id	sid	tid	token	lemma	pos
ma-167	1	1	2023	2023	NUM
ma-167	1	2	ada	ada	PROPN
ma-167	1	3	academica	academica	PROPN
ma-167	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-167	1	5	.	.	PUNCT
ma-167	2	1	j.	j.	PROPN
ma-167	2	2	math	math	PROPN
ma-167	2	3	.	.	PUNCT
ma-167	3	1	anal	anal	ADJ
ma-167	3	2	.	.	PUNCT
ma-167	4	1	3	3	NUM
ma-167	4	2	(	(	PUNCT
ma-167	4	3	2023	2023	NUM
ma-167	4	4	)	)	PUNCT
ma-167	4	5	18doi	18doi	NUM
ma-167	4	6	:	:	PUNCT
ma-167	4	7	10.28924	10.28924	NUM
ma-167	4	8	/	/	SYM
ma-167	4	9	ada	ada	PROPN
ma-167	4	10	/	/	SYM
ma-167	4	11	ma.3.18	ma.3.18	PROPN
ma-167	4	12	a	a	DET
ma-167	4	13	modified	modify	VERB
ma-167	4	14	algorithms	algorithm	NOUN
ma-167	4	15	for	for	ADP
ma-167	4	16	new	new	ADJ
ma-167	4	17	krasnoselskii	krasnoselskii	PROPN
ma-167	4	18	’s	’s	PART
ma-167	4	19	type	type	NOUN
ma-167	4	20	for	for	ADP
ma-167	4	21	strongly	strongly	ADV
ma-167	4	22	monotone	monotone	ADJ
ma-167	4	23	and	and	CCONJ
ma-167	4	24	lipschitz	lipschitz	NOUN
ma-167	4	25	mappings	mapping	NOUN
ma-167	4	26	furmose	furmose	NOUN
ma-167	4	27	mendy	mendy	PROPN
ma-167	4	28	,	,	PUNCT
ma-167	4	29	john	john	PROPN
ma-167	4	30	t	t	PROPN
ma-167	4	31	mendy∗	mendy∗	PROPN
ma-167	4	32	university	university	PROPN
ma-167	4	33	of	of	ADP
ma-167	4	34	the	the	DET
ma-167	4	35	gambia	gambia	PROPN
ma-167	4	36	,	,	PUNCT
ma-167	4	37	gambia	gambia	PROPN
ma-167	4	38	furmosemendy111@gmail.com	furmosemendy111@gmail.com	PROPN
ma-167	4	39	,	,	PUNCT
ma-167	4	40	jt.mendy@yahoo.com	jt.mendy@yahoo.com	PROPN
ma-167	4	41	∗correspondence	∗correspondence	PROPN
ma-167	4	42	:	:	PUNCT
ma-167	5	1	jt.mendy@yahoo.com	jt.mendy@yahoo.com	PROPN
ma-167	5	2	abstract	abstract	PROPN
ma-167	5	3	.	.	PUNCT
ma-167	6	1	let	let	VERB
ma-167	6	2	e	e	PRON
ma-167	6	3	be	be	AUX
ma-167	6	4	a	a	DET
ma-167	6	5	2	2	NUM
ma-167	6	6	uniformly	uniformly	ADV
ma-167	6	7	smooth	smooth	ADJ
ma-167	6	8	and	and	CCONJ
ma-167	6	9	convex	convex	VERB
ma-167	6	10	real	real	ADJ
ma-167	6	11	banach	banach	NOUN
ma-167	6	12	space	space	NOUN
ma-167	6	13	and	and	CCONJ
ma-167	6	14	let	let	VERB
ma-167	6	15	a	a	DET
ma-167	6	16	mapping	mapping	NOUN
ma-167	6	17	a	a	DET
ma-167	6	18	:	:	PUNCT
ma-167	6	19	e	e	X
ma-167	6	20	→	→	SYM
ma-167	6	21	e∗be	e∗be	NOUN
ma-167	6	22	lipschitz	lipschitz	NOUN
ma-167	6	23	and	and	CCONJ
ma-167	6	24	strongly	strongly	ADV
ma-167	6	25	monotone	monotone	ADJ
ma-167	6	26	such	such	ADJ
ma-167	6	27	that	that	SCONJ
ma-167	6	28	a−1(0	a−1(0	PRON
ma-167	6	29	)	)	PUNCT
ma-167	6	30	6=	6=	ADP
ma-167	6	31	∅.	∅.	VERB
ma-167	6	32	for	for	ADP
ma-167	6	33	an	an	DET
ma-167	6	34	arbitrary	arbitrary	ADJ
ma-167	6	35	(	(	PUNCT
ma-167	6	36	{	{	PUNCT
ma-167	6	37	x1	x1	PROPN
ma-167	6	38	}	}	PUNCT
ma-167	6	39	,	,	PUNCT
ma-167	6	40	{	{	PUNCT
ma-167	6	41	y1	y1	NOUN
ma-167	6	42	}	}	PUNCT
ma-167	6	43	)	)	PUNCT
ma-167	6	44	∈	∈	PROPN
ma-167	6	45	e	e	NOUN
ma-167	6	46	,	,	PUNCT
ma-167	6	47	wedefine	wedefine	VERB
ma-167	6	48	the	the	DET
ma-167	6	49	sequences	sequence	NOUN
ma-167	6	50	{	{	PUNCT
ma-167	6	51	xn	xn	NUM
ma-167	6	52	}	}	PUNCT
ma-167	6	53	and	and	CCONJ
ma-167	6	54	{	{	PUNCT
ma-167	6	55	yn	yn	NOUN
ma-167	6	56	}	}	PUNCT
ma-167	6	57	by	by	ADP
ma-167	6	58	{	{	PUNCT
ma-167	6	59	yn	yn	X
ma-167	6	60	=	=	SYM
ma-167	6	61	xn	xn	PROPN
ma-167	6	62	−	−	PROPN
ma-167	6	63	θnj−1(axn	θnj−1(axn	NOUN
ma-167	6	64	)	)	PUNCT
ma-167	6	65	,	,	PUNCT
ma-167	6	66	n	n	X
ma-167	6	67	≥	≥	NUM
ma-167	6	68	1	1	NUM
ma-167	6	69	xn+1	xn+1	X
ma-167	6	70	=	=	SYM
ma-167	6	71	yn	yn	PROPN
ma-167	6	72	−	−	PROPN
ma-167	6	73	λnj−1(ayn	λnj−1(ayn	PROPN
ma-167	6	74	)	)	PUNCT
ma-167	6	75	,	,	PUNCT
ma-167	6	76	n	n	PRON
ma-167	6	77	≥	≥	NOUN
ma-167	6	78	1where	1where	NUM
ma-167	6	79	λn	λn	NOUN
ma-167	6	80	and	and	CCONJ
ma-167	6	81	θn	θn	PROPN
ma-167	6	82	are	be	AUX
ma-167	6	83	positive	positive	ADJ
ma-167	6	84	real	real	ADJ
ma-167	6	85	number	number	NOUN
ma-167	6	86	and	and	CCONJ
ma-167	6	87	j	j	PROPN
ma-167	6	88	is	be	AUX
ma-167	6	89	the	the	DET
ma-167	6	90	duality	duality	NOUN
ma-167	6	91	mapping	mapping	NOUN
ma-167	6	92	of	of	ADP
ma-167	6	93	e.	e.	PROPN
ma-167	6	94	letting	letting	PROPN
ma-167	6	95	(	(	PUNCT
ma-167	6	96	λn	λn	NOUN
ma-167	6	97	,	,	PUNCT
ma-167	6	98	θn	θn	NOUN
ma-167	6	99	)	)	PUNCT
ma-167	6	100	∈	∈	PROPN
ma-167	6	101	(	(	PUNCT
ma-167	6	102	0	0	NUM
ma-167	6	103	,	,	PUNCT
ma-167	6	104	1	1	NUM
ma-167	6	105	)	)	PUNCT
ma-167	6	106	,	,	PUNCT
ma-167	6	107	then	then	ADV
ma-167	6	108	xn	xn	PROPN
ma-167	6	109	and	and	CCONJ
ma-167	6	110	yn	yn	PRON
ma-167	6	111	converges	converge	VERB
ma-167	6	112	strongly	strongly	ADV
ma-167	6	113	to	to	ADP
ma-167	6	114	ρ∗	ρ∗	PROPN
ma-167	6	115	,	,	PUNCT
ma-167	6	116	a	a	DET
ma-167	6	117	unique	unique	ADJ
ma-167	6	118	solution	solution	NOUN
ma-167	6	119	of	of	ADP
ma-167	6	120	the	the	DET
ma-167	6	121	equation	equation	NOUN
ma-167	6	122	ax	ax	NOUN
ma-167	6	123	=	=	NOUN
ma-167	6	124	0	0	X
ma-167	6	125	.	.	PUNCT
ma-167	7	1	we	we	PRON
ma-167	7	2	also	also	ADV
ma-167	7	3	appliedour	appliedour	ADJ
ma-167	7	4	algorithm	algorithm	NOUN
ma-167	7	5	in	in	ADP
ma-167	7	6	convex	convex	NOUN
ma-167	7	7	minimization	minimization	NOUN
ma-167	7	8	and	and	CCONJ
ma-167	7	9	also	also	ADV
ma-167	7	10	proved	prove	VERB
ma-167	7	11	the	the	DET
ma-167	7	12	convergence	convergence	NOUN
ma-167	7	13	of	of	ADP
ma-167	7	14	it	it	PRON
ma-167	7	15	in	in	ADP
ma-167	7	16	lp	lp	PROPN
ma-167	7	17	,	,	PUNCT
ma-167	7	18	`	`	PUNCT
ma-167	7	19	p	p	NOUN
ma-167	7	20	or	or	CCONJ
ma-167	7	21	wm	wm	PROPN
ma-167	7	22	,	,	PUNCT
ma-167	7	23	p	p	X
ma-167	7	24	.	.	PUNCT
ma-167	8	1	at	at	ADP
ma-167	8	2	theend	theend	NOUN
ma-167	8	3	we	we	PRON
ma-167	8	4	proposed	propose	VERB
ma-167	8	5	the	the	DET
ma-167	8	6	algorithm	algorithm	NOUN
ma-167	8	7	of	of	ADP
ma-167	8	8	it	it	PRON
ma-167	8	9	in	in	ADP
ma-167	8	10	lp(ω	lp(ω	PROPN
ma-167	8	11	)	)	PUNCT
ma-167	8	12	and	and	CCONJ
ma-167	8	13	its	its	PRON
ma-167	8	14	inverse	inverse	NOUN
ma-167	8	15	lq(ω	lq(ω	NOUN
ma-167	8	16	)	)	PUNCT
ma-167	8	17	.	.	PUNCT
ma-167	9	1	1	1	X
ma-167	9	2	.	.	X
ma-167	9	3	introduction	introduction	NOUN
ma-167	9	4	definition	definition	NOUN
ma-167	9	5	1.1	1.1	NUM
ma-167	9	6	.	.	PUNCT
ma-167	10	1	a	a	DET
ma-167	10	2	map	map	NOUN
ma-167	10	3	a	a	DET
ma-167	10	4	:	:	PUNCT
ma-167	10	5	e	e	X
ma-167	10	6	→	→	SYM
ma-167	10	7	e∗	e∗	PROPN
ma-167	10	8	is	be	AUX
ma-167	10	9	called	call	VERB
ma-167	10	10	monotone	monotone	ADJ
ma-167	10	11	if	if	SCONJ
ma-167	10	12	for	for	ADP
ma-167	10	13	each	each	DET
ma-167	10	14	x	x	NOUN
ma-167	10	15	,	,	PUNCT
ma-167	10	16	y	y	PROPN
ma-167	10	17	∈	∈	PROPN
ma-167	10	18	e	e	PROPN
ma-167	10	19	,	,	PUNCT
ma-167	10	20	the	the	DET
ma-167	10	21	following	following	ADJ
ma-167	10	22	inequalityholds	inequalityhold	NOUN
ma-167	10	23	:	:	PUNCT
ma-167	10	24	〈	〈	NOUN
ma-167	10	25	ax	ax	NOUN
ma-167	10	26	−	−	PROPN
ma-167	10	27	ay	ay	NOUN
ma-167	10	28	,	,	PUNCT
ma-167	10	29	x	x	NOUN
ma-167	10	30	−	−	PROPN
ma-167	10	31	y	y	PROPN
ma-167	10	32	〉	〉	PROPN
ma-167	10	33	≥	≥	NOUN
ma-167	10	34	0a	0a	PROPN
ma-167	10	35	is	be	AUX
ma-167	10	36	called	call	VERB
ma-167	10	37	strongly	strongly	ADV
ma-167	10	38	monotone	monotone	ADJ
ma-167	10	39	if	if	SCONJ
ma-167	10	40	there	there	PRON
ma-167	10	41	exists	exist	VERB
ma-167	10	42	k	k	PROPN
ma-167	10	43	∈	∈	PROPN
ma-167	10	44	(	(	PUNCT
ma-167	10	45	0	0	NUM
ma-167	10	46	,	,	PUNCT
ma-167	10	47	1	1	NUM
ma-167	10	48	)	)	PUNCT
ma-167	10	49	such	such	ADJ
ma-167	10	50	that	that	PRON
ma-167	10	51	for	for	ADP
ma-167	10	52	each	each	DET
ma-167	10	53	x	x	NOUN
ma-167	10	54	,	,	PUNCT
ma-167	10	55	y	y	PROPN
ma-167	10	56	∈	∈	PROPN
ma-167	10	57	e	e	PROPN
ma-167	10	58	,	,	PUNCT
ma-167	10	59	the	the	DET
ma-167	10	60	followinginequality	followinginequality	NOUN
ma-167	10	61	holds	hold	VERB
ma-167	10	62	:	:	PUNCT
ma-167	10	63	〈	〈	NOUN
ma-167	10	64	ax	ax	NOUN
ma-167	11	1	−	−	PROPN
ma-167	11	2	ay	ay	NOUN
ma-167	11	3	,	,	PUNCT
ma-167	11	4	x	x	NOUN
ma-167	11	5	−	−	PROPN
ma-167	11	6	y	y	PROPN
ma-167	11	7	〉	〉	PROPN
ma-167	11	8	≥	≥	NOUN
ma-167	11	9	k‖x	k‖x	PROPN
ma-167	11	10	−	−	PROPN
ma-167	11	11	y‖2a	y‖2a	NOUN
ma-167	11	12	map	map	VERB
ma-167	11	13	a	a	DET
ma-167	11	14	:	:	PUNCT
ma-167	11	15	e	e	X
ma-167	11	16	→	→	SYM
ma-167	11	17	e	e	X
ma-167	11	18	is	be	AUX
ma-167	11	19	called	call	VERB
ma-167	11	20	accretive	accretive	ADJ
ma-167	11	21	if	if	SCONJ
ma-167	11	22	for	for	ADP
ma-167	11	23	each	each	DET
ma-167	11	24	x	x	NOUN
ma-167	11	25	,	,	PUNCT
ma-167	11	26	y	y	PROPN
ma-167	11	27	∈	∈	PROPN
ma-167	11	28	e	e	NOUN
ma-167	11	29	,	,	PUNCT
ma-167	11	30	there	there	PRON
ma-167	11	31	exists	exist	VERB
ma-167	11	32	j(x	j(x	PROPN
ma-167	11	33	−	−	PROPN
ma-167	11	34	y	y	PROPN
ma-167	11	35	)	)	PUNCT
ma-167	11	36	∈	∈	PROPN
ma-167	11	37	j(x	j(x	PROPN
ma-167	11	38	−	−	PROPN
ma-167	11	39	y	y	PROPN
ma-167	11	40	)	)	PUNCT
ma-167	11	41	suchthat	suchthat	VERB
ma-167	11	42	〈	〈	NOUN
ma-167	11	43	ax	ax	NOUN
ma-167	11	44	−	−	PROPN
ma-167	11	45	ay	ay	NOUN
ma-167	11	46	,	,	PUNCT
ma-167	11	47	j(x	j(x	PROPN
ma-167	11	48	−	−	PROPN
ma-167	11	49	y	y	PROPN
ma-167	11	50	)	)	PUNCT
ma-167	11	51	〉	〉	PROPN
ma-167	11	52	≥	≥	NOUN
ma-167	11	53	0a	0a	PROPN
ma-167	11	54	is	be	AUX
ma-167	11	55	called	call	VERB
ma-167	11	56	strongly	strongly	ADV
ma-167	11	57	accretive	accretive	ADJ
ma-167	11	58	if	if	SCONJ
ma-167	11	59	there	there	PRON
ma-167	11	60	exists	exist	VERB
ma-167	11	61	k	k	PROPN
ma-167	11	62	∈	∈	PROPN
ma-167	11	63	(	(	PUNCT
ma-167	11	64	0	0	NUM
ma-167	11	65	,	,	PUNCT
ma-167	11	66	1	1	NUM
ma-167	11	67	)	)	PUNCT
ma-167	11	68	such	such	ADJ
ma-167	11	69	that	that	PRON
ma-167	11	70	for	for	ADP
ma-167	11	71	each	each	DET
ma-167	11	72	x	x	NOUN
ma-167	11	73	,	,	PUNCT
ma-167	11	74	y	y	PROPN
ma-167	11	75	∈	∈	PROPN
ma-167	11	76	e	e	NOUN
ma-167	11	77	,	,	PUNCT
ma-167	11	78	there	there	PRON
ma-167	11	79	exists	exist	VERB
ma-167	11	80	j(x	j(x	PROPN
ma-167	11	81	−	−	PROPN
ma-167	11	82	y	y	PROPN
ma-167	11	83	)	)	PUNCT
ma-167	11	84	∈	∈	PROPN
ma-167	11	85	j(x	j(x	PROPN
ma-167	11	86	−	−	PROPN
ma-167	11	87	y	y	PROPN
ma-167	11	88	)	)	PUNCT
ma-167	11	89	such	such	ADJ
ma-167	11	90	that	that	SCONJ
ma-167	11	91	〈	〈	PROPN
ma-167	11	92	ax	ax	NOUN
ma-167	11	93	−	−	PROPN
ma-167	11	94	ay	ay	NOUN
ma-167	11	95	,	,	PUNCT
ma-167	11	96	j(x	j(x	PROPN
ma-167	11	97	−	−	PROPN
ma-167	11	98	y	y	PROPN
ma-167	11	99	)	)	PUNCT
ma-167	11	100	〉	〉	PROPN
ma-167	11	101	≥	≥	NOUN
ma-167	11	102	k‖x	k‖x	NOUN
ma-167	11	103	−	−	PROPN
ma-167	11	104	y‖2	y‖2	PRON
ma-167	11	105	received	receive	VERB
ma-167	11	106	:	:	PUNCT
ma-167	11	107	23	23	NUM
ma-167	11	108	apr	apr	NOUN
ma-167	11	109	2023	2023	NUM
ma-167	11	110	.	.	PUNCT
ma-167	12	1	key	key	ADJ
ma-167	12	2	words	word	NOUN
ma-167	12	3	and	and	CCONJ
ma-167	12	4	phrases	phrase	NOUN
ma-167	12	5	.	.	PUNCT
ma-167	13	1	krasnoselskii	krasnoselskii	ADJ
ma-167	13	2	-	-	PUNCT
ma-167	13	3	type	type	NOUN
ma-167	13	4	algorithm	algorithm	NOUN
ma-167	13	5	;	;	PUNCT
ma-167	13	6	monotone	monotone	ADJ
ma-167	13	7	operators	operator	NOUN
ma-167	13	8	;	;	PUNCT
ma-167	13	9	lipschitz	lipschitz	VERB
ma-167	13	10	mappings.1	mappings.1	PROPN
ma-167	13	11	https://adac.ee	https://adac.ee	PROPN
ma-167	13	12	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	13	13	https://orcid.org/0000-0002-3774-0761	https://orcid.org/0000-0002-3774-0761	PROPN
ma-167	13	14	eur	eur	PROPN
ma-167	13	15	.	.	PUNCT
ma-167	14	1	j.	j.	PROPN
ma-167	14	2	math	math	PROPN
ma-167	14	3	.	.	PUNCT
ma-167	15	1	anal	anal	PROPN
ma-167	15	2	.	.	PUNCT
ma-167	16	1	10.28924	10.28924	NUM
ma-167	16	2	/	/	SYM
ma-167	16	3	ada	ada	PROPN
ma-167	16	4	/	/	SYM
ma-167	16	5	ma.3.18	ma.3.18	PROPN
ma-167	16	6	2a	2a	NUM
ma-167	16	7	map	map	VERB
ma-167	16	8	a	a	DET
ma-167	16	9	:	:	PUNCT
ma-167	16	10	e	e	X
ma-167	16	11	→	→	SYM
ma-167	16	12	e∗	e∗	PROPN
ma-167	16	13	is	be	AUX
ma-167	16	14	called	call	VERB
ma-167	16	15	lipschitzian	lipschitzian	ADJ
ma-167	16	16	,	,	PUNCT
ma-167	16	17	if	if	SCONJ
ma-167	16	18	for	for	ADP
ma-167	16	19	each	each	DET
ma-167	16	20	constant	constant	ADJ
ma-167	16	21	l	l	NOUN
ma-167	16	22	>	>	X
ma-167	16	23	0	0	PUNCT
ma-167	17	1	and	and	CCONJ
ma-167	17	2	for	for	ADP
ma-167	17	3	all	all	DET
ma-167	17	4	x	x	NOUN
ma-167	17	5	,	,	PUNCT
ma-167	17	6	y	y	PROPN
ma-167	17	7	∈	∈	PROPN
ma-167	17	8	e	e	NOUN
ma-167	17	9	,	,	PUNCT
ma-167	17	10	thefollowing	thefollowe	VERB
ma-167	17	11	inequality	inequality	NOUN
ma-167	17	12	holds	hold	VERB
ma-167	17	13	:	:	PUNCT
ma-167	18	1	i	i	PRON
ma-167	18	2	):	):	PUNCT
ma-167	18	3	〈	〈	NOUN
ma-167	18	4	ax	ax	NOUN
ma-167	18	5	−	−	PROPN
ma-167	18	6	ay	ay	NOUN
ma-167	18	7	〉	〉	PROPN
ma-167	18	8	≤	≤	NUM
ma-167	18	9	l‖x	l‖x	PROPN
ma-167	18	10	−	−	PROPN
ma-167	18	11	y‖	y‖	PROPN
ma-167	18	12	ii	ii	PROPN
ma-167	18	13	):	):	PUNCT
ma-167	18	14	l2(d2	l2(d2	ADJ
ma-167	18	15	−	−	PROPN
ma-167	18	16	1	1	NUM
ma-167	18	17	)	)	PUNCT
ma-167	18	18	<	<	X
ma-167	18	19	k2	k2	PROPN
ma-167	18	20	many	many	ADJ
ma-167	18	21	physical	physical	ADJ
ma-167	18	22	problems	problem	NOUN
ma-167	18	23	in	in	ADP
ma-167	18	24	applications	application	NOUN
ma-167	18	25	can	can	AUX
ma-167	18	26	be	be	AUX
ma-167	18	27	modeled	model	VERB
ma-167	18	28	in	in	ADP
ma-167	18	29	the	the	DET
ma-167	18	30	following	follow	VERB
ma-167	18	31	form	form	NOUN
ma-167	18	32	:	:	PUNCT
ma-167	18	33	find	find	VERB
ma-167	18	34	x	x	X
ma-167	18	35	∈	∈	NOUN
ma-167	18	36	h	h	NOUN
ma-167	18	37	suchthat	suchthat	PROPN
ma-167	18	38	0	0	NUM
ma-167	18	39	∈	∈	NOUN
ma-167	18	40	ax	ax	NOUN
ma-167	18	41	(	(	PUNCT
ma-167	18	42	1.1)where	1.1)where	NUM
ma-167	18	43	a	a	PRON
ma-167	18	44	is	be	AUX
ma-167	18	45	a	a	DET
ma-167	18	46	monotone	monotone	ADJ
ma-167	18	47	operator	operator	NOUN
ma-167	18	48	on	on	ADP
ma-167	18	49	a	a	DET
ma-167	18	50	real	real	ADJ
ma-167	18	51	hilbert	hilbert	NOUN
ma-167	18	52	space	space	NOUN
ma-167	18	53	h.	h.	PROPN
ma-167	18	54	typical	typical	ADJ
ma-167	18	55	examples	example	NOUN
ma-167	18	56	where	where	SCONJ
ma-167	18	57	monotone	monotone	ADJ
ma-167	18	58	oper	oper	NOUN
ma-167	18	59	-	-	PUNCT
ma-167	18	60	ators	ator	NOUN
ma-167	18	61	occur	occur	VERB
ma-167	18	62	and	and	CCONJ
ma-167	18	63	satisfy	satisfy	VERB
ma-167	18	64	the	the	DET
ma-167	18	65	inclusion	inclusion	NOUN
ma-167	18	66	0	0	NUM
ma-167	18	67	∈	∈	NOUN
ma-167	18	68	ax	ax	NOUN
ma-167	18	69	include	include	VERB
ma-167	18	70	the	the	DET
ma-167	18	71	equilibrium	equilibrium	NOUN
ma-167	18	72	state	state	NOUN
ma-167	18	73	of	of	ADP
ma-167	18	74	evolution	evolution	NOUN
ma-167	18	75	equations	equation	NOUN
ma-167	18	76	andcritical	andcritical	ADJ
ma-167	18	77	points	point	NOUN
ma-167	18	78	of	of	ADP
ma-167	18	79	some	some	DET
ma-167	18	80	functionals	functional	NOUN
ma-167	18	81	and	and	CCONJ
ma-167	18	82	convex	convex	NOUN
ma-167	18	83	optimization	optimization	NOUN
ma-167	18	84	,	,	PUNCT
ma-167	18	85	linear	linear	ADJ
ma-167	18	86	programing	programing	NOUN
ma-167	18	87	,	,	PUNCT
ma-167	18	88	monotone	monotone	ADJ
ma-167	18	89	inclusionsand	inclusionsand	NOUN
ma-167	18	90	elliptic	elliptic	PROPN
ma-167	18	91	differential	differential	NOUN
ma-167	18	92	equations	equation	NOUN
ma-167	18	93	defined	define	VERB
ma-167	18	94	on	on	ADP
ma-167	18	95	hilbert	hilbert	NOUN
ma-167	18	96	spaces	space	NOUN
ma-167	18	97	(	(	PUNCT
ma-167	18	98	see	see	VERB
ma-167	18	99	e.g.	e.g.	ADV
ma-167	18	100	,	,	PUNCT
ma-167	18	101	browder	browder	NOUN
ma-167	19	1	[	[	X
ma-167	19	2	2	2	NUM
ma-167	19	3	]	]	PUNCT
ma-167	19	4	,	,	PUNCT
ma-167	19	5	mustafa	mustafa	PROPN
ma-167	20	1	[	[	X
ma-167	20	2	19],stephen	19],stephen	NUM
ma-167	20	3	[	[	X
ma-167	20	4	26	26	NUM
ma-167	20	5	]	]	PUNCT
ma-167	20	6	,	,	PUNCT
ma-167	20	7	sina	sina	PROPN
ma-167	21	1	[	[	X
ma-167	21	2	24	24	NUM
ma-167	21	3	]	]	PUNCT
ma-167	21	4	,	,	PUNCT
ma-167	21	5	mendy	mendy	PROPN
ma-167	21	6	et	et	PROPN
ma-167	21	7	al	al	PROPN
ma-167	21	8	,	,	PUNCT
ma-167	21	9	[	[	X
ma-167	21	10	17	17	NUM
ma-167	21	11	]	]	PUNCT
ma-167	21	12	and	and	CCONJ
ma-167	21	13	chidume	chidume	VERB
ma-167	21	14	[	[	X
ma-167	21	15	3	3	NUM
ma-167	21	16	]	]	NUM
ma-167	21	17	)	)	PUNCT
ma-167	21	18	.	.	PUNCT
ma-167	22	1	for	for	ADP
ma-167	22	2	precisely	precisely	ADV
ma-167	22	3	,	,	PUNCT
ma-167	22	4	the	the	DET
ma-167	22	5	classical	classical	ADJ
ma-167	22	6	convexoptimization	convexoptimization	NOUN
ma-167	22	7	problem	problem	NOUN
ma-167	22	8	:	:	PUNCT
ma-167	22	9	let	let	VERB
ma-167	22	10	h	h	NOUN
ma-167	22	11	:	:	PUNCT
ma-167	22	12	h	h	NOUN
ma-167	22	13	→	→	PUNCT
ma-167	22	14	r	r	NOUN
ma-167	22	15	∪	∪	X
ma-167	22	16	{	{	PUNCT
ma-167	22	17	+	+	NOUN
ma-167	22	18	∞	∞	NOUN
ma-167	22	19	}	}	PUNCT
ma-167	22	20	be	be	AUX
ma-167	22	21	a	a	DET
ma-167	22	22	proper	proper	ADJ
ma-167	22	23	convex	convex	NOUN
ma-167	22	24	function	function	NOUN
ma-167	22	25	.	.	PUNCT
ma-167	23	1	the	the	DET
ma-167	23	2	sub	sub	NOUN
ma-167	23	3	-	-	NOUN
ma-167	23	4	differential	differential	NOUN
ma-167	23	5	of	of	ADP
ma-167	23	6	h	h	NOUN
ma-167	23	7	at	at	ADP
ma-167	23	8	x	x	PROPN
ma-167	23	9	∈	∈	PROPN
ma-167	23	10	h	h	NOUN
ma-167	23	11	;	;	PUNCT
ma-167	23	12	is	be	AUX
ma-167	23	13	defined	define	VERB
ma-167	23	14	by	by	ADP
ma-167	23	15	∂h	∂h	PROPN
ma-167	23	16	:	:	PUNCT
ma-167	23	17	h	h	NOUN
ma-167	23	18	→	→	SYM
ma-167	23	19	2h	2h	NUM
ma-167	23	20	∂(x	∂(x	NOUN
ma-167	23	21	)	)	PUNCT
ma-167	23	22	=	=	PRON
ma-167	23	23	{	{	PUNCT
ma-167	23	24	x∗	x∗	PROPN
ma-167	23	25	∈	∈	PROPN
ma-167	23	26	h	h	NOUN
ma-167	23	27	:	:	PUNCT
ma-167	23	28	h(y)−	h(y)−	PROPN
ma-167	23	29	h(x	h(x	PROPN
ma-167	23	30	)	)	PUNCT
ma-167	23	31	≥	≥	NOUN
ma-167	23	32	〈	〈	PROPN
ma-167	23	33	y	y	PROPN
ma-167	23	34	−	−	PROPN
ma-167	23	35	x	x	SYM
ma-167	23	36	,	,	PUNCT
ma-167	23	37	x∗〉,∀y	x∗〉,∀y	PROPN
ma-167	23	38	∈	∈	PROPN
ma-167	23	39	h	h	NOUN
ma-167	23	40	}	}	PUNCT
ma-167	23	41	.	.	PUNCT
ma-167	24	1	(	(	PUNCT
ma-167	24	2	1.2	1.2	NUM
ma-167	24	3	)	)	PUNCT
ma-167	24	4	clearly	clearly	ADV
ma-167	24	5	,	,	PUNCT
ma-167	24	6	∂h	∂h	PROPN
ma-167	24	7	:	:	PUNCT
ma-167	24	8	h	h	PROPN
ma-167	25	1	→	→	PUNCT
ma-167	25	2	2his	2his	PRON
ma-167	25	3	monotone	monotone	ADJ
ma-167	25	4	operator	operator	NOUN
ma-167	25	5	on	on	ADP
ma-167	25	6	h	h	NOUN
ma-167	25	7	,	,	PUNCT
ma-167	25	8	and	and	CCONJ
ma-167	25	9	0	0	NUM
ma-167	25	10	∈	∈	PROPN
ma-167	25	11	∂(x0	∂(x0	PROPN
ma-167	25	12	)	)	PUNCT
ma-167	25	13	if	if	SCONJ
ma-167	25	14	and	and	CCONJ
ma-167	25	15	only	only	ADV
ma-167	25	16	if	if	SCONJ
ma-167	25	17	x0	x0	PROPN
ma-167	25	18	is	be	AUX
ma-167	25	19	a	a	DET
ma-167	25	20	minimizer	minimizer	NOUN
ma-167	25	21	of	of	ADP
ma-167	25	22	h.	h.	PROPN
ma-167	25	23	in	in	ADP
ma-167	25	24	the	the	DET
ma-167	25	25	case	case	NOUN
ma-167	25	26	of	of	ADP
ma-167	25	27	setting	set	VERB
ma-167	25	28	∂(x	∂(x	NOUN
ma-167	25	29	)	)	PUNCT
ma-167	25	30	≡	≡	PROPN
ma-167	25	31	a	a	PRON
ma-167	25	32	;	;	PUNCT
ma-167	25	33	solving	solve	VERB
ma-167	25	34	the	the	DET
ma-167	25	35	inclusion	inclusion	NOUN
ma-167	25	36	0	0	NUM
ma-167	25	37	∈	∈	NOUN
ma-167	25	38	ax	ax	NOUN
ma-167	25	39	is	be	AUX
ma-167	25	40	solving	solve	VERB
ma-167	25	41	for	for	ADP
ma-167	25	42	a	a	DET
ma-167	25	43	minimizer	minimizer	NOUN
ma-167	25	44	of	of	ADP
ma-167	25	45	h.there	h.there	NOUN
ma-167	25	46	have	have	AUX
ma-167	25	47	been	be	AUX
ma-167	25	48	fruitful	fruitful	ADJ
ma-167	25	49	works	work	NOUN
ma-167	25	50	on	on	ADP
ma-167	25	51	approximating	approximate	VERB
ma-167	25	52	zero	zero	NUM
ma-167	25	53	point	point	NOUN
ma-167	25	54	of	of	ADP
ma-167	25	55	a	a	PRON
ma-167	25	56	in	in	ADP
ma-167	25	57	hilbert	hilbert	NOUN
ma-167	25	58	spaces	space	NOUN
ma-167	25	59	(	(	PUNCT
ma-167	25	60	see	see	VERB
ma-167	25	61	e.g.	e.g.	ADV
ma-167	25	62	,takahashi	,takahashi	PUNCT
ma-167	25	63	and	and	CCONJ
ma-167	25	64	ueda	ueda	PRON
ma-167	26	1	[	[	X
ma-167	26	2	31	31	NUM
ma-167	26	3	]	]	PUNCT
ma-167	26	4	,	,	PUNCT
ma-167	26	5	song	song	NOUN
ma-167	26	6	and	and	CCONJ
ma-167	26	7	chen	chen	PROPN
ma-167	27	1	[	[	X
ma-167	27	2	25	25	NUM
ma-167	27	3	]	]	PUNCT
ma-167	27	4	,	,	PUNCT
ma-167	27	5	and	and	CCONJ
ma-167	27	6	cho	cho	NOUN
ma-167	27	7	et	et	PROPN
ma-167	27	8	al	al	PROPN
ma-167	27	9	.	.	PUNCT
ma-167	28	1	[	[	X
ma-167	28	2	9	9	NUM
ma-167	28	3	]	]	PUNCT
ma-167	28	4	)	)	PUNCT
ma-167	28	5	.	.	PUNCT
ma-167	29	1	the	the	DET
ma-167	29	2	proximal	proximal	ADJ
ma-167	29	3	point	point	NOUN
ma-167	29	4	algorithm	algorithm	NOUN
ma-167	29	5	(	(	PUNCT
ma-167	29	6	ppa	ppa	PROPN
ma-167	29	7	)	)	PUNCT
ma-167	29	8	is	be	AUX
ma-167	29	9	recognized	recognize	VERB
ma-167	29	10	as	as	ADP
ma-167	29	11	a	a	DET
ma-167	29	12	powerful	powerful	ADJ
ma-167	29	13	and	and	CCONJ
ma-167	29	14	successful	successful	ADJ
ma-167	29	15	algorithm	algorithm	NOUN
ma-167	29	16	in	in	ADP
ma-167	29	17	finding	find	VERB
ma-167	29	18	a	a	DET
ma-167	29	19	numerical	numerical	ADJ
ma-167	29	20	solution	solution	NOUN
ma-167	29	21	ofmonotone	ofmonotone	NOUN
ma-167	29	22	operators	operator	NOUN
ma-167	29	23	equation	equation	NOUN
ma-167	29	24	0	0	NUM
ma-167	29	25	∈	∈	NOUN
ma-167	29	26	ax	ax	NOUN
ma-167	29	27	which	which	PRON
ma-167	29	28	was	be	AUX
ma-167	29	29	introduced	introduce	VERB
ma-167	29	30	by	by	ADP
ma-167	29	31	martinet	martinet	NOUN
ma-167	29	32	[	[	X
ma-167	29	33	13	13	NUM
ma-167	29	34	]	]	PUNCT
ma-167	29	35	and	and	CCONJ
ma-167	29	36	studied	study	VERB
ma-167	29	37	furtherby	furtherby	PROPN
ma-167	29	38	rockafellar	rockafellar	ADJ
ma-167	30	1	[	[	X
ma-167	30	2	22	22	NUM
ma-167	30	3	]	]	PUNCT
ma-167	30	4	and	and	CCONJ
ma-167	30	5	a	a	DET
ma-167	30	6	host	host	NOUN
ma-167	30	7	of	of	ADP
ma-167	30	8	other	other	ADJ
ma-167	30	9	authors	author	NOUN
ma-167	30	10	.	.	PUNCT
ma-167	31	1	that	that	PRON
ma-167	31	2	is	is	ADV
ma-167	31	3	,	,	PUNCT
ma-167	31	4	given	give	VERB
ma-167	31	5	xk	xk	PROPN
ma-167	31	6	∈	∈	PROPN
ma-167	31	7	h	h	NOUN
ma-167	31	8	;	;	PUNCT
ma-167	31	9	xn+1	xn+1	PROPN
ma-167	31	10	=	=	SYM
ma-167	31	11	jλnxn	jλnxn	PROPN
ma-167	31	12	.	.	PUNCT
ma-167	32	1	(	(	PUNCT
ma-167	32	2	1.3	1.3	NUM
ma-167	32	3	)	)	PUNCT
ma-167	32	4	where	where	SCONJ
ma-167	32	5	jλn	jλn	NOUN
ma-167	32	6	=	=	PUNCT
ma-167	32	7	(	(	PUNCT
ma-167	32	8	i	i	PRON
ma-167	32	9	+	+	NUM
ma-167	32	10	λna)−1	λna)−1	NOUN
ma-167	32	11	is	be	AUX
ma-167	32	12	the	the	DET
ma-167	32	13	resolvent	resolvent	NOUN
ma-167	32	14	of	of	ADP
ma-167	32	15	operator	operator	NOUN
ma-167	32	16	a.	a.	NOUN
ma-167	32	17	since	since	SCONJ
ma-167	32	18	rockafellar	rockafellar	ADJ
ma-167	33	1	[	[	X
ma-167	33	2	22	22	NUM
ma-167	33	3	]	]	PUNCT
ma-167	33	4	only	only	ADV
ma-167	33	5	obtained	obtain	VERB
ma-167	33	6	theweak	theweak	NOUN
ma-167	33	7	convergence	convergence	NOUN
ma-167	33	8	of	of	ADP
ma-167	33	9	the	the	DET
ma-167	33	10	algorithm	algorithm	NOUN
ma-167	33	11	1.3	1.3	NUM
ma-167	33	12	as	as	ADP
ma-167	33	13	λn	λn	PROPN
ma-167	33	14	→∞	→∞	NUM
ma-167	33	15	;	;	PUNCT
ma-167	33	16	so	so	ADV
ma-167	33	17	he	he	PRON
ma-167	33	18	proposed	propose	VERB
ma-167	33	19	two	two	NUM
ma-167	33	20	open	open	ADJ
ma-167	33	21	questions	question	NOUN
ma-167	33	22	for	for	ADP
ma-167	33	23	obtainingthe	obtainingthe	PRON
ma-167	33	24	strong	strong	ADJ
ma-167	33	25	convergence	convergence	NOUN
ma-167	33	26	of	of	ADP
ma-167	33	27	the	the	DET
ma-167	33	28	proximal	proximal	ADJ
ma-167	33	29	point	point	NOUN
ma-167	33	30	algorithm	algorithm	NOUN
ma-167	33	31	:	:	PUNCT
ma-167	33	32	(	(	PUNCT
ma-167	33	33	1	1	X
ma-167	33	34	)	)	PUNCT
ma-167	33	35	does	do	AUX
ma-167	33	36	the	the	DET
ma-167	33	37	proximal	proximal	ADJ
ma-167	33	38	point	point	NOUN
ma-167	33	39	algorithmalways	algorithmalway	VERB
ma-167	33	40	converge	converge	VERB
ma-167	33	41	weakly	weakly	ADV
ma-167	33	42	?	?	PUNCT
ma-167	34	1	(	(	PUNCT
ma-167	34	2	2	2	X
ma-167	34	3	)	)	PUNCT
ma-167	34	4	can	can	AUX
ma-167	34	5	the	the	DET
ma-167	34	6	proximal	proximal	ADJ
ma-167	34	7	point	point	NOUN
ma-167	34	8	algorithm	algorithm	NOUN
ma-167	34	9	be	be	AUX
ma-167	34	10	modified	modify	VERB
ma-167	34	11	to	to	PART
ma-167	34	12	guarantee	guarantee	VERB
ma-167	34	13	strongconvergence	strongconvergence	NOUN
ma-167	34	14	?	?	PUNCT
ma-167	35	1	in	in	ADP
ma-167	35	2	studying	study	VERB
ma-167	35	3	the	the	DET
ma-167	35	4	strong	strong	ADJ
ma-167	35	5	convergence	convergence	NOUN
ma-167	35	6	,	,	PUNCT
ma-167	35	7	many	many	ADJ
ma-167	35	8	authors	author	NOUN
ma-167	35	9	have	have	AUX
ma-167	35	10	modified	modify	VERB
ma-167	35	11	the	the	DET
ma-167	35	12	proximal	proximal	ADJ
ma-167	35	13	pointalgorithm	pointalgorithm	NOUN
ma-167	35	14	(	(	PUNCT
ma-167	35	15	ppa	ppa	PROPN
ma-167	35	16	)	)	PUNCT
ma-167	35	17	to	to	PART
ma-167	35	18	guarantee	guarantee	VERB
ma-167	35	19	strong	strong	ADJ
ma-167	35	20	convergence	convergence	NOUN
ma-167	35	21	under	under	ADP
ma-167	35	22	different	different	ADJ
ma-167	35	23	settings	setting	NOUN
ma-167	35	24	,	,	PUNCT
ma-167	35	25	see	see	VERB
ma-167	35	26	e.g.	e.g.	ADV
ma-167	35	27	,	,	PUNCT
ma-167	36	1	takahashi	takahashi	PROPN
ma-167	37	1	[	[	X
ma-167	37	2	29],reich	29],reich	PROPN
ma-167	38	1	[	[	X
ma-167	38	2	20	20	NUM
ma-167	38	3	]	]	PUNCT
ma-167	38	4	,	,	PUNCT
ma-167	38	5	lehdili	lehdili	NOUN
ma-167	38	6	and	and	CCONJ
ma-167	38	7	moudafi	moudafi	NOUN
ma-167	38	8	[	[	X
ma-167	38	9	12	12	NUM
ma-167	38	10	]	]	PUNCT
ma-167	38	11	,	,	PUNCT
ma-167	38	12	chidume	chidume	VERB
ma-167	38	13	et	et	PROPN
ma-167	38	14	al	al	PROPN
ma-167	38	15	.	.	PUNCT
ma-167	39	1	[	[	X
ma-167	39	2	6	6	NUM
ma-167	39	3	]	]	PUNCT
ma-167	39	4	,	,	PUNCT
ma-167	39	5	and	and	CCONJ
ma-167	39	6	the	the	DET
ma-167	39	7	references	reference	NOUN
ma-167	39	8	therein.let	therein.let	VERB
ma-167	39	9	e	e	PRON
ma-167	39	10	be	be	AUX
ma-167	39	11	a	a	DET
ma-167	39	12	real	real	ADV
ma-167	39	13	normed	normed	ADJ
ma-167	39	14	space	space	NOUN
ma-167	39	15	,	,	PUNCT
ma-167	39	16	e∗	e∗	NOUN
ma-167	39	17	its	its	PRON
ma-167	39	18	topological	topological	ADJ
ma-167	39	19	dual	dual	ADJ
ma-167	39	20	space	space	NOUN
ma-167	39	21	.	.	PUNCT
ma-167	40	1	the	the	DET
ma-167	40	2	map	map	NOUN
ma-167	40	3	j	j	NOUN
ma-167	40	4	:	:	PUNCT
ma-167	40	5	e	e	X
ma-167	40	6	→	→	SYM
ma-167	40	7	2e	2e	PROPN
ma-167	40	8	∗	∗	NOUN
ma-167	40	9	defined	define	VERB
ma-167	40	10	by	by	ADP
ma-167	40	11	jx	jx	PROPN
ma-167	40	12	:	:	PUNCT
ma-167	40	13	{	{	PUNCT
ma-167	40	14	x∗	x∗	PROPN
ma-167	40	15	∈	∈	PROPN
ma-167	40	16	e∗	e∗	NOUN
ma-167	40	17	:	:	PUNCT
ma-167	40	18	〈	〈	PROPN
ma-167	40	19	x	x	X
ma-167	40	20	,	,	PUNCT
ma-167	40	21	x∗	x∗	PROPN
ma-167	40	22	〉	〉	NOUN
ma-167	40	23	=	=	SYM
ma-167	40	24	‖x‖.‖x∗‖	‖x‖.‖x∗‖	PROPN
ma-167	40	25	=	=	PUNCT
ma-167	40	26	‖x‖2	‖x‖2	VERB
ma-167	40	27	=	=	SYM
ma-167	40	28	‖x∗‖2	‖x∗‖2	NOUN
ma-167	40	29	}	}	PUNCT
ma-167	40	30	.	.	PUNCT
ma-167	41	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	41	2	eur	eur	PROPN
ma-167	41	3	.	.	PUNCT
ma-167	42	1	j.	j.	PROPN
ma-167	42	2	math	math	PROPN
ma-167	42	3	.	.	PUNCT
ma-167	43	1	anal	anal	PROPN
ma-167	43	2	.	.	PUNCT
ma-167	44	1	10.28924	10.28924	NUM
ma-167	44	2	/	/	SYM
ma-167	44	3	ada	ada	PROPN
ma-167	44	4	/	/	SYM
ma-167	44	5	ma.3.18	ma.3.18	PROPN
ma-167	44	6	3is	3is	PROPN
ma-167	44	7	called	call	VERB
ma-167	44	8	the	the	DET
ma-167	44	9	normalized	normalize	VERB
ma-167	44	10	duality	duality	NOUN
ma-167	44	11	map	map	NOUN
ma-167	44	12	on	on	ADP
ma-167	44	13	e.	e.	PROPN
ma-167	44	14	where	where	SCONJ
ma-167	44	15	〈	〈	PROPN
ma-167	44	16	,	,	PUNCT
ma-167	44	17	〉	〉	PROPN
ma-167	44	18	denotes	denote	VERB
ma-167	44	19	the	the	DET
ma-167	44	20	generalized	generalized	ADJ
ma-167	44	21	duality	duality	NOUN
ma-167	44	22	pairingbetween	pairingbetween	PROPN
ma-167	44	23	e	e	NOUN
ma-167	44	24	and	and	CCONJ
ma-167	44	25	e∗.in	e∗.in	AUX
ma-167	44	26	a	a	DET
ma-167	44	27	hilbert	hilbert	NOUN
ma-167	44	28	space	space	NOUN
ma-167	44	29	,	,	PUNCT
ma-167	44	30	the	the	DET
ma-167	44	31	normalized	normalize	VERB
ma-167	44	32	duality	duality	NOUN
ma-167	44	33	map	map	NOUN
ma-167	44	34	is	be	AUX
ma-167	44	35	the	the	DET
ma-167	44	36	identity	identity	NOUN
ma-167	44	37	map	map	NOUN
ma-167	44	38	.	.	PUNCT
ma-167	45	1	hence	hence	ADV
ma-167	45	2	,	,	PUNCT
ma-167	45	3	in	in	ADP
ma-167	45	4	hilbert	hilbert	PROPN
ma-167	45	5	spaces	space	NOUN
ma-167	45	6	,	,	PUNCT
ma-167	45	7	monotonicity	monotonicity	NOUN
ma-167	45	8	and	and	CCONJ
ma-167	45	9	accretivity	accretivity	NOUN
ma-167	45	10	coincide	coincide	NOUN
ma-167	45	11	.	.	PUNCT
ma-167	46	1	for	for	ADP
ma-167	46	2	an	an	DET
ma-167	46	3	accretive	accretive	ADJ
ma-167	46	4	-	-	PUNCT
ma-167	46	5	type	type	NOUN
ma-167	46	6	operator	operator	NOUN
ma-167	46	7	a	a	PRON
ma-167	46	8	,	,	PUNCT
ma-167	46	9	solutions	solution	NOUN
ma-167	46	10	of	of	ADP
ma-167	46	11	the	the	DET
ma-167	46	12	equation	equation	NOUN
ma-167	46	13	ax	ax	NOUN
ma-167	46	14	=	=	NOUN
ma-167	46	15	0	0	NUM
ma-167	46	16	,	,	PUNCT
ma-167	46	17	in	in	ADP
ma-167	46	18	many	many	ADJ
ma-167	46	19	cases	case	NOUN
ma-167	46	20	,	,	PUNCT
ma-167	46	21	represent	represent	VERB
ma-167	46	22	the	the	DET
ma-167	46	23	equilibrium	equilibrium	NOUN
ma-167	46	24	state	state	NOUN
ma-167	46	25	of	of	ADP
ma-167	46	26	somedynamical	somedynamical	ADJ
ma-167	46	27	system	system	NOUN
ma-167	46	28	(	(	PUNCT
ma-167	46	29	see	see	VERB
ma-167	46	30	,	,	PUNCT
ma-167	46	31	for	for	ADP
ma-167	46	32	example	example	NOUN
ma-167	46	33	,	,	PUNCT
ma-167	46	34	[	[	X
ma-167	46	35	29	29	NUM
ma-167	46	36	]	]	PUNCT
ma-167	46	37	,	,	PUNCT
ma-167	46	38	page	page	NOUN
ma-167	46	39	116	116	NUM
ma-167	46	40	)	)	PUNCT
ma-167	46	41	.	.	PUNCT
ma-167	47	1	to	to	PART
ma-167	47	2	approximate	approximate	VERB
ma-167	47	3	a	a	DET
ma-167	47	4	solution	solution	NOUN
ma-167	47	5	of	of	ADP
ma-167	47	6	ax	ax	NOUN
ma-167	47	7	=	=	SYM
ma-167	47	8	0	0	NUM
ma-167	47	9	,	,	PUNCT
ma-167	47	10	assumingexistence	assumingexistence	NOUN
ma-167	47	11	,	,	PUNCT
ma-167	47	12	where	where	SCONJ
ma-167	47	13	a	a	DET
ma-167	47	14	:	:	PUNCT
ma-167	47	15	e	e	X
ma-167	47	16	→	→	SYM
ma-167	47	17	e	e	X
ma-167	47	18	is	be	AUX
ma-167	47	19	of	of	ADP
ma-167	47	20	accretive	accretive	ADJ
ma-167	47	21	type	type	NOUN
ma-167	47	22	,	,	PUNCT
ma-167	47	23	browder	browder	NOUN
ma-167	48	1	[	[	X
ma-167	48	2	2	2	NUM
ma-167	48	3	]	]	PUNCT
ma-167	48	4	defined	define	VERB
ma-167	48	5	an	an	DET
ma-167	48	6	operator	operator	NOUN
ma-167	48	7	t	t	NOUN
ma-167	48	8	:	:	PUNCT
ma-167	48	9	e	e	X
ma-167	48	10	→	→	SYM
ma-167	48	11	e	e	X
ma-167	48	12	by	by	ADP
ma-167	48	13	t	t	PROPN
ma-167	48	14	:	:	PUNCT
ma-167	48	15	=	=	SYM
ma-167	49	1	i	i	PRON
ma-167	49	2	−	−	VERB
ma-167	50	1	a	a	X
ma-167	50	2	,	,	PUNCT
ma-167	50	3	where	where	SCONJ
ma-167	50	4	i	i	PRON
ma-167	50	5	is	be	AUX
ma-167	50	6	the	the	DET
ma-167	50	7	identity	identity	NOUN
ma-167	50	8	map	map	NOUN
ma-167	50	9	on	on	ADP
ma-167	50	10	e.	e.	PROPN
ma-167	50	11	he	he	PRON
ma-167	50	12	called	call	VERB
ma-167	50	13	such	such	DET
ma-167	50	14	an	an	DET
ma-167	50	15	operator	operator	NOUN
ma-167	50	16	pseudo-contractive.it	pseudo-contractive.it	NOUN
ma-167	50	17	is	be	AUX
ma-167	50	18	trivial	trivial	ADJ
ma-167	50	19	to	to	PART
ma-167	50	20	observe	observe	VERB
ma-167	50	21	that	that	SCONJ
ma-167	50	22	zeros	zero	NOUN
ma-167	50	23	of	of	ADP
ma-167	50	24	a	a	DET
ma-167	50	25	correspond	correspond	NOUN
ma-167	50	26	to	to	ADP
ma-167	50	27	fixed	fix	VERB
ma-167	50	28	points	point	NOUN
ma-167	50	29	of	of	ADP
ma-167	50	30	t	t	PROPN
ma-167	50	31	.	.	PUNCT
ma-167	51	1	for	for	ADP
ma-167	51	2	lipschitz	lipschitz	VERB
ma-167	51	3	stronglypseudo	stronglypseudo	NOUN
ma-167	51	4	-	-	PUNCT
ma-167	51	5	contractive	contractive	ADJ
ma-167	51	6	maps	map	NOUN
ma-167	51	7	,	,	PUNCT
ma-167	51	8	chidume	chidume	VERB
ma-167	51	9	[	[	X
ma-167	51	10	6	6	NUM
ma-167	51	11	]	]	PUNCT
ma-167	51	12	proved	prove	VERB
ma-167	51	13	the	the	DET
ma-167	51	14	following	follow	VERB
ma-167	51	15	theorem	theorem	ADJ
ma-167	51	16	.	.	PUNCT
ma-167	51	17	theorem	theorem	VERB
ma-167	51	18	1.1	1.1	NUM
ma-167	51	19	.	.	PUNCT
ma-167	52	1	(	(	PUNCT
ma-167	52	2	chidume	chidume	NOUN
ma-167	52	3	,	,	PUNCT
ma-167	52	4	[	[	X
ma-167	52	5	7	7	NUM
ma-167	52	6	]	]	PUNCT
ma-167	52	7	.	.	PUNCT
ma-167	53	1	let	let	VERB
ma-167	53	2	e	e	NOUN
ma-167	53	3	=	=	SYM
ma-167	53	4	lp	lp	PROPN
ma-167	53	5	,	,	PUNCT
ma-167	53	6	2	2	NUM
ma-167	53	7	≤	≤	NOUN
ma-167	53	8	p	p	X
ma-167	53	9	<	<	X
ma-167	53	10	8	8	NUM
ma-167	53	11	,	,	PUNCT
ma-167	53	12	and	and	CCONJ
ma-167	53	13	k	k	PROPN
ma-167	53	14	⊂	⊂	PROPN
ma-167	53	15	e	e	X
ma-167	53	16	be	be	AUX
ma-167	53	17	nonempty	nonempty	ADV
ma-167	53	18	closed	close	VERB
ma-167	53	19	convex	convex	NOUN
ma-167	53	20	and	and	CCONJ
ma-167	53	21	bounded	bound	VERB
ma-167	53	22	.	.	PUNCT
ma-167	54	1	let	let	VERB
ma-167	54	2	t	t	NOUN
ma-167	54	3	:	:	PUNCT
ma-167	54	4	k	k	PROPN
ma-167	54	5	→	→	PUNCT
ma-167	54	6	k	k	X
ma-167	54	7	be	be	AUX
ma-167	54	8	a	a	DET
ma-167	54	9	strongly	strongly	ADV
ma-167	54	10	pseudo	pseudo	NOUN
ma-167	54	11	-	-	ADJ
ma-167	54	12	contractive	contractive	ADJ
ma-167	54	13	and	and	CCONJ
ma-167	54	14	lipschitz	lipschitz	NOUN
ma-167	54	15	map	map	NOUN
ma-167	54	16	.	.	PUNCT
ma-167	55	1	for	for	ADP
ma-167	55	2	arbitrary	arbitrary	ADJ
ma-167	55	3	x0	x0	PROPN
ma-167	55	4	∈	∈	PROPN
ma-167	55	5	k	k	NOUN
ma-167	55	6	,	,	PUNCT
ma-167	55	7	let	let	VERB
ma-167	55	8	a	a	DET
ma-167	55	9	sequence	sequence	NOUN
ma-167	55	10	{	{	PUNCT
ma-167	55	11	xn	xn	NOUN
ma-167	55	12	}	}	PUNCT
ma-167	55	13	be	be	AUX
ma-167	55	14	defined	define	VERB
ma-167	55	15	iteratively	iteratively	ADV
ma-167	55	16	by	by	ADP
ma-167	55	17	xn+1	xn+1	PROPN
ma-167	55	18	=	=	SYM
ma-167	55	19	(	(	PUNCT
ma-167	55	20	1	1	NUM
ma-167	55	21	−	−	NOUN
ma-167	55	22	λn)xn	λn)xn	PRON
ma-167	56	1	+	+	CCONJ
ma-167	56	2	λntxn	λntxn	ADJ
ma-167	56	3	,	,	PUNCT
ma-167	56	4	n	n	X
ma-167	56	5	≥	≥	NOUN
ma-167	56	6	0	0	NUM
ma-167	56	7	,	,	PUNCT
ma-167	56	8	where	where	SCONJ
ma-167	56	9	{	{	PUNCT
ma-167	56	10	λn	λn	NOUN
ma-167	56	11	}	}	PUNCT
ma-167	56	12	⊂	⊂	PROPN
ma-167	56	13	(	(	PUNCT
ma-167	56	14	0	0	NUM
ma-167	56	15	,	,	PUNCT
ma-167	56	16	1	1	NUM
ma-167	56	17	)	)	PUNCT
ma-167	56	18	satisfies	satisfy	VERB
ma-167	56	19	the	the	DET
ma-167	56	20	following	follow	VERB
ma-167	56	21	conditions	condition	NOUN
ma-167	56	22	:	:	PUNCT
ma-167	56	23	,	,	PUNCT
ma-167	56	24	(	(	PUNCT
ma-167	56	25	i	i	NOUN
ma-167	56	26	)	)	PUNCT
ma-167	57	1	∞∑	∞∑	NUM
ma-167	57	2	n=1	n=1	PROPN
ma-167	57	3	λn	λn	PROPN
ma-167	57	4	=	=	NOUN
ma-167	57	5	∞	∞	PROPN
ma-167	57	6	,	,	PUNCT
ma-167	57	7	(	(	PUNCT
ma-167	57	8	i	i	PRON
ma-167	57	9	i	i	PROPN
ma-167	57	10	)	)	PUNCT
ma-167	58	1	∞∑	∞∑	NUM
ma-167	58	2	n=1	n=1	PROPN
ma-167	58	3	λ2n	λ2n	PUNCT
ma-167	58	4	≤	≤	PROPN
ma-167	58	5	∞.	∞.	PROPN
ma-167	58	6	then	then	ADV
ma-167	58	7	{	{	PUNCT
ma-167	58	8	xn	xn	X
ma-167	58	9	}	}	PUNCT
ma-167	58	10	converges	converge	VERB
ma-167	58	11	strongly	strongly	ADV
ma-167	58	12	to	to	ADP
ma-167	58	13	the	the	DET
ma-167	58	14	unique	unique	ADJ
ma-167	58	15	fixed	fix	VERB
ma-167	58	16	point	point	NOUN
ma-167	58	17	of	of	ADP
ma-167	58	18	t	t	PROPN
ma-167	58	19	.	.	PUNCT
ma-167	59	1	by	by	ADP
ma-167	59	2	setting	set	VERB
ma-167	59	3	t	t	NOUN
ma-167	59	4	:	:	PUNCT
ma-167	60	1	=	=	SYM
ma-167	61	1	i	i	PRON
ma-167	61	2	−	−	VERB
ma-167	61	3	a	a	PRON
ma-167	61	4	in	in	ADP
ma-167	61	5	theorem	theorem	NOUN
ma-167	61	6	1.1	1.1	NUM
ma-167	61	7	,	,	PUNCT
ma-167	61	8	the	the	DET
ma-167	61	9	following	follow	VERB
ma-167	61	10	theorem	theorem	NOUN
ma-167	61	11	for	for	ADP
ma-167	61	12	approximating	approximate	VERB
ma-167	61	13	a	a	DET
ma-167	61	14	solution	solution	NOUN
ma-167	61	15	of	of	ADP
ma-167	61	16	ax	ax	NOUN
ma-167	61	17	=	=	NOUN
ma-167	61	18	0	0	NUM
ma-167	61	19	where	where	SCONJ
ma-167	61	20	a	a	PRON
ma-167	61	21	is	be	AUX
ma-167	61	22	a	a	DET
ma-167	61	23	strongly	strongly	ADV
ma-167	61	24	accretive	accretive	ADJ
ma-167	61	25	and	and	CCONJ
ma-167	61	26	bounded	bound	VERB
ma-167	61	27	operator	operator	NOUN
ma-167	61	28	can	can	AUX
ma-167	61	29	be	be	AUX
ma-167	61	30	proved.unfortunately	proved.unfortunately	ADV
ma-167	61	31	,	,	PUNCT
ma-167	61	32	the	the	DET
ma-167	61	33	success	success	NOUN
ma-167	61	34	achieved	achieve	VERB
ma-167	61	35	in	in	ADP
ma-167	61	36	using	use	VERB
ma-167	61	37	geometric	geometric	ADJ
ma-167	61	38	properties	property	NOUN
ma-167	61	39	developed	develop	VERB
ma-167	61	40	from	from	ADP
ma-167	61	41	the	the	DET
ma-167	61	42	mid-1980sto	mid-1980sto	NOUN
ma-167	61	43	early	early	ADJ
ma-167	61	44	1990s	1990	NOUN
ma-167	61	45	in	in	ADP
ma-167	61	46	approximating	approximate	VERB
ma-167	61	47	zeros	zero	NOUN
ma-167	61	48	of	of	ADP
ma-167	61	49	accretive	accretive	ADJ
ma-167	61	50	-	-	PUNCT
ma-167	61	51	type	type	NOUN
ma-167	61	52	mappings	mapping	NOUN
ma-167	61	53	has	have	AUX
ma-167	61	54	not	not	PART
ma-167	61	55	carried	carry	VERB
ma-167	61	56	over	over	ADP
ma-167	61	57	to	to	ADP
ma-167	61	58	approx	approx	NOUN
ma-167	61	59	-	-	PUNCT
ma-167	61	60	imating	imate	VERB
ma-167	61	61	zeros	zero	NOUN
ma-167	61	62	of	of	ADP
ma-167	61	63	monotone	monotone	NOUN
ma-167	61	64	-	-	PUNCT
ma-167	61	65	type	type	NOUN
ma-167	61	66	operators	operator	NOUN
ma-167	61	67	in	in	ADP
ma-167	61	68	general	general	ADJ
ma-167	61	69	banach	banach	NOUN
ma-167	61	70	spaces	space	VERB
ma-167	61	71	.	.	PUNCT
ma-167	62	1	part	part	NOUN
ma-167	62	2	of	of	ADP
ma-167	62	3	the	the	DET
ma-167	62	4	problem	problem	NOUN
ma-167	62	5	is	be	AUX
ma-167	62	6	thatsince	thatsince	NOUN
ma-167	62	7	a	a	DET
ma-167	62	8	maps	map	NOUN
ma-167	62	9	e	e	NOUN
ma-167	62	10	to	to	ADP
ma-167	62	11	e∗	e∗	PROPN
ma-167	62	12	,	,	PUNCT
ma-167	62	13	for	for	ADP
ma-167	62	14	xn	xn	PROPN
ma-167	62	15	∈	∈	PROPN
ma-167	62	16	e	e	PROPN
ma-167	62	17	,	,	PUNCT
ma-167	62	18	axn	axn	PROPN
ma-167	62	19	is	be	AUX
ma-167	62	20	in	in	ADP
ma-167	62	21	e∗.	e∗.	NOUN
ma-167	62	22	consequently	consequently	ADV
ma-167	62	23	,	,	PUNCT
ma-167	62	24	a	a	DET
ma-167	62	25	recursion	recursion	NOUN
ma-167	62	26	formula	formula	NOUN
ma-167	62	27	containing	contain	VERB
ma-167	62	28	xnand	xnand	PROPN
ma-167	62	29	axn	axn	PROPN
ma-167	62	30	may	may	AUX
ma-167	62	31	not	not	PART
ma-167	62	32	be	be	AUX
ma-167	62	33	well	well	ADV
ma-167	62	34	defined	define	VERB
ma-167	62	35	.	.	PUNCT
ma-167	63	1	attempts	attempt	NOUN
ma-167	63	2	have	have	AUX
ma-167	63	3	been	be	AUX
ma-167	63	4	made	make	VERB
ma-167	63	5	to	to	PART
ma-167	63	6	overcome	overcome	VERB
ma-167	63	7	this	this	DET
ma-167	63	8	difficulty	difficulty	NOUN
ma-167	63	9	by	by	ADP
ma-167	63	10	introduc	introduc	PROPN
ma-167	63	11	-	-	PUNCT
ma-167	63	12	ing	ing	NOUN
ma-167	63	13	the	the	DET
ma-167	63	14	inverse	inverse	NOUN
ma-167	63	15	of	of	ADP
ma-167	63	16	the	the	DET
ma-167	63	17	normalized	normalize	VERB
ma-167	63	18	duality	duality	NOUN
ma-167	63	19	mapping	mapping	NOUN
ma-167	63	20	in	in	ADP
ma-167	63	21	the	the	DET
ma-167	63	22	recursion	recursion	NOUN
ma-167	63	23	formulas	formula	NOUN
ma-167	63	24	for	for	ADP
ma-167	63	25	approximating	approximate	VERB
ma-167	63	26	zerosof	zerosof	NOUN
ma-167	63	27	monotone	monotone	NOUN
ma-167	63	28	-	-	PUNCT
ma-167	63	29	type	type	NOUN
ma-167	63	30	mappings.examples	mappings.example	NOUN
ma-167	63	31	chidume	chidume	NOUN
ma-167	63	32	[	[	X
ma-167	63	33	4	4	NUM
ma-167	63	34	]	]	PUNCT
ma-167	63	35	,	,	PUNCT
ma-167	63	36	[	[	X
ma-167	63	37	5	5	NUM
ma-167	63	38	]	]	PUNCT
ma-167	63	39	,	,	PUNCT
ma-167	63	40	moudafi	moudafi	PROPN
ma-167	64	1	[	[	X
ma-167	64	2	18	18	NUM
ma-167	64	3	]	]	PUNCT
ma-167	64	4	,	,	PUNCT
ma-167	64	5	reich	reich	PROPN
ma-167	65	1	[	[	X
ma-167	65	2	21	21	NUM
ma-167	65	3	]	]	PUNCT
ma-167	65	4	,	,	PUNCT
ma-167	65	5	takahashi	takahashi	PROPN
ma-167	66	1	[	[	X
ma-167	66	2	30],zegeye	30],zegeye	NUM
ma-167	66	3	[	[	X
ma-167	66	4	37	37	NUM
ma-167	66	5	]	]	PUNCT
ma-167	66	6	,	,	PUNCT
ma-167	66	7	djitte	djitte	NOUN
ma-167	66	8	[	[	X
ma-167	66	9	17	17	NUM
ma-167	66	10	]	]	PUNCT
ma-167	66	11	,	,	PUNCT
ma-167	66	12	mendy	mendy	X
ma-167	66	13	[	[	PUNCT
ma-167	66	14	[	[	X
ma-167	66	15	15	15	NUM
ma-167	66	16	]	]	PUNCT
ma-167	66	17	,	,	PUNCT
ma-167	66	18	[	[	X
ma-167	66	19	10]]motivated	10]]motivate	VERB
ma-167	66	20	by	by	ADP
ma-167	66	21	approximating	approximate	VERB
ma-167	66	22	zeros	zero	NOUN
ma-167	66	23	of	of	ADP
ma-167	66	24	monotone	monotone	ADJ
ma-167	66	25	mappings	mapping	NOUN
ma-167	66	26	,	,	PUNCT
ma-167	66	27	chidume	chidume	VERB
ma-167	66	28	et	et	PROPN
ma-167	66	29	al	al	PROPN
ma-167	66	30	.	.	PUNCT
ma-167	67	1	[	[	X
ma-167	67	2	8	8	NUM
ma-167	67	3	]	]	PUNCT
ma-167	67	4	proposed	propose	VERB
ma-167	67	5	akrasnoselskii	akrasnoselskii	VERB
ma-167	67	6	-	-	PUNCT
ma-167	67	7	type	type	NOUN
ma-167	67	8	scheme	scheme	NOUN
ma-167	67	9	and	and	CCONJ
ma-167	67	10	proved	prove	VERB
ma-167	67	11	a	a	DET
ma-167	67	12	strong	strong	ADJ
ma-167	67	13	convergence	convergence	NOUN
ma-167	67	14	theorem	theorem	VERB
ma-167	67	15	in	in	ADP
ma-167	67	16	lp	lp	NOUN
ma-167	67	17	,	,	PUNCT
ma-167	67	18	2	2	NUM
ma-167	67	19	≤	≤	NOUN
ma-167	67	20	p	p	NOUN
ma-167	67	21	<	<	X
ma-167	67	22	∞.	∞.	PROPN
ma-167	67	23	in	in	ADP
ma-167	67	24	fact	fact	NOUN
ma-167	67	25	,	,	PUNCT
ma-167	67	26	they	they	PRON
ma-167	67	27	obtained	obtain	VERB
ma-167	67	28	the	the	DET
ma-167	67	29	following	following	ADJ
ma-167	67	30	result	result	NOUN
ma-167	67	31	.	.	PUNCT
ma-167	68	1	theorem	theorem	VERB
ma-167	68	2	1.2	1.2	NUM
ma-167	68	3	.	.	PUNCT
ma-167	69	1	(	(	PUNCT
ma-167	69	2	chidume	chidume	VERB
ma-167	69	3	et	et	PROPN
ma-167	69	4	al	al	PROPN
ma-167	69	5	.	.	PUNCT
ma-167	70	1	[	[	X
ma-167	70	2	8	8	NUM
ma-167	70	3	]	]	PUNCT
ma-167	70	4	)	)	PUNCT
ma-167	70	5	.	.	PUNCT
ma-167	71	1	let	let	VERB
ma-167	71	2	x	x	SYM
ma-167	71	3	=	=	SYM
ma-167	71	4	lp	lp	ADJ
ma-167	71	5	,	,	PUNCT
ma-167	71	6	2	2	NUM
ma-167	71	7	≤	≤	NOUN
ma-167	71	8	p	p	X
ma-167	71	9	<	<	X
ma-167	71	10	∞	∞	PROPN
ma-167	71	11	,	,	PUNCT
ma-167	71	12	and	and	CCONJ
ma-167	71	13	a	a	PRON
ma-167	71	14	:	:	PUNCT
ma-167	71	15	x	x	X
ma-167	71	16	→	→	SYM
ma-167	71	17	x∗	x∗	X
ma-167	71	18	be	be	AUX
ma-167	71	19	a	a	DET
ma-167	71	20	lipschitz	lipschitz	NOUN
ma-167	71	21	map	map	NOUN
ma-167	71	22	.	.	PUNCT
ma-167	72	1	assume	assume	VERB
ma-167	72	2	that	that	SCONJ
ma-167	72	3	there	there	PRON
ma-167	72	4	exists	exist	VERB
ma-167	72	5	a	a	DET
ma-167	72	6	constant	constant	ADJ
ma-167	72	7	k	k	PROPN
ma-167	72	8	∈	∈	PROPN
ma-167	72	9	(	(	PUNCT
ma-167	72	10	0	0	NUM
ma-167	72	11	,	,	PUNCT
ma-167	72	12	1	1	NUM
ma-167	72	13	)	)	PUNCT
ma-167	72	14	such	such	ADJ
ma-167	72	15	that	that	SCONJ
ma-167	72	16	a	a	DET
ma-167	72	17	satisfies	satisfie	NOUN
ma-167	72	18	the	the	DET
ma-167	72	19	condition	condition	NOUN
ma-167	72	20	〈	〈	NOUN
ma-167	72	21	ax	ax	NOUN
ma-167	72	22	−	−	PROPN
ma-167	72	23	ay	ay	NOUN
ma-167	72	24	,	,	PUNCT
ma-167	72	25	x	x	NOUN
ma-167	72	26	−	−	PROPN
ma-167	72	27	y	y	PROPN
ma-167	72	28	〉	〉	PROPN
ma-167	72	29	≥	≥	NOUN
ma-167	72	30	k‖x	k‖x	PROPN
ma-167	72	31	−	−	PROPN
ma-167	73	1	y‖	y‖	PROPN
ma-167	74	1	p	p	PROPN
ma-167	74	2	p−1	p−1	PROPN
ma-167	74	3	(	(	PUNCT
ma-167	74	4	1.4	1.4	NUM
ma-167	74	5	)	)	PUNCT
ma-167	74	6	and	and	CCONJ
ma-167	74	7	that	that	SCONJ
ma-167	74	8	a−1(0	a−1(0	PRON
ma-167	74	9	)	)	PUNCT
ma-167	75	1	6=	6=	ADP
ma-167	75	2	∅.	∅.	VERB
ma-167	75	3	for	for	ADP
ma-167	75	4	arbitrary	arbitrary	ADJ
ma-167	75	5	x1	x1	PROPN
ma-167	75	6	∈	∈	PROPN
ma-167	75	7	x	x	PUNCT
ma-167	75	8	,	,	PUNCT
ma-167	75	9	define	define	VERB
ma-167	75	10	the	the	DET
ma-167	75	11	sequence	sequence	NOUN
ma-167	75	12	{	{	PUNCT
ma-167	75	13	xn	xn	PUNCT
ma-167	75	14	}	}	PUNCT
ma-167	75	15	iteratively	iteratively	ADV
ma-167	75	16	by	by	ADP
ma-167	75	17	xn+1	xn+1	PROPN
ma-167	75	18	=	=	SYM
ma-167	75	19	j−1(jxn	j−1(jxn	PROPN
ma-167	75	20	−	−	PROPN
ma-167	75	21	λnaxn	λnaxn	PROPN
ma-167	75	22	)	)	PUNCT
ma-167	76	1	n	n	PRON
ma-167	76	2	≥	≥	NOUN
ma-167	76	3	0	0	NUM
ma-167	76	4	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	76	5	eur	eur	PROPN
ma-167	76	6	.	.	PUNCT
ma-167	77	1	j.	j.	PROPN
ma-167	77	2	math	math	PROPN
ma-167	77	3	.	.	PUNCT
ma-167	78	1	anal	anal	PROPN
ma-167	78	2	.	.	PUNCT
ma-167	79	1	10.28924	10.28924	NUM
ma-167	79	2	/	/	SYM
ma-167	79	3	ada	ada	PROPN
ma-167	79	4	/	/	SYM
ma-167	79	5	ma.3.18	ma.3.18	NOUN
ma-167	79	6	4	4	NUM
ma-167	79	7	where	where	SCONJ
ma-167	79	8	λn	λn	PROPN
ma-167	79	9	∈	∈	PROPN
ma-167	79	10	(	(	PUNCT
ma-167	79	11	0	0	NUM
ma-167	79	12	,	,	PUNCT
ma-167	79	13	δp	δp	NOUN
ma-167	79	14	)	)	PUNCT
ma-167	79	15	and	and	CCONJ
ma-167	79	16	δp	δp	ADV
ma-167	79	17	is	be	AUX
ma-167	79	18	some	some	DET
ma-167	79	19	positive	positive	ADJ
ma-167	79	20	constant	constant	NOUN
ma-167	79	21	.	.	PUNCT
ma-167	80	1	then	then	ADV
ma-167	80	2	the	the	DET
ma-167	80	3	sequence	sequence	NOUN
ma-167	80	4	{	{	PUNCT
ma-167	80	5	xn	xn	NOUN
ma-167	80	6	}	}	PUNCT
ma-167	80	7	converges	converge	VERB
ma-167	80	8	strongly	strongly	ADV
ma-167	80	9	to	to	ADP
ma-167	80	10	the	the	DET
ma-167	80	11	unique	unique	ADJ
ma-167	80	12	solution	solution	NOUN
ma-167	80	13	of	of	ADP
ma-167	80	14	the	the	DET
ma-167	80	15	equation	equation	NOUN
ma-167	80	16	ax	ax	NOUN
ma-167	80	17	=	=	NOUN
ma-167	80	18	0	0	X
ma-167	80	19	.	.	PUNCT
ma-167	81	1	in	in	ADP
ma-167	81	2	[	[	X
ma-167	81	3	8	8	NUM
ma-167	81	4	]	]	PUNCT
ma-167	81	5	,	,	PUNCT
ma-167	81	6	the	the	DET
ma-167	81	7	authors	author	NOUN
ma-167	81	8	posed	pose	VERB
ma-167	81	9	the	the	DET
ma-167	81	10	following	follow	VERB
ma-167	81	11	open	open	ADJ
ma-167	81	12	problem	problem	NOUN
ma-167	81	13	.	.	PUNCT
ma-167	82	1	if	if	SCONJ
ma-167	82	2	e	e	PROPN
ma-167	82	3	=	=	SYM
ma-167	82	4	lp	lp	PROPN
ma-167	82	5	,	,	PUNCT
ma-167	82	6	2	2	NUM
ma-167	82	7	≤	≤	NOUN
ma-167	82	8	p	p	X
ma-167	82	9	<	<	X
ma-167	82	10	∞	∞	PROPN
ma-167	82	11	,	,	PUNCT
ma-167	82	12	attempts	attempt	VERB
ma-167	82	13	to	to	PART
ma-167	82	14	obtainstrong	obtainstrong	VERB
ma-167	82	15	convergence	convergence	NOUN
ma-167	82	16	of	of	ADP
ma-167	82	17	the	the	DET
ma-167	82	18	krasnoselskii	krasnoselskii	NOUN
ma-167	82	19	-	-	PUNCT
ma-167	82	20	type	type	NOUN
ma-167	82	21	sequence	sequence	NOUN
ma-167	82	22	defined	define	VERB
ma-167	82	23	for	for	ADP
ma-167	82	24	x0	x0	PROPN
ma-167	82	25	∈	∈	PROPN
ma-167	82	26	e	e	X
ma-167	82	27	by	by	ADP
ma-167	82	28	xn+1	xn+1	PROPN
ma-167	82	29	=	=	SYM
ma-167	82	30	j−1(jxn	j−1(jxn	PROPN
ma-167	82	31	−	−	PROPN
ma-167	82	32	λnaxn	λnaxn	PROPN
ma-167	82	33	)	)	PUNCT
ma-167	82	34	n	n	PRON
ma-167	82	35	≥	≥	NOUN
ma-167	82	36	0	0	NUM
ma-167	82	37	to	to	ADP
ma-167	82	38	a	a	DET
ma-167	82	39	solution	solution	NOUN
ma-167	82	40	of	of	ADP
ma-167	82	41	the	the	DET
ma-167	82	42	equation	equation	NOUN
ma-167	82	43	ax	ax	NOUN
ma-167	82	44	=	=	NOUN
ma-167	82	45	0	0	NUM
ma-167	82	46	,	,	PUNCT
ma-167	82	47	where	where	SCONJ
ma-167	82	48	a	a	PRON
ma-167	82	49	is	be	AUX
ma-167	82	50	strongly	strongly	ADV
ma-167	82	51	monotone	monotone	ADJ
ma-167	82	52	and	and	CCONJ
ma-167	82	53	lipschitz	lipschitz	NOUN
ma-167	82	54	,	,	PUNCT
ma-167	82	55	have	have	AUX
ma-167	82	56	notyielded	notyielde	VERB
ma-167	82	57	any	any	DET
ma-167	82	58	positive	positive	ADJ
ma-167	82	59	result.following	result.followe	VERB
ma-167	82	60	the	the	DET
ma-167	82	61	works	work	NOUN
ma-167	82	62	of	of	ADP
ma-167	82	63	chidume	chidume	PROPN
ma-167	82	64	et	et	PROPN
ma-167	82	65	al	al	PROPN
ma-167	83	1	[	[	X
ma-167	83	2	8	8	NUM
ma-167	83	3	]	]	PUNCT
ma-167	83	4	,	,	PUNCT
ma-167	83	5	and	and	CCONJ
ma-167	83	6	motivation	motivation	NOUN
ma-167	83	7	of	of	ADP
ma-167	83	8	finding	find	VERB
ma-167	83	9	the	the	DET
ma-167	83	10	zeros	zero	NOUN
ma-167	83	11	of	of	ADP
ma-167	83	12	the	the	DET
ma-167	83	13	monotonetype	monotonetype	ADJ
ma-167	83	14	mapping	mapping	NOUN
ma-167	83	15	,	,	PUNCT
ma-167	83	16	several	several	ADJ
ma-167	83	17	strong	strong	ADJ
ma-167	83	18	convergence	convergence	NOUN
ma-167	83	19	results	result	NOUN
ma-167	83	20	have	have	AUX
ma-167	83	21	been	be	AUX
ma-167	83	22	established	establish	VERB
ma-167	83	23	by	by	ADP
ma-167	83	24	various	various	ADJ
ma-167	83	25	authors	author	NOUN
ma-167	83	26	(	(	PUNCT
ma-167	83	27	seee.g	seee.g	X
ma-167	83	28	[	[	X
ma-167	83	29	17	17	NUM
ma-167	83	30	]	]	PUNCT
ma-167	83	31	,	,	PUNCT
ma-167	83	32	[	[	X
ma-167	83	33	10	10	NUM
ma-167	83	34	]	]	PUNCT
ma-167	83	35	,	,	PUNCT
ma-167	83	36	[	[	X
ma-167	83	37	15	15	NUM
ma-167	83	38	]	]	PUNCT
ma-167	83	39	,	,	PUNCT
ma-167	84	1	[	[	X
ma-167	84	2	23	23	NUM
ma-167	84	3	]	]	PUNCT
ma-167	84	4	,	,	PUNCT
ma-167	84	5	[	[	X
ma-167	84	6	16]).following	16]).followe	VERB
ma-167	84	7	this	this	DET
ma-167	84	8	great	great	ADJ
ma-167	84	9	work	work	NOUN
ma-167	84	10	,	,	PUNCT
ma-167	84	11	in	in	ADP
ma-167	84	12	2023	2023	NUM
ma-167	84	13	,	,	PUNCT
ma-167	84	14	mendy	mendy	PROPN
ma-167	84	15	[	[	X
ma-167	84	16	16	16	NUM
ma-167	84	17	]	]	PUNCT
ma-167	84	18	constructed	construct	VERB
ma-167	84	19	the	the	DET
ma-167	84	20	following	follow	VERB
ma-167	84	21	two	two	NUM
ma-167	84	22	-	-	PUNCT
ma-167	84	23	step	step	NOUN
ma-167	84	24	proximalalgorithm	proximalalgorithm	NOUN
ma-167	84	25	for	for	ADP
ma-167	84	26	the	the	DET
ma-167	84	27	zero	zero	NUM
ma-167	84	28	point	point	NOUN
ma-167	84	29	of	of	ADP
ma-167	84	30	monotone	monotone	ADJ
ma-167	84	31	mapping	mapping	NOUN
ma-167	84	32	and	and	CCONJ
ma-167	84	33	proof	proof	NOUN
ma-167	84	34	a	a	DET
ma-167	84	35	strong	strong	ADJ
ma-167	84	36	convergency	convergency	NOUN
ma-167	84	37	of	of	ADP
ma-167	84	38	the	the	DET
ma-167	84	39	sequences	sequence	NOUN
ma-167	84	40	{	{	PUNCT
ma-167	84	41	xn	xn	PUNCT
ma-167	84	42	}	}	PUNCT
ma-167	84	43	and	and	CCONJ
ma-167	84	44	{	{	PUNCT
ma-167	84	45	yn	yn	NOUN
ma-167	84	46	}	}	PUNCT
ma-167	84	47	to	to	ADP
ma-167	84	48	a	a	DET
ma-167	84	49	unique	unique	ADJ
ma-167	84	50	point	point	NOUN
ma-167	84	51	x∗	x∗	PROPN
ma-167	84	52	∈	∈	PROPN
ma-167	84	53	a−1(0	a−1(0	PROPN
ma-167	84	54	)	)	PUNCT
ma-167	84	55	.	.	PUNCT
ma-167	85	1	{	{	PUNCT
ma-167	86	1	yn+1	yn+1	PROPN
ma-167	86	2	=	=	SYM
ma-167	86	3	j−1(jxn	j−1(jxn	PROPN
ma-167	86	4	−	−	PROPN
ma-167	86	5	λnaxn	λnaxn	PROPN
ma-167	86	6	)	)	PUNCT
ma-167	86	7	,	,	PUNCT
ma-167	86	8	n	n	PRON
ma-167	86	9	≥	≥	X
ma-167	86	10	0	0	NUM
ma-167	86	11	xn+1	xn+1	PROPN
ma-167	86	12	=	=	SYM
ma-167	86	13	j−1(jyn+1	j−1(jyn+1	NUM
ma-167	86	14	−	−	NOUN
ma-167	86	15	λn+1ayn+1	λn+1ayn+1	NOUN
ma-167	86	16	)	)	PUNCT
ma-167	86	17	,	,	PUNCT
ma-167	86	18	n	n	PRON
ma-167	86	19	≥	≥	NOUN
ma-167	86	20	0	0	NUM
ma-167	86	21	(	(	PUNCT
ma-167	86	22	1.5	1.5	NUM
ma-167	86	23	)	)	PUNCT
ma-167	86	24	in	in	ADP
ma-167	86	25	this	this	DET
ma-167	86	26	paper	paper	NOUN
ma-167	86	27	,	,	PUNCT
ma-167	86	28	we	we	PRON
ma-167	86	29	study	study	VERB
ma-167	86	30	the	the	DET
ma-167	86	31	two	two	NUM
ma-167	86	32	step	step	NOUN
ma-167	86	33	size	size	NOUN
ma-167	86	34	of	of	ADP
ma-167	86	35	the	the	DET
ma-167	86	36	new	new	ADJ
ma-167	86	37	krasnoselskii	krasnoselskii	ADJ
ma-167	86	38	-	-	PUNCT
ma-167	86	39	type	type	NOUN
ma-167	86	40	algorithm	algorithm	NOUN
ma-167	86	41	introduced	introduce	VERB
ma-167	86	42	bysene	bysene	NOUN
ma-167	86	43	et	et	PROPN
ma-167	86	44	al	al	PROPN
ma-167	86	45	.	.	PUNCT
ma-167	87	1	[	[	X
ma-167	87	2	23	23	NUM
ma-167	87	3	]	]	PUNCT
ma-167	87	4	and	and	CCONJ
ma-167	87	5	prove	prove	VERB
ma-167	87	6	a	a	DET
ma-167	87	7	strong	strong	ADJ
ma-167	87	8	convergence	convergence	NOUN
ma-167	87	9	theorem	theorem	VERB
ma-167	87	10	to	to	PART
ma-167	87	11	approximate	approximate	VERB
ma-167	87	12	the	the	DET
ma-167	87	13	unique	unique	ADJ
ma-167	87	14	zero	zero	NUM
ma-167	87	15	of	of	ADP
ma-167	87	16	alipschitz	alipschitz	NOUN
ma-167	87	17	and	and	CCONJ
ma-167	87	18	strongly	strongly	ADV
ma-167	87	19	monotone	monotone	ADJ
ma-167	87	20	mapping	mapping	NOUN
ma-167	87	21	2−uniformly	2−uniformly	ADV
ma-167	87	22	smooth	smooth	ADJ
ma-167	87	23	and	and	CCONJ
ma-167	87	24	convex	convex	VERB
ma-167	87	25	real	real	ADJ
ma-167	87	26	banach	banach	NOUN
ma-167	87	27	space	space	NOUN
ma-167	87	28	for	for	ADP
ma-167	87	29	p	p	PRON
ma-167	87	30	≥	≥	NUM
ma-167	87	31	2	2	NUM
ma-167	87	32	.	.	PUNCT
ma-167	88	1	this	this	DET
ma-167	88	2	class	class	NOUN
ma-167	88	3	of	of	ADP
ma-167	88	4	banach	banach	NOUN
ma-167	88	5	spaces	space	NOUN
ma-167	88	6	contains	contain	VERB
ma-167	88	7	all	all	DET
ma-167	88	8	lp	lp	ADJ
ma-167	88	9	-	-	NOUN
ma-167	88	10	spaces	space	NOUN
ma-167	88	11	,	,	PUNCT
ma-167	88	12	2	2	NUM
ma-167	88	13	≤	≤	NOUN
ma-167	88	14	p	p	X
ma-167	88	15	<	<	X
ma-167	88	16	∞	∞	PROPN
ma-167	88	17	and	and	CCONJ
ma-167	88	18	sobolev	sobolev	ADJ
ma-167	88	19	space	space	NOUN
ma-167	88	20	.	.	PUNCT
ma-167	89	1	thenwe	thenwe	PROPN
ma-167	89	2	apply	apply	VERB
ma-167	89	3	our	our	PRON
ma-167	89	4	results	result	NOUN
ma-167	89	5	to	to	ADP
ma-167	89	6	the	the	DET
ma-167	89	7	convex	convex	PROPN
ma-167	89	8	minimization	minimization	NOUN
ma-167	89	9	problem	problem	NOUN
ma-167	89	10	.	.	PUNCT
ma-167	90	1	finally	finally	ADV
ma-167	90	2	,	,	PUNCT
ma-167	90	3	our	our	PRON
ma-167	90	4	method	method	NOUN
ma-167	90	5	of	of	ADP
ma-167	90	6	proof	proof	NOUN
ma-167	90	7	generalizedand	generalizedand	VERB
ma-167	90	8	extended	extend	VERB
ma-167	90	9	various	various	ADJ
ma-167	90	10	authors	author	NOUN
ma-167	90	11	in	in	ADP
ma-167	90	12	this	this	DET
ma-167	90	13	way	way	NOUN
ma-167	90	14	of	of	ADP
ma-167	90	15	work	work	NOUN
ma-167	90	16	.	.	PUNCT
ma-167	91	1	2	2	X
ma-167	91	2	.	.	X
ma-167	91	3	preliminaries	preliminary	NOUN
ma-167	91	4	let	let	VERB
ma-167	91	5	e	e	PRON
ma-167	91	6	be	be	AUX
ma-167	91	7	a	a	DET
ma-167	91	8	normed	normed	ADJ
ma-167	91	9	linear	linear	ADJ
ma-167	91	10	space	space	NOUN
ma-167	91	11	.	.	PUNCT
ma-167	92	1	e	e	NOUN
ma-167	92	2	is	be	AUX
ma-167	92	3	said	say	VERB
ma-167	92	4	to	to	PART
ma-167	92	5	be	be	AUX
ma-167	92	6	smooth	smooth	ADJ
ma-167	92	7	if	if	SCONJ
ma-167	92	8	lim	lim	PROPN
ma-167	92	9	t→0	t→0	PUNCT
ma-167	92	10	‖x	‖x	NOUN
ma-167	93	1	+	+	CCONJ
ma-167	93	2	ty‖	ty‖	PRON
ma-167	93	3	−	−	PROPN
ma-167	93	4	‖x‖	‖x‖	PROPN
ma-167	93	5	t	t	PROPN
ma-167	93	6	(	(	PUNCT
ma-167	93	7	2.1	2.1	NUM
ma-167	93	8	)	)	PUNCT
ma-167	93	9	exist	exist	VERB
ma-167	93	10	for	for	ADP
ma-167	93	11	each	each	DET
ma-167	93	12	x	x	NOUN
ma-167	93	13	,	,	PUNCT
ma-167	93	14	y	y	PROPN
ma-167	93	15	∈	∈	PROPN
ma-167	93	16	se	se	X
ma-167	93	17	(	(	PUNCT
ma-167	93	18	here	here	ADV
ma-167	93	19	se	se	X
ma-167	93	20	:	:	PUNCT
ma-167	93	21	=	=	SYM
ma-167	93	22	{	{	PUNCT
ma-167	93	23	x	x	PUNCT
ma-167	93	24	∈	∈	PROPN
ma-167	93	25	e	e	NOUN
ma-167	93	26	:	:	PUNCT
ma-167	93	27	||x	||x	NOUN
ma-167	93	28	||	||	PUNCT
ma-167	94	1	=	=	SYM
ma-167	94	2	1	1	X
ma-167	94	3	}	}	PUNCT
ma-167	94	4	is	be	AUX
ma-167	94	5	the	the	DET
ma-167	94	6	unit	unit	NOUN
ma-167	94	7	sphere	sphere	NOUN
ma-167	94	8	of	of	ADP
ma-167	94	9	e	e	NOUN
ma-167	94	10	)	)	PUNCT
ma-167	94	11	.	.	PUNCT
ma-167	95	1	e	e	NOUN
ma-167	95	2	is	be	AUX
ma-167	95	3	said	say	VERB
ma-167	95	4	to	to	PART
ma-167	95	5	beuniformly	beuniformly	ADV
ma-167	95	6	smooth	smooth	VERB
ma-167	95	7	if	if	SCONJ
ma-167	95	8	it	it	PRON
ma-167	95	9	is	be	AUX
ma-167	95	10	smooth	smooth	ADJ
ma-167	95	11	and	and	CCONJ
ma-167	95	12	the	the	DET
ma-167	95	13	limit	limit	NOUN
ma-167	95	14	is	be	AUX
ma-167	95	15	attained	attain	VERB
ma-167	95	16	uniformly	uniformly	ADV
ma-167	95	17	for	for	ADP
ma-167	95	18	each	each	DET
ma-167	95	19	x	x	NOUN
ma-167	95	20	,	,	PUNCT
ma-167	95	21	y	y	PROPN
ma-167	95	22	∈	∈	PROPN
ma-167	95	23	se	se	X
ma-167	95	24	,	,	PUNCT
ma-167	95	25	and	and	CCONJ
ma-167	95	26	e	e	AUX
ma-167	95	27	isfréchet	isfréchet	ADV
ma-167	95	28	differentiable	differentiable	ADJ
ma-167	95	29	if	if	SCONJ
ma-167	95	30	it	it	PRON
ma-167	95	31	is	be	AUX
ma-167	95	32	smooth	smooth	ADJ
ma-167	95	33	and	and	CCONJ
ma-167	95	34	the	the	DET
ma-167	95	35	limit	limit	NOUN
ma-167	95	36	is	be	AUX
ma-167	95	37	attained	attain	VERB
ma-167	95	38	uniformly	uniformly	ADV
ma-167	95	39	for	for	ADP
ma-167	95	40	y	y	PROPN
ma-167	95	41	∈	∈	PROPN
ma-167	95	42	se	se	X
ma-167	95	43	.let	.let	PUNCT
ma-167	96	1	e	e	X
ma-167	96	2	be	be	AUX
ma-167	96	3	a	a	DET
ma-167	96	4	real	real	ADV
ma-167	96	5	normed	normed	ADJ
ma-167	96	6	linear	linear	ADJ
ma-167	96	7	space	space	NOUN
ma-167	96	8	of	of	ADP
ma-167	96	9	dimension	dimension	NOUN
ma-167	96	10	≥	≥	NOUN
ma-167	96	11	2	2	NUM
ma-167	96	12	.	.	PUNCT
ma-167	97	1	the	the	DET
ma-167	97	2	modulus	modulus	NOUN
ma-167	97	3	of	of	ADP
ma-167	97	4	smoothness	smoothness	NOUN
ma-167	97	5	of	of	ADP
ma-167	97	6	e	e	PROPN
ma-167	97	7	,	,	PUNCT
ma-167	97	8	ρe	ρe	INTJ
ma-167	97	9	,	,	PUNCT
ma-167	97	10	isdefined	isdefine	VERB
ma-167	97	11	by	by	ADP
ma-167	97	12	:	:	PUNCT
ma-167	97	13	ρe(τ	ρe(τ	NUM
ma-167	97	14	)	)	PUNCT
ma-167	97	15	:	:	PUNCT
ma-167	98	1	=	=	SYM
ma-167	98	2	sup	sup	INTJ
ma-167	98	3	{	{	PUNCT
ma-167	98	4	‖x	‖x	NOUN
ma-167	98	5	+	+	PUNCT
ma-167	99	1	y‖+	y‖+	ADJ
ma-167	99	2	‖x	‖x	PUNCT
ma-167	99	3	−	−	PROPN
ma-167	99	4	y‖	y‖	NOUN
ma-167	99	5	2	2	NUM
ma-167	99	6	−	−	NOUN
ma-167	99	7	1	1	NUM
ma-167	99	8	:	:	PUNCT
ma-167	99	9	‖x‖	‖x‖	VERB
ma-167	99	10	=	=	SYM
ma-167	99	11	1	1	NUM
ma-167	99	12	,	,	PUNCT
ma-167	99	13	‖y‖	‖y‖	PROPN
ma-167	99	14	=	=	SYM
ma-167	99	15	τ	τ	PROPN
ma-167	99	16	}	}	PUNCT
ma-167	99	17	;	;	PUNCT
ma-167	99	18	τ	τ	X
ma-167	99	19	>	>	X
ma-167	99	20	0	0	PROPN
ma-167	99	21	.	.	PUNCT
ma-167	100	1	a	a	DET
ma-167	100	2	normed	normed	ADJ
ma-167	100	3	linear	linear	ADJ
ma-167	100	4	space	space	NOUN
ma-167	100	5	e	e	NOUN
ma-167	100	6	is	be	AUX
ma-167	100	7	called	call	VERB
ma-167	100	8	uniformly	uniformly	ADV
ma-167	100	9	smooth	smooth	ADJ
ma-167	100	10	if	if	SCONJ
ma-167	100	11	lim	lim	PROPN
ma-167	100	12	τ→0	τ→0	X
ma-167	100	13	ρe(τ	ρe(τ	NUM
ma-167	100	14	)	)	PUNCT
ma-167	100	15	τ	τ	X
ma-167	101	1	=	=	SYM
ma-167	101	2	0	0	PROPN
ma-167	101	3	.	.	PUNCT
ma-167	102	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	102	2	eur	eur	PROPN
ma-167	102	3	.	.	PUNCT
ma-167	103	1	j.	j.	PROPN
ma-167	103	2	math	math	PROPN
ma-167	103	3	.	.	PUNCT
ma-167	104	1	anal	anal	PROPN
ma-167	104	2	.	.	PUNCT
ma-167	105	1	10.28924	10.28924	NUM
ma-167	105	2	/	/	SYM
ma-167	105	3	ada	ada	PROPN
ma-167	105	4	/	/	SYM
ma-167	105	5	ma.3.18	ma.3.18	NOUN
ma-167	105	6	5if	5if	NOUN
ma-167	105	7	there	there	PRON
ma-167	105	8	exist	exist	VERB
ma-167	105	9	a	a	DET
ma-167	105	10	constant	constant	ADJ
ma-167	105	11	c	c	NOUN
ma-167	105	12	>	>	PUNCT
ma-167	105	13	0	0	PUNCT
ma-167	106	1	and	and	CCONJ
ma-167	106	2	a	a	DET
ma-167	106	3	real	real	ADJ
ma-167	106	4	number	number	NOUN
ma-167	106	5	q	q	PUNCT
ma-167	106	6	>	>	X
ma-167	106	7	1	1	NUM
ma-167	106	8	such	such	ADJ
ma-167	106	9	that	that	SCONJ
ma-167	106	10	ρe(τ	ρe(τ	NUM
ma-167	106	11	)	)	PUNCT
ma-167	106	12	≤	≤	NUM
ma-167	106	13	cτq	cτq	NOUN
ma-167	106	14	,	,	PUNCT
ma-167	106	15	then	then	ADV
ma-167	106	16	e	e	PROPN
ma-167	106	17	is	be	AUX
ma-167	106	18	said	say	VERB
ma-167	106	19	tobe	tobe	ADJ
ma-167	106	20	q	q	ADJ
ma-167	106	21	-	-	PUNCT
ma-167	106	22	uniformly	uniformly	ADJ
ma-167	106	23	smooth.a	smooth.a	NOUN
ma-167	106	24	normed	norme	VERB
ma-167	106	25	linear	linear	ADJ
ma-167	106	26	space	space	NOUN
ma-167	106	27	e	e	NOUN
ma-167	106	28	is	be	AUX
ma-167	106	29	said	say	VERB
ma-167	106	30	to	to	PART
ma-167	106	31	be	be	AUX
ma-167	106	32	strictly	strictly	ADV
ma-167	106	33	convex	convex	ADJ
ma-167	107	1	if	if	SCONJ
ma-167	107	2	:	:	PUNCT
ma-167	107	3	‖x‖	‖x‖	PROPN
ma-167	107	4	=	=	SYM
ma-167	107	5	‖y‖	‖y‖	PROPN
ma-167	107	6	=	=	SYM
ma-167	107	7	1	1	NUM
ma-167	107	8	,	,	PUNCT
ma-167	107	9	x	x	SYM
ma-167	107	10	6=	6=	NUM
ma-167	107	11	y	y	PROPN
ma-167	107	12	⇒	⇒	VERB
ma-167	107	13	∥∥∥x	∥∥∥x	PROPN
ma-167	108	1	+	+	CCONJ
ma-167	108	2	y	y	PROPN
ma-167	108	3	2	2	NUM
ma-167	108	4	∥∥∥	∥∥∥	PROPN
ma-167	108	5	<	<	X
ma-167	108	6	1	1	NUM
ma-167	108	7	.	.	PUNCT
ma-167	109	1	the	the	DET
ma-167	109	2	modulus	modulus	NOUN
ma-167	109	3	of	of	ADP
ma-167	109	4	convexity	convexity	NOUN
ma-167	109	5	of	of	ADP
ma-167	109	6	e	e	NOUN
ma-167	109	7	is	be	AUX
ma-167	109	8	the	the	DET
ma-167	109	9	function	function	NOUN
ma-167	109	10	δe	δe	NOUN
ma-167	109	11	:	:	PUNCT
ma-167	109	12	(	(	PUNCT
ma-167	109	13	0	0	NUM
ma-167	109	14	,	,	PUNCT
ma-167	109	15	2]→	2]→	NOUN
ma-167	110	1	[	[	X
ma-167	110	2	0	0	NUM
ma-167	110	3	,	,	PUNCT
ma-167	110	4	1	1	NUM
ma-167	110	5	]	]	PUNCT
ma-167	110	6	defined	define	VERB
ma-167	110	7	by	by	ADP
ma-167	110	8	:	:	PUNCT
ma-167	110	9	δe(ε	δe(ε	NUM
ma-167	110	10	)	)	PUNCT
ma-167	110	11	:	:	PUNCT
ma-167	110	12	=	=	SYM
ma-167	110	13	inf	inf	NOUN
ma-167	110	14	{	{	PUNCT
ma-167	110	15	1−	1−	NUM
ma-167	110	16	1	1	NUM
ma-167	110	17	2	2	NUM
ma-167	110	18	‖x	‖x	NUM
ma-167	110	19	+	+	CCONJ
ma-167	110	20	y‖	y‖	NOUN
ma-167	110	21	:	:	PUNCT
ma-167	111	1	‖x‖	‖x‖	PROPN
ma-167	111	2	=	=	PUNCT
ma-167	111	3	‖y‖	‖y‖	PROPN
ma-167	111	4	=	=	SYM
ma-167	111	5	1	1	NUM
ma-167	111	6	,	,	PUNCT
ma-167	111	7	‖x	‖x	NOUN
ma-167	112	1	−	−	PROPN
ma-167	112	2	y‖	y‖	PROPN
ma-167	112	3	≥	≥	X
ma-167	112	4	ε	ε	PROPN
ma-167	112	5	}	}	PUNCT
ma-167	112	6	.	.	PUNCT
ma-167	113	1	e	e	NOUN
ma-167	113	2	is	be	AUX
ma-167	113	3	uniformly	uniformly	ADV
ma-167	113	4	convex	convex	ADJ
ma-167	113	5	if	if	SCONJ
ma-167	113	6	and	and	CCONJ
ma-167	113	7	only	only	ADV
ma-167	113	8	if	if	SCONJ
ma-167	113	9	δe(ε	δe(ε	NOUN
ma-167	113	10	)	)	PUNCT
ma-167	113	11	>	>	X
ma-167	113	12	0	0	PUNCT
ma-167	114	1	for	for	ADP
ma-167	114	2	every	every	DET
ma-167	114	3	ε	ε	PROPN
ma-167	114	4	∈	∈	PROPN
ma-167	114	5	(	(	PUNCT
ma-167	114	6	0	0	NUM
ma-167	114	7	,	,	PUNCT
ma-167	114	8	2	2	NUM
ma-167	114	9	]	]	PUNCT
ma-167	114	10	.	.	PUNCT
ma-167	115	1	for	for	ADP
ma-167	115	2	p	p	PROPN
ma-167	115	3	>	>	X
ma-167	115	4	1	1	NUM
ma-167	115	5	,	,	PUNCT
ma-167	115	6	e	e	PROPN
ma-167	115	7	is	be	AUX
ma-167	115	8	said	say	VERB
ma-167	115	9	to	to	PART
ma-167	115	10	be	be	AUX
ma-167	115	11	p	p	NOUN
ma-167	115	12	-	-	PUNCT
ma-167	115	13	uniformly	uniformly	ADV
ma-167	115	14	convex	convex	NOUN
ma-167	115	15	if	if	SCONJ
ma-167	115	16	there	there	PRON
ma-167	115	17	exists	exist	VERB
ma-167	115	18	a	a	DET
ma-167	115	19	constant	constant	ADJ
ma-167	115	20	c	c	NOUN
ma-167	115	21	>	>	X
ma-167	115	22	0	0	NUM
ma-167	115	23	such	such	ADJ
ma-167	115	24	that	that	SCONJ
ma-167	115	25	δe(ε	δe(ε	NUM
ma-167	115	26	)	)	PUNCT
ma-167	115	27	≥	≥	NOUN
ma-167	115	28	cεp	cεp	VERB
ma-167	115	29	for	for	ADP
ma-167	115	30	all	all	DET
ma-167	115	31	ε	ε	PROPN
ma-167	115	32	∈	∈	PROPN
ma-167	115	33	(	(	PUNCT
ma-167	115	34	0	0	NUM
ma-167	115	35	,	,	PUNCT
ma-167	115	36	2	2	NUM
ma-167	115	37	]	]	PUNCT
ma-167	115	38	.	.	PUNCT
ma-167	116	1	observethat	observethat	INTJ
ma-167	116	2	every	every	DET
ma-167	116	3	p	p	NOUN
ma-167	116	4	-	-	PUNCT
ma-167	116	5	uniformly	uniformly	ADV
ma-167	116	6	convex	convex	NOUN
ma-167	116	7	space	space	NOUN
ma-167	116	8	is	be	AUX
ma-167	116	9	uniformly	uniformly	ADV
ma-167	116	10	convex.typical	convex.typical	ADJ
ma-167	116	11	examples	example	NOUN
ma-167	116	12	of	of	ADP
ma-167	116	13	such	such	ADJ
ma-167	116	14	spaces	space	NOUN
ma-167	116	15	are	be	AUX
ma-167	116	16	the	the	DET
ma-167	116	17	lp	lp	NOUN
ma-167	116	18	,	,	PUNCT
ma-167	116	19	`	`	PUNCT
ma-167	116	20	p	p	PROPN
ma-167	116	21	and	and	CCONJ
ma-167	116	22	wm	wm	PROPN
ma-167	116	23	p	p	PROPN
ma-167	116	24	spaces	space	VERB
ma-167	116	25	for	for	ADP
ma-167	116	26	1	1	NUM
ma-167	116	27	<	<	X
ma-167	116	28	p	p	X
ma-167	116	29	<	<	X
ma-167	116	30	∞	∞	NUM
ma-167	116	31	where	where	SCONJ
ma-167	116	32	,	,	PUNCT
ma-167	116	33	lp	lp	PROPN
ma-167	116	34	(	(	PUNCT
ma-167	116	35	or	or	CCONJ
ma-167	116	36	lp	lp	NOUN
ma-167	116	37	)	)	PUNCT
ma-167	116	38	or	or	CCONJ
ma-167	116	39	wm	wm	ADP
ma-167	116	40	p	p	NOUN
ma-167	116	41	is	be	AUX
ma-167	116	42	{	{	PUNCT
ma-167	116	43	2−	2−	NUM
ma-167	116	44	uniformly	uniformly	ADV
ma-167	116	45	smooth	smooth	ADJ
ma-167	116	46	and	and	CCONJ
ma-167	116	47	p	p	NOUN
ma-167	116	48	−	−	NOUN
ma-167	116	49	uniformly	uniformly	ADV
ma-167	116	50	convex	convex	NOUN
ma-167	116	51	if	if	SCONJ
ma-167	116	52	2	2	NUM
ma-167	116	53	≤	≤	NOUN
ma-167	116	54	p	p	NOUN
ma-167	116	55	<	<	X
ma-167	116	56	∞	∞	PROPN
ma-167	116	57	;	;	PUNCT
ma-167	116	58	2−	2−	NUM
ma-167	116	59	uniformly	uniformly	ADV
ma-167	116	60	convex	convex	VERB
ma-167	116	61	and	and	CCONJ
ma-167	116	62	p	p	NOUN
ma-167	116	63	−	−	NOUN
ma-167	116	64	uniformly	uniformly	ADV
ma-167	116	65	smooth	smooth	ADJ
ma-167	116	66	if	if	SCONJ
ma-167	116	67	1	1	NUM
ma-167	116	68	<	<	X
ma-167	116	69	p	p	X
ma-167	116	70	<	<	X
ma-167	116	71	2	2	NUM
ma-167	116	72	.	.	NOUN
ma-167	116	73	remark	remark	NOUN
ma-167	116	74	1	1	NUM
ma-167	116	75	.	.	PUNCT
ma-167	117	1	note	note	VERB
ma-167	117	2	also	also	ADV
ma-167	117	3	that	that	SCONJ
ma-167	117	4	duality	duality	NOUN
ma-167	117	5	mapping	mapping	NOUN
ma-167	117	6	exists	exist	VERB
ma-167	117	7	in	in	ADP
ma-167	117	8	each	each	DET
ma-167	117	9	banach	banach	NOUN
ma-167	117	10	space.we	space.we	PRON
ma-167	117	11	recall	recall	VERB
ma-167	117	12	from	from	ADP
ma-167	117	13	[	[	X
ma-167	117	14	11	11	NUM
ma-167	117	15	]	]	PUNCT
ma-167	117	16	someof	someof	NOUN
ma-167	117	17	the	the	DET
ma-167	117	18	examples	example	NOUN
ma-167	117	19	of	of	ADP
ma-167	117	20	this	this	DET
ma-167	117	21	mapping	mapping	NOUN
ma-167	117	22	in	in	ADP
ma-167	117	23	`	`	PUNCT
ma-167	117	24	p	p	X
ma-167	117	25	,	,	PUNCT
ma-167	117	26	lp	lp	ADJ
ma-167	117	27	,	,	PUNCT
ma-167	117	28	wm	wm	PROPN
ma-167	117	29	,	,	PUNCT
ma-167	117	30	p−spaces	p−space	NOUN
ma-167	117	31	,	,	PUNCT
ma-167	117	32	1	1	NUM
ma-167	117	33	<	<	X
ma-167	117	34	p	p	X
ma-167	117	35	<	<	X
ma-167	117	36	∞	∞	NUM
ma-167	117	37	•	•	NOUN
ma-167	117	38	`	`	PUNCT
ma-167	117	39	p	p	X
ma-167	117	40	:	:	PUNCT
ma-167	117	41	jx	jx	PROPN
ma-167	117	42	=	=	PUNCT
ma-167	117	43	‖x‖2−p`p	‖x‖2−p`p	PROPN
ma-167	117	44	y	y	PROPN
ma-167	117	45	∈	∈	PROPN
ma-167	117	46	`	`	PUNCT
ma-167	117	47	q	q	INTJ
ma-167	117	48	,	,	PUNCT
ma-167	117	49	x	x	SYM
ma-167	117	50	=	=	SYM
ma-167	117	51	(	(	PUNCT
ma-167	117	52	x1	x1	PROPN
ma-167	117	53	,	,	PUNCT
ma-167	117	54	x2	x2	PROPN
ma-167	117	55	,	,	PUNCT
ma-167	117	56	...	...	PUNCT
ma-167	117	57	,	,	PUNCT
ma-167	117	58	xn	xn	PROPN
ma-167	117	59	,	,	PUNCT
ma-167	117	60	...	...	PUNCT
ma-167	117	61	)	)	PUNCT
ma-167	117	62	,	,	PUNCT
ma-167	117	63	y	y	PROPN
ma-167	117	64	=	=	PUNCT
ma-167	117	65	(	(	PUNCT
ma-167	117	66	x1|x1|p−2	x1|x1|p−2	PROPN
ma-167	117	67	,	,	PUNCT
ma-167	117	68	x2|x2|p−2	x2|x2|p−2	PROPN
ma-167	117	69	,	,	PUNCT
ma-167	117	70	...	...	PUNCT
ma-167	117	71	,	,	PUNCT
ma-167	117	72	xn|xn|p−2	xn|xn|p−2	PROPN
ma-167	117	73	,	,	PUNCT
ma-167	117	74	...	...	PUNCT
ma-167	117	75	)	)	PUNCT
ma-167	118	1	•	•	X
ma-167	118	2	lp	lp	INTJ
ma-167	118	3	:	:	PUNCT
ma-167	118	4	ju	ju	NOUN
ma-167	118	5	=	=	SYM
ma-167	118	6	‖u‖2−plp	‖u‖2−plp	PROPN
ma-167	118	7	|u|p−2u	|u|p−2u	NOUN
ma-167	118	8	∈	∈	PROPN
ma-167	118	9	lq	lq	VERB
ma-167	118	10	•	•	NOUN
ma-167	118	11	wm	wm	PROPN
ma-167	118	12	,	,	PUNCT
ma-167	118	13	p	p	NOUN
ma-167	118	14	:	:	PUNCT
ma-167	118	15	ju	ju	NOUN
ma-167	118	16	=	=	SYM
ma-167	118	17	‖u‖2−pwm	‖u‖2−pwm	PROPN
ma-167	118	18	,	,	PUNCT
ma-167	118	19	p	p	NOUN
ma-167	118	20	∑	∑	ADV
ma-167	118	21	|α≤m|	|α≤m|	NOUN
ma-167	118	22	(	(	PUNCT
ma-167	118	23	−1)|α|dα(|dαu|p−2dαu	−1)|α|dα(|dαu|p−2dαu	ADJ
ma-167	118	24	)	)	PUNCT
ma-167	118	25	∈	∈	PROPN
ma-167	118	26	w−m	w−m	NOUN
ma-167	118	27	,	,	PUNCT
ma-167	118	28	p	p	NOUN
ma-167	118	29	in	in	ADP
ma-167	118	30	lp	lp	NOUN
ma-167	118	31	,	,	PUNCT
ma-167	118	32	`	`	PUNCT
ma-167	118	33	p	p	PROPN
ma-167	118	34	and	and	CCONJ
ma-167	118	35	wm	wm	PROPN
ma-167	118	36	,	,	PUNCT
ma-167	118	37	p	p	NOUN
ma-167	118	38	spaces	space	VERB
ma-167	118	39	for	for	ADP
ma-167	118	40	1	1	NUM
ma-167	118	41	<	<	X
ma-167	118	42	p	p	X
ma-167	118	43	<	<	X
ma-167	118	44	∞	∞	PROPN
ma-167	118	45	are	be	AUX
ma-167	118	46	q−uniformly	q−uniformly	ADV
ma-167	118	47	smooth	smooth	ADJ
ma-167	118	48	real	real	ADJ
ma-167	118	49	banach	banach	NOUN
ma-167	118	50	spaces	space	VERB
ma-167	118	51	with	with	ADP
ma-167	118	52	q	q	NOUN
ma-167	118	53	,	,	PUNCT
ma-167	118	54	as	as	SCONJ
ma-167	118	55	q	q	NOUN
ma-167	118	56	=	=	SYM
ma-167	118	57	min{2	min{2	NOUN
ma-167	118	58	,	,	PUNCT
ma-167	118	59	p	p	X
ma-167	118	60	}	}	PUNCT
ma-167	118	61	and	and	CCONJ
ma-167	118	62	dq	dq	ADP
ma-167	118	63	≥	≥	NUM
ma-167	118	64	1	1	NUM
ma-167	118	65	(	(	PUNCT
ma-167	118	66	2.2	2.2	NUM
ma-167	118	67	)	)	PUNCT
ma-167	118	68	is	be	AUX
ma-167	118	69	given	give	VERB
ma-167	118	70	by	by	ADP
ma-167	118	71	dq	dq	PROPN
ma-167	118	72	=	=	PUNCT
ma-167	118	73	{	{	PUNCT
ma-167	118	74	1+τq−1	1+τq−1	NUM
ma-167	118	75	(	(	PUNCT
ma-167	118	76	1+τ)q−1	1+τ)q−1	NUM
ma-167	118	77	,	,	PUNCT
ma-167	118	78	i	i	PRON
ma-167	118	79	f	f	NOUN
ma-167	119	1	1	1	NUM
ma-167	119	2	<	<	X
ma-167	119	3	p	p	X
ma-167	119	4	<	<	X
ma-167	119	5	2	2	NUM
ma-167	119	6	;	;	PUNCT
ma-167	119	7	p	p	PRON
ma-167	119	8	−	−	PROPN
ma-167	119	9	1	1	NUM
ma-167	119	10	,	,	PUNCT
ma-167	119	11	i	i	PRON
ma-167	119	12	f	f	NOUN
ma-167	119	13	2	2	NUM
ma-167	119	14	≤	≤	NOUN
ma-167	120	1	p	p	NOUN
ma-167	120	2	<	<	X
ma-167	120	3	∞.	∞.	PROPN
ma-167	120	4	(	(	PUNCT
ma-167	120	5	2.3	2.3	NUM
ma-167	120	6	)	)	PUNCT
ma-167	120	7	and	and	CCONJ
ma-167	120	8	τ(0	τ(0	PROPN
ma-167	120	9	,	,	PUNCT
ma-167	120	10	1	1	NUM
ma-167	120	11	)	)	PUNCT
ma-167	120	12	as	as	ADP
ma-167	120	13	the	the	DET
ma-167	120	14	unique	unique	ADJ
ma-167	120	15	solution	solution	NOUN
ma-167	120	16	of	of	ADP
ma-167	120	17	the	the	DET
ma-167	120	18	equation	equation	NOUN
ma-167	120	19	(	(	PUNCT
ma-167	120	20	q	q	NOUN
ma-167	120	21	−	−	PROPN
ma-167	120	22	2)tq−1	2)tq−1	NUM
ma-167	120	23	+	+	CCONJ
ma-167	120	24	(	(	PUNCT
ma-167	120	25	q	q	PROPN
ma-167	120	26	−	−	PROPN
ma-167	120	27	1)tq−2	1)tq−2	NUM
ma-167	120	28	−	−	NOUN
ma-167	120	29	1	1	NUM
ma-167	120	30	=	=	SYM
ma-167	120	31	0	0	NUM
ma-167	121	1	it	it	PRON
ma-167	121	2	is	be	AUX
ma-167	121	3	well	well	ADV
ma-167	121	4	known	know	VERB
ma-167	121	5	that	that	SCONJ
ma-167	121	6	•	•	NUM
ma-167	121	7	e	e	NOUN
ma-167	121	8	is	be	AUX
ma-167	121	9	smooth	smooth	ADJ
ma-167	121	10	if	if	SCONJ
ma-167	122	1	and	and	CCONJ
ma-167	122	2	only	only	ADV
ma-167	122	3	if	if	SCONJ
ma-167	122	4	j	j	PROPN
ma-167	122	5	is	be	AUX
ma-167	122	6	single	single	ADV
ma-167	122	7	-	-	PUNCT
ma-167	122	8	valued	value	VERB
ma-167	122	9	.	.	PUNCT
ma-167	123	1	•	•	INTJ
ma-167	123	2	if	if	SCONJ
ma-167	123	3	e	e	NOUN
ma-167	123	4	is	be	AUX
ma-167	123	5	uniformly	uniformly	ADV
ma-167	123	6	smooth	smooth	ADJ
ma-167	123	7	then	then	ADV
ma-167	123	8	j	j	PROPN
ma-167	123	9	is	be	AUX
ma-167	123	10	uniformly	uniformly	ADV
ma-167	123	11	continuous	continuous	ADJ
ma-167	123	12	on	on	ADP
ma-167	123	13	bounded	bounded	ADJ
ma-167	123	14	subsets	subset	NOUN
ma-167	123	15	of	of	ADP
ma-167	123	16	e.	e.	PROPN
ma-167	123	17	•	•	PROPN
ma-167	124	1	if	if	SCONJ
ma-167	124	2	e	e	NOUN
ma-167	124	3	is	be	AUX
ma-167	124	4	reflexive	reflexive	ADJ
ma-167	124	5	and	and	CCONJ
ma-167	124	6	strictly	strictly	ADV
ma-167	124	7	convex	convex	VERB
ma-167	124	8	dual	dual	ADV
ma-167	124	9	then	then	ADV
ma-167	124	10	j−1	j−1	PROPN
ma-167	124	11	is	be	AUX
ma-167	124	12	single	single	ADV
ma-167	124	13	-	-	PUNCT
ma-167	124	14	valued	value	VERB
ma-167	124	15	,	,	PUNCT
ma-167	124	16	one	one	NUM
ma-167	124	17	-	-	PUNCT
ma-167	124	18	to	to	ADP
ma-167	124	19	-	-	PUNCT
ma-167	124	20	one	one	NUM
ma-167	124	21	,	,	PUNCT
ma-167	124	22	surjective	surjective	ADJ
ma-167	124	23	,	,	PUNCT
ma-167	124	24	uniformly	uniformly	ADV
ma-167	124	25	continuous	continuous	ADJ
ma-167	124	26	on	on	ADP
ma-167	124	27	bounded	bounded	ADJ
ma-167	124	28	subsets	subset	NOUN
ma-167	124	29	and	and	CCONJ
ma-167	124	30	it	it	PRON
ma-167	124	31	is	be	AUX
ma-167	124	32	the	the	DET
ma-167	124	33	duality	duality	NOUN
ma-167	124	34	mapping	mapping	NOUN
ma-167	124	35	from	from	ADP
ma-167	124	36	e∗	e∗	NOUN
ma-167	124	37	into	into	ADP
ma-167	124	38	e	e	PROPN
ma-167	124	39	and	and	CCONJ
ma-167	124	40	j−1j	j−1j	NOUN
ma-167	124	41	=	=	PUNCT
ma-167	124	42	ie	ie	X
ma-167	124	43	and	and	CCONJ
ma-167	124	44	jj−1	jj−1	PROPN
ma-167	124	45	=	=	PUNCT
ma-167	124	46	ie	ie	X
ma-167	124	47	.	.	PUNCT
ma-167	125	1	•	•	X
ma-167	125	2	j−1	j−1	PROPN
ma-167	125	3	is	be	AUX
ma-167	125	4	uniformly	uniformly	ADV
ma-167	125	5	continuous	continuous	ADJ
ma-167	125	6	if	if	SCONJ
ma-167	125	7	and	and	CCONJ
ma-167	125	8	only	only	ADV
ma-167	125	9	if	if	SCONJ
ma-167	125	10	it	it	PRON
ma-167	125	11	has	have	VERB
ma-167	125	12	a	a	DET
ma-167	125	13	modulus	modulus	NOUN
ma-167	125	14	of	of	ADP
ma-167	125	15	continuity	continuity	NOUN
ma-167	125	16	.	.	PUNCT
ma-167	126	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	126	2	eur	eur	PROPN
ma-167	126	3	.	.	PUNCT
ma-167	127	1	j.	j.	PROPN
ma-167	127	2	math	math	PROPN
ma-167	127	3	.	.	PUNCT
ma-167	128	1	anal	anal	PROPN
ma-167	128	2	.	.	PUNCT
ma-167	129	1	10.28924	10.28924	NUM
ma-167	129	2	/	/	SYM
ma-167	129	3	ada	ada	PROPN
ma-167	129	4	/	/	SYM
ma-167	129	5	ma.3.18	ma.3.18	NOUN
ma-167	129	6	6	6	NUM
ma-167	129	7	lemma	lemma	PROPN
ma-167	129	8	2.1	2.1	NUM
ma-167	129	9	(	(	PUNCT
ma-167	129	10	xu	xu	PROPN
ma-167	130	1	[	[	X
ma-167	130	2	32	32	NUM
ma-167	130	3	]	]	PUNCT
ma-167	130	4	)	)	PUNCT
ma-167	130	5	.	.	PUNCT
ma-167	131	1	.	.	PUNCT
ma-167	132	1	let	let	VERB
ma-167	132	2	q	q	PRON
ma-167	132	3	>	>	X
ma-167	132	4	1	1	NUM
ma-167	132	5	be	be	AUX
ma-167	132	6	a	a	DET
ma-167	132	7	real	real	ADJ
ma-167	132	8	number	number	NOUN
ma-167	132	9	and	and	CCONJ
ma-167	132	10	e	e	NOUN
ma-167	132	11	be	be	AUX
ma-167	132	12	a	a	DET
ma-167	132	13	banach	banach	NOUN
ma-167	132	14	space	space	NOUN
ma-167	132	15	.	.	PUNCT
ma-167	133	1	then	then	ADV
ma-167	133	2	the	the	DET
ma-167	133	3	following	follow	VERB
ma-167	133	4	assertion	assertion	NOUN
ma-167	133	5	are	be	AUX
ma-167	133	6	equivalent	equivalent	ADJ
ma-167	133	7	i	i	PRON
ma-167	133	8	):	):	PUNCT
ma-167	133	9	e	e	NOUN
ma-167	133	10	is	be	AUX
ma-167	133	11	q−uniformly	q−uniformly	ADV
ma-167	133	12	smooth	smooth	PROPN
ma-167	133	13	ii	ii	NOUN
ma-167	133	14	):	):	PUNCT
ma-167	133	15	there	there	PRON
ma-167	133	16	exists	exist	VERB
ma-167	133	17	a	a	DET
ma-167	133	18	constant	constant	ADJ
ma-167	133	19	dn	dn	NOUN
ma-167	133	20	>	>	X
ma-167	133	21	0	0	PROPN
ma-167	133	22	,	,	PUNCT
ma-167	133	23	such	such	ADJ
ma-167	133	24	that	that	PRON
ma-167	133	25	for	for	ADP
ma-167	133	26	all	all	DET
ma-167	133	27	x	x	NOUN
ma-167	133	28	,	,	PUNCT
ma-167	133	29	y	y	PROPN
ma-167	133	30	∈	∈	PROPN
ma-167	133	31	e	e	NOUN
ma-167	133	32	,	,	PUNCT
ma-167	133	33	then	then	ADV
ma-167	133	34	the	the	DET
ma-167	133	35	following	follow	VERB
ma-167	133	36	holds	hold	VERB
ma-167	133	37	‖x	‖x	NOUN
ma-167	133	38	+	+	CCONJ
ma-167	133	39	q‖q	q‖q	NOUN
ma-167	133	40	≤	≤	NUM
ma-167	133	41	‖x‖q	‖x‖q	NOUN
ma-167	133	42	+	+	CCONJ
ma-167	133	43	q〈y	q〈y	PUNCT
ma-167	133	44	,	,	PUNCT
ma-167	133	45	jq(x)〉+	jq(x)〉+	PROPN
ma-167	133	46	dq‖y‖q	dq‖y‖q	PROPN
ma-167	133	47	.	.	PUNCT
ma-167	134	1	(	(	PUNCT
ma-167	134	2	2.4	2.4	NUM
ma-167	134	3	)	)	PUNCT
ma-167	134	4	3	3	NUM
ma-167	134	5	.	.	X
ma-167	134	6	main	main	ADJ
ma-167	134	7	result	result	NOUN
ma-167	134	8	we	we	PRON
ma-167	134	9	now	now	ADV
ma-167	134	10	prove	prove	VERB
ma-167	134	11	the	the	DET
ma-167	134	12	following	follow	VERB
ma-167	134	13	result	result	NOUN
ma-167	134	14	theorem	theorem	VERB
ma-167	134	15	3.1	3.1	NUM
ma-167	134	16	.	.	PUNCT
ma-167	135	1	let	let	VERB
ma-167	135	2	e	e	PRON
ma-167	135	3	be	be	AUX
ma-167	135	4	a	a	DET
ma-167	135	5	2	2	NUM
ma-167	135	6	uniformly	uniformly	ADV
ma-167	135	7	smooth	smooth	ADJ
ma-167	135	8	and	and	CCONJ
ma-167	135	9	convex	convex	VERB
ma-167	135	10	real	real	ADJ
ma-167	135	11	banach	banach	NOUN
ma-167	135	12	space	space	NOUN
ma-167	135	13	and	and	CCONJ
ma-167	135	14	let	let	VERB
ma-167	135	15	a	a	DET
ma-167	135	16	mapping	mapping	NOUN
ma-167	135	17	a	a	DET
ma-167	135	18	:	:	PUNCT
ma-167	135	19	e	e	X
ma-167	135	20	→	→	SYM
ma-167	135	21	e∗	e∗	PROPN
ma-167	135	22	be	be	AUX
ma-167	135	23	lipschitz	lipschitz	NOUN
ma-167	135	24	strongly	strongly	ADV
ma-167	135	25	monotone	monotone	ADJ
ma-167	135	26	such	such	ADJ
ma-167	135	27	that	that	SCONJ
ma-167	135	28	a−1(0	a−1(0	PRON
ma-167	135	29	)	)	PUNCT
ma-167	135	30	6=	6=	ADP
ma-167	135	31	∅.	∅.	VERB
ma-167	135	32	for	for	ADP
ma-167	135	33	an	an	DET
ma-167	135	34	arbitrary	arbitrary	ADJ
ma-167	135	35	(	(	PUNCT
ma-167	135	36	{	{	PUNCT
ma-167	135	37	x1	x1	PROPN
ma-167	135	38	}	}	PUNCT
ma-167	135	39	,	,	PUNCT
ma-167	135	40	{	{	PUNCT
ma-167	135	41	y1	y1	NOUN
ma-167	135	42	}	}	PUNCT
ma-167	135	43	)	)	PUNCT
ma-167	136	1	∈	∈	PROPN
ma-167	137	1	e	e	NOUN
ma-167	137	2	,	,	PUNCT
ma-167	137	3	we	we	PRON
ma-167	137	4	define	define	VERB
ma-167	137	5	the	the	DET
ma-167	137	6	sequences	sequence	NOUN
ma-167	137	7	{	{	PUNCT
ma-167	137	8	xn	xn	NUM
ma-167	137	9	}	}	PUNCT
ma-167	137	10	and	and	CCONJ
ma-167	137	11	{	{	PUNCT
ma-167	137	12	yn	yn	NOUN
ma-167	137	13	}	}	PUNCT
ma-167	137	14	by	by	ADP
ma-167	137	15	{	{	PUNCT
ma-167	137	16	yn	yn	X
ma-167	137	17	=	=	SYM
ma-167	137	18	xn	xn	PROPN
ma-167	137	19	−	−	PROPN
ma-167	137	20	θnj−1(axn	θnj−1(axn	NOUN
ma-167	137	21	)	)	PUNCT
ma-167	137	22	,	,	PUNCT
ma-167	137	23	n	n	X
ma-167	137	24	≥	≥	NUM
ma-167	137	25	1	1	NUM
ma-167	137	26	xn+1	xn+1	X
ma-167	137	27	=	=	SYM
ma-167	137	28	yn	yn	PROPN
ma-167	137	29	−	−	PROPN
ma-167	137	30	λnj−1(ayn	λnj−1(ayn	PROPN
ma-167	137	31	)	)	PUNCT
ma-167	137	32	,	,	PUNCT
ma-167	137	33	n	n	X
ma-167	137	34	≥	≥	NOUN
ma-167	137	35	1	1	NUM
ma-167	137	36	(	(	PUNCT
ma-167	137	37	3.1	3.1	NUM
ma-167	137	38	)	)	PUNCT
ma-167	137	39	where	where	SCONJ
ma-167	137	40	λn	λn	NOUN
ma-167	137	41	and	and	CCONJ
ma-167	137	42	θn	θn	PROPN
ma-167	137	43	are	be	AUX
ma-167	137	44	positive	positive	ADJ
ma-167	137	45	real	real	ADJ
ma-167	137	46	number	number	NOUN
ma-167	137	47	and	and	CCONJ
ma-167	137	48	j	j	PROPN
ma-167	137	49	is	be	AUX
ma-167	137	50	the	the	DET
ma-167	137	51	duality	duality	NOUN
ma-167	137	52	mapping	mapping	NOUN
ma-167	137	53	of	of	ADP
ma-167	137	54	e.	e.	PROPN
ma-167	137	55	letting	letting	PROPN
ma-167	137	56	(	(	PUNCT
ma-167	137	57	λn	λn	NOUN
ma-167	137	58	,	,	PUNCT
ma-167	137	59	θn	θn	NOUN
ma-167	137	60	)	)	PUNCT
ma-167	137	61	∈	∈	PROPN
ma-167	137	62	(	(	PUNCT
ma-167	137	63	0	0	NUM
ma-167	137	64	,	,	PUNCT
ma-167	137	65	1	1	NUM
ma-167	137	66	)	)	PUNCT
ma-167	137	67	,	,	PUNCT
ma-167	137	68	then	then	ADV
ma-167	137	69	{	{	PUNCT
ma-167	137	70	xn	xn	PUNCT
ma-167	137	71	}	}	PUNCT
ma-167	137	72	and	and	CCONJ
ma-167	137	73	{	{	PUNCT
ma-167	137	74	yn	yn	NOUN
ma-167	137	75	}	}	PUNCT
ma-167	137	76	converges	converge	VERB
ma-167	137	77	strongly	strongly	ADV
ma-167	137	78	to	to	ADP
ma-167	137	79	ρ∗	ρ∗	PROPN
ma-167	137	80	,	,	PUNCT
ma-167	137	81	a	a	DET
ma-167	137	82	unique	unique	ADJ
ma-167	137	83	solution	solution	NOUN
ma-167	137	84	of	of	ADP
ma-167	137	85	the	the	DET
ma-167	137	86	equation	equation	NOUN
ma-167	137	87	ax	ax	NOUN
ma-167	137	88	=	=	NOUN
ma-167	137	89	0	0	X
ma-167	137	90	.	.	PUNCT
ma-167	138	1	proof	proof	NOUN
ma-167	138	2	.	.	PUNCT
ma-167	139	1	letting	let	VERB
ma-167	139	2	ρ∗	ρ∗	PROPN
ma-167	139	3	=	=	PUNCT
ma-167	139	4	x∗	x∗	PROPN
ma-167	139	5	∈	∈	PROPN
ma-167	139	6	e	e	X
ma-167	139	7	be	be	AUX
ma-167	139	8	the	the	DET
ma-167	139	9	unique	unique	ADJ
ma-167	139	10	solution	solution	NOUN
ma-167	139	11	of	of	ADP
ma-167	139	12	ax	ax	NOUN
ma-167	139	13	=	=	NOUN
ma-167	139	14	0	0	NUM
ma-167	139	15	.	.	PUNCT
ma-167	140	1	from	from	ADP
ma-167	140	2	inequality	inequality	NOUN
ma-167	140	3	2.4	2.4	NUM
ma-167	140	4	in	in	ADP
ma-167	140	5	lemma	lemma	PROPN
ma-167	140	6	2.1with	2.1with	PROPN
ma-167	140	7	3.1	3.1	NUM
ma-167	140	8	,	,	PUNCT
ma-167	140	9	knowingly	knowingly	ADV
ma-167	140	10	that	that	SCONJ
ma-167	140	11	‖j−1w‖	‖j−1w‖	PROPN
ma-167	140	12	=	=	SYM
ma-167	140	13	‖w‖	‖w‖	PROPN
ma-167	140	14	for	for	ADP
ma-167	140	15	all	all	DET
ma-167	140	16	w	w	PROPN
ma-167	140	17	∈	∈	PROPN
ma-167	140	18	e∗	e∗	NOUN
ma-167	140	19	,	,	PUNCT
ma-167	140	20	then	then	ADV
ma-167	140	21	we	we	PRON
ma-167	140	22	have	have	VERB
ma-167	140	23	the	the	DET
ma-167	140	24	following	follow	VERB
ma-167	140	25	estimates	estimate	NOUN
ma-167	140	26	:	:	PUNCT
ma-167	140	27	‖xn+1	‖xn+1	NUM
ma-167	141	1	−	−	PROPN
ma-167	141	2	ρ∗‖2	ρ∗‖2	PROPN
ma-167	141	3	=	=	SYM
ma-167	141	4	‖yn	‖yn	PROPN
ma-167	141	5	−	−	PROPN
ma-167	141	6	ρ∗	ρ∗	NOUN
ma-167	141	7	−	−	PROPN
ma-167	141	8	λnj−1(ayn)‖2	λnj−1(ayn)‖2	X
ma-167	142	1	=	=	SYM
ma-167	142	2	‖λnj−1(ayn)‖2	‖λnj−1(ayn)‖2	NUM
ma-167	143	1	−	−	NOUN
ma-167	143	2	2〈yn	2〈yn	NUM
ma-167	143	3	−	−	ADP
ma-167	143	4	ρ∗	ρ∗	PROPN
ma-167	143	5	,	,	PUNCT
ma-167	143	6	j(λnj	j(λnj	PROPN
ma-167	143	7	−1(ayn))〉+	−1(ayn))〉+	PROPN
ma-167	143	8	d2‖yn	d2‖yn	PROPN
ma-167	143	9	−	−	PROPN
ma-167	143	10	ρ∗‖2	ρ∗‖2	PROPN
ma-167	143	11	≤	≤	PUNCT
ma-167	143	12	λ2n‖(ayn)‖2	λ2n‖(ayn)‖2	NOUN
ma-167	143	13	−	−	PROPN
ma-167	143	14	2λn〈yn	2λn〈yn	NUM
ma-167	143	15	−	−	PROPN
ma-167	143	16	ρ∗	ρ∗	PROPN
ma-167	143	17	,	,	PUNCT
ma-167	143	18	ayn)〉+	ayn)〉+	PROPN
ma-167	143	19	d2‖yn	d2‖yn	VERB
ma-167	143	20	−	−	PROPN
ma-167	143	21	ρ∗‖2	ρ∗‖2	PROPN
ma-167	143	22	≤	≤	NOUN
ma-167	143	23	λ2nl	λ2nl	PUNCT
ma-167	143	24	2‖yn	2‖yn	NOUN
ma-167	143	25	−	−	PROPN
ma-167	143	26	ρ∗‖2	ρ∗‖2	PROPN
ma-167	143	27	−	−	PROPN
ma-167	143	28	2λnk‖yn	2λnk‖yn	NOUN
ma-167	143	29	−	−	PROPN
ma-167	143	30	ρ∗‖2	ρ∗‖2	PROPN
ma-167	143	31	+	+	CCONJ
ma-167	143	32	d2‖yn	d2‖yn	NOUN
ma-167	143	33	−	−	PROPN
ma-167	143	34	ρ∗‖2	ρ∗‖2	PROPN
ma-167	143	35	=	=	PRON
ma-167	143	36	(	(	PUNCT
ma-167	143	37	λ2nl	λ2nl	X
ma-167	143	38	2	2	NUM
ma-167	143	39	−	−	PROPN
ma-167	143	40	2kλn	2kλn	NUM
ma-167	143	41	+	+	NUM
ma-167	143	42	d2	d2	PROPN
ma-167	143	43	)	)	PUNCT
ma-167	144	1	‖yn	‖yn	PUNCT
ma-167	144	2	−	−	PROPN
ma-167	144	3	ρ∗‖2	ρ∗‖2	PROPN
ma-167	144	4	(	(	PUNCT
ma-167	144	5	3.2	3.2	NUM
ma-167	144	6	)	)	PUNCT
ma-167	144	7	for	for	ADP
ma-167	144	8	the	the	DET
ma-167	144	9	fact	fact	NOUN
ma-167	144	10	that	that	SCONJ
ma-167	144	11	0	0	PUNCT
ma-167	144	12	<	<	X
ma-167	144	13	(	(	PUNCT
ma-167	144	14	λ2nl	λ2nl	X
ma-167	144	15	2	2	NUM
ma-167	144	16	−	−	PROPN
ma-167	144	17	2kλn	2kλn	NUM
ma-167	144	18	+	+	NUM
ma-167	144	19	d2	d2	PROPN
ma-167	144	20	)	)	PUNCT
ma-167	144	21	<	<	X
ma-167	144	22	1	1	NUM
ma-167	144	23	,	,	PUNCT
ma-167	144	24	we	we	PRON
ma-167	144	25	have	have	VERB
ma-167	144	26	the	the	DET
ma-167	144	27	following	follow	VERB
ma-167	144	28	‖xn+1	‖xn+1	PUNCT
ma-167	144	29	−	−	PROPN
ma-167	144	30	ρ∗‖2	ρ∗‖2	PROPN
ma-167	144	31	≤	≤	NUM
ma-167	144	32	δ(λ1)‖yn	δ(λ1)‖yn	PROPN
ma-167	144	33	−	−	PROPN
ma-167	144	34	ρ∗‖2	ρ∗‖2	PROPN
ma-167	144	35	(	(	PUNCT
ma-167	144	36	3.3	3.3	NUM
ma-167	144	37	)	)	PUNCT
ma-167	144	38	where	where	SCONJ
ma-167	144	39	δ(λ1	δ(λ1	NOUN
ma-167	144	40	)	)	PUNCT
ma-167	144	41	=	=	SYM
ma-167	144	42	(	(	PUNCT
ma-167	144	43	λ2nl	λ2nl	X
ma-167	144	44	2	2	NUM
ma-167	144	45	−	−	PROPN
ma-167	144	46	2kλn	2kλn	PROPN
ma-167	144	47	+	+	NUM
ma-167	144	48	d2	d2	PROPN
ma-167	144	49	)	)	PUNCT
ma-167	144	50	.using	.use	VERB
ma-167	144	51	3.1	3.1	NUM
ma-167	144	52	,	,	PUNCT
ma-167	144	53	lipschitz	lipschitz	VERB
ma-167	144	54	property	property	NOUN
ma-167	144	55	of	of	ADP
ma-167	144	56	a	a	PRON
ma-167	144	57	,	,	PUNCT
ma-167	144	58	with	with	ADP
ma-167	144	59	the	the	DET
ma-167	144	60	same	same	ADJ
ma-167	144	61	computational	computational	NOUN
ma-167	144	62	we	we	PRON
ma-167	144	63	have	have	VERB
ma-167	144	64	the	the	DET
ma-167	144	65	following	follow	VERB
ma-167	144	66	:	:	PUNCT
ma-167	144	67	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	144	68	eur	eur	PROPN
ma-167	144	69	.	.	PUNCT
ma-167	145	1	j.	j.	PROPN
ma-167	145	2	math	math	PROPN
ma-167	145	3	.	.	PUNCT
ma-167	146	1	anal	anal	PROPN
ma-167	146	2	.	.	PUNCT
ma-167	147	1	10.28924	10.28924	NUM
ma-167	147	2	/	/	SYM
ma-167	147	3	ada	ada	PROPN
ma-167	147	4	/	/	SYM
ma-167	147	5	ma.3.18	ma.3.18	NOUN
ma-167	147	6	7	7	NUM
ma-167	147	7	‖yn	‖yn	PROPN
ma-167	147	8	−	−	PROPN
ma-167	147	9	ρ∗‖2	ρ∗‖2	PROPN
ma-167	147	10	=	=	SYM
ma-167	147	11	‖xn	‖xn	PROPN
ma-167	147	12	−	−	PROPN
ma-167	147	13	ρ∗	ρ∗	PROPN
ma-167	147	14	−	−	PROPN
ma-167	147	15	θnj−1(axn)‖2	θnj−1(axn)‖2	PROPN
ma-167	147	16	=	=	SYM
ma-167	147	17	‖θnj−1(axn)‖2	‖θnj−1(axn)‖2	NUM
ma-167	148	1	−	−	NOUN
ma-167	148	2	2〈xn	2〈xn	PROPN
ma-167	149	1	−	−	PROPN
ma-167	149	2	ρ∗	ρ∗	PROPN
ma-167	149	3	,	,	PUNCT
ma-167	149	4	j(θnj	j(θnj	VERB
ma-167	149	5	−1(axn))〉+	−1(axn))〉+	PRON
ma-167	149	6	d2‖xn	d2‖xn	PROPN
ma-167	149	7	−	−	PROPN
ma-167	149	8	ρ∗‖2	ρ∗‖2	PROPN
ma-167	149	9	≤	≤	ADV
ma-167	149	10	θ2n‖(axn)‖2	θ2n‖(axn)‖2	PROPN
ma-167	149	11	−	−	PROPN
ma-167	149	12	2θn〈xn	2θn〈xn	NUM
ma-167	149	13	−	−	PROPN
ma-167	149	14	ρ∗	ρ∗	PROPN
ma-167	149	15	,	,	PUNCT
ma-167	149	16	axn)〉+	axn)〉+	PROPN
ma-167	149	17	d2‖xn	d2‖xn	PROPN
ma-167	149	18	−	−	PROPN
ma-167	149	19	ρ∗‖2	ρ∗‖2	PROPN
ma-167	149	20	≤	≤	NOUN
ma-167	149	21	θ2nl	θ2nl	NUM
ma-167	149	22	2‖xn	2‖xn	NUM
ma-167	149	23	−	−	PROPN
ma-167	149	24	ρ∗‖2	ρ∗‖2	PROPN
ma-167	149	25	−	−	PROPN
ma-167	149	26	2θnk‖xn	2θnk‖xn	PROPN
ma-167	150	1	−	−	PROPN
ma-167	150	2	ρ∗‖2	ρ∗‖2	PROPN
ma-167	150	3	+	+	CCONJ
ma-167	151	1	d2‖xn	d2‖xn	PROPN
ma-167	151	2	−	−	PROPN
ma-167	151	3	ρ∗‖2	ρ∗‖2	PROPN
ma-167	151	4	=	=	PRON
ma-167	151	5	(	(	PUNCT
ma-167	151	6	θ2nl	θ2nl	X
ma-167	151	7	2	2	NUM
ma-167	151	8	−	−	PROPN
ma-167	151	9	2kθn	2kθn	NUM
ma-167	151	10	+	+	CCONJ
ma-167	151	11	d2	d2	PROPN
ma-167	151	12	)	)	PUNCT
ma-167	151	13	‖xn	‖xn	PROPN
ma-167	151	14	−	−	PROPN
ma-167	151	15	ρ∗‖2	ρ∗‖2	PROPN
ma-167	151	16	(	(	PUNCT
ma-167	151	17	3.4	3.4	NUM
ma-167	151	18	)	)	PUNCT
ma-167	151	19	again	again	ADV
ma-167	151	20	,	,	PUNCT
ma-167	151	21	with	with	ADP
ma-167	151	22	the	the	DET
ma-167	151	23	fact	fact	NOUN
ma-167	151	24	that	that	SCONJ
ma-167	151	25	0	0	PUNCT
ma-167	151	26	<	<	X
ma-167	151	27	(	(	PUNCT
ma-167	151	28	θ2nl	θ2nl	X
ma-167	151	29	2	2	NUM
ma-167	151	30	−	−	PROPN
ma-167	151	31	2kθn	2kθn	NUM
ma-167	151	32	+	+	CCONJ
ma-167	151	33	d2	d2	PROPN
ma-167	151	34	)	)	PUNCT
ma-167	151	35	<	<	X
ma-167	152	1	1	1	NUM
ma-167	152	2	,	,	PUNCT
ma-167	152	3	we	we	PRON
ma-167	152	4	have	have	VERB
ma-167	152	5	the	the	DET
ma-167	152	6	following	follow	VERB
ma-167	152	7	‖yn	‖yn	PROPN
ma-167	152	8	−	−	PROPN
ma-167	152	9	ρ∗‖2	ρ∗‖2	PROPN
ma-167	152	10	≤	≤	PUNCT
ma-167	153	1	δ(λ2)‖xn	δ(λ2)‖xn	PROPN
ma-167	153	2	−	−	PROPN
ma-167	153	3	ρ∗‖2	ρ∗‖2	PROPN
ma-167	153	4	(	(	PUNCT
ma-167	153	5	3.5	3.5	NUM
ma-167	153	6	)	)	PUNCT
ma-167	153	7	where	where	SCONJ
ma-167	153	8	δ(λ2	δ(λ2	NOUN
ma-167	153	9	)	)	PUNCT
ma-167	153	10	=	=	NOUN
ma-167	153	11	(	(	PUNCT
ma-167	153	12	θ2nl	θ2nl	X
ma-167	153	13	2	2	NUM
ma-167	153	14	−	−	PROPN
ma-167	153	15	2kθn	2kθn	NUM
ma-167	153	16	+	+	CCONJ
ma-167	153	17	d2	d2	PROPN
ma-167	153	18	)	)	PUNCT
ma-167	153	19	putting	put	VERB
ma-167	153	20	3.5	3.5	NUM
ma-167	153	21	in	in	ADP
ma-167	153	22	3.3	3.3	NUM
ma-167	153	23	,	,	PUNCT
ma-167	153	24	we	we	PRON
ma-167	153	25	have	have	VERB
ma-167	153	26	the	the	DET
ma-167	153	27	following	follow	VERB
ma-167	153	28	‖xn+1	‖xn+1	PUNCT
ma-167	153	29	−	−	PROPN
ma-167	153	30	ρ∗‖2	ρ∗‖2	PROPN
ma-167	153	31	≤	≤	ADV
ma-167	153	32	δ(λ1)δ(λ2)‖xn	δ(λ1)δ(λ2)‖xn	PROPN
ma-167	153	33	−	−	PROPN
ma-167	153	34	ρ∗‖2	ρ∗‖2	PROPN
ma-167	153	35	(	(	PUNCT
ma-167	153	36	3.6	3.6	NUM
ma-167	153	37	)	)	PUNCT
ma-167	153	38	‖xn+1	‖xn+1	NUM
ma-167	153	39	−	−	PROPN
ma-167	153	40	ρ∗‖	ρ∗‖	PROPN
ma-167	153	41	≤	≤	PROPN
ma-167	153	42	√	√	PUNCT
ma-167	153	43	δ(λ1)δ(λ2)‖xn	δ(λ1)δ(λ2)‖xn	NUM
ma-167	153	44	−	−	NUM
ma-167	153	45	ρ∗‖	ρ∗‖	PROPN
ma-167	153	46	(	(	PUNCT
ma-167	153	47	3.7	3.7	NUM
ma-167	153	48	)	)	PUNCT
ma-167	153	49	‖xn+1	‖xn+1	NUM
ma-167	153	50	−	−	PROPN
ma-167	153	51	ρ∗‖	ρ∗‖	PROPN
ma-167	153	52	≤	≤	PROPN
ma-167	153	53	µ‖xn	µ‖xn	PROPN
ma-167	153	54	−	−	PROPN
ma-167	153	55	ρ∗‖where	ρ∗‖where	NOUN
ma-167	153	56	µ	µ	NOUN
ma-167	153	57	=	=	PUNCT
ma-167	153	58	√	√	NOUN
ma-167	153	59	δ(λ1)δ(λ2).therefore	δ(λ1)δ(λ2).therefore	ADP
ma-167	153	60	the	the	DET
ma-167	153	61	sequences	sequence	NOUN
ma-167	153	62	{	{	PUNCT
ma-167	153	63	xn	xn	NUM
ma-167	153	64	}	}	PUNCT
ma-167	153	65	and	and	CCONJ
ma-167	153	66	{	{	PUNCT
ma-167	153	67	yn	yn	NOUN
ma-167	153	68	}	}	PUNCT
ma-167	153	69	converges	converge	VERB
ma-167	153	70	strongly	strongly	ADV
ma-167	153	71	to	to	PART
ma-167	153	72	ρ∗.	ρ∗.	VERB
ma-167	153	73	this	this	DET
ma-167	153	74	complete	complete	ADJ
ma-167	153	75	the	the	DET
ma-167	153	76	proof	proof	NOUN
ma-167	153	77	.	.	PUNCT
ma-167	154	1	�	�	PROPN
ma-167	154	2	corollary	corollary	NOUN
ma-167	154	3	3.1	3.1	NUM
ma-167	154	4	.	.	PUNCT
ma-167	155	1	let	let	VERB
ma-167	155	2	e	e	NOUN
ma-167	155	3	=	=	SYM
ma-167	155	4	lp	lp	PROPN
ma-167	155	5	,	,	PUNCT
ma-167	155	6	2	2	NUM
ma-167	155	7	≤	≤	NOUN
ma-167	156	1	p	p	X
ma-167	156	2	<	<	X
ma-167	156	3	∞	∞	PROPN
ma-167	156	4	,	,	PUNCT
ma-167	156	5	and	and	CCONJ
ma-167	156	6	a	a	DET
ma-167	156	7	:	:	PUNCT
ma-167	156	8	e	e	X
ma-167	156	9	→	→	SYM
ma-167	156	10	e∗	e∗	PROPN
ma-167	156	11	be	be	AUX
ma-167	156	12	a	a	DET
ma-167	156	13	lipschitz	lipschitz	NOUN
ma-167	156	14	strongly	strongly	ADV
ma-167	156	15	monotone	monotone	ADJ
ma-167	156	16	mapping	mapping	NOUN
ma-167	156	17	such	such	ADJ
ma-167	156	18	that	that	SCONJ
ma-167	156	19	a−1(0	a−1(0	PRON
ma-167	156	20	)	)	PUNCT
ma-167	156	21	6=	6=	ADP
ma-167	156	22	∅.	∅.	VERB
ma-167	156	23	for	for	ADP
ma-167	156	24	arbitrary	arbitrary	ADJ
ma-167	156	25	(	(	PUNCT
ma-167	156	26	x1	x1	PROPN
ma-167	156	27	,	,	PUNCT
ma-167	156	28	y1	y1	ADJ
ma-167	156	29	)	)	PUNCT
ma-167	156	30	∈	∈	PROPN
ma-167	156	31	e	e	NOUN
ma-167	156	32	,	,	PUNCT
ma-167	156	33	define	define	VERB
ma-167	156	34	the	the	DET
ma-167	156	35	sequence	sequence	NOUN
ma-167	156	36	{	{	PUNCT
ma-167	156	37	xn	xn	PUNCT
ma-167	156	38	}	}	PUNCT
ma-167	156	39	and	and	CCONJ
ma-167	156	40	{	{	PUNCT
ma-167	156	41	yn	yn	NOUN
ma-167	156	42	}	}	PUNCT
ma-167	156	43	iteratively	iteratively	ADV
ma-167	156	44	by	by	ADP
ma-167	156	45	{	{	PUNCT
ma-167	156	46	yn	yn	X
ma-167	156	47	=	=	SYM
ma-167	156	48	xn	xn	PROPN
ma-167	156	49	−	−	PROPN
ma-167	156	50	θnj−1(axn	θnj−1(axn	NOUN
ma-167	156	51	)	)	PUNCT
ma-167	156	52	,	,	PUNCT
ma-167	156	53	n	n	X
ma-167	156	54	≥	≥	NUM
ma-167	156	55	1	1	NUM
ma-167	156	56	xn+1	xn+1	X
ma-167	156	57	=	=	SYM
ma-167	156	58	yn	yn	PROPN
ma-167	156	59	−	−	PROPN
ma-167	156	60	λnj−1(ayn	λnj−1(ayn	PROPN
ma-167	156	61	)	)	PUNCT
ma-167	156	62	,	,	PUNCT
ma-167	156	63	n	n	X
ma-167	156	64	≥	≥	NOUN
ma-167	156	65	1	1	NUM
ma-167	156	66	(	(	PUNCT
ma-167	156	67	3.8	3.8	NUM
ma-167	156	68	)	)	PUNCT
ma-167	156	69	where	where	SCONJ
ma-167	156	70	λn	λn	NOUN
ma-167	156	71	and	and	CCONJ
ma-167	156	72	θn	θn	PROPN
ma-167	156	73	are	be	AUX
ma-167	156	74	positive	positive	ADJ
ma-167	156	75	real	real	ADJ
ma-167	156	76	number	number	NOUN
ma-167	156	77	and	and	CCONJ
ma-167	156	78	j	j	PROPN
ma-167	156	79	is	be	AUX
ma-167	156	80	the	the	DET
ma-167	156	81	duality	duality	NOUN
ma-167	156	82	mapping	mapping	NOUN
ma-167	156	83	of	of	ADP
ma-167	156	84	e.	e.	PROPN
ma-167	156	85	letting	letting	PROPN
ma-167	156	86	(	(	PUNCT
ma-167	156	87	λn	λn	NOUN
ma-167	156	88	,	,	PUNCT
ma-167	156	89	θn	θn	NOUN
ma-167	156	90	)	)	PUNCT
ma-167	156	91	∈	∈	PROPN
ma-167	156	92	(	(	PUNCT
ma-167	156	93	0	0	NUM
ma-167	156	94	,	,	PUNCT
ma-167	156	95	1	1	NUM
ma-167	156	96	)	)	PUNCT
ma-167	156	97	,	,	PUNCT
ma-167	156	98	then	then	ADV
ma-167	156	99	xn	xn	PROPN
ma-167	156	100	and	and	CCONJ
ma-167	156	101	yn	yn	PRON
ma-167	156	102	converges	converge	VERB
ma-167	156	103	strongly	strongly	ADV
ma-167	156	104	to	to	ADP
ma-167	156	105	ρ∗	ρ∗	PROPN
ma-167	156	106	,	,	PUNCT
ma-167	156	107	a	a	DET
ma-167	156	108	unique	unique	ADJ
ma-167	156	109	solution	solution	NOUN
ma-167	156	110	of	of	ADP
ma-167	156	111	the	the	DET
ma-167	156	112	equation	equation	NOUN
ma-167	156	113	ax	ax	NOUN
ma-167	157	1	=	=	NOUN
ma-167	157	2	0	0	X
ma-167	157	3	.	.	PUNCT
ma-167	157	4	proof	proof	NOUN
ma-167	157	5	.	.	PUNCT
ma-167	158	1	since	since	SCONJ
ma-167	158	2	e	e	PROPN
ma-167	158	3	=	=	SYM
ma-167	158	4	lp	lp	PROPN
ma-167	158	5	spaces	space	NOUN
ma-167	158	6	,	,	PUNCT
ma-167	158	7	2	2	NUM
ma-167	158	8	≤	≤	NOUN
ma-167	158	9	p	p	X
ma-167	158	10	<	<	X
ma-167	158	11	∞	∞	PROPN
ma-167	158	12	,	,	PUNCT
ma-167	158	13	are	be	AUX
ma-167	158	14	2−uniformly	2−uniformly	ADV
ma-167	158	15	smooth	smooth	ADJ
ma-167	158	16	and	and	CCONJ
ma-167	158	17	convex	convex	VERB
ma-167	158	18	real	real	ADJ
ma-167	158	19	banach	banach	NOUN
ma-167	158	20	spaces	space	VERB
ma-167	158	21	,	,	PUNCT
ma-167	158	22	then	then	ADV
ma-167	158	23	the	the	DET
ma-167	158	24	proof	proof	NOUN
ma-167	158	25	follows	follow	VERB
ma-167	158	26	from	from	ADP
ma-167	158	27	theorem	theorem	ADJ
ma-167	158	28	3.1	3.1	NUM
ma-167	158	29	.	.	PUNCT
ma-167	158	30	�	�	PROPN
ma-167	158	31	4	4	NUM
ma-167	158	32	.	.	PUNCT
ma-167	158	33	convergence	convergence	NOUN
ma-167	158	34	in	in	ADP
ma-167	158	35	lp	lp	NOUN
ma-167	158	36	,	,	PUNCT
ma-167	158	37	`	`	PUNCT
ma-167	158	38	p	p	NOUN
ma-167	158	39	or	or	CCONJ
ma-167	158	40	wm	wm	PROPN
ma-167	158	41	,	,	PUNCT
ma-167	158	42	p	p	X
ma-167	158	43	,	,	PUNCT
ma-167	158	44	2	2	NUM
ma-167	158	45	≤	≤	NOUN
ma-167	158	46	p	p	PRON
ma-167	158	47	<	<	X
ma-167	158	48	∞	∞	NOUN
ma-167	158	49	theorem	theorem	VERB
ma-167	158	50	4.1	4.1	NUM
ma-167	158	51	.	.	PUNCT
ma-167	159	1	let	let	VERB
ma-167	159	2	e	e	PRON
ma-167	159	3	be	be	AUX
ma-167	159	4	a	a	DET
ma-167	159	5	2	2	NUM
ma-167	159	6	uniformly	uniformly	ADV
ma-167	159	7	smooth	smooth	ADJ
ma-167	159	8	and	and	CCONJ
ma-167	159	9	convex	convex	VERB
ma-167	159	10	real	real	ADJ
ma-167	159	11	banach	banach	NOUN
ma-167	159	12	space	space	NOUN
ma-167	159	13	either	either	CCONJ
ma-167	159	14	lp	lp	ADP
ma-167	159	15	,	,	PUNCT
ma-167	159	16	`	`	PUNCT
ma-167	159	17	p	p	NOUN
ma-167	159	18	or	or	CCONJ
ma-167	159	19	w	w	NOUN
ma-167	159	20	m	m	PROPN
ma-167	159	21	,	,	PUNCT
ma-167	159	22	p	p	X
ma-167	159	23	,	,	PUNCT
ma-167	159	24	2	2	NUM
ma-167	159	25	≤	≤	NOUN
ma-167	160	1	p	p	NOUN
ma-167	160	2	<	<	X
ma-167	160	3	∞	∞	NOUN
ma-167	160	4	with	with	ADP
ma-167	160	5	it	it	PRON
ma-167	160	6	dual	dual	ADJ
ma-167	160	7	e∗.	e∗.	NOUN
ma-167	160	8	let	let	VERB
ma-167	160	9	a	a	DET
ma-167	160	10	mapping	mapping	NOUN
ma-167	160	11	a	a	DET
ma-167	160	12	:	:	PUNCT
ma-167	160	13	e	e	X
ma-167	160	14	→	→	SYM
ma-167	160	15	e∗	e∗	PROPN
ma-167	160	16	be	be	AUX
ma-167	160	17	lipschitz	lipschitz	ADJ
ma-167	160	18	and	and	CCONJ
ma-167	160	19	strongly	strongly	ADV
ma-167	160	20	monotone	monotone	ADJ
ma-167	160	21	such	such	ADJ
ma-167	160	22	that	that	SCONJ
ma-167	160	23	a−1(0	a−1(0	PRON
ma-167	160	24	)	)	PUNCT
ma-167	160	25	6=	6=	ADP
ma-167	160	26	∅.	∅.	VERB
ma-167	160	27	for	for	ADP
ma-167	160	28	an	an	DET
ma-167	160	29	arbitrary	arbitrary	ADJ
ma-167	160	30	(	(	PUNCT
ma-167	160	31	{	{	PUNCT
ma-167	160	32	x1	x1	PROPN
ma-167	160	33	}	}	PUNCT
ma-167	160	34	,	,	PUNCT
ma-167	160	35	{	{	PUNCT
ma-167	160	36	y1	y1	NOUN
ma-167	160	37	}	}	PUNCT
ma-167	160	38	)	)	PUNCT
ma-167	161	1	∈	∈	PROPN
ma-167	162	1	e	e	NOUN
ma-167	162	2	,	,	PUNCT
ma-167	162	3	we	we	PRON
ma-167	162	4	define	define	VERB
ma-167	162	5	the	the	DET
ma-167	162	6	sequences	sequence	NOUN
ma-167	162	7	{	{	PUNCT
ma-167	162	8	xn	xn	NUM
ma-167	162	9	}	}	PUNCT
ma-167	162	10	and	and	CCONJ
ma-167	162	11	{	{	PUNCT
ma-167	162	12	yn	yn	NOUN
ma-167	162	13	}	}	PUNCT
ma-167	162	14	by	by	ADP
ma-167	162	15	3.1	3.1	NUM
ma-167	162	16	converges	converge	NOUN
ma-167	162	17	strongly	strongly	ADV
ma-167	162	18	to	to	ADP
ma-167	162	19	ρ∗	ρ∗	PROPN
ma-167	162	20	,	,	PUNCT
ma-167	162	21	a	a	DET
ma-167	162	22	unique	unique	ADJ
ma-167	162	23	solution	solution	NOUN
ma-167	162	24	of	of	ADP
ma-167	162	25	the	the	DET
ma-167	162	26	equation	equation	NOUN
ma-167	162	27	ax	ax	NOUN
ma-167	162	28	=	=	NOUN
ma-167	162	29	0	0	X
ma-167	162	30	.	.	PUNCT
ma-167	163	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	163	2	eur	eur	PROPN
ma-167	163	3	.	.	PUNCT
ma-167	164	1	j.	j.	PROPN
ma-167	164	2	math	math	PROPN
ma-167	164	3	.	.	PUNCT
ma-167	165	1	anal	anal	PROPN
ma-167	165	2	.	.	PUNCT
ma-167	166	1	10.28924	10.28924	NUM
ma-167	166	2	/	/	SYM
ma-167	166	3	ada	ada	PROPN
ma-167	166	4	/	/	SYM
ma-167	166	5	ma.3.18	ma.3.18	ADJ
ma-167	166	6	8	8	NUM
ma-167	166	7	proof	proof	NOUN
ma-167	166	8	.	.	PUNCT
ma-167	167	1	since	since	SCONJ
ma-167	167	2	lp	lp	NOUN
ma-167	167	3	,	,	PUNCT
ma-167	167	4	`	`	PUNCT
ma-167	167	5	p	p	NOUN
ma-167	167	6	or	or	CCONJ
ma-167	167	7	wm	wm	PROPN
ma-167	167	8	,	,	PUNCT
ma-167	167	9	p	p	X
ma-167	167	10	,	,	PUNCT
ma-167	167	11	2	2	NUM
ma-167	167	12	≤	≤	NOUN
ma-167	167	13	p	p	NOUN
ma-167	167	14	<	<	X
ma-167	167	15	∞	∞	PROPN
ma-167	167	16	are	be	AUX
ma-167	167	17	2−	2−	NUM
ma-167	167	18	uniformly	uniformly	ADV
ma-167	167	19	smooth	smooth	ADJ
ma-167	167	20	banach	banach	NOUN
ma-167	167	21	spaces	space	NOUN
ma-167	167	22	,	,	PUNCT
ma-167	167	23	then	then	ADV
ma-167	167	24	with	with	ADP
ma-167	167	25	thesame	thesame	ADJ
ma-167	167	26	computation	computation	NOUN
ma-167	167	27	in	in	ADP
ma-167	167	28	3.1	3.1	NUM
ma-167	167	29	,	,	PUNCT
ma-167	167	30	the	the	DET
ma-167	167	31	proof	proof	NOUN
ma-167	167	32	follows	follow	VERB
ma-167	167	33	.	.	PUNCT
ma-167	168	1	�	�	PROPN
ma-167	168	2	corollary	corollary	NOUN
ma-167	168	3	4.1	4.1	NUM
ma-167	168	4	.	.	PUNCT
ma-167	169	1	let	let	VERB
ma-167	169	2	e	e	PRON
ma-167	169	3	be	be	AUX
ma-167	169	4	a	a	DET
ma-167	169	5	banach	banach	NOUN
ma-167	169	6	space	space	NOUN
ma-167	169	7	either	either	CCONJ
ma-167	169	8	lp	lp	ADP
ma-167	169	9	,	,	PUNCT
ma-167	169	10	`	`	PUNCT
ma-167	169	11	p	p	NOUN
ma-167	169	12	or	or	CCONJ
ma-167	169	13	wm	wm	PROPN
ma-167	169	14	,	,	PUNCT
ma-167	169	15	p	p	X
ma-167	169	16	,	,	PUNCT
ma-167	169	17	2	2	NUM
ma-167	169	18	≤	≤	NOUN
ma-167	170	1	p	p	NOUN
ma-167	170	2	<	<	X
ma-167	170	3	∞	∞	NOUN
ma-167	170	4	with	with	ADP
ma-167	170	5	it	it	PRON
ma-167	170	6	dual	dual	ADJ
ma-167	170	7	e∗.	e∗.	NOUN
ma-167	170	8	let	let	VERB
ma-167	170	9	a	a	DET
ma-167	170	10	mapping	mapping	NOUN
ma-167	170	11	a	a	DET
ma-167	170	12	:	:	PUNCT
ma-167	170	13	e	e	X
ma-167	170	14	→	→	SYM
ma-167	170	15	e∗	e∗	PROPN
ma-167	170	16	be	be	AUX
ma-167	170	17	lipschitz	lipschitz	ADJ
ma-167	170	18	and	and	CCONJ
ma-167	170	19	strongly	strongly	ADV
ma-167	170	20	monotone	monotone	ADJ
ma-167	170	21	such	such	ADJ
ma-167	170	22	that	that	SCONJ
ma-167	170	23	a−1(0	a−1(0	PRON
ma-167	170	24	)	)	PUNCT
ma-167	170	25	6=	6=	ADP
ma-167	170	26	∅.	∅.	VERB
ma-167	170	27	for	for	ADP
ma-167	170	28	an	an	DET
ma-167	170	29	arbitrary	arbitrary	ADJ
ma-167	170	30	(	(	PUNCT
ma-167	170	31	{	{	PUNCT
ma-167	170	32	x1	x1	PROPN
ma-167	170	33	}	}	PUNCT
ma-167	170	34	,	,	PUNCT
ma-167	170	35	{	{	PUNCT
ma-167	170	36	y1	y1	NOUN
ma-167	170	37	}	}	PUNCT
ma-167	170	38	)	)	PUNCT
ma-167	171	1	∈	∈	PROPN
ma-167	172	1	e	e	NOUN
ma-167	172	2	,	,	PUNCT
ma-167	172	3	we	we	PRON
ma-167	172	4	define	define	VERB
ma-167	172	5	the	the	DET
ma-167	172	6	sequences	sequence	NOUN
ma-167	172	7	{	{	PUNCT
ma-167	172	8	xn	xn	NUM
ma-167	172	9	}	}	PUNCT
ma-167	172	10	and	and	CCONJ
ma-167	172	11	{	{	PUNCT
ma-167	172	12	yn	yn	NOUN
ma-167	172	13	}	}	PUNCT
ma-167	172	14	by	by	ADP
ma-167	172	15	3.1	3.1	NUM
ma-167	172	16	converges	converge	NOUN
ma-167	172	17	strongly	strongly	ADV
ma-167	172	18	to	to	ADP
ma-167	172	19	ρ∗	ρ∗	PROPN
ma-167	172	20	,	,	PUNCT
ma-167	172	21	a	a	DET
ma-167	172	22	unique	unique	ADJ
ma-167	172	23	solution	solution	NOUN
ma-167	172	24	of	of	ADP
ma-167	172	25	the	the	DET
ma-167	172	26	equation	equation	NOUN
ma-167	172	27	ax	ax	NOUN
ma-167	172	28	=	=	NOUN
ma-167	172	29	0	0	X
ma-167	172	30	.	.	PUNCT
ma-167	173	1	proof	proof	NOUN
ma-167	173	2	.	.	PUNCT
ma-167	174	1	since	since	SCONJ
ma-167	174	2	lp	lp	NOUN
ma-167	174	3	,	,	PUNCT
ma-167	174	4	`	`	PUNCT
ma-167	174	5	p	p	NOUN
ma-167	174	6	or	or	CCONJ
ma-167	174	7	wm	wm	PROPN
ma-167	174	8	,	,	PUNCT
ma-167	174	9	p	p	X
ma-167	174	10	,	,	PUNCT
ma-167	174	11	2	2	NUM
ma-167	174	12	≤	≤	NOUN
ma-167	174	13	p	p	NOUN
ma-167	174	14	<	<	X
ma-167	174	15	∞	∞	PROPN
ma-167	174	16	are	be	AUX
ma-167	174	17	2−	2−	NUM
ma-167	174	18	uniformly	uniformly	ADV
ma-167	174	19	smooth	smooth	ADJ
ma-167	174	20	banach	banach	NOUN
ma-167	174	21	spaces	space	NOUN
ma-167	174	22	,	,	PUNCT
ma-167	174	23	then	then	ADV
ma-167	174	24	fromtheorem	fromtheorem	VERB
ma-167	174	25	4.1	4.1	NUM
ma-167	174	26	with	with	ADP
ma-167	174	27	the	the	DET
ma-167	174	28	same	same	ADJ
ma-167	174	29	computation	computation	NOUN
ma-167	174	30	in	in	ADP
ma-167	174	31	3.1	3.1	NUM
ma-167	174	32	,	,	PUNCT
ma-167	174	33	the	the	DET
ma-167	174	34	proof	proof	NOUN
ma-167	174	35	follows	follow	VERB
ma-167	174	36	.	.	PUNCT
ma-167	175	1	�	�	PROPN
ma-167	175	2	5	5	NUM
ma-167	175	3	.	.	PUNCT
ma-167	175	4	application	application	NOUN
ma-167	175	5	to	to	PART
ma-167	175	6	convex	convex	VERB
ma-167	175	7	minimization	minimization	NOUN
ma-167	175	8	problem	problem	NOUN
ma-167	175	9	now	now	ADV
ma-167	175	10	,	,	PUNCT
ma-167	175	11	we	we	PRON
ma-167	175	12	present	present	VERB
ma-167	175	13	a	a	DET
ma-167	175	14	convex	convex	ADJ
ma-167	175	15	minimization	minimization	NOUN
ma-167	175	16	problem	problem	NOUN
ma-167	175	17	for	for	ADP
ma-167	175	18	a	a	DET
ma-167	175	19	convex	convex	NOUN
ma-167	175	20	function	function	NOUN
ma-167	175	21	∇	∇	NOUN
ma-167	175	22	:	:	PUNCT
ma-167	175	23	e	e	X
ma-167	175	24	→	→	SYM
ma-167	175	25	r.the	r.the	DET
ma-167	175	26	following	follow	VERB
ma-167	175	27	results	result	NOUN
ma-167	175	28	are	be	AUX
ma-167	175	29	well	well	ADV
ma-167	175	30	known	know	VERB
ma-167	175	31	.	.	PUNCT
ma-167	176	1	remark	remark	NOUN
ma-167	176	2	2	2	NUM
ma-167	176	3	.	.	PUNCT
ma-167	177	1	let	let	VERB
ma-167	177	2	∆	∆	PROPN
ma-167	177	3	:	:	PUNCT
ma-167	178	1	e	e	X
ma-167	178	2	→	→	SYM
ma-167	178	3	r	r	NOUN
ma-167	178	4	be	be	AUX
ma-167	178	5	a	a	DET
ma-167	178	6	differentiable	differentiable	ADJ
ma-167	178	7	convex	convex	NOUN
ma-167	178	8	function	function	NOUN
ma-167	178	9	and	and	CCONJ
ma-167	178	10	ρ∗	ρ∗	PROPN
ma-167	178	11	∈	∈	PROPN
ma-167	178	12	e	e	NOUN
ma-167	178	13	,	,	PUNCT
ma-167	178	14	then	then	ADV
ma-167	178	15	the	the	DET
ma-167	178	16	point	point	NOUN
ma-167	178	17	ρ∗	ρ∗	PROPN
ma-167	178	18	is	be	AUX
ma-167	178	19	aminimizer	aminimizer	NOUN
ma-167	178	20	of	of	ADP
ma-167	178	21	∇	∇	X
ma-167	178	22	on	on	ADP
ma-167	178	23	e	e	NOUN
ma-167	178	24	if	if	SCONJ
ma-167	178	25	and	and	CCONJ
ma-167	178	26	only	only	ADV
ma-167	178	27	if	if	SCONJ
ma-167	178	28	d∇(ρ∗	d∇(ρ∗	ADV
ma-167	178	29	)	)	PUNCT
ma-167	178	30	=	=	SYM
ma-167	179	1	0	0	X
ma-167	179	2	.	.	PUNCT
ma-167	180	1	definition	definition	NOUN
ma-167	180	2	5.1	5.1	NUM
ma-167	180	3	.	.	PUNCT
ma-167	181	1	a	a	DET
ma-167	181	2	function	function	NOUN
ma-167	181	3	∇	∇	NOUN
ma-167	181	4	:	:	PUNCT
ma-167	181	5	e	e	X
ma-167	181	6	→	→	SYM
ma-167	181	7	r	r	NOUN
ma-167	181	8	is	be	AUX
ma-167	181	9	said	say	VERB
ma-167	181	10	to	to	PART
ma-167	181	11	be	be	AUX
ma-167	181	12	strongly	strongly	ADV
ma-167	181	13	convex	convex	ADJ
ma-167	181	14	if	if	SCONJ
ma-167	181	15	there	there	PRON
ma-167	181	16	exists	exist	VERB
ma-167	181	17	γ	γ	X
ma-167	181	18	>	>	X
ma-167	181	19	0	0	NUM
ma-167	181	20	such	such	ADJ
ma-167	181	21	thatthe	thatthe	NOUN
ma-167	181	22	following	follow	VERB
ma-167	181	23	condition	condition	NOUN
ma-167	181	24	holds	hold	VERB
ma-167	181	25	:	:	PUNCT
ma-167	182	1	∇(βx	∇(βx	X
ma-167	182	2	+	+	CCONJ
ma-167	182	3	(	(	PUNCT
ma-167	182	4	1−	1−	NUM
ma-167	182	5	β)y	β)y	SYM
ma-167	182	6	)	)	PUNCT
ma-167	182	7	≤	≤	NUM
ma-167	182	8	β∇x	β∇x	PUNCT
ma-167	183	1	+	+	CCONJ
ma-167	183	2	(	(	PUNCT
ma-167	183	3	1−	1−	NUM
ma-167	183	4	β)∇y	β)∇y	NOUN
ma-167	183	5	−	−	PROPN
ma-167	183	6	γ‖x	γ‖x	CCONJ
ma-167	183	7	−	−	PROPN
ma-167	183	8	y‖2	y‖2	PROPN
ma-167	183	9	(	(	PUNCT
ma-167	183	10	5.1	5.1	NUM
ma-167	183	11	)	)	PUNCT
ma-167	183	12	for	for	ADP
ma-167	183	13	every	every	DET
ma-167	183	14	x	x	PROPN
ma-167	183	15	,	,	PUNCT
ma-167	183	16	y	y	PROPN
ma-167	183	17	∈	∈	PROPN
ma-167	183	18	e	e	X
ma-167	183	19	with	with	ADP
ma-167	183	20	x	x	SYM
ma-167	183	21	6=	6=	PROPN
ma-167	183	22	y	y	PROPN
ma-167	183	23	and	and	CCONJ
ma-167	183	24	β	β	X
ma-167	183	25	∈	∈	PROPN
ma-167	183	26	(	(	PUNCT
ma-167	183	27	0	0	NUM
ma-167	183	28	,	,	PUNCT
ma-167	183	29	1	1	NUM
ma-167	183	30	)	)	PUNCT
ma-167	183	31	,	,	PUNCT
ma-167	183	32	lemma	lemma	PROPN
ma-167	183	33	5.2	5.2	NUM
ma-167	183	34	.	.	PUNCT
ma-167	184	1	let	let	VERB
ma-167	184	2	e	e	PRON
ma-167	184	3	be	be	AUX
ma-167	184	4	normed	norme	VERB
ma-167	184	5	linear	linear	ADJ
ma-167	184	6	space	space	NOUN
ma-167	184	7	and∇	and∇	X
ma-167	184	8	:	:	PUNCT
ma-167	185	1	e	e	X
ma-167	185	2	→	→	PUNCT
ma-167	185	3	r	r	NOUN
ma-167	185	4	a	a	DET
ma-167	185	5	convex	convex	ADJ
ma-167	185	6	differentiable	differentiable	ADJ
ma-167	185	7	function	function	NOUN
ma-167	185	8	.	.	PUNCT
ma-167	186	1	suppose	suppose	VERB
ma-167	186	2	that	that	SCONJ
ma-167	186	3	∇	∇	PROPN
ma-167	186	4	is	be	AUX
ma-167	186	5	strongly	strongly	ADV
ma-167	186	6	convex	convex	ADJ
ma-167	186	7	.	.	PUNCT
ma-167	187	1	then	then	ADV
ma-167	187	2	the	the	DET
ma-167	187	3	differential	differential	ADJ
ma-167	187	4	map	map	NOUN
ma-167	187	5	d∇	d∇	PROPN
ma-167	187	6	:	:	PUNCT
ma-167	187	7	e	e	X
ma-167	187	8	→	→	SYM
ma-167	187	9	e∗	e∗	PROPN
ma-167	187	10	is	be	AUX
ma-167	187	11	strongly	strongly	ADV
ma-167	187	12	monotone	monotone	ADJ
ma-167	187	13	,	,	PUNCT
ma-167	187	14	i.e.	i.e.	X
ma-167	187	15	,	,	PUNCT
ma-167	187	16	there	there	PRON
ma-167	187	17	exists	exist	VERB
ma-167	187	18	k	k	PROPN
ma-167	187	19	>	>	X
ma-167	187	20	0	0	NUM
ma-167	188	1	such	such	ADJ
ma-167	188	2	that	that	SCONJ
ma-167	188	3	〈	〈	PROPN
ma-167	188	4	d∇x	d∇x	PROPN
ma-167	188	5	−	−	PROPN
ma-167	188	6	d∇y	d∇y	PROPN
ma-167	188	7	,	,	PUNCT
ma-167	188	8	x	x	PUNCT
ma-167	188	9	−	−	PROPN
ma-167	188	10	y	y	PROPN
ma-167	188	11	〉	〉	PROPN
ma-167	188	12	≥	≥	NOUN
ma-167	188	13	k‖x	k‖x	NOUN
ma-167	188	14	−	−	PROPN
ma-167	188	15	y‖2	y‖2	X
ma-167	188	16	∀	∀	X
ma-167	188	17	x	x	X
ma-167	188	18	,	,	PUNCT
ma-167	188	19	y	y	PROPN
ma-167	188	20	∈	∈	PROPN
ma-167	188	21	e.	e.	PROPN
ma-167	188	22	(	(	PUNCT
ma-167	188	23	5.2	5.2	NUM
ma-167	188	24	)	)	PUNCT
ma-167	188	25	now	now	ADV
ma-167	188	26	we	we	PRON
ma-167	188	27	present	present	VERB
ma-167	188	28	the	the	DET
ma-167	188	29	following	follow	VERB
ma-167	188	30	result	result	NOUN
ma-167	188	31	.	.	PUNCT
ma-167	189	1	theorem	theorem	VERB
ma-167	189	2	5.3	5.3	NUM
ma-167	189	3	.	.	PUNCT
ma-167	190	1	let	let	VERB
ma-167	190	2	d∇	d∇	PROPN
ma-167	190	3	:	:	PUNCT
ma-167	190	4	e∗	e∗	PROPN
ma-167	190	5	→	→	SYM
ma-167	190	6	e	e	AUX
ma-167	190	7	be	be	AUX
ma-167	190	8	a	a	DET
ma-167	190	9	l	l	NOUN
ma-167	190	10	-	-	ADJ
ma-167	190	11	lipschitz	lipschitz	ADJ
ma-167	190	12	continuous	continuous	ADJ
ma-167	190	13	and	and	CCONJ
ma-167	190	14	strongly	strongly	ADV
ma-167	190	15	monotone	monotone	ADJ
ma-167	190	16	mapping	mapping	NOUN
ma-167	190	17	such	such	ADJ
ma-167	190	18	that	that	DET
ma-167	190	19	d∇−1(0	d∇−1(0	NOUN
ma-167	190	20	)	)	PUNCT
ma-167	190	21	6=	6=	ADP
ma-167	190	22	∅.	∅.	ADV
ma-167	190	23	let	let	VERB
ma-167	190	24	e	e	NOUN
ma-167	190	25	=	=	SYM
ma-167	190	26	lp	lp	PROPN
ma-167	190	27	,	,	PUNCT
ma-167	190	28	p	p	PRON
ma-167	190	29	≥	≥	NUM
ma-167	190	30	2	2	NUM
ma-167	190	31	and	and	CCONJ
ma-167	190	32	∇	∇	X
ma-167	190	33	:	:	PUNCT
ma-167	190	34	e	e	X
ma-167	190	35	→	→	SYM
ma-167	190	36	r	r	NOUN
ma-167	190	37	be	be	AUX
ma-167	190	38	a	a	DET
ma-167	190	39	differentiable	differentiable	ADJ
ma-167	190	40	,	,	PUNCT
ma-167	190	41	strongly	strongly	ADV
ma-167	190	42	convex	convex	VERB
ma-167	190	43	real	real	ADV
ma-167	190	44	-	-	PUNCT
ma-167	190	45	valued	value	VERB
ma-167	190	46	function	function	NOUN
ma-167	190	47	.	.	PUNCT
ma-167	191	1	for	for	ADP
ma-167	191	2	given	give	VERB
ma-167	191	3	x1	x1	PROPN
ma-167	191	4	,	,	PUNCT
ma-167	191	5	y1	y1	PROPN
ma-167	191	6	∈	∈	PROPN
ma-167	191	7	e	e	NOUN
ma-167	191	8	,	,	PUNCT
ma-167	191	9	define	define	VERB
ma-167	191	10	the	the	DET
ma-167	191	11	sequence	sequence	NOUN
ma-167	191	12	{	{	PUNCT
ma-167	191	13	xn	xn	PUNCT
ma-167	191	14	}	}	PUNCT
ma-167	191	15	and	and	CCONJ
ma-167	191	16	{	{	PUNCT
ma-167	191	17	yn	yn	NOUN
ma-167	191	18	}	}	PUNCT
ma-167	191	19	as	as	SCONJ
ma-167	191	20	follows	follow	VERB
ma-167	191	21	:	:	PUNCT
ma-167	191	22	{	{	PUNCT
ma-167	191	23	yn	yn	X
ma-167	191	24	=	=	PUNCT
ma-167	191	25	xn	xn	PROPN
ma-167	192	1	−	−	PROPN
ma-167	192	2	θnd∇xn	θnd∇xn	NOUN
ma-167	192	3	)	)	PUNCT
ma-167	192	4	,	,	PUNCT
ma-167	192	5	n	n	PRON
ma-167	192	6	≥	≥	NUM
ma-167	192	7	1	1	NUM
ma-167	192	8	xn+1	xn+1	X
ma-167	192	9	=	=	SYM
ma-167	192	10	yn	yn	PROPN
ma-167	192	11	−	−	PROPN
ma-167	192	12	λnd∇yn	λnd∇yn	PROPN
ma-167	192	13	)	)	PUNCT
ma-167	192	14	,	,	PUNCT
ma-167	192	15	n	n	X
ma-167	192	16	≥	≥	NOUN
ma-167	192	17	1	1	NUM
ma-167	192	18	(	(	PUNCT
ma-167	192	19	5.3	5.3	NUM
ma-167	192	20	)	)	PUNCT
ma-167	192	21	where	where	SCONJ
ma-167	192	22	the	the	DET
ma-167	192	23	sequences	sequence	NOUN
ma-167	192	24	{	{	PUNCT
ma-167	192	25	λn	λn	NOUN
ma-167	192	26	}	}	PUNCT
ma-167	192	27	and	and	CCONJ
ma-167	192	28	{	{	PUNCT
ma-167	192	29	θn	θn	NOUN
ma-167	192	30	}	}	PUNCT
ma-167	192	31	,	,	PUNCT
ma-167	192	32	are	be	AUX
ma-167	192	33	in	in	ADP
ma-167	192	34	the	the	DET
ma-167	192	35	interval	interval	NOUN
ma-167	192	36	[	[	X
ma-167	192	37	0	0	NUM
ma-167	192	38	,	,	PUNCT
ma-167	192	39	1	1	NUM
ma-167	192	40	]	]	PUNCT
ma-167	192	41	.	.	PUNCT
ma-167	193	1	then	then	ADV
ma-167	193	2	∇	∇	PROPN
ma-167	193	3	has	have	VERB
ma-167	193	4	a	a	DET
ma-167	193	5	unique	unique	ADJ
ma-167	193	6	minimizer	minimizer	NOUN
ma-167	193	7	ρ∗	ρ∗	PROPN
ma-167	193	8	∈	∈	PROPN
ma-167	193	9	e	e	NOUN
ma-167	193	10	such	such	ADJ
ma-167	193	11	that	that	SCONJ
ma-167	193	12	if	if	SCONJ
ma-167	193	13	(	(	PUNCT
ma-167	193	14	λn	λn	NOUN
ma-167	193	15	,	,	PUNCT
ma-167	193	16	θn	θn	ADJ
ma-167	193	17	)	)	PUNCT
ma-167	193	18	∈	∈	PROPN
ma-167	194	1	[	[	X
ma-167	194	2	0	0	NUM
ma-167	194	3	,	,	PUNCT
ma-167	194	4	1	1	NUM
ma-167	194	5	]	]	PUNCT
ma-167	194	6	,	,	PUNCT
ma-167	194	7	the	the	DET
ma-167	194	8	sequence	sequence	NOUN
ma-167	194	9	{	{	PUNCT
ma-167	194	10	xn	xn	PUNCT
ma-167	194	11	}	}	PUNCT
ma-167	194	12	and	and	CCONJ
ma-167	194	13	{	{	PUNCT
ma-167	194	14	yn	yn	NOUN
ma-167	194	15	}	}	PUNCT
ma-167	194	16	converges	converge	VERB
ma-167	194	17	strongly	strongly	ADV
ma-167	194	18	to	to	PART
ma-167	194	19	ρ∗.	ρ∗.	VERB
ma-167	194	20	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	194	21	eur	eur	PROPN
ma-167	194	22	.	.	PUNCT
ma-167	195	1	j.	j.	PROPN
ma-167	195	2	math	math	PROPN
ma-167	195	3	.	.	PUNCT
ma-167	196	1	anal	anal	PROPN
ma-167	196	2	.	.	PUNCT
ma-167	197	1	10.28924	10.28924	NUM
ma-167	197	2	/	/	SYM
ma-167	197	3	ada	ada	PROPN
ma-167	197	4	/	/	SYM
ma-167	197	5	ma.3.18	ma.3.18	ADJ
ma-167	197	6	9	9	NUM
ma-167	197	7	proof	proof	NOUN
ma-167	197	8	.	.	PUNCT
ma-167	198	1	from	from	ADP
ma-167	198	2	remark	remark	NOUN
ma-167	198	3	2	2	NUM
ma-167	198	4	it	it	PRON
ma-167	198	5	follows	follow	VERB
ma-167	198	6	that	that	SCONJ
ma-167	198	7	∇	∇	PROPN
ma-167	198	8	has	have	VERB
ma-167	198	9	a	a	DET
ma-167	198	10	unique	unique	ADJ
ma-167	198	11	minimizer	minimizer	NOUN
ma-167	198	12	ρ∗	ρ∗	NOUN
ma-167	198	13	and	and	CCONJ
ma-167	198	14	is	be	AUX
ma-167	198	15	obtained	obtain	VERB
ma-167	198	16	by	by	ADP
ma-167	198	17	d∇(ρ∗	d∇(ρ∗	NOUN
ma-167	198	18	)	)	PUNCT
ma-167	198	19	=	=	SYM
ma-167	199	1	0.from	0.from	NUM
ma-167	199	2	lemma	lemma	PROPN
ma-167	199	3	5.2	5.2	NUM
ma-167	199	4	and	and	CCONJ
ma-167	199	5	using	use	VERB
ma-167	199	6	the	the	DET
ma-167	199	7	fact	fact	NOUN
ma-167	199	8	that	that	SCONJ
ma-167	199	9	the	the	DET
ma-167	199	10	differential	differential	ADJ
ma-167	199	11	mapping	mapping	NOUN
ma-167	199	12	d∇	d∇	PROPN
ma-167	199	13	:	:	PUNCT
ma-167	199	14	e	e	X
ma-167	199	15	→	→	SYM
ma-167	199	16	e∗	e∗	PROPN
ma-167	199	17	is	be	AUX
ma-167	199	18	lipschitz	lipschitz	ADJ
ma-167	199	19	,	,	PUNCT
ma-167	199	20	considering	consider	VERB
ma-167	199	21	the	the	DET
ma-167	199	22	result	result	NOUN
ma-167	199	23	of	of	ADP
ma-167	199	24	theorem	theorem	NOUN
ma-167	199	25	3.1	3.1	NUM
ma-167	199	26	,	,	PUNCT
ma-167	199	27	we	we	PRON
ma-167	199	28	can	can	AUX
ma-167	199	29	complete	complete	VERB
ma-167	199	30	the	the	DET
ma-167	199	31	proof	proof	NOUN
ma-167	199	32	.	.	PUNCT
ma-167	200	1	�	�	PROPN
ma-167	200	2	6	6	NUM
ma-167	200	3	.	.	PUNCT
ma-167	201	1	the	the	DET
ma-167	201	2	proposed	propose	VERB
ma-167	201	3	algorithm	algorithm	NOUN
ma-167	201	4	in	in	ADP
ma-167	201	5	lp(ω	lp(ω	PROPN
ma-167	201	6	)	)	PUNCT
ma-167	201	7	now	now	ADV
ma-167	201	8	,	,	PUNCT
ma-167	201	9	from	from	ADP
ma-167	201	10	[	[	X
ma-167	201	11	14	14	NUM
ma-167	201	12	]	]	PUNCT
ma-167	201	13	,	,	PUNCT
ma-167	201	14	the	the	DET
ma-167	201	15	duality	duality	NOUN
ma-167	201	16	mapping	mapping	NOUN
ma-167	201	17	j	j	PROPN
ma-167	201	18	is	be	AUX
ma-167	201	19	known	know	VERB
ma-167	201	20	precisely	precisely	ADV
ma-167	201	21	in	in	ADP
ma-167	201	22	lp(ω	lp(ω	NOUN
ma-167	201	23	)	)	PUNCT
ma-167	201	24	for	for	ADP
ma-167	201	25	1	1	NUM
ma-167	201	26	<	<	X
ma-167	201	27	p	p	X
ma-167	201	28	<	<	X
ma-167	201	29	∞	∞	NUM
ma-167	201	30	by	by	ADP
ma-167	201	31	jv	jv	NOUN
ma-167	201	32	=	=	SYM
ma-167	201	33	‖v‖2−plp	‖v‖2−plp	PROPN
ma-167	201	34	|v	|v	ADV
ma-167	201	35	|p−2v	|p−2v	PUNCT
ma-167	201	36	,	,	PUNCT
ma-167	201	37	∀v	∀v	PROPN
ma-167	201	38	∈	∈	PROPN
ma-167	201	39	lp(ω	lp(ω	X
ma-167	201	40	)	)	PUNCT
ma-167	201	41	and	and	CCONJ
ma-167	201	42	if	if	SCONJ
ma-167	201	43	lp(ω	lp(ω	NOUN
ma-167	201	44	)	)	PUNCT
ma-167	201	45	is	be	AUX
ma-167	201	46	reflexive	reflexive	ADJ
ma-167	201	47	,	,	PUNCT
ma-167	201	48	smooth	smooth	ADJ
ma-167	201	49	and	and	CCONJ
ma-167	201	50	strictly	strictly	ADV
ma-167	201	51	convex	convex	VERB
ma-167	201	52	real	real	ADJ
ma-167	201	53	banach	banach	NOUN
ma-167	201	54	space	space	NOUN
ma-167	201	55	,	,	PUNCT
ma-167	201	56	for	for	ADP
ma-167	201	57	1	1	NUM
ma-167	201	58	<	<	X
ma-167	201	59	p	p	X
ma-167	201	60	<	<	X
ma-167	201	61	∞	∞	PROPN
ma-167	201	62	,	,	PUNCT
ma-167	201	63	then	then	ADV
ma-167	201	64	theduality	theduality	NOUN
ma-167	201	65	mapping	mapping	PROPN
ma-167	201	66	j	j	PROPN
ma-167	201	67	is	be	AUX
ma-167	201	68	surjective	surjective	ADJ
ma-167	201	69	,	,	PUNCT
ma-167	201	70	one	one	NUM
ma-167	201	71	-	-	PUNCT
ma-167	201	72	to	to	ADP
ma-167	201	73	-	-	PUNCT
ma-167	201	74	one	one	NUM
ma-167	201	75	and	and	CCONJ
ma-167	201	76	its	its	PRON
ma-167	201	77	inverse	inverse	NOUN
ma-167	201	78	j−1	j−1	PROPN
ma-167	201	79	is	be	AUX
ma-167	201	80	given	give	VERB
ma-167	201	81	by	by	ADP
ma-167	201	82	ju	ju	NOUN
ma-167	202	1	=	=	NOUN
ma-167	202	2	‖‖2−ql	‖‖2−ql	NUM
ma-167	202	3	|u|q−2u,∀u	|u|q−2u,∀u	PUNCT
ma-167	202	4	∈	∈	PROPN
ma-167	202	5	lq(ω	lq(ω	NOUN
ma-167	202	6	)	)	PUNCT
ma-167	202	7	with	with	ADP
ma-167	202	8	1	1	NUM
ma-167	202	9	p	p	NOUN
ma-167	203	1	+	+	NOUN
ma-167	203	2	1	1	NUM
ma-167	203	3	q	q	NOUN
ma-167	203	4	=	=	SYM
ma-167	203	5	1now	1now	PROPN
ma-167	203	6	from	from	ADP
ma-167	203	7	3.1	3.1	NUM
ma-167	203	8	,	,	PUNCT
ma-167	203	9	we	we	PRON
ma-167	203	10	defined	define	VERB
ma-167	203	11	x1	x1	PROPN
ma-167	203	12	,	,	PUNCT
ma-167	203	13	y1	y1	PROPN
ma-167	203	14	∈	∈	PROPN
ma-167	203	15	lq(ω	lq(ω	NOUN
ma-167	203	16	)	)	PUNCT
ma-167	203	17	{	{	PUNCT
ma-167	203	18	yn	yn	NOUN
ma-167	203	19	=	=	PUNCT
ma-167	203	20	xn	xn	PROPN
ma-167	204	1	−	−	PROPN
ma-167	204	2	θn‖axn‖2−qlq	θn‖axn‖2−qlq	ADV
ma-167	204	3	|axn|2−qlq	|axn|2−qlq	ADJ
ma-167	204	4	axn	axn	PROPN
ma-167	204	5	,	,	PUNCT
ma-167	204	6	n	n	PRON
ma-167	204	7	≥	≥	NUM
ma-167	204	8	1	1	NUM
ma-167	204	9	xn+1	xn+1	X
ma-167	204	10	=	=	SYM
ma-167	204	11	yn	yn	PROPN
ma-167	204	12	−	−	PROPN
ma-167	204	13	λn‖ayn‖2−qlq	λn‖ayn‖2−qlq	PROPN
ma-167	204	14	|ayn|2−qlq	|ayn|2−qlq	PROPN
ma-167	204	15	ayn	ayn	PROPN
ma-167	204	16	,	,	PUNCT
ma-167	204	17	n	n	CCONJ
ma-167	204	18	≥	≥	NUM
ma-167	204	19	1	1	NUM
ma-167	204	20	(	(	PUNCT
ma-167	204	21	6.1	6.1	NUM
ma-167	204	22	)	)	PUNCT
ma-167	204	23	conclusion	conclusion	NOUN
ma-167	204	24	in	in	ADP
ma-167	204	25	this	this	DET
ma-167	204	26	paper	paper	NOUN
ma-167	204	27	,	,	PUNCT
ma-167	204	28	we	we	PRON
ma-167	204	29	proposed	propose	VERB
ma-167	204	30	and	and	CCONJ
ma-167	204	31	analyzed	analyze	VERB
ma-167	204	32	the	the	DET
ma-167	204	33	strong	strong	ADJ
ma-167	204	34	convergence	convergence	NOUN
ma-167	204	35	theorem	theorem	NOUN
ma-167	204	36	of	of	ADP
ma-167	204	37	two	two	NUM
ma-167	204	38	step	step	NOUN
ma-167	204	39	size	size	NOUN
ma-167	204	40	of	of	ADP
ma-167	204	41	thenew	thenew	ADJ
ma-167	204	42	krasnoselskii	krasnoselskii	ADJ
ma-167	204	43	-	-	PUNCT
ma-167	204	44	type	type	NOUN
ma-167	204	45	algorithm	algorithm	NOUN
ma-167	204	46	introduced	introduce	VERB
ma-167	204	47	by	by	ADP
ma-167	204	48	sene	sene	PROPN
ma-167	204	49	et	et	PROPN
ma-167	204	50	al	al	PROPN
ma-167	204	51	.	.	PUNCT
ma-167	205	1	[	[	X
ma-167	205	2	7	7	X
ma-167	205	3	]	]	PUNCT
ma-167	205	4	and	and	CCONJ
ma-167	205	5	prove	prove	VERB
ma-167	205	6	a	a	DET
ma-167	205	7	strong	strong	ADJ
ma-167	205	8	convergencetheorem	convergencetheorem	NOUN
ma-167	205	9	to	to	PART
ma-167	205	10	approximate	approximate	VERB
ma-167	205	11	the	the	DET
ma-167	205	12	unique	unique	ADJ
ma-167	205	13	zero	zero	NUM
ma-167	205	14	of	of	ADP
ma-167	205	15	a	a	DET
ma-167	205	16	lipschitz	lipschitz	NOUN
ma-167	205	17	strongly	strongly	ADV
ma-167	205	18	monotone	monotone	ADJ
ma-167	205	19	mapping	mapping	NOUN
ma-167	205	20	2−uniformlysmooth	2−uniformlysmooth	NOUN
ma-167	205	21	and	and	CCONJ
ma-167	205	22	p−uniformly	p−uniformly	PRON
ma-167	205	23	convex	convex	NOUN
ma-167	205	24	real	real	ADJ
ma-167	205	25	banach	banach	NOUN
ma-167	205	26	space	space	NOUN
ma-167	205	27	for	for	ADP
ma-167	205	28	p	p	PRON
ma-167	205	29	≥	≥	NUM
ma-167	205	30	2	2	NUM
ma-167	205	31	.	.	PUNCT
ma-167	206	1	this	this	DET
ma-167	206	2	class	class	NOUN
ma-167	206	3	of	of	ADP
ma-167	206	4	banach	banach	NOUN
ma-167	206	5	spaces	space	NOUN
ma-167	206	6	containsall	containsall	VERB
ma-167	206	7	lp	lp	NOUN
ma-167	206	8	-	-	NOUN
ma-167	206	9	spaces	space	NOUN
ma-167	206	10	,	,	PUNCT
ma-167	206	11	2	2	NUM
ma-167	206	12	≤	≤	NOUN
ma-167	206	13	p	p	PRON
ma-167	206	14	<	<	X
ma-167	206	15	∞	∞	PROPN
ma-167	206	16	and	and	CCONJ
ma-167	206	17	sobolev	sobolev	ADJ
ma-167	206	18	space	space	NOUN
ma-167	206	19	.	.	PUNCT
ma-167	207	1	then	then	ADV
ma-167	207	2	we	we	PRON
ma-167	207	3	apply	apply	VERB
ma-167	207	4	our	our	PRON
ma-167	207	5	results	result	NOUN
ma-167	207	6	to	to	ADP
ma-167	207	7	the	the	DET
ma-167	207	8	convex	convex	ADJ
ma-167	207	9	minimizationproblem	minimizationproblem	NOUN
ma-167	207	10	.	.	PUNCT
ma-167	208	1	we	we	PRON
ma-167	208	2	also	also	ADV
ma-167	208	3	complemented	complement	VERB
ma-167	208	4	and	and	CCONJ
ma-167	208	5	generalized	generalized	ADJ
ma-167	208	6	previous	previous	ADJ
ma-167	208	7	worked	work	VERB
ma-167	208	8	been	be	AUX
ma-167	208	9	done	do	VERB
ma-167	208	10	under	under	ADP
ma-167	208	11	this	this	DET
ma-167	208	12	setting	setting	NOUN
ma-167	208	13	.	.	PUNCT
ma-167	209	1	references	reference	NOUN
ma-167	209	2	[	[	X
ma-167	209	3	1	1	NUM
ma-167	209	4	]	]	X
ma-167	209	5	ya	ya	PROPN
ma-167	209	6	.	.	PROPN
ma-167	209	7	alber	alber	PROPN
ma-167	209	8	,	,	PUNCT
ma-167	209	9	i.	i.	PROPN
ma-167	209	10	ryazantseva	ryazantseva	PROPN
ma-167	209	11	,	,	PUNCT
ma-167	209	12	nonlinear	nonlinear	ADJ
ma-167	209	13	ill	ill	ADV
ma-167	209	14	posed	pose	VERB
ma-167	209	15	problems	problem	NOUN
ma-167	209	16	of	of	ADP
ma-167	209	17	monotone	monotone	ADJ
ma-167	209	18	type	type	NOUN
ma-167	209	19	,	,	PUNCT
ma-167	209	20	springer	springer	NOUN
ma-167	209	21	,	,	PUNCT
ma-167	209	22	london	london	PROPN
ma-167	209	23	,	,	PUNCT
ma-167	209	24	uk	uk	PROPN
ma-167	209	25	,	,	PUNCT
ma-167	209	26	2006.[2	2006.[2	NUM
ma-167	209	27	]	]	X
ma-167	209	28	f.e	f.e	PROPN
ma-167	209	29	.	.	PROPN
ma-167	209	30	browder	browder	PROPN
ma-167	209	31	,	,	PUNCT
ma-167	209	32	nonlinear	nonlinear	ADJ
ma-167	209	33	mappings	mapping	NOUN
ma-167	209	34	of	of	ADP
ma-167	209	35	nonexpansive	nonexpansive	ADJ
ma-167	209	36	and	and	CCONJ
ma-167	209	37	accretive	accretive	ADJ
ma-167	209	38	type	type	NOUN
ma-167	209	39	in	in	ADP
ma-167	209	40	banach	banach	NOUN
ma-167	209	41	spaces	space	NOUN
ma-167	209	42	,	,	PUNCT
ma-167	209	43	bull	bull	NOUN
ma-167	209	44	.	.	PUNCT
ma-167	210	1	amer	amer	PROPN
ma-167	210	2	.	.	PUNCT
ma-167	210	3	math	math	PROPN
ma-167	210	4	.	.	PUNCT
ma-167	211	1	soc	soc	PROPN
ma-167	211	2	.	.	PUNCT
ma-167	212	1	73(1967	73(1967	NUM
ma-167	212	2	)	)	PUNCT
ma-167	212	3	875	875	NUM
ma-167	212	4	-	-	SYM
ma-167	212	5	882	882	NUM
ma-167	212	6	.	.	PUNCT
ma-167	213	1	https://doi.org/10.1090/s0002-9904-1967-11823-8.[3	https://doi.org/10.1090/s0002-9904-1967-11823-8.[3	NOUN
ma-167	213	2	]	]	X
ma-167	213	3	c.e	c.e	PROPN
ma-167	213	4	.	.	PROPN
ma-167	213	5	chidume	chidume	PROPN
ma-167	213	6	,	,	PUNCT
ma-167	213	7	m.o	m.o	PROPN
ma-167	213	8	.	.	PROPN
ma-167	213	9	osilike	osilike	ADJ
ma-167	213	10	,	,	PUNCT
ma-167	213	11	iterative	iterative	ADJ
ma-167	213	12	solution	solution	NOUN
ma-167	213	13	of	of	ADP
ma-167	213	14	nonlinear	nonlinear	ADJ
ma-167	213	15	integral	integral	ADJ
ma-167	213	16	equations	equation	NOUN
ma-167	213	17	of	of	ADP
ma-167	213	18	hammerstein	hammerstein	PROPN
ma-167	213	19	-	-	PUNCT
ma-167	213	20	type	type	NOUN
ma-167	213	21	,	,	PUNCT
ma-167	213	22	j.	j.	PROPN
ma-167	213	23	niger	niger	PROPN
ma-167	213	24	.	.	PUNCT
ma-167	214	1	math.soc	math.soc	PROPN
ma-167	214	2	.	.	PUNCT
ma-167	214	3	appl	appl	PROPN
ma-167	214	4	.	.	PUNCT
ma-167	215	1	anal	anal	PROPN
ma-167	215	2	.	.	PUNCT
ma-167	216	1	11	11	NUM
ma-167	216	2	(	(	PUNCT
ma-167	216	3	1992	1992	NUM
ma-167	216	4	)	)	PUNCT
ma-167	216	5	9	9	NUM
ma-167	216	6	-	-	SYM
ma-167	216	7	18.[4	18.[4	NUM
ma-167	216	8	]	]	X
ma-167	216	9	c.e	c.e	PROPN
ma-167	216	10	.	.	PROPN
ma-167	216	11	chidume	chidume	PROPN
ma-167	216	12	,	,	PUNCT
ma-167	216	13	iterative	iterative	ADJ
ma-167	216	14	approximation	approximation	NOUN
ma-167	216	15	of	of	ADP
ma-167	216	16	fixed	fix	VERB
ma-167	216	17	points	point	NOUN
ma-167	216	18	of	of	ADP
ma-167	216	19	lipschitzian	lipschitzian	ADJ
ma-167	216	20	strictly	strictly	ADV
ma-167	216	21	pseudocontractive	pseudocontractive	ADJ
ma-167	216	22	mappings	mapping	NOUN
ma-167	216	23	,	,	PUNCT
ma-167	216	24	proc	proc	NOUN
ma-167	216	25	.	.	PUNCT
ma-167	217	1	amer.math	amer.math	NUM
ma-167	217	2	.	.	PUNCT
ma-167	218	1	soc	soc	PROPN
ma-167	218	2	.	.	PUNCT
ma-167	219	1	99	99	NUM
ma-167	219	2	(	(	PUNCT
ma-167	219	3	1987	1987	NUM
ma-167	219	4	)	)	PUNCT
ma-167	219	5	283	283	NUM
ma-167	219	6	-	-	SYM
ma-167	219	7	283	283	NUM
ma-167	219	8	.	.	PUNCT
ma-167	220	1	https://doi.org/10.1090/s0002-9939-1987-0870786-4.[5	https://doi.org/10.1090/s0002-9939-1987-0870786-4.[5	PROPN
ma-167	220	2	]	]	X
ma-167	220	3	c.e	c.e	PROPN
ma-167	220	4	.	.	PROPN
ma-167	220	5	chidume	chidume	PROPN
ma-167	220	6	,	,	PUNCT
ma-167	220	7	m.o	m.o	PROPN
ma-167	220	8	.	.	PROPN
ma-167	220	9	osilike	osilike	PROPN
ma-167	220	10	,	,	PUNCT
ma-167	220	11	iterative	iterative	ADJ
ma-167	220	12	solutions	solution	NOUN
ma-167	220	13	of	of	ADP
ma-167	220	14	nonlinear	nonlinear	ADJ
ma-167	220	15	accretive	accretive	ADJ
ma-167	220	16	operator	operator	NOUN
ma-167	220	17	equations	equation	NOUN
ma-167	220	18	in	in	ADP
ma-167	220	19	arbitrary	arbitrary	ADJ
ma-167	220	20	banach	banach	NOUN
ma-167	220	21	spaces	space	NOUN
ma-167	220	22	,	,	PUNCT
ma-167	220	23	nonlinear	nonlinear	ADJ
ma-167	220	24	anal	anal	NOUN
ma-167	220	25	.	.	PUNCT
ma-167	220	26	:	:	PUNCT
ma-167	221	1	theory	theory	NOUN
ma-167	221	2	meth	meth	NOUN
ma-167	221	3	.	.	PUNCT
ma-167	222	1	appl	appl	PROPN
ma-167	222	2	.	.	PUNCT
ma-167	223	1	36	36	NUM
ma-167	223	2	(	(	PUNCT
ma-167	223	3	1999	1999	NUM
ma-167	223	4	)	)	PUNCT
ma-167	223	5	863	863	NUM
ma-167	223	6	-	-	SYM
ma-167	223	7	872	872	NUM
ma-167	223	8	.	.	PUNCT
ma-167	224	1	https://doi.org/10.1016/s0362-546x(97)00611-1.[6	https://doi.org/10.1016/s0362-546x(97)00611-1.[6	NOUN
ma-167	224	2	]	]	PUNCT
ma-167	224	3	c.e	c.e	PROPN
ma-167	224	4	.	.	PROPN
ma-167	224	5	chidume	chidume	PROPN
ma-167	224	6	,	,	PUNCT
ma-167	224	7	a.	a.	PROPN
ma-167	224	8	adamu	adamu	PROPN
ma-167	224	9	,	,	PUNCT
ma-167	224	10	l.c	l.c	PROPN
ma-167	224	11	.	.	PROPN
ma-167	224	12	okereke	okereke	PROPN
ma-167	224	13	,	,	PUNCT
ma-167	224	14	a	a	DET
ma-167	224	15	krasnoselskii	krasnoselskii	ADJ
ma-167	224	16	-	-	PUNCT
ma-167	224	17	type	type	NOUN
ma-167	224	18	algorithm	algorithm	NOUN
ma-167	224	19	for	for	ADP
ma-167	224	20	approximating	approximate	VERB
ma-167	224	21	solutions	solution	NOUN
ma-167	224	22	of	of	ADP
ma-167	224	23	variationalinequality	variationalinequality	NOUN
ma-167	224	24	problems	problem	NOUN
ma-167	224	25	and	and	CCONJ
ma-167	224	26	convex	convex	VERB
ma-167	224	27	feasibility	feasibility	NOUN
ma-167	224	28	problems	problem	NOUN
ma-167	224	29	.	.	PUNCT
ma-167	225	1	j.	j.	PROPN
ma-167	225	2	nonlinear	nonlinear	PROPN
ma-167	225	3	var	var	PROPN
ma-167	225	4	.	.	PUNCT
ma-167	226	1	anal	anal	ADJ
ma-167	226	2	.	.	PUNCT
ma-167	226	3	2	2	NUM
ma-167	226	4	(	(	PUNCT
ma-167	226	5	2018	2018	NUM
ma-167	226	6	)	)	PUNCT
ma-167	226	7	203	203	NUM
ma-167	226	8	-	-	SYM
ma-167	226	9	218.[7	218.[7	NUM
ma-167	226	10	]	]	X
ma-167	226	11	c.e	c.e	PROPN
ma-167	226	12	.	.	PROPN
ma-167	226	13	chidume	chidume	PROPN
ma-167	226	14	,	,	PUNCT
ma-167	226	15	iterative	iterative	ADJ
ma-167	226	16	approximation	approximation	NOUN
ma-167	226	17	of	of	ADP
ma-167	226	18	fixed	fix	VERB
ma-167	226	19	points	point	NOUN
ma-167	226	20	of	of	ADP
ma-167	226	21	lipschitzian	lipschitzian	ADJ
ma-167	226	22	strictly	strictly	ADV
ma-167	226	23	pseudo	pseudo	ADJ
ma-167	226	24	-	-	ADJ
ma-167	226	25	contractive	contractive	ADJ
ma-167	226	26	mappings	mapping	NOUN
ma-167	226	27	,	,	PUNCT
ma-167	226	28	proc.amer	proc.amer	PROPN
ma-167	226	29	.	.	PUNCT
ma-167	227	1	math	math	NOUN
ma-167	227	2	.	.	PUNCT
ma-167	228	1	soc	soc	PROPN
ma-167	228	2	.	.	PUNCT
ma-167	229	1	99	99	NUM
ma-167	229	2	(	(	PUNCT
ma-167	229	3	1987	1987	NUM
ma-167	229	4	)	)	PUNCT
ma-167	229	5	283	283	NUM
ma-167	229	6	-	-	SYM
ma-167	229	7	288	288	NUM
ma-167	229	8	.	.	PUNCT
ma-167	230	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	231	1	https://doi.org/10.1090/s0002-9904-1967-11823-8	https://doi.org/10.1090/s0002-9904-1967-11823-8	PROPN
ma-167	231	2	https://doi.org/10.1090/s0002-9939-1987-0870786-4	https://doi.org/10.1090/s0002-9939-1987-0870786-4	PROPN
ma-167	231	3	https://doi.org/10.1016/s0362-546x(97)00611-1	https://doi.org/10.1016/s0362-546x(97)00611-1	PROPN
ma-167	231	4	eur	eur	PROPN
ma-167	231	5	.	.	PUNCT
ma-167	232	1	j.	j.	PROPN
ma-167	232	2	math	math	PROPN
ma-167	232	3	.	.	PUNCT
ma-167	233	1	anal	anal	PROPN
ma-167	233	2	.	.	PUNCT
ma-167	234	1	10.28924	10.28924	NUM
ma-167	234	2	/	/	SYM
ma-167	234	3	ada	ada	PROPN
ma-167	234	4	/	/	SYM
ma-167	234	5	ma.3.18	ma.3.18	NOUN
ma-167	234	6	10	10	NUM
ma-167	235	1	[	[	NOUN
ma-167	235	2	8	8	NUM
ma-167	235	3	]	]	X
ma-167	235	4	c.e	c.e	PROPN
ma-167	235	5	.	.	PROPN
ma-167	235	6	chidume	chidume	PROPN
ma-167	235	7	,	,	PUNCT
ma-167	235	8	a.u	a.u	PROPN
ma-167	235	9	.	.	PROPN
ma-167	235	10	bello	bello	PROPN
ma-167	235	11	,	,	PUNCT
ma-167	235	12	b.	b.	PROPN
ma-167	235	13	usman	usman	PROPN
ma-167	235	14	,	,	PUNCT
ma-167	235	15	krasnoselskii	krasnoselskii	NOUN
ma-167	235	16	-	-	PUNCT
ma-167	235	17	type	type	NOUN
ma-167	235	18	algorithm	algorithm	NOUN
ma-167	235	19	for	for	ADP
ma-167	235	20	zeros	zero	NOUN
ma-167	235	21	of	of	ADP
ma-167	235	22	strongly	strongly	ADV
ma-167	235	23	monotone	monotone	ADJ
ma-167	235	24	lipschitz	lipschitz	NOUN
ma-167	235	25	maps	map	NOUN
ma-167	235	26	inclassical	inclassical	ADJ
ma-167	235	27	banach	banach	NOUN
ma-167	235	28	spaces	space	NOUN
ma-167	235	29	,	,	PUNCT
ma-167	235	30	springerplus	springerplus	NOUN
ma-167	235	31	.	.	PROPN
ma-167	235	32	4	4	NUM
ma-167	235	33	(	(	PUNCT
ma-167	235	34	2015	2015	NUM
ma-167	235	35	)	)	PUNCT
ma-167	235	36	297.[9	297.[9	NUM
ma-167	235	37	]	]	SYM
ma-167	235	38	s.y	s.y	PROPN
ma-167	235	39	.	.	PUNCT
ma-167	235	40	cho	cho	PROPN
ma-167	235	41	,	,	PUNCT
ma-167	235	42	x.	x.	PROPN
ma-167	235	43	qin	qin	PROPN
ma-167	235	44	,	,	PUNCT
ma-167	235	45	l.	l.	PROPN
ma-167	235	46	wang	wang	PROPN
ma-167	235	47	,	,	PUNCT
ma-167	235	48	strong	strong	ADJ
ma-167	235	49	convergence	convergence	NOUN
ma-167	235	50	of	of	ADP
ma-167	235	51	a	a	DET
ma-167	235	52	splitting	splitting	NOUN
ma-167	235	53	algorithm	algorithm	NOUN
ma-167	235	54	for	for	ADP
ma-167	235	55	treating	treat	VERB
ma-167	235	56	monotone	monotone	ADJ
ma-167	235	57	operators	operator	NOUN
ma-167	235	58	,	,	PUNCT
ma-167	235	59	fixed	fix	VERB
ma-167	235	60	pointtheory	pointtheory	NOUN
ma-167	235	61	appl	appl	NOUN
ma-167	235	62	.	.	PUNCT
ma-167	236	1	2014	2014	NUM
ma-167	236	2	(	(	PUNCT
ma-167	236	3	2014	2014	NUM
ma-167	236	4	)	)	PUNCT
ma-167	236	5	94	94	NUM
ma-167	236	6	.	.	PUNCT
ma-167	237	1	https://doi.org/10.1186/1687-1812-2014-94.[10	https://doi.org/10.1186/1687-1812-2014-94.[10	NOUN
ma-167	237	2	]	]	PUNCT
ma-167	237	3	n.	n.	NOUN
ma-167	237	4	djitte	djitte	PROPN
ma-167	237	5	,	,	PUNCT
ma-167	237	6	j.t	j.t	PROPN
ma-167	237	7	.	.	PROPN
ma-167	237	8	mendy	mendy	PROPN
ma-167	237	9	,	,	PUNCT
ma-167	237	10	t.m.m	t.m.m	NOUN
ma-167	237	11	.	.	PUNCT
ma-167	237	12	sow	sow	NOUN
ma-167	237	13	,	,	PUNCT
ma-167	237	14	computation	computation	NOUN
ma-167	237	15	of	of	ADP
ma-167	237	16	zeros	zero	NOUN
ma-167	237	17	of	of	ADP
ma-167	237	18	monotone	monotone	ADJ
ma-167	237	19	type	type	NOUN
ma-167	237	20	mappings	mapping	NOUN
ma-167	237	21	:	:	PUNCT
ma-167	237	22	on	on	ADP
ma-167	237	23	chidume	chidume	PROPN
ma-167	237	24	’s	’s	PART
ma-167	237	25	open	open	ADJ
ma-167	237	26	problem	problem	NOUN
ma-167	237	27	,	,	PUNCT
ma-167	237	28	j.aust	j.aust	PROPN
ma-167	237	29	.	.	PUNCT
ma-167	237	30	math	math	NOUN
ma-167	237	31	.	.	PUNCT
ma-167	238	1	soc	soc	PROPN
ma-167	238	2	.	.	PUNCT
ma-167	239	1	108	108	NUM
ma-167	239	2	(	(	PUNCT
ma-167	239	3	2020	2020	NUM
ma-167	239	4	)	)	PUNCT
ma-167	239	5	278	278	NUM
ma-167	239	6	-	-	SYM
ma-167	239	7	288	288	NUM
ma-167	239	8	.	.	PUNCT
ma-167	240	1	https://doi.org/10.1017/s1446788719000545.[11	https://doi.org/10.1017/s1446788719000545.[11	X
ma-167	240	2	]	]	X
ma-167	240	3	i.	i.	PROPN
ma-167	240	4	cioranescu	cioranescu	PROPN
ma-167	240	5	,	,	PUNCT
ma-167	240	6	geometry	geometry	NOUN
ma-167	240	7	of	of	ADP
ma-167	240	8	banach	banach	NOUN
ma-167	240	9	spaces	space	NOUN
ma-167	240	10	,	,	PUNCT
ma-167	240	11	duality	duality	NOUN
ma-167	240	12	mappings	mapping	NOUN
ma-167	240	13	and	and	CCONJ
ma-167	240	14	nonlinear	nonlinear	ADJ
ma-167	240	15	problems	problem	NOUN
ma-167	240	16	,	,	PUNCT
ma-167	240	17	mathematics	mathematic	NOUN
ma-167	240	18	and	and	CCONJ
ma-167	240	19	its	its	PRON
ma-167	240	20	ap	ap	NOUN
ma-167	240	21	-	-	NOUN
ma-167	240	22	plications	plication	NOUN
ma-167	240	23	,	,	PUNCT
ma-167	240	24	62	62	NUM
ma-167	240	25	,	,	PUNCT
ma-167	240	26	springer	springer	NOUN
ma-167	240	27	,	,	PUNCT
ma-167	240	28	dordrecht	dordrecht	PROPN
ma-167	240	29	,	,	PUNCT
ma-167	240	30	1990.[12	1990.[12	PROPN
ma-167	240	31	]	]	X
ma-167	240	32	n.	n.	PROPN
ma-167	240	33	lehdili	lehdili	PROPN
ma-167	240	34	,	,	PUNCT
ma-167	240	35	a.	a.	NOUN
ma-167	240	36	moudafi	moudafi	PROPN
ma-167	240	37	,	,	PUNCT
ma-167	240	38	combining	combine	VERB
ma-167	240	39	the	the	DET
ma-167	240	40	proximal	proximal	ADJ
ma-167	240	41	algorithm	algorithm	NOUN
ma-167	240	42	and	and	CCONJ
ma-167	240	43	tikhonov	tikhonov	NOUN
ma-167	240	44	regularization	regularization	NOUN
ma-167	240	45	,	,	PUNCT
ma-167	240	46	optimization	optimization	NOUN
ma-167	240	47	.	.	PUNCT
ma-167	241	1	37	37	NUM
ma-167	241	2	(	(	PUNCT
ma-167	241	3	1996)239	1996)239	NUM
ma-167	241	4	-	-	PUNCT
ma-167	241	5	252	252	NUM
ma-167	241	6	.	.	PUNCT
ma-167	242	1	https://doi.org/10.1080/02331939608844217.[13	https://doi.org/10.1080/02331939608844217.[13	PROPN
ma-167	242	2	]	]	X
ma-167	242	3	b.	b.	PROPN
ma-167	242	4	martinet	martinet	PROPN
ma-167	242	5	,	,	PUNCT
ma-167	242	6	breve	breve	PROPN
ma-167	242	7	communication	communication	NOUN
ma-167	242	8	.	.	PUNCT
ma-167	243	1	regularisation	regularisation	NOUN
ma-167	243	2	d’inequations	d’inequation	NOUN
ma-167	243	3	variationnelles	variationnelle	NOUN
ma-167	243	4	par	par	NOUN
ma-167	243	5	approximations	approximation	NOUN
ma-167	243	6	successives	successive	NOUN
ma-167	243	7	,	,	PUNCT
ma-167	243	8	rev.fran	rev.fran	NOUN
ma-167	243	9	dinf	dinf	NOUN
ma-167	243	10	.	.	PUNCT
ma-167	244	1	rech	rech	PROPN
ma-167	244	2	.	.	PUNCT
ma-167	245	1	oper	oper	PROPN
ma-167	245	2	.	.	PROPN
ma-167	245	3	4	4	NUM
ma-167	245	4	(	(	PUNCT
ma-167	245	5	1970	1970	NUM
ma-167	245	6	)	)	PUNCT
ma-167	245	7	154	154	NUM
ma-167	245	8	-	-	SYM
ma-167	245	9	158	158	NUM
ma-167	245	10	.	.	PUNCT
ma-167	246	1	https://doi.org/10.1051/m2an/197004r301541.[14	https://doi.org/10.1051/m2an/197004r301541.[14	PROPN
ma-167	246	2	]	]	X
ma-167	246	3	j.t	j.t	PROPN
ma-167	246	4	.	.	PROPN
ma-167	246	5	mendy	mendy	PROPN
ma-167	246	6	,	,	PUNCT
ma-167	246	7	m.	m.	NOUN
ma-167	246	8	sene	sene	PROPN
ma-167	246	9	,	,	PUNCT
ma-167	246	10	n.	n.	NOUN
ma-167	246	11	djitte	djitte	NOUN
ma-167	246	12	,	,	PUNCT
ma-167	246	13	explicit	explicit	ADJ
ma-167	246	14	algorithm	algorithm	NOUN
ma-167	246	15	for	for	ADP
ma-167	246	16	hammerstein	hammerstein	PROPN
ma-167	246	17	equations	equation	NOUN
ma-167	246	18	with	with	ADP
ma-167	246	19	bounded	bounded	PROPN
ma-167	246	20	,	,	PUNCT
ma-167	246	21	hemi	hemi	NOUN
ma-167	246	22	-	-	ADJ
ma-167	246	23	continuous	continuous	ADJ
ma-167	246	24	andmonotone	andmonotone	NOUN
ma-167	246	25	mappings	mapping	NOUN
ma-167	246	26	,	,	PUNCT
ma-167	246	27	minimax	minimax	NOUN
ma-167	246	28	theory	theory	NOUN
ma-167	246	29	appl	appl	NOUN
ma-167	246	30	.	.	PUNCT
ma-167	247	1	02	02	NUM
ma-167	247	2	(	(	PUNCT
ma-167	247	3	2017	2017	NUM
ma-167	247	4	)	)	PUNCT
ma-167	247	5	319	319	NUM
ma-167	247	6	-	-	SYM
ma-167	247	7	343.[15	343.[15	NUM
ma-167	247	8	]	]	PUNCT
ma-167	247	9	j.	j.	PROPN
ma-167	247	10	mendy	mendy	PROPN
ma-167	247	11	,	,	PUNCT
ma-167	247	12	r.	r.	PROPN
ma-167	247	13	shukla	shukla	PROPN
ma-167	247	14	,	,	PUNCT
ma-167	247	15	viscosity	viscosity	NOUN
ma-167	247	16	like	like	ADP
ma-167	247	17	implicit	implicit	ADJ
ma-167	247	18	methods	method	NOUN
ma-167	247	19	for	for	ADP
ma-167	247	20	zeros	zero	NOUN
ma-167	247	21	of	of	ADP
ma-167	247	22	monotone	monotone	ADJ
ma-167	247	23	operators	operator	NOUN
ma-167	247	24	in	in	ADP
ma-167	247	25	banach	banach	NOUN
ma-167	247	26	spaces	space	NOUN
ma-167	247	27	,	,	PUNCT
ma-167	247	28	khayyam	khayyam	PROPN
ma-167	247	29	j.math	j.math	PROPN
ma-167	247	30	.	.	PROPN
ma-167	247	31	8	8	NUM
ma-167	247	32	(	(	PUNCT
ma-167	247	33	2022	2022	NUM
ma-167	247	34	)	)	PUNCT
ma-167	247	35	53	53	NUM
ma-167	247	36	-	-	SYM
ma-167	247	37	72.[16	72.[16	PROPN
ma-167	247	38	]	]	X
ma-167	247	39	j.	j.	PROPN
ma-167	247	40	mendy	mendy	PROPN
ma-167	247	41	,	,	PUNCT
ma-167	247	42	f.	f.	PROPN
ma-167	247	43	mendy	mendy	PROPN
ma-167	247	44	,	,	PUNCT
ma-167	247	45	two	two	NUM
ma-167	247	46	step	step	NOUN
ma-167	247	47	size	size	NOUN
ma-167	247	48	algorithms	algorithm	NOUN
ma-167	247	49	for	for	ADP
ma-167	247	50	strong	strong	ADJ
ma-167	247	51	convergence	convergence	NOUN
ma-167	247	52	for	for	ADP
ma-167	247	53	a	a	DET
ma-167	247	54	monotone	monotone	ADJ
ma-167	247	55	operator	operator	NOUN
ma-167	247	56	in	in	ADP
ma-167	247	57	banach	banach	NOUN
ma-167	247	58	spaces	space	NOUN
ma-167	247	59	,	,	PUNCT
ma-167	247	60	int	int	NOUN
ma-167	247	61	.	.	PUNCT
ma-167	248	1	j.	j.	PROPN
ma-167	248	2	nonlinear	nonlinear	PROPN
ma-167	248	3	anal	anal	PROPN
ma-167	248	4	.	.	PUNCT
ma-167	249	1	appl	appl	PROPN
ma-167	249	2	.	.	PUNCT
ma-167	250	1	in	in	ADP
ma-167	250	2	press	press	NOUN
ma-167	250	3	.	.	PUNCT
ma-167	251	1	https://doi.org/10.22075/ijnaa.2023.27501.3626.[17	https://doi.org/10.22075/ijnaa.2023.27501.3626.[17	NUM
ma-167	251	2	]	]	X
ma-167	251	3	j.t	j.t	PROPN
ma-167	251	4	.	.	PROPN
ma-167	251	5	mendy	mendy	PROPN
ma-167	251	6	,	,	PUNCT
ma-167	251	7	m.	m.	NOUN
ma-167	251	8	sene	sene	PROPN
ma-167	251	9	,	,	PUNCT
ma-167	251	10	n.	n.	NOUN
ma-167	251	11	djitte	djitte	PROPN
ma-167	251	12	,	,	PUNCT
ma-167	251	13	algorithm	algorithm	NOUN
ma-167	251	14	for	for	ADP
ma-167	251	15	zeros	zero	NOUN
ma-167	251	16	of	of	ADP
ma-167	251	17	maximal	maximal	ADJ
ma-167	251	18	monotone	monotone	ADJ
ma-167	251	19	mappings	mapping	NOUN
ma-167	251	20	in	in	ADP
ma-167	251	21	classical	classical	ADJ
ma-167	251	22	banach	banach	NOUN
ma-167	251	23	spaces	space	NOUN
ma-167	251	24	,	,	PUNCT
ma-167	251	25	int.j	int.j	PROPN
ma-167	251	26	.	.	PROPN
ma-167	251	27	math	math	NOUN
ma-167	251	28	.	.	PUNCT
ma-167	252	1	anal	anal	ADJ
ma-167	252	2	.	.	PUNCT
ma-167	253	1	11	11	NUM
ma-167	253	2	(	(	PUNCT
ma-167	253	3	2017	2017	NUM
ma-167	253	4	)	)	PUNCT
ma-167	253	5	551	551	NUM
ma-167	253	6	-	-	SYM
ma-167	253	7	570	570	NUM
ma-167	253	8	.	.	PUNCT
ma-167	254	1	https://doi.org/10.12988/ijma.2017.7112.[18	https://doi.org/10.12988/ijma.2017.7112.[18	X
ma-167	254	2	]	]	PUNCT
ma-167	255	1	a.	a.	NOUN
ma-167	255	2	moudafi	moudafi	PROPN
ma-167	255	3	,	,	PUNCT
ma-167	255	4	viscosity	viscosity	NOUN
ma-167	255	5	approximation	approximation	NOUN
ma-167	255	6	methods	method	NOUN
ma-167	255	7	for	for	ADP
ma-167	255	8	fixed	fix	VERB
ma-167	255	9	-	-	PUNCT
ma-167	255	10	points	point	NOUN
ma-167	255	11	problems	problem	NOUN
ma-167	255	12	,	,	PUNCT
ma-167	255	13	j.	j.	PROPN
ma-167	255	14	math	math	PROPN
ma-167	255	15	.	.	PUNCT
ma-167	256	1	anal	anal	PROPN
ma-167	256	2	.	.	PUNCT
ma-167	256	3	appl	appl	PROPN
ma-167	256	4	.	.	PUNCT
ma-167	257	1	241	241	NUM
ma-167	257	2	(	(	PUNCT
ma-167	257	3	2000	2000	NUM
ma-167	257	4	)	)	PUNCT
ma-167	257	5	46	46	NUM
ma-167	257	6	-	-	SYM
ma-167	257	7	55	55	NUM
ma-167	257	8	.	.	PUNCT
ma-167	258	1	https://doi.org/10.1006/jmaa.1999.6615.[19	https://doi.org/10.1006/jmaa.1999.6615.[19	X
ma-167	258	2	]	]	X
ma-167	258	3	m.	m.	NOUN
ma-167	258	4	turkyilmazoglu	turkyilmazoglu	NOUN
ma-167	258	5	,	,	PUNCT
ma-167	258	6	approximate	approximate	ADJ
ma-167	258	7	analytical	analytical	ADJ
ma-167	258	8	solution	solution	NOUN
ma-167	258	9	of	of	ADP
ma-167	258	10	the	the	DET
ma-167	258	11	nonlinear	nonlinear	ADJ
ma-167	258	12	system	system	NOUN
ma-167	258	13	of	of	ADP
ma-167	258	14	differential	differential	ADJ
ma-167	258	15	equations	equation	NOUN
ma-167	258	16	having	have	VERB
ma-167	258	17	asymp	asymp	NOUN
ma-167	258	18	-	-	PUNCT
ma-167	258	19	totically	totically	ADV
ma-167	258	20	stable	stable	ADJ
ma-167	258	21	equilibrium	equilibrium	NOUN
ma-167	258	22	,	,	PUNCT
ma-167	258	23	filomat	filomat	NOUN
ma-167	258	24	.	.	PROPN
ma-167	258	25	31	31	NUM
ma-167	258	26	(	(	PUNCT
ma-167	258	27	2017	2017	NUM
ma-167	258	28	)	)	PUNCT
ma-167	258	29	2633	2633	NUM
ma-167	258	30	-	-	SYM
ma-167	258	31	2641	2641	NUM
ma-167	258	32	.	.	PUNCT
ma-167	259	1	https://doi.org/10.2298/fil1709633t.[20	https://doi.org/10.2298/fil1709633t.[20	ADV
ma-167	259	2	]	]	PUNCT
ma-167	259	3	s.	s.	PROPN
ma-167	259	4	reich	reich	PROPN
ma-167	259	5	,	,	PUNCT
ma-167	259	6	a	a	DET
ma-167	259	7	weak	weak	ADJ
ma-167	259	8	convergence	convergence	NOUN
ma-167	259	9	theorem	theorem	NOUN
ma-167	259	10	for	for	ADP
ma-167	259	11	alternating	alternate	VERB
ma-167	259	12	methods	method	NOUN
ma-167	259	13	with	with	ADP
ma-167	259	14	bergman	bergman	PROPN
ma-167	259	15	distance	distance	PROPN
ma-167	259	16	.	.	PUNCT
ma-167	260	1	in	in	ADP
ma-167	260	2	:	:	PUNCT
ma-167	260	3	a.g	a.g	PROPN
ma-167	260	4	.	.	PROPN
ma-167	260	5	kartsatos	kartsato	NOUN
ma-167	260	6	,	,	PUNCT
ma-167	260	7	(	(	PUNCT
ma-167	260	8	ed.)theory	ed.)theory	NOUN
ma-167	260	9	and	and	CCONJ
ma-167	260	10	applications	application	NOUN
ma-167	260	11	of	of	ADP
ma-167	260	12	nonlinear	nonlinear	ADJ
ma-167	260	13	operators	operator	NOUN
ma-167	260	14	of	of	ADP
ma-167	260	15	accrective	accrective	ADJ
ma-167	260	16	and	and	CCONJ
ma-167	260	17	monotone	monotone	ADJ
ma-167	260	18	type	type	NOUN
ma-167	260	19	.	.	PUNCT
ma-167	261	1	lecture	lecture	NOUN
ma-167	261	2	notes	note	NOUN
ma-167	261	3	in	in	ADP
ma-167	261	4	pure	pure	ADJ
ma-167	261	5	andapplied	andapplie	VERB
ma-167	261	6	mathematics	mathematic	NOUN
ma-167	261	7	,	,	PUNCT
ma-167	261	8	vol	vol	NOUN
ma-167	261	9	.	.	PROPN
ma-167	261	10	178	178	NUM
ma-167	261	11	.	.	PUNCT
ma-167	262	1	new	new	PROPN
ma-167	262	2	york	york	PROPN
ma-167	262	3	:	:	PUNCT
ma-167	262	4	dekker	dekker	PROPN
ma-167	262	5	,	,	PUNCT
ma-167	262	6	(	(	PUNCT
ma-167	262	7	1996	1996	NUM
ma-167	262	8	)	)	PUNCT
ma-167	262	9	,	,	PUNCT
ma-167	263	1	pp	pp	PROPN
ma-167	263	2	.	.	PUNCT
ma-167	264	1	313	313	NUM
ma-167	264	2	-	-	SYM
ma-167	264	3	318.[21	318.[21	NUM
ma-167	264	4	]	]	PUNCT
ma-167	264	5	s.	s.	PROPN
ma-167	264	6	reich	reich	PROPN
ma-167	264	7	,	,	PUNCT
ma-167	264	8	s.	s.	PROPN
ma-167	264	9	sabach	sabach	PROPN
ma-167	264	10	,	,	PUNCT
ma-167	264	11	two	two	NUM
ma-167	264	12	strong	strong	ADJ
ma-167	264	13	convergence	convergence	NOUN
ma-167	264	14	theorems	theorem	NOUN
ma-167	264	15	for	for	ADP
ma-167	264	16	a	a	DET
ma-167	264	17	proximal	proximal	ADJ
ma-167	264	18	method	method	NOUN
ma-167	264	19	in	in	ADP
ma-167	264	20	reflexive	reflexive	ADJ
ma-167	264	21	banach	banach	NOUN
ma-167	264	22	spaces	space	NOUN
ma-167	264	23	,	,	PUNCT
ma-167	264	24	num.funct	num.funct	ADJ
ma-167	264	25	.	.	PUNCT
ma-167	265	1	anal	anal	PROPN
ma-167	265	2	.	.	PUNCT
ma-167	266	1	optim	optim	PROPN
ma-167	266	2	.	.	PUNCT
ma-167	267	1	31	31	NUM
ma-167	267	2	(	(	PUNCT
ma-167	267	3	2010	2010	NUM
ma-167	267	4	)	)	PUNCT
ma-167	267	5	22	22	NUM
ma-167	267	6	-	-	SYM
ma-167	267	7	44	44	NUM
ma-167	267	8	.	.	PUNCT
ma-167	268	1	https://doi.org/10.1080/01630560903499852.[22	https://doi.org/10.1080/01630560903499852.[22	NOUN
ma-167	268	2	]	]	PUNCT
ma-167	268	3	r.t	r.t	PROPN
ma-167	268	4	.	.	PROPN
ma-167	268	5	rockafellar	rockafellar	PROPN
ma-167	268	6	,	,	PUNCT
ma-167	268	7	on	on	ADP
ma-167	268	8	the	the	DET
ma-167	268	9	maximality	maximality	NOUN
ma-167	268	10	of	of	ADP
ma-167	268	11	sums	sum	NOUN
ma-167	268	12	of	of	ADP
ma-167	268	13	nonlinear	nonlinear	ADJ
ma-167	268	14	monotone	monotone	ADJ
ma-167	268	15	operators	operator	NOUN
ma-167	268	16	,	,	PUNCT
ma-167	268	17	trans	trans	PROPN
ma-167	268	18	.	.	PROPN
ma-167	269	1	amer	amer	PROPN
ma-167	269	2	.	.	PUNCT
ma-167	269	3	math	math	PROPN
ma-167	269	4	.	.	PUNCT
ma-167	270	1	soc	soc	PROPN
ma-167	270	2	.	.	PUNCT
ma-167	271	1	149	149	NUM
ma-167	271	2	(	(	PUNCT
ma-167	271	3	1970)75	1970)75	NUM
ma-167	271	4	-	-	SYM
ma-167	271	5	88	88	NUM
ma-167	271	6	.	.	PUNCT
ma-167	272	1	https://doi.org/10.1090/s0002-9947-1970-0282272-5.[23	https://doi.org/10.1090/s0002-9947-1970-0282272-5.[23	PROPN
ma-167	272	2	]	]	PUNCT
ma-167	272	3	m.	m.	NOUN
ma-167	272	4	sene	sene	PROPN
ma-167	272	5	,	,	PUNCT
ma-167	272	6	m.	m.	NOUN
ma-167	272	7	ndiaye	ndiaye	NOUN
ma-167	272	8	,	,	PUNCT
ma-167	272	9	n.	n.	NOUN
ma-167	272	10	djitte	djitte	PROPN
ma-167	272	11	,	,	PUNCT
ma-167	272	12	a	a	DET
ma-167	272	13	new	new	ADJ
ma-167	272	14	krasnoselskii?s	krasnoselskii?s	PROPN
ma-167	272	15	type	type	NOUN
ma-167	272	16	algorithm	algorithm	NOUN
ma-167	272	17	for	for	ADP
ma-167	272	18	zeros	zero	NOUN
ma-167	272	19	of	of	ADP
ma-167	272	20	strongly	strongly	ADV
ma-167	272	21	monotone	monotone	ADJ
ma-167	272	22	and	and	CCONJ
ma-167	272	23	lipschitzmappings	lipschitzmapping	NOUN
ma-167	272	24	,	,	PUNCT
ma-167	272	25	creat	creat	PROPN
ma-167	272	26	.	.	PUNCT
ma-167	273	1	math	math	PROPN
ma-167	273	2	.	.	PUNCT
ma-167	274	1	inf	inf	PROPN
ma-167	274	2	.	.	PROPN
ma-167	275	1	31	31	NUM
ma-167	275	2	(	(	PUNCT
ma-167	275	3	2022	2022	NUM
ma-167	275	4	)	)	PUNCT
ma-167	275	5	109	109	NUM
ma-167	275	6	-	-	SYM
ma-167	275	7	120	120	NUM
ma-167	275	8	.	.	PUNCT
ma-167	276	1	https://doi.org/10.37193/cmi.2022.01.11.[24	https://doi.org/10.37193/cmi.2022.01.11.[24	PROPN
ma-167	276	2	]	]	PUNCT
ma-167	277	1	k.	k.	PROPN
ma-167	277	2	sina	sina	PROPN
ma-167	277	3	,	,	PUNCT
ma-167	277	4	a.	a.	PROPN
ma-167	277	5	ali	ali	PROPN
ma-167	277	6	,	,	PUNCT
ma-167	277	7	analytical	analytical	ADJ
ma-167	277	8	solution	solution	NOUN
ma-167	277	9	of	of	ADP
ma-167	277	10	linear	linear	ADJ
ma-167	277	11	ordinary	ordinary	ADJ
ma-167	277	12	differential	differential	ADJ
ma-167	277	13	equations	equation	NOUN
ma-167	277	14	by	by	ADP
ma-167	277	15	differential	differential	ADJ
ma-167	277	16	transfer	transfer	NOUN
ma-167	277	17	,	,	PUNCT
ma-167	277	18	elect	elect	PROPN
ma-167	277	19	.	.	PUNCT
ma-167	278	1	j.	j.	PROPN
ma-167	278	2	diff.equ	diff.equ	PROPN
ma-167	278	3	.	.	PROPN
ma-167	278	4	79	79	NUM
ma-167	278	5	(	(	PUNCT
ma-167	278	6	2003	2003	NUM
ma-167	278	7	)	)	PUNCT
ma-167	278	8	1	1	NUM
ma-167	278	9	-	-	SYM
ma-167	278	10	18.[25	18.[25	NUM
ma-167	278	11	]	]	X
ma-167	278	12	y.	y.	PROPN
ma-167	278	13	song	song	PROPN
ma-167	278	14	,	,	PUNCT
ma-167	278	15	r.	r.	PROPN
ma-167	278	16	chen	chen	PROPN
ma-167	278	17	,	,	PUNCT
ma-167	278	18	strong	strong	ADJ
ma-167	278	19	convergence	convergence	NOUN
ma-167	278	20	theorems	theorem	VERB
ma-167	278	21	on	on	ADP
ma-167	278	22	an	an	DET
ma-167	278	23	iterative	iterative	NOUN
ma-167	278	24	method	method	NOUN
ma-167	278	25	for	for	ADP
ma-167	278	26	a	a	DET
ma-167	278	27	family	family	NOUN
ma-167	278	28	of	of	ADP
ma-167	278	29	finite	finite	PROPN
ma-167	278	30	nonexpansive	nonexpansive	PROPN
ma-167	278	31	mappings	mapping	NOUN
ma-167	278	32	,	,	PUNCT
ma-167	278	33	appl	appl	PROPN
ma-167	278	34	.	.	PROPN
ma-167	278	35	math	math	PROPN
ma-167	278	36	.	.	PUNCT
ma-167	279	1	comp	comp	PROPN
ma-167	279	2	.	.	PUNCT
ma-167	280	1	180	180	NUM
ma-167	280	2	(	(	PUNCT
ma-167	280	3	2006	2006	NUM
ma-167	280	4	)	)	PUNCT
ma-167	280	5	275	275	NUM
ma-167	280	6	-	-	SYM
ma-167	280	7	287	287	NUM
ma-167	280	8	.	.	PUNCT
ma-167	281	1	https://doi.org/10.1016/j.amc.2005.12.013.[26	https://doi.org/10.1016/j.amc.2005.12.013.[26	PROPN
ma-167	281	2	]	]	PUNCT
ma-167	281	3	s.b	s.b	PROPN
ma-167	281	4	.	.	PROPN
ma-167	281	5	duffull	duffull	PROPN
ma-167	281	6	,	,	PUNCT
ma-167	281	7	an	an	DET
ma-167	281	8	inductive	inductive	ADJ
ma-167	281	9	approximation	approximation	NOUN
ma-167	281	10	to	to	ADP
ma-167	281	11	the	the	DET
ma-167	281	12	solution	solution	NOUN
ma-167	281	13	of	of	ADP
ma-167	281	14	systems	system	NOUN
ma-167	281	15	of	of	ADP
ma-167	281	16	nonlinear	nonlinear	ADJ
ma-167	281	17	ordinary	ordinary	ADJ
ma-167	281	18	differential	differential	NOUN
ma-167	281	19	equationsin	equationsin	NOUN
ma-167	281	20	pharmacokinetics	pharmacokinetic	NOUN
ma-167	281	21	-	-	PUNCT
ma-167	281	22	pharmacodynamics	pharmacodynamic	NOUN
ma-167	281	23	,	,	PUNCT
ma-167	281	24	j.	j.	PROPN
ma-167	281	25	theor	theor	PROPN
ma-167	281	26	.	.	PUNCT
ma-167	282	1	comput	comput	PROPN
ma-167	282	2	.	.	PUNCT
ma-167	283	1	sci	sci	PROPN
ma-167	283	2	.	.	PROPN
ma-167	283	3	1	1	NUM
ma-167	283	4	(	(	PUNCT
ma-167	283	5	2014	2014	NUM
ma-167	283	6	)	)	PUNCT
ma-167	283	7	1000119	1000119	NUM
ma-167	283	8	.	.	PUNCT
ma-167	284	1	https://doi.org/10.4172/	https://doi.org/10.4172/	PROPN
ma-167	284	2	jtco.1000119.[27	jtco.1000119.[27	PROPN
ma-167	284	3	]	]	PUNCT
ma-167	284	4	s.	s.	PROPN
ma-167	284	5	kamimura	kamimura	PROPN
ma-167	284	6	,	,	PUNCT
ma-167	284	7	w.	w.	PROPN
ma-167	284	8	takahashi	takahashi	PROPN
ma-167	284	9	,	,	PUNCT
ma-167	284	10	strong	strong	ADJ
ma-167	284	11	convergence	convergence	NOUN
ma-167	284	12	of	of	ADP
ma-167	284	13	proximal	proximal	ADJ
ma-167	284	14	-	-	PUNCT
ma-167	284	15	type	type	NOUN
ma-167	284	16	algorithm	algorithm	NOUN
ma-167	284	17	in	in	ADP
ma-167	284	18	banach	banach	NOUN
ma-167	284	19	space	space	NOUN
ma-167	284	20	,	,	PUNCT
ma-167	284	21	siam	siam	PROPN
ma-167	284	22	j.	j.	PROPN
ma-167	284	23	optim	optim	PROPN
ma-167	284	24	.	.	PUNCT
ma-167	285	1	13(2002	13(2002	NUM
ma-167	285	2	)	)	PUNCT
ma-167	285	3	938	938	NUM
ma-167	285	4	-	-	SYM
ma-167	285	5	945.[28	945.[28	PROPN
ma-167	285	6	]	]	PUNCT
ma-167	285	7	s.	s.	PROPN
ma-167	285	8	reich	reich	PROPN
ma-167	285	9	,	,	PUNCT
ma-167	285	10	constructive	constructive	ADJ
ma-167	285	11	techniques	technique	NOUN
ma-167	285	12	for	for	ADP
ma-167	285	13	accretive	accretive	ADJ
ma-167	285	14	and	and	CCONJ
ma-167	285	15	monotone	monotone	ADJ
ma-167	285	16	operators	operator	NOUN
ma-167	285	17	,	,	PUNCT
ma-167	285	18	in	in	ADP
ma-167	285	19	:	:	PUNCT
ma-167	285	20	applied	apply	VERB
ma-167	285	21	non	non	ADJ
ma-167	285	22	-	-	ADJ
ma-167	285	23	linear	linear	ADJ
ma-167	285	24	analysis	analysis	NOUN
ma-167	285	25	,	,	PUNCT
ma-167	285	26	academicpress	academicpress	ADJ
ma-167	285	27	,	,	PUNCT
ma-167	285	28	new	new	PROPN
ma-167	285	29	york	york	PROPN
ma-167	285	30	,	,	PUNCT
ma-167	285	31	1979	1979	NUM
ma-167	285	32	,	,	PUNCT
ma-167	285	33	335	335	NUM
ma-167	285	34	-	-	SYM
ma-167	285	35	345	345	NUM
ma-167	285	36	.	.	PUNCT
ma-167	286	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	286	2	https://doi.org/10.1186/1687-1812-2014-94	https://doi.org/10.1186/1687-1812-2014-94	PROPN
ma-167	286	3	https://doi.org/10.1017/s1446788719000545	https://doi.org/10.1017/s1446788719000545	PROPN
ma-167	286	4	https://doi.org/10.1080/02331939608844217	https://doi.org/10.1080/02331939608844217	NOUN
ma-167	286	5	https://doi.org/10.1051/m2an/197004r301541	https://doi.org/10.1051/m2an/197004r301541	PUNCT
ma-167	286	6	https://doi.org/10.22075/ijnaa.2023.27501.3626	https://doi.org/10.22075/ijnaa.2023.27501.3626	NUM
ma-167	286	7	https://doi.org/10.12988/ijma.2017.7112	https://doi.org/10.12988/ijma.2017.7112	PROPN
ma-167	286	8	https://doi.org/10.1006/jmaa.1999.6615	https://doi.org/10.1006/jmaa.1999.6615	PROPN
ma-167	286	9	https://doi.org/10.2298/fil1709633	https://doi.org/10.2298/fil1709633	NOUN
ma-167	286	10	t	t	X
ma-167	286	11	https://doi.org/10.1080/01630560903499852	https://doi.org/10.1080/01630560903499852	ADV
ma-167	286	12	https://doi.org/10.1090/s0002-9947-1970-0282272-5	https://doi.org/10.1090/s0002-9947-1970-0282272-5	NOUN
ma-167	286	13	https://doi.org/10.37193/cmi.2022.01.11	https://doi.org/10.37193/cmi.2022.01.11	NOUN
ma-167	286	14	https://doi.org/10.1016/j.amc.2005.12.013	https://doi.org/10.1016/j.amc.2005.12.013	NOUN
ma-167	286	15	https://doi.org/10.4172/jtco.1000119	https://doi.org/10.4172/jtco.1000119	X
ma-167	286	16	https://doi.org/10.4172/jtco.1000119	https://doi.org/10.4172/jtco.1000119	ADJ
ma-167	286	17	eur	eur	NOUN
ma-167	286	18	.	.	PUNCT
ma-167	287	1	j.	j.	PROPN
ma-167	287	2	math	math	PROPN
ma-167	287	3	.	.	PUNCT
ma-167	288	1	anal	anal	PROPN
ma-167	288	2	.	.	PUNCT
ma-167	289	1	10.28924	10.28924	NUM
ma-167	289	2	/	/	SYM
ma-167	289	3	ada	ada	PROPN
ma-167	289	4	/	/	SYM
ma-167	289	5	ma.3.18	ma.3.18	NOUN
ma-167	289	6	11	11	NUM
ma-167	290	1	[	[	X
ma-167	290	2	29	29	NUM
ma-167	290	3	]	]	PUNCT
ma-167	290	4	w.	w.	PROPN
ma-167	290	5	takahashi	takahashi	PROPN
ma-167	290	6	,	,	PUNCT
ma-167	290	7	non	non	ADJ
ma-167	290	8	-	-	ADJ
ma-167	290	9	linear	linear	ADJ
ma-167	290	10	functional	functional	ADJ
ma-167	290	11	analysis	analysis	NOUN
ma-167	290	12	-	-	PUNCT
ma-167	290	13	fixed	fix	VERB
ma-167	290	14	point	point	NOUN
ma-167	290	15	theory	theory	NOUN
ma-167	290	16	and	and	CCONJ
ma-167	290	17	its	its	PRON
ma-167	290	18	applications	application	NOUN
ma-167	290	19	.	.	PUNCT
ma-167	291	1	yokohama	yokohama	PROPN
ma-167	291	2	:	:	PUNCT
ma-167	291	3	yokohamapublishers	yokohamapublishers	PROPN
ma-167	291	4	inc	inc	PROPN
ma-167	291	5	.	.	PROPN
ma-167	291	6	(	(	PUNCT
ma-167	291	7	2000	2000	NUM
ma-167	291	8	)	)	PUNCT
ma-167	291	9	.	.	PUNCT
ma-167	292	1	(	(	PUNCT
ma-167	292	2	in	in	ADP
ma-167	292	3	japanese).[30	japanese).[30	PROPN
ma-167	292	4	]	]	PUNCT
ma-167	292	5	w.	w.	PROPN
ma-167	292	6	takahashi	takahashi	PROPN
ma-167	292	7	,	,	PUNCT
ma-167	292	8	nonlinear	nonlinear	ADJ
ma-167	292	9	functional	functional	ADJ
ma-167	292	10	analysis	analysis	NOUN
ma-167	292	11	.	.	PUNCT
ma-167	293	1	yokohama	yokohama	PROPN
ma-167	293	2	:	:	PUNCT
ma-167	293	3	yokohama	yokohama	PROPN
ma-167	293	4	publishers	publisher	NOUN
ma-167	293	5	.	.	PUNCT
ma-167	294	1	(	(	PUNCT
ma-167	294	2	2000).[31	2000).[31	X
ma-167	294	3	]	]	X
ma-167	294	4	w.	w.	PROPN
ma-167	294	5	takahashi	takahashi	PROPN
ma-167	294	6	,	,	PUNCT
ma-167	294	7	y.	y.	PROPN
ma-167	294	8	ueda	ueda	PROPN
ma-167	294	9	,	,	PUNCT
ma-167	294	10	on	on	ADP
ma-167	294	11	reich	reich	PROPN
ma-167	294	12	’s	’s	PART
ma-167	294	13	strong	strong	ADJ
ma-167	294	14	convergence	convergence	NOUN
ma-167	294	15	theorems	theorem	NOUN
ma-167	294	16	for	for	ADP
ma-167	294	17	resolvents	resolvent	NOUN
ma-167	294	18	of	of	ADP
ma-167	294	19	accretive	accretive	ADJ
ma-167	294	20	operators	operator	NOUN
ma-167	294	21	,	,	PUNCT
ma-167	294	22	j.	j.	PROPN
ma-167	294	23	math	math	PROPN
ma-167	294	24	.	.	PUNCT
ma-167	295	1	anal.appl	anal.appl	PROPN
ma-167	295	2	.	.	PROPN
ma-167	296	1	104	104	NUM
ma-167	296	2	(	(	PUNCT
ma-167	296	3	1984	1984	NUM
ma-167	296	4	)	)	PUNCT
ma-167	296	5	546	546	NUM
ma-167	296	6	-	-	SYM
ma-167	296	7	553	553	NUM
ma-167	296	8	.	.	PUNCT
ma-167	297	1	https://doi.org/10.1016/0022-247x(84)90019-2.[32	https://doi.org/10.1016/0022-247x(84)90019-2.[32	NOUN
ma-167	297	2	]	]	X
ma-167	297	3	h.k	h.k	PROPN
ma-167	297	4	.	.	PROPN
ma-167	297	5	xu	xu	PROPN
ma-167	297	6	,	,	PUNCT
ma-167	297	7	inequalities	inequality	NOUN
ma-167	297	8	in	in	ADP
ma-167	297	9	banach	banach	NOUN
ma-167	297	10	spaces	space	NOUN
ma-167	297	11	with	with	ADP
ma-167	297	12	applications	application	NOUN
ma-167	297	13	,	,	PUNCT
ma-167	297	14	nonlinear	nonlinear	ADJ
ma-167	297	15	anal	anal	NOUN
ma-167	297	16	.	.	PUNCT
ma-167	297	17	:	:	PUNCT
ma-167	298	1	theory	theory	NOUN
ma-167	298	2	meth	meth	NOUN
ma-167	298	3	.	.	PUNCT
ma-167	299	1	appl	appl	PROPN
ma-167	299	2	.	.	PUNCT
ma-167	300	1	16	16	NUM
ma-167	300	2	(	(	PUNCT
ma-167	300	3	1991	1991	NUM
ma-167	300	4	)	)	PUNCT
ma-167	300	5	1127	1127	NUM
ma-167	300	6	-	-	SYM
ma-167	300	7	1138	1138	NUM
ma-167	300	8	.	.	PUNCT
ma-167	301	1	https://doi.org/10.1016/0362-546x(91)90200-k.[33	https://doi.org/10.1016/0362-546x(91)90200-k.[33	PROPN
ma-167	301	2	]	]	X
ma-167	301	3	ya	ya	PROPN
ma-167	301	4	.	.	PROPN
ma-167	301	5	alber	alber	PROPN
ma-167	301	6	,	,	PUNCT
ma-167	301	7	metric	metric	ADJ
ma-167	301	8	and	and	CCONJ
ma-167	301	9	generalized	generalized	ADJ
ma-167	301	10	projection	projection	NOUN
ma-167	301	11	operator	operator	NOUN
ma-167	301	12	in	in	ADP
ma-167	301	13	banach	banach	NOUN
ma-167	301	14	space	space	NOUN
ma-167	301	15	:	:	PUNCT
ma-167	301	16	properties	property	NOUN
ma-167	301	17	and	and	CCONJ
ma-167	301	18	applications	application	NOUN
ma-167	301	19	,	,	PUNCT
ma-167	301	20	in	in	ADP
ma-167	301	21	:	:	PUNCT
ma-167	301	22	theory	theory	NOUN
ma-167	301	23	andapplications	andapplication	NOUN
ma-167	301	24	of	of	ADP
ma-167	301	25	nonlinear	nonlinear	ADJ
ma-167	301	26	operators	operator	NOUN
ma-167	301	27	of	of	ADP
ma-167	301	28	accretive	accretive	ADJ
ma-167	301	29	and	and	CCONJ
ma-167	301	30	monotone	monotone	ADJ
ma-167	301	31	type	type	NOUN
ma-167	301	32	(	(	PUNCT
ma-167	301	33	ed	ed	NOUN
ma-167	301	34	.	.	PUNCT
ma-167	301	35	a.	a.	PROPN
ma-167	301	36	g.	g.	PROPN
ma-167	301	37	kartsatos	kartsatos	PROPN
ma-167	301	38	)	)	PUNCT
ma-167	301	39	(	(	PUNCT
ma-167	301	40	marcel	marcel	PROPN
ma-167	301	41	dekker	dekker	PROPN
ma-167	301	42	,	,	PUNCT
ma-167	301	43	newyork	newyork	PROPN
ma-167	301	44	,	,	PUNCT
ma-167	301	45	1996	1996	NUM
ma-167	301	46	)	)	PUNCT
ma-167	301	47	,	,	PUNCT
ma-167	301	48	15	15	NUM
ma-167	301	49	-	-	SYM
ma-167	301	50	50.[34	50.[34	PROPN
ma-167	301	51	]	]	X
ma-167	301	52	ya	ya	PROPN
ma-167	301	53	.	.	PROPN
ma-167	301	54	alber	alber	PROPN
ma-167	301	55	,	,	PUNCT
ma-167	301	56	s.	s.	PROPN
ma-167	301	57	guerre	guerre	PROPN
ma-167	301	58	-	-	PUNCT
ma-167	301	59	delabiere	delabiere	PROPN
ma-167	301	60	,	,	PUNCT
ma-167	301	61	on	on	ADP
ma-167	301	62	the	the	DET
ma-167	301	63	projection	projection	NOUN
ma-167	301	64	methods	method	NOUN
ma-167	301	65	for	for	ADP
ma-167	301	66	fixed	fix	VERB
ma-167	301	67	point	point	NOUN
ma-167	301	68	problems	problem	NOUN
ma-167	301	69	,	,	PUNCT
ma-167	301	70	analysis	analysis	NOUN
ma-167	301	71	(	(	PUNCT
ma-167	301	72	munich	munich	PROPN
ma-167	301	73	)	)	PUNCT
ma-167	301	74	.	.	PUNCT
ma-167	302	1	21	21	NUM
ma-167	302	2	(	(	PUNCT
ma-167	302	3	2001)17	2001)17	NUM
ma-167	302	4	-	-	SYM
ma-167	302	5	39.[35	39.[35	PROPN
ma-167	302	6	]	]	X
ma-167	302	7	y.	y.	PROPN
ma-167	302	8	tang	tang	PROPN
ma-167	302	9	,	,	PUNCT
ma-167	302	10	strong	strong	ADJ
ma-167	302	11	convergence	convergence	NOUN
ma-167	302	12	of	of	ADP
ma-167	302	13	new	new	ADJ
ma-167	302	14	algorithm	algorithm	NOUN
ma-167	302	15	for	for	ADP
ma-167	302	16	monotone	monotone	ADJ
ma-167	302	17	operator	operator	NOUN
ma-167	302	18	in	in	ADP
ma-167	302	19	banach	banach	NOUN
ma-167	302	20	spaces	space	NOUN
ma-167	302	21	,	,	PUNCT
ma-167	302	22	num	num	PROPN
ma-167	302	23	.	.	PUNCT
ma-167	302	24	funct	funct	PROPN
ma-167	302	25	.	.	PUNCT
ma-167	303	1	anal	anal	PROPN
ma-167	303	2	.	.	PUNCT
ma-167	304	1	optim.40	optim.40	PROPN
ma-167	304	2	(	(	PUNCT
ma-167	304	3	2019	2019	NUM
ma-167	304	4	)	)	PUNCT
ma-167	304	5	1426	1426	NUM
ma-167	304	6	-	-	SYM
ma-167	304	7	1447	1447	NUM
ma-167	304	8	.	.	PUNCT
ma-167	305	1	https://doi.org/10.1080/01630563.2019.1606825.[36	https://doi.org/10.1080/01630563.2019.1606825.[36	PROPN
ma-167	305	2	]	]	PUNCT
ma-167	305	3	y.	y.	PROPN
ma-167	305	4	tang	tang	PROPN
ma-167	305	5	,	,	PUNCT
ma-167	305	6	strong	strong	ADJ
ma-167	305	7	convergence	convergence	NOUN
ma-167	305	8	of	of	ADP
ma-167	305	9	new	new	ADJ
ma-167	305	10	algorithm	algorithm	NOUN
ma-167	305	11	for	for	ADP
ma-167	305	12	monotone	monotone	ADJ
ma-167	305	13	operator	operator	NOUN
ma-167	305	14	in	in	ADP
ma-167	305	15	banach	banach	NOUN
ma-167	305	16	spaces	space	NOUN
ma-167	305	17	,	,	PUNCT
ma-167	305	18	num	num	PROPN
ma-167	305	19	.	.	PUNCT
ma-167	305	20	funct	funct	PROPN
ma-167	305	21	.	.	PUNCT
ma-167	306	1	anal	anal	PROPN
ma-167	306	2	.	.	PUNCT
ma-167	307	1	optim.40	optim.40	PROPN
ma-167	307	2	(	(	PUNCT
ma-167	307	3	2019	2019	NUM
ma-167	307	4	)	)	PUNCT
ma-167	307	5	1426	1426	NUM
ma-167	307	6	-	-	SYM
ma-167	307	7	1447	1447	NUM
ma-167	307	8	.	.	PUNCT
ma-167	308	1	https://doi.org/10.1080/01630563.2019.1606825.[37	https://doi.org/10.1080/01630563.2019.1606825.[37	PROPN
ma-167	308	2	]	]	PUNCT
ma-167	309	1	h.	h.	PROPN
ma-167	309	2	zegeye	zegeye	PROPN
ma-167	309	3	,	,	PUNCT
ma-167	309	4	n.	n.	PROPN
ma-167	309	5	shahzad	shahzad	PROPN
ma-167	309	6	,	,	PUNCT
ma-167	309	7	an	an	DET
ma-167	309	8	algorithm	algorithm	NOUN
ma-167	309	9	for	for	ADP
ma-167	309	10	a	a	DET
ma-167	309	11	common	common	ADJ
ma-167	309	12	minimum	minimum	ADJ
ma-167	309	13	-	-	PUNCT
ma-167	309	14	norm	norm	NOUN
ma-167	309	15	zero	zero	NUM
ma-167	309	16	of	of	ADP
ma-167	309	17	a	a	DET
ma-167	309	18	finite	finite	ADJ
ma-167	309	19	family	family	NOUN
ma-167	309	20	of	of	ADP
ma-167	309	21	monotone	monotone	ADJ
ma-167	309	22	mappings	mapping	NOUN
ma-167	309	23	inbanach	inbanach	ADJ
ma-167	309	24	spaces	space	NOUN
ma-167	309	25	,	,	PUNCT
ma-167	309	26	j.	j.	PROPN
ma-167	309	27	ineq	ineq	PROPN
ma-167	309	28	.	.	PUNCT
ma-167	310	1	appl	appl	PROPN
ma-167	310	2	.	.	PUNCT
ma-167	311	1	2013	2013	NUM
ma-167	311	2	(	(	PUNCT
ma-167	311	3	2013	2013	NUM
ma-167	311	4	)	)	PUNCT
ma-167	311	5	566	566	NUM
ma-167	311	6	.	.	PUNCT
ma-167	312	1	https://doi.org/10.1186/1029-242x-2013-566	https://doi.org/10.1186/1029-242x-2013-566	PROPN
ma-167	312	2	.	.	PUNCT
ma-167	313	1	https://doi.org/10.28924/ada/ma.3.18	https://doi.org/10.28924/ada/ma.3.18	PROPN
ma-167	313	2	https://doi.org/10.1016/0022-247x(84)90019-2	https://doi.org/10.1016/0022-247x(84)90019-2	PROPN
ma-167	313	3	https://doi.org/10.1016/0362-546x(91)90200-k	https://doi.org/10.1016/0362-546x(91)90200-k	PROPN
ma-167	313	4	https://doi.org/10.1080/01630563.2019.1606825	https://doi.org/10.1080/01630563.2019.1606825	PROPN
ma-167	313	5	https://doi.org/10.1080/01630563.2019.1606825	https://doi.org/10.1080/01630563.2019.1606825	PROPN
ma-167	314	1	https://doi.org/10.1186/1029-242x-2013-566	https://doi.org/10.1186/1029-242x-2013-566	PROPN
ma-167	314	2	1	1	NUM
ma-167	314	3	.	.	PUNCT
ma-167	314	4	introduction	introduction	NOUN
ma-167	314	5	2	2	NUM
ma-167	314	6	.	.	PUNCT
ma-167	314	7	preliminaries	preliminary	NOUN
ma-167	314	8	3	3	NUM
ma-167	314	9	.	.	X
ma-167	314	10	main	main	ADJ
ma-167	314	11	result	result	NOUN
ma-167	314	12	4	4	NUM
ma-167	314	13	.	.	X
ma-167	314	14	convergence	convergence	NOUN
ma-167	314	15	in	in	ADP
ma-167	314	16	lp	lp	NOUN
ma-167	314	17	,	,	PUNCT
ma-167	314	18	p	p	NOUN
ma-167	314	19	or	or	CCONJ
ma-167	314	20	wm	wm	PROPN
ma-167	314	21	,	,	PUNCT
ma-167	314	22	p	p	X
ma-167	314	23	,	,	PUNCT
ma-167	314	24	2p	2p	NOUN
ma-167	314	25	<	<	X
ma-167	314	26	5	5	NUM
ma-167	314	27	.	.	PUNCT
ma-167	314	28	application	application	NOUN
ma-167	314	29	to	to	PART
ma-167	314	30	convex	convex	VERB
ma-167	314	31	minimization	minimization	NOUN
ma-167	314	32	problem	problem	NOUN
ma-167	314	33	6	6	NUM
ma-167	314	34	.	.	PUNCT
ma-167	315	1	the	the	DET
ma-167	315	2	proposed	propose	VERB
ma-167	315	3	algorithm	algorithm	NOUN
ma-167	315	4	in	in	ADP
ma-167	315	5	lp	lp	PROPN
ma-167	315	6	(	(	PUNCT
ma-167	315	7	)	)	PUNCT
ma-167	315	8	conclusion	conclusion	NOUN
ma-167	315	9	references	reference	NOUN