id	sid	tid	token	lemma	pos
ejpam-3756	1	1	european	european	PROPN
ejpam-3756	1	2	journal	journal	PROPN
ejpam-3756	1	3	of	of	ADP
ejpam-3756	1	4	pure	pure	ADJ
ejpam-3756	1	5	and	and	CCONJ
ejpam-3756	1	6	applied	apply	VERB
ejpam-3756	1	7	mathematics	mathematic	NOUN
ejpam-3756	1	8	vol	vol	NOUN
ejpam-3756	1	9	.	.	PROPN
ejpam-3756	2	1	13	13	NUM
ejpam-3756	2	2	,	,	PUNCT
ejpam-3756	2	3	no	no	INTJ
ejpam-3756	2	4	.	.	NOUN
ejpam-3756	2	5	5	5	NUM
ejpam-3756	2	6	,	,	PUNCT
ejpam-3756	2	7	2020	2020	NUM
ejpam-3756	2	8	,	,	PUNCT
ejpam-3756	2	9	1110	1110	NUM
ejpam-3756	2	10	-	-	SYM
ejpam-3756	2	11	1130	1130	NUM
ejpam-3756	2	12	issn	issn	PROPN
ejpam-3756	2	13	1307	1307	NUM
ejpam-3756	2	14	-	-	SYM
ejpam-3756	2	15	5543	5543	NUM
ejpam-3756	2	16	–	–	PUNCT
ejpam-3756	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3756	2	18	published	publish	VERB
ejpam-3756	2	19	by	by	ADP
ejpam-3756	2	20	new	new	PROPN
ejpam-3756	2	21	york	york	PROPN
ejpam-3756	2	22	business	business	PROPN
ejpam-3756	2	23	global	global	ADJ
ejpam-3756	2	24	special	special	ADJ
ejpam-3756	2	25	issue	issue	NOUN
ejpam-3756	2	26	dedicated	dedicate	VERB
ejpam-3756	2	27	to	to	ADP
ejpam-3756	2	28	professor	professor	NOUN
ejpam-3756	2	29	hari	hari	PROPN
ejpam-3756	2	30	m.	m.	PROPN
ejpam-3756	2	31	srivastava	srivastava	PROPN
ejpam-3756	2	32	on	on	ADP
ejpam-3756	2	33	the	the	DET
ejpam-3756	2	34	occasion	occasion	NOUN
ejpam-3756	2	35	of	of	ADP
ejpam-3756	2	36	his	his	PRON
ejpam-3756	2	37	80th	80th	ADJ
ejpam-3756	2	38	birthday	birthday	NOUN
ejpam-3756	2	39	solution	solution	NOUN
ejpam-3756	2	40	of	of	ADP
ejpam-3756	2	41	delay	delay	NOUN
ejpam-3756	2	42	differential	differential	ADJ
ejpam-3756	2	43	equation	equation	NOUN
ejpam-3756	2	44	via	via	ADP
ejpam-3756	2	45	n	n	PROPN
ejpam-3756	2	46	v	v	NUM
ejpam-3756	2	47	1	1	NUM
ejpam-3756	2	48	iteration	iteration	NOUN
ejpam-3756	2	49	algorithm	algorithm	NOUN
ejpam-3756	2	50	nisha	nisha	PROPN
ejpam-3756	2	51	sharma1	sharma1	PROPN
ejpam-3756	2	52	,	,	PUNCT
ejpam-3756	2	53	lakshmi	lakshmi	PROPN
ejpam-3756	2	54	narayan	narayan	PROPN
ejpam-3756	2	55	mishra2,∗	mishra2,∗	PROPN
ejpam-3756	2	56	,	,	PUNCT
ejpam-3756	2	57	vishnu	vishnu	PROPN
ejpam-3756	2	58	narayan	narayan	PROPN
ejpam-3756	2	59	mishra3	mishra3	PROPN
ejpam-3756	2	60	,	,	PUNCT
ejpam-3756	2	61	shikha	shikha	PROPN
ejpam-3756	2	62	pandey4	pandey4	PROPN
ejpam-3756	2	63	1	1	NUM
ejpam-3756	2	64	department	department	NOUN
ejpam-3756	2	65	of	of	ADP
ejpam-3756	2	66	mathematics	mathematic	NOUN
ejpam-3756	2	67	,	,	PUNCT
ejpam-3756	2	68	assistant	assistant	NOUN
ejpam-3756	2	69	professor	professor	NOUN
ejpam-3756	2	70	,	,	PUNCT
ejpam-3756	2	71	pt	pt	PROPN
ejpam-3756	2	72	.	.	PROPN
ejpam-3756	2	73	j.l.n	j.l.n	PROPN
ejpam-3756	2	74	.	.	PUNCT
ejpam-3756	3	1	govt	govt	PROPN
ejpam-3756	3	2	.	.	PUNCT
ejpam-3756	4	1	college	college	PROPN
ejpam-3756	4	2	,	,	PUNCT
ejpam-3756	4	3	faridabad	faridabad	PROPN
ejpam-3756	4	4	,	,	PUNCT
ejpam-3756	4	5	haryana	haryana	PROPN
ejpam-3756	4	6	121	121	NUM
ejpam-3756	4	7	002	002	NUM
ejpam-3756	4	8	,	,	PUNCT
ejpam-3756	4	9	india	india	PROPN
ejpam-3756	4	10	2	2	NUM
ejpam-3756	4	11	department	department	NOUN
ejpam-3756	4	12	of	of	ADP
ejpam-3756	4	13	mathematics	mathematic	NOUN
ejpam-3756	4	14	,	,	PUNCT
ejpam-3756	4	15	school	school	NOUN
ejpam-3756	4	16	of	of	ADP
ejpam-3756	4	17	advanced	advanced	ADJ
ejpam-3756	4	18	sciences	science	NOUN
ejpam-3756	4	19	,	,	PUNCT
ejpam-3756	4	20	vellore	vellore	PROPN
ejpam-3756	4	21	institute	institute	PROPN
ejpam-3756	4	22	of	of	ADP
ejpam-3756	4	23	technology	technology	PROPN
ejpam-3756	4	24	(	(	PUNCT
ejpam-3756	4	25	vit	vit	NOUN
ejpam-3756	4	26	)	)	PUNCT
ejpam-3756	4	27	university	university	NOUN
ejpam-3756	4	28	,	,	PUNCT
ejpam-3756	4	29	vellore	vellore	VERB
ejpam-3756	4	30	632	632	NUM
ejpam-3756	4	31	014	014	NUM
ejpam-3756	4	32	,	,	PUNCT
ejpam-3756	4	33	tamil	tamil	PROPN
ejpam-3756	4	34	nadu	nadu	PROPN
ejpam-3756	4	35	,	,	PUNCT
ejpam-3756	4	36	india	india	PROPN
ejpam-3756	4	37	3	3	NUM
ejpam-3756	4	38	department	department	PROPN
ejpam-3756	4	39	of	of	ADP
ejpam-3756	4	40	mathematics	mathematic	NOUN
ejpam-3756	4	41	,	,	PUNCT
ejpam-3756	4	42	indira	indira	PROPN
ejpam-3756	4	43	gandhi	gandhi	PROPN
ejpam-3756	4	44	national	national	PROPN
ejpam-3756	4	45	tribal	tribal	PROPN
ejpam-3756	4	46	university	university	PROPN
ejpam-3756	4	47	,	,	PUNCT
ejpam-3756	4	48	lalpur	lalpur	PROPN
ejpam-3756	4	49	,	,	PUNCT
ejpam-3756	4	50	amarkantak	amarkantak	ADJ
ejpam-3756	4	51	,	,	PUNCT
ejpam-3756	4	52	anuppur	anuppur	NOUN
ejpam-3756	4	53	,	,	PUNCT
ejpam-3756	4	54	madhya	madhya	PROPN
ejpam-3756	4	55	pradesh	pradesh	PROPN
ejpam-3756	4	56	484	484	NUM
ejpam-3756	4	57	887	887	NUM
ejpam-3756	4	58	,	,	PUNCT
ejpam-3756	4	59	india	india	PROPN
ejpam-3756	4	60	4	4	NUM
ejpam-3756	4	61	department	department	NOUN
ejpam-3756	4	62	of	of	ADP
ejpam-3756	4	63	mathematics	mathematic	NOUN
ejpam-3756	4	64	,	,	PUNCT
ejpam-3756	4	65	school	school	NOUN
ejpam-3756	4	66	of	of	ADP
ejpam-3756	4	67	sciences	science	NOUN
ejpam-3756	4	68	and	and	CCONJ
ejpam-3756	4	69	languages	language	NOUN
ejpam-3756	4	70	,	,	PUNCT
ejpam-3756	4	71	vit	vit	PROPN
ejpam-3756	4	72	-	-	PUNCT
ejpam-3756	4	73	ap	ap	PROPN
ejpam-3756	4	74	university	university	PROPN
ejpam-3756	4	75	,	,	PUNCT
ejpam-3756	4	76	amaravati	amaravati	VERB
ejpam-3756	4	77	522	522	NUM
ejpam-3756	4	78	237	237	NUM
ejpam-3756	4	79	,	,	PUNCT
ejpam-3756	4	80	andhra	andhra	PROPN
ejpam-3756	4	81	pradesh	pradesh	PROPN
ejpam-3756	4	82	,	,	PUNCT
ejpam-3756	4	83	india	india	PROPN
ejpam-3756	4	84	abstract	abstract	PROPN
ejpam-3756	4	85	.	.	PUNCT
ejpam-3756	5	1	the	the	DET
ejpam-3756	5	2	aim	aim	NOUN
ejpam-3756	5	3	of	of	ADP
ejpam-3756	5	4	this	this	DET
ejpam-3756	5	5	paper	paper	NOUN
ejpam-3756	5	6	is	be	AUX
ejpam-3756	5	7	to	to	PART
ejpam-3756	5	8	define	define	VERB
ejpam-3756	5	9	a	a	DET
ejpam-3756	5	10	new	new	ADJ
ejpam-3756	5	11	iteration	iteration	NOUN
ejpam-3756	5	12	scheme	scheme	NOUN
ejpam-3756	5	13	nv	nv	PROPN
ejpam-3756	5	14	1	1	NUM
ejpam-3756	5	15	which	which	PRON
ejpam-3756	5	16	converges	converge	VERB
ejpam-3756	5	17	to	to	ADP
ejpam-3756	5	18	a	a	DET
ejpam-3756	5	19	fixed	fix	VERB
ejpam-3756	5	20	point	point	NOUN
ejpam-3756	5	21	faster	fast	ADV
ejpam-3756	5	22	than	than	ADP
ejpam-3756	5	23	some	some	DET
ejpam-3756	5	24	previously	previously	ADV
ejpam-3756	5	25	existing	exist	VERB
ejpam-3756	5	26	methods	method	NOUN
ejpam-3756	5	27	such	such	ADJ
ejpam-3756	5	28	as	as	ADP
ejpam-3756	5	29	picard	picard	NOUN
ejpam-3756	5	30	,	,	PUNCT
ejpam-3756	5	31	mann	mann	PROPN
ejpam-3756	5	32	,	,	PUNCT
ejpam-3756	5	33	ishikawa	ishikawa	PROPN
ejpam-3756	5	34	,	,	PUNCT
ejpam-3756	5	35	noor	noor	PROPN
ejpam-3756	5	36	,	,	PUNCT
ejpam-3756	5	37	sp	sp	NOUN
ejpam-3756	5	38	,	,	PUNCT
ejpam-3756	5	39	cr	cr	PROPN
ejpam-3756	5	40	,	,	PUNCT
ejpam-3756	5	41	s	s	PROPN
ejpam-3756	5	42	,	,	PUNCT
ejpam-3756	5	43	picard	picard	NOUN
ejpam-3756	5	44	-	-	PUNCT
ejpam-3756	5	45	s	s	PROPN
ejpam-3756	5	46	,	,	PUNCT
ejpam-3756	5	47	garodia	garodia	NOUN
ejpam-3756	5	48	,	,	PUNCT
ejpam-3756	5	49	k	k	PROPN
ejpam-3756	5	50	and	and	CCONJ
ejpam-3756	5	51	k∗	k∗	PROPN
ejpam-3756	5	52	methods	method	NOUN
ejpam-3756	5	53	etc	etc	X
ejpam-3756	5	54	.	.	PUNCT
ejpam-3756	6	1	the	the	DET
ejpam-3756	6	2	effectiveness	effectiveness	NOUN
ejpam-3756	6	3	and	and	CCONJ
ejpam-3756	6	4	efficiency	efficiency	NOUN
ejpam-3756	6	5	of	of	ADP
ejpam-3756	6	6	our	our	PRON
ejpam-3756	6	7	algorithm	algorithm	NOUN
ejpam-3756	6	8	is	be	AUX
ejpam-3756	6	9	confirmed	confirm	VERB
ejpam-3756	6	10	by	by	ADP
ejpam-3756	6	11	numerical	numerical	ADJ
ejpam-3756	6	12	example	example	NOUN
ejpam-3756	6	13	and	and	CCONJ
ejpam-3756	6	14	some	some	DET
ejpam-3756	6	15	strong	strong	ADJ
ejpam-3756	6	16	convergence	convergence	NOUN
ejpam-3756	6	17	,	,	PUNCT
ejpam-3756	6	18	weak	weak	ADJ
ejpam-3756	6	19	convergence	convergence	NOUN
ejpam-3756	6	20	,	,	PUNCT
ejpam-3756	6	21	t	t	NOUN
ejpam-3756	6	22	-stability	-stability	PROPN
ejpam-3756	6	23	and	and	CCONJ
ejpam-3756	6	24	data	datum	NOUN
ejpam-3756	6	25	dependence	dependence	NOUN
ejpam-3756	6	26	results	result	NOUN
ejpam-3756	6	27	for	for	ADP
ejpam-3756	6	28	contraction	contraction	NOUN
ejpam-3756	6	29	mapping	mapping	NOUN
ejpam-3756	6	30	are	be	AUX
ejpam-3756	6	31	also	also	ADV
ejpam-3756	6	32	proven	prove	VERB
ejpam-3756	6	33	.	.	PUNCT
ejpam-3756	7	1	moreover	moreover	ADV
ejpam-3756	7	2	,	,	PUNCT
ejpam-3756	7	3	it	it	PRON
ejpam-3756	7	4	is	be	AUX
ejpam-3756	7	5	shown	show	VERB
ejpam-3756	7	6	that	that	SCONJ
ejpam-3756	7	7	differential	differential	ADJ
ejpam-3756	7	8	equation	equation	NOUN
ejpam-3756	7	9	with	with	ADP
ejpam-3756	7	10	retarted	retarted	ADJ
ejpam-3756	7	11	argument	argument	NOUN
ejpam-3756	7	12	is	be	AUX
ejpam-3756	7	13	solved	solve	VERB
ejpam-3756	7	14	using	use	VERB
ejpam-3756	7	15	nv	nv	PROPN
ejpam-3756	7	16	1	1	NUM
ejpam-3756	7	17	iteration	iteration	NOUN
ejpam-3756	7	18	process	process	NOUN
ejpam-3756	7	19	.	.	PUNCT
ejpam-3756	8	1	2020	2020	NUM
ejpam-3756	8	2	mathematics	mathematic	NOUN
ejpam-3756	8	3	subject	subject	NOUN
ejpam-3756	8	4	classifications	classification	NOUN
ejpam-3756	8	5	:	:	PUNCT
ejpam-3756	8	6	47h09	47h09	NUM
ejpam-3756	8	7	,	,	PUNCT
ejpam-3756	8	8	47h10	47h10	PRON
ejpam-3756	8	9	key	key	ADJ
ejpam-3756	8	10	words	word	NOUN
ejpam-3756	8	11	and	and	CCONJ
ejpam-3756	8	12	phrases	phrase	NOUN
ejpam-3756	8	13	:	:	PUNCT
ejpam-3756	8	14	iteration	iteration	NOUN
ejpam-3756	8	15	schemes	scheme	NOUN
ejpam-3756	8	16	,	,	PUNCT
ejpam-3756	8	17	nv	nv	PROPN
ejpam-3756	8	18	1	1	NUM
ejpam-3756	8	19	iteration	iteration	NOUN
ejpam-3756	8	20	scheme	scheme	NOUN
ejpam-3756	8	21	,	,	PUNCT
ejpam-3756	8	22	convergence	convergence	NOUN
ejpam-3756	8	23	analysis	analysis	NOUN
ejpam-3756	8	24	,	,	PUNCT
ejpam-3756	8	25	t	t	NOUN
ejpam-3756	8	26	−	−	PROPN
ejpam-3756	8	27	stability	stability	NOUN
ejpam-3756	8	28	,	,	PUNCT
ejpam-3756	8	29	data	datum	NOUN
ejpam-3756	8	30	dependency	dependency	NOUN
ejpam-3756	8	31	∗corresponding	∗corresponde	VERB
ejpam-3756	8	32	author	author	NOUN
ejpam-3756	8	33	.	.	PUNCT
ejpam-3756	9	1	doi	doi	NOUN
ejpam-3756	9	2	:	:	PUNCT
ejpam-3756	9	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3756	https://doi.org/10.29020/nybg.ejpam.v13i5.3756	PROPN
ejpam-3756	9	4	email	email	NOUN
ejpam-3756	9	5	addresses	address	VERB
ejpam-3756	9	6	:	:	PUNCT
ejpam-3756	9	7	nnishaa.bhardwaj@gmail.com	nnishaa.bhardwaj@gmail.com	X
ejpam-3756	9	8	(	(	PUNCT
ejpam-3756	9	9	n.	n.	PROPN
ejpam-3756	9	10	sharma	sharma	PROPN
ejpam-3756	9	11	)	)	PUNCT
ejpam-3756	9	12	,	,	PUNCT
ejpam-3756	9	13	lakshminarayanmishra04@gmail.com	lakshminarayanmishra04@gmail.com	PROPN
ejpam-3756	9	14	(	(	PUNCT
ejpam-3756	9	15	l.n	l.n	PROPN
ejpam-3756	9	16	.	.	PROPN
ejpam-3756	9	17	mishra	mishra	PROPN
ejpam-3756	9	18	)	)	PUNCT
ejpam-3756	9	19	,	,	PUNCT
ejpam-3756	9	20	vishnunarayanmishra@gmail.com	vishnunarayanmishra@gmail.com	X
ejpam-3756	9	21	(	(	PUNCT
ejpam-3756	9	22	v.n	v.n	PROPN
ejpam-3756	9	23	.	.	PROPN
ejpam-3756	9	24	mishra	mishra	PROPN
ejpam-3756	9	25	)	)	PUNCT
ejpam-3756	9	26	,	,	PUNCT
ejpam-3756	9	27	sp1486@gmail.com	sp1486@gmail.com	X
ejpam-3756	9	28	(	(	PUNCT
ejpam-3756	9	29	s.	s.	PROPN
ejpam-3756	9	30	pandey	pandey	PROPN
ejpam-3756	9	31	)	)	PUNCT
ejpam-3756	9	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3756	9	33	1110	1110	NUM
ejpam-3756	10	1	c	c	NOUN
ejpam-3756	10	2	©	©	PROPN
ejpam-3756	10	3	2020	2020	NUM
ejpam-3756	10	4	ejpam	ejpam	VERB
ejpam-3756	10	5	all	all	DET
ejpam-3756	10	6	rights	right	NOUN
ejpam-3756	10	7	reserved	reserve	VERB
ejpam-3756	10	8	.	.	PUNCT
ejpam-3756	11	1	l.n	l.n	PROPN
ejpam-3756	11	2	mishra	mishra	PROPN
ejpam-3756	11	3	et	et	PROPN
ejpam-3756	11	4	al	al	PROPN
ejpam-3756	11	5	.	.	PUNCT
ejpam-3756	11	6	/	/	SYM
ejpam-3756	11	7	eur	eur	PROPN
ejpam-3756	11	8	.	.	PUNCT
ejpam-3756	12	1	j.	j.	PROPN
ejpam-3756	12	2	pure	pure	PROPN
ejpam-3756	12	3	appl	appl	PROPN
ejpam-3756	12	4	.	.	PROPN
ejpam-3756	12	5	math	math	PROPN
ejpam-3756	12	6	,	,	PUNCT
ejpam-3756	12	7	13	13	NUM
ejpam-3756	12	8	(	(	PUNCT
ejpam-3756	12	9	5	5	NUM
ejpam-3756	12	10	)	)	PUNCT
ejpam-3756	12	11	(	(	PUNCT
ejpam-3756	12	12	2020	2020	NUM
ejpam-3756	12	13	)	)	PUNCT
ejpam-3756	12	14	,	,	PUNCT
ejpam-3756	12	15	1110	1110	NUM
ejpam-3756	12	16	-	-	SYM
ejpam-3756	12	17	1130	1130	NUM
ejpam-3756	12	18	1111	1111	NUM
ejpam-3756	12	19	1	1	NUM
ejpam-3756	12	20	.	.	PUNCT
ejpam-3756	13	1	introduction	introduction	NOUN
ejpam-3756	13	2	throughout	throughout	ADP
ejpam-3756	13	3	in	in	ADP
ejpam-3756	13	4	this	this	DET
ejpam-3756	13	5	paper	paper	NOUN
ejpam-3756	13	6	,	,	PUNCT
ejpam-3756	13	7	we	we	PRON
ejpam-3756	13	8	will	will	AUX
ejpam-3756	13	9	denote	denote	VERB
ejpam-3756	13	10	set	set	NOUN
ejpam-3756	13	11	of	of	ADP
ejpam-3756	13	12	natural	natural	ADJ
ejpam-3756	13	13	numbers	number	NOUN
ejpam-3756	13	14	by	by	ADP
ejpam-3756	13	15	n	n	NOUN
ejpam-3756	13	16	and	and	CCONJ
ejpam-3756	13	17	set	set	VERB
ejpam-3756	13	18	of	of	ADP
ejpam-3756	13	19	real	real	ADJ
ejpam-3756	13	20	numbers	number	NOUN
ejpam-3756	13	21	by	by	ADP
ejpam-3756	13	22	r.	r.	PROPN
ejpam-3756	13	23	a	a	DET
ejpam-3756	13	24	mapping	mapping	NOUN
ejpam-3756	13	25	t	t	NOUN
ejpam-3756	13	26	on	on	ADP
ejpam-3756	13	27	a	a	DET
ejpam-3756	13	28	subset	subset	NOUN
ejpam-3756	13	29	c	c	NOUN
ejpam-3756	13	30	of	of	ADP
ejpam-3756	13	31	a	a	DET
ejpam-3756	13	32	banach	banach	NOUN
ejpam-3756	13	33	space	space	NOUN
ejpam-3756	13	34	e	e	NOUN
ejpam-3756	13	35	is	be	AUX
ejpam-3756	13	36	said	say	VERB
ejpam-3756	13	37	to	to	PART
ejpam-3756	13	38	be	be	AUX
ejpam-3756	13	39	nonexpansive	nonexpansive	ADJ
ejpam-3756	13	40	if	if	SCONJ
ejpam-3756	13	41	||tx−	||tx−	NOUN
ejpam-3756	13	42	ty||	ty||	NOUN
ejpam-3756	13	43	≤	≤	NUM
ejpam-3756	14	1	||x−	||x−	PROPN
ejpam-3756	14	2	y||	y||	NOUN
ejpam-3756	14	3	,	,	PUNCT
ejpam-3756	14	4	for	for	ADP
ejpam-3756	14	5	all	all	DET
ejpam-3756	14	6	x	x	NOUN
ejpam-3756	14	7	,	,	PUNCT
ejpam-3756	14	8	y	y	PROPN
ejpam-3756	14	9	∈	∈	PROPN
ejpam-3756	14	10	c.	c.	PROPN
ejpam-3756	14	11	an	an	DET
ejpam-3756	14	12	element	element	NOUN
ejpam-3756	14	13	q	q	PROPN
ejpam-3756	14	14	∈	∈	PROPN
ejpam-3756	14	15	c	c	NOUN
ejpam-3756	14	16	is	be	AUX
ejpam-3756	14	17	said	say	VERB
ejpam-3756	14	18	to	to	PART
ejpam-3756	14	19	be	be	AUX
ejpam-3756	14	20	a	a	DET
ejpam-3756	14	21	fixed	fix	VERB
ejpam-3756	14	22	point	point	NOUN
ejpam-3756	14	23	of	of	ADP
ejpam-3756	14	24	t	t	PROPN
ejpam-3756	14	25	if	if	SCONJ
ejpam-3756	14	26	q	q	PROPN
ejpam-3756	14	27	=	=	SYM
ejpam-3756	14	28	t	t	X
ejpam-3756	14	29	(	(	PUNCT
ejpam-3756	14	30	q	q	NOUN
ejpam-3756	14	31	)	)	PUNCT
ejpam-3756	14	32	.	.	PUNCT
ejpam-3756	15	1	from	from	ADP
ejpam-3756	15	2	now	now	ADV
ejpam-3756	15	3	on	on	ADV
ejpam-3756	15	4	,	,	PUNCT
ejpam-3756	15	5	we	we	PRON
ejpam-3756	15	6	will	will	AUX
ejpam-3756	15	7	denote	denote	VERB
ejpam-3756	15	8	set	set	NOUN
ejpam-3756	15	9	of	of	ADP
ejpam-3756	15	10	all	all	DET
ejpam-3756	15	11	fixed	fix	VERB
ejpam-3756	15	12	points	point	NOUN
ejpam-3756	15	13	of	of	ADP
ejpam-3756	15	14	t	t	PROPN
ejpam-3756	15	15	by	by	ADP
ejpam-3756	15	16	tf	tf	PROPN
ejpam-3756	15	17	.	.	PUNCT
ejpam-3756	16	1	a	a	DET
ejpam-3756	16	2	mapping	mapping	NOUN
ejpam-3756	16	3	t	t	NOUN
ejpam-3756	16	4	:	:	PUNCT
ejpam-3756	16	5	c	c	X
ejpam-3756	16	6	→	→	PUNCT
ejpam-3756	16	7	c	c	PROPN
ejpam-3756	16	8	is	be	AUX
ejpam-3756	16	9	said	say	VERB
ejpam-3756	16	10	to	to	PART
ejpam-3756	16	11	be	be	AUX
ejpam-3756	16	12	quasinonexpansive	quasinonexpansive	ADJ
ejpam-3756	16	13	mappings	mapping	NOUN
ejpam-3756	16	14	if	if	SCONJ
ejpam-3756	16	15	tf	tf	PROPN
ejpam-3756	16	16	6=	6=	NOUN
ejpam-3756	16	17	∅	∅	NOUN
ejpam-3756	16	18	and	and	CCONJ
ejpam-3756	16	19	||tx	||tx	NOUN
ejpam-3756	16	20	−	−	PROPN
ejpam-3756	16	21	tq||	tq||	ADJ
ejpam-3756	16	22	≤	≤	ADJ
ejpam-3756	16	23	||x	||x	NOUN
ejpam-3756	16	24	−	−	PROPN
ejpam-3756	16	25	q||	q||	PROPN
ejpam-3756	16	26	for	for	ADP
ejpam-3756	16	27	all	all	DET
ejpam-3756	16	28	x	x	SYM
ejpam-3756	16	29	∈	∈	PROPN
ejpam-3756	16	30	c	c	NOUN
ejpam-3756	16	31	and	and	CCONJ
ejpam-3756	16	32	q	q	PROPN
ejpam-3756	16	33	∈	∈	PROPN
ejpam-3756	17	1	tf	tf	INTJ
ejpam-3756	17	2	.	.	PUNCT
ejpam-3756	18	1	the	the	DET
ejpam-3756	18	2	existence	existence	NOUN
ejpam-3756	18	3	of	of	ADP
ejpam-3756	18	4	fixed	fix	VERB
ejpam-3756	18	5	points	point	NOUN
ejpam-3756	18	6	for	for	ADP
ejpam-3756	18	7	nonexpansive	nonexpansive	ADJ
ejpam-3756	18	8	mappings	mapping	NOUN
ejpam-3756	18	9	in	in	ADP
ejpam-3756	18	10	the	the	DET
ejpam-3756	18	11	setting	setting	NOUN
ejpam-3756	18	12	of	of	ADP
ejpam-3756	18	13	banach	banach	NOUN
ejpam-3756	18	14	spaces	space	NOUN
ejpam-3756	18	15	was	be	AUX
ejpam-3756	18	16	studied	study	VERB
ejpam-3756	18	17	independently	independently	ADV
ejpam-3756	18	18	by	by	ADP
ejpam-3756	18	19	browder	browder	NOUN
ejpam-3756	18	20	[	[	X
ejpam-3756	18	21	3	3	NUM
ejpam-3756	18	22	]	]	PUNCT
ejpam-3756	18	23	,	,	PUNCT
ejpam-3756	18	24	gohde	gohde	NOUN
ejpam-3756	18	25	[	[	X
ejpam-3756	18	26	6	6	NUM
ejpam-3756	18	27	]	]	PUNCT
ejpam-3756	18	28	and	and	CCONJ
ejpam-3756	18	29	kirk	kirk	NOUN
ejpam-3756	19	1	[	[	X
ejpam-3756	19	2	8	8	NUM
ejpam-3756	19	3	]	]	PUNCT
ejpam-3756	19	4	.	.	PUNCT
ejpam-3756	20	1	they	they	PRON
ejpam-3756	20	2	proved	prove	VERB
ejpam-3756	20	3	that	that	SCONJ
ejpam-3756	20	4	,	,	PUNCT
ejpam-3756	20	5	if	if	SCONJ
ejpam-3756	20	6	c	c	PROPN
ejpam-3756	20	7	is	be	AUX
ejpam-3756	20	8	nonempty	nonempty	ADV
ejpam-3756	20	9	closed	close	VERB
ejpam-3756	20	10	bounded	bounded	ADJ
ejpam-3756	20	11	and	and	CCONJ
ejpam-3756	20	12	convex	convex	PROPN
ejpam-3756	20	13	subset	subset	NOUN
ejpam-3756	20	14	of	of	ADP
ejpam-3756	20	15	a	a	DET
ejpam-3756	20	16	uniformly	uniformly	ADV
ejpam-3756	20	17	convex	convex	NOUN
ejpam-3756	20	18	banach	banach	NOUN
ejpam-3756	20	19	space	space	NOUN
ejpam-3756	20	20	,	,	PUNCT
ejpam-3756	20	21	then	then	ADV
ejpam-3756	20	22	every	every	DET
ejpam-3756	20	23	nonexpansive	nonexpansive	ADJ
ejpam-3756	20	24	mapping	mapping	NOUN
ejpam-3756	20	25	t	t	NOUN
ejpam-3756	20	26	:	:	PUNCT
ejpam-3756	20	27	c	c	X
ejpam-3756	20	28	→	→	SYM
ejpam-3756	20	29	c	c	PROPN
ejpam-3756	20	30	has	have	VERB
ejpam-3756	20	31	at	at	ADP
ejpam-3756	20	32	-	-	PUNCT
ejpam-3756	20	33	least	least	ADJ
ejpam-3756	20	34	one	one	NUM
ejpam-3756	20	35	fixed	fix	VERB
ejpam-3756	20	36	point	point	NOUN
ejpam-3756	20	37	.	.	PUNCT
ejpam-3756	21	1	a	a	DET
ejpam-3756	21	2	numbers	number	NOUN
ejpam-3756	21	3	of	of	ADP
ejpam-3756	21	4	generalization	generalization	NOUN
ejpam-3756	21	5	of	of	ADP
ejpam-3756	21	6	nonexpansive	nonexpansive	ADJ
ejpam-3756	21	7	mappings	mapping	NOUN
ejpam-3756	21	8	have	have	AUX
ejpam-3756	21	9	been	be	AUX
ejpam-3756	21	10	considered	consider	VERB
ejpam-3756	21	11	by	by	ADP
ejpam-3756	21	12	some	some	DET
ejpam-3756	21	13	authors	author	NOUN
ejpam-3756	21	14	in	in	ADP
ejpam-3756	21	15	recent	recent	ADJ
ejpam-3756	21	16	years	year	NOUN
ejpam-3756	21	17	.	.	PUNCT
ejpam-3756	22	1	it	it	PRON
ejpam-3756	22	2	is	be	AUX
ejpam-3756	22	3	natural	natural	ADJ
ejpam-3756	22	4	to	to	PART
ejpam-3756	22	5	study	study	VERB
ejpam-3756	22	6	the	the	DET
ejpam-3756	22	7	computation	computation	NOUN
ejpam-3756	22	8	of	of	ADP
ejpam-3756	22	9	fixed	fix	VERB
ejpam-3756	22	10	points	point	NOUN
ejpam-3756	22	11	for	for	ADP
ejpam-3756	22	12	the	the	DET
ejpam-3756	22	13	known	know	VERB
ejpam-3756	22	14	existence	existence	NOUN
ejpam-3756	22	15	results	result	NOUN
ejpam-3756	22	16	,	,	PUNCT
ejpam-3756	22	17	which	which	PRON
ejpam-3756	22	18	is	be	AUX
ejpam-3756	22	19	not	not	PART
ejpam-3756	22	20	an	an	DET
ejpam-3756	22	21	easy	easy	ADJ
ejpam-3756	22	22	task	task	NOUN
ejpam-3756	22	23	.	.	PUNCT
ejpam-3756	23	1	the	the	DET
ejpam-3756	23	2	banach	banach	NOUN
ejpam-3756	23	3	contraction	contraction	NOUN
ejpam-3756	23	4	mapping	mapping	NOUN
ejpam-3756	23	5	principle	principle	NOUN
ejpam-3756	23	6	uses	use	VERB
ejpam-3756	23	7	picard	picard	PROPN
ejpam-3756	23	8	iteration	iteration	NOUN
ejpam-3756	23	9	process	process	NOUN
ejpam-3756	23	10	xn+1	xn+1	NUM
ejpam-3756	24	1	=	=	PUNCT
ejpam-3756	24	2	txn	txn	NOUN
ejpam-3756	24	3	for	for	ADP
ejpam-3756	24	4	approximation	approximation	NOUN
ejpam-3756	24	5	of	of	ADP
ejpam-3756	24	6	the	the	DET
ejpam-3756	24	7	unique	unique	ADJ
ejpam-3756	24	8	fixed	fix	VERB
ejpam-3756	24	9	point	point	NOUN
ejpam-3756	24	10	.	.	PUNCT
ejpam-3756	25	1	some	some	DET
ejpam-3756	25	2	other	other	ADJ
ejpam-3756	25	3	well	well	ADV
ejpam-3756	25	4	-	-	PUNCT
ejpam-3756	25	5	known	know	VERB
ejpam-3756	25	6	iteration	iteration	NOUN
ejpam-3756	25	7	schemes	scheme	NOUN
ejpam-3756	25	8	are	be	AUX
ejpam-3756	25	9	mann	mann	NOUN
ejpam-3756	25	10	[	[	X
ejpam-3756	25	11	9	9	NUM
ejpam-3756	25	12	]	]	PUNCT
ejpam-3756	25	13	,	,	PUNCT
ejpam-3756	25	14	ishikawa	ishikawa	PROPN
ejpam-3756	26	1	[	[	X
ejpam-3756	26	2	7	7	NUM
ejpam-3756	26	3	]	]	PUNCT
ejpam-3756	26	4	,	,	PUNCT
ejpam-3756	26	5	s	s	X
ejpam-3756	27	1	[	[	X
ejpam-3756	27	2	13	13	NUM
ejpam-3756	27	3	]	]	PUNCT
ejpam-3756	27	4	,	,	PUNCT
ejpam-3756	27	5	noor	noor	PROPN
ejpam-3756	28	1	[	[	X
ejpam-3756	28	2	10	10	NUM
ejpam-3756	28	3	]	]	PUNCT
ejpam-3756	28	4	,	,	PUNCT
ejpam-3756	28	5	abbas	abbas	PROPN
ejpam-3756	29	1	[	[	X
ejpam-3756	29	2	1	1	NUM
ejpam-3756	29	3	]	]	PUNCT
ejpam-3756	29	4	,	,	PUNCT
ejpam-3756	29	5	thakur	thakur	PROPN
ejpam-3756	29	6	et	et	PROPN
ejpam-3756	29	7	.	.	PUNCT
ejpam-3756	30	1	al	al	PROPN
ejpam-3756	30	2	.	.	PUNCT
ejpam-3756	31	1	[	[	X
ejpam-3756	31	2	4	4	X
ejpam-3756	31	3	]	]	PUNCT
ejpam-3756	31	4	and	and	CCONJ
ejpam-3756	31	5	so	so	ADV
ejpam-3756	31	6	on	on	ADV
ejpam-3756	31	7	.	.	PUNCT
ejpam-3756	32	1	speed	speed	NOUN
ejpam-3756	32	2	of	of	ADP
ejpam-3756	32	3	convergence	convergence	NOUN
ejpam-3756	32	4	plays	play	VERB
ejpam-3756	32	5	an	an	DET
ejpam-3756	32	6	important	important	ADJ
ejpam-3756	32	7	role	role	NOUN
ejpam-3756	32	8	for	for	ADP
ejpam-3756	32	9	an	an	DET
ejpam-3756	32	10	iteration	iteration	NOUN
ejpam-3756	32	11	process	process	NOUN
ejpam-3756	32	12	to	to	PART
ejpam-3756	32	13	be	be	AUX
ejpam-3756	32	14	preferred	prefer	VERB
ejpam-3756	32	15	on	on	ADP
ejpam-3756	32	16	another	another	DET
ejpam-3756	32	17	iteration	iteration	NOUN
ejpam-3756	32	18	process	process	NOUN
ejpam-3756	32	19	.	.	PUNCT
ejpam-3756	33	1	rhoades	rhoade	NOUN
ejpam-3756	34	1	[	[	X
ejpam-3756	34	2	12	12	NUM
ejpam-3756	34	3	]	]	PUNCT
ejpam-3756	34	4	mentioned	mention	VERB
ejpam-3756	34	5	that	that	SCONJ
ejpam-3756	34	6	the	the	DET
ejpam-3756	34	7	mann	mann	PROPN
ejpam-3756	34	8	iteration	iteration	NOUN
ejpam-3756	34	9	process	process	NOUN
ejpam-3756	34	10	for	for	ADP
ejpam-3756	34	11	decreasing	decrease	VERB
ejpam-3756	34	12	function	function	NOUN
ejpam-3756	34	13	converge	converge	VERB
ejpam-3756	34	14	faster	fast	ADV
ejpam-3756	34	15	than	than	ADP
ejpam-3756	34	16	the	the	DET
ejpam-3756	34	17	ishikawa	ishikawa	PROPN
ejpam-3756	34	18	iteration	iteration	NOUN
ejpam-3756	34	19	process	process	NOUN
ejpam-3756	34	20	and	and	CCONJ
ejpam-3756	34	21	for	for	ADP
ejpam-3756	34	22	increasing	increase	VERB
ejpam-3756	34	23	function	function	NOUN
ejpam-3756	34	24	the	the	DET
ejpam-3756	34	25	ishikawa	ishikawa	PROPN
ejpam-3756	34	26	iteration	iteration	NOUN
ejpam-3756	34	27	process	process	NOUN
ejpam-3756	34	28	is	be	AUX
ejpam-3756	34	29	better	well	ADJ
ejpam-3756	34	30	than	than	ADP
ejpam-3756	34	31	the	the	DET
ejpam-3756	34	32	mann	mann	PROPN
ejpam-3756	34	33	iteration	iteration	NOUN
ejpam-3756	34	34	process	process	NOUN
ejpam-3756	34	35	.	.	PUNCT
ejpam-3756	35	1	more	more	ADJ
ejpam-3756	35	2	details	detail	NOUN
ejpam-3756	35	3	can	can	AUX
ejpam-3756	35	4	be	be	AUX
ejpam-3756	35	5	found	find	VERB
ejpam-3756	35	6	in	in	ADP
ejpam-3756	35	7	[	[	X
ejpam-3756	35	8	16	16	NUM
ejpam-3756	35	9	]	]	PUNCT
ejpam-3756	35	10	,	,	PUNCT
ejpam-3756	35	11	[	[	X
ejpam-3756	35	12	18	18	NUM
ejpam-3756	35	13	]	]	PUNCT
ejpam-3756	35	14	,	,	PUNCT
ejpam-3756	35	15	[	[	X
ejpam-3756	35	16	15	15	NUM
ejpam-3756	35	17	]	]	PUNCT
ejpam-3756	35	18	,	,	PUNCT
ejpam-3756	35	19	[	[	X
ejpam-3756	35	20	19	19	NUM
ejpam-3756	35	21	]	]	PUNCT
ejpam-3756	35	22	,	,	PUNCT
ejpam-3756	35	23	[	[	X
ejpam-3756	35	24	5	5	NUM
ejpam-3756	35	25	]	]	PUNCT
ejpam-3756	35	26	.	.	PUNCT
ejpam-3756	36	1	the	the	DET
ejpam-3756	36	2	most	most	ADV
ejpam-3756	36	3	popular	popular	ADJ
ejpam-3756	36	4	and	and	CCONJ
ejpam-3756	36	5	simplest	simplest	ADJ
ejpam-3756	36	6	iteration	iteration	NOUN
ejpam-3756	36	7	method	method	NOUN
ejpam-3756	36	8	is	be	AUX
ejpam-3756	36	9	formulated	formulate	VERB
ejpam-3756	36	10	by	by	ADP
ejpam-3756	36	11	{	{	PUNCT
ejpam-3756	36	12	p0	p0	PROPN
ejpam-3756	36	13	∈	∈	PROPN
ejpam-3756	36	14	c	c	NOUN
ejpam-3756	36	15	pn+1	pn+1	NOUN
ejpam-3756	36	16	=	=	SYM
ejpam-3756	36	17	tpn	tpn	PROPN
ejpam-3756	36	18	,	,	PUNCT
ejpam-3756	36	19	n	n	NOUN
ejpam-3756	36	20	∈	∈	PROPN
ejpam-3756	36	21	n	n	CCONJ
ejpam-3756	36	22	(	(	PUNCT
ejpam-3756	36	23	1.3	1.3	NUM
ejpam-3756	36	24	)	)	PUNCT
ejpam-3756	36	25	and	and	CCONJ
ejpam-3756	36	26	is	be	AUX
ejpam-3756	36	27	known	know	VERB
ejpam-3756	36	28	as	as	ADP
ejpam-3756	36	29	picard	picard	NOUN
ejpam-3756	36	30	iteration	iteration	NOUN
ejpam-3756	36	31	method	method	NOUN
ejpam-3756	36	32	,	,	PUNCT
ejpam-3756	36	33	which	which	PRON
ejpam-3756	36	34	is	be	AUX
ejpam-3756	36	35	communally	communally	ADV
ejpam-3756	36	36	used	use	VERB
ejpam-3756	36	37	to	to	PART
ejpam-3756	36	38	approximate	approximate	VERB
ejpam-3756	36	39	fixed	fix	VERB
ejpam-3756	36	40	point	point	NOUN
ejpam-3756	36	41	of	of	ADP
ejpam-3756	36	42	contraction	contraction	NOUN
ejpam-3756	36	43	mappings	mapping	NOUN
ejpam-3756	36	44	satisfying	satisfy	VERB
ejpam-3756	36	45	‖tx−	‖tx−	NOUN
ejpam-3756	36	46	ty‖	ty‖	PROPN
ejpam-3756	36	47	≤	≤	NOUN
ejpam-3756	36	48	µ‖x−	µ‖x−	X
ejpam-3756	36	49	y‖	y‖	PROPN
ejpam-3756	36	50	,	,	PUNCT
ejpam-3756	36	51	µ	µ	X
ejpam-3756	36	52	∈	∈	X
ejpam-3756	36	53	(	(	PUNCT
ejpam-3756	36	54	0	0	NUM
ejpam-3756	36	55	,	,	PUNCT
ejpam-3756	36	56	1	1	NUM
ejpam-3756	36	57	)	)	PUNCT
ejpam-3756	36	58	,	,	PUNCT
ejpam-3756	36	59	(	(	PUNCT
ejpam-3756	36	60	1.4	1.4	NUM
ejpam-3756	36	61	)	)	PUNCT
ejpam-3756	36	62	for	for	ADP
ejpam-3756	36	63	all	all	DET
ejpam-3756	36	64	x	x	NOUN
ejpam-3756	36	65	,	,	PUNCT
ejpam-3756	36	66	y	y	PROPN
ejpam-3756	36	67	∈	∈	PROPN
ejpam-3756	36	68	c.	c.	NOUN
ejpam-3756	37	1	the	the	DET
ejpam-3756	37	2	subsequent	subsequent	ADJ
ejpam-3756	37	3	iteration	iteration	NOUN
ejpam-3756	37	4	methods	method	NOUN
ejpam-3756	37	5	are	be	AUX
ejpam-3756	37	6	mention	mention	NOUN
ejpam-3756	37	7	to	to	ADP
ejpam-3756	37	8	as	as	ADP
ejpam-3756	37	9	mann	mann	PROPN
ejpam-3756	37	10	,	,	PUNCT
ejpam-3756	37	11	ishikawa	ishikawa	PROPN
ejpam-3756	37	12	,	,	PUNCT
ejpam-3756	37	13	noor	noor	PROPN
ejpam-3756	37	14	,	,	PUNCT
ejpam-3756	37	15	sp	sp	NOUN
ejpam-3756	37	16	,	,	PUNCT
ejpam-3756	37	17	s	s	PROPN
ejpam-3756	37	18	,	,	PUNCT
ejpam-3756	37	19	cr	cr	NOUN
ejpam-3756	37	20	,	,	PUNCT
ejpam-3756	37	21	picard	picard	PROPN
ejpam-3756	37	22	-	-	PUNCT
ejpam-3756	37	23	s	s	PROPN
ejpam-3756	37	24	,	,	PUNCT
ejpam-3756	37	25	garodia	garodia	PROPN
ejpam-3756	37	26	’s	’s	PART
ejpam-3756	37	27	,	,	PUNCT
ejpam-3756	37	28	k	k	PROPN
ejpam-3756	37	29	and	and	CCONJ
ejpam-3756	37	30	k∗	k∗	PROPN
ejpam-3756	37	31	iteration	iteration	NOUN
ejpam-3756	37	32	methods	method	NOUN
ejpam-3756	37	33	,	,	PUNCT
ejpam-3756	37	34	respectively	respectively	ADV
ejpam-3756	37	35	:	:	PUNCT
ejpam-3756	37	36	{	{	PUNCT
ejpam-3756	37	37	v0	v0	PROPN
ejpam-3756	37	38	∈	∈	PROPN
ejpam-3756	37	39	c	c	X
ejpam-3756	37	40	,	,	PUNCT
ejpam-3756	37	41	ζn+1	ζn+1	ADJ
ejpam-3756	37	42	=	=	SYM
ejpam-3756	37	43	(	(	PUNCT
ejpam-3756	37	44	1−	1−	NUM
ejpam-3756	37	45	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	37	46	+	+	CCONJ
ejpam-3756	37	47	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	37	48	,	,	PUNCT
ejpam-3756	37	49	n	n	PRON
ejpam-3756	37	50	∈	∈	PROPN
ejpam-3756	37	51	n	n	CCONJ
ejpam-3756	37	52	,	,	PUNCT
ejpam-3756	37	53	(	(	PUNCT
ejpam-3756	37	54	1.5	1.5	NUM
ejpam-3756	37	55	)	)	PUNCT
ejpam-3756	37	56			PRON
ejpam-3756	37	57	v0	v0	VERB
ejpam-3756	37	58	∈	∈	PROPN
ejpam-3756	37	59	c	c	X
ejpam-3756	37	60	,	,	PUNCT
ejpam-3756	37	61	vn+1	vn+1	X
ejpam-3756	37	62	=	=	SYM
ejpam-3756	37	63	(	(	PUNCT
ejpam-3756	37	64	1−	1−	NUM
ejpam-3756	37	65	σ0n)vn	σ0n)vn	PROPN
ejpam-3756	37	66	+	+	CCONJ
ejpam-3756	37	67	σ0ntwn	σ0ntwn	PROPN
ejpam-3756	37	68	,	,	PUNCT
ejpam-3756	37	69	wn	wn	NOUN
ejpam-3756	37	70	=	=	SYM
ejpam-3756	37	71	(	(	PUNCT
ejpam-3756	37	72	1−	1−	NUM
ejpam-3756	37	73	σ1n)vn	σ1n)vn	PROPN
ejpam-3756	37	74	+	+	CCONJ
ejpam-3756	37	75	σ1ntvn	σ1ntvn	NOUN
ejpam-3756	37	76	,	,	PUNCT
ejpam-3756	37	77	n	n	PROPN
ejpam-3756	37	78	∈	∈	PROPN
ejpam-3756	37	79	n	n	CCONJ
ejpam-3756	37	80	,	,	PUNCT
ejpam-3756	37	81	(	(	PUNCT
ejpam-3756	37	82	1.6	1.6	NUM
ejpam-3756	37	83	)	)	PUNCT
ejpam-3756	37	84	l.n	l.n	PROPN
ejpam-3756	37	85	mishra	mishra	PROPN
ejpam-3756	37	86	et	et	PROPN
ejpam-3756	37	87	al	al	PROPN
ejpam-3756	37	88	.	.	PUNCT
ejpam-3756	37	89	/	/	SYM
ejpam-3756	37	90	eur	eur	PROPN
ejpam-3756	37	91	.	.	PUNCT
ejpam-3756	38	1	j.	j.	PROPN
ejpam-3756	38	2	pure	pure	PROPN
ejpam-3756	38	3	appl	appl	PROPN
ejpam-3756	38	4	.	.	PROPN
ejpam-3756	38	5	math	math	PROPN
ejpam-3756	38	6	,	,	PUNCT
ejpam-3756	38	7	13	13	NUM
ejpam-3756	38	8	(	(	PUNCT
ejpam-3756	38	9	5	5	NUM
ejpam-3756	38	10	)	)	PUNCT
ejpam-3756	38	11	(	(	PUNCT
ejpam-3756	38	12	2020	2020	NUM
ejpam-3756	38	13	)	)	PUNCT
ejpam-3756	38	14	,	,	PUNCT
ejpam-3756	38	15	1110	1110	NUM
ejpam-3756	38	16	-	-	SYM
ejpam-3756	38	17	1130	1130	NUM
ejpam-3756	38	18	1112	1112	NUM
ejpam-3756	38	19			PROPN
ejpam-3756	38	20	w0	w0	PROPN
ejpam-3756	38	21	∈	∈	PROPN
ejpam-3756	38	22	c	c	X
ejpam-3756	38	23	,	,	PUNCT
ejpam-3756	38	24	wn+1	wn+1	X
ejpam-3756	38	25	=	=	SYM
ejpam-3756	38	26	(	(	PUNCT
ejpam-3756	38	27	1−	1−	NUM
ejpam-3756	38	28	σ0n)wn	σ0n)wn	NOUN
ejpam-3756	38	29	+	+	CCONJ
ejpam-3756	38	30	σ0ntwn	σ0ntwn	ADJ
ejpam-3756	38	31	,	,	PUNCT
ejpam-3756	38	32	vn	vn	NOUN
ejpam-3756	38	33	=	=	SYM
ejpam-3756	38	34	(	(	PUNCT
ejpam-3756	38	35	1−	1−	NUM
ejpam-3756	38	36	σ1n)wn	σ1n)wn	NOUN
ejpam-3756	38	37	+	+	CCONJ
ejpam-3756	38	38	σ1ntun	σ1ntun	NUM
ejpam-3756	38	39	,	,	PUNCT
ejpam-3756	38	40	un	un	PROPN
ejpam-3756	38	41	=	=	SYM
ejpam-3756	38	42	(	(	PUNCT
ejpam-3756	38	43	1−	1−	NUM
ejpam-3756	38	44	σ2n)wn	σ2n)wn	NOUN
ejpam-3756	38	45	+	+	CCONJ
ejpam-3756	38	46	σ2ntwn	σ2ntwn	ADJ
ejpam-3756	38	47	,	,	PUNCT
ejpam-3756	38	48	n	n	NOUN
ejpam-3756	38	49	∈	∈	PROPN
ejpam-3756	38	50	n	n	CCONJ
ejpam-3756	38	51	,	,	PUNCT
ejpam-3756	38	52	(	(	PUNCT
ejpam-3756	38	53	1.7	1.7	NUM
ejpam-3756	38	54	)	)	PUNCT
ejpam-3756	38	55			VERB
ejpam-3756	39	1	q0	q0	VERB
ejpam-3756	39	2	∈	∈	PROPN
ejpam-3756	39	3	c	c	X
ejpam-3756	39	4	,	,	PUNCT
ejpam-3756	39	5	qn+1	qn+1	PROPN
ejpam-3756	39	6	=	=	SYM
ejpam-3756	39	7	(	(	PUNCT
ejpam-3756	39	8	1−	1−	NUM
ejpam-3756	39	9	σ0n)rn	σ0n)rn	NOUN
ejpam-3756	39	10	+	+	CCONJ
ejpam-3756	39	11	σ0ntrn	σ0ntrn	NOUN
ejpam-3756	39	12	,	,	PUNCT
ejpam-3756	39	13	rn	rn	NOUN
ejpam-3756	39	14	=	=	SYM
ejpam-3756	39	15	(	(	PUNCT
ejpam-3756	39	16	1−	1−	NUM
ejpam-3756	39	17	σ1n)sn	σ1n)sn	X
ejpam-3756	39	18	+	+	CCONJ
ejpam-3756	39	19	σ1ntsn	σ1ntsn	ADJ
ejpam-3756	39	20	,	,	PUNCT
ejpam-3756	39	21	sn	sn	NOUN
ejpam-3756	39	22	=	=	SYM
ejpam-3756	39	23	(	(	PUNCT
ejpam-3756	39	24	1−	1−	NUM
ejpam-3756	39	25	σ2n)qn	σ2n)qn	NOUN
ejpam-3756	39	26	+	+	CCONJ
ejpam-3756	39	27	σ2ntqn	σ2ntqn	PROPN
ejpam-3756	39	28	,	,	PUNCT
ejpam-3756	39	29	n	n	PROPN
ejpam-3756	39	30	∈	∈	PROPN
ejpam-3756	39	31	n	n	CCONJ
ejpam-3756	39	32	,	,	PUNCT
ejpam-3756	39	33	(	(	PUNCT
ejpam-3756	39	34	1.8	1.8	NUM
ejpam-3756	39	35	)	)	PUNCT
ejpam-3756	40	1			NOUN
ejpam-3756	40	2	t0	t0	X
ejpam-3756	40	3	∈	∈	PROPN
ejpam-3756	40	4	c	c	X
ejpam-3756	40	5	,	,	PUNCT
ejpam-3756	40	6	tn+1	tn+1	PROPN
ejpam-3756	40	7	=	=	SYM
ejpam-3756	40	8	(	(	PUNCT
ejpam-3756	40	9	1−	1−	NUM
ejpam-3756	40	10	σ0n)ttn	σ0n)ttn	NOUN
ejpam-3756	40	11	+	+	PROPN
ejpam-3756	40	12	σ0ntun	σ0ntun	PROPN
ejpam-3756	40	13	,	,	PUNCT
ejpam-3756	40	14	un	un	PROPN
ejpam-3756	40	15	=	=	SYM
ejpam-3756	40	16	(	(	PUNCT
ejpam-3756	40	17	1−	1−	NUM
ejpam-3756	40	18	σ1n)tn	σ1n)tn	NOUN
ejpam-3756	40	19	+	+	CCONJ
ejpam-3756	40	20	σ1nttn	σ1nttn	NOUN
ejpam-3756	40	21	,	,	PUNCT
ejpam-3756	40	22	n	n	PROPN
ejpam-3756	40	23	∈	∈	PROPN
ejpam-3756	40	24	n	n	CCONJ
ejpam-3756	40	25	,	,	PUNCT
ejpam-3756	40	26	(	(	PUNCT
ejpam-3756	40	27	1.9	1.9	NUM
ejpam-3756	40	28	)	)	PUNCT
ejpam-3756	40	29			VERB
ejpam-3756	40	30	u0	u0	PROPN
ejpam-3756	40	31	∈	∈	PROPN
ejpam-3756	40	32	c	c	X
ejpam-3756	40	33	,	,	PUNCT
ejpam-3756	40	34	un+1	un+1	NOUN
ejpam-3756	40	35	=	=	SYM
ejpam-3756	40	36	(	(	PUNCT
ejpam-3756	40	37	1−	1−	NUM
ejpam-3756	40	38	σ0n)vn	σ0n)vn	PROPN
ejpam-3756	40	39	+	+	CCONJ
ejpam-3756	40	40	σ0ntvn	σ0ntvn	PROPN
ejpam-3756	40	41	,	,	PUNCT
ejpam-3756	40	42	vn	vn	NOUN
ejpam-3756	40	43	=	=	SYM
ejpam-3756	40	44	(	(	PUNCT
ejpam-3756	40	45	1−	1−	NUM
ejpam-3756	40	46	σ1n)tun	σ1n)tun	PROPN
ejpam-3756	40	47	+	+	CCONJ
ejpam-3756	40	48	σ1ntwn	σ1ntwn	PROPN
ejpam-3756	40	49	,	,	PUNCT
ejpam-3756	40	50	un	un	PROPN
ejpam-3756	40	51	=	=	SYM
ejpam-3756	40	52	(	(	PUNCT
ejpam-3756	40	53	1−	1−	NUM
ejpam-3756	40	54	σ2n)un	σ2n)un	VERB
ejpam-3756	40	55	+	+	CCONJ
ejpam-3756	40	56	σ2ntun	σ2ntun	NOUN
ejpam-3756	40	57	,	,	PUNCT
ejpam-3756	40	58	n	n	NOUN
ejpam-3756	40	59	∈	∈	PROPN
ejpam-3756	40	60	n	n	CCONJ
ejpam-3756	40	61	,	,	PUNCT
ejpam-3756	40	62	(	(	PUNCT
ejpam-3756	40	63	1.10	1.10	NUM
ejpam-3756	40	64	)	)	PUNCT
ejpam-3756	40	65			NOUN
ejpam-3756	40	66	0	0	X
ejpam-3756	41	1	∈	∈	PROPN
ejpam-3756	41	2	c	c	X
ejpam-3756	41	3	,	,	PUNCT
ejpam-3756	41	4	n+1	n+1	PROPN
ejpam-3756	41	5	=	=	SYM
ejpam-3756	41	6	tkn	tkn	PROPN
ejpam-3756	41	7	,	,	PUNCT
ejpam-3756	41	8	kn	kn	PROPN
ejpam-3756	41	9	=	=	PUNCT
ejpam-3756	41	10	(	(	PUNCT
ejpam-3756	41	11	1−	1−	NUM
ejpam-3756	41	12	σ0n)tn	σ0n)tn	NOUN
ejpam-3756	41	13	+	+	CCONJ
ejpam-3756	41	14	σ0nt`n	σ0nt`n	NOUN
ejpam-3756	41	15	,	,	PUNCT
ejpam-3756	41	16	`	`	PUNCT
ejpam-3756	41	17	n	n	X
ejpam-3756	41	18	=	=	SYM
ejpam-3756	41	19	(	(	PUNCT
ejpam-3756	41	20	1−	1−	NUM
ejpam-3756	41	21	σ1n)n	σ1n)n	PROPN
ejpam-3756	41	22	+	+	CCONJ
ejpam-3756	41	23	σ1ntn	σ1ntn	NUM
ejpam-3756	41	24	,	,	PUNCT
ejpam-3756	41	25	n	n	X
ejpam-3756	41	26	∈	∈	PROPN
ejpam-3756	41	27	n	n	CCONJ
ejpam-3756	41	28	,	,	PUNCT
ejpam-3756	41	29	(	(	PUNCT
ejpam-3756	41	30	1.11	1.11	NUM
ejpam-3756	41	31	)	)	PUNCT
ejpam-3756	41	32			X
ejpam-3756	41	33	x′′0	x′′0	PUNCT
ejpam-3756	42	1	∈	∈	PROPN
ejpam-3756	42	2	c	c	PROPN
ejpam-3756	42	3	,	,	PUNCT
ejpam-3756	42	4	x′′n+1	x′′n+1	PROPN
ejpam-3756	42	5	=	=	PUNCT
ejpam-3756	42	6	ty′′n	ty′′n	PROPN
ejpam-3756	42	7	,	,	PUNCT
ejpam-3756	42	8	y′′n	y′′n	PROPN
ejpam-3756	42	9	=	=	SYM
ejpam-3756	42	10	(	(	PUNCT
ejpam-3756	42	11	1−	1−	NUM
ejpam-3756	42	12	σ0n)z′′n	σ0n)z′′n	NOUN
ejpam-3756	42	13	+	+	CCONJ
ejpam-3756	42	14	σ0ntz	σ0ntz	VERB
ejpam-3756	42	15	′′	′′	PROPN
ejpam-3756	42	16	n	n	CCONJ
ejpam-3756	42	17	,	,	PUNCT
ejpam-3756	42	18	z′′n	z′′n	PROPN
ejpam-3756	42	19	=	=	SYM
ejpam-3756	42	20	tx′′n	tx′′n	NOUN
ejpam-3756	42	21	,	,	PUNCT
ejpam-3756	42	22	n	n	PROPN
ejpam-3756	42	23	∈	∈	PROPN
ejpam-3756	42	24	n	n	CCONJ
ejpam-3756	42	25	,	,	PUNCT
ejpam-3756	42	26	(	(	PUNCT
ejpam-3756	42	27	1.12	1.12	NUM
ejpam-3756	42	28	)	)	PUNCT
ejpam-3756	42	29			NOUN
ejpam-3756	42	30	ζ0	ζ0	VERB
ejpam-3756	42	31	∈	∈	PROPN
ejpam-3756	42	32	c	c	X
ejpam-3756	42	33	,	,	PUNCT
ejpam-3756	42	34	ζn+1	ζn+1	ADJ
ejpam-3756	42	35	=	=	SYM
ejpam-3756	42	36	tηn	tηn	PROPN
ejpam-3756	42	37	,	,	PUNCT
ejpam-3756	42	38	ηn	ηn	PROPN
ejpam-3756	42	39	=	=	SYM
ejpam-3756	42	40	t	t	PROPN
ejpam-3756	42	41	(	(	PUNCT
ejpam-3756	42	42	(	(	PUNCT
ejpam-3756	42	43	1−	1−	NUM
ejpam-3756	42	44	σ0n)tζn	σ0n)tζn	NOUN
ejpam-3756	42	45	+	+	CCONJ
ejpam-3756	42	46	σ0ntθn	σ0ntθn	NUM
ejpam-3756	42	47	)	)	PUNCT
ejpam-3756	42	48	,	,	PUNCT
ejpam-3756	42	49	θn	θn	ADP
ejpam-3756	42	50	=	=	SYM
ejpam-3756	42	51	(	(	PUNCT
ejpam-3756	42	52	1−	1−	NUM
ejpam-3756	42	53	σ1n)ζn	σ1n)ζn	NOUN
ejpam-3756	42	54	+	+	CCONJ
ejpam-3756	42	55	σ1ntζn	σ1ntζn	ADJ
ejpam-3756	42	56	,	,	PUNCT
ejpam-3756	42	57	n	n	NOUN
ejpam-3756	42	58	∈	∈	PROPN
ejpam-3756	42	59	n	n	CCONJ
ejpam-3756	42	60	(	(	PUNCT
ejpam-3756	42	61	1.13	1.13	NUM
ejpam-3756	42	62	)	)	PUNCT
ejpam-3756	42	63	l.n	l.n	PROPN
ejpam-3756	42	64	mishra	mishra	PROPN
ejpam-3756	42	65	et	et	PROPN
ejpam-3756	42	66	al	al	PROPN
ejpam-3756	42	67	.	.	PUNCT
ejpam-3756	42	68	/	/	SYM
ejpam-3756	42	69	eur	eur	PROPN
ejpam-3756	42	70	.	.	PUNCT
ejpam-3756	43	1	j.	j.	PROPN
ejpam-3756	43	2	pure	pure	PROPN
ejpam-3756	43	3	appl	appl	PROPN
ejpam-3756	43	4	.	.	PROPN
ejpam-3756	43	5	math	math	PROPN
ejpam-3756	43	6	,	,	PUNCT
ejpam-3756	43	7	13	13	NUM
ejpam-3756	43	8	(	(	PUNCT
ejpam-3756	43	9	5	5	NUM
ejpam-3756	43	10	)	)	PUNCT
ejpam-3756	43	11	(	(	PUNCT
ejpam-3756	43	12	2020	2020	NUM
ejpam-3756	43	13	)	)	PUNCT
ejpam-3756	43	14	,	,	PUNCT
ejpam-3756	43	15	1110	1110	NUM
ejpam-3756	43	16	-	-	SYM
ejpam-3756	43	17	1130	1130	NUM
ejpam-3756	43	18	1113	1113	NUM
ejpam-3756	43	19			NOUN
ejpam-3756	43	20	x′0	x′0	ADP
ejpam-3756	43	21	∈	∈	PROPN
ejpam-3756	43	22	c	c	X
ejpam-3756	43	23	,	,	PUNCT
ejpam-3756	43	24	x′n+1	x′n+1	PROPN
ejpam-3756	44	1	=	=	SYM
ejpam-3756	44	2	ty′n	ty′n	PROPN
ejpam-3756	44	3	,	,	PUNCT
ejpam-3756	44	4	y′n	y′n	NOUN
ejpam-3756	44	5	=	=	PROPN
ejpam-3756	44	6	t	t	PROPN
ejpam-3756	44	7	(	(	PUNCT
ejpam-3756	44	8	(	(	PUNCT
ejpam-3756	44	9	1−	1−	NUM
ejpam-3756	44	10	σ0n)z′n	σ0n)z′n	NOUN
ejpam-3756	44	11	+	+	CCONJ
ejpam-3756	44	12	σ0ntz	σ0ntz	PROPN
ejpam-3756	44	13	′	′	NUM
ejpam-3756	44	14	n	n	CCONJ
ejpam-3756	44	15	)	)	PUNCT
ejpam-3756	44	16	,	,	PUNCT
ejpam-3756	44	17	z′n	z′n	X
ejpam-3756	44	18	=	=	SYM
ejpam-3756	44	19	(	(	PUNCT
ejpam-3756	44	20	1−	1−	NUM
ejpam-3756	44	21	σ1n)x′n	σ1n)x′n	NOUN
ejpam-3756	44	22	+	+	CCONJ
ejpam-3756	44	23	σ1ntx	σ1ntx	ADJ
ejpam-3756	44	24	′	′	NUM
ejpam-3756	44	25	n	n	CCONJ
ejpam-3756	44	26	,	,	PUNCT
ejpam-3756	44	27	n	n	CCONJ
ejpam-3756	44	28	∈	∈	PROPN
ejpam-3756	44	29	n	n	CCONJ
ejpam-3756	44	30	(	(	PUNCT
ejpam-3756	44	31	1.14	1.14	NUM
ejpam-3756	44	32	)	)	PUNCT
ejpam-3756	44	33	where	where	SCONJ
ejpam-3756	44	34	αn	αn	NOUN
ejpam-3756	44	35	,	,	PUNCT
ejpam-3756	44	36	βn	βn	ADV
ejpam-3756	44	37	∈	∈	PROPN
ejpam-3756	44	38	(	(	PUNCT
ejpam-3756	44	39	0	0	NUM
ejpam-3756	44	40	,	,	PUNCT
ejpam-3756	44	41	1	1	NUM
ejpam-3756	44	42	)	)	PUNCT
ejpam-3756	44	43	.	.	PUNCT
ejpam-3756	45	1	2	2	X
ejpam-3756	45	2	.	.	X
ejpam-3756	45	3	preliminaries	preliminary	NOUN
ejpam-3756	45	4	the	the	DET
ejpam-3756	45	5	following	follow	VERB
ejpam-3756	45	6	definitions	definition	NOUN
ejpam-3756	45	7	about	about	ADP
ejpam-3756	45	8	the	the	DET
ejpam-3756	45	9	rate	rate	NOUN
ejpam-3756	45	10	of	of	ADP
ejpam-3756	45	11	convergence	convergence	NOUN
ejpam-3756	45	12	are	be	AUX
ejpam-3756	45	13	due	due	ADJ
ejpam-3756	45	14	to	to	ADP
ejpam-3756	45	15	berinde	berinde	NOUN
ejpam-3756	45	16	[	[	X
ejpam-3756	45	17	2	2	NUM
ejpam-3756	45	18	]	]	PUNCT
ejpam-3756	45	19	.	.	PUNCT
ejpam-3756	46	1	definition	definition	NOUN
ejpam-3756	46	2	1	1	NUM
ejpam-3756	46	3	.	.	PUNCT
ejpam-3756	47	1	let	let	VERB
ejpam-3756	47	2	{	{	PUNCT
ejpam-3756	47	3	an}∞n=0	an}∞n=0	X
ejpam-3756	47	4	and	and	CCONJ
ejpam-3756	47	5	{	{	PUNCT
ejpam-3756	47	6	bn}∞n=0	bn}∞n=0	NUM
ejpam-3756	47	7	be	be	AUX
ejpam-3756	47	8	two	two	NUM
ejpam-3756	47	9	sequences	sequence	NOUN
ejpam-3756	47	10	of	of	ADP
ejpam-3756	47	11	real	real	ADJ
ejpam-3756	47	12	numbers	number	NOUN
ejpam-3756	47	13	with	with	ADP
ejpam-3756	47	14	limits	limit	NOUN
ejpam-3756	47	15	a	a	PRON
ejpam-3756	47	16	and	and	CCONJ
ejpam-3756	47	17	c	c	NOUN
ejpam-3756	47	18	,	,	PUNCT
ejpam-3756	47	19	respectively	respectively	ADV
ejpam-3756	47	20	.	.	PUNCT
ejpam-3756	48	1	assume	assume	VERB
ejpam-3756	48	2	that	that	SCONJ
ejpam-3756	48	3	there	there	PRON
ejpam-3756	48	4	exists	exist	VERB
ejpam-3756	48	5	lim	lim	PROPN
ejpam-3756	48	6	n→∞	n→∞	X
ejpam-3756	48	7	|an	|an	X
ejpam-3756	48	8	−	−	PROPN
ejpam-3756	48	9	a|	a|	PROPN
ejpam-3756	48	10	|bn	|bn	NUM
ejpam-3756	49	1	−	−	NOUN
ejpam-3756	49	2	b|	b|	PROPN
ejpam-3756	49	3	=	=	PUNCT
ejpam-3756	49	4	`	`	PUNCT
ejpam-3756	49	5	,	,	PUNCT
ejpam-3756	49	6	(	(	PUNCT
ejpam-3756	49	7	1.15	1.15	NUM
ejpam-3756	49	8	)	)	PUNCT
ejpam-3756	49	9	(	(	PUNCT
ejpam-3756	49	10	i	i	NOUN
ejpam-3756	49	11	)	)	PUNCT
ejpam-3756	49	12	if	if	SCONJ
ejpam-3756	49	13	`	`	PUNCT
ejpam-3756	49	14	=	=	SYM
ejpam-3756	49	15	0	0	NUM
ejpam-3756	49	16	,	,	PUNCT
ejpam-3756	49	17	then	then	ADV
ejpam-3756	49	18	we	we	PRON
ejpam-3756	49	19	say	say	VERB
ejpam-3756	49	20	that	that	SCONJ
ejpam-3756	49	21	{	{	PUNCT
ejpam-3756	49	22	an}∞n=0	an}∞n=0	X
ejpam-3756	49	23	converges	converge	VERB
ejpam-3756	49	24	faster	fast	ADV
ejpam-3756	49	25	to	to	ADP
ejpam-3756	49	26	a	a	DET
ejpam-3756	49	27	than	than	ADP
ejpam-3756	49	28	{	{	PUNCT
ejpam-3756	49	29	bn}∞n=0	bn}∞n=0	NUM
ejpam-3756	49	30	to	to	ADP
ejpam-3756	49	31	c.	c.	PROPN
ejpam-3756	49	32	(	(	PUNCT
ejpam-3756	49	33	ii	ii	PROPN
ejpam-3756	49	34	)	)	PUNCT
ejpam-3756	49	35	if	if	SCONJ
ejpam-3756	49	36	0	0	NUM
ejpam-3756	49	37	<	<	X
ejpam-3756	49	38	`	`	PUNCT
ejpam-3756	49	39	<	<	X
ejpam-3756	49	40	∞	∞	PROPN
ejpam-3756	49	41	,	,	PUNCT
ejpam-3756	49	42	then	then	ADV
ejpam-3756	49	43	we	we	PRON
ejpam-3756	49	44	say	say	VERB
ejpam-3756	49	45	that	that	SCONJ
ejpam-3756	49	46	{	{	PUNCT
ejpam-3756	49	47	an}∞n=0	an}∞n=0	X
ejpam-3756	49	48	and	and	CCONJ
ejpam-3756	49	49	{	{	PUNCT
ejpam-3756	49	50	bn}∞n=0	bn}∞n=0	X
ejpam-3756	49	51	have	have	VERB
ejpam-3756	49	52	the	the	DET
ejpam-3756	49	53	same	same	ADJ
ejpam-3756	49	54	rate	rate	NOUN
ejpam-3756	49	55	of	of	ADP
ejpam-3756	49	56	convergence	convergence	NOUN
ejpam-3756	49	57	.	.	PUNCT
ejpam-3756	50	1	definition	definition	NOUN
ejpam-3756	50	2	2	2	NUM
ejpam-3756	50	3	.	.	PUNCT
ejpam-3756	50	4	suppose	suppose	VERB
ejpam-3756	50	5	that	that	SCONJ
ejpam-3756	50	6	for	for	ADP
ejpam-3756	50	7	two	two	NUM
ejpam-3756	50	8	fixed	fix	VERB
ejpam-3756	50	9	point	point	NOUN
ejpam-3756	50	10	iteration	iteration	NOUN
ejpam-3756	50	11	processes	process	NOUN
ejpam-3756	50	12	{	{	PUNCT
ejpam-3756	50	13	un}∞n=0	un}∞n=0	VERB
ejpam-3756	50	14	and	and	CCONJ
ejpam-3756	50	15	{	{	PUNCT
ejpam-3756	50	16	vn}∞n=0	vn}∞n=0	X
ejpam-3756	50	17	both	both	PRON
ejpam-3756	50	18	converging	converge	VERB
ejpam-3756	50	19	to	to	ADP
ejpam-3756	50	20	the	the	DET
ejpam-3756	50	21	same	same	ADJ
ejpam-3756	50	22	fixed	fix	VERB
ejpam-3756	50	23	point	point	NOUN
ejpam-3756	50	24	p	p	NOUN
ejpam-3756	50	25	,	,	PUNCT
ejpam-3756	50	26	the	the	DET
ejpam-3756	50	27	following	follow	VERB
ejpam-3756	50	28	error	error	NOUN
ejpam-3756	50	29	estimates	estimate	VERB
ejpam-3756	50	30	‖un	‖un	PROPN
ejpam-3756	50	31	−	−	PROPN
ejpam-3756	50	32	p‖	p‖	NOUN
ejpam-3756	50	33	≤	≤	PUNCT
ejpam-3756	50	34	an	an	DET
ejpam-3756	50	35	(	(	PUNCT
ejpam-3756	50	36	1.16	1.16	NUM
ejpam-3756	50	37	)	)	PUNCT
ejpam-3756	50	38	for	for	ADP
ejpam-3756	50	39	all	all	PRON
ejpam-3756	50	40	n	n	PRON
ejpam-3756	50	41	∈	∈	PROPN
ejpam-3756	50	42	n	n	CCONJ
ejpam-3756	50	43	‖vn	‖vn	PROPN
ejpam-3756	50	44	−	−	PROPN
ejpam-3756	50	45	p‖	p‖	NOUN
ejpam-3756	50	46	≤	≤	NUM
ejpam-3756	50	47	bn	bn	PROPN
ejpam-3756	50	48	(	(	PUNCT
ejpam-3756	50	49	1.17	1.17	NUM
ejpam-3756	50	50	)	)	PUNCT
ejpam-3756	50	51	for	for	ADP
ejpam-3756	50	52	all	all	DET
ejpam-3756	50	53	n	n	PRON
ejpam-3756	50	54	∈	∈	PROPN
ejpam-3756	50	55	n	n	CCONJ
ejpam-3756	50	56	,	,	PUNCT
ejpam-3756	50	57	are	be	AUX
ejpam-3756	50	58	available	available	ADJ
ejpam-3756	50	59	where	where	SCONJ
ejpam-3756	50	60	{	{	PUNCT
ejpam-3756	50	61	an}∞n=0	an}∞n=0	X
ejpam-3756	50	62	and	and	CCONJ
ejpam-3756	50	63	{	{	PUNCT
ejpam-3756	50	64	bn}∞n=0	bn}∞n=0	NUM
ejpam-3756	50	65	are	be	AUX
ejpam-3756	50	66	two	two	NUM
ejpam-3756	50	67	sequences	sequence	NOUN
ejpam-3756	50	68	of	of	ADP
ejpam-3756	50	69	positive	positive	ADJ
ejpam-3756	50	70	numbers	number	NOUN
ejpam-3756	50	71	(	(	PUNCT
ejpam-3756	50	72	converging	converge	VERB
ejpam-3756	50	73	to	to	ADP
ejpam-3756	50	74	zero	zero	NUM
ejpam-3756	50	75	)	)	PUNCT
ejpam-3756	50	76	.	.	PUNCT
ejpam-3756	51	1	if	if	SCONJ
ejpam-3756	51	2	{	{	PUNCT
ejpam-3756	51	3	an}∞n=0	an}∞n=0	X
ejpam-3756	51	4	converges	converge	VERB
ejpam-3756	51	5	faster	fast	ADV
ejpam-3756	51	6	than	than	ADP
ejpam-3756	51	7	{	{	PUNCT
ejpam-3756	51	8	bn}∞n=0	bn}∞n=0	NUM
ejpam-3756	51	9	,	,	PUNCT
ejpam-3756	51	10	then	then	ADV
ejpam-3756	51	11	{	{	PUNCT
ejpam-3756	51	12	un}∞n=0	un}∞n=0	X
ejpam-3756	51	13	converges	converge	VERB
ejpam-3756	51	14	faster	fast	ADV
ejpam-3756	51	15	than	than	ADP
ejpam-3756	51	16	{	{	PUNCT
ejpam-3756	51	17	vn}∞n=0	vn}∞n=0	X
ejpam-3756	51	18	to	to	AUX
ejpam-3756	51	19	p.	p.	VERB
ejpam-3756	51	20	recent	recent	ADJ
ejpam-3756	51	21	study	study	NOUN
ejpam-3756	51	22	of	of	ADP
ejpam-3756	51	23	ullah	ullah	PROPN
ejpam-3756	51	24	and	and	CCONJ
ejpam-3756	51	25	muhammad	muhammad	PROPN
ejpam-3756	51	26	(	(	PUNCT
ejpam-3756	51	27	1.14	1.14	NUM
ejpam-3756	51	28	)	)	PUNCT
ejpam-3756	51	29	,	,	PUNCT
ejpam-3756	51	30	hussin	hussin	PROPN
ejpam-3756	51	31	et	et	PROPN
ejpam-3756	51	32	.	.	PUNCT
ejpam-3756	52	1	al	al	PROPN
ejpam-3756	52	2	.	.	PUNCT
ejpam-3756	53	1	(	(	PUNCT
ejpam-3756	53	2	1.13	1.13	NUM
ejpam-3756	53	3	)	)	PUNCT
ejpam-3756	53	4	proved	prove	VERB
ejpam-3756	53	5	that	that	SCONJ
ejpam-3756	53	6	their	their	PRON
ejpam-3756	53	7	iterative	iterative	NOUN
ejpam-3756	53	8	methods	method	NOUN
ejpam-3756	53	9	converges	converge	VERB
ejpam-3756	53	10	faster	fast	ADV
ejpam-3756	53	11	than	than	ADP
ejpam-3756	53	12	all	all	DET
ejpam-3756	53	13	the	the	DET
ejpam-3756	53	14	above	above	ADJ
ejpam-3756	53	15	mentioned	mention	VERB
ejpam-3756	53	16	iterative	iterative	NOUN
ejpam-3756	53	17	methods	method	NOUN
ejpam-3756	53	18	for	for	ADP
ejpam-3756	53	19	a	a	DET
ejpam-3756	53	20	different	different	ADJ
ejpam-3756	53	21	class	class	NOUN
ejpam-3756	53	22	of	of	ADP
ejpam-3756	53	23	mappings	mapping	NOUN
ejpam-3756	53	24	which	which	PRON
ejpam-3756	53	25	include	include	VERB
ejpam-3756	53	26	the	the	DET
ejpam-3756	53	27	aforementioned	aforementioned	ADJ
ejpam-3756	53	28	class	class	NOUN
ejpam-3756	53	29	of	of	ADP
ejpam-3756	53	30	contraction	contraction	NOUN
ejpam-3756	53	31	operators	operator	NOUN
ejpam-3756	53	32	.	.	PUNCT
ejpam-3756	54	1	now	now	ADV
ejpam-3756	54	2	,	,	PUNCT
ejpam-3756	54	3	the	the	DET
ejpam-3756	54	4	question	question	NOUN
ejpam-3756	54	5	arises	arise	VERB
ejpam-3756	54	6	whether	whether	SCONJ
ejpam-3756	54	7	it	it	PRON
ejpam-3756	54	8	is	be	AUX
ejpam-3756	54	9	possible	possible	ADJ
ejpam-3756	54	10	to	to	PART
ejpam-3756	54	11	find	find	VERB
ejpam-3756	54	12	scheme	scheme	NOUN
ejpam-3756	54	13	which	which	PRON
ejpam-3756	54	14	is	be	AUX
ejpam-3756	54	15	faster	fast	ADJ
ejpam-3756	54	16	than	than	ADP
ejpam-3756	54	17	k∗.	k∗.	PROPN
ejpam-3756	54	18	inspired	inspire	VERB
ejpam-3756	54	19	by	by	ADP
ejpam-3756	54	20	the	the	DET
ejpam-3756	54	21	works	work	NOUN
ejpam-3756	54	22	mentioned	mention	VERB
ejpam-3756	54	23	above	above	ADV
ejpam-3756	54	24	,	,	PUNCT
ejpam-3756	54	25	we	we	PRON
ejpam-3756	54	26	introduce	introduce	VERB
ejpam-3756	54	27	the	the	DET
ejpam-3756	54	28	following	follow	VERB
ejpam-3756	54	29	iteration	iteration	NOUN
ejpam-3756	54	30	method	method	NOUN
ejpam-3756	54	31	l.n	l.n	PROPN
ejpam-3756	54	32	mishra	mishra	PROPN
ejpam-3756	54	33	et	et	PROPN
ejpam-3756	54	34	al	al	PROPN
ejpam-3756	54	35	.	.	PUNCT
ejpam-3756	54	36	/	/	SYM
ejpam-3756	54	37	eur	eur	PROPN
ejpam-3756	54	38	.	.	PUNCT
ejpam-3756	55	1	j.	j.	PROPN
ejpam-3756	55	2	pure	pure	PROPN
ejpam-3756	55	3	appl	appl	PROPN
ejpam-3756	55	4	.	.	PROPN
ejpam-3756	55	5	math	math	PROPN
ejpam-3756	55	6	,	,	PUNCT
ejpam-3756	55	7	13	13	NUM
ejpam-3756	55	8	(	(	PUNCT
ejpam-3756	55	9	5	5	NUM
ejpam-3756	55	10	)	)	PUNCT
ejpam-3756	55	11	(	(	PUNCT
ejpam-3756	55	12	2020	2020	NUM
ejpam-3756	55	13	)	)	PUNCT
ejpam-3756	55	14	,	,	PUNCT
ejpam-3756	55	15	1110	1110	NUM
ejpam-3756	55	16	-	-	SYM
ejpam-3756	55	17	1130	1130	NUM
ejpam-3756	55	18	1114	1114	NUM
ejpam-3756	55	19	namely	namely	ADV
ejpam-3756	55	20	nv	nv	PROPN
ejpam-3756	55	21	1	1	NUM
ejpam-3756	55	22	iteration	iteration	NOUN
ejpam-3756	55	23	:	:	PUNCT
ejpam-3756	56	1			X
ejpam-3756	56	2	ζ0	ζ0	PROPN
ejpam-3756	56	3	∈	∈	PROPN
ejpam-3756	56	4	c	c	X
ejpam-3756	56	5	,	,	PUNCT
ejpam-3756	56	6	θn	θn	PROPN
ejpam-3756	56	7	=	=	PROPN
ejpam-3756	56	8	t	t	PROPN
ejpam-3756	56	9	(	(	PUNCT
ejpam-3756	56	10	(	(	PUNCT
ejpam-3756	56	11	1−	1−	NUM
ejpam-3756	56	12	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	56	13	+	+	CCONJ
ejpam-3756	56	14	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	56	15	)	)	PUNCT
ejpam-3756	56	16	,	,	PUNCT
ejpam-3756	56	17	ηn	ηn	PROPN
ejpam-3756	56	18	=	=	PUNCT
ejpam-3756	56	19	tθn	tθn	PROPN
ejpam-3756	56	20	,	,	PUNCT
ejpam-3756	56	21	ζn+1	ζn+1	ADJ
ejpam-3756	56	22	=	=	SYM
ejpam-3756	56	23	tηn	tηn	PROPN
ejpam-3756	56	24	,	,	PUNCT
ejpam-3756	56	25	n	n	PROPN
ejpam-3756	56	26	∈	∈	PROPN
ejpam-3756	56	27	n	n	CCONJ
ejpam-3756	56	28	,	,	PUNCT
ejpam-3756	56	29	(	(	PUNCT
ejpam-3756	56	30	1.18	1.18	NUM
ejpam-3756	56	31	)	)	PUNCT
ejpam-3756	56	32	let	let	VERB
ejpam-3756	56	33	e	e	PRON
ejpam-3756	56	34	be	be	AUX
ejpam-3756	56	35	a	a	DET
ejpam-3756	56	36	banach	banach	NOUN
ejpam-3756	56	37	space	space	NOUN
ejpam-3756	56	38	and	and	CCONJ
ejpam-3756	56	39	c	c	PROPN
ejpam-3756	56	40	be	be	AUX
ejpam-3756	56	41	a	a	DET
ejpam-3756	56	42	nonempty	nonempty	ADV
ejpam-3756	56	43	closed	close	VERB
ejpam-3756	56	44	convex	convex	NOUN
ejpam-3756	56	45	subset	subset	NOUN
ejpam-3756	56	46	of	of	ADP
ejpam-3756	56	47	e.	e.	PROPN
ejpam-3756	56	48	let	let	AUX
ejpam-3756	56	49	{	{	PUNCT
ejpam-3756	56	50	xn	xn	VERB
ejpam-3756	56	51	}	}	PUNCT
ejpam-3756	56	52	be	be	AUX
ejpam-3756	56	53	a	a	DET
ejpam-3756	56	54	bounded	bounded	ADJ
ejpam-3756	56	55	sequence	sequence	NOUN
ejpam-3756	56	56	in	in	ADP
ejpam-3756	56	57	c.	c.	NOUN
ejpam-3756	56	58	for	for	ADP
ejpam-3756	56	59	x	x	PROPN
ejpam-3756	56	60	∈	∈	PROPN
ejpam-3756	56	61	e	e	NOUN
ejpam-3756	56	62	,	,	PUNCT
ejpam-3756	56	63	set	set	VERB
ejpam-3756	56	64	r(x	r(x	PROPN
ejpam-3756	56	65	,	,	PUNCT
ejpam-3756	56	66	{	{	PUNCT
ejpam-3756	56	67	xn	xn	NOUN
ejpam-3756	56	68	}	}	PUNCT
ejpam-3756	56	69	)	)	PUNCT
ejpam-3756	57	1	=	=	SYM
ejpam-3756	57	2	lim	lim	PROPN
ejpam-3756	57	3	sup	sup	NOUN
ejpam-3756	57	4	n→∞	n→∞	X
ejpam-3756	58	1	||x−	||x−	NOUN
ejpam-3756	58	2	xn||	xn||	PROPN
ejpam-3756	58	3	.	.	PUNCT
ejpam-3756	59	1	the	the	DET
ejpam-3756	59	2	asymptotic	asymptotic	ADJ
ejpam-3756	59	3	radius	radius	NOUN
ejpam-3756	59	4	of	of	ADP
ejpam-3756	59	5	{	{	PUNCT
ejpam-3756	59	6	xn	xn	PROPN
ejpam-3756	59	7	}	}	PUNCT
ejpam-3756	59	8	relative	relative	ADJ
ejpam-3756	59	9	to	to	ADP
ejpam-3756	59	10	c	c	PROPN
ejpam-3756	59	11	is	be	AUX
ejpam-3756	59	12	given	give	VERB
ejpam-3756	59	13	by	by	ADP
ejpam-3756	59	14	r(c	r(c	PROPN
ejpam-3756	59	15	,	,	PUNCT
ejpam-3756	59	16	{	{	PUNCT
ejpam-3756	59	17	xn	xn	NOUN
ejpam-3756	59	18	}	}	PUNCT
ejpam-3756	59	19	)	)	PUNCT
ejpam-3756	60	1	=	=	SYM
ejpam-3756	60	2	inf{r(x	inf{r(x	PROPN
ejpam-3756	60	3	,	,	PUNCT
ejpam-3756	60	4	{	{	PUNCT
ejpam-3756	60	5	xn	xn	NOUN
ejpam-3756	60	6	}	}	PUNCT
ejpam-3756	60	7	)	)	PUNCT
ejpam-3756	60	8	:	:	PUNCT
ejpam-3756	61	1	x	x	X
ejpam-3756	61	2	∈	∈	NOUN
ejpam-3756	61	3	c	c	NOUN
ejpam-3756	61	4	}	}	PUNCT
ejpam-3756	61	5	.	.	PUNCT
ejpam-3756	62	1	the	the	DET
ejpam-3756	62	2	asymptotic	asymptotic	ADJ
ejpam-3756	62	3	centre	centre	NOUN
ejpam-3756	62	4	of	of	ADP
ejpam-3756	62	5	{	{	PUNCT
ejpam-3756	62	6	xn	xn	NOUN
ejpam-3756	62	7	}	}	PUNCT
ejpam-3756	62	8	relative	relative	ADJ
ejpam-3756	62	9	to	to	ADP
ejpam-3756	62	10	c	c	PROPN
ejpam-3756	62	11	is	be	AUX
ejpam-3756	62	12	the	the	DET
ejpam-3756	62	13	set	set	NOUN
ejpam-3756	62	14	a(c	a(c	NOUN
ejpam-3756	62	15	,	,	PUNCT
ejpam-3756	62	16	{	{	PUNCT
ejpam-3756	62	17	xn	xn	NOUN
ejpam-3756	62	18	}	}	PUNCT
ejpam-3756	62	19	)	)	PUNCT
ejpam-3756	63	1	=	=	PRON
ejpam-3756	63	2	{	{	PUNCT
ejpam-3756	63	3	x	x	PUNCT
ejpam-3756	63	4	∈	∈	PROPN
ejpam-3756	63	5	c	c	NOUN
ejpam-3756	63	6	:	:	PUNCT
ejpam-3756	63	7	r(x	r(x	NOUN
ejpam-3756	63	8	,	,	PUNCT
ejpam-3756	63	9	{	{	PUNCT
ejpam-3756	63	10	xn	xn	NOUN
ejpam-3756	63	11	}	}	PUNCT
ejpam-3756	63	12	)	)	PUNCT
ejpam-3756	63	13	=	=	PUNCT
ejpam-3756	64	1	r(c	r(c	X
ejpam-3756	64	2	,	,	PUNCT
ejpam-3756	64	3	{	{	PUNCT
ejpam-3756	64	4	xn	xn	NOUN
ejpam-3756	64	5	}	}	PUNCT
ejpam-3756	64	6	)	)	PUNCT
ejpam-3756	64	7	}	}	PUNCT
ejpam-3756	64	8	.	.	PUNCT
ejpam-3756	65	1	it	it	PRON
ejpam-3756	65	2	is	be	AUX
ejpam-3756	65	3	well	well	ADV
ejpam-3756	65	4	-	-	PUNCT
ejpam-3756	65	5	known	know	VERB
ejpam-3756	65	6	that	that	SCONJ
ejpam-3756	65	7	in	in	ADP
ejpam-3756	65	8	a	a	DET
ejpam-3756	65	9	uniformly	uniformly	ADJ
ejpam-3756	65	10	convex	convex	NOUN
ejpam-3756	65	11	banach	banach	NOUN
ejpam-3756	65	12	spaces	space	NOUN
ejpam-3756	65	13	,	,	PUNCT
ejpam-3756	65	14	a(c	a(c	PROPN
ejpam-3756	65	15	,	,	PUNCT
ejpam-3756	65	16	xn	xn	NUM
ejpam-3756	65	17	)	)	PUNCT
ejpam-3756	65	18	consists	consist	VERB
ejpam-3756	65	19	of	of	ADP
ejpam-3756	65	20	exactly	exactly	ADV
ejpam-3756	65	21	one	one	NUM
ejpam-3756	65	22	point	point	NOUN
ejpam-3756	65	23	.	.	PUNCT
ejpam-3756	66	1	also	also	ADV
ejpam-3756	66	2	,	,	PUNCT
ejpam-3756	66	3	a(c	a(c	PROPN
ejpam-3756	66	4	,	,	PUNCT
ejpam-3756	66	5	xn	xn	NUM
ejpam-3756	66	6	)	)	PUNCT
ejpam-3756	66	7	is	be	AUX
ejpam-3756	66	8	nonempty	nonempty	ADJ
ejpam-3756	66	9	and	and	CCONJ
ejpam-3756	66	10	convex	convex	VERB
ejpam-3756	66	11	in	in	ADP
ejpam-3756	66	12	the	the	DET
ejpam-3756	66	13	case	case	NOUN
ejpam-3756	66	14	when	when	SCONJ
ejpam-3756	66	15	c	c	NOUN
ejpam-3756	66	16	is	be	AUX
ejpam-3756	66	17	weakly	weakly	ADV
ejpam-3756	66	18	compact	compact	ADJ
ejpam-3756	66	19	and	and	CCONJ
ejpam-3756	66	20	convex	convex	NOUN
ejpam-3756	66	21	,	,	PUNCT
ejpam-3756	66	22	see	see	VERB
ejpam-3756	66	23	e.g.	e.g.	ADV
ejpam-3756	66	24	,	,	PUNCT
ejpam-3756	66	25	[	[	X
ejpam-3756	66	26	14	14	NUM
ejpam-3756	66	27	,	,	PUNCT
ejpam-3756	66	28	17	17	NUM
ejpam-3756	66	29	]	]	PUNCT
ejpam-3756	66	30	.	.	PUNCT
ejpam-3756	67	1	following	follow	VERB
ejpam-3756	67	2	are	be	AUX
ejpam-3756	67	3	some	some	DET
ejpam-3756	67	4	basic	basic	ADJ
ejpam-3756	67	5	definitions	definition	NOUN
ejpam-3756	67	6	and	and	CCONJ
ejpam-3756	67	7	results	result	NOUN
ejpam-3756	67	8	.	.	PUNCT
ejpam-3756	68	1	definition	definition	NOUN
ejpam-3756	68	2	3	3	NUM
ejpam-3756	68	3	.	.	PUNCT
ejpam-3756	69	1	a	a	DET
ejpam-3756	69	2	banach	banach	NOUN
ejpam-3756	69	3	space	space	NOUN
ejpam-3756	69	4	e	e	NOUN
ejpam-3756	69	5	is	be	AUX
ejpam-3756	69	6	said	say	VERB
ejpam-3756	69	7	to	to	PART
ejpam-3756	69	8	be	be	AUX
ejpam-3756	69	9	uniformly	uniformly	ADV
ejpam-3756	69	10	convex	convex	ADJ
ejpam-3756	69	11	if	if	SCONJ
ejpam-3756	69	12	for	for	ADP
ejpam-3756	69	13	each	each	DET
ejpam-3756	69	14	ε	ε	PROPN
ejpam-3756	69	15	∈	∈	PROPN
ejpam-3756	69	16	(	(	PUNCT
ejpam-3756	69	17	0	0	NUM
ejpam-3756	69	18	,	,	PUNCT
ejpam-3756	69	19	2	2	NUM
ejpam-3756	69	20	]	]	PUNCT
ejpam-3756	69	21	,	,	PUNCT
ejpam-3756	69	22	there	there	PRON
ejpam-3756	69	23	is	be	VERB
ejpam-3756	69	24	a	a	DET
ejpam-3756	69	25	λ	λ	X
ejpam-3756	69	26	>	>	X
ejpam-3756	69	27	0	0	NUM
ejpam-3756	69	28	such	such	ADJ
ejpam-3756	69	29	that	that	PRON
ejpam-3756	69	30	for	for	ADP
ejpam-3756	69	31	every	every	DET
ejpam-3756	69	32	x	x	NOUN
ejpam-3756	69	33	,	,	PUNCT
ejpam-3756	69	34	y	y	PROPN
ejpam-3756	69	35	∈	∈	PROPN
ejpam-3756	69	36	e	e	NOUN
ejpam-3756	69	37	,	,	PUNCT
ejpam-3756	69	38	||x||	||x||	ADV
ejpam-3756	69	39	≤	≤	NOUN
ejpam-3756	69	40	1	1	NUM
ejpam-3756	69	41	||y||	||y||	X
ejpam-3756	69	42	≤	≤	NUM
ejpam-3756	70	1	1	1	NUM
ejpam-3756	70	2	||x−	||x−	PROPN
ejpam-3756	70	3	y||	y||	NOUN
ejpam-3756	70	4	>	>	X
ejpam-3756	70	5	ε	ε	PROPN
ejpam-3756	71	1			NOUN
ejpam-3756	71	2	=	=	SYM
ejpam-3756	71	3	⇒	⇒	ADJ
ejpam-3756	71	4	1	1	NUM
ejpam-3756	71	5	2	2	NUM
ejpam-3756	71	6	||x+	||x+	NUM
ejpam-3756	71	7	y||	y||	NOUN
ejpam-3756	71	8	≤	≤	NOUN
ejpam-3756	71	9	(	(	PUNCT
ejpam-3756	71	10	1−	1−	NUM
ejpam-3756	71	11	λ	λ	NOUN
ejpam-3756	71	12	)	)	PUNCT
ejpam-3756	71	13	.	.	PUNCT
ejpam-3756	72	1	definition	definition	NOUN
ejpam-3756	72	2	4	4	NUM
ejpam-3756	72	3	.	.	PUNCT
ejpam-3756	73	1	[	[	X
ejpam-3756	73	2	11	11	NUM
ejpam-3756	73	3	]	]	X
ejpam-3756	73	4	a	a	DET
ejpam-3756	73	5	banach	banach	NOUN
ejpam-3756	73	6	space	space	NOUN
ejpam-3756	73	7	e	e	NOUN
ejpam-3756	73	8	is	be	AUX
ejpam-3756	73	9	said	say	VERB
ejpam-3756	73	10	to	to	PART
ejpam-3756	73	11	have	have	VERB
ejpam-3756	73	12	opial	opial	NOUN
ejpam-3756	73	13	’s	’s	PART
ejpam-3756	73	14	property	property	NOUN
ejpam-3756	73	15	if	if	SCONJ
ejpam-3756	73	16	for	for	ADP
ejpam-3756	73	17	each	each	DET
ejpam-3756	73	18	sequence	sequence	NOUN
ejpam-3756	73	19	{	{	PUNCT
ejpam-3756	73	20	xn	xn	NOUN
ejpam-3756	73	21	}	}	PUNCT
ejpam-3756	73	22	in	in	ADP
ejpam-3756	73	23	e	e	NOUN
ejpam-3756	73	24	which	which	PRON
ejpam-3756	73	25	weakly	weakly	ADJ
ejpam-3756	73	26	converges	converge	VERB
ejpam-3756	73	27	to	to	ADP
ejpam-3756	73	28	x	x	SYM
ejpam-3756	73	29	∈	∈	PROPN
ejpam-3756	73	30	e	e	NOUN
ejpam-3756	73	31	and	and	CCONJ
ejpam-3756	73	32	for	for	ADP
ejpam-3756	73	33	every	every	DET
ejpam-3756	73	34	y	y	PROPN
ejpam-3756	73	35	∈	∈	PROPN
ejpam-3756	73	36	e	e	NOUN
ejpam-3756	73	37	,	,	PUNCT
ejpam-3756	73	38	it	it	PRON
ejpam-3756	73	39	follows	follow	VERB
ejpam-3756	73	40	the	the	DET
ejpam-3756	73	41	following	follow	VERB
ejpam-3756	73	42	lim	lim	PROPN
ejpam-3756	73	43	sup	sup	VERB
ejpam-3756	73	44	n→∞	n→∞	NUM
ejpam-3756	73	45	||xn	||xn	NOUN
ejpam-3756	73	46	−	−	NOUN
ejpam-3756	73	47	x||	x||	PROPN
ejpam-3756	74	1	<	<	X
ejpam-3756	74	2	lim	lim	PROPN
ejpam-3756	74	3	sup	sup	X
ejpam-3756	74	4	n→∞	n→∞	NUM
ejpam-3756	74	5	||xn	||xn	NOUN
ejpam-3756	74	6	−	−	NOUN
ejpam-3756	74	7	y||	y||	PROPN
ejpam-3756	74	8	.	.	PUNCT
ejpam-3756	75	1	definition	definition	NOUN
ejpam-3756	75	2	5	5	NUM
ejpam-3756	75	3	.	.	PUNCT
ejpam-3756	76	1	let	let	VERB
ejpam-3756	76	2	e	e	NOUN
ejpam-3756	76	3	and	and	CCONJ
ejpam-3756	76	4	e	e	X
ejpam-3756	76	5	′	′	NOUN
ejpam-3756	76	6	be	be	AUX
ejpam-3756	76	7	two	two	NUM
ejpam-3756	76	8	banach	banach	NOUN
ejpam-3756	76	9	spaces	space	NOUN
ejpam-3756	76	10	and	and	CCONJ
ejpam-3756	76	11	let	let	VERB
ejpam-3756	76	12	t	t	NOUN
ejpam-3756	76	13	:	:	PUNCT
ejpam-3756	77	1	e	e	X
ejpam-3756	77	2	−→	−→	NOUN
ejpam-3756	77	3	e	e	NOUN
ejpam-3756	77	4	′	′	NOUN
ejpam-3756	77	5	.	.	PUNCT
ejpam-3756	78	1	then	then	ADV
ejpam-3756	78	2	the	the	DET
ejpam-3756	78	3	mapping	mapping	NOUN
ejpam-3756	78	4	t	t	PROPN
ejpam-3756	78	5	is	be	AUX
ejpam-3756	78	6	said	say	VERB
ejpam-3756	78	7	to	to	PART
ejpam-3756	78	8	be	be	AUX
ejpam-3756	78	9	demiclosed	demiclose	VERB
ejpam-3756	78	10	if	if	SCONJ
ejpam-3756	78	11	x	x	X
ejpam-3756	78	12	⇀	⇀	PUNCT
ejpam-3756	78	13	x	x	PUNCT
ejpam-3756	78	14	∈	∈	NOUN
ejpam-3756	78	15	e	e	NOUN
ejpam-3756	78	16	and	and	CCONJ
ejpam-3756	78	17	txn	txn	VERB
ejpam-3756	79	1	⇀	⇀	NUM
ejpam-3756	80	1	y	y	NOUN
ejpam-3756	80	2	in	in	ADP
ejpam-3756	80	3	e	e	NOUN
ejpam-3756	81	1	′	′	NUM
ejpam-3756	81	2	imply	imply	VERB
ejpam-3756	81	3	tx	tx	PROPN
ejpam-3756	82	1	=	=	PUNCT
ejpam-3756	82	2	y.	y.	PROPN
ejpam-3756	82	3	lemma	lemma	PROPN
ejpam-3756	82	4	1	1	X
ejpam-3756	82	5	.	.	PUNCT
ejpam-3756	83	1	let	let	VERB
ejpam-3756	83	2	c	c	PRON
ejpam-3756	83	3	be	be	AUX
ejpam-3756	83	4	a	a	DET
ejpam-3756	83	5	non	non	ADJ
ejpam-3756	83	6	-	-	ADJ
ejpam-3756	83	7	empty	empty	ADJ
ejpam-3756	83	8	closed	closed	ADJ
ejpam-3756	83	9	convex	convex	NOUN
ejpam-3756	83	10	subset	subset	NOUN
ejpam-3756	83	11	of	of	ADP
ejpam-3756	83	12	a	a	DET
ejpam-3756	83	13	uniformly	uniformly	ADJ
ejpam-3756	83	14	convex	convex	NOUN
ejpam-3756	83	15	banach	banach	NOUN
ejpam-3756	83	16	space	space	NOUN
ejpam-3756	83	17	e	e	NOUN
ejpam-3756	83	18	and	and	CCONJ
ejpam-3756	83	19	t	t	PROPN
ejpam-3756	83	20	be	be	AUX
ejpam-3756	83	21	a	a	DET
ejpam-3756	83	22	non	non	ADJ
ejpam-3756	83	23	-	-	ADJ
ejpam-3756	83	24	expansive	expansive	ADJ
ejpam-3756	83	25	on	on	ADP
ejpam-3756	83	26	c.	c.	PROPN
ejpam-3756	84	1	then	then	ADV
ejpam-3756	84	2	i	i	PRON
ejpam-3756	84	3	−	−	PROPN
ejpam-3756	84	4	t	t	PROPN
ejpam-3756	84	5	is	be	AUX
ejpam-3756	84	6	demiclosed	demiclose	VERB
ejpam-3756	84	7	at	at	ADP
ejpam-3756	84	8	0	0	NUM
ejpam-3756	84	9	.	.	PUNCT
ejpam-3756	85	1	l.n	l.n	PROPN
ejpam-3756	85	2	mishra	mishra	PROPN
ejpam-3756	85	3	et	et	PROPN
ejpam-3756	85	4	al	al	PROPN
ejpam-3756	85	5	.	.	PUNCT
ejpam-3756	85	6	/	/	SYM
ejpam-3756	85	7	eur	eur	PROPN
ejpam-3756	85	8	.	.	PUNCT
ejpam-3756	86	1	j.	j.	PROPN
ejpam-3756	86	2	pure	pure	PROPN
ejpam-3756	86	3	appl	appl	PROPN
ejpam-3756	86	4	.	.	PROPN
ejpam-3756	86	5	math	math	PROPN
ejpam-3756	86	6	,	,	PUNCT
ejpam-3756	86	7	13	13	NUM
ejpam-3756	86	8	(	(	PUNCT
ejpam-3756	86	9	5	5	NUM
ejpam-3756	86	10	)	)	PUNCT
ejpam-3756	86	11	(	(	PUNCT
ejpam-3756	86	12	2020	2020	NUM
ejpam-3756	86	13	)	)	PUNCT
ejpam-3756	86	14	,	,	PUNCT
ejpam-3756	86	15	1110	1110	NUM
ejpam-3756	86	16	-	-	SYM
ejpam-3756	86	17	1130	1130	NUM
ejpam-3756	86	18	1115	1115	NUM
ejpam-3756	86	19	3	3	NUM
ejpam-3756	86	20	.	.	PUNCT
ejpam-3756	86	21	convergence	convergence	NOUN
ejpam-3756	86	22	analysis	analysis	NOUN
ejpam-3756	86	23	theorem	theorem	VERB
ejpam-3756	86	24	1	1	X
ejpam-3756	86	25	.	.	PUNCT
ejpam-3756	86	26	suppose	suppose	VERB
ejpam-3756	86	27	that	that	SCONJ
ejpam-3756	86	28	there	there	PRON
ejpam-3756	86	29	is	be	VERB
ejpam-3756	86	30	a	a	DET
ejpam-3756	86	31	banach	banach	NOUN
ejpam-3756	86	32	space	space	NOUN
ejpam-3756	86	33	e	e	NOUN
ejpam-3756	86	34	,	,	PUNCT
ejpam-3756	86	35	having	having	AUX
ejpam-3756	86	36	subset	subset	VERB
ejpam-3756	86	37	c	c	NOUN
ejpam-3756	86	38	,	,	PUNCT
ejpam-3756	86	39	which	which	PRON
ejpam-3756	86	40	is	be	AUX
ejpam-3756	86	41	nonempty	nonempty	ADV
ejpam-3756	86	42	closed	closed	ADJ
ejpam-3756	86	43	and	and	CCONJ
ejpam-3756	86	44	convex	convex	NOUN
ejpam-3756	86	45	.	.	PUNCT
ejpam-3756	87	1	also	also	ADV
ejpam-3756	87	2	,	,	PUNCT
ejpam-3756	87	3	let	let	VERB
ejpam-3756	87	4	there	there	PRON
ejpam-3756	87	5	be	be	AUX
ejpam-3756	87	6	a	a	DET
ejpam-3756	87	7	contraction	contraction	NOUN
ejpam-3756	87	8	mapping	mapping	NOUN
ejpam-3756	87	9	t	t	NOUN
ejpam-3756	87	10	:	:	PUNCT
ejpam-3756	87	11	c	c	X
ejpam-3756	87	12	→	→	SYM
ejpam-3756	87	13	c.	c.	PROPN
ejpam-3756	87	14	let	let	VERB
ejpam-3756	87	15	{	{	PUNCT
ejpam-3756	87	16	ζn}∞n=0	ζn}∞n=0	PUNCT
ejpam-3756	87	17	be	be	AUX
ejpam-3756	87	18	an	an	DET
ejpam-3756	87	19	iterative	iterative	NOUN
ejpam-3756	87	20	sequence	sequence	NOUN
ejpam-3756	87	21	generated	generate	VERB
ejpam-3756	87	22	by	by	ADP
ejpam-3756	87	23	nv	nv	PROPN
ejpam-3756	87	24	1	1	NUM
ejpam-3756	87	25	and	and	CCONJ
ejpam-3756	87	26	with	with	ADP
ejpam-3756	87	27	real	real	ADJ
ejpam-3756	87	28	sequences	sequence	NOUN
ejpam-3756	87	29	{	{	PUNCT
ejpam-3756	87	30	σ0n}∞n=0	σ0n}∞n=0	X
ejpam-3756	87	31	and	and	CCONJ
ejpam-3756	87	32	{	{	PUNCT
ejpam-3756	87	33	σ1n}∞n=0	σ1n}∞n=0	PROPN
ejpam-3756	87	34	∈	∈	PROPN
ejpam-3756	88	1	[	[	X
ejpam-3756	88	2	0	0	NUM
ejpam-3756	88	3	,	,	PUNCT
ejpam-3756	88	4	1	1	NUM
ejpam-3756	88	5	]	]	PUNCT
ejpam-3756	89	1	such	such	ADJ
ejpam-3756	89	2	that	that	SCONJ
ejpam-3756	89	3	∑∞	∑∞	NOUN
ejpam-3756	89	4	n=0	n=0	PROPN
ejpam-3756	90	1	σ	σ	NOUN
ejpam-3756	90	2	0	0	NUM
ejpam-3756	90	3	nσ	nσ	NOUN
ejpam-3756	90	4	1	1	NUM
ejpam-3756	90	5	n	n	NOUN
ejpam-3756	90	6	=	=	SYM
ejpam-3756	90	7	∞.	∞.	PROPN
ejpam-3756	90	8	then	then	ADV
ejpam-3756	90	9	,	,	PUNCT
ejpam-3756	90	10	{	{	PUNCT
ejpam-3756	90	11	ζn}∞n=0	ζn}∞n=0	X
ejpam-3756	90	12	converges	converge	VERB
ejpam-3756	90	13	strongly	strongly	ADV
ejpam-3756	90	14	to	to	ADP
ejpam-3756	90	15	a	a	DET
ejpam-3756	90	16	fixed	fix	VERB
ejpam-3756	90	17	point	point	NOUN
ejpam-3756	90	18	of	of	ADP
ejpam-3756	90	19	t	t	PROPN
ejpam-3756	90	20	.	.	PUNCT
ejpam-3756	91	1	proof	proof	NOUN
ejpam-3756	91	2	.	.	PUNCT
ejpam-3756	92	1	it	it	PRON
ejpam-3756	92	2	is	be	AUX
ejpam-3756	92	3	obvious	obvious	ADJ
ejpam-3756	92	4	from	from	ADP
ejpam-3756	92	5	banach	banach	NOUN
ejpam-3756	92	6	contraction	contraction	NOUN
ejpam-3756	92	7	theorem	theorem	VERB
ejpam-3756	92	8	that	that	DET
ejpam-3756	92	9	existence	existence	NOUN
ejpam-3756	92	10	and	and	CCONJ
ejpam-3756	92	11	uniqueness	uniqueness	NOUN
ejpam-3756	92	12	of	of	ADP
ejpam-3756	92	13	fixed	fix	VERB
ejpam-3756	92	14	point	point	NOUN
ejpam-3756	92	15	xδ	xδ	PROPN
ejpam-3756	92	16	is	be	AUX
ejpam-3756	92	17	guaranteed	guarantee	VERB
ejpam-3756	92	18	.	.	PUNCT
ejpam-3756	93	1	now	now	ADV
ejpam-3756	93	2	,	,	PUNCT
ejpam-3756	93	3	it	it	PRON
ejpam-3756	93	4	is	be	AUX
ejpam-3756	93	5	to	to	PART
ejpam-3756	93	6	show	show	VERB
ejpam-3756	93	7	that	that	SCONJ
ejpam-3756	93	8	ζn	ζn	PROPN
ejpam-3756	93	9	→	→	SYM
ejpam-3756	93	10	xδ	xδ	PROPN
ejpam-3756	93	11	for	for	ADP
ejpam-3756	93	12	n	n	PROPN
ejpam-3756	93	13	→	→	SYM
ejpam-3756	93	14	∞.	∞.	PROPN
ejpam-3756	93	15	from	from	ADP
ejpam-3756	93	16	nv	nv	PROPN
ejpam-3756	93	17	1	1	NUM
ejpam-3756	93	18	iteration	iteration	NOUN
ejpam-3756	93	19	scheme	scheme	NOUN
ejpam-3756	93	20	it	it	PRON
ejpam-3756	93	21	follows	follow	VERB
ejpam-3756	93	22	that	that	SCONJ
ejpam-3756	93	23	,	,	PUNCT
ejpam-3756	93	24	‖θn	‖θn	PROPN
ejpam-3756	93	25	−	−	PROPN
ejpam-3756	93	26	xδ‖	xδ‖	PROPN
ejpam-3756	94	1	=	=	SYM
ejpam-3756	94	2	‖t	‖t	NOUN
ejpam-3756	94	3	(	(	PUNCT
ejpam-3756	94	4	(	(	PUNCT
ejpam-3756	94	5	1−	1−	NUM
ejpam-3756	94	6	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	95	1	+	+	CCONJ
ejpam-3756	95	2	σ0ntζn)−	σ0ntζn)−	X
ejpam-3756	95	3	xδ‖	xδ‖	PUNCT
ejpam-3756	95	4	=	=	SYM
ejpam-3756	95	5	‖t	‖t	NOUN
ejpam-3756	95	6	(	(	PUNCT
ejpam-3756	95	7	(	(	PUNCT
ejpam-3756	95	8	1−	1−	NUM
ejpam-3756	95	9	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	95	10	+	+	CCONJ
ejpam-3756	95	11	σ0ntζn)−	σ0ntζn)−	PROPN
ejpam-3756	95	12	txδ‖	txδ‖	NOUN
ejpam-3756	95	13	≤	≤	NUM
ejpam-3756	95	14	ξ‖(1−	ξ‖(1−	NOUN
ejpam-3756	95	15	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	95	16	+	+	CCONJ
ejpam-3756	95	17	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	95	18	−	−	NOUN
ejpam-3756	95	19	xδ‖	xδ‖	PROPN
ejpam-3756	95	20	≤	≤	NOUN
ejpam-3756	95	21	ξ(1−	ξ(1−	NOUN
ejpam-3756	95	22	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	95	23	−	−	PROPN
ejpam-3756	95	24	xδ‖+	xδ‖+	PUNCT
ejpam-3756	96	1	ξσ0n‖tζn	ξσ0n‖tζn	NOUN
ejpam-3756	96	2	−	−	ADP
ejpam-3756	96	3	txδ‖	txδ‖	NOUN
ejpam-3756	96	4	≤	≤	NUM
ejpam-3756	96	5	ξ(1−	ξ(1−	NOUN
ejpam-3756	96	6	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	96	7	−	−	PROPN
ejpam-3756	96	8	xδ‖+	xδ‖+	PUNCT
ejpam-3756	96	9	σ0nξ	σ0nξ	PUNCT
ejpam-3756	97	1	2‖ζn	2‖ζn	NOUN
ejpam-3756	97	2	−	−	NOUN
ejpam-3756	97	3	xδ‖	xδ‖	PROPN
ejpam-3756	98	1	=	=	SYM
ejpam-3756	98	2	ξ(1−	ξ(1−	PROPN
ejpam-3756	98	3	(	(	PUNCT
ejpam-3756	98	4	1−	1−	NUM
ejpam-3756	98	5	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	98	6	−	−	PROPN
ejpam-3756	98	7	xδ‖	xδ‖	PROPN
ejpam-3756	99	1	also	also	ADV
ejpam-3756	99	2	,	,	PUNCT
ejpam-3756	99	3	‖ηn	‖ηn	PROPN
ejpam-3756	99	4	−	−	NOUN
ejpam-3756	99	5	xδ‖	xδ‖	PROPN
ejpam-3756	99	6	≤	≤	NOUN
ejpam-3756	99	7	‖tθn	‖tθn	NOUN
ejpam-3756	99	8	−	−	NOUN
ejpam-3756	99	9	xδ‖	xδ‖	PUNCT
ejpam-3756	100	1	=	=	SYM
ejpam-3756	100	2	‖tθn	‖tθn	PROPN
ejpam-3756	100	3	−	−	NOUN
ejpam-3756	100	4	txδ‖	txδ‖	NOUN
ejpam-3756	100	5	≤	≤	PUNCT
ejpam-3756	101	1	ξ‖θn	ξ‖θn	PROPN
ejpam-3756	101	2	−	−	NOUN
ejpam-3756	101	3	xδ‖	xδ‖	NOUN
ejpam-3756	101	4	using	use	VERB
ejpam-3756	101	5	the	the	DET
ejpam-3756	101	6	value	value	NOUN
ejpam-3756	101	7	of	of	ADP
ejpam-3756	101	8	‖θn	‖θn	PROPN
ejpam-3756	101	9	−	−	PROPN
ejpam-3756	101	10	xδ‖	xδ‖	PROPN
ejpam-3756	101	11	,	,	PUNCT
ejpam-3756	101	12	we	we	PRON
ejpam-3756	101	13	have	have	VERB
ejpam-3756	101	14	‖ηn	‖ηn	NUM
ejpam-3756	101	15	−	−	NOUN
ejpam-3756	101	16	xδ‖	xδ‖	PROPN
ejpam-3756	101	17	≤	≤	NUM
ejpam-3756	101	18	ξ2(1−	ξ2(1−	ADP
ejpam-3756	101	19	(	(	PUNCT
ejpam-3756	101	20	1−	1−	NUM
ejpam-3756	101	21	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	PROPN
ejpam-3756	101	22	−	−	PROPN
ejpam-3756	101	23	xδ‖	xδ‖	PROPN
ejpam-3756	101	24	similarly	similarly	ADV
ejpam-3756	101	25	,	,	PUNCT
ejpam-3756	101	26	we	we	PRON
ejpam-3756	101	27	have	have	VERB
ejpam-3756	101	28	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	101	29	−	−	NOUN
ejpam-3756	101	30	xδ‖	xδ‖	PROPN
ejpam-3756	102	1	=	=	SYM
ejpam-3756	102	2	‖tηn	‖tηn	PROPN
ejpam-3756	102	3	−	−	PROPN
ejpam-3756	102	4	xδ‖	xδ‖	PROPN
ejpam-3756	103	1	=	=	SYM
ejpam-3756	103	2	‖tηn	‖tηn	PROPN
ejpam-3756	103	3	−	−	PROPN
ejpam-3756	103	4	txδ‖	txδ‖	NOUN
ejpam-3756	103	5	=	=	SYM
ejpam-3756	104	1	ξ‖ηn	ξ‖ηn	PROPN
ejpam-3756	104	2	−	−	NOUN
ejpam-3756	104	3	xδ‖	xδ‖	NOUN
ejpam-3756	105	1	using	use	VERB
ejpam-3756	105	2	the	the	DET
ejpam-3756	105	3	value	value	NOUN
ejpam-3756	105	4	of	of	ADP
ejpam-3756	105	5	‖ηn	‖ηn	NUM
ejpam-3756	105	6	−	−	NOUN
ejpam-3756	105	7	xδ‖	xδ‖	PROPN
ejpam-3756	105	8	and	and	CCONJ
ejpam-3756	105	9	‖ζn	‖ζn	NUM
ejpam-3756	105	10	−	−	NOUN
ejpam-3756	105	11	xδ‖	xδ‖	PROPN
ejpam-3756	105	12	,	,	PUNCT
ejpam-3756	105	13	we	we	PRON
ejpam-3756	105	14	have	have	VERB
ejpam-3756	105	15	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	105	16	−	−	NOUN
ejpam-3756	105	17	xδ‖	xδ‖	PROPN
ejpam-3756	105	18	≤	≤	ADV
ejpam-3756	105	19	ξ3(1−	ξ3(1−	ADP
ejpam-3756	105	20	(	(	PUNCT
ejpam-3756	105	21	1−	1−	NUM
ejpam-3756	105	22	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	105	23	−	−	PROPN
ejpam-3756	105	24	xδ‖	xδ‖	PROPN
ejpam-3756	106	1	now	now	ADV
ejpam-3756	106	2	,	,	PUNCT
ejpam-3756	106	3	inductively	inductively	ADV
ejpam-3756	106	4	using	use	VERB
ejpam-3756	106	5	the	the	DET
ejpam-3756	106	6	behaviour	behaviour	NOUN
ejpam-3756	106	7	of	of	ADP
ejpam-3756	106	8	sequence	sequence	NOUN
ejpam-3756	106	9	,	,	PUNCT
ejpam-3756	106	10	we	we	PRON
ejpam-3756	106	11	have	have	VERB
ejpam-3756	106	12	‖ζn	‖ζn	NUM
ejpam-3756	106	13	−	−	NOUN
ejpam-3756	106	14	xδ‖	xδ‖	PROPN
ejpam-3756	106	15	≤	≤	NOUN
ejpam-3756	106	16	ξ3(1−	ξ3(1−	ADP
ejpam-3756	106	17	(	(	PUNCT
ejpam-3756	106	18	1−	1−	NUM
ejpam-3756	106	19	ξ)σ0n−1)‖xn−1	ξ)σ0n−1)‖xn−1	PROPN
ejpam-3756	106	20	−	−	PROPN
ejpam-3756	106	21	xδ‖	xδ‖	PROPN
ejpam-3756	107	1	l.n	l.n	PROPN
ejpam-3756	107	2	mishra	mishra	PROPN
ejpam-3756	107	3	et	et	PROPN
ejpam-3756	107	4	al	al	PROPN
ejpam-3756	107	5	.	.	PUNCT
ejpam-3756	107	6	/	/	SYM
ejpam-3756	107	7	eur	eur	PROPN
ejpam-3756	107	8	.	.	PUNCT
ejpam-3756	108	1	j.	j.	PROPN
ejpam-3756	108	2	pure	pure	PROPN
ejpam-3756	108	3	appl	appl	PROPN
ejpam-3756	108	4	.	.	PROPN
ejpam-3756	108	5	math	math	PROPN
ejpam-3756	108	6	,	,	PUNCT
ejpam-3756	108	7	13	13	NUM
ejpam-3756	108	8	(	(	PUNCT
ejpam-3756	108	9	5	5	NUM
ejpam-3756	108	10	)	)	PUNCT
ejpam-3756	108	11	(	(	PUNCT
ejpam-3756	108	12	2020	2020	NUM
ejpam-3756	108	13	)	)	PUNCT
ejpam-3756	108	14	,	,	PUNCT
ejpam-3756	108	15	1110	1110	NUM
ejpam-3756	108	16	-	-	SYM
ejpam-3756	108	17	1130	1130	NUM
ejpam-3756	108	18	1116	1116	NUM
ejpam-3756	108	19	‖xn−1	‖xn−1	ADP
ejpam-3756	108	20	−	−	ADP
ejpam-3756	108	21	xδ‖	xδ‖	PROPN
ejpam-3756	108	22	≤	≤	ADV
ejpam-3756	108	23	ξ3(1−	ξ3(1−	ADP
ejpam-3756	108	24	(	(	PUNCT
ejpam-3756	108	25	1−	1−	NUM
ejpam-3756	108	26	ξ)σ0n−2)‖xn−2	ξ)σ0n−2)‖xn−2	PROPN
ejpam-3756	108	27	−	−	PROPN
ejpam-3756	108	28	xδ‖	xδ‖	PROPN
ejpam-3756	109	1	the	the	DET
ejpam-3756	109	2	repetition	repetition	NOUN
ejpam-3756	109	3	results	result	VERB
ejpam-3756	109	4	‖x1	‖x1	NOUN
ejpam-3756	109	5	−	−	PROPN
ejpam-3756	109	6	xδ‖	xδ‖	PROPN
ejpam-3756	110	1	≤	≤	NOUN
ejpam-3756	110	2	ξ3(1−	ξ3(1−	ADP
ejpam-3756	110	3	(	(	PUNCT
ejpam-3756	110	4	1−	1−	NUM
ejpam-3756	110	5	ξ)σ00)‖ζ0	ξ)σ00)‖ζ0	NOUN
ejpam-3756	110	6	−	−	NOUN
ejpam-3756	110	7	xδ‖	xδ‖	NOUN
ejpam-3756	111	1	proceeding	proceed	VERB
ejpam-3756	111	2	in	in	ADP
ejpam-3756	111	3	the	the	DET
ejpam-3756	111	4	same	same	ADJ
ejpam-3756	111	5	manner	manner	NOUN
ejpam-3756	111	6	,	,	PUNCT
ejpam-3756	111	7	we	we	PRON
ejpam-3756	111	8	have	have	VERB
ejpam-3756	111	9	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	111	10	−	−	NOUN
ejpam-3756	111	11	xδ‖	xδ‖	PROPN
ejpam-3756	112	1	≤	≤	NUM
ejpam-3756	113	1	‖ζ0	‖ζ0	ADJ
ejpam-3756	113	2	−	−	NUM
ejpam-3756	113	3	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	113	4	)	)	PUNCT
ejpam-3756	113	5	n∏	n∏	PROPN
ejpam-3756	113	6	k=0	k=0	PROPN
ejpam-3756	113	7	(	(	PUNCT
ejpam-3756	113	8	1−	1−	NUM
ejpam-3756	113	9	(	(	PUNCT
ejpam-3756	113	10	1−	1−	NUM
ejpam-3756	113	11	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	113	12	)	)	PUNCT
ejpam-3756	113	13	where	where	SCONJ
ejpam-3756	113	14	(	(	PUNCT
ejpam-3756	113	15	1−σ0n(1−	1−σ0n(1−	NUM
ejpam-3756	113	16	ξ	ξ	NOUN
ejpam-3756	113	17	)	)	PUNCT
ejpam-3756	113	18	)	)	PUNCT
ejpam-3756	114	1	∈	∈	PROPN
ejpam-3756	114	2	(	(	PUNCT
ejpam-3756	114	3	0	0	NUM
ejpam-3756	114	4	,	,	PUNCT
ejpam-3756	114	5	1	1	NUM
ejpam-3756	114	6	)	)	PUNCT
ejpam-3756	114	7	because	because	SCONJ
ejpam-3756	114	8	ξ	ξ	PROPN
ejpam-3756	114	9	∈	∈	PROPN
ejpam-3756	114	10	(	(	PUNCT
ejpam-3756	114	11	0	0	NUM
ejpam-3756	114	12	,	,	PUNCT
ejpam-3756	114	13	1	1	NUM
ejpam-3756	114	14	)	)	PUNCT
ejpam-3756	114	15	and	and	CCONJ
ejpam-3756	114	16	σ0n	σ0n	PUNCT
ejpam-3756	114	17	∈	∈	PROPN
ejpam-3756	115	1	[	[	X
ejpam-3756	115	2	0	0	NUM
ejpam-3756	115	3	,	,	PUNCT
ejpam-3756	115	4	1	1	NUM
ejpam-3756	115	5	]	]	PUNCT
ejpam-3756	115	6	,	,	PUNCT
ejpam-3756	115	7	for	for	ADP
ejpam-3756	115	8	all	all	DET
ejpam-3756	115	9	n	n	DET
ejpam-3756	115	10	∈	∈	PROPN
ejpam-3756	115	11	n	n	CCONJ
ejpam-3756	115	12	,	,	PUNCT
ejpam-3756	115	13	since	since	SCONJ
ejpam-3756	115	14	we	we	PRON
ejpam-3756	115	15	know	know	VERB
ejpam-3756	115	16	that	that	SCONJ
ejpam-3756	115	17	1−	1−	NUM
ejpam-3756	115	18	x	x	SYM
ejpam-3756	115	19	≤	≤	NUM
ejpam-3756	115	20	e−x	e−x	NOUN
ejpam-3756	115	21	for	for	ADP
ejpam-3756	115	22	all	all	DET
ejpam-3756	115	23	x	x	SYM
ejpam-3756	115	24	∈	∈	PROPN
ejpam-3756	116	1	[	[	X
ejpam-3756	116	2	0	0	NUM
ejpam-3756	116	3	,	,	PUNCT
ejpam-3756	116	4	1	1	NUM
ejpam-3756	116	5	]	]	PUNCT
ejpam-3756	116	6	,	,	PUNCT
ejpam-3756	116	7	so	so	SCONJ
ejpam-3756	116	8	from	from	ADP
ejpam-3756	116	9	the	the	DET
ejpam-3756	116	10	above	above	ADJ
ejpam-3756	116	11	inequality	inequality	NOUN
ejpam-3756	116	12	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	116	13	−	−	PROPN
ejpam-3756	116	14	xδ‖	xδ‖	PROPN
ejpam-3756	116	15	≤	≤	NUM
ejpam-3756	116	16	‖ζ0	‖ζ0	ADJ
ejpam-3756	116	17	−	−	NUM
ejpam-3756	116	18	xδ‖ξ3(n+1	xδ‖ξ3(n+1	PROPN
ejpam-3756	116	19	)	)	PUNCT
ejpam-3756	116	20	e(1−ξ	e(1−ξ	NOUN
ejpam-3756	116	21	)	)	PUNCT
ejpam-3756	117	1	∑n	∑n	PROPN
ejpam-3756	117	2	k=0	k=0	PROPN
ejpam-3756	117	3	σ	σ	PROPN
ejpam-3756	117	4	0	0	NUM
ejpam-3756	118	1	k	k	X
ejpam-3756	118	2	.	.	PUNCT
ejpam-3756	119	1	taking	take	VERB
ejpam-3756	119	2	the	the	DET
ejpam-3756	119	3	limit	limit	NOUN
ejpam-3756	119	4	both	both	DET
ejpam-3756	119	5	sides	side	NOUN
ejpam-3756	119	6	of	of	ADP
ejpam-3756	119	7	this	this	DET
ejpam-3756	119	8	inequality	inequality	NOUN
ejpam-3756	119	9	,	,	PUNCT
ejpam-3756	119	10	it	it	PRON
ejpam-3756	119	11	yields	yield	VERB
ejpam-3756	119	12	lim	lim	PROPN
ejpam-3756	119	13	n→∞	n→∞	X
ejpam-3756	119	14	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	119	15	−	−	NOUN
ejpam-3756	119	16	xδ‖	xδ‖	PROPN
ejpam-3756	120	1	=	=	SYM
ejpam-3756	120	2	0	0	PROPN
ejpam-3756	120	3	,	,	PUNCT
ejpam-3756	120	4	which	which	PRON
ejpam-3756	120	5	implies	imply	VERB
ejpam-3756	120	6	that	that	SCONJ
ejpam-3756	120	7	ζn	ζn	PROPN
ejpam-3756	120	8	→	→	SYM
ejpam-3756	120	9	xδ	xδ	PROPN
ejpam-3756	120	10	for	for	ADP
ejpam-3756	120	11	n→∞	n→∞	NUM
ejpam-3756	120	12	,	,	PUNCT
ejpam-3756	120	13	as	as	SCONJ
ejpam-3756	120	14	required	require	VERB
ejpam-3756	120	15	.	.	PUNCT
ejpam-3756	121	1	theorem	theorem	NOUN
ejpam-3756	121	2	2	2	NUM
ejpam-3756	121	3	.	.	PUNCT
ejpam-3756	121	4	suppose	suppose	VERB
ejpam-3756	121	5	that	that	SCONJ
ejpam-3756	121	6	there	there	PRON
ejpam-3756	121	7	is	be	VERB
ejpam-3756	121	8	a	a	DET
ejpam-3756	121	9	banach	banach	NOUN
ejpam-3756	121	10	space	space	NOUN
ejpam-3756	121	11	e	e	NOUN
ejpam-3756	121	12	,	,	PUNCT
ejpam-3756	121	13	having	having	AUX
ejpam-3756	121	14	subset	subset	VERB
ejpam-3756	121	15	c	c	NOUN
ejpam-3756	121	16	,	,	PUNCT
ejpam-3756	121	17	which	which	PRON
ejpam-3756	121	18	is	be	AUX
ejpam-3756	121	19	nonempty	nonempty	ADV
ejpam-3756	121	20	closed	closed	ADJ
ejpam-3756	121	21	and	and	CCONJ
ejpam-3756	121	22	convex	convex	VERB
ejpam-3756	121	23	and	and	CCONJ
ejpam-3756	121	24	also	also	ADV
ejpam-3756	121	25	that	that	SCONJ
ejpam-3756	121	26	there	there	PRON
ejpam-3756	121	27	is	be	VERB
ejpam-3756	121	28	a	a	DET
ejpam-3756	121	29	contraction	contraction	NOUN
ejpam-3756	121	30	mapping	mapping	NOUN
ejpam-3756	121	31	t	t	NOUN
ejpam-3756	121	32	on	on	ADP
ejpam-3756	121	33	c	c	PROPN
ejpam-3756	121	34	with	with	ADP
ejpam-3756	121	35	a	a	DET
ejpam-3756	121	36	fixed	fixed	ADJ
ejpam-3756	121	37	point	point	NOUN
ejpam-3756	121	38	xδ	xδ	PROPN
ejpam-3756	121	39	.	.	PUNCT
ejpam-3756	122	1	for	for	ADP
ejpam-3756	122	2	given	give	VERB
ejpam-3756	122	3	x′0	x′0	NOUN
ejpam-3756	122	4	=	=	PUNCT
ejpam-3756	122	5	ζ0	ζ0	NOUN
ejpam-3756	122	6	∈	∈	PROPN
ejpam-3756	122	7	c	c	NOUN
ejpam-3756	122	8	,	,	PUNCT
ejpam-3756	122	9	let	let	VERB
ejpam-3756	122	10	{	{	PUNCT
ejpam-3756	122	11	ζn}∞n=0	ζn}∞n=0	X
ejpam-3756	122	12	and	and	CCONJ
ejpam-3756	122	13	{	{	PUNCT
ejpam-3756	122	14	x′n}∞n=0	x′n}∞n=0	ADV
ejpam-3756	122	15	be	be	AUX
ejpam-3756	122	16	the	the	DET
ejpam-3756	122	17	iterative	iterative	NOUN
ejpam-3756	122	18	sequences	sequence	NOUN
ejpam-3756	122	19	generated	generate	VERB
ejpam-3756	122	20	by	by	ADP
ejpam-3756	122	21	nv	nv	PROPN
ejpam-3756	122	22	1	1	NUM
ejpam-3756	122	23	and	and	CCONJ
ejpam-3756	122	24	k∗	k∗	VERB
ejpam-3756	122	25	respectively	respectively	ADV
ejpam-3756	122	26	,	,	PUNCT
ejpam-3756	122	27	with	with	ADP
ejpam-3756	122	28	real	real	ADJ
ejpam-3756	122	29	sequences	sequence	NOUN
ejpam-3756	122	30	{	{	PUNCT
ejpam-3756	122	31	σ0n}∞n=0	σ0n}∞n=0	VERB
ejpam-3756	122	32	,	,	PUNCT
ejpam-3756	122	33	{	{	PUNCT
ejpam-3756	122	34	σ1n}∞n=0	σ1n}∞n=0	PROPN
ejpam-3756	122	35	∈	∈	PROPN
ejpam-3756	122	36	(	(	PUNCT
ejpam-3756	122	37	0	0	NUM
ejpam-3756	122	38	,	,	PUNCT
ejpam-3756	122	39	1	1	NUM
ejpam-3756	122	40	)	)	PUNCT
ejpam-3756	122	41	such	such	ADJ
ejpam-3756	122	42	that	that	DET
ejpam-3756	122	43	∑∞	∑∞	NOUN
ejpam-3756	122	44	k=0	k=0	PROPN
ejpam-3756	122	45	σ	σ	X
ejpam-3756	122	46	0	0	NUM
ejpam-3756	123	1	n	n	PROPN
ejpam-3756	123	2	=	=	SYM
ejpam-3756	123	3	∞	∞	PROPN
ejpam-3756	123	4	and	and	CCONJ
ejpam-3756	123	5	for	for	ADP
ejpam-3756	123	6	all	all	DET
ejpam-3756	123	7	n	n	PRON
ejpam-3756	123	8	∈	∈	PROPN
ejpam-3756	123	9	n.	n.	NOUN
ejpam-3756	123	10	then	then	ADV
ejpam-3756	123	11	nv	nv	PROPN
ejpam-3756	123	12	1	1	NUM
ejpam-3756	123	13	converges	converge	NOUN
ejpam-3756	123	14	to	to	ADP
ejpam-3756	123	15	xδ	xδ	PRON
ejpam-3756	123	16	faster	fast	ADV
ejpam-3756	123	17	than	than	SCONJ
ejpam-3756	123	18	k∗	k∗	VERB
ejpam-3756	123	19	iteration	iteration	NOUN
ejpam-3756	123	20	scheme	scheme	NOUN
ejpam-3756	123	21	.	.	PUNCT
ejpam-3756	124	1	proof	proof	NOUN
ejpam-3756	124	2	.	.	PUNCT
ejpam-3756	125	1	using	use	VERB
ejpam-3756	125	2	the	the	DET
ejpam-3756	125	3	result	result	NOUN
ejpam-3756	125	4	of	of	ADP
ejpam-3756	125	5	theorem	theorem	NOUN
ejpam-3756	125	6	1	1	NUM
ejpam-3756	125	7	it	it	PRON
ejpam-3756	125	8	is	be	AUX
ejpam-3756	125	9	clear	clear	ADJ
ejpam-3756	125	10	that	that	SCONJ
ejpam-3756	125	11	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	126	1	−	−	NOUN
ejpam-3756	126	2	xδ‖	xδ‖	PROPN
ejpam-3756	126	3	≤	≤	NUM
ejpam-3756	126	4	‖ζ0	‖ζ0	ADJ
ejpam-3756	126	5	−	−	NUM
ejpam-3756	126	6	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	126	7	)	)	PUNCT
ejpam-3756	126	8	n∏	n∏	PROPN
ejpam-3756	126	9	k=0	k=0	PROPN
ejpam-3756	126	10	(	(	PUNCT
ejpam-3756	126	11	1−	1−	NUM
ejpam-3756	126	12	(	(	PUNCT
ejpam-3756	126	13	1−	1−	NUM
ejpam-3756	126	14	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	126	15	)	)	PUNCT
ejpam-3756	126	16	now	now	ADV
ejpam-3756	126	17	,	,	PUNCT
ejpam-3756	126	18	for	for	ADP
ejpam-3756	126	19	the	the	DET
ejpam-3756	126	20	k∗	k∗	PROPN
ejpam-3756	126	21	iteration	iteration	NOUN
ejpam-3756	126	22	scheme	scheme	NOUN
ejpam-3756	126	23	,	,	PUNCT
ejpam-3756	126	24	‖z′n	‖z′n	VERB
ejpam-3756	126	25	−	−	NOUN
ejpam-3756	126	26	xδ‖	xδ‖	PROPN
ejpam-3756	126	27	=	=	SYM
ejpam-3756	126	28	‖(1−	‖(1−	PROPN
ejpam-3756	126	29	σ1n)x′n	σ1n)x′n	PROPN
ejpam-3756	126	30	+	+	CCONJ
ejpam-3756	126	31	σ0ntx	σ0ntx	NUM
ejpam-3756	126	32	′	′	NUM
ejpam-3756	126	33	n	n	CCONJ
ejpam-3756	126	34	−	−	PROPN
ejpam-3756	126	35	xδ‖	xδ‖	PROPN
ejpam-3756	126	36	≤	≤	NOUN
ejpam-3756	126	37	(	(	PUNCT
ejpam-3756	126	38	1−	1−	NUM
ejpam-3756	126	39	σ1n)‖x′n	σ1n)‖x′n	NOUN
ejpam-3756	126	40	−	−	PROPN
ejpam-3756	126	41	xδ‖+	xδ‖+	PUNCT
ejpam-3756	127	1	σ0n‖tx′n	σ0n‖tx′n	PROPN
ejpam-3756	127	2	−	−	NOUN
ejpam-3756	127	3	txδ‖	txδ‖	NOUN
ejpam-3756	127	4	≤	≤	NUM
ejpam-3756	127	5	(	(	PUNCT
ejpam-3756	127	6	1−	1−	NUM
ejpam-3756	127	7	σ1n)‖x′n	σ1n)‖x′n	NOUN
ejpam-3756	127	8	−	−	PROPN
ejpam-3756	127	9	xδ‖+	xδ‖+	PROPN
ejpam-3756	128	1	ξσ0n‖x′n	ξσ0n‖x′n	PROPN
ejpam-3756	129	1	−	−	NOUN
ejpam-3756	129	2	xδ‖	xδ‖	PROPN
ejpam-3756	129	3	≤	≤	NOUN
ejpam-3756	129	4	(	(	PUNCT
ejpam-3756	129	5	1−	1−	NUM
ejpam-3756	129	6	σ1n(1−	σ1n(1−	NOUN
ejpam-3756	129	7	ξ))‖x′n	ξ))‖x′n	NOUN
ejpam-3756	129	8	−	−	PROPN
ejpam-3756	129	9	xδ‖	xδ‖	PROPN
ejpam-3756	129	10	similarly	similarly	ADV
ejpam-3756	129	11	‖y′n	‖y′n	VERB
ejpam-3756	129	12	−	−	PRON
ejpam-3756	130	1	xδ‖	xδ‖	PROPN
ejpam-3756	130	2	≤	≤	ADJ
ejpam-3756	130	3	‖t	‖t	NOUN
ejpam-3756	130	4	(	(	PUNCT
ejpam-3756	130	5	(	(	PUNCT
ejpam-3756	130	6	σ0nz	σ0nz	X
ejpam-3756	130	7	′	′	NUM
ejpam-3756	130	8	n	n	NOUN
ejpam-3756	130	9	+	+	CCONJ
ejpam-3756	130	10	(	(	PUNCT
ejpam-3756	130	11	1−	1−	NUM
ejpam-3756	130	12	σ0n)tz′n)−	σ0n)tz′n)−	NUM
ejpam-3756	130	13	xδ‖	xδ‖	PROPN
ejpam-3756	131	1	l.n	l.n	PROPN
ejpam-3756	131	2	mishra	mishra	PROPN
ejpam-3756	131	3	et	et	PROPN
ejpam-3756	131	4	al	al	PROPN
ejpam-3756	131	5	.	.	PUNCT
ejpam-3756	131	6	/	/	SYM
ejpam-3756	131	7	eur	eur	PROPN
ejpam-3756	131	8	.	.	PUNCT
ejpam-3756	132	1	j.	j.	PROPN
ejpam-3756	132	2	pure	pure	PROPN
ejpam-3756	132	3	appl	appl	PROPN
ejpam-3756	132	4	.	.	PROPN
ejpam-3756	132	5	math	math	PROPN
ejpam-3756	132	6	,	,	PUNCT
ejpam-3756	132	7	13	13	NUM
ejpam-3756	132	8	(	(	PUNCT
ejpam-3756	132	9	5	5	NUM
ejpam-3756	132	10	)	)	PUNCT
ejpam-3756	132	11	(	(	PUNCT
ejpam-3756	132	12	2020	2020	NUM
ejpam-3756	132	13	)	)	PUNCT
ejpam-3756	132	14	,	,	PUNCT
ejpam-3756	132	15	1110	1110	NUM
ejpam-3756	132	16	-	-	SYM
ejpam-3756	132	17	1130	1130	NUM
ejpam-3756	132	18	1117	1117	NUM
ejpam-3756	132	19	≤	≤	NOUN
ejpam-3756	132	20	ξ‖σ0nz′n	ξ‖σ0nz′n	NUM
ejpam-3756	132	21	+	+	CCONJ
ejpam-3756	132	22	(	(	PUNCT
ejpam-3756	132	23	1−	1−	NUM
ejpam-3756	132	24	σ0n)tz′n	σ0n)tz′n	NOUN
ejpam-3756	132	25	−	−	PROPN
ejpam-3756	132	26	xδ‖	xδ‖	PROPN
ejpam-3756	133	1	≤	≤	NUM
ejpam-3756	133	2	ξσ0n‖z′n	ξσ0n‖z′n	NOUN
ejpam-3756	133	3	−	−	PROPN
ejpam-3756	133	4	xδ‖+	xδ‖+	PUNCT
ejpam-3756	134	1	(	(	PUNCT
ejpam-3756	134	2	1−	1−	NUM
ejpam-3756	134	3	σ0n)‖tz′n	σ0n)‖tz′n	NOUN
ejpam-3756	134	4	−	−	NOUN
ejpam-3756	134	5	xδ‖	xδ‖	PROPN
ejpam-3756	134	6	≤	≤	ADJ
ejpam-3756	134	7	ξσ0n‖z′n	ξσ0n‖z′n	NOUN
ejpam-3756	134	8	−	−	PROPN
ejpam-3756	134	9	xδ‖+	xδ‖+	PUNCT
ejpam-3756	135	1	ξ(1−	ξ(1−	PROPN
ejpam-3756	135	2	σ0n)ξ‖z′n	σ0n)ξ‖z′n	PRON
ejpam-3756	135	3	−	−	PROPN
ejpam-3756	135	4	xδ‖	xδ‖	PROPN
ejpam-3756	136	1	≤	≤	ADV
ejpam-3756	136	2	ξ(1−	ξ(1−	PROPN
ejpam-3756	136	3	(	(	PUNCT
ejpam-3756	136	4	1−	1−	NUM
ejpam-3756	136	5	ξ)σ0n)‖z′n	ξ)σ0n)‖z′n	NOUN
ejpam-3756	136	6	−	−	NOUN
ejpam-3756	136	7	xδ‖	xδ‖	PROPN
ejpam-3756	136	8	≤	≤	ADV
ejpam-3756	136	9	ξ(1−	ξ(1−	X
ejpam-3756	136	10	(	(	PUNCT
ejpam-3756	136	11	1−	1−	NUM
ejpam-3756	136	12	ξ)σ0n)(1−	ξ)σ0n)(1−	NOUN
ejpam-3756	136	13	(	(	PUNCT
ejpam-3756	136	14	1−	1−	NUM
ejpam-3756	136	15	ξ)σ1n)‖x′n	ξ)σ1n)‖x′n	NOUN
ejpam-3756	136	16	−	−	PROPN
ejpam-3756	136	17	xδ‖	xδ‖	PROPN
ejpam-3756	136	18	similarly	similarly	ADV
ejpam-3756	136	19	,	,	PUNCT
ejpam-3756	136	20	‖x′n+1	‖x′n+1	VERB
ejpam-3756	136	21	−	−	PROPN
ejpam-3756	136	22	xδ‖	xδ‖	PROPN
ejpam-3756	137	1	=	=	SYM
ejpam-3756	137	2	‖ty′n	‖ty′n	NUM
ejpam-3756	137	3	−	−	NUM
ejpam-3756	137	4	xδ‖	xδ‖	PROPN
ejpam-3756	137	5	≤	≤	PROPN
ejpam-3756	137	6	ξ‖y′n	ξ‖y′n	NOUN
ejpam-3756	137	7	−	−	PROPN
ejpam-3756	137	8	xδ‖	xδ‖	NOUN
ejpam-3756	137	9	using	use	VERB
ejpam-3756	137	10	the	the	DET
ejpam-3756	137	11	value	value	NOUN
ejpam-3756	137	12	of	of	ADP
ejpam-3756	137	13	‖y′n	‖y′n	NOUN
ejpam-3756	137	14	−	−	ADP
ejpam-3756	137	15	xδ‖	xδ‖	PROPN
ejpam-3756	137	16	and	and	CCONJ
ejpam-3756	137	17	by	by	ADP
ejpam-3756	137	18	using	use	VERB
ejpam-3756	137	19	the	the	DET
ejpam-3756	137	20	fact	fact	NOUN
ejpam-3756	137	21	that	that	SCONJ
ejpam-3756	137	22	(	(	PUNCT
ejpam-3756	137	23	1−	1−	NUM
ejpam-3756	137	24	(	(	PUNCT
ejpam-3756	137	25	1−	1−	NUM
ejpam-3756	137	26	ξ)σ1n	ξ)σ1n	NOUN
ejpam-3756	137	27	)	)	PUNCT
ejpam-3756	137	28	<	<	X
ejpam-3756	137	29	0	0	PUNCT
ejpam-3756	138	1	and	and	CCONJ
ejpam-3756	138	2	finally	finally	ADV
ejpam-3756	138	3	we	we	PRON
ejpam-3756	138	4	have	have	AUX
ejpam-3756	138	5	‖x′n+1	‖x′n+1	VERB
ejpam-3756	138	6	−	−	PROPN
ejpam-3756	138	7	xδ‖	xδ‖	PROPN
ejpam-3756	139	1	≤	≤	NUM
ejpam-3756	139	2	ξ2(1−	ξ2(1−	ADP
ejpam-3756	139	3	(	(	PUNCT
ejpam-3756	139	4	1−	1−	NUM
ejpam-3756	139	5	ξ)σ0n	ξ)σ0n	ADJ
ejpam-3756	139	6	)	)	PUNCT
ejpam-3756	139	7	‖x′n	‖x′n	NOUN
ejpam-3756	139	8	−	−	NOUN
ejpam-3756	139	9	xδ‖	xδ‖	PROPN
ejpam-3756	139	10	≤	≤	NOUN
ejpam-3756	140	1	ξ2(ξ	ξ2(ξ	NUM
ejpam-3756	140	2	−	−	PROPN
ejpam-3756	140	3	(	(	PUNCT
ejpam-3756	140	4	1−	1−	NUM
ejpam-3756	140	5	ξ)σ0n−1)‖x′n−1	ξ)σ0n−1)‖x′n−1	NOUN
ejpam-3756	140	6	−	−	NOUN
ejpam-3756	140	7	xδ‖	xδ‖	PROPN
ejpam-3756	141	1	also	also	ADV
ejpam-3756	141	2	,	,	PUNCT
ejpam-3756	141	3	‖x′n−1	‖x′n−1	PROPN
ejpam-3756	141	4	−	−	NOUN
ejpam-3756	141	5	xδ‖	xδ‖	PROPN
ejpam-3756	141	6	≤	≤	NUM
ejpam-3756	141	7	ξ2(1−	ξ2(1−	ADP
ejpam-3756	141	8	(	(	PUNCT
ejpam-3756	141	9	1−	1−	NUM
ejpam-3756	141	10	ξ)σ0n−2)‖x′n−2	ξ)σ0n−2)‖x′n−2	NOUN
ejpam-3756	141	11	−	−	PROPN
ejpam-3756	141	12	xδ‖	xδ‖	PROPN
ejpam-3756	142	1	continually	continually	ADV
ejpam-3756	142	2	,	,	PUNCT
ejpam-3756	142	3	we	we	PRON
ejpam-3756	142	4	have	have	VERB
ejpam-3756	142	5	‖x′1	‖x′1	NUM
ejpam-3756	142	6	−	−	NOUN
ejpam-3756	142	7	xδ‖	xδ‖	PROPN
ejpam-3756	142	8	≤	≤	NUM
ejpam-3756	143	1	ξ2(1−	ξ2(1−	ADP
ejpam-3756	143	2	(	(	PUNCT
ejpam-3756	143	3	1−	1−	NUM
ejpam-3756	143	4	ξ)σ00)‖x′0	ξ)σ00)‖x′0	NUM
ejpam-3756	143	5	−	−	NOUN
ejpam-3756	143	6	xδ‖	xδ‖	PUNCT
ejpam-3756	144	1	so	so	ADV
ejpam-3756	144	2	,	,	PUNCT
ejpam-3756	144	3	it	it	PRON
ejpam-3756	144	4	is	be	AUX
ejpam-3756	144	5	quite	quite	ADV
ejpam-3756	144	6	obvious	obvious	ADJ
ejpam-3756	144	7	that	that	SCONJ
ejpam-3756	144	8	the	the	DET
ejpam-3756	144	9	following	follow	VERB
ejpam-3756	144	10	deduction	deduction	NOUN
ejpam-3756	144	11	‖x′n+1	‖x′n+1	PROPN
ejpam-3756	144	12	−	−	PROPN
ejpam-3756	144	13	xδ‖	xδ‖	PROPN
ejpam-3756	144	14	≤	≤	NUM
ejpam-3756	144	15	‖x′0	‖x′0	PROPN
ejpam-3756	144	16	−	−	PROPN
ejpam-3756	144	17	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	144	18	)	)	PUNCT
ejpam-3756	144	19	n∏	n∏	PROPN
ejpam-3756	144	20	k=0	k=0	PROPN
ejpam-3756	144	21	(	(	PUNCT
ejpam-3756	144	22	1−	1−	NUM
ejpam-3756	144	23	(	(	PUNCT
ejpam-3756	144	24	1−	1−	NUM
ejpam-3756	144	25	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	144	26	)	)	PUNCT
ejpam-3756	144	27	is	be	AUX
ejpam-3756	144	28	correct	correct	ADJ
ejpam-3756	144	29	.	.	PUNCT
ejpam-3756	145	1	now	now	ADV
ejpam-3756	145	2	,	,	PUNCT
ejpam-3756	145	3	let	let	VERB
ejpam-3756	145	4	rn	rn	X
ejpam-3756	145	5	=	=	NOUN
ejpam-3756	146	1	‖ζ0	‖ζ0	ADJ
ejpam-3756	146	2	−	−	NUM
ejpam-3756	146	3	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	146	4	)	)	PUNCT
ejpam-3756	146	5	n∏	n∏	PROPN
ejpam-3756	146	6	k=0	k=0	PROPN
ejpam-3756	146	7	(	(	PUNCT
ejpam-3756	146	8	1−	1−	NUM
ejpam-3756	146	9	(	(	PUNCT
ejpam-3756	146	10	1−	1−	NUM
ejpam-3756	146	11	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	146	12	)	)	PUNCT
ejpam-3756	146	13	and	and	CCONJ
ejpam-3756	146	14	pn	pn	PROPN
ejpam-3756	146	15	=	=	PROPN
ejpam-3756	146	16	‖x′0	‖x′0	PROPN
ejpam-3756	146	17	−	−	PROPN
ejpam-3756	146	18	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	146	19	)	)	PUNCT
ejpam-3756	146	20	n∏	n∏	PROPN
ejpam-3756	147	1	k=1	k=1	NOUN
ejpam-3756	147	2	(	(	PUNCT
ejpam-3756	147	3	1−	1−	NUM
ejpam-3756	147	4	(	(	PUNCT
ejpam-3756	147	5	1−	1−	NUM
ejpam-3756	147	6	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	147	7	)	)	PUNCT
ejpam-3756	147	8	then	then	ADV
ejpam-3756	147	9	pn	pn	PROPN
ejpam-3756	147	10	rn	rn	PROPN
ejpam-3756	147	11	=	=	PROPN
ejpam-3756	147	12	‖x′0	‖x′0	PROPN
ejpam-3756	147	13	−	−	PROPN
ejpam-3756	147	14	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	147	15	)	)	PUNCT
ejpam-3756	148	1	∏n	∏n	PROPN
ejpam-3756	148	2	k=0(1−	k=0(1−	PROPN
ejpam-3756	148	3	(	(	PUNCT
ejpam-3756	148	4	1−	1−	NUM
ejpam-3756	148	5	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	148	6	)	)	PUNCT
ejpam-3756	148	7	‖ζ0	‖ζ0	ADJ
ejpam-3756	148	8	−	−	NUM
ejpam-3756	148	9	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	148	10	)	)	PUNCT
ejpam-3756	148	11	∏n	∏n	PROPN
ejpam-3756	148	12	k=0(1−	k=0(1−	PROPN
ejpam-3756	148	13	(	(	PUNCT
ejpam-3756	148	14	1−	1−	NUM
ejpam-3756	148	15	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	148	16	)	)	PUNCT
ejpam-3756	148	17	approaches	approach	VERB
ejpam-3756	148	18	to	to	ADP
ejpam-3756	148	19	0	0	NUM
ejpam-3756	148	20	as	as	ADP
ejpam-3756	148	21	n	n	PRON
ejpam-3756	148	22	approaches	approach	NOUN
ejpam-3756	148	23	to	to	ADP
ejpam-3756	148	24	∞.	∞.	PROPN
ejpam-3756	148	25	thus	thus	ADV
ejpam-3756	148	26	,	,	PUNCT
ejpam-3756	148	27	{	{	PUNCT
ejpam-3756	148	28	ζn	ζn	NOUN
ejpam-3756	148	29	}	}	PUNCT
ejpam-3756	148	30	is	be	AUX
ejpam-3756	148	31	a	a	DET
ejpam-3756	148	32	sequence	sequence	NOUN
ejpam-3756	148	33	defined	define	VERB
ejpam-3756	148	34	in	in	ADP
ejpam-3756	148	35	nv	nv	PROPN
ejpam-3756	148	36	1	1	NUM
ejpam-3756	148	37	iteration	iteration	NOUN
ejpam-3756	148	38	defined	define	VERB
ejpam-3756	148	39	by	by	ADP
ejpam-3756	148	40	(	(	PUNCT
ejpam-3756	148	41	1.14	1.14	NUM
ejpam-3756	148	42	)	)	PUNCT
ejpam-3756	148	43	,	,	PUNCT
ejpam-3756	148	44	then	then	ADV
ejpam-3756	148	45	{	{	PUNCT
ejpam-3756	148	46	ζn	ζn	NOUN
ejpam-3756	148	47	}	}	PUNCT
ejpam-3756	148	48	converges	converge	VERB
ejpam-3756	148	49	faster	fast	ADV
ejpam-3756	148	50	than	than	ADP
ejpam-3756	148	51	the	the	DET
ejpam-3756	148	52	iteration	iteration	NOUN
ejpam-3756	148	53	scheme	scheme	NOUN
ejpam-3756	148	54	of	of	ADP
ejpam-3756	148	55	ullah	ullah	PROPN
ejpam-3756	148	56	and	and	CCONJ
ejpam-3756	148	57	muhhamad	muhhamad	NOUN
ejpam-3756	148	58	known	know	VERB
ejpam-3756	148	59	as	as	ADP
ejpam-3756	148	60	k∗.	k∗.	PROPN
ejpam-3756	148	61	l.n	l.n	PROPN
ejpam-3756	148	62	mishra	mishra	PROPN
ejpam-3756	148	63	et	et	PROPN
ejpam-3756	148	64	al	al	PROPN
ejpam-3756	148	65	.	.	PUNCT
ejpam-3756	148	66	/	/	SYM
ejpam-3756	148	67	eur	eur	PROPN
ejpam-3756	148	68	.	.	PUNCT
ejpam-3756	149	1	j.	j.	PROPN
ejpam-3756	149	2	pure	pure	PROPN
ejpam-3756	149	3	appl	appl	PROPN
ejpam-3756	149	4	.	.	PROPN
ejpam-3756	149	5	math	math	PROPN
ejpam-3756	149	6	,	,	PUNCT
ejpam-3756	149	7	13	13	NUM
ejpam-3756	149	8	(	(	PUNCT
ejpam-3756	149	9	5	5	NUM
ejpam-3756	149	10	)	)	PUNCT
ejpam-3756	149	11	(	(	PUNCT
ejpam-3756	149	12	2020	2020	NUM
ejpam-3756	149	13	)	)	PUNCT
ejpam-3756	149	14	,	,	PUNCT
ejpam-3756	149	15	1110	1110	NUM
ejpam-3756	149	16	-	-	SYM
ejpam-3756	149	17	1130	1130	NUM
ejpam-3756	149	18	1118	1118	NUM
ejpam-3756	149	19	theorem	theorem	NOUN
ejpam-3756	149	20	3	3	X
ejpam-3756	149	21	.	.	PUNCT
ejpam-3756	149	22	suppose	suppose	VERB
ejpam-3756	149	23	that	that	SCONJ
ejpam-3756	149	24	there	there	PRON
ejpam-3756	149	25	is	be	VERB
ejpam-3756	149	26	a	a	DET
ejpam-3756	149	27	banach	banach	NOUN
ejpam-3756	149	28	space	space	NOUN
ejpam-3756	149	29	e	e	NOUN
ejpam-3756	149	30	,	,	PUNCT
ejpam-3756	149	31	having	having	AUX
ejpam-3756	149	32	subset	subset	VERB
ejpam-3756	149	33	c	c	NOUN
ejpam-3756	149	34	,	,	PUNCT
ejpam-3756	149	35	which	which	PRON
ejpam-3756	149	36	is	be	AUX
ejpam-3756	149	37	nonempty	nonempty	ADV
ejpam-3756	149	38	closed	closed	ADJ
ejpam-3756	149	39	and	and	CCONJ
ejpam-3756	149	40	convex	convex	VERB
ejpam-3756	149	41	and	and	CCONJ
ejpam-3756	149	42	also	also	ADV
ejpam-3756	149	43	that	that	SCONJ
ejpam-3756	149	44	there	there	PRON
ejpam-3756	149	45	is	be	VERB
ejpam-3756	149	46	a	a	DET
ejpam-3756	149	47	contraction	contraction	NOUN
ejpam-3756	149	48	mapping	mapping	NOUN
ejpam-3756	149	49	t	t	NOUN
ejpam-3756	149	50	with	with	ADP
ejpam-3756	149	51	contraction	contraction	NOUN
ejpam-3756	149	52	factor	factor	NOUN
ejpam-3756	149	53	ξ	ξ	X
ejpam-3756	149	54	∈	∈	PROPN
ejpam-3756	149	55	(	(	PUNCT
ejpam-3756	149	56	0	0	NUM
ejpam-3756	149	57	,	,	PUNCT
ejpam-3756	149	58	1	1	NUM
ejpam-3756	149	59	)	)	PUNCT
ejpam-3756	149	60	such	such	ADJ
ejpam-3756	149	61	that	that	SCONJ
ejpam-3756	149	62	tf	tf	PROPN
ejpam-3756	149	63	6=	6=	ADP
ejpam-3756	149	64	∅.	∅.	VERB
ejpam-3756	149	65	if	if	SCONJ
ejpam-3756	149	66	{	{	PUNCT
ejpam-3756	149	67	ζn	ζn	NOUN
ejpam-3756	149	68	}	}	PUNCT
ejpam-3756	149	69	is	be	AUX
ejpam-3756	149	70	a	a	DET
ejpam-3756	149	71	sequence	sequence	NOUN
ejpam-3756	149	72	defined	define	VERB
ejpam-3756	149	73	in	in	ADP
ejpam-3756	149	74	nv	nv	PROPN
ejpam-3756	149	75	1	1	NUM
ejpam-3756	149	76	iteration	iteration	NOUN
ejpam-3756	149	77	defined	define	VERB
ejpam-3756	149	78	by	by	ADP
ejpam-3756	149	79	(	(	PUNCT
ejpam-3756	149	80	1.14	1.14	NUM
ejpam-3756	149	81	)	)	PUNCT
ejpam-3756	149	82	,	,	PUNCT
ejpam-3756	149	83	then	then	ADV
ejpam-3756	149	84	{	{	PUNCT
ejpam-3756	149	85	x′′n	x′′n	PROPN
ejpam-3756	149	86	}	}	PUNCT
ejpam-3756	149	87	converges	converge	VERB
ejpam-3756	149	88	faster	fast	ADV
ejpam-3756	149	89	than	than	ADP
ejpam-3756	149	90	the	the	DET
ejpam-3756	149	91	iteration	iteration	NOUN
ejpam-3756	149	92	scheme	scheme	NOUN
ejpam-3756	149	93	of	of	ADP
ejpam-3756	149	94	garodia	garodia	NOUN
ejpam-3756	149	95	and	and	CCONJ
ejpam-3756	149	96	uddin	uddin	PROPN
ejpam-3756	149	97	defined	define	VERB
ejpam-3756	149	98	by	by	ADP
ejpam-3756	149	99	(	(	PUNCT
ejpam-3756	149	100	1.12	1.12	NUM
ejpam-3756	149	101	)	)	PUNCT
ejpam-3756	149	102	.	.	PUNCT
ejpam-3756	150	1	proof	proof	NOUN
ejpam-3756	150	2	.	.	PUNCT
ejpam-3756	151	1	using	use	VERB
ejpam-3756	151	2	the	the	DET
ejpam-3756	151	3	result	result	NOUN
ejpam-3756	151	4	of	of	ADP
ejpam-3756	151	5	theorem	theorem	NOUN
ejpam-3756	151	6	1	1	NUM
ejpam-3756	151	7	it	it	PRON
ejpam-3756	151	8	is	be	AUX
ejpam-3756	151	9	clear	clear	ADJ
ejpam-3756	151	10	that	that	SCONJ
ejpam-3756	151	11	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	152	1	−	−	NOUN
ejpam-3756	152	2	xδ‖	xδ‖	PROPN
ejpam-3756	152	3	≤	≤	NUM
ejpam-3756	152	4	‖ζ0	‖ζ0	ADJ
ejpam-3756	152	5	−	−	NUM
ejpam-3756	152	6	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	152	7	)	)	PUNCT
ejpam-3756	152	8	n∏	n∏	PROPN
ejpam-3756	152	9	k=0	k=0	PROPN
ejpam-3756	152	10	(	(	PUNCT
ejpam-3756	152	11	1−	1−	NUM
ejpam-3756	152	12	σ0k(1−	σ0k(1−	PROPN
ejpam-3756	152	13	ξ	ξ	PROPN
ejpam-3756	152	14	)	)	PUNCT
ejpam-3756	152	15	)	)	PUNCT
ejpam-3756	152	16	now	now	ADV
ejpam-3756	152	17	,	,	PUNCT
ejpam-3756	152	18	for	for	ADP
ejpam-3756	152	19	scheme	scheme	NOUN
ejpam-3756	152	20	(	(	PUNCT
ejpam-3756	152	21	1.12	1.12	NUM
ejpam-3756	152	22	)	)	PUNCT
ejpam-3756	152	23	,	,	PUNCT
ejpam-3756	152	24	‖z′′n	‖z′′n	NOUN
ejpam-3756	152	25	−	−	PROPN
ejpam-3756	152	26	xδ‖	xδ‖	PROPN
ejpam-3756	152	27	=	=	SYM
ejpam-3756	152	28	‖tx′′n	‖tx′′n	NOUN
ejpam-3756	152	29	−	−	PROPN
ejpam-3756	152	30	xδ‖	xδ‖	PROPN
ejpam-3756	152	31	≤	≤	PROPN
ejpam-3756	152	32	ξ‖x′′n	ξ‖x′′n	NOUN
ejpam-3756	152	33	−	−	PROPN
ejpam-3756	152	34	xδ‖	xδ‖	PROPN
ejpam-3756	153	1	‖y′′n	‖y′′n	NOUN
ejpam-3756	153	2	−	−	PROPN
ejpam-3756	153	3	xδ‖	xδ‖	PROPN
ejpam-3756	154	1	=	=	SYM
ejpam-3756	154	2	‖(1−	‖(1−	PROPN
ejpam-3756	154	3	σ0n)z′′n	σ0n)z′′n	NOUN
ejpam-3756	154	4	−	−	NOUN
ejpam-3756	154	5	σ0ntz′′n	σ0ntz′′n	NOUN
ejpam-3756	154	6	−	−	NOUN
ejpam-3756	154	7	xδ‖	xδ‖	PROPN
ejpam-3756	155	1	≤	≤	ADV
ejpam-3756	155	2	‖(1−	‖(1−	PROPN
ejpam-3756	155	3	σ0n)z′′n	σ0n)z′′n	NOUN
ejpam-3756	155	4	−	−	NOUN
ejpam-3756	155	5	σ0ntz′′n	σ0ntz′′n	NOUN
ejpam-3756	155	6	−	−	NOUN
ejpam-3756	155	7	xδ‖	xδ‖	PROPN
ejpam-3756	155	8	≤	≤	NOUN
ejpam-3756	155	9	(	(	PUNCT
ejpam-3756	155	10	1−	1−	NUM
ejpam-3756	155	11	σ0n)‖z′′n	σ0n)‖z′′n	NOUN
ejpam-3756	155	12	−	−	PROPN
ejpam-3756	155	13	xδ‖+	xδ‖+	PROPN
ejpam-3756	155	14	ξσ0n‖tz′′n	ξσ0n‖tz′′n	NOUN
ejpam-3756	156	1	−	−	NOUN
ejpam-3756	157	1	xδ‖	xδ‖	PROPN
ejpam-3756	157	2	]	]	X
ejpam-3756	157	3	≤	≤	NUM
ejpam-3756	157	4	(	(	PUNCT
ejpam-3756	157	5	1−	1−	NUM
ejpam-3756	157	6	σ0n)‖z′′n	σ0n)‖z′′n	NOUN
ejpam-3756	157	7	−	−	NOUN
ejpam-3756	157	8	xδ‖+	xδ‖+	PUNCT
ejpam-3756	158	1	ξσ0n‖z′′n	ξσ0n‖z′′n	PROPN
ejpam-3756	158	2	−	−	PROPN
ejpam-3756	158	3	xδ‖	xδ‖	PROPN
ejpam-3756	159	1	=	=	SYM
ejpam-3756	159	2	(	(	PUNCT
ejpam-3756	159	3	1−	1−	NUM
ejpam-3756	159	4	(	(	PUNCT
ejpam-3756	159	5	1−	1−	NUM
ejpam-3756	159	6	ξ)σ0n)‖z′′n	ξ)σ0n)‖z′′n	NOUN
ejpam-3756	159	7	−	−	NOUN
ejpam-3756	159	8	xδ‖	xδ‖	PUNCT
ejpam-3756	160	1	thus	thus	ADV
ejpam-3756	160	2	,	,	PUNCT
ejpam-3756	160	3	‖x′′n+1	‖x′′n+1	PROPN
ejpam-3756	160	4	−	−	NOUN
ejpam-3756	160	5	xδ‖	xδ‖	PROPN
ejpam-3756	160	6	=	=	SYM
ejpam-3756	160	7	‖ty′′n	‖ty′′n	NOUN
ejpam-3756	160	8	−	−	NOUN
ejpam-3756	160	9	xδ‖	xδ‖	PROPN
ejpam-3756	160	10	≤	≤	PROPN
ejpam-3756	160	11	ξ‖y′′n	ξ‖y′′n	PROPN
ejpam-3756	160	12	−	−	PROPN
ejpam-3756	160	13	xδ‖	xδ‖	NOUN
ejpam-3756	161	1	using	use	VERB
ejpam-3756	161	2	the	the	DET
ejpam-3756	161	3	value	value	NOUN
ejpam-3756	161	4	of	of	ADP
ejpam-3756	161	5	‖y′′n	‖y′′n	NOUN
ejpam-3756	161	6	−	−	NOUN
ejpam-3756	161	7	xδ‖	xδ‖	PROPN
ejpam-3756	161	8	and	and	CCONJ
ejpam-3756	161	9	using	use	VERB
ejpam-3756	161	10	the	the	DET
ejpam-3756	161	11	inductive	inductive	ADJ
ejpam-3756	161	12	behaviour	behaviour	NOUN
ejpam-3756	161	13	,	,	PUNCT
ejpam-3756	161	14	we	we	PRON
ejpam-3756	161	15	have	have	VERB
ejpam-3756	161	16	‖x′′n+1	‖x′′n+1	NUM
ejpam-3756	161	17	−	−	NOUN
ejpam-3756	161	18	xδ‖	xδ‖	PROPN
ejpam-3756	162	1	=	=	SYM
ejpam-3756	162	2	ξ2(1−	ξ2(1−	PROPN
ejpam-3756	162	3	(	(	PUNCT
ejpam-3756	162	4	1−	1−	NUM
ejpam-3756	162	5	ξ)σ0n)‖x′′n	ξ)σ0n)‖x′′n	NOUN
ejpam-3756	162	6	−	−	NOUN
ejpam-3756	162	7	xδ‖	xδ‖	PROPN
ejpam-3756	163	1	‖x′′n	‖x′′n	NOUN
ejpam-3756	163	2	−	−	PROPN
ejpam-3756	163	3	xδ‖	xδ‖	PROPN
ejpam-3756	163	4	=	=	SYM
ejpam-3756	164	1	ξ2(1−	ξ2(1−	PROPN
ejpam-3756	164	2	(	(	PUNCT
ejpam-3756	164	3	1−	1−	NUM
ejpam-3756	164	4	ξ)σ0n−1)‖x′′n−1	ξ)σ0n−1)‖x′′n−1	NOUN
ejpam-3756	164	5	−	−	PROPN
ejpam-3756	164	6	xδ‖	xδ‖	PROPN
ejpam-3756	164	7	‖x′′n−1	‖x′′n−1	ADP
ejpam-3756	164	8	−	−	PROPN
ejpam-3756	164	9	xδ‖	xδ‖	PROPN
ejpam-3756	164	10	=	=	SYM
ejpam-3756	165	1	ξ2(1−	ξ2(1−	PROPN
ejpam-3756	165	2	(	(	PUNCT
ejpam-3756	165	3	1−	1−	NUM
ejpam-3756	165	4	ξ)σ0n−2)‖x′′n−2	ξ)σ0n−2)‖x′′n−2	NOUN
ejpam-3756	165	5	−	−	PROPN
ejpam-3756	165	6	xδ‖	xδ‖	PROPN
ejpam-3756	165	7	on	on	ADP
ejpam-3756	165	8	combining	combine	VERB
ejpam-3756	165	9	all	all	DET
ejpam-3756	165	10	the	the	DET
ejpam-3756	165	11	inequalities	inequality	NOUN
ejpam-3756	165	12	,	,	PUNCT
ejpam-3756	165	13	we	we	PRON
ejpam-3756	165	14	have	have	VERB
ejpam-3756	165	15	‖x′′n+1	‖x′′n+1	NUM
ejpam-3756	165	16	−	−	NOUN
ejpam-3756	166	1	xδ‖	xδ‖	PROPN
ejpam-3756	166	2	≤	≤	NUM
ejpam-3756	166	3	‖x′′0	‖x′′0	ADJ
ejpam-3756	166	4	−	−	PROPN
ejpam-3756	166	5	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	166	6	)	)	PUNCT
ejpam-3756	166	7	n∏	n∏	PROPN
ejpam-3756	166	8	k=0	k=0	PROPN
ejpam-3756	166	9	(	(	PUNCT
ejpam-3756	166	10	1−	1−	NUM
ejpam-3756	166	11	σ0k(1−	σ0k(1−	PROPN
ejpam-3756	166	12	ξ	ξ	PROPN
ejpam-3756	166	13	)	)	PUNCT
ejpam-3756	166	14	)	)	PUNCT
ejpam-3756	166	15	let	let	VERB
ejpam-3756	166	16	rn	rn	PROPN
ejpam-3756	166	17	=	=	NOUN
ejpam-3756	167	1	‖ζ0	‖ζ0	ADJ
ejpam-3756	167	2	−	−	NUM
ejpam-3756	167	3	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	167	4	)	)	PUNCT
ejpam-3756	167	5	n∏	n∏	PROPN
ejpam-3756	167	6	k=0	k=0	PROPN
ejpam-3756	167	7	(	(	PUNCT
ejpam-3756	167	8	1−	1−	NUM
ejpam-3756	167	9	(	(	PUNCT
ejpam-3756	167	10	1−	1−	NUM
ejpam-3756	167	11	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	167	12	)	)	PUNCT
ejpam-3756	167	13	l.n	l.n	PROPN
ejpam-3756	167	14	mishra	mishra	PROPN
ejpam-3756	167	15	et	et	PROPN
ejpam-3756	167	16	al	al	PROPN
ejpam-3756	167	17	.	.	PUNCT
ejpam-3756	167	18	/	/	SYM
ejpam-3756	167	19	eur	eur	PROPN
ejpam-3756	167	20	.	.	PUNCT
ejpam-3756	168	1	j.	j.	PROPN
ejpam-3756	168	2	pure	pure	PROPN
ejpam-3756	168	3	appl	appl	PROPN
ejpam-3756	168	4	.	.	PROPN
ejpam-3756	168	5	math	math	PROPN
ejpam-3756	168	6	,	,	PUNCT
ejpam-3756	168	7	13	13	NUM
ejpam-3756	168	8	(	(	PUNCT
ejpam-3756	168	9	5	5	NUM
ejpam-3756	168	10	)	)	PUNCT
ejpam-3756	168	11	(	(	PUNCT
ejpam-3756	168	12	2020	2020	NUM
ejpam-3756	168	13	)	)	PUNCT
ejpam-3756	168	14	,	,	PUNCT
ejpam-3756	168	15	1110	1110	NUM
ejpam-3756	168	16	-	-	SYM
ejpam-3756	168	17	1130	1130	NUM
ejpam-3756	168	18	1119	1119	NUM
ejpam-3756	168	19	and	and	CCONJ
ejpam-3756	168	20	pn	pn	NOUN
ejpam-3756	168	21	=	=	SYM
ejpam-3756	168	22	‖x′′0	‖x′′0	NOUN
ejpam-3756	168	23	−	−	PROPN
ejpam-3756	168	24	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	168	25	)	)	PUNCT
ejpam-3756	168	26	n∏	n∏	PROPN
ejpam-3756	169	1	k=0	k=0	PROPN
ejpam-3756	169	2	(	(	PUNCT
ejpam-3756	169	3	1−	1−	NUM
ejpam-3756	169	4	(	(	PUNCT
ejpam-3756	169	5	1−	1−	NUM
ejpam-3756	169	6	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	169	7	)	)	PUNCT
ejpam-3756	169	8	then	then	ADV
ejpam-3756	169	9	pn	pn	PROPN
ejpam-3756	169	10	rn	rn	PROPN
ejpam-3756	169	11	=	=	PROPN
ejpam-3756	169	12	‖x′′0	‖x′′0	NOUN
ejpam-3756	169	13	−	−	PROPN
ejpam-3756	169	14	xδ‖ξ2(n+1	xδ‖ξ2(n+1	PROPN
ejpam-3756	169	15	)	)	PUNCT
ejpam-3756	169	16	∏n	∏n	PROPN
ejpam-3756	169	17	k=0(1−	k=0(1−	PROPN
ejpam-3756	169	18	(	(	PUNCT
ejpam-3756	169	19	1−	1−	NUM
ejpam-3756	169	20	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	169	21	)	)	PUNCT
ejpam-3756	169	22	‖ζ0	‖ζ0	ADJ
ejpam-3756	169	23	−	−	NUM
ejpam-3756	169	24	xδ‖ξ3(n+1	xδ‖ξ3(n+1	NUM
ejpam-3756	169	25	)	)	PUNCT
ejpam-3756	169	26	∏n	∏n	PROPN
ejpam-3756	169	27	k=0(1−	k=0(1−	PROPN
ejpam-3756	169	28	(	(	PUNCT
ejpam-3756	169	29	1−	1−	NUM
ejpam-3756	169	30	ξ)σ0k	ξ)σ0k	NOUN
ejpam-3756	169	31	)	)	PUNCT
ejpam-3756	169	32	approaches	approach	VERB
ejpam-3756	169	33	to	to	ADP
ejpam-3756	169	34	0	0	NUM
ejpam-3756	169	35	as	as	ADP
ejpam-3756	169	36	n	n	PRON
ejpam-3756	169	37	approaches	approach	NOUN
ejpam-3756	169	38	to	to	ADP
ejpam-3756	169	39	∞.	∞.	PROPN
ejpam-3756	169	40	thus	thus	ADV
ejpam-3756	169	41	{	{	PUNCT
ejpam-3756	169	42	ζn	ζn	NOUN
ejpam-3756	169	43	}	}	PUNCT
ejpam-3756	169	44	is	be	AUX
ejpam-3756	169	45	a	a	DET
ejpam-3756	169	46	sequence	sequence	NOUN
ejpam-3756	169	47	defined	define	VERB
ejpam-3756	169	48	in	in	ADP
ejpam-3756	169	49	nv	nv	PROPN
ejpam-3756	169	50	1	1	NUM
ejpam-3756	169	51	iteration	iteration	NOUN
ejpam-3756	169	52	defined	define	VERB
ejpam-3756	169	53	by	by	ADP
ejpam-3756	169	54	(	(	PUNCT
ejpam-3756	169	55	1.14	1.14	NUM
ejpam-3756	169	56	)	)	PUNCT
ejpam-3756	169	57	,	,	PUNCT
ejpam-3756	169	58	then	then	ADV
ejpam-3756	169	59	{	{	PUNCT
ejpam-3756	169	60	ζn	ζn	NOUN
ejpam-3756	169	61	}	}	PUNCT
ejpam-3756	169	62	converges	converge	VERB
ejpam-3756	169	63	faster	fast	ADV
ejpam-3756	169	64	than	than	ADP
ejpam-3756	169	65	the	the	DET
ejpam-3756	169	66	iteration	iteration	NOUN
ejpam-3756	169	67	scheme	scheme	NOUN
ejpam-3756	169	68	of	of	ADP
ejpam-3756	169	69	garodia	garodia	NOUN
ejpam-3756	169	70	and	and	CCONJ
ejpam-3756	169	71	uddin	uddin	PROPN
ejpam-3756	169	72	defined	define	VERB
ejpam-3756	169	73	by	by	ADP
ejpam-3756	169	74	(	(	PUNCT
ejpam-3756	169	75	1.12	1.12	NUM
ejpam-3756	169	76	)	)	PUNCT
ejpam-3756	169	77	.	.	PUNCT
ejpam-3756	170	1	lemma	lemma	PROPN
ejpam-3756	170	2	2	2	X
ejpam-3756	170	3	.	.	PUNCT
ejpam-3756	171	1	let	let	VERB
ejpam-3756	171	2	c	c	PRON
ejpam-3756	171	3	be	be	AUX
ejpam-3756	171	4	a	a	DET
ejpam-3756	171	5	nonempty	nonempty	ADV
ejpam-3756	171	6	closed	close	VERB
ejpam-3756	171	7	convex	convex	NOUN
ejpam-3756	171	8	subset	subset	NOUN
ejpam-3756	171	9	of	of	ADP
ejpam-3756	171	10	a	a	DET
ejpam-3756	171	11	uniformly	uniformly	ADJ
ejpam-3756	171	12	convex	convex	NOUN
ejpam-3756	171	13	banach	banach	NOUN
ejpam-3756	171	14	space	space	NOUN
ejpam-3756	171	15	e	e	NOUN
ejpam-3756	171	16	and	and	CCONJ
ejpam-3756	171	17	a	a	DET
ejpam-3756	171	18	nonexpansive	nonexpansive	ADJ
ejpam-3756	171	19	self	self	NOUN
ejpam-3756	171	20	mapping	mapping	NOUN
ejpam-3756	171	21	t	t	NOUN
ejpam-3756	171	22	on	on	ADP
ejpam-3756	171	23	c	c	PROPN
ejpam-3756	171	24	with	with	ADP
ejpam-3756	171	25	tf	tf	PROPN
ejpam-3756	171	26	6=	6=	ADP
ejpam-3756	171	27	∅.	∅.	ADV
ejpam-3756	171	28	let	let	VERB
ejpam-3756	171	29	{	{	PUNCT
ejpam-3756	171	30	ζn	ζn	PART
ejpam-3756	171	31	}	}	PUNCT
ejpam-3756	171	32	be	be	AUX
ejpam-3756	171	33	an	an	DET
ejpam-3756	171	34	iterative	iterative	NOUN
ejpam-3756	171	35	sequence	sequence	NOUN
ejpam-3756	171	36	defined	define	VERB
ejpam-3756	171	37	as	as	ADP
ejpam-3756	171	38	nv	nv	PROPN
ejpam-3756	171	39	1	1	NUM
ejpam-3756	171	40	.	.	PUNCT
ejpam-3756	172	1	then	then	ADV
ejpam-3756	172	2	limn→∞	limn→∞	PROPN
ejpam-3756	172	3	‖ζn	‖ζn	NUM
ejpam-3756	172	4	−	−	PROPN
ejpam-3756	172	5	xδ‖	xδ‖	PROPN
ejpam-3756	172	6	exists	exist	VERB
ejpam-3756	172	7	for	for	ADP
ejpam-3756	172	8	all	all	PRON
ejpam-3756	172	9	xδ	xδ	PROPN
ejpam-3756	172	10	∈	∈	PROPN
ejpam-3756	172	11	tf	tf	INTJ
ejpam-3756	172	12	.	.	PUNCT
ejpam-3756	173	1	proof	proof	NOUN
ejpam-3756	173	2	.	.	PUNCT
ejpam-3756	174	1	from	from	ADP
ejpam-3756	174	2	nv	nv	PROPN
ejpam-3756	174	3	1	1	NUM
ejpam-3756	174	4	iteration	iteration	NOUN
ejpam-3756	174	5	scheme	scheme	NOUN
ejpam-3756	174	6	it	it	PRON
ejpam-3756	174	7	follows	follow	VERB
ejpam-3756	174	8	that	that	SCONJ
ejpam-3756	174	9	,	,	PUNCT
ejpam-3756	174	10	‖θn	‖θn	PROPN
ejpam-3756	174	11	−	−	PROPN
ejpam-3756	174	12	xδ‖	xδ‖	PROPN
ejpam-3756	175	1	=	=	SYM
ejpam-3756	175	2	‖t	‖t	NOUN
ejpam-3756	175	3	(	(	PUNCT
ejpam-3756	175	4	(	(	PUNCT
ejpam-3756	175	5	1−	1−	NUM
ejpam-3756	175	6	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	176	1	+	+	CCONJ
ejpam-3756	176	2	σ0ntζn)−	σ0ntζn)−	X
ejpam-3756	176	3	xδ‖	xδ‖	PUNCT
ejpam-3756	176	4	=	=	SYM
ejpam-3756	176	5	‖t	‖t	NOUN
ejpam-3756	176	6	(	(	PUNCT
ejpam-3756	176	7	(	(	PUNCT
ejpam-3756	176	8	1−	1−	NUM
ejpam-3756	176	9	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	176	10	+	+	CCONJ
ejpam-3756	176	11	σ0ntζn)−	σ0ntζn)−	PROPN
ejpam-3756	176	12	txδ‖	txδ‖	NOUN
ejpam-3756	176	13	≤	≤	NUM
ejpam-3756	176	14	‖(1−	‖(1−	NUM
ejpam-3756	176	15	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	176	16	+	+	CCONJ
ejpam-3756	176	17	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	176	18	−	−	NOUN
ejpam-3756	176	19	xδ‖	xδ‖	PROPN
ejpam-3756	176	20	≤	≤	NOUN
ejpam-3756	176	21	(	(	PUNCT
ejpam-3756	176	22	1−	1−	NUM
ejpam-3756	176	23	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	176	24	−	−	PROPN
ejpam-3756	176	25	xδ‖+	xδ‖+	PUNCT
ejpam-3756	177	1	σ0n‖tζn	σ0n‖tζn	PROPN
ejpam-3756	177	2	−	−	NOUN
ejpam-3756	177	3	txδ‖	txδ‖	NOUN
ejpam-3756	177	4	≤	≤	NUM
ejpam-3756	177	5	(	(	PUNCT
ejpam-3756	177	6	1−	1−	NUM
ejpam-3756	177	7	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	177	8	−	−	PROPN
ejpam-3756	177	9	xδ‖+	xδ‖+	PUNCT
ejpam-3756	178	1	σ0n‖ζn	σ0n‖ζn	PROPN
ejpam-3756	178	2	−	−	NOUN
ejpam-3756	178	3	xδ‖	xδ‖	PROPN
ejpam-3756	178	4	≤	≤	NOUN
ejpam-3756	178	5	‖ζn	‖ζn	NUM
ejpam-3756	178	6	−	−	NOUN
ejpam-3756	178	7	xδ‖	xδ‖	PROPN
ejpam-3756	179	1	‖ηn	‖ηn	NUM
ejpam-3756	179	2	−	−	NOUN
ejpam-3756	179	3	xδ‖	xδ‖	PROPN
ejpam-3756	179	4	≤	≤	NOUN
ejpam-3756	179	5	‖tθn	‖tθn	NOUN
ejpam-3756	179	6	−	−	NOUN
ejpam-3756	179	7	xδ‖	xδ‖	PUNCT
ejpam-3756	180	1	=	=	SYM
ejpam-3756	180	2	‖tθn	‖tθn	PROPN
ejpam-3756	180	3	−	−	NOUN
ejpam-3756	180	4	txδ‖	txδ‖	NOUN
ejpam-3756	180	5	≤	≤	NOUN
ejpam-3756	180	6	‖θn	‖θn	NUM
ejpam-3756	180	7	−	−	NOUN
ejpam-3756	180	8	xδ‖	xδ‖	NOUN
ejpam-3756	180	9	using	use	VERB
ejpam-3756	180	10	the	the	DET
ejpam-3756	180	11	value	value	NOUN
ejpam-3756	180	12	of	of	ADP
ejpam-3756	180	13	‖θn	‖θn	PROPN
ejpam-3756	180	14	−	−	PROPN
ejpam-3756	180	15	xδ‖	xδ‖	PROPN
ejpam-3756	180	16	,	,	PUNCT
ejpam-3756	180	17	we	we	PRON
ejpam-3756	180	18	have	have	VERB
ejpam-3756	180	19	‖ηn	‖ηn	NUM
ejpam-3756	180	20	−	−	NOUN
ejpam-3756	181	1	xδ‖	xδ‖	PROPN
ejpam-3756	181	2	≤	≤	NOUN
ejpam-3756	181	3	‖ζn	‖ζn	NUM
ejpam-3756	181	4	−	−	NOUN
ejpam-3756	181	5	xδ‖	xδ‖	PROPN
ejpam-3756	181	6	similarly	similarly	ADV
ejpam-3756	181	7	,	,	PUNCT
ejpam-3756	181	8	we	we	PRON
ejpam-3756	181	9	have	have	VERB
ejpam-3756	181	10	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	181	11	−	−	NOUN
ejpam-3756	181	12	xδ‖	xδ‖	PROPN
ejpam-3756	182	1	=	=	SYM
ejpam-3756	182	2	‖tηn	‖tηn	PROPN
ejpam-3756	182	3	−	−	PROPN
ejpam-3756	182	4	xδ‖	xδ‖	PROPN
ejpam-3756	183	1	=	=	SYM
ejpam-3756	183	2	‖tηn	‖tηn	ADP
ejpam-3756	183	3	−	−	PROPN
ejpam-3756	183	4	txδ‖	txδ‖	NOUN
ejpam-3756	183	5	≤	≤	NOUN
ejpam-3756	184	1	‖ηn	‖ηn	NUM
ejpam-3756	184	2	−	−	NOUN
ejpam-3756	184	3	xδ‖	xδ‖	PROPN
ejpam-3756	185	1	using	use	VERB
ejpam-3756	185	2	the	the	DET
ejpam-3756	185	3	value	value	NOUN
ejpam-3756	185	4	of	of	ADP
ejpam-3756	185	5	‖ηn	‖ηn	NUM
ejpam-3756	185	6	−	−	NOUN
ejpam-3756	185	7	xδ‖	xδ‖	PROPN
ejpam-3756	185	8	,	,	PUNCT
ejpam-3756	185	9	we	we	PRON
ejpam-3756	185	10	have	have	VERB
ejpam-3756	185	11	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	185	12	−	−	NOUN
ejpam-3756	186	1	xδ‖	xδ‖	PROPN
ejpam-3756	186	2	≤	≤	NOUN
ejpam-3756	186	3	‖ζn	‖ζn	NUM
ejpam-3756	186	4	−	−	NOUN
ejpam-3756	186	5	xδ‖	xδ‖	PROPN
ejpam-3756	187	1	l.n	l.n	PROPN
ejpam-3756	187	2	mishra	mishra	PROPN
ejpam-3756	187	3	et	et	PROPN
ejpam-3756	187	4	al	al	PROPN
ejpam-3756	187	5	.	.	PUNCT
ejpam-3756	187	6	/	/	SYM
ejpam-3756	187	7	eur	eur	PROPN
ejpam-3756	187	8	.	.	PUNCT
ejpam-3756	188	1	j.	j.	PROPN
ejpam-3756	188	2	pure	pure	PROPN
ejpam-3756	188	3	appl	appl	PROPN
ejpam-3756	188	4	.	.	PROPN
ejpam-3756	188	5	math	math	PROPN
ejpam-3756	188	6	,	,	PUNCT
ejpam-3756	188	7	13	13	NUM
ejpam-3756	188	8	(	(	PUNCT
ejpam-3756	188	9	5	5	NUM
ejpam-3756	188	10	)	)	PUNCT
ejpam-3756	188	11	(	(	PUNCT
ejpam-3756	188	12	2020	2020	NUM
ejpam-3756	188	13	)	)	PUNCT
ejpam-3756	188	14	,	,	PUNCT
ejpam-3756	188	15	1110	1110	NUM
ejpam-3756	188	16	-	-	SYM
ejpam-3756	188	17	1130	1130	NUM
ejpam-3756	188	18	1120	1120	NUM
ejpam-3756	188	19	which	which	PRON
ejpam-3756	188	20	confirms	confirm	VERB
ejpam-3756	188	21	the	the	DET
ejpam-3756	188	22	existence	existence	NOUN
ejpam-3756	188	23	of	of	ADP
ejpam-3756	188	24	limn→∞	limn→∞	PROPN
ejpam-3756	188	25	‖ζn	‖ζn	NUM
ejpam-3756	188	26	−	−	PROPN
ejpam-3756	188	27	xδ‖	xδ‖	PROPN
ejpam-3756	188	28	for	for	ADP
ejpam-3756	188	29	all	all	PRON
ejpam-3756	188	30	xδ	xδ	PROPN
ejpam-3756	188	31	∈	∈	PROPN
ejpam-3756	189	1	tf	tf	INTJ
ejpam-3756	189	2	.	.	PUNCT
ejpam-3756	190	1	since	since	SCONJ
ejpam-3756	190	2	,	,	PUNCT
ejpam-3756	190	3	{	{	PUNCT
ejpam-3756	190	4	‖ζn	‖ζn	NUM
ejpam-3756	190	5	−	−	NOUN
ejpam-3756	190	6	xδ‖	xδ‖	PROPN
ejpam-3756	190	7	}	}	PUNCT
ejpam-3756	190	8	is	be	AUX
ejpam-3756	190	9	bounded	bound	VERB
ejpam-3756	190	10	and	and	CCONJ
ejpam-3756	190	11	non	non	ADJ
ejpam-3756	190	12	-	-	ADJ
ejpam-3756	190	13	increasing	increase	VERB
ejpam-3756	190	14	for	for	ADP
ejpam-3756	190	15	all	all	PRON
ejpam-3756	190	16	xδ	xδ	PROPN
ejpam-3756	190	17	∈	∈	PROPN
ejpam-3756	190	18	tf	tf	INTJ
ejpam-3756	190	19	.	.	PUNCT
ejpam-3756	191	1	now	now	ADV
ejpam-3756	191	2	,	,	PUNCT
ejpam-3756	191	3	we	we	PRON
ejpam-3756	191	4	prove	prove	VERB
ejpam-3756	191	5	the	the	DET
ejpam-3756	191	6	weak	weak	ADJ
ejpam-3756	191	7	convergence	convergence	NOUN
ejpam-3756	191	8	of	of	ADP
ejpam-3756	191	9	nv	nv	PROPN
ejpam-3756	191	10	1	1	NUM
ejpam-3756	191	11	iteration	iteration	NOUN
ejpam-3756	191	12	process	process	NOUN
ejpam-3756	191	13	.	.	PUNCT
ejpam-3756	192	1	theorem	theorem	ADJ
ejpam-3756	192	2	4	4	NUM
ejpam-3756	192	3	.	.	PUNCT
ejpam-3756	192	4	suppose	suppose	VERB
ejpam-3756	192	5	that	that	SCONJ
ejpam-3756	192	6	there	there	PRON
ejpam-3756	192	7	is	be	VERB
ejpam-3756	192	8	a	a	DET
ejpam-3756	192	9	uniformly	uniformly	ADJ
ejpam-3756	192	10	banach	banach	NOUN
ejpam-3756	192	11	space	space	NOUN
ejpam-3756	192	12	e	e	NOUN
ejpam-3756	192	13	,	,	PUNCT
ejpam-3756	192	14	having	have	VERB
ejpam-3756	192	15	a	a	DET
ejpam-3756	192	16	nonempty	nonempty	ADJ
ejpam-3756	192	17	subset	subset	NOUN
ejpam-3756	192	18	c	c	NOUN
ejpam-3756	192	19	,	,	PUNCT
ejpam-3756	192	20	which	which	PRON
ejpam-3756	192	21	is	be	AUX
ejpam-3756	192	22	nonempty	nonempty	ADV
ejpam-3756	192	23	closed	close	VERB
ejpam-3756	192	24	and	and	CCONJ
ejpam-3756	192	25	convex	convex	VERB
ejpam-3756	192	26	satisfying	satisfy	VERB
ejpam-3756	192	27	opial	opial	NOUN
ejpam-3756	192	28	’s	’s	PART
ejpam-3756	192	29	condition	condition	NOUN
ejpam-3756	192	30	and	and	CCONJ
ejpam-3756	192	31	also	also	ADV
ejpam-3756	192	32	that	that	SCONJ
ejpam-3756	192	33	there	there	PRON
ejpam-3756	192	34	is	be	VERB
ejpam-3756	192	35	a	a	DET
ejpam-3756	192	36	nonexpansive	nonexpansive	ADJ
ejpam-3756	192	37	mapping	mapping	NOUN
ejpam-3756	192	38	t	t	NOUN
ejpam-3756	192	39	:	:	PUNCT
ejpam-3756	192	40	c	c	X
ejpam-3756	192	41	→	→	SYM
ejpam-3756	192	42	c	c	NOUN
ejpam-3756	192	43	with	with	ADP
ejpam-3756	192	44	tf	tf	PROPN
ejpam-3756	192	45	6=	6=	ADP
ejpam-3756	192	46	∅.	∅.	VERB
ejpam-3756	192	47	if	if	SCONJ
ejpam-3756	192	48	{	{	PUNCT
ejpam-3756	192	49	ζn	ζn	NOUN
ejpam-3756	192	50	}	}	PUNCT
ejpam-3756	192	51	is	be	AUX
ejpam-3756	192	52	an	an	DET
ejpam-3756	192	53	iterative	iterative	NOUN
ejpam-3756	192	54	sequence	sequence	NOUN
ejpam-3756	192	55	defined	define	VERB
ejpam-3756	192	56	by	by	ADP
ejpam-3756	192	57	nv	nv	PROPN
ejpam-3756	192	58	1	1	NUM
ejpam-3756	192	59	,	,	PUNCT
ejpam-3756	192	60	then	then	ADV
ejpam-3756	192	61	{	{	PUNCT
ejpam-3756	192	62	ζn	ζn	NOUN
ejpam-3756	192	63	}	}	PUNCT
ejpam-3756	192	64	converges	converge	VERB
ejpam-3756	192	65	weakly	weakly	ADV
ejpam-3756	192	66	to	to	ADP
ejpam-3756	192	67	a	a	DET
ejpam-3756	192	68	fixed	fix	VERB
ejpam-3756	192	69	point	point	NOUN
ejpam-3756	192	70	of	of	ADP
ejpam-3756	192	71	t	t	PROPN
ejpam-3756	192	72	.	.	PUNCT
ejpam-3756	193	1	proof	proof	NOUN
ejpam-3756	193	2	.	.	PUNCT
ejpam-3756	194	1	let	let	VERB
ejpam-3756	194	2	xδ	xδ	PROPN
ejpam-3756	194	3	∈	∈	PROPN
ejpam-3756	195	1	tf	tf	INTJ
ejpam-3756	195	2	.	.	PUNCT
ejpam-3756	196	1	then	then	ADV
ejpam-3756	196	2	from	from	ADP
ejpam-3756	196	3	lemma	lemma	PROPN
ejpam-3756	196	4	2	2	NUM
ejpam-3756	196	5	,	,	PUNCT
ejpam-3756	196	6	it	it	PRON
ejpam-3756	196	7	is	be	AUX
ejpam-3756	196	8	obvious	obvious	ADJ
ejpam-3756	196	9	that	that	SCONJ
ejpam-3756	196	10	limn→∞	limn→∞	PROPN
ejpam-3756	196	11	‖ζn	‖ζn	NUM
ejpam-3756	196	12	−	−	NOUN
ejpam-3756	196	13	xδ‖	xδ‖	PROPN
ejpam-3756	196	14	exists	exist	VERB
ejpam-3756	196	15	.	.	PUNCT
ejpam-3756	197	1	to	to	PART
ejpam-3756	197	2	prove	prove	VERB
ejpam-3756	197	3	weak	weak	ADJ
ejpam-3756	197	4	convergence	convergence	NOUN
ejpam-3756	197	5	of	of	ADP
ejpam-3756	197	6	nv	nv	PROPN
ejpam-3756	197	7	1	1	NUM
ejpam-3756	197	8	iterative	iterative	NOUN
ejpam-3756	197	9	process	process	NOUN
ejpam-3756	197	10	,	,	PUNCT
ejpam-3756	197	11	it	it	PRON
ejpam-3756	197	12	is	be	AUX
ejpam-3756	197	13	to	to	PART
ejpam-3756	197	14	be	be	AUX
ejpam-3756	197	15	shown	show	VERB
ejpam-3756	197	16	that	that	SCONJ
ejpam-3756	197	17	{	{	PUNCT
ejpam-3756	197	18	ζn	ζn	NOUN
ejpam-3756	197	19	}	}	PUNCT
ejpam-3756	197	20	has	have	VERB
ejpam-3756	197	21	a	a	DET
ejpam-3756	197	22	weak	weak	ADJ
ejpam-3756	197	23	subsequential	subsequential	ADJ
ejpam-3756	197	24	limit	limit	NOUN
ejpam-3756	197	25	in	in	ADP
ejpam-3756	197	26	tf	tf	PROPN
ejpam-3756	197	27	.	.	PUNCT
ejpam-3756	198	1	let	let	VERB
ejpam-3756	198	2	{	{	PUNCT
ejpam-3756	198	3	xnu	xnu	PROPN
ejpam-3756	198	4	}	}	PUNCT
ejpam-3756	198	5	and	and	CCONJ
ejpam-3756	198	6	{	{	PUNCT
ejpam-3756	198	7	xnv	xnv	PROPN
ejpam-3756	198	8	}	}	PUNCT
ejpam-3756	198	9	are	be	AUX
ejpam-3756	198	10	the	the	DET
ejpam-3756	198	11	subsequences	subsequence	NOUN
ejpam-3756	198	12	of	of	ADP
ejpam-3756	198	13	{	{	PUNCT
ejpam-3756	198	14	ζn	ζn	NOUN
ejpam-3756	198	15	}	}	PUNCT
ejpam-3756	198	16	,	,	PUNCT
ejpam-3756	198	17	converges	converge	VERB
ejpam-3756	198	18	to	to	ADP
ejpam-3756	198	19	u	u	NOUN
ejpam-3756	198	20	and	and	CCONJ
ejpam-3756	198	21	v	v	ADP
ejpam-3756	198	22	respectively	respectively	ADV
ejpam-3756	198	23	.	.	PUNCT
ejpam-3756	199	1	using	use	VERB
ejpam-3756	199	2	lemma	lemma	PROPN
ejpam-3756	199	3	2	2	NUM
ejpam-3756	199	4	limn→∞	limn→∞	PROPN
ejpam-3756	199	5	‖tn	‖tn	NUM
ejpam-3756	199	6	−	−	NOUN
ejpam-3756	199	7	ζn‖	ζn‖	NOUN
ejpam-3756	199	8	=	=	SYM
ejpam-3756	199	9	0	0	NUM
ejpam-3756	199	10	,	,	PUNCT
ejpam-3756	199	11	i	i	PRON
ejpam-3756	199	12	−	−	PROPN
ejpam-3756	199	13	t	t	PROPN
ejpam-3756	199	14	is	be	AUX
ejpam-3756	199	15	demiclosed	demiclose	VERB
ejpam-3756	199	16	at	at	ADP
ejpam-3756	199	17	0	0	NUM
ejpam-3756	199	18	.	.	PUNCT
ejpam-3756	200	1	so	so	ADV
ejpam-3756	200	2	u	u	PROPN
ejpam-3756	200	3	,	,	PUNCT
ejpam-3756	200	4	v	v	NOUN
ejpam-3756	200	5	∈	∈	NOUN
ejpam-3756	201	1	tf	tf	INTJ
ejpam-3756	201	2	.	.	PUNCT
ejpam-3756	202	1	next	next	ADV
ejpam-3756	202	2	,	,	PUNCT
ejpam-3756	202	3	to	to	PART
ejpam-3756	202	4	show	show	VERB
ejpam-3756	202	5	the	the	DET
ejpam-3756	202	6	uniqueness	uniqueness	NOUN
ejpam-3756	202	7	,	,	PUNCT
ejpam-3756	202	8	we	we	PRON
ejpam-3756	202	9	assume	assume	VERB
ejpam-3756	202	10	that	that	SCONJ
ejpam-3756	202	11	limn→∞	limn→∞	PROPN
ejpam-3756	202	12	‖ζn	‖ζn	NUM
ejpam-3756	202	13	−	−	PROPN
ejpam-3756	202	14	u‖	u‖	NOUN
ejpam-3756	202	15	and	and	CCONJ
ejpam-3756	202	16	limn→∞	limn→∞	PRON
ejpam-3756	202	17	‖ζn	‖ζn	PUNCT
ejpam-3756	202	18	−	−	PROPN
ejpam-3756	202	19	v‖	v‖	NOUN
ejpam-3756	202	20	exists	exist	VERB
ejpam-3756	202	21	.	.	PUNCT
ejpam-3756	203	1	assuming	assume	VERB
ejpam-3756	203	2	u	u	PROPN
ejpam-3756	203	3	6=	6=	PROPN
ejpam-3756	203	4	v.	v.	CCONJ
ejpam-3756	203	5	then	then	ADV
ejpam-3756	203	6	using	use	VERB
ejpam-3756	203	7	opial	opial	ADJ
ejpam-3756	203	8	’s	’s	PART
ejpam-3756	203	9	condition	condition	NOUN
ejpam-3756	203	10	,	,	PUNCT
ejpam-3756	203	11	we	we	PRON
ejpam-3756	203	12	have	have	VERB
ejpam-3756	203	13	lim	lim	PROPN
ejpam-3756	203	14	n→∞	n→∞	X
ejpam-3756	203	15	‖ζn	‖ζn	NUM
ejpam-3756	203	16	−	−	PROPN
ejpam-3756	203	17	u‖	u‖	NOUN
ejpam-3756	203	18	=	=	PROPN
ejpam-3756	203	19	lim	lim	PROPN
ejpam-3756	203	20	n→∞	n→∞	X
ejpam-3756	204	1	‖xnu	‖xnu	PROPN
ejpam-3756	204	2	−	−	PROPN
ejpam-3756	204	3	u‖	u‖	PROPN
ejpam-3756	204	4	<	<	X
ejpam-3756	204	5	lim	lim	PROPN
ejpam-3756	204	6	n→∞	n→∞	X
ejpam-3756	204	7	‖xnu	‖xnu	PROPN
ejpam-3756	204	8	−	−	PROPN
ejpam-3756	204	9	v‖	v‖	NOUN
ejpam-3756	204	10	=	=	PRON
ejpam-3756	204	11	lim	lim	PROPN
ejpam-3756	204	12	n→∞	n→∞	X
ejpam-3756	204	13	‖ζn	‖ζn	NUM
ejpam-3756	204	14	−	−	PROPN
ejpam-3756	204	15	v‖	v‖	NOUN
ejpam-3756	204	16	=	=	PRON
ejpam-3756	205	1	lim	lim	PROPN
ejpam-3756	205	2	n→∞	n→∞	X
ejpam-3756	206	1	‖xnv	‖xnv	NUM
ejpam-3756	206	2	−	−	PROPN
ejpam-3756	206	3	v‖	v‖	NOUN
ejpam-3756	206	4	<	<	X
ejpam-3756	206	5	lim	lim	PROPN
ejpam-3756	206	6	n→∞	n→∞	X
ejpam-3756	206	7	‖xnv	‖xnv	NUM
ejpam-3756	206	8	−	−	NOUN
ejpam-3756	207	1	u‖	u‖	NOUN
ejpam-3756	208	1	=	=	PROPN
ejpam-3756	208	2	lim	lim	PROPN
ejpam-3756	208	3	n→∞	n→∞	X
ejpam-3756	209	1	‖ζn	‖ζn	NUM
ejpam-3756	209	2	−	−	PROPN
ejpam-3756	209	3	u‖	u‖	NOUN
ejpam-3756	209	4	which	which	PRON
ejpam-3756	209	5	is	be	AUX
ejpam-3756	209	6	a	a	DET
ejpam-3756	209	7	contradiction	contradiction	NOUN
ejpam-3756	209	8	,	,	PUNCT
ejpam-3756	209	9	so	so	CCONJ
ejpam-3756	209	10	u	u	X
ejpam-3756	210	1	=	=	PROPN
ejpam-3756	210	2	v.	v.	ADP
ejpam-3756	210	3	so	so	ADV
ejpam-3756	210	4	,	,	PUNCT
ejpam-3756	210	5	{	{	PUNCT
ejpam-3756	210	6	ζn	ζn	PART
ejpam-3756	210	7	}	}	PUNCT
ejpam-3756	210	8	converges	converge	VERB
ejpam-3756	210	9	weakly	weakly	ADV
ejpam-3756	210	10	to	to	ADP
ejpam-3756	210	11	a	a	DET
ejpam-3756	210	12	fixed	fix	VERB
ejpam-3756	210	13	point	point	NOUN
ejpam-3756	210	14	of	of	ADP
ejpam-3756	210	15	t	t	PROPN
ejpam-3756	210	16	.	.	PUNCT
ejpam-3756	211	1	now	now	ADV
ejpam-3756	211	2	,	,	PUNCT
ejpam-3756	211	3	we	we	PRON
ejpam-3756	211	4	prove	prove	VERB
ejpam-3756	211	5	the	the	DET
ejpam-3756	211	6	strong	strong	ADJ
ejpam-3756	211	7	convergence	convergence	NOUN
ejpam-3756	211	8	of	of	ADP
ejpam-3756	211	9	nv	nv	PROPN
ejpam-3756	211	10	1	1	NUM
ejpam-3756	211	11	iteration	iteration	NOUN
ejpam-3756	211	12	process	process	NOUN
ejpam-3756	211	13	.	.	PUNCT
ejpam-3756	212	1	theorem	theorem	NOUN
ejpam-3756	212	2	5	5	NUM
ejpam-3756	212	3	.	.	PUNCT
ejpam-3756	212	4	suppose	suppose	VERB
ejpam-3756	212	5	that	that	SCONJ
ejpam-3756	212	6	there	there	PRON
ejpam-3756	212	7	is	be	VERB
ejpam-3756	212	8	a	a	DET
ejpam-3756	212	9	uniformly	uniformly	ADJ
ejpam-3756	212	10	banach	banach	NOUN
ejpam-3756	212	11	space	space	NOUN
ejpam-3756	212	12	e	e	NOUN
ejpam-3756	212	13	,	,	PUNCT
ejpam-3756	212	14	having	have	VERB
ejpam-3756	212	15	a	a	DET
ejpam-3756	212	16	nonempty	nonempty	ADJ
ejpam-3756	212	17	subset	subset	NOUN
ejpam-3756	212	18	c	c	NOUN
ejpam-3756	212	19	,	,	PUNCT
ejpam-3756	212	20	which	which	PRON
ejpam-3756	212	21	is	be	AUX
ejpam-3756	212	22	nonempty	nonempty	ADV
ejpam-3756	212	23	closed	closed	ADJ
ejpam-3756	212	24	and	and	CCONJ
ejpam-3756	212	25	convex	convex	NOUN
ejpam-3756	212	26	.	.	PUNCT
ejpam-3756	213	1	also	also	ADV
ejpam-3756	213	2	,	,	PUNCT
ejpam-3756	213	3	there	there	PRON
ejpam-3756	213	4	be	be	VERB
ejpam-3756	213	5	a	a	DET
ejpam-3756	213	6	nonexpansive	nonexpansive	ADJ
ejpam-3756	213	7	mapping	mapping	NOUN
ejpam-3756	213	8	t	t	NOUN
ejpam-3756	213	9	:	:	PUNCT
ejpam-3756	213	10	c	c	X
ejpam-3756	213	11	→	→	SYM
ejpam-3756	213	12	c	c	NOUN
ejpam-3756	213	13	with	with	ADP
ejpam-3756	213	14	tf	tf	PROPN
ejpam-3756	213	15	6=	6=	PROPN
ejpam-3756	213	16	φ	φ	PROPN
ejpam-3756	213	17	.	.	PUNCT
ejpam-3756	214	1	if	if	SCONJ
ejpam-3756	214	2	{	{	PUNCT
ejpam-3756	214	3	ζn	ζn	NOUN
ejpam-3756	214	4	}	}	PUNCT
ejpam-3756	214	5	is	be	AUX
ejpam-3756	214	6	an	an	DET
ejpam-3756	214	7	iterative	iterative	NOUN
ejpam-3756	214	8	sequence	sequence	NOUN
ejpam-3756	214	9	defined	define	VERB
ejpam-3756	214	10	by	by	ADP
ejpam-3756	214	11	nv	nv	PROPN
ejpam-3756	214	12	1	1	NUM
ejpam-3756	214	13	,	,	PUNCT
ejpam-3756	214	14	then	then	ADV
ejpam-3756	214	15	{	{	PUNCT
ejpam-3756	214	16	ζn	ζn	NOUN
ejpam-3756	214	17	}	}	PUNCT
ejpam-3756	214	18	converges	converge	VERB
ejpam-3756	214	19	strongly	strongly	ADV
ejpam-3756	214	20	to	to	ADP
ejpam-3756	214	21	a	a	DET
ejpam-3756	214	22	point	point	NOUN
ejpam-3756	214	23	of	of	ADP
ejpam-3756	214	24	tf	tf	PROPN
ejpam-3756	214	25	iff	iff	PROPN
ejpam-3756	214	26	lim	lim	PROPN
ejpam-3756	214	27	infn→∞	infn→∞	PROPN
ejpam-3756	214	28	d(ζn	d(ζn	PROPN
ejpam-3756	214	29	,	,	PUNCT
ejpam-3756	214	30	tf	tf	INTJ
ejpam-3756	214	31	)	)	PUNCT
ejpam-3756	215	1	=	=	PUNCT
ejpam-3756	215	2	0	0	X
ejpam-3756	215	3	.	.	PUNCT
ejpam-3756	216	1	proof	proof	NOUN
ejpam-3756	216	2	.	.	PUNCT
ejpam-3756	217	1	if	if	SCONJ
ejpam-3756	217	2	a	a	DET
ejpam-3756	217	3	sequence	sequence	NOUN
ejpam-3756	217	4	{	{	PUNCT
ejpam-3756	217	5	ζn	ζn	NOUN
ejpam-3756	217	6	}	}	PUNCT
ejpam-3756	217	7	converges	converge	NOUN
ejpam-3756	217	8	to	to	ADP
ejpam-3756	217	9	a	a	DET
ejpam-3756	217	10	fixed	fixed	ADJ
ejpam-3756	217	11	point	point	NOUN
ejpam-3756	217	12	q	q	PROPN
ejpam-3756	217	13	∈	∈	PROPN
ejpam-3756	218	1	tf	tf	INTJ
ejpam-3756	218	2	,	,	PUNCT
ejpam-3756	218	3	then	then	ADV
ejpam-3756	218	4	it	it	PRON
ejpam-3756	218	5	is	be	AUX
ejpam-3756	218	6	obvious	obvious	ADJ
ejpam-3756	218	7	that	that	SCONJ
ejpam-3756	218	8	lim	lim	PROPN
ejpam-3756	218	9	infn→∞	infn→∞	PROPN
ejpam-3756	218	10	d(ζn	d(ζn	PROPN
ejpam-3756	218	11	,	,	PUNCT
ejpam-3756	218	12	tf	tf	INTJ
ejpam-3756	218	13	)	)	PUNCT
ejpam-3756	218	14	=	=	PUNCT
ejpam-3756	219	1	0	0	X
ejpam-3756	219	2	.	.	X
ejpam-3756	220	1	for	for	ADP
ejpam-3756	220	2	converse	converse	NOUN
ejpam-3756	220	3	,	,	PUNCT
ejpam-3756	220	4	lim	lim	PROPN
ejpam-3756	220	5	infn→∞	infn→∞	PROPN
ejpam-3756	220	6	d(ζn	d(ζn	PROPN
ejpam-3756	220	7	,	,	PUNCT
ejpam-3756	220	8	tf	tf	INTJ
ejpam-3756	220	9	)	)	PUNCT
ejpam-3756	221	1	=	=	PUNCT
ejpam-3756	221	2	0	0	X
ejpam-3756	221	3	.	.	PUNCT
ejpam-3756	222	1	from	from	ADP
ejpam-3756	222	2	lemma	lemma	PROPN
ejpam-3756	222	3	2	2	NUM
ejpam-3756	222	4	,	,	PUNCT
ejpam-3756	222	5	we	we	PRON
ejpam-3756	222	6	have	have	VERB
ejpam-3756	222	7	the	the	DET
ejpam-3756	222	8	existence	existence	NOUN
ejpam-3756	222	9	of	of	ADP
ejpam-3756	222	10	lim	lim	PROPN
ejpam-3756	222	11	infn→∞	infn→∞	PROPN
ejpam-3756	222	12	‖ζn−	‖ζn−	PROPN
ejpam-3756	222	13	q‖	q‖	NOUN
ejpam-3756	222	14	for	for	ADP
ejpam-3756	222	15	all	all	DET
ejpam-3756	222	16	q	q	PROPN
ejpam-3756	222	17	∈	∈	PROPN
ejpam-3756	222	18	tf	tf	INTJ
ejpam-3756	222	19	,	,	PUNCT
ejpam-3756	222	20	we	we	PRON
ejpam-3756	222	21	have	have	VERB
ejpam-3756	222	22	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	222	23	−	−	PROPN
ejpam-3756	223	1	q‖	q‖	NOUN
ejpam-3756	223	2	≤	≤	ADV
ejpam-3756	223	3	‖ζn	‖ζn	NUM
ejpam-3756	223	4	−	−	PROPN
ejpam-3756	223	5	q‖	q‖	NOUN
ejpam-3756	223	6	for	for	ADP
ejpam-3756	223	7	any	any	DET
ejpam-3756	223	8	q	q	NOUN
ejpam-3756	223	9	∈	∈	PROPN
ejpam-3756	224	1	tf	tf	X
ejpam-3756	224	2	l.n	l.n	PROPN
ejpam-3756	224	3	mishra	mishra	PROPN
ejpam-3756	224	4	et	et	PROPN
ejpam-3756	224	5	al	al	PROPN
ejpam-3756	224	6	.	.	PUNCT
ejpam-3756	224	7	/	/	SYM
ejpam-3756	224	8	eur	eur	PROPN
ejpam-3756	224	9	.	.	PUNCT
ejpam-3756	225	1	j.	j.	PROPN
ejpam-3756	225	2	pure	pure	PROPN
ejpam-3756	225	3	appl	appl	PROPN
ejpam-3756	225	4	.	.	PROPN
ejpam-3756	225	5	math	math	PROPN
ejpam-3756	225	6	,	,	PUNCT
ejpam-3756	225	7	13	13	NUM
ejpam-3756	225	8	(	(	PUNCT
ejpam-3756	225	9	5	5	NUM
ejpam-3756	225	10	)	)	PUNCT
ejpam-3756	225	11	(	(	PUNCT
ejpam-3756	225	12	2020	2020	NUM
ejpam-3756	225	13	)	)	PUNCT
ejpam-3756	225	14	,	,	PUNCT
ejpam-3756	225	15	1110	1110	NUM
ejpam-3756	225	16	-	-	SYM
ejpam-3756	225	17	1130	1130	NUM
ejpam-3756	225	18	1121	1121	NUM
ejpam-3756	225	19	which	which	PRON
ejpam-3756	225	20	yields	yield	VERB
ejpam-3756	225	21	d(ζn+1	d(ζn+1	PROPN
ejpam-3756	225	22	,	,	PUNCT
ejpam-3756	225	23	tf	tf	INTJ
ejpam-3756	225	24	)	)	PUNCT
ejpam-3756	225	25	≤	≤	NOUN
ejpam-3756	225	26	d(ζn	d(ζn	NOUN
ejpam-3756	225	27	,	,	PUNCT
ejpam-3756	225	28	tf	tf	INTJ
ejpam-3756	225	29	)	)	PUNCT
ejpam-3756	225	30	which	which	PRON
ejpam-3756	225	31	implies	imply	VERB
ejpam-3756	225	32	that	that	SCONJ
ejpam-3756	225	33	{	{	PUNCT
ejpam-3756	225	34	d(ζn	d(ζn	NOUN
ejpam-3756	225	35	,	,	PUNCT
ejpam-3756	225	36	tf	tf	INTJ
ejpam-3756	225	37	)	)	PUNCT
ejpam-3756	225	38	}	}	PUNCT
ejpam-3756	225	39	is	be	AUX
ejpam-3756	225	40	a	a	DET
ejpam-3756	225	41	decreasing	decrease	VERB
ejpam-3756	225	42	sequence	sequence	NOUN
ejpam-3756	225	43	which	which	PRON
ejpam-3756	225	44	is	be	AUX
ejpam-3756	225	45	bounded	bound	VERB
ejpam-3756	225	46	below	below	ADV
ejpam-3756	225	47	by	by	ADP
ejpam-3756	225	48	zero	zero	NUM
ejpam-3756	225	49	.	.	PUNCT
ejpam-3756	226	1	results	result	NOUN
ejpam-3756	226	2	,	,	PUNCT
ejpam-3756	226	3	limn→∞	limn→∞	PROPN
ejpam-3756	226	4	d(ζn	d(ζn	NOUN
ejpam-3756	226	5	,	,	PUNCT
ejpam-3756	226	6	tf	tf	INTJ
ejpam-3756	226	7	)	)	PUNCT
ejpam-3756	227	1	=	=	SYM
ejpam-3756	227	2	0	0	PUNCT
ejpam-3756	228	1	now	now	ADV
ejpam-3756	228	2	,	,	PUNCT
ejpam-3756	228	3	to	to	PART
ejpam-3756	228	4	prove	prove	VERB
ejpam-3756	228	5	that	that	SCONJ
ejpam-3756	228	6	{	{	PUNCT
ejpam-3756	228	7	ζn	ζn	NOUN
ejpam-3756	228	8	}	}	PUNCT
ejpam-3756	228	9	is	be	AUX
ejpam-3756	228	10	a	a	DET
ejpam-3756	228	11	cauchy	cauchy	ADJ
ejpam-3756	228	12	sequence	sequence	NOUN
ejpam-3756	228	13	in	in	ADP
ejpam-3756	228	14	c.	c.	NOUN
ejpam-3756	228	15	let	let	VERB
ejpam-3756	228	16	ε	ε	PROPN
ejpam-3756	228	17	>	>	X
ejpam-3756	228	18	0	0	PUNCT
ejpam-3756	228	19	be	be	AUX
ejpam-3756	228	20	arbitrarily	arbitrarily	ADV
ejpam-3756	228	21	chosen	choose	VERB
ejpam-3756	228	22	.	.	PUNCT
ejpam-3756	229	1	since	since	SCONJ
ejpam-3756	229	2	,	,	PUNCT
ejpam-3756	229	3	lim	lim	PROPN
ejpam-3756	229	4	infn→∞	infn→∞	PROPN
ejpam-3756	229	5	d(ζn	d(ζn	PROPN
ejpam-3756	229	6	,	,	PUNCT
ejpam-3756	229	7	tf	tf	INTJ
ejpam-3756	229	8	)	)	PUNCT
ejpam-3756	230	1	=	=	SYM
ejpam-3756	230	2	0	0	NUM
ejpam-3756	230	3	,	,	PUNCT
ejpam-3756	230	4	there	there	PRON
ejpam-3756	230	5	is	be	VERB
ejpam-3756	230	6	an	an	DET
ejpam-3756	230	7	existence	existence	NOUN
ejpam-3756	230	8	of	of	ADP
ejpam-3756	230	9	n0	n0	NUM
ejpam-3756	230	10	in	in	ADP
ejpam-3756	230	11	such	such	DET
ejpam-3756	230	12	a	a	DET
ejpam-3756	230	13	manner	manner	NOUN
ejpam-3756	230	14	that	that	SCONJ
ejpam-3756	230	15	∀	∀	VERB
ejpam-3756	230	16	n	n	PRON
ejpam-3756	230	17	≥	≥	NOUN
ejpam-3756	230	18	n0	n0	NUM
ejpam-3756	230	19	,	,	PUNCT
ejpam-3756	230	20	we	we	PRON
ejpam-3756	230	21	have	have	VERB
ejpam-3756	230	22	d(ζn	d(ζn	NOUN
ejpam-3756	230	23	,	,	PUNCT
ejpam-3756	230	24	tf	tf	INTJ
ejpam-3756	230	25	)	)	PUNCT
ejpam-3756	230	26	<	<	X
ejpam-3756	230	27	ε	ε	PROPN
ejpam-3756	230	28	4	4	NUM
ejpam-3756	230	29	particularly	particularly	ADV
ejpam-3756	230	30	,	,	PUNCT
ejpam-3756	230	31	inf{‖xn0	inf{‖xn0	PROPN
ejpam-3756	230	32	−	−	PROPN
ejpam-3756	230	33	q‖	q‖	NOUN
ejpam-3756	230	34	:	:	PUNCT
ejpam-3756	230	35	q	q	PUNCT
ejpam-3756	230	36	∈	∈	NOUN
ejpam-3756	230	37	tf	tf	X
ejpam-3756	230	38	}	}	PUNCT
ejpam-3756	230	39	<	<	X
ejpam-3756	230	40	ε	ε	PROPN
ejpam-3756	231	1	so	so	SCONJ
ejpam-3756	231	2	there	there	PRON
ejpam-3756	231	3	must	must	AUX
ejpam-3756	231	4	be	be	AUX
ejpam-3756	231	5	an	an	DET
ejpam-3756	231	6	existence	existence	NOUN
ejpam-3756	231	7	of	of	ADP
ejpam-3756	231	8	α	α	PROPN
ejpam-3756	231	9	∈	∈	PROPN
ejpam-3756	231	10	tf	tf	X
ejpam-3756	231	11	in	in	ADP
ejpam-3756	231	12	such	such	DET
ejpam-3756	231	13	a	a	DET
ejpam-3756	231	14	manner	manner	NOUN
ejpam-3756	231	15	that	that	PRON
ejpam-3756	231	16	‖xn0	‖xn0	ADJ
ejpam-3756	231	17	−	−	PROPN
ejpam-3756	231	18	α‖	α‖	NOUN
ejpam-3756	231	19	<	<	X
ejpam-3756	231	20	ε	ε	PROPN
ejpam-3756	231	21	.	.	PUNCT
ejpam-3756	232	1	thus	thus	ADV
ejpam-3756	232	2	,	,	PUNCT
ejpam-3756	232	3	for	for	ADP
ejpam-3756	232	4	m	m	PROPN
ejpam-3756	232	5	,	,	PUNCT
ejpam-3756	232	6	n	n	PRON
ejpam-3756	232	7	≥	≥	NOUN
ejpam-3756	232	8	n0	n0	NUM
ejpam-3756	232	9	,	,	PUNCT
ejpam-3756	232	10	we	we	PRON
ejpam-3756	232	11	have	have	VERB
ejpam-3756	232	12	‖xn+m	‖xn+m	VERB
ejpam-3756	232	13	−	−	ADP
ejpam-3756	232	14	ζn	ζn	PRON
ejpam-3756	232	15	≤	≤	PROPN
ejpam-3756	232	16	‖xn+m	‖xn+m	PROPN
ejpam-3756	232	17	−	−	PUNCT
ejpam-3756	232	18	α‖+	α‖+	PROPN
ejpam-3756	232	19	‖ζn	‖ζn	NUM
ejpam-3756	232	20	−	−	PROPN
ejpam-3756	233	1	α‖	α‖	NOUN
ejpam-3756	233	2	<	<	X
ejpam-3756	233	3	2‖xn0	2‖xn0	NUM
ejpam-3756	234	1	−	−	PUNCT
ejpam-3756	234	2	α‖	α‖	NOUN
ejpam-3756	234	3	<	<	X
ejpam-3756	234	4	2	2	NUM
ejpam-3756	234	5	ε	ε	PROPN
ejpam-3756	234	6	2	2	NUM
ejpam-3756	234	7	=	=	SYM
ejpam-3756	234	8	ε	ε	PROPN
ejpam-3756	234	9	which	which	PRON
ejpam-3756	234	10	proves	prove	VERB
ejpam-3756	234	11	the	the	DET
ejpam-3756	234	12	cauchy	cauchy	ADJ
ejpam-3756	234	13	behaviour	behaviour	NOUN
ejpam-3756	234	14	of	of	ADP
ejpam-3756	234	15	{	{	PUNCT
ejpam-3756	234	16	ζn	ζn	NOUN
ejpam-3756	234	17	}	}	PUNCT
ejpam-3756	234	18	.	.	PUNCT
ejpam-3756	235	1	since	since	SCONJ
ejpam-3756	235	2	it	it	PRON
ejpam-3756	235	3	is	be	AUX
ejpam-3756	235	4	given	give	VERB
ejpam-3756	235	5	that	that	SCONJ
ejpam-3756	235	6	c	c	PROPN
ejpam-3756	235	7	is	be	AUX
ejpam-3756	235	8	a	a	DET
ejpam-3756	235	9	closed	closed	ADJ
ejpam-3756	235	10	subset	subset	NOUN
ejpam-3756	235	11	of	of	ADP
ejpam-3756	235	12	a	a	DET
ejpam-3756	235	13	banach	banach	NOUN
ejpam-3756	235	14	space	space	NOUN
ejpam-3756	235	15	e	e	NOUN
ejpam-3756	235	16	,	,	PUNCT
ejpam-3756	235	17	therefore	therefore	ADV
ejpam-3756	235	18	the	the	DET
ejpam-3756	235	19	convergence	convergence	NOUN
ejpam-3756	235	20	of	of	ADP
ejpam-3756	235	21	{	{	PUNCT
ejpam-3756	235	22	ζn	ζn	NOUN
ejpam-3756	235	23	}	}	PUNCT
ejpam-3756	235	24	in	in	ADP
ejpam-3756	235	25	c	c	PROPN
ejpam-3756	235	26	is	be	AUX
ejpam-3756	235	27	confirmed	confirm	VERB
ejpam-3756	235	28	.	.	PUNCT
ejpam-3756	236	1	let	let	VERB
ejpam-3756	236	2	limn→∞	limn→∞	PROPN
ejpam-3756	236	3	ζn	ζn	ADP
ejpam-3756	236	4	=	=	SYM
ejpam-3756	236	5	α	α	PROPN
ejpam-3756	236	6	for	for	ADP
ejpam-3756	236	7	some	some	DET
ejpam-3756	236	8	α	α	PROPN
ejpam-3756	236	9	∈	∈	PROPN
ejpam-3756	236	10	b.	b.	PROPN
ejpam-3756	236	11	now	now	ADV
ejpam-3756	236	12	using	use	VERB
ejpam-3756	236	13	,	,	PUNCT
ejpam-3756	236	14	limn→∞	limn→∞	PROPN
ejpam-3756	236	15	‖tζn	‖tζn	VERB
ejpam-3756	236	16	−	−	ADP
ejpam-3756	236	17	ζn‖	ζn‖	PROPN
ejpam-3756	236	18	=	=	SYM
ejpam-3756	236	19	0	0	NUM
ejpam-3756	236	20	,	,	PUNCT
ejpam-3756	236	21	we	we	PRON
ejpam-3756	236	22	get	get	VERB
ejpam-3756	236	23	‖α−	‖α−	NUM
ejpam-3756	236	24	tα‖	tα‖	PROPN
ejpam-3756	236	25	≤	≤	NUM
ejpam-3756	236	26	‖α−	‖α−	PROPN
ejpam-3756	236	27	ζn‖+	ζn‖+	PROPN
ejpam-3756	236	28	‖ζn	‖ζn	NUM
ejpam-3756	236	29	−	−	PROPN
ejpam-3756	236	30	tζn‖+	tζn‖+	PROPN
ejpam-3756	236	31	‖tζn	‖tζn	PROPN
ejpam-3756	236	32	−	−	NOUN
ejpam-3756	236	33	tα‖	tα‖	PROPN
ejpam-3756	236	34	≤	≤	NUM
ejpam-3756	236	35	‖α−	‖α−	PROPN
ejpam-3756	236	36	ζn‖+	ζn‖+	PROPN
ejpam-3756	236	37	‖ζn	‖ζn	NUM
ejpam-3756	236	38	−	−	PROPN
ejpam-3756	236	39	tζn‖+	tζn‖+	PROPN
ejpam-3756	236	40	‖ζn	‖ζn	PUNCT
ejpam-3756	236	41	−	−	PROPN
ejpam-3756	236	42	α‖	α‖	NOUN
ejpam-3756	236	43	which	which	PRON
ejpam-3756	236	44	proves	prove	VERB
ejpam-3756	236	45	that	that	SCONJ
ejpam-3756	236	46	‖α	‖α	PROPN
ejpam-3756	236	47	−	−	NOUN
ejpam-3756	237	1	tα‖	tα‖	PROPN
ejpam-3756	237	2	approaches	approach	VERB
ejpam-3756	237	3	to	to	ADP
ejpam-3756	237	4	0	0	NUM
ejpam-3756	237	5	as	as	ADP
ejpam-3756	237	6	n	n	PRON
ejpam-3756	237	7	approaches	approach	NOUN
ejpam-3756	237	8	to	to	ADP
ejpam-3756	237	9	∞.	∞.	PROPN
ejpam-3756	237	10	this	this	PRON
ejpam-3756	237	11	shows	show	VERB
ejpam-3756	237	12	that	that	SCONJ
ejpam-3756	237	13	α	α	PROPN
ejpam-3756	237	14	=	=	SYM
ejpam-3756	237	15	tα	tα	PROPN
ejpam-3756	237	16	.	.	PUNCT
ejpam-3756	238	1	this	this	PRON
ejpam-3756	238	2	proves	prove	VERB
ejpam-3756	238	3	our	our	PRON
ejpam-3756	238	4	result	result	NOUN
ejpam-3756	238	5	.	.	PUNCT
ejpam-3756	239	1	4	4	X
ejpam-3756	239	2	.	.	X
ejpam-3756	239	3	numerical	numerical	ADJ
ejpam-3756	239	4	example	example	NOUN
ejpam-3756	239	5	in	in	ADP
ejpam-3756	239	6	this	this	DET
ejpam-3756	239	7	section	section	NOUN
ejpam-3756	239	8	,	,	PUNCT
ejpam-3756	239	9	an	an	DET
ejpam-3756	239	10	example	example	NOUN
ejpam-3756	239	11	is	be	AUX
ejpam-3756	239	12	to	to	PART
ejpam-3756	239	13	be	be	AUX
ejpam-3756	239	14	given	give	VERB
ejpam-3756	239	15	which	which	PRON
ejpam-3756	239	16	confirms	confirm	VERB
ejpam-3756	239	17	the	the	DET
ejpam-3756	239	18	behaviour	behaviour	NOUN
ejpam-3756	239	19	of	of	ADP
ejpam-3756	239	20	nv	nv	PROPN
ejpam-3756	239	21	1	1	NUM
ejpam-3756	239	22	.	.	PUNCT
ejpam-3756	240	1	in	in	ADP
ejpam-3756	240	2	order	order	NOUN
ejpam-3756	240	3	to	to	PART
ejpam-3756	240	4	support	support	VERB
ejpam-3756	240	5	the	the	DET
ejpam-3756	240	6	proof	proof	NOUN
ejpam-3756	240	7	of	of	ADP
ejpam-3756	240	8	theorems	theorem	NOUN
ejpam-3756	240	9	2	2	NUM
ejpam-3756	240	10	and	and	CCONJ
ejpam-3756	240	11	3	3	NUM
ejpam-3756	240	12	,	,	PUNCT
ejpam-3756	240	13	we	we	PRON
ejpam-3756	240	14	will	will	AUX
ejpam-3756	240	15	use	use	VERB
ejpam-3756	240	16	a	a	DET
ejpam-3756	240	17	numerical	numerical	ADJ
ejpam-3756	240	18	example	example	NOUN
ejpam-3756	240	19	as	as	ADP
ejpam-3756	240	20	follow	follow	VERB
ejpam-3756	240	21	example	example	NOUN
ejpam-3756	240	22	.	.	PUNCT
ejpam-3756	241	1	assuming	assume	VERB
ejpam-3756	241	2	e	e	X
ejpam-3756	241	3	=	=	PUNCT
ejpam-3756	241	4	(	(	PUNCT
ejpam-3756	241	5	−∞,∞	−∞,∞	NOUN
ejpam-3756	241	6	)	)	PUNCT
ejpam-3756	241	7	and	and	CCONJ
ejpam-3756	241	8	c	c	NOUN
ejpam-3756	241	9	=	=	PUNCT
ejpam-3756	242	1	[	[	X
ejpam-3756	242	2	1	1	NUM
ejpam-3756	242	3	,	,	PUNCT
ejpam-3756	242	4	50	50	NUM
ejpam-3756	242	5	]	]	PUNCT
ejpam-3756	242	6	.	.	PUNCT
ejpam-3756	243	1	let	let	VERB
ejpam-3756	243	2	t	t	NOUN
ejpam-3756	243	3	:	:	PUNCT
ejpam-3756	243	4	c	c	X
ejpam-3756	243	5	→	→	PUNCT
ejpam-3756	243	6	c	c	X
ejpam-3756	243	7	be	be	AUX
ejpam-3756	243	8	mapping	mapping	NOUN
ejpam-3756	243	9	defined	define	VERB
ejpam-3756	243	10	as	as	ADP
ejpam-3756	243	11	t	t	PROPN
ejpam-3756	243	12	(	(	PUNCT
ejpam-3756	243	13	x	x	NOUN
ejpam-3756	243	14	)	)	PUNCT
ejpam-3756	243	15	=	=	SYM
ejpam-3756	244	1	√	√	NUM
ejpam-3756	244	2	x2	x2	NUM
ejpam-3756	244	3	−	−	PROPN
ejpam-3756	244	4	9x+	9x+	NUM
ejpam-3756	244	5	54	54	NUM
ejpam-3756	244	6	for	for	ADP
ejpam-3756	244	7	all	all	DET
ejpam-3756	244	8	x	x	SYM
ejpam-3756	244	9	∈	∈	PROPN
ejpam-3756	244	10	c.	c.	NOUN
ejpam-3756	244	11	clearly	clearly	ADV
ejpam-3756	244	12	,	,	PUNCT
ejpam-3756	244	13	x	x	SYM
ejpam-3756	244	14	=	=	SYM
ejpam-3756	244	15	5	5	NUM
ejpam-3756	244	16	is	be	AUX
ejpam-3756	244	17	the	the	DET
ejpam-3756	244	18	fixed	fix	VERB
ejpam-3756	244	19	point	point	NOUN
ejpam-3756	244	20	of	of	ADP
ejpam-3756	244	21	t	t	PROPN
ejpam-3756	244	22	.	.	PUNCT
ejpam-3756	245	1	set	set	VERB
ejpam-3756	245	2	σ0n	σ0n	X
ejpam-3756	245	3	=	=	SYM
ejpam-3756	245	4	σ1n	σ1n	X
ejpam-3756	245	5	=	=	PUNCT
ejpam-3756	245	6	σ2n	σ2n	NOUN
ejpam-3756	245	7	=	=	PUNCT
ejpam-3756	245	8	0.75	0.75	NUM
ejpam-3756	245	9	for	for	ADP
ejpam-3756	245	10	all	all	DET
ejpam-3756	245	11	n	n	PRON
ejpam-3756	245	12	∈	∈	PROPN
ejpam-3756	245	13	n.	n.	NOUN
ejpam-3756	245	14	choose	choose	VERB
ejpam-3756	245	15	initial	initial	ADJ
ejpam-3756	245	16	value	value	NOUN
ejpam-3756	245	17	as	as	ADP
ejpam-3756	245	18	40	40	NUM
ejpam-3756	245	19	.	.	PUNCT
ejpam-3756	246	1	then	then	ADV
ejpam-3756	246	2	,	,	PUNCT
ejpam-3756	246	3	we	we	PRON
ejpam-3756	246	4	get	get	VERB
ejpam-3756	246	5	the	the	DET
ejpam-3756	246	6	following	follow	VERB
ejpam-3756	246	7	table	table	NOUN
ejpam-3756	246	8	and	and	CCONJ
ejpam-3756	246	9	graph	graph	NOUN
ejpam-3756	246	10	.	.	PUNCT
ejpam-3756	247	1	also	also	ADV
ejpam-3756	247	2	,	,	PUNCT
ejpam-3756	247	3	in	in	ADP
ejpam-3756	247	4	table	table	NOUN
ejpam-3756	247	5	nv	nv	PROPN
ejpam-3756	247	6	1	1	NUM
ejpam-3756	247	7	is	be	AUX
ejpam-3756	247	8	represented	represent	VERB
ejpam-3756	247	9	by	by	ADP
ejpam-3756	247	10	np	np	INTJ
ejpam-3756	247	11	of	of	ADP
ejpam-3756	247	12	iteration	iteration	NOUN
ejpam-3756	247	13	values	value	NOUN
ejpam-3756	247	14	:	:	PUNCT
ejpam-3756	247	15	l.n	l.n	PROPN
ejpam-3756	247	16	mishra	mishra	PROPN
ejpam-3756	247	17	et	et	PROPN
ejpam-3756	247	18	al	al	PROPN
ejpam-3756	247	19	.	.	PUNCT
ejpam-3756	247	20	/	/	SYM
ejpam-3756	247	21	eur	eur	PROPN
ejpam-3756	247	22	.	.	PUNCT
ejpam-3756	248	1	j.	j.	PROPN
ejpam-3756	248	2	pure	pure	PROPN
ejpam-3756	248	3	appl	appl	PROPN
ejpam-3756	248	4	.	.	PROPN
ejpam-3756	248	5	math	math	PROPN
ejpam-3756	248	6	,	,	PUNCT
ejpam-3756	248	7	13	13	NUM
ejpam-3756	248	8	(	(	PUNCT
ejpam-3756	248	9	5	5	NUM
ejpam-3756	248	10	)	)	PUNCT
ejpam-3756	248	11	(	(	PUNCT
ejpam-3756	248	12	2020	2020	NUM
ejpam-3756	248	13	)	)	PUNCT
ejpam-3756	248	14	,	,	PUNCT
ejpam-3756	248	15	1110	1110	NUM
ejpam-3756	248	16	-	-	SYM
ejpam-3756	248	17	1130	1130	NUM
ejpam-3756	248	18	1122	1122	NUM
ejpam-3756	248	19	l.n	l.n	PROPN
ejpam-3756	248	20	mishra	mishra	PROPN
ejpam-3756	248	21	et	et	PROPN
ejpam-3756	248	22	al	al	PROPN
ejpam-3756	248	23	.	.	PUNCT
ejpam-3756	248	24	/	/	SYM
ejpam-3756	248	25	eur	eur	PROPN
ejpam-3756	248	26	.	.	PUNCT
ejpam-3756	249	1	j.	j.	PROPN
ejpam-3756	249	2	pure	pure	PROPN
ejpam-3756	249	3	appl	appl	PROPN
ejpam-3756	249	4	.	.	PROPN
ejpam-3756	249	5	math	math	PROPN
ejpam-3756	249	6	,	,	PUNCT
ejpam-3756	249	7	13	13	NUM
ejpam-3756	249	8	(	(	PUNCT
ejpam-3756	249	9	5	5	NUM
ejpam-3756	249	10	)	)	PUNCT
ejpam-3756	249	11	(	(	PUNCT
ejpam-3756	249	12	2020	2020	NUM
ejpam-3756	249	13	)	)	PUNCT
ejpam-3756	249	14	,	,	PUNCT
ejpam-3756	249	15	1110	1110	NUM
ejpam-3756	249	16	-	-	SYM
ejpam-3756	249	17	1130	1130	NUM
ejpam-3756	249	18	1123	1123	NUM
ejpam-3756	249	19	figure	figure	NOUN
ejpam-3756	249	20	1	1	NUM
ejpam-3756	249	21	:	:	PUNCT
ejpam-3756	249	22	comparison	comparison	NOUN
ejpam-3756	249	23	graph	graph	NOUN
ejpam-3756	249	24	based	base	VERB
ejpam-3756	249	25	on	on	ADP
ejpam-3756	249	26	numerical	numerical	ADJ
ejpam-3756	249	27	example	example	NOUN
ejpam-3756	249	28	to	to	PART
ejpam-3756	249	29	prove	prove	VERB
ejpam-3756	249	30	the	the	DET
ejpam-3756	249	31	efficiency	efficiency	NOUN
ejpam-3756	249	32	of	of	ADP
ejpam-3756	249	33	nv	nv	PROPN
ejpam-3756	249	34	1	1	NUM
ejpam-3756	249	35	.	.	PUNCT
ejpam-3756	250	1	thus	thus	ADV
ejpam-3756	250	2	,	,	PUNCT
ejpam-3756	250	3	it	it	PRON
ejpam-3756	250	4	is	be	AUX
ejpam-3756	250	5	evident	evident	ADJ
ejpam-3756	250	6	from	from	ADP
ejpam-3756	250	7	the	the	DET
ejpam-3756	250	8	above	above	ADJ
ejpam-3756	250	9	table	table	NOUN
ejpam-3756	250	10	and	and	CCONJ
ejpam-3756	250	11	graph	graph	NOUN
ejpam-3756	250	12	that	that	SCONJ
ejpam-3756	250	13	the	the	DET
ejpam-3756	250	14	newly	newly	ADV
ejpam-3756	250	15	defined	define	VERB
ejpam-3756	250	16	iteration	iteration	NOUN
ejpam-3756	250	17	scheme	scheme	NOUN
ejpam-3756	250	18	nv	nv	PROPN
ejpam-3756	250	19	1	1	NUM
ejpam-3756	250	20	converges	converge	VERB
ejpam-3756	250	21	much	much	ADV
ejpam-3756	250	22	faster	fast	ADV
ejpam-3756	250	23	and	and	CCONJ
ejpam-3756	250	24	is	be	AUX
ejpam-3756	250	25	more	more	ADV
ejpam-3756	250	26	efficient	efficient	ADJ
ejpam-3756	250	27	than	than	ADP
ejpam-3756	250	28	many	many	ADJ
ejpam-3756	250	29	iteration	iteration	NOUN
ejpam-3756	250	30	schemes	scheme	NOUN
ejpam-3756	250	31	in	in	ADP
ejpam-3756	250	32	exiting	exit	VERB
ejpam-3756	250	33	literature	literature	NOUN
ejpam-3756	250	34	.	.	PUNCT
ejpam-3756	251	1	5	5	NUM
ejpam-3756	251	2	.	.	X
ejpam-3756	251	3	t	t	NOUN
ejpam-3756	251	4	-	-	PUNCT
ejpam-3756	251	5	stability	stability	NOUN
ejpam-3756	251	6	of	of	ADP
ejpam-3756	251	7	n	n	PRON
ejpam-3756	251	8	v	v	NOUN
ejpam-3756	251	9	1	1	NUM
ejpam-3756	251	10	iteration	iteration	NOUN
ejpam-3756	251	11	algorithm	algorithm	NOUN
ejpam-3756	251	12	now	now	ADV
ejpam-3756	251	13	,	,	PUNCT
ejpam-3756	251	14	we	we	PRON
ejpam-3756	251	15	prove	prove	VERB
ejpam-3756	251	16	the	the	DET
ejpam-3756	251	17	stability	stability	NOUN
ejpam-3756	251	18	of	of	ADP
ejpam-3756	251	19	nv	nv	PROPN
ejpam-3756	251	20	1	1	NUM
ejpam-3756	251	21	.	.	PUNCT
ejpam-3756	252	1	theorem	theorem	NOUN
ejpam-3756	252	2	6	6	NUM
ejpam-3756	252	3	.	.	PUNCT
ejpam-3756	253	1	suppose	suppose	VERB
ejpam-3756	253	2	that	that	SCONJ
ejpam-3756	253	3	there	there	PRON
ejpam-3756	253	4	is	be	VERB
ejpam-3756	253	5	a	a	DET
ejpam-3756	253	6	banach	banach	NOUN
ejpam-3756	253	7	space	space	NOUN
ejpam-3756	253	8	e	e	NOUN
ejpam-3756	253	9	,	,	PUNCT
ejpam-3756	253	10	having	having	AUX
ejpam-3756	253	11	subset	subset	VERB
ejpam-3756	253	12	c	c	NOUN
ejpam-3756	253	13	,	,	PUNCT
ejpam-3756	253	14	which	which	PRON
ejpam-3756	253	15	is	be	AUX
ejpam-3756	253	16	nonempty	nonempty	ADV
ejpam-3756	253	17	closed	closed	ADJ
ejpam-3756	253	18	and	and	CCONJ
ejpam-3756	253	19	convex	convex	NOUN
ejpam-3756	253	20	.	.	PUNCT
ejpam-3756	254	1	also	also	ADV
ejpam-3756	254	2	,	,	PUNCT
ejpam-3756	254	3	let	let	VERB
ejpam-3756	254	4	there	there	PRON
ejpam-3756	254	5	be	be	AUX
ejpam-3756	254	6	a	a	DET
ejpam-3756	254	7	contraction	contraction	NOUN
ejpam-3756	254	8	mapping	mapping	NOUN
ejpam-3756	254	9	t	t	NOUN
ejpam-3756	254	10	:	:	PUNCT
ejpam-3756	254	11	c	c	X
ejpam-3756	254	12	→	→	SYM
ejpam-3756	254	13	c.	c.	PROPN
ejpam-3756	254	14	let	let	VERB
ejpam-3756	254	15	{	{	PUNCT
ejpam-3756	254	16	ζn}∞n=0	ζn}∞n=0	PUNCT
ejpam-3756	254	17	be	be	AUX
ejpam-3756	254	18	an	an	DET
ejpam-3756	254	19	iterative	iterative	NOUN
ejpam-3756	254	20	sequence	sequence	NOUN
ejpam-3756	254	21	generated	generate	VERB
ejpam-3756	254	22	by	by	ADP
ejpam-3756	254	23	nv	nv	PROPN
ejpam-3756	254	24	1	1	NUM
ejpam-3756	254	25	and	and	CCONJ
ejpam-3756	254	26	with	with	ADP
ejpam-3756	254	27	real	real	ADJ
ejpam-3756	254	28	sequence	sequence	NOUN
ejpam-3756	254	29	{	{	PUNCT
ejpam-3756	254	30	σ0n	σ0n	ADV
ejpam-3756	254	31	}	}	PUNCT
ejpam-3756	254	32	∞	∞	NUM
ejpam-3756	254	33	n=0	n=0	PUNCT
ejpam-3756	254	34	∈	∈	PROPN
ejpam-3756	255	1	[	[	X
ejpam-3756	255	2	0	0	NUM
ejpam-3756	255	3	,	,	PUNCT
ejpam-3756	255	4	1	1	NUM
ejpam-3756	255	5	]	]	PUNCT
ejpam-3756	255	6	such	such	ADJ
ejpam-3756	255	7	that∑∞	that∑∞	NOUN
ejpam-3756	255	8	n=0	n=0	PROPN
ejpam-3756	256	1	σ	σ	NOUN
ejpam-3756	256	2	0	0	NUM
ejpam-3756	257	1	n	n	PROPN
ejpam-3756	257	2	=	=	NOUN
ejpam-3756	257	3	∞.	∞.	PROPN
ejpam-3756	257	4	then	then	ADV
ejpam-3756	257	5	the	the	DET
ejpam-3756	257	6	iteration	iteration	NOUN
ejpam-3756	257	7	algorithm	algorithm	NOUN
ejpam-3756	257	8	defined	define	VERB
ejpam-3756	257	9	as	as	ADP
ejpam-3756	257	10	nv	nv	PROPN
ejpam-3756	257	11	1	1	NUM
ejpam-3756	257	12	is	be	AUX
ejpam-3756	257	13	t	t	NOUN
ejpam-3756	257	14	−	−	NOUN
ejpam-3756	257	15	stable	stable	ADJ
ejpam-3756	257	16	.	.	PUNCT
ejpam-3756	258	1	proof	proof	NOUN
ejpam-3756	258	2	.	.	PUNCT
ejpam-3756	259	1	let	let	VERB
ejpam-3756	259	2	an	an	DET
ejpam-3756	259	3	arbitrary	arbitrary	ADJ
ejpam-3756	259	4	sequence	sequence	NOUN
ejpam-3756	259	5	{	{	PUNCT
ejpam-3756	259	6	tn}∞n=0	tn}∞n=0	X
ejpam-3756	259	7	⊂	⊂	X
ejpam-3756	259	8	e	e	NOUN
ejpam-3756	259	9	in	in	ADP
ejpam-3756	259	10	c	c	PROPN
ejpam-3756	259	11	,	,	PUNCT
ejpam-3756	259	12	generated	generate	VERB
ejpam-3756	259	13	by	by	ADP
ejpam-3756	259	14	nv	nv	PROPN
ejpam-3756	259	15	1	1	NUM
ejpam-3756	259	16	and	and	CCONJ
ejpam-3756	259	17	now	now	ADV
ejpam-3756	259	18	defined	define	VERB
ejpam-3756	259	19	as	as	ADP
ejpam-3756	259	20	ζn+1	ζn+1	ADJ
ejpam-3756	259	21	=	=	NOUN
ejpam-3756	259	22	f(t	f(t	NOUN
ejpam-3756	259	23	,	,	PUNCT
ejpam-3756	259	24	ζn	ζn	NOUN
ejpam-3756	259	25	)	)	PUNCT
ejpam-3756	259	26	converges	converge	VERB
ejpam-3756	259	27	to	to	ADP
ejpam-3756	259	28	a	a	DET
ejpam-3756	259	29	fixed	fixed	ADJ
ejpam-3756	259	30	point	point	NOUN
ejpam-3756	259	31	xδ	xδ	PROPN
ejpam-3756	259	32	(	(	PUNCT
ejpam-3756	259	33	by	by	ADP
ejpam-3756	259	34	theorem	theorem	NOUN
ejpam-3756	259	35	1	1	NUM
ejpam-3756	259	36	)	)	PUNCT
ejpam-3756	259	37	and	and	CCONJ
ejpam-3756	259	38	εn	εn	ADJ
ejpam-3756	259	39	=	=	SYM
ejpam-3756	259	40	‖tn+1−f(t	‖tn+1−f(t	PROPN
ejpam-3756	259	41	,	,	PUNCT
ejpam-3756	259	42	tn)‖.	tn)‖.	ADJ
ejpam-3756	259	43	we	we	PRON
ejpam-3756	259	44	will	will	AUX
ejpam-3756	259	45	prove	prove	VERB
ejpam-3756	259	46	that	that	SCONJ
ejpam-3756	259	47	limn→∞	limn→∞	PROPN
ejpam-3756	259	48	tn	tn	NOUN
ejpam-3756	259	49	=	=	SYM
ejpam-3756	259	50	p.	p.	NOUN
ejpam-3756	259	51	let	let	VERB
ejpam-3756	259	52	limn→∞	limn→∞	PROPN
ejpam-3756	259	53	εn	εn	ADJ
ejpam-3756	259	54	=	=	SYM
ejpam-3756	259	55	0	0	NUM
ejpam-3756	259	56	,	,	PUNCT
ejpam-3756	259	57	as	as	ADP
ejpam-3756	259	58	from	from	ADP
ejpam-3756	259	59	theorem	theorem	NOUN
ejpam-3756	259	60	1	1	NUM
ejpam-3756	259	61	using	use	VERB
ejpam-3756	259	62	the	the	DET
ejpam-3756	259	63	inequality	inequality	NOUN
ejpam-3756	259	64	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	259	65	−	−	PROPN
ejpam-3756	260	1	xδ‖	xδ‖	PROPN
ejpam-3756	260	2	≤	≤	PROPN
ejpam-3756	260	3	ξ3(ξ	ξ3(ξ	NUM
ejpam-3756	260	4	−	−	PROPN
ejpam-3756	260	5	(	(	PUNCT
ejpam-3756	260	6	1−	1−	NUM
ejpam-3756	260	7	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	PROPN
ejpam-3756	260	8	−	−	PROPN
ejpam-3756	260	9	xδ‖	xδ‖	PROPN
ejpam-3756	261	1	(	(	PUNCT
ejpam-3756	261	2	-14	-14	NUM
ejpam-3756	261	3	)	)	PUNCT
ejpam-3756	261	4	we	we	PRON
ejpam-3756	261	5	have	have	VERB
ejpam-3756	261	6	,	,	PUNCT
ejpam-3756	261	7	‖tn+1	‖tn+1	ADV
ejpam-3756	261	8	−	−	PRON
ejpam-3756	262	1	xδ‖	xδ‖	PROPN
ejpam-3756	262	2	≤	≤	PROPN
ejpam-3756	262	3	‖tn+1	‖tn+1	NOUN
ejpam-3756	262	4	−	−	PRON
ejpam-3756	262	5	f(t	f(t	PROPN
ejpam-3756	262	6	,	,	PUNCT
ejpam-3756	262	7	tn)‖+	tn)‖+	PUNCT
ejpam-3756	262	8	|f(t	|f(t	NOUN
ejpam-3756	262	9	,	,	PUNCT
ejpam-3756	262	10	tn)−	tn)−	PRON
ejpam-3756	262	11	xδ‖	xδ‖	PUNCT
ejpam-3756	263	1	=	=	PUNCT
ejpam-3756	263	2	εn	εn	ADJ
ejpam-3756	263	3	+	+	CCONJ
ejpam-3756	263	4	∥∥∥∥∥t	∥∥∥∥∥t	PROPN
ejpam-3756	263	5	(	(	PUNCT
ejpam-3756	263	6	t	t	PROPN
ejpam-3756	263	7	(	(	PUNCT
ejpam-3756	263	8	t	t	PROPN
ejpam-3756	263	9	(	(	PUNCT
ejpam-3756	263	10	(	(	PUNCT
ejpam-3756	263	11	1−	1−	NUM
ejpam-3756	263	12	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	263	13	)	)	PUNCT
ejpam-3756	263	14	)	)	PUNCT
ejpam-3756	264	1	+	+	CCONJ
ejpam-3756	264	2	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	264	3	)	)	PUNCT
ejpam-3756	264	4	−	−	PROPN
ejpam-3756	265	1	xδ	xδ	PROPN
ejpam-3756	265	2	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3756	265	3	l.n	l.n	PROPN
ejpam-3756	265	4	mishra	mishra	PROPN
ejpam-3756	265	5	et	et	PROPN
ejpam-3756	265	6	al	al	PROPN
ejpam-3756	265	7	.	.	PUNCT
ejpam-3756	265	8	/	/	SYM
ejpam-3756	265	9	eur	eur	PROPN
ejpam-3756	265	10	.	.	PUNCT
ejpam-3756	266	1	j.	j.	PROPN
ejpam-3756	266	2	pure	pure	PROPN
ejpam-3756	266	3	appl	appl	PROPN
ejpam-3756	266	4	.	.	PROPN
ejpam-3756	266	5	math	math	PROPN
ejpam-3756	266	6	,	,	PUNCT
ejpam-3756	266	7	13	13	NUM
ejpam-3756	266	8	(	(	PUNCT
ejpam-3756	266	9	5	5	NUM
ejpam-3756	266	10	)	)	PUNCT
ejpam-3756	266	11	(	(	PUNCT
ejpam-3756	266	12	2020	2020	NUM
ejpam-3756	266	13	)	)	PUNCT
ejpam-3756	266	14	,	,	PUNCT
ejpam-3756	266	15	1110	1110	NUM
ejpam-3756	266	16	-	-	SYM
ejpam-3756	266	17	1130	1130	NUM
ejpam-3756	266	18	1124	1124	NUM
ejpam-3756	266	19	≤	≤	NOUN
ejpam-3756	266	20	ξ3(1−	ξ3(1−	ADP
ejpam-3756	266	21	(	(	PUNCT
ejpam-3756	266	22	1−	1−	NUM
ejpam-3756	266	23	ξ)σ0n)‖tn	ξ)σ0n)‖tn	NOUN
ejpam-3756	266	24	−	−	PROPN
ejpam-3756	266	25	xδ‖+	xδ‖+	PUNCT
ejpam-3756	267	1	εn	εn	PROPN
ejpam-3756	267	2	.	.	PUNCT
ejpam-3756	268	1	define	define	VERB
ejpam-3756	268	2	ψn	ψn	NOUN
ejpam-3756	269	1	=	=	PUNCT
ejpam-3756	269	2	‖tn	‖tn	NUM
ejpam-3756	269	3	−	−	NOUN
ejpam-3756	269	4	xδ‖	xδ‖	PROPN
ejpam-3756	269	5	,	,	PUNCT
ejpam-3756	269	6	φn	φn	ADP
ejpam-3756	269	7	=	=	PUNCT
ejpam-3756	269	8	(	(	PUNCT
ejpam-3756	269	9	1−	1−	NUM
ejpam-3756	269	10	ξ)σ0n	ξ)σ0n	ADJ
ejpam-3756	269	11	∈	∈	PROPN
ejpam-3756	269	12	(	(	PUNCT
ejpam-3756	269	13	0	0	NUM
ejpam-3756	269	14	,	,	PUNCT
ejpam-3756	269	15	1	1	NUM
ejpam-3756	269	16	)	)	PUNCT
ejpam-3756	269	17	and	and	CCONJ
ejpam-3756	269	18	ϕ	ϕ	X
ejpam-3756	269	19	=	=	SYM
ejpam-3756	269	20	εn	εn	ADJ
ejpam-3756	269	21	,	,	PUNCT
ejpam-3756	269	22	which	which	PRON
ejpam-3756	269	23	implies	imply	VERB
ejpam-3756	269	24	that	that	SCONJ
ejpam-3756	269	25	ϕn	ϕn	INTJ
ejpam-3756	269	26	φn	φn	ADP
ejpam-3756	269	27	→	→	SYM
ejpam-3756	269	28	0	0	PUNCT
ejpam-3756	269	29	as	as	ADP
ejpam-3756	269	30	n→∞.	n→∞.	ADJ
ejpam-3756	269	31	thus	thus	ADV
ejpam-3756	269	32	all	all	DET
ejpam-3756	269	33	the	the	DET
ejpam-3756	269	34	conditions	condition	NOUN
ejpam-3756	269	35	of	of	ADP
ejpam-3756	269	36	lemma	lemma	PROPN
ejpam-3756	269	37	2	2	NUM
ejpam-3756	269	38	are	be	AUX
ejpam-3756	269	39	satisfied	satisfy	VERB
ejpam-3756	269	40	by	by	ADP
ejpam-3756	269	41	above	above	ADP
ejpam-3756	269	42	inequality	inequality	NOUN
ejpam-3756	269	43	.	.	PUNCT
ejpam-3756	270	1	hence	hence	ADV
ejpam-3756	270	2	,	,	PUNCT
ejpam-3756	270	3	we	we	PRON
ejpam-3756	270	4	get	get	VERB
ejpam-3756	270	5	limn→∞	limn→∞	PRON
ejpam-3756	270	6	tn	tn	NOUN
ejpam-3756	270	7	=	=	SYM
ejpam-3756	270	8	p	p	NOUN
ejpam-3756	270	9	,	,	PUNCT
ejpam-3756	270	10	we	we	PRON
ejpam-3756	270	11	have	have	AUX
ejpam-3756	270	12	εn	εn	ADJ
ejpam-3756	270	13	=	=	NOUN
ejpam-3756	270	14	‖tn+1	‖tn+1	NOUN
ejpam-3756	270	15	−	−	PRON
ejpam-3756	270	16	f(t	f(t	NOUN
ejpam-3756	270	17	,	,	PUNCT
ejpam-3756	270	18	tn)‖	tn)‖	NOUN
ejpam-3756	270	19	≤	≤	NUM
ejpam-3756	270	20	‖tn+1	‖tn+1	NOUN
ejpam-3756	270	21	−	−	PROPN
ejpam-3756	270	22	xδ‖	xδ‖	PROPN
ejpam-3756	271	1	−	−	NOUN
ejpam-3756	271	2	‖f(t	‖f(t	ADP
ejpam-3756	271	3	,	,	PUNCT
ejpam-3756	271	4	tn)−	tn)−	PRON
ejpam-3756	271	5	xδ‖	xδ‖	PROPN
ejpam-3756	272	1	≤	≤	NUM
ejpam-3756	272	2	ξ3(ξ	ξ3(ξ	NUM
ejpam-3756	272	3	−	−	PROPN
ejpam-3756	272	4	(	(	PUNCT
ejpam-3756	272	5	1−	1−	NUM
ejpam-3756	272	6	ξ)σ0n)‖tn	ξ)σ0n)‖tn	NOUN
ejpam-3756	272	7	−	−	PROPN
ejpam-3756	272	8	xδ‖+	xδ‖+	PROPN
ejpam-3756	273	1	εn	εn	ADP
ejpam-3756	273	2	this	this	PRON
ejpam-3756	273	3	implies	imply	VERB
ejpam-3756	273	4	that	that	SCONJ
ejpam-3756	273	5	limn→∞	limn→∞	PROPN
ejpam-3756	273	6	tn	tn	NOUN
ejpam-3756	273	7	=	=	SYM
ejpam-3756	273	8	0	0	PROPN
ejpam-3756	273	9	.	.	PUNCT
ejpam-3756	274	1	this	this	PRON
ejpam-3756	274	2	also	also	ADV
ejpam-3756	274	3	implies	imply	VERB
ejpam-3756	274	4	that	that	SCONJ
ejpam-3756	274	5	nv	nv	PROPN
ejpam-3756	274	6	1	1	NUM
ejpam-3756	274	7	is	be	AUX
ejpam-3756	274	8	t	t	NOUN
ejpam-3756	274	9	−	−	NOUN
ejpam-3756	274	10	stable	stable	ADJ
ejpam-3756	274	11	with	with	ADP
ejpam-3756	274	12	respect	respect	NOUN
ejpam-3756	274	13	to	to	ADP
ejpam-3756	274	14	t	t	PROPN
ejpam-3756	274	15	.	.	PUNCT
ejpam-3756	275	1	6	6	X
ejpam-3756	275	2	.	.	X
ejpam-3756	275	3	data	datum	NOUN
ejpam-3756	275	4	dependence	dependence	NOUN
ejpam-3756	275	5	result	result	NOUN
ejpam-3756	275	6	in	in	ADP
ejpam-3756	275	7	this	this	DET
ejpam-3756	275	8	section	section	NOUN
ejpam-3756	275	9	we	we	PRON
ejpam-3756	275	10	establish	establish	VERB
ejpam-3756	275	11	some	some	DET
ejpam-3756	275	12	data	datum	NOUN
ejpam-3756	275	13	dependence	dependence	NOUN
ejpam-3756	275	14	result	result	NOUN
ejpam-3756	275	15	.	.	PUNCT
ejpam-3756	276	1	theorem	theorem	ADJ
ejpam-3756	276	2	7	7	NUM
ejpam-3756	276	3	.	.	PUNCT
ejpam-3756	277	1	let	let	VERB
ejpam-3756	277	2	t̃	t̃	PROPN
ejpam-3756	277	3	be	be	AUX
ejpam-3756	277	4	an	an	DET
ejpam-3756	277	5	approximate	approximate	ADJ
ejpam-3756	277	6	operator	operator	NOUN
ejpam-3756	277	7	of	of	ADP
ejpam-3756	277	8	a	a	DET
ejpam-3756	277	9	contraction	contraction	NOUN
ejpam-3756	277	10	mapping	mapping	NOUN
ejpam-3756	277	11	t	t	NOUN
ejpam-3756	277	12	.	.	PUNCT
ejpam-3756	278	1	let	let	VERB
ejpam-3756	278	2	{	{	PUNCT
ejpam-3756	278	3	ζn}∞n=0	ζn}∞n=0	VERB
ejpam-3756	278	4	be	be	AUX
ejpam-3756	278	5	an	an	DET
ejpam-3756	278	6	iterative	iterative	NOUN
ejpam-3756	278	7	sequence	sequence	NOUN
ejpam-3756	278	8	defines	define	NOUN
ejpam-3756	278	9	as	as	ADP
ejpam-3756	278	10	nv	nv	PROPN
ejpam-3756	278	11	1	1	NUM
ejpam-3756	278	12	for	for	ADP
ejpam-3756	278	13	t	t	PROPN
ejpam-3756	278	14	and	and	CCONJ
ejpam-3756	278	15	defined	define	VERB
ejpam-3756	278	16	an	an	DET
ejpam-3756	278	17	iterative	iterative	NOUN
ejpam-3756	278	18	sequence	sequence	NOUN
ejpam-3756	278	19	{	{	PUNCT
ejpam-3756	278	20	ζ̃n	ζ̃n	NOUN
ejpam-3756	278	21	}	}	PUNCT
ejpam-3756	278	22	∞	∞	NUM
ejpam-3756	278	23	n=0	n=0	NUM
ejpam-3756	278	24	for	for	ADP
ejpam-3756	278	25	t̃	t̃	PROPN
ejpam-3756	278	26	,	,	PUNCT
ejpam-3756	278	27	as	as	SCONJ
ejpam-3756	278	28	follows	follow	VERB
ejpam-3756	278	29	constructed	construct	VERB
ejpam-3756	278	30	as	as	ADP
ejpam-3756	278	31	,	,	PUNCT
ejpam-3756	278	32	for	for	ADP
ejpam-3756	278	33	arbitrary	arbitrary	ADJ
ejpam-3756	278	34	ζ̃0	ζ̃0	PROPN
ejpam-3756	278	35	∈	∈	PROPN
ejpam-3756	278	36	x	x	X
ejpam-3756	278	37	by	by	NOUN
ejpam-3756	278	38	θ̃n	θ̃n	X
ejpam-3756	278	39	=	=	X
ejpam-3756	278	40	t̃	t̃	PROPN
ejpam-3756	278	41	(	(	PUNCT
ejpam-3756	278	42	(	(	PUNCT
ejpam-3756	278	43	1−	1−	NUM
ejpam-3756	278	44	σ0n)ζ̃n	σ0n)ζ̃n	NOUN
ejpam-3756	278	45	+	+	CCONJ
ejpam-3756	278	46	σ0nt̃	σ0nt̃	PROPN
ejpam-3756	278	47	ζ̃n	ζ̃n	NOUN
ejpam-3756	278	48	)	)	PUNCT
ejpam-3756	278	49	η̃n	η̃n	NOUN
ejpam-3756	278	50	=	=	PUNCT
ejpam-3756	278	51	t̃	t̃	PROPN
ejpam-3756	278	52	θ̃n	θ̃n	VERB
ejpam-3756	278	53	ζ̃n+1	ζ̃n+1	NOUN
ejpam-3756	278	54	=	=	SYM
ejpam-3756	278	55	t̃	t̃	PROPN
ejpam-3756	278	56	η̃n	η̃n	NOUN
ejpam-3756	278	57	n	n	PRON
ejpam-3756	278	58	∈	∈	NOUN
ejpam-3756	278	59	n	n	CCONJ
ejpam-3756	278	60	where	where	SCONJ
ejpam-3756	278	61	real	real	ADJ
ejpam-3756	278	62	sequence	sequence	NOUN
ejpam-3756	278	63	{	{	PUNCT
ejpam-3756	278	64	σ0n	σ0n	ADV
ejpam-3756	278	65	}	}	PUNCT
ejpam-3756	278	66	∞	∞	NUM
ejpam-3756	278	67	n=0	n=0	PUNCT
ejpam-3756	278	68	in	in	ADP
ejpam-3756	278	69	[	[	X
ejpam-3756	278	70	0,1	0,1	NUM
ejpam-3756	278	71	]	]	PUNCT
ejpam-3756	278	72	satisfying	satisfy	VERB
ejpam-3756	278	73	1	1	NUM
ejpam-3756	278	74	2	2	NUM
ejpam-3756	278	75	≤	≤	NUM
ejpam-3756	278	76	σ0n	σ0n	PUNCT
ejpam-3756	278	77	,	,	PUNCT
ejpam-3756	278	78	for	for	ADP
ejpam-3756	278	79	all	all	DET
ejpam-3756	278	80	n	n	DET
ejpam-3756	278	81	∈	∈	NOUN
ejpam-3756	278	82	n	n	NOUN
ejpam-3756	278	83	and	and	CCONJ
ejpam-3756	278	84	∑	∑	ADV
ejpam-3756	278	85	σ0n	σ0n	PROPN
ejpam-3756	278	86	=	=	PUNCT
ejpam-3756	278	87	∞.	∞.	PROPN
ejpam-3756	278	88	also	also	ADV
ejpam-3756	278	89	,	,	PUNCT
ejpam-3756	278	90	if	if	SCONJ
ejpam-3756	278	91	tp	tp	ADP
ejpam-3756	278	92	=	=	PUNCT
ejpam-3756	278	93	p	p	PROPN
ejpam-3756	278	94	and	and	CCONJ
ejpam-3756	278	95	t̃	t̃	PROPN
ejpam-3756	278	96	p̃	p̃	PROPN
ejpam-3756	278	97	=	=	SYM
ejpam-3756	278	98	p̃	p̃	PROPN
ejpam-3756	278	99	such	such	ADJ
ejpam-3756	278	100	that	that	SCONJ
ejpam-3756	278	101	limn→∞	limn→∞	ADJ
ejpam-3756	278	102	ζ̃	ζ̃	PROPN
ejpam-3756	278	103	=	=	SYM
ejpam-3756	278	104	p̃	p̃	PROPN
ejpam-3756	278	105	,	,	PUNCT
ejpam-3756	278	106	then	then	ADV
ejpam-3756	278	107	we	we	PRON
ejpam-3756	278	108	have	have	VERB
ejpam-3756	278	109	‖p−	‖p−	PROPN
ejpam-3756	278	110	p̃‖	p̃‖	ADJ
ejpam-3756	278	111	≤	≤	NOUN
ejpam-3756	278	112	11ε	11ε	NUM
ejpam-3756	278	113	1−	1−	NUM
ejpam-3756	278	114	ξ	ξ	X
ejpam-3756	278	115	.	.	PUNCT
ejpam-3756	279	1	proof	proof	NOUN
ejpam-3756	279	2	.	.	PUNCT
ejpam-3756	280	1	using	use	VERB
ejpam-3756	280	2	{	{	PUNCT
ejpam-3756	280	3	ζn}∞n=0	ζn}∞n=0	PUNCT
ejpam-3756	280	4	and	and	CCONJ
ejpam-3756	280	5	{	{	PUNCT
ejpam-3756	280	6	ζ̃n	ζ̃n	NOUN
ejpam-3756	280	7	}	}	PUNCT
ejpam-3756	280	8	∞	∞	NUM
ejpam-3756	280	9	n=0	n=0	NUM
ejpam-3756	280	10	,	,	PUNCT
ejpam-3756	280	11	we	we	PRON
ejpam-3756	280	12	have	have	VERB
ejpam-3756	280	13	‖θn	‖θn	NUM
ejpam-3756	280	14	−	−	PUNCT
ejpam-3756	280	15	θ̃n‖	θ̃n‖	PROPN
ejpam-3756	280	16	=	=	SYM
ejpam-3756	280	17	∥∥∥∥∥t	∥∥∥∥∥t	PROPN
ejpam-3756	280	18	(	(	PUNCT
ejpam-3756	280	19	(	(	PUNCT
ejpam-3756	280	20	1−	1−	NUM
ejpam-3756	280	21	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	281	1	+	+	CCONJ
ejpam-3756	281	2	σ0ntζn)−	σ0ntζn)−	PROPN
ejpam-3756	281	3	t̃	t̃	PROPN
ejpam-3756	281	4	(	(	PUNCT
ejpam-3756	281	5	(	(	PUNCT
ejpam-3756	281	6	1−	1−	NUM
ejpam-3756	281	7	σ0n)ζ̃n	σ0n)ζ̃n	NOUN
ejpam-3756	281	8	+	+	CCONJ
ejpam-3756	281	9	σ0nt̃	σ0nt̃	PROPN
ejpam-3756	281	10	ζ̃n	ζ̃n	NOUN
ejpam-3756	281	11	)	)	PUNCT
ejpam-3756	281	12	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3756	281	13	≤	≤	NUM
ejpam-3756	281	14	∥∥∥∥∥t	∥∥∥∥∥t	PROPN
ejpam-3756	281	15	(	(	PUNCT
ejpam-3756	281	16	(	(	PUNCT
ejpam-3756	281	17	1−	1−	NUM
ejpam-3756	281	18	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	281	19	+	+	CCONJ
ejpam-3756	281	20	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	281	21	)	)	PUNCT
ejpam-3756	281	22	−	−	PROPN
ejpam-3756	281	23	t	t	NOUN
ejpam-3756	281	24	(	(	PUNCT
ejpam-3756	281	25	(	(	PUNCT
ejpam-3756	281	26	1−	1−	NUM
ejpam-3756	281	27	σ0n)ζ̃n	σ0n)ζ̃n	NOUN
ejpam-3756	281	28	+	+	CCONJ
ejpam-3756	281	29	σ0nt̃	σ0nt̃	NOUN
ejpam-3756	281	30	ζ̃n	ζ̃n	NOUN
ejpam-3756	281	31	)	)	PUNCT
ejpam-3756	282	1	+	+	CCONJ
ejpam-3756	282	2	t	t	X
ejpam-3756	282	3	(	(	PUNCT
ejpam-3756	282	4	(	(	PUNCT
ejpam-3756	282	5	1−	1−	NUM
ejpam-3756	282	6	σ0n)ζ̃n	σ0n)ζ̃n	NOUN
ejpam-3756	282	7	+	+	CCONJ
ejpam-3756	282	8	σ0nt̃	σ0nt̃	NOUN
ejpam-3756	282	9	ζ̃n	ζ̃n	NOUN
ejpam-3756	282	10	)	)	PUNCT
ejpam-3756	283	1	−	−	PROPN
ejpam-3756	284	1	t̃	t̃	PROPN
ejpam-3756	284	2	(	(	PUNCT
ejpam-3756	284	3	(	(	PUNCT
ejpam-3756	284	4	1−	1−	NUM
ejpam-3756	284	5	σ0n)ζ̃n	σ0n)ζ̃n	NOUN
ejpam-3756	284	6	+	+	CCONJ
ejpam-3756	284	7	σ0nt̃	σ0nt̃	NOUN
ejpam-3756	284	8	ζ̃n	ζ̃n	NOUN
ejpam-3756	284	9	)	)	PUNCT
ejpam-3756	284	10	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-3756	284	11	≤	≤	ADV
ejpam-3756	284	12	ξ	ξ	X
ejpam-3756	284	13	(	(	PUNCT
ejpam-3756	284	14	(	(	PUNCT
ejpam-3756	284	15	1−	1−	NUM
ejpam-3756	284	16	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	284	17	−	−	PROPN
ejpam-3756	284	18	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	284	19	σ0n‖tζn	σ0n‖tζn	NOUN
ejpam-3756	284	20	−	−	PROPN
ejpam-3756	284	21	t̃	t̃	PROPN
ejpam-3756	284	22	ζ̃n)‖	ζ̃n)‖	NUM
ejpam-3756	284	23	)	)	PUNCT
ejpam-3756	285	1	+	+	CCONJ
ejpam-3756	285	2	ε	ε	PROPN
ejpam-3756	285	3	l.n	l.n	PROPN
ejpam-3756	285	4	mishra	mishra	PROPN
ejpam-3756	285	5	et	et	PROPN
ejpam-3756	285	6	al	al	PROPN
ejpam-3756	285	7	.	.	PUNCT
ejpam-3756	285	8	/	/	SYM
ejpam-3756	285	9	eur	eur	PROPN
ejpam-3756	285	10	.	.	PUNCT
ejpam-3756	286	1	j.	j.	PROPN
ejpam-3756	286	2	pure	pure	PROPN
ejpam-3756	286	3	appl	appl	PROPN
ejpam-3756	286	4	.	.	PROPN
ejpam-3756	286	5	math	math	PROPN
ejpam-3756	286	6	,	,	PUNCT
ejpam-3756	286	7	13	13	NUM
ejpam-3756	286	8	(	(	PUNCT
ejpam-3756	286	9	5	5	NUM
ejpam-3756	286	10	)	)	PUNCT
ejpam-3756	286	11	(	(	PUNCT
ejpam-3756	286	12	2020	2020	NUM
ejpam-3756	286	13	)	)	PUNCT
ejpam-3756	286	14	,	,	PUNCT
ejpam-3756	286	15	1110	1110	NUM
ejpam-3756	286	16	-	-	SYM
ejpam-3756	286	17	1130	1130	NUM
ejpam-3756	286	18	1125	1125	NUM
ejpam-3756	287	1	≤	≤	NOUN
ejpam-3756	287	2	ξ	ξ	X
ejpam-3756	287	3	(	(	PUNCT
ejpam-3756	287	4	(	(	PUNCT
ejpam-3756	287	5	1−	1−	NUM
ejpam-3756	287	6	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	287	7	−	−	PROPN
ejpam-3756	287	8	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	287	9	σ0n	σ0n	ADP
ejpam-3756	287	10	(	(	PUNCT
ejpam-3756	287	11	‖tζn	‖tζn	PROPN
ejpam-3756	287	12	−	−	PROPN
ejpam-3756	287	13	t	t	PROPN
ejpam-3756	287	14	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	287	15	‖t	‖t	PROPN
ejpam-3756	287	16	ζ̃n	ζ̃n	NOUN
ejpam-3756	287	17	−	−	PROPN
ejpam-3756	287	18	t̃	t̃	PROPN
ejpam-3756	287	19	ζ̃n)‖	ζ̃n)‖	NUM
ejpam-3756	287	20	)	)	PUNCT
ejpam-3756	287	21	)	)	PUNCT
ejpam-3756	288	1	+	+	CCONJ
ejpam-3756	288	2	ε	ε	PROPN
ejpam-3756	288	3	≤	≤	PROPN
ejpam-3756	288	4	ξ	ξ	PROPN
ejpam-3756	288	5	(	(	PUNCT
ejpam-3756	288	6	(	(	PUNCT
ejpam-3756	288	7	1−	1−	NUM
ejpam-3756	288	8	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	288	9	−	−	PROPN
ejpam-3756	288	10	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	288	11	σ0n	σ0n	ADP
ejpam-3756	288	12	(	(	PUNCT
ejpam-3756	288	13	ξ(‖ζn	ξ(‖ζn	X
ejpam-3756	288	14	−	−	ADP
ejpam-3756	288	15	ζ̃n‖	ζ̃n‖	NOUN
ejpam-3756	288	16	)	)	PUNCT
ejpam-3756	289	1	+	+	NUM
ejpam-3756	289	2	ε+	ε+	X
ejpam-3756	289	3	ε	ε	PROPN
ejpam-3756	289	4	)	)	PUNCT
ejpam-3756	289	5	)	)	PUNCT
ejpam-3756	290	1	+	+	CCONJ
ejpam-3756	290	2	ε	ε	PROPN
ejpam-3756	290	3	≤	≤	PROPN
ejpam-3756	290	4	ξ(1−	ξ(1−	PROPN
ejpam-3756	290	5	(	(	PUNCT
ejpam-3756	290	6	1−	1−	NUM
ejpam-3756	290	7	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	290	8	−	−	PROPN
ejpam-3756	290	9	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	290	10	ξσ0nε+	ξσ0nε+	ADJ
ejpam-3756	290	11	ε	ε	PROPN
ejpam-3756	290	12	in	in	ADP
ejpam-3756	290	13	similar	similar	ADJ
ejpam-3756	290	14	manner	manner	NOUN
ejpam-3756	290	15	,	,	PUNCT
ejpam-3756	290	16	we	we	PRON
ejpam-3756	290	17	have	have	VERB
ejpam-3756	290	18	‖ηn	‖ηn	NUM
ejpam-3756	290	19	−	−	PROPN
ejpam-3756	290	20	η̃n‖	η̃n‖	NOUN
ejpam-3756	290	21	=	=	SYM
ejpam-3756	290	22	‖tθn	‖tθn	PRON
ejpam-3756	291	1	−	−	PROPN
ejpam-3756	291	2	t̃	t̃	PROPN
ejpam-3756	291	3	θ̃n‖	θ̃n‖	NOUN
ejpam-3756	291	4	‖ηn	‖ηn	NUM
ejpam-3756	291	5	−	−	PUNCT
ejpam-3756	291	6	η̃n‖	η̃n‖	NOUN
ejpam-3756	291	7	=	=	SYM
ejpam-3756	291	8	‖tθn	‖tθn	PRON
ejpam-3756	291	9	−	−	PROPN
ejpam-3756	291	10	t	t	NOUN
ejpam-3756	291	11	θ̃n	θ̃n	X
ejpam-3756	291	12	+	+	NUM
ejpam-3756	291	13	t	t	NOUN
ejpam-3756	291	14	θ̃n	θ̃n	VERB
ejpam-3756	291	15	−	−	PROPN
ejpam-3756	291	16	t̃	t̃	PROPN
ejpam-3756	291	17	θ̃n‖	θ̃n‖	NOUN
ejpam-3756	291	18	≤	≤	NOUN
ejpam-3756	291	19	‖tθn	‖tθn	NOUN
ejpam-3756	291	20	−	−	PROPN
ejpam-3756	291	21	t	t	PROPN
ejpam-3756	291	22	θ̃n‖+	θ̃n‖+	PROPN
ejpam-3756	291	23	‖t	‖t	PROPN
ejpam-3756	291	24	θ̃n	θ̃n	VERB
ejpam-3756	291	25	−	−	PROPN
ejpam-3756	291	26	t̃	t̃	PROPN
ejpam-3756	291	27	θ̃n‖	θ̃n‖	NOUN
ejpam-3756	291	28	≤	≤	NOUN
ejpam-3756	292	1	ξ‖θn	ξ‖θn	PROPN
ejpam-3756	292	2	−	−	NOUN
ejpam-3756	292	3	θ̃‖+	θ̃‖+	PROPN
ejpam-3756	292	4	ε	ε	PROPN
ejpam-3756	292	5	on	on	ADP
ejpam-3756	292	6	substituting	substitute	VERB
ejpam-3756	292	7	the	the	DET
ejpam-3756	292	8	value	value	NOUN
ejpam-3756	292	9	of	of	ADP
ejpam-3756	292	10	‖θn	‖θn	NUM
ejpam-3756	292	11	−	−	PUNCT
ejpam-3756	292	12	θ̃n‖	θ̃n‖	NOUN
ejpam-3756	292	13	,	,	PUNCT
ejpam-3756	292	14	we	we	PRON
ejpam-3756	292	15	have	have	VERB
ejpam-3756	292	16	‖ηn	‖ηn	NUM
ejpam-3756	292	17	−	−	PUNCT
ejpam-3756	292	18	η̃n‖	η̃n‖	NOUN
ejpam-3756	292	19	≤	≤	NOUN
ejpam-3756	292	20	ξ	ξ	PROPN
ejpam-3756	292	21	(	(	PUNCT
ejpam-3756	292	22	ξ(1−	ξ(1−	X
ejpam-3756	292	23	(	(	PUNCT
ejpam-3756	292	24	1−	1−	NUM
ejpam-3756	292	25	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	292	26	−	−	PROPN
ejpam-3756	292	27	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	292	28	ξσ0nε+	ξσ0nε+	ADJ
ejpam-3756	292	29	ε	ε	PROPN
ejpam-3756	292	30	)	)	PUNCT
ejpam-3756	293	1	+	+	CCONJ
ejpam-3756	293	2	ε	ε	PROPN
ejpam-3756	293	3	in	in	ADP
ejpam-3756	293	4	a	a	DET
ejpam-3756	293	5	similar	similar	ADJ
ejpam-3756	293	6	manner	manner	NOUN
ejpam-3756	293	7	,	,	PUNCT
ejpam-3756	293	8	we	we	PRON
ejpam-3756	293	9	have	have	VERB
ejpam-3756	293	10	‖ζn+	‖ζn+	NOUN
ejpam-3756	293	11	−	−	NOUN
ejpam-3756	293	12	ζ̃n+1‖	ζ̃n+1‖	X
ejpam-3756	293	13	=	=	SYM
ejpam-3756	293	14	‖tηn	‖tηn	ADP
ejpam-3756	293	15	−	−	PROPN
ejpam-3756	293	16	t̃	t̃	PROPN
ejpam-3756	293	17	η̃n‖	η̃n‖	PROPN
ejpam-3756	293	18	‖ζn	‖ζn	NUM
ejpam-3756	293	19	−	−	PROPN
ejpam-3756	293	20	ζ̃n‖	ζ̃n‖	NOUN
ejpam-3756	293	21	=	=	SYM
ejpam-3756	294	1	‖tηn	‖tηn	PROPN
ejpam-3756	294	2	−	−	PROPN
ejpam-3756	294	3	t	t	NOUN
ejpam-3756	294	4	η̃n	η̃n	NOUN
ejpam-3756	294	5	+	+	CCONJ
ejpam-3756	294	6	t	t	NOUN
ejpam-3756	294	7	η̃n	η̃n	NOUN
ejpam-3756	294	8	−	−	PROPN
ejpam-3756	294	9	t̃	t̃	PROPN
ejpam-3756	294	10	η̃n‖	η̃n‖	PROPN
ejpam-3756	294	11	≤	≤	NUM
ejpam-3756	294	12	‖tηn	‖tηn	ADP
ejpam-3756	294	13	−	−	PROPN
ejpam-3756	294	14	t	t	PROPN
ejpam-3756	294	15	η̃n‖+	η̃n‖+	PROPN
ejpam-3756	294	16	‖t	‖t	NOUN
ejpam-3756	294	17	η̃n	η̃n	NOUN
ejpam-3756	295	1	−	−	PROPN
ejpam-3756	295	2	t̃	t̃	PROPN
ejpam-3756	295	3	η̃n‖	η̃n‖	PROPN
ejpam-3756	295	4	≤	≤	NOUN
ejpam-3756	296	1	ξ‖ηn	ξ‖ηn	DET
ejpam-3756	296	2	−	−	PROPN
ejpam-3756	296	3	η̃‖+	η̃‖+	PROPN
ejpam-3756	296	4	ε	ε	PROPN
ejpam-3756	296	5	on	on	ADP
ejpam-3756	296	6	substituting	substitute	VERB
ejpam-3756	296	7	the	the	DET
ejpam-3756	296	8	value	value	NOUN
ejpam-3756	296	9	of	of	ADP
ejpam-3756	296	10	‖ηn	‖ηn	NUM
ejpam-3756	296	11	−	−	NOUN
ejpam-3756	296	12	η̃n‖	η̃n‖	NOUN
ejpam-3756	296	13	,	,	PUNCT
ejpam-3756	296	14	we	we	PRON
ejpam-3756	296	15	have	have	VERB
ejpam-3756	296	16	‖ζn	‖ζn	NUM
ejpam-3756	296	17	−	−	NUM
ejpam-3756	296	18	ζ̃n‖	ζ̃n‖	PROPN
ejpam-3756	296	19	≤	≤	NOUN
ejpam-3756	296	20	ξ	ξ	X
ejpam-3756	296	21	(	(	PUNCT
ejpam-3756	296	22	ξ(1−	ξ(1−	X
ejpam-3756	296	23	(	(	PUNCT
ejpam-3756	296	24	1−	1−	NUM
ejpam-3756	296	25	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	296	26	−	−	PROPN
ejpam-3756	296	27	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	296	28	ξσ0nε+	ξσ0nε+	ADJ
ejpam-3756	296	29	ε	ε	PROPN
ejpam-3756	296	30	)	)	PUNCT
ejpam-3756	297	1	+	+	CCONJ
ejpam-3756	297	2	ε	ε	PROPN
ejpam-3756	297	3	using	use	VERB
ejpam-3756	297	4	{	{	PUNCT
ejpam-3756	297	5	σ0n	σ0n	ADV
ejpam-3756	297	6	}	}	PUNCT
ejpam-3756	297	7	∞	∞	NUM
ejpam-3756	297	8	n=0	n=0	PUNCT
ejpam-3756	297	9	in	in	ADP
ejpam-3756	297	10	[	[	X
ejpam-3756	297	11	0,1	0,1	NUM
ejpam-3756	297	12	]	]	PUNCT
ejpam-3756	297	13	and	and	CCONJ
ejpam-3756	297	14	ξ	ξ	X
ejpam-3756	297	15	∈	∈	PROPN
ejpam-3756	297	16	(	(	PUNCT
ejpam-3756	297	17	0	0	NUM
ejpam-3756	297	18	,	,	PUNCT
ejpam-3756	297	19	1	1	NUM
ejpam-3756	297	20	)	)	PUNCT
ejpam-3756	297	21	and	and	CCONJ
ejpam-3756	297	22	combining	combine	VERB
ejpam-3756	297	23	the	the	DET
ejpam-3756	297	24	above	above	ADJ
ejpam-3756	297	25	inequalities	inequality	NOUN
ejpam-3756	297	26	of	of	ADP
ejpam-3756	297	27	same	same	ADJ
ejpam-3756	297	28	theorem	theorem	NOUN
ejpam-3756	297	29	,	,	PUNCT
ejpam-3756	297	30	we	we	PRON
ejpam-3756	297	31	have	have	VERB
ejpam-3756	297	32	‖ζn	‖ζn	NUM
ejpam-3756	297	33	−	−	NUM
ejpam-3756	297	34	ζ̃n‖	ζ̃n‖	PROPN
ejpam-3756	297	35	≤	≤	NUM
ejpam-3756	297	36	(	(	PUNCT
ejpam-3756	297	37	1−	1−	NUM
ejpam-3756	297	38	(	(	PUNCT
ejpam-3756	297	39	1−	1−	NUM
ejpam-3756	297	40	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	PROPN
ejpam-3756	297	41	−	−	PROPN
ejpam-3756	297	42	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	297	43	σ0nε+	σ0nε+	VERB
ejpam-3756	297	44	5ε	5ε	NUM
ejpam-3756	297	45	≤	≤	NOUN
ejpam-3756	297	46	(	(	PUNCT
ejpam-3756	297	47	1−	1−	NUM
ejpam-3756	297	48	(	(	PUNCT
ejpam-3756	297	49	1−	1−	NUM
ejpam-3756	297	50	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	NOUN
ejpam-3756	297	51	−	−	PROPN
ejpam-3756	297	52	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	297	53	σ0nε	σ0nε	PUNCT
ejpam-3756	297	54	+	+	CCONJ
ejpam-3756	297	55	5(1−	5(1−	NUM
ejpam-3756	297	56	σ0n	σ0n	SYM
ejpam-3756	298	1	+	+	CCONJ
ejpam-3756	298	2	σ0n)ε	σ0n)ε	X
ejpam-3756	299	1	‖ζn	‖ζn	NUM
ejpam-3756	300	1	−	−	NUM
ejpam-3756	300	2	ζ̃n‖	ζ̃n‖	PROPN
ejpam-3756	300	3	≤	≤	NUM
ejpam-3756	300	4	(	(	PUNCT
ejpam-3756	301	1	1−	1−	NUM
ejpam-3756	301	2	(	(	PUNCT
ejpam-3756	301	3	1−	1−	NUM
ejpam-3756	301	4	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	PROPN
ejpam-3756	301	5	−	−	PROPN
ejpam-3756	301	6	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	301	7	σ0n(1−	σ0n(1−	X
ejpam-3756	301	8	ξ	ξ	PROPN
ejpam-3756	301	9	)	)	PUNCT
ejpam-3756	301	10	11ε	11ε	NUM
ejpam-3756	302	1	1−	1−	NUM
ejpam-3756	302	2	ξ	ξ	X
ejpam-3756	302	3	l.n	l.n	PROPN
ejpam-3756	302	4	mishra	mishra	PROPN
ejpam-3756	302	5	et	et	PROPN
ejpam-3756	302	6	al	al	PROPN
ejpam-3756	302	7	.	.	PUNCT
ejpam-3756	302	8	/	/	SYM
ejpam-3756	302	9	eur	eur	PROPN
ejpam-3756	302	10	.	.	PUNCT
ejpam-3756	303	1	j.	j.	PROPN
ejpam-3756	303	2	pure	pure	PROPN
ejpam-3756	303	3	appl	appl	PROPN
ejpam-3756	303	4	.	.	PROPN
ejpam-3756	303	5	math	math	PROPN
ejpam-3756	303	6	,	,	PUNCT
ejpam-3756	303	7	13	13	NUM
ejpam-3756	303	8	(	(	PUNCT
ejpam-3756	303	9	5	5	NUM
ejpam-3756	303	10	)	)	PUNCT
ejpam-3756	303	11	(	(	PUNCT
ejpam-3756	303	12	2020	2020	NUM
ejpam-3756	303	13	)	)	PUNCT
ejpam-3756	303	14	,	,	PUNCT
ejpam-3756	303	15	1110	1110	NUM
ejpam-3756	303	16	-	-	SYM
ejpam-3756	303	17	1130	1130	NUM
ejpam-3756	303	18	1126	1126	NUM
ejpam-3756	303	19	let	let	VERB
ejpam-3756	303	20	ψn	ψn	VERB
ejpam-3756	304	1	=	=	SYM
ejpam-3756	304	2	‖ζn	‖ζn	NUM
ejpam-3756	305	1	−	−	NOUN
ejpam-3756	305	2	ζ̃n‖	ζ̃n‖	NOUN
ejpam-3756	305	3	,	,	PUNCT
ejpam-3756	305	4	φn	φn	NOUN
ejpam-3756	305	5	=	=	PUNCT
ejpam-3756	305	6	(	(	PUNCT
ejpam-3756	305	7	1−	1−	NUM
ejpam-3756	305	8	σ0n)(1−	σ0n)(1−	PROPN
ejpam-3756	305	9	ξ	ξ	X
ejpam-3756	305	10	)	)	PUNCT
ejpam-3756	305	11	,	,	PUNCT
ejpam-3756	305	12	ϕn	ϕn	ADP
ejpam-3756	305	13	=	=	NOUN
ejpam-3756	305	14	11ε	11ε	NUM
ejpam-3756	305	15	1−ξ	1−ξ	NUM
ejpam-3756	305	16	,	,	PUNCT
ejpam-3756	305	17	then	then	ADV
ejpam-3756	305	18	from	from	ADP
ejpam-3756	305	19	the	the	DET
ejpam-3756	305	20	lemma	lemma	PROPN
ejpam-3756	305	21	2	2	NUM
ejpam-3756	305	22	,	,	PUNCT
ejpam-3756	305	23	we	we	PRON
ejpam-3756	305	24	have	have	VERB
ejpam-3756	305	25	0	0	NUM
ejpam-3756	305	26	≤	≤	NOUN
ejpam-3756	305	27	lim	lim	PROPN
ejpam-3756	305	28	sup	sup	VERB
ejpam-3756	305	29	n→∞	n→∞	NUM
ejpam-3756	306	1	‖ζn	‖ζn	NUM
ejpam-3756	307	1	−	−	NUM
ejpam-3756	308	1	ζ̃n‖	ζ̃n‖	PROPN
ejpam-3756	308	2	≤	≤	PROPN
ejpam-3756	308	3	lim	lim	PROPN
ejpam-3756	308	4	sup	sup	VERB
ejpam-3756	308	5	n→∞	n→∞	NUM
ejpam-3756	308	6	11ε	11ε	X
ejpam-3756	308	7	1−	1−	NUM
ejpam-3756	309	1	ξ	ξ	X
ejpam-3756	309	2	considering	consider	VERB
ejpam-3756	309	3	the	the	DET
ejpam-3756	309	4	result	result	NOUN
ejpam-3756	309	5	of	of	ADP
ejpam-3756	309	6	theorem	theorem	NOUN
ejpam-3756	309	7	1	1	NUM
ejpam-3756	309	8	we	we	PRON
ejpam-3756	309	9	have	have	VERB
ejpam-3756	309	10	lim	lim	NOUN
ejpam-3756	309	11	supn→∞	supn→∞	PROPN
ejpam-3756	309	12	ζn	ζn	ADP
ejpam-3756	309	13	=	=	PUNCT
ejpam-3756	309	14	p	p	NOUN
ejpam-3756	309	15	and	and	CCONJ
ejpam-3756	309	16	by	by	ADP
ejpam-3756	309	17	the	the	DET
ejpam-3756	309	18	assumption	assumption	NOUN
ejpam-3756	309	19	we	we	PRON
ejpam-3756	309	20	have	have	VERB
ejpam-3756	309	21	that	that	DET
ejpam-3756	309	22	lim	lim	PROPN
ejpam-3756	309	23	supn→∞	supn→∞	PROPN
ejpam-3756	309	24	ζ̃n	ζ̃n	NOUN
ejpam-3756	309	25	=	=	PUNCT
ejpam-3756	309	26	p̃.	p̃.	NOUN
ejpam-3756	309	27	using	use	VERB
ejpam-3756	309	28	the	the	DET
ejpam-3756	309	29	results	result	NOUN
ejpam-3756	309	30	together	together	ADV
ejpam-3756	309	31	with	with	ADP
ejpam-3756	309	32	‖ζn	‖ζn	NUM
ejpam-3756	309	33	−	−	NUM
ejpam-3756	309	34	ζ̃n‖	ζ̃n‖	PROPN
ejpam-3756	309	35	≤	≤	NUM
ejpam-3756	309	36	(	(	PUNCT
ejpam-3756	309	37	1−	1−	NUM
ejpam-3756	309	38	(	(	PUNCT
ejpam-3756	309	39	1−	1−	NUM
ejpam-3756	309	40	ξ)σ0n)‖ζn	ξ)σ0n)‖ζn	PROPN
ejpam-3756	309	41	−	−	PROPN
ejpam-3756	309	42	ζ̃n‖+	ζ̃n‖+	PROPN
ejpam-3756	309	43	σ0n(1−	σ0n(1−	X
ejpam-3756	309	44	ξ	ξ	PROPN
ejpam-3756	309	45	)	)	PUNCT
ejpam-3756	309	46	11ε	11ε	NUM
ejpam-3756	309	47	1−	1−	NUM
ejpam-3756	309	48	ξ	ξ	NOUN
ejpam-3756	309	49	we	we	PRON
ejpam-3756	309	50	have	have	VERB
ejpam-3756	309	51	,	,	PUNCT
ejpam-3756	309	52	‖p−	‖p−	PROPN
ejpam-3756	309	53	p̃n‖	p̃n‖	PROPN
ejpam-3756	309	54	≤	≤	X
ejpam-3756	309	55	11ε	11ε	NUM
ejpam-3756	309	56	1−ξ	1−ξ	NUM
ejpam-3756	309	57	as	as	SCONJ
ejpam-3756	309	58	required	require	VERB
ejpam-3756	309	59	.	.	PUNCT
ejpam-3756	310	1	7	7	X
ejpam-3756	310	2	.	.	X
ejpam-3756	310	3	an	an	DET
ejpam-3756	310	4	application	application	NOUN
ejpam-3756	310	5	let	let	VERB
ejpam-3756	310	6	a	a	DET
ejpam-3756	310	7	banach	banach	NOUN
ejpam-3756	310	8	space	space	NOUN
ejpam-3756	310	9	(	(	PUNCT
ejpam-3756	310	10	e([a	e([a	NOUN
ejpam-3756	310	11	,	,	PUNCT
ejpam-3756	310	12	b	b	NOUN
ejpam-3756	310	13	]	]	X
ejpam-3756	310	14	)	)	PUNCT
ejpam-3756	310	15	,	,	PUNCT
ejpam-3756	310	16	||.||∞	||.||∞	PROPN
ejpam-3756	310	17	)	)	PUNCT
ejpam-3756	310	18	which	which	PRON
ejpam-3756	310	19	is	be	AUX
ejpam-3756	310	20	space	space	NOUN
ejpam-3756	310	21	of	of	ADP
ejpam-3756	310	22	all	all	DET
ejpam-3756	310	23	continuous	continuous	ADJ
ejpam-3756	310	24	real	real	ADJ
ejpam-3756	310	25	valued	value	VERB
ejpam-3756	310	26	functions	function	NOUN
ejpam-3756	310	27	on	on	ADP
ejpam-3756	310	28	a	a	DET
ejpam-3756	310	29	closed	closed	ADJ
ejpam-3756	310	30	interval	interval	NOUN
ejpam-3756	310	31	[	[	X
ejpam-3756	310	32	a	a	X
ejpam-3756	310	33	,	,	PUNCT
ejpam-3756	310	34	b	b	X
ejpam-3756	310	35	]	]	X
ejpam-3756	310	36	a	a	PRON
ejpam-3756	310	37	with	with	ADP
ejpam-3756	310	38	endowed	endow	VERB
ejpam-3756	310	39	chebyshev	chebyshev	NOUN
ejpam-3756	310	40	norm	norm	NOUN
ejpam-3756	310	41	‖x−	‖x−	PROPN
ejpam-3756	310	42	y‖∞	y‖∞	NUM
ejpam-3756	310	43	=	=	SYM
ejpam-3756	310	44	max	max	PROPN
ejpam-3756	310	45	t∈[a	t∈[a	NOUN
ejpam-3756	310	46	,	,	PUNCT
ejpam-3756	310	47	b	b	NOUN
ejpam-3756	310	48	]	]	PUNCT
ejpam-3756	310	49	|x(t)−	|x(t)−	PROPN
ejpam-3756	310	50	y(t)|	y(t)|	NUM
ejpam-3756	310	51	.	.	PUNCT
ejpam-3756	311	1	in	in	ADP
ejpam-3756	311	2	this	this	DET
ejpam-3756	311	3	section	section	NOUN
ejpam-3756	311	4	solution	solution	NOUN
ejpam-3756	311	5	of	of	ADP
ejpam-3756	311	6	a	a	DET
ejpam-3756	311	7	particular	particular	ADJ
ejpam-3756	311	8	delay	delay	NOUN
ejpam-3756	311	9	differential	differential	NOUN
ejpam-3756	311	10	equation	equation	NOUN
ejpam-3756	311	11	has	have	VERB
ejpam-3756	311	12	a	a	DET
ejpam-3756	311	13	solution	solution	NOUN
ejpam-3756	311	14	generated	generate	VERB
ejpam-3756	311	15	by	by	ADP
ejpam-3756	311	16	nv	nv	PROPN
ejpam-3756	311	17	1	1	NUM
ejpam-3756	311	18	iteration	iteration	NOUN
ejpam-3756	311	19	scheme	scheme	NOUN
ejpam-3756	311	20	.	.	PUNCT
ejpam-3756	312	1	x′(t	x′(t	X
ejpam-3756	312	2	)	)	PUNCT
ejpam-3756	312	3	=	=	PUNCT
ejpam-3756	312	4	f(t	f(t	NOUN
ejpam-3756	312	5	,	,	PUNCT
ejpam-3756	312	6	x(t	x(t	PROPN
ejpam-3756	312	7	)	)	PUNCT
ejpam-3756	312	8	,	,	PUNCT
ejpam-3756	312	9	x(t−	x(t−	PROPN
ejpam-3756	312	10	τ	τ	PROPN
ejpam-3756	312	11	)	)	PUNCT
ejpam-3756	312	12	)	)	PUNCT
ejpam-3756	312	13	,	,	PUNCT
ejpam-3756	312	14	t	t	PROPN
ejpam-3756	312	15	∈	∈	PROPN
ejpam-3756	313	1	[	[	X
ejpam-3756	313	2	t0	t0	PROPN
ejpam-3756	313	3	,	,	PUNCT
ejpam-3756	313	4	b	b	X
ejpam-3756	313	5	]	]	X
ejpam-3756	313	6	(	(	PUNCT
ejpam-3756	313	7	7.1	7.1	NUM
ejpam-3756	313	8	)	)	PUNCT
ejpam-3756	313	9	with	with	ADP
ejpam-3756	313	10	initial	initial	ADJ
ejpam-3756	313	11	condition	condition	NOUN
ejpam-3756	313	12	x(t	x(t	PROPN
ejpam-3756	313	13	)	)	PUNCT
ejpam-3756	313	14	=	=	SYM
ejpam-3756	313	15	ψ(t	ψ(t	PROPN
ejpam-3756	313	16	)	)	PUNCT
ejpam-3756	313	17	,	,	PUNCT
ejpam-3756	313	18	t	t	PROPN
ejpam-3756	313	19	∈	∈	PROPN
ejpam-3756	314	1	[	[	X
ejpam-3756	314	2	t0	t0	X
ejpam-3756	314	3	−	−	PROPN
ejpam-3756	314	4	τ	τ	PROPN
ejpam-3756	314	5	,	,	PUNCT
ejpam-3756	314	6	t0	t0	PROPN
ejpam-3756	314	7	]	]	PUNCT
ejpam-3756	314	8	.	.	PUNCT
ejpam-3756	315	1	(	(	PUNCT
ejpam-3756	315	2	7.2	7.2	NUM
ejpam-3756	315	3	)	)	PUNCT
ejpam-3756	315	4	we	we	PRON
ejpam-3756	315	5	opine	opine	VERB
ejpam-3756	315	6	that	that	SCONJ
ejpam-3756	315	7	the	the	DET
ejpam-3756	315	8	following	follow	VERB
ejpam-3756	315	9	conditions	condition	NOUN
ejpam-3756	315	10	are	be	AUX
ejpam-3756	315	11	performed	perform	VERB
ejpam-3756	315	12	(	(	PUNCT
ejpam-3756	315	13	i	i	NOUN
ejpam-3756	315	14	)	)	PUNCT
ejpam-3756	315	15	t0	t0	PROPN
ejpam-3756	315	16	,	,	PUNCT
ejpam-3756	315	17	b	b	PROPN
ejpam-3756	315	18	∈	∈	PROPN
ejpam-3756	315	19	r	r	PROPN
ejpam-3756	315	20	,	,	PUNCT
ejpam-3756	315	21	τ	τ	X
ejpam-3756	315	22	>	>	X
ejpam-3756	315	23	0	0	NUM
ejpam-3756	315	24	;	;	PUNCT
ejpam-3756	315	25	(	(	PUNCT
ejpam-3756	315	26	ii	ii	NOUN
ejpam-3756	315	27	)	)	PUNCT
ejpam-3756	315	28	f	f	PROPN
ejpam-3756	315	29	∈	∈	PROPN
ejpam-3756	315	30	e([t0	e([t0	NOUN
ejpam-3756	315	31	,	,	PUNCT
ejpam-3756	315	32	b]×	b]×	NOUN
ejpam-3756	315	33	r2,r	r2,r	PROPN
ejpam-3756	315	34	)	)	PUNCT
ejpam-3756	315	35	;	;	PUNCT
ejpam-3756	315	36	(	(	PUNCT
ejpam-3756	315	37	iii	iii	X
ejpam-3756	315	38	)	)	PUNCT
ejpam-3756	315	39	ψ	ψ	NOUN
ejpam-3756	315	40	∈	∈	PROPN
ejpam-3756	315	41	e([t0	e([t0	PROPN
ejpam-3756	315	42	−	−	PROPN
ejpam-3756	315	43	τ	τ	PROPN
ejpam-3756	315	44	,	,	PUNCT
ejpam-3756	315	45	b],r	b],r	NOUN
ejpam-3756	315	46	)	)	PUNCT
ejpam-3756	315	47	;	;	PUNCT
ejpam-3756	315	48	(	(	PUNCT
ejpam-3756	315	49	iv	iv	X
ejpam-3756	315	50	)	)	PUNCT
ejpam-3756	315	51	if	if	SCONJ
ejpam-3756	315	52	2lf	2lf	ADJ
ejpam-3756	315	53	(	(	PUNCT
ejpam-3756	315	54	b−	b−	PROPN
ejpam-3756	315	55	t0	t0	PROPN
ejpam-3756	315	56	)	)	PUNCT
ejpam-3756	315	57	<	<	X
ejpam-3756	315	58	1	1	NUM
ejpam-3756	315	59	,	,	PUNCT
ejpam-3756	315	60	there	there	PRON
ejpam-3756	315	61	exist	exist	VERB
ejpam-3756	315	62	lf	lf	ADP
ejpam-3756	315	63	>	>	X
ejpam-3756	315	64	0	0	NUM
ejpam-3756	315	65	such	such	ADJ
ejpam-3756	315	66	that	that	SCONJ
ejpam-3756	315	67	|f(t	|f(t	NOUN
ejpam-3756	315	68	,	,	PUNCT
ejpam-3756	315	69	u1	u1	NOUN
ejpam-3756	315	70	,	,	PUNCT
ejpam-3756	315	71	u2)−	u2)−	ADJ
ejpam-3756	315	72	f(t	f(t	NOUN
ejpam-3756	315	73	,	,	PUNCT
ejpam-3756	315	74	v1	v1	NOUN
ejpam-3756	315	75	,	,	PUNCT
ejpam-3756	315	76	v2)|	v2)|	PROPN
ejpam-3756	315	77	≤	≤	NUM
ejpam-3756	315	78	lf	lf	ADP
ejpam-3756	315	79	2∑	2∑	NUM
ejpam-3756	315	80	n=0	n=0	SYM
ejpam-3756	315	81	|ui	|ui	NUM
ejpam-3756	315	82	−	−	PROPN
ejpam-3756	315	83	vi|	vi|	NOUN
ejpam-3756	315	84	,	,	PUNCT
ejpam-3756	315	85	(	(	PUNCT
ejpam-3756	315	86	7.3	7.3	NUM
ejpam-3756	315	87	)	)	PUNCT
ejpam-3756	315	88	∀ui	∀ui	PROPN
ejpam-3756	315	89	,	,	PUNCT
ejpam-3756	315	90	vi	vi	PROPN
ejpam-3756	315	91	∈	∈	PROPN
ejpam-3756	315	92	r	r	NOUN
ejpam-3756	315	93	,	,	PUNCT
ejpam-3756	315	94	i	i	NOUN
ejpam-3756	315	95	=	=	NOUN
ejpam-3756	315	96	1	1	NUM
ejpam-3756	315	97	,	,	PUNCT
ejpam-3756	315	98	2	2	NUM
ejpam-3756	315	99	,	,	PUNCT
ejpam-3756	315	100	t	t	PROPN
ejpam-3756	315	101	∈	∈	PROPN
ejpam-3756	316	1	[	[	X
ejpam-3756	316	2	t0	t0	PROPN
ejpam-3756	316	3	,	,	PUNCT
ejpam-3756	316	4	b	b	NOUN
ejpam-3756	316	5	]	]	X
ejpam-3756	316	6	,	,	PUNCT
ejpam-3756	316	7	l.n	l.n	PROPN
ejpam-3756	316	8	mishra	mishra	PROPN
ejpam-3756	316	9	et	et	PROPN
ejpam-3756	316	10	al	al	PROPN
ejpam-3756	316	11	.	.	PUNCT
ejpam-3756	316	12	/	/	SYM
ejpam-3756	316	13	eur	eur	PROPN
ejpam-3756	316	14	.	.	PUNCT
ejpam-3756	317	1	j.	j.	PROPN
ejpam-3756	317	2	pure	pure	PROPN
ejpam-3756	317	3	appl	appl	PROPN
ejpam-3756	317	4	.	.	PROPN
ejpam-3756	317	5	math	math	PROPN
ejpam-3756	317	6	,	,	PUNCT
ejpam-3756	317	7	13	13	NUM
ejpam-3756	317	8	(	(	PUNCT
ejpam-3756	317	9	5	5	NUM
ejpam-3756	317	10	)	)	PUNCT
ejpam-3756	317	11	(	(	PUNCT
ejpam-3756	317	12	2020	2020	NUM
ejpam-3756	317	13	)	)	PUNCT
ejpam-3756	317	14	,	,	PUNCT
ejpam-3756	317	15	1110	1110	NUM
ejpam-3756	317	16	-	-	SYM
ejpam-3756	317	17	1130	1130	NUM
ejpam-3756	317	18	1127	1127	NUM
ejpam-3756	317	19	by	by	ADP
ejpam-3756	317	20	a	a	DET
ejpam-3756	317	21	solution	solution	NOUN
ejpam-3756	317	22	of	of	ADP
ejpam-3756	317	23	the	the	DET
ejpam-3756	317	24	problem	problem	NOUN
ejpam-3756	317	25	(	(	PUNCT
ejpam-3756	317	26	7.1)-(7.2	7.1)-(7.2	NUM
ejpam-3756	317	27	)	)	PUNCT
ejpam-3756	317	28	we	we	PRON
ejpam-3756	317	29	understand	understand	VERB
ejpam-3756	317	30	function	function	NOUN
ejpam-3756	317	31	x	x	X
ejpam-3756	317	32	∈	∈	PROPN
ejpam-3756	317	33	e([t0−τ	e([t0−τ	PROPN
ejpam-3756	317	34	,	,	PUNCT
ejpam-3756	317	35	b],r	b],r	VERB
ejpam-3756	317	36	)	)	PUNCT
ejpam-3756	318	1	⋂	⋂	PROPN
ejpam-3756	318	2	e1([t0	e1([t0	NOUN
ejpam-3756	318	3	,	,	PUNCT
ejpam-3756	318	4	b],r	b],r	NOUN
ejpam-3756	318	5	)	)	PUNCT
ejpam-3756	318	6	.	.	PUNCT
ejpam-3756	319	1	the	the	DET
ejpam-3756	319	2	problem	problem	NOUN
ejpam-3756	319	3	(	(	PUNCT
ejpam-3756	319	4	7.1)-(7.2	7.1)-(7.2	NUM
ejpam-3756	319	5	)	)	PUNCT
ejpam-3756	319	6	can	can	AUX
ejpam-3756	319	7	be	be	AUX
ejpam-3756	319	8	reformulated	reformulate	VERB
ejpam-3756	319	9	in	in	ADP
ejpam-3756	319	10	the	the	DET
ejpam-3756	319	11	following	follow	VERB
ejpam-3756	319	12	form	form	NOUN
ejpam-3756	319	13	of	of	ADP
ejpam-3756	319	14	integral	integral	ADJ
ejpam-3756	319	15	x(t	x(t	NOUN
ejpam-3756	319	16	)	)	PUNCT
ejpam-3756	320	1	=	=	PRON
ejpam-3756	320	2	{	{	PUNCT
ejpam-3756	320	3	ψ(t	ψ(t	PROPN
ejpam-3756	320	4	)	)	PUNCT
ejpam-3756	320	5	,	,	PUNCT
ejpam-3756	320	6	t	t	PROPN
ejpam-3756	320	7	∈	∈	PROPN
ejpam-3756	321	1	[	[	X
ejpam-3756	321	2	t0	t0	X
ejpam-3756	321	3	−	−	PROPN
ejpam-3756	321	4	τ	τ	PROPN
ejpam-3756	321	5	,	,	PUNCT
ejpam-3756	321	6	t0	t0	PROPN
ejpam-3756	321	7	]	]	PUNCT
ejpam-3756	321	8	ψ(t0	ψ(t0	NOUN
ejpam-3756	321	9	)	)	PUNCT
ejpam-3756	322	1	+	+	CCONJ
ejpam-3756	322	2	∫	∫	PROPN
ejpam-3756	322	3	t	t	PROPN
ejpam-3756	322	4	t0	t0	PROPN
ejpam-3756	322	5	f(s	f(s	PROPN
ejpam-3756	322	6	,	,	PUNCT
ejpam-3756	322	7	x(s	x(s	PROPN
ejpam-3756	322	8	)	)	PUNCT
ejpam-3756	322	9	,	,	PUNCT
ejpam-3756	322	10	x(s−	x(s−	PROPN
ejpam-3756	322	11	τ))ds	τ))ds	PROPN
ejpam-3756	322	12	,	,	PUNCT
ejpam-3756	322	13	t	t	PROPN
ejpam-3756	322	14	∈	∈	PROPN
ejpam-3756	323	1	[	[	X
ejpam-3756	323	2	t0	t0	PROPN
ejpam-3756	323	3	,	,	PUNCT
ejpam-3756	323	4	b	b	NOUN
ejpam-3756	323	5	]	]	X
ejpam-3756	323	6	.	.	PUNCT
ejpam-3756	324	1	(	(	PUNCT
ejpam-3756	324	2	7.4	7.4	NUM
ejpam-3756	324	3	)	)	PUNCT
ejpam-3756	324	4	theorem	theorem	NOUN
ejpam-3756	324	5	8	8	NUM
ejpam-3756	324	6	.	.	PUNCT
ejpam-3756	324	7	suppose	suppose	VERB
ejpam-3756	324	8	that	that	SCONJ
ejpam-3756	324	9	conditions	condition	NOUN
ejpam-3756	324	10	(	(	PUNCT
ejpam-3756	324	11	1)-(4	1)-(4	NUM
ejpam-3756	324	12	)	)	PUNCT
ejpam-3756	324	13	are	be	AUX
ejpam-3756	324	14	satisfied	satisfied	ADJ
ejpam-3756	324	15	.	.	PUNCT
ejpam-3756	325	1	then	then	ADV
ejpam-3756	325	2	the	the	DET
ejpam-3756	325	3	problem	problem	NOUN
ejpam-3756	325	4	(	(	PUNCT
ejpam-3756	325	5	7.1)-(7.4	7.1)-(7.4	NUM
ejpam-3756	325	6	)	)	PUNCT
ejpam-3756	325	7	has	have	VERB
ejpam-3756	325	8	a	a	DET
ejpam-3756	325	9	unique	unique	ADJ
ejpam-3756	325	10	solution	solution	NOUN
ejpam-3756	325	11	in	in	ADP
ejpam-3756	325	12	e([t0	e([t0	PROPN
ejpam-3756	325	13	−	−	PROPN
ejpam-3756	325	14	τ	τ	PROPN
ejpam-3756	325	15	,	,	PUNCT
ejpam-3756	325	16	b],r	b],r	PROPN
ejpam-3756	325	17	)	)	PUNCT
ejpam-3756	325	18	⋂	⋂	PROPN
ejpam-3756	325	19	e1([t0	e1([t0	NOUN
ejpam-3756	325	20	,	,	PUNCT
ejpam-3756	325	21	b],r	b],r	NOUN
ejpam-3756	325	22	)	)	PUNCT
ejpam-3756	325	23	.	.	PUNCT
ejpam-3756	326	1	proof	proof	NOUN
ejpam-3756	326	2	.	.	PUNCT
ejpam-3756	327	1	let	let	VERB
ejpam-3756	327	2	{	{	PUNCT
ejpam-3756	327	3	ζn}∞n=0	ζn}∞n=0	PUNCT
ejpam-3756	327	4	be	be	AUX
ejpam-3756	327	5	an	an	DET
ejpam-3756	327	6	iterative	iterative	NOUN
ejpam-3756	327	7	sequence	sequence	NOUN
ejpam-3756	327	8	generative	generative	NOUN
ejpam-3756	327	9	by	by	ADP
ejpam-3756	327	10	nv	nv	PROPN
ejpam-3756	327	11	k	k	PROPN
ejpam-3756	327	12	iteration	iteration	NOUN
ejpam-3756	327	13	method	method	NOUN
ejpam-3756	327	14	(	(	PUNCT
ejpam-3756	327	15	1.18	1.18	NUM
ejpam-3756	327	16	)	)	PUNCT
ejpam-3756	327	17	for	for	ADP
ejpam-3756	327	18	the	the	DET
ejpam-3756	327	19	operator	operator	NOUN
ejpam-3756	327	20	tx(t	tx(t	NOUN
ejpam-3756	327	21	)	)	PUNCT
ejpam-3756	327	22	=	=	PRON
ejpam-3756	327	23	{	{	PUNCT
ejpam-3756	327	24	ψ(t	ψ(t	PROPN
ejpam-3756	327	25	)	)	PUNCT
ejpam-3756	327	26	,	,	PUNCT
ejpam-3756	327	27	t	t	PROPN
ejpam-3756	327	28	∈	∈	PROPN
ejpam-3756	328	1	[	[	X
ejpam-3756	328	2	t0	t0	X
ejpam-3756	328	3	−	−	PROPN
ejpam-3756	328	4	τ	τ	PROPN
ejpam-3756	328	5	,	,	PUNCT
ejpam-3756	328	6	t0	t0	PROPN
ejpam-3756	328	7	]	]	PUNCT
ejpam-3756	328	8	ψ(t0	ψ(t0	NOUN
ejpam-3756	328	9	)	)	PUNCT
ejpam-3756	329	1	+	+	CCONJ
ejpam-3756	329	2	∫	∫	PROPN
ejpam-3756	329	3	t	t	PROPN
ejpam-3756	329	4	t0	t0	PROPN
ejpam-3756	329	5	f(s	f(s	PROPN
ejpam-3756	329	6	,	,	PUNCT
ejpam-3756	329	7	x(s	x(s	PROPN
ejpam-3756	329	8	)	)	PUNCT
ejpam-3756	329	9	,	,	PUNCT
ejpam-3756	329	10	x(s−	x(s−	PROPN
ejpam-3756	329	11	τ))ds	τ))ds	PROPN
ejpam-3756	329	12	,	,	PUNCT
ejpam-3756	329	13	t	t	PROPN
ejpam-3756	329	14	∈	∈	PROPN
ejpam-3756	330	1	[	[	X
ejpam-3756	330	2	t0	t0	PROPN
ejpam-3756	330	3	,	,	PUNCT
ejpam-3756	330	4	b	b	NOUN
ejpam-3756	330	5	]	]	X
ejpam-3756	330	6	.	.	PUNCT
ejpam-3756	331	1	(	(	PUNCT
ejpam-3756	331	2	7.5	7.5	NUM
ejpam-3756	331	3	)	)	PUNCT
ejpam-3756	331	4	let	let	VERB
ejpam-3756	331	5	xδ	xδ	PRON
ejpam-3756	331	6	denote	denote	VERB
ejpam-3756	331	7	the	the	DET
ejpam-3756	331	8	fixed	fixed	ADJ
ejpam-3756	331	9	point	point	NOUN
ejpam-3756	331	10	of	of	ADP
ejpam-3756	331	11	t	t	PROPN
ejpam-3756	331	12	.	.	PUNCT
ejpam-3756	332	1	we	we	PRON
ejpam-3756	332	2	will	will	AUX
ejpam-3756	332	3	show	show	VERB
ejpam-3756	332	4	that	that	SCONJ
ejpam-3756	332	5	ζn	ζn	PROPN
ejpam-3756	332	6	→	→	SYM
ejpam-3756	332	7	xδ	xδ	PROPN
ejpam-3756	332	8	as	as	ADP
ejpam-3756	332	9	n→∞.	n→∞.	NUM
ejpam-3756	332	10	for	for	ADP
ejpam-3756	332	11	t	t	PROPN
ejpam-3756	332	12	∈	∈	PROPN
ejpam-3756	333	1	[	[	X
ejpam-3756	333	2	t0	t0	X
ejpam-3756	333	3	−	−	PROPN
ejpam-3756	333	4	τ	τ	PROPN
ejpam-3756	333	5	,	,	PUNCT
ejpam-3756	333	6	t0	t0	PROPN
ejpam-3756	333	7	]	]	PUNCT
ejpam-3756	333	8	,	,	PUNCT
ejpam-3756	333	9	it	it	PRON
ejpam-3756	333	10	is	be	AUX
ejpam-3756	333	11	easy	easy	ADJ
ejpam-3756	333	12	to	to	PART
ejpam-3756	333	13	see	see	VERB
ejpam-3756	333	14	that	that	SCONJ
ejpam-3756	333	15	ζn	ζn	PROPN
ejpam-3756	333	16	→	→	SYM
ejpam-3756	333	17	xδ	xδ	PROPN
ejpam-3756	333	18	as	as	ADP
ejpam-3756	333	19	n→∞.	n→∞.	NUM
ejpam-3756	333	20	for	for	ADP
ejpam-3756	333	21	t	t	PROPN
ejpam-3756	333	22	∈	∈	PROPN
ejpam-3756	333	23	[	[	X
ejpam-3756	333	24	t0	t0	PROPN
ejpam-3756	333	25	,	,	PUNCT
ejpam-3756	333	26	b	b	X
ejpam-3756	333	27	]	]	X
ejpam-3756	333	28	we	we	PRON
ejpam-3756	333	29	obtain	obtain	VERB
ejpam-3756	333	30	‖θn	‖θn	NUM
ejpam-3756	333	31	−	−	PROPN
ejpam-3756	333	32	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	333	33	=	=	SYM
ejpam-3756	333	34	‖t	‖t	PROPN
ejpam-3756	333	35	(	(	PUNCT
ejpam-3756	333	36	(	(	PUNCT
ejpam-3756	333	37	1−	1−	NUM
ejpam-3756	333	38	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	333	39	+	+	CCONJ
ejpam-3756	333	40	σ0ntζn)−	σ0ntζn)−	PROPN
ejpam-3756	333	41	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	333	42	=	=	SYM
ejpam-3756	333	43	‖t	‖t	PROPN
ejpam-3756	333	44	(	(	PUNCT
ejpam-3756	333	45	(	(	PUNCT
ejpam-3756	333	46	1−	1−	NUM
ejpam-3756	333	47	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	333	48	+	+	CCONJ
ejpam-3756	333	49	σ0ntζn)−	σ0ntζn)−	PROPN
ejpam-3756	333	50	txδ‖	txδ‖	NOUN
ejpam-3756	333	51	≤	≤	NUM
ejpam-3756	333	52	‖(1−	‖(1−	NUM
ejpam-3756	333	53	σ0n)ζn	σ0n)ζn	NOUN
ejpam-3756	333	54	+	+	CCONJ
ejpam-3756	333	55	σ0ntζn	σ0ntζn	ADJ
ejpam-3756	333	56	−	−	NOUN
ejpam-3756	333	57	xδ‖	xδ‖	PROPN
ejpam-3756	333	58	≤	≤	NOUN
ejpam-3756	333	59	(	(	PUNCT
ejpam-3756	333	60	1−	1−	NUM
ejpam-3756	333	61	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	334	1	−	−	PROPN
ejpam-3756	334	2	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	334	3	+	+	CCONJ
ejpam-3756	334	4	σ0n	σ0n	PROPN
ejpam-3756	334	5	max	max	PROPN
ejpam-3756	334	6	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	334	7	,	,	PUNCT
ejpam-3756	334	8	b	b	X
ejpam-3756	334	9	]	]	X
ejpam-3756	334	10	|tζn	|tζn	PROPN
ejpam-3756	334	11	−	−	PROPN
ejpam-3756	334	12	txδ|	txδ|	PROPN
ejpam-3756	334	13	=	=	PRON
ejpam-3756	334	14	(	(	PUNCT
ejpam-3756	334	15	1−	1−	NUM
ejpam-3756	334	16	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	335	1	−	−	PROPN
ejpam-3756	335	2	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	335	3	+	+	CCONJ
ejpam-3756	335	4	σ0n	σ0n	PROPN
ejpam-3756	335	5	max	max	PROPN
ejpam-3756	335	6	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	335	7	,	,	PUNCT
ejpam-3756	335	8	b	b	X
ejpam-3756	335	9	]	]	X
ejpam-3756	335	10	∣∣∣∣ψ(t0	∣∣∣∣ψ(t0	PROPN
ejpam-3756	335	11	)	)	PUNCT
ejpam-3756	336	1	+	+	CCONJ
ejpam-3756	336	2	∫	∫	PROPN
ejpam-3756	336	3	t	t	PROPN
ejpam-3756	336	4	t0	t0	PROPN
ejpam-3756	336	5	f(s	f(s	PROPN
ejpam-3756	336	6	,	,	PUNCT
ejpam-3756	336	7	x(s	x(s	PROPN
ejpam-3756	336	8	)	)	PUNCT
ejpam-3756	336	9	,	,	PUNCT
ejpam-3756	336	10	x(s−	x(s−	PROPN
ejpam-3756	336	11	τ))ds	τ))ds	PUNCT
ejpam-3756	336	12	−	−	PROPN
ejpam-3756	336	13	ψ(t0)−	ψ(t0)−	PROPN
ejpam-3756	336	14	∫	∫	PROPN
ejpam-3756	336	15	t	t	PROPN
ejpam-3756	336	16	t0	t0	PROPN
ejpam-3756	336	17	f(s	f(s	PROPN
ejpam-3756	336	18	,	,	PUNCT
ejpam-3756	336	19	xδ(s	xδ(s	PROPN
ejpam-3756	336	20	)	)	PUNCT
ejpam-3756	336	21	,	,	PUNCT
ejpam-3756	336	22	xδ(s−	xδ(s−	PROPN
ejpam-3756	336	23	τ))ds	τ))ds	X
ejpam-3756	336	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3756	336	25	=	=	SYM
ejpam-3756	336	26	(	(	PUNCT
ejpam-3756	336	27	1−	1−	NUM
ejpam-3756	336	28	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	336	29	−	−	PROPN
ejpam-3756	336	30	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	337	1	+	+	CCONJ
ejpam-3756	337	2	σ0n	σ0n	PROPN
ejpam-3756	337	3	max	max	PROPN
ejpam-3756	337	4	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	337	5	,	,	PUNCT
ejpam-3756	337	6	b	b	X
ejpam-3756	337	7	]	]	X
ejpam-3756	337	8	∣∣∣∣ψ(t0	∣∣∣∣ψ(t0	PROPN
ejpam-3756	337	9	)	)	PUNCT
ejpam-3756	338	1	+	+	CCONJ
ejpam-3756	338	2	∫	∫	PROPN
ejpam-3756	338	3	t	t	PROPN
ejpam-3756	338	4	t0	t0	PROPN
ejpam-3756	338	5	f(s	f(s	PROPN
ejpam-3756	338	6	,	,	PUNCT
ejpam-3756	338	7	x(s	x(s	PROPN
ejpam-3756	338	8	)	)	PUNCT
ejpam-3756	338	9	,	,	PUNCT
ejpam-3756	338	10	x(s−	x(s−	PROPN
ejpam-3756	338	11	τ))ds	τ))ds	PUNCT
ejpam-3756	338	12	−	−	PROPN
ejpam-3756	338	13	ψ(t0)−	ψ(t0)−	PROPN
ejpam-3756	338	14	∫	∫	PROPN
ejpam-3756	338	15	t	t	PROPN
ejpam-3756	338	16	t0	t0	PROPN
ejpam-3756	338	17	f(s	f(s	PROPN
ejpam-3756	338	18	,	,	PUNCT
ejpam-3756	338	19	xδ(s	xδ(s	PROPN
ejpam-3756	338	20	)	)	PUNCT
ejpam-3756	338	21	,	,	PUNCT
ejpam-3756	338	22	xδ(s−	xδ(s−	PROPN
ejpam-3756	338	23	τ))ds	τ))ds	X
ejpam-3756	338	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3756	338	25	=	=	SYM
ejpam-3756	338	26	(	(	PUNCT
ejpam-3756	338	27	1−	1−	NUM
ejpam-3756	338	28	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	338	29	−	−	PROPN
ejpam-3756	338	30	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	339	1	+	+	CCONJ
ejpam-3756	339	2	σ0n	σ0n	PROPN
ejpam-3756	339	3	max	max	PROPN
ejpam-3756	339	4	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	339	5	,	,	PUNCT
ejpam-3756	339	6	b	b	X
ejpam-3756	339	7	]	]	X
ejpam-3756	339	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	339	9	∫	∫	PROPN
ejpam-3756	339	10	t	t	PROPN
ejpam-3756	339	11	t0	t0	PROPN
ejpam-3756	339	12	f(s	f(s	PROPN
ejpam-3756	339	13	,	,	PUNCT
ejpam-3756	339	14	x(s	x(s	PROPN
ejpam-3756	339	15	)	)	PUNCT
ejpam-3756	339	16	,	,	PUNCT
ejpam-3756	339	17	x(s−	x(s−	PROPN
ejpam-3756	339	18	τ))ds	τ))ds	PUNCT
ejpam-3756	340	1	−	−	NOUN
ejpam-3756	340	2	∫	∫	PROPN
ejpam-3756	340	3	t	t	PROPN
ejpam-3756	340	4	t0	t0	PROPN
ejpam-3756	340	5	f(s	f(s	PROPN
ejpam-3756	340	6	,	,	PUNCT
ejpam-3756	340	7	xδ(s	xδ(s	PROPN
ejpam-3756	340	8	)	)	PUNCT
ejpam-3756	340	9	,	,	PUNCT
ejpam-3756	340	10	xδ(s−	xδ(s−	PROPN
ejpam-3756	340	11	τ))ds	τ))ds	X
ejpam-3756	340	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3756	340	13	=	=	SYM
ejpam-3756	340	14	(	(	PUNCT
ejpam-3756	340	15	1−	1−	NUM
ejpam-3756	340	16	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	340	17	−	−	PROPN
ejpam-3756	340	18	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	341	1	+	+	CCONJ
ejpam-3756	341	2	σ0n	σ0n	PROPN
ejpam-3756	341	3	max	max	PROPN
ejpam-3756	341	4	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	341	5	,	,	PUNCT
ejpam-3756	341	6	b	b	X
ejpam-3756	341	7	]	]	X
ejpam-3756	342	1	∫	∫	PROPN
ejpam-3756	342	2	t	t	PROPN
ejpam-3756	342	3	t0	t0	PROPN
ejpam-3756	342	4	∣∣∣∣f(s	∣∣∣∣f(s	PROPN
ejpam-3756	342	5	,	,	PUNCT
ejpam-3756	342	6	x(s	x(s	PROPN
ejpam-3756	342	7	)	)	PUNCT
ejpam-3756	342	8	,	,	PUNCT
ejpam-3756	342	9	x(s−	x(s−	PROPN
ejpam-3756	342	10	τ	τ	PROPN
ejpam-3756	342	11	)	)	PUNCT
ejpam-3756	342	12	)	)	PUNCT
ejpam-3756	343	1	−	−	PROPN
ejpam-3756	344	1	f(s	f(s	PROPN
ejpam-3756	344	2	,	,	PUNCT
ejpam-3756	344	3	xδ(s	xδ(s	PROPN
ejpam-3756	344	4	)	)	PUNCT
ejpam-3756	344	5	,	,	PUNCT
ejpam-3756	344	6	xδ(s−	xδ(s−	PROPN
ejpam-3756	344	7	τ))ds	τ))ds	PROPN
ejpam-3756	344	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	344	9	l.n	l.n	PROPN
ejpam-3756	344	10	mishra	mishra	PROPN
ejpam-3756	344	11	et	et	PROPN
ejpam-3756	344	12	al	al	PROPN
ejpam-3756	344	13	.	.	PUNCT
ejpam-3756	344	14	/	/	SYM
ejpam-3756	344	15	eur	eur	PROPN
ejpam-3756	344	16	.	.	PUNCT
ejpam-3756	345	1	j.	j.	PROPN
ejpam-3756	345	2	pure	pure	PROPN
ejpam-3756	345	3	appl	appl	PROPN
ejpam-3756	345	4	.	.	PROPN
ejpam-3756	345	5	math	math	PROPN
ejpam-3756	345	6	,	,	PUNCT
ejpam-3756	345	7	13	13	NUM
ejpam-3756	345	8	(	(	PUNCT
ejpam-3756	345	9	5	5	NUM
ejpam-3756	345	10	)	)	PUNCT
ejpam-3756	345	11	(	(	PUNCT
ejpam-3756	345	12	2020	2020	NUM
ejpam-3756	345	13	)	)	PUNCT
ejpam-3756	345	14	,	,	PUNCT
ejpam-3756	345	15	1110	1110	NUM
ejpam-3756	345	16	-	-	SYM
ejpam-3756	345	17	1130	1130	NUM
ejpam-3756	345	18	1128	1128	NUM
ejpam-3756	345	19	=	=	SYM
ejpam-3756	345	20	(	(	PUNCT
ejpam-3756	345	21	1−	1−	NUM
ejpam-3756	345	22	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	346	1	−	−	PROPN
ejpam-3756	346	2	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	346	3	+	+	CCONJ
ejpam-3756	346	4	σ0n	σ0n	PROPN
ejpam-3756	346	5	max	max	PROPN
ejpam-3756	346	6	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	346	7	,	,	PUNCT
ejpam-3756	346	8	b	b	X
ejpam-3756	346	9	]	]	X
ejpam-3756	346	10	∫	∫	PROPN
ejpam-3756	346	11	t	t	PROPN
ejpam-3756	346	12	t0	t0	PROPN
ejpam-3756	346	13	lf	lf	PROPN
ejpam-3756	346	14	(	(	PUNCT
ejpam-3756	346	15	|ζn(s)−	|ζn(s)−	X
ejpam-3756	346	16	xδ(s)|	xδ(s)|	PUNCT
ejpam-3756	347	1	+	+	CCONJ
ejpam-3756	347	2	|ζn(s−	|ζn(s−	PROPN
ejpam-3756	347	3	τ)−	τ)−	PROPN
ejpam-3756	347	4	xδ(s−	xδ(s−	PROPN
ejpam-3756	347	5	τ)|	τ)|	PROPN
ejpam-3756	347	6	)	)	PUNCT
ejpam-3756	347	7	ds	ds	PROPN
ejpam-3756	347	8	=	=	SYM
ejpam-3756	347	9	(	(	PUNCT
ejpam-3756	347	10	1−	1−	NUM
ejpam-3756	347	11	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	347	12	−	−	PROPN
ejpam-3756	347	13	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	348	1	+	+	CCONJ
ejpam-3756	348	2	σ0n	σ0n	PROPN
ejpam-3756	348	3	max	max	PROPN
ejpam-3756	348	4	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	348	5	,	,	PUNCT
ejpam-3756	348	6	b	b	X
ejpam-3756	348	7	]	]	X
ejpam-3756	349	1	∫	∫	PROPN
ejpam-3756	349	2	t	t	PROPN
ejpam-3756	349	3	t0	t0	PROPN
ejpam-3756	349	4	lf	lf	PROPN
ejpam-3756	349	5	(	(	PUNCT
ejpam-3756	349	6	|ζn(s)−	|ζn(s)−	PROPN
ejpam-3756	349	7	xδ(s)|+	xδ(s)|+	PROPN
ejpam-3756	349	8	|ζn(s−	|ζn(s−	PROPN
ejpam-3756	349	9	τ	τ	X
ejpam-3756	349	10	)	)	PUNCT
ejpam-3756	349	11	−	−	PROPN
ejpam-3756	349	12	xδ(s−	xδ(s−	PROPN
ejpam-3756	350	1	τ)|	τ)|	NOUN
ejpam-3756	350	2	)	)	PUNCT
ejpam-3756	351	1	ds	ds	PROPN
ejpam-3756	351	2	=	=	SYM
ejpam-3756	351	3	(	(	PUNCT
ejpam-3756	351	4	1−	1−	NUM
ejpam-3756	351	5	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	351	6	−	−	PROPN
ejpam-3756	351	7	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	351	8	+	+	CCONJ
ejpam-3756	351	9	σ0nlf	σ0nlf	PROPN
ejpam-3756	351	10	(	(	PUNCT
ejpam-3756	351	11	max	max	PROPN
ejpam-3756	351	12	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	351	13	,	,	PUNCT
ejpam-3756	351	14	b	b	X
ejpam-3756	351	15	]	]	PUNCT
ejpam-3756	351	16	|ζn(s)−	|ζn(s)−	PROPN
ejpam-3756	352	1	xδ(s)|+	xδ(s)|+	PROPN
ejpam-3756	352	2	max	max	PROPN
ejpam-3756	352	3	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	352	4	,	,	PUNCT
ejpam-3756	352	5	b	b	X
ejpam-3756	352	6	]	]	X
ejpam-3756	352	7	|ζn(s−	|ζn(s−	PROPN
ejpam-3756	352	8	τ	τ	PROPN
ejpam-3756	352	9	)	)	PUNCT
ejpam-3756	352	10	−	−	PROPN
ejpam-3756	352	11	xδ(s−	xδ(s−	PROPN
ejpam-3756	353	1	τ)|	τ)|	PROPN
ejpam-3756	353	2	)	)	PUNCT
ejpam-3756	353	3	∫	∫	PROPN
ejpam-3756	353	4	t	t	PROPN
ejpam-3756	353	5	t0	t0	PROPN
ejpam-3756	353	6	ds	ds	X
ejpam-3756	353	7	=	=	SYM
ejpam-3756	353	8	(	(	PUNCT
ejpam-3756	353	9	1−	1−	NUM
ejpam-3756	353	10	σ0n)‖ζn	σ0n)‖ζn	PROPN
ejpam-3756	353	11	−	−	PROPN
ejpam-3756	353	12	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	353	13	+	+	CCONJ
ejpam-3756	353	14	2σ0nlf	2σ0nlf	NUM
ejpam-3756	353	15	(	(	PUNCT
ejpam-3756	353	16	b−	b−	NOUN
ejpam-3756	353	17	t0)‖ζn	t0)‖ζn	CCONJ
ejpam-3756	353	18	−	−	NOUN
ejpam-3756	353	19	xδ‖	xδ‖	PROPN
ejpam-3756	354	1	‖θn	‖θn	NUM
ejpam-3756	354	2	−	−	PROPN
ejpam-3756	354	3	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	354	4	=	=	PUNCT
ejpam-3756	355	1	[	[	PUNCT
ejpam-3756	355	2	1−	1−	NUM
ejpam-3756	355	3	σ0n(1−	σ0n(1−	PROPN
ejpam-3756	355	4	2lf	2lf	ADJ
ejpam-3756	355	5	(	(	PUNCT
ejpam-3756	355	6	b−	b−	PROPN
ejpam-3756	355	7	t0	t0	PROPN
ejpam-3756	355	8	)	)	PUNCT
ejpam-3756	355	9	)	)	PUNCT
ejpam-3756	355	10	]	]	PUNCT
ejpam-3756	356	1	‖ζn	‖ζn	NUM
ejpam-3756	356	2	−	−	NOUN
ejpam-3756	356	3	xδ‖	xδ‖	PROPN
ejpam-3756	356	4	(	(	PUNCT
ejpam-3756	356	5	7.6	7.6	NUM
ejpam-3756	356	6	)	)	PUNCT
ejpam-3756	356	7	similarly	similarly	ADV
ejpam-3756	356	8	,	,	PUNCT
ejpam-3756	356	9	we	we	PRON
ejpam-3756	356	10	have	have	VERB
ejpam-3756	356	11	‖ηn	‖ηn	NUM
ejpam-3756	356	12	−	−	NUM
ejpam-3756	356	13	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	356	14	=	=	SYM
ejpam-3756	356	15	‖tθn	‖tθn	PROPN
ejpam-3756	357	1	−	−	PROPN
ejpam-3756	357	2	txδ‖∞	txδ‖∞	PROPN
ejpam-3756	357	3	=	=	PROPN
ejpam-3756	357	4	max	max	PROPN
ejpam-3756	357	5	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	357	6	,	,	PUNCT
ejpam-3756	357	7	b	b	X
ejpam-3756	357	8	]	]	X
ejpam-3756	357	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	357	10	∫	∫	PROPN
ejpam-3756	357	11	t	t	PROPN
ejpam-3756	357	12	t0	t0	PROPN
ejpam-3756	357	13	f(s	f(s	PROPN
ejpam-3756	357	14	,	,	PUNCT
ejpam-3756	357	15	θn(s	θn(	NOUN
ejpam-3756	357	16	)	)	PUNCT
ejpam-3756	357	17	,	,	PUNCT
ejpam-3756	357	18	θn(s−	θn(s−	PUNCT
ejpam-3756	357	19	τ))−	τ))−	PRON
ejpam-3756	357	20	f(s	f(s	PROPN
ejpam-3756	357	21	,	,	PUNCT
ejpam-3756	357	22	xδ(s	xδ(s	PROPN
ejpam-3756	357	23	)	)	PUNCT
ejpam-3756	357	24	,	,	PUNCT
ejpam-3756	357	25	xδ(s−	xδ(s−	PUNCT
ejpam-3756	357	26	τ))]ds	τ))]ds	PUNCT
ejpam-3756	357	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	357	28	≤	≤	NUM
ejpam-3756	357	29	max	max	PROPN
ejpam-3756	357	30	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	357	31	,	,	PUNCT
ejpam-3756	357	32	b	b	X
ejpam-3756	357	33	]	]	X
ejpam-3756	357	34	∫	∫	PROPN
ejpam-3756	357	35	t	t	PROPN
ejpam-3756	357	36	t0	t0	PROPN
ejpam-3756	357	37	∣∣∣∣f(s	∣∣∣∣f(s	PROPN
ejpam-3756	357	38	,	,	PUNCT
ejpam-3756	357	39	θn(s	θn(	NOUN
ejpam-3756	357	40	)	)	PUNCT
ejpam-3756	357	41	,	,	PUNCT
ejpam-3756	357	42	θn(s−	θn(s−	PUNCT
ejpam-3756	357	43	τ))−	τ))−	PRON
ejpam-3756	357	44	f(s	f(s	PROPN
ejpam-3756	357	45	,	,	PUNCT
ejpam-3756	357	46	xδ(s	xδ(s	PROPN
ejpam-3756	357	47	)	)	PUNCT
ejpam-3756	357	48	,	,	PUNCT
ejpam-3756	357	49	xδ(s−	xδ(s−	PROPN
ejpam-3756	357	50	τ	τ	PROPN
ejpam-3756	357	51	)	)	PUNCT
ejpam-3756	357	52	)	)	PUNCT
ejpam-3756	357	53	∣∣∣∣ds	∣∣∣∣ds	NOUN
ejpam-3756	357	54	=	=	PROPN
ejpam-3756	357	55	max	max	PROPN
ejpam-3756	357	56	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	357	57	,	,	PUNCT
ejpam-3756	357	58	b	b	X
ejpam-3756	357	59	]	]	X
ejpam-3756	357	60	∫	∫	PROPN
ejpam-3756	357	61	t	t	PROPN
ejpam-3756	357	62	t0	t0	PROPN
ejpam-3756	357	63	lf	lf	PROPN
ejpam-3756	357	64	(	(	PUNCT
ejpam-3756	357	65	|θn(s)−	|θn(s)−	PROPN
ejpam-3756	357	66	xδ(s)|+	xδ(s)|+	PROPN
ejpam-3756	357	67	|θn(s−	|θn(s−	PROPN
ejpam-3756	357	68	τ)−	τ)−	PROPN
ejpam-3756	357	69	xδ(s−	xδ(s−	PROPN
ejpam-3756	358	1	τ)|	τ)|	PROPN
ejpam-3756	358	2	)	)	PUNCT
ejpam-3756	359	1	ds	ds	ADP
ejpam-3756	359	2	‖ηn	‖ηn	NUM
ejpam-3756	359	3	−	−	NUM
ejpam-3756	359	4	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	359	5	≤	≤	PROPN
ejpam-3756	359	6	2lf	2lf	ADJ
ejpam-3756	359	7	(	(	PUNCT
ejpam-3756	359	8	b−	b−	PROPN
ejpam-3756	359	9	t0)‖θn	t0)‖θn	PROPN
ejpam-3756	359	10	−	−	PROPN
ejpam-3756	359	11	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	359	12	(	(	PUNCT
ejpam-3756	359	13	7.7	7.7	NUM
ejpam-3756	359	14	)	)	PUNCT
ejpam-3756	359	15	and	and	CCONJ
ejpam-3756	359	16	hence	hence	ADV
ejpam-3756	359	17	,	,	PUNCT
ejpam-3756	359	18	we	we	PRON
ejpam-3756	359	19	have	have	VERB
ejpam-3756	359	20	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	360	1	−	−	PROPN
ejpam-3756	360	2	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	360	3	=	=	SYM
ejpam-3756	360	4	‖tηn	‖tηn	PROPN
ejpam-3756	360	5	−	−	PROPN
ejpam-3756	360	6	txδ‖∞	txδ‖∞	PROPN
ejpam-3756	360	7	=	=	PUNCT
ejpam-3756	360	8	max	max	PROPN
ejpam-3756	360	9	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	360	10	,	,	PUNCT
ejpam-3756	360	11	b	b	X
ejpam-3756	360	12	]	]	X
ejpam-3756	360	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	360	14	∫	∫	PROPN
ejpam-3756	360	15	t	t	PROPN
ejpam-3756	360	16	t0	t0	PROPN
ejpam-3756	360	17	f(s	f(s	PROPN
ejpam-3756	360	18	,	,	PUNCT
ejpam-3756	360	19	ηn(s	ηn(s	X
ejpam-3756	360	20	)	)	PUNCT
ejpam-3756	360	21	,	,	PUNCT
ejpam-3756	360	22	ηn(s−	ηn(s−	VERB
ejpam-3756	360	23	τ))−	τ))−	PRON
ejpam-3756	360	24	f(s	f(s	PROPN
ejpam-3756	360	25	,	,	PUNCT
ejpam-3756	360	26	xδ(s	xδ(s	PROPN
ejpam-3756	360	27	)	)	PUNCT
ejpam-3756	360	28	,	,	PUNCT
ejpam-3756	360	29	xδ(s−	xδ(s−	PUNCT
ejpam-3756	361	1	τ))]ds	τ))]ds	PUNCT
ejpam-3756	361	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3756	361	3	≤	≤	NUM
ejpam-3756	361	4	max	max	PROPN
ejpam-3756	361	5	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	361	6	,	,	PUNCT
ejpam-3756	361	7	b	b	X
ejpam-3756	361	8	]	]	X
ejpam-3756	361	9	∫	∫	PROPN
ejpam-3756	361	10	t	t	PROPN
ejpam-3756	361	11	t0	t0	PROPN
ejpam-3756	361	12	∣∣∣∣f(s	∣∣∣∣f(s	PROPN
ejpam-3756	361	13	,	,	PUNCT
ejpam-3756	361	14	ηn(s	ηn(s	NOUN
ejpam-3756	361	15	)	)	PUNCT
ejpam-3756	361	16	,	,	PUNCT
ejpam-3756	361	17	ηn(s−	ηn(s−	VERB
ejpam-3756	361	18	τ))−	τ))−	PRON
ejpam-3756	361	19	f(s	f(s	PROPN
ejpam-3756	361	20	,	,	PUNCT
ejpam-3756	361	21	xδ(s	xδ(s	PROPN
ejpam-3756	361	22	)	)	PUNCT
ejpam-3756	361	23	,	,	PUNCT
ejpam-3756	361	24	xδ(s−	xδ(s−	PROPN
ejpam-3756	361	25	τ	τ	PROPN
ejpam-3756	361	26	)	)	PUNCT
ejpam-3756	361	27	)	)	PUNCT
ejpam-3756	361	28	∣∣∣∣ds	∣∣∣∣ds	NOUN
ejpam-3756	361	29	=	=	PROPN
ejpam-3756	361	30	max	max	PROPN
ejpam-3756	361	31	t∈[t0−τ	t∈[t0−τ	PROPN
ejpam-3756	361	32	,	,	PUNCT
ejpam-3756	361	33	b	b	X
ejpam-3756	361	34	]	]	X
ejpam-3756	361	35	∫	∫	PROPN
ejpam-3756	361	36	t	t	PROPN
ejpam-3756	361	37	t0	t0	PROPN
ejpam-3756	361	38	lf	lf	PROPN
ejpam-3756	361	39	(	(	PUNCT
ejpam-3756	361	40	|ηn(s)−	|ηn(s)−	PROPN
ejpam-3756	361	41	xδ(s)|+	xδ(s)|+	PROPN
ejpam-3756	362	1	|ηn(s−	|ηn(s−	PROPN
ejpam-3756	362	2	τ)−	τ)−	PROPN
ejpam-3756	362	3	xδ(s−	xδ(s−	PROPN
ejpam-3756	362	4	τ)|	τ)|	PROPN
ejpam-3756	362	5	)	)	PUNCT
ejpam-3756	363	1	ds	ds	PROPN
ejpam-3756	363	2	‖ζn	‖ζn	NUM
ejpam-3756	363	3	−	−	PUNCT
ejpam-3756	363	4	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	363	5	≤	≤	PROPN
ejpam-3756	363	6	2lf	2lf	ADJ
ejpam-3756	363	7	(	(	PUNCT
ejpam-3756	363	8	b−	b−	PROPN
ejpam-3756	363	9	t0)‖ηn	t0)‖ηn	PROPN
ejpam-3756	363	10	−	−	PROPN
ejpam-3756	363	11	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	363	12	(	(	PUNCT
ejpam-3756	363	13	7.7	7.7	NUM
ejpam-3756	363	14	)	)	PUNCT
ejpam-3756	363	15	using	use	VERB
ejpam-3756	363	16	the	the	DET
ejpam-3756	363	17	equations	equation	NOUN
ejpam-3756	363	18	(	(	PUNCT
ejpam-3756	363	19	7.6	7.6	NUM
ejpam-3756	363	20	)	)	PUNCT
ejpam-3756	363	21	,	,	PUNCT
ejpam-3756	363	22	(	(	PUNCT
ejpam-3756	363	23	7.7	7.7	NUM
ejpam-3756	363	24	)	)	PUNCT
ejpam-3756	363	25	and	and	CCONJ
ejpam-3756	363	26	(	(	PUNCT
ejpam-3756	363	27	7.8	7.8	NUM
ejpam-3756	363	28	)	)	PUNCT
ejpam-3756	363	29	‖ζn+1	‖ζn+1	PROPN
ejpam-3756	363	30	−	−	PROPN
ejpam-3756	363	31	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	363	32	≤	≤	NUM
ejpam-3756	364	1	4l2	4l2	NUM
ejpam-3756	365	1	f	f	X
ejpam-3756	365	2	(	(	PUNCT
ejpam-3756	365	3	b−	b−	PROPN
ejpam-3756	365	4	t0)2‖ηn	t0)2‖ηn	PROPN
ejpam-3756	365	5	−	−	PROPN
ejpam-3756	365	6	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	365	7	references	reference	VERB
ejpam-3756	365	8	1129	1129	NUM
ejpam-3756	365	9	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	365	10	−	−	PROPN
ejpam-3756	365	11	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	365	12	≤	≤	NUM
ejpam-3756	366	1	4l2	4l2	NUM
ejpam-3756	367	1	f	f	X
ejpam-3756	367	2	(	(	PUNCT
ejpam-3756	367	3	b−	b−	NOUN
ejpam-3756	367	4	t0)2	t0)2	X
ejpam-3756	367	5	[	[	PUNCT
ejpam-3756	367	6	1−	1−	NUM
ejpam-3756	367	7	σ0n(1−	σ0n(1−	PROPN
ejpam-3756	367	8	2lf	2lf	ADJ
ejpam-3756	367	9	(	(	PUNCT
ejpam-3756	367	10	b−	b−	PROPN
ejpam-3756	367	11	t0	t0	PROPN
ejpam-3756	367	12	)	)	PUNCT
ejpam-3756	367	13	)	)	PUNCT
ejpam-3756	367	14	]	]	PUNCT
ejpam-3756	368	1	‖ζn	‖ζn	NUM
ejpam-3756	368	2	−	−	NOUN
ejpam-3756	368	3	xδ‖	xδ‖	PROPN
ejpam-3756	368	4	proceeding	proceed	VERB
ejpam-3756	368	5	in	in	ADP
ejpam-3756	368	6	the	the	DET
ejpam-3756	368	7	same	same	ADJ
ejpam-3756	368	8	manner	manner	NOUN
ejpam-3756	368	9	,	,	PUNCT
ejpam-3756	368	10	we	we	PRON
ejpam-3756	368	11	have	have	VERB
ejpam-3756	368	12	‖ζn	‖ζn	NUM
ejpam-3756	368	13	−	−	PROPN
ejpam-3756	368	14	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	368	15	≤	≤	PROPN
ejpam-3756	368	16	[	[	PUNCT
ejpam-3756	368	17	1−	1−	NUM
ejpam-3756	368	18	σ0n−1(1−	σ0n−1(1−	PROPN
ejpam-3756	368	19	2lf	2lf	ADJ
ejpam-3756	368	20	(	(	PUNCT
ejpam-3756	368	21	b−	b−	PROPN
ejpam-3756	368	22	t0	t0	PROPN
ejpam-3756	368	23	)	)	PUNCT
ejpam-3756	368	24	)	)	PUNCT
ejpam-3756	368	25	]	]	PUNCT
ejpam-3756	369	1	‖ζn−1	‖ζn−1	PROPN
ejpam-3756	369	2	−	−	PROPN
ejpam-3756	369	3	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	369	4	and	and	CCONJ
ejpam-3756	369	5	‖ζn−1	‖ζn−1	PROPN
ejpam-3756	369	6	−	−	PROPN
ejpam-3756	369	7	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	369	8	≤	≤	PROPN
ejpam-3756	369	9	[	[	PUNCT
ejpam-3756	369	10	1−	1−	NUM
ejpam-3756	369	11	σ0n−2(1−	σ0n−2(1−	PROPN
ejpam-3756	369	12	2lf	2lf	ADJ
ejpam-3756	369	13	(	(	PUNCT
ejpam-3756	369	14	b−	b−	PROPN
ejpam-3756	369	15	t0	t0	PROPN
ejpam-3756	369	16	)	)	PUNCT
ejpam-3756	369	17	)	)	PUNCT
ejpam-3756	369	18	]	]	PUNCT
ejpam-3756	370	1	‖ζn−2	‖ζn−2	ADV
ejpam-3756	370	2	−	−	PROPN
ejpam-3756	370	3	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	370	4	and	and	CCONJ
ejpam-3756	370	5	hence	hence	ADV
ejpam-3756	370	6	we	we	PRON
ejpam-3756	370	7	have	have	VERB
ejpam-3756	370	8	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	370	9	−	−	PROPN
ejpam-3756	370	10	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	370	11	≤	≤	PROPN
ejpam-3756	370	12	n∏	n∏	PROPN
ejpam-3756	370	13	k=0	k=0	PROPN
ejpam-3756	370	14	[	[	PUNCT
ejpam-3756	370	15	1−	1−	NUM
ejpam-3756	370	16	σ0k(1−	σ0k(1−	PROPN
ejpam-3756	370	17	2lf	2lf	ADJ
ejpam-3756	370	18	(	(	PUNCT
ejpam-3756	370	19	b−	b−	PROPN
ejpam-3756	370	20	t0	t0	PROPN
ejpam-3756	370	21	)	)	PUNCT
ejpam-3756	370	22	)	)	PUNCT
ejpam-3756	370	23	]	]	PUNCT
ejpam-3756	371	1	‖ζ0	‖ζ0	ADV
ejpam-3756	371	2	−	−	X
ejpam-3756	372	1	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	372	2	(	(	PUNCT
ejpam-3756	372	3	7.9	7.9	NUM
ejpam-3756	372	4	)	)	PUNCT
ejpam-3756	372	5	where	where	SCONJ
ejpam-3756	372	6	[	[	X
ejpam-3756	372	7	1−σ0k(1−2lf	1−σ0k(1−2lf	NUM
ejpam-3756	372	8	(	(	PUNCT
ejpam-3756	372	9	b−	b−	PROPN
ejpam-3756	372	10	t0	t0	PROPN
ejpam-3756	372	11	)	)	PUNCT
ejpam-3756	372	12	)	)	PUNCT
ejpam-3756	373	1	∈	∈	PROPN
ejpam-3756	373	2	(	(	PUNCT
ejpam-3756	373	3	0	0	NUM
ejpam-3756	373	4	,	,	PUNCT
ejpam-3756	373	5	1	1	NUM
ejpam-3756	373	6	)	)	PUNCT
ejpam-3756	373	7	because	because	SCONJ
ejpam-3756	373	8	σ0k	σ0k	PROPN
ejpam-3756	373	9	∈	∈	PROPN
ejpam-3756	373	10	(	(	PUNCT
ejpam-3756	373	11	0	0	NUM
ejpam-3756	373	12	,	,	PUNCT
ejpam-3756	373	13	1	1	NUM
ejpam-3756	373	14	)	)	PUNCT
ejpam-3756	373	15	,	,	PUNCT
ejpam-3756	373	16	for	for	ADP
ejpam-3756	373	17	all	all	DET
ejpam-3756	373	18	natural	natural	ADJ
ejpam-3756	373	19	numbers	number	NOUN
ejpam-3756	373	20	n.	n.	NOUN
ejpam-3756	373	21	also	also	ADV
ejpam-3756	373	22	,	,	PUNCT
ejpam-3756	373	23	since	since	SCONJ
ejpam-3756	373	24	(	(	PUNCT
ejpam-3756	373	25	1−	1−	NUM
ejpam-3756	373	26	x	x	NOUN
ejpam-3756	373	27	)	)	PUNCT
ejpam-3756	373	28	≤	≤	NUM
ejpam-3756	373	29	e−x	e−x	NOUN
ejpam-3756	373	30	for	for	ADP
ejpam-3756	373	31	all	all	DET
ejpam-3756	373	32	x	x	SYM
ejpam-3756	373	33	∈	∈	PROPN
ejpam-3756	374	1	[	[	X
ejpam-3756	374	2	0	0	NUM
ejpam-3756	374	3	,	,	PUNCT
ejpam-3756	374	4	1	1	NUM
ejpam-3756	374	5	]	]	PUNCT
ejpam-3756	374	6	,	,	PUNCT
ejpam-3756	374	7	from	from	ADP
ejpam-3756	374	8	(	(	PUNCT
ejpam-3756	374	9	7.9	7.9	NUM
ejpam-3756	374	10	)	)	PUNCT
ejpam-3756	374	11	we	we	PRON
ejpam-3756	374	12	can	can	AUX
ejpam-3756	374	13	easily	easily	ADV
ejpam-3756	374	14	conclude	conclude	VERB
ejpam-3756	374	15	that	that	SCONJ
ejpam-3756	374	16	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	374	17	−	−	PROPN
ejpam-3756	374	18	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	374	19	≤	≤	PROPN
ejpam-3756	375	1	‖ζ0	‖ζ0	ADJ
ejpam-3756	375	2	−	−	PROPN
ejpam-3756	375	3	xδ‖	xδ‖	PROPN
ejpam-3756	376	1	e(1−(2lf	e(1−(2lf	X
ejpam-3756	377	1	(	(	PUNCT
ejpam-3756	377	2	b−t0	b−t0	NOUN
ejpam-3756	377	3	)	)	PUNCT
ejpam-3756	377	4	)	)	PUNCT
ejpam-3756	377	5	)	)	PUNCT
ejpam-3756	378	1	∑∞	∑∞	NOUN
ejpam-3756	378	2	k=0	k=0	PROPN
ejpam-3756	378	3	σ	σ	PROPN
ejpam-3756	378	4	0	0	NUM
ejpam-3756	379	1	k	k	X
ejpam-3756	379	2	(	(	PUNCT
ejpam-3756	379	3	7.10	7.10	NUM
ejpam-3756	379	4	)	)	PUNCT
ejpam-3756	379	5	which	which	PRON
ejpam-3756	379	6	led	lead	VERB
ejpam-3756	379	7	us	we	PRON
ejpam-3756	379	8	to	to	ADP
ejpam-3756	379	9	limn→∞	limn→∞	PROPN
ejpam-3756	379	10	‖ζn+1	‖ζn+1	PUNCT
ejpam-3756	380	1	−	−	PROPN
ejpam-3756	380	2	xδ‖∞	xδ‖∞	PROPN
ejpam-3756	380	3	=	=	PUNCT
ejpam-3756	380	4	0	0	NUM
ejpam-3756	380	5	when	when	SCONJ
ejpam-3756	380	6	taking	take	VERB
ejpam-3756	380	7	limits	limit	NOUN
ejpam-3756	380	8	of	of	ADP
ejpam-3756	380	9	both	both	DET
ejpam-3756	380	10	sides	side	NOUN
ejpam-3756	380	11	of	of	ADP
ejpam-3756	380	12	equation	equation	NOUN
ejpam-3756	380	13	(	(	PUNCT
ejpam-3756	380	14	7.10	7.10	NUM
ejpam-3756	380	15	)	)	PUNCT
ejpam-3756	380	16	.	.	PUNCT
ejpam-3756	381	1	8	8	X
ejpam-3756	381	2	.	.	X
ejpam-3756	381	3	conclusion	conclusion	NOUN
ejpam-3756	381	4	a	a	DET
ejpam-3756	381	5	whole	whole	ADJ
ejpam-3756	381	6	new	new	ADJ
ejpam-3756	381	7	iteration	iteration	NOUN
ejpam-3756	381	8	scheme	scheme	NOUN
ejpam-3756	381	9	namely	namely	ADV
ejpam-3756	381	10	nv	nv	PROPN
ejpam-3756	381	11	1	1	NUM
ejpam-3756	381	12	having	have	VERB
ejpam-3756	381	13	rate	rate	NOUN
ejpam-3756	381	14	of	of	ADP
ejpam-3756	381	15	convergence	convergence	NOUN
ejpam-3756	381	16	,	,	PUNCT
ejpam-3756	381	17	faster	fast	ADV
ejpam-3756	381	18	than	than	SCONJ
ejpam-3756	381	19	almost	almost	ADV
ejpam-3756	381	20	all	all	PRON
ejpam-3756	381	21	pre	pre	ADJ
ejpam-3756	381	22	-	-	ADJ
ejpam-3756	381	23	existing	exist	VERB
ejpam-3756	381	24	iteration	iteration	NOUN
ejpam-3756	381	25	schemes	scheme	NOUN
ejpam-3756	381	26	to	to	PART
ejpam-3756	381	27	find	find	VERB
ejpam-3756	381	28	the	the	DET
ejpam-3756	381	29	solution	solution	NOUN
ejpam-3756	381	30	with	with	ADP
ejpam-3756	381	31	minimum	minimum	ADJ
ejpam-3756	381	32	possible	possible	ADJ
ejpam-3756	381	33	steps	step	NOUN
ejpam-3756	381	34	is	be	AUX
ejpam-3756	381	35	established	establish	VERB
ejpam-3756	381	36	.	.	PUNCT
ejpam-3756	382	1	references	reference	NOUN
ejpam-3756	382	2	[	[	X
ejpam-3756	382	3	1	1	NUM
ejpam-3756	382	4	]	]	PUNCT
ejpam-3756	382	5	m.	m.	NOUN
ejpam-3756	382	6	abbas	abbas	PROPN
ejpam-3756	382	7	and	and	CCONJ
ejpam-3756	382	8	t.	t.	PROPN
ejpam-3756	382	9	nazir	nazir	PROPN
ejpam-3756	382	10	.	.	PUNCT
ejpam-3756	383	1	a	a	DET
ejpam-3756	383	2	new	new	ADJ
ejpam-3756	383	3	faster	fast	ADJ
ejpam-3756	383	4	iteration	iteration	NOUN
ejpam-3756	383	5	process	process	NOUN
ejpam-3756	383	6	applied	apply	VERB
ejpam-3756	383	7	to	to	ADP
ejpam-3756	383	8	constrained	constrain	VERB
ejpam-3756	383	9	minimization	minimization	NOUN
ejpam-3756	383	10	and	and	CCONJ
ejpam-3756	383	11	feasibility	feasibility	NOUN
ejpam-3756	383	12	problems	problem	NOUN
ejpam-3756	383	13	.	.	PUNCT
ejpam-3756	384	1	mat	mat	PROPN
ejpam-3756	384	2	.	.	PROPN
ejpam-3756	384	3	vesnik	vesnik	PROPN
ejpam-3756	384	4	,	,	PUNCT
ejpam-3756	384	5	66(2):223–229	66(2):223–229	PROPN
ejpam-3756	384	6	,	,	PUNCT
ejpam-3756	384	7	2014	2014	NUM
ejpam-3756	384	8	.	.	PUNCT
ejpam-3756	385	1	[	[	X
ejpam-3756	385	2	2	2	X
ejpam-3756	385	3	]	]	PUNCT
ejpam-3756	385	4	v.	v.	ADP
ejpam-3756	385	5	berinde	berinde	NOUN
ejpam-3756	385	6	.	.	PUNCT
ejpam-3756	386	1	iterative	iterative	NOUN
ejpam-3756	386	2	approximation	approximation	NOUN
ejpam-3756	386	3	of	of	ADP
ejpam-3756	386	4	fixed	fix	VERB
ejpam-3756	386	5	points	point	NOUN
ejpam-3756	386	6	.	.	PUNCT
ejpam-3756	387	1	springer	springer	NOUN
ejpam-3756	387	2	,	,	PUNCT
ejpam-3756	387	3	berlin	berlin	PROPN
ejpam-3756	387	4	,	,	PUNCT
ejpam-3756	387	5	2007	2007	NUM
ejpam-3756	387	6	.	.	PUNCT
ejpam-3756	388	1	[	[	X
ejpam-3756	388	2	3	3	X
ejpam-3756	388	3	]	]	X
ejpam-3756	388	4	f.e	f.e	PROPN
ejpam-3756	388	5	.	.	PROPN
ejpam-3756	388	6	browder	browder	PROPN
ejpam-3756	388	7	.	.	PUNCT
ejpam-3756	389	1	nonexpansive	nonexpansive	PROPN
ejpam-3756	389	2	nonlinear	nonlinear	PROPN
ejpam-3756	389	3	operators	operator	NOUN
ejpam-3756	389	4	in	in	ADP
ejpam-3756	389	5	a	a	DET
ejpam-3756	389	6	banach	banach	NOUN
ejpam-3756	389	7	space	space	NOUN
ejpam-3756	389	8	.	.	PUNCT
ejpam-3756	390	1	proc	proc	NOUN
ejpam-3756	390	2	.	.	PUNCT
ejpam-3756	391	1	nat	nat	PROPN
ejpam-3756	391	2	.	.	PUNCT
ejpam-3756	392	1	acad	acad	PROPN
ejpam-3756	392	2	.	.	PUNCT
ejpam-3756	393	1	sci	sci	PROPN
ejpam-3756	393	2	.	.	PROPN
ejpam-3756	393	3	usa	usa	PROPN
ejpam-3756	393	4	.	.	PROPN
ejpam-3756	393	5	,	,	PUNCT
ejpam-3756	393	6	54:1041–1044	54:1041–1044	PROPN
ejpam-3756	393	7	,	,	PUNCT
ejpam-3756	393	8	1965	1965	NUM
ejpam-3756	393	9	.	.	PUNCT
ejpam-3756	394	1	[	[	X
ejpam-3756	394	2	4	4	X
ejpam-3756	394	3	]	]	X
ejpam-3756	394	4	d.	d.	PROPN
ejpam-3756	394	5	thakur	thakur	PROPN
ejpam-3756	394	6	b.s	b.s	PROPN
ejpam-3756	394	7	.	.	PROPN
ejpam-3756	394	8	thakur	thakur	PROPN
ejpam-3756	394	9	and	and	CCONJ
ejpam-3756	394	10	m.	m.	NOUN
ejpam-3756	394	11	postolache	postolache	PROPN
ejpam-3756	394	12	.	.	PUNCT
ejpam-3756	395	1	a	a	DET
ejpam-3756	395	2	new	new	ADJ
ejpam-3756	395	3	iterative	iterative	NOUN
ejpam-3756	395	4	scheme	scheme	NOUN
ejpam-3756	395	5	for	for	ADP
ejpam-3756	395	6	numerical	numerical	ADJ
ejpam-3756	395	7	reckoning	reckon	VERB
ejpam-3756	395	8	fixed	fix	VERB
ejpam-3756	395	9	points	point	NOUN
ejpam-3756	395	10	of	of	ADP
ejpam-3756	395	11	suzuki	suzuki	PROPN
ejpam-3756	395	12	’s	’s	PART
ejpam-3756	395	13	generalized	generalize	VERB
ejpam-3756	395	14	nonexpansive	nonexpansive	ADJ
ejpam-3756	395	15	mappings	mapping	NOUN
ejpam-3756	395	16	.	.	PUNCT
ejpam-3756	396	1	app	app	PROPN
ejpam-3756	396	2	.	.	PROPN
ejpam-3756	396	3	math	math	PROPN
ejpam-3756	396	4	.	.	PUNCT
ejpam-3756	397	1	comp	comp	PROPN
ejpam-3756	397	2	.	.	PUNCT
ejpam-3756	397	3	,	,	PUNCT
ejpam-3756	397	4	275:147–155	275:147–155	NUM
ejpam-3756	397	5	,	,	PUNCT
ejpam-3756	397	6	2016	2016	NUM
ejpam-3756	397	7	.	.	PUNCT
ejpam-3756	398	1	references	reference	NOUN
ejpam-3756	398	2	1130	1130	NUM
ejpam-3756	398	3	[	[	X
ejpam-3756	398	4	5	5	NUM
ejpam-3756	398	5	]	]	PUNCT
ejpam-3756	398	6	izhar	izhar	PROPN
ejpam-3756	398	7	c.	c.	PROPN
ejpam-3756	398	8	garodia	garodia	PROPN
ejpam-3756	398	9	,	,	PUNCT
ejpam-3756	398	10	uddin	uddin	PROPN
ejpam-3756	398	11	.	.	PUNCT
ejpam-3756	399	1	solution	solution	NOUN
ejpam-3756	399	2	of	of	ADP
ejpam-3756	399	3	a	a	DET
ejpam-3756	399	4	nonlinear	nonlinear	ADJ
ejpam-3756	399	5	integral	integral	ADJ
ejpam-3756	399	6	equation	equation	NOUN
ejpam-3756	399	7	via	via	ADP
ejpam-3756	399	8	new	new	ADJ
ejpam-3756	399	9	fixed	fix	VERB
ejpam-3756	399	10	point	point	NOUN
ejpam-3756	399	11	iteration	iteration	NOUN
ejpam-3756	399	12	process	process	NOUN
ejpam-3756	399	13	.	.	PUNCT
ejpam-3756	400	1	arxiv:1809.03771v1	arxiv:1809.03771v1	NUM
ejpam-3756	401	1	[	[	X
ejpam-3756	401	2	math.f.a	math.f.a	X
ejpam-3756	401	3	]	]	PUNCT
ejpam-3756	401	4	,	,	PUNCT
ejpam-3756	401	5	11	11	NUM
ejpam-3756	401	6	sep	sep	PROPN
ejpam-3756	401	7	2018	2018	NUM
ejpam-3756	401	8	.	.	PUNCT
ejpam-3756	402	1	[	[	X
ejpam-3756	402	2	6	6	NUM
ejpam-3756	402	3	]	]	PUNCT
ejpam-3756	402	4	d.	d.	NOUN
ejpam-3756	402	5	gohde	gohde	PROPN
ejpam-3756	402	6	.	.	PUNCT
ejpam-3756	403	1	zum	zum	PROPN
ejpam-3756	403	2	prinzip	prinzip	NOUN
ejpam-3756	403	3	der	der	NOUN
ejpam-3756	403	4	kontraktiven	kontraktiven	NOUN
ejpam-3756	403	5	abbildung	abbildung	PROPN
ejpam-3756	403	6	.	.	PUNCT
ejpam-3756	404	1	math	math	NOUN
ejpam-3756	404	2	.	.	PUNCT
ejpam-3756	405	1	nachr	nachr	PROPN
ejpam-3756	405	2	.	.	PUNCT
ejpam-3756	405	3	,	,	PUNCT
ejpam-3756	406	1	30:251–258	30:251–258	PROPN
ejpam-3756	406	2	,	,	PUNCT
ejpam-3756	406	3	1965	1965	NUM
ejpam-3756	406	4	.	.	PUNCT
ejpam-3756	407	1	[	[	X
ejpam-3756	407	2	7	7	X
ejpam-3756	407	3	]	]	X
ejpam-3756	407	4	s.	s.	PROPN
ejpam-3756	407	5	ishikawa	ishikawa	PROPN
ejpam-3756	407	6	.	.	PUNCT
ejpam-3756	407	7	fixed	fix	VERB
ejpam-3756	407	8	points	point	NOUN
ejpam-3756	407	9	by	by	ADP
ejpam-3756	407	10	a	a	DET
ejpam-3756	407	11	new	new	ADJ
ejpam-3756	407	12	iteration	iteration	NOUN
ejpam-3756	407	13	method	method	NOUN
ejpam-3756	407	14	.	.	PUNCT
ejpam-3756	408	1	proc	proc	NOUN
ejpam-3756	408	2	.	.	PUNCT
ejpam-3756	409	1	am	be	AUX
ejpam-3756	409	2	.	.	PUNCT
ejpam-3756	410	1	math	math	NOUN
ejpam-3756	410	2	.	.	PUNCT
ejpam-3756	411	1	soc	soc	PROPN
ejpam-3756	411	2	.	.	PUNCT
ejpam-3756	411	3	,	,	PUNCT
ejpam-3756	411	4	44:147	44:147	NOUN
ejpam-3756	411	5	–	–	PUNCT
ejpam-3756	411	6	150	150	NUM
ejpam-3756	411	7	,	,	PUNCT
ejpam-3756	411	8	1974	1974	NUM
ejpam-3756	411	9	.	.	PUNCT
ejpam-3756	412	1	[	[	X
ejpam-3756	412	2	8	8	NUM
ejpam-3756	412	3	]	]	X
ejpam-3756	412	4	w.a	w.a	PROPN
ejpam-3756	412	5	.	.	PROPN
ejpam-3756	412	6	kirk	kirk	PROPN
ejpam-3756	412	7	.	.	PUNCT
ejpam-3756	413	1	a	a	DET
ejpam-3756	413	2	fixed	fix	VERB
ejpam-3756	413	3	point	point	NOUN
ejpam-3756	413	4	theorem	theorem	NOUN
ejpam-3756	413	5	for	for	ADP
ejpam-3756	413	6	mappings	mapping	NOUN
ejpam-3756	413	7	which	which	PRON
ejpam-3756	413	8	do	do	AUX
ejpam-3756	413	9	not	not	PART
ejpam-3756	413	10	increase	increase	VERB
ejpam-3756	413	11	distance	distance	NOUN
ejpam-3756	413	12	.	.	PUNCT
ejpam-3756	414	1	am	be	AUX
ejpam-3756	414	2	.	.	PUNCT
ejpam-3756	415	1	math	math	NOUN
ejpam-3756	415	2	.	.	PUNCT
ejpam-3756	416	1	monthly	monthly	ADJ
ejpam-3756	416	2	,	,	PUNCT
ejpam-3756	416	3	72:1004–1006	72:1004–1006	NOUN
ejpam-3756	416	4	,	,	PUNCT
ejpam-3756	416	5	1965	1965	NUM
ejpam-3756	416	6	.	.	PUNCT
ejpam-3756	417	1	[	[	X
ejpam-3756	417	2	9	9	NUM
ejpam-3756	417	3	]	]	X
ejpam-3756	417	4	w.r	w.r	PROPN
ejpam-3756	417	5	.	.	PROPN
ejpam-3756	417	6	mann	mann	PROPN
ejpam-3756	417	7	.	.	PUNCT
ejpam-3756	418	1	mean	mean	VERB
ejpam-3756	418	2	value	value	NOUN
ejpam-3756	418	3	methods	method	NOUN
ejpam-3756	418	4	in	in	ADP
ejpam-3756	418	5	iterations	iteration	NOUN
ejpam-3756	418	6	.	.	PUNCT
ejpam-3756	419	1	proc	proc	NOUN
ejpam-3756	419	2	.	.	PUNCT
ejpam-3756	420	1	am	be	AUX
ejpam-3756	420	2	.	.	PUNCT
ejpam-3756	421	1	math	math	NOUN
ejpam-3756	421	2	.	.	PUNCT
ejpam-3756	422	1	soc	soc	PROPN
ejpam-3756	422	2	.	.	PUNCT
ejpam-3756	422	3	,	,	PUNCT
ejpam-3756	422	4	4:506–510	4:506–510	NUM
ejpam-3756	422	5	,	,	PUNCT
ejpam-3756	422	6	1953	1953	NUM
ejpam-3756	422	7	.	.	PUNCT
ejpam-3756	423	1	[	[	X
ejpam-3756	423	2	10	10	NUM
ejpam-3756	423	3	]	]	X
ejpam-3756	423	4	m.a	m.a	PROPN
ejpam-3756	423	5	.	.	PROPN
ejpam-3756	423	6	noor	noor	PROPN
ejpam-3756	423	7	.	.	PUNCT
ejpam-3756	424	1	new	new	ADJ
ejpam-3756	424	2	approximation	approximation	NOUN
ejpam-3756	424	3	schemes	scheme	NOUN
ejpam-3756	424	4	for	for	ADP
ejpam-3756	424	5	general	general	ADJ
ejpam-3756	424	6	variational	variational	ADJ
ejpam-3756	424	7	inequalities	inequality	NOUN
ejpam-3756	424	8	.	.	PUNCT
ejpam-3756	425	1	j.	j.	PROPN
ejpam-3756	425	2	math	math	PROPN
ejpam-3756	425	3	.	.	PUNCT
ejpam-3756	426	1	anal	anal	PROPN
ejpam-3756	426	2	.	.	PUNCT
ejpam-3756	427	1	appl	appl	PROPN
ejpam-3756	427	2	.	.	PROPN
ejpam-3756	427	3	,	,	PUNCT
ejpam-3756	427	4	251(1):217–229	251(1):217–229	NUM
ejpam-3756	427	5	,	,	PUNCT
ejpam-3756	427	6	2000	2000	NUM
ejpam-3756	427	7	.	.	PUNCT
ejpam-3756	428	1	[	[	X
ejpam-3756	428	2	11	11	NUM
ejpam-3756	428	3	]	]	PUNCT
ejpam-3756	428	4	z.	z.	PROPN
ejpam-3756	428	5	opial	opial	PROPN
ejpam-3756	428	6	.	.	PUNCT
ejpam-3756	429	1	weak	weak	ADJ
ejpam-3756	429	2	and	and	CCONJ
ejpam-3756	429	3	strong	strong	ADJ
ejpam-3756	429	4	convergence	convergence	NOUN
ejpam-3756	429	5	of	of	ADP
ejpam-3756	429	6	the	the	DET
ejpam-3756	429	7	sequence	sequence	NOUN
ejpam-3756	429	8	of	of	ADP
ejpam-3756	429	9	successive	successive	ADJ
ejpam-3756	429	10	approximations	approximation	NOUN
ejpam-3756	429	11	for	for	ADP
ejpam-3756	429	12	nonexpansive	nonexpansive	ADJ
ejpam-3756	429	13	mappings	mapping	NOUN
ejpam-3756	429	14	.	.	PUNCT
ejpam-3756	430	1	bull	bull	NOUN
ejpam-3756	430	2	.	.	PUNCT
ejpam-3756	431	1	am	be	AUX
ejpam-3756	431	2	.	.	PUNCT
ejpam-3756	432	1	math	math	NOUN
ejpam-3756	432	2	.	.	PUNCT
ejpam-3756	433	1	soc	soc	PROPN
ejpam-3756	433	2	.	.	PUNCT
ejpam-3756	433	3	,	,	PUNCT
ejpam-3756	434	1	73:591–597	73:591–597	NOUN
ejpam-3756	434	2	,	,	PUNCT
ejpam-3756	434	3	1967	1967	NUM
ejpam-3756	434	4	.	.	PUNCT
ejpam-3756	435	1	[	[	X
ejpam-3756	435	2	12	12	NUM
ejpam-3756	435	3	]	]	X
ejpam-3756	435	4	b.e	b.e	PROPN
ejpam-3756	435	5	.	.	PROPN
ejpam-3756	435	6	rhoades	rhoade	NOUN
ejpam-3756	435	7	.	.	PUNCT
ejpam-3756	436	1	some	some	DET
ejpam-3756	436	2	fixed	fix	VERB
ejpam-3756	436	3	point	point	NOUN
ejpam-3756	436	4	iteration	iteration	NOUN
ejpam-3756	436	5	procedures	procedure	NOUN
ejpam-3756	436	6	.	.	PUNCT
ejpam-3756	437	1	int	int	NOUN
ejpam-3756	437	2	.	.	PUNCT
ejpam-3756	438	1	j.	j.	PROPN
ejpam-3756	438	2	math	math	PROPN
ejpam-3756	438	3	.	.	PUNCT
ejpam-3756	439	1	math	math	NOUN
ejpam-3756	439	2	.	.	PUNCT
ejpam-3756	440	1	sci	sci	PROPN
ejpam-3756	440	2	.	.	PROPN
ejpam-3756	440	3	,	,	PUNCT
ejpam-3756	440	4	14:1–16	14:1–16	NUM
ejpam-3756	440	5	,	,	PUNCT
ejpam-3756	440	6	1991	1991	NUM
ejpam-3756	440	7	.	.	PUNCT
ejpam-3756	441	1	[	[	X
ejpam-3756	441	2	13	13	NUM
ejpam-3756	441	3	]	]	PUNCT
ejpam-3756	441	4	d.	d.	PROPN
ejpam-3756	441	5	o’regan	o’regan	PROPN
ejpam-3756	441	6	r.p	r.p	PROPN
ejpam-3756	441	7	.	.	PROPN
ejpam-3756	441	8	agarwal	agarwal	PROPN
ejpam-3756	441	9	and	and	CCONJ
ejpam-3756	441	10	d.r	d.r	PROPN
ejpam-3756	441	11	.	.	PROPN
ejpam-3756	441	12	sahu	sahu	PROPN
ejpam-3756	441	13	.	.	PUNCT
ejpam-3756	442	1	iterative	iterative	ADJ
ejpam-3756	442	2	construction	construction	NOUN
ejpam-3756	442	3	of	of	ADP
ejpam-3756	442	4	fixed	fix	VERB
ejpam-3756	442	5	points	point	NOUN
ejpam-3756	442	6	of	of	ADP
ejpam-3756	442	7	nearly	nearly	ADV
ejpam-3756	442	8	asymptotically	asymptotically	ADV
ejpam-3756	442	9	nonexpansive	nonexpansive	ADJ
ejpam-3756	442	10	mappings	mapping	NOUN
ejpam-3756	442	11	.	.	PUNCT
ejpam-3756	443	1	j.	j.	PROPN
ejpam-3756	443	2	nonlinear	nonlinear	PROPN
ejpam-3756	443	3	convex	convex	PROPN
ejpam-3756	443	4	anal	anal	NOUN
ejpam-3756	443	5	.	.	PUNCT
ejpam-3756	443	6	,	,	PUNCT
ejpam-3756	443	7	8(1):61	8(1):61	NUM
ejpam-3756	443	8	–	–	PUNCT
ejpam-3756	443	9	79	79	NUM
ejpam-3756	443	10	,	,	PUNCT
ejpam-3756	443	11	2007	2007	NUM
ejpam-3756	443	12	.	.	PUNCT
ejpam-3756	444	1	[	[	X
ejpam-3756	444	2	14	14	NUM
ejpam-3756	444	3	]	]	X
ejpam-3756	444	4	d.	d.	PROPN
ejpam-3756	444	5	o’regan	o’regan	PROPN
ejpam-3756	444	6	r.p	r.p	PROPN
ejpam-3756	444	7	.	.	PROPN
ejpam-3756	444	8	agarwal	agarwal	PROPN
ejpam-3756	444	9	and	and	CCONJ
ejpam-3756	444	10	d.r	d.r	PROPN
ejpam-3756	444	11	.	.	PROPN
ejpam-3756	444	12	sahu	sahu	PROPN
ejpam-3756	444	13	.	.	PUNCT
ejpam-3756	445	1	fixed	fix	VERB
ejpam-3756	445	2	point	point	NOUN
ejpam-3756	445	3	theory	theory	NOUN
ejpam-3756	445	4	for	for	ADP
ejpam-3756	445	5	lipschitziantype	lipschitziantype	ADJ
ejpam-3756	445	6	mappings	mapping	NOUN
ejpam-3756	445	7	with	with	ADP
ejpam-3756	445	8	applications	application	NOUN
ejpam-3756	445	9	series	series	NOUN
ejpam-3756	445	10	.	.	PUNCT
ejpam-3756	446	1	topological	topological	ADJ
ejpam-3756	446	2	fixed	fix	VERB
ejpam-3756	446	3	point	point	NOUN
ejpam-3756	446	4	theory	theory	NOUN
ejpam-3756	446	5	and	and	CCONJ
ejpam-3756	446	6	its	its	PRON
ejpam-3756	446	7	applications	application	NOUN
ejpam-3756	446	8	,	,	PUNCT
ejpam-3756	446	9	springer	springer	NOUN
ejpam-3756	446	10	,	,	PUNCT
ejpam-3756	446	11	new	new	PROPN
ejpam-3756	446	12	york	york	PROPN
ejpam-3756	446	13	,	,	PUNCT
ejpam-3756	446	14	6:1004–1006	6:1004–1006	PROPN
ejpam-3756	446	15	,	,	PUNCT
ejpam-3756	446	16	2009	2009	NUM
ejpam-3756	446	17	.	.	PUNCT
ejpam-3756	447	1	[	[	X
ejpam-3756	447	2	15	15	NUM
ejpam-3756	447	3	]	]	X
ejpam-3756	447	4	j.	j.	PROPN
ejpam-3756	447	5	schu	schu	PROPN
ejpam-3756	447	6	.	.	PUNCT
ejpam-3756	448	1	weak	weak	ADJ
ejpam-3756	448	2	and	and	CCONJ
ejpam-3756	448	3	strong	strong	ADJ
ejpam-3756	448	4	convergence	convergence	NOUN
ejpam-3756	448	5	to	to	ADP
ejpam-3756	448	6	fixed	fix	VERB
ejpam-3756	448	7	points	point	NOUN
ejpam-3756	448	8	of	of	ADP
ejpam-3756	448	9	asymtotically	asymtotically	ADV
ejpam-3756	448	10	nonexpansive	nonexpansive	ADJ
ejpam-3756	448	11	mappings	mapping	NOUN
ejpam-3756	448	12	.	.	PUNCT
ejpam-3756	449	1	bull	bull	NOUN
ejpam-3756	449	2	.	.	PUNCT
ejpam-3756	450	1	austral	austral	PROPN
ejpam-3756	450	2	.	.	PUNCT
ejpam-3756	450	3	math	math	NOUN
ejpam-3756	450	4	.	.	PUNCT
ejpam-3756	451	1	soc	soc	PROPN
ejpam-3756	451	2	.	.	PUNCT
ejpam-3756	451	3	,	,	PUNCT
ejpam-3756	451	4	43:153–159	43:153–159	PROPN
ejpam-3756	451	5	,	,	PUNCT
ejpam-3756	451	6	1991	1991	NUM
ejpam-3756	451	7	.	.	PUNCT
ejpam-3756	452	1	[	[	X
ejpam-3756	452	2	16	16	NUM
ejpam-3756	452	3	]	]	PUNCT
ejpam-3756	452	4	t.	t.	PROPN
ejpam-3756	452	5	suzuki	suzuki	PROPN
ejpam-3756	452	6	.	.	PUNCT
ejpam-3756	453	1	fixed	fix	VERB
ejpam-3756	453	2	point	point	NOUN
ejpam-3756	453	3	theorems	theorem	NOUN
ejpam-3756	453	4	and	and	CCONJ
ejpam-3756	453	5	convergence	convergence	NOUN
ejpam-3756	453	6	theorems	theorem	NOUN
ejpam-3756	453	7	for	for	ADP
ejpam-3756	453	8	some	some	DET
ejpam-3756	453	9	generalized	generalize	VERB
ejpam-3756	453	10	nonexpansive	nonexpansive	ADJ
ejpam-3756	453	11	mappings	mapping	NOUN
ejpam-3756	453	12	.	.	PUNCT
ejpam-3756	454	1	j.	j.	PROPN
ejpam-3756	454	2	math	math	PROPN
ejpam-3756	454	3	.	.	PUNCT
ejpam-3756	455	1	anal	anal	PROPN
ejpam-3756	455	2	.	.	PUNCT
ejpam-3756	456	1	appl	appl	PROPN
ejpam-3756	456	2	.	.	PROPN
ejpam-3756	456	3	,	,	PUNCT
ejpam-3756	456	4	340:1088–1095	340:1088–1095	PROPN
ejpam-3756	456	5	,	,	PUNCT
ejpam-3756	456	6	2008	2008	NUM
ejpam-3756	456	7	.	.	PUNCT
ejpam-3756	457	1	[	[	X
ejpam-3756	457	2	17	17	NUM
ejpam-3756	457	3	]	]	X
ejpam-3756	457	4	w.	w.	PROPN
ejpam-3756	457	5	takahashi	takahashi	PROPN
ejpam-3756	457	6	.	.	PUNCT
ejpam-3756	458	1	nonlinear	nonlinear	ADJ
ejpam-3756	458	2	functional	functional	ADJ
ejpam-3756	458	3	analysis	analysis	NOUN
ejpam-3756	458	4	.	.	PUNCT
ejpam-3756	459	1	yokohoma	yokohoma	NOUN
ejpam-3756	459	2	publishers	publisher	NOUN
ejpam-3756	459	3	,	,	PUNCT
ejpam-3756	459	4	yokohoma	yokohoma	NOUN
ejpam-3756	459	5	,	,	PUNCT
ejpam-3756	459	6	2000	2000	NUM
ejpam-3756	459	7	.	.	PUNCT
ejpam-3756	460	1	[	[	X
ejpam-3756	460	2	18	18	NUM
ejpam-3756	460	3	]	]	PUNCT
ejpam-3756	460	4	k.	k.	PROPN
ejpam-3756	460	5	ullah	ullah	PROPN
ejpam-3756	460	6	and	and	CCONJ
ejpam-3756	460	7	m.	m.	PROPN
ejpam-3756	460	8	arshad	arshad	PROPN
ejpam-3756	460	9	.	.	PUNCT
ejpam-3756	461	1	new	new	ADJ
ejpam-3756	461	2	three	three	NUM
ejpam-3756	461	3	-	-	PUNCT
ejpam-3756	461	4	step	step	NOUN
ejpam-3756	461	5	iteration	iteration	NOUN
ejpam-3756	461	6	process	process	NOUN
ejpam-3756	461	7	and	and	CCONJ
ejpam-3756	461	8	fixed	fix	VERB
ejpam-3756	461	9	point	point	NOUN
ejpam-3756	461	10	approximation	approximation	NOUN
ejpam-3756	461	11	in	in	ADP
ejpam-3756	461	12	banach	banach	NOUN
ejpam-3756	461	13	spaces	space	NOUN
ejpam-3756	461	14	.	.	PUNCT
ejpam-3756	462	1	j.	j.	PROPN
ejpam-3756	462	2	nonlinear	nonlinear	PROPN
ejpam-3756	462	3	topl	topl	PROPN
ejpam-3756	462	4	.	.	PUNCT
ejpam-3756	463	1	algebra	algebra	NOUN
ejpam-3756	463	2	,	,	PUNCT
ejpam-3756	463	3	7(2):87–100	7(2):87–100	NUM
ejpam-3756	463	4	,	,	PUNCT
ejpam-3756	463	5	2018	2018	NUM
ejpam-3756	463	6	.	.	PUNCT
ejpam-3756	464	1	[	[	X
ejpam-3756	464	2	19	19	NUM
ejpam-3756	464	3	]	]	PUNCT
ejpam-3756	464	4	x.	x.	NOUN
ejpam-3756	464	5	weng	weng	PROPN
ejpam-3756	464	6	.	.	PUNCT
ejpam-3756	465	1	fixed	fix	VERB
ejpam-3756	465	2	point	point	NOUN
ejpam-3756	465	3	iteration	iteration	NOUN
ejpam-3756	465	4	for	for	ADP
ejpam-3756	465	5	local	local	ADJ
ejpam-3756	465	6	strictly	strictly	ADV
ejpam-3756	465	7	pseudocontractive	pseudocontractive	ADJ
ejpam-3756	465	8	mapping	mapping	NOUN
ejpam-3756	465	9	.	.	PUNCT
ejpam-3756	466	1	proc	proc	PROPN
ejpam-3756	466	2	.	.	PUNCT
ejpam-3756	467	1	amer.math	amer.math	NUM
ejpam-3756	467	2	.	.	PUNCT
ejpam-3756	468	1	soc	soc	PROPN
ejpam-3756	468	2	.	.	PUNCT
ejpam-3756	468	3	,	,	PUNCT
ejpam-3756	468	4	113:727–731	113:727–731	NUM
ejpam-3756	468	5	,	,	PUNCT
ejpam-3756	468	6	1991	1991	NUM
ejpam-3756	468	7	.	.	PUNCT