)	)	PUNCT
ejpam-3407	270	32	which	which	PRON
ejpam-3407	270	33	is	be	AUX
ejpam-3407	270	34	also	also	ADV
ejpam-3407	270	35	the	the	DET
ejpam-3407	270	36	solution	solution	NOUN
ejpam-3407	270	37	(	(	PUNCT
ejpam-3407	270	38	24	24	NUM
ejpam-3407	270	39	)	)	PUNCT
ejpam-3407	270	40	.	.	PUNCT
ejpam-3407	271	1	then	then	ADV
ejpam-3407	271	2	,	,	PUNCT
ejpam-3407	271	3	we	we	PRON
ejpam-3407	271	4	have	have	VERB
ejpam-3407	271	5	|v(s)−	|v(s)−	NUM
ejpam-3407	271	6	z(s)|	z(s)|	X
ejpam-3407	271	7	=	=	SYM
ejpam-3407	271	8	∣	∣	PROPN
ejpam-3407	271	9	∣	∣	ADJ
ejpam-3407	271	10	∣	∣	ADJ
ejpam-3407	271	11	∣	∣	ADJ
ejpam-3407	271	12	∫	∫	PROPN
ejpam-3407	271	13	1	1	NUM
ejpam-3407	271	14	0	0	NUM
ejpam-3407	271	15	r(s	r(s	PROPN
ejpam-3407	271	16	,	,	PUNCT
ejpam-3407	271	17	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	271	18	,	,	PUNCT
ejpam-3407	271	19	v(γ))dγ	v(γ))dγ	VERB
ejpam-3407	271	20	−	−	PROPN
ejpam-3407	271	21	z(s	z(s	PROPN
ejpam-3407	271	22	)	)	PUNCT
ejpam-3407	271	23	∣	∣	ADJ
ejpam-3407	271	24	∣	∣	ADJ
ejpam-3407	271	25	∣	∣	ADJ
ejpam-3407	271	26	∣	∣	ADJ
ejpam-3407	271	27	=	=	PUNCT
ejpam-3407	271	28	∣	∣	ADJ
ejpam-3407	271	29	∣	∣	ADJ
ejpam-3407	271	30	∣	∣	ADJ
ejpam-3407	271	31	∣	∣	ADJ
ejpam-3407	271	32	∫	∫	PROPN
ejpam-3407	271	33	1	1	NUM
ejpam-3407	271	34	0	0	NUM
ejpam-3407	271	35	r(s	r(s	PROPN
ejpam-3407	271	36	,	,	PUNCT
ejpam-3407	271	37	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	271	38	,	,	PUNCT
ejpam-3407	271	39	v(γ))dγ	v(γ))dγ	VERB
ejpam-3407	271	40	−	−	PROPN
ejpam-3407	271	41	∫	∫	PROPN
ejpam-3407	271	42	1	1	NUM
ejpam-3407	272	1	0	0	NUM
ejpam-3407	272	2	r(s	r(s	PROPN
ejpam-3407	272	3	,	,	PUNCT
ejpam-3407	272	4	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	272	5	,	,	PUNCT
ejpam-3407	272	6	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	272	7	+	+	CCONJ
ejpam-3407	272	8	∫	∫	PROPN
ejpam-3407	272	9	1	1	NUM
ejpam-3407	272	10	0	0	NUM
ejpam-3407	272	11	r(s	r(s	PROPN
ejpam-3407	272	12	,	,	PUNCT
ejpam-3407	272	13	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	272	14	,	,	PUNCT
ejpam-3407	272	15	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	272	16	−	−	PROPN
ejpam-3407	272	17	z(s	z(s	PROPN
ejpam-3407	272	18	)	)	PUNCT
ejpam-3407	272	19	∣	∣	ADJ
ejpam-3407	272	20	∣	∣	ADJ
ejpam-3407	272	21	∣	∣	ADJ
ejpam-3407	272	22	∣	∣	ADJ
ejpam-3407	272	23	≤	≤	NUM
ejpam-3407	272	24	∫	∫	NOUN
ejpam-3407	272	25	1	1	NUM
ejpam-3407	272	26	0	0	X
ejpam-3407	272	27	|r(s	|r(s	NOUN
ejpam-3407	272	28	,	,	PUNCT
ejpam-3407	272	29	γ)|q(γ	γ)|q(γ	NOUN
ejpam-3407	272	30	,	,	PUNCT
ejpam-3407	272	31	v(γ))−q(γ	v(γ))−q(γ	PRON
ejpam-3407	272	32	,	,	PUNCT
ejpam-3407	272	33	z(γ))|dγ	z(γ))|dγ	X
ejpam-3407	272	34	+	+	CCONJ
ejpam-3407	272	35	∣	∣	ADJ
ejpam-3407	272	36	∣	∣	ADJ
ejpam-3407	272	37	∣	∣	ADJ
ejpam-3407	272	38	∣	∣	ADJ
ejpam-3407	272	39	z(s)−	z(s)−	PROPN
ejpam-3407	272	40	∫	∫	PROPN
ejpam-3407	272	41	1	1	NUM
ejpam-3407	272	42	0	0	NUM
ejpam-3407	272	43	r(s	r(s	PROPN
ejpam-3407	272	44	,	,	PUNCT
ejpam-3407	272	45	γ)q(γ	γ)q(γ	PROPN
ejpam-3407	272	46	,	,	PUNCT
ejpam-3407	272	47	z(γ))dγ	z(γ))dγ	PROPN
ejpam-3407	272	48	∣	∣	PROPN
ejpam-3407	272	49	∣	∣	ADJ
ejpam-3407	272	50	∣	∣	ADJ
ejpam-3407	272	51	∣	∣	PROPN
ejpam-3407	272	52	.	.	PUNCT
ejpam-3407	273	1	which	which	PRON
ejpam-3407	273	2	implies	imply	VERB
ejpam-3407	273	3	that	that	SCONJ
ejpam-3407	273	4	‖v	‖v	NOUN
ejpam-3407	273	5	−	−	PROPN
ejpam-3407	273	6	z‖	z‖	NOUN
ejpam-3407	273	7	≤	≤	NOUN
ejpam-3407	273	8	2b	2b	NOUN
ejpam-3407	273	9	(	(	PUNCT
ejpam-3407	273	10	2−	2−	NUM
ejpam-3407	273	11	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	273	12	)	)	PUNCT
ejpam-3407	273	13	‖v	‖v	NOUN
ejpam-3407	274	1	−	−	PROPN
ejpam-3407	275	1	z‖+	z‖+	NOUN
ejpam-3407	275	2	2εφ(s	2εφ(s	NUM
ejpam-3407	275	3	)	)	PUNCT
ejpam-3407	275	4	(	(	PUNCT
ejpam-3407	275	5	2−	2−	NUM
ejpam-3407	275	6	δ)γ(p	δ)γ(p	NOUN
ejpam-3407	275	7	)	)	PUNCT
ejpam-3407	275	8	,	,	PUNCT
ejpam-3407	275	9	(	(	PUNCT
ejpam-3407	275	10	25	25	NUM
ejpam-3407	275	11	)	)	PUNCT
ejpam-3407	275	12	from	from	ADP
ejpam-3407	275	13	which	which	PRON
ejpam-3407	275	14	we	we	PRON
ejpam-3407	275	15	get	get	VERB
ejpam-3407	275	16	‖v	‖v	NOUN
ejpam-3407	275	17	−	−	PROPN
ejpam-3407	275	18	z‖	z‖	NOUN
ejpam-3407	275	19	≤	≤	NOUN
ejpam-3407	275	20	εckφ(s),where	εckφ(s),where	ADP
ejpam-3407	275	21	ck	ck	PROPN
ejpam-3407	275	22	=	=	SYM
ejpam-3407	275	23	2	2	NUM
ejpam-3407	275	24	(	(	PUNCT
ejpam-3407	275	25	2−	2−	NUM
ejpam-3407	275	26	δ)γ(p)−	δ)γ(p)−	NOUN
ejpam-3407	275	27	2b	2b	NOUN
ejpam-3407	275	28	>	>	X
ejpam-3407	275	29	0	0	X
ejpam-3407	275	30	.	.	PUNCT
ejpam-3407	276	1	(	(	PUNCT
ejpam-3407	276	2	26	26	NUM
ejpam-3407	276	3	)	)	PUNCT
ejpam-3407	276	4	therefore	therefore	ADV
ejpam-3407	276	5	the	the	DET
ejpam-3407	276	6	solutions	solution	NOUN
ejpam-3407	276	7	of	of	ADP
ejpam-3407	276	8	bvp	bvp	NOUN
ejpam-3407	276	9	(	(	PUNCT
ejpam-3407	276	10	1	1	X
ejpam-3407	276	11	)	)	PUNCT
ejpam-3407	276	12	are	be	AUX
ejpam-3407	276	13	ulam	ulam	NOUN
ejpam-3407	276	14	-	-	PUNCT
ejpam-3407	276	15	hyers	hyer	NOUN
ejpam-3407	276	16	-	-	PUNCT
ejpam-3407	276	17	rassias	rassia	NOUN
ejpam-3407	276	18	stable	stable	ADJ
ejpam-3407	276	19	.	.	PUNCT
ejpam-3407	277	1	when	when	SCONJ
ejpam-3407	277	2	,	,	PUNCT
ejpam-3407	277	3	we	we	PRON
ejpam-3407	277	4	substitute	substitute	VERB
ejpam-3407	277	5	ϕ(ε	ϕ(ε	NOUN
ejpam-3407	277	6	)	)	PUNCT
ejpam-3407	277	7	=	=	SYM
ejpam-3407	277	8	ckεφ(s	ckεφ(s	NOUN
ejpam-3407	277	9	)	)	PUNCT
ejpam-3407	277	10	,	,	PUNCT
ejpam-3407	277	11	ϕ(0	ϕ(0	PROPN
ejpam-3407	277	12	)	)	PUNCT
ejpam-3407	278	1	=	=	PUNCT
ejpam-3407	279	1	0	0	X
ejpam-3407	279	2	.	.	PUNCT
ejpam-3407	280	1	then	then	ADV
ejpam-3407	280	2	consequently	consequently	ADV
ejpam-3407	280	3	generalized	generalize	VERB
ejpam-3407	280	4	ulam	ulam	PROPN
ejpam-3407	280	5	-	-	PUNCT
ejpam-3407	280	6	hyers	hyer	NOUN
ejpam-3407	280	7	-	-	PUNCT
ejpam-3407	280	8	rassias	rassias	PROPN
ejpam-3407	280	9	stability	stability	NOUN
ejpam-3407	280	10	for	for	ADP
ejpam-3407	280	11	the	the	DET
ejpam-3407	280	12	solutions	solution	NOUN
ejpam-3407	280	13	of	of	ADP
ejpam-3407	280	14	bvp	bvp	NOUN
ejpam-3407	280	15	(	(	PUNCT
ejpam-3407	280	16	1	1	X
ejpam-3407	280	17	)	)	PUNCT
ejpam-3407	280	18	are	be	AUX
ejpam-3407	280	19	obtained	obtain	VERB
ejpam-3407	280	20	.	.	PUNCT
ejpam-3407	281	1	5	5	X
ejpam-3407	281	2	.	.	X
ejpam-3407	281	3	examples	example	NOUN
ejpam-3407	281	4	in	in	ADP
ejpam-3407	281	5	the	the	DET
ejpam-3407	281	6	concern	concern	NOUN
ejpam-3407	281	7	section	section	NOUN
ejpam-3407	281	8	,	,	PUNCT
ejpam-3407	281	9	we	we	PRON
ejpam-3407	281	10	provide	provide	VERB
ejpam-3407	281	11	two	two	NUM
ejpam-3407	281	12	examples	example	NOUN
ejpam-3407	281	13	of	of	ADP
ejpam-3407	281	14	concern	concern	NOUN
ejpam-3407	281	15	problem	problem	NOUN
ejpam-3407	281	16	(	(	PUNCT
ejpam-3407	281	17	1	1	NUM
ejpam-3407	281	18	)	)	PUNCT
ejpam-3407	281	19	.	.	PUNCT
ejpam-3407	282	1	we	we	PRON
ejpam-3407	282	2	find	find	VERB
ejpam-3407	282	3	iterative	iterative	NOUN
ejpam-3407	282	4	solution	solution	NOUN
ejpam-3407	282	5	for	for	ADP
ejpam-3407	282	6	the	the	DET
ejpam-3407	282	7	extremal	extremal	ADJ
ejpam-3407	282	8	solution	solution	NOUN
ejpam-3407	282	9	of	of	ADP
ejpam-3407	282	10	the	the	DET
ejpam-3407	282	11	considered	consider	VERB
ejpam-3407	282	12	examples	example	NOUN
ejpam-3407	282	13	.	.	PUNCT
ejpam-3407	283	1	we	we	PRON
ejpam-3407	283	2	also	also	ADV
ejpam-3407	283	3	provide	provide	VERB
ejpam-3407	283	4	error	error	NOUN
ejpam-3407	283	5	estimates	estimate	NOUN
ejpam-3407	283	6	for	for	ADP
ejpam-3407	283	7	the	the	DET
ejpam-3407	283	8	extremal	extremal	ADJ
ejpam-3407	283	9	solutions	solution	NOUN
ejpam-3407	283	10	.	.	PUNCT
ejpam-3407	284	1	furthermore	furthermore	ADV
ejpam-3407	284	2	,	,	PUNCT
ejpam-3407	284	3	stability	stability	NOUN
ejpam-3407	284	4	analysis	analysis	NOUN
ejpam-3407	284	5	and	and	CCONJ
ejpam-3407	284	6	error	error	NOUN
ejpam-3407	284	7	estimates	estimate	NOUN
ejpam-3407	284	8	for	for	ADP
ejpam-3407	284	9	the	the	DET
ejpam-3407	284	10	solution	solution	NOUN
ejpam-3407	284	11	of	of	ADP
ejpam-3407	284	12	examples	example	NOUN
ejpam-3407	284	13	of	of	ADP
ejpam-3407	284	14	the	the	DET
ejpam-3407	284	15	problem	problem	NOUN
ejpam-3407	284	16	(	(	PUNCT
ejpam-3407	284	17	1	1	X
ejpam-3407	284	18	)	)	PUNCT
ejpam-3407	284	19	is	be	AUX
ejpam-3407	284	20	also	also	ADV
ejpam-3407	284	21	our	our	PRON
ejpam-3407	284	22	concern	concern	NOUN
ejpam-3407	284	23	.	.	PUNCT
ejpam-3407	285	1	in	in	ADP
ejpam-3407	285	2	addition	addition	NOUN
ejpam-3407	285	3	,	,	PUNCT
ejpam-3407	285	4	we	we	PRON
ejpam-3407	285	5	provide	provide	VERB
ejpam-3407	285	6	various	various	ADJ
ejpam-3407	285	7	plots	plot	NOUN
ejpam-3407	285	8	view	view	NOUN
ejpam-3407	285	9	of	of	ADP
ejpam-3407	285	10	every	every	DET
ejpam-3407	285	11	example	example	NOUN
ejpam-3407	285	12	of	of	ADP
ejpam-3407	285	13	problem	problem	NOUN
ejpam-3407	285	14	(	(	PUNCT
ejpam-3407	285	15	1	1	NUM
ejpam-3407	285	16	)	)	PUNCT
ejpam-3407	285	17	.	.	PUNCT
ejpam-3407	286	1	example	example	NOUN
ejpam-3407	287	1	1	1	NUM
ejpam-3407	287	2	.	.	X
ejpam-3407	287	3			PROPN
ejpam-3407	287	4			VERB
ejpam-3407	287	5			PRON
ejpam-3407	287	6			ADJ
ejpam-3407	287	7			ADJ
ejpam-3407	287	8	cd	cd	NOUN
ejpam-3407	287	9	5	5	NUM
ejpam-3407	287	10	2	2	NUM
ejpam-3407	287	11	z(s	z(s	PROPN
ejpam-3407	287	12	)	)	PUNCT
ejpam-3407	288	1	+	+	NOUN
ejpam-3407	288	2	q	q	X
ejpam-3407	288	3	(	(	PUNCT
ejpam-3407	288	4	s	s	PROPN
ejpam-3407	288	5	,	,	PUNCT
ejpam-3407	288	6	z(s	z(s	PROPN
ejpam-3407	288	7	)	)	PUNCT
ejpam-3407	288	8	)	)	PUNCT
ejpam-3407	289	1	=	=	PUNCT
ejpam-3407	289	2	0	0	NUM
ejpam-3407	289	3	,	,	PUNCT
ejpam-3407	289	4	s	s	VERB
ejpam-3407	289	5	∈	∈	PROPN
ejpam-3407	290	1	[	[	X
ejpam-3407	290	2	0	0	NUM
ejpam-3407	290	3	,	,	PUNCT
ejpam-3407	290	4	1	1	NUM
ejpam-3407	290	5	]	]	PUNCT
ejpam-3407	290	6	,	,	PUNCT
ejpam-3407	290	7	z(0	z(0	X
ejpam-3407	290	8	)	)	PUNCT
ejpam-3407	290	9	=	=	SYM
ejpam-3407	290	10	z′′(s	z′′(s	NUM
ejpam-3407	290	11	)	)	PUNCT
ejpam-3407	290	12	∣	∣	ADJ
ejpam-3407	290	13	∣	∣	ADJ
ejpam-3407	290	14	s=0	s=0	PUNCT
ejpam-3407	290	15	=	=	SYM
ejpam-3407	290	16	0	0	NUM
ejpam-3407	290	17	,	,	PUNCT
ejpam-3407	290	18	z(1	z(1	PROPN
ejpam-3407	290	19	)	)	PUNCT
ejpam-3407	290	20	=	=	SYM
ejpam-3407	290	21	1	1	NUM
ejpam-3407	290	22	2	2	NUM
ejpam-3407	290	23	∫	∫	NOUN
ejpam-3407	290	24	1	1	NUM
ejpam-3407	290	25	0	0	NUM
ejpam-3407	290	26	z(s)ds	z(s)ds	NOUN
ejpam-3407	290	27	.	.	PUNCT
ejpam-3407	291	1	(	(	PUNCT
ejpam-3407	291	2	27	27	NUM
ejpam-3407	291	3	)	)	PUNCT
ejpam-3407	291	4	where	where	SCONJ
ejpam-3407	291	5	q	q	X
ejpam-3407	291	6	(	(	PUNCT
ejpam-3407	291	7	s	s	PROPN
ejpam-3407	291	8	,	,	PUNCT
ejpam-3407	291	9	z(s	z(s	PROPN
ejpam-3407	291	10	)	)	PUNCT
ejpam-3407	291	11	)	)	PUNCT
ejpam-3407	292	1	=	=	SYM
ejpam-3407	292	2	√	√	NUM
ejpam-3407	292	3	z(s	z(s	NUM
ejpam-3407	292	4	)	)	PUNCT
ejpam-3407	293	1	+	+	CCONJ
ejpam-3407	293	2	sin2[t	sin2[t	ADJ
ejpam-3407	293	3	exp(z(s	exp(z(s	NOUN
ejpam-3407	293	4	)	)	PUNCT
ejpam-3407	293	5	)	)	PUNCT
ejpam-3407	293	6	]	]	PUNCT
ejpam-3407	294	1	+	+	CCONJ
ejpam-3407	294	2	log[1	log[1	ADJ
ejpam-3407	294	3	+	+	CCONJ
ejpam-3407	294	4	z(s	z(s	PROPN
ejpam-3407	294	5	)	)	PUNCT
ejpam-3407	294	6	]	]	PUNCT
ejpam-3407	294	7	.	.	PUNCT
ejpam-3407	295	1	let	let	VERB
ejpam-3407	295	2	say	say	VERB
ejpam-3407	295	3	n	n	NOUN
ejpam-3407	295	4	=	=	SYM
ejpam-3407	295	5	4	4	NUM
ejpam-3407	295	6	is	be	AUX
ejpam-3407	295	7	large	large	ADJ
ejpam-3407	295	8	enough.then	enough.then	ADV
ejpam-3407	295	9	,	,	PUNCT
ejpam-3407	295	10	approximate	approximate	ADJ
ejpam-3407	295	11	minimal	minimal	ADJ
ejpam-3407	295	12	and	and	CCONJ
ejpam-3407	295	13	maximal	maximal	ADJ
ejpam-3407	295	14	solutions	solution	NOUN
ejpam-3407	295	15	are	be	AUX
ejpam-3407	295	16	given	give	VERB
ejpam-3407	295	17	by	by	ADP
ejpam-3407	295	18	z(s	z(s	PROPN
ejpam-3407	295	19	)	)	PUNCT
ejpam-3407	295	20	=	=	PUNCT
ejpam-3407	296	1	z4(s	z4(s	X
ejpam-3407	296	2	)	)	PUNCT
ejpam-3407	296	3	=	=	SYM
ejpam-3407	296	4	∫	∫	PROPN
ejpam-3407	296	5	1	1	NUM
ejpam-3407	296	6	0	0	NUM
ejpam-3407	296	7	r(s	r(s	PROPN
ejpam-3407	296	8	,	,	PUNCT
ejpam-3407	296	9	γ)q	γ)q	X
ejpam-3407	296	10	(	(	PUNCT
ejpam-3407	296	11	γ	γ	X
ejpam-3407	296	12	,	,	PUNCT
ejpam-3407	296	13	z3(γ	z3(γ	NUM
ejpam-3407	296	14	)	)	PUNCT
ejpam-3407	296	15	)	)	PUNCT
ejpam-3407	297	1	dγ	dγ	ADP
ejpam-3407	297	2	,	,	PUNCT
ejpam-3407	297	3	z∗(s	z∗(s	PROPN
ejpam-3407	297	4	)	)	PUNCT
ejpam-3407	297	5	=	=	SYM
ejpam-3407	297	6	z∗4(s	z∗4(s	PROPN
ejpam-3407	297	7	)	)	PUNCT
ejpam-3407	297	8	=	=	SYM
ejpam-3407	298	1	∫	∫	PROPN
ejpam-3407	298	2	1	1	NUM
ejpam-3407	298	3	0	0	NUM
ejpam-3407	298	4	r(s	r(s	PROPN
ejpam-3407	298	5	,	,	PUNCT
ejpam-3407	298	6	γ)q	γ)q	X
ejpam-3407	298	7	(	(	PUNCT
ejpam-3407	298	8	γ	γ	X
ejpam-3407	298	9	,	,	PUNCT
ejpam-3407	298	10	z∗3(γ	z∗3(γ	PROPN
ejpam-3407	298	11	)	)	PUNCT
ejpam-3407	298	12	)	)	PUNCT
ejpam-3407	299	1	dγ	dγ	PROPN
ejpam-3407	299	2	.	.	PUNCT
ejpam-3407	300	1	(	(	PUNCT
ejpam-3407	300	2	28	28	NUM
ejpam-3407	300	3	)	)	PUNCT
ejpam-3407	300	4	k.	k.	NOUN
ejpam-3407	301	1	shah	shah	PROPN
ejpam-3407	301	2	et	et	PROPN
ejpam-3407	301	3	al	al	PROPN
ejpam-3407	301	4	.	.	PUNCT
ejpam-3407	301	5	/	/	SYM
ejpam-3407	301	6	eur	eur	PROPN
ejpam-3407	301	7	.	.	PUNCT
ejpam-3407	302	1	j.	j.	PROPN
ejpam-3407	302	2	pure	pure	PROPN
ejpam-3407	302	3	appl	appl	PROPN
ejpam-3407	302	4	.	.	PROPN
ejpam-3407	302	5	math	math	PROPN
ejpam-3407	302	6	,	,	PUNCT
ejpam-3407	302	7	12	12	NUM
ejpam-3407	302	8	(	(	PUNCT
ejpam-3407	302	9	2	2	NUM
ejpam-3407	302	10	)	)	PUNCT
ejpam-3407	302	11	(	(	PUNCT
ejpam-3407	302	12	2019	2019	NUM
ejpam-3407	302	13	)	)	PUNCT
ejpam-3407	302	14	,	,	PUNCT
ejpam-3407	302	15	432	432	NUM
ejpam-3407	302	16	-	-	SYM
ejpam-3407	302	17	447	447	NUM
ejpam-3407	302	18	443	443	NUM
ejpam-3407	302	19	let	let	VERB
ejpam-3407	302	20	b	b	NOUN
ejpam-3407	302	21	=	=	SYM
ejpam-3407	302	22	0.00001	0.00001	NUM
ejpam-3407	302	23	and	and	CCONJ
ejpam-3407	302	24	the	the	DET
ejpam-3407	302	25	lower	low	ADJ
ejpam-3407	302	26	and	and	CCONJ
ejpam-3407	302	27	upper	upper	ADJ
ejpam-3407	302	28	solutions	solution	NOUN
ejpam-3407	302	29	of	of	ADP
ejpam-3407	302	30	bvp	bvp	PROPN
ejpam-3407	302	31	(	(	PUNCT
ejpam-3407	302	32	1	1	X
ejpam-3407	302	33	)	)	PUNCT
ejpam-3407	302	34	are	be	AUX
ejpam-3407	302	35	z0	z0	PROPN
ejpam-3407	302	36	=	=	PUNCT
ejpam-3407	302	37	−0.2	−0.2	PROPN
ejpam-3407	302	38	,	,	PUNCT
ejpam-3407	302	39	and	and	CCONJ
ejpam-3407	302	40	z∗0	z∗0	PROPN
ejpam-3407	302	41	=	=	PUNCT
ejpam-3407	302	42	0.2	0.2	NUM
ejpam-3407	302	43	respectively	respectively	ADV
ejpam-3407	302	44	.	.	PUNCT
ejpam-3407	303	1	then	then	ADV
ejpam-3407	303	2	we	we	PRON
ejpam-3407	303	3	have	have	VERB
ejpam-3407	303	4	∆	∆	PROPN
ejpam-3407	303	5	=	=	SYM
ejpam-3407	303	6	2b	2b	NOUN
ejpam-3407	303	7	(	(	PUNCT
ejpam-3407	303	8	2−δ)γ(p	2−δ)γ(p	NUM
ejpam-3407	303	9	)	)	PUNCT
ejpam-3407	303	10	=	=	NOUN
ejpam-3407	303	11	0.000010030	0.000010030	NUM
ejpam-3407	303	12	<	<	X
ejpam-3407	303	13	1	1	NUM
ejpam-3407	303	14	.	.	PUNCT
ejpam-3407	304	1	therefore	therefore	ADV
ejpam-3407	304	2	,	,	PUNCT
ejpam-3407	304	3	the	the	DET
ejpam-3407	304	4	error	error	NOUN
ejpam-3407	304	5	estimates	estimate	NOUN
ejpam-3407	304	6	are	be	AUX
ejpam-3407	304	7	:	:	PUNCT
ejpam-3407	304	8	e3	e3	X
ejpam-3407	304	9	=	=	SYM
ejpam-3407	304	10	‖z(s)−	‖z(s)−	NUM
ejpam-3407	304	11	z3(s)‖	z3(s)‖	NOUN
ejpam-3407	304	12	≤	≤	NOUN
ejpam-3407	304	13	∆3	∆3	AUX
ejpam-3407	304	14	1−∆	1−∆	NUM
ejpam-3407	304	15	×	×	NOUN
ejpam-3407	304	16	e1	e1	NOUN
ejpam-3407	304	17	≤	≤	NOUN
ejpam-3407	304	18	1.00904832686×	1.00904832686×	NUM
ejpam-3407	304	19	10−15	10−15	PROPN
ejpam-3407	304	20	max	max	PROPN
ejpam-3407	304	21	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	304	22	]	]	PUNCT
ejpam-3407	304	23	|z1(s	|z1(s	PROPN
ejpam-3407	304	24	)	)	PUNCT
ejpam-3407	304	25	+	+	NUM
ejpam-3407	304	26	0.2|	0.2|	NUM
ejpam-3407	304	27	≃	≃	VERB
ejpam-3407	304	28	2.22668549047×	2.22668549047×	PROPN
ejpam-3407	304	29	10−16	10−16	PROPN
ejpam-3407	304	30	,	,	PUNCT
ejpam-3407	304	31	e∗3	e∗3	NOUN
ejpam-3407	304	32	=	=	PUNCT
ejpam-3407	304	33	‖z(s)−	‖z(s)−	NUM
ejpam-3407	304	34	z∗3(s)‖	z∗3(s)‖	NOUN
ejpam-3407	304	35	≤	≤	NOUN
ejpam-3407	304	36	∆3	∆3	PRON
ejpam-3407	304	37	1−∆	1−∆	NUM
ejpam-3407	304	38	×	×	NOUN
ejpam-3407	304	39	e∗1	e∗1	ADJ
ejpam-3407	304	40	≤	≤	NUM
ejpam-3407	304	41	1.00904832686×	1.00904832686×	NUM
ejpam-3407	304	42	10−15	10−15	PROPN
ejpam-3407	304	43	max	max	PROPN
ejpam-3407	304	44	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	304	45	]	]	PUNCT
ejpam-3407	304	46	|0.2−	|0.2−	PROPN
ejpam-3407	304	47	z∗1(s)|	z∗1(s)|	PROPN
ejpam-3407	304	48	≃	≃	VERB
ejpam-3407	304	49	2.01809665372×	2.01809665372×	NUM
ejpam-3407	304	50	10−16	10−16	VERB
ejpam-3407	304	51	.	.	PUNCT
ejpam-3407	305	1	the	the	DET
ejpam-3407	305	2	maximal	maximal	ADJ
ejpam-3407	305	3	and	and	CCONJ
ejpam-3407	305	4	minimal	minimal	ADJ
ejpam-3407	305	5	solutions	solution	NOUN
ejpam-3407	305	6	of	of	ADP
ejpam-3407	305	7	the	the	DET
ejpam-3407	305	8	example	example	NOUN
ejpam-3407	305	9	(	(	PUNCT
ejpam-3407	305	10	1	1	X
ejpam-3407	305	11	)	)	PUNCT
ejpam-3407	305	12	are	be	AUX
ejpam-3407	305	13	plotted	plot	VERB
ejpam-3407	305	14	in	in	ADP
ejpam-3407	305	15	the	the	DET
ejpam-3407	305	16	figure	figure	NOUN
ejpam-3407	305	17	1	1	NUM
ejpam-3407	305	18	.	.	PUNCT
ejpam-3407	306	1	clearly	clearly	ADV
ejpam-3407	306	2	,	,	PUNCT
ejpam-3407	306	3	the	the	DET
ejpam-3407	306	4	condition	condition	NOUN
ejpam-3407	306	5	∆	∆	X
ejpam-3407	306	6	<	<	X
ejpam-3407	306	7	1	1	NUM
ejpam-3407	306	8	is	be	AUX
ejpam-3407	306	9	sufficient	sufficient	ADJ
ejpam-3407	306	10	for	for	ADP
ejpam-3407	306	11	various	various	ADJ
ejpam-3407	306	12	kinds	kind	NOUN
ejpam-3407	306	13	of	of	ADP
ejpam-3407	306	14	ulam	ulam	ADJ
ejpam-3407	306	15	stabilities	stability	NOUN
ejpam-3407	306	16	for	for	ADP
ejpam-3407	306	17	the	the	DET
ejpam-3407	306	18	extremal	extremal	ADJ
ejpam-3407	306	19	solution	solution	NOUN
ejpam-3407	306	20	of	of	ADP
ejpam-3407	306	21	the	the	DET
ejpam-3407	306	22	example	example	NOUN
ejpam-3407	306	23	(	(	PUNCT
ejpam-3407	306	24	1	1	NUM
ejpam-3407	306	25	)	)	PUNCT
ejpam-3407	306	26	.	.	PUNCT
ejpam-3407	307	1	the	the	DET
ejpam-3407	307	2	stability	stability	NOUN
ejpam-3407	307	3	of	of	ADP
ejpam-3407	307	4	extremal	extremal	ADJ
ejpam-3407	307	5	solutions	solution	NOUN
ejpam-3407	307	6	is	be	AUX
ejpam-3407	307	7	also	also	ADV
ejpam-3407	307	8	obvious	obvious	ADJ
ejpam-3407	307	9	from	from	ADP
ejpam-3407	307	10	plots	plot	NOUN
ejpam-3407	307	11	in	in	ADP
ejpam-3407	307	12	the	the	DET
ejpam-3407	307	13	given	give	VERB
ejpam-3407	307	14	figure	figure	NOUN
ejpam-3407	307	15	1	1	NUM
ejpam-3407	307	16	.	.	NOUN
ejpam-3407	307	17	0	0	NUM
ejpam-3407	307	18	0.1	0.1	NUM
ejpam-3407	307	19	0.2	0.2	NUM
ejpam-3407	307	20	0.3	0.3	NUM
ejpam-3407	307	21	0.4	0.4	NUM
ejpam-3407	307	22	0.5	0.5	NUM
ejpam-3407	307	23	0.6	0.6	NUM
ejpam-3407	307	24	0.7	0.7	NUM
ejpam-3407	307	25	0.8	0.8	NUM
ejpam-3407	307	26	0.9	0.9	NUM
ejpam-3407	307	27	1	1	NUM
ejpam-3407	307	28	-0.05	-0.05	NUM
ejpam-3407	307	29	0	0	NUM
ejpam-3407	307	30	0.05	0.05	NUM
ejpam-3407	307	31	0.1	0.1	NUM
ejpam-3407	307	32	0.15	0.15	NUM
ejpam-3407	307	33	0	0	NUM
ejpam-3407	307	34	0.1	0.1	NUM
ejpam-3407	307	35	0.2	0.2	NUM
ejpam-3407	307	36	0.3	0.3	NUM
ejpam-3407	307	37	0.4	0.4	NUM
ejpam-3407	307	38	0.5	0.5	NUM
ejpam-3407	307	39	0.6	0.6	NUM
ejpam-3407	307	40	0.7	0.7	NUM
ejpam-3407	307	41	0.8	0.8	NUM
ejpam-3407	307	42	0.9	0.9	NUM
ejpam-3407	307	43	1	1	NUM
ejpam-3407	307	44	0	0	NUM
ejpam-3407	307	45	0.05	0.05	NUM
ejpam-3407	307	46	0.1	0.1	NUM
ejpam-3407	307	47	0.15	0.15	NUM
ejpam-3407	307	48	z	z	NOUN
ejpam-3407	307	49	*	*	PUNCT
ejpam-3407	307	50	1	1	NUM
ejpam-3407	307	51	(	(	PUNCT
ejpam-3407	307	52	s)=maximal	s)=maximal	ADJ
ejpam-3407	307	53	solution	solution	NOUN
ejpam-3407	307	54	z	z	NOUN
ejpam-3407	307	55	1	1	NUM
ejpam-3407	307	56	(	(	PUNCT
ejpam-3407	307	57	s)=minimal	s)=minimal	ADJ
ejpam-3407	307	58	solution	solution	NOUN
ejpam-3407	307	59	z	z	NOUN
ejpam-3407	307	60	*	*	SYM
ejpam-3407	307	61	2	2	NUM
ejpam-3407	307	62	(	(	PUNCT
ejpam-3407	307	63	s)=maximal	s)=maximal	ADJ
ejpam-3407	307	64	solution	solution	NOUN
ejpam-3407	307	65	z	z	NOUN
ejpam-3407	307	66	2	2	NUM
ejpam-3407	307	67	(	(	PUNCT
ejpam-3407	307	68	s)=minimal	s)=minimal	ADJ
ejpam-3407	307	69	solution	solution	NOUN
ejpam-3407	307	70	figure	figure	NOUN
ejpam-3407	307	71	1	1	NUM
ejpam-3407	307	72	a	a	DET
ejpam-3407	307	73	line	line	NOUN
ejpam-3407	307	74	graph	graph	NOUN
ejpam-3407	307	75	of	of	ADP
ejpam-3407	307	76	the	the	DET
ejpam-3407	307	77	extremal	extremal	ADJ
ejpam-3407	307	78	solutions	solution	NOUN
ejpam-3407	307	79	of	of	ADP
ejpam-3407	307	80	the	the	DET
ejpam-3407	307	81	example	example	NOUN
ejpam-3407	307	82	1	1	NUM
ejpam-3407	307	83	.	.	PUNCT
ejpam-3407	307	84	example	example	NOUN
ejpam-3407	308	1	2	2	NUM
ejpam-3407	308	2	.	.	X
ejpam-3407	308	3			PROPN
ejpam-3407	308	4			VERB
ejpam-3407	308	5			PRON
ejpam-3407	308	6			ADJ
ejpam-3407	308	7			ADJ
ejpam-3407	308	8	cd	cd	PROPN
ejpam-3407	308	9	11	11	NUM
ejpam-3407	308	10	4	4	NUM
ejpam-3407	308	11	z(s	z(s	PROPN
ejpam-3407	308	12	)	)	PUNCT
ejpam-3407	309	1	+	+	NOUN
ejpam-3407	309	2	q	q	X
ejpam-3407	309	3	(	(	PUNCT
ejpam-3407	309	4	s	s	PROPN
ejpam-3407	309	5	,	,	PUNCT
ejpam-3407	309	6	z(s	z(s	PROPN
ejpam-3407	309	7	)	)	PUNCT
ejpam-3407	309	8	)	)	PUNCT
ejpam-3407	310	1	=	=	PUNCT
ejpam-3407	310	2	0	0	NUM
ejpam-3407	310	3	,	,	PUNCT
ejpam-3407	310	4	s	s	VERB
ejpam-3407	310	5	∈	∈	PROPN
ejpam-3407	311	1	[	[	X
ejpam-3407	311	2	0	0	NUM
ejpam-3407	311	3	,	,	PUNCT
ejpam-3407	311	4	1	1	NUM
ejpam-3407	311	5	]	]	PUNCT
ejpam-3407	311	6	,	,	PUNCT
ejpam-3407	311	7	z(0	z(0	X
ejpam-3407	311	8	)	)	PUNCT
ejpam-3407	311	9	=	=	SYM
ejpam-3407	311	10	z′′(s	z′′(s	NUM
ejpam-3407	311	11	)	)	PUNCT
ejpam-3407	311	12	∣	∣	ADJ
ejpam-3407	311	13	∣	∣	ADJ
ejpam-3407	311	14	s=0	s=0	PUNCT
ejpam-3407	311	15	=	=	SYM
ejpam-3407	311	16	0	0	NUM
ejpam-3407	311	17	,	,	PUNCT
ejpam-3407	311	18	z(1	z(1	PROPN
ejpam-3407	311	19	)	)	PUNCT
ejpam-3407	311	20	=	=	SYM
ejpam-3407	311	21	1	1	NUM
ejpam-3407	311	22	10	10	NUM
ejpam-3407	311	23	∫	∫	PROPN
ejpam-3407	311	24	1	1	NUM
ejpam-3407	311	25	0	0	NUM
ejpam-3407	311	26	z(s)ds	z(s)ds	NOUN
ejpam-3407	311	27	.	.	PUNCT
ejpam-3407	312	1	(	(	PUNCT
ejpam-3407	312	2	29	29	NUM
ejpam-3407	312	3	)	)	PUNCT
ejpam-3407	312	4	where	where	SCONJ
ejpam-3407	312	5	q	q	X
ejpam-3407	312	6	(	(	PUNCT
ejpam-3407	312	7	s	s	PROPN
ejpam-3407	312	8	,	,	PUNCT
ejpam-3407	312	9	z(s	z(s	PROPN
ejpam-3407	312	10	)	)	PUNCT
ejpam-3407	312	11	)	)	PUNCT
ejpam-3407	313	1	=	=	PUNCT
ejpam-3407	313	2	t	t	NOUN
ejpam-3407	313	3	√	√	NUM
ejpam-3407	313	4	z(s)+	z(s)+	NUM
ejpam-3407	313	5	exp(z(s	exp(z(s	NOUN
ejpam-3407	313	6	)	)	PUNCT
ejpam-3407	313	7	.	.	PUNCT
ejpam-3407	314	1	let	let	VERB
ejpam-3407	314	2	say	say	VERB
ejpam-3407	314	3	n	n	NOUN
ejpam-3407	314	4	=	=	SYM
ejpam-3407	314	5	4	4	NUM
ejpam-3407	314	6	is	be	AUX
ejpam-3407	314	7	large	large	ADJ
ejpam-3407	314	8	enough	enough	ADV
ejpam-3407	314	9	.	.	PUNCT
ejpam-3407	315	1	then	then	ADV
ejpam-3407	315	2	,	,	PUNCT
ejpam-3407	315	3	approximate	approximate	VERB
ejpam-3407	315	4	minimal	minimal	ADJ
ejpam-3407	315	5	and	and	CCONJ
ejpam-3407	315	6	maximal	maximal	ADJ
ejpam-3407	315	7	solutions	solution	NOUN
ejpam-3407	315	8	are	be	AUX
ejpam-3407	315	9	given	give	VERB
ejpam-3407	315	10	by	by	ADP
ejpam-3407	315	11	z(s	z(s	PROPN
ejpam-3407	315	12	)	)	PUNCT
ejpam-3407	315	13	=	=	PUNCT
ejpam-3407	316	1	z4(s	z4(s	X
ejpam-3407	316	2	)	)	PUNCT
ejpam-3407	316	3	=	=	SYM
ejpam-3407	316	4	∫	∫	PROPN
ejpam-3407	316	5	1	1	NUM
ejpam-3407	316	6	0	0	NUM
ejpam-3407	316	7	r(s	r(s	PROPN
ejpam-3407	316	8	,	,	PUNCT
ejpam-3407	316	9	γ)q	γ)q	X
ejpam-3407	316	10	(	(	PUNCT
ejpam-3407	316	11	γ	γ	X
ejpam-3407	316	12	,	,	PUNCT
ejpam-3407	316	13	z3(γ	z3(γ	NUM
ejpam-3407	316	14	)	)	PUNCT
ejpam-3407	316	15	)	)	PUNCT
ejpam-3407	317	1	dγ	dγ	ADP
ejpam-3407	317	2	,	,	PUNCT
ejpam-3407	317	3	z∗(s	z∗(s	PROPN
ejpam-3407	317	4	)	)	PUNCT
ejpam-3407	317	5	=	=	SYM
ejpam-3407	317	6	z∗4(s	z∗4(s	PROPN
ejpam-3407	317	7	)	)	PUNCT
ejpam-3407	317	8	=	=	SYM
ejpam-3407	318	1	∫	∫	PROPN
ejpam-3407	318	2	1	1	NUM
ejpam-3407	318	3	0	0	NUM
ejpam-3407	318	4	r(s	r(s	PROPN
ejpam-3407	318	5	,	,	PUNCT
ejpam-3407	318	6	γ)q	γ)q	X
ejpam-3407	318	7	(	(	PUNCT
ejpam-3407	318	8	γ	γ	X
ejpam-3407	318	9	,	,	PUNCT
ejpam-3407	318	10	z∗3(γ	z∗3(γ	PROPN
ejpam-3407	318	11	)	)	PUNCT
ejpam-3407	318	12	)	)	PUNCT
ejpam-3407	319	1	dγ	dγ	PROPN
ejpam-3407	319	2	.	.	PUNCT
ejpam-3407	320	1	(	(	PUNCT
ejpam-3407	320	2	30	30	NUM
ejpam-3407	320	3	)	)	PUNCT
ejpam-3407	320	4	k.	k.	NOUN
ejpam-3407	321	1	shah	shah	PROPN
ejpam-3407	321	2	et	et	PROPN
ejpam-3407	321	3	al	al	PROPN
ejpam-3407	321	4	.	.	PUNCT
ejpam-3407	321	5	/	/	SYM
ejpam-3407	321	6	eur	eur	PROPN
ejpam-3407	321	7	.	.	PUNCT
ejpam-3407	322	1	j.	j.	PROPN
ejpam-3407	322	2	pure	pure	PROPN
ejpam-3407	322	3	appl	appl	PROPN
ejpam-3407	322	4	.	.	PROPN
ejpam-3407	322	5	math	math	PROPN
ejpam-3407	322	6	,	,	PUNCT
ejpam-3407	322	7	12	12	NUM
ejpam-3407	322	8	(	(	PUNCT
ejpam-3407	322	9	2	2	NUM
ejpam-3407	322	10	)	)	PUNCT
ejpam-3407	322	11	(	(	PUNCT
ejpam-3407	322	12	2019	2019	NUM
ejpam-3407	322	13	)	)	PUNCT
ejpam-3407	322	14	,	,	PUNCT
ejpam-3407	322	15	432	432	NUM
ejpam-3407	322	16	-	-	SYM
ejpam-3407	322	17	447	447	NUM
ejpam-3407	322	18	444	444	NUM
ejpam-3407	322	19	let	let	VERB
ejpam-3407	322	20	b	b	NOUN
ejpam-3407	322	21	=	=	SYM
ejpam-3407	322	22	0.00001	0.00001	NUM
ejpam-3407	322	23	and	and	CCONJ
ejpam-3407	322	24	the	the	DET
ejpam-3407	322	25	lower	low	ADJ
ejpam-3407	322	26	and	and	CCONJ
ejpam-3407	322	27	upper	upper	ADJ
ejpam-3407	322	28	solutions	solution	NOUN
ejpam-3407	322	29	of	of	ADP
ejpam-3407	322	30	bvp	bvp	NOUN
ejpam-3407	322	31	(	(	PUNCT
ejpam-3407	322	32	2	2	X
ejpam-3407	322	33	)	)	PUNCT
ejpam-3407	322	34	are	be	AUX
ejpam-3407	322	35	z0	z0	PROPN
ejpam-3407	322	36	=	=	SYM
ejpam-3407	322	37	−0.5	−0.5	PROPN
ejpam-3407	322	38	,	,	PUNCT
ejpam-3407	322	39	and	and	CCONJ
ejpam-3407	322	40	z∗0	z∗0	NOUN
ejpam-3407	322	41	=	=	SYM
ejpam-3407	322	42	0.5	0.5	NUM
ejpam-3407	322	43	respectively	respectively	ADV
ejpam-3407	322	44	.	.	PUNCT
ejpam-3407	323	1	then	then	ADV
ejpam-3407	323	2	,	,	PUNCT
ejpam-3407	323	3	we	we	PRON
ejpam-3407	323	4	have	have	VERB
ejpam-3407	323	5	∆	∆	PROPN
ejpam-3407	323	6	=	=	SYM
ejpam-3407	323	7	2b	2b	NOUN
ejpam-3407	323	8	(	(	PUNCT
ejpam-3407	323	9	2−δ)γ(p	2−δ)γ(p	NUM
ejpam-3407	323	10	)	)	PUNCT
ejpam-3407	323	11	=	=	PUNCT
ejpam-3407	324	1	6.5448e−06	6.5448e−06	NUM
ejpam-3407	324	2	<	<	X
ejpam-3407	324	3	1	1	NUM
ejpam-3407	324	4	.	.	PUNCT
ejpam-3407	324	5	therefore	therefore	ADV
ejpam-3407	324	6	,	,	PUNCT
ejpam-3407	324	7	the	the	DET
ejpam-3407	324	8	corresponding	corresponding	ADJ
ejpam-3407	324	9	estimates	estimate	NOUN
ejpam-3407	324	10	of	of	ADP
ejpam-3407	324	11	error	error	NOUN
ejpam-3407	324	12	are	be	AUX
ejpam-3407	324	13	:	:	PUNCT
ejpam-3407	324	14	e3	e3	X
ejpam-3407	324	15	=	=	SYM
ejpam-3407	324	16	‖z(s)−	‖z(s)−	NUM
ejpam-3407	324	17	z3(s)‖	z3(s)‖	NOUN
ejpam-3407	324	18	≤	≤	NOUN
ejpam-3407	324	19	∆3	∆3	AUX
ejpam-3407	324	20	1−∆	1−∆	NUM
ejpam-3407	324	21	×	×	NOUN
ejpam-3407	324	22	e1	e1	NOUN
ejpam-3407	324	23	≤	≤	NOUN
ejpam-3407	324	24	2.8034×	2.8034×	NUM
ejpam-3407	324	25	10−16	10−16	PROPN
ejpam-3407	324	26	max	max	PROPN
ejpam-3407	324	27	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	324	28	]	]	PUNCT
ejpam-3407	324	29	|z1(s	|z1(s	PROPN
ejpam-3407	324	30	)	)	PUNCT
ejpam-3407	324	31	+	+	NUM
ejpam-3407	324	32	0.5|	0.5|	NUM
ejpam-3407	324	33	≃	≃	NOUN
ejpam-3407	324	34	1.5469×	1.5469×	NUM
ejpam-3407	324	35	10−16	10−16	PROPN
ejpam-3407	324	36	,	,	PUNCT
ejpam-3407	324	37	e∗3	e∗3	NOUN
ejpam-3407	324	38	=	=	PUNCT
ejpam-3407	324	39	‖z(s)−	‖z(s)−	NUM
ejpam-3407	324	40	z∗3(s)‖	z∗3(s)‖	NOUN
ejpam-3407	324	41	≤	≤	NOUN
ejpam-3407	324	42	∆3	∆3	PRON
ejpam-3407	324	43	1−∆	1−∆	NUM
ejpam-3407	324	44	×	×	NOUN
ejpam-3407	324	45	e∗1	e∗1	ADJ
ejpam-3407	324	46	≤	≤	NUM
ejpam-3407	324	47	2.8034×	2.8034×	NUM
ejpam-3407	324	48	10−16	10−16	PROPN
ejpam-3407	324	49	max	max	PROPN
ejpam-3407	324	50	s∈[0,1	s∈[0,1	PROPN
ejpam-3407	324	51	]	]	PUNCT
ejpam-3407	324	52	|0.5−	|0.5−	PUNCT
ejpam-3407	324	53	z∗1(s)|	z∗1(s)|	PROPN
ejpam-3407	324	54	≃	≃	VERB
ejpam-3407	324	55	1.4017×	1.4017×	NUM
ejpam-3407	324	56	10−16	10−16	PROPN
ejpam-3407	324	57	.	.	PUNCT
ejpam-3407	325	1	the	the	DET
ejpam-3407	325	2	maximal	maximal	ADJ
ejpam-3407	325	3	and	and	CCONJ
ejpam-3407	325	4	minimal	minimal	ADJ
ejpam-3407	325	5	solutions	solution	NOUN
ejpam-3407	325	6	of	of	ADP
ejpam-3407	325	7	the	the	DET
ejpam-3407	325	8	example	example	NOUN
ejpam-3407	325	9	(	(	PUNCT
ejpam-3407	325	10	2	2	X
ejpam-3407	325	11	)	)	PUNCT
ejpam-3407	325	12	are	be	AUX
ejpam-3407	325	13	plotted	plot	VERB
ejpam-3407	325	14	in	in	ADP
ejpam-3407	325	15	the	the	DET
ejpam-3407	325	16	figure	figure	NOUN
ejpam-3407	325	17	2	2	NUM
ejpam-3407	325	18	.	.	PUNCT
ejpam-3407	326	1	clearly	clearly	ADV
ejpam-3407	326	2	,	,	PUNCT
ejpam-3407	326	3	the	the	DET
ejpam-3407	326	4	condition	condition	NOUN
ejpam-3407	326	5	∆	∆	X
ejpam-3407	326	6	<	<	X
ejpam-3407	326	7	1	1	NUM
ejpam-3407	326	8	is	be	AUX
ejpam-3407	326	9	sufficient	sufficient	ADJ
ejpam-3407	326	10	for	for	ADP
ejpam-3407	326	11	various	various	ADJ
ejpam-3407	326	12	kinds	kind	NOUN
ejpam-3407	326	13	of	of	ADP
ejpam-3407	326	14	ulam	ulam	ADJ
ejpam-3407	326	15	stabilities	stability	NOUN
ejpam-3407	326	16	for	for	ADP
ejpam-3407	326	17	the	the	DET
ejpam-3407	326	18	extremal	extremal	ADJ
ejpam-3407	326	19	solution	solution	NOUN
ejpam-3407	326	20	of	of	ADP
ejpam-3407	326	21	the	the	DET
ejpam-3407	326	22	example	example	NOUN
ejpam-3407	326	23	(	(	PUNCT
ejpam-3407	326	24	2	2	NUM
ejpam-3407	326	25	)	)	PUNCT
ejpam-3407	326	26	.	.	PUNCT
ejpam-3407	327	1	the	the	DET
ejpam-3407	327	2	stability	stability	NOUN
ejpam-3407	327	3	of	of	ADP
ejpam-3407	327	4	extremal	extremal	ADJ
ejpam-3407	327	5	solutions	solution	NOUN
ejpam-3407	327	6	is	be	AUX
ejpam-3407	327	7	also	also	ADV
ejpam-3407	327	8	obvious	obvious	ADJ
ejpam-3407	327	9	from	from	ADP
ejpam-3407	327	10	plots	plot	NOUN
ejpam-3407	327	11	in	in	ADP
ejpam-3407	327	12	the	the	DET
ejpam-3407	327	13	given	give	VERB
ejpam-3407	327	14	figure	figure	NOUN
ejpam-3407	327	15	2	2	NUM
ejpam-3407	327	16	.	.	NOUN
ejpam-3407	327	17	0	0	NUM
ejpam-3407	327	18	0.1	0.1	NUM
ejpam-3407	327	19	0.2	0.2	NUM
ejpam-3407	327	20	0.3	0.3	NUM
ejpam-3407	327	21	0.4	0.4	NUM
ejpam-3407	327	22	0.5	0.5	NUM
ejpam-3407	327	23	0.6	0.6	NUM
ejpam-3407	327	24	0.7	0.7	NUM
ejpam-3407	327	25	0.8	0.8	NUM
ejpam-3407	327	26	0.9	0.9	NUM
ejpam-3407	327	27	1	1	NUM
ejpam-3407	327	28	0	0	NUM
ejpam-3407	327	29	0.05	0.05	NUM
ejpam-3407	327	30	0.1	0.1	NUM
ejpam-3407	327	31	0.15	0.15	NUM
ejpam-3407	327	32	0.2	0.2	NUM
ejpam-3407	327	33	0	0	NUM
ejpam-3407	327	34	0.1	0.1	NUM
ejpam-3407	327	35	0.2	0.2	NUM
ejpam-3407	327	36	0.3	0.3	NUM
ejpam-3407	327	37	0.4	0.4	NUM
ejpam-3407	327	38	0.5	0.5	NUM
ejpam-3407	327	39	0.6	0.6	NUM
ejpam-3407	327	40	0.7	0.7	NUM
ejpam-3407	327	41	0.8	0.8	NUM
ejpam-3407	327	42	0.9	0.9	NUM
ejpam-3407	327	43	1	1	NUM
ejpam-3407	327	44	0	0	NUM
ejpam-3407	327	45	0.05	0.05	NUM
ejpam-3407	327	46	0.1	0.1	NUM
ejpam-3407	327	47	0.15	0.15	NUM
ejpam-3407	327	48	z	z	NOUN
ejpam-3407	327	49	*	*	PUNCT
ejpam-3407	327	50	1	1	NUM
ejpam-3407	327	51	(	(	PUNCT
ejpam-3407	327	52	s)=maximal	s)=maximal	ADJ
ejpam-3407	327	53	solution	solution	NOUN
ejpam-3407	327	54	z	z	NOUN
ejpam-3407	327	55	1	1	NUM
ejpam-3407	327	56	(	(	PUNCT
ejpam-3407	327	57	s)=minimal	s)=minimal	ADJ
ejpam-3407	327	58	solution	solution	NOUN
ejpam-3407	327	59	z	z	NOUN
ejpam-3407	327	60	*	*	SYM
ejpam-3407	327	61	2	2	NUM
ejpam-3407	327	62	(	(	PUNCT
ejpam-3407	327	63	s)=maximal	s)=maximal	ADJ
ejpam-3407	327	64	solution	solution	NOUN
ejpam-3407	327	65	z	z	NOUN
ejpam-3407	327	66	2	2	NUM
ejpam-3407	327	67	(	(	PUNCT
ejpam-3407	327	68	s)=minimal	s)=minimal	ADJ
ejpam-3407	327	69	solution	solution	NOUN
ejpam-3407	327	70	figure	figure	NOUN
ejpam-3407	327	71	.	.	PUNCT
ejpam-3407	328	1	2	2	NUM
ejpam-3407	328	2	a	a	DET
ejpam-3407	328	3	line	line	NOUN
ejpam-3407	328	4	graph	graph	NOUN
ejpam-3407	328	5	of	of	ADP
ejpam-3407	328	6	the	the	DET
ejpam-3407	328	7	extremal	extremal	ADJ
ejpam-3407	328	8	solutions	solution	NOUN
ejpam-3407	328	9	of	of	ADP
ejpam-3407	328	10	the	the	DET
ejpam-3407	328	11	example	example	NOUN
ejpam-3407	328	12	2	2	NUM
ejpam-3407	328	13	.	.	NOUN
ejpam-3407	328	14	6	6	NUM
ejpam-3407	328	15	.	.	X
ejpam-3407	329	1	conclusion	conclusion	NOUN
ejpam-3407	329	2	we	we	PRON
ejpam-3407	329	3	have	have	AUX
ejpam-3407	329	4	successfully	successfully	ADV
ejpam-3407	329	5	investigated	investigate	VERB
ejpam-3407	329	6	sufficient	sufficient	ADJ
ejpam-3407	329	7	conditions	condition	NOUN
ejpam-3407	329	8	for	for	ADP
ejpam-3407	329	9	maximal	maximal	ADJ
ejpam-3407	329	10	and	and	CCONJ
ejpam-3407	329	11	minimal	minimal	ADJ
ejpam-3407	329	12	solutions	solution	NOUN
ejpam-3407	329	13	using	use	VERB
ejpam-3407	329	14	monotone	monotone	ADJ
ejpam-3407	329	15	iterative	iterative	NOUN
ejpam-3407	329	16	schemes	scheme	NOUN
ejpam-3407	329	17	together	together	ADV
ejpam-3407	329	18	with	with	ADP
ejpam-3407	329	19	upper	upper	ADJ
ejpam-3407	329	20	and	and	CCONJ
ejpam-3407	329	21	lower	low	ADJ
ejpam-3407	329	22	solutions	solution	NOUN
ejpam-3407	329	23	method	method	NOUN
ejpam-3407	329	24	.	.	PUNCT
ejpam-3407	330	1	we	we	PRON
ejpam-3407	330	2	also	also	ADV
ejpam-3407	330	3	provided	provide	VERB
ejpam-3407	330	4	maximum	maximum	ADJ
ejpam-3407	330	5	error	error	NOUN
ejpam-3407	330	6	estimates	estimate	NOUN
ejpam-3407	330	7	for	for	ADP
ejpam-3407	330	8	the	the	DET
ejpam-3407	330	9	solutions	solution	NOUN
ejpam-3407	330	10	.	.	PUNCT
ejpam-3407	331	1	the	the	DET
ejpam-3407	331	2	obtained	obtain	VERB
ejpam-3407	331	3	results	result	NOUN
ejpam-3407	331	4	were	be	AUX
ejpam-3407	331	5	verified	verify	VERB
ejpam-3407	331	6	by	by	ADP
ejpam-3407	331	7	plotting	plot	VERB
ejpam-3407	331	8	the	the	DET
ejpam-3407	331	9	graph	graph	NOUN
ejpam-3407	331	10	of	of	ADP
ejpam-3407	331	11	the	the	DET
ejpam-3407	331	12	illustrative	illustrative	ADJ
ejpam-3407	331	13	problem	problem	NOUN
ejpam-3407	331	14	.	.	PUNCT
ejpam-3407	332	1	acknowledgements	acknowledgement	NOUN
ejpam-3407	332	2	the	the	DET
ejpam-3407	332	3	authors	author	NOUN
ejpam-3407	332	4	would	would	AUX
ejpam-3407	332	5	like	like	VERB
ejpam-3407	332	6	to	to	PART
ejpam-3407	332	7	thank	thank	VERB
ejpam-3407	332	8	the	the	DET
ejpam-3407	332	9	reviewers	reviewer	NOUN
ejpam-3407	332	10	of	of	ADP
ejpam-3407	332	11	this	this	DET
ejpam-3407	332	12	paper	paper	NOUN
ejpam-3407	332	13	for	for	ADP
ejpam-3407	332	14	their	their	PRON
ejpam-3407	332	15	valuable	valuable	ADJ
ejpam-3407	332	16	comments	comment	NOUN
ejpam-3407	332	17	on	on	ADP
ejpam-3407	332	18	the	the	DET
ejpam-3407	332	19	earlier	early	ADJ
ejpam-3407	332	20	version	version	NOUN
ejpam-3407	332	21	of	of	ADP
ejpam-3407	332	22	the	the	DET
ejpam-3407	332	23	paper	paper	NOUN
ejpam-3407	332	24	.	.	PUNCT
ejpam-3407	333	1	they	they	PRON
ejpam-3407	333	2	would	would	AUX
ejpam-3407	333	3	also	also	ADV
ejpam-3407	333	4	like	like	VERB
ejpam-3407	333	5	to	to	PART
ejpam-3407	333	6	acknowledge	acknowledge	VERB
ejpam-3407	333	7	prof	prof	PROPN
ejpam-3407	333	8	.	.	PUNCT
ejpam-3407	334	1	dr	dr	PROPN
ejpam-3407	334	2	.	.	PROPN
ejpam-3407	334	3	salim	salim	PROPN
ejpam-3407	334	4	ur	ur	PROPN
ejpam-3407	334	5	rehman	rehman	PROPN
ejpam-3407	334	6	,	,	PUNCT
ejpam-3407	334	7	v.c	v.c	PROPN
ejpam-3407	334	8	.	.	PROPN
ejpam-3407	334	9	sarhad	sarhad	PROPN
ejpam-3407	334	10	university	university	PROPN
ejpam-3407	334	11	of	of	ADP
ejpam-3407	334	12	science	science	PROPN
ejpam-3407	334	13	and	and	CCONJ
ejpam-3407	334	14	i.	i.	PROPN
ejpam-3407	334	15	t	t	PROPN
ejpam-3407	334	16	,	,	PUNCT
ejpam-3407	334	17	for	for	ADP
ejpam-3407	334	18	providing	provide	VERB
ejpam-3407	334	19	excellent	excellent	ADJ
ejpam-3407	334	20	research	research	NOUN
ejpam-3407	334	21	references	reference	NOUN
ejpam-3407	334	22	445	445	NUM
ejpam-3407	334	23	and	and	CCONJ
ejpam-3407	334	24	academic	academic	ADJ
ejpam-3407	334	25	environment	environment	NOUN
ejpam-3407	334	26	.	.	PUNCT
ejpam-3407	335	1	funding	funding	NOUN
ejpam-3407	335	2	source	source	NOUN
ejpam-3407	335	3	:	:	PUNCT
ejpam-3407	335	4	we	we	PRON
ejpam-3407	335	5	remark	remark	VERB
ejpam-3407	335	6	that	that	SCONJ
ejpam-3407	335	7	this	this	DET
ejpam-3407	335	8	work	work	NOUN
ejpam-3407	335	9	has	have	AUX
ejpam-3407	335	10	been	be	AUX
ejpam-3407	335	11	supported	support	VERB
ejpam-3407	335	12	by	by	ADP
ejpam-3407	335	13	the	the	DET
ejpam-3407	335	14	hec	hec	PROPN
ejpam-3407	335	15	of	of	ADP
ejpam-3407	335	16	pakistan	pakistan	PROPN
ejpam-3407	335	17	,	,	PUNCT
ejpam-3407	335	18	grant	grant	VERB
ejpam-3407	335	19	no	no	DET
ejpam-3407	335	20	:	:	PUNCT
ejpam-3407	335	21	10039	10039	NUM
ejpam-3407	335	22	/	/	SYM
ejpam-3407	335	23	kpk/	kpk/	NOUN
ejpam-3407	335	24	nrpu	nrpu	NOUN
ejpam-3407	335	25	/	/	SYM
ejpam-3407	335	26	r&d	r&d	NOUN
ejpam-3407	335	27	/	/	SYM
ejpam-3407	335	28	hec/	hec/	ADJ
ejpam-3407	335	29	2017	2017	NUM
ejpam-3407	335	30	and	and	CCONJ
ejpam-3407	335	31	he	he	PRON
ejpam-3407	335	32	d	d	PROPN
ejpam-3407	335	33	of	of	ADP
ejpam-3407	335	34	kpk	kpk	PROPN
ejpam-3407	335	35	,	,	PUNCT
ejpam-3407	335	36	government	government	NOUN
ejpam-3407	335	37	of	of	ADP
ejpam-3407	335	38	pakistan	pakistan	PROPN
ejpam-3407	335	39	at	at	ADP
ejpam-3407	335	40	grant	grant	PROPN
ejpam-3407	335	41	no	no	NOUN
ejpam-3407	335	42	:	:	PUNCT
ejpam-3407	335	43	heref-46	heref-46	ADJ
ejpam-3407	335	44	authors	author	NOUN
ejpam-3407	335	45	contributions	contribution	NOUN
ejpam-3407	335	46	:	:	PUNCT
ejpam-3407	335	47	all	all	DET
ejpam-3407	335	48	authors	author	NOUN
ejpam-3407	335	49	jointly	jointly	ADV
ejpam-3407	335	50	worked	work	VERB
ejpam-3407	335	51	on	on	ADP
ejpam-3407	335	52	the	the	DET
ejpam-3407	335	53	results	result	NOUN
ejpam-3407	335	54	and	and	CCONJ
ejpam-3407	335	55	they	they	PRON
ejpam-3407	335	56	read	read	VERB
ejpam-3407	335	57	and	and	CCONJ
ejpam-3407	335	58	approved	approve	VERB
ejpam-3407	335	59	the	the	DET
ejpam-3407	335	60	final	final	ADJ
ejpam-3407	335	61	manuscript	manuscript	NOUN
ejpam-3407	335	62	.	.	PUNCT
ejpam-3407	336	1	conflict	conflict	NOUN
ejpam-3407	336	2	of	of	ADP
ejpam-3407	336	3	interest	interest	NOUN
ejpam-3407	336	4	:	:	PUNCT
ejpam-3407	336	5	it	it	PRON
ejpam-3407	336	6	is	be	AUX
ejpam-3407	336	7	declared	declare	VERB
ejpam-3407	336	8	that	that	SCONJ
ejpam-3407	336	9	no	no	DET
ejpam-3407	336	10	conflict	conflict	NOUN
ejpam-3407	336	11	of	of	ADP
ejpam-3407	336	12	interest	interest	NOUN
ejpam-3407	336	13	exist	exist	VERB
ejpam-3407	336	14	regarding	regard	VERB
ejpam-3407	336	15	this	this	DET
ejpam-3407	336	16	paper	paper	NOUN
ejpam-3407	336	17	.	.	PUNCT
ejpam-3407	337	1	references	reference	NOUN
ejpam-3407	337	2	[	[	X
ejpam-3407	337	3	1	1	NUM
ejpam-3407	337	4	]	]	PUNCT
ejpam-3407	337	5	a.	a.	NOUN
ejpam-3407	337	6	a.	a.	NOUN
ejpam-3407	337	7	kilbas	kilbas	PROPN
ejpam-3407	337	8	,	,	PUNCT
ejpam-3407	337	9	o.i	o.i	PROPN
ejpam-3407	337	10	.	.	PROPN
ejpam-3407	337	11	marichev	marichev	PROPN
ejpam-3407	337	12	and	and	CCONJ
ejpam-3407	337	13	s.	s.	PROPN
ejpam-3407	337	14	g.	g.	PROPN
ejpam-3407	337	15	samko	samko	PROPN
ejpam-3407	337	16	.	.	PUNCT
ejpam-3407	338	1	fractional	fractional	ADJ
ejpam-3407	338	2	integrals	integral	NOUN
ejpam-3407	338	3	and	and	CCONJ
ejpam-3407	338	4	derivatives	derivative	NOUN
ejpam-3407	338	5	(	(	PUNCT
ejpam-3407	338	6	theory	theory	NOUN
ejpam-3407	338	7	and	and	CCONJ
ejpam-3407	338	8	applications	application	NOUN
ejpam-3407	338	9	)	)	PUNCT
ejpam-3407	338	10	.	.	PUNCT
ejpam-3407	339	1	gordon	gordon	PROPN
ejpam-3407	339	2	and	and	CCONJ
ejpam-3407	339	3	breach	breach	PROPN
ejpam-3407	339	4	,	,	PUNCT
ejpam-3407	339	5	switzerland	switzerland	PROPN
ejpam-3407	339	6	,	,	PUNCT
ejpam-3407	339	7	1993	1993	NUM
ejpam-3407	339	8	.	.	PUNCT
ejpam-3407	340	1	[	[	X
ejpam-3407	340	2	2	2	X
ejpam-3407	340	3	]	]	PUNCT
ejpam-3407	340	4	k.	k.	PROPN
ejpam-3407	340	5	s.	s.	PROPN
ejpam-3407	340	6	miller	miller	PROPN
ejpam-3407	340	7	and	and	CCONJ
ejpam-3407	340	8	b.	b.	PROPN
ejpam-3407	340	9	ross	ross	PROPN
ejpam-3407	340	10	.	.	PUNCT
ejpam-3407	341	1	an	an	DET
ejpam-3407	341	2	introduction	introduction	NOUN
ejpam-3407	341	3	to	to	ADP
ejpam-3407	341	4	the	the	DET
ejpam-3407	341	5	fractional	fractional	ADJ
ejpam-3407	341	6	calculus	calculus	NOUN
ejpam-3407	341	7	and	and	CCONJ
ejpam-3407	341	8	fractional	fractional	ADJ
ejpam-3407	341	9	differential	differential	ADJ
ejpam-3407	341	10	equations	equation	NOUN
ejpam-3407	341	11	.	.	PUNCT
ejpam-3407	342	1	wiley	wiley	PROPN
ejpam-3407	342	2	,	,	PUNCT
ejpam-3407	342	3	new	new	PROPN
ejpam-3407	342	4	york	york	PROPN
ejpam-3407	342	5	,	,	PUNCT
ejpam-3407	342	6	1993	1993	NUM
ejpam-3407	342	7	.	.	PUNCT
ejpam-3407	343	1	[	[	X
ejpam-3407	343	2	3	3	NUM
ejpam-3407	343	3	]	]	X
ejpam-3407	343	4	i.	i.	NOUN
ejpam-3407	343	5	podlubny	podlubny	PROPN
ejpam-3407	343	6	.	.	PUNCT
ejpam-3407	344	1	fractional	fractional	ADJ
ejpam-3407	344	2	differential	differential	ADJ
ejpam-3407	344	3	equations	equation	NOUN
ejpam-3407	344	4	,	,	PUNCT
ejpam-3407	344	5	mathematics	mathematic	NOUN
ejpam-3407	344	6	in	in	ADP
ejpam-3407	344	7	science	science	NOUN
ejpam-3407	344	8	and	and	CCONJ
ejpam-3407	344	9	engineering	engineering	NOUN
ejpam-3407	344	10	.	.	PUNCT
ejpam-3407	345	1	academic	academic	ADJ
ejpam-3407	345	2	press	press	NOUN
ejpam-3407	345	3	,	,	PUNCT
ejpam-3407	345	4	new	new	PROPN
ejpam-3407	345	5	york	york	PROPN
ejpam-3407	345	6	,	,	PUNCT
ejpam-3407	345	7	1999	1999	NUM
ejpam-3407	345	8	.	.	PUNCT
ejpam-3407	346	1	[	[	X
ejpam-3407	346	2	4	4	NUM
ejpam-3407	346	3	]	]	PUNCT
ejpam-3407	346	4	r.	r.	NOUN
ejpam-3407	346	5	hilfer	hilfer	PROPN
ejpam-3407	346	6	.	.	PUNCT
ejpam-3407	347	1	applications	application	NOUN
ejpam-3407	347	2	of	of	ADP
ejpam-3407	347	3	fractional	fractional	ADJ
ejpam-3407	347	4	calculus	calculus	NOUN
ejpam-3407	347	5	in	in	ADP
ejpam-3407	347	6	physics	physics	PROPN
ejpam-3407	347	7	.	.	PUNCT
ejpam-3407	348	1	world	world	PROPN
ejpam-3407	348	2	scientific	scientific	PROPN
ejpam-3407	348	3	,	,	PUNCT
ejpam-3407	348	4	singapore	singapore	PROPN
ejpam-3407	348	5	,	,	PUNCT
ejpam-3407	348	6	2000	2000	NUM
ejpam-3407	348	7	.	.	PUNCT
ejpam-3407	349	1	[	[	X
ejpam-3407	349	2	5	5	NUM
ejpam-3407	349	3	]	]	PUNCT
ejpam-3407	349	4	a.	a.	NOUN
ejpam-3407	349	5	a.	a.	NOUN
ejpam-3407	349	6	kilbas	kilbas	PROPN
ejpam-3407	349	7	,	,	PUNCT
ejpam-3407	349	8	h.	h.	PROPN
ejpam-3407	349	9	m.	m.	PROPN
ejpam-3407	349	10	srivastava	srivastava	PROPN
ejpam-3407	349	11	and	and	CCONJ
ejpam-3407	349	12	j.j	j.j	PROPN
ejpam-3407	349	13	.	.	PROPN
ejpam-3407	349	14	trujillo	trujillo	PROPN
ejpam-3407	349	15	.	.	PUNCT
ejpam-3407	349	16	theory	theory	NOUN
ejpam-3407	349	17	and	and	CCONJ
ejpam-3407	349	18	applications	application	NOUN
ejpam-3407	349	19	of	of	ADP
ejpam-3407	349	20	fractional	fractional	ADJ
ejpam-3407	349	21	differential	differential	ADJ
ejpam-3407	349	22	equations	equation	NOUN
ejpam-3407	349	23	.	.	PUNCT
ejpam-3407	350	1	elsevier	elsevier	PROPN
ejpam-3407	350	2	,	,	PUNCT
ejpam-3407	350	3	amsterdam	amsterdam	PROPN
ejpam-3407	350	4	,	,	PUNCT
ejpam-3407	350	5	2006	2006	NUM
ejpam-3407	350	6	.	.	PUNCT
ejpam-3407	351	1	[	[	X
ejpam-3407	351	2	6	6	NUM
ejpam-3407	351	3	]	]	PUNCT
ejpam-3407	351	4	m.	m.	NOUN
ejpam-3407	351	5	benchohra	benchohra	NOUN
ejpam-3407	351	6	,	,	PUNCT
ejpam-3407	351	7	j.	j.	PROPN
ejpam-3407	351	8	r.	r.	PROPN
ejpam-3407	351	9	graef	graef	PROPN
ejpam-3407	351	10	,	,	PUNCT
ejpam-3407	351	11	and	and	CCONJ
ejpam-3407	351	12	s.	s.	PROPN
ejpam-3407	351	13	hamani	hamani	PROPN
ejpam-3407	351	14	.	.	PUNCT
ejpam-3407	352	1	existence	existence	NOUN
ejpam-3407	352	2	results	result	VERB
ejpam-3407	352	3	for	for	ADP
ejpam-3407	352	4	boundary	boundary	ADJ
ejpam-3407	352	5	value	value	NOUN
ejpam-3407	352	6	problems	problem	NOUN
ejpam-3407	352	7	with	with	ADP
ejpam-3407	352	8	nonlinear	nonlinear	ADJ
ejpam-3407	352	9	fractional	fractional	ADJ
ejpam-3407	352	10	differential	differential	ADJ
ejpam-3407	352	11	equations	equation	NOUN
ejpam-3407	352	12	.	.	PUNCT
ejpam-3407	353	1	applied	apply	VERB
ejpam-3407	353	2	analysis	analysis	NOUN
ejpam-3407	353	3	,	,	PUNCT
ejpam-3407	353	4	87:851	87:851	NUM
ejpam-3407	353	5	–	–	PUNCT
ejpam-3407	353	6	863	863	NUM
ejpam-3407	353	7	,	,	PUNCT
ejpam-3407	353	8	2008	2008	NUM
ejpam-3407	353	9	.	.	PUNCT
ejpam-3407	354	1	[	[	X
ejpam-3407	354	2	7	7	X
ejpam-3407	354	3	]	]	X
ejpam-3407	354	4	r.	r.	PROPN
ejpam-3407	354	5	p.	p.	PROPN
ejpam-3407	354	6	agarwal	agarwal	PROPN
ejpam-3407	354	7	,	,	PUNCT
ejpam-3407	354	8	m.	m.	NOUN
ejpam-3407	354	9	belmekki	belmekki	PROPN
ejpam-3407	354	10	and	and	CCONJ
ejpam-3407	354	11	m.	m.	NOUN
ejpam-3407	354	12	benchohra	benchohra	NOUN
ejpam-3407	354	13	.	.	PUNCT
ejpam-3407	355	1	a	a	DET
ejpam-3407	355	2	survey	survey	NOUN
ejpam-3407	355	3	on	on	ADP
ejpam-3407	355	4	semilinear	semilinear	ADJ
ejpam-3407	355	5	differential	differential	NOUN
ejpam-3407	355	6	equations	equation	NOUN
ejpam-3407	355	7	and	and	CCONJ
ejpam-3407	355	8	inclusions	inclusion	NOUN
ejpam-3407	355	9	involving	involve	VERB
ejpam-3407	355	10	riemann	riemann	PROPN
ejpam-3407	355	11	-	-	PUNCT
ejpam-3407	355	12	liouville	liouville	VERB
ejpam-3407	355	13	fractional	fractional	ADJ
ejpam-3407	355	14	derivative	derivative	NOUN
ejpam-3407	355	15	.	.	PUNCT
ejpam-3407	356	1	advances	advance	NOUN
ejpam-3407	356	2	in	in	ADP
ejpam-3407	356	3	.	.	PUNCT
ejpam-3407	357	1	difference	difference	NOUN
ejpam-3407	357	2	equations	equation	NOUN
ejpam-3407	357	3	,	,	PUNCT
ejpam-3407	357	4	2009:14	2009:14	NUM
ejpam-3407	357	5	pages	page	NOUN
ejpam-3407	357	6	,	,	PUNCT
ejpam-3407	357	7	2009	2009	NUM
ejpam-3407	357	8	.	.	PUNCT
ejpam-3407	358	1	[	[	X
ejpam-3407	358	2	8	8	NUM
ejpam-3407	358	3	]	]	X
ejpam-3407	358	4	r.	r.	PROPN
ejpam-3407	358	5	p.	p.	PROPN
ejpam-3407	358	6	agarwal	agarwal	PROPN
ejpam-3407	358	7	,	,	PUNCT
ejpam-3407	358	8	m.	m.	NOUN
ejpam-3407	358	9	benchohra	benchohra	NOUN
ejpam-3407	358	10	and	and	CCONJ
ejpam-3407	358	11	s.	s.	PROPN
ejpam-3407	358	12	hamani	hamani	PROPN
ejpam-3407	358	13	.	.	PUNCT
ejpam-3407	359	1	a	a	DET
ejpam-3407	359	2	survey	survey	NOUN
ejpam-3407	359	3	on	on	ADP
ejpam-3407	359	4	existence	existence	NOUN
ejpam-3407	359	5	results	result	NOUN
ejpam-3407	359	6	for	for	ADP
ejpam-3407	359	7	boundary	boundary	ADJ
ejpam-3407	359	8	value	value	NOUN
ejpam-3407	359	9	problems	problem	NOUN
ejpam-3407	359	10	of	of	ADP
ejpam-3407	359	11	nonlinear	nonlinear	ADJ
ejpam-3407	359	12	fractional	fractional	ADJ
ejpam-3407	359	13	differential	differential	ADJ
ejpam-3407	359	14	equations	equation	NOUN
ejpam-3407	359	15	and	and	CCONJ
ejpam-3407	359	16	inclusions	inclusion	NOUN
ejpam-3407	359	17	.	.	PUNCT
ejpam-3407	360	1	acta	acta	PROPN
ejpam-3407	360	2	applicandae	applicandae	PROPN
ejpam-3407	360	3	mathematicae	mathematicae	PROPN
ejpam-3407	360	4	,	,	PUNCT
ejpam-3407	360	5	109:973–1033	109:973–1033	NUM
ejpam-3407	360	6	,	,	PUNCT
ejpam-3407	360	7	2012	2012	NUM
ejpam-3407	360	8	.	.	PUNCT
ejpam-3407	361	1	[	[	X
ejpam-3407	361	2	9	9	NUM
ejpam-3407	361	3	]	]	PUNCT
ejpam-3407	361	4	w.yang	w.yang	X
ejpam-3407	361	5	.	.	PUNCT
ejpam-3407	361	6	positive	positive	ADJ
ejpam-3407	361	7	solution	solution	NOUN
ejpam-3407	361	8	to	to	ADP
ejpam-3407	361	9	nonzero	nonzero	PROPN
ejpam-3407	361	10	boundary	boundary	ADJ
ejpam-3407	361	11	values	value	NOUN
ejpam-3407	361	12	problem	problem	NOUN
ejpam-3407	361	13	for	for	ADP
ejpam-3407	361	14	a	a	DET
ejpam-3407	361	15	coupled	couple	VERB
ejpam-3407	361	16	systemof	systemof	ADJ
ejpam-3407	361	17	nonlinear	nonlinear	ADJ
ejpam-3407	361	18	fractional	fractional	ADJ
ejpam-3407	361	19	differential	differential	NOUN
ejpam-3407	361	20	equations	equation	NOUN
ejpam-3407	361	21	.	.	PUNCT
ejpam-3407	362	1	computer	computer	NOUN
ejpam-3407	362	2	and	and	CCONJ
ejpam-3407	362	3	mathematics	mathematic	NOUN
ejpam-3407	362	4	with	with	ADP
ejpam-3407	362	5	applications	application	NOUN
ejpam-3407	362	6	,	,	PUNCT
ejpam-3407	362	7	63:288–297	63:288–297	PROPN
ejpam-3407	362	8	,	,	PUNCT
ejpam-3407	362	9	2012	2012	NUM
ejpam-3407	362	10	.	.	PUNCT
ejpam-3407	363	1	[	[	X
ejpam-3407	363	2	10	10	NUM
ejpam-3407	363	3	]	]	X
ejpam-3407	363	4	k.shah	k.shah	PROPN
ejpam-3407	363	5	and	and	CCONJ
ejpam-3407	363	6	r.a	r.a	PROPN
ejpam-3407	363	7	.	.	PROPN
ejpam-3407	363	8	khan	khan	PROPN
ejpam-3407	363	9	.	.	PUNCT
ejpam-3407	364	1	iterative	iterative	NOUN
ejpam-3407	364	2	solutions	solution	NOUN
ejpam-3407	364	3	to	to	ADP
ejpam-3407	364	4	a	a	DET
ejpam-3407	364	5	coupled	couple	VERB
ejpam-3407	364	6	system	system	NOUN
ejpam-3407	364	7	of	of	ADP
ejpam-3407	364	8	nonlinear	nonlinear	ADJ
ejpam-3407	364	9	fractional	fractional	ADJ
ejpam-3407	364	10	differential	differential	NOUN
ejpam-3407	364	11	equations.journal	equations.journal	PROPN
ejpam-3407	364	12	of	of	ADP
ejpam-3407	364	13	fractional	fractional	ADJ
ejpam-3407	364	14	calcculus	calcculus	ADJ
ejpam-3407	364	15	and	and	CCONJ
ejpam-3407	364	16	applications	application	NOUN
ejpam-3407	364	17	,	,	PUNCT
ejpam-3407	364	18	7(2):40–50	7(2):40–50	NUM
ejpam-3407	364	19	,	,	PUNCT
ejpam-3407	364	20	2016	2016	NUM
ejpam-3407	364	21	.	.	PUNCT
ejpam-3407	365	1	references	reference	NOUN
ejpam-3407	365	2	446	446	NUM
ejpam-3407	365	3	[	[	SYM
ejpam-3407	365	4	11	11	NUM
ejpam-3407	365	5	]	]	PUNCT
ejpam-3407	365	6	k.	k.	PROPN
ejpam-3407	365	7	shah	shah	PROPN
ejpam-3407	365	8	,	,	PUNCT
ejpam-3407	365	9	h.	h.	PROPN
ejpam-3407	365	10	khalil	khalil	PROPN
ejpam-3407	365	11	and	and	CCONJ
ejpam-3407	365	12	r.	r.	PROPN
ejpam-3407	365	13	a.	a.	PROPN
ejpam-3407	365	14	khan	khan	PROPN
ejpam-3407	365	15	.	.	PUNCT
ejpam-3407	366	1	upper	upper	ADJ
ejpam-3407	366	2	and	and	CCONJ
ejpam-3407	366	3	lower	low	ADJ
ejpam-3407	366	4	solutions	solution	NOUN
ejpam-3407	366	5	to	to	ADP
ejpam-3407	366	6	a	a	DET
ejpam-3407	366	7	coupled	couple	VERB
ejpam-3407	366	8	system	system	NOUN
ejpam-3407	366	9	of	of	ADP
ejpam-3407	366	10	nonlinear	nonlinear	ADJ
ejpam-3407	366	11	fractional	fractional	ADJ
ejpam-3407	366	12	differential	differential	ADJ
ejpam-3407	366	13	equations	equation	NOUN
ejpam-3407	366	14	.	.	PUNCT
ejpam-3407	367	1	progress	progress	NOUN
ejpam-3407	367	2	in	in	ADP
ejpam-3407	367	3	fractional	fractional	ADJ
ejpam-3407	367	4	differntial	differntial	ADJ
ejpam-3407	367	5	equations	equation	NOUN
ejpam-3407	367	6	applications	application	NOUN
ejpam-3407	367	7	,	,	PUNCT
ejpam-3407	367	8	1(1):1–10	1(1):1–10	NUM
ejpam-3407	367	9	,	,	PUNCT
ejpam-3407	367	10	2016	2016	NUM
ejpam-3407	367	11	.	.	PUNCT
ejpam-3407	368	1	[	[	X
ejpam-3407	368	2	12	12	NUM
ejpam-3407	368	3	]	]	PUNCT
ejpam-3407	368	4	b.	b.	PROPN
ejpam-3407	368	5	ahmad	ahmad	PROPN
ejpam-3407	368	6	and	and	CCONJ
ejpam-3407	368	7	j.	j.	PROPN
ejpam-3407	368	8	j.	j.	PROPN
ejpam-3407	368	9	nieto	nieto	PROPN
ejpam-3407	368	10	.	.	PUNCT
ejpam-3407	369	1	existence	existence	NOUN
ejpam-3407	369	2	results	result	VERB
ejpam-3407	369	3	for	for	ADP
ejpam-3407	369	4	a	a	DET
ejpam-3407	369	5	coupled	couple	VERB
ejpam-3407	369	6	system	system	NOUN
ejpam-3407	369	7	of	of	ADP
ejpam-3407	369	8	nonlinear	nonlinear	ADJ
ejpam-3407	369	9	fractional	fractional	ADJ
ejpam-3407	369	10	differential	differential	ADJ
ejpam-3407	369	11	equations	equation	NOUN
ejpam-3407	369	12	with	with	ADP
ejpam-3407	369	13	three	three	NUM
ejpam-3407	369	14	-	-	PUNCT
ejpam-3407	369	15	point	point	NOUN
ejpam-3407	369	16	boundary	boundary	ADJ
ejpam-3407	369	17	conditions.computer	conditions.computer	NOUN
ejpam-3407	369	18	and	and	CCONJ
ejpam-3407	369	19	mathematics	mathematic	NOUN
ejpam-3407	369	20	with	with	ADP
ejpam-3407	369	21	applications	application	NOUN
ejpam-3407	369	22	,	,	PUNCT
ejpam-3407	369	23	58:1838–1843	58:1838–1843	NUM
ejpam-3407	369	24	,	,	PUNCT
ejpam-3407	369	25	2009	2009	NUM
ejpam-3407	369	26	.	.	PUNCT
ejpam-3407	370	1	[	[	X
ejpam-3407	370	2	13	13	NUM
ejpam-3407	370	3	]	]	X
ejpam-3407	370	4	g.s	g.s	PROPN
ejpam-3407	370	5	.	.	PROPN
ejpam-3407	370	6	ladde	ladde	PROPN
ejpam-3407	370	7	,	,	PUNCT
ejpam-3407	370	8	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-3407	370	9	and	and	CCONJ
ejpam-3407	370	10	a.s	a.s	PROPN
ejpam-3407	370	11	.	.	PROPN
ejpam-3407	370	12	vatsala	vatsala	PROPN
ejpam-3407	370	13	.	.	PUNCT
ejpam-3407	371	1	monotone	monotone	ADJ
ejpam-3407	371	2	iterative	iterative	NOUN
ejpam-3407	371	3	technique	technique	NOUN
ejpam-3407	371	4	for	for	ADP
ejpam-3407	371	5	nonlinear	nonlinear	ADJ
ejpam-3407	371	6	differential	differential	ADJ
ejpam-3407	371	7	equations	equation	NOUN
ejpam-3407	371	8	.	.	PUNCT
ejpam-3407	372	1	pitman	pitman	PROPN
ejpam-3407	372	2	publishing	publishing	PROPN
ejpam-3407	372	3	inc	inc	PROPN
ejpam-3407	372	4	.	.	PROPN
ejpam-3407	372	5	,	,	PUNCT
ejpam-3407	372	6	boston	boston	PROPN
ejpam-3407	372	7	,	,	PUNCT
ejpam-3407	372	8	1985	1985	NUM
ejpam-3407	372	9	.	.	PUNCT
ejpam-3407	373	1	[	[	X
ejpam-3407	373	2	14	14	NUM
ejpam-3407	373	3	]	]	PUNCT
ejpam-3407	373	4	s.	s.	PROPN
ejpam-3407	373	5	zhang	zhang	PROPN
ejpam-3407	373	6	.	.	PUNCT
ejpam-3407	374	1	monotone	monotone	ADJ
ejpam-3407	374	2	iterative	iterative	NOUN
ejpam-3407	374	3	method	method	NOUN
ejpam-3407	374	4	for	for	ADP
ejpam-3407	374	5	initial	initial	ADJ
ejpam-3407	374	6	value	value	NOUN
ejpam-3407	374	7	problem	problem	NOUN
ejpam-3407	374	8	involving	involve	VERB
ejpam-3407	374	9	riemannliouville	riemannliouville	NOUN
ejpam-3407	374	10	fractional	fractional	ADJ
ejpam-3407	374	11	derivatives	derivative	NOUN
ejpam-3407	374	12	.	.	PUNCT
ejpam-3407	375	1	nonlinear	nonlinear	ADJ
ejpam-3407	375	2	analysis	analysis	NOUN
ejpam-3407	375	3	:	:	PUNCT
ejpam-3407	375	4	theory	theory	NOUN
ejpam-3407	375	5	methods	method	NOUN
ejpam-3407	375	6	and	and	CCONJ
ejpam-3407	375	7	applications	application	NOUN
ejpam-3407	375	8	,	,	PUNCT
ejpam-3407	375	9	71(5):2087–2093	71(5):2087–2093	NUM
ejpam-3407	375	10	,	,	PUNCT
ejpam-3407	375	11	2009	2009	NUM
ejpam-3407	375	12	.	.	PUNCT
ejpam-3407	376	1	[	[	X
ejpam-3407	376	2	15	15	NUM
ejpam-3407	376	3	]	]	X
ejpam-3407	376	4	f.a	f.a	PROPN
ejpam-3407	376	5	.	.	PROPN
ejpam-3407	376	6	mcrae	mcrae	PROPN
ejpam-3407	376	7	.	.	PUNCT
ejpam-3407	377	1	monotone	monotone	ADJ
ejpam-3407	377	2	iterative	iterative	NOUN
ejpam-3407	377	3	technique	technique	NOUN
ejpam-3407	377	4	and	and	CCONJ
ejpam-3407	377	5	existence	existence	NOUN
ejpam-3407	377	6	results	result	NOUN
ejpam-3407	377	7	for	for	ADP
ejpam-3407	377	8	fractional	fractional	ADJ
ejpam-3407	377	9	differential	differential	ADJ
ejpam-3407	377	10	equations	equation	NOUN
ejpam-3407	377	11	.	.	PUNCT
ejpam-3407	378	1	nonlinear	nonlinear	ADJ
ejpam-3407	378	2	analysis	analysis	NOUN
ejpam-3407	378	3	:	:	PUNCT
ejpam-3407	378	4	theory	theory	NOUN
ejpam-3407	378	5	methods	method	NOUN
ejpam-3407	378	6	and	and	CCONJ
ejpam-3407	378	7	applications	application	NOUN
ejpam-3407	378	8	,	,	PUNCT
ejpam-3407	378	9	71(12):6093	71(12):6093	NUM
ejpam-3407	378	10	–	–	PUNCT
ejpam-3407	378	11	6096	6096	NUM
ejpam-3407	378	12	,	,	PUNCT
ejpam-3407	378	13	2009	2009	NUM
ejpam-3407	378	14	.	.	PUNCT
ejpam-3407	379	1	[	[	X
ejpam-3407	379	2	16	16	NUM
ejpam-3407	379	3	]	]	PUNCT
ejpam-3407	379	4	m.	m.	NOUN
ejpam-3407	379	5	al	al	PROPN
ejpam-3407	379	6	-	-	PUNCT
ejpam-3407	379	7	refai	refai	PROPN
ejpam-3407	379	8	,	,	PUNCT
ejpam-3407	379	9	m.	m.	PROPN
ejpam-3407	379	10	ali	ali	PROPN
ejpam-3407	379	11	hajji	hajji	PROPN
ejpam-3407	379	12	.	.	PUNCT
ejpam-3407	380	1	monotone	monotone	ADJ
ejpam-3407	380	2	iterative	iterative	NOUN
ejpam-3407	380	3	sequences	sequence	NOUN
ejpam-3407	380	4	for	for	ADP
ejpam-3407	380	5	nonlinear	nonlinear	ADJ
ejpam-3407	380	6	boundary	boundary	ADJ
ejpam-3407	380	7	value	value	NOUN
ejpam-3407	380	8	problems	problem	NOUN
ejpam-3407	380	9	of	of	ADP
ejpam-3407	380	10	fractional	fractional	ADJ
ejpam-3407	380	11	order	order	NOUN
ejpam-3407	380	12	.	.	PUNCT
ejpam-3407	381	1	nonlinear	nonlinear	ADJ
ejpam-3407	381	2	analysis	analysis	NOUN
ejpam-3407	381	3	:	:	PUNCT
ejpam-3407	381	4	theory	theory	NOUN
ejpam-3407	381	5	methods	method	NOUN
ejpam-3407	381	6	and	and	CCONJ
ejpam-3407	381	7	applications	application	NOUN
ejpam-3407	381	8	,	,	PUNCT
ejpam-3407	381	9	74(11):3531–3539	74(11):3531–3539	NOUN
ejpam-3407	381	10	,	,	PUNCT
ejpam-3407	381	11	2011	2011	NUM
ejpam-3407	381	12	.	.	PUNCT
ejpam-3407	382	1	[	[	X
ejpam-3407	382	2	17	17	NUM
ejpam-3407	382	3	]	]	X
ejpam-3407	382	4	g.	g.	PROPN
ejpam-3407	382	5	wang	wang	PROPN
ejpam-3407	382	6	,	,	PUNCT
ejpam-3407	382	7	r.p	r.p	PROPN
ejpam-3407	382	8	.	.	PROPN
ejpam-3407	382	9	agarwal	agarwal	PROPN
ejpam-3407	382	10	,	,	PUNCT
ejpam-3407	382	11	a.	a.	PROPN
ejpam-3407	382	12	cabada	cabada	PROPN
ejpam-3407	382	13	.	.	PUNCT
ejpam-3407	383	1	existence	existence	NOUN
ejpam-3407	383	2	results	result	NOUN
ejpam-3407	383	3	and	and	CCONJ
ejpam-3407	383	4	the	the	DET
ejpam-3407	383	5	monotone	monotone	ADJ
ejpam-3407	383	6	iterative	iterative	NOUN
ejpam-3407	383	7	technique	technique	NOUN
ejpam-3407	383	8	for	for	ADP
ejpam-3407	383	9	systems	system	NOUN
ejpam-3407	383	10	of	of	ADP
ejpam-3407	383	11	nonlinear	nonlinear	ADJ
ejpam-3407	383	12	fractional	fractional	ADJ
ejpam-3407	383	13	differential	differential	ADJ
ejpam-3407	383	14	equations	equation	NOUN
ejpam-3407	383	15	.	.	PUNCT
ejpam-3407	384	1	applied	apply	VERB
ejpam-3407	384	2	mathematical	mathematical	ADJ
ejpam-3407	384	3	letter	letter	NOUN
ejpam-3407	384	4	,	,	PUNCT
ejpam-3407	384	5	25(6):1019	25(6):1019	NUM
ejpam-3407	384	6	-	-	SYM
ejpam-3407	384	7	1024	1024	NUM
ejpam-3407	384	8	,	,	PUNCT
ejpam-3407	384	9	2012	2012	NUM
ejpam-3407	384	10	.	.	PUNCT
ejpam-3407	385	1	[	[	X
ejpam-3407	385	2	18	18	NUM
ejpam-3407	385	3	]	]	X
ejpam-3407	385	4	e.	e.	PROPN
ejpam-3407	385	5	zeidler	zeidler	PROPN
ejpam-3407	385	6	.	.	PUNCT
ejpam-3407	386	1	nonlinear	nonlinear	ADJ
ejpam-3407	386	2	functional	functional	ADJ
ejpam-3407	386	3	analysis	analysis	NOUN
ejpam-3407	386	4	and	and	CCONJ
ejpam-3407	386	5	its	its	PRON
ejpam-3407	386	6	applications	application	NOUN
ejpam-3407	386	7	,	,	PUNCT
ejpam-3407	386	8	part	part	PROPN
ejpam-3407	386	9	ii	ii	PROPN
ejpam-3407	386	10	/	/	SYM
ejpam-3407	386	11	b	b	PROPN
ejpam-3407	386	12	:	:	PUNCT
ejpam-3407	386	13	nonlinear	nonlinear	ADJ
ejpam-3407	386	14	monotone	monotone	ADJ
ejpam-3407	386	15	operators	operator	NOUN
ejpam-3407	386	16	.	.	PUNCT
ejpam-3407	387	1	springer	springer	PROPN
ejpam-3407	387	2	verlag	verlag	PROPN
ejpam-3407	387	3	,	,	PUNCT
ejpam-3407	387	4	new	new	PROPN
ejpam-3407	387	5	york	york	PROPN
ejpam-3407	387	6	,	,	PUNCT
ejpam-3407	387	7	1989	1989	NUM
ejpam-3407	387	8	.	.	PUNCT
ejpam-3407	388	1	[	[	X
ejpam-3407	388	2	19	19	NUM
ejpam-3407	388	3	]	]	X
ejpam-3407	388	4	n.xu	n.xu	ADJ
ejpam-3407	388	5	,	,	PUNCT
ejpam-3407	388	6	w.liu	w.liu	PROPN
ejpam-3407	388	7	.	.	PUNCT
ejpam-3407	388	8	iterative	iterative	NOUN
ejpam-3407	388	9	solutions	solution	NOUN
ejpam-3407	388	10	for	for	ADP
ejpam-3407	388	11	a	a	DET
ejpam-3407	388	12	coupled	couple	VERB
ejpam-3407	388	13	system	system	NOUN
ejpam-3407	388	14	of	of	ADP
ejpam-3407	388	15	fractional	fractional	ADJ
ejpam-3407	388	16	differential	differential	ADJ
ejpam-3407	388	17	-	-	PUNCT
ejpam-3407	388	18	integral	integral	ADJ
ejpam-3407	388	19	equations	equation	NOUN
ejpam-3407	388	20	with	with	ADP
ejpam-3407	388	21	twopoint	twopoint	NOUN
ejpam-3407	388	22	boundary	boundary	ADJ
ejpam-3407	388	23	conditions.applied	conditions.applied	ADJ
ejpam-3407	388	24	mathematics	mathematic	NOUN
ejpam-3407	388	25	and	and	CCONJ
ejpam-3407	388	26	computation	computation	NOUN
ejpam-3407	388	27	,	,	PUNCT
ejpam-3407	388	28	244:903–911	244:903–911	NUM
ejpam-3407	388	29	,	,	PUNCT
ejpam-3407	388	30	2014	2014	NUM
ejpam-3407	388	31	.	.	PUNCT
ejpam-3407	389	1	[	[	X
ejpam-3407	389	2	20	20	NUM
ejpam-3407	389	3	]	]	PUNCT
ejpam-3407	389	4	x.	x.	NOUN
ejpam-3407	389	5	liu	liu	PROPN
ejpam-3407	389	6	,	,	PUNCT
ejpam-3407	389	7	m.	m.	PROPN
ejpam-3407	389	8	jia	jia	PROPN
ejpam-3407	389	9	.	.	PUNCT
ejpam-3407	389	10	multiple	multiple	ADJ
ejpam-3407	389	11	solutions	solution	NOUN
ejpam-3407	389	12	for	for	ADP
ejpam-3407	389	13	fractional	fractional	ADJ
ejpam-3407	389	14	differential	differential	ADJ
ejpam-3407	389	15	equations	equation	NOUN
ejpam-3407	389	16	with	with	ADP
ejpam-3407	389	17	nonlinear	nonlinear	ADJ
ejpam-3407	389	18	boundary	boundary	ADJ
ejpam-3407	389	19	conditions	condition	NOUN
ejpam-3407	389	20	.	.	PUNCT
ejpam-3407	390	1	computer	computer	NOUN
ejpam-3407	390	2	and	and	CCONJ
ejpam-3407	390	3	mathematics	mathematic	NOUN
ejpam-3407	390	4	with	with	ADP
ejpam-3407	390	5	applications	application	NOUN
ejpam-3407	390	6	,	,	PUNCT
ejpam-3407	390	7	59:2880–2886	59:2880–2886	NUM
ejpam-3407	390	8	,	,	PUNCT
ejpam-3407	390	9	2010	2010	NUM
ejpam-3407	390	10	.	.	PUNCT
ejpam-3407	391	1	[	[	X
ejpam-3407	391	2	21	21	NUM
ejpam-3407	391	3	]	]	PUNCT
ejpam-3407	391	4	z.	z.	PROPN
ejpam-3407	392	1	he	he	PRON
ejpam-3407	392	2	,	,	PUNCT
ejpam-3407	392	3	x.	x.	NOUN
ejpam-3407	392	4	he	he	PRON
ejpam-3407	392	5	.	.	PUNCT
ejpam-3407	393	1	monotone	monotone	ADJ
ejpam-3407	393	2	iterative	iterative	NOUN
ejpam-3407	393	3	technique	technique	NOUN
ejpam-3407	393	4	for	for	ADP
ejpam-3407	393	5	impulsive	impulsive	ADJ
ejpam-3407	393	6	integro	integro	ADJ
ejpam-3407	393	7	-	-	PUNCT
ejpam-3407	393	8	differential	differential	NOUN
ejpam-3407	393	9	equations	equation	NOUN
ejpam-3407	393	10	with	with	ADP
ejpam-3407	393	11	periodic	periodic	ADJ
ejpam-3407	393	12	boundary	boundary	ADJ
ejpam-3407	393	13	conditions.computer	conditions.computer	NOUN
ejpam-3407	393	14	and	and	CCONJ
ejpam-3407	393	15	mathematics	mathematic	NOUN
ejpam-3407	393	16	with	with	ADP
ejpam-3407	393	17	applications	application	NOUN
ejpam-3407	393	18	,	,	PUNCT
ejpam-3407	393	19	48:73–84	48:73–84	NOUN
ejpam-3407	393	20	,	,	PUNCT
ejpam-3407	393	21	2004	2004	NUM
ejpam-3407	393	22	.	.	PUNCT
ejpam-3407	394	1	[	[	X
ejpam-3407	394	2	22	22	NUM
ejpam-3407	394	3	]	]	X
ejpam-3407	394	4	c.	c.	PROPN
ejpam-3407	394	5	de	de	PROPN
ejpam-3407	394	6	coster	coster	PROPN
ejpam-3407	394	7	,	,	PUNCT
ejpam-3407	394	8	p.	p.	NOUN
ejpam-3407	394	9	habets	habet	NOUN
ejpam-3407	394	10	.	.	PUNCT
ejpam-3407	395	1	two	two	NUM
ejpam-3407	395	2	-	-	PUNCT
ejpam-3407	395	3	point	point	NOUN
ejpam-3407	395	4	boundary	boundary	ADJ
ejpam-3407	395	5	value	value	NOUN
ejpam-3407	395	6	problems	problem	NOUN
ejpam-3407	395	7	:	:	PUNCT
ejpam-3407	395	8	lower	low	ADJ
ejpam-3407	395	9	and	and	CCONJ
ejpam-3407	395	10	upper	upper	ADJ
ejpam-3407	395	11	solutions	solution	NOUN
ejpam-3407	395	12	.	.	PUNCT
ejpam-3407	396	1	elsevier	elsevier	NOUN
ejpam-3407	396	2	,	,	PUNCT
ejpam-3407	396	3	amsterdam	amsterdam	PROPN
ejpam-3407	396	4	,	,	PUNCT
ejpam-3407	396	5	2006	2006	NUM
ejpam-3407	396	6	.	.	PUNCT
ejpam-3407	397	1	[	[	X
ejpam-3407	397	2	23	23	NUM
ejpam-3407	397	3	]	]	X
ejpam-3407	397	4	f.	f.	PROPN
ejpam-3407	397	5	li	li	PROPN
ejpam-3407	397	6	,	,	PUNCT
ejpam-3407	397	7	m.	m.	PROPN
ejpam-3407	397	8	jia	jia	PROPN
ejpam-3407	397	9	,	,	PUNCT
ejpam-3407	397	10	x.	x.	PROPN
ejpam-3407	397	11	liu	liu	PROPN
ejpam-3407	397	12	,	,	PUNCT
ejpam-3407	397	13	c.	c.	PROPN
ejpam-3407	397	14	li	li	PROPN
ejpam-3407	397	15	,	,	PUNCT
ejpam-3407	397	16	g.	g.	PROPN
ejpam-3407	397	17	li	li	PROPN
ejpam-3407	397	18	.	.	PROPN
ejpam-3407	397	19	existence	existence	NOUN
ejpam-3407	397	20	and	and	CCONJ
ejpam-3407	397	21	uniqueness	uniqueness	NOUN
ejpam-3407	397	22	of	of	ADP
ejpam-3407	397	23	solutions	solution	NOUN
ejpam-3407	397	24	of	of	ADP
ejpam-3407	397	25	secendorder	secendorder	NOUN
ejpam-3407	397	26	three	three	NUM
ejpam-3407	397	27	-	-	PUNCT
ejpam-3407	397	28	point	point	NOUN
ejpam-3407	397	29	boundary	boundary	ADJ
ejpam-3407	397	30	value	value	NOUN
ejpam-3407	397	31	problems	problem	NOUN
ejpam-3407	397	32	with	with	ADP
ejpam-3407	397	33	upper	upper	ADJ
ejpam-3407	397	34	and	and	CCONJ
ejpam-3407	397	35	lower	low	ADJ
ejpam-3407	397	36	solutions	solution	NOUN
ejpam-3407	397	37	in	in	ADP
ejpam-3407	397	38	the	the	DET
ejpam-3407	397	39	references	reference	NOUN
ejpam-3407	397	40	447	447	NUM
ejpam-3407	397	41	reverse	reverse	ADJ
ejpam-3407	397	42	order.nonlinear	order.nonlinear	NOUN
ejpam-3407	397	43	analysis	analysis	NOUN
ejpam-3407	397	44	:	:	PUNCT
ejpam-3407	397	45	theory	theory	NOUN
ejpam-3407	397	46	methods	method	NOUN
ejpam-3407	397	47	and	and	CCONJ
ejpam-3407	397	48	applications	application	NOUN
ejpam-3407	397	49	,	,	PUNCT
ejpam-3407	397	50	68:2381–2388	68:2381–2388	NUM
ejpam-3407	397	51	,	,	PUNCT
ejpam-3407	397	52	2008	2008	NUM
ejpam-3407	397	53	.	.	PUNCT
ejpam-3407	398	1	[	[	X
ejpam-3407	398	2	24	24	NUM
ejpam-3407	398	3	]	]	X
ejpam-3407	398	4	f.	f.	PROPN
ejpam-3407	398	5	li	li	PROPN
ejpam-3407	398	6	,	,	PUNCT
ejpam-3407	398	7	j.	j.	PROPN
ejpam-3407	398	8	sun	sun	PROPN
ejpam-3407	398	9	,	,	PUNCT
ejpam-3407	398	10	m.	m.	PROPN
ejpam-3407	398	11	jia	jia	PROPN
ejpam-3407	398	12	.	.	PUNCT
ejpam-3407	399	1	monotone	monotone	ADJ
ejpam-3407	399	2	iterative	iterative	NOUN
ejpam-3407	399	3	method	method	NOUN
ejpam-3407	399	4	for	for	ADP
ejpam-3407	399	5	the	the	DET
ejpam-3407	399	6	second	second	ADJ
ejpam-3407	399	7	-	-	PUNCT
ejpam-3407	399	8	order	order	NOUN
ejpam-3407	399	9	threepoint	threepoint	NOUN
ejpam-3407	399	10	boundary	boundary	ADJ
ejpam-3407	399	11	value	value	NOUN
ejpam-3407	399	12	problem	problem	NOUN
ejpam-3407	399	13	with	with	ADP
ejpam-3407	399	14	upper	upper	ADJ
ejpam-3407	399	15	and	and	CCONJ
ejpam-3407	399	16	lower	low	ADJ
ejpam-3407	399	17	solutions	solution	NOUN
ejpam-3407	399	18	in	in	ADP
ejpam-3407	399	19	the	the	DET
ejpam-3407	399	20	reversed	reverse	VERB
ejpam-3407	399	21	order.computer	order.computer	NOUN
ejpam-3407	399	22	and	and	CCONJ
ejpam-3407	399	23	mathematics	mathematic	NOUN
ejpam-3407	399	24	with	with	ADP
ejpam-3407	399	25	applications	application	NOUN
ejpam-3407	399	26	,	,	PUNCT
ejpam-3407	399	27	217:4840–4847	217:4840–4847	NOUN
ejpam-3407	399	28	,	,	PUNCT
ejpam-3407	399	29	2011	2011	NUM
ejpam-3407	399	30	.	.	PUNCT
ejpam-3407	400	1	[	[	X
ejpam-3407	400	2	25	25	NUM
ejpam-3407	400	3	]	]	X
ejpam-3407	400	4	r.	r.	PROPN
ejpam-3407	400	5	a.	a.	PROPN
ejpam-3407	400	6	khan	khan	PROPN
ejpam-3407	400	7	.	.	PUNCT
ejpam-3407	401	1	existence	existence	NOUN
ejpam-3407	401	2	and	and	CCONJ
ejpam-3407	401	3	approximation	approximation	NOUN
ejpam-3407	401	4	of	of	ADP
ejpam-3407	401	5	solutions	solution	NOUN
ejpam-3407	401	6	to	to	ADP
ejpam-3407	401	7	three	three	NUM
ejpam-3407	401	8	-	-	PUNCT
ejpam-3407	401	9	point	point	NOUN
ejpam-3407	401	10	boundary	boundary	ADJ
ejpam-3407	401	11	value	value	NOUN
ejpam-3407	401	12	problems	problem	NOUN
ejpam-3407	401	13	for	for	ADP
ejpam-3407	401	14	fractional	fractional	ADJ
ejpam-3407	401	15	differential	differential	ADJ
ejpam-3407	401	16	equations	equation	NOUN
ejpam-3407	401	17	.	.	PUNCT
ejpam-3407	402	1	electronic	electronic	ADJ
ejpam-3407	402	2	journal	journal	NOUN
ejpam-3407	402	3	of	of	ADP
ejpam-3407	402	4	qualitative	qualitative	ADJ
ejpam-3407	402	5	theory	theory	NOUN
ejpam-3407	402	6	of	of	ADP
ejpam-3407	402	7	differential	differential	ADJ
ejpam-3407	402	8	equations	equation	NOUN
ejpam-3407	402	9	,	,	PUNCT
ejpam-3407	402	10	58:1–8	58:1–8	NUM
ejpam-3407	402	11	,	,	PUNCT
ejpam-3407	402	12	2011	2011	NUM
ejpam-3407	402	13	.	.	PUNCT
ejpam-3407	403	1	[	[	X
ejpam-3407	403	2	26	26	NUM
ejpam-3407	403	3	]	]	X
ejpam-3407	403	4	kamal	kamal	PROPN
ejpam-3407	403	5	shah	shah	PROPN
ejpam-3407	403	6	and	and	CCONJ
ejpam-3407	403	7	rahmat	rahmat	PROPN
ejpam-3407	403	8	ali	ali	PROPN
ejpam-3407	403	9	khan	khan	PROPN
ejpam-3407	403	10	.	.	PUNCT
ejpam-3407	404	1	iterative	iterative	NOUN
ejpam-3407	404	2	scheme	scheme	NOUN
ejpam-3407	404	3	for	for	ADP
ejpam-3407	404	4	a	a	DET
ejpam-3407	404	5	coupled	couple	VERB
ejpam-3407	404	6	system	system	NOUN
ejpam-3407	404	7	of	of	ADP
ejpam-3407	404	8	fractional	fractional	ADJ
ejpam-3407	404	9	-	-	PUNCT
ejpam-3407	404	10	order	order	NOUN
ejpam-3407	404	11	differential	differential	ADJ
ejpam-3407	404	12	equations	equation	NOUN
ejpam-3407	404	13	with	with	ADP
ejpam-3407	404	14	three	three	NUM
ejpam-3407	404	15	-	-	PUNCT
ejpam-3407	404	16	point	point	NOUN
ejpam-3407	404	17	boundary	boundary	ADJ
ejpam-3407	404	18	conditions.mathematical	conditions.mathematical	ADJ
ejpam-3407	404	19	methods	method	NOUN
ejpam-3407	404	20	in	in	ADP
ejpam-3407	404	21	the	the	DET
ejpam-3407	404	22	applied	apply	VERB
ejpam-3407	404	23	sciences	science	NOUN
ejpam-3407	404	24	,	,	PUNCT
ejpam-3407	404	25	2016:7	2016:7	NUM
ejpam-3407	404	26	pages	page	NOUN
ejpam-3407	404	27	,	,	PUNCT
ejpam-3407	404	28	2016	2016	NUM
ejpam-3407	404	29	.	.	PUNCT
ejpam-3407	405	1	[	[	X
ejpam-3407	405	2	27	27	NUM
ejpam-3407	405	3	]	]	X
ejpam-3407	405	4	i.	i.	PROPN
ejpam-3407	405	5	a.	a.	PROPN
ejpam-3407	405	6	rus	rus	PROPN
ejpam-3407	405	7	.	.	PUNCT
ejpam-3407	406	1	ulam	ulam	PROPN
ejpam-3407	406	2	stabilities	stability	NOUN
ejpam-3407	406	3	of	of	ADP
ejpam-3407	406	4	ordinary	ordinary	ADJ
ejpam-3407	406	5	differential	differential	ADJ
ejpam-3407	406	6	equations	equation	NOUN
ejpam-3407	406	7	in	in	ADP
ejpam-3407	406	8	a	a	DET
ejpam-3407	406	9	banach	banach	NOUN
ejpam-3407	406	10	space	space	NOUN
ejpam-3407	406	11	.	.	PUNCT
ejpam-3407	407	1	carpathian	carpathian	PROPN
ejpam-3407	407	2	j.	j.	PROPN
ejpam-3407	407	3	math	math	PROPN
ejpam-3407	407	4	.	.	PROPN
ejpam-3407	407	5	,	,	PUNCT
ejpam-3407	407	6	26:103–107	26:103–107	PROPN
ejpam-3407	407	7	,	,	PUNCT
ejpam-3407	407	8	2010	2010	NUM
ejpam-3407	407	9	.	.	PUNCT
ejpam-3407	408	1	[	[	X
ejpam-3407	408	2	28	28	NUM
ejpam-3407	408	3	]	]	X
ejpam-3407	408	4	t.	t.	PROPN
ejpam-3407	408	5	m.	m.	NOUN
ejpam-3407	408	6	rassias	rassias	PROPN
ejpam-3407	408	7	.	.	PUNCT
ejpam-3407	409	1	on	on	ADP
ejpam-3407	409	2	the	the	DET
ejpam-3407	409	3	stability	stability	NOUN
ejpam-3407	409	4	of	of	ADP
ejpam-3407	409	5	the	the	DET
ejpam-3407	409	6	linear	linear	ADJ
ejpam-3407	409	7	mapping	mapping	NOUN
ejpam-3407	409	8	in	in	ADP
ejpam-3407	409	9	banach	banach	NOUN
ejpam-3407	409	10	spaces	space	NOUN
ejpam-3407	409	11	.	.	PUNCT
ejpam-3407	410	1	proc	proc	NOUN
ejpam-3407	410	2	.	.	PUNCT
ejpam-3407	411	1	amer	amer	PROPN
ejpam-3407	411	2	.	.	PUNCT
ejpam-3407	411	3	math	math	PROPN
ejpam-3407	411	4	.	.	PUNCT
ejpam-3407	412	1	soc	soc	PROPN
ejpam-3407	412	2	.	.	PUNCT
ejpam-3407	412	3	,	,	PUNCT
ejpam-3407	412	4	72:297–300	72:297–300	PROPN
ejpam-3407	412	5	,	,	PUNCT
ejpam-3407	412	6	1978	1978	NUM
ejpam-3407	412	7	.	.	PUNCT
ejpam-3407	413	1	[	[	X
ejpam-3407	413	2	29	29	NUM
ejpam-3407	413	3	]	]	X
ejpam-3407	413	4	t.	t.	PROPN
ejpam-3407	413	5	m.	m.	NOUN
ejpam-3407	413	6	rassias	rassias	PROPN
ejpam-3407	413	7	.	.	PUNCT
ejpam-3407	414	1	on	on	ADP
ejpam-3407	414	2	the	the	DET
ejpam-3407	414	3	stability	stability	NOUN
ejpam-3407	414	4	of	of	ADP
ejpam-3407	414	5	functional	functional	ADJ
ejpam-3407	414	6	equations	equation	NOUN
ejpam-3407	414	7	and	and	CCONJ
ejpam-3407	414	8	a	a	DET
ejpam-3407	414	9	problem	problem	NOUN
ejpam-3407	414	10	of	of	ADP
ejpam-3407	414	11	ulam	ulam	PROPN
ejpam-3407	414	12	.	.	PUNCT
ejpam-3407	415	1	acta	acta	PROPN
ejpam-3407	415	2	.	.	PUNCT
ejpam-3407	416	1	appl	appl	PROPN
ejpam-3407	416	2	.	.	PROPN
ejpam-3407	416	3	math	math	PROPN
ejpam-3407	416	4	.	.	PUNCT
ejpam-3407	416	5	,	,	PUNCT
ejpam-3407	416	6	26:23–130	26:23–130	NUM
ejpam-3407	416	7	,	,	PUNCT
ejpam-3407	416	8	2000	2000	NUM
ejpam-3407	416	9	.	.	PUNCT
ejpam-3407	417	1	[	[	X
ejpam-3407	417	2	30	30	NUM
ejpam-3407	417	3	]	]	X
ejpam-3407	417	4	m.	m.	NOUN
ejpam-3407	417	5	li	li	PROPN
ejpam-3407	417	6	,	,	PUNCT
ejpam-3407	417	7	j.	j.	PROPN
ejpam-3407	417	8	wang	wang	PROPN
ejpam-3407	417	9	,	,	PUNCT
ejpam-3407	417	10	d.	d.	PROPN
ejpam-3407	417	11	o’regan	o’regan	PROPN
ejpam-3407	417	12	.	.	PUNCT
ejpam-3407	418	1	existence	existence	PROPN
ejpam-3407	418	2	and	and	CCONJ
ejpam-3407	418	3	ulam	ulam	PROPN
ejpam-3407	418	4	’s	’s	PART
ejpam-3407	418	5	stability	stability	NOUN
ejpam-3407	418	6	for	for	ADP
ejpam-3407	418	7	conformable	conformable	ADJ
ejpam-3407	418	8	fractional	fractional	ADJ
ejpam-3407	418	9	differential	differential	ADJ
ejpam-3407	418	10	equations	equation	NOUN
ejpam-3407	418	11	with	with	ADP
ejpam-3407	418	12	constant	constant	ADJ
ejpam-3407	418	13	coefficients	coefficient	NOUN
ejpam-3407	418	14	.	.	PUNCT
ejpam-3407	419	1	bull	bull	NOUN
ejpam-3407	419	2	.	.	PUNCT
ejpam-3407	420	1	malays	malays	PROPN
ejpam-3407	420	2	.	.	PUNCT
ejpam-3407	421	1	math	math	NOUN
ejpam-3407	421	2	.	.	PUNCT
ejpam-3407	422	1	sci	sci	PROPN
ejpam-3407	422	2	.	.	PROPN
ejpam-3407	422	3	soc	soc	PROPN
ejpam-3407	422	4	.	.	PUNCT
ejpam-3407	423	1	2017	2017	NUM
ejpam-3407	423	2	;	;	PUNCT
ejpam-3407	423	3	doi:10.1007	doi:10.1007	X
ejpam-3407	423	4	/	/	SYM
ejpam-3407	423	5	s40840	s40840	PROPN
ejpam-3407	423	6	-	-	PUNCT
ejpam-3407	423	7	017	017	NUM
ejpam-3407	423	8	-	-	PUNCT
ejpam-3407	423	9	0576	0576	NUM
ejpam-3407	423	10	-	-	SYM
ejpam-3407	423	11	7	7	NUM
ejpam-3407	423	12	.	.	PUNCT
ejpam-3407	424	1	[	[	X
ejpam-3407	424	2	31	31	NUM
ejpam-3407	424	3	]	]	PUNCT
ejpam-3407	424	4	j.	j.	PROPN
ejpam-3407	424	5	wang	wang	PROPN
ejpam-3407	424	6	,	,	PUNCT
ejpam-3407	424	7	m.	m.	NOUN
ejpam-3407	424	8	fečkan	fečkan	PROPN
ejpam-3407	424	9	,	,	PUNCT
ejpam-3407	424	10	y.	y.	PROPN
ejpam-3407	424	11	zhou	zhou	PROPN
ejpam-3407	424	12	.	.	PUNCT
ejpam-3407	425	1	fractional	fractional	ADJ
ejpam-3407	425	2	order	order	NOUN
ejpam-3407	425	3	differential	differential	NOUN
ejpam-3407	425	4	switched	switch	VERB
ejpam-3407	425	5	systems	system	NOUN
ejpam-3407	425	6	with	with	ADP
ejpam-3407	425	7	coupled	couple	VERB
ejpam-3407	425	8	nonlocal	nonlocal	ADJ
ejpam-3407	425	9	initial	initial	ADJ
ejpam-3407	425	10	and	and	CCONJ
ejpam-3407	425	11	impulsive	impulsive	ADJ
ejpam-3407	425	12	conditions	condition	NOUN
ejpam-3407	425	13	.	.	PUNCT
ejpam-3407	426	1	bull	bull	NOUN
ejpam-3407	426	2	.	.	PUNCT
ejpam-3407	427	1	sci	sci	PROPN
ejpam-3407	427	2	.	.	PUNCT
ejpam-3407	427	3	math	math	PROPN
ejpam-3407	427	4	.	.	PUNCT
ejpam-3407	427	5	,	,	PUNCT
ejpam-3407	427	6	141:727–746	141:727–746	NUM
ejpam-3407	427	7	,	,	PUNCT
ejpam-3407	427	8	2017	2017	NUM
ejpam-3407	427	9	.	.	PUNCT
ejpam-3407	428	1	[	[	X
ejpam-3407	428	2	32	32	NUM
ejpam-3407	428	3	]	]	PUNCT
ejpam-3407	428	4	alberto	alberto	PROPN
ejpam-3407	428	5	cabada1	cabada1	PROPN
ejpam-3407	428	6	and	and	CCONJ
ejpam-3407	428	7	guotao	guotao	PROPN
ejpam-3407	428	8	wang	wang	PROPN
ejpam-3407	428	9	.	.	PUNCT
ejpam-3407	429	1	positive	positive	ADJ
ejpam-3407	429	2	solutions	solution	NOUN
ejpam-3407	429	3	of	of	ADP
ejpam-3407	429	4	nonlinear	nonlinear	ADJ
ejpam-3407	429	5	fractional	fractional	ADJ
ejpam-3407	429	6	differential	differential	ADJ
ejpam-3407	429	7	equations	equation	NOUN
ejpam-3407	429	8	with	with	ADP
ejpam-3407	429	9	integral	integral	ADJ
ejpam-3407	429	10	boundary	boundary	ADJ
ejpam-3407	429	11	value	value	NOUN
ejpam-3407	429	12	conditions.journal	conditions.journal	PROPN
ejpam-3407	429	13	of	of	ADP
ejpam-3407	429	14	mathematical	mathematical	ADJ
ejpam-3407	429	15	analysis	analysis	NOUN
ejpam-3407	429	16	and	and	CCONJ
ejpam-3407	429	17	applications	application	NOUN
ejpam-3407	429	18	,	,	PUNCT
ejpam-3407	429	19	389(1):403–411	389(1):403–411	NUM
ejpam-3407	429	20	,	,	PUNCT
ejpam-3407	429	21	2013	2013	NUM
ejpam-3407	429	22	.	.	PUNCT
ejpam-3407	430	1	[	[	X
ejpam-3407	430	2	33	33	NUM
ejpam-3407	430	3	]	]	X
ejpam-3407	430	4	sajjad	sajjad	PROPN
ejpam-3407	430	5	ali	ali	PROPN
ejpam-3407	430	6	.	.	PROPN
ejpam-3407	431	1	kamal	kamal	PROPN
ejpam-3407	431	2	shah	shah	PROPN
ejpam-3407	431	3	and	and	CCONJ
ejpam-3407	431	4	fahd	fahd	PROPN
ejpam-3407	431	5	jarad	jarad	PROPN
ejpam-3407	431	6	.	.	PUNCT
ejpam-3407	432	1	on	on	ADP
ejpam-3407	432	2	stable	stable	ADJ
ejpam-3407	432	3	iterative	iterative	NOUN
ejpam-3407	432	4	solutions	solution	NOUN
ejpam-3407	432	5	for	for	ADP
ejpam-3407	432	6	a	a	DET
ejpam-3407	432	7	class	class	NOUN
ejpam-3407	432	8	of	of	ADP
ejpam-3407	432	9	boundary	boundary	ADJ
ejpam-3407	432	10	value	value	NOUN
ejpam-3407	432	11	problem	problem	NOUN
ejpam-3407	432	12	of	of	ADP
ejpam-3407	432	13	nonlinear	nonlinear	ADJ
ejpam-3407	432	14	fractional	fractional	ADJ
ejpam-3407	432	15	order	order	NOUN
ejpam-3407	432	16	differential	differential	VERB
ejpam-3407	432	17	equations.math	equations.math	PROPN
ejpam-3407	432	18	meth	meth	PROPN
ejpam-3407	432	19	appl	appl	PROPN
ejpam-3407	432	20	sci	sci	PROPN
ejpam-3407	432	21	.	.	PROPN
ejpam-3407	432	22	2018:1–13	2018:1–13	NUM
ejpam-3407	432	23	,	,	PUNCT
ejpam-3407	432	24	2018	2018	NUM
ejpam-3407	432	25	.	.	PUNCT
ejpam-3407	433	1	[	[	X
ejpam-3407	433	2	34	34	NUM
ejpam-3407	433	3	]	]	SYM
ejpam-3407	433	4	th	th	X
ejpam-3407	433	5	.	.	PUNCT
ejpam-3407	433	6	m.	m.	NOUN
ejpam-3407	433	7	rassias	rassias	PROPN
ejpam-3407	433	8	and	and	CCONJ
ejpam-3407	433	9	j.	j.	PROPN
ejpam-3407	433	10	brzdek	brzdek	PROPN
ejpam-3407	433	11	.	.	PUNCT
ejpam-3407	434	1	functional	functional	ADJ
ejpam-3407	434	2	equations	equation	NOUN
ejpam-3407	434	3	in	in	ADP
ejpam-3407	434	4	mathematical	mathematical	ADJ
ejpam-3407	434	5	analysis	analysis	NOUN
ejpam-3407	434	6	-in	-in	ADP
ejpam-3407	434	7	honor	honor	NOUN
ejpam-3407	434	8	of	of	ADP
ejpam-3407	434	9	s.	s.	PROPN
ejpam-3407	434	10	m.	m.	PROPN
ejpam-3407	434	11	ulam	ulam	PROPN
ejpam-3407	434	12	.	.	PROPN
ejpam-3407	434	13	springer	springer	PROPN
ejpam-3407	434	14	,	,	PUNCT
ejpam-3407	434	15	new	new	PROPN
ejpam-3407	434	16	york	york	PROPN
ejpam-3407	434	17	,	,	PUNCT
ejpam-3407	434	18	2012	2012	NUM
ejpam-3407	434	19	.	.	PUNCT
ejpam-3407	435	1	[	[	X
ejpam-3407	435	2	35	35	NUM
ejpam-3407	435	3	]	]	SYM
ejpam-3407	435	4	pl	pl	PROPN
ejpam-3407	435	5	.	.	PROPN
ejpam-3407	435	6	kannappan	kannappan	PROPN
ejpam-3407	435	7	.	.	PUNCT
ejpam-3407	436	1	functional	functional	ADJ
ejpam-3407	436	2	equations	equation	NOUN
ejpam-3407	436	3	and	and	CCONJ
ejpam-3407	436	4	inequalities	inequality	NOUN
ejpam-3407	436	5	with	with	ADP
ejpam-3407	436	6	applications	application	NOUN
ejpam-3407	436	7	.	.	PUNCT
ejpam-3407	436	8	springer	springer	NOUN
ejpam-3407	436	9	,	,	PUNCT
ejpam-3407	436	10	2009	2009	NUM
ejpam-3407	436	11	.	.	PUNCT
ejpam-3407	437	1	[	[	X
ejpam-3407	437	2	36	36	NUM
ejpam-3407	437	3	]	]	X
ejpam-3407	437	4	michael	michael	PROPN
ejpam-3407	437	5	th	th	PROPN
ejpam-3407	437	6	.	.	PUNCT
ejpam-3407	437	7	rassias	rassias	PROPN
ejpam-3407	437	8	.	.	PUNCT
ejpam-3407	438	1	solution	solution	NOUN
ejpam-3407	438	2	of	of	ADP
ejpam-3407	438	3	a	a	DET
ejpam-3407	438	4	functional	functional	ADJ
ejpam-3407	438	5	equation	equation	NOUN
ejpam-3407	438	6	problem	problem	NOUN
ejpam-3407	438	7	of	of	ADP
ejpam-3407	438	8	steven	steven	PROPN
ejpam-3407	438	9	butler.octogon	butler.octogon	PROPN
ejpam-3407	438	10	math	math	NOUN
ejpam-3407	438	11	.	.	PUNCT
ejpam-3407	439	1	mag	mag	INTJ
ejpam-3407	439	2	.	.	PROPN
ejpam-3407	439	3	,	,	PUNCT
ejpam-3407	439	4	12	12	NUM
ejpam-3407	439	5	:	:	SYM
ejpam-3407	439	6	152	152	NUM
ejpam-3407	439	7	–	–	SYM
ejpam-3407	439	8	153	153	NUM
ejpam-3407	439	9	,	,	PUNCT
ejpam-3407	439	10	2004	2004	NUM
ejpam-3407	439	11	.	.	PUNCT