id	sid	tid	token	lemma	pos
ma-27	1	1	2021	2021	NUM
ma-27	1	2	ada	ada	PROPN
ma-27	1	3	academica	academica	PROPN
ma-27	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-27	1	5	.	.	PUNCT
ma-27	2	1	j.	j.	PROPN
ma-27	2	2	math	math	PROPN
ma-27	2	3	.	.	PUNCT
ma-27	3	1	anal	anal	ADJ
ma-27	3	2	.	.	PUNCT
ma-27	4	1	1	1	NUM
ma-27	4	2	(	(	PUNCT
ma-27	4	3	2021	2021	NUM
ma-27	4	4	)	)	PUNCT
ma-27	4	5	106	106	NUM
ma-27	4	6	-	-	SYM
ma-27	4	7	132doi	132doi	NUM
ma-27	4	8	:	:	PUNCT
ma-27	4	9	10.28924	10.28924	NUM
ma-27	4	10	/	/	SYM
ma-27	4	11	ada	ada	PROPN
ma-27	4	12	/	/	SYM
ma-27	4	13	ma.1.106	ma.1.106	PROPN
ma-27	4	14	new	new	ADJ
ma-27	4	15	iterative	iterative	NOUN
ma-27	4	16	algorithm	algorithm	NOUN
ma-27	4	17	for	for	ADP
ma-27	4	18	solving	solve	VERB
ma-27	4	19	constrained	constrain	VERB
ma-27	4	20	convex	convex	NOUN
ma-27	4	21	minimization	minimization	NOUN
ma-27	4	22	problem	problem	NOUN
ma-27	4	23	and	and	CCONJ
ma-27	4	24	split	split	VERB
ma-27	4	25	feasibility	feasibility	NOUN
ma-27	4	26	problem	problem	NOUN
ma-27	4	27	austine	austine	NOUN
ma-27	4	28	efut	efut	PROPN
ma-27	4	29	ofem1,∗	ofem1,∗	PROPN
ma-27	4	30	,	,	PUNCT
ma-27	4	31	unwana	unwana	PROPN
ma-27	4	32	effiong	effiong	PROPN
ma-27	4	33	udofia2	udofia2	NOUN
ma-27	4	34	,	,	PUNCT
ma-27	4	35	donatus	donatus	X
ma-27	4	36	ikechi	ikechi	PROPN
ma-27	4	37	igbokwe3	igbokwe3	PROPN
ma-27	4	38	1department	1department	NUM
ma-27	4	39	of	of	ADP
ma-27	4	40	mathematics	mathematic	NOUN
ma-27	4	41	,	,	PUNCT
ma-27	4	42	university	university	NOUN
ma-27	4	43	of	of	ADP
ma-27	4	44	uyo	uyo	PROPN
ma-27	4	45	,	,	PUNCT
ma-27	4	46	uyo	uyo	PROPN
ma-27	4	47	,	,	PUNCT
ma-27	4	48	nigeria	nigeria	PROPN
ma-27	4	49	ofemaustine@gmail.com	ofemaustine@gmail.com	X
ma-27	5	1	2department	2department	NUM
ma-27	5	2	of	of	ADP
ma-27	5	3	mathematics	mathematic	NOUN
ma-27	5	4	and	and	CCONJ
ma-27	5	5	statistics	statistic	NOUN
ma-27	5	6	,	,	PUNCT
ma-27	5	7	akwa	akwa	ADJ
ma-27	5	8	ibom	ibom	ADJ
ma-27	5	9	state	state	NOUN
ma-27	5	10	university	university	PROPN
ma-27	5	11	,	,	PUNCT
ma-27	5	12	ikot	ikot	PROPN
ma-27	5	13	akpaden	akpaden	PROPN
ma-27	5	14	,	,	PUNCT
ma-27	5	15	mkpatenin	mkpatenin	PROPN
ma-27	5	16	,	,	PUNCT
ma-27	5	17	nigeria	nigeria	PROPN
ma-27	5	18	unwanaudofia.aksu@yahoo.com	unwanaudofia.aksu@yahoo.com	PROPN
ma-27	5	19	3department	3department	NUM
ma-27	5	20	of	of	ADP
ma-27	5	21	mathematics	mathematic	NOUN
ma-27	5	22	,	,	PUNCT
ma-27	5	23	michael	michael	PROPN
ma-27	5	24	okpara	okpara	PROPN
ma-27	5	25	university	university	PROPN
ma-27	5	26	of	of	ADP
ma-27	5	27	agriculture	agriculture	PROPN
ma-27	5	28	,	,	PUNCT
ma-27	5	29	umudike	umudike	NOUN
ma-27	5	30	,	,	PUNCT
ma-27	5	31	nigeria	nigeria	PROPN
ma-27	5	32	igbokwedi@yahoo.com	igbokwedi@yahoo.com	PUNCT
ma-27	6	1	∗correspondence	∗correspondence	NOUN
ma-27	6	2	:	:	PUNCT
ma-27	6	3	ofemaustine@gmail.com	ofemaustine@gmail.com	X
ma-27	6	4	abstract	abstract	ADJ
ma-27	6	5	.	.	PUNCT
ma-27	7	1	the	the	DET
ma-27	7	2	purpose	purpose	NOUN
ma-27	7	3	of	of	ADP
ma-27	7	4	this	this	DET
ma-27	7	5	paper	paper	NOUN
ma-27	7	6	is	be	AUX
ma-27	7	7	to	to	PART
ma-27	7	8	introduce	introduce	VERB
ma-27	7	9	a	a	DET
ma-27	7	10	new	new	ADJ
ma-27	7	11	iterative	iterative	NOUN
ma-27	7	12	algorithm	algorithm	NOUN
ma-27	7	13	to	to	PART
ma-27	7	14	approximate	approximate	VERB
ma-27	7	15	the	the	DET
ma-27	7	16	fixedpoints	fixedpoint	NOUN
ma-27	7	17	of	of	ADP
ma-27	7	18	almost	almost	ADV
ma-27	7	19	contraction	contraction	NOUN
ma-27	7	20	mappings	mapping	NOUN
ma-27	7	21	and	and	CCONJ
ma-27	7	22	generalized	generalize	VERB
ma-27	7	23	α	α	NUM
ma-27	7	24	-	-	PUNCT
ma-27	7	25	nonexpansive	nonexpansive	ADJ
ma-27	7	26	mappings	mapping	NOUN
ma-27	7	27	.	.	PUNCT
ma-27	8	1	also	also	ADV
ma-27	8	2	,	,	PUNCT
ma-27	8	3	we	we	PRON
ma-27	8	4	show	show	VERB
ma-27	8	5	thatour	thatour	NOUN
ma-27	8	6	proposed	propose	VERB
ma-27	8	7	iterative	iterative	NOUN
ma-27	8	8	algorithm	algorithm	NOUN
ma-27	8	9	converges	converge	VERB
ma-27	8	10	weakly	weakly	ADJ
ma-27	8	11	and	and	CCONJ
ma-27	8	12	strongly	strongly	ADV
ma-27	8	13	to	to	ADP
ma-27	8	14	the	the	DET
ma-27	8	15	fixed	fix	VERB
ma-27	8	16	points	point	NOUN
ma-27	8	17	of	of	ADP
ma-27	8	18	almost	almost	ADV
ma-27	8	19	contrac	contrac	ADJ
ma-27	8	20	-	-	PUNCT
ma-27	8	21	tion	tion	NOUN
ma-27	8	22	mappings	mapping	NOUN
ma-27	8	23	and	and	CCONJ
ma-27	8	24	generalized	generalize	VERB
ma-27	8	25	α	α	NUM
ma-27	8	26	-	-	PUNCT
ma-27	8	27	nonexpansive	nonexpansive	ADJ
ma-27	8	28	mappings	mapping	NOUN
ma-27	8	29	.	.	PUNCT
ma-27	9	1	furthermore	furthermore	ADV
ma-27	9	2	,	,	PUNCT
ma-27	9	3	it	it	PRON
ma-27	9	4	is	be	AUX
ma-27	9	5	proved	prove	VERB
ma-27	9	6	analytically	analytically	ADV
ma-27	9	7	thatour	thatour	ADJ
ma-27	9	8	new	new	ADJ
ma-27	9	9	iterative	iterative	NOUN
ma-27	9	10	algorithm	algorithm	NOUN
ma-27	9	11	converges	converge	VERB
ma-27	9	12	faster	fast	ADV
ma-27	9	13	than	than	ADP
ma-27	9	14	one	one	NUM
ma-27	9	15	of	of	ADP
ma-27	9	16	the	the	DET
ma-27	9	17	leading	lead	VERB
ma-27	9	18	iterative	iterative	NOUN
ma-27	9	19	algorithms	algorithm	NOUN
ma-27	9	20	in	in	ADP
ma-27	9	21	the	the	DET
ma-27	9	22	liter	liter	NOUN
ma-27	9	23	-	-	PUNCT
ma-27	9	24	ature	ature	NOUN
ma-27	9	25	for	for	ADP
ma-27	9	26	almost	almost	ADV
ma-27	9	27	contraction	contraction	NOUN
ma-27	9	28	mappings	mapping	NOUN
ma-27	9	29	.	.	PUNCT
ma-27	10	1	some	some	DET
ma-27	10	2	numerical	numerical	ADJ
ma-27	10	3	examples	example	NOUN
ma-27	10	4	are	be	AUX
ma-27	10	5	also	also	ADV
ma-27	10	6	provided	provide	VERB
ma-27	10	7	and	and	CCONJ
ma-27	10	8	used	use	VERB
ma-27	10	9	to	to	ADP
ma-27	10	10	showthat	showthat	ADP
ma-27	10	11	our	our	PRON
ma-27	10	12	new	new	ADJ
ma-27	10	13	iterative	iterative	NOUN
ma-27	10	14	algorithm	algorithm	NOUN
ma-27	10	15	has	have	VERB
ma-27	10	16	better	well	ADJ
ma-27	10	17	rate	rate	NOUN
ma-27	10	18	of	of	ADP
ma-27	10	19	convergence	convergence	NOUN
ma-27	10	20	than	than	ADP
ma-27	10	21	all	all	PRON
ma-27	10	22	of	of	ADP
ma-27	10	23	s	s	NOUN
ma-27	10	24	,	,	PUNCT
ma-27	10	25	picard	picard	NOUN
ma-27	10	26	-	-	PUNCT
ma-27	10	27	s	s	PROPN
ma-27	10	28	,	,	PUNCT
ma-27	10	29	thakur	thakur	PROPN
ma-27	10	30	andm	andm	PROPN
ma-27	10	31	iterative	iterative	VERB
ma-27	10	32	algorithms	algorithm	NOUN
ma-27	10	33	for	for	ADP
ma-27	10	34	almost	almost	ADV
ma-27	10	35	contraction	contraction	NOUN
ma-27	10	36	mappings	mapping	NOUN
ma-27	10	37	and	and	CCONJ
ma-27	10	38	generalized	generalize	VERB
ma-27	10	39	α	α	PRON
ma-27	10	40	-	-	ADJ
ma-27	10	41	nonexpansive	nonexpansive	ADJ
ma-27	10	42	mappings.again	mappings.again	NOUN
ma-27	10	43	,	,	PUNCT
ma-27	10	44	we	we	PRON
ma-27	10	45	show	show	VERB
ma-27	10	46	that	that	SCONJ
ma-27	10	47	the	the	DET
ma-27	10	48	proposed	propose	VERB
ma-27	10	49	iterative	iterative	NOUN
ma-27	10	50	algorithm	algorithm	NOUN
ma-27	10	51	is	be	AUX
ma-27	10	52	stable	stable	ADJ
ma-27	10	53	with	with	ADP
ma-27	10	54	respect	respect	NOUN
ma-27	10	55	to	to	ADP
ma-27	10	56	t	t	NOUN
ma-27	10	57	and	and	CCONJ
ma-27	10	58	data	datum	NOUN
ma-27	10	59	dependentfor	dependentfor	ADP
ma-27	10	60	almost	almost	ADV
ma-27	10	61	contraction	contraction	NOUN
ma-27	10	62	mappings	mapping	NOUN
ma-27	10	63	.	.	PUNCT
ma-27	11	1	some	some	DET
ma-27	11	2	applications	application	NOUN
ma-27	11	3	of	of	ADP
ma-27	11	4	our	our	PRON
ma-27	11	5	main	main	ADJ
ma-27	11	6	results	result	NOUN
ma-27	11	7	and	and	CCONJ
ma-27	11	8	new	new	ADJ
ma-27	11	9	iterative	iterative	NOUN
ma-27	11	10	algorithmare	algorithmare	NOUN
ma-27	11	11	considered	consider	VERB
ma-27	11	12	.	.	PUNCT
ma-27	12	1	the	the	DET
ma-27	12	2	results	result	NOUN
ma-27	12	3	in	in	ADP
ma-27	12	4	this	this	DET
ma-27	12	5	article	article	NOUN
ma-27	12	6	are	be	AUX
ma-27	12	7	improvements	improvement	NOUN
ma-27	12	8	,	,	PUNCT
ma-27	12	9	generalizations	generalization	NOUN
ma-27	12	10	and	and	CCONJ
ma-27	12	11	extensions	extension	NOUN
ma-27	12	12	of	of	ADP
ma-27	12	13	severalrelevant	severalrelevant	ADJ
ma-27	12	14	results	result	NOUN
ma-27	12	15	existing	exist	VERB
ma-27	12	16	in	in	ADP
ma-27	12	17	the	the	DET
ma-27	12	18	literature	literature	NOUN
ma-27	12	19	.	.	PUNCT
ma-27	13	1	1	1	X
ma-27	13	2	.	.	X
ma-27	13	3	introduction	introduction	NOUN
ma-27	13	4	fixed	fix	VERB
ma-27	13	5	point	point	NOUN
ma-27	13	6	theory	theory	NOUN
ma-27	13	7	is	be	AUX
ma-27	13	8	concerned	concern	VERB
ma-27	13	9	with	with	ADP
ma-27	13	10	solution	solution	NOUN
ma-27	13	11	of	of	ADP
ma-27	13	12	the	the	DET
ma-27	13	13	equation	equation	NOUN
ma-27	13	14	t	t	NOUN
ma-27	13	15	`	`	PUNCT
ma-27	13	16	=	=	PRON
ma-27	13	17	`	`	PUNCT
ma-27	13	18	,	,	PUNCT
ma-27	13	19	(	(	PUNCT
ma-27	13	20	1.1	1.1	NUM
ma-27	13	21	)	)	PUNCT
ma-27	13	22	where	where	SCONJ
ma-27	13	23	t	t	NOUN
ma-27	13	24	could	could	AUX
ma-27	13	25	be	be	AUX
ma-27	13	26	a	a	DET
ma-27	13	27	nonlinear	nonlinear	ADJ
ma-27	13	28	operator	operator	NOUN
ma-27	13	29	defined	define	VERB
ma-27	13	30	on	on	ADP
ma-27	13	31	a	a	DET
ma-27	13	32	metric	metric	ADJ
ma-27	13	33	space	space	NOUN
ma-27	13	34	.	.	PUNCT
ma-27	14	1	any	any	DET
ma-27	14	2	`	`	PUNCT
ma-27	14	3	that	that	SCONJ
ma-27	14	4	solves	solve	NOUN
ma-27	14	5	(	(	PUNCT
ma-27	14	6	1.1	1.1	NUM
ma-27	14	7	)	)	PUNCT
ma-27	14	8	is	be	AUX
ma-27	14	9	calledthe	calledthe	DET
ma-27	14	10	fixed	fix	VERB
ma-27	14	11	point	point	NOUN
ma-27	14	12	of	of	ADP
ma-27	14	13	t	t	PROPN
ma-27	14	14	and	and	CCONJ
ma-27	14	15	the	the	DET
ma-27	14	16	collection	collection	NOUN
ma-27	14	17	all	all	DET
ma-27	14	18	such	such	ADJ
ma-27	14	19	elements	element	NOUN
ma-27	14	20	is	be	AUX
ma-27	14	21	denoted	denote	VERB
ma-27	14	22	by	by	ADP
ma-27	14	23	f	f	PROPN
ma-27	14	24	(	(	PUNCT
ma-27	14	25	t	t	PROPN
ma-27	14	26	)	)	PUNCT
ma-27	14	27	.	.	PUNCT
ma-27	15	1	fixed	fix	VERB
ma-27	15	2	point	point	NOUN
ma-27	15	3	theory	theory	NOUN
ma-27	15	4	is	be	AUX
ma-27	15	5	received	receive	VERB
ma-27	15	6	:	:	PUNCT
ma-27	15	7	10	10	NUM
ma-27	15	8	sep	sep	NOUN
ma-27	15	9	2021	2021	NUM
ma-27	15	10	.	.	PUNCT
ma-27	16	1	key	key	ADJ
ma-27	16	2	words	word	NOUN
ma-27	16	3	and	and	CCONJ
ma-27	16	4	phrases	phrase	NOUN
ma-27	16	5	.	.	PUNCT
ma-27	17	1	stability	stability	NOUN
ma-27	17	2	;	;	PUNCT
ma-27	17	3	almost	almost	ADV
ma-27	17	4	contraction	contraction	NOUN
ma-27	17	5	map	map	NOUN
ma-27	17	6	;	;	PUNCT
ma-27	17	7	generalized	generalized	ADJ
ma-27	17	8	α	α	PROPN
ma-27	17	9	-	-	PUNCT
ma-27	17	10	nonexpansive	nonexpansive	ADJ
ma-27	17	11	mapping	mapping	NOUN
ma-27	17	12	;	;	PUNCT
ma-27	17	13	data	datum	NOUN
ma-27	17	14	dependence;iterative	dependence;iterative	PROPN
ma-27	17	15	algorithm	algorithm	NOUN
ma-27	17	16	;	;	PUNCT
ma-27	17	17	constrained	constrain	VERB
ma-27	17	18	convex	convex	PROPN
ma-27	17	19	minimization	minimization	NOUN
ma-27	17	20	problem	problem	NOUN
ma-27	17	21	;	;	PUNCT
ma-27	17	22	split	split	VERB
ma-27	17	23	feasibility	feasibility	NOUN
ma-27	17	24	problem.106	problem.106	NOUN
ma-27	17	25	https://adac.ee	https://adac.ee	PROPN
ma-27	17	26	https://doi.org/10.28924/ada/ma.1.106	https://doi.org/10.28924/ada/ma.1.106	NOUN
ma-27	17	27	https://orcid.org/0000-0001-8064-2326	https://orcid.org/0000-0001-8064-2326	ADP
ma-27	17	28	eur	eur	NOUN
ma-27	17	29	.	.	PUNCT
ma-27	18	1	j.	j.	PROPN
ma-27	18	2	math	math	PROPN
ma-27	18	3	.	.	PUNCT
ma-27	19	1	anal	anal	ADJ
ma-27	19	2	.	.	PUNCT
ma-27	20	1	1	1	NUM
ma-27	20	2	(	(	PUNCT
ma-27	20	3	2021	2021	NUM
ma-27	20	4	)	)	PUNCT
ma-27	20	5	107an	107an	NOUN
ma-27	20	6	area	area	NOUN
ma-27	20	7	in	in	ADP
ma-27	20	8	nonlinear	nonlinear	ADJ
ma-27	20	9	analysis	analysis	NOUN
ma-27	20	10	that	that	PRON
ma-27	20	11	has	have	AUX
ma-27	20	12	become	become	VERB
ma-27	20	13	very	very	ADV
ma-27	20	14	attractive	attractive	ADJ
ma-27	20	15	and	and	CCONJ
ma-27	20	16	interesting	interesting	ADJ
ma-27	20	17	with	with	ADP
ma-27	20	18	a	a	DET
ma-27	20	19	large	large	ADJ
ma-27	20	20	numberof	numberof	NOUN
ma-27	20	21	applications	application	NOUN
ma-27	20	22	in	in	ADP
ma-27	20	23	various	various	ADJ
ma-27	20	24	fields	field	NOUN
ma-27	20	25	of	of	ADP
ma-27	20	26	mathematics	mathematic	NOUN
ma-27	20	27	and	and	CCONJ
ma-27	20	28	other	other	ADJ
ma-27	20	29	branches	branch	NOUN
ma-27	20	30	of	of	ADP
ma-27	20	31	science	science	NOUN
ma-27	20	32	.	.	PUNCT
ma-27	21	1	fixed	fix	VERB
ma-27	21	2	point	point	NOUN
ma-27	21	3	theoryhas	theoryhas	PROPN
ma-27	21	4	remained	remain	VERB
ma-27	21	5	not	not	PART
ma-27	21	6	only	only	ADV
ma-27	21	7	a	a	DET
ma-27	21	8	field	field	NOUN
ma-27	21	9	with	with	ADP
ma-27	21	10	a	a	DET
ma-27	21	11	huge	huge	ADJ
ma-27	21	12	development	development	NOUN
ma-27	21	13	,	,	PUNCT
ma-27	21	14	but	but	CCONJ
ma-27	21	15	also	also	ADV
ma-27	21	16	a	a	DET
ma-27	21	17	very	very	ADV
ma-27	21	18	helpful	helpful	ADJ
ma-27	21	19	means	mean	NOUN
ma-27	21	20	for	for	ADP
ma-27	21	21	solvingvarious	solvingvarious	ADJ
ma-27	21	22	problems	problem	NOUN
ma-27	21	23	in	in	ADP
ma-27	21	24	different	different	ADJ
ma-27	21	25	fields	field	NOUN
ma-27	21	26	of	of	ADP
ma-27	21	27	mathematics	mathematic	NOUN
ma-27	21	28	.	.	PUNCT
ma-27	22	1	it	it	PRON
ma-27	22	2	is	be	AUX
ma-27	22	3	well	well	ADV
ma-27	22	4	known	know	VERB
ma-27	22	5	that	that	SCONJ
ma-27	22	6	fixed	fix	VERB
ma-27	22	7	point	point	NOUN
ma-27	22	8	theorems	theorem	NOUN
ma-27	22	9	areused	areuse	VERB
ma-27	22	10	for	for	ADP
ma-27	22	11	proving	prove	VERB
ma-27	22	12	the	the	DET
ma-27	22	13	existence	existence	NOUN
ma-27	22	14	and	and	CCONJ
ma-27	22	15	uniqueness	uniqueness	NOUN
ma-27	22	16	to	to	ADP
ma-27	22	17	various	various	ADJ
ma-27	22	18	mathematical	mathematical	ADJ
ma-27	22	19	models	model	NOUN
ma-27	22	20	like	like	ADP
ma-27	22	21	differential	differential	ADJ
ma-27	22	22	,	,	PUNCT
ma-27	22	23	integral	integral	ADJ
ma-27	22	24	and	and	CCONJ
ma-27	22	25	partial	partial	ADJ
ma-27	22	26	differential	differential	ADJ
ma-27	22	27	equations	equation	NOUN
ma-27	22	28	and	and	CCONJ
ma-27	22	29	variational	variational	ADJ
ma-27	22	30	inequalities	inequality	NOUN
ma-27	22	31	problems	problem	NOUN
ma-27	22	32	etc	etc	X
ma-27	22	33	.	.	X
ma-27	22	34	,	,	PUNCT
ma-27	22	35	representingphenomena	representingphenomena	NOUN
ma-27	22	36	arising	arise	VERB
ma-27	22	37	in	in	ADP
ma-27	22	38	different	different	ADJ
ma-27	22	39	fields	field	NOUN
ma-27	22	40	such	such	ADJ
ma-27	22	41	as	as	ADP
ma-27	22	42	steady	steady	ADJ
ma-27	22	43	state	state	NOUN
ma-27	22	44	temperature	temperature	NOUN
ma-27	22	45	distribution	distribution	NOUN
ma-27	22	46	,	,	PUNCT
ma-27	22	47	chemical	chemical	NOUN
ma-27	22	48	equa	equa	NOUN
ma-27	22	49	-	-	PUNCT
ma-27	22	50	tions	tion	NOUN
ma-27	22	51	,	,	PUNCT
ma-27	22	52	neutron	neutron	NOUN
ma-27	22	53	transport	transport	NOUN
ma-27	22	54	theory	theory	NOUN
ma-27	22	55	,	,	PUNCT
ma-27	22	56	economic	economic	ADJ
ma-27	22	57	theories	theory	NOUN
ma-27	22	58	,	,	PUNCT
ma-27	22	59	epidemics	epidemic	NOUN
ma-27	22	60	and	and	CCONJ
ma-27	22	61	flow	flow	NOUN
ma-27	22	62	of	of	ADP
ma-27	22	63	fluids	fluid	NOUN
ma-27	22	64	.	.	PUNCT
ma-27	23	1	furthermore	furthermore	ADV
ma-27	23	2	,	,	PUNCT
ma-27	23	3	itas	ita	VERB
ma-27	23	4	also	also	ADV
ma-27	23	5	significant	significant	ADJ
ma-27	23	6	in	in	ADP
ma-27	23	7	the	the	DET
ma-27	23	8	field	field	NOUN
ma-27	23	9	of	of	ADP
ma-27	23	10	computer	computer	NOUN
ma-27	23	11	science	science	NOUN
ma-27	23	12	,	,	PUNCT
ma-27	23	13	image	image	NOUN
ma-27	23	14	processing	processing	NOUN
ma-27	23	15	,	,	PUNCT
ma-27	23	16	artificial	artificial	ADJ
ma-27	23	17	intelligence	intelligence	NOUN
ma-27	23	18	,	,	PUNCT
ma-27	23	19	deci	deci	PROPN
ma-27	23	20	-	-	PUNCT
ma-27	23	21	sion	sion	NOUN
ma-27	23	22	making	making	NOUN
ma-27	23	23	,	,	PUNCT
ma-27	23	24	population	population	NOUN
ma-27	23	25	dynamics	dynamic	NOUN
ma-27	23	26	,	,	PUNCT
ma-27	23	27	computer	computer	NOUN
ma-27	23	28	science	science	NOUN
ma-27	23	29	,	,	PUNCT
ma-27	23	30	operational	operational	ADJ
ma-27	23	31	research	research	NOUN
ma-27	23	32	,	,	PUNCT
ma-27	23	33	industrial	industrial	ADJ
ma-27	23	34	engineering	engineering	NOUN
ma-27	23	35	,	,	PUNCT
ma-27	23	36	pattern	pattern	NOUN
ma-27	23	37	recognition	recognition	NOUN
ma-27	23	38	,	,	PUNCT
ma-27	23	39	medicine	medicine	NOUN
ma-27	23	40	,	,	PUNCT
ma-27	23	41	group	group	NOUN
ma-27	23	42	health	health	NOUN
ma-27	23	43	underwriting	underwriting	NOUN
ma-27	23	44	,	,	PUNCT
ma-27	23	45	management	management	NOUN
ma-27	23	46	and	and	CCONJ
ma-27	23	47	many	many	ADJ
ma-27	23	48	others.existence	others.existence	NOUN
ma-27	23	49	theorem	theorem	NOUN
ma-27	23	50	is	be	AUX
ma-27	23	51	concerned	concern	VERB
ma-27	23	52	with	with	ADP
ma-27	23	53	establishing	establish	VERB
ma-27	23	54	sufficient	sufficient	ADJ
ma-27	23	55	conditions	condition	NOUN
ma-27	23	56	in	in	ADP
ma-27	23	57	which	which	PRON
ma-27	23	58	the	the	DET
ma-27	23	59	equation	equation	NOUN
ma-27	23	60	(	(	PUNCT
ma-27	23	61	1.1)will	1.1)will	NUM
ma-27	23	62	have	have	VERB
ma-27	23	63	solution	solution	NOUN
ma-27	23	64	,	,	PUNCT
ma-27	23	65	but	but	CCONJ
ma-27	23	66	does	do	AUX
ma-27	23	67	not	not	PART
ma-27	23	68	necessarily	necessarily	ADV
ma-27	23	69	show	show	VERB
ma-27	23	70	how	how	SCONJ
ma-27	23	71	to	to	PART
ma-27	23	72	find	find	VERB
ma-27	23	73	such	such	ADJ
ma-27	23	74	solution	solution	NOUN
ma-27	23	75	.	.	PUNCT
ma-27	24	1	on	on	ADP
ma-27	24	2	the	the	DET
ma-27	24	3	other	other	ADJ
ma-27	24	4	hand	hand	NOUN
ma-27	24	5	,	,	PUNCT
ma-27	24	6	iteration	iteration	NOUN
ma-27	24	7	method	method	NOUN
ma-27	24	8	of	of	ADP
ma-27	24	9	fixed	fix	VERB
ma-27	24	10	points	point	NOUN
ma-27	24	11	is	be	AUX
ma-27	24	12	concerned	concern	VERB
ma-27	24	13	with	with	ADP
ma-27	24	14	approximation	approximation	NOUN
ma-27	24	15	or	or	CCONJ
ma-27	24	16	computation	computation	NOUN
ma-27	24	17	of	of	ADP
ma-27	24	18	sequences	sequence	NOUN
ma-27	24	19	whichconverge	whichconverge	VERB
ma-27	24	20	to	to	ADP
ma-27	24	21	the	the	DET
ma-27	24	22	solution	solution	NOUN
ma-27	24	23	of	of	ADP
ma-27	24	24	(	(	PUNCT
ma-27	24	25	1.1	1.1	NUM
ma-27	24	26	)	)	PUNCT
ma-27	24	27	.	.	PUNCT
ma-27	25	1	when	when	SCONJ
ma-27	25	2	existence	existence	NOUN
ma-27	25	3	of	of	ADP
ma-27	25	4	a	a	DET
ma-27	25	5	fixed	fix	VERB
ma-27	25	6	point	point	NOUN
ma-27	25	7	of	of	ADP
ma-27	25	8	an	an	DET
ma-27	25	9	operator	operator	NOUN
ma-27	25	10	is	be	AUX
ma-27	25	11	guaranteed	guarantee	VERB
ma-27	25	12	,	,	PUNCT
ma-27	25	13	obtaining	obtain	VERB
ma-27	25	14	constructive	constructive	ADJ
ma-27	25	15	technique	technique	NOUN
ma-27	25	16	for	for	ADP
ma-27	25	17	finding	find	VERB
ma-27	25	18	such	such	DET
ma-27	25	19	a	a	DET
ma-27	25	20	fixed	fix	VERB
ma-27	25	21	point	point	NOUN
ma-27	25	22	is	be	AUX
ma-27	25	23	also	also	ADV
ma-27	25	24	paramount.in	paramount.in	NUM
ma-27	25	25	2003	2003	NUM
ma-27	25	26	,	,	PUNCT
ma-27	25	27	berinde	berinde	VERB
ma-27	25	28	[	[	X
ma-27	25	29	6	6	NUM
ma-27	25	30	]	]	PUNCT
ma-27	25	31	introduced	introduce	VERB
ma-27	25	32	the	the	DET
ma-27	25	33	concept	concept	NOUN
ma-27	25	34	of	of	ADP
ma-27	25	35	weak	weak	ADJ
ma-27	25	36	contraction	contraction	NOUN
ma-27	25	37	mappings	mapping	NOUN
ma-27	25	38	which	which	PRON
ma-27	25	39	is	be	AUX
ma-27	25	40	also	also	ADV
ma-27	25	41	knownas	knowna	NOUN
ma-27	25	42	almost	almost	ADV
ma-27	25	43	contraction	contraction	NOUN
ma-27	25	44	mappings	mapping	NOUN
ma-27	25	45	.	.	PUNCT
ma-27	26	1	he	he	PRON
ma-27	26	2	showed	show	VERB
ma-27	26	3	that	that	SCONJ
ma-27	26	4	the	the	DET
ma-27	26	5	class	class	NOUN
ma-27	26	6	of	of	ADP
ma-27	26	7	almost	almost	ADV
ma-27	26	8	contraction	contraction	NOUN
ma-27	26	9	mappings	mapping	NOUN
ma-27	26	10	is	be	AUX
ma-27	26	11	moregeneral	moregeneral	ADJ
ma-27	26	12	than	than	ADP
ma-27	26	13	the	the	DET
ma-27	26	14	class	class	NOUN
ma-27	26	15	of	of	ADP
ma-27	26	16	zamfirescu	zamfirescu	PROPN
ma-27	26	17	mappings	mapping	NOUN
ma-27	27	1	[	[	X
ma-27	27	2	41	41	NUM
ma-27	27	3	]	]	PUNCT
ma-27	28	1	which	which	PRON
ma-27	28	2	includes	include	VERB
ma-27	28	3	contraction	contraction	NOUN
ma-27	28	4	mappings	mapping	NOUN
ma-27	28	5	,	,	PUNCT
ma-27	28	6	kannanmappings	kannanmapping	NOUN
ma-27	29	1	[	[	X
ma-27	29	2	22	22	NUM
ma-27	29	3	]	]	PUNCT
ma-27	29	4	and	and	CCONJ
ma-27	29	5	chatterjea	chatterjea	ADJ
ma-27	29	6	mappings	mapping	NOUN
ma-27	30	1	[	[	X
ma-27	30	2	10].throughout	10].throughout	NUM
ma-27	30	3	this	this	DET
ma-27	30	4	paper	paper	NOUN
ma-27	30	5	,	,	PUNCT
ma-27	30	6	let	let	VERB
ma-27	30	7	ω	ω	PUNCT
ma-27	30	8	denote	denote	VERB
ma-27	30	9	a	a	DET
ma-27	30	10	banach	banach	NOUN
ma-27	30	11	space	space	NOUN
ma-27	30	12	and	and	CCONJ
ma-27	30	13	λ	λ	X
ma-27	30	14	a	a	DET
ma-27	30	15	nonempty	nonempty	ADV
ma-27	30	16	closed	close	VERB
ma-27	30	17	convex	convex	NOUN
ma-27	30	18	subset	subset	NOUN
ma-27	30	19	of	of	ADP
ma-27	30	20	ω	ω	PROPN
ma-27	30	21	.	.	PUNCT
ma-27	31	1	let	let	VERB
ma-27	31	2	r	r	PRON
ma-27	31	3	stand	stand	VERB
ma-27	31	4	for	for	ADP
ma-27	31	5	set	set	NOUN
ma-27	31	6	of	of	ADP
ma-27	31	7	real	real	ADJ
ma-27	31	8	numbers	number	NOUN
ma-27	31	9	.	.	PUNCT
ma-27	32	1	definition	definition	NOUN
ma-27	32	2	1.1	1.1	NUM
ma-27	32	3	.	.	PUNCT
ma-27	33	1	a	a	DET
ma-27	33	2	mapping	mapping	NOUN
ma-27	33	3	t	t	NOUN
ma-27	33	4	:	:	PUNCT
ma-27	33	5	λ	λ	X
ma-27	33	6	→	→	SYM
ma-27	33	7	λ	λ	PROPN
ma-27	33	8	is	be	AUX
ma-27	33	9	called	call	VERB
ma-27	33	10	almost	almost	ADV
ma-27	33	11	contraction	contraction	NOUN
ma-27	33	12	if	if	SCONJ
ma-27	33	13	there	there	PRON
ma-27	33	14	exists	exist	VERB
ma-27	33	15	a	a	DET
ma-27	33	16	constant	constant	ADJ
ma-27	33	17	γ	γ	X
ma-27	33	18	∈	∈	PROPN
ma-27	33	19	(	(	PUNCT
ma-27	33	20	0	0	NUM
ma-27	33	21	,	,	PUNCT
ma-27	33	22	1	1	NUM
ma-27	33	23	)	)	PUNCT
ma-27	33	24	and	and	CCONJ
ma-27	33	25	some	some	DET
ma-27	33	26	constant	constant	ADJ
ma-27	33	27	l	l	NOUN
ma-27	33	28	≥	≥	NOUN
ma-27	33	29	0	0	NUM
ma-27	33	30	,	,	PUNCT
ma-27	33	31	such	such	ADJ
ma-27	33	32	that	that	SCONJ
ma-27	33	33	‖t`−	‖t`−	PUNCT
ma-27	33	34	tζ‖	tζ‖	PROPN
ma-27	33	35	≤	≤	VERB
ma-27	33	36	γ‖`−	γ‖`−	PRON
ma-27	33	37	ζ‖+	ζ‖+	PROPN
ma-27	33	38	l‖`−	l‖`−	NOUN
ma-27	33	39	t`‖	t`‖	NOUN
ma-27	33	40	,	,	PUNCT
ma-27	33	41	∀	∀	PUNCT
ma-27	34	1	`	`	PUNCT
ma-27	34	2	,	,	PUNCT
ma-27	34	3	ζ	ζ	PROPN
ma-27	34	4	∈	∈	PROPN
ma-27	34	5	λ	λ	PROPN
ma-27	34	6	.	.	PUNCT
ma-27	34	7	(	(	PUNCT
ma-27	34	8	1.2	1.2	NUM
ma-27	34	9	)	)	PUNCT
ma-27	34	10	definition	definition	NOUN
ma-27	34	11	1.2	1.2	NUM
ma-27	34	12	.	.	PUNCT
ma-27	35	1	a	a	DET
ma-27	35	2	mapping	mapping	NOUN
ma-27	35	3	t	t	NOUN
ma-27	35	4	:	:	PUNCT
ma-27	35	5	λ	λ	X
ma-27	35	6	→	→	SYM
ma-27	35	7	λ	λ	PROPN
ma-27	35	8	is	be	AUX
ma-27	35	9	said	say	VERB
ma-27	35	10	to	to	PART
ma-27	35	11	be	be	AUX
ma-27	35	12	suzuki	suzuki	NOUN
ma-27	35	13	generalized	generalize	VERB
ma-27	35	14	nonexpansive	nonexpansive	ADJ
ma-27	35	15	if	if	SCONJ
ma-27	35	16	for	for	ADP
ma-27	35	17	all	all	PRON
ma-27	35	18	`	`	PUNCT
ma-27	35	19	,	,	PUNCT
ma-27	35	20	ζ	ζ	PROPN
ma-27	35	21	∈	∈	PROPN
ma-27	35	22	λ	λ	NOUN
ma-27	35	23	,	,	PUNCT
ma-27	35	24	we	we	PRON
ma-27	35	25	have	have	VERB
ma-27	35	26	1	1	NUM
ma-27	35	27	2	2	NUM
ma-27	35	28	‖`−	‖`−	NUM
ma-27	35	29	t`‖	t`‖	NOUN
ma-27	35	30	≤	≤	NOUN
ma-27	35	31	‖`−	‖`−	NUM
ma-27	35	32	ζ‖	ζ‖	NOUN
ma-27	35	33	=	=	NOUN
ma-27	35	34	⇒	⇒	NOUN
ma-27	35	35	‖t`−	‖t`−	NUM
ma-27	35	36	tζ‖	tζ‖	PROPN
ma-27	35	37	≤	≤	VERB
ma-27	35	38	‖`−	‖`−	NUM
ma-27	35	39	ζ‖.	ζ‖.	NOUN
ma-27	35	40	suzuki	suzuki	NOUN
ma-27	35	41	generalized	generalize	VERB
ma-27	35	42	nonexpansive	nonexpansive	ADJ
ma-27	35	43	mappings	mapping	NOUN
ma-27	35	44	is	be	AUX
ma-27	35	45	also	also	ADV
ma-27	35	46	known	know	VERB
ma-27	35	47	as	as	ADP
ma-27	35	48	mappings	mapping	NOUN
ma-27	35	49	satisfying	satisfy	VERB
ma-27	35	50	condition	condition	NOUN
ma-27	35	51	(	(	PUNCT
ma-27	35	52	c).in	c).in	PROPN
ma-27	36	1	[	[	X
ma-27	36	2	33	33	NUM
ma-27	36	3	]	]	PUNCT
ma-27	36	4	,	,	PUNCT
ma-27	36	5	suzuki	suzuki	PROPN
ma-27	36	6	showed	show	VERB
ma-27	36	7	that	that	SCONJ
ma-27	36	8	the	the	DET
ma-27	36	9	class	class	NOUN
ma-27	36	10	of	of	ADP
ma-27	36	11	suzuki	suzuki	PROPN
ma-27	36	12	generalized	generalize	VERB
ma-27	36	13	nonexpansive	nonexpansive	ADJ
ma-27	36	14	mappings	mapping	NOUN
ma-27	36	15	is	be	AUX
ma-27	36	16	more	more	ADJ
ma-27	36	17	generalthan	generalthan	NOUN
ma-27	36	18	the	the	DET
ma-27	36	19	class	class	NOUN
ma-27	36	20	of	of	ADP
ma-27	36	21	nonexpansive	nonexpansive	ADJ
ma-27	36	22	mappings	mapping	NOUN
ma-27	36	23	and	and	CCONJ
ma-27	36	24	obtained	obtain	VERB
ma-27	36	25	some	some	DET
ma-27	36	26	fixed	fix	VERB
ma-27	36	27	points	point	NOUN
ma-27	36	28	and	and	CCONJ
ma-27	36	29	convergence	convergence	NOUN
ma-27	36	30	theorems	theorem	NOUN
ma-27	36	31	.	.	PUNCT
ma-27	37	1	definition	definition	NOUN
ma-27	37	2	1.3	1.3	NUM
ma-27	37	3	.	.	PUNCT
ma-27	38	1	a	a	DET
ma-27	38	2	mapping	mapping	NOUN
ma-27	38	3	t	t	NOUN
ma-27	38	4	:	:	PUNCT
ma-27	38	5	λ→	λ→	PUNCT
ma-27	38	6	λ	λ	NOUN
ma-27	38	7	is	be	AUX
ma-27	38	8	said	say	VERB
ma-27	38	9	to	to	PART
ma-27	38	10	be	be	AUX
ma-27	38	11	α	α	X
ma-27	38	12	-	-	NOUN
ma-27	38	13	nonexpansive	nonexpansive	ADJ
ma-27	38	14	if	if	SCONJ
ma-27	38	15	there	there	PRON
ma-27	38	16	exists	exist	VERB
ma-27	38	17	α	α	PRON
ma-27	38	18	∈	∈	PROPN
ma-27	39	1	[	[	X
ma-27	39	2	0	0	NUM
ma-27	39	3	,	,	PUNCT
ma-27	39	4	1	1	X
ma-27	39	5	)	)	PUNCT
ma-27	39	6	suchthat	suchthat	VERB
ma-27	39	7	‖t`−	‖t`−	PRON
ma-27	39	8	tζ‖2	tζ‖2	PROPN
ma-27	39	9	≤	≤	NUM
ma-27	39	10	α‖t`−	α‖t`−	NOUN
ma-27	39	11	ζ‖2	ζ‖2	ADP
ma-27	39	12	+	+	CCONJ
ma-27	40	1	α‖`−	α‖`−	PROPN
ma-27	40	2	tζ‖2	tζ‖2	PROPN
ma-27	40	3	+	+	CCONJ
ma-27	40	4	(	(	PUNCT
ma-27	40	5	1−	1−	NUM
ma-27	40	6	2α)‖`−	2α)‖`−	NUM
ma-27	40	7	ζ‖2	ζ‖2	NOUN
ma-27	40	8	,	,	PUNCT
ma-27	40	9	eur	eur	PROPN
ma-27	40	10	.	.	PUNCT
ma-27	41	1	j.	j.	PROPN
ma-27	41	2	math	math	PROPN
ma-27	41	3	.	.	PUNCT
ma-27	42	1	anal	anal	ADJ
ma-27	42	2	.	.	PUNCT
ma-27	43	1	1	1	NUM
ma-27	43	2	(	(	PUNCT
ma-27	43	3	2021	2021	NUM
ma-27	43	4	)	)	PUNCT
ma-27	44	1	108for	108for	NUM
ma-27	44	2	all	all	DET
ma-27	44	3	`	`	PUNCT
ma-27	44	4	,	,	PUNCT
ma-27	44	5	ζ	ζ	PROPN
ma-27	44	6	∈	∈	PROPN
ma-27	44	7	λ	λ	PROPN
ma-27	44	8	.	.	PUNCT
ma-27	45	1	the	the	DET
ma-27	45	2	class	class	NOUN
ma-27	45	3	of	of	ADP
ma-27	45	4	α	α	PROPN
ma-27	45	5	-	-	PUNCT
ma-27	45	6	nonexpansive	nonexpansive	ADJ
ma-27	45	7	mappings	mapping	NOUN
ma-27	45	8	was	be	AUX
ma-27	45	9	introduced	introduce	VERB
ma-27	45	10	in	in	ADP
ma-27	45	11	2011	2011	NUM
ma-27	45	12	by	by	ADP
ma-27	45	13	aoyama	aoyama	PROPN
ma-27	45	14	and	and	CCONJ
ma-27	45	15	kohsaka	kohsaka	ADV
ma-27	46	1	[	[	X
ma-27	46	2	3]as	3]as	NUM
ma-27	46	3	generalization	generalization	NOUN
ma-27	46	4	of	of	ADP
ma-27	46	5	nonexpansive	nonexpansive	ADJ
ma-27	46	6	mappings	mapping	NOUN
ma-27	46	7	and	and	CCONJ
ma-27	46	8	further	far	ADV
ma-27	46	9	obtained	obtain	VERB
ma-27	46	10	some	some	DET
ma-27	46	11	convergence	convergence	NOUN
ma-27	46	12	results	result	NOUN
ma-27	46	13	.	.	PUNCT
ma-27	47	1	itis	itis	NOUN
ma-27	47	2	worthy	worthy	ADJ
ma-27	47	3	noting	note	VERB
ma-27	47	4	that	that	SCONJ
ma-27	47	5	nonexpansive	nonexpansive	ADJ
ma-27	47	6	mappings	mapping	NOUN
ma-27	47	7	are	be	AUX
ma-27	47	8	continuous	continuous	ADJ
ma-27	47	9	on	on	ADP
ma-27	47	10	their	their	PRON
ma-27	47	11	domains	domain	NOUN
ma-27	47	12	,	,	PUNCT
ma-27	47	13	but	but	CCONJ
ma-27	47	14	suzuki	suzuki	NOUN
ma-27	47	15	-	-	ADJ
ma-27	47	16	typegeneralized	typegeneralize	VERB
ma-27	47	17	nonexpansive	nonexpansive	ADJ
ma-27	47	18	mappings	mapping	NOUN
ma-27	47	19	and	and	CCONJ
ma-27	47	20	α	α	NUM
ma-27	47	21	-	-	PUNCT
ma-27	47	22	nonexpansive	nonexpansive	ADJ
ma-27	47	23	mappings	mapping	NOUN
ma-27	47	24	need	need	AUX
ma-27	47	25	not	not	PART
ma-27	47	26	be	be	AUX
ma-27	47	27	continuous	continuous	ADJ
ma-27	47	28	(	(	PUNCT
ma-27	47	29	see[33	see[33	NOUN
ma-27	47	30	]	]	PUNCT
ma-27	47	31	)	)	PUNCT
ma-27	47	32	.	.	PUNCT
ma-27	48	1	clearly	clearly	ADV
ma-27	48	2	,	,	PUNCT
ma-27	48	3	every	every	DET
ma-27	48	4	nonexpansive	nonexpansive	ADJ
ma-27	48	5	mapping	mapping	NOUN
ma-27	48	6	is	be	AUX
ma-27	48	7	an	an	DET
ma-27	48	8	α	α	NOUN
ma-27	48	9	-	-	PUNCT
ma-27	48	10	nonexpansive	nonexpansive	ADJ
ma-27	48	11	mapping	mapping	NOUN
ma-27	48	12	with	with	ADP
ma-27	48	13	α	α	PROPN
ma-27	48	14	=	=	SYM
ma-27	48	15	0	0	PUNCT
ma-27	48	16	(	(	PUNCT
ma-27	48	17	i.e.	i.e.	X
ma-27	48	18	,	,	PUNCT
ma-27	48	19	0	0	NUM
ma-27	48	20	-	-	PUNCT
ma-27	48	21	nonexpansive	nonexpansive	ADJ
ma-27	48	22	)	)	PUNCT
ma-27	48	23	and	and	CCONJ
ma-27	48	24	every	every	DET
ma-27	48	25	α	α	PROPN
ma-27	48	26	-	-	PUNCT
ma-27	48	27	nonexpansive	nonexpansive	ADJ
ma-27	48	28	mapping	mapping	NOUN
ma-27	48	29	with	with	ADP
ma-27	48	30	a	a	DET
ma-27	48	31	nonempty	nonempty	ADV
ma-27	48	32	fixed	fix	VERB
ma-27	48	33	point	point	NOUN
ma-27	48	34	set	set	NOUN
ma-27	48	35	is	be	AUX
ma-27	48	36	quasinonex	quasinonex	ADV
ma-27	48	37	-	-	PUNCT
ma-27	48	38	pansive	pansive	ADJ
ma-27	48	39	.	.	PUNCT
ma-27	49	1	definition	definition	NOUN
ma-27	49	2	1.4	1.4	NUM
ma-27	49	3	.	.	PUNCT
ma-27	50	1	a	a	DET
ma-27	50	2	mapping	mapping	NOUN
ma-27	50	3	t	t	NOUN
ma-27	50	4	:	:	PUNCT
ma-27	50	5	λ	λ	X
ma-27	50	6	→	→	SYM
ma-27	50	7	λ	λ	PROPN
ma-27	50	8	is	be	AUX
ma-27	50	9	said	say	VERB
ma-27	50	10	to	to	PART
ma-27	50	11	be	be	AUX
ma-27	50	12	generalized	generalize	VERB
ma-27	50	13	α	α	PRON
ma-27	50	14	-	-	NOUN
ma-27	50	15	nonexpansive	nonexpansive	ADJ
ma-27	50	16	if	if	SCONJ
ma-27	50	17	there	there	PRON
ma-27	50	18	exists	exist	VERB
ma-27	50	19	α	α	PRON
ma-27	50	20	∈	∈	PROPN
ma-27	51	1	[	[	X
ma-27	51	2	0	0	NUM
ma-27	51	3	,	,	PUNCT
ma-27	51	4	1	1	NUM
ma-27	51	5	)	)	PUNCT
ma-27	51	6	such	such	ADJ
ma-27	51	7	that	that	SCONJ
ma-27	51	8	1	1	NUM
ma-27	51	9	2	2	NUM
ma-27	51	10	‖`−	‖`−	NUM
ma-27	51	11	t`‖	t`‖	NOUN
ma-27	51	12	≤	≤	NOUN
ma-27	51	13	‖`−	‖`−	NUM
ma-27	51	14	ζ‖	ζ‖	NOUN
ma-27	51	15	implies	imply	VERB
ma-27	51	16	‖t`−	‖t`−	PUNCT
ma-27	51	17	tζ‖	tζ‖	PROPN
ma-27	51	18	≤	≤	NUM
ma-27	51	19	α‖t`−	α‖t`−	ADJ
ma-27	51	20	ζ‖+	ζ‖+	PROPN
ma-27	51	21	α‖tζ	α‖tζ	PROPN
ma-27	51	22	−	−	NOUN
ma-27	51	23	`	`	PUNCT
ma-27	51	24	‖+	‖+	NUM
ma-27	51	25	(	(	PUNCT
ma-27	51	26	1−	1−	NUM
ma-27	51	27	2α)‖`−	2α)‖`−	NUM
ma-27	51	28	ζ‖	ζ‖	NOUN
ma-27	51	29	for	for	ADP
ma-27	51	30	all	all	DET
ma-27	51	31	`	`	PUNCT
ma-27	51	32	,	,	PUNCT
ma-27	51	33	ζ	ζ	PROPN
ma-27	51	34	∈	∈	PROPN
ma-27	51	35	λ	λ	NOUN
ma-27	51	36	.	.	PUNCT
ma-27	52	1	in	in	ADP
ma-27	52	2	[	[	X
ma-27	52	3	26	26	NUM
ma-27	52	4	]	]	PUNCT
ma-27	52	5	,	,	PUNCT
ma-27	52	6	pant	pant	NOUN
ma-27	52	7	and	and	CCONJ
ma-27	52	8	shukla	shukla	NOUN
ma-27	52	9	introduced	introduce	VERB
ma-27	52	10	a	a	DET
ma-27	52	11	wider	wide	ADJ
ma-27	52	12	class	class	NOUN
ma-27	52	13	of	of	ADP
ma-27	52	14	nonexpansive	nonexpansive	ADJ
ma-27	52	15	mappings	mapping	NOUN
ma-27	52	16	in	in	ADP
ma-27	52	17	banach	banach	ADV
ma-27	52	18	spacesknown	spacesknown	ADJ
ma-27	52	19	as	as	SCONJ
ma-27	52	20	generalized	generalize	VERB
ma-27	52	21	α	α	NUM
ma-27	52	22	-	-	PUNCT
ma-27	52	23	nonexpansive	nonexpansive	ADJ
ma-27	52	24	mappings	mapping	NOUN
ma-27	52	25	which	which	PRON
ma-27	52	26	contains	contain	VERB
ma-27	52	27	the	the	DET
ma-27	52	28	class	class	NOUN
ma-27	52	29	of	of	ADP
ma-27	52	30	suzuki	suzuki	PROPN
ma-27	52	31	generalizednonexpansive	generalizednonexpansive	PROPN
ma-27	52	32	mappings.it	mappings.it	X
ma-27	52	33	is	be	AUX
ma-27	52	34	well	well	ADV
ma-27	52	35	known	know	VERB
ma-27	52	36	that	that	SCONJ
ma-27	52	37	the	the	DET
ma-27	52	38	case	case	NOUN
ma-27	52	39	of	of	ADP
ma-27	52	40	contraction	contraction	NOUN
ma-27	52	41	mappings	mapping	NOUN
ma-27	52	42	is	be	AUX
ma-27	52	43	simple	simple	ADJ
ma-27	52	44	and	and	CCONJ
ma-27	52	45	carries	carry	VERB
ma-27	52	46	most	most	ADJ
ma-27	52	47	of	of	ADP
ma-27	52	48	the	the	DET
ma-27	52	49	goodbehavior	goodbehavior	NOUN
ma-27	52	50	using	use	VERB
ma-27	52	51	picard	picard	PROPN
ma-27	52	52	iterative	iterative	NOUN
ma-27	52	53	algorithm	algorithm	NOUN
ma-27	52	54	.	.	PUNCT
ma-27	53	1	but	but	CCONJ
ma-27	53	2	when	when	SCONJ
ma-27	53	3	we	we	PRON
ma-27	53	4	move	move	VERB
ma-27	53	5	to	to	ADP
ma-27	53	6	the	the	DET
ma-27	53	7	case	case	NOUN
ma-27	53	8	of	of	ADP
ma-27	53	9	nonexpansive	nonexpansive	ADJ
ma-27	53	10	mappings	mapping	NOUN
ma-27	53	11	,	,	PUNCT
ma-27	53	12	the	the	DET
ma-27	53	13	picard	picard	NOUN
ma-27	53	14	iterative	iterative	NOUN
ma-27	53	15	algorithm	algorithm	NOUN
ma-27	53	16	need	need	AUX
ma-27	53	17	not	not	PART
ma-27	53	18	converge	converge	VERB
ma-27	53	19	to	to	ADP
ma-27	53	20	a	a	DET
ma-27	53	21	fixed	fix	VERB
ma-27	53	22	point	point	NOUN
ma-27	53	23	.	.	PUNCT
ma-27	54	1	apparently	apparently	ADV
ma-27	54	2	,	,	PUNCT
ma-27	54	3	the	the	DET
ma-27	54	4	conclusion	conclusion	NOUN
ma-27	54	5	ofbanach	ofbanach	NOUN
ma-27	54	6	contraction	contraction	NOUN
ma-27	54	7	principle	principle	NOUN
ma-27	54	8	fails	fail	VERB
ma-27	54	9	for	for	ADP
ma-27	54	10	nonexpansive	nonexpansive	ADJ
ma-27	54	11	mappings	mapping	NOUN
ma-27	54	12	even	even	ADV
ma-27	54	13	if	if	SCONJ
ma-27	54	14	λ	λ	NOUN
ma-27	54	15	is	be	AUX
ma-27	54	16	compact	compact	ADJ
ma-27	54	17	.	.	PUNCT
ma-27	55	1	as	as	ADP
ma-27	55	2	an	an	DET
ma-27	55	3	example	example	NOUN
ma-27	55	4	,	,	PUNCT
ma-27	55	5	one	one	PRON
ma-27	55	6	may	may	AUX
ma-27	55	7	consider	consider	VERB
ma-27	55	8	a	a	DET
ma-27	55	9	geometric	geometric	ADJ
ma-27	55	10	rotation	rotation	NOUN
ma-27	55	11	on	on	ADP
ma-27	55	12	the	the	DET
ma-27	55	13	unit	unit	NOUN
ma-27	55	14	circle	circle	NOUN
ma-27	55	15	in	in	ADP
ma-27	55	16	the	the	DET
ma-27	55	17	plane	plane	NOUN
ma-27	55	18	r2.the	r2.the	DET
ma-27	55	19	limitation	limitation	NOUN
ma-27	55	20	of	of	ADP
ma-27	55	21	picard	picard	PROPN
ma-27	55	22	iterative	iterative	NOUN
ma-27	55	23	algorithm	algorithm	NOUN
ma-27	55	24	gave	give	VERB
ma-27	55	25	many	many	ADJ
ma-27	55	26	researchers	researcher	NOUN
ma-27	55	27	in	in	ADP
ma-27	55	28	nonlinear	nonlinear	ADJ
ma-27	55	29	analysis	analysis	NOUN
ma-27	55	30	the	the	DET
ma-27	55	31	roomto	roomto	NOUN
ma-27	55	32	construct	construct	VERB
ma-27	55	33	more	more	ADV
ma-27	55	34	efficient	efficient	ADJ
ma-27	55	35	iterative	iterative	NOUN
ma-27	55	36	algorithms	algorithm	NOUN
ma-27	55	37	for	for	ADP
ma-27	55	38	approximating	approximate	VERB
ma-27	55	39	the	the	DET
ma-27	55	40	fixed	fix	VERB
ma-27	55	41	points	point	NOUN
ma-27	55	42	of	of	ADP
ma-27	55	43	nonexpansivemappings	nonexpansivemapping	NOUN
ma-27	55	44	and	and	CCONJ
ma-27	55	45	other	other	ADJ
ma-27	55	46	classes	class	NOUN
ma-27	55	47	of	of	ADP
ma-27	55	48	mappings	mapping	NOUN
ma-27	55	49	which	which	PRON
ma-27	55	50	are	be	AUX
ma-27	55	51	more	more	ADV
ma-27	55	52	general	general	ADJ
ma-27	55	53	than	than	ADP
ma-27	55	54	the	the	DET
ma-27	55	55	class	class	NOUN
ma-27	55	56	of	of	ADP
ma-27	55	57	nonexpansivemappings.some	nonexpansivemappings.some	VERB
ma-27	55	58	notable	notable	ADJ
ma-27	55	59	iterative	iterative	NOUN
ma-27	55	60	algorithms	algorithm	NOUN
ma-27	55	61	in	in	ADP
ma-27	55	62	the	the	DET
ma-27	55	63	existing	exist	VERB
ma-27	55	64	literature	literature	NOUN
ma-27	55	65	are	be	AUX
ma-27	55	66	:	:	PUNCT
ma-27	55	67	mann	mann	PROPN
ma-27	56	1	[	[	X
ma-27	56	2	24	24	NUM
ma-27	56	3	]	]	PUNCT
ma-27	56	4	,	,	PUNCT
ma-27	56	5	ishikawa	ishikawa	PROPN
ma-27	57	1	[	[	X
ma-27	57	2	21	21	NUM
ma-27	57	3	]	]	PUNCT
ma-27	57	4	,	,	PUNCT
ma-27	57	5	noor[25	noor[25	PROPN
ma-27	57	6	]	]	PUNCT
ma-27	57	7	,	,	PUNCT
ma-27	57	8	argawal	argawal	VERB
ma-27	57	9	et	et	PROPN
ma-27	57	10	al	al	PROPN
ma-27	57	11	.	.	PUNCT
ma-27	58	1	[	[	X
ma-27	58	2	2	2	NUM
ma-27	58	3	]	]	PUNCT
ma-27	58	4	,	,	PUNCT
ma-27	58	5	abbas	abbas	PROPN
ma-27	58	6	and	and	CCONJ
ma-27	58	7	nazir	nazir	PROPN
ma-27	58	8	[	[	X
ma-27	58	9	1	1	NUM
ma-27	58	10	]	]	PUNCT
ma-27	58	11	,	,	PUNCT
ma-27	58	12	sp	sp	ADP
ma-27	58	13	[	[	X
ma-27	58	14	27	27	NUM
ma-27	58	15	]	]	PUNCT
ma-27	58	16	,	,	PUNCT
ma-27	58	17	s	s	X
ma-27	58	18	*	*	PUNCT
ma-27	59	1	[	[	X
ma-27	59	2	20	20	NUM
ma-27	59	3	]	]	PUNCT
ma-27	59	4	,	,	PUNCT
ma-27	59	5	cr	cr	X
ma-27	60	1	[	[	X
ma-27	60	2	12	12	NUM
ma-27	60	3	]	]	PUNCT
ma-27	60	4	,	,	PUNCT
ma-27	60	5	normal	normal	ADJ
ma-27	60	6	-	-	PUNCT
ma-27	60	7	s	s	X
ma-27	61	1	[	[	X
ma-27	61	2	28	28	NUM
ma-27	61	3	]	]	X
ma-27	61	4	,	,	PUNCT
ma-27	61	5	picard	picard	NOUN
ma-27	61	6	-	-	PUNCT
ma-27	61	7	s	s	X
ma-27	62	1	[	[	X
ma-27	62	2	17],thakur	17],thakur	NUM
ma-27	62	3	[	[	SYM
ma-27	62	4	36	36	NUM
ma-27	62	5	]	]	PUNCT
ma-27	62	6	,	,	PUNCT
ma-27	62	7	thakur	thakur	PROPN
ma-27	62	8	new	new	ADJ
ma-27	62	9	[	[	X
ma-27	62	10	37	37	NUM
ma-27	62	11	]	]	PUNCT
ma-27	62	12	,	,	PUNCT
ma-27	62	13	m	m	VERB
ma-27	62	14	[	[	X
ma-27	62	15	39	39	NUM
ma-27	62	16	]	]	PUNCT
ma-27	62	17	,	,	PUNCT
ma-27	62	18	m	m	VERB
ma-27	62	19	*	*	PUNCT
ma-27	63	1	[	[	X
ma-27	63	2	38	38	NUM
ma-27	63	3	]	]	PUNCT
ma-27	63	4	,	,	PUNCT
ma-27	63	5	garodia	garodia	NOUN
ma-27	63	6	and	and	CCONJ
ma-27	63	7	uddin	uddin	PROPN
ma-27	63	8	[	[	X
ma-27	63	9	16	16	NUM
ma-27	63	10	]	]	PUNCT
ma-27	63	11	,	,	PUNCT
ma-27	63	12	two	two	NUM
ma-27	63	13	-	-	PUNCT
ma-27	63	14	step	step	NOUN
ma-27	63	15	mann	mann	NOUN
ma-27	63	16	[	[	X
ma-27	63	17	35	35	NUM
ma-27	63	18	]	]	SYM
ma-27	63	19	iterativealgorithms	iterativealgorithm	NOUN
ma-27	63	20	and	and	CCONJ
ma-27	63	21	many	many	ADJ
ma-27	63	22	others.in	others.in	NUM
ma-27	63	23	2007	2007	NUM
ma-27	63	24	,	,	PUNCT
ma-27	63	25	the	the	DET
ma-27	63	26	s	s	NOUN
ma-27	63	27	iterative	iterative	NOUN
ma-27	63	28	algorithm	algorithm	NOUN
ma-27	63	29	was	be	AUX
ma-27	63	30	introduced	introduce	VERB
ma-27	63	31	by	by	ADP
ma-27	63	32	argawal	argawal	NOUN
ma-27	63	33	et	et	PROPN
ma-27	63	34	al	al	PROPN
ma-27	63	35	.	.	PUNCT
ma-27	64	1	[	[	X
ma-27	64	2	2	2	X
ma-27	64	3	]	]	PUNCT
ma-27	64	4	as	as	ADP
ma-27	64	5	follows:	follows:	PROPN
ma-27	64	6	ψ0	ψ0	NOUN
ma-27	64	7	∈	∈	PROPN
ma-27	64	8	λ	λ	PROPN
ma-27	64	9	,	,	PUNCT
ma-27	64	10	µs	µs	X
ma-27	64	11	=	=	PUNCT
ma-27	64	12	(	(	PUNCT
ma-27	64	13	1−	1−	NUM
ma-27	64	14	βs)ψs	βs)ψs	PUNCT
ma-27	64	15	+	+	NUM
ma-27	64	16	βstψs	βstψs	NOUN
ma-27	64	17	,	,	PUNCT
ma-27	64	18	ψs+1	ψs+1	X
ma-27	64	19	=	=	SYM
ma-27	64	20	(	(	PUNCT
ma-27	64	21	1−	1−	NUM
ma-27	64	22	δs)tψs	δs)tψs	PROPN
ma-27	64	23	+	+	CCONJ
ma-27	64	24	δstµs	δstµs	PROPN
ma-27	64	25	,	,	PUNCT
ma-27	64	26	∀s	∀s	PROPN
ma-27	64	27	≥	≥	NUM
ma-27	64	28	1	1	NUM
ma-27	64	29	,	,	PUNCT
ma-27	64	30	(	(	PUNCT
ma-27	64	31	1.3	1.3	NUM
ma-27	64	32	)	)	PUNCT
ma-27	64	33	where	where	SCONJ
ma-27	64	34	{	{	PUNCT
ma-27	64	35	δs	δs	NOUN
ma-27	64	36	}	}	PUNCT
ma-27	64	37	and	and	CCONJ
ma-27	64	38	{	{	PUNCT
ma-27	64	39	βs	βs	X
ma-27	64	40	}	}	PUNCT
ma-27	64	41	are	be	AUX
ma-27	64	42	sequences	sequence	NOUN
ma-27	64	43	in	in	ADP
ma-27	64	44	[	[	X
ma-27	64	45	0,1	0,1	NUM
ma-27	64	46	]	]	PUNCT
ma-27	64	47	.	.	PUNCT
ma-27	65	1	eur	eur	PROPN
ma-27	65	2	.	.	PUNCT
ma-27	66	1	j.	j.	PROPN
ma-27	66	2	math	math	PROPN
ma-27	66	3	.	.	PUNCT
ma-27	67	1	anal	anal	ADJ
ma-27	67	2	.	.	PUNCT
ma-27	68	1	1	1	NUM
ma-27	68	2	(	(	PUNCT
ma-27	68	3	2021	2021	NUM
ma-27	68	4	)	)	PUNCT
ma-27	68	5	109	109	NUM
ma-27	68	6	in	in	ADP
ma-27	68	7	2014	2014	NUM
ma-27	68	8	,	,	PUNCT
ma-27	68	9	the	the	DET
ma-27	68	10	picard	picard	NOUN
ma-27	68	11	-	-	PUNCT
ma-27	68	12	s	s	PART
ma-27	68	13	iterative	iterative	NOUN
ma-27	68	14	algorithm	algorithm	NOUN
ma-27	68	15	was	be	AUX
ma-27	68	16	introduced	introduce	VERB
ma-27	68	17	by	by	ADP
ma-27	68	18	gursoy	gursoy	NOUN
ma-27	68	19	and	and	CCONJ
ma-27	68	20	karakaya	karakaya	VERB
ma-27	69	1	[	[	X
ma-27	69	2	17	17	NUM
ma-27	69	3	]	]	PUNCT
ma-27	69	4	as	as	ADP
ma-27	69	5	follows:	follows:	PROPN
ma-27	69	6	u0	u0	PROPN
ma-27	69	7	∈	∈	PROPN
ma-27	69	8	λ	λ	PROPN
ma-27	69	9	,	,	PUNCT
ma-27	69	10	ϕs	ϕs	ADP
ma-27	69	11	=	=	SYM
ma-27	69	12	(	(	PUNCT
ma-27	69	13	1−	1−	NUM
ma-27	69	14	βs)us	βs)us	SYM
ma-27	69	15	+	+	NUM
ma-27	69	16	βstus	βstus	NOUN
ma-27	69	17	,	,	PUNCT
ma-27	69	18	%	%	NOUN
ma-27	69	19	s	s	PART
ma-27	69	20	=	=	X
ma-27	69	21	(	(	PUNCT
ma-27	69	22	1−	1−	NUM
ma-27	69	23	δs)tus	δs)tus	X
ma-27	69	24	+	+	CCONJ
ma-27	69	25	δstϕs	δstϕs	ADJ
ma-27	69	26	,	,	PUNCT
ma-27	69	27	us+1	us+1	PROPN
ma-27	69	28	=	=	PUNCT
ma-27	69	29	t%s	t%s	INTJ
ma-27	69	30	,	,	PUNCT
ma-27	69	31	∀s	∀s	PROPN
ma-27	69	32	≥	≥	NUM
ma-27	69	33	1	1	NUM
ma-27	69	34	,	,	PUNCT
ma-27	69	35	(	(	PUNCT
ma-27	69	36	1.4	1.4	NUM
ma-27	69	37	)	)	PUNCT
ma-27	69	38	where	where	SCONJ
ma-27	69	39	{	{	PUNCT
ma-27	69	40	δs	δs	NOUN
ma-27	69	41	}	}	PUNCT
ma-27	69	42	and	and	CCONJ
ma-27	69	43	{	{	PUNCT
ma-27	69	44	βs	βs	X
ma-27	69	45	}	}	PUNCT
ma-27	69	46	are	be	AUX
ma-27	69	47	sequences	sequence	NOUN
ma-27	69	48	in	in	ADP
ma-27	69	49	[	[	X
ma-27	69	50	0,1	0,1	NUM
ma-27	69	51	]	]	PUNCT
ma-27	69	52	.	.	PUNCT
ma-27	70	1	the	the	DET
ma-27	70	2	authors	author	NOUN
ma-27	70	3	showed	show	VERB
ma-27	70	4	with	with	ADP
ma-27	70	5	the	the	DET
ma-27	70	6	aid	aid	NOUN
ma-27	70	7	of	of	ADP
ma-27	70	8	an	an	DET
ma-27	70	9	example	example	NOUN
ma-27	70	10	thatpicard	thatpicard	ADJ
ma-27	70	11	-	-	PUNCT
ma-27	70	12	s	s	NOUN
ma-27	70	13	iterative	iterative	NOUN
ma-27	70	14	algorithm	algorithm	NOUN
ma-27	70	15	(	(	PUNCT
ma-27	70	16	1.4	1.4	NUM
ma-27	70	17	)	)	PUNCT
ma-27	70	18	converges	converge	NOUN
ma-27	70	19	at	at	ADP
ma-27	70	20	a	a	DET
ma-27	70	21	rate	rate	NOUN
ma-27	70	22	faster	fast	ADV
ma-27	70	23	than	than	ADP
ma-27	70	24	all	all	PRON
ma-27	70	25	of	of	ADP
ma-27	70	26	picard	picard	NOUN
ma-27	70	27	,	,	PUNCT
ma-27	70	28	mann	mann	PROPN
ma-27	70	29	,	,	PUNCT
ma-27	70	30	ishikawa	ishikawa	PROPN
ma-27	70	31	,	,	PUNCT
ma-27	70	32	noor	noor	PROPN
ma-27	70	33	,	,	PUNCT
ma-27	70	34	sp	sp	NOUN
ma-27	70	35	,	,	PUNCT
ma-27	70	36	cr	cr	PROPN
ma-27	70	37	,	,	PUNCT
ma-27	70	38	s	s	PROPN
ma-27	70	39	,	,	PUNCT
ma-27	70	40	s	s	NOUN
ma-27	70	41	*	*	NOUN
ma-27	70	42	,	,	PUNCT
ma-27	70	43	abbas	abbas	PROPN
ma-27	70	44	and	and	CCONJ
ma-27	70	45	nazir	nazir	PROPN
ma-27	70	46	,	,	PUNCT
ma-27	70	47	normal	normal	ADJ
ma-27	70	48	-	-	PUNCT
ma-27	70	49	s	s	X
ma-27	70	50	and	and	CCONJ
ma-27	70	51	two	two	NUM
ma-27	70	52	-	-	PUNCT
ma-27	70	53	step	step	NOUN
ma-27	70	54	mann	mann	PROPN
ma-27	70	55	iterative	iterative	NOUN
ma-27	70	56	algorithms	algorithm	NOUN
ma-27	70	57	forcontraction	forcontraction	NOUN
ma-27	70	58	mappings.in	mappings.in	PROPN
ma-27	70	59	2016	2016	NUM
ma-27	70	60	,	,	PUNCT
ma-27	70	61	thakur	thakur	PROPN
ma-27	70	62	et	et	PROPN
ma-27	70	63	al	al	PROPN
ma-27	70	64	.	.	PUNCT
ma-27	71	1	[	[	X
ma-27	71	2	37	37	NUM
ma-27	71	3	]	]	PUNCT
ma-27	71	4	introduced	introduce	VERB
ma-27	71	5	the	the	DET
ma-27	71	6	following	follow	VERB
ma-27	71	7	three	three	NUM
ma-27	71	8	steps	step	NOUN
ma-27	71	9	iterative	iterative	NOUN
ma-27	71	10	algorithm:	algorithm:	NOUN
ma-27	71	11	ω0	ω0	PROPN
ma-27	71	12	∈	∈	PROPN
ma-27	71	13	λ	λ	NOUN
ma-27	71	14	,	,	PUNCT
ma-27	71	15	ρs	ρs	ADV
ma-27	71	16	=	=	PUNCT
ma-27	71	17	(	(	PUNCT
ma-27	71	18	1−	1−	NUM
ma-27	71	19	βs)ωs	βs)ωs	PUNCT
ma-27	71	20	+	+	NUM
ma-27	71	21	βstωs	βstωs	NOUN
ma-27	71	22	,	,	PUNCT
ma-27	71	23	vs	vs	ADP
ma-27	71	24	=	=	PROPN
ma-27	71	25	t	t	PROPN
ma-27	71	26	(	(	PUNCT
ma-27	71	27	(	(	PUNCT
ma-27	71	28	1−	1−	NUM
ma-27	71	29	δs)ωs	δs)ωs	PUNCT
ma-27	71	30	+	+	NUM
ma-27	71	31	δsρs	δsρs	ADJ
ma-27	71	32	)	)	PUNCT
ma-27	71	33	,	,	PUNCT
ma-27	71	34	ωs+1	ωs+1	NUM
ma-27	72	1	=	=	NOUN
ma-27	72	2	tvs	tv	NOUN
ma-27	72	3	,	,	PUNCT
ma-27	72	4	∀s	∀s	X
ma-27	72	5	≥	≥	NUM
ma-27	72	6	1	1	NUM
ma-27	72	7	,	,	PUNCT
ma-27	72	8	(	(	PUNCT
ma-27	72	9	1.5	1.5	NUM
ma-27	72	10	)	)	PUNCT
ma-27	72	11	where	where	SCONJ
ma-27	72	12	{	{	PUNCT
ma-27	72	13	δs	δs	NOUN
ma-27	72	14	}	}	PUNCT
ma-27	72	15	and	and	CCONJ
ma-27	72	16	{	{	PUNCT
ma-27	72	17	βs	βs	X
ma-27	72	18	}	}	PUNCT
ma-27	72	19	are	be	AUX
ma-27	72	20	sequences	sequence	NOUN
ma-27	72	21	in	in	ADP
ma-27	72	22	[	[	X
ma-27	72	23	0,1	0,1	NUM
ma-27	72	24	]	]	PUNCT
ma-27	72	25	.	.	PUNCT
ma-27	73	1	with	with	ADP
ma-27	73	2	the	the	DET
ma-27	73	3	help	help	NOUN
ma-27	73	4	of	of	ADP
ma-27	73	5	numerical	numerical	ADJ
ma-27	73	6	example	example	NOUN
ma-27	73	7	,	,	PUNCT
ma-27	73	8	they	they	PRON
ma-27	73	9	proved	prove	VERB
ma-27	73	10	that(1.5	that(1.5	NOUN
ma-27	73	11	)	)	PUNCT
ma-27	73	12	is	be	AUX
ma-27	73	13	faster	fast	ADJ
ma-27	73	14	than	than	ADP
ma-27	73	15	picard	picard	NOUN
ma-27	73	16	,	,	PUNCT
ma-27	73	17	mann	mann	PROPN
ma-27	73	18	,	,	PUNCT
ma-27	73	19	ishikawa	ishikawa	PROPN
ma-27	73	20	,	,	PUNCT
ma-27	73	21	agarwal	agarwal	PROPN
ma-27	73	22	,	,	PUNCT
ma-27	73	23	noor	noor	PROPN
ma-27	73	24	and	and	CCONJ
ma-27	73	25	abbas	abbas	PROPN
ma-27	73	26	iterative	iterative	NOUN
ma-27	73	27	algorithm	algorithm	NOUN
ma-27	73	28	for	for	ADP
ma-27	73	29	suzukigeneralized	suzukigeneralize	VERB
ma-27	73	30	nonexpansive	nonexpansive	ADJ
ma-27	73	31	mappings.in	mappings.in	PROPN
ma-27	73	32	2018	2018	NUM
ma-27	73	33	,	,	PUNCT
ma-27	73	34	ullah	ullah	PROPN
ma-27	73	35	and	and	CCONJ
ma-27	73	36	arshad	arshad	VERB
ma-27	74	1	[	[	X
ma-27	74	2	39	39	NUM
ma-27	74	3	]	]	PUNCT
ma-27	74	4	introduced	introduce	VERB
ma-27	74	5	m	m	PROPN
ma-27	74	6	iterative	iterative	NOUN
ma-27	74	7	algorithm	algorithm	NOUN
ma-27	74	8	as	as	ADP
ma-27	74	9	follows:	follows:	PROPN
ma-27	74	10	m0	m0	PROPN
ma-27	74	11	∈	∈	PROPN
ma-27	74	12	λ	λ	PROPN
ma-27	74	13	,	,	PUNCT
ma-27	74	14	cs	cs	X
ma-27	74	15	=	=	SYM
ma-27	74	16	(	(	PUNCT
ma-27	74	17	1−	1−	NUM
ma-27	74	18	δs)ms	δs)ms	PUNCT
ma-27	74	19	+	+	PUNCT
ma-27	74	20	δstms	δstms	NOUN
ma-27	74	21	,	,	PUNCT
ma-27	74	22	ds	ds	ADJ
ma-27	74	23	=	=	SYM
ma-27	74	24	tcs	tcs	NOUN
ma-27	74	25	,	,	PUNCT
ma-27	74	26	ms+1	ms+1	PROPN
ma-27	74	27	=	=	SYM
ma-27	74	28	tds	tds	PROPN
ma-27	74	29	,	,	PUNCT
ma-27	74	30	∀s	∀s	PROPN
ma-27	74	31	≥	≥	NUM
ma-27	74	32	1	1	NUM
ma-27	74	33	,	,	PUNCT
ma-27	74	34	(	(	PUNCT
ma-27	74	35	1.6	1.6	NUM
ma-27	74	36	)	)	PUNCT
ma-27	74	37	where	where	SCONJ
ma-27	74	38	{	{	PUNCT
ma-27	74	39	δs	δs	NOUN
ma-27	74	40	}	}	PUNCT
ma-27	74	41	is	be	AUX
ma-27	74	42	a	a	DET
ma-27	74	43	sequence	sequence	NOUN
ma-27	74	44	in	in	ADP
ma-27	74	45	[	[	X
ma-27	74	46	0,1	0,1	NUM
ma-27	74	47	]	]	PUNCT
ma-27	74	48	.	.	PUNCT
ma-27	75	1	numerically	numerically	ADV
ma-27	75	2	they	they	PRON
ma-27	75	3	showed	show	VERB
ma-27	75	4	that	that	SCONJ
ma-27	75	5	m	m	VERB
ma-27	75	6	iterative	iterative	ADJ
ma-27	75	7	algorithm	algorithm	NOUN
ma-27	75	8	(	(	PUNCT
ma-27	75	9	1.2)converges	1.2)converge	NOUN
ma-27	75	10	faster	fast	ADV
ma-27	75	11	than	than	ADP
ma-27	75	12	s	s	NOUN
ma-27	75	13	iterative	iterative	NOUN
ma-27	75	14	algorithm	algorithm	NOUN
ma-27	75	15	(	(	PUNCT
ma-27	75	16	1.3	1.3	NUM
ma-27	75	17	)	)	PUNCT
ma-27	75	18	and	and	CCONJ
ma-27	75	19	picard	picard	NOUN
ma-27	75	20	-	-	PUNCT
ma-27	75	21	s	s	PART
ma-27	75	22	iterative	iterative	NOUN
ma-27	75	23	algorithm	algorithm	NOUN
ma-27	75	24	(	(	PUNCT
ma-27	75	25	1.4	1.4	NUM
ma-27	75	26	)	)	PUNCT
ma-27	75	27	for	for	ADP
ma-27	75	28	suzukigeneralized	suzukigeneralize	VERB
ma-27	75	29	nonexpansive	nonexpansive	ADJ
ma-27	75	30	mappings	mapping	NOUN
ma-27	75	31	.	.	PUNCT
ma-27	76	1	also	also	ADV
ma-27	76	2	,	,	PUNCT
ma-27	76	3	they	they	PRON
ma-27	76	4	noted	note	VERB
ma-27	76	5	that	that	SCONJ
ma-27	76	6	the	the	DET
ma-27	76	7	speed	speed	NOUN
ma-27	76	8	of	of	ADP
ma-27	76	9	convergence	convergence	NOUN
ma-27	76	10	of	of	ADP
ma-27	76	11	picard	picard	NOUN
ma-27	76	12	-	-	PUNCT
ma-27	76	13	siterative	siterative	ADJ
ma-27	76	14	algorithm	algorithm	NOUN
ma-27	76	15	(	(	PUNCT
ma-27	76	16	1.4	1.4	NUM
ma-27	76	17	)	)	PUNCT
ma-27	76	18	and	and	CCONJ
ma-27	76	19	thakur	thakur	PROPN
ma-27	76	20	iterative	iterative	NOUN
ma-27	76	21	algorithm	algorithm	NOUN
ma-27	76	22	(	(	PUNCT
ma-27	76	23	1.5	1.5	NUM
ma-27	76	24	)	)	PUNCT
ma-27	76	25	are	be	AUX
ma-27	76	26	almost	almost	ADV
ma-27	76	27	same.motivated	same.motivate	VERB
ma-27	76	28	by	by	ADP
ma-27	76	29	the	the	DET
ma-27	76	30	above	above	ADJ
ma-27	76	31	results	result	NOUN
ma-27	76	32	,	,	PUNCT
ma-27	76	33	in	in	ADP
ma-27	76	34	this	this	DET
ma-27	76	35	paper	paper	NOUN
ma-27	76	36	,	,	PUNCT
ma-27	76	37	we	we	PRON
ma-27	76	38	construct	construct	VERB
ma-27	76	39	a	a	DET
ma-27	76	40	new	new	ADJ
ma-27	76	41	four	four	NUM
ma-27	76	42	step	step	NOUN
ma-27	76	43	iterative	iterative	NOUN
ma-27	76	44	algorithmwhich	algorithmwhich	PROPN
ma-27	76	45	outperforms	outperform	VERB
ma-27	76	46	the	the	DET
ma-27	76	47	iterative	iterative	ADJ
ma-27	76	48	algorithm	algorithm	NOUN
ma-27	76	49	(	(	PUNCT
ma-27	76	50	1.6	1.6	NUM
ma-27	76	51	)	)	PUNCT
ma-27	76	52	in	in	ADP
ma-27	76	53	terms	term	NOUN
ma-27	76	54	of	of	ADP
ma-27	76	55	convergence	convergence	NOUN
ma-27	76	56	rate	rate	NOUN
ma-27	76	57	for	for	ADP
ma-27	76	58	almost	almost	ADV
ma-27	76	59	contractionmappings	contractionmapping	NOUN
ma-27	76	60	as	as	SCONJ
ma-27	76	61	follows	follow	VERB
ma-27	76	62	:	:	PUNCT
ma-27	76	63			NUM
ma-27	77	1	`	`	PUNCT
ma-27	77	2	0	0	NUM
ma-27	77	3	∈	∈	PROPN
ma-27	77	4	λ	λ	PROPN
ma-27	77	5	,	,	PUNCT
ma-27	77	6	gs	gs	NOUN
ma-27	77	7	=	=	PUNCT
ma-27	77	8	(	(	PUNCT
ma-27	77	9	1−	1−	NUM
ma-27	77	10	βs)`s	βs)`s	NOUN
ma-27	78	1	+	+	CCONJ
ma-27	78	2	βst`s	βst`s	PROPN
ma-27	78	3	,	,	PUNCT
ma-27	78	4	ws	ws	NOUN
ma-27	78	5	=	=	SYM
ma-27	78	6	(	(	PUNCT
ma-27	78	7	1−	1−	NUM
ma-27	78	8	δs)t`s	δs)t`s	NOUN
ma-27	78	9	+	+	CCONJ
ma-27	78	10	δstgs	δstgs	NOUN
ma-27	78	11	,	,	PUNCT
ma-27	78	12	ζs	ζs	ADP
ma-27	78	13	=	=	SYM
ma-27	78	14	tws	tws	PROPN
ma-27	78	15	,	,	PUNCT
ma-27	78	16	`	`	PUNCT
ma-27	78	17	s+1	s+1	PRON
ma-27	78	18	=	=	PUNCT
ma-27	78	19	tζs	tζs	NOUN
ma-27	78	20	,	,	PUNCT
ma-27	78	21	∀s	∀s	PROPN
ma-27	78	22	≥	≥	NUM
ma-27	78	23	1	1	NUM
ma-27	78	24	,	,	PUNCT
ma-27	78	25	(	(	PUNCT
ma-27	78	26	1.7	1.7	NUM
ma-27	78	27	)	)	PUNCT
ma-27	78	28	where	where	SCONJ
ma-27	78	29	{	{	PUNCT
ma-27	78	30	δs	δs	NOUN
ma-27	78	31	}	}	PUNCT
ma-27	78	32	and	and	CCONJ
ma-27	78	33	{	{	PUNCT
ma-27	78	34	βs	βs	X
ma-27	78	35	}	}	PUNCT
ma-27	78	36	are	be	AUX
ma-27	78	37	sequences	sequence	NOUN
ma-27	78	38	in	in	ADP
ma-27	78	39	[	[	X
ma-27	78	40	0,1	0,1	NUM
ma-27	78	41	]	]	PUNCT
ma-27	78	42	.	.	PUNCT
ma-27	79	1	eur	eur	PROPN
ma-27	79	2	.	.	PUNCT
ma-27	80	1	j.	j.	PROPN
ma-27	80	2	math	math	PROPN
ma-27	80	3	.	.	PUNCT
ma-27	81	1	anal	anal	ADJ
ma-27	81	2	.	.	PUNCT
ma-27	82	1	1	1	NUM
ma-27	82	2	(	(	PUNCT
ma-27	82	3	2021	2021	NUM
ma-27	82	4	)	)	PUNCT
ma-27	83	1	110the	110the	DET
ma-27	83	2	purpose	purpose	NOUN
ma-27	83	3	of	of	ADP
ma-27	83	4	this	this	DET
ma-27	83	5	paper	paper	NOUN
ma-27	83	6	is	be	AUX
ma-27	83	7	to	to	PART
ma-27	83	8	prove	prove	VERB
ma-27	83	9	analytically	analytically	ADV
ma-27	83	10	that	that	SCONJ
ma-27	83	11	our	our	PRON
ma-27	83	12	new	new	ADJ
ma-27	83	13	iterative	iterative	NOUN
ma-27	83	14	algorithm	algorithm	NOUN
ma-27	83	15	convergesfaster	convergesfaster	NOUN
ma-27	83	16	than	than	ADP
ma-27	83	17	(	(	PUNCT
ma-27	83	18	1.6	1.6	NUM
ma-27	83	19	)	)	PUNCT
ma-27	83	20	for	for	ADP
ma-27	83	21	almost	almost	ADV
ma-27	83	22	contraction	contraction	NOUN
ma-27	83	23	mappings	mapping	NOUN
ma-27	83	24	.	.	PUNCT
ma-27	84	1	in	in	ADP
ma-27	84	2	order	order	NOUN
ma-27	84	3	to	to	PART
ma-27	84	4	support	support	VERB
ma-27	84	5	our	our	PRON
ma-27	84	6	analytical	analytical	ADJ
ma-27	84	7	proof	proof	NOUN
ma-27	84	8	,	,	PUNCT
ma-27	84	9	weuse	weuse	VERB
ma-27	84	10	some	some	DET
ma-27	84	11	new	new	ADJ
ma-27	84	12	examples	example	NOUN
ma-27	84	13	to	to	PART
ma-27	84	14	show	show	VERB
ma-27	84	15	that	that	SCONJ
ma-27	84	16	our	our	PRON
ma-27	84	17	iterative	iterative	NOUN
ma-27	84	18	algorithm	algorithm	NOUN
ma-27	84	19	(	(	PUNCT
ma-27	84	20	1.7	1.7	NUM
ma-27	84	21	)	)	PUNCT
ma-27	84	22	converges	converge	VERB
ma-27	84	23	faster	fast	ADV
ma-27	84	24	than	than	ADP
ma-27	84	25	(	(	PUNCT
ma-27	84	26	1.6	1.6	NUM
ma-27	84	27	)	)	PUNCT
ma-27	84	28	anda	anda	PROPN
ma-27	84	29	number	number	NOUN
ma-27	84	30	of	of	ADP
ma-27	84	31	other	other	ADJ
ma-27	84	32	leading	leading	ADJ
ma-27	84	33	iterative	iterative	NOUN
ma-27	84	34	algorithms	algorithm	NOUN
ma-27	84	35	in	in	ADP
ma-27	84	36	the	the	DET
ma-27	84	37	literature	literature	NOUN
ma-27	84	38	.	.	PUNCT
ma-27	85	1	we	we	PRON
ma-27	85	2	also	also	ADV
ma-27	85	3	prove	prove	VERB
ma-27	85	4	the	the	DET
ma-27	85	5	weak	weak	ADJ
ma-27	85	6	andstrong	andstrong	NOUN
ma-27	85	7	convergence	convergence	NOUN
ma-27	85	8	of	of	ADP
ma-27	85	9	new	new	ADJ
ma-27	85	10	iterative	iterative	NOUN
ma-27	85	11	algorithm	algorithm	NOUN
ma-27	85	12	(	(	PUNCT
ma-27	85	13	1.7	1.7	NUM
ma-27	85	14	)	)	PUNCT
ma-27	85	15	to	to	ADP
ma-27	85	16	the	the	DET
ma-27	85	17	fixed	fix	VERB
ma-27	85	18	points	point	NOUN
ma-27	85	19	generalized	generalize	VERB
ma-27	85	20	α	α	NOUN
ma-27	85	21	-	-	NOUN
ma-27	85	22	nonexpansivemappings	nonexpansivemapping	NOUN
ma-27	85	23	in	in	ADP
ma-27	85	24	a	a	DET
ma-27	85	25	uniformly	uniformly	ADJ
ma-27	85	26	convex	convex	NOUN
ma-27	85	27	banach	banach	NOUN
ma-27	85	28	spaces	space	VERB
ma-27	85	29	.	.	PUNCT
ma-27	86	1	furthermore	furthermore	ADV
ma-27	86	2	,	,	PUNCT
ma-27	86	3	we	we	PRON
ma-27	86	4	show	show	VERB
ma-27	86	5	that	that	SCONJ
ma-27	86	6	our	our	PRON
ma-27	86	7	new	new	ADJ
ma-27	86	8	iterativealgorithm	iterativealgorithm	NOUN
ma-27	86	9	is	be	AUX
ma-27	86	10	t	t	NOUN
ma-27	86	11	-stable	-stable	ADJ
ma-27	86	12	and	and	CCONJ
ma-27	86	13	data	datum	NOUN
ma-27	86	14	dependent	dependent	ADJ
ma-27	86	15	.	.	PUNCT
ma-27	87	1	finally	finally	ADV
ma-27	87	2	,	,	PUNCT
ma-27	87	3	we	we	PRON
ma-27	87	4	use	use	VERB
ma-27	87	5	our	our	PRON
ma-27	87	6	new	new	ADJ
ma-27	87	7	iterative	iterative	NOUN
ma-27	87	8	algorithm	algorithm	NOUN
ma-27	87	9	(	(	PUNCT
ma-27	87	10	1.7	1.7	NUM
ma-27	87	11	)	)	PUNCT
ma-27	87	12	tosolve	tosolve	VERB
ma-27	87	13	a	a	DET
ma-27	87	14	constrained	constrain	VERB
ma-27	87	15	convex	convex	NOUN
ma-27	87	16	minimization	minimization	NOUN
ma-27	87	17	problem	problem	NOUN
ma-27	87	18	and	and	CCONJ
ma-27	87	19	a	a	DET
ma-27	87	20	split	split	NOUN
ma-27	87	21	feasibility	feasibility	NOUN
ma-27	87	22	problem	problem	NOUN
ma-27	87	23	.	.	PUNCT
ma-27	88	1	2	2	X
ma-27	88	2	.	.	NUM
ma-27	88	3	preliminaries	preliminary	NOUN
ma-27	88	4	the	the	DET
ma-27	88	5	following	follow	VERB
ma-27	88	6	definitions	definition	NOUN
ma-27	88	7	,	,	PUNCT
ma-27	88	8	propositions	proposition	NOUN
ma-27	88	9	and	and	CCONJ
ma-27	88	10	lemmas	lemma	NOUN
ma-27	88	11	will	will	AUX
ma-27	88	12	be	be	AUX
ma-27	88	13	useful	useful	ADJ
ma-27	88	14	in	in	ADP
ma-27	88	15	proving	prove	VERB
ma-27	88	16	our	our	PRON
ma-27	88	17	main	main	ADJ
ma-27	88	18	results	result	NOUN
ma-27	88	19	.	.	PUNCT
ma-27	89	1	definition	definition	NOUN
ma-27	89	2	2.1	2.1	NUM
ma-27	89	3	.	.	PUNCT
ma-27	90	1	a	a	DET
ma-27	90	2	banach	banach	NOUN
ma-27	90	3	space	space	NOUN
ma-27	90	4	ω	ω	PROPN
ma-27	90	5	is	be	AUX
ma-27	90	6	said	say	VERB
ma-27	90	7	to	to	PART
ma-27	90	8	be	be	AUX
ma-27	90	9	uniformly	uniformly	ADV
ma-27	90	10	convex	convex	ADJ
ma-27	90	11	if	if	SCONJ
ma-27	90	12	for	for	ADP
ma-27	90	13	each	each	DET
ma-27	90	14	ε	ε	PROPN
ma-27	90	15	∈	∈	PROPN
ma-27	90	16	(	(	PUNCT
ma-27	90	17	0	0	NUM
ma-27	90	18	,	,	PUNCT
ma-27	90	19	2	2	NUM
ma-27	90	20	]	]	PUNCT
ma-27	90	21	,	,	PUNCT
ma-27	90	22	there	there	PRON
ma-27	90	23	exists	exist	VERB
ma-27	90	24	δ	δ	PROPN
ma-27	90	25	>	>	X
ma-27	90	26	0	0	NUM
ma-27	91	1	such	such	ADJ
ma-27	91	2	that	that	PRON
ma-27	91	3	for	for	ADP
ma-27	91	4	`	`	PUNCT
ma-27	91	5	,	,	PUNCT
ma-27	91	6	ζ	ζ	PROPN
ma-27	91	7	∈	∈	PROPN
ma-27	91	8	ω	ω	X
ma-27	91	9	satisfying	satisfy	VERB
ma-27	91	10	‖`‖	‖`‖	NUM
ma-27	91	11	≤	≤	NUM
ma-27	91	12	1	1	NUM
ma-27	91	13	,	,	PUNCT
ma-27	91	14	‖ζ‖	‖ζ‖	PROPN
ma-27	91	15	≤	≤	ADV
ma-27	91	16	1	1	NUM
ma-27	91	17	and	and	CCONJ
ma-27	91	18	‖`−	‖`−	NUM
ma-27	91	19	ζ‖	ζ‖	NOUN
ma-27	91	20	>	>	X
ma-27	91	21	ε	ε	PROPN
ma-27	91	22	,	,	PUNCT
ma-27	91	23	we	we	PRON
ma-27	91	24	have	have	VERB
ma-27	91	25	∥∥∥	∥∥∥	NUM
ma-27	91	26	`	`	PUNCT
ma-27	91	27	+	+	ADJ
ma-27	91	28	ζ2	ζ2	NOUN
ma-27	91	29	∥∥∥	∥∥∥	PROPN
ma-27	91	30	<	<	X
ma-27	91	31	1−	1−	NUM
ma-27	91	32	δ	δ	PROPN
ma-27	91	33	.	.	PUNCT
ma-27	92	1	definition	definition	NOUN
ma-27	92	2	2.2	2.2	NUM
ma-27	92	3	.	.	PUNCT
ma-27	93	1	a	a	DET
ma-27	93	2	banach	banach	NOUN
ma-27	93	3	space	space	NOUN
ma-27	93	4	ω	ω	PROPN
ma-27	93	5	is	be	AUX
ma-27	93	6	said	say	VERB
ma-27	93	7	to	to	PART
ma-27	93	8	satisfy	satisfy	VERB
ma-27	93	9	opial	opial	PROPN
ma-27	93	10	’s	’s	PART
ma-27	93	11	condition	condition	NOUN
ma-27	93	12	if	if	SCONJ
ma-27	93	13	for	for	ADP
ma-27	93	14	any	any	DET
ma-27	93	15	sequence	sequence	NOUN
ma-27	93	16	{	{	PUNCT
ma-27	93	17	`	`	PUNCT
ma-27	93	18	s	s	X
ma-27	93	19	}	}	PUNCT
ma-27	93	20	in	in	ADP
ma-27	93	21	ω	ω	NUM
ma-27	93	22	which	which	PRON
ma-27	93	23	converges	converge	VERB
ma-27	93	24	weakly	weakly	ADJ
ma-27	93	25	to	to	ADP
ma-27	93	26	`	`	PUNCT
ma-27	93	27	∈	∈	PROPN
ma-27	93	28	ω	ω	PROPN
ma-27	93	29	implies	imply	VERB
ma-27	93	30	lim	lim	PROPN
ma-27	93	31	sup	sup	NOUN
ma-27	93	32	s→∞	s→∞	NUM
ma-27	93	33	‖`s	‖`s	PRON
ma-27	93	34	−	−	PUNCT
ma-27	93	35	`	`	PUNCT
ma-27	93	36	‖	‖	PROPN
ma-27	93	37	<	<	X
ma-27	93	38	lim	lim	PROPN
ma-27	93	39	sup	sup	NOUN
ma-27	93	40	s→∞	s→∞	NUM
ma-27	93	41	‖`s	‖`s	PUNCT
ma-27	94	1	−	−	PROPN
ma-27	94	2	ζ‖	ζ‖	NOUN
ma-27	94	3	,	,	PUNCT
ma-27	94	4	∀	∀	NOUN
ma-27	94	5	ζ	ζ	NOUN
ma-27	94	6	∈	∈	PROPN
ma-27	94	7	ω	ω	NOUN
ma-27	94	8	with	with	ADP
ma-27	94	9	ζ	ζ	PROPN
ma-27	94	10	6=	6=	NUM
ma-27	94	11	`	`	PUNCT
ma-27	94	12	.	.	PUNCT
ma-27	95	1	definition	definition	NOUN
ma-27	95	2	2.3	2.3	NUM
ma-27	95	3	.	.	PUNCT
ma-27	96	1	let	let	VERB
ma-27	96	2	{	{	PUNCT
ma-27	96	3	`	`	PUNCT
ma-27	96	4	s	s	AUX
ma-27	96	5	}	}	PUNCT
ma-27	96	6	be	be	AUX
ma-27	96	7	a	a	DET
ma-27	96	8	bounded	bounded	ADJ
ma-27	96	9	sequence	sequence	NOUN
ma-27	96	10	in	in	ADP
ma-27	96	11	ω	ω	PROPN
ma-27	96	12	.	.	PUNCT
ma-27	97	1	for	for	ADP
ma-27	97	2	`	`	PUNCT
ma-27	97	3	∈	∈	PROPN
ma-27	97	4	λ	λ	PROPN
ma-27	97	5	⊂	⊂	PROPN
ma-27	97	6	ω	ω	PROPN
ma-27	97	7	,	,	PUNCT
ma-27	97	8	we	we	PRON
ma-27	97	9	put	put	VERB
ma-27	97	10	r	r	NOUN
ma-27	97	11	(	(	PUNCT
ma-27	97	12	`	`	PUNCT
ma-27	97	13	,	,	PUNCT
ma-27	97	14	{	{	PUNCT
ma-27	97	15	`	`	PUNCT
ma-27	97	16	s	s	X
ma-27	97	17	}	}	PUNCT
ma-27	97	18	)	)	PUNCT
ma-27	98	1	=	=	SYM
ma-27	98	2	lim	lim	PROPN
ma-27	98	3	sup	sup	NOUN
ma-27	98	4	s→∞	s→∞	NUM
ma-27	98	5	‖`s	‖`s	INTJ
ma-27	98	6	−	−	PUNCT
ma-27	99	1	`	`	PUNCT
ma-27	99	2	‖.	‖.	X
ma-27	99	3	the	the	DET
ma-27	99	4	asymptotic	asymptotic	ADJ
ma-27	99	5	radius	radius	NOUN
ma-27	99	6	of	of	ADP
ma-27	99	7	{	{	PUNCT
ma-27	99	8	`	`	PUNCT
ma-27	99	9	s	s	PART
ma-27	99	10	}	}	PUNCT
ma-27	99	11	relative	relative	ADJ
ma-27	99	12	to	to	ADP
ma-27	99	13	λ	λ	PROPN
ma-27	99	14	is	be	AUX
ma-27	99	15	defined	define	VERB
ma-27	99	16	by	by	ADP
ma-27	99	17	r(λ	r(λ	NOUN
ma-27	99	18	,	,	PUNCT
ma-27	99	19	{	{	PUNCT
ma-27	99	20	`	`	PUNCT
ma-27	99	21	s	s	X
ma-27	99	22	}	}	PUNCT
ma-27	99	23	)	)	PUNCT
ma-27	100	1	=	=	SYM
ma-27	100	2	inf{r	inf{r	NOUN
ma-27	100	3	(	(	PUNCT
ma-27	100	4	`	`	PUNCT
ma-27	100	5	,	,	PUNCT
ma-27	100	6	{	{	PUNCT
ma-27	100	7	`	`	PUNCT
ma-27	100	8	s	s	X
ma-27	100	9	}	}	PUNCT
ma-27	100	10	)	)	PUNCT
ma-27	100	11	:	:	PUNCT
ma-27	100	12	`	`	PUNCT
ma-27	100	13	∈	∈	PROPN
ma-27	100	14	λ	λ	NOUN
ma-27	100	15	}	}	PUNCT
ma-27	100	16	.	.	PUNCT
ma-27	101	1	the	the	DET
ma-27	101	2	asymptotic	asymptotic	ADJ
ma-27	101	3	center	center	NOUN
ma-27	101	4	of	of	ADP
ma-27	101	5	{	{	PUNCT
ma-27	101	6	`	`	PUNCT
ma-27	101	7	s	s	PART
ma-27	101	8	}	}	PUNCT
ma-27	101	9	relative	relative	ADJ
ma-27	101	10	to	to	ADP
ma-27	101	11	λ	λ	PROPN
ma-27	101	12	is	be	AUX
ma-27	101	13	given	give	VERB
ma-27	101	14	as	as	ADP
ma-27	101	15	:	:	PUNCT
ma-27	101	16	a(λ	a(λ	ADV
ma-27	101	17	,	,	PUNCT
ma-27	101	18	{	{	PUNCT
ma-27	101	19	`	`	PUNCT
ma-27	101	20	s	s	X
ma-27	101	21	}	}	PUNCT
ma-27	101	22	)	)	PUNCT
ma-27	101	23	=	=	PRON
ma-27	102	1	{	{	PUNCT
ma-27	102	2	`	`	PUNCT
ma-27	102	3	∈	∈	PROPN
ma-27	102	4	λ	λ	X
ma-27	102	5	:	:	PUNCT
ma-27	102	6	r	r	X
ma-27	102	7	(	(	PUNCT
ma-27	102	8	`	`	PUNCT
ma-27	102	9	,	,	PUNCT
ma-27	102	10	{	{	PUNCT
ma-27	102	11	`	`	PUNCT
ma-27	102	12	s	s	X
ma-27	102	13	}	}	PUNCT
ma-27	102	14	)	)	PUNCT
ma-27	102	15	=	=	SYM
ma-27	102	16	r(λ	r(λ	NOUN
ma-27	102	17	,	,	PUNCT
ma-27	102	18	{	{	PUNCT
ma-27	102	19	`	`	PUNCT
ma-27	102	20	s	s	NOUN
ma-27	102	21	}	}	PUNCT
ma-27	102	22	)	)	PUNCT
ma-27	102	23	}	}	PUNCT
ma-27	102	24	.	.	PUNCT
ma-27	103	1	in	in	ADP
ma-27	103	2	a	a	DET
ma-27	103	3	uniformly	uniformly	ADJ
ma-27	103	4	convex	convex	NOUN
ma-27	103	5	banach	banach	NOUN
ma-27	103	6	space	space	NOUN
ma-27	103	7	,	,	PUNCT
ma-27	103	8	it	it	PRON
ma-27	103	9	is	be	AUX
ma-27	103	10	well	well	ADV
ma-27	103	11	known	know	VERB
ma-27	103	12	that	that	SCONJ
ma-27	103	13	a(λ	a(λ	ADV
ma-27	103	14	,	,	PUNCT
ma-27	103	15	{	{	PUNCT
ma-27	103	16	`	`	PUNCT
ma-27	103	17	s	s	X
ma-27	103	18	}	}	PUNCT
ma-27	103	19	)	)	PUNCT
ma-27	103	20	consist	consist	NOUN
ma-27	103	21	of	of	ADP
ma-27	103	22	exactly	exactly	ADV
ma-27	103	23	one	one	NUM
ma-27	103	24	point	point	NOUN
ma-27	103	25	.	.	PUNCT
ma-27	104	1	definition	definition	NOUN
ma-27	104	2	2.4	2.4	NUM
ma-27	104	3	.	.	PUNCT
ma-27	105	1	[	[	X
ma-27	105	2	5	5	NUM
ma-27	105	3	]	]	X
ma-27	105	4	let	let	VERB
ma-27	105	5	{	{	PUNCT
ma-27	105	6	as	as	ADP
ma-27	105	7	}	}	PUNCT
ma-27	105	8	and	and	CCONJ
ma-27	105	9	{	{	PUNCT
ma-27	105	10	bs	bs	NOUN
ma-27	105	11	}	}	PUNCT
ma-27	105	12	be	be	AUX
ma-27	105	13	two	two	NUM
ma-27	105	14	sequences	sequence	NOUN
ma-27	105	15	of	of	ADP
ma-27	105	16	real	real	ADJ
ma-27	105	17	numbers	number	NOUN
ma-27	105	18	that	that	PRON
ma-27	105	19	converge	converge	VERB
ma-27	105	20	to	to	ADP
ma-27	105	21	a	a	PRON
ma-27	105	22	and	and	CCONJ
ma-27	105	23	brespectively	brespectively	ADV
ma-27	105	24	,	,	PUNCT
ma-27	105	25	and	and	CCONJ
ma-27	105	26	assume	assume	VERB
ma-27	105	27	that	that	SCONJ
ma-27	105	28	there	there	PRON
ma-27	105	29	exists	exist	VERB
ma-27	105	30	k	k	PROPN
ma-27	105	31	=	=	SYM
ma-27	105	32	lim	lim	PROPN
ma-27	105	33	s→∞	s→∞	PROPN
ma-27	105	34	‖as	‖as	PROPN
ma-27	105	35	−	−	PROPN
ma-27	105	36	a‖	a‖	PROPN
ma-27	105	37	‖bs	‖bs	PROPN
ma-27	106	1	−	−	PROPN
ma-27	106	2	b‖	b‖	PROPN
ma-27	106	3	.	.	PUNCT
ma-27	107	1	then,(r1	then,(r1	X
ma-27	107	2	)	)	PUNCT
ma-27	108	1	if	if	SCONJ
ma-27	108	2	k	k	PROPN
ma-27	108	3	=	=	SYM
ma-27	108	4	0	0	PROPN
ma-27	108	5	,	,	PUNCT
ma-27	108	6	we	we	PRON
ma-27	108	7	say	say	VERB
ma-27	108	8	that	that	SCONJ
ma-27	108	9	{	{	PUNCT
ma-27	108	10	as	as	SCONJ
ma-27	108	11	}	}	PUNCT
ma-27	108	12	converges	converge	VERB
ma-27	108	13	faster	fast	ADV
ma-27	108	14	to	to	ADP
ma-27	108	15	a	a	DET
ma-27	108	16	than	than	ADP
ma-27	108	17	{	{	PUNCT
ma-27	108	18	bs	bs	NOUN
ma-27	108	19	}	}	PUNCT
ma-27	108	20	does	do	AUX
ma-27	108	21	to	to	ADP
ma-27	108	22	b.(r2	b.(r2	VERB
ma-27	108	23	)	)	PUNCT
ma-27	108	24	if	if	SCONJ
ma-27	108	25	0	0	NUM
ma-27	108	26	<	<	X
ma-27	108	27	k	k	X
ma-27	108	28	<	<	X
ma-27	108	29	∞	∞	PROPN
ma-27	108	30	,	,	PUNCT
ma-27	108	31	we	we	PRON
ma-27	108	32	say	say	VERB
ma-27	108	33	that	that	SCONJ
ma-27	108	34	{	{	PUNCT
ma-27	108	35	as	as	SCONJ
ma-27	108	36	}	}	PUNCT
ma-27	108	37	and	and	CCONJ
ma-27	108	38	{	{	PUNCT
ma-27	108	39	bs	bs	NOUN
ma-27	108	40	}	}	PUNCT
ma-27	108	41	have	have	VERB
ma-27	108	42	the	the	DET
ma-27	108	43	same	same	ADJ
ma-27	108	44	rate	rate	NOUN
ma-27	108	45	of	of	ADP
ma-27	108	46	convergence	convergence	NOUN
ma-27	108	47	.	.	PUNCT
ma-27	109	1	eur	eur	PROPN
ma-27	109	2	.	.	PUNCT
ma-27	110	1	j.	j.	PROPN
ma-27	110	2	math	math	PROPN
ma-27	110	3	.	.	PUNCT
ma-27	111	1	anal	anal	ADJ
ma-27	111	2	.	.	PUNCT
ma-27	112	1	1	1	NUM
ma-27	112	2	(	(	PUNCT
ma-27	112	3	2021	2021	NUM
ma-27	112	4	)	)	PUNCT
ma-27	112	5	111	111	NUM
ma-27	112	6	definition	definition	NOUN
ma-27	112	7	2.5	2.5	NUM
ma-27	112	8	.	.	PUNCT
ma-27	113	1	[	[	X
ma-27	113	2	5	5	NUM
ma-27	113	3	]	]	X
ma-27	113	4	let	let	VERB
ma-27	113	5	{	{	PUNCT
ma-27	113	6	ηs	ηs	VERB
ma-27	113	7	}	}	PUNCT
ma-27	113	8	and	and	CCONJ
ma-27	113	9	{	{	PUNCT
ma-27	113	10	φs	φs	PART
ma-27	113	11	}	}	PUNCT
ma-27	113	12	be	be	AUX
ma-27	113	13	two	two	NUM
ma-27	113	14	fixed	fix	VERB
ma-27	113	15	point	point	NOUN
ma-27	113	16	iteration	iteration	NOUN
ma-27	113	17	processes	process	NOUN
ma-27	113	18	that	that	PRON
ma-27	113	19	converge	converge	VERB
ma-27	113	20	to	to	ADP
ma-27	113	21	thesame	thesame	ADJ
ma-27	113	22	point	point	NOUN
ma-27	113	23	z	z	NOUN
ma-27	113	24	,	,	PUNCT
ma-27	113	25	the	the	DET
ma-27	113	26	error	error	NOUN
ma-27	113	27	estimates	estimate	VERB
ma-27	113	28	‖ηs	‖ηs	PRON
ma-27	113	29	−	−	PROPN
ma-27	113	30	z‖	z‖	X
ma-27	113	31	≤	≤	NOUN
ma-27	113	32	as	as	ADP
ma-27	113	33	,	,	PUNCT
ma-27	113	34	∀	∀	X
ma-27	113	35	s	s	NOUN
ma-27	113	36	≥	≥	NOUN
ma-27	113	37	1	1	NUM
ma-27	113	38	,	,	PUNCT
ma-27	113	39	‖φs	‖φs	PROPN
ma-27	113	40	−	−	PROPN
ma-27	113	41	z‖	z‖	NOUN
ma-27	113	42	≤	≤	NUM
ma-27	113	43	bs	b	NOUN
ma-27	113	44	,	,	PUNCT
ma-27	113	45	∀	∀	X
ma-27	113	46	s	s	PART
ma-27	113	47	≥	≥	NOUN
ma-27	113	48	1	1	NUM
ma-27	113	49	,	,	PUNCT
ma-27	113	50	are	be	AUX
ma-27	113	51	available	available	ADJ
ma-27	113	52	where	where	SCONJ
ma-27	113	53	{	{	PUNCT
ma-27	113	54	as	as	SCONJ
ma-27	113	55	}	}	PUNCT
ma-27	113	56	and	and	CCONJ
ma-27	113	57	{	{	PUNCT
ma-27	113	58	bs	bs	NOUN
ma-27	113	59	}	}	PUNCT
ma-27	113	60	are	be	AUX
ma-27	113	61	two	two	NUM
ma-27	113	62	sequences	sequence	NOUN
ma-27	113	63	of	of	ADP
ma-27	113	64	positive	positive	ADJ
ma-27	113	65	numbers	number	NOUN
ma-27	113	66	converging	converge	VERB
ma-27	113	67	to	to	ADP
ma-27	113	68	zero	zero	NUM
ma-27	113	69	.	.	PUNCT
ma-27	114	1	thenwe	thenwe	PROPN
ma-27	114	2	say	say	VERB
ma-27	114	3	that	that	SCONJ
ma-27	114	4	{	{	PUNCT
ma-27	114	5	ηs	ηs	NOUN
ma-27	114	6	}	}	PUNCT
ma-27	114	7	converges	converge	NOUN
ma-27	114	8	faster	fast	ADV
ma-27	114	9	to	to	ADP
ma-27	114	10	z	z	NOUN
ma-27	114	11	than	than	SCONJ
ma-27	114	12	{	{	PUNCT
ma-27	114	13	φs	φs	PART
ma-27	114	14	}	}	PUNCT
ma-27	114	15	does	do	VERB
ma-27	114	16	if	if	SCONJ
ma-27	114	17	{	{	PUNCT
ma-27	114	18	as	as	SCONJ
ma-27	114	19	}	}	PUNCT
ma-27	114	20	converges	converge	NOUN
ma-27	114	21	faster	fast	ADV
ma-27	114	22	than	than	ADP
ma-27	114	23	{	{	PUNCT
ma-27	114	24	bs	bs	NOUN
ma-27	114	25	}	}	PUNCT
ma-27	114	26	.	.	PUNCT
ma-27	115	1	definition	definition	NOUN
ma-27	115	2	2.6	2.6	NUM
ma-27	115	3	.	.	PUNCT
ma-27	116	1	[	[	X
ma-27	116	2	5	5	X
ma-27	116	3	]	]	PUNCT
ma-27	116	4	let	let	VERB
ma-27	116	5	t	t	NOUN
ma-27	116	6	,	,	PUNCT
ma-27	116	7	t̃	t̃	PROPN
ma-27	116	8	:	:	PUNCT
ma-27	116	9	λ→	λ→	PUNCT
ma-27	116	10	λ	λ	NOUN
ma-27	116	11	be	be	VERB
ma-27	116	12	two	two	NUM
ma-27	116	13	operators	operator	NOUN
ma-27	116	14	.	.	PUNCT
ma-27	117	1	we	we	PRON
ma-27	117	2	say	say	VERB
ma-27	117	3	that	that	SCONJ
ma-27	117	4	t̃	t̃	PROPN
ma-27	117	5	is	be	AUX
ma-27	117	6	an	an	DET
ma-27	117	7	approximate	approximate	ADJ
ma-27	117	8	operatorfor	operatorfor	PROPN
ma-27	117	9	t	t	PROPN
ma-27	117	10	if	if	SCONJ
ma-27	117	11	for	for	ADP
ma-27	117	12	some	some	DET
ma-27	117	13	ε	ε	PROPN
ma-27	117	14	>	>	X
ma-27	117	15	0	0	PROPN
ma-27	117	16	,	,	PUNCT
ma-27	117	17	we	we	PRON
ma-27	117	18	have	have	VERB
ma-27	117	19	‖t`−	‖t`−	PUNCT
ma-27	117	20	t̃	t̃	PROPN
ma-27	117	21	`	`	PUNCT
ma-27	117	22	‖	‖	PROPN
ma-27	117	23	≤	≤	PROPN
ma-27	117	24	ε	ε	PROPN
ma-27	117	25	,	,	PUNCT
ma-27	117	26	∀	∀	PUNCT
ma-27	117	27	`	`	PUNCT
ma-27	117	28	∈	∈	PROPN
ma-27	117	29	λ	λ	PROPN
ma-27	117	30	.	.	PROPN
ma-27	117	31	definition	definition	NOUN
ma-27	117	32	2.7	2.7	NUM
ma-27	117	33	.	.	PUNCT
ma-27	118	1	[	[	X
ma-27	118	2	18	18	NUM
ma-27	118	3	]	]	PUNCT
ma-27	118	4	let	let	AUX
ma-27	118	5	{	{	PUNCT
ma-27	118	6	ys	ys	AUX
ma-27	118	7	}	}	PUNCT
ma-27	118	8	be	be	AUX
ma-27	118	9	any	any	DET
ma-27	118	10	sequence	sequence	NOUN
ma-27	118	11	in	in	ADP
ma-27	118	12	λ	λ	PROPN
ma-27	118	13	.	.	PUNCT
ma-27	119	1	then	then	ADV
ma-27	119	2	,	,	PUNCT
ma-27	119	3	an	an	DET
ma-27	119	4	iteration	iteration	NOUN
ma-27	119	5	process	process	NOUN
ma-27	119	6	`	`	PUNCT
ma-27	119	7	s+1	s+1	PROPN
ma-27	119	8	=	=	SYM
ma-27	119	9	f	f	PROPN
ma-27	119	10	(	(	PUNCT
ma-27	119	11	t	t	PROPN
ma-27	119	12	,	,	PUNCT
ma-27	119	13	ys),which	ys),which	PRON
ma-27	119	14	converges	converge	VERB
ma-27	119	15	to	to	ADP
ma-27	119	16	fixed	fix	VERB
ma-27	119	17	point	point	NOUN
ma-27	119	18	z	z	NOUN
ma-27	119	19	,	,	PUNCT
ma-27	119	20	is	be	AUX
ma-27	119	21	said	say	VERB
ma-27	119	22	to	to	PART
ma-27	119	23	be	be	AUX
ma-27	119	24	stable	stable	ADJ
ma-27	119	25	with	with	ADP
ma-27	119	26	respect	respect	NOUN
ma-27	119	27	to	to	ADP
ma-27	119	28	t	t	NOUN
ma-27	119	29	,	,	PUNCT
ma-27	119	30	if	if	SCONJ
ma-27	119	31	for	for	ADP
ma-27	119	32	εs	εs	PROPN
ma-27	119	33	=	=	SYM
ma-27	119	34	‖ys+1−f	‖ys+1−f	PROPN
ma-27	119	35	(	(	PUNCT
ma-27	119	36	t	t	PROPN
ma-27	119	37	,	,	PUNCT
ma-27	119	38	ys)‖	ys)‖	PROPN
ma-27	119	39	,	,	PUNCT
ma-27	119	40	∀	∀	PUNCT
ma-27	119	41	s	s	NOUN
ma-27	119	42	∈	∈	PROPN
ma-27	119	43	n	n	CCONJ
ma-27	119	44	,	,	PUNCT
ma-27	119	45	we	we	PRON
ma-27	119	46	have	have	VERB
ma-27	119	47	lim	lim	PROPN
ma-27	119	48	s→∞	s→∞	NOUN
ma-27	120	1	εs	εs	ADP
ma-27	120	2	=	=	PUNCT
ma-27	120	3	0⇔	0⇔	NOUN
ma-27	120	4	lim	lim	PROPN
ma-27	120	5	s→∞	s→∞	PROPN
ma-27	120	6	ys	ys	NOUN
ma-27	120	7	=	=	PROPN
ma-27	120	8	z.	z.	PROPN
ma-27	120	9	definition	definition	NOUN
ma-27	120	10	2.8	2.8	NUM
ma-27	120	11	.	.	PUNCT
ma-27	121	1	[	[	X
ma-27	121	2	31	31	NUM
ma-27	121	3	]	]	PUNCT
ma-27	121	4	a	a	DET
ma-27	121	5	mapping	mapping	NOUN
ma-27	121	6	t	t	NOUN
ma-27	121	7	:	:	PUNCT
ma-27	121	8	λ	λ	X
ma-27	121	9	→	→	SYM
ma-27	121	10	λ	λ	PROPN
ma-27	121	11	is	be	AUX
ma-27	121	12	said	say	VERB
ma-27	121	13	to	to	PART
ma-27	121	14	satisfy	satisfy	VERB
ma-27	121	15	condition	condition	NOUN
ma-27	121	16	(	(	PUNCT
ma-27	121	17	i	i	NOUN
ma-27	121	18	)	)	PUNCT
ma-27	121	19	if	if	SCONJ
ma-27	121	20	a	a	DET
ma-27	121	21	nondecreasingfunction	nondecreasingfunction	NOUN
ma-27	121	22	f	f	X
ma-27	121	23	:	:	PUNCT
ma-27	122	1	[	[	X
ma-27	122	2	0,∞	0,∞	NOUN
ma-27	122	3	)	)	PUNCT
ma-27	122	4	→	→	PUNCT
ma-27	123	1	[	[	X
ma-27	123	2	0,∞	0,∞	NOUN
ma-27	123	3	)	)	PUNCT
ma-27	123	4	exists	exist	VERB
ma-27	123	5	with	with	ADP
ma-27	123	6	f	f	PROPN
ma-27	123	7	(	(	PUNCT
ma-27	123	8	0	0	NUM
ma-27	123	9	)	)	PUNCT
ma-27	123	10	=	=	SYM
ma-27	123	11	0	0	NUM
ma-27	123	12	and	and	CCONJ
ma-27	123	13	for	for	ADP
ma-27	123	14	all	all	DET
ma-27	123	15	r	r	NOUN
ma-27	123	16	>	>	X
ma-27	123	17	0	0	PUNCT
ma-27	124	1	then	then	ADV
ma-27	124	2	f	f	X
ma-27	124	3	(	(	PUNCT
ma-27	124	4	r	r	NOUN
ma-27	124	5	)	)	PUNCT
ma-27	124	6	>	>	X
ma-27	124	7	0	0	NUM
ma-27	125	1	such	such	ADJ
ma-27	125	2	that	that	SCONJ
ma-27	125	3	‖`−	‖`−	NUM
ma-27	125	4	t`‖	t`‖	PROPN
ma-27	125	5	≥	≥	NOUN
ma-27	125	6	f	f	X
ma-27	125	7	(	(	PUNCT
ma-27	125	8	d	d	X
ma-27	125	9	(	(	PUNCT
ma-27	125	10	`	`	PUNCT
ma-27	125	11	,	,	PUNCT
ma-27	125	12	f	f	PROPN
ma-27	125	13	(	(	PUNCT
ma-27	125	14	t	t	PROPN
ma-27	125	15	)	)	PUNCT
ma-27	125	16	)	)	PUNCT
ma-27	125	17	)	)	PUNCT
ma-27	125	18	)	)	PUNCT
ma-27	126	1	for	for	ADP
ma-27	126	2	all	all	DET
ma-27	126	3	`	`	PUNCT
ma-27	126	4	∈	∈	PROPN
ma-27	126	5	λ	λ	PROPN
ma-27	126	6	,	,	PUNCT
ma-27	126	7	where	where	SCONJ
ma-27	126	8	d	d	X
ma-27	126	9	(	(	PUNCT
ma-27	126	10	`	`	PUNCT
ma-27	126	11	,	,	PUNCT
ma-27	126	12	f	f	PROPN
ma-27	126	13	(	(	PUNCT
ma-27	126	14	t	t	PROPN
ma-27	126	15	)	)	PUNCT
ma-27	126	16	)	)	PUNCT
ma-27	127	1	=	=	SYM
ma-27	127	2	infz∈f	infz∈f	PROPN
ma-27	127	3	(	(	PUNCT
ma-27	127	4	t	t	PROPN
ma-27	127	5	)	)	PUNCT
ma-27	128	1	‖`−	‖`−	NUM
ma-27	128	2	z‖.	z‖.	NOUN
ma-27	128	3	proposition	proposition	NOUN
ma-27	128	4	2.9	2.9	NUM
ma-27	128	5	.	.	PUNCT
ma-27	129	1	[	[	X
ma-27	129	2	26	26	NUM
ma-27	129	3	]	]	PUNCT
ma-27	129	4	let	let	VERB
ma-27	129	5	λ	λ	PART
ma-27	129	6	be	be	AUX
ma-27	129	7	a	a	DET
ma-27	129	8	nonempty	nonempty	ADJ
ma-27	129	9	subset	subset	NOUN
ma-27	129	10	of	of	ADP
ma-27	129	11	a	a	DET
ma-27	129	12	banach	banach	NOUN
ma-27	129	13	space	space	NOUN
ma-27	129	14	ω	ω	PROPN
ma-27	129	15	.	.	PUNCT
ma-27	129	16	suppose	suppose	VERB
ma-27	130	1	t	t	NOUN
ma-27	130	2	:	:	PUNCT
ma-27	130	3	λ	λ	X
ma-27	130	4	→	→	SYM
ma-27	130	5	λ	λ	PROPN
ma-27	130	6	is	be	AUX
ma-27	130	7	any	any	DET
ma-27	130	8	mapping	mapping	NOUN
ma-27	130	9	.	.	PUNCT
ma-27	131	1	then(i	then(i	VERB
ma-27	131	2	)	)	PUNCT
ma-27	131	3	if	if	SCONJ
ma-27	131	4	t	t	PROPN
ma-27	131	5	is	be	AUX
ma-27	131	6	a	a	DET
ma-27	131	7	suzuki	suzuki	NOUN
ma-27	131	8	generalized	generalize	VERB
ma-27	131	9	nonexpansive	nonexpansive	PROPN
ma-27	131	10	mapping	mapping	NOUN
ma-27	131	11	,	,	PUNCT
ma-27	131	12	it	it	PRON
ma-27	131	13	follows	follow	VERB
ma-27	131	14	that	that	SCONJ
ma-27	131	15	t	t	PROPN
ma-27	131	16	is	be	AUX
ma-27	131	17	a	a	DET
ma-27	131	18	generalized	generalized	ADJ
ma-27	131	19	α	α	NOUN
ma-27	131	20	-	-	PUNCT
ma-27	131	21	nonexpansive	nonexpansive	ADJ
ma-27	131	22	mapping.(ii	mapping.(ii	NOUN
ma-27	131	23	)	)	PUNCT
ma-27	131	24	every	every	DET
ma-27	131	25	generalized	generalized	ADJ
ma-27	131	26	α	α	PRON
ma-27	131	27	-	-	PUNCT
ma-27	131	28	nonexpansive	nonexpansive	ADJ
ma-27	131	29	mapping	mapping	NOUN
ma-27	131	30	with	with	ADP
ma-27	131	31	a	a	DET
ma-27	131	32	nonempty	nonempty	ADV
ma-27	131	33	fixed	fix	VERB
ma-27	131	34	point	point	NOUN
ma-27	131	35	set	set	NOUN
ma-27	131	36	is	be	AUX
ma-27	131	37	quasinonexpansive	quasinonexpansive	ADJ
ma-27	131	38	mapping.(ii	mapping.(ii	NOUN
ma-27	131	39	)	)	PUNCT
ma-27	131	40	if	if	SCONJ
ma-27	131	41	t	t	PROPN
ma-27	131	42	is	be	AUX
ma-27	131	43	a	a	DET
ma-27	131	44	generalized	generalized	ADJ
ma-27	131	45	α	α	PRON
ma-27	131	46	-	-	PUNCT
ma-27	131	47	nonexpansive	nonexpansive	ADJ
ma-27	131	48	mapping	mapping	NOUN
ma-27	131	49	,	,	PUNCT
ma-27	131	50	then	then	ADV
ma-27	131	51	f	f	PROPN
ma-27	131	52	(	(	PUNCT
ma-27	131	53	t	t	PROPN
ma-27	131	54	)	)	PUNCT
ma-27	131	55	is	be	AUX
ma-27	131	56	closed	close	VERB
ma-27	131	57	.	.	PUNCT
ma-27	132	1	moreover	moreover	ADV
ma-27	132	2	,	,	PUNCT
ma-27	132	3	if	if	SCONJ
ma-27	132	4	ω	ω	NOUN
ma-27	132	5	is	be	AUX
ma-27	132	6	strictly	strictly	ADV
ma-27	132	7	convex	convex	ADJ
ma-27	132	8	and	and	CCONJ
ma-27	132	9	λ	λ	PROPN
ma-27	132	10	is	be	AUX
ma-27	132	11	convex	convex	PROPN
ma-27	132	12	,	,	PUNCT
ma-27	132	13	then	then	ADV
ma-27	132	14	f	f	PROPN
ma-27	132	15	(	(	PUNCT
ma-27	132	16	t	t	PROPN
ma-27	132	17	)	)	PUNCT
ma-27	132	18	is	be	AUX
ma-27	132	19	also	also	ADV
ma-27	132	20	convex.(iv	convex.(iv	ADJ
ma-27	132	21	)	)	PUNCT
ma-27	133	1	if	if	SCONJ
ma-27	133	2	t	t	PROPN
ma-27	133	3	is	be	AUX
ma-27	133	4	a	a	DET
ma-27	133	5	generalized	generalized	ADJ
ma-27	133	6	α	α	PRON
ma-27	133	7	-	-	PUNCT
ma-27	133	8	nonexpansive	nonexpansive	ADJ
ma-27	133	9	mapping	mapping	NOUN
ma-27	133	10	,	,	PUNCT
ma-27	133	11	then	then	ADV
ma-27	133	12	the	the	DET
ma-27	133	13	following	follow	VERB
ma-27	133	14	inequality	inequality	NOUN
ma-27	133	15	holds	hold	VERB
ma-27	133	16	:	:	PUNCT
ma-27	133	17	‖`−	‖`−	NUM
ma-27	133	18	tζ‖	tζ‖	PROPN
ma-27	133	19	≤	≤	NUM
ma-27	133	20	(	(	PUNCT
ma-27	133	21	3	3	NUM
ma-27	133	22	+	+	CCONJ
ma-27	133	23	α	α	PROPN
ma-27	133	24	1−	1−	NUM
ma-27	133	25	α	α	NOUN
ma-27	133	26	)	)	PUNCT
ma-27	134	1	‖`−	‖`−	NUM
ma-27	134	2	t`‖+	t`‖+	VERB
ma-27	134	3	‖`−	‖`−	NUM
ma-27	134	4	ζ‖	ζ‖	NOUN
ma-27	134	5	,	,	PUNCT
ma-27	134	6	∀	∀	PUNCT
ma-27	134	7	`	`	PUNCT
ma-27	134	8	,	,	PUNCT
ma-27	134	9	ζ	ζ	PROPN
ma-27	134	10	∈	∈	PROPN
ma-27	134	11	λ	λ	PROPN
ma-27	134	12	.	.	PUNCT
ma-27	134	13	lemma	lemma	PROPN
ma-27	134	14	2.10	2.10	NUM
ma-27	134	15	.	.	PUNCT
ma-27	135	1	[	[	X
ma-27	135	2	26	26	NUM
ma-27	135	3	]	]	PUNCT
ma-27	135	4	let	let	VERB
ma-27	135	5	t	t	NOUN
ma-27	135	6	be	be	AUX
ma-27	135	7	a	a	DET
ma-27	135	8	self	self	NOUN
ma-27	135	9	mapping	mapping	NOUN
ma-27	135	10	on	on	ADP
ma-27	135	11	a	a	DET
ma-27	135	12	subset	subset	ADJ
ma-27	135	13	λ	λ	NOUN
ma-27	135	14	of	of	ADP
ma-27	135	15	a	a	DET
ma-27	135	16	banach	banach	NOUN
ma-27	135	17	space	space	NOUN
ma-27	135	18	ω	ω	NOUN
ma-27	135	19	which	which	PRON
ma-27	135	20	satisfies	satisfy	VERB
ma-27	135	21	opial	opial	ADJ
ma-27	135	22	’s	’s	PART
ma-27	135	23	condition	condition	NOUN
ma-27	135	24	.	.	PUNCT
ma-27	136	1	suppose	suppose	VERB
ma-27	136	2	t	t	PROPN
ma-27	136	3	is	be	AUX
ma-27	136	4	a	a	DET
ma-27	136	5	generalized	generalized	ADJ
ma-27	136	6	α	α	PRON
ma-27	136	7	-	-	PUNCT
ma-27	136	8	nonexpansive	nonexpansive	ADJ
ma-27	136	9	mapping	mapping	NOUN
ma-27	136	10	.	.	PUNCT
ma-27	137	1	if	if	SCONJ
ma-27	137	2	{	{	PUNCT
ma-27	137	3	`	`	PUNCT
ma-27	137	4	s	s	X
ma-27	137	5	}	}	PUNCT
ma-27	137	6	converges	converge	VERB
ma-27	137	7	weakly	weakly	ADV
ma-27	137	8	to	to	ADP
ma-27	137	9	z	z	PROPN
ma-27	137	10	and	and	CCONJ
ma-27	137	11	lim	lim	PROPN
ma-27	137	12	s→∞	s→∞	PROPN
ma-27	137	13	‖t`s	‖t`s	ADJ
ma-27	137	14	−	−	NOUN
ma-27	137	15	`	`	PUNCT
ma-27	137	16	s‖	s‖	NOUN
ma-27	137	17	=	=	SYM
ma-27	137	18	0	0	NUM
ma-27	137	19	,	,	PUNCT
ma-27	137	20	then	then	ADV
ma-27	137	21	tz	tz	PROPN
ma-27	137	22	=	=	PROPN
ma-27	137	23	z	z	PROPN
ma-27	137	24	.	.	PUNCT
ma-27	138	1	that	that	PRON
ma-27	138	2	is	be	AUX
ma-27	138	3	,	,	PUNCT
ma-27	138	4	i	i	PRON
ma-27	138	5	−	−	PROPN
ma-27	138	6	t	t	PROPN
ma-27	138	7	is	be	AUX
ma-27	138	8	demiclosed	demiclose	VERB
ma-27	138	9	at	at	ADP
ma-27	138	10	zero	zero	NUM
ma-27	138	11	.	.	PUNCT
ma-27	139	1	lemma	lemma	PROPN
ma-27	139	2	2.11	2.11	NUM
ma-27	139	3	.	.	PUNCT
ma-27	140	1	[	[	X
ma-27	140	2	33	33	NUM
ma-27	140	3	]	]	PUNCT
ma-27	140	4	let	let	VERB
ma-27	140	5	t	t	NOUN
ma-27	140	6	be	be	AUX
ma-27	140	7	a	a	DET
ma-27	140	8	self	self	NOUN
ma-27	140	9	mapping	mapping	NOUN
ma-27	140	10	on	on	ADP
ma-27	140	11	a	a	DET
ma-27	140	12	weakly	weakly	ADJ
ma-27	140	13	compact	compact	ADJ
ma-27	140	14	convex	convex	NOUN
ma-27	140	15	subset	subset	VERB
ma-27	140	16	λ	λ	PROPN
ma-27	140	17	of	of	ADP
ma-27	140	18	a	a	DET
ma-27	140	19	banach	banach	NOUN
ma-27	140	20	space	space	NOUN
ma-27	140	21	ω	ω	NOUN
ma-27	140	22	with	with	ADP
ma-27	140	23	the	the	DET
ma-27	140	24	opial	opial	NOUN
ma-27	140	25	’s	’s	PART
ma-27	140	26	property	property	NOUN
ma-27	140	27	.	.	PUNCT
ma-27	141	1	if	if	SCONJ
ma-27	141	2	t	t	PROPN
ma-27	141	3	is	be	AUX
ma-27	141	4	a	a	DET
ma-27	141	5	suzuki	suzuki	NOUN
ma-27	141	6	generalized	generalize	VERB
ma-27	141	7	nonexpansive	nonexpansive	PROPN
ma-27	141	8	mapping	mapping	NOUN
ma-27	141	9	,	,	PUNCT
ma-27	141	10	then	then	ADV
ma-27	141	11	t	t	PROPN
ma-27	141	12	has	have	VERB
ma-27	141	13	a	a	DET
ma-27	141	14	fixed	fix	VERB
ma-27	141	15	point	point	NOUN
ma-27	141	16	.	.	PUNCT
ma-27	142	1	eur	eur	PROPN
ma-27	142	2	.	.	PUNCT
ma-27	143	1	j.	j.	PROPN
ma-27	143	2	math	math	PROPN
ma-27	143	3	.	.	PUNCT
ma-27	144	1	anal	anal	ADJ
ma-27	144	2	.	.	PUNCT
ma-27	145	1	1	1	NUM
ma-27	145	2	(	(	PUNCT
ma-27	145	3	2021	2021	NUM
ma-27	145	4	)	)	PUNCT
ma-27	145	5	112	112	NUM
ma-27	145	6	lemma	lemma	PROPN
ma-27	145	7	2.12	2.12	NUM
ma-27	145	8	.	.	PUNCT
ma-27	146	1	[	[	X
ma-27	146	2	40	40	NUM
ma-27	146	3	]	]	PUNCT
ma-27	146	4	let	let	VERB
ma-27	146	5	{	{	PUNCT
ma-27	146	6	‘s	‘s	NOUN
ma-27	146	7	}	}	PUNCT
ma-27	146	8	and	and	CCONJ
ma-27	146	9	{	{	PUNCT
ma-27	146	10	λs	λs	AUX
ma-27	146	11	}	}	PUNCT
ma-27	146	12	be	be	AUX
ma-27	146	13	nonnegative	nonnegative	ADJ
ma-27	146	14	real	real	ADJ
ma-27	146	15	sequences	sequence	NOUN
ma-27	146	16	satisfying	satisfy	VERB
ma-27	146	17	the	the	DET
ma-27	146	18	following	follow	VERB
ma-27	146	19	inequalities	inequality	NOUN
ma-27	146	20	:	:	PUNCT
ma-27	146	21	‘	'	PUNCT
ma-27	146	22	s+1	s+1	ADJ
ma-27	146	23	≤	≤	NUM
ma-27	146	24	(	(	PUNCT
ma-27	146	25	1−	1−	NUM
ma-27	146	26	σs)‘s	σs)‘s	PROPN
ma-27	146	27	+	+	CCONJ
ma-27	146	28	λs	λs	ADP
ma-27	146	29	,	,	PUNCT
ma-27	146	30	where	where	SCONJ
ma-27	146	31	σs	σs	ADP
ma-27	146	32	∈	∈	PROPN
ma-27	146	33	(	(	PUNCT
ma-27	146	34	0	0	NUM
ma-27	146	35	,	,	PUNCT
ma-27	146	36	1	1	NUM
ma-27	146	37	)	)	PUNCT
ma-27	146	38	for	for	ADP
ma-27	146	39	all	all	DET
ma-27	146	40	s	s	PROPN
ma-27	146	41	∈	∈	PROPN
ma-27	146	42	n	n	CCONJ
ma-27	146	43	,	,	PUNCT
ma-27	146	44	∞∑	∞∑	PROPN
ma-27	146	45	s=0	s=0	X
ma-27	146	46	σs	σs	ADP
ma-27	146	47	=	=	PROPN
ma-27	146	48	∞	∞	PROPN
ma-27	146	49	and	and	CCONJ
ma-27	146	50	lim	lim	PROPN
ma-27	146	51	s→∞	s→∞	NOUN
ma-27	146	52	s	s	PART
ma-27	146	53	σs	σs	ADP
ma-27	146	54	=	=	SYM
ma-27	146	55	0	0	PROPN
ma-27	146	56	,	,	PUNCT
ma-27	146	57	then	then	ADV
ma-27	146	58	lim	lim	PROPN
ma-27	146	59	s→∞	s→∞	PROPN
ma-27	146	60	‘s	‘s	PART
ma-27	147	1	=	=	NOUN
ma-27	147	2	0	0	X
ma-27	147	3	.	.	PUNCT
ma-27	148	1	lemma	lemma	PROPN
ma-27	148	2	2.13	2.13	NUM
ma-27	148	3	.	.	PUNCT
ma-27	149	1	[	[	X
ma-27	149	2	32	32	NUM
ma-27	149	3	]	]	PUNCT
ma-27	149	4	let	let	AUX
ma-27	149	5	{	{	PUNCT
ma-27	149	6	‘s	‘s	PRON
ma-27	149	7	}	}	PUNCT
ma-27	149	8	be	be	AUX
ma-27	149	9	a	a	DET
ma-27	149	10	nonnegative	nonnegative	ADJ
ma-27	149	11	real	real	ADJ
ma-27	149	12	sequence	sequence	NOUN
ma-27	149	13	and	and	CCONJ
ma-27	149	14	there	there	PRON
ma-27	149	15	exits	exit	VERB
ma-27	149	16	an	an	DET
ma-27	149	17	s0	s0	PROPN
ma-27	149	18	∈	∈	PROPN
ma-27	149	19	n	n	PRON
ma-27	149	20	such	such	ADJ
ma-27	149	21	that	that	PRON
ma-27	149	22	for	for	ADP
ma-27	149	23	all	all	DET
ma-27	149	24	s	s	PART
ma-27	149	25	≥	≥	NOUN
ma-27	149	26	s0	s0	NOUN
ma-27	149	27	satisfying	satisfy	VERB
ma-27	149	28	the	the	DET
ma-27	149	29	following	follow	VERB
ma-27	149	30	condition	condition	NOUN
ma-27	149	31	:	:	PUNCT
ma-27	149	32	‘	'	PUNCT
ma-27	149	33	s+1	s+1	ADJ
ma-27	149	34	≤	≤	NUM
ma-27	149	35	(	(	PUNCT
ma-27	149	36	1−	1−	NUM
ma-27	149	37	σs)‘s	σs)‘s	PROPN
ma-27	149	38	+	+	CCONJ
ma-27	149	39	σsλs	σsλs	PROPN
ma-27	149	40	,	,	PUNCT
ma-27	149	41	where	where	SCONJ
ma-27	149	42	σs	σs	ADP
ma-27	149	43	∈	∈	PROPN
ma-27	149	44	(	(	PUNCT
ma-27	149	45	0	0	NUM
ma-27	149	46	,	,	PUNCT
ma-27	149	47	1	1	NUM
ma-27	149	48	)	)	PUNCT
ma-27	149	49	for	for	ADP
ma-27	149	50	all	all	DET
ma-27	149	51	s	s	PROPN
ma-27	149	52	∈	∈	PROPN
ma-27	149	53	n	n	CCONJ
ma-27	149	54	,	,	PUNCT
ma-27	149	55	∞∑	∞∑	PROPN
ma-27	149	56	s=0	s=0	X
ma-27	149	57	σs	σs	ADP
ma-27	149	58	=	=	PROPN
ma-27	149	59	∞	∞	PROPN
ma-27	149	60	and	and	CCONJ
ma-27	149	61	λs	λs	ADP
ma-27	149	62	≥	≥	NOUN
ma-27	149	63	0	0	NUM
ma-27	149	64	for	for	ADP
ma-27	149	65	all	all	DET
ma-27	149	66	s	s	PART
ma-27	149	67	∈	∈	NOUN
ma-27	149	68	n	n	CCONJ
ma-27	149	69	,	,	PUNCT
ma-27	149	70	then	then	ADV
ma-27	149	71	0	0	NUM
ma-27	149	72	≤	≤	NOUN
ma-27	149	73	lim	lim	PROPN
ma-27	149	74	sup	sup	NOUN
ma-27	149	75	s→∞	s→∞	NOUN
ma-27	149	76	‘s	‘s	PROPN
ma-27	149	77	≤	≤	ADJ
ma-27	149	78	lim	lim	PROPN
ma-27	149	79	sup	sup	NOUN
ma-27	149	80	s→∞	s→∞	NOUN
ma-27	149	81	λs	λs	ADV
ma-27	149	82	.	.	PUNCT
ma-27	150	1	lemma	lemma	PROPN
ma-27	150	2	2.14	2.14	NUM
ma-27	150	3	.	.	PUNCT
ma-27	151	1	[	[	X
ma-27	151	2	29	29	NUM
ma-27	151	3	]	]	PUNCT
ma-27	151	4	suppose	suppose	VERB
ma-27	151	5	ω	ω	NOUN
ma-27	151	6	is	be	AUX
ma-27	151	7	a	a	DET
ma-27	151	8	uniformly	uniformly	ADV
ma-27	151	9	convex	convex	NOUN
ma-27	151	10	banach	banach	NOUN
ma-27	151	11	space	space	NOUN
ma-27	151	12	and	and	CCONJ
ma-27	151	13	{	{	PUNCT
ma-27	151	14	ιs	ιs	NOUN
ma-27	151	15	}	}	PUNCT
ma-27	151	16	is	be	AUX
ma-27	151	17	any	any	DET
ma-27	151	18	sequence	sequence	NOUN
ma-27	151	19	satisfying	satisfy	VERB
ma-27	151	20	0	0	PUNCT
ma-27	151	21	<	<	X
ma-27	151	22	p	p	X
ma-27	151	23	≤	≤	NUM
ma-27	151	24	ιs	ιs	PUNCT
ma-27	151	25	≤	≤	NUM
ma-27	151	26	q	q	NOUN
ma-27	151	27	<	<	X
ma-27	151	28	1	1	NUM
ma-27	151	29	for	for	ADP
ma-27	151	30	all	all	DET
ma-27	151	31	s	s	PART
ma-27	151	32	≥	≥	NOUN
ma-27	151	33	1	1	NUM
ma-27	151	34	.	.	PUNCT
ma-27	152	1	suppose	suppose	VERB
ma-27	152	2	{	{	PUNCT
ma-27	152	3	`	`	PUNCT
ma-27	152	4	s	s	X
ma-27	152	5	}	}	PUNCT
ma-27	152	6	and	and	CCONJ
ma-27	152	7	{	{	PUNCT
ma-27	152	8	ζs	ζs	PART
ma-27	152	9	}	}	PUNCT
ma-27	152	10	are	be	AUX
ma-27	152	11	any	any	DET
ma-27	152	12	sequences	sequence	NOUN
ma-27	152	13	of	of	ADP
ma-27	152	14	ω	ω	NUM
ma-27	152	15	such	such	ADJ
ma-27	152	16	that	that	SCONJ
ma-27	152	17	lim	lim	PROPN
ma-27	152	18	sup	sup	NOUN
ma-27	152	19	s→∞	s→∞	NUM
ma-27	152	20	‖`s‖	‖`s‖	PROPN
ma-27	152	21	≤	≤	NUM
ma-27	152	22	x	x	X
ma-27	152	23	,	,	PUNCT
ma-27	152	24	lim	lim	PROPN
ma-27	152	25	sup	sup	NOUN
ma-27	152	26	s→∞	s→∞	NUM
ma-27	153	1	‖ζs‖	‖ζs‖	INTJ
ma-27	154	1	≤	≤	ADV
ma-27	154	2	x	x	PUNCT
ma-27	154	3	and	and	CCONJ
ma-27	154	4	lim	lim	PROPN
ma-27	154	5	sup	sup	NOUN
ma-27	154	6	s→∞	s→∞	NOUN
ma-27	154	7	‖ιs`s	‖ιs`s	PROPN
ma-27	155	1	+	+	CCONJ
ma-27	155	2	(	(	PUNCT
ma-27	155	3	1	1	NUM
ma-27	155	4	−	−	NOUN
ma-27	155	5	ιs)ζs‖	ιs)ζs‖	NOUN
ma-27	156	1	=	=	NOUN
ma-27	156	2	x	x	AUX
ma-27	156	3	hold	hold	VERB
ma-27	156	4	for	for	ADP
ma-27	156	5	some	some	DET
ma-27	156	6	x	x	PUNCT
ma-27	156	7	≥	≥	NOUN
ma-27	156	8	0	0	NUM
ma-27	156	9	.	.	PUNCT
ma-27	157	1	then	then	ADV
ma-27	157	2	lim	lim	PROPN
ma-27	157	3	s→∞	s→∞	PROPN
ma-27	157	4	‖`s	‖`s	PROPN
ma-27	158	1	−	−	PUNCT
ma-27	159	1	ζs‖	ζs‖	PROPN
ma-27	159	2	=	=	SYM
ma-27	159	3	0	0	PROPN
ma-27	159	4	.	.	NOUN
ma-27	159	5	3	3	X
ma-27	159	6	.	.	X
ma-27	159	7	rate	rate	NOUN
ma-27	159	8	of	of	ADP
ma-27	159	9	convergence	convergence	NOUN
ma-27	159	10	in	in	ADP
ma-27	159	11	this	this	DET
ma-27	159	12	section	section	NOUN
ma-27	159	13	,	,	PUNCT
ma-27	159	14	we	we	PRON
ma-27	159	15	will	will	AUX
ma-27	159	16	prove	prove	VERB
ma-27	159	17	that	that	SCONJ
ma-27	159	18	our	our	PRON
ma-27	159	19	new	new	ADJ
ma-27	159	20	iterative	iterative	NOUN
ma-27	159	21	algorithm	algorithm	NOUN
ma-27	159	22	(	(	PUNCT
ma-27	159	23	1.7	1.7	NUM
ma-27	159	24	)	)	PUNCT
ma-27	159	25	converges	converge	VERB
ma-27	159	26	faster	fast	ADV
ma-27	159	27	than	than	ADP
ma-27	159	28	theiterative	theiterative	ADJ
ma-27	159	29	algorithm	algorithm	NOUN
ma-27	159	30	(	(	PUNCT
ma-27	159	31	1.6	1.6	NUM
ma-27	159	32	)	)	PUNCT
ma-27	159	33	for	for	ADP
ma-27	159	34	almost	almost	ADV
ma-27	159	35	contraction	contraction	NOUN
ma-27	159	36	mappings	mapping	NOUN
ma-27	159	37	.	.	PUNCT
ma-27	160	1	theorem	theorem	VERB
ma-27	160	2	3.1	3.1	NUM
ma-27	160	3	.	.	PUNCT
ma-27	161	1	let	let	VERB
ma-27	161	2	ω	ω	NUM
ma-27	161	3	be	be	AUX
ma-27	161	4	a	a	DET
ma-27	161	5	banach	banach	NOUN
ma-27	161	6	space	space	NOUN
ma-27	161	7	and	and	CCONJ
ma-27	161	8	let	let	VERB
ma-27	161	9	λ	λ	NOUN
ma-27	161	10	be	be	AUX
ma-27	161	11	a	a	DET
ma-27	161	12	nonempty	nonempty	ADV
ma-27	161	13	closed	close	VERB
ma-27	161	14	convex	convex	NOUN
ma-27	161	15	subset	subset	NOUN
ma-27	161	16	of	of	ADP
ma-27	161	17	ω	ω	PROPN
ma-27	161	18	.	.	PUNCT
ma-27	162	1	let	let	VERB
ma-27	162	2	t	t	NOUN
ma-27	162	3	:	:	PUNCT
ma-27	162	4	λ→	λ→	PUNCT
ma-27	162	5	λ	λ	NOUN
ma-27	162	6	be	be	AUX
ma-27	162	7	a	a	DET
ma-27	162	8	mapping	mapping	NOUN
ma-27	162	9	satisfying	satisfy	VERB
ma-27	162	10	(	(	PUNCT
ma-27	162	11	1.2	1.2	NUM
ma-27	162	12	)	)	PUNCT
ma-27	162	13	with	with	ADP
ma-27	162	14	f	f	PROPN
ma-27	162	15	(	(	PUNCT
ma-27	162	16	t	t	PROPN
ma-27	162	17	)	)	PUNCT
ma-27	163	1	6=	6=	ADP
ma-27	163	2	∅.	∅.	ADV
ma-27	163	3	let	let	VERB
ma-27	163	4	{	{	PUNCT
ma-27	163	5	`	`	PUNCT
ma-27	163	6	s	s	AUX
ma-27	163	7	}	}	PUNCT
ma-27	163	8	be	be	AUX
ma-27	163	9	the	the	DET
ma-27	163	10	iterative	iterative	ADJ
ma-27	163	11	algorithm	algorithm	NOUN
ma-27	163	12	defined	define	VERB
ma-27	163	13	by	by	ADP
ma-27	163	14	(	(	PUNCT
ma-27	163	15	1.7	1.7	NUM
ma-27	163	16	)	)	PUNCT
ma-27	163	17	with	with	ADP
ma-27	163	18	sequences	sequence	NOUN
ma-27	163	19	{	{	PUNCT
ma-27	163	20	δs	δs	NOUN
ma-27	163	21	}	}	PUNCT
ma-27	163	22	,	,	PUNCT
ma-27	163	23	{	{	PUNCT
ma-27	163	24	βs	βs	NOUN
ma-27	163	25	}	}	PUNCT
ma-27	163	26	∈	∈	PROPN
ma-27	164	1	[	[	X
ma-27	164	2	0	0	NUM
ma-27	164	3	,	,	PUNCT
ma-27	164	4	1	1	NUM
ma-27	164	5	]	]	PUNCT
ma-27	164	6	such	such	ADJ
ma-27	164	7	that	that	SCONJ
ma-27	164	8	∞∑	∞∑	NUM
ma-27	164	9	s=0	s=0	NOUN
ma-27	164	10	δsβs	δsβs	NOUN
ma-27	164	11	=	=	SYM
ma-27	164	12	∞	∞	PROPN
ma-27	164	13	,	,	PUNCT
ma-27	164	14	then	then	ADV
ma-27	164	15	{	{	PUNCT
ma-27	164	16	`	`	PUNCT
ma-27	164	17	s	s	X
ma-27	164	18	}	}	PUNCT
ma-27	164	19	converges	converge	VERB
ma-27	164	20	strongly	strongly	ADV
ma-27	164	21	to	to	ADP
ma-27	164	22	a	a	DET
ma-27	164	23	unique	unique	ADJ
ma-27	164	24	fixed	fix	VERB
ma-27	164	25	point	point	NOUN
ma-27	164	26	of	of	ADP
ma-27	164	27	t	t	PROPN
ma-27	164	28	.	.	PUNCT
ma-27	165	1	proof	proof	NOUN
ma-27	165	2	.	.	PUNCT
ma-27	166	1	let	let	VERB
ma-27	166	2	z	z	NOUN
ma-27	166	3	∈	∈	PROPN
ma-27	166	4	f	f	X
ma-27	166	5	(	(	PUNCT
ma-27	166	6	t	t	PROPN
ma-27	166	7	)	)	PUNCT
ma-27	166	8	and	and	CCONJ
ma-27	166	9	from	from	ADP
ma-27	166	10	(	(	PUNCT
ma-27	166	11	1.7	1.7	NUM
ma-27	166	12	)	)	PUNCT
ma-27	166	13	,	,	PUNCT
ma-27	166	14	we	we	PRON
ma-27	166	15	have	have	AUX
ma-27	166	16	get	get	VERB
ma-27	166	17	‖gs	‖gs	PRON
ma-27	166	18	−	−	NOUN
ma-27	166	19	z‖	z‖	NOUN
ma-27	166	20	=	=	SYM
ma-27	167	1	‖(1−	‖(1−	PROPN
ma-27	167	2	βs)`s	βs)`s	NOUN
ma-27	168	1	+	+	CCONJ
ma-27	168	2	βst`s	βst`s	PROPN
ma-27	168	3	−	−	NOUN
ma-27	168	4	z‖	z‖	NOUN
ma-27	168	5	≤	≤	NOUN
ma-27	168	6	(	(	PUNCT
ma-27	168	7	1−	1−	NUM
ma-27	168	8	βs)‖`s	βs)‖`s	PUNCT
ma-27	168	9	−	−	PUNCT
ma-27	168	10	z‖+	z‖+	NOUN
ma-27	168	11	βs‖t`s	βs‖t`s	NOUN
ma-27	169	1	−	−	PROPN
ma-27	169	2	z‖	z‖	NOUN
ma-27	169	3	≤	≤	NOUN
ma-27	169	4	(	(	PUNCT
ma-27	169	5	1−	1−	NUM
ma-27	169	6	βs)‖`s	βs)‖`s	PUNCT
ma-27	170	1	−	−	PUNCT
ma-27	170	2	z‖+	z‖+	X
ma-27	170	3	βsγ‖`s	βsγ‖`s	PUNCT
ma-27	170	4	−	−	NOUN
ma-27	170	5	z‖	z‖	NOUN
ma-27	170	6	=	=	SYM
ma-27	170	7	(	(	PUNCT
ma-27	170	8	1−	1−	NUM
ma-27	170	9	(	(	PUNCT
ma-27	170	10	1−	1−	NUM
ma-27	170	11	γ)βs)‖`s	γ)βs)‖`s	NUM
ma-27	170	12	−	−	PROPN
ma-27	170	13	z‖.	z‖.	X
ma-27	170	14	(	(	PUNCT
ma-27	170	15	3.1	3.1	NUM
ma-27	170	16	)	)	PUNCT
ma-27	170	17	eur	eur	PROPN
ma-27	170	18	.	.	PUNCT
ma-27	171	1	j.	j.	PROPN
ma-27	171	2	math	math	PROPN
ma-27	171	3	.	.	PUNCT
ma-27	172	1	anal	anal	ADJ
ma-27	172	2	.	.	PUNCT
ma-27	173	1	1	1	NUM
ma-27	173	2	(	(	PUNCT
ma-27	173	3	2021	2021	NUM
ma-27	173	4	)	)	PUNCT
ma-27	174	1	113using	113using	PROPN
ma-27	174	2	(	(	PUNCT
ma-27	174	3	1.7	1.7	NUM
ma-27	174	4	)	)	PUNCT
ma-27	174	5	and	and	CCONJ
ma-27	174	6	(	(	PUNCT
ma-27	174	7	3.1	3.1	NUM
ma-27	174	8	)	)	PUNCT
ma-27	174	9	,	,	PUNCT
ma-27	174	10	we	we	PRON
ma-27	174	11	have	have	VERB
ma-27	174	12	‖ws	‖ws	NUM
ma-27	174	13	−	−	PROPN
ma-27	174	14	z‖	z‖	NOUN
ma-27	174	15	=	=	SYM
ma-27	174	16	‖(1−	‖(1−	ADJ
ma-27	174	17	δs)t`s	δs)t`s	NOUN
ma-27	174	18	+	+	CCONJ
ma-27	174	19	δstgs	δstgs	NOUN
ma-27	174	20	−	−	PROPN
ma-27	174	21	z‖	z‖	NOUN
ma-27	174	22	≤	≤	NOUN
ma-27	174	23	(	(	PUNCT
ma-27	174	24	1−	1−	NUM
ma-27	174	25	δs)‖t`s	δs)‖t`s	PROPN
ma-27	174	26	−	−	PROPN
ma-27	174	27	z‖+	z‖+	PROPN
ma-27	174	28	δs‖tgs	δs‖tg	VERB
ma-27	174	29	−	−	PROPN
ma-27	174	30	z‖	z‖	NOUN
ma-27	174	31	≤	≤	NUM
ma-27	174	32	γ(1−	γ(1−	PROPN
ma-27	175	1	δs)‖`s	δs)‖`s	X
ma-27	175	2	−	−	PROPN
ma-27	176	1	z‖+	z‖+	NOUN
ma-27	176	2	γδs‖gs	γδs‖gs	PROPN
ma-27	177	1	−	−	NOUN
ma-27	177	2	z‖	z‖	NOUN
ma-27	177	3	≤	≤	NUM
ma-27	177	4	γ(1−	γ(1−	PROPN
ma-27	177	5	δs)‖`s	δs)‖`s	X
ma-27	177	6	−	−	NOUN
ma-27	177	7	z‖+	z‖+	NOUN
ma-27	177	8	γδs(1−	γδs(1−	VERB
ma-27	177	9	(	(	PUNCT
ma-27	177	10	1−	1−	NUM
ma-27	177	11	γ)βs)‖`s	γ)βs)‖`s	NUM
ma-27	177	12	−	−	NOUN
ma-27	177	13	z‖	z‖	NOUN
ma-27	177	14	=	=	SYM
ma-27	177	15	γ(1−	γ(1−	PROPN
ma-27	177	16	(	(	PUNCT
ma-27	177	17	1−	1−	NUM
ma-27	177	18	γ)δsβs)‖`s	γ)δsβs)‖`s	PROPN
ma-27	177	19	−	−	PROPN
ma-27	177	20	z‖.	z‖.	X
ma-27	177	21	(	(	PUNCT
ma-27	177	22	3.2	3.2	NUM
ma-27	177	23	)	)	PUNCT
ma-27	177	24	from	from	ADP
ma-27	177	25	(	(	PUNCT
ma-27	177	26	1.7	1.7	NUM
ma-27	177	27	)	)	PUNCT
ma-27	177	28	and	and	CCONJ
ma-27	177	29	(	(	PUNCT
ma-27	177	30	3.2	3.2	NUM
ma-27	177	31	)	)	PUNCT
ma-27	177	32	,	,	PUNCT
ma-27	177	33	we	we	PRON
ma-27	177	34	obtain	obtain	VERB
ma-27	177	35	‖ζs	‖ζ	NOUN
ma-27	177	36	−	−	PROPN
ma-27	177	37	z‖	z‖	NOUN
ma-27	177	38	=	=	SYM
ma-27	177	39	‖tws	‖tws	NOUN
ma-27	178	1	−	−	PROPN
ma-27	178	2	z‖	z‖	NOUN
ma-27	178	3	≤	≤	X
ma-27	178	4	γ‖ws	γ‖ws	PROPN
ma-27	178	5	−	−	PROPN
ma-27	178	6	z‖	z‖	NOUN
ma-27	178	7	≤	≤	NUM
ma-27	178	8	γ2(1−	γ2(1−	PROPN
ma-27	179	1	(	(	PUNCT
ma-27	179	2	1−	1−	NUM
ma-27	179	3	γ)δsβs)‖`s	γ)δsβs)‖`s	PROPN
ma-27	179	4	−	−	PROPN
ma-27	179	5	z‖.	z‖.	X
ma-27	179	6	(	(	PUNCT
ma-27	179	7	3.3	3.3	NUM
ma-27	179	8	)	)	PUNCT
ma-27	179	9	using	use	VERB
ma-27	179	10	(	(	PUNCT
ma-27	179	11	1.7	1.7	NUM
ma-27	179	12	)	)	PUNCT
ma-27	179	13	and	and	CCONJ
ma-27	179	14	(	(	PUNCT
ma-27	179	15	3.3	3.3	NUM
ma-27	179	16	)	)	PUNCT
ma-27	179	17	,	,	PUNCT
ma-27	179	18	we	we	PRON
ma-27	179	19	have	have	VERB
ma-27	179	20	‖`s+1	‖`s+1	ADJ
ma-27	179	21	−	−	PROPN
ma-27	179	22	z‖	z‖	NOUN
ma-27	179	23	=	=	SYM
ma-27	179	24	‖tζs	‖tζs	NOUN
ma-27	179	25	−	−	NOUN
ma-27	179	26	z‖	z‖	NOUN
ma-27	179	27	≤	≤	NOUN
ma-27	180	1	γ‖ζs	γ‖ζs	ADP
ma-27	180	2	−	−	PROPN
ma-27	180	3	z‖	z‖	NOUN
ma-27	180	4	≤	≤	NUM
ma-27	180	5	γ3(1−	γ3(1−	ADV
ma-27	180	6	(	(	PUNCT
ma-27	180	7	1−	1−	NUM
ma-27	180	8	γ)δsβs)‖`s	γ)δsβs)‖`s	PROPN
ma-27	180	9	−	−	PROPN
ma-27	180	10	z‖.	z‖.	X
ma-27	180	11	(	(	PUNCT
ma-27	180	12	3.4	3.4	NUM
ma-27	180	13	)	)	PUNCT
ma-27	180	14	from	from	ADP
ma-27	180	15	(	(	PUNCT
ma-27	180	16	3.4	3.4	NUM
ma-27	180	17	)	)	PUNCT
ma-27	180	18	,	,	PUNCT
ma-27	180	19	we	we	PRON
ma-27	180	20	have	have	VERB
ma-27	180	21	the	the	DET
ma-27	180	22	following	follow	VERB
ma-27	180	23	inequalities	inequality	NOUN
ma-27	180	24	:	:	PUNCT
ma-27	180	25	‖`s+1	‖`s+1	ADJ
ma-27	180	26	−	−	PROPN
ma-27	180	27	z‖	z‖	NOUN
ma-27	180	28	≤	≤	NUM
ma-27	180	29	γ3(1−	γ3(1−	ADV
ma-27	180	30	(	(	PUNCT
ma-27	180	31	1−	1−	NUM
ma-27	180	32	γ)δsβs)‖`s	γ)δsβs)‖`s	PROPN
ma-27	180	33	−	−	PROPN
ma-27	180	34	z‖	z‖	NOUN
ma-27	180	35	≤	≤	NUM
ma-27	180	36	γ3(1−	γ3(1−	ADV
ma-27	180	37	(	(	PUNCT
ma-27	180	38	1−	1−	NUM
ma-27	180	39	γ)δs−1βs−1)‖`s−1	γ)δs−1βs−1)‖`s−1	PROPN
ma-27	180	40	−	−	PROPN
ma-27	180	41	z‖	z‖	NOUN
ma-27	180	42	...	...	PUNCT
ma-27	180	43	‖`1	‖`1	PUNCT
ma-27	180	44	−	−	NOUN
ma-27	180	45	z‖	z‖	NOUN
ma-27	180	46	≤	≤	NUM
ma-27	180	47	γ3(1−	γ3(1−	ADV
ma-27	181	1	(	(	PUNCT
ma-27	181	2	1−	1−	NUM
ma-27	181	3	γ)δ0β0)‖`0	γ)δ0β0)‖`0	PROPN
ma-27	181	4	−	−	PROPN
ma-27	181	5	z‖.	z‖.	NOUN
ma-27	181	6	(	(	PUNCT
ma-27	181	7	3.5	3.5	NUM
ma-27	181	8	)	)	PUNCT
ma-27	181	9	from	from	ADP
ma-27	181	10	(	(	PUNCT
ma-27	181	11	3.5	3.5	NUM
ma-27	181	12	)	)	PUNCT
ma-27	181	13	,	,	PUNCT
ma-27	181	14	we	we	PRON
ma-27	181	15	get	get	VERB
ma-27	181	16	‖`s+1	‖`s+1	ADJ
ma-27	181	17	−	−	PROPN
ma-27	181	18	z‖	z‖	NOUN
ma-27	181	19	≤	≤	NUM
ma-27	181	20	‖`0	‖`0	PUNCT
ma-27	181	21	−	−	PROPN
ma-27	181	22	z‖γ3(s+1	z‖γ3(s+1	PROPN
ma-27	181	23	)	)	PUNCT
ma-27	181	24	s∏	s∏	PROPN
ma-27	181	25	t=0	t=0	X
ma-27	181	26	(	(	PUNCT
ma-27	181	27	1−	1−	NUM
ma-27	181	28	(	(	PUNCT
ma-27	181	29	1−	1−	NUM
ma-27	181	30	γ)δtβt	γ)δtβt	NUM
ma-27	181	31	)	)	PUNCT
ma-27	181	32	.	.	PUNCT
ma-27	182	1	(	(	PUNCT
ma-27	182	2	3.6	3.6	NUM
ma-27	182	3	)	)	PUNCT
ma-27	182	4	since	since	SCONJ
ma-27	182	5	γ	γ	PROPN
ma-27	182	6	∈	∈	PROPN
ma-27	182	7	(	(	PUNCT
ma-27	182	8	0	0	NUM
ma-27	182	9	,	,	PUNCT
ma-27	182	10	1	1	NUM
ma-27	182	11	)	)	PUNCT
ma-27	182	12	,	,	PUNCT
ma-27	182	13	δt	δt	AUX
ma-27	182	14	,	,	PUNCT
ma-27	182	15	βt	βt	VERB
ma-27	182	16	∈	∈	PROPN
ma-27	183	1	[	[	X
ma-27	183	2	0	0	NUM
ma-27	183	3	,	,	PUNCT
ma-27	183	4	1	1	NUM
ma-27	183	5	]	]	PUNCT
ma-27	183	6	for	for	ADP
ma-27	183	7	all	all	DET
ma-27	183	8	t	t	NOUN
ma-27	183	9	∈	∈	PRON
ma-27	183	10	n	n	CCONJ
ma-27	183	11	,	,	PUNCT
ma-27	183	12	it	it	PRON
ma-27	183	13	follows	follow	VERB
ma-27	183	14	that	that	SCONJ
ma-27	183	15	(	(	PUNCT
ma-27	183	16	1−	1−	NUM
ma-27	183	17	(	(	PUNCT
ma-27	183	18	1−	1−	NUM
ma-27	183	19	γ)δtβt	γ)δtβt	NOUN
ma-27	183	20	)	)	PUNCT
ma-27	183	21	∈	∈	PROPN
ma-27	183	22	(	(	PUNCT
ma-27	183	23	0	0	NUM
ma-27	183	24	,	,	PUNCT
ma-27	183	25	1	1	NUM
ma-27	183	26	)	)	PUNCT
ma-27	183	27	.	.	PUNCT
ma-27	184	1	since	since	SCONJ
ma-27	184	2	fromclassical	fromclassical	ADJ
ma-27	184	3	analysis	analysis	NOUN
ma-27	184	4	we	we	PRON
ma-27	184	5	know	know	VERB
ma-27	184	6	that	that	SCONJ
ma-27	184	7	1−	1−	NUM
ma-27	184	8	`	`	PUNCT
ma-27	184	9	≤	≤	NOUN
ma-27	185	1	e−	e−	PROPN
ma-27	185	2	`	`	PUNCT
ma-27	185	3	for	for	ADP
ma-27	185	4	all	all	DET
ma-27	185	5	`	`	PUNCT
ma-27	185	6	∈	∈	PROPN
ma-27	185	7	[	[	X
ma-27	185	8	0	0	NUM
ma-27	185	9	,	,	PUNCT
ma-27	185	10	1	1	NUM
ma-27	185	11	]	]	PUNCT
ma-27	185	12	,	,	PUNCT
ma-27	185	13	thus	thus	ADV
ma-27	185	14	from	from	ADP
ma-27	185	15	(	(	PUNCT
ma-27	185	16	3.6	3.6	NUM
ma-27	185	17	)	)	PUNCT
ma-27	185	18	,	,	PUNCT
ma-27	185	19	we	we	PRON
ma-27	185	20	have	have	VERB
ma-27	185	21	‖`s+1	‖`s+1	ADJ
ma-27	185	22	−	−	PROPN
ma-27	185	23	z‖	z‖	NOUN
ma-27	185	24	≤	≤	NUM
ma-27	185	25	γ3(s+1)‖`0	γ3(s+1)‖`0	NOUN
ma-27	185	26	−	−	PROPN
ma-27	185	27	z‖	z‖	NOUN
ma-27	185	28	e	e	X
ma-27	185	29	(	(	PUNCT
ma-27	185	30	1−γ	1−γ	NUM
ma-27	185	31	)	)	PUNCT
ma-27	185	32	s∑	s∑	PROPN
ma-27	185	33	t=0	t=0	PROPN
ma-27	185	34	δtβt	δtβt	ADJ
ma-27	185	35	.	.	PUNCT
ma-27	186	1	(	(	PUNCT
ma-27	186	2	3.7	3.7	NUM
ma-27	186	3	)	)	PUNCT
ma-27	186	4	if	if	SCONJ
ma-27	186	5	we	we	PRON
ma-27	186	6	take	take	VERB
ma-27	186	7	the	the	DET
ma-27	186	8	limits	limit	NOUN
ma-27	186	9	of	of	ADP
ma-27	186	10	both	both	DET
ma-27	186	11	sides	side	NOUN
ma-27	186	12	of	of	ADP
ma-27	186	13	(	(	PUNCT
ma-27	186	14	3.7	3.7	NUM
ma-27	186	15	)	)	PUNCT
ma-27	186	16	,	,	PUNCT
ma-27	186	17	we	we	PRON
ma-27	186	18	get	get	VERB
ma-27	186	19	lim	lim	PROPN
ma-27	186	20	s→∞	s→∞	PROPN
ma-27	187	1	‖`s	‖`s	PROPN
ma-27	187	2	−	−	PROPN
ma-27	187	3	z‖	z‖	NOUN
ma-27	187	4	=	=	SYM
ma-27	187	5	0	0	X
ma-27	187	6	.	.	PUNCT
ma-27	187	7	�	�	PROPN
ma-27	187	8	eur	eur	PROPN
ma-27	187	9	.	.	PUNCT
ma-27	188	1	j.	j.	PROPN
ma-27	188	2	math	math	PROPN
ma-27	188	3	.	.	PUNCT
ma-27	189	1	anal	anal	ADJ
ma-27	189	2	.	.	PUNCT
ma-27	190	1	1	1	NUM
ma-27	190	2	(	(	PUNCT
ma-27	190	3	2021	2021	NUM
ma-27	190	4	)	)	PUNCT
ma-27	190	5	114	114	NUM
ma-27	190	6	theorem	theorem	NOUN
ma-27	190	7	3.2	3.2	NUM
ma-27	190	8	.	.	PUNCT
ma-27	191	1	let	let	VERB
ma-27	191	2	ω	ω	NOUN
ma-27	191	3	be	be	AUX
ma-27	191	4	a	a	DET
ma-27	191	5	banach	banach	NOUN
ma-27	191	6	space	space	NOUN
ma-27	191	7	and	and	CCONJ
ma-27	191	8	let	let	VERB
ma-27	191	9	λ	λ	NOUN
ma-27	191	10	be	be	AUX
ma-27	191	11	a	a	DET
ma-27	191	12	nonempty	nonempty	ADV
ma-27	191	13	closed	close	VERB
ma-27	191	14	convex	convex	NOUN
ma-27	191	15	subset	subset	NOUN
ma-27	191	16	of	of	ADP
ma-27	191	17	ω	ω	PROPN
ma-27	191	18	.	.	PUNCT
ma-27	192	1	let	let	VERB
ma-27	192	2	t	t	NOUN
ma-27	192	3	:	:	PUNCT
ma-27	192	4	λ	λ	X
ma-27	192	5	→	→	SYM
ma-27	192	6	λ	λ	X
ma-27	192	7	be	be	AUX
ma-27	192	8	a	a	DET
ma-27	192	9	mapping	mapping	NOUN
ma-27	192	10	satisfying	satisfy	VERB
ma-27	192	11	(	(	PUNCT
ma-27	192	12	1.2	1.2	NUM
ma-27	192	13	)	)	PUNCT
ma-27	192	14	with	with	ADP
ma-27	192	15	f	f	PROPN
ma-27	192	16	(	(	PUNCT
ma-27	192	17	t	t	PROPN
ma-27	192	18	)	)	PUNCT
ma-27	192	19	6=	6=	ADP
ma-27	192	20	∅.	∅.	VERB
ma-27	192	21	for	for	ADP
ma-27	192	22	given	give	VERB
ma-27	192	23	`	`	PUNCT
ma-27	192	24	0	0	NUM
ma-27	192	25	=	=	SYM
ma-27	192	26	m0	m0	PROPN
ma-27	192	27	∈	∈	PROPN
ma-27	192	28	λ	λ	PROPN
ma-27	192	29	,	,	PUNCT
ma-27	192	30	let	let	VERB
ma-27	192	31	{	{	PUNCT
ma-27	192	32	`	`	PUNCT
ma-27	192	33	s	s	X
ma-27	192	34	}	}	PUNCT
ma-27	192	35	and	and	CCONJ
ma-27	192	36	{	{	PUNCT
ma-27	192	37	ms	ms	NOUN
ma-27	192	38	}	}	PUNCT
ma-27	192	39	be	be	VERB
ma-27	192	40	the	the	DET
ma-27	192	41	iterative	iterative	ADJ
ma-27	192	42	algorithms	algorithms	NOUN
ma-27	192	43	defined	define	VERB
ma-27	192	44	by	by	ADP
ma-27	192	45	(	(	PUNCT
ma-27	192	46	1.7	1.7	NUM
ma-27	192	47	)	)	PUNCT
ma-27	192	48	and	and	CCONJ
ma-27	192	49	(	(	PUNCT
ma-27	192	50	1.6	1.6	NUM
ma-27	192	51	)	)	PUNCT
ma-27	192	52	,	,	PUNCT
ma-27	192	53	respectively	respectively	ADV
ma-27	192	54	,	,	PUNCT
ma-27	192	55	with	with	ADP
ma-27	192	56	real	real	ADJ
ma-27	192	57	sequences	sequence	NOUN
ma-27	192	58	{	{	PUNCT
ma-27	192	59	δs	δs	NOUN
ma-27	192	60	}	}	PUNCT
ma-27	192	61	and	and	CCONJ
ma-27	192	62	{	{	PUNCT
ma-27	192	63	βs	β	NOUN
ma-27	192	64	}	}	PUNCT
ma-27	192	65	in	in	ADP
ma-27	192	66	[	[	X
ma-27	192	67	0,1	0,1	NUM
ma-27	192	68	]	]	PUNCT
ma-27	192	69	such	such	ADJ
ma-27	192	70	that	that	DET
ma-27	192	71	δs	δs	VERB
ma-27	193	1	≤	≤	NUM
ma-27	193	2	δ	δ	PROPN
ma-27	193	3	<	<	X
ma-27	193	4	1	1	NUM
ma-27	193	5	and	and	CCONJ
ma-27	193	6	βs	βs	ADJ
ma-27	193	7	≤	≤	NUM
ma-27	193	8	β	β	X
ma-27	193	9	<	<	X
ma-27	193	10	1	1	NUM
ma-27	193	11	,	,	PUNCT
ma-27	193	12	for	for	ADP
ma-27	193	13	all	all	DET
ma-27	193	14	s	s	PART
ma-27	193	15	∈	∈	NOUN
ma-27	193	16	n	n	NOUN
ma-27	193	17	and	and	CCONJ
ma-27	193	18	for	for	ADP
ma-27	193	19	some	some	DET
ma-27	193	20	δ	δ	PROPN
ma-27	193	21	,	,	PUNCT
ma-27	193	22	β	β	X
ma-27	193	23	>	>	X
ma-27	193	24	0	0	X
ma-27	193	25	.	.	PUNCT
ma-27	194	1	then	then	ADV
ma-27	194	2	{	{	PUNCT
ma-27	194	3	`	`	PUNCT
ma-27	194	4	s	s	X
ma-27	194	5	}	}	PUNCT
ma-27	194	6	converges	converge	NOUN
ma-27	194	7	to	to	ADP
ma-27	194	8	z	z	NOUN
ma-27	194	9	faster	fast	ADV
ma-27	194	10	than	than	SCONJ
ma-27	194	11	{	{	PUNCT
ma-27	194	12	ms	ms	PROPN
ma-27	194	13	}	}	PUNCT
ma-27	194	14	does	do	VERB
ma-27	194	15	.	.	PUNCT
ma-27	195	1	proof	proof	NOUN
ma-27	195	2	.	.	PUNCT
ma-27	196	1	from	from	ADP
ma-27	196	2	(	(	PUNCT
ma-27	196	3	3.6	3.6	NUM
ma-27	196	4	)	)	PUNCT
ma-27	196	5	in	in	ADP
ma-27	196	6	theorem	theorem	ADJ
ma-27	196	7	3.1	3.1	NUM
ma-27	196	8	together	together	ADV
ma-27	196	9	with	with	ADP
ma-27	196	10	the	the	DET
ma-27	196	11	assumptions	assumption	NOUN
ma-27	196	12	αs	αs	ADP
ma-27	196	13	≤	≤	ADJ
ma-27	196	14	α	α	NOUN
ma-27	196	15	<	<	X
ma-27	196	16	1	1	NUM
ma-27	196	17	and	and	CCONJ
ma-27	196	18	βs	βs	ADJ
ma-27	196	19	≤	≤	NUM
ma-27	196	20	β	β	X
ma-27	196	21	<	<	X
ma-27	196	22	1	1	NUM
ma-27	196	23	,	,	PUNCT
ma-27	196	24	forall	forall	NOUN
ma-27	196	25	s	s	X
ma-27	196	26	∈	∈	NOUN
ma-27	196	27	n	n	NOUN
ma-27	196	28	and	and	CCONJ
ma-27	196	29	for	for	ADP
ma-27	196	30	some	some	DET
ma-27	196	31	α	α	NOUN
ma-27	196	32	,	,	PUNCT
ma-27	196	33	β	β	X
ma-27	196	34	>	>	X
ma-27	196	35	0	0	NUM
ma-27	196	36	,	,	PUNCT
ma-27	196	37	then	then	ADV
ma-27	196	38	we	we	PRON
ma-27	196	39	have	have	VERB
ma-27	196	40	‖`s+1	‖`s+1	ADJ
ma-27	196	41	−	−	PROPN
ma-27	196	42	z‖	z‖	NOUN
ma-27	196	43	≤	≤	NUM
ma-27	196	44	‖`0	‖`0	PUNCT
ma-27	196	45	−	−	PROPN
ma-27	196	46	z‖γ3(s+1	z‖γ3(s+1	PROPN
ma-27	196	47	)	)	PUNCT
ma-27	196	48	s∏	s∏	PROPN
ma-27	196	49	t=0	t=0	X
ma-27	196	50	(	(	PUNCT
ma-27	196	51	1−	1−	NUM
ma-27	196	52	(	(	PUNCT
ma-27	196	53	1−	1−	NUM
ma-27	196	54	γ)αtβt	γ)αtβt	NUM
ma-27	196	55	)	)	PUNCT
ma-27	197	1	=	=	PUNCT
ma-27	197	2	‖`0	‖`0	VERB
ma-27	197	3	−	−	PROPN
ma-27	197	4	z‖γ3(s+1)(1−	z‖γ3(s+1)(1−	PROPN
ma-27	197	5	(	(	PUNCT
ma-27	197	6	1−	1−	NUM
ma-27	197	7	γ)αβ)s+1	γ)αβ)s+1	NOUN
ma-27	197	8	.	.	PUNCT
ma-27	198	1	(	(	PUNCT
ma-27	198	2	3.8	3.8	NUM
ma-27	198	3	)	)	PUNCT
ma-27	198	4	similarly	similarly	ADV
ma-27	198	5	,	,	PUNCT
ma-27	198	6	from	from	ADP
ma-27	198	7	(	(	PUNCT
ma-27	198	8	1.6	1.6	NUM
ma-27	198	9	)	)	PUNCT
ma-27	198	10	,	,	PUNCT
ma-27	198	11	we	we	PRON
ma-27	198	12	get	get	VERB
ma-27	198	13	‖cs	‖cs	PROPN
ma-27	198	14	−	−	NOUN
ma-27	198	15	z‖	z‖	NOUN
ma-27	198	16	=	=	SYM
ma-27	198	17	‖(1−	‖(1−	PROPN
ma-27	198	18	δs)ms	δs)ms	PUNCT
ma-27	198	19	+	+	NUM
ma-27	198	20	δstms	δstms	NOUN
ma-27	198	21	−	−	NOUN
ma-27	198	22	z‖	z‖	NOUN
ma-27	198	23	≤	≤	NUM
ma-27	198	24	(	(	PUNCT
ma-27	198	25	1−	1−	NUM
ma-27	198	26	δs)‖ms	δs)‖ms	NOUN
ma-27	198	27	−	−	PROPN
ma-27	199	1	z‖+	z‖+	PROPN
ma-27	199	2	δs‖tms	δs‖tms	PROPN
ma-27	199	3	−	−	PROPN
ma-27	199	4	z‖	z‖	NOUN
ma-27	199	5	≤	≤	NUM
ma-27	199	6	(	(	PUNCT
ma-27	199	7	1−	1−	NUM
ma-27	199	8	δs)‖ms	δs)‖ms	NOUN
ma-27	199	9	−	−	PROPN
ma-27	200	1	z‖+	z‖+	NOUN
ma-27	200	2	δsγ‖mn	δsγ‖mn	PROPN
ma-27	200	3	−	−	PROPN
ma-27	200	4	z‖	z‖	NOUN
ma-27	200	5	=	=	SYM
ma-27	200	6	(	(	PUNCT
ma-27	200	7	1−	1−	NUM
ma-27	200	8	(	(	PUNCT
ma-27	200	9	1−	1−	NUM
ma-27	200	10	γ)δs)‖ms	γ)δs)‖ms	PROPN
ma-27	200	11	−	−	PROPN
ma-27	200	12	z‖.	z‖.	X
ma-27	200	13	(	(	PUNCT
ma-27	200	14	3.9	3.9	NUM
ma-27	200	15	)	)	PUNCT
ma-27	200	16	using	use	VERB
ma-27	200	17	(	(	PUNCT
ma-27	200	18	1.6	1.6	NUM
ma-27	200	19	)	)	PUNCT
ma-27	200	20	and	and	CCONJ
ma-27	200	21	(	(	PUNCT
ma-27	200	22	3.9	3.9	NUM
ma-27	200	23	)	)	PUNCT
ma-27	200	24	,	,	PUNCT
ma-27	200	25	we	we	PRON
ma-27	200	26	get	get	VERB
ma-27	200	27	‖ds	‖ds	PROPN
ma-27	200	28	−	−	PROPN
ma-27	200	29	z‖	z‖	NOUN
ma-27	200	30	=	=	SYM
ma-27	200	31	‖tcs	‖tcs	NOUN
ma-27	200	32	−	−	PROPN
ma-27	200	33	z‖	z‖	NOUN
ma-27	200	34	≤	≤	X
ma-27	201	1	γ‖cs	γ‖cs	ADP
ma-27	201	2	−	−	NOUN
ma-27	201	3	z‖	z‖	NOUN
ma-27	201	4	≤	≤	NUM
ma-27	201	5	γ(1−	γ(1−	PROPN
ma-27	201	6	(	(	PUNCT
ma-27	201	7	1−	1−	NUM
ma-27	201	8	γ)δs)‖ms	γ)δs)‖ms	PROPN
ma-27	201	9	−	−	PROPN
ma-27	201	10	z‖.	z‖.	NOUN
ma-27	201	11	(	(	PUNCT
ma-27	201	12	3.10	3.10	NUM
ma-27	201	13	)	)	PUNCT
ma-27	201	14	finally	finally	ADV
ma-27	201	15	,	,	PUNCT
ma-27	201	16	from	from	ADP
ma-27	201	17	(	(	PUNCT
ma-27	201	18	1.6	1.6	NUM
ma-27	201	19	)	)	PUNCT
ma-27	201	20	and	and	CCONJ
ma-27	201	21	(	(	PUNCT
ma-27	201	22	3.10	3.10	NUM
ma-27	201	23	)	)	PUNCT
ma-27	201	24	,	,	PUNCT
ma-27	201	25	we	we	PRON
ma-27	201	26	obtain	obtain	VERB
ma-27	201	27	‖ms+1	‖ms+1	ADP
ma-27	201	28	−	−	PROPN
ma-27	201	29	z‖	z‖	NOUN
ma-27	201	30	=	=	SYM
ma-27	201	31	‖tds	‖tds	PROPN
ma-27	201	32	−	−	PROPN
ma-27	201	33	z‖	z‖	NOUN
ma-27	201	34	≤	≤	X
ma-27	202	1	γ‖ds	γ‖ds	PROPN
ma-27	202	2	−	−	PROPN
ma-27	202	3	z‖	z‖	NOUN
ma-27	202	4	≤	≤	NUM
ma-27	202	5	γ2(1−	γ2(1−	PROPN
ma-27	203	1	(	(	PUNCT
ma-27	203	2	1−	1−	NUM
ma-27	203	3	γ)δs)‖ms	γ)δs)‖ms	PROPN
ma-27	203	4	−	−	PROPN
ma-27	203	5	z‖.	z‖.	NOUN
ma-27	203	6	(	(	PUNCT
ma-27	203	7	3.11	3.11	NUM
ma-27	203	8	)	)	PUNCT
ma-27	203	9	from	from	ADP
ma-27	203	10	(	(	PUNCT
ma-27	203	11	3.11	3.11	NUM
ma-27	203	12	)	)	PUNCT
ma-27	203	13	,	,	PUNCT
ma-27	203	14	we	we	PRON
ma-27	203	15	have	have	VERB
ma-27	203	16	the	the	DET
ma-27	203	17	following	follow	VERB
ma-27	203	18	inequalities	inequality	NOUN
ma-27	203	19	:	:	PUNCT
ma-27	203	20	‖ms+1	‖ms+1	ADP
ma-27	203	21	−	−	PROPN
ma-27	203	22	z‖	z‖	NOUN
ma-27	203	23	≤	≤	NUM
ma-27	203	24	γ2(1−	γ2(1−	PROPN
ma-27	204	1	(	(	PUNCT
ma-27	204	2	1−	1−	NUM
ma-27	204	3	γ)δs)‖ms	γ)δs)‖ms	NOUN
ma-27	204	4	−	−	PROPN
ma-27	204	5	z‖	z‖	NOUN
ma-27	204	6	≤	≤	NUM
ma-27	204	7	γ2(1−	γ2(1−	PROPN
ma-27	205	1	(	(	PUNCT
ma-27	205	2	1−	1−	NUM
ma-27	205	3	γ)δs−1)‖ms−1	γ)δs−1)‖ms−1	NOUN
ma-27	205	4	−	−	NOUN
ma-27	205	5	z‖	z‖	NOUN
ma-27	205	6	...	...	PUNCT
ma-27	205	7	‖m1	‖m1	NOUN
ma-27	205	8	−	−	NOUN
ma-27	205	9	z‖	z‖	NOUN
ma-27	205	10	≤	≤	NUM
ma-27	205	11	γ2(1−	γ2(1−	PROPN
ma-27	206	1	(	(	PUNCT
ma-27	206	2	1−	1−	NUM
ma-27	206	3	γ)δ0)‖m0	γ)δ0)‖m0	PROPN
ma-27	206	4	−	−	PROPN
ma-27	206	5	z‖.	z‖.	X
ma-27	206	6	(	(	PUNCT
ma-27	206	7	3.12	3.12	NUM
ma-27	206	8	)	)	PUNCT
ma-27	206	9	eur	eur	PROPN
ma-27	206	10	.	.	PUNCT
ma-27	207	1	j.	j.	PROPN
ma-27	207	2	math	math	PROPN
ma-27	207	3	.	.	PUNCT
ma-27	208	1	anal	anal	ADJ
ma-27	208	2	.	.	PUNCT
ma-27	209	1	1	1	NUM
ma-27	209	2	(	(	PUNCT
ma-27	209	3	2021	2021	NUM
ma-27	209	4	)	)	PUNCT
ma-27	210	1	115from	115from	PROPN
ma-27	210	2	(	(	PUNCT
ma-27	210	3	3.12	3.12	NUM
ma-27	210	4	)	)	PUNCT
ma-27	210	5	,	,	PUNCT
ma-27	210	6	we	we	PRON
ma-27	210	7	get	get	VERB
ma-27	210	8	‖ms+1	‖ms+1	ADP
ma-27	210	9	−	−	PROPN
ma-27	210	10	z‖	z‖	NOUN
ma-27	210	11	≤	≤	NUM
ma-27	210	12	‖m0	‖m0	PROPN
ma-27	210	13	−	−	PROPN
ma-27	210	14	z‖γ2(s+1	z‖γ2(s+1	PROPN
ma-27	210	15	)	)	PUNCT
ma-27	210	16	s∏	s∏	PROPN
ma-27	210	17	t=0	t=0	X
ma-27	210	18	(	(	PUNCT
ma-27	210	19	1−	1−	NUM
ma-27	210	20	(	(	PUNCT
ma-27	210	21	1−	1−	NUM
ma-27	210	22	γ)δt	γ)δt	PROPN
ma-27	210	23	)	)	PUNCT
ma-27	210	24	.	.	PUNCT
ma-27	211	1	since	since	SCONJ
ma-27	211	2	δs	δs	ADP
ma-27	211	3	≤	≤	NUM
ma-27	211	4	δ	δ	PROPN
ma-27	211	5	<	<	X
ma-27	211	6	1	1	NUM
ma-27	211	7	and	and	CCONJ
ma-27	211	8	βs	βs	ADJ
ma-27	211	9	≤	≤	NUM
ma-27	211	10	β	β	X
ma-27	211	11	<	<	X
ma-27	211	12	1	1	NUM
ma-27	211	13	,	,	PUNCT
ma-27	211	14	for	for	ADP
ma-27	211	15	all	all	DET
ma-27	211	16	s	s	PART
ma-27	211	17	∈	∈	NOUN
ma-27	211	18	n	n	NOUN
ma-27	211	19	and	and	CCONJ
ma-27	211	20	for	for	ADP
ma-27	211	21	some	some	DET
ma-27	211	22	δ	δ	PROPN
ma-27	211	23	,	,	PUNCT
ma-27	211	24	β	β	X
ma-27	211	25	>	>	X
ma-27	211	26	0	0	NUM
ma-27	211	27	,	,	PUNCT
ma-27	211	28	then	then	ADV
ma-27	211	29	we	we	PRON
ma-27	211	30	have	have	VERB
ma-27	211	31	‖ms+1	‖ms+1	ADP
ma-27	211	32	−	−	PROPN
ma-27	211	33	z‖	z‖	NOUN
ma-27	212	1	≤	≤	NUM
ma-27	213	1	‖m0	‖m0	PROPN
ma-27	214	1	−	−	PROPN
ma-27	214	2	z‖γ2(s+1	z‖γ2(s+1	PROPN
ma-27	214	3	)	)	PUNCT
ma-27	214	4	s∏	s∏	PROPN
ma-27	214	5	t=0	t=0	X
ma-27	214	6	(	(	PUNCT
ma-27	214	7	1−	1−	NUM
ma-27	214	8	(	(	PUNCT
ma-27	214	9	1−	1−	NUM
ma-27	214	10	γ)δt	γ)δt	PROPN
ma-27	214	11	)	)	PUNCT
ma-27	214	12	=	=	SYM
ma-27	214	13	‖m0	‖m0	NOUN
ma-27	214	14	−	−	PROPN
ma-27	214	15	z‖γ2(s+1)(1−	z‖γ2(s+1)(1−	NOUN
ma-27	214	16	(	(	PUNCT
ma-27	214	17	1−	1−	NUM
ma-27	214	18	γ)δ)s+1	γ)δ)s+1	PROPN
ma-27	214	19	.	.	PUNCT
ma-27	215	1	set	set	VERB
ma-27	215	2	as	as	ADP
ma-27	215	3	=	=	SYM
ma-27	215	4	‖`0	‖`0	PROPN
ma-27	215	5	−	−	PROPN
ma-27	215	6	z‖γ3(s+1)(1−	z‖γ3(s+1)(1−	PROPN
ma-27	215	7	(	(	PUNCT
ma-27	215	8	1−	1−	NUM
ma-27	215	9	γ)δ)s+1	γ)δ)s+1	PROPN
ma-27	215	10	,	,	PUNCT
ma-27	215	11	and	and	CCONJ
ma-27	215	12	bs	bs	X
ma-27	215	13	=	=	PUNCT
ma-27	215	14	‖`0	‖`0	VERB
ma-27	216	1	−	−	PROPN
ma-27	216	2	z‖γ2(s+1)(1−	z‖γ2(s+1)(1−	NOUN
ma-27	216	3	(	(	PUNCT
ma-27	216	4	1−	1−	NUM
ma-27	216	5	γ)δ)s+1	γ)δ)s+1	PROPN
ma-27	216	6	.	.	PUNCT
ma-27	217	1	(	(	PUNCT
ma-27	217	2	3.13	3.13	NUM
ma-27	217	3	)	)	PUNCT
ma-27	217	4	hence	hence	ADV
ma-27	217	5	,	,	PUNCT
ma-27	217	6	as	as	ADP
ma-27	217	7	bs	bs	PROPN
ma-27	217	8	=	=	SYM
ma-27	217	9	‖`0	‖`0	PROPN
ma-27	217	10	−	−	PROPN
ma-27	217	11	z‖γ3(s+1)(1−	z‖γ3(s+1)(1−	PROPN
ma-27	217	12	(	(	PUNCT
ma-27	217	13	1−	1−	NUM
ma-27	217	14	γ)δβ)s+1	γ)δβ)s+1	PROPN
ma-27	217	15	‖m0	‖m0	NOUN
ma-27	217	16	−	−	PROPN
ma-27	217	17	z‖γ2(s+1)(1−	z‖γ2(s+1)(1−	NOUN
ma-27	217	18	(	(	PUNCT
ma-27	217	19	1−	1−	NUM
ma-27	217	20	γ)δ)s+1	γ)δ)s+1	PROPN
ma-27	217	21	→	→	SYM
ma-27	217	22	0	0	PUNCT
ma-27	217	23	as	as	ADP
ma-27	217	24	s	s	PRON
ma-27	217	25	→∞.	→∞.	X
ma-27	217	26	this	this	PRON
ma-27	217	27	implies	imply	VERB
ma-27	217	28	that	that	SCONJ
ma-27	217	29	our	our	PRON
ma-27	217	30	new	new	ADJ
ma-27	217	31	iterative	iterative	NOUN
ma-27	217	32	algorithm	algorithm	NOUN
ma-27	217	33	(	(	PUNCT
ma-27	217	34	1.7	1.7	NUM
ma-27	217	35	)	)	PUNCT
ma-27	217	36	converges	converge	VERB
ma-27	217	37	faster	fast	ADV
ma-27	217	38	to	to	ADP
ma-27	217	39	z	z	NOUN
ma-27	217	40	than	than	ADP
ma-27	217	41	m	m	PROPN
ma-27	217	42	iterative	iterative	NOUN
ma-27	217	43	algorithm(1.6	algorithm(1.6	ADJ
ma-27	217	44	)	)	PUNCT
ma-27	217	45	.	.	PUNCT
ma-27	218	1	�	�	PROPN
ma-27	218	2	in	in	ADP
ma-27	218	3	order	order	NOUN
ma-27	218	4	to	to	PART
ma-27	218	5	support	support	VERB
ma-27	218	6	analytical	analytical	ADJ
ma-27	218	7	prove	prove	NOUN
ma-27	218	8	in	in	ADP
ma-27	218	9	theorem	theorem	ADJ
ma-27	218	10	3.2	3.2	NUM
ma-27	218	11	and	and	CCONJ
ma-27	218	12	demonstrate	demonstrate	VERB
ma-27	218	13	the	the	DET
ma-27	218	14	advantage	advantage	NOUN
ma-27	218	15	of	of	ADP
ma-27	218	16	our	our	PRON
ma-27	218	17	newiterative	newiterative	ADJ
ma-27	218	18	algorithm	algorithm	NOUN
ma-27	218	19	(	(	PUNCT
ma-27	218	20	1.7	1.7	NUM
ma-27	218	21	)	)	PUNCT
ma-27	218	22	,	,	PUNCT
ma-27	218	23	we	we	PRON
ma-27	218	24	give	give	VERB
ma-27	218	25	the	the	DET
ma-27	218	26	following	follow	VERB
ma-27	218	27	example	example	NOUN
ma-27	218	28	.	.	PUNCT
ma-27	219	1	example	example	NOUN
ma-27	219	2	3.3	3.3	NUM
ma-27	219	3	.	.	PUNCT
ma-27	220	1	let	let	VERB
ma-27	220	2	ω	ω	NOUN
ma-27	220	3	=	=	PUNCT
ma-27	220	4	<	<	X
ma-27	220	5	and	and	CCONJ
ma-27	220	6	λ	λ	NOUN
ma-27	220	7	=	=	PUNCT
ma-27	221	1	[	[	X
ma-27	221	2	1	1	NUM
ma-27	221	3	,	,	PUNCT
ma-27	221	4	50	50	NUM
ma-27	221	5	]	]	PUNCT
ma-27	221	6	.	.	PUNCT
ma-27	222	1	let	let	VERB
ma-27	222	2	t	t	NOUN
ma-27	222	3	:	:	PUNCT
ma-27	222	4	λ	λ	X
ma-27	222	5	→	→	SYM
ma-27	222	6	λ	λ	X
ma-27	222	7	be	be	AUX
ma-27	222	8	a	a	DET
ma-27	222	9	mapping	mapping	NOUN
ma-27	222	10	defined	define	VERB
ma-27	222	11	by	by	ADP
ma-27	222	12	t	t	PROPN
ma-27	222	13	(	(	PUNCT
ma-27	222	14	`	`	PUNCT
ma-27	222	15	)	)	PUNCT
ma-27	222	16	=	=	SYM
ma-27	223	1	√	√	NUM
ma-27	223	2	`	`	PUNCT
ma-27	223	3	2	2	NUM
ma-27	223	4	−	−	PROPN
ma-27	223	5	8`+	8`+	NUM
ma-27	223	6	40	40	NUM
ma-27	223	7	.	.	PUNCT
ma-27	224	1	obviously	obviously	ADV
ma-27	224	2	,	,	PUNCT
ma-27	224	3	5	5	NUM
ma-27	224	4	is	be	AUX
ma-27	224	5	the	the	DET
ma-27	224	6	fixed	fix	VERB
ma-27	224	7	point	point	NOUN
ma-27	224	8	of	of	ADP
ma-27	224	9	t	t	PROPN
ma-27	224	10	.	.	PUNCT
ma-27	225	1	take	take	VERB
ma-27	225	2	δs	δs	NOUN
ma-27	225	3	=	=	PUNCT
ma-27	225	4	βs	β	NOUN
ma-27	226	1	=	=	SYM
ma-27	226	2	3	3	NUM
ma-27	226	3	4	4	NUM
ma-27	226	4	,	,	PUNCT
ma-27	226	5	with	with	ADP
ma-27	226	6	an	an	DET
ma-27	226	7	initial	initial	ADJ
ma-27	226	8	value	value	NOUN
ma-27	226	9	of	of	ADP
ma-27	226	10	`	`	PUNCT
ma-27	226	11	1	1	NUM
ma-27	226	12	=	=	SYM
ma-27	226	13	50	50	NUM
ma-27	226	14	.	.	PUNCT
ma-27	227	1	by	by	ADP
ma-27	227	2	writing	write	VERB
ma-27	227	3	all	all	DET
ma-27	227	4	the	the	DET
ma-27	227	5	codes	code	NOUN
ma-27	227	6	in	in	ADP
ma-27	227	7	matlab	matlab	PROPN
ma-27	227	8	(	(	PUNCT
ma-27	227	9	r2015a	r2015a	PROPN
ma-27	227	10	)	)	PUNCT
ma-27	227	11	for	for	ADP
ma-27	227	12	example	example	NOUN
ma-27	227	13	3.3	3.3	NUM
ma-27	227	14	,	,	PUNCT
ma-27	227	15	we	we	PRON
ma-27	227	16	obtain	obtain	VERB
ma-27	227	17	the	the	DET
ma-27	227	18	following	follow	VERB
ma-27	227	19	com	com	NOUN
ma-27	227	20	-	-	PUNCT
ma-27	227	21	parison	parison	NOUN
ma-27	227	22	table	table	NOUN
ma-27	227	23	1	1	NUM
ma-27	227	24	and	and	CCONJ
ma-27	227	25	figure	figure	VERB
ma-27	227	26	1	1	NUM
ma-27	227	27	.	.	PUNCT
ma-27	227	28	eur	eur	PROPN
ma-27	227	29	.	.	PUNCT
ma-27	228	1	j.	j.	PROPN
ma-27	228	2	math	math	PROPN
ma-27	228	3	.	.	PUNCT
ma-27	229	1	anal	anal	ADJ
ma-27	229	2	.	.	PUNCT
ma-27	230	1	1	1	NUM
ma-27	230	2	(	(	PUNCT
ma-27	230	3	2021	2021	NUM
ma-27	230	4	)	)	PUNCT
ma-27	230	5	116	116	NUM
ma-27	230	6	table	table	NOUN
ma-27	230	7	1	1	NUM
ma-27	230	8	.	.	PUNCT
ma-27	230	9	comparison	comparison	NOUN
ma-27	230	10	of	of	ADP
ma-27	230	11	convergence	convergence	NOUN
ma-27	230	12	behaviour	behaviour	NOUN
ma-27	230	13	of	of	ADP
ma-27	230	14	our	our	PRON
ma-27	230	15	new	new	ADJ
ma-27	230	16	iterative	iterative	NOUN
ma-27	230	17	algorithm	algorithm	NOUN
ma-27	230	18	withs	with	NOUN
ma-27	230	19	,	,	PUNCT
ma-27	230	20	picard	picard	NOUN
ma-27	230	21	-	-	PUNCT
ma-27	230	22	s	s	PROPN
ma-27	230	23	,	,	PUNCT
ma-27	230	24	thakur	thakur	NOUN
ma-27	230	25	and	and	CCONJ
ma-27	230	26	m	m	PROPN
ma-27	230	27	iterative	iterative	ADJ
ma-27	230	28	algorithms.step	algorithms.step	PROPN
ma-27	230	29	s	s	NOUN
ma-27	230	30	picard	picard	NOUN
ma-27	230	31	-	-	PUNCT
ma-27	230	32	s	s	PART
ma-27	231	1	thakur	thakur	PROPN
ma-27	231	2	m	m	VERB
ma-27	231	3	new1	new1	PROPN
ma-27	231	4	50.00000000	50.00000000	NUM
ma-27	231	5	50.00000000	50.00000000	NUM
ma-27	231	6	50.00000000	50.00000000	NUM
ma-27	231	7	50.00000000	50.00000000	NUM
ma-27	231	8	50.000000002	50.000000002	NUM
ma-27	231	9	44.16905011	44.16905011	NUM
ma-27	231	10	40.46668490	40.46668490	NUM
ma-27	231	11	40.46648707	40.46648707	NUM
ma-27	231	12	39.77487312	39.77487312	NUM
ma-27	231	13	36.794280913	36.794280913	NUM
ma-27	231	14	38.40054569	38.40054569	NUM
ma-27	231	15	31.13624438	31.13624438	NUM
ma-27	231	16	31.13566491	31.13566491	NUM
ma-27	231	17	29.79220887	29.79220887	NUM
ma-27	231	18	24.079581494	24.079581494	NUM
ma-27	231	19	32.71513008	32.71513008	NUM
ma-27	231	20	22.15533283	22.15533283	NUM
ma-27	231	21	22.15389446	22.15389446	NUM
ma-27	231	22	20.25245189	20.25245189	NUM
ma-27	231	23	12.593214715	12.593214715	NUM
ma-27	231	24	27.14503094	27.14503094	NUM
ma-27	231	25	13.88761070	13.88761070	NUM
ma-27	231	26	13.88380778	13.88380778	NUM
ma-27	231	27	11.71208997	11.71208997	NUM
ma-27	231	28	5.609365616	5.609365616	NUM
ma-27	231	29	21.74399379	21.74399379	NUM
ma-27	231	30	7.46589475	7.46589475	NUM
ma-27	231	31	7.45557218	7.45557218	NUM
ma-27	231	32	6.06597569	6.06597569	NUM
ma-27	231	33	5.003558697	5.003558697	NUM
ma-27	231	34	16.60935306	16.60935306	NUM
ma-27	232	1	5.14776230	5.14776230	NUM
ma-27	232	2	5.14203305	5.14203305	NUM
ma-27	232	3	5.02641919	5.02641919	NUM
ma-27	232	4	5.000015698	5.000015698	NUM
ma-27	232	5	11.93484164	11.93484164	NUM
ma-27	232	6	5.00348330	5.00348330	NUM
ma-27	232	7	5.00331403	5.00331403	NUM
ma-27	232	8	5.00042732	5.00042732	NUM
ma-27	232	9	5.000000009	5.000000009	NUM
ma-27	232	10	8.12786414	8.12786414	NUM
ma-27	232	11	5.00007676	5.00007676	NUM
ma-27	232	12	5.00007301	5.00007301	NUM
ma-27	232	13	5.00000684	5.00000684	NUM
ma-27	232	14	5.0000000010	5.0000000010	NUM
ma-27	232	15	5.84725921	5.84725921	NUM
ma-27	232	16	5.00000169	5.00000169	NUM
ma-27	232	17	5.00000161	5.00000161	NUM
ma-27	232	18	5.00000011	5.00000011	NUM
ma-27	232	19	5.0000000011	5.0000000011	NUM
ma-27	232	20	5.12789697	5.12789697	NUM
ma-27	232	21	5.00000004	5.00000004	NUM
ma-27	232	22	5.00000004	5.00000004	NUM
ma-27	232	23	5.00000000	5.00000000	NUM
ma-27	232	24	5.0000000012	5.0000000012	NUM
ma-27	232	25	5.01483168	5.01483168	NUM
ma-27	232	26	5.00000000	5.00000000	NUM
ma-27	232	27	5.00000000	5.00000000	NUM
ma-27	232	28	5.00000000	5.00000000	NUM
ma-27	232	29	5.0000000013	5.0000000013	NUM
ma-27	232	30	5.00164168	5.00164168	NUM
ma-27	232	31	5.00000000	5.00000000	NUM
ma-27	232	32	5.00000000	5.00000000	NUM
ma-27	232	33	5.00000000	5.00000000	NUM
ma-27	232	34	5.00000000	5.00000000	NUM
ma-27	232	35	iteration	iteration	NOUN
ma-27	232	36	number	number	NOUN
ma-27	232	37	s	s	PART
ma-27	232	38	2	2	NUM
ma-27	232	39	4	4	NUM
ma-27	232	40	6	6	NUM
ma-27	232	41	8	8	NUM
ma-27	232	42	10	10	NUM
ma-27	232	43	12	12	NUM
ma-27	232	44	14	14	NUM
ma-27	232	45	s	s	NOUN
ma-27	232	46	eq	eq	NOUN
ma-27	232	47	ue	ue	PROPN
ma-27	232	48	nc	nc	PROPN
ma-27	232	49	e	e	PROPN
ma-27	232	50	va	va	PROPN
ma-27	232	51	lu	lu	PROPN
ma-27	232	52	es	es	VERB
ma-27	232	53	5	5	NUM
ma-27	232	54	10	10	NUM
ma-27	232	55	15	15	NUM
ma-27	232	56	20	20	NUM
ma-27	232	57	25	25	NUM
ma-27	232	58	30	30	NUM
ma-27	232	59	35	35	NUM
ma-27	232	60	40	40	NUM
ma-27	232	61	45	45	NUM
ma-27	232	62	50	50	NUM
ma-27	232	63	new	new	ADJ
ma-27	232	64	iteration	iteration	NOUN
ma-27	232	65	m	m	PROPN
ma-27	232	66	iteration	iteration	NOUN
ma-27	232	67	thakur	thakur	PROPN
ma-27	232	68	iteration	iteration	NOUN
ma-27	232	69	picard	picard	PROPN
ma-27	232	70	-	-	PUNCT
ma-27	232	71	s	s	PART
ma-27	232	72	iteration	iteration	NOUN
ma-27	232	73	s	s	PART
ma-27	232	74	iteration	iteration	NOUN
ma-27	232	75	figure	figure	NOUN
ma-27	232	76	1	1	NUM
ma-27	232	77	.	.	PUNCT
ma-27	233	1	graph	graph	NOUN
ma-27	233	2	corresponding	correspond	VERB
ma-27	233	3	to	to	ADP
ma-27	233	4	table	table	NOUN
ma-27	233	5	1	1	NUM
ma-27	233	6	.	.	PUNCT
ma-27	233	7	eur	eur	PROPN
ma-27	233	8	.	.	PUNCT
ma-27	234	1	j.	j.	PROPN
ma-27	234	2	math	math	PROPN
ma-27	234	3	.	.	PUNCT
ma-27	235	1	anal	anal	ADJ
ma-27	235	2	.	.	PUNCT
ma-27	236	1	1	1	NUM
ma-27	236	2	(	(	PUNCT
ma-27	236	3	2021	2021	NUM
ma-27	236	4	)	)	PUNCT
ma-27	236	5	1174	1174	NUM
ma-27	236	6	.	.	PUNCT
ma-27	237	1	convergence	convergence	NOUN
ma-27	237	2	results	result	NOUN
ma-27	237	3	in	in	ADP
ma-27	237	4	this	this	DET
ma-27	237	5	section	section	NOUN
ma-27	237	6	,	,	PUNCT
ma-27	237	7	we	we	PRON
ma-27	237	8	will	will	AUX
ma-27	237	9	prove	prove	VERB
ma-27	237	10	the	the	DET
ma-27	237	11	weak	weak	ADJ
ma-27	237	12	and	and	CCONJ
ma-27	237	13	strong	strong	ADJ
ma-27	237	14	convergence	convergence	NOUN
ma-27	237	15	of	of	ADP
ma-27	237	16	our	our	PRON
ma-27	237	17	new	new	ADJ
ma-27	237	18	iterative	iterative	NOUN
ma-27	237	19	algorithm	algorithm	NOUN
ma-27	237	20	(	(	PUNCT
ma-27	237	21	1.7)for	1.7)for	ADP
ma-27	237	22	generalized	generalize	VERB
ma-27	237	23	α	α	PRON
ma-27	237	24	–	–	PUNCT
ma-27	237	25	nonexpansive	nonexpansive	ADJ
ma-27	237	26	mappings	mapping	NOUN
ma-27	237	27	in	in	ADP
ma-27	237	28	the	the	DET
ma-27	237	29	framework	framework	NOUN
ma-27	237	30	of	of	ADP
ma-27	237	31	uniformly	uniformly	ADV
ma-27	237	32	convex	convex	VERB
ma-27	237	33	banach	banach	NOUN
ma-27	237	34	spaces.firstly	spaces.firstly	ADV
ma-27	237	35	,	,	PUNCT
ma-27	237	36	we	we	PRON
ma-27	237	37	will	will	AUX
ma-27	237	38	state	state	VERB
ma-27	237	39	and	and	CCONJ
ma-27	237	40	prove	prove	VERB
ma-27	237	41	the	the	DET
ma-27	237	42	following	follow	VERB
ma-27	237	43	lemmas	lemma	NOUN
ma-27	237	44	which	which	PRON
ma-27	237	45	will	will	AUX
ma-27	237	46	be	be	AUX
ma-27	237	47	useful	useful	ADJ
ma-27	237	48	in	in	ADP
ma-27	237	49	obtaining	obtain	VERB
ma-27	237	50	our	our	PRON
ma-27	237	51	mainresults	mainresult	NOUN
ma-27	237	52	.	.	PUNCT
ma-27	238	1	lemma	lemma	PROPN
ma-27	238	2	4.1	4.1	NUM
ma-27	238	3	.	.	PUNCT
ma-27	239	1	let	let	VERB
ma-27	239	2	ω	ω	NUM
ma-27	239	3	be	be	AUX
ma-27	239	4	a	a	DET
ma-27	239	5	banach	banach	NOUN
ma-27	239	6	space	space	NOUN
ma-27	239	7	and	and	CCONJ
ma-27	239	8	λ	λ	PROPN
ma-27	239	9	be	be	AUX
ma-27	239	10	a	a	DET
ma-27	239	11	nonempty	nonempty	ADV
ma-27	239	12	closed	close	VERB
ma-27	239	13	convex	convex	NOUN
ma-27	239	14	subset	subset	NOUN
ma-27	239	15	of	of	ADP
ma-27	239	16	ω	ω	PROPN
ma-27	239	17	.	.	PUNCT
ma-27	240	1	let	let	VERB
ma-27	240	2	t	t	NOUN
ma-27	240	3	:	:	PUNCT
ma-27	240	4	λ	λ	X
ma-27	240	5	→	→	SYM
ma-27	240	6	λ	λ	X
ma-27	240	7	be	be	AUX
ma-27	240	8	a	a	DET
ma-27	240	9	generalized	generalized	ADJ
ma-27	240	10	α	α	NOUN
ma-27	240	11	–	–	PUNCT
ma-27	240	12	nonexpansive	nonexpansive	ADJ
ma-27	240	13	mapping	mapping	NOUN
ma-27	240	14	with	with	ADP
ma-27	240	15	f	f	PROPN
ma-27	240	16	(	(	PUNCT
ma-27	240	17	t	t	PROPN
ma-27	240	18	)	)	PUNCT
ma-27	240	19	6=	6=	ADP
ma-27	240	20	∅.	∅.	ADP
ma-27	240	21	if	if	SCONJ
ma-27	240	22	{	{	PUNCT
ma-27	240	23	`	`	PUNCT
ma-27	240	24	s	s	X
ma-27	240	25	}	}	PUNCT
ma-27	240	26	is	be	AUX
ma-27	240	27	the	the	DET
ma-27	240	28	iterative	iterative	ADJ
ma-27	240	29	algorithm	algorithm	NOUN
ma-27	240	30	defined	define	VERB
ma-27	240	31	by	by	ADP
ma-27	240	32	(	(	PUNCT
ma-27	240	33	1.7	1.7	NUM
ma-27	240	34	)	)	PUNCT
ma-27	240	35	,	,	PUNCT
ma-27	240	36	then	then	ADV
ma-27	240	37	lim	lim	PROPN
ma-27	240	38	s→∞	s→∞	PROPN
ma-27	240	39	‖`s	‖`s	PROPN
ma-27	241	1	−	−	DET
ma-27	241	2	z‖	z‖	NOUN
ma-27	241	3	exists	exist	VERB
ma-27	241	4	for	for	ADP
ma-27	241	5	all	all	PRON
ma-27	241	6	z	z	NOUN
ma-27	241	7	∈	∈	PROPN
ma-27	241	8	f	f	X
ma-27	241	9	(	(	PUNCT
ma-27	241	10	t	t	PROPN
ma-27	241	11	)	)	PUNCT
ma-27	241	12	.	.	PUNCT
ma-27	242	1	proof	proof	NOUN
ma-27	242	2	.	.	PUNCT
ma-27	243	1	let	let	VERB
ma-27	243	2	z	z	NOUN
ma-27	243	3	∈	∈	PROPN
ma-27	243	4	f	f	X
ma-27	243	5	(	(	PUNCT
ma-27	243	6	t	t	PROPN
ma-27	243	7	)	)	PUNCT
ma-27	243	8	.	.	PUNCT
ma-27	244	1	by	by	ADP
ma-27	244	2	proposition	proposition	NOUN
ma-27	244	3	2.9(ii	2.9(ii	NUM
ma-27	244	4	)	)	PUNCT
ma-27	244	5	,	,	PUNCT
ma-27	244	6	we	we	PRON
ma-27	244	7	know	know	VERB
ma-27	244	8	that	that	SCONJ
ma-27	244	9	every	every	DET
ma-27	244	10	suzuki	suzuki	NOUN
ma-27	244	11	generalized	generalize	VERB
ma-27	244	12	nonexpansivemapping	nonexpansivemapping	NOUN
ma-27	244	13	with	with	ADP
ma-27	244	14	f	f	PROPN
ma-27	244	15	(	(	PUNCT
ma-27	244	16	t	t	PROPN
ma-27	244	17	)	)	PUNCT
ma-27	244	18	6=	6=	ADP
ma-27	244	19	∅	∅	NOUN
ma-27	244	20	is	be	AUX
ma-27	244	21	quasi	quasi	ADJ
ma-27	244	22	-	-	ADJ
ma-27	244	23	nonexpansive	nonexpansive	ADJ
ma-27	244	24	mapping	mapping	NOUN
ma-27	244	25	.	.	PUNCT
ma-27	245	1	then	then	ADV
ma-27	245	2	,	,	PUNCT
ma-27	245	3	from	from	ADP
ma-27	245	4	(	(	PUNCT
ma-27	245	5	1.7	1.7	NUM
ma-27	245	6	)	)	PUNCT
ma-27	245	7	,	,	PUNCT
ma-27	245	8	we	we	PRON
ma-27	245	9	have	have	VERB
ma-27	245	10	‖gs	‖gs	NUM
ma-27	245	11	−	−	NOUN
ma-27	245	12	z‖	z‖	NOUN
ma-27	245	13	=	=	SYM
ma-27	245	14	‖(1−	‖(1−	PROPN
ma-27	246	1	βs)`s	βs)`s	NOUN
ma-27	247	1	+	+	CCONJ
ma-27	248	1	βst`s	βst`s	PROPN
ma-27	248	2	−	−	NOUN
ma-27	248	3	z‖	z‖	NOUN
ma-27	248	4	≤	≤	NOUN
ma-27	248	5	(	(	PUNCT
ma-27	248	6	1−	1−	NUM
ma-27	248	7	βs)‖`s	βs)‖`s	PUNCT
ma-27	248	8	−	−	PUNCT
ma-27	248	9	z‖+	z‖+	NOUN
ma-27	248	10	βs‖t`s	βs‖t`s	NOUN
ma-27	249	1	−	−	PROPN
ma-27	249	2	z‖	z‖	NOUN
ma-27	249	3	≤	≤	NOUN
ma-27	249	4	(	(	PUNCT
ma-27	249	5	1−	1−	NUM
ma-27	249	6	βs)‖`s	βs)‖`s	PUNCT
ma-27	250	1	−	−	PUNCT
ma-27	250	2	z‖+	z‖+	NOUN
ma-27	250	3	βs‖`s	βs‖`s	PROPN
ma-27	250	4	−	−	PROPN
ma-27	250	5	z‖	z‖	NOUN
ma-27	250	6	=	=	SYM
ma-27	251	1	‖`s	‖`s	PROPN
ma-27	251	2	−	−	PROPN
ma-27	251	3	z‖.	z‖.	X
ma-27	251	4	(	(	PUNCT
ma-27	251	5	4.1	4.1	NUM
ma-27	251	6	)	)	PUNCT
ma-27	251	7	using	use	VERB
ma-27	251	8	(	(	PUNCT
ma-27	251	9	1.7	1.7	NUM
ma-27	251	10	)	)	PUNCT
ma-27	251	11	and	and	CCONJ
ma-27	251	12	(	(	PUNCT
ma-27	251	13	4.1	4.1	NUM
ma-27	251	14	)	)	PUNCT
ma-27	251	15	,	,	PUNCT
ma-27	251	16	we	we	PRON
ma-27	251	17	obtain	obtain	VERB
ma-27	251	18	‖ws	‖ws	NUM
ma-27	251	19	−	−	PROPN
ma-27	251	20	z‖	z‖	NOUN
ma-27	251	21	=	=	SYM
ma-27	251	22	‖(1−	‖(1−	ADJ
ma-27	251	23	δs)t`s	δs)t`s	NOUN
ma-27	251	24	+	+	CCONJ
ma-27	251	25	δstgs	δstgs	NOUN
ma-27	251	26	−	−	PROPN
ma-27	251	27	z‖	z‖	NOUN
ma-27	251	28	≤	≤	NOUN
ma-27	251	29	(	(	PUNCT
ma-27	251	30	1−	1−	NUM
ma-27	251	31	δs)‖t`s	δs)‖t`s	PROPN
ma-27	251	32	−	−	PROPN
ma-27	251	33	z‖+	z‖+	PROPN
ma-27	251	34	δs‖tgs	δs‖tg	VERB
ma-27	251	35	−	−	PROPN
ma-27	251	36	z‖	z‖	NOUN
ma-27	251	37	≤	≤	NUM
ma-27	251	38	(	(	PUNCT
ma-27	251	39	1−	1−	NUM
ma-27	251	40	δs)‖`s	δs)‖`s	PROPN
ma-27	251	41	−	−	PROPN
ma-27	251	42	z‖+	z‖+	NOUN
ma-27	251	43	δs‖gs	δs‖gs	NOUN
ma-27	251	44	−	−	ADP
ma-27	251	45	z‖	z‖	NOUN
ma-27	251	46	≤	≤	NOUN
ma-27	251	47	(	(	PUNCT
ma-27	251	48	1−	1−	NUM
ma-27	251	49	δs)‖`s	δs)‖`s	PROPN
ma-27	251	50	−	−	NOUN
ma-27	251	51	z‖+	z‖+	NOUN
ma-27	252	1	δs‖`s	δs‖`s	NOUN
ma-27	252	2	−	−	NOUN
ma-27	252	3	z‖	z‖	NOUN
ma-27	252	4	=	=	SYM
ma-27	253	1	‖`s	‖`s	PROPN
ma-27	253	2	−	−	PROPN
ma-27	253	3	z‖.	z‖.	X
ma-27	253	4	(	(	PUNCT
ma-27	253	5	4.2	4.2	NUM
ma-27	253	6	)	)	PUNCT
ma-27	253	7	again	again	ADV
ma-27	253	8	,	,	PUNCT
ma-27	253	9	using	use	VERB
ma-27	253	10	(	(	PUNCT
ma-27	253	11	1.7	1.7	NUM
ma-27	253	12	)	)	PUNCT
ma-27	253	13	and	and	CCONJ
ma-27	253	14	(	(	PUNCT
ma-27	253	15	4.2	4.2	NUM
ma-27	253	16	)	)	PUNCT
ma-27	253	17	,	,	PUNCT
ma-27	253	18	we	we	PRON
ma-27	253	19	get	get	VERB
ma-27	253	20	‖ζs	‖ζ	NOUN
ma-27	253	21	−	−	PROPN
ma-27	253	22	z‖	z‖	NOUN
ma-27	253	23	=	=	SYM
ma-27	253	24	‖tws	‖tws	NOUN
ma-27	254	1	−	−	PROPN
ma-27	254	2	z‖	z‖	NOUN
ma-27	254	3	≤	≤	NUM
ma-27	254	4	‖ws	‖ws	NUM
ma-27	254	5	−	−	PROPN
ma-27	254	6	z‖	z‖	NOUN
ma-27	254	7	≤	≤	X
ma-27	255	1	‖`s	‖`s	PRON
ma-27	255	2	−	−	PROPN
ma-27	255	3	z‖.	z‖.	X
ma-27	255	4	(	(	PUNCT
ma-27	255	5	4.3	4.3	NUM
ma-27	255	6	)	)	PUNCT
ma-27	255	7	lastly	lastly	ADV
ma-27	255	8	,	,	PUNCT
ma-27	255	9	from	from	ADP
ma-27	255	10	(	(	PUNCT
ma-27	255	11	1.7	1.7	NUM
ma-27	255	12	)	)	PUNCT
ma-27	255	13	and	and	CCONJ
ma-27	255	14	(	(	PUNCT
ma-27	255	15	4.3	4.3	NUM
ma-27	255	16	)	)	PUNCT
ma-27	255	17	,	,	PUNCT
ma-27	255	18	we	we	PRON
ma-27	255	19	have	have	AUX
ma-27	255	20	‖`s	‖`s	NOUN
ma-27	255	21	−	−	NOUN
ma-27	255	22	z‖	z‖	NOUN
ma-27	255	23	=	=	SYM
ma-27	255	24	‖tζs	‖tζs	NOUN
ma-27	255	25	−	−	PROPN
ma-27	255	26	z‖	z‖	NOUN
ma-27	255	27	≤	≤	NUM
ma-27	256	1	‖ζs	‖ζs	PROPN
ma-27	256	2	−	−	PROPN
ma-27	256	3	z‖	z‖	NOUN
ma-27	256	4	≤	≤	X
ma-27	257	1	‖`s	‖`s	PRON
ma-27	257	2	−	−	PROPN
ma-27	257	3	z‖.	z‖.	X
ma-27	257	4	(	(	PUNCT
ma-27	257	5	4.4	4.4	NUM
ma-27	257	6	)	)	PUNCT
ma-27	257	7	this	this	PRON
ma-27	257	8	implies	imply	VERB
ma-27	257	9	that	that	SCONJ
ma-27	257	10	{	{	PUNCT
ma-27	257	11	‖`s	‖`s	NOUN
ma-27	257	12	−	−	PROPN
ma-27	257	13	z‖	z‖	PROPN
ma-27	257	14	}	}	PUNCT
ma-27	257	15	is	be	AUX
ma-27	257	16	bounded	bound	VERB
ma-27	257	17	and	and	CCONJ
ma-27	257	18	nondecreasing	nondecrease	VERB
ma-27	257	19	for	for	ADP
ma-27	257	20	all	all	DET
ma-27	257	21	z	z	NOUN
ma-27	257	22	∈	∈	PROPN
ma-27	257	23	f	f	X
ma-27	257	24	(	(	PUNCT
ma-27	257	25	t	t	PROPN
ma-27	257	26	)	)	PUNCT
ma-27	257	27	.	.	PUNCT
ma-27	258	1	hence	hence	ADV
ma-27	258	2	,	,	PUNCT
ma-27	258	3	lim	lim	PROPN
ma-27	258	4	s→∞	s→∞	PROPN
ma-27	258	5	‖`s	‖`s	PROPN
ma-27	258	6	−	−	PROPN
ma-27	258	7	z‖exists	z‖exists	PROPN
ma-27	258	8	.	.	PUNCT
ma-27	259	1	�	�	PROPN
ma-27	259	2	eur	eur	PROPN
ma-27	259	3	.	.	PUNCT
ma-27	260	1	j.	j.	PROPN
ma-27	260	2	math	math	PROPN
ma-27	260	3	.	.	PUNCT
ma-27	261	1	anal	anal	ADJ
ma-27	261	2	.	.	PUNCT
ma-27	262	1	1	1	NUM
ma-27	262	2	(	(	PUNCT
ma-27	262	3	2021	2021	NUM
ma-27	262	4	)	)	PUNCT
ma-27	263	1	118	118	NUM
ma-27	263	2	lemma	lemma	PROPN
ma-27	263	3	4.2	4.2	NUM
ma-27	263	4	.	.	PUNCT
ma-27	264	1	let	let	VERB
ma-27	264	2	ω	ω	PRON
ma-27	264	3	be	be	AUX
ma-27	264	4	a	a	DET
ma-27	264	5	uniformly	uniformly	ADV
ma-27	264	6	convex	convex	NOUN
ma-27	264	7	banach	banach	NOUN
ma-27	264	8	space	space	NOUN
ma-27	264	9	and	and	CCONJ
ma-27	264	10	λ	λ	PROPN
ma-27	264	11	be	be	AUX
ma-27	264	12	a	a	DET
ma-27	264	13	nonempty	nonempty	ADV
ma-27	264	14	closed	close	VERB
ma-27	264	15	convex	convex	NOUN
ma-27	264	16	subset	subset	NOUN
ma-27	264	17	of	of	ADP
ma-27	264	18	ω	ω	PROPN
ma-27	264	19	.	.	PUNCT
ma-27	265	1	let	let	VERB
ma-27	265	2	t	t	NOUN
ma-27	265	3	:	:	PUNCT
ma-27	265	4	λ	λ	X
ma-27	265	5	→	→	SYM
ma-27	265	6	λ	λ	X
ma-27	265	7	be	be	AUX
ma-27	265	8	a	a	DET
ma-27	265	9	generalized	generalized	ADJ
ma-27	265	10	α	α	PRON
ma-27	265	11	–	–	PUNCT
ma-27	265	12	nonexpansive	nonexpansive	ADJ
ma-27	265	13	mapping	mapping	NOUN
ma-27	265	14	.	.	PUNCT
ma-27	266	1	suppose	suppose	VERB
ma-27	266	2	{	{	PUNCT
ma-27	266	3	`	`	PUNCT
ma-27	266	4	s	s	X
ma-27	266	5	}	}	PUNCT
ma-27	266	6	is	be	AUX
ma-27	266	7	the	the	DET
ma-27	266	8	iterative	iterative	ADJ
ma-27	266	9	algorithm	algorithm	NOUN
ma-27	266	10	defined	define	VERB
ma-27	266	11	by	by	ADP
ma-27	266	12	(	(	PUNCT
ma-27	266	13	1.7	1.7	NUM
ma-27	266	14	)	)	PUNCT
ma-27	266	15	.	.	PUNCT
ma-27	267	1	then	then	ADV
ma-27	267	2	,	,	PUNCT
ma-27	267	3	f	f	PROPN
ma-27	267	4	(	(	PUNCT
ma-27	267	5	t	t	PROPN
ma-27	267	6	)	)	PUNCT
ma-27	267	7	6=	6=	ADP
ma-27	267	8	∅	∅	NOUN
ma-27	267	9	if	if	SCONJ
ma-27	267	10	and	and	CCONJ
ma-27	267	11	only	only	ADV
ma-27	267	12	if	if	SCONJ
ma-27	267	13	{	{	PUNCT
ma-27	267	14	`	`	PUNCT
ma-27	267	15	s	s	AUX
ma-27	267	16	}	}	PUNCT
ma-27	267	17	is	be	AUX
ma-27	267	18	bounded	bound	VERB
ma-27	267	19	and	and	CCONJ
ma-27	267	20	lim	lim	PROPN
ma-27	267	21	s→∞	s→∞	PROPN
ma-27	267	22	‖t`s−	‖t`s−	PROPN
ma-27	267	23	`	`	PUNCT
ma-27	267	24	s‖	s‖	NOUN
ma-27	267	25	=	=	SYM
ma-27	267	26	0	0	X
ma-27	267	27	.	.	PUNCT
ma-27	268	1	proof	proof	NOUN
ma-27	268	2	.	.	PUNCT
ma-27	269	1	suppose	suppose	VERB
ma-27	269	2	f	f	PROPN
ma-27	269	3	(	(	PUNCT
ma-27	269	4	t	t	PROPN
ma-27	269	5	)	)	PUNCT
ma-27	269	6	6=	6=	ADP
ma-27	269	7	∅	∅	NOUN
ma-27	269	8	and	and	CCONJ
ma-27	269	9	let	let	VERB
ma-27	269	10	z	z	NOUN
ma-27	269	11	∈	∈	PROPN
ma-27	269	12	f	f	X
ma-27	269	13	(	(	PUNCT
ma-27	269	14	t	t	PROPN
ma-27	269	15	)	)	PUNCT
ma-27	269	16	.	.	PUNCT
ma-27	270	1	then	then	ADV
ma-27	270	2	,	,	PUNCT
ma-27	270	3	by	by	ADP
ma-27	270	4	lemma	lemma	PROPN
ma-27	270	5	4.1	4.1	NUM
ma-27	270	6	,	,	PUNCT
ma-27	270	7	lim	lim	PROPN
ma-27	270	8	s→∞	s→∞	PROPN
ma-27	270	9	‖`s	‖`s	PROPN
ma-27	271	1	−	−	PROPN
ma-27	271	2	z‖	z‖	NOUN
ma-27	271	3	exists	exist	VERB
ma-27	271	4	and	and	CCONJ
ma-27	271	5	{	{	PUNCT
ma-27	271	6	`	`	PUNCT
ma-27	271	7	s	s	X
ma-27	271	8	}	}	PUNCT
ma-27	271	9	isbounded	isbounde	VERB
ma-27	271	10	.	.	PUNCT
ma-27	272	1	put	put	VERB
ma-27	272	2	lim	lim	PROPN
ma-27	272	3	s→∞	s→∞	PROPN
ma-27	272	4	‖`s	‖`s	PROPN
ma-27	272	5	−	−	NOUN
ma-27	272	6	z‖	z‖	NOUN
ma-27	272	7	=	=	PUNCT
ma-27	273	1	x.	x.	NOUN
ma-27	273	2	(	(	PUNCT
ma-27	273	3	4.5	4.5	NUM
ma-27	273	4	)	)	PUNCT
ma-27	273	5	from	from	ADP
ma-27	273	6	(	(	PUNCT
ma-27	273	7	4.4	4.4	NUM
ma-27	273	8	)	)	PUNCT
ma-27	273	9	and	and	CCONJ
ma-27	273	10	(	(	PUNCT
ma-27	273	11	4.5	4.5	NUM
ma-27	273	12	)	)	PUNCT
ma-27	273	13	,	,	PUNCT
ma-27	273	14	we	we	PRON
ma-27	273	15	obtain	obtain	VERB
ma-27	273	16	lim	lim	NOUN
ma-27	273	17	sup	sup	NOUN
ma-27	273	18	s→∞	s→∞	NUM
ma-27	273	19	‖gs	‖gs	NUM
ma-27	273	20	−	−	PROPN
ma-27	273	21	z‖	z‖	NOUN
ma-27	273	22	≤	≤	NUM
ma-27	273	23	lim	lim	PROPN
ma-27	273	24	sup	sup	NOUN
ma-27	273	25	s→∞	s→∞	NUM
ma-27	273	26	‖`s	‖`s	ADJ
ma-27	273	27	−	−	NOUN
ma-27	273	28	z‖	z‖	NOUN
ma-27	273	29	=	=	PUNCT
ma-27	273	30	x.	x.	NOUN
ma-27	273	31	(	(	PUNCT
ma-27	273	32	4.6	4.6	NUM
ma-27	273	33	)	)	PUNCT
ma-27	273	34	from	from	ADP
ma-27	273	35	proposition	proposition	NOUN
ma-27	273	36	2.9(ii	2.9(ii	NUM
ma-27	273	37	)	)	PUNCT
ma-27	273	38	,	,	PUNCT
ma-27	273	39	we	we	PRON
ma-27	273	40	know	know	VERB
ma-27	273	41	that	that	SCONJ
ma-27	273	42	every	every	DET
ma-27	273	43	generalized	generalized	ADJ
ma-27	273	44	α	α	NOUN
ma-27	273	45	–	–	PUNCT
ma-27	273	46	nonexpansive	nonexpansive	ADJ
ma-27	273	47	mapping	mapping	NOUN
ma-27	273	48	with	with	ADP
ma-27	273	49	f	f	PROPN
ma-27	273	50	(	(	PUNCT
ma-27	273	51	t	t	PROPN
ma-27	273	52	)	)	PUNCT
ma-27	273	53	6=	6=	PUNCT
ma-27	274	1	∅is	∅i	NOUN
ma-27	274	2	quasi	quasi	ADJ
ma-27	274	3	-	-	ADJ
ma-27	274	4	nonexpansive	nonexpansive	ADJ
ma-27	274	5	mapping	mapping	NOUN
ma-27	274	6	.	.	PUNCT
ma-27	275	1	so	so	SCONJ
ma-27	275	2	that	that	SCONJ
ma-27	275	3	we	we	PRON
ma-27	275	4	have	have	VERB
ma-27	275	5	lim	lim	PROPN
ma-27	275	6	sup	sup	NOUN
ma-27	275	7	s→∞	s→∞	NUM
ma-27	275	8	‖t`s	‖t`s	ADJ
ma-27	275	9	−	−	DET
ma-27	275	10	z‖	z‖	NOUN
ma-27	276	1	≤	≤	X
ma-27	276	2	lim	lim	PROPN
ma-27	276	3	sup	sup	NOUN
ma-27	276	4	s→∞	s→∞	NUM
ma-27	276	5	‖`s	‖`s	ADJ
ma-27	276	6	−	−	NOUN
ma-27	276	7	z‖	z‖	NOUN
ma-27	276	8	=	=	PUNCT
ma-27	276	9	x.	x.	NOUN
ma-27	276	10	(	(	PUNCT
ma-27	276	11	4.7	4.7	NUM
ma-27	276	12	)	)	PUNCT
ma-27	276	13	again	again	ADV
ma-27	276	14	,	,	PUNCT
ma-27	276	15	using	use	VERB
ma-27	276	16	(	(	PUNCT
ma-27	276	17	1.7	1.7	NUM
ma-27	276	18	)	)	PUNCT
ma-27	276	19	,	,	PUNCT
ma-27	276	20	we	we	PRON
ma-27	276	21	get	get	VERB
ma-27	276	22	‖`s+1	‖`s+1	ADJ
ma-27	276	23	−	−	NOUN
ma-27	276	24	z‖	z‖	NOUN
ma-27	276	25	=	=	SYM
ma-27	276	26	‖tζs	‖tζs	NOUN
ma-27	276	27	−	−	PROPN
ma-27	276	28	z‖	z‖	NOUN
ma-27	276	29	≤	≤	NUM
ma-27	277	1	‖ζs	‖ζs	PROPN
ma-27	277	2	−	−	PROPN
ma-27	277	3	z‖	z‖	NOUN
ma-27	277	4	=	=	SYM
ma-27	277	5	‖tws	‖tws	NOUN
ma-27	277	6	−	−	PROPN
ma-27	277	7	z‖	z‖	NOUN
ma-27	277	8	≤	≤	NUM
ma-27	277	9	‖ws	‖ws	NUM
ma-27	277	10	−	−	PROPN
ma-27	277	11	z‖	z‖	NOUN
ma-27	277	12	=	=	SYM
ma-27	277	13	‖(1−	‖(1−	ADJ
ma-27	277	14	δs)t`s	δs)t`s	NOUN
ma-27	277	15	+	+	CCONJ
ma-27	277	16	δstgs	δstgs	NOUN
ma-27	277	17	−	−	PROPN
ma-27	277	18	z‖	z‖	NOUN
ma-27	277	19	≤	≤	NOUN
ma-27	277	20	(	(	PUNCT
ma-27	277	21	1−	1−	NUM
ma-27	277	22	δs)‖t`s	δs)‖t`s	PROPN
ma-27	278	1	−	−	PROPN
ma-27	278	2	z‖+	z‖+	PROPN
ma-27	278	3	δs‖tgs	δs‖tg	VERB
ma-27	278	4	−	−	PROPN
ma-27	278	5	z‖	z‖	NOUN
ma-27	278	6	≤	≤	NUM
ma-27	278	7	(	(	PUNCT
ma-27	278	8	1−	1−	NUM
ma-27	278	9	δs)‖`s	δs)‖`s	PROPN
ma-27	278	10	−	−	PROPN
ma-27	278	11	z‖+	z‖+	NOUN
ma-27	278	12	δs‖gs	δs‖gs	VERB
ma-27	278	13	−	−	ADP
ma-27	278	14	z‖	z‖	NOUN
ma-27	278	15	=	=	SYM
ma-27	279	1	‖`s	‖`s	PROPN
ma-27	279	2	−	−	NOUN
ma-27	279	3	z‖	z‖	NOUN
ma-27	279	4	−	−	PROPN
ma-27	280	1	δs‖`s	δs‖`s	PROPN
ma-27	280	2	−	−	PROPN
ma-27	280	3	z‖+	z‖+	NOUN
ma-27	280	4	δs‖gs	δs‖gs	NOUN
ma-27	280	5	−	−	PROPN
ma-27	280	6	z‖.	z‖.	X
ma-27	280	7	(	(	PUNCT
ma-27	280	8	4.8	4.8	NUM
ma-27	280	9	)	)	PUNCT
ma-27	280	10	from	from	ADP
ma-27	280	11	(	(	PUNCT
ma-27	280	12	4.8	4.8	NUM
ma-27	280	13	)	)	PUNCT
ma-27	280	14	,	,	PUNCT
ma-27	280	15	we	we	PRON
ma-27	280	16	have	have	VERB
ma-27	280	17	‖`s+1	‖`s+1	ADJ
ma-27	280	18	−	−	PROPN
ma-27	280	19	z‖	z‖	NOUN
ma-27	280	20	−	−	PROPN
ma-27	280	21	‖`s	‖`s	PROPN
ma-27	280	22	−	−	ADP
ma-27	280	23	z‖	z‖	NOUN
ma-27	280	24	δs	δs	VERB
ma-27	280	25	≤	≤	NUM
ma-27	280	26	‖gs	‖gs	PROPN
ma-27	280	27	−	−	PROPN
ma-27	280	28	z‖	z‖	NOUN
ma-27	280	29	−	−	PROPN
ma-27	281	1	‖`s	‖`s	PROPN
ma-27	281	2	−	−	PROPN
ma-27	281	3	z‖.	z‖.	X
ma-27	281	4	(	(	PUNCT
ma-27	281	5	4.9	4.9	NUM
ma-27	281	6	)	)	PUNCT
ma-27	281	7	since	since	SCONJ
ma-27	281	8	δs	δs	ADP
ma-27	281	9	∈	∈	PROPN
ma-27	282	1	[	[	X
ma-27	282	2	0	0	NUM
ma-27	282	3	,	,	PUNCT
ma-27	282	4	1	1	NUM
ma-27	282	5	]	]	PUNCT
ma-27	282	6	,	,	PUNCT
ma-27	282	7	then	then	ADV
ma-27	282	8	from	from	ADP
ma-27	282	9	(	(	PUNCT
ma-27	282	10	4.9	4.9	NUM
ma-27	282	11	)	)	PUNCT
ma-27	282	12	,	,	PUNCT
ma-27	282	13	we	we	PRON
ma-27	282	14	have	have	VERB
ma-27	282	15	‖`s+1	‖`s+1	ADJ
ma-27	282	16	−	−	PROPN
ma-27	282	17	z‖	z‖	NOUN
ma-27	282	18	−	−	PROPN
ma-27	283	1	‖`s	‖`s	PROPN
ma-27	283	2	−	−	PROPN
ma-27	283	3	z‖	z‖	NOUN
ma-27	283	4	≤	≤	NOUN
ma-27	283	5	‖`s+1	‖`s+1	ADJ
ma-27	283	6	−	−	PROPN
ma-27	283	7	z‖	z‖	NOUN
ma-27	283	8	−	−	PROPN
ma-27	284	1	‖`s	‖`s	PROPN
ma-27	284	2	−	−	ADP
ma-27	284	3	z‖	z‖	NOUN
ma-27	284	4	δs	δs	VERB
ma-27	284	5	≤	≤	NUM
ma-27	284	6	‖gs	‖gs	PROPN
ma-27	284	7	−	−	PROPN
ma-27	284	8	z‖	z‖	NOUN
ma-27	284	9	−	−	PROPN
ma-27	285	1	‖`s	‖`s	PROPN
ma-27	285	2	−	−	PROPN
ma-27	285	3	z‖	z‖	NOUN
ma-27	285	4	,	,	PUNCT
ma-27	285	5	which	which	PRON
ma-27	285	6	implies	imply	VERB
ma-27	285	7	that	that	SCONJ
ma-27	285	8	‖`s+1	‖`s+1	ADJ
ma-27	285	9	−	−	PROPN
ma-27	285	10	z‖	z‖	NOUN
ma-27	285	11	≤	≤	NOUN
ma-27	285	12	‖gs	‖gs	PUNCT
ma-27	285	13	−	−	PROPN
ma-27	285	14	z‖.	z‖.	NOUN
ma-27	285	15	therefore	therefore	ADV
ma-27	285	16	,	,	PUNCT
ma-27	285	17	from	from	ADP
ma-27	285	18	(	(	PUNCT
ma-27	285	19	4.5	4.5	NUM
ma-27	285	20	)	)	PUNCT
ma-27	285	21	,	,	PUNCT
ma-27	285	22	we	we	PRON
ma-27	285	23	obtain	obtain	VERB
ma-27	285	24	x	x	SYM
ma-27	285	25	≤	≤	NUM
ma-27	285	26	lim	lim	PROPN
ma-27	285	27	inf	inf	PROPN
ma-27	285	28	s→∞	s→∞	PROPN
ma-27	285	29	‖gs	‖gs	NUM
ma-27	285	30	−	−	PROPN
ma-27	285	31	z‖.	z‖.	NOUN
ma-27	285	32	(	(	PUNCT
ma-27	285	33	4.10	4.10	NUM
ma-27	285	34	)	)	PUNCT
ma-27	285	35	eur	eur	PROPN
ma-27	285	36	.	.	PUNCT
ma-27	286	1	j.	j.	PROPN
ma-27	286	2	math	math	PROPN
ma-27	286	3	.	.	PUNCT
ma-27	287	1	anal	anal	ADJ
ma-27	287	2	.	.	PUNCT
ma-27	288	1	1	1	NUM
ma-27	288	2	(	(	PUNCT
ma-27	288	3	2021	2021	NUM
ma-27	288	4	)	)	PUNCT
ma-27	289	1	119from	119from	PROPN
ma-27	289	2	(	(	PUNCT
ma-27	289	3	4.6	4.6	NUM
ma-27	289	4	)	)	PUNCT
ma-27	289	5	and	and	CCONJ
ma-27	289	6	(	(	PUNCT
ma-27	289	7	4.10	4.10	NUM
ma-27	289	8	)	)	PUNCT
ma-27	289	9	we	we	PRON
ma-27	289	10	obtain	obtain	VERB
ma-27	289	11	x	x	X
ma-27	289	12	=	=	SYM
ma-27	289	13	lim	lim	NOUN
ma-27	289	14	s→∞	s→∞	NUM
ma-27	289	15	‖gn	‖gn	NUM
ma-27	289	16	−	−	PROPN
ma-27	289	17	z‖	z‖	NOUN
ma-27	289	18	=	=	SYM
ma-27	289	19	lim	lim	PROPN
ma-27	289	20	s→∞	s→∞	NOUN
ma-27	289	21	‖(1−	‖(1−	PROPN
ma-27	289	22	βs)`s	βs)`s	NOUN
ma-27	290	1	+	+	CCONJ
ma-27	290	2	βst`s	βst`s	PROPN
ma-27	290	3	−	−	NOUN
ma-27	290	4	z‖	z‖	NOUN
ma-27	290	5	=	=	SYM
ma-27	290	6	lim	lim	PROPN
ma-27	290	7	s→∞	s→∞	NUM
ma-27	291	1	‖(1−	‖(1−	PROPN
ma-27	291	2	βs)(`s	βs)(`s	PROPN
ma-27	291	3	−	−	PROPN
ma-27	291	4	z	z	NOUN
ma-27	291	5	)	)	PUNCT
ma-27	292	1	+	+	CCONJ
ma-27	292	2	βs(t`s	βs(t`s	SYM
ma-27	293	1	−	−	ADP
ma-27	293	2	z)‖	z)‖	NOUN
ma-27	294	1	=	=	SYM
ma-27	294	2	lim	lim	PROPN
ma-27	294	3	s→∞	s→∞	PROPN
ma-27	294	4	‖βs(t`s	‖βs(t`s	PUNCT
ma-27	294	5	−	−	PROPN
ma-27	294	6	z	z	NOUN
ma-27	294	7	)	)	PUNCT
ma-27	295	1	+	+	CCONJ
ma-27	295	2	(	(	PUNCT
ma-27	295	3	1−	1−	NUM
ma-27	295	4	βs)(`s	βs)(`s	PROPN
ma-27	295	5	−	−	PROPN
ma-27	296	1	z)‖.	z)‖.	NOUN
ma-27	296	2	(	(	PUNCT
ma-27	296	3	4.11	4.11	NUM
ma-27	296	4	)	)	PUNCT
ma-27	296	5	from	from	ADP
ma-27	296	6	(	(	PUNCT
ma-27	296	7	4.5	4.5	NUM
ma-27	296	8	)	)	PUNCT
ma-27	296	9	,	,	PUNCT
ma-27	296	10	(	(	PUNCT
ma-27	296	11	4.7	4.7	NUM
ma-27	296	12	)	)	PUNCT
ma-27	296	13	,	,	PUNCT
ma-27	296	14	(	(	PUNCT
ma-27	296	15	4.11	4.11	NUM
ma-27	296	16	)	)	PUNCT
ma-27	296	17	and	and	CCONJ
ma-27	296	18	lemma	lemma	PROPN
ma-27	296	19	2.14	2.14	NUM
ma-27	296	20	,	,	PUNCT
ma-27	296	21	we	we	PRON
ma-27	296	22	obtain	obtain	VERB
ma-27	296	23	lim	lim	PROPN
ma-27	296	24	s→∞	s→∞	PROPN
ma-27	296	25	‖t`s	‖t`s	ADJ
ma-27	296	26	−	−	NOUN
ma-27	296	27	`	`	PUNCT
ma-27	296	28	s‖	s‖	NOUN
ma-27	296	29	=	=	SYM
ma-27	296	30	0	0	NUM
ma-27	296	31	.	.	PUNCT
ma-27	297	1	(	(	PUNCT
ma-27	297	2	4.12	4.12	NUM
ma-27	297	3	)	)	PUNCT
ma-27	297	4	conversely	conversely	ADV
ma-27	297	5	,	,	PUNCT
ma-27	297	6	assume	assume	VERB
ma-27	297	7	that	that	SCONJ
ma-27	297	8	{	{	PUNCT
ma-27	297	9	`	`	PUNCT
ma-27	297	10	s	s	X
ma-27	297	11	}	}	PUNCT
ma-27	297	12	is	be	AUX
ma-27	297	13	bounded	bound	VERB
ma-27	297	14	and	and	CCONJ
ma-27	297	15	lim	lim	PROPN
ma-27	298	1	s→∞	s→∞	PROPN
ma-27	298	2	‖t`s−`s‖	‖t`s−`s‖	NOUN
ma-27	298	3	=	=	PUNCT
ma-27	298	4	0	0	X
ma-27	298	5	.	.	PUNCT
ma-27	299	1	let	let	VERB
ma-27	299	2	z	z	NOUN
ma-27	299	3	∈	∈	PROPN
ma-27	299	4	a(λ	a(λ	PROPN
ma-27	299	5	,	,	PUNCT
ma-27	299	6	{	{	PUNCT
ma-27	299	7	`	`	PUNCT
ma-27	299	8	s	s	X
ma-27	299	9	}	}	PUNCT
ma-27	299	10	)	)	PUNCT
ma-27	299	11	,	,	PUNCT
ma-27	299	12	by	by	ADP
ma-27	299	13	definition2.3	definition2.3	NOUN
ma-27	299	14	and	and	CCONJ
ma-27	299	15	proposition	proposition	NOUN
ma-27	299	16	2.9(iv	2.9(iv	NUM
ma-27	299	17	)	)	PUNCT
ma-27	299	18	,	,	PUNCT
ma-27	299	19	we	we	PRON
ma-27	299	20	have	have	VERB
ma-27	299	21	(	(	PUNCT
ma-27	299	22	tz	tz	NOUN
ma-27	299	23	,	,	PUNCT
ma-27	299	24	{	{	PUNCT
ma-27	299	25	`	`	PUNCT
ma-27	299	26	s	s	X
ma-27	299	27	}	}	PUNCT
ma-27	299	28	)	)	PUNCT
ma-27	300	1	=	=	SYM
ma-27	300	2	lim	lim	PROPN
ma-27	300	3	sup	sup	NOUN
ma-27	300	4	s→∞	s→∞	NUM
ma-27	300	5	‖`s	‖`s	PUNCT
ma-27	300	6	−	−	NOUN
ma-27	300	7	tz‖	tz‖	PROPN
ma-27	300	8	≤	≤	NUM
ma-27	300	9	lim	lim	PROPN
ma-27	300	10	sup	sup	NOUN
ma-27	300	11	s→∞	s→∞	NUM
ma-27	300	12	(	(	PUNCT
ma-27	300	13	(	(	PUNCT
ma-27	300	14	3	3	NUM
ma-27	300	15	+	+	NOUN
ma-27	300	16	α	α	X
ma-27	300	17	)	)	PUNCT
ma-27	300	18	(	(	PUNCT
ma-27	300	19	1−	1−	NUM
ma-27	300	20	α	α	NOUN
ma-27	300	21	)	)	PUNCT
ma-27	300	22	‖t`s	‖t`s	ADJ
ma-27	300	23	−	−	NOUN
ma-27	300	24	`	`	PUNCT
ma-27	300	25	s‖+	s‖+	VERB
ma-27	300	26	‖`s	‖`s	PRON
ma-27	300	27	−	−	NOUN
ma-27	300	28	z‖	z‖	NOUN
ma-27	300	29	)	)	PUNCT
ma-27	301	1	=	=	SYM
ma-27	301	2	lim	lim	PROPN
ma-27	301	3	sup	sup	NOUN
ma-27	301	4	s→∞	s→∞	NUM
ma-27	301	5	‖`s	‖`s	ADJ
ma-27	301	6	−	−	NOUN
ma-27	301	7	z‖	z‖	NOUN
ma-27	301	8	=	=	SYM
ma-27	301	9	r(z	r(z	NOUN
ma-27	301	10	,	,	PUNCT
ma-27	301	11	{	{	PUNCT
ma-27	301	12	`	`	PUNCT
ma-27	301	13	s	s	NOUN
ma-27	301	14	}	}	PUNCT
ma-27	301	15	)	)	PUNCT
ma-27	301	16	.	.	PUNCT
ma-27	302	1	(	(	PUNCT
ma-27	302	2	4.13	4.13	X
ma-27	302	3	)	)	PUNCT
ma-27	302	4	this	this	PRON
ma-27	302	5	implies	imply	VERB
ma-27	302	6	that	that	SCONJ
ma-27	302	7	z	z	PROPN
ma-27	302	8	∈	∈	PROPN
ma-27	302	9	a(λ	a(λ	PROPN
ma-27	302	10	,	,	PUNCT
ma-27	302	11	{	{	PUNCT
ma-27	302	12	`	`	PUNCT
ma-27	302	13	s	s	X
ma-27	302	14	}	}	PUNCT
ma-27	302	15	)	)	PUNCT
ma-27	302	16	.	.	PUNCT
ma-27	303	1	since	since	SCONJ
ma-27	303	2	ω	ω	PROPN
ma-27	303	3	is	be	AUX
ma-27	303	4	uniformly	uniformly	ADV
ma-27	303	5	convex	convex	NOUN
ma-27	303	6	,	,	PUNCT
ma-27	303	7	a(λ	a(λ	ADV
ma-27	303	8	,	,	PUNCT
ma-27	303	9	{	{	PUNCT
ma-27	303	10	`	`	PUNCT
ma-27	303	11	s	s	X
ma-27	303	12	}	}	PUNCT
ma-27	303	13	)	)	PUNCT
ma-27	303	14	is	be	AUX
ma-27	303	15	singleton	singleton	NOUN
ma-27	303	16	,	,	PUNCT
ma-27	303	17	thus	thus	ADV
ma-27	303	18	wehave	wehave	VERB
ma-27	303	19	tz	tz	NOUN
ma-27	303	20	=	=	SYM
ma-27	303	21	z	z	PROPN
ma-27	303	22	.	.	PUNCT
ma-27	304	1	�	�	PROPN
ma-27	304	2	theorem	theorem	VERB
ma-27	304	3	4.3	4.3	NUM
ma-27	304	4	.	.	PUNCT
ma-27	305	1	let	let	VERB
ma-27	305	2	ω	ω	NUM
ma-27	305	3	,	,	PUNCT
ma-27	305	4	λ	λ	PROPN
ma-27	305	5	,	,	PUNCT
ma-27	305	6	t	t	PROPN
ma-27	305	7	be	be	AUX
ma-27	305	8	same	same	ADJ
ma-27	305	9	as	as	ADP
ma-27	305	10	in	in	ADP
ma-27	305	11	lemma	lemma	PROPN
ma-27	305	12	4.2	4.2	NUM
ma-27	305	13	.	.	PUNCT
ma-27	306	1	suppose	suppose	VERB
ma-27	306	2	tat	tat	PROPN
ma-27	306	3	ω	ω	PROPN
ma-27	306	4	satisfies	satisfie	NOUN
ma-27	306	5	opial	opial	NOUN
ma-27	306	6	’s	’s	PART
ma-27	306	7	condition	condition	NOUN
ma-27	306	8	and	and	CCONJ
ma-27	306	9	f	f	PROPN
ma-27	306	10	(	(	PUNCT
ma-27	306	11	t	t	PROPN
ma-27	306	12	)	)	PUNCT
ma-27	306	13	6=	6=	ADP
ma-27	306	14	∅.	∅.	ADP
ma-27	306	15	then	then	ADV
ma-27	306	16	,	,	PUNCT
ma-27	306	17	the	the	DET
ma-27	306	18	sequence	sequence	NOUN
ma-27	306	19	{	{	PUNCT
ma-27	306	20	`	`	PUNCT
ma-27	306	21	s	s	X
ma-27	306	22	}	}	PUNCT
ma-27	306	23	defined	define	VERB
ma-27	306	24	by	by	ADP
ma-27	306	25	(	(	PUNCT
ma-27	306	26	1.7	1.7	NUM
ma-27	306	27	)	)	PUNCT
ma-27	306	28	converges	converge	VERB
ma-27	306	29	weakly	weakly	ADJ
ma-27	306	30	to	to	ADP
ma-27	306	31	a	a	DET
ma-27	306	32	fixed	fix	VERB
ma-27	306	33	point	point	NOUN
ma-27	306	34	of	of	ADP
ma-27	306	35	t	t	PROPN
ma-27	306	36	.	.	PUNCT
ma-27	307	1	proof	proof	NOUN
ma-27	307	2	.	.	PUNCT
ma-27	308	1	let	let	VERB
ma-27	308	2	z	z	NOUN
ma-27	308	3	∈	∈	PROPN
ma-27	308	4	f	f	X
ma-27	308	5	(	(	PUNCT
ma-27	308	6	t	t	PROPN
ma-27	308	7	)	)	PUNCT
ma-27	308	8	,	,	PUNCT
ma-27	308	9	then	then	ADV
ma-27	308	10	by	by	ADP
ma-27	308	11	lemma	lemma	PROPN
ma-27	308	12	4.1	4.1	NUM
ma-27	308	13	,	,	PUNCT
ma-27	308	14	we	we	PRON
ma-27	308	15	have	have	VERB
ma-27	308	16	lim	lim	PROPN
ma-27	309	1	s→∞	s→∞	PROPN
ma-27	309	2	‖`s	‖`s	PROPN
ma-27	309	3	−	−	PRON
ma-27	309	4	z‖	z‖	NOUN
ma-27	309	5	exists	exist	VERB
ma-27	309	6	.	.	PUNCT
ma-27	310	1	now	now	ADV
ma-27	310	2	we	we	PRON
ma-27	310	3	show	show	VERB
ma-27	310	4	that	that	SCONJ
ma-27	310	5	{	{	PUNCT
ma-27	310	6	`	`	PUNCT
ma-27	310	7	s}has	s}has	ADJ
ma-27	310	8	weak	weak	ADJ
ma-27	310	9	sequential	sequential	ADJ
ma-27	310	10	limit	limit	NOUN
ma-27	310	11	in	in	ADP
ma-27	310	12	f	f	PROPN
ma-27	310	13	(	(	PUNCT
ma-27	310	14	t	t	PROPN
ma-27	310	15	)	)	PUNCT
ma-27	310	16	.	.	PUNCT
ma-27	311	1	let	let	VERB
ma-27	311	2	`	`	PUNCT
ma-27	311	3	and	and	CCONJ
ma-27	311	4	ζ	ζ	NOUN
ma-27	311	5	be	be	AUX
ma-27	311	6	weak	weak	ADJ
ma-27	311	7	limits	limit	NOUN
ma-27	311	8	of	of	ADP
ma-27	311	9	the	the	DET
ma-27	311	10	subsequences	subsequence	NOUN
ma-27	311	11	{	{	PUNCT
ma-27	311	12	`	`	PUNCT
ma-27	311	13	sj	sj	INTJ
ma-27	311	14	}	}	PUNCT
ma-27	311	15	and	and	CCONJ
ma-27	311	16	{	{	PUNCT
ma-27	311	17	`	`	PUNCT
ma-27	311	18	sk}of	sk}of	ADJ
ma-27	311	19	{	{	PUNCT
ma-27	311	20	`	`	PUNCT
ma-27	311	21	s	s	PART
ma-27	311	22	}	}	PUNCT
ma-27	311	23	,	,	PUNCT
ma-27	311	24	respectively	respectively	ADV
ma-27	311	25	.	.	PUNCT
ma-27	312	1	by	by	ADP
ma-27	312	2	lemma	lemma	PROPN
ma-27	312	3	4.2	4.2	NUM
ma-27	312	4	,	,	PUNCT
ma-27	312	5	we	we	PRON
ma-27	312	6	have	have	VERB
ma-27	312	7	lim	lim	PROPN
ma-27	312	8	s→∞	s→∞	PROPN
ma-27	312	9	‖t`s	‖t`s	ADJ
ma-27	312	10	−	−	NOUN
ma-27	312	11	`	`	PUNCT
ma-27	312	12	s‖	s‖	NOUN
ma-27	312	13	=	=	SYM
ma-27	312	14	0	0	NUM
ma-27	312	15	and	and	CCONJ
ma-27	312	16	from	from	ADP
ma-27	312	17	lemma	lemma	PROPN
ma-27	312	18	2.10	2.10	NUM
ma-27	312	19	,	,	PUNCT
ma-27	312	20	i	i	PRON
ma-27	312	21	−	−	PROPN
ma-27	312	22	t	t	PROPN
ma-27	312	23	isdemiclosed	isdemiclose	VERB
ma-27	312	24	at	at	ADP
ma-27	312	25	zero	zero	NUM
ma-27	312	26	.	.	PUNCT
ma-27	313	1	it	it	PRON
ma-27	313	2	follows	follow	VERB
ma-27	313	3	that	that	SCONJ
ma-27	313	4	(	(	PUNCT
ma-27	313	5	i	i	PRON
ma-27	313	6	−	−	PROPN
ma-27	313	7	t	t	NOUN
ma-27	313	8	)	)	PUNCT
ma-27	313	9	`	`	PUNCT
ma-27	313	10	=	=	SYM
ma-27	313	11	0	0	NUM
ma-27	313	12	implies	imply	VERB
ma-27	313	13	`	`	PUNCT
ma-27	313	14	=	=	SYM
ma-27	313	15	t	t	PROPN
ma-27	313	16	`	`	PUNCT
ma-27	313	17	,	,	PUNCT
ma-27	313	18	similarly	similarly	ADV
ma-27	313	19	tζ	tζ	X
ma-27	313	20	=	=	NOUN
ma-27	313	21	ζ.next	ζ.next	PROPN
ma-27	313	22	we	we	PRON
ma-27	313	23	show	show	VERB
ma-27	313	24	uniqueness	uniqueness	NOUN
ma-27	313	25	.	.	PUNCT
ma-27	314	1	suppose	suppose	VERB
ma-27	314	2	`	`	PUNCT
ma-27	314	3	6=	6=	SYM
ma-27	314	4	ζ	ζ	NOUN
ma-27	314	5	,	,	PUNCT
ma-27	314	6	then	then	ADV
ma-27	314	7	by	by	ADP
ma-27	314	8	opial	opial	NOUN
ma-27	314	9	’s	’s	PART
ma-27	314	10	property	property	NOUN
ma-27	314	11	,	,	PUNCT
ma-27	314	12	we	we	PRON
ma-27	314	13	obtain	obtain	VERB
ma-27	314	14	lim	lim	PROPN
ma-27	314	15	s→∞	s→∞	PROPN
ma-27	314	16	‖`s	‖`s	PROPN
ma-27	314	17	−	−	PUNCT
ma-27	314	18	`	`	PUNCT
ma-27	314	19	‖	‖	PROPN
ma-27	314	20	=	=	SYM
ma-27	314	21	lim	lim	PROPN
ma-27	314	22	sj→∞	sj→∞	PROPN
ma-27	314	23	‖`sj	‖`sj	VERB
ma-27	314	24	−	−	PROPN
ma-27	314	25	`	`	PUNCT
ma-27	314	26	‖	‖	PROPN
ma-27	314	27	<	<	X
ma-27	314	28	lim	lim	PROPN
ma-27	314	29	sj→∞	sj→∞	PROPN
ma-27	314	30	‖`sj	‖`sj	VERB
ma-27	314	31	−	−	NOUN
ma-27	314	32	ζ‖	ζ‖	NOUN
ma-27	314	33	=	=	SYM
ma-27	314	34	lim	lim	PROPN
ma-27	314	35	s→∞	s→∞	PROPN
ma-27	314	36	‖`s	‖`s	PROPN
ma-27	314	37	−	−	PROPN
ma-27	314	38	ζ‖	ζ‖	NOUN
ma-27	314	39	=	=	PROPN
ma-27	314	40	lim	lim	PROPN
ma-27	314	41	sk→∞	sk→∞	NOUN
ma-27	314	42	‖`sk	‖`sk	VERB
ma-27	314	43	−	−	PROPN
ma-27	314	44	ζ‖	ζ‖	NOUN
ma-27	314	45	<	<	X
ma-27	314	46	lim	lim	PROPN
ma-27	314	47	sk→∞	sk→∞	ADV
ma-27	314	48	‖`sk	‖`sk	VERB
ma-27	314	49	−	−	NOUN
ma-27	314	50	`	`	PUNCT
ma-27	314	51	‖	‖	PROPN
ma-27	314	52	=	=	SYM
ma-27	314	53	lim	lim	PROPN
ma-27	314	54	s→∞	s→∞	PROPN
ma-27	314	55	‖`s	‖`s	PROPN
ma-27	314	56	−	−	PUNCT
ma-27	314	57	`	`	PUNCT
ma-27	314	58	‖	‖	NUM
ma-27	314	59	,	,	PUNCT
ma-27	314	60	(	(	PUNCT
ma-27	314	61	4.14	4.14	NUM
ma-27	314	62	)	)	PUNCT
ma-27	314	63	which	which	PRON
ma-27	314	64	is	be	AUX
ma-27	314	65	a	a	DET
ma-27	314	66	contradiction	contradiction	NOUN
ma-27	314	67	,	,	PUNCT
ma-27	314	68	so	so	CCONJ
ma-27	314	69	`	`	PUNCT
ma-27	314	70	=	=	SYM
ma-27	314	71	ζ	ζ	X
ma-27	314	72	.	.	PUNCT
ma-27	315	1	hence	hence	ADV
ma-27	315	2	,	,	PUNCT
ma-27	315	3	{	{	PUNCT
ma-27	315	4	`	`	PUNCT
ma-27	315	5	s	s	X
ma-27	315	6	}	}	PUNCT
ma-27	315	7	converges	converge	VERB
ma-27	315	8	weakly	weakly	ADV
ma-27	315	9	to	to	ADP
ma-27	315	10	a	a	DET
ma-27	315	11	fixed	fix	VERB
ma-27	315	12	point	point	NOUN
ma-27	315	13	of	of	ADP
ma-27	315	14	t	t	PROPN
ma-27	315	15	.	.	PUNCT
ma-27	316	1	�	�	PROPN
ma-27	316	2	eur	eur	PROPN
ma-27	316	3	.	.	PUNCT
ma-27	317	1	j.	j.	PROPN
ma-27	317	2	math	math	PROPN
ma-27	317	3	.	.	PUNCT
ma-27	318	1	anal	anal	ADJ
ma-27	318	2	.	.	PUNCT
ma-27	319	1	1	1	NUM
ma-27	319	2	(	(	PUNCT
ma-27	319	3	2021	2021	NUM
ma-27	319	4	)	)	PUNCT
ma-27	320	1	120	120	NUM
ma-27	320	2	theorem	theorem	VERB
ma-27	320	3	4.4	4.4	NUM
ma-27	320	4	.	.	PUNCT
ma-27	321	1	let	let	VERB
ma-27	321	2	ω	ω	NUM
ma-27	321	3	,	,	PUNCT
ma-27	321	4	λ	λ	PROPN
ma-27	321	5	,	,	PUNCT
ma-27	321	6	t	t	PROPN
ma-27	321	7	be	be	AUX
ma-27	321	8	same	same	ADJ
ma-27	321	9	as	as	ADP
ma-27	321	10	in	in	ADP
ma-27	321	11	lemma	lemma	PROPN
ma-27	321	12	4.2	4.2	NUM
ma-27	321	13	.	.	PUNCT
ma-27	322	1	then	then	ADV
ma-27	322	2	,	,	PUNCT
ma-27	322	3	the	the	DET
ma-27	322	4	iterative	iterative	NOUN
ma-27	322	5	algorithm	algorithm	NOUN
ma-27	322	6	{	{	PUNCT
ma-27	322	7	`	`	PUNCT
ma-27	322	8	s	s	X
ma-27	322	9	}	}	PUNCT
ma-27	322	10	defined	define	VERB
ma-27	322	11	by	by	ADP
ma-27	322	12	(	(	PUNCT
ma-27	322	13	1.7	1.7	NUM
ma-27	322	14	)	)	PUNCT
ma-27	322	15	converges	converge	VERB
ma-27	322	16	strongly	strongly	ADV
ma-27	322	17	to	to	ADP
ma-27	322	18	a	a	DET
ma-27	322	19	point	point	NOUN
ma-27	322	20	of	of	ADP
ma-27	322	21	f	f	PROPN
ma-27	322	22	(	(	PUNCT
ma-27	322	23	t	t	PROPN
ma-27	322	24	)	)	PUNCT
ma-27	322	25	if	if	SCONJ
ma-27	323	1	and	and	CCONJ
ma-27	323	2	only	only	ADV
ma-27	323	3	if	if	SCONJ
ma-27	323	4	lim	lim	PROPN
ma-27	323	5	inf	inf	PROPN
ma-27	323	6	s→∞	s→∞	PROPN
ma-27	323	7	d(`s	d(`	NOUN
ma-27	323	8	,	,	PUNCT
ma-27	323	9	f	f	PROPN
ma-27	323	10	(	(	PUNCT
ma-27	323	11	t	t	PROPN
ma-27	323	12	)	)	PUNCT
ma-27	323	13	)	)	PUNCT
ma-27	324	1	=	=	PUNCT
ma-27	324	2	0	0	NUM
ma-27	324	3	,	,	PUNCT
ma-27	324	4	where	where	SCONJ
ma-27	324	5	d(`s	d(`	NOUN
ma-27	324	6	,	,	PUNCT
ma-27	324	7	f	f	PROPN
ma-27	324	8	(	(	PUNCT
ma-27	324	9	t	t	PROPN
ma-27	324	10	)	)	PUNCT
ma-27	324	11	)	)	PUNCT
ma-27	325	1	=	=	PRON
ma-27	325	2	inf{‖`−	inf{‖`−	NOUN
ma-27	325	3	z‖	z‖	VERB
ma-27	325	4	:	:	PUNCT
ma-27	325	5	z	z	PROPN
ma-27	325	6	∈	∈	PROPN
ma-27	326	1	f	f	X
ma-27	326	2	(	(	PUNCT
ma-27	326	3	t	t	PROPN
ma-27	326	4	)	)	PUNCT
ma-27	326	5	}	}	PUNCT
ma-27	326	6	.	.	PUNCT
ma-27	327	1	proof	proof	NOUN
ma-27	327	2	.	.	PUNCT
ma-27	328	1	necessity	necessity	NOUN
ma-27	328	2	is	be	AUX
ma-27	328	3	obvious	obvious	ADJ
ma-27	328	4	.	.	PUNCT
ma-27	329	1	assume	assume	VERB
ma-27	329	2	that	that	SCONJ
ma-27	329	3	lim	lim	PROPN
ma-27	329	4	inf	inf	PROPN
ma-27	329	5	s→∞	s→∞	PROPN
ma-27	329	6	d(`s	d(`	NOUN
ma-27	329	7	,	,	PUNCT
ma-27	329	8	f	f	PROPN
ma-27	329	9	(	(	PUNCT
ma-27	329	10	t	t	PROPN
ma-27	329	11	)	)	PUNCT
ma-27	329	12	)	)	PUNCT
ma-27	330	1	=	=	PUNCT
ma-27	330	2	0	0	X
ma-27	330	3	.	.	PUNCT
ma-27	330	4	from	from	ADP
ma-27	330	5	lemma	lemma	PROPN
ma-27	330	6	4.1	4.1	NUM
ma-27	330	7	,	,	PUNCT
ma-27	330	8	we	we	PRON
ma-27	330	9	have	have	VERB
ma-27	330	10	lim	lim	PROPN
ma-27	330	11	s→∞	s→∞	PROPN
ma-27	331	1	‖`s	‖`s	PROPN
ma-27	332	1	−	−	PROPN
ma-27	332	2	z‖	z‖	NOUN
ma-27	332	3	exists	exist	VERB
ma-27	332	4	for	for	ADP
ma-27	332	5	all	all	PRON
ma-27	332	6	z	z	NOUN
ma-27	332	7	∈	∈	PROPN
ma-27	332	8	f	f	X
ma-27	332	9	(	(	PUNCT
ma-27	332	10	t	t	PROPN
ma-27	332	11	)	)	PUNCT
ma-27	332	12	,	,	PUNCT
ma-27	332	13	it	it	PRON
ma-27	332	14	follows	follow	VERB
ma-27	332	15	that	that	SCONJ
ma-27	332	16	lim	lim	PROPN
ma-27	332	17	inf	inf	PROPN
ma-27	332	18	s→∞	s→∞	PROPN
ma-27	332	19	d(`s	d(`	NOUN
ma-27	332	20	,	,	PUNCT
ma-27	332	21	f	f	PROPN
ma-27	332	22	(	(	PUNCT
ma-27	332	23	t	t	PROPN
ma-27	332	24	)	)	PUNCT
ma-27	332	25	)	)	PUNCT
ma-27	332	26	exists	exist	VERB
ma-27	332	27	.	.	PUNCT
ma-27	333	1	but	but	CCONJ
ma-27	333	2	by	by	ADP
ma-27	333	3	hypothesis	hypothesis	NOUN
ma-27	333	4	,	,	PUNCT
ma-27	333	5	lim	lim	PROPN
ma-27	333	6	inf	inf	PROPN
ma-27	333	7	s→∞	s→∞	PROPN
ma-27	333	8	d(`s	d(`	NOUN
ma-27	333	9	,	,	PUNCT
ma-27	333	10	f	f	PROPN
ma-27	333	11	(	(	PUNCT
ma-27	333	12	t	t	PROPN
ma-27	333	13	)	)	PUNCT
ma-27	333	14	)	)	PUNCT
ma-27	334	1	=	=	SYM
ma-27	334	2	0	0	NUM
ma-27	334	3	,	,	PUNCT
ma-27	334	4	thus	thus	ADV
ma-27	334	5	lim	lim	NOUN
ma-27	334	6	s→∞	s→∞	PROPN
ma-27	334	7	d(`s	d(`	NOUN
ma-27	334	8	,	,	PUNCT
ma-27	334	9	f	f	PROPN
ma-27	334	10	(	(	PUNCT
ma-27	334	11	t	t	PROPN
ma-27	334	12	)	)	PUNCT
ma-27	334	13	)	)	PUNCT
ma-27	335	1	=	=	PUNCT
ma-27	335	2	0	0	X
ma-27	335	3	.	.	PUNCT
ma-27	336	1	next	next	ADV
ma-27	336	2	we	we	PRON
ma-27	336	3	prove	prove	VERB
ma-27	336	4	that	that	SCONJ
ma-27	336	5	{	{	PUNCT
ma-27	336	6	`	`	PUNCT
ma-27	336	7	s	s	AUX
ma-27	336	8	}	}	PUNCT
ma-27	336	9	is	be	AUX
ma-27	336	10	a	a	DET
ma-27	336	11	cauchy	cauchy	ADJ
ma-27	336	12	sequencein	sequencein	NOUN
ma-27	336	13	λ	λ	PROPN
ma-27	336	14	.	.	PROPN
ma-27	337	1	since	since	SCONJ
ma-27	337	2	lim	lim	PROPN
ma-27	337	3	inf	inf	PROPN
ma-27	337	4	s→∞	s→∞	PROPN
ma-27	337	5	d(`s	d(`	NOUN
ma-27	337	6	,	,	PUNCT
ma-27	337	7	f	f	PROPN
ma-27	337	8	(	(	PUNCT
ma-27	337	9	t	t	PROPN
ma-27	337	10	)	)	PUNCT
ma-27	337	11	)	)	PUNCT
ma-27	338	1	=	=	PUNCT
ma-27	338	2	0	0	NUM
ma-27	338	3	,	,	PUNCT
ma-27	338	4	then	then	ADV
ma-27	338	5	given	give	VERB
ma-27	338	6	ε	ε	PROPN
ma-27	338	7	>	>	X
ma-27	338	8	0	0	PROPN
ma-27	338	9	,	,	PUNCT
ma-27	338	10	there	there	PRON
ma-27	338	11	exists	exist	VERB
ma-27	338	12	s0	s0	PROPN
ma-27	338	13	∈	∈	PROPN
ma-27	338	14	n	n	PRON
ma-27	338	15	such	such	ADJ
ma-27	338	16	that	that	SCONJ
ma-27	338	17	,	,	PUNCT
ma-27	338	18	for	for	ADP
ma-27	338	19	all	all	DET
ma-27	338	20	s	s	NOUN
ma-27	338	21	,	,	PUNCT
ma-27	338	22	n	n	PRON
ma-27	338	23	≥	≥	NOUN
ma-27	338	24	s0,we	s0,we	PROPN
ma-27	338	25	have	have	VERB
ma-27	338	26	d(`s	d(`	NOUN
ma-27	338	27	,	,	PUNCT
ma-27	338	28	f	f	PROPN
ma-27	338	29	(	(	PUNCT
ma-27	338	30	t	t	PROPN
ma-27	338	31	)	)	PUNCT
ma-27	338	32	)	)	PUNCT
ma-27	339	1	≤	≤	NUM
ma-27	339	2	ε	ε	PROPN
ma-27	339	3	2	2	NUM
ma-27	339	4	,	,	PUNCT
ma-27	339	5	d(`n	d(`n	ADV
ma-27	339	6	,	,	PUNCT
ma-27	339	7	f	f	PROPN
ma-27	339	8	(	(	PUNCT
ma-27	339	9	t	t	PROPN
ma-27	339	10	)	)	PUNCT
ma-27	339	11	)	)	PUNCT
ma-27	339	12	≤	≤	NUM
ma-27	339	13	ε	ε	PROPN
ma-27	339	14	2	2	NUM
ma-27	339	15	.	.	PUNCT
ma-27	340	1	thus	thus	ADV
ma-27	340	2	,	,	PUNCT
ma-27	340	3	we	we	PRON
ma-27	340	4	have	have	VERB
ma-27	340	5	‖`s	‖`s	NOUN
ma-27	340	6	−	−	ADP
ma-27	340	7	`	`	PUNCT
ma-27	340	8	n‖	n‖	VERB
ma-27	340	9	≤	≤	ADJ
ma-27	341	1	‖`s	‖`s	PROPN
ma-27	341	2	−	−	PUNCT
ma-27	342	1	z‖+	z‖+	NUM
ma-27	342	2	‖`n	‖`n	PROPN
ma-27	342	3	−	−	PROPN
ma-27	342	4	z‖	z‖	VERB
ma-27	342	5	≤	≤	NUM
ma-27	342	6	d(`s	d(`	NOUN
ma-27	342	7	,	,	PUNCT
ma-27	342	8	f	f	PROPN
ma-27	342	9	(	(	PUNCT
ma-27	342	10	t	t	PROPN
ma-27	342	11	)	)	PUNCT
ma-27	342	12	)	)	PUNCT
ma-27	343	1	+	+	CCONJ
ma-27	343	2	d(`n	d(`n	X
ma-27	343	3	,	,	PUNCT
ma-27	343	4	f	f	PROPN
ma-27	343	5	(	(	PUNCT
ma-27	343	6	t	t	PROPN
ma-27	343	7	)	)	PUNCT
ma-27	343	8	)	)	PUNCT
ma-27	343	9	≤	≤	NUM
ma-27	343	10	ε	ε	PROPN
ma-27	343	11	2	2	NUM
ma-27	343	12	+	+	CCONJ
ma-27	343	13	ε	ε	PROPN
ma-27	343	14	2	2	NUM
ma-27	343	15	=	=	SYM
ma-27	343	16	ε	ε	PROPN
ma-27	343	17	.	.	PUNCT
ma-27	344	1	hence	hence	ADV
ma-27	344	2	{	{	PUNCT
ma-27	344	3	`	`	PUNCT
ma-27	344	4	s	s	AUX
ma-27	344	5	}	}	PUNCT
ma-27	344	6	is	be	AUX
ma-27	344	7	a	a	DET
ma-27	344	8	cauchy	cauchy	ADJ
ma-27	344	9	sequence	sequence	NOUN
ma-27	344	10	in	in	ADP
ma-27	344	11	λ	λ	PROPN
ma-27	344	12	.	.	PUNCT
ma-27	345	1	since	since	SCONJ
ma-27	345	2	λ	λ	PROPN
ma-27	345	3	is	be	AUX
ma-27	345	4	closed	closed	ADJ
ma-27	345	5	,	,	PUNCT
ma-27	345	6	therefore	therefore	ADV
ma-27	345	7	there	there	PRON
ma-27	345	8	exists	exist	VERB
ma-27	345	9	a	a	DET
ma-27	345	10	point	point	NOUN
ma-27	345	11	`	`	PUNCT
ma-27	345	12	1	1	NUM
ma-27	345	13	∈	∈	NOUN
ma-27	345	14	λsuch	λsuch	ADJ
ma-27	345	15	that	that	SCONJ
ma-27	345	16	lim	lim	PROPN
ma-27	345	17	s→∞	s→∞	PRON
ma-27	345	18	`	`	PUNCT
ma-27	345	19	s	s	VERB
ma-27	345	20	=	=	PUNCT
ma-27	345	21	`	`	PUNCT
ma-27	345	22	1	1	NUM
ma-27	345	23	.	.	PUNCT
ma-27	346	1	since	since	SCONJ
ma-27	346	2	lim	lim	PROPN
ma-27	346	3	s→∞	s→∞	PROPN
ma-27	346	4	d(`s	d(`	NOUN
ma-27	346	5	,	,	PUNCT
ma-27	346	6	f	f	PROPN
ma-27	346	7	(	(	PUNCT
ma-27	346	8	t	t	PROPN
ma-27	346	9	)	)	PUNCT
ma-27	346	10	)	)	PUNCT
ma-27	347	1	=	=	PUNCT
ma-27	347	2	0	0	X
ma-27	347	3	,	,	PUNCT
ma-27	347	4	it	it	PRON
ma-27	347	5	implies	imply	VERB
ma-27	347	6	that	that	SCONJ
ma-27	347	7	lim	lim	PROPN
ma-27	347	8	s→∞	s→∞	PRON
ma-27	347	9	d(`1	d(`1	PROPN
ma-27	347	10	,	,	PUNCT
ma-27	347	11	f	f	PROPN
ma-27	347	12	(	(	PUNCT
ma-27	347	13	t	t	PROPN
ma-27	347	14	)	)	PUNCT
ma-27	347	15	)	)	PUNCT
ma-27	348	1	=	=	PUNCT
ma-27	348	2	0	0	X
ma-27	348	3	.	.	PUNCT
ma-27	349	1	hence	hence	ADV
ma-27	349	2	,	,	PUNCT
ma-27	349	3	`	`	PUNCT
ma-27	349	4	1	1	NUM
ma-27	349	5	∈	∈	PROPN
ma-27	349	6	f	f	X
ma-27	349	7	(	(	PUNCT
ma-27	349	8	t	t	PROPN
ma-27	349	9	)	)	PUNCT
ma-27	349	10	since	since	SCONJ
ma-27	349	11	f	f	PROPN
ma-27	349	12	(	(	PUNCT
ma-27	349	13	t	t	PROPN
ma-27	349	14	)	)	PUNCT
ma-27	349	15	closed	close	VERB
ma-27	349	16	.	.	PUNCT
ma-27	350	1	�	�	PROPN
ma-27	350	2	theorem	theorem	VERB
ma-27	350	3	4.5	4.5	NUM
ma-27	350	4	.	.	PUNCT
ma-27	351	1	let	let	VERB
ma-27	351	2	ω	ω	NUM
ma-27	351	3	,	,	PUNCT
ma-27	351	4	λ	λ	PROPN
ma-27	351	5	,	,	PUNCT
ma-27	351	6	t	t	PROPN
ma-27	351	7	be	be	AUX
ma-27	351	8	same	same	ADJ
ma-27	351	9	as	as	ADP
ma-27	351	10	in	in	ADP
ma-27	351	11	lemma	lemma	PROPN
ma-27	351	12	4.2	4.2	NUM
ma-27	351	13	.	.	PUNCT
ma-27	352	1	if	if	SCONJ
ma-27	352	2	t	t	PROPN
ma-27	352	3	satisfies	satisfy	VERB
ma-27	352	4	condition	condition	NOUN
ma-27	352	5	(	(	PUNCT
ma-27	352	6	i	i	NOUN
ma-27	352	7	)	)	PUNCT
ma-27	352	8	,	,	PUNCT
ma-27	352	9	then	then	ADV
ma-27	352	10	the	the	DET
ma-27	352	11	iterative	iterative	ADJ
ma-27	352	12	algorithm	algorithm	NOUN
ma-27	352	13	{	{	PUNCT
ma-27	352	14	`	`	PUNCT
ma-27	352	15	s	s	X
ma-27	352	16	}	}	PUNCT
ma-27	352	17	defined	define	VERB
ma-27	352	18	by	by	ADP
ma-27	352	19	(	(	PUNCT
ma-27	352	20	1.7	1.7	NUM
ma-27	352	21	)	)	PUNCT
ma-27	352	22	converges	converge	VERB
ma-27	352	23	strongly	strongly	ADV
ma-27	352	24	to	to	ADP
ma-27	352	25	a	a	DET
ma-27	352	26	fixed	fix	VERB
ma-27	352	27	point	point	NOUN
ma-27	352	28	of	of	ADP
ma-27	352	29	t	t	PROPN
ma-27	352	30	.	.	PUNCT
ma-27	353	1	proof	proof	NOUN
ma-27	353	2	.	.	PUNCT
ma-27	354	1	we	we	PRON
ma-27	354	2	have	have	AUX
ma-27	354	3	shown	show	VERB
ma-27	354	4	in	in	ADP
ma-27	354	5	lemma	lemma	PROPN
ma-27	354	6	4.2	4.2	NUM
ma-27	354	7	that	that	PRON
ma-27	354	8	lim	lim	PROPN
ma-27	354	9	s→∞	s→∞	AUX
ma-27	354	10	‖t`s	‖t`s	ADJ
ma-27	354	11	−	−	NOUN
ma-27	355	1	`	`	PUNCT
ma-27	355	2	s‖	s‖	NOUN
ma-27	355	3	=	=	SYM
ma-27	355	4	0	0	NUM
ma-27	355	5	.	.	PUNCT
ma-27	356	1	(	(	PUNCT
ma-27	356	2	4.15	4.15	NUM
ma-27	356	3	)	)	PUNCT
ma-27	356	4	using	use	VERB
ma-27	356	5	condition	condition	NOUN
ma-27	356	6	(	(	PUNCT
ma-27	356	7	i	i	NOUN
ma-27	356	8	)	)	PUNCT
ma-27	356	9	in	in	ADP
ma-27	356	10	definition	definition	NOUN
ma-27	356	11	2.8	2.8	NUM
ma-27	356	12	and	and	CCONJ
ma-27	356	13	(	(	PUNCT
ma-27	356	14	4.15	4.15	NUM
ma-27	356	15	)	)	PUNCT
ma-27	356	16	,	,	PUNCT
ma-27	356	17	we	we	PRON
ma-27	356	18	get	get	VERB
ma-27	356	19	lim	lim	PROPN
ma-27	356	20	s→∞	s→∞	PROPN
ma-27	356	21	f	f	PROPN
ma-27	356	22	(	(	PUNCT
ma-27	356	23	d(`s	d(`	NOUN
ma-27	356	24	,	,	PUNCT
ma-27	356	25	f	f	PROPN
ma-27	356	26	(	(	PUNCT
ma-27	356	27	t	t	PROPN
ma-27	356	28	)	)	PUNCT
ma-27	356	29	)	)	PUNCT
ma-27	356	30	)	)	PUNCT
ma-27	357	1	≤	≤	PROPN
ma-27	357	2	lim	lim	PROPN
ma-27	357	3	s→∞	s→∞	PROPN
ma-27	357	4	‖t`s	‖t`s	ADJ
ma-27	357	5	−	−	NOUN
ma-27	357	6	`	`	PUNCT
ma-27	357	7	s‖	s‖	NOUN
ma-27	357	8	=	=	SYM
ma-27	357	9	0	0	NUM
ma-27	357	10	,	,	PUNCT
ma-27	357	11	(	(	PUNCT
ma-27	357	12	4.16	4.16	NUM
ma-27	357	13	)	)	PUNCT
ma-27	357	14	i.e.	i.e.	X
ma-27	357	15	,	,	PUNCT
ma-27	357	16	lim	lim	PROPN
ma-27	357	17	s→∞	s→∞	PROPN
ma-27	357	18	f	f	PROPN
ma-27	357	19	(	(	PUNCT
ma-27	357	20	d(`s	d(`	NOUN
ma-27	357	21	,	,	PUNCT
ma-27	357	22	f	f	PROPN
ma-27	357	23	(	(	PUNCT
ma-27	357	24	t	t	PROPN
ma-27	357	25	)	)	PUNCT
ma-27	357	26	)	)	PUNCT
ma-27	357	27	)	)	PUNCT
ma-27	358	1	=	=	PUNCT
ma-27	358	2	0	0	X
ma-27	358	3	.	.	PUNCT
ma-27	359	1	since	since	SCONJ
ma-27	359	2	f	f	PROPN
ma-27	359	3	:	:	PUNCT
ma-27	359	4	[	[	X
ma-27	359	5	0,∞	0,∞	NOUN
ma-27	359	6	)	)	PUNCT
ma-27	359	7	→	→	PUNCT
ma-27	359	8	[	[	X
ma-27	359	9	0,∞	0,∞	NUM
ma-27	359	10	)	)	PUNCT
ma-27	359	11	is	be	AUX
ma-27	359	12	a	a	DET
ma-27	359	13	nondecreasing	nondecrease	VERB
ma-27	359	14	function	function	NOUN
ma-27	359	15	satisfying	satisfy	VERB
ma-27	359	16	f	f	PROPN
ma-27	359	17	(	(	PUNCT
ma-27	359	18	0	0	NUM
ma-27	359	19	)	)	PUNCT
ma-27	359	20	=	=	SYM
ma-27	359	21	0	0	NUM
ma-27	359	22	,	,	PUNCT
ma-27	359	23	f	f	X
ma-27	359	24	(	(	PUNCT
ma-27	359	25	r	r	NOUN
ma-27	359	26	)	)	PUNCT
ma-27	359	27	>	>	X
ma-27	359	28	0	0	PUNCT
ma-27	360	1	for	for	ADP
ma-27	360	2	all	all	DET
ma-27	360	3	r	r	NOUN
ma-27	360	4	∈	∈	PROPN
ma-27	360	5	(	(	PUNCT
ma-27	360	6	0,∞	0,∞	NOUN
ma-27	360	7	)	)	PUNCT
ma-27	360	8	,	,	PUNCT
ma-27	360	9	we	we	PRON
ma-27	360	10	have	have	VERB
ma-27	360	11	lim	lim	PROPN
ma-27	360	12	s→∞	s→∞	PROPN
ma-27	360	13	d(`s	d(`	NOUN
ma-27	360	14	,	,	PUNCT
ma-27	360	15	f	f	PROPN
ma-27	360	16	(	(	PUNCT
ma-27	360	17	t	t	PROPN
ma-27	360	18	)	)	PUNCT
ma-27	360	19	)	)	PUNCT
ma-27	361	1	=	=	PUNCT
ma-27	361	2	0	0	X
ma-27	361	3	.	.	PUNCT
ma-27	362	1	(	(	PUNCT
ma-27	362	2	4.17	4.17	NUM
ma-27	362	3	)	)	PUNCT
ma-27	362	4	from	from	ADP
ma-27	362	5	theorem	theorem	ADJ
ma-27	362	6	4.4	4.4	NUM
ma-27	362	7	,	,	PUNCT
ma-27	362	8	then	then	ADV
ma-27	362	9	sequence	sequence	NOUN
ma-27	362	10	{	{	PUNCT
ma-27	362	11	`	`	PUNCT
ma-27	362	12	s	s	PART
ma-27	362	13	}	}	PUNCT
ma-27	362	14	converges	converge	VERB
ma-27	362	15	strongly	strongly	ADV
ma-27	362	16	to	to	ADP
ma-27	362	17	a	a	DET
ma-27	362	18	point	point	NOUN
ma-27	362	19	of	of	ADP
ma-27	362	20	f	f	PROPN
ma-27	362	21	(	(	PUNCT
ma-27	362	22	t	t	PROPN
ma-27	362	23	)	)	PUNCT
ma-27	362	24	.	.	PUNCT
ma-27	363	1	�	�	PROPN
ma-27	363	2	eur	eur	PROPN
ma-27	363	3	.	.	PUNCT
ma-27	364	1	j.	j.	PROPN
ma-27	364	2	math	math	PROPN
ma-27	364	3	.	.	PUNCT
ma-27	365	1	anal	anal	ADJ
ma-27	365	2	.	.	PUNCT
ma-27	366	1	1	1	NUM
ma-27	366	2	(	(	PUNCT
ma-27	366	3	2021	2021	NUM
ma-27	366	4	)	)	PUNCT
ma-27	366	5	1215	1215	NUM
ma-27	366	6	.	.	PUNCT
ma-27	367	1	numerical	numerical	ADJ
ma-27	367	2	result	result	NOUN
ma-27	367	3	in	in	ADP
ma-27	367	4	this	this	DET
ma-27	367	5	section	section	NOUN
ma-27	367	6	,	,	PUNCT
ma-27	367	7	we	we	PRON
ma-27	367	8	provide	provide	VERB
ma-27	367	9	an	an	DET
ma-27	367	10	example	example	NOUN
ma-27	367	11	of	of	ADP
ma-27	367	12	generalized	generalized	ADJ
ma-27	367	13	α	α	PROPN
ma-27	367	14	-	-	PUNCT
ma-27	367	15	nonexpansive	nonexpansive	ADJ
ma-27	367	16	mapping	mapping	NOUN
ma-27	367	17	which	which	PRON
ma-27	367	18	is	be	AUX
ma-27	367	19	notsuzuki	notsuzuki	NOUN
ma-27	367	20	generalized	generalize	VERB
ma-27	367	21	nonexpansive	nonexpansive	ADJ
ma-27	367	22	mapping	mapping	NOUN
ma-27	367	23	.	.	PUNCT
ma-27	368	1	with	with	ADP
ma-27	368	2	the	the	DET
ma-27	368	3	aid	aid	NOUN
ma-27	368	4	of	of	ADP
ma-27	368	5	the	the	DET
ma-27	368	6	provided	provide	VERB
ma-27	368	7	example	example	NOUN
ma-27	368	8	,	,	PUNCT
ma-27	368	9	we	we	PRON
ma-27	368	10	will	will	AUX
ma-27	368	11	provethat	provethat	VERB
ma-27	368	12	our	our	PRON
ma-27	368	13	new	new	ADJ
ma-27	368	14	iterative	iterative	NOUN
ma-27	368	15	algorithm	algorithm	NOUN
ma-27	368	16	(	(	PUNCT
ma-27	368	17	1.7	1.7	NUM
ma-27	368	18	)	)	PUNCT
ma-27	368	19	outperforms	outperform	VERB
ma-27	368	20	a	a	DET
ma-27	368	21	number	number	NOUN
ma-27	368	22	of	of	ADP
ma-27	368	23	iterative	iterative	ADJ
ma-27	368	24	algorithms	algorithm	NOUN
ma-27	368	25	in	in	ADP
ma-27	368	26	the	the	DET
ma-27	368	27	existingliterature	existingliterature	NOUN
ma-27	368	28	in	in	ADP
ma-27	368	29	terms	term	NOUN
ma-27	368	30	of	of	ADP
ma-27	368	31	convergence	convergence	NOUN
ma-27	368	32	.	.	PUNCT
ma-27	368	33	example	example	NOUN
ma-27	369	1	5.1	5.1	NUM
ma-27	369	2	.	.	PUNCT
ma-27	370	1	let	let	VERB
ma-27	370	2	λ	λ	INTJ
ma-27	370	3	=	=	PUNCT
ma-27	371	1	[	[	X
ma-27	371	2	0,∞	0,∞	X
ma-27	371	3	)	)	PUNCT
ma-27	371	4	be	be	AUX
ma-27	371	5	endowed	endow	VERB
ma-27	371	6	with	with	ADP
ma-27	371	7	the	the	DET
ma-27	371	8	usual	usual	ADJ
ma-27	371	9	norm	norm	NOUN
ma-27	371	10	|	|	ADV
ma-27	371	11	·	·	PUNCT
ma-27	372	1	|	|	ADV
ma-27	372	2	and	and	CCONJ
ma-27	372	3	let	let	VERB
ma-27	372	4	t	t	NOUN
ma-27	372	5	:	:	PUNCT
ma-27	373	1	λ	λ	X
ma-27	373	2	→	→	SYM
ma-27	373	3	λ	λ	PROPN
ma-27	373	4	be	be	VERB
ma-27	373	5	definedas	defineda	NOUN
ma-27	373	6	:	:	PUNCT
ma-27	373	7	t	t	X
ma-27	373	8	`	`	PUNCT
ma-27	373	9	=	=	PRON
ma-27	373	10	{	{	PUNCT
ma-27	373	11	0	0	NUM
ma-27	373	12	,	,	PUNCT
ma-27	373	13	if	if	SCONJ
ma-27	373	14	`	`	PUNCT
ma-27	373	15	∈	∈	PROPN
ma-27	374	1	[	[	X
ma-27	374	2	0	0	NUM
ma-27	374	3	,	,	PUNCT
ma-27	374	4	15	15	NUM
ma-27	374	5	)	)	PUNCT
ma-27	374	6	,	,	PUNCT
ma-27	374	7	3	3	NUM
ma-27	374	8	`	`	SYM
ma-27	374	9	4	4	NUM
ma-27	374	10	,	,	PUNCT
ma-27	374	11	if	if	SCONJ
ma-27	374	12	`	`	PUNCT
ma-27	374	13	∈	∈	PROPN
ma-27	374	14	[	[	X
ma-27	374	15	15	15	NUM
ma-27	374	16	,	,	PUNCT
ma-27	374	17	∞	∞	PROPN
ma-27	374	18	)	)	PUNCT
ma-27	374	19	.	.	PUNCT
ma-27	375	1	(	(	PUNCT
ma-27	375	2	5.1	5.1	NUM
ma-27	375	3	)	)	PUNCT
ma-27	375	4	firstly	firstly	ADV
ma-27	375	5	,	,	PUNCT
ma-27	375	6	we	we	PRON
ma-27	375	7	show	show	VERB
ma-27	375	8	that	that	SCONJ
ma-27	375	9	t	t	PROPN
ma-27	375	10	does	do	AUX
ma-27	375	11	not	not	PART
ma-27	375	12	satisfy	satisfy	VERB
ma-27	375	13	condition	condition	NOUN
ma-27	375	14	(	(	PUNCT
ma-27	375	15	c	c	NOUN
ma-27	375	16	)	)	PUNCT
ma-27	375	17	.	.	PUNCT
ma-27	376	1	to	to	PART
ma-27	376	2	see	see	VERB
ma-27	376	3	this	this	PRON
ma-27	376	4	,	,	PUNCT
ma-27	376	5	let	let	VERB
ma-27	376	6	`	`	PUNCT
ma-27	376	7	=	=	SYM
ma-27	376	8	1	1	NUM
ma-27	376	9	15	15	NUM
ma-27	376	10	and	and	CCONJ
ma-27	376	11	ζ	ζ	NOUN
ma-27	376	12	=	=	SYM
ma-27	376	13	1	1	NUM
ma-27	376	14	5	5	NUM
ma-27	376	15	,	,	PUNCT
ma-27	376	16	then	then	ADV
ma-27	376	17	1	1	NUM
ma-27	376	18	2	2	NUM
ma-27	376	19	|`−	|`−	NUM
ma-27	376	20	t`|	t`|	NUM
ma-27	376	21	=	=	SYM
ma-27	376	22	1	1	NUM
ma-27	376	23	30	30	NUM
ma-27	376	24	<	<	SYM
ma-27	376	25	2	2	NUM
ma-27	376	26	15	15	NUM
ma-27	376	27	=	=	NOUN
ma-27	376	28	|`−	|`−	NUM
ma-27	376	29	ζ|	ζ|	PROPN
ma-27	376	30	.	.	PUNCT
ma-27	377	1	but	but	CCONJ
ma-27	377	2	|t`−	|t`−	ADJ
ma-27	377	3	tζ|	tζ|	NOUN
ma-27	377	4	=	=	NOUN
ma-27	377	5	3ζ	3ζ	NOUN
ma-27	377	6	4	4	NUM
ma-27	377	7	=	=	SYM
ma-27	377	8	3	3	NUM
ma-27	377	9	20	20	NUM
ma-27	377	10	>	>	SYM
ma-27	377	11	2	2	NUM
ma-27	377	12	15	15	NUM
ma-27	377	13	=	=	NOUN
ma-27	377	14	|`−	|`−	NUM
ma-27	377	15	ζ|	ζ|	PROPN
ma-27	377	16	.	.	PUNCT
ma-27	378	1	hence	hence	ADV
ma-27	378	2	,	,	PUNCT
ma-27	378	3	t	t	PROPN
ma-27	378	4	does	do	AUX
ma-27	378	5	not	not	PART
ma-27	378	6	satisfy	satisfy	VERB
ma-27	378	7	condition	condition	NOUN
ma-27	378	8	(	(	PUNCT
ma-27	378	9	c	c	NOUN
ma-27	378	10	)	)	PUNCT
ma-27	378	11	,	,	PUNCT
ma-27	378	12	which	which	PRON
ma-27	378	13	implies	imply	VERB
ma-27	378	14	that	that	SCONJ
ma-27	378	15	t	t	PROPN
ma-27	378	16	is	be	AUX
ma-27	378	17	not	not	PART
ma-27	378	18	a	a	DET
ma-27	378	19	suzuki	suzuki	NOUN
ma-27	378	20	generalized	generalize	VERB
ma-27	378	21	nonex	nonex	ADV
ma-27	378	22	-	-	PUNCT
ma-27	378	23	pansive	pansive	ADJ
ma-27	378	24	mapping.now	mapping.now	NOUN
ma-27	378	25	we	we	PRON
ma-27	378	26	show	show	VERB
ma-27	378	27	that	that	SCONJ
ma-27	378	28	t	t	PROPN
ma-27	378	29	is	be	AUX
ma-27	378	30	a	a	DET
ma-27	378	31	generalized	generalized	ADJ
ma-27	378	32	α	α	PRON
ma-27	378	33	-	-	PUNCT
ma-27	378	34	nonexpansive	nonexpansive	ADJ
ma-27	378	35	mapping	mapping	NOUN
ma-27	378	36	with	with	ADP
ma-27	378	37	α	α	PROPN
ma-27	378	38	=	=	SYM
ma-27	378	39	1	1	NUM
ma-27	378	40	3	3	NUM
ma-27	378	41	(	(	PUNCT
ma-27	378	42	i.e.	i.e.	X
ma-27	378	43	,	,	PUNCT
ma-27	378	44	generalized	generalize	VERB
ma-27	378	45	1	1	NUM
ma-27	378	46	3	3	NUM
ma-27	378	47	-	-	NUM
ma-27	378	48	nonexpansive	nonexpansive	ADJ
ma-27	378	49	)	)	PUNCT
ma-27	378	50	.	.	PUNCT
ma-27	379	1	we	we	PRON
ma-27	379	2	consider	consider	VERB
ma-27	379	3	the	the	DET
ma-27	379	4	following	follow	VERB
ma-27	379	5	cases	case	NOUN
ma-27	379	6	:	:	PUNCT
ma-27	379	7	case	case	NOUN
ma-27	379	8	(	(	PUNCT
ma-27	379	9	a	a	X
ma-27	379	10	):	):	PUNCT
ma-27	379	11	when	when	SCONJ
ma-27	379	12	`	`	PUNCT
ma-27	379	13	,	,	PUNCT
ma-27	379	14	ζ	ζ	PROPN
ma-27	379	15	∈	∈	NOUN
ma-27	379	16	[	[	X
ma-27	379	17	0	0	NUM
ma-27	379	18	,	,	PUNCT
ma-27	379	19	15	15	NUM
ma-27	379	20	)	)	PUNCT
ma-27	379	21	,	,	PUNCT
ma-27	379	22	we	we	PRON
ma-27	379	23	have	have	VERB
ma-27	379	24	1	1	NUM
ma-27	379	25	3	3	NUM
ma-27	379	26	|t`−	|t`−	ADJ
ma-27	379	27	ζ|+	ζ|+	NOUN
ma-27	379	28	1	1	NUM
ma-27	379	29	3	3	NUM
ma-27	379	30	|`−	|`−	NUM
ma-27	379	31	tζ|+	tζ|+	VERB
ma-27	379	32	1	1	NUM
ma-27	379	33	3	3	NUM
ma-27	379	34	|`−	|`−	NUM
ma-27	379	35	ζ|	ζ|	PROPN
ma-27	379	36	≥	≥	X
ma-27	379	37	0	0	NUM
ma-27	379	38	=	=	NUM
ma-27	379	39	|t`−	|t`−	ADJ
ma-27	379	40	tζ|	tζ|	PROPN
ma-27	379	41	.	.	PUNCT
ma-27	380	1	case	case	NOUN
ma-27	380	2	(	(	PUNCT
ma-27	380	3	b	b	NOUN
ma-27	380	4	):	):	PUNCT
ma-27	380	5	when	when	SCONJ
ma-27	380	6	`	`	PUNCT
ma-27	380	7	,	,	PUNCT
ma-27	380	8	ζ	ζ	PROPN
ma-27	380	9	∈	∈	NOUN
ma-27	380	10	[	[	X
ma-27	380	11	15	15	NUM
ma-27	380	12	,	,	PUNCT
ma-27	380	13	∞	∞	PROPN
ma-27	380	14	)	)	PUNCT
ma-27	380	15	,	,	PUNCT
ma-27	380	16	we	we	PRON
ma-27	380	17	obtain	obtain	VERB
ma-27	380	18	1	1	NUM
ma-27	380	19	3	3	NUM
ma-27	380	20	|t`−	|t`−	ADJ
ma-27	380	21	ζ|+	ζ|+	NOUN
ma-27	380	22	1	1	NUM
ma-27	380	23	3	3	NUM
ma-27	380	24	|`−	|`−	NUM
ma-27	380	25	tζ|+	tζ|+	VERB
ma-27	380	26	1	1	NUM
ma-27	380	27	3	3	NUM
ma-27	380	28	|`−	|`−	NUM
ma-27	380	29	ζ|	ζ|	PROPN
ma-27	380	30	=	=	SYM
ma-27	380	31	1	1	NUM
ma-27	380	32	3	3	NUM
ma-27	380	33	∣∣∣∣3`4	∣∣∣∣3`4	ADP
ma-27	380	34	−	−	PROPN
ma-27	380	35	ζ	ζ	PROPN
ma-27	380	36	∣∣∣∣+	∣∣∣∣+	PROPN
ma-27	380	37	1	1	NUM
ma-27	380	38	3	3	NUM
ma-27	380	39	∣∣∣∣`−	∣∣∣∣`−	NOUN
ma-27	380	40	3ζ	3ζ	NOUN
ma-27	380	41	4	4	NUM
ma-27	380	42	∣∣∣∣+	∣∣∣∣+	NOUN
ma-27	380	43	1	1	NUM
ma-27	380	44	3	3	NUM
ma-27	380	45	|`−	|`−	NUM
ma-27	380	46	ζ|	ζ|	PROPN
ma-27	380	47	≥	≥	NOUN
ma-27	380	48	1	1	NUM
ma-27	380	49	3	3	NUM
ma-27	380	50	∣∣∣∣(3	∣∣∣∣(3	ADV
ma-27	380	51	`	`	NUM
ma-27	380	52	4	4	NUM
ma-27	380	53	−	−	NOUN
ma-27	380	54	ζ	ζ	NOUN
ma-27	380	55	)	)	PUNCT
ma-27	381	1	+	+	CCONJ
ma-27	381	2	(	(	PUNCT
ma-27	381	3	`	`	PUNCT
ma-27	381	4	−	−	PROPN
ma-27	381	5	3ζ	3ζ	NOUN
ma-27	381	6	4	4	NUM
ma-27	381	7	)	)	PUNCT
ma-27	381	8	∣∣∣∣+	∣∣∣∣+	PROPN
ma-27	381	9	1	1	NUM
ma-27	381	10	3	3	NUM
ma-27	381	11	|`−	|`−	NUM
ma-27	381	12	ζ|	ζ|	PROPN
ma-27	381	13	=	=	SYM
ma-27	381	14	7	7	NUM
ma-27	381	15	12	12	NUM
ma-27	381	16	|`−	|`−	NUM
ma-27	381	17	ζ|+	ζ|+	NOUN
ma-27	381	18	1	1	NUM
ma-27	381	19	3	3	NUM
ma-27	381	20	|`−	|`−	NUM
ma-27	381	21	ζ|	ζ|	PROPN
ma-27	381	22	=	=	SYM
ma-27	381	23	11	11	NUM
ma-27	381	24	12	12	NUM
ma-27	381	25	|`−	|`−	NUM
ma-27	381	26	ζ|	ζ|	PROPN
ma-27	381	27	≥	≥	NOUN
ma-27	381	28	3	3	NUM
ma-27	381	29	4	4	NUM
ma-27	381	30	|`−	|`−	NUM
ma-27	381	31	ζ|	ζ|	PROPN
ma-27	381	32	=	=	PUNCT
ma-27	381	33	|t`−	|t`−	ADJ
ma-27	381	34	tζ|	tζ|	PROPN
ma-27	381	35	.	.	PUNCT
ma-27	382	1	eur	eur	PROPN
ma-27	382	2	.	.	PUNCT
ma-27	383	1	j.	j.	PROPN
ma-27	383	2	math	math	PROPN
ma-27	383	3	.	.	PUNCT
ma-27	384	1	anal	anal	ADJ
ma-27	384	2	.	.	PUNCT
ma-27	385	1	1	1	NUM
ma-27	385	2	(	(	PUNCT
ma-27	385	3	2021	2021	NUM
ma-27	385	4	)	)	PUNCT
ma-27	385	5	122	122	NUM
ma-27	385	6	case	case	NOUN
ma-27	385	7	(	(	PUNCT
ma-27	385	8	c	c	NOUN
ma-27	385	9	):	):	PUNCT
ma-27	385	10	when	when	SCONJ
ma-27	385	11	`	`	PUNCT
ma-27	385	12	∈	∈	PROPN
ma-27	385	13	[	[	X
ma-27	385	14	15	15	NUM
ma-27	385	15	,	,	PUNCT
ma-27	385	16	∞	∞	PROPN
ma-27	385	17	)	)	PUNCT
ma-27	385	18	and	and	CCONJ
ma-27	385	19	ζ	ζ	NOUN
ma-27	385	20	∈	∈	PROPN
ma-27	386	1	[	[	X
ma-27	386	2	0	0	NUM
ma-27	386	3	,	,	PUNCT
ma-27	386	4	15	15	NUM
ma-27	386	5	)	)	PUNCT
ma-27	386	6	,	,	PUNCT
ma-27	386	7	we	we	PRON
ma-27	386	8	get	get	VERB
ma-27	386	9	1	1	NUM
ma-27	386	10	3	3	NUM
ma-27	386	11	|t`−	|t`−	ADJ
ma-27	386	12	ζ|+	ζ|+	NOUN
ma-27	386	13	1	1	NUM
ma-27	386	14	3	3	NUM
ma-27	386	15	|`−	|`−	NUM
ma-27	386	16	tζ|+	tζ|+	VERB
ma-27	386	17	1	1	NUM
ma-27	386	18	3	3	NUM
ma-27	387	1	|`−	|`−	NUM
ma-27	387	2	ζ|	ζ|	PROPN
ma-27	387	3	=	=	SYM
ma-27	387	4	1	1	NUM
ma-27	387	5	3	3	NUM
ma-27	387	6	∣∣∣∣3`4	∣∣∣∣3`4	ADP
ma-27	387	7	−	−	PROPN
ma-27	387	8	ζ	ζ	X
ma-27	387	9	∣∣∣∣+	∣∣∣∣+	PROPN
ma-27	387	10	1	1	NUM
ma-27	387	11	3	3	NUM
ma-27	387	12	|`|+	|`|+	ADJ
ma-27	387	13	1	1	NUM
ma-27	387	14	3	3	NUM
ma-27	387	15	|`−	|`−	NUM
ma-27	387	16	ζ|	ζ|	PROPN
ma-27	387	17	≥	≥	NOUN
ma-27	387	18	1	1	NUM
ma-27	387	19	3	3	NUM
ma-27	387	20	∣∣∣∣3`4	∣∣∣∣3`4	ADP
ma-27	387	21	−	−	PROPN
ma-27	387	22	ζ	ζ	X
ma-27	387	23	∣∣∣∣+	∣∣∣∣+	PROPN
ma-27	387	24	1	1	NUM
ma-27	387	25	3	3	NUM
ma-27	387	26	|`−	|`−	NUM
ma-27	387	27	ζ|	ζ|	PROPN
ma-27	387	28	≥	≥	NOUN
ma-27	387	29	7	7	NUM
ma-27	387	30	`	`	SYM
ma-27	387	31	12	12	NUM
ma-27	387	32	=	=	NOUN
ma-27	387	33	|t`−	|t`−	ADJ
ma-27	387	34	tζ|	tζ|	NOUN
ma-27	387	35	.	.	PUNCT
ma-27	388	1	hence	hence	ADV
ma-27	388	2	,	,	PUNCT
ma-27	388	3	t	t	PROPN
ma-27	388	4	is	be	AUX
ma-27	388	5	generalized	generalize	VERB
ma-27	388	6	α	α	DET
ma-27	388	7	-	-	PUNCT
ma-27	388	8	nonexpansive	nonexpansive	ADJ
ma-27	388	9	mapping	mapping	NOUN
ma-27	388	10	with	with	ADP
ma-27	388	11	α	α	PROPN
ma-27	388	12	=	=	SYM
ma-27	388	13	1	1	NUM
ma-27	388	14	3	3	NUM
ma-27	388	15	(	(	PUNCT
ma-27	388	16	i.e.	i.e.	X
ma-27	388	17	,	,	PUNCT
ma-27	388	18	generalized	generalize	VERB
ma-27	388	19	1	1	NUM
ma-27	388	20	3	3	NUM
ma-27	388	21	-	-	NUM
ma-27	388	22	nonexpansive)with	nonexpansive)with	NOUN
ma-27	388	23	f	f	X
ma-27	388	24	(	(	PUNCT
ma-27	388	25	t	t	PROPN
ma-27	388	26	)	)	PUNCT
ma-27	388	27	=	=	PUNCT
ma-27	389	1	{	{	PUNCT
ma-27	389	2	0}.with	0}.with	ADP
ma-27	389	3	the	the	DET
ma-27	389	4	aid	aid	NOUN
ma-27	389	5	of	of	ADP
ma-27	389	6	matlab	matlab	PROPN
ma-27	389	7	(	(	PUNCT
ma-27	389	8	r2015a	r2015a	PROPN
ma-27	389	9	)	)	PUNCT
ma-27	389	10	,	,	PUNCT
ma-27	389	11	we	we	PRON
ma-27	389	12	obtain	obtain	VERB
ma-27	389	13	the	the	DET
ma-27	389	14	following	follow	VERB
ma-27	389	15	comparison	comparison	NOUN
ma-27	389	16	table	table	NOUN
ma-27	389	17	2	2	NUM
ma-27	389	18	and	and	CCONJ
ma-27	389	19	figure	figure	VERB
ma-27	389	20	2	2	NUM
ma-27	389	21	forvarious	forvarious	ADJ
ma-27	389	22	iterative	iterative	NOUN
ma-27	389	23	algorithms	algorithm	NOUN
ma-27	389	24	with	with	ADP
ma-27	389	25	control	control	NOUN
ma-27	389	26	sequences	sequence	NOUN
ma-27	389	27	δs	δs	NOUN
ma-27	389	28	=	=	SYM
ma-27	389	29	0.65	0.65	NUM
ma-27	389	30	,	,	PUNCT
ma-27	389	31	βs	βs	X
ma-27	389	32	=	=	SYM
ma-27	389	33	0.8	0.8	NUM
ma-27	389	34	and	and	CCONJ
ma-27	389	35	initial	initial	ADJ
ma-27	389	36	guess	guess	NOUN
ma-27	389	37	`	`	PUNCT
ma-27	389	38	1	1	NUM
ma-27	389	39	=	=	SYM
ma-27	389	40	50	50	NUM
ma-27	389	41	.	.	PUNCT
ma-27	389	42	table	table	NOUN
ma-27	389	43	2	2	NUM
ma-27	389	44	.	.	PUNCT
ma-27	389	45	comparison	comparison	NOUN
ma-27	389	46	of	of	ADP
ma-27	389	47	convergence	convergence	NOUN
ma-27	389	48	behaviour	behaviour	NOUN
ma-27	389	49	of	of	ADP
ma-27	389	50	our	our	PRON
ma-27	389	51	new	new	ADJ
ma-27	389	52	iterative	iterative	NOUN
ma-27	389	53	algorithm	algorithm	NOUN
ma-27	389	54	withs	with	NOUN
ma-27	389	55	,	,	PUNCT
ma-27	389	56	picard	picard	NOUN
ma-27	389	57	-	-	PUNCT
ma-27	389	58	s	s	PROPN
ma-27	389	59	,	,	PUNCT
ma-27	389	60	thakur	thakur	NOUN
ma-27	389	61	and	and	CCONJ
ma-27	389	62	m	m	PROPN
ma-27	389	63	iterative	iterative	ADJ
ma-27	389	64	algorithms.step	algorithms.step	PROPN
ma-27	389	65	s	s	NOUN
ma-27	389	66	picard	picard	NOUN
ma-27	389	67	-	-	PUNCT
ma-27	389	68	s	s	PART
ma-27	390	1	thakur	thakur	PROPN
ma-27	390	2	m	m	VERB
ma-27	390	3	new1	new1	PROPN
ma-27	390	4	50.00000000	50.00000000	NUM
ma-27	390	5	50.00000000	50.00000000	NUM
ma-27	390	6	50.00000000	50.00000000	NUM
ma-27	390	7	50.00000000	50.00000000	NUM
ma-27	390	8	50.000000002	50.000000002	NUM
ma-27	390	9	32.62500000	32.62500000	NUM
ma-27	390	10	24.46875000	24.46875000	NUM
ma-27	390	11	24.46875000	24.46875000	NUM
ma-27	390	12	23.55468750	23.55468750	NUM
ma-27	390	13	18.351562503	18.351562503	NUM
ma-27	390	14	21.28781250	21.28781250	NUM
ma-27	390	15	11.97439453	11.97439453	NUM
ma-27	390	16	11.97439453	11.97439453	NUM
ma-27	390	17	11.09646606	11.09646606	NUM
ma-27	390	18	6.735596924	6.735596924	NUM
ma-27	390	19	13.89029766	13.89029766	NUM
ma-27	390	20	5.85996932	5.85996932	NUM
ma-27	390	21	5.85996932	5.85996932	NUM
ma-27	390	22	5.22747581	5.22747581	NUM
ma-27	390	23	2.472174565	2.472174565	NUM
ma-27	390	24	9.06341922	9.06341922	NUM
ma-27	390	25	2.86772249	2.86772249	NUM
ma-27	390	26	2.86772249	2.86772249	NUM
ma-27	390	27	2.46263118	2.46263118	NUM
ma-27	390	28	0.000000006	0.000000006	NUM
ma-27	390	29	5.91388104	5.91388104	NUM
ma-27	390	30	1.40339169	1.40339169	NUM
ma-27	390	31	1.40339169	1.40339169	NUM
ma-27	390	32	1.16013016	1.16013016	NUM
ma-27	390	33	0.000000007	0.000000007	NUM
ma-27	390	34	3.85880738	3.85880738	NUM
ma-27	390	35	0.00000000	0.00000000	NUM
ma-27	390	36	0.00000000	0.00000000	NUM
ma-27	390	37	0.00000000	0.00000000	NUM
ma-27	390	38	0.000000008	0.000000008	NUM
ma-27	390	39	2.51787182	2.51787182	NUM
ma-27	390	40	0.00000000	0.00000000	NUM
ma-27	390	41	0.00000000	0.00000000	NUM
ma-27	390	42	0.00000000	0.00000000	NUM
ma-27	390	43	0.000000009	0.000000009	NUM
ma-27	390	44	1.64291136	1.64291136	NUM
ma-27	390	45	0.00000000	0.00000000	NUM
ma-27	390	46	0.00000000	0.00000000	NUM
ma-27	390	47	0.00000000	0.00000000	NUM
ma-27	390	48	0.00000000	0.00000000	NUM
ma-27	390	49	iteration	iteration	NOUN
ma-27	390	50	number	number	NOUN
ma-27	390	51	s	s	PART
ma-27	390	52	1	1	NUM
ma-27	390	53	2	2	NUM
ma-27	390	54	3	3	NUM
ma-27	390	55	4	4	NUM
ma-27	390	56	5	5	NUM
ma-27	390	57	6	6	NUM
ma-27	390	58	7	7	NUM
ma-27	390	59	8	8	NUM
ma-27	390	60	9	9	NUM
ma-27	390	61	s	s	NOUN
ma-27	390	62	eq	eq	NOUN
ma-27	390	63	ue	ue	PROPN
ma-27	390	64	nc	nc	PROPN
ma-27	390	65	e	e	PROPN
ma-27	390	66	va	va	PROPN
ma-27	390	67	lu	lu	PROPN
ma-27	390	68	es	es	NOUN
ma-27	390	69	0	0	NUM
ma-27	390	70	5	5	NUM
ma-27	390	71	10	10	NUM
ma-27	390	72	15	15	NUM
ma-27	390	73	20	20	NUM
ma-27	390	74	25	25	NUM
ma-27	390	75	30	30	NUM
ma-27	390	76	35	35	NUM
ma-27	390	77	40	40	NUM
ma-27	390	78	45	45	NUM
ma-27	390	79	50	50	NUM
ma-27	390	80	new	new	ADJ
ma-27	390	81	iteration	iteration	NOUN
ma-27	390	82	m	m	PROPN
ma-27	390	83	iteration	iteration	NOUN
ma-27	390	84	thakur	thakur	PROPN
ma-27	390	85	iteration	iteration	NOUN
ma-27	390	86	picard	picard	PROPN
ma-27	390	87	-	-	PUNCT
ma-27	390	88	s	s	PART
ma-27	390	89	iteration	iteration	NOUN
ma-27	390	90	s	s	PART
ma-27	390	91	iteration	iteration	NOUN
ma-27	390	92	figure	figure	NOUN
ma-27	390	93	2	2	NUM
ma-27	390	94	.	.	PUNCT
ma-27	391	1	graph	graph	NOUN
ma-27	391	2	corresponding	correspond	VERB
ma-27	391	3	to	to	ADP
ma-27	391	4	table	table	NOUN
ma-27	391	5	2	2	NUM
ma-27	391	6	.	.	PUNCT
ma-27	391	7	from	from	ADP
ma-27	391	8	the	the	DET
ma-27	391	9	above	above	ADJ
ma-27	391	10	table	table	NOUN
ma-27	391	11	2	2	NUM
ma-27	391	12	and	and	CCONJ
ma-27	391	13	figure	figure	NOUN
ma-27	391	14	2	2	NUM
ma-27	391	15	,	,	PUNCT
ma-27	391	16	it	it	PRON
ma-27	391	17	is	be	AUX
ma-27	391	18	clear	clear	ADJ
ma-27	391	19	that	that	SCONJ
ma-27	391	20	our	our	PRON
ma-27	391	21	new	new	ADJ
ma-27	391	22	iterative	iterative	NOUN
ma-27	391	23	algorithm	algorithm	NOUN
ma-27	391	24	(	(	PUNCT
ma-27	391	25	1.7	1.7	NUM
ma-27	391	26	)	)	PUNCT
ma-27	391	27	outperformsa	outperformsa	ADJ
ma-27	391	28	number	number	NOUN
ma-27	391	29	of	of	ADP
ma-27	391	30	existing	exist	VERB
ma-27	391	31	iterative	iterative	NOUN
ma-27	391	32	algorithms	algorithm	NOUN
ma-27	391	33	.	.	PUNCT
ma-27	392	1	eur	eur	PROPN
ma-27	392	2	.	.	PUNCT
ma-27	393	1	j.	j.	PROPN
ma-27	393	2	math	math	PROPN
ma-27	393	3	.	.	PUNCT
ma-27	394	1	anal	anal	ADJ
ma-27	394	2	.	.	PUNCT
ma-27	395	1	1	1	NUM
ma-27	395	2	(	(	PUNCT
ma-27	395	3	2021	2021	NUM
ma-27	395	4	)	)	PUNCT
ma-27	395	5	1236	1236	NUM
ma-27	395	6	.	.	PUNCT
ma-27	396	1	stability	stability	NOUN
ma-27	396	2	result	result	VERB
ma-27	396	3	our	our	PRON
ma-27	396	4	aim	aim	NOUN
ma-27	396	5	in	in	ADP
ma-27	396	6	this	this	DET
ma-27	396	7	section	section	NOUN
ma-27	396	8	is	be	AUX
ma-27	396	9	to	to	PART
ma-27	396	10	show	show	VERB
ma-27	396	11	that	that	SCONJ
ma-27	396	12	our	our	PRON
ma-27	396	13	new	new	ADJ
ma-27	396	14	iterative	iterative	NOUN
ma-27	396	15	algorithm	algorithm	NOUN
ma-27	396	16	(	(	PUNCT
ma-27	396	17	1.7	1.7	NUM
ma-27	396	18	)	)	PUNCT
ma-27	396	19	is	be	AUX
ma-27	396	20	t	t	PROPN
ma-27	396	21	–	–	PUNCT
ma-27	396	22	stable	stable	ADJ
ma-27	396	23	.	.	PUNCT
ma-27	397	1	theorem	theorem	NOUN
ma-27	397	2	6.1	6.1	NUM
ma-27	397	3	.	.	PUNCT
ma-27	398	1	let	let	VERB
ma-27	398	2	ω	ω	NUM
ma-27	398	3	be	be	AUX
ma-27	398	4	a	a	DET
ma-27	398	5	banach	banach	NOUN
ma-27	398	6	space	space	NOUN
ma-27	398	7	and	and	CCONJ
ma-27	398	8	λ	λ	PROPN
ma-27	398	9	be	be	AUX
ma-27	398	10	a	a	DET
ma-27	398	11	nonempty	nonempty	ADV
ma-27	398	12	closed	close	VERB
ma-27	398	13	convex	convex	NOUN
ma-27	398	14	subset	subset	NOUN
ma-27	398	15	of	of	ADP
ma-27	398	16	ω	ω	PROPN
ma-27	398	17	.	.	PUNCT
ma-27	399	1	let	let	VERB
ma-27	399	2	t	t	NOUN
ma-27	399	3	be	be	AUX
ma-27	399	4	a	a	DET
ma-27	399	5	mapping	mapping	NOUN
ma-27	399	6	satisfy	satisfy	NOUN
ma-27	399	7	(	(	PUNCT
ma-27	399	8	1.2	1.2	NUM
ma-27	399	9	)	)	PUNCT
ma-27	399	10	.	.	PUNCT
ma-27	400	1	let	let	VERB
ma-27	400	2	{	{	PUNCT
ma-27	400	3	`	`	PUNCT
ma-27	400	4	s	s	AUX
ma-27	400	5	}	}	PUNCT
ma-27	400	6	be	be	AUX
ma-27	400	7	the	the	DET
ma-27	400	8	iterative	iterative	ADJ
ma-27	400	9	algorithm	algorithm	NOUN
ma-27	400	10	defined	define	VERB
ma-27	400	11	by	by	ADP
ma-27	400	12	(	(	PUNCT
ma-27	400	13	1.7	1.7	NUM
ma-27	400	14	)	)	PUNCT
ma-27	400	15	with	with	ADP
ma-27	400	16	sequences	sequence	NOUN
ma-27	400	17	δs	δs	NOUN
ma-27	400	18	and	and	CCONJ
ma-27	400	19	βs	βs	ADP
ma-27	400	20	∈	∈	PROPN
ma-27	401	1	[	[	X
ma-27	401	2	0	0	NUM
ma-27	401	3	,	,	PUNCT
ma-27	401	4	1	1	NUM
ma-27	401	5	]	]	PUNCT
ma-27	402	1	such	such	ADJ
ma-27	402	2	that	that	SCONJ
ma-27	402	3	∑∞	∑∞	NOUN
ma-27	402	4	s=0	s=0	X
ma-27	402	5	δsβs	δsβs	PRON
ma-27	402	6	=	=	NUM
ma-27	402	7	∞.	∞.	PROPN
ma-27	402	8	then	then	ADV
ma-27	402	9	the	the	DET
ma-27	402	10	iterative	iterative	ADJ
ma-27	402	11	algorithm	algorithm	NOUN
ma-27	402	12	(	(	PUNCT
ma-27	402	13	1.7	1.7	NUM
ma-27	402	14	)	)	PUNCT
ma-27	402	15	is	be	AUX
ma-27	402	16	t	t	PROPN
ma-27	402	17	–	–	PUNCT
ma-27	402	18	stable	stable	ADJ
ma-27	402	19	.	.	PUNCT
ma-27	403	1	proof	proof	NOUN
ma-27	403	2	.	.	PUNCT
ma-27	404	1	let	let	VERB
ma-27	404	2	{	{	PUNCT
ma-27	404	3	ys	ys	VERB
ma-27	404	4	}	}	PUNCT
ma-27	404	5	⊂	⊂	PROPN
ma-27	404	6	ω	ω	NOUN
ma-27	404	7	be	be	AUX
ma-27	404	8	an	an	DET
ma-27	404	9	arbitrary	arbitrary	ADJ
ma-27	404	10	sequence	sequence	NOUN
ma-27	404	11	in	in	ADP
ma-27	404	12	λ	λ	PROPN
ma-27	404	13	and	and	CCONJ
ma-27	404	14	suppose	suppose	VERB
ma-27	404	15	that	that	SCONJ
ma-27	404	16	the	the	DET
ma-27	404	17	sequence	sequence	NOUN
ma-27	404	18	iterativelygenerated	iterativelygenerate	VERB
ma-27	404	19	by	by	ADP
ma-27	404	20	(	(	PUNCT
ma-27	404	21	1.7	1.7	NUM
ma-27	404	22	)	)	PUNCT
ma-27	404	23	is	be	AUX
ma-27	404	24	`	`	PUNCT
ma-27	404	25	s+1	s+1	PROPN
ma-27	404	26	=	=	SYM
ma-27	404	27	f	f	X
ma-27	404	28	(	(	PUNCT
ma-27	404	29	g	g	NOUN
ma-27	404	30	,	,	PUNCT
ma-27	404	31	ys	ys	NOUN
ma-27	404	32	)	)	PUNCT
ma-27	404	33	converging	converge	VERB
ma-27	404	34	to	to	ADP
ma-27	404	35	a	a	DET
ma-27	404	36	unique	unique	ADJ
ma-27	404	37	point	point	NOUN
ma-27	404	38	z	z	NOUN
ma-27	404	39	and	and	CCONJ
ma-27	404	40	that	that	SCONJ
ma-27	404	41	εs	εs	ADP
ma-27	404	42	=	=	SYM
ma-27	404	43	‖ys+1−f	‖ys+1−f	PROPN
ma-27	404	44	(	(	PUNCT
ma-27	404	45	t	t	PROPN
ma-27	404	46	,	,	PUNCT
ma-27	404	47	ys)‖.to	ys)‖.to	PRON
ma-27	404	48	prove	prove	VERB
ma-27	404	49	that	that	SCONJ
ma-27	404	50	(	(	PUNCT
ma-27	404	51	1.7	1.7	NUM
ma-27	404	52	)	)	PUNCT
ma-27	404	53	is	be	AUX
ma-27	404	54	t	t	NOUN
ma-27	404	55	-stable	-stable	PROPN
ma-27	404	56	,	,	PUNCT
ma-27	404	57	we	we	PRON
ma-27	404	58	have	have	VERB
ma-27	404	59	to	to	PART
ma-27	404	60	show	show	VERB
ma-27	404	61	that	that	SCONJ
ma-27	404	62	lim	lim	PROPN
ma-27	404	63	s→∞	s→∞	NOUN
ma-27	405	1	εs	εs	ADP
ma-27	405	2	=	=	PUNCT
ma-27	405	3	0⇔	0⇔	NOUN
ma-27	405	4	lim	lim	PROPN
ma-27	405	5	s→∞	s→∞	PROPN
ma-27	405	6	ys	ys	NOUN
ma-27	405	7	=	=	NOUN
ma-27	405	8	z	z	PROPN
ma-27	405	9	.let	.let	PUNCT
ma-27	406	1	lim	lim	PROPN
ma-27	406	2	s→∞	s→∞	PROPN
ma-27	406	3	εs	εs	PROPN
ma-27	406	4	=	=	ADJ
ma-27	406	5	0	0	PROPN
ma-27	406	6	.	.	PUNCT
ma-27	407	1	then	then	ADV
ma-27	407	2	from	from	ADP
ma-27	407	3	(	(	PUNCT
ma-27	407	4	1.7	1.7	NUM
ma-27	407	5	)	)	PUNCT
ma-27	407	6	and	and	CCONJ
ma-27	407	7	(	(	PUNCT
ma-27	407	8	1.6	1.6	NUM
ma-27	407	9	)	)	PUNCT
ma-27	407	10	,	,	PUNCT
ma-27	407	11	we	we	PRON
ma-27	407	12	obtain	obtain	VERB
ma-27	407	13	‖ys+1	‖ys+1	PUNCT
ma-27	407	14	−	−	PROPN
ma-27	407	15	z‖	z‖	NOUN
ma-27	408	1	=	=	SYM
ma-27	408	2	‖ys+1	‖ys+1	PUNCT
ma-27	409	1	−	−	PROPN
ma-27	409	2	f	f	PROPN
ma-27	409	3	(	(	PUNCT
ma-27	409	4	t	t	PROPN
ma-27	409	5	,	,	PUNCT
ma-27	409	6	ys	ys	NOUN
ma-27	409	7	)	)	PUNCT
ma-27	410	1	+	+	NUM
ma-27	410	2	f	f	X
ma-27	410	3	(	(	PUNCT
ma-27	410	4	t	t	PROPN
ma-27	410	5	,	,	PUNCT
ma-27	410	6	ys)−	ys)−	VERB
ma-27	410	7	z‖	z‖	PROPN
ma-27	410	8	≤	≤	NUM
ma-27	411	1	‖ys+1	‖ys+1	PUNCT
ma-27	412	1	−	−	PROPN
ma-27	412	2	f	f	PROPN
ma-27	412	3	(	(	PUNCT
ma-27	412	4	t	t	PROPN
ma-27	412	5	,	,	PUNCT
ma-27	412	6	ys)‖+	ys)‖+	PROPN
ma-27	412	7	‖f	‖f	PROPN
ma-27	412	8	(	(	PUNCT
ma-27	412	9	t	t	PROPN
ma-27	412	10	,	,	PUNCT
ma-27	412	11	ys)−	ys)−	X
ma-27	412	12	z‖	z‖	NOUN
ma-27	412	13	=	=	SYM
ma-27	412	14	εs	εs	ADP
ma-27	412	15	+	+	ADJ
ma-27	412	16	‖f	‖f	ADP
ma-27	412	17	(	(	PUNCT
ma-27	412	18	t	t	PROPN
ma-27	412	19	,	,	PUNCT
ma-27	412	20	ys)−	ys)−	X
ma-27	412	21	z‖	z‖	NOUN
ma-27	413	1	=	=	SYM
ma-27	413	2	εs	εs	ADP
ma-27	413	3	+	+	X
ma-27	413	4	‖t	‖t	NOUN
ma-27	413	5	(	(	PUNCT
ma-27	413	6	t	t	PROPN
ma-27	413	7	(	(	PUNCT
ma-27	413	8	(	(	PUNCT
ma-27	413	9	1−	1−	NUM
ma-27	413	10	δs)tys	δs)tys	X
ma-27	413	11	+	+	X
ma-27	413	12	δst	δst	NOUN
ma-27	413	13	(	(	PUNCT
ma-27	413	14	(	(	PUNCT
ma-27	413	15	1−	1−	NUM
ma-27	413	16	βs)ys	βs)ys	PUNCT
ma-27	414	1	+	+	PUNCT
ma-27	414	2	βstys)))−	βstys)))−	NOUN
ma-27	414	3	z‖	z‖	NOUN
ma-27	414	4	=	=	SYM
ma-27	414	5	γ3(1−	γ3(1−	X
ma-27	414	6	(	(	PUNCT
ma-27	414	7	1−	1−	NUM
ma-27	414	8	γ)δsβs)‖ys	γ)δsβs)‖ys	PUNCT
ma-27	415	1	−	−	PROPN
ma-27	415	2	z‖+	z‖+	NOUN
ma-27	415	3	εs	εs	VERB
ma-27	415	4	.	.	PUNCT
ma-27	416	1	(	(	PUNCT
ma-27	416	2	6.1	6.1	NUM
ma-27	416	3	)	)	PUNCT
ma-27	416	4	for	for	ADP
ma-27	416	5	all	all	PRON
ma-27	416	6	s	s	PART
ma-27	416	7	≥	≥	NOUN
ma-27	416	8	1	1	NUM
ma-27	416	9	,	,	PUNCT
ma-27	416	10	put	put	VERB
ma-27	416	11	θs	θ	NOUN
ma-27	416	12	=	=	PUNCT
ma-27	417	1	‖ys	‖ys	NUM
ma-27	417	2	−	−	NUM
ma-27	417	3	z‖	z‖	NOUN
ma-27	417	4	,	,	PUNCT
ma-27	417	5	σs	σs	ADP
ma-27	417	6	=	=	SYM
ma-27	417	7	(	(	PUNCT
ma-27	417	8	1−	1−	NUM
ma-27	417	9	γ)δsβs	γ)δsβs	NOUN
ma-27	417	10	∈	∈	PROPN
ma-27	417	11	(	(	PUNCT
ma-27	417	12	0	0	NUM
ma-27	417	13	,	,	PUNCT
ma-27	417	14	1	1	NUM
ma-27	417	15	)	)	PUNCT
ma-27	417	16	,	,	PUNCT
ma-27	417	17	λs	λs	ADP
ma-27	417	18	=	=	NOUN
ma-27	417	19	εs	εs	VERB
ma-27	417	20	.	.	PUNCT
ma-27	418	1	since	since	SCONJ
ma-27	418	2	lim	lim	PROPN
ma-27	418	3	s→∞	s→∞	VERB
ma-27	418	4	εs	εs	ADP
ma-27	418	5	=	=	ADJ
ma-27	418	6	0	0	NUM
ma-27	418	7	,	,	PUNCT
ma-27	418	8	this	this	PRON
ma-27	418	9	implies	imply	VERB
ma-27	418	10	that	that	SCONJ
ma-27	418	11	λs	λs	NOUN
ma-27	418	12	σs	σs	ADP
ma-27	418	13	=	=	VERB
ma-27	418	14	εs	εs	PROPN
ma-27	418	15	(	(	PUNCT
ma-27	418	16	1−γ)δsβs	1−γ)δsβs	NUM
ma-27	418	17	→	→	SYM
ma-27	418	18	0	0	NUM
ma-27	418	19	as	as	SCONJ
ma-27	418	20	s	s	PRON
ma-27	418	21	→∞.	→∞.	X
ma-27	418	22	apparently	apparently	ADV
ma-27	418	23	,	,	PUNCT
ma-27	418	24	all	all	DET
ma-27	418	25	the	the	DET
ma-27	418	26	conditionsof	conditionsof	NOUN
ma-27	418	27	lemma	lemma	PROPN
ma-27	418	28	2.12	2.12	NUM
ma-27	418	29	are	be	AUX
ma-27	418	30	fulfilled	fulfil	VERB
ma-27	418	31	.	.	PUNCT
ma-27	419	1	hence	hence	ADV
ma-27	419	2	,	,	PUNCT
ma-27	419	3	from	from	ADP
ma-27	419	4	lemma	lemma	PROPN
ma-27	419	5	2.12	2.12	NUM
ma-27	419	6	we	we	PRON
ma-27	419	7	have	have	VERB
ma-27	419	8	lim	lim	PROPN
ma-27	419	9	s→∞	s→∞	NOUN
ma-27	419	10	ys	ys	NOUN
ma-27	420	1	=	=	NOUN
ma-27	420	2	z	z	NOUN
ma-27	420	3	.conversely	.conversely	ADV
ma-27	420	4	,	,	PUNCT
ma-27	420	5	let	let	VERB
ma-27	420	6	lim	lim	PROPN
ma-27	420	7	s→∞	s→∞	NOUN
ma-27	420	8	ys	ys	NOUN
ma-27	420	9	=	=	NOUN
ma-27	420	10	z	z	PROPN
ma-27	420	11	.	.	PUNCT
ma-27	421	1	the	the	PRON
ma-27	421	2	we	we	PRON
ma-27	421	3	have	have	VERB
ma-27	421	4	εs	εs	NOUN
ma-27	421	5	=	=	PUNCT
ma-27	421	6	‖ys+1	‖ys+1	PUNCT
ma-27	422	1	−	−	PROPN
ma-27	422	2	f	f	PROPN
ma-27	422	3	(	(	PUNCT
ma-27	422	4	t	t	PROPN
ma-27	422	5	,	,	PUNCT
ma-27	422	6	ys)‖	ys)‖	PROPN
ma-27	422	7	=	=	PUNCT
ma-27	422	8	‖ys+1	‖ys+1	PUNCT
ma-27	422	9	−	−	PUNCT
ma-27	422	10	z	z	NOUN
ma-27	423	1	+	+	NOUN
ma-27	423	2	z	z	NOUN
ma-27	424	1	−	−	PROPN
ma-27	424	2	f	f	PROPN
ma-27	424	3	(	(	PUNCT
ma-27	424	4	t	t	PROPN
ma-27	424	5	,	,	PUNCT
ma-27	424	6	ys)‖	ys)‖	PROPN
ma-27	424	7	≤	≤	NUM
ma-27	424	8	‖ys+1	‖ys+1	PUNCT
ma-27	425	1	−	−	PUNCT
ma-27	425	2	z‖+	z‖+	NOUN
ma-27	425	3	‖f	‖f	PUNCT
ma-27	425	4	(	(	PUNCT
ma-27	425	5	t	t	PROPN
ma-27	425	6	,	,	PUNCT
ma-27	425	7	ys)−	ys)−	VERB
ma-27	425	8	z‖	z‖	PROPN
ma-27	425	9	≤	≤	NUM
ma-27	426	1	‖ys+1	‖ys+1	PUNCT
ma-27	427	1	−	−	PROPN
ma-27	428	1	z‖+	z‖+	INTJ
ma-27	428	2	γ3(1−	γ3(1−	PROPN
ma-27	428	3	(	(	PUNCT
ma-27	428	4	1−	1−	NUM
ma-27	428	5	γ)δsβs)‖ys	γ)δsβs)‖ys	PROPN
ma-27	428	6	−	−	PROPN
ma-27	428	7	z‖.	z‖.	X
ma-27	428	8	(	(	PUNCT
ma-27	428	9	6.2	6.2	NUM
ma-27	428	10	)	)	PUNCT
ma-27	428	11	from	from	ADP
ma-27	428	12	(	(	PUNCT
ma-27	428	13	6.2	6.2	NUM
ma-27	428	14	)	)	PUNCT
ma-27	428	15	,	,	PUNCT
ma-27	428	16	it	it	PRON
ma-27	428	17	follows	follow	VERB
ma-27	428	18	that	that	SCONJ
ma-27	428	19	lim	lim	PROPN
ma-27	428	20	s→∞	s→∞	NOUN
ma-27	428	21	εs	εs	ADP
ma-27	428	22	=	=	ADJ
ma-27	428	23	0	0	NUM
ma-27	428	24	.	.	PUNCT
ma-27	429	1	hence	hence	ADV
ma-27	429	2	,	,	PUNCT
ma-27	429	3	our	our	PRON
ma-27	429	4	new	new	ADJ
ma-27	429	5	iterative	iterative	NOUN
ma-27	429	6	algorithm	algorithm	NOUN
ma-27	429	7	(	(	PUNCT
ma-27	429	8	1.7	1.7	NUM
ma-27	429	9	)	)	PUNCT
ma-27	429	10	is	be	AUX
ma-27	429	11	stable	stable	ADJ
ma-27	429	12	withrespect	withrespect	ADJ
ma-27	429	13	to	to	ADP
ma-27	429	14	t	t	PROPN
ma-27	429	15	.	.	PUNCT
ma-27	430	1	�	�	PROPN
ma-27	430	2	7	7	NUM
ma-27	430	3	.	.	PUNCT
ma-27	430	4	data	datum	NOUN
ma-27	430	5	dependence	dependence	NOUN
ma-27	430	6	result	result	NOUN
ma-27	430	7	in	in	ADP
ma-27	430	8	this	this	DET
ma-27	430	9	section	section	NOUN
ma-27	430	10	,	,	PUNCT
ma-27	430	11	we	we	PRON
ma-27	430	12	obtain	obtain	VERB
ma-27	430	13	data	datum	NOUN
ma-27	430	14	dependence	dependence	NOUN
ma-27	430	15	result	result	NOUN
ma-27	430	16	for	for	ADP
ma-27	430	17	the	the	DET
ma-27	430	18	mapping	mapping	NOUN
ma-27	430	19	t	t	NOUN
ma-27	430	20	satisfying	satisfying	NOUN
ma-27	430	21	(	(	PUNCT
ma-27	430	22	1.2	1.2	NUM
ma-27	430	23	)	)	PUNCT
ma-27	430	24	by	by	ADP
ma-27	430	25	utilizingour	utilizingour	PRON
ma-27	430	26	new	new	ADJ
ma-27	430	27	iterative	iterative	NOUN
ma-27	430	28	algorithm	algorithm	NOUN
ma-27	430	29	(	(	PUNCT
ma-27	430	30	1.7	1.7	NUM
ma-27	430	31	)	)	PUNCT
ma-27	430	32	.	.	PUNCT
ma-27	431	1	eur	eur	PROPN
ma-27	431	2	.	.	PUNCT
ma-27	432	1	j.	j.	PROPN
ma-27	432	2	math	math	PROPN
ma-27	432	3	.	.	PUNCT
ma-27	433	1	anal	anal	ADJ
ma-27	433	2	.	.	PUNCT
ma-27	434	1	1	1	NUM
ma-27	434	2	(	(	PUNCT
ma-27	434	3	2021	2021	NUM
ma-27	434	4	)	)	PUNCT
ma-27	434	5	124	124	NUM
ma-27	434	6	theorem	theorem	VERB
ma-27	434	7	7.1	7.1	NUM
ma-27	434	8	.	.	PUNCT
ma-27	435	1	let	let	VERB
ma-27	435	2	t̃	t̃	PROPN
ma-27	435	3	be	be	AUX
ma-27	435	4	an	an	DET
ma-27	435	5	approximate	approximate	ADJ
ma-27	435	6	operator	operator	NOUN
ma-27	435	7	of	of	ADP
ma-27	435	8	a	a	DET
ma-27	435	9	mapping	mapping	NOUN
ma-27	435	10	t	t	NOUN
ma-27	435	11	satisfying	satisfying	NOUN
ma-27	435	12	(	(	PUNCT
ma-27	435	13	1.2	1.2	NUM
ma-27	435	14	)	)	PUNCT
ma-27	435	15	.	.	PUNCT
ma-27	436	1	let	let	VERB
ma-27	436	2	{	{	PUNCT
ma-27	436	3	`	`	PUNCT
ma-27	436	4	s	s	AUX
ma-27	436	5	}	}	PUNCT
ma-27	436	6	be	be	AUX
ma-27	436	7	an	an	DET
ma-27	436	8	iterative	iterative	NOUN
ma-27	436	9	sequence	sequence	NOUN
ma-27	436	10	generated	generate	VERB
ma-27	436	11	by	by	ADP
ma-27	436	12	(	(	PUNCT
ma-27	436	13	1.7	1.7	NUM
ma-27	436	14	)	)	PUNCT
ma-27	436	15	for	for	ADP
ma-27	436	16	t	t	NOUN
ma-27	436	17	and	and	CCONJ
ma-27	436	18	define	define	VERB
ma-27	436	19	an	an	DET
ma-27	436	20	iterative	iterative	NOUN
ma-27	436	21	algorithm	algorithm	NOUN
ma-27	436	22	as	as	ADP
ma-27	436	23	follows:	follows:	PROPN
ma-27	436	24	˜̀	˜̀	NOUN
ma-27	436	25	0	0	NUM
ma-27	436	26	∈	∈	PROPN
ma-27	436	27	λ	λ	NOUN
ma-27	436	28	,	,	PUNCT
ma-27	436	29	g̃s	g̃s	NOUN
ma-27	436	30	=	=	SYM
ma-27	436	31	(	(	PUNCT
ma-27	436	32	1−	1−	NUM
ma-27	436	33	βs)˜̀	βs)˜̀	X
ma-27	436	34	s	s	PART
ma-27	436	35	+	+	NUM
ma-27	436	36	βs	βs	ADJ
ma-27	436	37	t̃	t̃	PROPN
ma-27	436	38	˜̀	˜̀	NOUN
ma-27	436	39	s	s	NOUN
ma-27	436	40	,	,	PUNCT
ma-27	436	41	w̃s	w̃s	PROPN
ma-27	436	42	=	=	SYM
ma-27	436	43	(	(	PUNCT
ma-27	436	44	1−	1−	NUM
ma-27	436	45	δs)t̃	δs)t̃	PROPN
ma-27	436	46	˜̀	˜̀	NOUN
ma-27	436	47	s	s	PART
ma-27	436	48	+	+	NOUN
ma-27	436	49	δs	δs	ADP
ma-27	436	50	t̃	t̃	PROPN
ma-27	436	51	g̃s	g̃s	NOUN
ma-27	436	52	,	,	PUNCT
ma-27	436	53	ζ̃s	ζ̃s	NOUN
ma-27	436	54	=	=	SYM
ma-27	436	55	t̃	t̃	PROPN
ma-27	436	56	w̃s	w̃s	NOUN
ma-27	436	57	,	,	PUNCT
ma-27	436	58	˜̀	˜̀	NOUN
ma-27	436	59	s+1	s+1	NOUN
ma-27	436	60	=	=	SYM
ma-27	436	61	t̃	t̃	PROPN
ma-27	436	62	ζ̃s	ζ̃s	NOUN
ma-27	436	63	,	,	PUNCT
ma-27	436	64	∀s	∀s	PROPN
ma-27	436	65	≥	≥	NUM
ma-27	436	66	1	1	NUM
ma-27	436	67	,	,	PUNCT
ma-27	436	68	(	(	PUNCT
ma-27	436	69	7.1	7.1	NUM
ma-27	436	70	)	)	PUNCT
ma-27	436	71	where	where	SCONJ
ma-27	436	72	{	{	PUNCT
ma-27	436	73	δs	δs	NOUN
ma-27	436	74	}	}	PUNCT
ma-27	436	75	and	and	CCONJ
ma-27	436	76	{	{	PUNCT
ma-27	436	77	βs	βs	X
ma-27	436	78	}	}	PUNCT
ma-27	436	79	are	be	AUX
ma-27	436	80	sequences	sequence	NOUN
ma-27	436	81	in	in	ADP
ma-27	436	82	[	[	X
ma-27	436	83	0	0	NUM
ma-27	436	84	,	,	PUNCT
ma-27	436	85	1	1	NUM
ma-27	436	86	]	]	PUNCT
ma-27	436	87	satisfying	satisfy	VERB
ma-27	436	88	the	the	DET
ma-27	436	89	following	follow	VERB
ma-27	436	90	conditions:(i	conditions:(i	NOUN
ma-27	436	91	)	)	PUNCT
ma-27	436	92	12	12	NUM
ma-27	436	93	≤	≤	ADV
ma-27	436	94	δsβs	δsβs	ADV
ma-27	436	95	,	,	PUNCT
ma-27	436	96	∀	∀	NOUN
ma-27	436	97	s	s	NOUN
ma-27	436	98	∈	∈	NOUN
ma-27	436	99	n,(ii	n,(ii	NUM
ma-27	436	100	)	)	PUNCT
ma-27	437	1	∞∑	∞∑	NUM
ma-27	437	2	s=0	s=0	NOUN
ma-27	437	3	δsβs	δsβs	PRON
ma-27	437	4	=	=	NUM
ma-27	437	5	∞.	∞.	PROPN
ma-27	437	6	if	if	SCONJ
ma-27	437	7	tz	tz	NOUN
ma-27	437	8	=	=	SYM
ma-27	437	9	z	z	PROPN
ma-27	437	10	and	and	CCONJ
ma-27	437	11	t̃	t̃	PROPN
ma-27	437	12	z̃	z̃	PROPN
ma-27	437	13	=	=	SYM
ma-27	437	14	z̃	z̃	PROPN
ma-27	437	15	such	such	ADJ
ma-27	437	16	that	that	SCONJ
ma-27	437	17	lim	lim	PROPN
ma-27	437	18	s→∞	s→∞	PROPN
ma-27	437	19	˜̀	˜̀	NOUN
ma-27	437	20	s	s	PART
ma-27	437	21	=	=	SYM
ma-27	437	22	z̃	z̃	PROPN
ma-27	437	23	,	,	PUNCT
ma-27	437	24	we	we	PRON
ma-27	437	25	have	have	VERB
ma-27	437	26	‖z	‖z	NOUN
ma-27	437	27	−	−	NOUN
ma-27	437	28	z̃‖	z̃‖	NUM
ma-27	437	29	≤	≤	NUM
ma-27	437	30	7ε	7ε	NOUN
ma-27	437	31	1−	1−	NUM
ma-27	437	32	γ	γ	NOUN
ma-27	437	33	,	,	PUNCT
ma-27	437	34	where	where	SCONJ
ma-27	437	35	ε	ε	PROPN
ma-27	437	36	>	>	X
ma-27	437	37	0	0	NUM
ma-27	437	38	is	be	AUX
ma-27	437	39	a	a	DET
ma-27	437	40	fixed	fix	VERB
ma-27	437	41	number	number	NOUN
ma-27	437	42	.	.	PUNCT
ma-27	438	1	proof	proof	NOUN
ma-27	438	2	.	.	PUNCT
ma-27	439	1	using	use	VERB
ma-27	439	2	(	(	PUNCT
ma-27	439	3	1.7	1.7	NUM
ma-27	439	4	)	)	PUNCT
ma-27	439	5	,	,	PUNCT
ma-27	439	6	(	(	PUNCT
ma-27	439	7	1.2	1.2	NUM
ma-27	439	8	)	)	PUNCT
ma-27	439	9	and	and	CCONJ
ma-27	439	10	(	(	PUNCT
ma-27	439	11	7.1	7.1	NUM
ma-27	439	12	)	)	PUNCT
ma-27	439	13	,	,	PUNCT
ma-27	439	14	we	we	PRON
ma-27	439	15	have	have	VERB
ma-27	439	16	‖`s+1	‖`s+1	ADJ
ma-27	439	17	−	−	PROPN
ma-27	439	18	˜̀	˜̀	PROPN
ma-27	439	19	s+1‖	s+1‖	PROPN
ma-27	439	20	=	=	X
ma-27	439	21	‖tζs	‖tζs	NOUN
ma-27	439	22	−	−	PROPN
ma-27	439	23	t̃	t̃	PROPN
ma-27	439	24	ζ̃s‖	ζ̃s‖	PROPN
ma-27	439	25	=	=	SYM
ma-27	439	26	‖tζs	‖tζs	NOUN
ma-27	439	27	−	−	PROPN
ma-27	439	28	t	t	PROPN
ma-27	439	29	ζ̃s	ζ̃s	NOUN
ma-27	439	30	+	+	SYM
ma-27	439	31	t	t	NOUN
ma-27	439	32	ζ̃s	ζ̃s	NOUN
ma-27	439	33	−	−	PROPN
ma-27	439	34	t̃	t̃	PROPN
ma-27	439	35	ζ̃s‖	ζ̃s‖	PROPN
ma-27	439	36	≤	≤	NUM
ma-27	439	37	‖tζs	‖tζs	NOUN
ma-27	439	38	−	−	PROPN
ma-27	439	39	t	t	PROPN
ma-27	439	40	ζ̃s‖+	ζ̃s‖+	PROPN
ma-27	439	41	‖t	‖t	NOUN
ma-27	439	42	ζ̃s	ζ̃s	NOUN
ma-27	439	43	−	−	NOUN
ma-27	439	44	t̃	t̃	PROPN
ma-27	439	45	ζ̃s‖	ζ̃s‖	PROPN
ma-27	439	46	≤	≤	NOUN
ma-27	440	1	γ‖ζs	γ‖ζs	PROPN
ma-27	440	2	−	−	NOUN
ma-27	440	3	ζ̃s‖+	ζ̃s‖+	ADV
ma-27	440	4	l‖ζs	l‖ζs	DET
ma-27	440	5	−	−	NOUN
ma-27	440	6	tζs‖+	tζs‖+	NOUN
ma-27	440	7	ε	ε	PROPN
ma-27	440	8	.	.	PUNCT
ma-27	440	9	(	(	PUNCT
ma-27	440	10	7.2	7.2	NUM
ma-27	440	11	)	)	PUNCT
ma-27	440	12	from	from	ADP
ma-27	440	13	(	(	PUNCT
ma-27	440	14	1.7	1.7	NUM
ma-27	440	15	)	)	PUNCT
ma-27	440	16	,	,	PUNCT
ma-27	440	17	(	(	PUNCT
ma-27	440	18	1.2	1.2	NUM
ma-27	440	19	)	)	PUNCT
ma-27	440	20	and	and	CCONJ
ma-27	440	21	(	(	PUNCT
ma-27	440	22	7.1	7.1	NUM
ma-27	440	23	)	)	PUNCT
ma-27	440	24	,	,	PUNCT
ma-27	440	25	we	we	PRON
ma-27	440	26	have	have	VERB
ma-27	440	27	‖ζs	‖ζ	NOUN
ma-27	440	28	−	−	PROPN
ma-27	440	29	ζ̃s‖	ζ̃s‖	PROPN
ma-27	440	30	=	=	PUNCT
ma-27	440	31	‖tws	‖tws	ADP
ma-27	440	32	−	−	PROPN
ma-27	441	1	t̃	t̃	PROPN
ma-27	441	2	w̃s‖	w̃s‖	PROPN
ma-27	441	3	=	=	PUNCT
ma-27	442	1	‖tws	‖tws	NUM
ma-27	443	1	−	−	PROPN
ma-27	443	2	t	t	NOUN
ma-27	443	3	w̃s	w̃s	NOUN
ma-27	443	4	+	+	CCONJ
ma-27	443	5	t	t	NOUN
ma-27	443	6	w̃s	w̃s	NOUN
ma-27	443	7	−	−	NOUN
ma-27	443	8	t̃	t̃	PROPN
ma-27	443	9	w̃s‖	w̃s‖	PROPN
ma-27	443	10	≤	≤	NOUN
ma-27	443	11	‖tws	‖tws	PUNCT
ma-27	444	1	−	−	PROPN
ma-27	444	2	t	t	PROPN
ma-27	444	3	w̃s‖+	w̃s‖+	PROPN
ma-27	444	4	‖t	‖t	PUNCT
ma-27	444	5	w̃s	w̃s	NOUN
ma-27	445	1	−	−	NOUN
ma-27	445	2	t̃	t̃	PROPN
ma-27	445	3	w̃s‖	w̃s‖	PROPN
ma-27	445	4	≤	≤	PUNCT
ma-27	446	1	γ‖ws	γ‖ws	PROPN
ma-27	446	2	−	−	NUM
ma-27	446	3	w̃s‖+	w̃s‖+	ADJ
ma-27	447	1	l‖ws	l‖ws	PROPN
ma-27	447	2	−	−	PROPN
ma-27	447	3	tws‖+	tws‖+	PROPN
ma-27	447	4	ε	ε	PROPN
ma-27	447	5	.	.	PUNCT
ma-27	448	1	(	(	PUNCT
ma-27	448	2	7.3	7.3	NUM
ma-27	448	3	)	)	PUNCT
ma-27	448	4	putting	put	VERB
ma-27	448	5	(	(	PUNCT
ma-27	448	6	7.3	7.3	NUM
ma-27	448	7	)	)	PUNCT
ma-27	448	8	into	into	ADP
ma-27	448	9	(	(	PUNCT
ma-27	448	10	7.2	7.2	NUM
ma-27	448	11	)	)	PUNCT
ma-27	448	12	,	,	PUNCT
ma-27	448	13	we	we	PRON
ma-27	448	14	have	have	VERB
ma-27	448	15	‖`s+1	‖`s+1	ADJ
ma-27	448	16	−	−	PROPN
ma-27	448	17	˜̀	˜̀	PROPN
ma-27	448	18	s+1‖	s+1‖	PROPN
ma-27	448	19	≤	≤	NUM
ma-27	448	20	γ2‖ws	γ2‖ws	ADP
ma-27	448	21	−	−	PROPN
ma-27	448	22	w̃s‖+	w̃s‖+	NOUN
ma-27	448	23	γl‖ws	γl‖ws	PUNCT
ma-27	448	24	−	−	NUM
ma-27	448	25	tws‖	tws‖	PUNCT
ma-27	449	1	+	+	PROPN
ma-27	449	2	γε+	γε+	NOUN
ma-27	449	3	l‖ζs	l‖ζs	PRON
ma-27	449	4	−	−	NOUN
ma-27	449	5	tζs‖+	tζs‖+	NOUN
ma-27	449	6	ε	ε	PROPN
ma-27	449	7	.	.	PUNCT
ma-27	450	1	(	(	PUNCT
ma-27	450	2	7.4	7.4	NUM
ma-27	450	3	)	)	PUNCT
ma-27	450	4	eur	eur	NOUN
ma-27	450	5	.	.	PUNCT
ma-27	451	1	j.	j.	PROPN
ma-27	451	2	math	math	PROPN
ma-27	451	3	.	.	PUNCT
ma-27	452	1	anal	anal	ADJ
ma-27	452	2	.	.	PUNCT
ma-27	453	1	1	1	NUM
ma-27	453	2	(	(	PUNCT
ma-27	453	3	2021	2021	NUM
ma-27	453	4	)	)	PUNCT
ma-27	454	1	125again	125again	PROPN
ma-27	454	2	,	,	PUNCT
ma-27	454	3	using	use	VERB
ma-27	454	4	(	(	PUNCT
ma-27	454	5	1.7	1.7	NUM
ma-27	454	6	)	)	PUNCT
ma-27	454	7	,	,	PUNCT
ma-27	454	8	(	(	PUNCT
ma-27	454	9	1.2	1.2	NUM
ma-27	454	10	)	)	PUNCT
ma-27	454	11	and	and	CCONJ
ma-27	454	12	(	(	PUNCT
ma-27	454	13	7.1	7.1	NUM
ma-27	454	14	)	)	PUNCT
ma-27	455	1	,	,	PUNCT
ma-27	455	2	we	we	PRON
ma-27	455	3	get	get	VERB
ma-27	455	4	‖ws	‖ws	NUM
ma-27	455	5	−	−	PROPN
ma-27	455	6	w̃s‖	w̃s‖	PROPN
ma-27	455	7	=	=	SYM
ma-27	455	8	(	(	PUNCT
ma-27	455	9	1−	1−	NUM
ma-27	455	10	δs)‖t`s	δs)‖t`s	PROPN
ma-27	456	1	−	−	PROPN
ma-27	456	2	t̃	t̃	PROPN
ma-27	456	3	˜̀	˜̀	NOUN
ma-27	456	4	s‖+	s‖+	NOUN
ma-27	456	5	δs‖tgs	δs‖tg	VERB
ma-27	456	6	−	−	PROPN
ma-27	456	7	t̃	t̃	PROPN
ma-27	456	8	g̃s‖	g̃s‖	PROPN
ma-27	456	9	≤	≤	NOUN
ma-27	456	10	(	(	PUNCT
ma-27	456	11	1−	1−	NUM
ma-27	456	12	δs){‖t`s	δs){‖t`s	ADV
ma-27	456	13	−	−	PROPN
ma-27	456	14	t	t	NOUN
ma-27	456	15	˜̀	˜̀	NOUN
ma-27	456	16	s‖+	s‖+	PROPN
ma-27	456	17	‖t	‖t	PROPN
ma-27	456	18	˜̀	˜̀	NOUN
ma-27	456	19	s	s	PART
ma-27	456	20	−	−	PROPN
ma-27	456	21	t̃	t̃	PROPN
ma-27	456	22	˜̀	˜̀	NOUN
ma-27	456	23	s‖	s‖	NOUN
ma-27	456	24	}	}	PUNCT
ma-27	456	25	+	+	NOUN
ma-27	456	26	δs{‖tgs	δs{‖tgs	PROPN
ma-27	456	27	−	−	PROPN
ma-27	456	28	t	t	PROPN
ma-27	456	29	g̃s‖+	g̃s‖+	PROPN
ma-27	456	30	‖t	‖t	PROPN
ma-27	456	31	g̃s	g̃s	NOUN
ma-27	457	1	−	−	PROPN
ma-27	457	2	t̃	t̃	PROPN
ma-27	457	3	g̃s‖	g̃s‖	PROPN
ma-27	457	4	}	}	PUNCT
ma-27	457	5	≤	≤	NOUN
ma-27	457	6	(	(	PUNCT
ma-27	457	7	1−	1−	NUM
ma-27	457	8	δs){γ‖`s	δs){γ‖`s	NOUN
ma-27	458	1	−	−	PROPN
ma-27	459	1	˜̀	˜̀	NOUN
ma-27	459	2	s‖+	s‖+	X
ma-27	459	3	l‖`s	l‖`	VERB
ma-27	460	1	−	−	NUM
ma-27	460	2	t`s‖+	t`s‖+	ADJ
ma-27	460	3	ε	ε	PROPN
ma-27	460	4	}	}	PUNCT
ma-27	460	5	+	+	NOUN
ma-27	460	6	δs{γ‖gs	δs{γ‖gs	NOUN
ma-27	460	7	−	−	ADJ
ma-27	460	8	g̃s‖+	g̃s‖+	ADJ
ma-27	460	9	l‖gs	l‖gs	PROPN
ma-27	460	10	−	−	PROPN
ma-27	460	11	tgs‖+	tgs‖+	NOUN
ma-27	460	12	ε	ε	PROPN
ma-27	460	13	}	}	PUNCT
ma-27	460	14	.	.	PUNCT
ma-27	461	1	(	(	PUNCT
ma-27	461	2	7.5	7.5	NUM
ma-27	461	3	)	)	PUNCT
ma-27	461	4	using	use	VERB
ma-27	461	5	(	(	PUNCT
ma-27	461	6	1.7	1.7	NUM
ma-27	461	7	)	)	PUNCT
ma-27	461	8	,	,	PUNCT
ma-27	461	9	(	(	PUNCT
ma-27	461	10	1.2	1.2	NUM
ma-27	461	11	)	)	PUNCT
ma-27	461	12	and	and	CCONJ
ma-27	461	13	(	(	PUNCT
ma-27	461	14	7.1	7.1	NUM
ma-27	461	15	)	)	PUNCT
ma-27	461	16	,	,	PUNCT
ma-27	461	17	we	we	PRON
ma-27	461	18	get	get	VERB
ma-27	461	19	‖gs	‖gs	NUM
ma-27	461	20	−	−	PROPN
ma-27	461	21	g̃s‖	g̃s‖	PROPN
ma-27	461	22	≤	≤	NOUN
ma-27	461	23	(	(	PUNCT
ma-27	461	24	1−	1−	NUM
ma-27	461	25	βs)‖`s	βs)‖`s	PUNCT
ma-27	462	1	−	−	PROPN
ma-27	462	2	˜̀	˜̀	NOUN
ma-27	462	3	s‖+	s‖+	X
ma-27	462	4	βs‖t`s	βs‖t`s	NOUN
ma-27	463	1	−	−	ADP
ma-27	463	2	t̃	t̃	PROPN
ma-27	463	3	˜̀	˜̀	NOUN
ma-27	463	4	s‖	s‖	NOUN
ma-27	463	5	≤	≤	NUM
ma-27	463	6	(	(	PUNCT
ma-27	463	7	1−	1−	NUM
ma-27	463	8	βs)‖`s	βs)‖`s	PUNCT
ma-27	464	1	−	−	PROPN
ma-27	464	2	˜̀	˜̀	NOUN
ma-27	464	3	s‖+	s‖+	NOUN
ma-27	464	4	βs{‖t`s	βs{‖t`s	SYM
ma-27	464	5	−	−	ADP
ma-27	464	6	t	t	NOUN
ma-27	464	7	˜̀	˜̀	NOUN
ma-27	464	8	s‖+	s‖+	PROPN
ma-27	464	9	‖t	‖t	PROPN
ma-27	464	10	˜̀	˜̀	NOUN
ma-27	464	11	s	s	PART
ma-27	464	12	−	−	PROPN
ma-27	464	13	t̃	t̃	PROPN
ma-27	464	14	˜̀	˜̀	NOUN
ma-27	464	15	s‖	s‖	NOUN
ma-27	464	16	}	}	PUNCT
ma-27	464	17	≤	≤	NOUN
ma-27	464	18	(	(	PUNCT
ma-27	464	19	1−	1−	NUM
ma-27	464	20	βs)‖`s	βs)‖`s	PUNCT
ma-27	464	21	−	−	PROPN
ma-27	465	1	˜̀	˜̀	NOUN
ma-27	465	2	s‖+	s‖+	ADJ
ma-27	465	3	βs{γ‖`s	βs{γ‖`s	PROPN
ma-27	465	4	−	−	PROPN
ma-27	466	1	˜̀	˜̀	NOUN
ma-27	466	2	s‖+	s‖+	X
ma-27	466	3	l‖`s	l‖`	VERB
ma-27	466	4	−	−	NUM
ma-27	466	5	t`s‖+	t`s‖+	ADJ
ma-27	466	6	ε	ε	NOUN
ma-27	466	7	}	}	PUNCT
ma-27	466	8	=	=	PUNCT
ma-27	467	1	[	[	X
ma-27	467	2	1−	1−	NUM
ma-27	467	3	(	(	PUNCT
ma-27	467	4	1−	1−	NUM
ma-27	467	5	γ)βs	γ)βs	PROPN
ma-27	467	6	]	]	PUNCT
ma-27	467	7	‖`s	‖`s	PROPN
ma-27	467	8	−	−	PROPN
ma-27	467	9	˜̀	˜̀	NOUN
ma-27	467	10	s‖+	s‖+	X
ma-27	467	11	βsl‖`s	βsl‖`s	PUNCT
ma-27	468	1	−	−	NUM
ma-27	468	2	t`s‖+	t`s‖+	ADJ
ma-27	468	3	βsε	βsε	NOUN
ma-27	469	1	(	(	PUNCT
ma-27	469	2	7.6	7.6	NUM
ma-27	469	3	)	)	PUNCT
ma-27	469	4	using	use	VERB
ma-27	469	5	(	(	PUNCT
ma-27	469	6	7.6	7.6	NUM
ma-27	469	7	)	)	PUNCT
ma-27	469	8	and	and	CCONJ
ma-27	469	9	(	(	PUNCT
ma-27	469	10	7.5	7.5	NUM
ma-27	469	11	)	)	PUNCT
ma-27	469	12	,	,	PUNCT
ma-27	469	13	we	we	PRON
ma-27	469	14	have	have	VERB
ma-27	469	15	‖ws	‖ws	NUM
ma-27	469	16	−	−	PROPN
ma-27	469	17	w̃s‖	w̃s‖	PROPN
ma-27	469	18	≤	≤	NUM
ma-27	469	19	(	(	PUNCT
ma-27	469	20	1−	1−	NUM
ma-27	469	21	δs){γ‖`s	δs){γ‖`s	NOUN
ma-27	470	1	−	−	PROPN
ma-27	471	1	˜̀	˜̀	NOUN
ma-27	471	2	s‖+	s‖+	X
ma-27	471	3	l‖`s	l‖`	VERB
ma-27	471	4	−	−	NUM
ma-27	471	5	t`s‖+	t`s‖+	ADJ
ma-27	471	6	ε	ε	PROPN
ma-27	471	7	}	}	PUNCT
ma-27	471	8	+	+	PROPN
ma-27	471	9	δs{γ[1−	δs{γ[1−	NOUN
ma-27	471	10	(	(	PUNCT
ma-27	471	11	1−	1−	NUM
ma-27	471	12	γ)βs	γ)βs	PROPN
ma-27	471	13	]	]	PUNCT
ma-27	472	1	‖`s	‖`s	PROPN
ma-27	472	2	−	−	PROPN
ma-27	472	3	˜̀	˜̀	NOUN
ma-27	472	4	s‖+	s‖+	NOUN
ma-27	472	5	γβ‖`s	γβ‖`s	PROPN
ma-27	472	6	−	−	ADP
ma-27	472	7	t`s‖+	t`s‖+	ADJ
ma-27	472	8	γβsε	γβsε	NOUN
ma-27	472	9	}	}	PUNCT
ma-27	472	10	=	=	SYM
ma-27	472	11	γ[1−	γ[1−	X
ma-27	472	12	(	(	PUNCT
ma-27	472	13	1−	1−	NUM
ma-27	472	14	γ)δsβs	γ)δsβs	NOUN
ma-27	473	1	]	]	X
ma-27	473	2	‖`s	‖`s	PROPN
ma-27	473	3	−	−	PROPN
ma-27	473	4	˜̀	˜̀	NOUN
ma-27	473	5	s‖+	s‖+	X
ma-27	473	6	(	(	PUNCT
ma-27	473	7	1−	1−	NUM
ma-27	473	8	δs)l‖`s	δs)l‖`s	NOUN
ma-27	473	9	−	−	NOUN
ma-27	473	10	t`s‖	t`s‖	NOUN
ma-27	473	11	+	+	NOUN
ma-27	473	12	(	(	PUNCT
ma-27	473	13	1−	1−	NUM
ma-27	473	14	δs)ε+	δs)ε+	NOUN
ma-27	473	15	γδsβsl‖`s	γδsβsl‖`s	PROPN
ma-27	473	16	−	−	ADP
ma-27	473	17	t`s‖+	t`s‖+	ADJ
ma-27	473	18	γδsβsε	γδsβsε	NOUN
ma-27	473	19	.	.	PUNCT
ma-27	474	1	(	(	PUNCT
ma-27	474	2	7.7	7.7	NUM
ma-27	474	3	)	)	PUNCT
ma-27	474	4	substituting	substituting	NOUN
ma-27	474	5	(	(	PUNCT
ma-27	474	6	7.7	7.7	NUM
ma-27	474	7	)	)	PUNCT
ma-27	474	8	into	into	ADP
ma-27	474	9	(	(	PUNCT
ma-27	474	10	7.4	7.4	NUM
ma-27	474	11	)	)	PUNCT
ma-27	474	12	,	,	PUNCT
ma-27	474	13	we	we	PRON
ma-27	474	14	obtain	obtain	VERB
ma-27	474	15	‖`s+1	‖`s+1	ADJ
ma-27	474	16	−	−	PROPN
ma-27	474	17	˜̀	˜̀	PROPN
ma-27	474	18	s+1‖	s+1‖	PROPN
ma-27	474	19	≤	≤	PROPN
ma-27	474	20	γ3[1−	γ3[1−	PROPN
ma-27	474	21	(	(	PUNCT
ma-27	474	22	1−	1−	NUM
ma-27	474	23	γ)δsβs	γ)δsβs	PRON
ma-27	474	24	]	]	X
ma-27	475	1	‖`s	‖`s	PROPN
ma-27	475	2	−	−	PROPN
ma-27	475	3	˜̀	˜̀	NOUN
ma-27	475	4	s‖+	s‖+	NOUN
ma-27	475	5	γ2(1−	γ2(1−	PROPN
ma-27	475	6	δs)l‖`s	δs)l‖`s	PROPN
ma-27	475	7	−	−	PROPN
ma-27	475	8	t`s‖	t`s‖	NOUN
ma-27	476	1	+	+	NOUN
ma-27	476	2	γ2(1−	γ2(1−	PROPN
ma-27	476	3	δs)ε+	δs)ε+	NOUN
ma-27	476	4	γ3δsβsl‖`s	γ3δsβsl‖`s	NOUN
ma-27	476	5	−	−	ADP
ma-27	476	6	t`s‖+	t`s‖+	ADJ
ma-27	476	7	γ3δsβsε	γ3δsβsε	NOUN
ma-27	476	8	+	+	NOUN
ma-27	476	9	γl‖ws	γl‖ws	PUNCT
ma-27	476	10	−	−	NOUN
ma-27	476	11	tws‖+	tws‖+	NOUN
ma-27	476	12	γε+	γε+	NOUN
ma-27	477	1	l‖ζs	l‖ζs	DET
ma-27	477	2	−	−	NOUN
ma-27	477	3	tζs‖+	tζs‖+	NOUN
ma-27	477	4	ε	ε	PROPN
ma-27	477	5	.	.	PUNCT
ma-27	477	6	(	(	PUNCT
ma-27	477	7	7.8	7.8	NUM
ma-27	477	8	)	)	PUNCT
ma-27	477	9	since	since	SCONJ
ma-27	477	10	γ	γ	X
ma-27	477	11	,	,	PUNCT
ma-27	477	12	γ2	γ2	PROPN
ma-27	477	13	,	,	PUNCT
ma-27	477	14	γ3	γ3	NOUN
ma-27	477	15	∈	∈	PROPN
ma-27	477	16	(	(	PUNCT
ma-27	477	17	0	0	NUM
ma-27	477	18	,	,	PUNCT
ma-27	477	19	1	1	NUM
ma-27	477	20	)	)	PUNCT
ma-27	477	21	and	and	CCONJ
ma-27	477	22	δs	δs	NOUN
ma-27	477	23	,	,	PUNCT
ma-27	477	24	βs	βs	X
ma-27	477	25	∈	∈	PROPN
ma-27	478	1	[	[	X
ma-27	478	2	0	0	NUM
ma-27	478	3	,	,	PUNCT
ma-27	478	4	1	1	NUM
ma-27	478	5	]	]	PUNCT
ma-27	478	6	,	,	PUNCT
ma-27	478	7	then	then	ADV
ma-27	478	8	(	(	PUNCT
ma-27	478	9	7.8	7.8	NUM
ma-27	478	10	)	)	PUNCT
ma-27	478	11	becomes	become	VERB
ma-27	478	12	‖`s+1	‖`s+1	ADJ
ma-27	478	13	−	−	PROPN
ma-27	478	14	˜̀	˜̀	PROPN
ma-27	478	15	s+1‖	s+1‖	PROPN
ma-27	478	16	≤	≤	X
ma-27	479	1	[	[	X
ma-27	479	2	1−	1−	NUM
ma-27	479	3	(	(	PUNCT
ma-27	479	4	1−	1−	NUM
ma-27	479	5	γ)δsβs	γ)δsβs	NOUN
ma-27	479	6	]	]	X
ma-27	479	7	‖`s	‖`s	PROPN
ma-27	479	8	−	−	PROPN
ma-27	479	9	˜̀	˜̀	NOUN
ma-27	479	10	s‖+	s‖+	X
ma-27	479	11	l‖`s	l‖`	VERB
ma-27	479	12	−	−	PRON
ma-27	479	13	t`s‖	t`s‖	NOUN
ma-27	480	1	+	+	NOUN
ma-27	480	2	δsβsl‖`s	δsβsl‖`s	PROPN
ma-27	480	3	−	−	NOUN
ma-27	480	4	t`s‖+	t`s‖+	ADJ
ma-27	480	5	l‖ws	l‖ws	PROPN
ma-27	480	6	−	−	PROPN
ma-27	480	7	tws‖	tws‖	NOUN
ma-27	480	8	+	+	PUNCT
ma-27	480	9	l‖ζs	l‖ζs	DET
ma-27	480	10	−	−	NOUN
ma-27	480	11	tζs‖+	tζs‖+	NOUN
ma-27	480	12	δsβsε+	δsβsε+	ADP
ma-27	480	13	3ε	3ε	NUM
ma-27	480	14	.	.	PUNCT
ma-27	481	1	(	(	PUNCT
ma-27	481	2	7.9	7.9	NUM
ma-27	481	3	)	)	PUNCT
ma-27	481	4	by	by	ADP
ma-27	481	5	our	our	PRON
ma-27	481	6	assumption	assumption	NOUN
ma-27	481	7	(	(	PUNCT
ma-27	481	8	i	i	NOUN
ma-27	481	9	)	)	PUNCT
ma-27	481	10	that	that	SCONJ
ma-27	481	11	12	12	NUM
ma-27	481	12	≤	≤	NUM
ma-27	481	13	δsβs	δsβs	ADV
ma-27	481	14	,	,	PUNCT
ma-27	481	15	we	we	PRON
ma-27	481	16	have	have	VERB
ma-27	481	17	1−	1−	NUM
ma-27	481	18	δsβs	δsβs	PROPN
ma-27	481	19	≤	≤	NUM
ma-27	481	20	δsβs	δsβs	ADJ
ma-27	481	21	⇒	⇒	NOUN
ma-27	481	22	1	1	NUM
ma-27	481	23	=	=	SYM
ma-27	481	24	1−	1−	NUM
ma-27	481	25	δsβs	δsβs	NOUN
ma-27	482	1	+	+	NUM
ma-27	482	2	δsβs	δsβs	ADJ
ma-27	482	3	≤	≤	NUM
ma-27	482	4	δsβs	δsβs	NOUN
ma-27	483	1	+	+	CCONJ
ma-27	483	2	δsβs	δsβs	ADJ
ma-27	483	3	=	=	SYM
ma-27	483	4	2δsβs	2δsβs	NUM
ma-27	483	5	.	.	PUNCT
ma-27	484	1	eur	eur	PROPN
ma-27	484	2	.	.	PUNCT
ma-27	485	1	j.	j.	PROPN
ma-27	485	2	math	math	PROPN
ma-27	485	3	.	.	PUNCT
ma-27	486	1	anal	anal	ADJ
ma-27	486	2	.	.	PUNCT
ma-27	487	1	1	1	NUM
ma-27	487	2	(	(	PUNCT
ma-27	487	3	2021	2021	NUM
ma-27	487	4	)	)	PUNCT
ma-27	488	1	126this	126this	PROPN
ma-27	488	2	yields	yield	VERB
ma-27	488	3	‖`s+1	‖`s+1	ADJ
ma-27	488	4	−	−	PROPN
ma-27	488	5	˜̀	˜̀	PROPN
ma-27	488	6	s+1‖	s+1‖	PROPN
ma-27	488	7	≤	≤	X
ma-27	489	1	[	[	X
ma-27	489	2	1−	1−	NUM
ma-27	489	3	(	(	PUNCT
ma-27	489	4	1−	1−	NUM
ma-27	489	5	γ)δsβs	γ)δsβs	NOUN
ma-27	489	6	]	]	X
ma-27	489	7	‖`s	‖`s	PROPN
ma-27	489	8	−	−	PROPN
ma-27	489	9	˜̀	˜̀	NOUN
ma-27	489	10	s‖+	s‖+	VERB
ma-27	489	11	3δsβsl‖`s	3δsβsl‖`s	NUM
ma-27	489	12	−	−	NOUN
ma-27	489	13	t`s‖	t`s‖	NOUN
ma-27	489	14	+2δsβsl‖ws	+2δsβsl‖ws	ADJ
ma-27	489	15	−	−	PROPN
ma-27	489	16	tws‖+	tws‖+	NOUN
ma-27	489	17	2δsβsl‖ζs	2δsβsl‖ζs	NUM
ma-27	489	18	−	−	NOUN
ma-27	489	19	tζs‖+	tζs‖+	NOUN
ma-27	489	20	7δsβsε	7δsβsε	NUM
ma-27	489	21	=	=	SYM
ma-27	489	22	(	(	PUNCT
ma-27	489	23	1−	1−	NUM
ma-27	489	24	(	(	PUNCT
ma-27	489	25	1−	1−	NUM
ma-27	489	26	γ)δsβs)‖`s	γ)δsβs)‖`s	PROPN
ma-27	489	27	−	−	PROPN
ma-27	489	28	˜̀	˜̀	NOUN
ma-27	489	29	s‖	s‖	NOUN
ma-27	489	30	+	+	ADJ
ma-27	489	31	δsβs(1−	δsβs(1−	PROPN
ma-27	489	32	γ)×	γ)×	SYM
ma-27	489	33	{	{	PUNCT
ma-27	489	34	3l‖`s	3l‖`s	NUM
ma-27	489	35	−	−	NOUN
ma-27	489	36	t`s‖+	t`s‖+	ADJ
ma-27	489	37	2l‖ws	2l‖ws	NUM
ma-27	489	38	−	−	PROPN
ma-27	489	39	tws‖	tws‖	PUNCT
ma-27	489	40	(	(	PUNCT
ma-27	489	41	1−	1−	NUM
ma-27	489	42	γ	γ	X
ma-27	489	43	)	)	PUNCT
ma-27	489	44	+	+	NUM
ma-27	489	45	2l‖ζs	2l‖ζs	NUM
ma-27	489	46	−	−	NOUN
ma-27	489	47	tζs‖+	tζs‖+	NOUN
ma-27	489	48	7ε	7ε	NOUN
ma-27	489	49	(	(	PUNCT
ma-27	489	50	1−	1−	NUM
ma-27	489	51	γ	γ	NOUN
ma-27	489	52	)	)	PUNCT
ma-27	489	53	}	}	PUNCT
ma-27	489	54	.	.	PUNCT
ma-27	490	1	(	(	PUNCT
ma-27	490	2	7.10	7.10	NUM
ma-27	490	3	)	)	PUNCT
ma-27	490	4	set	set	NOUN
ma-27	490	5	θs	θs	X
ma-27	490	6	=	=	PUNCT
ma-27	490	7	‖`s	‖`s	PROPN
ma-27	491	1	−	−	NOUN
ma-27	491	2	˜̀	˜̀	NOUN
ma-27	491	3	s‖	s‖	NOUN
ma-27	491	4	σs	σs	ADP
ma-27	491	5	=	=	PUNCT
ma-27	491	6	(	(	PUNCT
ma-27	491	7	1−	1−	NUM
ma-27	491	8	γ)δsβs	γ)δsβs	NOUN
ma-27	491	9	∈	∈	PROPN
ma-27	491	10	(	(	PUNCT
ma-27	491	11	0	0	NUM
ma-27	491	12	,	,	PUNCT
ma-27	491	13	1	1	NUM
ma-27	491	14	)	)	PUNCT
ma-27	491	15	λs	λs	NOUN
ma-27	492	1	=	=	PUNCT
ma-27	493	1	{	{	PUNCT
ma-27	493	2	3l‖`s	3l‖`s	NUM
ma-27	493	3	−	−	NOUN
ma-27	493	4	t`s‖+	t`s‖+	ADJ
ma-27	493	5	2l‖ws	2l‖ws	NUM
ma-27	493	6	−	−	NOUN
ma-27	493	7	tws‖+	tws‖+	PROPN
ma-27	493	8	2l‖ζs	2l‖ζs	NUM
ma-27	493	9	−	−	NOUN
ma-27	493	10	tζs‖+	tζs‖+	NOUN
ma-27	493	11	7ε	7ε	NOUN
ma-27	493	12	(	(	PUNCT
ma-27	493	13	1−	1−	NUM
ma-27	493	14	γ	γ	NOUN
ma-27	493	15	)	)	PUNCT
ma-27	493	16	}	}	PUNCT
ma-27	493	17	from	from	ADP
ma-27	493	18	theorem	theorem	ADJ
ma-27	493	19	3.1	3.1	NUM
ma-27	493	20	,	,	PUNCT
ma-27	493	21	we	we	PRON
ma-27	493	22	know	know	VERB
ma-27	493	23	that	that	SCONJ
ma-27	493	24	lim	lim	PROPN
ma-27	493	25	s→∞	s→∞	PRON
ma-27	493	26	`	`	PUNCT
ma-27	493	27	s	s	VERB
ma-27	493	28	=	=	NOUN
ma-27	493	29	z	z	NOUN
ma-27	493	30	and	and	CCONJ
ma-27	493	31	since	since	SCONJ
ma-27	493	32	tz	tz	PROPN
ma-27	493	33	=	=	SYM
ma-27	493	34	z	z	PROPN
ma-27	493	35	,	,	PUNCT
ma-27	493	36	it	it	PRON
ma-27	493	37	follows	follow	VERB
ma-27	493	38	that	that	SCONJ
ma-27	493	39	lim	lim	PROPN
ma-27	493	40	s→∞	s→∞	PROPN
ma-27	494	1	‖`s	‖`s	PROPN
ma-27	494	2	−	−	NOUN
ma-27	494	3	t`s‖	t`s‖	NOUN
ma-27	495	1	=	=	SYM
ma-27	495	2	lim	lim	PROPN
ma-27	495	3	s→∞	s→∞	PROPN
ma-27	495	4	‖ws	‖ws	NUM
ma-27	495	5	−	−	PROPN
ma-27	495	6	tws‖	tws‖	PUNCT
ma-27	495	7	=	=	SYM
ma-27	495	8	lim	lim	PROPN
ma-27	495	9	s→∞	s→∞	NOUN
ma-27	496	1	‖ζs	‖ζs	PROPN
ma-27	496	2	−	−	PROPN
ma-27	496	3	gζs‖	gζs‖	NOUN
ma-27	496	4	=	=	NOUN
ma-27	496	5	0	0	X
ma-27	496	6	.	.	PUNCT
ma-27	496	7	using	use	VERB
ma-27	496	8	lemma	lemma	PROPN
ma-27	496	9	2.13	2.13	NUM
ma-27	496	10	,	,	PUNCT
ma-27	496	11	we	we	PRON
ma-27	496	12	get	get	VERB
ma-27	496	13	0	0	NUM
ma-27	496	14	≤	≤	NOUN
ma-27	496	15	lim	lim	PROPN
ma-27	496	16	sup	sup	NOUN
ma-27	496	17	s→∞	s→∞	NUM
ma-27	496	18	‖`s	‖`s	PRON
ma-27	497	1	−	−	NOUN
ma-27	497	2	˜̀	˜̀	NOUN
ma-27	497	3	s‖	s‖	NOUN
ma-27	497	4	≤	≤	NUM
ma-27	497	5	lim	lim	PROPN
ma-27	497	6	sup	sup	PROPN
ma-27	497	7	s→∞	s→∞	NUM
ma-27	497	8	7ε	7ε	NOUN
ma-27	497	9	(	(	PUNCT
ma-27	497	10	1−	1−	NUM
ma-27	497	11	γ	γ	NOUN
ma-27	497	12	)	)	PUNCT
ma-27	497	13	.	.	PUNCT
ma-27	498	1	(	(	PUNCT
ma-27	498	2	7.11	7.11	NUM
ma-27	498	3	)	)	PUNCT
ma-27	498	4	since	since	SCONJ
ma-27	498	5	by	by	ADP
ma-27	498	6	theorem	theorem	NOUN
ma-27	498	7	3.1	3.1	NUM
ma-27	498	8	,	,	PUNCT
ma-27	498	9	we	we	PRON
ma-27	498	10	have	have	VERB
ma-27	498	11	that	that	DET
ma-27	498	12	lim	lim	PROPN
ma-27	498	13	s→∞	s→∞	PRON
ma-27	498	14	`	`	PUNCT
ma-27	498	15	s	s	VERB
ma-27	498	16	=	=	NOUN
ma-27	498	17	z	z	NOUN
ma-27	498	18	and	and	CCONJ
ma-27	498	19	from	from	ADP
ma-27	498	20	our	our	PRON
ma-27	498	21	hypothesis	hypothesis	NOUN
ma-27	498	22	lim	lim	NOUN
ma-27	498	23	s→∞	s→∞	PROPN
ma-27	498	24	˜̀	˜̀	NOUN
ma-27	498	25	s	s	PART
ma-27	498	26	=	=	SYM
ma-27	498	27	z̃	z̃	PROPN
ma-27	498	28	,	,	PUNCT
ma-27	499	1	it	it	PRON
ma-27	499	2	followsfrom	followsfrom	VERB
ma-27	499	3	(	(	PUNCT
ma-27	499	4	7.11	7.11	NUM
ma-27	499	5	)	)	PUNCT
ma-27	499	6	that	that	SCONJ
ma-27	499	7	‖z	‖z	NOUN
ma-27	499	8	−	−	NOUN
ma-27	499	9	z̃‖	z̃‖	NUM
ma-27	499	10	≤	≤	NUM
ma-27	499	11	7ε	7ε	NOUN
ma-27	499	12	(	(	PUNCT
ma-27	499	13	1−	1−	NUM
ma-27	499	14	γ	γ	NOUN
ma-27	499	15	)	)	PUNCT
ma-27	499	16	.	.	PUNCT
ma-27	500	1	this	this	PRON
ma-27	500	2	completes	complete	VERB
ma-27	500	3	the	the	DET
ma-27	500	4	proof	proof	NOUN
ma-27	500	5	.	.	PUNCT
ma-27	501	1	�	�	PROPN
ma-27	501	2	8	8	NUM
ma-27	501	3	.	.	PUNCT
ma-27	502	1	some	some	DET
ma-27	502	2	applications	application	NOUN
ma-27	502	3	in	in	ADP
ma-27	502	4	this	this	DET
ma-27	502	5	section	section	NOUN
ma-27	502	6	,	,	PUNCT
ma-27	502	7	we	we	PRON
ma-27	502	8	will	will	AUX
ma-27	502	9	prove	prove	VERB
ma-27	502	10	that	that	SCONJ
ma-27	502	11	the	the	DET
ma-27	502	12	sequence	sequence	NOUN
ma-27	502	13	generated	generate	VERB
ma-27	502	14	by	by	ADP
ma-27	502	15	our	our	PRON
ma-27	502	16	new	new	ADJ
ma-27	502	17	iterative	iterative	NOUN
ma-27	502	18	algorithm	algorithm	NOUN
ma-27	502	19	(	(	PUNCT
ma-27	502	20	1.7)converges	1.7)converge	NOUN
ma-27	502	21	strongly	strongly	ADV
ma-27	502	22	to	to	ADP
ma-27	502	23	solutions	solution	NOUN
ma-27	502	24	of	of	ADP
ma-27	502	25	the	the	DET
ma-27	502	26	constrained	constrain	VERB
ma-27	502	27	convex	convex	NOUN
ma-27	502	28	minimization	minimization	NOUN
ma-27	502	29	problem	problem	NOUN
ma-27	502	30	and	and	CCONJ
ma-27	502	31	split	split	VERB
ma-27	502	32	feasibilityproblem.now	feasibilityproblem.now	NOUN
ma-27	502	33	,	,	PUNCT
ma-27	502	34	we	we	PRON
ma-27	502	35	present	present	VERB
ma-27	502	36	the	the	DET
ma-27	502	37	definitions	definition	NOUN
ma-27	502	38	of	of	ADP
ma-27	502	39	some	some	DET
ma-27	502	40	operators	operator	NOUN
ma-27	502	41	that	that	PRON
ma-27	502	42	will	will	AUX
ma-27	502	43	we	we	PRON
ma-27	502	44	be	be	AUX
ma-27	502	45	important	important	ADJ
ma-27	502	46	in	in	ADP
ma-27	502	47	proving	prove	VERB
ma-27	502	48	our	our	PRON
ma-27	502	49	mainresults	mainresult	NOUN
ma-27	502	50	.	.	PUNCT
ma-27	503	1	let	let	VERB
ma-27	503	2	h	h	PRON
ma-27	503	3	be	be	AUX
ma-27	503	4	a	a	DET
ma-27	503	5	hilbert	hilbert	NOUN
ma-27	503	6	space	space	NOUN
ma-27	503	7	and	and	CCONJ
ma-27	503	8	let	let	VERB
ma-27	503	9	c	c	PRON
ma-27	503	10	be	be	AUX
ma-27	503	11	a	a	DET
ma-27	503	12	nonempty	nonempty	ADV
ma-27	503	13	closed	close	VERB
ma-27	503	14	and	and	CCONJ
ma-27	503	15	convex	convex	PROPN
ma-27	503	16	subset	subset	NOUN
ma-27	503	17	of	of	ADP
ma-27	503	18	h.	h.	PROPN
ma-27	503	19	definition	definition	NOUN
ma-27	503	20	8.1	8.1	NUM
ma-27	503	21	.	.	PUNCT
ma-27	504	1	let	let	VERB
ma-27	504	2	t	t	NOUN
ma-27	504	3	:	:	PUNCT
ma-27	504	4	c	c	X
ma-27	504	5	→	→	PUNCT
ma-27	504	6	c	c	X
ma-27	504	7	be	be	AUX
ma-27	504	8	a	a	DET
ma-27	504	9	mapping	mapping	NOUN
ma-27	504	10	.	.	PUNCT
ma-27	505	1	then	then	ADV
ma-27	505	2	t	t	PROPN
ma-27	505	3	is	be	AUX
ma-27	505	4	said	say	VERB
ma-27	505	5	to	to	ADP
ma-27	505	6	be:(i	be:(i	NOUN
ma-27	505	7	)	)	PUNCT
ma-27	506	1	nonexpansive	nonexpansive	PROPN
ma-27	506	2	,	,	PUNCT
ma-27	506	3	if	if	SCONJ
ma-27	506	4	‖t`−	‖t`−	PUNCT
ma-27	506	5	tζ‖	tζ‖	PROPN
ma-27	506	6	≤	≤	NOUN
ma-27	506	7	‖`−	‖`−	NUM
ma-27	506	8	ζ‖	ζ‖	NOUN
ma-27	506	9	,	,	PUNCT
ma-27	506	10	for	for	ADP
ma-27	506	11	all	all	DET
ma-27	506	12	`	`	PUNCT
ma-27	506	13	,	,	PUNCT
ma-27	506	14	ζ	ζ	PROPN
ma-27	506	15	∈	∈	PROPN
ma-27	506	16	c	c	X
ma-27	506	17	;	;	PUNCT
ma-27	506	18	eur	eur	PROPN
ma-27	506	19	.	.	PUNCT
ma-27	507	1	j.	j.	PROPN
ma-27	507	2	math	math	PROPN
ma-27	507	3	.	.	PUNCT
ma-27	508	1	anal	anal	ADJ
ma-27	508	2	.	.	PUNCT
ma-27	509	1	1	1	NUM
ma-27	509	2	(	(	PUNCT
ma-27	509	3	2021	2021	NUM
ma-27	509	4	)	)	PUNCT
ma-27	509	5	127(ii	127(ii	NUM
ma-27	509	6	)	)	PUNCT
ma-27	509	7	lipschitz	lipschitz	NOUN
ma-27	509	8	continuous	continuous	ADJ
ma-27	509	9	,	,	PUNCT
ma-27	509	10	if	if	SCONJ
ma-27	509	11	there	there	PRON
ma-27	509	12	exists	exist	VERB
ma-27	509	13	l	l	NOUN
ma-27	509	14	>	>	X
ma-27	509	15	0	0	PUNCT
ma-27	510	1	such	such	ADJ
ma-27	510	2	‖t`−	‖t`−	NUM
ma-27	510	3	tζ‖	tζ‖	PROPN
ma-27	510	4	≤	≤	X
ma-27	510	5	l‖`−	l‖`−	PUNCT
ma-27	510	6	ζ‖	ζ‖	NOUN
ma-27	510	7	,	,	PUNCT
ma-27	510	8	for	for	ADP
ma-27	510	9	all	all	PRON
ma-27	510	10	`	`	PUNCT
ma-27	510	11	,	,	PUNCT
ma-27	510	12	ζ	ζ	PROPN
ma-27	510	13	∈	∈	NOUN
ma-27	510	14	c	c	X
ma-27	510	15	;	;	PUNCT
ma-27	510	16	(	(	PUNCT
ma-27	510	17	iii	iii	X
ma-27	510	18	)	)	PUNCT
ma-27	510	19	monotone	monotone	NOUN
ma-27	510	20	if	if	SCONJ
ma-27	510	21	,	,	PUNCT
ma-27	510	22	〈	〈	PROPN
ma-27	510	23	t`−	t`−	NOUN
ma-27	510	24	tζ	tζ	ADP
ma-27	510	25	,	,	PUNCT
ma-27	510	26	`	`	PUNCT
ma-27	510	27	−	−	PUNCT
ma-27	510	28	ζ	ζ	PROPN
ma-27	510	29	〉	〉	PROPN
ma-27	510	30	≥	≥	NOUN
ma-27	510	31	0	0	NUM
ma-27	510	32	,	,	PUNCT
ma-27	510	33	for	for	ADP
ma-27	510	34	all	all	DET
ma-27	510	35	`	`	PUNCT
ma-27	510	36	,	,	PUNCT
ma-27	510	37	ζ	ζ	PROPN
ma-27	510	38	∈	∈	NOUN
ma-27	510	39	c	c	NOUN
ma-27	510	40	;	;	PUNCT
ma-27	510	41	(	(	PUNCT
ma-27	510	42	8.1	8.1	NUM
ma-27	510	43	)	)	PUNCT
ma-27	510	44	(	(	PUNCT
ma-27	510	45	iv	iv	X
ma-27	510	46	)	)	PUNCT
ma-27	510	47	$	$	SYM
ma-27	510	48	-strongly	-strongly	ADV
ma-27	510	49	monotone	monotone	ADJ
ma-27	510	50	if	if	SCONJ
ma-27	510	51	there	there	PRON
ma-27	510	52	exists	exist	VERB
ma-27	510	53	$	$	SYM
ma-27	510	54	>	>	PUNCT
ma-27	510	55	0	0	NUM
ma-27	510	56	,	,	PUNCT
ma-27	510	57	such	such	ADJ
ma-27	510	58	that	that	SCONJ
ma-27	510	59	〈	〈	PROPN
ma-27	510	60	`	`	PUNCT
ma-27	510	61	−	−	PROPN
ma-27	510	62	ζ	ζ	PROPN
ma-27	510	63	,	,	PUNCT
ma-27	510	64	t	t	NOUN
ma-27	510	65	`	`	PUNCT
ma-27	510	66	−	−	PROPN
ma-27	510	67	tζ	tζ	INTJ
ma-27	510	68	〉	〉	PROPN
ma-27	510	69	≥	≥	NOUN
ma-27	510	70	$	$	SYM
ma-27	510	71	‖`−	‖`−	NUM
ma-27	510	72	ζ‖	ζ‖	NOUN
ma-27	510	73	,	,	PUNCT
ma-27	510	74	for	for	ADP
ma-27	510	75	all	all	DET
ma-27	510	76	`	`	PUNCT
ma-27	510	77	,	,	PUNCT
ma-27	510	78	ζ	ζ	PROPN
ma-27	510	79	∈	∈	PROPN
ma-27	510	80	c.	c.	NOUN
ma-27	510	81	(	(	PUNCT
ma-27	510	82	8.2	8.2	NUM
ma-27	510	83	)	)	PUNCT
ma-27	510	84	for	for	ADP
ma-27	510	85	any	any	DET
ma-27	510	86	`	`	PUNCT
ma-27	510	87	∈	∈	PROPN
ma-27	510	88	h	h	NOUN
ma-27	510	89	,	,	PUNCT
ma-27	510	90	we	we	PRON
ma-27	510	91	define	define	VERB
ma-27	510	92	the	the	DET
ma-27	510	93	map	map	NOUN
ma-27	510	94	pc	pc	NOUN
ma-27	510	95	:	:	PUNCT
ma-27	510	96	h	h	NOUN
ma-27	510	97	→	→	SYM
ma-27	510	98	c	c	NOUN
ma-27	510	99	satisfying	satisfy	VERB
ma-27	510	100	‖`−	‖`−	NUM
ma-27	510	101	pc`‖	pc`‖	NOUN
ma-27	510	102	≤	≤	NOUN
ma-27	510	103	‖`−	‖`−	NUM
ma-27	510	104	ζ‖	ζ‖	NOUN
ma-27	510	105	,	,	PUNCT
ma-27	510	106	for	for	ADP
ma-27	510	107	all	all	DET
ma-27	510	108	ζ	ζ	PROPN
ma-27	510	109	∈	∈	PROPN
ma-27	510	110	c.	c.	NOUN
ma-27	510	111	pc	pc	NOUN
ma-27	510	112	is	be	AUX
ma-27	510	113	called	call	VERB
ma-27	510	114	the	the	DET
ma-27	510	115	metric	metric	ADJ
ma-27	510	116	projection	projection	NOUN
ma-27	510	117	of	of	ADP
ma-27	510	118	h	h	NOUN
ma-27	510	119	onto	onto	ADP
ma-27	510	120	c.	c.	NOUN
ma-27	510	121	it	it	PRON
ma-27	510	122	is	be	AUX
ma-27	510	123	well	well	ADV
ma-27	510	124	known	know	VERB
ma-27	510	125	that	that	SCONJ
ma-27	510	126	pc	pc	NOUN
ma-27	510	127	is	be	AUX
ma-27	510	128	nonexpansive	nonexpansive	ADJ
ma-27	510	129	.	.	PUNCT
ma-27	511	1	8.1	8.1	NUM
ma-27	511	2	.	.	PUNCT
ma-27	512	1	application	application	NOUN
ma-27	512	2	to	to	ADP
ma-27	512	3	constrained	constrain	VERB
ma-27	512	4	convex	convex	NOUN
ma-27	512	5	minimization	minimization	NOUN
ma-27	512	6	problem.consider	problem.consider	NUM
ma-27	512	7	the	the	DET
ma-27	512	8	following	follow	VERB
ma-27	512	9	constrained	constrain	VERB
ma-27	512	10	convex	convex	NOUN
ma-27	512	11	minimization	minimization	NOUN
ma-27	512	12	problem	problem	NOUN
ma-27	512	13	:	:	PUNCT
ma-27	512	14	minimize	minimize	VERB
ma-27	512	15	{	{	PUNCT
ma-27	512	16	f	f	X
ma-27	512	17	(	(	PUNCT
ma-27	512	18	`	`	PUNCT
ma-27	512	19	)	)	PUNCT
ma-27	512	20	:	:	PUNCT
ma-27	512	21	`	`	PUNCT
ma-27	512	22	∈	∈	NOUN
ma-27	512	23	c	c	NOUN
ma-27	512	24	}	}	PUNCT
ma-27	512	25	,	,	PUNCT
ma-27	512	26	(	(	PUNCT
ma-27	512	27	8.3	8.3	NUM
ma-27	512	28	)	)	PUNCT
ma-27	512	29	where	where	SCONJ
ma-27	512	30	f	f	NOUN
ma-27	512	31	:	:	PUNCT
ma-27	512	32	c	c	X
ma-27	512	33	→	→	PUNCT
ma-27	512	34	r	r	NOUN
ma-27	512	35	is	be	AUX
ma-27	512	36	a	a	DET
ma-27	512	37	real	real	ADV
ma-27	512	38	-	-	PUNCT
ma-27	512	39	valued	value	VERB
ma-27	512	40	function	function	NOUN
ma-27	512	41	.	.	PUNCT
ma-27	513	1	the	the	DET
ma-27	513	2	minimization	minimization	NOUN
ma-27	513	3	problem	problem	NOUN
ma-27	513	4	(	(	PUNCT
ma-27	513	5	8.3	8.3	NUM
ma-27	513	6	)	)	PUNCT
ma-27	513	7	is	be	AUX
ma-27	513	8	consistent	consistent	ADJ
ma-27	513	9	if	if	SCONJ
ma-27	513	10	it	it	PRON
ma-27	513	11	hasa	hasa	VERB
ma-27	513	12	solution	solution	NOUN
ma-27	513	13	.	.	PUNCT
ma-27	514	1	throughout	throughout	ADP
ma-27	514	2	this	this	DET
ma-27	514	3	paper	paper	NOUN
ma-27	514	4	,	,	PUNCT
ma-27	514	5	we	we	PRON
ma-27	514	6	shall	shall	AUX
ma-27	514	7	use	use	VERB
ma-27	514	8	γ	γ	NOUN
ma-27	514	9	to	to	PART
ma-27	514	10	stand	stand	VERB
ma-27	514	11	for	for	ADP
ma-27	514	12	the	the	DET
ma-27	514	13	solution	solution	NOUN
ma-27	514	14	set	set	VERB
ma-27	514	15	of	of	ADP
ma-27	514	16	the	the	DET
ma-27	514	17	problem(8.3	problem(8.3	NOUN
ma-27	514	18	)	)	PUNCT
ma-27	514	19	.	.	PUNCT
ma-27	515	1	it	it	PRON
ma-27	515	2	is	be	AUX
ma-27	515	3	worthy	worthy	ADJ
ma-27	515	4	noting	note	VERB
ma-27	515	5	that	that	SCONJ
ma-27	515	6	f	f	PROPN
ma-27	515	7	is	be	AUX
ma-27	515	8	(	(	PUNCT
ma-27	515	9	fréchect	fréchect	NOUN
ma-27	515	10	)	)	PUNCT
ma-27	515	11	differentiable	differentiable	PROPN
ma-27	515	12	,	,	PUNCT
ma-27	515	13	the	the	DET
ma-27	515	14	gradient	gradient	NOUN
ma-27	515	15	-	-	PUNCT
ma-27	515	16	projection	projection	NOUN
ma-27	515	17	method	method	NOUN
ma-27	515	18	(	(	PUNCT
ma-27	515	19	gpm)generates	gpm)generate	VERB
ma-27	515	20	a	a	DET
ma-27	515	21	sequence	sequence	NOUN
ma-27	515	22	{	{	PUNCT
ma-27	515	23	`	`	PUNCT
ma-27	515	24	s	s	X
ma-27	515	25	}	}	PUNCT
ma-27	515	26	by	by	ADP
ma-27	515	27	using	use	VERB
ma-27	515	28	the	the	DET
ma-27	515	29	recursive	recursive	ADJ
ma-27	515	30	formula	formula	NOUN
ma-27	515	31	:	:	PUNCT
ma-27	515	32	{	{	PUNCT
ma-27	515	33	`	`	PUNCT
ma-27	515	34	0	0	NUM
ma-27	515	35	∈	∈	PROPN
ma-27	515	36	c	c	NOUN
ma-27	515	37	,	,	PUNCT
ma-27	515	38	`	`	PUNCT
ma-27	515	39	s+1	s+1	PRON
ma-27	515	40	=	=	PUNCT
ma-27	515	41	pc(`s	pc(`s	PROPN
ma-27	515	42	−	−	PROPN
ma-27	515	43	λ∇f	λ∇f	INTJ
ma-27	515	44	(	(	PUNCT
ma-27	515	45	`	`	PUNCT
ma-27	515	46	s	s	NOUN
ma-27	515	47	)	)	PUNCT
ma-27	515	48	)	)	PUNCT
ma-27	515	49	,	,	PUNCT
ma-27	515	50	for	for	SCONJ
ma-27	515	51	all	all	DET
ma-27	515	52	s	s	PART
ma-27	515	53	≥	≥	NOUN
ma-27	515	54	1	1	NUM
ma-27	515	55	.	.	PUNCT
ma-27	516	1	(	(	PUNCT
ma-27	516	2	8.4	8.4	NUM
ma-27	516	3	)	)	PUNCT
ma-27	516	4	in	in	ADP
ma-27	516	5	more	more	ADJ
ma-27	516	6	general	general	ADJ
ma-27	516	7	form	form	NOUN
ma-27	516	8	,	,	PUNCT
ma-27	516	9	(	(	PUNCT
ma-27	516	10	8.4	8.4	NUM
ma-27	516	11	)	)	PUNCT
ma-27	516	12	can	can	AUX
ma-27	516	13	be	be	AUX
ma-27	516	14	written	write	VERB
ma-27	516	15	as	as	ADP
ma-27	516	16	:	:	PUNCT
ma-27	516	17	{	{	PUNCT
ma-27	516	18	`	`	PUNCT
ma-27	516	19	0	0	NUM
ma-27	516	20	∈	∈	PROPN
ma-27	516	21	c	c	NOUN
ma-27	516	22	,	,	PUNCT
ma-27	516	23	`	`	PUNCT
ma-27	516	24	s+1	s+1	PRON
ma-27	516	25	=	=	PUNCT
ma-27	516	26	pc(`s	pc(`s	PROPN
ma-27	516	27	−	−	PROPN
ma-27	517	1	λs∇f	λs∇f	PROPN
ma-27	517	2	(	(	PUNCT
ma-27	517	3	`	`	PUNCT
ma-27	517	4	s	s	X
ma-27	517	5	)	)	PUNCT
ma-27	517	6	)	)	PUNCT
ma-27	517	7	,	,	PUNCT
ma-27	517	8	for	for	ADP
ma-27	517	9	all	all	DET
ma-27	517	10	s	s	PART
ma-27	517	11	≥	≥	NOUN
ma-27	517	12	1	1	NUM
ma-27	517	13	,	,	PUNCT
ma-27	517	14	(	(	PUNCT
ma-27	517	15	8.5	8.5	NUM
ma-27	517	16	)	)	PUNCT
ma-27	517	17	where	where	SCONJ
ma-27	517	18	λ	λ	PROPN
ma-27	517	19	and	and	CCONJ
ma-27	517	20	λs	λs	NOUN
ma-27	517	21	are	be	AUX
ma-27	517	22	positive	positive	ADJ
ma-27	517	23	real	real	ADJ
ma-27	517	24	numbers.it	numbers.it	NOUN
ma-27	517	25	is	be	AUX
ma-27	517	26	well	well	ADV
ma-27	517	27	known	know	VERB
ma-27	517	28	that	that	SCONJ
ma-27	517	29	if	if	SCONJ
ma-27	517	30	∇f	∇f	PROPN
ma-27	517	31	is	be	AUX
ma-27	517	32	$	$	SYM
ma-27	517	33	-strongly	-strongly	ADV
ma-27	517	34	monotone	monotone	ADJ
ma-27	517	35	and	and	CCONJ
ma-27	517	36	l	l	NOUN
ma-27	517	37	-	-	NOUN
ma-27	517	38	lipschitzian	lipschitzian	ADJ
ma-27	517	39	with	with	ADP
ma-27	517	40	$	$	SYM
ma-27	517	41	,	,	PUNCT
ma-27	517	42	l	l	NOUN
ma-27	517	43	>	>	X
ma-27	517	44	0	0	NUM
ma-27	517	45	,	,	PUNCT
ma-27	517	46	then	then	ADV
ma-27	517	47	theoperator	theoperator	NOUN
ma-27	517	48	t	t	PROPN
ma-27	517	49	=	=	PUNCT
ma-27	517	50	pc(i	pc(i	NUM
ma-27	517	51	−	−	PROPN
ma-27	517	52	λ∇f	λ∇f	PROPN
ma-27	517	53	)	)	PUNCT
ma-27	517	54	(	(	PUNCT
ma-27	517	55	8.6	8.6	NUM
ma-27	517	56	)	)	PUNCT
ma-27	517	57	is	be	AUX
ma-27	517	58	a	a	DET
ma-27	517	59	contraction	contraction	NOUN
ma-27	517	60	;	;	PUNCT
ma-27	517	61	thus	thus	ADV
ma-27	517	62	the	the	DET
ma-27	517	63	sequence	sequence	NOUN
ma-27	517	64	{	{	PUNCT
ma-27	517	65	`	`	PUNCT
ma-27	517	66	s	s	X
ma-27	517	67	}	}	PUNCT
ma-27	517	68	in	in	ADP
ma-27	517	69	(	(	PUNCT
ma-27	517	70	8.4	8.4	NUM
ma-27	517	71	)	)	PUNCT
ma-27	517	72	converges	converge	NOUN
ma-27	517	73	in	in	ADP
ma-27	517	74	norm	norm	NOUN
ma-27	517	75	to	to	ADP
ma-27	517	76	the	the	DET
ma-27	517	77	unique	unique	ADJ
ma-27	517	78	minimizer	minimizer	NOUN
ma-27	517	79	of	of	ADP
ma-27	517	80	(	(	PUNCT
ma-27	517	81	8.3).from	8.3).from	NUM
ma-27	517	82	[	[	X
ma-27	517	83	14	14	NUM
ma-27	517	84	,	,	PUNCT
ma-27	517	85	30	30	NUM
ma-27	517	86	]	]	PUNCT
ma-27	517	87	,	,	PUNCT
ma-27	517	88	we	we	PRON
ma-27	517	89	know	know	VERB
ma-27	517	90	that	that	SCONJ
ma-27	517	91	z	z	PROPN
ma-27	517	92	∈	∈	PROPN
ma-27	517	93	c	c	X
ma-27	517	94	solve	solve	VERB
ma-27	517	95	the	the	DET
ma-27	517	96	minimization	minimization	NOUN
ma-27	517	97	problem	problem	NOUN
ma-27	517	98	(	(	PUNCT
ma-27	517	99	8.3	8.3	NUM
ma-27	517	100	)	)	PUNCT
ma-27	518	1	if	if	SCONJ
ma-27	518	2	and	and	CCONJ
ma-27	518	3	only	only	ADV
ma-27	518	4	if	if	SCONJ
ma-27	518	5	z	z	NOUN
ma-27	518	6	solvesthe	solvesthe	VERB
ma-27	518	7	following	follow	VERB
ma-27	518	8	fixed	fix	VERB
ma-27	518	9	point	point	NOUN
ma-27	518	10	equation	equation	NOUN
ma-27	518	11	:	:	PUNCT
ma-27	518	12	z	z	NOUN
ma-27	518	13	=	=	SYM
ma-27	518	14	pc(i	pc(i	NUM
ma-27	518	15	−	−	PROPN
ma-27	518	16	λ∇f	λ∇f	X
ma-27	518	17	)	)	PUNCT
ma-27	518	18	z	z	NOUN
ma-27	518	19	,	,	PUNCT
ma-27	518	20	(	(	PUNCT
ma-27	518	21	8.7	8.7	NUM
ma-27	518	22	)	)	PUNCT
ma-27	518	23	eur	eur	PROPN
ma-27	518	24	.	.	PUNCT
ma-27	519	1	j.	j.	PROPN
ma-27	519	2	math	math	PROPN
ma-27	519	3	.	.	PUNCT
ma-27	520	1	anal	anal	ADJ
ma-27	520	2	.	.	PUNCT
ma-27	521	1	1	1	NUM
ma-27	521	2	(	(	PUNCT
ma-27	521	3	2021	2021	NUM
ma-27	521	4	)	)	PUNCT
ma-27	522	1	128where	128where	PROPN
ma-27	522	2	λ	λ	X
ma-27	522	3	>	>	X
ma-27	522	4	0	0	NUM
ma-27	522	5	is	be	AUX
ma-27	522	6	any	any	DET
ma-27	522	7	fixed	fix	VERB
ma-27	522	8	positive	positive	ADJ
ma-27	522	9	number	number	NOUN
ma-27	522	10	.	.	PUNCT
ma-27	523	1	the	the	DET
ma-27	523	2	operator	operator	NOUN
ma-27	523	3	t	t	NOUN
ma-27	523	4	=	=	PUNCT
ma-27	523	5	pc(i	pc(i	NUM
ma-27	523	6	−	−	PROPN
ma-27	523	7	λ∇f	λ∇f	PROPN
ma-27	523	8	)	)	PUNCT
ma-27	523	9	is	be	AUX
ma-27	523	10	well	well	ADV
ma-27	523	11	known	know	VERB
ma-27	523	12	tobe	tobe	NOUN
ma-27	523	13	nonexpansive	nonexpansive	ADJ
ma-27	523	14	(	(	PUNCT
ma-27	523	15	see	see	VERB
ma-27	523	16	[	[	X
ma-27	523	17	14	14	NUM
ma-27	523	18	,	,	PUNCT
ma-27	523	19	30	30	NUM
ma-27	523	20	]	]	PUNCT
ma-27	523	21	and	and	CCONJ
ma-27	523	22	the	the	DET
ma-27	523	23	references	reference	NOUN
ma-27	523	24	therein	therein	ADV
ma-27	523	25	)	)	PUNCT
ma-27	523	26	.	.	PUNCT
ma-27	524	1	several	several	ADJ
ma-27	524	2	authors	author	NOUN
ma-27	524	3	have	have	AUX
ma-27	524	4	have	have	VERB
ma-27	524	5	considereddifferent	considereddifferent	NOUN
ma-27	524	6	iterative	iterative	NOUN
ma-27	524	7	algorithm	algorithm	NOUN
ma-27	524	8	for	for	ADP
ma-27	524	9	constrained	constrain	VERB
ma-27	524	10	convex	convex	NOUN
ma-27	524	11	minimization	minimization	NOUN
ma-27	524	12	problems	problem	NOUN
ma-27	524	13	(	(	PUNCT
ma-27	524	14	see	see	VERB
ma-27	524	15	[	[	X
ma-27	524	16	4	4	NUM
ma-27	524	17	,	,	PUNCT
ma-27	524	18	9	9	NUM
ma-27	524	19	,	,	PUNCT
ma-27	524	20	13	13	NUM
ma-27	524	21	,	,	PUNCT
ma-27	524	22	19	19	NUM
ma-27	524	23	,	,	PUNCT
ma-27	524	24	34	34	NUM
ma-27	524	25	]	]	X
ma-27	524	26	andthe	andthe	ADJ
ma-27	524	27	references	reference	NOUN
ma-27	524	28	therein	therein	ADV
ma-27	524	29	)	)	PUNCT
ma-27	524	30	.	.	PUNCT
ma-27	525	1	we	we	PRON
ma-27	525	2	now	now	ADV
ma-27	525	3	give	give	VERB
ma-27	525	4	our	our	PRON
ma-27	525	5	main	main	ADJ
ma-27	525	6	results	result	NOUN
ma-27	525	7	theorem	theorem	VERB
ma-27	525	8	8.2	8.2	NUM
ma-27	525	9	.	.	PUNCT
ma-27	526	1	let	let	VERB
ma-27	526	2	c	c	PRON
ma-27	526	3	be	be	AUX
ma-27	526	4	a	a	DET
ma-27	526	5	nonempty	nonempty	ADV
ma-27	526	6	closed	close	VERB
ma-27	526	7	convex	convex	NOUN
ma-27	526	8	subset	subset	NOUN
ma-27	526	9	of	of	ADP
ma-27	526	10	a	a	DET
ma-27	526	11	real	real	ADJ
ma-27	526	12	hilbert	hilbert	NOUN
ma-27	526	13	space	space	NOUN
ma-27	526	14	h.	h.	PROPN
ma-27	526	15	supposed	suppose	VERB
ma-27	526	16	that	that	SCONJ
ma-27	526	17	the	the	DET
ma-27	526	18	minimization	minimization	NOUN
ma-27	526	19	problem	problem	NOUN
ma-27	526	20	(	(	PUNCT
ma-27	526	21	8.3	8.3	NUM
ma-27	526	22	)	)	PUNCT
ma-27	526	23	is	be	AUX
ma-27	526	24	consistent	consistent	ADJ
ma-27	526	25	and	and	CCONJ
ma-27	526	26	let	let	VERB
ma-27	526	27	γ	γ	PRON
ma-27	526	28	denote	denote	VERB
ma-27	526	29	the	the	DET
ma-27	526	30	solution	solution	NOUN
ma-27	526	31	set	set	VERB
ma-27	526	32	.	.	PUNCT
ma-27	527	1	supposed	suppose	VERB
ma-27	527	2	that	that	SCONJ
ma-27	527	3	the	the	DET
ma-27	527	4	gradient	gradient	NOUN
ma-27	527	5	∇f	∇f	PROPN
ma-27	527	6	is	be	AUX
ma-27	527	7	l	l	NOUN
ma-27	527	8	-	-	ADJ
ma-27	527	9	lipschitzian	lipschitzian	ADJ
ma-27	527	10	with	with	ADP
ma-27	527	11	constant	constant	ADJ
ma-27	527	12	l	l	NOUN
ma-27	527	13	>	>	X
ma-27	527	14	0	0	X
ma-27	527	15	.	.	PUNCT
ma-27	528	1	let	let	VERB
ma-27	528	2	{	{	PUNCT
ma-27	528	3	`	`	PUNCT
ma-27	528	4	s	s	AUX
ma-27	528	5	}	}	PUNCT
ma-27	528	6	be	be	AUX
ma-27	528	7	the	the	DET
ma-27	528	8	sequence	sequence	NOUN
ma-27	528	9	generated	generate	VERB
ma-27	528	10	iteratively	iteratively	ADV
ma-27	528	11	by	by	ADP
ma-27	528	12			PROPN
ma-27	528	13	`	`	PUNCT
ma-27	528	14	0	0	NUM
ma-27	528	15	∈	∈	PROPN
ma-27	528	16	c	c	NOUN
ma-27	528	17	,	,	PUNCT
ma-27	528	18	gs	gs	NOUN
ma-27	528	19	=	=	PUNCT
ma-27	528	20	(	(	PUNCT
ma-27	528	21	1−	1−	NUM
ma-27	528	22	βs)`s	βs)`s	NOUN
ma-27	529	1	+	+	CCONJ
ma-27	530	1	βspc(i	βspc(i	PRON
ma-27	530	2	−	−	PROPN
ma-27	530	3	λ∇f	λ∇f	INTJ
ma-27	530	4	)	)	PUNCT
ma-27	530	5	`	`	PUNCT
ma-27	530	6	s	s	X
ma-27	530	7	ws	ws	NOUN
ma-27	530	8	=	=	SYM
ma-27	530	9	(	(	PUNCT
ma-27	530	10	1−	1−	NUM
ma-27	530	11	δs)pc(i	δs)pc(i	PROPN
ma-27	530	12	−	−	PROPN
ma-27	530	13	λ∇f	λ∇f	X
ma-27	530	14	)	)	PUNCT
ma-27	530	15	`	`	PUNCT
ma-27	530	16	s	s	VERB
ma-27	531	1	+	+	X
ma-27	531	2	δspc(i	δspc(i	INTJ
ma-27	531	3	−	−	PROPN
ma-27	531	4	λ∇f	λ∇f	X
ma-27	531	5	)	)	PUNCT
ma-27	531	6	gs	gs	PROPN
ma-27	531	7	ζs	ζs	ADP
ma-27	531	8	=	=	NOUN
ma-27	531	9	pc(i	pc(i	NOUN
ma-27	531	10	−	−	PROPN
ma-27	531	11	λ∇f	λ∇f	X
ma-27	531	12	)	)	PUNCT
ma-27	531	13	ws	ws	NOUN
ma-27	531	14	`	`	PUNCT
ma-27	531	15	s+1	s+1	PROPN
ma-27	531	16	=	=	PUNCT
ma-27	531	17	pc(i	pc(i	NUM
ma-27	531	18	−	−	PROPN
ma-27	531	19	λ∇f	λ∇f	X
ma-27	531	20	)	)	PUNCT
ma-27	531	21	ζs	ζs	ADP
ma-27	531	22	,	,	PUNCT
ma-27	531	23	∀s	∀s	PROPN
ma-27	531	24	≥	≥	PROPN
ma-27	531	25	1	1	NUM
ma-27	531	26	.	.	PUNCT
ma-27	531	27	(	(	PUNCT
ma-27	531	28	8.8	8.8	NUM
ma-27	531	29	)	)	PUNCT
ma-27	531	30	where	where	SCONJ
ma-27	531	31	{	{	PUNCT
ma-27	531	32	δs	δs	NOUN
ma-27	531	33	}	}	PUNCT
ma-27	531	34	,	,	PUNCT
ma-27	531	35	{	{	PUNCT
ma-27	531	36	βs	βs	PRON
ma-27	531	37	}	}	PUNCT
ma-27	531	38	are	be	AUX
ma-27	531	39	sequences	sequence	NOUN
ma-27	531	40	in	in	ADP
ma-27	531	41	[	[	X
ma-27	531	42	0,1	0,1	NUM
ma-27	531	43	]	]	PUNCT
ma-27	531	44	and	and	CCONJ
ma-27	531	45	λ	λ	X
ma-27	531	46	∈	∈	PROPN
ma-27	531	47	(	(	PUNCT
ma-27	531	48	0	0	NUM
ma-27	531	49	,	,	PUNCT
ma-27	531	50	l2	l2	NOUN
ma-27	531	51	)	)	PUNCT
ma-27	531	52	.	.	PUNCT
ma-27	532	1	then	then	ADV
ma-27	532	2	the	the	DET
ma-27	532	3	sequence	sequence	NOUN
ma-27	532	4	{	{	PUNCT
ma-27	532	5	`	`	PUNCT
ma-27	532	6	s	s	PART
ma-27	532	7	}	}	PUNCT
ma-27	532	8	converges	converge	VERB
ma-27	532	9	strongly	strongly	ADV
ma-27	532	10	to	to	ADP
ma-27	532	11	a	a	DET
ma-27	532	12	minimizer	minimizer	NOUN
ma-27	532	13	z	z	NOUN
ma-27	532	14	of	of	ADP
ma-27	532	15	(	(	PUNCT
ma-27	532	16	8.3	8.3	NUM
ma-27	532	17	)	)	PUNCT
ma-27	532	18	.	.	PUNCT
ma-27	533	1	8.2	8.2	NUM
ma-27	533	2	.	.	PUNCT
ma-27	533	3	application	application	NOUN
ma-27	533	4	to	to	PART
ma-27	533	5	split	split	VERB
ma-27	533	6	feasibility	feasibility	NOUN
ma-27	533	7	problem.for	problem.for	ADP
ma-27	533	8	modeling	model	VERB
ma-27	533	9	inverse	inverse	NOUN
ma-27	533	10	problems	problem	NOUN
ma-27	533	11	which	which	PRON
ma-27	533	12	emanate	emanate	VERB
ma-27	533	13	from	from	ADP
ma-27	533	14	phase	phase	NOUN
ma-27	533	15	retrieval	retrieval	NOUN
ma-27	533	16	and	and	CCONJ
ma-27	533	17	medical	medical	ADJ
ma-27	533	18	image	image	NOUN
ma-27	533	19	reconstruc	reconstruc	NOUN
ma-27	533	20	-	-	PUNCT
ma-27	533	21	tion	tion	NOUN
ma-27	533	22	,	,	PUNCT
ma-27	533	23	in	in	ADP
ma-27	533	24	1994	1994	NUM
ma-27	533	25	,	,	PUNCT
ma-27	533	26	censor	censor	VERB
ma-27	533	27	and	and	CCONJ
ma-27	533	28	elfving	elfve	VERB
ma-27	533	29	[	[	X
ma-27	533	30	11	11	NUM
ma-27	533	31	]	]	PUNCT
ma-27	533	32	firstly	firstly	ADV
ma-27	533	33	introduced	introduce	VERB
ma-27	533	34	the	the	DET
ma-27	533	35	following	follow	VERB
ma-27	533	36	split	split	NOUN
ma-27	533	37	feasibility	feasibility	NOUN
ma-27	533	38	problem	problem	NOUN
ma-27	533	39	(	(	PUNCT
ma-27	533	40	sfp)in	sfp)in	ADJ
ma-27	533	41	finite	finite	ADJ
ma-27	533	42	-	-	ADJ
ma-27	533	43	dimensional	dimensional	ADJ
ma-27	533	44	hilbert	hilbert	NOUN
ma-27	533	45	spaces.let	spaces.let	X
ma-27	533	46	c	c	PROPN
ma-27	533	47	and	and	CCONJ
ma-27	533	48	q	q	NOUN
ma-27	533	49	be	be	AUX
ma-27	533	50	nonempty	nonempty	ADV
ma-27	533	51	closed	close	VERB
ma-27	533	52	convex	convex	ADJ
ma-27	533	53	subsets	subset	NOUN
ma-27	533	54	of	of	ADP
ma-27	533	55	the	the	DET
ma-27	533	56	hilbert	hilbert	NOUN
ma-27	533	57	spaces	space	NOUN
ma-27	533	58	h1	h1	PROPN
ma-27	533	59	and	and	CCONJ
ma-27	533	60	h2	h2	NOUN
ma-27	533	61	,	,	PUNCT
ma-27	533	62	respectivelyand	respectivelyand	VERB
ma-27	533	63	a	a	DET
ma-27	533	64	:	:	PUNCT
ma-27	533	65	h1	h1	PROPN
ma-27	533	66	→	→	SYM
ma-27	533	67	h2	h2	PROPN
ma-27	533	68	be	be	AUX
ma-27	533	69	a	a	DET
ma-27	533	70	bounded	bounded	ADJ
ma-27	533	71	linear	linear	ADJ
ma-27	533	72	operator	operator	NOUN
ma-27	533	73	.	.	PUNCT
ma-27	534	1	then	then	ADV
ma-27	534	2	the	the	DET
ma-27	534	3	split	split	NOUN
ma-27	534	4	feasibility	feasibility	NOUN
ma-27	534	5	problem	problem	NOUN
ma-27	534	6	(	(	PUNCT
ma-27	534	7	sfp	sfp	NOUN
ma-27	534	8	)	)	PUNCT
ma-27	534	9	isformulated	isformulate	VERB
ma-27	534	10	to	to	PART
ma-27	534	11	find	find	VERB
ma-27	534	12	z	z	X
ma-27	534	13	∈	∈	PROPN
ma-27	534	14	c	c	NOUN
ma-27	535	1	such	such	ADJ
ma-27	535	2	that	that	SCONJ
ma-27	535	3	az	az	PROPN
ma-27	535	4	∈	∈	PROPN
ma-27	535	5	q.	q.	PROPN
ma-27	535	6	(	(	PUNCT
ma-27	535	7	8.9)sfp	8.9)sfp	PROPN
ma-27	535	8	has	have	VERB
ma-27	535	9	many	many	ADJ
ma-27	535	10	applications	application	NOUN
ma-27	535	11	,	,	PUNCT
ma-27	535	12	it	it	PRON
ma-27	535	13	has	have	AUX
ma-27	535	14	been	be	AUX
ma-27	535	15	found	find	VERB
ma-27	535	16	that	that	SCONJ
ma-27	535	17	sfp	sfp	PROPN
ma-27	535	18	can	can	AUX
ma-27	535	19	been	be	AUX
ma-27	535	20	used	use	VERB
ma-27	535	21	in	in	ADP
ma-27	535	22	many	many	ADJ
ma-27	535	23	areas	area	NOUN
ma-27	535	24	such	such	ADJ
ma-27	535	25	asimage	asimage	NOUN
ma-27	535	26	restoration	restoration	NOUN
ma-27	535	27	,	,	PUNCT
ma-27	535	28	computer	computer	NOUN
ma-27	535	29	tomograph	tomograph	NOUN
ma-27	535	30	,	,	PUNCT
ma-27	535	31	radiation	radiation	NOUN
ma-27	535	32	therapy	therapy	NOUN
ma-27	535	33	treatment	treatment	NOUN
ma-27	535	34	planning	planning	NOUN
ma-27	535	35	.	.	PUNCT
ma-27	536	1	there	there	PRON
ma-27	536	2	exists	exist	VERB
ma-27	536	3	someiterative	someiterative	ADJ
ma-27	536	4	several	several	ADJ
ma-27	536	5	iterative	iterative	NOUN
ma-27	536	6	methods	method	NOUN
ma-27	536	7	for	for	ADP
ma-27	536	8	solving	solve	VERB
ma-27	536	9	split	split	VERB
ma-27	536	10	feasibility	feasibility	NOUN
ma-27	536	11	problems	problem	NOUN
ma-27	536	12	,	,	PUNCT
ma-27	536	13	see	see	VERB
ma-27	536	14	,	,	PUNCT
ma-27	536	15	for	for	ADP
ma-27	536	16	instance	instance	NOUN
ma-27	536	17	[	[	X
ma-27	536	18	8	8	NUM
ma-27	536	19	,	,	PUNCT
ma-27	536	20	15,30].in	15,30].in	NUM
ma-27	536	21	2002	2002	NUM
ma-27	536	22	,	,	PUNCT
ma-27	536	23	byrne	byrne	ADJ
ma-27	536	24	[	[	X
ma-27	536	25	8	8	NUM
ma-27	536	26	]	]	PUNCT
ma-27	536	27	applied	apply	VERB
ma-27	536	28	the	the	DET
ma-27	536	29	forward	forward	ADV
ma-27	536	30	-	-	PUNCT
ma-27	536	31	backward	backward	ADJ
ma-27	536	32	method	method	NOUN
ma-27	536	33	,	,	PUNCT
ma-27	536	34	a	a	DET
ma-27	536	35	type	type	NOUN
ma-27	536	36	of	of	ADP
ma-27	536	37	projection	projection	NOUN
ma-27	536	38	gradient	gradient	NOUN
ma-27	536	39	methodto	methodto	PROPN
ma-27	536	40	approximate	approximate	NOUN
ma-27	536	41	(	(	PUNCT
ma-27	536	42	8.9	8.9	NUM
ma-27	536	43	)	)	PUNCT
ma-27	536	44	.	.	PUNCT
ma-27	537	1	the	the	DET
ma-27	537	2	so	so	ADV
ma-27	537	3	called	call	VERB
ma-27	537	4	cq	cq	ADJ
ma-27	537	5	-	-	PUNCT
ma-27	537	6	iterative	iterative	NOUN
ma-27	537	7	procedure	procedure	NOUN
ma-27	537	8	is	be	AUX
ma-27	537	9	defined	define	VERB
ma-27	537	10	as	as	SCONJ
ma-27	537	11	follows	follow	VERB
ma-27	537	12	:	:	PUNCT
ma-27	537	13	`	`	PUNCT
ma-27	538	1	s+1	s+1	PRON
ma-27	538	2	=	=	SYM
ma-27	538	3	pc	pc	NOUN
ma-27	539	1	[	[	X
ma-27	539	2	i	i	PRON
ma-27	539	3	−	−	VERB
ma-27	539	4	γa∗(1−	γa∗(1−	PROPN
ma-27	539	5	pq)a]`n	pq)a]`n	NOUN
ma-27	539	6	,	,	PUNCT
ma-27	539	7	∀	∀	X
ma-27	539	8	n	n	PRON
ma-27	539	9	≥	≥	NOUN
ma-27	539	10	1	1	NUM
ma-27	539	11	,	,	PUNCT
ma-27	539	12	(	(	PUNCT
ma-27	539	13	8.10	8.10	NUM
ma-27	539	14	)	)	PUNCT
ma-27	539	15	where	where	SCONJ
ma-27	539	16	γ	γ	X
ma-27	539	17	∈	∈	PROPN
ma-27	539	18	(	(	PUNCT
ma-27	539	19	0	0	NUM
ma-27	539	20	,	,	PUNCT
ma-27	539	21	2	2	NUM
ma-27	539	22	‖a‖2	‖a‖2	NOUN
ma-27	539	23	)	)	PUNCT
ma-27	539	24	with	with	ADP
ma-27	539	25	λ	λ	NOUN
ma-27	539	26	being	be	AUX
ma-27	539	27	the	the	DET
ma-27	539	28	spectral	spectral	ADJ
ma-27	539	29	radius	radius	NOUN
ma-27	539	30	of	of	ADP
ma-27	539	31	the	the	PRON
ma-27	539	32	of	of	ADP
ma-27	539	33	operator	operator	NOUN
ma-27	539	34	a∗a	a∗a	SYM
ma-27	539	35	,	,	PUNCT
ma-27	539	36	pc	pc	NOUN
ma-27	539	37	and	and	CCONJ
ma-27	539	38	pq	pq	VERB
ma-27	539	39	denotethe	denotethe	DET
ma-27	539	40	projections	projection	NOUN
ma-27	539	41	onto	onto	ADP
ma-27	539	42	sets	set	NOUN
ma-27	539	43	c	c	PROPN
ma-27	539	44	and	and	CCONJ
ma-27	539	45	q	q	NOUN
ma-27	539	46	,	,	PUNCT
ma-27	539	47	respectively	respectively	ADV
ma-27	539	48	,	,	PUNCT
ma-27	539	49	and	and	CCONJ
ma-27	539	50	a∗	a∗	PROPN
ma-27	539	51	:	:	PUNCT
ma-27	539	52	h∗2	h∗2	PROPN
ma-27	539	53	→	→	SYM
ma-27	539	54	h∗1	h∗1	PROPN
ma-27	539	55	is	be	AUX
ma-27	539	56	the	the	DET
ma-27	539	57	adjoint	adjoint	NOUN
ma-27	539	58	of	of	ADP
ma-27	539	59	a.we	a.we	PRON
ma-27	539	60	assume	assume	VERB
ma-27	539	61	that	that	SCONJ
ma-27	539	62	the	the	DET
ma-27	539	63	solution	solution	NOUN
ma-27	539	64	set	set	VERB
ma-27	539	65	γ	γ	NOUN
ma-27	539	66	of	of	ADP
ma-27	539	67	the	the	DET
ma-27	539	68	sfp	sfp	NOUN
ma-27	539	69	(	(	PUNCT
ma-27	539	70	8.10	8.10	NUM
ma-27	539	71	)	)	PUNCT
ma-27	539	72	is	be	AUX
ma-27	539	73	nonempty	nonempty	ADJ
ma-27	539	74	,	,	PUNCT
ma-27	539	75	let	let	VERB
ma-27	539	76	γ	γ	X
ma-27	539	77	=	=	PRON
ma-27	539	78	{	{	PUNCT
ma-27	539	79	`	`	PUNCT
ma-27	539	80	∈	∈	PROPN
ma-27	539	81	c	c	NOUN
ma-27	539	82	:	:	PUNCT
ma-27	539	83	a	a	DET
ma-27	539	84	`	`	PUNCT
ma-27	539	85	∈	∈	ADJ
ma-27	539	86	q	q	NOUN
ma-27	539	87	}	}	PUNCT
ma-27	539	88	=	=	SYM
ma-27	539	89	c	c	NOUN
ma-27	539	90	∩	∩	X
ma-27	539	91	a−1q	a−1q	PROPN
ma-27	539	92	,	,	PUNCT
ma-27	539	93	then	then	ADV
ma-27	539	94	γ	γ	PROPN
ma-27	539	95	is	be	AUX
ma-27	539	96	closed	closed	ADJ
ma-27	539	97	,	,	PUNCT
ma-27	539	98	convex	convex	VERB
ma-27	539	99	and	and	CCONJ
ma-27	539	100	nonempty	nonempty	ADV
ma-27	539	101	set	set	VERB
ma-27	539	102	.	.	PUNCT
ma-27	540	1	eur	eur	PROPN
ma-27	540	2	.	.	PUNCT
ma-27	541	1	j.	j.	PROPN
ma-27	541	2	math	math	PROPN
ma-27	541	3	.	.	PUNCT
ma-27	542	1	anal	anal	ADJ
ma-27	542	2	.	.	PUNCT
ma-27	543	1	1	1	NUM
ma-27	543	2	(	(	PUNCT
ma-27	543	3	2021	2021	NUM
ma-27	543	4	)	)	PUNCT
ma-27	544	1	129	129	NUM
ma-27	544	2	lemma	lemma	PROPN
ma-27	544	3	8.3	8.3	NUM
ma-27	544	4	.	.	PUNCT
ma-27	545	1	[	[	X
ma-27	545	2	15	15	NUM
ma-27	545	3	]	]	PUNCT
ma-27	545	4	let	let	VERB
ma-27	545	5	operator	operator	NOUN
ma-27	545	6	t	t	NOUN
ma-27	545	7	=	=	SYM
ma-27	545	8	pc	pc	NOUN
ma-27	546	1	[	[	X
ma-27	546	2	i	i	NOUN
ma-27	546	3	−	−	VERB
ma-27	546	4	γa∗(i	γa∗(i	NOUN
ma-27	546	5	−	−	PROPN
ma-27	546	6	pq)a	pq)a	PROPN
ma-27	546	7	]	]	PUNCT
ma-27	546	8	,	,	PUNCT
ma-27	546	9	where	where	SCONJ
ma-27	546	10	γ	γ	X
ma-27	546	11	∈	∈	PROPN
ma-27	546	12	(	(	PUNCT
ma-27	546	13	0	0	NUM
ma-27	546	14	,	,	PUNCT
ma-27	546	15	2	2	NUM
ma-27	546	16	‖a‖2	‖a‖2	NOUN
ma-27	546	17	)	)	PUNCT
ma-27	546	18	.	.	PUNCT
ma-27	547	1	then	then	ADV
ma-27	547	2	,	,	PUNCT
ma-27	547	3	t	t	PROPN
ma-27	547	4	is	be	AUX
ma-27	547	5	said	say	VERB
ma-27	547	6	to	to	PART
ma-27	547	7	be	be	AUX
ma-27	547	8	a	a	DET
ma-27	547	9	nonexpansive	nonexpansive	ADJ
ma-27	547	10	map	map	NOUN
ma-27	547	11	.	.	PUNCT
ma-27	548	1	since	since	SCONJ
ma-27	548	2	by	by	ADP
ma-27	548	3	our	our	PRON
ma-27	548	4	assumption	assumption	NOUN
ma-27	548	5	γ	γ	X
ma-27	548	6	6=	6=	PROPN
ma-27	548	7	∅	∅	NOUN
ma-27	548	8	,	,	PUNCT
ma-27	548	9	then	then	ADV
ma-27	548	10	it	it	PRON
ma-27	548	11	is	be	AUX
ma-27	548	12	clear	clear	ADJ
ma-27	548	13	that	that	SCONJ
ma-27	548	14	any	any	DET
ma-27	548	15	z	z	NOUN
ma-27	548	16	∈	∈	PROPN
ma-27	548	17	c	c	NOUN
ma-27	548	18	solves	solve	NOUN
ma-27	548	19	(	(	PUNCT
ma-27	548	20	8.9	8.9	NUM
ma-27	548	21	)	)	PUNCT
ma-27	548	22	if	if	SCONJ
ma-27	548	23	and	and	CCONJ
ma-27	548	24	only	only	ADV
ma-27	548	25	if	if	SCONJ
ma-27	548	26	it	it	PRON
ma-27	548	27	solvesthe	solvesthe	DET
ma-27	548	28	fixed	fix	VERB
ma-27	548	29	point	point	NOUN
ma-27	548	30	equation	equation	NOUN
ma-27	548	31	:	:	PUNCT
ma-27	548	32	t	t	NOUN
ma-27	548	33	=	=	SYM
ma-27	548	34	pc[i	pc[i	PROPN
ma-27	548	35	−	−	PROPN
ma-27	548	36	γa∗(i	γa∗(i	NOUN
ma-27	548	37	−	−	PROPN
ma-27	548	38	pq)a]z	pq)a]z	VERB
ma-27	548	39	=	=	PUNCT
ma-27	548	40	z	z	PROPN
ma-27	548	41	,	,	PUNCT
ma-27	548	42	z	z	PROPN
ma-27	548	43	∈	∈	PROPN
ma-27	548	44	c.	c.	PROPN
ma-27	548	45	thus	thus	ADV
ma-27	548	46	,	,	PUNCT
ma-27	548	47	f	f	PROPN
ma-27	548	48	(	(	PUNCT
ma-27	548	49	t	t	PROPN
ma-27	548	50	)	)	PUNCT
ma-27	549	1	=	=	SYM
ma-27	549	2	γ	γ	X
ma-27	549	3	=	=	SYM
ma-27	549	4	c	c	PROPN
ma-27	549	5	∩	∩	X
ma-27	549	6	a−1q	a−1q	PROPN
ma-27	549	7	,	,	PUNCT
ma-27	549	8	i.e.	i.e.	X
ma-27	549	9	,	,	PUNCT
ma-27	549	10	the	the	DET
ma-27	549	11	solution	solution	NOUN
ma-27	549	12	set	set	VERB
ma-27	549	13	γ	γ	X
ma-27	549	14	is	be	AUX
ma-27	549	15	equal	equal	ADJ
ma-27	549	16	the	the	DET
ma-27	549	17	set	set	NOUN
ma-27	549	18	of	of	ADP
ma-27	549	19	fixed	fix	VERB
ma-27	549	20	point	point	NOUN
ma-27	549	21	of	of	ADP
ma-27	549	22	the	the	DET
ma-27	549	23	map	map	NOUN
ma-27	549	24	t	t	NOUN
ma-27	549	25	.for	.for	PUNCT
ma-27	549	26	more	more	ADV
ma-27	549	27	explicit	explicit	ADJ
ma-27	549	28	explanation	explanation	NOUN
ma-27	549	29	,	,	PUNCT
ma-27	549	30	the	the	DET
ma-27	549	31	reader	reader	NOUN
ma-27	549	32	can	can	AUX
ma-27	549	33	see	see	VERB
ma-27	549	34	[	[	X
ma-27	549	35	42,43].now	42,43].now	NOUN
ma-27	549	36	,	,	PUNCT
ma-27	549	37	to	to	PART
ma-27	549	38	prove	prove	VERB
ma-27	549	39	our	our	PRON
ma-27	549	40	main	main	ADJ
ma-27	549	41	results	result	NOUN
ma-27	549	42	in	in	ADP
ma-27	549	43	this	this	DET
ma-27	549	44	part	part	NOUN
ma-27	549	45	,	,	PUNCT
ma-27	549	46	we	we	PRON
ma-27	549	47	will	will	AUX
ma-27	549	48	consider	consider	VERB
ma-27	549	49	the	the	DET
ma-27	549	50	following	follow	VERB
ma-27	549	51	scheme:	scheme:	ADJ
ma-27	549	52	`	`	PUNCT
ma-27	549	53	0	0	NUM
ma-27	549	54	∈	∈	PROPN
ma-27	549	55	c	c	NOUN
ma-27	549	56	,	,	PUNCT
ma-27	549	57	gs	gs	NOUN
ma-27	549	58	=	=	PUNCT
ma-27	549	59	(	(	PUNCT
ma-27	549	60	1−	1−	NUM
ma-27	549	61	βs)`s	βs)`s	NOUN
ma-27	550	1	+	+	NUM
ma-27	550	2	βspc	βspc	NOUN
ma-27	551	1	[	[	X
ma-27	551	2	i	i	PRON
ma-27	551	3	−	−	VERB
ma-27	551	4	γa∗(i	γa∗(i	NOUN
ma-27	551	5	−	−	PROPN
ma-27	551	6	pq)a]`s	pq)a]`s	PROPN
ma-27	551	7	ws	ws	NOUN
ma-27	551	8	=	=	SYM
ma-27	551	9	(	(	PUNCT
ma-27	551	10	1−	1−	NUM
ma-27	551	11	δs)pc	δs)pc	PROPN
ma-27	552	1	[	[	X
ma-27	552	2	i	i	PRON
ma-27	552	3	−	−	VERB
ma-27	552	4	γa∗(i	γa∗(i	NOUN
ma-27	552	5	−	−	PROPN
ma-27	552	6	pq)a]`s	pq)a]`s	PROPN
ma-27	552	7	+	+	CCONJ
ma-27	552	8	δspc	δspc	NOUN
ma-27	553	1	[	[	X
ma-27	553	2	i	i	PRON
ma-27	553	3	−	−	VERB
ma-27	553	4	γa∗(i	γa∗(i	NOUN
ma-27	553	5	−	−	PROPN
ma-27	553	6	pq)a]gs	pq)a]gs	PROPN
ma-27	553	7	ζs	ζs	ADP
ma-27	553	8	=	=	VERB
ma-27	553	9	pc	pc	NOUN
ma-27	554	1	[	[	X
ma-27	554	2	i	i	PRON
ma-27	554	3	−	−	VERB
ma-27	554	4	γa∗(i	γa∗(i	NOUN
ma-27	554	5	−	−	PUNCT
ma-27	555	1	pq)a]ws	pq)a]ws	NOUN
ma-27	555	2	`	`	PUNCT
ma-27	555	3	s+1	s+1	NOUN
ma-27	555	4	=	=	PUNCT
ma-27	555	5	pc	pc	NOUN
ma-27	556	1	[	[	X
ma-27	556	2	i	i	PRON
ma-27	556	3	−	−	VERB
ma-27	556	4	γa∗(i	γa∗(i	NOUN
ma-27	556	5	−	−	PROPN
ma-27	556	6	pq)a]ζs	pq)a]ζs	PROPN
ma-27	556	7	,	,	PUNCT
ma-27	556	8	(	(	PUNCT
ma-27	556	9	8.11	8.11	NUM
ma-27	556	10	)	)	PUNCT
ma-27	556	11	for	for	ADP
ma-27	556	12	all	all	PRON
ma-27	556	13	s	s	PART
ma-27	556	14	≥	≥	NOUN
ma-27	556	15	1	1	NUM
ma-27	556	16	,	,	PUNCT
ma-27	556	17	where	where	SCONJ
ma-27	556	18	{	{	PUNCT
ma-27	556	19	δs	δs	NOUN
ma-27	556	20	}	}	PUNCT
ma-27	556	21	,	,	PUNCT
ma-27	556	22	{	{	PUNCT
ma-27	556	23	βs	βs	PRON
ma-27	556	24	}	}	PUNCT
ma-27	556	25	are	be	AUX
ma-27	556	26	sequences	sequence	NOUN
ma-27	556	27	in	in	ADP
ma-27	556	28	[	[	X
ma-27	556	29	0,1	0,1	NUM
ma-27	556	30	]	]	PUNCT
ma-27	556	31	and	and	CCONJ
ma-27	556	32	γ	γ	X
ma-27	556	33	∈	∈	PROPN
ma-27	556	34	(	(	PUNCT
ma-27	556	35	0	0	NUM
ma-27	556	36	,	,	PUNCT
ma-27	556	37	2	2	NUM
ma-27	556	38	‖a‖2	‖a‖2	NOUN
ma-27	556	39	)	)	PUNCT
ma-27	556	40	.	.	PUNCT
ma-27	557	1	theorem	theorem	NOUN
ma-27	557	2	8.4	8.4	NUM
ma-27	557	3	.	.	PUNCT
ma-27	558	1	let	let	VERB
ma-27	558	2	{	{	PUNCT
ma-27	558	3	`	`	PUNCT
ma-27	558	4	s	s	AUX
ma-27	558	5	}	}	PUNCT
ma-27	558	6	be	be	AUX
ma-27	558	7	the	the	DET
ma-27	558	8	sequence	sequence	NOUN
ma-27	558	9	iteratively	iteratively	ADV
ma-27	558	10	generated	generate	VERB
ma-27	558	11	by	by	ADP
ma-27	558	12	(	(	PUNCT
ma-27	558	13	8.11	8.11	NUM
ma-27	558	14	)	)	PUNCT
ma-27	558	15	.	.	PUNCT
ma-27	559	1	then	then	ADV
ma-27	559	2	,	,	PUNCT
ma-27	559	3	{	{	PUNCT
ma-27	559	4	`	`	PUNCT
ma-27	559	5	s	s	AUX
ma-27	559	6	}	}	PUNCT
ma-27	559	7	converses	converse	VERB
ma-27	559	8	weakly	weakly	ADJ
ma-27	559	9	to	to	ADP
ma-27	559	10	an	an	DET
ma-27	559	11	element	element	NOUN
ma-27	559	12	in	in	ADP
ma-27	559	13	γ	γ	PROPN
ma-27	559	14	.	.	PUNCT
ma-27	559	15	proof	proof	NOUN
ma-27	559	16	.	.	PUNCT
ma-27	560	1	since	since	SCONJ
ma-27	560	2	t	t	NOUN
ma-27	560	3	=	=	SYM
ma-27	560	4	pc	pc	NOUN
ma-27	560	5	[	[	X
ma-27	560	6	i	i	NOUN
ma-27	560	7	−	−	VERB
ma-27	560	8	γa∗(i	γa∗(i	NOUN
ma-27	560	9	−	−	PROPN
ma-27	560	10	pq)a	pq)a	PROPN
ma-27	560	11	]	]	PUNCT
ma-27	560	12	is	be	AUX
ma-27	560	13	a	a	DET
ma-27	560	14	nonexpansive	nonexpansive	ADJ
ma-27	560	15	map	map	NOUN
ma-27	560	16	and	and	CCONJ
ma-27	560	17	by	by	ADP
ma-27	560	18	proposition	proposition	NOUN
ma-27	560	19	2.9	2.9	NUM
ma-27	560	20	we	we	PRON
ma-27	560	21	knowthat	knowthat	INTJ
ma-27	560	22	every	every	DET
ma-27	560	23	generalized	generalized	ADJ
ma-27	560	24	α	α	PROPN
ma-27	560	25	-	-	PUNCT
ma-27	560	26	nonexpansive	nonexpansive	ADJ
ma-27	560	27	map	map	NOUN
ma-27	560	28	is	be	AUX
ma-27	560	29	nonexpansive	nonexpansive	ADJ
ma-27	560	30	map	map	NOUN
ma-27	560	31	with	with	ADP
ma-27	560	32	α	α	NOUN
ma-27	560	33	=	=	SYM
ma-27	560	34	0	0	PUNCT
ma-27	560	35	(	(	PUNCT
ma-27	560	36	i.e.	i.e.	X
ma-27	560	37	,	,	PUNCT
ma-27	560	38	0	0	X
ma-27	560	39	-	-	PUNCT
ma-27	560	40	nonexpansive),so	nonexpansive),so	PRON
ma-27	560	41	the	the	DET
ma-27	560	42	conclusion	conclusion	NOUN
ma-27	560	43	follows	follow	VERB
ma-27	560	44	from	from	ADP
ma-27	560	45	theorem	theorem	ADJ
ma-27	560	46	4.3	4.3	NUM
ma-27	560	47	.	.	PUNCT
ma-27	560	48	�	�	PROPN
ma-27	560	49	theorem	theorem	VERB
ma-27	560	50	8.5	8.5	NUM
ma-27	560	51	.	.	PUNCT
ma-27	561	1	if	if	SCONJ
ma-27	561	2	{	{	PUNCT
ma-27	561	3	`	`	PUNCT
ma-27	561	4	s	s	X
ma-27	561	5	}	}	PUNCT
ma-27	561	6	is	be	AUX
ma-27	561	7	the	the	DET
ma-27	561	8	sequence	sequence	NOUN
ma-27	561	9	generated	generate	VERB
ma-27	561	10	by	by	ADP
ma-27	561	11	the	the	DET
ma-27	561	12	iterative	iterative	NOUN
ma-27	561	13	scheme	scheme	NOUN
ma-27	561	14	(	(	PUNCT
ma-27	561	15	8.11	8.11	NUM
ma-27	561	16	)	)	PUNCT
ma-27	561	17	.	.	PUNCT
ma-27	562	1	then	then	ADV
ma-27	562	2	{	{	PUNCT
ma-27	562	3	`	`	PUNCT
ma-27	562	4	s	s	AUX
ma-27	562	5	}	}	PUNCT
ma-27	562	6	converges	converge	VERB
ma-27	562	7	strongly	strongly	ADV
ma-27	562	8	the	the	DET
ma-27	562	9	an	an	DET
ma-27	562	10	element	element	NOUN
ma-27	562	11	in	in	ADP
ma-27	562	12	γ	γ	PROPN
ma-27	562	13	if	if	SCONJ
ma-27	562	14	and	and	CCONJ
ma-27	562	15	only	only	ADV
ma-27	562	16	if	if	SCONJ
ma-27	562	17	lim	lim	PROPN
ma-27	562	18	inf	inf	NOUN
ma-27	562	19	s→∞	s→∞	PROPN
ma-27	562	20	d(`s	d(`	NOUN
ma-27	562	21	,	,	PUNCT
ma-27	562	22	γ	γ	NOUN
ma-27	562	23	)	)	PUNCT
ma-27	562	24	=	=	SYM
ma-27	562	25	0	0	X
ma-27	562	26	.	.	PUNCT
ma-27	563	1	proof	proof	NOUN
ma-27	563	2	.	.	PUNCT
ma-27	564	1	since	since	SCONJ
ma-27	564	2	t	t	NOUN
ma-27	564	3	=	=	SYM
ma-27	564	4	pc	pc	NOUN
ma-27	564	5	[	[	X
ma-27	564	6	i	i	NOUN
ma-27	564	7	−	−	VERB
ma-27	564	8	γa∗(i	γa∗(i	NOUN
ma-27	564	9	−	−	PROPN
ma-27	564	10	pq)a	pq)a	PROPN
ma-27	564	11	]	]	PUNCT
ma-27	564	12	is	be	AUX
ma-27	564	13	nonexpansive	nonexpansive	ADJ
ma-27	564	14	map	map	NOUN
ma-27	564	15	,	,	PUNCT
ma-27	564	16	then	then	ADV
ma-27	564	17	the	the	DET
ma-27	564	18	conclusion	conclusion	NOUN
ma-27	564	19	of	of	ADP
ma-27	564	20	the	the	DET
ma-27	564	21	prooffollows	prooffollow	NOUN
ma-27	564	22	from	from	ADP
ma-27	564	23	theorem	theorem	ADJ
ma-27	564	24	4.4	4.4	NUM
ma-27	564	25	.	.	PUNCT
ma-27	564	26	�	�	PROPN
ma-27	564	27	theorem	theorem	VERB
ma-27	564	28	8.6	8.6	NUM
ma-27	564	29	.	.	PUNCT
ma-27	565	1	if	if	SCONJ
ma-27	565	2	t	t	NOUN
ma-27	565	3	=	=	SYM
ma-27	565	4	pc	pc	NOUN
ma-27	566	1	[	[	X
ma-27	566	2	i	i	NOUN
ma-27	566	3	−	−	VERB
ma-27	566	4	γa∗(i	γa∗(i	NOUN
ma-27	566	5	−	−	PROPN
ma-27	566	6	pq)a	pq)a	PROPN
ma-27	566	7	]	]	PUNCT
ma-27	566	8	satisfies	satisfie	NOUN
ma-27	566	9	condition	condition	NOUN
ma-27	566	10	(	(	PUNCT
ma-27	566	11	i	i	NOUN
ma-27	566	12	)	)	PUNCT
ma-27	566	13	and	and	CCONJ
ma-27	566	14	{	{	PUNCT
ma-27	566	15	`	`	PUNCT
ma-27	566	16	s	s	X
ma-27	566	17	}	}	PUNCT
ma-27	566	18	is	be	AUX
ma-27	566	19	the	the	DET
ma-27	566	20	sequence	sequence	NOUN
ma-27	566	21	iteratively	iteratively	ADV
ma-27	566	22	defined	define	VERB
ma-27	566	23	by	by	ADP
ma-27	566	24	(	(	PUNCT
ma-27	566	25	8.11	8.11	NUM
ma-27	566	26	)	)	PUNCT
ma-27	566	27	,	,	PUNCT
ma-27	566	28	then	then	ADV
ma-27	566	29	{	{	PUNCT
ma-27	566	30	`	`	PUNCT
ma-27	566	31	s	s	X
ma-27	566	32	}	}	PUNCT
ma-27	566	33	converges	converge	VERB
ma-27	566	34	strongly	strongly	ADV
ma-27	566	35	to	to	ADP
ma-27	566	36	a	a	DET
ma-27	566	37	point	point	NOUN
ma-27	566	38	in	in	ADP
ma-27	566	39	γ	γ	PROPN
ma-27	566	40	.	.	PUNCT
ma-27	566	41	proof	proof	NOUN
ma-27	566	42	.	.	PUNCT
ma-27	567	1	the	the	DET
ma-27	567	2	result	result	NOUN
ma-27	567	3	follows	follow	VERB
ma-27	567	4	from	from	ADP
ma-27	567	5	theorem	theorem	ADJ
ma-27	567	6	4.5	4.5	NUM
ma-27	567	7	.	.	PUNCT
ma-27	568	1	�	�	PROPN
ma-27	568	2	9	9	NUM
ma-27	568	3	.	.	PUNCT
ma-27	568	4	conclusion	conclusion	NOUN
ma-27	568	5	in	in	ADP
ma-27	568	6	this	this	DET
ma-27	568	7	paper	paper	NOUN
ma-27	568	8	,	,	PUNCT
ma-27	568	9	we	we	PRON
ma-27	568	10	have	have	AUX
ma-27	568	11	shown	show	VERB
ma-27	568	12	numerically	numerically	ADV
ma-27	568	13	and	and	CCONJ
ma-27	568	14	analytically	analytically	ADV
ma-27	568	15	that	that	SCONJ
ma-27	568	16	our	our	PRON
ma-27	568	17	new	new	ADJ
ma-27	568	18	iterative	iterative	NOUN
ma-27	568	19	algorithm	algorithm	NOUN
ma-27	568	20	(	(	PUNCT
ma-27	568	21	1.7)has	1.7)has	NUM
ma-27	568	22	a	a	DET
ma-27	568	23	better	well	ADJ
ma-27	568	24	rate	rate	NOUN
ma-27	568	25	of	of	ADP
ma-27	568	26	convergence	convergence	NOUN
ma-27	568	27	than	than	ADP
ma-27	568	28	m	m	VERB
ma-27	568	29	iterative	iterative	ADJ
ma-27	568	30	algorithm	algorithm	NOUN
ma-27	568	31	and	and	CCONJ
ma-27	568	32	some	some	DET
ma-27	568	33	other	other	ADJ
ma-27	568	34	well	well	ADV
ma-27	568	35	known	know	VERB
ma-27	568	36	existingiterative	existingiterative	ADJ
ma-27	568	37	algorithms	algorithm	NOUN
ma-27	568	38	in	in	ADP
ma-27	568	39	the	the	DET
ma-27	568	40	literature	literature	NOUN
ma-27	568	41	for	for	ADP
ma-27	568	42	almost	almost	ADV
ma-27	568	43	contraction	contraction	VERB
ma-27	568	44	mapping	mapping	NOUN
ma-27	568	45	and	and	CCONJ
ma-27	568	46	generalized	generalize	VERB
ma-27	568	47	α	α	NOUN
ma-27	568	48	-	-	NOUN
ma-27	568	49	nonexpansivemappings	nonexpansivemapping	NOUN
ma-27	568	50	.	.	PUNCT
ma-27	569	1	also	also	ADV
ma-27	569	2	,	,	PUNCT
ma-27	569	3	it	it	PRON
ma-27	569	4	is	be	AUX
ma-27	569	5	shown	show	VERB
ma-27	569	6	that	that	SCONJ
ma-27	569	7	our	our	PRON
ma-27	569	8	new	new	ADJ
ma-27	569	9	iterative	iterative	NOUN
ma-27	569	10	algorithm	algorithm	NOUN
ma-27	569	11	(	(	PUNCT
ma-27	569	12	1.7	1.7	NUM
ma-27	569	13	)	)	PUNCT
ma-27	569	14	is	be	AUX
ma-27	569	15	t	t	PROPN
ma-27	569	16	–	–	PUNCT
ma-27	569	17	stable	stable	ADJ
ma-27	569	18	and	and	CCONJ
ma-27	569	19	data	datum	NOUN
ma-27	569	20	dependent	dependent	ADJ
ma-27	569	21	eur	eur	PROPN
ma-27	569	22	.	.	PUNCT
ma-27	570	1	j.	j.	PROPN
ma-27	570	2	math	math	PROPN
ma-27	570	3	.	.	PUNCT
ma-27	571	1	anal	anal	ADJ
ma-27	571	2	.	.	PUNCT
ma-27	572	1	1	1	NUM
ma-27	572	2	(	(	PUNCT
ma-27	572	3	2021	2021	NUM
ma-27	572	4	)	)	PUNCT
ma-27	573	1	130which	130which	PROPN
ma-27	573	2	make	make	VERB
ma-27	573	3	it	it	PRON
ma-27	573	4	reliable	reliable	ADJ
ma-27	573	5	.	.	PUNCT
ma-27	574	1	as	as	ADP
ma-27	574	2	some	some	DET
ma-27	574	3	applications	application	NOUN
ma-27	574	4	of	of	ADP
ma-27	574	5	our	our	PRON
ma-27	574	6	new	new	ADJ
ma-27	574	7	iterative	iterative	NOUN
ma-27	574	8	algorithm	algorithm	NOUN
ma-27	574	9	(	(	PUNCT
ma-27	574	10	1.7	1.7	NUM
ma-27	574	11	)	)	PUNCT
ma-27	574	12	,	,	PUNCT
ma-27	574	13	it	it	PRON
ma-27	574	14	is	be	AUX
ma-27	574	15	used	use	VERB
ma-27	574	16	tofind	tofind	VERB
ma-27	574	17	the	the	DET
ma-27	574	18	solutions	solution	NOUN
ma-27	574	19	of	of	ADP
ma-27	574	20	constrained	constrain	VERB
ma-27	574	21	convex	convex	NOUN
ma-27	574	22	minimization	minimization	NOUN
ma-27	574	23	problem	problem	NOUN
ma-27	574	24	and	and	CCONJ
ma-27	574	25	split	split	VERB
ma-27	574	26	feasibility	feasibility	NOUN
ma-27	574	27	problem	problem	NOUN
ma-27	574	28	.	.	PUNCT
ma-27	575	1	now	now	ADV
ma-27	575	2	,	,	PUNCT
ma-27	575	3	owing	owe	VERB
ma-27	575	4	to	to	ADP
ma-27	575	5	the	the	DET
ma-27	575	6	fact	fact	NOUN
ma-27	575	7	that	that	SCONJ
ma-27	575	8	the	the	DET
ma-27	575	9	class	class	NOUN
ma-27	575	10	of	of	ADP
ma-27	575	11	generalized	generalized	ADJ
ma-27	575	12	α	α	PROPN
ma-27	575	13	-	-	PUNCT
ma-27	575	14	nonexpansive	nonexpansive	ADJ
ma-27	575	15	mappings	mapping	NOUN
ma-27	575	16	which	which	PRON
ma-27	575	17	is	be	AUX
ma-27	575	18	considered	consider	VERB
ma-27	575	19	inour	inour	ADJ
ma-27	575	20	paper	paper	NOUN
ma-27	575	21	is	be	AUX
ma-27	575	22	more	more	ADV
ma-27	575	23	general	general	ADJ
ma-27	575	24	than	than	ADP
ma-27	575	25	the	the	DET
ma-27	575	26	class	class	NOUN
ma-27	575	27	of	of	ADP
ma-27	575	28	suzuki	suzuki	PROPN
ma-27	575	29	generalized	generalize	VERB
ma-27	575	30	nonexpansive	nonexpansive	ADJ
ma-27	575	31	mappings	mapping	NOUN
ma-27	575	32	which	which	PRON
ma-27	575	33	hasbeen	hasbeen	ADV
ma-27	575	34	considered	consider	VERB
ma-27	575	35	by	by	ADP
ma-27	575	36	ullah	ullah	PROPN
ma-27	575	37	and	and	CCONJ
ma-27	575	38	arshad	arshad	VERB
ma-27	575	39	[	[	X
ma-27	575	40	39	39	NUM
ma-27	575	41	]	]	PUNCT
ma-27	575	42	for	for	ADP
ma-27	575	43	m	m	PROPN
ma-27	575	44	iteration	iteration	NOUN
ma-27	575	45	,	,	PUNCT
ma-27	575	46	it	it	PRON
ma-27	575	47	implies	imply	VERB
ma-27	575	48	that	that	SCONJ
ma-27	575	49	our	our	PRON
ma-27	575	50	results	result	NOUN
ma-27	575	51	generalizeand	generalizeand	NOUN
ma-27	575	52	improve	improve	VERB
ma-27	575	53	the	the	DET
ma-27	575	54	results	result	NOUN
ma-27	575	55	in	in	ADP
ma-27	575	56	ullah	ullah	PROPN
ma-27	575	57	and	and	CCONJ
ma-27	575	58	arshad	arshad	VERB
ma-27	576	1	[	[	X
ma-27	576	2	39	39	NUM
ma-27	576	3	]	]	PUNCT
ma-27	576	4	and	and	CCONJ
ma-27	576	5	several	several	ADJ
ma-27	576	6	other	other	ADJ
ma-27	576	7	related	related	ADJ
ma-27	576	8	results	result	NOUN
ma-27	576	9	existing	exist	VERB
ma-27	576	10	in	in	ADP
ma-27	576	11	theliterature	theliterature	NOUN
ma-27	576	12	.	.	PUNCT
ma-27	577	1	references	reference	NOUN
ma-27	577	2	[	[	X
ma-27	577	3	1	1	NUM
ma-27	577	4	]	]	PUNCT
ma-27	577	5	m.	m.	NOUN
ma-27	577	6	abbas	abbas	PROPN
ma-27	577	7	and	and	CCONJ
ma-27	577	8	t.	t.	PROPN
ma-27	577	9	nazir	nazir	PROPN
ma-27	577	10	,	,	PUNCT
ma-27	577	11	a	a	DET
ma-27	577	12	new	new	ADJ
ma-27	577	13	faster	fast	ADJ
ma-27	577	14	iteration	iteration	NOUN
ma-27	577	15	process	process	NOUN
ma-27	577	16	applied	apply	VERB
ma-27	577	17	to	to	ADP
ma-27	577	18	constrained	constrain	VERB
ma-27	577	19	minimization	minimization	NOUN
ma-27	577	20	and	and	CCONJ
ma-27	577	21	feasibility	feasibility	NOUN
ma-27	577	22	problems	problem	NOUN
ma-27	577	23	,	,	PUNCT
ma-27	577	24	mat	mat	NOUN
ma-27	577	25	.	.	PUNCT
ma-27	577	26	vesn	vesn	PROPN
ma-27	577	27	.	.	PUNCT
ma-27	578	1	66(2014	66(2014	NUM
ma-27	578	2	)	)	PUNCT
ma-27	578	3	,	,	PUNCT
ma-27	578	4	223–234.[2	223–234.[2	NUM
ma-27	578	5	]	]	PUNCT
ma-27	578	6	r.	r.	PROPN
ma-27	578	7	p.	p.	PROPN
ma-27	578	8	agarwal	agarwal	PROPN
ma-27	578	9	,	,	PUNCT
ma-27	578	10	d.	d.	PROPN
ma-27	578	11	o.	o.	PROPN
ma-27	578	12	regan	regan	PROPN
ma-27	578	13	and	and	CCONJ
ma-27	578	14	d.	d.	PROPN
ma-27	578	15	r.	r.	PROPN
ma-27	578	16	sahu	sahu	PROPN
ma-27	578	17	,	,	PUNCT
ma-27	578	18	iterative	iterative	ADJ
ma-27	578	19	construction	construction	NOUN
ma-27	578	20	of	of	ADP
ma-27	578	21	fixed	fix	VERB
ma-27	578	22	points	point	NOUN
ma-27	578	23	of	of	ADP
ma-27	578	24	nearly	nearly	ADV
ma-27	578	25	asymptotically	asymptotically	ADV
ma-27	578	26	nonex	nonex	ADJ
ma-27	578	27	-	-	PUNCT
ma-27	578	28	pansive	pansive	ADJ
ma-27	578	29	mappings	mapping	NOUN
ma-27	578	30	,	,	PUNCT
ma-27	578	31	j.	j.	PROPN
ma-27	578	32	nonlinear	nonlinear	PROPN
ma-27	578	33	convex	convex	PROPN
ma-27	578	34	anal	anal	NOUN
ma-27	578	35	.	.	PUNCT
ma-27	579	1	8(2007	8(2007	NUM
ma-27	579	2	)	)	PUNCT
ma-27	579	3	,	,	PUNCT
ma-27	579	4	61–79.[3	61–79.[3	NOUN
ma-27	579	5	]	]	PUNCT
ma-27	579	6	k.	k.	PROPN
ma-27	579	7	aoyama	aoyama	PROPN
ma-27	579	8	and	and	CCONJ
ma-27	579	9	f.	f.	PROPN
ma-27	579	10	kohsaka	kohsaka	PROPN
ma-27	579	11	,	,	PUNCT
ma-27	579	12	fixed	fix	VERB
ma-27	579	13	point	point	NOUN
ma-27	579	14	theorem	theorem	NOUN
ma-27	579	15	for	for	ADP
ma-27	579	16	α	α	NOUN
ma-27	579	17	-	-	PUNCT
ma-27	579	18	nonexpansive	nonexpansive	ADJ
ma-27	579	19	mappings	mapping	NOUN
ma-27	579	20	in	in	ADP
ma-27	579	21	banach	banach	NOUN
ma-27	579	22	spaces	space	NOUN
ma-27	579	23	,	,	PUNCT
ma-27	579	24	nonlinear	nonlinear	NOUN
ma-27	579	25	anal.74(13	anal.74(13	NUM
ma-27	579	26	)	)	PUNCT
ma-27	579	27	(	(	PUNCT
ma-27	579	28	2011	2011	NUM
ma-27	579	29	)	)	PUNCT
ma-27	579	30	,	,	PUNCT
ma-27	579	31	4387–4391.[4	4387–4391.[4	PROPN
ma-27	579	32	]	]	X
ma-27	579	33	a.	a.	NOUN
ma-27	579	34	bejenaru	bejenaru	PROPN
ma-27	579	35	and	and	CCONJ
ma-27	579	36	m.	m.	PROPN
ma-27	579	37	postolache	postolache	PROPN
ma-27	579	38	,	,	PUNCT
ma-27	579	39	partially	partially	ADV
ma-27	579	40	projective	projective	ADJ
ma-27	579	41	algorithm	algorithm	NOUN
ma-27	579	42	for	for	ADP
ma-27	579	43	the	the	DET
ma-27	579	44	split	split	NOUN
ma-27	579	45	feasibility	feasibility	NOUN
ma-27	579	46	problem	problem	NOUN
ma-27	579	47	with	with	ADP
ma-27	579	48	visualization	visualization	NOUN
ma-27	579	49	ofthe	ofthe	NOUN
ma-27	579	50	solution	solution	NOUN
ma-27	579	51	set	set	NOUN
ma-27	579	52	,	,	PUNCT
ma-27	579	53	symmetry	symmetry	NOUN
ma-27	579	54	,	,	PUNCT
ma-27	579	55	12	12	NUM
ma-27	579	56	(	(	PUNCT
ma-27	579	57	2020	2020	NUM
ma-27	579	58	)	)	PUNCT
ma-27	579	59	,	,	PUNCT
ma-27	579	60	608.[5	608.[5	NUM
ma-27	579	61	]	]	X
ma-27	579	62	v.	v.	CCONJ
ma-27	579	63	berinde	berinde	NOUN
ma-27	579	64	,	,	PUNCT
ma-27	579	65	picard	picard	NOUN
ma-27	579	66	iteration	iteration	NOUN
ma-27	579	67	converges	converge	VERB
ma-27	579	68	faster	fast	ADV
ma-27	579	69	than	than	ADP
ma-27	579	70	mann	mann	PROPN
ma-27	579	71	iteration	iteration	NOUN
ma-27	579	72	for	for	ADP
ma-27	579	73	a	a	DET
ma-27	579	74	class	class	NOUN
ma-27	579	75	of	of	ADP
ma-27	579	76	quasicontractive	quasicontractive	ADJ
ma-27	579	77	operators	operator	NOUN
ma-27	579	78	,	,	PUNCT
ma-27	579	79	fixedpoint	fixedpoint	NOUN
ma-27	579	80	theory	theory	NOUN
ma-27	579	81	appl	appl	NOUN
ma-27	579	82	.	.	PROPN
ma-27	579	83	2	2	NUM
ma-27	579	84	(	(	PUNCT
ma-27	579	85	2004	2004	NUM
ma-27	579	86	)	)	PUNCT
ma-27	579	87	,	,	PUNCT
ma-27	580	1	97–105.[6	97–105.[6	X
ma-27	580	2	]	]	X
ma-27	580	3	v.	v.	CCONJ
ma-27	580	4	berinde	berinde	NOUN
ma-27	580	5	,	,	PUNCT
ma-27	580	6	on	on	ADP
ma-27	580	7	the	the	DET
ma-27	580	8	approximation	approximation	NOUN
ma-27	580	9	of	of	ADP
ma-27	580	10	fixed	fix	VERB
ma-27	580	11	points	point	NOUN
ma-27	580	12	of	of	ADP
ma-27	580	13	weak	weak	ADJ
ma-27	580	14	contractive	contractive	ADJ
ma-27	580	15	mapping	mapping	NOUN
ma-27	580	16	,	,	PUNCT
ma-27	580	17	carpath	carpath	PROPN
ma-27	580	18	.	.	PUNCT
ma-27	581	1	j.	j.	PROPN
ma-27	581	2	math	math	PROPN
ma-27	581	3	.	.	PUNCT
ma-27	582	1	19(2003	19(2003	NUM
ma-27	582	2	)	)	PUNCT
ma-27	582	3	,	,	PUNCT
ma-27	582	4	7–22.[7	7–22.[7	NUM
ma-27	582	5	]	]	X
ma-27	582	6	a.	a.	NOUN
ma-27	582	7	bielecki	bielecki	PROPN
ma-27	582	8	,	,	PUNCT
ma-27	582	9	une	une	PROPN
ma-27	582	10	remarque	remarque	X
ma-27	582	11	sur	sur	PROPN
ma-27	582	12	l’application	l’application	PROPN
ma-27	582	13	de	de	PROPN
ma-27	582	14	la	la	X
ma-27	582	15	méthode	méthode	X
ma-27	582	16	de	de	X
ma-27	582	17	banach	banach	PROPN
ma-27	582	18	–	–	PUNCT
ma-27	582	19	cocciopoli	cocciopoli	NOUN
ma-27	582	20	-	-	PUNCT
ma-27	582	21	tichonov	tichonov	NOUN
ma-27	582	22	dans	dan	NOUN
ma-27	582	23	la	la	X
ma-27	582	24	thórie	thórie	PROPN
ma-27	582	25	del’équation	del’équation	NOUN
ma-27	582	26	s	s	PART
ma-27	582	27	=	=	SYM
ma-27	582	28	f	f	X
ma-27	582	29	(	(	PUNCT
ma-27	582	30	x	x	PROPN
ma-27	582	31	,	,	PUNCT
ma-27	582	32	y	y	PROPN
ma-27	582	33	,	,	PUNCT
ma-27	582	34	z	z	PROPN
ma-27	582	35	,	,	PUNCT
ma-27	582	36	p	p	X
ma-27	582	37	,	,	PUNCT
ma-27	582	38	q	q	NOUN
ma-27	582	39	)	)	PUNCT
ma-27	582	40	,	,	PUNCT
ma-27	582	41	bull	bull	NOUN
ma-27	582	42	.	.	PUNCT
ma-27	583	1	pol	pol	PROPN
ma-27	583	2	.	.	PUNCT
ma-27	584	1	acad	acad	PROPN
ma-27	584	2	.	.	PUNCT
ma-27	585	1	sci	sci	PROPN
ma-27	585	2	.	.	PUNCT
ma-27	585	3	math	math	PROPN
ma-27	585	4	.	.	PUNCT
ma-27	586	1	4(1956	4(1956	NUM
ma-27	586	2	)	)	PUNCT
ma-27	586	3	,	,	PUNCT
ma-27	586	4	265–357.[8	265–357.[8	NUM
ma-27	586	5	]	]	X
ma-27	586	6	c.	c.	PROPN
ma-27	586	7	byrne	byrne	PROPN
ma-27	586	8	,	,	PUNCT
ma-27	586	9	iterative	iterative	ADJ
ma-27	586	10	oblique	oblique	ADJ
ma-27	586	11	projection	projection	NOUN
ma-27	586	12	onto	onto	ADP
ma-27	586	13	convex	convex	NOUN
ma-27	586	14	sets	set	NOUN
ma-27	586	15	and	and	CCONJ
ma-27	586	16	the	the	DET
ma-27	586	17	split	split	ADJ
ma-27	586	18	feasibility	feasibility	NOUN
ma-27	586	19	problem	problem	NOUN
ma-27	586	20	,	,	PUNCT
ma-27	586	21	inverse	inverse	NOUN
ma-27	586	22	problems	problem	NOUN
ma-27	586	23	,	,	PUNCT
ma-27	586	24	18(2)(2002	18(2)(2002	NUM
ma-27	586	25	)	)	PUNCT
ma-27	586	26	,	,	PUNCT
ma-27	586	27	441–453.[9	441–453.[9	X
ma-27	586	28	]	]	X
ma-27	586	29	g.	g.	PROPN
ma-27	586	30	cai	cai	PROPN
ma-27	586	31	,	,	PUNCT
ma-27	586	32	y.	y.	PROPN
ma-27	586	33	shehu	shehu	PROPN
ma-27	586	34	,	,	PUNCT
ma-27	586	35	an	an	DET
ma-27	586	36	iterative	iterative	NOUN
ma-27	586	37	algorithm	algorithm	NOUN
ma-27	586	38	for	for	ADP
ma-27	586	39	fixed	fix	VERB
ma-27	586	40	point	point	NOUN
ma-27	586	41	problem	problem	NOUN
ma-27	586	42	and	and	CCONJ
ma-27	586	43	convex	convex	ADJ
ma-27	586	44	minimization	minimization	NOUN
ma-27	586	45	problem	problem	NOUN
ma-27	586	46	with	with	ADP
ma-27	586	47	applications	application	NOUN
ma-27	586	48	,	,	PUNCT
ma-27	586	49	fixed	fix	VERB
ma-27	586	50	point	point	NOUN
ma-27	586	51	theory	theory	NOUN
ma-27	586	52	appl	appl	NOUN
ma-27	586	53	.	.	PROPN
ma-27	587	1	2015	2015	NUM
ma-27	587	2	(	(	PUNCT
ma-27	587	3	2015	2015	NUM
ma-27	587	4	)	)	PUNCT
ma-27	587	5	7	7	NUM
ma-27	587	6	.	.	PUNCT
ma-27	588	1	https://doi.org/10.1186/s13663-014-0253-6.[10	https://doi.org/10.1186/s13663-014-0253-6.[10	PROPN
ma-27	588	2	]	]	X
ma-27	589	1	s.k	s.k	AUX
ma-27	589	2	.	.	PUNCT
ma-27	589	3	chatterjea	chatterjea	PROPN
ma-27	589	4	,	,	PUNCT
ma-27	589	5	fixed	fix	VERB
ma-27	589	6	point	point	NOUN
ma-27	589	7	theorems	theorem	NOUN
ma-27	589	8	,	,	PUNCT
ma-27	589	9	c	c	PROPN
ma-27	589	10	r	r	NOUN
ma-27	589	11	acad	acad	PROPN
ma-27	589	12	bulg	bulg	PROPN
ma-27	589	13	sci	sci	PROPN
ma-27	589	14	.	.	PROPN
ma-27	589	15	25(1972	25(1972	NUM
ma-27	589	16	)	)	PUNCT
ma-27	589	17	,	,	PUNCT
ma-27	589	18	727–730.[11	727–730.[11	PROPN
ma-27	589	19	]	]	X
ma-27	589	20	y.	y.	NOUN
ma-27	589	21	censor	censor	NOUN
ma-27	589	22	and	and	CCONJ
ma-27	589	23	t.	t.	PROPN
ma-27	589	24	elfving	elfving	NOUN
ma-27	589	25	,	,	PUNCT
ma-27	589	26	a	a	DET
ma-27	589	27	multiprojection	multiprojection	NOUN
ma-27	589	28	algorithm	algorithm	NOUN
ma-27	589	29	using	use	VERB
ma-27	589	30	bregman	bregman	NOUN
ma-27	589	31	projections	projection	NOUN
ma-27	589	32	in	in	ADP
ma-27	589	33	a	a	DET
ma-27	589	34	product	product	NOUN
ma-27	589	35	space	space	NOUN
ma-27	589	36	,	,	PUNCT
ma-27	589	37	numer	numer	NOUN
ma-27	589	38	.	.	PUNCT
ma-27	590	1	algo	algo	PROPN
ma-27	590	2	-	-	PUNCT
ma-27	590	3	rithms	rithms	PROPN
ma-27	590	4	,	,	PUNCT
ma-27	590	5	8(2–4	8(2–4	NUM
ma-27	590	6	)	)	PUNCT
ma-27	590	7	(	(	PUNCT
ma-27	590	8	1994	1994	NUM
ma-27	590	9	)	)	PUNCT
ma-27	590	10	,	,	PUNCT
ma-27	590	11	221–239.[12	221–239.[12	PROPN
ma-27	590	12	]	]	X
ma-27	590	13	r.	r.	NOUN
ma-27	590	14	chugh	chugh	NOUN
ma-27	590	15	,	,	PUNCT
ma-27	590	16	v.	v.	PROPN
ma-27	590	17	kumar	kumar	PROPN
ma-27	590	18	and	and	CCONJ
ma-27	590	19	s.	s.	PROPN
ma-27	590	20	kumar	kumar	PROPN
ma-27	590	21	,	,	PUNCT
ma-27	590	22	strong	strong	ADJ
ma-27	590	23	convergence	convergence	NOUN
ma-27	590	24	of	of	ADP
ma-27	590	25	a	a	DET
ma-27	590	26	new	new	ADJ
ma-27	590	27	three	three	NUM
ma-27	590	28	step	step	NOUN
ma-27	590	29	iterative	iterative	NOUN
ma-27	590	30	scheme	scheme	NOUN
ma-27	590	31	in	in	ADP
ma-27	590	32	banach	banach	NOUN
ma-27	590	33	spaces	space	NOUN
ma-27	590	34	,	,	PUNCT
ma-27	590	35	amer	amer	PROPN
ma-27	590	36	.	.	PUNCT
ma-27	591	1	j.	j.	PROPN
ma-27	591	2	comp	comp	PROPN
ma-27	591	3	.	.	PUNCT
ma-27	592	1	math	math	NOUN
ma-27	592	2	.	.	PUNCT
ma-27	593	1	2(2012	2(2012	NUM
ma-27	593	2	)	)	PUNCT
ma-27	593	3	,	,	PUNCT
ma-27	593	4	345–357.[13	345–357.[13	NUM
ma-27	593	5	]	]	X
ma-27	593	6	q.l	q.l	PROPN
ma-27	593	7	.	.	PROPN
ma-27	593	8	dong	dong	PROPN
ma-27	593	9	,	,	PUNCT
ma-27	593	10	x.h	x.h	PROPN
ma-27	593	11	.	.	PROPN
ma-27	593	12	li	li	PROPN
ma-27	593	13	,	,	PUNCT
ma-27	593	14	d.	d.	PROPN
ma-27	593	15	kitkuan	kitkuan	PROPN
ma-27	593	16	,	,	PUNCT
ma-27	593	17	y.j	y.j	PROPN
ma-27	593	18	.	.	PUNCT
ma-27	593	19	cho	cho	PROPN
ma-27	593	20	,	,	PUNCT
ma-27	593	21	p.	p.	PROPN
ma-27	593	22	kumam	kumam	PROPN
ma-27	593	23	,	,	PUNCT
ma-27	593	24	some	some	DET
ma-27	593	25	algorithms	algorithm	NOUN
ma-27	593	26	for	for	ADP
ma-27	593	27	classes	class	NOUN
ma-27	593	28	of	of	ADP
ma-27	593	29	split	split	NOUN
ma-27	593	30	feasibility	feasibility	NOUN
ma-27	593	31	problems	problem	NOUN
ma-27	593	32	involvingparamonotone	involvingparamonotone	NOUN
ma-27	593	33	equilibria	equilibrium	NOUN
ma-27	593	34	and	and	CCONJ
ma-27	593	35	convex	convex	VERB
ma-27	593	36	optimization	optimization	NOUN
ma-27	593	37	,	,	PUNCT
ma-27	593	38	j.	j.	PROPN
ma-27	593	39	inequal	inequal	PROPN
ma-27	593	40	.	.	PUNCT
ma-27	594	1	appl	appl	PROPN
ma-27	594	2	.	.	PROPN
ma-27	595	1	2019	2019	NUM
ma-27	595	2	(	(	PUNCT
ma-27	595	3	2019	2019	NUM
ma-27	595	4	)	)	PUNCT
ma-27	595	5	77	77	NUM
ma-27	595	6	.	.	PUNCT
ma-27	596	1	https://doi.org/10.1186/	https://doi.org/10.1186/	PROPN
ma-27	596	2	s13660	s13660	PROPN
ma-27	596	3	-	-	PUNCT
ma-27	596	4	019	019	NUM
ma-27	596	5	-	-	PUNCT
ma-27	596	6	2030	2030	NUM
ma-27	596	7	-	-	SYM
ma-27	596	8	x.[14	x.[14	PROPN
ma-27	596	9	]	]	PUNCT
ma-27	596	10	c.	c.	PROPN
ma-27	596	11	d.	d.	PROPN
ma-27	596	12	enyi	enyi	PROPN
ma-27	596	13	and	and	CCONJ
ma-27	596	14	m.	m.	PROPN
ma-27	596	15	e.	e.	PROPN
ma-27	596	16	soh	soh	PROPN
ma-27	596	17	,	,	PUNCT
ma-27	596	18	modified	modify	VERB
ma-27	596	19	gradient	gradient	NOUN
ma-27	596	20	-	-	PUNCT
ma-27	596	21	projection	projection	NOUN
ma-27	596	22	algorithm	algorithm	NOUN
ma-27	596	23	for	for	ADP
ma-27	596	24	solving	solve	VERB
ma-27	596	25	convex	convex	ADJ
ma-27	596	26	minimization	minimization	NOUN
ma-27	596	27	problem	problem	NOUN
ma-27	596	28	in	in	ADP
ma-27	596	29	hilbertspaces	hilbertspace	NOUN
ma-27	596	30	,	,	PUNCT
ma-27	596	31	iaeng	iaeng	PROPN
ma-27	596	32	international	international	PROPN
ma-27	596	33	journal	journal	PROPN
ma-27	596	34	of	of	ADP
ma-27	596	35	applied	apply	VERB
ma-27	596	36	mathematics	mathematic	NOUN
ma-27	596	37	,	,	PUNCT
ma-27	596	38	44	44	NUM
ma-27	596	39	(	(	PUNCT
ma-27	596	40	2014	2014	NUM
ma-27	596	41	)	)	PUNCT
ma-27	596	42	,	,	PUNCT
ma-27	596	43	3.[15	3.[15	NUM
ma-27	596	44	]	]	PUNCT
ma-27	596	45	m.	m.	NOUN
ma-27	596	46	feng	feng	PROPN
ma-27	596	47	,	,	PUNCT
ma-27	596	48	l.	l.	PROPN
ma-27	596	49	shi	shi	PROPN
ma-27	596	50	and	and	CCONJ
ma-27	596	51	r.	r.	PROPN
ma-27	596	52	chen	chen	PROPN
ma-27	596	53	,	,	PUNCT
ma-27	596	54	a	a	DET
ma-27	596	55	new	new	ADJ
ma-27	596	56	three	three	NUM
ma-27	596	57	-	-	PUNCT
ma-27	596	58	step	step	NOUN
ma-27	596	59	iterative	iterative	NOUN
ma-27	596	60	algorithm	algorithm	NOUN
ma-27	596	61	for	for	ADP
ma-27	596	62	solving	solve	VERB
ma-27	596	63	the	the	DET
ma-27	596	64	split	split	NOUN
ma-27	596	65	feasibility	feasibility	NOUN
ma-27	596	66	problem	problem	NOUN
ma-27	596	67	,	,	PUNCT
ma-27	596	68	u.p.b.sci	u.p.b.sci	NOUN
ma-27	596	69	.	.	PUNCT
ma-27	597	1	bull	bull	NOUN
ma-27	597	2	.	.	PUNCT
ma-27	597	3	,	,	PUNCT
ma-27	597	4	series	series	PROPN
ma-27	597	5	a	a	PROPN
ma-27	597	6	,	,	PUNCT
ma-27	597	7	81	81	NUM
ma-27	597	8	(	(	PUNCT
ma-27	597	9	2019	2019	NUM
ma-27	597	10	)	)	PUNCT
ma-27	597	11	,	,	PUNCT
ma-27	597	12	93	93	NUM
ma-27	597	13	-	-	SYM
ma-27	597	14	102.[16	102.[16	NUM
ma-27	597	15	]	]	PUNCT
ma-27	597	16	c.	c.	PROPN
ma-27	597	17	garodia	garodia	NOUN
ma-27	597	18	and	and	CCONJ
ma-27	597	19	i.	i.	PROPN
ma-27	597	20	uddin	uddin	PROPN
ma-27	597	21	,	,	PUNCT
ma-27	597	22	a	a	DET
ma-27	597	23	new	new	ADJ
ma-27	597	24	fixed	fix	VERB
ma-27	597	25	point	point	NOUN
ma-27	597	26	algorithm	algorithm	NOUN
ma-27	597	27	for	for	ADP
ma-27	597	28	finding	find	VERB
ma-27	597	29	the	the	DET
ma-27	597	30	solution	solution	NOUN
ma-27	597	31	of	of	ADP
ma-27	597	32	a	a	DET
ma-27	597	33	delay	delay	NOUN
ma-27	597	34	differential	differential	NOUN
ma-27	597	35	equation	equation	NOUN
ma-27	597	36	,	,	PUNCT
ma-27	597	37	aimsmath	aimsmath	PROPN
ma-27	597	38	.	.	PUNCT
ma-27	598	1	5(2020	5(2020	X
ma-27	598	2	)	)	PUNCT
ma-27	598	3	,	,	PUNCT
ma-27	598	4	3182–3200.[17	3182–3200.[17	PROPN
ma-27	598	5	]	]	X
ma-27	598	6	f.	f.	PROPN
ma-27	598	7	gursoy	gursoy	PROPN
ma-27	598	8	and	and	CCONJ
ma-27	598	9	v	v	ADP
ma-27	598	10	karakaya	karakaya	NOUN
ma-27	598	11	,	,	PUNCT
ma-27	598	12	a	a	DET
ma-27	598	13	picard	picard	NOUN
ma-27	598	14	–	–	PUNCT
ma-27	598	15	s	s	NOUN
ma-27	598	16	hybrid	hybrid	ADJ
ma-27	598	17	type	type	NOUN
ma-27	598	18	iteration	iteration	NOUN
ma-27	598	19	method	method	NOUN
ma-27	598	20	for	for	ADP
ma-27	598	21	solving	solve	VERB
ma-27	598	22	a	a	DET
ma-27	598	23	differential	differential	ADJ
ma-27	598	24	equation	equation	NOUN
ma-27	598	25	with	with	ADP
ma-27	598	26	retardedargument	retardedargument	NOUN
ma-27	598	27	,	,	PUNCT
ma-27	598	28	(	(	PUNCT
ma-27	598	29	2014	2014	NUM
ma-27	598	30	)	)	PUNCT
ma-27	598	31	,	,	PUNCT
ma-27	598	32	arxiv:1403.2546v2	arxiv:1403.2546v2	PROPN
ma-27	598	33	.	.	PUNCT
ma-27	599	1	https://doi.org/10.1186/s13663-014-0253-6	https://doi.org/10.1186/s13663-014-0253-6	NUM
ma-27	600	1	https://doi.org/10.1186/s13660-019-2030-x	https://doi.org/10.1186/s13660-019-2030-x	PROPN
ma-27	600	2	https://doi.org/10.1186/s13660-019-2030-x	https://doi.org/10.1186/s13660-019-2030-x	PROPN
ma-27	600	3	eur	eur	PROPN
ma-27	600	4	.	.	PUNCT
ma-27	601	1	j.	j.	PROPN
ma-27	601	2	math	math	PROPN
ma-27	601	3	.	.	PUNCT
ma-27	602	1	anal	anal	ADJ
ma-27	602	2	.	.	PUNCT
ma-27	603	1	1	1	NUM
ma-27	603	2	(	(	PUNCT
ma-27	603	3	2021	2021	NUM
ma-27	603	4	)	)	PUNCT
ma-27	604	1	131	131	NUM
ma-27	605	1	[	[	SYM
ma-27	605	2	18	18	NUM
ma-27	605	3	]	]	PUNCT
ma-27	605	4	m.	m.	NOUN
ma-27	605	5	a.	a.	NOUN
ma-27	605	6	harder	hard	ADV
ma-27	605	7	,	,	PUNCT
ma-27	605	8	fixed	fix	VERB
ma-27	605	9	point	point	NOUN
ma-27	605	10	theory	theory	NOUN
ma-27	605	11	and	and	CCONJ
ma-27	605	12	stability	stability	NOUN
ma-27	605	13	results	result	NOUN
ma-27	605	14	for	for	ADP
ma-27	605	15	fixed	fix	VERB
ma-27	605	16	point	point	NOUN
ma-27	605	17	iteration	iteration	NOUN
ma-27	605	18	procedures	procedure	NOUN
ma-27	605	19	.	.	PUNCT
ma-27	606	1	phd	phd	NOUN
ma-27	606	2	thesis	thesis	PROPN
ma-27	606	3	,	,	PUNCT
ma-27	606	4	university	university	NOUN
ma-27	606	5	ofmissouri	ofmissouri	NOUN
ma-27	606	6	-	-	PUNCT
ma-27	606	7	rolla	rolla	PROPN
ma-27	606	8	,	,	PUNCT
ma-27	606	9	missouri	missouri	PROPN
ma-27	606	10	(	(	PUNCT
ma-27	606	11	2008).[19	2008).[19	PROPN
ma-27	606	12	]	]	X
ma-27	606	13	s.	s.	PROPN
ma-27	606	14	he	he	PROPN
ma-27	606	15	and	and	CCONJ
ma-27	606	16	z.	z.	PROPN
ma-27	606	17	zhao	zhao	PROPN
ma-27	606	18	,	,	PUNCT
ma-27	606	19	strong	strong	ADJ
ma-27	606	20	convergence	convergence	NOUN
ma-27	606	21	of	of	ADP
ma-27	606	22	a	a	DET
ma-27	606	23	relaxed	relaxed	ADJ
ma-27	606	24	cq	cq	NOUN
ma-27	606	25	algorithm	algorithm	NOUN
ma-27	606	26	for	for	ADP
ma-27	606	27	the	the	DET
ma-27	606	28	split	split	NOUN
ma-27	606	29	feasibility	feasibility	NOUN
ma-27	606	30	problem	problem	NOUN
ma-27	606	31	,	,	PUNCT
ma-27	606	32	j.	j.	PROPN
ma-27	606	33	inequal	inequal	PROPN
ma-27	606	34	.	.	PUNCT
ma-27	607	1	appl.2013	appl.2013	ADP
ma-27	607	2	(	(	PUNCT
ma-27	607	3	2013	2013	NUM
ma-27	607	4	)	)	PUNCT
ma-27	607	5	,	,	PUNCT
ma-27	607	6	197	197	NUM
ma-27	607	7	.	.	PUNCT
ma-27	607	8	.[20	.[20	PROPN
ma-27	607	9	]	]	PUNCT
ma-27	607	10	i.	i.	PROPN
ma-27	607	11	karahan	karahan	PROPN
ma-27	607	12	and	and	CCONJ
ma-27	607	13	m.	m.	PROPN
ma-27	607	14	ozdemir	ozdemir	PROPN
ma-27	607	15	,	,	PUNCT
ma-27	607	16	a	a	DET
ma-27	607	17	general	general	ADJ
ma-27	607	18	iterative	iterative	NOUN
ma-27	607	19	method	method	NOUN
ma-27	607	20	for	for	ADP
ma-27	607	21	approximation	approximation	NOUN
ma-27	607	22	of	of	ADP
ma-27	607	23	fixed	fix	VERB
ma-27	607	24	points	point	NOUN
ma-27	607	25	and	and	CCONJ
ma-27	607	26	their	their	PRON
ma-27	607	27	applications	application	NOUN
ma-27	607	28	,	,	PUNCT
ma-27	607	29	adv.fixed	adv.fixe	VERB
ma-27	607	30	point	point	NOUN
ma-27	607	31	theory	theory	NOUN
ma-27	607	32	,	,	PUNCT
ma-27	607	33	3(2013	3(2013	NUM
ma-27	607	34	)	)	PUNCT
ma-27	607	35	,	,	PUNCT
ma-27	607	36	510–526.[21	510–526.[21	NUM
ma-27	607	37	]	]	X
ma-27	607	38	s.	s.	PROPN
ma-27	607	39	ishikawa	ishikawa	PROPN
ma-27	607	40	,	,	PUNCT
ma-27	607	41	fixed	fix	VERB
ma-27	607	42	points	point	NOUN
ma-27	607	43	by	by	ADP
ma-27	607	44	a	a	DET
ma-27	607	45	new	new	ADJ
ma-27	607	46	iteration	iteration	NOUN
ma-27	607	47	method	method	NOUN
ma-27	607	48	.	.	PUNCT
ma-27	608	1	proc	proc	NOUN
ma-27	608	2	.	.	PUNCT
ma-27	609	1	am	be	AUX
ma-27	609	2	.	.	PUNCT
ma-27	610	1	math	math	NOUN
ma-27	610	2	.	.	PUNCT
ma-27	611	1	soc	soc	PROPN
ma-27	611	2	.	.	PUNCT
ma-27	612	1	44(1974	44(1974	NUM
ma-27	612	2	)	)	PUNCT
ma-27	613	1	,	,	PUNCT
ma-27	613	2	147–150.[22	147–150.[22	NOUN
ma-27	613	3	]	]	PUNCT
ma-27	613	4	r.	r.	PROPN
ma-27	613	5	kannan	kannan	PROPN
ma-27	613	6	,	,	PUNCT
ma-27	613	7	some	some	DET
ma-27	613	8	results	result	NOUN
ma-27	613	9	on	on	ADP
ma-27	613	10	fixed	fix	VERB
ma-27	613	11	point	point	NOUN
ma-27	613	12	.	.	PUNCT
ma-27	614	1	bull	bull	PROPN
ma-27	614	2	calcutta	calcutta	PROPN
ma-27	614	3	math	math	NOUN
ma-27	614	4	.	.	PUNCT
ma-27	615	1	soc	soc	PROPN
ma-27	615	2	.	.	PUNCT
ma-27	616	1	10	10	NUM
ma-27	616	2	(	(	PUNCT
ma-27	616	3	1968	1968	NUM
ma-27	616	4	)	)	PUNCT
ma-27	616	5	,	,	PUNCT
ma-27	616	6	71–76.[23	71–76.[23	NUM
ma-27	616	7	]	]	X
ma-27	616	8	k.	k.	PROPN
ma-27	616	9	maleknejad	maleknejad	PROPN
ma-27	616	10	and	and	CCONJ
ma-27	616	11	m.	m.	NOUN
ma-27	616	12	hadizadeh	hadizadeh	NOUN
ma-27	616	13	,	,	PUNCT
ma-27	616	14	a	a	DET
ma-27	616	15	new	new	ADJ
ma-27	616	16	computational	computational	ADJ
ma-27	616	17	method	method	NOUN
ma-27	616	18	for	for	ADP
ma-27	616	19	volterra	volterra	NOUN
ma-27	616	20	–	–	PUNCT
ma-27	616	21	fredholm	fredholm	ADJ
ma-27	616	22	integral	integral	ADJ
ma-27	616	23	equations	equation	NOUN
ma-27	616	24	,	,	PUNCT
ma-27	617	1	comput.math	comput.math	NUM
ma-27	617	2	.	.	PUNCT
ma-27	617	3	appl	appl	PROPN
ma-27	617	4	.	.	PUNCT
ma-27	618	1	37	37	NUM
ma-27	618	2	(	(	PUNCT
ma-27	618	3	1999	1999	NUM
ma-27	618	4	)	)	PUNCT
ma-27	618	5	,	,	PUNCT
ma-27	618	6	1–8.[24	1–8.[24	NUM
ma-27	618	7	]	]	X
ma-27	618	8	w.	w.	PROPN
ma-27	618	9	r.	r.	PROPN
ma-27	618	10	mann	mann	PROPN
ma-27	618	11	,	,	PUNCT
ma-27	618	12	mean	mean	ADJ
ma-27	618	13	value	value	NOUN
ma-27	618	14	methods	method	NOUN
ma-27	618	15	in	in	ADP
ma-27	618	16	iteration	iteration	NOUN
ma-27	618	17	,	,	PUNCT
ma-27	618	18	proc	proc	NOUN
ma-27	618	19	.	.	PUNCT
ma-27	618	20	am	be	AUX
ma-27	618	21	.	.	PUNCT
ma-27	619	1	math	math	NOUN
ma-27	619	2	.	.	PUNCT
ma-27	620	1	soc	soc	PROPN
ma-27	620	2	.	.	PUNCT
ma-27	621	1	4(1953	4(1953	NUM
ma-27	621	2	)	)	PUNCT
ma-27	621	3	,	,	PUNCT
ma-27	621	4	506–510.[25	506–510.[25	NUM
ma-27	621	5	]	]	PUNCT
ma-27	622	1	m.	m.	NOUN
ma-27	622	2	a.	a.	PROPN
ma-27	622	3	noor	noor	PROPN
ma-27	622	4	,	,	PUNCT
ma-27	622	5	new	new	ADJ
ma-27	622	6	approximation	approximation	NOUN
ma-27	622	7	schemes	scheme	NOUN
ma-27	622	8	for	for	ADP
ma-27	622	9	general	general	ADJ
ma-27	622	10	variational	variational	ADJ
ma-27	622	11	inequalities	inequality	NOUN
ma-27	622	12	,	,	PUNCT
ma-27	622	13	j.	j.	PROPN
ma-27	622	14	math	math	PROPN
ma-27	622	15	anal	anal	PROPN
ma-27	622	16	appl	appl	PROPN
ma-27	622	17	.	.	PUNCT
ma-27	622	18	251(2000	251(2000	NUM
ma-27	622	19	)	)	PUNCT
ma-27	622	20	,	,	PUNCT
ma-27	622	21	217–229.[26	217–229.[26	X
ma-27	622	22	]	]	X
ma-27	622	23	d.	d.	PROPN
ma-27	622	24	pant	pant	PROPN
ma-27	622	25	and	and	CCONJ
ma-27	622	26	r.	r.	PROPN
ma-27	622	27	shukla	shukla	PROPN
ma-27	622	28	,	,	PUNCT
ma-27	622	29	approximating	approximate	VERB
ma-27	622	30	fixed	fix	VERB
ma-27	622	31	points	point	NOUN
ma-27	622	32	of	of	ADP
ma-27	622	33	generalized	generalized	ADJ
ma-27	622	34	α	α	PROPN
ma-27	622	35	-	-	PUNCT
ma-27	622	36	nonexpansive	nonexpansive	ADJ
ma-27	622	37	mappings	mapping	NOUN
ma-27	622	38	in	in	ADP
ma-27	622	39	banach	banach	NOUN
ma-27	622	40	spaces	space	NOUN
ma-27	622	41	,	,	PUNCT
ma-27	622	42	numer	numer	PROPN
ma-27	622	43	.	.	PUNCT
ma-27	623	1	funct	funct	PROPN
ma-27	623	2	.	.	PUNCT
ma-27	624	1	anal	anal	PROPN
ma-27	624	2	.	.	PUNCT
ma-27	625	1	optim	optim	PROPN
ma-27	625	2	.	.	PUNCT
ma-27	626	1	38(2	38(2	NUM
ma-27	626	2	)	)	PUNCT
ma-27	626	3	(	(	PUNCT
ma-27	626	4	2017	2017	NUM
ma-27	626	5	)	)	PUNCT
ma-27	626	6	,	,	PUNCT
ma-27	627	1	248–266.[27	248–266.[27	PROPN
ma-27	627	2	]	]	X
ma-27	627	3	w.	w.	PROPN
ma-27	627	4	phuengrattana	phuengrattana	PROPN
ma-27	627	5	and	and	CCONJ
ma-27	627	6	s.	s.	PROPN
ma-27	627	7	suantai	suantai	PROPN
ma-27	627	8	,	,	PUNCT
ma-27	627	9	on	on	ADP
ma-27	627	10	the	the	DET
ma-27	627	11	rate	rate	NOUN
ma-27	627	12	of	of	ADP
ma-27	627	13	convergence	convergence	NOUN
ma-27	627	14	of	of	ADP
ma-27	627	15	mann	mann	PROPN
ma-27	627	16	,	,	PUNCT
ma-27	627	17	ishikawa	ishikawa	PROPN
ma-27	627	18	,	,	PUNCT
ma-27	627	19	noor	noor	PROPN
ma-27	627	20	and	and	CCONJ
ma-27	627	21	sp	sp	NOUN
ma-27	627	22	-	-	PUNCT
ma-27	627	23	iterations	iteration	NOUN
ma-27	627	24	forcontinuous	forcontinuous	ADJ
ma-27	627	25	functions	function	NOUN
ma-27	627	26	on	on	ADP
ma-27	627	27	an	an	DET
ma-27	627	28	arbitrary	arbitrary	ADJ
ma-27	627	29	interval	interval	NOUN
ma-27	627	30	,	,	PUNCT
ma-27	627	31	j.	j.	PROPN
ma-27	627	32	comput	comput	PROPN
ma-27	627	33	.	.	PUNCT
ma-27	628	1	appl	appl	PROPN
ma-27	628	2	.	.	PROPN
ma-27	628	3	math	math	NOUN
ma-27	628	4	.	.	PUNCT
ma-27	629	1	235(2011	235(2011	NUM
ma-27	629	2	)	)	PUNCT
ma-27	629	3	,	,	PUNCT
ma-27	629	4	3006–3014.[28	3006–3014.[28	X
ma-27	629	5	]	]	X
ma-27	629	6	d.	d.	PROPN
ma-27	629	7	r.	r.	PROPN
ma-27	629	8	sahu	sahu	PROPN
ma-27	629	9	and	and	CCONJ
ma-27	629	10	a.	a.	NOUN
ma-27	629	11	petrusel	petrusel	NOUN
ma-27	629	12	,	,	PUNCT
ma-27	629	13	strong	strong	ADJ
ma-27	629	14	convergence	convergence	NOUN
ma-27	629	15	of	of	ADP
ma-27	629	16	iterative	iterative	ADJ
ma-27	629	17	methods	method	NOUN
ma-27	629	18	by	by	ADP
ma-27	629	19	strictly	strictly	ADV
ma-27	629	20	pseudocontractive	pseudocontractive	ADJ
ma-27	629	21	mappings	mapping	NOUN
ma-27	629	22	inbanach	inbanach	ADJ
ma-27	629	23	spaces	space	NOUN
ma-27	629	24	.	.	PUNCT
ma-27	630	1	nonlinear	nonlinear	ADJ
ma-27	630	2	anal	anal	PROPN
ma-27	630	3	.	.	PUNCT
ma-27	631	1	theory	theory	NOUN
ma-27	631	2	methods	method	NOUN
ma-27	631	3	appl	appl	PROPN
ma-27	631	4	.	.	PUNCT
ma-27	632	1	74(2011	74(2011	NOUN
ma-27	632	2	)	)	PUNCT
ma-27	632	3	,	,	PUNCT
ma-27	632	4	6012–6023.[29	6012–6023.[29	NUM
ma-27	632	5	]	]	X
ma-27	632	6	j.	j.	PROPN
ma-27	632	7	schu	schu	PROPN
ma-27	632	8	,	,	PUNCT
ma-27	632	9	weak	weak	ADJ
ma-27	632	10	and	and	CCONJ
ma-27	632	11	strong	strong	ADJ
ma-27	632	12	convergence	convergence	NOUN
ma-27	632	13	to	to	ADP
ma-27	632	14	fixed	fix	VERB
ma-27	632	15	points	point	NOUN
ma-27	632	16	of	of	ADP
ma-27	632	17	asymptotically	asymptotically	ADV
ma-27	632	18	nonexpansive	nonexpansive	ADJ
ma-27	632	19	mappings	mapping	NOUN
ma-27	632	20	,	,	PUNCT
ma-27	632	21	b.	b.	PROPN
ma-27	632	22	aust	aust	PROPN
ma-27	632	23	.	.	PUNCT
ma-27	633	1	math	math	PROPN
ma-27	633	2	.	.	PUNCT
ma-27	634	1	soc.43(1991	soc.43(1991	PROPN
ma-27	634	2	)	)	PUNCT
ma-27	634	3	,	,	PUNCT
ma-27	635	1	153–159.[30	153–159.[30	PROPN
ma-27	635	2	]	]	X
ma-27	635	3	y.	y.	PROPN
ma-27	635	4	shehu	shehu	PROPN
ma-27	635	5	,	,	PUNCT
ma-27	635	6	o.	o.	PROPN
ma-27	635	7	s.	s.	PROPN
ma-27	635	8	iyiola	iyiola	PROPN
ma-27	635	9	and	and	CCONJ
ma-27	635	10	c.	c.	PROPN
ma-27	635	11	d.	d.	PROPN
ma-27	635	12	enyi	enyi	PROPN
ma-27	635	13	,	,	PUNCT
ma-27	635	14	iterative	iterative	NOUN
ma-27	635	15	approximation	approximation	NOUN
ma-27	635	16	of	of	ADP
ma-27	635	17	solutions	solution	NOUN
ma-27	635	18	for	for	ADP
ma-27	635	19	constrained	constrain	VERB
ma-27	635	20	convex	convex	NOUN
ma-27	635	21	minimizationproblem	minimizationproblem	NOUN
ma-27	635	22	,	,	PUNCT
ma-27	635	23	arab	arab	PROPN
ma-27	635	24	j.	j.	PROPN
ma-27	635	25	math	math	PROPN
ma-27	635	26	.	.	PUNCT
ma-27	636	1	2(2013	2(2013	NUM
ma-27	636	2	)	)	PUNCT
ma-27	636	3	,	,	PUNCT
ma-27	637	1	393–402.[31	393–402.[31	X
ma-27	637	2	]	]	X
ma-27	637	3	h.	h.	PROPN
ma-27	637	4	f.	f.	PROPN
ma-27	637	5	senter	senter	PROPN
ma-27	637	6	and	and	CCONJ
ma-27	637	7	w.	w.	PROPN
ma-27	637	8	g.	g.	PROPN
ma-27	637	9	dotson	dotson	PROPN
ma-27	637	10	,	,	PUNCT
ma-27	637	11	approximating	approximate	VERB
ma-27	637	12	fixed	fix	VERB
ma-27	637	13	points	point	NOUN
ma-27	637	14	of	of	ADP
ma-27	637	15	nonexpansive	nonexpansive	ADJ
ma-27	637	16	mapping	mapping	NOUN
ma-27	637	17	,	,	PUNCT
ma-27	637	18	proc	proc	PROPN
ma-27	637	19	.	.	PUNCT
ma-27	638	1	amer	amer	PROPN
ma-27	638	2	.	.	PUNCT
ma-27	638	3	math	math	PROPN
ma-27	638	4	.	.	PUNCT
ma-27	639	1	soc.44(1974	soc.44(1974	PROPN
ma-27	639	2	)	)	PUNCT
ma-27	639	3	,	,	PUNCT
ma-27	640	1	375–380.[32	375–380.[32	PROPN
ma-27	640	2	]	]	PUNCT
ma-27	640	3	s.	s.	PROPN
ma-27	640	4	m.	m.	PROPN
ma-27	640	5	soltuz	soltuz	PROPN
ma-27	640	6	and	and	CCONJ
ma-27	640	7	t.	t.	PROPN
ma-27	640	8	grosan	grosan	PROPN
ma-27	640	9	,	,	PUNCT
ma-27	640	10	data	datum	NOUN
ma-27	640	11	dependence	dependence	NOUN
ma-27	640	12	for	for	ADP
ma-27	640	13	ishikawa	ishikawa	PROPN
ma-27	640	14	iteration	iteration	NOUN
ma-27	640	15	when	when	SCONJ
ma-27	640	16	dealing	deal	VERB
ma-27	640	17	with	with	ADP
ma-27	640	18	contractive	contractive	ADJ
ma-27	640	19	like	like	ADP
ma-27	640	20	operators	operator	NOUN
ma-27	640	21	,	,	PUNCT
ma-27	640	22	fixed	fix	VERB
ma-27	640	23	point	point	NOUN
ma-27	640	24	theory	theory	NOUN
ma-27	640	25	appl	appl	PROPN
ma-27	640	26	.	.	PROPN
ma-27	640	27	,	,	PUNCT
ma-27	640	28	(	(	PUNCT
ma-27	640	29	2008)2008	2008)2008	NOUN
ma-27	640	30	,	,	PUNCT
ma-27	640	31	242916.[33	242916.[33	NUM
ma-27	640	32	]	]	X
ma-27	640	33	t.	t.	PROPN
ma-27	640	34	suzuki	suzuki	PROPN
ma-27	640	35	,	,	PUNCT
ma-27	640	36	fixed	fix	VERB
ma-27	640	37	point	point	NOUN
ma-27	640	38	theorems	theorem	NOUN
ma-27	640	39	and	and	CCONJ
ma-27	640	40	convergence	convergence	NOUN
ma-27	640	41	theorems	theorem	NOUN
ma-27	640	42	for	for	ADP
ma-27	640	43	some	some	DET
ma-27	640	44	generalized	generalize	VERB
ma-27	640	45	nonexpansive	nonexpansive	ADJ
ma-27	640	46	mappings	mapping	NOUN
ma-27	640	47	,	,	PUNCT
ma-27	640	48	j.	j.	PROPN
ma-27	640	49	math.anal	math.anal	PROPN
ma-27	640	50	.	.	PROPN
ma-27	640	51	appl	appl	PROPN
ma-27	640	52	.	.	PROPN
ma-27	640	53	math	math	PROPN
ma-27	640	54	.	.	PUNCT
ma-27	641	1	340(2008	340(2008	NUM
ma-27	641	2	)	)	PUNCT
ma-27	641	3	,	,	PUNCT
ma-27	641	4	1088–10995.[34	1088–10995.[34	NUM
ma-27	641	5	]	]	X
ma-27	641	6	j.	j.	PROPN
ma-27	641	7	tang	tang	PROPN
ma-27	641	8	,	,	PUNCT
ma-27	641	9	s.	s.	PROPN
ma-27	641	10	chang	chang	PROPN
ma-27	641	11	,	,	PUNCT
ma-27	641	12	strong	strong	ADJ
ma-27	641	13	convergence	convergence	NOUN
ma-27	641	14	theorem	theorem	NOUN
ma-27	641	15	of	of	ADP
ma-27	641	16	two	two	NUM
ma-27	641	17	-	-	PUNCT
ma-27	641	18	step	step	NOUN
ma-27	641	19	iterative	iterative	NOUN
ma-27	641	20	algorithm	algorithm	NOUN
ma-27	641	21	for	for	ADP
ma-27	641	22	split	split	ADJ
ma-27	641	23	feasibility	feasibility	NOUN
ma-27	641	24	problems	problem	NOUN
ma-27	641	25	,	,	PUNCT
ma-27	641	26	j	j	PROPN
ma-27	641	27	inequalappl	inequalappl	NOUN
ma-27	641	28	.	.	PUNCT
ma-27	642	1	2014	2014	NUM
ma-27	642	2	(	(	PUNCT
ma-27	642	3	2014	2014	NUM
ma-27	642	4	)	)	PUNCT
ma-27	642	5	280	280	NUM
ma-27	642	6	.	.	PUNCT
ma-27	643	1	https://doi.org/10.1186/1029-242x-2014-280.[35	https://doi.org/10.1186/1029-242x-2014-280.[35	PROPN
ma-27	643	2	]	]	X
ma-27	643	3	s.	s.	PROPN
ma-27	643	4	thianwan	thianwan	PROPN
ma-27	643	5	,	,	PUNCT
ma-27	643	6	common	common	ADJ
ma-27	643	7	fixed	fix	VERB
ma-27	643	8	points	point	NOUN
ma-27	643	9	of	of	ADP
ma-27	643	10	new	new	ADJ
ma-27	643	11	iterations	iteration	NOUN
ma-27	643	12	for	for	ADP
ma-27	643	13	two	two	NUM
ma-27	643	14	asymptotically	asymptotically	ADV
ma-27	643	15	nonexpansive	nonexpansive	ADJ
ma-27	643	16	nonself	nonself	NOUN
ma-27	643	17	-	-	PUNCT
ma-27	643	18	mappings	mapping	NOUN
ma-27	643	19	in	in	ADP
ma-27	643	20	abanach	abanach	ADJ
ma-27	643	21	space	space	NOUN
ma-27	643	22	,	,	PUNCT
ma-27	643	23	j.f	j.f	ADP
ma-27	643	24	comput	comput	NOUN
ma-27	643	25	.	.	PUNCT
ma-27	644	1	appl	appl	PROPN
ma-27	644	2	.	.	PROPN
ma-27	644	3	math	math	NOUN
ma-27	644	4	.	.	PUNCT
ma-27	645	1	224(2009	224(2009	NUM
ma-27	645	2	)	)	PUNCT
ma-27	645	3	,	,	PUNCT
ma-27	645	4	688–695.[36	688–695.[36	PROPN
ma-27	645	5	]	]	PUNCT
ma-27	645	6	d.	d.	PROPN
ma-27	645	7	thakur	thakur	PROPN
ma-27	645	8	,	,	PUNCT
ma-27	645	9	b.	b.	PROPN
ma-27	645	10	s.	s.	PROPN
ma-27	645	11	thakur	thakur	PROPN
ma-27	645	12	,	,	PUNCT
ma-27	645	13	m.	m.	NOUN
ma-27	645	14	postolache	postolache	PROPN
ma-27	645	15	,	,	PUNCT
ma-27	645	16	a	a	DET
ma-27	645	17	new	new	ADJ
ma-27	645	18	iterative	iterative	NOUN
ma-27	645	19	scheme	scheme	NOUN
ma-27	645	20	for	for	ADP
ma-27	645	21	numerical	numerical	ADJ
ma-27	645	22	reckoning	reckon	VERB
ma-27	645	23	fixed	fix	VERB
ma-27	645	24	points	point	NOUN
ma-27	645	25	of	of	ADP
ma-27	645	26	suzuki’sgeneralized	suzuki’sgeneralize	VERB
ma-27	645	27	nonexpansive	nonexpansive	ADJ
ma-27	645	28	mappings	mapping	NOUN
ma-27	645	29	,	,	PUNCT
ma-27	645	30	appl	appl	PROPN
ma-27	645	31	.	.	PROPN
ma-27	645	32	math	math	NOUN
ma-27	645	33	.	.	PUNCT
ma-27	646	1	comput	comput	NOUN
ma-27	646	2	.	.	PUNCT
ma-27	647	1	275	275	NUM
ma-27	647	2	(	(	PUNCT
ma-27	647	3	2016	2016	NUM
ma-27	647	4	)	)	PUNCT
ma-27	647	5	,	,	PUNCT
ma-27	647	6	147–155.[37	147–155.[37	PROPN
ma-27	647	7	]	]	X
ma-27	647	8	b.	b.	PROPN
ma-27	647	9	s.	s.	PROPN
ma-27	647	10	thakur	thakur	PROPN
ma-27	647	11	,	,	PUNCT
ma-27	647	12	d.	d.	PROPN
ma-27	647	13	thakur	thakur	PROPN
ma-27	647	14	and	and	CCONJ
ma-27	647	15	m.	m.	PROPN
ma-27	647	16	postolache	postolache	PROPN
ma-27	647	17	,	,	PUNCT
ma-27	647	18	a	a	DET
ma-27	647	19	new	new	ADJ
ma-27	647	20	iterative	iterative	NOUN
ma-27	647	21	scheme	scheme	NOUN
ma-27	647	22	for	for	ADP
ma-27	647	23	numerical	numerical	ADJ
ma-27	647	24	reckoning	reckon	VERB
ma-27	647	25	fixed	fix	VERB
ma-27	647	26	points	point	NOUN
ma-27	647	27	of	of	ADP
ma-27	647	28	suzuki’sgeneralized	suzuki’sgeneralize	VERB
ma-27	647	29	nonexpansive	nonexpansive	ADJ
ma-27	647	30	mappings	mapping	NOUN
ma-27	647	31	,	,	PUNCT
ma-27	647	32	appl	appl	PROPN
ma-27	647	33	.	.	PROPN
ma-27	647	34	math	math	PROPN
ma-27	647	35	.	.	PUNCT
ma-27	648	1	comput	comput	NOUN
ma-27	648	2	.	.	PUNCT
ma-27	649	1	275(2016	275(2016	NUM
ma-27	649	2	)	)	PUNCT
ma-27	649	3	,	,	PUNCT
ma-27	649	4	147–155.[38	147–155.[38	PROPN
ma-27	649	5	]	]	X
ma-27	649	6	k.	k.	PROPN
ma-27	649	7	ullah	ullah	PROPN
ma-27	649	8	and	and	CCONJ
ma-27	649	9	m.	m.	PROPN
ma-27	649	10	arshad	arshad	PROPN
ma-27	649	11	,	,	PUNCT
ma-27	649	12	new	new	ADJ
ma-27	649	13	iteration	iteration	NOUN
ma-27	649	14	process	process	NOUN
ma-27	649	15	and	and	CCONJ
ma-27	649	16	numerical	numerical	ADJ
ma-27	649	17	reckoning	reckon	VERB
ma-27	649	18	fixed	fix	VERB
ma-27	649	19	points	point	NOUN
ma-27	649	20	in	in	ADP
ma-27	649	21	banach	banach	NOUN
ma-27	649	22	spaces	space	NOUN
ma-27	649	23	,	,	PUNCT
ma-27	649	24	universitypolitehnica	universitypolitehnica	PROPN
ma-27	649	25	of	of	ADP
ma-27	649	26	bucharest	buchar	ADJ
ma-27	649	27	scientific	scientific	ADJ
ma-27	649	28	bulletin	bulletin	NOUN
ma-27	649	29	series	series	PROPN
ma-27	649	30	a	a	PROPN
ma-27	649	31	,	,	PUNCT
ma-27	649	32	79	79	NUM
ma-27	649	33	(	(	PUNCT
ma-27	649	34	2017	2017	NUM
ma-27	649	35	)	)	PUNCT
ma-27	649	36	,	,	PUNCT
ma-27	649	37	113–122.[39	113–122.[39	NUM
ma-27	649	38	]	]	X
ma-27	649	39	k.	k.	PROPN
ma-27	649	40	ullah	ullah	PROPN
ma-27	649	41	and	and	CCONJ
ma-27	649	42	m.	m.	PROPN
ma-27	649	43	arshad	arshad	PROPN
ma-27	649	44	,	,	PUNCT
ma-27	649	45	numerical	numerical	ADJ
ma-27	649	46	reckoning	reckon	VERB
ma-27	649	47	fixed	fix	VERB
ma-27	649	48	points	point	NOUN
ma-27	649	49	for	for	ADP
ma-27	649	50	suzuki	suzuki	PROPN
ma-27	649	51	’s	’s	PART
ma-27	649	52	generalized	generalize	VERB
ma-27	649	53	nonexpansive	nonexpansive	ADJ
ma-27	649	54	mappings	mapping	NOUN
ma-27	649	55	vianew	vianew	ADJ
ma-27	649	56	iteration	iteration	NOUN
ma-27	649	57	process	process	NOUN
ma-27	649	58	,	,	PUNCT
ma-27	649	59	filomat	filomat	NOUN
ma-27	649	60	,	,	PUNCT
ma-27	649	61	32(2018	32(2018	NUM
ma-27	649	62	)	)	PUNCT
ma-27	649	63	,	,	PUNCT
ma-27	649	64	187–196.[40	187–196.[40	NOUN
ma-27	649	65	]	]	PUNCT
ma-27	649	66	x.	x.	NOUN
ma-27	649	67	weng	weng	PROPN
ma-27	649	68	,	,	PUNCT
ma-27	649	69	fixed	fix	VERB
ma-27	649	70	point	point	NOUN
ma-27	649	71	iteration	iteration	NOUN
ma-27	649	72	for	for	ADP
ma-27	649	73	local	local	ADJ
ma-27	649	74	strictly	strictly	ADV
ma-27	649	75	pseudocontractive	pseudocontractive	ADJ
ma-27	649	76	mapping	mapping	NOUN
ma-27	649	77	,	,	PUNCT
ma-27	649	78	proc	proc	PROPN
ma-27	649	79	.	.	PUNCT
ma-27	650	1	am	be	AUX
ma-27	650	2	.	.	PUNCT
ma-27	651	1	math	math	NOUN
ma-27	651	2	.	.	PUNCT
ma-27	652	1	soc	soc	PROPN
ma-27	652	2	.	.	PUNCT
ma-27	653	1	113(1991	113(1991	NUM
ma-27	653	2	)	)	PUNCT
ma-27	654	1	,	,	PUNCT
ma-27	654	2	727–731.[41	727–731.[41	PROPN
ma-27	654	3	]	]	PUNCT
ma-27	654	4	t.	t.	PROPN
ma-27	654	5	zamfirescu	zamfirescu	PROPN
ma-27	654	6	,	,	PUNCT
ma-27	654	7	fixed	fix	VERB
ma-27	654	8	point	point	NOUN
ma-27	654	9	theorems	theorem	NOUN
ma-27	654	10	in	in	ADP
ma-27	654	11	metric	metric	ADJ
ma-27	654	12	spaces	space	NOUN
ma-27	654	13	,	,	PUNCT
ma-27	654	14	arch	arch	NOUN
ma-27	654	15	.	.	PUNCT
ma-27	655	1	math	math	NOUN
ma-27	655	2	.	.	PUNCT
ma-27	656	1	(	(	PUNCT
ma-27	656	2	basel	basel	PROPN
ma-27	656	3	)	)	PUNCT
ma-27	656	4	.	.	PUNCT
ma-27	657	1	23	23	NUM
ma-27	657	2	(	(	PUNCT
ma-27	657	3	1972	1972	NUM
ma-27	657	4	)	)	PUNCT
ma-27	657	5	,	,	PUNCT
ma-27	657	6	292–298	292–298	NUM
ma-27	657	7	.	.	PUNCT
ma-27	658	1	https://doi.org/10.1186/1029-242x-2014-280	https://doi.org/10.1186/1029-242x-2014-280	PROPN
ma-27	658	2	eur	eur	PROPN
ma-27	658	3	.	.	PUNCT
ma-27	659	1	j.	j.	PROPN
ma-27	659	2	math	math	PROPN
ma-27	659	3	.	.	PUNCT
ma-27	660	1	anal	anal	ADJ
ma-27	660	2	.	.	PUNCT
ma-27	661	1	1	1	NUM
ma-27	661	2	(	(	PUNCT
ma-27	661	3	2021	2021	NUM
ma-27	661	4	)	)	PUNCT
ma-27	662	1	132	132	NUM
ma-27	662	2	[	[	X
ma-27	662	3	42	42	NUM
ma-27	662	4	]	]	X
ma-27	662	5	h.k	h.k	PROPN
ma-27	662	6	.	.	PROPN
ma-27	662	7	xu	xu	PROPN
ma-27	662	8	,	,	PUNCT
ma-27	662	9	a	a	DET
ma-27	662	10	variable	variable	ADJ
ma-27	662	11	krasnosel’skii	krasnosel’skii	NOUN
ma-27	662	12	-	-	PUNCT
ma-27	662	13	mann	mann	PROPN
ma-27	662	14	algorithm	algorithm	NOUN
ma-27	662	15	and	and	CCONJ
ma-27	662	16	the	the	DET
ma-27	662	17	multiple	multiple	ADV
ma-27	662	18	-	-	PUNCT
ma-27	662	19	set	set	VERB
ma-27	662	20	split	split	NOUN
ma-27	662	21	feasibility	feasibility	NOUN
ma-27	662	22	problem	problem	NOUN
ma-27	662	23	,	,	PUNCT
ma-27	662	24	inverse	inverse	NOUN
ma-27	662	25	probl.22(6	probl.22(6	NOUN
ma-27	662	26	)	)	PUNCT
ma-27	662	27	(	(	PUNCT
ma-27	662	28	2006	2006	NUM
ma-27	662	29	)	)	PUNCT
ma-27	662	30	,	,	PUNCT
ma-27	662	31	2021–2034.[43	2021–2034.[43	NUM
ma-27	662	32	]	]	X
ma-27	662	33	h.k	h.k	PROPN
ma-27	662	34	.	.	PROPN
ma-27	662	35	xu	xu	PROPN
ma-27	662	36	,	,	PUNCT
ma-27	662	37	iterative	iterative	NOUN
ma-27	662	38	methods	method	NOUN
ma-27	662	39	for	for	ADP
ma-27	662	40	the	the	DET
ma-27	662	41	split	split	NOUN
ma-27	662	42	feasibility	feasibility	NOUN
ma-27	662	43	problem	problem	NOUN
ma-27	662	44	in	in	ADP
ma-27	662	45	infinite	infinite	ADJ
ma-27	662	46	-	-	PUNCT
ma-27	662	47	dimensional	dimensional	ADJ
ma-27	662	48	hilbert	hilbert	NOUN
ma-27	662	49	spaces	space	NOUN
ma-27	662	50	.	.	PUNCT
ma-27	663	1	inverse	inverse	PROPN
ma-27	663	2	probl	probl	NOUN
ma-27	663	3	.	.	PUNCT
ma-27	664	1	26(2010	26(2010	NUM
ma-27	664	2	)	)	PUNCT
ma-27	664	3	,	,	PUNCT
ma-27	664	4	105018	105018	NUM
ma-27	664	5	.	.	PUNCT
ma-27	665	1	17	17	NUM
ma-27	665	2	pp	pp	NOUN
ma-27	665	3	.	.	PUNCT
ma-27	666	1	1	1	X
ma-27	666	2	.	.	X
ma-27	666	3	introduction	introduction	NOUN
ma-27	666	4	2	2	NUM
ma-27	666	5	.	.	PUNCT
ma-27	666	6	preliminaries	preliminary	NOUN
ma-27	666	7	3	3	NUM
ma-27	666	8	.	.	PUNCT
ma-27	666	9	rate	rate	NOUN
ma-27	666	10	of	of	ADP
ma-27	666	11	convergence	convergence	NOUN
ma-27	666	12	4	4	NUM
ma-27	666	13	.	.	PUNCT
ma-27	666	14	convergence	convergence	NOUN
ma-27	666	15	results	result	VERB
ma-27	666	16	5	5	NUM
ma-27	666	17	.	.	PUNCT
ma-27	667	1	numerical	numerical	PROPN
ma-27	667	2	result	result	PROPN
ma-27	667	3	6	6	NUM
ma-27	667	4	.	.	PUNCT
ma-27	668	1	stability	stability	NOUN
ma-27	668	2	result	result	VERB
ma-27	668	3	7	7	NUM
ma-27	668	4	.	.	PUNCT
ma-27	668	5	data	datum	NOUN
ma-27	668	6	dependence	dependence	NOUN
ma-27	668	7	result	result	VERB
ma-27	668	8	8	8	NUM
ma-27	668	9	.	.	PUNCT
ma-27	669	1	some	some	DET
ma-27	669	2	applications	application	NOUN
ma-27	669	3	8.1	8.1	NUM
ma-27	669	4	.	.	PUNCT
ma-27	670	1	application	application	NOUN
ma-27	670	2	to	to	ADP
ma-27	670	3	constrained	constrain	VERB
ma-27	670	4	convex	convex	NOUN
ma-27	670	5	minimization	minimization	NOUN
ma-27	670	6	problem	problem	NOUN
ma-27	670	7	8.2	8.2	NUM
ma-27	670	8	.	.	PUNCT
ma-27	671	1	application	application	NOUN
ma-27	671	2	to	to	PART
ma-27	671	3	split	split	VERB
ma-27	671	4	feasibility	feasibility	NOUN
ma-27	671	5	problem	problem	NOUN
ma-27	671	6	9	9	NUM
ma-27	671	7	.	.	PUNCT
ma-27	672	1	conclusion	conclusion	NOUN
ma-27	672	2	references	reference	NOUN