id	sid	tid	token	lemma	pos
ma-61	1	1	2022	2022	NUM
ma-61	1	2	ada	ada	PROPN
ma-61	1	3	academica	academica	PROPN
ma-61	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-61	1	5	.	.	PUNCT
ma-61	2	1	j.	j.	PROPN
ma-61	2	2	math	math	PROPN
ma-61	2	3	.	.	PUNCT
ma-61	3	1	anal	anal	ADJ
ma-61	3	2	.	.	PUNCT
ma-61	3	3	2	2	NUM
ma-61	3	4	(	(	PUNCT
ma-61	3	5	2022	2022	NUM
ma-61	3	6	)	)	PUNCT
ma-61	3	7	6doi	6doi	NOUN
ma-61	3	8	:	:	PUNCT
ma-61	3	9	10.28924	10.28924	NUM
ma-61	3	10	/	/	SYM
ma-61	3	11	ada	ada	PROPN
ma-61	3	12	/	/	SYM
ma-61	3	13	ma.2.6	ma.2.6	PROPN
ma-61	3	14	solving	solve	VERB
ma-61	3	15	equilibrium	equilibrium	NOUN
ma-61	3	16	problem	problem	NOUN
ma-61	3	17	and	and	CCONJ
ma-61	3	18	fixed	fix	VERB
ma-61	3	19	point	point	NOUN
ma-61	3	20	problem	problem	NOUN
ma-61	3	21	by	by	ADP
ma-61	3	22	normal	normal	ADJ
ma-61	3	23	s	s	NOUN
ma-61	3	24	-	-	PUNCT
ma-61	3	25	iteration	iteration	NOUN
ma-61	3	26	process	process	NOUN
ma-61	3	27	in	in	ADP
ma-61	3	28	hilbert	hilbert	PROPN
ma-61	3	29	space	space	PROPN
ma-61	3	30	shamshad	shamshad	PROPN
ma-61	3	31	husain	husain	PROPN
ma-61	3	32	,	,	PUNCT
ma-61	3	33	mohd	mohd	PROPN
ma-61	3	34	asad∗	asad∗	PROPN
ma-61	3	35	department	department	PROPN
ma-61	3	36	of	of	ADP
ma-61	3	37	applied	apply	VERB
ma-61	3	38	mathematics	mathematic	NOUN
ma-61	3	39	,	,	PUNCT
ma-61	3	40	faculty	faculty	NOUN
ma-61	3	41	of	of	ADP
ma-61	3	42	engineering	engineering	NOUN
ma-61	3	43	and	and	CCONJ
ma-61	3	44	technology	technology	NOUN
ma-61	3	45	,	,	PUNCT
ma-61	3	46	aligarh	aligarh	PROPN
ma-61	3	47	muslim	muslim	PROPN
ma-61	3	48	university	university	PROPN
ma-61	3	49	,	,	PUNCT
ma-61	3	50	aligarh	aligarh	PROPN
ma-61	3	51	,	,	PUNCT
ma-61	3	52	india	india	PROPN
ma-61	3	53	s_husain68@yahoo.com	s_husain68@yahoo.com	PROPN
ma-61	3	54	,	,	PUNCT
ma-61	3	55	masad19932015@gmail.com	masad19932015@gmail.com	X
ma-61	4	1	∗correspondence	∗correspondence	NOUN
ma-61	4	2	:	:	PUNCT
ma-61	4	3	masad19932015@gmail.com	masad19932015@gmail.com	X
ma-61	4	4	abstract	abstract	PROPN
ma-61	4	5	.	.	PUNCT
ma-61	5	1	the	the	DET
ma-61	5	2	main	main	ADJ
ma-61	5	3	purpose	purpose	NOUN
ma-61	5	4	of	of	ADP
ma-61	5	5	this	this	DET
ma-61	5	6	paper	paper	NOUN
ma-61	5	7	is	be	AUX
ma-61	5	8	to	to	PART
ma-61	5	9	find	find	VERB
ma-61	5	10	a	a	DET
ma-61	5	11	common	common	ADJ
ma-61	5	12	element	element	NOUN
ma-61	5	13	in	in	ADP
ma-61	5	14	the	the	DET
ma-61	5	15	solution	solution	NOUN
ma-61	5	16	set	set	VERB
ma-61	5	17	of	of	ADP
ma-61	5	18	equilibriumproblem	equilibriumproblem	NOUN
ma-61	5	19	and	and	CCONJ
ma-61	5	20	fixed	fix	VERB
ma-61	5	21	point	point	NOUN
ma-61	5	22	problem	problem	NOUN
ma-61	5	23	of	of	ADP
ma-61	5	24	non	non	ADJ
ma-61	5	25	-	-	ADJ
ma-61	5	26	expansive	expansive	ADJ
ma-61	5	27	mappings	mapping	NOUN
ma-61	5	28	in	in	ADP
ma-61	5	29	the	the	DET
ma-61	5	30	real	real	ADJ
ma-61	5	31	hilbert	hilbert	NOUN
ma-61	5	32	space	space	NOUN
ma-61	5	33	with	with	ADP
ma-61	5	34	the	the	DET
ma-61	5	35	helpof	helpof	VERB
ma-61	5	36	normal	normal	ADJ
ma-61	5	37	s	s	NOUN
ma-61	5	38	-	-	PUNCT
ma-61	5	39	iteration	iteration	NOUN
ma-61	5	40	process	process	NOUN
ma-61	5	41	.	.	PUNCT
ma-61	6	1	also	also	ADV
ma-61	6	2	,	,	PUNCT
ma-61	6	3	under	under	ADP
ma-61	6	4	some	some	DET
ma-61	6	5	acceptable	acceptable	ADJ
ma-61	6	6	assumptions	assumption	NOUN
ma-61	6	7	,	,	PUNCT
ma-61	6	8	we	we	PRON
ma-61	6	9	prove	prove	VERB
ma-61	6	10	the	the	DET
ma-61	6	11	sequencesinduced	sequencesinduce	VERB
ma-61	6	12	by	by	ADP
ma-61	6	13	above	above	ADV
ma-61	6	14	stated	stated	ADJ
ma-61	6	15	process	process	NOUN
ma-61	6	16	converge	converge	VERB
ma-61	6	17	weakly	weakly	ADV
ma-61	6	18	to	to	ADP
ma-61	6	19	a	a	DET
ma-61	6	20	point	point	NOUN
ma-61	6	21	in	in	ADP
ma-61	6	22	the	the	DET
ma-61	6	23	solution	solution	NOUN
ma-61	6	24	set	set	VERB
ma-61	6	25	of	of	ADP
ma-61	6	26	above	above	ADP
ma-61	6	27	statedproblems	statedproblem	NOUN
ma-61	6	28	.	.	PUNCT
ma-61	7	1	at	at	ADP
ma-61	7	2	the	the	DET
ma-61	7	3	end	end	NOUN
ma-61	7	4	,	,	PUNCT
ma-61	7	5	we	we	PRON
ma-61	7	6	give	give	VERB
ma-61	7	7	a	a	DET
ma-61	7	8	numerical	numerical	ADJ
ma-61	7	9	example	example	NOUN
ma-61	7	10	to	to	PART
ma-61	7	11	justify	justify	VERB
ma-61	7	12	our	our	PRON
ma-61	7	13	work	work	NOUN
ma-61	7	14	.	.	PUNCT
ma-61	8	1	the	the	DET
ma-61	8	2	results	result	NOUN
ma-61	8	3	studied	study	VERB
ma-61	8	4	in	in	ADP
ma-61	8	5	thiswork	thiswork	NOUN
ma-61	8	6	philosophize	philosophize	NOUN
ma-61	8	7	and	and	CCONJ
ma-61	8	8	boost	boost	VERB
ma-61	8	9	some	some	DET
ma-61	8	10	contemporary	contemporary	ADJ
ma-61	8	11	and	and	CCONJ
ma-61	8	12	known	known	ADJ
ma-61	8	13	results	result	NOUN
ma-61	8	14	in	in	ADP
ma-61	8	15	this	this	DET
ma-61	8	16	direction	direction	NOUN
ma-61	8	17	.	.	PUNCT
ma-61	9	1	1	1	X
ma-61	9	2	.	.	X
ma-61	9	3	introduction	introduction	NOUN
ma-61	9	4	and	and	CCONJ
ma-61	9	5	auxiliary	auxiliary	ADJ
ma-61	9	6	results	result	NOUN
ma-61	9	7	everywhere	everywhere	ADV
ma-61	9	8	in	in	ADP
ma-61	9	9	this	this	DET
ma-61	9	10	paper	paper	NOUN
ma-61	9	11	except	except	SCONJ
ma-61	9	12	stated	state	VERB
ma-61	9	13	otherwise	otherwise	ADV
ma-61	9	14	,	,	PUNCT
ma-61	9	15	let	let	VERB
ma-61	9	16	h	h	PRON
ma-61	9	17	be	be	AUX
ma-61	9	18	a	a	DET
ma-61	9	19	real	real	ADJ
ma-61	9	20	hilbert	hilbert	NOUN
ma-61	9	21	space	space	NOUN
ma-61	9	22	equipped	equip	VERB
ma-61	9	23	withinner	withinner	NOUN
ma-61	9	24	product	product	NOUN
ma-61	9	25	〈	〈	PROPN
ma-61	9	26	·	·	PROPN
ma-61	9	27	,	,	PUNCT
ma-61	9	28	·	·	PUNCT
ma-61	9	29	〉	〉	NUM
ma-61	9	30	and	and	CCONJ
ma-61	10	1	induced	induce	VERB
ma-61	10	2	norm	norm	NOUN
ma-61	10	3	‖	‖	PROPN
ma-61	10	4	·	·	PUNCT
ma-61	10	5	‖.	‖.	PROPN
ma-61	10	6	let	let	VERB
ma-61	10	7	c	c	PRON
ma-61	10	8	be	be	AUX
ma-61	10	9	a	a	DET
ma-61	10	10	non	non	ADJ
ma-61	10	11	-	-	ADJ
ma-61	10	12	empty	empty	ADJ
ma-61	10	13	closed	closed	ADJ
ma-61	10	14	and	and	CCONJ
ma-61	10	15	convex	convex	PROPN
ma-61	10	16	subset	subset	NOUN
ma-61	10	17	of	of	ADP
ma-61	10	18	h.	h.	PROPN
ma-61	10	19	we	we	PRON
ma-61	10	20	denote	denote	VERB
ma-61	10	21	strong	strong	ADJ
ma-61	10	22	and	and	CCONJ
ma-61	10	23	weak	weak	ADJ
ma-61	10	24	convergence	convergence	NOUN
ma-61	10	25	of	of	ADP
ma-61	10	26	a	a	DET
ma-61	10	27	sequence	sequence	NOUN
ma-61	10	28	{	{	PUNCT
ma-61	10	29	xn	xn	NOUN
ma-61	10	30	}	}	PUNCT
ma-61	10	31	∈	∈	NOUN
ma-61	10	32	h	h	NOUN
ma-61	10	33	by	by	ADP
ma-61	10	34	the	the	DET
ma-61	10	35	symbols	symbol	NOUN
ma-61	10	36	→	→	PUNCT
ma-61	10	37	and	and	CCONJ
ma-61	10	38	⇀	⇀	PROPN
ma-61	10	39	respectively.let	respectively.let	X
ma-61	10	40	t	t	NOUN
ma-61	10	41	:	:	PUNCT
ma-61	10	42	c	c	X
ma-61	10	43	→	→	PUNCT
ma-61	10	44	h	h	PROPN
ma-61	10	45	be	be	AUX
ma-61	10	46	a	a	DET
ma-61	10	47	nonexpansive	nonexpansive	ADJ
ma-61	10	48	mapping	mapping	NOUN
ma-61	10	49	.	.	PUNCT
ma-61	11	1	the	the	DET
ma-61	11	2	so	so	ADV
ma-61	11	3	called	call	VERB
ma-61	11	4	fixed	fix	VERB
ma-61	11	5	point	point	NOUN
ma-61	11	6	problem	problem	NOUN
ma-61	11	7	for	for	ADP
ma-61	11	8	mapping	mapping	NOUN
ma-61	11	9	t	t	PROPN
ma-61	11	10	is	be	AUX
ma-61	11	11	tofind	tofind	ADJ
ma-61	11	12	an	an	DET
ma-61	11	13	element	element	NOUN
ma-61	11	14	p	p	PROPN
ma-61	11	15	∈	∈	PROPN
ma-61	11	16	c	c	NOUN
ma-61	12	1	such	such	ADJ
ma-61	12	2	that	that	PRON
ma-61	12	3	tp	tp	NOUN
ma-61	12	4	=	=	PUNCT
ma-61	13	1	p.	p.	NOUN
ma-61	13	2	(	(	PUNCT
ma-61	13	3	1	1	X
ma-61	13	4	)	)	PUNCT
ma-61	13	5	denote	denote	VERB
ma-61	13	6	the	the	DET
ma-61	13	7	set	set	NOUN
ma-61	13	8	of	of	ADP
ma-61	13	9	solution	solution	NOUN
ma-61	13	10	of	of	ADP
ma-61	13	11	the	the	DET
ma-61	13	12	problem	problem	NOUN
ma-61	13	13	(	(	PUNCT
ma-61	13	14	1	1	NUM
ma-61	13	15	)	)	PUNCT
ma-61	13	16	by	by	ADP
ma-61	13	17	fix(t	fix(t	PROPN
ma-61	13	18	)	)	PUNCT
ma-61	14	1	=	=	PRON
ma-61	15	1	{	{	PUNCT
ma-61	15	2	p	p	X
ma-61	15	3	∈	∈	PROPN
ma-61	15	4	c	c	NOUN
ma-61	15	5	:	:	PUNCT
ma-61	15	6	tp	tp	X
ma-61	15	7	=	=	SYM
ma-61	15	8	p	p	X
ma-61	15	9	}	}	PUNCT
ma-61	15	10	.	.	PUNCT
ma-61	16	1	t	t	PROPN
ma-61	16	2	is	be	AUX
ma-61	16	3	said	say	VERB
ma-61	16	4	to	to	PART
ma-61	16	5	benonexpansive	benonexpansive	VERB
ma-61	16	6	iff	iff	PROPN
ma-61	16	7	‖tp	‖tp	PROPN
ma-61	16	8	−	−	PROPN
ma-61	16	9	tq‖2	tq‖2	PROPN
ma-61	16	10	≤	≤	NUM
ma-61	16	11	‖p	‖p	PROPN
ma-61	17	1	−	−	PROPN
ma-61	17	2	q‖2	q‖2	NOUN
ma-61	17	3	,	,	PUNCT
ma-61	17	4	∀	∀	X
ma-61	17	5	p	p	NOUN
ma-61	17	6	,	,	PUNCT
ma-61	17	7	q	q	PROPN
ma-61	17	8	∈	∈	PROPN
ma-61	17	9	c.	c.	NOUN
ma-61	17	10	received	receive	VERB
ma-61	17	11	:	:	PUNCT
ma-61	17	12	10	10	NUM
ma-61	17	13	dec	dec	PROPN
ma-61	17	14	2021	2021	NUM
ma-61	17	15	.	.	PUNCT
ma-61	18	1	key	key	ADJ
ma-61	18	2	words	word	NOUN
ma-61	18	3	and	and	CCONJ
ma-61	18	4	phrases	phrase	NOUN
ma-61	18	5	.	.	PUNCT
ma-61	19	1	equilibrium	equilibrium	NOUN
ma-61	19	2	problem	problem	NOUN
ma-61	19	3	;	;	PUNCT
ma-61	19	4	normal	normal	ADJ
ma-61	19	5	s	s	NOUN
ma-61	19	6	-	-	NOUN
ma-61	19	7	iteration	iteration	NOUN
ma-61	19	8	;	;	PUNCT
ma-61	19	9	fixed	fix	VERB
ma-61	19	10	point	point	NOUN
ma-61	19	11	problem	problem	NOUN
ma-61	19	12	;	;	PUNCT
ma-61	19	13	hilbert	hilbert	NOUN
ma-61	19	14	space	space	NOUN
ma-61	19	15	;	;	PUNCT
ma-61	19	16	non	non	ADJ
ma-61	19	17	-	-	ADJ
ma-61	19	18	expansivemapping	expansivemapping	ADJ
ma-61	19	19	.	.	PUNCT
ma-61	20	1	1	1	NUM
ma-61	20	2	https://adac.ee	https://adac.ee	PROPN
ma-61	20	3	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	20	4	eur	eur	PROPN
ma-61	20	5	.	.	PUNCT
ma-61	21	1	j.	j.	PROPN
ma-61	21	2	math	math	PROPN
ma-61	21	3	.	.	PUNCT
ma-61	22	1	anal	anal	PROPN
ma-61	22	2	.	.	PUNCT
ma-61	23	1	10.28924	10.28924	NUM
ma-61	23	2	/	/	SYM
ma-61	23	3	ada	ada	PROPN
ma-61	23	4	/	/	SYM
ma-61	23	5	ma.2.6	ma.2.6	PROPN
ma-61	23	6	2	2	NUM
ma-61	23	7	in	in	ADP
ma-61	23	8	2011	2011	NUM
ma-61	23	9	,	,	PUNCT
ma-61	23	10	d.r	d.r	PROPN
ma-61	23	11	.	.	PROPN
ma-61	23	12	sahu	sahu	PROPN
ma-61	24	1	[	[	X
ma-61	24	2	4	4	NUM
ma-61	24	3	]	]	PUNCT
ma-61	24	4	studied	study	VERB
ma-61	24	5	problem	problem	NOUN
ma-61	24	6	(	(	PUNCT
ma-61	24	7	1	1	NUM
ma-61	24	8	)	)	PUNCT
ma-61	24	9	and	and	CCONJ
ma-61	24	10	proposed	propose	VERB
ma-61	24	11	an	an	DET
ma-61	24	12	iterative	iterative	NOUN
ma-61	24	13	method	method	NOUN
ma-61	24	14	known	know	VERB
ma-61	24	15	as	as	ADP
ma-61	24	16	normals	normal	NOUN
ma-61	24	17	-	-	PUNCT
ma-61	24	18	iteration	iteration	NOUN
ma-61	24	19	process	process	NOUN
ma-61	24	20	which	which	PRON
ma-61	24	21	is	be	AUX
ma-61	24	22	defied	defy	VERB
ma-61	24	23	as	as	SCONJ
ma-61	24	24	follows	follow	VERB
ma-61	24	25	:	:	PUNCT
ma-61	24	26	let	let	VERB
ma-61	24	27	x1	x1	PROPN
ma-61	24	28	∈	∈	PROPN
ma-61	24	29	c	c	AUX
ma-61	24	30	be	be	AUX
ma-61	24	31	chosen	choose	VERB
ma-61	24	32	arbitrarily	arbitrarily	ADV
ma-61	24	33	,	,	PUNCT
ma-61	24	34	yn	yn	PROPN
ma-61	24	35	=	=	PUNCT
ma-61	24	36	(	(	PUNCT
ma-61	24	37	1−	1−	NUM
ma-61	24	38	αn)xn	αn)xn	PROPN
ma-61	25	1	+	+	CCONJ
ma-61	25	2	αntxn	αntxn	NOUN
ma-61	25	3	,	,	PUNCT
ma-61	25	4	xn+1	xn+1	PROPN
ma-61	25	5	=	=	SYM
ma-61	25	6	tyn	tyn	PROPN
ma-61	25	7	,	,	PUNCT
ma-61	25	8	∀	∀	X
ma-61	25	9	n	n	PRON
ma-61	25	10	≥	≥	NOUN
ma-61	25	11	1	1	NUM
ma-61	25	12	,	,	PUNCT
ma-61	25	13	(	(	PUNCT
ma-61	25	14	2	2	X
ma-61	25	15	)	)	PUNCT
ma-61	25	16	where	where	SCONJ
ma-61	25	17	{	{	PUNCT
ma-61	25	18	αn	αn	NOUN
ma-61	25	19	}	}	PUNCT
ma-61	25	20	⊂	⊂	PROPN
ma-61	25	21	(	(	PUNCT
ma-61	25	22	0	0	NUM
ma-61	25	23	,	,	PUNCT
ma-61	25	24	1	1	NUM
ma-61	25	25	)	)	PUNCT
ma-61	25	26	.	.	PUNCT
ma-61	26	1	under	under	ADP
ma-61	26	2	some	some	DET
ma-61	26	3	acceptable	acceptable	ADJ
ma-61	26	4	conditions	condition	NOUN
ma-61	26	5	of	of	ADP
ma-61	26	6	{	{	PUNCT
ma-61	26	7	αn	αn	NOUN
ma-61	26	8	}	}	PUNCT
ma-61	26	9	,	,	PUNCT
ma-61	26	10	sahu	sahu	PROPN
ma-61	26	11	proved	prove	VERB
ma-61	26	12	that	that	SCONJ
ma-61	26	13	the	the	DET
ma-61	26	14	sequence	sequence	NOUN
ma-61	26	15	{	{	PUNCT
ma-61	26	16	xn	xn	NOUN
ma-61	26	17	}	}	PUNCT
ma-61	26	18	induced	induce	VERB
ma-61	26	19	by	by	ADP
ma-61	26	20	the	the	DET
ma-61	26	21	algorithm	algorithm	NOUN
ma-61	26	22	(	(	PUNCT
ma-61	26	23	2	2	X
ma-61	26	24	)	)	PUNCT
ma-61	26	25	converges	converge	VERB
ma-61	26	26	weakly	weakly	ADJ
ma-61	26	27	to	to	ADP
ma-61	26	28	an	an	DET
ma-61	26	29	element	element	NOUN
ma-61	26	30	of	of	ADP
ma-61	26	31	solution	solution	NOUN
ma-61	26	32	set	set	VERB
ma-61	26	33	of	of	ADP
ma-61	26	34	problem	problem	NOUN
ma-61	26	35	(	(	PUNCT
ma-61	26	36	1).the	1).the	DET
ma-61	26	37	performance	performance	NOUN
ma-61	26	38	of	of	ADP
ma-61	26	39	normal	normal	ADJ
ma-61	26	40	s	s	NOUN
ma-61	26	41	-	-	PUNCT
ma-61	26	42	iteration	iteration	NOUN
ma-61	26	43	process	process	NOUN
ma-61	26	44	is	be	AUX
ma-61	26	45	much	much	ADV
ma-61	26	46	better	well	ADJ
ma-61	26	47	than	than	ADP
ma-61	26	48	mann	mann	PROPN
ma-61	26	49	and	and	CCONJ
ma-61	26	50	picard	picard	PROPN
ma-61	26	51	iterationprocess	iterationprocess	NOUN
ma-61	26	52	for	for	ADP
ma-61	26	53	nonexpansive	nonexpansive	ADJ
ma-61	26	54	mappings(see	mappings(see	NOUN
ma-61	27	1	[	[	X
ma-61	27	2	4	4	NUM
ma-61	27	3	]	]	PUNCT
ma-61	27	4	,	,	PUNCT
ma-61	28	1	[	[	X
ma-61	28	2	5]).elsewhere	5]).elsewhere	NUM
ma-61	28	3	,	,	PUNCT
ma-61	28	4	let	let	VERB
ma-61	28	5	f	f	PRON
ma-61	28	6	:	:	PUNCT
ma-61	28	7	c	c	X
ma-61	28	8	×	×	NOUN
ma-61	28	9	c	c	NOUN
ma-61	28	10	→	→	PUNCT
ma-61	28	11	r	r	NOUN
ma-61	28	12	be	be	AUX
ma-61	28	13	a	a	DET
ma-61	28	14	bifunction	bifunction	NOUN
ma-61	28	15	such	such	ADJ
ma-61	28	16	that	that	PRON
ma-61	28	17	for	for	ADP
ma-61	28	18	all	all	DET
ma-61	28	19	p	p	NOUN
ma-61	28	20	∈	∈	PROPN
ma-61	28	21	c	c	NOUN
ma-61	28	22	,	,	PUNCT
ma-61	28	23	f	f	PROPN
ma-61	28	24	(	(	PUNCT
ma-61	28	25	p	p	X
ma-61	28	26	,	,	PUNCT
ma-61	28	27	p	p	NOUN
ma-61	28	28	)	)	PUNCT
ma-61	28	29	=	=	SYM
ma-61	29	1	0	0	X
ma-61	29	2	.	.	PUNCT
ma-61	30	1	then	then	ADV
ma-61	30	2	the	the	DET
ma-61	30	3	socalled	socalled	ADJ
ma-61	30	4	equilibrium	equilibrium	NOUN
ma-61	30	5	problem	problem	NOUN
ma-61	30	6	is	be	AUX
ma-61	30	7	to	to	PART
ma-61	30	8	find	find	VERB
ma-61	30	9	p	p	X
ma-61	30	10	∈	∈	PROPN
ma-61	30	11	c	c	NOUN
ma-61	30	12	such	such	ADJ
ma-61	30	13	that	that	SCONJ
ma-61	30	14	f	f	PROPN
ma-61	30	15	(	(	PUNCT
ma-61	30	16	p	p	X
ma-61	30	17	,	,	PUNCT
ma-61	30	18	q	q	NOUN
ma-61	30	19	)	)	PUNCT
ma-61	30	20	≥	≥	NOUN
ma-61	30	21	0	0	NUM
ma-61	30	22	,	,	PUNCT
ma-61	30	23	∀	∀	PUNCT
ma-61	30	24	q	q	PROPN
ma-61	30	25	∈	∈	PROPN
ma-61	30	26	c.	c.	NOUN
ma-61	30	27	(	(	PUNCT
ma-61	30	28	3	3	X
ma-61	30	29	)	)	PUNCT
ma-61	30	30	denote	denote	VERB
ma-61	30	31	the	the	DET
ma-61	30	32	solution	solution	NOUN
ma-61	30	33	set	set	VERB
ma-61	30	34	of	of	ADP
ma-61	30	35	problem	problem	NOUN
ma-61	30	36	(	(	PUNCT
ma-61	30	37	3	3	NUM
ma-61	30	38	)	)	PUNCT
ma-61	30	39	by	by	ADP
ma-61	30	40	ep	ep	PROPN
ma-61	30	41	(	(	PUNCT
ma-61	30	42	f	f	PROPN
ma-61	30	43	)	)	PUNCT
ma-61	30	44	.	.	PUNCT
ma-61	31	1	problem	problem	NOUN
ma-61	31	2	(	(	PUNCT
ma-61	31	3	3	3	X
ma-61	31	4	)	)	PUNCT
ma-61	31	5	contains	contain	VERB
ma-61	31	6	nash	nash	PROPN
ma-61	31	7	equilibrium	equilibrium	PROPN
ma-61	31	8	prob	prob	PROPN
ma-61	31	9	-	-	PUNCT
ma-61	31	10	lems	lem	NOUN
ma-61	31	11	,	,	PUNCT
ma-61	31	12	fixed	fix	VERB
ma-61	31	13	point	point	NOUN
ma-61	31	14	problems	problem	NOUN
ma-61	31	15	,	,	PUNCT
ma-61	31	16	variational	variational	ADJ
ma-61	31	17	inequality	inequality	NOUN
ma-61	31	18	problems	problem	NOUN
ma-61	31	19	,	,	PUNCT
ma-61	31	20	minimization	minimization	NOUN
ma-61	31	21	problems	problem	NOUN
ma-61	31	22	and	and	CCONJ
ma-61	31	23	optimizationproblems	optimizationproblem	NOUN
ma-61	31	24	as	as	ADP
ma-61	31	25	its	its	PRON
ma-61	31	26	special	special	ADJ
ma-61	31	27	cases(see	cases(see	NOUN
ma-61	32	1	[	[	X
ma-61	32	2	7	7	NUM
ma-61	32	3	,	,	PUNCT
ma-61	32	4	16]).in	16]).in	NUM
ma-61	32	5	this	this	DET
ma-61	32	6	paper	paper	NOUN
ma-61	32	7	,	,	PUNCT
ma-61	32	8	we	we	PRON
ma-61	32	9	consider	consider	VERB
ma-61	32	10	a	a	DET
ma-61	32	11	problem	problem	NOUN
ma-61	32	12	which	which	PRON
ma-61	32	13	is	be	AUX
ma-61	32	14	formulated	formulate	VERB
ma-61	32	15	as	as	SCONJ
ma-61	32	16	follows	follow	VERB
ma-61	32	17	:	:	PUNCT
ma-61	32	18	find	find	VERB
ma-61	32	19	p	p	X
ma-61	32	20	∈	∈	PROPN
ma-61	32	21	c	c	NOUN
ma-61	32	22	,	,	PUNCT
ma-61	32	23	such	such	ADJ
ma-61	32	24	that	that	SCONJ
ma-61	32	25	p	p	PROPN
ma-61	32	26	∈	∈	PROPN
ma-61	32	27	ω	ω	NOUN
ma-61	32	28	:	:	PUNCT
ma-61	32	29	=	=	SYM
ma-61	32	30	fix(t	fix(t	PROPN
ma-61	32	31	)	)	PUNCT
ma-61	32	32	∩	∩	NOUN
ma-61	32	33	ep	ep	PROPN
ma-61	32	34	(	(	PUNCT
ma-61	32	35	f	f	PROPN
ma-61	32	36	)	)	PUNCT
ma-61	32	37	.	.	PUNCT
ma-61	33	1	(	(	PUNCT
ma-61	33	2	4	4	X
ma-61	33	3	)	)	PUNCT
ma-61	33	4	in	in	ADP
ma-61	33	5	past	past	ADJ
ma-61	33	6	few	few	ADJ
ma-61	33	7	years	year	NOUN
ma-61	33	8	,	,	PUNCT
ma-61	33	9	many	many	ADJ
ma-61	33	10	researchers	researcher	NOUN
ma-61	33	11	have	have	AUX
ma-61	33	12	found	find	VERB
ma-61	33	13	a	a	DET
ma-61	33	14	common	common	ADJ
ma-61	33	15	solution	solution	NOUN
ma-61	33	16	of	of	ADP
ma-61	33	17	problem	problem	NOUN
ma-61	33	18	(	(	PUNCT
ma-61	33	19	4	4	NUM
ma-61	33	20	)	)	PUNCT
ma-61	33	21	by	by	ADP
ma-61	33	22	varioustechniques(see	varioustechniques(see	NOUN
ma-61	34	1	[	[	X
ma-61	34	2	4	4	NUM
ma-61	34	3	]	]	PUNCT
ma-61	34	4	,	,	PUNCT
ma-61	34	5	[	[	X
ma-61	34	6	3	3	NUM
ma-61	34	7	]	]	PUNCT
ma-61	34	8	,	,	PUNCT
ma-61	34	9	[	[	X
ma-61	34	10	2	2	NUM
ma-61	34	11	]	]	PUNCT
ma-61	34	12	,	,	PUNCT
ma-61	34	13	[	[	X
ma-61	34	14	12	12	NUM
ma-61	34	15	]	]	PUNCT
ma-61	34	16	,	,	PUNCT
ma-61	35	1	[	[	X
ma-61	35	2	1	1	NUM
ma-61	35	3	]	]	PUNCT
ma-61	35	4	,	,	PUNCT
ma-61	35	5	[	[	X
ma-61	35	6	14	14	NUM
ma-61	35	7	]	]	PUNCT
ma-61	35	8	,	,	PUNCT
ma-61	35	9	[	[	X
ma-61	35	10	10	10	NUM
ma-61	35	11	]	]	NUM
ma-61	35	12	)	)	PUNCT
ma-61	35	13	.	.	PUNCT
ma-61	36	1	impelled	impel	VERB
ma-61	36	2	and	and	CCONJ
ma-61	36	3	inspired	inspire	VERB
ma-61	36	4	by	by	ADP
ma-61	36	5	these	these	DET
ma-61	36	6	approaches	approach	NOUN
ma-61	36	7	,	,	PUNCT
ma-61	36	8	the	the	DET
ma-61	36	9	mainobjective	mainobjective	NOUN
ma-61	36	10	of	of	ADP
ma-61	36	11	this	this	DET
ma-61	36	12	paper	paper	NOUN
ma-61	36	13	is	be	AUX
ma-61	36	14	to	to	PART
ma-61	36	15	find	find	VERB
ma-61	36	16	a	a	DET
ma-61	36	17	common	common	ADJ
ma-61	36	18	element	element	NOUN
ma-61	36	19	in	in	ADP
ma-61	36	20	the	the	DET
ma-61	36	21	solution	solution	NOUN
ma-61	36	22	set	set	VERB
ma-61	36	23	of	of	ADP
ma-61	36	24	problem	problem	NOUN
ma-61	36	25	(	(	PUNCT
ma-61	36	26	4	4	NUM
ma-61	36	27	)	)	PUNCT
ma-61	36	28	with	with	ADP
ma-61	36	29	the	the	DET
ma-61	36	30	helpof	helpof	VERB
ma-61	36	31	normal	normal	ADJ
ma-61	36	32	s	s	NOUN
ma-61	36	33	-	-	PUNCT
ma-61	36	34	iteration	iteration	NOUN
ma-61	36	35	process	process	NOUN
ma-61	36	36	in	in	ADP
ma-61	36	37	the	the	DET
ma-61	36	38	framework	framework	NOUN
ma-61	36	39	of	of	ADP
ma-61	36	40	real	real	ADJ
ma-61	36	41	hilbert	hilbert	NOUN
ma-61	36	42	space	space	NOUN
ma-61	36	43	.	.	PUNCT
ma-61	37	1	also	also	ADV
ma-61	37	2	we	we	PRON
ma-61	37	3	prove	prove	VERB
ma-61	37	4	some	some	DET
ma-61	37	5	weakconvergence	weakconvergence	NOUN
ma-61	37	6	theorem	theorem	VERB
ma-61	37	7	under	under	ADP
ma-61	37	8	some	some	DET
ma-61	37	9	acceptable	acceptable	ADJ
ma-61	37	10	conditions.now	conditions.now	NOUN
ma-61	37	11	we	we	PRON
ma-61	37	12	define	define	VERB
ma-61	37	13	some	some	DET
ma-61	37	14	basic	basic	ADJ
ma-61	37	15	auxiliary	auxiliary	ADJ
ma-61	37	16	results	result	NOUN
ma-61	37	17	which	which	PRON
ma-61	37	18	are	be	AUX
ma-61	37	19	very	very	ADV
ma-61	37	20	helpful	helpful	ADJ
ma-61	37	21	throughout	throughout	ADP
ma-61	37	22	this	this	DET
ma-61	37	23	work.the	work.the	DET
ma-61	37	24	metric	metric	ADJ
ma-61	37	25	projection	projection	NOUN
ma-61	37	26	pc	pc	NOUN
ma-61	37	27	from	from	ADP
ma-61	37	28	h	h	NOUN
ma-61	37	29	into	into	ADP
ma-61	37	30	c	c	PROPN
ma-61	37	31	is	be	AUX
ma-61	37	32	defined	define	VERB
ma-61	37	33	as	as	ADP
ma-61	37	34	:	:	PUNCT
ma-61	37	35	for	for	ADP
ma-61	37	36	any	any	DET
ma-61	37	37	p	p	NOUN
ma-61	37	38	∈	∈	PROPN
ma-61	37	39	c	c	NOUN
ma-61	37	40	,	,	PUNCT
ma-61	37	41	‖p	‖p	PROPN
ma-61	37	42	−	−	NOUN
ma-61	38	1	pc(p)‖	pc(p)‖	PROPN
ma-61	38	2	≤	≤	PROPN
ma-61	38	3	‖p	‖p	PROPN
ma-61	38	4	−	−	PROPN
ma-61	39	1	q‖	q‖	NOUN
ma-61	39	2	,	,	PUNCT
ma-61	39	3	∀	∀	PUNCT
ma-61	39	4	q	q	PROPN
ma-61	39	5	∈	∈	PROPN
ma-61	39	6	c.	c.	NOUN
ma-61	39	7	it	it	PRON
ma-61	39	8	is	be	AUX
ma-61	39	9	to	to	PART
ma-61	39	10	be	be	AUX
ma-61	39	11	noted	note	VERB
ma-61	39	12	that	that	SCONJ
ma-61	39	13	the	the	DET
ma-61	39	14	metric	metric	ADJ
ma-61	39	15	projection	projection	NOUN
ma-61	39	16	is	be	AUX
ma-61	39	17	nonexpansive	nonexpansive	ADJ
ma-61	39	18	.	.	PUNCT
ma-61	40	1	further	far	ADV
ma-61	40	2	for	for	ADP
ma-61	40	3	any	any	DET
ma-61	40	4	p	p	PROPN
ma-61	40	5	∈	∈	PROPN
ma-61	40	6	h	h	NOUN
ma-61	40	7	and	and	CCONJ
ma-61	40	8	s	s	PROPN
ma-61	40	9	∈	∈	PROPN
ma-61	40	10	c	c	X
ma-61	40	11	,	,	PUNCT
ma-61	40	12	s	s	NOUN
ma-61	40	13	=	=	NOUN
ma-61	40	14	pc(p	pc(p	NOUN
ma-61	40	15	)	)	PUNCT
ma-61	40	16	⇐	⇐	ADJ
ma-61	40	17	⇒	⇒	NOUN
ma-61	40	18	〈	〈	PROPN
ma-61	40	19	p	p	PROPN
ma-61	40	20	−	−	PROPN
ma-61	40	21	s	s	NOUN
ma-61	40	22	,	,	PUNCT
ma-61	40	23	s	s	AUX
ma-61	40	24	−	−	PROPN
ma-61	40	25	q	q	SYM
ma-61	40	26	〉	〉	PROPN
ma-61	40	27	≥	≥	NUM
ma-61	40	28	0	0	NUM
ma-61	40	29	,	,	PUNCT
ma-61	40	30	∀	∀	PUNCT
ma-61	40	31	q	q	PROPN
ma-61	40	32	∈	∈	PROPN
ma-61	40	33	c.	c.	NOUN
ma-61	40	34	a	a	DET
ma-61	40	35	mapping	mapping	NOUN
ma-61	40	36	t	t	PROPN
ma-61	40	37	is	be	AUX
ma-61	40	38	said	say	VERB
ma-61	40	39	to	to	PART
ma-61	40	40	be	be	AUX
ma-61	40	41	monotone	monotone	ADJ
ma-61	40	42	iff	iff	NOUN
ma-61	40	43	for	for	ADP
ma-61	40	44	all	all	DET
ma-61	40	45	p	p	NOUN
ma-61	40	46	,	,	PUNCT
ma-61	40	47	q	q	PROPN
ma-61	40	48	∈	∈	PROPN
ma-61	40	49	h	h	NOUN
ma-61	40	50	〈	〈	PROPN
ma-61	40	51	tp	tp	X
ma-61	40	52	−	−	PROPN
ma-61	40	53	tq	tq	ADP
ma-61	40	54	,	,	PUNCT
ma-61	40	55	p	p	NOUN
ma-61	40	56	−	−	PROPN
ma-61	40	57	q	q	NOUN
ma-61	40	58	〉	〉	PROPN
ma-61	40	59	≥	≥	NOUN
ma-61	40	60	0	0	NUM
ma-61	40	61	.	.	PUNCT
ma-61	41	1	lemma	lemma	PROPN
ma-61	41	2	1.1	1.1	NUM
ma-61	41	3	.	.	PUNCT
ma-61	42	1	[	[	X
ma-61	42	2	9	9	NUM
ma-61	42	3	]	]	PUNCT
ma-61	42	4	let	let	VERB
ma-61	42	5	h	h	PRON
ma-61	42	6	be	be	AUX
ma-61	42	7	a	a	DET
ma-61	42	8	hilbert	hilbert	NOUN
ma-61	42	9	space	space	NOUN
ma-61	42	10	.	.	PUNCT
ma-61	43	1	then	then	ADV
ma-61	43	2	for	for	ADP
ma-61	43	3	all	all	DET
ma-61	43	4	p	p	NOUN
ma-61	43	5	,	,	PUNCT
ma-61	43	6	q	q	PROPN
ma-61	43	7	∈	∈	PROPN
ma-61	43	8	h	h	NOUN
ma-61	43	9	and	and	CCONJ
ma-61	43	10	α	α	NOUN
ma-61	43	11	∈	∈	PROPN
ma-61	44	1	[	[	X
ma-61	44	2	0	0	NUM
ma-61	44	3	,	,	PUNCT
ma-61	44	4	1	1	NUM
ma-61	44	5	]	]	PUNCT
ma-61	44	6	the	the	DET
ma-61	44	7	followings	following	NOUN
ma-61	44	8	hold:(i	hold:(i	NOUN
ma-61	44	9	)	)	PUNCT
ma-61	44	10	‖p	‖p	PROPN
ma-61	44	11	−	−	PROPN
ma-61	45	1	q‖2	q‖2	PROPN
ma-61	45	2	=	=	SYM
ma-61	45	3	‖p‖2	‖p‖2	NOUN
ma-61	46	1	−	−	NOUN
ma-61	46	2	‖q‖2	‖q‖2	ADP
ma-61	46	3	−	−	NUM
ma-61	46	4	2〈p	2〈p	NOUN
ma-61	47	1	−	−	PROPN
ma-61	47	2	q	q	INTJ
ma-61	47	3	,	,	PUNCT
ma-61	47	4	q〉;(ii	q〉;(ii	ADJ
ma-61	47	5	)	)	PUNCT
ma-61	47	6	‖p	‖p	NOUN
ma-61	47	7	+	+	CCONJ
ma-61	47	8	q‖2	q‖2	VERB
ma-61	47	9	≤	≤	NUM
ma-61	47	10	‖p‖2	‖p‖2	NOUN
ma-61	48	1	+	+	CCONJ
ma-61	48	2	2〈q	2〈q	ADJ
ma-61	48	3	,	,	PUNCT
ma-61	48	4	p	p	X
ma-61	48	5	+	+	X
ma-61	48	6	q〉;(iii	q〉;(iii	NOUN
ma-61	48	7	)	)	PUNCT
ma-61	48	8	‖αp	‖αp	NOUN
ma-61	48	9	+	+	CCONJ
ma-61	48	10	(	(	PUNCT
ma-61	48	11	1−	1−	NUM
ma-61	48	12	α)q‖2	α)q‖2	PROPN
ma-61	48	13	=	=	PUNCT
ma-61	49	1	α‖p‖2	α‖p‖2	PROPN
ma-61	49	2	+	+	X
ma-61	49	3	(	(	PUNCT
ma-61	49	4	1−	1−	NUM
ma-61	49	5	α)‖q‖2	α)‖q‖2	NUM
ma-61	49	6	−	−	PROPN
ma-61	49	7	α(1−	α(1−	PROPN
ma-61	49	8	α)‖p	α)‖p	PROPN
ma-61	49	9	−	−	PROPN
ma-61	49	10	q‖2	q‖2	PROPN
ma-61	49	11	.	.	PUNCT
ma-61	50	1	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	50	2	eur	eur	PROPN
ma-61	50	3	.	.	PUNCT
ma-61	51	1	j.	j.	PROPN
ma-61	51	2	math	math	PROPN
ma-61	51	3	.	.	PUNCT
ma-61	52	1	anal	anal	PROPN
ma-61	52	2	.	.	PUNCT
ma-61	53	1	10.28924	10.28924	NUM
ma-61	53	2	/	/	SYM
ma-61	53	3	ada	ada	PROPN
ma-61	53	4	/	/	SYM
ma-61	53	5	ma.2.6	ma.2.6	PROPN
ma-61	53	6	3	3	NUM
ma-61	53	7	assumption	assumption	NOUN
ma-61	53	8	1.1	1.1	NUM
ma-61	53	9	.	.	PUNCT
ma-61	54	1	[	[	X
ma-61	54	2	6	6	NUM
ma-61	54	3	]	]	PUNCT
ma-61	54	4	let	let	VERB
ma-61	54	5	f	f	NOUN
ma-61	54	6	:	:	PUNCT
ma-61	54	7	c	c	X
ma-61	54	8	×	×	NOUN
ma-61	54	9	c	c	NOUN
ma-61	54	10	→	→	PUNCT
ma-61	54	11	r	r	NOUN
ma-61	54	12	be	be	AUX
ma-61	54	13	a	a	DET
ma-61	54	14	bi	bi	ADJ
ma-61	54	15	-	-	NOUN
ma-61	54	16	function	function	NOUN
ma-61	54	17	satisfying	satisfy	VERB
ma-61	54	18	the	the	DET
ma-61	54	19	subsequent	subsequent	ADJ
ma-61	54	20	conditions:(i	conditions:(i	NOUN
ma-61	54	21	)	)	PUNCT
ma-61	55	1	f	f	PROPN
ma-61	55	2	(	(	PUNCT
ma-61	55	3	p	p	X
ma-61	55	4	,	,	PUNCT
ma-61	55	5	p	p	NOUN
ma-61	55	6	)	)	PUNCT
ma-61	55	7	≥	≥	NOUN
ma-61	55	8	0	0	NUM
ma-61	55	9	,	,	PUNCT
ma-61	55	10	∀	∀	PUNCT
ma-61	55	11	p	p	NOUN
ma-61	55	12	∈	∈	PROPN
ma-61	55	13	c;(ii	c;(ii	PROPN
ma-61	55	14	)	)	PUNCT
ma-61	56	1	f	f	PROPN
ma-61	56	2	is	be	AUX
ma-61	56	3	monotone	monotone	ADJ
ma-61	56	4	,	,	PUNCT
ma-61	56	5	i.e.	i.e.	X
ma-61	56	6	f	f	X
ma-61	56	7	(	(	PUNCT
ma-61	56	8	p	p	X
ma-61	56	9	,	,	PUNCT
ma-61	56	10	q	q	NOUN
ma-61	56	11	)	)	PUNCT
ma-61	57	1	+	+	NUM
ma-61	57	2	f	f	X
ma-61	57	3	(	(	PUNCT
ma-61	57	4	q	q	NOUN
ma-61	57	5	,	,	PUNCT
ma-61	57	6	p	p	NOUN
ma-61	57	7	)	)	PUNCT
ma-61	57	8	≤	≤	NOUN
ma-61	57	9	0	0	NUM
ma-61	57	10	,	,	PUNCT
ma-61	57	11	∀	∀	X
ma-61	57	12	p	p	NOUN
ma-61	57	13	,	,	PUNCT
ma-61	57	14	q	q	PROPN
ma-61	57	15	∈	∈	PROPN
ma-61	57	16	c;(iii	c;(iii	PRON
ma-61	57	17	)	)	PUNCT
ma-61	57	18	f	f	PROPN
ma-61	57	19	is	be	AUX
ma-61	57	20	upper	upper	ADJ
ma-61	57	21	semi	semi	ADV
ma-61	57	22	continuous	continuous	ADJ
ma-61	57	23	,	,	PUNCT
ma-61	57	24	i.e.	i.e.	X
ma-61	57	25	for	for	ADP
ma-61	57	26	each	each	DET
ma-61	57	27	p	p	X
ma-61	57	28	,	,	PUNCT
ma-61	57	29	q	q	X
ma-61	57	30	,	,	PUNCT
ma-61	57	31	s	s	VERB
ma-61	57	32	∈	∈	PROPN
ma-61	57	33	c	c	NOUN
ma-61	57	34	,	,	PUNCT
ma-61	57	35	lim	lim	PROPN
ma-61	57	36	t→0	t→0	PROPN
ma-61	57	37	supf	supf	PROPN
ma-61	57	38	(	(	PUNCT
ma-61	57	39	λs	λs	X
ma-61	58	1	+	+	PUNCT
ma-61	58	2	(	(	PUNCT
ma-61	58	3	1−	1−	NUM
ma-61	58	4	λ)p	λ)p	NOUN
ma-61	58	5	,	,	PUNCT
ma-61	58	6	q	q	NOUN
ma-61	58	7	)	)	PUNCT
ma-61	58	8	≤	≤	NUM
ma-61	58	9	f	f	X
ma-61	58	10	(	(	PUNCT
ma-61	58	11	p	p	X
ma-61	58	12	,	,	PUNCT
ma-61	58	13	q	q	NOUN
ma-61	58	14	)	)	PUNCT
ma-61	58	15	;	;	PUNCT
ma-61	58	16	(	(	PUNCT
ma-61	58	17	5	5	X
ma-61	58	18	)	)	PUNCT
ma-61	58	19	(	(	PUNCT
ma-61	58	20	iv	iv	X
ma-61	58	21	)	)	PUNCT
ma-61	58	22	for	for	ADP
ma-61	58	23	each	each	DET
ma-61	58	24	fixed	fix	VERB
ma-61	58	25	p	p	NOUN
ma-61	58	26	∈	∈	PROPN
ma-61	58	27	c	c	NOUN
ma-61	58	28	,	,	PUNCT
ma-61	58	29	the	the	DET
ma-61	58	30	function	function	NOUN
ma-61	58	31	q	q	PROPN
ma-61	58	32	7→	7→	NUM
ma-61	58	33	f	f	NOUN
ma-61	58	34	(	(	PUNCT
ma-61	58	35	p	p	X
ma-61	58	36	,	,	PUNCT
ma-61	58	37	q	q	NOUN
ma-61	58	38	)	)	PUNCT
ma-61	58	39	is	be	AUX
ma-61	58	40	convex	convex	ADJ
ma-61	58	41	and	and	CCONJ
ma-61	58	42	lower	low	ADJ
ma-61	58	43	semi	semi	ADV
ma-61	58	44	continuous	continuous	ADJ
ma-61	58	45	;	;	PUNCT
ma-61	58	46	lemma	lemma	PROPN
ma-61	58	47	1.2	1.2	NUM
ma-61	58	48	.	.	PUNCT
ma-61	59	1	[	[	X
ma-61	59	2	7	7	X
ma-61	59	3	]	]	PUNCT
ma-61	59	4	assume	assume	VERB
ma-61	59	5	that	that	SCONJ
ma-61	59	6	the	the	DET
ma-61	59	7	bi	bi	NOUN
ma-61	59	8	-	-	NOUN
ma-61	59	9	function	function	ADJ
ma-61	59	10	f	f	NOUN
ma-61	59	11	:	:	PUNCT
ma-61	59	12	c	c	X
ma-61	59	13	×	×	NOUN
ma-61	59	14	c	c	NOUN
ma-61	59	15	→	→	SYM
ma-61	59	16	r	r	NOUN
ma-61	59	17	satisfy	satisfy	VERB
ma-61	59	18	the	the	DET
ma-61	59	19	conditions	condition	NOUN
ma-61	59	20	of	of	ADP
ma-61	59	21	assumption1.1	assumption1.1	NOUN
ma-61	59	22	.	.	PUNCT
ma-61	60	1	then	then	ADV
ma-61	60	2	for	for	ADP
ma-61	60	3	fixed	fix	VERB
ma-61	60	4	r	r	NOUN
ma-61	60	5	>	>	PUNCT
ma-61	60	6	0	0	NUM
ma-61	61	1	and	and	CCONJ
ma-61	61	2	p	p	PROPN
ma-61	61	3	∈	∈	PROPN
ma-61	61	4	h	h	NOUN
ma-61	61	5	,	,	PUNCT
ma-61	61	6	there	there	PRON
ma-61	61	7	exists	exist	VERB
ma-61	61	8	s	s	PROPN
ma-61	61	9	∈	∈	NOUN
ma-61	61	10	c	c	NOUN
ma-61	62	1	such	such	ADJ
ma-61	62	2	that	that	SCONJ
ma-61	62	3	f	f	PROPN
ma-61	62	4	(	(	PUNCT
ma-61	62	5	q	q	X
ma-61	62	6	,	,	PUNCT
ma-61	62	7	p	p	NOUN
ma-61	62	8	)	)	PUNCT
ma-61	62	9	+	+	CCONJ
ma-61	62	10	1	1	NUM
ma-61	62	11	r	r	NOUN
ma-61	62	12	〈	〈	PROPN
ma-61	62	13	q	q	NOUN
ma-61	62	14	−	−	PROPN
ma-61	62	15	p	p	NOUN
ma-61	62	16	,	,	PUNCT
ma-61	62	17	p	p	NOUN
ma-61	62	18	−	−	PROPN
ma-61	62	19	s	s	PROPN
ma-61	62	20	〉	〉	PROPN
ma-61	62	21	≥	≥	NUM
ma-61	62	22	0	0	NUM
ma-61	62	23	,	,	PUNCT
ma-61	62	24	∀	∀	PUNCT
ma-61	62	25	q	q	PROPN
ma-61	62	26	∈	∈	PROPN
ma-61	62	27	c.	c.	NOUN
ma-61	62	28	(	(	PUNCT
ma-61	62	29	6	6	NUM
ma-61	62	30	)	)	PUNCT
ma-61	62	31	lemma	lemma	PROPN
ma-61	62	32	1.3	1.3	NUM
ma-61	62	33	.	.	PUNCT
ma-61	63	1	[	[	X
ma-61	63	2	12	12	NUM
ma-61	63	3	]	]	PUNCT
ma-61	63	4	assume	assume	VERB
ma-61	63	5	that	that	SCONJ
ma-61	63	6	the	the	DET
ma-61	63	7	bi	bi	NOUN
ma-61	63	8	-	-	NOUN
ma-61	63	9	function	function	ADJ
ma-61	63	10	f	f	NOUN
ma-61	63	11	:	:	PUNCT
ma-61	63	12	c	c	X
ma-61	63	13	×	×	NOUN
ma-61	63	14	c	c	NOUN
ma-61	63	15	→	→	SYM
ma-61	63	16	r	r	NOUN
ma-61	63	17	satisfy	satisfy	VERB
ma-61	63	18	the	the	DET
ma-61	63	19	conditions	condition	NOUN
ma-61	63	20	of	of	ADP
ma-61	63	21	assumption1.1	assumption1.1	NOUN
ma-61	63	22	.	.	PUNCT
ma-61	64	1	if	if	SCONJ
ma-61	64	2	for	for	ADP
ma-61	64	3	r	r	NOUN
ma-61	64	4	>	>	X
ma-61	64	5	0	0	PUNCT
ma-61	65	1	and	and	CCONJ
ma-61	65	2	p	p	PROPN
ma-61	65	3	∈	∈	PROPN
ma-61	65	4	h	h	NOUN
ma-61	65	5	,	,	PUNCT
ma-61	65	6	defined	define	VERB
ma-61	65	7	a	a	DET
ma-61	65	8	mapping	mapping	NOUN
ma-61	65	9	t	t	NOUN
ma-61	65	10	fr	fr	NOUN
ma-61	65	11	:	:	PUNCT
ma-61	65	12	h	h	NOUN
ma-61	65	13	→	→	SYM
ma-61	65	14	c	c	PROPN
ma-61	65	15	as	as	SCONJ
ma-61	65	16	follows	follow	VERB
ma-61	65	17	:	:	PUNCT
ma-61	66	1	t	t	PROPN
ma-61	66	2	fr	fr	NOUN
ma-61	67	1	(	(	PUNCT
ma-61	67	2	p	p	X
ma-61	67	3	)	)	PUNCT
ma-61	67	4	=	=	NOUN
ma-61	67	5	{	{	PUNCT
ma-61	67	6	s	s	NOUN
ma-61	67	7	∈	∈	X
ma-61	67	8	c	c	NOUN
ma-61	67	9	:	:	PUNCT
ma-61	67	10	f	f	X
ma-61	67	11	(	(	PUNCT
ma-61	67	12	s	s	PROPN
ma-61	67	13	,	,	PUNCT
ma-61	67	14	q	q	NOUN
ma-61	67	15	)	)	PUNCT
ma-61	67	16	+	+	CCONJ
ma-61	67	17	1	1	NUM
ma-61	67	18	r	r	NOUN
ma-61	67	19	〈	〈	PROPN
ma-61	67	20	q	q	NOUN
ma-61	67	21	−	−	PROPN
ma-61	67	22	s	s	PROPN
ma-61	67	23	,	,	PUNCT
ma-61	67	24	s	s	VERB
ma-61	67	25	−	−	PROPN
ma-61	67	26	p	p	X
ma-61	67	27	〉	〉	PROPN
ma-61	67	28	≥	≥	NUM
ma-61	67	29	0	0	NUM
ma-61	67	30	,	,	PUNCT
ma-61	67	31	∀	∀	PUNCT
ma-61	67	32	q	q	NOUN
ma-61	68	1	∈	∈	PROPN
ma-61	68	2	c	c	NOUN
ma-61	68	3	}	}	PUNCT
ma-61	68	4	.	.	PUNCT
ma-61	69	1	(	(	PUNCT
ma-61	69	2	7	7	X
ma-61	69	3	)	)	PUNCT
ma-61	69	4	then	then	ADV
ma-61	69	5	the	the	DET
ma-61	69	6	followings	following	NOUN
ma-61	69	7	hold:(i	hold:(i	NOUN
ma-61	69	8	)	)	PUNCT
ma-61	70	1	t	t	PROPN
ma-61	70	2	fr	fr	PROPN
ma-61	70	3	is	be	AUX
ma-61	70	4	non	non	ADJ
ma-61	70	5	-	-	ADJ
ma-61	70	6	empty	empty	ADJ
ma-61	70	7	and	and	CCONJ
ma-61	70	8	single	single	ADJ
ma-61	70	9	valued.(ii	valued.(ii	ADJ
ma-61	70	10	)	)	PUNCT
ma-61	71	1	t	t	PROPN
ma-61	71	2	fr	fr	NOUN
ma-61	71	3	is	be	AUX
ma-61	71	4	firmly	firmly	ADV
ma-61	71	5	non	non	ADJ
ma-61	71	6	-	-	ADJ
ma-61	71	7	expansive	expansive	ADJ
ma-61	71	8	,	,	PUNCT
ma-61	71	9	i.e.	i.e.	X
ma-61	71	10	,	,	PUNCT
ma-61	71	11	‖t	‖t	ADJ
ma-61	71	12	fr	fr	NOUN
ma-61	72	1	(	(	PUNCT
ma-61	72	2	p)−	p)−	NOUN
ma-61	72	3	t	t	NOUN
ma-61	72	4	fr	fr	INTJ
ma-61	72	5	(	(	PUNCT
ma-61	72	6	q)‖2	q)‖2	NOUN
ma-61	72	7	≤	≤	PUNCT
ma-61	73	1	〈	〈	PROPN
ma-61	73	2	t	t	PROPN
ma-61	73	3	fr	fr	NOUN
ma-61	73	4	(	(	PUNCT
ma-61	73	5	p)−	p)−	NOUN
ma-61	73	6	t	t	NOUN
ma-61	74	1	fr	fr	INTJ
ma-61	74	2	(	(	PUNCT
ma-61	74	3	q	q	X
ma-61	74	4	)	)	PUNCT
ma-61	74	5	,	,	PUNCT
ma-61	74	6	p	p	NOUN
ma-61	74	7	−	−	PROPN
ma-61	74	8	q	q	NOUN
ma-61	74	9	〉	〉	NOUN
ma-61	74	10	∀	∀	NOUN
ma-61	75	1	p	p	NOUN
ma-61	75	2	,	,	PUNCT
ma-61	75	3	q	q	PROPN
ma-61	75	4	∈	∈	PROPN
ma-61	75	5	h.	h.	PROPN
ma-61	75	6	(	(	PUNCT
ma-61	75	7	iii	iii	X
ma-61	75	8	)	)	PUNCT
ma-61	75	9	fix(t	fix(t	PROPN
ma-61	75	10	fr	fr	NOUN
ma-61	75	11	)	)	PUNCT
ma-61	76	1	=	=	SYM
ma-61	76	2	ep(f	ep(f	NUM
ma-61	76	3	)	)	PUNCT
ma-61	77	1	.(iv	.(iv	PROPN
ma-61	77	2	)	)	PUNCT
ma-61	78	1	ep(f	ep(f	PUNCT
ma-61	79	1	)	)	PUNCT
ma-61	79	2	is	be	AUX
ma-61	79	3	closed	close	VERB
ma-61	79	4	and	and	CCONJ
ma-61	79	5	convex	convex	PROPN
ma-61	79	6	.	.	PUNCT
ma-61	80	1	lemma	lemma	PROPN
ma-61	80	2	1.4	1.4	NUM
ma-61	80	3	.	.	PUNCT
ma-61	81	1	[	[	X
ma-61	81	2	11	11	NUM
ma-61	81	3	]	]	X
ma-61	81	4	let	let	AUX
ma-61	81	5	{	{	PUNCT
ma-61	81	6	an	an	PRON
ma-61	81	7	}	}	PUNCT
ma-61	81	8	be	be	AUX
ma-61	81	9	a	a	DET
ma-61	81	10	sequence	sequence	NOUN
ma-61	81	11	of	of	ADP
ma-61	81	12	non	non	NOUN
ma-61	81	13	negetive	negetive	ADJ
ma-61	81	14	real	real	ADJ
ma-61	81	15	numbers	number	NOUN
ma-61	81	16	such	such	ADJ
ma-61	81	17	that	that	PRON
ma-61	81	18	an+1	an+1	ADJ
ma-61	81	19	≤	≤	NOUN
ma-61	81	20	(	(	PUNCT
ma-61	81	21	1−	1−	NUM
ma-61	81	22	αn)an	αn)an	NUM
ma-61	81	23	+	+	CCONJ
ma-61	81	24	αnδn	αnδn	NOUN
ma-61	81	25	+	+	SYM
ma-61	81	26	γn	γn	NUM
ma-61	81	27	,	,	PUNCT
ma-61	81	28	∀	∀	X
ma-61	81	29	n	n	PRON
ma-61	81	30	≥	≥	NOUN
ma-61	81	31	0	0	NUM
ma-61	81	32	,	,	PUNCT
ma-61	81	33	where	where	SCONJ
ma-61	81	34	αn	αn	NOUN
ma-61	81	35	∈	∈	PROPN
ma-61	81	36	(	(	PUNCT
ma-61	81	37	0	0	NUM
ma-61	81	38	,	,	PUNCT
ma-61	81	39	1	1	NUM
ma-61	81	40	)	)	PUNCT
ma-61	81	41	and	and	CCONJ
ma-61	81	42	δn	δn	NOUN
ma-61	82	1	⊂	⊂	PROPN
ma-61	82	2	r	r	NOUN
ma-61	82	3	satisfies	satisfy	VERB
ma-61	82	4	the	the	DET
ma-61	82	5	following	follow	VERB
ma-61	82	6	conditions:(i	conditions:(i	NOUN
ma-61	82	7	)	)	PUNCT
ma-61	82	8	∑∞n=0	∑∞n=0	PROPN
ma-61	82	9	αn	αn	NOUN
ma-61	82	10	=	=	SYM
ma-61	82	11	∞;(ii	∞;(ii	ADJ
ma-61	82	12	)	)	PUNCT
ma-61	82	13	lim	lim	PROPN
ma-61	82	14	n→∞	n→∞	NUM
ma-61	82	15	supδn	supδn	NOUN
ma-61	82	16	≤	≤	NOUN
ma-61	82	17	0.(iii	0.(iii	PUNCT
ma-61	82	18	)	)	PUNCT
ma-61	82	19	γn	γn	ADP
ma-61	82	20	≥	≥	NOUN
ma-61	82	21	0	0	NUM
ma-61	82	22	(	(	PUNCT
ma-61	82	23	n	n	CCONJ
ma-61	82	24	≥	≥	NOUN
ma-61	82	25	1	1	NUM
ma-61	82	26	)	)	PUNCT
ma-61	82	27	,	,	PUNCT
ma-61	82	28	∑	∑	ADP
ma-61	82	29	γn	γn	ADP
ma-61	82	30	<	<	X
ma-61	82	31	∞.then	∞.then	PROPN
ma-61	82	32	lim	lim	NOUN
ma-61	82	33	n→∞	n→∞	NUM
ma-61	82	34	an	an	DET
ma-61	82	35	=	=	NOUN
ma-61	82	36	0	0	X
ma-61	82	37	.	.	PUNCT
ma-61	83	1	lemma	lemma	PROPN
ma-61	83	2	1.5	1.5	NUM
ma-61	83	3	.	.	PUNCT
ma-61	84	1	[	[	X
ma-61	84	2	13	13	NUM
ma-61	84	3	]	]	PUNCT
ma-61	84	4	let	let	VERB
ma-61	84	5	c	c	PRON
ma-61	84	6	be	be	AUX
ma-61	84	7	a	a	DET
ma-61	84	8	closed	closed	ADJ
ma-61	84	9	and	and	CCONJ
ma-61	84	10	convex	convex	NOUN
ma-61	84	11	subset	subset	NOUN
ma-61	84	12	of	of	ADP
ma-61	84	13	h	h	PROPN
ma-61	84	14	and	and	CCONJ
ma-61	84	15	t	t	PROPN
ma-61	84	16	:	:	PUNCT
ma-61	84	17	c	c	X
ma-61	84	18	→	→	PUNCT
ma-61	84	19	c	c	X
ma-61	84	20	be	be	AUX
ma-61	84	21	a	a	DET
ma-61	84	22	non	non	ADJ
ma-61	84	23	-	-	ADJ
ma-61	84	24	expansivemapping	expansivemapping	ADJ
ma-61	84	25	.	.	PUNCT
ma-61	85	1	then(i	then(i	NOUN
ma-61	85	2	)	)	PUNCT
ma-61	85	3	fix(t	fix(t	PROPN
ma-61	85	4	)	)	PUNCT
ma-61	85	5	is	be	AUX
ma-61	85	6	a	a	DET
ma-61	85	7	closed	closed	ADJ
ma-61	85	8	and	and	CCONJ
ma-61	85	9	convex	convex	NOUN
ma-61	85	10	subset	subset	NOUN
ma-61	85	11	of	of	ADP
ma-61	85	12	c;(ii	c;(ii	PROPN
ma-61	85	13	)	)	PUNCT
ma-61	86	1	i	i	PRON
ma-61	86	2	−	−	PROPN
ma-61	86	3	t	t	PROPN
ma-61	86	4	is	be	AUX
ma-61	86	5	demiclosed	demiclose	VERB
ma-61	86	6	at	at	ADP
ma-61	86	7	0	0	NUM
ma-61	86	8	.	.	PUNCT
ma-61	87	1	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	87	2	eur	eur	PROPN
ma-61	87	3	.	.	PUNCT
ma-61	88	1	j.	j.	PROPN
ma-61	88	2	math	math	PROPN
ma-61	88	3	.	.	PUNCT
ma-61	89	1	anal	anal	PROPN
ma-61	89	2	.	.	PUNCT
ma-61	90	1	10.28924	10.28924	NUM
ma-61	90	2	/	/	SYM
ma-61	90	3	ada	ada	PROPN
ma-61	90	4	/	/	SYM
ma-61	90	5	ma.2.6	ma.2.6	PROPN
ma-61	90	6	4	4	NUM
ma-61	90	7	lemma	lemma	PROPN
ma-61	90	8	1.6	1.6	NUM
ma-61	90	9	.	.	PUNCT
ma-61	91	1	[	[	X
ma-61	91	2	8	8	NUM
ma-61	91	3	]	]	PUNCT
ma-61	91	4	let	let	VERB
ma-61	91	5	f	f	NOUN
ma-61	91	6	:	:	PUNCT
ma-61	91	7	c	c	X
ma-61	91	8	×	×	NOUN
ma-61	91	9	c	c	NOUN
ma-61	91	10	→	→	PUNCT
ma-61	91	11	r	r	NOUN
ma-61	91	12	be	be	AUX
ma-61	91	13	a	a	DET
ma-61	91	14	non	non	ADJ
ma-61	91	15	linear	linear	PROPN
ma-61	91	16	bi	bi	NOUN
ma-61	91	17	-	-	NOUN
ma-61	91	18	function	function	NOUN
ma-61	91	19	satisfying	satisfy	VERB
ma-61	91	20	the	the	DET
ma-61	91	21	assumption	assumption	NOUN
ma-61	91	22	1.1	1.1	NUM
ma-61	91	23	andlet	andlet	NOUN
ma-61	91	24	t	t	PROPN
ma-61	91	25	fr	fr	INTJ
ma-61	91	26	be	be	AUX
ma-61	91	27	defined	define	VERB
ma-61	91	28	as	as	ADP
ma-61	91	29	above	above	ADV
ma-61	91	30	in	in	ADP
ma-61	91	31	lemma	lemma	PROPN
ma-61	91	32	1.3	1.3	NUM
ma-61	91	33	.	.	PUNCT
ma-61	92	1	if	if	SCONJ
ma-61	92	2	for	for	ADP
ma-61	92	3	r	r	NOUN
ma-61	92	4	>	>	X
ma-61	92	5	0	0	NUM
ma-61	92	6	,	,	PUNCT
ma-61	92	7	let	let	VERB
ma-61	92	8	p	p	PRON
ma-61	92	9	,	,	PUNCT
ma-61	92	10	q	q	PROPN
ma-61	92	11	∈	∈	PROPN
ma-61	92	12	h	h	NOUN
ma-61	92	13	and	and	CCONJ
ma-61	92	14	r1	r1	PROPN
ma-61	92	15	,	,	PUNCT
ma-61	92	16	r2	r2	PROPN
ma-61	92	17	>	>	X
ma-61	92	18	0	0	NUM
ma-61	92	19	,	,	PUNCT
ma-61	92	20	then	then	ADV
ma-61	92	21	‖t	‖t	PROPN
ma-61	92	22	fr2	fr2	PROPN
ma-61	92	23	(	(	PUNCT
ma-61	92	24	q)−	q)−	PROPN
ma-61	92	25	t	t	PROPN
ma-61	92	26	fr1	fr1	PROPN
ma-61	92	27	(	(	PUNCT
ma-61	92	28	p)‖	p)‖	VERB
ma-61	92	29	≤	≤	NUM
ma-61	93	1	‖q	‖q	ADP
ma-61	93	2	−	−	PUNCT
ma-61	93	3	p‖+	p‖+	NOUN
ma-61	93	4	∣∣∣∣	∣∣∣∣	PROPN
ma-61	93	5	r2	r2	PROPN
ma-61	93	6	−	−	PROPN
ma-61	93	7	r1r2	r1r2	PUNCT
ma-61	93	8	∣∣∣∣‖t	∣∣∣∣‖t	NOUN
ma-61	93	9	fr2	fr2	PROPN
ma-61	93	10	(	(	PUNCT
ma-61	93	11	q)−	q)−	PROPN
ma-61	93	12	q‖.	q‖.	VERB
ma-61	93	13	lemma	lemma	PROPN
ma-61	93	14	1.7	1.7	NUM
ma-61	93	15	.	.	PUNCT
ma-61	94	1	[	[	X
ma-61	94	2	15	15	NUM
ma-61	94	3	]	]	X
ma-61	94	4	let	let	VERB
ma-61	94	5	xn	xn	PROPN
ma-61	95	1	and	and	CCONJ
ma-61	95	2	yn	yn	PROPN
ma-61	95	3	be	be	VERB
ma-61	95	4	two	two	NUM
ma-61	95	5	bounded	bounded	ADJ
ma-61	95	6	sequences	sequence	NOUN
ma-61	95	7	in	in	ADP
ma-61	95	8	a	a	DET
ma-61	95	9	banach	banach	NOUN
ma-61	95	10	space	space	NOUN
ma-61	95	11	x	x	PUNCT
ma-61	95	12	and	and	CCONJ
ma-61	95	13	let	let	VERB
ma-61	95	14	βn	βn	VERB
ma-61	95	15	be	be	AUX
ma-61	95	16	asequence	asequence	NOUN
ma-61	95	17	in	in	ADP
ma-61	95	18	[	[	X
ma-61	95	19	0	0	NUM
ma-61	95	20	,	,	PUNCT
ma-61	95	21	1	1	NUM
ma-61	95	22	]	]	PUNCT
ma-61	95	23	which	which	PRON
ma-61	95	24	satisfy	satisfy	VERB
ma-61	95	25	the	the	DET
ma-61	95	26	following	following	ADJ
ma-61	95	27	conditions	condition	NOUN
ma-61	95	28	:	:	PUNCT
ma-61	95	29	0	0	PUNCT
ma-61	95	30	<	<	X
ma-61	95	31	lim	lim	PROPN
ma-61	95	32	n→∞	n→∞	PROPN
ma-61	95	33	inf	inf	PROPN
ma-61	95	34	βn	βn	PROPN
ma-61	95	35	≤	≤	PROPN
ma-61	95	36	lim	lim	PROPN
ma-61	95	37	n→∞	n→∞	NUM
ma-61	95	38	supβn	supβn	NOUN
ma-61	95	39	<	<	X
ma-61	95	40	1	1	X
ma-61	95	41	.	.	PUNCT
ma-61	95	42	suppose	suppose	VERB
ma-61	95	43	xn+1	xn+1	X
ma-61	96	1	=	=	SYM
ma-61	97	1	(	(	PUNCT
ma-61	97	2	1−	1−	NUM
ma-61	97	3	βn)zn	βn)zn	PUNCT
ma-61	98	1	+	+	NUM
ma-61	98	2	βnxn	βnxn	NOUN
ma-61	98	3	for	for	ADP
ma-61	98	4	all	all	DET
ma-61	98	5	integers	integer	NOUN
ma-61	98	6	n	n	PRON
ma-61	98	7	≥	≥	NOUN
ma-61	98	8	0	0	NUM
ma-61	98	9	,	,	PUNCT
ma-61	98	10	and	and	CCONJ
ma-61	98	11	lim	lim	PROPN
ma-61	98	12	n→∞	n→∞	NUM
ma-61	98	13	sup	sup	NOUN
ma-61	98	14	(	(	PUNCT
ma-61	98	15	‖zn+1	‖zn+1	NOUN
ma-61	98	16	−	−	PROPN
ma-61	98	17	zn‖	zn‖	PROPN
ma-61	98	18	−	−	PROPN
ma-61	98	19	‖xn+1	‖xn+1	NUM
ma-61	98	20	−	−	PROPN
ma-61	98	21	xn‖	xn‖	PROPN
ma-61	98	22	)	)	PUNCT
ma-61	98	23	≤	≤	NOUN
ma-61	98	24	0	0	NUM
ma-61	98	25	,	,	PUNCT
ma-61	98	26	then	then	ADV
ma-61	98	27	lim	lim	PROPN
ma-61	98	28	n→∞	n→∞	X
ma-61	98	29	‖xn	‖xn	PROPN
ma-61	98	30	−	−	PROPN
ma-61	98	31	zn‖	zn‖	PROPN
ma-61	98	32	=	=	PUNCT
ma-61	98	33	0	0	NUM
ma-61	98	34	.	.	NOUN
ma-61	98	35	2	2	NUM
ma-61	98	36	.	.	X
ma-61	98	37	main	main	ADJ
ma-61	98	38	result	result	NOUN
ma-61	98	39	in	in	ADP
ma-61	98	40	this	this	DET
ma-61	98	41	section	section	NOUN
ma-61	98	42	we	we	PRON
ma-61	98	43	study	study	VERB
ma-61	98	44	and	and	CCONJ
ma-61	98	45	analyze	analyze	VERB
ma-61	98	46	normal	normal	ADJ
ma-61	98	47	s	s	NOUN
ma-61	98	48	-	-	PUNCT
ma-61	98	49	iteration	iteration	NOUN
ma-61	98	50	process	process	NOUN
ma-61	98	51	for	for	ADP
ma-61	98	52	solving	solve	VERB
ma-61	98	53	equilibrium	equilibrium	NOUN
ma-61	98	54	problemand	problemand	NOUN
ma-61	98	55	fixed	fix	VERB
ma-61	98	56	point	point	NOUN
ma-61	98	57	problem	problem	NOUN
ma-61	98	58	for	for	ADP
ma-61	98	59	nonexpansive	nonexpansive	ADJ
ma-61	98	60	mapping	mapping	NOUN
ma-61	98	61	and	and	CCONJ
ma-61	98	62	its	its	PRON
ma-61	98	63	convergence	convergence	NOUN
ma-61	98	64	analysis	analysis	NOUN
ma-61	98	65	.	.	PUNCT
ma-61	99	1	theorem	theorem	VERB
ma-61	99	2	2.1	2.1	NUM
ma-61	99	3	.	.	PUNCT
ma-61	100	1	let	let	AUX
ma-61	100	2	c	c	NOUN
ma-61	100	3	⊂	⊂	PROPN
ma-61	100	4	h	h	PROPN
ma-61	100	5	be	be	AUX
ma-61	100	6	a	a	DET
ma-61	100	7	nonempty	nonempty	ADV
ma-61	100	8	closed	close	VERB
ma-61	100	9	and	and	CCONJ
ma-61	100	10	convex	convex	ADJ
ma-61	100	11	subsets	subset	NOUN
ma-61	100	12	of	of	ADP
ma-61	100	13	h.	h.	PROPN
ma-61	100	14	let	let	VERB
ma-61	100	15	f	f	NOUN
ma-61	100	16	:	:	PUNCT
ma-61	100	17	c	c	X
ma-61	100	18	×	×	NOUN
ma-61	100	19	c	c	NOUN
ma-61	100	20	→	→	SYM
ma-61	100	21	r	r	NOUN
ma-61	100	22	bea	bea	PROPN
ma-61	100	23	nonlinear	nonlinear	ADJ
ma-61	100	24	bifunction	bifunction	NOUN
ma-61	100	25	satisfying	satisfy	VERB
ma-61	100	26	assumption	assumption	NOUN
ma-61	100	27	1.1	1.1	NUM
ma-61	100	28	.	.	PUNCT
ma-61	101	1	let	let	AUX
ma-61	101	2	t	t	NOUN
ma-61	101	3	:	:	PUNCT
ma-61	101	4	c	c	X
ma-61	101	5	→	→	PUNCT
ma-61	101	6	h	h	PROPN
ma-61	101	7	be	be	AUX
ma-61	101	8	a	a	DET
ma-61	101	9	nonexpansive	nonexpansive	ADJ
ma-61	101	10	mapping	mapping	NOUN
ma-61	101	11	suchthat	suchthat	VERB
ma-61	101	12	fix(t	fix(t	PROPN
ma-61	101	13	)	)	PUNCT
ma-61	101	14	6=	6=	PUNCT
ma-61	101	15	.	.	PUNCT
ma-61	102	1	assume	assume	VERB
ma-61	102	2	that	that	SCONJ
ma-61	102	3	ω	ω	X
ma-61	102	4	:	:	PUNCT
ma-61	102	5	=	=	SYM
ma-61	102	6	fix(t	fix(t	PROPN
ma-61	102	7	)	)	PUNCT
ma-61	102	8	∩	∩	NOUN
ma-61	102	9	ep	ep	PROPN
ma-61	102	10	(	(	PUNCT
ma-61	102	11	f	f	PROPN
ma-61	102	12	)	)	PUNCT
ma-61	102	13	6=	6=	PUNCT
ma-61	102	14	.	.	PUNCT
ma-61	103	1	let	let	VERB
ma-61	103	2	{	{	PUNCT
ma-61	103	3	xn}be	xn}be	PROPN
ma-61	103	4	a	a	DET
ma-61	103	5	sequence	sequence	NOUN
ma-61	103	6	defined	define	VERB
ma-61	103	7	as	as	ADP
ma-61	103	8	follows	follow	VERB
ma-61	103	9	:	:	PUNCT
ma-61	103	10	choose	choose	VERB
ma-61	103	11	x1	x1	PROPN
ma-61	103	12	∈	∈	PROPN
ma-61	103	13	h	h	NOUN
ma-61	103	14	arbitrarily	arbitrarily	ADV
ma-61	103	15	,	,	PUNCT
ma-61	103	16	yn	yn	PROPN
ma-61	103	17	=	=	PROPN
ma-61	103	18	t	t	PROPN
ma-61	103	19	frn	frn	PROPN
ma-61	103	20	(	(	PUNCT
ma-61	103	21	xn	xn	PROPN
ma-61	103	22	)	)	PUNCT
ma-61	103	23	,	,	PUNCT
ma-61	103	24	zn	zn	X
ma-61	103	25	=	=	SYM
ma-61	103	26	(	(	PUNCT
ma-61	103	27	1−	1−	NUM
ma-61	103	28	αn)yn	αn)yn	NUM
ma-61	103	29	+	+	CCONJ
ma-61	103	30	αntyn	αntyn	NOUN
ma-61	103	31	,	,	PUNCT
ma-61	103	32	xn+1	xn+1	PROPN
ma-61	104	1	=	=	SYM
ma-61	104	2	tzn	tzn	PROPN
ma-61	104	3	,	,	PUNCT
ma-61	104	4	∀	∀	X
ma-61	104	5	n	n	PRON
ma-61	104	6	≥	≥	NOUN
ma-61	104	7	1	1	NUM
ma-61	104	8	,	,	PUNCT
ma-61	104	9	(	(	PUNCT
ma-61	104	10	8)	8)	NUM
ma-61	104	11	where	where	SCONJ
ma-61	104	12	{	{	PUNCT
ma-61	104	13	αn	αn	NOUN
ma-61	104	14	}	}	PUNCT
ma-61	104	15	⊂	⊂	PROPN
ma-61	105	1	[	[	X
ma-61	105	2	0	0	NUM
ma-61	105	3	,	,	PUNCT
ma-61	105	4	1	1	NUM
ma-61	105	5	]	]	PUNCT
ma-61	105	6	and	and	CCONJ
ma-61	105	7	{	{	PUNCT
ma-61	105	8	rn	rn	PROPN
ma-61	105	9	}	}	PUNCT
ma-61	105	10	⊂	⊂	PROPN
ma-61	105	11	(	(	PUNCT
ma-61	105	12	0	0	NUM
ma-61	105	13	,	,	PUNCT
ma-61	105	14	∞	∞	PROPN
ma-61	105	15	)	)	PUNCT
ma-61	105	16	satisfying	satisfy	VERB
ma-61	105	17	the	the	DET
ma-61	105	18	following	follow	VERB
ma-61	105	19	conditions	condition	NOUN
ma-61	105	20	:	:	PUNCT
ma-61	105	21	c1	c1	NOUN
ma-61	105	22	:	:	PUNCT
ma-61	105	23	lim	lim	PROPN
ma-61	105	24	n→∞	n→∞	X
ma-61	105	25	αn	αn	NOUN
ma-61	105	26	=	=	SYM
ma-61	105	27	0	0	NUM
ma-61	105	28	,	,	PUNCT
ma-61	105	29	∑∞	∑∞	NOUN
ma-61	105	30	n=1	n=1	ADP
ma-61	105	31	αn(1−	αn(1−	PROPN
ma-61	105	32	αn	αn	NOUN
ma-61	105	33	)	)	PUNCT
ma-61	105	34	=	=	SYM
ma-61	105	35	∞	∞	PROPN
ma-61	105	36	,	,	PUNCT
ma-61	105	37	∑∞	∑∞	NOUN
ma-61	105	38	n=1	n=1	PROPN
ma-61	105	39	|αn	|αn	PROPN
ma-61	105	40	−	−	PROPN
ma-61	105	41	αn−1|	αn−1|	SYM
ma-61	105	42	<	<	X
ma-61	105	43	∞	∞	PROPN
ma-61	105	44	;	;	PUNCT
ma-61	105	45	c2	c2	PROPN
ma-61	105	46	:	:	PUNCT
ma-61	105	47	lim	lim	PROPN
ma-61	105	48	n→∞	n→∞	PROPN
ma-61	106	1	inf	inf	PROPN
ma-61	106	2	rn	rn	PROPN
ma-61	106	3	>	>	PROPN
ma-61	106	4	0	0	NUM
ma-61	106	5	,	,	PUNCT
ma-61	106	6	∑∞	∑∞	NOUN
ma-61	106	7	n=0	n=0	NUM
ma-61	106	8	|rn+1	|rn+1	VERB
ma-61	106	9	−	−	NOUN
ma-61	106	10	rn|	rn|	NOUN
ma-61	106	11	<	<	X
ma-61	106	12	∞;then	∞;then	ADV
ma-61	106	13	the	the	DET
ma-61	106	14	sequence	sequence	NOUN
ma-61	106	15	{	{	PUNCT
ma-61	106	16	xn	xn	NOUN
ma-61	106	17	}	}	PUNCT
ma-61	106	18	induced	induce	VERB
ma-61	106	19	by	by	ADP
ma-61	106	20	process	process	NOUN
ma-61	106	21	(	(	PUNCT
ma-61	106	22	8)	8)	NUM
ma-61	106	23	converges	converge	VERB
ma-61	106	24	weakly	weakly	ADV
ma-61	106	25	to	to	ADP
ma-61	106	26	an	an	DET
ma-61	106	27	element	element	NOUN
ma-61	106	28	in	in	ADP
ma-61	106	29	ω	ω	PROPN
ma-61	106	30	.	.	PUNCT
ma-61	107	1	proof	proof	NOUN
ma-61	107	2	.	.	PUNCT
ma-61	108	1	take	take	VERB
ma-61	108	2	p	p	NOUN
ma-61	108	3	∈	∈	PROPN
ma-61	108	4	ω	ω	NOUN
ma-61	108	5	.	.	PUNCT
ma-61	109	1	then	then	ADV
ma-61	109	2	by	by	ADP
ma-61	109	3	process	process	NOUN
ma-61	109	4	(	(	PUNCT
ma-61	109	5	8)	8)	NUM
ma-61	109	6	,	,	PUNCT
ma-61	109	7	we	we	PRON
ma-61	109	8	obtain	obtain	VERB
ma-61	109	9	‖xn+1	‖xn+1	PUNCT
ma-61	110	1	−	−	PROPN
ma-61	110	2	p‖	p‖	NOUN
ma-61	110	3	=	=	SYM
ma-61	110	4	‖tzn	‖tzn	PROPN
ma-61	110	5	−	−	PROPN
ma-61	110	6	p‖	p‖	NOUN
ma-61	110	7	≤	≤	PUNCT
ma-61	111	1	‖zn	‖zn	NUM
ma-61	111	2	−	−	PROPN
ma-61	111	3	p‖	p‖	NOUN
ma-61	111	4	,	,	PUNCT
ma-61	111	5	≤	≤	X
ma-61	111	6	‖(1−	‖(1−	PROPN
ma-61	111	7	αn)yn	αn)yn	NUM
ma-61	111	8	+	+	CCONJ
ma-61	111	9	αntyn	αntyn	NOUN
ma-61	111	10	−	−	PROPN
ma-61	111	11	p‖	p‖	NOUN
ma-61	111	12	,	,	PUNCT
ma-61	111	13	≤	≤	NUM
ma-61	111	14	(	(	PUNCT
ma-61	111	15	1−	1−	NUM
ma-61	111	16	αn)‖yn	αn)‖yn	NOUN
ma-61	111	17	−	−	NOUN
ma-61	111	18	p‖+	p‖+	NOUN
ma-61	111	19	αn‖tyn	αn‖tyn	PRON
ma-61	111	20	−	−	PROPN
ma-61	111	21	p‖	p‖	NOUN
ma-61	111	22	,	,	PUNCT
ma-61	111	23	≤	≤	NUM
ma-61	111	24	(	(	PUNCT
ma-61	111	25	1−	1−	NUM
ma-61	111	26	αn)‖yn	αn)‖yn	NOUN
ma-61	111	27	−	−	NOUN
ma-61	111	28	p‖+	p‖+	ADV
ma-61	111	29	αn‖yn	αn‖yn	ADP
ma-61	111	30	−	−	PROPN
ma-61	112	1	p‖	p‖	NOUN
ma-61	112	2	,	,	PUNCT
ma-61	112	3	≤	≤	PROPN
ma-61	112	4	‖yn	‖yn	PUNCT
ma-61	112	5	−	−	PROPN
ma-61	112	6	p‖	p‖	NOUN
ma-61	112	7	≤	≤	PUNCT
ma-61	112	8	‖t	‖t	PROPN
ma-61	112	9	frn	frn	PROPN
ma-61	112	10	(	(	PUNCT
ma-61	112	11	xn)−	xn)−	PROPN
ma-61	112	12	p‖	p‖	NOUN
ma-61	112	13	,	,	PUNCT
ma-61	112	14	≤	≤	ADJ
ma-61	112	15	‖xn	‖xn	PUNCT
ma-61	112	16	−	−	PROPN
ma-61	112	17	p‖.	p‖.	NOUN
ma-61	112	18	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	112	19	eur	eur	NOUN
ma-61	112	20	.	.	PUNCT
ma-61	113	1	j.	j.	PROPN
ma-61	113	2	math	math	PROPN
ma-61	113	3	.	.	PUNCT
ma-61	114	1	anal	anal	PROPN
ma-61	114	2	.	.	PUNCT
ma-61	115	1	10.28924	10.28924	NUM
ma-61	115	2	/	/	SYM
ma-61	115	3	ada	ada	PROPN
ma-61	115	4	/	/	SYM
ma-61	115	5	ma.2.6	ma.2.6	PROPN
ma-61	115	6	5by	5by	NOUN
ma-61	115	7	using	use	VERB
ma-61	115	8	mathematical	mathematical	ADJ
ma-61	115	9	induction	induction	NOUN
ma-61	115	10	,	,	PUNCT
ma-61	115	11	we	we	PRON
ma-61	115	12	have	have	VERB
ma-61	115	13	‖xn+1	‖xn+1	NUM
ma-61	115	14	−	−	PROPN
ma-61	115	15	p‖	p‖	NOUN
ma-61	115	16	≤	≤	PUNCT
ma-61	115	17	‖xn	‖xn	PUNCT
ma-61	115	18	−	−	PROPN
ma-61	115	19	p‖	p‖	NOUN
ma-61	115	20	≤	≤	NUM
ma-61	116	1	‖x1	‖x1	NOUN
ma-61	117	1	−	−	PROPN
ma-61	117	2	p‖	p‖	NOUN
ma-61	117	3	,	,	PUNCT
ma-61	117	4	∀	∀	X
ma-61	117	5	n	n	PRON
ma-61	117	6	≥	≥	NOUN
ma-61	117	7	1	1	NUM
ma-61	117	8	.	.	PUNCT
ma-61	118	1	hence	hence	ADV
ma-61	118	2	the	the	DET
ma-61	118	3	sequence	sequence	NOUN
ma-61	118	4	{	{	PUNCT
ma-61	118	5	xn	xn	PUNCT
ma-61	118	6	}	}	PUNCT
ma-61	118	7	is	be	AUX
ma-61	118	8	bounded	bound	VERB
ma-61	118	9	and	and	CCONJ
ma-61	118	10	so	so	ADV
ma-61	118	11	are	be	AUX
ma-61	118	12	the	the	DET
ma-61	118	13	sequences	sequence	NOUN
ma-61	118	14	{	{	PUNCT
ma-61	118	15	yn	yn	NOUN
ma-61	118	16	}	}	PUNCT
ma-61	118	17	,	,	PUNCT
ma-61	118	18	{	{	PUNCT
ma-61	118	19	zn	zn	X
ma-61	118	20	}	}	PUNCT
ma-61	118	21	,	,	PUNCT
ma-61	118	22	{	{	PUNCT
ma-61	118	23	tyn	tyn	NOUN
ma-61	118	24	}	}	PUNCT
ma-61	118	25	and	and	CCONJ
ma-61	118	26	{	{	PUNCT
ma-61	118	27	tzn	tzn	NOUN
ma-61	118	28	}	}	PUNCT
ma-61	118	29	arealso	arealso	ADV
ma-61	118	30	bounded.let	bounded.let	X
ma-61	118	31	m	m	PROPN
ma-61	118	32	=	=	ADJ
ma-61	118	33	supn≥0{‖yn	supn≥0{‖yn	NOUN
ma-61	118	34	−	−	NOUN
ma-61	118	35	xn‖+	xn‖+	PUNCT
ma-61	119	1	‖xn	‖xn	PROPN
ma-61	119	2	−	−	PROPN
ma-61	119	3	q‖2	q‖2	PROPN
ma-61	119	4	+	+	CCONJ
ma-61	119	5	‖tyn‖+	‖tyn‖+	NOUN
ma-61	119	6	‖tzn‖}.since	‖tzn‖}.since	NOUN
ma-61	119	7	yn	yn	PROPN
ma-61	119	8	=	=	PROPN
ma-61	119	9	t	t	PROPN
ma-61	119	10	frn	frn	PROPN
ma-61	119	11	(	(	PUNCT
ma-61	119	12	xn	xn	PROPN
ma-61	119	13	)	)	PUNCT
ma-61	119	14	and	and	CCONJ
ma-61	119	15	yn−1	yn−1	NOUN
ma-61	119	16	=	=	SYM
ma-61	119	17	t	t	PROPN
ma-61	119	18	frn−1(xn−1	frn−1(xn−1	PROPN
ma-61	119	19	)	)	PUNCT
ma-61	119	20	,	,	PUNCT
ma-61	119	21	then	then	ADV
ma-61	119	22	we	we	PRON
ma-61	119	23	obtain	obtain	VERB
ma-61	119	24	f	f	PROPN
ma-61	119	25	(	(	PUNCT
ma-61	119	26	yn	yn	PROPN
ma-61	119	27	,	,	PUNCT
ma-61	119	28	q	q	NOUN
ma-61	119	29	)	)	PUNCT
ma-61	120	1	+	+	CCONJ
ma-61	120	2	1	1	NUM
ma-61	120	3	rn	rn	ADP
ma-61	120	4	〈	〈	PROPN
ma-61	120	5	q	q	PROPN
ma-61	120	6	−	−	PROPN
ma-61	120	7	yn	yn	PROPN
ma-61	120	8	,	,	PUNCT
ma-61	120	9	yn	yn	PROPN
ma-61	120	10	−	−	PROPN
ma-61	121	1	xn	xn	PROPN
ma-61	121	2	〉	〉	PROPN
ma-61	121	3	≥	≥	NUM
ma-61	121	4	0	0	NUM
ma-61	121	5	,	,	PUNCT
ma-61	121	6	∀	∀	PUNCT
ma-61	121	7	q	q	NOUN
ma-61	121	8	∈	∈	PROPN
ma-61	121	9	c	c	NOUN
ma-61	121	10	,	,	PUNCT
ma-61	121	11	(	(	PUNCT
ma-61	121	12	9	9	X
ma-61	121	13	)	)	PUNCT
ma-61	121	14	f	f	NOUN
ma-61	121	15	(	(	PUNCT
ma-61	121	16	yn−1	yn−1	PROPN
ma-61	121	17	,	,	PUNCT
ma-61	121	18	q	q	NOUN
ma-61	121	19	)	)	PUNCT
ma-61	122	1	+	+	CCONJ
ma-61	122	2	1	1	NUM
ma-61	122	3	rn−1	rn−1	PROPN
ma-61	122	4	〈	〈	PROPN
ma-61	122	5	q	q	NOUN
ma-61	122	6	−	−	PROPN
ma-61	122	7	yn−1	yn−1	PROPN
ma-61	122	8	,	,	PUNCT
ma-61	122	9	yn−1	yn−1	ADJ
ma-61	122	10	−	−	PROPN
ma-61	122	11	xn−1	xn−1	PROPN
ma-61	122	12	〉	〉	PROPN
ma-61	122	13	≥	≥	NUM
ma-61	122	14	0	0	NUM
ma-61	122	15	,	,	PUNCT
ma-61	122	16	∀	∀	PUNCT
ma-61	122	17	q	q	PROPN
ma-61	122	18	∈	∈	PROPN
ma-61	122	19	c.	c.	NOUN
ma-61	122	20	(	(	PUNCT
ma-61	122	21	10	10	NUM
ma-61	122	22	)	)	PUNCT
ma-61	122	23	replace	replace	NOUN
ma-61	122	24	q	q	NOUN
ma-61	122	25	by	by	ADP
ma-61	122	26	yn	yn	PRON
ma-61	122	27	in	in	ADP
ma-61	122	28	(	(	PUNCT
ma-61	122	29	10	10	NUM
ma-61	122	30	)	)	PUNCT
ma-61	122	31	and	and	CCONJ
ma-61	122	32	q	q	X
ma-61	122	33	by	by	ADP
ma-61	122	34	qn−1	qn−1	PROPN
ma-61	122	35	in	in	ADP
ma-61	122	36	(	(	PUNCT
ma-61	122	37	9	9	NUM
ma-61	122	38	)	)	PUNCT
ma-61	122	39	and	and	CCONJ
ma-61	122	40	adding	add	VERB
ma-61	122	41	them	they	PRON
ma-61	122	42	with	with	ADP
ma-61	122	43	the	the	DET
ma-61	122	44	assumption	assumption	NOUN
ma-61	122	45	1.1(ii),we	1.1(ii),we	NUM
ma-61	122	46	obtain	obtain	VERB
ma-61	122	47	〈	〈	PROPN
ma-61	122	48	yn	yn	NOUN
ma-61	122	49	−	−	PROPN
ma-61	122	50	yn−1	yn−1	PROPN
ma-61	122	51	,	,	PUNCT
ma-61	122	52	yn−1	yn−1	ADJ
ma-61	122	53	−	−	PROPN
ma-61	122	54	xn−1	xn−1	PROPN
ma-61	122	55	rn−1	rn−1	PROPN
ma-61	122	56	−	−	PROPN
ma-61	122	57	yn	yn	INTJ
ma-61	122	58	−	−	PROPN
ma-61	122	59	xn	xn	PROPN
ma-61	122	60	rn	rn	PROPN
ma-61	122	61	〉	〉	PROPN
ma-61	122	62	≥	≥	NUM
ma-61	122	63	0	0	NUM
ma-61	122	64	,	,	PUNCT
ma-61	122	65	and	and	CCONJ
ma-61	122	66	hence	hence	ADV
ma-61	122	67	〈	〈	PROPN
ma-61	122	68	yn	yn	PRON
ma-61	122	69	−	−	PROPN
ma-61	122	70	yn−1	yn−1	PROPN
ma-61	122	71	,	,	PUNCT
ma-61	122	72	yn−1	yn−1	ADJ
ma-61	122	73	−	−	PROPN
ma-61	122	74	yn	yn	INTJ
ma-61	122	75	−	−	NOUN
ma-61	122	76	xn−1	xn−1	PROPN
ma-61	122	77	−	−	PROPN
ma-61	122	78	rn−1	rn−1	PROPN
ma-61	122	79	rn	rn	PROPN
ma-61	122	80	(	(	PUNCT
ma-61	122	81	yn	yn	PROPN
ma-61	122	82	−	−	PROPN
ma-61	123	1	xn	xn	X
ma-61	123	2	)	)	PUNCT
ma-61	123	3	〉	〉	PROPN
ma-61	123	4	≥	≥	NUM
ma-61	123	5	0	0	NUM
ma-61	123	6	.	.	PUNCT
ma-61	124	1	this	this	PRON
ma-61	124	2	implies	imply	VERB
ma-61	124	3	that	that	SCONJ
ma-61	124	4	by	by	ADP
ma-61	124	5	using	use	VERB
ma-61	124	6	lemma	lemma	PROPN
ma-61	124	7	1.6	1.6	NUM
ma-61	124	8	‖yn	‖yn	PROPN
ma-61	124	9	−	−	PROPN
ma-61	124	10	yn−1‖2	yn−1‖2	NOUN
ma-61	124	11	≤	≤	PUNCT
ma-61	125	1	〈	〈	PROPN
ma-61	125	2	yn	yn	PROPN
ma-61	125	3	−	−	PROPN
ma-61	125	4	yn−1	yn−1	PROPN
ma-61	125	5	,	,	PUNCT
ma-61	125	6	xn	xn	PROPN
ma-61	126	1	−	−	PROPN
ma-61	127	1	xn−1	xn−1	PROPN
ma-61	127	2	+	+	CCONJ
ma-61	127	3	(	(	PUNCT
ma-61	127	4	1−	1−	NUM
ma-61	127	5	rn−1	rn−1	PROPN
ma-61	127	6	rn	rn	PROPN
ma-61	127	7	)	)	PUNCT
ma-61	127	8	(	(	PUNCT
ma-61	127	9	yn	yn	INTJ
ma-61	127	10	−	−	PROPN
ma-61	127	11	xn	xn	PROPN
ma-61	127	12	)	)	PUNCT
ma-61	127	13	〉	〉	PROPN
ma-61	127	14	,	,	PUNCT
ma-61	127	15	≤	≤	PROPN
ma-61	127	16	‖yn	‖yn	PROPN
ma-61	127	17	−	−	PROPN
ma-61	127	18	yn−1‖	yn−1‖	PROPN
ma-61	127	19	{	{	PUNCT
ma-61	127	20	‖xn	‖xn	PROPN
ma-61	127	21	−	−	PROPN
ma-61	127	22	xn−1‖+	xn−1‖+	NOUN
ma-61	127	23	∣∣∣∣	∣∣∣∣	PROPN
ma-61	127	24	rn	rn	PROPN
ma-61	127	25	−	−	PRON
ma-61	127	26	rn−1rn	rn−1rn	ADJ
ma-61	127	27	∣∣∣∣‖yn	∣∣∣∣‖yn	NOUN
ma-61	127	28	−	−	NOUN
ma-61	127	29	xn‖	xn‖	PROPN
ma-61	127	30	}	}	PUNCT
ma-61	127	31	,	,	PUNCT
ma-61	128	1	‖yn	‖yn	PROPN
ma-61	128	2	−	−	PROPN
ma-61	128	3	yn−1‖	yn−1‖	PROPN
ma-61	128	4	≤	≤	PROPN
ma-61	128	5	‖xn	‖xn	PUNCT
ma-61	128	6	−	−	PROPN
ma-61	128	7	xn−1‖+	xn−1‖+	NOUN
ma-61	128	8	∣∣∣∣	∣∣∣∣	PROPN
ma-61	128	9	rn	rn	PROPN
ma-61	128	10	−	−	PRON
ma-61	128	11	rn−1rn	rn−1rn	ADJ
ma-61	128	12	∣∣∣∣‖yn	∣∣∣∣‖yn	NOUN
ma-61	128	13	−	−	NOUN
ma-61	128	14	xn‖	xn‖	PROPN
ma-61	128	15	,	,	PUNCT
ma-61	128	16	from	from	ADP
ma-61	128	17	process	process	NOUN
ma-61	128	18	(	(	PUNCT
ma-61	128	19	8)(c2	8)(c2	NUM
ma-61	128	20	)	)	PUNCT
ma-61	128	21	,	,	PUNCT
ma-61	128	22	we	we	PRON
ma-61	128	23	have	have	VERB
ma-61	128	24	lim	lim	PROPN
ma-61	128	25	n→∞	n→∞	NUM
ma-61	128	26	inf	inf	PROPN
ma-61	128	27	rn	rn	PROPN
ma-61	128	28	>	>	PROPN
ma-61	128	29	0	0	PROPN
ma-61	128	30	.	.	PUNCT
ma-61	129	1	therefore	therefore	ADV
ma-61	129	2	there	there	PRON
ma-61	129	3	exists	exist	VERB
ma-61	129	4	r	r	NOUN
ma-61	129	5	>	>	X
ma-61	129	6	0	0	NUM
ma-61	129	7	such	such	ADJ
ma-61	129	8	that	that	PRON
ma-61	129	9	rn	rn	PROPN
ma-61	129	10	>	>	X
ma-61	129	11	r	r	NOUN
ma-61	129	12	forlarge	forlarge	NOUN
ma-61	129	13	enough	enough	ADV
ma-61	129	14	n	n	PRON
ma-61	129	15	∈	∈	PROPN
ma-61	129	16	n.	n.	NOUN
ma-61	129	17	then	then	ADV
ma-61	129	18	for	for	ADP
ma-61	129	19	n	n	PRON
ma-61	129	20	≥	≥	NUM
ma-61	129	21	1	1	NUM
ma-61	129	22	,	,	PUNCT
ma-61	129	23	‖yn	‖yn	PROPN
ma-61	129	24	−	−	PROPN
ma-61	129	25	yn−1‖	yn−1‖	PROPN
ma-61	129	26	≤	≤	PROPN
ma-61	130	1	‖xn	‖xn	PUNCT
ma-61	130	2	−	−	NOUN
ma-61	130	3	xn−1‖+	xn−1‖+	NOUN
ma-61	130	4	1	1	NUM
ma-61	130	5	r	r	NOUN
ma-61	130	6	|rn	|rn	NUM
ma-61	130	7	−	−	NOUN
ma-61	130	8	rn−1|m	rn−1|m	ADJ
ma-61	130	9	.	.	PUNCT
ma-61	131	1	(	(	PUNCT
ma-61	131	2	11	11	X
ma-61	131	3	)	)	PUNCT
ma-61	131	4	consider	consider	VERB
ma-61	131	5	‖xn+1	‖xn+1	NOUN
ma-61	131	6	−	−	NOUN
ma-61	131	7	xn‖	xn‖	PROPN
ma-61	132	1	=	=	SYM
ma-61	132	2	‖tzn	‖tzn	ADJ
ma-61	133	1	−	−	NOUN
ma-61	133	2	tzn−1‖	tzn−1‖	PROPN
ma-61	133	3	≤	≤	NOUN
ma-61	134	1	‖zn	‖zn	NUM
ma-61	134	2	−	−	PROPN
ma-61	134	3	zn−1‖	zn−1‖	PROPN
ma-61	134	4	,	,	PUNCT
ma-61	134	5	≤	≤	X
ma-61	134	6	‖(1−	‖(1−	PROPN
ma-61	134	7	αn)yn	αn)yn	NUM
ma-61	134	8	+	+	NUM
ma-61	134	9	αntyn	αntyn	NOUN
ma-61	134	10	−	−	PROPN
ma-61	134	11	(	(	PUNCT
ma-61	134	12	1−	1−	NUM
ma-61	134	13	αn−1)yn−1	αn−1)yn−1	NOUN
ma-61	134	14	−	−	PROPN
ma-61	134	15	αn−1tyn−1‖	αn−1tyn−1‖	NOUN
ma-61	134	16	,	,	PUNCT
ma-61	134	17	≤	≤	X
ma-61	134	18	‖(1−	‖(1−	NUM
ma-61	134	19	αn)yn	αn)yn	NUM
ma-61	134	20	−	−	PROPN
ma-61	134	21	(	(	PUNCT
ma-61	134	22	1−	1−	NUM
ma-61	134	23	αn)yn−1	αn)yn−1	NUM
ma-61	134	24	+	+	CCONJ
ma-61	134	25	(	(	PUNCT
ma-61	134	26	1−	1−	NUM
ma-61	134	27	αn)yn−1	αn)yn−1	ADJ
ma-61	134	28	−	−	PROPN
ma-61	135	1	(	(	PUNCT
ma-61	135	2	1−	1−	NUM
ma-61	135	3	αn−1)yn−1	αn−1)yn−1	NOUN
ma-61	136	1	+	+	CCONJ
ma-61	136	2	αntyn	αntyn	PROPN
ma-61	137	1	−	−	PROPN
ma-61	137	2	αntyn−1	αntyn−1	PROPN
ma-61	138	1	+	+	NOUN
ma-61	138	2	−αntyn−1	−αntyn−1	PROPN
ma-61	138	3	−	−	PROPN
ma-61	138	4	αn−1tyn−1‖	αn−1tyn−1‖	NOUN
ma-61	138	5	,	,	PUNCT
ma-61	138	6	≤	≤	NUM
ma-61	138	7	(	(	PUNCT
ma-61	138	8	1−	1−	NUM
ma-61	138	9	αn)‖yn	αn)‖yn	NOUN
ma-61	138	10	−	−	NOUN
ma-61	138	11	yn−1‖+	yn−1‖+	NUM
ma-61	138	12	2|αn	2|αn	NUM
ma-61	138	13	−	−	NOUN
ma-61	138	14	αn−1|m	αn−1|m	NOUN
ma-61	138	15	+	+	CCONJ
ma-61	138	16	αn‖yn	αn‖yn	ADP
ma-61	138	17	−	−	PROPN
ma-61	138	18	yn−1‖	yn−1‖	PROPN
ma-61	138	19	,	,	PUNCT
ma-61	138	20	≤	≤	PROPN
ma-61	138	21	‖yn	‖yn	NUM
ma-61	138	22	−	−	NOUN
ma-61	138	23	yn−1‖+	yn−1‖+	NUM
ma-61	138	24	2|αn	2|αn	NUM
ma-61	138	25	−	−	NOUN
ma-61	138	26	αn−1|m	αn−1|m	NOUN
ma-61	138	27	.	.	PUNCT
ma-61	139	1	(	(	PUNCT
ma-61	139	2	12	12	NUM
ma-61	139	3	)	)	PUNCT
ma-61	139	4	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	139	5	eur	eur	PROPN
ma-61	139	6	.	.	PUNCT
ma-61	140	1	j.	j.	PROPN
ma-61	140	2	math	math	PROPN
ma-61	140	3	.	.	PUNCT
ma-61	141	1	anal	anal	PROPN
ma-61	141	2	.	.	PUNCT
ma-61	142	1	10.28924	10.28924	NUM
ma-61	142	2	/	/	SYM
ma-61	142	3	ada	ada	PROPN
ma-61	142	4	/	/	SYM
ma-61	142	5	ma.2.6	ma.2.6	PROPN
ma-61	142	6	6using	6using	NUM
ma-61	142	7	(	(	PUNCT
ma-61	142	8	11	11	NUM
ma-61	142	9	)	)	PUNCT
ma-61	142	10	and	and	CCONJ
ma-61	142	11	(	(	PUNCT
ma-61	142	12	12	12	NUM
ma-61	142	13	)	)	PUNCT
ma-61	142	14	,	,	PUNCT
ma-61	142	15	we	we	PRON
ma-61	142	16	obtain	obtain	VERB
ma-61	142	17	‖xn+1	‖xn+1	PUNCT
ma-61	142	18	−	−	NOUN
ma-61	142	19	xn‖	xn‖	PROPN
ma-61	142	20	≤	≤	PROPN
ma-61	143	1	‖xn	‖xn	PUNCT
ma-61	144	1	−	−	NOUN
ma-61	144	2	xn−1‖+	xn−1‖+	NOUN
ma-61	144	3	1	1	NUM
ma-61	144	4	r	r	NOUN
ma-61	144	5	|rn	|rn	NUM
ma-61	144	6	−	−	NOUN
ma-61	144	7	rn−1|m	rn−1|m	ADJ
ma-61	145	1	+	+	CCONJ
ma-61	145	2	2|αn	2|αn	NUM
ma-61	145	3	−	−	NOUN
ma-61	145	4	αn−1|m	αn−1|m	NOUN
ma-61	145	5	.	.	PUNCT
ma-61	146	1	(	(	PUNCT
ma-61	146	2	13	13	NUM
ma-61	146	3	)	)	PUNCT
ma-61	146	4	by	by	ADP
ma-61	146	5	applying	apply	VERB
ma-61	146	6	lemma	lemma	PROPN
ma-61	146	7	1.4	1.4	NUM
ma-61	146	8	,	,	PUNCT
ma-61	146	9	we	we	PRON
ma-61	146	10	obtain	obtain	VERB
ma-61	146	11	lim	lim	PROPN
ma-61	146	12	n→∞	n→∞	X
ma-61	146	13	‖xn+1	‖xn+1	NUM
ma-61	146	14	−	−	NOUN
ma-61	146	15	xn‖	xn‖	PROPN
ma-61	147	1	=	=	SYM
ma-61	147	2	0	0	PROPN
ma-61	147	3	.	.	PUNCT
ma-61	148	1	(	(	PUNCT
ma-61	148	2	14	14	NUM
ma-61	148	3	)	)	PUNCT
ma-61	148	4	by	by	ADP
ma-61	148	5	using	use	VERB
ma-61	148	6	process	process	NOUN
ma-61	148	7	(	(	PUNCT
ma-61	148	8	8)(c1)(c2	8)(c1)(c2	NUM
ma-61	148	9	)	)	PUNCT
ma-61	148	10	along	along	ADP
ma-61	148	11	with	with	ADP
ma-61	148	12	lemma	lemma	PROPN
ma-61	148	13	1.7	1.7	NUM
ma-61	148	14	and	and	CCONJ
ma-61	148	15	(	(	PUNCT
ma-61	148	16	13	13	NUM
ma-61	148	17	)	)	PUNCT
ma-61	148	18	,	,	PUNCT
ma-61	148	19	we	we	PRON
ma-61	148	20	obtain	obtain	VERB
ma-61	148	21	lim	lim	PROPN
ma-61	148	22	n→∞	n→∞	X
ma-61	149	1	‖xn	‖xn	PROPN
ma-61	149	2	−	−	PROPN
ma-61	149	3	zn‖	zn‖	PROPN
ma-61	149	4	=	=	SYM
ma-61	149	5	0	0	NUM
ma-61	149	6	.	.	PUNCT
ma-61	149	7	(	(	PUNCT
ma-61	149	8	15	15	NUM
ma-61	149	9	)	)	PUNCT
ma-61	149	10	furthermore	furthermore	ADV
ma-61	149	11	,	,	PUNCT
ma-61	149	12	for	for	ADP
ma-61	149	13	any	any	DET
ma-61	149	14	p	p	PROPN
ma-61	149	15	∈	∈	PROPN
ma-61	149	16	ω	ω	NOUN
ma-61	149	17	,	,	PUNCT
ma-61	149	18	we	we	PRON
ma-61	149	19	have	have	VERB
ma-61	149	20	from	from	ADP
ma-61	149	21	process	process	NOUN
ma-61	149	22	(	(	PUNCT
ma-61	149	23	8)	8)	NUM
ma-61	149	24	‖yn	‖yn	PROPN
ma-61	149	25	−	−	PROPN
ma-61	149	26	p‖2	p‖2	PROPN
ma-61	149	27	=	=	PROPN
ma-61	149	28	‖t	‖t	PROPN
ma-61	149	29	frn	frn	PROPN
ma-61	149	30	(	(	PUNCT
ma-61	149	31	xn)−	xn)−	PROPN
ma-61	149	32	p‖2	p‖2	PROPN
ma-61	149	33	,	,	PUNCT
ma-61	149	34	≤	≤	PUNCT
ma-61	149	35	〈	〈	PROPN
ma-61	149	36	t	t	PROPN
ma-61	149	37	frn	frn	PROPN
ma-61	149	38	(	(	PUNCT
ma-61	149	39	xn)−	xn)−	PROPN
ma-61	149	40	t	t	PROPN
ma-61	149	41	frn	frn	PROPN
ma-61	149	42	(	(	PUNCT
ma-61	149	43	p	p	NOUN
ma-61	149	44	)	)	PUNCT
ma-61	149	45	,	,	PUNCT
ma-61	149	46	xn	xn	PROPN
ma-61	150	1	−	−	PROPN
ma-61	151	1	p	p	PRON
ma-61	151	2	〉	〉	PROPN
ma-61	151	3	,	,	PUNCT
ma-61	151	4	≤	≤	PUNCT
ma-61	151	5	〈	〈	PROPN
ma-61	151	6	yn	yn	PROPN
ma-61	151	7	−	−	PROPN
ma-61	151	8	p	p	PROPN
ma-61	151	9	,	,	PUNCT
ma-61	151	10	xn	xn	PROPN
ma-61	152	1	−	−	PROPN
ma-61	153	1	p	p	PRON
ma-61	153	2	〉	〉	PROPN
ma-61	153	3	,	,	PUNCT
ma-61	153	4	≤	≤	NUM
ma-61	153	5	1	1	NUM
ma-61	153	6	2	2	NUM
ma-61	153	7	{	{	PUNCT
ma-61	153	8	‖yn	‖yn	PROPN
ma-61	153	9	−	−	PROPN
ma-61	153	10	p‖2	p‖2	PROPN
ma-61	153	11	+	+	CCONJ
ma-61	153	12	‖xn	‖xn	PROPN
ma-61	153	13	−	−	PROPN
ma-61	153	14	p‖2	p‖2	PROPN
ma-61	153	15	−	−	PROPN
ma-61	153	16	‖xn	‖xn	PROPN
ma-61	153	17	−	−	PROPN
ma-61	153	18	yn‖2	yn‖2	PROPN
ma-61	153	19	}	}	PUNCT
ma-61	153	20	,	,	PUNCT
ma-61	153	21	≤	≤	ADJ
ma-61	153	22	‖xn	‖xn	PROPN
ma-61	153	23	−	−	PROPN
ma-61	153	24	p‖2	p‖2	PROPN
ma-61	153	25	−	−	PROPN
ma-61	153	26	‖xn	‖xn	PROPN
ma-61	153	27	−	−	PUNCT
ma-61	153	28	yn‖2	yn‖2	PROPN
ma-61	153	29	.	.	PUNCT
ma-61	154	1	(	(	PUNCT
ma-61	154	2	16	16	NUM
ma-61	154	3	)	)	PUNCT
ma-61	154	4	from	from	ADP
ma-61	154	5	convaxity	convaxity	NOUN
ma-61	154	6	of	of	ADP
ma-61	154	7	function	function	NOUN
ma-61	154	8	x	x	PROPN
ma-61	154	9	7→	7→	NUM
ma-61	154	10	‖x‖2	‖x‖2	VERB
ma-61	154	11	and	and	CCONJ
ma-61	154	12	(	(	PUNCT
ma-61	154	13	16	16	NUM
ma-61	154	14	)	)	PUNCT
ma-61	154	15	,	,	PUNCT
ma-61	154	16	we	we	PRON
ma-61	154	17	obtain	obtain	VERB
ma-61	154	18	‖xn+1	‖xn+1	PUNCT
ma-61	154	19	−	−	PROPN
ma-61	154	20	p‖2	p‖2	PROPN
ma-61	154	21	=	=	SYM
ma-61	154	22	‖tzn	‖tzn	X
ma-61	155	1	−	−	PROPN
ma-61	155	2	p‖2	p‖2	PROPN
ma-61	155	3	,	,	PUNCT
ma-61	155	4	≤	≤	NUM
ma-61	155	5	‖zn	‖zn	NUM
ma-61	155	6	−	−	PROPN
ma-61	155	7	p‖2	p‖2	PROPN
ma-61	155	8	,	,	PUNCT
ma-61	155	9	≤	≤	NOUN
ma-61	155	10	‖(1−	‖(1−	PROPN
ma-61	155	11	αn)yn	αn)yn	NUM
ma-61	155	12	+	+	CCONJ
ma-61	155	13	αntyn	αntyn	NOUN
ma-61	155	14	−	−	PROPN
ma-61	155	15	p‖2	p‖2	PROPN
ma-61	155	16	,	,	PUNCT
ma-61	155	17	≤	≤	NUM
ma-61	155	18	(	(	PUNCT
ma-61	155	19	1−	1−	NUM
ma-61	155	20	αn)‖yn	αn)‖yn	NOUN
ma-61	155	21	−	−	PROPN
ma-61	155	22	p‖2	p‖2	PROPN
ma-61	155	23	+	+	CCONJ
ma-61	155	24	αn‖tyn	αn‖tyn	X
ma-61	155	25	−	−	PROPN
ma-61	155	26	p‖2	p‖2	PROPN
ma-61	155	27	,	,	PUNCT
ma-61	155	28	≤	≤	NUM
ma-61	155	29	‖yn	‖yn	PROPN
ma-61	155	30	−	−	PROPN
ma-61	155	31	p‖2	p‖2	PROPN
ma-61	155	32	,	,	PUNCT
ma-61	155	33	≤	≤	ADJ
ma-61	155	34	‖xn	‖xn	PROPN
ma-61	155	35	−	−	PROPN
ma-61	155	36	p‖2	p‖2	PROPN
ma-61	155	37	−	−	PROPN
ma-61	156	1	‖xn	‖xn	PROPN
ma-61	156	2	−	−	PUNCT
ma-61	156	3	yn‖2	yn‖2	PROPN
ma-61	156	4	.	.	PUNCT
ma-61	157	1	and	and	CCONJ
ma-61	157	2	so	so	ADV
ma-61	157	3	,	,	PUNCT
ma-61	157	4	‖xn	‖xn	PROPN
ma-61	157	5	−	−	PROPN
ma-61	157	6	yn‖2	yn‖2	PROPN
ma-61	157	7	≤	≤	PROPN
ma-61	157	8	‖xn	‖xn	PROPN
ma-61	157	9	−	−	PROPN
ma-61	157	10	p‖2	p‖2	PROPN
ma-61	157	11	−	−	PROPN
ma-61	157	12	‖xn+1	‖xn+1	PROPN
ma-61	157	13	−	−	PROPN
ma-61	157	14	p‖2	p‖2	PROPN
ma-61	157	15	,	,	PUNCT
ma-61	157	16	≤	≤	NUM
ma-61	157	17	(	(	PUNCT
ma-61	157	18	‖xn	‖xn	PROPN
ma-61	157	19	−	−	PROPN
ma-61	157	20	p‖	p‖	NOUN
ma-61	157	21	−	−	PROPN
ma-61	157	22	‖xn+1	‖xn+1	PROPN
ma-61	157	23	−	−	PROPN
ma-61	157	24	p‖)(‖xn	p‖)(‖xn	X
ma-61	157	25	−	−	PROPN
ma-61	157	26	p‖+	p‖+	NOUN
ma-61	157	27	‖xn+1	‖xn+1	PUNCT
ma-61	157	28	−	−	PROPN
ma-61	157	29	p‖	p‖	NOUN
ma-61	157	30	)	)	PUNCT
ma-61	157	31	,	,	PUNCT
ma-61	157	32	≤	≤	X
ma-61	157	33	‖xn	‖xn	PROPN
ma-61	157	34	−	−	PROPN
ma-61	157	35	xn+1‖(‖xn	xn+1‖(‖xn	PROPN
ma-61	157	36	−	−	PROPN
ma-61	157	37	p‖+	p‖+	PROPN
ma-61	157	38	‖xn+1	‖xn+1	PUNCT
ma-61	157	39	−	−	PROPN
ma-61	157	40	p‖	p‖	NOUN
ma-61	157	41	)	)	PUNCT
ma-61	157	42	.	.	PUNCT
ma-61	158	1	since	since	SCONJ
ma-61	158	2	the	the	DET
ma-61	158	3	sequence	sequence	NOUN
ma-61	158	4	{	{	PUNCT
ma-61	158	5	xn	xn	PUNCT
ma-61	158	6	}	}	PUNCT
ma-61	158	7	is	be	AUX
ma-61	158	8	bounded	bound	VERB
ma-61	158	9	and	and	CCONJ
ma-61	158	10	lim	lim	PROPN
ma-61	158	11	n→∞	n→∞	X
ma-61	158	12	‖xn+1	‖xn+1	NUM
ma-61	158	13	−	−	NOUN
ma-61	158	14	xn‖	xn‖	PROPN
ma-61	159	1	=	=	SYM
ma-61	159	2	0	0	X
ma-61	159	3	.	.	PUNCT
ma-61	160	1	we	we	PRON
ma-61	160	2	have	have	VERB
ma-61	160	3	lim	lim	PROPN
ma-61	160	4	n→∞	n→∞	X
ma-61	161	1	‖xn	‖xn	PROPN
ma-61	161	2	−	−	PROPN
ma-61	161	3	yn‖	yn‖	NOUN
ma-61	161	4	=	=	NOUN
ma-61	161	5	0	0	PROPN
ma-61	161	6	.	.	PUNCT
ma-61	162	1	(	(	PUNCT
ma-61	162	2	17	17	NUM
ma-61	162	3	)	)	PUNCT
ma-61	162	4	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	162	5	eur	eur	PROPN
ma-61	162	6	.	.	PUNCT
ma-61	163	1	j.	j.	PROPN
ma-61	163	2	math	math	PROPN
ma-61	163	3	.	.	PUNCT
ma-61	164	1	anal	anal	PROPN
ma-61	164	2	.	.	PUNCT
ma-61	165	1	10.28924	10.28924	NUM
ma-61	165	2	/	/	SYM
ma-61	165	3	ada	ada	PROPN
ma-61	165	4	/	/	SYM
ma-61	165	5	ma.2.6	ma.2.6	PROPN
ma-61	165	6	7further	7further	PROPN
ma-61	165	7	,	,	PUNCT
ma-61	165	8	‖xn+1	‖xn+1	NUM
ma-61	165	9	−	−	PROPN
ma-61	165	10	p‖2	p‖2	PROPN
ma-61	165	11	=	=	SYM
ma-61	165	12	‖tzn	‖tzn	X
ma-61	166	1	−	−	PROPN
ma-61	166	2	p‖2	p‖2	PROPN
ma-61	166	3	,	,	PUNCT
ma-61	166	4	≤	≤	NUM
ma-61	166	5	‖zn	‖zn	NUM
ma-61	166	6	−	−	PROPN
ma-61	166	7	p‖2	p‖2	PROPN
ma-61	166	8	,	,	PUNCT
ma-61	166	9	≤	≤	NOUN
ma-61	166	10	‖(1−	‖(1−	PROPN
ma-61	166	11	αn)yn	αn)yn	NUM
ma-61	166	12	+	+	CCONJ
ma-61	166	13	αntyn	αntyn	NOUN
ma-61	166	14	−	−	PROPN
ma-61	166	15	p‖2	p‖2	PROPN
ma-61	166	16	,	,	PUNCT
ma-61	166	17	≤	≤	NUM
ma-61	166	18	(	(	PUNCT
ma-61	166	19	1−	1−	NUM
ma-61	166	20	αn)‖yn	αn)‖yn	NOUN
ma-61	166	21	−	−	PROPN
ma-61	166	22	p‖2	p‖2	PROPN
ma-61	166	23	+	+	CCONJ
ma-61	166	24	αn‖tyn	αn‖tyn	X
ma-61	166	25	−	−	PROPN
ma-61	166	26	p‖2	p‖2	PROPN
ma-61	166	27	−	−	PROPN
ma-61	166	28	αn(1−	αn(1−	PROPN
ma-61	166	29	αn)‖yn	αn)‖yn	NOUN
ma-61	166	30	−	−	NOUN
ma-61	166	31	tyn‖2	tyn‖2	ADV
ma-61	166	32	,	,	PUNCT
ma-61	166	33	≤	≤	PROPN
ma-61	166	34	‖yn	‖yn	PUNCT
ma-61	166	35	−	−	PROPN
ma-61	166	36	p‖2	p‖2	PROPN
ma-61	166	37	−	−	PROPN
ma-61	166	38	αn(1−	αn(1−	PROPN
ma-61	166	39	αn)‖yn	αn)‖yn	NOUN
ma-61	166	40	−	−	NOUN
ma-61	166	41	tyn‖2	tyn‖2	ADV
ma-61	166	42	,	,	PUNCT
ma-61	166	43	≤	≤	ADJ
ma-61	166	44	‖xn	‖xn	PROPN
ma-61	166	45	−	−	PROPN
ma-61	166	46	p‖2	p‖2	PROPN
ma-61	166	47	−	−	PROPN
ma-61	166	48	‖xn	‖xn	PROPN
ma-61	166	49	−	−	PUNCT
ma-61	166	50	yn‖2	yn‖2	PROPN
ma-61	166	51	−	−	PROPN
ma-61	166	52	αn(1−	αn(1−	PROPN
ma-61	166	53	αn)‖yn	αn)‖yn	NOUN
ma-61	166	54	−	−	NOUN
ma-61	166	55	tyn‖2	tyn‖2	ADV
ma-61	166	56	,	,	PUNCT
ma-61	166	57	and	and	CCONJ
ma-61	166	58	so	so	ADV
ma-61	166	59	,	,	PUNCT
ma-61	166	60	αn(1−	αn(1−	ADJ
ma-61	166	61	αn)‖yn	αn)‖yn	NOUN
ma-61	166	62	−	−	NOUN
ma-61	166	63	tyn‖2	tyn‖2	PROPN
ma-61	166	64	≤	≤	PROPN
ma-61	166	65	‖xn	‖xn	PUNCT
ma-61	166	66	−	−	PROPN
ma-61	166	67	p‖2	p‖2	PROPN
ma-61	166	68	−	−	PROPN
ma-61	166	69	‖xn+1	‖xn+1	PROPN
ma-61	166	70	−	−	PROPN
ma-61	166	71	p‖2	p‖2	PROPN
ma-61	166	72	−	−	PROPN
ma-61	167	1	‖xn	‖xn	PROPN
ma-61	167	2	−	−	PUNCT
ma-61	167	3	yn‖2	yn‖2	PROPN
ma-61	167	4	,	,	PUNCT
ma-61	167	5	≤	≤	NUM
ma-61	167	6	‖xn	‖xn	PROPN
ma-61	167	7	−	−	PROPN
ma-61	167	8	xn+1‖(‖xn	xn+1‖(‖xn	PROPN
ma-61	167	9	−	−	PROPN
ma-61	167	10	p‖+	p‖+	NOUN
ma-61	167	11	‖xn+1	‖xn+1	PUNCT
ma-61	167	12	−	−	PROPN
ma-61	167	13	p‖)−	p‖)−	X
ma-61	167	14	‖xn	‖xn	PROPN
ma-61	167	15	−	−	PUNCT
ma-61	167	16	yn‖2	yn‖2	PROPN
ma-61	167	17	,	,	PUNCT
ma-61	167	18	using	use	VERB
ma-61	167	19	process	process	NOUN
ma-61	167	20	(	(	PUNCT
ma-61	167	21	8)(c1	8)(c1	NUM
ma-61	167	22	)	)	PUNCT
ma-61	167	23	,	,	PUNCT
ma-61	167	24	(	(	PUNCT
ma-61	167	25	14	14	NUM
ma-61	167	26	)	)	PUNCT
ma-61	167	27	and	and	CCONJ
ma-61	167	28	(	(	PUNCT
ma-61	167	29	17	17	NUM
ma-61	167	30	)	)	PUNCT
ma-61	167	31	,	,	PUNCT
ma-61	167	32	we	we	PRON
ma-61	167	33	obtain	obtain	VERB
ma-61	167	34	lim	lim	PROPN
ma-61	167	35	n→∞	n→∞	X
ma-61	168	1	‖yn	‖yn	PROPN
ma-61	168	2	−	−	PROPN
ma-61	168	3	tyn‖	tyn‖	NOUN
ma-61	168	4	=	=	SYM
ma-61	168	5	0	0	NUM
ma-61	168	6	.	.	PUNCT
ma-61	169	1	(	(	PUNCT
ma-61	169	2	18	18	NUM
ma-61	169	3	)	)	PUNCT
ma-61	169	4	consider	consider	VERB
ma-61	169	5	‖zn	‖zn	NUM
ma-61	169	6	−	−	NOUN
ma-61	169	7	tzn‖	tzn‖	ADV
ma-61	169	8	≤	≤	NOUN
ma-61	170	1	‖zn	‖zn	NUM
ma-61	170	2	−	−	PROPN
ma-61	170	3	yn‖+	yn‖+	PROPN
ma-61	170	4	‖yn	‖yn	PROPN
ma-61	170	5	−	−	PROPN
ma-61	170	6	tyn‖+	tyn‖+	SCONJ
ma-61	170	7	‖tyn	‖tyn	DET
ma-61	170	8	−	−	NOUN
ma-61	170	9	tzn‖	tzn‖	ADV
ma-61	170	10	,	,	PUNCT
ma-61	170	11	(	(	PUNCT
ma-61	170	12	19	19	NUM
ma-61	170	13	)	)	PUNCT
ma-61	170	14	≤	≤	NOUN
ma-61	171	1	‖zn	‖zn	NUM
ma-61	171	2	−	−	PROPN
ma-61	171	3	yn‖+	yn‖+	PROPN
ma-61	171	4	‖yn	‖yn	PROPN
ma-61	171	5	−	−	PROPN
ma-61	171	6	tyn‖+	tyn‖+	PROPN
ma-61	171	7	‖yn	‖yn	NOUN
ma-61	171	8	−	−	PROPN
ma-61	171	9	zn‖.	zn‖.	NOUN
ma-61	171	10	(	(	PUNCT
ma-61	171	11	20	20	NUM
ma-61	171	12	)	)	PUNCT
ma-61	171	13	by	by	ADP
ma-61	171	14	using	use	VERB
ma-61	171	15	(	(	PUNCT
ma-61	171	16	15	15	NUM
ma-61	171	17	)	)	PUNCT
ma-61	171	18	and	and	CCONJ
ma-61	171	19	(	(	PUNCT
ma-61	171	20	18	18	NUM
ma-61	171	21	)	)	PUNCT
ma-61	171	22	,	,	PUNCT
ma-61	171	23	we	we	PRON
ma-61	171	24	obtain	obtain	VERB
ma-61	171	25	lim	lim	PROPN
ma-61	171	26	n→∞	n→∞	X
ma-61	172	1	‖zn	‖zn	NUM
ma-61	172	2	−	−	NOUN
ma-61	172	3	tzn‖	tzn‖	ADV
ma-61	172	4	=	=	NOUN
ma-61	172	5	0	0	NUM
ma-61	172	6	.	.	PUNCT
ma-61	173	1	(	(	PUNCT
ma-61	173	2	21	21	NUM
ma-61	173	3	)	)	PUNCT
ma-61	173	4	since	since	SCONJ
ma-61	173	5	{	{	PUNCT
ma-61	173	6	xn	xn	X
ma-61	173	7	}	}	PUNCT
ma-61	173	8	is	be	AUX
ma-61	173	9	bounded	bound	VERB
ma-61	173	10	.	.	PUNCT
ma-61	174	1	there	there	PRON
ma-61	174	2	exists	exist	VERB
ma-61	174	3	a	a	DET
ma-61	174	4	subsequence	subsequence	NOUN
ma-61	174	5	{	{	PUNCT
ma-61	174	6	xni	xni	PROPN
ma-61	174	7	}	}	PUNCT
ma-61	174	8	⊂	⊂	PROPN
ma-61	174	9	{	{	PUNCT
ma-61	174	10	xn	xn	X
ma-61	174	11	}	}	PUNCT
ma-61	174	12	such	such	ADJ
ma-61	174	13	that	that	SCONJ
ma-61	174	14	xn	xn	PROPN
ma-61	175	1	⇀	⇀	NUM
ma-61	175	2	p̂.	p̂.	PROPN
ma-61	175	3	since	since	SCONJ
ma-61	175	4	lim	lim	PROPN
ma-61	175	5	n→∞	n→∞	X
ma-61	176	1	‖xn	‖xn	PROPN
ma-61	176	2	−	−	PROPN
ma-61	176	3	yn‖	yn‖	NOUN
ma-61	176	4	=	=	SYM
ma-61	176	5	0	0	PROPN
ma-61	176	6	and	and	CCONJ
ma-61	176	7	{	{	PUNCT
ma-61	176	8	yn	yn	NOUN
ma-61	176	9	}	}	PUNCT
ma-61	176	10	is	be	AUX
ma-61	176	11	bounded	bound	VERB
ma-61	176	12	,	,	PUNCT
ma-61	176	13	this	this	PRON
ma-61	176	14	implies	imply	VERB
ma-61	176	15	that	that	SCONJ
ma-61	176	16	yni	yni	VERB
ma-61	176	17	⇀	⇀	NUM
ma-61	176	18	p̂	p̂	X
ma-61	176	19	∈	∈	PROPN
ma-61	176	20	c.	c.	NOUN
ma-61	176	21	now	now	ADV
ma-61	176	22	by	by	ADP
ma-61	176	23	(	(	PUNCT
ma-61	176	24	18	18	NUM
ma-61	176	25	)	)	PUNCT
ma-61	176	26	we	we	PRON
ma-61	176	27	have	have	AUX
ma-61	176	28	‖tyni	‖tyni	NOUN
ma-61	176	29	−	−	PROPN
ma-61	176	30	yni‖	yni‖	PROPN
ma-61	176	31	→	→	SYM
ma-61	176	32	0	0	NUM
ma-61	176	33	.	.	PUNCT
ma-61	177	1	(	(	PUNCT
ma-61	177	2	22	22	NUM
ma-61	177	3	)	)	PUNCT
ma-61	177	4	from	from	ADP
ma-61	177	5	(	(	PUNCT
ma-61	177	6	22	22	NUM
ma-61	177	7	)	)	PUNCT
ma-61	177	8	and	and	CCONJ
ma-61	177	9	lemma	lemma	PROPN
ma-61	177	10	1.5	1.5	NUM
ma-61	177	11	,	,	PUNCT
ma-61	177	12	we	we	PRON
ma-61	177	13	conclude	conclude	VERB
ma-61	177	14	that	that	PRON
ma-61	177	15	p̂	p̂	NOUN
ma-61	177	16	∈	∈	PROPN
ma-61	177	17	fix(t	fix(t	PROPN
ma-61	177	18	)	)	PUNCT
ma-61	177	19	.next	.next	NUM
ma-61	178	1	we	we	PRON
ma-61	178	2	prove	prove	VERB
ma-61	178	3	that	that	SCONJ
ma-61	178	4	p̂	p̂	NOUN
ma-61	178	5	∈	∈	PROPN
ma-61	178	6	ep	ep	PROPN
ma-61	178	7	(	(	PUNCT
ma-61	178	8	f	f	PROPN
ma-61	178	9	)	)	PUNCT
ma-61	178	10	.	.	PUNCT
ma-61	179	1	since	since	SCONJ
ma-61	179	2	yn	yn	PROPN
ma-61	179	3	=	=	PROPN
ma-61	179	4	t	t	PROPN
ma-61	179	5	frn	frn	PROPN
ma-61	179	6	(	(	PUNCT
ma-61	179	7	xn	xn	PROPN
ma-61	179	8	)	)	PUNCT
ma-61	179	9	,	,	PUNCT
ma-61	179	10	we	we	PRON
ma-61	179	11	have	have	VERB
ma-61	179	12	f	f	PROPN
ma-61	179	13	(	(	PUNCT
ma-61	179	14	yn	yn	PROPN
ma-61	179	15	,	,	PUNCT
ma-61	179	16	q	q	NOUN
ma-61	179	17	)	)	PUNCT
ma-61	180	1	+	+	CCONJ
ma-61	180	2	1	1	NUM
ma-61	180	3	rn	rn	ADP
ma-61	180	4	〈	〈	PROPN
ma-61	180	5	q	q	PROPN
ma-61	180	6	−	−	PROPN
ma-61	180	7	yn	yn	PROPN
ma-61	180	8	,	,	PUNCT
ma-61	180	9	yn	yn	PROPN
ma-61	180	10	−	−	PROPN
ma-61	181	1	xn	xn	PROPN
ma-61	181	2	〉	〉	PROPN
ma-61	181	3	≥	≥	NUM
ma-61	181	4	0	0	NUM
ma-61	181	5	,	,	PUNCT
ma-61	181	6	∀	∀	PUNCT
ma-61	182	1	q	q	NOUN
ma-61	182	2	∈	∈	PROPN
ma-61	182	3	c.by	c.by	PROPN
ma-61	182	4	using	use	VERB
ma-61	182	5	assumption	assumption	NOUN
ma-61	182	6	1.1(ii	1.1(ii	NUM
ma-61	182	7	)	)	PUNCT
ma-61	182	8	,	,	PUNCT
ma-61	182	9	we	we	PRON
ma-61	182	10	obtain	obtain	VERB
ma-61	182	11	1	1	NUM
ma-61	182	12	rn	rn	ADP
ma-61	182	13	〈	〈	PROPN
ma-61	182	14	q	q	PROPN
ma-61	182	15	−	−	PROPN
ma-61	182	16	yn	yn	PROPN
ma-61	182	17	,	,	PUNCT
ma-61	182	18	yn	yn	PROPN
ma-61	182	19	−	−	PROPN
ma-61	183	1	xn	xn	PROPN
ma-61	183	2	〉	〉	PROPN
ma-61	183	3	≥	≥	NOUN
ma-61	183	4	f	f	PROPN
ma-61	183	5	(	(	PUNCT
ma-61	183	6	q	q	PROPN
ma-61	183	7	,	,	PUNCT
ma-61	183	8	yn	yn	PROPN
ma-61	183	9	)	)	PUNCT
ma-61	183	10	,	,	PUNCT
ma-61	183	11	and	and	CCONJ
ma-61	183	12	so	so	ADV
ma-61	183	13	,	,	PUNCT
ma-61	183	14	〈	〈	PROPN
ma-61	183	15	q	q	X
ma-61	183	16	−	−	PROPN
ma-61	183	17	yni	yni	NOUN
ma-61	183	18	,	,	PUNCT
ma-61	183	19	yni	yni	VERB
ma-61	183	20	−	−	PROPN
ma-61	183	21	xni	xni	PROPN
ma-61	183	22	rni	rni	PROPN
ma-61	183	23	〉	〉	PROPN
ma-61	183	24	≥	≥	PROPN
ma-61	183	25	f	f	PROPN
ma-61	183	26	(	(	PUNCT
ma-61	183	27	q	q	ADJ
ma-61	183	28	,	,	PUNCT
ma-61	183	29	yni	yni	NOUN
ma-61	183	30	)	)	PUNCT
ma-61	183	31	.	.	PUNCT
ma-61	184	1	(	(	PUNCT
ma-61	184	2	23	23	NUM
ma-61	184	3	)	)	PUNCT
ma-61	184	4	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	184	5	eur	eur	PROPN
ma-61	184	6	.	.	PUNCT
ma-61	185	1	j.	j.	PROPN
ma-61	185	2	math	math	PROPN
ma-61	185	3	.	.	PUNCT
ma-61	186	1	anal	anal	PROPN
ma-61	186	2	.	.	PUNCT
ma-61	187	1	10.28924	10.28924	NUM
ma-61	187	2	/	/	SYM
ma-61	187	3	ada	ada	PROPN
ma-61	187	4	/	/	SYM
ma-61	187	5	ma.2.6	ma.2.6	PROPN
ma-61	187	6	8	8	NUM
ma-61	187	7	since	since	SCONJ
ma-61	187	8	‖yni−xni	‖yni−xni	NUM
ma-61	187	9	‖rni	‖rni	PROPN
ma-61	187	10	≤	≤	NUM
ma-61	187	11	‖yni−xni	‖yni−xni	NUM
ma-61	187	12	‖r	‖r	PROPN
ma-61	187	13	→	→	SYM
ma-61	187	14	0	0	NUM
ma-61	187	15	and	and	CCONJ
ma-61	187	16	yni	yni	VERB
ma-61	187	17	⇀	⇀	NUM
ma-61	187	18	p̂	p̂	NOUN
ma-61	187	19	,	,	PUNCT
ma-61	187	20	therefore	therefore	ADV
ma-61	187	21	by	by	ADP
ma-61	187	22	assumption	assumption	NOUN
ma-61	187	23	1.1(iv	1.1(iv	NUM
ma-61	187	24	)	)	PUNCT
ma-61	187	25	,	,	PUNCT
ma-61	187	26	we	we	PRON
ma-61	187	27	obtain	obtain	VERB
ma-61	187	28	lim	lim	PROPN
ma-61	187	29	ni→∞	ni→∞	PROPN
ma-61	187	30	inf	inf	PROPN
ma-61	187	31	f	f	X
ma-61	187	32	(	(	PUNCT
ma-61	187	33	q	q	ADJ
ma-61	187	34	,	,	PUNCT
ma-61	187	35	yni	yni	NOUN
ma-61	187	36	)	)	PUNCT
ma-61	187	37	≤	≤	NOUN
ma-61	188	1	lim	lim	PROPN
ma-61	188	2	ni→∞	ni→∞	PROPN
ma-61	188	3	〈	〈	PROPN
ma-61	188	4	q	q	PROPN
ma-61	188	5	−	−	PROPN
ma-61	188	6	yni	yni	NOUN
ma-61	188	7	,	,	PUNCT
ma-61	188	8	yni	yni	VERB
ma-61	189	1	−	−	PROPN
ma-61	189	2	xni	xni	PROPN
ma-61	189	3	rni	rni	PROPN
ma-61	189	4	〉	〉	PROPN
ma-61	189	5	=	=	SYM
ma-61	189	6	0	0	PROPN
ma-61	189	7	.	.	PUNCT
ma-61	190	1	that	that	PRON
ma-61	190	2	is	be	AUX
ma-61	190	3	,	,	PUNCT
ma-61	190	4	f	f	PROPN
ma-61	190	5	(	(	PUNCT
ma-61	190	6	q	q	NOUN
ma-61	190	7	,	,	PUNCT
ma-61	190	8	p̂	p̂	NOUN
ma-61	190	9	)	)	PUNCT
ma-61	190	10	≤	≤	NUM
ma-61	190	11	0	0	NUM
ma-61	190	12	,	,	PUNCT
ma-61	190	13	∀	∀	PUNCT
ma-61	190	14	q	q	PROPN
ma-61	190	15	∈	∈	PROPN
ma-61	190	16	c.	c.	NOUN
ma-61	190	17	(	(	PUNCT
ma-61	190	18	24	24	NUM
ma-61	190	19	)	)	PUNCT
ma-61	190	20	further	far	ADV
ma-61	190	21	for	for	ADP
ma-61	190	22	any	any	DET
ma-61	190	23	λ	λ	PROPN
ma-61	190	24	∈	∈	PROPN
ma-61	190	25	(	(	PUNCT
ma-61	190	26	0	0	NUM
ma-61	190	27	,	,	PUNCT
ma-61	190	28	1	1	NUM
ma-61	190	29	)	)	PUNCT
ma-61	190	30	and	and	CCONJ
ma-61	190	31	q	q	ADJ
ma-61	190	32	∈	∈	PROPN
ma-61	190	33	c	c	X
ma-61	190	34	,	,	PUNCT
ma-61	190	35	let	let	VERB
ma-61	190	36	qλ	qλ	NOUN
ma-61	190	37	=	=	PUNCT
ma-61	190	38	λq	λq	INTJ
ma-61	191	1	+	+	CCONJ
ma-61	191	2	(	(	PUNCT
ma-61	191	3	1	1	NUM
ma-61	191	4	−	−	PROPN
ma-61	191	5	λ)p̂	λ)p̂	PROPN
ma-61	191	6	,	,	PUNCT
ma-61	191	7	then	then	ADV
ma-61	191	8	qλ	qλ	PROPN
ma-61	191	9	∈	∈	PROPN
ma-61	191	10	c	c	PROPN
ma-61	192	1	and	and	CCONJ
ma-61	192	2	so	so	ADV
ma-61	192	3	we	we	PRON
ma-61	192	4	have	have	VERB
ma-61	192	5	f	f	PROPN
ma-61	192	6	(	(	PUNCT
ma-61	192	7	qλ	qλ	PROPN
ma-61	192	8	,	,	PUNCT
ma-61	192	9	p̂	p̂	X
ma-61	192	10	)	)	PUNCT
ma-61	192	11	≤	≤	NUM
ma-61	192	12	0	0	NUM
ma-61	192	13	.	.	PUNCT
ma-61	193	1	it	it	PRON
ma-61	193	2	follows	follow	VERB
ma-61	193	3	from	from	ADP
ma-61	193	4	the	the	DET
ma-61	193	5	assumption	assumption	NOUN
ma-61	193	6	1.1	1.1	NUM
ma-61	193	7	and	and	CCONJ
ma-61	193	8	(	(	PUNCT
ma-61	193	9	24	24	NUM
ma-61	193	10	)	)	PUNCT
ma-61	193	11	,	,	PUNCT
ma-61	193	12	that	that	SCONJ
ma-61	193	13	0	0	X
ma-61	193	14	=	=	SYM
ma-61	193	15	f	f	X
ma-61	193	16	(	(	PUNCT
ma-61	193	17	qλ	qλ	PROPN
ma-61	193	18	,	,	PUNCT
ma-61	193	19	qλ	qλ	PROPN
ma-61	193	20	)	)	PUNCT
ma-61	193	21	,	,	PUNCT
ma-61	193	22	≤	≤	PROPN
ma-61	193	23	λf	λf	PROPN
ma-61	193	24	(	(	PUNCT
ma-61	193	25	qλ	qλ	PROPN
ma-61	193	26	,	,	PUNCT
ma-61	193	27	q	q	PROPN
ma-61	193	28	)	)	PUNCT
ma-61	193	29	+	+	CCONJ
ma-61	193	30	(	(	PUNCT
ma-61	193	31	1−	1−	NUM
ma-61	193	32	λ)f	λ)f	X
ma-61	193	33	(	(	PUNCT
ma-61	193	34	qλ	qλ	PROPN
ma-61	193	35	,	,	PUNCT
ma-61	193	36	p̂	p̂	NOUN
ma-61	193	37	)	)	PUNCT
ma-61	193	38	,	,	PUNCT
ma-61	193	39	≤	≤	NUM
ma-61	193	40	λf	λf	PROPN
ma-61	193	41	(	(	PUNCT
ma-61	193	42	qλ	qλ	PROPN
ma-61	193	43	,	,	PUNCT
ma-61	193	44	q	q	NOUN
ma-61	193	45	)	)	PUNCT
ma-61	193	46	.	.	PUNCT
ma-61	194	1	this	this	PRON
ma-61	194	2	implies	imply	VERB
ma-61	194	3	that	that	SCONJ
ma-61	194	4	f	f	PROPN
ma-61	194	5	(	(	PUNCT
ma-61	194	6	qλ	qλ	PROPN
ma-61	194	7	,	,	PUNCT
ma-61	194	8	q	q	NOUN
ma-61	194	9	)	)	PUNCT
ma-61	194	10	≥	≥	NOUN
ma-61	194	11	0	0	NUM
ma-61	194	12	,	,	PUNCT
ma-61	194	13	∀λ	∀λ	X
ma-61	194	14	∈	∈	PROPN
ma-61	194	15	(	(	PUNCT
ma-61	194	16	0	0	NUM
ma-61	194	17	,	,	PUNCT
ma-61	194	18	1	1	NUM
ma-61	194	19	)	)	PUNCT
ma-61	194	20	.	.	PUNCT
ma-61	195	1	letting	let	VERB
ma-61	195	2	λ	λ	X
ma-61	195	3	→	→	X
ma-61	195	4	0	0	NUM
ma-61	195	5	+	+	NUM
ma-61	195	6	by	by	ADP
ma-61	195	7	assumption	assumption	NOUN
ma-61	195	8	1.1	1.1	NUM
ma-61	195	9	,	,	PUNCT
ma-61	195	10	we	we	PRON
ma-61	195	11	have	have	VERB
ma-61	195	12	f	f	X
ma-61	195	13	(	(	PUNCT
ma-61	195	14	p̂	p̂	X
ma-61	195	15	,	,	PUNCT
ma-61	195	16	q	q	NOUN
ma-61	195	17	)	)	PUNCT
ma-61	195	18	≥	≥	NOUN
ma-61	195	19	0	0	NUM
ma-61	195	20	,	,	PUNCT
ma-61	195	21	∀	∀	PUNCT
ma-61	195	22	q	q	PROPN
ma-61	195	23	∈	∈	PROPN
ma-61	195	24	c.	c.	NOUN
ma-61	195	25	this	this	PRON
ma-61	195	26	implies	imply	VERB
ma-61	195	27	that	that	SCONJ
ma-61	195	28	p̂	p̂	NOUN
ma-61	195	29	∈	∈	PROPN
ma-61	195	30	ep	ep	PROPN
ma-61	195	31	(	(	PUNCT
ma-61	195	32	f	f	PROPN
ma-61	195	33	)	)	PUNCT
ma-61	195	34	and	and	CCONJ
ma-61	195	35	hence	hence	ADV
ma-61	195	36	p̂	p̂	X
ma-61	195	37	∈	∈	PROPN
ma-61	195	38	ω	ω	X
ma-61	195	39	.	.	PUNCT
ma-61	196	1	this	this	PRON
ma-61	196	2	completes	complete	VERB
ma-61	196	3	theproof	theproof	NOUN
ma-61	196	4	.	.	PUNCT
ma-61	197	1	�	�	PROPN
ma-61	197	2	3	3	NUM
ma-61	197	3	.	.	PUNCT
ma-61	197	4	numerical	numerical	ADJ
ma-61	197	5	example	example	NOUN
ma-61	197	6	here	here	ADV
ma-61	197	7	we	we	PRON
ma-61	197	8	give	give	VERB
ma-61	197	9	numerical	numerical	ADJ
ma-61	197	10	examples	example	NOUN
ma-61	197	11	for	for	ADP
ma-61	197	12	supporting	support	VERB
ma-61	197	13	our	our	PRON
ma-61	197	14	main	main	ADJ
ma-61	197	15	results	result	NOUN
ma-61	197	16	.	.	PUNCT
ma-61	198	1	all	all	DET
ma-61	198	2	codes	code	NOUN
ma-61	198	3	are	be	AUX
ma-61	198	4	done	do	VERB
ma-61	198	5	by	by	ADP
ma-61	198	6	matlab2021a	matlab2021a	PROPN
ma-61	198	7	.	.	PUNCT
ma-61	199	1	example	example	NOUN
ma-61	199	2	3.1	3.1	NUM
ma-61	199	3	.	.	PUNCT
ma-61	200	1	set	set	VERB
ma-61	200	2	h	h	NOUN
ma-61	201	1	=	=	SYM
ma-61	201	2	r.	r.	PROPN
ma-61	201	3	let	let	VERB
ma-61	201	4	c	c	NOUN
ma-61	201	5	=	=	PUNCT
ma-61	202	1	[	[	X
ma-61	202	2	0	0	NUM
ma-61	202	3	+	+	ADJ
ma-61	202	4	∞	∞	NUM
ma-61	202	5	)	)	PUNCT
ma-61	202	6	.	.	PUNCT
ma-61	203	1	suppose	suppose	VERB
ma-61	203	2	t	t	NOUN
ma-61	203	3	:	:	PUNCT
ma-61	203	4	c	c	PROPN
ma-61	203	5	→	→	SYM
ma-61	203	6	h	h	NOUN
ma-61	203	7	,	,	PUNCT
ma-61	203	8	is	be	AUX
ma-61	203	9	defined	define	VERB
ma-61	203	10	by	by	ADP
ma-61	203	11	t	t	PROPN
ma-61	203	12	(	(	PUNCT
ma-61	203	13	p	p	NOUN
ma-61	203	14	)	)	PUNCT
ma-61	203	15	=	=	PUNCT
ma-61	204	1	p	p	NOUN
ma-61	204	2	3	3	NUM
ma-61	204	3	.	.	PUNCT
ma-61	205	1	it	it	PRON
ma-61	205	2	can	can	AUX
ma-61	205	3	be	be	AUX
ma-61	205	4	easily	easily	ADV
ma-61	205	5	seen	see	VERB
ma-61	205	6	that	that	SCONJ
ma-61	205	7	,	,	PUNCT
ma-61	205	8	here	here	ADV
ma-61	205	9	fix(t	fix(t	PROPN
ma-61	205	10	)	)	PUNCT
ma-61	206	1	=	=	PUNCT
ma-61	206	2	{	{	PUNCT
ma-61	206	3	0	0	NUM
ma-61	206	4	}	}	PUNCT
ma-61	206	5	.	.	PUNCT
ma-61	207	1	also	also	ADV
ma-61	207	2	,	,	PUNCT
ma-61	207	3	we	we	PRON
ma-61	207	4	define	define	VERB
ma-61	207	5	f	f	PROPN
ma-61	207	6	(	(	PUNCT
ma-61	207	7	s	s	PROPN
ma-61	207	8	,	,	PUNCT
ma-61	207	9	q	q	NOUN
ma-61	207	10	)	)	PUNCT
ma-61	207	11	=	=	NOUN
ma-61	207	12	3q2	3q2	NUM
ma-61	207	13	+	+	CCONJ
ma-61	207	14	2sq	2sq	ADJ
ma-61	207	15	−	−	PROPN
ma-61	207	16	5s2	5s2	NUM
ma-61	207	17	,	,	PUNCT
ma-61	207	18	it	it	PRON
ma-61	207	19	is	be	AUX
ma-61	207	20	easy	easy	ADJ
ma-61	207	21	to	to	PART
ma-61	207	22	check	check	VERB
ma-61	207	23	that	that	PRON
ma-61	207	24	f	f	PROPN
ma-61	207	25	satisfy	satisfy	VERB
ma-61	207	26	the	the	DET
ma-61	207	27	conditions	condition	NOUN
ma-61	207	28	of	of	ADP
ma-61	207	29	assumption	assumption	NOUN
ma-61	207	30	1.1	1.1	NUM
ma-61	207	31	.	.	PUNCT
ma-61	208	1	so	so	ADV
ma-61	208	2	,	,	PUNCT
ma-61	208	3	for	for	ADP
ma-61	208	4	rn	rn	NOUN
ma-61	208	5	=	=	SYM
ma-61	208	6	r	r	NOUN
ma-61	208	7	>	>	X
ma-61	208	8	0	0	NUM
ma-61	208	9	,	,	PUNCT
ma-61	208	10	t	t	PROPN
ma-61	208	11	fr	fr	NOUN
ma-61	208	12	(	(	PUNCT
ma-61	208	13	p	p	NOUN
ma-61	208	14	)	)	PUNCT
ma-61	208	15	is	be	AUX
ma-61	208	16	non	non	ADJ
ma-61	208	17	-	-	ADJ
ma-61	208	18	empty	empty	ADJ
ma-61	208	19	and	and	CCONJ
ma-61	208	20	single	single	ADV
ma-61	208	21	-	-	PUNCT
ma-61	208	22	valued	value	VERB
ma-61	208	23	for	for	ADP
ma-61	208	24	each	each	DET
ma-61	208	25	p	p	PROPN
ma-61	208	26	∈	∈	PROPN
ma-61	208	27	c.	c.	NOUN
ma-61	208	28	hence	hence	ADV
ma-61	208	29	for	for	ADP
ma-61	208	30	r	r	NOUN
ma-61	208	31	>	>	X
ma-61	208	32	0	0	NUM
ma-61	208	33	,	,	PUNCT
ma-61	208	34	there	there	PRON
ma-61	208	35	exists	exist	VERB
ma-61	208	36	s	s	PROPN
ma-61	208	37	∈	∈	NOUN
ma-61	208	38	c	c	NOUN
ma-61	208	39	such	such	ADJ
ma-61	209	1	that	that	SCONJ
ma-61	209	2	f	f	PROPN
ma-61	209	3	(	(	PUNCT
ma-61	209	4	s	s	PROPN
ma-61	209	5	,	,	PUNCT
ma-61	209	6	q	q	NOUN
ma-61	209	7	)	)	PUNCT
ma-61	209	8	+	+	CCONJ
ma-61	209	9	1	1	NUM
ma-61	209	10	r	r	NOUN
ma-61	209	11	〈	〈	PROPN
ma-61	209	12	q	q	NOUN
ma-61	209	13	−	−	PROPN
ma-61	209	14	s	s	PROPN
ma-61	209	15	,	,	PUNCT
ma-61	209	16	s	s	VERB
ma-61	209	17	−	−	PROPN
ma-61	209	18	p	p	X
ma-61	209	19	〉	〉	PROPN
ma-61	209	20	≥	≥	NOUN
ma-61	209	21	0	0	NUM
ma-61	209	22	∀	∀	NOUN
ma-61	210	1	q	q	X
ma-61	210	2	∈	∈	PROPN
ma-61	210	3	c	c	NOUN
ma-61	210	4	,	,	PUNCT
ma-61	210	5	which	which	PRON
ma-61	210	6	is	be	AUX
ma-61	210	7	equivalent	equivalent	ADJ
ma-61	210	8	to	to	ADP
ma-61	210	9	3rq2	3rq2	NUM
ma-61	210	10	+	+	CCONJ
ma-61	210	11	(	(	PUNCT
ma-61	210	12	s	s	VERB
ma-61	210	13	−	−	PROPN
ma-61	210	14	p	p	NOUN
ma-61	210	15	+	+	NUM
ma-61	210	16	2r	2r	NUM
ma-61	210	17	s)q	s)q	PUNCT
ma-61	211	1	+	+	CCONJ
ma-61	211	2	(	(	PUNCT
ma-61	211	3	ps	ps	INTJ
ma-61	211	4	−	−	PROPN
ma-61	211	5	5r	5r	NUM
ma-61	211	6	s2	s2	NOUN
ma-61	211	7	−	−	PROPN
ma-61	211	8	s2	s2	PROPN
ma-61	211	9	)	)	PUNCT
ma-61	211	10	≥	≥	NOUN
ma-61	211	11	0	0	NUM
ma-61	211	12	,	,	PUNCT
ma-61	211	13	∀	∀	PUNCT
ma-61	211	14	q	q	PROPN
ma-61	211	15	∈	∈	PROPN
ma-61	211	16	c.	c.	NOUN
ma-61	211	17	after	after	ADP
ma-61	211	18	solving	solve	VERB
ma-61	211	19	the	the	DET
ma-61	211	20	above	above	ADJ
ma-61	211	21	inequality	inequality	NOUN
ma-61	211	22	,	,	PUNCT
ma-61	211	23	we	we	PRON
ma-61	211	24	get	get	VERB
ma-61	211	25	s	s	NOUN
ma-61	211	26	=	=	PUNCT
ma-61	211	27	p	p	NOUN
ma-61	211	28	1	1	NUM
ma-61	211	29	+	+	NOUN
ma-61	211	30	8r	8r	NUM
ma-61	211	31	for	for	ADP
ma-61	211	32	each	each	DET
ma-61	211	33	r	r	NOUN
ma-61	211	34	>	>	X
ma-61	211	35	0	0	PUNCT
ma-61	212	1	i.e.	i.e.	X
ma-61	212	2	t	t	X
ma-61	212	3	fr	fr	INTJ
ma-61	212	4	(	(	PUNCT
ma-61	212	5	p	p	X
ma-61	212	6	)	)	PUNCT
ma-61	212	7	=	=	PUNCT
ma-61	213	1	p	p	VERB
ma-61	213	2	1	1	NUM
ma-61	213	3	+	+	NOUN
ma-61	213	4	8r	8r	NUM
ma-61	213	5	for	for	ADP
ma-61	213	6	each	each	DET
ma-61	213	7	r	r	NOUN
ma-61	213	8	>	>	X
ma-61	213	9	0	0	X
ma-61	213	10	.	.	PUNCT
ma-61	214	1	it	it	PRON
ma-61	214	2	can	can	AUX
ma-61	214	3	be	be	AUX
ma-61	214	4	easily	easily	ADV
ma-61	214	5	seen	see	VERB
ma-61	214	6	that	that	SCONJ
ma-61	214	7	here	here	ADV
ma-61	214	8	ep	ep	PROPN
ma-61	214	9	(	(	PUNCT
ma-61	214	10	f	f	PROPN
ma-61	214	11	)	)	PUNCT
ma-61	214	12	=	=	PUNCT
ma-61	214	13	{	{	PUNCT
ma-61	214	14	0	0	NUM
ma-61	214	15	}	}	PUNCT
ma-61	214	16	.	.	PUNCT
ma-61	215	1	this	this	PRON
ma-61	215	2	implies	imply	VERB
ma-61	215	3	that	that	SCONJ
ma-61	215	4	ω	ω	X
ma-61	215	5	:	:	PUNCT
ma-61	215	6	=	=	PUNCT
ma-61	215	7	fix(t	fix(t	PROPN
ma-61	215	8	)	)	PUNCT
ma-61	215	9	∩ep	∩ep	NOUN
ma-61	215	10	(	(	PUNCT
ma-61	215	11	f	f	NOUN
ma-61	215	12	)	)	PUNCT
ma-61	215	13	=	=	PUNCT
ma-61	215	14	{	{	PUNCT
ma-61	215	15	0	0	NUM
ma-61	215	16	}	}	PUNCT
ma-61	215	17	.	.	PUNCT
ma-61	216	1	now	now	ADV
ma-61	216	2	,	,	PUNCT
ma-61	216	3	let	let	VERB
ma-61	216	4	us	we	PRON
ma-61	216	5	choose	choose	VERB
ma-61	216	6	r	r	NOUN
ma-61	216	7	=	=	SYM
ma-61	216	8	1	1	NUM
ma-61	216	9	8	8	NUM
ma-61	216	10	,	,	PUNCT
ma-61	216	11	and	and	CCONJ
ma-61	216	12	{	{	PUNCT
ma-61	216	13	αn	αn	NOUN
ma-61	216	14	}	}	PUNCT
ma-61	216	15	=	=	SYM
ma-61	216	16	1	1	NUM
ma-61	216	17	(	(	PUNCT
ma-61	216	18	n+6	n+6	NUM
ma-61	216	19	)	)	PUNCT
ma-61	216	20	.	.	PUNCT
ma-61	217	1	{	{	PUNCT
ma-61	217	2	αn	αn	NOUN
ma-61	217	3	}	}	PUNCT
ma-61	217	4	satisfy	satisfy	VERB
ma-61	217	5	the	the	DET
ma-61	217	6	conditions	condition	NOUN
ma-61	217	7	of	of	ADP
ma-61	217	8	main	main	ADJ
ma-61	217	9	result	result	NOUN
ma-61	217	10	.	.	PUNCT
ma-61	218	1	table	table	NOUN
ma-61	218	2	.	.	PUNCT
ma-61	219	1	for	for	ADP
ma-61	219	2	different	different	ADJ
ma-61	219	3	initial	initial	ADJ
ma-61	219	4	value	value	NOUN
ma-61	219	5	,	,	PUNCT
ma-61	219	6	we	we	PRON
ma-61	219	7	present	present	VERB
ma-61	219	8	a	a	DET
ma-61	219	9	table	table	NOUN
ma-61	219	10	of	of	ADP
ma-61	219	11	iterations	iteration	NOUN
ma-61	219	12	here	here	ADV
ma-61	219	13	.	.	PUNCT
ma-61	220	1	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	220	2	eur	eur	PROPN
ma-61	220	3	.	.	PUNCT
ma-61	221	1	j.	j.	PROPN
ma-61	221	2	math	math	PROPN
ma-61	221	3	.	.	PUNCT
ma-61	222	1	anal	anal	PROPN
ma-61	222	2	.	.	PUNCT
ma-61	223	1	10.28924	10.28924	NUM
ma-61	223	2	/	/	SYM
ma-61	223	3	ada	ada	PROPN
ma-61	223	4	/	/	SYM
ma-61	223	5	ma.2.6	ma.2.6	PROPN
ma-61	223	6	9	9	NUM
ma-61	223	7	no	no	NOUN
ma-61	223	8	.	.	PUNCT
ma-61	223	9	of	of	ADP
ma-61	223	10	iterations	iteration	NOUN
ma-61	223	11	x0	x0	PROPN
ma-61	223	12	=	=	PUNCT
ma-61	223	13	1	1	NUM
ma-61	223	14	x0	x0	NOUN
ma-61	223	15	=	=	SYM
ma-61	223	16	−11	−11	NOUN
ma-61	223	17	1.000000	1.000000	NUM
ma-61	223	18	-1.0000002	-1.0000002	NOUN
ma-61	223	19	0.150794	0.150794	NUM
ma-61	223	20	-0.1419233	-0.1419233	NOUN
ma-61	223	21	0.023038	0.023038	NUM
ma-61	223	22	-0.0204074	-0.0204074	NOUN
ma-61	223	23	0.003555	0.003555	NUM
ma-61	223	24	-0.0029645	-0.0029645	NOUN
ma-61	223	25	0.000553	0.000553	NUM
ma-61	223	26	-0.0004346	-0.0004346	NOUN
ma-61	223	27	0.000087	0.000087	NUM
ma-61	223	28	-0.0000647	-0.0000647	NOUN
ma-61	223	29	0.000014	0.000014	NUM
ma-61	223	30	-0.0000098	-0.0000098	NOUN
ma-61	223	31	0.000002	0.000002	NUM
ma-61	223	32	-0.0000019	-0.0000019	X
ma-61	223	33	0.000000	0.000000	NUM
ma-61	223	34	0.000000	0.000000	NUM
ma-61	223	35	0	0	NUM
ma-61	223	36	2	2	NUM
ma-61	223	37	4	4	NUM
ma-61	223	38	6	6	NUM
ma-61	223	39	8	8	NUM
ma-61	223	40	10	10	NUM
ma-61	223	41	12	12	NUM
ma-61	223	42	14	14	NUM
ma-61	223	43	16	16	NUM
ma-61	223	44	18	18	NUM
ma-61	223	45	20	20	NUM
ma-61	223	46	number	number	NOUN
ma-61	223	47	of	of	ADP
ma-61	223	48	iterations	iteration	NOUN
ma-61	223	49	-1	-1	ADP
ma-61	223	50	-0.8	-0.8	PROPN
ma-61	223	51	-0.6	-0.6	X
ma-61	223	52	-0.4	-0.4	X
ma-61	223	53	-0.2	-0.2	PROPN
ma-61	223	54	0	0	NUM
ma-61	223	55	0.2	0.2	NUM
ma-61	223	56	0.4	0.4	NUM
ma-61	223	57	0.6	0.6	NUM
ma-61	223	58	0.8	0.8	NUM
ma-61	223	59	1	1	NUM
ma-61	223	60	x	x	SYM
ma-61	223	61	n	n	PROPN
ma-61	223	62	x	x	SYM
ma-61	223	63	0	0	PUNCT
ma-61	224	1	=	=	SYM
ma-61	224	2	1	1	NUM
ma-61	224	3	x	x	SYM
ma-61	224	4	0	0	NUM
ma-61	224	5	=	=	SYM
ma-61	224	6	-1	-1	NOUN
ma-61	224	7	figure	figure	NOUN
ma-61	224	8	1	1	NUM
ma-61	224	9	.	.	PUNCT
ma-61	224	10	graphical	graphical	ADJ
ma-61	224	11	representation	representation	NOUN
ma-61	224	12	of	of	ADP
ma-61	224	13	sequence	sequence	NOUN
ma-61	224	14	{	{	PUNCT
ma-61	224	15	xn	xn	NOUN
ma-61	224	16	}	}	PUNCT
ma-61	224	17	for	for	ADP
ma-61	224	18	different	different	ADJ
ma-61	224	19	choices	choice	NOUN
ma-61	224	20	of	of	ADP
ma-61	224	21	initialvalue	initialvalue	NOUN
ma-61	224	22	x0	x0	PROPN
ma-61	224	23	.	.	PUNCT
ma-61	225	1	references	reference	NOUN
ma-61	225	2	[	[	X
ma-61	225	3	1	1	NUM
ma-61	225	4	]	]	PUNCT
ma-61	225	5	a.	a.	NOUN
ma-61	225	6	moudafi	moudafi	PROPN
ma-61	225	7	,	,	PUNCT
ma-61	225	8	m.	m.	NOUN
ma-61	225	9	théra	théra	NOUN
ma-61	225	10	,	,	PUNCT
ma-61	225	11	proximal	proximal	ADJ
ma-61	225	12	and	and	CCONJ
ma-61	225	13	dynamical	dynamical	ADJ
ma-61	225	14	approaches	approach	NOUN
ma-61	225	15	to	to	ADP
ma-61	225	16	equilibrium	equilibrium	NOUN
ma-61	225	17	problems	problem	NOUN
ma-61	225	18	,	,	PUNCT
ma-61	225	19	in	in	ADP
ma-61	225	20	:	:	PUNCT
ma-61	225	21	m.	m.	NOUN
ma-61	225	22	théra	théra	PROPN
ma-61	225	23	,	,	PUNCT
ma-61	225	24	r.	r.	PROPN
ma-61	225	25	tichatschke(eds	tichatschke(eds	PROPN
ma-61	225	26	.	.	PUNCT
ma-61	225	27	)	)	PUNCT
ma-61	225	28	,	,	PUNCT
ma-61	225	29	ill	ill	ADV
ma-61	225	30	-	-	PUNCT
ma-61	225	31	posed	pose	VERB
ma-61	225	32	variational	variational	ADJ
ma-61	225	33	problems	problem	NOUN
ma-61	225	34	and	and	CCONJ
ma-61	225	35	regularization	regularization	NOUN
ma-61	225	36	techniques	technique	NOUN
ma-61	225	37	,	,	PUNCT
ma-61	225	38	springer	springer	NOUN
ma-61	225	39	berlin	berlin	PROPN
ma-61	225	40	heidelberg	heidelberg	PROPN
ma-61	225	41	,	,	PUNCT
ma-61	225	42	berlin	berlin	PROPN
ma-61	225	43	,	,	PUNCT
ma-61	225	44	heidel	heidel	PROPN
ma-61	225	45	-	-	PUNCT
ma-61	225	46	berg	berg	PROPN
ma-61	225	47	,	,	PUNCT
ma-61	225	48	1999	1999	NUM
ma-61	225	49	:	:	PUNCT
ma-61	225	50	pp	pp	ADP
ma-61	225	51	.	.	PUNCT
ma-61	226	1	187–201	187–201	NUM
ma-61	226	2	.	.	PUNCT
ma-61	226	3	https://doi.org/10.1007/978-3-642-45780-7_12.[2	https://doi.org/10.1007/978-3-642-45780-7_12.[2	X
ma-61	226	4	]	]	X
ma-61	226	5	a.	a.	NOUN
ma-61	226	6	moudafi	moudafi	PROPN
ma-61	226	7	,	,	PUNCT
ma-61	226	8	viscosity	viscosity	NOUN
ma-61	226	9	approximation	approximation	NOUN
ma-61	226	10	methods	method	NOUN
ma-61	226	11	for	for	ADP
ma-61	226	12	fixed	fix	VERB
ma-61	226	13	-	-	PUNCT
ma-61	226	14	points	point	NOUN
ma-61	226	15	problems	problem	NOUN
ma-61	226	16	,	,	PUNCT
ma-61	226	17	j.	j.	PROPN
ma-61	226	18	math	math	PROPN
ma-61	226	19	.	.	PUNCT
ma-61	227	1	anal	anal	PROPN
ma-61	227	2	.	.	PUNCT
ma-61	227	3	appl	appl	PROPN
ma-61	227	4	.	.	PUNCT
ma-61	228	1	241	241	NUM
ma-61	228	2	(	(	PUNCT
ma-61	228	3	2000	2000	NUM
ma-61	228	4	)	)	PUNCT
ma-61	228	5	46–55	46–55	NUM
ma-61	228	6	.	.	PUNCT
ma-61	229	1	https://doi.org/10.1006/jmaa.1999.6615	https://doi.org/10.1006/jmaa.1999.6615	NOUN
ma-61	229	2	.	.	PUNCT
ma-61	230	1	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	230	2	https://doi.org/10.1007/978-3-642-45780-7_12	https://doi.org/10.1007/978-3-642-45780-7_12	PROPN
ma-61	230	3	https://doi.org/10.1006/jmaa.1999.6615	https://doi.org/10.1006/jmaa.1999.6615	PROPN
ma-61	230	4	eur	eur	NOUN
ma-61	230	5	.	.	PUNCT
ma-61	231	1	j.	j.	PROPN
ma-61	231	2	math	math	PROPN
ma-61	231	3	.	.	PUNCT
ma-61	232	1	anal	anal	PROPN
ma-61	232	2	.	.	PUNCT
ma-61	233	1	10.28924	10.28924	NUM
ma-61	233	2	/	/	SYM
ma-61	233	3	ada	ada	PROPN
ma-61	233	4	/	/	SYM
ma-61	233	5	ma.2.6	ma.2.6	PROPN
ma-61	233	6	10	10	NUM
ma-61	234	1	[	[	X
ma-61	234	2	3	3	NUM
ma-61	234	3	]	]	X
ma-61	234	4	s.d	s.d	PROPN
ma-61	234	5	.	.	PROPN
ma-61	234	6	flam	flam	PROPN
ma-61	234	7	,	,	PUNCT
ma-61	234	8	a.s	a.s	PROPN
ma-61	234	9	.	.	PROPN
ma-61	234	10	antipin	antipin	PROPN
ma-61	234	11	,	,	PUNCT
ma-61	234	12	equilibrium	equilibrium	NOUN
ma-61	234	13	programming	programming	NOUN
ma-61	234	14	using	use	VERB
ma-61	234	15	proximal	proximal	ADJ
ma-61	234	16	-	-	PUNCT
ma-61	234	17	like	like	ADJ
ma-61	234	18	algorithms	algorithm	NOUN
ma-61	234	19	,	,	PUNCT
ma-61	234	20	math	math	NOUN
ma-61	234	21	.	.	PUNCT
ma-61	235	1	program	program	NOUN
ma-61	235	2	.	.	PUNCT
ma-61	236	1	78	78	NUM
ma-61	236	2	(	(	PUNCT
ma-61	236	3	1996	1996	NUM
ma-61	236	4	)	)	PUNCT
ma-61	237	1	29–41	29–41	NUM
ma-61	237	2	.	.	PUNCT
ma-61	238	1	https://doi.org/10.1007/bf02614504.[4	https://doi.org/10.1007/bf02614504.[4	X
ma-61	238	2	]	]	X
ma-61	238	3	d.	d.	PROPN
ma-61	238	4	r.	r.	PROPN
ma-61	238	5	sahu	sahu	PROPN
ma-61	238	6	,	,	PUNCT
ma-61	238	7	applications	application	NOUN
ma-61	238	8	of	of	ADP
ma-61	238	9	the	the	DET
ma-61	238	10	s	s	NOUN
ma-61	238	11	-	-	PUNCT
ma-61	238	12	iteration	iteration	NOUN
ma-61	238	13	process	process	NOUN
ma-61	238	14	to	to	ADP
ma-61	238	15	constrained	constrain	VERB
ma-61	238	16	minimization	minimization	NOUN
ma-61	238	17	problems	problem	NOUN
ma-61	238	18	and	and	CCONJ
ma-61	238	19	split	split	ADJ
ma-61	238	20	feasibilityproblems	feasibilityproblem	NOUN
ma-61	238	21	,	,	PUNCT
ma-61	238	22	fixed	fix	VERB
ma-61	238	23	point	point	NOUN
ma-61	238	24	theory	theory	NOUN
ma-61	238	25	,	,	PUNCT
ma-61	238	26	12	12	NUM
ma-61	238	27	(	(	PUNCT
ma-61	238	28	2011	2011	NUM
ma-61	238	29	)	)	PUNCT
ma-61	238	30	187–204.[5	187–204.[5	NUM
ma-61	238	31	]	]	X
ma-61	238	32	d.r	d.r	PROPN
ma-61	238	33	.	.	PROPN
ma-61	238	34	sahu	sahu	PROPN
ma-61	238	35	,	,	PUNCT
ma-61	238	36	a.	a.	NOUN
ma-61	238	37	pitea	pitea	NOUN
ma-61	238	38	,	,	PUNCT
ma-61	238	39	m.	m.	PROPN
ma-61	238	40	verma	verma	PROPN
ma-61	238	41	,	,	PUNCT
ma-61	238	42	a	a	DET
ma-61	238	43	new	new	ADJ
ma-61	238	44	iteration	iteration	NOUN
ma-61	238	45	technique	technique	NOUN
ma-61	238	46	for	for	ADP
ma-61	238	47	nonlinear	nonlinear	ADJ
ma-61	238	48	operators	operator	NOUN
ma-61	238	49	as	as	ADP
ma-61	238	50	concerns	concern	NOUN
ma-61	238	51	convex	convex	VERB
ma-61	238	52	programmingand	programmingand	NOUN
ma-61	238	53	feasibility	feasibility	NOUN
ma-61	238	54	problems	problem	NOUN
ma-61	238	55	,	,	PUNCT
ma-61	238	56	numer	numer	PROPN
ma-61	238	57	.	.	PROPN
ma-61	238	58	algor	algor	PROPN
ma-61	238	59	.	.	PUNCT
ma-61	239	1	83	83	NUM
ma-61	239	2	(	(	PUNCT
ma-61	239	3	2020	2020	NUM
ma-61	239	4	)	)	PUNCT
ma-61	240	1	421–449	421–449	NUM
ma-61	240	2	.	.	PUNCT
ma-61	241	1	https://doi.org/10.1007/s11075-019-00688-9.[6	https://doi.org/10.1007/s11075-019-00688-9.[6	PROPN
ma-61	241	2	]	]	PUNCT
ma-61	241	3	h.	h.	PROPN
ma-61	241	4	mahdioui	mahdioui	PROPN
ma-61	241	5	,	,	PUNCT
ma-61	241	6	o.	o.	PROPN
ma-61	241	7	chadli	chadli	PROPN
ma-61	241	8	,	,	PUNCT
ma-61	241	9	on	on	ADP
ma-61	241	10	a	a	DET
ma-61	241	11	system	system	NOUN
ma-61	241	12	of	of	ADP
ma-61	241	13	generalized	generalized	ADJ
ma-61	241	14	mixed	mixed	ADJ
ma-61	241	15	equilibrium	equilibrium	NOUN
ma-61	241	16	problems	problem	NOUN
ma-61	241	17	involving	involve	VERB
ma-61	241	18	variational	variational	ADJ
ma-61	241	19	-	-	PUNCT
ma-61	241	20	like	like	ADJ
ma-61	241	21	inequalitiesin	inequalitiesin	NOUN
ma-61	241	22	banach	banach	NOUN
ma-61	241	23	spaces	space	VERB
ma-61	241	24	:	:	PUNCT
ma-61	241	25	existence	existence	NOUN
ma-61	241	26	and	and	CCONJ
ma-61	241	27	algorithmic	algorithmic	ADJ
ma-61	241	28	aspects	aspect	NOUN
ma-61	241	29	,	,	PUNCT
ma-61	241	30	adv	adv	PROPN
ma-61	241	31	.	.	PUNCT
ma-61	241	32	oper	oper	PROPN
ma-61	241	33	.	.	PUNCT
ma-61	242	1	res	res	PROPN
ma-61	242	2	.	.	PROPN
ma-61	242	3	2012	2012	NUM
ma-61	242	4	(	(	PUNCT
ma-61	242	5	2012	2012	NUM
ma-61	242	6	)	)	PUNCT
ma-61	242	7	843486	843486	NUM
ma-61	242	8	.	.	PUNCT
ma-61	243	1	https://doi.org/10	https://doi.org/10	PROPN
ma-61	243	2	.	.	PUNCT
ma-61	244	1	1155/2012/843486.[7	1155/2012/843486.[7	NUM
ma-61	244	2	]	]	X
ma-61	244	3	e.	e.	PROPN
ma-61	244	4	blum	blum	PROPN
ma-61	244	5	,	,	PUNCT
ma-61	244	6	w.	w.	PROPN
ma-61	244	7	oettli	oettli	PROPN
ma-61	244	8	,	,	PUNCT
ma-61	244	9	from	from	ADP
ma-61	244	10	optimization	optimization	NOUN
ma-61	244	11	and	and	CCONJ
ma-61	244	12	variational	variational	ADJ
ma-61	244	13	inequalities	inequality	NOUN
ma-61	244	14	to	to	ADP
ma-61	244	15	equilibrium	equilibrium	NOUN
ma-61	244	16	problems	problem	NOUN
ma-61	244	17	.	.	PUNCT
ma-61	245	1	the	the	DET
ma-61	245	2	math	math	NOUN
ma-61	245	3	.	.	PUNCT
ma-61	246	1	students	student	NOUN
ma-61	246	2	,	,	PUNCT
ma-61	246	3	63(1994	63(1994	NUM
ma-61	246	4	)	)	PUNCT
ma-61	246	5	,	,	PUNCT
ma-61	246	6	123–145.[8	123–145.[8	NUM
ma-61	246	7	]	]	X
ma-61	246	8	f.	f.	PROPN
ma-61	246	9	cianciaruso	cianciaruso	PROPN
ma-61	246	10	,	,	PUNCT
ma-61	246	11	g.	g.	PROPN
ma-61	246	12	marino	marino	PROPN
ma-61	246	13	,	,	PUNCT
ma-61	246	14	l.	l.	PROPN
ma-61	246	15	muglia	muglia	PROPN
ma-61	246	16	,	,	PUNCT
ma-61	246	17	y.	y.	PROPN
ma-61	246	18	yao	yao	PROPN
ma-61	246	19	,	,	PUNCT
ma-61	246	20	a	a	DET
ma-61	246	21	hybrid	hybrid	ADJ
ma-61	246	22	projection	projection	NOUN
ma-61	246	23	algorithm	algorithm	NOUN
ma-61	246	24	for	for	ADP
ma-61	246	25	finding	find	VERB
ma-61	246	26	solutions	solution	NOUN
ma-61	246	27	of	of	ADP
ma-61	246	28	mixedequilibrium	mixedequilibrium	NOUN
ma-61	246	29	problem	problem	NOUN
ma-61	246	30	and	and	CCONJ
ma-61	246	31	variational	variational	ADJ
ma-61	246	32	inequality	inequality	NOUN
ma-61	246	33	problem	problem	NOUN
ma-61	246	34	,	,	PUNCT
ma-61	246	35	fixed	fix	VERB
ma-61	246	36	point	point	NOUN
ma-61	246	37	theory	theory	NOUN
ma-61	246	38	appl	appl	NOUN
ma-61	246	39	.	.	PUNCT
ma-61	247	1	2010	2010	NUM
ma-61	247	2	(	(	PUNCT
ma-61	247	3	2010	2010	NUM
ma-61	247	4	)	)	PUNCT
ma-61	248	1	383740.https://doi.org/10.1155/2010/383740.[9	383740.https://doi.org/10.1155/2010/383740.[9	NOUN
ma-61	248	2	]	]	X
ma-61	248	3	h.h	h.h	PROPN
ma-61	248	4	.	.	PROPN
ma-61	248	5	bauschke	bauschke	PROPN
ma-61	248	6	,	,	PUNCT
ma-61	248	7	p.l	p.l	PROPN
ma-61	248	8	.	.	PROPN
ma-61	248	9	combettes	combette	NOUN
ma-61	248	10	,	,	PUNCT
ma-61	248	11	convex	convex	VERB
ma-61	248	12	analysis	analysis	NOUN
ma-61	248	13	and	and	CCONJ
ma-61	248	14	monotone	monotone	ADJ
ma-61	248	15	operator	operator	NOUN
ma-61	248	16	theory	theory	NOUN
ma-61	248	17	in	in	ADP
ma-61	248	18	hilbert	hilbert	PROPN
ma-61	248	19	spaces	space	NOUN
ma-61	248	20	,	,	PUNCT
ma-61	248	21	2nded	2nded	NUM
ma-61	248	22	.	.	NOUN
ma-61	248	23	2017	2017	NUM
ma-61	248	24	,	,	PUNCT
ma-61	248	25	springer	springer	NOUN
ma-61	248	26	international	international	ADJ
ma-61	248	27	publishing	publishing	NOUN
ma-61	248	28	:	:	PUNCT
ma-61	248	29	imprint	imprint	NOUN
ma-61	248	30	:	:	PUNCT
ma-61	248	31	springer	springer	NOUN
ma-61	248	32	,	,	PUNCT
ma-61	248	33	cham	cham	PROPN
ma-61	248	34	,	,	PUNCT
ma-61	248	35	2017	2017	NUM
ma-61	248	36	.	.	PUNCT
ma-61	249	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-61	249	2	978	978	NUM
ma-61	249	3	-	-	SYM
ma-61	249	4	3	3	NUM
ma-61	249	5	-	-	NUM
ma-61	249	6	319	319	NUM
ma-61	249	7	-	-	PUNCT
ma-61	249	8	48311	48311	NUM
ma-61	249	9	-	-	PUNCT
ma-61	249	10	5.[10	5.[10	NUM
ma-61	249	11	]	]	PUNCT
ma-61	249	12	h.-k	h.-k	PROPN
ma-61	249	13	.	.	PUNCT
ma-61	250	1	xu	xu	INTJ
ma-61	250	2	,	,	PUNCT
ma-61	250	3	viscosity	viscosity	NOUN
ma-61	250	4	approximation	approximation	NOUN
ma-61	250	5	methods	method	NOUN
ma-61	250	6	for	for	ADP
ma-61	250	7	nonexpansive	nonexpansive	ADJ
ma-61	250	8	mappings	mapping	NOUN
ma-61	250	9	,	,	PUNCT
ma-61	250	10	j.	j.	PROPN
ma-61	250	11	math	math	PROPN
ma-61	250	12	.	.	PUNCT
ma-61	251	1	anal	anal	PROPN
ma-61	251	2	.	.	PUNCT
ma-61	251	3	appl.298	appl.298	PROPN
ma-61	251	4	(	(	PUNCT
ma-61	251	5	2004	2004	NUM
ma-61	251	6	)	)	PUNCT
ma-61	252	1	279–291	279–291	NUM
ma-61	252	2	.	.	PUNCT
ma-61	253	1	https://doi.org/10.1016/j.jmaa.2004.04.059.[11	https://doi.org/10.1016/j.jmaa.2004.04.059.[11	ADV
ma-61	253	2	]	]	PUNCT
ma-61	253	3	h.-k	h.-k	PROPN
ma-61	253	4	.	.	PUNCT
ma-61	254	1	xu	xu	INTJ
ma-61	254	2	,	,	PUNCT
ma-61	254	3	iterative	iterative	NOUN
ma-61	254	4	algorithms	algorithm	NOUN
ma-61	254	5	for	for	ADP
ma-61	254	6	nonlinear	nonlinear	ADJ
ma-61	254	7	operators	operator	NOUN
ma-61	254	8	,	,	PUNCT
ma-61	254	9	j.	j.	PROPN
ma-61	254	10	lond	lond	PROPN
ma-61	254	11	.	.	PUNCT
ma-61	255	1	math	math	PROPN
ma-61	255	2	.	.	PUNCT
ma-61	256	1	soc	soc	PROPN
ma-61	256	2	.	.	PUNCT
ma-61	257	1	66	66	NUM
ma-61	257	2	(	(	PUNCT
ma-61	257	3	2002	2002	NUM
ma-61	257	4	)	)	PUNCT
ma-61	258	1	240–256	240–256	NUM
ma-61	258	2	.	.	PUNCT
ma-61	258	3	https://doi.org/	https://doi.org/	VERB
ma-61	258	4	10.1112	10.1112	NUM
ma-61	258	5	/	/	SYM
ma-61	258	6	s0024610702003332.[12	s0024610702003332.[12	PROPN
ma-61	258	7	]	]	X
ma-61	258	8	p.l	p.l	PROPN
ma-61	258	9	.	.	PROPN
ma-61	258	10	combettes	combettes	PROPN
ma-61	258	11	,	,	PUNCT
ma-61	258	12	s.a	s.a	PROPN
ma-61	258	13	.	.	PROPN
ma-61	258	14	hirstoaga	hirstoaga	PROPN
ma-61	258	15	,	,	PUNCT
ma-61	258	16	equilibrium	equilibrium	NOUN
ma-61	258	17	programming	programming	NOUN
ma-61	258	18	in	in	ADP
ma-61	258	19	hilbert	hilbert	PROPN
ma-61	258	20	spaces	space	NOUN
ma-61	258	21	,	,	PUNCT
ma-61	258	22	j.	j.	PROPN
ma-61	258	23	nonlinear	nonlinear	PROPN
ma-61	258	24	convex	convex	PROPN
ma-61	258	25	anal	anal	NOUN
ma-61	258	26	.	.	PUNCT
ma-61	259	1	6	6	NUM
ma-61	259	2	(	(	PUNCT
ma-61	259	3	2005)117–136.[13	2005)117–136.[13	NOUN
ma-61	259	4	]	]	PUNCT
ma-61	259	5	q.	q.	PROPN
ma-61	259	6	zhang	zhang	PROPN
ma-61	259	7	,	,	PUNCT
ma-61	259	8	c.	c.	PROPN
ma-61	259	9	cheng	cheng	PROPN
ma-61	259	10	,	,	PUNCT
ma-61	259	11	strong	strong	ADJ
ma-61	259	12	convergence	convergence	NOUN
ma-61	259	13	theorem	theorem	NOUN
ma-61	259	14	for	for	ADP
ma-61	259	15	a	a	DET
ma-61	259	16	family	family	NOUN
ma-61	259	17	of	of	ADP
ma-61	259	18	lipschitz	lipschitz	VERB
ma-61	259	19	pseudocontractive	pseudocontractive	ADJ
ma-61	259	20	mappings	mapping	NOUN
ma-61	259	21	in	in	ADP
ma-61	259	22	a	a	DET
ma-61	259	23	hilbertspace	hilbertspace	NOUN
ma-61	259	24	,	,	PUNCT
ma-61	259	25	math	math	NOUN
ma-61	259	26	.	.	PUNCT
ma-61	260	1	computer	computer	NOUN
ma-61	260	2	model	model	NOUN
ma-61	260	3	.	.	PUNCT
ma-61	261	1	48	48	NUM
ma-61	261	2	(	(	PUNCT
ma-61	261	3	2008	2008	NUM
ma-61	261	4	)	)	PUNCT
ma-61	262	1	480–485	480–485	NUM
ma-61	262	2	.	.	PUNCT
ma-61	263	1	https://doi.org/10.1016/j.mcm.2007.09.014.[14	https://doi.org/10.1016/j.mcm.2007.09.014.[14	PROPN
ma-61	263	2	]	]	PUNCT
ma-61	263	3	s.	s.	PROPN
ma-61	263	4	takahashi	takahashi	PROPN
ma-61	263	5	,	,	PUNCT
ma-61	263	6	w.	w.	PROPN
ma-61	263	7	takahashi	takahashi	PROPN
ma-61	263	8	,	,	PUNCT
ma-61	263	9	viscosity	viscosity	NOUN
ma-61	263	10	approximation	approximation	NOUN
ma-61	263	11	methods	method	NOUN
ma-61	263	12	for	for	ADP
ma-61	263	13	equilibrium	equilibrium	NOUN
ma-61	263	14	problems	problem	NOUN
ma-61	263	15	and	and	CCONJ
ma-61	263	16	fixed	fix	VERB
ma-61	263	17	point	point	NOUN
ma-61	263	18	problems	problem	NOUN
ma-61	263	19	inhilbert	inhilbert	PROPN
ma-61	263	20	spaces	space	NOUN
ma-61	263	21	,	,	PUNCT
ma-61	263	22	j.	j.	PROPN
ma-61	263	23	math	math	PROPN
ma-61	263	24	.	.	PUNCT
ma-61	264	1	anal	anal	PROPN
ma-61	264	2	.	.	PUNCT
ma-61	264	3	appl	appl	PROPN
ma-61	264	4	.	.	PUNCT
ma-61	265	1	331	331	NUM
ma-61	265	2	(	(	PUNCT
ma-61	265	3	2007	2007	NUM
ma-61	265	4	)	)	PUNCT
ma-61	265	5	506–515	506–515	NUM
ma-61	265	6	.	.	PUNCT
ma-61	266	1	https://doi.org/10.1016/j.jmaa.2006.08.036.[15	https://doi.org/10.1016/j.jmaa.2006.08.036.[15	X
ma-61	266	2	]	]	PUNCT
ma-61	266	3	t.	t.	PROPN
ma-61	266	4	suzuki	suzuki	PROPN
ma-61	266	5	,	,	PUNCT
ma-61	266	6	strong	strong	ADJ
ma-61	266	7	convergence	convergence	NOUN
ma-61	266	8	of	of	ADP
ma-61	266	9	krasnoselskii	krasnoselskii	PROPN
ma-61	266	10	and	and	CCONJ
ma-61	266	11	mann	mann	PROPN
ma-61	266	12	’s	’s	PART
ma-61	266	13	type	type	NOUN
ma-61	266	14	sequences	sequence	NOUN
ma-61	266	15	for	for	ADP
ma-61	266	16	one	one	NUM
ma-61	266	17	-	-	PUNCT
ma-61	266	18	parameter	parameter	NOUN
ma-61	266	19	nonexpansive	nonexpansive	ADJ
ma-61	266	20	semi	semi	NOUN
ma-61	266	21	-	-	NOUN
ma-61	266	22	groups	group	NOUN
ma-61	266	23	without	without	ADP
ma-61	266	24	bochner	bochner	NOUN
ma-61	266	25	integrals	integral	NOUN
ma-61	266	26	,	,	PUNCT
ma-61	266	27	j.	j.	PROPN
ma-61	266	28	math	math	PROPN
ma-61	266	29	.	.	PUNCT
ma-61	267	1	anal	anal	PROPN
ma-61	267	2	.	.	PUNCT
ma-61	267	3	appl	appl	PROPN
ma-61	267	4	.	.	PUNCT
ma-61	268	1	305	305	NUM
ma-61	268	2	(	(	PUNCT
ma-61	268	3	2005	2005	NUM
ma-61	268	4	)	)	PUNCT
ma-61	269	1	227–239	227–239	NUM
ma-61	269	2	.	.	PUNCT
ma-61	270	1	https://doi.org/10.1016/j.jmaa	https://doi.org/10.1016/j.jmaa	NOUN
ma-61	270	2	.	.	PUNCT
ma-61	271	1	2004.11.017.[16	2004.11.017.[16	NUM
ma-61	271	2	]	]	X
ma-61	272	1	s.	s.	PROPN
ma-61	272	2	husain	husain	PROPN
ma-61	272	3	,	,	PUNCT
ma-61	272	4	n.	n.	PROPN
ma-61	272	5	singh	singh	PROPN
ma-61	272	6	,	,	PUNCT
ma-61	272	7	∆-convergence	∆-convergence	NOUN
ma-61	272	8	for	for	ADP
ma-61	272	9	proximal	proximal	ADJ
ma-61	272	10	point	point	NOUN
ma-61	272	11	algorithm	algorithm	NOUN
ma-61	272	12	and	and	CCONJ
ma-61	272	13	fixed	fix	VERB
ma-61	272	14	point	point	NOUN
ma-61	272	15	problem	problem	NOUN
ma-61	272	16	in	in	ADP
ma-61	272	17	cat(0	cat(0	ADJ
ma-61	272	18	)	)	PUNCT
ma-61	272	19	spaces	space	NOUN
ma-61	272	20	,	,	PUNCT
ma-61	272	21	fixedpoint	fixedpoint	NOUN
ma-61	272	22	theory	theory	NOUN
ma-61	272	23	appl	appl	NOUN
ma-61	272	24	.	.	PROPN
ma-61	272	25	2019	2019	NUM
ma-61	272	26	(	(	PUNCT
ma-61	272	27	2019	2019	NUM
ma-61	272	28	)	)	PUNCT
ma-61	272	29	,	,	PUNCT
ma-61	272	30	8	8	NUM
ma-61	272	31	.	.	PUNCT
ma-61	272	32	https://doi.org/10.1186/s13663-019-0658-3	https://doi.org/10.1186/s13663-019-0658-3	NUM
ma-61	272	33	.	.	PUNCT
ma-61	273	1	https://doi.org/10.28924/ada/ma.2.6	https://doi.org/10.28924/ada/ma.2.6	PROPN
ma-61	273	2	https://doi.org/10.1007/bf02614504	https://doi.org/10.1007/bf02614504	PROPN
ma-61	273	3	https://doi.org/10.1007/s11075-019-00688-9	https://doi.org/10.1007/s11075-019-00688-9	PROPN
ma-61	273	4	https://doi.org/10.1155/2012/843486	https://doi.org/10.1155/2012/843486	PROPN
ma-61	273	5	https://doi.org/10.1155/2012/843486	https://doi.org/10.1155/2012/843486	PROPN
ma-61	273	6	https://doi.org/10.1007/978-3-319-48311-5	https://doi.org/10.1007/978-3-319-48311-5	PROPN
ma-61	273	7	https://doi.org/10.1007/978-3-319-48311-5	https://doi.org/10.1007/978-3-319-48311-5	PROPN
ma-61	273	8	https://doi.org/10.1016/j.jmaa.2004.04.059	https://doi.org/10.1016/j.jmaa.2004.04.059	PROPN
ma-61	273	9	https://doi.org/10.1112/s0024610702003332	https://doi.org/10.1112/s0024610702003332	PROPN
ma-61	274	1	https://doi.org/10.1112/s0024610702003332	https://doi.org/10.1112/s0024610702003332	PROPN
ma-61	274	2	https://doi.org/10.1016/j.mcm.2007.09.014	https://doi.org/10.1016/j.mcm.2007.09.014	PROPN
ma-61	274	3	https://doi.org/10.1016/j.jmaa.2006.08.036	https://doi.org/10.1016/j.jmaa.2006.08.036	PROPN
ma-61	274	4	https://doi.org/10.1016/j.jmaa.2004.11.017	https://doi.org/10.1016/j.jmaa.2004.11.017	PROPN
ma-61	274	5	https://doi.org/10.1016/j.jmaa.2004.11.017	https://doi.org/10.1016/j.jmaa.2004.11.017	NUM
ma-61	274	6	https://doi.org/10.1186/s13663-019-0658-3	https://doi.org/10.1186/s13663-019-0658-3	NUM
ma-61	274	7	1	1	NUM
ma-61	274	8	.	.	PUNCT
ma-61	275	1	introduction	introduction	NOUN
ma-61	275	2	and	and	CCONJ
ma-61	275	3	auxiliary	auxiliary	ADJ
ma-61	275	4	results	result	NOUN
ma-61	275	5	2	2	NUM
ma-61	275	6	.	.	X
ma-61	275	7	main	main	ADJ
ma-61	275	8	result	result	NOUN
ma-61	275	9	3	3	NUM
ma-61	275	10	.	.	PUNCT
ma-61	275	11	numerical	numerical	PROPN
ma-61	275	12	example	example	NOUN
ma-61	275	13	references	reference	NOUN