id	sid	tid	token	lemma	pos
ma-198	1	1	2024	2024	NUM
ma-198	1	2	ada	ada	PROPN
ma-198	1	3	academica	academica	PROPN
ma-198	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-198	1	5	.	.	PUNCT
ma-198	2	1	j.	j.	PROPN
ma-198	2	2	math	math	PROPN
ma-198	2	3	.	.	PUNCT
ma-198	3	1	anal	anal	ADJ
ma-198	3	2	.	.	PUNCT
ma-198	4	1	4	4	NUM
ma-198	4	2	(	(	PUNCT
ma-198	4	3	2024	2024	NUM
ma-198	4	4	)	)	PUNCT
ma-198	5	1	2doi	2doi	NUM
ma-198	5	2	:	:	PUNCT
ma-198	5	3	10.28924	10.28924	NUM
ma-198	5	4	/	/	SYM
ma-198	5	5	ada	ada	PROPN
ma-198	5	6	/	/	SYM
ma-198	5	7	ma.4.2	ma.4.2	PROPN
ma-198	5	8	modified	modify	VERB
ma-198	5	9	viscosity	viscosity	NOUN
ma-198	5	10	iterative	iterative	NOUN
ma-198	5	11	algorithm	algorithm	NOUN
ma-198	5	12	for	for	ADP
ma-198	5	13	solving	solve	VERB
ma-198	5	14	variational	variational	ADJ
ma-198	5	15	inclusion	inclusion	NOUN
ma-198	5	16	and	and	CCONJ
ma-198	5	17	fixed	fix	VERB
ma-198	5	18	point	point	NOUN
ma-198	5	19	problems	problem	NOUN
ma-198	5	20	in	in	ADP
ma-198	5	21	real	real	ADJ
ma-198	5	22	hilbert	hilbert	NOUN
ma-198	5	23	space	space	NOUN
ma-198	5	24	furmose	furmose	PROPN
ma-198	5	25	mendy1,∗	mendy1,∗	NOUN
ma-198	5	26	,	,	PUNCT
ma-198	5	27	john	john	PROPN
ma-198	5	28	t	t	PROPN
ma-198	5	29	mendy2,∗	mendy2,∗	VERB
ma-198	5	30	1department	1department	NUM
ma-198	5	31	of	of	ADP
ma-198	5	32	mathematics	mathematic	NOUN
ma-198	5	33	,	,	PUNCT
ma-198	5	34	university	university	PROPN
ma-198	5	35	of	of	ADP
ma-198	5	36	toledo	toledo	PROPN
ma-198	5	37	,	,	PUNCT
ma-198	5	38	usa	usa	PROPN
ma-198	5	39	furmosemendy111@gmail.com	furmosemendy111@gmail.com	PROPN
ma-198	6	1	2department	2department	NUM
ma-198	6	2	of	of	ADP
ma-198	6	3	mathematics	mathematic	NOUN
ma-198	6	4	,	,	PUNCT
ma-198	6	5	universita	universita	PROPN
ma-198	6	6	degli	degli	PROPN
ma-198	6	7	studi	studi	PROPN
ma-198	6	8	dell’aquila	dell’aquila	PROPN
ma-198	6	9	,	,	PUNCT
ma-198	6	10	italy	italy	PROPN
ma-198	6	11	,	,	PUNCT
ma-198	6	12	67010	67010	NUM
ma-198	6	13	,	,	PUNCT
ma-198	6	14	coppito	coppito	ADJ
ma-198	6	15	,	,	PUNCT
ma-198	6	16	via	via	ADP
ma-198	6	17	vetoio	vetoio	PROPN
ma-198	6	18	,	,	PUNCT
ma-198	6	19	italy	italy	PROPN
ma-198	6	20	johntgracemendy@gmail.com	johntgracemendy@gmail.com	X
ma-198	7	1	∗correspondence	∗correspondence	NOUN
ma-198	7	2	:	:	PUNCT
ma-198	7	3	furmosemendy111@gmail.com	furmosemendy111@gmail.com	X
ma-198	7	4	abstract	abstract	ADJ
ma-198	7	5	.	.	PUNCT
ma-198	8	1	this	this	DET
ma-198	8	2	paper	paper	NOUN
ma-198	8	3	introduces	introduce	VERB
ma-198	8	4	a	a	DET
ma-198	8	5	new	new	ADJ
ma-198	8	6	iterative	iterative	NOUN
ma-198	8	7	algorithm	algorithm	NOUN
ma-198	8	8	,	,	PUNCT
ma-198	8	9	called	call	VERB
ma-198	8	10	the	the	DET
ma-198	8	11	modified	modify	VERB
ma-198	8	12	viscosity	viscosity	NOUN
ma-198	8	13	iterativealgorithm	iterativealgorithm	NOUN
ma-198	8	14	,	,	PUNCT
ma-198	8	15	designed	design	VERB
ma-198	8	16	to	to	PART
ma-198	8	17	solve	solve	VERB
ma-198	8	18	problems	problem	NOUN
ma-198	8	19	related	relate	VERB
ma-198	8	20	to	to	ADP
ma-198	8	21	variational	variational	ADJ
ma-198	8	22	inclusion	inclusion	NOUN
ma-198	8	23	and	and	CCONJ
ma-198	8	24	fixed	fix	VERB
ma-198	8	25	point	point	NOUN
ma-198	8	26	in	in	ADP
ma-198	8	27	real	real	ADJ
ma-198	8	28	hilbertspaces	hilbertspace	NOUN
ma-198	8	29	.	.	PUNCT
ma-198	9	1	the	the	DET
ma-198	9	2	algorithm	algorithm	NOUN
ma-198	9	3	is	be	AUX
ma-198	9	4	specifically	specifically	ADV
ma-198	9	5	tailored	tailor	VERB
ma-198	9	6	to	to	PART
ma-198	9	7	handle	handle	VERB
ma-198	9	8	multivalued	multivalued	ADJ
ma-198	9	9	quasi	quasi	ADJ
ma-198	9	10	-	-	ADJ
ma-198	9	11	nonexpansive	nonexpansive	ADJ
ma-198	9	12	and	and	CCONJ
ma-198	9	13	demi	demi	NOUN
ma-198	9	14	-	-	PUNCT
ma-198	9	15	contractive	contractive	ADJ
ma-198	9	16	operators	operator	NOUN
ma-198	9	17	.	.	PUNCT
ma-198	10	1	the	the	DET
ma-198	10	2	convergence	convergence	NOUN
ma-198	10	3	properties	property	NOUN
ma-198	10	4	of	of	ADP
ma-198	10	5	the	the	DET
ma-198	10	6	algorithm	algorithm	NOUN
ma-198	10	7	are	be	AUX
ma-198	10	8	analyzed	analyze	VERB
ma-198	10	9	and	and	CCONJ
ma-198	10	10	established	establish	VERB
ma-198	10	11	,	,	PUNCT
ma-198	10	12	ensuring	ensure	VERB
ma-198	10	13	its	its	PRON
ma-198	10	14	effectiveness	effectiveness	NOUN
ma-198	10	15	in	in	ADP
ma-198	10	16	finding	find	VERB
ma-198	10	17	solutions	solution	NOUN
ma-198	10	18	for	for	ADP
ma-198	10	19	complex	complex	ADJ
ma-198	10	20	mathematical	mathematical	ADJ
ma-198	10	21	problems	problem	NOUN
ma-198	10	22	in	in	ADP
ma-198	10	23	the	the	DET
ma-198	10	24	field	field	NOUN
ma-198	10	25	of	of	ADP
ma-198	10	26	opti	opti	NOUN
ma-198	10	27	-	-	PUNCT
ma-198	10	28	mization	mization	NOUN
ma-198	10	29	and	and	CCONJ
ma-198	10	30	equilibrium	equilibrium	NOUN
ma-198	10	31	.	.	PUNCT
ma-198	11	1	1	1	X
ma-198	11	2	.	.	X
ma-198	11	3	introduction	introduction	NOUN
ma-198	11	4	variational	variational	ADJ
ma-198	11	5	inclusion	inclusion	NOUN
ma-198	11	6	and	and	CCONJ
ma-198	11	7	fixed	fix	VERB
ma-198	11	8	point	point	NOUN
ma-198	11	9	problems	problem	NOUN
ma-198	11	10	involving	involve	VERB
ma-198	11	11	multivalued	multivalue	VERB
ma-198	11	12	quasi	quasi	PROPN
ma-198	11	13	nonexpansive	nonexpansive	PROPN
ma-198	11	14	anddemicontractive	anddemicontractive	PROPN
ma-198	11	15	operators	operator	NOUN
ma-198	11	16	play	play	VERB
ma-198	11	17	a	a	DET
ma-198	11	18	crucial	crucial	ADJ
ma-198	11	19	role	role	NOUN
ma-198	11	20	in	in	ADP
ma-198	11	21	the	the	DET
ma-198	11	22	field	field	NOUN
ma-198	11	23	of	of	ADP
ma-198	11	24	mathematics	mathematic	NOUN
ma-198	11	25	,	,	PUNCT
ma-198	11	26	particularly	particularly	ADV
ma-198	11	27	in	in	ADP
ma-198	11	28	real	real	ADJ
ma-198	11	29	hilbertspaces.the	hilbertspaces.the	DET
ma-198	11	30	study	study	NOUN
ma-198	11	31	of	of	ADP
ma-198	11	32	variational	variational	ADJ
ma-198	11	33	inclusion	inclusion	NOUN
ma-198	11	34	and	and	CCONJ
ma-198	11	35	fixed	fix	VERB
ma-198	11	36	point	point	NOUN
ma-198	11	37	problems	problem	NOUN
ma-198	11	38	originated	originate	VERB
ma-198	11	39	from	from	ADP
ma-198	11	40	the	the	DET
ma-198	11	41	theory	theory	NOUN
ma-198	11	42	of	of	ADP
ma-198	11	43	opti	opti	PROPN
ma-198	11	44	-	-	PUNCT
ma-198	11	45	mization	mization	NOUN
ma-198	11	46	and	and	CCONJ
ma-198	11	47	nonlinear	nonlinear	ADJ
ma-198	11	48	analysis	analysis	NOUN
ma-198	11	49	,	,	PUNCT
ma-198	11	50	and	and	CCONJ
ma-198	11	51	in	in	ADP
ma-198	11	52	the	the	DET
ma-198	11	53	mid−20th	mid−20th	NOUN
ma-198	11	54	century	century	NOUN
ma-198	11	55	,	,	PUNCT
ma-198	11	56	mathematicians	mathematician	NOUN
ma-198	11	57	began	begin	VERB
ma-198	11	58	investigatingproblems	investigatingproblem	NOUN
ma-198	11	59	involving	involve	VERB
ma-198	11	60	finding	find	VERB
ma-198	11	61	points	point	NOUN
ma-198	11	62	that	that	PRON
ma-198	11	63	satisfy	satisfy	VERB
ma-198	11	64	certain	certain	ADJ
ma-198	11	65	inclusion	inclusion	NOUN
ma-198	11	66	and	and	CCONJ
ma-198	11	67	fixed	fix	VERB
ma-198	11	68	point	point	NOUN
ma-198	11	69	conditions	condition	NOUN
ma-198	11	70	.	.	PUNCT
ma-198	12	1	over	over	ADP
ma-198	12	2	time	time	NOUN
ma-198	12	3	,	,	PUNCT
ma-198	12	4	research	research	NOUN
ma-198	12	5	in	in	ADP
ma-198	12	6	this	this	DET
ma-198	12	7	area	area	NOUN
ma-198	12	8	expanded	expand	VERB
ma-198	12	9	and	and	CCONJ
ma-198	12	10	became	become	VERB
ma-198	12	11	an	an	DET
ma-198	12	12	essential	essential	ADJ
ma-198	12	13	part	part	NOUN
ma-198	12	14	of	of	ADP
ma-198	12	15	functional	functional	ADJ
ma-198	12	16	analysis	analysis	NOUN
ma-198	12	17	and	and	CCONJ
ma-198	12	18	optimiza	optimiza	ADJ
ma-198	12	19	-	-	PUNCT
ma-198	12	20	tion	tion	NOUN
ma-198	12	21	theory	theory	NOUN
ma-198	12	22	.	.	PUNCT
ma-198	13	1	they	they	PRON
ma-198	13	2	are	be	AUX
ma-198	13	3	widely	widely	ADV
ma-198	13	4	-	-	PUNCT
ma-198	13	5	used	use	VERB
ma-198	13	6	in	in	ADP
ma-198	13	7	applications	application	NOUN
ma-198	13	8	in	in	ADP
ma-198	13	9	diverse	diverse	ADJ
ma-198	13	10	fields	field	NOUN
ma-198	13	11	such	such	ADJ
ma-198	13	12	as	as	ADP
ma-198	13	13	engineering	engineering	NOUN
ma-198	13	14	,	,	PUNCT
ma-198	13	15	economics	economic	NOUN
ma-198	13	16	,	,	PUNCT
ma-198	13	17	physics	physics	NOUN
ma-198	13	18	,	,	PUNCT
ma-198	13	19	and	and	CCONJ
ma-198	13	20	computer	computer	NOUN
ma-198	13	21	science	science	NOUN
ma-198	13	22	.	.	PUNCT
ma-198	14	1	they	they	PRON
ma-198	14	2	provide	provide	VERB
ma-198	14	3	a	a	DET
ma-198	14	4	framework	framework	NOUN
ma-198	14	5	to	to	PART
ma-198	14	6	model	model	VERB
ma-198	14	7	and	and	CCONJ
ma-198	14	8	solve	solve	VERB
ma-198	14	9	various	various	ADJ
ma-198	14	10	real	real	ADJ
ma-198	14	11	-	-	PUNCT
ma-198	14	12	worldproblems	worldproblem	NOUN
ma-198	14	13	,	,	PUNCT
ma-198	14	14	including	include	VERB
ma-198	14	15	equilibrium	equilibrium	NOUN
ma-198	14	16	problems	problem	NOUN
ma-198	14	17	,	,	PUNCT
ma-198	14	18	optimization	optimization	NOUN
ma-198	14	19	problems	problem	NOUN
ma-198	14	20	,	,	PUNCT
ma-198	14	21	and	and	CCONJ
ma-198	14	22	variational	variational	ADJ
ma-198	14	23	inequalities.fixed	inequalities.fixe	VERB
ma-198	14	24	point	point	NOUN
ma-198	14	25	problems	problem	NOUN
ma-198	14	26	,	,	PUNCT
ma-198	14	27	on	on	ADP
ma-198	14	28	the	the	DET
ma-198	14	29	other	other	ADJ
ma-198	14	30	hand	hand	NOUN
ma-198	14	31	,	,	PUNCT
ma-198	14	32	deal	deal	VERB
ma-198	14	33	with	with	ADP
ma-198	14	34	finding	find	VERB
ma-198	14	35	points	point	NOUN
ma-198	14	36	that	that	PRON
ma-198	14	37	remain	remain	VERB
ma-198	14	38	unchanged	unchanged	ADJ
ma-198	14	39	underthe	underthe	ADJ
ma-198	14	40	action	action	NOUN
ma-198	14	41	of	of	ADP
ma-198	14	42	an	an	DET
ma-198	14	43	operator	operator	NOUN
ma-198	14	44	.	.	PUNCT
ma-198	15	1	the	the	DET
ma-198	15	2	concept	concept	NOUN
ma-198	15	3	of	of	ADP
ma-198	15	4	fixed	fix	VERB
ma-198	15	5	points	point	NOUN
ma-198	15	6	has	have	VERB
ma-198	15	7	profound	profound	ADJ
ma-198	15	8	implications	implication	NOUN
ma-198	15	9	in	in	ADP
ma-198	15	10	mathematicsand	mathematicsand	NOUN
ma-198	15	11	its	its	PRON
ma-198	15	12	applications	application	NOUN
ma-198	15	13	.	.	PUNCT
ma-198	16	1	a	a	DET
ma-198	16	2	wide	wide	ADJ
ma-198	16	3	range	range	NOUN
ma-198	16	4	of	of	ADP
ma-198	16	5	problems	problem	NOUN
ma-198	16	6	in	in	ADP
ma-198	16	7	analysis	analysis	NOUN
ma-198	16	8	,	,	PUNCT
ma-198	16	9	differential	differential	ADJ
ma-198	16	10	equations	equation	NOUN
ma-198	16	11	,	,	PUNCT
ma-198	16	12	and	and	CCONJ
ma-198	16	13	optimization	optimization	NOUN
ma-198	16	14	received	receive	VERB
ma-198	16	15	:	:	PUNCT
ma-198	16	16	22	22	NUM
ma-198	16	17	nov	nov	PROPN
ma-198	16	18	2023	2023	NUM
ma-198	16	19	.	.	PUNCT
ma-198	17	1	key	key	ADJ
ma-198	17	2	words	word	NOUN
ma-198	17	3	and	and	CCONJ
ma-198	17	4	phrases	phrase	NOUN
ma-198	17	5	.	.	PUNCT
ma-198	18	1	iterative	iterative	NOUN
ma-198	18	2	algorithm	algorithm	NOUN
ma-198	18	3	,	,	PUNCT
ma-198	18	4	quasi	quasi	ADJ
ma-198	18	5	-	-	ADJ
ma-198	18	6	nonexpansive	nonexpansive	ADJ
ma-198	18	7	,	,	PUNCT
ma-198	18	8	multivalued	multivalued	ADJ
ma-198	18	9	demiclosed	demiclosed	ADJ
ma-198	18	10	mapping	mapping	NOUN
ma-198	18	11	,	,	PUNCT
ma-198	18	12	hilbert	hilbert	NOUN
ma-198	18	13	space	space	NOUN
ma-198	18	14	,	,	PUNCT
ma-198	18	15	variational	variational	ADJ
ma-198	18	16	inequality	inequality	NOUN
ma-198	18	17	,	,	PUNCT
ma-198	18	18	strongly	strongly	ADV
ma-198	18	19	monotone	monotone	ADJ
ma-198	18	20	mappings	mapping	NOUN
ma-198	18	21	.	.	PUNCT
ma-198	19	1	1	1	NUM
ma-198	19	2	https://adac.ee	https://adac.ee	PROPN
ma-198	19	3	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	19	4	https://orcid.org/0009-0000-3806-629x	https://orcid.org/0009-0000-3806-629x	PROPN
ma-198	19	5	https://orcid.org/0000-0002-3774-0761	https://orcid.org/0000-0002-3774-0761	VERB
ma-198	19	6	eur	eur	PROPN
ma-198	19	7	.	.	PUNCT
ma-198	20	1	j.	j.	PROPN
ma-198	20	2	math	math	PROPN
ma-198	20	3	.	.	PUNCT
ma-198	21	1	anal	anal	PROPN
ma-198	21	2	.	.	PUNCT
ma-198	22	1	10.28924	10.28924	NUM
ma-198	22	2	/	/	SYM
ma-198	22	3	ada	ada	PROPN
ma-198	22	4	/	/	SYM
ma-198	22	5	ma.4.2	ma.4.2	PROPN
ma-198	22	6	2theory	2theory	NUM
ma-198	22	7	can	can	AUX
ma-198	22	8	be	be	AUX
ma-198	22	9	reduced	reduce	VERB
ma-198	22	10	to	to	ADP
ma-198	22	11	fixed	fix	VERB
ma-198	22	12	point	point	NOUN
ma-198	22	13	problems	problem	NOUN
ma-198	22	14	.	.	PUNCT
ma-198	23	1	they	they	PRON
ma-198	23	2	serve	serve	VERB
ma-198	23	3	as	as	ADP
ma-198	23	4	powerful	powerful	ADJ
ma-198	23	5	tools	tool	NOUN
ma-198	23	6	to	to	PART
ma-198	23	7	prove	prove	VERB
ma-198	23	8	the	the	DET
ma-198	23	9	exis	exis	NOUN
ma-198	23	10	-	-	PUNCT
ma-198	23	11	tence	tence	NOUN
ma-198	23	12	and	and	CCONJ
ma-198	23	13	uniqueness	uniqueness	NOUN
ma-198	23	14	of	of	ADP
ma-198	23	15	solutions	solution	NOUN
ma-198	23	16	,	,	PUNCT
ma-198	23	17	compute	compute	NOUN
ma-198	23	18	approximations	approximation	NOUN
ma-198	23	19	,	,	PUNCT
ma-198	23	20	and	and	CCONJ
ma-198	23	21	establish	establish	VERB
ma-198	23	22	convergence	convergence	NOUN
ma-198	23	23	propertiesof	propertiesof	NOUN
ma-198	23	24	iterative	iterative	NOUN
ma-198	23	25	algorithms	algorithm	NOUN
ma-198	23	26	.	.	PUNCT
ma-198	24	1	whilst	whilst	SCONJ
ma-198	24	2	multivalued	multivalue	VERB
ma-198	24	3	quasi	quasi	ADJ
ma-198	24	4	nonexpansive	nonexpansive	PROPN
ma-198	24	5	operators	operator	NOUN
ma-198	24	6	play	play	VERB
ma-198	24	7	a	a	DET
ma-198	24	8	pivotal	pivotal	ADJ
ma-198	24	9	role	role	NOUN
ma-198	24	10	in	in	ADP
ma-198	24	11	vari	vari	ADJ
ma-198	24	12	-	-	ADJ
ma-198	24	13	ational	ational	ADJ
ma-198	24	14	inclusion	inclusion	NOUN
ma-198	24	15	and	and	CCONJ
ma-198	24	16	fixed	fix	VERB
ma-198	24	17	point	point	NOUN
ma-198	24	18	problems	problem	NOUN
ma-198	24	19	.	.	PUNCT
ma-198	25	1	these	these	DET
ma-198	25	2	operators	operator	NOUN
ma-198	25	3	possess	possess	VERB
ma-198	25	4	certain	certain	ADJ
ma-198	25	5	properties	property	NOUN
ma-198	25	6	that	that	PRON
ma-198	25	7	ensurethe	ensurethe	DET
ma-198	25	8	stability	stability	NOUN
ma-198	25	9	and	and	CCONJ
ma-198	25	10	convergence	convergence	NOUN
ma-198	25	11	of	of	ADP
ma-198	25	12	iterative	iterative	ADJ
ma-198	25	13	algorithms	algorithm	NOUN
ma-198	25	14	.	.	PUNCT
ma-198	26	1	they	they	PRON
ma-198	26	2	have	have	VERB
ma-198	26	3	applications	application	NOUN
ma-198	26	4	in	in	ADP
ma-198	26	5	image	image	NOUN
ma-198	26	6	processing	processing	NOUN
ma-198	26	7	,	,	PUNCT
ma-198	26	8	signal	signal	NOUN
ma-198	26	9	estimation	estimation	NOUN
ma-198	26	10	,	,	PUNCT
ma-198	26	11	and	and	CCONJ
ma-198	26	12	constrained	constrained	ADJ
ma-198	26	13	optimization	optimization	NOUN
ma-198	26	14	,	,	PUNCT
ma-198	26	15	among	among	ADP
ma-198	26	16	others.moreover	others.moreover	ADV
ma-198	26	17	,	,	PUNCT
ma-198	26	18	fixed	fix	VERB
ma-198	26	19	point	point	NOUN
ma-198	26	20	theory	theory	NOUN
ma-198	26	21	for	for	ADP
ma-198	26	22	multivalued	multivalued	ADJ
ma-198	26	23	mappings	mapping	NOUN
ma-198	26	24	has	have	AUX
ma-198	26	25	also	also	ADV
ma-198	26	26	contributed	contribute	VERB
ma-198	26	27	to	to	ADP
ma-198	26	28	the	the	DET
ma-198	26	29	developmentof	developmentof	NOUN
ma-198	26	30	related	relate	VERB
ma-198	26	31	areas	area	NOUN
ma-198	26	32	of	of	ADP
ma-198	26	33	research	research	NOUN
ma-198	26	34	,	,	PUNCT
ma-198	26	35	such	such	ADJ
ma-198	26	36	as	as	ADP
ma-198	26	37	operator	operator	NOUN
ma-198	26	38	theory	theory	NOUN
ma-198	26	39	,	,	PUNCT
ma-198	26	40	topological	topological	ADJ
ma-198	26	41	degree	degree	NOUN
ma-198	26	42	theory	theory	NOUN
ma-198	26	43	,	,	PUNCT
ma-198	26	44	and	and	CCONJ
ma-198	26	45	convex	convex	ADJ
ma-198	26	46	anal	anal	ADJ
ma-198	26	47	-	-	PUNCT
ma-198	26	48	ysis	ysis	NOUN
ma-198	26	49	.	.	PUNCT
ma-198	27	1	by	by	ADP
ma-198	27	2	investigating	investigate	VERB
ma-198	27	3	the	the	DET
ma-198	27	4	properties	property	NOUN
ma-198	27	5	and	and	CCONJ
ma-198	27	6	behavior	behavior	NOUN
ma-198	27	7	of	of	ADP
ma-198	27	8	fixed	fix	VERB
ma-198	27	9	points	point	NOUN
ma-198	27	10	in	in	ADP
ma-198	27	11	multivalued	multivalued	ADJ
ma-198	27	12	mappings	mapping	NOUN
ma-198	27	13	,	,	PUNCT
ma-198	27	14	math	math	NOUN
ma-198	27	15	-	-	PUNCT
ma-198	27	16	ematicians	ematician	NOUN
ma-198	27	17	have	have	AUX
ma-198	27	18	gained	gain	VERB
ma-198	27	19	a	a	DET
ma-198	27	20	deeper	deep	ADJ
ma-198	27	21	understanding	understanding	NOUN
ma-198	27	22	of	of	ADP
ma-198	27	23	these	these	DET
ma-198	27	24	fields	field	NOUN
ma-198	27	25	and	and	CCONJ
ma-198	27	26	have	have	AUX
ma-198	27	27	been	be	AUX
ma-198	27	28	able	able	ADJ
ma-198	27	29	to	to	PART
ma-198	27	30	establishconnections	establishconnections	VERB
ma-198	27	31	and	and	CCONJ
ma-198	27	32	develop	develop	VERB
ma-198	27	33	new	new	ADJ
ma-198	27	34	techniques.(see	techniques.(see	NOUN
ma-198	27	35	,	,	PUNCT
ma-198	27	36	[	[	X
ma-198	27	37	30	30	NUM
ma-198	27	38	]	]	PUNCT
ma-198	27	39	,	,	PUNCT
ma-198	27	40	[	[	X
ma-198	27	41	10	10	NUM
ma-198	27	42	,	,	PUNCT
ma-198	27	43	11	11	NUM
ma-198	27	44	]	]	PUNCT
ma-198	27	45	,	,	PUNCT
ma-198	27	46	[	[	X
ma-198	27	47	2	2	NUM
ma-198	27	48	]	]	PUNCT
ma-198	27	49	,	,	PUNCT
ma-198	27	50	[	[	X
ma-198	27	51	7	7	NUM
ma-198	27	52	]	]	PUNCT
ma-198	27	53	,	,	PUNCT
ma-198	27	54	[	[	X
ma-198	27	55	33	33	NUM
ma-198	27	56	]	]	PUNCT
ma-198	27	57	,	,	PUNCT
ma-198	27	58	[	[	X
ma-198	27	59	9	9	NUM
ma-198	27	60	]	]	PUNCT
ma-198	27	61	and	and	CCONJ
ma-198	27	62	[	[	X
ma-198	27	63	26]).demicontractive	26]).demicontractive	NUM
ma-198	27	64	operators	operator	NOUN
ma-198	27	65	,	,	PUNCT
ma-198	27	66	on	on	ADP
ma-198	27	67	the	the	DET
ma-198	27	68	other	other	ADJ
ma-198	27	69	hand	hand	NOUN
ma-198	27	70	,	,	PUNCT
ma-198	27	71	exhibit	exhibit	VERB
ma-198	27	72	properties	property	NOUN
ma-198	27	73	of	of	ADP
ma-198	27	74	both	both	CCONJ
ma-198	27	75	contractive	contractive	ADJ
ma-198	27	76	and	and	CCONJ
ma-198	27	77	nonex	nonex	ADV
ma-198	27	78	-	-	PUNCT
ma-198	27	79	pansive	pansive	ADJ
ma-198	27	80	operators	operator	NOUN
ma-198	27	81	.	.	PUNCT
ma-198	28	1	they	they	PRON
ma-198	28	2	are	be	AUX
ma-198	28	3	broadly	broadly	ADV
ma-198	28	4	used	use	VERB
ma-198	28	5	in	in	ADP
ma-198	28	6	the	the	DET
ma-198	28	7	study	study	NOUN
ma-198	28	8	of	of	ADP
ma-198	28	9	variational	variational	ADJ
ma-198	28	10	inequalities	inequality	NOUN
ma-198	28	11	and	and	CCONJ
ma-198	28	12	play	play	VERB
ma-198	28	13	a	a	DET
ma-198	28	14	crucialrole	crucialrole	NOUN
ma-198	28	15	in	in	ADP
ma-198	28	16	convex	convex	NOUN
ma-198	28	17	analysis	analysis	NOUN
ma-198	28	18	and	and	CCONJ
ma-198	28	19	optimization	optimization	NOUN
ma-198	28	20	theory	theory	NOUN
ma-198	28	21	.	.	PUNCT
ma-198	29	1	they	they	PRON
ma-198	29	2	provide	provide	VERB
ma-198	29	3	a	a	DET
ma-198	29	4	bridge	bridge	NOUN
ma-198	29	5	between	between	ADP
ma-198	29	6	nonlinear	nonlinear	ADJ
ma-198	29	7	andlinear	andlinear	NOUN
ma-198	29	8	problems	problem	NOUN
ma-198	29	9	,	,	PUNCT
ma-198	29	10	enabling	enable	VERB
ma-198	29	11	the	the	DET
ma-198	29	12	development	development	NOUN
ma-198	29	13	of	of	ADP
ma-198	29	14	efficient	efficient	ADJ
ma-198	29	15	numerical	numerical	ADJ
ma-198	29	16	methods	method	NOUN
ma-198	29	17	for	for	ADP
ma-198	29	18	solving	solve	VERB
ma-198	29	19	variationalproblems	variationalproblem	NOUN
ma-198	29	20	arising	arise	VERB
ma-198	29	21	in	in	ADP
ma-198	29	22	diverse	diverse	ADJ
ma-198	29	23	areas.viscosity	areas.viscosity	PROPN
ma-198	29	24	iterative	iterative	NOUN
ma-198	29	25	algorithms	algorithm	NOUN
ma-198	29	26	have	have	AUX
ma-198	29	27	been	be	AUX
ma-198	29	28	extensively	extensively	ADV
ma-198	29	29	studied	study	VERB
ma-198	29	30	in	in	ADP
ma-198	29	31	recent	recent	ADJ
ma-198	29	32	years	year	NOUN
ma-198	29	33	for	for	ADP
ma-198	29	34	finding	find	VERB
ma-198	29	35	commonfixed	commonfixe	VERB
ma-198	29	36	points	point	NOUN
ma-198	29	37	of	of	ADP
ma-198	29	38	single	single	ADV
ma-198	29	39	-	-	PUNCT
ma-198	29	40	valued	value	VERB
ma-198	29	41	nonexpansive	nonexpansive	ADJ
ma-198	29	42	mappings	mapping	NOUN
ma-198	29	43	and	and	CCONJ
ma-198	29	44	solving	solve	VERB
ma-198	29	45	variational	variational	ADJ
ma-198	29	46	inequality	inequality	NOUN
ma-198	29	47	problems.these	problems.these	ADJ
ma-198	29	48	investigations	investigation	NOUN
ma-198	29	49	have	have	AUX
ma-198	29	50	built	build	VERB
ma-198	29	51	upon	upon	SCONJ
ma-198	29	52	the	the	DET
ma-198	29	53	concepts	concept	NOUN
ma-198	29	54	of	of	ADP
ma-198	29	55	viscosity	viscosity	NOUN
ma-198	29	56	solutions	solution	NOUN
ma-198	29	57	introduced	introduce	VERB
ma-198	29	58	by	by	ADP
ma-198	29	59	variousresearchers	variousresearcher	NOUN
ma-198	29	60	.	.	PUNCT
ma-198	30	1	(	(	PUNCT
ma-198	30	2	see	see	VERB
ma-198	30	3	e.g	e.g	X
ma-198	31	1	[	[	X
ma-198	31	2	6	6	NUM
ma-198	31	3	]	]	PUNCT
ma-198	31	4	,	,	PUNCT
ma-198	31	5	[	[	X
ma-198	31	6	25	25	NUM
ma-198	31	7	]	]	PUNCT
ma-198	31	8	,	,	PUNCT
ma-198	31	9	[	[	X
ma-198	31	10	5	5	NUM
ma-198	31	11	]	]	PUNCT
ma-198	31	12	,	,	PUNCT
ma-198	31	13	[	[	X
ma-198	31	14	29	29	NUM
ma-198	31	15	]	]	PUNCT
ma-198	31	16	,	,	PUNCT
ma-198	32	1	[	[	X
ma-198	32	2	23	23	NUM
ma-198	32	3	]	]	PUNCT
ma-198	32	4	,	,	PUNCT
ma-198	33	1	[	[	X
ma-198	33	2	19	19	NUM
ma-198	33	3	]	]	PUNCT
ma-198	33	4	,	,	PUNCT
ma-198	33	5	[	[	X
ma-198	33	6	28]).throughout	28]).throughout	ADP
ma-198	33	7	this	this	DET
ma-198	33	8	paper	paper	NOUN
ma-198	33	9	,	,	PUNCT
ma-198	33	10	we	we	PRON
ma-198	33	11	denote	denote	VERB
ma-198	33	12	h	h	NOUN
ma-198	33	13	to	to	PART
ma-198	33	14	be	be	AUX
ma-198	33	15	real	real	ADJ
ma-198	33	16	hilbert	hilbert	NOUN
ma-198	33	17	space	space	NOUN
ma-198	33	18	with	with	ADP
ma-198	33	19	the	the	DET
ma-198	33	20	inner	inner	ADJ
ma-198	33	21	product	product	NOUN
ma-198	33	22	〈	〈	PROPN
ma-198	33	23	.	.	PROPN
ma-198	33	24	,	,	PUNCT
ma-198	33	25	.	.	PUNCT
ma-198	34	1	〉	〉	PROPN
ma-198	34	2	inducedby	inducedby	ADV
ma-198	34	3	the	the	DET
ma-198	34	4	norm	norm	NOUN
ma-198	34	5	‖.‖.	‖.‖.	PROPN
ma-198	34	6	let	let	VERB
ma-198	34	7	k	k	NOUN
ma-198	34	8	,	,	PUNCT
ma-198	34	9	to	to	PART
ma-198	34	10	be	be	AUX
ma-198	34	11	a	a	DET
ma-198	34	12	nonempty	nonempty	ADJ
ma-198	34	13	,	,	PUNCT
ma-198	34	14	closed	closed	ADJ
ma-198	34	15	and	and	CCONJ
ma-198	34	16	convex	convex	PROPN
ma-198	34	17	subset	subset	NOUN
ma-198	34	18	of	of	ADP
ma-198	34	19	h.an	h.an	NOUN
ma-198	34	20	operator	operator	NOUN
ma-198	34	21	a	a	DET
ma-198	34	22	:	:	PUNCT
ma-198	34	23	h	h	NOUN
ma-198	34	24	→	→	SYM
ma-198	34	25	h	h	NOUN
ma-198	34	26	is	be	AUX
ma-198	34	27	said	say	VERB
ma-198	34	28	to	to	PART
ma-198	34	29	be	be	AUX
ma-198	34	30	lipschitz	lipschitz	NOUN
ma-198	34	31	if	if	SCONJ
ma-198	34	32	there	there	PRON
ma-198	34	33	exists	exist	VERB
ma-198	34	34	a	a	DET
ma-198	34	35	constant	constant	ADJ
ma-198	34	36	l	l	NOUN
ma-198	34	37	>	>	X
ma-198	34	38	0	0	NUM
ma-198	34	39	such	such	ADJ
ma-198	34	40	that	that	PRON
ma-198	34	41	‖ax	‖ax	PUNCT
ma-198	35	1	−	−	NOUN
ma-198	35	2	ay‖	ay‖	PROPN
ma-198	35	3	≤	≤	PUNCT
ma-198	35	4	l‖x	l‖x	PROPN
ma-198	35	5	−	−	PROPN
ma-198	35	6	y‖,∀x	y‖,∀x	NOUN
ma-198	35	7	,	,	PUNCT
ma-198	35	8	y	y	PROPN
ma-198	35	9	∈	∈	PROPN
ma-198	35	10	h	h	NOUN
ma-198	35	11	(	(	PUNCT
ma-198	35	12	1.1	1.1	NUM
ma-198	35	13	)	)	PUNCT
ma-198	35	14	a	a	DET
ma-198	35	15	:	:	PUNCT
ma-198	35	16	h	h	NOUN
ma-198	35	17	→	→	SYM
ma-198	35	18	h	h	NOUN
ma-198	35	19	is	be	AUX
ma-198	35	20	said	say	VERB
ma-198	35	21	to	to	PART
ma-198	35	22	be	be	AUX
ma-198	35	23	strongly	strongly	ADV
ma-198	35	24	positive	positive	ADJ
ma-198	35	25	if	if	SCONJ
ma-198	35	26	there	there	PRON
ma-198	35	27	exists	exist	VERB
ma-198	35	28	a	a	DET
ma-198	35	29	constant	constant	ADJ
ma-198	35	30	k	k	X
ma-198	35	31	>	>	X
ma-198	35	32	0	0	NUM
ma-198	35	33	such	such	ADJ
ma-198	35	34	that	that	SCONJ
ma-198	35	35	〈	〈	PROPN
ma-198	35	36	ax	ax	NOUN
ma-198	35	37	,	,	PUNCT
ma-198	35	38	x	x	PROPN
ma-198	35	39	〉	〉	NUM
ma-198	35	40	≥	≥	NOUN
ma-198	35	41	k‖x‖2	k‖x‖2	PROPN
ma-198	35	42	,	,	PUNCT
ma-198	35	43	∀x	∀x	X
ma-198	35	44	∈	∈	PROPN
ma-198	35	45	h	h	NOUN
ma-198	35	46	(	(	PUNCT
ma-198	35	47	1.2	1.2	NUM
ma-198	35	48	)	)	PUNCT
ma-198	35	49	a	a	DET
ma-198	35	50	:	:	PUNCT
ma-198	35	51	h	h	NOUN
ma-198	35	52	→	→	SYM
ma-198	35	53	h	h	NOUN
ma-198	35	54	is	be	AUX
ma-198	35	55	said	say	VERB
ma-198	35	56	to	to	PART
ma-198	35	57	be	be	AUX
ma-198	35	58	k−strongly	k−strongly	ADV
ma-198	35	59	monotone	monotone	ADJ
ma-198	35	60	if	if	SCONJ
ma-198	35	61	there	there	PRON
ma-198	35	62	exists	exist	VERB
ma-198	35	63	a	a	DET
ma-198	35	64	constant	constant	ADJ
ma-198	35	65	k	k	PROPN
ma-198	35	66	∈	∈	PROPN
ma-198	35	67	(	(	PUNCT
ma-198	35	68	0	0	NUM
ma-198	35	69	,	,	PUNCT
ma-198	35	70	1	1	NUM
ma-198	35	71	)	)	PUNCT
ma-198	35	72	such	such	ADJ
ma-198	35	73	that	that	SCONJ
ma-198	35	74	〈	〈	PROPN
ma-198	35	75	ax	ax	NOUN
ma-198	35	76	−	−	PROPN
ma-198	35	77	ay	ay	INTJ
ma-198	35	78	,	,	PUNCT
ma-198	35	79	x	x	PROPN
ma-198	35	80	−	−	NOUN
ma-198	36	1	y〉h	y〉h	PROPN
ma-198	36	2	≥	≥	PROPN
ma-198	36	3	k‖x	k‖x	PROPN
ma-198	36	4	−	−	PROPN
ma-198	36	5	y‖2	y‖2	PROPN
ma-198	36	6	,	,	PUNCT
ma-198	36	7	∀x	∀x	NUM
ma-198	36	8	,	,	PUNCT
ma-198	36	9	y	y	PROPN
ma-198	36	10	∈	∈	PROPN
ma-198	36	11	h	h	NOUN
ma-198	36	12	(	(	PUNCT
ma-198	36	13	1.3	1.3	NUM
ma-198	36	14	)	)	PUNCT
ma-198	36	15	definition	definition	NOUN
ma-198	36	16	1.1	1.1	NUM
ma-198	36	17	.	.	PUNCT
ma-198	37	1	a	a	DET
ma-198	37	2	multivalued	multivalue	VERB
ma-198	37	3	mapping(1	mapping(1	NOUN
ma-198	37	4	)	)	PUNCT
ma-198	37	5	t	t	NOUN
ma-198	37	6	:	:	PUNCT
ma-198	37	7	d(t	d(t	PROPN
ma-198	37	8	)	)	PUNCT
ma-198	37	9	⊆	⊆	NUM
ma-198	37	10	h	h	NOUN
ma-198	37	11	→	→	SYM
ma-198	37	12	cb(d	cb(d	NOUN
ma-198	37	13	)	)	PUNCT
ma-198	37	14	is	be	AUX
ma-198	37	15	called	call	VERB
ma-198	37	16	l−lipschitzian	l−lipschitzian	ADJ
ma-198	37	17	if	if	SCONJ
ma-198	37	18	there	there	PRON
ma-198	37	19	exists	exist	VERB
ma-198	37	20	l	l	NOUN
ma-198	37	21	>	>	X
ma-198	37	22	0	0	NUM
ma-198	37	23	,	,	PUNCT
ma-198	37	24	such	such	ADJ
ma-198	37	25	that	that	DET
ma-198	37	26	h(tx	h(tx	PROPN
ma-198	37	27	,	,	PUNCT
ma-198	37	28	t	t	PROPN
ma-198	37	29	y	y	PROPN
ma-198	37	30	)	)	PUNCT
ma-198	37	31	≤	≤	NUM
ma-198	37	32	l‖x	l‖x	PROPN
ma-198	37	33	−	−	PROPN
ma-198	37	34	y‖,∀x	y‖,∀x	NOUN
ma-198	37	35	,	,	PUNCT
ma-198	37	36	y	y	PROPN
ma-198	37	37	∈	∈	PROPN
ma-198	37	38	d(t	d(t	PROPN
ma-198	37	39	)	)	PUNCT
ma-198	37	40	and	and	CCONJ
ma-198	37	41	t	t	PROPN
ma-198	37	42	is	be	AUX
ma-198	37	43	contraction	contraction	NOUN
ma-198	37	44	if	if	SCONJ
ma-198	37	45	l	l	PROPN
ma-198	37	46	∈	∈	PROPN
ma-198	37	47	(	(	PUNCT
ma-198	37	48	0	0	NUM
ma-198	37	49	,	,	PUNCT
ma-198	37	50	1	1	NUM
ma-198	37	51	)	)	PUNCT
ma-198	37	52	and	and	CCONJ
ma-198	37	53	noneaxpansive	noneaxpansive	ADJ
ma-198	37	54	if	if	SCONJ
ma-198	37	55	l	l	NOUN
ma-198	37	56	=	=	SYM
ma-198	37	57	1.(2	1.(2	X
ma-198	37	58	)	)	PUNCT
ma-198	37	59	t	t	PROPN
ma-198	37	60	is	be	AUX
ma-198	37	61	called	call	VERB
ma-198	37	62	quasi	quasi	ADJ
ma-198	37	63	-	-	ADJ
ma-198	37	64	nonexpansive	nonexpansive	ADJ
ma-198	37	65	if	if	SCONJ
ma-198	37	66	h(tx	h(tx	PROPN
ma-198	37	67	,	,	PUNCT
ma-198	37	68	tp	tp	NOUN
ma-198	37	69	)	)	PUNCT
ma-198	37	70	≤	≤	NUM
ma-198	37	71	‖x	‖x	PUNCT
ma-198	38	1	−	−	PROPN
ma-198	38	2	p‖	p‖	NOUN
ma-198	38	3	,	,	PUNCT
ma-198	38	4	∀x	∀x	X
ma-198	38	5	∈	∈	PROPN
ma-198	38	6	d(t	d(t	PROPN
ma-198	38	7	)	)	PUNCT
ma-198	38	8	,	,	PUNCT
ma-198	38	9	p	p	PROPN
ma-198	38	10	∈	∈	PROPN
ma-198	38	11	f	f	PROPN
ma-198	38	12	ix(t	ix(t	ADJ
ma-198	38	13	)	)	PUNCT
ma-198	38	14	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	38	15	eur	eur	NOUN
ma-198	38	16	.	.	PUNCT
ma-198	39	1	j.	j.	PROPN
ma-198	39	2	math	math	PROPN
ma-198	39	3	.	.	PUNCT
ma-198	40	1	anal	anal	PROPN
ma-198	40	2	.	.	PUNCT
ma-198	41	1	10.28924	10.28924	NUM
ma-198	41	2	/	/	SYM
ma-198	41	3	ada	ada	PROPN
ma-198	41	4	/	/	SYM
ma-198	41	5	ma.4.2	ma.4.2	PROPN
ma-198	41	6	3(3	3(3	NUM
ma-198	41	7	)	)	PUNCT
ma-198	41	8	t	t	NOUN
ma-198	41	9	:	:	PUNCT
ma-198	41	10	d(t	d(t	PROPN
ma-198	41	11	)	)	PUNCT
ma-198	41	12	⊆	⊆	NUM
ma-198	41	13	h	h	NOUN
ma-198	41	14	→	→	SYM
ma-198	41	15	cb(d	cb(d	NOUN
ma-198	41	16	)	)	PUNCT
ma-198	41	17	is	be	AUX
ma-198	41	18	said	say	VERB
ma-198	41	19	to	to	PART
ma-198	41	20	be	be	AUX
ma-198	41	21	k−stritly	k−stritly	ADV
ma-198	41	22	pseudo	pseudo	NOUN
ma-198	41	23	-	-	ADJ
ma-198	41	24	contractive	contractive	ADJ
ma-198	41	25	,	,	PUNCT
ma-198	41	26	if	if	SCONJ
ma-198	41	27	there	there	PRON
ma-198	41	28	exists	exist	VERB
ma-198	41	29	k	k	PROPN
ma-198	41	30	∈	∈	PROPN
ma-198	41	31	(	(	PUNCT
ma-198	41	32	0	0	NUM
ma-198	41	33	,	,	PUNCT
ma-198	41	34	1	1	NUM
ma-198	41	35	)	)	PUNCT
ma-198	41	36	such	such	ADJ
ma-198	41	37	that	that	PRON
ma-198	41	38	for	for	ADP
ma-198	41	39	all	all	DET
ma-198	41	40	x	x	NOUN
ma-198	41	41	,	,	PUNCT
ma-198	41	42	y	y	PROPN
ma-198	41	43	∈	∈	PROPN
ma-198	41	44	d(t	d(t	PROPN
ma-198	41	45	)	)	PUNCT
ma-198	41	46	,	,	PUNCT
ma-198	41	47	the	the	DET
ma-198	41	48	following	follow	VERB
ma-198	41	49	holds	hold	VERB
ma-198	41	50	;	;	PUNCT
ma-198	41	51	(	(	PUNCT
ma-198	41	52	h(tx	h(tx	PROPN
ma-198	41	53	,	,	PUNCT
ma-198	41	54	t	t	PROPN
ma-198	41	55	y	y	PROPN
ma-198	41	56	)	)	PUNCT
ma-198	41	57	)	)	PUNCT
ma-198	41	58	2	2	NUM
ma-198	41	59	≤	≤	NUM
ma-198	41	60	‖x	‖x	PUNCT
ma-198	42	1	−	−	PROPN
ma-198	43	1	y‖2	y‖2	X
ma-198	44	1	+	+	CCONJ
ma-198	45	1	k‖(i	k‖(i	NOUN
ma-198	45	2	−	−	PROPN
ma-198	45	3	t	t	NOUN
ma-198	45	4	)	)	PUNCT
ma-198	45	5	x	x	SYM
ma-198	46	1	−	−	PROPN
ma-198	46	2	(	(	PUNCT
ma-198	46	3	i	i	PRON
ma-198	46	4	−	−	PROPN
ma-198	46	5	t	t	NOUN
ma-198	46	6	)	)	PUNCT
ma-198	46	7	y‖2	y‖2	PROPN
ma-198	46	8	,	,	PUNCT
ma-198	46	9	if	if	SCONJ
ma-198	46	10	k	k	PROPN
ma-198	46	11	=	=	SYM
ma-198	46	12	1	1	NUM
ma-198	46	13	,	,	PUNCT
ma-198	46	14	the	the	DET
ma-198	46	15	map	map	NOUN
ma-198	46	16	t	t	PROPN
ma-198	46	17	is	be	AUX
ma-198	46	18	said	say	VERB
ma-198	46	19	to	to	PART
ma-198	46	20	be	be	AUX
ma-198	46	21	pseudocontractive.(4	pseudocontractive.(4	PROPN
ma-198	46	22	)	)	PUNCT
ma-198	47	1	[	[	X
ma-198	47	2	26	26	NUM
ma-198	47	3	]	]	X
ma-198	47	4	t	t	NOUN
ma-198	47	5	:	:	PUNCT
ma-198	47	6	d(t	d(t	PROPN
ma-198	47	7	)	)	PUNCT
ma-198	48	1	⊆	⊆	NUM
ma-198	48	2	e	e	X
ma-198	48	3	→	→	SYM
ma-198	48	4	2e	2e	PROPN
ma-198	48	5	is	be	AUX
ma-198	48	6	said	say	VERB
ma-198	48	7	to	to	PART
ma-198	48	8	be	be	AUX
ma-198	48	9	demicontractive	demicontractive	ADJ
ma-198	48	10	if	if	SCONJ
ma-198	48	11	f	f	PROPN
ma-198	48	12	ix(t	ix(t	ADV
ma-198	48	13	)	)	PUNCT
ma-198	48	14	6=	6=	ADP
ma-198	48	15	∅	∅	NOUN
ma-198	48	16	and	and	CCONJ
ma-198	48	17	for	for	ADP
ma-198	48	18	all	all	PRON
ma-198	48	19	p	p	NOUN
ma-198	48	20	∈	∈	PROPN
ma-198	48	21	f	f	NOUN
ma-198	48	22	ix(t	ix(t	PROPN
ma-198	48	23	)	)	PUNCT
ma-198	48	24	,	,	PUNCT
ma-198	48	25	x	x	PROPN
ma-198	48	26	∈	∈	PROPN
ma-198	48	27	d(t	d(t	PROPN
ma-198	48	28	)	)	PUNCT
ma-198	48	29	there	there	PRON
ma-198	48	30	exists	exist	VERB
ma-198	48	31	k	k	PROPN
ma-198	48	32	∈	∈	PROPN
ma-198	48	33	(	(	PUNCT
ma-198	48	34	0	0	NUM
ma-198	48	35	,	,	PUNCT
ma-198	48	36	1	1	NUM
ma-198	48	37	)	)	PUNCT
ma-198	49	1	such	such	ADJ
ma-198	49	2	that	that	SCONJ
ma-198	49	3	(	(	PUNCT
ma-198	49	4	h(tx	h(tx	PROPN
ma-198	49	5	,	,	PUNCT
ma-198	49	6	tp	tp	NOUN
ma-198	49	7	)	)	PUNCT
ma-198	49	8	)	)	PUNCT
ma-198	49	9	2	2	NUM
ma-198	49	10	≤	≤	NUM
ma-198	49	11	‖x	‖x	PUNCT
ma-198	49	12	−	−	PROPN
ma-198	49	13	p‖2	p‖2	PROPN
ma-198	49	14	+	+	CCONJ
ma-198	49	15	kd(x	kd(x	NOUN
ma-198	49	16	,	,	PUNCT
ma-198	49	17	t	t	PROPN
ma-198	49	18	x)2	x)2	PROPN
ma-198	49	19	.	.	PUNCT
ma-198	50	1	if	if	SCONJ
ma-198	50	2	k	k	PROPN
ma-198	50	3	=	=	SYM
ma-198	50	4	1	1	NUM
ma-198	50	5	,	,	PUNCT
ma-198	50	6	the	the	DET
ma-198	50	7	map	map	NOUN
ma-198	50	8	t	t	PROPN
ma-198	50	9	is	be	AUX
ma-198	50	10	said	say	VERB
ma-198	50	11	to	to	PART
ma-198	50	12	be	be	AUX
ma-198	50	13	hemicontractive	hemicontractive	ADJ
ma-198	50	14	.	.	PUNCT
ma-198	51	1	let	let	VERB
ma-198	51	2	(	(	PUNCT
ma-198	51	3	x	x	NOUN
ma-198	51	4	,	,	PUNCT
ma-198	51	5	d	d	NOUN
ma-198	51	6	)	)	PUNCT
ma-198	51	7	be	be	AUX
ma-198	51	8	a	a	DET
ma-198	51	9	metric	metric	ADJ
ma-198	51	10	space	space	NOUN
ma-198	51	11	,	,	PUNCT
ma-198	51	12	k	k	X
ma-198	51	13	be	be	AUX
ma-198	51	14	a	a	DET
ma-198	51	15	nonempty	nonempty	ADJ
ma-198	51	16	subset	subset	NOUN
ma-198	51	17	of	of	ADP
ma-198	51	18	x	x	PUNCT
ma-198	51	19	and	and	CCONJ
ma-198	51	20	t	t	PROPN
ma-198	51	21	:	:	PUNCT
ma-198	52	1	k	k	X
ma-198	52	2	→	→	SYM
ma-198	52	3	2k	2k	PROPN
ma-198	52	4	be	be	AUX
ma-198	52	5	a	a	DET
ma-198	52	6	multivaluedmapping	multivaluedmapping	NOUN
ma-198	52	7	.	.	PUNCT
ma-198	53	1	an	an	DET
ma-198	53	2	element	element	NOUN
ma-198	53	3	x	x	SYM
ma-198	53	4	∈	∈	PROPN
ma-198	53	5	k	k	PROPN
ma-198	53	6	is	be	AUX
ma-198	53	7	called	call	VERB
ma-198	53	8	a	a	DET
ma-198	53	9	fixed	fix	VERB
ma-198	53	10	point	point	NOUN
ma-198	53	11	of	of	ADP
ma-198	53	12	t	t	PROPN
ma-198	53	13	if	if	SCONJ
ma-198	53	14	x	x	PROPN
ma-198	53	15	∈	∈	PROPN
ma-198	53	16	tx	tx	PROPN
ma-198	53	17	.	.	PUNCT
ma-198	54	1	the	the	DET
ma-198	54	2	fixed	fix	VERB
ma-198	54	3	point	point	NOUN
ma-198	54	4	set	set	NOUN
ma-198	54	5	of	of	ADP
ma-198	54	6	t	t	PROPN
ma-198	54	7	isdenoted	isdenote	VERB
ma-198	54	8	by	by	ADP
ma-198	54	9	f	f	PROPN
ma-198	54	10	ix(t	ix(t	PROPN
ma-198	54	11	)	)	PUNCT
ma-198	54	12	:	:	PUNCT
ma-198	55	1	=	=	SYM
ma-198	55	2	{	{	PUNCT
ma-198	55	3	x	x	PROPN
ma-198	55	4	∈	∈	PROPN
ma-198	55	5	d(t	d(t	PROPN
ma-198	55	6	)	)	PUNCT
ma-198	55	7	:	:	PUNCT
ma-198	56	1	x	x	X
ma-198	56	2	∈	∈	PROPN
ma-198	56	3	tx	tx	PROPN
ma-198	56	4	}	}	PUNCT
ma-198	56	5	where	where	SCONJ
ma-198	56	6	d(t	d(t	PROPN
ma-198	56	7	)	)	PUNCT
ma-198	56	8	:	:	PUNCT
ma-198	56	9	=	=	SYM
ma-198	56	10	{	{	PUNCT
ma-198	56	11	x	x	PUNCT
ma-198	56	12	∈	∈	PROPN
ma-198	56	13	x	x	X
ma-198	56	14	:	:	PUNCT
ma-198	56	15	tx	tx	PROPN
ma-198	56	16	6=	6=	ADP
ma-198	56	17	∅	∅	NOUN
ma-198	56	18	}	}	PUNCT
ma-198	56	19	.	.	PUNCT
ma-198	57	1	it	it	PRON
ma-198	57	2	is	be	AUX
ma-198	57	3	easy	easy	ADJ
ma-198	57	4	to	to	PART
ma-198	57	5	seethat	seethat	VERB
ma-198	57	6	single	single	ADV
ma-198	57	7	-	-	PUNCT
ma-198	57	8	valued	value	VERB
ma-198	57	9	mapping	mapping	NOUN
ma-198	57	10	is	be	AUX
ma-198	57	11	a	a	DET
ma-198	57	12	particular	particular	ADJ
ma-198	57	13	case	case	NOUN
ma-198	57	14	of	of	ADP
ma-198	57	15	multivalued	multivalue	VERB
ma-198	57	16	mapping.let	mapping.let	X
ma-198	57	17	d	d	NOUN
ma-198	57	18	be	be	AUX
ma-198	57	19	a	a	DET
ma-198	57	20	nonempty	nonempty	ADJ
ma-198	57	21	suset	suset	NOUN
ma-198	57	22	of	of	ADP
ma-198	57	23	a	a	DET
ma-198	57	24	normed	normed	ADJ
ma-198	57	25	linear	linear	PROPN
ma-198	57	26	space	space	NOUN
ma-198	57	27	e.	e.	PROPN
ma-198	58	1	the	the	DET
ma-198	58	2	set	set	PROPN
ma-198	58	3	d	d	PROPN
ma-198	58	4	is	be	AUX
ma-198	58	5	called	call	VERB
ma-198	58	6	proximinal	proximinal	ADJ
ma-198	58	7	(	(	PUNCT
ma-198	58	8	see	see	VERB
ma-198	58	9	[	[	X
ma-198	58	10	13])if	13])if	NUM
ma-198	58	11	for	for	ADP
ma-198	58	12	each	each	DET
ma-198	58	13	ψ	ψ	X
ma-198	58	14	∈	∈	PROPN
ma-198	58	15	e	e	NOUN
ma-198	58	16	,	,	PUNCT
ma-198	58	17	there	there	PRON
ma-198	58	18	exists	exist	VERB
ma-198	58	19	u	u	NOUN
ma-198	58	20	∈	∈	PROPN
ma-198	58	21	d	d	ADP
ma-198	58	22	such	such	ADJ
ma-198	58	23	that	that	DET
ma-198	58	24	d(x	d(x	PROPN
ma-198	58	25	,	,	PUNCT
ma-198	58	26	u	u	NOUN
ma-198	58	27	)	)	PUNCT
ma-198	58	28	:	:	PUNCT
ma-198	59	1	=	=	SYM
ma-198	59	2	inf{‖x	inf{‖x	PUNCT
ma-198	60	1	−	−	PROPN
ma-198	60	2	y‖	y‖	NOUN
ma-198	60	3	:	:	PUNCT
ma-198	60	4	y	y	PROPN
ma-198	60	5	∈	∈	PROPN
ma-198	60	6	d},∀x	d},∀x	NOUN
ma-198	60	7	,	,	PUNCT
ma-198	60	8	y	y	PROPN
ma-198	60	9	∈	∈	PROPN
ma-198	60	10	e	e	X
ma-198	60	11	(	(	PUNCT
ma-198	60	12	1.4	1.4	NUM
ma-198	60	13	)	)	PUNCT
ma-198	60	14	where	where	SCONJ
ma-198	60	15	d(x	d(x	PROPN
ma-198	60	16	,	,	PUNCT
ma-198	60	17	y	y	NOUN
ma-198	60	18	)	)	PUNCT
ma-198	60	19	:	:	PUNCT
ma-198	60	20	=	=	PUNCT
ma-198	60	21	‖x	‖x	NOUN
ma-198	61	1	−	−	NOUN
ma-198	61	2	y‖	y‖	PROPN
ma-198	61	3	for	for	ADP
ma-198	61	4	all	all	DET
ma-198	61	5	x	x	NOUN
ma-198	61	6	,	,	PUNCT
ma-198	61	7	y	y	PROPN
ma-198	61	8	∈	∈	PROPN
ma-198	61	9	e.	e.	PROPN
ma-198	62	1	every	every	DET
ma-198	62	2	closed	closed	ADJ
ma-198	62	3	,	,	PUNCT
ma-198	62	4	nonempty	nonempty	ADJ
ma-198	62	5	and	and	CCONJ
ma-198	62	6	convex	convex	ADJ
ma-198	62	7	set	set	NOUN
ma-198	62	8	of	of	ADP
ma-198	62	9	real	real	ADJ
ma-198	62	10	hilbertspace	hilbertspace	NOUN
ma-198	62	11	is	be	AUX
ma-198	62	12	proximinal	proximinal	ADJ
ma-198	62	13	.	.	PUNCT
ma-198	63	1	the	the	DET
ma-198	63	2	family	family	NOUN
ma-198	63	3	of	of	ADP
ma-198	63	4	nonempty	nonempty	X
ma-198	63	5	closed	close	VERB
ma-198	63	6	bounded	bounded	ADJ
ma-198	63	7	subsets	subset	NOUN
ma-198	63	8	,	,	PUNCT
ma-198	63	9	nonempty	nonempty	ADJ
ma-198	63	10	compact	compact	ADJ
ma-198	63	11	subsets	subset	NOUN
ma-198	63	12	,	,	PUNCT
ma-198	63	13	and	and	CCONJ
ma-198	63	14	nonempty	nonempty	ADJ
ma-198	63	15	proximinal	proximinal	ADJ
ma-198	63	16	bounded	bounded	ADJ
ma-198	63	17	subsets	subset	NOUN
ma-198	63	18	be	be	AUX
ma-198	63	19	donated	donate	VERB
ma-198	63	20	as	as	ADP
ma-198	63	21	cb(d	cb(d	NOUN
ma-198	63	22	)	)	PUNCT
ma-198	63	23	,	,	PUNCT
ma-198	63	24	k(d	k(d	PROPN
ma-198	63	25	)	)	PUNCT
ma-198	63	26	and	and	CCONJ
ma-198	63	27	p	p	X
ma-198	63	28	(	(	PUNCT
ma-198	63	29	d	d	PROPN
ma-198	63	30	)	)	PUNCT
ma-198	63	31	respectively.let	respectively.let	PROPN
ma-198	63	32	a	a	PRON
ma-198	63	33	,	,	PUNCT
ma-198	63	34	b	b	PROPN
ma-198	63	35	∈	∈	PROPN
ma-198	63	36	cb(d	cb(d	NOUN
ma-198	63	37	)	)	PUNCT
ma-198	63	38	.	.	PUNCT
ma-198	64	1	then	then	ADV
ma-198	64	2	the	the	DET
ma-198	64	3	hausdorff	hausdorff	NOUN
ma-198	64	4	metric	metric	ADJ
ma-198	64	5	in	in	ADP
ma-198	64	6	h	h	NOUN
ma-198	64	7	is	be	AUX
ma-198	64	8	defined	define	VERB
ma-198	64	9	by	by	ADP
ma-198	64	10	h(a	h(a	PROPN
ma-198	64	11	,	,	PUNCT
ma-198	64	12	b	b	NOUN
ma-198	64	13	)	)	PUNCT
ma-198	64	14	=	=	SYM
ma-198	64	15	max	max	PROPN
ma-198	64	16	{	{	PUNCT
ma-198	64	17	sup	sup	PROPN
ma-198	64	18	a∈a	a∈a	PRON
ma-198	64	19	d(a	d(a	PROPN
ma-198	64	20	,	,	PUNCT
ma-198	64	21	b	b	NOUN
ma-198	64	22	)	)	PUNCT
ma-198	64	23	,	,	PUNCT
ma-198	64	24	sup	sup	NOUN
ma-198	64	25	b∈b	b∈b	NOUN
ma-198	64	26	d(b	d(b	PROPN
ma-198	64	27	,	,	PUNCT
ma-198	64	28	a	a	PRON
ma-198	64	29	)	)	PUNCT
ma-198	64	30	}	}	PUNCT
ma-198	64	31	.	.	PUNCT
ma-198	65	1	(	(	PUNCT
ma-198	65	2	1.5	1.5	NUM
ma-198	65	3	)	)	PUNCT
ma-198	65	4	let	let	VERB
ma-198	65	5	a	a	DET
ma-198	65	6	:	:	PUNCT
ma-198	65	7	d(a	d(a	PROPN
ma-198	65	8	)	)	PUNCT
ma-198	66	1	⊂	⊂	PROPN
ma-198	66	2	h	h	X
ma-198	66	3	→	→	SYM
ma-198	66	4	2h	2h	NUM
ma-198	66	5	be	be	VERB
ma-198	66	6	a	a	DET
ma-198	66	7	multivalued	multivalue	VERB
ma-198	66	8	operator	operator	NOUN
ma-198	66	9	.	.	PUNCT
ma-198	67	1	then	then	ADV
ma-198	67	2	a	a	PRON
ma-198	67	3	is	be	AUX
ma-198	67	4	monotone	monotone	ADJ
ma-198	67	5	if	if	SCONJ
ma-198	67	6	(	(	PUNCT
ma-198	67	7	x	x	NOUN
ma-198	67	8	,	,	PUNCT
ma-198	67	9	u	u	NOUN
ma-198	67	10	)	)	PUNCT
ma-198	67	11	,	,	PUNCT
ma-198	67	12	(	(	PUNCT
ma-198	67	13	y	y	PROPN
ma-198	67	14	,	,	PUNCT
ma-198	67	15	v	v	NOUN
ma-198	67	16	)	)	PUNCT
ma-198	67	17	∈	∈	NOUN
ma-198	67	18	d(a)such	d(a)such	ADJ
ma-198	67	19	that	that	SCONJ
ma-198	67	20	g(a	g(a	PROPN
ma-198	67	21	)	)	PUNCT
ma-198	67	22	:	:	PUNCT
ma-198	68	1	=	=	SYM
ma-198	68	2	{	{	PUNCT
ma-198	68	3	x	x	NOUN
ma-198	68	4	,	,	PUNCT
ma-198	68	5	u	u	NOUN
ma-198	68	6	)	)	PUNCT
ma-198	68	7	:	:	PUNCT
ma-198	68	8	x	x	PUNCT
ma-198	68	9	∈	∈	PROPN
ma-198	68	10	d(a	d(a	PROPN
ma-198	68	11	)	)	PUNCT
ma-198	68	12	,	,	PUNCT
ma-198	68	13	u	u	NOUN
ma-198	68	14	∈	∈	NOUN
ma-198	68	15	ax	ax	NOUN
ma-198	68	16	}	}	PUNCT
ma-198	68	17	(	(	PUNCT
ma-198	68	18	1.6	1.6	NUM
ma-198	68	19	)	)	PUNCT
ma-198	68	20	a	a	DET
ma-198	68	21	monotone	monotone	ADJ
ma-198	68	22	mapping	mapping	NOUN
ma-198	68	23	a	a	DET
ma-198	68	24	:	:	PUNCT
ma-198	68	25	h	h	NOUN
ma-198	68	26	→	→	SYM
ma-198	68	27	2h	2h	NUM
ma-198	68	28	is	be	AUX
ma-198	68	29	said	say	VERB
ma-198	68	30	to	to	PART
ma-198	68	31	be	be	AUX
ma-198	68	32	maximal	maximal	ADJ
ma-198	68	33	if	if	SCONJ
ma-198	68	34	its	its	PRON
ma-198	68	35	graph	graph	NOUN
ma-198	68	36	g(a	g(a	PROPN
ma-198	68	37	)	)	PUNCT
ma-198	68	38	is	be	AUX
ma-198	68	39	not	not	PART
ma-198	68	40	properly	properly	ADV
ma-198	68	41	containedin	containedin	VERB
ma-198	68	42	the	the	DET
ma-198	68	43	graph	graph	NOUN
ma-198	68	44	of	of	ADP
ma-198	68	45	any	any	DET
ma-198	68	46	other	other	ADJ
ma-198	68	47	monotone	monotone	NOUN
ma-198	68	48	mapping.a	mapping.a	NOUN
ma-198	68	49	mapping	mapping	NOUN
ma-198	68	50	a	a	DET
ma-198	68	51	:	:	PUNCT
ma-198	68	52	h	h	NOUN
ma-198	68	53	→	→	SYM
ma-198	68	54	h	h	NOUN
ma-198	68	55	is	be	AUX
ma-198	68	56	said	say	VERB
ma-198	68	57	to	to	PART
ma-198	68	58	be	be	AUX
ma-198	68	59	α−inverse	α−inverse	ADV
ma-198	68	60	strongly	strongly	ADV
ma-198	68	61	if	if	SCONJ
ma-198	68	62	there	there	PRON
ma-198	68	63	exits	exit	VERB
ma-198	68	64	a	a	DET
ma-198	68	65	constant	constant	ADJ
ma-198	68	66	α	α	NOUN
ma-198	68	67	>	>	X
ma-198	68	68	0	0	NUM
ma-198	68	69	such	such	ADJ
ma-198	68	70	that	that	SCONJ
ma-198	68	71	〈	〈	PROPN
ma-198	68	72	ax	ax	NOUN
ma-198	68	73	−	−	PROPN
ma-198	69	1	ay	ay	INTJ
ma-198	69	2	,	,	PUNCT
ma-198	69	3	x	x	PROPN
ma-198	69	4	−	−	NOUN
ma-198	69	5	y〉h	y〉h	PROPN
ma-198	69	6	≥	≥	X
ma-198	70	1	α‖ax	α‖ax	PROPN
ma-198	70	2	−	−	PROPN
ma-198	70	3	ay‖2	ay‖2	NOUN
ma-198	70	4	,	,	PUNCT
ma-198	70	5	∀x	∀x	X
ma-198	70	6	,	,	PUNCT
ma-198	70	7	y	y	PROPN
ma-198	70	8	∈	∈	PROPN
ma-198	70	9	h	h	NOUN
ma-198	70	10	(	(	PUNCT
ma-198	70	11	1.7	1.7	NUM
ma-198	70	12	)	)	PUNCT
ma-198	70	13	remark	remark	NOUN
ma-198	70	14	1.2	1.2	NUM
ma-198	70	15	.	.	PUNCT
ma-198	71	1	it	it	PRON
ma-198	71	2	can	can	AUX
ma-198	71	3	be	be	AUX
ma-198	71	4	seen	see	VERB
ma-198	71	5	that	that	SCONJ
ma-198	71	6	every	every	DET
ma-198	71	7	α−inverse	α−inverse	NOUN
ma-198	71	8	strongly	strongly	ADV
ma-198	71	9	monotone	monotone	ADJ
ma-198	71	10	mapping	mapping	NOUN
ma-198	71	11	is	be	AUX
ma-198	71	12	1	1	NUM
ma-198	71	13	α	α	PRON
ma-198	71	14	−lipschitzmonotone	−lipschitzmonotone	NOUN
ma-198	71	15	.	.	PUNCT
ma-198	72	1	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	72	2	eur	eur	NOUN
ma-198	72	3	.	.	PUNCT
ma-198	73	1	j.	j.	PROPN
ma-198	73	2	math	math	PROPN
ma-198	73	3	.	.	PUNCT
ma-198	74	1	anal	anal	PROPN
ma-198	74	2	.	.	PUNCT
ma-198	75	1	10.28924	10.28924	NUM
ma-198	75	2	/	/	SYM
ma-198	75	3	ada	ada	PROPN
ma-198	75	4	/	/	SYM
ma-198	75	5	ma.4.2	ma.4.2	PROPN
ma-198	75	6	4	4	NUM
ma-198	75	7	let	let	VERB
ma-198	75	8	a	a	DET
ma-198	75	9	:	:	PUNCT
ma-198	75	10	h	h	NOUN
ma-198	75	11	→	→	SYM
ma-198	75	12	h	h	NOUN
ma-198	75	13	be	be	AUX
ma-198	75	14	a	a	DET
ma-198	75	15	single	single	ADV
ma-198	75	16	-	-	PUNCT
ma-198	75	17	valued	value	VERB
ma-198	75	18	nonlinear	nonlinear	ADJ
ma-198	75	19	mapping	mapping	NOUN
ma-198	75	20	and	and	CCONJ
ma-198	75	21	π	π	NOUN
ma-198	75	22	:	:	PUNCT
ma-198	75	23	h	h	NOUN
ma-198	75	24	→	→	SYM
ma-198	75	25	2h	2h	NUM
ma-198	75	26	be	be	VERB
ma-198	75	27	a	a	DET
ma-198	75	28	set	set	NOUN
ma-198	75	29	-	-	PUNCT
ma-198	75	30	valued	value	VERB
ma-198	75	31	mapping.then	mapping.then	PROPN
ma-198	75	32	the	the	DET
ma-198	75	33	variational	variational	ADJ
ma-198	75	34	inclusion	inclusion	NOUN
ma-198	75	35	problem	problem	NOUN
ma-198	75	36	is	be	AUX
ma-198	75	37	as	as	SCONJ
ma-198	75	38	follows	follow	VERB
ma-198	75	39	:	:	PUNCT
ma-198	75	40	find	find	VERB
ma-198	75	41	x	x	X
ma-198	75	42	∈	∈	PROPN
ma-198	75	43	h	h	NOUN
ma-198	75	44	,	,	PUNCT
ma-198	75	45	such	such	ADJ
ma-198	75	46	that	that	SCONJ
ma-198	75	47	ω	ω	NUM
ma-198	75	48	∈m(x	∈m(x	PROPN
ma-198	75	49	)	)	PUNCT
ma-198	75	50	+	+	X
ma-198	75	51	a(x	a(x	NOUN
ma-198	75	52	)	)	PUNCT
ma-198	75	53	(	(	PUNCT
ma-198	75	54	1.8	1.8	NUM
ma-198	75	55	)	)	PUNCT
ma-198	75	56	where	where	SCONJ
ma-198	75	57	ω	ω	PROPN
ma-198	75	58	is	be	AUX
ma-198	75	59	the	the	DET
ma-198	75	60	zero	zero	NUM
ma-198	75	61	vector	vector	NOUN
ma-198	75	62	in	in	ADP
ma-198	75	63	h.	h.	PROPN
ma-198	75	64	we	we	PRON
ma-198	75	65	denote	denote	VERB
ma-198	75	66	the	the	DET
ma-198	75	67	solution	solution	NOUN
ma-198	75	68	of	of	ADP
ma-198	75	69	the	the	DET
ma-198	75	70	problem	problem	NOUN
ma-198	75	71	(	(	PUNCT
ma-198	75	72	1.8	1.8	NUM
ma-198	75	73	)	)	PUNCT
ma-198	75	74	by	by	ADP
ma-198	75	75	s(m	s(m	PROPN
ma-198	75	76	,	,	PUNCT
ma-198	75	77	a	a	PRON
ma-198	75	78	)	)	PUNCT
ma-198	75	79	.	.	PUNCT
ma-198	76	1	if	if	SCONJ
ma-198	76	2	ω	ω	PROPN
ma-198	76	3	=	=	SYM
ma-198	76	4	athen	athen	PROPN
ma-198	76	5	,	,	PUNCT
ma-198	76	6	problem	problem	NOUN
ma-198	76	7	(	(	PUNCT
ma-198	76	8	1.8	1.8	NUM
ma-198	76	9	)	)	PUNCT
ma-198	76	10	becomes	become	VERB
ma-198	76	11	the	the	DET
ma-198	76	12	inclusion	inclusion	NOUN
ma-198	76	13	problem	problem	NOUN
ma-198	76	14	by	by	ADP
ma-198	76	15	rockafellar	rockafellar	ADJ
ma-198	76	16	[	[	X
ma-198	76	17	16].further	16].further	NUM
ma-198	76	18	readings	reading	NOUN
ma-198	76	19	on	on	ADP
ma-198	76	20	zeros	zero	NOUN
ma-198	76	21	ofinclusion	ofinclusion	NOUN
ma-198	76	22	problem	problem	NOUN
ma-198	76	23	(	(	PUNCT
ma-198	76	24	see	see	VERB
ma-198	76	25	[	[	X
ma-198	76	26	17	17	NUM
ma-198	76	27	]	]	PUNCT
ma-198	76	28	,	,	PUNCT
ma-198	76	29	[	[	X
ma-198	76	30	18	18	NUM
ma-198	76	31	]	]	PUNCT
ma-198	76	32	,	,	PUNCT
ma-198	76	33	[	[	X
ma-198	76	34	19	19	NUM
ma-198	76	35	]	]	PUNCT
ma-198	76	36	,	,	PUNCT
ma-198	76	37	[	[	X
ma-198	76	38	8	8	NUM
ma-198	76	39	]	]	PUNCT
ma-198	76	40	,	,	PUNCT
ma-198	76	41	[	[	X
ma-198	76	42	12	12	NUM
ma-198	76	43	]	]	PUNCT
ma-198	76	44	)	)	PUNCT
ma-198	76	45	let	let	VERB
ma-198	76	46	a	a	DET
ma-198	76	47	set	set	ADJ
ma-198	76	48	value	value	NOUN
ma-198	76	49	mapping	mapping	NOUN
ma-198	76	50	m	m	NOUN
ma-198	76	51	:	:	PUNCT
ma-198	76	52	h	h	PROPN
ma-198	76	53	→	→	SYM
ma-198	76	54	2h	2h	NUM
ma-198	76	55	be	be	VERB
ma-198	76	56	maximal	maximal	ADJ
ma-198	76	57	monotone	monotone	ADJ
ma-198	76	58	.	.	PUNCT
ma-198	77	1	we	we	PRON
ma-198	77	2	define	define	VERB
ma-198	77	3	a	a	DET
ma-198	77	4	resolvent	resolvent	ADJ
ma-198	77	5	operator	operator	NOUN
ma-198	77	6	jm	jm	PROPN
ma-198	77	7	λgenerated	λgenerate	VERB
ma-198	77	8	by	by	ADP
ma-198	77	9	π	π	PROPN
ma-198	77	10	and	and	CCONJ
ma-198	77	11	λ	λ	PROPN
ma-198	77	12	as	as	SCONJ
ma-198	77	13	follows	follow	VERB
ma-198	77	14	jm	jm	PROPN
ma-198	77	15	λ	λ	PROPN
ma-198	77	16	=	=	PRON
ma-198	77	17	(	(	PUNCT
ma-198	77	18	i	i	PRON
ma-198	77	19	−	−	VERB
ma-198	78	1	λm)−1(x),∀x	λm)−1(x),∀x	X
ma-198	78	2	∈	∈	PROPN
ma-198	78	3	h	h	NOUN
ma-198	78	4	(	(	PUNCT
ma-198	78	5	1.9	1.9	NUM
ma-198	78	6	)	)	PUNCT
ma-198	78	7	where	where	SCONJ
ma-198	78	8	λ	λ	PROPN
ma-198	78	9	is	be	AUX
ma-198	78	10	a	a	DET
ma-198	78	11	positive	positive	ADJ
ma-198	78	12	number	number	NOUN
ma-198	78	13	.	.	PUNCT
ma-198	79	1	it	it	PRON
ma-198	79	2	is	be	AUX
ma-198	79	3	easily	easily	ADV
ma-198	79	4	to	to	PART
ma-198	79	5	see	see	VERB
ma-198	79	6	that	that	SCONJ
ma-198	79	7	the	the	DET
ma-198	79	8	resolvent	resolvent	ADJ
ma-198	79	9	operator	operator	NOUN
ma-198	79	10	jm	jm	PROPN
ma-198	79	11	λ	λ	PROPN
ma-198	79	12	is	be	AUX
ma-198	79	13	single	single	ADJ
ma-198	79	14	valuednonexpensive	valuednonexpensive	NOUN
ma-198	79	15	and	and	CCONJ
ma-198	79	16	1−inverse	1−inverse	NOUN
ma-198	79	17	strongly	strongly	ADV
ma-198	79	18	monotone	monotone	ADJ
ma-198	79	19	,	,	PUNCT
ma-198	79	20	and	and	CCONJ
ma-198	79	21	moreover	moreover	ADV
ma-198	79	22	,	,	PUNCT
ma-198	79	23	a	a	DET
ma-198	79	24	solution	solution	NOUN
ma-198	79	25	of	of	ADP
ma-198	79	26	the	the	DET
ma-198	79	27	problem	problem	NOUN
ma-198	79	28	(	(	PUNCT
ma-198	79	29	1.8	1.8	NUM
ma-198	79	30	)	)	PUNCT
ma-198	79	31	isa	isa	NOUN
ma-198	79	32	fixed	fix	VERB
ma-198	79	33	point	point	NOUN
ma-198	79	34	of	of	ADP
ma-198	79	35	the	the	DET
ma-198	79	36	operator	operator	NOUN
ma-198	79	37	jm	jm	PROPN
ma-198	79	38	λ	λ	PROPN
ma-198	79	39	(	(	PUNCT
ma-198	79	40	i	i	PRON
ma-198	79	41	−	−	PROPN
ma-198	79	42	λa	λa	NOUN
ma-198	79	43	)	)	PUNCT
ma-198	79	44	,	,	PUNCT
ma-198	79	45	∀λ	∀λ	X
ma-198	79	46	>	>	X
ma-198	79	47	0	0	PROPN
ma-198	79	48	(	(	PUNCT
ma-198	79	49	see	see	VERB
ma-198	79	50	[	[	X
ma-198	79	51	4]).let	4]).let	NUM
ma-198	79	52	t	t	NOUN
ma-198	79	53	:	:	PUNCT
ma-198	79	54	h	h	NOUN
ma-198	79	55	→	→	SYM
ma-198	79	56	p	p	X
ma-198	79	57	(	(	PUNCT
ma-198	79	58	h	h	NOUN
ma-198	79	59	)	)	PUNCT
ma-198	79	60	be	be	AUX
ma-198	79	61	multivalued	multivalue	VERB
ma-198	79	62	map	map	NOUN
ma-198	79	63	and	and	CCONJ
ma-198	79	64	pt	pt	INTJ
ma-198	79	65	:	:	PUNCT
ma-198	79	66	h	h	NOUN
ma-198	79	67	→	→	SYM
ma-198	79	68	cb(h	cb(h	X
ma-198	79	69	)	)	PUNCT
ma-198	79	70	be	be	AUX
ma-198	79	71	defined	define	VERB
ma-198	79	72	by	by	ADP
ma-198	79	73	pt	pt	X
ma-198	79	74	(	(	PUNCT
ma-198	79	75	x	x	NOUN
ma-198	79	76	)	)	PUNCT
ma-198	79	77	=	=	SYM
ma-198	79	78	{	{	PUNCT
ma-198	79	79	y	y	PROPN
ma-198	79	80	∈	∈	PROPN
ma-198	79	81	tx	tx	PROPN
ma-198	79	82	:	:	PUNCT
ma-198	79	83	‖y	‖y	PUNCT
ma-198	80	1	−	−	PUNCT
ma-198	80	2	x‖	x‖	X
ma-198	80	3	=	=	SYM
ma-198	80	4	d(x	d(x	PROPN
ma-198	80	5	,	,	PUNCT
ma-198	80	6	t	t	PROPN
ma-198	80	7	x	x	PROPN
ma-198	80	8	)	)	PUNCT
ma-198	80	9	}	}	PUNCT
ma-198	80	10	(	(	PUNCT
ma-198	80	11	1.10	1.10	NUM
ma-198	80	12	)	)	PUNCT
ma-198	80	13	see	see	VERB
ma-198	80	14	examples	example	NOUN
ma-198	80	15	of	of	ADP
ma-198	80	16	a	a	DET
ma-198	80	17	multivalued	multivalue	VERB
ma-198	80	18	mapping	mapping	NOUN
ma-198	80	19	t	t	NOUN
ma-198	80	20	with	with	ADP
ma-198	80	21	f	f	PROPN
ma-198	80	22	ix(t	ix(t	ADV
ma-198	80	23	)	)	PUNCT
ma-198	81	1	6=	6=	ADP
ma-198	81	2	∅	∅	NOUN
ma-198	81	3	,	,	PUNCT
ma-198	81	4	t	t	PROPN
ma-198	81	5	p	p	NOUN
ma-198	81	6	=	=	X
ma-198	81	7	{	{	PUNCT
ma-198	81	8	q	q	X
ma-198	81	9	}	}	PUNCT
ma-198	81	10	for	for	ADP
ma-198	81	11	all	all	DET
ma-198	81	12	q	q	PROPN
ma-198	81	13	∈	∈	PROPN
ma-198	81	14	tp	tp	X
ma-198	81	15	which	which	PRON
ma-198	81	16	ptis	ptis	NOUN
ma-198	81	17	a	a	DET
ma-198	81	18	demicontractive	demicontractive	ADJ
ma-198	81	19	-	-	PUNCT
ma-198	81	20	type	type	NOUN
ma-198	81	21	but	but	CCONJ
ma-198	81	22	not	not	PART
ma-198	81	23	a	a	DET
ma-198	81	24	k−strictly	k−strictly	ADV
ma-198	81	25	pseudocontractive	pseudocontractive	ADJ
ma-198	81	26	-	-	PUNCT
ma-198	81	27	type	type	NOUN
ma-198	81	28	mapping	mapping	NOUN
ma-198	81	29	in	in	ADP
ma-198	81	30	mendy	mendy	PROPN
ma-198	81	31	et	et	PROPN
ma-198	81	32	al	al	PROPN
ma-198	82	1	[	[	X
ma-198	82	2	?	?	X
ma-198	82	3	]	]	X
ma-198	82	4	to	to	PART
ma-198	82	5	prove	prove	VERB
ma-198	82	6	that	that	SCONJ
ma-198	82	7	a	a	DET
ma-198	82	8	multivalued	multivalue	VERB
ma-198	82	9	mapping	mapping	NOUN
ma-198	82	10	t	t	NOUN
ma-198	82	11	with	with	ADP
ma-198	82	12	f	f	PROPN
ma-198	82	13	ix(t	ix(t	ADV
ma-198	82	14	)	)	PUNCT
ma-198	82	15	6=	6=	ADP
ma-198	82	16	∅	∅	NOUN
ma-198	82	17	and	and	CCONJ
ma-198	82	18	tp	tp	ADP
ma-198	82	19	=	=	PUNCT
ma-198	82	20	{	{	PUNCT
ma-198	82	21	q	q	X
ma-198	82	22	}	}	PUNCT
ma-198	82	23	for	for	ADP
ma-198	82	24	all	all	DET
ma-198	82	25	q	q	PROPN
ma-198	82	26	∈	∈	PROPN
ma-198	82	27	tp	tp	NOUN
ma-198	82	28	is	be	AUX
ma-198	82	29	ademicontractive	ademicontractive	ADJ
ma-198	82	30	-	-	PUNCT
ma-198	82	31	type	type	NOUN
ma-198	82	32	but	but	CCONJ
ma-198	82	33	not	not	PART
ma-198	82	34	a	a	DET
ma-198	82	35	k	k	NOUN
ma-198	82	36	-	-	PUNCT
ma-198	82	37	strictly	strictly	ADV
ma-198	82	38	pseudocontractive	pseudocontractive	ADJ
ma-198	82	39	-	-	PUNCT
ma-198	82	40	type	type	NOUN
ma-198	82	41	mapping	mapping	NOUN
ma-198	82	42	,	,	PUNCT
ma-198	82	43	we	we	PRON
ma-198	82	44	need	need	VERB
ma-198	82	45	to	to	PART
ma-198	82	46	demonstratethe	demonstratethe	VERB
ma-198	82	47	following	follow	VERB
ma-198	82	48	three	three	NUM
ma-198	82	49	steps	step	NOUN
ma-198	82	50	:	:	PUNCT
ma-198	82	51	step	step	NOUN
ma-198	82	52	1.3	1.3	NUM
ma-198	82	53	.	.	PUNCT
ma-198	83	1	show	show	VERB
ma-198	83	2	that	that	SCONJ
ma-198	83	3	t	t	PROPN
ma-198	83	4	is	be	AUX
ma-198	83	5	demicontractive-type.to	demicontractive-type.to	NOUN
ma-198	83	6	prove	prove	VERB
ma-198	83	7	that	that	SCONJ
ma-198	83	8	t	t	PROPN
ma-198	83	9	is	be	AUX
ma-198	83	10	demicontractive	demicontractive	ADJ
ma-198	83	11	-	-	PUNCT
ma-198	83	12	type	type	NOUN
ma-198	83	13	,	,	PUNCT
ma-198	83	14	we	we	PRON
ma-198	83	15	need	need	VERB
ma-198	83	16	to	to	PART
ma-198	83	17	show	show	VERB
ma-198	83	18	that	that	SCONJ
ma-198	83	19	for	for	ADP
ma-198	83	20	all	all	PRON
ma-198	83	21	p	p	NOUN
ma-198	83	22	∈	∈	PROPN
ma-198	83	23	f	f	NOUN
ma-198	83	24	ix(t	ix(t	ADV
ma-198	83	25	)	)	PUNCT
ma-198	83	26	and	and	CCONJ
ma-198	83	27	x	x	PUNCT
ma-198	83	28	∈	∈	PROPN
ma-198	83	29	d(t	d(t	PROPN
ma-198	83	30	)	)	PUNCT
ma-198	83	31	,	,	PUNCT
ma-198	83	32	there	there	PRON
ma-198	83	33	exists	exist	VERB
ma-198	83	34	k	k	PROPN
ma-198	83	35	∈	∈	PROPN
ma-198	83	36	(	(	PUNCT
ma-198	83	37	0	0	NUM
ma-198	83	38	,	,	PUNCT
ma-198	83	39	1	1	NUM
ma-198	83	40	)	)	PUNCT
ma-198	83	41	such	such	ADJ
ma-198	83	42	that	that	SCONJ
ma-198	83	43	(	(	PUNCT
ma-198	83	44	h(tx	h(tx	PROPN
ma-198	83	45	,	,	PUNCT
ma-198	83	46	tp	tp	NOUN
ma-198	83	47	)	)	PUNCT
ma-198	83	48	)	)	PUNCT
ma-198	83	49	2	2	NUM
ma-198	83	50	≤	≤	NUM
ma-198	83	51	‖x	‖x	PUNCT
ma-198	84	1	−	−	PROPN
ma-198	84	2	p‖2	p‖2	PROPN
ma-198	84	3	+	+	CCONJ
ma-198	84	4	kd(x	kd(x	NOUN
ma-198	84	5	,	,	PUNCT
ma-198	84	6	t	t	PROPN
ma-198	84	7	x)2	x)2	PROPN
ma-198	84	8	.	.	PUNCT
ma-198	85	1	since	since	SCONJ
ma-198	85	2	tp	tp	NUM
ma-198	85	3	=	=	PUNCT
ma-198	85	4	{	{	PUNCT
ma-198	85	5	q	q	X
ma-198	85	6	}	}	PUNCT
ma-198	85	7	for	for	ADP
ma-198	85	8	all	all	DET
ma-198	85	9	q	q	PROPN
ma-198	85	10	∈	∈	PROPN
ma-198	85	11	tp	tp	NOUN
ma-198	85	12	,	,	PUNCT
ma-198	85	13	we	we	PRON
ma-198	85	14	have	have	VERB
ma-198	85	15	tp	tp	VERB
ma-198	85	16	=	=	PUNCT
ma-198	85	17	{	{	PUNCT
ma-198	85	18	p	p	X
ma-198	85	19	}	}	PUNCT
ma-198	85	20	for	for	ADP
ma-198	85	21	all	all	PRON
ma-198	85	22	p	p	NOUN
ma-198	85	23	∈	∈	PROPN
ma-198	85	24	f	f	NOUN
ma-198	85	25	ix(t	ix(t	PROPN
ma-198	85	26	)	)	PUNCT
ma-198	85	27	.	.	PUNCT
ma-198	86	1	thus	thus	ADV
ma-198	86	2	,	,	PUNCT
ma-198	86	3	for	for	ADP
ma-198	86	4	any	any	DET
ma-198	86	5	x	x	PROPN
ma-198	86	6	∈	∈	PROPN
ma-198	86	7	d(t	d(t	PROPN
ma-198	86	8	)	)	PUNCT
ma-198	86	9	,	,	PUNCT
ma-198	86	10	tx	tx	PROPN
ma-198	86	11	=	=	PUNCT
ma-198	86	12	{	{	PUNCT
ma-198	86	13	φ	φ	NOUN
ma-198	86	14	}	}	PUNCT
ma-198	86	15	for	for	ADP
ma-198	86	16	some	some	DET
ma-198	86	17	φ	φ	NOUN
ma-198	86	18	∈	∈	PROPN
ma-198	86	19	f	f	PROPN
ma-198	86	20	ix(t	ix(t	ADV
ma-198	86	21	)	)	PUNCT
ma-198	86	22	.now	.now	PROPN
ma-198	86	23	,	,	PUNCT
ma-198	86	24	consider	consider	VERB
ma-198	86	25	the	the	DET
ma-198	86	26	case	case	NOUN
ma-198	86	27	when	when	SCONJ
ma-198	86	28	x	x	PROPN
ma-198	86	29	=	=	SYM
ma-198	86	30	φ	φ	PROPN
ma-198	86	31	.	.	PUNCT
ma-198	87	1	in	in	ADP
ma-198	87	2	this	this	DET
ma-198	87	3	case	case	NOUN
ma-198	87	4	,	,	PUNCT
ma-198	87	5	we	we	PRON
ma-198	87	6	have	have	VERB
ma-198	87	7	h(tx	h(tx	NUM
ma-198	87	8	,	,	PUNCT
ma-198	87	9	tp	tp	NOUN
ma-198	87	10	)	)	PUNCT
ma-198	87	11	=	=	SYM
ma-198	87	12	h(tφ	h(tφ	PROPN
ma-198	87	13	,	,	PUNCT
ma-198	87	14	tp	tp	NOUN
ma-198	87	15	)	)	PUNCT
ma-198	87	16	=	=	SYM
ma-198	87	17	h({φ	h({φ	PROPN
ma-198	87	18	}	}	PUNCT
ma-198	87	19	,	,	PUNCT
ma-198	87	20	{	{	PUNCT
ma-198	87	21	p	p	NOUN
ma-198	87	22	}	}	PUNCT
ma-198	87	23	)	)	PUNCT
ma-198	87	24	=	=	SYM
ma-198	88	1	0	0	X
ma-198	88	2	.	.	PUNCT
ma-198	89	1	therefore	therefore	ADV
ma-198	89	2	,	,	PUNCT
ma-198	89	3	the	the	DET
ma-198	89	4	inequality	inequality	NOUN
ma-198	89	5	holds	hold	VERB
ma-198	89	6	for	for	ADP
ma-198	89	7	any	any	DET
ma-198	89	8	k	k	PROPN
ma-198	89	9	∈	∈	PROPN
ma-198	89	10	(	(	PUNCT
ma-198	89	11	0	0	NUM
ma-198	89	12	,	,	PUNCT
ma-198	89	13	1	1	NUM
ma-198	89	14	)	)	PUNCT
ma-198	89	15	.	.	PUNCT
ma-198	90	1	step	step	NOUN
ma-198	90	2	1.4	1.4	NUM
ma-198	90	3	.	.	PUNCT
ma-198	91	1	show	show	VERB
ma-198	91	2	that	that	SCONJ
ma-198	91	3	t	t	PROPN
ma-198	91	4	is	be	AUX
ma-198	91	5	not	not	PART
ma-198	91	6	k	k	ADJ
ma-198	91	7	-	-	PUNCT
ma-198	91	8	strictly	strictly	ADV
ma-198	91	9	pseudocontractive-type.to	pseudocontractive-type.to	ADV
ma-198	91	10	prove	prove	NOUN
ma-198	91	11	that	that	SCONJ
ma-198	91	12	t	t	PROPN
ma-198	91	13	is	be	AUX
ma-198	91	14	not	not	PART
ma-198	91	15	k	k	ADJ
ma-198	91	16	-	-	PUNCT
ma-198	91	17	strictly	strictly	ADV
ma-198	91	18	pseudocontractive	pseudocontractive	ADJ
ma-198	91	19	-	-	PUNCT
ma-198	91	20	type	type	NOUN
ma-198	91	21	,	,	PUNCT
ma-198	91	22	we	we	PRON
ma-198	91	23	need	need	VERB
ma-198	91	24	to	to	PART
ma-198	91	25	show	show	VERB
ma-198	91	26	that	that	SCONJ
ma-198	91	27	there	there	PRON
ma-198	91	28	does	do	VERB
ma-198	91	29	notexist	notexist	NOUN
ma-198	91	30	a	a	DET
ma-198	91	31	constant	constant	ADJ
ma-198	91	32	k	k	PROPN
ma-198	91	33	∈	∈	PROPN
ma-198	91	34	(	(	PUNCT
ma-198	91	35	0	0	NUM
ma-198	91	36	,	,	PUNCT
ma-198	91	37	1	1	NUM
ma-198	91	38	)	)	PUNCT
ma-198	91	39	such	such	ADJ
ma-198	91	40	that	that	SCONJ
ma-198	91	41	(	(	PUNCT
ma-198	91	42	h(tx	h(tx	PROPN
ma-198	91	43	,	,	PUNCT
ma-198	91	44	tp	tp	NOUN
ma-198	91	45	)	)	PUNCT
ma-198	91	46	)	)	PUNCT
ma-198	91	47	2	2	NUM
ma-198	91	48	≤	≤	PROPN
ma-198	91	49	k‖x	k‖x	PROPN
ma-198	91	50	−	−	PROPN
ma-198	91	51	p‖2	p‖2	PROPN
ma-198	91	52	+	+	CCONJ
ma-198	91	53	kd(x	kd(x	NOUN
ma-198	91	54	,	,	PUNCT
ma-198	91	55	t	t	PROPN
ma-198	91	56	x)2	x)2	VERB
ma-198	91	57	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	91	58	eur	eur	NOUN
ma-198	91	59	.	.	PUNCT
ma-198	92	1	j.	j.	PROPN
ma-198	92	2	math	math	PROPN
ma-198	92	3	.	.	PUNCT
ma-198	93	1	anal	anal	PROPN
ma-198	93	2	.	.	PUNCT
ma-198	94	1	10.28924	10.28924	NUM
ma-198	94	2	/	/	SYM
ma-198	94	3	ada	ada	PROPN
ma-198	94	4	/	/	SYM
ma-198	94	5	ma.4.2	ma.4.2	PROPN
ma-198	94	6	5for	5for	NUM
ma-198	94	7	all	all	DET
ma-198	94	8	p	p	NOUN
ma-198	94	9	∈	∈	PROPN
ma-198	94	10	f	f	NOUN
ma-198	94	11	ix(t	ix(t	ADV
ma-198	94	12	)	)	PUNCT
ma-198	94	13	and	and	CCONJ
ma-198	94	14	x	x	PUNCT
ma-198	94	15	∈	∈	PROPN
ma-198	94	16	d(t	d(t	PROPN
ma-198	94	17	)	)	PUNCT
ma-198	94	18	.from	.from	ADP
ma-198	94	19	step	step	NOUN
ma-198	94	20	1.3	1.3	NUM
ma-198	94	21	,	,	PUNCT
ma-198	94	22	we	we	PRON
ma-198	94	23	know	know	VERB
ma-198	94	24	that	that	SCONJ
ma-198	94	25	h(tx	h(tx	NUM
ma-198	94	26	,	,	PUNCT
ma-198	94	27	tp	tp	NOUN
ma-198	94	28	)	)	PUNCT
ma-198	94	29	=	=	SYM
ma-198	94	30	0	0	NUM
ma-198	95	1	for	for	ADP
ma-198	95	2	any	any	DET
ma-198	95	3	p	p	NOUN
ma-198	95	4	∈	∈	PROPN
ma-198	95	5	f	f	PROPN
ma-198	95	6	ix(t	ix(t	ADV
ma-198	95	7	)	)	PUNCT
ma-198	95	8	and	and	CCONJ
ma-198	95	9	x	x	PUNCT
ma-198	95	10	∈	∈	PROPN
ma-198	95	11	d(t	d(t	PROPN
ma-198	95	12	)	)	PUNCT
ma-198	95	13	.	.	PUNCT
ma-198	96	1	therefore	therefore	ADV
ma-198	96	2	,	,	PUNCT
ma-198	96	3	theinequality	theinequality	NOUN
ma-198	96	4	reduces	reduce	VERB
ma-198	96	5	to	to	ADP
ma-198	96	6	0	0	NUM
ma-198	96	7	≤	≤	NUM
ma-198	96	8	k‖x	k‖x	PROPN
ma-198	96	9	−	−	PROPN
ma-198	96	10	p‖2	p‖2	PROPN
ma-198	96	11	for	for	ADP
ma-198	96	12	all	all	PRON
ma-198	96	13	p	p	NOUN
ma-198	96	14	∈	∈	PROPN
ma-198	96	15	f	f	NOUN
ma-198	96	16	ix(t	ix(t	ADV
ma-198	96	17	)	)	PUNCT
ma-198	96	18	and	and	CCONJ
ma-198	96	19	x	x	PUNCT
ma-198	96	20	∈	∈	PROPN
ma-198	96	21	d(t	d(t	PROPN
ma-198	96	22	)	)	PUNCT
ma-198	96	23	.	.	PUNCT
ma-198	97	1	however	however	ADV
ma-198	97	2	,	,	PUNCT
ma-198	97	3	this	this	DET
ma-198	97	4	inequality	inequality	NOUN
ma-198	97	5	can	can	AUX
ma-198	97	6	not	not	PART
ma-198	97	7	hold	hold	VERB
ma-198	97	8	for	for	ADP
ma-198	97	9	all	all	PRON
ma-198	97	10	x	x	SYM
ma-198	97	11	6=	6=	ADP
ma-198	97	12	p	p	NOUN
ma-198	97	13	since	since	SCONJ
ma-198	97	14	itimplies	itimplie	VERB
ma-198	97	15	k	k	PROPN
ma-198	97	16	≥	≥	NUM
ma-198	97	17	1	1	NUM
ma-198	97	18	‖x−p‖2	‖x−p‖2	PROPN
ma-198	97	19	,	,	PUNCT
ma-198	97	20	which	which	PRON
ma-198	97	21	contradicts	contradict	VERB
ma-198	97	22	the	the	DET
ma-198	97	23	requirement	requirement	NOUN
ma-198	97	24	that	that	SCONJ
ma-198	97	25	k	k	PROPN
ma-198	97	26	∈	∈	PROPN
ma-198	97	27	(	(	PUNCT
ma-198	97	28	0	0	NUM
ma-198	97	29	,	,	PUNCT
ma-198	97	30	1	1	NUM
ma-198	97	31	)	)	PUNCT
ma-198	97	32	.	.	PUNCT
ma-198	98	1	step	step	NOUN
ma-198	98	2	1.5	1.5	NUM
ma-198	98	3	.	.	PUNCT
ma-198	99	1	show	show	VERB
ma-198	99	2	that	that	SCONJ
ma-198	99	3	pt	pt	PROPN
ma-198	99	4	is	be	AUX
ma-198	99	5	a	a	DET
ma-198	99	6	demicontractive-type.let	demicontractive-type.let	NOUN
ma-198	99	7	pt	pt	NOUN
ma-198	99	8	denote	denote	VERB
ma-198	99	9	the	the	DET
ma-198	99	10	projection	projection	NOUN
ma-198	99	11	operator	operator	NOUN
ma-198	99	12	associated	associate	VERB
ma-198	99	13	with	with	ADP
ma-198	99	14	multivalued	multivalue	VERB
ma-198	99	15	mapping	mapping	NOUN
ma-198	99	16	t	t	NOUN
ma-198	99	17	.	.	PUNCT
ma-198	100	1	since	since	SCONJ
ma-198	100	2	tp	tp	NUM
ma-198	100	3	=	=	PUNCT
ma-198	100	4	{	{	PUNCT
ma-198	100	5	q}for	q}for	VERB
ma-198	100	6	all	all	DET
ma-198	100	7	q	q	PROPN
ma-198	100	8	∈	∈	PROPN
ma-198	100	9	tp	tp	NOUN
ma-198	100	10	,	,	PUNCT
ma-198	100	11	pt	pt	X
ma-198	100	12	is	be	AUX
ma-198	100	13	the	the	DET
ma-198	100	14	single	single	ADV
ma-198	100	15	-	-	PUNCT
ma-198	100	16	valued	value	VERB
ma-198	100	17	mapping	mapping	NOUN
ma-198	100	18	that	that	PRON
ma-198	100	19	assigns	assign	VERB
ma-198	100	20	each	each	DET
ma-198	100	21	p	p	PROPN
ma-198	100	22	∈	∈	PROPN
ma-198	100	23	f	f	PROPN
ma-198	100	24	ix(t	ix(t	ADV
ma-198	100	25	)	)	PUNCT
ma-198	100	26	to	to	ADP
ma-198	100	27	itself.consider	itself.consider	PROPN
ma-198	100	28	p	p	PRON
ma-198	100	29	,	,	PUNCT
ma-198	100	30	x	x	SYM
ma-198	100	31	∈	∈	PROPN
ma-198	100	32	f	f	PROPN
ma-198	100	33	ix(t	ix(t	PROPN
ma-198	100	34	)	)	PUNCT
ma-198	100	35	,	,	PUNCT
ma-198	100	36	with	with	SCONJ
ma-198	100	37	x	x	PROPN
ma-198	100	38	6=	6=	PROPN
ma-198	100	39	p.	p.	NOUN
ma-198	100	40	then	then	ADV
ma-198	100	41	tx	tx	VERB
ma-198	100	42	=	=	PUNCT
ma-198	100	43	tp	tp	PROPN
ma-198	100	44	and	and	CCONJ
ma-198	100	45	‖x	‖x	NOUN
ma-198	101	1	−	−	PROPN
ma-198	101	2	p‖	p‖	NOUN
ma-198	101	3	>	>	X
ma-198	101	4	0	0	X
ma-198	101	5	.	.	PUNCT
ma-198	102	1	furthermore	furthermore	ADV
ma-198	102	2	,	,	PUNCT
ma-198	102	3	d(x	d(x	PROPN
ma-198	102	4	,	,	PUNCT
ma-198	102	5	t	t	NOUN
ma-198	102	6	x	x	X
ma-198	102	7	)	)	PUNCT
ma-198	102	8	=	=	SYM
ma-198	102	9	d(p	d(p	PROPN
ma-198	102	10	,	,	PUNCT
ma-198	102	11	tp	tp	NOUN
ma-198	102	12	)	)	PUNCT
ma-198	102	13	=	=	SYM
ma-198	102	14	0	0	PUNCT
ma-198	102	15	since	since	SCONJ
ma-198	102	16	x	x	X
ma-198	102	17	,	,	PUNCT
ma-198	102	18	p	p	PROPN
ma-198	102	19	∈	∈	PROPN
ma-198	102	20	f	f	PROPN
ma-198	102	21	ix(t	ix(t	PROPN
ma-198	102	22	)	)	PUNCT
ma-198	102	23	.using	.use	VERB
ma-198	102	24	these	these	DET
ma-198	102	25	values	value	NOUN
ma-198	102	26	,	,	PUNCT
ma-198	102	27	let	let	VERB
ma-198	102	28	’s	’s	NOUN
ma-198	102	29	rearrange	rearrange	VERB
ma-198	102	30	the	the	DET
ma-198	102	31	original	original	ADJ
ma-198	102	32	inequality	inequality	NOUN
ma-198	102	33	:	:	PUNCT
ma-198	102	34	(	(	PUNCT
ma-198	102	35	h(tx	h(tx	NUM
ma-198	102	36	,	,	PUNCT
ma-198	102	37	tp	tp	NOUN
ma-198	102	38	)	)	PUNCT
ma-198	102	39	)	)	PUNCT
ma-198	102	40	2	2	NUM
ma-198	102	41	≤	≤	NUM
ma-198	102	42	‖x	‖x	PUNCT
ma-198	103	1	−	−	PROPN
ma-198	103	2	p‖2	p‖2	PROPN
ma-198	103	3	+	+	CCONJ
ma-198	103	4	kd(x	kd(x	NOUN
ma-198	103	5	,	,	PUNCT
ma-198	103	6	t	t	PROPN
ma-198	103	7	x)2	x)2	PROPN
ma-198	103	8	0	0	NUM
ma-198	104	1	≤	≤	NUM
ma-198	104	2	‖x	‖x	PUNCT
ma-198	105	1	−	−	PROPN
ma-198	105	2	p‖2	p‖2	PROPN
ma-198	105	3	+	+	CCONJ
ma-198	105	4	kd(x	kd(x	NOUN
ma-198	105	5	,	,	PUNCT
ma-198	105	6	t	t	PROPN
ma-198	105	7	x)2	x)2	PROPN
ma-198	105	8	.	.	PUNCT
ma-198	106	1	since	since	SCONJ
ma-198	106	2	‖x−p‖	‖x−p‖	PROPN
ma-198	106	3	>	>	X
ma-198	106	4	0	0	NUM
ma-198	106	5	,	,	PUNCT
ma-198	106	6	the	the	DET
ma-198	106	7	inequality	inequality	NOUN
ma-198	106	8	can	can	AUX
ma-198	106	9	only	only	ADV
ma-198	106	10	hold	hold	VERB
ma-198	106	11	if	if	SCONJ
ma-198	106	12	k	k	PROPN
ma-198	106	13	=	=	NOUN
ma-198	106	14	0	0	X
ma-198	106	15	.	.	PUNCT
ma-198	107	1	however	however	ADV
ma-198	107	2	,	,	PUNCT
ma-198	107	3	k	k	PROPN
ma-198	107	4	∈	∈	PROPN
ma-198	107	5	(	(	PUNCT
ma-198	107	6	0	0	NUM
ma-198	107	7	,	,	PUNCT
ma-198	107	8	1	1	NUM
ma-198	107	9	)	)	PUNCT
ma-198	107	10	by	by	ADP
ma-198	107	11	definition	definition	NOUN
ma-198	107	12	,	,	PUNCT
ma-198	107	13	so	so	ADV
ma-198	107	14	ptcannot	ptcannot	ADV
ma-198	107	15	satisfy	satisfy	VERB
ma-198	107	16	the	the	DET
ma-198	107	17	inequality	inequality	NOUN
ma-198	107	18	for	for	ADP
ma-198	107	19	any	any	DET
ma-198	107	20	k	k	PROPN
ma-198	107	21	∈	∈	PROPN
ma-198	107	22	(	(	PUNCT
ma-198	107	23	0	0	NUM
ma-198	107	24	,	,	PUNCT
ma-198	107	25	1	1	NUM
ma-198	107	26	)	)	PUNCT
ma-198	107	27	.	.	PUNCT
ma-198	108	1	hence	hence	ADV
ma-198	108	2	,	,	PUNCT
ma-198	108	3	pt	pt	X
ma-198	108	4	is	be	AUX
ma-198	108	5	not	not	PART
ma-198	108	6	a	a	DET
ma-198	108	7	k	k	NOUN
ma-198	108	8	-	-	PUNCT
ma-198	108	9	strictly	strictly	ADV
ma-198	108	10	pseudocontractive	pseudocontractive	ADJ
ma-198	108	11	-	-	PUNCT
ma-198	108	12	type	type	NOUN
ma-198	108	13	mapping	mapping	NOUN
ma-198	108	14	.	.	PUNCT
ma-198	109	1	a	a	DET
ma-198	109	2	popular	popular	ADJ
ma-198	109	3	method	method	NOUN
ma-198	109	4	for	for	ADP
ma-198	109	5	solving	solve	VERB
ma-198	109	6	problem	problem	NOUN
ma-198	109	7	(	(	PUNCT
ma-198	109	8	1.8	1.8	NUM
ma-198	109	9	)	)	PUNCT
ma-198	109	10	is	be	AUX
ma-198	109	11	the	the	DET
ma-198	109	12	well	well	ADV
ma-198	109	13	-	-	PUNCT
ma-198	109	14	known	know	VERB
ma-198	109	15	forward	forward	ADJ
ma-198	109	16	-	-	PUNCT
ma-198	109	17	backward	backward	ADJ
ma-198	109	18	splitting	splitting	NOUN
ma-198	109	19	methodintroduced	methodintroduce	VERB
ma-198	109	20	by	by	ADP
ma-198	109	21	passty	passty	NOUN
ma-198	109	22	[	[	X
ma-198	109	23	14	14	NUM
ma-198	109	24	]	]	PUNCT
ma-198	109	25	and	and	CCONJ
ma-198	109	26	lions	lion	NOUN
ma-198	109	27	and	and	CCONJ
ma-198	109	28	mercier	merci	ADJ
ma-198	109	29	[	[	X
ma-198	109	30	27].the	27].the	DET
ma-198	109	31	method	method	NOUN
ma-198	109	32	is	be	AUX
ma-198	109	33	formulated	formulate	VERB
ma-198	109	34	as	as	ADP
ma-198	109	35	xn+1	xn+1	PROPN
ma-198	109	36	=	=	SYM
ma-198	109	37	(	(	PUNCT
ma-198	109	38	i	i	PRON
ma-198	109	39	−	−	X
ma-198	109	40	λnm)−1(i	λnm)−1(i	VERB
ma-198	109	41	−	−	PROPN
ma-198	110	1	λna)x	λna)x	PROPN
ma-198	110	2	,	,	PUNCT
ma-198	110	3	λn	λn	X
ma-198	110	4	>	>	X
ma-198	110	5	0	0	NUM
ma-198	110	6	.	.	PUNCT
ma-198	111	1	(	(	PUNCT
ma-198	111	2	1.11	1.11	NUM
ma-198	111	3	)	)	PUNCT
ma-198	111	4	under	under	ADP
ma-198	111	5	the	the	DET
ma-198	111	6	condition	condition	NOUN
ma-198	111	7	that	that	SCONJ
ma-198	111	8	dom(m	dom(m	PROPN
ma-198	111	9	)	)	PUNCT
ma-198	111	10	⊂	⊂	PROPN
ma-198	111	11	dom(a	dom(a	PROPN
ma-198	111	12	)	)	PUNCT
ma-198	111	13	.	.	PUNCT
ma-198	112	1	it	it	PRON
ma-198	112	2	was	be	AUX
ma-198	112	3	known	know	VERB
ma-198	112	4	in	in	ADP
ma-198	112	5	[	[	X
ma-198	112	6	31	31	NUM
ma-198	112	7	]	]	PUNCT
ma-198	112	8	,	,	PUNCT
ma-198	112	9	that	that	DET
ma-198	112	10	weak	weak	ADJ
ma-198	112	11	convergence	convergence	NOUN
ma-198	112	12	of(1.11	of(1.11	NOUN
ma-198	112	13	)	)	PUNCT
ma-198	112	14	requires	require	VERB
ma-198	112	15	quite	quite	ADV
ma-198	112	16	restrictive	restrictive	ADJ
ma-198	112	17	assumptions	assumption	NOUN
ma-198	112	18	on	on	ADP
ma-198	112	19	a	a	PRON
ma-198	112	20	and	and	CCONJ
ma-198	112	21	π	π	NOUN
ma-198	112	22	,	,	PUNCT
ma-198	112	23	such	such	ADJ
ma-198	112	24	that	that	SCONJ
ma-198	112	25	the	the	DET
ma-198	112	26	inverse	inverse	NOUN
ma-198	112	27	of	of	ADP
ma-198	112	28	a	a	PRON
ma-198	112	29	is	be	AUX
ma-198	112	30	stronglymonotone	stronglymonotone	NOUN
ma-198	112	31	or	or	CCONJ
ma-198	112	32	π	π	PROPN
ma-198	112	33	is	be	AUX
ma-198	112	34	lipschitz	lipschitz	VERB
ma-198	112	35	continuous	continuous	ADJ
ma-198	112	36	and	and	CCONJ
ma-198	112	37	monotone	monotone	ADJ
ma-198	112	38	and	and	CCONJ
ma-198	112	39	the	the	DET
ma-198	112	40	operator	operator	NOUN
ma-198	112	41	(	(	PUNCT
ma-198	112	42	a+m	a+m	NUM
ma-198	112	43	)	)	PUNCT
ma-198	112	44	is	be	AUX
ma-198	112	45	strongly	strongly	ADV
ma-198	112	46	monotoneon	monotoneon	PROPN
ma-198	112	47	dom(b	dom(b	PROPN
ma-198	112	48	)	)	PUNCT
ma-198	112	49	.	.	PUNCT
ma-198	113	1	tseng	tseng	PROPN
ma-198	113	2	in	in	ADP
ma-198	113	3	[	[	X
ma-198	113	4	20	20	NUM
ma-198	113	5	]	]	PUNCT
ma-198	113	6	and	and	CCONJ
ma-198	113	7	gibali	gibali	VERB
ma-198	113	8	and	and	CCONJ
ma-198	113	9	thong	thong	NOUN
ma-198	113	10	in	in	ADP
ma-198	113	11	[	[	X
ma-198	113	12	24	24	NUM
ma-198	113	13	]	]	PUNCT
ma-198	113	14	extended	extended	ADJ
ma-198	113	15	and	and	CCONJ
ma-198	113	16	improved	improve	VERB
ma-198	113	17	results	result	NOUN
ma-198	113	18	of	of	ADP
ma-198	113	19	g.h-g.chen	g.h-g.chen	PROPN
ma-198	113	20	and	and	CCONJ
ma-198	113	21	r.t	r.t	PROPN
ma-198	113	22	.	.	PROPN
ma-198	113	23	rockafellar	rockafellar	PROPN
ma-198	114	1	[	[	X
ma-198	114	2	31].most	31].most	NUM
ma-198	114	3	recently	recently	ADV
ma-198	114	4	,	,	PUNCT
ma-198	114	5	sow	sow	VERB
ma-198	114	6	[	[	X
ma-198	114	7	28	28	NUM
ma-198	114	8	]	]	PUNCT
ma-198	114	9	introduced	introduce	VERB
ma-198	114	10	and	and	CCONJ
ma-198	114	11	studied	study	VERB
ma-198	114	12	a	a	DET
ma-198	114	13	new	new	ADJ
ma-198	114	14	iterative	iterative	NOUN
ma-198	114	15	algorithm	algorithm	NOUN
ma-198	114	16	and	and	CCONJ
ma-198	114	17	prove	prove	VERB
ma-198	114	18	convergencetheorems	convergencetheorem	NOUN
ma-198	114	19	for	for	ADP
ma-198	114	20	variation	variation	NOUN
ma-198	114	21	inclusion	inclusion	NOUN
ma-198	114	22	problem	problem	NOUN
ma-198	114	23	(	(	PUNCT
ma-198	114	24	1.8	1.8	NUM
ma-198	114	25	)	)	PUNCT
ma-198	114	26	and	and	CCONJ
ma-198	114	27	fixed	fix	VERB
ma-198	114	28	point	point	NOUN
ma-198	114	29	problem	problem	NOUN
ma-198	114	30	involving	involve	VERB
ma-198	114	31	multivalued	multivalue	VERB
ma-198	114	32	demi	demi	NOUN
ma-198	114	33	-	-	PUNCT
ma-198	114	34	contractive	contractive	ADJ
ma-198	114	35	and	and	CCONJ
ma-198	114	36	quasi	quasi	ADJ
ma-198	114	37	-	-	ADJ
ma-198	114	38	nonexpansive	nonexpansive	ADJ
ma-198	114	39	mappings	mapping	NOUN
ma-198	114	40	in	in	ADP
ma-198	114	41	hilbert	hilbert	PROPN
ma-198	114	42	spaces	space	NOUN
ma-198	114	43	.	.	PUNCT
ma-198	115	1	they	they	PRON
ma-198	115	2	defined	define	VERB
ma-198	115	3	the	the	DET
ma-198	115	4	sequence	sequence	NOUN
ma-198	115	5	{	{	PUNCT
ma-198	115	6	ψn	ψn	NOUN
ma-198	115	7	}	}	PUNCT
ma-198	115	8	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NOUN
ma-198	115	9	eur	eur	NOUN
ma-198	115	10	.	.	PUNCT
ma-198	116	1	j.	j.	PROPN
ma-198	116	2	math	math	PROPN
ma-198	116	3	.	.	PUNCT
ma-198	117	1	anal	anal	PROPN
ma-198	117	2	.	.	PUNCT
ma-198	118	1	10.28924	10.28924	NUM
ma-198	118	2	/	/	SYM
ma-198	118	3	ada	ada	NOUN
ma-198	118	4	/	/	SYM
ma-198	118	5	ma.4.2	ma.4.2	PROPN
ma-198	118	6	6as	6as	NOUN
ma-198	118	7	follows	follow	VERB
ma-198	118	8			NOUN
ma-198	118	9	δn	δn	ADJ
ma-198	118	10	=	=	PUNCT
ma-198	118	11	jm	jm	PROPN
ma-198	118	12	λn	λn	PROPN
ma-198	118	13	(	(	PUNCT
ma-198	118	14	i	i	PRON
ma-198	118	15	−	−	PROPN
ma-198	118	16	λna)xn	λna)xn	NOUN
ma-198	118	17	,	,	PUNCT
ma-198	118	18	yn	yn	PROPN
ma-198	118	19	=	=	PUNCT
ma-198	118	20	θnδn	θnδn	PROPN
ma-198	118	21	+	+	CCONJ
ma-198	118	22	(	(	PUNCT
ma-198	118	23	1−	1−	NUM
ma-198	118	24	θn)vn	θn)vn	ADP
ma-198	118	25	,	,	PUNCT
ma-198	118	26	vn	vn	PROPN
ma-198	118	27	∈	∈	PROPN
ma-198	118	28	tδn	tδn	X
ma-198	118	29	,	,	PUNCT
ma-198	118	30	zn	zn	PROPN
ma-198	118	31	=	=	SYM
ma-198	118	32	βnyn	βnyn	PROPN
ma-198	118	33	+	+	CCONJ
ma-198	118	34	(	(	PUNCT
ma-198	118	35	1−	1−	NUM
ma-198	118	36	βn)un	βn)un	NUM
ma-198	118	37	,	,	PUNCT
ma-198	118	38	un	un	PROPN
ma-198	118	39	∈	∈	PROPN
ma-198	118	40	t2yn	t2yn	NUM
ma-198	118	41	,	,	PUNCT
ma-198	118	42	xn+1	xn+1	X
ma-198	118	43	=	=	PUNCT
ma-198	118	44	pk(αnγf	pk(αnγf	X
ma-198	118	45	(	(	PUNCT
ma-198	118	46	xn	xn	X
ma-198	118	47	)	)	PUNCT
ma-198	119	1	+	+	CCONJ
ma-198	119	2	(	(	PUNCT
ma-198	119	3	1−	1−	NUM
ma-198	119	4	ηαnb)zn	ηαnb)zn	NOUN
ma-198	119	5	)	)	PUNCT
ma-198	119	6	(	(	PUNCT
ma-198	119	7	1.12	1.12	NUM
ma-198	119	8	)	)	PUNCT
ma-198	119	9	and	and	CCONJ
ma-198	119	10	prove	prove	VERB
ma-198	119	11	that	that	SCONJ
ma-198	119	12	under	under	ADP
ma-198	119	13	certain	certain	ADJ
ma-198	119	14	conditions	condition	NOUN
ma-198	119	15	,	,	PUNCT
ma-198	119	16	the	the	DET
ma-198	119	17	sequence	sequence	NOUN
ma-198	119	18	{	{	PUNCT
ma-198	119	19	xn	xn	NOUN
ma-198	119	20	}	}	PUNCT
ma-198	119	21	converges	converge	VERB
ma-198	119	22	strongly	strongly	ADV
ma-198	119	23	to	to	ADP
ma-198	119	24	a	a	DET
ma-198	119	25	unique	unique	ADJ
ma-198	119	26	fixedpoint	fixedpoint	NOUN
ma-198	119	27	that	that	PRON
ma-198	119	28	solved	solve	VERB
ma-198	119	29	the	the	DET
ma-198	119	30	variational	variational	ADJ
ma-198	119	31	inequality.it	inequality.it	NUM
ma-198	119	32	is	be	AUX
ma-198	119	33	our	our	PRON
ma-198	119	34	purpose	purpose	NOUN
ma-198	119	35	in	in	ADP
ma-198	119	36	this	this	DET
ma-198	119	37	paper	paper	NOUN
ma-198	119	38	to	to	PART
ma-198	119	39	construct	construct	VERB
ma-198	119	40	a	a	DET
ma-198	119	41	new	new	ADJ
ma-198	119	42	iteration	iteration	NOUN
ma-198	119	43	process	process	NOUN
ma-198	119	44	,	,	PUNCT
ma-198	119	45	that	that	PRON
ma-198	119	46	modifies	modify	VERB
ma-198	119	47	that	that	PRON
ma-198	119	48	of	of	ADP
ma-198	119	49	sow	sow	NOUN
ma-198	119	50	[	[	X
ma-198	119	51	28]and	28]and	NUM
ma-198	119	52	prove	prove	VERB
ma-198	119	53	that	that	SCONJ
ma-198	119	54	the	the	DET
ma-198	119	55	corresponding	correspond	VERB
ma-198	119	56	sequence	sequence	NOUN
ma-198	119	57	{	{	PUNCT
ma-198	119	58	xn	xn	NOUN
ma-198	119	59	}	}	PUNCT
ma-198	119	60	converges	converge	VERB
ma-198	119	61	strongly	strongly	ADV
ma-198	119	62	to	to	ADP
ma-198	119	63	a	a	DET
ma-198	119	64	common	common	ADJ
ma-198	119	65	point	point	NOUN
ma-198	119	66	of	of	ADP
ma-198	119	67	aninclusion	aninclusion	NOUN
ma-198	119	68	problem	problem	NOUN
ma-198	119	69	and	and	CCONJ
ma-198	119	70	fixed	fix	VERB
ma-198	119	71	point	point	NOUN
ma-198	119	72	of	of	ADP
ma-198	119	73	a	a	DET
ma-198	119	74	family	family	NOUN
ma-198	119	75	of	of	ADP
ma-198	119	76	multivalued	multivalued	ADJ
ma-198	119	77	demicontractive	demicontractive	ADJ
ma-198	119	78	and	and	CCONJ
ma-198	119	79	quasi	quasi	NOUN
ma-198	119	80	-	-	NOUN
ma-198	119	81	nonexpansivemappings	nonexpansivemapping	NOUN
ma-198	119	82	in	in	ADP
ma-198	119	83	hilbert	hilbert	PROPN
ma-198	119	84	spaces	space	NOUN
ma-198	119	85	without	without	ADP
ma-198	119	86	any	any	DET
ma-198	119	87	compactness	compactness	NOUN
ma-198	119	88	.	.	PUNCT
ma-198	120	1	our	our	PRON
ma-198	120	2	theorems	theorem	NOUN
ma-198	120	3	generalize	generalize	VERB
ma-198	120	4	and	and	CCONJ
ma-198	120	5	extend	extend	VERB
ma-198	120	6	that	that	DET
ma-198	120	7	ofsow	ofsow	NOUN
ma-198	120	8	[	[	X
ma-198	120	9	28	28	NUM
ma-198	120	10	]	]	PUNCT
ma-198	120	11	,	,	PUNCT
ma-198	120	12	and	and	CCONJ
ma-198	120	13	many	many	ADJ
ma-198	120	14	other	other	ADJ
ma-198	120	15	results	result	NOUN
ma-198	120	16	in	in	ADP
ma-198	120	17	this	this	DET
ma-198	120	18	directions	direction	NOUN
ma-198	120	19	.	.	PUNCT
ma-198	121	1	2	2	X
ma-198	121	2	.	.	NUM
ma-198	121	3	preliminaries	preliminary	NOUN
ma-198	121	4	the	the	DET
ma-198	121	5	following	follow	VERB
ma-198	121	6	lemmas	lemmas	PROPN
ma-198	121	7	will	will	AUX
ma-198	121	8	play	play	VERB
ma-198	121	9	a	a	DET
ma-198	121	10	crucial	crucial	ADJ
ma-198	121	11	role	role	NOUN
ma-198	121	12	in	in	ADP
ma-198	121	13	the	the	DET
ma-198	121	14	sequel.let	sequel.let	X
ma-198	121	15	k	k	X
ma-198	121	16	be	be	AUX
ma-198	121	17	a	a	DET
ma-198	121	18	nonempty	nonempty	ADJ
ma-198	121	19	,	,	PUNCT
ma-198	121	20	closed	closed	ADJ
ma-198	121	21	convex	convex	NOUN
ma-198	121	22	subset	subset	NOUN
ma-198	121	23	of	of	ADP
ma-198	121	24	h.	h.	PROPN
ma-198	121	25	the	the	DET
ma-198	121	26	nearest	near	ADJ
ma-198	121	27	point	point	NOUN
ma-198	121	28	projection	projection	NOUN
ma-198	121	29	from	from	SCONJ
ma-198	121	30	h	h	NOUN
ma-198	121	31	to	to	PART
ma-198	121	32	kdenoted	kdenote	VERB
ma-198	121	33	by	by	ADP
ma-198	121	34	pk	pk	NOUN
ma-198	121	35	,	,	PUNCT
ma-198	121	36	assigns	assign	NOUN
ma-198	121	37	to	to	ADP
ma-198	121	38	each	each	DET
ma-198	121	39	ψ	ψ	X
ma-198	121	40	∈	∈	NOUN
ma-198	121	41	h	h	NOUN
ma-198	121	42	the	the	DET
ma-198	121	43	unique	unique	ADJ
ma-198	121	44	point	point	NOUN
ma-198	121	45	of	of	ADP
ma-198	121	46	k	k	PROPN
ma-198	121	47	,	,	PUNCT
ma-198	121	48	pkψ	pkψ	NOUN
ma-198	121	49	such	such	ADJ
ma-198	121	50	that	that	SCONJ
ma-198	121	51	‖x	‖x	PROPN
ma-198	121	52	−	−	PROPN
ma-198	121	53	pkx‖	pkx‖	VERB
ma-198	121	54	≤	≤	NUM
ma-198	121	55	‖x	‖x	PUNCT
ma-198	122	1	−	−	PROPN
ma-198	122	2	y‖	y‖	PROPN
ma-198	122	3	,	,	PUNCT
ma-198	122	4	for	for	ADP
ma-198	122	5	all	all	DET
ma-198	122	6	y	y	PROPN
ma-198	122	7	∈	∈	PROPN
ma-198	122	8	k	k	NOUN
ma-198	122	9	,	,	PUNCT
ma-198	122	10	and	and	CCONJ
ma-198	122	11	for	for	ADP
ma-198	122	12	every	every	DET
ma-198	122	13	x	x	SYM
ma-198	122	14	∈	∈	PROPN
ma-198	122	15	h	h	NOUN
ma-198	122	16	,	,	PUNCT
ma-198	122	17	〈	〈	PROPN
ma-198	122	18	x	x	X
ma-198	122	19	−	−	PROPN
ma-198	122	20	pkx	pkx	PROPN
ma-198	122	21	,	,	PUNCT
ma-198	122	22	y	y	PROPN
ma-198	122	23	−	−	PROPN
ma-198	122	24	pkx	pkx	VERB
ma-198	122	25	〉	〉	PROPN
ma-198	122	26	≤	≤	NUM
ma-198	122	27	0	0	NUM
ma-198	122	28	,	,	PUNCT
ma-198	122	29	∀y	∀y	PROPN
ma-198	122	30	∈	∈	PROPN
ma-198	122	31	k	k	X
ma-198	122	32	(	(	PUNCT
ma-198	122	33	2.1	2.1	NUM
ma-198	122	34	)	)	PUNCT
ma-198	122	35	lemma	lemma	PROPN
ma-198	122	36	2.1	2.1	NUM
ma-198	122	37	.	.	PUNCT
ma-198	123	1	[	[	X
ma-198	123	2	27	27	NUM
ma-198	123	3	]	]	PUNCT
ma-198	123	4	.	.	PUNCT
ma-198	124	1	let	let	VERB
ma-198	124	2	π	π	NOUN
ma-198	124	3	:	:	PUNCT
ma-198	124	4	h	h	NOUN
ma-198	124	5	→	→	SYM
ma-198	124	6	2h	2h	NUM
ma-198	124	7	be	be	VERB
ma-198	124	8	a	a	DET
ma-198	124	9	maximal	maximal	ADJ
ma-198	124	10	monotone	monotone	ADJ
ma-198	124	11	mapping	mapping	NOUN
ma-198	124	12	,	,	PUNCT
ma-198	124	13	and	and	CCONJ
ma-198	124	14	λ	λ	INTJ
ma-198	124	15	:	:	PUNCT
ma-198	124	16	h	h	NOUN
ma-198	124	17	→	→	PUNCT
ma-198	124	18	h	h	NOUN
ma-198	124	19	be	be	AUX
ma-198	124	20	lipschitz	lipschitz	ADJ
ma-198	124	21	and	and	CCONJ
ma-198	124	22	continuous	continuous	ADJ
ma-198	124	23	monotone	monotone	ADJ
ma-198	124	24	mapping	mapping	NOUN
ma-198	124	25	.	.	PUNCT
ma-198	125	1	then	then	ADV
ma-198	125	2	(	(	PUNCT
ma-198	125	3	π	π	PROPN
ma-198	125	4	+	+	CCONJ
ma-198	125	5	λ	λ	NOUN
ma-198	125	6	)	)	PUNCT
ma-198	125	7	:	:	PUNCT
ma-198	125	8	h	h	NOUN
ma-198	125	9	→	→	SYM
ma-198	125	10	2h	2h	NUM
ma-198	125	11	is	be	AUX
ma-198	125	12	a	a	DET
ma-198	125	13	maximal	maximal	ADJ
ma-198	125	14	monotone	monotone	ADJ
ma-198	125	15	mapping	mapping	NOUN
ma-198	125	16	.	.	PUNCT
ma-198	126	1	lemma	lemma	PROPN
ma-198	126	2	2.2	2.2	NUM
ma-198	126	3	.	.	PUNCT
ma-198	127	1	[	[	X
ma-198	127	2	28	28	NUM
ma-198	127	3	]	]	PUNCT
ma-198	127	4	.	.	PUNCT
ma-198	128	1	let	let	VERB
ma-198	128	2	h	h	PRON
ma-198	128	3	be	be	AUX
ma-198	128	4	real	real	ADJ
ma-198	128	5	hilbert	hilbert	NOUN
ma-198	128	6	space	space	NOUN
ma-198	128	7	and	and	CCONJ
ma-198	128	8	λ	λ	PROPN
ma-198	128	9	:	:	PUNCT
ma-198	128	10	h	h	PROPN
ma-198	128	11	→	→	PUNCT
ma-198	128	12	h	h	NOUN
ma-198	128	13	be	be	VERB
ma-198	128	14	an	an	DET
ma-198	128	15	α−inverse	α−inverse	NOUN
ma-198	128	16	strongly	strongly	ADV
ma-198	128	17	monotone	monotone	ADJ
ma-198	128	18	mapping	mapping	NOUN
ma-198	128	19	.	.	PUNCT
ma-198	129	1	then	then	ADV
ma-198	129	2	,	,	PUNCT
ma-198	129	3	(	(	PUNCT
ma-198	129	4	i	i	PRON
ma-198	129	5	−	−	PROPN
ma-198	129	6	θλ	θλ	VERB
ma-198	129	7	)	)	PUNCT
ma-198	129	8	is	be	AUX
ma-198	129	9	nonexpansive	nonexpansive	ADJ
ma-198	129	10	mapping	mapping	NOUN
ma-198	129	11	for	for	ADP
ma-198	129	12	all	all	DET
ma-198	129	13	ψ	ψ	NOUN
ma-198	129	14	,	,	PUNCT
ma-198	129	15	π	π	PROPN
ma-198	129	16	∈	∈	PROPN
ma-198	129	17	h	h	NOUN
ma-198	129	18	and	and	CCONJ
ma-198	129	19	θ	θ	PROPN
ma-198	129	20	∈	∈	PROPN
ma-198	130	1	[	[	X
ma-198	130	2	0	0	NUM
ma-198	130	3	,	,	PUNCT
ma-198	130	4	2α	2α	NOUN
ma-198	130	5	]	]	PUNCT
ma-198	130	6	such	such	ADJ
ma-198	130	7	that	that	DET
ma-198	130	8	‖(i	‖(i	NOUN
ma-198	130	9	−	−	NOUN
ma-198	130	10	θa)x	θa)x	NOUN
ma-198	130	11	−	−	PROPN
ma-198	130	12	(	(	PUNCT
ma-198	130	13	i	i	PRON
ma-198	130	14	−	−	PROPN
ma-198	130	15	θay‖2	θay‖2	X
ma-198	130	16	≤	≤	ADJ
ma-198	130	17	‖x	‖x	X
ma-198	131	1	−	−	PROPN
ma-198	132	1	y‖2	y‖2	X
ma-198	132	2	+	+	CCONJ
ma-198	132	3	θ(θ	θ(θ	PROPN
ma-198	132	4	−	−	PROPN
ma-198	132	5	2α)‖ax	2α)‖ax	NUM
ma-198	132	6	−	−	NOUN
ma-198	132	7	ay‖2	ay‖2	NOUN
ma-198	132	8	(	(	PUNCT
ma-198	132	9	2.2	2.2	NUM
ma-198	132	10	)	)	PUNCT
ma-198	132	11	lemma	lemma	PROPN
ma-198	132	12	2.3	2.3	NUM
ma-198	132	13	.	.	PUNCT
ma-198	133	1	[	[	X
ma-198	133	2	24	24	NUM
ma-198	133	3	]	]	PUNCT
ma-198	133	4	.	.	PUNCT
ma-198	134	1	assume	assume	VERB
ma-198	134	2	that	that	SCONJ
ma-198	134	3	{	{	PUNCT
ma-198	134	4	an	an	PRON
ma-198	134	5	}	}	PUNCT
ma-198	134	6	is	be	AUX
ma-198	134	7	a	a	DET
ma-198	134	8	sequence	sequence	NOUN
ma-198	134	9	of	of	ADP
ma-198	134	10	nonnegative	nonnegative	ADJ
ma-198	134	11	real	real	ADJ
ma-198	134	12	numbers	number	NOUN
ma-198	134	13	such	such	ADJ
ma-198	134	14	that	that	DET
ma-198	134	15	an+1	an+1	NOUN
ma-198	134	16	=	=	SYM
ma-198	134	17	(	(	PUNCT
ma-198	134	18	1	1	NUM
ma-198	134	19	−	−	NOUN
ma-198	134	20	bn)an	bn)an	X
ma-198	135	1	+	+	CCONJ
ma-198	135	2	σn	σn	NOUN
ma-198	135	3	for	for	ADP
ma-198	135	4	all	all	DET
ma-198	135	5	n	n	PRON
ma-198	135	6	≥	≥	NOUN
ma-198	135	7	0	0	NUM
ma-198	135	8	,	,	PUNCT
ma-198	135	9	where	where	SCONJ
ma-198	135	10	{	{	PUNCT
ma-198	135	11	αn	αn	NOUN
ma-198	135	12	}	}	PUNCT
ma-198	135	13	is	be	AUX
ma-198	135	14	a	a	DET
ma-198	135	15	sequence	sequence	NOUN
ma-198	135	16	in	in	ADP
ma-198	135	17	(	(	PUNCT
ma-198	135	18	0	0	NUM
ma-198	135	19	,	,	PUNCT
ma-198	135	20	1	1	NUM
ma-198	135	21	)	)	PUNCT
ma-198	135	22	and	and	CCONJ
ma-198	135	23	{	{	PUNCT
ma-198	135	24	σn	σn	NOUN
ma-198	135	25	}	}	PUNCT
ma-198	135	26	is	be	AUX
ma-198	135	27	a	a	DET
ma-198	135	28	sequence	sequence	NOUN
ma-198	135	29	in	in	ADP
ma-198	135	30	r	r	NOUN
ma-198	135	31	such	such	ADJ
ma-198	135	32	that	that	SCONJ
ma-198	135	33	i	i	PRON
ma-198	135	34	)	)	PUNCT
ma-198	135	35	∞∑	∞∑	PRON
ma-198	135	36	n=0	n=0	NUM
ma-198	135	37	bn	bn	NOUN
ma-198	135	38	=	=	NUM
ma-198	135	39	∞	∞	PROPN
ma-198	135	40	,	,	PUNCT
ma-198	135	41	i	i	PRON
ma-198	135	42	i	i	PROPN
ma-198	135	43	)	)	PUNCT
ma-198	136	1	lim	lim	PROPN
ma-198	136	2	n→∞	n→∞	NUM
ma-198	136	3	sup	sup	NOUN
ma-198	136	4	σn	σn	NOUN
ma-198	136	5	bn	bn	NOUN
ma-198	136	6	≤	≤	NUM
ma-198	136	7	0	0	NUM
ma-198	136	8	.	.	PUNCT
ma-198	137	1	then	then	ADV
ma-198	137	2	lim	lim	PROPN
ma-198	137	3	n→∞	n→∞	PRON
ma-198	137	4	an	an	DET
ma-198	137	5	=	=	SYM
ma-198	137	6	0	0	NUM
ma-198	137	7	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NOUN
ma-198	137	8	eur	eur	NOUN
ma-198	137	9	.	.	PUNCT
ma-198	138	1	j.	j.	PROPN
ma-198	138	2	math	math	PROPN
ma-198	138	3	.	.	PUNCT
ma-198	139	1	anal	anal	PROPN
ma-198	139	2	.	.	PUNCT
ma-198	140	1	10.28924	10.28924	NUM
ma-198	140	2	/	/	SYM
ma-198	140	3	ada	ada	PROPN
ma-198	140	4	/	/	SYM
ma-198	140	5	ma.4.2	ma.4.2	PROPN
ma-198	140	6	7	7	NUM
ma-198	140	7	lemma	lemma	PROPN
ma-198	140	8	2.4	2.4	NUM
ma-198	140	9	.	.	PUNCT
ma-198	141	1	(	(	PUNCT
ma-198	141	2	wang	wang	PROPN
ma-198	142	1	[	[	X
ma-198	142	2	1	1	NUM
ma-198	142	3	]	]	PUNCT
ma-198	142	4	)	)	PUNCT
ma-198	142	5	.	.	PUNCT
ma-198	143	1	let	let	VERB
ma-198	143	2	h	h	PRON
ma-198	143	3	be	be	AUX
ma-198	143	4	a	a	DET
ma-198	143	5	real	real	ADJ
ma-198	143	6	hilbert	hilbert	NOUN
ma-198	143	7	space	space	NOUN
ma-198	143	8	.	.	PUNCT
ma-198	144	1	let	let	VERB
ma-198	144	2	k	k	PRON
ma-198	144	3	be	be	AUX
ma-198	144	4	a	a	DET
ma-198	144	5	nonempty	nonempty	ADV
ma-198	144	6	closed	close	VERB
ma-198	144	7	convex	convex	NOUN
ma-198	144	8	subset	subset	NOUN
ma-198	144	9	of	of	ADP
ma-198	144	10	h.	h.	PROPN
ma-198	144	11	a	a	DET
ma-198	144	12	:	:	PUNCT
ma-198	144	13	h	h	NOUN
ma-198	144	14	→	→	SYM
ma-198	144	15	h	h	PROPN
ma-198	144	16	be	be	AUX
ma-198	144	17	k−	k−	NOUN
ma-198	144	18	strongly	strongly	ADV
ma-198	144	19	monotone	monotone	ADJ
ma-198	144	20	and	and	CCONJ
ma-198	144	21	l−	l−	NOUN
ma-198	144	22	lipschitzian	lipschitzian	ADJ
ma-198	144	23	operator	operator	NOUN
ma-198	144	24	with	with	ADP
ma-198	144	25	k	k	PROPN
ma-198	144	26	>	>	X
ma-198	144	27	0	0	PUNCT
ma-198	145	1	and	and	CCONJ
ma-198	145	2	l	l	NOUN
ma-198	145	3	>	>	X
ma-198	145	4	0	0	X
ma-198	145	5	.	.	PUNCT
ma-198	145	6	assume	assume	VERB
ma-198	145	7	that	that	SCONJ
ma-198	145	8	0	0	NUM
ma-198	145	9	<	<	X
ma-198	145	10	η	η	X
ma-198	145	11	<	<	X
ma-198	145	12	2k	2k	PROPN
ma-198	145	13	l2	l2	NOUN
ma-198	145	14	and	and	CCONJ
ma-198	145	15	τ	τ	PROPN
ma-198	145	16	=	=	SYM
ma-198	145	17	η	η	PROPN
ma-198	145	18	(	(	PUNCT
ma-198	145	19	k	k	PROPN
ma-198	145	20	−	−	PROPN
ma-198	145	21	l2η	l2η	PROPN
ma-198	145	22	2	2	NUM
ma-198	145	23	)	)	PUNCT
ma-198	145	24	.	.	PUNCT
ma-198	146	1	then	then	ADV
ma-198	146	2	for	for	ADP
ma-198	146	3	each	each	DET
ma-198	146	4	t	t	NOUN
ma-198	146	5	∈	∈	PROPN
ma-198	146	6	(	(	PUNCT
ma-198	146	7	0,min	0,min	NUM
ma-198	146	8	(	(	PUNCT
ma-198	146	9	1	1	NUM
ma-198	146	10	,	,	PUNCT
ma-198	146	11	1	1	NUM
ma-198	146	12	τ	τ	NOUN
ma-198	146	13	)	)	PUNCT
ma-198	146	14	)	)	PUNCT
ma-198	146	15	,	,	PUNCT
ma-198	146	16	we	we	PRON
ma-198	146	17	have	have	AUX
ma-198	146	18	‖(i	‖(i	NOUN
ma-198	146	19	−	−	PROPN
ma-198	147	1	tηa)x	tηa)x	ADJ
ma-198	147	2	−	−	PROPN
ma-198	148	1	(	(	PUNCT
ma-198	148	2	i	i	PRON
ma-198	148	3	−	−	VERB
ma-198	148	4	tηa)y‖	tηa)y‖	NOUN
ma-198	148	5	≤	≤	NUM
ma-198	149	1	(	(	PUNCT
ma-198	149	2	i	i	PRON
ma-198	149	3	−	−	PROPN
ma-198	150	1	tτ)‖x	tτ)‖x	PROPN
ma-198	151	1	−	−	PROPN
ma-198	151	2	y‖	y‖	PROPN
ma-198	151	3	,	,	PUNCT
ma-198	151	4	∀x	∀x	NUM
ma-198	151	5	,	,	PUNCT
ma-198	151	6	y	y	PROPN
ma-198	151	7	∈	∈	PROPN
ma-198	151	8	h	h	NOUN
ma-198	151	9	(	(	PUNCT
ma-198	151	10	2.3	2.3	NUM
ma-198	151	11	)	)	PUNCT
ma-198	151	12	lemma	lemma	PROPN
ma-198	151	13	2.5	2.5	NUM
ma-198	151	14	.	.	PUNCT
ma-198	152	1	[	[	X
ma-198	152	2	29	29	NUM
ma-198	152	3	]	]	PUNCT
ma-198	152	4	.	.	PUNCT
ma-198	153	1	let	let	VERB
ma-198	153	2	h	h	PRON
ma-198	153	3	be	be	AUX
ma-198	153	4	a	a	DET
ma-198	153	5	real	real	ADJ
ma-198	153	6	hilbert	hilbert	NOUN
ma-198	153	7	space	space	NOUN
ma-198	153	8	.	.	PUNCT
ma-198	154	1	then	then	ADV
ma-198	154	2	for	for	ADP
ma-198	154	3	every	every	DET
ma-198	154	4	x	x	NOUN
ma-198	154	5	,	,	PUNCT
ma-198	154	6	y	y	PROPN
ma-198	154	7	∈	∈	PROPN
ma-198	154	8	h	h	NOUN
ma-198	154	9	,	,	PUNCT
ma-198	154	10	and	and	CCONJ
ma-198	154	11	every	every	DET
ma-198	154	12	λ	λ	PROPN
ma-198	154	13	∈	∈	PROPN
ma-198	154	14	(	(	PUNCT
ma-198	154	15	0	0	NUM
ma-198	154	16	,	,	PUNCT
ma-198	154	17	1	1	NUM
ma-198	154	18	)	)	PUNCT
ma-198	154	19	,	,	PUNCT
ma-198	154	20	the	the	DET
ma-198	154	21	following	follow	VERB
ma-198	154	22	holds	hold	VERB
ma-198	154	23	:	:	PUNCT
ma-198	155	1	i	i	PRON
ma-198	155	2	):	):	PUNCT
ma-198	155	3	‖x	‖x	NOUN
ma-198	155	4	−	−	PROPN
ma-198	155	5	y‖2	y‖2	PROPN
ma-198	155	6	≤	≤	PROPN
ma-198	155	7	‖x‖2	‖x‖2	VERB
ma-198	156	1	+	+	X
ma-198	156	2	2〈y	2〈y	INTJ
ma-198	156	3	,	,	PUNCT
ma-198	156	4	x	x	PROPN
ma-198	157	1	+	+	NUM
ma-198	157	2	y	y	PROPN
ma-198	157	3	〉	〉	PROPN
ma-198	157	4	ii	ii	PROPN
ma-198	157	5	:	:	PUNCT
ma-198	157	6	‖λx	‖λx	NUM
ma-198	157	7	+	+	CCONJ
ma-198	157	8	(	(	PUNCT
ma-198	157	9	1−	1−	NUM
ma-198	157	10	λ)y‖2	λ)y‖2	PROPN
ma-198	157	11	≤	≤	ADV
ma-198	157	12	λ‖x‖2	λ‖x‖2	PROPN
ma-198	157	13	+	+	CCONJ
ma-198	157	14	(	(	PUNCT
ma-198	157	15	1−	1−	NUM
ma-198	157	16	λ)‖y‖2	λ)‖y‖2	NOUN
ma-198	158	1	−	−	PROPN
ma-198	158	2	(	(	PUNCT
ma-198	158	3	1−	1−	NUM
ma-198	158	4	λ)λ‖x	λ)λ‖x	NOUN
ma-198	158	5	−	−	PROPN
ma-198	158	6	y‖2	y‖2	NOUN
ma-198	158	7	.	.	PROPN
ma-198	159	1	3	3	NUM
ma-198	159	2	.	.	X
ma-198	159	3	main	main	ADJ
ma-198	159	4	results	result	NOUN
ma-198	159	5	in	in	ADP
ma-198	159	6	this	this	DET
ma-198	159	7	section	section	NOUN
ma-198	159	8	,	,	PUNCT
ma-198	159	9	we	we	PRON
ma-198	159	10	study	study	VERB
ma-198	159	11	the	the	DET
ma-198	159	12	convergence	convergence	NOUN
ma-198	159	13	properties	property	NOUN
ma-198	159	14	of	of	ADP
ma-198	159	15	the	the	DET
ma-198	159	16	iterative	iterative	NOUN
ma-198	159	17	algorithm	algorithm	NOUN
ma-198	159	18	which	which	PRON
ma-198	159	19	is	be	AUX
ma-198	159	20	based	base	VERB
ma-198	159	21	onviscosity	onviscosity	NOUN
ma-198	159	22	algorithm	algorithm	NOUN
ma-198	159	23	and	and	CCONJ
ma-198	159	24	forward	forward	ADV
ma-198	159	25	backward	backward	ADJ
ma-198	159	26	splitting	splitting	NOUN
ma-198	159	27	method	method	NOUN
ma-198	159	28	.	.	PUNCT
ma-198	160	1	we	we	PRON
ma-198	160	2	now	now	ADV
ma-198	160	3	prove	prove	VERB
ma-198	160	4	the	the	DET
ma-198	160	5	following	follow	VERB
ma-198	160	6	theorem	theorem	VERB
ma-198	160	7	.	.	PUNCT
ma-198	160	8	theorem	theorem	PROPN
ma-198	160	9	3.1	3.1	NUM
ma-198	160	10	.	.	PUNCT
ma-198	161	1	let	let	VERB
ma-198	161	2	h	h	PRON
ma-198	161	3	be	be	AUX
ma-198	161	4	a	a	DET
ma-198	161	5	real	real	ADJ
ma-198	161	6	hilbert	hilbert	NOUN
ma-198	161	7	space	space	NOUN
ma-198	161	8	and	and	CCONJ
ma-198	161	9	k	k	PROPN
ma-198	161	10	be	be	AUX
ma-198	161	11	a	a	DET
ma-198	161	12	nonempty	nonempty	ADJ
ma-198	161	13	,	,	PUNCT
ma-198	161	14	closed	closed	ADJ
ma-198	161	15	convex	convex	NOUN
ma-198	161	16	subset	subset	NOUN
ma-198	161	17	of	of	ADP
ma-198	161	18	h.	h.	PROPN
ma-198	161	19	let	let	VERB
ma-198	161	20	a	a	PRON
ma-198	161	21	:	:	PUNCT
ma-198	161	22	k	k	X
ma-198	161	23	→	→	PUNCT
ma-198	161	24	h	h	NOUN
ma-198	161	25	be	be	AUX
ma-198	161	26	an	an	DET
ma-198	161	27	α−inverse	α−inverse	NOUN
ma-198	161	28	strongly	strongly	ADV
ma-198	161	29	monotone	monotone	ADJ
ma-198	161	30	operator	operator	NOUN
ma-198	161	31	and	and	CCONJ
ma-198	161	32	let	let	VERB
ma-198	161	33	b	b	NOUN
ma-198	161	34	:	:	PUNCT
ma-198	161	35	h	h	NOUN
ma-198	161	36	→	→	PUNCT
ma-198	161	37	h	h	NOUN
ma-198	161	38	be	be	AUX
ma-198	161	39	an	an	DET
ma-198	161	40	k−strongly	k−strongly	ADV
ma-198	161	41	monotone	monotone	ADJ
ma-198	161	42	and	and	CCONJ
ma-198	161	43	l−lipschitzian	l−lipschitzian	ADJ
ma-198	161	44	operator	operator	NOUN
ma-198	161	45	.	.	PUNCT
ma-198	162	1	let	let	VERB
ma-198	162	2	f	f	NOUN
ma-198	162	3	:	:	PUNCT
ma-198	162	4	k→	k→	PUNCT
ma-198	162	5	h	h	NOUN
ma-198	162	6	be	be	AUX
ma-198	162	7	an	an	DET
ma-198	162	8	b−lipschitzian	b−lipschitzian	ADJ
ma-198	162	9	mapping	mapping	NOUN
ma-198	162	10	and	and	CCONJ
ma-198	162	11	m	m	PRON
ma-198	162	12	:	:	PUNCT
ma-198	162	13	h	h	NOUN
ma-198	162	14	→	→	SYM
ma-198	162	15	2h	2h	NUM
ma-198	162	16	be	be	VERB
ma-198	162	17	a	a	DET
ma-198	162	18	maximal	maximal	ADJ
ma-198	162	19	monotone	monotone	ADJ
ma-198	162	20	mapping	mapping	NOUN
ma-198	162	21	such	such	ADJ
ma-198	162	22	that	that	SCONJ
ma-198	162	23	the	the	DET
ma-198	162	24	domain	domain	NOUN
ma-198	162	25	of	of	ADP
ma-198	162	26	m	m	PROPN
ma-198	162	27	is	be	AUX
ma-198	162	28	included	include	VERB
ma-198	162	29	in	in	ADP
ma-198	162	30	k.	k.	PROPN
ma-198	162	31	let	let	VERB
ma-198	162	32	t1	t1	NOUN
ma-198	162	33	,	,	PUNCT
ma-198	162	34	t2	t2	NOUN
ma-198	162	35	:	:	PUNCT
ma-198	162	36	k	k	X
ma-198	162	37	→	→	SYM
ma-198	162	38	cb(k	cb(k	AUX
ma-198	162	39	)	)	PUNCT
ma-198	162	40	be	be	AUX
ma-198	162	41	a	a	DET
ma-198	162	42	multivalued	multivalue	VERB
ma-198	162	43	β−	β−	PRON
ma-198	162	44	demicontractive	demicontractive	ADJ
ma-198	162	45	mapping	mapping	NOUN
ma-198	162	46	and	and	CCONJ
ma-198	162	47	t3	t3	NOUN
ma-198	162	48	:	:	PUNCT
ma-198	163	1	k	k	X
ma-198	163	2	→	→	SYM
ma-198	163	3	cb(k	cb(k	AUX
ma-198	163	4	)	)	PUNCT
ma-198	163	5	be	be	AUX
ma-198	163	6	a	a	DET
ma-198	163	7	multivalued	multivalued	ADJ
ma-198	163	8	quasi	quasi	ADJ
ma-198	163	9	-	-	ADJ
ma-198	163	10	nonexpansive	nonexpansive	ADJ
ma-198	163	11	mapping	mapping	NOUN
ma-198	163	12	.	.	PUNCT
ma-198	164	1	assume	assume	VERB
ma-198	164	2	that	that	SCONJ
ma-198	164	3	0	0	NUM
ma-198	164	4	<	<	X
ma-198	164	5	η	η	X
ma-198	164	6	<	<	X
ma-198	164	7	2k	2k	PROPN
ma-198	164	8	l2	l2	NOUN
ma-198	164	9	,	,	PUNCT
ma-198	164	10	0	0	PUNCT
ma-198	164	11	<	<	X
ma-198	164	12	γb	γb	X
ma-198	164	13	<	<	X
ma-198	164	14	τ	τ	PROPN
ma-198	164	15	,	,	PUNCT
ma-198	164	16	where	where	SCONJ
ma-198	164	17	τ	τ	PROPN
ma-198	164	18	=	=	SYM
ma-198	164	19	η	η	PROPN
ma-198	164	20	(	(	PUNCT
ma-198	164	21	k	k	PROPN
ma-198	164	22	−	−	PROPN
ma-198	164	23	l2η	l2η	PROPN
ma-198	164	24	2	2	NUM
ma-198	164	25	)	)	PUNCT
ma-198	164	26	,	,	PUNCT
ma-198	164	27	and	and	CCONJ
ma-198	164	28	i	i	PRON
ma-198	164	29	−	−	PROPN
ma-198	165	1	t1	t1	INTJ
ma-198	165	2	,	,	PUNCT
ma-198	165	3	i	i	PRON
ma-198	165	4	−	−	PROPN
ma-198	165	5	t2	t2	NOUN
ma-198	165	6	and	and	CCONJ
ma-198	165	7	i	i	PRON
ma-198	166	1	−	−	PROPN
ma-198	166	2	t3	t3	PROPN
ma-198	166	3	are	be	AUX
ma-198	166	4	demiclosed	demiclose	VERB
ma-198	166	5	at	at	ADP
ma-198	166	6	origin	origin	NOUN
ma-198	166	7	,	,	PUNCT
ma-198	166	8	such	such	ADJ
ma-198	166	9	that	that	SCONJ
ma-198	166	10	ω	ω	NOUN
ma-198	166	11	:	:	PUNCT
ma-198	166	12	=	=	SYM
ma-198	166	13	f	f	X
ma-198	166	14	ix(t1	ix(t1	X
ma-198	166	15	)	)	PUNCT
ma-198	166	16	∩	∩	PROPN
ma-198	166	17	f	f	PROPN
ma-198	166	18	ix(t2	ix(t2	NOUN
ma-198	166	19	)	)	PUNCT
ma-198	166	20	∩	∩	PROPN
ma-198	166	21	f	f	PROPN
ma-198	166	22	ix(t3	ix(t3	PROPN
ma-198	166	23	)	)	PUNCT
ma-198	166	24	∩	∩	PROPN
ma-198	166	25	s(m	s(m	PROPN
ma-198	166	26	,	,	PUNCT
ma-198	166	27	a	a	PRON
ma-198	166	28	)	)	PUNCT
ma-198	166	29	6=	6=	ADP
ma-198	166	30	∅	∅	NOUN
ma-198	166	31	and	and	CCONJ
ma-198	166	32	t1q	t1q	NUM
ma-198	166	33	=	=	SYM
ma-198	166	34	t2q	t2q	PROPN
ma-198	166	35	=	=	SYM
ma-198	166	36	t3q	t3q	PROPN
ma-198	167	1	=	=	SYM
ma-198	168	1	{	{	PUNCT
ma-198	168	2	q},∀q	q},∀q	PROPN
ma-198	168	3	∈	∈	PROPN
ma-198	168	4	ω	ω	PROPN
ma-198	168	5	.	.	PUNCT
ma-198	169	1	for	for	ADP
ma-198	169	2	given	give	VERB
ma-198	169	3	x0	x0	PROPN
ma-198	169	4	∈	∈	PROPN
ma-198	169	5	k	k	NOUN
ma-198	169	6	,	,	PUNCT
ma-198	169	7	let	let	VERB
ma-198	169	8	{	{	PUNCT
ma-198	169	9	xn	xn	AUX
ma-198	169	10	}	}	PUNCT
ma-198	169	11	be	be	AUX
ma-198	169	12	generated	generate	VERB
ma-198	169	13	by	by	ADP
ma-198	169	14	the	the	DET
ma-198	169	15	algorithm:	algorithm:	PROPN
ma-198	169	16	δn	δn	NOUN
ma-198	169	17	=	=	PUNCT
ma-198	169	18	jmλn(i	jmλn(i	PROPN
ma-198	169	19	−	−	PROPN
ma-198	169	20	λna)xn	λna)xn	NOUN
ma-198	169	21	;	;	PUNCT
ma-198	169	22	yn	yn	PROPN
ma-198	169	23	=	=	PUNCT
ma-198	169	24	θnδn	θnδn	PROPN
ma-198	169	25	+	+	CCONJ
ma-198	169	26	(	(	PUNCT
ma-198	169	27	1−	1−	NUM
ma-198	169	28	θn)vn	θn)vn	ADP
ma-198	169	29	,	,	PUNCT
ma-198	169	30	vn	vn	PROPN
ma-198	169	31	∈	∈	PROPN
ma-198	169	32	t1δn	t1δn	PROPN
ma-198	169	33	;	;	PUNCT
ma-198	169	34	zn	zn	PROPN
ma-198	169	35	=	=	SYM
ma-198	169	36	βnyn	βnyn	PROPN
ma-198	169	37	+	+	CCONJ
ma-198	169	38	(	(	PUNCT
ma-198	169	39	1−	1−	NUM
ma-198	169	40	βn)un	βn)un	NUM
ma-198	169	41	,	,	PUNCT
ma-198	169	42	un	un	PROPN
ma-198	169	43	∈	∈	PROPN
ma-198	169	44	t2yn	t2yn	NUM
ma-198	169	45	;	;	PUNCT
ma-198	169	46	tn	tn	PROPN
ma-198	169	47	=	=	SYM
ma-198	169	48	γnzn	γnzn	NOUN
ma-198	169	49	+	+	CCONJ
ma-198	169	50	(	(	PUNCT
ma-198	169	51	1−	1−	NUM
ma-198	169	52	γn)wn	γn)wn	NOUN
ma-198	169	53	,	,	PUNCT
ma-198	169	54	wn	wn	PROPN
ma-198	169	55	∈	∈	PROPN
ma-198	169	56	t3zn	t3zn	PUNCT
ma-198	169	57	;	;	PUNCT
ma-198	169	58	xn+1	xn+1	X
ma-198	169	59	=	=	SYM
ma-198	169	60	pk(αnγf	pk(αnγf	X
ma-198	169	61	(	(	PUNCT
ma-198	169	62	xn	xn	X
ma-198	169	63	)	)	PUNCT
ma-198	169	64	+	+	CCONJ
ma-198	169	65	(	(	PUNCT
ma-198	169	66	i	i	PRON
ma-198	169	67	−	−	PROPN
ma-198	169	68	ηαnb)tn	ηαnb)tn	NOUN
ma-198	169	69	)	)	PUNCT
ma-198	169	70	(	(	PUNCT
ma-198	169	71	3.1	3.1	NUM
ma-198	169	72	)	)	PUNCT
ma-198	169	73	where	where	SCONJ
ma-198	169	74	{	{	PUNCT
ma-198	169	75	βn	βn	NOUN
ma-198	169	76	}	}	PUNCT
ma-198	169	77	,	,	PUNCT
ma-198	169	78	{	{	PUNCT
ma-198	169	79	γn	γn	NOUN
ma-198	169	80	}	}	PUNCT
ma-198	169	81	,	,	PUNCT
ma-198	169	82	{	{	PUNCT
ma-198	169	83	θn	θn	NOUN
ma-198	169	84	}	}	PUNCT
ma-198	169	85	,	,	PUNCT
ma-198	169	86	{	{	PUNCT
ma-198	169	87	µn	µn	NOUN
ma-198	169	88	}	}	PUNCT
ma-198	169	89	,	,	PUNCT
ma-198	169	90	{	{	PUNCT
ma-198	169	91	λn	λn	NOUN
ma-198	169	92	}	}	PUNCT
ma-198	169	93	and	and	CCONJ
ma-198	169	94	{	{	PUNCT
ma-198	169	95	αn	αn	NOUN
ma-198	169	96	}	}	PUNCT
ma-198	169	97	are	be	AUX
ma-198	169	98	real	real	ADJ
ma-198	169	99	sequence	sequence	NOUN
ma-198	169	100	in	in	ADP
ma-198	169	101	(	(	PUNCT
ma-198	169	102	0	0	NUM
ma-198	169	103	,	,	PUNCT
ma-198	169	104	1	1	X
ma-198	169	105	)	)	PUNCT
ma-198	169	106	satisfying	satisfy	VERB
ma-198	169	107	the	the	DET
ma-198	169	108	following	follow	VERB
ma-198	169	109	conditions	condition	NOUN
ma-198	169	110	i	i	PRON
ma-198	169	111	):	):	PUNCT
ma-198	169	112	lim	lim	PROPN
ma-198	169	113	n→∞	n→∞	NUM
ma-198	169	114	αn	αn	NOUN
ma-198	170	1	=	=	NOUN
ma-198	170	2	0	0	NUM
ma-198	171	1	∞∑	∞∑	NUM
ma-198	171	2	n=0	n=0	NUM
ma-198	171	3	αn	αn	NOUN
ma-198	171	4	<	<	X
ma-198	171	5	∞	∞	PROPN
ma-198	171	6	,	,	PUNCT
ma-198	171	7	λn	λn	PROPN
ma-198	171	8	∈	∈	PROPN
ma-198	172	1	[	[	X
ma-198	172	2	a	a	X
ma-198	172	3	,	,	PUNCT
ma-198	172	4	b	b	NOUN
ma-198	172	5	]	]	X
ma-198	172	6	⊂	⊂	X
ma-198	172	7	(	(	PUNCT
ma-198	172	8	0,min{1	0,min{1	NUM
ma-198	172	9	,	,	PUNCT
ma-198	172	10	2α	2α	NOUN
ma-198	172	11	}	}	PUNCT
ma-198	172	12	)	)	PUNCT
ma-198	172	13	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	172	14	eur	eur	NOUN
ma-198	172	15	.	.	PUNCT
ma-198	173	1	j.	j.	PROPN
ma-198	173	2	math	math	PROPN
ma-198	173	3	.	.	PUNCT
ma-198	174	1	anal	anal	PROPN
ma-198	174	2	.	.	PUNCT
ma-198	175	1	10.28924	10.28924	NUM
ma-198	175	2	/	/	SYM
ma-198	175	3	ada	ada	PROPN
ma-198	175	4	/	/	SYM
ma-198	175	5	ma.4.2	ma.4.2	PROPN
ma-198	175	6	8	8	NUM
ma-198	175	7	ii	ii	NOUN
ma-198	175	8	):	):	PUNCT
ma-198	175	9	lim	lim	PROPN
ma-198	175	10	n→∞	n→∞	PRON
ma-198	175	11	inf(1−	inf(1−	VERB
ma-198	175	12	βn)(βn	βn)(βn	PUNCT
ma-198	175	13	−	−	PROPN
ma-198	175	14	β	β	X
ma-198	175	15	)	)	PUNCT
ma-198	175	16	>	>	X
ma-198	175	17	0	0	PUNCT
ma-198	175	18	and	and	CCONJ
ma-198	175	19	lim	lim	PROPN
ma-198	175	20	n→∞	n→∞	PRON
ma-198	175	21	inf(1−	inf(1−	VERB
ma-198	175	22	θn)(θn	θn)(θn	PUNCT
ma-198	175	23	−	−	NOUN
ma-198	175	24	β	β	NOUN
ma-198	175	25	)	)	PUNCT
ma-198	175	26	>	>	X
ma-198	175	27	0	0	NUM
ma-198	175	28	,	,	PUNCT
ma-198	175	29	(	(	PUNCT
ma-198	175	30	βn	βn	NOUN
ma-198	175	31	,	,	PUNCT
ma-198	175	32	θn	θn	ADJ
ma-198	175	33	)	)	PUNCT
ma-198	175	34	∈	∈	PROPN
ma-198	175	35	(	(	PUNCT
ma-198	175	36	β	β	X
ma-198	175	37	,	,	PUNCT
ma-198	175	38	1	1	NUM
ma-198	175	39	)	)	PUNCT
ma-198	175	40	iii	iii	PROPN
ma-198	175	41	):	):	PUNCT
ma-198	175	42	limn→∞	limn→∞	PROPN
ma-198	175	43	inf(1−	inf(1−	VERB
ma-198	175	44	γn)γn	γn)γn	PROPN
ma-198	175	45	)	)	PUNCT
ma-198	175	46	>	>	X
ma-198	175	47	0	0	PUNCT
ma-198	176	1	then	then	ADV
ma-198	176	2	,	,	PUNCT
ma-198	176	3	the	the	DET
ma-198	176	4	sequences	sequence	NOUN
ma-198	176	5	defined	define	VERB
ma-198	176	6	in	in	ADP
ma-198	176	7	(	(	PUNCT
ma-198	176	8	3.1	3.1	NUM
ma-198	176	9	)	)	PUNCT
ma-198	176	10	,	,	PUNCT
ma-198	176	11	that	that	ADV
ma-198	176	12	is	be	AUX
ma-198	176	13	{	{	PUNCT
ma-198	176	14	xn	xn	PUNCT
ma-198	176	15	}	}	PUNCT
ma-198	176	16	and	and	CCONJ
ma-198	176	17	{	{	PUNCT
ma-198	176	18	δn	δn	NOUN
ma-198	176	19	}	}	PUNCT
ma-198	176	20	converge	converge	VERB
ma-198	176	21	strongly	strongly	ADV
ma-198	176	22	to	to	ADP
ma-198	176	23	unique	unique	ADJ
ma-198	176	24	solution	solution	NOUN
ma-198	176	25	x∗	x∗	PROPN
ma-198	176	26	∈	∈	PROPN
ma-198	176	27	ω	ω	PROPN
ma-198	176	28	,	,	PUNCT
ma-198	176	29	which	which	PRON
ma-198	176	30	also	also	ADV
ma-198	176	31	solve	solve	VERB
ma-198	176	32	the	the	DET
ma-198	176	33	following	follow	VERB
ma-198	176	34	variational	variational	ADJ
ma-198	176	35	inequality	inequality	NOUN
ma-198	176	36	:	:	PUNCT
ma-198	176	37	〈	〈	PROPN
ma-198	176	38	ηbx∗	ηbx∗	NOUN
ma-198	176	39	−	−	PROPN
ma-198	176	40	γf	γf	PROPN
ma-198	176	41	(	(	PUNCT
ma-198	176	42	x∗	x∗	PROPN
ma-198	176	43	)	)	PUNCT
ma-198	176	44	,	,	PUNCT
ma-198	176	45	x∗	x∗	PROPN
ma-198	176	46	−	−	PROPN
ma-198	177	1	q	q	NOUN
ma-198	177	2	〉	〉	NOUN
ma-198	177	3	≤	≤	NUM
ma-198	177	4	0	0	NUM
ma-198	177	5	,	,	PUNCT
ma-198	177	6	∀q	∀q	PROPN
ma-198	177	7	∈	∈	PROPN
ma-198	177	8	ω	ω	PROPN
ma-198	177	9	(	(	PUNCT
ma-198	177	10	3.2	3.2	NUM
ma-198	177	11	)	)	PUNCT
ma-198	177	12	proof	proof	NOUN
ma-198	177	13	.	.	PUNCT
ma-198	178	1	from	from	ADP
ma-198	178	2	the	the	DET
ma-198	178	3	choice	choice	NOUN
ma-198	178	4	of	of	ADP
ma-198	178	5	η	η	PROPN
ma-198	178	6	and	and	CCONJ
ma-198	178	7	γ	γ	X
ma-198	178	8	from	from	ADP
ma-198	178	9	[	[	X
ma-198	178	10	?	?	PUNCT
ma-198	178	11	]	]	X
ma-198	178	12	,	,	PUNCT
ma-198	178	13	(	(	PUNCT
ma-198	178	14	ηφ	ηφ	AUX
ma-198	178	15	−	−	PROPN
ma-198	178	16	γψ	γψ	CCONJ
ma-198	178	17	)	)	PUNCT
ma-198	178	18	is	be	AUX
ma-198	178	19	strongly	strongly	ADV
ma-198	178	20	monotone	monotone	ADJ
ma-198	178	21	,	,	PUNCT
ma-198	178	22	then	then	ADV
ma-198	178	23	the	the	DET
ma-198	178	24	variationalinequality	variationalinequality	NOUN
ma-198	178	25	(	(	PUNCT
ma-198	178	26	3.2	3.2	NUM
ma-198	178	27	)	)	PUNCT
ma-198	178	28	has	have	VERB
ma-198	178	29	a	a	DET
ma-198	178	30	unique	unique	ADJ
ma-198	178	31	solution	solution	NOUN
ma-198	178	32	.	.	PUNCT
ma-198	179	1	we	we	PRON
ma-198	179	2	will	will	AUX
ma-198	179	3	first	first	ADV
ma-198	179	4	show	show	VERB
ma-198	179	5	that	that	SCONJ
ma-198	179	6	there	there	PRON
ma-198	179	7	is	be	VERB
ma-198	179	8	only	only	ADV
ma-198	179	9	one	one	NUM
ma-198	179	10	solution.lets	solution.let	NOUN
ma-198	179	11	assume	assume	VERB
ma-198	179	12	that	that	SCONJ
ma-198	179	13	by	by	ADP
ma-198	179	14	contradiction	contradiction	NOUN
ma-198	179	15	that	that	SCONJ
ma-198	179	16	there	there	PRON
ma-198	179	17	exist	exist	VERB
ma-198	179	18	two	two	NUM
ma-198	179	19	points	point	NOUN
ma-198	179	20	x∗	x∗	NOUN
ma-198	179	21	,	,	PUNCT
ma-198	179	22	y∗	y∗	PROPN
ma-198	179	23	∈	∈	PROPN
ma-198	179	24	ω	ω	NOUN
ma-198	179	25	which	which	PRON
ma-198	179	26	are	be	AUX
ma-198	179	27	two	two	NUM
ma-198	179	28	solutionof	solutionof	NOUN
ma-198	179	29	the	the	DET
ma-198	179	30	given	give	VERB
ma-198	179	31	inequality	inequality	NOUN
ma-198	179	32	,	,	PUNCT
ma-198	179	33	and	and	CCONJ
ma-198	179	34	x∗	x∗	PROPN
ma-198	179	35	6=	6=	SYM
ma-198	179	36	y∗	y∗	ADV
ma-198	179	37	,	,	PUNCT
ma-198	179	38	then	then	ADV
ma-198	179	39	we	we	PRON
ma-198	179	40	have	have	VERB
ma-198	179	41	〈	〈	AUX
ma-198	179	42	ηbx∗	ηbx∗	VERB
ma-198	179	43	−	−	PROPN
ma-198	179	44	γf	γf	PROPN
ma-198	179	45	(	(	PUNCT
ma-198	179	46	x∗	x∗	PROPN
ma-198	179	47	)	)	PUNCT
ma-198	179	48	,	,	PUNCT
ma-198	179	49	x∗	x∗	PROPN
ma-198	180	1	−	−	PROPN
ma-198	180	2	y∗	y∗	PROPN
ma-198	180	3	〉	〉	PROPN
ma-198	180	4	≤	≤	NOUN
ma-198	180	5	0	0	NUM
ma-198	180	6	(	(	PUNCT
ma-198	180	7	3.3	3.3	NUM
ma-198	180	8	)	)	PUNCT
ma-198	180	9	and	and	CCONJ
ma-198	180	10	〈	〈	ADP
ma-198	180	11	ηby∗	ηby∗	ADJ
ma-198	180	12	−	−	PROPN
ma-198	180	13	γf	γf	PROPN
ma-198	180	14	(	(	PUNCT
ma-198	180	15	y∗	y∗	PROPN
ma-198	180	16	)	)	PUNCT
ma-198	180	17	,	,	PUNCT
ma-198	180	18	y∗	y∗	ADV
ma-198	180	19	−	−	ADP
ma-198	180	20	x∗	x∗	PROPN
ma-198	180	21	〉	〉	NOUN
ma-198	180	22	≤	≤	NOUN
ma-198	180	23	0	0	NUM
ma-198	181	1	(	(	PUNCT
ma-198	181	2	3.4	3.4	NUM
ma-198	181	3	)	)	PUNCT
ma-198	181	4	therefore	therefore	ADV
ma-198	181	5	from	from	ADP
ma-198	181	6	(	(	PUNCT
ma-198	181	7	3.3	3.3	NUM
ma-198	181	8	)	)	PUNCT
ma-198	181	9	and	and	CCONJ
ma-198	181	10	(	(	PUNCT
ma-198	181	11	3.4	3.4	NUM
ma-198	181	12	)	)	PUNCT
ma-198	181	13	,	,	PUNCT
ma-198	181	14	we	we	PRON
ma-198	181	15	have	have	VERB
ma-198	181	16	〈	〈	PROPN
ma-198	181	17	ηby∗	ηby∗	ADJ
ma-198	181	18	−	−	PROPN
ma-198	182	1	ηbx∗	ηbx∗	NOUN
ma-198	183	1	+	+	CCONJ
ma-198	184	1	γf	γf	PROPN
ma-198	184	2	(	(	PUNCT
ma-198	184	3	x∗)−	x∗)−	PRON
ma-198	184	4	γf	γf	PROPN
ma-198	184	5	(	(	PUNCT
ma-198	184	6	y∗	y∗	PROPN
ma-198	184	7	)	)	PUNCT
ma-198	184	8	,	,	PUNCT
ma-198	184	9	y∗	y∗	ADV
ma-198	184	10	−	−	ADP
ma-198	184	11	x∗	x∗	PROPN
ma-198	184	12	〉	〉	NOUN
ma-198	184	13	≤	≤	NOUN
ma-198	184	14	0	0	NUM
ma-198	185	1	(	(	PUNCT
ma-198	185	2	3.5	3.5	NUM
ma-198	185	3	)	)	PUNCT
ma-198	185	4	now	now	ADV
ma-198	185	5	from	from	ADP
ma-198	185	6	the	the	DET
ma-198	185	7	assumption	assumption	NOUN
ma-198	186	1	that	that	SCONJ
ma-198	186	2	l2η	l2η	PROPN
ma-198	186	3	2	2	NUM
ma-198	186	4	>	>	SYM
ma-198	186	5	0	0	NUM
ma-198	186	6	⇔	⇔	X
ma-198	186	7	α−	α−	ADP
ma-198	186	8	l2η	l2η	PROPN
ma-198	186	9	2	2	NUM
ma-198	186	10	<	<	X
ma-198	186	11	α	α	PROPN
ma-198	186	12	⇔	⇔	PROPN
ma-198	186	13	η	η	PROPN
ma-198	186	14	(	(	PUNCT
ma-198	186	15	α−	α−	ADP
ma-198	186	16	l2η	l2η	PROPN
ma-198	186	17	2	2	NUM
ma-198	186	18	)	)	PUNCT
ma-198	186	19	<	<	X
ma-198	186	20	αη	αη	X
ma-198	186	21	⇔	⇔	X
ma-198	186	22	τ	τ	X
ma-198	186	23	<	<	X
ma-198	186	24	αη	αη	X
ma-198	186	25	so	so	ADV
ma-198	186	26	that	that	SCONJ
ma-198	186	27	0	0	NUM
ma-198	186	28	<	<	X
ma-198	186	29	γ	γ	X
ma-198	186	30	<	<	X
ma-198	186	31	τ	τ	X
ma-198	186	32	<	<	X
ma-198	186	33	αη	αη	ADP
ma-198	186	34	〈	〈	PROPN
ma-198	186	35	ηby∗	ηby∗	ADJ
ma-198	186	36	−	−	PROPN
ma-198	186	37	ηbx∗	ηbx∗	NOUN
ma-198	186	38	+	+	CCONJ
ma-198	186	39	γf	γf	PROPN
ma-198	186	40	(	(	PUNCT
ma-198	186	41	x∗)−	x∗)−	PRON
ma-198	186	42	γf	γf	PROPN
ma-198	186	43	(	(	PUNCT
ma-198	186	44	y∗	y∗	PROPN
ma-198	186	45	)	)	PUNCT
ma-198	186	46	,	,	PUNCT
ma-198	186	47	y∗	y∗	ADV
ma-198	186	48	−	−	ADP
ma-198	186	49	x∗	x∗	PROPN
ma-198	186	50	〉	〉	NOUN
ma-198	186	51	=	=	PUNCT
ma-198	187	1	〈	〈	VERB
ma-198	187	2	ηby∗	ηby∗	ADJ
ma-198	187	3	−	−	PROPN
ma-198	187	4	ηbx∗	ηbx∗	PROPN
ma-198	187	5	,	,	PUNCT
ma-198	187	6	y∗	y∗	ADV
ma-198	187	7	−	−	PROPN
ma-198	187	8	x∗	x∗	PROPN
ma-198	187	9	〉	〉	NOUN
ma-198	187	10	−	−	NOUN
ma-198	188	1	〈	〈	PROPN
ma-198	188	2	γf	γf	PROPN
ma-198	188	3	(	(	PUNCT
ma-198	188	4	y∗)−	y∗)−	NOUN
ma-198	188	5	γf	γf	PROPN
ma-198	188	6	(	(	PUNCT
ma-198	188	7	x∗	x∗	PROPN
ma-198	188	8	)	)	PUNCT
ma-198	188	9	,	,	PUNCT
ma-198	188	10	y∗	y∗	ADV
ma-198	188	11	−	−	ADP
ma-198	189	1	x∗	x∗	PROPN
ma-198	189	2	〉	〉	NOUN
ma-198	189	3	=	=	PUNCT
ma-198	190	1	〈	〈	VERB
ma-198	190	2	ηby∗	ηby∗	ADJ
ma-198	190	3	−	−	PROPN
ma-198	190	4	ηbx∗	ηbx∗	PROPN
ma-198	190	5	,	,	PUNCT
ma-198	190	6	y∗	y∗	ADV
ma-198	190	7	−	−	PROPN
ma-198	190	8	x∗	x∗	PROPN
ma-198	190	9	〉	〉	PROPN
ma-198	190	10	−	−	NOUN
ma-198	190	11	γ‖f	γ‖f	ADJ
ma-198	190	12	(	(	PUNCT
ma-198	190	13	y∗)−	y∗)−	PROPN
ma-198	190	14	f	f	X
ma-198	190	15	(	(	PUNCT
ma-198	190	16	x∗)‖‖y∗	x∗)‖‖y∗	PROPN
ma-198	190	17	−	−	PROPN
ma-198	190	18	x∗‖	x∗‖	PROPN
ma-198	190	19	≥	≥	NOUN
ma-198	190	20	αη‖x∗	αη‖x∗	NUM
ma-198	190	21	−	−	PROPN
ma-198	190	22	y∗‖2	y∗‖2	PROPN
ma-198	190	23	−	−	PROPN
ma-198	190	24	γρ‖x∗	γρ‖x∗	NOUN
ma-198	190	25	−	−	NOUN
ma-198	191	1	y∗‖2	y∗‖2	PROPN
ma-198	191	2	=	=	SYM
ma-198	191	3	(	(	PUNCT
ma-198	191	4	αη	αη	ADP
ma-198	191	5	−	−	PROPN
ma-198	191	6	γρ)‖x∗	γρ)‖x∗	PROPN
ma-198	191	7	−	−	PROPN
ma-198	192	1	y∗‖2	y∗‖2	PROPN
ma-198	192	2	and	and	CCONJ
ma-198	192	3	this	this	PRON
ma-198	192	4	is	be	AUX
ma-198	192	5	a	a	DET
ma-198	192	6	contradiction	contradiction	NOUN
ma-198	192	7	to	to	ADP
ma-198	192	8	(	(	PUNCT
ma-198	192	9	3.5	3.5	NUM
ma-198	192	10	)	)	PUNCT
ma-198	192	11	,	,	PUNCT
ma-198	192	12	and	and	CCONJ
ma-198	192	13	hence	hence	ADV
ma-198	192	14	x∗	x∗	PROPN
ma-198	193	1	=	=	SYM
ma-198	193	2	y∗	y∗	PROPN
ma-198	193	3	,	,	PUNCT
ma-198	193	4	which	which	PRON
ma-198	193	5	is	be	AUX
ma-198	193	6	required	require	VERB
ma-198	193	7	.	.	PUNCT
ma-198	194	1	again	again	ADV
ma-198	194	2	,	,	PUNCT
ma-198	194	3	we	we	PRON
ma-198	194	4	note	note	VERB
ma-198	194	5	that	that	SCONJ
ma-198	194	6	theoperator	theoperator	NOUN
ma-198	194	7	pk[i	pk[i	PROPN
ma-198	194	8	+	+	CCONJ
ma-198	194	9	(	(	PUNCT
ma-198	194	10	αγf	αγf	NOUN
ma-198	194	11	−	−	PROPN
ma-198	194	12	ηαb	ηαb	PROPN
ma-198	194	13	)	)	PUNCT
ma-198	194	14	]	]	PUNCT
ma-198	194	15	is	be	AUX
ma-198	194	16	a	a	DET
ma-198	194	17	contradiction	contradiction	NOUN
ma-198	194	18	.	.	PUNCT
ma-198	195	1	now	now	ADV
ma-198	195	2	for	for	ADP
ma-198	195	3	any	any	DET
ma-198	195	4	fixed	fix	VERB
ma-198	195	5	point	point	NOUN
ma-198	195	6	α0	α0	PROPN
ma-198	195	7	∈	∈	PROPN
ma-198	195	8	(	(	PUNCT
ma-198	195	9	0,min	0,min	NUM
ma-198	195	10	{	{	PUNCT
ma-198	195	11	1	1	NUM
ma-198	195	12	,	,	PUNCT
ma-198	195	13	1	1	NUM
ma-198	195	14	τ	τ	PROPN
ma-198	195	15	}	}	PUNCT
ma-198	195	16	)	)	PUNCT
ma-198	195	17	,	,	PUNCT
ma-198	195	18	and	and	CCONJ
ma-198	195	19	∀x	∀x	NUM
ma-198	195	20	,	,	PUNCT
ma-198	195	21	y	y	PROPN
ma-198	195	22	∈	∈	PROPN
ma-198	195	23	h	h	NOUN
ma-198	195	24	,	,	PUNCT
ma-198	195	25	we	we	PRON
ma-198	195	26	have	have	AUX
ma-198	195	27	,	,	PUNCT
ma-198	195	28	by	by	ADP
ma-198	195	29	lemma	lemma	PROPN
ma-198	195	30	(	(	PUNCT
ma-198	195	31	2.4	2.4	NUM
ma-198	195	32	)	)	PUNCT
ma-198	195	33	,	,	PUNCT
ma-198	195	34	and	and	CCONJ
ma-198	195	35	letting	let	VERB
ma-198	195	36	φ	φ	X
ma-198	195	37	=	=	PUNCT
ma-198	196	1	[	[	X
ma-198	196	2	i	i	X
ma-198	196	3	+	+	CCONJ
ma-198	196	4	(	(	PUNCT
ma-198	196	5	α0γf	α0γf	NUM
ma-198	196	6	−	−	NOUN
ma-198	196	7	ηα0b)]x	ηα0b)]x	NOUN
ma-198	196	8	and	and	CCONJ
ma-198	196	9	θ	θ	NOUN
ma-198	196	10	=	=	PUNCT
ma-198	197	1	[	[	X
ma-198	197	2	i	i	X
ma-198	197	3	+	+	CCONJ
ma-198	197	4	(	(	PUNCT
ma-198	197	5	α0γf	α0γf	NUM
ma-198	197	6	−	−	NOUN
ma-198	197	7	ηα0b)]y	ηα0b)]y	NOUN
ma-198	197	8	,	,	PUNCT
ma-198	197	9	we	we	PRON
ma-198	197	10	have	have	VERB
ma-198	197	11	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	ADJ
ma-198	197	12	eur	eur	NOUN
ma-198	197	13	.	.	PUNCT
ma-198	198	1	j.	j.	PROPN
ma-198	198	2	math	math	PROPN
ma-198	198	3	.	.	PUNCT
ma-198	199	1	anal	anal	PROPN
ma-198	199	2	.	.	PUNCT
ma-198	200	1	10.28924	10.28924	NUM
ma-198	200	2	/	/	SYM
ma-198	200	3	ada	ada	PROPN
ma-198	200	4	/	/	SYM
ma-198	200	5	ma.4.2	ma.4.2	PROPN
ma-198	200	6	9	9	NUM
ma-198	200	7	‖pkφ−	‖pkφ−	PROPN
ma-198	200	8	pkθ‖	pkθ‖	ADP
ma-198	200	9	≤	≤	NOUN
ma-198	200	10	‖[i	‖[i	PROPN
ma-198	201	1	+	+	CCONJ
ma-198	201	2	(	(	PUNCT
ma-198	201	3	α0γf	α0γf	NUM
ma-198	201	4	−	−	PROPN
ma-198	201	5	ηα0b)]x	ηα0b)]x	NOUN
ma-198	201	6	−	−	PROPN
ma-198	201	7	(	(	PUNCT
ma-198	202	1	[	[	X
ma-198	202	2	i	i	X
ma-198	202	3	+	+	X
ma-198	202	4	(	(	PUNCT
ma-198	202	5	α0γf	α0γf	NUM
ma-198	202	6	−	−	PROPN
ma-198	202	7	ηα0b)]y)‖	ηα0b)]y)‖	PROPN
ma-198	202	8	≤	≤	ADJ
ma-198	202	9	α0γ‖f	α0γ‖f	PROPN
ma-198	202	10	(	(	PUNCT
ma-198	202	11	x)−	x)−	PROPN
ma-198	202	12	f	f	PROPN
ma-198	202	13	(	(	PUNCT
ma-198	202	14	y)‖+	y)‖+	NOUN
ma-198	202	15	‖(i	‖(i	NOUN
ma-198	202	16	−	−	PROPN
ma-198	202	17	ηα0b)x	ηα0b)x	ADV
ma-198	202	18	−	−	PROPN
ma-198	202	19	(	(	PUNCT
ma-198	202	20	i	i	PRON
ma-198	202	21	−	−	VERB
ma-198	202	22	ηα0b)y‖	ηα0b)y‖	VERB
ma-198	202	23	≤	≤	NUM
ma-198	202	24	α0γρ‖x	α0γρ‖x	NOUN
ma-198	202	25	−	−	PROPN
ma-198	203	1	y‖+	y‖+	PROPN
ma-198	203	2	(	(	PUNCT
ma-198	203	3	i	i	PRON
ma-198	203	4	−	−	PROPN
ma-198	203	5	ατ)‖x	ατ)‖x	PROPN
ma-198	203	6	−	−	PROPN
ma-198	203	7	y‖	y‖	PROPN
ma-198	203	8	≤	≤	NUM
ma-198	203	9	(	(	PUNCT
ma-198	203	10	i	i	PRON
ma-198	203	11	−	−	PROPN
ma-198	203	12	α0(τ	α0(τ	NUM
ma-198	203	13	−	−	NOUN
ma-198	203	14	γρ))‖x	γρ))‖x	PROPN
ma-198	203	15	−	−	PROPN
ma-198	203	16	y‖	y‖	PROPN
ma-198	203	17	thus	thus	ADV
ma-198	203	18	,	,	PUNCT
ma-198	203	19	by	by	ADP
ma-198	203	20	banach	banach	NOUN
ma-198	203	21	contraction	contraction	NOUN
ma-198	203	22	principle	principle	NOUN
ma-198	203	23	,	,	PUNCT
ma-198	203	24	the	the	DET
ma-198	203	25	mapping	mapping	NOUN
ma-198	203	26	pk[i	pk[i	PROPN
ma-198	203	27	+	+	CCONJ
ma-198	203	28	(	(	PUNCT
ma-198	203	29	αγf	αγf	NOUN
ma-198	203	30	−	−	PROPN
ma-198	203	31	ηαb	ηαb	PROPN
ma-198	203	32	)	)	PUNCT
ma-198	203	33	]	]	PUNCT
ma-198	203	34	has	have	VERB
ma-198	203	35	a	a	DET
ma-198	203	36	fixed	fix	VERB
ma-198	203	37	point	point	NOUN
ma-198	203	38	,	,	PUNCT
ma-198	203	39	say	say	VERB
ma-198	203	40	x̂	x̂	PUNCT
ma-198	204	1	=	=	PUNCT
ma-198	204	2	pk[i+	pk[i+	NOUN
ma-198	204	3	(	(	PUNCT
ma-198	204	4	αγf	αγf	NOUN
ma-198	204	5	−ηαb	−ηαb	NOUN
ma-198	204	6	)	)	PUNCT
ma-198	204	7	]	]	PUNCT
ma-198	204	8	and	and	CCONJ
ma-198	204	9	as	as	ADP
ma-198	204	10	such	such	ADJ
ma-198	204	11	,	,	PUNCT
ma-198	204	12	from	from	ADP
ma-198	204	13	(	(	PUNCT
ma-198	204	14	2.1	2.1	NUM
ma-198	204	15	)	)	PUNCT
ma-198	204	16	,	,	PUNCT
ma-198	204	17	it	it	PRON
ma-198	204	18	is	be	AUX
ma-198	204	19	similar	similar	ADJ
ma-198	204	20	in	in	ADP
ma-198	204	21	value	value	NOUN
ma-198	204	22	to	to	ADP
ma-198	204	23	the	the	DET
ma-198	204	24	variational	variational	ADJ
ma-198	204	25	inequalitybelow	inequalitybelow	NOUN
ma-198	205	1	〈	〈	PROPN
ma-198	205	2	ηbx̂	ηbx̂	PROPN
ma-198	205	3	−	−	PROPN
ma-198	205	4	γf	γf	PROPN
ma-198	205	5	(	(	PUNCT
ma-198	205	6	x̂	x̂	NUM
ma-198	205	7	)	)	PUNCT
ma-198	205	8	,	,	PUNCT
ma-198	205	9	x̂	x̂	PUNCT
ma-198	206	1	−	−	PUNCT
ma-198	207	1	q	q	NOUN
ma-198	207	2	〉	〉	NOUN
ma-198	207	3	≤	≤	NUM
ma-198	207	4	0,∀q	0,∀q	NOUN
ma-198	208	1	∈	∈	PROPN
ma-198	208	2	ω	ω	NOUN
ma-198	208	3	now	now	ADV
ma-198	208	4	we	we	PRON
ma-198	208	5	continue	continue	VERB
ma-198	208	6	with	with	ADP
ma-198	208	7	the	the	DET
ma-198	208	8	proof	proof	NOUN
ma-198	208	9	of	of	ADP
ma-198	208	10	theorem	theorem	NOUN
ma-198	208	11	(	(	PUNCT
ma-198	208	12	3.1)let	3.1)let	NUM
ma-198	208	13	q	q	NOUN
ma-198	208	14	∈	∈	PROPN
ma-198	208	15	ω	ω	PROPN
ma-198	208	16	with	with	ADP
ma-198	208	17	the	the	DET
ma-198	208	18	fact	fact	NOUN
ma-198	208	19	that	that	SCONJ
ma-198	208	20	jπ	jπ	PROPN
ma-198	208	21	λn	λn	PROPN
ma-198	208	22	is	be	AUX
ma-198	208	23	1−inverse	1−inverse	ADV
ma-198	208	24	strongly	strongly	ADV
ma-198	208	25	monotone	monotone	ADJ
ma-198	208	26	,	,	PUNCT
ma-198	208	27	and	and	CCONJ
ma-198	208	28	from	from	ADP
ma-198	208	29	[	[	X
ma-198	208	30	?	?	PUNCT
ma-198	208	31	]	]	X
ma-198	208	32	,	,	PUNCT
ma-198	208	33	we	we	PRON
ma-198	208	34	have	have	AUX
ma-198	208	35	thefollowing	thefollowe	VERB
ma-198	208	36	‖δn	‖δn	NUM
ma-198	208	37	−	−	PROPN
ma-198	208	38	q‖2	q‖2	VERB
ma-198	208	39	≤	≤	NUM
ma-198	208	40	‖xn	‖xn	PROPN
ma-198	208	41	−	−	PROPN
ma-198	208	42	q‖2	q‖2	PROPN
ma-198	208	43	therefore	therefore	ADV
ma-198	208	44	from	from	ADP
ma-198	208	45	(	(	PUNCT
ma-198	208	46	3.6	3.6	NUM
ma-198	208	47	)	)	PUNCT
ma-198	208	48	,	,	PUNCT
ma-198	208	49	we	we	PRON
ma-198	208	50	have	have	VERB
ma-198	208	51	‖δn	‖δn	NUM
ma-198	208	52	−	−	PROPN
ma-198	208	53	q‖	q‖	NOUN
ma-198	208	54	≤	≤	ADV
ma-198	208	55	‖xn	‖xn	NUM
ma-198	208	56	−	−	NOUN
ma-198	208	57	q‖	q‖	NOUN
ma-198	208	58	(	(	PUNCT
ma-198	208	59	3.6	3.6	NUM
ma-198	208	60	)	)	PUNCT
ma-198	208	61	from	from	ADP
ma-198	208	62	lemma	lemma	PROPN
ma-198	208	63	(	(	PUNCT
ma-198	208	64	2.5	2.5	NUM
ma-198	208	65	)	)	PUNCT
ma-198	208	66	,	,	PUNCT
ma-198	208	67	with	with	ADP
ma-198	208	68	(	(	PUNCT
ma-198	208	69	3.1	3.1	NUM
ma-198	208	70	)	)	PUNCT
ma-198	208	71	,	,	PUNCT
ma-198	208	72	and	and	CCONJ
ma-198	208	73	,	,	PUNCT
ma-198	208	74	for	for	ADP
ma-198	208	75	the	the	DET
ma-198	208	76	fact	fact	NOUN
ma-198	208	77	that	that	SCONJ
ma-198	208	78	t1q	t1q	NUM
ma-198	208	79	=	=	SYM
ma-198	208	80	{	{	PUNCT
ma-198	208	81	q	q	NOUN
ma-198	208	82	}	}	PUNCT
ma-198	208	83	,	,	PUNCT
ma-198	208	84	t1	t1	PROPN
ma-198	208	85	is	be	AUX
ma-198	208	86	β−demicontrative	β−demicontrative	NUM
ma-198	208	87	,	,	PUNCT
ma-198	208	88	we	we	PRON
ma-198	208	89	have	have	VERB
ma-198	208	90	‖yn	‖yn	NUM
ma-198	208	91	−	−	PROPN
ma-198	208	92	q‖2	q‖2	PROPN
ma-198	208	93	=	=	PUNCT
ma-198	208	94	‖θn(δn	‖θn(δn	PROPN
ma-198	208	95	−	−	PROPN
ma-198	208	96	q	q	NOUN
ma-198	208	97	)	)	PUNCT
ma-198	209	1	+	+	CCONJ
ma-198	209	2	(	(	PUNCT
ma-198	209	3	1−	1−	NUM
ma-198	209	4	θn)(vn	θn)(vn	NUM
ma-198	209	5	−	−	PROPN
ma-198	209	6	q)‖2	q)‖2	NOUN
ma-198	209	7	=	=	PUNCT
ma-198	209	8	θn‖δn	θn‖δn	PUNCT
ma-198	209	9	−	−	PROPN
ma-198	209	10	q‖2	q‖2	PROPN
ma-198	209	11	+	+	CCONJ
ma-198	209	12	(	(	PUNCT
ma-198	209	13	1−	1−	NUM
ma-198	209	14	θn)‖vn	θn)‖vn	NOUN
ma-198	209	15	−	−	ADP
ma-198	209	16	q‖2	q‖2	VERB
ma-198	209	17	−	−	PROPN
ma-198	209	18	(	(	PUNCT
ma-198	209	19	1−	1−	NUM
ma-198	209	20	θn)θn‖vn	θn)θn‖vn	NUM
ma-198	209	21	−	−	PROPN
ma-198	209	22	δn‖2	δn‖2	PROPN
ma-198	209	23	≤	≤	NOUN
ma-198	209	24	θn‖δn	θn‖δn	VERB
ma-198	209	25	−	−	PROPN
ma-198	209	26	q‖2	q‖2	PROPN
ma-198	209	27	+	+	CCONJ
ma-198	209	28	(	(	PUNCT
ma-198	209	29	1−	1−	NUM
ma-198	209	30	θn)h(t1δn	θn)h(t1δn	NOUN
ma-198	209	31	,	,	PUNCT
ma-198	209	32	t1q)2	t1q)2	PROPN
ma-198	209	33	−	−	PROPN
ma-198	209	34	(	(	PUNCT
ma-198	209	35	1−	1−	NUM
ma-198	209	36	θn)θn‖vn	θn)θn‖vn	NUM
ma-198	209	37	−	−	PROPN
ma-198	209	38	δn‖2	δn‖2	PROPN
ma-198	209	39	≤	≤	NOUN
ma-198	209	40	θn‖δn	θn‖δn	VERB
ma-198	209	41	−	−	PROPN
ma-198	209	42	q‖2	q‖2	PROPN
ma-198	209	43	+	+	CCONJ
ma-198	209	44	(	(	PUNCT
ma-198	209	45	1−	1−	NUM
ma-198	209	46	θn)[‖δn	θn)[‖δn	CCONJ
ma-198	209	47	−	−	PROPN
ma-198	209	48	q‖2	q‖2	PROPN
ma-198	209	49	+	+	CCONJ
ma-198	209	50	βd(δn	βd(δn	PROPN
ma-198	209	51	,	,	PUNCT
ma-198	209	52	t1δn)2]−	t1δn)2]−	ADJ
ma-198	209	53	(	(	PUNCT
ma-198	209	54	1−	1−	NUM
ma-198	209	55	θn)θn‖vn	θn)θn‖vn	NUM
ma-198	209	56	−	−	PROPN
ma-198	210	1	δn‖2	δn‖2	PROPN
ma-198	210	2	≤	≤	NOUN
ma-198	211	1	‖δn	‖δn	NUM
ma-198	211	2	−	−	PROPN
ma-198	211	3	q‖2	q‖2	PROPN
ma-198	211	4	−	−	PROPN
ma-198	211	5	(	(	PUNCT
ma-198	211	6	1−	1−	NUM
ma-198	211	7	θn)(θn	θn)(θn	SYM
ma-198	211	8	−	−	PROPN
ma-198	211	9	β)‖vn	β)‖vn	PUNCT
ma-198	211	10	−	−	PROPN
ma-198	212	1	δn‖2	δn‖2	PROPN
ma-198	212	2	(	(	PUNCT
ma-198	212	3	3.7	3.7	NUM
ma-198	212	4	)	)	PUNCT
ma-198	212	5	thus	thus	ADV
ma-198	212	6	,	,	PUNCT
ma-198	212	7	we	we	PRON
ma-198	212	8	have	have	VERB
ma-198	212	9	‖yn	‖yn	PROPN
ma-198	212	10	−	−	PROPN
ma-198	212	11	q‖2	q‖2	NOUN
ma-198	212	12	≤	≤	NOUN
ma-198	213	1	‖δn	‖δn	NUM
ma-198	213	2	−	−	PROPN
ma-198	213	3	q‖2	q‖2	PROPN
ma-198	213	4	−	−	PROPN
ma-198	213	5	(	(	PUNCT
ma-198	213	6	1−	1−	NUM
ma-198	213	7	θn)(θn	θn)(θn	SYM
ma-198	213	8	−	−	PROPN
ma-198	213	9	β)‖vn	β)‖vn	PUNCT
ma-198	213	10	−	−	PROPN
ma-198	214	1	δn‖2	δn‖2	PROPN
ma-198	214	2	since	since	SCONJ
ma-198	214	3	θn	θn	X
ma-198	214	4	∈	∈	PROPN
ma-198	214	5	(	(	PUNCT
ma-198	214	6	β	β	X
ma-198	214	7	,	,	PUNCT
ma-198	214	8	1	1	NUM
ma-198	214	9	)	)	PUNCT
ma-198	214	10	,	,	PUNCT
ma-198	214	11	we	we	PRON
ma-198	214	12	have	have	VERB
ma-198	214	13	‖yn	‖yn	PROPN
ma-198	214	14	−	−	PROPN
ma-198	214	15	q‖2	q‖2	NOUN
ma-198	214	16	≤	≤	NOUN
ma-198	214	17	‖δn	‖δn	NUM
ma-198	214	18	−	−	NOUN
ma-198	214	19	q‖2	q‖2	VERB
ma-198	214	20	again	again	ADV
ma-198	214	21	from	from	ADP
ma-198	214	22	lemma	lemma	PROPN
ma-198	214	23	(	(	PUNCT
ma-198	214	24	2.5	2.5	NUM
ma-198	214	25	)	)	PUNCT
ma-198	214	26	,	,	PUNCT
ma-198	214	27	with	with	ADP
ma-198	214	28	(	(	PUNCT
ma-198	214	29	3.1	3.1	NUM
ma-198	214	30	)	)	PUNCT
ma-198	214	31	,	,	PUNCT
ma-198	214	32	and	and	CCONJ
ma-198	214	33	,	,	PUNCT
ma-198	214	34	for	for	ADP
ma-198	214	35	the	the	DET
ma-198	214	36	fact	fact	NOUN
ma-198	214	37	that	that	SCONJ
ma-198	214	38	t2q	t2q	AUX
ma-198	214	39	=	=	SYM
ma-198	214	40	{	{	PUNCT
ma-198	214	41	q	q	X
ma-198	214	42	}	}	PUNCT
ma-198	214	43	,	,	PUNCT
ma-198	214	44	t2	t2	PROPN
ma-198	214	45	is	be	AUX
ma-198	214	46	β−demicontrative	β−demicontrative	ADJ
ma-198	214	47	,	,	PUNCT
ma-198	214	48	wehave	wehave	VERB
ma-198	214	49	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	214	50	eur	eur	NOUN
ma-198	214	51	.	.	PUNCT
ma-198	215	1	j.	j.	PROPN
ma-198	215	2	math	math	PROPN
ma-198	215	3	.	.	PUNCT
ma-198	216	1	anal	anal	PROPN
ma-198	216	2	.	.	PUNCT
ma-198	217	1	10.28924	10.28924	NUM
ma-198	217	2	/	/	SYM
ma-198	217	3	ada	ada	PROPN
ma-198	217	4	/	/	SYM
ma-198	217	5	ma.4.2	ma.4.2	PROPN
ma-198	217	6	10	10	NUM
ma-198	217	7	‖zn	‖zn	NUM
ma-198	217	8	−	−	PROPN
ma-198	217	9	q‖2	q‖2	NOUN
ma-198	218	1	=	=	PUNCT
ma-198	218	2	‖βn(yn	‖βn(yn	PROPN
ma-198	218	3	−	−	PROPN
ma-198	218	4	q	q	NOUN
ma-198	218	5	)	)	PUNCT
ma-198	218	6	+	+	CCONJ
ma-198	218	7	(	(	PUNCT
ma-198	218	8	1−	1−	NUM
ma-198	218	9	βn)(un	βn)(un	NUM
ma-198	218	10	−	−	NOUN
ma-198	218	11	q)‖2	q)‖2	NOUN
ma-198	218	12	=	=	PUNCT
ma-198	218	13	βn‖yn	βn‖yn	NOUN
ma-198	219	1	−	−	PROPN
ma-198	219	2	q‖2	q‖2	VERB
ma-198	219	3	+	+	CCONJ
ma-198	219	4	(	(	PUNCT
ma-198	219	5	1−	1−	NUM
ma-198	219	6	βn)‖un	βn)‖un	ADP
ma-198	219	7	−	−	PROPN
ma-198	219	8	q‖2	q‖2	PROPN
ma-198	219	9	−	−	PROPN
ma-198	220	1	(	(	PUNCT
ma-198	220	2	1−	1−	NUM
ma-198	220	3	βn)βn‖un	βn)βn‖un	NOUN
ma-198	220	4	−	−	PUNCT
ma-198	220	5	yn‖2	yn‖2	PROPN
ma-198	220	6	≤	≤	PROPN
ma-198	220	7	βn‖yn	βn‖yn	PUNCT
ma-198	221	1	−	−	PROPN
ma-198	221	2	q‖2	q‖2	VERB
ma-198	221	3	+	+	CCONJ
ma-198	221	4	(	(	PUNCT
ma-198	221	5	1−	1−	NUM
ma-198	221	6	βn)h(t2yn	βn)h(t2yn	NOUN
ma-198	221	7	,	,	PUNCT
ma-198	221	8	t2q)2	t2q)2	PROPN
ma-198	221	9	−	−	PROPN
ma-198	221	10	(	(	PUNCT
ma-198	221	11	1−	1−	NUM
ma-198	221	12	βn)βn‖un	βn)βn‖un	NOUN
ma-198	221	13	−	−	PUNCT
ma-198	221	14	yn‖2	yn‖2	PROPN
ma-198	221	15	≤	≤	PROPN
ma-198	221	16	βn‖yn	βn‖yn	PUNCT
ma-198	222	1	−	−	PROPN
ma-198	222	2	q‖2	q‖2	VERB
ma-198	222	3	+	+	CCONJ
ma-198	222	4	(	(	PUNCT
ma-198	222	5	1−	1−	NUM
ma-198	222	6	βn)[‖yn	βn)[‖yn	NUM
ma-198	222	7	−	−	PROPN
ma-198	222	8	q‖2	q‖2	PROPN
ma-198	222	9	+	+	CCONJ
ma-198	222	10	βd(yn	βd(yn	NOUN
ma-198	222	11	,	,	PUNCT
ma-198	222	12	t2yn)2]−	t2yn)2]−	CCONJ
ma-198	222	13	(	(	PUNCT
ma-198	222	14	1−	1−	NUM
ma-198	222	15	βn)βn‖un	βn)βn‖un	NOUN
ma-198	222	16	−	−	PROPN
ma-198	222	17	yn‖2	yn‖2	PROPN
ma-198	222	18	≤	≤	PROPN
ma-198	222	19	‖yn	‖yn	PROPN
ma-198	222	20	−	−	PROPN
ma-198	222	21	q‖2	q‖2	PROPN
ma-198	222	22	−	−	PROPN
ma-198	222	23	(	(	PUNCT
ma-198	222	24	1−	1−	NUM
ma-198	222	25	βn)(βn	βn)(βn	PUNCT
ma-198	223	1	−	−	PROPN
ma-198	223	2	β)‖un	β)‖un	PUNCT
ma-198	224	1	−	−	PUNCT
ma-198	224	2	yn‖2	yn‖2	PROPN
ma-198	224	3	(	(	PUNCT
ma-198	224	4	3.8	3.8	NUM
ma-198	224	5	)	)	PUNCT
ma-198	224	6	thus	thus	ADV
ma-198	224	7	,	,	PUNCT
ma-198	224	8	we	we	PRON
ma-198	224	9	have	have	VERB
ma-198	224	10	‖zn	‖zn	NUM
ma-198	224	11	−	−	PROPN
ma-198	224	12	q‖2	q‖2	VERB
ma-198	224	13	≤	≤	NUM
ma-198	224	14	‖yn	‖yn	NUM
ma-198	224	15	−	−	PROPN
ma-198	225	1	q‖2	q‖2	PROPN
ma-198	225	2	−	−	PROPN
ma-198	225	3	(	(	PUNCT
ma-198	225	4	1−	1−	NUM
ma-198	225	5	βn)(βn	βn)(βn	PUNCT
ma-198	225	6	−	−	PROPN
ma-198	225	7	β)‖un	β)‖un	PUNCT
ma-198	226	1	−	−	PROPN
ma-198	226	2	yn‖2	yn‖2	PROPN
ma-198	226	3	since	since	SCONJ
ma-198	226	4	βn	βn	PROPN
ma-198	226	5	∈	∈	PROPN
ma-198	226	6	(	(	PUNCT
ma-198	226	7	β	β	X
ma-198	226	8	,	,	PUNCT
ma-198	226	9	1	1	NUM
ma-198	226	10	)	)	PUNCT
ma-198	226	11	,	,	PUNCT
ma-198	226	12	we	we	PRON
ma-198	226	13	have	have	VERB
ma-198	226	14	‖zn	‖zn	NUM
ma-198	226	15	−	−	PROPN
ma-198	226	16	q‖2	q‖2	VERB
ma-198	226	17	≤	≤	NUM
ma-198	226	18	‖yn	‖yn	NUM
ma-198	226	19	−	−	PROPN
ma-198	226	20	q‖2	q‖2	VERB
ma-198	226	21	now	now	ADV
ma-198	226	22	,	,	PUNCT
ma-198	226	23	using	use	VERB
ma-198	226	24	the	the	DET
ma-198	226	25	fact	fact	NOUN
ma-198	226	26	that	that	SCONJ
ma-198	226	27	t3q	t3q	PROPN
ma-198	226	28	=	=	SYM
ma-198	226	29	q	q	X
ma-198	226	30	,	,	PUNCT
ma-198	226	31	we	we	PRON
ma-198	226	32	have	have	AUX
ma-198	226	33	the	the	DET
ma-198	226	34	following	follow	VERB
ma-198	226	35	estimates	estimate	NOUN
ma-198	226	36	‖tn	‖tn	PUNCT
ma-198	226	37	−	−	PROPN
ma-198	226	38	q‖	q‖	NOUN
ma-198	226	39	=	=	SYM
ma-198	226	40	‖γnzn	‖γnzn	NOUN
ma-198	227	1	+	+	CCONJ
ma-198	227	2	(	(	PUNCT
ma-198	227	3	1−	1−	NUM
ma-198	227	4	γn)wn	γn)wn	PUNCT
ma-198	227	5	−	−	PROPN
ma-198	227	6	q‖	q‖	NOUN
ma-198	227	7	≤	≤	ADV
ma-198	227	8	γn‖zn	γn‖zn	NOUN
ma-198	228	1	−	−	ADP
ma-198	228	2	q‖+	q‖+	ADJ
ma-198	228	3	(	(	PUNCT
ma-198	228	4	1−	1−	NUM
ma-198	228	5	γn)‖wn	γn)‖wn	ADJ
ma-198	228	6	−	−	PROPN
ma-198	229	1	q‖	q‖	NOUN
ma-198	229	2	≤	≤	ADV
ma-198	230	1	γn‖zn	γn‖zn	NOUN
ma-198	230	2	−	−	ADP
ma-198	230	3	q‖+	q‖+	ADJ
ma-198	230	4	(	(	PUNCT
ma-198	230	5	1−	1−	NUM
ma-198	230	6	γn)h(t3z	γn)h(t3z	NUM
ma-198	230	7	,	,	PUNCT
ma-198	230	8	t3q	t3q	PROPN
ma-198	230	9	)	)	PUNCT
ma-198	230	10	≤	≤	NOUN
ma-198	231	1	γn‖zn	γn‖zn	NUM
ma-198	231	2	−	−	ADP
ma-198	231	3	q‖+	q‖+	ADJ
ma-198	231	4	(	(	PUNCT
ma-198	231	5	1−	1−	NUM
ma-198	231	6	γn)‖zn	γn)‖zn	ADV
ma-198	231	7	−	−	PROPN
ma-198	232	1	q‖	q‖	NOUN
ma-198	232	2	≤	≤	ADV
ma-198	233	1	‖zn	‖zn	NUM
ma-198	233	2	−	−	NOUN
ma-198	233	3	q‖	q‖	NOUN
ma-198	233	4	(	(	PUNCT
ma-198	233	5	3.9	3.9	NUM
ma-198	233	6	)	)	PUNCT
ma-198	233	7	hence	hence	ADV
ma-198	233	8	,	,	PUNCT
ma-198	233	9	we	we	PRON
ma-198	233	10	can	can	AUX
ma-198	233	11	see	see	VERB
ma-198	233	12	that	that	SCONJ
ma-198	233	13	‖tn	‖tn	NUM
ma-198	233	14	−	−	PROPN
ma-198	233	15	q‖	q‖	NOUN
ma-198	233	16	≤	≤	SCONJ
ma-198	234	1	‖zn	‖zn	NUM
ma-198	234	2	−	−	NOUN
ma-198	234	3	q‖	q‖	NOUN
ma-198	234	4	≤	≤	SCONJ
ma-198	234	5	‖yn	‖yn	NUM
ma-198	234	6	−	−	NOUN
ma-198	234	7	q‖	q‖	NOUN
ma-198	234	8	≤	≤	VERB
ma-198	234	9	‖δn	‖δn	NUM
ma-198	234	10	−	−	PROPN
ma-198	234	11	q‖	q‖	NOUN
ma-198	234	12	≤	≤	ADV
ma-198	234	13	‖xn	‖xn	NUM
ma-198	234	14	−	−	NOUN
ma-198	234	15	q‖	q‖	NOUN
ma-198	234	16	(	(	PUNCT
ma-198	234	17	3.10	3.10	NUM
ma-198	234	18	)	)	PUNCT
ma-198	234	19	using	use	VERB
ma-198	234	20	(	(	PUNCT
ma-198	234	21	3.1	3.1	NUM
ma-198	234	22	)	)	PUNCT
ma-198	234	23	,	,	PUNCT
ma-198	234	24	inequality	inequality	NOUN
ma-198	234	25	(	(	PUNCT
ma-198	234	26	3.10	3.10	NUM
ma-198	234	27	)	)	PUNCT
ma-198	234	28	and	and	CCONJ
ma-198	234	29	lemma	lemma	PROPN
ma-198	234	30	(	(	PUNCT
ma-198	234	31	2.4	2.4	NUM
ma-198	234	32	)	)	PUNCT
ma-198	234	33	‖xn+1	‖xn+1	PUNCT
ma-198	234	34	−	−	PROPN
ma-198	234	35	q‖	q‖	NOUN
ma-198	234	36	≤	≤	ADV
ma-198	234	37	‖(αnγf	‖(αnγf	NOUN
ma-198	234	38	(	(	PUNCT
ma-198	234	39	xn	xn	PROPN
ma-198	234	40	)	)	PUNCT
ma-198	235	1	+	+	CCONJ
ma-198	235	2	(	(	PUNCT
ma-198	235	3	i	i	PRON
ma-198	235	4	−	−	VERB
ma-198	235	5	ηαnb)tn)−	ηαnb)tn)−	PROPN
ma-198	235	6	q‖	q‖	NOUN
ma-198	235	7	≤	≤	ADJ
ma-198	235	8	‖αnγ(f	‖αnγ(f	PROPN
ma-198	235	9	(	(	PUNCT
ma-198	235	10	xn)−	xn)−	X
ma-198	235	11	f	f	X
ma-198	235	12	(	(	PUNCT
ma-198	235	13	q))‖+	q))‖+	PROPN
ma-198	235	14	(	(	PUNCT
ma-198	235	15	1−	1−	NUM
ma-198	235	16	τα)‖tn	τα)‖tn	NOUN
ma-198	235	17	−	−	PROPN
ma-198	235	18	q)‖+	q)‖+	NOUN
ma-198	235	19	α‖γf	α‖γf	PROPN
ma-198	235	20	(	(	PUNCT
ma-198	235	21	q)−	q)−	PROPN
ma-198	235	22	ηαb‖	ηαb‖	NOUN
ma-198	235	23	≤	≤	NOUN
ma-198	235	24	αnγ‖f	αnγ‖f	NUM
ma-198	235	25	(	(	PUNCT
ma-198	235	26	xn)−	xn)−	X
ma-198	235	27	f	f	X
ma-198	235	28	(	(	PUNCT
ma-198	235	29	q)‖+	q)‖+	PROPN
ma-198	235	30	(	(	PUNCT
ma-198	235	31	1−	1−	NUM
ma-198	235	32	τα)‖xn	τα)‖xn	SYM
ma-198	235	33	−	−	PROPN
ma-198	235	34	q)‖+	q)‖+	VERB
ma-198	235	35	α‖γf	α‖γf	PROPN
ma-198	235	36	(	(	PUNCT
ma-198	235	37	q)−	q)−	PROPN
ma-198	235	38	ηαb‖	ηαb‖	NOUN
ma-198	235	39	≤	≤	PUNCT
ma-198	235	40	αnbγ‖xn	αnbγ‖xn	PROPN
ma-198	235	41	−	−	PROPN
ma-198	235	42	q‖+	q‖+	PROPN
ma-198	235	43	(	(	PUNCT
ma-198	235	44	1−	1−	NUM
ma-198	235	45	τα)‖xn	τα)‖xn	SYM
ma-198	235	46	−	−	PROPN
ma-198	235	47	q)‖+	q)‖+	VERB
ma-198	235	48	α‖γf	α‖γf	PROPN
ma-198	235	49	(	(	PUNCT
ma-198	235	50	q)−	q)−	PROPN
ma-198	235	51	ηαb‖	ηαb‖	NOUN
ma-198	235	52	≤	≤	NOUN
ma-198	235	53	(	(	PUNCT
ma-198	235	54	1−	1−	NUM
ma-198	235	55	α(τ	α(τ	NUM
ma-198	235	56	−	−	NOUN
ma-198	235	57	bγ))‖xn	bγ))‖xn	PROPN
ma-198	235	58	−	−	PROPN
ma-198	235	59	q)‖+	q)‖+	PROPN
ma-198	235	60	α‖γf	α‖γf	PROPN
ma-198	235	61	(	(	PUNCT
ma-198	235	62	q)−	q)−	PROPN
ma-198	235	63	ηαb‖	ηαb‖	PUNCT
ma-198	235	64	≤	≤	ADJ
ma-198	235	65	max	max	PROPN
ma-198	235	66	{	{	PUNCT
ma-198	235	67	‖xn	‖xn	PROPN
ma-198	235	68	−	−	NOUN
ma-198	235	69	q‖	q‖	NOUN
ma-198	235	70	,	,	PUNCT
ma-198	235	71	‖γf	‖γf	PROPN
ma-198	235	72	(	(	PUNCT
ma-198	235	73	q)−	q)−	PROPN
ma-198	235	74	ηbq‖	ηbq‖	VERB
ma-198	235	75	τ	τ	PROPN
ma-198	235	76	−	−	NOUN
ma-198	235	77	bγ	bγ	PROPN
ma-198	235	78	}	}	PUNCT
ma-198	235	79	.	.	PUNCT
ma-198	236	1	therefore	therefore	ADV
ma-198	236	2	,	,	PUNCT
ma-198	236	3	by	by	ADP
ma-198	236	4	induction	induction	NOUN
ma-198	236	5	,	,	PUNCT
ma-198	236	6	it	it	PRON
ma-198	236	7	is	be	AUX
ma-198	236	8	easy	easy	ADJ
ma-198	236	9	to	to	PART
ma-198	236	10	see	see	VERB
ma-198	236	11	that	that	PRON
ma-198	236	12	‖xn+1	‖xn+1	NOUN
ma-198	236	13	−	−	PROPN
ma-198	236	14	q‖	q‖	NOUN
ma-198	236	15	≤	≤	PROPN
ma-198	236	16	max	max	PROPN
ma-198	236	17	{	{	PUNCT
ma-198	236	18	‖x0	‖x0	PROPN
ma-198	236	19	−	−	PROPN
ma-198	237	1	q‖	q‖	NOUN
ma-198	237	2	,	,	PUNCT
ma-198	237	3	‖γf	‖γf	PROPN
ma-198	237	4	(	(	PUNCT
ma-198	237	5	q)−	q)−	PROPN
ma-198	237	6	ηbq‖	ηbq‖	VERB
ma-198	237	7	τ	τ	PROPN
ma-198	237	8	−	−	PROPN
ma-198	237	9	bγ	bγ	PROPN
ma-198	237	10	}	}	PUNCT
ma-198	237	11	,	,	PUNCT
ma-198	237	12	∀n	∀n	NUM
ma-198	237	13	≥	≥	NOUN
ma-198	237	14	1	1	NUM
ma-198	237	15	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NOUN
ma-198	237	16	eur	eur	NOUN
ma-198	237	17	.	.	PUNCT
ma-198	238	1	j.	j.	PROPN
ma-198	238	2	math	math	PROPN
ma-198	238	3	.	.	PUNCT
ma-198	239	1	anal	anal	PROPN
ma-198	239	2	.	.	PUNCT
ma-198	240	1	10.28924	10.28924	NUM
ma-198	240	2	/	/	SYM
ma-198	240	3	ada	ada	PROPN
ma-198	240	4	/	/	SYM
ma-198	240	5	ma.4.2	ma.4.2	PROPN
ma-198	240	6	11hence	11hence	NUM
ma-198	240	7	{	{	PUNCT
ma-198	240	8	xn	xn	NUM
ma-198	240	9	}	}	PUNCT
ma-198	240	10	,	,	PUNCT
ma-198	240	11	{	{	PUNCT
ma-198	240	12	f	f	X
ma-198	240	13	(	(	PUNCT
ma-198	240	14	xn	xn	PROPN
ma-198	240	15	)	)	PUNCT
ma-198	240	16	}	}	PUNCT
ma-198	240	17	and	and	CCONJ
ma-198	240	18	{	{	PUNCT
ma-198	240	19	bxn	bxn	PROPN
ma-198	240	20	}	}	PUNCT
ma-198	240	21	are	be	AUX
ma-198	240	22	bounded.secondly	bounded.secondly	ADV
ma-198	240	23	,	,	PUNCT
ma-198	240	24	we	we	PRON
ma-198	240	25	now	now	ADV
ma-198	240	26	have	have	VERB
ma-198	240	27	the	the	DET
ma-198	240	28	following	follow	VERB
ma-198	240	29	estimates	estimate	NOUN
ma-198	240	30	.	.	PUNCT
ma-198	241	1	from	from	ADP
ma-198	241	2	(	(	PUNCT
ma-198	241	3	3.1	3.1	NUM
ma-198	241	4	)	)	PUNCT
ma-198	241	5	and	and	CCONJ
ma-198	241	6	lemma	lemma	PROPN
ma-198	241	7	(	(	PUNCT
ma-198	241	8	2.5	2.5	NUM
ma-198	241	9	)	)	PUNCT
ma-198	241	10	,	,	PUNCT
ma-198	241	11	we	we	PRON
ma-198	241	12	have	have	VERB
ma-198	241	13	‖xn+1	‖xn+1	NOUN
ma-198	241	14	−	−	PROPN
ma-198	241	15	q‖2	q‖2	NOUN
ma-198	241	16	≤	≤	ADJ
ma-198	241	17	‖αn(γf	‖αn(γf	NOUN
ma-198	241	18	(	(	PUNCT
ma-198	241	19	xn)−	xn)−	NOUN
ma-198	241	20	ηbq	ηbq	ADV
ma-198	241	21	)	)	PUNCT
ma-198	242	1	+	+	CCONJ
ma-198	242	2	(	(	PUNCT
ma-198	242	3	i	i	PRON
ma-198	242	4	−	−	PROPN
ma-198	242	5	ηαnb)(tn	ηαnb)(tn	PROPN
ma-198	242	6	−	−	PROPN
ma-198	242	7	q)‖2	q)‖2	NOUN
ma-198	242	8	≤	≤	ADV
ma-198	242	9	α2	α2	VERB
ma-198	242	10	n‖γf	n‖γf	PROPN
ma-198	242	11	(	(	PUNCT
ma-198	242	12	xn)−	xn)−	NOUN
ma-198	242	13	ηbq‖2	ηbq‖2	X
ma-198	242	14	+	+	CCONJ
ma-198	242	15	(	(	PUNCT
ma-198	242	16	1−	1−	NUM
ma-198	242	17	ταn)2‖tn	ταn)2‖tn	NOUN
ma-198	242	18	−	−	PROPN
ma-198	242	19	q‖2	q‖2	PROPN
ma-198	242	20	+	+	CCONJ
ma-198	242	21	2αn(1−	2αn(1−	NUM
ma-198	242	22	ταn)‖γf	ταn)‖γf	NUM
ma-198	242	23	(	(	PUNCT
ma-198	242	24	xn)−	xn)−	PROPN
ma-198	242	25	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	242	26	−	−	PROPN
ma-198	242	27	q‖	q‖	NOUN
ma-198	242	28	≤	≤	ADV
ma-198	242	29	α2	α2	PROPN
ma-198	242	30	n‖γf	n‖γf	PROPN
ma-198	242	31	(	(	PUNCT
ma-198	242	32	xn)−	xn)−	NOUN
ma-198	242	33	ηbq‖2	ηbq‖2	X
ma-198	242	34	+	+	CCONJ
ma-198	242	35	(	(	PUNCT
ma-198	242	36	1−	1−	NUM
ma-198	242	37	ταn)2‖zn	ταn)2‖zn	NOUN
ma-198	242	38	−	−	PROPN
ma-198	242	39	q‖2	q‖2	VERB
ma-198	243	1	+	+	CCONJ
ma-198	243	2	2αn(1−	2αn(1−	NUM
ma-198	243	3	ταn)‖γf	ταn)‖γf	NUM
ma-198	243	4	(	(	PUNCT
ma-198	243	5	xn)−	xn)−	PROPN
ma-198	243	6	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	243	7	−	−	PROPN
ma-198	243	8	q‖	q‖	NOUN
ma-198	243	9	≤	≤	ADV
ma-198	243	10	α2	α2	PROPN
ma-198	243	11	n‖γf	n‖γf	PROPN
ma-198	243	12	(	(	PUNCT
ma-198	243	13	xn)−	xn)−	NOUN
ma-198	243	14	ηbq‖2	ηbq‖2	X
ma-198	243	15	+	+	CCONJ
ma-198	243	16	(	(	PUNCT
ma-198	243	17	1−	1−	NUM
ma-198	243	18	ταn)2‖yn	ταn)2‖yn	NOUN
ma-198	243	19	−	−	PROPN
ma-198	243	20	q‖2	q‖2	VERB
ma-198	243	21	−	−	PROPN
ma-198	243	22	(	(	PUNCT
ma-198	243	23	1−	1−	NUM
ma-198	244	1	ταn)2(1−	ταn)2(1−	PROPN
ma-198	244	2	βn)(βn	βn)(βn	PUNCT
ma-198	244	3	−	−	PROPN
ma-198	244	4	β)‖un	β)‖un	PUNCT
ma-198	245	1	−	−	PUNCT
ma-198	245	2	yn‖2	yn‖2	PROPN
ma-198	245	3	+	+	CCONJ
ma-198	246	1	2αn(1−	2αn(1−	NUM
ma-198	246	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	246	3	(	(	PUNCT
ma-198	246	4	xn)−	xn)−	PROPN
ma-198	246	5	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	246	6	−	−	PROPN
ma-198	246	7	q‖	q‖	NOUN
ma-198	246	8	≤	≤	ADV
ma-198	246	9	α2	α2	PROPN
ma-198	246	10	n‖γf	n‖γf	PROPN
ma-198	246	11	(	(	PUNCT
ma-198	246	12	xn)−	xn)−	NOUN
ma-198	246	13	ηbq‖2	ηbq‖2	X
ma-198	246	14	+	+	CCONJ
ma-198	247	1	(	(	PUNCT
ma-198	247	2	1−	1−	NUM
ma-198	247	3	ταn)2‖δn	ταn)2‖δn	NUM
ma-198	247	4	−	−	PROPN
ma-198	247	5	q‖2	q‖2	PROPN
ma-198	247	6	−	−	PROPN
ma-198	247	7	(	(	PUNCT
ma-198	247	8	1−	1−	NUM
ma-198	247	9	ταn)2(1−	ταn)2(1−	PROPN
ma-198	247	10	θn)(θn	θn)(θn	PUNCT
ma-198	247	11	−	−	PROPN
ma-198	247	12	β)‖vn	β)‖vn	PUNCT
ma-198	247	13	−	−	PROPN
ma-198	248	1	δn‖2	δn‖2	INTJ
ma-198	248	2	−	−	PROPN
ma-198	248	3	(	(	PUNCT
ma-198	248	4	1−	1−	NUM
ma-198	248	5	ταn)2(1−	ταn)2(1−	PROPN
ma-198	248	6	βn)(βn	βn)(βn	PUNCT
ma-198	248	7	−	−	PROPN
ma-198	248	8	β)‖un	β)‖un	PUNCT
ma-198	249	1	−	−	PUNCT
ma-198	249	2	yn‖2	yn‖2	PROPN
ma-198	249	3	+	+	CCONJ
ma-198	250	1	2αn(1−	2αn(1−	NUM
ma-198	250	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	250	3	(	(	PUNCT
ma-198	250	4	xn)−	xn)−	PROPN
ma-198	250	5	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	250	6	−	−	PROPN
ma-198	250	7	q‖	q‖	NOUN
ma-198	250	8	≤	≤	ADV
ma-198	250	9	α2	α2	PROPN
ma-198	250	10	n‖γf	n‖γf	PROPN
ma-198	250	11	(	(	PUNCT
ma-198	250	12	xn)−	xn)−	NOUN
ma-198	250	13	ηbq‖2	ηbq‖2	X
ma-198	251	1	+	+	CCONJ
ma-198	251	2	(	(	PUNCT
ma-198	251	3	1−	1−	NUM
ma-198	251	4	ταn)2‖xn	ταn)2‖xn	SYM
ma-198	251	5	−	−	PROPN
ma-198	251	6	q‖2	q‖2	PROPN
ma-198	251	7	−	−	PROPN
ma-198	251	8	(	(	PUNCT
ma-198	251	9	1−	1−	NUM
ma-198	251	10	ταn)2(1−	ταn)2(1−	PROPN
ma-198	251	11	θn)(θn	θn)(θn	PUNCT
ma-198	251	12	−	−	PROPN
ma-198	251	13	β)‖vn	β)‖vn	PUNCT
ma-198	251	14	−	−	PROPN
ma-198	251	15	δn‖2	δn‖2	INTJ
ma-198	251	16	−	−	PROPN
ma-198	251	17	(	(	PUNCT
ma-198	251	18	1−	1−	NUM
ma-198	251	19	ταn)2(1−	ταn)2(1−	PROPN
ma-198	251	20	βn)(βn	βn)(βn	PUNCT
ma-198	251	21	−	−	PROPN
ma-198	251	22	β)‖un	β)‖un	PUNCT
ma-198	252	1	−	−	PUNCT
ma-198	252	2	yn‖2	yn‖2	PROPN
ma-198	252	3	+	+	CCONJ
ma-198	253	1	2αn(1−	2αn(1−	NUM
ma-198	253	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	253	3	(	(	PUNCT
ma-198	253	4	xn)−	xn)−	PROPN
ma-198	253	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	253	6	−	−	PROPN
ma-198	253	7	q‖	q‖	NOUN
ma-198	253	8	≤	≤	SCONJ
ma-198	253	9	‖xn	‖xn	PROPN
ma-198	253	10	−	−	PROPN
ma-198	253	11	q‖2	q‖2	PROPN
ma-198	253	12	+	+	CCONJ
ma-198	253	13	α2	α2	ADJ
ma-198	253	14	n‖γf	n‖γf	PROPN
ma-198	253	15	(	(	PUNCT
ma-198	253	16	xn)−	xn)−	PROPN
ma-198	253	17	ηbq‖2	ηbq‖2	ADP
ma-198	253	18	−	−	PROPN
ma-198	254	1	αn(2τ	αn(2τ	PROPN
ma-198	254	2	−	−	PROPN
ma-198	254	3	τ2αn)‖xn	τ2αn)‖xn	PROPN
ma-198	254	4	−	−	PROPN
ma-198	254	5	q‖2	q‖2	PROPN
ma-198	254	6	−	−	PROPN
ma-198	254	7	(	(	PUNCT
ma-198	254	8	1−	1−	NUM
ma-198	254	9	ταn)2(1−	ταn)2(1−	PROPN
ma-198	254	10	θn)(θn	θn)(θn	PUNCT
ma-198	254	11	−	−	PROPN
ma-198	254	12	β)‖vn	β)‖vn	PUNCT
ma-198	254	13	−	−	PROPN
ma-198	255	1	δn‖2	δn‖2	INTJ
ma-198	255	2	−	−	PROPN
ma-198	255	3	(	(	PUNCT
ma-198	255	4	1−	1−	NUM
ma-198	255	5	ταn)2(1−	ταn)2(1−	PROPN
ma-198	255	6	βn)(βn	βn)(βn	PUNCT
ma-198	255	7	−	−	PROPN
ma-198	255	8	β)‖un	β)‖un	PUNCT
ma-198	256	1	−	−	PUNCT
ma-198	256	2	yn‖2	yn‖2	PROPN
ma-198	256	3	+	+	CCONJ
ma-198	257	1	2αn(1−	2αn(1−	NUM
ma-198	257	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	257	3	(	(	PUNCT
ma-198	257	4	xn)−	xn)−	PROPN
ma-198	257	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	257	6	−	−	PROPN
ma-198	258	1	q‖	q‖	NOUN
ma-198	258	2	therefore	therefore	ADV
ma-198	258	3	(	(	PUNCT
ma-198	258	4	1−	1−	NUM
ma-198	258	5	ταn)2	ταn)2	PROPN
ma-198	258	6	[	[	PUNCT
ma-198	258	7	(	(	PUNCT
ma-198	258	8	1−	1−	NUM
ma-198	258	9	θn)(θn	θn)(θn	SYM
ma-198	258	10	−	−	PROPN
ma-198	258	11	β)‖vn	β)‖vn	PUNCT
ma-198	258	12	−	−	PROPN
ma-198	259	1	δn‖2	δn‖2	X
ma-198	259	2	+	+	CCONJ
ma-198	259	3	(	(	PUNCT
ma-198	259	4	1−	1−	NUM
ma-198	259	5	βn)(βn	βn)(βn	PUNCT
ma-198	259	6	−	−	PROPN
ma-198	259	7	β)‖un	β)‖un	PUNCT
ma-198	259	8	−	−	PUNCT
ma-198	259	9	yn‖2	yn‖2	PROPN
ma-198	259	10	]	]	PUNCT
ma-198	259	11	≤	≤	NUM
ma-198	259	12	‖xn	‖xn	PROPN
ma-198	259	13	−	−	PROPN
ma-198	259	14	q‖2	q‖2	PROPN
ma-198	259	15	−	−	PROPN
ma-198	259	16	‖xn+1	‖xn+1	NUM
ma-198	259	17	−	−	PROPN
ma-198	260	1	q‖2	q‖2	VERB
ma-198	260	2	−	−	PROPN
ma-198	260	3	αn(2τ	αn(2τ	NOUN
ma-198	260	4	−	−	PROPN
ma-198	260	5	τ2αn)‖xn	τ2αn)‖xn	PROPN
ma-198	260	6	−	−	PROPN
ma-198	260	7	q‖2	q‖2	PROPN
ma-198	260	8	+	+	CCONJ
ma-198	261	1	2αn(1−	2αn(1−	NUM
ma-198	261	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	261	3	(	(	PUNCT
ma-198	261	4	xn)−	xn)−	PROPN
ma-198	261	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	262	1	−	−	PROPN
ma-198	263	1	q‖	q‖	PROPN
ma-198	263	2	+	+	CCONJ
ma-198	263	3	α2	α2	ADJ
ma-198	263	4	n‖γf	n‖γf	PROPN
ma-198	263	5	(	(	PUNCT
ma-198	263	6	xn)−	xn)−	NOUN
ma-198	263	7	ηbq‖2	ηbq‖2	ADP
ma-198	263	8	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	263	9	eur	eur	NOUN
ma-198	263	10	.	.	PUNCT
ma-198	264	1	j.	j.	PROPN
ma-198	264	2	math	math	PROPN
ma-198	264	3	.	.	PUNCT
ma-198	265	1	anal	anal	PROPN
ma-198	265	2	.	.	PUNCT
ma-198	266	1	10.28924	10.28924	NUM
ma-198	266	2	/	/	SYM
ma-198	266	3	ada	ada	PROPN
ma-198	266	4	/	/	SYM
ma-198	266	5	ma.4.2	ma.4.2	PROPN
ma-198	266	6	12due	12due	NOUN
ma-198	266	7	to	to	ADP
ma-198	266	8	the	the	DET
ma-198	266	9	boundedness	boundedness	NOUN
ma-198	266	10	of	of	ADP
ma-198	266	11	{	{	PUNCT
ma-198	266	12	f	f	PROPN
ma-198	266	13	(	(	PUNCT
ma-198	266	14	xn	xn	PROPN
ma-198	266	15	)	)	PUNCT
ma-198	266	16	}	}	PUNCT
ma-198	266	17	and	and	CCONJ
ma-198	266	18	{	{	PUNCT
ma-198	266	19	xn	xn	NOUN
ma-198	266	20	}	}	PUNCT
ma-198	266	21	,	,	PUNCT
ma-198	266	22	and	and	CCONJ
ma-198	266	23	for	for	ADP
ma-198	266	24	some	some	PRON
ma-198	266	25	constant	constant	ADJ
ma-198	266	26	m	m	NOUN
ma-198	266	27	>	>	X
ma-198	266	28	0	0	NUM
ma-198	266	29	,	,	PUNCT
ma-198	266	30	we	we	PRON
ma-198	266	31	have	have	VERB
ma-198	266	32	(	(	PUNCT
ma-198	266	33	1−	1−	NUM
ma-198	266	34	ταn)2	ταn)2	PROPN
ma-198	266	35	[	[	PUNCT
ma-198	266	36	(	(	PUNCT
ma-198	266	37	1−	1−	NUM
ma-198	266	38	θn)(θn	θn)(θn	SYM
ma-198	266	39	−	−	PROPN
ma-198	266	40	β)‖vn	β)‖vn	PUNCT
ma-198	266	41	−	−	PROPN
ma-198	267	1	δn‖2	δn‖2	X
ma-198	267	2	+	+	CCONJ
ma-198	267	3	(	(	PUNCT
ma-198	267	4	1−	1−	NUM
ma-198	267	5	βn)(βn	βn)(βn	PUNCT
ma-198	267	6	−	−	PROPN
ma-198	267	7	β)‖un	β)‖un	PUNCT
ma-198	267	8	−	−	PUNCT
ma-198	267	9	yn‖2	yn‖2	PROPN
ma-198	267	10	]	]	PUNCT
ma-198	267	11	≤	≤	NUM
ma-198	267	12	‖xn	‖xn	PROPN
ma-198	267	13	−	−	PROPN
ma-198	267	14	q‖2	q‖2	PROPN
ma-198	267	15	−	−	PROPN
ma-198	267	16	‖xn+1	‖xn+1	NUM
ma-198	267	17	−	−	PROPN
ma-198	268	1	q‖2	q‖2	NOUN
ma-198	268	2	+	+	NUM
ma-198	268	3	αnm	αnm	NOUN
ma-198	268	4	(	(	PUNCT
ma-198	268	5	3.11	3.11	NUM
ma-198	268	6	)	)	PUNCT
ma-198	268	7	we	we	PRON
ma-198	268	8	now	now	ADV
ma-198	268	9	show	show	VERB
ma-198	268	10	that	that	SCONJ
ma-198	268	11	xn	xn	PROPN
ma-198	269	1	→	→	SYM
ma-198	269	2	x	x	X
ma-198	269	3	.	.	PUNCT
ma-198	270	1	we	we	PRON
ma-198	270	2	then	then	ADV
ma-198	270	3	consider	consider	VERB
ma-198	270	4	two	two	NUM
ma-198	270	5	cases	case	NOUN
ma-198	270	6	.	.	PUNCT
ma-198	271	1	case	case	NOUN
ma-198	271	2	1	1	NUM
ma-198	271	3	:	:	PUNCT
ma-198	271	4	assuming	assume	VERB
ma-198	271	5	that	that	SCONJ
ma-198	271	6	the	the	DET
ma-198	271	7	sequence	sequence	NOUN
ma-198	271	8	{	{	PUNCT
ma-198	271	9	‖xn−q‖	‖xn−q‖	PROPN
ma-198	271	10	}	}	PUNCT
ma-198	271	11	is	be	AUX
ma-198	271	12	monotonically	monotonically	ADV
ma-198	271	13	decreasing	decrease	VERB
ma-198	271	14	.	.	PUNCT
ma-198	272	1	then	then	ADV
ma-198	272	2	{	{	PUNCT
ma-198	272	3	‖xn−q‖}must	‖xn−q‖}must	X
ma-198	272	4	be	be	AUX
ma-198	272	5	a	a	DET
ma-198	272	6	convergent	convergent	NOUN
ma-198	272	7	sequence	sequence	NOUN
ma-198	272	8	.	.	PUNCT
ma-198	273	1	therefore	therefore	ADV
ma-198	273	2	,	,	PUNCT
ma-198	273	3	we	we	PRON
ma-198	273	4	have	have	VERB
ma-198	273	5	lim	lim	PROPN
ma-198	273	6	n→∞	n→∞	X
ma-198	274	1	[	[	X
ma-198	274	2	‖xn	‖xn	PROPN
ma-198	274	3	−	−	PROPN
ma-198	274	4	q‖2	q‖2	PROPN
ma-198	274	5	−	−	PROPN
ma-198	274	6	‖xn+1	‖xn+1	NOUN
ma-198	274	7	−	−	NOUN
ma-198	274	8	q‖2	q‖2	NOUN
ma-198	274	9	]	]	X
ma-198	274	10	=	=	SYM
ma-198	274	11	0	0	NUM
ma-198	274	12	,	,	PUNCT
ma-198	274	13	(	(	PUNCT
ma-198	274	14	3.12	3.12	NUM
ma-198	274	15	)	)	PUNCT
ma-198	274	16	this	this	PRON
ma-198	274	17	implies	imply	VERB
ma-198	274	18	that	that	SCONJ
ma-198	274	19	from	from	ADP
ma-198	274	20	(	(	PUNCT
ma-198	274	21	3.11	3.11	NUM
ma-198	274	22	)	)	PUNCT
ma-198	274	23	,	,	PUNCT
ma-198	275	1	that	that	SCONJ
ma-198	275	2	lim	lim	PROPN
ma-198	275	3	n→∞	n→∞	X
ma-198	275	4	(	(	PUNCT
ma-198	275	5	1−	1−	NUM
ma-198	275	6	θn)(θn	θn)(θn	SYM
ma-198	275	7	−	−	PROPN
ma-198	275	8	β)‖vn	β)‖vn	PUNCT
ma-198	275	9	−	−	PROPN
ma-198	276	1	δn‖2	δn‖2	PROPN
ma-198	276	2	=	=	SYM
ma-198	276	3	0	0	NUM
ma-198	276	4	(	(	PUNCT
ma-198	276	5	3.13	3.13	NUM
ma-198	276	6	)	)	PUNCT
ma-198	276	7	and	and	CCONJ
ma-198	276	8	lim	lim	PROPN
ma-198	276	9	n→∞	n→∞	X
ma-198	276	10	(	(	PUNCT
ma-198	276	11	1−	1−	NUM
ma-198	276	12	βn)(βn	βn)(βn	PUNCT
ma-198	276	13	−	−	PROPN
ma-198	276	14	β)‖un	β)‖un	PUNCT
ma-198	277	1	−	−	PUNCT
ma-198	277	2	yn‖2	yn‖2	PROPN
ma-198	277	3	=	=	SYM
ma-198	277	4	0	0	NUM
ma-198	277	5	(	(	PUNCT
ma-198	277	6	3.14	3.14	NUM
ma-198	277	7	)	)	PUNCT
ma-198	277	8	since	since	SCONJ
ma-198	277	9	lim	lim	PROPN
ma-198	277	10	n→∞	n→∞	NUM
ma-198	277	11	inf(1	inf(1	NOUN
ma-198	277	12	−	−	PROPN
ma-198	277	13	θn)(θn	θn)(θn	ADP
ma-198	277	14	−	−	PROPN
ma-198	277	15	β	β	X
ma-198	277	16	)	)	PUNCT
ma-198	277	17	>	>	X
ma-198	277	18	0	0	PUNCT
ma-198	278	1	and	and	CCONJ
ma-198	278	2	lim	lim	PROPN
ma-198	278	3	n→∞	n→∞	NUM
ma-198	278	4	inf(1	inf(1	NOUN
ma-198	278	5	−	−	PROPN
ma-198	278	6	βn)(βn	βn)(βn	PUNCT
ma-198	278	7	−	−	PROPN
ma-198	278	8	β	β	X
ma-198	278	9	)	)	PUNCT
ma-198	278	10	>	>	X
ma-198	278	11	0	0	NUM
ma-198	278	12	,	,	PUNCT
ma-198	278	13	with	with	ADP
ma-198	278	14	the	the	DET
ma-198	278	15	fact	fact	NOUN
ma-198	278	16	that	that	SCONJ
ma-198	278	17	vn	vn	PROPN
ma-198	278	18	∈	∈	PROPN
ma-198	278	19	t1δn	t1δn	PUNCT
ma-198	278	20	and	and	CCONJ
ma-198	278	21	un	un	PROPN
ma-198	278	22	∈	∈	PROPN
ma-198	278	23	t2yn	t2yn	NUM
ma-198	278	24	,	,	PUNCT
ma-198	278	25	it	it	PRON
ma-198	278	26	follows	follow	VERB
ma-198	278	27	that	that	SCONJ
ma-198	278	28	lim	lim	PROPN
ma-198	278	29	n→∞	n→∞	X
ma-198	278	30	d(δn	d(δn	PROPN
ma-198	278	31	,	,	PUNCT
ma-198	278	32	t1δn	t1δn	PUNCT
ma-198	278	33	)	)	PUNCT
ma-198	278	34	=	=	SYM
ma-198	278	35	0	0	PUNCT
ma-198	278	36	(	(	PUNCT
ma-198	278	37	3.15	3.15	NUM
ma-198	278	38	)	)	PUNCT
ma-198	278	39	and	and	CCONJ
ma-198	278	40	lim	lim	PROPN
ma-198	278	41	n→∞	n→∞	X
ma-198	278	42	d(yn	d(yn	PROPN
ma-198	278	43	,	,	PUNCT
ma-198	278	44	t2yn	t2yn	NUM
ma-198	278	45	)	)	PUNCT
ma-198	278	46	=	=	SYM
ma-198	278	47	0	0	PUNCT
ma-198	279	1	(	(	PUNCT
ma-198	279	2	3.16	3.16	NUM
ma-198	279	3	)	)	PUNCT
ma-198	279	4	observing	observe	VERB
ma-198	279	5	that	that	SCONJ
ma-198	279	6	‖yn	‖yn	PROPN
ma-198	279	7	−	−	PROPN
ma-198	279	8	δn‖	δn‖	NOUN
ma-198	279	9	=	=	SYM
ma-198	279	10	‖θnδn	‖θnδn	NOUN
ma-198	280	1	+	+	CCONJ
ma-198	280	2	(	(	PUNCT
ma-198	280	3	1−	1−	NUM
ma-198	280	4	θn)vn	θn)vn	ADP
ma-198	280	5	−	−	NOUN
ma-198	280	6	δn‖	δn‖	NOUN
ma-198	280	7	=	=	PUNCT
ma-198	280	8	‖θnδn	‖θnδn	NOUN
ma-198	281	1	+	+	CCONJ
ma-198	281	2	(	(	PUNCT
ma-198	281	3	1−	1−	NUM
ma-198	281	4	θn)vn	θn)vn	SYM
ma-198	281	5	−	−	PROPN
ma-198	281	6	δn	δn	NOUN
ma-198	281	7	+	+	CCONJ
ma-198	281	8	θnδn	θnδn	PROPN
ma-198	281	9	−	−	PROPN
ma-198	281	10	θnδn‖	θnδn‖	X
ma-198	281	11	=	=	PRON
ma-198	282	1	(	(	PUNCT
ma-198	282	2	1−	1−	NUM
ma-198	282	3	θn)‖vn	θn)‖vn	NOUN
ma-198	282	4	−	−	NUM
ma-198	282	5	δn‖	δn‖	PROPN
ma-198	282	6	≤	≤	PUNCT
ma-198	283	1	‖vn	‖vn	PROPN
ma-198	283	2	−	−	PROPN
ma-198	283	3	δn‖	δn‖	PROPN
ma-198	283	4	(	(	PUNCT
ma-198	283	5	3.17	3.17	NUM
ma-198	283	6	)	)	PUNCT
ma-198	283	7	taking	take	VERB
ma-198	283	8	the	the	DET
ma-198	283	9	limits	limit	NOUN
ma-198	283	10	and	and	CCONJ
ma-198	283	11	from	from	ADP
ma-198	283	12	(	(	PUNCT
ma-198	283	13	3.13	3.13	NUM
ma-198	283	14	)	)	PUNCT
ma-198	283	15	,	,	PUNCT
ma-198	283	16	we	we	PRON
ma-198	283	17	can	can	AUX
ma-198	283	18	see	see	VERB
ma-198	283	19	that	that	SCONJ
ma-198	283	20	lim	lim	PROPN
ma-198	283	21	n→∞	n→∞	X
ma-198	284	1	‖yn	‖yn	PROPN
ma-198	284	2	−	−	PROPN
ma-198	284	3	δn‖	δn‖	PROPN
ma-198	284	4	=	=	SYM
ma-198	284	5	0	0	NUM
ma-198	284	6	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	284	7	eur	eur	NOUN
ma-198	284	8	.	.	PUNCT
ma-198	285	1	j.	j.	PROPN
ma-198	285	2	math	math	PROPN
ma-198	285	3	.	.	PUNCT
ma-198	286	1	anal	anal	PROPN
ma-198	286	2	.	.	PUNCT
ma-198	287	1	10.28924	10.28924	NUM
ma-198	287	2	/	/	SYM
ma-198	287	3	ada	ada	PROPN
ma-198	287	4	/	/	SYM
ma-198	287	5	ma.4.2	ma.4.2	PROPN
ma-198	287	6	13	13	NUM
ma-198	287	7	‖zn	‖zn	NUM
ma-198	287	8	−	−	NOUN
ma-198	287	9	yn‖	yn‖	NOUN
ma-198	287	10	=	=	PUNCT
ma-198	287	11	‖βnyn	‖βnyn	PROPN
ma-198	287	12	+	+	CCONJ
ma-198	287	13	(	(	PUNCT
ma-198	287	14	1−	1−	NUM
ma-198	287	15	βn)un	βn)un	PUNCT
ma-198	287	16	−	−	NOUN
ma-198	287	17	yn‖	yn‖	NOUN
ma-198	287	18	=	=	PUNCT
ma-198	287	19	‖βnyn	‖βnyn	PROPN
ma-198	287	20	+	+	CCONJ
ma-198	287	21	(	(	PUNCT
ma-198	287	22	1−	1−	NUM
ma-198	287	23	βn)un	βn)un	SYM
ma-198	287	24	−	−	PROPN
ma-198	287	25	yn	yn	PROPN
ma-198	287	26	+	+	NUM
ma-198	287	27	βnyn	βnyn	PROPN
ma-198	287	28	−	−	PROPN
ma-198	287	29	βnyn‖	βnyn‖	PROPN
ma-198	287	30	=	=	PUNCT
ma-198	287	31	(	(	PUNCT
ma-198	287	32	1−	1−	NUM
ma-198	287	33	βn)‖un	βn)‖un	ADP
ma-198	287	34	−	−	NOUN
ma-198	288	1	yn‖	yn‖	PROPN
ma-198	288	2	≤	≤	PROPN
ma-198	288	3	‖un	‖un	PROPN
ma-198	288	4	−	−	PROPN
ma-198	288	5	yn‖	yn‖	NOUN
ma-198	288	6	(	(	PUNCT
ma-198	288	7	3.18	3.18	NUM
ma-198	288	8	)	)	PUNCT
ma-198	288	9	again	again	ADV
ma-198	288	10	,	,	PUNCT
ma-198	288	11	from	from	ADP
ma-198	288	12	(	(	PUNCT
ma-198	288	13	3.14	3.14	NUM
ma-198	288	14	)	)	PUNCT
ma-198	288	15	,	,	PUNCT
ma-198	288	16	we	we	PRON
ma-198	288	17	can	can	AUX
ma-198	288	18	see	see	VERB
ma-198	288	19	that	that	SCONJ
ma-198	288	20	lim	lim	PROPN
ma-198	288	21	n→∞	n→∞	PRON
ma-198	289	1	‖zn	‖zn	NUM
ma-198	289	2	−	−	NOUN
ma-198	289	3	yn‖	yn‖	NOUN
ma-198	289	4	=	=	NOUN
ma-198	289	5	0	0	PUNCT
ma-198	290	1	‖zn	‖zn	NUM
ma-198	290	2	−	−	NOUN
ma-198	290	3	δn‖	δn‖	NOUN
ma-198	290	4	=	=	PUNCT
ma-198	291	1	‖zn	‖zn	NUM
ma-198	291	2	−	−	PROPN
ma-198	292	1	yn	yn	PROPN
ma-198	292	2	+	+	CCONJ
ma-198	292	3	yn	yn	PROPN
ma-198	292	4	−	−	PROPN
ma-198	292	5	δn‖	δn‖	PROPN
ma-198	292	6	≤	≤	NOUN
ma-198	293	1	‖zn	‖zn	NUM
ma-198	293	2	−	−	PROPN
ma-198	293	3	yn‖+	yn‖+	PROPN
ma-198	293	4	‖yn	‖yn	PROPN
ma-198	293	5	−	−	PROPN
ma-198	293	6	δn‖	δn‖	PROPN
ma-198	293	7	hence	hence	ADV
ma-198	293	8	lim	lim	PROPN
ma-198	293	9	n→∞	n→∞	X
ma-198	294	1	‖zn	‖zn	NUM
ma-198	294	2	−	−	PROPN
ma-198	294	3	δn‖	δn‖	PROPN
ma-198	294	4	=	=	SYM
ma-198	294	5	0now	0now	PROPN
ma-198	294	6	from	from	ADP
ma-198	294	7	lemma	lemma	PROPN
ma-198	294	8	(	(	PUNCT
ma-198	294	9	2.2	2.2	NUM
ma-198	294	10	)	)	PUNCT
ma-198	294	11	,	,	PUNCT
ma-198	294	12	lemma	lemma	PROPN
ma-198	294	13	(	(	PUNCT
ma-198	294	14	2.4	2.4	NUM
ma-198	294	15	)	)	PUNCT
ma-198	294	16	and	and	CCONJ
ma-198	294	17	(	(	PUNCT
ma-198	294	18	3.1	3.1	NUM
ma-198	294	19	)	)	PUNCT
ma-198	294	20	,	,	PUNCT
ma-198	294	21	we	we	PRON
ma-198	294	22	have	have	VERB
ma-198	294	23	the	the	DET
ma-198	294	24	following	follow	VERB
ma-198	294	25	‖xn+1	‖xn+1	PUNCT
ma-198	294	26	−	−	PROPN
ma-198	294	27	q‖2	q‖2	VERB
ma-198	294	28	≤	≤	ADJ
ma-198	294	29	‖αn(γf	‖αn(γf	NOUN
ma-198	294	30	(	(	PUNCT
ma-198	294	31	xn)−	xn)−	NOUN
ma-198	294	32	ηbq	ηbq	ADV
ma-198	294	33	)	)	PUNCT
ma-198	295	1	+	+	CCONJ
ma-198	295	2	(	(	PUNCT
ma-198	295	3	i	i	PRON
ma-198	295	4	−	−	PROPN
ma-198	295	5	ηαnb)(tn	ηαnb)(tn	PROPN
ma-198	295	6	−	−	PROPN
ma-198	295	7	q)‖2	q)‖2	NOUN
ma-198	295	8	≤	≤	ADV
ma-198	295	9	α2	α2	VERB
ma-198	295	10	n‖γf	n‖γf	PROPN
ma-198	295	11	(	(	PUNCT
ma-198	295	12	xn)−	xn)−	PUNCT
ma-198	295	13	ηb‖2	ηb‖2	PROPN
ma-198	295	14	+	+	CCONJ
ma-198	295	15	(	(	PUNCT
ma-198	295	16	1−	1−	NUM
ma-198	295	17	τα)2‖tn	τα)2‖tn	NOUN
ma-198	295	18	−	−	PROPN
ma-198	295	19	q‖2	q‖2	VERB
ma-198	295	20	+	+	CCONJ
ma-198	295	21	2αn(1−	2αn(1−	NUM
ma-198	295	22	ταn)‖γf	ταn)‖γf	NUM
ma-198	295	23	(	(	PUNCT
ma-198	295	24	xn)−	xn)−	PROPN
ma-198	295	25	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	295	26	−	−	PROPN
ma-198	295	27	q‖	q‖	NOUN
ma-198	295	28	≤	≤	ADV
ma-198	295	29	α2	α2	PROPN
ma-198	295	30	n‖γf	n‖γf	PROPN
ma-198	295	31	(	(	PUNCT
ma-198	295	32	xn)−	xn)−	PUNCT
ma-198	295	33	ηb‖2	ηb‖2	PROPN
ma-198	295	34	+	+	CCONJ
ma-198	295	35	(	(	PUNCT
ma-198	295	36	1−	1−	NUM
ma-198	295	37	ταn)2‖δn	ταn)2‖δn	NUM
ma-198	295	38	−	−	PROPN
ma-198	295	39	q‖2	q‖2	PROPN
ma-198	296	1	+	+	CCONJ
ma-198	296	2	2αn(1−	2αn(1−	NUM
ma-198	296	3	ταn)‖γf	ταn)‖γf	NUM
ma-198	296	4	(	(	PUNCT
ma-198	296	5	xn)−	xn)−	PROPN
ma-198	296	6	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	296	7	−	−	PROPN
ma-198	296	8	q‖	q‖	NOUN
ma-198	296	9	≤	≤	ADV
ma-198	296	10	α2	α2	PROPN
ma-198	296	11	n‖γf	n‖γf	PROPN
ma-198	296	12	(	(	PUNCT
ma-198	296	13	xn)−	xn)−	PUNCT
ma-198	296	14	ηb‖2	ηb‖2	PROPN
ma-198	296	15	+	+	CCONJ
ma-198	296	16	(	(	PUNCT
ma-198	296	17	1−	1−	NUM
ma-198	296	18	ταn)2‖jmλn(1−	ταn)2‖jmλn(1−	PUNCT
ma-198	296	19	λa)xn	λa)xn	PRON
ma-198	297	1	−	−	PROPN
ma-198	297	2	jmλn(1−	jmλn(1−	PROPN
ma-198	297	3	λa)q‖2	λa)q‖2	X
ma-198	297	4	+	+	CCONJ
ma-198	298	1	2αn(1−	2αn(1−	NUM
ma-198	298	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	298	3	(	(	PUNCT
ma-198	298	4	xn)−	xn)−	PROPN
ma-198	298	5	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	298	6	−	−	PROPN
ma-198	298	7	q‖	q‖	NOUN
ma-198	298	8	≤	≤	ADV
ma-198	298	9	α2	α2	PROPN
ma-198	298	10	n‖γf	n‖γf	PROPN
ma-198	298	11	(	(	PUNCT
ma-198	298	12	xn)−	xn)−	PUNCT
ma-198	298	13	ηb‖2	ηb‖2	PROPN
ma-198	298	14	+	+	CCONJ
ma-198	298	15	(	(	PUNCT
ma-198	298	16	1−	1−	NUM
ma-198	298	17	ταn)2	ταn)2	PROPN
ma-198	298	18	[	[	PUNCT
ma-198	298	19	‖xn	‖xn	PROPN
ma-198	298	20	−	−	PROPN
ma-198	298	21	q‖2	q‖2	NOUN
ma-198	298	22	+	+	CCONJ
ma-198	298	23	a(b	a(b	ADP
ma-198	298	24	−	−	PROPN
ma-198	298	25	2α)‖axn	2α)‖axn	NUM
ma-198	298	26	−	−	PROPN
ma-198	298	27	aq‖2	aq‖2	VERB
ma-198	298	28	]	]	PUNCT
ma-198	299	1	+	+	CCONJ
ma-198	299	2	2αn(1−	2αn(1−	NUM
ma-198	299	3	ταn)‖γf	ταn)‖γf	NUM
ma-198	299	4	(	(	PUNCT
ma-198	299	5	xn)−	xn)−	PROPN
ma-198	299	6	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	299	7	−	−	PROPN
ma-198	299	8	q‖	q‖	PROPN
ma-198	299	9	≤	≤	ADV
ma-198	299	10	α2	α2	PROPN
ma-198	299	11	n‖γf	n‖γf	PROPN
ma-198	299	12	(	(	PUNCT
ma-198	299	13	xn)−	xn)−	PUNCT
ma-198	299	14	ηb‖2	ηb‖2	PROPN
ma-198	299	15	+	+	SYM
ma-198	299	16	‖xn	‖xn	PROPN
ma-198	299	17	−	−	PROPN
ma-198	299	18	q‖2	q‖2	PROPN
ma-198	299	19	−	−	PROPN
ma-198	299	20	αn(2τ	αn(2τ	NOUN
ma-198	299	21	−	−	PROPN
ma-198	299	22	τ2αn)‖xn	τ2αn)‖xn	PROPN
ma-198	299	23	−	−	PROPN
ma-198	300	1	q‖2	q‖2	PROPN
ma-198	301	1	−	−	PROPN
ma-198	302	1	(	(	PUNCT
ma-198	302	2	1−	1−	NUM
ma-198	302	3	τα)2a(2α−	τα)2a(2α−	PUNCT
ma-198	302	4	b)‖axn	b)‖axn	PROPN
ma-198	302	5	−	−	PROPN
ma-198	302	6	aq‖2	aq‖2	PROPN
ma-198	302	7	(	(	PUNCT
ma-198	302	8	3.19	3.19	NUM
ma-198	302	9	)	)	PUNCT
ma-198	302	10	+	+	CCONJ
ma-198	303	1	2αn(1−	2αn(1−	NUM
ma-198	303	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	303	3	(	(	PUNCT
ma-198	303	4	xn)−	xn)−	PROPN
ma-198	303	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	303	6	−	−	PROPN
ma-198	303	7	q‖	q‖	NOUN
ma-198	303	8	therefore	therefore	ADV
ma-198	303	9	,	,	PUNCT
ma-198	303	10	from	from	ADP
ma-198	303	11	(	(	PUNCT
ma-198	303	12	3.19),and	3.19),and	NUM
ma-198	303	13	with	with	ADP
ma-198	303	14	a	a	DET
ma-198	303	15	constant	constant	ADJ
ma-198	303	16	d	d	X
ma-198	303	17	>	>	X
ma-198	303	18	0	0	PROPN
ma-198	303	19	,	,	PUNCT
ma-198	303	20	we	we	PRON
ma-198	303	21	have	have	VERB
ma-198	303	22	(	(	PUNCT
ma-198	303	23	1−	1−	NUM
ma-198	303	24	τα)2a(2α−	τα)2a(2α−	PUNCT
ma-198	304	1	b)‖axn	b)‖axn	PROPN
ma-198	304	2	−	−	PROPN
ma-198	304	3	aq‖2	aq‖2	VERB
ma-198	304	4	≤	≤	ADJ
ma-198	304	5	‖xn	‖xn	PUNCT
ma-198	304	6	−	−	PUNCT
ma-198	304	7	q)‖2	q)‖2	NOUN
ma-198	304	8	−	−	NOUN
ma-198	304	9	‖xn+1	‖xn+1	NUM
ma-198	304	10	−	−	PROPN
ma-198	304	11	q)‖2	q)‖2	NOUN
ma-198	304	12	+	+	CCONJ
ma-198	304	13	αnd	αnd	NOUN
ma-198	304	14	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	ADJ
ma-198	304	15	eur	eur	NOUN
ma-198	304	16	.	.	PUNCT
ma-198	305	1	j.	j.	PROPN
ma-198	305	2	math	math	PROPN
ma-198	305	3	.	.	PUNCT
ma-198	306	1	anal	anal	PROPN
ma-198	306	2	.	.	PUNCT
ma-198	307	1	10.28924	10.28924	NUM
ma-198	307	2	/	/	SYM
ma-198	307	3	ada	ada	PROPN
ma-198	307	4	/	/	SYM
ma-198	307	5	ma.4.2	ma.4.2	PROPN
ma-198	307	6	14since	14since	NUM
ma-198	307	7	,	,	PUNCT
ma-198	307	8	lim	lim	PROPN
ma-198	307	9	n→∞	n→∞	NUM
ma-198	307	10	αn	αn	NOUN
ma-198	307	11	=	=	SYM
ma-198	307	12	0	0	NUM
ma-198	307	13	,	,	PUNCT
ma-198	307	14	and	and	CCONJ
ma-198	307	15	from	from	ADP
ma-198	307	16	the	the	DET
ma-198	307	17	inequality	inequality	NOUN
ma-198	307	18	(	(	PUNCT
ma-198	307	19	3.12	3.12	NUM
ma-198	307	20	)	)	PUNCT
ma-198	307	21	,	,	PUNCT
ma-198	307	22	with	with	ADP
ma-198	307	23	the	the	DET
ma-198	307	24	fact	fact	NOUN
ma-198	307	25	that	that	SCONJ
ma-198	307	26	{	{	PUNCT
ma-198	307	27	xn	xn	X
ma-198	307	28	}	}	PUNCT
ma-198	307	29	is	be	AUX
ma-198	307	30	bounded	bound	VERB
ma-198	307	31	,	,	PUNCT
ma-198	307	32	wehave	wehave	PROPN
ma-198	307	33	lim	lim	PROPN
ma-198	307	34	n→∞	n→∞	X
ma-198	308	1	‖axn	‖axn	PROPN
ma-198	308	2	−	−	PROPN
ma-198	308	3	aq‖2	aq‖2	PROPN
ma-198	308	4	=	=	SYM
ma-198	308	5	0	0	PUNCT
ma-198	308	6	(	(	PUNCT
ma-198	308	7	3.20	3.20	NUM
ma-198	308	8	)	)	PUNCT
ma-198	308	9	since	since	SCONJ
ma-198	308	10	jmλn	jmλn	PROPN
ma-198	308	11	is	be	AUX
ma-198	308	12	1−inverse	1−inverse	ADV
ma-198	308	13	strongly	strongly	ADV
ma-198	308	14	monotone	monotone	ADJ
ma-198	308	15	,	,	PUNCT
ma-198	308	16	and	and	CCONJ
ma-198	308	17	‖tn−q‖	‖tn−q‖	VERB
ma-198	308	18	≤	≤	ADJ
ma-198	308	19	‖δn−q‖	‖δn−q‖	NOUN
ma-198	308	20	,	,	PUNCT
ma-198	308	21	we	we	PRON
ma-198	308	22	have	have	VERB
ma-198	308	23	the	the	DET
ma-198	308	24	following	follow	VERB
ma-198	308	25	‖tn	‖tn	PROPN
ma-198	308	26	−	−	PROPN
ma-198	308	27	q‖2	q‖2	PROPN
ma-198	308	28	=	=	SYM
ma-198	308	29	‖j(m	‖j(m	PROPN
ma-198	308	30	)	)	PUNCT
ma-198	308	31	λn	λn	NOUN
ma-198	308	32	(	(	PUNCT
ma-198	308	33	i	i	PRON
ma-198	308	34	−	−	PROPN
ma-198	308	35	λna)xn	λna)xn	NOUN
ma-198	308	36	−	−	PROPN
ma-198	308	37	jmλn(i	jmλn(i	PROPN
ma-198	308	38	−	−	PROPN
ma-198	308	39	λna)q‖2	λna)q‖2	PUNCT
ma-198	308	40	≤	≤	PROPN
ma-198	308	41	〈	〈	PROPN
ma-198	308	42	tn	tn	PROPN
ma-198	308	43	−	−	PROPN
ma-198	308	44	q	q	NOUN
ma-198	308	45	,	,	PUNCT
ma-198	308	46	(	(	PUNCT
ma-198	308	47	i	i	PRON
ma-198	308	48	−	−	VERB
ma-198	308	49	λna)xn	λna)xn	NOUN
ma-198	308	50	−	−	PROPN
ma-198	309	1	(	(	PUNCT
ma-198	309	2	i	i	PRON
ma-198	309	3	−	−	VERB
ma-198	310	1	λna)q	λna)q	NOUN
ma-198	310	2	〉	〉	NOUN
ma-198	310	3	=	=	SYM
ma-198	310	4	1	1	NUM
ma-198	310	5	2	2	NUM
ma-198	310	6	[	[	PUNCT
ma-198	310	7	‖(i	‖(i	NOUN
ma-198	310	8	−	−	NOUN
ma-198	310	9	λna)xn	λna)xn	NOUN
ma-198	311	1	−	−	PROPN
ma-198	312	1	(	(	PUNCT
ma-198	312	2	i	i	PRON
ma-198	312	3	−	−	PROPN
ma-198	312	4	λna)q‖2	λna)q‖2	X
ma-198	313	1	+	+	CCONJ
ma-198	313	2	‖tn	‖tn	NUM
ma-198	313	3	−	−	NOUN
ma-198	313	4	q‖2	q‖2	VERB
ma-198	313	5	−	−	PROPN
ma-198	313	6	‖(i	‖(i	NOUN
ma-198	313	7	−	−	NOUN
ma-198	313	8	λna)xn	λna)xn	NOUN
ma-198	314	1	−	−	PROPN
ma-198	315	1	(	(	PUNCT
ma-198	315	2	i	i	PRON
ma-198	315	3	−	−	PROPN
ma-198	316	1	λna)q	λna)q	NOUN
ma-198	316	2	−	−	PROPN
ma-198	316	3	(	(	PUNCT
ma-198	316	4	tn	tn	NOUN
ma-198	316	5	−	−	PROPN
ma-198	316	6	q)‖2	q)‖2	NOUN
ma-198	316	7	]	]	PUNCT
ma-198	316	8	≤	≤	NUM
ma-198	316	9	1	1	NUM
ma-198	316	10	2	2	NUM
ma-198	316	11	[	[	PUNCT
ma-198	316	12	‖xn	‖xn	PROPN
ma-198	316	13	−	−	PROPN
ma-198	316	14	q‖2	q‖2	PROPN
ma-198	316	15	+	+	CCONJ
ma-198	317	1	‖tn	‖tn	NUM
ma-198	317	2	−	−	NOUN
ma-198	317	3	q‖2	q‖2	VERB
ma-198	317	4	−	−	PROPN
ma-198	317	5	‖xn	‖xn	PROPN
ma-198	317	6	−	−	PUNCT
ma-198	317	7	tn‖2	tn‖2	PROPN
ma-198	317	8	+	+	NOUN
ma-198	317	9	2λn〈tn	2λn〈tn	NUM
ma-198	317	10	−	−	NOUN
ma-198	318	1	q	q	NOUN
ma-198	318	2	,	,	PUNCT
ma-198	318	3	axn	axn	PROPN
ma-198	318	4	−	−	PROPN
ma-198	318	5	aq	aq	NOUN
ma-198	318	6	〉	〉	NOUN
ma-198	318	7	−	−	NOUN
ma-198	318	8	λ2	λ2	PROPN
ma-198	318	9	n‖axn	n‖axn	NUM
ma-198	318	10	−	−	NOUN
ma-198	318	11	a)q)‖2	a)q)‖2	NOUN
ma-198	318	12	]	]	PUNCT
ma-198	318	13	≤	≤	NUM
ma-198	318	14	‖xn	‖xn	PROPN
ma-198	318	15	−	−	PROPN
ma-198	318	16	q‖2	q‖2	PROPN
ma-198	318	17	−	−	PROPN
ma-198	318	18	‖xn	‖xn	PROPN
ma-198	318	19	−	−	PUNCT
ma-198	318	20	tn‖2	tn‖2	NOUN
ma-198	318	21	+	+	NOUN
ma-198	318	22	2λn〈xn	2λn〈xn	NUM
ma-198	318	23	−	−	NOUN
ma-198	319	1	q	q	NOUN
ma-198	319	2	,	,	PUNCT
ma-198	319	3	axn	axn	PROPN
ma-198	319	4	−	−	PROPN
ma-198	319	5	aq	aq	NOUN
ma-198	319	6	〉	〉	NOUN
ma-198	319	7	−	−	NOUN
ma-198	319	8	λ2	λ2	PROPN
ma-198	319	9	n‖axn	n‖axn	NUM
ma-198	319	10	−	−	PROPN
ma-198	319	11	aq‖2	aq‖2	PROPN
ma-198	319	12	this	this	PRON
ma-198	319	13	gives	give	VERB
ma-198	319	14	us	we	PRON
ma-198	319	15	‖tn	‖tn	PROPN
ma-198	319	16	−	−	NOUN
ma-198	319	17	q‖2	q‖2	VERB
ma-198	319	18	≤	≤	NUM
ma-198	319	19	‖xn	‖xn	PROPN
ma-198	319	20	−	−	PROPN
ma-198	319	21	q‖2	q‖2	PROPN
ma-198	319	22	−	−	PROPN
ma-198	319	23	‖xn	‖xn	PROPN
ma-198	319	24	−	−	PUNCT
ma-198	319	25	tn‖2	tn‖2	PROPN
ma-198	319	26	+	+	NOUN
ma-198	319	27	2λn〈tn	2λn〈tn	NUM
ma-198	319	28	−	−	NOUN
ma-198	320	1	q	q	NOUN
ma-198	320	2	,	,	PUNCT
ma-198	320	3	axn	axn	PROPN
ma-198	320	4	−	−	PROPN
ma-198	320	5	aq	aq	NOUN
ma-198	320	6	〉	〉	NOUN
ma-198	320	7	−	−	NOUN
ma-198	320	8	λ2	λ2	PROPN
ma-198	320	9	n‖axn	n‖axn	NUM
ma-198	320	10	−	−	PROPN
ma-198	320	11	aq‖2	aq‖2	PROPN
ma-198	320	12	(	(	PUNCT
ma-198	320	13	3.21	3.21	NUM
ma-198	320	14	)	)	PUNCT
ma-198	320	15	therefore	therefore	ADV
ma-198	320	16	‖xn+1	‖xn+1	NUM
ma-198	320	17	−	−	PROPN
ma-198	320	18	q‖2	q‖2	VERB
ma-198	320	19	≤	≤	ADJ
ma-198	320	20	‖αn(γf	‖αn(γf	NOUN
ma-198	320	21	(	(	PUNCT
ma-198	320	22	xn)−	xn)−	NOUN
ma-198	320	23	ηbq	ηbq	ADV
ma-198	320	24	)	)	PUNCT
ma-198	321	1	+	+	CCONJ
ma-198	321	2	(	(	PUNCT
ma-198	321	3	i	i	PRON
ma-198	321	4	−	−	PROPN
ma-198	321	5	ηαnb)(tn	ηαnb)(tn	PROPN
ma-198	321	6	−	−	PROPN
ma-198	321	7	q)‖2	q)‖2	NOUN
ma-198	321	8	≤	≤	ADV
ma-198	321	9	α2	α2	VERB
ma-198	321	10	n‖γf	n‖γf	PROPN
ma-198	321	11	(	(	PUNCT
ma-198	321	12	xn)−	xn)−	PUNCT
ma-198	321	13	ηb‖2	ηb‖2	PROPN
ma-198	321	14	+	+	CCONJ
ma-198	321	15	(	(	PUNCT
ma-198	321	16	1−	1−	NUM
ma-198	321	17	ταn)2‖tn	ταn)2‖tn	NOUN
ma-198	321	18	−	−	PROPN
ma-198	321	19	q‖2	q‖2	PROPN
ma-198	321	20	+	+	CCONJ
ma-198	321	21	2αn(1−	2αn(1−	NUM
ma-198	321	22	ταn)‖γf	ταn)‖γf	NUM
ma-198	321	23	(	(	PUNCT
ma-198	321	24	xn)−	xn)−	PROPN
ma-198	321	25	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	321	26	−	−	PROPN
ma-198	321	27	q‖	q‖	NOUN
ma-198	321	28	≤	≤	ADV
ma-198	321	29	α2	α2	PROPN
ma-198	321	30	n‖γf	n‖γf	PROPN
ma-198	321	31	(	(	PUNCT
ma-198	321	32	xn)−	xn)−	PUNCT
ma-198	321	33	ηb‖2	ηb‖2	PROPN
ma-198	321	34	+	+	CCONJ
ma-198	321	35	(	(	PUNCT
ma-198	321	36	1−	1−	NUM
ma-198	321	37	ταn)2	ταn)2	PROPN
ma-198	321	38	[	[	PUNCT
ma-198	321	39	‖xn	‖xn	PROPN
ma-198	321	40	−	−	PROPN
ma-198	321	41	q‖2	q‖2	VERB
ma-198	321	42	−	−	PROPN
ma-198	321	43	‖xn	‖xn	PROPN
ma-198	321	44	−	−	PUNCT
ma-198	321	45	tn‖2	tn‖2	PROPN
ma-198	321	46	+	+	NOUN
ma-198	321	47	2λn〈tn	2λn〈tn	NUM
ma-198	321	48	−	−	NOUN
ma-198	322	1	q	q	NOUN
ma-198	322	2	,	,	PUNCT
ma-198	322	3	axn	axn	PROPN
ma-198	322	4	−	−	PROPN
ma-198	322	5	aq	aq	NOUN
ma-198	322	6	〉	〉	NOUN
ma-198	322	7	−	−	NOUN
ma-198	322	8	λ2	λ2	PROPN
ma-198	322	9	n‖axn	n‖axn	NUM
ma-198	322	10	−	−	X
ma-198	322	11	aq‖2	aq‖2	PROPN
ma-198	322	12	]	]	PUNCT
ma-198	323	1	+	+	CCONJ
ma-198	323	2	2αn(1−	2αn(1−	NUM
ma-198	323	3	ταn)‖γf	ταn)‖γf	NUM
ma-198	323	4	(	(	PUNCT
ma-198	323	5	xn)−	xn)−	PROPN
ma-198	323	6	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	323	7	−	−	PROPN
ma-198	323	8	q‖	q‖	PROPN
ma-198	323	9	≤	≤	ADV
ma-198	323	10	α2	α2	PROPN
ma-198	323	11	n‖γf	n‖γf	PROPN
ma-198	323	12	(	(	PUNCT
ma-198	323	13	xn)−	xn)−	PUNCT
ma-198	323	14	ηb‖2	ηb‖2	PROPN
ma-198	323	15	+	+	CCONJ
ma-198	323	16	(	(	PUNCT
ma-198	323	17	1−	1−	NUM
ma-198	323	18	ταn)2‖xn	ταn)2‖xn	SYM
ma-198	323	19	−	−	PROPN
ma-198	323	20	q‖2	q‖2	PROPN
ma-198	323	21	−	−	PROPN
ma-198	323	22	(	(	PUNCT
ma-198	323	23	1−	1−	NUM
ma-198	323	24	ταn)2‖xn	ταn)2‖xn	INTJ
ma-198	323	25	−	−	PUNCT
ma-198	323	26	tn‖2	tn‖2	PROPN
ma-198	323	27	+	+	PROPN
ma-198	323	28	2λn(1−	2λn(1−	NUM
ma-198	323	29	ταn)2〈tn	ταn)2〈tn	SYM
ma-198	324	1	−	−	NOUN
ma-198	324	2	q	q	INTJ
ma-198	324	3	,	,	PUNCT
ma-198	324	4	axn	axn	PROPN
ma-198	324	5	−	−	PROPN
ma-198	324	6	aq	aq	NOUN
ma-198	324	7	〉	〉	NOUN
ma-198	324	8	−	−	PROPN
ma-198	324	9	λ2	λ2	PROPN
ma-198	324	10	n(1−	n(1−	PROPN
ma-198	324	11	ταn)2‖axn	ταn)2‖axn	NUM
ma-198	324	12	−	−	PROPN
ma-198	324	13	aq‖2	aq‖2	PROPN
ma-198	324	14	+	+	CCONJ
ma-198	325	1	2αn(1−	2αn(1−	NUM
ma-198	325	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	325	3	(	(	PUNCT
ma-198	325	4	xn)−	xn)−	PROPN
ma-198	325	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	325	6	−	−	PROPN
ma-198	325	7	q‖	q‖	NOUN
ma-198	325	8	(	(	PUNCT
ma-198	325	9	3.22	3.22	NUM
ma-198	325	10	)	)	PUNCT
ma-198	325	11	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NOUN
ma-198	325	12	eur	eur	NOUN
ma-198	325	13	.	.	PUNCT
ma-198	326	1	j.	j.	PROPN
ma-198	326	2	math	math	PROPN
ma-198	326	3	.	.	PUNCT
ma-198	327	1	anal	anal	PROPN
ma-198	327	2	.	.	PUNCT
ma-198	328	1	10.28924	10.28924	NUM
ma-198	328	2	/	/	SYM
ma-198	328	3	ada	ada	PROPN
ma-198	328	4	/	/	SYM
ma-198	328	5	ma.4.2	ma.4.2	PROPN
ma-198	328	6	15thus	15thus	NUM
ma-198	328	7	,	,	PUNCT
ma-198	328	8	from	from	ADP
ma-198	328	9	(	(	PUNCT
ma-198	328	10	3.25	3.25	NUM
ma-198	328	11	)	)	PUNCT
ma-198	328	12	,	,	PUNCT
ma-198	328	13	we	we	PRON
ma-198	328	14	have	have	VERB
ma-198	328	15	(	(	PUNCT
ma-198	328	16	1−	1−	NUM
ma-198	328	17	ταn)2‖xn	ταn)2‖xn	INTJ
ma-198	328	18	−	−	PUNCT
ma-198	328	19	tn‖2	tn‖2	PROPN
ma-198	328	20	≤	≤	ADJ
ma-198	328	21	α2	α2	ADJ
ma-198	328	22	n‖γf	n‖γf	PROPN
ma-198	328	23	(	(	PUNCT
ma-198	328	24	xn)−	xn)−	PUNCT
ma-198	328	25	ηb‖2	ηb‖2	PROPN
ma-198	328	26	+	+	SYM
ma-198	328	27	‖xn	‖xn	PROPN
ma-198	328	28	−	−	NOUN
ma-198	328	29	q‖2	q‖2	PROPN
ma-198	329	1	−	−	PROPN
ma-198	329	2	‖xn+1	‖xn+1	NUM
ma-198	329	3	−	−	PROPN
ma-198	330	1	q‖2	q‖2	PROPN
ma-198	330	2	(	(	PUNCT
ma-198	330	3	3.23	3.23	NUM
ma-198	330	4	)	)	PUNCT
ma-198	330	5	−	−	PROPN
ma-198	331	1	αnτ(2−	αnτ(2−	NOUN
ma-198	331	2	ταn)‖xn	ταn)‖xn	PROPN
ma-198	331	3	−	−	PROPN
ma-198	331	4	q‖2	q‖2	VERB
ma-198	331	5	+	+	CCONJ
ma-198	331	6	2λn(1−	2λn(1−	NUM
ma-198	331	7	ταn)2〈tn	ταn)2〈tn	SYM
ma-198	332	1	−	−	NOUN
ma-198	332	2	q	q	INTJ
ma-198	332	3	,	,	PUNCT
ma-198	332	4	axn	axn	PROPN
ma-198	332	5	−	−	PROPN
ma-198	332	6	aq	aq	NOUN
ma-198	332	7	〉	〉	NOUN
ma-198	332	8	−	−	PROPN
ma-198	332	9	λ2	λ2	PROPN
ma-198	332	10	n(1−	n(1−	PROPN
ma-198	332	11	ταn)2‖axn	ταn)2‖axn	NUM
ma-198	332	12	−	−	PROPN
ma-198	332	13	aq‖2	aq‖2	PROPN
ma-198	332	14	+	+	CCONJ
ma-198	333	1	2αn(1−	2αn(1−	NUM
ma-198	333	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	333	3	(	(	PUNCT
ma-198	333	4	xn)−	xn)−	PROPN
ma-198	333	5	ηbq‖‖xn	ηbq‖‖xn	PROPN
ma-198	333	6	−	−	PROPN
ma-198	333	7	q‖	q‖	AUX
ma-198	333	8	therefor	therefor	VERB
ma-198	333	9	,	,	PUNCT
ma-198	333	10	since	since	SCONJ
ma-198	333	11	αn	αn	NOUN
ma-198	333	12	→	→	SYM
ma-198	333	13	0	0	NUM
ma-198	333	14	as	as	ADP
ma-198	333	15	n	n	X
ma-198	333	16	→∞	→∞	NOUN
ma-198	333	17	with	with	ADP
ma-198	333	18	inequalities	inequality	NOUN
ma-198	333	19	(	(	PUNCT
ma-198	333	20	3.12	3.12	NUM
ma-198	333	21	)	)	PUNCT
ma-198	333	22	and	and	CCONJ
ma-198	333	23	(	(	PUNCT
ma-198	333	24	3.20	3.20	NUM
ma-198	333	25	)	)	PUNCT
ma-198	333	26	,	,	PUNCT
ma-198	333	27	we	we	PRON
ma-198	333	28	have	have	VERB
ma-198	333	29	lim	lim	PROPN
ma-198	333	30	n→∞	n→∞	X
ma-198	334	1	‖xn	‖xn	PROPN
ma-198	334	2	−	−	PROPN
ma-198	334	3	tn‖	tn‖	NOUN
ma-198	334	4	=	=	SYM
ma-198	334	5	0	0	NUM
ma-198	334	6	from	from	ADP
ma-198	334	7	(	(	PUNCT
ma-198	334	8	3.10	3.10	NUM
ma-198	334	9	)	)	PUNCT
ma-198	334	10	and	and	CCONJ
ma-198	334	11	lemma	lemma	PROPN
ma-198	334	12	(	(	PUNCT
ma-198	334	13	2.5	2.5	NUM
ma-198	334	14	)	)	PUNCT
ma-198	334	15	with	with	ADP
ma-198	334	16	the	the	DET
ma-198	334	17	fact	fact	NOUN
ma-198	334	18	that	that	SCONJ
ma-198	334	19	t3	t3	PROPN
ma-198	334	20	is	be	AUX
ma-198	334	21	quasi	quasi	ADJ
ma-198	334	22	-	-	ADJ
ma-198	334	23	nonexpansive	nonexpansive	ADJ
ma-198	334	24	,	,	PUNCT
ma-198	334	25	we	we	PRON
ma-198	334	26	have	have	AUX
ma-198	334	27	thefollowing	thefollowing	NOUN
ma-198	334	28	estimate	estimate	NOUN
ma-198	335	1	‖tn	‖tn	PUNCT
ma-198	335	2	−	−	NOUN
ma-198	335	3	q‖2	q‖2	PROPN
ma-198	335	4	=	=	PUNCT
ma-198	335	5	‖γnzn	‖γnzn	NOUN
ma-198	335	6	+	+	CCONJ
ma-198	335	7	(	(	PUNCT
ma-198	335	8	1−	1−	NUM
ma-198	335	9	γn)wn	γn)wn	SYM
ma-198	335	10	−	−	NOUN
ma-198	335	11	q‖2	q‖2	PROPN
ma-198	335	12	=	=	PUNCT
ma-198	335	13	γn‖zn	γn‖zn	NUM
ma-198	335	14	−	−	PROPN
ma-198	336	1	q‖2	q‖2	VERB
ma-198	336	2	+	+	CCONJ
ma-198	336	3	(	(	PUNCT
ma-198	336	4	1−	1−	NUM
ma-198	336	5	γn)‖wn	γn)‖wn	PROPN
ma-198	336	6	−	−	PROPN
ma-198	336	7	q‖2	q‖2	VERB
ma-198	336	8	−	−	PROPN
ma-198	336	9	(	(	PUNCT
ma-198	336	10	1−	1−	NUM
ma-198	336	11	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	336	12	−	−	PROPN
ma-198	336	13	zn‖2	zn‖2	NOUN
ma-198	336	14	=	=	PUNCT
ma-198	336	15	γn‖zn	γn‖zn	NUM
ma-198	337	1	−	−	PROPN
ma-198	338	1	q‖2	q‖2	VERB
ma-198	338	2	+	+	CCONJ
ma-198	338	3	(	(	PUNCT
ma-198	338	4	1−	1−	NUM
ma-198	338	5	γn)h(t3zn	γn)h(t3zn	PROPN
ma-198	338	6	,	,	PUNCT
ma-198	338	7	t3q)2	t3q)2	PROPN
ma-198	338	8	−	−	PROPN
ma-198	338	9	(	(	PUNCT
ma-198	338	10	1−	1−	NUM
ma-198	338	11	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	338	12	−	−	PROPN
ma-198	338	13	zn‖2	zn‖2	NOUN
ma-198	338	14	=	=	PUNCT
ma-198	339	1	γn‖zn	γn‖zn	NUM
ma-198	339	2	−	−	PROPN
ma-198	340	1	q‖2	q‖2	VERB
ma-198	340	2	+	+	CCONJ
ma-198	340	3	(	(	PUNCT
ma-198	340	4	1−	1−	NUM
ma-198	340	5	γn)‖zn	γn)‖zn	ADJ
ma-198	340	6	−	−	PROPN
ma-198	340	7	q‖2	q‖2	VERB
ma-198	340	8	−	−	PROPN
ma-198	340	9	(	(	PUNCT
ma-198	340	10	1−	1−	NUM
ma-198	340	11	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	340	12	−	−	PROPN
ma-198	340	13	zn‖2	zn‖2	NOUN
ma-198	340	14	≤	≤	PROPN
ma-198	340	15	‖xn	‖xn	PROPN
ma-198	340	16	−	−	PROPN
ma-198	340	17	q‖2	q‖2	PROPN
ma-198	340	18	−	−	PROPN
ma-198	340	19	(	(	PUNCT
ma-198	340	20	1−	1−	NUM
ma-198	340	21	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	340	22	−	−	PROPN
ma-198	340	23	zn‖2	zn‖2	NOUN
ma-198	340	24	(	(	PUNCT
ma-198	340	25	3.24	3.24	NUM
ma-198	340	26	)	)	PUNCT
ma-198	340	27	therefore	therefore	ADV
ma-198	340	28	‖xn+1	‖xn+1	NUM
ma-198	340	29	−	−	PROPN
ma-198	340	30	q‖2	q‖2	VERB
ma-198	340	31	≤	≤	ADJ
ma-198	340	32	‖αn(γf	‖αn(γf	NOUN
ma-198	340	33	(	(	PUNCT
ma-198	340	34	xn)−	xn)−	NOUN
ma-198	340	35	ηbq	ηbq	ADV
ma-198	340	36	)	)	PUNCT
ma-198	341	1	+	+	CCONJ
ma-198	341	2	(	(	PUNCT
ma-198	341	3	i	i	PRON
ma-198	341	4	−	−	PROPN
ma-198	341	5	ηαnb)(tn	ηαnb)(tn	PROPN
ma-198	341	6	−	−	PROPN
ma-198	341	7	q)‖2	q)‖2	NOUN
ma-198	341	8	≤	≤	ADV
ma-198	341	9	α2	α2	VERB
ma-198	341	10	n‖γf	n‖γf	PROPN
ma-198	341	11	(	(	PUNCT
ma-198	341	12	xn)−	xn)−	PUNCT
ma-198	341	13	ηb‖2	ηb‖2	PROPN
ma-198	341	14	+	+	CCONJ
ma-198	341	15	(	(	PUNCT
ma-198	341	16	1−	1−	NUM
ma-198	341	17	ταn)2‖tn	ταn)2‖tn	NOUN
ma-198	341	18	−	−	PROPN
ma-198	341	19	q‖2	q‖2	PROPN
ma-198	341	20	+	+	CCONJ
ma-198	341	21	2αn(1−	2αn(1−	NUM
ma-198	341	22	ταn)‖γf	ταn)‖γf	NUM
ma-198	341	23	(	(	PUNCT
ma-198	341	24	xn)−	xn)−	PROPN
ma-198	341	25	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	341	26	−	−	PROPN
ma-198	341	27	q‖	q‖	NOUN
ma-198	341	28	≤	≤	ADV
ma-198	341	29	α2	α2	PROPN
ma-198	341	30	n‖γf	n‖γf	PROPN
ma-198	341	31	(	(	PUNCT
ma-198	341	32	xn)−	xn)−	PUNCT
ma-198	341	33	ηb‖2	ηb‖2	PROPN
ma-198	341	34	+	+	CCONJ
ma-198	341	35	(	(	PUNCT
ma-198	341	36	1−	1−	NUM
ma-198	341	37	ταn)2	ταn)2	PROPN
ma-198	341	38	[	[	PUNCT
ma-198	341	39	‖xn	‖xn	PROPN
ma-198	341	40	−	−	PROPN
ma-198	341	41	q‖2	q‖2	PROPN
ma-198	341	42	−	−	PROPN
ma-198	341	43	(	(	PUNCT
ma-198	341	44	1−	1−	NUM
ma-198	341	45	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	341	46	−	−	PROPN
ma-198	341	47	zn‖2	zn‖2	NOUN
ma-198	341	48	]	]	PUNCT
ma-198	342	1	+	+	CCONJ
ma-198	342	2	2αn(1−	2αn(1−	NUM
ma-198	342	3	ταn)‖γf	ταn)‖γf	NUM
ma-198	342	4	(	(	PUNCT
ma-198	342	5	xn)−	xn)−	PROPN
ma-198	342	6	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	342	7	−	−	PROPN
ma-198	342	8	q‖	q‖	NOUN
ma-198	342	9	≤	≤	ADV
ma-198	342	10	α2	α2	PROPN
ma-198	342	11	n‖γf	n‖γf	PROPN
ma-198	342	12	(	(	PUNCT
ma-198	342	13	xn)−	xn)−	PUNCT
ma-198	342	14	ηb‖2	ηb‖2	PROPN
ma-198	342	15	+	+	CCONJ
ma-198	342	16	(	(	PUNCT
ma-198	342	17	1−	1−	NUM
ma-198	342	18	ταn)2‖xn	ταn)2‖xn	SYM
ma-198	342	19	−	−	PROPN
ma-198	342	20	q‖2	q‖2	PROPN
ma-198	342	21	−	−	PROPN
ma-198	342	22	(	(	PUNCT
ma-198	342	23	1−	1−	NUM
ma-198	342	24	ταn)2(1−	ταn)2(1−	PROPN
ma-198	342	25	γn)γn‖wn	γn)γn‖wn	PRON
ma-198	342	26	−	−	PROPN
ma-198	342	27	zn‖2	zn‖2	NOUN
ma-198	342	28	+	+	CCONJ
ma-198	343	1	2αn(1−	2αn(1−	NUM
ma-198	343	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	343	3	(	(	PUNCT
ma-198	343	4	xn)−	xn)−	PROPN
ma-198	343	5	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	343	6	−	−	PROPN
ma-198	343	7	q‖	q‖	NOUN
ma-198	343	8	hence	hence	ADV
ma-198	343	9	,	,	PUNCT
ma-198	343	10	we	we	PRON
ma-198	343	11	have	have	VERB
ma-198	343	12	the	the	DET
ma-198	343	13	following	follow	VERB
ma-198	343	14	(	(	PUNCT
ma-198	343	15	1−	1−	NUM
ma-198	343	16	ταn)2(1−	ταn)2(1−	PROPN
ma-198	343	17	γn)γn‖wn	γn)γn‖wn	PRON
ma-198	343	18	−	−	PROPN
ma-198	343	19	zn‖2	zn‖2	PROPN
ma-198	343	20	≤	≤	PROPN
ma-198	343	21	α2	α2	NOUN
ma-198	343	22	n‖γf	n‖γf	PROPN
ma-198	343	23	(	(	PUNCT
ma-198	343	24	xn)−	xn)−	X
ma-198	343	25	ηb‖2	ηb‖2	PROPN
ma-198	343	26	−	−	NOUN
ma-198	343	27	ταn(2−	ταn(2−	VERB
ma-198	343	28	ταn)‖xn	ταn)‖xn	PROPN
ma-198	343	29	−	−	PROPN
ma-198	343	30	q‖2	q‖2	PROPN
ma-198	344	1	+	+	CCONJ
ma-198	345	1	‖xn	‖xn	PROPN
ma-198	345	2	−	−	PROPN
ma-198	345	3	q‖2	q‖2	AUX
ma-198	345	4	−	−	PROPN
ma-198	345	5	‖xn+1	‖xn+1	NUM
ma-198	345	6	−	−	PROPN
ma-198	345	7	q‖2	q‖2	NOUN
ma-198	345	8	+	+	CCONJ
ma-198	346	1	2αn(1−	2αn(1−	NUM
ma-198	346	2	ταn)‖γf	ταn)‖γf	NUM
ma-198	346	3	(	(	PUNCT
ma-198	346	4	xn)−	xn)−	PROPN
ma-198	346	5	ηbq‖‖tn	ηbq‖‖tn	PROPN
ma-198	346	6	−	−	PROPN
ma-198	346	7	q‖	q‖	ADV
ma-198	346	8	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	346	9	eur	eur	NOUN
ma-198	346	10	.	.	PUNCT
ma-198	347	1	j.	j.	PROPN
ma-198	347	2	math	math	PROPN
ma-198	347	3	.	.	PUNCT
ma-198	348	1	anal	anal	PROPN
ma-198	348	2	.	.	PUNCT
ma-198	349	1	10.28924	10.28924	NUM
ma-198	349	2	/	/	SYM
ma-198	349	3	ada	ada	PROPN
ma-198	349	4	/	/	SYM
ma-198	349	5	ma.4.2	ma.4.2	PROPN
ma-198	349	6	16therefor	16therefor	NUM
ma-198	349	7	,	,	PUNCT
ma-198	349	8	since	since	SCONJ
ma-198	349	9	αn	αn	NOUN
ma-198	349	10	→	→	SYM
ma-198	349	11	0	0	NUM
ma-198	349	12	as	as	ADP
ma-198	349	13	n	n	X
ma-198	349	14	→∞	→∞	NOUN
ma-198	349	15	with	with	ADP
ma-198	349	16	inequalities	inequality	NOUN
ma-198	349	17	(	(	PUNCT
ma-198	349	18	3.12	3.12	NUM
ma-198	349	19	)	)	PUNCT
ma-198	349	20	and	and	CCONJ
ma-198	349	21	(	(	PUNCT
ma-198	349	22	3.20	3.20	NUM
ma-198	349	23	)	)	PUNCT
ma-198	349	24	,	,	PUNCT
ma-198	349	25	we	we	PRON
ma-198	349	26	have	have	VERB
ma-198	349	27	(	(	PUNCT
ma-198	349	28	1−	1−	NUM
ma-198	349	29	ταn)2(1−	ταn)2(1−	PROPN
ma-198	349	30	γn)γn‖wn	γn)γn‖wn	PRON
ma-198	349	31	−	−	PROPN
ma-198	349	32	zn‖2	zn‖2	PROPN
ma-198	349	33	≤	≤	NOUN
ma-198	349	34	0	0	NUM
ma-198	349	35	from	from	ADP
ma-198	349	36	this	this	PRON
ma-198	349	37	we	we	PRON
ma-198	349	38	have	have	VERB
ma-198	349	39	lim	lim	PROPN
ma-198	349	40	n→∞	n→∞	X
ma-198	349	41	(	(	PUNCT
ma-198	349	42	1−	1−	NUM
ma-198	349	43	γn)γn‖wn	γn)γn‖wn	NOUN
ma-198	349	44	−	−	PROPN
ma-198	349	45	zn‖2	zn‖2	NOUN
ma-198	349	46	=	=	SYM
ma-198	349	47	0	0	NUM
ma-198	350	1	(	(	PUNCT
ma-198	350	2	3.25	3.25	NUM
ma-198	350	3	)	)	PUNCT
ma-198	350	4	since	since	SCONJ
ma-198	350	5	lim	lim	PROPN
ma-198	350	6	n→∞	n→∞	X
ma-198	350	7	inf((1−	inf((1−	PROPN
ma-198	350	8	γn)γn	γn)γn	X
ma-198	350	9	)	)	PUNCT
ma-198	350	10	>	>	X
ma-198	350	11	0	0	PUNCT
ma-198	351	1	lim	lim	PROPN
ma-198	351	2	n→∞	n→∞	NUM
ma-198	351	3	‖wn	‖wn	NUM
ma-198	351	4	−	−	PROPN
ma-198	351	5	zn‖	zn‖	PROPN
ma-198	351	6	=	=	SYM
ma-198	351	7	0	0	PUNCT
ma-198	351	8	(	(	PUNCT
ma-198	351	9	3.26	3.26	NUM
ma-198	351	10	)	)	PUNCT
ma-198	351	11	again	again	ADV
ma-198	351	12	,	,	PUNCT
ma-198	351	13	with	with	ADP
ma-198	351	14	w	w	PROPN
ma-198	351	15	∈	∈	PROPN
ma-198	351	16	t3zn	t3zn	X
ma-198	351	17	lim	lim	PROPN
ma-198	351	18	n→∞	n→∞	NUM
ma-198	351	19	d(zn	d(zn	PROPN
ma-198	351	20	,	,	PUNCT
ma-198	351	21	t3zn	t3zn	X
ma-198	351	22	)	)	PUNCT
ma-198	351	23	=	=	SYM
ma-198	351	24	0	0	PUNCT
ma-198	351	25	(	(	PUNCT
ma-198	351	26	3.27	3.27	NUM
ma-198	351	27	)	)	PUNCT
ma-198	351	28	moreover	moreover	ADV
ma-198	351	29	,	,	PUNCT
ma-198	351	30	since	since	SCONJ
ma-198	351	31	h	h	NOUN
ma-198	351	32	is	be	AUX
ma-198	351	33	reflexive	reflexive	ADJ
ma-198	351	34	and	and	CCONJ
ma-198	351	35	{	{	PUNCT
ma-198	351	36	xn	xn	X
ma-198	351	37	}	}	PUNCT
ma-198	351	38	is	be	AUX
ma-198	351	39	bounded	bound	VERB
ma-198	351	40	,	,	PUNCT
ma-198	351	41	we	we	PRON
ma-198	351	42	then	then	ADV
ma-198	351	43	prove	prove	VERB
ma-198	351	44	that	that	SCONJ
ma-198	351	45	lim	lim	PROPN
ma-198	351	46	n→+∞	n→+∞	VERB
ma-198	351	47	sup〈ηbx∗	sup〈ηbx∗	NOUN
ma-198	351	48	−	−	PROPN
ma-198	351	49	γf	γf	PROPN
ma-198	351	50	(	(	PUNCT
ma-198	351	51	x∗	x∗	PROPN
ma-198	351	52	)	)	PUNCT
ma-198	351	53	,	,	PUNCT
ma-198	351	54	x∗	x∗	PROPN
ma-198	351	55	−	−	PROPN
ma-198	352	1	xn	xn	SYM
ma-198	352	2	〉	〉	PROPN
ma-198	352	3	≤	≤	NUM
ma-198	352	4	0	0	NUM
ma-198	352	5	.	.	PUNCT
ma-198	353	1	we	we	PRON
ma-198	353	2	let	let	VERB
ma-198	353	3	the	the	DET
ma-198	353	4	subsequence	subsequence	NOUN
ma-198	353	5	{	{	PUNCT
ma-198	353	6	xni	xni	NOUN
ma-198	353	7	}	}	PUNCT
ma-198	353	8	of	of	ADP
ma-198	353	9	{	{	PUNCT
ma-198	353	10	xn	xn	INTJ
ma-198	353	11	}	}	PUNCT
ma-198	353	12	to	to	PART
ma-198	353	13	converge	converge	VERB
ma-198	353	14	weakly	weakly	ADV
ma-198	353	15	to	to	ADP
ma-198	353	16	x∗∗	x∗∗	PROPN
ma-198	353	17	in	in	ADP
ma-198	353	18	k	k	PROPN
ma-198	353	19	,	,	PUNCT
ma-198	353	20	and	and	CCONJ
ma-198	353	21	lim	lim	PROPN
ma-198	353	22	n→+∞	n→+∞	PROPN
ma-198	353	23	〈	〈	PROPN
ma-198	353	24	ηbx∗	ηbx∗	NOUN
ma-198	353	25	−	−	PROPN
ma-198	353	26	γf	γf	PROPN
ma-198	353	27	(	(	PUNCT
ma-198	353	28	x∗	x∗	PROPN
ma-198	353	29	)	)	PUNCT
ma-198	353	30	,	,	PUNCT
ma-198	353	31	x∗	x∗	PROPN
ma-198	353	32	−	−	PROPN
ma-198	354	1	xn	xn	SYM
ma-198	354	2	〉	〉	PROPN
ma-198	354	3	=	=	SYM
ma-198	354	4	lim	lim	PROPN
ma-198	354	5	n→+∞	n→+∞	PROPN
ma-198	354	6	〈	〈	PROPN
ma-198	354	7	ηbx∗	ηbx∗	NOUN
ma-198	354	8	−	−	PROPN
ma-198	354	9	γf	γf	PROPN
ma-198	354	10	(	(	PUNCT
ma-198	354	11	x∗	x∗	PROPN
ma-198	354	12	)	)	PUNCT
ma-198	354	13	,	,	PUNCT
ma-198	354	14	x∗	x∗	PROPN
ma-198	355	1	−	−	PROPN
ma-198	355	2	xni	xni	PROPN
ma-198	355	3	〉	〉	PROPN
ma-198	355	4	again	again	ADV
ma-198	355	5	,	,	PUNCT
ma-198	355	6	since	since	SCONJ
ma-198	355	7	i−t1	i−t1	NOUN
ma-198	355	8	,	,	PUNCT
ma-198	355	9	i−t2	i−t2	PUNCT
ma-198	355	10	and	and	CCONJ
ma-198	355	11	i−t3	i−t3	NOUN
ma-198	355	12	satisfies	satisfy	VERB
ma-198	355	13	the	the	DET
ma-198	355	14	demiclosed	demiclosed	ADJ
ma-198	355	15	principle	principle	NOUN
ma-198	355	16	and	and	CCONJ
ma-198	355	17	from	from	ADP
ma-198	355	18	(	(	PUNCT
ma-198	355	19	3.32	3.32	NUM
ma-198	355	20	)	)	PUNCT
ma-198	355	21	,	,	PUNCT
ma-198	355	22	(	(	PUNCT
ma-198	355	23	3.16)and	3.16)and	NUM
ma-198	355	24	(	(	PUNCT
ma-198	355	25	3.27	3.27	NUM
ma-198	355	26	)	)	PUNCT
ma-198	355	27	,	,	PUNCT
ma-198	355	28	we	we	PRON
ma-198	355	29	obtain	obtain	VERB
ma-198	355	30	x∗∗	x∗∗	PROPN
ma-198	355	31	∈	∈	PROPN
ma-198	355	32	f	f	PROPN
ma-198	355	33	ix(t1)∩f	ix(t1)∩f	PROPN
ma-198	355	34	ix(t2)∩f	ix(t2)∩f	PROPN
ma-198	355	35	ix(t3	ix(t3	PROPN
ma-198	355	36	)	)	PUNCT
ma-198	355	37	.	.	PUNCT
ma-198	356	1	we	we	PRON
ma-198	356	2	now	now	ADV
ma-198	356	3	show	show	VERB
ma-198	356	4	that	that	SCONJ
ma-198	356	5	x∗∗	x∗∗	PROPN
ma-198	356	6	∈	∈	PROPN
ma-198	356	7	s(m	s(m	PROPN
ma-198	356	8	,	,	PUNCT
ma-198	356	9	a).since	a).since	PROPN
ma-198	356	10	a	a	PRON
ma-198	356	11	is	be	AUX
ma-198	356	12	α−inverse	α−inverse	NOUN
ma-198	356	13	strongly	strongly	ADV
ma-198	356	14	monotone	monotone	ADJ
ma-198	356	15	,	,	PUNCT
ma-198	356	16	and	and	CCONJ
ma-198	356	17	lipschitz	lipschitz	VERB
ma-198	356	18	continuous	continuous	ADJ
ma-198	356	19	mapping	mapping	NOUN
ma-198	356	20	.	.	PUNCT
ma-198	357	1	then	then	ADV
ma-198	357	2	fromlemma	fromlemma	PROPN
ma-198	357	3	(	(	PUNCT
ma-198	357	4	2.1	2.1	NUM
ma-198	357	5	)	)	PUNCT
ma-198	357	6	,	,	PUNCT
ma-198	357	7	it	it	PRON
ma-198	357	8	follows	follow	VERB
ma-198	357	9	that	that	SCONJ
ma-198	357	10	(	(	PUNCT
ma-198	357	11	m+	m+	NOUN
ma-198	357	12	a	a	NOUN
ma-198	357	13	)	)	PUNCT
ma-198	357	14	is	be	AUX
ma-198	357	15	maximal	maximal	ADJ
ma-198	357	16	monotone.let	monotone.let	X
ma-198	357	17	(	(	PUNCT
ma-198	357	18	ν	ν	NOUN
ma-198	357	19	,	,	PUNCT
ma-198	357	20	g	g	NOUN
ma-198	357	21	)	)	PUNCT
ma-198	357	22	∈	∈	PROPN
ma-198	357	23	g(m	g(m	VERB
ma-198	357	24	+	+	CCONJ
ma-198	357	25	a	a	X
ma-198	357	26	)	)	PUNCT
ma-198	357	27	,	,	PUNCT
ma-198	357	28	that	that	PRON
ma-198	357	29	is	be	AUX
ma-198	357	30	g	g	PROPN
ma-198	357	31	−	−	PROPN
ma-198	357	32	aν	aν	NOUN
ma-198	357	33	∈	∈	PROPN
ma-198	357	34	m(ν	m(ν	PROPN
ma-198	357	35	)	)	PUNCT
ma-198	357	36	.	.	PUNCT
ma-198	358	1	since	since	SCONJ
ma-198	358	2	δni	δni	PROPN
ma-198	358	3	=	=	SYM
ma-198	358	4	jmλni	jmλni	PROPN
ma-198	358	5	(	(	PUNCT
ma-198	358	6	xni	xni	PROPN
ma-198	358	7	)	)	PUNCT
ma-198	359	1	−	−	PROPN
ma-198	359	2	λniaxni	λniaxni	NOUN
ma-198	359	3	)	)	PUNCT
ma-198	359	4	,	,	PUNCT
ma-198	359	5	wehave	wehave	NOUN
ma-198	359	6	xni	xni	PROPN
ma-198	360	1	−	−	PROPN
ma-198	360	2	λni	λni	INTJ
ma-198	360	3	xni	xni	PROPN
ma-198	360	4	∈	∈	PROPN
ma-198	360	5	(	(	PUNCT
ma-198	360	6	i	i	NOUN
ma-198	360	7	+	+	CCONJ
ma-198	360	8	λnim)δni	λnim)δni	NOUN
ma-198	360	9	,	,	PUNCT
ma-198	360	10	that	that	PRON
ma-198	360	11	is	be	AUX
ma-198	360	12	1	1	NUM
ma-198	360	13	λni	λni	NOUN
ma-198	360	14	(	(	PUNCT
ma-198	360	15	xni	xni	PROPN
ma-198	360	16	−	−	PROPN
ma-198	360	17	δni	δni	PROPN
ma-198	360	18	−	−	PROPN
ma-198	360	19	λniaxni	λniaxni	PROPN
ma-198	360	20	)	)	PUNCT
ma-198	360	21	∈	∈	PROPN
ma-198	360	22	m(δni	m(δni	PROPN
ma-198	360	23	)	)	PUNCT
ma-198	360	24	.	.	PUNCT
ma-198	361	1	by	by	ADP
ma-198	361	2	maximalmonotonocity	maximalmonotonocity	NOUN
ma-198	361	3	of	of	ADP
ma-198	361	4	(	(	PUNCT
ma-198	361	5	m+	m+	NOUN
ma-198	361	6	a	a	NOUN
ma-198	361	7	)	)	PUNCT
ma-198	361	8	,	,	PUNCT
ma-198	361	9	gives	give	VERB
ma-198	361	10	〈	〈	PROPN
ma-198	361	11	ν	ν	NOUN
ma-198	361	12	−	−	PROPN
ma-198	361	13	δni	δni	PROPN
ma-198	361	14	,	,	PUNCT
ma-198	361	15	g	g	PROPN
ma-198	361	16	−	−	PROPN
ma-198	361	17	aν	aν	NOUN
ma-198	361	18	−	−	PROPN
ma-198	361	19	1	1	NUM
ma-198	361	20	λni	λni	NOUN
ma-198	361	21	(	(	PUNCT
ma-198	361	22	xni	xni	PROPN
ma-198	361	23	−	−	PROPN
ma-198	361	24	δni	δni	PROPN
ma-198	361	25	−	−	PROPN
ma-198	361	26	λniaxni	λniaxni	PROPN
ma-198	361	27	)	)	PUNCT
ma-198	361	28	≥	≥	NOUN
ma-198	361	29	0	0	NUM
ma-198	362	1	and	and	CCONJ
ma-198	362	2	,	,	PUNCT
ma-198	362	3	therefore	therefore	ADV
ma-198	362	4	〈	〈	PROPN
ma-198	362	5	ν	ν	PROPN
ma-198	362	6	−	−	PROPN
ma-198	362	7	δni	δni	PROPN
ma-198	362	8	,	,	PUNCT
ma-198	362	9	g	g	PROPN
ma-198	362	10	〉	〉	PROPN
ma-198	362	11	≥	≥	NOUN
ma-198	362	12	〈	〈	PROPN
ma-198	362	13	ν	ν	PROPN
ma-198	362	14	−	−	PROPN
ma-198	362	15	δni	δni	PROPN
ma-198	362	16	,	,	PUNCT
ma-198	362	17	aν	aν	NOUN
ma-198	362	18	−	−	NOUN
ma-198	362	19	1	1	NUM
ma-198	362	20	λni	λni	NOUN
ma-198	362	21	(	(	PUNCT
ma-198	362	22	xni	xni	PROPN
ma-198	362	23	−	−	PROPN
ma-198	362	24	δni	δni	PROPN
ma-198	362	25	−	−	PROPN
ma-198	362	26	λniaxni	λniaxni	PROPN
ma-198	362	27	)	)	PUNCT
ma-198	362	28	〉	〉	NOUN
ma-198	362	29	=	=	SYM
ma-198	362	30	〈	〈	PROPN
ma-198	362	31	ν	ν	X
ma-198	362	32	−	−	PROPN
ma-198	362	33	δni	δni	PROPN
ma-198	362	34	,	,	PUNCT
ma-198	362	35	aν	aν	NOUN
ma-198	362	36	−	−	NOUN
ma-198	362	37	aδni	aδni	PROPN
ma-198	362	38	+	+	SYM
ma-198	362	39	aδni	aδni	ADJ
ma-198	362	40	+	+	CCONJ
ma-198	362	41	1	1	NUM
ma-198	362	42	λni	λni	NOUN
ma-198	362	43	(	(	PUNCT
ma-198	362	44	xni	xni	PROPN
ma-198	362	45	−	−	PROPN
ma-198	362	46	δni	δni	PROPN
ma-198	362	47	−	−	PROPN
ma-198	362	48	λniaxni	λniaxni	PROPN
ma-198	362	49	)	)	PUNCT
ma-198	362	50	〉	〉	PROPN
ma-198	362	51	≥	≥	NOUN
ma-198	362	52	〈	〈	PROPN
ma-198	363	1	ν	ν	PROPN
ma-198	363	2	−	−	PROPN
ma-198	363	3	δni	δni	PROPN
ma-198	363	4	,	,	PUNCT
ma-198	363	5	aν	aν	NOUN
ma-198	363	6	−	−	PROPN
ma-198	363	7	axni	axni	PROPN
ma-198	363	8	〉	〉	PROPN
ma-198	363	9	+	+	CCONJ
ma-198	364	1	〈	〈	PROPN
ma-198	364	2	ν	ν	X
ma-198	364	3	−	−	PROPN
ma-198	364	4	δni	δni	PROPN
ma-198	364	5	,	,	PUNCT
ma-198	364	6	1	1	NUM
ma-198	364	7	λni	λni	NOUN
ma-198	364	8	(	(	PUNCT
ma-198	364	9	xni	xni	PROPN
ma-198	364	10	−	−	PROPN
ma-198	364	11	δni	δni	PROPN
ma-198	364	12	〉	〉	PROPN
ma-198	364	13	it	it	PRON
ma-198	364	14	then	then	ADV
ma-198	364	15	follows	follow	VERB
ma-198	364	16	from	from	ADP
ma-198	364	17	‖δn	‖δn	NUM
ma-198	364	18	−	−	NOUN
ma-198	364	19	xn‖	xn‖	PROPN
ma-198	364	20	→	→	SYM
ma-198	364	21	0	0	NUM
ma-198	364	22	,	,	PUNCT
ma-198	364	23	‖aδn	‖aδn	PROPN
ma-198	364	24	−	−	PROPN
ma-198	364	25	axn‖	axn‖	NOUN
ma-198	364	26	→	→	SYM
ma-198	364	27	0	0	NUM
ma-198	364	28	and	and	CCONJ
ma-198	364	29	δni	δni	PROPN
ma-198	364	30	→	→	SYM
ma-198	364	31	x∗∗	x∗∗	PROPN
ma-198	364	32	weakly	weakly	ADJ
ma-198	365	1	that	that	SCONJ
ma-198	365	2	lim	lim	PROPN
ma-198	365	3	n→∞	n→∞	X
ma-198	366	1	〈	〈	PROPN
ma-198	366	2	ν	ν	PROPN
ma-198	366	3	−	−	PROPN
ma-198	366	4	δni	δni	PROPN
ma-198	366	5	,	,	PUNCT
ma-198	366	6	g	g	PROPN
ma-198	366	7	〉	〉	NOUN
ma-198	366	8	=	=	SYM
ma-198	366	9	〈	〈	PROPN
ma-198	366	10	ν	ν	NOUN
ma-198	366	11	−	−	NOUN
ma-198	366	12	x∗∗	x∗∗	PROPN
ma-198	366	13	,	,	PUNCT
ma-198	366	14	g	g	PROPN
ma-198	366	15	〉	〉	NOUN
ma-198	366	16	and	and	CCONJ
ma-198	366	17	hence	hence	ADV
ma-198	366	18	x∗∗	x∗∗	PROPN
ma-198	366	19	∈	∈	PROPN
ma-198	366	20	s(π	s(π	PROPN
ma-198	366	21	,	,	PUNCT
ma-198	366	22	a	a	PRON
ma-198	366	23	)	)	PUNCT
ma-198	366	24	.	.	PUNCT
ma-198	367	1	therefore	therefore	ADV
ma-198	367	2	,	,	PUNCT
ma-198	367	3	x∗∗	x∗∗	PROPN
ma-198	367	4	∈	∈	PROPN
ma-198	367	5	ω	ω	PROPN
ma-198	367	6	,	,	PUNCT
ma-198	367	7	on	on	ADP
ma-198	367	8	the	the	DET
ma-198	367	9	other	other	ADJ
ma-198	367	10	hand	hand	NOUN
ma-198	367	11	,	,	PUNCT
ma-198	367	12	for	for	ADP
ma-198	367	13	the	the	DET
ma-198	367	14	fact	fact	NOUN
ma-198	367	15	that	that	SCONJ
ma-198	367	16	x∗	x∗	PROPN
ma-198	367	17	solves	solve	VERB
ma-198	367	18	the	the	DET
ma-198	367	19	variational	variational	ADJ
ma-198	367	20	inequality	inequality	NOUN
ma-198	367	21	(	(	PUNCT
ma-198	367	22	3.30	3.30	NUM
ma-198	367	23	)	)	PUNCT
ma-198	367	24	.	.	PUNCT
ma-198	368	1	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	368	2	eur	eur	NOUN
ma-198	368	3	.	.	PUNCT
ma-198	369	1	j.	j.	PROPN
ma-198	369	2	math	math	PROPN
ma-198	369	3	.	.	PUNCT
ma-198	370	1	anal	anal	PROPN
ma-198	370	2	.	.	PUNCT
ma-198	371	1	10.28924	10.28924	NUM
ma-198	371	2	/	/	SYM
ma-198	371	3	ada	ada	PROPN
ma-198	371	4	/	/	SYM
ma-198	371	5	ma.4.2	ma.4.2	PROPN
ma-198	371	6	17	17	NUM
ma-198	371	7	lim	lim	NOUN
ma-198	371	8	n→+∞	n→+∞	VERB
ma-198	371	9	sup〈ηbx∗	sup〈ηbx∗	NOUN
ma-198	371	10	−	−	PROPN
ma-198	371	11	γf	γf	PROPN
ma-198	371	12	(	(	PUNCT
ma-198	371	13	x∗	x∗	PROPN
ma-198	371	14	)	)	PUNCT
ma-198	371	15	,	,	PUNCT
ma-198	371	16	x∗	x∗	PROPN
ma-198	372	1	−	−	PROPN
ma-198	373	1	xn	xn	SYM
ma-198	373	2	〉	〉	PROPN
ma-198	373	3	=	=	SYM
ma-198	373	4	lim	lim	PROPN
ma-198	373	5	n→+∞	n→+∞	VERB
ma-198	373	6	sup〈ηbx∗	sup〈ηbx∗	NOUN
ma-198	373	7	−	−	PROPN
ma-198	373	8	γf	γf	PROPN
ma-198	373	9	(	(	PUNCT
ma-198	373	10	x∗	x∗	PROPN
ma-198	373	11	)	)	PUNCT
ma-198	373	12	,	,	PUNCT
ma-198	373	13	x∗	x∗	PROPN
ma-198	374	1	−	−	PROPN
ma-198	375	1	xni	xni	PROPN
ma-198	376	1	〉	〉	PROPN
ma-198	377	1	=	=	PUNCT
ma-198	378	1	〈	〈	PROPN
ma-198	378	2	ηbx∗	ηbx∗	NOUN
ma-198	378	3	−	−	PROPN
ma-198	378	4	γf	γf	PROPN
ma-198	378	5	(	(	PUNCT
ma-198	378	6	x∗	x∗	PROPN
ma-198	378	7	)	)	PUNCT
ma-198	378	8	,	,	PUNCT
ma-198	378	9	x∗	x∗	PROPN
ma-198	378	10	−	−	PROPN
ma-198	379	1	x∗∗	x∗∗	PROPN
ma-198	379	2	〉	〉	PROPN
ma-198	379	3	≤	≤	NUM
ma-198	379	4	0	0	NUM
ma-198	379	5	(	(	PUNCT
ma-198	379	6	3.28	3.28	NUM
ma-198	379	7	)	)	PUNCT
ma-198	379	8	lastly	lastly	ADV
ma-198	379	9	,	,	PUNCT
ma-198	379	10	we	we	PRON
ma-198	379	11	now	now	ADV
ma-198	379	12	prove	prove	VERB
ma-198	379	13	that	that	SCONJ
ma-198	379	14	lim	lim	PROPN
ma-198	379	15	n→∞	n→∞	PRON
ma-198	379	16	‖xn	‖xn	PROPN
ma-198	379	17	−	−	PROPN
ma-198	379	18	x∗‖	x∗‖	X
ma-198	379	19	=	=	SYM
ma-198	379	20	0	0	PROPN
ma-198	379	21	,	,	PUNCT
ma-198	379	22	that	that	PRON
ma-198	379	23	is	is	ADV
ma-198	379	24	xn	xn	PROPN
ma-198	379	25	→	→	SYM
ma-198	379	26	x∗	x∗	PROPN
ma-198	379	27	as	as	ADP
ma-198	379	28	n	n	PROPN
ma-198	379	29	→∞.	→∞.	SYM
ma-198	379	30	‖xn+1	‖xn+1	PROPN
ma-198	379	31	−	−	PROPN
ma-198	379	32	x∗‖2	x∗‖2	PROPN
ma-198	379	33	≤	≤	NUM
ma-198	379	34	‖αnγf	‖αnγf	PUNCT
ma-198	379	35	(	(	PUNCT
ma-198	379	36	xn	xn	X
ma-198	379	37	)	)	PUNCT
ma-198	380	1	+	+	CCONJ
ma-198	380	2	(	(	PUNCT
ma-198	380	3	i	i	PRON
ma-198	380	4	−	−	PROPN
ma-198	380	5	ηαnb)tn	ηαnb)tn	NOUN
ma-198	380	6	−	−	PROPN
ma-198	380	7	x∗‖2	x∗‖2	PROPN
ma-198	380	8	≤	≤	X
ma-198	380	9	‖αn(γf	‖αn(γf	NOUN
ma-198	380	10	(	(	PUNCT
ma-198	380	11	xn)−	xn)−	NOUN
ma-198	380	12	γf	γf	PROPN
ma-198	380	13	(	(	PUNCT
ma-198	380	14	x∗	x∗	PROPN
ma-198	380	15	)	)	PUNCT
ma-198	380	16	)	)	PUNCT
ma-198	381	1	+	+	CCONJ
ma-198	381	2	(	(	PUNCT
ma-198	381	3	i	i	PRON
ma-198	381	4	−	−	PROPN
ma-198	381	5	ηαnb)tn	ηαnb)tn	NOUN
ma-198	381	6	−	−	PROPN
ma-198	381	7	x∗‖2	x∗‖2	PROPN
ma-198	382	1	+	+	CCONJ
ma-198	383	1	2αn〈ηbx∗	2αn〈ηbx∗	NUM
ma-198	383	2	−	−	NOUN
ma-198	383	3	γf	γf	PROPN
ma-198	383	4	(	(	PUNCT
ma-198	383	5	x∗	x∗	PROPN
ma-198	383	6	)	)	PUNCT
ma-198	383	7	,	,	PUNCT
ma-198	383	8	x∗	x∗	PROPN
ma-198	383	9	−	−	PROPN
ma-198	384	1	xn+1	xn+1	NUM
ma-198	384	2	〉	〉	PROPN
ma-198	384	3	≤	≤	NOUN
ma-198	384	4	[	[	PUNCT
ma-198	384	5	αnγ‖f	αnγ‖f	NUM
ma-198	384	6	(	(	PUNCT
ma-198	384	7	xn)−	xn)−	NOUN
ma-198	384	8	f	f	X
ma-198	384	9	(	(	PUNCT
ma-198	384	10	x∗)‖+	x∗)‖+	NUM
ma-198	384	11	‖(i	‖(i	PROPN
ma-198	384	12	−	−	PROPN
ma-198	384	13	ηαnb)(tn	ηαnb)(tn	PROPN
ma-198	384	14	−	−	PROPN
ma-198	384	15	x∗)‖	x∗)‖	PUNCT
ma-198	385	1	]	]	SYM
ma-198	385	2	2	2	X
ma-198	385	3	+	+	NUM
ma-198	385	4	2αn〈ηbx∗	2αn〈ηbx∗	NUM
ma-198	385	5	−	−	NOUN
ma-198	385	6	γf	γf	PROPN
ma-198	385	7	(	(	PUNCT
ma-198	385	8	x∗	x∗	PROPN
ma-198	385	9	)	)	PUNCT
ma-198	385	10	,	,	PUNCT
ma-198	385	11	x∗	x∗	PROPN
ma-198	385	12	−	−	PROPN
ma-198	386	1	xn+1	xn+1	NUM
ma-198	386	2	〉	〉	PROPN
ma-198	386	3	≤	≤	NOUN
ma-198	386	4	[	[	PUNCT
ma-198	386	5	αnγb‖xn	αnγb‖xn	PROPN
ma-198	386	6	−	−	PROPN
ma-198	386	7	x∗‖+	x∗‖+	PROPN
ma-198	386	8	(	(	PUNCT
ma-198	386	9	1−	1−	NUM
ma-198	386	10	ταn)‖xn	ταn)‖xn	X
ma-198	386	11	−	−	PROPN
ma-198	386	12	x∗‖	x∗‖	X
ma-198	386	13	]	]	SYM
ma-198	386	14	2	2	NUM
ma-198	386	15	+	+	NUM
ma-198	386	16	2αn〈ηbx∗	2αn〈ηbx∗	NUM
ma-198	386	17	−	−	NOUN
ma-198	386	18	γf	γf	PROPN
ma-198	386	19	(	(	PUNCT
ma-198	386	20	x∗	x∗	PROPN
ma-198	386	21	)	)	PUNCT
ma-198	386	22	,	,	PUNCT
ma-198	386	23	x∗	x∗	PROPN
ma-198	386	24	−	−	PROPN
ma-198	386	25	xn+1	xn+1	NUM
ma-198	386	26	〉	〉	PROPN
ma-198	386	27	≤	≤	NOUN
ma-198	386	28	[	[	PUNCT
ma-198	386	29	1−	1−	NUM
ma-198	386	30	αn(τ	αn(τ	NUM
ma-198	386	31	−	−	PROPN
ma-198	386	32	γb	γb	PROPN
ma-198	386	33	)	)	PUNCT
ma-198	386	34	]	]	PUNCT
ma-198	386	35	2	2	NUM
ma-198	386	36	‖xn	‖xn	PROPN
ma-198	386	37	−	−	PROPN
ma-198	386	38	x∗‖2	x∗‖2	PROPN
ma-198	387	1	+	+	CCONJ
ma-198	388	1	2αn〈ηbx∗	2αn〈ηbx∗	NUM
ma-198	388	2	−	−	NOUN
ma-198	388	3	γf	γf	PROPN
ma-198	388	4	(	(	PUNCT
ma-198	388	5	x∗	x∗	PROPN
ma-198	388	6	)	)	PUNCT
ma-198	388	7	,	,	PUNCT
ma-198	388	8	x∗	x∗	PROPN
ma-198	388	9	−	−	PROPN
ma-198	389	1	xn+1	xn+1	NUM
ma-198	389	2	〉	〉	PROPN
ma-198	389	3	≤	≤	NOUN
ma-198	389	4	[	[	PUNCT
ma-198	389	5	1−	1−	NUM
ma-198	389	6	αn(τ	αn(τ	NUM
ma-198	389	7	−	−	NUM
ma-198	389	8	γb	γb	PROPN
ma-198	389	9	)	)	PUNCT
ma-198	389	10	]	]	PUNCT
ma-198	390	1	‖xn	‖xn	PROPN
ma-198	390	2	−	−	PUNCT
ma-198	390	3	x∗‖2	x∗‖2	PROPN
ma-198	391	1	+	+	CCONJ
ma-198	392	1	2αn〈ηbx∗	2αn〈ηbx∗	NUM
ma-198	392	2	−	−	NOUN
ma-198	392	3	γf	γf	PROPN
ma-198	392	4	(	(	PUNCT
ma-198	392	5	x∗	x∗	PROPN
ma-198	392	6	)	)	PUNCT
ma-198	392	7	,	,	PUNCT
ma-198	392	8	x∗	x∗	PROPN
ma-198	392	9	−	−	PROPN
ma-198	393	1	xn+1	xn+1	PROPN
ma-198	393	2	〉	〉	PROPN
ma-198	393	3	thus	thus	ADV
ma-198	393	4	,	,	PUNCT
ma-198	393	5	from	from	ADP
ma-198	393	6	lemma	lemma	PROPN
ma-198	393	7	(	(	PUNCT
ma-198	393	8	2.3	2.3	NUM
ma-198	393	9	)	)	PUNCT
ma-198	393	10	,	,	PUNCT
ma-198	393	11	it	it	PRON
ma-198	393	12	follows	follow	VERB
ma-198	393	13	that	that	SCONJ
ma-198	393	14	ψn	ψn	INTJ
ma-198	393	15	→	→	SYM
ma-198	393	16	ψ∗	ψ∗	NOUN
ma-198	393	17	as	as	ADP
ma-198	393	18	n	n	PROPN
ma-198	393	19	→∞	→∞	PROPN
ma-198	393	20	,	,	PUNCT
ma-198	393	21	where	where	SCONJ
ma-198	393	22	bn	bn	NOUN
ma-198	393	23	=	=	NOUN
ma-198	393	24	αn(τ	αn(τ	NUM
ma-198	394	1	−	−	PROPN
ma-198	394	2	γb	γb	NOUN
ma-198	394	3	)	)	PUNCT
ma-198	394	4	,	,	PUNCT
ma-198	394	5	an	an	DET
ma-198	394	6	=	=	SYM
ma-198	394	7	‖xn	‖xn	PROPN
ma-198	394	8	−	−	NOUN
ma-198	394	9	x∗‖2	x∗‖2	PROPN
ma-198	394	10	and	and	CCONJ
ma-198	394	11	σn	σn	NOUN
ma-198	394	12	=	=	SYM
ma-198	394	13	2αn〈ηbx∗	2αn〈ηbx∗	PROPN
ma-198	394	14	−	−	NOUN
ma-198	394	15	γf	γf	PROPN
ma-198	394	16	(	(	PUNCT
ma-198	394	17	x∗	x∗	PROPN
ma-198	394	18	)	)	PUNCT
ma-198	394	19	,	,	PUNCT
ma-198	394	20	x∗	x∗	PROPN
ma-198	394	21	−	−	PROPN
ma-198	395	1	xn+1	xn+1	NUM
ma-198	395	2	〉	〉	PROPN
ma-198	395	3	case	case	NOUN
ma-198	395	4	2	2	NUM
ma-198	395	5	:	:	PUNCT
ma-198	395	6	suppose	suppose	VERB
ma-198	395	7	that	that	SCONJ
ma-198	395	8	the	the	DET
ma-198	395	9	sequence	sequence	NOUN
ma-198	395	10	{	{	PUNCT
ma-198	395	11	‖xn	‖xn	PROPN
ma-198	395	12	−	−	NUM
ma-198	395	13	x∗‖	x∗‖	PROPN
ma-198	395	14	}	}	PUNCT
ma-198	395	15	is	be	AUX
ma-198	395	16	monotonically	monotonically	ADV
ma-198	395	17	increasing	increase	VERB
ma-198	395	18	.	.	PUNCT
ma-198	396	1	set	set	VERB
ma-198	396	2	wn	wn	NOUN
ma-198	397	1	:	:	PUNCT
ma-198	397	2	=	=	SYM
ma-198	397	3	‖xn	‖xn	PROPN
ma-198	397	4	−	−	NUM
ma-198	397	5	x∗‖2	x∗‖2	PROPN
ma-198	397	6	and	and	CCONJ
ma-198	397	7	τ	τ	PROPN
ma-198	397	8	:	:	PUNCT
ma-198	397	9	=	=	SYM
ma-198	397	10	n→	n→	X
ma-198	397	11	n	n	CCONJ
ma-198	397	12	be	be	AUX
ma-198	397	13	a	a	DET
ma-198	397	14	mapping	mapping	NOUN
ma-198	397	15	for	for	ADP
ma-198	397	16	all	all	PRON
ma-198	397	17	n	n	DET
ma-198	397	18	≥	≥	NOUN
ma-198	397	19	n0	n0	NUM
ma-198	397	20	(	(	PUNCT
ma-198	397	21	for	for	ADP
ma-198	397	22	some	some	DET
ma-198	397	23	n0	n0	NUM
ma-198	397	24	sufficient	sufficient	ADJ
ma-198	397	25	large	large	ADJ
ma-198	397	26	)	)	PUNCT
ma-198	397	27	,	,	PUNCT
ma-198	397	28	by	by	ADP
ma-198	397	29	τn	τn	ADP
ma-198	397	30	:	:	PUNCT
ma-198	397	31	=	=	SYM
ma-198	397	32	max{k	max{k	PROPN
ma-198	397	33	∈	∈	PROPN
ma-198	397	34	n	n	NOUN
ma-198	397	35	:	:	PUNCT
ma-198	397	36	k	k	PROPN
ma-198	397	37	≤	≤	PROPN
ma-198	397	38	n	n	CCONJ
ma-198	397	39	,	,	PUNCT
ma-198	397	40	wk	wk	ADP
ma-198	397	41	≤wk+1	≤wk+1	NOUN
ma-198	397	42	}	}	PUNCT
ma-198	397	43	.	.	PUNCT
ma-198	398	1	then	then	ADV
ma-198	398	2	,	,	PUNCT
ma-198	398	3	τ	τ	PROPN
ma-198	398	4	is	be	AUX
ma-198	398	5	a	a	DET
ma-198	398	6	nondecreasing	nondecrease	VERB
ma-198	398	7	sequence	sequence	NOUN
ma-198	398	8	,	,	PUNCT
ma-198	398	9	such	such	ADJ
ma-198	398	10	that	that	SCONJ
ma-198	398	11	τn	τn	ADP
ma-198	398	12	→∞	→∞	NOUN
ma-198	398	13	as	as	ADP
ma-198	398	14	n	n	PROPN
ma-198	398	15	→∞	→∞	PROPN
ma-198	398	16	and	and	CCONJ
ma-198	398	17	wτ(n	wτ(n	NOUN
ma-198	398	18	)	)	PUNCT
ma-198	398	19	≤wτ(n)+1	≤wτ(n)+1	NOUN
ma-198	398	20	}	}	PUNCT
ma-198	398	21	for	for	ADP
ma-198	398	22	all	all	DET
ma-198	398	23	n	n	PRON
ma-198	398	24	≥	≥	NOUN
ma-198	398	25	n0	n0	NUM
ma-198	398	26	.	.	PUNCT
ma-198	399	1	now	now	ADV
ma-198	399	2	,	,	PUNCT
ma-198	399	3	from	from	ADP
ma-198	399	4	(	(	PUNCT
ma-198	399	5	3.11	3.11	NUM
ma-198	399	6	)	)	PUNCT
ma-198	399	7	,	,	PUNCT
ma-198	399	8	we	we	PRON
ma-198	399	9	have	have	VERB
ma-198	399	10	(	(	PUNCT
ma-198	399	11	1−	1−	NUM
ma-198	399	12	ατ(n)τ	ατ(n)τ	NUM
ma-198	399	13	)	)	PUNCT
ma-198	399	14	[	[	PUNCT
ma-198	399	15	(	(	PUNCT
ma-198	399	16	1−	1−	NUM
ma-198	399	17	θn)(θn	θn)(θn	PUNCT
ma-198	399	18	−	−	PROPN
ma-198	399	19	β)‖vτ(n	β)‖vτ(n	NOUN
ma-198	399	20	)	)	PUNCT
ma-198	399	21	−	−	NOUN
ma-198	400	1	δτ(n)‖2	δτ(n)‖2	ADJ
ma-198	400	2	+	+	CCONJ
ma-198	400	3	(	(	PUNCT
ma-198	400	4	1−	1−	NUM
ma-198	400	5	βn)(βn	βn)(βn	PUNCT
ma-198	400	6	−	−	PROPN
ma-198	400	7	β)‖uτ(n	β)‖uτ(n	NOUN
ma-198	400	8	)	)	PUNCT
ma-198	400	9	−	−	PROPN
ma-198	400	10	yτ(n)‖2	yτ(n)‖2	VERB
ma-198	400	11	]	]	PUNCT
ma-198	401	1	≤	≤	NUM
ma-198	401	2	2ατ(n)m	2ατ(n)m	PROPN
ma-198	401	3	(	(	PUNCT
ma-198	401	4	3.29	3.29	NUM
ma-198	401	5	)	)	PUNCT
ma-198	401	6	lim	lim	NOUN
ma-198	401	7	n→+∞	n→+∞	PROPN
ma-198	401	8	τ(1−ατ(n	τ(1−ατ(n	PROPN
ma-198	401	9	)	)	PUNCT
ma-198	401	10	)	)	PUNCT
ma-198	402	1	[	[	PUNCT
ma-198	402	2	(	(	PUNCT
ma-198	402	3	1−θτ(n))(θτ(n)−β)‖vτ(n)−δτ(n)‖2+(1−βτ(n))(βτ(n)−β)‖uτ(n)−yτ(n)‖2	1−θτ(n))(θτ(n)−β)‖vτ(n)−δτ(n)‖2+(1−βτ(n))(βτ(n)−β)‖uτ(n)−yτ(n)‖2	NUM
ma-198	402	4	]	]	PUNCT
ma-198	402	5	=	=	SYM
ma-198	402	6	0	0	PUNCT
ma-198	402	7	since	since	SCONJ
ma-198	402	8	(	(	PUNCT
ma-198	402	9	βτ(n	βτ(n	NOUN
ma-198	402	10	)	)	PUNCT
ma-198	402	11	,	,	PUNCT
ma-198	402	12	θτ(n	θτ(n	NOUN
ma-198	402	13	)	)	PUNCT
ma-198	402	14	)	)	PUNCT
ma-198	403	1	∈	∈	PROPN
ma-198	403	2	(	(	PUNCT
ma-198	403	3	β	β	X
ma-198	403	4	,	,	PUNCT
ma-198	403	5	1	1	NUM
ma-198	403	6	)	)	PUNCT
ma-198	403	7	and	and	CCONJ
ma-198	403	8	lim	lim	PROPN
ma-198	403	9	n→∞	n→∞	PROPN
ma-198	403	10	inf	inf	PROPN
ma-198	403	11	γτ(n)(1−	γτ(n)(1−	X
ma-198	403	12	γτ(n	γτ(n	NOUN
ma-198	403	13	)	)	PUNCT
ma-198	403	14	)	)	PUNCT
ma-198	403	15	>	>	X
ma-198	403	16	0	0	NUM
ma-198	403	17	,	,	PUNCT
ma-198	403	18	we	we	PRON
ma-198	403	19	have	have	VERB
ma-198	403	20	lim	lim	PROPN
ma-198	403	21	n→∞	n→∞	NUM
ma-198	403	22	‖uτ(n	‖uτ(n	PUNCT
ma-198	403	23	)	)	PUNCT
ma-198	404	1	−	−	PROPN
ma-198	404	2	yτ(n)‖	yτ(n)‖	PROPN
ma-198	405	1	=	=	SYM
ma-198	405	2	0	0	PROPN
ma-198	406	1	and	and	CCONJ
ma-198	406	2	lim	lim	PROPN
ma-198	406	3	n→∞	n→∞	X
ma-198	406	4	‖vτ(n	‖vτ(n	PROPN
ma-198	406	5	)	)	PUNCT
ma-198	407	1	−	−	PROPN
ma-198	408	1	δτ(n)‖	δτ(n)‖	PROPN
ma-198	408	2	=	=	SYM
ma-198	408	3	0	0	NUM
ma-198	408	4	with	with	ADP
ma-198	408	5	vτ(n	vτ(n	PUNCT
ma-198	408	6	)	)	PUNCT
ma-198	408	7	∈	∈	PROPN
ma-198	408	8	t1δτ(n	t1δτ(n	PROPN
ma-198	408	9	)	)	PUNCT
ma-198	408	10	and	and	CCONJ
ma-198	408	11	uτ(n	uτ(n	NOUN
ma-198	408	12	)	)	PUNCT
ma-198	408	13	∈	∈	PROPN
ma-198	408	14	t2yτ(n	t2yτ(n	PROPN
ma-198	408	15	)	)	PUNCT
ma-198	409	1	,	,	PUNCT
ma-198	409	2	it	it	PRON
ma-198	409	3	follows	follow	VERB
ma-198	409	4	that	that	SCONJ
ma-198	409	5	lim	lim	PROPN
ma-198	409	6	n→∞	n→∞	X
ma-198	409	7	d	d	NOUN
ma-198	409	8	(	(	PUNCT
ma-198	409	9	δτ(n	δτ(n	NOUN
ma-198	409	10	)	)	PUNCT
ma-198	409	11	,	,	PUNCT
ma-198	409	12	t1δτ(n	t1δτ(n	PROPN
ma-198	409	13	)	)	PUNCT
ma-198	409	14	)	)	PUNCT
ma-198	410	1	=	=	SYM
ma-198	410	2	0	0	PUNCT
ma-198	410	3	and	and	CCONJ
ma-198	410	4	lim	lim	PROPN
ma-198	410	5	n→∞	n→∞	PROPN
ma-198	411	1	d	d	NOUN
ma-198	411	2	(	(	PUNCT
ma-198	411	3	yτ(n	yτ(n	NOUN
ma-198	411	4	)	)	PUNCT
ma-198	411	5	,	,	PUNCT
ma-198	411	6	t2yτ(n	t2yτ(n	PROPN
ma-198	411	7	)	)	PUNCT
ma-198	411	8	)	)	PUNCT
ma-198	412	1	=	=	SYM
ma-198	412	2	0	0	NUM
ma-198	412	3	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	412	4	eur	eur	NOUN
ma-198	412	5	.	.	PUNCT
ma-198	413	1	j.	j.	PROPN
ma-198	413	2	math	math	PROPN
ma-198	413	3	.	.	PUNCT
ma-198	414	1	anal	anal	PROPN
ma-198	414	2	.	.	PUNCT
ma-198	415	1	10.28924	10.28924	NUM
ma-198	415	2	/	/	SYM
ma-198	415	3	ada	ada	PROPN
ma-198	415	4	/	/	SYM
ma-198	415	5	ma.4.2	ma.4.2	PROPN
ma-198	415	6	18following	18followe	VERB
ma-198	415	7	the	the	DET
ma-198	415	8	same	same	ADJ
ma-198	415	9	argument	argument	NOUN
ma-198	415	10	in	in	ADP
ma-198	415	11	case	case	NOUN
ma-198	415	12	1	1	NUM
ma-198	415	13	,	,	PUNCT
ma-198	415	14	we	we	PRON
ma-198	415	15	conclude	conclude	VERB
ma-198	415	16	that	that	SCONJ
ma-198	415	17	lim	lim	PROPN
ma-198	415	18	τ(n)→+∞	τ(n)→+∞	VERB
ma-198	415	19	sup〈ηbx∗	sup〈ηbx∗	ADJ
ma-198	415	20	−	−	PROPN
ma-198	415	21	γf	γf	PROPN
ma-198	415	22	(	(	PUNCT
ma-198	415	23	x∗	x∗	PROPN
ma-198	415	24	)	)	PUNCT
ma-198	415	25	,	,	PUNCT
ma-198	415	26	x∗	x∗	PROPN
ma-198	415	27	−	−	PROPN
ma-198	416	1	xτ(n)+1	xτ(n)+1	PROPN
ma-198	416	2	〉	〉	PROPN
ma-198	416	3	≤	≤	NOUN
ma-198	416	4	0	0	PUNCT
ma-198	417	1	therefore	therefore	ADV
ma-198	417	2	,	,	PUNCT
ma-198	417	3	for	for	ADP
ma-198	417	4	all	all	DET
ma-198	417	5	n	n	PRON
ma-198	417	6	≥	≥	NOUN
ma-198	417	7	n0,and	n0,and	NOUN
ma-198	417	8	from	from	ADP
ma-198	417	9	3.29	3.29	NUM
ma-198	417	10	,	,	PUNCT
ma-198	417	11	we	we	PRON
ma-198	417	12	have	have	VERB
ma-198	417	13	0	0	NUM
ma-198	417	14	≤	≤	PROPN
ma-198	417	15	‖xτ(n)+1	‖xτ(n)+1	PROPN
ma-198	417	16	−	−	PROPN
ma-198	417	17	x∗‖2	x∗‖2	PROPN
ma-198	417	18	−	−	PROPN
ma-198	417	19	‖xτ(n	‖xτ(n	NOUN
ma-198	417	20	)	)	PUNCT
ma-198	417	21	−	−	PROPN
ma-198	418	1	x∗‖2	x∗‖2	PROPN
ma-198	418	2	≤	≤	PROPN
ma-198	418	3	ατ(n)[−αn(τ	ατ(n)[−αn(τ	PROPN
ma-198	418	4	−	−	PROPN
ma-198	418	5	γb)‖xτ(n	γb)‖xτ(n	PROPN
ma-198	418	6	)	)	PUNCT
ma-198	418	7	−	−	NOUN
ma-198	418	8	x∗)‖2	x∗)‖2	VERB
ma-198	419	1	+	+	CCONJ
ma-198	419	2	2ατ(n)〈ηbx∗	2ατ(n)〈ηbx∗	NUM
ma-198	419	3	−	−	NOUN
ma-198	420	1	γf	γf	PROPN
ma-198	420	2	(	(	PUNCT
ma-198	420	3	x∗	x∗	PROPN
ma-198	420	4	)	)	PUNCT
ma-198	420	5	,	,	PUNCT
ma-198	420	6	xτ(n)+1	xτ(n)+1	PROPN
ma-198	420	7	−	−	PROPN
ma-198	420	8	x∗	x∗	PROPN
ma-198	420	9	〉	〉	PROPN
ma-198	420	10	‖xτ(n	‖xτ(n	NOUN
ma-198	420	11	)	)	PUNCT
ma-198	421	1	−	−	PROPN
ma-198	421	2	x∗‖2	x∗‖2	PROPN
ma-198	421	3	≤	≤	ADV
ma-198	421	4	2	2	NUM
ma-198	421	5	τ	τ	NOUN
ma-198	421	6	−	−	NOUN
ma-198	421	7	γb	γb	NOUN
ma-198	422	1	〈	〈	PROPN
ma-198	422	2	ηbx	ηbx	NOUN
ma-198	422	3	∗	∗	NOUN
ma-198	422	4	−	−	NOUN
ma-198	422	5	γf	γf	PROPN
ma-198	422	6	(	(	PUNCT
ma-198	422	7	x∗	x∗	PROPN
ma-198	422	8	)	)	PUNCT
ma-198	422	9	,	,	PUNCT
ma-198	422	10	xτ(n)+1	xτ(n)+1	PROPN
ma-198	423	1	−	−	PROPN
ma-198	423	2	x∗	x∗	PROPN
ma-198	423	3	〉	〉	PROPN
ma-198	423	4	then	then	ADV
ma-198	423	5	we	we	PRON
ma-198	423	6	have	have	VERB
ma-198	423	7	lim	lim	PROPN
ma-198	423	8	n→∞	n→∞	NUM
ma-198	423	9	‖xτ(n	‖xτ(n	NOUN
ma-198	423	10	)	)	PUNCT
ma-198	423	11	−	−	NOUN
ma-198	424	1	x∗‖2	x∗‖2	PROPN
ma-198	425	1	=	=	NOUN
ma-198	425	2	0	0	X
ma-198	425	3	.	.	PUNCT
ma-198	426	1	therefore	therefore	ADV
ma-198	426	2	lim	lim	PROPN
ma-198	426	3	n→∞	n→∞	NUM
ma-198	426	4	wτ(n	wτ(n	PUNCT
ma-198	426	5	)	)	PUNCT
ma-198	427	1	=	=	VERB
ma-198	427	2	lim	lim	PROPN
ma-198	427	3	n→∞	n→∞	X
ma-198	427	4	wτ(n)+1	wτ(n)+1	ADV
ma-198	427	5	=	=	SYM
ma-198	427	6	0.furthermore	0.furthermore	NUM
ma-198	427	7	,	,	PUNCT
ma-198	427	8	for	for	ADP
ma-198	427	9	all	all	DET
ma-198	427	10	n	n	PRON
ma-198	427	11	≥	≥	NOUN
ma-198	427	12	n0	n0	NUM
ma-198	427	13	,	,	PUNCT
ma-198	427	14	we	we	PRON
ma-198	427	15	have	have	VERB
ma-198	427	16	wτ(n	wτ(n	NOUN
ma-198	427	17	)	)	PUNCT
ma-198	427	18	≤	≤	NOUN
ma-198	428	1	wτ(n)+1	wτ(n)+1	ADV
ma-198	428	2	if	if	SCONJ
ma-198	428	3	n	n	X
ma-198	428	4	6=	6=	X
ma-198	428	5	τ(n	τ(n	NOUN
ma-198	428	6	)	)	PUNCT
ma-198	428	7	(	(	PUNCT
ma-198	428	8	that	that	PRON
ma-198	428	9	is	be	AUX
ma-198	428	10	n	n	PRON
ma-198	428	11	>	>	PUNCT
ma-198	428	12	τ(n),because	τ(n),because	NOUN
ma-198	428	13	wj	wj	X
ma-198	428	14	>	>	SYM
ma-198	428	15	wj+1	wj+1	PROPN
ma-198	428	16	,	,	PUNCT
ma-198	428	17	f	f	NOUN
ma-198	428	18	or	or	CCONJ
ma-198	428	19	τ(n	τ(n	PROPN
ma-198	428	20	+	+	CCONJ
ma-198	428	21	1	1	X
ma-198	428	22	)	)	PUNCT
ma-198	428	23	≤	≤	NUM
ma-198	428	24	j	j	PROPN
ma-198	428	25	≤	≤	PROPN
ma-198	428	26	n.hence	n.hence	NOUN
ma-198	428	27	,	,	PUNCT
ma-198	428	28	0	0	NUM
ma-198	428	29	≤wτ(n	≤wτ(n	NUM
ma-198	428	30	)	)	PUNCT
ma-198	428	31	≤	≤	NUM
ma-198	428	32	max	max	PROPN
ma-198	428	33	{	{	PUNCT
ma-198	428	34	wτ(n),wτ(n)+1	wτ(n),wτ(n)+1	NOUN
ma-198	428	35	}	}	PUNCT
ma-198	428	36	=	=	SYM
ma-198	428	37	wτ(n)+1	wτ(n)+1	PROPN
ma-198	428	38	.	.	PUNCT
ma-198	429	1	therefore	therefore	ADV
ma-198	429	2	,	,	PUNCT
ma-198	429	3	wn	wn	PROPN
ma-198	429	4	→	→	X
ma-198	429	5	0	0	NUM
ma-198	429	6	,	,	PUNCT
ma-198	429	7	as	as	ADP
ma-198	429	8	n	n	PROPN
ma-198	429	9	→	→	SYM
ma-198	429	10	∞	∞	PROPN
ma-198	429	11	and	and	CCONJ
ma-198	429	12	this	this	PRON
ma-198	429	13	implies	imply	VERB
ma-198	429	14	that	that	SCONJ
ma-198	429	15	xn	xn	PROPN
ma-198	429	16	→	→	SYM
ma-198	429	17	x∗	x∗	PROPN
ma-198	429	18	as	as	ADP
ma-198	429	19	n	n	X
ma-198	429	20	→∞.	→∞.	PROPN
ma-198	429	21	this	this	PRON
ma-198	429	22	complete	complete	VERB
ma-198	429	23	the	the	DET
ma-198	429	24	proof	proof	NOUN
ma-198	429	25	.	.	PUNCT
ma-198	430	1	�	�	PROPN
ma-198	430	2	now	now	ADV
ma-198	430	3	using	use	VERB
ma-198	430	4	theorem	theorem	NOUN
ma-198	430	5	(	(	PUNCT
ma-198	430	6	3.1	3.1	NUM
ma-198	430	7	)	)	PUNCT
ma-198	430	8	,	,	PUNCT
ma-198	430	9	and	and	CCONJ
ma-198	430	10	multivalued	multivalued	ADJ
ma-198	430	11	mappings	mapping	NOUN
ma-198	430	12	are	be	AUX
ma-198	430	13	nonexpansive	nonexpansive	ADJ
ma-198	430	14	mappings	mapping	NOUN
ma-198	430	15	with	with	ADP
ma-198	430	16	convexvalues	convexvalue	NOUN
ma-198	430	17	without	without	ADP
ma-198	430	18	demiclosed	demiclosed	ADJ
ma-198	430	19	assumptions	assumption	NOUN
ma-198	430	20	in	in	ADP
ma-198	430	21	the	the	DET
ma-198	430	22	following	follow	VERB
ma-198	430	23	theorem	theorem	NOUN
ma-198	430	24	.	.	PUNCT
ma-198	430	25	theorem	theorem	PROPN
ma-198	430	26	3.2	3.2	NUM
ma-198	430	27	.	.	PUNCT
ma-198	431	1	let	let	VERB
ma-198	431	2	h	h	PRON
ma-198	431	3	be	be	AUX
ma-198	431	4	a	a	DET
ma-198	431	5	real	real	ADJ
ma-198	431	6	hilbert	hilbert	NOUN
ma-198	431	7	space	space	NOUN
ma-198	431	8	and	and	CCONJ
ma-198	431	9	k	k	PROPN
ma-198	431	10	be	be	AUX
ma-198	431	11	a	a	DET
ma-198	431	12	nonempty	nonempty	ADJ
ma-198	431	13	,	,	PUNCT
ma-198	431	14	closed	closed	ADJ
ma-198	431	15	convex	convex	NOUN
ma-198	431	16	subset	subset	NOUN
ma-198	431	17	of	of	ADP
ma-198	431	18	h.	h.	PROPN
ma-198	431	19	let	let	VERB
ma-198	431	20	a	a	PRON
ma-198	431	21	:	:	PUNCT
ma-198	431	22	k	k	X
ma-198	431	23	→	→	PUNCT
ma-198	431	24	h	h	NOUN
ma-198	431	25	be	be	AUX
ma-198	431	26	an	an	DET
ma-198	431	27	α−inverse	α−inverse	NOUN
ma-198	431	28	strongly	strongly	ADV
ma-198	431	29	monotone	monotone	ADJ
ma-198	431	30	operator	operator	NOUN
ma-198	431	31	and	and	CCONJ
ma-198	431	32	let	let	VERB
ma-198	431	33	b	b	NOUN
ma-198	431	34	:	:	PUNCT
ma-198	431	35	h	h	NOUN
ma-198	431	36	→	→	PUNCT
ma-198	431	37	h	h	NOUN
ma-198	431	38	be	be	AUX
ma-198	431	39	an	an	DET
ma-198	431	40	k−strongly	k−strongly	ADV
ma-198	431	41	monotone	monotone	ADJ
ma-198	431	42	and	and	CCONJ
ma-198	431	43	l−lipschitzian	l−lipschitzian	ADJ
ma-198	431	44	operator	operator	NOUN
ma-198	431	45	.	.	PUNCT
ma-198	432	1	let	let	VERB
ma-198	432	2	f	f	NOUN
ma-198	432	3	:	:	PUNCT
ma-198	432	4	k	k	X
ma-198	432	5	→	→	PUNCT
ma-198	432	6	h	h	NOUN
ma-198	432	7	be	be	AUX
ma-198	432	8	an	an	DET
ma-198	432	9	b−lipschitzian	b−lipschitzian	ADJ
ma-198	432	10	mapping	mapping	NOUN
ma-198	432	11	and	and	CCONJ
ma-198	432	12	m	m	PRON
ma-198	432	13	:	:	PUNCT
ma-198	432	14	h	h	NOUN
ma-198	432	15	→	→	SYM
ma-198	432	16	2h	2h	NUM
ma-198	432	17	be	be	VERB
ma-198	432	18	a	a	DET
ma-198	432	19	maximal	maximal	ADJ
ma-198	432	20	monotone	monotone	ADJ
ma-198	432	21	mapping	mapping	NOUN
ma-198	432	22	such	such	ADJ
ma-198	432	23	that	that	SCONJ
ma-198	432	24	the	the	DET
ma-198	432	25	domain	domain	NOUN
ma-198	432	26	of	of	ADP
ma-198	432	27	m	m	PROPN
ma-198	432	28	is	be	AUX
ma-198	432	29	included	include	VERB
ma-198	432	30	in	in	ADP
ma-198	432	31	k.	k.	PROPN
ma-198	432	32	let	let	VERB
ma-198	432	33	t1	t1	NOUN
ma-198	432	34	,	,	PUNCT
ma-198	432	35	t2	t2	NOUN
ma-198	432	36	:	:	PUNCT
ma-198	432	37	k	k	X
ma-198	432	38	→	→	SYM
ma-198	432	39	cb(k	cb(k	AUX
ma-198	432	40	)	)	PUNCT
ma-198	432	41	be	be	AUX
ma-198	432	42	a	a	DET
ma-198	432	43	multivalued	multivalue	VERB
ma-198	432	44	β−	β−	PRON
ma-198	432	45	demicontractive	demicontractive	ADJ
ma-198	432	46	mapping	mapping	NOUN
ma-198	432	47	and	and	CCONJ
ma-198	432	48	t3	t3	NOUN
ma-198	432	49	:	:	PUNCT
ma-198	433	1	k	k	X
ma-198	433	2	→	→	SYM
ma-198	433	3	cb(k	cb(k	AUX
ma-198	433	4	)	)	PUNCT
ma-198	433	5	be	be	AUX
ma-198	433	6	a	a	DET
ma-198	433	7	multivalued	multivalued	ADJ
ma-198	433	8	quasi	quasi	ADJ
ma-198	433	9	-	-	ADJ
ma-198	433	10	nonexpansive	nonexpansive	ADJ
ma-198	433	11	mapping	mapping	NOUN
ma-198	433	12	such	such	ADJ
ma-198	433	13	that	that	SCONJ
ma-198	433	14	ω	ω	NOUN
ma-198	433	15	:	:	PUNCT
ma-198	433	16	=	=	SYM
ma-198	433	17	f	f	PROPN
ma-198	433	18	ix(t1)∩f	ix(t1)∩f	PROPN
ma-198	433	19	ix(t2)∩f	ix(t2)∩f	PROPN
ma-198	433	20	ix(t3)∩s(π	ix(t3)∩s(π	PROPN
ma-198	433	21	,	,	PUNCT
ma-198	433	22	λ	λ	NOUN
ma-198	433	23	)	)	PUNCT
ma-198	433	24	6=	6=	ADP
ma-198	433	25	∅	∅	NOUN
ma-198	433	26	and	and	CCONJ
ma-198	433	27	t1q	t1q	NUM
ma-198	433	28	=	=	SYM
ma-198	433	29	t2q	t2q	PROPN
ma-198	433	30	=	=	SYM
ma-198	433	31	t3q	t3q	PROPN
ma-198	433	32	=	=	SYM
ma-198	433	33	{	{	PUNCT
ma-198	433	34	q},∀q	q},∀q	PROPN
ma-198	433	35	∈	∈	PROPN
ma-198	433	36	ω	ω	PROPN
ma-198	433	37	.	.	PUNCT
ma-198	434	1	for	for	SCONJ
ma-198	434	2	given	give	VERB
ma-198	434	3	x0	x0	PROPN
ma-198	434	4	∈	∈	PROPN
ma-198	434	5	k	k	NOUN
ma-198	434	6	,	,	PUNCT
ma-198	434	7	let	let	VERB
ma-198	434	8	{	{	PUNCT
ma-198	434	9	xn	xn	AUX
ma-198	434	10	}	}	PUNCT
ma-198	434	11	be	be	AUX
ma-198	434	12	generated	generate	VERB
ma-198	434	13	by	by	ADP
ma-198	434	14	the	the	DET
ma-198	434	15	algorithm:	algorithm:	PROPN
ma-198	434	16	δn	δn	NOUN
ma-198	434	17	=	=	PUNCT
ma-198	434	18	jmλn(i	jmλn(i	PROPN
ma-198	434	19	−	−	PROPN
ma-198	434	20	λna)xn	λna)xn	NOUN
ma-198	434	21	;	;	PUNCT
ma-198	434	22	yn	yn	PROPN
ma-198	434	23	=	=	PUNCT
ma-198	434	24	θnδn	θnδn	PROPN
ma-198	434	25	+	+	CCONJ
ma-198	434	26	(	(	PUNCT
ma-198	434	27	1−	1−	NUM
ma-198	434	28	θn)vn	θn)vn	ADP
ma-198	434	29	,	,	PUNCT
ma-198	434	30	vn	vn	PROPN
ma-198	434	31	∈	∈	PROPN
ma-198	434	32	t1δn	t1δn	PROPN
ma-198	434	33	;	;	PUNCT
ma-198	434	34	zn	zn	PROPN
ma-198	434	35	=	=	SYM
ma-198	434	36	βnyn	βnyn	PROPN
ma-198	434	37	+	+	CCONJ
ma-198	434	38	(	(	PUNCT
ma-198	434	39	1−	1−	NUM
ma-198	434	40	βn)un	βn)un	NUM
ma-198	434	41	,	,	PUNCT
ma-198	434	42	un	un	PROPN
ma-198	434	43	∈	∈	PROPN
ma-198	434	44	t2yn	t2yn	NUM
ma-198	434	45	;	;	PUNCT
ma-198	434	46	tn	tn	PROPN
ma-198	434	47	=	=	SYM
ma-198	434	48	γnzn	γnzn	NOUN
ma-198	434	49	+	+	CCONJ
ma-198	434	50	(	(	PUNCT
ma-198	434	51	1−	1−	NUM
ma-198	434	52	γn)wn	γn)wn	NOUN
ma-198	434	53	,	,	PUNCT
ma-198	434	54	wn	wn	PROPN
ma-198	434	55	∈	∈	PROPN
ma-198	434	56	t3zn	t3zn	PUNCT
ma-198	434	57	;	;	PUNCT
ma-198	434	58	xn+1	xn+1	X
ma-198	434	59	=	=	SYM
ma-198	434	60	pk(αnγf	pk(αnγf	X
ma-198	434	61	(	(	PUNCT
ma-198	434	62	xn	xn	X
ma-198	434	63	)	)	PUNCT
ma-198	434	64	+	+	CCONJ
ma-198	434	65	(	(	PUNCT
ma-198	434	66	i	i	PRON
ma-198	434	67	−	−	PROPN
ma-198	434	68	ηαnb)tn	ηαnb)tn	NOUN
ma-198	434	69	)	)	PUNCT
ma-198	434	70	(	(	PUNCT
ma-198	434	71	3.30	3.30	NUM
ma-198	434	72	)	)	PUNCT
ma-198	434	73	where	where	SCONJ
ma-198	434	74	{	{	PUNCT
ma-198	434	75	βn	βn	NOUN
ma-198	434	76	}	}	PUNCT
ma-198	434	77	,	,	PUNCT
ma-198	434	78	{	{	PUNCT
ma-198	434	79	γn	γn	NOUN
ma-198	434	80	}	}	PUNCT
ma-198	434	81	,	,	PUNCT
ma-198	434	82	{	{	PUNCT
ma-198	434	83	θn	θn	NOUN
ma-198	434	84	}	}	PUNCT
ma-198	434	85	,	,	PUNCT
ma-198	434	86	{	{	PUNCT
ma-198	434	87	λn	λn	NOUN
ma-198	434	88	}	}	PUNCT
ma-198	434	89	and	and	CCONJ
ma-198	434	90	{	{	PUNCT
ma-198	434	91	αn	αn	NOUN
ma-198	434	92	}	}	PUNCT
ma-198	434	93	are	be	AUX
ma-198	434	94	real	real	ADJ
ma-198	434	95	sequence	sequence	NOUN
ma-198	434	96	in	in	ADP
ma-198	434	97	(	(	PUNCT
ma-198	434	98	0	0	NUM
ma-198	434	99	,	,	PUNCT
ma-198	434	100	1	1	X
ma-198	434	101	)	)	PUNCT
ma-198	434	102	satisfying	satisfy	VERB
ma-198	434	103	the	the	DET
ma-198	434	104	following	follow	VERB
ma-198	434	105	conditions	condition	NOUN
ma-198	434	106	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	PROPN
ma-198	434	107	eur	eur	NOUN
ma-198	434	108	.	.	PUNCT
ma-198	435	1	j.	j.	PROPN
ma-198	435	2	math	math	PROPN
ma-198	435	3	.	.	PUNCT
ma-198	436	1	anal	anal	PROPN
ma-198	436	2	.	.	PUNCT
ma-198	437	1	10.28924	10.28924	NUM
ma-198	437	2	/	/	SYM
ma-198	437	3	ada	ada	PROPN
ma-198	437	4	/	/	SYM
ma-198	437	5	ma.4.2	ma.4.2	PROPN
ma-198	437	6	19	19	NUM
ma-198	437	7	i	i	NOUN
ma-198	437	8	):	):	PUNCT
ma-198	437	9	lim	lim	PROPN
ma-198	437	10	n→∞	n→∞	NUM
ma-198	437	11	αn	αn	NOUN
ma-198	438	1	=	=	NOUN
ma-198	438	2	0	0	NUM
ma-198	439	1	∞∑	∞∑	NUM
ma-198	439	2	n=0	n=0	NUM
ma-198	439	3	αn	αn	NOUN
ma-198	439	4	<	<	X
ma-198	439	5	∞	∞	PROPN
ma-198	439	6	ii	ii	PROPN
ma-198	439	7	):	):	PUNCT
ma-198	439	8	lim	lim	PROPN
ma-198	439	9	n→∞	n→∞	PRON
ma-198	439	10	inf(1−	inf(1−	VERB
ma-198	439	11	βn)(βn	βn)(βn	PUNCT
ma-198	439	12	−	−	PROPN
ma-198	439	13	β	β	X
ma-198	439	14	)	)	PUNCT
ma-198	439	15	>	>	X
ma-198	439	16	0	0	PUNCT
ma-198	439	17	and	and	CCONJ
ma-198	439	18	lim	lim	PROPN
ma-198	439	19	n→∞	n→∞	PRON
ma-198	439	20	inf(1−	inf(1−	VERB
ma-198	439	21	θn)(θn	θn)(θn	PUNCT
ma-198	439	22	−	−	NOUN
ma-198	439	23	β	β	NOUN
ma-198	439	24	)	)	PUNCT
ma-198	439	25	>	>	X
ma-198	439	26	0	0	NUM
ma-198	439	27	,	,	PUNCT
ma-198	439	28	(	(	PUNCT
ma-198	439	29	βn	βn	NOUN
ma-198	439	30	,	,	PUNCT
ma-198	439	31	θn	θn	ADJ
ma-198	439	32	)	)	PUNCT
ma-198	439	33	∈	∈	PROPN
ma-198	439	34	(	(	PUNCT
ma-198	439	35	β	β	X
ma-198	439	36	,	,	PUNCT
ma-198	439	37	1	1	NUM
ma-198	439	38	)	)	PUNCT
ma-198	439	39	iii	iii	PROPN
ma-198	439	40	):	):	PUNCT
ma-198	439	41	limn→∞	limn→∞	PROPN
ma-198	439	42	inf(1−	inf(1−	VERB
ma-198	439	43	γn)γn	γn)γn	PROPN
ma-198	439	44	)	)	PUNCT
ma-198	439	45	>	>	X
ma-198	439	46	0	0	PUNCT
ma-198	439	47	assume	assume	VERB
ma-198	439	48	that	that	SCONJ
ma-198	439	49	0	0	NUM
ma-198	439	50	<	<	X
ma-198	439	51	η	η	X
ma-198	439	52	<	<	X
ma-198	439	53	2k	2k	PROPN
ma-198	439	54	l2	l2	NOUN
ma-198	439	55	,	,	PUNCT
ma-198	439	56	0	0	PUNCT
ma-198	439	57	<	<	X
ma-198	439	58	γb	γb	X
ma-198	439	59	<	<	X
ma-198	439	60	τ	τ	PROPN
ma-198	439	61	,	,	PUNCT
ma-198	439	62	where	where	SCONJ
ma-198	439	63	τ	τ	PROPN
ma-198	439	64	=	=	SYM
ma-198	439	65	η	η	PROPN
ma-198	439	66	(	(	PUNCT
ma-198	439	67	k	k	PROPN
ma-198	439	68	−	−	PROPN
ma-198	439	69	l2η	l2η	PROPN
ma-198	439	70	2	2	NUM
ma-198	439	71	)	)	PUNCT
ma-198	439	72	,	,	PUNCT
ma-198	439	73	and	and	CCONJ
ma-198	439	74	the	the	DET
ma-198	439	75	sequences	sequence	NOUN
ma-198	439	76	defined	define	VERB
ma-198	439	77	in	in	ADP
ma-198	439	78	(	(	PUNCT
ma-198	439	79	3.30	3.30	NUM
ma-198	439	80	)	)	PUNCT
ma-198	439	81	,	,	PUNCT
ma-198	439	82	that	that	ADV
ma-198	439	83	is	be	AUX
ma-198	439	84	{	{	PUNCT
ma-198	439	85	xn	xn	PUNCT
ma-198	439	86	}	}	PUNCT
ma-198	439	87	and	and	CCONJ
ma-198	439	88	{	{	PUNCT
ma-198	439	89	δn	δn	NOUN
ma-198	439	90	}	}	PUNCT
ma-198	439	91	converge	converge	VERB
ma-198	439	92	strongly	strongly	ADV
ma-198	439	93	to	to	ADP
ma-198	439	94	unique	unique	ADJ
ma-198	439	95	solution	solution	NOUN
ma-198	439	96	x∗	x∗	PROPN
ma-198	439	97	∈	∈	PROPN
ma-198	439	98	ω	ω	PROPN
ma-198	439	99	,	,	PUNCT
ma-198	439	100	which	which	PRON
ma-198	439	101	also	also	ADV
ma-198	439	102	solve	solve	VERB
ma-198	439	103	the	the	DET
ma-198	439	104	following	follow	VERB
ma-198	439	105	variational	variational	ADJ
ma-198	439	106	inequality	inequality	NOUN
ma-198	439	107	:	:	PUNCT
ma-198	439	108	〈	〈	PROPN
ma-198	439	109	ηbx∗	ηbx∗	NOUN
ma-198	439	110	−	−	PROPN
ma-198	439	111	γf	γf	PROPN
ma-198	439	112	(	(	PUNCT
ma-198	439	113	x∗	x∗	PROPN
ma-198	439	114	)	)	PUNCT
ma-198	439	115	,	,	PUNCT
ma-198	439	116	x∗	x∗	PROPN
ma-198	439	117	−	−	PROPN
ma-198	440	1	q	q	NOUN
ma-198	440	2	〉	〉	NOUN
ma-198	440	3	≤	≤	NUM
ma-198	440	4	0	0	NUM
ma-198	440	5	,	,	PUNCT
ma-198	440	6	∀q	∀q	PROPN
ma-198	440	7	∈	∈	PROPN
ma-198	440	8	ω	ω	PROPN
ma-198	440	9	(	(	PUNCT
ma-198	440	10	3.31	3.31	NUM
ma-198	440	11	)	)	PUNCT
ma-198	440	12	proof	proof	NOUN
ma-198	440	13	.	.	PUNCT
ma-198	441	1	since	since	SCONJ
ma-198	441	2	every	every	DET
ma-198	441	3	multivalued	multivalue	VERB
ma-198	441	4	nonexpansive	nonexpansive	ADJ
ma-198	441	5	mapping	mapping	NOUN
ma-198	441	6	is	be	AUX
ma-198	441	7	quasi	quasi	ADJ
ma-198	441	8	-	-	ADJ
ma-198	441	9	nonexpansive	nonexpansive	ADJ
ma-198	441	10	and	and	CCONJ
ma-198	441	11	demicontractive	demicontractive	ADJ
ma-198	441	12	,	,	PUNCT
ma-198	441	13	then	then	ADV
ma-198	441	14	,	,	PUNCT
ma-198	441	15	the	the	DET
ma-198	441	16	proof	proof	NOUN
ma-198	441	17	follows	follow	VERB
ma-198	441	18	theorem	theorem	VERB
ma-198	441	19	3.10	3.10	NUM
ma-198	441	20	�	�	PROPN
ma-198	441	21	now	now	ADV
ma-198	441	22	using	use	VERB
ma-198	441	23	the	the	DET
ma-198	441	24	same	same	ADJ
ma-198	441	25	argument	argument	NOUN
ma-198	441	26	of	of	ADP
ma-198	441	27	the	the	DET
ma-198	441	28	proof	proof	NOUN
ma-198	441	29	in	in	ADP
ma-198	441	30	theorem	theorem	NOUN
ma-198	441	31	(	(	PUNCT
ma-198	441	32	3.1	3.1	NUM
ma-198	441	33	)	)	PUNCT
ma-198	441	34	in	in	ADP
ma-198	441	35	theorem	theorem	NOUN
ma-198	441	36	(	(	PUNCT
ma-198	441	37	3.3	3.3	NUM
ma-198	441	38	)	)	PUNCT
ma-198	441	39	,	,	PUNCT
ma-198	441	40	we	we	PRON
ma-198	441	41	achieved	achieve	VERB
ma-198	441	42	thedesired	thedesire	VERB
ma-198	441	43	results	result	NOUN
ma-198	441	44	.	.	PUNCT
ma-198	442	1	in	in	ADP
ma-198	442	2	theorem	theorem	NOUN
ma-198	442	3	(	(	PUNCT
ma-198	442	4	3.3	3.3	NUM
ma-198	442	5	)	)	PUNCT
ma-198	442	6	,	,	PUNCT
ma-198	442	7	we	we	PRON
ma-198	442	8	let	let	VERB
ma-198	442	9	t1	t1	NOUN
ma-198	442	10	=	=	SYM
ma-198	442	11	pt1	pt1	PROPN
ma-198	442	12	,	,	PUNCT
ma-198	442	13	t2	t2	NOUN
ma-198	442	14	=	=	SYM
ma-198	442	15	pt2	pt2	PROPN
ma-198	442	16	and	and	CCONJ
ma-198	442	17	t3	t3	PROPN
ma-198	442	18	=	=	PUNCT
ma-198	442	19	pt3	pt3	NOUN
ma-198	442	20	without	without	ADP
ma-198	442	21	the	the	DET
ma-198	442	22	assumptionsthat	assumptionsthat	ADV
ma-198	443	1	t1q	t1q	NUM
ma-198	443	2	=	=	SYM
ma-198	443	3	t2q	t2q	PROPN
ma-198	443	4	=	=	SYM
ma-198	443	5	t3q	t3q	PROPN
ma-198	443	6	=	=	SYM
ma-198	443	7	{	{	PUNCT
ma-198	443	8	q},∀q	q},∀q	PROPN
ma-198	443	9	∈	∈	PROPN
ma-198	443	10	ω	ω	NOUN
ma-198	443	11	theorem	theorem	VERB
ma-198	443	12	3.3	3.3	NUM
ma-198	443	13	.	.	PUNCT
ma-198	444	1	let	let	VERB
ma-198	444	2	h	h	PRON
ma-198	444	3	be	be	AUX
ma-198	444	4	a	a	DET
ma-198	444	5	real	real	ADJ
ma-198	444	6	hilbert	hilbert	NOUN
ma-198	444	7	space	space	NOUN
ma-198	444	8	and	and	CCONJ
ma-198	444	9	k	k	PROPN
ma-198	444	10	be	be	AUX
ma-198	444	11	a	a	DET
ma-198	444	12	nonempty	nonempty	ADJ
ma-198	444	13	,	,	PUNCT
ma-198	444	14	closed	closed	ADJ
ma-198	444	15	convex	convex	NOUN
ma-198	444	16	subset	subset	NOUN
ma-198	444	17	of	of	ADP
ma-198	444	18	h.	h.	PROPN
ma-198	444	19	let	let	VERB
ma-198	444	20	a	a	PRON
ma-198	444	21	:	:	PUNCT
ma-198	444	22	k	k	X
ma-198	444	23	→	→	PUNCT
ma-198	444	24	h	h	NOUN
ma-198	444	25	be	be	AUX
ma-198	444	26	an	an	DET
ma-198	444	27	α−inverse	α−inverse	NOUN
ma-198	444	28	strongly	strongly	ADV
ma-198	444	29	monotone	monotone	ADJ
ma-198	444	30	operator	operator	NOUN
ma-198	444	31	and	and	CCONJ
ma-198	444	32	let	let	VERB
ma-198	444	33	b	b	NOUN
ma-198	444	34	:	:	PUNCT
ma-198	444	35	h	h	NOUN
ma-198	444	36	→	→	PUNCT
ma-198	444	37	h	h	NOUN
ma-198	444	38	be	be	AUX
ma-198	444	39	an	an	DET
ma-198	444	40	k−strongly	k−strongly	ADV
ma-198	444	41	monotone	monotone	ADJ
ma-198	444	42	and	and	CCONJ
ma-198	444	43	l−lipschitzian	l−lipschitzian	ADJ
ma-198	444	44	operator	operator	NOUN
ma-198	444	45	.	.	PUNCT
ma-198	445	1	let	let	VERB
ma-198	445	2	f	f	NOUN
ma-198	445	3	:	:	PUNCT
ma-198	445	4	k	k	X
ma-198	445	5	→	→	PUNCT
ma-198	445	6	h	h	NOUN
ma-198	445	7	be	be	AUX
ma-198	445	8	an	an	DET
ma-198	445	9	b−lipschitzian	b−lipschitzian	ADJ
ma-198	445	10	mapping	mapping	NOUN
ma-198	445	11	and	and	CCONJ
ma-198	445	12	m	m	PRON
ma-198	445	13	:	:	PUNCT
ma-198	445	14	h	h	NOUN
ma-198	445	15	→	→	SYM
ma-198	445	16	2h	2h	NUM
ma-198	445	17	be	be	VERB
ma-198	445	18	a	a	DET
ma-198	445	19	maximal	maximal	ADJ
ma-198	445	20	monotone	monotone	ADJ
ma-198	445	21	mapping	mapping	NOUN
ma-198	445	22	such	such	ADJ
ma-198	445	23	that	that	SCONJ
ma-198	445	24	the	the	DET
ma-198	445	25	domain	domain	NOUN
ma-198	445	26	of	of	ADP
ma-198	445	27	m	m	PROPN
ma-198	445	28	is	be	AUX
ma-198	445	29	included	include	VERB
ma-198	445	30	in	in	ADP
ma-198	445	31	k.	k.	PROPN
ma-198	445	32	let	let	VERB
ma-198	445	33	t1	t1	NOUN
ma-198	445	34	,	,	PUNCT
ma-198	445	35	t2	t2	NOUN
ma-198	445	36	:	:	PUNCT
ma-198	445	37	k	k	X
ma-198	445	38	→	→	SYM
ma-198	445	39	cb(k	cb(k	AUX
ma-198	445	40	)	)	PUNCT
ma-198	445	41	be	be	AUX
ma-198	445	42	a	a	DET
ma-198	445	43	multivalued	multivalue	VERB
ma-198	445	44	β−	β−	PRON
ma-198	445	45	demicontractive	demicontractive	ADJ
ma-198	445	46	mapping	mapping	NOUN
ma-198	445	47	and	and	CCONJ
ma-198	445	48	t3	t3	NOUN
ma-198	445	49	:	:	PUNCT
ma-198	446	1	k	k	X
ma-198	446	2	→	→	SYM
ma-198	446	3	cb(k	cb(k	AUX
ma-198	446	4	)	)	PUNCT
ma-198	446	5	be	be	AUX
ma-198	446	6	a	a	DET
ma-198	446	7	multivalued	multivalued	ADJ
ma-198	446	8	quasi	quasi	ADJ
ma-198	446	9	-	-	ADJ
ma-198	446	10	nonexpansive	nonexpansive	ADJ
ma-198	446	11	mapping	mapping	NOUN
ma-198	446	12	such	such	ADJ
ma-198	446	13	that	that	SCONJ
ma-198	446	14	ω	ω	NOUN
ma-198	446	15	:	:	PUNCT
ma-198	446	16	=	=	SYM
ma-198	446	17	f	f	PROPN
ma-198	446	18	ix(t1)∩f	ix(t1)∩f	PROPN
ma-198	446	19	ix(t2)∩f	ix(t2)∩f	PROPN
ma-198	446	20	ix(t3)∩s(m	ix(t3)∩s(m	PROPN
ma-198	446	21	,	,	PUNCT
ma-198	446	22	a	a	PRON
ma-198	446	23	)	)	PUNCT
ma-198	446	24	6=	6=	ADP
ma-198	446	25	∅.	∅.	VERB
ma-198	446	26	for	for	ADP
ma-198	446	27	given	give	VERB
ma-198	446	28	x0	x0	PROPN
ma-198	446	29	∈	∈	PROPN
ma-198	446	30	k	k	NOUN
ma-198	446	31	,	,	PUNCT
ma-198	446	32	let	let	VERB
ma-198	446	33	{	{	PUNCT
ma-198	446	34	xn	xn	AUX
ma-198	446	35	}	}	PUNCT
ma-198	446	36	be	be	AUX
ma-198	446	37	generated	generate	VERB
ma-198	446	38	by	by	ADP
ma-198	446	39	the	the	DET
ma-198	446	40	algorithm:	algorithm:	PROPN
ma-198	446	41	δn	δn	NOUN
ma-198	446	42	=	=	PUNCT
ma-198	446	43	jmλn(i	jmλn(i	PROPN
ma-198	446	44	−	−	PROPN
ma-198	446	45	λna)xn	λna)xn	NOUN
ma-198	446	46	;	;	PUNCT
ma-198	446	47	yn	yn	PROPN
ma-198	446	48	=	=	PUNCT
ma-198	446	49	θnδn	θnδn	PROPN
ma-198	446	50	+	+	CCONJ
ma-198	446	51	(	(	PUNCT
ma-198	446	52	1−	1−	NUM
ma-198	446	53	θn)vn	θn)vn	ADP
ma-198	446	54	,	,	PUNCT
ma-198	446	55	vn	vn	PROPN
ma-198	446	56	∈	∈	PROPN
ma-198	446	57	t1δn	t1δn	PROPN
ma-198	446	58	;	;	PUNCT
ma-198	446	59	zn	zn	PROPN
ma-198	446	60	=	=	SYM
ma-198	446	61	βnyn	βnyn	PROPN
ma-198	446	62	+	+	CCONJ
ma-198	446	63	(	(	PUNCT
ma-198	446	64	1−	1−	NUM
ma-198	446	65	βn)un	βn)un	NUM
ma-198	446	66	,	,	PUNCT
ma-198	446	67	un	un	PROPN
ma-198	446	68	∈	∈	PROPN
ma-198	446	69	t2yn	t2yn	NUM
ma-198	446	70	;	;	PUNCT
ma-198	446	71	tn	tn	PROPN
ma-198	446	72	=	=	SYM
ma-198	446	73	γnzn	γnzn	NOUN
ma-198	447	1	+	+	CCONJ
ma-198	447	2	(	(	PUNCT
ma-198	447	3	1−	1−	NUM
ma-198	447	4	γn)wn	γn)wn	NOUN
ma-198	447	5	,	,	PUNCT
ma-198	447	6	wn	wn	PROPN
ma-198	447	7	∈	∈	PROPN
ma-198	447	8	t3zn	t3zn	PUNCT
ma-198	447	9	;	;	PUNCT
ma-198	447	10	xn+1	xn+1	X
ma-198	447	11	=	=	SYM
ma-198	448	1	pk(αnγf	pk(αnγf	X
ma-198	448	2	(	(	PUNCT
ma-198	448	3	xn	xn	X
ma-198	448	4	)	)	PUNCT
ma-198	449	1	+	+	CCONJ
ma-198	449	2	(	(	PUNCT
ma-198	449	3	i	i	PRON
ma-198	449	4	−	−	PROPN
ma-198	449	5	ηαnb)tn	ηαnb)tn	NOUN
ma-198	449	6	)	)	PUNCT
ma-198	449	7	(	(	PUNCT
ma-198	449	8	3.32	3.32	NUM
ma-198	449	9	)	)	PUNCT
ma-198	449	10	where	where	SCONJ
ma-198	449	11	{	{	PUNCT
ma-198	449	12	βn	βn	NOUN
ma-198	449	13	}	}	PUNCT
ma-198	449	14	,	,	PUNCT
ma-198	449	15	{	{	PUNCT
ma-198	449	16	γn	γn	NOUN
ma-198	449	17	}	}	PUNCT
ma-198	449	18	,	,	PUNCT
ma-198	449	19	{	{	PUNCT
ma-198	449	20	θn	θn	NOUN
ma-198	449	21	}	}	PUNCT
ma-198	449	22	,	,	PUNCT
ma-198	449	23	{	{	PUNCT
ma-198	449	24	λn	λn	NOUN
ma-198	449	25	}	}	PUNCT
ma-198	449	26	and	and	CCONJ
ma-198	449	27	{	{	PUNCT
ma-198	449	28	αn	αn	NOUN
ma-198	449	29	}	}	PUNCT
ma-198	449	30	are	be	AUX
ma-198	449	31	real	real	ADJ
ma-198	449	32	sequence	sequence	NOUN
ma-198	449	33	in	in	ADP
ma-198	449	34	(	(	PUNCT
ma-198	449	35	0	0	NUM
ma-198	449	36	,	,	PUNCT
ma-198	449	37	1	1	X
ma-198	449	38	)	)	PUNCT
ma-198	449	39	satisfying	satisfy	VERB
ma-198	449	40	the	the	DET
ma-198	449	41	following	follow	VERB
ma-198	449	42	conditions	condition	NOUN
ma-198	449	43	i	i	PRON
ma-198	449	44	):	):	PUNCT
ma-198	449	45	lim	lim	PROPN
ma-198	449	46	n→∞	n→∞	NUM
ma-198	449	47	αn	αn	NOUN
ma-198	450	1	=	=	NOUN
ma-198	450	2	0	0	NUM
ma-198	451	1	∞∑	∞∑	NUM
ma-198	451	2	n=0	n=0	NUM
ma-198	451	3	αn	αn	NOUN
ma-198	451	4	<	<	NOUN
ma-198	451	5	∞	∞	NUM
ma-198	451	6	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	ADJ
ma-198	451	7	eur	eur	NOUN
ma-198	451	8	.	.	PUNCT
ma-198	452	1	j.	j.	PROPN
ma-198	452	2	math	math	PROPN
ma-198	452	3	.	.	PUNCT
ma-198	453	1	anal	anal	PROPN
ma-198	453	2	.	.	PUNCT
ma-198	454	1	10.28924	10.28924	NUM
ma-198	454	2	/	/	SYM
ma-198	454	3	ada	ada	PROPN
ma-198	454	4	/	/	SYM
ma-198	454	5	ma.4.2	ma.4.2	PROPN
ma-198	454	6	20	20	NUM
ma-198	454	7	ii	ii	NOUN
ma-198	454	8	):	):	PUNCT
ma-198	454	9	lim	lim	PROPN
ma-198	454	10	n→∞	n→∞	PRON
ma-198	454	11	inf(1−	inf(1−	VERB
ma-198	454	12	βn)(βn	βn)(βn	PUNCT
ma-198	454	13	−	−	PROPN
ma-198	454	14	β	β	X
ma-198	454	15	)	)	PUNCT
ma-198	454	16	>	>	X
ma-198	454	17	0	0	PUNCT
ma-198	454	18	and	and	CCONJ
ma-198	454	19	lim	lim	PROPN
ma-198	454	20	n→∞	n→∞	PRON
ma-198	454	21	inf(1−	inf(1−	VERB
ma-198	454	22	θn)(θn	θn)(θn	PUNCT
ma-198	454	23	−	−	NOUN
ma-198	454	24	β	β	NOUN
ma-198	454	25	)	)	PUNCT
ma-198	454	26	>	>	X
ma-198	455	1	0	0	NUM
ma-198	455	2	,	,	PUNCT
ma-198	455	3	(	(	PUNCT
ma-198	455	4	βn	βn	NOUN
ma-198	455	5	,	,	PUNCT
ma-198	455	6	θn	θn	ADJ
ma-198	455	7	)	)	PUNCT
ma-198	455	8	∈	∈	PROPN
ma-198	455	9	(	(	PUNCT
ma-198	455	10	β	β	X
ma-198	455	11	,	,	PUNCT
ma-198	455	12	1	1	NUM
ma-198	455	13	)	)	PUNCT
ma-198	455	14	iii	iii	PROPN
ma-198	455	15	):	):	PUNCT
ma-198	455	16	limn→∞	limn→∞	PROPN
ma-198	455	17	inf(1−	inf(1−	VERB
ma-198	455	18	γn)γn	γn)γn	PROPN
ma-198	455	19	)	)	PUNCT
ma-198	455	20	>	>	X
ma-198	455	21	0	0	PUNCT
ma-198	455	22	assume	assume	VERB
ma-198	455	23	that	that	SCONJ
ma-198	455	24	0	0	NUM
ma-198	455	25	<	<	X
ma-198	455	26	η	η	X
ma-198	455	27	<	<	X
ma-198	455	28	2k	2k	PROPN
ma-198	455	29	l2	l2	NOUN
ma-198	455	30	,	,	PUNCT
ma-198	455	31	0	0	PUNCT
ma-198	455	32	<	<	X
ma-198	455	33	γb	γb	X
ma-198	455	34	<	<	X
ma-198	455	35	τ	τ	PROPN
ma-198	455	36	,	,	PUNCT
ma-198	455	37	where	where	SCONJ
ma-198	455	38	τ	τ	PROPN
ma-198	455	39	=	=	SYM
ma-198	455	40	η	η	PROPN
ma-198	455	41	(	(	PUNCT
ma-198	455	42	k−	k−	PROPN
ma-198	455	43	l2η	l2η	PROPN
ma-198	455	44	2	2	NUM
ma-198	455	45	)	)	PUNCT
ma-198	455	46	,	,	PUNCT
ma-198	455	47	and	and	CCONJ
ma-198	455	48	i−pt1	i−pt1	NOUN
ma-198	455	49	,	,	PUNCT
ma-198	455	50	i−pt2	i−pt2	NOUN
ma-198	455	51	and	and	CCONJ
ma-198	455	52	i−pt3	i−pt3	ADV
ma-198	455	53	are	be	AUX
ma-198	455	54	demiclosed	demiclose	VERB
ma-198	455	55	at	at	ADP
ma-198	455	56	origin	origin	NOUN
ma-198	455	57	.	.	PUNCT
ma-198	456	1	hence	hence	ADV
ma-198	456	2	,	,	PUNCT
ma-198	456	3	the	the	DET
ma-198	456	4	sequences	sequence	NOUN
ma-198	456	5	defined	define	VERB
ma-198	456	6	in	in	ADP
ma-198	456	7	(	(	PUNCT
ma-198	456	8	3.32	3.32	NUM
ma-198	456	9	)	)	PUNCT
ma-198	456	10	,	,	PUNCT
ma-198	456	11	that	that	ADV
ma-198	456	12	is	be	AUX
ma-198	456	13	{	{	PUNCT
ma-198	456	14	xn	xn	PUNCT
ma-198	456	15	}	}	PUNCT
ma-198	456	16	and	and	CCONJ
ma-198	456	17	{	{	PUNCT
ma-198	456	18	δn	δn	NOUN
ma-198	456	19	}	}	PUNCT
ma-198	456	20	converge	converge	VERB
ma-198	456	21	strongly	strongly	ADV
ma-198	456	22	to	to	ADP
ma-198	456	23	unique	unique	ADJ
ma-198	456	24	solution	solution	NOUN
ma-198	456	25	x∗	x∗	PROPN
ma-198	456	26	∈	∈	PROPN
ma-198	456	27	ω	ω	PROPN
ma-198	456	28	,	,	PUNCT
ma-198	456	29	which	which	PRON
ma-198	456	30	also	also	ADV
ma-198	456	31	solve	solve	VERB
ma-198	456	32	the	the	DET
ma-198	456	33	following	follow	VERB
ma-198	456	34	variational	variational	ADJ
ma-198	456	35	inequality	inequality	NOUN
ma-198	456	36	:	:	PUNCT
ma-198	456	37	〈	〈	PROPN
ma-198	456	38	ηbx∗	ηbx∗	NOUN
ma-198	456	39	−	−	PROPN
ma-198	456	40	γf	γf	PROPN
ma-198	456	41	(	(	PUNCT
ma-198	456	42	x∗	x∗	PROPN
ma-198	456	43	)	)	PUNCT
ma-198	456	44	,	,	PUNCT
ma-198	456	45	x∗	x∗	PROPN
ma-198	456	46	−	−	PROPN
ma-198	457	1	q	q	NOUN
ma-198	457	2	〉	〉	NOUN
ma-198	457	3	≤	≤	NUM
ma-198	457	4	0	0	NUM
ma-198	457	5	,	,	PUNCT
ma-198	457	6	∀q	∀q	PROPN
ma-198	457	7	∈	∈	PROPN
ma-198	457	8	ω	ω	PROPN
ma-198	457	9	(	(	PUNCT
ma-198	457	10	3.33	3.33	NUM
ma-198	457	11	)	)	PUNCT
ma-198	457	12	4	4	NUM
ma-198	457	13	.	.	X
ma-198	457	14	conclusion	conclusion	VERB
ma-198	457	15	the	the	DET
ma-198	457	16	modified	modify	VERB
ma-198	457	17	general	general	ADJ
ma-198	457	18	viscosity	viscosity	NOUN
ma-198	457	19	iterative	iterative	NOUN
ma-198	457	20	process	process	NOUN
ma-198	457	21	presented	present	VERB
ma-198	457	22	in	in	ADP
ma-198	457	23	this	this	DET
ma-198	457	24	research	research	NOUN
ma-198	457	25	offers	offer	VERB
ma-198	457	26	a	a	DET
ma-198	457	27	powerful	powerful	ADJ
ma-198	457	28	toolfor	toolfor	NOUN
ma-198	457	29	solving	solve	VERB
ma-198	457	30	variational	variational	ADJ
ma-198	457	31	inclusion	inclusion	NOUN
ma-198	457	32	and	and	CCONJ
ma-198	457	33	fixed	fix	VERB
ma-198	457	34	point	point	NOUN
ma-198	457	35	problems	problem	NOUN
ma-198	457	36	involving	involve	VERB
ma-198	457	37	and	and	CCONJ
ma-198	457	38	and	and	CCONJ
ma-198	457	39	fixed	fix	VERB
ma-198	457	40	point	point	NOUN
ma-198	457	41	problem	problem	NOUN
ma-198	457	42	withrespectively	withrespectively	ADV
ma-198	457	43	set	set	NOUN
ma-198	457	44	-	-	PUNCT
ma-198	457	45	valued	value	VERB
ma-198	457	46	maximal	maximal	ADJ
ma-198	457	47	monotone	monotone	ADJ
ma-198	457	48	mapping	mapping	NOUN
ma-198	457	49	and	and	CCONJ
ma-198	457	50	inverse	inverse	NOUN
ma-198	457	51	strongly	strongly	ADV
ma-198	457	52	monotone	monotone	ADJ
ma-198	457	53	and	and	CCONJ
ma-198	457	54	multivaluedquasi	multivaluedquasi	NOUN
ma-198	457	55	-	-	PUNCT
ma-198	457	56	nonexpansive	nonexpansive	ADJ
ma-198	457	57	and	and	CCONJ
ma-198	457	58	demicontractive	demicontractive	ADJ
ma-198	457	59	operators	operator	NOUN
ma-198	457	60	.	.	PUNCT
ma-198	458	1	our	our	PRON
ma-198	458	2	theorem	theorem	NOUN
ma-198	458	3	presents	present	VERB
ma-198	458	4	a	a	DET
ma-198	458	5	new	new	ADJ
ma-198	458	6	and	and	CCONJ
ma-198	458	7	a	a	DET
ma-198	458	8	modifiedalgorithm	modifiedalgorithm	NOUN
ma-198	458	9	for	for	ADP
ma-198	458	10	solving	solve	VERB
ma-198	458	11	simultaneously	simultaneously	ADV
ma-198	458	12	variational	variational	ADJ
ma-198	458	13	inclusion	inclusion	NOUN
ma-198	458	14	problem	problem	NOUN
ma-198	458	15	and	and	CCONJ
ma-198	458	16	fixed	fix	VERB
ma-198	458	17	point	point	NOUN
ma-198	458	18	problem	problem	NOUN
ma-198	458	19	withrespectively	withrespectively	ADV
ma-198	458	20	set	set	NOUN
ma-198	458	21	-	-	PUNCT
ma-198	458	22	valued	value	VERB
ma-198	458	23	maximal	maximal	ADJ
ma-198	458	24	monotone	monotone	ADJ
ma-198	458	25	mapping	mapping	NOUN
ma-198	458	26	and	and	CCONJ
ma-198	458	27	inverse	inverse	NOUN
ma-198	458	28	strongly	strongly	ADV
ma-198	458	29	monotone	monotone	ADJ
ma-198	458	30	and	and	CCONJ
ma-198	458	31	multival	multival	NOUN
ma-198	458	32	-	-	PUNCT
ma-198	458	33	ued	ue	VERB
ma-198	458	34	demicontractive	demicontractive	ADJ
ma-198	458	35	and	and	CCONJ
ma-198	458	36	quasi	quasi	ADJ
ma-198	458	37	-	-	ADJ
ma-198	458	38	nonexpansive	nonexpansive	ADJ
ma-198	458	39	mappings	mapping	NOUN
ma-198	458	40	.	.	PUNCT
ma-198	459	1	the	the	DET
ma-198	459	2	result	result	NOUN
ma-198	459	3	we	we	PRON
ma-198	459	4	show	show	VERB
ma-198	459	5	here	here	ADV
ma-198	459	6	improves	improve	VERB
ma-198	459	7	andextends	andextend	NOUN
ma-198	459	8	the	the	DET
ma-198	459	9	corresponding	corresponding	ADJ
ma-198	459	10	results	result	NOUN
ma-198	459	11	of	of	ADP
ma-198	459	12	some	some	DET
ma-198	459	13	authors	author	NOUN
ma-198	459	14	and	and	CCONJ
ma-198	459	15	many	many	ADJ
ma-198	459	16	other	other	ADJ
ma-198	459	17	recent	recent	ADJ
ma-198	459	18	results	result	NOUN
ma-198	459	19	using	use	VERB
ma-198	459	20	forward	forward	ADV
ma-198	459	21	-	-	PUNCT
ma-198	459	22	backward	backward	ADJ
ma-198	459	23	splitting	splitting	NOUN
ma-198	459	24	method	method	NOUN
ma-198	459	25	and	and	CCONJ
ma-198	459	26	general	general	ADJ
ma-198	459	27	iterative	iterative	NOUN
ma-198	459	28	algorithm	algorithm	NOUN
ma-198	459	29	that	that	PRON
ma-198	459	30	gives	give	VERB
ma-198	459	31	a	a	DET
ma-198	459	32	strong	strong	ADJ
ma-198	459	33	convergence	convergence	NOUN
ma-198	459	34	to	to	PART
ma-198	459	35	aunique	aunique	VERB
ma-198	459	36	solution	solution	NOUN
ma-198	459	37	.	.	PUNCT
ma-198	460	1	references	reference	NOUN
ma-198	460	2	[	[	X
ma-198	460	3	1	1	X
ma-198	460	4	]	]	PUNCT
ma-198	460	5	s.	s.	PROPN
ma-198	460	6	wang	wang	PROPN
ma-198	460	7	,	,	PUNCT
ma-198	460	8	a	a	DET
ma-198	460	9	general	general	ADJ
ma-198	460	10	iterative	iterative	NOUN
ma-198	460	11	method	method	NOUN
ma-198	460	12	for	for	ADP
ma-198	460	13	an	an	DET
ma-198	460	14	infinite	infinite	ADJ
ma-198	460	15	family	family	NOUN
ma-198	460	16	of	of	ADP
ma-198	460	17	strictly	strictly	ADV
ma-198	460	18	pseudo	pseudo	ADJ
ma-198	460	19	-	-	ADJ
ma-198	460	20	contractive	contractive	ADJ
ma-198	460	21	mappings	mapping	NOUN
ma-198	460	22	in	in	ADP
ma-198	460	23	hilbert	hilbert	PROPN
ma-198	460	24	spaces	space	NOUN
ma-198	460	25	,	,	PUNCT
ma-198	460	26	appl	appl	PROPN
ma-198	460	27	.	.	PROPN
ma-198	460	28	math	math	PROPN
ma-198	460	29	.	.	PUNCT
ma-198	461	1	lett	lett	PROPN
ma-198	461	2	.	.	PROPN
ma-198	462	1	24	24	NUM
ma-198	462	2	(	(	PUNCT
ma-198	462	3	2011	2011	NUM
ma-198	462	4	)	)	PUNCT
ma-198	462	5	,	,	PUNCT
ma-198	462	6	901	901	NUM
ma-198	462	7	-	-	SYM
ma-198	462	8	907	907	NUM
ma-198	462	9	.	.	PUNCT
ma-198	463	1	https://doi.org/10.1016/j.aml.2010.12.048.[2	https://doi.org/10.1016/j.aml.2010.12.048.[2	ADV
ma-198	463	2	]	]	PUNCT
ma-198	463	3	j.	j.	PROPN
ma-198	463	4	geanakoplos	geanakoplos	PROPN
ma-198	463	5	,	,	PUNCT
ma-198	463	6	nash	nash	PROPN
ma-198	463	7	and	and	CCONJ
ma-198	463	8	walras	walras	PRON
ma-198	463	9	equilibrium	equilibrium	NOUN
ma-198	463	10	via	via	ADP
ma-198	463	11	brouwer	brouwer	PROPN
ma-198	463	12	,	,	PUNCT
ma-198	463	13	econ	econ	PROPN
ma-198	463	14	.	.	PUNCT
ma-198	464	1	theory	theory	NOUN
ma-198	464	2	,	,	PUNCT
ma-198	464	3	21	21	NUM
ma-198	464	4	(	(	PUNCT
ma-198	464	5	2003	2003	NUM
ma-198	464	6	)	)	PUNCT
ma-198	464	7	,	,	PUNCT
ma-198	464	8	585	585	NUM
ma-198	464	9	-	-	SYM
ma-198	464	10	603.[3	603.[3	NUM
ma-198	464	11	]	]	X
ma-198	464	12	s.	s.	PROPN
ma-198	464	13	kakutani	kakutani	PROPN
ma-198	464	14	,	,	PUNCT
ma-198	464	15	a	a	DET
ma-198	464	16	generalization	generalization	NOUN
ma-198	464	17	of	of	ADP
ma-198	464	18	brouwers	brouwer	NOUN
ma-198	464	19	fied	fie	VERB
ma-198	464	20	point	point	NOUN
ma-198	464	21	theorem	theorem	ADJ
ma-198	464	22	,	,	PUNCT
ma-198	464	23	duke	duke	PROPN
ma-198	464	24	math	math	PROPN
ma-198	464	25	.	.	PUNCT
ma-198	465	1	j.	j.	PROPN
ma-198	465	2	8	8	NUM
ma-198	465	3	(	(	PUNCT
ma-198	465	4	1941	1941	NUM
ma-198	465	5	)	)	PUNCT
ma-198	465	6	,	,	PUNCT
ma-198	465	7	457459.[4	457459.[4	NUM
ma-198	465	8	]	]	X
ma-198	465	9	b.	b.	PROPN
ma-198	465	10	lemaire	lemaire	PROPN
ma-198	465	11	,	,	PUNCT
ma-198	465	12	which	which	PRON
ma-198	465	13	fied	fie	VERB
ma-198	465	14	point	point	NOUN
ma-198	465	15	does	do	AUX
ma-198	465	16	the	the	DET
ma-198	465	17	iteration	iteration	NOUN
ma-198	465	18	method	method	NOUN
ma-198	465	19	select	select	ADJ
ma-198	465	20	?	?	PUNCT
ma-198	466	1	recent	recent	ADJ
ma-198	466	2	advances	advance	NOUN
ma-198	466	3	in	in	ADP
ma-198	466	4	optimization	optimization	NOUN
ma-198	466	5	(	(	PUNCT
ma-198	466	6	trier	tri	ADJ
ma-198	466	7	,	,	PUNCT
ma-198	466	8	1996),lecture	1996),lecture	NUM
ma-198	466	9	notes	note	NOUN
ma-198	466	10	in	in	ADP
ma-198	466	11	economics	economic	NOUN
ma-198	466	12	and	and	CCONJ
ma-198	466	13	mathematical	mathematical	ADJ
ma-198	466	14	systems	system	NOUN
ma-198	466	15	,	,	PUNCT
ma-198	466	16	springer	springer	NOUN
ma-198	466	17	,	,	PUNCT
ma-198	466	18	berlin	berlin	PROPN
ma-198	466	19	,	,	PUNCT
ma-198	466	20	54	54	NUM
ma-198	466	21	-	-	SYM
ma-198	466	22	167	167	NUM
ma-198	466	23	,	,	PUNCT
ma-198	466	24	1997.[5	1997.[5	NUM
ma-198	466	25	]	]	X
ma-198	466	26	g.	g.	PROPN
ma-198	466	27	marino	marino	PROPN
ma-198	466	28	,	,	PUNCT
ma-198	466	29	h.k	h.k	PROPN
ma-198	466	30	.	.	PROPN
ma-198	466	31	xu	xu	PROPN
ma-198	466	32	,	,	PUNCT
ma-198	466	33	a	a	DET
ma-198	466	34	general	general	ADJ
ma-198	466	35	iterative	iterative	NOUN
ma-198	466	36	method	method	NOUN
ma-198	466	37	for	for	ADP
ma-198	466	38	nonexpansive	nonexpansive	ADJ
ma-198	466	39	mappings	mapping	NOUN
ma-198	466	40	in	in	ADP
ma-198	466	41	hibert	hibert	NOUN
ma-198	466	42	spaces	space	NOUN
ma-198	466	43	,	,	PUNCT
ma-198	466	44	j.	j.	PROPN
ma-198	466	45	math	math	PROPN
ma-198	466	46	.	.	PUNCT
ma-198	467	1	anal	anal	PROPN
ma-198	467	2	.	.	PUNCT
ma-198	468	1	appl.318	appl.318	PROPN
ma-198	468	2	(	(	PUNCT
ma-198	468	3	2006	2006	NUM
ma-198	468	4	)	)	PUNCT
ma-198	468	5	,	,	PUNCT
ma-198	468	6	43	43	NUM
ma-198	468	7	-	-	SYM
ma-198	468	8	52.[6	52.[6	NUM
ma-198	468	9	]	]	PUNCT
ma-198	468	10	a.	a.	NOUN
ma-198	468	11	moudafi	moudafi	PROPN
ma-198	468	12	,	,	PUNCT
ma-198	468	13	viscosity	viscosity	NOUN
ma-198	468	14	approximation	approximation	NOUN
ma-198	468	15	methods	method	NOUN
ma-198	468	16	for	for	ADP
ma-198	468	17	fied	fied	ADJ
ma-198	468	18	point	point	NOUN
ma-198	468	19	problems	problem	NOUN
ma-198	468	20	,	,	PUNCT
ma-198	468	21	j.	j.	PROPN
ma-198	468	22	math	math	PROPN
ma-198	468	23	.	.	PUNCT
ma-198	469	1	anal	anal	PROPN
ma-198	469	2	.	.	PUNCT
ma-198	469	3	appl	appl	PROPN
ma-198	469	4	.	.	PUNCT
ma-198	470	1	241	241	NUM
ma-198	470	2	(	(	PUNCT
ma-198	470	3	2000	2000	NUM
ma-198	470	4	)	)	PUNCT
ma-198	470	5	,	,	PUNCT
ma-198	470	6	46	46	NUM
ma-198	470	7	-	-	PUNCT
ma-198	470	8	55.[7	55.[7	NUM
ma-198	470	9	]	]	PUNCT
ma-198	470	10	t.m.m	t.m.m	NOUN
ma-198	470	11	.	.	PUNCT
ma-198	470	12	sow	sow	PROPN
ma-198	470	13	,	,	PUNCT
ma-198	470	14	m.	m.	NOUN
ma-198	470	15	sene	sene	PROPN
ma-198	470	16	,	,	PUNCT
ma-198	470	17	n.	n.	NOUN
ma-198	470	18	djitte	djitte	PROPN
ma-198	470	19	,	,	PUNCT
ma-198	470	20	strong	strong	ADJ
ma-198	470	21	convergence	convergence	NOUN
ma-198	470	22	theorems	theorem	NOUN
ma-198	470	23	for	for	ADP
ma-198	470	24	a	a	DET
ma-198	470	25	common	common	ADJ
ma-198	470	26	fied	fied	ADJ
ma-198	470	27	point	point	NOUN
ma-198	470	28	of	of	ADP
ma-198	470	29	a	a	DET
ma-198	470	30	fiite	fiite	ADJ
ma-198	470	31	family	family	NOUN
ma-198	470	32	of	of	ADP
ma-198	470	33	multi	multi	NOUN
ma-198	470	34	-	-	NOUN
ma-198	470	35	valuedmappings	valuedmapping	NOUN
ma-198	470	36	in	in	ADP
ma-198	470	37	certain	certain	ADJ
ma-198	470	38	banach	banach	NOUN
ma-198	470	39	spaces	space	NOUN
ma-198	470	40	,	,	PUNCT
ma-198	470	41	int	int	NOUN
ma-198	470	42	.	.	PUNCT
ma-198	471	1	j.	j.	PROPN
ma-198	471	2	math	math	PROPN
ma-198	471	3	.	.	PUNCT
ma-198	472	1	anal	anal	ADJ
ma-198	472	2	.	.	PUNCT
ma-198	473	1	9	9	NUM
ma-198	473	2	(	(	PUNCT
ma-198	473	3	2015	2015	NUM
ma-198	473	4	)	)	PUNCT
ma-198	473	5	,	,	PUNCT
ma-198	473	6	437	437	NUM
ma-198	473	7	-	-	SYM
ma-198	473	8	452.[8	452.[8	NUM
ma-198	473	9	]	]	X
ma-198	473	10	j.t	j.t	PROPN
ma-198	473	11	.	.	PROPN
ma-198	473	12	mendy	mendy	PROPN
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ma-198	473	14	f.	f.	PROPN
ma-198	473	15	mendy	mendy	PROPN
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ma-198	473	17	two	two	NUM
ma-198	473	18	step	step	NOUN
ma-198	473	19	size	size	NOUN
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ma-198	473	21	for	for	ADP
ma-198	473	22	strong	strong	ADJ
ma-198	473	23	convergence	convergence	NOUN
ma-198	473	24	for	for	ADP
ma-198	473	25	a	a	DET
ma-198	473	26	monotone	monotone	ADJ
ma-198	473	27	operator	operator	NOUN
ma-198	473	28	in	in	ADP
ma-198	473	29	banach	banach	NOUN
ma-198	473	30	spaces	space	NOUN
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ma-198	473	32	int	int	NOUN
ma-198	473	33	.	.	PUNCT
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ma-198	476	3	2023	2023	NUM
ma-198	476	4	)	)	PUNCT
ma-198	476	5	,	,	PUNCT
ma-198	476	6	217	217	NUM
ma-198	476	7	-	-	SYM
ma-198	476	8	225	225	NUM
ma-198	476	9	.	.	PUNCT
ma-198	477	1	https://doi.org/10.22075/ijnaa.2023.27501.3626.[9	https://doi.org/10.22075/ijnaa.2023.27501.3626.[9	PROPN
ma-198	477	2	]	]	X
ma-198	477	3	f.	f.	PROPN
ma-198	477	4	mendy	mendy	PROPN
ma-198	477	5	,	,	PUNCT
ma-198	477	6	j.	j.	PROPN
ma-198	477	7	t	t	PROPN
ma-198	477	8	mendy	mendy	PROPN
ma-198	477	9	,	,	PUNCT
ma-198	477	10	j.	j.	PROPN
ma-198	477	11	bah	bah	PROPN
ma-198	477	12	,	,	PUNCT
ma-198	477	13	g.	g.	PROPN
ma-198	477	14	mendy	mendy	PROPN
ma-198	477	15	,	,	PUNCT
ma-198	477	16	convergence	convergence	NOUN
ma-198	477	17	analysis	analysis	NOUN
ma-198	477	18	of	of	ADP
ma-198	477	19	viscosity	viscosity	NOUN
ma-198	477	20	implicit	implicit	ADJ
ma-198	477	21	rules	rule	NOUN
ma-198	477	22	of	of	ADP
ma-198	477	23	asymptotically	asymptotically	ADV
ma-198	477	24	non	non	ADJ
ma-198	477	25	-	-	ADJ
ma-198	477	26	expansive	expansive	ADJ
ma-198	477	27	mappings	mapping	NOUN
ma-198	477	28	in	in	ADP
ma-198	477	29	hilbert	hilbert	PROPN
ma-198	477	30	spaces	space	NOUN
ma-198	477	31	,	,	PUNCT
ma-198	477	32	int	int	NOUN
ma-198	477	33	.	.	PUNCT
ma-198	478	1	j.	j.	PROPN
ma-198	478	2	theor	theor	PROPN
ma-198	478	3	.	.	PUNCT
ma-198	479	1	appl	appl	PROPN
ma-198	479	2	.	.	PROPN
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ma-198	479	4	.	.	PUNCT
ma-198	480	1	9	9	NUM
ma-198	480	2	(	(	PUNCT
ma-198	480	3	2023	2023	NUM
ma-198	480	4	)	)	PUNCT
ma-198	480	5	,	,	PUNCT
ma-198	480	6	14	14	NUM
ma-198	480	7	-	-	SYM
ma-198	480	8	22	22	NUM
ma-198	480	9	.	.	PUNCT
ma-198	481	1	https://doi.org/10.11648/j	https://doi.org/10.11648/j	NOUN
ma-198	481	2	.	.	PUNCT
ma-198	482	1	ijtam.20230902.12.[10	ijtam.20230902.12.[10	PROPN
ma-198	482	2	]	]	X
ma-198	482	3	j.f	j.f	PROPN
ma-198	482	4	.	.	PROPN
ma-198	482	5	nash	nash	PROPN
ma-198	482	6	,	,	PUNCT
ma-198	482	7	non	non	ADJ
ma-198	482	8	-	-	ADJ
ma-198	482	9	cooperative	cooperative	ADJ
ma-198	482	10	games	game	NOUN
ma-198	482	11	,	,	PUNCT
ma-198	482	12	ann	ann	PROPN
ma-198	482	13	.	.	PROPN
ma-198	482	14	math	math	PROPN
ma-198	482	15	.	.	PUNCT
ma-198	483	1	second	second	ADJ
ma-198	483	2	series	series	NOUN
ma-198	483	3	.	.	PUNCT
ma-198	484	1	54	54	NUM
ma-198	484	2	(	(	PUNCT
ma-198	484	3	1951	1951	NUM
ma-198	484	4	)	)	PUNCT
ma-198	485	1	,	,	PUNCT
ma-198	485	2	286	286	NUM
ma-198	485	3	-	-	SYM
ma-198	485	4	295.[11	295.[11	NUM
ma-198	485	5	]	]	X
ma-198	485	6	j.f	j.f	PROPN
ma-198	485	7	.	.	PROPN
ma-198	485	8	nash	nash	PROPN
ma-198	485	9	,	,	PUNCT
ma-198	485	10	equilibrium	equilibrium	NOUN
ma-198	485	11	points	point	NOUN
ma-198	485	12	in	in	ADP
ma-198	485	13	n	n	CCONJ
ma-198	485	14	-	-	PUNCT
ma-198	485	15	person	person	NOUN
ma-198	485	16	games	game	NOUN
ma-198	485	17	,	,	PUNCT
ma-198	485	18	proc	proc	NOUN
ma-198	485	19	.	.	PUNCT
ma-198	486	1	nat	nat	PROPN
ma-198	486	2	.	.	PUNCT
ma-198	487	1	acad	acad	PROPN
ma-198	487	2	.	.	PUNCT
ma-198	488	1	sci	sci	PROPN
ma-198	488	2	.	.	PUNCT
ma-198	488	3	u.s.a	u.s.a	PROPN
ma-198	488	4	.	.	PROPN
ma-198	488	5	36	36	NUM
ma-198	488	6	(	(	PUNCT
ma-198	488	7	1950	1950	NUM
ma-198	488	8	)	)	PUNCT
ma-198	488	9	,	,	PUNCT
ma-198	488	10	48	48	NUM
ma-198	488	11	-	-	SYM
ma-198	488	12	49.[12	49.[12	PROPN
ma-198	488	13	]	]	X
ma-198	488	14	f.	f.	PROPN
ma-198	488	15	mendy	mendy	PROPN
ma-198	488	16	,	,	PUNCT
ma-198	488	17	j.t	j.t	PROPN
ma-198	488	18	.	.	PROPN
ma-198	488	19	mendy	mendy	PROPN
ma-198	488	20	,	,	PUNCT
ma-198	488	21	a	a	DET
ma-198	488	22	modified	modify	VERB
ma-198	488	23	algorithms	algorithm	NOUN
ma-198	488	24	for	for	ADP
ma-198	488	25	new	new	ADJ
ma-198	488	26	krasnoselskii	krasnoselskii	PROPN
ma-198	488	27	’s	’s	PART
ma-198	488	28	type	type	NOUN
ma-198	488	29	for	for	ADP
ma-198	488	30	strongly	strongly	ADV
ma-198	488	31	monotone	monotone	ADJ
ma-198	488	32	and	and	CCONJ
ma-198	488	33	lipschitzmappings	lipschitzmapping	NOUN
ma-198	488	34	,	,	PUNCT
ma-198	488	35	eur	eur	PROPN
ma-198	488	36	.	.	PUNCT
ma-198	489	1	j.	j.	PROPN
ma-198	489	2	math	math	PROPN
ma-198	489	3	.	.	PUNCT
ma-198	490	1	anal	anal	ADJ
ma-198	490	2	.	.	PUNCT
ma-198	491	1	3	3	NUM
ma-198	491	2	(	(	PUNCT
ma-198	491	3	2023	2023	NUM
ma-198	491	4	)	)	PUNCT
ma-198	491	5	,	,	PUNCT
ma-198	491	6	18	18	NUM
ma-198	491	7	-	-	SYM
ma-198	491	8	18	18	NUM
ma-198	491	9	.	.	PUNCT
ma-198	492	1	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	492	2	https://doi.org/10.1016/j.aml.2010.12.048	https://doi.org/10.1016/j.aml.2010.12.048	ADJ
ma-198	492	3	https://doi.org/10.22075/ijnaa.2023.27501.3626	https://doi.org/10.22075/ijnaa.2023.27501.3626	NUM
ma-198	492	4	https://doi.org/10.11648/j.ijtam.20230902.12	https://doi.org/10.11648/j.ijtam.20230902.12	NOUN
ma-198	492	5	https://doi.org/10.11648/j.ijtam.20230902.12	https://doi.org/10.11648/j.ijtam.20230902.12	NOUN
ma-198	492	6	eur	eur	ADJ
ma-198	492	7	.	.	PUNCT
ma-198	493	1	j.	j.	PROPN
ma-198	493	2	math	math	PROPN
ma-198	493	3	.	.	PUNCT
ma-198	494	1	anal	anal	PROPN
ma-198	494	2	.	.	PUNCT
ma-198	495	1	10.28924	10.28924	NUM
ma-198	495	2	/	/	SYM
ma-198	495	3	ada	ada	PROPN
ma-198	495	4	/	/	SYM
ma-198	495	5	ma.4.2	ma.4.2	PROPN
ma-198	495	6	21	21	NUM
ma-198	495	7	[	[	SYM
ma-198	495	8	13	13	NUM
ma-198	495	9	]	]	PUNCT
ma-198	495	10	b.	b.	PROPN
ma-198	495	11	panyanak	panyanak	PROPN
ma-198	495	12	,	,	PUNCT
ma-198	495	13	endpoints	endpoint	NOUN
ma-198	495	14	of	of	ADP
ma-198	495	15	multivalued	multivalued	ADJ
ma-198	495	16	nonexpansive	nonexpansive	ADJ
ma-198	495	17	mappings	mapping	NOUN
ma-198	495	18	in	in	ADP
ma-198	495	19	geodesic	geodesic	ADJ
ma-198	495	20	spaces	space	NOUN
ma-198	495	21	,	,	PUNCT
ma-198	495	22	fixed	fix	VERB
ma-198	495	23	point	point	NOUN
ma-198	495	24	theory	theory	NOUN
ma-198	495	25	appl	appl	NOUN
ma-198	495	26	.	.	PUNCT
ma-198	495	27	2015(2015	2015(2015	NUM
ma-198	495	28	)	)	PUNCT
ma-198	495	29	,	,	PUNCT
ma-198	495	30	147.[14	147.[14	PROPN
ma-198	495	31	]	]	X
ma-198	495	32	g.b	g.b	PROPN
ma-198	495	33	.	.	PROPN
ma-198	495	34	passty	passty	PROPN
ma-198	495	35	,	,	PUNCT
ma-198	495	36	ergodic	ergodic	ADJ
ma-198	495	37	convergence	convergence	NOUN
ma-198	495	38	to	to	ADP
ma-198	495	39	a	a	DET
ma-198	495	40	zero	zero	NUM
ma-198	495	41	of	of	ADP
ma-198	495	42	the	the	DET
ma-198	495	43	sum	sum	NOUN
ma-198	495	44	of	of	ADP
ma-198	495	45	monotone	monotone	ADJ
ma-198	495	46	operators	operator	NOUN
ma-198	495	47	in	in	ADP
ma-198	495	48	hilbert	hilbert	PROPN
ma-198	495	49	spaces	space	NOUN
ma-198	495	50	,	,	PUNCT
ma-198	495	51	j.	j.	PROPN
ma-198	495	52	math	math	PROPN
ma-198	495	53	.	.	PUNCT
ma-198	496	1	anal	anal	PROPN
ma-198	496	2	.	.	PUNCT
ma-198	497	1	appl.72	appl.72	PROPN
ma-198	497	2	(	(	PUNCT
ma-198	497	3	1979	1979	NUM
ma-198	497	4	)	)	PUNCT
ma-198	497	5	,	,	PUNCT
ma-198	497	6	383	383	NUM
ma-198	497	7	-	-	SYM
ma-198	497	8	390.[15	390.[15	NUM
ma-198	497	9	]	]	X
ma-198	497	10	t.l	t.l	PROPN
ma-198	497	11	.	.	PROPN
ma-198	497	12	hicks	hicks	PROPN
ma-198	497	13	,	,	PUNCT
ma-198	497	14	j.d	j.d	PROPN
ma-198	497	15	.	.	PROPN
ma-198	497	16	kubicek	kubicek	PROPN
ma-198	497	17	,	,	PUNCT
ma-198	497	18	on	on	ADP
ma-198	497	19	the	the	DET
ma-198	497	20	mann	mann	PROPN
ma-198	497	21	iteration	iteration	NOUN
ma-198	497	22	process	process	NOUN
ma-198	497	23	in	in	ADP
ma-198	497	24	a	a	DET
ma-198	497	25	hilbert	hilbert	NOUN
ma-198	497	26	space	space	NOUN
ma-198	497	27	,	,	PUNCT
ma-198	497	28	j.	j.	PROPN
ma-198	497	29	math	math	PROPN
ma-198	497	30	.	.	PUNCT
ma-198	498	1	anal	anal	PROPN
ma-198	498	2	.	.	PUNCT
ma-198	499	1	appl	appl	PROPN
ma-198	499	2	.	.	PROPN
ma-198	500	1	59	59	NUM
ma-198	500	2	(	(	PUNCT
ma-198	500	3	1977	1977	NUM
ma-198	500	4	)	)	PUNCT
ma-198	500	5	,	,	PUNCT
ma-198	500	6	498	498	NUM
ma-198	500	7	-	-	SYM
ma-198	500	8	504.[16	504.[16	NUM
ma-198	500	9	]	]	PUNCT
ma-198	500	10	r.	r.	PROPN
ma-198	500	11	t.	t.	PROPN
ma-198	500	12	rockafellar	rockafellar	PROPN
ma-198	500	13	,	,	PUNCT
ma-198	500	14	monotone	monotone	ADJ
ma-198	500	15	operators	operator	NOUN
ma-198	500	16	and	and	CCONJ
ma-198	500	17	the	the	DET
ma-198	500	18	proximal	proximal	ADJ
ma-198	500	19	point	point	NOUN
ma-198	500	20	algorithm	algorithm	NOUN
ma-198	500	21	,	,	PUNCT
ma-198	500	22	siam	siam	PROPN
ma-198	500	23	j.	j.	PROPN
ma-198	500	24	control	control	PROPN
ma-198	500	25	optim	optim	PROPN
ma-198	500	26	.	.	PUNCT
ma-198	501	1	14	14	NUM
ma-198	501	2	(	(	PUNCT
ma-198	501	3	1976	1976	NUM
ma-198	501	4	)	)	PUNCT
ma-198	501	5	,	,	PUNCT
ma-198	501	6	877	877	NUM
ma-198	501	7	-	-	SYM
ma-198	501	8	898.[17	898.[17	NUM
ma-198	501	9	]	]	PUNCT
ma-198	501	10	n.	n.	NOUN
ma-198	501	11	djitte	djitte	PROPN
ma-198	501	12	,	,	PUNCT
ma-198	501	13	j.t	j.t	PROPN
ma-198	501	14	.	.	PROPN
ma-198	501	15	mendy	mendy	PROPN
ma-198	501	16	,	,	PUNCT
ma-198	501	17	t.m.m	t.m.m	NOUN
ma-198	501	18	.	.	PUNCT
ma-198	501	19	sow	sow	NOUN
ma-198	501	20	,	,	PUNCT
ma-198	501	21	computation	computation	NOUN
ma-198	501	22	of	of	ADP
ma-198	501	23	zeros	zero	NOUN
ma-198	501	24	of	of	ADP
ma-198	501	25	monotone	monotone	ADJ
ma-198	501	26	type	type	NOUN
ma-198	501	27	mappings	mapping	NOUN
ma-198	501	28	:	:	PUNCT
ma-198	501	29	on	on	ADP
ma-198	501	30	chidume	chidume	PROPN
ma-198	501	31	’s	’s	PART
ma-198	501	32	open	open	ADJ
ma-198	501	33	problem	problem	NOUN
ma-198	501	34	,	,	PUNCT
ma-198	501	35	j.	j.	PROPN
ma-198	501	36	aust	aust	PROPN
ma-198	501	37	.	.	PUNCT
ma-198	501	38	math	math	PROPN
ma-198	501	39	.	.	PUNCT
ma-198	502	1	soc	soc	PROPN
ma-198	502	2	.	.	PUNCT
ma-198	503	1	108	108	NUM
ma-198	503	2	(	(	PUNCT
ma-198	503	3	2020	2020	NUM
ma-198	503	4	)	)	PUNCT
ma-198	503	5	,	,	PUNCT
ma-198	503	6	278	278	NUM
ma-198	503	7	-	-	SYM
ma-198	503	8	288.[18	288.[18	NUM
ma-198	503	9	]	]	X
ma-198	503	10	j.t	j.t	PROPN
ma-198	503	11	.	.	PROPN
ma-198	503	12	mendy	mendy	PROPN
ma-198	503	13	,	,	PUNCT
ma-198	503	14	m.	m.	NOUN
ma-198	503	15	sene	sene	PROPN
ma-198	503	16	,	,	PUNCT
ma-198	503	17	n.	n.	NOUN
ma-198	503	18	djitte	djitte	PROPN
ma-198	503	19	,	,	PUNCT
ma-198	503	20	algorithm	algorithm	NOUN
ma-198	503	21	for	for	ADP
ma-198	503	22	zeros	zero	NOUN
ma-198	503	23	of	of	ADP
ma-198	503	24	maximal	maximal	ADJ
ma-198	503	25	monotone	monotone	ADJ
ma-198	503	26	mappings	mapping	NOUN
ma-198	503	27	in	in	ADP
ma-198	503	28	classical	classical	ADJ
ma-198	503	29	banach	banach	NOUN
ma-198	503	30	spaces	space	NOUN
ma-198	503	31	.	.	PUNCT
ma-198	504	1	int.j	int.j	PROPN
ma-198	504	2	.	.	PUNCT
ma-198	504	3	math	math	NOUN
ma-198	504	4	.	.	PUNCT
ma-198	505	1	anal	anal	ADJ
ma-198	505	2	.	.	PUNCT
ma-198	506	1	11	11	NUM
ma-198	506	2	(	(	PUNCT
ma-198	506	3	2017	2017	NUM
ma-198	506	4	)	)	PUNCT
ma-198	506	5	,	,	PUNCT
ma-198	507	1	551	551	NUM
ma-198	507	2	-	-	SYM
ma-198	507	3	570.[19	570.[19	NUM
ma-198	507	4	]	]	X
ma-198	507	5	j.t	j.t	PROPN
ma-198	507	6	.	.	PROPN
ma-198	507	7	mendy	mendy	PROPN
ma-198	507	8	,	,	PUNCT
ma-198	507	9	r.	r.	PROPN
ma-198	507	10	shukla	shukla	PROPN
ma-198	507	11	,	,	PUNCT
ma-198	507	12	viscosity	viscosity	NOUN
ma-198	507	13	like	like	ADP
ma-198	507	14	implicit	implicit	ADJ
ma-198	507	15	methods	method	NOUN
ma-198	507	16	for	for	ADP
ma-198	507	17	zeros	zero	NOUN
ma-198	507	18	of	of	ADP
ma-198	507	19	monotone	monotone	ADJ
ma-198	507	20	operators	operator	NOUN
ma-198	507	21	in	in	ADP
ma-198	507	22	banach	banach	NOUN
ma-198	507	23	spaces	space	NOUN
ma-198	507	24	.	.	PUNCT
ma-198	508	1	khayyamj	khayyamj	NOUN
ma-198	508	2	.	.	PUNCT
ma-198	509	1	math	math	NOUN
ma-198	509	2	.	.	PUNCT
ma-198	510	1	8	8	NUM
ma-198	510	2	(	(	PUNCT
ma-198	510	3	2022	2022	NUM
ma-198	510	4	)	)	PUNCT
ma-198	510	5	,	,	PUNCT
ma-198	511	1	53	53	NUM
ma-198	511	2	-	-	SYM
ma-198	511	3	72.[20	72.[20	PROPN
ma-198	511	4	]	]	PUNCT
ma-198	511	5	p.	p.	PROPN
ma-198	511	6	tseng	tseng	PROPN
ma-198	511	7	,	,	PUNCT
ma-198	511	8	a	a	DET
ma-198	511	9	modifid	modifid	ADJ
ma-198	511	10	forward	forward	ADJ
ma-198	511	11	-	-	PUNCT
ma-198	511	12	backward	backward	ADJ
ma-198	511	13	splitting	splitting	NOUN
ma-198	511	14	method	method	NOUN
ma-198	511	15	for	for	ADP
ma-198	511	16	maximal	maximal	ADJ
ma-198	511	17	monotone	monotone	ADJ
ma-198	511	18	mappings	mapping	NOUN
ma-198	511	19	,	,	PUNCT
ma-198	511	20	siam	siam	PROPN
ma-198	511	21	j.	j.	PROPN
ma-198	511	22	control	control	PROPN
ma-198	511	23	optim	optim	PROPN
ma-198	511	24	.	.	PUNCT
ma-198	512	1	38(2000	38(2000	NUM
ma-198	512	2	)	)	PUNCT
ma-198	512	3	,	,	PUNCT
ma-198	512	4	431	431	NUM
ma-198	512	5	-	-	SYM
ma-198	512	6	446.[21	446.[21	NUM
ma-198	512	7	]	]	PUNCT
ma-198	512	8	h.k	h.k	PROPN
ma-198	512	9	.	.	PROPN
ma-198	512	10	xu	xu	PROPN
ma-198	512	11	,	,	PUNCT
ma-198	512	12	an	an	DET
ma-198	512	13	iterative	iterative	NOUN
ma-198	512	14	approach	approach	NOUN
ma-198	512	15	to	to	ADP
ma-198	512	16	quadratic	quadratic	ADJ
ma-198	512	17	optimization	optimization	NOUN
ma-198	512	18	,	,	PUNCT
ma-198	512	19	j.	j.	PROPN
ma-198	512	20	optim	optim	PROPN
ma-198	512	21	.	.	PUNCT
ma-198	513	1	theory	theory	NOUN
ma-198	513	2	appl	appl	PROPN
ma-198	513	3	.	.	PUNCT
ma-198	514	1	116	116	NUM
ma-198	514	2	(	(	PUNCT
ma-198	514	3	2003	2003	NUM
ma-198	514	4	)	)	PUNCT
ma-198	514	5	,	,	PUNCT
ma-198	514	6	659	659	NUM
ma-198	514	7	-	-	SYM
ma-198	514	8	678.[22	678.[22	PROPN
ma-198	514	9	]	]	X
ma-198	514	10	y.b	y.b	PROPN
ma-198	514	11	.	.	PROPN
ma-198	514	12	el	el	PROPN
ma-198	514	13	yekheir	yekheir	PROPN
ma-198	514	14	,	,	PUNCT
ma-198	514	15	j.t	j.t	PROPN
ma-198	514	16	.	.	PROPN
ma-198	514	17	mendy	mendy	PROPN
ma-198	514	18	,	,	PUNCT
ma-198	514	19	t.m.m	t.m.m	NOUN
ma-198	514	20	.	.	PUNCT
ma-198	514	21	sow	sow	PROPN
ma-198	514	22	,	,	PUNCT
ma-198	514	23	n.	n.	NOUN
ma-198	514	24	djitte	djitte	NOUN
ma-198	514	25	,	,	PUNCT
ma-198	514	26	proximal	proximal	ADJ
ma-198	514	27	point	point	NOUN
ma-198	514	28	algorithms	algorithm	NOUN
ma-198	514	29	for	for	ADP
ma-198	514	30	fixed	fix	VERB
ma-198	514	31	point	point	NOUN
ma-198	514	32	problem	problem	NOUN
ma-198	514	33	and	and	CCONJ
ma-198	514	34	convexminimization	convexminimization	NOUN
ma-198	514	35	problem	problem	NOUN
ma-198	514	36	,	,	PUNCT
ma-198	514	37	int	int	NOUN
ma-198	514	38	.	.	PUNCT
ma-198	515	1	j.	j.	PROPN
ma-198	515	2	math	math	PROPN
ma-198	515	3	.	.	PUNCT
ma-198	516	1	anal	anal	ADJ
ma-198	516	2	.	.	PUNCT
ma-198	517	1	14	14	NUM
ma-198	517	2	(	(	PUNCT
ma-198	517	3	2020	2020	NUM
ma-198	517	4	)	)	PUNCT
ma-198	517	5	,	,	PUNCT
ma-198	517	6	27	27	NUM
ma-198	517	7	-	-	SYM
ma-198	517	8	44.[23	44.[23	NUM
ma-198	517	9	]	]	X
ma-198	517	10	s.b	s.b	PROPN
ma-198	517	11	.	.	PROPN
ma-198	517	12	mendy	mendy	PROPN
ma-198	517	13	,	,	PUNCT
ma-198	517	14	j.t	j.t	PROPN
ma-198	517	15	.	.	PROPN
ma-198	517	16	mendy	mendy	PROPN
ma-198	517	17	,	,	PUNCT
ma-198	517	18	a.	a.	PROPN
ma-198	517	19	jobe	jobe	PROPN
ma-198	517	20	,	,	PUNCT
ma-198	517	21	the	the	DET
ma-198	517	22	generalized	generalized	ADJ
ma-198	517	23	viscosity	viscosity	NOUN
ma-198	517	24	implicit	implicit	ADJ
ma-198	517	25	rules	rule	NOUN
ma-198	517	26	of	of	ADP
ma-198	517	27	asymptotically	asymptotically	ADV
ma-198	517	28	nonexpansive	nonexpansive	ADJ
ma-198	517	29	mappingsin	mappingsin	PROPN
ma-198	517	30	hilbert	hilbert	PROPN
ma-198	517	31	spaces	space	NOUN
ma-198	517	32	,	,	PUNCT
ma-198	517	33	eur	eur	PROPN
ma-198	517	34	.	.	PUNCT
ma-198	518	1	j.	j.	PROPN
ma-198	518	2	math	math	PROPN
ma-198	518	3	.	.	PUNCT
ma-198	519	1	anal	anal	ADJ
ma-198	519	2	.	.	PUNCT
ma-198	520	1	1	1	NUM
ma-198	520	2	(	(	PUNCT
ma-198	520	3	2021	2021	NUM
ma-198	520	4	)	)	PUNCT
ma-198	520	5	,	,	PUNCT
ma-198	520	6	19	19	NUM
ma-198	520	7	-	-	SYM
ma-198	520	8	33.[24	33.[24	NUM
ma-198	520	9	]	]	PUNCT
ma-198	520	10	h.k	h.k	PROPN
ma-198	520	11	.	.	PROPN
ma-198	520	12	xu	xu	PROPN
ma-198	520	13	,	,	PUNCT
ma-198	520	14	inequalities	inequality	NOUN
ma-198	520	15	in	in	ADP
ma-198	520	16	banach	banach	NOUN
ma-198	520	17	spaces	space	NOUN
ma-198	520	18	with	with	ADP
ma-198	520	19	applications	application	NOUN
ma-198	520	20	,	,	PUNCT
ma-198	520	21	nonlinear	nonlinear	ADJ
ma-198	520	22	anal	anal	NOUN
ma-198	520	23	.	.	PUNCT
ma-198	521	1	tma	tma	PROPN
ma-198	521	2	.	.	PROPN
ma-198	522	1	16	16	NUM
ma-198	522	2	(	(	PUNCT
ma-198	522	3	1991	1991	NUM
ma-198	522	4	)	)	PUNCT
ma-198	522	5	,	,	PUNCT
ma-198	522	6	1127	1127	NUM
ma-198	522	7	-	-	SYM
ma-198	522	8	1138.[25	1138.[25	NUM
ma-198	522	9	]	]	X
ma-198	522	10	j.t	j.t	PROPN
ma-198	522	11	.	.	PROPN
ma-198	522	12	mendy	mendy	PROPN
ma-198	522	13	,	,	PUNCT
ma-198	522	14	the	the	DET
ma-198	522	15	viscosity	viscosity	NOUN
ma-198	522	16	iterative	iterative	NOUN
ma-198	522	17	algorithms	algorithm	NOUN
ma-198	522	18	for	for	ADP
ma-198	522	19	the	the	DET
ma-198	522	20	implicit	implicit	ADJ
ma-198	522	21	double	double	ADJ
ma-198	522	22	midpoint	midpoint	NOUN
ma-198	522	23	rule	rule	NOUN
ma-198	522	24	of	of	ADP
ma-198	522	25	nonexpansive	nonexpansive	ADJ
ma-198	522	26	mappings	mapping	NOUN
ma-198	522	27	inhilbert	inhilbert	PROPN
ma-198	522	28	spaces	space	NOUN
ma-198	522	29	,	,	PUNCT
ma-198	522	30	amer	amer	PROPN
ma-198	522	31	.	.	PUNCT
ma-198	523	1	j.	j.	PROPN
ma-198	523	2	math	math	PROPN
ma-198	523	3	.	.	PUNCT
ma-198	524	1	anal	anal	PROPN
ma-198	524	2	.	.	PUNCT
ma-198	525	1	8	8	NUM
ma-198	525	2	(	(	PUNCT
ma-198	525	3	2020	2020	NUM
ma-198	525	4	)	)	PUNCT
ma-198	525	5	,	,	PUNCT
ma-198	525	6	1	1	NUM
ma-198	525	7	-	-	SYM
ma-198	525	8	8.[26	8.[26	NUM
ma-198	525	9	]	]	X
ma-198	525	10	t.l	t.l	PROPN
ma-198	525	11	.	.	PROPN
ma-198	525	12	hicks	hicks	PROPN
ma-198	525	13	,	,	PUNCT
ma-198	525	14	j.d	j.d	PROPN
ma-198	525	15	.	.	PROPN
ma-198	525	16	kubicek	kubicek	PROPN
ma-198	525	17	,	,	PUNCT
ma-198	525	18	on	on	ADP
ma-198	525	19	the	the	DET
ma-198	525	20	mann	mann	PROPN
ma-198	525	21	iteration	iteration	NOUN
ma-198	525	22	process	process	NOUN
ma-198	525	23	in	in	ADP
ma-198	525	24	a	a	DET
ma-198	525	25	hilbert	hilbert	NOUN
ma-198	525	26	space	space	NOUN
ma-198	525	27	,	,	PUNCT
ma-198	525	28	j.	j.	PROPN
ma-198	525	29	math	math	PROPN
ma-198	525	30	.	.	PUNCT
ma-198	526	1	anal	anal	PROPN
ma-198	526	2	.	.	PUNCT
ma-198	527	1	appl	appl	PROPN
ma-198	527	2	.	.	PROPN
ma-198	528	1	59	59	NUM
ma-198	528	2	(	(	PUNCT
ma-198	528	3	1977	1977	NUM
ma-198	528	4	)	)	PUNCT
ma-198	528	5	,	,	PUNCT
ma-198	528	6	498	498	NUM
ma-198	528	7	-	-	SYM
ma-198	528	8	504.[27	504.[27	PROPN
ma-198	528	9	]	]	X
ma-198	528	10	p.l	p.l	PROPN
ma-198	528	11	.	.	PROPN
ma-198	528	12	lions	lion	NOUN
ma-198	528	13	,	,	PUNCT
ma-198	528	14	b.	b.	PROPN
ma-198	528	15	mercier	mercier	NOUN
ma-198	528	16	,	,	PUNCT
ma-198	528	17	splitting	split	VERB
ma-198	528	18	algorithms	algorithm	NOUN
ma-198	528	19	for	for	ADP
ma-198	528	20	the	the	DET
ma-198	528	21	sum	sum	NOUN
ma-198	528	22	of	of	ADP
ma-198	528	23	two	two	NUM
ma-198	528	24	nonlinear	nonlinear	ADJ
ma-198	528	25	operators	operator	NOUN
ma-198	528	26	,	,	PUNCT
ma-198	528	27	siam	siam	PROPN
ma-198	528	28	j.	j.	PROPN
ma-198	528	29	numer	numer	PROPN
ma-198	528	30	.	.	PUNCT
ma-198	529	1	anal	anal	PROPN
ma-198	529	2	.	.	PUNCT
ma-198	530	1	16	16	NUM
ma-198	530	2	(	(	PUNCT
ma-198	530	3	1979),964	1979),964	NUM
ma-198	530	4	-	-	SYM
ma-198	530	5	979.[28	979.[28	NUM
ma-198	530	6	]	]	PUNCT
ma-198	530	7	t.m.m	t.m.m	NOUN
ma-198	530	8	.	.	PUNCT
ma-198	530	9	sow	sow	NOUN
ma-198	530	10	,	,	PUNCT
ma-198	530	11	general	general	ADJ
ma-198	530	12	viscosity	viscosity	NOUN
ma-198	530	13	iterative	iterative	NOUN
ma-198	530	14	process	process	NOUN
ma-198	530	15	for	for	ADP
ma-198	530	16	solving	solve	VERB
ma-198	530	17	variational	variational	ADJ
ma-198	530	18	inclusion	inclusion	NOUN
ma-198	530	19	and	and	CCONJ
ma-198	530	20	fixed	fix	VERB
ma-198	530	21	point	point	NOUN
ma-198	530	22	problems	problem	NOUN
ma-198	530	23	involvingmultivuled	involvingmultivule	VERB
ma-198	530	24	quasi	quasi	ADJ
ma-198	530	25	-	-	ADJ
ma-198	530	26	nonexpansive	nonexpansive	ADJ
ma-198	530	27	and	and	CCONJ
ma-198	530	28	demicontractive	demicontractive	ADJ
ma-198	530	29	operators	operator	NOUN
ma-198	530	30	with	with	ADP
ma-198	530	31	applications	application	NOUN
ma-198	530	32	,	,	PUNCT
ma-198	530	33	math	math	NOUN
ma-198	530	34	.	.	PUNCT
ma-198	531	1	anal	anal	PROPN
ma-198	531	2	.	.	PUNCT
ma-198	532	1	convex	convex	PROPN
ma-198	532	2	optim	optim	ADJ
ma-198	532	3	.	.	PUNCT
ma-198	532	4	1	1	NUM
ma-198	532	5	(	(	PUNCT
ma-198	532	6	2020),75	2020),75	NUM
ma-198	532	7	-	-	SYM
ma-198	532	8	91.[29	91.[29	NUM
ma-198	532	9	]	]	X
ma-198	532	10	c.e	c.e	PROPN
ma-198	532	11	.	.	PROPN
ma-198	532	12	chidume	chidume	PROPN
ma-198	532	13	,	,	PUNCT
ma-198	532	14	geometric	geometric	ADJ
ma-198	532	15	properties	property	NOUN
ma-198	532	16	of	of	ADP
ma-198	532	17	banach	banach	NOUN
ma-198	532	18	space	space	NOUN
ma-198	532	19	and	and	CCONJ
ma-198	532	20	nonlinear	nonlinear	ADJ
ma-198	532	21	iterations	iteration	NOUN
ma-198	532	22	,	,	PUNCT
ma-198	532	23	series	series	NOUN
ma-198	532	24	:	:	PUNCT
ma-198	532	25	lecture	lecture	VERB
ma-198	532	26	notesin	notesin	ADJ
ma-198	532	27	mathematics	mathematic	NOUN
ma-198	532	28	,	,	PUNCT
ma-198	532	29	springer	springer	NOUN
ma-198	532	30	,	,	PUNCT
ma-198	532	31	berlin	berlin	PROPN
ma-198	532	32	,	,	PUNCT
ma-198	532	33	2009.[30	2009.[30	PROPN
ma-198	532	34	]	]	X
ma-198	532	35	f.e	f.e	PROPN
ma-198	532	36	.	.	PROPN
ma-198	532	37	browder	browder	PROPN
ma-198	532	38	,	,	PUNCT
ma-198	532	39	convergenge	convergenge	NOUN
ma-198	532	40	theorem	theorem	NOUN
ma-198	532	41	for	for	ADP
ma-198	532	42	sequence	sequence	NOUN
ma-198	532	43	of	of	ADP
ma-198	532	44	nonlinear	nonlinear	ADJ
ma-198	532	45	operator	operator	NOUN
ma-198	532	46	in	in	ADP
ma-198	532	47	banach	banach	NOUN
ma-198	532	48	spaces	space	NOUN
ma-198	532	49	,	,	PUNCT
ma-198	532	50	math	math	NOUN
ma-198	532	51	.	.	PUNCT
ma-198	533	1	zeitsch	zeitsch	PROPN
ma-198	533	2	.	.	PROPN
ma-198	533	3	100	100	NUM
ma-198	533	4	(	(	PUNCT
ma-198	533	5	1967),201	1967),201	NOUN
ma-198	533	6	-	-	SYM
ma-198	533	7	225.[31	225.[31	NUM
ma-198	533	8	]	]	X
ma-198	533	9	g.h.g	g.h.g	NOUN
ma-198	533	10	.	.	PUNCT
ma-198	534	1	chen	chen	PROPN
ma-198	534	2	,	,	PUNCT
ma-198	534	3	r.t	r.t	PROPN
ma-198	534	4	.	.	PROPN
ma-198	534	5	rockafellar	rockafellar	PROPN
ma-198	534	6	,	,	PUNCT
ma-198	534	7	convergence	convergence	NOUN
ma-198	534	8	rates	rate	NOUN
ma-198	534	9	in	in	ADP
ma-198	534	10	forward	forward	ADV
ma-198	534	11	-	-	PUNCT
ma-198	534	12	backward	backward	ADJ
ma-198	534	13	splitting	splitting	NOUN
ma-198	534	14	,	,	PUNCT
ma-198	534	15	siam	siam	PROPN
ma-198	534	16	j.	j.	PROPN
ma-198	534	17	optim	optim	PROPN
ma-198	534	18	.	.	PROPN
ma-198	534	19	7	7	NUM
ma-198	534	20	(	(	PUNCT
ma-198	534	21	1997	1997	NUM
ma-198	534	22	)	)	PUNCT
ma-198	534	23	,	,	PUNCT
ma-198	534	24	421	421	NUM
ma-198	534	25	-	-	SYM
ma-198	534	26	444.[32	444.[32	PROPN
ma-198	534	27	]	]	X
ma-198	534	28	c.e	c.e	PROPN
ma-198	534	29	.	.	PROPN
ma-198	534	30	chidume	chidume	PROPN
ma-198	534	31	,	,	PUNCT
ma-198	534	32	geometric	geometric	ADJ
ma-198	534	33	properties	property	NOUN
ma-198	534	34	of	of	ADP
ma-198	534	35	banach	banach	NOUN
ma-198	534	36	spaces	space	NOUN
ma-198	534	37	and	and	CCONJ
ma-198	534	38	nonlinear	nonlinear	ADJ
ma-198	534	39	iterations	iteration	NOUN
ma-198	534	40	,	,	PUNCT
ma-198	534	41	springer	springer	NOUN
ma-198	534	42	verlag	verlag	PROPN
ma-198	534	43	series	series	PROPN
ma-198	534	44	:	:	PUNCT
ma-198	534	45	lecturenotes	lecturenote	VERB
ma-198	534	46	in	in	ADP
ma-198	534	47	mathematics	mathematic	NOUN
ma-198	534	48	,	,	PUNCT
ma-198	534	49	2009.[33	2009.[33	NUM
ma-198	534	50	]	]	X
ma-198	534	51	c.e	c.e	PROPN
ma-198	534	52	.	.	PROPN
ma-198	534	53	chidume	chidume	PROPN
ma-198	534	54	,	,	PUNCT
ma-198	534	55	c.o	c.o	PROPN
ma-198	534	56	.	.	PROPN
ma-198	534	57	chidume	chidume	PROPN
ma-198	534	58	,	,	PUNCT
ma-198	534	59	n.	n.	NOUN
ma-198	534	60	djitte	djitte	PROPN
ma-198	534	61	,	,	PUNCT
ma-198	534	62	m.s	m.s	PROPN
ma-198	534	63	.	.	PROPN
ma-198	534	64	minjibir	minjibir	PROPN
ma-198	534	65	,	,	PUNCT
ma-198	534	66	convergence	convergence	NOUN
ma-198	534	67	theorems	theorem	NOUN
ma-198	534	68	for	for	ADP
ma-198	534	69	fixed	fix	VERB
ma-198	534	70	points	point	NOUN
ma-198	534	71	of	of	ADP
ma-198	534	72	multivalued	multivalue	VERB
ma-198	534	73	strictlypseudocontractive	strictlypseudocontractive	ADJ
ma-198	534	74	mappings	mapping	NOUN
ma-198	534	75	in	in	ADP
ma-198	534	76	hilbert	hilbert	PROPN
ma-198	534	77	spaces	space	NOUN
ma-198	534	78	,	,	PUNCT
ma-198	534	79	abstr	abstr	PROPN
ma-198	534	80	.	.	PUNCT
ma-198	535	1	appl	appl	PROPN
ma-198	535	2	.	.	PUNCT
ma-198	536	1	anal	anal	PROPN
ma-198	536	2	.	.	PUNCT
ma-198	537	1	2013	2013	NUM
ma-198	537	2	(	(	PUNCT
ma-198	537	3	2013	2013	NUM
ma-198	537	4	)	)	PUNCT
ma-198	537	5	,	,	PUNCT
ma-198	537	6	629468	629468	NUM
ma-198	537	7	.	.	PUNCT
ma-198	538	1	https://doi.org/10.28924/ada/ma.4.2	https://doi.org/10.28924/ada/ma.4.2	NUM
ma-198	538	2	1	1	NUM
ma-198	538	3	.	.	PUNCT
ma-198	538	4	introduction	introduction	NOUN
ma-198	538	5	2	2	NUM
ma-198	538	6	.	.	PUNCT
ma-198	538	7	preliminaries	preliminary	NOUN
ma-198	538	8	3	3	NUM
ma-198	538	9	.	.	X
ma-198	538	10	main	main	ADJ
ma-198	538	11	results	result	NOUN
ma-198	538	12	4	4	NUM
ma-198	538	13	.	.	PUNCT
ma-198	539	1	conclusion	conclusion	NOUN
ma-198	539	2	references	reference	NOUN