id	sid	tid	token	lemma	pos
ma-218	1	1	2024	2024	NUM
ma-218	1	2	ada	ada	PROPN
ma-218	1	3	academica	academica	PROPN
ma-218	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-218	1	5	.	.	PUNCT
ma-218	2	1	j.	j.	PROPN
ma-218	2	2	math	math	PROPN
ma-218	2	3	.	.	PUNCT
ma-218	3	1	anal	anal	ADJ
ma-218	3	2	.	.	PUNCT
ma-218	4	1	4	4	NUM
ma-218	4	2	(	(	PUNCT
ma-218	4	3	2024	2024	NUM
ma-218	4	4	)	)	PUNCT
ma-218	5	1	8doi	8doi	NUM
ma-218	5	2	:	:	PUNCT
ma-218	5	3	10.28924	10.28924	NUM
ma-218	5	4	/	/	SYM
ma-218	5	5	ada	ada	PROPN
ma-218	5	6	/	/	SYM
ma-218	5	7	ma.4.8	ma.4.8	VERB
ma-218	5	8	hybrid	hybrid	ADJ
ma-218	5	9	inertial	inertial	ADJ
ma-218	5	10	iterative	iterative	NOUN
ma-218	5	11	method	method	NOUN
ma-218	5	12	for	for	ADP
ma-218	5	13	fixed	fix	VERB
ma-218	5	14	point	point	NOUN
ma-218	5	15	,	,	PUNCT
ma-218	5	16	variational	variational	ADJ
ma-218	5	17	inequality	inequality	NOUN
ma-218	5	18	and	and	CCONJ
ma-218	5	19	generalized	generalize	VERB
ma-218	5	20	mixed	mixed	ADJ
ma-218	5	21	equilibrium	equilibrium	NOUN
ma-218	5	22	problems	problem	NOUN
ma-218	5	23	in	in	ADP
ma-218	5	24	banach	banach	NOUN
ma-218	5	25	space	space	NOUN
ma-218	5	26	lawal	lawal	PROPN
ma-218	5	27	umar1,∗	umar1,∗	PROPN
ma-218	5	28	,	,	PUNCT
ma-218	5	29	yusuf	yusuf	PROPN
ma-218	5	30	ibrahim2	ibrahim2	PROPN
ma-218	5	31	,	,	PUNCT
ma-218	5	32	m.s	m.s	PROPN
ma-218	5	33	.	.	PUNCT
ma-218	5	34	lawan3	lawan3	PROPN
ma-218	5	35	1department	1department	NUM
ma-218	5	36	of	of	ADP
ma-218	5	37	mathematics	mathematic	NOUN
ma-218	5	38	,	,	PUNCT
ma-218	5	39	federal	federal	ADJ
ma-218	5	40	college	college	NOUN
ma-218	5	41	of	of	ADP
ma-218	5	42	education	education	NOUN
ma-218	5	43	,	,	PUNCT
ma-218	5	44	zaria	zaria	PROPN
ma-218	5	45	kaduna	kaduna	PROPN
ma-218	5	46	,	,	PUNCT
ma-218	5	47	nigeria	nigeria	PROPN
ma-218	5	48	lawalu4@gmail.com	lawalu4@gmail.com	X
ma-218	6	1	2department	2department	NUM
ma-218	6	2	of	of	ADP
ma-218	6	3	mathematics	mathematic	NOUN
ma-218	6	4	,	,	PUNCT
ma-218	6	5	saadatu	saadatu	PROPN
ma-218	6	6	rimi	rimi	PROPN
ma-218	6	7	university	university	PROPN
ma-218	6	8	of	of	ADP
ma-218	6	9	education	education	PROPN
ma-218	6	10	,	,	PUNCT
ma-218	6	11	kumbotso	kumbotso	PROPN
ma-218	6	12	kano	kano	PROPN
ma-218	6	13	,	,	PUNCT
ma-218	6	14	nigeria	nigeria	PROPN
ma-218	6	15	danustazz@gmail.com	danustazz@gmail.com	X
ma-218	7	1	3department	3department	NUM
ma-218	7	2	of	of	ADP
ma-218	7	3	mathematics	mathematic	NOUN
ma-218	7	4	and	and	CCONJ
ma-218	7	5	statistics	statistic	NOUN
ma-218	7	6	,	,	PUNCT
ma-218	7	7	kaduna	kaduna	PROPN
ma-218	7	8	polytechnic	polytechnic	PROPN
ma-218	7	9	kaduna	kaduna	PROPN
ma-218	7	10	,	,	PUNCT
ma-218	7	11	nigeria	nigeria	PROPN
ma-218	8	1	mslawankh@yahoo.com	mslawankh@yahoo.com	PROPN
ma-218	8	2	∗correspondence	∗correspondence	NOUN
ma-218	8	3	:	:	PUNCT
ma-218	8	4	lawalu4@gmail.com	lawalu4@gmail.com	X
ma-218	8	5	abstract	abstract	ADJ
ma-218	8	6	.	.	PUNCT
ma-218	9	1	in	in	ADP
ma-218	9	2	this	this	DET
ma-218	9	3	paper	paper	NOUN
ma-218	9	4	,	,	PUNCT
ma-218	9	5	we	we	PRON
ma-218	9	6	introduced	introduce	VERB
ma-218	9	7	a	a	DET
ma-218	9	8	hybrid	hybrid	ADJ
ma-218	9	9	inertial	inertial	ADJ
ma-218	9	10	iterative	iterative	NOUN
ma-218	9	11	method	method	NOUN
ma-218	9	12	which	which	PRON
ma-218	9	13	converges	converge	VERB
ma-218	9	14	stronglyto	stronglyto	VERB
ma-218	9	15	a	a	DET
ma-218	9	16	common	common	ADJ
ma-218	9	17	element	element	NOUN
ma-218	9	18	of	of	ADP
ma-218	9	19	solution	solution	NOUN
ma-218	9	20	of	of	ADP
ma-218	9	21	generalized	generalized	ADJ
ma-218	9	22	mixed	mixed	ADJ
ma-218	9	23	equilibrium	equilibrium	NOUN
ma-218	9	24	,	,	PUNCT
ma-218	9	25	variational	variational	ADJ
ma-218	9	26	inequality	inequality	NOUN
ma-218	9	27	and	and	CCONJ
ma-218	9	28	fixedpoint	fixedpoint	NOUN
ma-218	9	29	problems	problem	NOUN
ma-218	9	30	in	in	ADP
ma-218	9	31	a	a	DET
ma-218	9	32	two	two	NUM
ma-218	9	33	uniformly	uniformly	ADV
ma-218	9	34	smooth	smooth	ADJ
ma-218	9	35	and	and	CCONJ
ma-218	9	36	uniformly	uniformly	ADV
ma-218	9	37	convex	convex	VERB
ma-218	9	38	banach	banach	NOUN
ma-218	9	39	space	space	NOUN
ma-218	9	40	.	.	PUNCT
ma-218	10	1	our	our	PRON
ma-218	10	2	hybrid	hybrid	ADJ
ma-218	10	3	inertialiterative	inertialiterative	ADJ
ma-218	10	4	method	method	NOUN
ma-218	10	5	,	,	PUNCT
ma-218	10	6	techniques	technique	NOUN
ma-218	10	7	of	of	ADP
ma-218	10	8	proof	proof	NOUN
ma-218	10	9	and	and	CCONJ
ma-218	10	10	corollaries	corollary	NOUN
ma-218	10	11	improves	improve	VERB
ma-218	10	12	,	,	PUNCT
ma-218	10	13	extends	extend	VERB
ma-218	10	14	and	and	CCONJ
ma-218	10	15	generalizes	generalize	VERB
ma-218	10	16	many	many	ADJ
ma-218	10	17	resultsin	resultsin	NOUN
ma-218	10	18	the	the	DET
ma-218	10	19	literature	literature	NOUN
ma-218	10	20	.	.	PUNCT
ma-218	11	1	1	1	X
ma-218	11	2	.	.	X
ma-218	11	3	introduction	introduction	NOUN
ma-218	11	4	let	let	VERB
ma-218	11	5	b	b	PROPN
ma-218	11	6	denotes	denote	NOUN
ma-218	11	7	a	a	DET
ma-218	11	8	real	real	ADJ
ma-218	11	9	banach	banach	NOUN
ma-218	11	10	space	space	NOUN
ma-218	11	11	with	with	ADP
ma-218	11	12	b∗	b∗	ADJ
ma-218	11	13	as	as	ADP
ma-218	11	14	the	the	DET
ma-218	11	15	dual	dual	ADJ
ma-218	11	16	space	space	NOUN
ma-218	11	17	of	of	ADP
ma-218	11	18	b.	b.	PROPN
ma-218	11	19	we	we	PRON
ma-218	11	20	consider	consider	VERB
ma-218	11	21	〈	〈	PROPN
ma-218	11	22	τ1	τ1	NOUN
ma-218	11	23	,	,	PUNCT
ma-218	11	24	j	j	PROPN
ma-218	11	25	〉	〉	PROPN
ma-218	11	26	as	as	ADP
ma-218	11	27	thevalue	thevalue	NOUN
ma-218	11	28	of	of	ADP
ma-218	11	29	the	the	DET
ma-218	11	30	functional	functional	ADJ
ma-218	11	31	j	j	PROPN
ma-218	11	32	∈	∈	PROPN
ma-218	11	33	b∗	b∗	ADV
ma-218	11	34	at	at	ADP
ma-218	11	35	τ1	τ1	PROPN
ma-218	11	36	∈	∈	PROPN
ma-218	11	37	b	b	PROPN
ma-218	11	38	and	and	CCONJ
ma-218	11	39	‖	‖	PROPN
ma-218	11	40	.	.	PUNCT
ma-218	12	1	‖	‖	PROPN
ma-218	12	2	as	as	ADP
ma-218	12	3	the	the	DET
ma-218	12	4	norm	norm	NOUN
ma-218	12	5	of	of	ADP
ma-218	12	6	b	b	NOUN
ma-218	12	7	or	or	CCONJ
ma-218	12	8	b∗.	b∗.	NOUN
ma-218	12	9	let	let	VERB
ma-218	12	10	c	c	NOUN
ma-218	12	11	6=	6=	NOUN
ma-218	12	12	∅	∅	NOUN
ma-218	12	13	be	be	AUX
ma-218	12	14	subset	subset	VERB
ma-218	12	15	of	of	ADP
ma-218	12	16	b.	b.	PROPN
ma-218	12	17	a	a	DET
ma-218	12	18	mapping	mapping	NOUN
ma-218	12	19	j	j	NOUN
ma-218	12	20	:	:	PUNCT
ma-218	12	21	b	b	X
ma-218	12	22	−→	−→	NOUN
ma-218	12	23	2b	2b	NUM
ma-218	12	24	∗	∗	NOUN
ma-218	12	25	is	be	AUX
ma-218	12	26	called	call	VERB
ma-218	12	27	normalized	normalize	VERB
ma-218	12	28	duality	duality	NOUN
ma-218	12	29	provided	provide	VERB
ma-218	12	30	that	that	SCONJ
ma-218	12	31	jτ1	jτ1	NOUN
ma-218	12	32	=	=	PRON
ma-218	12	33	{	{	PUNCT
ma-218	12	34	τ2	τ2	NOUN
ma-218	12	35	∈	∈	PROPN
ma-218	12	36	b∗	b∗	ADV
ma-218	12	37	:	:	PUNCT
ma-218	12	38	〈	〈	PROPN
ma-218	12	39	τ2	τ2	NOUN
ma-218	12	40	,	,	PUNCT
ma-218	12	41	τ1	τ1	NOUN
ma-218	12	42	〉	〉	NOUN
ma-218	12	43	=	=	PUNCT
ma-218	13	1	‖τ1	‖τ1	DET
ma-218	13	2	‖2=	‖2=	PROPN
ma-218	13	3	‖τ2	‖τ2	PROPN
ma-218	13	4	‖2},∀τ1	‖2},∀τ1	PROPN
ma-218	13	5	∈	∈	PROPN
ma-218	13	6	b.	b.	NOUN
ma-218	13	7	we	we	PRON
ma-218	13	8	denotes	denote	VERB
ma-218	13	9	the	the	DET
ma-218	13	10	short	short	ADJ
ma-218	13	11	form	form	NOUN
ma-218	13	12	gmep	gmep	NOUN
ma-218	13	13	as	as	ADP
ma-218	13	14	generalized	generalize	VERB
ma-218	13	15	mixed	mixed	ADJ
ma-218	13	16	equilibrium	equilibrium	NOUN
ma-218	13	17	problem	problem	NOUN
ma-218	13	18	:	:	PUNCT
ma-218	13	19	find	find	VERB
ma-218	13	20	v1	v1	NOUN
ma-218	13	21	∈	∈	NOUN
ma-218	13	22	c	c	NOUN
ma-218	13	23	suchthat	suchthat	PROPN
ma-218	13	24	d(v1	d(v1	VERB
ma-218	13	25	,	,	PUNCT
ma-218	13	26	v2	v2	PROPN
ma-218	13	27	)	)	PUNCT
ma-218	14	1	+	+	CCONJ
ma-218	14	2	〈	〈	PROPN
ma-218	14	3	gv1	gv1	NOUN
ma-218	14	4	,	,	PUNCT
ma-218	14	5	v2	v2	PROPN
ma-218	14	6	−	−	NOUN
ma-218	14	7	v1〉+	v1〉+	NUM
ma-218	14	8	ϑ(v1	ϑ(v1	NOUN
ma-218	14	9	,	,	PUNCT
ma-218	14	10	v2)−	v2)−	NOUN
ma-218	14	11	ϑ(v1	ϑ(v1	NOUN
ma-218	14	12	,	,	PUNCT
ma-218	14	13	v1	v1	NOUN
ma-218	14	14	)	)	PUNCT
ma-218	14	15	≥	≥	NOUN
ma-218	14	16	0	0	NUM
ma-218	14	17	,	,	PUNCT
ma-218	14	18	∀v2	∀v2	X
ma-218	14	19	∈	∈	PROPN
ma-218	14	20	c	c	AUX
ma-218	14	21	,	,	PUNCT
ma-218	14	22	(	(	PUNCT
ma-218	14	23	1.1	1.1	NUM
ma-218	14	24	)	)	PUNCT
ma-218	14	25	where	where	SCONJ
ma-218	14	26	d	d	NOUN
ma-218	14	27	,	,	PUNCT
ma-218	14	28	ϑ	ϑ	X
ma-218	14	29	:	:	PUNCT
ma-218	14	30	c	c	X
ma-218	14	31	×	×	NOUN
ma-218	14	32	c	c	NOUN
ma-218	14	33	−→	−→	NOUN
ma-218	14	34	r	r	NOUN
ma-218	14	35	and	and	CCONJ
ma-218	14	36	g	g	NOUN
ma-218	14	37	:	:	PUNCT
ma-218	14	38	c	c	X
ma-218	14	39	−→	−→	ADJ
ma-218	14	40	b∗	b∗	ADJ
ma-218	14	41	denotes	denote	VERB
ma-218	14	42	the	the	DET
ma-218	14	43	bifunctions	bifunction	NOUN
ma-218	14	44	and	and	CCONJ
ma-218	14	45	a	a	DET
ma-218	14	46	nonlinear	nonlinear	ADJ
ma-218	14	47	mappingrespectively	mappingrespectively	NOUN
ma-218	14	48	,	,	PUNCT
ma-218	14	49	also	also	ADV
ma-218	14	50	r	r	NOUN
ma-218	14	51	is	be	AUX
ma-218	14	52	consider	consider	VERB
ma-218	14	53	as	as	ADP
ma-218	14	54	the	the	DET
ma-218	14	55	set	set	NOUN
ma-218	14	56	of	of	ADP
ma-218	14	57	all	all	DET
ma-218	14	58	real	real	ADJ
ma-218	14	59	numbers	number	NOUN
ma-218	14	60	.	.	PUNCT
ma-218	15	1	then	then	ADV
ma-218	15	2	,	,	PUNCT
ma-218	15	3	sol(gmep	sol(gmep	NOUN
ma-218	15	4	(	(	PUNCT
ma-218	15	5	1.1	1.1	NUM
ma-218	15	6	)	)	PUNCT
ma-218	15	7	)	)	PUNCT
ma-218	15	8	is	be	AUX
ma-218	15	9	consideras	considera	NOUN
ma-218	15	10	the	the	DET
ma-218	15	11	solution	solution	NOUN
ma-218	15	12	set	set	VERB
ma-218	15	13	of	of	ADP
ma-218	15	14	gmep.(1.1	gmep.(1.1	NOUN
ma-218	15	15	)	)	PUNCT
ma-218	15	16	.	.	PUNCT
ma-218	16	1	received	receive	VERB
ma-218	16	2	:	:	PUNCT
ma-218	16	3	16	16	NUM
ma-218	16	4	jan	jan	PROPN
ma-218	16	5	2024	2024	NUM
ma-218	16	6	.	.	PUNCT
ma-218	17	1	key	key	ADJ
ma-218	17	2	words	word	NOUN
ma-218	17	3	and	and	CCONJ
ma-218	17	4	phrases	phrase	NOUN
ma-218	17	5	.	.	PUNCT
ma-218	18	1	hybrid	hybrid	ADJ
ma-218	18	2	inertial	inertial	ADJ
ma-218	18	3	iterative	iterative	NOUN
ma-218	18	4	method	method	NOUN
ma-218	18	5	;	;	PUNCT
ma-218	18	6	fixed	fix	VERB
ma-218	18	7	point	point	NOUN
ma-218	18	8	problem	problem	NOUN
ma-218	18	9	;	;	PUNCT
ma-218	18	10	variational	variational	ADJ
ma-218	18	11	inequality	inequality	NOUN
ma-218	18	12	problem;generalized	problem;generalize	VERB
ma-218	18	13	mixed	mixed	ADJ
ma-218	18	14	equilibrium	equilibrium	NOUN
ma-218	18	15	problem	problem	NOUN
ma-218	18	16	.	.	PUNCT
ma-218	19	1	1	1	NUM
ma-218	19	2	https://adac.ee	https://adac.ee	PROPN
ma-218	19	3	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	19	4	eur	eur	PROPN
ma-218	19	5	.	.	PUNCT
ma-218	20	1	j.	j.	PROPN
ma-218	20	2	math	math	PROPN
ma-218	20	3	.	.	PUNCT
ma-218	21	1	anal	anal	PROPN
ma-218	21	2	.	.	PUNCT
ma-218	22	1	10.28924	10.28924	NUM
ma-218	22	2	/	/	SYM
ma-218	22	3	ada	ada	PROPN
ma-218	22	4	/	/	SYM
ma-218	22	5	ma.4.8	ma.4.8	VERB
ma-218	22	6	2if	2if	NOUN
ma-218	22	7	g	g	PROPN
ma-218	22	8	≡	≡	PROPN
ma-218	22	9	0	0	NUM
ma-218	22	10	,	,	PUNCT
ma-218	22	11	gmep	gmep	NOUN
ma-218	22	12	(	(	PUNCT
ma-218	22	13	1.1	1.1	NUM
ma-218	22	14	)	)	PUNCT
ma-218	22	15	reduces	reduce	VERB
ma-218	22	16	to	to	PART
ma-218	22	17	generalized	generalize	VERB
ma-218	22	18	equilibrium	equilibrium	NOUN
ma-218	22	19	problem	problem	NOUN
ma-218	22	20	(	(	PUNCT
ma-218	22	21	with	with	ADP
ma-218	22	22	gep	gep	PROPN
ma-218	22	23	as	as	ADP
ma-218	22	24	the	the	DET
ma-218	22	25	short	short	ADJ
ma-218	22	26	form):find	form):find	PROPN
ma-218	22	27	v1	v1	PROPN
ma-218	22	28	∈	∈	PROPN
ma-218	22	29	c	c	NOUN
ma-218	22	30	such	such	ADJ
ma-218	22	31	that	that	DET
ma-218	22	32	d(v1	d(v1	NOUN
ma-218	22	33	,	,	PUNCT
ma-218	22	34	v2	v2	PROPN
ma-218	22	35	)	)	PUNCT
ma-218	22	36	+	+	NUM
ma-218	22	37	ϑ(v1	ϑ(v1	NOUN
ma-218	22	38	,	,	PUNCT
ma-218	22	39	v2)−	v2)−	X
ma-218	22	40	ϑ(v1	ϑ(v1	NOUN
ma-218	22	41	,	,	PUNCT
ma-218	22	42	v1	v1	NOUN
ma-218	22	43	)	)	PUNCT
ma-218	22	44	≥	≥	NOUN
ma-218	22	45	0,∀v2	0,∀v2	NOUN
ma-218	23	1	∈	∈	PROPN
ma-218	23	2	c.	c.	NOUN
ma-218	23	3	(	(	PUNCT
ma-218	23	4	1.2	1.2	NUM
ma-218	23	5	)	)	PUNCT
ma-218	23	6	then	then	ADV
ma-218	23	7	,	,	PUNCT
ma-218	23	8	sol(gep	sol(gep	NOUN
ma-218	23	9	(	(	PUNCT
ma-218	23	10	1.2	1.2	NUM
ma-218	23	11	)	)	PUNCT
ma-218	23	12	)	)	PUNCT
ma-218	23	13	is	be	AUX
ma-218	23	14	represent	represent	VERB
ma-218	23	15	the	the	DET
ma-218	23	16	solution	solution	NOUN
ma-218	23	17	set	set	VERB
ma-218	23	18	of	of	ADP
ma-218	23	19	gep	gep	PROPN
ma-218	23	20	(	(	PUNCT
ma-218	23	21	1.2).if	1.2).if	NUM
ma-218	23	22	g	g	PROPN
ma-218	23	23	≡	≡	PROPN
ma-218	23	24	0	0	PUNCT
ma-218	23	25	and	and	CCONJ
ma-218	23	26	ϑ	ϑ	X
ma-218	23	27	≡	≡	PROPN
ma-218	23	28	0	0	NUM
ma-218	23	29	,	,	PUNCT
ma-218	23	30	gmep	gmep	NOUN
ma-218	23	31	(	(	PUNCT
ma-218	23	32	1.1	1.1	NUM
ma-218	23	33	)	)	PUNCT
ma-218	23	34	becomes	become	VERB
ma-218	23	35	equilibrium	equilibrium	NOUN
ma-218	23	36	problem	problem	NOUN
ma-218	23	37	(	(	PUNCT
ma-218	23	38	with	with	ADP
ma-218	23	39	ep	ep	PROPN
ma-218	23	40	as	as	ADP
ma-218	23	41	the	the	DET
ma-218	23	42	short	short	ADJ
ma-218	23	43	form	form	NOUN
ma-218	23	44	)	)	PUNCT
ma-218	24	1	[	[	X
ma-218	24	2	3]:find	3]:find	NUM
ma-218	24	3	v1	v1	NOUN
ma-218	24	4	∈	∈	NOUN
ma-218	24	5	c	c	NOUN
ma-218	24	6	such	such	ADJ
ma-218	24	7	that	that	DET
ma-218	24	8	d(v1	d(v1	NOUN
ma-218	24	9	,	,	PUNCT
ma-218	24	10	v2	v2	PROPN
ma-218	24	11	)	)	PUNCT
ma-218	24	12	≥	≥	NOUN
ma-218	24	13	0,∀v2	0,∀v2	NOUN
ma-218	25	1	∈	∈	PROPN
ma-218	25	2	c.	c.	NOUN
ma-218	25	3	(	(	PUNCT
ma-218	25	4	1.3	1.3	NUM
ma-218	25	5	)	)	PUNCT
ma-218	25	6	then	then	ADV
ma-218	25	7	,	,	PUNCT
ma-218	25	8	sol(ep	sol(ep	ADJ
ma-218	25	9	(	(	PUNCT
ma-218	25	10	1.3	1.3	NUM
ma-218	25	11	)	)	PUNCT
ma-218	25	12	)	)	PUNCT
ma-218	25	13	is	be	AUX
ma-218	25	14	consider	consider	VERB
ma-218	25	15	as	as	ADP
ma-218	25	16	the	the	DET
ma-218	25	17	solution	solution	NOUN
ma-218	25	18	set	set	VERB
ma-218	25	19	of	of	ADP
ma-218	25	20	ep.(1.3).if	ep.(1.3).if	PROPN
ma-218	25	21	d	d	X
ma-218	25	22	≡	≡	PROPN
ma-218	25	23	0	0	NUM
ma-218	25	24	and	and	CCONJ
ma-218	25	25	ϑ	ϑ	X
ma-218	25	26	≡	≡	PROPN
ma-218	25	27	0	0	NUM
ma-218	25	28	,	,	PUNCT
ma-218	25	29	gmep	gmep	NOUN
ma-218	25	30	(	(	PUNCT
ma-218	25	31	1.1	1.1	NUM
ma-218	25	32	)	)	PUNCT
ma-218	25	33	reduces	reduce	VERB
ma-218	25	34	to	to	ADP
ma-218	25	35	variational	variational	ADJ
ma-218	25	36	inequality	inequality	NOUN
ma-218	25	37	problem	problem	NOUN
ma-218	25	38	(	(	PUNCT
ma-218	25	39	with	with	ADP
ma-218	25	40	v	v	NOUN
ma-218	25	41	ip	ip	NOUN
ma-218	25	42	as	as	ADP
ma-218	25	43	theshort	theshort	NOUN
ma-218	25	44	form	form	NOUN
ma-218	25	45	):	):	PUNCT
ma-218	25	46	find	find	VERB
ma-218	25	47	v1	v1	NOUN
ma-218	25	48	∈	∈	NOUN
ma-218	25	49	c	c	NOUN
ma-218	26	1	such	such	ADJ
ma-218	26	2	that	that	SCONJ
ma-218	26	3	〈	〈	PROPN
ma-218	26	4	gv1	gv1	NOUN
ma-218	26	5	,	,	PUNCT
ma-218	26	6	v2	v2	PROPN
ma-218	26	7	−	−	PROPN
ma-218	26	8	v1	v1	PROPN
ma-218	26	9	〉	〉	PROPN
ma-218	26	10	≥	≥	NOUN
ma-218	26	11	0,∀v2	0,∀v2	NOUN
ma-218	26	12	∈	∈	PROPN
ma-218	26	13	c.	c.	NOUN
ma-218	26	14	(	(	PUNCT
ma-218	26	15	1.4	1.4	NUM
ma-218	26	16	)	)	PUNCT
ma-218	26	17	then	then	ADV
ma-218	26	18	,	,	PUNCT
ma-218	26	19	sol(v	sol(v	PROPN
ma-218	26	20	ip	ip	NOUN
ma-218	26	21	(	(	PUNCT
ma-218	26	22	1.4	1.4	NUM
ma-218	26	23	)	)	PUNCT
ma-218	26	24	)	)	PUNCT
ma-218	26	25	is	be	AUX
ma-218	26	26	consider	consider	VERB
ma-218	26	27	as	as	ADP
ma-218	26	28	the	the	DET
ma-218	26	29	solution	solution	NOUN
ma-218	26	30	set	set	VERB
ma-218	26	31	of	of	ADP
ma-218	26	32	v	v	NUM
ma-218	26	33	ip	ip	NOUN
ma-218	26	34	(	(	PUNCT
ma-218	26	35	1.4	1.4	NUM
ma-218	26	36	)	)	PUNCT
ma-218	26	37	.	.	PUNCT
ma-218	27	1	definition	definition	NOUN
ma-218	27	2	1.1	1.1	NUM
ma-218	27	3	.	.	PUNCT
ma-218	28	1	let	let	VERB
ma-218	28	2	t	t	NOUN
ma-218	28	3	:	:	PUNCT
ma-218	28	4	c	c	AUX
ma-218	28	5	−→	−→	NOUN
ma-218	28	6	c	c	AUX
ma-218	28	7	be	be	AUX
ma-218	28	8	a	a	DET
ma-218	28	9	mapping	mapping	NOUN
ma-218	28	10	[	[	X
ma-218	28	11	6	6	NUM
ma-218	28	12	]	]	PUNCT
ma-218	28	13	,	,	PUNCT
ma-218	28	14	then(i	then(i	PROPN
ma-218	28	15	)	)	PUNCT
ma-218	28	16	a	a	DET
ma-218	28	17	point	point	NOUN
ma-218	28	18	v1	v1	NOUN
ma-218	28	19	∈	∈	NOUN
ma-218	28	20	c	c	NOUN
ma-218	28	21	is	be	AUX
ma-218	28	22	called	call	VERB
ma-218	28	23	fixed	fix	VERB
ma-218	28	24	point	point	NOUN
ma-218	28	25	of	of	ADP
ma-218	28	26	t	t	PROPN
ma-218	28	27	provided	provide	VERB
ma-218	28	28	that	that	SCONJ
ma-218	28	29	f	f	PROPN
ma-218	28	30	(	(	PUNCT
ma-218	28	31	t	t	PROPN
ma-218	28	32	)	)	PUNCT
ma-218	28	33	=	=	PUNCT
ma-218	28	34	{	{	PUNCT
ma-218	28	35	v1	v1	PROPN
ma-218	28	36	∈	∈	PROPN
ma-218	28	37	c	c	NOUN
ma-218	28	38	:	:	PUNCT
ma-218	28	39	tv1	tv1	PROPN
ma-218	28	40	=	=	SYM
ma-218	28	41	v1	v1	PROPN
ma-218	28	42	}	}	PUNCT
ma-218	28	43	6=	6=	NUM
ma-218	28	44	∅;(ii	∅;(ii	NOUN
ma-218	28	45	)	)	PUNCT
ma-218	28	46	a	a	DET
ma-218	28	47	point	point	NOUN
ma-218	28	48	v0	v0	NOUN
ma-218	28	49	∈	∈	NOUN
ma-218	28	50	c	c	NOUN
ma-218	28	51	is	be	AUX
ma-218	28	52	called	call	VERB
ma-218	28	53	an	an	DET
ma-218	28	54	asymptotic	asymptotic	ADJ
ma-218	28	55	fixed	fix	VERB
ma-218	28	56	point	point	NOUN
ma-218	28	57	of	of	ADP
ma-218	28	58	t	t	PROPN
ma-218	28	59	provided	provide	VERB
ma-218	28	60	that	that	SCONJ
ma-218	28	61	{	{	PUNCT
ma-218	28	62	vn	vn	NOUN
ma-218	28	63	}	}	PUNCT
ma-218	28	64	⊂	⊂	PROPN
ma-218	28	65	c	c	X
ma-218	28	66	,	,	PUNCT
ma-218	28	67	vn	vn	PROPN
ma-218	28	68	⇀	⇀	NUM
ma-218	29	1	v0	v0	PROPN
ma-218	29	2	suchthat	suchthat	PROPN
ma-218	29	3	lim	lim	PROPN
ma-218	29	4	n→∞	n→∞	PRON
ma-218	29	5	‖	‖	PROPN
ma-218	29	6	vn	vn	PROPN
ma-218	29	7	−	−	PROPN
ma-218	29	8	tvn	tvn	PROPN
ma-218	29	9	‖=	‖=	PROPN
ma-218	29	10	0	0	X
ma-218	29	11	.	.	PUNCT
ma-218	30	1	the	the	DET
ma-218	30	2	set	set	NOUN
ma-218	30	3	of	of	ADP
ma-218	30	4	asymptotic	asymptotic	ADJ
ma-218	30	5	fixed	fix	VERB
ma-218	30	6	point	point	NOUN
ma-218	30	7	of	of	ADP
ma-218	30	8	t	t	PROPN
ma-218	30	9	is	be	AUX
ma-218	30	10	denoted	denote	VERB
ma-218	30	11	by	by	ADP
ma-218	30	12	f̂	f̂	PROPN
ma-218	30	13	(	(	PUNCT
ma-218	30	14	t	t	PROPN
ma-218	30	15	)	)	PUNCT
ma-218	30	16	;	;	PUNCT
ma-218	30	17	(	(	PUNCT
ma-218	30	18	iii	iii	X
ma-218	30	19	)	)	PUNCT
ma-218	30	20	t	t	PROPN
ma-218	30	21	is	be	AUX
ma-218	30	22	called	call	VERB
ma-218	30	23	quasi−φ−nonexpansive	quasi−φ−nonexpansive	PROPN
ma-218	30	24	provided	provide	VERB
ma-218	30	25	that	that	SCONJ
ma-218	30	26	φ(v0	φ(v0	NOUN
ma-218	30	27	,	,	PUNCT
ma-218	30	28	t	t	PROPN
ma-218	30	29	v	v	NOUN
ma-218	30	30	)	)	PUNCT
ma-218	30	31	≤	≤	NOUN
ma-218	30	32	φ(v0	φ(v0	NOUN
ma-218	30	33	,	,	PUNCT
ma-218	30	34	v	v	NOUN
ma-218	30	35	)	)	PUNCT
ma-218	30	36	and	and	CCONJ
ma-218	30	37	f	f	PROPN
ma-218	30	38	(	(	PUNCT
ma-218	30	39	t	t	PROPN
ma-218	30	40	)	)	PUNCT
ma-218	30	41	6=	6=	ADP
ma-218	30	42	∅	∅	NOUN
ma-218	30	43	,	,	PUNCT
ma-218	30	44	∀v	∀v	PROPN
ma-218	30	45	∈	∈	PROPN
ma-218	30	46	c	c	X
ma-218	30	47	,	,	PUNCT
ma-218	30	48	v0	v0	PROPN
ma-218	30	49	∈	∈	PROPN
ma-218	30	50	f	f	X
ma-218	30	51	(	(	PUNCT
ma-218	30	52	t	t	PROPN
ma-218	30	53	)	)	PUNCT
ma-218	30	54	;	;	PUNCT
ma-218	30	55	(	(	PUNCT
ma-218	30	56	iv	iv	X
ma-218	30	57	)	)	PUNCT
ma-218	30	58	t	t	PROPN
ma-218	30	59	is	be	AUX
ma-218	30	60	called	call	VERB
ma-218	30	61	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	30	62	nonexpansive	nonexpansive	ADJ
ma-218	30	63	provided	provide	VERB
ma-218	30	64	that	that	SCONJ
ma-218	30	65	f	f	PROPN
ma-218	30	66	(	(	PUNCT
ma-218	30	67	t	t	PROPN
ma-218	30	68	)	)	PUNCT
ma-218	30	69	6=	6=	ADP
ma-218	30	70	∅	∅	NOUN
ma-218	30	71	and	and	CCONJ
ma-218	30	72	there	there	PRON
ma-218	30	73	exists	exist	VERB
ma-218	30	74	asequence	asequence	NOUN
ma-218	30	75	{	{	PUNCT
ma-218	30	76	kn	kn	PROPN
ma-218	30	77	}	}	PUNCT
ma-218	30	78	⊂	⊂	PROPN
ma-218	31	1	[	[	X
ma-218	31	2	1,∞	1,∞	NUM
ma-218	31	3	)	)	PUNCT
ma-218	31	4	with	with	ADP
ma-218	31	5	kn	kn	PROPN
ma-218	31	6	−→	−→	NOUN
ma-218	31	7	1	1	NUM
ma-218	31	8	as	as	ADP
ma-218	31	9	n	n	X
ma-218	31	10	→∞	→∞	PROPN
ma-218	31	11	such	such	ADJ
ma-218	31	12	that	that	SCONJ
ma-218	31	13	φ(v0	φ(v0	NOUN
ma-218	31	14	,	,	PUNCT
ma-218	31	15	t	t	PROPN
ma-218	31	16	nv	nv	PROPN
ma-218	31	17	)	)	PUNCT
ma-218	31	18	≤	≤	NOUN
ma-218	32	1	knφ(v0	knφ(v0	PROPN
ma-218	32	2	,	,	PUNCT
ma-218	32	3	v	v	NOUN
ma-218	32	4	)	)	PUNCT
ma-218	32	5	,	,	PUNCT
ma-218	32	6	∀v	∀v	PROPN
ma-218	32	7	∈	∈	PROPN
ma-218	32	8	c	c	X
ma-218	32	9	,	,	PUNCT
ma-218	32	10	v0	v0	PROPN
ma-218	32	11	∈	∈	PROPN
ma-218	32	12	f	f	X
ma-218	32	13	(	(	PUNCT
ma-218	32	14	t	t	PROPN
ma-218	32	15	)	)	PUNCT
ma-218	32	16	,	,	PUNCT
ma-218	32	17	n	n	X
ma-218	32	18	≥	≥	NOUN
ma-218	32	19	1	1	NUM
ma-218	32	20	.	.	PUNCT
ma-218	32	21	definition	definition	NOUN
ma-218	32	22	1.2	1.2	NUM
ma-218	32	23	.	.	PUNCT
ma-218	33	1	a	a	DET
ma-218	33	2	function	function	NOUN
ma-218	33	3	t	t	NOUN
ma-218	33	4	:	:	PUNCT
ma-218	33	5	c	c	X
ma-218	33	6	−→	−→	NOUN
ma-218	33	7	b∗	b∗	ADJ
ma-218	33	8	is	be	AUX
ma-218	33	9	said	say	VERB
ma-218	33	10	to	to	PART
ma-218	33	11	be	be	AUX
ma-218	33	12	[	[	X
ma-218	33	13	6	6	NUM
ma-218	33	14	]	]	PUNCT
ma-218	33	15	:(	:(	PUNCT
ma-218	34	1	i	i	NOUN
ma-218	34	2	)	)	PUNCT
ma-218	34	3	monotone	monotone	ADJ
ma-218	34	4	if	if	SCONJ
ma-218	34	5	〈	〈	PROPN
ma-218	34	6	τ1	τ1	ADP
ma-218	34	7	−	−	PROPN
ma-218	34	8	τ2	τ2	PROPN
ma-218	34	9	,	,	PUNCT
ma-218	34	10	t	t	NOUN
ma-218	34	11	τ1	τ1	NOUN
ma-218	34	12	−	−	PROPN
ma-218	35	1	tτ2	tτ2	PROPN
ma-218	35	2	〉	〉	PROPN
ma-218	35	3	≥	≥	NUM
ma-218	35	4	0	0	NUM
ma-218	35	5	,	,	PUNCT
ma-218	35	6	∀τ1	∀τ1	ADP
ma-218	35	7	,	,	PUNCT
ma-218	35	8	τ2	τ2	PROPN
ma-218	35	9	∈	∈	PROPN
ma-218	35	10	b;(ii	b;(ii	PROPN
ma-218	35	11	)	)	PUNCT
ma-218	35	12	γ−inverse	γ−inverse	X
ma-218	35	13	strongly	strongly	ADV
ma-218	35	14	monotone	monotone	ADJ
ma-218	35	15	(	(	PUNCT
ma-218	35	16	with	with	SCONJ
ma-218	35	17	i	i	PRON
ma-218	35	18	sm	sm	VERB
ma-218	35	19	as	as	ADP
ma-218	35	20	short	short	ADJ
ma-218	35	21	form	form	NOUN
ma-218	35	22	)	)	PUNCT
ma-218	35	23	if	if	SCONJ
ma-218	35	24	∃γ	∃γ	NOUN
ma-218	35	25	>	>	X
ma-218	35	26	0	0	NUM
ma-218	36	1	such	such	ADJ
ma-218	36	2	that	that	SCONJ
ma-218	36	3	〈	〈	PROPN
ma-218	36	4	τ1	τ1	NOUN
ma-218	36	5	−	−	NOUN
ma-218	36	6	τ2	τ2	PROPN
ma-218	36	7	,	,	PUNCT
ma-218	36	8	t	t	NOUN
ma-218	36	9	τ1	τ1	NOUN
ma-218	36	10	−	−	PROPN
ma-218	37	1	tτ2	tτ2	PROPN
ma-218	38	1	〉	〉	PROPN
ma-218	38	2	≥	≥	NOUN
ma-218	38	3	γ	γ	PROPN
ma-218	38	4	‖	‖	PROPN
ma-218	38	5	tτ1	tτ1	PRON
ma-218	38	6	−	−	NOUN
ma-218	38	7	tτ2	tτ2	NOUN
ma-218	38	8	‖2	‖2	NOUN
ma-218	38	9	,	,	PUNCT
ma-218	38	10	∀τ1	∀τ1	ADP
ma-218	38	11	,	,	PUNCT
ma-218	38	12	τ2	τ2	PROPN
ma-218	38	13	∈	∈	PROPN
ma-218	38	14	b	b	NOUN
ma-218	38	15	;	;	PUNCT
ma-218	38	16	(	(	PUNCT
ma-218	38	17	iii	iii	X
ma-218	38	18	)	)	PUNCT
ma-218	38	19	lipschitz	lipschitz	NOUN
ma-218	38	20	continuous	continuous	ADJ
ma-218	38	21	if	if	SCONJ
ma-218	38	22	∃l	∃l	PROPN
ma-218	38	23	>	>	X
ma-218	38	24	0	0	NUM
ma-218	38	25	such	such	ADJ
ma-218	38	26	that	that	SCONJ
ma-218	38	27	‖	‖	PROPN
ma-218	38	28	tτ1	tτ1	DET
ma-218	38	29	−	−	NOUN
ma-218	38	30	tτ2	tτ2	NOUN
ma-218	38	31	‖≤	‖≤	PROPN
ma-218	38	32	l	l	NOUN
ma-218	38	33	‖	‖	PROPN
ma-218	38	34	τ1	τ1	NOUN
ma-218	38	35	−	−	PROPN
ma-218	38	36	τ2	τ2	PROPN
ma-218	38	37	‖	‖	PROPN
ma-218	38	38	,	,	PUNCT
ma-218	38	39	∀τ1	∀τ1	ADP
ma-218	38	40	,	,	PUNCT
ma-218	38	41	τ2	τ2	PROPN
ma-218	38	42	∈	∈	PROPN
ma-218	38	43	b.	b.	NOUN
ma-218	39	1	if	if	SCONJ
ma-218	39	2	t	t	PROPN
ma-218	39	3	is	be	AUX
ma-218	39	4	γ	γ	X
ma-218	39	5	−	−	PROPN
ma-218	40	1	i	i	PRON
ma-218	40	2	sm	sm	VERB
ma-218	40	3	,	,	PUNCT
ma-218	40	4	then	then	ADV
ma-218	40	5	it	it	PRON
ma-218	40	6	is	be	AUX
ma-218	40	7	lipschitz	lipschitz	NOUN
ma-218	40	8	continuous	continuous	ADJ
ma-218	40	9	with	with	ADP
ma-218	40	10	1	1	NUM
ma-218	40	11	γ	γ	NOUN
ma-218	40	12	as	as	ADP
ma-218	40	13	a	a	DET
ma-218	40	14	constant	constant	ADJ
ma-218	40	15	.	.	PUNCT
ma-218	41	1	definition	definition	NOUN
ma-218	41	2	1.3	1.3	NUM
ma-218	41	3	.	.	PUNCT
ma-218	42	1	a	a	DET
ma-218	42	2	mapping	mapping	NOUN
ma-218	42	3	πc	πc	VERB
ma-218	42	4	:	:	PUNCT
ma-218	42	5	b	b	X
ma-218	42	6	−→	−→	NOUN
ma-218	42	7	c	c	PROPN
ma-218	42	8	is	be	AUX
ma-218	42	9	called	call	VERB
ma-218	42	10	generalized	generalized	ADJ
ma-218	42	11	projection	projection	NOUN
ma-218	43	1	[	[	X
ma-218	43	2	6	6	NUM
ma-218	43	3	]	]	PUNCT
ma-218	43	4	,	,	PUNCT
ma-218	43	5	provided	provide	VERB
ma-218	43	6	that	that	PRON
ma-218	43	7	πcτ1	πcτ1	NOUN
ma-218	43	8	=	=	X
ma-218	43	9	v0	v0	PROPN
ma-218	43	10	,	,	PUNCT
ma-218	43	11	for	for	ADP
ma-218	43	12	any	any	DET
ma-218	43	13	τ1	τ1	NOUN
ma-218	43	14	∈	∈	PROPN
ma-218	43	15	b	b	PROPN
ma-218	43	16	and	and	CCONJ
ma-218	43	17	v0	v0	NOUN
ma-218	43	18	be	be	VERB
ma-218	43	19	the	the	DET
ma-218	43	20	solution	solution	NOUN
ma-218	43	21	of	of	ADP
ma-218	43	22	φ(v0	φ(v0	NOUN
ma-218	43	23	,	,	PUNCT
ma-218	43	24	τ1	τ1	NOUN
ma-218	43	25	)	)	PUNCT
ma-218	43	26	=	=	SYM
ma-218	43	27	inf	inf	NOUN
ma-218	43	28	v∈c	v∈c	NOUN
ma-218	43	29	φ(v	φ(v	ADV
ma-218	43	30	,	,	PUNCT
ma-218	43	31	τ1	τ1	NOUN
ma-218	43	32	)	)	PUNCT
ma-218	43	33	.	.	PUNCT
ma-218	44	1	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PRON
ma-218	44	2	eur	eur	PROPN
ma-218	44	3	.	.	PUNCT
ma-218	45	1	j.	j.	PROPN
ma-218	45	2	math	math	PROPN
ma-218	45	3	.	.	PUNCT
ma-218	46	1	anal	anal	PROPN
ma-218	46	2	.	.	PUNCT
ma-218	47	1	10.28924	10.28924	NUM
ma-218	47	2	/	/	SYM
ma-218	47	3	ada	ada	PROPN
ma-218	47	4	/	/	SYM
ma-218	47	5	ma.4.8	ma.4.8	VERB
ma-218	47	6	3an	3an	ADJ
ma-218	47	7	inertial	inertial	NOUN
ma-218	47	8	-	-	PUNCT
ma-218	47	9	type	type	NOUN
ma-218	47	10	algorithm	algorithm	NOUN
ma-218	47	11	is	be	AUX
ma-218	47	12	a	a	DET
ma-218	47	13	method	method	NOUN
ma-218	47	14	for	for	ADP
ma-218	47	15	speeding	speed	VERB
ma-218	47	16	the	the	DET
ma-218	47	17	convergence	convergence	NOUN
ma-218	47	18	of	of	ADP
ma-218	47	19	the	the	DET
ma-218	47	20	sequence	sequence	NOUN
ma-218	47	21	of	of	ADP
ma-218	47	22	an	an	DET
ma-218	47	23	algorithmintroduced	algorithmintroduce	VERB
ma-218	47	24	by	by	ADP
ma-218	47	25	polyak	polyak	NOUN
ma-218	47	26	[	[	X
ma-218	47	27	16	16	NUM
ma-218	47	28	]	]	PUNCT
ma-218	47	29	.	.	PUNCT
ma-218	48	1	numerous	numerous	ADJ
ma-218	48	2	problems	problem	NOUN
ma-218	48	3	have	have	AUX
ma-218	48	4	been	be	AUX
ma-218	48	5	approximated	approximate	VERB
ma-218	48	6	by	by	ADP
ma-218	48	7	using	use	VERB
ma-218	48	8	inertial	inertial	ADJ
ma-218	48	9	algorithms	algorithm	NOUN
ma-218	48	10	(	(	PUNCT
ma-218	48	11	for	for	SCONJ
ma-218	48	12	more	more	ADJ
ma-218	48	13	details	detail	NOUN
ma-218	48	14	see	see	VERB
ma-218	48	15	,	,	PUNCT
ma-218	48	16	[	[	X
ma-218	48	17	4	4	NUM
ma-218	48	18	,	,	PUNCT
ma-218	48	19	5	5	NUM
ma-218	48	20	,	,	PUNCT
ma-218	48	21	12	12	NUM
ma-218	48	22	]	]	PUNCT
ma-218	48	23	and	and	CCONJ
ma-218	48	24	the	the	DET
ma-218	48	25	references	reference	NOUN
ma-218	48	26	therein	therein	ADV
ma-218	48	27	)	)	PUNCT
ma-218	48	28	.	.	PUNCT
ma-218	49	1	mainge	mainge	VERB
ma-218	49	2	[	[	X
ma-218	49	3	13	13	NUM
ma-218	49	4	]	]	PUNCT
ma-218	49	5	proposed	propose	VERB
ma-218	49	6	and	and	CCONJ
ma-218	49	7	studied	study	VERB
ma-218	49	8	thedevelopment	thedevelopment	NOUN
ma-218	49	9	of	of	ADP
ma-218	49	10	an	an	DET
ma-218	49	11	inertialtype	inertialtype	NOUN
ma-218	49	12	algorithm	algorithm	NOUN
ma-218	49	13	method	method	NOUN
ma-218	49	14	as	as	SCONJ
ma-218	49	15	follows	follow	VERB
ma-218	49	16	:	:	PUNCT
ma-218	49	17	{	{	PUNCT
ma-218	49	18	un	un	PROPN
ma-218	49	19	=	=	SYM
ma-218	49	20	ωn	ωn	PROPN
ma-218	49	21	+	+	PROPN
ma-218	49	22	θn(ωn	θn(ωn	PROPN
ma-218	49	23	−	−	PROPN
ma-218	49	24	ωn−1	ωn−1	PROPN
ma-218	49	25	)	)	PUNCT
ma-218	49	26	,	,	PUNCT
ma-218	49	27	ωn+1	ωn+1	NUM
ma-218	49	28	=	=	SYM
ma-218	49	29	(	(	PUNCT
ma-218	49	30	1−	1−	NUM
ma-218	49	31	δn)un	δn)un	PUNCT
ma-218	49	32	+	+	CCONJ
ma-218	49	33	δntun.takahashi	δntun.takahashi	NUM
ma-218	49	34	and	and	CCONJ
ma-218	49	35	zembayashi	zembayashi	PROPN
ma-218	49	36	[	[	X
ma-218	49	37	17	17	NUM
ma-218	49	38	]	]	PUNCT
ma-218	49	39	proposed	propose	VERB
ma-218	49	40	an	an	DET
ma-218	49	41	iterative	iterative	NOUN
ma-218	49	42	process	process	NOUN
ma-218	49	43	which	which	PRON
ma-218	49	44	converges	converge	VERB
ma-218	49	45	strongly	strongly	ADV
ma-218	49	46	to	to	ADP
ma-218	49	47	a	a	DET
ma-218	49	48	commonelement	commonelement	NOUN
ma-218	49	49	of	of	ADP
ma-218	49	50	solution	solution	NOUN
ma-218	49	51	of	of	ADP
ma-218	49	52	equilibrium	equilibrium	NOUN
ma-218	49	53	problem	problem	NOUN
ma-218	49	54	and	and	CCONJ
ma-218	49	55	fixed	fix	VERB
ma-218	49	56	point	point	NOUN
ma-218	49	57	problem	problem	NOUN
ma-218	49	58	of	of	ADP
ma-218	49	59	relatively	relatively	ADV
ma-218	49	60	nonexpansivemapping	nonexpansivemapping	ADJ
ma-218	49	61	.	.	PUNCT
ma-218	50	1	furthermore	furthermore	ADV
ma-218	50	2	,	,	PUNCT
ma-218	50	3	the	the	DET
ma-218	50	4	generalization	generalization	NOUN
ma-218	50	5	of	of	ADP
ma-218	50	6	the	the	DET
ma-218	50	7	proposed	propose	VERB
ma-218	50	8	iterative	iterative	NOUN
ma-218	50	9	process	process	NOUN
ma-218	50	10	[	[	X
ma-218	50	11	17	17	NUM
ma-218	50	12	]	]	PUNCT
ma-218	50	13	have	have	AUX
ma-218	50	14	been	be	AUX
ma-218	50	15	carriedout	carriedout	VERB
ma-218	50	16	by	by	ADP
ma-218	50	17	many	many	ADJ
ma-218	50	18	researchers	researcher	NOUN
ma-218	50	19	(	(	PUNCT
ma-218	50	20	for	for	SCONJ
ma-218	50	21	more	more	ADJ
ma-218	50	22	details	detail	NOUN
ma-218	50	23	see	see	VERB
ma-218	50	24	,	,	PUNCT
ma-218	50	25	[	[	X
ma-218	50	26	7	7	NUM
ma-218	50	27	,	,	PUNCT
ma-218	50	28	8	8	NUM
ma-218	50	29	,	,	PUNCT
ma-218	50	30	11	11	NUM
ma-218	50	31	,	,	PUNCT
ma-218	50	32	18	18	NUM
ma-218	50	33	,	,	PUNCT
ma-218	50	34	20	20	NUM
ma-218	50	35	]	]	PUNCT
ma-218	50	36	and	and	CCONJ
ma-218	50	37	the	the	DET
ma-218	50	38	references	reference	NOUN
ma-218	50	39	therein	therein	ADV
ma-218	50	40	)	)	PUNCT
ma-218	50	41	.	.	PUNCT
ma-218	51	1	kazmiand	kazmiand	PROPN
ma-218	51	2	ali	ali	PROPN
ma-218	52	1	[	[	X
ma-218	52	2	10	10	NUM
ma-218	52	3	]	]	PUNCT
ma-218	52	4	introduced	introduce	VERB
ma-218	52	5	an	an	DET
ma-218	52	6	iterative	iterative	NOUN
ma-218	52	7	algorithm	algorithm	NOUN
ma-218	52	8	for	for	ADP
ma-218	52	9	solving	solve	VERB
ma-218	52	10	a	a	DET
ma-218	52	11	common	common	ADJ
ma-218	52	12	solution	solution	NOUN
ma-218	52	13	of	of	ADP
ma-218	52	14	ep.(1.3	ep.(1.3	PROPN
ma-218	52	15	)	)	PUNCT
ma-218	52	16	.	.	PUNCT
ma-218	53	1	and	and	CCONJ
ma-218	53	2	fixedpoint	fixedpoint	NOUN
ma-218	53	3	problemof	problemof	NOUN
ma-218	53	4	quasi−φ−	quasi−φ−	PROPN
ma-218	53	5	asymptotically	asymptotically	ADV
ma-218	53	6	nonexpansive	nonexpansive	ADJ
ma-218	53	7	mapping	mapping	NOUN
ma-218	53	8	.	.	PUNCT
ma-218	54	1	alansari	alansari	PROPN
ma-218	54	2	et	et	PROPN
ma-218	54	3	al	al	PROPN
ma-218	54	4	.	.	PUNCT
ma-218	55	1	[	[	X
ma-218	55	2	1	1	X
ma-218	55	3	]	]	PUNCT
ma-218	55	4	studied	study	VERB
ma-218	55	5	an	an	DET
ma-218	55	6	inertial	inertial	ADJ
ma-218	55	7	iterative	iterative	NOUN
ma-218	55	8	method	method	NOUN
ma-218	55	9	for	for	ADP
ma-218	55	10	finding	find	VERB
ma-218	55	11	a	a	DET
ma-218	55	12	common	common	ADJ
ma-218	55	13	solution	solution	NOUN
ma-218	55	14	of	of	ADP
ma-218	55	15	generalizedequilibrium	generalizedequilibrium	NOUN
ma-218	55	16	,	,	PUNCT
ma-218	55	17	variational	variational	ADJ
ma-218	55	18	inequality	inequality	NOUN
ma-218	55	19	and	and	CCONJ
ma-218	55	20	fixed	fix	VERB
ma-218	55	21	point	point	NOUN
ma-218	55	22	problems	problem	NOUN
ma-218	55	23	using	use	VERB
ma-218	55	24	the	the	DET
ma-218	55	25	sequences	sequence	NOUN
ma-218	55	26	{	{	PUNCT
ma-218	55	27	xn	xn	PUNCT
ma-218	55	28	}	}	PUNCT
ma-218	55	29	and	and	CCONJ
ma-218	55	30	{	{	PUNCT
ma-218	55	31	zn}generated	zn}generate	VERB
ma-218	55	32	by	by	ADP
ma-218	55	33	the	the	DET
ma-218	55	34	iterative	iterative	NOUN
ma-218	55	35	algorithm:	algorithm:	PROPN
ma-218	55	36	x0	x0	PROPN
ma-218	56	1	=	=	PUNCT
ma-218	56	2	x1	x1	PROPN
ma-218	56	3	,	,	PUNCT
ma-218	56	4	z0	z0	PROPN
ma-218	56	5	∈	∈	PROPN
ma-218	56	6	c	c	PROPN
ma-218	56	7	,	,	PUNCT
ma-218	56	8	c0	c0	NOUN
ma-218	56	9	:	:	PUNCT
ma-218	56	10	=	=	SYM
ma-218	56	11	c	c	X
ma-218	56	12	;	;	PUNCT
ma-218	56	13	µn	µn	PROPN
ma-218	56	14	=	=	SYM
ma-218	56	15	xn	xn	PROPN
ma-218	57	1	+	+	NUM
ma-218	57	2	αn(xn	αn(xn	PROPN
ma-218	57	3	−	−	PROPN
ma-218	57	4	xn−1	xn−1	PROPN
ma-218	57	5	)	)	PUNCT
ma-218	57	6	;	;	PUNCT
ma-218	57	7	yn	yn	PROPN
ma-218	57	8	=	=	PUNCT
ma-218	57	9	πcj	πcj	PROPN
ma-218	57	10	−1(jµn	−1(jµn	PROPN
ma-218	57	11	−	−	PROPN
ma-218	57	12	wngµn	wngµn	PROPN
ma-218	57	13	)	)	PUNCT
ma-218	57	14	;	;	PUNCT
ma-218	57	15	un	un	PROPN
ma-218	57	16	=	=	PROPN
ma-218	57	17	j−1(δnjzn	j−1(δnjzn	PROPN
ma-218	58	1	+	+	CCONJ
ma-218	58	2	(	(	PUNCT
ma-218	58	3	1−	1−	NUM
ma-218	58	4	δn)jtyn	δn)jtyn	PROPN
ma-218	58	5	)	)	PUNCT
ma-218	58	6	;	;	PUNCT
ma-218	58	7	zn+1	zn+1	X
ma-218	58	8	=	=	SYM
ma-218	58	9	trnun	trnun	NOUN
ma-218	58	10	;	;	PUNCT
ma-218	58	11	cn	cn	PROPN
ma-218	58	12	=	=	PUNCT
ma-218	58	13	{	{	PUNCT
ma-218	58	14	u	u	NOUN
ma-218	58	15	∈	∈	PROPN
ma-218	58	16	c	c	NOUN
ma-218	58	17	:	:	PUNCT
ma-218	58	18	φ(u	φ(u	NOUN
ma-218	58	19	,	,	PUNCT
ma-218	58	20	zn+1	zn+1	NOUN
ma-218	58	21	)	)	PUNCT
ma-218	58	22	≤	≤	PROPN
ma-218	58	23	δnφ(u	δnφ(u	PROPN
ma-218	58	24	,	,	PUNCT
ma-218	58	25	zn	zn	PROPN
ma-218	58	26	)	)	PUNCT
ma-218	59	1	+	+	CCONJ
ma-218	59	2	(	(	PUNCT
ma-218	59	3	1−	1−	NUM
ma-218	59	4	δn)φ(u	δn)φ(u	NOUN
ma-218	59	5	,	,	PUNCT
ma-218	59	6	µn	µn	NOUN
ma-218	59	7	)	)	PUNCT
ma-218	59	8	;	;	PUNCT
ma-218	59	9	qn	qn	NOUN
ma-218	59	10	=	=	SYM
ma-218	59	11	〈	〈	PROPN
ma-218	59	12	u	u	NOUN
ma-218	59	13	∈	∈	NOUN
ma-218	59	14	c	c	NOUN
ma-218	59	15	:	:	PUNCT
ma-218	59	16	xn	xn	PROPN
ma-218	60	1	−	−	PROPN
ma-218	60	2	u	u	PROPN
ma-218	60	3	,	,	PUNCT
ma-218	60	4	jxn	jxn	PROPN
ma-218	60	5	−	−	PROPN
ma-218	60	6	jx0	jx0	NOUN
ma-218	60	7	〉	〉	NOUN
ma-218	60	8	≤	≤	NOUN
ma-218	60	9	0	0	NUM
ma-218	60	10	}	}	PUNCT
ma-218	60	11	;	;	PUNCT
ma-218	60	12	xn+1	xn+1	X
ma-218	60	13	=	=	SYM
ma-218	60	14	πcn∩qnx0,∀n	πcn∩qnx0,∀n	X
ma-218	60	15	≥	≥	NOUN
ma-218	60	16	0,where	0,where	ADP
ma-218	60	17	{	{	PUNCT
ma-218	60	18	αn	αn	NOUN
ma-218	60	19	}	}	PUNCT
ma-218	60	20	⊂	⊂	PROPN
ma-218	60	21	(	(	PUNCT
ma-218	60	22	0	0	NUM
ma-218	60	23	,	,	PUNCT
ma-218	60	24	1	1	NUM
ma-218	60	25	)	)	PUNCT
ma-218	60	26	,	,	PUNCT
ma-218	60	27	{	{	PUNCT
ma-218	60	28	wn	wn	PROPN
ma-218	60	29	}	}	PUNCT
ma-218	60	30	⊂	⊂	PROPN
ma-218	60	31	(	(	PUNCT
ma-218	60	32	0,∞	0,∞	NOUN
ma-218	60	33	)	)	PUNCT
ma-218	60	34	,	,	PUNCT
ma-218	60	35	{	{	PUNCT
ma-218	60	36	δn	δn	NOUN
ma-218	60	37	}	}	PUNCT
ma-218	60	38	⊂	⊂	PROPN
ma-218	61	1	[	[	X
ma-218	61	2	0	0	NUM
ma-218	61	3	,	,	PUNCT
ma-218	61	4	1	1	NUM
ma-218	61	5	]	]	PUNCT
ma-218	61	6	and	and	CCONJ
ma-218	61	7	{	{	PUNCT
ma-218	61	8	rn	rn	PROPN
ma-218	61	9	}	}	PUNCT
ma-218	61	10	⊂	⊂	PROPN
ma-218	62	1	[	[	X
ma-218	62	2	a,∞	a,∞	PROPN
ma-218	62	3	)	)	PUNCT
ma-218	62	4	,	,	PUNCT
ma-218	62	5	for	for	ADP
ma-218	62	6	some	some	DET
ma-218	62	7	a	a	DET
ma-218	62	8	>	>	X
ma-218	62	9	0	0	NUM
ma-218	62	10	.	.	PUNCT
ma-218	63	1	then	then	ADV
ma-218	63	2	,	,	PUNCT
ma-218	63	3	{	{	PUNCT
ma-218	63	4	xn}converges	xn}converge	NOUN
ma-218	63	5	strongly	strongly	ADV
ma-218	63	6	to	to	ADP
ma-218	63	7	$	$	SYM
ma-218	63	8	=	=	NOUN
ma-218	63	9	πγx0.farid	πγx0.farid	PUNCT
ma-218	63	10	et	et	NOUN
ma-218	63	11	al	al	PROPN
ma-218	63	12	.	.	PUNCT
ma-218	64	1	[	[	X
ma-218	64	2	6	6	NUM
ma-218	64	3	]	]	PUNCT
ma-218	64	4	proposed	propose	VERB
ma-218	64	5	the	the	DET
ma-218	64	6	following	follow	VERB
ma-218	64	7	inertial	inertial	ADJ
ma-218	64	8	algorithm	algorithm	NOUN
ma-218	64	9	for	for	ADP
ma-218	64	10	approximating	approximate	VERB
ma-218	64	11	a	a	DET
ma-218	64	12	common	common	ADJ
ma-218	64	13	solution	solution	NOUN
ma-218	64	14	ofgeneralized	ofgeneralize	VERB
ma-218	64	15	mixed	mixed	ADJ
ma-218	64	16	equilibrium	equilibrium	NOUN
ma-218	64	17	problem	problem	NOUN
ma-218	64	18	,	,	PUNCT
ma-218	64	19	variational	variational	ADJ
ma-218	64	20	inequality	inequality	NOUN
ma-218	64	21	problem	problem	NOUN
ma-218	64	22	and	and	CCONJ
ma-218	64	23	fixed	fix	VERB
ma-218	64	24	point	point	NOUN
ma-218	64	25	problem	problem	NOUN
ma-218	64	26	forfamily	forfamily	ADV
ma-218	64	27	of	of	ADP
ma-218	64	28	quasi−φ−nonexpansive	quasi−φ−nonexpansive	ADJ
ma-218	64	29	mappings	mapping	NOUN
ma-218	64	30	:	:	PUNCT
ma-218	64	31	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	64	32	eur	eur	PROPN
ma-218	64	33	.	.	PUNCT
ma-218	65	1	j.	j.	PROPN
ma-218	65	2	math	math	PROPN
ma-218	65	3	.	.	PUNCT
ma-218	66	1	anal	anal	PROPN
ma-218	66	2	.	.	PUNCT
ma-218	67	1	10.28924	10.28924	NUM
ma-218	67	2	/	/	SYM
ma-218	67	3	ada	ada	PROPN
ma-218	67	4	/	/	SYM
ma-218	67	5	ma.4.8	ma.4.8	VERB
ma-218	67	6	4	4	NUM
ma-218	67	7			NOUN
ma-218	67	8	x0	x0	PROPN
ma-218	67	9	,	,	PUNCT
ma-218	67	10	x1	x1	PROPN
ma-218	67	11	∈	∈	PROPN
ma-218	68	1	q	q	NOUN
ma-218	68	2	,	,	PUNCT
ma-218	68	3	q1	q1	PROPN
ma-218	68	4	:	:	PUNCT
ma-218	68	5	=	=	SYM
ma-218	69	1	q	q	ADJ
ma-218	69	2	;	;	PUNCT
ma-218	69	3	ωn	ωn	ADP
ma-218	69	4	=	=	PUNCT
ma-218	69	5	xn	xn	PROPN
ma-218	70	1	+	+	NUM
ma-218	70	2	θn(xn	θn(xn	NOUN
ma-218	70	3	−	−	NOUN
ma-218	70	4	xn−1	xn−1	PROPN
ma-218	70	5	)	)	PUNCT
ma-218	70	6	;	;	PUNCT
ma-218	70	7	yn	yn	PROPN
ma-218	70	8	=	=	PUNCT
ma-218	70	9	πqj	πqj	VERB
ma-218	70	10	−1(jωn	−1(jωn	NOUN
ma-218	70	11	−	−	PROPN
ma-218	70	12	wnqωn	wnqωn	ADJ
ma-218	70	13	)	)	PUNCT
ma-218	70	14	;	;	PUNCT
ma-218	70	15	vn	vn	PROPN
ma-218	70	16	=	=	SYM
ma-218	70	17	j−1(δn,0jωn	j−1(δn,0jωn	PROPN
ma-218	70	18	+	+	CCONJ
ma-218	70	19	n∑	n∑	ADJ
ma-218	70	20	i=1	i=1	PROPN
ma-218	70	21	δn	δn	NOUN
ma-218	70	22	,	,	PUNCT
ma-218	70	23	ijtiωn	ijtiωn	NOUN
ma-218	70	24	)	)	PUNCT
ma-218	70	25	;	;	PUNCT
ma-218	70	26	zn	zn	X
ma-218	70	27	=	=	SYM
ma-218	71	1	j−1(αnjyn	j−1(αnjyn	X
ma-218	71	2	+	+	NUM
ma-218	71	3	(	(	PUNCT
ma-218	71	4	1−	1−	NUM
ma-218	71	5	αn)jvn	αn)jvn	NOUN
ma-218	71	6	)	)	PUNCT
ma-218	71	7	;	;	PUNCT
ma-218	71	8	un	un	PROPN
ma-218	71	9	=	=	PROPN
ma-218	71	10	trnzn	trnzn	NOUN
ma-218	71	11	;	;	PUNCT
ma-218	71	12	qn	qn	NOUN
ma-218	71	13	=	=	X
ma-218	71	14	{	{	PUNCT
ma-218	71	15	u	u	NOUN
ma-218	71	16	∈	∈	PROPN
ma-218	71	17	q	q	NOUN
ma-218	71	18	:	:	PUNCT
ma-218	71	19	φ(u	φ(u	NOUN
ma-218	71	20	,	,	PUNCT
ma-218	71	21	un	un	ADJ
ma-218	71	22	)	)	PUNCT
ma-218	71	23	≤	≤	NOUN
ma-218	71	24	φ(u	φ(u	NOUN
ma-218	71	25	,	,	PUNCT
ma-218	71	26	ωn	ωn	NUM
ma-218	71	27	)	)	PUNCT
ma-218	71	28	;	;	PUNCT
ma-218	71	29	qn	qn	PROPN
ma-218	71	30	=	=	SYM
ma-218	71	31	〈	〈	PROPN
ma-218	71	32	u	u	NOUN
ma-218	71	33	∈	∈	NOUN
ma-218	71	34	q	q	NOUN
ma-218	71	35	:	:	PUNCT
ma-218	71	36	xn	xn	PROPN
ma-218	72	1	−	−	PROPN
ma-218	72	2	u	u	PROPN
ma-218	72	3	,	,	PUNCT
ma-218	72	4	jxn	jxn	PROPN
ma-218	72	5	−	−	PROPN
ma-218	72	6	jx0	jx0	NOUN
ma-218	72	7	〉	〉	NOUN
ma-218	72	8	≤	≤	NOUN
ma-218	72	9	0	0	NUM
ma-218	72	10	}	}	PUNCT
ma-218	72	11	;	;	PUNCT
ma-218	72	12	xn+1	xn+1	X
ma-218	72	13	=	=	SYM
ma-218	72	14	πqn∩qnx0,∀n	πqn∩qnx0,∀n	X
ma-218	72	15	≥	≥	NOUN
ma-218	72	16	1	1	NUM
ma-218	72	17	.	.	PUNCT
ma-218	72	18	consider	consider	VERB
ma-218	72	19	{	{	PUNCT
ma-218	72	20	δn	δn	VERB
ma-218	72	21	,	,	PUNCT
ma-218	72	22	i	i	PROPN
ma-218	72	23	}	}	PUNCT
ma-218	72	24	and	and	CCONJ
ma-218	72	25	{	{	PUNCT
ma-218	72	26	αn	αn	NOUN
ma-218	72	27	}	}	PUNCT
ma-218	72	28	⊂	⊂	PROPN
ma-218	73	1	[	[	X
ma-218	73	2	0	0	NUM
ma-218	73	3	,	,	PUNCT
ma-218	73	4	1	1	NUM
ma-218	73	5	]	]	PUNCT
ma-218	73	6	,	,	PUNCT
ma-218	73	7	{	{	PUNCT
ma-218	73	8	wn	wn	PROPN
ma-218	73	9	}	}	PUNCT
ma-218	73	10	⊂	⊂	PROPN
ma-218	73	11	(	(	PUNCT
ma-218	73	12	0,∞	0,∞	NOUN
ma-218	73	13	)	)	PUNCT
ma-218	73	14	,	,	PUNCT
ma-218	73	15	{	{	PUNCT
ma-218	73	16	θn	θn	NOUN
ma-218	73	17	}	}	PUNCT
ma-218	73	18	⊂	⊂	PROPN
ma-218	73	19	(	(	PUNCT
ma-218	73	20	0	0	NUM
ma-218	73	21	,	,	PUNCT
ma-218	73	22	1	1	NUM
ma-218	73	23	)	)	PUNCT
ma-218	73	24	and	and	CCONJ
ma-218	73	25	{	{	PUNCT
ma-218	73	26	rn	rn	PROPN
ma-218	73	27	}	}	PUNCT
ma-218	73	28	⊂	⊂	PROPN
ma-218	74	1	[	[	X
ma-218	74	2	a,∞	a,∞	PROPN
ma-218	74	3	)	)	PUNCT
ma-218	74	4	,	,	PUNCT
ma-218	74	5	for	for	ADP
ma-218	74	6	some	some	DET
ma-218	74	7	a	a	DET
ma-218	74	8	>	>	X
ma-218	74	9	0	0	NUM
ma-218	74	10	.	.	PUNCT
ma-218	75	1	it	it	PRON
ma-218	75	2	has	have	AUX
ma-218	75	3	been	be	AUX
ma-218	75	4	proved	prove	VERB
ma-218	75	5	that	that	SCONJ
ma-218	75	6	{	{	PUNCT
ma-218	75	7	xn	xn	X
ma-218	75	8	}	}	PUNCT
ma-218	75	9	is	be	AUX
ma-218	75	10	a	a	DET
ma-218	75	11	strong	strong	ADJ
ma-218	75	12	convergent	convergent	NOUN
ma-218	75	13	to	to	ADP
ma-218	75	14	x̂	x̂	PUNCT
ma-218	75	15	=	=	PUNCT
ma-218	75	16	πωx0.motivated	πωx0.motivated	PUNCT
ma-218	75	17	and	and	CCONJ
ma-218	75	18	inspired	inspire	VERB
ma-218	75	19	by	by	ADP
ma-218	75	20	the	the	DET
ma-218	75	21	work	work	NOUN
ma-218	75	22	of	of	ADP
ma-218	75	23	kazmi	kazmi	PROPN
ma-218	75	24	and	and	CCONJ
ma-218	75	25	ali	ali	PROPN
ma-218	76	1	[	[	X
ma-218	76	2	10	10	NUM
ma-218	76	3	]	]	PUNCT
ma-218	76	4	,	,	PUNCT
ma-218	76	5	alansari	alansari	PROPN
ma-218	76	6	et	et	PROPN
ma-218	76	7	al	al	PROPN
ma-218	76	8	.	.	PUNCT
ma-218	77	1	[	[	X
ma-218	77	2	1	1	X
ma-218	77	3	]	]	PUNCT
ma-218	77	4	and	and	CCONJ
ma-218	77	5	farid	farid	PROPN
ma-218	77	6	et	et	PROPN
ma-218	77	7	al	al	PROPN
ma-218	77	8	.	.	PUNCT
ma-218	78	1	[	[	X
ma-218	78	2	6	6	NUM
ma-218	78	3	]	]	PUNCT
ma-218	78	4	.	.	PUNCT
ma-218	78	5	weproposed	wepropose	VERB
ma-218	78	6	a	a	DET
ma-218	78	7	hybrid	hybrid	ADJ
ma-218	78	8	inertial	inertial	ADJ
ma-218	78	9	iterative	iterative	NOUN
ma-218	78	10	algorithm	algorithm	NOUN
ma-218	78	11	for	for	ADP
ma-218	78	12	approximating	approximate	VERB
ma-218	78	13	a	a	DET
ma-218	78	14	common	common	ADJ
ma-218	78	15	solution	solution	NOUN
ma-218	78	16	of	of	ADP
ma-218	78	17	gmep.(1.1	gmep.(1.1	NOUN
ma-218	78	18	)	)	PUNCT
ma-218	78	19	,	,	PUNCT
ma-218	78	20	v	v	NOUN
ma-218	78	21	ip	ip	NOUN
ma-218	78	22	(	(	PUNCT
ma-218	78	23	1.4	1.4	NUM
ma-218	78	24	)	)	PUNCT
ma-218	78	25	and	and	CCONJ
ma-218	78	26	fixed	fix	VERB
ma-218	78	27	point	point	NOUN
ma-218	78	28	problem	problem	NOUN
ma-218	78	29	for	for	ADP
ma-218	78	30	a	a	DET
ma-218	78	31	family	family	NOUN
ma-218	78	32	of	of	ADP
ma-218	78	33	two	two	NUM
ma-218	78	34	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	78	35	nonexpansive	nonexpansive	ADJ
ma-218	78	36	map	map	NOUN
ma-218	78	37	-	-	PUNCT
ma-218	78	38	pings	ping	NOUN
ma-218	78	39	in	in	ADP
ma-218	78	40	twouniformly	twouniformly	ADJ
ma-218	78	41	convex	convex	NOUN
ma-218	78	42	and	and	CCONJ
ma-218	78	43	uniformly	uniformly	ADV
ma-218	78	44	smooth	smooth	ADJ
ma-218	78	45	banach	banach	NOUN
ma-218	78	46	spaces	space	VERB
ma-218	78	47	.	.	PUNCT
ma-218	79	1	our	our	PRON
ma-218	79	2	result	result	NOUN
ma-218	79	3	extends	extend	VERB
ma-218	79	4	andimproves	andimprove	VERB
ma-218	79	5	the	the	DET
ma-218	79	6	results	result	NOUN
ma-218	79	7	of	of	ADP
ma-218	79	8	kazmi	kazmi	PROPN
ma-218	79	9	and	and	CCONJ
ma-218	79	10	ali	ali	PROPN
ma-218	80	1	[	[	X
ma-218	80	2	10	10	NUM
ma-218	80	3	]	]	PUNCT
ma-218	80	4	,	,	PUNCT
ma-218	80	5	alansari	alansari	PROPN
ma-218	80	6	et	et	PROPN
ma-218	80	7	al	al	PROPN
ma-218	80	8	.	.	PUNCT
ma-218	81	1	[	[	X
ma-218	81	2	1	1	X
ma-218	81	3	]	]	PUNCT
ma-218	81	4	and	and	CCONJ
ma-218	81	5	farid	farid	PROPN
ma-218	81	6	et	et	PROPN
ma-218	81	7	al	al	PROPN
ma-218	81	8	.	.	PUNCT
ma-218	82	1	[	[	X
ma-218	82	2	6	6	NUM
ma-218	82	3	]	]	PUNCT
ma-218	82	4	,	,	PUNCT
ma-218	82	5	many	many	ADJ
ma-218	82	6	results	result	VERB
ma-218	82	7	inthe	inthe	ADJ
ma-218	82	8	literature	literature	NOUN
ma-218	82	9	.	.	PUNCT
ma-218	83	1	2	2	X
ma-218	83	2	.	.	X
ma-218	83	3	preliminaries	preliminary	NOUN
ma-218	83	4	let	let	VERB
ma-218	83	5	w	w	NOUN
ma-218	83	6	=	=	PRON
ma-218	83	7	{	{	PUNCT
ma-218	83	8	τ1	τ1	PROPN
ma-218	83	9	∈	∈	PROPN
ma-218	83	10	b	b	PROPN
ma-218	83	11	:	:	PUNCT
ma-218	83	12	‖	‖	PROPN
ma-218	83	13	τ1	τ1	NOUN
ma-218	83	14	‖=	‖=	NOUN
ma-218	83	15	1	1	NUM
ma-218	83	16	}	}	PUNCT
ma-218	83	17	be	be	AUX
ma-218	83	18	the	the	DET
ma-218	83	19	unit	unit	NOUN
ma-218	83	20	sphere	sphere	NOUN
ma-218	83	21	of	of	ADP
ma-218	83	22	b.	b.	PROPN
ma-218	83	23	if	if	SCONJ
ma-218	83	24	for	for	ADP
ma-218	83	25	any	any	DET
ma-218	83	26	ε	ε	PROPN
ma-218	83	27	∈	∈	PROPN
ma-218	83	28	(	(	PUNCT
ma-218	83	29	0	0	NUM
ma-218	83	30	,	,	PUNCT
ma-218	83	31	2	2	NUM
ma-218	83	32	]	]	PUNCT
ma-218	83	33	there	there	PRON
ma-218	83	34	exists	exist	VERB
ma-218	83	35	δ	δ	PROPN
ma-218	83	36	>	>	X
ma-218	83	37	0	0	PUNCT
ma-218	84	1	suchthat	suchthat	PROPN
ma-218	84	2	‖	‖	ADJ
ma-218	84	3	τ1	τ1	NOUN
ma-218	84	4	−	−	NOUN
ma-218	84	5	τ2	τ2	PROPN
ma-218	84	6	‖≥	‖≥	ADJ
ma-218	84	7	ε	ε	PROPN
ma-218	85	1	=	=	AUX
ma-218	85	2	⇒	⇒	NOUN
ma-218	85	3	‖	‖	PROPN
ma-218	85	4	τ1	τ1	NOUN
ma-218	85	5	+	+	CCONJ
ma-218	85	6	τ2	τ2	PROPN
ma-218	85	7	‖	‖	ADJ
ma-218	85	8	2	2	NUM
ma-218	85	9	≤	≤	NUM
ma-218	85	10	1−	1−	NUM
ma-218	85	11	δ	δ	PROPN
ma-218	85	12	,	,	PUNCT
ma-218	85	13	∀τ1	∀τ1	ADP
ma-218	85	14	,	,	PUNCT
ma-218	85	15	τ2	τ2	PROPN
ma-218	85	16	∈	∈	PROPN
ma-218	85	17	w	w	NOUN
ma-218	85	18	,	,	PUNCT
ma-218	85	19	then	then	ADV
ma-218	85	20	b	b	PROPN
ma-218	85	21	is	be	AUX
ma-218	85	22	called	call	VERB
ma-218	85	23	uniformly	uniformly	ADV
ma-218	85	24	convex	convex	NOUN
ma-218	85	25	.	.	PUNCT
ma-218	86	1	b	b	NOUN
ma-218	86	2	is	be	AUX
ma-218	86	3	called	call	VERB
ma-218	86	4	strictly	strictly	ADV
ma-218	86	5	convex	convex	ADJ
ma-218	86	6	if	if	SCONJ
ma-218	86	7	‖	‖	PROPN
ma-218	86	8	τ1	τ1	NOUN
ma-218	86	9	+	+	CCONJ
ma-218	86	10	τ2	τ2	NOUN
ma-218	86	11	‖	‖	ADJ
ma-218	86	12	2	2	NUM
ma-218	86	13	<	<	X
ma-218	86	14	1	1	NUM
ma-218	86	15	,	,	PUNCT
ma-218	86	16	∀τ1	∀τ1	ADP
ma-218	86	17	,	,	PUNCT
ma-218	86	18	τ2	τ2	PROPN
ma-218	86	19	∈	∈	PROPN
ma-218	86	20	w	w	NOUN
ma-218	86	21	and	and	CCONJ
ma-218	86	22	τ1	τ1	PROPN
ma-218	86	23	6=	6=	SYM
ma-218	86	24	τ2	τ2	NOUN
ma-218	86	25	.	.	PUNCT
ma-218	87	1	the	the	DET
ma-218	87	2	space	space	NOUN
ma-218	87	3	b	b	PROPN
ma-218	87	4	is	be	AUX
ma-218	87	5	called	call	VERB
ma-218	87	6	smooth	smooth	ADJ
ma-218	87	7	if	if	SCONJ
ma-218	87	8	lim	lim	PROPN
ma-218	87	9	t→0	t→0	ADP
ma-218	87	10	‖	‖	PROPN
ma-218	87	11	τ1	τ1	PROPN
ma-218	87	12	+	+	CCONJ
ma-218	87	13	tτ2	tτ2	VERB
ma-218	87	14	‖	‖	PROPN
ma-218	87	15	−	−	PROPN
ma-218	87	16	‖	‖	PROPN
ma-218	87	17	τ1	τ1	PROPN
ma-218	87	18	‖	‖	PROPN
ma-218	87	19	t	t	PROPN
ma-218	87	20	exists	exist	VERB
ma-218	87	21	,	,	PUNCT
ma-218	87	22	∀τ1	∀τ1	PUNCT
ma-218	87	23	,	,	PUNCT
ma-218	87	24	τ2	τ2	PROPN
ma-218	87	25	∈	∈	PROPN
ma-218	87	26	w	w	NOUN
ma-218	87	27	and	and	CCONJ
ma-218	87	28	also	also	ADV
ma-218	87	29	is	be	AUX
ma-218	87	30	said	say	VERB
ma-218	87	31	to	to	PART
ma-218	87	32	be	be	AUX
ma-218	87	33	uniformly	uniformly	ADV
ma-218	87	34	smooth	smooth	ADJ
ma-218	87	35	if	if	SCONJ
ma-218	87	36	the	the	DET
ma-218	87	37	limitis	limitis	NOUN
ma-218	87	38	attained	attain	VERB
ma-218	87	39	uniformly	uniformly	ADV
ma-218	87	40	,	,	PUNCT
ma-218	87	41	∀τ1	∀τ1	ADP
ma-218	87	42	,	,	PUNCT
ma-218	87	43	τ2	τ2	PROPN
ma-218	87	44	∈	∈	PROPN
ma-218	87	45	w.a	w.a	PROPN
ma-218	87	46	function	function	PROPN
ma-218	87	47	φ	φ	PROPN
ma-218	87	48	:	:	PUNCT
ma-218	88	1	b	b	X
ma-218	88	2	×	×	NOUN
ma-218	88	3	b	b	NOUN
ma-218	88	4	−→	−→	NOUN
ma-218	88	5	r	r	NOUN
ma-218	88	6	defined	define	VERB
ma-218	88	7	by	by	ADP
ma-218	88	8	φ(τ1	φ(τ1	NOUN
ma-218	88	9	,	,	PUNCT
ma-218	88	10	τ2	τ2	NOUN
ma-218	88	11	)	)	PUNCT
ma-218	88	12	=	=	NOUN
ma-218	88	13	‖	‖	PROPN
ma-218	88	14	τ1	τ1	PROPN
ma-218	88	15	‖2	‖2	NOUN
ma-218	88	16	−2〈τ1	−2〈τ1	NOUN
ma-218	88	17	,	,	PUNCT
ma-218	88	18	jτ2〉+	jτ2〉+	PROPN
ma-218	88	19	‖τ2	‖τ2	PROPN
ma-218	88	20	‖2	‖2	PROPN
ma-218	88	21	,	,	PUNCT
ma-218	88	22	∀τ1	∀τ1	ADP
ma-218	88	23	,	,	PUNCT
ma-218	88	24	τ2	τ2	PROPN
ma-218	88	25	∈	∈	PROPN
ma-218	88	26	b.	b.	NOUN
ma-218	88	27	is	be	AUX
ma-218	88	28	consider	consider	VERB
ma-218	88	29	as	as	ADP
ma-218	88	30	lyapunov	lyapunov	PROPN
ma-218	88	31	functional	functional	ADJ
ma-218	88	32	.	.	PUNCT
ma-218	89	1	from	from	ADP
ma-218	89	2	the	the	DET
ma-218	89	3	definition	definition	NOUN
ma-218	89	4	of	of	ADP
ma-218	89	5	φ	φ	PROPN
ma-218	89	6	,	,	PUNCT
ma-218	89	7	the	the	DET
ma-218	89	8	following	follow	VERB
ma-218	89	9	properties	property	NOUN
ma-218	89	10	can	can	AUX
ma-218	89	11	be	be	AUX
ma-218	89	12	veri	veri	NOUN
ma-218	89	13	-	-	PUNCT
ma-218	89	14	fied	fie	VERB
ma-218	89	15	[	[	X
ma-218	89	16	6	6	NUM
ma-218	89	17	]	]	NUM
ma-218	89	18	:	:	PUNCT
ma-218	89	19	(	(	PUNCT
ma-218	89	20	l1	l1	PROPN
ma-218	89	21	)	)	PUNCT
ma-218	89	22	(	(	PUNCT
ma-218	89	23	‖	‖	PROPN
ma-218	89	24	τ1	τ1	PROPN
ma-218	89	25	‖	‖	PROPN
ma-218	90	1	−	−	PROPN
ma-218	90	2	‖	‖	PROPN
ma-218	90	3	τ2	τ2	PROPN
ma-218	90	4	‖)2	‖)2	PROPN
ma-218	90	5	≤	≤	NOUN
ma-218	90	6	φ(τ1	φ(τ1	NOUN
ma-218	90	7	,	,	PUNCT
ma-218	90	8	τ2	τ2	NOUN
ma-218	90	9	)	)	PUNCT
ma-218	90	10	≤	≤	NOUN
ma-218	90	11	(	(	PUNCT
ma-218	90	12	‖	‖	PROPN
ma-218	90	13	τ1	τ1	NOUN
ma-218	90	14	‖	‖	PROPN
ma-218	90	15	+	+	CCONJ
ma-218	90	16	‖	‖	PROPN
ma-218	90	17	τ2	τ2	PROPN
ma-218	90	18	‖)2	‖)2	PROPN
ma-218	90	19	,	,	PUNCT
ma-218	90	20	∀τ1	∀τ1	ADP
ma-218	90	21	,	,	PUNCT
ma-218	90	22	τ2	τ2	PROPN
ma-218	90	23	∈	∈	PROPN
ma-218	90	24	b	b	NOUN
ma-218	90	25	;	;	PUNCT
ma-218	90	26	(	(	PUNCT
ma-218	90	27	l2	l2	NOUN
ma-218	90	28	)	)	PUNCT
ma-218	90	29	φ(τ1	φ(τ1	PROPN
ma-218	90	30	,	,	PUNCT
ma-218	90	31	j	j	PROPN
ma-218	90	32	−1(λjτ2	−1(λjτ2	NUM
ma-218	90	33	+	+	CCONJ
ma-218	90	34	(	(	PUNCT
ma-218	90	35	1−	1−	NUM
ma-218	90	36	λ)jτ3	λ)jτ3	NOUN
ma-218	90	37	)	)	PUNCT
ma-218	90	38	)	)	PUNCT
ma-218	90	39	≤	≤	NUM
ma-218	91	1	λφ(τ1	λφ(τ1	NOUN
ma-218	91	2	,	,	PUNCT
ma-218	91	3	τ2	τ2	NOUN
ma-218	91	4	)	)	PUNCT
ma-218	92	1	+	+	CCONJ
ma-218	92	2	(	(	PUNCT
ma-218	92	3	1−	1−	NUM
ma-218	92	4	λ)φ(τ1	λ)φ(τ1	NOUN
ma-218	92	5	,	,	PUNCT
ma-218	92	6	τ3	τ3	PROPN
ma-218	92	7	)	)	PUNCT
ma-218	92	8	,	,	PUNCT
ma-218	92	9	∀τ1	∀τ1	PROPN
ma-218	92	10	,	,	PUNCT
ma-218	92	11	τ2	τ2	PROPN
ma-218	92	12	,	,	PUNCT
ma-218	92	13	τ3	τ3	NOUN
ma-218	92	14	∈	∈	PROPN
ma-218	92	15	b	b	PROPN
ma-218	92	16	,	,	PUNCT
ma-218	92	17	(	(	PUNCT
ma-218	92	18	l3	l3	NOUN
ma-218	92	19	)	)	PUNCT
ma-218	92	20	φ(τ1	φ(τ1	PROPN
ma-218	92	21	,	,	PUNCT
ma-218	92	22	τ2	τ2	NOUN
ma-218	92	23	)	)	PUNCT
ma-218	93	1	=	=	NOUN
ma-218	93	2	‖	‖	PROPN
ma-218	93	3	τ1	τ1	PROPN
ma-218	93	4	‖	‖	PROPN
ma-218	93	5	‖	‖	PROPN
ma-218	93	6	jτ1	jτ1	NOUN
ma-218	94	1	−	−	PROPN
ma-218	94	2	jτ2	jτ2	NOUN
ma-218	94	3	‖	‖	PROPN
ma-218	94	4	+	+	CCONJ
ma-218	94	5	‖	‖	PROPN
ma-218	94	6	τ2	τ2	PROPN
ma-218	94	7	‖	‖	PROPN
ma-218	94	8	‖	‖	PROPN
ma-218	94	9	τ1	τ1	PROPN
ma-218	94	10	−	−	PROPN
ma-218	94	11	τ2	τ2	PROPN
ma-218	94	12	‖	‖	PROPN
ma-218	94	13	,	,	PUNCT
ma-218	94	14	∀τ1	∀τ1	ADP
ma-218	94	15	,	,	PUNCT
ma-218	95	1	τ2	τ2	PROPN
ma-218	95	2	∈	∈	PROPN
ma-218	95	3	b.	b.	NOUN
ma-218	96	1	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PRON
ma-218	96	2	eur	eur	PROPN
ma-218	96	3	.	.	PUNCT
ma-218	97	1	j.	j.	PROPN
ma-218	97	2	math	math	PROPN
ma-218	97	3	.	.	PUNCT
ma-218	98	1	anal	anal	PROPN
ma-218	98	2	.	.	PUNCT
ma-218	99	1	10.28924	10.28924	NUM
ma-218	99	2	/	/	SYM
ma-218	99	3	ada	ada	PROPN
ma-218	99	4	/	/	SYM
ma-218	99	5	ma.4.8	ma.4.8	ADJ
ma-218	99	6	5	5	NUM
ma-218	99	7	remark	remark	NOUN
ma-218	99	8	2.1	2.1	NUM
ma-218	99	9	.	.	PUNCT
ma-218	100	1	consider	consider	VERB
ma-218	100	2	b	b	NOUN
ma-218	100	3	as	as	ADV
ma-218	100	4	smooth	smooth	ADJ
ma-218	100	5	,	,	PUNCT
ma-218	100	6	strictly	strictly	ADV
ma-218	100	7	convex	convex	VERB
ma-218	100	8	and	and	CCONJ
ma-218	100	9	reflexive	reflexive	ADJ
ma-218	100	10	banach	banach	NOUN
ma-218	100	11	space	space	NOUN
ma-218	100	12	,	,	PUNCT
ma-218	100	13	then	then	ADV
ma-218	100	14	φ(τ1	φ(τ1	NOUN
ma-218	100	15	,	,	PUNCT
ma-218	100	16	τ2	τ2	NOUN
ma-218	100	17	)	)	PUNCT
ma-218	100	18	=	=	SYM
ma-218	101	1	0	0	NUM
ma-218	101	2	⇐	⇐	ADJ
ma-218	101	3	⇒	⇒	NOUN
ma-218	101	4	τ1	τ1	NOUN
ma-218	101	5	=	=	SYM
ma-218	101	6	τ2	τ2	PROPN
ma-218	101	7	,	,	PUNCT
ma-218	101	8	∀τ1	∀τ1	ADP
ma-218	101	9	,	,	PUNCT
ma-218	101	10	τ2	τ2	PROPN
ma-218	101	11	∈	∈	PROPN
ma-218	101	12	b.	b.	PROPN
ma-218	101	13	lemma	lemma	PROPN
ma-218	101	14	2.2	2.2	NUM
ma-218	101	15	.	.	PUNCT
ma-218	102	1	[	[	X
ma-218	102	2	9	9	NUM
ma-218	102	3	]	]	PUNCT
ma-218	102	4	let	let	VERB
ma-218	102	5	c	c	NOUN
ma-218	102	6	6=	6=	NOUN
ma-218	102	7	∅	∅	NOUN
ma-218	102	8	be	be	AUX
ma-218	102	9	closed	close	VERB
ma-218	102	10	convex	convex	NOUN
ma-218	102	11	subset	subset	NOUN
ma-218	102	12	of	of	ADP
ma-218	102	13	a	a	DET
ma-218	102	14	stricly	stricly	ADV
ma-218	102	15	convex	convex	NOUN
ma-218	102	16	,	,	PUNCT
ma-218	102	17	reflexive	reflexive	ADJ
ma-218	102	18	and	and	CCONJ
ma-218	102	19	smooth	smooth	ADJ
ma-218	102	20	banach	banach	NOUN
ma-218	102	21	space	space	NOUN
ma-218	102	22	b.	b.	PROPN
ma-218	103	1	then	then	ADV
ma-218	103	2	,	,	PUNCT
ma-218	103	3	∃	∃	PROPN
ma-218	103	4	a	a	DET
ma-218	103	5	unique	unique	ADJ
ma-218	103	6	element	element	NOUN
ma-218	103	7	τ0	τ0	NOUN
ma-218	103	8	∈	∈	NOUN
ma-218	103	9	c	c	NOUN
ma-218	103	10	such	such	ADJ
ma-218	103	11	that	that	PRON
ma-218	103	12	φ(τ0	φ(τ0	PROPN
ma-218	103	13	,	,	PUNCT
ma-218	103	14	τ1	τ1	NOUN
ma-218	103	15	)	)	PUNCT
ma-218	103	16	=	=	SYM
ma-218	103	17	inf	inf	NOUN
ma-218	103	18	v∈c	v∈c	NOUN
ma-218	103	19	φ(v	φ(v	ADV
ma-218	103	20	,	,	PUNCT
ma-218	103	21	τ1	τ1	NOUN
ma-218	103	22	)	)	PUNCT
ma-218	103	23	,	,	PUNCT
ma-218	103	24	for	for	ADP
ma-218	103	25	τ1	τ1	PROPN
ma-218	103	26	∈	∈	PROPN
ma-218	103	27	b.	b.	PROPN
ma-218	103	28	lemma	lemma	PROPN
ma-218	103	29	2.3	2.3	NUM
ma-218	103	30	.	.	PUNCT
ma-218	104	1	[	[	X
ma-218	104	2	15	15	NUM
ma-218	104	3	]	]	X
ma-218	104	4	let	let	VERB
ma-218	104	5	b	b	PRON
ma-218	104	6	be	be	AUX
ma-218	104	7	a	a	DET
ma-218	104	8	uniformly	uniformly	ADJ
ma-218	104	9	convex	convex	NOUN
ma-218	104	10	and	and	CCONJ
ma-218	104	11	smooth	smooth	ADJ
ma-218	104	12	banach	banach	NOUN
ma-218	104	13	space	space	NOUN
ma-218	104	14	,	,	PUNCT
ma-218	105	1	c	c	PROPN
ma-218	105	2	⊂	⊂	PROPN
ma-218	105	3	b	b	PROPN
ma-218	105	4	be	be	AUX
ma-218	105	5	closed	close	VERB
ma-218	105	6	convex	convex	NOUN
ma-218	105	7	and	and	CCONJ
ma-218	105	8	t	t	NOUN
ma-218	105	9	:	:	PUNCT
ma-218	106	1	c	c	AUX
ma-218	106	2	−→	−→	NOUN
ma-218	106	3	c	c	AUX
ma-218	106	4	be	be	AUX
ma-218	106	5	closed	close	VERB
ma-218	106	6	and	and	CCONJ
ma-218	106	7	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	106	8	nonexpansive	nonexpansive	ADJ
ma-218	106	9	mapping	mapping	NOUN
ma-218	106	10	.	.	PUNCT
ma-218	107	1	then	then	ADV
ma-218	107	2	,	,	PUNCT
ma-218	107	3	f	f	PROPN
ma-218	107	4	(	(	PUNCT
ma-218	107	5	t	t	PROPN
ma-218	107	6	)	)	PUNCT
ma-218	107	7	is	be	AUX
ma-218	107	8	closed	close	VERB
ma-218	107	9	and	and	CCONJ
ma-218	107	10	convex	convex	PROPN
ma-218	107	11	.	.	PUNCT
ma-218	108	1	lemma	lemma	PROPN
ma-218	108	2	2.4	2.4	NUM
ma-218	108	3	.	.	PUNCT
ma-218	109	1	[	[	X
ma-218	109	2	14	14	NUM
ma-218	109	3	]	]	PUNCT
ma-218	109	4	let	let	VERB
ma-218	109	5	c	c	NOUN
ma-218	109	6	6=	6=	NOUN
ma-218	109	7	∅	∅	NOUN
ma-218	109	8	be	be	AUX
ma-218	109	9	closed	close	VERB
ma-218	109	10	convex	convex	NOUN
ma-218	109	11	subset	subset	NOUN
ma-218	109	12	of	of	ADP
ma-218	109	13	b	b	PROPN
ma-218	109	14	and	and	CCONJ
ma-218	109	15	q	q	NOUN
ma-218	109	16	:	:	PUNCT
ma-218	109	17	c	c	AUX
ma-218	109	18	−→	−→	ADV
ma-218	109	19	b∗	b∗	ADV
ma-218	109	20	be	be	AUX
ma-218	109	21	monotone	monotone	ADJ
ma-218	109	22	and	and	CCONJ
ma-218	109	23	hemicontinuous	hemicontinuous	ADJ
ma-218	109	24	function	function	NOUN
ma-218	109	25	.	.	PUNCT
ma-218	110	1	then	then	ADV
ma-218	110	2	v	v	X
ma-218	110	3	ip	ip	NOUN
ma-218	110	4	(	(	PUNCT
ma-218	110	5	1.4	1.4	NUM
ma-218	110	6	)	)	PUNCT
ma-218	110	7	.	.	PUNCT
ma-218	111	1	is	be	AUX
ma-218	111	2	closed	close	VERB
ma-218	111	3	and	and	CCONJ
ma-218	111	4	convex	convex	VERB
ma-218	111	5	lemma	lemma	PROPN
ma-218	111	6	2.5	2.5	NUM
ma-218	111	7	.	.	PUNCT
ma-218	112	1	[	[	X
ma-218	112	2	19	19	NUM
ma-218	112	3	]	]	X
ma-218	112	4	let	let	VERB
ma-218	112	5	b	b	X
ma-218	112	6	be	be	AUX
ma-218	112	7	a	a	DET
ma-218	112	8	2−uniformly	2−uniformly	ADJ
ma-218	112	9	convex	convex	NOUN
ma-218	112	10	and	and	CCONJ
ma-218	112	11	smooth	smooth	ADJ
ma-218	112	12	banach	banach	NOUN
ma-218	112	13	space	space	NOUN
ma-218	112	14	.	.	PUNCT
ma-218	113	1	then	then	ADV
ma-218	113	2	,	,	PUNCT
ma-218	113	3	τ1	τ1	NOUN
ma-218	113	4	,	,	PUNCT
ma-218	113	5	τ2	τ2	PROPN
ma-218	113	6	∈	∈	PROPN
ma-218	113	7	b	b	PROPN
ma-218	113	8	,	,	PUNCT
ma-218	113	9	φ(τ1	φ(τ1	NOUN
ma-218	113	10	,	,	PUNCT
ma-218	113	11	τ2	τ2	PROPN
ma-218	113	12	)	)	PUNCT
ma-218	113	13	≥	≥	NOUN
ma-218	114	1	δ	δ	PROPN
ma-218	114	2	‖	‖	PROPN
ma-218	114	3	τ1	τ1	PROPN
ma-218	114	4	−	−	NOUN
ma-218	114	5	τ2	τ2	NOUN
ma-218	114	6	‖2	‖2	NOUN
ma-218	114	7	,	,	PUNCT
ma-218	114	8	where	where	SCONJ
ma-218	114	9	0	0	X
ma-218	114	10	<	<	X
ma-218	114	11	δ	δ	PROPN
ma-218	114	12	≤	≤	ADV
ma-218	114	13	1	1	NUM
ma-218	114	14	and	and	CCONJ
ma-218	114	15	called	call	VERB
ma-218	114	16	two	two	NUM
ma-218	114	17	-	-	PUNCT
ma-218	114	18	uniformly	uniformly	ADV
ma-218	114	19	convex	convex	NOUN
ma-218	114	20	constant	constant	ADJ
ma-218	114	21	.	.	PUNCT
ma-218	115	1	lemma	lemma	PROPN
ma-218	115	2	2.6	2.6	NUM
ma-218	115	3	.	.	PUNCT
ma-218	116	1	[	[	X
ma-218	116	2	19	19	NUM
ma-218	116	3	]	]	X
ma-218	116	4	let	let	VERB
ma-218	116	5	b	b	X
ma-218	116	6	be	be	AUX
ma-218	116	7	a	a	DET
ma-218	116	8	two	two	NUM
ma-218	116	9	-	-	PUNCT
ma-218	116	10	uniformly	uniformly	ADV
ma-218	116	11	convex	convex	NOUN
ma-218	116	12	banach	banach	NOUN
ma-218	116	13	space	space	NOUN
ma-218	116	14	,	,	PUNCT
ma-218	116	15	then	then	ADV
ma-218	116	16	‖	‖	PROPN
ma-218	116	17	τ1	τ1	PROPN
ma-218	116	18	−	−	NOUN
ma-218	116	19	τ2	τ2	NOUN
ma-218	116	20	‖≤	‖≤	PROPN
ma-218	116	21	2	2	NUM
ma-218	116	22	δ	δ	NOUN
ma-218	116	23	‖	‖	ADJ
ma-218	116	24	jτ1	jτ1	NOUN
ma-218	116	25	−	−	PROPN
ma-218	116	26	jτ2	jτ2	PROPN
ma-218	116	27	‖	‖	PROPN
ma-218	116	28	,	,	PUNCT
ma-218	116	29	∀τ1	∀τ1	ADP
ma-218	116	30	,	,	PUNCT
ma-218	116	31	τ2	τ2	PROPN
ma-218	116	32	∈	∈	PROPN
ma-218	116	33	b	b	NOUN
ma-218	116	34	,	,	PUNCT
ma-218	116	35	where	where	SCONJ
ma-218	116	36	0	0	X
ma-218	116	37	<	<	X
ma-218	116	38	δ	δ	PROPN
ma-218	116	39	≤	≤	ADV
ma-218	116	40	1	1	NUM
ma-218	116	41	.	.	PUNCT
ma-218	117	1	lemma	lemma	PROPN
ma-218	117	2	2.7	2.7	NUM
ma-218	117	3	.	.	PUNCT
ma-218	118	1	[	[	X
ma-218	118	2	9	9	NUM
ma-218	118	3	]	]	PUNCT
ma-218	118	4	let	let	VERB
ma-218	118	5	e	e	PRON
ma-218	118	6	be	be	AUX
ma-218	118	7	a	a	DET
ma-218	118	8	smooth	smooth	ADJ
ma-218	118	9	and	and	CCONJ
ma-218	118	10	uniformly	uniformly	ADV
ma-218	118	11	convex	convex	VERB
ma-218	118	12	banach	banach	NOUN
ma-218	118	13	space	space	NOUN
ma-218	118	14	and	and	CCONJ
ma-218	118	15	let	let	VERB
ma-218	118	16	{	{	PUNCT
ma-218	118	17	un	un	VERB
ma-218	118	18	}	}	PUNCT
ma-218	118	19	and	and	CCONJ
ma-218	118	20	{	{	PUNCT
ma-218	118	21	vn	vn	NOUN
ma-218	118	22	}	}	PUNCT
ma-218	118	23	be	be	AUX
ma-218	118	24	sequences	sequence	NOUN
ma-218	118	25	in	in	ADP
ma-218	118	26	e	e	NOUN
ma-218	118	27	such	such	ADJ
ma-218	118	28	that	that	SCONJ
ma-218	118	29	either	either	CCONJ
ma-218	118	30	{	{	PUNCT
ma-218	118	31	un	un	PROPN
ma-218	118	32	}	}	PUNCT
ma-218	118	33	or	or	CCONJ
ma-218	118	34	{	{	PUNCT
ma-218	118	35	vn	vn	NOUN
ma-218	118	36	}	}	PUNCT
ma-218	118	37	is	be	AUX
ma-218	118	38	bounded	bound	VERB
ma-218	118	39	.	.	PUNCT
ma-218	119	1	if	if	SCONJ
ma-218	119	2	lim	lim	PROPN
ma-218	119	3	n→∞	n→∞	PRON
ma-218	119	4	φ(un	φ(un	PROPN
ma-218	119	5	,	,	PUNCT
ma-218	119	6	vn	vn	NOUN
ma-218	119	7	)	)	PUNCT
ma-218	119	8	=	=	SYM
ma-218	119	9	0	0	NUM
ma-218	119	10	,	,	PUNCT
ma-218	119	11	then	then	ADV
ma-218	119	12	lim	lim	PROPN
ma-218	119	13	n→∞	n→∞	PROPN
ma-218	119	14	‖	‖	PROPN
ma-218	119	15	un	un	PROPN
ma-218	119	16	−	−	PROPN
ma-218	119	17	vn	vn	PROPN
ma-218	119	18	‖=	‖=	PROPN
ma-218	119	19	0	0	X
ma-218	119	20	.	.	PROPN
ma-218	119	21	remark	remark	PROPN
ma-218	119	22	2.8	2.8	NUM
ma-218	119	23	.	.	PUNCT
ma-218	120	1	by	by	ADP
ma-218	120	2	considering	consider	VERB
ma-218	120	3	(	(	PUNCT
ma-218	120	4	l3	l3	NOUN
ma-218	120	5	)	)	PUNCT
ma-218	120	6	,	,	PUNCT
ma-218	120	7	it	it	PRON
ma-218	120	8	is	be	AUX
ma-218	120	9	observe	observe	VERB
ma-218	120	10	that	that	SCONJ
ma-218	120	11	the	the	DET
ma-218	120	12	converse	converse	NOUN
ma-218	120	13	of	of	ADP
ma-218	120	14	lemma	lemma	PROPN
ma-218	120	15	2.7	2.7	NUM
ma-218	120	16	is	be	AUX
ma-218	120	17	true	true	ADJ
ma-218	120	18	,	,	PUNCT
ma-218	120	19	providedthat	providedthat	NOUN
ma-218	120	20	{	{	PUNCT
ma-218	120	21	un	un	PROPN
ma-218	120	22	}	}	PUNCT
ma-218	120	23	and	and	CCONJ
ma-218	120	24	{	{	PUNCT
ma-218	120	25	vn	vn	NOUN
ma-218	120	26	}	}	PUNCT
ma-218	120	27	are	be	AUX
ma-218	120	28	bounded	bound	VERB
ma-218	120	29	lemma	lemma	PROPN
ma-218	120	30	2.9	2.9	NUM
ma-218	120	31	.	.	PUNCT
ma-218	121	1	[	[	X
ma-218	121	2	2	2	X
ma-218	121	3	]	]	PUNCT
ma-218	121	4	let	let	VERB
ma-218	121	5	c	c	NOUN
ma-218	121	6	6=	6=	NOUN
ma-218	121	7	∅	∅	NOUN
ma-218	121	8	be	be	AUX
ma-218	121	9	closed	close	VERB
ma-218	121	10	convex	convex	NOUN
ma-218	121	11	subset	subset	NOUN
ma-218	121	12	of	of	ADP
ma-218	121	13	a	a	DET
ma-218	121	14	stricly	stricly	ADV
ma-218	121	15	convex	convex	NOUN
ma-218	121	16	,	,	PUNCT
ma-218	121	17	reflexive	reflexive	ADJ
ma-218	121	18	and	and	CCONJ
ma-218	121	19	smooth	smooth	ADJ
ma-218	121	20	banach	banach	NOUN
ma-218	121	21	space	space	NOUN
ma-218	121	22	b.	b.	PROPN
ma-218	122	1	then	then	ADV
ma-218	122	2	,	,	PUNCT
ma-218	122	3	φ(v	φ(v	ADV
ma-218	122	4	,	,	PUNCT
ma-218	122	5	πcτ1	πcτ1	NOUN
ma-218	122	6	)	)	PUNCT
ma-218	123	1	+	+	CCONJ
ma-218	123	2	φ(πcτ1	φ(πcτ1	NOUN
ma-218	123	3	,	,	PUNCT
ma-218	123	4	τ1	τ1	NOUN
ma-218	123	5	)	)	PUNCT
ma-218	123	6	≤	≤	NOUN
ma-218	123	7	(	(	PUNCT
ma-218	123	8	v	v	NOUN
ma-218	123	9	,	,	PUNCT
ma-218	123	10	τ1	τ1	NOUN
ma-218	123	11	)	)	PUNCT
ma-218	123	12	,	,	PUNCT
ma-218	123	13	∀v	∀v	PROPN
ma-218	123	14	∈	∈	PROPN
ma-218	123	15	c	c	X
ma-218	123	16	,	,	PUNCT
ma-218	123	17	τ1	τ1	PROPN
ma-218	123	18	∈	∈	PROPN
ma-218	123	19	b.	b.	PROPN
ma-218	124	1	and	and	CCONJ
ma-218	124	2	,	,	PUNCT
ma-218	124	3	so	so	ADV
ma-218	124	4	for	for	ADP
ma-218	124	5	any	any	DET
ma-218	124	6	τ1	τ1	NOUN
ma-218	124	7	∈	∈	PROPN
ma-218	124	8	b	b	PROPN
ma-218	124	9	and	and	CCONJ
ma-218	124	10	v	v	ADP
ma-218	124	11	∈	∈	NOUN
ma-218	124	12	c	c	X
ma-218	124	13	,	,	PUNCT
ma-218	124	14	u	u	NOUN
ma-218	124	15	=	=	NOUN
ma-218	124	16	πcτ1	πcτ1	NOUN
ma-218	124	17	⇐	⇐	ADJ
ma-218	124	18	⇒	⇒	NOUN
ma-218	124	19	〈	〈	PROPN
ma-218	124	20	v	v	ADP
ma-218	124	21	−	−	PROPN
ma-218	124	22	u	u	PROPN
ma-218	124	23	,	,	PUNCT
ma-218	124	24	jτ1	jτ1	X
ma-218	124	25	−	−	PROPN
ma-218	124	26	jv	jv	PROPN
ma-218	124	27	〉	〉	PROPN
ma-218	124	28	,	,	PUNCT
ma-218	124	29	∀u	∀u	NOUN
ma-218	124	30	∈	∈	PROPN
ma-218	124	31	c.	c.	NOUN
ma-218	124	32	assumption	assumption	NOUN
ma-218	124	33	1	1	NUM
ma-218	124	34	:	:	PUNCT
ma-218	124	35	consider	consider	VERB
ma-218	124	36	d	d	NOUN
ma-218	124	37	:	:	PUNCT
ma-218	124	38	c	c	X
ma-218	124	39	×	×	NOUN
ma-218	124	40	c	c	NOUN
ma-218	124	41	−→	−→	NOUN
ma-218	124	42	r	r	NOUN
ma-218	124	43	as	as	ADP
ma-218	124	44	a	a	DET
ma-218	124	45	bifunction	bifunction	NOUN
ma-218	124	46	satisfies	satisfy	VERB
ma-218	124	47	the	the	DET
ma-218	124	48	following	follow	VERB
ma-218	124	49	assumptions	assumption	NOUN
ma-218	124	50	[	[	X
ma-218	124	51	3	3	NUM
ma-218	124	52	]	]	X
ma-218	124	53	:	:	PUNCT
ma-218	124	54	(	(	PUNCT
ma-218	124	55	d1	d1	NOUN
ma-218	124	56	)	)	PUNCT
ma-218	124	57	d(v	d(v	PROPN
ma-218	124	58	,	,	PUNCT
ma-218	124	59	v	v	NOUN
ma-218	124	60	)	)	PUNCT
ma-218	124	61	=	=	PUNCT
ma-218	125	1	0,∀v	0,∀v	NUM
ma-218	125	2	∈	∈	PROPN
ma-218	125	3	c	c	NOUN
ma-218	125	4	;	;	PUNCT
ma-218	125	5	(	(	PUNCT
ma-218	125	6	d2	d2	PROPN
ma-218	125	7	)	)	PUNCT
ma-218	125	8	d	d	NOUN
ma-218	125	9	is	be	AUX
ma-218	125	10	monotone	monotone	ADJ
ma-218	125	11	,	,	PUNCT
ma-218	125	12	1.e	1.e	NUM
ma-218	125	13	,	,	PUNCT
ma-218	125	14	d(v	d(v	PROPN
ma-218	125	15	,	,	PUNCT
ma-218	125	16	u	u	NOUN
ma-218	125	17	)	)	PUNCT
ma-218	126	1	+	+	ADP
ma-218	126	2	d(u	d(u	PROPN
ma-218	126	3	,	,	PUNCT
ma-218	126	4	v	v	NOUN
ma-218	126	5	)	)	PUNCT
ma-218	126	6	≤	≤	NOUN
ma-218	126	7	0	0	NUM
ma-218	126	8	,	,	PUNCT
ma-218	126	9	∀v	∀v	NOUN
ma-218	126	10	,	,	PUNCT
ma-218	126	11	u	u	PROPN
ma-218	126	12	∈	∈	PROPN
ma-218	126	13	c	c	X
ma-218	126	14	;	;	PUNCT
ma-218	126	15	(	(	PUNCT
ma-218	126	16	d3	d3	PROPN
ma-218	126	17	)	)	PUNCT
ma-218	126	18	the	the	DET
ma-218	126	19	mapping	mapping	NOUN
ma-218	126	20	v	v	ADP
ma-218	126	21	7→	7→	NUM
ma-218	126	22	d(v	d(v	ADJ
ma-218	126	23	,	,	PUNCT
ma-218	126	24	u	u	NOUN
ma-218	126	25	)	)	PUNCT
ma-218	126	26	is	be	AUX
ma-218	126	27	upper	upper	ADJ
ma-218	126	28	hemicontinuity	hemicontinuity	NOUN
ma-218	126	29	,	,	PUNCT
ma-218	126	30	∀	∀	NOUN
ma-218	126	31	u	u	NOUN
ma-218	126	32	∈	∈	PROPN
ma-218	126	33	c.	c.	PROPN
ma-218	126	34	(	(	PUNCT
ma-218	126	35	d4	d4	PROPN
ma-218	126	36	)	)	PUNCT
ma-218	126	37	the	the	DET
ma-218	126	38	mapping	mapping	NOUN
ma-218	126	39	u	u	NOUN
ma-218	126	40	7→	7→	ADV
ma-218	126	41	d(v	d(v	PROPN
ma-218	126	42	,	,	PUNCT
ma-218	126	43	u	u	NOUN
ma-218	126	44	)	)	PUNCT
ma-218	126	45	,	,	PUNCT
ma-218	126	46	u	u	PROPN
ma-218	126	47	∈	∈	PROPN
ma-218	126	48	c	c	NOUN
ma-218	126	49	is	be	AUX
ma-218	126	50	convex	convex	ADJ
ma-218	126	51	and	and	CCONJ
ma-218	126	52	lower	low	ADJ
ma-218	126	53	semicontinuous	semicontinuous	ADJ
ma-218	126	54	.	.	PUNCT
ma-218	127	1	assumption	assumption	NOUN
ma-218	127	2	2	2	NUM
ma-218	127	3	:	:	PUNCT
ma-218	127	4	also	also	ADV
ma-218	127	5	consider	consider	VERB
ma-218	127	6	ϑ	ϑ	X
ma-218	127	7	:	:	PUNCT
ma-218	127	8	c×c	c×c	X
ma-218	127	9	−→	−→	ADJ
ma-218	127	10	r	r	NOUN
ma-218	127	11	as	as	ADP
ma-218	127	12	a	a	DET
ma-218	127	13	bifunction	bifunction	NOUN
ma-218	127	14	satisfying	satisfy	VERB
ma-218	127	15	the	the	DET
ma-218	127	16	following	follow	VERB
ma-218	127	17	assumptions	assumption	NOUN
ma-218	127	18	:	:	PUNCT
ma-218	127	19	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	127	20	eur	eur	PROPN
ma-218	127	21	.	.	PUNCT
ma-218	128	1	j.	j.	PROPN
ma-218	128	2	math	math	PROPN
ma-218	128	3	.	.	PUNCT
ma-218	129	1	anal	anal	PROPN
ma-218	129	2	.	.	PUNCT
ma-218	130	1	10.28924	10.28924	NUM
ma-218	130	2	/	/	SYM
ma-218	130	3	ada	ada	PROPN
ma-218	130	4	/	/	SYM
ma-218	130	5	ma.4.8	ma.4.8	ADJ
ma-218	130	6	6	6	NUM
ma-218	130	7	(	(	PUNCT
ma-218	130	8	ϑ1	ϑ1	PROPN
ma-218	130	9	)	)	PUNCT
ma-218	130	10	ϑ	ϑ	PROPN
ma-218	130	11	is	be	AUX
ma-218	130	12	skew	skew	ADJ
ma-218	130	13	-	-	PUNCT
ma-218	130	14	symmetric	symmetric	ADJ
ma-218	130	15	,	,	PUNCT
ma-218	130	16	i.e.	i.e.	X
ma-218	130	17	,	,	PUNCT
ma-218	130	18	ϑ(v	ϑ(v	PROPN
ma-218	130	19	,	,	PUNCT
ma-218	130	20	v)−	v)−	PROPN
ma-218	130	21	ϑ(v	ϑ(v	PROPN
ma-218	130	22	,	,	PUNCT
ma-218	130	23	u)−	u)−	PROPN
ma-218	130	24	ϑ(u	ϑ(u	X
ma-218	130	25	,	,	PUNCT
ma-218	130	26	v	v	NOUN
ma-218	130	27	)	)	PUNCT
ma-218	131	1	+	+	CCONJ
ma-218	131	2	ϑ(u	ϑ(u	X
ma-218	131	3	,	,	PUNCT
ma-218	131	4	u	u	NOUN
ma-218	131	5	)	)	PUNCT
ma-218	131	6	≥	≥	NUM
ma-218	131	7	0,∀v	0,∀v	X
ma-218	131	8	,	,	PUNCT
ma-218	131	9	u	u	PROPN
ma-218	131	10	∈	∈	PROPN
ma-218	131	11	c	c	X
ma-218	131	12	;	;	PUNCT
ma-218	131	13	(	(	PUNCT
ma-218	131	14	ϑ2	ϑ2	NOUN
ma-218	131	15	)	)	PUNCT
ma-218	131	16	ϑ	ϑ	PROPN
ma-218	131	17	is	be	AUX
ma-218	131	18	convex	convex	ADJ
ma-218	131	19	in	in	ADP
ma-218	131	20	the	the	DET
ma-218	131	21	second	second	ADJ
ma-218	131	22	argument	argument	NOUN
ma-218	131	23	;	;	PUNCT
ma-218	131	24	(	(	PUNCT
ma-218	131	25	ϑ3	ϑ3	NOUN
ma-218	131	26	)	)	PUNCT
ma-218	131	27	ϑ	ϑ	PROPN
ma-218	131	28	is	be	AUX
ma-218	131	29	continuous	continuous	ADJ
ma-218	131	30	.	.	PUNCT
ma-218	132	1	lemma	lemma	PROPN
ma-218	132	2	2.10	2.10	NUM
ma-218	132	3	.	.	PUNCT
ma-218	133	1	[	[	X
ma-218	133	2	1	1	NUM
ma-218	133	3	,	,	PUNCT
ma-218	133	4	6	6	NUM
ma-218	133	5	,	,	PUNCT
ma-218	133	6	21	21	NUM
ma-218	133	7	]	]	PUNCT
ma-218	133	8	let	let	VERB
ma-218	133	9	b	b	NOUN
ma-218	133	10	a	a	DET
ma-218	133	11	uniformly	uniformly	ADV
ma-218	133	12	smooth	smooth	ADJ
ma-218	133	13	,	,	PUNCT
ma-218	133	14	strictly	strictly	ADV
ma-218	133	15	convex	convex	VERB
ma-218	133	16	and	and	CCONJ
ma-218	133	17	reflexive	reflexive	ADJ
ma-218	133	18	banach	banach	NOUN
ma-218	133	19	space	space	NOUN
ma-218	133	20	and	and	CCONJ
ma-218	133	21	c	c	PROPN
ma-218	133	22	⊂	⊂	PROPN
ma-218	133	23	b	b	PROPN
ma-218	133	24	be	be	AUX
ma-218	133	25	closed	close	VERB
ma-218	133	26	.	.	PUNCT
ma-218	134	1	let	let	VERB
ma-218	134	2	g	g	NOUN
ma-218	134	3	:	:	PUNCT
ma-218	134	4	c	c	AUX
ma-218	134	5	−→	−→	ADV
ma-218	134	6	b∗	b∗	ADV
ma-218	134	7	be	be	AUX
ma-218	134	8	a	a	DET
ma-218	134	9	continuous	continuous	ADJ
ma-218	134	10	and	and	CCONJ
ma-218	134	11	monotone	monotone	ADJ
ma-218	134	12	mapping	mapping	NOUN
ma-218	134	13	,	,	PUNCT
ma-218	135	1	d	d	NOUN
ma-218	135	2	:	:	PUNCT
ma-218	135	3	c	c	X
ma-218	135	4	×	×	NOUN
ma-218	135	5	c	c	NOUN
ma-218	135	6	−→	−→	NOUN
ma-218	135	7	r	r	NOUN
ma-218	135	8	be	be	VERB
ma-218	135	9	a	a	DET
ma-218	135	10	bifunction	bifunction	NOUN
ma-218	135	11	satisfying	satisfy	VERB
ma-218	135	12	assumptions	assumption	NOUN
ma-218	135	13	1	1	NUM
ma-218	135	14	and	and	CCONJ
ma-218	135	15	ϑ	ϑ	X
ma-218	135	16	:	:	PUNCT
ma-218	135	17	c	c	X
ma-218	135	18	×c	×c	X
ma-218	135	19	−→	−→	NOUN
ma-218	135	20	r	r	NOUN
ma-218	135	21	be	be	VERB
ma-218	135	22	a	a	DET
ma-218	135	23	bifunction	bifunction	NOUN
ma-218	135	24	satisfying	satisfy	VERB
ma-218	135	25	assumptions	assumption	NOUN
ma-218	135	26	2	2	NUM
ma-218	135	27	.	.	X
ma-218	135	28	for	for	ADP
ma-218	135	29	any	any	DET
ma-218	135	30	given	give	VERB
ma-218	135	31	number	number	NOUN
ma-218	135	32	r	r	NOUN
ma-218	135	33	>	>	X
ma-218	135	34	0	0	NUM
ma-218	135	35	and	and	CCONJ
ma-218	135	36	τ1	τ1	ADP
ma-218	135	37	∈	∈	PROPN
ma-218	135	38	b	b	PROPN
ma-218	135	39	,	,	PUNCT
ma-218	135	40	define	define	VERB
ma-218	135	41	a	a	DET
ma-218	135	42	mapping	mapping	NOUN
ma-218	135	43	tr	tr	VERB
ma-218	135	44	:	:	PUNCT
ma-218	135	45	b	b	X
ma-218	135	46	−→	−→	NOUN
ma-218	135	47	c	c	VERB
ma-218	135	48	by	by	ADP
ma-218	135	49	tr	tr	NOUN
ma-218	135	50	(	(	PUNCT
ma-218	135	51	τ1	τ1	NOUN
ma-218	135	52	)	)	PUNCT
ma-218	135	53	=	=	PUNCT
ma-218	136	1	{	{	PUNCT
ma-218	136	2	u	u	NOUN
ma-218	136	3	∈	∈	PROPN
ma-218	136	4	c	c	NOUN
ma-218	136	5	:	:	PUNCT
ma-218	136	6	d(u	d(u	PROPN
ma-218	136	7	,	,	PUNCT
ma-218	136	8	v	v	NOUN
ma-218	136	9	)	)	PUNCT
ma-218	136	10	+	+	CCONJ
ma-218	137	1	〈	〈	PROPN
ma-218	137	2	v	v	ADJ
ma-218	137	3	−	−	PROPN
ma-218	137	4	u	u	NOUN
ma-218	137	5	,	,	PUNCT
ma-218	137	6	gu〉+	gu〉+	VERB
ma-218	137	7	1	1	NUM
ma-218	137	8	r	r	NOUN
ma-218	137	9	〈	〈	PROPN
ma-218	137	10	v	v	ADP
ma-218	137	11	−	−	PROPN
ma-218	137	12	u	u	PROPN
ma-218	137	13	,	,	PUNCT
ma-218	137	14	ju	ju	PROPN
ma-218	137	15	−	−	PROPN
ma-218	137	16	jτ1〉+	jτ1〉+	NOUN
ma-218	137	17	ψ(u	ψ(u	PROPN
ma-218	137	18	,	,	PUNCT
ma-218	137	19	v)−	v)−	PROPN
ma-218	137	20	ψ(u	ψ(u	PROPN
ma-218	137	21	,	,	PUNCT
ma-218	137	22	u	u	NOUN
ma-218	137	23	)	)	PUNCT
ma-218	137	24	≥	≥	NOUN
ma-218	137	25	0,∀y	0,∀y	NUM
ma-218	138	1	∈	∈	PROPN
ma-218	138	2	c	c	X
ma-218	138	3	}	}	PUNCT
ma-218	138	4	,	,	PUNCT
ma-218	138	5	∀v	∀v	PROPN
ma-218	138	6	∈	∈	PROPN
ma-218	138	7	b.	b.	NOUN
ma-218	139	1	the	the	DET
ma-218	139	2	mapping	mapping	NOUN
ma-218	139	3	tr	tr	VERB
ma-218	139	4	has	have	VERB
ma-218	139	5	the	the	DET
ma-218	139	6	following	follow	VERB
ma-218	139	7	properties	property	NOUN
ma-218	139	8	:	:	PUNCT
ma-218	139	9	(	(	PUNCT
ma-218	139	10	p1	p1	NOUN
ma-218	139	11	)	)	PUNCT
ma-218	139	12	tr	tr	VERB
ma-218	139	13	is	be	AUX
ma-218	139	14	single	single	ADJ
ma-218	139	15	-	-	PUNCT
ma-218	139	16	valued	value	VERB
ma-218	139	17	;	;	PUNCT
ma-218	139	18	(	(	PUNCT
ma-218	139	19	p2	p2	X
ma-218	139	20	)	)	PUNCT
ma-218	140	1	tr	tr	VERB
ma-218	140	2	is	be	AUX
ma-218	140	3	a	a	DET
ma-218	140	4	firmly	firmly	ADV
ma-218	140	5	nonexpansive	nonexpansive	ADJ
ma-218	140	6	type	type	NOUN
ma-218	140	7	mapping	mapping	NOUN
ma-218	140	8	,	,	PUNCT
ma-218	140	9	for	for	ADP
ma-218	140	10	all	all	DET
ma-218	140	11	τ1	τ1	NOUN
ma-218	140	12	,	,	PUNCT
ma-218	140	13	τ2	τ2	PROPN
ma-218	140	14	∈	∈	PROPN
ma-218	140	15	b	b	NOUN
ma-218	140	16	,	,	PUNCT
ma-218	140	17	〈	〈	PROPN
ma-218	140	18	trτ1	trτ1	PROPN
ma-218	140	19	−	−	PROPN
ma-218	140	20	trτ2	trτ2	PROPN
ma-218	140	21	,	,	PUNCT
ma-218	140	22	jtrτ1	jtrτ1	ADJ
ma-218	141	1	−	−	PUNCT
ma-218	141	2	jtrτ2	jtrτ2	X
ma-218	142	1	〉	〉	NOUN
ma-218	142	2	≤	≤	PUNCT
ma-218	143	1	〈	〈	PROPN
ma-218	143	2	trτ1	trτ1	PROPN
ma-218	143	3	−	−	PROPN
ma-218	143	4	trτ2	trτ2	PROPN
ma-218	143	5	,	,	PUNCT
ma-218	143	6	jτ1	jτ1	NOUN
ma-218	143	7	−	−	PROPN
ma-218	143	8	jτ2	jτ2	PROPN
ma-218	143	9	〉	〉	PROPN
ma-218	143	10	,	,	PUNCT
ma-218	143	11	(	(	PUNCT
ma-218	143	12	p3	p3	PROPN
ma-218	143	13	)	)	PUNCT
ma-218	143	14	f	f	PROPN
ma-218	143	15	(	(	PUNCT
ma-218	143	16	tr	tr	NOUN
ma-218	143	17	)	)	PUNCT
ma-218	143	18	=	=	NOUN
ma-218	143	19	sol(gmep	sol(gmep	NOUN
ma-218	143	20	(	(	PUNCT
ma-218	143	21	1.1	1.1	NUM
ma-218	143	22	)	)	PUNCT
ma-218	143	23	)	)	PUNCT
ma-218	143	24	is	be	AUX
ma-218	143	25	closed	close	VERB
ma-218	143	26	convex	convex	NOUN
ma-218	143	27	set	set	NOUN
ma-218	143	28	of	of	ADP
ma-218	143	29	c	c	PROPN
ma-218	143	30	;	;	PUNCT
ma-218	143	31	(	(	PUNCT
ma-218	143	32	p4	p4	ADJ
ma-218	143	33	)	)	PUNCT
ma-218	143	34	tr	tr	VERB
ma-218	143	35	is	be	AUX
ma-218	143	36	quasi−φ−	quasi−φ−	PROPN
ma-218	143	37	nonexpansive	nonexpansive	NOUN
ma-218	143	38	;	;	PUNCT
ma-218	143	39	(	(	PUNCT
ma-218	143	40	p5	p5	ADJ
ma-218	143	41	)	)	PUNCT
ma-218	143	42	φ(v0	φ(v0	NOUN
ma-218	143	43	,	,	PUNCT
ma-218	143	44	trτ1	trτ1	PROPN
ma-218	143	45	)	)	PUNCT
ma-218	144	1	+	+	CCONJ
ma-218	144	2	φ(trτ1	φ(trτ1	ADJ
ma-218	144	3	,	,	PUNCT
ma-218	144	4	τ1	τ1	NOUN
ma-218	144	5	)	)	PUNCT
ma-218	144	6	≤	≤	NOUN
ma-218	144	7	φ(v0	φ(v0	NOUN
ma-218	144	8	,	,	PUNCT
ma-218	144	9	τ1	τ1	NOUN
ma-218	144	10	)	)	PUNCT
ma-218	144	11	,	,	PUNCT
ma-218	144	12	∀v0	∀v0	PROPN
ma-218	144	13	∈	∈	PROPN
ma-218	144	14	f	f	PROPN
ma-218	144	15	(	(	PUNCT
ma-218	144	16	tr	tr	VERB
ma-218	144	17	)	)	PUNCT
ma-218	144	18	,	,	PUNCT
ma-218	144	19	τ1	τ1	PROPN
ma-218	144	20	∈	∈	PROPN
ma-218	144	21	b.	b.	PROPN
ma-218	144	22	furthermore	furthermore	ADV
ma-218	144	23	,	,	PUNCT
ma-218	144	24	consider	consider	VERB
ma-218	144	25	the	the	DET
ma-218	144	26	map	map	NOUN
ma-218	144	27	φ	φ	X
ma-218	144	28	:	:	PUNCT
ma-218	144	29	b	b	X
ma-218	144	30	×	×	NOUN
ma-218	144	31	b∗	b∗	ADJ
ma-218	144	32	−→	−→	NOUN
ma-218	144	33	r	r	NOUN
ma-218	144	34	,	,	PUNCT
ma-218	144	35	defined	define	VERB
ma-218	144	36	by	by	ADP
ma-218	144	37	φ(τ1	φ(τ1	NOUN
ma-218	144	38	,	,	PUNCT
ma-218	145	1	τ	τ	PROPN
ma-218	145	2	∗	∗	NOUN
ma-218	145	3	1	1	NUM
ma-218	145	4	)	)	PUNCT
ma-218	146	1	=	=	NOUN
ma-218	146	2	‖	‖	PROPN
ma-218	146	3	τ1	τ1	NOUN
ma-218	146	4	‖2	‖2	NOUN
ma-218	146	5	−〈τ1	−〈τ1	VERB
ma-218	146	6	,	,	PUNCT
ma-218	146	7	τ	τ	PROPN
ma-218	146	8	∗	∗	PROPN
ma-218	146	9	1	1	NUM
ma-218	146	10	〉	〉	PROPN
ma-218	146	11	+	+	CCONJ
ma-218	146	12	‖	‖	ADJ
ma-218	146	13	τ∗1	τ∗1	ADJ
ma-218	146	14	‖2	‖2	NOUN
ma-218	146	15	observe	observe	VERB
ma-218	146	16	that	that	SCONJ
ma-218	146	17	φ(τ1	φ(τ1	NOUN
ma-218	146	18	,	,	PUNCT
ma-218	146	19	τ	τ	PROPN
ma-218	146	20	∗	∗	NOUN
ma-218	146	21	1	1	NUM
ma-218	146	22	)	)	PUNCT
ma-218	146	23	=	=	SYM
ma-218	146	24	φ(τ1	φ(τ1	PROPN
ma-218	146	25	,	,	PUNCT
ma-218	146	26	j	j	PROPN
ma-218	146	27	−1τ∗1	−1τ∗1	PROPN
ma-218	146	28	)	)	PUNCT
ma-218	146	29	lemma	lemma	PROPN
ma-218	146	30	2.11	2.11	NUM
ma-218	146	31	.	.	PUNCT
ma-218	147	1	[	[	X
ma-218	147	2	2	2	X
ma-218	147	3	]	]	PUNCT
ma-218	147	4	let	let	VERB
ma-218	147	5	b	b	PRON
ma-218	147	6	be	be	AUX
ma-218	147	7	a	a	DET
ma-218	147	8	strictly	strictly	ADV
ma-218	147	9	convex	convex	ADJ
ma-218	147	10	,	,	PUNCT
ma-218	147	11	smooth	smooth	ADJ
ma-218	147	12	and	and	CCONJ
ma-218	147	13	reflexive	reflexive	ADJ
ma-218	147	14	banach	banach	NOUN
ma-218	147	15	space	space	NOUN
ma-218	147	16	.	.	PUNCT
ma-218	148	1	then	then	ADV
ma-218	148	2	φ(τ1	φ(τ1	VERB
ma-218	148	3	,	,	PUNCT
ma-218	148	4	τ	τ	PROPN
ma-218	148	5	∗	∗	NOUN
ma-218	148	6	1	1	NUM
ma-218	148	7	)	)	PUNCT
ma-218	148	8	+	+	NUM
ma-218	148	9	2〈j−1τ∗1	2〈j−1τ∗1	NOUN
ma-218	148	10	−	−	NOUN
ma-218	148	11	τ1	τ1	NOUN
ma-218	148	12	,	,	PUNCT
ma-218	148	13	τ	τ	PROPN
ma-218	148	14	∗	∗	NOUN
ma-218	148	15	2	2	NUM
ma-218	148	16	〉	〉	PROPN
ma-218	148	17	≤	≤	NOUN
ma-218	148	18	φ(τ1	φ(τ1	NOUN
ma-218	148	19	,	,	PUNCT
ma-218	148	20	τ	τ	PROPN
ma-218	148	21	∗	∗	NOUN
ma-218	148	22	1	1	NUM
ma-218	148	23	+	+	NUM
ma-218	148	24	τ∗2	τ∗2	NOUN
ma-218	148	25	)	)	PUNCT
ma-218	148	26	,	,	PUNCT
ma-218	148	27	∀τ1	∀τ1	PROPN
ma-218	148	28	∈	∈	PROPN
ma-218	148	29	b	b	PROPN
ma-218	148	30	,	,	PUNCT
ma-218	148	31	τ∗1	τ∗1	ADV
ma-218	148	32	,	,	PUNCT
ma-218	148	33	τ∗2	τ∗2	PROPN
ma-218	148	34	∈	∈	PROPN
ma-218	148	35	b∗.	b∗.	NOUN
ma-218	148	36	3	3	X
ma-218	148	37	.	.	X
ma-218	148	38	main	main	ADJ
ma-218	148	39	results	result	NOUN
ma-218	148	40	theorem	theorem	VERB
ma-218	148	41	3.1	3.1	NUM
ma-218	148	42	.	.	PUNCT
ma-218	149	1	let	let	VERB
ma-218	149	2	c	c	PRON
ma-218	149	3	be	be	AUX
ma-218	149	4	a	a	DET
ma-218	149	5	nonempty	nonempty	ADV
ma-218	149	6	closed	close	VERB
ma-218	149	7	and	and	CCONJ
ma-218	149	8	convex	convex	NOUN
ma-218	149	9	subset	subset	NOUN
ma-218	149	10	of	of	ADP
ma-218	149	11	a	a	DET
ma-218	149	12	2−uniformly	2−uniformly	ADV
ma-218	149	13	smooth	smooth	ADJ
ma-218	149	14	and	and	CCONJ
ma-218	149	15	uniformly	uniformly	ADV
ma-218	149	16	convex	convex	VERB
ma-218	149	17	banach	banach	NOUN
ma-218	149	18	space	space	NOUN
ma-218	149	19	b	b	NOUN
ma-218	149	20	with	with	ADP
ma-218	149	21	b∗	b∗	ADJ
ma-218	149	22	as	as	ADP
ma-218	149	23	the	the	DET
ma-218	149	24	dual	dual	ADJ
ma-218	149	25	space	space	NOUN
ma-218	149	26	of	of	ADP
ma-218	149	27	b.	b.	PROPN
ma-218	149	28	let	let	VERB
ma-218	149	29	q	q	NOUN
ma-218	149	30	:	:	PUNCT
ma-218	149	31	−→	−→	ADJ
ma-218	149	32	b∗	b∗	ADJ
ma-218	149	33	be	be	AUX
ma-218	149	34	a	a	DET
ma-218	149	35	γ−ism	γ−ism	NOUN
ma-218	149	36	mapping	mapping	NOUN
ma-218	149	37	with	with	ADP
ma-218	149	38	γ	γ	X
ma-218	149	39	∈	∈	PROPN
ma-218	149	40	(	(	PUNCT
ma-218	149	41	0	0	NUM
ma-218	149	42	,	,	PUNCT
ma-218	149	43	1	1	NUM
ma-218	149	44	)	)	PUNCT
ma-218	149	45	as	as	ADP
ma-218	149	46	a	a	DET
ma-218	149	47	constant	constant	ADJ
ma-218	149	48	.	.	PUNCT
ma-218	150	1	let	let	VERB
ma-218	150	2	d	d	NOUN
ma-218	150	3	:	:	PUNCT
ma-218	150	4	c	c	X
ma-218	150	5	×	×	NOUN
ma-218	150	6	c	c	NOUN
ma-218	150	7	−→	−→	NOUN
ma-218	150	8	r	r	NOUN
ma-218	150	9	be	be	VERB
ma-218	150	10	a	a	DET
ma-218	150	11	bifunction	bifunction	NOUN
ma-218	150	12	satisfying	satisfy	VERB
ma-218	150	13	assumption	assumption	NOUN
ma-218	150	14	1	1	NUM
ma-218	150	15	,	,	PUNCT
ma-218	150	16	ϑ	ϑ	X
ma-218	150	17	:	:	PUNCT
ma-218	150	18	c	c	AUX
ma-218	150	19	×	×	NOUN
ma-218	150	20	c	c	NOUN
ma-218	150	21	−→	−→	NOUN
ma-218	150	22	r	r	NOUN
ma-218	150	23	be	be	VERB
ma-218	150	24	a	a	DET
ma-218	150	25	bifunction	bifunction	NOUN
ma-218	150	26	satisfying	satisfy	VERB
ma-218	150	27	assumption	assumption	NOUN
ma-218	150	28	2	2	NUM
ma-218	150	29	and	and	CCONJ
ma-218	150	30	g	g	NOUN
ma-218	150	31	:	:	PUNCT
ma-218	150	32	c	c	AUX
ma-218	150	33	−→	−→	ADV
ma-218	150	34	b∗	b∗	ADV
ma-218	150	35	be	be	AUX
ma-218	150	36	a	a	DET
ma-218	150	37	monotone	monotone	ADJ
ma-218	150	38	and	and	CCONJ
ma-218	150	39	continuous	continuous	ADJ
ma-218	150	40	mapping	mapping	NOUN
ma-218	150	41	.	.	PUNCT
ma-218	151	1	let	let	VERB
ma-218	151	2	ti	ti	NOUN
ma-218	151	3	:	:	PUNCT
ma-218	151	4	c	c	X
ma-218	151	5	−→	−→	NOUN
ma-218	151	6	c	c	PROPN
ma-218	151	7	and	and	CCONJ
ma-218	151	8	si	si	INTJ
ma-218	151	9	:	:	PUNCT
ma-218	151	10	c	c	AUX
ma-218	151	11	−→	−→	NOUN
ma-218	151	12	c	c	NOUN
ma-218	151	13	,	,	PUNCT
ma-218	151	14	for	for	ADP
ma-218	151	15	each	each	DET
ma-218	151	16	i	i	NOUN
ma-218	151	17	=	=	NOUN
ma-218	151	18	1	1	NUM
ma-218	151	19	,	,	PUNCT
ma-218	151	20	2	2	NUM
ma-218	151	21	,	,	PUNCT
ma-218	151	22	...	...	PUNCT
ma-218	151	23	,	,	PUNCT
ma-218	151	24	n	n	X
ma-218	151	25	be	be	AUX
ma-218	151	26	two	two	NUM
ma-218	151	27	finite	finite	ADJ
ma-218	151	28	family	family	NOUN
ma-218	151	29	of	of	ADP
ma-218	151	30	closed	closed	ADJ
ma-218	151	31	li−lipschitz	li−lipschitz	PROPN
ma-218	151	32	continuous	continuous	ADJ
ma-218	151	33	and	and	CCONJ
ma-218	151	34	uniformly	uniformly	ADV
ma-218	151	35	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	151	36	nonexpansive	nonexpansive	ADJ
ma-218	151	37	mappings	mapping	NOUN
ma-218	152	1	such	such	ADJ
ma-218	152	2	that	that	DET
ma-218	152	3	ω	ω	NOUN
ma-218	152	4	:	:	PUNCT
ma-218	152	5	=	=	SYM
ma-218	152	6	(	(	PUNCT
ma-218	152	7	∩ni=1	∩ni=1	INTJ
ma-218	152	8	f	f	PROPN
ma-218	152	9	(	(	PUNCT
ma-218	152	10	ti	ti	NOUN
ma-218	152	11	)	)	PUNCT
ma-218	152	12	)	)	PUNCT
ma-218	152	13	∩	∩	NOUN
ma-218	152	14	(	(	PUNCT
ma-218	152	15	∩ni=1	∩ni=1	ADP
ma-218	152	16	f	f	PROPN
ma-218	152	17	(	(	PUNCT
ma-218	152	18	si	si	NOUN
ma-218	152	19	)	)	PUNCT
ma-218	152	20	)	)	PUNCT
ma-218	152	21	∩	∩	ADJ
ma-218	152	22	sol	sol	NOUN
ma-218	152	23	(	(	PUNCT
ma-218	152	24	v	v	NOUN
ma-218	152	25	ip	ip	NOUN
ma-218	152	26	(	(	PUNCT
ma-218	152	27	1.4	1.4	NUM
ma-218	152	28	)	)	PUNCT
ma-218	152	29	)	)	PUNCT
ma-218	152	30	∩	∩	ADJ
ma-218	152	31	sol	sol	NOUN
ma-218	152	32	(	(	PUNCT
ma-218	152	33	gmep	gmep	X
ma-218	152	34	(	(	PUNCT
ma-218	152	35	1.1	1.1	NUM
ma-218	152	36	)	)	PUNCT
ma-218	152	37	)	)	PUNCT
ma-218	152	38	6=	6=	ADP
ma-218	152	39	∅.	∅.	ADV
ma-218	152	40	let	let	VERB
ma-218	152	41	{	{	PUNCT
ma-218	152	42	xn	xn	NOUN
ma-218	152	43	}	}	PUNCT
ma-218	152	44	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	152	45	eur	eur	NOUN
ma-218	152	46	.	.	PUNCT
ma-218	153	1	j.	j.	PROPN
ma-218	153	2	math	math	PROPN
ma-218	153	3	.	.	PUNCT
ma-218	154	1	anal	anal	PROPN
ma-218	154	2	.	.	PUNCT
ma-218	155	1	10.28924	10.28924	NUM
ma-218	155	2	/	/	SYM
ma-218	155	3	ada	ada	PROPN
ma-218	155	4	/	/	SYM
ma-218	155	5	ma.4.8	ma.4.8	PROPN
ma-218	155	6	7	7	NUM
ma-218	155	7	generated	generate	VERB
ma-218	155	8	by	by	ADP
ma-218	155	9	algorithm	algorithm	NOUN
ma-218	155	10	:	:	PUNCT
ma-218	155	11			NOUN
ma-218	155	12	x0	x0	PROPN
ma-218	155	13	,	,	PUNCT
ma-218	155	14	x1	x1	PROPN
ma-218	155	15	∈	∈	PROPN
ma-218	155	16	c	c	X
ma-218	155	17	,	,	PUNCT
ma-218	155	18	c1	c1	NOUN
ma-218	155	19	:	:	PUNCT
ma-218	155	20	=	=	SYM
ma-218	155	21	c	c	X
ma-218	155	22	,	,	PUNCT
ma-218	155	23	ωn	ωn	PROPN
ma-218	155	24	=	=	SYM
ma-218	155	25	xn	xn	PROPN
ma-218	156	1	+	+	NUM
ma-218	156	2	αn(xn	αn(xn	PROPN
ma-218	156	3	−	−	PROPN
ma-218	156	4	xn−1	xn−1	PROPN
ma-218	156	5	)	)	PUNCT
ma-218	156	6	,	,	PUNCT
ma-218	157	1	vn	vn	PROPN
ma-218	157	2	=	=	PUNCT
ma-218	157	3	πcj	πcj	PROPN
ma-218	157	4	−1(jωn	−1(jωn	NOUN
ma-218	157	5	−	−	PROPN
ma-218	157	6	βnqωn	βnqωn	PROPN
ma-218	157	7	)	)	PUNCT
ma-218	157	8	,	,	PUNCT
ma-218	157	9	yn	yn	PROPN
ma-218	157	10	=	=	PUNCT
ma-218	158	1	j−1(µn,0jωn	j−1(µn,0jωn	PROPN
ma-218	158	2	+	+	CCONJ
ma-218	158	3	n∑	n∑	ADJ
ma-218	158	4	i=1	i=1	PROPN
ma-218	158	5	µn	µn	PROPN
ma-218	158	6	,	,	PUNCT
ma-218	158	7	ijt	ijt	VERB
ma-218	158	8	n	n	ADV
ma-218	158	9	i	i	PRON
ma-218	158	10	ωn	ωn	PROPN
ma-218	158	11	)	)	PUNCT
ma-218	158	12	;	;	PUNCT
ma-218	158	13	zn	zn	PROPN
ma-218	158	14	=	=	SYM
ma-218	158	15	j−1(ηn,0jvn	j−1(ηn,0jvn	PROPN
ma-218	159	1	+	+	CCONJ
ma-218	160	1	n∑	n∑	PROPN
ma-218	160	2	i=1	i=1	PROPN
ma-218	161	1	ηn	ηn	PROPN
ma-218	161	2	,	,	PUNCT
ma-218	161	3	ijs	ijs	PROPN
ma-218	162	1	n	n	PROPN
ma-218	162	2	i	i	PROPN
ma-218	162	3	yn	yn	PROPN
ma-218	162	4	)	)	PUNCT
ma-218	162	5	,	,	PUNCT
ma-218	162	6	un	un	PROPN
ma-218	162	7	=	=	PROPN
ma-218	162	8	trnzn	trnzn	PROPN
ma-218	162	9	,	,	PUNCT
ma-218	162	10	cn+1	cn+1	X
ma-218	162	11	=	=	SYM
ma-218	162	12	{	{	PUNCT
ma-218	162	13	u	u	NOUN
ma-218	162	14	∈	∈	PROPN
ma-218	162	15	cn	cn	PROPN
ma-218	162	16	:	:	PUNCT
ma-218	162	17	φ(u	φ(u	NOUN
ma-218	162	18	,	,	PUNCT
ma-218	162	19	un	un	ADJ
ma-218	162	20	)	)	PUNCT
ma-218	162	21	≤	≤	NOUN
ma-218	162	22	k2	k2	NOUN
ma-218	162	23	nφ(u	nφ(u	NOUN
ma-218	162	24	,	,	PUNCT
ma-218	162	25	ωn	ωn	NOUN
ma-218	162	26	)	)	PUNCT
ma-218	162	27	}	}	PUNCT
ma-218	162	28	,	,	PUNCT
ma-218	162	29	xn+1	xn+1	PROPN
ma-218	162	30	=	=	SYM
ma-218	162	31	πcn+1	πcn+1	NOUN
ma-218	162	32	x0	x0	PROPN
ma-218	162	33	,	,	PUNCT
ma-218	162	34	∀n	∀n	NUM
ma-218	162	35	≥	≥	NOUN
ma-218	162	36	1	1	NUM
ma-218	162	37	,	,	PUNCT
ma-218	162	38	(	(	PUNCT
ma-218	162	39	3.1	3.1	NUM
ma-218	162	40	)	)	PUNCT
ma-218	162	41	where	where	SCONJ
ma-218	162	42	{	{	PUNCT
ma-218	162	43	αn	αn	NOUN
ma-218	162	44	}	}	PUNCT
ma-218	162	45	⊂	⊂	PROPN
ma-218	162	46	(	(	PUNCT
ma-218	162	47	0	0	NUM
ma-218	162	48	,	,	PUNCT
ma-218	162	49	1	1	NUM
ma-218	162	50	)	)	PUNCT
ma-218	162	51	,	,	PUNCT
ma-218	162	52	{	{	PUNCT
ma-218	162	53	µn	µn	PROPN
ma-218	162	54	,	,	PUNCT
ma-218	162	55	i	i	PRON
ma-218	162	56	}	}	PUNCT
ma-218	162	57	⊂	⊂	PROPN
ma-218	163	1	[	[	X
ma-218	163	2	0	0	NUM
ma-218	163	3	,	,	PUNCT
ma-218	163	4	1	1	NUM
ma-218	163	5	]	]	PUNCT
ma-218	163	6	and	and	CCONJ
ma-218	163	7	{	{	PUNCT
ma-218	163	8	ηn	ηn	INTJ
ma-218	163	9	,	,	PUNCT
ma-218	163	10	i	i	PROPN
ma-218	163	11	}	}	PUNCT
ma-218	163	12	⊂	⊂	X
ma-218	163	13	(	(	PUNCT
ma-218	163	14	0	0	NUM
ma-218	163	15	,	,	PUNCT
ma-218	163	16	1	1	NUM
ma-218	163	17	]	]	PUNCT
ma-218	163	18	satisfying	satisfy	VERB
ma-218	163	19	the	the	DET
ma-218	163	20	following	follow	VERB
ma-218	163	21	conditions	condition	NOUN
ma-218	163	22	:	:	PUNCT
ma-218	163	23	(	(	PUNCT
ma-218	163	24	s1	s1	NOUN
ma-218	163	25	)	)	PUNCT
ma-218	163	26	n∑	n∑	NOUN
ma-218	163	27	i=0	i=0	PROPN
ma-218	163	28	µn	µn	PROPN
ma-218	163	29	,	,	PUNCT
ma-218	163	30	i	i	PRON
ma-218	163	31	=	=	NOUN
ma-218	163	32	1	1	NUM
ma-218	163	33	;	;	PUNCT
ma-218	163	34	(	(	PUNCT
ma-218	163	35	s2	s2	PROPN
ma-218	163	36	)	)	PUNCT
ma-218	163	37	n∑	n∑	NOUN
ma-218	164	1	i=0	i=0	PROPN
ma-218	164	2	ηn	ηn	INTJ
ma-218	164	3	,	,	PUNCT
ma-218	164	4	i	i	PRON
ma-218	164	5	=	=	NOUN
ma-218	164	6	1	1	NUM
ma-218	164	7	;	;	PUNCT
ma-218	164	8	(	(	PUNCT
ma-218	164	9	s3	s3	PROPN
ma-218	164	10	)	)	PUNCT
ma-218	164	11	lim	lim	PROPN
ma-218	164	12	sup	sup	VERB
ma-218	164	13	n→∞	n→∞	NUM
ma-218	165	1	ηn,0	ηn,0	NOUN
ma-218	165	2	<	<	X
ma-218	165	3	1	1	NUM
ma-218	165	4	;	;	PUNCT
ma-218	165	5	(	(	PUNCT
ma-218	165	6	s4	s4	PROPN
ma-218	165	7	)	)	PUNCT
ma-218	165	8	for	for	ADP
ma-218	165	9	same	same	ADJ
ma-218	165	10	a	a	DET
ma-218	165	11	>	>	X
ma-218	165	12	0	0	NUM
ma-218	165	13	,	,	PUNCT
ma-218	165	14	rn	rn	PROPN
ma-218	165	15	∈	∈	PROPN
ma-218	166	1	[	[	X
ma-218	166	2	a,∞	a,∞	PROPN
ma-218	166	3	)	)	PUNCT
ma-218	166	4	;	;	PUNCT
ma-218	166	5	(	(	PUNCT
ma-218	166	6	s5	s5	X
ma-218	166	7	)	)	PUNCT
ma-218	166	8	{	{	PUNCT
ma-218	166	9	βn	βn	NOUN
ma-218	166	10	}	}	PUNCT
ma-218	166	11	⊂	⊂	PROPN
ma-218	166	12	(	(	PUNCT
ma-218	166	13	0,∞	0,∞	NOUN
ma-218	166	14	)	)	PUNCT
ma-218	166	15	satisfying	satisfy	VERB
ma-218	166	16	the	the	DET
ma-218	166	17	condition	condition	NOUN
ma-218	166	18	0	0	PUNCT
ma-218	166	19	<	<	X
ma-218	166	20	lim	lim	PROPN
ma-218	166	21	inf	inf	PROPN
ma-218	166	22	n→∞	n→∞	X
ma-218	167	1	βn	βn	NOUN
ma-218	167	2	<	<	X
ma-218	167	3	δ2γ	δ2γ	PROPN
ma-218	167	4	2	2	NUM
ma-218	167	5	,	,	PUNCT
ma-218	167	6	where	where	SCONJ
ma-218	167	7	0	0	X
ma-218	167	8	<	<	X
ma-218	167	9	δ	δ	PROPN
ma-218	167	10	≤	≤	ADV
ma-218	167	11	1	1	NUM
ma-218	167	12	.	.	PUNCT
ma-218	168	1	then	then	ADV
ma-218	168	2	,	,	PUNCT
ma-218	168	3	{	{	PUNCT
ma-218	168	4	xn	xn	X
ma-218	168	5	}	}	PUNCT
ma-218	168	6	converges	converge	VERB
ma-218	168	7	strongly	strongly	ADV
ma-218	168	8	to	to	ADP
ma-218	168	9	$	$	SYM
ma-218	168	10	,	,	PUNCT
ma-218	168	11	where	where	SCONJ
ma-218	168	12	$	$	SYM
ma-218	168	13	=	=	SYM
ma-218	168	14	πωx0	πωx0	PROPN
ma-218	168	15	is	be	AUX
ma-218	168	16	consider	consider	VERB
ma-218	168	17	as	as	ADP
ma-218	168	18	the	the	DET
ma-218	168	19	generalized	generalized	ADJ
ma-218	168	20	projection	projection	NOUN
ma-218	168	21	of	of	ADP
ma-218	168	22	$	$	SYM
ma-218	168	23	onto	onto	ADP
ma-218	168	24	ω	ω	NUM
ma-218	168	25	.	.	PUNCT
ma-218	169	1	proof	proof	NOUN
ma-218	169	2	.	.	PUNCT
ma-218	170	1	we	we	PRON
ma-218	170	2	consider	consider	VERB
ma-218	170	3	the	the	DET
ma-218	170	4	proof	proof	NOUN
ma-218	170	5	in	in	ADP
ma-218	170	6	the	the	DET
ma-218	170	7	following	follow	VERB
ma-218	170	8	steps	step	NOUN
ma-218	170	9	:	:	PUNCT
ma-218	170	10	step	step	NOUN
ma-218	170	11	1	1	NUM
ma-218	170	12	:	:	PUNCT
ma-218	170	13	we	we	PRON
ma-218	170	14	show	show	VERB
ma-218	170	15	that	that	SCONJ
ma-218	170	16	cn+1	cn+1	NOUN
ma-218	170	17	is	be	AUX
ma-218	170	18	closed	close	VERB
ma-218	170	19	and	and	CCONJ
ma-218	170	20	convex	convex	VERB
ma-218	170	21	for	for	ADP
ma-218	170	22	each	each	DET
ma-218	170	23	n	n	PRON
ma-218	170	24	≥	≥	NOUN
ma-218	170	25	1	1	NUM
ma-218	170	26	and	and	CCONJ
ma-218	170	27	{	{	PUNCT
ma-218	170	28	xn	xn	X
ma-218	170	29	}	}	PUNCT
ma-218	170	30	is	be	AUX
ma-218	170	31	well	well	ADV
ma-218	170	32	defined.observe	defined.observe	VERB
ma-218	170	33	clearly	clearly	ADV
ma-218	170	34	that	that	DET
ma-218	170	35	c1	c1	NOUN
ma-218	171	1	=	=	PUNCT
ma-218	171	2	c	c	PROPN
ma-218	171	3	is	be	AUX
ma-218	171	4	closed	closed	ADJ
ma-218	171	5	and	and	CCONJ
ma-218	171	6	convex	convex	PROPN
ma-218	171	7	.	.	PUNCT
ma-218	172	1	suppose	suppose	VERB
ma-218	172	2	that	that	SCONJ
ma-218	172	3	cn	cn	PROPN
ma-218	172	4	is	be	AUX
ma-218	172	5	closed	closed	ADJ
ma-218	172	6	and	and	CCONJ
ma-218	172	7	convex	convex	VERB
ma-218	172	8	for	for	ADP
ma-218	172	9	each	each	DET
ma-218	172	10	n	n	PRON
ma-218	172	11	∈	∈	PROPN
ma-218	172	12	n.	n.	NOUN
ma-218	172	13	now	now	ADV
ma-218	172	14	,	,	PUNCT
ma-218	172	15	we	we	PRON
ma-218	172	16	know	know	VERB
ma-218	172	17	from	from	ADP
ma-218	172	18	3.1	3.1	NUM
ma-218	173	1	that	that	PRON
ma-218	173	2	for	for	ADP
ma-218	173	3	any	any	DET
ma-218	173	4	u	u	PROPN
ma-218	173	5	∈	∈	PROPN
ma-218	173	6	cn	cn	PROPN
ma-218	173	7	,	,	PUNCT
ma-218	173	8	φ(u	φ(u	NOUN
ma-218	173	9	,	,	PUNCT
ma-218	173	10	un	un	ADJ
ma-218	173	11	)	)	PUNCT
ma-218	173	12	≤	≤	NOUN
ma-218	173	13	k2	k2	NOUN
ma-218	173	14	nφ(u	nφ(u	NOUN
ma-218	173	15	,	,	PUNCT
ma-218	173	16	ωn	ωn	X
ma-218	173	17	)	)	PUNCT
ma-218	173	18	⇐	⇐	ADJ
ma-218	173	19	⇒	⇒	NOUN
ma-218	173	20	(	(	PUNCT
ma-218	173	21	1−	1−	NUM
ma-218	173	22	k2	k2	PROPN
ma-218	173	23	n	n	PROPN
ma-218	173	24	)	)	PUNCT
ma-218	173	25	[	[	PUNCT
ma-218	173	26	‖	‖	NUM
ma-218	173	27	u	u	NOUN
ma-218	173	28	‖2	‖2	NOUN
ma-218	173	29	−2(1−	−2(1−	PROPN
ma-218	173	30	k2	k2	NOUN
ma-218	173	31	n	n	NOUN
ma-218	173	32	)	)	PUNCT
ma-218	173	33	〈	〈	PROPN
ma-218	173	34	u	u	NOUN
ma-218	173	35	,	,	PUNCT
ma-218	173	36	jun〉+	jun〉+	NOUN
ma-218	173	37	2k2	2k2	NUM
ma-218	173	38	n	n	PRON
ma-218	173	39	〈	〈	PROPN
ma-218	173	40	u	u	NOUN
ma-218	173	41	,	,	PUNCT
ma-218	173	42	jωn	jωn	NOUN
ma-218	173	43	−	−	PROPN
ma-218	173	44	jun	jun	PROPN
ma-218	173	45	〉	〉	PROPN
ma-218	173	46	]	]	PUNCT
ma-218	173	47	≤	≤	NUM
ma-218	173	48	k2	k2	X
ma-218	173	49	n	n	CCONJ
ma-218	173	50	‖	‖	PROPN
ma-218	173	51	ωn	ωn	NOUN
ma-218	173	52	‖2	‖2	NOUN
ma-218	174	1	−	−	PROPN
ma-218	174	2	‖	‖	PROPN
ma-218	174	3	un	un	PROPN
ma-218	174	4	‖2	‖2	NOUN
ma-218	174	5	.	.	PUNCT
ma-218	175	1	then	then	ADV
ma-218	175	2	,	,	PUNCT
ma-218	175	3	cn+1	cn+1	PROPN
ma-218	175	4	is	be	AUX
ma-218	175	5	closed	close	VERB
ma-218	175	6	and	and	CCONJ
ma-218	175	7	convex	convex	PROPN
ma-218	175	8	.	.	PUNCT
ma-218	175	9	implies	imply	VERB
ma-218	175	10	that	that	PRON
ma-218	175	11	πcn+1	πcn+1	NOUN
ma-218	175	12	x0	x0	PROPN
ma-218	175	13	is	be	AUX
ma-218	175	14	well	well	ADV
ma-218	175	15	defined	define	VERB
ma-218	175	16	∀n	∀n	NUM
ma-218	175	17	≥	≥	NOUN
ma-218	175	18	1	1	NUM
ma-218	175	19	,	,	PUNCT
ma-218	175	20	also	also	ADV
ma-218	175	21	{	{	PUNCT
ma-218	175	22	xn	xn	X
ma-218	175	23	}	}	PUNCT
ma-218	175	24	is	be	AUX
ma-218	175	25	welldefined	welldefine	VERB
ma-218	175	26	.	.	PUNCT
ma-218	176	1	furthermore	furthermore	ADV
ma-218	176	2	since	since	SCONJ
ma-218	176	3	ω	ω	PROPN
ma-218	176	4	6=	6=	ADP
ma-218	176	5	∅	∅	NOUN
ma-218	176	6	,	,	PUNCT
ma-218	176	7	by	by	ADP
ma-218	176	8	considering	consider	VERB
ma-218	176	9	lemma	lemma	PROPN
ma-218	176	10	2.3	2.3	NUM
ma-218	176	11	,	,	PUNCT
ma-218	176	12	2.4	2.4	NUM
ma-218	176	13	and	and	CCONJ
ma-218	176	14	2.10	2.10	NUM
ma-218	176	15	we	we	PRON
ma-218	176	16	conclude	conclude	VERB
ma-218	176	17	that	that	SCONJ
ma-218	176	18	ω	ω	NOUN
ma-218	176	19	isclosed	isclose	VERB
ma-218	176	20	and	and	CCONJ
ma-218	176	21	convex	convex	NOUN
ma-218	176	22	,	,	PUNCT
ma-218	176	23	and	and	CCONJ
ma-218	176	24	so	so	ADV
ma-218	176	25	πωx0	πωx0	PROPN
ma-218	176	26	is	be	AUX
ma-218	176	27	well	well	ADV
ma-218	176	28	defined	define	VERB
ma-218	176	29	.	.	PUNCT
ma-218	177	1	step	step	NOUN
ma-218	177	2	2	2	NUM
ma-218	177	3	:	:	PUNCT
ma-218	177	4	we	we	PRON
ma-218	177	5	show	show	VERB
ma-218	177	6	that	that	SCONJ
ma-218	177	7	ω	ω	PROPN
ma-218	177	8	⊂	⊂	PROPN
ma-218	177	9	cn	cn	PROPN
ma-218	177	10	,	,	PUNCT
ma-218	177	11	∀n	∀n	NUM
ma-218	177	12	≥	≥	NOUN
ma-218	177	13	1	1	X
ma-218	177	14	.	.	PUNCT
ma-218	178	1	it	it	PRON
ma-218	178	2	is	be	AUX
ma-218	178	3	obvious	obvious	ADJ
ma-218	178	4	that	that	SCONJ
ma-218	178	5	ω	ω	PROPN
ma-218	178	6	⊂	⊂	PROPN
ma-218	178	7	c1	c1	PROPN
ma-218	178	8	=	=	PROPN
ma-218	178	9	c.	c.	PROPN
ma-218	178	10	suppose	suppose	VERB
ma-218	178	11	that	that	SCONJ
ma-218	178	12	ω	ω	PROPN
ma-218	178	13	⊂	⊂	PROPN
ma-218	178	14	cn	cn	PROPN
ma-218	178	15	forsome	forsome	PROPN
ma-218	178	16	n	n	NUM
ma-218	178	17	≥	≥	NOUN
ma-218	178	18	1	1	NUM
ma-218	178	19	.	.	PUNCT
ma-218	179	1	let	let	VERB
ma-218	179	2	x̂	x̂	PUNCT
ma-218	179	3	∈	∈	PROPN
ma-218	179	4	ω	ω	PROPN
ma-218	179	5	,	,	PUNCT
ma-218	179	6	from	from	ADP
ma-218	179	7	the	the	DET
ma-218	179	8	definition	definition	NOUN
ma-218	179	9	of	of	ADP
ma-218	179	10	φ	φ	PROPN
ma-218	179	11	,	,	PUNCT
ma-218	179	12	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	179	13	nonexpansive	nonexpansive	ADJ
ma-218	179	14	mapping	mapping	NOUN
ma-218	179	15	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	179	16	eur	eur	NOUN
ma-218	179	17	.	.	PUNCT
ma-218	180	1	j.	j.	PROPN
ma-218	180	2	math	math	PROPN
ma-218	180	3	.	.	PUNCT
ma-218	181	1	anal	anal	PROPN
ma-218	181	2	.	.	PUNCT
ma-218	182	1	10.28924	10.28924	NUM
ma-218	182	2	/	/	SYM
ma-218	182	3	ada	ada	PROPN
ma-218	182	4	/	/	SYM
ma-218	182	5	ma.4.8	ma.4.8	VERB
ma-218	182	6	8of	8of	ADJ
ma-218	182	7	si	si	NOUN
ma-218	182	8	and	and	CCONJ
ma-218	182	9	convexity	convexity	NOUN
ma-218	182	10	of	of	ADP
ma-218	182	11	‖	‖	PROPN
ma-218	182	12	.	.	PUNCT
ma-218	183	1	‖2	‖2	NOUN
ma-218	183	2	we	we	PRON
ma-218	183	3	have	have	VERB
ma-218	183	4	the	the	DET
ma-218	183	5	following	follow	VERB
ma-218	183	6	estimate	estimate	NOUN
ma-218	183	7	:	:	PUNCT
ma-218	183	8	φ(x̂	φ(x̂	NOUN
ma-218	183	9	,	,	PUNCT
ma-218	183	10	un	un	PROPN
ma-218	183	11	)	)	PUNCT
ma-218	184	1	=	=	SYM
ma-218	184	2	φ(x̂	φ(x̂	NOUN
ma-218	184	3	,	,	PUNCT
ma-218	184	4	trnzn	trnzn	NOUN
ma-218	184	5	)	)	PUNCT
ma-218	184	6	≤	≤	NUM
ma-218	184	7	φ(x̂	φ(x̂	PROPN
ma-218	184	8	,	,	PUNCT
ma-218	184	9	zn	zn	PROPN
ma-218	184	10	)	)	PUNCT
ma-218	184	11	(	(	PUNCT
ma-218	184	12	3.2	3.2	NUM
ma-218	184	13	)	)	PUNCT
ma-218	184	14	=	=	SYM
ma-218	184	15	φ	φ	PROPN
ma-218	184	16	(	(	PUNCT
ma-218	184	17	x̂	x̂	PROPN
ma-218	184	18	,	,	PUNCT
ma-218	184	19	j−1(ηn,0jvn	j−1(ηn,0jvn	PROPN
ma-218	185	1	+	+	CCONJ
ma-218	186	1	n∑	n∑	PROPN
ma-218	186	2	i=1	i=1	PROPN
ma-218	187	1	ηn	ηn	PROPN
ma-218	187	2	,	,	PUNCT
ma-218	187	3	ijs	ijs	PROPN
ma-218	188	1	n	n	PROPN
ma-218	188	2	i	i	PROPN
ma-218	188	3	yn	yn	PROPN
ma-218	188	4	)	)	PUNCT
ma-218	188	5	)	)	PUNCT
ma-218	189	1	=	=	PUNCT
ma-218	189	2	‖	‖	PROPN
ma-218	189	3	x̂	x̂	NOUN
ma-218	189	4	‖2	‖2	NOUN
ma-218	189	5	−2(〈x̂	−2(〈x̂	NOUN
ma-218	189	6	,	,	PUNCT
ma-218	189	7	ηn,0jvn	ηn,0jvn	PROPN
ma-218	189	8	+	+	CCONJ
ma-218	190	1	n∑	n∑	PROPN
ma-218	191	1	i=1	i=1	PROPN
ma-218	192	1	ηn	ηn	PROPN
ma-218	192	2	,	,	PUNCT
ma-218	192	3	ijs	ijs	PROPN
ma-218	193	1	n	n	PROPN
ma-218	193	2	i	i	PROPN
ma-218	193	3	yn	yn	PROPN
ma-218	193	4	〉	〉	PROPN
ma-218	193	5	)	)	PUNCT
ma-218	193	6	+	+	SYM
ma-218	193	7	‖ηn,0jvn	‖ηn,0jvn	PROPN
ma-218	194	1	+	+	CCONJ
ma-218	195	1	n∑	n∑	NOUN
ma-218	195	2	i=1	i=1	PROPN
ma-218	195	3	ηn	ηn	PROPN
ma-218	195	4	,	,	PUNCT
ma-218	195	5	ijs	ijs	PROPN
ma-218	196	1	n	n	PROPN
ma-218	196	2	i	i	PRON
ma-218	196	3	yn‖2	yn‖2	PROPN
ma-218	197	1	≤	≤	PROPN
ma-218	197	2	‖	‖	PROPN
ma-218	197	3	x̂	x̂	PROPN
ma-218	198	1	‖2	‖2	NOUN
ma-218	198	2	−2ηn,0〈x̂	−2ηn,0〈x̂	NOUN
ma-218	198	3	,	,	PUNCT
ma-218	198	4	jvn	jvn	PROPN
ma-218	198	5	〉	〉	PROPN
ma-218	198	6	−	−	NUM
ma-218	199	1	2	2	NUM
ma-218	199	2	n∑	n∑	NOUN
ma-218	199	3	i=1	i=1	PROPN
ma-218	200	1	ηn	ηn	ADJ
ma-218	200	2	,	,	PUNCT
ma-218	200	3	i	i	PRON
ma-218	200	4	〈	〈	PROPN
ma-218	200	5	x̂	x̂	PROPN
ma-218	200	6	,	,	PUNCT
ma-218	200	7	jsni	jsni	NOUN
ma-218	200	8	yn〉+	yn〉+	PROPN
ma-218	201	1	ηn,0‖jvn‖2	ηn,0‖jvn‖2	PROPN
ma-218	201	2	+	+	NUM
ma-218	201	3	n∑	n∑	NOUN
ma-218	201	4	i=1	i=1	PROPN
ma-218	201	5	ηn	ηn	ADJ
ma-218	201	6	,	,	PUNCT
ma-218	201	7	i‖jsni	i‖jsni	VERB
ma-218	201	8	yn‖2	yn‖2	PROPN
ma-218	201	9	=	=	NOUN
ma-218	201	10	ηn,0	ηn,0	PROPN
ma-218	201	11	(	(	PUNCT
ma-218	201	12	‖x̂‖2	‖x̂‖2	PROPN
ma-218	201	13	−	−	PROPN
ma-218	201	14	2〈x̂	2〈x̂	NOUN
ma-218	201	15	,	,	PUNCT
ma-218	201	16	jvn〉+	jvn〉+	PROPN
ma-218	201	17	‖vn‖2	‖vn‖2	PROPN
ma-218	201	18	)	)	PUNCT
ma-218	202	1	+	+	CCONJ
ma-218	203	1	n∑	n∑	X
ma-218	203	2	i=1	i=1	PROPN
ma-218	204	1	ηn	ηn	ADJ
ma-218	204	2	,	,	PUNCT
ma-218	204	3	i	i	PRON
ma-218	204	4	(	(	PUNCT
ma-218	204	5	‖x̂‖2	‖x̂‖2	PROPN
ma-218	204	6	−	−	PROPN
ma-218	204	7	2〈x̂	2〈x̂	NOUN
ma-218	204	8	,	,	PUNCT
ma-218	204	9	jsni	jsni	NOUN
ma-218	204	10	yn〉+	yn〉+	PROPN
ma-218	204	11	‖sni	‖sni	PROPN
ma-218	204	12	yn‖2	yn‖2	PROPN
ma-218	204	13	)	)	PUNCT
ma-218	205	1	=	=	SYM
ma-218	205	2	ηn,0φ(x̂	ηn,0φ(x̂	PROPN
ma-218	205	3	,	,	PUNCT
ma-218	205	4	vn	vn	PROPN
ma-218	205	5	)	)	PUNCT
ma-218	206	1	+	+	CCONJ
ma-218	206	2	n∑	n∑	X
ma-218	206	3	i=1	i=1	PROPN
ma-218	206	4	ηn	ηn	ADJ
ma-218	206	5	,	,	PUNCT
ma-218	206	6	iφ(x̂	iφ(x̂	NOUN
ma-218	206	7	,	,	PUNCT
ma-218	206	8	sni	sni	PROPN
ma-218	206	9	yn	yn	PROPN
ma-218	206	10	)	)	PUNCT
ma-218	206	11	≤	≤	PUNCT
ma-218	207	1	ηn,0φ(x̂	ηn,0φ(x̂	PROPN
ma-218	207	2	,	,	PUNCT
ma-218	207	3	vn	vn	PROPN
ma-218	207	4	)	)	PUNCT
ma-218	208	1	+	+	CCONJ
ma-218	208	2	kn	kn	PROPN
ma-218	208	3	n∑	n∑	PROPN
ma-218	208	4	i=1	i=1	PROPN
ma-218	208	5	ηn	ηn	ADJ
ma-218	208	6	,	,	PUNCT
ma-218	208	7	iφ(x̂	iφ(x̂	NOUN
ma-218	208	8	,	,	PUNCT
ma-218	208	9	yn	yn	PROPN
ma-218	208	10	)	)	PUNCT
ma-218	208	11	(	(	PUNCT
ma-218	208	12	3.3	3.3	NUM
ma-218	208	13	)	)	PUNCT
ma-218	208	14	similarly	similarly	ADV
ma-218	208	15	,	,	PUNCT
ma-218	208	16	by	by	ADP
ma-218	208	17	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	208	18	nonexpansive	nonexpansive	ADJ
ma-218	208	19	of	of	ADP
ma-218	208	20	ti	ti	PROPN
ma-218	208	21	,	,	PUNCT
ma-218	208	22	definition	definition	NOUN
ma-218	208	23	of	of	ADP
ma-218	208	24	φ	φ	PROPN
ma-218	208	25	and	and	CCONJ
ma-218	208	26	convexity	convexity	NOUN
ma-218	208	27	of	of	ADP
ma-218	208	28	‖	‖	PROPN
ma-218	208	29	.	.	PUNCT
ma-218	209	1	‖2,we	‖2,we	NUM
ma-218	209	2	estimate	estimate	NOUN
ma-218	209	3	as	as	SCONJ
ma-218	209	4	follows	follow	VERB
ma-218	209	5	:	:	PUNCT
ma-218	209	6	φ(x̂	φ(x̂	NOUN
ma-218	209	7	,	,	PUNCT
ma-218	209	8	yn	yn	PROPN
ma-218	209	9	)	)	PUNCT
ma-218	209	10	=	=	SYM
ma-218	210	1	φ	φ	PROPN
ma-218	210	2	(	(	PUNCT
ma-218	210	3	x̂	x̂	NUM
ma-218	210	4	,	,	PUNCT
ma-218	210	5	j−1(µn,0jωn	j−1(µn,0jωn	ADP
ma-218	210	6	+	+	CCONJ
ma-218	210	7	n∑	n∑	ADJ
ma-218	210	8	i=1	i=1	PROPN
ma-218	210	9	µn	µn	PROPN
ma-218	210	10	,	,	PUNCT
ma-218	210	11	ijt	ijt	VERB
ma-218	210	12	n	n	ADV
ma-218	210	13	i	i	PRON
ma-218	210	14	ωn	ωn	VERB
ma-218	210	15	)	)	PUNCT
ma-218	210	16	)	)	PUNCT
ma-218	211	1	=	=	PUNCT
ma-218	211	2	‖	‖	PROPN
ma-218	211	3	x̂	x̂	NOUN
ma-218	211	4	‖2	‖2	NOUN
ma-218	211	5	−2(〈x̂	−2(〈x̂	PUNCT
ma-218	211	6	,	,	PUNCT
ma-218	211	7	µn,0jωn	µn,0jωn	VERB
ma-218	211	8	+	+	CCONJ
ma-218	211	9	n∑	n∑	ADJ
ma-218	211	10	i=1	i=1	PROPN
ma-218	211	11	µn	µn	PROPN
ma-218	211	12	,	,	PUNCT
ma-218	211	13	ijt	ijt	VERB
ma-218	211	14	n	n	ADV
ma-218	211	15	i	i	PRON
ma-218	211	16	ωn〉)+	ωn〉)+	X
ma-218	212	1	‖	‖	ADJ
ma-218	212	2	µn,0jωn	µn,0jωn	PROPN
ma-218	212	3	+	+	CCONJ
ma-218	212	4	n∑	n∑	ADJ
ma-218	212	5	i=1	i=1	PROPN
ma-218	212	6	µn	µn	PROPN
ma-218	212	7	,	,	PUNCT
ma-218	212	8	ijt	ijt	VERB
ma-218	212	9	n	n	ADV
ma-218	212	10	i	i	PRON
ma-218	212	11	ωn	ωn	VERB
ma-218	212	12	‖2	‖2	VERB
ma-218	212	13	≤	≤	NUM
ma-218	213	1	‖	‖	PROPN
ma-218	213	2	x̂	x̂	PROPN
ma-218	213	3	‖2	‖2	NOUN
ma-218	213	4	−2µn,0〈x̂	−2µn,0〈x̂	NOUN
ma-218	213	5	,	,	PUNCT
ma-218	213	6	jωn	jωn	VERB
ma-218	213	7	〉	〉	NOUN
ma-218	213	8	−	−	NUM
ma-218	214	1	2	2	NUM
ma-218	214	2	n∑	n∑	NOUN
ma-218	214	3	i=1	i=1	PROPN
ma-218	214	4	µn	µn	PROPN
ma-218	214	5	,	,	PUNCT
ma-218	214	6	i	i	PRON
ma-218	214	7	〈	〈	PROPN
ma-218	214	8	x̂	x̂	PROPN
ma-218	214	9	,	,	PUNCT
ma-218	214	10	jt	jt	PROPN
ma-218	214	11	ni	ni	PROPN
ma-218	214	12	ωn〉+	ωn〉+	PROPN
ma-218	214	13	µn,0‖jωn‖2	µn,0‖jωn‖2	PROPN
ma-218	214	14	+	+	NUM
ma-218	214	15	n∑	n∑	ADJ
ma-218	214	16	i=1	i=1	PROPN
ma-218	214	17	µn	µn	PROPN
ma-218	214	18	,	,	PUNCT
ma-218	214	19	i‖jt	i‖jt	PROPN
ma-218	214	20	ni	ni	NOUN
ma-218	214	21	ωn‖2	ωn‖2	PROPN
ma-218	214	22	=	=	PROPN
ma-218	214	23	µn,0	µn,0	PROPN
ma-218	214	24	(	(	PUNCT
ma-218	214	25	‖x̂‖2	‖x̂‖2	PROPN
ma-218	214	26	−	−	PROPN
ma-218	214	27	2〈x̂	2〈x̂	NOUN
ma-218	214	28	,	,	PUNCT
ma-218	214	29	jωn〉+	jωn〉+	PROPN
ma-218	214	30	‖ωn‖2	‖ωn‖2	PROPN
ma-218	214	31	)	)	PUNCT
ma-218	215	1	+	+	NUM
ma-218	215	2	n∑	n∑	X
ma-218	215	3	i=1	i=1	NUM
ma-218	215	4	µn	µn	PROPN
ma-218	215	5	,	,	PUNCT
ma-218	215	6	i	i	PRON
ma-218	215	7	(	(	PUNCT
ma-218	215	8	‖	‖	PROPN
ma-218	215	9	x̂	x̂	PROPN
ma-218	215	10	‖2	‖2	NOUN
ma-218	215	11	−2〈x̂	−2〈x̂	PROPN
ma-218	215	12	,	,	PUNCT
ma-218	215	13	jt	jt	PROPN
ma-218	215	14	ni	ni	PROPN
ma-218	215	15	ωn〉+	ωn〉+	PROPN
ma-218	215	16	‖t	‖t	PROPN
ma-218	215	17	ni	ni	PROPN
ma-218	215	18	ωn‖2	ωn‖2	PROPN
ma-218	215	19	)	)	PUNCT
ma-218	216	1	=	=	SYM
ma-218	216	2	µn,0φ(x̂	µn,0φ(x̂	NOUN
ma-218	216	3	,	,	PUNCT
ma-218	216	4	ωn	ωn	PRON
ma-218	216	5	)	)	PUNCT
ma-218	217	1	+	+	NUM
ma-218	217	2	n∑	n∑	ADJ
ma-218	217	3	i=1	i=1	PROPN
ma-218	217	4	µn	µn	PROPN
ma-218	217	5	,	,	PUNCT
ma-218	217	6	iφ(x̂	iφ(x̂	NOUN
ma-218	217	7	,	,	PUNCT
ma-218	217	8	t	t	PROPN
ma-218	217	9	ni	ni	PROPN
ma-218	217	10	ωn	ωn	PROPN
ma-218	217	11	)	)	PUNCT
ma-218	217	12	≤	≤	NOUN
ma-218	218	1	µn,0φ(x̂	µn,0φ(x̂	NOUN
ma-218	218	2	,	,	PUNCT
ma-218	218	3	ωn	ωn	PRON
ma-218	218	4	)	)	PUNCT
ma-218	219	1	+	+	CCONJ
ma-218	219	2	kn	kn	PROPN
ma-218	219	3	n∑	n∑	PROPN
ma-218	219	4	i=1	i=1	PROPN
ma-218	219	5	µn	µn	PROPN
ma-218	219	6	,	,	PUNCT
ma-218	219	7	iφ(x̂	iφ(x̂	NOUN
ma-218	219	8	,	,	PUNCT
ma-218	219	9	ωn	ωn	NOUN
ma-218	219	10	)	)	PUNCT
ma-218	219	11	≤	≤	NOUN
ma-218	220	1	knµn,0φ(x̂	knµn,0φ(x̂	ADJ
ma-218	220	2	,	,	PUNCT
ma-218	220	3	ωn	ωn	PROPN
ma-218	220	4	)	)	PUNCT
ma-218	221	1	+	+	CCONJ
ma-218	221	2	kn	kn	PROPN
ma-218	221	3	n∑	n∑	PROPN
ma-218	221	4	i=1	i=1	PROPN
ma-218	221	5	µn	µn	PROPN
ma-218	221	6	,	,	PUNCT
ma-218	221	7	iφ(x̂	iφ(x̂	NOUN
ma-218	221	8	,	,	PUNCT
ma-218	221	9	ωn	ωn	NUM
ma-218	221	10	)	)	PUNCT
ma-218	221	11	=	=	SYM
ma-218	221	12	knφ(x̂	knφ(x̂	NOUN
ma-218	221	13	,	,	PUNCT
ma-218	221	14	ωn	ωn	PROPN
ma-218	221	15	)	)	PUNCT
ma-218	221	16	(	(	PUNCT
ma-218	221	17	3.4	3.4	NUM
ma-218	221	18	)	)	PUNCT
ma-218	221	19	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	221	20	eur	eur	NOUN
ma-218	221	21	.	.	PUNCT
ma-218	222	1	j.	j.	PROPN
ma-218	222	2	math	math	PROPN
ma-218	222	3	.	.	PUNCT
ma-218	223	1	anal	anal	PROPN
ma-218	223	2	.	.	PUNCT
ma-218	224	1	10.28924	10.28924	NUM
ma-218	224	2	/	/	SYM
ma-218	224	3	ada	ada	PROPN
ma-218	224	4	/	/	SYM
ma-218	224	5	ma.4.8	ma.4.8	PROPN
ma-218	224	6	9it	9it	NOUN
ma-218	224	7	has	have	AUX
ma-218	224	8	been	be	AUX
ma-218	224	9	observe	observe	VERB
ma-218	224	10	from	from	ADP
ma-218	224	11	(	(	PUNCT
ma-218	224	12	3.3	3.3	NUM
ma-218	224	13	)	)	PUNCT
ma-218	224	14	and	and	CCONJ
ma-218	224	15	(	(	PUNCT
ma-218	224	16	3.4	3.4	NUM
ma-218	224	17	)	)	PUNCT
ma-218	224	18	that	that	PRON
ma-218	224	19	φ(x̂	φ(x̂	PROPN
ma-218	224	20	,	,	PUNCT
ma-218	224	21	un	un	PROPN
ma-218	224	22	)	)	PUNCT
ma-218	224	23	≤	≤	PUNCT
ma-218	225	1	ηn,0φ(x̂	ηn,0φ(x̂	PROPN
ma-218	225	2	,	,	PUNCT
ma-218	225	3	vn	vn	PROPN
ma-218	225	4	)	)	PUNCT
ma-218	226	1	+	+	CCONJ
ma-218	226	2	kn	kn	PROPN
ma-218	226	3	n∑	n∑	PROPN
ma-218	227	1	i=1	i=1	PROPN
ma-218	228	1	ηn	ηn	ADJ
ma-218	228	2	,	,	PUNCT
ma-218	228	3	i	i	PRON
ma-218	228	4	[	[	PUNCT
ma-218	228	5	knφ(x̂	knφ(x̂	PROPN
ma-218	228	6	,	,	PUNCT
ma-218	228	7	ωn	ωn	PROPN
ma-218	228	8	)	)	PUNCT
ma-218	228	9	]	]	PUNCT
ma-218	229	1	=	=	SYM
ma-218	229	2	ηn,0φ(x̂	ηn,0φ(x̂	PROPN
ma-218	229	3	,	,	PUNCT
ma-218	229	4	vn	vn	PROPN
ma-218	229	5	)	)	PUNCT
ma-218	229	6	+	+	CCONJ
ma-218	229	7	k2	k2	PROPN
ma-218	229	8	n	n	PROPN
ma-218	229	9	n∑	n∑	NOUN
ma-218	229	10	i=1	i=1	PROPN
ma-218	229	11	ηn	ηn	ADJ
ma-218	229	12	,	,	PUNCT
ma-218	229	13	iφ(x̂	iφ(x̂	NOUN
ma-218	229	14	,	,	PUNCT
ma-218	229	15	ωn	ωn	NOUN
ma-218	229	16	)	)	PUNCT
ma-218	229	17	≤	≤	NOUN
ma-218	229	18	k2	k2	PROPN
ma-218	229	19	nηn,0φ(x̂	nηn,0φ(x̂	PROPN
ma-218	229	20	,	,	PUNCT
ma-218	229	21	vn	vn	PROPN
ma-218	229	22	)	)	PUNCT
ma-218	229	23	+	+	CCONJ
ma-218	229	24	k2	k2	PROPN
ma-218	229	25	n	n	PROPN
ma-218	229	26	n∑	n∑	NOUN
ma-218	229	27	i=1	i=1	PROPN
ma-218	229	28	ηn	ηn	ADJ
ma-218	229	29	,	,	PUNCT
ma-218	229	30	iφ(x̂	iφ(x̂	NOUN
ma-218	229	31	,	,	PUNCT
ma-218	229	32	ωn	ωn	NUM
ma-218	229	33	)	)	PUNCT
ma-218	229	34	(	(	PUNCT
ma-218	229	35	3.5	3.5	NUM
ma-218	229	36	)	)	PUNCT
ma-218	229	37	also	also	ADV
ma-218	229	38	,	,	PUNCT
ma-218	229	39	by	by	ADP
ma-218	229	40	lemma	lemma	PROPN
ma-218	229	41	2.6	2.6	NUM
ma-218	229	42	and	and	CCONJ
ma-218	229	43	2.11	2.11	NUM
ma-218	229	44	,	,	PUNCT
ma-218	229	45	we	we	PRON
ma-218	229	46	estimate	estimate	VERB
ma-218	229	47	as	as	ADP
ma-218	229	48	:	:	PUNCT
ma-218	229	49	φ(x̂	φ(x̂	NOUN
ma-218	229	50	,	,	PUNCT
ma-218	229	51	vn	vn	PROPN
ma-218	229	52	)	)	PUNCT
ma-218	229	53	=	=	SYM
ma-218	229	54	φ	φ	PROPN
ma-218	229	55	(	(	PUNCT
ma-218	229	56	x̂	x̂	NUM
ma-218	229	57	,	,	PUNCT
ma-218	229	58	πcj	πcj	PROPN
ma-218	229	59	−1(jωn	−1(jωn	NOUN
ma-218	229	60	−	−	PROPN
ma-218	229	61	βnqωn	βnqωn	PROPN
ma-218	229	62	)	)	PUNCT
ma-218	229	63	)	)	PUNCT
ma-218	230	1	≤	≤	NUM
ma-218	230	2	φ	φ	PROPN
ma-218	230	3	(	(	PUNCT
ma-218	230	4	x̂	x̂	NUM
ma-218	230	5	,	,	PUNCT
ma-218	230	6	j−1(jωn	j−1(jωn	NOUN
ma-218	230	7	−	−	NOUN
ma-218	230	8	βnqωn	βnqωn	ADJ
ma-218	230	9	)	)	PUNCT
ma-218	230	10	)	)	PUNCT
ma-218	231	1	=	=	SYM
ma-218	231	2	φ	φ	PROPN
ma-218	231	3	(	(	PUNCT
ma-218	231	4	x̂	x̂	NUM
ma-218	231	5	,	,	PUNCT
ma-218	231	6	jωn	jωn	NOUN
ma-218	231	7	−	−	PROPN
ma-218	231	8	βnqωn	βnqωn	NOUN
ma-218	231	9	)	)	PUNCT
ma-218	231	10	≤	≤	NUM
ma-218	231	11	φ	φ	PROPN
ma-218	231	12	(	(	PUNCT
ma-218	231	13	x̂	x̂	NUM
ma-218	231	14	,	,	PUNCT
ma-218	231	15	(	(	PUNCT
ma-218	231	16	jωn	jωn	NOUN
ma-218	231	17	−	−	NOUN
ma-218	231	18	βnqωn	βnqωn	PRON
ma-218	231	19	)	)	PUNCT
ma-218	232	1	+	+	CCONJ
ma-218	232	2	βnqωn	βnqωn	ADJ
ma-218	232	3	)	)	PUNCT
ma-218	233	1	−	−	PROPN
ma-218	234	1	2〈j−1(jωn	2〈j−1(jωn	NUM
ma-218	234	2	−	−	NOUN
ma-218	234	3	βnqωn)−	βnqωn)−	X
ma-218	234	4	x̂	x̂	PUNCT
ma-218	234	5	,	,	PUNCT
ma-218	234	6	βnqωn	βnqωn	ADJ
ma-218	234	7	〉	〉	NOUN
ma-218	234	8	=	=	SYM
ma-218	234	9	φ(x̂	φ(x̂	PROPN
ma-218	234	10	,	,	PUNCT
ma-218	234	11	jωn)−	jωn)−	PROPN
ma-218	234	12	2βn〈j−1(jωn	2βn〈j−1(jωn	NUM
ma-218	234	13	−	−	PROPN
ma-218	234	14	βnqωn)−	βnqωn)−	X
ma-218	234	15	x̂	x̂	PUNCT
ma-218	234	16	,	,	PUNCT
ma-218	234	17	qωn	qωn	VERB
ma-218	234	18	〉	〉	NOUN
ma-218	234	19	=	=	SYM
ma-218	234	20	φ(x̂	φ(x̂	PROPN
ma-218	234	21	,	,	PUNCT
ma-218	234	22	ωn)−	ωn)−	X
ma-218	234	23	2〈ωn	2〈ωn	NUM
ma-218	234	24	−	−	NOUN
ma-218	234	25	x̂	x̂	NOUN
ma-218	234	26	,	,	PUNCT
ma-218	234	27	qωn	qωn	VERB
ma-218	234	28	〉	〉	NOUN
ma-218	234	29	−	−	PROPN
ma-218	234	30	2βn〈j−1(jωn	2βn〈j−1(jωn	NUM
ma-218	234	31	−	−	NOUN
ma-218	234	32	βnqωn)−	βnqωn)−	NOUN
ma-218	234	33	ωn	ωn	ADP
ma-218	234	34	,	,	PUNCT
ma-218	234	35	qωn	qωn	VERB
ma-218	234	36	〉	〉	NOUN
ma-218	234	37	=	=	SYM
ma-218	234	38	φ(x̂	φ(x̂	PROPN
ma-218	234	39	,	,	PUNCT
ma-218	234	40	ωn)−	ωn)−	X
ma-218	234	41	2〈ωn	2〈ωn	NUM
ma-218	234	42	−	−	NOUN
ma-218	234	43	x̂	x̂	NUM
ma-218	234	44	,	,	PUNCT
ma-218	234	45	qωn	qωn	VERB
ma-218	234	46	−qx̂	−qx̂	ADV
ma-218	234	47	〉	〉	NOUN
ma-218	235	1	−	−	NUM
ma-218	235	2	2βn〈j−1(jωn	2βn〈j−1(jωn	NUM
ma-218	235	3	−	−	NOUN
ma-218	235	4	βnqωn)−	βnqωn)−	NOUN
ma-218	235	5	ωn	ωn	ADP
ma-218	235	6	,	,	PUNCT
ma-218	235	7	qωn	qωn	VERB
ma-218	235	8	〉	〉	PROPN
ma-218	235	9	≤	≤	NOUN
ma-218	235	10	φ(x̂	φ(x̂	PROPN
ma-218	235	11	,	,	PUNCT
ma-218	235	12	ωn)−	ωn)−	NOUN
ma-218	235	13	2βnγ	2βnγ	PROPN
ma-218	235	14	‖	‖	PROPN
ma-218	235	15	qωn‖2	qωn‖2	NOUN
ma-218	236	1	+	+	CCONJ
ma-218	236	2	2βn	2βn	ADJ
ma-218	236	3	‖	‖	ADJ
ma-218	236	4	j−1(jωn	j−1(jωn	NOUN
ma-218	236	5	−qωn)−	−qωn)−	PROPN
ma-218	236	6	j−1jωn‖‖qωn‖2	j−1jωn‖‖qωn‖2	PROPN
ma-218	236	7	≤	≤	NUM
ma-218	236	8	φ(x̂	φ(x̂	PROPN
ma-218	236	9	,	,	PUNCT
ma-218	236	10	ωn)−	ωn)−	NOUN
ma-218	236	11	2βnγ	2βnγ	PROPN
ma-218	236	12	‖	‖	PROPN
ma-218	236	13	qωn	qωn	PROPN
ma-218	236	14	‖2	‖2	NOUN
ma-218	236	15	+	+	CCONJ
ma-218	236	16	4β2	4β2	NUM
ma-218	236	17	n	n	PRON
ma-218	236	18	δ2	δ2	VERB
ma-218	236	19	‖	‖	ADJ
ma-218	236	20	qωn	qωn	ADJ
ma-218	236	21	‖2	‖2	NOUN
ma-218	236	22	=	=	SYM
ma-218	236	23	φ(x̂	φ(x̂	NOUN
ma-218	236	24	,	,	PUNCT
ma-218	236	25	ωn)−	ωn)−	NOUN
ma-218	236	26	2βn	2βn	ADJ
ma-218	236	27	(	(	PUNCT
ma-218	236	28	γ	γ	X
ma-218	236	29	−	−	PROPN
ma-218	236	30	2βn	2βn	ADJ
ma-218	236	31	δ2	δ2	ADV
ma-218	236	32	)	)	PUNCT
ma-218	236	33	‖	‖	PROPN
ma-218	236	34	qωn	qωn	PROPN
ma-218	236	35	‖2	‖2	NOUN
ma-218	236	36	,	,	PUNCT
ma-218	236	37	(	(	PUNCT
ma-218	236	38	3.6	3.6	NUM
ma-218	236	39	)	)	PUNCT
ma-218	236	40	if	if	SCONJ
ma-218	236	41	follows	follow	VERB
ma-218	236	42	by	by	ADP
ma-218	236	43	combined	combine	VERB
ma-218	236	44	with	with	ADP
ma-218	236	45	βn	βn	NOUN
ma-218	236	46	<	<	X
ma-218	236	47	δ2	δ2	ADJ
ma-218	236	48	2	2	NUM
ma-218	236	49	that	that	DET
ma-218	236	50	φ(x̂	φ(x̂	NOUN
ma-218	236	51	,	,	PUNCT
ma-218	236	52	vn	vn	PROPN
ma-218	236	53	)	)	PUNCT
ma-218	236	54	≤	≤	PROPN
ma-218	236	55	φ(x̂	φ(x̂	NOUN
ma-218	236	56	,	,	PUNCT
ma-218	236	57	ωn	ωn	PROPN
ma-218	236	58	)	)	PUNCT
ma-218	236	59	(	(	PUNCT
ma-218	236	60	3.7	3.7	NUM
ma-218	236	61	)	)	PUNCT
ma-218	236	62	now	now	ADV
ma-218	236	63	,	,	PUNCT
ma-218	236	64	putting	put	VERB
ma-218	236	65	(	(	PUNCT
ma-218	236	66	3.7	3.7	NUM
ma-218	236	67	)	)	PUNCT
ma-218	236	68	in	in	ADP
ma-218	236	69	(	(	PUNCT
ma-218	236	70	3.5	3.5	NUM
ma-218	236	71	)	)	PUNCT
ma-218	236	72	leads	lead	VERB
ma-218	236	73	to	to	ADP
ma-218	236	74	φ(x̂	φ(x̂	PROPN
ma-218	236	75	,	,	PUNCT
ma-218	236	76	un	un	PROPN
ma-218	236	77	)	)	PUNCT
ma-218	236	78	≤	≤	NOUN
ma-218	236	79	k2	k2	PROPN
ma-218	236	80	nηn,0φ(x̂	nηn,0φ(x̂	NOUN
ma-218	236	81	,	,	PUNCT
ma-218	236	82	ωn	ωn	PROPN
ma-218	236	83	)	)	PUNCT
ma-218	236	84	+	+	CCONJ
ma-218	236	85	k2	k2	PROPN
ma-218	236	86	n	n	PROPN
ma-218	236	87	n∑	n∑	NOUN
ma-218	236	88	i=1	i=1	PROPN
ma-218	236	89	ηn	ηn	ADJ
ma-218	236	90	,	,	PUNCT
ma-218	236	91	iφ(x̂	iφ(x̂	NOUN
ma-218	236	92	,	,	PUNCT
ma-218	236	93	ωn	ωn	NUM
ma-218	236	94	)	)	PUNCT
ma-218	236	95	=	=	SYM
ma-218	237	1	(	(	PUNCT
ma-218	237	2	ηn,0	ηn,0	PROPN
ma-218	237	3	+	+	CCONJ
ma-218	238	1	n∑	n∑	NOUN
ma-218	238	2	i=1	i=1	ADP
ma-218	238	3	ηn	ηn	ADJ
ma-218	238	4	,	,	PUNCT
ma-218	238	5	i)k	i)k	NOUN
ma-218	238	6	2	2	NUM
ma-218	238	7	nφ(x̂	nφ(x̂	NOUN
ma-218	238	8	,	,	PUNCT
ma-218	238	9	ωn	ωn	NUM
ma-218	238	10	)	)	PUNCT
ma-218	238	11	=	=	SYM
ma-218	238	12	k2	k2	PROPN
ma-218	238	13	nφ(x̂	nφ(x̂	NOUN
ma-218	238	14	,	,	PUNCT
ma-218	238	15	ωn	ωn	PROPN
ma-218	238	16	)	)	PUNCT
ma-218	238	17	,	,	PUNCT
ma-218	238	18	which	which	PRON
ma-218	238	19	gives	give	VERB
ma-218	238	20	φ(x̂	φ(x̂	PROPN
ma-218	238	21	,	,	PUNCT
ma-218	238	22	un	un	PROPN
ma-218	238	23	)	)	PUNCT
ma-218	238	24	≤	≤	NOUN
ma-218	238	25	k2	k2	PROPN
ma-218	238	26	nφ(x̂	nφ(x̂	NOUN
ma-218	238	27	,	,	PUNCT
ma-218	238	28	ωn	ωn	PROPN
ma-218	238	29	)	)	PUNCT
ma-218	238	30	,	,	PUNCT
ma-218	238	31	(	(	PUNCT
ma-218	238	32	3.8	3.8	NUM
ma-218	238	33	)	)	PUNCT
ma-218	238	34	therefore	therefore	ADV
ma-218	238	35	x̂	x̂	PUNCT
ma-218	238	36	∈	∈	PROPN
ma-218	238	37	cn+1	cn+1	PROPN
ma-218	238	38	,	,	PUNCT
ma-218	238	39	implies	imply	VERB
ma-218	238	40	that	that	SCONJ
ma-218	238	41	ω	ω	PROPN
ma-218	238	42	⊂	⊂	X
ma-218	238	43	cn+1	cn+1	PROPN
ma-218	238	44	.	.	PUNCT
ma-218	239	1	hence	hence	ADV
ma-218	239	2	ω	ω	PROPN
ma-218	239	3	⊂	⊂	PROPN
ma-218	239	4	cn	cn	PROPN
ma-218	239	5	,	,	PUNCT
ma-218	239	6	∀n	∀n	NUM
ma-218	239	7	≥	≥	NOUN
ma-218	239	8	1	1	X
ma-218	239	9	.	.	PUNCT
ma-218	240	1	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	240	2	eur	eur	PROPN
ma-218	240	3	.	.	PUNCT
ma-218	241	1	j.	j.	PROPN
ma-218	241	2	math	math	PROPN
ma-218	241	3	.	.	PUNCT
ma-218	242	1	anal	anal	PROPN
ma-218	242	2	.	.	PUNCT
ma-218	243	1	10.28924	10.28924	NUM
ma-218	243	2	/	/	SYM
ma-218	243	3	ada	ada	PROPN
ma-218	243	4	/	/	SYM
ma-218	243	5	ma.4.8	ma.4.8	PROPN
ma-218	243	6	10	10	NUM
ma-218	243	7	step	step	NOUN
ma-218	243	8	3	3	NUM
ma-218	243	9	:	:	PUNCT
ma-218	243	10	we	we	PRON
ma-218	243	11	show	show	VERB
ma-218	243	12	that	that	SCONJ
ma-218	243	13	{	{	PUNCT
ma-218	243	14	xn	xn	X
ma-218	243	15	}	}	PUNCT
ma-218	243	16	,	,	PUNCT
ma-218	243	17	{	{	PUNCT
ma-218	243	18	ωn	ωn	VERB
ma-218	243	19	}	}	PUNCT
ma-218	243	20	,	,	PUNCT
ma-218	243	21	{	{	PUNCT
ma-218	243	22	vn	vn	NOUN
ma-218	243	23	}	}	PUNCT
ma-218	243	24	,	,	PUNCT
ma-218	243	25	{	{	PUNCT
ma-218	243	26	yn	yn	X
ma-218	243	27	}	}	PUNCT
ma-218	243	28	,	,	PUNCT
ma-218	243	29	{	{	PUNCT
ma-218	243	30	zn	zn	X
ma-218	243	31	}	}	PUNCT
ma-218	243	32	and	and	CCONJ
ma-218	243	33	{	{	PUNCT
ma-218	243	34	un	un	PROPN
ma-218	243	35	}	}	PUNCT
ma-218	243	36	are	be	AUX
ma-218	243	37	bounded	bound	VERB
ma-218	243	38	and	and	CCONJ
ma-218	243	39	{	{	PUNCT
ma-218	243	40	xn	xn	X
ma-218	243	41	}	}	PUNCT
ma-218	243	42	is	be	AUX
ma-218	243	43	cauchy.we	cauchy.we	NOUN
ma-218	243	44	consider	consider	VERB
ma-218	243	45	xn	xn	X
ma-218	243	46	=	=	PUNCT
ma-218	244	1	πcnx0	πcnx0	NOUN
ma-218	244	2	and	and	CCONJ
ma-218	244	3	cn+1	cn+1	VERB
ma-218	244	4	⊂	⊂	PROPN
ma-218	244	5	cn	cn	PROPN
ma-218	244	6	,	,	PUNCT
ma-218	244	7	∀n	∀n	NUM
ma-218	244	8	≥	≥	NOUN
ma-218	244	9	1	1	NUM
ma-218	244	10	.	.	PUNCT
ma-218	245	1	then	then	ADV
ma-218	245	2	from	from	ADP
ma-218	245	3	lemma	lemma	PROPN
ma-218	245	4	2.9	2.9	NUM
ma-218	245	5	,	,	PUNCT
ma-218	245	6	we	we	PRON
ma-218	245	7	observe	observe	VERB
ma-218	245	8	that	that	SCONJ
ma-218	245	9	φ(xn	φ(xn	NOUN
ma-218	245	10	,	,	PUNCT
ma-218	245	11	x0	x0	PROPN
ma-218	245	12	)	)	PUNCT
ma-218	245	13	≤	≤	NUM
ma-218	245	14	φ(xn+1	φ(xn+1	PROPN
ma-218	245	15	,	,	PUNCT
ma-218	245	16	x0	x0	PROPN
ma-218	245	17	)	)	PUNCT
ma-218	245	18	hence	hence	ADV
ma-218	245	19	{	{	PUNCT
ma-218	245	20	φ(xn	φ(xn	PROPN
ma-218	245	21	,	,	PUNCT
ma-218	245	22	x0	x0	PROPN
ma-218	245	23	)	)	PUNCT
ma-218	245	24	}	}	PUNCT
ma-218	245	25	is	be	AUX
ma-218	245	26	non	non	ADJ
ma-218	245	27	decreasing	decrease	VERB
ma-218	245	28	.	.	PUNCT
ma-218	246	1	also	also	ADV
ma-218	246	2	it	it	PRON
ma-218	246	3	has	have	AUX
ma-218	246	4	been	be	AUX
ma-218	246	5	observe	observe	VERB
ma-218	246	6	that	that	SCONJ
ma-218	246	7	φ(xn	φ(xn	NOUN
ma-218	246	8	,	,	PUNCT
ma-218	246	9	x0	x0	NUM
ma-218	246	10	)	)	PUNCT
ma-218	246	11	=	=	SYM
ma-218	246	12	φ(πcnx0	φ(πcnx0	PROPN
ma-218	246	13	,	,	PUNCT
ma-218	246	14	x0	x0	PROPN
ma-218	246	15	)	)	PUNCT
ma-218	246	16	≤	≤	NUM
ma-218	246	17	φ(x̂	φ(x̂	PROPN
ma-218	246	18	,	,	PUNCT
ma-218	246	19	x0)−	x0)−	PROPN
ma-218	246	20	φ(x̂	φ(x̂	PROPN
ma-218	246	21	,	,	PUNCT
ma-218	246	22	xn	xn	PROPN
ma-218	246	23	)	)	PUNCT
ma-218	246	24	≤	≤	NUM
ma-218	246	25	φ(x̂	φ(x̂	PROPN
ma-218	246	26	,	,	PUNCT
ma-218	246	27	x0	x0	PROPN
ma-218	246	28	)	)	PUNCT
ma-218	246	29	,	,	PUNCT
ma-218	246	30	which	which	PRON
ma-218	246	31	gives	give	VERB
ma-218	246	32	that	that	SCONJ
ma-218	246	33	{	{	PUNCT
ma-218	246	34	φ(xn	φ(xn	PROPN
ma-218	246	35	,	,	PUNCT
ma-218	246	36	x0	x0	PROPN
ma-218	246	37	)	)	PUNCT
ma-218	246	38	}	}	PUNCT
ma-218	246	39	is	be	AUX
ma-218	246	40	bounded	bound	VERB
ma-218	246	41	and	and	CCONJ
ma-218	246	42	{	{	PUNCT
ma-218	246	43	xn	xn	X
ma-218	246	44	}	}	PUNCT
ma-218	246	45	is	be	AUX
ma-218	246	46	also	also	ADV
ma-218	246	47	bounded	bound	VERB
ma-218	246	48	.	.	PUNCT
ma-218	247	1	therefore	therefore	ADV
ma-218	247	2	,	,	PUNCT
ma-218	247	3	since	since	SCONJ
ma-218	247	4	{	{	PUNCT
ma-218	247	5	φ(xn	φ(xn	PROPN
ma-218	247	6	,	,	PUNCT
ma-218	247	7	x0	x0	PROPN
ma-218	247	8	)	)	PUNCT
ma-218	247	9	}	}	PUNCT
ma-218	247	10	nondecreasing	nondecrease	VERB
ma-218	247	11	.	.	PUNCT
ma-218	248	1	{	{	PUNCT
ma-218	248	2	φ(xn	φ(xn	PROPN
ma-218	248	3	,	,	PUNCT
ma-218	248	4	x0	x0	PROPN
ma-218	248	5	)	)	PUNCT
ma-218	248	6	}	}	PUNCT
ma-218	248	7	convergent	convergent	NOUN
ma-218	248	8	.	.	PUNCT
ma-218	249	1	taking	take	VERB
ma-218	249	2	the	the	DET
ma-218	249	3	advantage	advantage	NOUN
ma-218	249	4	of	of	ADP
ma-218	249	5	{	{	PUNCT
ma-218	249	6	xn	xn	NOUN
ma-218	249	7	}	}	PUNCT
ma-218	249	8	as	as	ADP
ma-218	249	9	a	a	DET
ma-218	249	10	bounded	bounded	ADJ
ma-218	249	11	sequence	sequence	NOUN
ma-218	249	12	impliesthat	impliesthat	NOUN
ma-218	249	13	{	{	PUNCT
ma-218	249	14	ωn	ωn	VERB
ma-218	249	15	}	}	PUNCT
ma-218	249	16	,	,	PUNCT
ma-218	249	17	{	{	PUNCT
ma-218	249	18	vn	vn	NOUN
ma-218	249	19	}	}	PUNCT
ma-218	249	20	,	,	PUNCT
ma-218	249	21	{	{	PUNCT
ma-218	249	22	yn	yn	X
ma-218	249	23	}	}	PUNCT
ma-218	249	24	,	,	PUNCT
ma-218	249	25	{	{	PUNCT
ma-218	249	26	zn	zn	X
ma-218	249	27	}	}	PUNCT
ma-218	249	28	and	and	CCONJ
ma-218	249	29	{	{	PUNCT
ma-218	249	30	un	un	PROPN
ma-218	249	31	}	}	PUNCT
ma-218	249	32	are	be	AUX
ma-218	249	33	all	all	PRON
ma-218	249	34	bounded	bound	VERB
ma-218	249	35	.	.	PUNCT
ma-218	250	1	also	also	ADV
ma-218	250	2	by	by	ADP
ma-218	250	3	lemma	lemma	PROPN
ma-218	250	4	2.9	2.9	NUM
ma-218	250	5	,	,	PUNCT
ma-218	250	6	we	we	PRON
ma-218	250	7	have	have	VERB
ma-218	250	8	φ(xm	φ(xm	NOUN
ma-218	250	9	,	,	PUNCT
ma-218	250	10	xn	xn	PROPN
ma-218	250	11	)	)	PUNCT
ma-218	251	1	=	=	SYM
ma-218	251	2	φ(xm	φ(xm	PROPN
ma-218	251	3	,	,	PUNCT
ma-218	251	4	πcnx0	πcnx0	NOUN
ma-218	251	5	)	)	PUNCT
ma-218	251	6	≤	≤	NOUN
ma-218	251	7	φ(xm	φ(xm	PROPN
ma-218	251	8	,	,	PUNCT
ma-218	251	9	x0)−	x0)−	PROPN
ma-218	251	10	φ(xn	φ(xn	PROPN
ma-218	251	11	,	,	PUNCT
ma-218	251	12	x0	x0	PROPN
ma-218	251	13	)	)	PUNCT
ma-218	252	1	−→	−→	NOUN
ma-218	252	2	0	0	NUM
ma-218	252	3	as	as	ADP
ma-218	252	4	n	n	CCONJ
ma-218	252	5	,	,	PUNCT
ma-218	252	6	m	m	VERB
ma-218	252	7	→∞.	→∞.	X
ma-218	252	8	(	(	PUNCT
ma-218	252	9	3.9	3.9	NUM
ma-218	252	10	)	)	PUNCT
ma-218	252	11	by	by	ADP
ma-218	252	12	lemma	lemma	PROPN
ma-218	252	13	2.7	2.7	NUM
ma-218	252	14	,	,	PUNCT
ma-218	252	15	we	we	PRON
ma-218	252	16	have	have	VERB
ma-218	252	17	lim	lim	PROPN
ma-218	252	18	n→∞	n→∞	PROPN
ma-218	252	19	‖	‖	PROPN
ma-218	252	20	xm	xm	PROPN
ma-218	253	1	−	−	NOUN
ma-218	253	2	xn	xn	PROPN
ma-218	254	1	‖=	‖=	PROPN
ma-218	254	2	0	0	X
ma-218	254	3	.	.	PUNCT
ma-218	255	1	hence	hence	ADV
ma-218	255	2	{	{	PUNCT
ma-218	255	3	xn	xn	X
ma-218	255	4	}	}	PUNCT
ma-218	255	5	is	be	AUX
ma-218	255	6	a	a	DET
ma-218	255	7	cauchy	cauchy	ADJ
ma-218	255	8	sequence	sequence	NOUN
ma-218	255	9	.	.	PUNCT
ma-218	256	1	step	step	NOUN
ma-218	256	2	4	4	NUM
ma-218	256	3	:	:	PUNCT
ma-218	256	4	we	we	PRON
ma-218	256	5	show	show	VERB
ma-218	256	6	that	that	SCONJ
ma-218	256	7	xn	xn	PROPN
ma-218	256	8	−→	−→	NOUN
ma-218	256	9	$	$	SYM
ma-218	256	10	,	,	PUNCT
ma-218	256	11	ωn	ωn	ADP
ma-218	256	12	−→	−→	ADV
ma-218	256	13	$	$	SYM
ma-218	256	14	,	,	PUNCT
ma-218	256	15	un	un	PROPN
ma-218	256	16	−→	−→	NOUN
ma-218	256	17	$	$	SYM
ma-218	256	18	,	,	PUNCT
ma-218	256	19	zn	zn	PROPN
ma-218	256	20	−→	−→	ADV
ma-218	256	21	$	$	SYM
ma-218	256	22	,	,	PUNCT
ma-218	256	23	yn	yn	PROPN
ma-218	256	24	−→	−→	ADV
ma-218	256	25	$	$	SYM
ma-218	256	26	and	and	CCONJ
ma-218	256	27	vn	vn	X
ma-218	256	28	−→	−→	ADJ
ma-218	256	29	$	$	ADP
ma-218	256	30	(	(	PUNCT
ma-218	256	31	as	as	ADP
ma-218	256	32	n	n	X
ma-218	256	33	→	→	SYM
ma-218	256	34	∞	∞	NUM
ma-218	256	35	)	)	PUNCT
ma-218	256	36	.	.	PUNCT
ma-218	257	1	since	since	SCONJ
ma-218	257	2	{	{	PUNCT
ma-218	257	3	xn	xn	X
ma-218	257	4	}	}	PUNCT
ma-218	257	5	is	be	AUX
ma-218	257	6	a	a	DET
ma-218	257	7	cauchy	cauchy	ADJ
ma-218	257	8	sequence	sequence	NOUN
ma-218	257	9	,	,	PUNCT
ma-218	257	10	then	then	ADV
ma-218	257	11	by	by	ADP
ma-218	257	12	the	the	DET
ma-218	257	13	closedness	closedness	NOUN
ma-218	257	14	of	of	ADP
ma-218	257	15	c	c	PROPN
ma-218	257	16	andthe	andthe	NOUN
ma-218	257	17	completeness	completeness	NOUN
ma-218	257	18	of	of	ADP
ma-218	257	19	b	b	PROPN
ma-218	257	20	,	,	PUNCT
ma-218	257	21	we	we	PRON
ma-218	257	22	can	can	AUX
ma-218	257	23	assume	assume	VERB
ma-218	257	24	that	that	SCONJ
ma-218	257	25	there	there	PRON
ma-218	257	26	exists	exist	VERB
ma-218	257	27	$	$	SYM
ma-218	257	28	∈	∈	NOUN
ma-218	257	29	c	c	NOUN
ma-218	257	30	such	such	ADJ
ma-218	257	31	that	that	SCONJ
ma-218	257	32	lim	lim	PROPN
ma-218	257	33	n→∞	n→∞	X
ma-218	257	34	xn	xn	PROPN
ma-218	257	35	=	=	PUNCT
ma-218	257	36	$	$	SYM
ma-218	257	37	.	.	PUNCT
ma-218	258	1	(	(	PUNCT
ma-218	258	2	3.10	3.10	NUM
ma-218	258	3	)	)	PUNCT
ma-218	258	4	now	now	ADV
ma-218	258	5	,	,	PUNCT
ma-218	258	6	setting	set	VERB
ma-218	258	7	m	m	PROPN
ma-218	258	8	=	=	SYM
ma-218	258	9	n	n	PROPN
ma-218	258	10	+	+	CCONJ
ma-218	258	11	1	1	NUM
ma-218	258	12	in	in	ADP
ma-218	258	13	(	(	PUNCT
ma-218	258	14	3.9	3.9	NUM
ma-218	258	15	)	)	PUNCT
ma-218	258	16	,	,	PUNCT
ma-218	258	17	we	we	PRON
ma-218	258	18	obtain	obtain	VERB
ma-218	258	19	lim	lim	PROPN
ma-218	258	20	n→∞	n→∞	NUM
ma-218	258	21	φ(xn+1	φ(xn+1	PROPN
ma-218	258	22	,	,	PUNCT
ma-218	258	23	xn	xn	PUNCT
ma-218	258	24	)	)	PUNCT
ma-218	258	25	=	=	SYM
ma-218	259	1	0	0	X
ma-218	259	2	.	.	PUNCT
ma-218	260	1	(	(	PUNCT
ma-218	260	2	3.11	3.11	NUM
ma-218	260	3	)	)	PUNCT
ma-218	260	4	using	use	VERB
ma-218	260	5	lemma	lemma	PROPN
ma-218	260	6	2.7	2.7	NUM
ma-218	260	7	,	,	PUNCT
ma-218	260	8	we	we	PRON
ma-218	260	9	get	get	VERB
ma-218	260	10	lim	lim	PROPN
ma-218	260	11	n→∞	n→∞	X
ma-218	260	12	‖xn+1	‖xn+1	NUM
ma-218	260	13	−	−	NOUN
ma-218	260	14	xn‖	xn‖	PROPN
ma-218	260	15	=	=	SYM
ma-218	260	16	0	0	PROPN
ma-218	260	17	.	.	PUNCT
ma-218	261	1	(	(	PUNCT
ma-218	261	2	3.12	3.12	NUM
ma-218	261	3	)	)	PUNCT
ma-218	261	4	we	we	PRON
ma-218	261	5	observe	observe	VERB
ma-218	261	6	from	from	ADP
ma-218	261	7	(	(	PUNCT
ma-218	261	8	3.1	3.1	NUM
ma-218	261	9	)	)	PUNCT
ma-218	261	10	that	that	PRON
ma-218	261	11	‖	‖	ADJ
ma-218	261	12	ωn	ωn	PRON
ma-218	261	13	−	−	PROPN
ma-218	261	14	xn	xn	PUNCT
ma-218	262	1	‖=‖	‖=‖	INTJ
ma-218	263	1	αn(xn	αn(xn	PROPN
ma-218	264	1	−	−	PROPN
ma-218	264	2	xn−1	xn−1	PROPN
ma-218	264	3	)	)	PUNCT
ma-218	264	4	‖≤‖	‖≤‖	PROPN
ma-218	264	5	xn	xn	X
ma-218	265	1	−	−	NOUN
ma-218	266	1	xn−1	xn−1	PROPN
ma-218	266	2	‖	‖	ADJ
ma-218	266	3	using	use	VERB
ma-218	266	4	(	(	PUNCT
ma-218	266	5	3.12	3.12	NUM
ma-218	266	6	)	)	PUNCT
ma-218	266	7	,	,	PUNCT
ma-218	266	8	we	we	PRON
ma-218	266	9	arrive	arrive	VERB
ma-218	266	10	at	at	ADP
ma-218	266	11	lim	lim	PROPN
ma-218	266	12	n→∞	n→∞	X
ma-218	267	1	‖ωn	‖ωn	NUM
ma-218	267	2	−	−	NOUN
ma-218	267	3	xn‖	xn‖	PROPN
ma-218	268	1	=	=	SYM
ma-218	268	2	0	0	PROPN
ma-218	268	3	.	.	PUNCT
ma-218	269	1	(	(	PUNCT
ma-218	269	2	3.13	3.13	NUM
ma-218	269	3	)	)	PUNCT
ma-218	269	4	by	by	ADP
ma-218	269	5	(	(	PUNCT
ma-218	269	6	3.10	3.10	NUM
ma-218	269	7	)	)	PUNCT
ma-218	269	8	and	and	CCONJ
ma-218	269	9	(	(	PUNCT
ma-218	269	10	3.13	3.13	NUM
ma-218	269	11	)	)	PUNCT
ma-218	269	12	,	,	PUNCT
ma-218	269	13	we	we	PRON
ma-218	269	14	conclude	conclude	VERB
ma-218	269	15	that	that	SCONJ
ma-218	269	16	lim	lim	PROPN
ma-218	269	17	n→∞	n→∞	X
ma-218	269	18	ωn	ωn	ADV
ma-218	269	19	=	=	PUNCT
ma-218	269	20	$	$	SYM
ma-218	269	21	.	.	PUNCT
ma-218	270	1	(	(	PUNCT
ma-218	270	2	3.14	3.14	NUM
ma-218	270	3	)	)	PUNCT
ma-218	270	4	taking	take	VERB
ma-218	270	5	the	the	DET
ma-218	270	6	advantage	advantage	NOUN
ma-218	270	7	of	of	ADP
ma-218	270	8	remark	remark	NOUN
ma-218	270	9	2.8	2.8	NUM
ma-218	270	10	,	,	PUNCT
ma-218	270	11	(	(	PUNCT
ma-218	270	12	3.13	3.13	NUM
ma-218	270	13	)	)	PUNCT
ma-218	270	14	and	and	CCONJ
ma-218	270	15	boundedness	boundedness	NOUN
ma-218	270	16	of	of	ADP
ma-218	270	17	{	{	PUNCT
ma-218	270	18	ωn	ωn	PROPN
ma-218	270	19	}	}	PUNCT
ma-218	270	20	,	,	PUNCT
ma-218	270	21	we	we	PRON
ma-218	270	22	get	get	VERB
ma-218	270	23	lim	lim	PROPN
ma-218	270	24	n→∞	n→∞	NUM
ma-218	270	25	φ(ωn	φ(ωn	PROPN
ma-218	270	26	,	,	PUNCT
ma-218	270	27	xn	xn	PROPN
ma-218	270	28	)	)	PUNCT
ma-218	270	29	=	=	SYM
ma-218	271	1	0	0	X
ma-218	271	2	.	.	PUNCT
ma-218	272	1	(	(	PUNCT
ma-218	272	2	3.15	3.15	NUM
ma-218	272	3	)	)	PUNCT
ma-218	272	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	272	5	eur	eur	NOUN
ma-218	272	6	.	.	PUNCT
ma-218	273	1	j.	j.	PROPN
ma-218	273	2	math	math	PROPN
ma-218	273	3	.	.	PUNCT
ma-218	274	1	anal	anal	PROPN
ma-218	274	2	.	.	PUNCT
ma-218	275	1	10.28924	10.28924	NUM
ma-218	275	2	/	/	SYM
ma-218	275	3	ada	ada	PROPN
ma-218	275	4	/	/	PROPN
ma-218	275	5	ma.4.8	ma.4.8	PROPN
ma-218	275	6	11also	11also	NUM
ma-218	275	7	,	,	PUNCT
ma-218	275	8	by	by	ADP
ma-218	275	9	(	(	PUNCT
ma-218	275	10	3.12	3.12	NUM
ma-218	275	11	)	)	PUNCT
ma-218	275	12	and	and	CCONJ
ma-218	275	13	(	(	PUNCT
ma-218	275	14	3.13	3.13	NUM
ma-218	275	15	)	)	PUNCT
ma-218	275	16	,	,	PUNCT
ma-218	275	17	we	we	PRON
ma-218	275	18	obtain	obtain	VERB
ma-218	275	19	lim	lim	PROPN
ma-218	275	20	n→∞	n→∞	X
ma-218	275	21	‖xn+1	‖xn+1	NUM
ma-218	275	22	−	−	ADP
ma-218	276	1	ωn	ωn	NUM
ma-218	276	2	‖=	‖=	PROPN
ma-218	276	3	0	0	PROPN
ma-218	276	4	.	.	PUNCT
ma-218	277	1	(	(	PUNCT
ma-218	277	2	3.16	3.16	NUM
ma-218	277	3	)	)	PUNCT
ma-218	277	4	using	use	VERB
ma-218	277	5	remark	remark	NOUN
ma-218	277	6	2.8	2.8	NUM
ma-218	277	7	,	,	PUNCT
ma-218	277	8	we	we	PRON
ma-218	277	9	present	present	VERB
ma-218	277	10	(	(	PUNCT
ma-218	277	11	3.16	3.16	NUM
ma-218	277	12	)	)	PUNCT
ma-218	277	13	as	as	ADP
ma-218	277	14	lim	lim	PROPN
ma-218	277	15	n→∞	n→∞	NUM
ma-218	277	16	φ(xn+1	φ(xn+1	PROPN
ma-218	277	17	,	,	PUNCT
ma-218	277	18	ωn	ωn	PRON
ma-218	277	19	)	)	PUNCT
ma-218	277	20	=	=	SYM
ma-218	278	1	0	0	X
ma-218	278	2	.	.	PUNCT
ma-218	279	1	(	(	PUNCT
ma-218	279	2	3.17	3.17	NUM
ma-218	279	3	)	)	PUNCT
ma-218	279	4	we	we	PRON
ma-218	279	5	observe	observe	VERB
ma-218	279	6	from	from	ADP
ma-218	279	7	xn+1	xn+1	PROPN
ma-218	279	8	=	=	SYM
ma-218	279	9	πcn+1	πcn+1	PUNCT
ma-218	279	10	x0	x0	PROPN
ma-218	279	11	∈	∈	PROPN
ma-218	279	12	cn+1	cn+1	NUM
ma-218	279	13	⊂	⊂	X
ma-218	279	14	cn	cn	PROPN
ma-218	279	15	and	and	CCONJ
ma-218	279	16	definition	definition	NOUN
ma-218	279	17	of	of	ADP
ma-218	279	18	cn	cn	PROPN
ma-218	279	19	that	that	SCONJ
ma-218	279	20	φ(xn+1	φ(xn+1	PROPN
ma-218	279	21	,	,	PUNCT
ma-218	279	22	un	un	ADJ
ma-218	279	23	)	)	PUNCT
ma-218	279	24	≤	≤	NOUN
ma-218	279	25	k2	k2	PROPN
ma-218	279	26	nφ(xn+1	nφ(xn+1	PROPN
ma-218	279	27	,	,	PUNCT
ma-218	279	28	ωn	ωn	PRON
ma-218	279	29	)	)	PUNCT
ma-218	279	30	using	use	VERB
ma-218	279	31	(	(	PUNCT
ma-218	279	32	3.17	3.17	NUM
ma-218	279	33	,	,	PUNCT
ma-218	279	34	)	)	PUNCT
ma-218	279	35	we	we	PRON
ma-218	279	36	obtain	obtain	VERB
ma-218	279	37	lim	lim	PROPN
ma-218	279	38	n→∞	n→∞	NUM
ma-218	279	39	φ(xn+1	φ(xn+1	PROPN
ma-218	279	40	,	,	PUNCT
ma-218	279	41	un	un	ADJ
ma-218	279	42	)	)	PUNCT
ma-218	280	1	=	=	SYM
ma-218	280	2	0	0	X
ma-218	280	3	.	.	X
ma-218	280	4	applying	apply	VERB
ma-218	280	5	lemma	lemma	PROPN
ma-218	280	6	2.7	2.7	NUM
ma-218	280	7	,	,	PUNCT
ma-218	280	8	we	we	PRON
ma-218	280	9	get	get	VERB
ma-218	280	10	lim	lim	PROPN
ma-218	280	11	n→∞	n→∞	X
ma-218	280	12	‖	‖	PROPN
ma-218	280	13	xn+1	xn+1	PROPN
ma-218	281	1	−	−	PROPN
ma-218	281	2	un	un	PROPN
ma-218	281	3	‖=	‖=	PROPN
ma-218	281	4	0	0	PROPN
ma-218	281	5	.	.	PUNCT
ma-218	282	1	(	(	PUNCT
ma-218	282	2	3.18	3.18	NUM
ma-218	282	3	)	)	PUNCT
ma-218	282	4	taking	take	VERB
ma-218	282	5	the	the	DET
ma-218	282	6	advantage	advantage	NOUN
ma-218	282	7	of	of	ADP
ma-218	282	8	triangular	triangular	NOUN
ma-218	282	9	inequality	inequality	NOUN
ma-218	282	10	,	,	PUNCT
ma-218	282	11	we	we	PRON
ma-218	282	12	present	present	VERB
ma-218	282	13	‖xn	‖xn	PROPN
ma-218	282	14	−	−	NOUN
ma-218	282	15	un‖	un‖	NOUN
ma-218	282	16	≤	≤	NUM
ma-218	282	17	‖xn	‖xn	PROPN
ma-218	282	18	−	−	NOUN
ma-218	282	19	xn+1‖+	xn+1‖+	PUNCT
ma-218	283	1	‖xn+1	‖xn+1	NUM
ma-218	283	2	−	−	NOUN
ma-218	283	3	un‖	un‖	NOUN
ma-218	283	4	by	by	ADP
ma-218	283	5	(	(	PUNCT
ma-218	283	6	3.12	3.12	NUM
ma-218	283	7	)	)	PUNCT
ma-218	283	8	and	and	CCONJ
ma-218	283	9	(	(	PUNCT
ma-218	283	10	3.18	3.18	NUM
ma-218	283	11	)	)	PUNCT
ma-218	283	12	,	,	PUNCT
ma-218	283	13	we	we	PRON
ma-218	283	14	obtain	obtain	VERB
ma-218	283	15	lim	lim	PROPN
ma-218	283	16	n→∞	n→∞	X
ma-218	283	17	‖	‖	PROPN
ma-218	283	18	xn	xn	PROPN
ma-218	284	1	−	−	PROPN
ma-218	284	2	un	un	PROPN
ma-218	284	3	‖=	‖=	PROPN
ma-218	284	4	0	0	PROPN
ma-218	284	5	.	.	PUNCT
ma-218	285	1	(	(	PUNCT
ma-218	285	2	3.19	3.19	NUM
ma-218	285	3	)	)	PUNCT
ma-218	285	4	it	it	PRON
ma-218	285	5	follows	follow	VERB
ma-218	285	6	from	from	ADP
ma-218	285	7	(	(	PUNCT
ma-218	285	8	3.10	3.10	NUM
ma-218	285	9	)	)	PUNCT
ma-218	285	10	and	and	CCONJ
ma-218	285	11	(	(	PUNCT
ma-218	285	12	3.19	3.19	NUM
ma-218	285	13	)	)	PUNCT
ma-218	285	14	that	that	PRON
ma-218	285	15	lim	lim	PROPN
ma-218	285	16	n→∞	n→∞	PRON
ma-218	285	17	un	un	PROPN
ma-218	285	18	=	=	PROPN
ma-218	285	19	$	$	SYM
ma-218	285	20	.	.	PUNCT
ma-218	286	1	(	(	PUNCT
ma-218	286	2	3.20	3.20	NUM
ma-218	286	3	)	)	PUNCT
ma-218	286	4	similarly	similarly	ADV
ma-218	286	5	,	,	PUNCT
ma-218	286	6	by	by	ADP
ma-218	286	7	definition	definition	NOUN
ma-218	286	8	of	of	ADP
ma-218	286	9	cn	cn	PROPN
ma-218	286	10	and	and	CCONJ
ma-218	286	11	xn+1	xn+1	NUM
ma-218	286	12	=	=	PUNCT
ma-218	286	13	πcn+1	πcn+1	PUNCT
ma-218	286	14	x0	x0	PROPN
ma-218	286	15	∈	∈	PROPN
ma-218	286	16	cn+1	cn+1	NUM
ma-218	286	17	⊂	⊂	X
ma-218	286	18	cn	cn	PROPN
ma-218	286	19	,	,	PUNCT
ma-218	286	20	we	we	PRON
ma-218	286	21	also	also	ADV
ma-218	286	22	present	present	VERB
ma-218	286	23	that	that	SCONJ
ma-218	286	24	φ(xn+1	φ(xn+1	PROPN
ma-218	286	25	,	,	PUNCT
ma-218	286	26	zn	zn	NOUN
ma-218	286	27	)	)	PUNCT
ma-218	286	28	≤	≤	NOUN
ma-218	286	29	k2	k2	PROPN
ma-218	286	30	nφ(xn+1	nφ(xn+1	PROPN
ma-218	286	31	,	,	PUNCT
ma-218	286	32	ωn	ωn	NUM
ma-218	286	33	)	)	PUNCT
ma-218	286	34	by	by	ADP
ma-218	286	35	applying	apply	VERB
ma-218	286	36	(	(	PUNCT
ma-218	286	37	3.17	3.17	NUM
ma-218	286	38	,	,	PUNCT
ma-218	286	39	)	)	PUNCT
ma-218	286	40	we	we	PRON
ma-218	286	41	arrive	arrive	VERB
ma-218	286	42	at	at	ADP
ma-218	286	43	lim	lim	PROPN
ma-218	286	44	n→∞	n→∞	NUM
ma-218	286	45	φ(xn+1	φ(xn+1	PROPN
ma-218	286	46	,	,	PUNCT
ma-218	286	47	zn	zn	NOUN
ma-218	286	48	)	)	PUNCT
ma-218	286	49	=	=	SYM
ma-218	287	1	0	0	X
ma-218	287	2	.	.	X
ma-218	287	3	using	use	VERB
ma-218	287	4	lemma	lemma	PROPN
ma-218	287	5	2.7	2.7	NUM
ma-218	287	6	,	,	PUNCT
ma-218	287	7	we	we	PRON
ma-218	287	8	have	have	VERB
ma-218	287	9	lim	lim	PROPN
ma-218	287	10	n→∞	n→∞	X
ma-218	287	11	‖	‖	PROPN
ma-218	287	12	xn+1	xn+1	PROPN
ma-218	288	1	−	−	PROPN
ma-218	288	2	zn	zn	PROPN
ma-218	288	3	‖=	‖=	PROPN
ma-218	288	4	0	0	PROPN
ma-218	288	5	.	.	PUNCT
ma-218	289	1	(	(	PUNCT
ma-218	289	2	3.21	3.21	NUM
ma-218	289	3	)	)	PUNCT
ma-218	289	4	taking	take	VERB
ma-218	289	5	into	into	ADP
ma-218	289	6	account	account	NOUN
ma-218	289	7	that	that	SCONJ
ma-218	289	8	‖xn	‖xn	PROPN
ma-218	289	9	−	−	PROPN
ma-218	289	10	zn‖	zn‖	PROPN
ma-218	289	11	≤	≤	PROPN
ma-218	290	1	‖xn	‖xn	PROPN
ma-218	290	2	−	−	NOUN
ma-218	290	3	xn+1‖+	xn+1‖+	PUNCT
ma-218	290	4	‖xn+1	‖xn+1	NUM
ma-218	291	1	−	−	PROPN
ma-218	291	2	zn‖	zn‖	PROPN
ma-218	291	3	using	use	VERB
ma-218	291	4	(	(	PUNCT
ma-218	291	5	3.12	3.12	NUM
ma-218	291	6	)	)	PUNCT
ma-218	291	7	and	and	CCONJ
ma-218	291	8	(	(	PUNCT
ma-218	291	9	3.21	3.21	NUM
ma-218	291	10	)	)	PUNCT
ma-218	291	11	,	,	PUNCT
ma-218	291	12	we	we	PRON
ma-218	291	13	get	get	VERB
ma-218	291	14	lim	lim	PROPN
ma-218	291	15	n→∞	n→∞	X
ma-218	291	16	‖	‖	PROPN
ma-218	291	17	xn	xn	PROPN
ma-218	292	1	−	−	PROPN
ma-218	292	2	zn	zn	PROPN
ma-218	292	3	‖=	‖=	PROPN
ma-218	292	4	0	0	PROPN
ma-218	292	5	.	.	PUNCT
ma-218	293	1	(	(	PUNCT
ma-218	293	2	3.22	3.22	NUM
ma-218	293	3	)	)	PUNCT
ma-218	293	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	293	5	eur	eur	NOUN
ma-218	293	6	.	.	PUNCT
ma-218	294	1	j.	j.	PROPN
ma-218	294	2	math	math	PROPN
ma-218	294	3	.	.	PUNCT
ma-218	295	1	anal	anal	PROPN
ma-218	295	2	.	.	PUNCT
ma-218	296	1	10.28924	10.28924	NUM
ma-218	296	2	/	/	SYM
ma-218	296	3	ada	ada	PROPN
ma-218	296	4	/	/	SYM
ma-218	296	5	ma.4.8	ma.4.8	ADJ
ma-218	296	6	12by	12by	PROPN
ma-218	296	7	considering(3.10	considering(3.10	NUM
ma-218	296	8	)	)	PUNCT
ma-218	296	9	and	and	CCONJ
ma-218	296	10	(	(	PUNCT
ma-218	296	11	3.22	3.22	NUM
ma-218	296	12	)	)	PUNCT
ma-218	296	13	,	,	PUNCT
ma-218	296	14	we	we	PRON
ma-218	296	15	obtain	obtain	VERB
ma-218	296	16	lim	lim	PROPN
ma-218	296	17	n→∞	n→∞	X
ma-218	296	18	zn	zn	PROPN
ma-218	296	19	=	=	SYM
ma-218	296	20	$	$	SYM
ma-218	296	21	.	.	PUNCT
ma-218	297	1	(	(	PUNCT
ma-218	297	2	3.23	3.23	NUM
ma-218	297	3	)	)	PUNCT
ma-218	297	4	also	also	ADV
ma-218	297	5	from	from	ADP
ma-218	297	6	the	the	DET
ma-218	297	7	definition	definition	NOUN
ma-218	297	8	of	of	ADP
ma-218	297	9	cn	cn	PROPN
ma-218	297	10	and	and	CCONJ
ma-218	297	11	xn+1	xn+1	NUM
ma-218	297	12	=	=	PUNCT
ma-218	297	13	πcn+1	πcn+1	PUNCT
ma-218	297	14	x0	x0	PROPN
ma-218	297	15	∈	∈	PROPN
ma-218	297	16	cn+1	cn+1	NUM
ma-218	298	1	⊂	⊂	X
ma-218	298	2	cn	cn	PROPN
ma-218	298	3	,	,	PUNCT
ma-218	298	4	we	we	PRON
ma-218	298	5	estimate	estimate	VERB
ma-218	298	6	as	as	ADP
ma-218	298	7	φ(xn+1	φ(xn+1	PROPN
ma-218	298	8	,	,	PUNCT
ma-218	298	9	yn	yn	NOUN
ma-218	298	10	)	)	PUNCT
ma-218	298	11	≤	≤	NOUN
ma-218	298	12	k2	k2	PROPN
ma-218	298	13	nφ(xn+1	nφ(xn+1	PROPN
ma-218	298	14	,	,	PUNCT
ma-218	298	15	ωn	ωn	PRON
ma-218	298	16	)	)	PUNCT
ma-218	298	17	by	by	ADP
ma-218	298	18	(	(	PUNCT
ma-218	298	19	3.17	3.17	NUM
ma-218	298	20	,	,	PUNCT
ma-218	298	21	)	)	PUNCT
ma-218	298	22	we	we	PRON
ma-218	298	23	get	get	VERB
ma-218	298	24	lim	lim	PROPN
ma-218	298	25	n→∞	n→∞	NUM
ma-218	298	26	φ(xn+1	φ(xn+1	PROPN
ma-218	298	27	,	,	PUNCT
ma-218	298	28	yn	yn	X
ma-218	298	29	)	)	PUNCT
ma-218	298	30	=	=	SYM
ma-218	299	1	0	0	X
ma-218	299	2	.	.	PUNCT
ma-218	300	1	it	it	PRON
ma-218	300	2	follows	follow	VERB
ma-218	300	3	from	from	ADP
ma-218	300	4	lemma	lemma	PROPN
ma-218	300	5	2.7	2.7	NUM
ma-218	300	6	that	that	PRON
ma-218	300	7	lim	lim	PROPN
ma-218	300	8	n→∞	n→∞	X
ma-218	300	9	‖	‖	PROPN
ma-218	300	10	xn+1	xn+1	PROPN
ma-218	300	11	−	−	PROPN
ma-218	301	1	yn	yn	INTJ
ma-218	301	2	‖=	‖=	NOUN
ma-218	301	3	0	0	PROPN
ma-218	301	4	.	.	PUNCT
ma-218	302	1	(	(	PUNCT
ma-218	302	2	3.24	3.24	NUM
ma-218	302	3	)	)	PUNCT
ma-218	302	4	by	by	ADP
ma-218	302	5	triangular	triangular	NOUN
ma-218	302	6	inequality	inequality	NOUN
ma-218	302	7	,	,	PUNCT
ma-218	302	8	we	we	PRON
ma-218	302	9	obtain	obtain	VERB
ma-218	302	10	‖xn	‖xn	PROPN
ma-218	302	11	−	−	NOUN
ma-218	302	12	yn‖	yn‖	NOUN
ma-218	302	13	≤	≤	PROPN
ma-218	303	1	‖xn	‖xn	PROPN
ma-218	303	2	−	−	NOUN
ma-218	303	3	xn+1‖+	xn+1‖+	PUNCT
ma-218	303	4	‖xn+1	‖xn+1	NUM
ma-218	304	1	−	−	NOUN
ma-218	304	2	yn‖	yn‖	NOUN
ma-218	304	3	also	also	ADV
ma-218	304	4	by	by	ADP
ma-218	304	5	(	(	PUNCT
ma-218	304	6	3.12	3.12	NUM
ma-218	304	7	)	)	PUNCT
ma-218	304	8	and	and	CCONJ
ma-218	304	9	(	(	PUNCT
ma-218	304	10	3.24	3.24	NUM
ma-218	304	11	)	)	PUNCT
ma-218	304	12	,	,	PUNCT
ma-218	304	13	we	we	PRON
ma-218	304	14	get	get	VERB
ma-218	304	15	lim	lim	PROPN
ma-218	304	16	n→∞	n→∞	X
ma-218	304	17	‖	‖	PROPN
ma-218	304	18	xn	xn	PROPN
ma-218	305	1	−	−	PROPN
ma-218	305	2	yn	yn	INTJ
ma-218	305	3	‖=	‖=	NOUN
ma-218	305	4	0	0	PROPN
ma-218	305	5	.	.	PUNCT
ma-218	306	1	(	(	PUNCT
ma-218	306	2	3.25	3.25	NUM
ma-218	306	3	)	)	PUNCT
ma-218	306	4	using	use	VERB
ma-218	306	5	(	(	PUNCT
ma-218	306	6	3.10	3.10	NUM
ma-218	306	7	)	)	PUNCT
ma-218	306	8	and	and	CCONJ
ma-218	306	9	(	(	PUNCT
ma-218	306	10	3.25	3.25	NUM
ma-218	306	11	)	)	PUNCT
ma-218	306	12	,	,	PUNCT
ma-218	306	13	we	we	PRON
ma-218	306	14	obtain	obtain	VERB
ma-218	306	15	lim	lim	PROPN
ma-218	306	16	n→∞	n→∞	X
ma-218	307	1	yn	yn	X
ma-218	307	2	=	=	PUNCT
ma-218	307	3	$	$	SYM
ma-218	307	4	.	.	PUNCT
ma-218	308	1	(	(	PUNCT
ma-218	308	2	3.26	3.26	NUM
ma-218	308	3	)	)	PUNCT
ma-218	308	4	finally	finally	ADV
ma-218	308	5	,	,	PUNCT
ma-218	308	6	by	by	ADP
ma-218	308	7	considering	consider	VERB
ma-218	308	8	xn+1	xn+1	NOUN
ma-218	308	9	=	=	SYM
ma-218	308	10	πcn+1	πcn+1	PUNCT
ma-218	308	11	x0	x0	PROPN
ma-218	308	12	∈	∈	PROPN
ma-218	308	13	cn+1	cn+1	NUM
ma-218	308	14	⊂	⊂	X
ma-218	308	15	cn	cn	PROPN
ma-218	308	16	and	and	CCONJ
ma-218	308	17	definition	definition	NOUN
ma-218	308	18	of	of	ADP
ma-218	308	19	cn	cn	PROPN
ma-218	308	20	,	,	PUNCT
ma-218	308	21	we	we	PRON
ma-218	308	22	present	present	VERB
ma-218	308	23	that	that	SCONJ
ma-218	308	24	φ(xn+1	φ(xn+1	PROPN
ma-218	308	25	,	,	PUNCT
ma-218	308	26	vn	vn	NOUN
ma-218	308	27	)	)	PUNCT
ma-218	308	28	≤	≤	NOUN
ma-218	308	29	k2	k2	PROPN
ma-218	308	30	nφ(xn+1	nφ(xn+1	PROPN
ma-218	308	31	,	,	PUNCT
ma-218	308	32	ωn	ωn	PRON
ma-218	308	33	)	)	PUNCT
ma-218	308	34	applying	apply	VERB
ma-218	308	35	(	(	PUNCT
ma-218	308	36	3.17	3.17	NUM
ma-218	308	37	,	,	PUNCT
ma-218	308	38	)	)	PUNCT
ma-218	308	39	we	we	PRON
ma-218	308	40	obtain	obtain	VERB
ma-218	308	41	lim	lim	PROPN
ma-218	308	42	n→∞	n→∞	NUM
ma-218	308	43	φ(xn+1	φ(xn+1	PROPN
ma-218	308	44	,	,	PUNCT
ma-218	308	45	vn	vn	X
ma-218	308	46	)	)	PUNCT
ma-218	308	47	=	=	SYM
ma-218	309	1	0	0	X
ma-218	309	2	.	.	PUNCT
ma-218	309	3	by	by	ADP
ma-218	309	4	lemma	lemma	PROPN
ma-218	309	5	2.7	2.7	NUM
ma-218	309	6	,	,	PUNCT
ma-218	309	7	we	we	PRON
ma-218	309	8	get	get	VERB
ma-218	309	9	lim	lim	PROPN
ma-218	309	10	n→∞	n→∞	X
ma-218	309	11	‖	‖	PROPN
ma-218	309	12	xn+1	xn+1	PROPN
ma-218	310	1	−	−	PROPN
ma-218	310	2	vn	vn	PROPN
ma-218	310	3	‖=	‖=	PROPN
ma-218	310	4	0	0	PROPN
ma-218	310	5	.	.	PUNCT
ma-218	311	1	(	(	PUNCT
ma-218	311	2	3.27	3.27	NUM
ma-218	311	3	)	)	PUNCT
ma-218	311	4	we	we	PRON
ma-218	311	5	consider	consider	VERB
ma-218	311	6	the	the	DET
ma-218	311	7	following	follow	VERB
ma-218	311	8	estimate	estimate	NOUN
ma-218	311	9	using	use	VERB
ma-218	311	10	triangular	triangular	NOUN
ma-218	311	11	inequality	inequality	NOUN
ma-218	311	12	‖xn	‖xn	PROPN
ma-218	311	13	−	−	PROPN
ma-218	311	14	vn‖	vn‖	PROPN
ma-218	311	15	≤	≤	NOUN
ma-218	311	16	‖xn	‖xn	PROPN
ma-218	311	17	−	−	NOUN
ma-218	311	18	xn+1‖+	xn+1‖+	PUNCT
ma-218	311	19	‖xn+1	‖xn+1	NUM
ma-218	312	1	−	−	NOUN
ma-218	312	2	vn‖	vn‖	NOUN
ma-218	312	3	using	use	VERB
ma-218	312	4	(	(	PUNCT
ma-218	312	5	3.12	3.12	NUM
ma-218	312	6	)	)	PUNCT
ma-218	312	7	and	and	CCONJ
ma-218	312	8	(	(	PUNCT
ma-218	312	9	3.27	3.27	NUM
ma-218	312	10	)	)	PUNCT
ma-218	312	11	,	,	PUNCT
ma-218	312	12	we	we	PRON
ma-218	312	13	obtain	obtain	VERB
ma-218	312	14	lim	lim	PROPN
ma-218	312	15	n→∞	n→∞	X
ma-218	313	1	‖	‖	PROPN
ma-218	313	2	xn	xn	PROPN
ma-218	314	1	−	−	PROPN
ma-218	314	2	vn	vn	PROPN
ma-218	314	3	‖=	‖=	PROPN
ma-218	314	4	0	0	PROPN
ma-218	314	5	.	.	PUNCT
ma-218	315	1	(	(	PUNCT
ma-218	315	2	3.28	3.28	NUM
ma-218	315	3	)	)	PUNCT
ma-218	315	4	using	use	VERB
ma-218	315	5	(	(	PUNCT
ma-218	315	6	3.10	3.10	NUM
ma-218	315	7	)	)	PUNCT
ma-218	315	8	and	and	CCONJ
ma-218	315	9	(	(	PUNCT
ma-218	315	10	3.28	3.28	NUM
ma-218	315	11	)	)	PUNCT
ma-218	315	12	,	,	PUNCT
ma-218	315	13	we	we	PRON
ma-218	315	14	obtain	obtain	VERB
ma-218	315	15	lim	lim	PROPN
ma-218	315	16	n→∞	n→∞	NUM
ma-218	315	17	vn	vn	X
ma-218	315	18	=	=	SYM
ma-218	315	19	$	$	SYM
ma-218	315	20	.	.	PUNCT
ma-218	316	1	(	(	PUNCT
ma-218	316	2	3.29	3.29	NUM
ma-218	316	3	)	)	PUNCT
ma-218	316	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	316	5	eur	eur	NOUN
ma-218	316	6	.	.	PUNCT
ma-218	317	1	j.	j.	PROPN
ma-218	317	2	math	math	PROPN
ma-218	317	3	.	.	PUNCT
ma-218	318	1	anal	anal	PROPN
ma-218	318	2	.	.	PUNCT
ma-218	319	1	10.28924	10.28924	NUM
ma-218	319	2	/	/	SYM
ma-218	319	3	ada	ada	PROPN
ma-218	319	4	/	/	SYM
ma-218	319	5	ma.4.8	ma.4.8	ADJ
ma-218	319	6	13	13	NUM
ma-218	319	7	step	step	NOUN
ma-218	319	8	4	4	NUM
ma-218	319	9	:	:	PUNCT
ma-218	319	10	we	we	PRON
ma-218	319	11	show	show	VERB
ma-218	319	12	that	that	SCONJ
ma-218	319	13	‖	‖	PROPN
ma-218	319	14	ωn	ωn	ADP
ma-218	319	15	−	−	PROPN
ma-218	319	16	t	t	PROPN
ma-218	319	17	ni	ni	PROPN
ma-218	319	18	ωn	ωn	ADP
ma-218	319	19	‖=‖	‖=‖	PROPN
ma-218	319	20	yn	yn	PROPN
ma-218	319	21	−	−	PROPN
ma-218	319	22	sni	sni	PROPN
ma-218	319	23	yn	yn	PROPN
ma-218	319	24	‖=	‖=	PROPN
ma-218	319	25	0	0	X
ma-218	319	26	.	.	PUNCT
ma-218	320	1	now	now	ADV
ma-218	320	2	,	,	PUNCT
ma-218	320	3	taking	take	VERB
ma-218	320	4	the	the	DET
ma-218	320	5	advantage	advantage	NOUN
ma-218	320	6	of	of	ADP
ma-218	320	7	j	j	PROPN
ma-218	320	8	asuniformly	asuniformly	ADJ
ma-218	320	9	continuity	continuity	NOUN
ma-218	320	10	on	on	ADP
ma-218	320	11	bounded	bounded	ADJ
ma-218	320	12	sets	set	NOUN
ma-218	320	13	,	,	PUNCT
ma-218	320	14	then	then	ADV
ma-218	320	15	it	it	PRON
ma-218	320	16	follows	follow	VERB
ma-218	320	17	from	from	ADP
ma-218	320	18	(	(	PUNCT
ma-218	320	19	3.16	3.16	NUM
ma-218	320	20	)	)	PUNCT
ma-218	320	21	and	and	CCONJ
ma-218	320	22	(	(	PUNCT
ma-218	320	23	3.24	3.24	NUM
ma-218	320	24	)	)	PUNCT
ma-218	320	25	that	that	PRON
ma-218	320	26	‖	‖	ADJ
ma-218	320	27	jωn	jωn	NOUN
ma-218	320	28	−	−	PROPN
ma-218	320	29	jxn+1	jxn+1	ADJ
ma-218	320	30	‖=‖	‖=‖	INTJ
ma-218	320	31	jxn+1	jxn+1	ADJ
ma-218	320	32	−	−	NOUN
ma-218	320	33	jyn	jyn	NOUN
ma-218	320	34	‖=	‖=	NOUN
ma-218	320	35	0	0	X
ma-218	320	36	.	.	PUNCT
ma-218	321	1	(	(	PUNCT
ma-218	321	2	3.30	3.30	NUM
ma-218	321	3	)	)	PUNCT
ma-218	321	4	from	from	ADP
ma-218	321	5	(	(	PUNCT
ma-218	321	6	3.1	3.1	NUM
ma-218	321	7	)	)	PUNCT
ma-218	321	8	,	,	PUNCT
ma-218	321	9	we	we	PRON
ma-218	321	10	observe	observe	VERB
ma-218	321	11	that	that	SCONJ
ma-218	321	12	‖jxn+1	‖jxn+1	VERB
ma-218	321	13	−	−	NOUN
ma-218	321	14	jyn	jyn	NOUN
ma-218	321	15	‖	‖	PROPN
ma-218	321	16	=	=	SYM
ma-218	321	17	‖	‖	PROPN
ma-218	321	18	jxn+1	jxn+1	ADJ
ma-218	321	19	−	−	PROPN
ma-218	321	20	(	(	PUNCT
ma-218	321	21	µn,0jωn	µn,0jωn	PROPN
ma-218	321	22	+	+	CCONJ
ma-218	321	23	n∑	n∑	ADJ
ma-218	321	24	i=1	i=1	PROPN
ma-218	321	25	µn	µn	PROPN
ma-218	321	26	,	,	PUNCT
ma-218	321	27	ijt	ijt	VERB
ma-218	321	28	n	n	ADV
ma-218	321	29	i	i	PRON
ma-218	321	30	ωn	ωn	VERB
ma-218	321	31	)	)	PUNCT
ma-218	321	32	‖	‖	PROPN
ma-218	321	33	=	=	SYM
ma-218	321	34	‖	‖	PROPN
ma-218	321	35	n∑	n∑	PROPN
ma-218	321	36	i=1	i=1	PROPN
ma-218	321	37	µn	µn	PROPN
ma-218	321	38	,	,	PUNCT
ma-218	321	39	ijxn+1	ijxn+1	VERB
ma-218	321	40	−	−	PROPN
ma-218	321	41	n∑	n∑	PROPN
ma-218	321	42	i=1	i=1	PROPN
ma-218	321	43	µn	µn	PROPN
ma-218	321	44	,	,	PUNCT
ma-218	321	45	ijt	ijt	VERB
ma-218	322	1	n	n	ADV
ma-218	322	2	i	i	PRON
ma-218	322	3	ωn	ωn	VERB
ma-218	323	1	+	+	PUNCT
ma-218	323	2	µn,0jxn+1	µn,0jxn+1	PROPN
ma-218	323	3	−	−	PROPN
ma-218	323	4	µn,0jωn	µn,0jωn	NOUN
ma-218	323	5	‖	‖	PROPN
ma-218	323	6	=	=	SYM
ma-218	323	7	‖	‖	PROPN
ma-218	323	8	n∑	n∑	PROPN
ma-218	323	9	i=1	i=1	PROPN
ma-218	323	10	µn	µn	PROPN
ma-218	323	11	,	,	PUNCT
ma-218	323	12	i	i	PRON
ma-218	323	13	(	(	PUNCT
ma-218	323	14	jxn+1	jxn+1	PROPN
ma-218	323	15	−	−	PROPN
ma-218	323	16	jt	jt	PROPN
ma-218	323	17	ni	ni	PROPN
ma-218	323	18	ωn	ωn	PROPN
ma-218	323	19	)	)	PUNCT
ma-218	324	1	+	+	CCONJ
ma-218	324	2	µn,0	µn,0	PROPN
ma-218	324	3	(	(	PUNCT
ma-218	324	4	jxn+1	jxn+1	ADJ
ma-218	324	5	−	−	NOUN
ma-218	324	6	jωn	jωn	NOUN
ma-218	324	7	)	)	PUNCT
ma-218	324	8	‖	‖	PROPN
ma-218	324	9	≥	≥	PROPN
ma-218	324	10	n∑	n∑	NOUN
ma-218	324	11	i=1	i=1	PROPN
ma-218	324	12	µn	µn	PROPN
ma-218	324	13	,	,	PUNCT
ma-218	324	14	i	i	PRON
ma-218	324	15	‖	‖	PROPN
ma-218	324	16	jxn+1	jxn+1	PROPN
ma-218	324	17	−	−	PROPN
ma-218	324	18	jt	jt	PROPN
ma-218	324	19	ni	ni	PROPN
ma-218	324	20	ωn	ωn	PROPN
ma-218	324	21	‖	‖	PROPN
ma-218	324	22	−µn,0	−µn,0	PROPN
ma-218	324	23	‖	‖	PROPN
ma-218	324	24	jωn	jωn	NOUN
ma-218	324	25	−	−	PROPN
ma-218	324	26	jxn+1	jxn+1	PROPN
ma-218	324	27	‖	‖	PROPN
ma-218	324	28	,	,	PUNCT
ma-218	324	29	this	this	PRON
ma-218	324	30	gives	give	VERB
ma-218	324	31	‖	‖	PROPN
ma-218	324	32	jxn+1	jxn+1	PROPN
ma-218	324	33	−	−	PROPN
ma-218	324	34	jt	jt	PROPN
ma-218	324	35	ni	ni	PROPN
ma-218	324	36	ωn	ωn	PROPN
ma-218	324	37	‖≤	‖≤	PROPN
ma-218	324	38	1	1	NUM
ma-218	324	39	n∑	n∑	NOUN
ma-218	324	40	i=1	i=1	PROPN
ma-218	324	41	µn	µn	PROPN
ma-218	324	42	,	,	PUNCT
ma-218	324	43	i	i	PRON
ma-218	324	44	[	[	PUNCT
ma-218	324	45	‖	‖	PROPN
ma-218	324	46	jxn+1	jxn+1	ADJ
ma-218	324	47	−	−	NOUN
ma-218	324	48	jyn	jyn	NOUN
ma-218	324	49	‖	‖	ADJ
ma-218	325	1	+	+	ADJ
ma-218	325	2	µn,0	µn,0	PROPN
ma-218	325	3	‖	‖	PROPN
ma-218	325	4	jωn	jωn	PROPN
ma-218	325	5	−	−	PROPN
ma-218	325	6	jxn+1	jxn+1	NOUN
ma-218	325	7	‖	‖	PROPN
ma-218	325	8	]	]	PUNCT
ma-218	325	9	.	.	PUNCT
ma-218	326	1	by	by	ADP
ma-218	326	2	(	(	PUNCT
ma-218	326	3	3.30	3.30	NUM
ma-218	326	4	)	)	PUNCT
ma-218	326	5	,	,	PUNCT
ma-218	326	6	we	we	PRON
ma-218	326	7	arrive	arrive	VERB
ma-218	326	8	at	at	ADP
ma-218	326	9	lim	lim	PROPN
ma-218	326	10	n→∞	n→∞	X
ma-218	326	11	‖	‖	PROPN
ma-218	326	12	jxn+1	jxn+1	PROPN
ma-218	327	1	−	−	PROPN
ma-218	327	2	jt	jt	PROPN
ma-218	327	3	ni	ni	PROPN
ma-218	327	4	ωn	ωn	PROPN
ma-218	327	5	‖=	‖=	PROPN
ma-218	327	6	0	0	NUM
ma-218	327	7	.	.	PUNCT
ma-218	328	1	as	as	SCONJ
ma-218	328	2	j−1	j−1	PROPN
ma-218	328	3	is	be	AUX
ma-218	328	4	uniform	uniform	ADJ
ma-218	328	5	norm	norm	NOUN
ma-218	328	6	-	-	PUNCT
ma-218	328	7	to	to	ADP
ma-218	328	8	-	-	PUNCT
ma-218	328	9	norm	norm	NOUN
ma-218	328	10	continuous	continuous	ADJ
ma-218	328	11	on	on	ADP
ma-218	328	12	bounded	bounded	ADJ
ma-218	328	13	sets	set	NOUN
ma-218	328	14	,	,	PUNCT
ma-218	328	15	we	we	PRON
ma-218	328	16	present	present	VERB
ma-218	328	17	that	that	SCONJ
ma-218	328	18	lim	lim	PROPN
ma-218	328	19	n→∞	n→∞	X
ma-218	328	20	‖	‖	PROPN
ma-218	328	21	xn+1	xn+1	PROPN
ma-218	329	1	−	−	PROPN
ma-218	329	2	t	t	PROPN
ma-218	329	3	ni	ni	PROPN
ma-218	329	4	ωn	ωn	PROPN
ma-218	329	5	‖=	‖=	PROPN
ma-218	329	6	0	0	PROPN
ma-218	329	7	.	.	PUNCT
ma-218	330	1	(	(	PUNCT
ma-218	330	2	3.31	3.31	NUM
ma-218	330	3	)	)	PUNCT
ma-218	330	4	taking	take	VERB
ma-218	330	5	into	into	ADP
ma-218	330	6	account	account	NOUN
ma-218	330	7	that	that	SCONJ
ma-218	330	8	‖	‖	PROPN
ma-218	330	9	ωn	ωn	ADP
ma-218	330	10	−	−	PROPN
ma-218	330	11	t	t	PROPN
ma-218	330	12	ni	ni	PROPN
ma-218	330	13	ωn	ωn	ADP
ma-218	330	14	‖≤‖	‖≤‖	PROPN
ma-218	330	15	ωn	ωn	ADP
ma-218	330	16	−	−	PROPN
ma-218	330	17	xn+1	xn+1	PROPN
ma-218	330	18	‖	‖	PROPN
ma-218	331	1	+	+	CCONJ
ma-218	331	2	‖	‖	PROPN
ma-218	331	3	xn+1	xn+1	PROPN
ma-218	332	1	−	−	PROPN
ma-218	332	2	t	t	PROPN
ma-218	332	3	ni	ni	PROPN
ma-218	332	4	ωn	ωn	PROPN
ma-218	332	5	‖	‖	PROPN
ma-218	332	6	by	by	ADP
ma-218	332	7	(	(	PUNCT
ma-218	332	8	3.16	3.16	NUM
ma-218	332	9	)	)	PUNCT
ma-218	332	10	and	and	CCONJ
ma-218	332	11	(	(	PUNCT
ma-218	332	12	3.31	3.31	NUM
ma-218	332	13	)	)	PUNCT
ma-218	332	14	,	,	PUNCT
ma-218	332	15	we	we	PRON
ma-218	332	16	obtain	obtain	VERB
ma-218	332	17	lim	lim	PROPN
ma-218	332	18	n→∞	n→∞	PRON
ma-218	332	19	‖	‖	PROPN
ma-218	332	20	ωn	ωn	ADP
ma-218	332	21	−	−	PROPN
ma-218	332	22	t	t	PROPN
ma-218	332	23	ni	ni	PROPN
ma-218	332	24	ωn	ωn	PROPN
ma-218	332	25	‖=	‖=	PROPN
ma-218	332	26	0	0	PROPN
ma-218	332	27	.	.	PUNCT
ma-218	333	1	(	(	PUNCT
ma-218	333	2	3.32	3.32	NUM
ma-218	333	3	)	)	PUNCT
ma-218	333	4	similarly	similarly	ADV
ma-218	333	5	,	,	PUNCT
ma-218	333	6	we	we	PRON
ma-218	333	7	observe	observe	VERB
ma-218	333	8	from	from	ADP
ma-218	333	9	(	(	PUNCT
ma-218	333	10	3.21	3.21	NUM
ma-218	333	11	)	)	PUNCT
ma-218	333	12	,	,	PUNCT
ma-218	333	13	(	(	PUNCT
ma-218	333	14	3.27	3.27	NUM
ma-218	333	15	)	)	PUNCT
ma-218	333	16	and	and	CCONJ
ma-218	333	17	by	by	ADP
ma-218	333	18	continuity	continuity	NOUN
ma-218	333	19	of	of	ADP
ma-218	333	20	j	j	PROPN
ma-218	333	21	that	that	SCONJ
ma-218	333	22	‖	‖	PROPN
ma-218	333	23	jxn+1	jxn+1	PROPN
ma-218	333	24	−	−	PROPN
ma-218	333	25	jzn	jzn	NOUN
ma-218	333	26	‖=‖	‖=‖	PROPN
ma-218	333	27	jxn+1	jxn+1	ADJ
ma-218	333	28	−	−	PROPN
ma-218	333	29	jvn	jvn	NOUN
ma-218	333	30	‖=	‖=	NOUN
ma-218	333	31	0	0	PROPN
ma-218	333	32	.	.	PUNCT
ma-218	334	1	(	(	PUNCT
ma-218	334	2	3.33	3.33	NUM
ma-218	334	3	)	)	PUNCT
ma-218	334	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	334	5	eur	eur	NOUN
ma-218	334	6	.	.	PUNCT
ma-218	335	1	j.	j.	PROPN
ma-218	335	2	math	math	PROPN
ma-218	335	3	.	.	PUNCT
ma-218	336	1	anal	anal	PROPN
ma-218	336	2	.	.	PUNCT
ma-218	337	1	10.28924	10.28924	NUM
ma-218	337	2	/	/	SYM
ma-218	337	3	ada	ada	PROPN
ma-218	337	4	/	/	SYM
ma-218	337	5	ma.4.8	ma.4.8	PROPN
ma-218	337	6	14also	14also	AUX
ma-218	337	7	by	by	ADP
ma-218	337	8	(	(	PUNCT
ma-218	337	9	3.1	3.1	NUM
ma-218	337	10	)	)	PUNCT
ma-218	337	11	,	,	PUNCT
ma-218	337	12	we	we	PRON
ma-218	337	13	observe	observe	VERB
ma-218	337	14	that	that	SCONJ
ma-218	337	15	‖	‖	PROPN
ma-218	337	16	jxn+1	jxn+1	ADJ
ma-218	337	17	−	−	PROPN
ma-218	337	18	jzn	jzn	NOUN
ma-218	337	19	‖	‖	PROPN
ma-218	337	20	=	=	SYM
ma-218	337	21	‖	‖	PROPN
ma-218	337	22	jxn+1	jxn+1	ADJ
ma-218	337	23	−	−	PROPN
ma-218	337	24	(	(	PUNCT
ma-218	337	25	ηn,0jvn	ηn,0jvn	PROPN
ma-218	337	26	+	+	CCONJ
ma-218	337	27	n∑	n∑	PROPN
ma-218	337	28	i=1	i=1	PROPN
ma-218	337	29	ηn	ηn	PROPN
ma-218	337	30	,	,	PUNCT
ma-218	337	31	ijs	ijs	PROPN
ma-218	338	1	n	n	PROPN
ma-218	338	2	i	i	PROPN
ma-218	338	3	yn	yn	PROPN
ma-218	338	4	)	)	PUNCT
ma-218	338	5	‖	‖	PROPN
ma-218	338	6	=	=	SYM
ma-218	339	1	‖	‖	PROPN
ma-218	339	2	n∑	n∑	PROPN
ma-218	339	3	i=1	i=1	PROPN
ma-218	339	4	ηn	ηn	ADJ
ma-218	339	5	,	,	PUNCT
ma-218	339	6	ijxn+1	ijxn+1	NOUN
ma-218	339	7	−	−	PROPN
ma-218	340	1	n∑	n∑	INTJ
ma-218	341	1	i=1	i=1	PROPN
ma-218	341	2	ηn	ηn	PROPN
ma-218	341	3	,	,	PUNCT
ma-218	341	4	ijs	ijs	PROPN
ma-218	342	1	n	n	PROPN
ma-218	342	2	i	i	PROPN
ma-218	342	3	yn	yn	PROPN
ma-218	342	4	+	+	CCONJ
ma-218	342	5	ηn,0jxn+1	ηn,0jxn+1	PROPN
ma-218	342	6	−	−	PROPN
ma-218	343	1	ηn,0jvn	ηn,0jvn	PROPN
ma-218	343	2	‖	‖	PROPN
ma-218	343	3	=	=	SYM
ma-218	343	4	‖	‖	PROPN
ma-218	343	5	n∑	n∑	PROPN
ma-218	343	6	i=1	i=1	PROPN
ma-218	343	7	ηn	ηn	ADJ
ma-218	343	8	,	,	PUNCT
ma-218	343	9	i	i	PRON
ma-218	343	10	(	(	PUNCT
ma-218	343	11	jxn+1	jxn+1	PROPN
ma-218	343	12	−	−	PROPN
ma-218	343	13	jsni	jsni	NOUN
ma-218	343	14	yn	yn	PROPN
ma-218	343	15	)	)	PUNCT
ma-218	344	1	+	+	CCONJ
ma-218	344	2	ηn,0	ηn,0	NOUN
ma-218	344	3	(	(	PUNCT
ma-218	344	4	jxn+1	jxn+1	ADJ
ma-218	344	5	−	−	PROPN
ma-218	344	6	jvn	jvn	NOUN
ma-218	344	7	)	)	PUNCT
ma-218	344	8	‖	‖	PROPN
ma-218	345	1	≥	≥	PROPN
ma-218	345	2	n∑	n∑	INTJ
ma-218	346	1	i=1	i=1	PROPN
ma-218	346	2	ηn	ηn	ADJ
ma-218	346	3	,	,	PUNCT
ma-218	346	4	i	i	PRON
ma-218	346	5	‖	‖	PROPN
ma-218	346	6	jxn+1	jxn+1	PROPN
ma-218	346	7	−	−	PROPN
ma-218	346	8	jsni	jsni	NOUN
ma-218	347	1	yn	yn	PROPN
ma-218	347	2	‖	‖	PROPN
ma-218	348	1	−ηn,0	−ηn,0	X
ma-218	348	2	‖	‖	ADJ
ma-218	348	3	jvn	jvn	NOUN
ma-218	348	4	−	−	PROPN
ma-218	348	5	jxn+1	jxn+1	PROPN
ma-218	348	6	‖	‖	PROPN
ma-218	348	7	,	,	PUNCT
ma-218	348	8	this	this	PRON
ma-218	348	9	implies	imply	VERB
ma-218	348	10	‖jxn+1	‖jxn+1	PUNCT
ma-218	348	11	−	−	PROPN
ma-218	348	12	jsni	jsni	PROPN
ma-218	348	13	yn‖	yn‖	PROPN
ma-218	348	14	≤	≤	ADV
ma-218	349	1	1	1	NUM
ma-218	349	2	n∑	n∑	NOUN
ma-218	349	3	i=1	i=1	PROPN
ma-218	350	1	ηn	ηn	ADJ
ma-218	350	2	,	,	PUNCT
ma-218	350	3	i	i	PRON
ma-218	350	4	[	[	PUNCT
ma-218	350	5	‖jxn+1	‖jxn+1	SYM
ma-218	350	6	−	−	PRON
ma-218	350	7	jzn‖+	jzn‖+	PROPN
ma-218	350	8	ηn,0‖jvn	ηn,0‖jvn	VERB
ma-218	350	9	−	−	PROPN
ma-218	350	10	jxn+1	jxn+1	PROPN
ma-218	350	11	‖	‖	PROPN
ma-218	350	12	]	]	PUNCT
ma-218	350	13	.	.	PUNCT
ma-218	351	1	also	also	ADV
ma-218	351	2	by	by	ADP
ma-218	351	3	(	(	PUNCT
ma-218	351	4	3.33	3.33	NUM
ma-218	351	5	)	)	PUNCT
ma-218	351	6	,	,	PUNCT
ma-218	351	7	we	we	PRON
ma-218	351	8	get	get	VERB
ma-218	351	9	lim	lim	PROPN
ma-218	351	10	n→∞	n→∞	X
ma-218	351	11	‖	‖	PROPN
ma-218	351	12	jxn+1	jxn+1	PROPN
ma-218	351	13	−	−	PROPN
ma-218	351	14	jsni	jsni	NOUN
ma-218	351	15	yn	yn	PROPN
ma-218	351	16	‖=	‖=	PROPN
ma-218	351	17	0	0	X
ma-218	351	18	.	.	PUNCT
ma-218	351	19	applying	apply	VERB
ma-218	351	20	j−1	j−1	PROPN
ma-218	351	21	as	as	ADP
ma-218	351	22	uniform	uniform	ADJ
ma-218	351	23	norm	norm	NOUN
ma-218	351	24	-	-	PUNCT
ma-218	351	25	to	to	ADP
ma-218	351	26	-	-	PUNCT
ma-218	351	27	norm	norm	NOUN
ma-218	351	28	continuous	continuous	ADJ
ma-218	351	29	on	on	ADP
ma-218	351	30	bounded	bounded	ADJ
ma-218	351	31	sets	set	NOUN
ma-218	351	32	,	,	PUNCT
ma-218	351	33	we	we	PRON
ma-218	351	34	have	have	VERB
ma-218	351	35	lim	lim	PROPN
ma-218	351	36	n→∞	n→∞	X
ma-218	351	37	‖	‖	PROPN
ma-218	351	38	xn+1	xn+1	PROPN
ma-218	352	1	−	−	PROPN
ma-218	352	2	sni	sni	PROPN
ma-218	352	3	yn	yn	PROPN
ma-218	352	4	‖=	‖=	PROPN
ma-218	352	5	0	0	PROPN
ma-218	352	6	.	.	PUNCT
ma-218	353	1	(	(	PUNCT
ma-218	353	2	3.34	3.34	NUM
ma-218	353	3	)	)	PUNCT
ma-218	353	4	by	by	ADP
ma-218	353	5	triangular	triangular	NOUN
ma-218	353	6	inequality	inequality	NOUN
ma-218	353	7	,	,	PUNCT
ma-218	353	8	we	we	PRON
ma-218	353	9	obtain	obtain	VERB
ma-218	353	10	‖	‖	PROPN
ma-218	354	1	yn	yn	PROPN
ma-218	354	2	−	−	PROPN
ma-218	354	3	sni	sni	PROPN
ma-218	354	4	yn	yn	PROPN
ma-218	354	5	‖≤‖	‖≤‖	PROPN
ma-218	354	6	yn	yn	PROPN
ma-218	354	7	−	−	PROPN
ma-218	354	8	xn+1	xn+1	PROPN
ma-218	354	9	‖	‖	PROPN
ma-218	354	10	+	+	CCONJ
ma-218	354	11	‖	‖	PROPN
ma-218	354	12	xn+1	xn+1	PROPN
ma-218	354	13	−	−	PROPN
ma-218	354	14	sni	sni	PROPN
ma-218	354	15	yn	yn	PROPN
ma-218	354	16	‖	‖	PROPN
ma-218	354	17	by	by	ADP
ma-218	354	18	(	(	PUNCT
ma-218	354	19	3.24	3.24	NUM
ma-218	354	20	)	)	PUNCT
ma-218	354	21	and	and	CCONJ
ma-218	354	22	(	(	PUNCT
ma-218	354	23	3.34	3.34	NUM
ma-218	354	24	)	)	PUNCT
ma-218	354	25	,	,	PUNCT
ma-218	354	26	we	we	PRON
ma-218	354	27	get	get	VERB
ma-218	354	28	lim	lim	PROPN
ma-218	354	29	n→∞	n→∞	X
ma-218	354	30	‖	‖	PROPN
ma-218	354	31	yn	yn	PROPN
ma-218	354	32	−	−	PROPN
ma-218	354	33	sni	sni	PROPN
ma-218	354	34	yn	yn	PROPN
ma-218	354	35	‖=	‖=	PROPN
ma-218	354	36	0	0	PROPN
ma-218	354	37	.	.	PUNCT
ma-218	355	1	(	(	PUNCT
ma-218	355	2	3.35	3.35	NUM
ma-218	355	3	)	)	PUNCT
ma-218	355	4	therefore	therefore	ADV
ma-218	355	5	by	by	ADP
ma-218	355	6	(	(	PUNCT
ma-218	355	7	3.32	3.32	NUM
ma-218	355	8	)	)	PUNCT
ma-218	355	9	and	and	CCONJ
ma-218	355	10	(	(	PUNCT
ma-218	355	11	3.35	3.35	NUM
ma-218	355	12	)	)	PUNCT
ma-218	355	13	,	,	PUNCT
ma-218	355	14	we	we	PRON
ma-218	355	15	conclude	conclude	VERB
ma-218	355	16	that	that	SCONJ
ma-218	355	17	lim	lim	PROPN
ma-218	355	18	n→∞	n→∞	PRON
ma-218	355	19	‖	‖	PROPN
ma-218	355	20	ωn	ωn	ADP
ma-218	355	21	−	−	PROPN
ma-218	355	22	t	t	PROPN
ma-218	355	23	ni	ni	PROPN
ma-218	355	24	ωn	ωn	PROPN
ma-218	355	25	‖=	‖=	PROPN
ma-218	355	26	lim	lim	PROPN
ma-218	355	27	n→∞	n→∞	X
ma-218	356	1	‖	‖	PROPN
ma-218	356	2	yn	yn	PROPN
ma-218	356	3	−	−	PROPN
ma-218	356	4	sni	sni	PROPN
ma-218	356	5	yn	yn	PROPN
ma-218	356	6	‖=	‖=	PROPN
ma-218	356	7	0	0	X
ma-218	356	8	.	.	PUNCT
ma-218	357	1	step	step	NOUN
ma-218	357	2	5	5	NUM
ma-218	357	3	:	:	PUNCT
ma-218	357	4	we	we	PRON
ma-218	357	5	show	show	VERB
ma-218	357	6	that	that	SCONJ
ma-218	357	7	$	$	SYM
ma-218	357	8	∈	∈	PROPN
ma-218	357	9	ω	ω	NOUN
ma-218	357	10	.	.	PUNCT
ma-218	357	11	to	to	PART
ma-218	357	12	show	show	VERB
ma-218	357	13	this	this	PRON
ma-218	357	14	we	we	PRON
ma-218	357	15	claim	claim	VERB
ma-218	357	16	as	as	SCONJ
ma-218	357	17	follows	follow	VERB
ma-218	357	18	:	:	PUNCT
ma-218	357	19	we	we	PRON
ma-218	357	20	claim	claim	VERB
ma-218	357	21	that	that	SCONJ
ma-218	357	22	$	$	SYM
ma-218	357	23	∈	∈	NOUN
ma-218	357	24	(	(	PUNCT
ma-218	357	25	∩ni=1	∩ni=1	PROPN
ma-218	357	26	f	f	PROPN
ma-218	357	27	(	(	PUNCT
ma-218	357	28	ti	ti	NOUN
ma-218	357	29	)	)	PUNCT
ma-218	357	30	)	)	PUNCT
ma-218	357	31	∩	∩	NOUN
ma-218	357	32	(	(	PUNCT
ma-218	357	33	∩ni=1	∩ni=1	ADP
ma-218	357	34	f	f	PROPN
ma-218	357	35	(	(	PUNCT
ma-218	357	36	si	si	NOUN
ma-218	357	37	)	)	PUNCT
ma-218	357	38	)	)	PUNCT
ma-218	357	39	.	.	PUNCT
ma-218	358	1	by	by	ADP
ma-218	358	2	triangular	triangular	NOUN
ma-218	358	3	inequality	inequality	NOUN
ma-218	358	4	for	for	ADP
ma-218	358	5	i	i	PRON
ma-218	358	6	≥	≥	NUM
ma-218	358	7	1	1	NUM
ma-218	358	8	,	,	PUNCT
ma-218	358	9	we	we	PRON
ma-218	358	10	have	have	VERB
ma-218	358	11	‖	‖	PROPN
ma-218	358	12	t	t	PROPN
ma-218	358	13	ni	ni	PROPN
ma-218	358	14	ωn	ωn	PROPN
ma-218	358	15	−$	−$	VERB
ma-218	358	16	‖≤‖	‖≤‖	PROPN
ma-218	358	17	t	t	PROPN
ma-218	358	18	ni	ni	PROPN
ma-218	358	19	ωn	ωn	ADP
ma-218	358	20	−	−	PROPN
ma-218	358	21	ωn	ωn	ADP
ma-218	358	22	‖	‖	PROPN
ma-218	358	23	+	+	CCONJ
ma-218	358	24	‖	‖	ADJ
ma-218	358	25	ωn	ωn	ADP
ma-218	358	26	−$	−$	VERB
ma-218	358	27	‖	‖	PROPN
ma-218	358	28	.	.	PUNCT
ma-218	359	1	using	use	VERB
ma-218	359	2	(	(	PUNCT
ma-218	359	3	3.14	3.14	NUM
ma-218	359	4	)	)	PUNCT
ma-218	359	5	and	and	CCONJ
ma-218	359	6	(	(	PUNCT
ma-218	359	7	3.32	3.32	NUM
ma-218	359	8	)	)	PUNCT
ma-218	359	9	,	,	PUNCT
ma-218	359	10	we	we	PRON
ma-218	359	11	arrive	arrive	VERB
ma-218	359	12	at	at	ADP
ma-218	359	13	lim	lim	PROPN
ma-218	359	14	n→∞	n→∞	PROPN
ma-218	359	15	‖	‖	PROPN
ma-218	359	16	t	t	PROPN
ma-218	359	17	ni	ni	PROPN
ma-218	359	18	ωn	ωn	PROPN
ma-218	359	19	−$	−$	VERB
ma-218	359	20	‖=	‖=	NOUN
ma-218	359	21	0	0	NUM
ma-218	359	22	.	.	PUNCT
ma-218	360	1	(	(	PUNCT
ma-218	360	2	3.36	3.36	NUM
ma-218	360	3	)	)	PUNCT
ma-218	360	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	360	5	eur	eur	NOUN
ma-218	360	6	.	.	PUNCT
ma-218	361	1	j.	j.	PROPN
ma-218	361	2	math	math	PROPN
ma-218	361	3	.	.	PUNCT
ma-218	362	1	anal	anal	PROPN
ma-218	362	2	.	.	PUNCT
ma-218	363	1	10.28924	10.28924	NUM
ma-218	363	2	/	/	SYM
ma-218	363	3	ada	ada	PROPN
ma-218	363	4	/	/	SYM
ma-218	363	5	ma.4.8	ma.4.8	PROPN
ma-218	363	6	15by	15by	ADJ
ma-218	363	7	the	the	DET
ma-218	363	8	assumption	assumption	NOUN
ma-218	363	9	that	that	SCONJ
ma-218	363	10	for	for	ADP
ma-218	363	11	each	each	DET
ma-218	363	12	ti	ti	NOUN
ma-218	363	13	is	be	AUX
ma-218	363	14	uniformly	uniformly	ADV
ma-218	363	15	li−lipschitz	li−lipschitz	X
ma-218	363	16	continuous	continuous	ADJ
ma-218	363	17	,	,	PUNCT
ma-218	363	18	we	we	PRON
ma-218	363	19	obtain	obtain	VERB
ma-218	363	20	‖t	‖t	NOUN
ma-218	363	21	n+1	n+1	PUNCT
ma-218	364	1	i	i	PRON
ma-218	364	2	ωn	ωn	VERB
ma-218	364	3	−	−	PROPN
ma-218	364	4	t	t	PROPN
ma-218	364	5	ni	ni	PROPN
ma-218	364	6	ωn‖	ωn‖	PROPN
ma-218	364	7	≤	≤	PROPN
ma-218	364	8	‖t	‖t	NOUN
ma-218	364	9	n+1	n+1	PUNCT
ma-218	365	1	i	i	PRON
ma-218	365	2	ωn	ωn	VERB
ma-218	365	3	−	−	PROPN
ma-218	366	1	t	t	NOUN
ma-218	367	1	n+1	n+1	PROPN
ma-218	368	1	i	i	PRON
ma-218	368	2	ωn+1‖+	ωn+1‖+	VERB
ma-218	369	1	‖t	‖t	NOUN
ma-218	369	2	n+1	n+1	PROPN
ma-218	370	1	i	i	PRON
ma-218	370	2	ωn+1	ωn+1	PROPN
ma-218	370	3	−	−	PRON
ma-218	370	4	ωn+1‖	ωn+1‖	PROPN
ma-218	370	5	+	+	CCONJ
ma-218	370	6	‖ωn+1	‖ωn+1	PUNCT
ma-218	370	7	−	−	PROPN
ma-218	370	8	ωn‖+	ωn‖+	PROPN
ma-218	371	1	‖ωn	‖ωn	NUM
ma-218	371	2	−	−	PROPN
ma-218	371	3	t	t	PROPN
ma-218	371	4	ni	ni	PROPN
ma-218	371	5	ωn‖	ωn‖	PROPN
ma-218	371	6	≤	≤	PROPN
ma-218	371	7	(	(	PUNCT
ma-218	371	8	li	li	PROPN
ma-218	371	9	+	+	PROPN
ma-218	371	10	1)‖ωn+1	1)‖ωn+1	PROPN
ma-218	371	11	−	−	PROPN
ma-218	371	12	ωn‖+	ωn‖+	PROPN
ma-218	371	13	‖t	‖t	NOUN
ma-218	371	14	n+1	n+1	PROPN
ma-218	372	1	i	i	PRON
ma-218	372	2	ωn+1	ωn+1	NUM
ma-218	372	3	−	−	NOUN
ma-218	372	4	ωn+1‖+	ωn+1‖+	NOUN
ma-218	373	1	‖ωn	‖ωn	NUM
ma-218	373	2	−	−	PROPN
ma-218	373	3	t	t	PROPN
ma-218	373	4	ni	ni	PROPN
ma-218	373	5	ωn‖.	ωn‖.	X
ma-218	373	6	by	by	ADP
ma-218	373	7	(	(	PUNCT
ma-218	373	8	3.12	3.12	NUM
ma-218	373	9	)	)	PUNCT
ma-218	373	10	and	and	CCONJ
ma-218	373	11	(	(	PUNCT
ma-218	373	12	3.32	3.32	NUM
ma-218	373	13	,	,	PUNCT
ma-218	373	14	)	)	PUNCT
ma-218	373	15	we	we	PRON
ma-218	373	16	get	get	VERB
ma-218	373	17	lim	lim	PROPN
ma-218	373	18	n→∞	n→∞	X
ma-218	373	19	‖t	‖t	PROPN
ma-218	373	20	n+1	n+1	PUNCT
ma-218	374	1	i	i	PRON
ma-218	374	2	ωn	ωn	VERB
ma-218	374	3	−	−	PROPN
ma-218	374	4	t	t	PROPN
ma-218	374	5	ni	ni	PROPN
ma-218	374	6	ωn‖	ωn‖	PROPN
ma-218	374	7	=	=	SYM
ma-218	374	8	0	0	NUM
ma-218	374	9	.	.	NOUN
ma-218	374	10	which	which	PRON
ma-218	374	11	yields	yield	VERB
ma-218	374	12	from	from	ADP
ma-218	374	13	(	(	PUNCT
ma-218	374	14	3.36	3.36	NUM
ma-218	374	15	)	)	PUNCT
ma-218	374	16	that	that	PRON
ma-218	374	17	lim	lim	PROPN
ma-218	374	18	n→∞	n→∞	PRON
ma-218	374	19	‖t	‖t	PROPN
ma-218	374	20	n+1	n+1	PUNCT
ma-218	374	21	i	i	PRON
ma-218	374	22	ωn	ωn	VERB
ma-218	374	23	−$‖	−$‖	NOUN
ma-218	374	24	=	=	SYM
ma-218	374	25	0	0	NUM
ma-218	374	26	,	,	PUNCT
ma-218	374	27	∀i	∀i	NOUN
ma-218	374	28	≥	≥	NOUN
ma-218	374	29	1	1	NUM
ma-218	374	30	.	.	PUNCT
ma-218	375	1	consequently	consequently	ADV
ma-218	375	2	,	,	PUNCT
ma-218	375	3	we	we	PRON
ma-218	375	4	get	get	VERB
ma-218	375	5	ti(t	ti(t	PUNCT
ma-218	375	6	ni	ni	PROPN
ma-218	375	7	)	)	PUNCT
ma-218	375	8	ωn	ωn	ADP
ma-218	375	9	−→	−→	NOUN
ma-218	375	10	$	$	ADP
ma-218	375	11	(	(	PUNCT
ma-218	375	12	as	as	ADP
ma-218	375	13	n	n	PROPN
ma-218	375	14	→∞	→∞	NOUN
ma-218	375	15	)	)	PUNCT
ma-218	375	16	.	.	PUNCT
ma-218	376	1	in	in	ADP
ma-218	376	2	view	view	NOUN
ma-218	376	3	of	of	ADP
ma-218	376	4	the	the	DET
ma-218	376	5	closedness	closedness	NOUN
ma-218	376	6	of	of	ADP
ma-218	376	7	ti	ti	NOUN
ma-218	376	8	,	,	PUNCT
ma-218	376	9	we	we	PRON
ma-218	376	10	arrive	arrive	VERB
ma-218	376	11	at	at	ADP
ma-218	376	12	ti$	ti$	X
ma-218	376	13	=	=	SYM
ma-218	376	14	$	$	SYM
ma-218	376	15	,	,	PUNCT
ma-218	376	16	∀i	∀i	NOUN
ma-218	376	17	≥	≥	NOUN
ma-218	376	18	1	1	NUM
ma-218	376	19	.	.	PUNCT
ma-218	377	1	thus	thus	ADV
ma-218	377	2	$	$	SYM
ma-218	377	3	∈	∈	NOUN
ma-218	377	4	∩ni=1f	∩ni=1f	X
ma-218	377	5	(	(	PUNCT
ma-218	377	6	ti	ti	NOUN
ma-218	377	7	)	)	PUNCT
ma-218	377	8	.	.	PUNCT
ma-218	378	1	furthermore	furthermore	ADV
ma-218	378	2	,	,	PUNCT
ma-218	378	3	following	follow	VERB
ma-218	378	4	similar	similar	ADJ
ma-218	378	5	argument	argument	NOUN
ma-218	378	6	as	as	ADP
ma-218	378	7	above	above	ADV
ma-218	378	8	,	,	PUNCT
ma-218	378	9	onecan	onecan	PROPN
ma-218	378	10	also	also	ADV
ma-218	378	11	claim	claim	VERB
ma-218	378	12	that	that	SCONJ
ma-218	378	13	$	$	SYM
ma-218	378	14	∈	∈	NOUN
ma-218	378	15	∩ni=1f	∩ni=1f	X
ma-218	378	16	(	(	PUNCT
ma-218	378	17	si	si	NOUN
ma-218	378	18	)	)	PUNCT
ma-218	378	19	.	.	PUNCT
ma-218	379	1	hence	hence	ADV
ma-218	379	2	$	$	SYM
ma-218	379	3	∈	∈	PRON
ma-218	379	4	(	(	PUNCT
ma-218	379	5	∩ni=1	∩ni=1	ADP
ma-218	379	6	f	f	PROPN
ma-218	379	7	(	(	PUNCT
ma-218	379	8	ti	ti	NOUN
ma-218	379	9	)	)	PUNCT
ma-218	379	10	)	)	PUNCT
ma-218	379	11	∩	∩	NOUN
ma-218	379	12	(	(	PUNCT
ma-218	379	13	∩ni=1	∩ni=1	ADP
ma-218	379	14	f	f	PROPN
ma-218	379	15	(	(	PUNCT
ma-218	379	16	si	si	NOUN
ma-218	379	17	)	)	PUNCT
ma-218	379	18	)	)	PUNCT
ma-218	379	19	.	.	PUNCT
ma-218	380	1	next	next	ADV
ma-218	380	2	,	,	PUNCT
ma-218	380	3	we	we	PRON
ma-218	380	4	claim	claim	VERB
ma-218	380	5	that	that	SCONJ
ma-218	380	6	$	$	SYM
ma-218	380	7	∈	∈	PROPN
ma-218	380	8	sol(v	sol(v	NOUN
ma-218	380	9	ip	ip	NOUN
ma-218	380	10	(	(	PUNCT
ma-218	380	11	1.4	1.4	NUM
ma-218	380	12	)	)	PUNCT
ma-218	380	13	)	)	PUNCT
ma-218	380	14	.	.	PUNCT
ma-218	381	1	consider	consider	VERB
ma-218	381	2	the	the	DET
ma-218	381	3	triangular	triangular	NOUN
ma-218	381	4	inequality	inequality	NOUN
ma-218	381	5	‖	‖	ADJ
ma-218	381	6	ωn	ωn	ADP
ma-218	381	7	−	−	PROPN
ma-218	381	8	zn	zn	NOUN
ma-218	381	9	‖≤‖	‖≤‖	PROPN
ma-218	381	10	ωn	ωn	ADP
ma-218	381	11	−	−	PROPN
ma-218	381	12	xn	xn	PUNCT
ma-218	381	13	‖	‖	PROPN
ma-218	381	14	+	+	CCONJ
ma-218	381	15	‖	‖	PROPN
ma-218	381	16	xn	xn	PROPN
ma-218	382	1	−	−	PROPN
ma-218	382	2	zn	zn	PROPN
ma-218	382	3	‖	‖	PROPN
ma-218	382	4	.	.	PUNCT
ma-218	383	1	using	use	VERB
ma-218	383	2	(	(	PUNCT
ma-218	383	3	3.13	3.13	NUM
ma-218	383	4	)	)	PUNCT
ma-218	383	5	and	and	CCONJ
ma-218	383	6	(	(	PUNCT
ma-218	383	7	3.22	3.22	NUM
ma-218	383	8	,	,	PUNCT
ma-218	383	9	)	)	PUNCT
ma-218	383	10	leads	lead	VERB
ma-218	383	11	to	to	ADP
ma-218	383	12	lim	lim	PROPN
ma-218	383	13	n→∞	n→∞	X
ma-218	384	1	‖	‖	PROPN
ma-218	384	2	ωn	ωn	ADP
ma-218	384	3	−	−	PROPN
ma-218	384	4	zn	zn	X
ma-218	384	5	‖=	‖=	PROPN
ma-218	384	6	0	0	PROPN
ma-218	384	7	.	.	PUNCT
ma-218	385	1	(	(	PUNCT
ma-218	385	2	3.37	3.37	NUM
ma-218	385	3	)	)	PUNCT
ma-218	385	4	from	from	ADP
ma-218	385	5	the	the	DET
ma-218	385	6	uniform	uniform	ADJ
ma-218	385	7	continuity	continuity	NOUN
ma-218	385	8	of	of	ADP
ma-218	385	9	j	j	PROPN
ma-218	385	10	on	on	ADP
ma-218	385	11	bounded	bounded	PROPN
ma-218	385	12	set	set	PROPN
ma-218	385	13	,	,	PUNCT
ma-218	385	14	we	we	PRON
ma-218	385	15	get	get	VERB
ma-218	385	16	lim	lim	PROPN
ma-218	385	17	n→∞	n→∞	X
ma-218	385	18	‖	‖	PROPN
ma-218	385	19	jωn	jωn	PROPN
ma-218	385	20	−	−	PROPN
ma-218	385	21	jzn	jzn	NOUN
ma-218	385	22	‖=	‖=	NOUN
ma-218	385	23	0	0	PROPN
ma-218	385	24	.	.	PUNCT
ma-218	386	1	(	(	PUNCT
ma-218	386	2	3.38	3.38	NUM
ma-218	386	3	)	)	PUNCT
ma-218	386	4	since	since	SCONJ
ma-218	386	5	x̂	x̂	NUM
ma-218	386	6	∈	∈	PROPN
ma-218	386	7	ω	ω	PROPN
ma-218	386	8	,	,	PUNCT
ma-218	386	9	then	then	ADV
ma-218	386	10	it	it	PRON
ma-218	386	11	follows	follow	VERB
ma-218	386	12	from	from	ADP
ma-218	386	13	(	(	PUNCT
ma-218	386	14	3.2	3.2	NUM
ma-218	386	15	)	)	PUNCT
ma-218	386	16	,	,	PUNCT
ma-218	386	17	(	(	PUNCT
ma-218	386	18	3.3	3.3	NUM
ma-218	386	19	)	)	PUNCT
ma-218	386	20	,	,	PUNCT
ma-218	386	21	(	(	PUNCT
ma-218	386	22	3.4	3.4	NUM
ma-218	386	23	)	)	PUNCT
ma-218	386	24	and	and	CCONJ
ma-218	386	25	(	(	PUNCT
ma-218	386	26	3.6	3.6	NUM
ma-218	386	27	)	)	PUNCT
ma-218	386	28	that	that	SCONJ
ma-218	386	29	φ(x̂	φ(x̂	NOUN
ma-218	386	30	,	,	PUNCT
ma-218	386	31	zn	zn	NOUN
ma-218	386	32	)	)	PUNCT
ma-218	386	33	≤	≤	NUM
ma-218	387	1	ηn,0	ηn,0	PROPN
ma-218	387	2	[	[	PUNCT
ma-218	387	3	φ(x̂	φ(x̂	NOUN
ma-218	387	4	,	,	PUNCT
ma-218	387	5	ωn)−	ωn)−	NOUN
ma-218	387	6	2βn	2βn	ADJ
ma-218	387	7	(	(	PUNCT
ma-218	387	8	γ	γ	X
ma-218	387	9	−	−	PROPN
ma-218	387	10	2βn	2βn	ADJ
ma-218	387	11	δ2	δ2	ADJ
ma-218	387	12	)	)	PUNCT
ma-218	387	13	‖qωn	‖qωn	NOUN
ma-218	387	14	‖2	‖2	NOUN
ma-218	387	15	]	]	PUNCT
ma-218	388	1	+	+	CCONJ
ma-218	389	1	kn	kn	PROPN
ma-218	389	2	n∑	n∑	PROPN
ma-218	390	1	i=1	i=1	PROPN
ma-218	391	1	ηn	ηn	ADJ
ma-218	391	2	,	,	PUNCT
ma-218	391	3	i	i	PRON
ma-218	391	4	[	[	PUNCT
ma-218	391	5	knφ(x̂	knφ(x̂	PROPN
ma-218	391	6	,	,	PUNCT
ma-218	391	7	ωn	ωn	PROPN
ma-218	391	8	)	)	PUNCT
ma-218	391	9	]	]	PUNCT
ma-218	392	1	≤	≤	PROPN
ma-218	392	2	k2	k2	PROPN
ma-218	392	3	nηn,0φ(x̂	nηn,0φ(x̂	NOUN
ma-218	392	4	,	,	PUNCT
ma-218	392	5	ωn	ωn	PROPN
ma-218	392	6	)	)	PUNCT
ma-218	392	7	+	+	CCONJ
ma-218	392	8	k2	k2	PROPN
ma-218	392	9	n	n	PROPN
ma-218	392	10	n∑	n∑	NOUN
ma-218	392	11	i=1	i=1	PROPN
ma-218	392	12	ηn	ηn	ADJ
ma-218	392	13	,	,	PUNCT
ma-218	392	14	iφ(x̂	iφ(x̂	NOUN
ma-218	392	15	,	,	PUNCT
ma-218	392	16	ωn)−	ωn)−	DET
ma-218	392	17	2βnηn,0	2βnηn,0	NUM
ma-218	392	18	(	(	PUNCT
ma-218	392	19	γ	γ	PROPN
ma-218	392	20	−	−	PROPN
ma-218	392	21	2βn	2βn	ADJ
ma-218	392	22	δ2	δ2	ADV
ma-218	392	23	)	)	PUNCT
ma-218	392	24	‖	‖	PROPN
ma-218	392	25	qωn	qωn	NOUN
ma-218	392	26	‖2	‖2	NOUN
ma-218	393	1	=	=	SYM
ma-218	393	2	k2	k2	ADJ
ma-218	393	3	nφ(x̂	nφ(x̂	NOUN
ma-218	393	4	,	,	PUNCT
ma-218	393	5	ωn)−	ωn)−	PRON
ma-218	393	6	2βnηn,0	2βnηn,0	NOUN
ma-218	393	7	(	(	PUNCT
ma-218	393	8	γ	γ	PROPN
ma-218	393	9	−	−	PROPN
ma-218	393	10	2βn	2βn	ADJ
ma-218	393	11	δ2	δ2	ADV
ma-218	393	12	)	)	PUNCT
ma-218	393	13	‖	‖	PROPN
ma-218	393	14	qωn	qωn	PROPN
ma-218	393	15	‖2	‖2	NOUN
ma-218	393	16	,	,	PUNCT
ma-218	393	17	implies	imply	VERB
ma-218	393	18	that	that	SCONJ
ma-218	393	19	2βnηn,0	2βnηn,0	NOUN
ma-218	393	20	(	(	PUNCT
ma-218	393	21	γ	γ	PROPN
ma-218	393	22	−	−	PROPN
ma-218	393	23	2βn	2βn	ADJ
ma-218	393	24	δ2	δ2	ADV
ma-218	393	25	)	)	PUNCT
ma-218	393	26	‖	‖	PROPN
ma-218	393	27	qωn	qωn	PROPN
ma-218	393	28	‖2≤	‖2≤	PROPN
ma-218	393	29	k2	k2	PROPN
ma-218	393	30	nφ(x̂	nφ(x̂	NOUN
ma-218	393	31	,	,	PUNCT
ma-218	393	32	ωn)−	ωn)−	PRON
ma-218	393	33	φ(x̂	φ(x̂	NOUN
ma-218	393	34	,	,	PUNCT
ma-218	393	35	zn	zn	PROPN
ma-218	393	36	)	)	PUNCT
ma-218	393	37	(	(	PUNCT
ma-218	393	38	3.39	3.39	NUM
ma-218	393	39	)	)	PUNCT
ma-218	393	40	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	393	41	eur	eur	NOUN
ma-218	393	42	.	.	PUNCT
ma-218	394	1	j.	j.	PROPN
ma-218	394	2	math	math	PROPN
ma-218	394	3	.	.	PUNCT
ma-218	395	1	anal	anal	PROPN
ma-218	395	2	.	.	PUNCT
ma-218	396	1	10.28924	10.28924	NUM
ma-218	396	2	/	/	SYM
ma-218	396	3	ada	ada	PROPN
ma-218	396	4	/	/	SYM
ma-218	396	5	ma.4.8	ma.4.8	PROPN
ma-218	396	6	16but	16but	PROPN
ma-218	396	7	k2	k2	PROPN
ma-218	396	8	nφ(x̂	nφ(x̂	PROPN
ma-218	396	9	,	,	PUNCT
ma-218	396	10	ωn)−	ωn)−	PRON
ma-218	396	11	φ(x̂	φ(x̂	NOUN
ma-218	396	12	,	,	PUNCT
ma-218	396	13	zn	zn	PROPN
ma-218	396	14	)	)	PUNCT
ma-218	396	15	=	=	SYM
ma-218	396	16	k2	k2	PROPN
ma-218	396	17	n	n	CCONJ
ma-218	396	18	[	[	PUNCT
ma-218	396	19	‖	‖	PROPN
ma-218	396	20	x̂	x̂	PROPN
ma-218	396	21	‖2	‖2	NOUN
ma-218	396	22	−2〈x̂	−2〈x̂	PROPN
ma-218	396	23	,	,	PUNCT
ma-218	396	24	jωn〉+	jωn〉+	PROPN
ma-218	396	25	‖	‖	PROPN
ma-218	396	26	ωn	ωn	PRON
ma-218	396	27	‖2	‖2	NOUN
ma-218	396	28	]	]	PUNCT
ma-218	396	29	−	−	PROPN
ma-218	397	1	[	[	PUNCT
ma-218	397	2	‖	‖	PROPN
ma-218	397	3	x̂	x̂	NOUN
ma-218	397	4	‖2	‖2	NOUN
ma-218	397	5	−2〈x̂	−2〈x̂	PROPN
ma-218	397	6	,	,	PUNCT
ma-218	397	7	jzn〉+	jzn〉+	PROPN
ma-218	397	8	‖	‖	PROPN
ma-218	397	9	zn	zn	PROPN
ma-218	397	10	‖2	‖2	NOUN
ma-218	397	11	]	]	PUNCT
ma-218	398	1	=	=	SYM
ma-218	398	2	(	(	PUNCT
ma-218	398	3	k2	k2	PROPN
ma-218	398	4	n	n	CCONJ
ma-218	398	5	−	−	PROPN
ma-218	398	6	1)‖x̂‖2	1)‖x̂‖2	NUM
ma-218	398	7	−	−	PROPN
ma-218	398	8	2(k2	2(k2	NUM
ma-218	398	9	n	n	CCONJ
ma-218	398	10	−	−	PROPN
ma-218	398	11	1)〈x̂	1)〈x̂	PROPN
ma-218	398	12	,	,	PUNCT
ma-218	398	13	jzn	jzn	PROPN
ma-218	398	14	〉	〉	PROPN
ma-218	398	15	−	−	PROPN
ma-218	398	16	2k2	2k2	NUM
ma-218	398	17	n	n	DET
ma-218	398	18	〈	〈	PROPN
ma-218	398	19	x̂	x̂	PROPN
ma-218	398	20	,	,	PUNCT
ma-218	398	21	jωn	jωn	NOUN
ma-218	398	22	−	−	PROPN
ma-218	398	23	jωn	jωn	NOUN
ma-218	398	24	〉	〉	PROPN
ma-218	399	1	+	+	CCONJ
ma-218	399	2	k2	k2	PROPN
ma-218	399	3	n‖ωn	n‖ωn	PROPN
ma-218	399	4	‖2	‖2	NOUN
ma-218	399	5	−	−	PROPN
ma-218	399	6	‖	‖	PROPN
ma-218	399	7	zn	zn	NOUN
ma-218	399	8	‖2	‖2	NOUN
ma-218	399	9	=	=	PUNCT
ma-218	399	10	(	(	PUNCT
ma-218	399	11	k2	k2	PROPN
ma-218	399	12	n	n	CCONJ
ma-218	399	13	−	−	PROPN
ma-218	399	14	1	1	NUM
ma-218	399	15	)	)	PUNCT
ma-218	399	16	‖	‖	PROPN
ma-218	399	17	x̂	x̂	PROPN
ma-218	399	18	‖2	‖2	NOUN
ma-218	399	19	−2(k2	−2(k2	PROPN
ma-218	400	1	n	n	CCONJ
ma-218	400	2	−	−	PROPN
ma-218	400	3	1)〈x̂	1)〈x̂	PROPN
ma-218	400	4	,	,	PUNCT
ma-218	400	5	jzn	jzn	PROPN
ma-218	400	6	〉	〉	PROPN
ma-218	400	7	−	−	PROPN
ma-218	400	8	2k2	2k2	NUM
ma-218	400	9	n	n	DET
ma-218	400	10	〈	〈	PROPN
ma-218	400	11	x̂	x̂	PROPN
ma-218	400	12	,	,	PUNCT
ma-218	400	13	jωn	jωn	NOUN
ma-218	400	14	−	−	PROPN
ma-218	400	15	jzn	jzn	PROPN
ma-218	400	16	〉	〉	PROPN
ma-218	400	17	+	+	CCONJ
ma-218	400	18	(	(	PUNCT
ma-218	400	19	k2	k2	ADJ
ma-218	400	20	n	n	CCONJ
ma-218	400	21	−	−	PROPN
ma-218	401	1	1)‖ωn	1)‖ωn	NUM
ma-218	401	2	‖2	‖2	NOUN
ma-218	401	3	+	+	CCONJ
ma-218	401	4	‖	‖	ADJ
ma-218	401	5	ωn	ωn	VERB
ma-218	401	6	‖2	‖2	NOUN
ma-218	401	7	−	−	PROPN
ma-218	401	8	‖	‖	PROPN
ma-218	401	9	zn	zn	PROPN
ma-218	401	10	‖2	‖2	NOUN
ma-218	401	11	≤	≤	PUNCT
ma-218	402	1	|	|	ADV
ma-218	402	2	(	(	PUNCT
ma-218	402	3	k2	k2	PROPN
ma-218	402	4	n	n	CCONJ
ma-218	402	5	−	−	PROPN
ma-218	402	6	1	1	NUM
ma-218	402	7	)	)	PUNCT
ma-218	402	8	‖	‖	PROPN
ma-218	402	9	x̂	x̂	NOUN
ma-218	402	10	‖2|	‖2|	PUNCT
ma-218	403	1	+	+	CCONJ
ma-218	403	2	|	|	ADV
ma-218	403	3	2(k2	2(k2	NUM
ma-218	403	4	n	n	CCONJ
ma-218	403	5	−	−	NOUN
ma-218	403	6	1)〈x̂	1)〈x̂	PROPN
ma-218	403	7	,	,	PUNCT
ma-218	403	8	jzn	jzn	PROPN
ma-218	403	9	〉	〉	PROPN
ma-218	404	1	|	|	ADV
ma-218	405	1	+	+	CCONJ
ma-218	405	2	|	|	ADV
ma-218	405	3	2k2	2k2	NUM
ma-218	405	4	n	n	PRON
ma-218	405	5	〈	〈	PROPN
ma-218	405	6	x̂	x̂	PROPN
ma-218	405	7	,	,	PUNCT
ma-218	405	8	jωn	jωn	NOUN
ma-218	405	9	−	−	PROPN
ma-218	405	10	jzn	jzn	PROPN
ma-218	405	11	〉	〉	PROPN
ma-218	406	1	|	|	ADV
ma-218	407	1	+	+	CCONJ
ma-218	407	2	|	|	ADV
ma-218	407	3	(	(	PUNCT
ma-218	407	4	k2	k2	PROPN
ma-218	407	5	n	n	CCONJ
ma-218	407	6	−	−	PROPN
ma-218	408	1	1)‖ωn	1)‖ωn	NUM
ma-218	408	2	‖2|	‖2|	PROPN
ma-218	408	3	+	+	CCONJ
ma-218	408	4	|‖	|‖	NOUN
ma-218	408	5	ωn	ωn	PRON
ma-218	408	6	‖2	‖2	NOUN
ma-218	409	1	+	+	CCONJ
ma-218	409	2	‖	‖	PROPN
ma-218	409	3	zn	zn	PROPN
ma-218	409	4	‖2|	‖2|	PROPN
ma-218	409	5	≤	≤	PROPN
ma-218	409	6	(	(	PUNCT
ma-218	409	7	k2	k2	NOUN
ma-218	409	8	n	n	CCONJ
ma-218	409	9	−	−	PROPN
ma-218	409	10	1	1	NUM
ma-218	409	11	)	)	PUNCT
ma-218	410	1	‖	‖	PROPN
ma-218	410	2	x̂	x̂	NOUN
ma-218	410	3	‖2	‖2	NOUN
ma-218	410	4	+2(k2	+2(k2	PUNCT
ma-218	410	5	n	n	CCONJ
ma-218	410	6	−	−	PROPN
ma-218	410	7	1	1	NUM
ma-218	410	8	)	)	PUNCT
ma-218	410	9	‖	‖	PROPN
ma-218	410	10	x̂	x̂	PROPN
ma-218	411	1	‖	‖	PROPN
ma-218	411	2	‖	‖	PROPN
ma-218	411	3	jzn	jzn	PROPN
ma-218	411	4	‖	‖	PROPN
ma-218	411	5	+2k2	+2k2	PROPN
ma-218	411	6	n	n	X
ma-218	411	7	‖	‖	PROPN
ma-218	411	8	x̂	x̂	PROPN
ma-218	412	1	‖	‖	PROPN
ma-218	412	2	‖	‖	PROPN
ma-218	412	3	jωn	jωn	PROPN
ma-218	412	4	−	−	PROPN
ma-218	412	5	jzn	jzn	NOUN
ma-218	412	6	‖	‖	PROPN
ma-218	412	7	+	+	CCONJ
ma-218	412	8	(	(	PUNCT
ma-218	412	9	‖	‖	PROPN
ma-218	412	10	ωn	ωn	X
ma-218	412	11	−	−	PROPN
ma-218	412	12	zn	zn	INTJ
ma-218	412	13	‖)(‖	‖)(‖	PUNCT
ma-218	412	14	ωn	ωn	ADP
ma-218	412	15	‖	‖	PROPN
ma-218	412	16	+	+	CCONJ
ma-218	412	17	‖	‖	PROPN
ma-218	412	18	zn	zn	PROPN
ma-218	412	19	‖	‖	PROPN
ma-218	412	20	)	)	PUNCT
ma-218	412	21	.	.	PUNCT
ma-218	413	1	since	since	SCONJ
ma-218	413	2	kn	kn	PROPN
ma-218	413	3	−→	−→	NOUN
ma-218	413	4	1	1	NUM
ma-218	413	5	as	as	ADP
ma-218	413	6	n	n	PROPN
ma-218	413	7	−→∞	−→∞	PROPN
ma-218	413	8	,	,	PUNCT
ma-218	413	9	then	then	ADV
ma-218	413	10	by	by	ADP
ma-218	413	11	(	(	PUNCT
ma-218	413	12	3.37	3.37	NUM
ma-218	413	13	)	)	PUNCT
ma-218	413	14	and	and	CCONJ
ma-218	413	15	(	(	PUNCT
ma-218	413	16	3.38	3.38	NUM
ma-218	413	17	,	,	PUNCT
ma-218	413	18	)	)	PUNCT
ma-218	413	19	we	we	PRON
ma-218	413	20	obtain	obtain	VERB
ma-218	413	21	lim	lim	PROPN
ma-218	413	22	n→∞	n→∞	X
ma-218	413	23	(	(	PUNCT
ma-218	413	24	k2	k2	PROPN
ma-218	413	25	nφ(x̂	nφ(x̂	NOUN
ma-218	413	26	,	,	PUNCT
ma-218	413	27	ωn)−	ωn)−	PRON
ma-218	413	28	φ(x̂	φ(x̂	NOUN
ma-218	413	29	,	,	PUNCT
ma-218	413	30	zn	zn	PROPN
ma-218	413	31	)	)	PUNCT
ma-218	413	32	)	)	PUNCT
ma-218	414	1	=	=	PUNCT
ma-218	414	2	0	0	X
ma-218	414	3	.	.	PUNCT
ma-218	415	1	(	(	PUNCT
ma-218	415	2	3.40	3.40	NUM
ma-218	415	3	)	)	PUNCT
ma-218	415	4	also	also	ADV
ma-218	415	5	since	since	SCONJ
ma-218	415	6	βnηn,0(γ	βnηn,0(γ	NOUN
ma-218	415	7	−	−	PROPN
ma-218	415	8	2βn	2βn	ADV
ma-218	415	9	δ2	δ2	ADV
ma-218	415	10	)	)	PUNCT
ma-218	415	11	>	>	X
ma-218	415	12	0	0	NUM
ma-218	415	13	,	,	PUNCT
ma-218	415	14	by	by	ADP
ma-218	415	15	(	(	PUNCT
ma-218	415	16	3.39	3.39	NUM
ma-218	415	17	)	)	PUNCT
ma-218	415	18	and	and	CCONJ
ma-218	415	19	(	(	PUNCT
ma-218	415	20	3.40	3.40	NUM
ma-218	415	21	)	)	PUNCT
ma-218	415	22	,	,	PUNCT
ma-218	415	23	we	we	PRON
ma-218	415	24	have	have	VERB
ma-218	415	25	lim	lim	PROPN
ma-218	415	26	n→∞	n→∞	PRON
ma-218	415	27	‖	‖	PROPN
ma-218	415	28	qωn	qωn	PROPN
ma-218	415	29	‖=	‖=	PROPN
ma-218	415	30	0	0	X
ma-218	415	31	.	.	PUNCT
ma-218	416	1	(	(	PUNCT
ma-218	416	2	3.41	3.41	NUM
ma-218	416	3	)	)	PUNCT
ma-218	416	4	taking	take	VERB
ma-218	416	5	the	the	DET
ma-218	416	6	advantage	advantage	NOUN
ma-218	416	7	of	of	ADP
ma-218	416	8	q	q	NOUN
ma-218	416	9	as	as	ADP
ma-218	416	10	γ	γ	X
ma-218	416	11	−	−	PROPN
ma-218	417	1	i	i	PRON
ma-218	417	2	sm	sm	INTJ
ma-218	418	1	and	and	CCONJ
ma-218	418	2	so	so	ADV
ma-218	418	3	1	1	NUM
ma-218	418	4	γ	γ	NOUN
ma-218	418	5	−lipschitz	−lipschitz	NOUN
ma-218	418	6	continuous	continuous	ADJ
ma-218	418	7	.	.	PUNCT
ma-218	419	1	therefore	therefore	ADV
ma-218	419	2	,	,	PUNCT
ma-218	419	3	it	it	PRON
ma-218	419	4	follows	follow	VERB
ma-218	419	5	from(3.38	from(3.38	NOUN
ma-218	419	6	)	)	PUNCT
ma-218	419	7	and	and	CCONJ
ma-218	419	8	(	(	PUNCT
ma-218	419	9	3.40	3.40	NUM
ma-218	419	10	)	)	PUNCT
ma-218	419	11	that	that	SCONJ
ma-218	419	12	$	$	SYM
ma-218	419	13	∈	∈	PROPN
ma-218	419	14	q−1(0	q−1(0	NOUN
ma-218	419	15	)	)	PUNCT
ma-218	419	16	.	.	PUNCT
ma-218	420	1	hence	hence	ADV
ma-218	420	2	,	,	PUNCT
ma-218	420	3	$	$	SYM
ma-218	420	4	∈	∈	NOUN
ma-218	420	5	sol(v	sol(v	NOUN
ma-218	420	6	ip	ip	NOUN
ma-218	420	7	(	(	PUNCT
ma-218	420	8	1.4	1.4	NUM
ma-218	420	9	)	)	PUNCT
ma-218	420	10	)	)	PUNCT
ma-218	420	11	.	.	PUNCT
ma-218	421	1	we	we	PRON
ma-218	421	2	also	also	ADV
ma-218	421	3	claim	claim	VERB
ma-218	421	4	that	that	SCONJ
ma-218	421	5	$	$	SYM
ma-218	421	6	∈	∈	NOUN
ma-218	421	7	sol(gmep	sol(gmep	NOUN
ma-218	421	8	(	(	PUNCT
ma-218	421	9	1.1	1.1	NUM
ma-218	421	10	)	)	PUNCT
ma-218	421	11	)	)	PUNCT
ma-218	421	12	.	.	PUNCT
ma-218	422	1	consider	consider	VERB
ma-218	422	2	the	the	DET
ma-218	422	3	triangular	triangular	NOUN
ma-218	422	4	inequality	inequality	NOUN
ma-218	422	5	‖	‖	PROPN
ma-218	422	6	un	un	PROPN
ma-218	422	7	−	−	PROPN
ma-218	422	8	zn	zn	PROPN
ma-218	422	9	‖≤‖	‖≤‖	PROPN
ma-218	422	10	un	un	PROPN
ma-218	422	11	−	−	PROPN
ma-218	422	12	xn	xn	PROPN
ma-218	422	13	‖	‖	PROPN
ma-218	423	1	+	+	CCONJ
ma-218	423	2	‖	‖	PROPN
ma-218	423	3	xn	xn	PROPN
ma-218	424	1	−	−	PROPN
ma-218	424	2	zn	zn	PROPN
ma-218	424	3	‖	‖	PROPN
ma-218	424	4	.	.	PUNCT
ma-218	425	1	by	by	ADP
ma-218	425	2	(	(	PUNCT
ma-218	425	3	3.19	3.19	NUM
ma-218	425	4	)	)	PUNCT
ma-218	425	5	and	and	CCONJ
ma-218	425	6	(	(	PUNCT
ma-218	425	7	3.22	3.22	NUM
ma-218	425	8	)	)	PUNCT
ma-218	425	9	,	,	PUNCT
ma-218	425	10	we	we	PRON
ma-218	425	11	get	get	VERB
ma-218	425	12	lim	lim	PROPN
ma-218	425	13	n→∞	n→∞	X
ma-218	425	14	‖	‖	PROPN
ma-218	425	15	un	un	PROPN
ma-218	425	16	−	−	PROPN
ma-218	425	17	zn	zn	PROPN
ma-218	425	18	‖=	‖=	PROPN
ma-218	425	19	0	0	PROPN
ma-218	425	20	.	.	PUNCT
ma-218	426	1	from	from	ADP
ma-218	426	2	uniform	uniform	ADJ
ma-218	426	3	continuity	continuity	NOUN
ma-218	426	4	of	of	ADP
ma-218	426	5	j	j	PROPN
ma-218	426	6	on	on	ADP
ma-218	426	7	bounded	bounded	ADJ
ma-218	426	8	sets	set	NOUN
ma-218	426	9	,	,	PUNCT
ma-218	426	10	we	we	PRON
ma-218	426	11	obtain	obtain	VERB
ma-218	426	12	lim	lim	PROPN
ma-218	426	13	n→∞	n→∞	X
ma-218	426	14	‖	‖	PROPN
ma-218	426	15	jun	jun	PROPN
ma-218	426	16	−	−	PROPN
ma-218	426	17	jzn	jzn	PROPN
ma-218	426	18	‖=	‖=	PROPN
ma-218	426	19	0	0	PROPN
ma-218	426	20	.	.	PUNCT
ma-218	427	1	(	(	PUNCT
ma-218	427	2	3.42	3.42	NUM
ma-218	427	3	)	)	PUNCT
ma-218	427	4	since	since	SCONJ
ma-218	427	5	rn	rn	PROPN
ma-218	427	6	≥	≥	PROPN
ma-218	427	7	a	a	PRON
ma-218	427	8	and	and	CCONJ
ma-218	427	9	by	by	ADP
ma-218	427	10	(	(	PUNCT
ma-218	427	11	3.42	3.42	NUM
ma-218	427	12	)	)	PUNCT
ma-218	427	13	,	,	PUNCT
ma-218	427	14	we	we	PRON
ma-218	427	15	have	have	VERB
ma-218	427	16	lim	lim	PROPN
ma-218	427	17	n→∞	n→∞	X
ma-218	427	18	‖	‖	PROPN
ma-218	427	19	jun	jun	PROPN
ma-218	427	20	−	−	PROPN
ma-218	427	21	jzn	jzn	PROPN
ma-218	427	22	‖	‖	PROPN
ma-218	427	23	rn	rn	PROPN
ma-218	427	24	=	=	PROPN
ma-218	427	25	0	0	PROPN
ma-218	427	26	.	.	PUNCT
ma-218	428	1	(	(	PUNCT
ma-218	428	2	3.43	3.43	NUM
ma-218	428	3	)	)	PUNCT
ma-218	428	4	equation	equation	NOUN
ma-218	428	5	un	un	PROPN
ma-218	428	6	=	=	NOUN
ma-218	428	7	trnzn	trnzn	PROPN
ma-218	428	8	implies	imply	VERB
ma-218	428	9	that	that	SCONJ
ma-218	428	10	h(un	h(un	PROPN
ma-218	428	11	,	,	PUNCT
ma-218	428	12	v	v	NOUN
ma-218	428	13	)	)	PUNCT
ma-218	428	14	+	+	CCONJ
ma-218	428	15	1	1	NUM
ma-218	428	16	rn	rn	ADP
ma-218	428	17	〈	〈	PROPN
ma-218	428	18	v	v	NOUN
ma-218	428	19	−	−	PROPN
ma-218	428	20	un	un	PROPN
ma-218	428	21	,	,	PUNCT
ma-218	428	22	jun	jun	PROPN
ma-218	428	23	−	−	PROPN
ma-218	428	24	jzn〉+	jzn〉+	PROPN
ma-218	428	25	ϑ(v	ϑ(v	PROPN
ma-218	428	26	,	,	PUNCT
ma-218	428	27	un)−	un)−	PROPN
ma-218	428	28	ϑ(un	ϑ(un	PROPN
ma-218	428	29	,	,	PUNCT
ma-218	428	30	un	un	PROPN
ma-218	428	31	)	)	PUNCT
ma-218	428	32	≥	≥	NOUN
ma-218	428	33	0	0	NUM
ma-218	428	34	,	,	PUNCT
ma-218	428	35	∀v	∀v	PROPN
ma-218	428	36	∈	∈	PROPN
ma-218	428	37	c.	c.	PROPN
ma-218	428	38	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	428	39	eur	eur	PROPN
ma-218	428	40	.	.	PUNCT
ma-218	429	1	j.	j.	PROPN
ma-218	429	2	math	math	PROPN
ma-218	429	3	.	.	PUNCT
ma-218	430	1	anal	anal	PROPN
ma-218	430	2	.	.	PUNCT
ma-218	431	1	10.28924	10.28924	NUM
ma-218	431	2	/	/	SYM
ma-218	431	3	ada	ada	PROPN
ma-218	431	4	/	/	SYM
ma-218	431	5	ma.4.8	ma.4.8	PROPN
ma-218	431	6	17where	17where	PROPN
ma-218	432	1	h(un	h(un	NOUN
ma-218	432	2	,	,	PUNCT
ma-218	432	3	v	v	NOUN
ma-218	432	4	)	)	PUNCT
ma-218	432	5	=	=	SYM
ma-218	432	6	d(un	d(un	PROPN
ma-218	432	7	,	,	PUNCT
ma-218	432	8	v	v	NOUN
ma-218	432	9	)	)	PUNCT
ma-218	432	10	+	+	CCONJ
ma-218	432	11	〈	〈	PROPN
ma-218	432	12	gun	gun	NOUN
ma-218	432	13	,	,	PUNCT
ma-218	432	14	v	v	ADP
ma-218	432	15	−	−	PROPN
ma-218	432	16	un	un	PROPN
ma-218	432	17	〉	〉	PROPN
ma-218	432	18	.	.	PUNCT
ma-218	433	1	by	by	ADP
ma-218	433	2	applying	apply	VERB
ma-218	433	3	assumption	assumption	NOUN
ma-218	433	4	(	(	PUNCT
ma-218	433	5	d2	d2	PROPN
ma-218	433	6	)	)	PUNCT
ma-218	433	7	,	,	PUNCT
ma-218	433	8	we	we	PRON
ma-218	433	9	obtain	obtain	VERB
ma-218	433	10	1	1	NUM
ma-218	433	11	rn	rn	ADP
ma-218	433	12	〈	〈	PROPN
ma-218	433	13	v	v	NOUN
ma-218	433	14	−	−	PROPN
ma-218	434	1	un	un	PROPN
ma-218	435	1	,	,	PUNCT
ma-218	435	2	jun	jun	PROPN
ma-218	435	3	−	−	PROPN
ma-218	435	4	jzn	jzn	PROPN
ma-218	435	5	〉	〉	PROPN
ma-218	435	6	≥	≥	PROPN
ma-218	435	7	−h(un	−h(un	PUNCT
ma-218	435	8	,	,	PUNCT
ma-218	435	9	v)−	v)−	PROPN
ma-218	435	10	ϑ(v	ϑ(v	PROPN
ma-218	435	11	,	,	PUNCT
ma-218	435	12	un	un	PROPN
ma-218	435	13	)	)	PUNCT
ma-218	435	14	+	+	CCONJ
ma-218	435	15	ϑ(un	ϑ(un	PROPN
ma-218	435	16	,	,	PUNCT
ma-218	435	17	un	un	PROPN
ma-218	435	18	)	)	PUNCT
ma-218	435	19	≥	≥	NOUN
ma-218	435	20	h(v	h(v	PROPN
ma-218	435	21	,	,	PUNCT
ma-218	435	22	un)−	un)−	ADJ
ma-218	435	23	ϑ(v	ϑ(v	PROPN
ma-218	435	24	,	,	PUNCT
ma-218	435	25	un	un	PROPN
ma-218	435	26	)	)	PUNCT
ma-218	435	27	+	+	CCONJ
ma-218	435	28	ϑ(un	ϑ(un	PROPN
ma-218	435	29	,	,	PUNCT
ma-218	435	30	un	un	PROPN
ma-218	435	31	)	)	PUNCT
ma-218	435	32	.	.	PUNCT
ma-218	436	1	letting	let	VERB
ma-218	436	2	n	n	PROPN
ma-218	436	3	−→∞	−→∞	PROPN
ma-218	436	4	,	,	PUNCT
ma-218	436	5	by	by	ADP
ma-218	436	6	assumption	assumption	NOUN
ma-218	436	7	(	(	PUNCT
ma-218	436	8	d4	d4	PROPN
ma-218	436	9	)	)	PUNCT
ma-218	436	10	and	and	CCONJ
ma-218	436	11	(	(	PUNCT
ma-218	436	12	3.43	3.43	NUM
ma-218	436	13	)	)	PUNCT
ma-218	436	14	,	,	PUNCT
ma-218	436	15	we	we	PRON
ma-218	436	16	get	get	VERB
ma-218	436	17	h(v	h(v	PROPN
ma-218	436	18	,	,	PUNCT
ma-218	436	19	$	$	SYM
ma-218	436	20	)	)	PUNCT
ma-218	437	1	−	−	PROPN
ma-218	438	1	ϑ(v	ϑ(v	PROPN
ma-218	438	2	,	,	PUNCT
ma-218	438	3	$	$	SYM
ma-218	438	4	)	)	PUNCT
ma-218	438	5	+	+	NUM
ma-218	438	6	ϑ($,$	ϑ($,$	NOUN
ma-218	438	7	)	)	PUNCT
ma-218	438	8	≤	≤	NOUN
ma-218	438	9	0	0	NUM
ma-218	438	10	,	,	PUNCT
ma-218	438	11	∀v	∀v	PROPN
ma-218	438	12	∈	∈	PROPN
ma-218	438	13	c.	c.	NOUN
ma-218	438	14	for	for	ADP
ma-218	438	15	all	all	PRON
ma-218	438	16	s	s	PART
ma-218	438	17	∈	∈	NOUN
ma-218	438	18	(	(	PUNCT
ma-218	438	19	0	0	NUM
ma-218	438	20	,	,	PUNCT
ma-218	438	21	1	1	NUM
ma-218	438	22	]	]	PUNCT
ma-218	438	23	and	and	CCONJ
ma-218	438	24	v	v	ADP
ma-218	438	25	∈	∈	NOUN
ma-218	438	26	c	c	NOUN
ma-218	438	27	,	,	PUNCT
ma-218	438	28	setting	set	VERB
ma-218	438	29	vs	vs	ADP
ma-218	438	30	:	:	PUNCT
ma-218	438	31	=	=	PUNCT
ma-218	438	32	sv	sv	INTJ
ma-218	439	1	+	+	CCONJ
ma-218	439	2	(	(	PUNCT
ma-218	439	3	1−	1−	NUM
ma-218	439	4	s)$.	s)$.	X
ma-218	439	5	therefore	therefore	ADV
ma-218	439	6	vs	vs	ADP
ma-218	439	7	∈	∈	PROPN
ma-218	439	8	c	c	NOUN
ma-218	439	9	and	and	CCONJ
ma-218	439	10	then	then	ADV
ma-218	439	11	,	,	PUNCT
ma-218	439	12	h(vs	h(vs	ADJ
ma-218	439	13	,	,	PUNCT
ma-218	439	14	$	$	SYM
ma-218	439	15	)	)	PUNCT
ma-218	439	16	−	−	PROPN
ma-218	439	17	ϑ(vs	ϑ(vs	PROPN
ma-218	439	18	,	,	PUNCT
ma-218	439	19	$	$	SYM
ma-218	439	20	)	)	PUNCT
ma-218	439	21	+	+	NUM
ma-218	439	22	ϑ($,$	ϑ($,$	NOUN
ma-218	439	23	)	)	PUNCT
ma-218	439	24	≤	≤	NOUN
ma-218	439	25	0	0	NUM
ma-218	439	26	.	.	PUNCT
ma-218	440	1	by	by	ADP
ma-218	440	2	assumption	assumption	NOUN
ma-218	440	3	(	(	PUNCT
ma-218	440	4	d1)−	d1)−	PROPN
ma-218	440	5	(	(	PUNCT
ma-218	440	6	d4	d4	PROPN
ma-218	440	7	)	)	PUNCT
ma-218	440	8	,	,	PUNCT
ma-218	440	9	we	we	PRON
ma-218	440	10	estimate	estimate	VERB
ma-218	440	11	as	as	ADP
ma-218	440	12	0	0	NUM
ma-218	440	13	=	=	SYM
ma-218	440	14	h(vs	h(vs	ADJ
ma-218	440	15	,	,	PUNCT
ma-218	440	16	vs	vs	ADP
ma-218	440	17	)	)	PUNCT
ma-218	440	18	≤	≤	NOUN
ma-218	440	19	sh(vs	sh(vs	ADJ
ma-218	440	20	,	,	PUNCT
ma-218	440	21	v	v	NOUN
ma-218	440	22	)	)	PUNCT
ma-218	440	23	+	+	CCONJ
ma-218	440	24	(	(	PUNCT
ma-218	440	25	1−	1−	NUM
ma-218	440	26	s)h(vs	s)h(vs	NUM
ma-218	440	27	,	,	PUNCT
ma-218	440	28	$	$	SYM
ma-218	440	29	)	)	PUNCT
ma-218	440	30	≤	≤	NOUN
ma-218	441	1	sh(vs	sh(vs	ADJ
ma-218	441	2	,	,	PUNCT
ma-218	441	3	v	v	NOUN
ma-218	441	4	)	)	PUNCT
ma-218	441	5	+	+	CCONJ
ma-218	441	6	(	(	PUNCT
ma-218	441	7	1−	1−	NUM
ma-218	441	8	s	s	NOUN
ma-218	441	9	)	)	PUNCT
ma-218	441	10	[	[	PUNCT
ma-218	441	11	ϑ(vs	ϑ(vs	PROPN
ma-218	441	12	,	,	PUNCT
ma-218	441	13	$	$	SYM
ma-218	441	14	)	)	PUNCT
ma-218	441	15	−	−	NOUN
ma-218	441	16	ϑ($,$	ϑ($,$	NOUN
ma-218	441	17	)	)	PUNCT
ma-218	441	18	]	]	PUNCT
ma-218	442	1	≤	≤	PROPN
ma-218	442	2	sh(vs	sh(vs	ADJ
ma-218	442	3	,	,	PUNCT
ma-218	442	4	v	v	NOUN
ma-218	442	5	)	)	PUNCT
ma-218	442	6	+	+	CCONJ
ma-218	442	7	(	(	PUNCT
ma-218	442	8	1−	1−	NUM
ma-218	442	9	s	s	NOUN
ma-218	442	10	)	)	PUNCT
ma-218	442	11	[	[	PUNCT
ma-218	442	12	ϑ(v	ϑ(v	NOUN
ma-218	442	13	,	,	PUNCT
ma-218	442	14	$	$	SYM
ma-218	442	15	)	)	PUNCT
ma-218	442	16	−	−	NOUN
ma-218	442	17	ϑ($,$	ϑ($,$	NOUN
ma-218	442	18	)	)	PUNCT
ma-218	442	19	]	]	PUNCT
ma-218	442	20	as	as	ADP
ma-218	442	21	s	s	PROPN
ma-218	442	22	>	>	X
ma-218	442	23	0	0	NUM
ma-218	442	24	,	,	PUNCT
ma-218	442	25	from	from	ADP
ma-218	442	26	assumption	assumption	NOUN
ma-218	442	27	(	(	PUNCT
ma-218	442	28	d3	d3	PROPN
ma-218	442	29	)	)	PUNCT
ma-218	442	30	,	,	PUNCT
ma-218	442	31	we	we	PRON
ma-218	442	32	conclude	conclude	VERB
ma-218	442	33	that	that	SCONJ
ma-218	442	34	h($	h($	PROPN
ma-218	442	35	,	,	PUNCT
ma-218	442	36	v	v	NOUN
ma-218	442	37	)	)	PUNCT
ma-218	443	1	+	+	NUM
ma-218	443	2	ϑ(v	ϑ(v	PROPN
ma-218	443	3	,	,	PUNCT
ma-218	443	4	$	$	SYM
ma-218	443	5	)	)	PUNCT
ma-218	443	6	−	−	NOUN
ma-218	443	7	ϑ($,$	ϑ($,$	NOUN
ma-218	443	8	)	)	PUNCT
ma-218	443	9	≥	≥	NOUN
ma-218	443	10	0	0	NUM
ma-218	443	11	,	,	PUNCT
ma-218	443	12	∀v	∀v	PROPN
ma-218	443	13	∈	∈	PROPN
ma-218	443	14	c.	c.	NOUN
ma-218	443	15	hence	hence	ADV
ma-218	443	16	,	,	PUNCT
ma-218	443	17	$	$	SYM
ma-218	443	18	∈	∈	NOUN
ma-218	443	19	sol(gmep	sol(gmep	NOUN
ma-218	443	20	(	(	PUNCT
ma-218	443	21	1.1	1.1	NUM
ma-218	443	22	)	)	PUNCT
ma-218	443	23	)	)	PUNCT
ma-218	443	24	.	.	PUNCT
ma-218	444	1	step	step	NOUN
ma-218	444	2	6	6	NUM
ma-218	444	3	:	:	PUNCT
ma-218	444	4	finally	finally	ADV
ma-218	444	5	we	we	PRON
ma-218	444	6	show	show	VERB
ma-218	444	7	that	that	SCONJ
ma-218	444	8	$	$	SYM
ma-218	444	9	=	=	SYM
ma-218	444	10	πωx0	πωx0	PROPN
ma-218	444	11	and	and	CCONJ
ma-218	444	12	so	so	ADV
ma-218	444	13	xn	xn	PROPN
ma-218	444	14	−→	−→	ADJ
ma-218	444	15	πωx0	πωx0	PROPN
ma-218	444	16	as	as	ADP
ma-218	444	17	n	n	PRON
ma-218	444	18	−→	−→	NOUN
ma-218	444	19	∞.	∞.	PROPN
ma-218	444	20	putting	put	VERB
ma-218	444	21	x∗	x∗	NOUN
ma-218	444	22	=	=	PUNCT
ma-218	445	1	πωx0,since	πωx0,since	NUM
ma-218	445	2	x∗	x∗	PROPN
ma-218	445	3	∈	∈	PROPN
ma-218	445	4	ω	ω	PROPN
ma-218	445	5	⊂	⊂	PROPN
ma-218	445	6	cn	cn	PROPN
ma-218	445	7	and	and	CCONJ
ma-218	445	8	xn	xn	PROPN
ma-218	445	9	=	=	SYM
ma-218	445	10	πωx0	πωx0	PROPN
ma-218	445	11	,	,	PUNCT
ma-218	445	12	we	we	PRON
ma-218	445	13	have	have	VERB
ma-218	445	14	φ(xn	φ(xn	NOUN
ma-218	445	15	,	,	PUNCT
ma-218	445	16	x0	x0	PROPN
ma-218	445	17	)	)	PUNCT
ma-218	445	18	≤	≤	NUM
ma-218	445	19	φ(x∗	φ(x∗	NOUN
ma-218	445	20	,	,	PUNCT
ma-218	445	21	x0	x0	PROPN
ma-218	445	22	)	)	PUNCT
ma-218	445	23	,	,	PUNCT
ma-218	445	24	∀n	∀n	NUM
ma-218	445	25	≥	≥	NOUN
ma-218	445	26	0	0	NUM
ma-218	445	27	.	.	PUNCT
ma-218	446	1	then	then	ADV
ma-218	446	2	φ($	φ($	ADV
ma-218	446	3	,	,	PUNCT
ma-218	446	4	x0	x0	NUM
ma-218	446	5	)	)	PUNCT
ma-218	447	1	=	=	SYM
ma-218	447	2	lim	lim	PROPN
ma-218	447	3	n→∞	n→∞	NUM
ma-218	447	4	φ(xn	φ(xn	PROPN
ma-218	447	5	,	,	PUNCT
ma-218	447	6	x0	x0	PROPN
ma-218	447	7	)	)	PUNCT
ma-218	447	8	≤	≤	NUM
ma-218	447	9	φ(x∗	φ(x∗	NOUN
ma-218	447	10	,	,	PUNCT
ma-218	447	11	x0	x0	PROPN
ma-218	447	12	)	)	PUNCT
ma-218	447	13	,	,	PUNCT
ma-218	447	14	implies	imply	VERB
ma-218	447	15	that	that	SCONJ
ma-218	447	16	$	$	SYM
ma-218	447	17	=	=	SYM
ma-218	447	18	x∗	x∗	NOUN
ma-218	447	19	and	and	CCONJ
ma-218	447	20	since	since	SCONJ
ma-218	447	21	x∗	x∗	PROPN
ma-218	447	22	=	=	SYM
ma-218	447	23	πωx0	πωx0	PROPN
ma-218	447	24	,	,	PUNCT
ma-218	447	25	then	then	ADV
ma-218	447	26	we	we	PRON
ma-218	447	27	conclude	conclude	VERB
ma-218	447	28	that	that	SCONJ
ma-218	447	29	xn	xn	PROPN
ma-218	448	1	−→	−→	ADJ
ma-218	448	2	$	$	SYM
ma-218	448	3	=	=	SYM
ma-218	448	4	πωx0	πωx0	PROPN
ma-218	448	5	,	,	PUNCT
ma-218	448	6	as	as	SCONJ
ma-218	448	7	n	n	NOUN
ma-218	448	8	→∞.this	→∞.this	PUNCT
ma-218	448	9	completes	complete	VERB
ma-218	448	10	the	the	DET
ma-218	448	11	proof	proof	NOUN
ma-218	448	12	.	.	PUNCT
ma-218	449	1	�	�	PROPN
ma-218	449	2	corollary	corollary	ADJ
ma-218	449	3	3.2	3.2	NUM
ma-218	449	4	.	.	PUNCT
ma-218	450	1	let	let	VERB
ma-218	450	2	c	c	PRON
ma-218	450	3	be	be	AUX
ma-218	450	4	a	a	DET
ma-218	450	5	nonempty	nonempty	ADV
ma-218	450	6	closed	close	VERB
ma-218	450	7	and	and	CCONJ
ma-218	450	8	convex	convex	NOUN
ma-218	450	9	subset	subset	NOUN
ma-218	450	10	of	of	ADP
ma-218	450	11	a	a	DET
ma-218	450	12	2−uniformly	2−uniformly	ADV
ma-218	450	13	smooth	smooth	ADJ
ma-218	450	14	and	and	CCONJ
ma-218	450	15	uniformly	uniformly	ADV
ma-218	450	16	convex	convex	VERB
ma-218	450	17	banach	banach	NOUN
ma-218	450	18	space	space	NOUN
ma-218	450	19	b	b	NOUN
ma-218	450	20	with	with	ADP
ma-218	450	21	b∗	b∗	ADJ
ma-218	450	22	as	as	ADP
ma-218	450	23	the	the	DET
ma-218	450	24	dual	dual	ADJ
ma-218	450	25	space	space	NOUN
ma-218	450	26	of	of	ADP
ma-218	450	27	b.	b.	PROPN
ma-218	450	28	let	let	VERB
ma-218	450	29	d	d	NOUN
ma-218	450	30	:	:	PUNCT
ma-218	450	31	c	c	X
ma-218	450	32	×	×	NOUN
ma-218	450	33	c	c	NOUN
ma-218	450	34	−→	−→	NOUN
ma-218	450	35	r	r	NOUN
ma-218	450	36	be	be	VERB
ma-218	450	37	a	a	DET
ma-218	450	38	bifunction	bifunction	NOUN
ma-218	450	39	satisfying	satisfy	VERB
ma-218	450	40	assumption	assumption	NOUN
ma-218	450	41	1	1	NUM
ma-218	450	42	,	,	PUNCT
ma-218	450	43	ϑ	ϑ	X
ma-218	450	44	:	:	PUNCT
ma-218	450	45	c	c	AUX
ma-218	450	46	×	×	NOUN
ma-218	450	47	c	c	NOUN
ma-218	450	48	−→	−→	NOUN
ma-218	450	49	r	r	NOUN
ma-218	450	50	be	be	VERB
ma-218	450	51	a	a	DET
ma-218	450	52	bifunction	bifunction	NOUN
ma-218	450	53	satisfying	satisfy	VERB
ma-218	450	54	assumption	assumption	NOUN
ma-218	450	55	2	2	NUM
ma-218	450	56	and	and	CCONJ
ma-218	450	57	g	g	NOUN
ma-218	450	58	:	:	PUNCT
ma-218	450	59	c	c	AUX
ma-218	450	60	−→	−→	ADV
ma-218	450	61	b∗	b∗	ADV
ma-218	450	62	be	be	AUX
ma-218	450	63	a	a	DET
ma-218	450	64	monotone	monotone	ADJ
ma-218	450	65	and	and	CCONJ
ma-218	450	66	continuous	continuous	ADJ
ma-218	450	67	mapping	mapping	NOUN
ma-218	450	68	.	.	PUNCT
ma-218	451	1	let	let	VERB
ma-218	451	2	ti	ti	NOUN
ma-218	451	3	:	:	PUNCT
ma-218	451	4	c	c	X
ma-218	451	5	−→	−→	NOUN
ma-218	451	6	c	c	PROPN
ma-218	451	7	and	and	CCONJ
ma-218	451	8	si	si	INTJ
ma-218	451	9	:	:	PUNCT
ma-218	451	10	c	c	AUX
ma-218	451	11	−→	−→	NOUN
ma-218	451	12	c	c	NOUN
ma-218	451	13	,	,	PUNCT
ma-218	451	14	for	for	ADP
ma-218	451	15	each	each	DET
ma-218	451	16	i	i	NOUN
ma-218	451	17	=	=	NOUN
ma-218	451	18	1	1	NUM
ma-218	451	19	,	,	PUNCT
ma-218	451	20	2	2	NUM
ma-218	451	21	,	,	PUNCT
ma-218	451	22	...	...	PUNCT
ma-218	451	23	,	,	PUNCT
ma-218	451	24	n	n	X
ma-218	451	25	be	be	AUX
ma-218	451	26	two	two	NUM
ma-218	451	27	finite	finite	ADJ
ma-218	451	28	family	family	NOUN
ma-218	451	29	of	of	ADP
ma-218	451	30	closed	closed	ADJ
ma-218	451	31	li−lipschitz	li−lipschitz	PROPN
ma-218	451	32	continuous	continuous	ADJ
ma-218	451	33	and	and	CCONJ
ma-218	451	34	uniformly	uniformly	ADV
ma-218	451	35	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PRON
ma-218	451	36	eur	eur	NOUN
ma-218	451	37	.	.	PUNCT
ma-218	452	1	j.	j.	PROPN
ma-218	452	2	math	math	PROPN
ma-218	452	3	.	.	PUNCT
ma-218	453	1	anal	anal	PROPN
ma-218	453	2	.	.	PUNCT
ma-218	454	1	10.28924	10.28924	NUM
ma-218	454	2	/	/	SYM
ma-218	454	3	ada	ada	PROPN
ma-218	454	4	/	/	SYM
ma-218	454	5	ma.4.8	ma.4.8	PROPN
ma-218	454	6	18	18	NUM
ma-218	454	7	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	454	8	nonexpansive	nonexpansive	ADJ
ma-218	454	9	mappings	mapping	NOUN
ma-218	454	10	such	such	ADJ
ma-218	454	11	that	that	DET
ma-218	454	12	ω	ω	NOUN
ma-218	454	13	:	:	PUNCT
ma-218	454	14	=	=	SYM
ma-218	454	15	(	(	PUNCT
ma-218	454	16	∩ni=1	∩ni=1	INTJ
ma-218	454	17	f	f	PROPN
ma-218	454	18	(	(	PUNCT
ma-218	454	19	ti	ti	NOUN
ma-218	454	20	)	)	PUNCT
ma-218	454	21	)	)	PUNCT
ma-218	454	22	∩	∩	NOUN
ma-218	454	23	(	(	PUNCT
ma-218	454	24	∩ni=1	∩ni=1	ADP
ma-218	454	25	f	f	PROPN
ma-218	454	26	(	(	PUNCT
ma-218	454	27	si	si	NOUN
ma-218	454	28	)	)	PUNCT
ma-218	454	29	)	)	PUNCT
ma-218	454	30	∩	∩	ADJ
ma-218	454	31	∩sol	∩sol	NOUN
ma-218	454	32	(	(	PUNCT
ma-218	454	33	gmep	gmep	X
ma-218	454	34	(	(	PUNCT
ma-218	454	35	1.1	1.1	NUM
ma-218	454	36	)	)	PUNCT
ma-218	454	37	)	)	PUNCT
ma-218	455	1	6=	6=	ADP
ma-218	455	2	∅.	∅.	ADV
ma-218	455	3	let	let	VERB
ma-218	455	4	{	{	PUNCT
ma-218	455	5	xn	xn	NOUN
ma-218	455	6	}	}	PUNCT
ma-218	455	7	generated	generate	VERB
ma-218	455	8	by	by	ADP
ma-218	455	9	algorithm	algorithm	NOUN
ma-218	455	10	:	:	PUNCT
ma-218	455	11			X
ma-218	455	12	x0	x0	PROPN
ma-218	455	13	,	,	PUNCT
ma-218	455	14	x1	x1	PROPN
ma-218	455	15	∈	∈	PROPN
ma-218	455	16	c	c	X
ma-218	455	17	,	,	PUNCT
ma-218	455	18	c1	c1	NOUN
ma-218	455	19	:	:	PUNCT
ma-218	456	1	=	=	SYM
ma-218	457	1	c	c	X
ma-218	457	2	,	,	PUNCT
ma-218	457	3	ωn	ωn	PROPN
ma-218	457	4	=	=	SYM
ma-218	457	5	xn	xn	PROPN
ma-218	458	1	+	+	NUM
ma-218	458	2	αn(xn	αn(xn	PROPN
ma-218	458	3	−	−	PROPN
ma-218	458	4	xn−1	xn−1	PROPN
ma-218	458	5	)	)	PUNCT
ma-218	458	6	,	,	PUNCT
ma-218	458	7	yn	yn	PROPN
ma-218	458	8	=	=	PUNCT
ma-218	459	1	j−1(µn,0jωn	j−1(µn,0jωn	PROPN
ma-218	459	2	+	+	CCONJ
ma-218	459	3	n∑	n∑	ADJ
ma-218	459	4	i=1	i=1	PROPN
ma-218	459	5	µn	µn	PROPN
ma-218	459	6	,	,	PUNCT
ma-218	459	7	ijt	ijt	VERB
ma-218	459	8	n	n	ADV
ma-218	459	9	i	i	PRON
ma-218	459	10	ωn	ωn	PROPN
ma-218	459	11	)	)	PUNCT
ma-218	459	12	;	;	PUNCT
ma-218	459	13	zn	zn	X
ma-218	459	14	=	=	PUNCT
ma-218	460	1	j−1(ηn,0jωn	j−1(ηn,0jωn	PROPN
ma-218	461	1	+	+	CCONJ
ma-218	462	1	n∑	n∑	INTJ
ma-218	462	2	i=1	i=1	PROPN
ma-218	462	3	ηn	ηn	PROPN
ma-218	462	4	,	,	PUNCT
ma-218	462	5	ijs	ijs	PROPN
ma-218	463	1	n	n	PROPN
ma-218	463	2	i	i	PROPN
ma-218	463	3	yn	yn	PROPN
ma-218	463	4	)	)	PUNCT
ma-218	463	5	,	,	PUNCT
ma-218	463	6	un	un	PROPN
ma-218	463	7	=	=	PROPN
ma-218	463	8	trnzn	trnzn	PROPN
ma-218	463	9	,	,	PUNCT
ma-218	463	10	cn+1	cn+1	X
ma-218	463	11	=	=	SYM
ma-218	463	12	{	{	PUNCT
ma-218	463	13	u	u	NOUN
ma-218	463	14	∈	∈	PROPN
ma-218	463	15	cn	cn	PROPN
ma-218	463	16	:	:	PUNCT
ma-218	463	17	φ(u	φ(u	NOUN
ma-218	463	18	,	,	PUNCT
ma-218	463	19	un	un	ADJ
ma-218	463	20	)	)	PUNCT
ma-218	463	21	≤	≤	NOUN
ma-218	463	22	k2	k2	NOUN
ma-218	463	23	nφ(u	nφ(u	NOUN
ma-218	463	24	,	,	PUNCT
ma-218	463	25	ωn	ωn	NOUN
ma-218	463	26	)	)	PUNCT
ma-218	463	27	}	}	PUNCT
ma-218	463	28	,	,	PUNCT
ma-218	463	29	xn+1	xn+1	PROPN
ma-218	463	30	=	=	SYM
ma-218	463	31	πcn+1	πcn+1	NOUN
ma-218	463	32	x0	x0	PROPN
ma-218	463	33	,	,	PUNCT
ma-218	463	34	∀n	∀n	NUM
ma-218	463	35	≥	≥	NOUN
ma-218	463	36	1	1	NUM
ma-218	463	37	,	,	PUNCT
ma-218	463	38	where	where	SCONJ
ma-218	463	39	{	{	PUNCT
ma-218	463	40	αn	αn	NOUN
ma-218	463	41	}	}	PUNCT
ma-218	463	42	⊂	⊂	PROPN
ma-218	463	43	(	(	PUNCT
ma-218	463	44	0	0	NUM
ma-218	463	45	,	,	PUNCT
ma-218	463	46	1	1	NUM
ma-218	463	47	)	)	PUNCT
ma-218	463	48	,	,	PUNCT
ma-218	463	49	{	{	PUNCT
ma-218	463	50	µn	µn	PROPN
ma-218	463	51	,	,	PUNCT
ma-218	463	52	i	i	PRON
ma-218	463	53	}	}	PUNCT
ma-218	463	54	⊂	⊂	PROPN
ma-218	464	1	[	[	X
ma-218	464	2	0	0	NUM
ma-218	464	3	,	,	PUNCT
ma-218	464	4	1	1	NUM
ma-218	464	5	]	]	PUNCT
ma-218	464	6	and	and	CCONJ
ma-218	464	7	{	{	PUNCT
ma-218	464	8	ηn	ηn	INTJ
ma-218	464	9	,	,	PUNCT
ma-218	464	10	i	i	PROPN
ma-218	464	11	}	}	PUNCT
ma-218	464	12	⊂	⊂	X
ma-218	464	13	(	(	PUNCT
ma-218	464	14	0	0	NUM
ma-218	464	15	,	,	PUNCT
ma-218	464	16	1	1	NUM
ma-218	464	17	]	]	PUNCT
ma-218	464	18	satisfying	satisfy	VERB
ma-218	464	19	the	the	DET
ma-218	464	20	following	follow	VERB
ma-218	464	21	conditions	condition	NOUN
ma-218	464	22	:	:	PUNCT
ma-218	464	23	(	(	PUNCT
ma-218	464	24	s1	s1	NOUN
ma-218	464	25	)	)	PUNCT
ma-218	464	26	n∑	n∑	NOUN
ma-218	464	27	i=0	i=0	PROPN
ma-218	464	28	µn	µn	PROPN
ma-218	464	29	,	,	PUNCT
ma-218	464	30	i	i	PRON
ma-218	464	31	=	=	NOUN
ma-218	464	32	1	1	NUM
ma-218	464	33	;	;	PUNCT
ma-218	464	34	(	(	PUNCT
ma-218	464	35	s2	s2	PROPN
ma-218	464	36	)	)	PUNCT
ma-218	464	37	n∑	n∑	NOUN
ma-218	465	1	i=0	i=0	PROPN
ma-218	465	2	ηn	ηn	INTJ
ma-218	465	3	,	,	PUNCT
ma-218	465	4	i	i	PRON
ma-218	465	5	=	=	NOUN
ma-218	465	6	1	1	NUM
ma-218	465	7	;	;	PUNCT
ma-218	465	8	(	(	PUNCT
ma-218	465	9	s3	s3	PROPN
ma-218	465	10	)	)	PUNCT
ma-218	465	11	lim	lim	PROPN
ma-218	465	12	sup	sup	VERB
ma-218	465	13	n→∞	n→∞	NUM
ma-218	466	1	ηn,0	ηn,0	NOUN
ma-218	466	2	<	<	X
ma-218	466	3	1	1	NUM
ma-218	466	4	;	;	PUNCT
ma-218	466	5	(	(	PUNCT
ma-218	466	6	s4	s4	PROPN
ma-218	466	7	)	)	PUNCT
ma-218	466	8	for	for	ADP
ma-218	466	9	same	same	ADJ
ma-218	466	10	a	a	DET
ma-218	466	11	>	>	X
ma-218	466	12	0	0	NUM
ma-218	466	13	,	,	PUNCT
ma-218	466	14	rn	rn	PROPN
ma-218	466	15	∈	∈	PROPN
ma-218	467	1	[	[	X
ma-218	467	2	a,∞	a,∞	PROPN
ma-218	467	3	)	)	PUNCT
ma-218	467	4	.	.	PUNCT
ma-218	468	1	then	then	ADV
ma-218	468	2	,	,	PUNCT
ma-218	468	3	{	{	PUNCT
ma-218	468	4	xn	xn	X
ma-218	468	5	}	}	PUNCT
ma-218	468	6	converges	converge	VERB
ma-218	468	7	strongly	strongly	ADV
ma-218	468	8	to	to	ADP
ma-218	468	9	$	$	SYM
ma-218	468	10	,	,	PUNCT
ma-218	468	11	where	where	SCONJ
ma-218	468	12	$	$	SYM
ma-218	468	13	=	=	SYM
ma-218	468	14	πωx0	πωx0	PROPN
ma-218	468	15	is	be	AUX
ma-218	468	16	consider	consider	VERB
ma-218	468	17	as	as	ADP
ma-218	468	18	the	the	DET
ma-218	468	19	generalized	generalized	ADJ
ma-218	468	20	projection	projection	NOUN
ma-218	468	21	of	of	ADP
ma-218	468	22	$	$	SYM
ma-218	468	23	onto	onto	ADP
ma-218	468	24	ω	ω	NUM
ma-218	468	25	.	.	PUNCT
ma-218	469	1	corollary	corollary	ADJ
ma-218	469	2	3.3	3.3	NUM
ma-218	469	3	.	.	PUNCT
ma-218	470	1	let	let	VERB
ma-218	470	2	c	c	PRON
ma-218	470	3	be	be	AUX
ma-218	470	4	a	a	DET
ma-218	470	5	nonempty	nonempty	ADV
ma-218	470	6	closed	close	VERB
ma-218	470	7	and	and	CCONJ
ma-218	470	8	convex	convex	NOUN
ma-218	470	9	subset	subset	NOUN
ma-218	470	10	of	of	ADP
ma-218	470	11	a	a	DET
ma-218	470	12	2−uniformly	2−uniformly	ADV
ma-218	470	13	smooth	smooth	ADJ
ma-218	470	14	and	and	CCONJ
ma-218	470	15	uniformly	uniformly	ADV
ma-218	470	16	convex	convex	VERB
ma-218	470	17	banach	banach	NOUN
ma-218	470	18	space	space	NOUN
ma-218	470	19	b	b	NOUN
ma-218	470	20	with	with	ADP
ma-218	470	21	b∗	b∗	ADJ
ma-218	470	22	as	as	ADP
ma-218	470	23	the	the	DET
ma-218	470	24	dual	dual	ADJ
ma-218	470	25	space	space	NOUN
ma-218	470	26	of	of	ADP
ma-218	470	27	b.	b.	PROPN
ma-218	470	28	let	let	VERB
ma-218	470	29	d	d	NOUN
ma-218	470	30	:	:	PUNCT
ma-218	470	31	c	c	X
ma-218	470	32	×	×	NOUN
ma-218	470	33	c	c	NOUN
ma-218	470	34	−→	−→	NOUN
ma-218	470	35	r	r	NOUN
ma-218	470	36	be	be	VERB
ma-218	470	37	a	a	DET
ma-218	470	38	bifunction	bifunction	NOUN
ma-218	470	39	satisfying	satisfy	VERB
ma-218	470	40	assumption	assumption	NOUN
ma-218	470	41	1	1	NUM
ma-218	470	42	and	and	CCONJ
ma-218	470	43	g	g	NOUN
ma-218	470	44	:	:	PUNCT
ma-218	470	45	c	c	AUX
ma-218	470	46	−→	−→	ADV
ma-218	470	47	b∗	b∗	ADV
ma-218	470	48	be	be	AUX
ma-218	470	49	a	a	DET
ma-218	470	50	monotone	monotone	ADJ
ma-218	470	51	and	and	CCONJ
ma-218	470	52	continuous	continuous	ADJ
ma-218	470	53	mapping	mapping	NOUN
ma-218	470	54	.	.	PUNCT
ma-218	471	1	let	let	VERB
ma-218	471	2	ti	ti	NOUN
ma-218	471	3	:	:	PUNCT
ma-218	471	4	c	c	X
ma-218	471	5	−→	−→	NOUN
ma-218	471	6	c	c	PROPN
ma-218	471	7	and	and	CCONJ
ma-218	471	8	si	si	INTJ
ma-218	471	9	:	:	PUNCT
ma-218	471	10	c	c	AUX
ma-218	471	11	−→	−→	NOUN
ma-218	471	12	c	c	NOUN
ma-218	471	13	,	,	PUNCT
ma-218	471	14	for	for	ADP
ma-218	471	15	each	each	DET
ma-218	471	16	i	i	NOUN
ma-218	471	17	=	=	NOUN
ma-218	471	18	1	1	NUM
ma-218	471	19	,	,	PUNCT
ma-218	471	20	2	2	NUM
ma-218	471	21	,	,	PUNCT
ma-218	471	22	...	...	PUNCT
ma-218	471	23	,	,	PUNCT
ma-218	471	24	n	n	X
ma-218	471	25	be	be	AUX
ma-218	471	26	two	two	NUM
ma-218	471	27	finite	finite	ADJ
ma-218	471	28	family	family	NOUN
ma-218	471	29	of	of	ADP
ma-218	471	30	closed	closed	ADJ
ma-218	471	31	li−lipschitz	li−lipschitz	PROPN
ma-218	471	32	continuous	continuous	ADJ
ma-218	471	33	and	and	CCONJ
ma-218	471	34	uniformly	uniformly	ADV
ma-218	471	35	quasi−φ−asymptotically	quasi−φ−asymptotically	ADV
ma-218	471	36	nonexpansive	nonexpansive	ADJ
ma-218	471	37	mappings	mapping	NOUN
ma-218	472	1	such	such	ADJ
ma-218	472	2	that	that	DET
ma-218	472	3	ω	ω	NOUN
ma-218	472	4	:	:	PUNCT
ma-218	472	5	=	=	SYM
ma-218	472	6	(	(	PUNCT
ma-218	472	7	∩ni=1	∩ni=1	INTJ
ma-218	472	8	f	f	PROPN
ma-218	472	9	(	(	PUNCT
ma-218	472	10	ti	ti	NOUN
ma-218	472	11	)	)	PUNCT
ma-218	472	12	)	)	PUNCT
ma-218	472	13	∩	∩	NOUN
ma-218	472	14	(	(	PUNCT
ma-218	472	15	∩ni=1	∩ni=1	ADP
ma-218	472	16	f	f	PROPN
ma-218	472	17	(	(	PUNCT
ma-218	472	18	si	si	NOUN
ma-218	472	19	)	)	PUNCT
ma-218	472	20	)	)	PUNCT
ma-218	472	21	∩	∩	ADJ
ma-218	472	22	∩sol	∩sol	NOUN
ma-218	472	23	(	(	PUNCT
ma-218	472	24	gep	gep	PROPN
ma-218	472	25	(	(	PUNCT
ma-218	472	26	1.2	1.2	NUM
ma-218	472	27	)	)	PUNCT
ma-218	472	28	)	)	PUNCT
ma-218	472	29	6=	6=	ADP
ma-218	472	30	∅.	∅.	ADV
ma-218	472	31	let	let	VERB
ma-218	472	32	{	{	PUNCT
ma-218	472	33	xn	xn	NOUN
ma-218	472	34	}	}	PUNCT
ma-218	472	35	generated	generate	VERB
ma-218	472	36	by	by	ADP
ma-218	472	37	algorithm	algorithm	NOUN
ma-218	472	38	:	:	PUNCT
ma-218	472	39			X
ma-218	472	40	x0	x0	PROPN
ma-218	472	41	,	,	PUNCT
ma-218	472	42	x1	x1	PROPN
ma-218	472	43	∈	∈	PROPN
ma-218	472	44	c	c	X
ma-218	472	45	,	,	PUNCT
ma-218	472	46	c1	c1	NOUN
ma-218	472	47	:	:	PUNCT
ma-218	472	48	=	=	SYM
ma-218	472	49	c	c	X
ma-218	472	50	,	,	PUNCT
ma-218	472	51	ωn	ωn	PROPN
ma-218	472	52	=	=	SYM
ma-218	472	53	xn	xn	PROPN
ma-218	473	1	+	+	NUM
ma-218	473	2	αn(xn	αn(xn	PROPN
ma-218	473	3	−	−	PROPN
ma-218	473	4	xn−1	xn−1	PROPN
ma-218	473	5	)	)	PUNCT
ma-218	473	6	,	,	PUNCT
ma-218	473	7	yn	yn	PROPN
ma-218	473	8	=	=	PUNCT
ma-218	474	1	j−1(µn,0jωn	j−1(µn,0jωn	PROPN
ma-218	474	2	+	+	CCONJ
ma-218	474	3	n∑	n∑	ADJ
ma-218	474	4	i=1	i=1	PROPN
ma-218	474	5	µn	µn	PROPN
ma-218	474	6	,	,	PUNCT
ma-218	474	7	ijt	ijt	VERB
ma-218	474	8	n	n	ADV
ma-218	474	9	i	i	PRON
ma-218	474	10	ωn	ωn	PROPN
ma-218	474	11	)	)	PUNCT
ma-218	474	12	;	;	PUNCT
ma-218	474	13	zn	zn	X
ma-218	474	14	=	=	PUNCT
ma-218	475	1	j−1(ηn,0jωn	j−1(ηn,0jωn	PROPN
ma-218	476	1	+	+	CCONJ
ma-218	477	1	n∑	n∑	INTJ
ma-218	477	2	i=1	i=1	PROPN
ma-218	477	3	ηn	ηn	PROPN
ma-218	477	4	,	,	PUNCT
ma-218	477	5	ijs	ijs	PROPN
ma-218	478	1	n	n	PROPN
ma-218	478	2	i	i	PROPN
ma-218	478	3	yn	yn	PROPN
ma-218	478	4	)	)	PUNCT
ma-218	478	5	,	,	PUNCT
ma-218	478	6	un	un	PROPN
ma-218	478	7	=	=	PROPN
ma-218	478	8	trnzn	trnzn	PROPN
ma-218	478	9	,	,	PUNCT
ma-218	478	10	cn+1	cn+1	X
ma-218	478	11	=	=	SYM
ma-218	478	12	{	{	PUNCT
ma-218	478	13	u	u	NOUN
ma-218	478	14	∈	∈	PROPN
ma-218	478	15	cn	cn	PROPN
ma-218	478	16	:	:	PUNCT
ma-218	478	17	φ(u	φ(u	NOUN
ma-218	478	18	,	,	PUNCT
ma-218	478	19	un	un	ADJ
ma-218	478	20	)	)	PUNCT
ma-218	478	21	≤	≤	NOUN
ma-218	478	22	k2	k2	NOUN
ma-218	478	23	nφ(u	nφ(u	NOUN
ma-218	478	24	,	,	PUNCT
ma-218	478	25	ωn	ωn	NOUN
ma-218	478	26	)	)	PUNCT
ma-218	478	27	}	}	PUNCT
ma-218	478	28	,	,	PUNCT
ma-218	478	29	xn+1	xn+1	PROPN
ma-218	478	30	=	=	SYM
ma-218	478	31	πcn+1	πcn+1	NOUN
ma-218	478	32	x0	x0	PROPN
ma-218	478	33	,	,	PUNCT
ma-218	478	34	∀n	∀n	NUM
ma-218	478	35	≥	≥	NOUN
ma-218	478	36	1	1	NUM
ma-218	478	37	,	,	PUNCT
ma-218	478	38	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	478	39	eur	eur	NOUN
ma-218	478	40	.	.	PUNCT
ma-218	479	1	j.	j.	PROPN
ma-218	479	2	math	math	PROPN
ma-218	479	3	.	.	PUNCT
ma-218	480	1	anal	anal	PROPN
ma-218	480	2	.	.	PUNCT
ma-218	481	1	10.28924	10.28924	NUM
ma-218	481	2	/	/	SYM
ma-218	481	3	ada	ada	PROPN
ma-218	481	4	/	/	SYM
ma-218	481	5	ma.4.8	ma.4.8	PROPN
ma-218	481	6	19	19	NUM
ma-218	482	1	where	where	SCONJ
ma-218	482	2	{	{	PUNCT
ma-218	482	3	αn	αn	NOUN
ma-218	482	4	}	}	PUNCT
ma-218	482	5	⊂	⊂	PROPN
ma-218	482	6	(	(	PUNCT
ma-218	482	7	0	0	NUM
ma-218	482	8	,	,	PUNCT
ma-218	482	9	1	1	NUM
ma-218	482	10	)	)	PUNCT
ma-218	482	11	,	,	PUNCT
ma-218	482	12	{	{	PUNCT
ma-218	482	13	µn	µn	PROPN
ma-218	482	14	,	,	PUNCT
ma-218	482	15	i	i	PRON
ma-218	482	16	}	}	PUNCT
ma-218	482	17	⊂	⊂	PROPN
ma-218	483	1	[	[	X
ma-218	483	2	0	0	NUM
ma-218	483	3	,	,	PUNCT
ma-218	483	4	1	1	NUM
ma-218	483	5	]	]	PUNCT
ma-218	483	6	and	and	CCONJ
ma-218	483	7	{	{	PUNCT
ma-218	483	8	ηn	ηn	INTJ
ma-218	483	9	,	,	PUNCT
ma-218	483	10	i	i	PROPN
ma-218	483	11	}	}	PUNCT
ma-218	483	12	⊂	⊂	X
ma-218	483	13	(	(	PUNCT
ma-218	483	14	0	0	NUM
ma-218	483	15	,	,	PUNCT
ma-218	483	16	1	1	NUM
ma-218	483	17	]	]	PUNCT
ma-218	483	18	satisfying	satisfy	VERB
ma-218	483	19	the	the	DET
ma-218	483	20	following	follow	VERB
ma-218	483	21	conditions	condition	NOUN
ma-218	483	22	:	:	PUNCT
ma-218	483	23	(	(	PUNCT
ma-218	483	24	s1	s1	NOUN
ma-218	483	25	)	)	PUNCT
ma-218	483	26	n∑	n∑	NOUN
ma-218	483	27	i=0	i=0	PROPN
ma-218	483	28	µn	µn	PROPN
ma-218	483	29	,	,	PUNCT
ma-218	483	30	i	i	PRON
ma-218	483	31	=	=	NOUN
ma-218	483	32	1	1	NUM
ma-218	483	33	;	;	PUNCT
ma-218	483	34	(	(	PUNCT
ma-218	483	35	s2	s2	PROPN
ma-218	483	36	)	)	PUNCT
ma-218	483	37	n∑	n∑	NOUN
ma-218	484	1	i=0	i=0	PROPN
ma-218	484	2	ηn	ηn	INTJ
ma-218	484	3	,	,	PUNCT
ma-218	484	4	i	i	PRON
ma-218	484	5	=	=	NOUN
ma-218	484	6	1	1	NUM
ma-218	484	7	;	;	PUNCT
ma-218	484	8	(	(	PUNCT
ma-218	484	9	s3	s3	PROPN
ma-218	484	10	)	)	PUNCT
ma-218	484	11	lim	lim	PROPN
ma-218	484	12	sup	sup	VERB
ma-218	484	13	n→∞	n→∞	NUM
ma-218	485	1	ηn,0	ηn,0	NOUN
ma-218	485	2	<	<	X
ma-218	485	3	1	1	NUM
ma-218	485	4	;	;	PUNCT
ma-218	485	5	(	(	PUNCT
ma-218	485	6	s4	s4	PROPN
ma-218	485	7	)	)	PUNCT
ma-218	485	8	for	for	ADP
ma-218	485	9	same	same	ADJ
ma-218	485	10	a	a	DET
ma-218	485	11	>	>	X
ma-218	485	12	0	0	NUM
ma-218	485	13	,	,	PUNCT
ma-218	485	14	rn	rn	PROPN
ma-218	485	15	∈	∈	PROPN
ma-218	486	1	[	[	X
ma-218	486	2	a,∞	a,∞	PROPN
ma-218	486	3	)	)	PUNCT
ma-218	486	4	.	.	PUNCT
ma-218	487	1	then	then	ADV
ma-218	487	2	,	,	PUNCT
ma-218	487	3	{	{	PUNCT
ma-218	487	4	xn	xn	X
ma-218	487	5	}	}	PUNCT
ma-218	487	6	converges	converge	VERB
ma-218	487	7	strongly	strongly	ADV
ma-218	487	8	to	to	ADP
ma-218	487	9	$	$	SYM
ma-218	487	10	,	,	PUNCT
ma-218	487	11	where	where	SCONJ
ma-218	487	12	$	$	SYM
ma-218	487	13	=	=	SYM
ma-218	487	14	πωx0	πωx0	PROPN
ma-218	487	15	is	be	AUX
ma-218	487	16	consider	consider	VERB
ma-218	487	17	as	as	ADP
ma-218	487	18	the	the	DET
ma-218	487	19	generalized	generalized	ADJ
ma-218	487	20	projection	projection	NOUN
ma-218	487	21	of	of	ADP
ma-218	487	22	$	$	SYM
ma-218	487	23	onto	onto	ADP
ma-218	487	24	ω	ω	NUM
ma-218	487	25	.	.	PROPN
ma-218	488	1	4	4	NUM
ma-218	488	2	.	.	X
ma-218	488	3	numerical	numerical	PROPN
ma-218	488	4	example	example	NOUN
ma-218	488	5	let	let	VERB
ma-218	488	6	b	b	NOUN
ma-218	488	7	=	=	SYM
ma-218	488	8	r	r	NOUN
ma-218	488	9	and	and	CCONJ
ma-218	488	10	c	c	NOUN
ma-218	488	11	=	=	PUNCT
ma-218	489	1	[	[	X
ma-218	489	2	0	0	NUM
ma-218	489	3	,	,	PUNCT
ma-218	489	4	1	1	NUM
ma-218	489	5	]	]	PUNCT
ma-218	489	6	.	.	PUNCT
ma-218	490	1	let	let	VERB
ma-218	490	2	q	q	NOUN
ma-218	490	3	:	:	PUNCT
ma-218	490	4	c	c	X
ma-218	490	5	→	→	PUNCT
ma-218	490	6	c	c	AUX
ma-218	490	7	be	be	AUX
ma-218	490	8	defined	define	VERB
ma-218	490	9	by	by	ADP
ma-218	490	10	qu	qu	X
ma-218	490	11	=	=	PROPN
ma-218	490	12	2u∀u	2u∀u	NUM
ma-218	490	13	∈	∈	PROPN
ma-218	490	14	c.	c.	NOUN
ma-218	490	15	define	define	VERB
ma-218	490	16	ϑ	ϑ	X
ma-218	490	17	:	:	PUNCT
ma-218	490	18	c×c	c×c	PROPN
ma-218	490	19	→	→	SYM
ma-218	490	20	r	r	NOUN
ma-218	490	21	,	,	PUNCT
ma-218	490	22	d	d	NOUN
ma-218	490	23	:	:	PUNCT
ma-218	491	1	c	c	X
ma-218	491	2	×	×	NOUN
ma-218	491	3	c	c	NOUN
ma-218	491	4	→	→	SYM
ma-218	491	5	r	r	NOUN
ma-218	491	6	,	,	PUNCT
ma-218	491	7	g	g	NOUN
ma-218	491	8	:	:	PUNCT
ma-218	491	9	c	c	NOUN
ma-218	491	10	→	→	SYM
ma-218	491	11	r	r	NOUN
ma-218	491	12	,	,	PUNCT
ma-218	491	13	q	q	NOUN
ma-218	491	14	:	:	PUNCT
ma-218	491	15	c	c	X
ma-218	491	16	→	→	SYM
ma-218	491	17	r	r	NOUN
ma-218	491	18	,	,	PUNCT
ma-218	491	19	ti	ti	NOUN
ma-218	491	20	:	:	PUNCT
ma-218	491	21	c	c	PROPN
ma-218	491	22	→	→	SYM
ma-218	491	23	c	c	PROPN
ma-218	491	24	and	and	CCONJ
ma-218	491	25	si	si	INTJ
ma-218	491	26	:	:	PUNCT
ma-218	491	27	c	c	X
ma-218	491	28	→	→	SYM
ma-218	491	29	c	c	NOUN
ma-218	491	30	by	by	ADP
ma-218	491	31	ϑ(u	ϑ(u	NOUN
ma-218	491	32	,	,	PUNCT
ma-218	491	33	v	v	NOUN
ma-218	491	34	)	)	PUNCT
ma-218	491	35	=	=	SYM
ma-218	491	36	0	0	NUM
ma-218	491	37	,	,	PUNCT
ma-218	491	38	d(u	d(u	PROPN
ma-218	491	39	,	,	PUNCT
ma-218	491	40	v	v	NOUN
ma-218	491	41	)	)	PUNCT
ma-218	491	42	=	=	SYM
ma-218	491	43	(	(	PUNCT
ma-218	491	44	u	u	NOUN
ma-218	491	45	+	+	NOUN
ma-218	491	46	v)(v	v)(v	NOUN
ma-218	491	47	−	−	ADP
ma-218	491	48	u	u	NOUN
ma-218	491	49	)	)	PUNCT
ma-218	491	50	,	,	PUNCT
ma-218	491	51	g(u	g(u	PROPN
ma-218	491	52	)	)	PUNCT
ma-218	491	53	=	=	SYM
ma-218	491	54	u	u	NOUN
ma-218	491	55	,	,	PUNCT
ma-218	491	56	q(u	q(u	ADJ
ma-218	491	57	)	)	PUNCT
ma-218	491	58	=	=	SYM
ma-218	491	59	2u	2u	NOUN
ma-218	491	60	and	and	CCONJ
ma-218	491	61	ti(u	ti(u	NUM
ma-218	491	62	)	)	PUNCT
ma-218	491	63	=	=	SYM
ma-218	491	64	si(u	si(u	NOUN
ma-218	491	65	)	)	PUNCT
ma-218	491	66	=	=	SYM
ma-218	491	67	1	1	NUM
ma-218	491	68	i+1u	i+1u	PROPN
ma-218	491	69	,	,	PUNCT
ma-218	491	70	respectively.setting	respectively.setting	NOUN
ma-218	491	71	{	{	PUNCT
ma-218	491	72	βn	βn	NOUN
ma-218	491	73	}	}	PUNCT
ma-218	491	74	=	=	PUNCT
ma-218	491	75	{	{	PUNCT
ma-218	491	76	0.9	0.9	NUM
ma-218	491	77	2n	2n	NUM
ma-218	491	78	}	}	PUNCT
ma-218	491	79	,	,	PUNCT
ma-218	491	80	rn	rn	PROPN
ma-218	491	81	=	=	NOUN
ma-218	491	82	1	1	NUM
ma-218	491	83	2	2	NUM
ma-218	491	84	,	,	PUNCT
ma-218	491	85	{	{	PUNCT
ma-218	491	86	αn	αn	NOUN
ma-218	491	87	}	}	PUNCT
ma-218	491	88	=	=	SYM
ma-218	491	89	0.9	0.9	NUM
ma-218	491	90	,	,	PUNCT
ma-218	491	91	µ0,n	µ0,n	PROPN
ma-218	491	92	=	=	SYM
ma-218	491	93	1	1	NUM
ma-218	491	94	2	2	NUM
ma-218	491	95	,	,	PUNCT
ma-218	491	96	∑ni=1	∑ni=1	PUNCT
ma-218	491	97	µn	µn	NOUN
ma-218	491	98	,	,	PUNCT
ma-218	491	99	i	i	PRON
ma-218	491	100	=	=	NOUN
ma-218	491	101	1	1	NUM
ma-218	491	102	2	2	NUM
ma-218	491	103	such	such	ADJ
ma-218	491	104	that	that	SCONJ
ma-218	491	105	∑ni=0	∑ni=0	PROPN
ma-218	491	106	µi	µi	PROPN
ma-218	491	107	,	,	PUNCT
ma-218	491	108	n	n	NOUN
ma-218	491	109	=	=	SYM
ma-218	491	110	1	1	NUM
ma-218	491	111	and	and	CCONJ
ma-218	491	112	η0,n	η0,n	PROPN
ma-218	491	113	=	=	SYM
ma-218	491	114	1	1	NUM
ma-218	491	115	3	3	NUM
ma-218	491	116	,	,	PUNCT
ma-218	491	117	∑ni=1	∑ni=1	INTJ
ma-218	491	118	ηn	ηn	ADJ
ma-218	491	119	,	,	PUNCT
ma-218	491	120	i	i	PRON
ma-218	491	121	=	=	NOUN
ma-218	491	122	2	2	NUM
ma-218	491	123	3	3	NUM
ma-218	491	124	so	so	SCONJ
ma-218	491	125	that	that	SCONJ
ma-218	491	126	∑ni=0	∑ni=0	PROPN
ma-218	491	127	ηi	ηi	NOUN
ma-218	491	128	,	,	PUNCT
ma-218	491	129	n	n	PROPN
ma-218	491	130	=	=	SYM
ma-218	491	131	1.let	1.let	PROPN
ma-218	491	132	{	{	PUNCT
ma-218	491	133	xn	xn	PROPN
ma-218	491	134	}	}	PUNCT
ma-218	491	135	be	be	AUX
ma-218	491	136	generated	generate	VERB
ma-218	491	137	by	by	ADP
ma-218	491	138	the	the	DET
ma-218	491	139	hybrid	hybrid	ADJ
ma-218	491	140	inertial	inertial	ADJ
ma-218	491	141	iterative	iterative	NOUN
ma-218	491	142	algorithm	algorithm	NOUN
ma-218	491	143	(	(	PUNCT
ma-218	491	144	3.1	3.1	NUM
ma-218	491	145	)	)	PUNCT
ma-218	491	146	converges	converge	NOUN
ma-218	491	147	to	to	ADP
ma-218	491	148	x∗	x∗	PROPN
ma-218	491	149	=	=	SYM
ma-218	491	150	{	{	PUNCT
ma-218	491	151	0	0	NUM
ma-218	491	152	}	}	PUNCT
ma-218	491	153	∈	∈	PROPN
ma-218	491	154	ω	ω	NOUN
ma-218	491	155	.	.	PUNCT
ma-218	492	1	proof	proof	NOUN
ma-218	492	2	.	.	PUNCT
ma-218	493	1	clearly	clearly	ADV
ma-218	493	2	ϑ	ϑ	X
ma-218	493	3	and	and	CCONJ
ma-218	493	4	d	d	NOUN
ma-218	493	5	satisfy	satisfy	NOUN
ma-218	493	6	assumptions	assumption	NOUN
ma-218	493	7	1	1	NUM
ma-218	493	8	and	and	CCONJ
ma-218	493	9	2	2	NUM
ma-218	493	10	,	,	PUNCT
ma-218	493	11	respectively	respectively	ADV
ma-218	493	12	,	,	PUNCT
ma-218	493	13	and	and	CCONJ
ma-218	493	14	g	g	NOUN
ma-218	493	15	is	be	AUX
ma-218	493	16	continuous	continuous	ADJ
ma-218	493	17	andmonotone	andmonotone	NOUN
ma-218	493	18	so	so	SCONJ
ma-218	493	19	that	that	DET
ma-218	493	20	sol(gmep	sol(gmep	NOUN
ma-218	493	21	(	(	PUNCT
ma-218	493	22	eq1.1	eq1.1	NOUN
ma-218	493	23	)	)	PUNCT
ma-218	493	24	)	)	PUNCT
ma-218	494	1	=	=	PUNCT
ma-218	494	2	{	{	PUNCT
ma-218	494	3	0	0	NUM
ma-218	494	4	}	}	PUNCT
ma-218	494	5	6=	6=	NOUN
ma-218	494	6	∅	∅	NOUN
ma-218	494	7	,	,	PUNCT
ma-218	494	8	sol(v	sol(v	PROPN
ma-218	494	9	ip	ip	NOUN
ma-218	494	10	(	(	PUNCT
ma-218	494	11	eq1.4	eq1.4	NOUN
ma-218	494	12	)	)	PUNCT
ma-218	494	13	)	)	PUNCT
ma-218	495	1	=	=	PUNCT
ma-218	495	2	{	{	PUNCT
ma-218	495	3	0	0	NUM
ma-218	495	4	}	}	PUNCT
ma-218	495	5	6=	6=	ADP
ma-218	495	6	∅.	∅.	NOUN
ma-218	495	7	obviously	obviously	ADV
ma-218	495	8	q	q	X
ma-218	495	9	is	be	AUX
ma-218	495	10	1	1	NUM
ma-218	495	11	2	2	NUM
ma-218	495	12	−	−	NOUN
ma-218	495	13	i	i	PRON
ma-218	495	14	sm	sm	VERB
ma-218	495	15	,	,	PUNCT
ma-218	495	16	and	and	CCONJ
ma-218	495	17	ti	ti	NOUN
ma-218	495	18	and	and	CCONJ
ma-218	495	19	si	si	PROPN
ma-218	495	20	are	be	AUX
ma-218	495	21	two	two	NUM
ma-218	495	22	finite	finite	ADJ
ma-218	495	23	families	family	NOUN
ma-218	495	24	of	of	ADP
ma-218	495	25	closed	closed	ADJ
ma-218	495	26	1	1	NUM
ma-218	495	27	-	-	PUNCT
ma-218	495	28	lipschitz	lipschitz	NOUN
ma-218	495	29	continuous	continuous	ADJ
ma-218	495	30	and	and	CCONJ
ma-218	495	31	uni	uni	ADJ
ma-218	495	32	-	-	ADJ
ma-218	495	33	formly	formly	ADJ
ma-218	495	34	quisi	quisi	VERB
ma-218	495	35	-	-	PUNCT
ma-218	495	36	φ	φ	VERB
ma-218	495	37	-	-	PUNCT
ma-218	495	38	asymptotically	asymptotically	ADV
ma-218	495	39	nonexpansive	nonexpansive	ADJ
ma-218	495	40	mappings	mapping	NOUN
ma-218	495	41	with	with	ADP
ma-218	495	42	f	f	PROPN
ma-218	495	43	ix(ti	ix(ti	PROPN
ma-218	495	44	)	)	PUNCT
ma-218	496	1	=	=	SYM
ma-218	496	2	f	f	X
ma-218	496	3	ix(si	ix(si	PROPN
ma-218	496	4	)	)	PUNCT
ma-218	497	1	=	=	PRON
ma-218	497	2	{	{	PUNCT
ma-218	497	3	0	0	NUM
ma-218	497	4	}	}	PUNCT
ma-218	497	5	.	.	PUNCT
ma-218	498	1	thus	thus	ADV
ma-218	498	2	ω	ω	X
ma-218	498	3	=	=	NOUN
ma-218	498	4	sol(gmep	sol(gmep	NOUN
ma-218	498	5	(	(	PUNCT
ma-218	498	6	eq1.1	eq1.1	NOUN
ma-218	498	7	)	)	PUNCT
ma-218	498	8	)	)	PUNCT
ma-218	498	9	∩	∩	PROPN
ma-218	498	10	sol(v	sol(v	PROPN
ma-218	498	11	ip	ip	NOUN
ma-218	498	12	(	(	PUNCT
ma-218	498	13	eq1.4	eq1.4	NOUN
ma-218	498	14	)	)	PUNCT
ma-218	498	15	)	)	PUNCT
ma-218	498	16	∩	∩	PROPN
ma-218	498	17	f	f	PROPN
ma-218	498	18	ix(ti	ix(ti	PROPN
ma-218	498	19	)	)	PUNCT
ma-218	498	20	∩	∩	PROPN
ma-218	498	21	f	f	PROPN
ma-218	498	22	ix(si	ix(si	PROPN
ma-218	498	23	)	)	PUNCT
ma-218	498	24	=	=	PRON
ma-218	498	25	{	{	PUNCT
ma-218	498	26	0	0	NUM
ma-218	498	27	}	}	PUNCT
ma-218	498	28	6=	6=	ADP
ma-218	498	29	∅.	∅.	ADP
ma-218	498	30	hence	hence	ADV
ma-218	498	31	,	,	PUNCT
ma-218	498	32	the	the	DET
ma-218	498	33	it	it	PRON
ma-218	498	34	-	-	PUNCT
ma-218	498	35	erative	erative	ADJ
ma-218	498	36	scheme	scheme	NOUN
ma-218	498	37	(	(	PUNCT
ma-218	498	38	3.1	3.1	NUM
ma-218	498	39	)	)	PUNCT
ma-218	498	40	becomes	become	VERB
ma-218	498	41	the	the	DET
ma-218	498	42	following	follow	VERB
ma-218	498	43	scheme	scheme	NOUN
ma-218	498	44	(	(	PUNCT
ma-218	498	45	4.1	4.1	NUM
ma-218	498	46	)	)	PUNCT
ma-218	498	47	after	after	ADP
ma-218	498	48	simplification:	simplification:	ADJ
ma-218	498	49	x0	x0	PROPN
ma-218	498	50	,	,	PUNCT
ma-218	498	51	x1	x1	PROPN
ma-218	498	52	∈	∈	PROPN
ma-218	498	53	c	c	X
ma-218	498	54	,	,	PUNCT
ma-218	498	55	c1	c1	NOUN
ma-218	498	56	:	:	PUNCT
ma-218	499	1	=	=	SYM
ma-218	499	2	c	c	X
ma-218	499	3	,	,	PUNCT
ma-218	499	4	ωn	ωn	PROPN
ma-218	499	5	=	=	SYM
ma-218	499	6	xn	xn	PROPN
ma-218	500	1	+	+	NUM
ma-218	500	2	0.9(xn	0.9(xn	NUM
ma-218	501	1	−	−	VERB
ma-218	501	2	xn−1	xn−1	PROPN
ma-218	501	3	)	)	PUNCT
ma-218	501	4	,	,	PUNCT
ma-218	501	5	yn	yn	X
ma-218	501	6	=	=	NOUN
ma-218	501	7	1	1	NUM
ma-218	501	8	2ωn	2ωn	NOUN
ma-218	501	9	+	+	CCONJ
ma-218	501	10	1	1	NUM
ma-218	501	11	2(n+1)ωn	2(n+1)ωn	NUM
ma-218	501	12	,	,	PUNCT
ma-218	501	13	zn	zn	NOUN
ma-218	501	14	=	=	SYM
ma-218	501	15	1	1	NUM
ma-218	501	16	3yn	3yn	NOUN
ma-218	501	17	+	+	CCONJ
ma-218	501	18	2	2	NUM
ma-218	501	19	3(n+1)vn	3(n+1)vn	NUM
ma-218	501	20	,	,	PUNCT
ma-218	501	21	un	un	PROPN
ma-218	501	22	=	=	PROPN
ma-218	501	23	2zn	2zn	PROPN
ma-218	501	24	7	7	NUM
ma-218	501	25	,	,	PUNCT
ma-218	501	26	cn+1	cn+1	VERB
ma-218	501	27	=	=	SYM
ma-218	501	28	[	[	PUNCT
ma-218	501	29	0	0	NUM
ma-218	501	30	,	,	PUNCT
ma-218	501	31	un+ωn	un+ωn	NOUN
ma-218	501	32	2	2	NUM
ma-218	501	33	]	]	PUNCT
ma-218	501	34	,	,	PUNCT
ma-218	501	35	xn+1	xn+1	PROPN
ma-218	501	36	=	=	SYM
ma-218	501	37	πcn+1x0	πcn+1x0	PROPN
ma-218	501	38	,	,	PUNCT
ma-218	501	39	∀n	∀n	NUM
ma-218	501	40	≥	≥	NOUN
ma-218	501	41	1	1	NUM
ma-218	501	42	,	,	PUNCT
ma-218	501	43	where	where	SCONJ
ma-218	501	44	,	,	PUNCT
ma-218	501	45	f	f	PROPN
ma-218	501	46	or	or	CCONJ
ma-218	501	47	πc	πc	VERB
ma-218	501	48	a	a	DET
ma-218	501	49	metr	metr	PROPN
ma-218	501	50	ic	ic	PROPN
ma-218	501	51	projection	projection	NOUN
ma-218	501	52	onto	onto	ADP
ma-218	501	53	c	c	PROPN
ma-218	501	54	,	,	PUNCT
ma-218	501	55	vn	vn	PROPN
ma-218	501	56	=	=	SYM
ma-218	501	57	πc(ωn	πc(ωn	PROPN
ma-218	501	58	−	−	PROPN
ma-218	501	59	βnqωn	βnqωn	PROPN
ma-218	501	60	)	)	PUNCT
ma-218	501	61	=	=	PUNCT
ma-218	502	1			PROPN
ma-218	502	2	0	0	NUM
ma-218	502	3	,	,	PUNCT
ma-218	502	4	ωn	ωn	ADP
ma-218	502	5	−	−	PROPN
ma-218	502	6	0.9	0.9	NUM
ma-218	502	7	2n	2n	NUM
ma-218	502	8	ωn	ωn	ADP
ma-218	502	9	<	<	X
ma-218	502	10	0	0	NUM
ma-218	502	11	1	1	NUM
ma-218	502	12	,	,	PUNCT
ma-218	502	13	ωn	ωn	ADP
ma-218	502	14	−	−	PROPN
ma-218	502	15	0.9	0.9	NUM
ma-218	502	16	2n	2n	NUM
ma-218	502	17	ωn	ωn	ADP
ma-218	502	18	>	>	X
ma-218	502	19	1	1	NUM
ma-218	502	20	ωn	ωn	ADP
ma-218	502	21	−	−	PROPN
ma-218	502	22	0.9	0.9	NUM
ma-218	502	23	2n	2n	NUM
ma-218	502	24	ωn	ωn	ADP
ma-218	502	25	,	,	PUNCT
ma-218	502	26	otherwise	otherwise	ADV
ma-218	502	27	.	.	PUNCT
ma-218	503	1	(	(	PUNCT
ma-218	503	2	4.1	4.1	NUM
ma-218	503	3	)	)	PUNCT
ma-218	503	4	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PROPN
ma-218	503	5	eur	eur	NOUN
ma-218	503	6	.	.	PUNCT
ma-218	504	1	j.	j.	PROPN
ma-218	504	2	math	math	PROPN
ma-218	504	3	.	.	PUNCT
ma-218	505	1	anal	anal	PROPN
ma-218	505	2	.	.	PUNCT
ma-218	506	1	10.28924	10.28924	NUM
ma-218	506	2	/	/	SYM
ma-218	506	3	ada	ada	PROPN
ma-218	506	4	/	/	PROPN
ma-218	506	5	ma.4.8	ma.4.8	PROPN
ma-218	506	6	20finally	20finally	ADV
ma-218	506	7	,	,	PUNCT
ma-218	506	8	using	use	VERB
ma-218	506	9	the	the	DET
ma-218	506	10	software	software	NOUN
ma-218	506	11	matlab	matlab	PROPN
ma-218	506	12	7.8.0	7.8.0	NUM
ma-218	506	13	,	,	PUNCT
ma-218	506	14	we	we	PRON
ma-218	506	15	have	have	VERB
ma-218	506	16	the	the	DET
ma-218	506	17	following	follow	VERB
ma-218	506	18	figure	figure	NOUN
ma-218	506	19	which	which	PRON
ma-218	506	20	shows	show	VERB
ma-218	506	21	that	that	SCONJ
ma-218	506	22	{	{	PUNCT
ma-218	506	23	xn}converges	xn}converge	NOUN
ma-218	506	24	to	to	PART
ma-218	506	25	{	{	PUNCT
ma-218	506	26	0	0	NUM
ma-218	506	27	}	}	PUNCT
ma-218	506	28	as	as	SCONJ
ma-218	506	29	n	n	X
ma-218	506	30	→∞.	→∞.	PUNCT
ma-218	506	31	figure	figure	NOUN
ma-218	506	32	1	1	NUM
ma-218	506	33	.	.	PUNCT
ma-218	507	1	convergence	convergence	NOUN
ma-218	507	2	of	of	ADP
ma-218	507	3	{	{	PUNCT
ma-218	507	4	xn	xn	NOUN
ma-218	507	5	}	}	PUNCT
ma-218	507	6	when	when	SCONJ
ma-218	507	7	x0	x0	PROPN
ma-218	507	8	=	=	PUNCT
ma-218	507	9	1.0	1.0	NUM
ma-218	507	10	and	and	CCONJ
ma-218	507	11	x1	x1	NOUN
ma-218	507	12	=	=	SYM
ma-218	507	13	0.5	0.5	NUM
ma-218	507	14	references	reference	NOUN
ma-218	507	15	[	[	X
ma-218	507	16	1	1	NUM
ma-218	507	17	]	]	PUNCT
ma-218	507	18	m.	m.	NOUN
ma-218	507	19	alansari	alansari	PROPN
ma-218	507	20	,	,	PUNCT
ma-218	507	21	r.	r.	PROPN
ma-218	507	22	ali	ali	PROPN
ma-218	507	23	and	and	CCONJ
ma-218	507	24	m.	m.	PROPN
ma-218	507	25	farid	farid	PROPN
ma-218	507	26	,	,	PUNCT
ma-218	507	27	strong	strong	ADJ
ma-218	507	28	convergence	convergence	NOUN
ma-218	507	29	of	of	ADP
ma-218	507	30	an	an	DET
ma-218	507	31	inertial	inertial	ADJ
ma-218	507	32	iterative	iterative	NOUN
ma-218	507	33	algorithm	algorithm	NOUN
ma-218	507	34	for	for	ADP
ma-218	507	35	variational	variational	ADJ
ma-218	507	36	inequalityproblem	inequalityproblem	NOUN
ma-218	507	37	,	,	PUNCT
ma-218	507	38	generalized	generalize	VERB
ma-218	507	39	equilibrium	equilibrium	NOUN
ma-218	507	40	problem	problem	NOUN
ma-218	507	41	and	and	CCONJ
ma-218	507	42	fixed	fix	VERB
ma-218	507	43	point	point	NOUN
ma-218	507	44	problem	problem	NOUN
ma-218	507	45	in	in	ADP
ma-218	507	46	a	a	DET
ma-218	507	47	banach	banach	NOUN
ma-218	507	48	space	space	NOUN
ma-218	507	49	,	,	PUNCT
ma-218	507	50	j.	j.	PROPN
ma-218	507	51	ineq	ineq	PROPN
ma-218	507	52	.	.	PUNCT
ma-218	508	1	appl	appl	PROPN
ma-218	508	2	.	.	PUNCT
ma-218	509	1	2020	2020	NUM
ma-218	509	2	(	(	PUNCT
ma-218	509	3	2020	2020	NUM
ma-218	509	4	)	)	PUNCT
ma-218	510	1	42.[2	42.[2	NUM
ma-218	510	2	]	]	X
ma-218	510	3	y.i	y.i	PROPN
ma-218	510	4	.	.	PROPN
ma-218	510	5	alber	alber	PROPN
ma-218	510	6	,	,	PUNCT
ma-218	510	7	metric	metric	ADJ
ma-218	510	8	and	and	CCONJ
ma-218	510	9	generalized	generalized	ADJ
ma-218	510	10	projection	projection	NOUN
ma-218	510	11	operators	operator	NOUN
ma-218	510	12	in	in	ADP
ma-218	510	13	banach	banach	NOUN
ma-218	510	14	spaces	space	NOUN
ma-218	510	15	,	,	PUNCT
ma-218	510	16	in	in	ADP
ma-218	510	17	:	:	PUNCT
ma-218	510	18	properties	property	NOUN
ma-218	510	19	and	and	CCONJ
ma-218	510	20	applications	application	NOUN
ma-218	510	21	,	,	PUNCT
ma-218	510	22	lect.note	lect.note	ADJ
ma-218	510	23	,	,	PUNCT
ma-218	510	24	pure	pure	ADJ
ma-218	510	25	.	.	PUNCT
ma-218	511	1	appl	appl	PROPN
ma-218	511	2	.	.	PROPN
ma-218	511	3	math	math	NOUN
ma-218	511	4	.	.	PUNCT
ma-218	512	1	8(1996	8(1996	NUM
ma-218	512	2	)	)	PUNCT
ma-218	512	3	,	,	PUNCT
ma-218	512	4	15–50.[3	15–50.[3	NUM
ma-218	512	5	]	]	X
ma-218	513	1	e.	e.	PROPN
ma-218	513	2	blum	blum	PROPN
ma-218	513	3	and	and	CCONJ
ma-218	513	4	w.	w.	PROPN
ma-218	513	5	oettli	oettli	PROPN
ma-218	513	6	,	,	PUNCT
ma-218	513	7	from	from	ADP
ma-218	513	8	optimization	optimization	NOUN
ma-218	513	9	and	and	CCONJ
ma-218	513	10	variational	variational	ADJ
ma-218	513	11	inequalities	inequality	NOUN
ma-218	513	12	to	to	ADP
ma-218	513	13	equilibrium	equilibrium	NOUN
ma-218	513	14	problems	problem	NOUN
ma-218	513	15	,	,	PUNCT
ma-218	513	16	math	math	NOUN
ma-218	513	17	.	.	PUNCT
ma-218	513	18	stud	stud	PROPN
ma-218	513	19	.	.	PUNCT
ma-218	514	1	63(1994	63(1994	NUM
ma-218	514	2	)	)	PUNCT
ma-218	514	3	123–145.[4	123–145.[4	NUM
ma-218	514	4	]	]	X
ma-218	514	5	r.i	r.i	PROPN
ma-218	514	6	.	.	PROPN
ma-218	514	7	bot	bot	PROPN
ma-218	514	8	,	,	PUNCT
ma-218	514	9	e.r	e.r	PROPN
ma-218	514	10	.	.	PROPN
ma-218	514	11	csetnek	csetnek	PROPN
ma-218	514	12	and	and	CCONJ
ma-218	514	13	c.	c.	PROPN
ma-218	514	14	hendrich	hendrich	PROPN
ma-218	514	15	,	,	PUNCT
ma-218	514	16	inertial	inertial	ADJ
ma-218	514	17	douglas	douglas	PROPN
ma-218	514	18	-	-	PUNCT
ma-218	514	19	racheord	racheord	NOUN
ma-218	514	20	splitting	splitting	NOUN
ma-218	514	21	for	for	ADP
ma-218	514	22	monotone	monotone	ADJ
ma-218	514	23	inclusion	inclusion	NOUN
ma-218	514	24	problems	problem	NOUN
ma-218	514	25	,	,	PUNCT
ma-218	514	26	appt.math	appt.math	NOUN
ma-218	514	27	.	.	PUNCT
ma-218	515	1	comp	comp	NOUN
ma-218	515	2	.	.	PUNCT
ma-218	516	1	256	256	NUM
ma-218	516	2	(	(	PUNCT
ma-218	516	3	2015	2015	NUM
ma-218	516	4	)	)	PUNCT
ma-218	516	5	472–487.[5	472–487.[5	NUM
ma-218	516	6	]	]	X
ma-218	516	7	r.i	r.i	PROPN
ma-218	516	8	.	.	PROPN
ma-218	516	9	bot	bot	PROPN
ma-218	516	10	and	and	CCONJ
ma-218	516	11	e.r	e.r	PROPN
ma-218	516	12	.	.	PROPN
ma-218	516	13	csetnek	csetnek	PROPN
ma-218	516	14	,	,	PUNCT
ma-218	516	15	an	an	DET
ma-218	516	16	inertial	inertial	NOUN
ma-218	516	17	forwardbackward	forwardbackward	ADP
ma-218	516	18	forward	forward	ADV
ma-218	516	19	primal	primal	ADJ
ma-218	516	20	-	-	PUNCT
ma-218	516	21	dual	dual	ADJ
ma-218	516	22	splitting	splitting	NOUN
ma-218	516	23	algorithm	algorithm	NOUN
ma-218	516	24	for	for	ADP
ma-218	516	25	solvingmonotone	solvingmonotone	NOUN
ma-218	516	26	inclusions	inclusion	NOUN
ma-218	516	27	problems	problem	NOUN
ma-218	516	28	,	,	PUNCT
ma-218	516	29	numer	numer	PROPN
ma-218	516	30	.	.	PROPN
ma-218	516	31	algor	algor	PROPN
ma-218	516	32	.	.	PUNCT
ma-218	517	1	71	71	NUM
ma-218	517	2	(	(	PUNCT
ma-218	517	3	2016	2016	NUM
ma-218	517	4	)	)	PUNCT
ma-218	517	5	519–540.[6	519–540.[6	NUM
ma-218	517	6	]	]	PUNCT
ma-218	517	7	m.	m.	NOUN
ma-218	517	8	farid	farid	PROPN
ma-218	517	9	,	,	PUNCT
ma-218	517	10	r.	r.	PROPN
ma-218	517	11	ali	ali	PROPN
ma-218	517	12	and	and	CCONJ
ma-218	517	13	k.r	k.r	PROPN
ma-218	517	14	.	.	PROPN
ma-218	517	15	kazmi	kazmi	PROPN
ma-218	517	16	,	,	PUNCT
ma-218	517	17	inertial	inertial	ADJ
ma-218	517	18	iterative	iterative	NOUN
ma-218	517	19	method	method	NOUN
ma-218	517	20	for	for	ADP
ma-218	517	21	a	a	DET
ma-218	517	22	generalized	generalize	VERB
ma-218	517	23	mixed	mixed	ADJ
ma-218	517	24	equilibrium	equilibrium	NOUN
ma-218	517	25	,	,	PUNCT
ma-218	517	26	variational	variational	ADJ
ma-218	517	27	inequalityand	inequalityand	NOUN
ma-218	517	28	a	a	DET
ma-218	517	29	fixed	fix	VERB
ma-218	517	30	point	point	NOUN
ma-218	517	31	problems	problem	NOUN
ma-218	517	32	for	for	ADP
ma-218	517	33	a	a	DET
ma-218	517	34	family	family	NOUN
ma-218	517	35	of	of	ADP
ma-218	517	36	quasi−φ−nonexpansive	quasi−φ−nonexpansive	ADJ
ma-218	517	37	mappings	mapping	NOUN
ma-218	517	38	,	,	PUNCT
ma-218	517	39	filomat	filomat	NOUN
ma-218	517	40	.	.	PROPN
ma-218	517	41	37	37	NUM
ma-218	517	42	(	(	PUNCT
ma-218	517	43	2023	2023	NUM
ma-218	517	44	)	)	PUNCT
ma-218	517	45	,	,	PUNCT
ma-218	517	46	6133	6133	NUM
ma-218	517	47	-	-	SYM
ma-218	517	48	6150.[7	6150.[7	NUM
ma-218	517	49	]	]	PUNCT
ma-218	517	50	s.	s.	PROPN
ma-218	517	51	gupta	gupta	PROPN
ma-218	517	52	,	,	PUNCT
ma-218	517	53	s.	s.	PROPN
ma-218	517	54	husain	husain	PROPN
ma-218	517	55	and	and	CCONJ
ma-218	517	56	v.n	v.n	PROPN
ma-218	517	57	.	.	PROPN
ma-218	517	58	mishra	mishra	PROPN
ma-218	517	59	,	,	PUNCT
ma-218	517	60	variationa	variationa	NOUN
ma-218	517	61	inclusion	inclusion	NOUN
ma-218	517	62	governed	govern	VERB
ma-218	517	63	by	by	ADP
ma-218	517	64	αβ	αβ	INTJ
ma-218	517	65	−	−	PROPN
ma-218	517	66	h	h	NOUN
ma-218	517	67	(	(	PUNCT
ma-218	517	68	(	(	PUNCT
ma-218	517	69	.	.	PUNCT
ma-218	517	70	,	,	PUNCT
ma-218	517	71	.	.	PUNCT
ma-218	517	72	)	)	PUNCT
ma-218	517	73	,	,	PUNCT
ma-218	517	74	(	(	PUNCT
ma-218	517	75	.	.	PUNCT
ma-218	517	76	,	,	PUNCT
ma-218	517	77	.)−	.)−	PROPN
ma-218	517	78	mixed	mixed	ADJ
ma-218	517	79	accretivemapping	accretivemapping	NOUN
ma-218	517	80	,	,	PUNCT
ma-218	517	81	filomat	filomat	NOUN
ma-218	517	82	,	,	PUNCT
ma-218	517	83	31	31	NUM
ma-218	517	84	(	(	PUNCT
ma-218	517	85	2017	2017	NUM
ma-218	517	86	)	)	PUNCT
ma-218	517	87	,	,	PUNCT
ma-218	517	88	6529–6542.[8	6529–6542.[8	PROPN
ma-218	517	89	]	]	PUNCT
ma-218	517	90	j.	j.	PROPN
ma-218	517	91	iqbal	iqbal	PROPN
ma-218	517	92	,	,	PUNCT
ma-218	517	93	v.n	v.n	PROPN
ma-218	517	94	.	.	PROPN
ma-218	517	95	mashra	mashra	PROPN
ma-218	517	96	w.a	w.a	PROPN
ma-218	517	97	.	.	PROPN
ma-218	517	98	mir	mir	PROPN
ma-218	517	99	,	,	PUNCT
ma-218	517	100	a.h	a.h	PROPN
ma-218	517	101	.	.	PROPN
ma-218	517	102	dar	dar	PROPN
ma-218	517	103	,	,	PUNCT
ma-218	517	104	m.	m.	NOUN
ma-218	517	105	ishiyak	ishiyak	NOUN
ma-218	517	106	and	and	CCONJ
ma-218	517	107	l.	l.	PROPN
ma-218	517	108	rathour	rathour	PROPN
ma-218	517	109	,	,	PUNCT
ma-218	517	110	generalized	generalize	VERB
ma-218	517	111	resolvent	resolvent	ADJ
ma-218	517	112	operator	operator	NOUN
ma-218	517	113	involving	involve	VERB
ma-218	517	114	g	g	PROPN
ma-218	517	115	(	(	PUNCT
ma-218	517	116	.	.	PUNCT
ma-218	517	117	,	,	PUNCT
ma-218	517	118	.)−	.)−	PROPN
ma-218	517	119	co	co	ADJ
ma-218	517	120	-	-	ADJ
ma-218	517	121	monotone	monotone	ADJ
ma-218	517	122	mapping	mapping	NOUN
ma-218	517	123	for	for	ADP
ma-218	517	124	solving	solve	VERB
ma-218	517	125	generalized	generalize	VERB
ma-218	517	126	variational	variational	ADJ
ma-218	517	127	inclusion	inclusion	NOUN
ma-218	517	128	problem	problem	NOUN
ma-218	517	129	,	,	PUNCT
ma-218	517	130	georgian	georgian	PROPN
ma-218	517	131	math	math	NOUN
ma-218	517	132	.	.	PUNCT
ma-218	518	1	j.	j.	PROPN
ma-218	518	2	3	3	NUM
ma-218	518	3	(	(	PUNCT
ma-218	518	4	2022),533–542.[9	2022),533–542.[9	NUM
ma-218	518	5	]	]	X
ma-218	518	6	s.	s.	PROPN
ma-218	518	7	kamimura	kamimura	PROPN
ma-218	518	8	and	and	CCONJ
ma-218	518	9	w.	w.	PROPN
ma-218	518	10	takahashi	takahashi	PROPN
ma-218	518	11	,	,	PUNCT
ma-218	518	12	strong	strong	ADJ
ma-218	518	13	convergence	convergence	NOUN
ma-218	518	14	of	of	ADP
ma-218	518	15	a	a	DET
ma-218	518	16	proximal	proximal	ADJ
ma-218	518	17	-	-	PUNCT
ma-218	518	18	type	type	NOUN
ma-218	518	19	algorithm	algorithm	NOUN
ma-218	518	20	in	in	ADP
ma-218	518	21	a	a	DET
ma-218	518	22	banach	banach	NOUN
ma-218	518	23	space	space	NOUN
ma-218	518	24	,	,	PUNCT
ma-218	518	25	siam	siam	PROPN
ma-218	518	26	j.	j.	PROPN
ma-218	518	27	optim.13	optim.13	PROPN
ma-218	518	28	(	(	PUNCT
ma-218	518	29	2002	2002	NUM
ma-218	518	30	)	)	PUNCT
ma-218	518	31	938–945	938–945	NUM
ma-218	518	32	.	.	PUNCT
ma-218	519	1	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PRON
ma-218	519	2	eur	eur	PROPN
ma-218	519	3	.	.	PUNCT
ma-218	520	1	j.	j.	PROPN
ma-218	520	2	math	math	PROPN
ma-218	520	3	.	.	PUNCT
ma-218	521	1	anal	anal	PROPN
ma-218	521	2	.	.	PUNCT
ma-218	522	1	10.28924	10.28924	NUM
ma-218	522	2	/	/	SYM
ma-218	522	3	ada	ada	PROPN
ma-218	522	4	/	/	SYM
ma-218	522	5	ma.4.8	ma.4.8	PROPN
ma-218	522	6	21	21	NUM
ma-218	523	1	[	[	X
ma-218	523	2	10	10	NUM
ma-218	523	3	]	]	X
ma-218	523	4	k.r	k.r	PROPN
ma-218	523	5	.	.	PROPN
ma-218	523	6	kazmi	kazmi	PROPN
ma-218	523	7	and	and	CCONJ
ma-218	523	8	r.	r.	PROPN
ma-218	523	9	ali	ali	PROPN
ma-218	523	10	,	,	PUNCT
ma-218	523	11	common	common	ADJ
ma-218	523	12	solution	solution	NOUN
ma-218	523	13	to	to	ADP
ma-218	523	14	an	an	DET
ma-218	523	15	problem	problem	NOUN
ma-218	523	16	and	and	CCONJ
ma-218	523	17	fixed	fix	VERB
ma-218	523	18	point	point	NOUN
ma-218	523	19	problem	problem	NOUN
ma-218	523	20	for	for	ADP
ma-218	523	21	an	an	DET
ma-218	523	22	asymptoticallyquasi−φ−nonexpansive	asymptoticallyquasi−φ−nonexpansive	ADJ
ma-218	523	23	mapping	mapping	NOUN
ma-218	523	24	in	in	ADP
ma-218	523	25	intermediate	intermediate	ADJ
ma-218	523	26	sense	sense	NOUN
ma-218	523	27	,	,	PUNCT
ma-218	523	28	racsam	racsam	PROPN
ma-218	523	29	,	,	PUNCT
ma-218	523	30	111	111	NUM
ma-218	523	31	(	(	PUNCT
ma-218	523	32	2017	2017	NUM
ma-218	523	33	)	)	PUNCT
ma-218	523	34	877–889.[11	877–889.[11	PROPN
ma-218	523	35	]	]	PUNCT
ma-218	523	36	l.	l.	PROPN
ma-218	523	37	umar	umar	PROPN
ma-218	523	38	,	,	PUNCT
ma-218	523	39	y.	y.	PROPN
ma-218	523	40	ibrahim	ibrahim	PROPN
ma-218	523	41	and	and	CCONJ
ma-218	523	42	t.m	t.m	PROPN
ma-218	523	43	.	.	PROPN
ma-218	523	44	kabir	kabir	PROPN
ma-218	523	45	,	,	PUNCT
ma-218	523	46	hybrid	hybrid	ADJ
ma-218	523	47	algorithm	algorithm	NOUN
ma-218	523	48	for	for	ADP
ma-218	523	49	solving	solve	VERB
ma-218	523	50	fixed	fix	VERB
ma-218	523	51	point	point	NOUN
ma-218	523	52	problem	problem	NOUN
ma-218	523	53	and	and	CCONJ
ma-218	523	54	generalized	generalize	VERB
ma-218	523	55	mixed	mixed	ADJ
ma-218	523	56	equi	equi	NOUN
ma-218	523	57	-	-	PUNCT
ma-218	523	58	librium	librium	NOUN
ma-218	523	59	problem	problem	NOUN
ma-218	523	60	in	in	ADP
ma-218	523	61	banach	banach	NOUN
ma-218	523	62	spaces	space	NOUN
ma-218	523	63	,	,	PUNCT
ma-218	523	64	uzbek	uzbek	PROPN
ma-218	523	65	math	math	PROPN
ma-218	523	66	.	.	PUNCT
ma-218	524	1	j.	j.	PROPN
ma-218	524	2	66	66	NUM
ma-218	524	3	(	(	PUNCT
ma-218	524	4	2022	2022	NUM
ma-218	524	5	)	)	PUNCT
ma-218	524	6	101–118.[12	101–118.[12	PROPN
ma-218	524	7	]	]	X
ma-218	524	8	l.	l.	PROPN
ma-218	524	9	umar	umar	PROPN
ma-218	524	10	,	,	PUNCT
ma-218	524	11	t.m	t.m	PROPN
ma-218	524	12	.	.	PROPN
ma-218	524	13	kabir	kabir	PROPN
ma-218	524	14	and	and	CCONJ
ma-218	524	15	i.u	i.u	PROPN
ma-218	524	16	.	.	PROPN
ma-218	524	17	haruna	haruna	PROPN
ma-218	524	18	,	,	PUNCT
ma-218	524	19	an	an	DET
ma-218	524	20	inertial	inertial	ADJ
ma-218	524	21	algorithm	algorithm	NOUN
ma-218	524	22	of	of	ADP
ma-218	524	23	generalized	generalize	VERB
ma-218	524	24	f	f	PROPN
ma-218	524	25	projection	projection	NOUN
ma-218	524	26	for	for	ADP
ma-218	524	27	maximal	maximal	ADJ
ma-218	524	28	monotoneoperators	monotoneoperator	NOUN
ma-218	524	29	and	and	CCONJ
ma-218	524	30	generalized	generalize	VERB
ma-218	524	31	mixed	mixed	ADJ
ma-218	524	32	equilibrium	equilibrium	NOUN
ma-218	524	33	problem	problem	NOUN
ma-218	524	34	in	in	ADP
ma-218	524	35	banach	banach	NOUN
ma-218	524	36	spaces	space	NOUN
ma-218	524	37	,	,	PUNCT
ma-218	524	38	afr	afr	PROPN
ma-218	524	39	.	.	PUNCT
ma-218	525	1	sci	sci	PROPN
ma-218	525	2	.	.	PROPN
ma-218	525	3	rep	rep	PROPN
ma-218	525	4	.	.	PROPN
ma-218	525	5	1	1	NUM
ma-218	525	6	(	(	PUNCT
ma-218	525	7	2022	2022	NUM
ma-218	525	8	)	)	PUNCT
ma-218	525	9	32–47.[13	32–47.[13	NUM
ma-218	525	10	]	]	X
ma-218	525	11	p.e	p.e	PROPN
ma-218	525	12	.	.	PROPN
ma-218	525	13	mainge	mainge	PROPN
ma-218	525	14	,	,	PUNCT
ma-218	525	15	convergence	convergence	NOUN
ma-218	525	16	theorem	theorem	NOUN
ma-218	525	17	for	for	ADP
ma-218	525	18	inertial	inertial	ADJ
ma-218	525	19	km	km	NOUN
ma-218	525	20	-	-	PUNCT
ma-218	525	21	type	type	NOUN
ma-218	525	22	algorithms	algorithms	NOUN
ma-218	525	23	j.	j.	PROPN
ma-218	525	24	comp	comp	PROPN
ma-218	525	25	.	.	PUNCT
ma-218	526	1	appl	appl	PROPN
ma-218	526	2	.	.	PROPN
ma-218	526	3	math	math	NOUN
ma-218	526	4	.	.	PUNCT
ma-218	527	1	219	219	NUM
ma-218	527	2	(	(	PUNCT
ma-218	527	3	2008	2008	NUM
ma-218	527	4	)	)	PUNCT
ma-218	528	1	223–236.[14	223–236.[14	NUM
ma-218	528	2	]	]	PUNCT
ma-218	528	3	k.	k.	PROPN
ma-218	528	4	nakajo	nakajo	PROPN
ma-218	528	5	,	,	PUNCT
ma-218	528	6	strong	strong	ADJ
ma-218	528	7	convergence	convergence	NOUN
ma-218	528	8	for	for	ADP
ma-218	528	9	gradient	gradient	ADJ
ma-218	528	10	projection	projection	NOUN
ma-218	528	11	method	method	NOUN
ma-218	528	12	and	and	CCONJ
ma-218	528	13	relatively	relatively	ADV
ma-218	528	14	nonexpansive	nonexpansive	ADJ
ma-218	528	15	mappings	mapping	NOUN
ma-218	528	16	in	in	ADP
ma-218	528	17	banachspaces	banachspace	NOUN
ma-218	528	18	,	,	PUNCT
ma-218	528	19	appl	appl	PROPN
ma-218	528	20	.	.	PROPN
ma-218	528	21	math	math	PROPN
ma-218	528	22	.	.	PUNCT
ma-218	529	1	comp	comp	PROPN
ma-218	529	2	.	.	PUNCT
ma-218	530	1	271	271	NUM
ma-218	530	2	(	(	PUNCT
ma-218	530	3	2017	2017	NUM
ma-218	530	4	)	)	PUNCT
ma-218	530	5	251–258.[15	251–258.[15	NOUN
ma-218	530	6	]	]	X
ma-218	531	1	x.l	x.l	PROPN
ma-218	531	2	.	.	PROPN
ma-218	531	3	qin	qin	PROPN
ma-218	531	4	,	,	PUNCT
ma-218	531	5	y.j	y.j	PROPN
ma-218	531	6	.	.	PROPN
ma-218	531	7	cho	cho	PROPN
ma-218	531	8	and	and	CCONJ
ma-218	531	9	s.m	s.m	PROPN
ma-218	531	10	.	.	PROPN
ma-218	531	11	kang	kang	PROPN
ma-218	531	12	,	,	PUNCT
ma-218	531	13	convergence	convergence	NOUN
ma-218	531	14	theorems	theorem	NOUN
ma-218	531	15	of	of	ADP
ma-218	531	16	common	common	ADJ
ma-218	531	17	elements	element	NOUN
ma-218	531	18	for	for	ADP
ma-218	531	19	equilibrium	equilibrium	NOUN
ma-218	531	20	problems	problem	NOUN
ma-218	531	21	and	and	CCONJ
ma-218	531	22	fixedpoint	fixedpoint	NOUN
ma-218	531	23	problems	problem	NOUN
ma-218	531	24	in	in	ADP
ma-218	531	25	a	a	DET
ma-218	531	26	banach	banach	NOUN
ma-218	531	27	spaces	space	NOUN
ma-218	531	28	,	,	PUNCT
ma-218	531	29	j.	j.	PROPN
ma-218	531	30	comp	comp	PROPN
ma-218	531	31	.	.	PUNCT
ma-218	532	1	appl	appl	PROPN
ma-218	532	2	.	.	PROPN
ma-218	532	3	math	math	PROPN
ma-218	532	4	.	.	PUNCT
ma-218	533	1	225	225	NUM
ma-218	533	2	(	(	PUNCT
ma-218	533	3	2009	2009	NUM
ma-218	533	4	)	)	PUNCT
ma-218	533	5	20–30.[16	20–30.[16	NUM
ma-218	533	6	]	]	X
ma-218	533	7	b.t	b.t	PROPN
ma-218	533	8	.	.	PROPN
ma-218	533	9	polyak	polyak	PROPN
ma-218	533	10	,	,	PUNCT
ma-218	533	11	some	some	DET
ma-218	533	12	methods	method	NOUN
ma-218	533	13	of	of	ADP
ma-218	533	14	speeding	speed	VERB
ma-218	533	15	up	up	ADP
ma-218	533	16	the	the	DET
ma-218	533	17	convergence	convergence	NOUN
ma-218	533	18	of	of	ADP
ma-218	533	19	iteration	iteration	NOUN
ma-218	533	20	methods	method	NOUN
ma-218	533	21	.	.	PUNCT
ma-218	534	1	ussr	ussr	ADJ
ma-218	534	2	comp	comp	PROPN
ma-218	534	3	.	.	PUNCT
ma-218	535	1	math	math	NOUN
ma-218	535	2	.	.	PUNCT
ma-218	536	1	phys	phy	NOUN
ma-218	536	2	.	.	PUNCT
ma-218	537	1	4	4	NUM
ma-218	537	2	(	(	PUNCT
ma-218	537	3	1964)1–7.[17	1964)1–7.[17	NUM
ma-218	537	4	]	]	PUNCT
ma-218	537	5	w.	w.	PROPN
ma-218	537	6	takahashi	takahashi	PROPN
ma-218	537	7	and	and	CCONJ
ma-218	537	8	k.	k.	PROPN
ma-218	537	9	zembayashi	zembayashi	PROPN
ma-218	537	10	,	,	PUNCT
ma-218	537	11	strong	strong	ADJ
ma-218	537	12	and	and	CCONJ
ma-218	537	13	weak	weak	ADJ
ma-218	537	14	convergence	convergence	NOUN
ma-218	537	15	theorem	theorem	NOUN
ma-218	537	16	for	for	ADP
ma-218	537	17	equilibrium	equilibrium	NOUN
ma-218	537	18	problem	problem	NOUN
ma-218	537	19	and	and	CCONJ
ma-218	537	20	relativelynonexpansive	relativelynonexpansive	ADJ
ma-218	537	21	mappings	mapping	NOUN
ma-218	537	22	in	in	ADP
ma-218	537	23	banach	banach	NOUN
ma-218	537	24	space	space	NOUN
ma-218	537	25	,	,	PUNCT
ma-218	537	26	nonlinear	nonlinear	ADJ
ma-218	537	27	anal	anal	NOUN
ma-218	537	28	.	.	PUNCT
ma-218	538	1	tma	tma	PROPN
ma-218	538	2	.	.	PROPN
ma-218	538	3	70	70	NUM
ma-218	538	4	(	(	PUNCT
ma-218	538	5	2009	2009	NUM
ma-218	538	6	)	)	PUNCT
ma-218	538	7	45–57.[18	45–57.[18	NUM
ma-218	538	8	]	]	PUNCT
ma-218	538	9	vandana	vandana	PROPN
ma-218	538	10	,	,	PUNCT
ma-218	538	11	r.	r.	PROPN
ma-218	538	12	dubey	dubey	PROPN
ma-218	538	13	,	,	PUNCT
ma-218	538	14	deepmala	deepmala	PROPN
ma-218	538	15	,	,	PUNCT
ma-218	538	16	l.n	l.n	PROPN
ma-218	538	17	.	.	PROPN
ma-218	538	18	mishra	mishra	PROPN
ma-218	538	19	and	and	CCONJ
ma-218	538	20	v.n	v.n	PROPN
ma-218	538	21	.	.	PROPN
ma-218	538	22	mishra	mishra	PROPN
ma-218	538	23	,	,	PUNCT
ma-218	538	24	duality	duality	NOUN
ma-218	538	25	relations	relation	NOUN
ma-218	538	26	for	for	ADP
ma-218	538	27	a	a	DET
ma-218	538	28	class	class	NOUN
ma-218	538	29	of	of	ADP
ma-218	538	30	a	a	DET
ma-218	538	31	multiobjective	multiobjective	ADJ
ma-218	538	32	factionprogramming	factionprogramming	NOUN
ma-218	538	33	problem	problem	NOUN
ma-218	538	34	involving	involve	VERB
ma-218	538	35	support	support	NOUN
ma-218	538	36	functions	function	NOUN
ma-218	538	37	,	,	PUNCT
ma-218	538	38	amer	amer	PROPN
ma-218	538	39	.	.	PUNCT
ma-218	539	1	j.	j.	PROPN
ma-218	539	2	oper	oper	PROPN
ma-218	539	3	.	.	PUNCT
ma-218	540	1	res	res	PROPN
ma-218	540	2	.	.	PROPN
ma-218	540	3	8	8	NUM
ma-218	540	4	(	(	PUNCT
ma-218	540	5	2018	2018	NUM
ma-218	540	6	)	)	PUNCT
ma-218	540	7	293–311.[19	293–311.[19	NOUN
ma-218	540	8	]	]	PUNCT
ma-218	541	1	h.k	h.k	PROPN
ma-218	541	2	.	.	PROPN
ma-218	541	3	xu	xu	PROPN
ma-218	541	4	,	,	PUNCT
ma-218	541	5	inequality	inequality	NOUN
ma-218	541	6	in	in	ADP
ma-218	541	7	banach	banach	NOUN
ma-218	541	8	space	space	NOUN
ma-218	541	9	with	with	ADP
ma-218	541	10	application	application	NOUN
ma-218	541	11	,	,	PUNCT
ma-218	541	12	nonlinear	nonlinear	ADJ
ma-218	541	13	.	.	PUNCT
ma-218	542	1	anal	anal	PROPN
ma-218	542	2	.	.	PUNCT
ma-218	543	1	tma	tma	PROPN
ma-218	543	2	.	.	PROPN
ma-218	544	1	16	16	NUM
ma-218	544	2	(	(	PUNCT
ma-218	544	3	1991	1991	NUM
ma-218	544	4	)	)	PUNCT
ma-218	545	1	11271138.[20	11271138.[20	NUM
ma-218	545	2	]	]	X
ma-218	545	3	c.	c.	PROPN
ma-218	545	4	zalinesco	zalinesco	PROPN
ma-218	545	5	,	,	PUNCT
ma-218	545	6	on	on	ADP
ma-218	545	7	uniformly	uniformly	ADV
ma-218	545	8	convex	convex	NOUN
ma-218	545	9	function	function	NOUN
ma-218	545	10	,	,	PUNCT
ma-218	545	11	j.	j.	PROPN
ma-218	545	12	math	math	PROPN
ma-218	545	13	.	.	PUNCT
ma-218	546	1	anal	anal	PROPN
ma-218	546	2	.	.	PUNCT
ma-218	546	3	appl	appl	PROPN
ma-218	546	4	.	.	PUNCT
ma-218	547	1	95	95	NUM
ma-218	547	2	(	(	PUNCT
ma-218	547	3	1983	1983	NUM
ma-218	547	4	)	)	PUNCT
ma-218	547	5	344–374.[21	344–374.[21	PROPN
ma-218	547	6	]	]	PUNCT
ma-218	548	1	h.	h.	PROPN
ma-218	548	2	zegeye	zegeye	PROPN
ma-218	548	3	,	,	PUNCT
ma-218	548	4	a	a	DET
ma-218	548	5	hybrid	hybrid	ADJ
ma-218	548	6	iterative	iterative	NOUN
ma-218	548	7	scheme	scheme	NOUN
ma-218	548	8	for	for	ADP
ma-218	548	9	equilibrium	equilibrium	NOUN
ma-218	548	10	problems	problem	NOUN
ma-218	548	11	,	,	PUNCT
ma-218	548	12	variational	variational	ADJ
ma-218	548	13	inequality	inequality	NOUN
ma-218	548	14	problems	problem	NOUN
ma-218	548	15	and	and	CCONJ
ma-218	548	16	common	common	ADJ
ma-218	548	17	fixedpoint	fixedpoint	NOUN
ma-218	548	18	problems	problem	NOUN
ma-218	548	19	in	in	ADP
ma-218	548	20	banach	banach	NOUN
ma-218	548	21	spaces	space	NOUN
ma-218	548	22	,	,	PUNCT
ma-218	548	23	nonlinear	nonlinear	ADJ
ma-218	548	24	anal	anal	NOUN
ma-218	548	25	.	.	PUNCT
ma-218	549	1	tma	tma	PROPN
ma-218	549	2	.	.	PROPN
ma-218	549	3	72	72	NUM
ma-218	549	4	(	(	PUNCT
ma-218	549	5	2010	2010	NUM
ma-218	549	6	)	)	PUNCT
ma-218	549	7	2136–2146	2136–2146	NUM
ma-218	549	8	.	.	PUNCT
ma-218	550	1	https://doi.org/10.28924/ada/ma.4.8	https://doi.org/10.28924/ada/ma.4.8	PRON
ma-218	550	2	1	1	NUM
ma-218	550	3	.	.	PUNCT
ma-218	550	4	introduction	introduction	NOUN
ma-218	550	5	2	2	NUM
ma-218	550	6	.	.	PUNCT
ma-218	550	7	preliminaries	preliminary	NOUN
ma-218	550	8	3	3	NUM
ma-218	550	9	.	.	X
ma-218	550	10	main	main	ADJ
ma-218	550	11	results	result	NOUN
ma-218	550	12	4	4	NUM
ma-218	550	13	.	.	PUNCT
ma-218	550	14	numerical	numerical	PROPN
ma-218	550	15	example	example	NOUN
ma-218	550	16	references	reference	NOUN