id	sid	tid	token	lemma	pos
ejpam-6173	1	1	european	european	PROPN
ejpam-6173	1	2	journal	journal	PROPN
ejpam-6173	1	3	of	of	ADP
ejpam-6173	1	4	pure	pure	ADJ
ejpam-6173	1	5	and	and	CCONJ
ejpam-6173	1	6	applied	applied	ADJ
ejpam-6173	1	7	mathematics	mathematic	NOUN
ejpam-6173	1	8	2025	2025	NUM
ejpam-6173	1	9	,	,	PUNCT
ejpam-6173	1	10	vol	vol	NOUN
ejpam-6173	1	11	.	.	PROPN
ejpam-6173	1	12	18	18	NUM
ejpam-6173	1	13	,	,	PUNCT
ejpam-6173	1	14	issue	issue	NOUN
ejpam-6173	1	15	3	3	NUM
ejpam-6173	1	16	,	,	PUNCT
ejpam-6173	1	17	article	article	NOUN
ejpam-6173	1	18	number	number	NOUN
ejpam-6173	1	19	6173	6173	NUM
ejpam-6173	1	20	issn	issn	VERB
ejpam-6173	1	21	1307	1307	NUM
ejpam-6173	1	22	-	-	SYM
ejpam-6173	1	23	5543	5543	NUM
ejpam-6173	1	24	–	–	PUNCT
ejpam-6173	1	25	ejpam.com	ejpam.com	X
ejpam-6173	1	26	published	publish	VERB
ejpam-6173	1	27	by	by	ADP
ejpam-6173	1	28	new	new	PROPN
ejpam-6173	1	29	york	york	PROPN
ejpam-6173	1	30	business	business	PROPN
ejpam-6173	1	31	global	global	ADJ
ejpam-6173	1	32	inertial	inertial	ADJ
ejpam-6173	1	33	iterative	iterative	NOUN
ejpam-6173	1	34	method	method	NOUN
ejpam-6173	1	35	for	for	ADP
ejpam-6173	1	36	generalized	generalized	ADJ
ejpam-6173	1	37	mixed	mixed	ADJ
ejpam-6173	1	38	equilibrium	equilibrium	NOUN
ejpam-6173	1	39	problem	problem	NOUN
ejpam-6173	1	40	and	and	CCONJ
ejpam-6173	1	41	fixed	fix	VERB
ejpam-6173	1	42	point	point	NOUN
ejpam-6173	1	43	problem	problem	NOUN
ejpam-6173	1	44	vahid	vahid	PROPN
ejpam-6173	1	45	darvish1	darvish1	PROPN
ejpam-6173	1	46	,	,	PUNCT
ejpam-6173	1	47	grace	grace	NOUN
ejpam-6173	1	48	nnennaya	nnennaya	NOUN
ejpam-6173	1	49	ogwo2,∗	ogwo2,∗	PROPN
ejpam-6173	1	50	,	,	PUNCT
ejpam-6173	1	51	olawale	olawale	ADJ
ejpam-6173	1	52	kazeem	kazeem	NOUN
ejpam-6173	1	53	oyewole3,4	oyewole3,4	PROPN
ejpam-6173	1	54	,	,	PUNCT
ejpam-6173	1	55	hammed	ham	VERB
ejpam-6173	1	56	anuoluwapo	anuoluwapo	PROPN
ejpam-6173	1	57	abass5,6	abass5,6	PROPN
ejpam-6173	1	58	,	,	PUNCT
ejpam-6173	1	59	amirbek	amirbek	PROPN
ejpam-6173	1	60	aminovich	aminovich	PROPN
ejpam-6173	1	61	ikramov6	ikramov6	PROPN
ejpam-6173	1	62	1	1	NUM
ejpam-6173	1	63	department	department	NOUN
ejpam-6173	1	64	of	of	ADP
ejpam-6173	1	65	mathematics	mathematic	NOUN
ejpam-6173	1	66	and	and	CCONJ
ejpam-6173	1	67	statistics	statistic	NOUN
ejpam-6173	1	68	,	,	PUNCT
ejpam-6173	1	69	nanjing	nanjing	PROPN
ejpam-6173	1	70	university	university	PROPN
ejpam-6173	1	71	of	of	ADP
ejpam-6173	1	72	information	information	NOUN
ejpam-6173	1	73	science	science	NOUN
ejpam-6173	1	74	and	and	CCONJ
ejpam-6173	1	75	technology	technology	NOUN
ejpam-6173	1	76	,	,	PUNCT
ejpam-6173	1	77	nanjing	nanjing	PROPN
ejpam-6173	1	78	china	china	PROPN
ejpam-6173	1	79	2	2	NUM
ejpam-6173	1	80	school	school	NOUN
ejpam-6173	1	81	of	of	ADP
ejpam-6173	1	82	mathematical	mathematical	ADJ
ejpam-6173	1	83	sciences	sciences	PROPN
ejpam-6173	1	84	,	,	PUNCT
ejpam-6173	1	85	zhejiang	zhejiang	PROPN
ejpam-6173	1	86	normal	normal	PROPN
ejpam-6173	1	87	university	university	PROPN
ejpam-6173	1	88	,	,	PUNCT
ejpam-6173	1	89	jinhua	jinhua	PROPN
ejpam-6173	1	90	321004	321004	NUM
ejpam-6173	1	91	,	,	PUNCT
ejpam-6173	1	92	china	china	PROPN
ejpam-6173	1	93	3	3	NUM
ejpam-6173	1	94	department	department	NOUN
ejpam-6173	1	95	of	of	ADP
ejpam-6173	1	96	mathematics	mathematic	NOUN
ejpam-6173	1	97	and	and	CCONJ
ejpam-6173	1	98	statistics	statistic	NOUN
ejpam-6173	1	99	,	,	PUNCT
ejpam-6173	1	100	tshwane	tshwane	NOUN
ejpam-6173	1	101	university	university	NOUN
ejpam-6173	1	102	of	of	ADP
ejpam-6173	1	103	technology	technology	PROPN
ejpam-6173	1	104	,	,	PUNCT
ejpam-6173	1	105	pmb	pmb	PROPN
ejpam-6173	1	106	007	007	NUM
ejpam-6173	1	107	,	,	PUNCT
ejpam-6173	1	108	arcadia	arcadia	PROPN
ejpam-6173	1	109	,	,	PUNCT
ejpam-6173	1	110	pretoria	pretoria	PROPN
ejpam-6173	1	111	,	,	PUNCT
ejpam-6173	1	112	south	south	PROPN
ejpam-6173	1	113	africa	africa	PROPN
ejpam-6173	1	114	4	4	NUM
ejpam-6173	1	115	department	department	NOUN
ejpam-6173	1	116	of	of	ADP
ejpam-6173	1	117	mathematics	mathematic	NOUN
ejpam-6173	1	118	,	,	PUNCT
ejpam-6173	1	119	saveetha	saveetha	PROPN
ejpam-6173	1	120	school	school	PROPN
ejpam-6173	1	121	of	of	ADP
ejpam-6173	1	122	engineering	engineering	PROPN
ejpam-6173	1	123	,	,	PUNCT
ejpam-6173	1	124	saveetha	saveetha	PROPN
ejpam-6173	1	125	institute	institute	PROPN
ejpam-6173	1	126	of	of	ADP
ejpam-6173	1	127	medical	medical	ADJ
ejpam-6173	1	128	and	and	CCONJ
ejpam-6173	1	129	technical	technical	ADJ
ejpam-6173	1	130	sciences	science	NOUN
ejpam-6173	1	131	,	,	PUNCT
ejpam-6173	1	132	saveetha	saveetha	PROPN
ejpam-6173	1	133	university	university	PROPN
ejpam-6173	1	134	,	,	PUNCT
ejpam-6173	1	135	chennai	chennai	VERB
ejpam-6173	1	136	602	602	NUM
ejpam-6173	1	137	105	105	NUM
ejpam-6173	1	138	,	,	PUNCT
ejpam-6173	1	139	tamil	tamil	PROPN
ejpam-6173	1	140	nadu	nadu	PROPN
ejpam-6173	1	141	,	,	PUNCT
ejpam-6173	1	142	india	india	PROPN
ejpam-6173	1	143	5	5	NUM
ejpam-6173	1	144	department	department	NOUN
ejpam-6173	1	145	of	of	ADP
ejpam-6173	1	146	mathematics	mathematic	NOUN
ejpam-6173	1	147	and	and	CCONJ
ejpam-6173	1	148	applied	apply	VERB
ejpam-6173	1	149	mathematics	mathematic	NOUN
ejpam-6173	1	150	,	,	PUNCT
ejpam-6173	1	151	sefako	sefako	ADJ
ejpam-6173	1	152	makgato	makgato	ADJ
ejpam-6173	1	153	health	health	PROPN
ejpam-6173	1	154	science	science	PROPN
ejpam-6173	1	155	university	university	PROPN
ejpam-6173	1	156	,	,	PUNCT
ejpam-6173	1	157	p.o	p.o	PROPN
ejpam-6173	1	158	.	.	PROPN
ejpam-6173	1	159	box	box	PROPN
ejpam-6173	1	160	94	94	PROPN
ejpam-6173	1	161	,	,	PUNCT
ejpam-6173	1	162	pretoria	pretoria	PROPN
ejpam-6173	1	163	0204	0204	NUM
ejpam-6173	1	164	,	,	PUNCT
ejpam-6173	1	165	south	south	PROPN
ejpam-6173	1	166	africa	africa	PROPN
ejpam-6173	2	1	6center	6center	NUM
ejpam-6173	2	2	of	of	ADP
ejpam-6173	2	3	research	research	NOUN
ejpam-6173	2	4	and	and	CCONJ
ejpam-6173	2	5	innovation	innovation	NOUN
ejpam-6173	2	6	,	,	PUNCT
ejpam-6173	3	1	asia	asia	PROPN
ejpam-6173	3	2	international	international	PROPN
ejpam-6173	3	3	university	university	PROPN
ejpam-6173	3	4	,	,	PUNCT
ejpam-6173	3	5	yangiobod	yangiobod	ADJ
ejpam-6173	3	6	mfy	mfy	NOUN
ejpam-6173	3	7	,	,	PUNCT
ejpam-6173	3	8	g‘ijduvon	g‘ijduvon	PROPN
ejpam-6173	3	9	street	street	PROPN
ejpam-6173	3	10	,	,	PUNCT
ejpam-6173	3	11	house	house	NOUN
ejpam-6173	3	12	74	74	NUM
ejpam-6173	3	13	,	,	PUNCT
ejpam-6173	3	14	bukhara	bukhara	PROPN
ejpam-6173	3	15	,	,	PUNCT
ejpam-6173	3	16	uzbekistan	uzbekistan	PROPN
ejpam-6173	3	17	abstract	abstract	NOUN
ejpam-6173	3	18	.	.	PUNCT
ejpam-6173	4	1	in	in	ADP
ejpam-6173	4	2	this	this	DET
ejpam-6173	4	3	paper	paper	NOUN
ejpam-6173	4	4	,	,	PUNCT
ejpam-6173	4	5	we	we	PRON
ejpam-6173	4	6	study	study	VERB
ejpam-6173	4	7	the	the	DET
ejpam-6173	4	8	generalized	generalize	VERB
ejpam-6173	4	9	mixed	mixed	ADJ
ejpam-6173	4	10	equilibrium	equilibrium	NOUN
ejpam-6173	4	11	problem	problem	NOUN
ejpam-6173	4	12	and	and	CCONJ
ejpam-6173	4	13	the	the	DET
ejpam-6173	4	14	fixed	fix	VERB
ejpam-6173	4	15	point	point	NOUN
ejpam-6173	4	16	problem	problem	NOUN
ejpam-6173	4	17	.	.	PUNCT
ejpam-6173	5	1	we	we	PRON
ejpam-6173	5	2	propose	propose	VERB
ejpam-6173	5	3	an	an	DET
ejpam-6173	5	4	inertial	inertial	ADJ
ejpam-6173	5	5	iterative	iterative	NOUN
ejpam-6173	5	6	method	method	NOUN
ejpam-6173	5	7	for	for	ADP
ejpam-6173	5	8	approximating	approximate	VERB
ejpam-6173	5	9	the	the	DET
ejpam-6173	5	10	common	common	ADJ
ejpam-6173	5	11	solution	solution	NOUN
ejpam-6173	5	12	of	of	ADP
ejpam-6173	5	13	a	a	DET
ejpam-6173	5	14	generalized	generalize	VERB
ejpam-6173	5	15	mixed	mixed	ADJ
ejpam-6173	5	16	equilibrium	equilibrium	NOUN
ejpam-6173	5	17	problem	problem	NOUN
ejpam-6173	5	18	of	of	ADP
ejpam-6173	5	19	a	a	DET
ejpam-6173	5	20	monotone	monotone	ADJ
ejpam-6173	5	21	mapping	mapping	NOUN
ejpam-6173	5	22	and	and	CCONJ
ejpam-6173	5	23	a	a	DET
ejpam-6173	5	24	fixed	fix	VERB
ejpam-6173	5	25	point	point	NOUN
ejpam-6173	5	26	problem	problem	NOUN
ejpam-6173	5	27	for	for	ADP
ejpam-6173	5	28	a	a	DET
ejpam-6173	5	29	bregman	bregman	NOUN
ejpam-6173	5	30	strongly	strongly	ADV
ejpam-6173	5	31	nonexpansive	nonexpansive	ADJ
ejpam-6173	5	32	mapping	mapping	NOUN
ejpam-6173	5	33	in	in	ADP
ejpam-6173	5	34	the	the	DET
ejpam-6173	5	35	framework	framework	NOUN
ejpam-6173	5	36	of	of	ADP
ejpam-6173	5	37	real	real	ADJ
ejpam-6173	5	38	reflexive	reflexive	ADJ
ejpam-6173	5	39	banach	banach	NOUN
ejpam-6173	5	40	spaces	space	VERB
ejpam-6173	5	41	.	.	PUNCT
ejpam-6173	6	1	under	under	ADP
ejpam-6173	6	2	certain	certain	ADJ
ejpam-6173	6	3	mild	mild	ADJ
ejpam-6173	6	4	conditions	condition	NOUN
ejpam-6173	6	5	,	,	PUNCT
ejpam-6173	6	6	we	we	PRON
ejpam-6173	6	7	obtain	obtain	VERB
ejpam-6173	6	8	a	a	DET
ejpam-6173	6	9	strong	strong	ADJ
ejpam-6173	6	10	convergence	convergence	NOUN
ejpam-6173	6	11	result	result	NOUN
ejpam-6173	6	12	of	of	ADP
ejpam-6173	6	13	the	the	DET
ejpam-6173	6	14	proposed	propose	VERB
ejpam-6173	6	15	method	method	NOUN
ejpam-6173	6	16	.	.	PUNCT
ejpam-6173	7	1	finally	finally	ADV
ejpam-6173	7	2	,	,	PUNCT
ejpam-6173	7	3	we	we	PRON
ejpam-6173	7	4	present	present	VERB
ejpam-6173	7	5	numerical	numerical	ADJ
ejpam-6173	7	6	examples	example	NOUN
ejpam-6173	7	7	to	to	PART
ejpam-6173	7	8	illustrate	illustrate	VERB
ejpam-6173	7	9	the	the	DET
ejpam-6173	7	10	applicability	applicability	NOUN
ejpam-6173	7	11	of	of	ADP
ejpam-6173	7	12	our	our	PRON
ejpam-6173	7	13	method	method	NOUN
ejpam-6173	7	14	.	.	PUNCT
ejpam-6173	8	1	2020	2020	NUM
ejpam-6173	8	2	mathematics	mathematic	NOUN
ejpam-6173	8	3	subject	subject	NOUN
ejpam-6173	8	4	classifications	classification	NOUN
ejpam-6173	8	5	:	:	PUNCT
ejpam-6173	8	6	47h05	47h05	NUM
ejpam-6173	8	7	,	,	PUNCT
ejpam-6173	8	8	47h09	47h09	NUM
ejpam-6173	8	9	,	,	PUNCT
ejpam-6173	8	10	47j05	47j05	NUM
ejpam-6173	8	11	,	,	PUNCT
ejpam-6173	8	12	49j25	49j25	DET
ejpam-6173	8	13	key	key	ADJ
ejpam-6173	8	14	words	word	NOUN
ejpam-6173	8	15	and	and	CCONJ
ejpam-6173	8	16	phrases	phrase	NOUN
ejpam-6173	8	17	:	:	PUNCT
ejpam-6173	8	18	generalized	generalize	VERB
ejpam-6173	8	19	mixed	mixed	ADJ
ejpam-6173	8	20	equilibrium	equilibrium	NOUN
ejpam-6173	8	21	problem	problem	NOUN
ejpam-6173	8	22	,	,	PUNCT
ejpam-6173	8	23	fixed	fix	VERB
ejpam-6173	8	24	point	point	NOUN
ejpam-6173	8	25	problem	problem	NOUN
ejpam-6173	8	26	,	,	PUNCT
ejpam-6173	8	27	inertial	inertial	ADJ
ejpam-6173	8	28	technique	technique	NOUN
ejpam-6173	8	29	,	,	PUNCT
ejpam-6173	8	30	bregman	bregman	NOUN
ejpam-6173	8	31	strongly	strongly	ADV
ejpam-6173	8	32	nonexpansive	nonexpansive	ADJ
ejpam-6173	8	33	mapping	mapping	NOUN
ejpam-6173	8	34	1	1	NUM
ejpam-6173	8	35	.	.	PUNCT
ejpam-6173	8	36	introduction	introduction	NOUN
ejpam-6173	8	37	let	let	VERB
ejpam-6173	8	38	e	e	PRON
ejpam-6173	8	39	be	be	AUX
ejpam-6173	8	40	a	a	DET
ejpam-6173	8	41	real	real	ADJ
ejpam-6173	8	42	reflexive	reflexive	ADJ
ejpam-6173	8	43	banach	banach	NOUN
ejpam-6173	8	44	space	space	NOUN
ejpam-6173	8	45	and	and	CCONJ
ejpam-6173	8	46	e∗	e∗	NOUN
ejpam-6173	8	47	be	be	AUX
ejpam-6173	8	48	its	its	PRON
ejpam-6173	8	49	dual	dual	ADJ
ejpam-6173	8	50	space	space	NOUN
ejpam-6173	8	51	.	.	PUNCT
ejpam-6173	9	1	let	let	VERB
ejpam-6173	9	2	c	c	PRON
ejpam-6173	9	3	be	be	AUX
ejpam-6173	9	4	a	a	DET
ejpam-6173	9	5	nonempty	nonempty	ADJ
ejpam-6173	9	6	,	,	PUNCT
ejpam-6173	9	7	closed	closed	ADJ
ejpam-6173	9	8	and	and	CCONJ
ejpam-6173	9	9	convex	convex	NOUN
ejpam-6173	9	10	subset	subset	NOUN
ejpam-6173	9	11	of	of	ADP
ejpam-6173	9	12	e	e	PROPN
ejpam-6173	9	13	,	,	PUNCT
ejpam-6173	9	14	θ	θ	NOUN
ejpam-6173	9	15	:	:	PUNCT
ejpam-6173	9	16	c	c	X
ejpam-6173	9	17	×	×	NOUN
ejpam-6173	9	18	c	c	NOUN
ejpam-6173	9	19	→	→	PUNCT
ejpam-6173	9	20	r	r	NOUN
ejpam-6173	9	21	a	a	DET
ejpam-6173	9	22	bifunction	bifunction	NOUN
ejpam-6173	9	23	,	,	PUNCT
ejpam-6173	9	24	ψ	ψ	X
ejpam-6173	9	25	:	:	PUNCT
ejpam-6173	9	26	c	c	X
ejpam-6173	9	27	→	→	SYM
ejpam-6173	9	28	e∗	e∗	PROPN
ejpam-6173	9	29	a	a	DET
ejpam-6173	9	30	nonlinear	nonlinear	ADJ
ejpam-6173	9	31	∗corresponding	∗corresponde	VERB
ejpam-6173	9	32	author	author	NOUN
ejpam-6173	9	33	.	.	PUNCT
ejpam-6173	10	1	doi	doi	NOUN
ejpam-6173	10	2	:	:	PUNCT
ejpam-6173	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6173	https://doi.org/10.29020/nybg.ejpam.v18i3.6173	NOUN
ejpam-6173	10	4	email	email	NOUN
ejpam-6173	10	5	addresses	address	NOUN
ejpam-6173	10	6	:	:	PUNCT
ejpam-6173	10	7	vahid.darvish@mail.com	vahid.darvish@mail.com	NUM
ejpam-6173	10	8	,	,	PUNCT
ejpam-6173	10	9	vdarvish@nuist.edu.cn	vdarvish@nuist.edu.cn	NOUN
ejpam-6173	10	10	(	(	PUNCT
ejpam-6173	10	11	v.	v.	X
ejpam-6173	10	12	darvish	darvish	PROPN
ejpam-6173	10	13	)	)	PUNCT
ejpam-6173	10	14	,	,	PUNCT
ejpam-6173	10	15	graceogwo@zjnu.edu.cn	graceogwo@zjnu.edu.cn	NOUN
ejpam-6173	10	16	(	(	PUNCT
ejpam-6173	10	17	g.	g.	PROPN
ejpam-6173	10	18	n.	n.	PROPN
ejpam-6173	10	19	ogwo	ogwo	PROPN
ejpam-6173	10	20	)	)	PUNCT
ejpam-6173	10	21	,	,	PUNCT
ejpam-6173	10	22	oyewoleolawalekazeem@gmail.com	oyewoleolawalekazeem@gmail.com	X
ejpam-6173	10	23	(	(	PUNCT
ejpam-6173	10	24	o.	o.	PROPN
ejpam-6173	10	25	k.	k.	PROPN
ejpam-6173	10	26	oyewole	oyewole	PROPN
ejpam-6173	10	27	)	)	PUNCT
ejpam-6173	10	28	,	,	PUNCT
ejpam-6173	10	29	hammedabass548@gmail.com,hammed.abass@smu.ac.za	hammedabass548@gmail.com,hammed.abass@smu.ac.za	PROPN
ejpam-6173	10	30	(	(	PUNCT
ejpam-6173	10	31	h.	h.	PROPN
ejpam-6173	10	32	a.	a.	PROPN
ejpam-6173	10	33	abass	abass	PROPN
ejpam-6173	10	34	)	)	PUNCT
ejpam-6173	10	35	,	,	PUNCT
ejpam-6173	10	36	amirbekikramov@oxu.uz	amirbekikramov@oxu.uz	PROPN
ejpam-6173	10	37	(	(	PUNCT
ejpam-6173	10	38	a.	a.	NOUN
ejpam-6173	10	39	a.	a.	PROPN
ejpam-6173	10	40	ikramov	ikramov	PROPN
ejpam-6173	10	41	)	)	PUNCT
ejpam-6173	10	42	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6173	10	43	1	1	NUM
ejpam-6173	10	44	copyright	copyright	NOUN
ejpam-6173	10	45	:	:	PUNCT
ejpam-6173	11	1	©	©	PROPN
ejpam-6173	11	2	2025	2025	NUM
ejpam-6173	11	3	the	the	DET
ejpam-6173	11	4	author(s	author(s	NOUN
ejpam-6173	11	5	)	)	PUNCT
ejpam-6173	11	6	.	.	PUNCT
ejpam-6173	12	1	(	(	PUNCT
ejpam-6173	12	2	cc	cc	NOUN
ejpam-6173	12	3	by	by	ADP
ejpam-6173	12	4	-	-	PUNCT
ejpam-6173	12	5	nc	nc	PROPN
ejpam-6173	12	6	4.0	4.0	NUM
ejpam-6173	12	7	)	)	PUNCT
ejpam-6173	12	8	v.	v.	ADP
ejpam-6173	12	9	darvish	darvish	PROPN
ejpam-6173	12	10	et	et	PROPN
ejpam-6173	12	11	al	al	PROPN
ejpam-6173	12	12	.	.	PUNCT
ejpam-6173	12	13	/	/	SYM
ejpam-6173	12	14	eur	eur	PROPN
ejpam-6173	12	15	.	.	PUNCT
ejpam-6173	13	1	j.	j.	PROPN
ejpam-6173	13	2	pure	pure	PROPN
ejpam-6173	13	3	appl	appl	PROPN
ejpam-6173	13	4	.	.	PROPN
ejpam-6173	13	5	math	math	PROPN
ejpam-6173	13	6	,	,	PUNCT
ejpam-6173	13	7	18	18	NUM
ejpam-6173	13	8	(	(	PUNCT
ejpam-6173	13	9	3	3	NUM
ejpam-6173	13	10	)	)	PUNCT
ejpam-6173	13	11	(	(	PUNCT
ejpam-6173	13	12	2025	2025	NUM
ejpam-6173	13	13	)	)	PUNCT
ejpam-6173	13	14	,	,	PUNCT
ejpam-6173	13	15	6173	6173	NUM
ejpam-6173	13	16	2	2	NUM
ejpam-6173	13	17	of	of	ADP
ejpam-6173	13	18	32	32	NUM
ejpam-6173	13	19	mapping	mapping	NOUN
ejpam-6173	13	20	and	and	CCONJ
ejpam-6173	13	21	φ	φ	NOUN
ejpam-6173	13	22	:	:	PUNCT
ejpam-6173	14	1	c	c	X
ejpam-6173	14	2	→	→	PUNCT
ejpam-6173	14	3	r	r	NOUN
ejpam-6173	14	4	a	a	DET
ejpam-6173	14	5	real	real	ADV
ejpam-6173	14	6	valued	value	VERB
ejpam-6173	14	7	function	function	NOUN
ejpam-6173	14	8	.	.	PUNCT
ejpam-6173	15	1	the	the	DET
ejpam-6173	15	2	generalized	generalize	VERB
ejpam-6173	15	3	mixed	mixed	ADJ
ejpam-6173	15	4	equilibrium	equilibrium	NOUN
ejpam-6173	15	5	problem	problem	NOUN
ejpam-6173	15	6	(	(	PUNCT
ejpam-6173	15	7	gmep	gmep	PROPN
ejpam-6173	15	8	)	)	PUNCT
ejpam-6173	15	9	is	be	AUX
ejpam-6173	15	10	defined	define	VERB
ejpam-6173	15	11	as	as	SCONJ
ejpam-6173	15	12	follows	follow	VERB
ejpam-6173	15	13	:	:	PUNCT
ejpam-6173	15	14	find	find	VERB
ejpam-6173	15	15	x	x	X
ejpam-6173	15	16	∈	∈	PROPN
ejpam-6173	15	17	c	c	NOUN
ejpam-6173	15	18	such	such	ADJ
ejpam-6173	15	19	that	that	SCONJ
ejpam-6173	15	20	θ(x	θ(x	PROPN
ejpam-6173	15	21	,	,	PUNCT
ejpam-6173	15	22	y	y	PROPN
ejpam-6173	15	23	)	)	PUNCT
ejpam-6173	16	1	+	+	CCONJ
ejpam-6173	16	2	⟨ψx	⟨ψx	PROPN
ejpam-6173	16	3	,	,	PUNCT
ejpam-6173	16	4	y	y	PROPN
ejpam-6173	16	5	−	−	PROPN
ejpam-6173	16	6	x⟩+	x⟩+	PROPN
ejpam-6173	16	7	φ(y	φ(y	PROPN
ejpam-6173	16	8	)	)	PUNCT
ejpam-6173	16	9	≥	≥	NOUN
ejpam-6173	16	10	φ(x	φ(x	PROPN
ejpam-6173	16	11	)	)	PUNCT
ejpam-6173	16	12	,	,	PUNCT
ejpam-6173	16	13	for	for	ADP
ejpam-6173	16	14	all	all	DET
ejpam-6173	16	15	y	y	PROPN
ejpam-6173	16	16	∈	∈	PROPN
ejpam-6173	16	17	c.	c.	NOUN
ejpam-6173	16	18	(	(	PUNCT
ejpam-6173	16	19	1.1	1.1	NUM
ejpam-6173	16	20	)	)	PUNCT
ejpam-6173	16	21	the	the	DET
ejpam-6173	16	22	set	set	NOUN
ejpam-6173	16	23	of	of	ADP
ejpam-6173	16	24	solutions	solution	NOUN
ejpam-6173	16	25	of	of	ADP
ejpam-6173	16	26	(	(	PUNCT
ejpam-6173	16	27	1.1	1.1	NUM
ejpam-6173	16	28	)	)	PUNCT
ejpam-6173	16	29	is	be	AUX
ejpam-6173	16	30	denoted	denote	VERB
ejpam-6173	16	31	by	by	ADP
ejpam-6173	16	32	gmep(θ	gmep(θ	PROPN
ejpam-6173	16	33	,	,	PUNCT
ejpam-6173	16	34	ψ	ψ	PROPN
ejpam-6173	16	35	,	,	PUNCT
ejpam-6173	16	36	φ	φ	NUM
ejpam-6173	16	37	)	)	PUNCT
ejpam-6173	16	38	,	,	PUNCT
ejpam-6173	16	39	that	that	PRON
ejpam-6173	16	40	is	be	AUX
ejpam-6173	16	41	gmep(θ	gmep(θ	PROPN
ejpam-6173	16	42	,	,	PUNCT
ejpam-6173	16	43	ψ	ψ	PROPN
ejpam-6173	16	44	,	,	PUNCT
ejpam-6173	16	45	φ	φ	NUM
ejpam-6173	16	46	)	)	PUNCT
ejpam-6173	17	1	=	=	PRON
ejpam-6173	17	2	{	{	PUNCT
ejpam-6173	17	3	x	x	PUNCT
ejpam-6173	17	4	∈	∈	PROPN
ejpam-6173	17	5	c	c	NOUN
ejpam-6173	17	6	:	:	PUNCT
ejpam-6173	17	7	θ(x	θ(x	PROPN
ejpam-6173	17	8	,	,	PUNCT
ejpam-6173	17	9	y	y	PROPN
ejpam-6173	17	10	)	)	PUNCT
ejpam-6173	17	11	+	+	CCONJ
ejpam-6173	17	12	⟨ψx	⟨ψx	PROPN
ejpam-6173	17	13	,	,	PUNCT
ejpam-6173	17	14	y	y	PROPN
ejpam-6173	17	15	−	−	PROPN
ejpam-6173	17	16	x⟩+	x⟩+	PROPN
ejpam-6173	17	17	φ(y	φ(y	PROPN
ejpam-6173	17	18	)	)	PUNCT
ejpam-6173	17	19	≥	≥	NOUN
ejpam-6173	17	20	φ(x	φ(x	PROPN
ejpam-6173	17	21	)	)	PUNCT
ejpam-6173	17	22	,	,	PUNCT
ejpam-6173	17	23	for	for	ADP
ejpam-6173	17	24	all	all	DET
ejpam-6173	17	25	y	y	PROPN
ejpam-6173	17	26	∈	∈	PROPN
ejpam-6173	17	27	c	c	X
ejpam-6173	17	28	}	}	PUNCT
ejpam-6173	17	29	.	.	PUNCT
ejpam-6173	18	1	in	in	ADP
ejpam-6173	18	2	particular	particular	ADJ
ejpam-6173	18	3	,	,	PUNCT
ejpam-6173	18	4	if	if	SCONJ
ejpam-6173	18	5	ψ	ψ	ADP
ejpam-6173	18	6	≡	≡	PROPN
ejpam-6173	18	7	0	0	NUM
ejpam-6173	18	8	,	,	PUNCT
ejpam-6173	18	9	the	the	DET
ejpam-6173	18	10	problem	problem	NOUN
ejpam-6173	18	11	(	(	PUNCT
ejpam-6173	18	12	1.1	1.1	NUM
ejpam-6173	18	13	)	)	PUNCT
ejpam-6173	18	14	is	be	AUX
ejpam-6173	18	15	reduced	reduce	VERB
ejpam-6173	18	16	to	to	ADP
ejpam-6173	18	17	the	the	DET
ejpam-6173	18	18	mixed	mixed	ADJ
ejpam-6173	18	19	equilibrium	equilibrium	NOUN
ejpam-6173	18	20	problem	problem	NOUN
ejpam-6173	18	21	(	(	PUNCT
ejpam-6173	18	22	mep	mep	PROPN
ejpam-6173	18	23	)	)	PUNCT
ejpam-6173	19	1	[	[	X
ejpam-6173	19	2	1	1	X
ejpam-6173	19	3	]	]	PUNCT
ejpam-6173	19	4	defined	define	VERB
ejpam-6173	19	5	as	as	SCONJ
ejpam-6173	19	6	follows	follow	VERB
ejpam-6173	19	7	:	:	PUNCT
ejpam-6173	19	8	find	find	VERB
ejpam-6173	19	9	x	x	X
ejpam-6173	19	10	∈	∈	PROPN
ejpam-6173	19	11	c	c	NOUN
ejpam-6173	19	12	such	such	ADJ
ejpam-6173	19	13	that	that	SCONJ
ejpam-6173	19	14	θ(x	θ(x	PROPN
ejpam-6173	19	15	,	,	PUNCT
ejpam-6173	19	16	y	y	PROPN
ejpam-6173	19	17	)	)	PUNCT
ejpam-6173	19	18	+	+	CCONJ
ejpam-6173	19	19	φ(y	φ(y	ADJ
ejpam-6173	19	20	)	)	PUNCT
ejpam-6173	19	21	≥	≥	NOUN
ejpam-6173	19	22	φ(x	φ(x	PROPN
ejpam-6173	19	23	)	)	PUNCT
ejpam-6173	19	24	,	,	PUNCT
ejpam-6173	19	25	for	for	ADP
ejpam-6173	19	26	all	all	DET
ejpam-6173	19	27	y	y	PROPN
ejpam-6173	19	28	∈	∈	PROPN
ejpam-6173	19	29	c.	c.	NOUN
ejpam-6173	19	30	(	(	PUNCT
ejpam-6173	19	31	1.2	1.2	NUM
ejpam-6173	19	32	)	)	PUNCT
ejpam-6173	19	33	the	the	DET
ejpam-6173	19	34	set	set	NOUN
ejpam-6173	19	35	of	of	ADP
ejpam-6173	19	36	solutions	solution	NOUN
ejpam-6173	19	37	of	of	ADP
ejpam-6173	19	38	(	(	PUNCT
ejpam-6173	19	39	1.2	1.2	NUM
ejpam-6173	19	40	)	)	PUNCT
ejpam-6173	19	41	is	be	AUX
ejpam-6173	19	42	denoted	denote	VERB
ejpam-6173	19	43	by	by	ADP
ejpam-6173	19	44	mep	mep	PROPN
ejpam-6173	19	45	(	(	PUNCT
ejpam-6173	19	46	θ	θ	PROPN
ejpam-6173	19	47	,	,	PUNCT
ejpam-6173	19	48	φ	φ	NUM
ejpam-6173	19	49	)	)	PUNCT
ejpam-6173	19	50	.	.	PUNCT
ejpam-6173	20	1	if	if	SCONJ
ejpam-6173	20	2	φ	φ	PROPN
ejpam-6173	20	3	≡	≡	PROPN
ejpam-6173	20	4	0	0	NUM
ejpam-6173	20	5	,	,	PUNCT
ejpam-6173	20	6	the	the	DET
ejpam-6173	20	7	problem	problem	NOUN
ejpam-6173	20	8	(	(	PUNCT
ejpam-6173	20	9	1.1	1.1	NUM
ejpam-6173	20	10	)	)	PUNCT
ejpam-6173	20	11	is	be	AUX
ejpam-6173	20	12	reduced	reduce	VERB
ejpam-6173	20	13	to	to	ADP
ejpam-6173	20	14	the	the	DET
ejpam-6173	20	15	generalized	generalized	ADJ
ejpam-6173	20	16	equilibrium	equilibrium	NOUN
ejpam-6173	20	17	problem	problem	NOUN
ejpam-6173	20	18	(	(	PUNCT
ejpam-6173	20	19	gep	gep	NOUN
ejpam-6173	20	20	)	)	PUNCT
ejpam-6173	21	1	[	[	X
ejpam-6173	21	2	2	2	X
ejpam-6173	21	3	]	]	PUNCT
ejpam-6173	21	4	defined	define	VERB
ejpam-6173	21	5	as	as	SCONJ
ejpam-6173	21	6	follows	follow	VERB
ejpam-6173	21	7	:	:	PUNCT
ejpam-6173	21	8	find	find	VERB
ejpam-6173	21	9	x	x	X
ejpam-6173	21	10	∈	∈	PROPN
ejpam-6173	21	11	c	c	NOUN
ejpam-6173	21	12	such	such	ADJ
ejpam-6173	21	13	that	that	SCONJ
ejpam-6173	21	14	θ(x	θ(x	PROPN
ejpam-6173	21	15	,	,	PUNCT
ejpam-6173	21	16	y	y	PROPN
ejpam-6173	21	17	)	)	PUNCT
ejpam-6173	22	1	+	+	CCONJ
ejpam-6173	22	2	⟨ψx	⟨ψx	PROPN
ejpam-6173	22	3	,	,	PUNCT
ejpam-6173	22	4	y	y	PROPN
ejpam-6173	22	5	−	−	PROPN
ejpam-6173	22	6	x⟩	x⟩	PUNCT
ejpam-6173	22	7	≥	≥	PROPN
ejpam-6173	22	8	0	0	NUM
ejpam-6173	22	9	,	,	PUNCT
ejpam-6173	22	10	for	for	ADP
ejpam-6173	22	11	all	all	DET
ejpam-6173	22	12	y	y	PROPN
ejpam-6173	22	13	∈	∈	PROPN
ejpam-6173	22	14	c.	c.	NOUN
ejpam-6173	22	15	(	(	PUNCT
ejpam-6173	22	16	1.3	1.3	NUM
ejpam-6173	22	17	)	)	PUNCT
ejpam-6173	22	18	the	the	DET
ejpam-6173	22	19	set	set	NOUN
ejpam-6173	22	20	of	of	ADP
ejpam-6173	22	21	solution	solution	NOUN
ejpam-6173	22	22	(	(	PUNCT
ejpam-6173	22	23	1.3	1.3	NUM
ejpam-6173	22	24	)	)	PUNCT
ejpam-6173	22	25	is	be	AUX
ejpam-6173	22	26	denoted	denote	VERB
ejpam-6173	22	27	by	by	ADP
ejpam-6173	22	28	gep	gep	PROPN
ejpam-6173	22	29	(	(	PUNCT
ejpam-6173	22	30	θ	θ	PROPN
ejpam-6173	22	31	,	,	PUNCT
ejpam-6173	22	32	ψ	ψ	NOUN
ejpam-6173	22	33	)	)	PUNCT
ejpam-6173	22	34	.	.	PUNCT
ejpam-6173	23	1	if	if	SCONJ
ejpam-6173	23	2	θ	θ	PROPN
ejpam-6173	23	3	≡	≡	PROPN
ejpam-6173	23	4	0	0	NUM
ejpam-6173	23	5	,	,	PUNCT
ejpam-6173	23	6	the	the	DET
ejpam-6173	23	7	problem	problem	NOUN
ejpam-6173	23	8	(	(	PUNCT
ejpam-6173	23	9	1.1	1.1	NUM
ejpam-6173	23	10	)	)	PUNCT
ejpam-6173	23	11	is	be	AUX
ejpam-6173	23	12	reduced	reduce	VERB
ejpam-6173	23	13	to	to	ADP
ejpam-6173	23	14	the	the	DET
ejpam-6173	23	15	mixed	mixed	ADJ
ejpam-6173	23	16	variational	variational	ADJ
ejpam-6173	23	17	inequality	inequality	NOUN
ejpam-6173	23	18	of	of	ADP
ejpam-6173	23	19	browder	browder	NOUN
ejpam-6173	23	20	type	type	NOUN
ejpam-6173	23	21	(	(	PUNCT
ejpam-6173	23	22	mvi	mvi	NOUN
ejpam-6173	23	23	)	)	PUNCT
ejpam-6173	24	1	[	[	X
ejpam-6173	24	2	3	3	X
ejpam-6173	24	3	]	]	PUNCT
ejpam-6173	24	4	defined	define	VERB
ejpam-6173	24	5	as	as	SCONJ
ejpam-6173	24	6	follows	follow	VERB
ejpam-6173	24	7	:	:	PUNCT
ejpam-6173	24	8	find	find	VERB
ejpam-6173	24	9	x	x	X
ejpam-6173	24	10	∈	∈	PROPN
ejpam-6173	24	11	c	c	NOUN
ejpam-6173	24	12	such	such	ADJ
ejpam-6173	24	13	that	that	PRON
ejpam-6173	24	14	⟨ψx	⟨ψx	PROPN
ejpam-6173	24	15	,	,	PUNCT
ejpam-6173	24	16	y	y	PROPN
ejpam-6173	24	17	−	−	PROPN
ejpam-6173	24	18	x⟩+	x⟩+	PROPN
ejpam-6173	24	19	φ(y	φ(y	PROPN
ejpam-6173	24	20	)	)	PUNCT
ejpam-6173	24	21	≥	≥	NOUN
ejpam-6173	24	22	φ(x	φ(x	PROPN
ejpam-6173	24	23	)	)	PUNCT
ejpam-6173	24	24	,	,	PUNCT
ejpam-6173	24	25	for	for	ADP
ejpam-6173	24	26	all	all	DET
ejpam-6173	24	27	y	y	PROPN
ejpam-6173	24	28	∈	∈	PROPN
ejpam-6173	24	29	c.	c.	NOUN
ejpam-6173	24	30	(	(	PUNCT
ejpam-6173	24	31	1.4	1.4	NUM
ejpam-6173	24	32	)	)	PUNCT
ejpam-6173	24	33	the	the	DET
ejpam-6173	24	34	set	set	NOUN
ejpam-6173	24	35	of	of	ADP
ejpam-6173	24	36	solution	solution	NOUN
ejpam-6173	24	37	of	of	ADP
ejpam-6173	24	38	(	(	PUNCT
ejpam-6173	24	39	1.4	1.4	NUM
ejpam-6173	24	40	)	)	PUNCT
ejpam-6173	24	41	is	be	AUX
ejpam-6173	24	42	denoted	denote	VERB
ejpam-6173	24	43	by	by	ADP
ejpam-6173	24	44	mv	mv	PROPN
ejpam-6173	24	45	i(φ	i(φ	PROPN
ejpam-6173	24	46	,	,	PUNCT
ejpam-6173	24	47	ψ	ψ	NOUN
ejpam-6173	24	48	)	)	PUNCT
ejpam-6173	24	49	.	.	PUNCT
ejpam-6173	25	1	if	if	SCONJ
ejpam-6173	25	2	ψ	ψ	PRON
ejpam-6173	25	3	≡	≡	PROPN
ejpam-6173	25	4	0	0	NUM
ejpam-6173	25	5	and	and	CCONJ
ejpam-6173	25	6	φ	φ	PROPN
ejpam-6173	25	7	≡	≡	PROPN
ejpam-6173	25	8	0	0	PROPN
ejpam-6173	25	9	,	,	PUNCT
ejpam-6173	25	10	the	the	DET
ejpam-6173	25	11	problem	problem	NOUN
ejpam-6173	25	12	(	(	PUNCT
ejpam-6173	25	13	1.1	1.1	NUM
ejpam-6173	25	14	)	)	PUNCT
ejpam-6173	25	15	is	be	AUX
ejpam-6173	25	16	reduced	reduce	VERB
ejpam-6173	25	17	to	to	ADP
ejpam-6173	25	18	the	the	DET
ejpam-6173	25	19	equilibrium	equilibrium	NOUN
ejpam-6173	25	20	problem	problem	NOUN
ejpam-6173	25	21	(	(	PUNCT
ejpam-6173	25	22	ep	ep	PROPN
ejpam-6173	25	23	)	)	PUNCT
ejpam-6173	26	1	[	[	X
ejpam-6173	26	2	4	4	X
ejpam-6173	26	3	]	]	PUNCT
ejpam-6173	26	4	for	for	ADP
ejpam-6173	26	5	finding	find	VERB
ejpam-6173	26	6	x	x	X
ejpam-6173	26	7	∈	∈	PROPN
ejpam-6173	26	8	c	c	NOUN
ejpam-6173	26	9	such	such	ADJ
ejpam-6173	26	10	that	that	SCONJ
ejpam-6173	26	11	θ(x	θ(x	PROPN
ejpam-6173	26	12	,	,	PUNCT
ejpam-6173	26	13	y	y	PROPN
ejpam-6173	26	14	)	)	PUNCT
ejpam-6173	26	15	≥	≥	NOUN
ejpam-6173	26	16	0	0	NUM
ejpam-6173	26	17	,	,	PUNCT
ejpam-6173	26	18	for	for	ADP
ejpam-6173	26	19	all	all	DET
ejpam-6173	26	20	y	y	PROPN
ejpam-6173	26	21	∈	∈	PROPN
ejpam-6173	26	22	c.	c.	NOUN
ejpam-6173	26	23	(	(	PUNCT
ejpam-6173	26	24	1.5	1.5	NUM
ejpam-6173	26	25	)	)	PUNCT
ejpam-6173	26	26	the	the	DET
ejpam-6173	26	27	set	set	NOUN
ejpam-6173	26	28	of	of	ADP
ejpam-6173	26	29	solutions	solution	NOUN
ejpam-6173	26	30	of	of	ADP
ejpam-6173	26	31	(	(	PUNCT
ejpam-6173	26	32	1.5	1.5	NUM
ejpam-6173	26	33	)	)	PUNCT
ejpam-6173	26	34	is	be	AUX
ejpam-6173	26	35	denoted	denote	VERB
ejpam-6173	26	36	by	by	ADP
ejpam-6173	26	37	ep	ep	PROPN
ejpam-6173	26	38	(	(	PUNCT
ejpam-6173	26	39	θ	θ	PROPN
ejpam-6173	26	40	)	)	PUNCT
ejpam-6173	26	41	.	.	PUNCT
ejpam-6173	27	1	we	we	PRON
ejpam-6173	27	2	observe	observe	VERB
ejpam-6173	27	3	that	that	SCONJ
ejpam-6173	27	4	(	(	PUNCT
ejpam-6173	27	5	1.1	1.1	NUM
ejpam-6173	27	6	)	)	PUNCT
ejpam-6173	27	7	generalizes	generalize	VERB
ejpam-6173	27	8	(	(	PUNCT
ejpam-6173	27	9	1.2)-(1.5	1.2)-(1.5	NUM
ejpam-6173	27	10	)	)	PUNCT
ejpam-6173	27	11	.	.	PUNCT
ejpam-6173	28	1	the	the	DET
ejpam-6173	28	2	equilibrium	equilibrium	NOUN
ejpam-6173	28	3	problem	problem	NOUN
ejpam-6173	28	4	was	be	AUX
ejpam-6173	28	5	introduced	introduce	VERB
ejpam-6173	28	6	by	by	ADP
ejpam-6173	28	7	blum	blum	NOUN
ejpam-6173	28	8	and	and	CCONJ
ejpam-6173	28	9	oettli	oettli	NOUN
ejpam-6173	29	1	[	[	X
ejpam-6173	29	2	4	4	NUM
ejpam-6173	29	3	]	]	PUNCT
ejpam-6173	29	4	and	and	CCONJ
ejpam-6173	29	5	noor	noor	PROPN
ejpam-6173	29	6	and	and	CCONJ
ejpam-6173	29	7	oettli	oettli	NOUN
ejpam-6173	30	1	[	[	X
ejpam-6173	30	2	5	5	NUM
ejpam-6173	30	3	]	]	PUNCT
ejpam-6173	30	4	in	in	ADP
ejpam-6173	30	5	1994	1994	NUM
ejpam-6173	30	6	,	,	PUNCT
ejpam-6173	30	7	and	and	CCONJ
ejpam-6173	30	8	has	have	AUX
ejpam-6173	30	9	had	have	VERB
ejpam-6173	30	10	a	a	DET
ejpam-6173	30	11	great	great	ADJ
ejpam-6173	30	12	impact	impact	NOUN
ejpam-6173	30	13	and	and	CCONJ
ejpam-6173	30	14	influence	influence	NOUN
ejpam-6173	30	15	in	in	ADP
ejpam-6173	30	16	the	the	DET
ejpam-6173	30	17	development	development	NOUN
ejpam-6173	30	18	of	of	ADP
ejpam-6173	30	19	several	several	ADJ
ejpam-6173	30	20	branches	branch	NOUN
ejpam-6173	30	21	of	of	ADP
ejpam-6173	30	22	pure	pure	ADJ
ejpam-6173	30	23	and	and	CCONJ
ejpam-6173	30	24	applied	applied	ADJ
ejpam-6173	30	25	sciences	science	NOUN
ejpam-6173	30	26	.	.	PUNCT
ejpam-6173	31	1	it	it	PRON
ejpam-6173	31	2	has	have	AUX
ejpam-6173	31	3	been	be	AUX
ejpam-6173	31	4	shown	show	VERB
ejpam-6173	31	5	that	that	SCONJ
ejpam-6173	31	6	equilibrium	equilibrium	NOUN
ejpam-6173	31	7	problem	problem	NOUN
ejpam-6173	31	8	theory	theory	NOUN
ejpam-6173	31	9	provides	provide	VERB
ejpam-6173	31	10	a	a	DET
ejpam-6173	31	11	novel	novel	ADJ
ejpam-6173	31	12	and	and	CCONJ
ejpam-6173	31	13	unified	unified	ADJ
ejpam-6173	31	14	treatment	treatment	NOUN
ejpam-6173	31	15	of	of	ADP
ejpam-6173	31	16	a	a	DET
ejpam-6173	31	17	wide	wide	ADJ
ejpam-6173	31	18	class	class	NOUN
ejpam-6173	31	19	of	of	ADP
ejpam-6173	31	20	problems	problem	NOUN
ejpam-6173	31	21	that	that	PRON
ejpam-6173	31	22	arise	arise	VERB
ejpam-6173	31	23	in	in	ADP
ejpam-6173	31	24	economics	economic	NOUN
ejpam-6173	31	25	,	,	PUNCT
ejpam-6173	31	26	finance	finance	NOUN
ejpam-6173	31	27	,	,	PUNCT
ejpam-6173	31	28	image	image	NOUN
ejpam-6173	31	29	reconstruction	reconstruction	NOUN
ejpam-6173	31	30	,	,	PUNCT
ejpam-6173	31	31	ecology	ecology	NOUN
ejpam-6173	31	32	,	,	PUNCT
ejpam-6173	31	33	transportation	transportation	NOUN
ejpam-6173	31	34	,	,	PUNCT
ejpam-6173	31	35	networks	network	NOUN
ejpam-6173	31	36	,	,	PUNCT
ejpam-6173	31	37	elasticity	elasticity	NOUN
ejpam-6173	31	38	,	,	PUNCT
ejpam-6173	31	39	and	and	CCONJ
ejpam-6173	31	40	optimization	optimization	NOUN
ejpam-6173	31	41	.	.	PUNCT
ejpam-6173	32	1	the	the	DET
ejpam-6173	32	2	ep	ep	PROPN
ejpam-6173	32	3	was	be	AUX
ejpam-6173	32	4	shown	show	VERB
ejpam-6173	32	5	in	in	ADP
ejpam-6173	32	6	[	[	X
ejpam-6173	32	7	4	4	NUM
ejpam-6173	32	8	]	]	PUNCT
ejpam-6173	32	9	to	to	PART
ejpam-6173	32	10	cover	cover	VERB
ejpam-6173	32	11	monotone	monotone	ADJ
ejpam-6173	32	12	inclusion	inclusion	NOUN
ejpam-6173	32	13	problems	problem	NOUN
ejpam-6173	32	14	,	,	PUNCT
ejpam-6173	32	15	saddle	saddle	NOUN
ejpam-6173	32	16	point	point	NOUN
ejpam-6173	32	17	problems	problem	NOUN
ejpam-6173	32	18	,	,	PUNCT
ejpam-6173	32	19	variational	variational	ADJ
ejpam-6173	32	20	inequality	inequality	NOUN
ejpam-6173	32	21	problems	problem	NOUN
ejpam-6173	32	22	,	,	PUNCT
ejpam-6173	32	23	minimization	minimization	NOUN
ejpam-6173	32	24	problems	problem	NOUN
ejpam-6173	32	25	,	,	PUNCT
ejpam-6173	32	26	optimization	optimization	NOUN
ejpam-6173	32	27	problems	problem	NOUN
ejpam-6173	32	28	,	,	PUNCT
ejpam-6173	32	29	variational	variational	ADJ
ejpam-6173	32	30	inequality	inequality	NOUN
ejpam-6173	32	31	problems	problem	NOUN
ejpam-6173	32	32	,	,	PUNCT
ejpam-6173	32	33	vector	vector	NOUN
ejpam-6173	32	34	equilibrium	equilibrium	NOUN
ejpam-6173	32	35	problems	problem	NOUN
ejpam-6173	32	36	,	,	PUNCT
ejpam-6173	32	37	nash	nash	PROPN
ejpam-6173	32	38	equilibrium	equilibrium	NOUN
ejpam-6173	32	39	problems	problem	NOUN
ejpam-6173	32	40	in	in	ADP
ejpam-6173	32	41	noncooperative	noncooperative	ADJ
ejpam-6173	32	42	games	game	NOUN
ejpam-6173	32	43	.	.	PUNCT
ejpam-6173	33	1	some	some	DET
ejpam-6173	33	2	methods	method	NOUN
ejpam-6173	33	3	have	have	AUX
ejpam-6173	33	4	been	be	AUX
ejpam-6173	33	5	proposed	propose	VERB
ejpam-6173	33	6	to	to	PART
ejpam-6173	33	7	solve	solve	VERB
ejpam-6173	33	8	the	the	DET
ejpam-6173	33	9	equilibrium	equilibrium	NOUN
ejpam-6173	33	10	problem	problem	NOUN
ejpam-6173	33	11	.	.	PUNCT
ejpam-6173	34	1	these	these	DET
ejpam-6173	34	2	methods	method	NOUN
ejpam-6173	34	3	include	include	VERB
ejpam-6173	34	4	the	the	DET
ejpam-6173	34	5	penalty	penalty	NOUN
ejpam-6173	34	6	and	and	CCONJ
ejpam-6173	34	7	gap	gap	NOUN
ejpam-6173	34	8	functions	function	NOUN
ejpam-6173	34	9	,	,	PUNCT
ejpam-6173	34	10	regularization	regularization	NOUN
ejpam-6173	34	11	,	,	PUNCT
ejpam-6173	34	12	extragradient	extragradient	NOUN
ejpam-6173	34	13	methods	method	NOUN
ejpam-6173	34	14	and	and	CCONJ
ejpam-6173	34	15	splitting	splitting	NOUN
ejpam-6173	34	16	methods	method	NOUN
ejpam-6173	34	17	(	(	PUNCT
ejpam-6173	34	18	see	see	VERB
ejpam-6173	34	19	[	[	X
ejpam-6173	34	20	6–10	6–10	NOUN
ejpam-6173	34	21	]	]	PUNCT
ejpam-6173	34	22	and	and	CCONJ
ejpam-6173	34	23	other	other	ADJ
ejpam-6173	34	24	references	reference	NOUN
ejpam-6173	34	25	therein	therein	ADV
ejpam-6173	34	26	)	)	PUNCT
ejpam-6173	34	27	.	.	PUNCT
ejpam-6173	35	1	for	for	ADP
ejpam-6173	35	2	solving	solve	VERB
ejpam-6173	35	3	the	the	DET
ejpam-6173	35	4	generalized	generalize	VERB
ejpam-6173	35	5	mixed	mixed	ADJ
ejpam-6173	35	6	equilibrium	equilibrium	NOUN
ejpam-6173	35	7	problem	problem	NOUN
ejpam-6173	35	8	,	,	PUNCT
ejpam-6173	35	9	let	let	VERB
ejpam-6173	35	10	us	we	PRON
ejpam-6173	35	11	assume	assume	VERB
ejpam-6173	35	12	that	that	SCONJ
ejpam-6173	35	13	the	the	DET
ejpam-6173	35	14	bifunction	bifunction	NOUN
ejpam-6173	35	15	θ	θ	NOUN
ejpam-6173	35	16	:	:	PUNCT
ejpam-6173	35	17	c	c	X
ejpam-6173	35	18	×	×	NOUN
ejpam-6173	35	19	c	c	NOUN
ejpam-6173	35	20	→	→	SYM
ejpam-6173	35	21	r	r	NOUN
ejpam-6173	35	22	satisfies	satisfy	VERB
ejpam-6173	35	23	the	the	DET
ejpam-6173	35	24	following	follow	VERB
ejpam-6173	35	25	conditions	condition	NOUN
ejpam-6173	35	26	:	:	PUNCT
ejpam-6173	35	27	v.	v.	X
ejpam-6173	35	28	darvish	darvish	PROPN
ejpam-6173	35	29	et	et	PROPN
ejpam-6173	35	30	al	al	PROPN
ejpam-6173	35	31	.	.	PUNCT
ejpam-6173	35	32	/	/	SYM
ejpam-6173	35	33	eur	eur	PROPN
ejpam-6173	35	34	.	.	PUNCT
ejpam-6173	36	1	j.	j.	PROPN
ejpam-6173	36	2	pure	pure	PROPN
ejpam-6173	36	3	appl	appl	PROPN
ejpam-6173	36	4	.	.	PROPN
ejpam-6173	36	5	math	math	PROPN
ejpam-6173	36	6	,	,	PUNCT
ejpam-6173	36	7	18	18	NUM
ejpam-6173	36	8	(	(	PUNCT
ejpam-6173	36	9	3	3	NUM
ejpam-6173	36	10	)	)	PUNCT
ejpam-6173	36	11	(	(	PUNCT
ejpam-6173	36	12	2025	2025	NUM
ejpam-6173	36	13	)	)	PUNCT
ejpam-6173	36	14	,	,	PUNCT
ejpam-6173	36	15	6173	6173	NUM
ejpam-6173	36	16	3	3	NUM
ejpam-6173	36	17	of	of	ADP
ejpam-6173	36	18	32	32	NUM
ejpam-6173	36	19	(	(	PUNCT
ejpam-6173	36	20	q1	q1	NOUN
ejpam-6173	36	21	)	)	PUNCT
ejpam-6173	36	22	θ(x	θ(x	PROPN
ejpam-6173	36	23	,	,	PUNCT
ejpam-6173	36	24	x	x	NOUN
ejpam-6173	36	25	)	)	PUNCT
ejpam-6173	36	26	=	=	SYM
ejpam-6173	36	27	0	0	NUM
ejpam-6173	36	28	for	for	ADP
ejpam-6173	36	29	all	all	DET
ejpam-6173	36	30	x	x	SYM
ejpam-6173	36	31	∈	∈	PROPN
ejpam-6173	36	32	c	c	X
ejpam-6173	36	33	;	;	PUNCT
ejpam-6173	36	34	(	(	PUNCT
ejpam-6173	36	35	q2	q2	NOUN
ejpam-6173	36	36	)	)	PUNCT
ejpam-6173	36	37	θ	θ	PROPN
ejpam-6173	36	38	is	be	AUX
ejpam-6173	36	39	monotone	monotone	ADJ
ejpam-6173	36	40	,	,	PUNCT
ejpam-6173	36	41	i.e.	i.e.	X
ejpam-6173	36	42	,	,	PUNCT
ejpam-6173	36	43	θ(x	θ(x	PROPN
ejpam-6173	36	44	,	,	PUNCT
ejpam-6173	36	45	y	y	PROPN
ejpam-6173	36	46	)	)	PUNCT
ejpam-6173	37	1	+	+	CCONJ
ejpam-6173	37	2	θ(y	θ(y	PROPN
ejpam-6173	37	3	,	,	PUNCT
ejpam-6173	37	4	x	x	NOUN
ejpam-6173	37	5	)	)	PUNCT
ejpam-6173	37	6	≤	≤	NUM
ejpam-6173	37	7	0	0	NUM
ejpam-6173	37	8	for	for	ADP
ejpam-6173	37	9	any	any	DET
ejpam-6173	37	10	x	x	NOUN
ejpam-6173	37	11	,	,	PUNCT
ejpam-6173	37	12	y	y	PROPN
ejpam-6173	37	13	∈	∈	PROPN
ejpam-6173	37	14	c	c	X
ejpam-6173	37	15	;	;	PUNCT
ejpam-6173	37	16	(	(	PUNCT
ejpam-6173	37	17	q3	q3	PROPN
ejpam-6173	37	18	)	)	PUNCT
ejpam-6173	37	19	for	for	ADP
ejpam-6173	37	20	each	each	DET
ejpam-6173	37	21	y	y	PROPN
ejpam-6173	37	22	∈	∈	PROPN
ejpam-6173	37	23	c	c	X
ejpam-6173	37	24	,	,	PUNCT
ejpam-6173	37	25	x	x	PROPN
ejpam-6173	37	26	7→	7→	NUM
ejpam-6173	37	27	θ(x	θ(x	PROPN
ejpam-6173	37	28	,	,	PUNCT
ejpam-6173	37	29	y	y	NOUN
ejpam-6173	37	30	)	)	PUNCT
ejpam-6173	37	31	is	be	AUX
ejpam-6173	37	32	upper	upper	ADJ
ejpam-6173	37	33	-	-	PUNCT
ejpam-6173	37	34	hemicontinuous	hemicontinuous	ADJ
ejpam-6173	37	35	,	,	PUNCT
ejpam-6173	37	36	i.e.	i.e.	X
ejpam-6173	37	37	,	,	PUNCT
ejpam-6173	37	38	for	for	ADP
ejpam-6173	37	39	each	each	DET
ejpam-6173	37	40	x	x	PROPN
ejpam-6173	37	41	,	,	PUNCT
ejpam-6173	37	42	y	y	PROPN
ejpam-6173	37	43	,	,	PUNCT
ejpam-6173	37	44	z	z	NOUN
ejpam-6173	37	45	∈	∈	PROPN
ejpam-6173	37	46	c	c	X
ejpam-6173	37	47	,	,	PUNCT
ejpam-6173	37	48	lim	lim	PROPN
ejpam-6173	37	49	sup	sup	PROPN
ejpam-6173	37	50	t	t	PROPN
ejpam-6173	37	51	↘	↘	PROPN
ejpam-6173	37	52	0	0	PROPN
ejpam-6173	37	53	θ(tz	θ(tz	PROPN
ejpam-6173	37	54	+	+	CCONJ
ejpam-6173	37	55	(	(	PUNCT
ejpam-6173	37	56	1−	1−	NUM
ejpam-6173	37	57	t)x	t)x	ADJ
ejpam-6173	37	58	,	,	PUNCT
ejpam-6173	37	59	y	y	NOUN
ejpam-6173	37	60	)	)	PUNCT
ejpam-6173	37	61	≤	≤	PROPN
ejpam-6173	37	62	θ(x	θ(x	PROPN
ejpam-6173	37	63	,	,	PUNCT
ejpam-6173	37	64	y	y	PROPN
ejpam-6173	37	65	)	)	PUNCT
ejpam-6173	37	66	;	;	PUNCT
ejpam-6173	37	67	(	(	PUNCT
ejpam-6173	37	68	q4	q4	PROPN
ejpam-6173	37	69	)	)	PUNCT
ejpam-6173	37	70	for	for	ADP
ejpam-6173	37	71	each	each	DET
ejpam-6173	37	72	x	x	SYM
ejpam-6173	37	73	∈	∈	PROPN
ejpam-6173	37	74	c	c	X
ejpam-6173	37	75	,	,	PUNCT
ejpam-6173	37	76	y	y	PROPN
ejpam-6173	37	77	7→	7→	PROPN
ejpam-6173	37	78	θ(x	θ(x	PROPN
ejpam-6173	37	79	,	,	PUNCT
ejpam-6173	37	80	y	y	NOUN
ejpam-6173	37	81	)	)	PUNCT
ejpam-6173	37	82	is	be	AUX
ejpam-6173	37	83	convex	convex	ADJ
ejpam-6173	37	84	and	and	CCONJ
ejpam-6173	37	85	lower	low	ADJ
ejpam-6173	37	86	semicontinuous	semicontinuous	ADJ
ejpam-6173	37	87	(	(	PUNCT
ejpam-6173	37	88	see	see	VERB
ejpam-6173	37	89	[	[	X
ejpam-6173	37	90	11	11	NUM
ejpam-6173	37	91	]	]	NUM
ejpam-6173	37	92	)	)	PUNCT
ejpam-6173	37	93	.	.	PUNCT
ejpam-6173	38	1	several	several	ADJ
ejpam-6173	38	2	authors	author	NOUN
ejpam-6173	38	3	have	have	AUX
ejpam-6173	38	4	studied	study	VERB
ejpam-6173	38	5	and	and	CCONJ
ejpam-6173	38	6	proposed	propose	VERB
ejpam-6173	38	7	various	various	ADJ
ejpam-6173	38	8	iterative	iterative	NOUN
ejpam-6173	38	9	methods	method	NOUN
ejpam-6173	38	10	for	for	ADP
ejpam-6173	38	11	studying	study	VERB
ejpam-6173	38	12	(	(	PUNCT
ejpam-6173	38	13	1.1	1.1	NUM
ejpam-6173	38	14	)	)	PUNCT
ejpam-6173	38	15	.	.	PUNCT
ejpam-6173	39	1	tuyen	tuyen	PROPN
ejpam-6173	40	1	[	[	X
ejpam-6173	40	2	12	12	NUM
ejpam-6173	40	3	]	]	PUNCT
ejpam-6173	40	4	introduced	introduce	VERB
ejpam-6173	40	5	a	a	DET
ejpam-6173	40	6	hybrid	hybrid	ADJ
ejpam-6173	40	7	projection	projection	NOUN
ejpam-6173	40	8	method	method	NOUN
ejpam-6173	40	9	for	for	ADP
ejpam-6173	40	10	solving	solve	VERB
ejpam-6173	40	11	systems	system	NOUN
ejpam-6173	40	12	of	of	ADP
ejpam-6173	40	13	gmep	gmep	NOUN
ejpam-6173	40	14	in	in	ADP
ejpam-6173	40	15	a	a	DET
ejpam-6173	40	16	reflexive	reflexive	ADJ
ejpam-6173	40	17	banach	banach	NOUN
ejpam-6173	40	18	space	space	NOUN
ejpam-6173	40	19	and	and	CCONJ
ejpam-6173	40	20	defined	define	VERB
ejpam-6173	40	21	it	it	PRON
ejpam-6173	40	22	as	as	ADP
ejpam-6173	40	23	follows:	follows:	X
ejpam-6173	40	24	yin	yin	NOUN
ejpam-6173	40	25	=	=	PUNCT
ejpam-6173	40	26	resfθi	resfθi	PROPN
ejpam-6173	40	27	,	,	PUNCT
ejpam-6173	40	28	ψi	ψi	NOUN
ejpam-6173	40	29	,	,	PUNCT
ejpam-6173	40	30	φi	φi	ADP
ejpam-6173	40	31	xn	xn	PROPN
ejpam-6173	40	32	,	,	PUNCT
ejpam-6173	40	33	i	i	PRON
ejpam-6173	40	34	=	=	NOUN
ejpam-6173	40	35	1	1	NUM
ejpam-6173	40	36	,	,	PUNCT
ejpam-6173	40	37	2	2	NUM
ejpam-6173	40	38	,	,	PUNCT
ejpam-6173	40	39	·	·	PUNCT
ejpam-6173	40	40	·	·	PUNCT
ejpam-6173	40	41	·	·	PUNCT
ejpam-6173	40	42	,	,	PUNCT
ejpam-6173	40	43	n	n	CCONJ
ejpam-6173	40	44	in	in	ADP
ejpam-6173	40	45	:	:	PUNCT
ejpam-6173	40	46	=	=	SYM
ejpam-6173	40	47	argmaxi=1,2	argmaxi=1,2	PROPN
ejpam-6173	40	48	·	·	SYM
ejpam-6173	40	49	·	·	PUNCT
ejpam-6173	40	50	·	·	PUNCT
ejpam-6173	40	51	,	,	PUNCT
ejpam-6173	40	52	n{df	n{df	PROPN
ejpam-6173	40	53	(	(	PUNCT
ejpam-6173	40	54	y	y	NOUN
ejpam-6173	40	55	i	i	PROPN
ejpam-6173	40	56	n	n	CCONJ
ejpam-6173	40	57	,	,	PUNCT
ejpam-6173	40	58	xn	xn	PROPN
ejpam-6173	40	59	)	)	PUNCT
ejpam-6173	40	60	}	}	PUNCT
ejpam-6173	40	61	,	,	PUNCT
ejpam-6173	40	62	ȳn	ȳn	PROPN
ejpam-6173	40	63	=	=	PUNCT
ejpam-6173	40	64	yinn	yinn	NOUN
ejpam-6173	40	65	cn	cn	NOUN
ejpam-6173	40	66	:	:	PUNCT
ejpam-6173	40	67	=	=	SYM
ejpam-6173	40	68	{	{	PUNCT
ejpam-6173	40	69	z	z	NOUN
ejpam-6173	40	70	∈	∈	PROPN
ejpam-6173	40	71	e	e	NOUN
ejpam-6173	40	72	:	:	PUNCT
ejpam-6173	40	73	df	df	PROPN
ejpam-6173	40	74	(	(	PUNCT
ejpam-6173	40	75	z	z	NOUN
ejpam-6173	40	76	,	,	PUNCT
ejpam-6173	40	77	ȳn	ȳn	PROPN
ejpam-6173	40	78	≤	≤	PROPN
ejpam-6173	40	79	df	df	NOUN
ejpam-6173	40	80	(	(	PUNCT
ejpam-6173	40	81	z	z	PROPN
ejpam-6173	40	82	,	,	PUNCT
ejpam-6173	40	83	xn	xn	PROPN
ejpam-6173	40	84	)	)	PUNCT
ejpam-6173	40	85	)	)	PUNCT
ejpam-6173	40	86	}	}	PUNCT
ejpam-6173	41	1	qn	qn	INTJ
ejpam-6173	41	2	:	:	PUNCT
ejpam-6173	41	3	=	=	SYM
ejpam-6173	41	4	{	{	PUNCT
ejpam-6173	41	5	z	z	NOUN
ejpam-6173	41	6	∈	∈	PROPN
ejpam-6173	41	7	e	e	NOUN
ejpam-6173	41	8	:	:	PUNCT
ejpam-6173	41	9	⟨∇f(x0)−∇f(xn	⟨∇f(x0)−∇f(xn	X
ejpam-6173	41	10	)	)	PUNCT
ejpam-6173	41	11	,	,	PUNCT
ejpam-6173	41	12	z	z	NOUN
ejpam-6173	41	13	−	−	NOUN
ejpam-6173	41	14	xn⟩	xn⟩	PROPN
ejpam-6173	41	15	≤	≤	NUM
ejpam-6173	41	16	0	0	NUM
ejpam-6173	41	17	}	}	PUNCT
ejpam-6173	41	18	xn+1	xn+1	PROPN
ejpam-6173	42	1	=	=	SYM
ejpam-6173	42	2	projcn∩qn	projcn∩qn	PROPN
ejpam-6173	42	3	(	(	PUNCT
ejpam-6173	42	4	x0	x0	PROPN
ejpam-6173	42	5	)	)	PUNCT
ejpam-6173	42	6	,	,	PUNCT
ejpam-6173	42	7	n	n	X
ejpam-6173	42	8	≥	≥	NOUN
ejpam-6173	42	9	0	0	NUM
ejpam-6173	42	10	.	.	PUNCT
ejpam-6173	43	1	the	the	DET
ejpam-6173	43	2	author	author	NOUN
ejpam-6173	43	3	obtained	obtain	VERB
ejpam-6173	43	4	a	a	DET
ejpam-6173	43	5	strong	strong	ADJ
ejpam-6173	43	6	convergence	convergence	NOUN
ejpam-6173	43	7	result	result	NOUN
ejpam-6173	43	8	of	of	ADP
ejpam-6173	43	9	the	the	DET
ejpam-6173	43	10	proposed	propose	VERB
ejpam-6173	43	11	method	method	NOUN
ejpam-6173	43	12	.	.	PUNCT
ejpam-6173	44	1	the	the	DET
ejpam-6173	44	2	limitation	limitation	NOUN
ejpam-6173	44	3	of	of	ADP
ejpam-6173	44	4	this	this	DET
ejpam-6173	44	5	method	method	NOUN
ejpam-6173	44	6	is	be	AUX
ejpam-6173	44	7	the	the	DET
ejpam-6173	44	8	fact	fact	NOUN
ejpam-6173	44	9	that	that	SCONJ
ejpam-6173	44	10	it	it	PRON
ejpam-6173	44	11	requires	require	VERB
ejpam-6173	44	12	the	the	DET
ejpam-6173	44	13	computation	computation	NOUN
ejpam-6173	44	14	of	of	ADP
ejpam-6173	44	15	subsets	subset	NOUN
ejpam-6173	44	16	of	of	ADP
ejpam-6173	44	17	cn	cn	PROPN
ejpam-6173	44	18	and	and	CCONJ
ejpam-6173	44	19	qn	qn	NOUN
ejpam-6173	44	20	which	which	PRON
ejpam-6173	44	21	can	can	AUX
ejpam-6173	44	22	be	be	AUX
ejpam-6173	44	23	computationally	computationally	ADV
ejpam-6173	44	24	expensive	expensive	ADJ
ejpam-6173	44	25	.	.	PUNCT
ejpam-6173	45	1	on	on	ADP
ejpam-6173	45	2	the	the	DET
ejpam-6173	45	3	other	other	ADJ
ejpam-6173	45	4	hand	hand	NOUN
ejpam-6173	45	5	,	,	PUNCT
ejpam-6173	45	6	another	another	DET
ejpam-6173	45	7	problem	problem	NOUN
ejpam-6173	45	8	of	of	ADP
ejpam-6173	45	9	interest	interest	NOUN
ejpam-6173	45	10	is	be	AUX
ejpam-6173	45	11	the	the	DET
ejpam-6173	45	12	fixed	fix	VERB
ejpam-6173	45	13	point	point	NOUN
ejpam-6173	45	14	problem	problem	NOUN
ejpam-6173	45	15	(	(	PUNCT
ejpam-6173	45	16	fpp	fpp	PROPN
ejpam-6173	45	17	)	)	PUNCT
ejpam-6173	45	18	.	.	PUNCT
ejpam-6173	46	1	let	let	VERB
ejpam-6173	46	2	t	t	NOUN
ejpam-6173	46	3	:	:	PUNCT
ejpam-6173	46	4	c	c	X
ejpam-6173	46	5	→	→	PUNCT
ejpam-6173	46	6	c	c	X
ejpam-6173	46	7	be	be	AUX
ejpam-6173	46	8	a	a	DET
ejpam-6173	46	9	nonlinear	nonlinear	ADJ
ejpam-6173	46	10	mapping	mapping	NOUN
ejpam-6173	46	11	.	.	PUNCT
ejpam-6173	47	1	a	a	DET
ejpam-6173	47	2	point	point	NOUN
ejpam-6173	47	3	x	x	X
ejpam-6173	47	4	∈	∈	NOUN
ejpam-6173	47	5	c	c	NOUN
ejpam-6173	47	6	is	be	AUX
ejpam-6173	47	7	a	a	DET
ejpam-6173	47	8	fixed	fix	VERB
ejpam-6173	47	9	point	point	NOUN
ejpam-6173	47	10	of	of	ADP
ejpam-6173	47	11	t	t	PROPN
ejpam-6173	47	12	if	if	SCONJ
ejpam-6173	47	13	tx	tx	PROPN
ejpam-6173	47	14	=	=	PUNCT
ejpam-6173	47	15	x.	x.	NOUN
ejpam-6173	47	16	let	let	VERB
ejpam-6173	47	17	f	f	PROPN
ejpam-6173	47	18	(	(	PUNCT
ejpam-6173	47	19	t	t	PROPN
ejpam-6173	47	20	)	)	PUNCT
ejpam-6173	47	21	denote	denote	VERB
ejpam-6173	47	22	the	the	DET
ejpam-6173	47	23	set	set	NOUN
ejpam-6173	47	24	of	of	ADP
ejpam-6173	47	25	fixed	fix	VERB
ejpam-6173	47	26	points	point	NOUN
ejpam-6173	47	27	,	,	PUNCT
ejpam-6173	47	28	that	that	PRON
ejpam-6173	47	29	is	be	AUX
ejpam-6173	47	30	f	f	PROPN
ejpam-6173	47	31	(	(	PUNCT
ejpam-6173	47	32	t	t	PROPN
ejpam-6173	47	33	)	)	PUNCT
ejpam-6173	47	34	=	=	PRON
ejpam-6173	48	1	{	{	PUNCT
ejpam-6173	48	2	x	x	PUNCT
ejpam-6173	48	3	∈	∈	PROPN
ejpam-6173	48	4	c	c	NOUN
ejpam-6173	48	5	:	:	PUNCT
ejpam-6173	48	6	tx	tx	PROPN
ejpam-6173	48	7	=	=	PUNCT
ejpam-6173	48	8	x	x	X
ejpam-6173	48	9	}	}	PUNCT
ejpam-6173	48	10	.	.	PUNCT
ejpam-6173	49	1	many	many	ADJ
ejpam-6173	49	2	problems	problem	NOUN
ejpam-6173	49	3	in	in	ADP
ejpam-6173	49	4	sciences	science	NOUN
ejpam-6173	49	5	and	and	CCONJ
ejpam-6173	49	6	engineering	engineering	NOUN
ejpam-6173	49	7	can	can	AUX
ejpam-6173	49	8	be	be	AUX
ejpam-6173	49	9	transformed	transform	VERB
ejpam-6173	49	10	into	into	ADP
ejpam-6173	49	11	a	a	DET
ejpam-6173	49	12	problem	problem	NOUN
ejpam-6173	49	13	of	of	ADP
ejpam-6173	49	14	finding	find	VERB
ejpam-6173	49	15	the	the	DET
ejpam-6173	49	16	solution	solution	NOUN
ejpam-6173	49	17	of	of	ADP
ejpam-6173	49	18	a	a	DET
ejpam-6173	49	19	fixed	fix	VERB
ejpam-6173	49	20	point	point	NOUN
ejpam-6173	49	21	problem	problem	NOUN
ejpam-6173	49	22	(	(	PUNCT
ejpam-6173	49	23	fpp	fpp	PROPN
ejpam-6173	49	24	)	)	PUNCT
ejpam-6173	49	25	of	of	ADP
ejpam-6173	49	26	a	a	DET
ejpam-6173	49	27	nonlinear	nonlinear	ADJ
ejpam-6173	49	28	mapping	mapping	NOUN
ejpam-6173	49	29	.	.	PUNCT
ejpam-6173	50	1	for	for	ADP
ejpam-6173	50	2	more	more	ADJ
ejpam-6173	50	3	information	information	NOUN
ejpam-6173	50	4	on	on	ADP
ejpam-6173	50	5	fixed	fix	VERB
ejpam-6173	50	6	point	point	NOUN
ejpam-6173	50	7	see	see	VERB
ejpam-6173	50	8	[	[	X
ejpam-6173	50	9	13–17	13–17	NUM
ejpam-6173	50	10	]	]	PUNCT
ejpam-6173	50	11	.	.	PUNCT
ejpam-6173	51	1	moudafi	moudafi	PROPN
ejpam-6173	52	1	[	[	X
ejpam-6173	52	2	18	18	NUM
ejpam-6173	52	3	]	]	PUNCT
ejpam-6173	52	4	introduced	introduce	VERB
ejpam-6173	52	5	the	the	DET
ejpam-6173	52	6	viscosity	viscosity	NOUN
ejpam-6173	52	7	approximation	approximation	NOUN
ejpam-6173	52	8	method	method	NOUN
ejpam-6173	52	9	for	for	ADP
ejpam-6173	52	10	a	a	DET
ejpam-6173	52	11	nonexpansive	nonexpansive	ADJ
ejpam-6173	52	12	mapping	mapping	NOUN
ejpam-6173	52	13	t	t	PROPN
ejpam-6173	52	14	and	and	CCONJ
ejpam-6173	52	15	defined	define	VERB
ejpam-6173	52	16	it	it	PRON
ejpam-6173	52	17	as	as	SCONJ
ejpam-6173	52	18	follows	follow	VERB
ejpam-6173	52	19	:	:	PUNCT
ejpam-6173	52	20	xn+1	xn+1	NUM
ejpam-6173	52	21	=	=	SYM
ejpam-6173	52	22	αnf(xn	αnf(xn	NOUN
ejpam-6173	52	23	)	)	PUNCT
ejpam-6173	53	1	+	+	CCONJ
ejpam-6173	53	2	(	(	PUNCT
ejpam-6173	53	3	1−	1−	NUM
ejpam-6173	53	4	αn)txn	αn)txn	NUM
ejpam-6173	53	5	,	,	PUNCT
ejpam-6173	53	6	n	n	PRON
ejpam-6173	53	7	≥	≥	NOUN
ejpam-6173	53	8	1	1	NUM
ejpam-6173	53	9	,	,	PUNCT
ejpam-6173	53	10	where	where	SCONJ
ejpam-6173	53	11	{	{	PUNCT
ejpam-6173	53	12	αn	αn	NOUN
ejpam-6173	53	13	}	}	PUNCT
ejpam-6173	53	14	⊂	⊂	PROPN
ejpam-6173	53	15	(	(	PUNCT
ejpam-6173	53	16	0	0	NUM
ejpam-6173	53	17	,	,	PUNCT
ejpam-6173	53	18	1	1	NUM
ejpam-6173	53	19	)	)	PUNCT
ejpam-6173	53	20	and	and	CCONJ
ejpam-6173	53	21	f	f	PROPN
ejpam-6173	53	22	is	be	AUX
ejpam-6173	53	23	a	a	DET
ejpam-6173	53	24	contraction	contraction	NOUN
ejpam-6173	53	25	mapping	mapping	NOUN
ejpam-6173	53	26	.	.	PUNCT
ejpam-6173	54	1	recently	recently	ADV
ejpam-6173	54	2	,	,	PUNCT
ejpam-6173	54	3	several	several	ADJ
ejpam-6173	54	4	authors	author	NOUN
ejpam-6173	54	5	have	have	AUX
ejpam-6173	54	6	studied	study	VERB
ejpam-6173	54	7	iterative	iterative	ADJ
ejpam-6173	54	8	algorithms	algorithm	NOUN
ejpam-6173	54	9	for	for	ADP
ejpam-6173	54	10	finding	find	VERB
ejpam-6173	54	11	a	a	DET
ejpam-6173	54	12	common	common	ADJ
ejpam-6173	54	13	solution	solution	NOUN
ejpam-6173	54	14	of	of	ADP
ejpam-6173	54	15	the	the	DET
ejpam-6173	54	16	ffp	ffp	PROPN
ejpam-6173	54	17	and	and	CCONJ
ejpam-6173	54	18	gmep	gmep	PROPN
ejpam-6173	54	19	.	.	PUNCT
ejpam-6173	55	1	in	in	ADP
ejpam-6173	55	2	particular	particular	ADJ
ejpam-6173	55	3	,	,	PUNCT
ejpam-6173	55	4	several	several	ADJ
ejpam-6173	55	5	authors	author	NOUN
ejpam-6173	55	6	have	have	AUX
ejpam-6173	55	7	considered	consider	VERB
ejpam-6173	55	8	the	the	DET
ejpam-6173	55	9	following	follow	VERB
ejpam-6173	55	10	problem	problem	NOUN
ejpam-6173	55	11	(	(	PUNCT
ejpam-6173	55	12	see	see	VERB
ejpam-6173	55	13	[	[	X
ejpam-6173	55	14	19–21	19–21	NUM
ejpam-6173	55	15	]	]	PUNCT
ejpam-6173	55	16	and	and	CCONJ
ejpam-6173	55	17	other	other	ADJ
ejpam-6173	55	18	references	reference	NOUN
ejpam-6173	55	19	therein	therein	ADV
ejpam-6173	55	20	):	):	PUNCT
ejpam-6173	55	21	find	find	VERB
ejpam-6173	55	22	x	x	X
ejpam-6173	55	23	∈	∈	PROPN
ejpam-6173	55	24	c	c	NOUN
ejpam-6173	55	25	such	such	ADJ
ejpam-6173	55	26	that	that	SCONJ
ejpam-6173	55	27	x	x	SYM
ejpam-6173	55	28	∈	∈	PROPN
ejpam-6173	55	29	f	f	X
ejpam-6173	55	30	(	(	PUNCT
ejpam-6173	55	31	t	t	PROPN
ejpam-6173	55	32	)	)	PUNCT
ejpam-6173	55	33	∩gmep(θ	∩gmep(θ	PROPN
ejpam-6173	55	34	,	,	PUNCT
ejpam-6173	55	35	ψ	ψ	X
ejpam-6173	55	36	,	,	PUNCT
ejpam-6173	55	37	φ	φ	NUM
ejpam-6173	55	38	)	)	PUNCT
ejpam-6173	55	39	.	.	PUNCT
ejpam-6173	56	1	the	the	DET
ejpam-6173	56	2	motivation	motivation	NOUN
ejpam-6173	56	3	for	for	ADP
ejpam-6173	56	4	studying	study	VERB
ejpam-6173	56	5	a	a	DET
ejpam-6173	56	6	common	common	ADJ
ejpam-6173	56	7	solution	solution	NOUN
ejpam-6173	56	8	problem	problem	NOUN
ejpam-6173	56	9	lies	lie	VERB
ejpam-6173	56	10	in	in	ADP
ejpam-6173	56	11	its	its	PRON
ejpam-6173	56	12	application	application	NOUN
ejpam-6173	56	13	to	to	ADP
ejpam-6173	56	14	problems	problem	NOUN
ejpam-6173	56	15	whose	whose	DET
ejpam-6173	56	16	constraints	constraint	NOUN
ejpam-6173	56	17	can	can	AUX
ejpam-6173	56	18	be	be	AUX
ejpam-6173	56	19	reformulated	reformulate	VERB
ejpam-6173	56	20	as	as	ADP
ejpam-6173	56	21	fpps	fpp	NOUN
ejpam-6173	56	22	and	and	CCONJ
ejpam-6173	56	23	gmeps	gmep	NOUN
ejpam-6173	56	24	.	.	PUNCT
ejpam-6173	57	1	for	for	ADP
ejpam-6173	57	2	instance	instance	NOUN
ejpam-6173	57	3	,	,	PUNCT
ejpam-6173	57	4	in	in	ADP
ejpam-6173	57	5	signal	signal	ADJ
ejpam-6173	57	6	processing	processing	NOUN
ejpam-6173	57	7	,	,	PUNCT
ejpam-6173	57	8	network	network	NOUN
ejpam-6173	57	9	resource	resource	NOUN
ejpam-6173	57	10	allocation	allocation	NOUN
ejpam-6173	57	11	,	,	PUNCT
ejpam-6173	57	12	among	among	ADP
ejpam-6173	57	13	others	other	NOUN
ejpam-6173	57	14	.	.	PUNCT
ejpam-6173	58	1	v.	v.	ADP
ejpam-6173	58	2	darvish	darvish	PROPN
ejpam-6173	58	3	et	et	PROPN
ejpam-6173	58	4	al	al	PROPN
ejpam-6173	58	5	.	.	PUNCT
ejpam-6173	58	6	/	/	SYM
ejpam-6173	58	7	eur	eur	PROPN
ejpam-6173	58	8	.	.	PUNCT
ejpam-6173	59	1	j.	j.	PROPN
ejpam-6173	59	2	pure	pure	PROPN
ejpam-6173	59	3	appl	appl	PROPN
ejpam-6173	59	4	.	.	PROPN
ejpam-6173	59	5	math	math	PROPN
ejpam-6173	59	6	,	,	PUNCT
ejpam-6173	59	7	18	18	NUM
ejpam-6173	59	8	(	(	PUNCT
ejpam-6173	59	9	3	3	NUM
ejpam-6173	59	10	)	)	PUNCT
ejpam-6173	59	11	(	(	PUNCT
ejpam-6173	59	12	2025	2025	NUM
ejpam-6173	59	13	)	)	PUNCT
ejpam-6173	59	14	,	,	PUNCT
ejpam-6173	59	15	6173	6173	NUM
ejpam-6173	59	16	4	4	NUM
ejpam-6173	59	17	of	of	ADP
ejpam-6173	59	18	32	32	NUM
ejpam-6173	59	19	recently	recently	ADV
ejpam-6173	59	20	,	,	PUNCT
ejpam-6173	59	21	takahashi	takahashi	PROPN
ejpam-6173	59	22	and	and	CCONJ
ejpam-6173	59	23	takahashi	takahashi	PROPN
ejpam-6173	60	1	[	[	X
ejpam-6173	60	2	22	22	NUM
ejpam-6173	60	3	]	]	PUNCT
ejpam-6173	60	4	introduced	introduce	VERB
ejpam-6173	60	5	the	the	DET
ejpam-6173	60	6	following	following	ADJ
ejpam-6173	60	7	iterative	iterative	NOUN
ejpam-6173	60	8	scheme	scheme	NOUN
ejpam-6173	60	9	for	for	ADP
ejpam-6173	60	10	solving	solve	VERB
ejpam-6173	60	11	gep	gep	PROPN
ejpam-6173	60	12	and	and	CCONJ
ejpam-6173	60	13	fpp	fpp	PROPN
ejpam-6173	60	14	of	of	ADP
ejpam-6173	60	15	a	a	DET
ejpam-6173	60	16	nonexpansive	nonexpansive	ADJ
ejpam-6173	60	17	mapping	mapping	NOUN
ejpam-6173	60	18	t	t	NOUN
ejpam-6173	60	19	in	in	ADP
ejpam-6173	60	20	a	a	DET
ejpam-6173	60	21	hilbert	hilbert	NOUN
ejpam-6173	60	22	space	space	NOUN
ejpam-6173	60	23	.	.	PUNCT
ejpam-6173	61	1	they	they	PRON
ejpam-6173	61	2	defined	define	VERB
ejpam-6173	61	3	the	the	DET
ejpam-6173	61	4	proposed	propose	VERB
ejpam-6173	61	5	method	method	NOUN
ejpam-6173	61	6	as	as	SCONJ
ejpam-6173	61	7	follows	follow	VERB
ejpam-6173	61	8	:	:	PUNCT
ejpam-6173	61	9	find	find	VERB
ejpam-6173	61	10	x1	x1	PROPN
ejpam-6173	61	11	,	,	PUNCT
ejpam-6173	61	12	z	z	PROPN
ejpam-6173	61	13	∈	∈	PROPN
ejpam-6173	61	14	c	c	NOUN
ejpam-6173	61	15	and	and	PROPN
ejpam-6173	61	16	zn	zn	PROPN
ejpam-6173	61	17	∈	∈	PROPN
ejpam-6173	61	18	c	c	NOUN
ejpam-6173	62	1	such	such	ADJ
ejpam-6173	62	2	that	that	DET
ejpam-6173	62	3	θ(zn	θ(zn	NOUN
ejpam-6173	62	4	,	,	PUNCT
ejpam-6173	62	5	y	y	PROPN
ejpam-6173	62	6	)	)	PUNCT
ejpam-6173	62	7	+	+	CCONJ
ejpam-6173	62	8	⟨bxn	⟨bxn	PROPN
ejpam-6173	62	9	,	,	PUNCT
ejpam-6173	62	10	y	y	PROPN
ejpam-6173	62	11	−	−	PROPN
ejpam-6173	62	12	zn⟩+	zn⟩+	PROPN
ejpam-6173	62	13	1	1	NUM
ejpam-6173	62	14	rn	rn	NOUN
ejpam-6173	62	15	⟨y	⟨y	NOUN
ejpam-6173	62	16	−	−	PROPN
ejpam-6173	62	17	zn	zn	PROPN
ejpam-6173	62	18	,	,	PUNCT
ejpam-6173	62	19	zn	zn	PROPN
ejpam-6173	62	20	−	−	PROPN
ejpam-6173	62	21	xn⟩	xn⟩	PROPN
ejpam-6173	62	22	≥	≥	PROPN
ejpam-6173	62	23	0	0	NUM
ejpam-6173	62	24	,	,	PUNCT
ejpam-6173	62	25	y	y	PROPN
ejpam-6173	62	26	∈	∈	PROPN
ejpam-6173	62	27	c	c	X
ejpam-6173	62	28	xn+1	xn+1	PROPN
ejpam-6173	63	1	=	=	SYM
ejpam-6173	64	1	βnxn	βnxn	NOUN
ejpam-6173	65	1	+	+	CCONJ
ejpam-6173	66	1	(	(	PUNCT
ejpam-6173	66	2	1−	1−	NUM
ejpam-6173	66	3	βn)t	βn)t	PROPN
ejpam-6173	66	4	[	[	PUNCT
ejpam-6173	66	5	αnz	αnz	NOUN
ejpam-6173	66	6	+	+	CCONJ
ejpam-6173	66	7	(	(	PUNCT
ejpam-6173	66	8	1−	1−	NUM
ejpam-6173	66	9	αn)zn	αn)zn	NUM
ejpam-6173	66	10	]	]	PUNCT
ejpam-6173	66	11	,	,	PUNCT
ejpam-6173	66	12	n	n	X
ejpam-6173	66	13	≥	≥	NOUN
ejpam-6173	66	14	1	1	NUM
ejpam-6173	66	15	{	{	PUNCT
ejpam-6173	66	16	αn	αn	NOUN
ejpam-6173	66	17	}	}	PUNCT
ejpam-6173	66	18	⊂	⊂	PROPN
ejpam-6173	66	19	(	(	PUNCT
ejpam-6173	66	20	0	0	NUM
ejpam-6173	66	21	,	,	PUNCT
ejpam-6173	66	22	1	1	NUM
ejpam-6173	66	23	)	)	PUNCT
ejpam-6173	66	24	,	,	PUNCT
ejpam-6173	66	25	{	{	PUNCT
ejpam-6173	66	26	βn	βn	NOUN
ejpam-6173	66	27	}	}	PUNCT
ejpam-6173	66	28	⊂	⊂	X
ejpam-6173	66	29	(	(	PUNCT
ejpam-6173	66	30	0	0	NUM
ejpam-6173	66	31	,	,	PUNCT
ejpam-6173	66	32	1	1	NUM
ejpam-6173	66	33	)	)	PUNCT
ejpam-6173	66	34	,	,	PUNCT
ejpam-6173	66	35	{	{	PUNCT
ejpam-6173	66	36	rn	rn	X
ejpam-6173	66	37	}	}	PUNCT
ejpam-6173	66	38	⊂	⊂	PROPN
ejpam-6173	66	39	(	(	PUNCT
ejpam-6173	66	40	0,+∞	0,+∞	NUM
ejpam-6173	66	41	)	)	PUNCT
ejpam-6173	66	42	and	and	CCONJ
ejpam-6173	66	43	b	b	NOUN
ejpam-6173	66	44	is	be	AUX
ejpam-6173	66	45	an	an	DET
ejpam-6173	66	46	α	α	NOUN
ejpam-6173	66	47	-	-	PUNCT
ejpam-6173	66	48	inverse	inverse	ADJ
ejpam-6173	66	49	strongly	strongly	ADV
ejpam-6173	66	50	monotone	monotone	ADJ
ejpam-6173	66	51	mapping	mapping	NOUN
ejpam-6173	66	52	.	.	PUNCT
ejpam-6173	67	1	the	the	DET
ejpam-6173	67	2	authors	author	NOUN
ejpam-6173	67	3	obtained	obtain	VERB
ejpam-6173	67	4	a	a	DET
ejpam-6173	67	5	strong	strong	ADJ
ejpam-6173	67	6	convergent	convergent	NOUN
ejpam-6173	67	7	result	result	NOUN
ejpam-6173	67	8	under	under	ADP
ejpam-6173	67	9	certain	certain	ADJ
ejpam-6173	67	10	conditions	condition	NOUN
ejpam-6173	67	11	.	.	PUNCT
ejpam-6173	68	1	eskandari	eskandari	ADJ
ejpam-6173	68	2	and	and	CCONJ
ejpam-6173	68	3	raeisi	raeisi	VERB
ejpam-6173	69	1	[	[	X
ejpam-6173	69	2	23	23	NUM
ejpam-6173	69	3	]	]	PUNCT
ejpam-6173	69	4	introduced	introduce	VERB
ejpam-6173	69	5	an	an	DET
ejpam-6173	69	6	iterative	iterative	NOUN
ejpam-6173	69	7	method	method	NOUN
ejpam-6173	69	8	for	for	ADP
ejpam-6173	69	9	approximating	approximate	VERB
ejpam-6173	69	10	a	a	DET
ejpam-6173	69	11	common	common	ADJ
ejpam-6173	69	12	solution	solution	NOUN
ejpam-6173	69	13	of	of	ADP
ejpam-6173	69	14	fpp	fpp	PROPN
ejpam-6173	69	15	of	of	ADP
ejpam-6173	69	16	bregman	bregman	PROPN
ejpam-6173	69	17	quasi	quasi	ADJ
ejpam-6173	69	18	-	-	ADJ
ejpam-6173	69	19	nonexpansive	nonexpansive	ADJ
ejpam-6173	69	20	mappings	mapping	NOUN
ejpam-6173	69	21	and	and	CCONJ
ejpam-6173	69	22	zeros	zero	NOUN
ejpam-6173	69	23	of	of	ADP
ejpam-6173	69	24	maximal	maximal	ADJ
ejpam-6173	69	25	monotone	monotone	ADJ
ejpam-6173	69	26	operators	operator	NOUN
ejpam-6173	69	27	.	.	PUNCT
ejpam-6173	70	1	they	they	PRON
ejpam-6173	70	2	defined	define	VERB
ejpam-6173	70	3	the	the	DET
ejpam-6173	70	4	algorithm	algorithm	NOUN
ejpam-6173	70	5	as	as	SCONJ
ejpam-6173	70	6	follows:	follows:	PROPN
ejpam-6173	70	7	x1	x1	PROPN
ejpam-6173	70	8	∈	∈	PROPN
ejpam-6173	70	9	e	e	NOUN
ejpam-6173	70	10	,	,	PUNCT
ejpam-6173	70	11	zn	zn	NOUN
ejpam-6173	70	12	=	=	PUNCT
ejpam-6173	70	13	resf	resf	VERB
ejpam-6173	70	14	λn	λn	NOUN
ejpam-6173	70	15	n	n	PRON
ejpam-6173	70	16	bn	bn	ADJ
ejpam-6173	70	17	◦	◦	NOUN
ejpam-6173	70	18	.	.	PUNCT
ejpam-6173	70	19	.	.	PUNCT
ejpam-6173	70	20	.	.	PUNCT
ejpam-6173	71	1	◦	◦	NOUN
ejpam-6173	71	2	resf	resf	NOUN
ejpam-6173	71	3	λ1	λ1	PROPN
ejpam-6173	71	4	nb1	nb1	PROPN
ejpam-6173	72	1	xn	xn	PROPN
ejpam-6173	72	2	,	,	PUNCT
ejpam-6173	72	3	yn	yn	X
ejpam-6173	72	4	=	=	PUNCT
ejpam-6173	72	5	βn∇f(zn	βn∇f(zn	PROPN
ejpam-6173	72	6	)	)	PUNCT
ejpam-6173	73	1	+	+	CCONJ
ejpam-6173	73	2	(	(	PUNCT
ejpam-6173	73	3	1−	1−	NUM
ejpam-6173	73	4	βn)∇f(tn(zn	βn)∇f(tn(zn	NOUN
ejpam-6173	73	5	)	)	PUNCT
ejpam-6173	73	6	)	)	PUNCT
ejpam-6173	74	1	,	,	PUNCT
ejpam-6173	74	2	xn+1	xn+1	PROPN
ejpam-6173	74	3	=	=	SYM
ejpam-6173	74	4	∇f∗(αn∇f(qn	∇f∗(αn∇f(qn	PROPN
ejpam-6173	74	5	)	)	PUNCT
ejpam-6173	74	6	+	+	CCONJ
ejpam-6173	74	7	(	(	PUNCT
ejpam-6173	74	8	1−	1−	NUM
ejpam-6173	74	9	αn)yn	αn)yn	NUM
ejpam-6173	74	10	)	)	PUNCT
ejpam-6173	74	11	,	,	PUNCT
ejpam-6173	74	12	where	where	SCONJ
ejpam-6173	74	13	{	{	PUNCT
ejpam-6173	74	14	αn	αn	NOUN
ejpam-6173	74	15	}	}	PUNCT
ejpam-6173	74	16	⊂	⊂	PROPN
ejpam-6173	74	17	(	(	PUNCT
ejpam-6173	74	18	0	0	NUM
ejpam-6173	74	19	,	,	PUNCT
ejpam-6173	74	20	1	1	NUM
ejpam-6173	74	21	)	)	PUNCT
ejpam-6173	74	22	.	.	PUNCT
ejpam-6173	75	1	under	under	ADP
ejpam-6173	75	2	certain	certain	ADJ
ejpam-6173	75	3	standard	standard	ADJ
ejpam-6173	75	4	conditions	condition	NOUN
ejpam-6173	75	5	,	,	PUNCT
ejpam-6173	75	6	the	the	DET
ejpam-6173	75	7	authors	author	NOUN
ejpam-6173	75	8	obtained	obtain	VERB
ejpam-6173	75	9	a	a	DET
ejpam-6173	75	10	strong	strong	ADJ
ejpam-6173	75	11	convergence	convergence	NOUN
ejpam-6173	75	12	result	result	NOUN
ejpam-6173	75	13	.	.	PUNCT
ejpam-6173	76	1	the	the	DET
ejpam-6173	76	2	ultimate	ultimate	ADJ
ejpam-6173	76	3	aim	aim	NOUN
ejpam-6173	76	4	of	of	ADP
ejpam-6173	76	5	every	every	DET
ejpam-6173	76	6	researcher	researcher	NOUN
ejpam-6173	76	7	is	be	AUX
ejpam-6173	76	8	to	to	PART
ejpam-6173	76	9	construct	construct	VERB
ejpam-6173	76	10	effective	effective	ADJ
ejpam-6173	76	11	iterative	iterative	NOUN
ejpam-6173	76	12	methods	method	NOUN
ejpam-6173	76	13	with	with	ADP
ejpam-6173	76	14	high	high	ADJ
ejpam-6173	76	15	convergence	convergence	NOUN
ejpam-6173	76	16	rates	rate	NOUN
ejpam-6173	76	17	to	to	ADP
ejpam-6173	76	18	the	the	DET
ejpam-6173	76	19	solutions	solution	NOUN
ejpam-6173	76	20	of	of	ADP
ejpam-6173	76	21	the	the	DET
ejpam-6173	76	22	optimization	optimization	NOUN
ejpam-6173	76	23	problem	problem	NOUN
ejpam-6173	76	24	under	under	ADP
ejpam-6173	76	25	consideration	consideration	NOUN
ejpam-6173	76	26	.	.	PUNCT
ejpam-6173	77	1	to	to	PART
ejpam-6173	77	2	achieve	achieve	VERB
ejpam-6173	77	3	this	this	DET
ejpam-6173	77	4	high	high	ADJ
ejpam-6173	77	5	rate	rate	NOUN
ejpam-6173	77	6	of	of	ADP
ejpam-6173	77	7	convergence	convergence	NOUN
ejpam-6173	77	8	,	,	PUNCT
ejpam-6173	77	9	authors	author	NOUN
ejpam-6173	77	10	employ	employ	VERB
ejpam-6173	77	11	the	the	DET
ejpam-6173	77	12	inertial	inertial	ADJ
ejpam-6173	77	13	technique	technique	NOUN
ejpam-6173	77	14	.	.	PUNCT
ejpam-6173	78	1	polyak	polyak	NOUN
ejpam-6173	79	1	[	[	X
ejpam-6173	79	2	24	24	NUM
ejpam-6173	79	3	]	]	PUNCT
ejpam-6173	79	4	introduced	introduce	VERB
ejpam-6173	79	5	the	the	DET
ejpam-6173	79	6	inertial	inertial	ADJ
ejpam-6173	79	7	extrapolation	extrapolation	NOUN
ejpam-6173	79	8	as	as	ADP
ejpam-6173	79	9	an	an	DET
ejpam-6173	79	10	acceleration	acceleration	NOUN
ejpam-6173	79	11	process	process	NOUN
ejpam-6173	79	12	to	to	PART
ejpam-6173	79	13	solve	solve	VERB
ejpam-6173	79	14	smooth	smooth	ADJ
ejpam-6173	79	15	convex	convex	NOUN
ejpam-6173	79	16	minimization	minimization	NOUN
ejpam-6173	79	17	problems	problem	NOUN
ejpam-6173	79	18	.	.	PUNCT
ejpam-6173	80	1	it	it	PRON
ejpam-6173	80	2	has	have	AUX
ejpam-6173	80	3	been	be	AUX
ejpam-6173	80	4	shown	show	VERB
ejpam-6173	80	5	by	by	ADP
ejpam-6173	80	6	several	several	ADJ
ejpam-6173	80	7	authors	author	NOUN
ejpam-6173	80	8	that	that	SCONJ
ejpam-6173	80	9	the	the	DET
ejpam-6173	80	10	inertial	inertial	ADJ
ejpam-6173	80	11	term	term	NOUN
ejpam-6173	80	12	improves	improve	VERB
ejpam-6173	80	13	the	the	DET
ejpam-6173	80	14	performance	performance	NOUN
ejpam-6173	80	15	of	of	ADP
ejpam-6173	80	16	iterative	iterative	ADJ
ejpam-6173	80	17	algorithms	algorithm	NOUN
ejpam-6173	80	18	numerically	numerically	ADV
ejpam-6173	80	19	in	in	ADP
ejpam-6173	80	20	terms	term	NOUN
ejpam-6173	80	21	of	of	ADP
ejpam-6173	80	22	the	the	DET
ejpam-6173	80	23	number	number	NOUN
ejpam-6173	80	24	of	of	ADP
ejpam-6173	80	25	iterations	iteration	NOUN
ejpam-6173	80	26	and	and	CCONJ
ejpam-6173	80	27	cpu	cpu	NOUN
ejpam-6173	80	28	time	time	NOUN
ejpam-6173	80	29	.	.	PUNCT
ejpam-6173	81	1	several	several	ADJ
ejpam-6173	81	2	authors	author	NOUN
ejpam-6173	81	3	have	have	AUX
ejpam-6173	81	4	studied	study	VERB
ejpam-6173	81	5	and	and	CCONJ
ejpam-6173	81	6	proposed	propose	VERB
ejpam-6173	81	7	iterative	iterative	NOUN
ejpam-6173	81	8	algorithms	algorithm	NOUN
ejpam-6173	81	9	with	with	ADP
ejpam-6173	81	10	the	the	DET
ejpam-6173	81	11	inertial	inertial	ADJ
ejpam-6173	81	12	technique	technique	NOUN
ejpam-6173	81	13	for	for	ADP
ejpam-6173	81	14	solving	solve	VERB
ejpam-6173	81	15	optimization	optimization	NOUN
ejpam-6173	81	16	problems	problem	NOUN
ejpam-6173	81	17	(	(	PUNCT
ejpam-6173	81	18	see	see	VERB
ejpam-6173	81	19	to	to	ADP
ejpam-6173	81	20	[	[	X
ejpam-6173	81	21	25–27	25–27	NUM
ejpam-6173	81	22	]	]	X
ejpam-6173	81	23	and	and	CCONJ
ejpam-6173	81	24	other	other	ADJ
ejpam-6173	81	25	references	reference	NOUN
ejpam-6173	81	26	therein	therein	ADV
ejpam-6173	81	27	)	)	PUNCT
ejpam-6173	81	28	.	.	PUNCT
ejpam-6173	82	1	motivated	motivate	VERB
ejpam-6173	82	2	by	by	ADP
ejpam-6173	82	3	the	the	DET
ejpam-6173	82	4	above	above	ADJ
ejpam-6173	82	5	mentioned	mention	VERB
ejpam-6173	82	6	methods	method	NOUN
ejpam-6173	82	7	in	in	ADP
ejpam-6173	82	8	the	the	DET
ejpam-6173	82	9	literature	literature	NOUN
ejpam-6173	82	10	and	and	CCONJ
ejpam-6173	82	11	the	the	DET
ejpam-6173	82	12	ongoing	ongoing	ADJ
ejpam-6173	82	13	research	research	NOUN
ejpam-6173	82	14	in	in	ADP
ejpam-6173	82	15	this	this	DET
ejpam-6173	82	16	area	area	NOUN
ejpam-6173	82	17	,	,	PUNCT
ejpam-6173	82	18	we	we	PRON
ejpam-6173	82	19	introduce	introduce	VERB
ejpam-6173	82	20	a	a	DET
ejpam-6173	82	21	new	new	ADJ
ejpam-6173	82	22	inertial	inertial	ADJ
ejpam-6173	82	23	iterative	iterative	NOUN
ejpam-6173	82	24	method	method	NOUN
ejpam-6173	82	25	for	for	ADP
ejpam-6173	82	26	approximating	approximate	VERB
ejpam-6173	82	27	the	the	DET
ejpam-6173	82	28	solutions	solution	NOUN
ejpam-6173	82	29	of	of	ADP
ejpam-6173	82	30	a	a	DET
ejpam-6173	82	31	generalized	generalize	VERB
ejpam-6173	82	32	mixed	mixed	ADJ
ejpam-6173	82	33	equilibrium	equilibrium	NOUN
ejpam-6173	82	34	problem	problem	NOUN
ejpam-6173	82	35	with	with	ADP
ejpam-6173	82	36	a	a	DET
ejpam-6173	82	37	maximal	maximal	ADJ
ejpam-6173	82	38	monotone	monotone	NOUN
ejpam-6173	82	39	mapping	mapping	NOUN
ejpam-6173	82	40	and	and	CCONJ
ejpam-6173	82	41	fixed	fix	VERB
ejpam-6173	82	42	point	point	NOUN
ejpam-6173	82	43	of	of	ADP
ejpam-6173	82	44	a	a	DET
ejpam-6173	82	45	bregman	bregman	NOUN
ejpam-6173	82	46	strongly	strongly	ADV
ejpam-6173	82	47	nonexpansive	nonexpansive	ADJ
ejpam-6173	82	48	mapping	mapping	NOUN
ejpam-6173	82	49	in	in	ADP
ejpam-6173	82	50	the	the	DET
ejpam-6173	82	51	framework	framework	NOUN
ejpam-6173	82	52	of	of	ADP
ejpam-6173	82	53	a	a	DET
ejpam-6173	82	54	reflexive	reflexive	ADJ
ejpam-6173	82	55	banach	banach	NOUN
ejpam-6173	82	56	space	space	NOUN
ejpam-6173	82	57	.	.	PUNCT
ejpam-6173	83	1	our	our	PRON
ejpam-6173	83	2	method	method	NOUN
ejpam-6173	83	3	does	do	AUX
ejpam-6173	83	4	not	not	PART
ejpam-6173	83	5	require	require	VERB
ejpam-6173	83	6	us	we	PRON
ejpam-6173	83	7	to	to	PART
ejpam-6173	83	8	compute	compute	VERB
ejpam-6173	83	9	subsets	subset	NOUN
ejpam-6173	83	10	of	of	ADP
ejpam-6173	83	11	cn	cn	PROPN
ejpam-6173	83	12	and	and	CCONJ
ejpam-6173	83	13	qn	qn	NOUN
ejpam-6173	83	14	.	.	PROPN
ejpam-6173	83	15	under	under	ADP
ejpam-6173	83	16	mild	mild	ADJ
ejpam-6173	83	17	condition	condition	NOUN
ejpam-6173	83	18	,	,	PUNCT
ejpam-6173	83	19	we	we	PRON
ejpam-6173	83	20	establish	establish	VERB
ejpam-6173	83	21	a	a	DET
ejpam-6173	83	22	strong	strong	ADJ
ejpam-6173	83	23	convergence	convergence	NOUN
ejpam-6173	83	24	result	result	NOUN
ejpam-6173	83	25	for	for	ADP
ejpam-6173	83	26	the	the	DET
ejpam-6173	83	27	proposed	propose	VERB
ejpam-6173	83	28	method	method	NOUN
ejpam-6173	83	29	.	.	PUNCT
ejpam-6173	84	1	finally	finally	ADV
ejpam-6173	84	2	,	,	PUNCT
ejpam-6173	84	3	we	we	PRON
ejpam-6173	84	4	present	present	VERB
ejpam-6173	84	5	numerical	numerical	ADJ
ejpam-6173	84	6	examples	example	NOUN
ejpam-6173	84	7	to	to	PART
ejpam-6173	84	8	illustrate	illustrate	VERB
ejpam-6173	84	9	the	the	DET
ejpam-6173	84	10	applicability	applicability	NOUN
ejpam-6173	84	11	of	of	ADP
ejpam-6173	84	12	our	our	PRON
ejpam-6173	84	13	proposed	propose	VERB
ejpam-6173	84	14	method	method	NOUN
ejpam-6173	84	15	.	.	PUNCT
ejpam-6173	85	1	the	the	DET
ejpam-6173	85	2	rest	rest	NOUN
ejpam-6173	85	3	of	of	ADP
ejpam-6173	85	4	the	the	DET
ejpam-6173	85	5	paper	paper	NOUN
ejpam-6173	85	6	is	be	AUX
ejpam-6173	85	7	organized	organize	VERB
ejpam-6173	85	8	as	as	SCONJ
ejpam-6173	85	9	follows	follow	VERB
ejpam-6173	85	10	:	:	PUNCT
ejpam-6173	85	11	in	in	ADP
ejpam-6173	85	12	section	section	NOUN
ejpam-6173	85	13	2	2	NUM
ejpam-6173	85	14	,	,	PUNCT
ejpam-6173	85	15	we	we	PRON
ejpam-6173	85	16	present	present	VERB
ejpam-6173	85	17	some	some	DET
ejpam-6173	85	18	basic	basic	ADJ
ejpam-6173	85	19	definitions	definition	NOUN
ejpam-6173	85	20	,	,	PUNCT
ejpam-6173	85	21	concepts	concept	NOUN
ejpam-6173	85	22	,	,	PUNCT
ejpam-6173	85	23	lemmas	lemmas	ADJ
ejpam-6173	85	24	,	,	PUNCT
ejpam-6173	85	25	and	and	CCONJ
ejpam-6173	85	26	results	result	NOUN
ejpam-6173	85	27	which	which	PRON
ejpam-6173	85	28	will	will	AUX
ejpam-6173	85	29	be	be	AUX
ejpam-6173	85	30	required	require	VERB
ejpam-6173	85	31	to	to	PART
ejpam-6173	85	32	obtain	obtain	VERB
ejpam-6173	85	33	the	the	DET
ejpam-6173	85	34	convergence	convergence	NOUN
ejpam-6173	85	35	analysis	analysis	NOUN
ejpam-6173	85	36	of	of	ADP
ejpam-6173	85	37	the	the	DET
ejpam-6173	85	38	proposed	propose	VERB
ejpam-6173	85	39	method	method	NOUN
ejpam-6173	85	40	.	.	PUNCT
ejpam-6173	86	1	in	in	ADP
ejpam-6173	86	2	section	section	NOUN
ejpam-6173	86	3	3	3	NUM
ejpam-6173	86	4	,	,	PUNCT
ejpam-6173	86	5	we	we	PRON
ejpam-6173	86	6	present	present	VERB
ejpam-6173	86	7	some	some	DET
ejpam-6173	86	8	required	require	VERB
ejpam-6173	86	9	assumptions	assumption	NOUN
ejpam-6173	86	10	and	and	CCONJ
ejpam-6173	86	11	introduce	introduce	VERB
ejpam-6173	86	12	our	our	PRON
ejpam-6173	86	13	proposed	propose	VERB
ejpam-6173	86	14	method	method	NOUN
ejpam-6173	86	15	.	.	PUNCT
ejpam-6173	87	1	in	in	ADP
ejpam-6173	87	2	section	section	NOUN
ejpam-6173	87	3	4	4	NUM
ejpam-6173	87	4	,	,	PUNCT
ejpam-6173	87	5	we	we	PRON
ejpam-6173	87	6	present	present	VERB
ejpam-6173	87	7	our	our	PRON
ejpam-6173	87	8	convergence	convergence	NOUN
ejpam-6173	87	9	analysis	analysis	NOUN
ejpam-6173	87	10	.	.	PUNCT
ejpam-6173	88	1	in	in	ADP
ejpam-6173	88	2	section	section	NOUN
ejpam-6173	88	3	5	5	NUM
ejpam-6173	88	4	,	,	PUNCT
ejpam-6173	88	5	we	we	PRON
ejpam-6173	88	6	present	present	VERB
ejpam-6173	88	7	numerical	numerical	ADJ
ejpam-6173	88	8	experiments	experiment	NOUN
ejpam-6173	88	9	in	in	ADP
ejpam-6173	88	10	comparisons	comparison	NOUN
ejpam-6173	88	11	with	with	ADP
ejpam-6173	88	12	other	other	ADJ
ejpam-6173	88	13	related	related	ADJ
ejpam-6173	88	14	methods	method	NOUN
ejpam-6173	88	15	to	to	PART
ejpam-6173	88	16	illustrate	illustrate	VERB
ejpam-6173	88	17	the	the	DET
ejpam-6173	88	18	effectiveness	effectiveness	NOUN
ejpam-6173	88	19	of	of	ADP
ejpam-6173	88	20	our	our	PRON
ejpam-6173	88	21	proposed	propose	VERB
ejpam-6173	88	22	method	method	NOUN
ejpam-6173	88	23	.	.	PUNCT
ejpam-6173	89	1	in	in	ADP
ejpam-6173	89	2	section	section	NOUN
ejpam-6173	89	3	6	6	NUM
ejpam-6173	89	4	,	,	PUNCT
ejpam-6173	89	5	we	we	PRON
ejpam-6173	89	6	present	present	VERB
ejpam-6173	89	7	a	a	DET
ejpam-6173	89	8	brief	brief	ADJ
ejpam-6173	89	9	summary	summary	NOUN
ejpam-6173	89	10	of	of	ADP
ejpam-6173	89	11	our	our	PRON
ejpam-6173	89	12	result	result	NOUN
ejpam-6173	89	13	.	.	PUNCT
ejpam-6173	90	1	v.	v.	ADP
ejpam-6173	90	2	darvish	darvish	PROPN
ejpam-6173	90	3	et	et	PROPN
ejpam-6173	90	4	al	al	PROPN
ejpam-6173	90	5	.	.	PUNCT
ejpam-6173	90	6	/	/	SYM
ejpam-6173	90	7	eur	eur	PROPN
ejpam-6173	90	8	.	.	PUNCT
ejpam-6173	91	1	j.	j.	PROPN
ejpam-6173	91	2	pure	pure	PROPN
ejpam-6173	91	3	appl	appl	PROPN
ejpam-6173	91	4	.	.	PROPN
ejpam-6173	91	5	math	math	PROPN
ejpam-6173	91	6	,	,	PUNCT
ejpam-6173	91	7	18	18	NUM
ejpam-6173	91	8	(	(	PUNCT
ejpam-6173	91	9	3	3	NUM
ejpam-6173	91	10	)	)	PUNCT
ejpam-6173	91	11	(	(	PUNCT
ejpam-6173	91	12	2025	2025	NUM
ejpam-6173	91	13	)	)	PUNCT
ejpam-6173	91	14	,	,	PUNCT
ejpam-6173	91	15	6173	6173	NUM
ejpam-6173	91	16	5	5	NUM
ejpam-6173	91	17	of	of	ADP
ejpam-6173	91	18	32	32	NUM
ejpam-6173	91	19	2	2	NUM
ejpam-6173	91	20	.	.	PUNCT
ejpam-6173	92	1	preliminaries	preliminary	NOUN
ejpam-6173	92	2	let	let	VERB
ejpam-6173	92	3	f	f	NOUN
ejpam-6173	92	4	:	:	PUNCT
ejpam-6173	92	5	e	e	X
ejpam-6173	92	6	→	→	PUNCT
ejpam-6173	92	7	(	(	PUNCT
ejpam-6173	92	8	−∞,+∞	−∞,+∞	ADV
ejpam-6173	92	9	]	]	PUNCT
ejpam-6173	92	10	be	be	AUX
ejpam-6173	92	11	a	a	DET
ejpam-6173	92	12	proper	proper	ADJ
ejpam-6173	92	13	,	,	PUNCT
ejpam-6173	92	14	lower	low	ADJ
ejpam-6173	92	15	semi	semi	ADJ
ejpam-6173	92	16	-	-	ADJ
ejpam-6173	92	17	continuous	continuous	ADJ
ejpam-6173	92	18	and	and	CCONJ
ejpam-6173	92	19	convex	convex	ADJ
ejpam-6173	92	20	function	function	NOUN
ejpam-6173	92	21	.	.	PUNCT
ejpam-6173	93	1	we	we	PRON
ejpam-6173	93	2	denote	denote	VERB
ejpam-6173	93	3	by	by	ADP
ejpam-6173	93	4	domf	domf	NOUN
ejpam-6173	93	5	,	,	PUNCT
ejpam-6173	93	6	the	the	DET
ejpam-6173	93	7	domain	domain	NOUN
ejpam-6173	93	8	of	of	ADP
ejpam-6173	93	9	f	f	PROPN
ejpam-6173	93	10	,	,	PUNCT
ejpam-6173	93	11	that	that	PRON
ejpam-6173	93	12	is	be	AUX
ejpam-6173	93	13	the	the	DET
ejpam-6173	93	14	set	set	NOUN
ejpam-6173	93	15	{	{	PUNCT
ejpam-6173	93	16	x	x	SYM
ejpam-6173	93	17	∈	∈	PROPN
ejpam-6173	93	18	e	e	NOUN
ejpam-6173	93	19	:	:	PUNCT
ejpam-6173	93	20	f(x	f(x	PROPN
ejpam-6173	93	21	)	)	PUNCT
ejpam-6173	93	22	<	<	X
ejpam-6173	94	1	+	+	PUNCT
ejpam-6173	94	2	∞	∞	NOUN
ejpam-6173	94	3	}	}	PUNCT
ejpam-6173	94	4	.	.	PUNCT
ejpam-6173	95	1	for	for	ADP
ejpam-6173	95	2	a	a	DET
ejpam-6173	95	3	sequence	sequence	NOUN
ejpam-6173	95	4	{	{	PUNCT
ejpam-6173	95	5	xn	xn	NOUN
ejpam-6173	95	6	}	}	PUNCT
ejpam-6173	95	7	in	in	ADP
ejpam-6173	95	8	e	e	NOUN
ejpam-6173	95	9	,	,	PUNCT
ejpam-6173	95	10	we	we	PRON
ejpam-6173	95	11	denote	denote	VERB
ejpam-6173	95	12	the	the	DET
ejpam-6173	95	13	strong	strong	ADJ
ejpam-6173	95	14	and	and	CCONJ
ejpam-6173	95	15	weak	weak	ADJ
ejpam-6173	95	16	convergence	convergence	NOUN
ejpam-6173	95	17	of	of	ADP
ejpam-6173	95	18	{	{	PUNCT
ejpam-6173	95	19	xn	xn	NOUN
ejpam-6173	95	20	}	}	PUNCT
ejpam-6173	95	21	to	to	ADP
ejpam-6173	95	22	x	x	SYM
ejpam-6173	95	23	∈	∈	PROPN
ejpam-6173	95	24	e	e	X
ejpam-6173	95	25	by	by	ADP
ejpam-6173	95	26	xn	xn	PROPN
ejpam-6173	95	27	→	→	SYM
ejpam-6173	95	28	x	x	PROPN
ejpam-6173	95	29	and	and	CCONJ
ejpam-6173	95	30	xn	xn	NUM
ejpam-6173	95	31	⇀	⇀	NUM
ejpam-6173	96	1	x	x	NOUN
ejpam-6173	96	2	,	,	PUNCT
ejpam-6173	96	3	respectively	respectively	ADV
ejpam-6173	96	4	.	.	PUNCT
ejpam-6173	97	1	let	let	VERB
ejpam-6173	97	2	x	x	PUNCT
ejpam-6173	97	3	∈	∈	PROPN
ejpam-6173	97	4	int(domf	int(domf	NOUN
ejpam-6173	97	5	)	)	PUNCT
ejpam-6173	97	6	,	,	PUNCT
ejpam-6173	97	7	the	the	DET
ejpam-6173	97	8	subdifferential	subdifferential	NOUN
ejpam-6173	97	9	of	of	ADP
ejpam-6173	97	10	f	f	PROPN
ejpam-6173	97	11	at	at	ADP
ejpam-6173	97	12	x	x	PROPN
ejpam-6173	97	13	is	be	AUX
ejpam-6173	97	14	the	the	DET
ejpam-6173	97	15	convex	convex	NOUN
ejpam-6173	97	16	set	set	VERB
ejpam-6173	97	17	defined	define	VERB
ejpam-6173	97	18	by	by	ADP
ejpam-6173	97	19	∂f(x	∂f(x	PROPN
ejpam-6173	97	20	)	)	PUNCT
ejpam-6173	97	21	=	=	PRON
ejpam-6173	98	1	{	{	PUNCT
ejpam-6173	98	2	x∗	x∗	PROPN
ejpam-6173	98	3	∈	∈	PROPN
ejpam-6173	98	4	e∗	e∗	NOUN
ejpam-6173	98	5	:	:	PUNCT
ejpam-6173	98	6	f(x	f(x	PROPN
ejpam-6173	98	7	)	)	PUNCT
ejpam-6173	99	1	+	+	CCONJ
ejpam-6173	100	1	⟨x∗	⟨x∗	PROPN
ejpam-6173	100	2	,	,	PUNCT
ejpam-6173	100	3	y	y	PROPN
ejpam-6173	100	4	−	−	PROPN
ejpam-6173	100	5	x⟩	x⟩	PUNCT
ejpam-6173	101	1	≤	≤	NUM
ejpam-6173	101	2	f(y	f(y	NOUN
ejpam-6173	101	3	)	)	PUNCT
ejpam-6173	101	4	,	,	PUNCT
ejpam-6173	101	5	for	for	ADP
ejpam-6173	101	6	all	all	DET
ejpam-6173	101	7	y	y	PROPN
ejpam-6173	101	8	∈	∈	PROPN
ejpam-6173	101	9	e	e	X
ejpam-6173	101	10	}	}	PUNCT
ejpam-6173	101	11	,	,	PUNCT
ejpam-6173	101	12	where	where	SCONJ
ejpam-6173	101	13	the	the	DET
ejpam-6173	101	14	fenchel	fenchel	PROPN
ejpam-6173	101	15	conjugate	conjugate	NOUN
ejpam-6173	101	16	of	of	ADP
ejpam-6173	101	17	f	f	PROPN
ejpam-6173	101	18	is	be	AUX
ejpam-6173	101	19	the	the	DET
ejpam-6173	101	20	function	function	NOUN
ejpam-6173	101	21	f∗	f∗	NOUN
ejpam-6173	101	22	:	:	PUNCT
ejpam-6173	101	23	e∗	e∗	PROPN
ejpam-6173	101	24	→	→	SYM
ejpam-6173	101	25	(	(	PUNCT
ejpam-6173	101	26	−∞,+∞	−∞,+∞	ADV
ejpam-6173	101	27	]	]	PUNCT
ejpam-6173	101	28	defined	define	VERB
ejpam-6173	101	29	by	by	ADP
ejpam-6173	101	30	f∗(x∗	f∗(x∗	NOUN
ejpam-6173	101	31	)	)	PUNCT
ejpam-6173	102	1	=	=	PUNCT
ejpam-6173	102	2	sup{⟨x∗	sup{⟨x∗	PROPN
ejpam-6173	102	3	,	,	PUNCT
ejpam-6173	102	4	x⟩	x⟩	PUNCT
ejpam-6173	103	1	−	−	PROPN
ejpam-6173	103	2	f(x	f(x	PROPN
ejpam-6173	103	3	)	)	PUNCT
ejpam-6173	103	4	:	:	PUNCT
ejpam-6173	104	1	x	x	X
ejpam-6173	104	2	∈	∈	PROPN
ejpam-6173	104	3	e	e	NOUN
ejpam-6173	104	4	,	,	PUNCT
ejpam-6173	104	5	x∗	x∗	PROPN
ejpam-6173	104	6	∈	∈	PROPN
ejpam-6173	104	7	e∗	e∗	PROPN
ejpam-6173	104	8	}	}	PUNCT
ejpam-6173	104	9	.	.	PUNCT
ejpam-6173	105	1	for	for	ADP
ejpam-6173	105	2	any	any	DET
ejpam-6173	105	3	x	x	SYM
ejpam-6173	105	4	∈	∈	PROPN
ejpam-6173	105	5	int(domf	int(domf	NOUN
ejpam-6173	105	6	)	)	PUNCT
ejpam-6173	105	7	,	,	PUNCT
ejpam-6173	105	8	the	the	DET
ejpam-6173	105	9	right	right	ADJ
ejpam-6173	105	10	-	-	PUNCT
ejpam-6173	105	11	hand	hand	NOUN
ejpam-6173	105	12	derivative	derivative	NOUN
ejpam-6173	105	13	of	of	ADP
ejpam-6173	105	14	f	f	PROPN
ejpam-6173	105	15	at	at	ADP
ejpam-6173	105	16	x	x	PROPN
ejpam-6173	105	17	in	in	ADP
ejpam-6173	105	18	the	the	DET
ejpam-6173	105	19	derivation	derivation	NOUN
ejpam-6173	105	20	y	y	PROPN
ejpam-6173	105	21	∈	∈	PROPN
ejpam-6173	105	22	e	e	NOUN
ejpam-6173	105	23	is	be	AUX
ejpam-6173	105	24	defined	define	VERB
ejpam-6173	105	25	by	by	ADP
ejpam-6173	105	26	f	f	PROPN
ejpam-6173	105	27	′	′	NUM
ejpam-6173	105	28	(	(	PUNCT
ejpam-6173	105	29	x	x	NOUN
ejpam-6173	105	30	,	,	PUNCT
ejpam-6173	105	31	y	y	PROPN
ejpam-6173	105	32	)	)	PUNCT
ejpam-6173	105	33	:	:	PUNCT
ejpam-6173	106	1	=	=	PROPN
ejpam-6173	106	2	lim	lim	PROPN
ejpam-6173	106	3	t	t	PROPN
ejpam-6173	106	4	↘	↘	PROPN
ejpam-6173	106	5	0	0	PROPN
ejpam-6173	106	6	f(x+	f(x+	NOUN
ejpam-6173	106	7	ty)−	ty)−	NUM
ejpam-6173	106	8	f(x	f(x	PROPN
ejpam-6173	106	9	)	)	PUNCT
ejpam-6173	106	10	t	t	PROPN
ejpam-6173	106	11	.	.	PUNCT
ejpam-6173	107	1	the	the	DET
ejpam-6173	107	2	function	function	NOUN
ejpam-6173	107	3	f	f	PROPN
ejpam-6173	107	4	is	be	AUX
ejpam-6173	107	5	called	call	VERB
ejpam-6173	107	6	gâteaux	gâteaux	ADV
ejpam-6173	107	7	differentiable	differentiable	ADJ
ejpam-6173	107	8	at	at	ADP
ejpam-6173	107	9	x	x	SYM
ejpam-6173	107	10	if	if	SCONJ
ejpam-6173	107	11	limt	limt	VERB
ejpam-6173	107	12	↘	↘	PROPN
ejpam-6173	107	13	0	0	SYM
ejpam-6173	107	14	f(x+ty)−f(x	f(x+ty)−f(x	PROPN
ejpam-6173	107	15	)	)	PUNCT
ejpam-6173	107	16	t	t	NOUN
ejpam-6173	107	17	exists	exist	VERB
ejpam-6173	107	18	for	for	ADP
ejpam-6173	107	19	all	all	DET
ejpam-6173	107	20	y	y	PROPN
ejpam-6173	107	21	∈	∈	PROPN
ejpam-6173	107	22	e.	e.	PROPN
ejpam-6173	107	23	in	in	ADP
ejpam-6173	107	24	this	this	DET
ejpam-6173	107	25	case	case	NOUN
ejpam-6173	107	26	,	,	PUNCT
ejpam-6173	107	27	f	f	PROPN
ejpam-6173	107	28	′	′	NUM
ejpam-6173	107	29	(	(	PUNCT
ejpam-6173	107	30	x	x	NOUN
ejpam-6173	107	31	,	,	PUNCT
ejpam-6173	107	32	y	y	NOUN
ejpam-6173	107	33	)	)	PUNCT
ejpam-6173	107	34	coincides	coincide	VERB
ejpam-6173	107	35	with	with	ADP
ejpam-6173	107	36	∇f(x	∇f(x	PROPN
ejpam-6173	107	37	)	)	PUNCT
ejpam-6173	107	38	,	,	PUNCT
ejpam-6173	107	39	the	the	DET
ejpam-6173	107	40	value	value	NOUN
ejpam-6173	107	41	of	of	ADP
ejpam-6173	107	42	the	the	DET
ejpam-6173	107	43	gradient	gradient	NOUN
ejpam-6173	107	44	(	(	PUNCT
ejpam-6173	107	45	∇f	∇f	NOUN
ejpam-6173	107	46	)	)	PUNCT
ejpam-6173	107	47	of	of	ADP
ejpam-6173	107	48	f	f	PROPN
ejpam-6173	107	49	at	at	ADP
ejpam-6173	107	50	x.	x.	NOUN
ejpam-6173	107	51	the	the	DET
ejpam-6173	107	52	function	function	NOUN
ejpam-6173	107	53	f	f	PROPN
ejpam-6173	107	54	is	be	AUX
ejpam-6173	107	55	called	call	VERB
ejpam-6173	107	56	gâteaux	gâteaux	ADV
ejpam-6173	107	57	differentiable	differentiable	ADJ
ejpam-6173	107	58	if	if	SCONJ
ejpam-6173	107	59	it	it	PRON
ejpam-6173	107	60	is	be	AUX
ejpam-6173	107	61	gâteaux	gâteaux	ADV
ejpam-6173	107	62	differentiable	differentiable	ADJ
ejpam-6173	107	63	for	for	ADP
ejpam-6173	107	64	any	any	DET
ejpam-6173	107	65	x	x	SYM
ejpam-6173	107	66	∈	∈	PROPN
ejpam-6173	107	67	int(domf	int(domf	NOUN
ejpam-6173	107	68	)	)	PUNCT
ejpam-6173	107	69	and	and	CCONJ
ejpam-6173	107	70	f	f	PROPN
ejpam-6173	107	71	is	be	AUX
ejpam-6173	107	72	called	call	VERB
ejpam-6173	107	73	fréchet	fréchet	NOUN
ejpam-6173	107	74	differentiable	differentiable	ADJ
ejpam-6173	107	75	at	at	ADP
ejpam-6173	107	76	x	x	SYM
ejpam-6173	107	77	if	if	SCONJ
ejpam-6173	107	78	this	this	DET
ejpam-6173	107	79	limit	limit	NOUN
ejpam-6173	107	80	is	be	AUX
ejpam-6173	107	81	attain	attain	VERB
ejpam-6173	107	82	uniformly	uniformly	ADV
ejpam-6173	107	83	for	for	ADP
ejpam-6173	107	84	all	all	DET
ejpam-6173	107	85	y	y	NOUN
ejpam-6173	107	86	which	which	PRON
ejpam-6173	107	87	satisfies	satisfy	VERB
ejpam-6173	107	88	∥y∥	∥y∥	NOUN
ejpam-6173	107	89	=	=	SYM
ejpam-6173	107	90	1	1	X
ejpam-6173	107	91	.	.	PUNCT
ejpam-6173	108	1	the	the	DET
ejpam-6173	108	2	function	function	NOUN
ejpam-6173	108	3	f	f	PROPN
ejpam-6173	108	4	is	be	AUX
ejpam-6173	108	5	uniformly	uniformly	ADV
ejpam-6173	108	6	fréchet	fréchet	VERB
ejpam-6173	108	7	differentiable	differentiable	ADJ
ejpam-6173	108	8	on	on	ADP
ejpam-6173	108	9	a	a	DET
ejpam-6173	108	10	subset	subset	NOUN
ejpam-6173	108	11	c	c	NOUN
ejpam-6173	108	12	of	of	ADP
ejpam-6173	108	13	e	e	PROPN
ejpam-6173	108	14	if	if	SCONJ
ejpam-6173	108	15	the	the	DET
ejpam-6173	108	16	limit	limit	NOUN
ejpam-6173	108	17	is	be	AUX
ejpam-6173	108	18	attained	attain	VERB
ejpam-6173	108	19	uniformly	uniformly	ADV
ejpam-6173	108	20	for	for	ADP
ejpam-6173	108	21	any	any	DET
ejpam-6173	108	22	x	x	SYM
ejpam-6173	108	23	∈	∈	PROPN
ejpam-6173	108	24	c	c	NOUN
ejpam-6173	108	25	and	and	CCONJ
ejpam-6173	108	26	∥y∥	∥y∥	NOUN
ejpam-6173	108	27	=	=	SYM
ejpam-6173	109	1	1	1	X
ejpam-6173	109	2	.	.	PUNCT
ejpam-6173	110	1	it	it	PRON
ejpam-6173	110	2	is	be	AUX
ejpam-6173	110	3	known	know	VERB
ejpam-6173	110	4	that	that	SCONJ
ejpam-6173	110	5	if	if	SCONJ
ejpam-6173	110	6	f	f	PROPN
ejpam-6173	110	7	is	be	AUX
ejpam-6173	110	8	gâteaux	gâteaux	ADV
ejpam-6173	110	9	differentiable	differentiable	ADJ
ejpam-6173	110	10	(	(	PUNCT
ejpam-6173	110	11	resp	resp	NOUN
ejpam-6173	110	12	.	.	PUNCT
ejpam-6173	111	1	fréchet	fréchet	PROPN
ejpam-6173	111	2	differentiable	differentiable	ADJ
ejpam-6173	111	3	)	)	PUNCT
ejpam-6173	111	4	on	on	ADP
ejpam-6173	111	5	int(domf	int(domf	NOUN
ejpam-6173	111	6	)	)	PUNCT
ejpam-6173	111	7	,	,	PUNCT
ejpam-6173	111	8	then	then	ADV
ejpam-6173	111	9	f	f	PROPN
ejpam-6173	111	10	is	be	AUX
ejpam-6173	111	11	continuous	continuous	ADJ
ejpam-6173	111	12	and	and	CCONJ
ejpam-6173	111	13	its	its	PRON
ejpam-6173	111	14	gâteaux	gâteaux	ADJ
ejpam-6173	111	15	derivative	derivative	ADJ
ejpam-6173	111	16	∇f	∇f	NOUN
ejpam-6173	111	17	is	be	AUX
ejpam-6173	111	18	norm	norm	NOUN
ejpam-6173	111	19	-	-	PUNCT
ejpam-6173	111	20	to	to	ADP
ejpam-6173	111	21	-	-	PUNCT
ejpam-6173	111	22	weak∗	weak∗	NOUN
ejpam-6173	111	23	continuous	continuous	ADJ
ejpam-6173	111	24	(	(	PUNCT
ejpam-6173	111	25	resp	resp	NOUN
ejpam-6173	111	26	.	.	PUNCT
ejpam-6173	112	1	continuous	continuous	ADJ
ejpam-6173	112	2	)	)	PUNCT
ejpam-6173	112	3	on	on	ADP
ejpam-6173	112	4	int(domf	int(domf	NOUN
ejpam-6173	112	5	)	)	PUNCT
ejpam-6173	112	6	(	(	PUNCT
ejpam-6173	112	7	see	see	VERB
ejpam-6173	112	8	[	[	X
ejpam-6173	112	9	28	28	NUM
ejpam-6173	112	10	]	]	NUM
ejpam-6173	112	11	)	)	PUNCT
ejpam-6173	112	12	.	.	PUNCT
ejpam-6173	113	1	let	let	VERB
ejpam-6173	113	2	f	f	NOUN
ejpam-6173	113	3	:	:	PUNCT
ejpam-6173	113	4	e	e	X
ejpam-6173	113	5	→	→	PUNCT
ejpam-6173	113	6	(	(	PUNCT
ejpam-6173	113	7	−∞,+∞	−∞,+∞	ADV
ejpam-6173	113	8	]	]	PUNCT
ejpam-6173	113	9	be	be	VERB
ejpam-6173	113	10	a	a	DET
ejpam-6173	113	11	gâteaux	gâteaux	ADV
ejpam-6173	113	12	differentiable	differentiable	ADJ
ejpam-6173	113	13	function	function	NOUN
ejpam-6173	113	14	.	.	PUNCT
ejpam-6173	114	1	the	the	DET
ejpam-6173	114	2	function	function	NOUN
ejpam-6173	114	3	df	df	NOUN
ejpam-6173	114	4	:	:	PUNCT
ejpam-6173	114	5	domf	domf	NOUN
ejpam-6173	114	6	×	×	PROPN
ejpam-6173	114	7	int(domf	int(domf	NOUN
ejpam-6173	114	8	)	)	PUNCT
ejpam-6173	114	9	→	→	PUNCT
ejpam-6173	114	10	[	[	X
ejpam-6173	114	11	0,+∞	0,+∞	NUM
ejpam-6173	114	12	)	)	PUNCT
ejpam-6173	114	13	defined	define	VERB
ejpam-6173	114	14	as	as	SCONJ
ejpam-6173	114	15	follows	follow	VERB
ejpam-6173	114	16	:	:	PUNCT
ejpam-6173	114	17	df	df	PROPN
ejpam-6173	114	18	(	(	PUNCT
ejpam-6173	114	19	x	x	NOUN
ejpam-6173	114	20	,	,	PUNCT
ejpam-6173	114	21	y	y	PROPN
ejpam-6173	114	22	)	)	PUNCT
ejpam-6173	114	23	:	:	PUNCT
ejpam-6173	114	24	=	=	PUNCT
ejpam-6173	114	25	f(x)−	f(x)−	PROPN
ejpam-6173	114	26	f(y)−	f(y)−	PROPN
ejpam-6173	114	27	⟨∇f(y	⟨∇f(y	PROPN
ejpam-6173	114	28	)	)	PUNCT
ejpam-6173	114	29	,	,	PUNCT
ejpam-6173	114	30	x−	x−	PROPN
ejpam-6173	114	31	y⟩	y⟩	PROPN
ejpam-6173	114	32	,	,	PUNCT
ejpam-6173	114	33	for	for	ADP
ejpam-6173	114	34	all	all	DET
ejpam-6173	114	35	x	x	SYM
ejpam-6173	114	36	∈	∈	PROPN
ejpam-6173	114	37	dom(f	dom(f	PROPN
ejpam-6173	114	38	)	)	PUNCT
ejpam-6173	114	39	,	,	PUNCT
ejpam-6173	114	40	y	y	PROPN
ejpam-6173	114	41	∈	∈	PROPN
ejpam-6173	114	42	int(dom(f	int(dom(f	PROPN
ejpam-6173	114	43	)	)	PUNCT
ejpam-6173	114	44	)	)	PUNCT
ejpam-6173	114	45	(	(	PUNCT
ejpam-6173	114	46	2.1	2.1	NUM
ejpam-6173	114	47	)	)	PUNCT
ejpam-6173	114	48	is	be	AUX
ejpam-6173	114	49	called	call	VERB
ejpam-6173	114	50	the	the	DET
ejpam-6173	114	51	bregman	bregman	NOUN
ejpam-6173	114	52	distance	distance	NOUN
ejpam-6173	114	53	with	with	ADP
ejpam-6173	114	54	respect	respect	NOUN
ejpam-6173	114	55	to	to	ADP
ejpam-6173	114	56	f	f	PROPN
ejpam-6173	114	57	,	,	PUNCT
ejpam-6173	114	58	[	[	X
ejpam-6173	114	59	29	29	NUM
ejpam-6173	114	60	]	]	PUNCT
ejpam-6173	114	61	.	.	PUNCT
ejpam-6173	115	1	remark	remark	PROPN
ejpam-6173	115	2	1	1	NUM
ejpam-6173	115	3	.	.	PUNCT
ejpam-6173	116	1	the	the	DET
ejpam-6173	116	2	bregman	bregman	NOUN
ejpam-6173	116	3	distance	distance	NOUN
ejpam-6173	116	4	has	have	VERB
ejpam-6173	116	5	the	the	DET
ejpam-6173	116	6	following	follow	VERB
ejpam-6173	116	7	properties	property	NOUN
ejpam-6173	116	8	:	:	PUNCT
ejpam-6173	116	9	(	(	PUNCT
ejpam-6173	116	10	i	i	NOUN
ejpam-6173	116	11	)	)	PUNCT
ejpam-6173	116	12	the	the	DET
ejpam-6173	116	13	three	three	NUM
ejpam-6173	116	14	-	-	PUNCT
ejpam-6173	116	15	point	point	NOUN
ejpam-6173	116	16	identity	identity	NOUN
ejpam-6173	116	17	,	,	PUNCT
ejpam-6173	116	18	for	for	ADP
ejpam-6173	116	19	any	any	DET
ejpam-6173	116	20	x	x	SYM
ejpam-6173	116	21	∈	∈	PROPN
ejpam-6173	116	22	domf	domf	NOUN
ejpam-6173	116	23	and	and	CCONJ
ejpam-6173	116	24	y	y	NOUN
ejpam-6173	116	25	,	,	PUNCT
ejpam-6173	116	26	z	z	PROPN
ejpam-6173	116	27	∈	∈	PROPN
ejpam-6173	116	28	int(domf	int(domf	NOUN
ejpam-6173	116	29	)	)	PUNCT
ejpam-6173	116	30	,	,	PUNCT
ejpam-6173	116	31	df	df	PROPN
ejpam-6173	116	32	(	(	PUNCT
ejpam-6173	116	33	x	x	NOUN
ejpam-6173	116	34	,	,	PUNCT
ejpam-6173	116	35	y	y	PROPN
ejpam-6173	116	36	)	)	PUNCT
ejpam-6173	117	1	+	+	NOUN
ejpam-6173	117	2	df	df	PROPN
ejpam-6173	117	3	(	(	PUNCT
ejpam-6173	117	4	y	y	NOUN
ejpam-6173	117	5	,	,	PUNCT
ejpam-6173	117	6	z)−df	z)−df	PROPN
ejpam-6173	117	7	(	(	PUNCT
ejpam-6173	117	8	x	x	X
ejpam-6173	117	9	,	,	PUNCT
ejpam-6173	117	10	z	z	NOUN
ejpam-6173	117	11	)	)	PUNCT
ejpam-6173	117	12	=	=	SYM
ejpam-6173	117	13	⟨∇f(z)−∇f(y	⟨∇f(z)−∇f(y	NUM
ejpam-6173	117	14	)	)	PUNCT
ejpam-6173	117	15	,	,	PUNCT
ejpam-6173	117	16	x−	x−	PROPN
ejpam-6173	117	17	y⟩	y⟩	PROPN
ejpam-6173	117	18	;	;	PUNCT
ejpam-6173	117	19	(	(	PUNCT
ejpam-6173	117	20	2.2	2.2	NUM
ejpam-6173	117	21	)	)	PUNCT
ejpam-6173	118	1	[	[	X
ejpam-6173	118	2	30	30	NUM
ejpam-6173	118	3	]	]	X
ejpam-6173	118	4	(	(	PUNCT
ejpam-6173	118	5	ii	ii	NOUN
ejpam-6173	118	6	)	)	PUNCT
ejpam-6173	118	7	the	the	DET
ejpam-6173	118	8	four	four	NUM
ejpam-6173	118	9	-	-	PUNCT
ejpam-6173	118	10	point	point	NOUN
ejpam-6173	118	11	identity	identity	NOUN
ejpam-6173	118	12	,	,	PUNCT
ejpam-6173	118	13	for	for	ADP
ejpam-6173	118	14	any	any	DET
ejpam-6173	118	15	y	y	PROPN
ejpam-6173	118	16	,	,	PUNCT
ejpam-6173	118	17	w	w	PROPN
ejpam-6173	118	18	∈	∈	NOUN
ejpam-6173	118	19	domf	domf	NOUN
ejpam-6173	118	20	and	and	CCONJ
ejpam-6173	118	21	x	x	NOUN
ejpam-6173	118	22	,	,	PUNCT
ejpam-6173	118	23	z	z	PROPN
ejpam-6173	118	24	∈	∈	PROPN
ejpam-6173	118	25	int(domf	int(domf	NOUN
ejpam-6173	118	26	)	)	PUNCT
ejpam-6173	118	27	,	,	PUNCT
ejpam-6173	118	28	df	df	PROPN
ejpam-6173	118	29	(	(	PUNCT
ejpam-6173	118	30	y	y	PROPN
ejpam-6173	118	31	,	,	PUNCT
ejpam-6173	118	32	x)−df	x)−df	PUNCT
ejpam-6173	119	1	(	(	PUNCT
ejpam-6173	119	2	y	y	NOUN
ejpam-6173	119	3	,	,	PUNCT
ejpam-6173	119	4	z)−df	z)−df	PROPN
ejpam-6173	119	5	(	(	PUNCT
ejpam-6173	119	6	w	w	NOUN
ejpam-6173	119	7	,	,	PUNCT
ejpam-6173	119	8	x	x	NOUN
ejpam-6173	119	9	)	)	PUNCT
ejpam-6173	120	1	+	+	NOUN
ejpam-6173	120	2	df	df	NOUN
ejpam-6173	120	3	(	(	PUNCT
ejpam-6173	120	4	w	w	PROPN
ejpam-6173	120	5	,	,	PUNCT
ejpam-6173	120	6	z	z	NOUN
ejpam-6173	120	7	)	)	PUNCT
ejpam-6173	120	8	=	=	SYM
ejpam-6173	120	9	⟨∇f(z)−∇f(x	⟨∇f(z)−∇f(x	NOUN
ejpam-6173	120	10	)	)	PUNCT
ejpam-6173	120	11	,	,	PUNCT
ejpam-6173	120	12	y	y	PROPN
ejpam-6173	120	13	−	−	PROPN
ejpam-6173	120	14	w⟩.	w⟩.	X
ejpam-6173	120	15	(	(	PUNCT
ejpam-6173	120	16	2.3	2.3	NUM
ejpam-6173	120	17	)	)	PUNCT
ejpam-6173	120	18	v.	v.	ADP
ejpam-6173	120	19	darvish	darvish	PROPN
ejpam-6173	120	20	et	et	PROPN
ejpam-6173	120	21	al	al	PROPN
ejpam-6173	120	22	.	.	PUNCT
ejpam-6173	120	23	/	/	SYM
ejpam-6173	120	24	eur	eur	PROPN
ejpam-6173	120	25	.	.	PUNCT
ejpam-6173	121	1	j.	j.	PROPN
ejpam-6173	121	2	pure	pure	PROPN
ejpam-6173	121	3	appl	appl	PROPN
ejpam-6173	121	4	.	.	PROPN
ejpam-6173	121	5	math	math	PROPN
ejpam-6173	121	6	,	,	PUNCT
ejpam-6173	121	7	18	18	NUM
ejpam-6173	121	8	(	(	PUNCT
ejpam-6173	121	9	3	3	NUM
ejpam-6173	121	10	)	)	PUNCT
ejpam-6173	121	11	(	(	PUNCT
ejpam-6173	121	12	2025	2025	NUM
ejpam-6173	121	13	)	)	PUNCT
ejpam-6173	121	14	,	,	PUNCT
ejpam-6173	121	15	6173	6173	NUM
ejpam-6173	121	16	6	6	NUM
ejpam-6173	121	17	of	of	ADP
ejpam-6173	121	18	32	32	NUM
ejpam-6173	121	19	definition	definition	NOUN
ejpam-6173	121	20	1	1	NUM
ejpam-6173	121	21	.	.	PUNCT
ejpam-6173	122	1	a	a	DET
ejpam-6173	122	2	gâteaux	gâteaux	ADV
ejpam-6173	122	3	differentiable	differentiable	ADJ
ejpam-6173	122	4	function	function	NOUN
ejpam-6173	122	5	f	f	PROPN
ejpam-6173	122	6	is	be	AUX
ejpam-6173	122	7	said	say	VERB
ejpam-6173	122	8	to	to	PART
ejpam-6173	122	9	be	be	AUX
ejpam-6173	122	10	γ	γ	X
ejpam-6173	122	11	-	-	ADJ
ejpam-6173	122	12	strongly	strongly	ADV
ejpam-6173	122	13	convex	convex	NOUN
ejpam-6173	122	14	if	if	SCONJ
ejpam-6173	122	15	there	there	PRON
ejpam-6173	122	16	exists	exist	VERB
ejpam-6173	122	17	a	a	DET
ejpam-6173	122	18	constant	constant	ADJ
ejpam-6173	122	19	γ	γ	X
ejpam-6173	122	20	>	>	X
ejpam-6173	122	21	0	0	NUM
ejpam-6173	122	22	such	such	ADJ
ejpam-6173	122	23	that	that	SCONJ
ejpam-6173	122	24	f(x	f(x	PROPN
ejpam-6173	122	25	)	)	PUNCT
ejpam-6173	122	26	≥	≥	NOUN
ejpam-6173	122	27	f(y	f(y	NOUN
ejpam-6173	122	28	)	)	PUNCT
ejpam-6173	123	1	+	+	CCONJ
ejpam-6173	123	2	⟨x−	⟨x−	PROPN
ejpam-6173	123	3	y,∇f(y)⟩+	y,∇f(y)⟩+	PROPN
ejpam-6173	123	4	γ	γ	NOUN
ejpam-6173	123	5	2	2	NUM
ejpam-6173	123	6	∥x−	∥x−	NUM
ejpam-6173	123	7	y∥2	y∥2	NOUN
ejpam-6173	123	8	,	,	PUNCT
ejpam-6173	123	9	for	for	ADP
ejpam-6173	123	10	all	all	DET
ejpam-6173	123	11	x	x	SYM
ejpam-6173	123	12	∈	∈	PROPN
ejpam-6173	123	13	dom(f	dom(f	PROPN
ejpam-6173	123	14	)	)	PUNCT
ejpam-6173	123	15	,	,	PUNCT
ejpam-6173	123	16	y	y	PROPN
ejpam-6173	123	17	∈	∈	PROPN
ejpam-6173	123	18	int(dom(f	int(dom(f	PROPN
ejpam-6173	123	19	)	)	PUNCT
ejpam-6173	123	20	)	)	PUNCT
ejpam-6173	123	21	.	.	PUNCT
ejpam-6173	124	1	lemma	lemma	PROPN
ejpam-6173	124	2	1	1	NUM
ejpam-6173	124	3	.	.	PUNCT
ejpam-6173	125	1	[	[	X
ejpam-6173	125	2	31	31	NUM
ejpam-6173	125	3	]	]	PUNCT
ejpam-6173	125	4	let	let	VERB
ejpam-6173	125	5	f	f	PRON
ejpam-6173	125	6	be	be	AUX
ejpam-6173	125	7	a	a	DET
ejpam-6173	125	8	strongly	strongly	ADV
ejpam-6173	125	9	convex	convex	ADJ
ejpam-6173	125	10	function	function	NOUN
ejpam-6173	125	11	with	with	ADP
ejpam-6173	125	12	constant	constant	ADJ
ejpam-6173	125	13	γ	γ	X
ejpam-6173	125	14	>	>	X
ejpam-6173	125	15	0	0	NUM
ejpam-6173	125	16	.	.	PUNCT
ejpam-6173	126	1	then	then	ADV
ejpam-6173	126	2	for	for	ADP
ejpam-6173	126	3	all	all	DET
ejpam-6173	126	4	y	y	PROPN
ejpam-6173	126	5	∈	∈	PROPN
ejpam-6173	126	6	dom(f	dom(f	PROPN
ejpam-6173	126	7	)	)	PUNCT
ejpam-6173	126	8	and	and	CCONJ
ejpam-6173	126	9	x	x	PUNCT
ejpam-6173	126	10	∈	∈	PROPN
ejpam-6173	126	11	int(dom(f	int(dom(f	PROPN
ejpam-6173	126	12	)	)	PUNCT
ejpam-6173	126	13	)	)	PUNCT
ejpam-6173	126	14	,	,	PUNCT
ejpam-6173	126	15	we	we	PRON
ejpam-6173	126	16	have	have	VERB
ejpam-6173	126	17	:	:	PUNCT
ejpam-6173	126	18	df	df	PROPN
ejpam-6173	126	19	(	(	PUNCT
ejpam-6173	126	20	x	x	NOUN
ejpam-6173	126	21	,	,	PUNCT
ejpam-6173	126	22	y	y	PROPN
ejpam-6173	126	23	)	)	PUNCT
ejpam-6173	126	24	≥	≥	PROPN
ejpam-6173	126	25	γ	γ	PROPN
ejpam-6173	126	26	2	2	NUM
ejpam-6173	126	27	∥x−	∥x−	PROPN
ejpam-6173	126	28	y∥2	y∥2	NOUN
ejpam-6173	126	29	,	,	PUNCT
ejpam-6173	126	30	(	(	PUNCT
ejpam-6173	126	31	2.4	2.4	NUM
ejpam-6173	126	32	)	)	PUNCT
ejpam-6173	126	33	where	where	SCONJ
ejpam-6173	126	34	df	df	PROPN
ejpam-6173	126	35	(	(	PUNCT
ejpam-6173	126	36	x	x	NOUN
ejpam-6173	126	37	,	,	PUNCT
ejpam-6173	126	38	y	y	PROPN
ejpam-6173	126	39	)	)	PUNCT
ejpam-6173	126	40	is	be	AUX
ejpam-6173	126	41	the	the	DET
ejpam-6173	126	42	bregman	bregman	NOUN
ejpam-6173	126	43	distance	distance	NOUN
ejpam-6173	126	44	with	with	ADP
ejpam-6173	126	45	respect	respect	NOUN
ejpam-6173	126	46	to	to	ADP
ejpam-6173	126	47	f.	f.	PROPN
ejpam-6173	126	48	the	the	DET
ejpam-6173	126	49	legendre	legendre	PROPN
ejpam-6173	126	50	function	function	PROPN
ejpam-6173	127	1	f	f	X
ejpam-6173	127	2	:	:	PUNCT
ejpam-6173	127	3	e	e	X
ejpam-6173	127	4	→	→	PUNCT
ejpam-6173	127	5	(	(	PUNCT
ejpam-6173	127	6	−∞,+∞	−∞,+∞	ADV
ejpam-6173	127	7	]	]	PUNCT
ejpam-6173	127	8	is	be	AUX
ejpam-6173	127	9	defined	define	VERB
ejpam-6173	127	10	in	in	ADP
ejpam-6173	127	11	[	[	X
ejpam-6173	127	12	32	32	NUM
ejpam-6173	127	13	]	]	PUNCT
ejpam-6173	127	14	.	.	PUNCT
ejpam-6173	128	1	it	it	PRON
ejpam-6173	128	2	is	be	AUX
ejpam-6173	128	3	well	well	ADV
ejpam-6173	128	4	known	know	VERB
ejpam-6173	128	5	that	that	SCONJ
ejpam-6173	128	6	in	in	ADP
ejpam-6173	128	7	reflexive	reflexive	ADJ
ejpam-6173	128	8	spaces	space	NOUN
ejpam-6173	128	9	,	,	PUNCT
ejpam-6173	128	10	f	f	PROPN
ejpam-6173	128	11	is	be	AUX
ejpam-6173	128	12	legendre	legendre	PROPN
ejpam-6173	128	13	function	function	PROPN
ejpam-6173	128	14	if	if	SCONJ
ejpam-6173	128	15	and	and	CCONJ
ejpam-6173	128	16	only	only	ADV
ejpam-6173	128	17	if	if	SCONJ
ejpam-6173	128	18	it	it	PRON
ejpam-6173	128	19	satisfies	satisfy	VERB
ejpam-6173	128	20	the	the	DET
ejpam-6173	128	21	following	follow	VERB
ejpam-6173	128	22	conditions	condition	NOUN
ejpam-6173	128	23	:	:	PUNCT
ejpam-6173	128	24	(	(	PUNCT
ejpam-6173	128	25	l1	l1	PROPN
ejpam-6173	128	26	)	)	PUNCT
ejpam-6173	128	27	the	the	DET
ejpam-6173	128	28	interior	interior	NOUN
ejpam-6173	128	29	of	of	ADP
ejpam-6173	128	30	the	the	DET
ejpam-6173	128	31	domain	domain	NOUN
ejpam-6173	128	32	of	of	ADP
ejpam-6173	128	33	f	f	PROPN
ejpam-6173	128	34	,	,	PUNCT
ejpam-6173	128	35	int(domf	int(domf	NOUN
ejpam-6173	128	36	)	)	PUNCT
ejpam-6173	128	37	,	,	PUNCT
ejpam-6173	128	38	is	be	AUX
ejpam-6173	128	39	nonempty	nonempty	ADJ
ejpam-6173	128	40	,	,	PUNCT
ejpam-6173	128	41	f	f	PROPN
ejpam-6173	128	42	is	be	AUX
ejpam-6173	128	43	gâteaux	gâteaux	ADV
ejpam-6173	128	44	differentiable	differentiable	ADJ
ejpam-6173	128	45	on	on	ADP
ejpam-6173	128	46	int(domf	int(domf	NOUN
ejpam-6173	128	47	)	)	PUNCT
ejpam-6173	128	48	and	and	CCONJ
ejpam-6173	128	49	domf	domf	NOUN
ejpam-6173	128	50	=	=	PUNCT
ejpam-6173	128	51	int(domf	int(domf	NOUN
ejpam-6173	128	52	)	)	PUNCT
ejpam-6173	128	53	;	;	PUNCT
ejpam-6173	128	54	(	(	PUNCT
ejpam-6173	128	55	l2	l2	NOUN
ejpam-6173	128	56	)	)	PUNCT
ejpam-6173	128	57	the	the	DET
ejpam-6173	128	58	interior	interior	NOUN
ejpam-6173	128	59	of	of	ADP
ejpam-6173	128	60	the	the	DET
ejpam-6173	128	61	domain	domain	NOUN
ejpam-6173	128	62	of	of	ADP
ejpam-6173	128	63	f∗	f∗	NOUN
ejpam-6173	128	64	,	,	PUNCT
ejpam-6173	128	65	int(domf∗	int(domf∗	NOUN
ejpam-6173	128	66	)	)	PUNCT
ejpam-6173	128	67	,	,	PUNCT
ejpam-6173	128	68	is	be	AUX
ejpam-6173	128	69	nonempty	nonempty	ADJ
ejpam-6173	128	70	,	,	PUNCT
ejpam-6173	128	71	f∗	f∗	NOUN
ejpam-6173	128	72	is	be	AUX
ejpam-6173	128	73	gâteaux	gâteaux	VERB
ejpam-6173	128	74	differentiable	differentiable	ADJ
ejpam-6173	128	75	on	on	ADP
ejpam-6173	128	76	int(domf∗	int(domf∗	NOUN
ejpam-6173	128	77	)	)	PUNCT
ejpam-6173	128	78	and	and	CCONJ
ejpam-6173	128	79	domf∗	domf∗	NOUN
ejpam-6173	128	80	=	=	SYM
ejpam-6173	128	81	int(domf∗	int(domf∗	NOUN
ejpam-6173	128	82	)	)	PUNCT
ejpam-6173	128	83	.	.	PUNCT
ejpam-6173	129	1	since	since	SCONJ
ejpam-6173	129	2	e	e	PROPN
ejpam-6173	129	3	is	be	AUX
ejpam-6173	129	4	reflexive	reflexive	ADJ
ejpam-6173	129	5	,	,	PUNCT
ejpam-6173	129	6	we	we	PRON
ejpam-6173	129	7	know	know	VERB
ejpam-6173	129	8	that	that	PRON
ejpam-6173	129	9	(	(	PUNCT
ejpam-6173	129	10	∂f)−1	∂f)−1	NOUN
ejpam-6173	129	11	=	=	SYM
ejpam-6173	129	12	∂f∗	∂f∗	NOUN
ejpam-6173	129	13	(	(	PUNCT
ejpam-6173	129	14	see	see	VERB
ejpam-6173	129	15	[	[	X
ejpam-6173	129	16	28	28	NUM
ejpam-6173	129	17	]	]	NUM
ejpam-6173	129	18	)	)	PUNCT
ejpam-6173	129	19	.	.	PUNCT
ejpam-6173	130	1	this	this	PRON
ejpam-6173	130	2	,	,	PUNCT
ejpam-6173	130	3	with	with	ADP
ejpam-6173	130	4	(	(	PUNCT
ejpam-6173	130	5	l1	l1	PROPN
ejpam-6173	130	6	)	)	PUNCT
ejpam-6173	130	7	and	and	CCONJ
ejpam-6173	130	8	(	(	PUNCT
ejpam-6173	130	9	l2	l2	NOUN
ejpam-6173	130	10	)	)	PUNCT
ejpam-6173	130	11	,	,	PUNCT
ejpam-6173	130	12	imply	imply	VERB
ejpam-6173	130	13	the	the	DET
ejpam-6173	130	14	following	follow	VERB
ejpam-6173	130	15	equalities	equality	NOUN
ejpam-6173	130	16	:	:	PUNCT
ejpam-6173	130	17	∇f	∇f	PROPN
ejpam-6173	130	18	=	=	SYM
ejpam-6173	130	19	(	(	PUNCT
ejpam-6173	130	20	∇f∗)−1	∇f∗)−1	NOUN
ejpam-6173	130	21	,	,	PUNCT
ejpam-6173	130	22	ran∇f	ran∇f	VERB
ejpam-6173	130	23	=	=	SYM
ejpam-6173	130	24	dom∇f∗	dom∇f∗	NOUN
ejpam-6173	130	25	=	=	PUNCT
ejpam-6173	130	26	int(domf∗	int(domf∗	NOUN
ejpam-6173	130	27	)	)	PUNCT
ejpam-6173	130	28	and	and	CCONJ
ejpam-6173	130	29	ran∇f∗	ran∇f∗	NOUN
ejpam-6173	130	30	=	=	SYM
ejpam-6173	130	31	dom(∇f	dom(∇f	PROPN
ejpam-6173	130	32	)	)	PUNCT
ejpam-6173	130	33	=	=	SYM
ejpam-6173	130	34	int(domf	int(domf	NOUN
ejpam-6173	130	35	)	)	PUNCT
ejpam-6173	130	36	,	,	PUNCT
ejpam-6173	130	37	where	where	SCONJ
ejpam-6173	130	38	ran∇f	ran∇f	NOUN
ejpam-6173	130	39	denotes	denote	VERB
ejpam-6173	130	40	the	the	DET
ejpam-6173	130	41	range	range	NOUN
ejpam-6173	130	42	of	of	ADP
ejpam-6173	130	43	∇f	∇f	PROPN
ejpam-6173	130	44	.	.	PUNCT
ejpam-6173	131	1	when	when	SCONJ
ejpam-6173	131	2	the	the	DET
ejpam-6173	131	3	subdifferential	subdifferential	NOUN
ejpam-6173	131	4	of	of	ADP
ejpam-6173	131	5	f	f	PROPN
ejpam-6173	131	6	is	be	AUX
ejpam-6173	131	7	single	single	ADV
ejpam-6173	131	8	-	-	PUNCT
ejpam-6173	131	9	valued	value	VERB
ejpam-6173	131	10	,	,	PUNCT
ejpam-6173	131	11	it	it	PRON
ejpam-6173	131	12	coincides	coincide	VERB
ejpam-6173	131	13	with	with	ADP
ejpam-6173	131	14	the	the	DET
ejpam-6173	131	15	gradient	gradient	NOUN
ejpam-6173	131	16	∂f	∂f	PROPN
ejpam-6173	131	17	=	=	SYM
ejpam-6173	131	18	∇f	∇f	PROPN
ejpam-6173	131	19	,	,	PUNCT
ejpam-6173	131	20	[	[	X
ejpam-6173	131	21	33	33	NUM
ejpam-6173	131	22	]	]	PUNCT
ejpam-6173	131	23	.	.	PUNCT
ejpam-6173	132	1	by	by	ADP
ejpam-6173	132	2	bauschke	bauschke	NOUN
ejpam-6173	132	3	et	et	PROPN
ejpam-6173	132	4	al	al	PROPN
ejpam-6173	132	5	.	.	PUNCT
ejpam-6173	133	1	[	[	X
ejpam-6173	133	2	32	32	NUM
ejpam-6173	133	3	]	]	PUNCT
ejpam-6173	133	4	the	the	DET
ejpam-6173	133	5	conditions	condition	NOUN
ejpam-6173	133	6	(	(	PUNCT
ejpam-6173	133	7	l1	l1	PROPN
ejpam-6173	133	8	)	)	PUNCT
ejpam-6173	133	9	and	and	CCONJ
ejpam-6173	133	10	(	(	PUNCT
ejpam-6173	133	11	l2	l2	NOUN
ejpam-6173	133	12	)	)	PUNCT
ejpam-6173	133	13	also	also	ADV
ejpam-6173	133	14	yields	yield	VERB
ejpam-6173	133	15	that	that	SCONJ
ejpam-6173	133	16	the	the	DET
ejpam-6173	133	17	function	function	NOUN
ejpam-6173	133	18	f	f	PROPN
ejpam-6173	133	19	and	and	CCONJ
ejpam-6173	133	20	f∗	f∗	NOUN
ejpam-6173	133	21	are	be	AUX
ejpam-6173	133	22	strictly	strictly	ADV
ejpam-6173	133	23	convex	convex	ADJ
ejpam-6173	133	24	on	on	ADP
ejpam-6173	133	25	the	the	DET
ejpam-6173	133	26	interior	interior	NOUN
ejpam-6173	133	27	of	of	ADP
ejpam-6173	133	28	their	their	PRON
ejpam-6173	133	29	respective	respective	ADJ
ejpam-6173	133	30	domains	domain	NOUN
ejpam-6173	133	31	.	.	PUNCT
ejpam-6173	134	1	if	if	SCONJ
ejpam-6173	134	2	e	e	PROPN
ejpam-6173	134	3	is	be	AUX
ejpam-6173	134	4	a	a	DET
ejpam-6173	134	5	smooth	smooth	ADJ
ejpam-6173	134	6	and	and	CCONJ
ejpam-6173	134	7	strictly	strictly	ADV
ejpam-6173	134	8	convex	convex	VERB
ejpam-6173	134	9	banach	banach	NOUN
ejpam-6173	134	10	space	space	NOUN
ejpam-6173	134	11	,	,	PUNCT
ejpam-6173	134	12	then	then	ADV
ejpam-6173	134	13	an	an	DET
ejpam-6173	134	14	important	important	ADJ
ejpam-6173	134	15	and	and	CCONJ
ejpam-6173	134	16	interesting	interesting	ADJ
ejpam-6173	134	17	legendre	legendre	PROPN
ejpam-6173	134	18	function	function	PROPN
ejpam-6173	134	19	is	be	AUX
ejpam-6173	134	20	f(x	f(x	PROPN
ejpam-6173	134	21	)	)	PUNCT
ejpam-6173	134	22	:	:	PUNCT
ejpam-6173	135	1	=	=	SYM
ejpam-6173	135	2	1	1	NUM
ejpam-6173	135	3	p∥x∥	p∥x∥	NOUN
ejpam-6173	135	4	p(1	p(1	NOUN
ejpam-6173	135	5	<	<	X
ejpam-6173	135	6	p	p	X
ejpam-6173	135	7	<	<	X
ejpam-6173	135	8	+	+	NOUN
ejpam-6173	135	9	∞	∞	NOUN
ejpam-6173	135	10	)	)	PUNCT
ejpam-6173	135	11	.	.	PUNCT
ejpam-6173	136	1	in	in	ADP
ejpam-6173	136	2	this	this	DET
ejpam-6173	136	3	case	case	NOUN
ejpam-6173	136	4	the	the	DET
ejpam-6173	136	5	gradient	gradient	ADJ
ejpam-6173	136	6	∇f	∇f	PROPN
ejpam-6173	136	7	of	of	ADP
ejpam-6173	136	8	f	f	PROPN
ejpam-6173	136	9	coincides	coincide	VERB
ejpam-6173	136	10	with	with	ADP
ejpam-6173	136	11	the	the	DET
ejpam-6173	136	12	generalized	generalized	ADJ
ejpam-6173	136	13	duality	duality	NOUN
ejpam-6173	136	14	mapping	mapping	NOUN
ejpam-6173	136	15	of	of	ADP
ejpam-6173	136	16	e	e	PROPN
ejpam-6173	136	17	,	,	PUNCT
ejpam-6173	136	18	i.e.	i.e.	X
ejpam-6173	136	19	,	,	PUNCT
ejpam-6173	136	20	∇f	∇f	PROPN
ejpam-6173	136	21	=	=	SYM
ejpam-6173	136	22	jp(1	jp(1	X
ejpam-6173	136	23	<	<	X
ejpam-6173	136	24	p	p	X
ejpam-6173	136	25	<	<	X
ejpam-6173	136	26	+	+	NOUN
ejpam-6173	136	27	∞	∞	NOUN
ejpam-6173	136	28	)	)	PUNCT
ejpam-6173	136	29	.	.	PUNCT
ejpam-6173	137	1	in	in	ADP
ejpam-6173	137	2	particular	particular	ADJ
ejpam-6173	137	3	,	,	PUNCT
ejpam-6173	137	4	∇f	∇f	PROPN
ejpam-6173	137	5	=	=	SYM
ejpam-6173	137	6	i	i	PROPN
ejpam-6173	137	7	,	,	PUNCT
ejpam-6173	137	8	the	the	DET
ejpam-6173	137	9	identity	identity	NOUN
ejpam-6173	137	10	mapping	mapping	NOUN
ejpam-6173	137	11	in	in	ADP
ejpam-6173	137	12	hilbert	hilbert	PROPN
ejpam-6173	137	13	spaces	space	NOUN
ejpam-6173	137	14	.	.	PUNCT
ejpam-6173	138	1	from	from	ADP
ejpam-6173	138	2	now	now	ADV
ejpam-6173	138	3	on	on	ADV
ejpam-6173	138	4	we	we	PRON
ejpam-6173	138	5	assume	assume	VERB
ejpam-6173	138	6	that	that	SCONJ
ejpam-6173	138	7	the	the	DET
ejpam-6173	138	8	convex	convex	PROPN
ejpam-6173	138	9	function	function	NOUN
ejpam-6173	138	10	f	f	NOUN
ejpam-6173	138	11	:	:	PUNCT
ejpam-6173	138	12	e	e	X
ejpam-6173	138	13	→	→	PUNCT
ejpam-6173	138	14	(	(	PUNCT
ejpam-6173	138	15	−∞,+∞	−∞,+∞	ADV
ejpam-6173	138	16	]	]	X
ejpam-6173	138	17	is	be	AUX
ejpam-6173	138	18	legendre	legendre	PROPN
ejpam-6173	138	19	.	.	PUNCT
ejpam-6173	139	1	in	in	ADP
ejpam-6173	139	2	connection	connection	NOUN
ejpam-6173	139	3	with	with	ADP
ejpam-6173	139	4	legendre	legendre	PROPN
ejpam-6173	139	5	functions	function	NOUN
ejpam-6173	139	6	,	,	PUNCT
ejpam-6173	139	7	see	see	VERB
ejpam-6173	139	8	also	also	ADV
ejpam-6173	139	9	the	the	DET
ejpam-6173	139	10	recent	recent	ADJ
ejpam-6173	139	11	paper	paper	NOUN
ejpam-6173	140	1	[	[	X
ejpam-6173	140	2	34	34	NUM
ejpam-6173	140	3	]	]	PUNCT
ejpam-6173	140	4	.	.	PUNCT
ejpam-6173	141	1	definition	definition	NOUN
ejpam-6173	141	2	2	2	NUM
ejpam-6173	141	3	.	.	PUNCT
ejpam-6173	142	1	let	let	VERB
ejpam-6173	142	2	f	f	NOUN
ejpam-6173	142	3	:	:	PUNCT
ejpam-6173	142	4	e	e	X
ejpam-6173	142	5	→	→	PUNCT
ejpam-6173	142	6	(	(	PUNCT
ejpam-6173	142	7	−∞,+∞	−∞,+∞	ADV
ejpam-6173	142	8	]	]	PUNCT
ejpam-6173	142	9	be	be	AUX
ejpam-6173	142	10	a	a	DET
ejpam-6173	142	11	convex	convex	NOUN
ejpam-6173	142	12	and	and	CCONJ
ejpam-6173	142	13	gâteaux	gâteaux	ADJ
ejpam-6173	142	14	differentiable	differentiable	ADJ
ejpam-6173	142	15	function	function	NOUN
ejpam-6173	142	16	.	.	PUNCT
ejpam-6173	143	1	the	the	DET
ejpam-6173	143	2	bregman	bregman	NOUN
ejpam-6173	143	3	projection	projection	NOUN
ejpam-6173	143	4	of	of	ADP
ejpam-6173	143	5	x	x	PROPN
ejpam-6173	143	6	∈	∈	PROPN
ejpam-6173	143	7	int(domf	int(domf	NOUN
ejpam-6173	143	8	)	)	PUNCT
ejpam-6173	143	9	onto	onto	ADP
ejpam-6173	143	10	the	the	DET
ejpam-6173	143	11	nonempty	nonempty	ADJ
ejpam-6173	143	12	,	,	PUNCT
ejpam-6173	143	13	closed	closed	ADJ
ejpam-6173	143	14	and	and	CCONJ
ejpam-6173	143	15	convex	convex	PROPN
ejpam-6173	143	16	subset	subset	VERB
ejpam-6173	143	17	c	c	PROPN
ejpam-6173	143	18	⊂	⊂	PROPN
ejpam-6173	143	19	domf	domf	PROPN
ejpam-6173	143	20	is	be	AUX
ejpam-6173	143	21	the	the	DET
ejpam-6173	143	22	necessary	necessary	ADJ
ejpam-6173	143	23	unique	unique	ADJ
ejpam-6173	143	24	vector	vector	NOUN
ejpam-6173	143	25	projfc(x	projfc(x	NOUN
ejpam-6173	143	26	)	)	PUNCT
ejpam-6173	143	27	∈	∈	PROPN
ejpam-6173	143	28	c	c	NOUN
ejpam-6173	143	29	satisfying	satisfy	VERB
ejpam-6173	143	30	df	df	PROPN
ejpam-6173	143	31	(	(	PUNCT
ejpam-6173	143	32	proj	proj	NOUN
ejpam-6173	143	33	f	f	PROPN
ejpam-6173	143	34	c(x	c(x	PROPN
ejpam-6173	143	35	)	)	PUNCT
ejpam-6173	143	36	,	,	PUNCT
ejpam-6173	143	37	x	x	X
ejpam-6173	143	38	)	)	PUNCT
ejpam-6173	143	39	=	=	SYM
ejpam-6173	143	40	inf{df	inf{df	X
ejpam-6173	143	41	(	(	PUNCT
ejpam-6173	143	42	y	y	NOUN
ejpam-6173	143	43	,	,	PUNCT
ejpam-6173	143	44	x	x	NOUN
ejpam-6173	143	45	)	)	PUNCT
ejpam-6173	143	46	:	:	PUNCT
ejpam-6173	143	47	y	y	PROPN
ejpam-6173	143	48	∈	∈	PROPN
ejpam-6173	143	49	c	c	X
ejpam-6173	143	50	}	}	PUNCT
ejpam-6173	143	51	.	.	PUNCT
ejpam-6173	144	1	remark	remark	NOUN
ejpam-6173	144	2	2	2	NUM
ejpam-6173	144	3	.	.	PUNCT
ejpam-6173	145	1	if	if	SCONJ
ejpam-6173	145	2	e	e	PROPN
ejpam-6173	145	3	is	be	AUX
ejpam-6173	145	4	a	a	DET
ejpam-6173	145	5	smooth	smooth	ADJ
ejpam-6173	145	6	and	and	CCONJ
ejpam-6173	145	7	strictly	strictly	ADV
ejpam-6173	145	8	convex	convex	VERB
ejpam-6173	145	9	banach	banach	NOUN
ejpam-6173	145	10	space	space	NOUN
ejpam-6173	145	11	and	and	CCONJ
ejpam-6173	145	12	f(x	f(x	NOUN
ejpam-6173	145	13	)	)	PUNCT
ejpam-6173	145	14	=	=	SYM
ejpam-6173	145	15	∥x∥2	∥x∥2	NOUN
ejpam-6173	145	16	for	for	ADP
ejpam-6173	145	17	all	all	DET
ejpam-6173	145	18	x	x	SYM
ejpam-6173	145	19	∈	∈	PROPN
ejpam-6173	145	20	e	e	NOUN
ejpam-6173	145	21	,	,	PUNCT
ejpam-6173	145	22	then	then	ADV
ejpam-6173	145	23	we	we	PRON
ejpam-6173	145	24	have	have	VERB
ejpam-6173	145	25	that	that	DET
ejpam-6173	145	26	∇f(x	∇f(x	NOUN
ejpam-6173	145	27	)	)	PUNCT
ejpam-6173	145	28	=	=	PUNCT
ejpam-6173	146	1	2jx	2jx	NOUN
ejpam-6173	146	2	for	for	ADP
ejpam-6173	146	3	all	all	DET
ejpam-6173	146	4	x	x	SYM
ejpam-6173	146	5	∈	∈	PROPN
ejpam-6173	146	6	e	e	NOUN
ejpam-6173	146	7	,	,	PUNCT
ejpam-6173	146	8	where	where	SCONJ
ejpam-6173	146	9	j	j	PROPN
ejpam-6173	146	10	is	be	AUX
ejpam-6173	146	11	the	the	DET
ejpam-6173	146	12	normalized	normalize	VERB
ejpam-6173	146	13	duality	duality	NOUN
ejpam-6173	146	14	v.	v.	ADP
ejpam-6173	146	15	darvish	darvish	PROPN
ejpam-6173	146	16	et	et	PROPN
ejpam-6173	146	17	al	al	PROPN
ejpam-6173	146	18	.	.	PUNCT
ejpam-6173	146	19	/	/	SYM
ejpam-6173	146	20	eur	eur	PROPN
ejpam-6173	146	21	.	.	PUNCT
ejpam-6173	147	1	j.	j.	PROPN
ejpam-6173	147	2	pure	pure	PROPN
ejpam-6173	147	3	appl	appl	PROPN
ejpam-6173	147	4	.	.	PROPN
ejpam-6173	147	5	math	math	PROPN
ejpam-6173	147	6	,	,	PUNCT
ejpam-6173	147	7	18	18	NUM
ejpam-6173	147	8	(	(	PUNCT
ejpam-6173	147	9	3	3	NUM
ejpam-6173	147	10	)	)	PUNCT
ejpam-6173	147	11	(	(	PUNCT
ejpam-6173	147	12	2025	2025	NUM
ejpam-6173	147	13	)	)	PUNCT
ejpam-6173	147	14	,	,	PUNCT
ejpam-6173	147	15	6173	6173	NUM
ejpam-6173	147	16	7	7	NUM
ejpam-6173	147	17	of	of	ADP
ejpam-6173	147	18	32	32	NUM
ejpam-6173	147	19	mapping	mapping	NOUN
ejpam-6173	147	20	from	from	ADP
ejpam-6173	147	21	e	e	NOUN
ejpam-6173	147	22	in	in	ADP
ejpam-6173	147	23	to	to	ADP
ejpam-6173	147	24	2e	2e	NOUN
ejpam-6173	147	25	∗	∗	NOUN
ejpam-6173	147	26	,	,	PUNCT
ejpam-6173	147	27	and	and	CCONJ
ejpam-6173	147	28	hence	hence	ADV
ejpam-6173	147	29	df	df	PROPN
ejpam-6173	147	30	(	(	PUNCT
ejpam-6173	147	31	x	x	NOUN
ejpam-6173	147	32	,	,	PUNCT
ejpam-6173	147	33	y	y	NOUN
ejpam-6173	147	34	)	)	PUNCT
ejpam-6173	147	35	reduced	reduce	VERB
ejpam-6173	147	36	to	to	ADP
ejpam-6173	147	37	ϕ(x	ϕ(x	PROPN
ejpam-6173	147	38	,	,	PUNCT
ejpam-6173	147	39	y	y	NOUN
ejpam-6173	147	40	)	)	PUNCT
ejpam-6173	147	41	=	=	SYM
ejpam-6173	147	42	∥x∥2−2⟨x	∥x∥2−2⟨x	PROPN
ejpam-6173	147	43	,	,	PUNCT
ejpam-6173	147	44	jy⟩+∥y∥2	jy⟩+∥y∥2	PROPN
ejpam-6173	147	45	,	,	PUNCT
ejpam-6173	147	46	for	for	ADP
ejpam-6173	147	47	all	all	DET
ejpam-6173	147	48	x	x	NOUN
ejpam-6173	147	49	,	,	PUNCT
ejpam-6173	147	50	y	y	PROPN
ejpam-6173	147	51	∈	∈	PROPN
ejpam-6173	147	52	e	e	NOUN
ejpam-6173	147	53	,	,	PUNCT
ejpam-6173	147	54	which	which	PRON
ejpam-6173	147	55	is	be	AUX
ejpam-6173	147	56	the	the	DET
ejpam-6173	147	57	lyapunov	lyapunov	ADJ
ejpam-6173	147	58	function	function	NOUN
ejpam-6173	147	59	introduced	introduce	VERB
ejpam-6173	147	60	by	by	ADP
ejpam-6173	147	61	alber	alber	PROPN
ejpam-6173	148	1	[	[	X
ejpam-6173	148	2	35	35	NUM
ejpam-6173	148	3	]	]	PUNCT
ejpam-6173	148	4	and	and	CCONJ
ejpam-6173	148	5	bregman	bregman	PROPN
ejpam-6173	148	6	projection	projection	NOUN
ejpam-6173	148	7	p	p	PROPN
ejpam-6173	148	8	f	f	PROPN
ejpam-6173	148	9	c(x	c(x	NOUN
ejpam-6173	148	10	)	)	PUNCT
ejpam-6173	148	11	reduces	reduce	VERB
ejpam-6173	148	12	to	to	ADP
ejpam-6173	148	13	the	the	DET
ejpam-6173	148	14	generalized	generalized	ADJ
ejpam-6173	148	15	projection	projection	NOUN
ejpam-6173	148	16	πc(x	πc(x	NOUN
ejpam-6173	148	17	)	)	PUNCT
ejpam-6173	148	18	which	which	PRON
ejpam-6173	148	19	is	be	AUX
ejpam-6173	148	20	defined	define	VERB
ejpam-6173	148	21	by	by	ADP
ejpam-6173	148	22	ϕ(πc(x	ϕ(πc(x	NOUN
ejpam-6173	148	23	)	)	PUNCT
ejpam-6173	148	24	,	,	PUNCT
ejpam-6173	148	25	x	x	X
ejpam-6173	148	26	)	)	PUNCT
ejpam-6173	148	27	=	=	SYM
ejpam-6173	148	28	min	min	PROPN
ejpam-6173	148	29	y∈c	y∈c	NOUN
ejpam-6173	148	30	ϕ(y	ϕ(y	PROPN
ejpam-6173	148	31	,	,	PUNCT
ejpam-6173	148	32	x	x	NOUN
ejpam-6173	148	33	)	)	PUNCT
ejpam-6173	148	34	.	.	PUNCT
ejpam-6173	149	1	if	if	SCONJ
ejpam-6173	149	2	e	e	PROPN
ejpam-6173	149	3	=	=	SYM
ejpam-6173	149	4	h	h	PROPN
ejpam-6173	149	5	,	,	PUNCT
ejpam-6173	149	6	a	a	DET
ejpam-6173	149	7	hilbert	hilbert	NOUN
ejpam-6173	149	8	space	space	NOUN
ejpam-6173	149	9	,	,	PUNCT
ejpam-6173	149	10	j	j	PROPN
ejpam-6173	149	11	is	be	AUX
ejpam-6173	149	12	the	the	DET
ejpam-6173	149	13	identity	identity	NOUN
ejpam-6173	149	14	mapping	mapping	NOUN
ejpam-6173	149	15	and	and	CCONJ
ejpam-6173	149	16	hence	hence	ADV
ejpam-6173	149	17	bregman	bregman	PROPN
ejpam-6173	149	18	projection	projection	PROPN
ejpam-6173	149	19	p	p	PROPN
ejpam-6173	149	20	f	f	PROPN
ejpam-6173	149	21	c(x	c(x	NOUN
ejpam-6173	149	22	)	)	PUNCT
ejpam-6173	149	23	reduced	reduce	VERB
ejpam-6173	149	24	to	to	ADP
ejpam-6173	149	25	the	the	DET
ejpam-6173	149	26	metric	metric	ADJ
ejpam-6173	149	27	projection	projection	NOUN
ejpam-6173	149	28	of	of	ADP
ejpam-6173	149	29	h	h	NOUN
ejpam-6173	149	30	onto	onto	ADP
ejpam-6173	149	31	c	c	NOUN
ejpam-6173	149	32	,	,	PUNCT
ejpam-6173	149	33	pc(x	pc(x	NOUN
ejpam-6173	149	34	)	)	PUNCT
ejpam-6173	149	35	.	.	PUNCT
ejpam-6173	150	1	definition	definition	NOUN
ejpam-6173	150	2	3	3	NUM
ejpam-6173	150	3	.	.	PUNCT
ejpam-6173	151	1	[	[	X
ejpam-6173	151	2	36	36	NUM
ejpam-6173	151	3	,	,	PUNCT
ejpam-6173	151	4	37	37	NUM
ejpam-6173	151	5	]	]	PUNCT
ejpam-6173	151	6	let	let	VERB
ejpam-6173	151	7	f	f	PRON
ejpam-6173	151	8	:	:	PUNCT
ejpam-6173	151	9	e	e	X
ejpam-6173	151	10	→	→	PUNCT
ejpam-6173	151	11	(	(	PUNCT
ejpam-6173	151	12	−∞,+∞	−∞,+∞	ADV
ejpam-6173	151	13	]	]	PUNCT
ejpam-6173	151	14	be	be	AUX
ejpam-6173	151	15	a	a	DET
ejpam-6173	151	16	convex	convex	NOUN
ejpam-6173	151	17	and	and	CCONJ
ejpam-6173	151	18	gâteaux	gâteaux	ADJ
ejpam-6173	151	19	differentiable	differentiable	ADJ
ejpam-6173	151	20	function	function	NOUN
ejpam-6173	151	21	.	.	PUNCT
ejpam-6173	152	1	f	f	PROPN
ejpam-6173	152	2	is	be	AUX
ejpam-6173	152	3	called	call	VERB
ejpam-6173	152	4	:	:	PUNCT
ejpam-6173	152	5	(	(	PUNCT
ejpam-6173	152	6	i	i	NOUN
ejpam-6173	152	7	)	)	PUNCT
ejpam-6173	152	8	totally	totally	ADV
ejpam-6173	152	9	convex	convex	VERB
ejpam-6173	152	10	at	at	ADP
ejpam-6173	152	11	x	x	PROPN
ejpam-6173	152	12	∈	∈	PROPN
ejpam-6173	152	13	int(domf	int(domf	NOUN
ejpam-6173	152	14	)	)	PUNCT
ejpam-6173	152	15	if	if	SCONJ
ejpam-6173	152	16	its	its	PRON
ejpam-6173	152	17	modulus	modulus	NOUN
ejpam-6173	152	18	of	of	ADP
ejpam-6173	152	19	total	total	ADJ
ejpam-6173	152	20	convexity	convexity	NOUN
ejpam-6173	152	21	at	at	ADP
ejpam-6173	152	22	x	x	NOUN
ejpam-6173	152	23	,	,	PUNCT
ejpam-6173	152	24	that	that	ADV
ejpam-6173	152	25	is	is	ADV
ejpam-6173	152	26	,	,	PUNCT
ejpam-6173	152	27	the	the	DET
ejpam-6173	152	28	function	function	NOUN
ejpam-6173	152	29	νf	νf	NOUN
ejpam-6173	152	30	:	:	PUNCT
ejpam-6173	152	31	int(domf)×	int(domf)×	PROPN
ejpam-6173	152	32	[	[	X
ejpam-6173	152	33	0,+∞	0,+∞	NUM
ejpam-6173	152	34	)	)	PUNCT
ejpam-6173	152	35	→	→	PUNCT
ejpam-6173	153	1	[	[	X
ejpam-6173	153	2	0,+∞	0,+∞	NUM
ejpam-6173	153	3	)	)	PUNCT
ejpam-6173	153	4	defined	define	VERB
ejpam-6173	153	5	by	by	ADP
ejpam-6173	153	6	νf	νf	NOUN
ejpam-6173	153	7	(	(	PUNCT
ejpam-6173	153	8	x	x	PROPN
ejpam-6173	153	9	,	,	PUNCT
ejpam-6173	153	10	t	t	PROPN
ejpam-6173	153	11	)	)	PUNCT
ejpam-6173	153	12	:	:	PUNCT
ejpam-6173	153	13	=	=	SYM
ejpam-6173	153	14	inf{df	inf{df	ADJ
ejpam-6173	153	15	(	(	PUNCT
ejpam-6173	153	16	y	y	NOUN
ejpam-6173	153	17	,	,	PUNCT
ejpam-6173	153	18	x	x	NOUN
ejpam-6173	153	19	)	)	PUNCT
ejpam-6173	153	20	:	:	PUNCT
ejpam-6173	153	21	y	y	PROPN
ejpam-6173	153	22	∈	∈	PROPN
ejpam-6173	153	23	domf	domf	NOUN
ejpam-6173	153	24	,	,	PUNCT
ejpam-6173	153	25	∥y	∥y	PROPN
ejpam-6173	153	26	−	−	PROPN
ejpam-6173	153	27	x∥	x∥	PROPN
ejpam-6173	153	28	=	=	SYM
ejpam-6173	153	29	t	t	PROPN
ejpam-6173	153	30	}	}	PUNCT
ejpam-6173	153	31	,	,	PUNCT
ejpam-6173	153	32	is	be	AUX
ejpam-6173	153	33	positive	positive	ADJ
ejpam-6173	153	34	whenever	whenever	SCONJ
ejpam-6173	153	35	t	t	PROPN
ejpam-6173	153	36	>	>	X
ejpam-6173	153	37	0	0	NUM
ejpam-6173	153	38	;	;	PUNCT
ejpam-6173	153	39	(	(	PUNCT
ejpam-6173	153	40	ii	ii	NOUN
ejpam-6173	153	41	)	)	PUNCT
ejpam-6173	153	42	totally	totally	ADV
ejpam-6173	153	43	convex	convex	VERB
ejpam-6173	153	44	if	if	SCONJ
ejpam-6173	153	45	it	it	PRON
ejpam-6173	153	46	is	be	AUX
ejpam-6173	153	47	totally	totally	ADV
ejpam-6173	153	48	convex	convex	ADJ
ejpam-6173	153	49	at	at	ADP
ejpam-6173	153	50	every	every	DET
ejpam-6173	153	51	point	point	NOUN
ejpam-6173	153	52	x	x	X
ejpam-6173	153	53	∈	∈	PROPN
ejpam-6173	153	54	int(domf	int(domf	NOUN
ejpam-6173	153	55	)	)	PUNCT
ejpam-6173	153	56	;	;	PUNCT
ejpam-6173	153	57	(	(	PUNCT
ejpam-6173	153	58	iii	iii	NOUN
ejpam-6173	153	59	)	)	PUNCT
ejpam-6173	153	60	totally	totally	ADV
ejpam-6173	153	61	convex	convex	VERB
ejpam-6173	153	62	on	on	ADP
ejpam-6173	153	63	bounded	bounded	ADJ
ejpam-6173	153	64	sets	set	NOUN
ejpam-6173	153	65	if	if	SCONJ
ejpam-6173	153	66	νf	νf	X
ejpam-6173	153	67	(	(	PUNCT
ejpam-6173	153	68	b	b	NOUN
ejpam-6173	153	69	,	,	PUNCT
ejpam-6173	153	70	t	t	PROPN
ejpam-6173	153	71	)	)	PUNCT
ejpam-6173	153	72	is	be	AUX
ejpam-6173	153	73	positive	positive	ADJ
ejpam-6173	153	74	for	for	ADP
ejpam-6173	153	75	any	any	DET
ejpam-6173	153	76	nonempty	nonempty	ADV
ejpam-6173	153	77	bounded	bound	VERB
ejpam-6173	153	78	subset	subset	PROPN
ejpam-6173	153	79	b	b	PROPN
ejpam-6173	153	80	of	of	ADP
ejpam-6173	153	81	e	e	PROPN
ejpam-6173	153	82	and	and	CCONJ
ejpam-6173	153	83	t	t	PROPN
ejpam-6173	153	84	>	>	X
ejpam-6173	153	85	0	0	PROPN
ejpam-6173	153	86	,	,	PUNCT
ejpam-6173	153	87	where	where	SCONJ
ejpam-6173	153	88	the	the	DET
ejpam-6173	153	89	modulus	modulus	NOUN
ejpam-6173	153	90	of	of	ADP
ejpam-6173	153	91	total	total	ADJ
ejpam-6173	153	92	convexity	convexity	NOUN
ejpam-6173	153	93	of	of	ADP
ejpam-6173	153	94	the	the	DET
ejpam-6173	153	95	function	function	NOUN
ejpam-6173	153	96	f	f	PROPN
ejpam-6173	153	97	on	on	ADP
ejpam-6173	153	98	the	the	DET
ejpam-6173	153	99	set	set	PROPN
ejpam-6173	153	100	b	b	PROPN
ejpam-6173	153	101	is	be	AUX
ejpam-6173	153	102	the	the	DET
ejpam-6173	153	103	function	function	NOUN
ejpam-6173	153	104	νf	νf	NOUN
ejpam-6173	153	105	:	:	PUNCT
ejpam-6173	153	106	int(domf)×	int(domf)×	PROPN
ejpam-6173	153	107	[	[	X
ejpam-6173	153	108	0,+∞	0,+∞	NUM
ejpam-6173	153	109	)	)	PUNCT
ejpam-6173	153	110	→	→	PUNCT
ejpam-6173	154	1	[	[	X
ejpam-6173	154	2	0,+∞	0,+∞	NUM
ejpam-6173	154	3	)	)	PUNCT
ejpam-6173	154	4	defined	define	VERB
ejpam-6173	154	5	by	by	ADP
ejpam-6173	154	6	νf	νf	NOUN
ejpam-6173	154	7	(	(	PUNCT
ejpam-6173	154	8	b	b	PROPN
ejpam-6173	154	9	,	,	PUNCT
ejpam-6173	154	10	t	t	PROPN
ejpam-6173	154	11	)	)	PUNCT
ejpam-6173	154	12	:	:	PUNCT
ejpam-6173	155	1	=	=	SYM
ejpam-6173	155	2	inf{νf	inf{νf	INTJ
ejpam-6173	155	3	(	(	PUNCT
ejpam-6173	155	4	x	x	X
ejpam-6173	155	5	,	,	PUNCT
ejpam-6173	155	6	t	t	PROPN
ejpam-6173	155	7	)	)	PUNCT
ejpam-6173	155	8	:	:	PUNCT
ejpam-6173	155	9	x	x	X
ejpam-6173	155	10	∈	∈	PROPN
ejpam-6173	155	11	b	b	NOUN
ejpam-6173	155	12	∩	∩	ADJ
ejpam-6173	155	13	domf	domf	NOUN
ejpam-6173	155	14	}	}	PUNCT
ejpam-6173	155	15	.	.	PUNCT
ejpam-6173	156	1	the	the	DET
ejpam-6173	156	2	set	set	VERB
ejpam-6173	156	3	levf≤(r	levf≤(r	NOUN
ejpam-6173	156	4	)	)	PUNCT
ejpam-6173	156	5	=	=	PRON
ejpam-6173	156	6	{	{	PUNCT
ejpam-6173	156	7	x	x	PUNCT
ejpam-6173	156	8	∈	∈	PROPN
ejpam-6173	156	9	e	e	NOUN
ejpam-6173	156	10	:	:	PUNCT
ejpam-6173	156	11	f(x	f(x	PROPN
ejpam-6173	156	12	)	)	PUNCT
ejpam-6173	156	13	≤	≤	NOUN
ejpam-6173	157	1	r	r	NOUN
ejpam-6173	157	2	}	}	PUNCT
ejpam-6173	157	3	for	for	ADP
ejpam-6173	157	4	some	some	DET
ejpam-6173	157	5	r	r	NOUN
ejpam-6173	157	6	∈	∈	NOUN
ejpam-6173	157	7	r	r	NOUN
ejpam-6173	157	8	is	be	AUX
ejpam-6173	157	9	called	call	VERB
ejpam-6173	157	10	a	a	DET
ejpam-6173	157	11	sublevel	sublevel	NOUN
ejpam-6173	157	12	of	of	ADP
ejpam-6173	157	13	f	f	PROPN
ejpam-6173	157	14	.	.	PUNCT
ejpam-6173	158	1	definition	definition	NOUN
ejpam-6173	158	2	4	4	NUM
ejpam-6173	158	3	.	.	PUNCT
ejpam-6173	159	1	[	[	X
ejpam-6173	159	2	37	37	NUM
ejpam-6173	159	3	,	,	PUNCT
ejpam-6173	159	4	38	38	NUM
ejpam-6173	159	5	]	]	PUNCT
ejpam-6173	159	6	the	the	DET
ejpam-6173	159	7	function	function	NOUN
ejpam-6173	159	8	f	f	NOUN
ejpam-6173	159	9	:	:	PUNCT
ejpam-6173	159	10	e	e	X
ejpam-6173	159	11	→	→	PUNCT
ejpam-6173	159	12	(	(	PUNCT
ejpam-6173	159	13	−∞,+∞	−∞,+∞	ADV
ejpam-6173	159	14	]	]	PUNCT
ejpam-6173	159	15	is	be	AUX
ejpam-6173	159	16	called	call	VERB
ejpam-6173	159	17	;	;	PUNCT
ejpam-6173	159	18	(	(	PUNCT
ejpam-6173	159	19	i	i	NOUN
ejpam-6173	159	20	)	)	PUNCT
ejpam-6173	159	21	cofinite	cofinite	NOUN
ejpam-6173	159	22	if	if	SCONJ
ejpam-6173	159	23	domf∗	domf∗	PROPN
ejpam-6173	159	24	=	=	SYM
ejpam-6173	159	25	e∗	e∗	PROPN
ejpam-6173	159	26	;	;	PUNCT
ejpam-6173	159	27	(	(	PUNCT
ejpam-6173	159	28	ii	ii	NOUN
ejpam-6173	159	29	)	)	PUNCT
ejpam-6173	159	30	coercive	coercive	ADJ
ejpam-6173	160	1	[	[	X
ejpam-6173	160	2	39	39	NUM
ejpam-6173	160	3	]	]	PUNCT
ejpam-6173	160	4	if	if	SCONJ
ejpam-6173	160	5	the	the	DET
ejpam-6173	160	6	sublevel	sublevel	NOUN
ejpam-6173	160	7	set	set	NOUN
ejpam-6173	160	8	of	of	ADP
ejpam-6173	160	9	f	f	PROPN
ejpam-6173	160	10	is	be	AUX
ejpam-6173	160	11	bounded	bound	VERB
ejpam-6173	160	12	;	;	PUNCT
ejpam-6173	160	13	equivalently	equivalently	ADV
ejpam-6173	160	14	,	,	PUNCT
ejpam-6173	160	15	lim	lim	PROPN
ejpam-6173	160	16	∥x∥→+∞	∥x∥→+∞	PROPN
ejpam-6173	160	17	f(x	f(x	PROPN
ejpam-6173	160	18	)	)	PUNCT
ejpam-6173	160	19	=	=	PUNCT
ejpam-6173	161	1	+	+	NUM
ejpam-6173	161	2	∞	∞	NUM
ejpam-6173	161	3	;	;	PUNCT
ejpam-6173	161	4	(	(	PUNCT
ejpam-6173	161	5	iii	iii	NOUN
ejpam-6173	161	6	)	)	PUNCT
ejpam-6173	161	7	strongly	strongly	ADV
ejpam-6173	161	8	coercive	coercive	ADJ
ejpam-6173	161	9	if	if	SCONJ
ejpam-6173	161	10	lim∥x∥→+∞	lim∥x∥→+∞	PROPN
ejpam-6173	161	11	f(x	f(x	PROPN
ejpam-6173	161	12	)	)	PUNCT
ejpam-6173	161	13	∥x∥	∥x∥	NOUN
ejpam-6173	162	1	=	=	PUNCT
ejpam-6173	163	1	+	+	NOUN
ejpam-6173	163	2	∞	∞	NUM
ejpam-6173	163	3	;	;	PUNCT
ejpam-6173	163	4	(	(	PUNCT
ejpam-6173	163	5	iv	iv	X
ejpam-6173	163	6	)	)	PUNCT
ejpam-6173	163	7	sequentially	sequentially	ADV
ejpam-6173	163	8	consistent	consistent	ADJ
ejpam-6173	163	9	if	if	SCONJ
ejpam-6173	163	10	for	for	ADP
ejpam-6173	163	11	any	any	DET
ejpam-6173	163	12	two	two	NUM
ejpam-6173	163	13	sequences	sequence	NOUN
ejpam-6173	163	14	{	{	PUNCT
ejpam-6173	163	15	xn	xn	NUM
ejpam-6173	163	16	}	}	PUNCT
ejpam-6173	163	17	and	and	CCONJ
ejpam-6173	163	18	{	{	PUNCT
ejpam-6173	163	19	yn	yn	NOUN
ejpam-6173	163	20	}	}	PUNCT
ejpam-6173	163	21	in	in	ADP
ejpam-6173	163	22	e	e	ADP
ejpam-6173	163	23	such	such	ADJ
ejpam-6173	163	24	that	that	SCONJ
ejpam-6173	163	25	{	{	PUNCT
ejpam-6173	163	26	xn	xn	X
ejpam-6173	163	27	}	}	PUNCT
ejpam-6173	163	28	is	be	AUX
ejpam-6173	163	29	bounded	bound	VERB
ejpam-6173	163	30	,	,	PUNCT
ejpam-6173	163	31	lim	lim	PROPN
ejpam-6173	163	32	n→+∞	n→+∞	VERB
ejpam-6173	163	33	df	df	PROPN
ejpam-6173	163	34	(	(	PUNCT
ejpam-6173	163	35	yn	yn	PROPN
ejpam-6173	163	36	,	,	PUNCT
ejpam-6173	163	37	xn	xn	PROPN
ejpam-6173	163	38	)	)	PUNCT
ejpam-6173	164	1	=	=	SYM
ejpam-6173	164	2	0	0	NUM
ejpam-6173	164	3	⇒	⇒	NOUN
ejpam-6173	164	4	lim	lim	PROPN
ejpam-6173	164	5	n→+∞	n→+∞	PROPN
ejpam-6173	164	6	∥yn	∥yn	PROPN
ejpam-6173	164	7	−	−	PROPN
ejpam-6173	164	8	xn∥	xn∥	PROPN
ejpam-6173	164	9	=	=	SYM
ejpam-6173	164	10	0	0	PROPN
ejpam-6173	164	11	.	.	PUNCT
ejpam-6173	165	1	lemma	lemma	PROPN
ejpam-6173	165	2	2	2	NUM
ejpam-6173	165	3	.	.	PUNCT
ejpam-6173	166	1	[	[	X
ejpam-6173	166	2	40	40	NUM
ejpam-6173	166	3	]	]	PUNCT
ejpam-6173	166	4	the	the	DET
ejpam-6173	166	5	function	function	NOUN
ejpam-6173	166	6	f	f	PROPN
ejpam-6173	166	7	is	be	AUX
ejpam-6173	166	8	totally	totally	ADV
ejpam-6173	166	9	convex	convex	ADJ
ejpam-6173	166	10	on	on	ADP
ejpam-6173	166	11	bounded	bounded	ADJ
ejpam-6173	166	12	subsets	subset	NOUN
ejpam-6173	166	13	if	if	SCONJ
ejpam-6173	166	14	and	and	CCONJ
ejpam-6173	166	15	only	only	ADV
ejpam-6173	166	16	if	if	SCONJ
ejpam-6173	166	17	it	it	PRON
ejpam-6173	166	18	is	be	AUX
ejpam-6173	166	19	sequentially	sequentially	ADV
ejpam-6173	166	20	consistent	consistent	ADJ
ejpam-6173	166	21	.	.	PUNCT
ejpam-6173	167	1	v.	v.	ADP
ejpam-6173	167	2	darvish	darvish	PROPN
ejpam-6173	167	3	et	et	PROPN
ejpam-6173	167	4	al	al	PROPN
ejpam-6173	167	5	.	.	PUNCT
ejpam-6173	167	6	/	/	SYM
ejpam-6173	167	7	eur	eur	PROPN
ejpam-6173	167	8	.	.	PUNCT
ejpam-6173	168	1	j.	j.	PROPN
ejpam-6173	168	2	pure	pure	PROPN
ejpam-6173	168	3	appl	appl	PROPN
ejpam-6173	168	4	.	.	PROPN
ejpam-6173	168	5	math	math	PROPN
ejpam-6173	168	6	,	,	PUNCT
ejpam-6173	168	7	18	18	NUM
ejpam-6173	168	8	(	(	PUNCT
ejpam-6173	168	9	3	3	NUM
ejpam-6173	168	10	)	)	PUNCT
ejpam-6173	168	11	(	(	PUNCT
ejpam-6173	168	12	2025	2025	NUM
ejpam-6173	168	13	)	)	PUNCT
ejpam-6173	168	14	,	,	PUNCT
ejpam-6173	168	15	6173	6173	NUM
ejpam-6173	168	16	8	8	NUM
ejpam-6173	168	17	of	of	ADP
ejpam-6173	168	18	32	32	NUM
ejpam-6173	168	19	lemma	lemma	PROPN
ejpam-6173	168	20	3	3	NUM
ejpam-6173	168	21	.	.	PUNCT
ejpam-6173	169	1	[	[	X
ejpam-6173	169	2	38	38	NUM
ejpam-6173	169	3	,	,	PUNCT
ejpam-6173	169	4	proposition	proposition	NOUN
ejpam-6173	169	5	2.3	2.3	NUM
ejpam-6173	169	6	]	]	PUNCT
ejpam-6173	169	7	if	if	SCONJ
ejpam-6173	169	8	f	f	PROPN
ejpam-6173	169	9	:	:	PUNCT
ejpam-6173	169	10	e	e	X
ejpam-6173	169	11	→	→	PUNCT
ejpam-6173	169	12	(	(	PUNCT
ejpam-6173	169	13	−∞,+∞	−∞,+∞	ADV
ejpam-6173	169	14	]	]	PUNCT
ejpam-6173	169	15	is	be	AUX
ejpam-6173	169	16	fréchet	fréchet	VERB
ejpam-6173	169	17	differentiable	differentiable	ADJ
ejpam-6173	169	18	and	and	CCONJ
ejpam-6173	169	19	totally	totally	ADV
ejpam-6173	169	20	convex	convex	ADJ
ejpam-6173	169	21	,	,	PUNCT
ejpam-6173	169	22	then	then	ADV
ejpam-6173	169	23	f	f	PROPN
ejpam-6173	169	24	is	be	AUX
ejpam-6173	169	25	cofinite	cofinite	VERB
ejpam-6173	169	26	.	.	PUNCT
ejpam-6173	170	1	lemma	lemma	PROPN
ejpam-6173	170	2	4	4	NUM
ejpam-6173	170	3	.	.	PUNCT
ejpam-6173	171	1	[	[	X
ejpam-6173	171	2	40	40	NUM
ejpam-6173	171	3	]	]	PUNCT
ejpam-6173	171	4	let	let	VERB
ejpam-6173	171	5	f	f	PRON
ejpam-6173	171	6	:	:	PUNCT
ejpam-6173	171	7	e	e	X
ejpam-6173	171	8	→	→	PUNCT
ejpam-6173	171	9	(	(	PUNCT
ejpam-6173	171	10	−∞,+∞	−∞,+∞	ADV
ejpam-6173	171	11	]	]	PUNCT
ejpam-6173	171	12	be	be	VERB
ejpam-6173	171	13	a	a	DET
ejpam-6173	171	14	convex	convex	NOUN
ejpam-6173	171	15	function	function	NOUN
ejpam-6173	171	16	whose	whose	DET
ejpam-6173	171	17	domain	domain	NOUN
ejpam-6173	171	18	contains	contain	VERB
ejpam-6173	171	19	at	at	ADV
ejpam-6173	171	20	least	least	ADV
ejpam-6173	171	21	two	two	NUM
ejpam-6173	171	22	points.then	points.then	ADV
ejpam-6173	171	23	the	the	DET
ejpam-6173	171	24	following	follow	VERB
ejpam-6173	171	25	statements	statement	NOUN
ejpam-6173	171	26	hold	hold	VERB
ejpam-6173	171	27	:	:	PUNCT
ejpam-6173	171	28	(	(	PUNCT
ejpam-6173	171	29	i	i	NOUN
ejpam-6173	171	30	)	)	PUNCT
ejpam-6173	171	31	f	f	PROPN
ejpam-6173	171	32	is	be	AUX
ejpam-6173	171	33	sequentially	sequentially	ADV
ejpam-6173	171	34	consistent	consistent	ADJ
ejpam-6173	171	35	if	if	SCONJ
ejpam-6173	171	36	and	and	CCONJ
ejpam-6173	171	37	only	only	ADV
ejpam-6173	171	38	if	if	SCONJ
ejpam-6173	171	39	it	it	PRON
ejpam-6173	171	40	is	be	AUX
ejpam-6173	171	41	totally	totally	ADV
ejpam-6173	171	42	convex	convex	ADJ
ejpam-6173	171	43	on	on	ADP
ejpam-6173	171	44	bounded	bounded	ADJ
ejpam-6173	171	45	sets	set	NOUN
ejpam-6173	171	46	;	;	PUNCT
ejpam-6173	171	47	(	(	PUNCT
ejpam-6173	171	48	ii	ii	NOUN
ejpam-6173	171	49	)	)	PUNCT
ejpam-6173	171	50	if	if	SCONJ
ejpam-6173	171	51	f	f	PROPN
ejpam-6173	171	52	is	be	AUX
ejpam-6173	171	53	lower	low	ADJ
ejpam-6173	171	54	semicontinuous	semicontinuous	ADJ
ejpam-6173	171	55	,	,	PUNCT
ejpam-6173	171	56	then	then	ADV
ejpam-6173	171	57	f	f	PROPN
ejpam-6173	171	58	is	be	AUX
ejpam-6173	171	59	sequentially	sequentially	ADV
ejpam-6173	171	60	consistent	consistent	ADJ
ejpam-6173	171	61	if	if	SCONJ
ejpam-6173	171	62	and	and	CCONJ
ejpam-6173	171	63	only	only	ADV
ejpam-6173	171	64	if	if	SCONJ
ejpam-6173	171	65	it	it	PRON
ejpam-6173	171	66	is	be	AUX
ejpam-6173	171	67	uniformly	uniformly	ADV
ejpam-6173	171	68	convex	convex	ADJ
ejpam-6173	171	69	on	on	ADP
ejpam-6173	171	70	bounded	bounded	ADJ
ejpam-6173	171	71	sets	set	NOUN
ejpam-6173	171	72	;	;	PUNCT
ejpam-6173	171	73	(	(	PUNCT
ejpam-6173	171	74	iii	iii	X
ejpam-6173	171	75	)	)	PUNCT
ejpam-6173	171	76	if	if	SCONJ
ejpam-6173	171	77	f	f	PROPN
ejpam-6173	171	78	is	be	AUX
ejpam-6173	171	79	uniformly	uniformly	ADV
ejpam-6173	171	80	strictly	strictly	ADV
ejpam-6173	171	81	convex	convex	VERB
ejpam-6173	171	82	on	on	ADP
ejpam-6173	171	83	bounded	bounded	ADJ
ejpam-6173	171	84	sets	set	NOUN
ejpam-6173	171	85	,	,	PUNCT
ejpam-6173	171	86	then	then	ADV
ejpam-6173	171	87	it	it	PRON
ejpam-6173	171	88	is	be	AUX
ejpam-6173	171	89	sequentially	sequentially	ADV
ejpam-6173	171	90	consistent	consistent	ADJ
ejpam-6173	171	91	and	and	CCONJ
ejpam-6173	171	92	the	the	DET
ejpam-6173	171	93	converse	converse	NOUN
ejpam-6173	171	94	implication	implication	NOUN
ejpam-6173	171	95	holds	hold	VERB
ejpam-6173	171	96	when	when	SCONJ
ejpam-6173	171	97	f	f	PROPN
ejpam-6173	171	98	is	be	AUX
ejpam-6173	171	99	lower	low	ADJ
ejpam-6173	171	100	semicontinuous	semicontinuous	ADJ
ejpam-6173	171	101	,	,	PUNCT
ejpam-6173	171	102	fréchet	fréchet	NOUN
ejpam-6173	171	103	differentiable	differentiable	ADJ
ejpam-6173	171	104	on	on	ADP
ejpam-6173	171	105	its	its	PRON
ejpam-6173	171	106	domain	domain	NOUN
ejpam-6173	171	107	and	and	CCONJ
ejpam-6173	171	108	fréchet	fréchet	VERB
ejpam-6173	171	109	derivative	derivative	ADJ
ejpam-6173	171	110	∇f	∇f	NOUN
ejpam-6173	171	111	is	be	AUX
ejpam-6173	171	112	uniformly	uniformly	ADV
ejpam-6173	171	113	continuous	continuous	ADJ
ejpam-6173	171	114	on	on	ADP
ejpam-6173	171	115	bounded	bounded	ADJ
ejpam-6173	171	116	sets	set	NOUN
ejpam-6173	171	117	.	.	PUNCT
ejpam-6173	172	1	lemma	lemma	PROPN
ejpam-6173	172	2	5	5	NUM
ejpam-6173	172	3	.	.	PUNCT
ejpam-6173	173	1	[	[	X
ejpam-6173	173	2	41	41	NUM
ejpam-6173	173	3	,	,	PUNCT
ejpam-6173	173	4	proposition	proposition	NOUN
ejpam-6173	173	5	2.1	2.1	NUM
ejpam-6173	173	6	]	]	PUNCT
ejpam-6173	173	7	let	let	VERB
ejpam-6173	173	8	f	f	PRON
ejpam-6173	173	9	:	:	PUNCT
ejpam-6173	173	10	e	e	X
ejpam-6173	173	11	→	→	SYM
ejpam-6173	173	12	r	r	NOUN
ejpam-6173	173	13	be	be	AUX
ejpam-6173	173	14	uniformly	uniformly	ADV
ejpam-6173	173	15	fréchet	fréchet	VERB
ejpam-6173	173	16	differentiable	differentiable	ADJ
ejpam-6173	173	17	and	and	CCONJ
ejpam-6173	173	18	bounded	bound	VERB
ejpam-6173	173	19	on	on	ADP
ejpam-6173	173	20	bounded	bounded	ADJ
ejpam-6173	173	21	subsets	subset	NOUN
ejpam-6173	173	22	of	of	ADP
ejpam-6173	173	23	e.	e.	PROPN
ejpam-6173	173	24	then	then	ADV
ejpam-6173	173	25	∇f	∇f	PROPN
ejpam-6173	173	26	is	be	AUX
ejpam-6173	173	27	uniformly	uniformly	ADV
ejpam-6173	173	28	continuous	continuous	ADJ
ejpam-6173	173	29	on	on	ADP
ejpam-6173	173	30	bounded	bounded	ADJ
ejpam-6173	173	31	subsets	subset	NOUN
ejpam-6173	173	32	of	of	ADP
ejpam-6173	173	33	e	e	PROPN
ejpam-6173	173	34	from	from	ADP
ejpam-6173	173	35	the	the	DET
ejpam-6173	173	36	strong	strong	ADJ
ejpam-6173	173	37	topology	topology	NOUN
ejpam-6173	173	38	of	of	ADP
ejpam-6173	173	39	e	e	PROPN
ejpam-6173	173	40	to	to	ADP
ejpam-6173	173	41	the	the	DET
ejpam-6173	173	42	strong	strong	ADJ
ejpam-6173	173	43	topology	topology	NOUN
ejpam-6173	173	44	of	of	ADP
ejpam-6173	173	45	e∗.	e∗.	NOUN
ejpam-6173	173	46	lemma	lemma	PROPN
ejpam-6173	173	47	6	6	NUM
ejpam-6173	173	48	.	.	PUNCT
ejpam-6173	174	1	[	[	X
ejpam-6173	174	2	38	38	NUM
ejpam-6173	174	3	,	,	PUNCT
ejpam-6173	174	4	lemma	lemma	PROPN
ejpam-6173	174	5	3.1	3.1	NUM
ejpam-6173	174	6	]	]	PUNCT
ejpam-6173	174	7	let	let	VERB
ejpam-6173	174	8	f	f	PRON
ejpam-6173	174	9	:	:	PUNCT
ejpam-6173	174	10	e	e	X
ejpam-6173	174	11	→	→	SYM
ejpam-6173	174	12	r	r	NOUN
ejpam-6173	174	13	be	be	AUX
ejpam-6173	174	14	a	a	DET
ejpam-6173	174	15	gâteaux	gâteaux	ADV
ejpam-6173	174	16	differentiable	differentiable	ADJ
ejpam-6173	174	17	and	and	CCONJ
ejpam-6173	174	18	totally	totally	ADV
ejpam-6173	174	19	convex	convex	ADJ
ejpam-6173	174	20	function	function	NOUN
ejpam-6173	174	21	.	.	PUNCT
ejpam-6173	175	1	if	if	SCONJ
ejpam-6173	175	2	x0	x0	PROPN
ejpam-6173	175	3	∈	∈	PROPN
ejpam-6173	175	4	e	e	NOUN
ejpam-6173	175	5	and	and	CCONJ
ejpam-6173	175	6	the	the	DET
ejpam-6173	175	7	sequence	sequence	NOUN
ejpam-6173	175	8	{	{	PUNCT
ejpam-6173	175	9	df	df	PROPN
ejpam-6173	175	10	(	(	PUNCT
ejpam-6173	175	11	xn	xn	PROPN
ejpam-6173	175	12	,	,	PUNCT
ejpam-6173	175	13	x0	x0	PROPN
ejpam-6173	175	14	)	)	PUNCT
ejpam-6173	175	15	}	}	PUNCT
ejpam-6173	175	16	is	be	AUX
ejpam-6173	175	17	bounded	bound	VERB
ejpam-6173	175	18	,	,	PUNCT
ejpam-6173	175	19	then	then	ADV
ejpam-6173	175	20	the	the	DET
ejpam-6173	175	21	sequence	sequence	NOUN
ejpam-6173	175	22	{	{	PUNCT
ejpam-6173	175	23	xn	xn	NOUN
ejpam-6173	175	24	}	}	PUNCT
ejpam-6173	175	25	is	be	AUX
ejpam-6173	175	26	also	also	ADV
ejpam-6173	175	27	bounded	bound	VERB
ejpam-6173	175	28	.	.	PUNCT
ejpam-6173	176	1	a	a	DET
ejpam-6173	176	2	mapping	mapping	NOUN
ejpam-6173	176	3	t	t	NOUN
ejpam-6173	176	4	is	be	AUX
ejpam-6173	176	5	said	say	VERB
ejpam-6173	176	6	to	to	PART
ejpam-6173	176	7	be	be	AUX
ejpam-6173	176	8	nonexpansive	nonexpansive	ADJ
ejpam-6173	176	9	if	if	SCONJ
ejpam-6173	176	10	∥tx	∥tx	NUM
ejpam-6173	176	11	−	−	PROPN
ejpam-6173	177	1	ty∥	ty∥	NOUN
ejpam-6173	177	2	≤	≤	ADV
ejpam-6173	178	1	∥x	∥x	PROPN
ejpam-6173	178	2	−	−	PROPN
ejpam-6173	178	3	y∥	y∥	NOUN
ejpam-6173	178	4	for	for	ADP
ejpam-6173	178	5	all	all	DET
ejpam-6173	178	6	x	x	NOUN
ejpam-6173	178	7	,	,	PUNCT
ejpam-6173	178	8	y	y	PROPN
ejpam-6173	178	9	∈	∈	PROPN
ejpam-6173	178	10	c.	c.	PROPN
ejpam-6173	178	11	t	t	PROPN
ejpam-6173	178	12	is	be	AUX
ejpam-6173	178	13	said	say	VERB
ejpam-6173	178	14	to	to	PART
ejpam-6173	178	15	be	be	AUX
ejpam-6173	178	16	quasi	quasi	ADJ
ejpam-6173	178	17	-	-	ADJ
ejpam-6173	178	18	nonexpansive	nonexpansive	ADJ
ejpam-6173	178	19	if	if	SCONJ
ejpam-6173	178	20	f	f	PROPN
ejpam-6173	178	21	(	(	PUNCT
ejpam-6173	178	22	t	t	PROPN
ejpam-6173	178	23	)	)	PUNCT
ejpam-6173	178	24	̸=	̸=	PROPN
ejpam-6173	178	25	∅	∅	NOUN
ejpam-6173	178	26	and	and	CCONJ
ejpam-6173	178	27	∥tx	∥tx	NUM
ejpam-6173	178	28	−	−	PROPN
ejpam-6173	178	29	p∥	p∥	NOUN
ejpam-6173	178	30	≤	≤	NOUN
ejpam-6173	178	31	∥x	∥x	PROPN
ejpam-6173	178	32	−	−	PROPN
ejpam-6173	178	33	p∥	p∥	NOUN
ejpam-6173	178	34	,	,	PUNCT
ejpam-6173	178	35	for	for	ADP
ejpam-6173	178	36	all	all	DET
ejpam-6173	178	37	x	x	SYM
ejpam-6173	178	38	∈	∈	PROPN
ejpam-6173	178	39	c	c	NOUN
ejpam-6173	178	40	and	and	CCONJ
ejpam-6173	178	41	p	p	NOUN
ejpam-6173	178	42	∈	∈	PROPN
ejpam-6173	179	1	f	f	X
ejpam-6173	179	2	(	(	PUNCT
ejpam-6173	179	3	t	t	PROPN
ejpam-6173	179	4	)	)	PUNCT
ejpam-6173	179	5	.	.	PUNCT
ejpam-6173	180	1	a	a	DET
ejpam-6173	180	2	point	point	NOUN
ejpam-6173	180	3	p	p	X
ejpam-6173	180	4	∈	∈	PROPN
ejpam-6173	180	5	c	c	NOUN
ejpam-6173	180	6	is	be	AUX
ejpam-6173	180	7	called	call	VERB
ejpam-6173	180	8	an	an	DET
ejpam-6173	180	9	asymptotic	asymptotic	ADJ
ejpam-6173	180	10	fixed	fix	VERB
ejpam-6173	180	11	point	point	NOUN
ejpam-6173	180	12	of	of	ADP
ejpam-6173	180	13	t	t	PROPN
ejpam-6173	180	14	(	(	PUNCT
ejpam-6173	180	15	see	see	VERB
ejpam-6173	180	16	[	[	X
ejpam-6173	180	17	42	42	NUM
ejpam-6173	180	18	]	]	PUNCT
ejpam-6173	180	19	)	)	PUNCT
ejpam-6173	180	20	if	if	SCONJ
ejpam-6173	180	21	c	c	PROPN
ejpam-6173	180	22	contains	contain	VERB
ejpam-6173	180	23	a	a	DET
ejpam-6173	180	24	sequence	sequence	NOUN
ejpam-6173	180	25	{	{	PUNCT
ejpam-6173	180	26	xn	xn	NOUN
ejpam-6173	180	27	}	}	PUNCT
ejpam-6173	180	28	which	which	PRON
ejpam-6173	180	29	converges	converge	VERB
ejpam-6173	180	30	weakly	weakly	ADV
ejpam-6173	180	31	to	to	ADP
ejpam-6173	180	32	p	p	NOUN
ejpam-6173	180	33	such	such	ADJ
ejpam-6173	180	34	that	that	PRON
ejpam-6173	180	35	limn→+∞	limn→+∞	VERB
ejpam-6173	180	36	∥xn	∥xn	PRON
ejpam-6173	180	37	−	−	PROPN
ejpam-6173	180	38	txn∥	txn∥	PROPN
ejpam-6173	181	1	=	=	NOUN
ejpam-6173	181	2	0	0	X
ejpam-6173	181	3	.	.	PUNCT
ejpam-6173	182	1	we	we	PRON
ejpam-6173	182	2	denote	denote	VERB
ejpam-6173	182	3	by	by	ADP
ejpam-6173	182	4	f̂	f̂	PROPN
ejpam-6173	182	5	(	(	PUNCT
ejpam-6173	182	6	t	t	PROPN
ejpam-6173	182	7	)	)	PUNCT
ejpam-6173	182	8	the	the	DET
ejpam-6173	182	9	set	set	NOUN
ejpam-6173	182	10	of	of	ADP
ejpam-6173	182	11	asymptotic	asymptotic	ADJ
ejpam-6173	182	12	fixed	fix	VERB
ejpam-6173	182	13	points	point	NOUN
ejpam-6173	182	14	of	of	ADP
ejpam-6173	182	15	t	t	PROPN
ejpam-6173	182	16	.	.	PUNCT
ejpam-6173	183	1	a	a	DET
ejpam-6173	183	2	mapping	mapping	NOUN
ejpam-6173	183	3	t	t	NOUN
ejpam-6173	183	4	:	:	PUNCT
ejpam-6173	183	5	c	c	X
ejpam-6173	183	6	→	→	SYM
ejpam-6173	183	7	int(domf	int(domf	NOUN
ejpam-6173	183	8	)	)	PUNCT
ejpam-6173	183	9	with	with	ADP
ejpam-6173	183	10	f	f	PROPN
ejpam-6173	183	11	(	(	PUNCT
ejpam-6173	183	12	t	t	PROPN
ejpam-6173	183	13	)	)	PUNCT
ejpam-6173	183	14	̸=	̸=	PROPN
ejpam-6173	183	15	∅	∅	NOUN
ejpam-6173	183	16	is	be	AUX
ejpam-6173	183	17	called	call	VERB
ejpam-6173	183	18	:	:	PUNCT
ejpam-6173	183	19	(	(	PUNCT
ejpam-6173	183	20	i	i	NOUN
ejpam-6173	183	21	)	)	PUNCT
ejpam-6173	183	22	quasi	quasi	NOUN
ejpam-6173	183	23	-	-	NOUN
ejpam-6173	183	24	bregman	bregman	NOUN
ejpam-6173	183	25	nonexpansive	nonexpansive	NOUN
ejpam-6173	184	1	[	[	X
ejpam-6173	184	2	38	38	NUM
ejpam-6173	184	3	]	]	PUNCT
ejpam-6173	184	4	with	with	ADP
ejpam-6173	184	5	respect	respect	NOUN
ejpam-6173	184	6	to	to	ADP
ejpam-6173	184	7	f	f	PROPN
ejpam-6173	184	8	if	if	SCONJ
ejpam-6173	184	9	df	df	PROPN
ejpam-6173	184	10	(	(	PUNCT
ejpam-6173	184	11	p	p	X
ejpam-6173	184	12	,	,	PUNCT
ejpam-6173	184	13	tx	tx	PROPN
ejpam-6173	184	14	)	)	PUNCT
ejpam-6173	184	15	≤	≤	NOUN
ejpam-6173	184	16	df	df	NOUN
ejpam-6173	184	17	(	(	PUNCT
ejpam-6173	184	18	p	p	X
ejpam-6173	184	19	,	,	PUNCT
ejpam-6173	184	20	x	x	NOUN
ejpam-6173	184	21	)	)	PUNCT
ejpam-6173	184	22	,	,	PUNCT
ejpam-6173	184	23	for	for	ADP
ejpam-6173	184	24	all	all	DET
ejpam-6173	184	25	x	x	SYM
ejpam-6173	184	26	∈	∈	PROPN
ejpam-6173	184	27	c	c	NOUN
ejpam-6173	184	28	,	,	PUNCT
ejpam-6173	184	29	p	p	PROPN
ejpam-6173	184	30	∈	∈	PROPN
ejpam-6173	184	31	f	f	X
ejpam-6173	184	32	(	(	PUNCT
ejpam-6173	184	33	t	t	PROPN
ejpam-6173	184	34	)	)	PUNCT
ejpam-6173	184	35	.	.	PUNCT
ejpam-6173	185	1	(	(	PUNCT
ejpam-6173	185	2	ii	ii	NOUN
ejpam-6173	185	3	)	)	PUNCT
ejpam-6173	185	4	bregman	bregman	NOUN
ejpam-6173	185	5	relatively	relatively	ADV
ejpam-6173	185	6	nonexpansive	nonexpansive	ADJ
ejpam-6173	186	1	[	[	X
ejpam-6173	186	2	38	38	NUM
ejpam-6173	186	3	,	,	PUNCT
ejpam-6173	186	4	43	43	NUM
ejpam-6173	186	5	]	]	PUNCT
ejpam-6173	186	6	with	with	ADP
ejpam-6173	186	7	respect	respect	NOUN
ejpam-6173	186	8	to	to	ADP
ejpam-6173	186	9	f	f	PROPN
ejpam-6173	186	10	if	if	SCONJ
ejpam-6173	186	11	,	,	PUNCT
ejpam-6173	186	12	df	df	PROPN
ejpam-6173	186	13	(	(	PUNCT
ejpam-6173	186	14	p	p	X
ejpam-6173	186	15	,	,	PUNCT
ejpam-6173	186	16	tx	tx	PROPN
ejpam-6173	186	17	)	)	PUNCT
ejpam-6173	186	18	≤	≤	NOUN
ejpam-6173	186	19	df	df	NOUN
ejpam-6173	186	20	(	(	PUNCT
ejpam-6173	186	21	p	p	X
ejpam-6173	186	22	,	,	PUNCT
ejpam-6173	186	23	x	x	NOUN
ejpam-6173	186	24	)	)	PUNCT
ejpam-6173	186	25	,	,	PUNCT
ejpam-6173	186	26	for	for	ADP
ejpam-6173	186	27	all	all	DET
ejpam-6173	186	28	x	x	SYM
ejpam-6173	186	29	∈	∈	PROPN
ejpam-6173	186	30	c	c	NOUN
ejpam-6173	186	31	,	,	PUNCT
ejpam-6173	186	32	p	p	PROPN
ejpam-6173	186	33	∈	∈	PROPN
ejpam-6173	186	34	f	f	X
ejpam-6173	186	35	(	(	PUNCT
ejpam-6173	186	36	t	t	PROPN
ejpam-6173	186	37	)	)	PUNCT
ejpam-6173	186	38	,	,	PUNCT
ejpam-6173	186	39	and	and	CCONJ
ejpam-6173	186	40	f̂	f̂	PROPN
ejpam-6173	186	41	(	(	PUNCT
ejpam-6173	186	42	t	t	PROPN
ejpam-6173	186	43	)	)	PUNCT
ejpam-6173	187	1	=	=	SYM
ejpam-6173	187	2	f	f	PROPN
ejpam-6173	187	3	(	(	PUNCT
ejpam-6173	187	4	t	t	PROPN
ejpam-6173	187	5	)	)	PUNCT
ejpam-6173	187	6	.	.	PUNCT
ejpam-6173	188	1	(	(	PUNCT
ejpam-6173	188	2	iii	iii	X
ejpam-6173	188	3	)	)	PUNCT
ejpam-6173	188	4	bregman	bregman	NOUN
ejpam-6173	188	5	strongly	strongly	ADV
ejpam-6173	188	6	nonexpansive	nonexpansive	ADJ
ejpam-6173	188	7	(	(	PUNCT
ejpam-6173	188	8	see	see	VERB
ejpam-6173	188	9	[	[	X
ejpam-6173	188	10	38	38	NUM
ejpam-6173	188	11	,	,	PUNCT
ejpam-6173	188	12	44	44	NUM
ejpam-6173	188	13	]	]	PUNCT
ejpam-6173	188	14	)	)	PUNCT
ejpam-6173	188	15	with	with	ADP
ejpam-6173	188	16	respect	respect	NOUN
ejpam-6173	188	17	to	to	ADP
ejpam-6173	188	18	f	f	PROPN
ejpam-6173	188	19	and	and	CCONJ
ejpam-6173	188	20	f̂	f̂	PROPN
ejpam-6173	188	21	(	(	PUNCT
ejpam-6173	188	22	t	t	PROPN
ejpam-6173	188	23	)	)	PUNCT
ejpam-6173	189	1	if	if	SCONJ
ejpam-6173	189	2	,	,	PUNCT
ejpam-6173	189	3	df	df	PROPN
ejpam-6173	189	4	(	(	PUNCT
ejpam-6173	189	5	p	p	X
ejpam-6173	189	6	,	,	PUNCT
ejpam-6173	189	7	tx	tx	PROPN
ejpam-6173	189	8	)	)	PUNCT
ejpam-6173	189	9	≤	≤	NOUN
ejpam-6173	189	10	df	df	NOUN
ejpam-6173	189	11	(	(	PUNCT
ejpam-6173	189	12	p	p	X
ejpam-6173	189	13	,	,	PUNCT
ejpam-6173	189	14	x	x	NOUN
ejpam-6173	189	15	)	)	PUNCT
ejpam-6173	189	16	,	,	PUNCT
ejpam-6173	189	17	for	for	ADP
ejpam-6173	189	18	all	all	DET
ejpam-6173	189	19	x	x	SYM
ejpam-6173	189	20	∈	∈	PROPN
ejpam-6173	189	21	c	c	NOUN
ejpam-6173	189	22	,	,	PUNCT
ejpam-6173	189	23	p	p	PROPN
ejpam-6173	189	24	∈	∈	PROPN
ejpam-6173	189	25	f̂	f̂	X
ejpam-6173	189	26	(	(	PUNCT
ejpam-6173	189	27	t	t	PROPN
ejpam-6173	189	28	)	)	PUNCT
ejpam-6173	189	29	and	and	CCONJ
ejpam-6173	189	30	,	,	PUNCT
ejpam-6173	189	31	if	if	SCONJ
ejpam-6173	189	32	whenever	whenever	ADV
ejpam-6173	189	33	{	{	PUNCT
ejpam-6173	189	34	xn	xn	X
ejpam-6173	189	35	}	}	PUNCT
ejpam-6173	189	36	⊂	⊂	PROPN
ejpam-6173	190	1	c	c	PROPN
ejpam-6173	190	2	is	be	AUX
ejpam-6173	190	3	bounded	bound	VERB
ejpam-6173	190	4	,	,	PUNCT
ejpam-6173	190	5	p	p	PROPN
ejpam-6173	190	6	∈	∈	PROPN
ejpam-6173	190	7	f̂	f̂	X
ejpam-6173	190	8	(	(	PUNCT
ejpam-6173	190	9	t	t	PROPN
ejpam-6173	190	10	)	)	PUNCT
ejpam-6173	190	11	,	,	PUNCT
ejpam-6173	190	12	and	and	CCONJ
ejpam-6173	190	13	lim	lim	PROPN
ejpam-6173	190	14	z→+∞	z→+∞	PROPN
ejpam-6173	190	15	(	(	PUNCT
ejpam-6173	190	16	df	df	PROPN
ejpam-6173	190	17	(	(	PUNCT
ejpam-6173	190	18	p	p	X
ejpam-6173	190	19	,	,	PUNCT
ejpam-6173	190	20	xn)−df	xn)−df	PROPN
ejpam-6173	191	1	(	(	PUNCT
ejpam-6173	191	2	p	p	NOUN
ejpam-6173	191	3	,	,	PUNCT
ejpam-6173	191	4	txn	txn	NOUN
ejpam-6173	191	5	)	)	PUNCT
ejpam-6173	191	6	)	)	PUNCT
ejpam-6173	192	1	=	=	SYM
ejpam-6173	192	2	0	0	X
ejpam-6173	192	3	,	,	PUNCT
ejpam-6173	192	4	it	it	PRON
ejpam-6173	192	5	follows	follow	VERB
ejpam-6173	192	6	that	that	SCONJ
ejpam-6173	192	7	lim	lim	PROPN
ejpam-6173	192	8	n→+∞	n→+∞	VERB
ejpam-6173	192	9	df	df	PROPN
ejpam-6173	192	10	(	(	PUNCT
ejpam-6173	192	11	xn	xn	PROPN
ejpam-6173	192	12	,	,	PUNCT
ejpam-6173	192	13	txn	txn	NOUN
ejpam-6173	192	14	)	)	PUNCT
ejpam-6173	192	15	=	=	SYM
ejpam-6173	193	1	0	0	X
ejpam-6173	193	2	.	.	PUNCT
ejpam-6173	194	1	v.	v.	ADP
ejpam-6173	194	2	darvish	darvish	PROPN
ejpam-6173	194	3	et	et	PROPN
ejpam-6173	194	4	al	al	PROPN
ejpam-6173	194	5	.	.	PUNCT
ejpam-6173	194	6	/	/	SYM
ejpam-6173	194	7	eur	eur	PROPN
ejpam-6173	194	8	.	.	PUNCT
ejpam-6173	195	1	j.	j.	PROPN
ejpam-6173	195	2	pure	pure	PROPN
ejpam-6173	195	3	appl	appl	PROPN
ejpam-6173	195	4	.	.	PROPN
ejpam-6173	195	5	math	math	PROPN
ejpam-6173	195	6	,	,	PUNCT
ejpam-6173	195	7	18	18	NUM
ejpam-6173	195	8	(	(	PUNCT
ejpam-6173	195	9	3	3	NUM
ejpam-6173	195	10	)	)	PUNCT
ejpam-6173	195	11	(	(	PUNCT
ejpam-6173	195	12	2025	2025	NUM
ejpam-6173	195	13	)	)	PUNCT
ejpam-6173	195	14	,	,	PUNCT
ejpam-6173	195	15	6173	6173	NUM
ejpam-6173	195	16	9	9	NUM
ejpam-6173	195	17	of	of	ADP
ejpam-6173	195	18	32	32	NUM
ejpam-6173	195	19	(	(	PUNCT
ejpam-6173	195	20	iv	iv	X
ejpam-6173	195	21	)	)	PUNCT
ejpam-6173	195	22	bregman	bregman	NOUN
ejpam-6173	195	23	firmly	firmly	ADV
ejpam-6173	195	24	nonexpansive	nonexpansive	ADJ
ejpam-6173	195	25	(	(	PUNCT
ejpam-6173	195	26	for	for	ADP
ejpam-6173	195	27	short	short	ADJ
ejpam-6173	195	28	bfne	bfne	NOUN
ejpam-6173	196	1	[	[	X
ejpam-6173	196	2	45	45	NUM
ejpam-6173	196	3	]	]	PUNCT
ejpam-6173	196	4	)	)	PUNCT
ejpam-6173	196	5	with	with	ADP
ejpam-6173	196	6	respect	respect	NOUN
ejpam-6173	196	7	to	to	ADP
ejpam-6173	196	8	f	f	PROPN
ejpam-6173	196	9	if	if	SCONJ
ejpam-6173	196	10	,	,	PUNCT
ejpam-6173	196	11	for	for	ADP
ejpam-6173	196	12	all	all	DET
ejpam-6173	196	13	x	x	NOUN
ejpam-6173	196	14	,	,	PUNCT
ejpam-6173	196	15	y	y	PROPN
ejpam-6173	196	16	∈	∈	PROPN
ejpam-6173	196	17	c	c	X
ejpam-6173	196	18	,	,	PUNCT
ejpam-6173	196	19	⟨∇f(tx)−∇f(ty	⟨∇f(tx)−∇f(ty	PROPN
ejpam-6173	196	20	)	)	PUNCT
ejpam-6173	196	21	,	,	PUNCT
ejpam-6173	196	22	tx−	tx−	X
ejpam-6173	196	23	ty⟩	ty⟩	NOUN
ejpam-6173	196	24	≤	≤	PROPN
ejpam-6173	196	25	⟨∇f(x)−∇f(y	⟨∇f(x)−∇f(y	NUM
ejpam-6173	196	26	)	)	PUNCT
ejpam-6173	196	27	,	,	PUNCT
ejpam-6173	196	28	tx−	tx−	X
ejpam-6173	196	29	ty⟩	ty⟩	PUNCT
ejpam-6173	196	30	equivalently	equivalently	ADV
ejpam-6173	196	31	,	,	PUNCT
ejpam-6173	196	32	df	df	PROPN
ejpam-6173	196	33	(	(	PUNCT
ejpam-6173	196	34	tx	tx	PROPN
ejpam-6173	196	35	,	,	PUNCT
ejpam-6173	196	36	ty)+df	ty)+df	NOUN
ejpam-6173	196	37	(	(	PUNCT
ejpam-6173	196	38	ty	ty	INTJ
ejpam-6173	196	39	,	,	PUNCT
ejpam-6173	196	40	tx)+df	tx)+df	PRON
ejpam-6173	196	41	(	(	PUNCT
ejpam-6173	196	42	tx	tx	PROPN
ejpam-6173	196	43	,	,	PUNCT
ejpam-6173	196	44	x)+df	x)+df	PROPN
ejpam-6173	196	45	(	(	PUNCT
ejpam-6173	196	46	ty	ty	INTJ
ejpam-6173	196	47	,	,	PUNCT
ejpam-6173	196	48	y	y	NOUN
ejpam-6173	196	49	)	)	PUNCT
ejpam-6173	196	50	≤	≤	NUM
ejpam-6173	196	51	df	df	NOUN
ejpam-6173	196	52	(	(	PUNCT
ejpam-6173	196	53	tx	tx	PROPN
ejpam-6173	196	54	,	,	PUNCT
ejpam-6173	196	55	y)+df	y)+df	PROPN
ejpam-6173	196	56	(	(	PUNCT
ejpam-6173	196	57	ty	ty	INTJ
ejpam-6173	196	58	,	,	PUNCT
ejpam-6173	196	59	x	x	NOUN
ejpam-6173	196	60	)	)	PUNCT
ejpam-6173	196	61	.	.	PUNCT
ejpam-6173	197	1	(	(	PUNCT
ejpam-6173	197	2	2.5	2.5	NUM
ejpam-6173	197	3	)	)	PUNCT
ejpam-6173	197	4	the	the	DET
ejpam-6173	197	5	existence	existence	NOUN
ejpam-6173	197	6	and	and	CCONJ
ejpam-6173	197	7	approximation	approximation	NOUN
ejpam-6173	197	8	of	of	ADP
ejpam-6173	197	9	bregman	bregman	NOUN
ejpam-6173	197	10	firmly	firmly	ADV
ejpam-6173	197	11	nonexpansive	nonexpansive	ADJ
ejpam-6173	197	12	mappings	mapping	NOUN
ejpam-6173	197	13	was	be	AUX
ejpam-6173	197	14	studied	study	VERB
ejpam-6173	197	15	in	in	ADP
ejpam-6173	197	16	[	[	X
ejpam-6173	197	17	42	42	NUM
ejpam-6173	197	18	]	]	PUNCT
ejpam-6173	197	19	.	.	PUNCT
ejpam-6173	198	1	it	it	PRON
ejpam-6173	198	2	is	be	AUX
ejpam-6173	198	3	also	also	ADV
ejpam-6173	198	4	known	know	VERB
ejpam-6173	198	5	that	that	SCONJ
ejpam-6173	198	6	if	if	SCONJ
ejpam-6173	198	7	t	t	PROPN
ejpam-6173	198	8	is	be	AUX
ejpam-6173	198	9	bregman	bregman	NOUN
ejpam-6173	198	10	firmly	firmly	ADV
ejpam-6173	198	11	nonexpansive	nonexpansive	ADJ
ejpam-6173	198	12	and	and	CCONJ
ejpam-6173	198	13	f	f	PROPN
ejpam-6173	198	14	is	be	AUX
ejpam-6173	198	15	legendre	legendre	PROPN
ejpam-6173	198	16	function	function	NOUN
ejpam-6173	198	17	which	which	PRON
ejpam-6173	198	18	is	be	AUX
ejpam-6173	198	19	bounded	bound	VERB
ejpam-6173	198	20	,	,	PUNCT
ejpam-6173	198	21	uniformly	uniformly	ADV
ejpam-6173	198	22	fréchet	fréchet	VERB
ejpam-6173	198	23	differentiable	differentiable	ADJ
ejpam-6173	198	24	and	and	CCONJ
ejpam-6173	198	25	totally	totally	ADV
ejpam-6173	198	26	convex	convex	VERB
ejpam-6173	198	27	on	on	ADP
ejpam-6173	198	28	bounded	bounded	ADJ
ejpam-6173	198	29	subset	subset	NOUN
ejpam-6173	198	30	of	of	ADP
ejpam-6173	198	31	e	e	NOUN
ejpam-6173	198	32	,	,	PUNCT
ejpam-6173	198	33	then	then	ADV
ejpam-6173	198	34	f	f	PROPN
ejpam-6173	198	35	(	(	PUNCT
ejpam-6173	198	36	t	t	PROPN
ejpam-6173	198	37	)	)	PUNCT
ejpam-6173	199	1	=	=	SYM
ejpam-6173	199	2	f̂	f̂	X
ejpam-6173	199	3	(	(	PUNCT
ejpam-6173	199	4	t	t	PROPN
ejpam-6173	199	5	)	)	PUNCT
ejpam-6173	199	6	and	and	CCONJ
ejpam-6173	199	7	f	f	PROPN
ejpam-6173	199	8	(	(	PUNCT
ejpam-6173	199	9	t	t	PROPN
ejpam-6173	199	10	)	)	PUNCT
ejpam-6173	199	11	is	be	AUX
ejpam-6173	199	12	closed	close	VERB
ejpam-6173	199	13	and	and	CCONJ
ejpam-6173	199	14	convex	convex	NOUN
ejpam-6173	199	15	.	.	PUNCT
ejpam-6173	200	1	it	it	PRON
ejpam-6173	200	2	also	also	ADV
ejpam-6173	200	3	follows	follow	VERB
ejpam-6173	200	4	that	that	SCONJ
ejpam-6173	200	5	every	every	DET
ejpam-6173	200	6	bregman	bregman	NOUN
ejpam-6173	200	7	firmly	firmly	ADV
ejpam-6173	200	8	nonexpansive	nonexpansive	ADJ
ejpam-6173	200	9	mapping	mapping	NOUN
ejpam-6173	200	10	is	be	AUX
ejpam-6173	200	11	bregman	bregman	NOUN
ejpam-6173	200	12	strongly	strongly	ADV
ejpam-6173	200	13	nonexpansive	nonexpansive	ADJ
ejpam-6173	200	14	with	with	ADP
ejpam-6173	200	15	respect	respect	NOUN
ejpam-6173	200	16	to	to	ADP
ejpam-6173	200	17	f	f	PROPN
ejpam-6173	200	18	(	(	PUNCT
ejpam-6173	200	19	t	t	PROPN
ejpam-6173	200	20	)	)	PUNCT
ejpam-6173	201	1	=	=	SYM
ejpam-6173	201	2	f̂	f̂	X
ejpam-6173	201	3	(	(	PUNCT
ejpam-6173	201	4	t	t	PROPN
ejpam-6173	201	5	)	)	PUNCT
ejpam-6173	201	6	.	.	PUNCT
ejpam-6173	202	1	lemma	lemma	PROPN
ejpam-6173	202	2	7	7	NUM
ejpam-6173	202	3	.	.	PUNCT
ejpam-6173	203	1	[	[	X
ejpam-6173	203	2	40	40	NUM
ejpam-6173	203	3	]	]	PUNCT
ejpam-6173	203	4	let	let	VERB
ejpam-6173	203	5	c	c	PRON
ejpam-6173	203	6	be	be	AUX
ejpam-6173	203	7	a	a	DET
ejpam-6173	203	8	nonempty	nonempty	ADJ
ejpam-6173	203	9	,	,	PUNCT
ejpam-6173	203	10	closed	closed	ADJ
ejpam-6173	203	11	and	and	CCONJ
ejpam-6173	203	12	convex	convex	PROPN
ejpam-6173	203	13	subset	subset	NOUN
ejpam-6173	203	14	of	of	ADP
ejpam-6173	203	15	e.	e.	PROPN
ejpam-6173	203	16	let	let	VERB
ejpam-6173	203	17	f	f	PROPN
ejpam-6173	203	18	:	:	PUNCT
ejpam-6173	203	19	e	e	X
ejpam-6173	203	20	→	→	SYM
ejpam-6173	203	21	r	r	NOUN
ejpam-6173	203	22	be	be	AUX
ejpam-6173	203	23	a	a	DET
ejpam-6173	203	24	gâteaux	gâteaux	ADV
ejpam-6173	203	25	differentiable	differentiable	ADJ
ejpam-6173	203	26	and	and	CCONJ
ejpam-6173	203	27	totally	totally	ADV
ejpam-6173	203	28	convex	convex	ADJ
ejpam-6173	203	29	function	function	NOUN
ejpam-6173	203	30	.	.	PUNCT
ejpam-6173	204	1	let	let	VERB
ejpam-6173	204	2	x	x	SYM
ejpam-6173	204	3	∈	∈	PROPN
ejpam-6173	204	4	e	e	NOUN
ejpam-6173	204	5	,	,	PUNCT
ejpam-6173	204	6	then	then	ADV
ejpam-6173	204	7	1	1	X
ejpam-6173	204	8	)	)	PUNCT
ejpam-6173	204	9	z	z	NOUN
ejpam-6173	204	10	=	=	SYM
ejpam-6173	204	11	projfc(x	projfc(x	NOUN
ejpam-6173	204	12	)	)	PUNCT
ejpam-6173	204	13	if	if	SCONJ
ejpam-6173	204	14	and	and	CCONJ
ejpam-6173	204	15	only	only	ADV
ejpam-6173	204	16	if	if	SCONJ
ejpam-6173	204	17	⟨∇f(x)−∇f(z	⟨∇f(x)−∇f(z	NOUN
ejpam-6173	204	18	)	)	PUNCT
ejpam-6173	204	19	,	,	PUNCT
ejpam-6173	204	20	y	y	PROPN
ejpam-6173	204	21	−	−	PROPN
ejpam-6173	204	22	z⟩	z⟩	NOUN
ejpam-6173	204	23	≤	≤	NUM
ejpam-6173	204	24	0	0	NUM
ejpam-6173	204	25	,	,	PUNCT
ejpam-6173	204	26	for	for	ADP
ejpam-6173	204	27	all	all	DET
ejpam-6173	204	28	y	y	PROPN
ejpam-6173	204	29	∈	∈	PROPN
ejpam-6173	204	30	c.	c.	PROPN
ejpam-6173	204	31	2	2	NUM
ejpam-6173	204	32	)	)	PUNCT
ejpam-6173	204	33	df	df	NOUN
ejpam-6173	204	34	(	(	PUNCT
ejpam-6173	204	35	y	y	PROPN
ejpam-6173	204	36	,	,	PUNCT
ejpam-6173	204	37	proj	proj	NOUN
ejpam-6173	204	38	f	f	PROPN
ejpam-6173	204	39	c(x	c(x	NOUN
ejpam-6173	204	40	)	)	PUNCT
ejpam-6173	204	41	)	)	PUNCT
ejpam-6173	205	1	+	+	ADP
ejpam-6173	205	2	df	df	NOUN
ejpam-6173	205	3	(	(	PUNCT
ejpam-6173	205	4	proj	proj	NOUN
ejpam-6173	205	5	f	f	PROPN
ejpam-6173	205	6	c(x	c(x	PROPN
ejpam-6173	205	7	)	)	PUNCT
ejpam-6173	205	8	,	,	PUNCT
ejpam-6173	205	9	x	x	X
ejpam-6173	205	10	)	)	PUNCT
ejpam-6173	205	11	≤	≤	NUM
ejpam-6173	205	12	df	df	NOUN
ejpam-6173	205	13	(	(	PUNCT
ejpam-6173	205	14	y	y	PROPN
ejpam-6173	205	15	,	,	PUNCT
ejpam-6173	205	16	x	x	NOUN
ejpam-6173	205	17	)	)	PUNCT
ejpam-6173	205	18	,	,	PUNCT
ejpam-6173	205	19	for	for	ADP
ejpam-6173	205	20	all	all	DET
ejpam-6173	205	21	x	x	SYM
ejpam-6173	205	22	∈	∈	PROPN
ejpam-6173	205	23	e	e	NOUN
ejpam-6173	205	24	,	,	PUNCT
ejpam-6173	205	25	y	y	PROPN
ejpam-6173	205	26	∈	∈	PROPN
ejpam-6173	205	27	c.	c.	PROPN
ejpam-6173	205	28	let	let	VERB
ejpam-6173	205	29	f	f	NOUN
ejpam-6173	205	30	:	:	PUNCT
ejpam-6173	205	31	e	e	X
ejpam-6173	205	32	→	→	SYM
ejpam-6173	205	33	r	r	NOUN
ejpam-6173	205	34	be	be	AUX
ejpam-6173	205	35	a	a	DET
ejpam-6173	205	36	convex	convex	NOUN
ejpam-6173	205	37	,	,	PUNCT
ejpam-6173	205	38	legendre	legendre	PROPN
ejpam-6173	205	39	and	and	CCONJ
ejpam-6173	205	40	gâteaux	gâteaux	ADJ
ejpam-6173	205	41	differentiable	differentiable	ADJ
ejpam-6173	205	42	function	function	NOUN
ejpam-6173	205	43	.	.	PUNCT
ejpam-6173	206	1	following	follow	VERB
ejpam-6173	206	2	[	[	X
ejpam-6173	206	3	35	35	NUM
ejpam-6173	206	4	]	]	PUNCT
ejpam-6173	206	5	and	and	CCONJ
ejpam-6173	206	6	[	[	X
ejpam-6173	206	7	29	29	NUM
ejpam-6173	206	8	]	]	PUNCT
ejpam-6173	206	9	,	,	PUNCT
ejpam-6173	206	10	we	we	PRON
ejpam-6173	206	11	make	make	VERB
ejpam-6173	206	12	use	use	NOUN
ejpam-6173	206	13	of	of	ADP
ejpam-6173	206	14	the	the	DET
ejpam-6173	206	15	function	function	NOUN
ejpam-6173	206	16	vf	vf	NOUN
ejpam-6173	206	17	:	:	PUNCT
ejpam-6173	206	18	e	e	PROPN
ejpam-6173	206	19	×	×	PROPN
ejpam-6173	206	20	e∗	e∗	PROPN
ejpam-6173	206	21	→	→	PUNCT
ejpam-6173	207	1	[	[	X
ejpam-6173	207	2	0,+∞	0,+∞	NUM
ejpam-6173	207	3	)	)	PUNCT
ejpam-6173	207	4	associated	associate	VERB
ejpam-6173	207	5	with	with	ADP
ejpam-6173	207	6	f	f	PROPN
ejpam-6173	207	7	,	,	PUNCT
ejpam-6173	207	8	which	which	PRON
ejpam-6173	207	9	is	be	AUX
ejpam-6173	207	10	defined	define	VERB
ejpam-6173	207	11	by	by	ADP
ejpam-6173	207	12	vf	vf	X
ejpam-6173	207	13	(	(	PUNCT
ejpam-6173	207	14	x	x	X
ejpam-6173	207	15	,	,	PUNCT
ejpam-6173	207	16	x	x	NOUN
ejpam-6173	207	17	∗	∗	NOUN
ejpam-6173	207	18	)	)	PUNCT
ejpam-6173	208	1	=	=	SYM
ejpam-6173	208	2	f(x)−	f(x)−	PROPN
ejpam-6173	208	3	⟨x∗	⟨x∗	PROPN
ejpam-6173	208	4	,	,	PUNCT
ejpam-6173	208	5	x⟩+	x⟩+	PROPN
ejpam-6173	208	6	f∗(x∗	f∗(x∗	PROPN
ejpam-6173	208	7	)	)	PUNCT
ejpam-6173	208	8	,	,	PUNCT
ejpam-6173	208	9	for	for	ADP
ejpam-6173	208	10	all	all	DET
ejpam-6173	208	11	x	x	SYM
ejpam-6173	208	12	∈	∈	PROPN
ejpam-6173	208	13	e	e	NOUN
ejpam-6173	208	14	,	,	PUNCT
ejpam-6173	208	15	x∗	x∗	PROPN
ejpam-6173	208	16	∈	∈	PROPN
ejpam-6173	208	17	e∗.	e∗.	NOUN
ejpam-6173	208	18	(	(	PUNCT
ejpam-6173	208	19	2.6	2.6	NUM
ejpam-6173	208	20	)	)	PUNCT
ejpam-6173	208	21	then	then	ADV
ejpam-6173	208	22	vf	vf	PROPN
ejpam-6173	208	23	is	be	AUX
ejpam-6173	208	24	nonexpansive	nonexpansive	ADJ
ejpam-6173	208	25	and	and	CCONJ
ejpam-6173	208	26	vf	vf	X
ejpam-6173	208	27	(	(	PUNCT
ejpam-6173	208	28	x	x	X
ejpam-6173	208	29	,	,	PUNCT
ejpam-6173	208	30	x	x	SYM
ejpam-6173	208	31	∗	∗	NOUN
ejpam-6173	208	32	)	)	PUNCT
ejpam-6173	209	1	=	=	SYM
ejpam-6173	209	2	df	df	NOUN
ejpam-6173	209	3	(	(	PUNCT
ejpam-6173	209	4	x,∇f∗(x∗	x,∇f∗(x∗	PROPN
ejpam-6173	209	5	)	)	PUNCT
ejpam-6173	209	6	)	)	PUNCT
ejpam-6173	209	7	for	for	ADP
ejpam-6173	209	8	all	all	DET
ejpam-6173	209	9	x	x	SYM
ejpam-6173	209	10	∈	∈	PROPN
ejpam-6173	209	11	e	e	NOUN
ejpam-6173	209	12	and	and	CCONJ
ejpam-6173	209	13	x∗	x∗	PROPN
ejpam-6173	209	14	∈	∈	PROPN
ejpam-6173	209	15	e∗.	e∗.	NOUN
ejpam-6173	210	1	moreover	moreover	ADV
ejpam-6173	210	2	,	,	PUNCT
ejpam-6173	210	3	by	by	ADP
ejpam-6173	210	4	the	the	DET
ejpam-6173	210	5	subdifferential	subdifferential	ADJ
ejpam-6173	210	6	inequality	inequality	NOUN
ejpam-6173	210	7	,	,	PUNCT
ejpam-6173	210	8	vf	vf	X
ejpam-6173	210	9	(	(	PUNCT
ejpam-6173	210	10	x	x	X
ejpam-6173	210	11	,	,	PUNCT
ejpam-6173	210	12	x	x	NOUN
ejpam-6173	210	13	∗	∗	NOUN
ejpam-6173	210	14	)	)	PUNCT
ejpam-6173	210	15	+	+	CCONJ
ejpam-6173	210	16	⟨y∗,∇f∗(x∗)−	⟨y∗,∇f∗(x∗)−	X
ejpam-6173	210	17	x⟩	x⟩	PUNCT
ejpam-6173	210	18	≤	≤	NUM
ejpam-6173	210	19	vf	vf	X
ejpam-6173	210	20	(	(	PUNCT
ejpam-6173	210	21	x	x	X
ejpam-6173	210	22	,	,	PUNCT
ejpam-6173	210	23	x	x	X
ejpam-6173	210	24	∗	∗	NOUN
ejpam-6173	210	25	+	+	CCONJ
ejpam-6173	210	26	y∗	y∗	ADV
ejpam-6173	210	27	)	)	PUNCT
ejpam-6173	210	28	(	(	PUNCT
ejpam-6173	210	29	2.7	2.7	NUM
ejpam-6173	210	30	)	)	PUNCT
ejpam-6173	210	31	for	for	ADP
ejpam-6173	210	32	all	all	DET
ejpam-6173	210	33	x	x	SYM
ejpam-6173	210	34	∈	∈	PROPN
ejpam-6173	210	35	e	e	NOUN
ejpam-6173	210	36	and	and	CCONJ
ejpam-6173	210	37	x∗	x∗	PROPN
ejpam-6173	210	38	,	,	PUNCT
ejpam-6173	210	39	y∗	y∗	PROPN
ejpam-6173	210	40	∈	∈	PROPN
ejpam-6173	210	41	e∗	e∗	NOUN
ejpam-6173	211	1	[	[	X
ejpam-6173	211	2	46	46	NUM
ejpam-6173	211	3	]	]	PUNCT
ejpam-6173	211	4	.	.	PUNCT
ejpam-6173	212	1	in	in	ADP
ejpam-6173	212	2	addition	addition	NOUN
ejpam-6173	212	3	,	,	PUNCT
ejpam-6173	212	4	if	if	SCONJ
ejpam-6173	212	5	f	f	PRON
ejpam-6173	212	6	:	:	PUNCT
ejpam-6173	212	7	e	e	X
ejpam-6173	212	8	→	→	PUNCT
ejpam-6173	212	9	(	(	PUNCT
ejpam-6173	212	10	−∞,+∞	−∞,+∞	ADV
ejpam-6173	212	11	]	]	PUNCT
ejpam-6173	212	12	is	be	AUX
ejpam-6173	212	13	a	a	DET
ejpam-6173	212	14	proper	proper	ADJ
ejpam-6173	212	15	lower	low	ADJ
ejpam-6173	212	16	semicontinuous	semicontinuous	ADJ
ejpam-6173	212	17	function	function	NOUN
ejpam-6173	212	18	,	,	PUNCT
ejpam-6173	212	19	then	then	ADV
ejpam-6173	212	20	f∗	f∗	NOUN
ejpam-6173	212	21	:	:	PUNCT
ejpam-6173	212	22	e∗	e∗	PROPN
ejpam-6173	212	23	→	→	SYM
ejpam-6173	212	24	(	(	PUNCT
ejpam-6173	212	25	−∞,+∞	−∞,+∞	ADV
ejpam-6173	212	26	]	]	PUNCT
ejpam-6173	212	27	is	be	AUX
ejpam-6173	212	28	a	a	DET
ejpam-6173	212	29	proper	proper	ADJ
ejpam-6173	212	30	weak∗	weak∗	NOUN
ejpam-6173	212	31	lower	lower	ADV
ejpam-6173	212	32	semicontinuous	semicontinuous	ADJ
ejpam-6173	212	33	and	and	CCONJ
ejpam-6173	212	34	convex	convex	ADJ
ejpam-6173	212	35	function	function	NOUN
ejpam-6173	212	36	(	(	PUNCT
ejpam-6173	212	37	see	see	VERB
ejpam-6173	212	38	[	[	X
ejpam-6173	212	39	47	47	NUM
ejpam-6173	212	40	]	]	NUM
ejpam-6173	212	41	)	)	PUNCT
ejpam-6173	212	42	.	.	PUNCT
ejpam-6173	213	1	hence	hence	ADV
ejpam-6173	213	2	,	,	PUNCT
ejpam-6173	213	3	vf	vf	X
ejpam-6173	213	4	is	be	AUX
ejpam-6173	213	5	convex	convex	ADJ
ejpam-6173	213	6	in	in	ADP
ejpam-6173	213	7	the	the	DET
ejpam-6173	213	8	second	second	ADJ
ejpam-6173	213	9	variable	variable	NOUN
ejpam-6173	213	10	.	.	PUNCT
ejpam-6173	214	1	thus	thus	ADV
ejpam-6173	214	2	,	,	PUNCT
ejpam-6173	214	3	for	for	ADP
ejpam-6173	214	4	all	all	DET
ejpam-6173	214	5	z	z	NOUN
ejpam-6173	214	6	∈	∈	PROPN
ejpam-6173	214	7	e	e	NOUN
ejpam-6173	214	8	,	,	PUNCT
ejpam-6173	214	9	df	df	PROPN
ejpam-6173	214	10	(	(	PUNCT
ejpam-6173	214	11	z,∇f∗	z,∇f∗	PROPN
ejpam-6173	214	12	(	(	PUNCT
ejpam-6173	214	13	n∑	n∑	NOUN
ejpam-6173	214	14	i=1	i=1	PROPN
ejpam-6173	214	15	ti∇f(xi	ti∇f(xi	NOUN
ejpam-6173	214	16	)	)	PUNCT
ejpam-6173	214	17	)	)	PUNCT
ejpam-6173	214	18	)	)	PUNCT
ejpam-6173	214	19	≤	≤	NUM
ejpam-6173	215	1	n∑	n∑	PROPN
ejpam-6173	215	2	i=1	i=1	PROPN
ejpam-6173	216	1	tidf	tidf	PROPN
ejpam-6173	216	2	(	(	PUNCT
ejpam-6173	216	3	z	z	NOUN
ejpam-6173	216	4	,	,	PUNCT
ejpam-6173	216	5	xi	xi	PROPN
ejpam-6173	216	6	)	)	PUNCT
ejpam-6173	216	7	,	,	PUNCT
ejpam-6173	216	8	(	(	PUNCT
ejpam-6173	216	9	2.8	2.8	NUM
ejpam-6173	216	10	)	)	PUNCT
ejpam-6173	216	11	where	where	SCONJ
ejpam-6173	216	12	{	{	PUNCT
ejpam-6173	216	13	xi}ni=1	xi}ni=1	PROPN
ejpam-6173	216	14	⊂	⊂	PROPN
ejpam-6173	216	15	e	e	PROPN
ejpam-6173	216	16	and	and	CCONJ
ejpam-6173	216	17	{	{	PUNCT
ejpam-6173	216	18	ti}ni=1	ti}ni=1	PROPN
ejpam-6173	216	19	⊂	⊂	X
ejpam-6173	216	20	(	(	PUNCT
ejpam-6173	216	21	0	0	NUM
ejpam-6173	216	22	,	,	PUNCT
ejpam-6173	216	23	1	1	NUM
ejpam-6173	216	24	)	)	PUNCT
ejpam-6173	216	25	with	with	ADP
ejpam-6173	216	26	∑n	∑n	PROPN
ejpam-6173	216	27	i=1	i=1	PROPN
ejpam-6173	216	28	ti	ti	NOUN
ejpam-6173	216	29	=	=	SYM
ejpam-6173	216	30	1	1	PROPN
ejpam-6173	216	31	.	.	PUNCT
ejpam-6173	217	1	v.	v.	ADP
ejpam-6173	217	2	darvish	darvish	PROPN
ejpam-6173	217	3	et	et	PROPN
ejpam-6173	217	4	al	al	PROPN
ejpam-6173	217	5	.	.	PUNCT
ejpam-6173	217	6	/	/	SYM
ejpam-6173	217	7	eur	eur	PROPN
ejpam-6173	217	8	.	.	PUNCT
ejpam-6173	218	1	j.	j.	PROPN
ejpam-6173	218	2	pure	pure	PROPN
ejpam-6173	218	3	appl	appl	PROPN
ejpam-6173	218	4	.	.	PROPN
ejpam-6173	218	5	math	math	PROPN
ejpam-6173	218	6	,	,	PUNCT
ejpam-6173	218	7	18	18	NUM
ejpam-6173	218	8	(	(	PUNCT
ejpam-6173	218	9	3	3	NUM
ejpam-6173	218	10	)	)	PUNCT
ejpam-6173	218	11	(	(	PUNCT
ejpam-6173	218	12	2025	2025	NUM
ejpam-6173	218	13	)	)	PUNCT
ejpam-6173	218	14	,	,	PUNCT
ejpam-6173	218	15	6173	6173	NUM
ejpam-6173	218	16	10	10	NUM
ejpam-6173	218	17	of	of	ADP
ejpam-6173	218	18	32	32	NUM
ejpam-6173	218	19	definition	definition	NOUN
ejpam-6173	218	20	5	5	NUM
ejpam-6173	218	21	.	.	PUNCT
ejpam-6173	219	1	let	let	VERB
ejpam-6173	219	2	br	br	VERB
ejpam-6173	219	3	=	=	PUNCT
ejpam-6173	219	4	{	{	PUNCT
ejpam-6173	219	5	x	x	SYM
ejpam-6173	219	6	∈	∈	PROPN
ejpam-6173	219	7	e	e	NOUN
ejpam-6173	219	8	:	:	PUNCT
ejpam-6173	219	9	∥x∥	∥x∥	NOUN
ejpam-6173	219	10	≤	≤	ADJ
ejpam-6173	219	11	r	r	NOUN
ejpam-6173	219	12	}	}	PUNCT
ejpam-6173	219	13	for	for	ADP
ejpam-6173	219	14	all	all	DET
ejpam-6173	219	15	r	r	NOUN
ejpam-6173	219	16	>	>	X
ejpam-6173	219	17	0	0	NUM
ejpam-6173	219	18	.	.	PUNCT
ejpam-6173	220	1	then	then	ADV
ejpam-6173	220	2	a	a	DET
ejpam-6173	220	3	function	function	NOUN
ejpam-6173	220	4	g	g	NOUN
ejpam-6173	220	5	:	:	PUNCT
ejpam-6173	220	6	e	e	X
ejpam-6173	220	7	−→	−→	NOUN
ejpam-6173	220	8	r	r	NOUN
ejpam-6173	220	9	is	be	AUX
ejpam-6173	220	10	said	say	VERB
ejpam-6173	220	11	to	to	PART
ejpam-6173	220	12	be	be	AUX
ejpam-6173	220	13	uniformly	uniformly	ADV
ejpam-6173	220	14	convex	convex	ADJ
ejpam-6173	220	15	on	on	ADP
ejpam-6173	220	16	bounded	bounded	ADJ
ejpam-6173	220	17	sets	set	NOUN
ejpam-6173	220	18	of	of	ADP
ejpam-6173	220	19	e	e	PROPN
ejpam-6173	221	1	[	[	X
ejpam-6173	221	2	48	48	NUM
ejpam-6173	221	3	]	]	PUNCT
ejpam-6173	221	4	if	if	SCONJ
ejpam-6173	221	5	ρr(t	ρr(t	NUM
ejpam-6173	221	6	)	)	PUNCT
ejpam-6173	221	7	>	>	X
ejpam-6173	221	8	0	0	PUNCT
ejpam-6173	222	1	for	for	ADP
ejpam-6173	222	2	all	all	DET
ejpam-6173	222	3	r	r	NOUN
ejpam-6173	222	4	,	,	PUNCT
ejpam-6173	222	5	t	t	X
ejpam-6173	222	6	>	>	X
ejpam-6173	222	7	0	0	NUM
ejpam-6173	222	8	where	where	SCONJ
ejpam-6173	222	9	ρr	ρr	ADV
ejpam-6173	222	10	:	:	PUNCT
ejpam-6173	222	11	[	[	X
ejpam-6173	222	12	0,+∞	0,+∞	NUM
ejpam-6173	222	13	)	)	PUNCT
ejpam-6173	222	14	−→	−→	NOUN
ejpam-6173	222	15	[	[	X
ejpam-6173	222	16	0,+∞	0,+∞	NUM
ejpam-6173	222	17	]	]	X
ejpam-6173	222	18	is	be	AUX
ejpam-6173	222	19	defined	define	VERB
ejpam-6173	222	20	by	by	ADP
ejpam-6173	222	21	ρr(t	ρr(t	NUM
ejpam-6173	222	22	)	)	PUNCT
ejpam-6173	223	1	=	=	SYM
ejpam-6173	223	2	inf	inf	PROPN
ejpam-6173	223	3	x	x	NOUN
ejpam-6173	223	4	,	,	PUNCT
ejpam-6173	223	5	y∈br,∥x−y∥=t	y∈br,∥x−y∥=t	NOUN
ejpam-6173	223	6	,	,	PUNCT
ejpam-6173	223	7	α∈(0,1	α∈(0,1	ADV
ejpam-6173	223	8	)	)	PUNCT
ejpam-6173	223	9	αg(x	αg(x	PUNCT
ejpam-6173	223	10	)	)	PUNCT
ejpam-6173	224	1	+	+	CCONJ
ejpam-6173	224	2	(	(	PUNCT
ejpam-6173	224	3	1−	1−	NUM
ejpam-6173	224	4	α)g(y)−	α)g(y)−	NUM
ejpam-6173	224	5	g[αx+	g[αx+	NOUN
ejpam-6173	224	6	(	(	PUNCT
ejpam-6173	224	7	1−	1−	NUM
ejpam-6173	224	8	α)y	α)y	X
ejpam-6173	224	9	]	]	PUNCT
ejpam-6173	224	10	α(1−	α(1−	PROPN
ejpam-6173	224	11	α	α	X
ejpam-6173	224	12	)	)	PUNCT
ejpam-6173	224	13	for	for	ADP
ejpam-6173	224	14	all	all	DET
ejpam-6173	224	15	t	t	PROPN
ejpam-6173	224	16	>	>	X
ejpam-6173	224	17	0	0	X
ejpam-6173	224	18	.	.	PUNCT
ejpam-6173	225	1	the	the	DET
ejpam-6173	225	2	function	function	NOUN
ejpam-6173	225	3	ρr	ρr	NOUN
ejpam-6173	225	4	is	be	AUX
ejpam-6173	225	5	called	call	VERB
ejpam-6173	225	6	the	the	DET
ejpam-6173	225	7	gauge	gauge	NOUN
ejpam-6173	225	8	of	of	ADP
ejpam-6173	225	9	uniform	uniform	ADJ
ejpam-6173	225	10	convexity	convexity	NOUN
ejpam-6173	225	11	of	of	ADP
ejpam-6173	225	12	g.	g.	PROPN
ejpam-6173	225	13	the	the	DET
ejpam-6173	225	14	function	function	NOUN
ejpam-6173	225	15	g	g	PROPN
ejpam-6173	225	16	is	be	AUX
ejpam-6173	225	17	said	say	VERB
ejpam-6173	225	18	to	to	PART
ejpam-6173	225	19	be	be	AUX
ejpam-6173	225	20	uniformly	uniformly	ADV
ejpam-6173	225	21	convex	convex	ADJ
ejpam-6173	225	22	if	if	SCONJ
ejpam-6173	225	23	the	the	DET
ejpam-6173	225	24	function	function	NOUN
ejpam-6173	225	25	δg	δg	VERB
ejpam-6173	225	26	:	:	PUNCT
ejpam-6173	226	1	[	[	X
ejpam-6173	226	2	0,+∞	0,+∞	NUM
ejpam-6173	226	3	)	)	PUNCT
ejpam-6173	227	1	−→	−→	NOUN
ejpam-6173	228	1	[	[	X
ejpam-6173	228	2	0,+∞	0,+∞	NUM
ejpam-6173	228	3	]	]	PUNCT
ejpam-6173	228	4	,	,	PUNCT
ejpam-6173	228	5	defined	define	VERB
ejpam-6173	228	6	by	by	ADP
ejpam-6173	228	7	δg(t	δg(t	NOUN
ejpam-6173	228	8	)	)	PUNCT
ejpam-6173	228	9	=	=	SYM
ejpam-6173	228	10	sup	sup	NOUN
ejpam-6173	228	11	∥x−y∥=t	∥x−y∥=t	NOUN
ejpam-6173	228	12	{	{	PUNCT
ejpam-6173	228	13	1	1	NUM
ejpam-6173	228	14	2	2	NUM
ejpam-6173	228	15	g(x	g(x	NOUN
ejpam-6173	228	16	)	)	PUNCT
ejpam-6173	229	1	+	+	CCONJ
ejpam-6173	229	2	1	1	NUM
ejpam-6173	229	3	2	2	NUM
ejpam-6173	229	4	g(y)−	g(y)−	NOUN
ejpam-6173	229	5	g	g	NOUN
ejpam-6173	229	6	(	(	PUNCT
ejpam-6173	229	7	x+	x+	PROPN
ejpam-6173	229	8	y	y	PROPN
ejpam-6173	229	9	2	2	NUM
ejpam-6173	229	10	)	)	PUNCT
ejpam-6173	229	11	}	}	PUNCT
ejpam-6173	229	12	satisfies	satisfy	VERB
ejpam-6173	229	13	that	that	SCONJ
ejpam-6173	229	14	limt↓0	limt↓0	PROPN
ejpam-6173	229	15	δg(t	δg(t	NUM
ejpam-6173	229	16	)	)	PUNCT
ejpam-6173	229	17	t	t	NOUN
ejpam-6173	229	18	=	=	SYM
ejpam-6173	229	19	0	0	X
ejpam-6173	229	20	.	.	PUNCT
ejpam-6173	230	1	lemma	lemma	PROPN
ejpam-6173	230	2	8	8	NUM
ejpam-6173	230	3	.	.	PUNCT
ejpam-6173	231	1	[	[	X
ejpam-6173	231	2	49	49	NUM
ejpam-6173	231	3	]	]	PUNCT
ejpam-6173	231	4	let	let	VERB
ejpam-6173	231	5	c	c	PRON
ejpam-6173	231	6	be	be	AUX
ejpam-6173	231	7	a	a	DET
ejpam-6173	231	8	nonempty	nonempty	ADJ
ejpam-6173	231	9	,	,	PUNCT
ejpam-6173	231	10	closed	closed	ADJ
ejpam-6173	231	11	and	and	CCONJ
ejpam-6173	231	12	convex	convex	PROPN
ejpam-6173	231	13	subset	subset	NOUN
ejpam-6173	231	14	of	of	ADP
ejpam-6173	231	15	int(domf	int(domf	NOUN
ejpam-6173	231	16	)	)	PUNCT
ejpam-6173	231	17	and	and	CCONJ
ejpam-6173	231	18	t	t	PROPN
ejpam-6173	231	19	:	:	PUNCT
ejpam-6173	231	20	c	c	X
ejpam-6173	231	21	→	→	PUNCT
ejpam-6173	231	22	c	c	X
ejpam-6173	231	23	be	be	AUX
ejpam-6173	231	24	a	a	DET
ejpam-6173	231	25	quasi	quasi	ADJ
ejpam-6173	231	26	-	-	ADJ
ejpam-6173	231	27	bregman	bregman	ADJ
ejpam-6173	231	28	nonexpansive	nonexpansive	ADJ
ejpam-6173	231	29	mappings	mapping	NOUN
ejpam-6173	231	30	with	with	ADP
ejpam-6173	231	31	respect	respect	NOUN
ejpam-6173	231	32	to	to	ADP
ejpam-6173	231	33	f	f	PROPN
ejpam-6173	231	34	.	.	PUNCT
ejpam-6173	232	1	then	then	ADV
ejpam-6173	232	2	f	f	PROPN
ejpam-6173	232	3	(	(	PUNCT
ejpam-6173	232	4	t	t	PROPN
ejpam-6173	232	5	)	)	PUNCT
ejpam-6173	232	6	is	be	AUX
ejpam-6173	232	7	closed	close	VERB
ejpam-6173	232	8	and	and	CCONJ
ejpam-6173	232	9	convex	convex	NOUN
ejpam-6173	232	10	.	.	PUNCT
ejpam-6173	233	1	definition	definition	NOUN
ejpam-6173	233	2	6	6	NUM
ejpam-6173	233	3	.	.	PUNCT
ejpam-6173	234	1	let	let	VERB
ejpam-6173	234	2	c	c	PRON
ejpam-6173	234	3	be	be	AUX
ejpam-6173	234	4	a	a	DET
ejpam-6173	234	5	nonempty	nonempty	ADJ
ejpam-6173	234	6	,	,	PUNCT
ejpam-6173	234	7	closed	closed	ADJ
ejpam-6173	234	8	and	and	CCONJ
ejpam-6173	234	9	convex	convex	ADJ
ejpam-6173	234	10	subsets	subset	NOUN
ejpam-6173	234	11	of	of	ADP
ejpam-6173	234	12	a	a	DET
ejpam-6173	234	13	real	real	ADJ
ejpam-6173	234	14	reflexive	reflexive	ADJ
ejpam-6173	234	15	banach	banach	NOUN
ejpam-6173	234	16	space	space	NOUN
ejpam-6173	234	17	and	and	CCONJ
ejpam-6173	234	18	let	let	VERB
ejpam-6173	234	19	φ	φ	PROPN
ejpam-6173	234	20	be	be	AUX
ejpam-6173	234	21	a	a	DET
ejpam-6173	234	22	lower	low	ADJ
ejpam-6173	234	23	semicontinuous	semicontinuous	ADJ
ejpam-6173	234	24	and	and	CCONJ
ejpam-6173	234	25	convex	convex	VERB
ejpam-6173	234	26	functional	functional	ADJ
ejpam-6173	234	27	from	from	ADP
ejpam-6173	234	28	c	c	NOUN
ejpam-6173	234	29	to	to	ADP
ejpam-6173	234	30	r	r	NOUN
ejpam-6173	234	31	and	and	CCONJ
ejpam-6173	234	32	ψ	ψ	NOUN
ejpam-6173	234	33	:	:	PUNCT
ejpam-6173	234	34	c	c	X
ejpam-6173	234	35	→	→	SYM
ejpam-6173	234	36	e∗	e∗	PROPN
ejpam-6173	234	37	be	be	AUX
ejpam-6173	234	38	a	a	DET
ejpam-6173	234	39	continuous	continuous	ADJ
ejpam-6173	234	40	monotone	monotone	ADJ
ejpam-6173	234	41	mapping	mapping	NOUN
ejpam-6173	234	42	.	.	PUNCT
ejpam-6173	235	1	let	let	VERB
ejpam-6173	235	2	θ	θ	NOUN
ejpam-6173	235	3	:	:	PUNCT
ejpam-6173	235	4	c	c	X
ejpam-6173	235	5	×	×	NOUN
ejpam-6173	235	6	c	c	NOUN
ejpam-6173	235	7	→	→	PUNCT
ejpam-6173	235	8	r	r	NOUN
ejpam-6173	235	9	be	be	AUX
ejpam-6173	235	10	a	a	DET
ejpam-6173	235	11	bifunctional	bifunctional	ADJ
ejpam-6173	235	12	satisfying	satisfying	NOUN
ejpam-6173	235	13	(	(	PUNCT
ejpam-6173	235	14	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	235	15	)	)	PUNCT
ejpam-6173	235	16	.	.	PUNCT
ejpam-6173	236	1	the	the	DET
ejpam-6173	236	2	mixed	mixed	ADJ
ejpam-6173	236	3	resolvent	resolvent	NOUN
ejpam-6173	236	4	of	of	ADP
ejpam-6173	236	5	θ	θ	PROPN
ejpam-6173	236	6	is	be	AUX
ejpam-6173	236	7	the	the	DET
ejpam-6173	236	8	operator	operator	NOUN
ejpam-6173	236	9	resfθ	resfθ	NOUN
ejpam-6173	236	10	,	,	PUNCT
ejpam-6173	236	11	φ	φ	X
ejpam-6173	236	12	,	,	PUNCT
ejpam-6173	236	13	ψ	ψ	X
ejpam-6173	236	14	:	:	PUNCT
ejpam-6173	236	15	e	e	X
ejpam-6173	236	16	→	→	SYM
ejpam-6173	236	17	2c	2c	NUM
ejpam-6173	236	18	resfθ	resfθ	NOUN
ejpam-6173	236	19	,	,	PUNCT
ejpam-6173	236	20	φ	φ	NOUN
ejpam-6173	236	21	,	,	PUNCT
ejpam-6173	236	22	ψ(x	ψ(x	NOUN
ejpam-6173	236	23	)	)	PUNCT
ejpam-6173	236	24	=	=	PRON
ejpam-6173	237	1	{	{	PUNCT
ejpam-6173	237	2	z	z	NOUN
ejpam-6173	237	3	∈	∈	PROPN
ejpam-6173	237	4	c	c	NOUN
ejpam-6173	237	5	:	:	PUNCT
ejpam-6173	238	1	θ(z	θ(z	NOUN
ejpam-6173	238	2	,	,	PUNCT
ejpam-6173	238	3	y	y	NOUN
ejpam-6173	238	4	)	)	PUNCT
ejpam-6173	238	5	+	+	CCONJ
ejpam-6173	238	6	φ(y	φ(y	ADJ
ejpam-6173	238	7	)	)	PUNCT
ejpam-6173	238	8	+	+	CCONJ
ejpam-6173	238	9	⟨ψz	⟨ψz	NOUN
ejpam-6173	238	10	,	,	PUNCT
ejpam-6173	238	11	y	y	PROPN
ejpam-6173	238	12	−	−	PROPN
ejpam-6173	238	13	z⟩+	z⟩+	PROPN
ejpam-6173	238	14	⟨∇f(z)−∇f(x	⟨∇f(z)−∇f(x	NOUN
ejpam-6173	238	15	)	)	PUNCT
ejpam-6173	238	16	,	,	PUNCT
ejpam-6173	238	17	y	y	PROPN
ejpam-6173	238	18	−	−	PROPN
ejpam-6173	238	19	z⟩	z⟩	NUM
ejpam-6173	238	20	≥	≥	PROPN
ejpam-6173	238	21	φ(z	φ(z	PROPN
ejpam-6173	238	22	)	)	PUNCT
ejpam-6173	238	23	,	,	PUNCT
ejpam-6173	238	24	for	for	ADP
ejpam-6173	238	25	all	all	DET
ejpam-6173	238	26	y	y	PROPN
ejpam-6173	238	27	∈	∈	PROPN
ejpam-6173	238	28	c	c	X
ejpam-6173	238	29	}	}	PUNCT
ejpam-6173	238	30	.	.	PUNCT
ejpam-6173	239	1	(	(	PUNCT
ejpam-6173	239	2	2.9	2.9	NUM
ejpam-6173	239	3	)	)	PUNCT
ejpam-6173	239	4	lemma	lemma	PROPN
ejpam-6173	239	5	9	9	NUM
ejpam-6173	239	6	.	.	PUNCT
ejpam-6173	240	1	[	[	X
ejpam-6173	240	2	50	50	NUM
ejpam-6173	240	3	]	]	PUNCT
ejpam-6173	240	4	let	let	VERB
ejpam-6173	240	5	f	f	PRON
ejpam-6173	240	6	:	:	PUNCT
ejpam-6173	240	7	e	e	X
ejpam-6173	240	8	→	→	PUNCT
ejpam-6173	240	9	(	(	PUNCT
ejpam-6173	240	10	−∞,+∞	−∞,+∞	ADV
ejpam-6173	240	11	]	]	PUNCT
ejpam-6173	240	12	be	be	VERB
ejpam-6173	240	13	a	a	DET
ejpam-6173	240	14	coercive	coercive	ADJ
ejpam-6173	240	15	and	and	CCONJ
ejpam-6173	240	16	gâteaux	gâteaux	ADJ
ejpam-6173	240	17	differentiable	differentiable	ADJ
ejpam-6173	240	18	function	function	NOUN
ejpam-6173	240	19	.	.	PUNCT
ejpam-6173	241	1	let	let	VERB
ejpam-6173	241	2	c	c	PRON
ejpam-6173	241	3	be	be	AUX
ejpam-6173	241	4	a	a	DET
ejpam-6173	241	5	closed	closed	ADJ
ejpam-6173	241	6	and	and	CCONJ
ejpam-6173	241	7	convex	convex	NOUN
ejpam-6173	241	8	subset	subset	NOUN
ejpam-6173	241	9	of	of	ADP
ejpam-6173	241	10	e.	e.	PROPN
ejpam-6173	241	11	assume	assume	VERB
ejpam-6173	241	12	that	that	SCONJ
ejpam-6173	241	13	φ	φ	PROPN
ejpam-6173	241	14	:	:	PUNCT
ejpam-6173	241	15	c	c	X
ejpam-6173	241	16	→	→	SYM
ejpam-6173	241	17	r	r	NOUN
ejpam-6173	241	18	be	be	AUX
ejpam-6173	241	19	a	a	DET
ejpam-6173	241	20	lower	low	ADJ
ejpam-6173	241	21	semicontinuous	semicontinuous	ADJ
ejpam-6173	241	22	and	and	CCONJ
ejpam-6173	241	23	convex	convex	ADJ
ejpam-6173	241	24	functional	functional	ADJ
ejpam-6173	241	25	,	,	PUNCT
ejpam-6173	241	26	ψ	ψ	X
ejpam-6173	241	27	:	:	PUNCT
ejpam-6173	241	28	c	c	X
ejpam-6173	241	29	→	→	SYM
ejpam-6173	241	30	e∗	e∗	PROPN
ejpam-6173	241	31	be	be	AUX
ejpam-6173	241	32	a	a	DET
ejpam-6173	241	33	continuous	continuous	ADJ
ejpam-6173	241	34	monotone	monotone	ADJ
ejpam-6173	241	35	mapping	mapping	NOUN
ejpam-6173	241	36	and	and	CCONJ
ejpam-6173	241	37	the	the	DET
ejpam-6173	241	38	bifunctional	bifunctional	ADJ
ejpam-6173	241	39	θ	θ	NOUN
ejpam-6173	241	40	:	:	PUNCT
ejpam-6173	242	1	c	c	X
ejpam-6173	242	2	×	×	NOUN
ejpam-6173	242	3	c	c	NOUN
ejpam-6173	242	4	→	→	SYM
ejpam-6173	242	5	r	r	NOUN
ejpam-6173	242	6	satisfies	satisfie	NOUN
ejpam-6173	242	7	conditions	condition	NOUN
ejpam-6173	242	8	(	(	PUNCT
ejpam-6173	242	9	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	242	10	)	)	PUNCT
ejpam-6173	242	11	,	,	PUNCT
ejpam-6173	242	12	then	then	ADV
ejpam-6173	242	13	dom(resfθ	dom(resfθ	PROPN
ejpam-6173	242	14	,	,	PUNCT
ejpam-6173	242	15	φ	φ	PROPN
ejpam-6173	242	16	,	,	PUNCT
ejpam-6173	242	17	ψ	ψ	NOUN
ejpam-6173	242	18	)	)	PUNCT
ejpam-6173	242	19	=	=	SYM
ejpam-6173	242	20	e.	e.	PROPN
ejpam-6173	242	21	lemma	lemma	PROPN
ejpam-6173	242	22	10	10	NUM
ejpam-6173	242	23	.	.	PUNCT
ejpam-6173	243	1	[	[	X
ejpam-6173	243	2	50	50	NUM
ejpam-6173	243	3	]	]	PUNCT
ejpam-6173	243	4	let	let	VERB
ejpam-6173	243	5	f	f	PRON
ejpam-6173	243	6	:	:	PUNCT
ejpam-6173	243	7	e	e	X
ejpam-6173	243	8	→	→	PUNCT
ejpam-6173	243	9	(	(	PUNCT
ejpam-6173	243	10	−∞,+∞	−∞,+∞	ADV
ejpam-6173	243	11	]	]	PUNCT
ejpam-6173	243	12	be	be	VERB
ejpam-6173	243	13	a	a	DET
ejpam-6173	243	14	legendre	legendre	NOUN
ejpam-6173	243	15	function	function	NOUN
ejpam-6173	243	16	.	.	PUNCT
ejpam-6173	244	1	let	let	VERB
ejpam-6173	244	2	c	c	PRON
ejpam-6173	244	3	be	be	AUX
ejpam-6173	244	4	a	a	DET
ejpam-6173	244	5	closed	closed	ADJ
ejpam-6173	244	6	and	and	CCONJ
ejpam-6173	244	7	convex	convex	NOUN
ejpam-6173	244	8	subset	subset	NOUN
ejpam-6173	244	9	of	of	ADP
ejpam-6173	244	10	e.	e.	PROPN
ejpam-6173	244	11	if	if	SCONJ
ejpam-6173	244	12	the	the	DET
ejpam-6173	244	13	bifunction	bifunction	NOUN
ejpam-6173	244	14	θ	θ	NOUN
ejpam-6173	244	15	:	:	PUNCT
ejpam-6173	244	16	c	c	X
ejpam-6173	244	17	×	×	NOUN
ejpam-6173	244	18	c	c	NOUN
ejpam-6173	244	19	→	→	SYM
ejpam-6173	244	20	r	r	NOUN
ejpam-6173	244	21	satisfies	satisfie	NOUN
ejpam-6173	244	22	conditions	condition	NOUN
ejpam-6173	244	23	(	(	PUNCT
ejpam-6173	244	24	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	244	25	)	)	PUNCT
ejpam-6173	244	26	,	,	PUNCT
ejpam-6173	244	27	then	then	ADV
ejpam-6173	244	28	(	(	PUNCT
ejpam-6173	244	29	i	i	NOUN
ejpam-6173	244	30	)	)	PUNCT
ejpam-6173	244	31	resfθ	resfθ	PROPN
ejpam-6173	244	32	,	,	PUNCT
ejpam-6173	244	33	φ	φ	X
ejpam-6173	244	34	,	,	PUNCT
ejpam-6173	244	35	ψ	ψ	X
ejpam-6173	244	36	is	be	AUX
ejpam-6173	244	37	single	single	ADV
ejpam-6173	244	38	-	-	PUNCT
ejpam-6173	244	39	valued	value	VERB
ejpam-6173	244	40	;	;	PUNCT
ejpam-6173	244	41	(	(	PUNCT
ejpam-6173	244	42	ii	ii	NOUN
ejpam-6173	244	43	)	)	PUNCT
ejpam-6173	244	44	resfθ	resfθ	PROPN
ejpam-6173	244	45	,	,	PUNCT
ejpam-6173	244	46	φ	φ	X
ejpam-6173	244	47	,	,	PUNCT
ejpam-6173	244	48	ψ	ψ	X
ejpam-6173	244	49	is	be	AUX
ejpam-6173	244	50	a	a	DET
ejpam-6173	244	51	bfne	bfne	ADJ
ejpam-6173	244	52	operator	operator	NOUN
ejpam-6173	244	53	;	;	PUNCT
ejpam-6173	244	54	(	(	PUNCT
ejpam-6173	244	55	iii	iii	X
ejpam-6173	244	56	)	)	PUNCT
ejpam-6173	244	57	f	f	PROPN
ejpam-6173	244	58	(	(	PUNCT
ejpam-6173	244	59	resfθ	resfθ	PROPN
ejpam-6173	244	60	,	,	PUNCT
ejpam-6173	244	61	φ	φ	X
ejpam-6173	244	62	,	,	PUNCT
ejpam-6173	244	63	ψ	ψ	X
ejpam-6173	244	64	)	)	PUNCT
ejpam-6173	245	1	=	=	SYM
ejpam-6173	245	2	gmep(θ	gmep(θ	PROPN
ejpam-6173	245	3	,	,	PUNCT
ejpam-6173	245	4	φ	φ	PROPN
ejpam-6173	245	5	,	,	PUNCT
ejpam-6173	245	6	ψ	ψ	NOUN
ejpam-6173	245	7	)	)	PUNCT
ejpam-6173	245	8	;	;	PUNCT
ejpam-6173	245	9	(	(	PUNCT
ejpam-6173	245	10	iv	iv	X
ejpam-6173	245	11	)	)	PUNCT
ejpam-6173	245	12	gmep(θ	gmep(θ	PROPN
ejpam-6173	245	13	,	,	PUNCT
ejpam-6173	245	14	φ	φ	PROPN
ejpam-6173	245	15	,	,	PUNCT
ejpam-6173	245	16	ψ	ψ	NOUN
ejpam-6173	245	17	)	)	PUNCT
ejpam-6173	245	18	is	be	AUX
ejpam-6173	245	19	closed	close	VERB
ejpam-6173	245	20	and	and	CCONJ
ejpam-6173	245	21	convex	convex	ADJ
ejpam-6173	245	22	;	;	PUNCT
ejpam-6173	245	23	(	(	PUNCT
ejpam-6173	245	24	v	v	NOUN
ejpam-6173	245	25	)	)	PUNCT
ejpam-6173	245	26	df	df	NOUN
ejpam-6173	245	27	(	(	PUNCT
ejpam-6173	245	28	p	p	X
ejpam-6173	245	29	,	,	PUNCT
ejpam-6173	245	30	resfθ	resfθ	PROPN
ejpam-6173	245	31	,	,	PUNCT
ejpam-6173	245	32	φ	φ	NOUN
ejpam-6173	245	33	,	,	PUNCT
ejpam-6173	245	34	ψ(x	ψ(x	NOUN
ejpam-6173	245	35	)	)	PUNCT
ejpam-6173	245	36	)	)	PUNCT
ejpam-6173	246	1	+	+	X
ejpam-6173	246	2	df	df	NOUN
ejpam-6173	246	3	(	(	PUNCT
ejpam-6173	246	4	resfθ	resfθ	PROPN
ejpam-6173	246	5	,	,	PUNCT
ejpam-6173	246	6	φ	φ	NOUN
ejpam-6173	246	7	,	,	PUNCT
ejpam-6173	246	8	ψ(x	ψ(x	NOUN
ejpam-6173	246	9	)	)	PUNCT
ejpam-6173	246	10	,	,	PUNCT
ejpam-6173	246	11	x	x	X
ejpam-6173	246	12	)	)	PUNCT
ejpam-6173	246	13	≤	≤	NUM
ejpam-6173	246	14	df	df	NOUN
ejpam-6173	246	15	(	(	PUNCT
ejpam-6173	246	16	p	p	X
ejpam-6173	246	17	,	,	PUNCT
ejpam-6173	246	18	x	x	NOUN
ejpam-6173	246	19	)	)	PUNCT
ejpam-6173	246	20	,	,	PUNCT
ejpam-6173	246	21	for	for	ADP
ejpam-6173	246	22	all	all	DET
ejpam-6173	246	23	p	p	PROPN
ejpam-6173	246	24	∈	∈	PROPN
ejpam-6173	246	25	f	f	X
ejpam-6173	246	26	(	(	PUNCT
ejpam-6173	246	27	resfθ	resfθ	PROPN
ejpam-6173	246	28	,	,	PUNCT
ejpam-6173	246	29	φ	φ	X
ejpam-6173	246	30	,	,	PUNCT
ejpam-6173	246	31	ψ	ψ	NOUN
ejpam-6173	246	32	)	)	PUNCT
ejpam-6173	246	33	,	,	PUNCT
ejpam-6173	246	34	x	x	PUNCT
ejpam-6173	246	35	∈	∈	PROPN
ejpam-6173	246	36	e.	e.	PROPN
ejpam-6173	246	37	v.	v.	PROPN
ejpam-6173	246	38	darvish	darvish	PROPN
ejpam-6173	246	39	et	et	PROPN
ejpam-6173	246	40	al	al	PROPN
ejpam-6173	246	41	.	.	PUNCT
ejpam-6173	246	42	/	/	SYM
ejpam-6173	246	43	eur	eur	PROPN
ejpam-6173	246	44	.	.	PUNCT
ejpam-6173	247	1	j.	j.	PROPN
ejpam-6173	247	2	pure	pure	PROPN
ejpam-6173	247	3	appl	appl	PROPN
ejpam-6173	247	4	.	.	PROPN
ejpam-6173	247	5	math	math	PROPN
ejpam-6173	247	6	,	,	PUNCT
ejpam-6173	247	7	18	18	NUM
ejpam-6173	247	8	(	(	PUNCT
ejpam-6173	247	9	3	3	NUM
ejpam-6173	247	10	)	)	PUNCT
ejpam-6173	247	11	(	(	PUNCT
ejpam-6173	247	12	2025	2025	NUM
ejpam-6173	247	13	)	)	PUNCT
ejpam-6173	247	14	,	,	PUNCT
ejpam-6173	247	15	6173	6173	NUM
ejpam-6173	247	16	11	11	NUM
ejpam-6173	247	17	of	of	ADP
ejpam-6173	247	18	32	32	NUM
ejpam-6173	247	19	let	let	VERB
ejpam-6173	247	20	θ	θ	NOUN
ejpam-6173	247	21	:	:	PUNCT
ejpam-6173	247	22	c	c	X
ejpam-6173	247	23	×	×	NOUN
ejpam-6173	247	24	c	c	NOUN
ejpam-6173	247	25	→	→	PUNCT
ejpam-6173	247	26	r	r	NOUN
ejpam-6173	247	27	be	be	AUX
ejpam-6173	247	28	a	a	DET
ejpam-6173	247	29	bifunction	bifunction	NOUN
ejpam-6173	247	30	and	and	CCONJ
ejpam-6173	247	31	define	define	VERB
ejpam-6173	247	32	the	the	DET
ejpam-6173	247	33	mapping	mapping	NOUN
ejpam-6173	247	34	bθ	bθ	NOUN
ejpam-6173	247	35	:	:	PUNCT
ejpam-6173	247	36	e	e	X
ejpam-6173	247	37	→	→	SYM
ejpam-6173	247	38	2e	2e	NUM
ejpam-6173	247	39	∗	∗	NOUN
ejpam-6173	247	40	in	in	ADP
ejpam-6173	247	41	the	the	DET
ejpam-6173	247	42	following	following	ADJ
ejpam-6173	247	43	way	way	NOUN
ejpam-6173	247	44	:	:	PUNCT
ejpam-6173	247	45	bθ(x	bθ(x	PUNCT
ejpam-6173	247	46	)	)	PUNCT
ejpam-6173	247	47	:	:	PUNCT
ejpam-6173	247	48	=	=	PUNCT
ejpam-6173	247	49			PUNCT
ejpam-6173	247	50	{	{	PUNCT
ejpam-6173	247	51	x∗	x∗	PROPN
ejpam-6173	247	52	∈	∈	PROPN
ejpam-6173	247	53	e∗	e∗	PROPN
ejpam-6173	247	54	:	:	PUNCT
ejpam-6173	247	55	θ(x	θ(x	PROPN
ejpam-6173	247	56	,	,	PUNCT
ejpam-6173	247	57	y	y	PROPN
ejpam-6173	247	58	)	)	PUNCT
ejpam-6173	247	59	+	+	CCONJ
ejpam-6173	247	60	φ(y	φ(y	ADJ
ejpam-6173	247	61	)	)	PUNCT
ejpam-6173	247	62	+	+	CCONJ
ejpam-6173	248	1	⟨ψx	⟨ψx	PROPN
ejpam-6173	248	2	,	,	PUNCT
ejpam-6173	248	3	y	y	PROPN
ejpam-6173	248	4	−	−	PROPN
ejpam-6173	248	5	x⟩	x⟩	PUNCT
ejpam-6173	248	6	≥	≥	PROPN
ejpam-6173	248	7	⟨x∗	⟨x∗	PROPN
ejpam-6173	248	8	,	,	PUNCT
ejpam-6173	248	9	y	y	PROPN
ejpam-6173	248	10	−	−	PROPN
ejpam-6173	248	11	x⟩+	x⟩+	PROPN
ejpam-6173	248	12	φ(x	φ(x	PROPN
ejpam-6173	248	13	)	)	PUNCT
ejpam-6173	248	14	for	for	ADP
ejpam-6173	248	15	all	all	DET
ejpam-6173	248	16	y	y	PROPN
ejpam-6173	248	17	∈	∈	PROPN
ejpam-6173	248	18	c	c	X
ejpam-6173	248	19	}	}	PUNCT
ejpam-6173	248	20	,	,	PUNCT
ejpam-6173	248	21	x	x	PUNCT
ejpam-6173	248	22	∈	∈	PROPN
ejpam-6173	248	23	c	c	NOUN
ejpam-6173	248	24	,	,	PUNCT
ejpam-6173	248	25	∅	∅	NOUN
ejpam-6173	248	26	x	x	SYM
ejpam-6173	248	27	/∈	/∈	PROPN
ejpam-6173	248	28	c.	c.	NOUN
ejpam-6173	248	29	(	(	PUNCT
ejpam-6173	248	30	2.10	2.10	NUM
ejpam-6173	248	31	)	)	PUNCT
ejpam-6173	248	32	lemma	lemma	PROPN
ejpam-6173	248	33	11	11	NUM
ejpam-6173	248	34	.	.	PUNCT
ejpam-6173	249	1	[	[	X
ejpam-6173	249	2	51	51	NUM
ejpam-6173	249	3	]	]	PUNCT
ejpam-6173	249	4	let	let	AUX
ejpam-6173	249	5	e	e	PRON
ejpam-6173	249	6	be	be	AUX
ejpam-6173	249	7	a	a	DET
ejpam-6173	249	8	banach	banach	NOUN
ejpam-6173	249	9	space	space	NOUN
ejpam-6173	249	10	and	and	CCONJ
ejpam-6173	249	11	f	f	NOUN
ejpam-6173	249	12	:	:	PUNCT
ejpam-6173	249	13	er	er	INTJ
ejpam-6173	249	14	be	be	AUX
ejpam-6173	249	15	a	a	DET
ejpam-6173	249	16	gâteaux	gâteaux	ADV
ejpam-6173	249	17	differentiable	differentiable	ADJ
ejpam-6173	249	18	function	function	NOUN
ejpam-6173	249	19	which	which	PRON
ejpam-6173	249	20	is	be	AUX
ejpam-6173	249	21	uniformly	uniformly	ADV
ejpam-6173	249	22	convex	convex	ADJ
ejpam-6173	249	23	on	on	ADP
ejpam-6173	249	24	bounded	bounded	ADJ
ejpam-6173	249	25	subsets	subset	NOUN
ejpam-6173	249	26	of	of	ADP
ejpam-6173	249	27	e.	e.	PROPN
ejpam-6173	249	28	suppose	suppose	VERB
ejpam-6173	249	29	that	that	SCONJ
ejpam-6173	249	30	{	{	PUNCT
ejpam-6173	249	31	xn	xn	X
ejpam-6173	249	32	}	}	PUNCT
ejpam-6173	249	33	and	and	CCONJ
ejpam-6173	249	34	{	{	PUNCT
ejpam-6173	249	35	yn	yn	NOUN
ejpam-6173	249	36	}	}	PUNCT
ejpam-6173	249	37	are	be	AUX
ejpam-6173	249	38	two	two	NUM
ejpam-6173	249	39	sequenecs	sequenec	NOUN
ejpam-6173	249	40	in	in	ADP
ejpam-6173	249	41	e.	e.	PROPN
ejpam-6173	249	42	then	then	ADV
ejpam-6173	249	43	,	,	PUNCT
ejpam-6173	249	44	lim	lim	PROPN
ejpam-6173	249	45	n→+∞	n→+∞	VERB
ejpam-6173	249	46	df	df	PROPN
ejpam-6173	249	47	(	(	PUNCT
ejpam-6173	249	48	xn	xn	PROPN
ejpam-6173	249	49	,	,	PUNCT
ejpam-6173	249	50	yn	yn	PROPN
ejpam-6173	249	51	)	)	PUNCT
ejpam-6173	249	52	=	=	SYM
ejpam-6173	249	53	0	0	PUNCT
ejpam-6173	250	1	if	if	SCONJ
ejpam-6173	250	2	and	and	CCONJ
ejpam-6173	250	3	only	only	ADV
ejpam-6173	250	4	if	if	SCONJ
ejpam-6173	250	5	lim	lim	PROPN
ejpam-6173	250	6	n→+∞	n→+∞	VERB
ejpam-6173	250	7	∥xn	∥xn	PROPN
ejpam-6173	250	8	−	−	PROPN
ejpam-6173	250	9	yn∥	yn∥	NOUN
ejpam-6173	250	10	=	=	SYM
ejpam-6173	250	11	0	0	X
ejpam-6173	250	12	.	.	PUNCT
ejpam-6173	251	1	lemma	lemma	PROPN
ejpam-6173	251	2	12	12	NUM
ejpam-6173	251	3	.	.	PUNCT
ejpam-6173	252	1	[	[	X
ejpam-6173	252	2	52	52	NUM
ejpam-6173	252	3	]	]	PUNCT
ejpam-6173	252	4	let	let	AUX
ejpam-6173	252	5	{	{	PUNCT
ejpam-6173	252	6	an	an	PRON
ejpam-6173	252	7	}	}	PUNCT
ejpam-6173	252	8	be	be	AUX
ejpam-6173	252	9	a	a	DET
ejpam-6173	252	10	sequence	sequence	NOUN
ejpam-6173	252	11	of	of	ADP
ejpam-6173	252	12	nonnegative	nonnegative	ADJ
ejpam-6173	252	13	real	real	ADJ
ejpam-6173	252	14	numbers	number	NOUN
ejpam-6173	252	15	,	,	PUNCT
ejpam-6173	252	16	{	{	PUNCT
ejpam-6173	252	17	αn	αn	NOUN
ejpam-6173	252	18	}	}	PUNCT
ejpam-6173	252	19	be	be	AUX
ejpam-6173	252	20	a	a	DET
ejpam-6173	252	21	sequence	sequence	NOUN
ejpam-6173	252	22	in	in	ADP
ejpam-6173	252	23	(	(	PUNCT
ejpam-6173	252	24	0	0	NUM
ejpam-6173	252	25	,	,	PUNCT
ejpam-6173	252	26	1	1	NUM
ejpam-6173	252	27	)	)	PUNCT
ejpam-6173	252	28	with	with	ADP
ejpam-6173	252	29	+	+	ADJ
ejpam-6173	252	30	∞∑	∞∑	NUM
ejpam-6173	252	31	n=1	n=1	ADP
ejpam-6173	252	32	αn	αn	NOUN
ejpam-6173	252	33	=	=	PUNCT
ejpam-6173	253	1	+	+	NOUN
ejpam-6173	253	2	∞	∞	NUM
ejpam-6173	253	3	and	and	CCONJ
ejpam-6173	253	4	{	{	PUNCT
ejpam-6173	253	5	bn	bn	PART
ejpam-6173	253	6	}	}	PUNCT
ejpam-6173	253	7	be	be	AUX
ejpam-6173	253	8	a	a	DET
ejpam-6173	253	9	sequence	sequence	NOUN
ejpam-6173	253	10	of	of	ADP
ejpam-6173	253	11	real	real	ADJ
ejpam-6173	253	12	numbers	number	NOUN
ejpam-6173	253	13	.	.	PUNCT
ejpam-6173	254	1	assume	assume	VERB
ejpam-6173	254	2	that	that	PRON
ejpam-6173	254	3	an+1	an+1	VERB
ejpam-6173	254	4	≤	≤	NOUN
ejpam-6173	254	5	(	(	PUNCT
ejpam-6173	254	6	1−	1−	NUM
ejpam-6173	254	7	αn)an	αn)an	PROPN
ejpam-6173	255	1	+	+	NUM
ejpam-6173	256	1	αnbn	αnbn	NOUN
ejpam-6173	256	2	,	,	PUNCT
ejpam-6173	256	3	for	for	ADP
ejpam-6173	256	4	all	all	DET
ejpam-6173	256	5	n	n	PRON
ejpam-6173	256	6	≥	≥	NOUN
ejpam-6173	256	7	1	1	NUM
ejpam-6173	256	8	.	.	PUNCT
ejpam-6173	257	1	if	if	SCONJ
ejpam-6173	257	2	lim	lim	PROPN
ejpam-6173	257	3	sup	sup	PROPN
ejpam-6173	257	4	k→+∞	k→+∞	PROPN
ejpam-6173	257	5	bnk	bnk	PROPN
ejpam-6173	257	6	≤	≤	NOUN
ejpam-6173	257	7	0	0	NUM
ejpam-6173	257	8	for	for	ADP
ejpam-6173	257	9	every	every	DET
ejpam-6173	257	10	subsequence	subsequence	NOUN
ejpam-6173	257	11	{	{	PUNCT
ejpam-6173	257	12	ank	ank	PROPN
ejpam-6173	257	13	}	}	PUNCT
ejpam-6173	257	14	of	of	ADP
ejpam-6173	257	15	{	{	PUNCT
ejpam-6173	257	16	an	an	PRON
ejpam-6173	257	17	}	}	PUNCT
ejpam-6173	257	18	satisfying	satisfy	VERB
ejpam-6173	257	19	lim	lim	PROPN
ejpam-6173	257	20	inf	inf	PROPN
ejpam-6173	257	21	k→+∞	k→+∞	PROPN
ejpam-6173	257	22	(	(	PUNCT
ejpam-6173	257	23	ank+1	ank+1	PROPN
ejpam-6173	257	24	−	−	PROPN
ejpam-6173	257	25	ank	ank	PROPN
ejpam-6173	257	26	)	)	PUNCT
ejpam-6173	257	27	≥	≥	PROPN
ejpam-6173	257	28	0	0	NUM
ejpam-6173	257	29	,	,	PUNCT
ejpam-6173	257	30	then	then	ADV
ejpam-6173	257	31	lim	lim	PROPN
ejpam-6173	257	32	n→+∞	n→+∞	VERB
ejpam-6173	257	33	an	an	DET
ejpam-6173	257	34	=	=	NOUN
ejpam-6173	257	35	0	0	NUM
ejpam-6173	257	36	.	.	NOUN
ejpam-6173	258	1	3	3	NUM
ejpam-6173	258	2	.	.	X
ejpam-6173	258	3	main	main	ADJ
ejpam-6173	258	4	result	result	NOUN
ejpam-6173	258	5	in	in	ADP
ejpam-6173	258	6	this	this	DET
ejpam-6173	258	7	section	section	NOUN
ejpam-6173	258	8	,	,	PUNCT
ejpam-6173	258	9	we	we	PRON
ejpam-6173	258	10	present	present	VERB
ejpam-6173	258	11	the	the	DET
ejpam-6173	258	12	assumptions	assumption	NOUN
ejpam-6173	258	13	under	under	ADP
ejpam-6173	258	14	which	which	PRON
ejpam-6173	258	15	our	our	PRON
ejpam-6173	258	16	convergence	convergence	NOUN
ejpam-6173	258	17	analysis	analysis	NOUN
ejpam-6173	258	18	will	will	AUX
ejpam-6173	258	19	be	be	AUX
ejpam-6173	258	20	obtained	obtain	VERB
ejpam-6173	258	21	.	.	PUNCT
ejpam-6173	259	1	furthermore	furthermore	ADV
ejpam-6173	259	2	,	,	PUNCT
ejpam-6173	259	3	we	we	PRON
ejpam-6173	259	4	present	present	VERB
ejpam-6173	259	5	our	our	PRON
ejpam-6173	259	6	proposed	propose	VERB
ejpam-6173	259	7	algorithm	algorithm	NOUN
ejpam-6173	259	8	.	.	PUNCT
ejpam-6173	260	1	assumption	assumption	NOUN
ejpam-6173	260	2	3.1	3.1	NUM
ejpam-6173	260	3	.	.	PUNCT
ejpam-6173	260	4	assumption	assumption	NOUN
ejpam-6173	260	5	a	a	PRON
ejpam-6173	260	6	:	:	PUNCT
ejpam-6173	260	7	(	(	PUNCT
ejpam-6173	260	8	a1	a1	NOUN
ejpam-6173	260	9	)	)	PUNCT
ejpam-6173	260	10	e	e	NOUN
ejpam-6173	260	11	is	be	AUX
ejpam-6173	260	12	a	a	DET
ejpam-6173	260	13	reflexive	reflexive	ADJ
ejpam-6173	260	14	banach	banach	NOUN
ejpam-6173	260	15	space	space	NOUN
ejpam-6173	260	16	with	with	ADP
ejpam-6173	260	17	dual	dual	ADJ
ejpam-6173	260	18	e∗	e∗	NOUN
ejpam-6173	260	19	and	and	CCONJ
ejpam-6173	260	20	c	c	PROPN
ejpam-6173	260	21	is	be	AUX
ejpam-6173	260	22	a	a	DET
ejpam-6173	260	23	nonempty	nonempty	ADJ
ejpam-6173	260	24	,	,	PUNCT
ejpam-6173	260	25	closed	closed	ADJ
ejpam-6173	260	26	and	and	CCONJ
ejpam-6173	260	27	convex	convex	PROPN
ejpam-6173	260	28	subset	subset	NOUN
ejpam-6173	260	29	of	of	ADP
ejpam-6173	260	30	int(dom(f	int(dom(f	NOUN
ejpam-6173	260	31	)	)	PUNCT
ejpam-6173	260	32	)	)	PUNCT
ejpam-6173	260	33	.	.	PUNCT
ejpam-6173	261	1	(	(	PUNCT
ejpam-6173	261	2	a2	a2	PROPN
ejpam-6173	261	3	)	)	PUNCT
ejpam-6173	261	4	t	t	NOUN
ejpam-6173	261	5	:	:	PUNCT
ejpam-6173	261	6	c	c	X
ejpam-6173	261	7	→	→	SYM
ejpam-6173	261	8	c	c	PROPN
ejpam-6173	261	9	is	be	AUX
ejpam-6173	261	10	a	a	DET
ejpam-6173	261	11	bregman	bregman	NOUN
ejpam-6173	261	12	strongly	strongly	ADV
ejpam-6173	261	13	nonexpansive	nonexpansive	ADJ
ejpam-6173	261	14	mapping	mapping	NOUN
ejpam-6173	261	15	such	such	ADJ
ejpam-6173	261	16	that	that	SCONJ
ejpam-6173	261	17	f	f	PROPN
ejpam-6173	261	18	(	(	PUNCT
ejpam-6173	261	19	t	t	PROPN
ejpam-6173	261	20	)	)	PUNCT
ejpam-6173	261	21	=	=	SYM
ejpam-6173	261	22	f̂	f̂	X
ejpam-6173	261	23	(	(	PUNCT
ejpam-6173	261	24	t	t	PROPN
ejpam-6173	261	25	)	)	PUNCT
ejpam-6173	261	26	and	and	CCONJ
ejpam-6173	261	27	t	t	PROPN
ejpam-6173	261	28	is	be	AUX
ejpam-6173	261	29	uniformly	uniformly	ADV
ejpam-6173	261	30	continuous	continuous	ADJ
ejpam-6173	261	31	.	.	PUNCT
ejpam-6173	262	1	(	(	PUNCT
ejpam-6173	262	2	a3	a3	NOUN
ejpam-6173	262	3	)	)	PUNCT
ejpam-6173	262	4	f	f	NOUN
ejpam-6173	262	5	:	:	PUNCT
ejpam-6173	263	1	e	e	X
ejpam-6173	263	2	→	→	SYM
ejpam-6173	263	3	r	r	NOUN
ejpam-6173	263	4	is	be	AUX
ejpam-6173	263	5	a	a	DET
ejpam-6173	263	6	super	super	ADV
ejpam-6173	263	7	coercive	coercive	ADJ
ejpam-6173	263	8	legendre	legendre	PROPN
ejpam-6173	263	9	function	function	NOUN
ejpam-6173	263	10	that	that	PRON
ejpam-6173	263	11	is	be	AUX
ejpam-6173	263	12	bounded	bound	VERB
ejpam-6173	263	13	,	,	PUNCT
ejpam-6173	263	14	uniformly	uniformly	ADV
ejpam-6173	263	15	fréchet	fréchet	VERB
ejpam-6173	263	16	differentiable	differentiable	ADJ
ejpam-6173	263	17	and	and	CCONJ
ejpam-6173	263	18	totally	totally	ADV
ejpam-6173	263	19	convex	convex	VERB
ejpam-6173	263	20	on	on	ADP
ejpam-6173	263	21	bounded	bounded	ADJ
ejpam-6173	263	22	subsets	subset	NOUN
ejpam-6173	263	23	of	of	ADP
ejpam-6173	263	24	e.	e.	PROPN
ejpam-6173	263	25	(	(	PUNCT
ejpam-6173	263	26	a4	a4	PROPN
ejpam-6173	263	27	)	)	PUNCT
ejpam-6173	263	28	bθj	bθj	NOUN
ejpam-6173	263	29	:	:	PUNCT
ejpam-6173	263	30	e	e	X
ejpam-6173	263	31	→	→	SYM
ejpam-6173	263	32	2e	2e	NUM
ejpam-6173	263	33	∗	∗	NOUN
ejpam-6173	263	34	,	,	PUNCT
ejpam-6173	263	35	j	j	PROPN
ejpam-6173	263	36	=	=	SYM
ejpam-6173	263	37	1	1	NUM
ejpam-6173	263	38	,	,	PUNCT
ejpam-6173	263	39	2	2	NUM
ejpam-6173	263	40	,	,	PUNCT
ejpam-6173	263	41	.	.	PUNCT
ejpam-6173	263	42	.	.	PUNCT
ejpam-6173	263	43	.	.	PUNCT
ejpam-6173	264	1	n	n	PRON
ejpam-6173	264	2	is	be	AUX
ejpam-6173	264	3	a	a	DET
ejpam-6173	264	4	maximal	maximal	ADJ
ejpam-6173	264	5	monotone	monotone	ADJ
ejpam-6173	264	6	mapping	mapping	NOUN
ejpam-6173	264	7	with	with	ADP
ejpam-6173	264	8	dom(bθj	dom(bθj	NOUN
ejpam-6173	264	9	)	)	PUNCT
ejpam-6173	265	1	⊂	⊂	PROPN
ejpam-6173	265	2	c.	c.	PROPN
ejpam-6173	265	3	(	(	PUNCT
ejpam-6173	265	4	a5	a5	PROPN
ejpam-6173	265	5	)	)	PUNCT
ejpam-6173	265	6	the	the	DET
ejpam-6173	265	7	solution	solution	NOUN
ejpam-6173	265	8	set	set	VERB
ejpam-6173	265	9	ω	ω	PROPN
ejpam-6173	265	10	=	=	SYM
ejpam-6173	265	11	f	f	PROPN
ejpam-6173	265	12	(	(	PUNCT
ejpam-6173	265	13	t	t	PROPN
ejpam-6173	265	14	)	)	PUNCT
ejpam-6173	265	15	∩	∩	NOUN
ejpam-6173	265	16	(	(	PUNCT
ejpam-6173	265	17	⋂n	⋂n	PROPN
ejpam-6173	265	18	j=1b	j=1b	PROPN
ejpam-6173	265	19	−1	−1	PROPN
ejpam-6173	265	20	θj	θj	NOUN
ejpam-6173	265	21	(	(	PUNCT
ejpam-6173	265	22	0∗	0∗	NOUN
ejpam-6173	265	23	)	)	PUNCT
ejpam-6173	265	24	)	)	PUNCT
ejpam-6173	266	1	̸=	̸=	PROPN
ejpam-6173	266	2	∅.	∅.	PRON
ejpam-6173	266	3	assumption	assumption	NOUN
ejpam-6173	266	4	b	b	PROPN
ejpam-6173	266	5	:	:	PUNCT
ejpam-6173	266	6	(	(	PUNCT
ejpam-6173	266	7	b1	b1	NOUN
ejpam-6173	266	8	)	)	PUNCT
ejpam-6173	266	9	let	let	VERB
ejpam-6173	266	10	{	{	PUNCT
ejpam-6173	266	11	αn	αn	VERB
ejpam-6173	266	12	}	}	PUNCT
ejpam-6173	266	13	and	and	CCONJ
ejpam-6173	266	14	{	{	PUNCT
ejpam-6173	266	15	βn	βn	NOUN
ejpam-6173	266	16	}	}	PUNCT
ejpam-6173	266	17	be	be	AUX
ejpam-6173	266	18	sequences	sequence	NOUN
ejpam-6173	266	19	in	in	ADP
ejpam-6173	266	20	[	[	X
ejpam-6173	266	21	0	0	NUM
ejpam-6173	266	22	,	,	PUNCT
ejpam-6173	266	23	1	1	NUM
ejpam-6173	266	24	]	]	PUNCT
ejpam-6173	266	25	satisfying	satisfy	VERB
ejpam-6173	266	26	the	the	DET
ejpam-6173	266	27	following	follow	VERB
ejpam-6173	266	28	lim	lim	PROPN
ejpam-6173	266	29	n→+∞	n→+∞	VERB
ejpam-6173	266	30	βn	βn	NOUN
ejpam-6173	267	1	=	=	SYM
ejpam-6173	267	2	0	0	NUM
ejpam-6173	267	3	and	and	CCONJ
ejpam-6173	267	4	+	+	ADJ
ejpam-6173	267	5	∞∑	∞∑	NOUN
ejpam-6173	267	6	n=1	n=1	ADP
ejpam-6173	267	7	βn	βn	NOUN
ejpam-6173	267	8	=	=	PUNCT
ejpam-6173	268	1	+	+	NUM
ejpam-6173	268	2	∞.	∞.	PROPN
ejpam-6173	268	3	0	0	NUM
ejpam-6173	268	4	<	<	X
ejpam-6173	268	5	lim	lim	PROPN
ejpam-6173	268	6	inf	inf	PROPN
ejpam-6173	268	7	n→+∞	n→+∞	VERB
ejpam-6173	268	8	αn	αn	NOUN
ejpam-6173	268	9	≤	≤	NOUN
ejpam-6173	268	10	lim	lim	PROPN
ejpam-6173	268	11	sup	sup	PROPN
ejpam-6173	268	12	n→+∞	n→+∞	VERB
ejpam-6173	268	13	αn	αn	NOUN
ejpam-6173	268	14	<	<	X
ejpam-6173	268	15	1	1	NUM
ejpam-6173	268	16	.	.	PUNCT
ejpam-6173	268	17	(	(	PUNCT
ejpam-6173	268	18	b2	b2	NOUN
ejpam-6173	268	19	)	)	PUNCT
ejpam-6173	268	20	let	let	VERB
ejpam-6173	268	21	θ	θ	PROPN
ejpam-6173	268	22	>	>	PUNCT
ejpam-6173	268	23	0	0	PUNCT
ejpam-6173	269	1	and	and	CCONJ
ejpam-6173	269	2	{	{	PUNCT
ejpam-6173	269	3	ξn	ξn	PROPN
ejpam-6173	269	4	}	}	PUNCT
ejpam-6173	269	5	be	be	AUX
ejpam-6173	269	6	a	a	DET
ejpam-6173	269	7	positive	positive	ADJ
ejpam-6173	269	8	sequence	sequence	NOUN
ejpam-6173	269	9	such	such	ADJ
ejpam-6173	269	10	that	that	SCONJ
ejpam-6173	269	11	lim	lim	PROPN
ejpam-6173	269	12	n→+∞	n→+∞	VERB
ejpam-6173	269	13	ξn	ξn	NOUN
ejpam-6173	269	14	βn	βn	NOUN
ejpam-6173	269	15	=	=	NOUN
ejpam-6173	269	16	0	0	PROPN
ejpam-6173	269	17	.	.	PUNCT
ejpam-6173	270	1	(	(	PUNCT
ejpam-6173	270	2	b3	b3	PROPN
ejpam-6173	270	3	)	)	PUNCT
ejpam-6173	270	4	let	let	VERB
ejpam-6173	270	5	{	{	PUNCT
ejpam-6173	270	6	qn	qn	NOUN
ejpam-6173	270	7	}	}	PUNCT
ejpam-6173	270	8	⊂	⊂	PROPN
ejpam-6173	271	1	e	e	PROPN
ejpam-6173	271	2	such	such	ADJ
ejpam-6173	271	3	that	that	SCONJ
ejpam-6173	271	4	lim	lim	PROPN
ejpam-6173	271	5	n→+∞	n→+∞	VERB
ejpam-6173	271	6	qn	qn	NOUN
ejpam-6173	271	7	=	=	X
ejpam-6173	271	8	q	q	PROPN
ejpam-6173	271	9	∈	∈	PROPN
ejpam-6173	271	10	e.	e.	PROPN
ejpam-6173	271	11	v.	v.	PROPN
ejpam-6173	271	12	darvish	darvish	PROPN
ejpam-6173	271	13	et	et	PROPN
ejpam-6173	271	14	al	al	PROPN
ejpam-6173	271	15	.	.	PUNCT
ejpam-6173	271	16	/	/	SYM
ejpam-6173	271	17	eur	eur	PROPN
ejpam-6173	271	18	.	.	PUNCT
ejpam-6173	272	1	j.	j.	PROPN
ejpam-6173	272	2	pure	pure	PROPN
ejpam-6173	272	3	appl	appl	PROPN
ejpam-6173	272	4	.	.	PROPN
ejpam-6173	272	5	math	math	PROPN
ejpam-6173	272	6	,	,	PUNCT
ejpam-6173	272	7	18	18	NUM
ejpam-6173	272	8	(	(	PUNCT
ejpam-6173	272	9	3	3	NUM
ejpam-6173	272	10	)	)	PUNCT
ejpam-6173	272	11	(	(	PUNCT
ejpam-6173	272	12	2025	2025	NUM
ejpam-6173	272	13	)	)	PUNCT
ejpam-6173	272	14	,	,	PUNCT
ejpam-6173	272	15	6173	6173	NUM
ejpam-6173	272	16	12	12	NUM
ejpam-6173	272	17	of	of	ADP
ejpam-6173	272	18	32	32	NUM
ejpam-6173	272	19	algorithm	algorithm	NOUN
ejpam-6173	272	20	3.2	3.2	NUM
ejpam-6173	272	21	.	.	PUNCT
ejpam-6173	273	1	common	common	ADJ
ejpam-6173	273	2	solution	solution	NOUN
ejpam-6173	273	3	of	of	ADP
ejpam-6173	273	4	generalized	generalized	ADJ
ejpam-6173	273	5	mixed	mixed	ADJ
ejpam-6173	273	6	equilibrium	equilibrium	NOUN
ejpam-6173	273	7	problem	problem	NOUN
ejpam-6173	273	8	and	and	CCONJ
ejpam-6173	273	9	fixed	fix	VERB
ejpam-6173	273	10	point	point	NOUN
ejpam-6173	273	11	problem	problem	NOUN
ejpam-6173	273	12	step	step	NOUN
ejpam-6173	273	13	0	0	NUM
ejpam-6173	273	14	:	:	PUNCT
ejpam-6173	273	15	let	let	VERB
ejpam-6173	273	16	x0	x0	PROPN
ejpam-6173	273	17	,	,	PUNCT
ejpam-6173	273	18	x1	x1	PROPN
ejpam-6173	273	19	∈	∈	PROPN
ejpam-6173	273	20	e	e	X
ejpam-6173	273	21	be	be	VERB
ejpam-6173	273	22	arbitrary	arbitrary	ADJ
ejpam-6173	273	23	initial	initial	ADJ
ejpam-6173	273	24	points	point	NOUN
ejpam-6173	273	25	and	and	CCONJ
ejpam-6173	273	26	set	set	VERB
ejpam-6173	273	27	n	n	NOUN
ejpam-6173	273	28	=	=	SYM
ejpam-6173	273	29	1	1	X
ejpam-6173	273	30	.	.	X
ejpam-6173	273	31	step	step	NOUN
ejpam-6173	273	32	1	1	NUM
ejpam-6173	273	33	:	:	PUNCT
ejpam-6173	273	34	given	give	VERB
ejpam-6173	273	35	the	the	DET
ejpam-6173	273	36	(	(	PUNCT
ejpam-6173	273	37	n	n	CCONJ
ejpam-6173	273	38	−	−	PROPN
ejpam-6173	273	39	1)th	1)th	NOUN
ejpam-6173	273	40	and	and	CCONJ
ejpam-6173	273	41	nth	nth	NOUN
ejpam-6173	273	42	iterates	iterate	NOUN
ejpam-6173	273	43	,	,	PUNCT
ejpam-6173	273	44	choose	choose	VERB
ejpam-6173	273	45	θn	θn	ADP
ejpam-6173	273	46	such	such	ADJ
ejpam-6173	273	47	that	that	SCONJ
ejpam-6173	273	48	0	0	NUM
ejpam-6173	273	49	≤	≤	NUM
ejpam-6173	273	50	θn	θn	ADP
ejpam-6173	273	51	≤	≤	NOUN
ejpam-6173	273	52	θ̂n	θ̂n	PUNCT
ejpam-6173	273	53	with	with	ADP
ejpam-6173	273	54	θ̂n	θ̂n	NUM
ejpam-6173	273	55	defined	define	VERB
ejpam-6173	273	56	by	by	ADP
ejpam-6173	273	57	θ̂n	θ̂n	ADP
ejpam-6173	273	58	=	=	PRON
ejpam-6173	273	59	{	{	PUNCT
ejpam-6173	273	60	min{θ	min{θ	PROPN
ejpam-6173	273	61	,	,	PUNCT
ejpam-6173	273	62	ξn	ξn	NOUN
ejpam-6173	273	63	∥xn−xn−1∥	∥xn−xn−1∥	NOUN
ejpam-6173	273	64	}	}	PUNCT
ejpam-6173	273	65	,	,	PUNCT
ejpam-6173	273	66	if	if	SCONJ
ejpam-6173	273	67	xn	xn	PROPN
ejpam-6173	273	68	̸=	̸=	PROPN
ejpam-6173	273	69	xn−1	xn−1	PROPN
ejpam-6173	273	70	,	,	PUNCT
ejpam-6173	273	71	θ	θ	PROPN
ejpam-6173	273	72	,	,	PUNCT
ejpam-6173	273	73	otherwise	otherwise	ADV
ejpam-6173	273	74	.	.	PUNCT
ejpam-6173	274	1	(	(	PUNCT
ejpam-6173	274	2	3.1	3.1	NUM
ejpam-6173	274	3	)	)	PUNCT
ejpam-6173	274	4	step	step	NOUN
ejpam-6173	274	5	2	2	NUM
ejpam-6173	274	6	:	:	PUNCT
ejpam-6173	274	7	compute	compute	PROPN
ejpam-6173	274	8	wn	wn	PROPN
ejpam-6173	275	1	=	=	SYM
ejpam-6173	275	2	∇f∗	∇f∗	PROPN
ejpam-6173	275	3	(	(	PUNCT
ejpam-6173	275	4	∇f(xn	∇f(xn	NOUN
ejpam-6173	275	5	)	)	PUNCT
ejpam-6173	275	6	+	+	NUM
ejpam-6173	275	7	θn	θn	ADJ
ejpam-6173	275	8	(	(	PUNCT
ejpam-6173	275	9	∇f(xn−1)−∇f(xn	∇f(xn−1)−∇f(xn	NOUN
ejpam-6173	275	10	)	)	PUNCT
ejpam-6173	275	11	)	)	PUNCT
ejpam-6173	275	12	)	)	PUNCT
ejpam-6173	275	13	zn	zn	X
ejpam-6173	275	14	=	=	SYM
ejpam-6173	275	15	resfbθn	resfbθn	PROPN
ejpam-6173	275	16	◦	◦	NOUN
ejpam-6173	275	17	·	·	PUNCT
ejpam-6173	275	18	·	·	PUNCT
ejpam-6173	275	19	·	·	PUNCT
ejpam-6173	276	1	◦	◦	NOUN
ejpam-6173	276	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	276	3	(	(	PUNCT
ejpam-6173	276	4	wn	wn	PROPN
ejpam-6173	276	5	)	)	PUNCT
ejpam-6173	276	6	yn	yn	PROPN
ejpam-6173	276	7	=	=	PUNCT
ejpam-6173	276	8	∇f∗	∇f∗	PROPN
ejpam-6173	276	9	(	(	PUNCT
ejpam-6173	276	10	βn∇f	βn∇f	NOUN
ejpam-6173	276	11	(	(	PUNCT
ejpam-6173	276	12	qn	qn	NOUN
ejpam-6173	276	13	)	)	PUNCT
ejpam-6173	276	14	+	+	CCONJ
ejpam-6173	276	15	(	(	PUNCT
ejpam-6173	276	16	1−	1−	NUM
ejpam-6173	276	17	βn)∇f	βn)∇f	X
ejpam-6173	276	18	(	(	PUNCT
ejpam-6173	276	19	t	t	PROPN
ejpam-6173	276	20	(	(	PUNCT
ejpam-6173	276	21	zn	zn	NOUN
ejpam-6173	276	22	)	)	PUNCT
ejpam-6173	276	23	)	)	PUNCT
ejpam-6173	276	24	)	)	PUNCT
ejpam-6173	276	25	xn+1	xn+1	X
ejpam-6173	277	1	=	=	SYM
ejpam-6173	277	2	∇f∗	∇f∗	PROPN
ejpam-6173	277	3	(	(	PUNCT
ejpam-6173	277	4	αn∇f	αn∇f	PROPN
ejpam-6173	277	5	(	(	PUNCT
ejpam-6173	277	6	wn	wn	PROPN
ejpam-6173	277	7	)	)	PUNCT
ejpam-6173	277	8	+	+	CCONJ
ejpam-6173	277	9	(	(	PUNCT
ejpam-6173	277	10	1−	1−	NUM
ejpam-6173	277	11	αn)∇f	αn)∇f	NOUN
ejpam-6173	277	12	(	(	PUNCT
ejpam-6173	277	13	t	t	PROPN
ejpam-6173	277	14	(	(	PUNCT
ejpam-6173	277	15	yn	yn	PROPN
ejpam-6173	277	16	)	)	PUNCT
ejpam-6173	277	17	)	)	PUNCT
ejpam-6173	277	18	)	)	PUNCT
ejpam-6173	277	19	.	.	PUNCT
ejpam-6173	278	1	set	set	VERB
ejpam-6173	278	2	n	n	NOUN
ejpam-6173	278	3	:	:	PUNCT
ejpam-6173	278	4	=	=	SYM
ejpam-6173	278	5	n+	n+	PUNCT
ejpam-6173	278	6	1	1	NUM
ejpam-6173	278	7	and	and	CCONJ
ejpam-6173	278	8	return	return	VERB
ejpam-6173	278	9	to	to	PART
ejpam-6173	278	10	step	step	VERB
ejpam-6173	278	11	1	1	NUM
ejpam-6173	278	12	.	.	PUNCT
ejpam-6173	278	13	remark	remark	NOUN
ejpam-6173	278	14	3	3	NUM
ejpam-6173	278	15	.	.	PUNCT
ejpam-6173	279	1	the	the	DET
ejpam-6173	279	2	inertial	inertial	ADJ
ejpam-6173	279	3	technique	technique	NOUN
ejpam-6173	279	4	used	use	VERB
ejpam-6173	279	5	in	in	ADP
ejpam-6173	279	6	step	step	NOUN
ejpam-6173	279	7	1	1	NUM
ejpam-6173	279	8	of	of	ADP
ejpam-6173	279	9	algorithm	algorithm	NOUN
ejpam-6173	279	10	1	1	NUM
ejpam-6173	279	11	can	can	AUX
ejpam-6173	279	12	be	be	AUX
ejpam-6173	279	13	easily	easily	ADV
ejpam-6173	279	14	implemented	implement	VERB
ejpam-6173	279	15	since	since	SCONJ
ejpam-6173	279	16	the	the	DET
ejpam-6173	279	17	value	value	NOUN
ejpam-6173	279	18	of	of	ADP
ejpam-6173	279	19	∥xn	∥xn	PRON
ejpam-6173	279	20	−	−	PROPN
ejpam-6173	279	21	xn−1∥	xn−1∥	PROPN
ejpam-6173	279	22	is	be	AUX
ejpam-6173	279	23	known	know	VERB
ejpam-6173	279	24	before	before	ADP
ejpam-6173	279	25	choosing	choose	VERB
ejpam-6173	279	26	θn	θn	PROPN
ejpam-6173	279	27	.	.	PUNCT
ejpam-6173	280	1	we	we	PRON
ejpam-6173	280	2	also	also	ADV
ejpam-6173	280	3	note	note	VERB
ejpam-6173	280	4	that	that	SCONJ
ejpam-6173	280	5	the	the	DET
ejpam-6173	280	6	restrictive	restrictive	ADJ
ejpam-6173	280	7	summability	summability	NOUN
ejpam-6173	280	8	condition	condition	NOUN
ejpam-6173	280	9	+	+	ADP
ejpam-6173	280	10	∞∑	∞∑	NUM
ejpam-6173	280	11	n=1	n=1	NUM
ejpam-6173	280	12	∥xn	∥xn	PROPN
ejpam-6173	280	13	−	−	PROPN
ejpam-6173	280	14	xn−1∥	xn−1∥	PROPN
ejpam-6173	280	15	<	<	X
ejpam-6173	281	1	+	+	NOUN
ejpam-6173	281	2	∞	∞	PROPN
ejpam-6173	281	3	often	often	ADV
ejpam-6173	281	4	used	use	VERB
ejpam-6173	281	5	by	by	ADP
ejpam-6173	281	6	several	several	ADJ
ejpam-6173	281	7	authors	author	NOUN
ejpam-6173	281	8	when	when	SCONJ
ejpam-6173	281	9	constructing	construct	VERB
ejpam-6173	281	10	initial	initial	ADJ
ejpam-6173	281	11	algorithms	algorithm	NOUN
ejpam-6173	281	12	is	be	AUX
ejpam-6173	281	13	dispensed	dispense	VERB
ejpam-6173	281	14	with	with	ADP
ejpam-6173	281	15	in	in	ADP
ejpam-6173	281	16	our	our	PRON
ejpam-6173	281	17	proposed	propose	VERB
ejpam-6173	281	18	algorithm	algorithm	NOUN
ejpam-6173	281	19	.	.	PUNCT
ejpam-6173	282	1	4	4	X
ejpam-6173	282	2	.	.	X
ejpam-6173	282	3	convergence	convergence	NOUN
ejpam-6173	282	4	analysis	analysis	NOUN
ejpam-6173	282	5	first	first	ADV
ejpam-6173	282	6	,	,	PUNCT
ejpam-6173	282	7	we	we	PRON
ejpam-6173	282	8	present	present	VERB
ejpam-6173	282	9	some	some	DET
ejpam-6173	282	10	lemmas	lemma	NOUN
ejpam-6173	282	11	which	which	PRON
ejpam-6173	282	12	will	will	AUX
ejpam-6173	282	13	be	be	AUX
ejpam-6173	282	14	needed	need	VERB
ejpam-6173	282	15	in	in	ADP
ejpam-6173	282	16	obtaining	obtain	VERB
ejpam-6173	282	17	our	our	PRON
ejpam-6173	282	18	convergence	convergence	NOUN
ejpam-6173	282	19	result	result	VERB
ejpam-6173	282	20	.	.	PUNCT
ejpam-6173	283	1	in	in	ADP
ejpam-6173	283	2	the	the	DET
ejpam-6173	283	3	following	follow	VERB
ejpam-6173	283	4	lemma	lemma	PROPN
ejpam-6173	283	5	,	,	PUNCT
ejpam-6173	283	6	we	we	PRON
ejpam-6173	283	7	obtain	obtain	VERB
ejpam-6173	283	8	some	some	DET
ejpam-6173	283	9	results	result	NOUN
ejpam-6173	283	10	for	for	ADP
ejpam-6173	283	11	the	the	DET
ejpam-6173	283	12	maximal	maximal	ADJ
ejpam-6173	283	13	operator	operator	NOUN
ejpam-6173	283	14	bθ	bθ	NOUN
ejpam-6173	283	15	from	from	ADP
ejpam-6173	283	16	the	the	DET
ejpam-6173	283	17	bifunction	bifunction	NOUN
ejpam-6173	283	18	θ	θ	PROPN
ejpam-6173	283	19	.	.	PUNCT
ejpam-6173	284	1	the	the	DET
ejpam-6173	284	2	main	main	ADJ
ejpam-6173	284	3	idea	idea	NOUN
ejpam-6173	284	4	of	of	ADP
ejpam-6173	284	5	the	the	DET
ejpam-6173	284	6	following	follow	VERB
ejpam-6173	284	7	lemma	lemma	PROPN
ejpam-6173	284	8	is	be	AUX
ejpam-6173	284	9	from	from	ADP
ejpam-6173	284	10	[	[	X
ejpam-6173	284	11	53	53	NUM
ejpam-6173	284	12	]	]	PUNCT
ejpam-6173	284	13	.	.	PUNCT
ejpam-6173	285	1	lemma	lemma	PROPN
ejpam-6173	285	2	13	13	NUM
ejpam-6173	285	3	.	.	PUNCT
ejpam-6173	286	1	let	let	VERB
ejpam-6173	286	2	f	f	NOUN
ejpam-6173	286	3	:	:	PUNCT
ejpam-6173	286	4	e	e	X
ejpam-6173	286	5	→	→	PUNCT
ejpam-6173	286	6	(	(	PUNCT
ejpam-6173	286	7	−∞,+∞	−∞,+∞	ADV
ejpam-6173	286	8	]	]	PUNCT
ejpam-6173	286	9	be	be	AUX
ejpam-6173	286	10	a	a	DET
ejpam-6173	286	11	supercoercive	supercoercive	NOUN
ejpam-6173	286	12	,	,	PUNCT
ejpam-6173	286	13	legendre	legendre	PROPN
ejpam-6173	286	14	,	,	PUNCT
ejpam-6173	286	15	fréchet	fréchet	NOUN
ejpam-6173	286	16	differentiable	differentiable	ADJ
ejpam-6173	286	17	and	and	CCONJ
ejpam-6173	286	18	totally	totally	ADV
ejpam-6173	286	19	convex	convex	ADJ
ejpam-6173	286	20	function	function	NOUN
ejpam-6173	286	21	.	.	PUNCT
ejpam-6173	287	1	let	let	VERB
ejpam-6173	287	2	c	c	PRON
ejpam-6173	287	3	be	be	AUX
ejpam-6173	287	4	a	a	DET
ejpam-6173	287	5	closed	closed	ADJ
ejpam-6173	287	6	and	and	CCONJ
ejpam-6173	287	7	convex	convex	NOUN
ejpam-6173	287	8	subset	subset	NOUN
ejpam-6173	287	9	of	of	ADP
ejpam-6173	287	10	e	e	NOUN
ejpam-6173	287	11	and	and	CCONJ
ejpam-6173	287	12	assume	assume	VERB
ejpam-6173	287	13	that	that	SCONJ
ejpam-6173	287	14	the	the	DET
ejpam-6173	287	15	bifunction	bifunction	NOUN
ejpam-6173	287	16	θ	θ	NOUN
ejpam-6173	287	17	:	:	PUNCT
ejpam-6173	287	18	c	c	X
ejpam-6173	287	19	×	×	NOUN
ejpam-6173	287	20	c	c	NOUN
ejpam-6173	287	21	→	→	SYM
ejpam-6173	287	22	r	r	NOUN
ejpam-6173	287	23	satisfies	satisfie	NOUN
ejpam-6173	287	24	conditions	condition	NOUN
ejpam-6173	287	25	(	(	PUNCT
ejpam-6173	287	26	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	287	27	)	)	PUNCT
ejpam-6173	287	28	and	and	CCONJ
ejpam-6173	287	29	ψ	ψ	NOUN
ejpam-6173	287	30	is	be	AUX
ejpam-6173	287	31	monotone	monotone	ADJ
ejpam-6173	287	32	.	.	PUNCT
ejpam-6173	288	1	then	then	ADV
ejpam-6173	288	2	(	(	PUNCT
ejpam-6173	288	3	1	1	X
ejpam-6173	288	4	)	)	PUNCT
ejpam-6173	288	5	gmep(θ	gmep(θ	PROPN
ejpam-6173	288	6	,	,	PUNCT
ejpam-6173	288	7	φ	φ	PROPN
ejpam-6173	288	8	,	,	PUNCT
ejpam-6173	288	9	ψ	ψ	NOUN
ejpam-6173	288	10	)	)	PUNCT
ejpam-6173	288	11	=	=	SYM
ejpam-6173	288	12	b−1	b−1	PROPN
ejpam-6173	288	13	θ	θ	PROPN
ejpam-6173	288	14	(	(	PUNCT
ejpam-6173	288	15	0∗	0∗	NUM
ejpam-6173	288	16	)	)	PUNCT
ejpam-6173	288	17	;	;	PUNCT
ejpam-6173	288	18	(	(	PUNCT
ejpam-6173	288	19	2	2	X
ejpam-6173	288	20	)	)	PUNCT
ejpam-6173	288	21	bθ	bθ	NOUN
ejpam-6173	288	22	is	be	AUX
ejpam-6173	288	23	a	a	DET
ejpam-6173	288	24	maximal	maximal	ADJ
ejpam-6173	288	25	monotone	monotone	ADJ
ejpam-6173	288	26	mapping	mapping	NOUN
ejpam-6173	288	27	;	;	PUNCT
ejpam-6173	288	28	(	(	PUNCT
ejpam-6173	288	29	3	3	X
ejpam-6173	288	30	)	)	PUNCT
ejpam-6173	288	31	resfθ	resfθ	PROPN
ejpam-6173	288	32	,	,	PUNCT
ejpam-6173	288	33	φ	φ	X
ejpam-6173	288	34	,	,	PUNCT
ejpam-6173	288	35	ψ	ψ	X
ejpam-6173	288	36	=	=	NOUN
ejpam-6173	288	37	resfbθ	resfbθ	NOUN
ejpam-6173	288	38	.	.	PUNCT
ejpam-6173	289	1	proof	proof	NOUN
ejpam-6173	289	2	.	.	PUNCT
ejpam-6173	290	1	(	(	PUNCT
ejpam-6173	290	2	1	1	X
ejpam-6173	290	3	)	)	PUNCT
ejpam-6173	290	4	if	if	SCONJ
ejpam-6173	290	5	x	x	SYM
ejpam-6173	290	6	∈	∈	PROPN
ejpam-6173	290	7	c	c	NOUN
ejpam-6173	290	8	then	then	ADV
ejpam-6173	290	9	from	from	ADP
ejpam-6173	290	10	the	the	DET
ejpam-6173	290	11	definition	definition	NOUN
ejpam-6173	290	12	of	of	ADP
ejpam-6173	290	13	the	the	DET
ejpam-6173	290	14	mapping	mapping	NOUN
ejpam-6173	290	15	bθ	bθ	NOUN
ejpam-6173	290	16	(	(	PUNCT
ejpam-6173	290	17	2.10	2.10	NUM
ejpam-6173	290	18	)	)	PUNCT
ejpam-6173	290	19	we	we	PRON
ejpam-6173	290	20	have	have	VERB
ejpam-6173	290	21	x	x	X
ejpam-6173	290	22	∈	∈	ADJ
ejpam-6173	290	23	b−1	b−1	PROPN
ejpam-6173	290	24	θ	θ	PROPN
ejpam-6173	290	25	(	(	PUNCT
ejpam-6173	290	26	0∗	0∗	NUM
ejpam-6173	290	27	)	)	PUNCT
ejpam-6173	290	28	⇔	⇔	PROPN
ejpam-6173	290	29	θ(x	θ(x	PROPN
ejpam-6173	290	30	,	,	PUNCT
ejpam-6173	290	31	y)+φ(y)+	y)+φ(y)+	NOUN
ejpam-6173	290	32	⟨ψx	⟨ψx	PROPN
ejpam-6173	290	33	,	,	PUNCT
ejpam-6173	290	34	y−x⟩	y−x⟩	PROPN
ejpam-6173	290	35	≥	≥	NOUN
ejpam-6173	290	36	φ(x	φ(x	PROPN
ejpam-6173	290	37	)	)	PUNCT
ejpam-6173	290	38	for	for	ADP
ejpam-6173	290	39	all	all	DET
ejpam-6173	290	40	y	y	PROPN
ejpam-6173	290	41	∈	∈	PROPN
ejpam-6173	290	42	c	c	PROPN
ejpam-6173	290	43	⇔	⇔	X
ejpam-6173	290	44	x	x	SYM
ejpam-6173	290	45	∈	∈	PROPN
ejpam-6173	290	46	gmep(θ	gmep(θ	PROPN
ejpam-6173	290	47	,	,	PUNCT
ejpam-6173	290	48	φ	φ	PROPN
ejpam-6173	290	49	,	,	PUNCT
ejpam-6173	290	50	ψ	ψ	NOUN
ejpam-6173	290	51	)	)	PUNCT
ejpam-6173	290	52	.	.	PUNCT
ejpam-6173	291	1	(	(	PUNCT
ejpam-6173	291	2	2	2	X
ejpam-6173	291	3	)	)	PUNCT
ejpam-6173	291	4	we	we	PRON
ejpam-6173	291	5	show	show	VERB
ejpam-6173	291	6	that	that	SCONJ
ejpam-6173	291	7	bθ	bθ	PROPN
ejpam-6173	291	8	is	be	AUX
ejpam-6173	291	9	monotone	monotone	ADJ
ejpam-6173	291	10	mapping	mapping	NOUN
ejpam-6173	291	11	.	.	PUNCT
ejpam-6173	292	1	let	let	VERB
ejpam-6173	292	2	(	(	PUNCT
ejpam-6173	292	3	x1	x1	ADJ
ejpam-6173	292	4	,	,	PUNCT
ejpam-6173	292	5	x	x	X
ejpam-6173	292	6	∗	∗	NOUN
ejpam-6173	292	7	1	1	NUM
ejpam-6173	292	8	)	)	PUNCT
ejpam-6173	292	9	and	and	CCONJ
ejpam-6173	292	10	(	(	PUNCT
ejpam-6173	292	11	x2	x2	PROPN
ejpam-6173	292	12	,	,	PUNCT
ejpam-6173	292	13	x	x	PROPN
ejpam-6173	292	14	∗	∗	NOUN
ejpam-6173	292	15	2	2	NUM
ejpam-6173	292	16	)	)	PUNCT
ejpam-6173	292	17	belong	belong	VERB
ejpam-6173	292	18	to	to	ADP
ejpam-6173	292	19	the	the	DET
ejpam-6173	292	20	graph	graph	NOUN
ejpam-6173	292	21	of	of	ADP
ejpam-6173	292	22	bθ	bθ	NOUN
ejpam-6173	292	23	.	.	PUNCT
ejpam-6173	293	1	by	by	ADP
ejpam-6173	293	2	the	the	DET
ejpam-6173	293	3	definition	definition	NOUN
ejpam-6173	293	4	of	of	ADP
ejpam-6173	293	5	the	the	DET
ejpam-6173	293	6	mapping	mapping	NOUN
ejpam-6173	293	7	bθ	bθ	ADV
ejpam-6173	293	8	,	,	PUNCT
ejpam-6173	293	9	we	we	PRON
ejpam-6173	293	10	have	have	VERB
ejpam-6173	293	11	θ(x1	θ(x1	ADJ
ejpam-6173	293	12	,	,	PUNCT
ejpam-6173	293	13	z	z	NOUN
ejpam-6173	293	14	)	)	PUNCT
ejpam-6173	293	15	+	+	CCONJ
ejpam-6173	294	1	φ(z	φ(z	NOUN
ejpam-6173	294	2	)	)	PUNCT
ejpam-6173	295	1	+	+	CCONJ
ejpam-6173	295	2	⟨ψx1	⟨ψx1	X
ejpam-6173	295	3	,	,	PUNCT
ejpam-6173	295	4	z	z	NOUN
ejpam-6173	295	5	−	−	PROPN
ejpam-6173	295	6	x1⟩	x1⟩	X
ejpam-6173	295	7	≥	≥	PROPN
ejpam-6173	295	8	⟨x∗1	⟨x∗1	PROPN
ejpam-6173	295	9	,	,	PUNCT
ejpam-6173	295	10	z	z	NOUN
ejpam-6173	295	11	−	−	PROPN
ejpam-6173	295	12	x1⟩+	x1⟩+	NUM
ejpam-6173	295	13	φ(x1	φ(x1	PROPN
ejpam-6173	295	14	)	)	PUNCT
ejpam-6173	295	15	v.	v.	ADP
ejpam-6173	295	16	darvish	darvish	PROPN
ejpam-6173	295	17	et	et	PROPN
ejpam-6173	295	18	al	al	PROPN
ejpam-6173	295	19	.	.	PUNCT
ejpam-6173	295	20	/	/	SYM
ejpam-6173	295	21	eur	eur	PROPN
ejpam-6173	295	22	.	.	PUNCT
ejpam-6173	296	1	j.	j.	PROPN
ejpam-6173	296	2	pure	pure	PROPN
ejpam-6173	296	3	appl	appl	PROPN
ejpam-6173	296	4	.	.	PROPN
ejpam-6173	296	5	math	math	PROPN
ejpam-6173	296	6	,	,	PUNCT
ejpam-6173	296	7	18	18	NUM
ejpam-6173	296	8	(	(	PUNCT
ejpam-6173	296	9	3	3	NUM
ejpam-6173	296	10	)	)	PUNCT
ejpam-6173	296	11	(	(	PUNCT
ejpam-6173	296	12	2025	2025	NUM
ejpam-6173	296	13	)	)	PUNCT
ejpam-6173	296	14	,	,	PUNCT
ejpam-6173	296	15	6173	6173	NUM
ejpam-6173	296	16	13	13	NUM
ejpam-6173	296	17	of	of	ADP
ejpam-6173	296	18	32	32	NUM
ejpam-6173	296	19	and	and	CCONJ
ejpam-6173	296	20	θ(x2	θ(x2	NOUN
ejpam-6173	296	21	,	,	PUNCT
ejpam-6173	296	22	z	z	NOUN
ejpam-6173	296	23	)	)	PUNCT
ejpam-6173	296	24	+	+	CCONJ
ejpam-6173	296	25	φ(z	φ(z	NOUN
ejpam-6173	296	26	)	)	PUNCT
ejpam-6173	296	27	+	+	NUM
ejpam-6173	296	28	⟨ψx2	⟨ψx2	NOUN
ejpam-6173	296	29	,	,	PUNCT
ejpam-6173	296	30	z	z	NOUN
ejpam-6173	296	31	−	−	PROPN
ejpam-6173	296	32	x2⟩	x2⟩	PUNCT
ejpam-6173	296	33	≥	≥	PROPN
ejpam-6173	297	1	⟨x∗2	⟨x∗2	ADJ
ejpam-6173	297	2	,	,	PUNCT
ejpam-6173	297	3	z	z	NOUN
ejpam-6173	297	4	−	−	PROPN
ejpam-6173	297	5	x2⟩+	x2⟩+	SYM
ejpam-6173	297	6	φ(x2	φ(x2	NOUN
ejpam-6173	297	7	)	)	PUNCT
ejpam-6173	297	8	for	for	ADP
ejpam-6173	297	9	any	any	DET
ejpam-6173	297	10	z	z	PROPN
ejpam-6173	297	11	∈	∈	PROPN
ejpam-6173	297	12	c.	c.	NOUN
ejpam-6173	297	13	in	in	ADP
ejpam-6173	297	14	particular	particular	ADJ
ejpam-6173	297	15	we	we	PRON
ejpam-6173	297	16	have	have	VERB
ejpam-6173	297	17	that	that	DET
ejpam-6173	297	18	θ(x1	θ(x1	ADJ
ejpam-6173	297	19	,	,	PUNCT
ejpam-6173	297	20	x2	x2	PROPN
ejpam-6173	297	21	)	)	PUNCT
ejpam-6173	297	22	+	+	NUM
ejpam-6173	297	23	φ(x2	φ(x2	NOUN
ejpam-6173	297	24	)	)	PUNCT
ejpam-6173	298	1	+	+	CCONJ
ejpam-6173	298	2	⟨ψx1	⟨ψx1	X
ejpam-6173	298	3	,	,	PUNCT
ejpam-6173	298	4	x2	x2	PROPN
ejpam-6173	298	5	−	−	PROPN
ejpam-6173	298	6	x1⟩	x1⟩	X
ejpam-6173	298	7	≥	≥	PROPN
ejpam-6173	298	8	⟨x∗1	⟨x∗1	PROPN
ejpam-6173	298	9	,	,	PUNCT
ejpam-6173	298	10	x2	x2	PROPN
ejpam-6173	298	11	−	−	PROPN
ejpam-6173	298	12	x1⟩+	x1⟩+	NUM
ejpam-6173	298	13	φ(x1	φ(x1	NOUN
ejpam-6173	298	14	)	)	PUNCT
ejpam-6173	298	15	(	(	PUNCT
ejpam-6173	298	16	4.1	4.1	NUM
ejpam-6173	298	17	)	)	PUNCT
ejpam-6173	298	18	and	and	CCONJ
ejpam-6173	298	19	θ(x2	θ(x2	NOUN
ejpam-6173	298	20	,	,	PUNCT
ejpam-6173	298	21	x1	x1	PROPN
ejpam-6173	298	22	)	)	PUNCT
ejpam-6173	299	1	+	+	NUM
ejpam-6173	299	2	φ(x1	φ(x1	NOUN
ejpam-6173	299	3	)	)	PUNCT
ejpam-6173	299	4	+	+	NUM
ejpam-6173	299	5	⟨ψx2	⟨ψx2	NOUN
ejpam-6173	299	6	,	,	PUNCT
ejpam-6173	299	7	x1	x1	PROPN
ejpam-6173	299	8	−	−	PROPN
ejpam-6173	299	9	x2⟩	x2⟩	PUNCT
ejpam-6173	299	10	≥	≥	PROPN
ejpam-6173	300	1	⟨x∗2	⟨x∗2	PROPN
ejpam-6173	300	2	,	,	PUNCT
ejpam-6173	300	3	x1	x1	PROPN
ejpam-6173	300	4	−	−	PROPN
ejpam-6173	300	5	x2⟩+	x2⟩+	NUM
ejpam-6173	300	6	φ(x2	φ(x2	NOUN
ejpam-6173	300	7	)	)	PUNCT
ejpam-6173	300	8	.	.	PUNCT
ejpam-6173	301	1	(	(	PUNCT
ejpam-6173	301	2	4.2	4.2	X
ejpam-6173	301	3	)	)	PUNCT
ejpam-6173	301	4	adding	add	VERB
ejpam-6173	301	5	equations	equation	NOUN
ejpam-6173	301	6	(	(	PUNCT
ejpam-6173	301	7	4.1	4.1	NUM
ejpam-6173	301	8	)	)	PUNCT
ejpam-6173	301	9	and	and	CCONJ
ejpam-6173	301	10	(	(	PUNCT
ejpam-6173	301	11	4.2	4.2	NUM
ejpam-6173	301	12	)	)	PUNCT
ejpam-6173	301	13	together	together	ADV
ejpam-6173	301	14	,	,	PUNCT
ejpam-6173	301	15	we	we	PRON
ejpam-6173	301	16	obtain	obtain	VERB
ejpam-6173	301	17	θ(x1	θ(x1	ADJ
ejpam-6173	301	18	,	,	PUNCT
ejpam-6173	301	19	x2	x2	PROPN
ejpam-6173	301	20	)	)	PUNCT
ejpam-6173	301	21	+	+	NUM
ejpam-6173	301	22	θ(x2	θ(x2	NOUN
ejpam-6173	301	23	,	,	PUNCT
ejpam-6173	301	24	x1	x1	PROPN
ejpam-6173	301	25	)	)	PUNCT
ejpam-6173	301	26	+	+	NUM
ejpam-6173	301	27	φ(x2	φ(x2	NOUN
ejpam-6173	301	28	)	)	PUNCT
ejpam-6173	301	29	+	+	NUM
ejpam-6173	301	30	φ(x1	φ(x1	NOUN
ejpam-6173	301	31	)	)	PUNCT
ejpam-6173	301	32	+	+	CCONJ
ejpam-6173	301	33	⟨ψx1	⟨ψx1	X
ejpam-6173	301	34	,	,	PUNCT
ejpam-6173	301	35	x2	x2	NOUN
ejpam-6173	301	36	−	−	NOUN
ejpam-6173	301	37	x1⟩+	x1⟩+	NUM
ejpam-6173	301	38	⟨ψx2	⟨ψx2	NOUN
ejpam-6173	301	39	,	,	PUNCT
ejpam-6173	302	1	x1	x1	PROPN
ejpam-6173	302	2	−	−	PROPN
ejpam-6173	302	3	x2⟩	x2⟩	PROPN
ejpam-6173	302	4	≥	≥	PROPN
ejpam-6173	302	5	⟨x∗1	⟨x∗1	VERB
ejpam-6173	302	6	,	,	PUNCT
ejpam-6173	303	1	x2	x2	PROPN
ejpam-6173	304	1	−	−	PROPN
ejpam-6173	304	2	x1⟩+	x1⟩+	PROPN
ejpam-6173	304	3	⟨x∗2	⟨x∗2	PROPN
ejpam-6173	304	4	,	,	PUNCT
ejpam-6173	304	5	x1	x1	PROPN
ejpam-6173	304	6	−	−	PROPN
ejpam-6173	304	7	x2⟩+	x2⟩+	SYM
ejpam-6173	304	8	φ(x1	φ(x1	NOUN
ejpam-6173	304	9	)	)	PUNCT
ejpam-6173	304	10	+	+	NUM
ejpam-6173	304	11	φ(x2	φ(x2	NOUN
ejpam-6173	304	12	)	)	PUNCT
ejpam-6173	304	13	.	.	PUNCT
ejpam-6173	305	1	by	by	ADP
ejpam-6173	305	2	(	(	PUNCT
ejpam-6173	305	3	a2	a2	PROPN
ejpam-6173	305	4	)	)	PUNCT
ejpam-6173	305	5	,	,	PUNCT
ejpam-6173	305	6	it	it	PRON
ejpam-6173	305	7	is	be	AUX
ejpam-6173	305	8	equivalent	equivalent	ADJ
ejpam-6173	305	9	to	to	PART
ejpam-6173	305	10	write	write	VERB
ejpam-6173	305	11	0	0	NUM
ejpam-6173	305	12	≥	≥	NOUN
ejpam-6173	305	13	θ(x1	θ(x1	NOUN
ejpam-6173	305	14	,	,	PUNCT
ejpam-6173	305	15	x2	x2	PROPN
ejpam-6173	305	16	)	)	PUNCT
ejpam-6173	305	17	+	+	NUM
ejpam-6173	305	18	θ(x2	θ(x2	NOUN
ejpam-6173	305	19	,	,	PUNCT
ejpam-6173	305	20	x1	x1	PROPN
ejpam-6173	305	21	)	)	PUNCT
ejpam-6173	306	1	+	+	CCONJ
ejpam-6173	306	2	⟨ψx1	⟨ψx1	X
ejpam-6173	306	3	−ψx2	−ψx2	NOUN
ejpam-6173	306	4	,	,	PUNCT
ejpam-6173	306	5	x2	x2	PROPN
ejpam-6173	306	6	−	−	PROPN
ejpam-6173	306	7	x1⟩	x1⟩	X
ejpam-6173	306	8	≥	≥	PROPN
ejpam-6173	306	9	⟨x∗1	⟨x∗1	VERB
ejpam-6173	306	10	−	−	PROPN
ejpam-6173	306	11	x∗2	x∗2	PROPN
ejpam-6173	306	12	,	,	PUNCT
ejpam-6173	306	13	x2	x2	PROPN
ejpam-6173	306	14	−	−	PROPN
ejpam-6173	306	15	x1⟩.	x1⟩.	PROPN
ejpam-6173	307	1	it	it	PRON
ejpam-6173	307	2	means	mean	VERB
ejpam-6173	307	3	that	that	SCONJ
ejpam-6173	307	4	⟨x∗1	⟨x∗1	VERB
ejpam-6173	307	5	−	−	PROPN
ejpam-6173	307	6	x∗2	x∗2	NOUN
ejpam-6173	307	7	,	,	PUNCT
ejpam-6173	308	1	x1	x1	PROPN
ejpam-6173	308	2	−	−	PROPN
ejpam-6173	308	3	x2⟩	x2⟩	PUNCT
ejpam-6173	308	4	≥	≥	NOUN
ejpam-6173	308	5	0	0	NUM
ejpam-6173	308	6	which	which	PRON
ejpam-6173	308	7	follows	follow	VERB
ejpam-6173	308	8	that	that	SCONJ
ejpam-6173	308	9	bθ	bθ	PROPN
ejpam-6173	308	10	is	be	AUX
ejpam-6173	308	11	a	a	DET
ejpam-6173	308	12	monotone	monotone	ADJ
ejpam-6173	308	13	mapping	mapping	NOUN
ejpam-6173	308	14	.	.	PUNCT
ejpam-6173	309	1	to	to	PART
ejpam-6173	309	2	show	show	VERB
ejpam-6173	309	3	that	that	SCONJ
ejpam-6173	309	4	bθ	bθ	PROPN
ejpam-6173	309	5	is	be	AUX
ejpam-6173	309	6	maximal	maximal	ADJ
ejpam-6173	309	7	monotone	monotone	ADJ
ejpam-6173	309	8	mapping	mapping	NOUN
ejpam-6173	309	9	,	,	PUNCT
ejpam-6173	309	10	it	it	PRON
ejpam-6173	309	11	is	be	AUX
ejpam-6173	309	12	enough	enough	ADJ
ejpam-6173	309	13	to	to	PART
ejpam-6173	309	14	show	show	VERB
ejpam-6173	309	15	that	that	SCONJ
ejpam-6173	309	16	ran(bθ	ran(bθ	NOUN
ejpam-6173	309	17	+	+	CCONJ
ejpam-6173	309	18	∇f	∇f	NOUN
ejpam-6173	309	19	)	)	PUNCT
ejpam-6173	309	20	=	=	SYM
ejpam-6173	309	21	e∗	e∗	NOUN
ejpam-6173	309	22	(	(	PUNCT
ejpam-6173	309	23	[	[	X
ejpam-6173	309	24	54	54	NUM
ejpam-6173	309	25	,	,	PUNCT
ejpam-6173	309	26	corollary	corollary	ADJ
ejpam-6173	309	27	2.3	2.3	NUM
ejpam-6173	309	28	]	]	PUNCT
ejpam-6173	309	29	)	)	PUNCT
ejpam-6173	309	30	.	.	PUNCT
ejpam-6173	310	1	let	let	VERB
ejpam-6173	310	2	x∗	x∗	PROPN
ejpam-6173	310	3	∈	∈	PROPN
ejpam-6173	310	4	e∗	e∗	NOUN
ejpam-6173	310	5	from	from	ADP
ejpam-6173	310	6	[	[	X
ejpam-6173	310	7	55	55	NUM
ejpam-6173	310	8	,	,	PUNCT
ejpam-6173	310	9	proposition	proposition	NOUN
ejpam-6173	310	10	2.3	2.3	NUM
ejpam-6173	310	11	]	]	PUNCT
ejpam-6173	310	12	and	and	CCONJ
ejpam-6173	310	13	[	[	X
ejpam-6173	310	14	48	48	NUM
ejpam-6173	310	15	,	,	PUNCT
ejpam-6173	310	16	theorem	theorem	VERB
ejpam-6173	310	17	3.5.10	3.5.10	NUM
ejpam-6173	310	18	]	]	PUNCT
ejpam-6173	310	19	,	,	PUNCT
ejpam-6173	310	20	we	we	PRON
ejpam-6173	310	21	have	have	VERB
ejpam-6173	310	22	that	that	SCONJ
ejpam-6173	310	23	f	f	PROPN
ejpam-6173	310	24	is	be	AUX
ejpam-6173	310	25	cofinite	cofinite	ADJ
ejpam-6173	310	26	and	and	CCONJ
ejpam-6173	310	27	therefore	therefore	ADV
ejpam-6173	310	28	ran∇f	ran∇f	VERB
ejpam-6173	310	29	=	=	SYM
ejpam-6173	310	30	intdomf∗	intdomf∗	NOUN
ejpam-6173	310	31	=	=	SYM
ejpam-6173	310	32	e∗	e∗	NOUN
ejpam-6173	310	33	which	which	PRON
ejpam-6173	310	34	follows	follow	VERB
ejpam-6173	310	35	that	that	SCONJ
ejpam-6173	310	36	∇f	∇f	PROPN
ejpam-6173	310	37	is	be	AUX
ejpam-6173	310	38	surjective	surjective	ADJ
ejpam-6173	310	39	.	.	PUNCT
ejpam-6173	311	1	so	so	ADV
ejpam-6173	311	2	,	,	PUNCT
ejpam-6173	311	3	there	there	PRON
ejpam-6173	311	4	exists	exist	VERB
ejpam-6173	311	5	x	x	X
ejpam-6173	311	6	∈	∈	PROPN
ejpam-6173	311	7	e	e	NOUN
ejpam-6173	311	8	such	such	ADJ
ejpam-6173	311	9	that	that	PRON
ejpam-6173	311	10	∇f(x	∇f(x	NUM
ejpam-6173	311	11	)	)	PUNCT
ejpam-6173	312	1	=	=	PUNCT
ejpam-6173	313	1	x∗.	x∗.	PROPN
ejpam-6173	314	1	from	from	ADP
ejpam-6173	314	2	lemma	lemma	PROPN
ejpam-6173	314	3	9	9	NUM
ejpam-6173	314	4	we	we	PRON
ejpam-6173	314	5	know	know	VERB
ejpam-6173	314	6	that	that	DET
ejpam-6173	314	7	dom(resfθ	dom(resfθ	VERB
ejpam-6173	314	8	,	,	PUNCT
ejpam-6173	314	9	φ	φ	NOUN
ejpam-6173	314	10	,	,	PUNCT
ejpam-6173	314	11	ψ	ψ	NOUN
ejpam-6173	314	12	)	)	PUNCT
ejpam-6173	314	13	=	=	SYM
ejpam-6173	314	14	e	e	NOUN
ejpam-6173	314	15	and	and	CCONJ
ejpam-6173	314	16	from	from	ADP
ejpam-6173	314	17	the	the	DET
ejpam-6173	314	18	definition	definition	NOUN
ejpam-6173	314	19	of	of	ADP
ejpam-6173	314	20	resfθ	resfθ	PROPN
ejpam-6173	314	21	,	,	PUNCT
ejpam-6173	314	22	φ	φ	X
ejpam-6173	314	23	,	,	PUNCT
ejpam-6173	314	24	ψ	ψ	VERB
ejpam-6173	314	25	we	we	PRON
ejpam-6173	314	26	obtain	obtain	VERB
ejpam-6173	314	27	θ	θ	PROPN
ejpam-6173	314	28	(	(	PUNCT
ejpam-6173	314	29	resfθ	resfθ	PROPN
ejpam-6173	314	30	,	,	PUNCT
ejpam-6173	314	31	φ	φ	NOUN
ejpam-6173	314	32	,	,	PUNCT
ejpam-6173	314	33	ψ(x1	ψ(x1	NOUN
ejpam-6173	314	34	)	)	PUNCT
ejpam-6173	314	35	,	,	PUNCT
ejpam-6173	314	36	x2	x2	PROPN
ejpam-6173	314	37	)	)	PUNCT
ejpam-6173	315	1	+	+	NUM
ejpam-6173	315	2	φ(x2	φ(x2	NOUN
ejpam-6173	315	3	)	)	PUNCT
ejpam-6173	316	1	+	+	CCONJ
ejpam-6173	316	2	⟨ψ(resfθ	⟨ψ(resfθ	PROPN
ejpam-6173	316	3	,	,	PUNCT
ejpam-6173	316	4	φ	φ	NOUN
ejpam-6173	316	5	,	,	PUNCT
ejpam-6173	316	6	ψ(x1	ψ(x1	NOUN
ejpam-6173	316	7	)	)	PUNCT
ejpam-6173	316	8	)	)	PUNCT
ejpam-6173	317	1	,	,	PUNCT
ejpam-6173	317	2	x2	x2	PROPN
ejpam-6173	317	3	−resfθ	−resfθ	PROPN
ejpam-6173	317	4	,	,	PUNCT
ejpam-6173	317	5	φ	φ	PROPN
ejpam-6173	317	6	,	,	PUNCT
ejpam-6173	317	7	ψ(x1)⟩	ψ(x1)⟩	PUNCT
ejpam-6173	318	1	+	+	ADV
ejpam-6173	318	2	⟨∇f(resfθ	⟨∇f(resfθ	VERB
ejpam-6173	318	3	,	,	PUNCT
ejpam-6173	318	4	φ	φ	NOUN
ejpam-6173	318	5	,	,	PUNCT
ejpam-6173	318	6	ψ(x1))−∇f(x1	ψ(x1))−∇f(x1	NOUN
ejpam-6173	318	7	)	)	PUNCT
ejpam-6173	318	8	,	,	PUNCT
ejpam-6173	318	9	x2	x2	PROPN
ejpam-6173	318	10	−resfθ	−resfθ	PROPN
ejpam-6173	318	11	,	,	PUNCT
ejpam-6173	318	12	φ	φ	PROPN
ejpam-6173	318	13	,	,	PUNCT
ejpam-6173	318	14	ψ(x1)⟩	ψ(x1)⟩	PROPN
ejpam-6173	318	15	≥	≥	PROPN
ejpam-6173	318	16	φ(resfθ	φ(resfθ	PROPN
ejpam-6173	318	17	,	,	PUNCT
ejpam-6173	318	18	φ	φ	NOUN
ejpam-6173	318	19	,	,	PUNCT
ejpam-6173	318	20	ψ(x1	ψ(x1	NOUN
ejpam-6173	318	21	)	)	PUNCT
ejpam-6173	318	22	)	)	PUNCT
ejpam-6173	319	1	for	for	ADP
ejpam-6173	319	2	any	any	DET
ejpam-6173	319	3	x2	x2	PROPN
ejpam-6173	319	4	∈	∈	PROPN
ejpam-6173	319	5	c.	c.	NOUN
ejpam-6173	319	6	it	it	PRON
ejpam-6173	319	7	follows	follow	VERB
ejpam-6173	319	8	that	that	SCONJ
ejpam-6173	319	9	θ	θ	PROPN
ejpam-6173	319	10	(	(	PUNCT
ejpam-6173	319	11	resfθ	resfθ	PROPN
ejpam-6173	319	12	,	,	PUNCT
ejpam-6173	319	13	φ	φ	NOUN
ejpam-6173	319	14	,	,	PUNCT
ejpam-6173	319	15	ψ(x1	ψ(x1	NOUN
ejpam-6173	319	16	)	)	PUNCT
ejpam-6173	319	17	,	,	PUNCT
ejpam-6173	319	18	x2	x2	PROPN
ejpam-6173	319	19	)	)	PUNCT
ejpam-6173	320	1	+	+	NUM
ejpam-6173	320	2	φ(x2	φ(x2	NOUN
ejpam-6173	320	3	)	)	PUNCT
ejpam-6173	321	1	+	+	CCONJ
ejpam-6173	321	2	⟨ψ(resfθ	⟨ψ(resfθ	PROPN
ejpam-6173	321	3	,	,	PUNCT
ejpam-6173	321	4	φ	φ	NOUN
ejpam-6173	321	5	,	,	PUNCT
ejpam-6173	321	6	ψ(x1	ψ(x1	NOUN
ejpam-6173	321	7	)	)	PUNCT
ejpam-6173	321	8	)	)	PUNCT
ejpam-6173	322	1	,	,	PUNCT
ejpam-6173	322	2	x2	x2	PROPN
ejpam-6173	322	3	−resfθ	−resfθ	PROPN
ejpam-6173	322	4	,	,	PUNCT
ejpam-6173	322	5	φ	φ	PROPN
ejpam-6173	322	6	,	,	PUNCT
ejpam-6173	322	7	ψ(x1)⟩	ψ(x1)⟩	PROPN
ejpam-6173	322	8	≥	≥	PROPN
ejpam-6173	322	9	⟨∇f(x1)−∇f(resfθ	⟨∇f(x1)−∇f(resfθ	PROPN
ejpam-6173	322	10	,	,	PUNCT
ejpam-6173	322	11	φ	φ	NOUN
ejpam-6173	322	12	,	,	PUNCT
ejpam-6173	322	13	ψ(x1	ψ(x1	NOUN
ejpam-6173	322	14	)	)	PUNCT
ejpam-6173	322	15	)	)	PUNCT
ejpam-6173	322	16	,	,	PUNCT
ejpam-6173	322	17	x2	x2	PROPN
ejpam-6173	322	18	−resfθ	−resfθ	PROPN
ejpam-6173	322	19	,	,	PUNCT
ejpam-6173	322	20	φ	φ	PROPN
ejpam-6173	322	21	,	,	PUNCT
ejpam-6173	322	22	ψ(x1)⟩	ψ(x1)⟩	PUNCT
ejpam-6173	323	1	+	+	ADV
ejpam-6173	323	2	φ(resfθ	φ(resfθ	ADJ
ejpam-6173	323	3	,	,	PUNCT
ejpam-6173	323	4	φ	φ	NOUN
ejpam-6173	323	5	,	,	PUNCT
ejpam-6173	323	6	ψ(x1	ψ(x1	NOUN
ejpam-6173	323	7	)	)	PUNCT
ejpam-6173	323	8	)	)	PUNCT
ejpam-6173	323	9	for	for	ADP
ejpam-6173	323	10	any	any	DET
ejpam-6173	323	11	x2	x2	PROPN
ejpam-6173	323	12	∈	∈	PROPN
ejpam-6173	323	13	c.	c.	NOUN
ejpam-6173	323	14	this	this	PRON
ejpam-6173	323	15	shows	show	VERB
ejpam-6173	323	16	that	that	SCONJ
ejpam-6173	323	17	∇f(x1)−∇f(resfθ	∇f(x1)−∇f(resfθ	PROPN
ejpam-6173	323	18	,	,	PUNCT
ejpam-6173	323	19	φ	φ	NOUN
ejpam-6173	323	20	,	,	PUNCT
ejpam-6173	323	21	ψ(x1	ψ(x1	NOUN
ejpam-6173	323	22	)	)	PUNCT
ejpam-6173	323	23	)	)	PUNCT
ejpam-6173	323	24	∈	∈	PROPN
ejpam-6173	323	25	bθ(resfθ	bθ(resfθ	PROPN
ejpam-6173	323	26	,	,	PUNCT
ejpam-6173	323	27	φ	φ	NOUN
ejpam-6173	323	28	,	,	PUNCT
ejpam-6173	323	29	ψ(x1	ψ(x1	NOUN
ejpam-6173	323	30	)	)	PUNCT
ejpam-6173	323	31	)	)	PUNCT
ejpam-6173	323	32	.	.	PUNCT
ejpam-6173	324	1	hence	hence	ADV
ejpam-6173	324	2	x∗	x∗	PROPN
ejpam-6173	324	3	=	=	SYM
ejpam-6173	324	4	∇f(x1	∇f(x1	PROPN
ejpam-6173	324	5	)	)	PUNCT
ejpam-6173	324	6	∈	∈	PROPN
ejpam-6173	324	7	(	(	PUNCT
ejpam-6173	324	8	∇f	∇f	NOUN
ejpam-6173	324	9	+	+	NOUN
ejpam-6173	324	10	bθ	bθ	NOUN
ejpam-6173	324	11	)	)	PUNCT
ejpam-6173	324	12	(	(	PUNCT
ejpam-6173	324	13	resfθ	resfθ	PROPN
ejpam-6173	324	14	,	,	PUNCT
ejpam-6173	324	15	φ	φ	NOUN
ejpam-6173	324	16	,	,	PUNCT
ejpam-6173	324	17	ψ(x1	ψ(x1	NOUN
ejpam-6173	324	18	)	)	PUNCT
ejpam-6173	324	19	)	)	PUNCT
ejpam-6173	324	20	.	.	PUNCT
ejpam-6173	325	1	(	(	PUNCT
ejpam-6173	325	2	4.3	4.3	NUM
ejpam-6173	325	3	)	)	PUNCT
ejpam-6173	325	4	it	it	PRON
ejpam-6173	325	5	follows	follow	VERB
ejpam-6173	325	6	that	that	SCONJ
ejpam-6173	325	7	x∗	x∗	PROPN
ejpam-6173	325	8	∈	∈	PROPN
ejpam-6173	325	9	ran(bθ	ran(bθ	X
ejpam-6173	326	1	+	+	CCONJ
ejpam-6173	326	2	∇f	∇f	NOUN
ejpam-6173	326	3	)	)	PUNCT
ejpam-6173	326	4	.	.	PUNCT
ejpam-6173	327	1	(	(	PUNCT
ejpam-6173	327	2	3	3	X
ejpam-6173	327	3	)	)	PUNCT
ejpam-6173	327	4	it	it	PRON
ejpam-6173	327	5	is	be	AUX
ejpam-6173	327	6	easy	easy	ADJ
ejpam-6173	327	7	to	to	PART
ejpam-6173	327	8	show	show	VERB
ejpam-6173	327	9	that	that	SCONJ
ejpam-6173	327	10	resfbθ	resfbθ	NOUN
ejpam-6173	327	11	is	be	AUX
ejpam-6173	327	12	single	single	ADJ
ejpam-6173	327	13	valued	value	VERB
ejpam-6173	327	14	.	.	PUNCT
ejpam-6173	328	1	from	from	ADP
ejpam-6173	328	2	lemma	lemma	PROPN
ejpam-6173	328	3	9	9	NUM
ejpam-6173	328	4	we	we	PRON
ejpam-6173	328	5	know	know	VERB
ejpam-6173	328	6	that	that	DET
ejpam-6173	328	7	resfθ	resfθ	VERB
ejpam-6173	328	8	,	,	PUNCT
ejpam-6173	328	9	φ	φ	X
ejpam-6173	328	10	,	,	PUNCT
ejpam-6173	328	11	ψ	ψ	X
ejpam-6173	328	12	is	be	AUX
ejpam-6173	328	13	single	single	ADV
ejpam-6173	328	14	valued	value	VERB
ejpam-6173	328	15	too	too	ADV
ejpam-6173	328	16	.	.	PUNCT
ejpam-6173	329	1	from	from	ADP
ejpam-6173	329	2	(	(	PUNCT
ejpam-6173	329	3	4.3	4.3	NUM
ejpam-6173	329	4	)	)	PUNCT
ejpam-6173	329	5	we	we	PRON
ejpam-6173	329	6	have	have	VERB
ejpam-6173	329	7	resfbθ	resfbθ	NOUN
ejpam-6173	329	8	=	=	SYM
ejpam-6173	329	9	(	(	PUNCT
ejpam-6173	329	10	bθ	bθ	PROPN
ejpam-6173	330	1	+	+	NOUN
ejpam-6173	330	2	∇f)−1	∇f)−1	NOUN
ejpam-6173	330	3	◦	◦	NOUN
ejpam-6173	330	4	∇f	∇f	NOUN
ejpam-6173	330	5	=	=	SYM
ejpam-6173	330	6	resfθ	resfθ	PROPN
ejpam-6173	330	7	,	,	PUNCT
ejpam-6173	330	8	φ	φ	NOUN
ejpam-6173	330	9	,	,	PUNCT
ejpam-6173	330	10	ψ	ψ	SYM
ejpam-6173	330	11	.	.	PROPN
ejpam-6173	331	1	v.	v.	ADP
ejpam-6173	331	2	darvish	darvish	PROPN
ejpam-6173	331	3	et	et	PROPN
ejpam-6173	331	4	al	al	PROPN
ejpam-6173	331	5	.	.	PUNCT
ejpam-6173	331	6	/	/	SYM
ejpam-6173	331	7	eur	eur	PROPN
ejpam-6173	331	8	.	.	PUNCT
ejpam-6173	332	1	j.	j.	PROPN
ejpam-6173	332	2	pure	pure	PROPN
ejpam-6173	332	3	appl	appl	PROPN
ejpam-6173	332	4	.	.	PROPN
ejpam-6173	332	5	math	math	PROPN
ejpam-6173	332	6	,	,	PUNCT
ejpam-6173	332	7	18	18	NUM
ejpam-6173	332	8	(	(	PUNCT
ejpam-6173	332	9	3	3	NUM
ejpam-6173	332	10	)	)	PUNCT
ejpam-6173	332	11	(	(	PUNCT
ejpam-6173	332	12	2025	2025	NUM
ejpam-6173	332	13	)	)	PUNCT
ejpam-6173	332	14	,	,	PUNCT
ejpam-6173	332	15	6173	6173	NUM
ejpam-6173	332	16	14	14	NUM
ejpam-6173	332	17	of	of	ADP
ejpam-6173	332	18	32	32	NUM
ejpam-6173	332	19	lemma	lemma	PROPN
ejpam-6173	332	20	14	14	NUM
ejpam-6173	332	21	.	.	PUNCT
ejpam-6173	333	1	let	let	VERB
ejpam-6173	333	2	{	{	PUNCT
ejpam-6173	333	3	xn	xn	VERB
ejpam-6173	333	4	}	}	PUNCT
ejpam-6173	333	5	be	be	AUX
ejpam-6173	333	6	a	a	DET
ejpam-6173	333	7	sequence	sequence	NOUN
ejpam-6173	333	8	generated	generate	VERB
ejpam-6173	333	9	by	by	ADP
ejpam-6173	333	10	algorithm	algorithm	NOUN
ejpam-6173	333	11	3.2	3.2	NUM
ejpam-6173	333	12	satisfying	satisfy	VERB
ejpam-6173	333	13	assumption	assumption	NOUN
ejpam-6173	333	14	3.1	3.1	NUM
ejpam-6173	333	15	(	(	PUNCT
ejpam-6173	333	16	a	a	PRON
ejpam-6173	333	17	and	and	CCONJ
ejpam-6173	333	18	b	b	NOUN
ejpam-6173	333	19	)	)	PUNCT
ejpam-6173	333	20	.	.	PUNCT
ejpam-6173	334	1	then	then	ADV
ejpam-6173	334	2	,	,	PUNCT
ejpam-6173	334	3	{	{	PUNCT
ejpam-6173	334	4	xn	xn	X
ejpam-6173	334	5	}	}	PUNCT
ejpam-6173	334	6	is	be	AUX
ejpam-6173	334	7	bounded	bound	VERB
ejpam-6173	334	8	.	.	PUNCT
ejpam-6173	335	1	proof	proof	NOUN
ejpam-6173	335	2	.	.	PUNCT
ejpam-6173	336	1	let	let	VERB
ejpam-6173	336	2	p	p	PROPN
ejpam-6173	336	3	∈	∈	PROPN
ejpam-6173	336	4	ω	ω	PROPN
ejpam-6173	336	5	.	.	PUNCT
ejpam-6173	337	1	then	then	ADV
ejpam-6173	337	2	,	,	PUNCT
ejpam-6173	337	3	from	from	ADP
ejpam-6173	337	4	lemma	lemma	PROPN
ejpam-6173	337	5	8	8	NUM
ejpam-6173	337	6	we	we	PRON
ejpam-6173	337	7	have	have	VERB
ejpam-6173	337	8	that	that	PRON
ejpam-6173	337	9	f	f	PROPN
ejpam-6173	337	10	(	(	PUNCT
ejpam-6173	337	11	t	t	PROPN
ejpam-6173	337	12	)	)	PUNCT
ejpam-6173	337	13	is	be	AUX
ejpam-6173	337	14	closed	close	VERB
ejpam-6173	337	15	and	and	CCONJ
ejpam-6173	337	16	convex	convex	PROPN
ejpam-6173	337	17	.	.	PUNCT
ejpam-6173	338	1	from	from	ADP
ejpam-6173	338	2	lemma	lemma	PROPN
ejpam-6173	338	3	10	10	NUM
ejpam-6173	338	4	and	and	CCONJ
ejpam-6173	338	5	the	the	DET
ejpam-6173	338	6	definition	definition	NOUN
ejpam-6173	338	7	of	of	ADP
ejpam-6173	338	8	zn	zn	PROPN
ejpam-6173	338	9	we	we	PRON
ejpam-6173	338	10	have	have	VERB
ejpam-6173	338	11	df	df	NOUN
ejpam-6173	338	12	(	(	PUNCT
ejpam-6173	338	13	p	p	X
ejpam-6173	338	14	,	,	PUNCT
ejpam-6173	338	15	zn	zn	NOUN
ejpam-6173	338	16	)	)	PUNCT
ejpam-6173	339	1	=	=	SYM
ejpam-6173	339	2	df	df	NOUN
ejpam-6173	339	3	(	(	PUNCT
ejpam-6173	339	4	p	p	NOUN
ejpam-6173	339	5	,	,	PUNCT
ejpam-6173	339	6	resfbθn	resfbθn	NOUN
ejpam-6173	339	7	◦	◦	NOUN
ejpam-6173	339	8	·	·	PUNCT
ejpam-6173	339	9	·	·	PUNCT
ejpam-6173	339	10	·	·	PUNCT
ejpam-6173	339	11	◦	◦	NOUN
ejpam-6173	339	12	resfbθ2	resfbθ2	NOUN
ejpam-6173	339	13	◦	◦	NOUN
ejpam-6173	339	14	resfbθ1	resfbθ1	PROPN
ejpam-6173	339	15	(	(	PUNCT
ejpam-6173	339	16	wn	wn	PROPN
ejpam-6173	339	17	)	)	PUNCT
ejpam-6173	339	18	)	)	PUNCT
ejpam-6173	340	1	≤	≤	NUM
ejpam-6173	340	2	df	df	NOUN
ejpam-6173	340	3	(	(	PUNCT
ejpam-6173	340	4	p	p	X
ejpam-6173	340	5	,	,	PUNCT
ejpam-6173	340	6	resfbθ1	resfbθ1	PROPN
ejpam-6173	340	7	(	(	PUNCT
ejpam-6173	340	8	wn	wn	PROPN
ejpam-6173	340	9	)	)	PUNCT
ejpam-6173	340	10	)	)	PUNCT
ejpam-6173	340	11	≤	≤	NUM
ejpam-6173	340	12	df	df	NOUN
ejpam-6173	340	13	(	(	PUNCT
ejpam-6173	340	14	p	p	X
ejpam-6173	340	15	,	,	PUNCT
ejpam-6173	340	16	wn	wn	PROPN
ejpam-6173	340	17	)	)	PUNCT
ejpam-6173	340	18	.	.	PUNCT
ejpam-6173	341	1	(	(	PUNCT
ejpam-6173	341	2	4.4	4.4	NUM
ejpam-6173	341	3	)	)	PUNCT
ejpam-6173	341	4	also	also	ADV
ejpam-6173	341	5	,	,	PUNCT
ejpam-6173	341	6	from	from	ADP
ejpam-6173	341	7	the	the	DET
ejpam-6173	341	8	definition	definition	NOUN
ejpam-6173	341	9	of	of	ADP
ejpam-6173	341	10	wn	wn	PROPN
ejpam-6173	341	11	and	and	CCONJ
ejpam-6173	341	12	(	(	PUNCT
ejpam-6173	341	13	2.8	2.8	NUM
ejpam-6173	341	14	)	)	PUNCT
ejpam-6173	341	15	,	,	PUNCT
ejpam-6173	341	16	we	we	PRON
ejpam-6173	341	17	obtain	obtain	VERB
ejpam-6173	341	18	df	df	NOUN
ejpam-6173	341	19	(	(	PUNCT
ejpam-6173	341	20	p	p	X
ejpam-6173	341	21	,	,	PUNCT
ejpam-6173	341	22	wn	wn	PROPN
ejpam-6173	341	23	)	)	PUNCT
ejpam-6173	341	24	≤	≤	NOUN
ejpam-6173	341	25	df	df	NOUN
ejpam-6173	341	26	(	(	PUNCT
ejpam-6173	341	27	p,∇f∗	p,∇f∗	X
ejpam-6173	341	28	(	(	PUNCT
ejpam-6173	341	29	∇f	∇f	PROPN
ejpam-6173	341	30	(	(	PUNCT
ejpam-6173	341	31	xn	xn	PROPN
ejpam-6173	341	32	)	)	PUNCT
ejpam-6173	342	1	+	+	NUM
ejpam-6173	342	2	θn	θn	ADJ
ejpam-6173	342	3	(	(	PUNCT
ejpam-6173	342	4	∇f	∇f	PROPN
ejpam-6173	342	5	(	(	PUNCT
ejpam-6173	342	6	xn−1)−∇f	xn−1)−∇f	X
ejpam-6173	342	7	(	(	PUNCT
ejpam-6173	342	8	xn	xn	PROPN
ejpam-6173	342	9	)	)	PUNCT
ejpam-6173	342	10	)	)	PUNCT
ejpam-6173	342	11	)	)	PUNCT
ejpam-6173	343	1	=	=	PRON
ejpam-6173	343	2	df	df	PROPN
ejpam-6173	343	3	(	(	PUNCT
ejpam-6173	343	4	p,∇f∗	p,∇f∗	X
ejpam-6173	343	5	(	(	PUNCT
ejpam-6173	343	6	(	(	PUNCT
ejpam-6173	343	7	1−	1−	NUM
ejpam-6173	343	8	θn)∇f	θn)∇f	NOUN
ejpam-6173	343	9	(	(	PUNCT
ejpam-6173	343	10	xn	xn	NUM
ejpam-6173	343	11	)	)	PUNCT
ejpam-6173	344	1	+	+	CCONJ
ejpam-6173	344	2	θn∇f	θn∇f	PROPN
ejpam-6173	344	3	(	(	PUNCT
ejpam-6173	344	4	xn−1	xn−1	PROPN
ejpam-6173	344	5	)	)	PUNCT
ejpam-6173	344	6	)	)	PUNCT
ejpam-6173	344	7	)	)	PUNCT
ejpam-6173	344	8	≤	≤	NOUN
ejpam-6173	344	9	(	(	PUNCT
ejpam-6173	344	10	1−	1−	NUM
ejpam-6173	344	11	θn)df	θn)df	X
ejpam-6173	344	12	(	(	PUNCT
ejpam-6173	344	13	p	p	X
ejpam-6173	344	14	,	,	PUNCT
ejpam-6173	344	15	xn	xn	PUNCT
ejpam-6173	344	16	)	)	PUNCT
ejpam-6173	344	17	+	+	CCONJ
ejpam-6173	344	18	θndf	θndf	NOUN
ejpam-6173	344	19	(	(	PUNCT
ejpam-6173	344	20	p	p	X
ejpam-6173	344	21	,	,	PUNCT
ejpam-6173	344	22	xn−1	xn−1	PROPN
ejpam-6173	344	23	)	)	PUNCT
ejpam-6173	344	24	.	.	PUNCT
ejpam-6173	345	1	(	(	PUNCT
ejpam-6173	345	2	4.5	4.5	NUM
ejpam-6173	345	3	)	)	PUNCT
ejpam-6173	345	4	also	also	ADV
ejpam-6173	345	5	,	,	PUNCT
ejpam-6173	345	6	df	df	PROPN
ejpam-6173	345	7	(	(	PUNCT
ejpam-6173	345	8	p	p	X
ejpam-6173	345	9	,	,	PUNCT
ejpam-6173	345	10	yn	yn	PROPN
ejpam-6173	345	11	)	)	PUNCT
ejpam-6173	345	12	=	=	SYM
ejpam-6173	345	13	df	df	PROPN
ejpam-6173	345	14	(	(	PUNCT
ejpam-6173	345	15	p,∇f∗	p,∇f∗	X
ejpam-6173	345	16	(	(	PUNCT
ejpam-6173	345	17	βn∇f	βn∇f	NOUN
ejpam-6173	345	18	(	(	PUNCT
ejpam-6173	345	19	qn	qn	NOUN
ejpam-6173	345	20	)	)	PUNCT
ejpam-6173	345	21	+	+	CCONJ
ejpam-6173	345	22	(	(	PUNCT
ejpam-6173	345	23	1−	1−	NUM
ejpam-6173	345	24	βn)∇f	βn)∇f	X
ejpam-6173	345	25	(	(	PUNCT
ejpam-6173	345	26	t	t	PROPN
ejpam-6173	345	27	(	(	PUNCT
ejpam-6173	345	28	zn	zn	NOUN
ejpam-6173	345	29	)	)	PUNCT
ejpam-6173	345	30	)	)	PUNCT
ejpam-6173	345	31	)	)	PUNCT
ejpam-6173	346	1	≤	≤	NUM
ejpam-6173	346	2	βndf	βndf	NOUN
ejpam-6173	346	3	(	(	PUNCT
ejpam-6173	346	4	p	p	X
ejpam-6173	346	5	,	,	PUNCT
ejpam-6173	346	6	qn	qn	NOUN
ejpam-6173	346	7	)	)	PUNCT
ejpam-6173	346	8	+	+	CCONJ
ejpam-6173	346	9	(	(	PUNCT
ejpam-6173	346	10	1−	1−	NUM
ejpam-6173	346	11	βn)df	βn)df	PUNCT
ejpam-6173	346	12	(	(	PUNCT
ejpam-6173	346	13	p	p	X
ejpam-6173	346	14	,	,	PUNCT
ejpam-6173	346	15	t	t	PROPN
ejpam-6173	346	16	(	(	PUNCT
ejpam-6173	346	17	zn	zn	NOUN
ejpam-6173	346	18	)	)	PUNCT
ejpam-6173	346	19	)	)	PUNCT
ejpam-6173	346	20	≤	≤	NUM
ejpam-6173	347	1	βndf	βndf	NOUN
ejpam-6173	347	2	(	(	PUNCT
ejpam-6173	347	3	p	p	X
ejpam-6173	347	4	,	,	PUNCT
ejpam-6173	347	5	qn	qn	NOUN
ejpam-6173	347	6	)	)	PUNCT
ejpam-6173	347	7	+	+	CCONJ
ejpam-6173	347	8	(	(	PUNCT
ejpam-6173	347	9	1−	1−	NUM
ejpam-6173	347	10	βn)df	βn)df	PUNCT
ejpam-6173	347	11	(	(	PUNCT
ejpam-6173	347	12	p	p	X
ejpam-6173	347	13	,	,	PUNCT
ejpam-6173	347	14	zn	zn	NOUN
ejpam-6173	347	15	)	)	PUNCT
ejpam-6173	347	16	≤	≤	NUM
ejpam-6173	347	17	βndf	βndf	NOUN
ejpam-6173	347	18	(	(	PUNCT
ejpam-6173	347	19	p	p	X
ejpam-6173	347	20	,	,	PUNCT
ejpam-6173	347	21	qn	qn	NOUN
ejpam-6173	347	22	)	)	PUNCT
ejpam-6173	347	23	+	+	CCONJ
ejpam-6173	347	24	(	(	PUNCT
ejpam-6173	347	25	1−	1−	NUM
ejpam-6173	347	26	βn)df	βn)df	PUNCT
ejpam-6173	347	27	(	(	PUNCT
ejpam-6173	347	28	p	p	X
ejpam-6173	347	29	,	,	PUNCT
ejpam-6173	347	30	wn	wn	PROPN
ejpam-6173	347	31	)	)	PUNCT
ejpam-6173	347	32	(	(	PUNCT
ejpam-6173	347	33	4.6	4.6	NUM
ejpam-6173	347	34	)	)	PUNCT
ejpam-6173	347	35	from	from	ADP
ejpam-6173	347	36	the	the	DET
ejpam-6173	347	37	definition	definition	NOUN
ejpam-6173	347	38	of	of	ADP
ejpam-6173	347	39	xn+1	xn+1	PROPN
ejpam-6173	347	40	and	and	CCONJ
ejpam-6173	347	41	(	(	PUNCT
ejpam-6173	347	42	2.8	2.8	NUM
ejpam-6173	347	43	)	)	PUNCT
ejpam-6173	347	44	,	,	PUNCT
ejpam-6173	347	45	we	we	PRON
ejpam-6173	347	46	obtain	obtain	VERB
ejpam-6173	347	47	df	df	NOUN
ejpam-6173	347	48	(	(	PUNCT
ejpam-6173	347	49	p	p	X
ejpam-6173	347	50	,	,	PUNCT
ejpam-6173	347	51	xn+1	xn+1	NUM
ejpam-6173	347	52	)	)	PUNCT
ejpam-6173	347	53	=	=	SYM
ejpam-6173	347	54	df	df	PROPN
ejpam-6173	347	55	(	(	PUNCT
ejpam-6173	347	56	p,∇f∗	p,∇f∗	X
ejpam-6173	347	57	(	(	PUNCT
ejpam-6173	347	58	αn∇f	αn∇f	NOUN
ejpam-6173	347	59	(	(	PUNCT
ejpam-6173	347	60	wn	wn	PROPN
ejpam-6173	347	61	)	)	PUNCT
ejpam-6173	347	62	+	+	CCONJ
ejpam-6173	347	63	(	(	PUNCT
ejpam-6173	347	64	1−	1−	NUM
ejpam-6173	347	65	αn)∇f	αn)∇f	NOUN
ejpam-6173	347	66	(	(	PUNCT
ejpam-6173	347	67	t	t	PROPN
ejpam-6173	347	68	(	(	PUNCT
ejpam-6173	347	69	yn	yn	PROPN
ejpam-6173	347	70	)	)	PUNCT
ejpam-6173	347	71	)	)	PUNCT
ejpam-6173	347	72	)	)	PUNCT
ejpam-6173	347	73	≤	≤	NUM
ejpam-6173	348	1	αndf	αndf	ADJ
ejpam-6173	348	2	(	(	PUNCT
ejpam-6173	348	3	p	p	X
ejpam-6173	348	4	,	,	PUNCT
ejpam-6173	348	5	wn	wn	PROPN
ejpam-6173	348	6	)	)	PUNCT
ejpam-6173	348	7	+	+	CCONJ
ejpam-6173	348	8	(	(	PUNCT
ejpam-6173	348	9	1−	1−	NUM
ejpam-6173	348	10	αn)df	αn)df	NUM
ejpam-6173	348	11	(	(	PUNCT
ejpam-6173	348	12	p	p	X
ejpam-6173	348	13	,	,	PUNCT
ejpam-6173	348	14	t	t	PROPN
ejpam-6173	348	15	(	(	PUNCT
ejpam-6173	348	16	yn	yn	PROPN
ejpam-6173	348	17	)	)	PUNCT
ejpam-6173	348	18	)	)	PUNCT
ejpam-6173	348	19	≤	≤	NUM
ejpam-6173	348	20	αndf	αndf	ADJ
ejpam-6173	348	21	(	(	PUNCT
ejpam-6173	348	22	p	p	X
ejpam-6173	348	23	,	,	PUNCT
ejpam-6173	348	24	wn	wn	PROPN
ejpam-6173	348	25	)	)	PUNCT
ejpam-6173	348	26	+	+	CCONJ
ejpam-6173	348	27	(	(	PUNCT
ejpam-6173	348	28	1−	1−	NUM
ejpam-6173	348	29	αn)df	αn)df	NUM
ejpam-6173	348	30	(	(	PUNCT
ejpam-6173	348	31	p	p	X
ejpam-6173	348	32	,	,	PUNCT
ejpam-6173	348	33	yn	yn	PROPN
ejpam-6173	348	34	)	)	PUNCT
ejpam-6173	348	35	≤	≤	NUM
ejpam-6173	348	36	αndf	αndf	ADJ
ejpam-6173	348	37	(	(	PUNCT
ejpam-6173	348	38	p	p	X
ejpam-6173	348	39	,	,	PUNCT
ejpam-6173	348	40	wn	wn	PROPN
ejpam-6173	348	41	)	)	PUNCT
ejpam-6173	348	42	+	+	CCONJ
ejpam-6173	348	43	(	(	PUNCT
ejpam-6173	348	44	1−	1−	NUM
ejpam-6173	348	45	αn	αn	NOUN
ejpam-6173	348	46	)	)	PUNCT
ejpam-6173	349	1	[	[	X
ejpam-6173	349	2	βndf	βndf	NOUN
ejpam-6173	349	3	(	(	PUNCT
ejpam-6173	349	4	p	p	X
ejpam-6173	349	5	,	,	PUNCT
ejpam-6173	349	6	qn	qn	NOUN
ejpam-6173	349	7	)	)	PUNCT
ejpam-6173	349	8	+	+	CCONJ
ejpam-6173	349	9	(	(	PUNCT
ejpam-6173	349	10	1−	1−	NUM
ejpam-6173	349	11	βn)df	βn)df	PUNCT
ejpam-6173	349	12	(	(	PUNCT
ejpam-6173	349	13	p	p	X
ejpam-6173	349	14	,	,	PUNCT
ejpam-6173	349	15	wn	wn	PROPN
ejpam-6173	349	16	)	)	PUNCT
ejpam-6173	349	17	]	]	PUNCT
ejpam-6173	350	1	=	=	PUNCT
ejpam-6173	350	2	βn	βn	X
ejpam-6173	350	3	(	(	PUNCT
ejpam-6173	350	4	1−	1−	NUM
ejpam-6173	350	5	αn)df	αn)df	NUM
ejpam-6173	350	6	(	(	PUNCT
ejpam-6173	350	7	p	p	X
ejpam-6173	350	8	,	,	PUNCT
ejpam-6173	350	9	qn	qn	NOUN
ejpam-6173	350	10	)	)	PUNCT
ejpam-6173	350	11	+	+	PUNCT
ejpam-6173	351	1	[	[	X
ejpam-6173	351	2	αn	αn	NOUN
ejpam-6173	351	3	+	+	CCONJ
ejpam-6173	351	4	(	(	PUNCT
ejpam-6173	351	5	1−	1−	NUM
ejpam-6173	351	6	αn	αn	NOUN
ejpam-6173	351	7	)	)	PUNCT
ejpam-6173	351	8	(	(	PUNCT
ejpam-6173	351	9	1−	1−	NUM
ejpam-6173	351	10	βn)]df	βn)]df	PUNCT
ejpam-6173	351	11	(	(	PUNCT
ejpam-6173	351	12	p	p	X
ejpam-6173	351	13	,	,	PUNCT
ejpam-6173	351	14	wn	wn	PROPN
ejpam-6173	351	15	)	)	PUNCT
ejpam-6173	351	16	≤	≤	NUM
ejpam-6173	351	17	βn	βn	PUNCT
ejpam-6173	351	18	(	(	PUNCT
ejpam-6173	351	19	1−	1−	NUM
ejpam-6173	351	20	αn)df	αn)df	NUM
ejpam-6173	351	21	(	(	PUNCT
ejpam-6173	351	22	p	p	X
ejpam-6173	351	23	,	,	PUNCT
ejpam-6173	351	24	qn	qn	NOUN
ejpam-6173	351	25	)	)	PUNCT
ejpam-6173	351	26	+	+	PUNCT
ejpam-6173	352	1	[	[	X
ejpam-6173	352	2	1−	1−	NUM
ejpam-6173	352	3	βn	βn	NOUN
ejpam-6173	352	4	(	(	PUNCT
ejpam-6173	352	5	1−	1−	NUM
ejpam-6173	352	6	αn	αn	NOUN
ejpam-6173	352	7	)	)	PUNCT
ejpam-6173	352	8	]	]	PUNCT
ejpam-6173	353	1	[	[	X
ejpam-6173	353	2	(	(	PUNCT
ejpam-6173	353	3	1−	1−	NUM
ejpam-6173	353	4	θn)df	θn)df	X
ejpam-6173	353	5	(	(	PUNCT
ejpam-6173	353	6	p	p	X
ejpam-6173	353	7	,	,	PUNCT
ejpam-6173	353	8	xn	xn	PUNCT
ejpam-6173	353	9	)	)	PUNCT
ejpam-6173	354	1	+	+	CCONJ
ejpam-6173	354	2	θndf	θndf	NOUN
ejpam-6173	354	3	(	(	PUNCT
ejpam-6173	354	4	p	p	X
ejpam-6173	354	5	,	,	PUNCT
ejpam-6173	354	6	xn−1	xn−1	PROPN
ejpam-6173	354	7	)	)	PUNCT
ejpam-6173	354	8	]	]	PUNCT
ejpam-6173	354	9	≤	≤	NUM
ejpam-6173	354	10	max	max	PROPN
ejpam-6173	354	11	{	{	PUNCT
ejpam-6173	354	12	df	df	PROPN
ejpam-6173	354	13	(	(	PUNCT
ejpam-6173	354	14	p	p	X
ejpam-6173	354	15	,	,	PUNCT
ejpam-6173	354	16	qn	qn	NOUN
ejpam-6173	354	17	)	)	PUNCT
ejpam-6173	354	18	,	,	PUNCT
ejpam-6173	354	19	df	df	PROPN
ejpam-6173	354	20	(	(	PUNCT
ejpam-6173	354	21	p	p	X
ejpam-6173	354	22	,	,	PUNCT
ejpam-6173	354	23	xn	xn	PROPN
ejpam-6173	354	24	)	)	PUNCT
ejpam-6173	354	25	,	,	PUNCT
ejpam-6173	354	26	df	df	PROPN
ejpam-6173	354	27	(	(	PUNCT
ejpam-6173	354	28	p	p	X
ejpam-6173	354	29	,	,	PUNCT
ejpam-6173	354	30	xn−1	xn−1	PROPN
ejpam-6173	354	31	)	)	PUNCT
ejpam-6173	354	32	}	}	PUNCT
ejpam-6173	354	33	.	.	PUNCT
ejpam-6173	355	1	(	(	PUNCT
ejpam-6173	355	2	4.7	4.7	NUM
ejpam-6173	355	3	)	)	PUNCT
ejpam-6173	355	4	since	since	SCONJ
ejpam-6173	355	5	{	{	PUNCT
ejpam-6173	355	6	qn	qn	AUX
ejpam-6173	355	7	}	}	PUNCT
ejpam-6173	355	8	is	be	AUX
ejpam-6173	355	9	bounded	bound	VERB
ejpam-6173	355	10	and	and	CCONJ
ejpam-6173	355	11	∇f	∇f	PROPN
ejpam-6173	355	12	is	be	AUX
ejpam-6173	355	13	bounded	bound	VERB
ejpam-6173	355	14	on	on	ADP
ejpam-6173	355	15	bounded	bounded	PROPN
ejpam-6173	355	16	subset	subset	NOUN
ejpam-6173	355	17	of	of	ADP
ejpam-6173	355	18	e	e	NOUN
ejpam-6173	355	19	,	,	PUNCT
ejpam-6173	355	20	there	there	PRON
ejpam-6173	355	21	exists	exist	VERB
ejpam-6173	355	22	a	a	DET
ejpam-6173	355	23	real	real	ADJ
ejpam-6173	355	24	number	number	NOUN
ejpam-6173	355	25	d	d	NOUN
ejpam-6173	355	26	>	>	X
ejpam-6173	355	27	0	0	NUM
ejpam-6173	355	28	such	such	ADJ
ejpam-6173	355	29	that	that	DET
ejpam-6173	355	30	df	df	NOUN
ejpam-6173	355	31	(	(	PUNCT
ejpam-6173	355	32	p	p	X
ejpam-6173	355	33	,	,	PUNCT
ejpam-6173	355	34	qn	qn	NOUN
ejpam-6173	355	35	)	)	PUNCT
ejpam-6173	355	36	≤	≤	NOUN
ejpam-6173	356	1	d	d	NOUN
ejpam-6173	356	2	,	,	PUNCT
ejpam-6173	356	3	for	for	ADP
ejpam-6173	356	4	all	all	DET
ejpam-6173	356	5	n	n	PRON
ejpam-6173	356	6	∈	∈	PROPN
ejpam-6173	356	7	n.	n.	NOUN
ejpam-6173	356	8	thus	thus	ADV
ejpam-6173	356	9	,	,	PUNCT
ejpam-6173	356	10	by	by	ADP
ejpam-6173	356	11	induction	induction	NOUN
ejpam-6173	356	12	,	,	PUNCT
ejpam-6173	356	13	we	we	PRON
ejpam-6173	356	14	have	have	VERB
ejpam-6173	356	15	df	df	NOUN
ejpam-6173	356	16	(	(	PUNCT
ejpam-6173	356	17	p	p	X
ejpam-6173	356	18	,	,	PUNCT
ejpam-6173	356	19	xn+1	xn+1	NUM
ejpam-6173	356	20	)	)	PUNCT
ejpam-6173	356	21	≤	≤	NUM
ejpam-6173	357	1	max	max	PROPN
ejpam-6173	357	2	{	{	PUNCT
ejpam-6173	357	3	d	d	PROPN
ejpam-6173	357	4	,	,	PUNCT
ejpam-6173	357	5	df	df	PROPN
ejpam-6173	357	6	(	(	PUNCT
ejpam-6173	357	7	p	p	X
ejpam-6173	357	8	,	,	PUNCT
ejpam-6173	357	9	xn	xn	PROPN
ejpam-6173	357	10	)	)	PUNCT
ejpam-6173	357	11	,	,	PUNCT
ejpam-6173	357	12	df	df	PROPN
ejpam-6173	357	13	(	(	PUNCT
ejpam-6173	357	14	p	p	X
ejpam-6173	357	15	,	,	PUNCT
ejpam-6173	357	16	xn−1	xn−1	PROPN
ejpam-6173	357	17	)	)	PUNCT
ejpam-6173	357	18	}	}	PUNCT
ejpam-6173	357	19	...	...	PUNCT
ejpam-6173	358	1	≤	≤	NUM
ejpam-6173	358	2	max	max	PROPN
ejpam-6173	358	3	{	{	PUNCT
ejpam-6173	358	4	d	d	PROPN
ejpam-6173	358	5	,	,	PUNCT
ejpam-6173	358	6	df	df	PROPN
ejpam-6173	358	7	(	(	PUNCT
ejpam-6173	358	8	p	p	X
ejpam-6173	358	9	,	,	PUNCT
ejpam-6173	358	10	xn0	xn0	PROPN
ejpam-6173	358	11	)	)	PUNCT
ejpam-6173	358	12	,	,	PUNCT
ejpam-6173	358	13	df	df	PROPN
ejpam-6173	358	14	(	(	PUNCT
ejpam-6173	358	15	p	p	X
ejpam-6173	358	16	,	,	PUNCT
ejpam-6173	358	17	xn0−1	xn0−1	PROPN
ejpam-6173	358	18	)	)	PUNCT
ejpam-6173	358	19	}	}	PUNCT
ejpam-6173	358	20	.	.	PUNCT
ejpam-6173	359	1	this	this	PRON
ejpam-6173	359	2	implies	imply	VERB
ejpam-6173	359	3	that	that	SCONJ
ejpam-6173	359	4	{	{	PUNCT
ejpam-6173	359	5	df	df	PROPN
ejpam-6173	359	6	(	(	PUNCT
ejpam-6173	359	7	p	p	X
ejpam-6173	359	8	,	,	PUNCT
ejpam-6173	359	9	xn	xn	PROPN
ejpam-6173	359	10	)	)	PUNCT
ejpam-6173	359	11	}	}	PUNCT
ejpam-6173	359	12	is	be	AUX
ejpam-6173	359	13	bounded	bound	VERB
ejpam-6173	359	14	.	.	PUNCT
ejpam-6173	360	1	hence	hence	ADV
ejpam-6173	360	2	,	,	PUNCT
ejpam-6173	360	3	from	from	ADP
ejpam-6173	360	4	lemma	lemma	PROPN
ejpam-6173	360	5	6	6	NUM
ejpam-6173	360	6	we	we	PRON
ejpam-6173	360	7	have	have	VERB
ejpam-6173	360	8	that	that	PRON
ejpam-6173	360	9	{	{	PUNCT
ejpam-6173	360	10	xn	xn	X
ejpam-6173	360	11	}	}	PUNCT
ejpam-6173	360	12	is	be	AUX
ejpam-6173	360	13	bounded	bound	VERB
ejpam-6173	360	14	.	.	PUNCT
ejpam-6173	361	1	consequently	consequently	ADV
ejpam-6173	361	2	,	,	PUNCT
ejpam-6173	361	3	{	{	PUNCT
ejpam-6173	361	4	wn	wn	X
ejpam-6173	361	5	}	}	PUNCT
ejpam-6173	361	6	,	,	PUNCT
ejpam-6173	361	7	{	{	PUNCT
ejpam-6173	361	8	zn	zn	X
ejpam-6173	361	9	}	}	PUNCT
ejpam-6173	361	10	and	and	CCONJ
ejpam-6173	361	11	{	{	PUNCT
ejpam-6173	361	12	yn	yn	NOUN
ejpam-6173	361	13	}	}	PUNCT
ejpam-6173	361	14	are	be	AUX
ejpam-6173	361	15	all	all	PRON
ejpam-6173	361	16	bounded	bound	VERB
ejpam-6173	361	17	.	.	PUNCT
ejpam-6173	362	1	v.	v.	ADP
ejpam-6173	362	2	darvish	darvish	PROPN
ejpam-6173	362	3	et	et	PROPN
ejpam-6173	362	4	al	al	PROPN
ejpam-6173	362	5	.	.	PUNCT
ejpam-6173	362	6	/	/	SYM
ejpam-6173	362	7	eur	eur	PROPN
ejpam-6173	362	8	.	.	PUNCT
ejpam-6173	363	1	j.	j.	PROPN
ejpam-6173	363	2	pure	pure	PROPN
ejpam-6173	363	3	appl	appl	PROPN
ejpam-6173	363	4	.	.	PROPN
ejpam-6173	363	5	math	math	PROPN
ejpam-6173	363	6	,	,	PUNCT
ejpam-6173	363	7	18	18	NUM
ejpam-6173	363	8	(	(	PUNCT
ejpam-6173	363	9	3	3	NUM
ejpam-6173	363	10	)	)	PUNCT
ejpam-6173	363	11	(	(	PUNCT
ejpam-6173	363	12	2025	2025	NUM
ejpam-6173	363	13	)	)	PUNCT
ejpam-6173	363	14	,	,	PUNCT
ejpam-6173	363	15	6173	6173	NUM
ejpam-6173	363	16	15	15	NUM
ejpam-6173	363	17	of	of	ADP
ejpam-6173	363	18	32	32	NUM
ejpam-6173	363	19	lemma	lemma	PROPN
ejpam-6173	363	20	15	15	NUM
ejpam-6173	363	21	.	.	PUNCT
ejpam-6173	364	1	let	let	VERB
ejpam-6173	364	2	{	{	PUNCT
ejpam-6173	364	3	xn	xn	VERB
ejpam-6173	364	4	}	}	PUNCT
ejpam-6173	364	5	be	be	AUX
ejpam-6173	364	6	a	a	DET
ejpam-6173	364	7	sequence	sequence	NOUN
ejpam-6173	364	8	generated	generate	VERB
ejpam-6173	364	9	by	by	ADP
ejpam-6173	364	10	algorithm	algorithm	NOUN
ejpam-6173	364	11	3.2	3.2	NUM
ejpam-6173	364	12	satisfying	satisfy	VERB
ejpam-6173	364	13	assumption	assumption	NOUN
ejpam-6173	364	14	3.1	3.1	NUM
ejpam-6173	364	15	(	(	PUNCT
ejpam-6173	364	16	a	a	PRON
ejpam-6173	364	17	and	and	CCONJ
ejpam-6173	364	18	b	b	NOUN
ejpam-6173	364	19	)	)	PUNCT
ejpam-6173	364	20	.	.	PUNCT
ejpam-6173	365	1	suppose	suppose	VERB
ejpam-6173	365	2	that	that	SCONJ
ejpam-6173	365	3	p	p	PROPN
ejpam-6173	365	4	∈	∈	PROPN
ejpam-6173	365	5	ω	ω	PROPN
ejpam-6173	365	6	.	.	PUNCT
ejpam-6173	366	1	then	then	ADV
ejpam-6173	366	2	,	,	PUNCT
ejpam-6173	366	3	the	the	DET
ejpam-6173	366	4	following	follow	VERB
ejpam-6173	366	5	holds	hold	VERB
ejpam-6173	366	6	:	:	PUNCT
ejpam-6173	366	7	(	(	PUNCT
ejpam-6173	366	8	i	i	NOUN
ejpam-6173	366	9	)	)	PUNCT
ejpam-6173	367	1	lim	lim	PROPN
ejpam-6173	367	2	n→+∞	n→+∞	PROPN
ejpam-6173	367	3	θn	θn	PROPN
ejpam-6173	368	1	[	[	X
ejpam-6173	368	2	df	df	X
ejpam-6173	368	3	(	(	PUNCT
ejpam-6173	368	4	p	p	NOUN
ejpam-6173	368	5	,	,	PUNCT
ejpam-6173	368	6	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	368	7	(	(	PUNCT
ejpam-6173	368	8	p	p	X
ejpam-6173	368	9	,	,	PUNCT
ejpam-6173	368	10	xn	xn	PROPN
ejpam-6173	368	11	)	)	PUNCT
ejpam-6173	368	12	)	)	PUNCT
ejpam-6173	369	1	=	=	PUNCT
ejpam-6173	369	2	0	0	X
ejpam-6173	369	3	.	.	PUNCT
ejpam-6173	369	4	(	(	PUNCT
ejpam-6173	369	5	ii	ii	NOUN
ejpam-6173	369	6	)	)	PUNCT
ejpam-6173	369	7	lim	lim	PROPN
ejpam-6173	369	8	n→+∞	n→+∞	VERB
ejpam-6173	370	1	θn	θn	ADP
ejpam-6173	370	2	βn	βn	PROPN
ejpam-6173	371	1	[	[	X
ejpam-6173	371	2	df	df	X
ejpam-6173	371	3	(	(	PUNCT
ejpam-6173	371	4	p	p	NOUN
ejpam-6173	371	5	,	,	PUNCT
ejpam-6173	371	6	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	372	1	(	(	PUNCT
ejpam-6173	372	2	p	p	X
ejpam-6173	372	3	,	,	PUNCT
ejpam-6173	372	4	xn	xn	PROPN
ejpam-6173	372	5	)	)	PUNCT
ejpam-6173	372	6	]	]	PUNCT
ejpam-6173	373	1	=	=	PUNCT
ejpam-6173	373	2	0	0	X
ejpam-6173	373	3	.	.	PUNCT
ejpam-6173	373	4	proof	proof	NOUN
ejpam-6173	373	5	.	.	PUNCT
ejpam-6173	374	1	(	(	PUNCT
ejpam-6173	374	2	i	i	NOUN
ejpam-6173	374	3	)	)	PUNCT
ejpam-6173	374	4	let	let	VERB
ejpam-6173	374	5	p	p	PROPN
ejpam-6173	374	6	∈	∈	PROPN
ejpam-6173	374	7	ω	ω	PROPN
ejpam-6173	374	8	.	.	PUNCT
ejpam-6173	375	1	from	from	ADP
ejpam-6173	375	2	(	(	PUNCT
ejpam-6173	375	3	3.1	3.1	NUM
ejpam-6173	375	4	)	)	PUNCT
ejpam-6173	375	5	,	,	PUNCT
ejpam-6173	375	6	we	we	PRON
ejpam-6173	375	7	have	have	VERB
ejpam-6173	375	8	θn	θn	ADP
ejpam-6173	375	9	∥xn	∥xn	PRON
ejpam-6173	375	10	−	−	PROPN
ejpam-6173	375	11	xn−1∥	xn−1∥	PROPN
ejpam-6173	375	12	≤	≤	PROPN
ejpam-6173	375	13	ξn	ξn	PROPN
ejpam-6173	375	14	,	,	PUNCT
ejpam-6173	375	15	for	for	ADP
ejpam-6173	375	16	each	each	DET
ejpam-6173	375	17	n	n	PRON
ejpam-6173	375	18	≥	≥	NOUN
ejpam-6173	375	19	1	1	NUM
ejpam-6173	375	20	.	.	PUNCT
ejpam-6173	376	1	(	(	PUNCT
ejpam-6173	376	2	4.8	4.8	NUM
ejpam-6173	376	3	)	)	PUNCT
ejpam-6173	376	4	from	from	ADP
ejpam-6173	376	5	assumption	assumption	NOUN
ejpam-6173	376	6	3.1(b2	3.1(b2	NOUN
ejpam-6173	376	7	)	)	PUNCT
ejpam-6173	376	8	,	,	PUNCT
ejpam-6173	376	9	we	we	PRON
ejpam-6173	376	10	have	have	VERB
ejpam-6173	376	11	that	that	SCONJ
ejpam-6173	376	12	lim	lim	PROPN
ejpam-6173	376	13	n→+∞	n→+∞	VERB
ejpam-6173	376	14	ξn	ξn	NOUN
ejpam-6173	376	15	βn	βn	NOUN
ejpam-6173	376	16	=	=	SYM
ejpam-6173	376	17	0	0	NUM
ejpam-6173	377	1	and	and	CCONJ
ejpam-6173	377	2	lim	lim	PROPN
ejpam-6173	377	3	n→+∞	n→+∞	VERB
ejpam-6173	377	4	βn	βn	NOUN
ejpam-6173	378	1	=	=	SYM
ejpam-6173	378	2	0	0	X
ejpam-6173	378	3	.	.	PUNCT
ejpam-6173	379	1	it	it	PRON
ejpam-6173	379	2	follows	follow	VERB
ejpam-6173	379	3	that	that	SCONJ
ejpam-6173	379	4	lim	lim	PROPN
ejpam-6173	379	5	n→+∞	n→+∞	VERB
ejpam-6173	379	6	ξn	ξn	PROPN
ejpam-6173	379	7	=	=	NOUN
ejpam-6173	379	8	0	0	NUM
ejpam-6173	379	9	.	.	PUNCT
ejpam-6173	380	1	hence	hence	ADV
ejpam-6173	380	2	,	,	PUNCT
ejpam-6173	380	3	we	we	PRON
ejpam-6173	380	4	have	have	VERB
ejpam-6173	380	5	that	that	PRON
ejpam-6173	380	6	lim	lim	PROPN
ejpam-6173	380	7	n→+∞	n→+∞	PROPN
ejpam-6173	380	8	θn	θn	PROPN
ejpam-6173	380	9	∥xn	∥xn	PROPN
ejpam-6173	380	10	−	−	PROPN
ejpam-6173	380	11	xn−1∥	xn−1∥	PROPN
ejpam-6173	380	12	≤	≤	PROPN
ejpam-6173	381	1	lim	lim	PROPN
ejpam-6173	381	2	n→+∞	n→+∞	VERB
ejpam-6173	381	3	ξn	ξn	PROPN
ejpam-6173	381	4	=	=	NOUN
ejpam-6173	381	5	0	0	PROPN
ejpam-6173	381	6	.	.	PUNCT
ejpam-6173	382	1	(	(	PUNCT
ejpam-6173	382	2	4.9	4.9	NUM
ejpam-6173	382	3	)	)	PUNCT
ejpam-6173	382	4	since	since	SCONJ
ejpam-6173	382	5	∇f	∇f	PROPN
ejpam-6173	382	6	is	be	AUX
ejpam-6173	382	7	norm	norm	NOUN
ejpam-6173	382	8	-	-	PUNCT
ejpam-6173	382	9	to	to	ADP
ejpam-6173	382	10	-	-	PUNCT
ejpam-6173	382	11	norm	norm	NOUN
ejpam-6173	382	12	continuous	continuous	ADJ
ejpam-6173	382	13	on	on	ADP
ejpam-6173	382	14	subsets	subset	NOUN
ejpam-6173	382	15	of	of	ADP
ejpam-6173	382	16	e	e	NOUN
ejpam-6173	382	17	,	,	PUNCT
ejpam-6173	382	18	we	we	PRON
ejpam-6173	382	19	have	have	VERB
ejpam-6173	382	20	that	that	PRON
ejpam-6173	382	21	lim	lim	PROPN
ejpam-6173	382	22	n→+∞	n→+∞	PROPN
ejpam-6173	383	1	θn	θn	ADP
ejpam-6173	383	2	∥∇f	∥∇f	NOUN
ejpam-6173	383	3	(	(	PUNCT
ejpam-6173	383	4	xn)−∇f	xn)−∇f	X
ejpam-6173	383	5	(	(	PUNCT
ejpam-6173	383	6	xn−1)∥	xn−1)∥	PROPN
ejpam-6173	383	7	=	=	SYM
ejpam-6173	383	8	0	0	PROPN
ejpam-6173	383	9	.	.	PUNCT
ejpam-6173	383	10	(	(	PUNCT
ejpam-6173	383	11	4.10	4.10	NUM
ejpam-6173	383	12	)	)	PUNCT
ejpam-6173	383	13	using	use	VERB
ejpam-6173	383	14	the	the	DET
ejpam-6173	383	15	three	three	NUM
ejpam-6173	383	16	-	-	PUNCT
ejpam-6173	383	17	point	point	NOUN
ejpam-6173	383	18	identity	identity	NOUN
ejpam-6173	383	19	,	,	PUNCT
ejpam-6173	383	20	df	df	PROPN
ejpam-6173	383	21	(	(	PUNCT
ejpam-6173	383	22	p	p	NOUN
ejpam-6173	383	23	,	,	PUNCT
ejpam-6173	383	24	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	383	25	(	(	PUNCT
ejpam-6173	383	26	p	p	X
ejpam-6173	383	27	,	,	PUNCT
ejpam-6173	383	28	xn	xn	PROPN
ejpam-6173	383	29	)	)	PUNCT
ejpam-6173	383	30	=	=	SYM
ejpam-6173	383	31	−df	−df	PROPN
ejpam-6173	383	32	(	(	PUNCT
ejpam-6173	383	33	xn−1	xn−1	PROPN
ejpam-6173	383	34	,	,	PUNCT
ejpam-6173	383	35	xn	xn	PUNCT
ejpam-6173	383	36	)	)	PUNCT
ejpam-6173	383	37	+	+	CCONJ
ejpam-6173	383	38	⟨∇f(xn)−∇f(xn−1	⟨∇f(xn)−∇f(xn−1	NOUN
ejpam-6173	383	39	)	)	PUNCT
ejpam-6173	383	40	,	,	PUNCT
ejpam-6173	383	41	xn−1	xn−1	PROPN
ejpam-6173	383	42	−	−	PROPN
ejpam-6173	383	43	p⟩.	p⟩.	INTJ
ejpam-6173	383	44	(	(	PUNCT
ejpam-6173	383	45	4.11	4.11	NUM
ejpam-6173	383	46	)	)	PUNCT
ejpam-6173	383	47	multiplying	multiplying	NOUN
ejpam-6173	383	48	(	(	PUNCT
ejpam-6173	383	49	4.11	4.11	NUM
ejpam-6173	383	50	)	)	PUNCT
ejpam-6173	383	51	by	by	ADP
ejpam-6173	383	52	θn	θn	SYM
ejpam-6173	383	53	,	,	PUNCT
ejpam-6173	383	54	we	we	PRON
ejpam-6173	383	55	have	have	VERB
ejpam-6173	383	56	θn[df	θn[df	NOUN
ejpam-6173	383	57	(	(	PUNCT
ejpam-6173	383	58	p	p	X
ejpam-6173	383	59	,	,	PUNCT
ejpam-6173	383	60	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	384	1	(	(	PUNCT
ejpam-6173	384	2	p	p	X
ejpam-6173	384	3	,	,	PUNCT
ejpam-6173	384	4	xn	xn	PROPN
ejpam-6173	384	5	)	)	PUNCT
ejpam-6173	384	6	]	]	PUNCT
ejpam-6173	385	1	=	=	PUNCT
ejpam-6173	385	2	−θndf	−θndf	NOUN
ejpam-6173	385	3	(	(	PUNCT
ejpam-6173	385	4	xn−1	xn−1	PROPN
ejpam-6173	385	5	,	,	PUNCT
ejpam-6173	385	6	xn	xn	PUNCT
ejpam-6173	385	7	)	)	PUNCT
ejpam-6173	385	8	+	+	CCONJ
ejpam-6173	385	9	θn⟨∇f(xn)−∇f(xn−1	θn⟨∇f(xn)−∇f(xn−1	NUM
ejpam-6173	385	10	)	)	PUNCT
ejpam-6173	385	11	,	,	PUNCT
ejpam-6173	385	12	xn−1	xn−1	PROPN
ejpam-6173	385	13	−	−	PROPN
ejpam-6173	385	14	p⟩.	p⟩.	INTJ
ejpam-6173	385	15	(	(	PUNCT
ejpam-6173	385	16	4.12	4.12	NUM
ejpam-6173	385	17	)	)	PUNCT
ejpam-6173	385	18	since	since	SCONJ
ejpam-6173	385	19	∇f	∇f	PROPN
ejpam-6173	385	20	is	be	AUX
ejpam-6173	385	21	bounded	bound	VERB
ejpam-6173	385	22	on	on	ADP
ejpam-6173	385	23	bounded	bounded	ADJ
ejpam-6173	385	24	sets	set	NOUN
ejpam-6173	385	25	(	(	PUNCT
ejpam-6173	385	26	assumption	assumption	NOUN
ejpam-6173	385	27	a3	a3	NOUN
ejpam-6173	385	28	)	)	PUNCT
ejpam-6173	385	29	,	,	PUNCT
ejpam-6173	385	30	there	there	PRON
ejpam-6173	385	31	exists	exist	VERB
ejpam-6173	385	32	l	l	NOUN
ejpam-6173	385	33	>	>	X
ejpam-6173	385	34	0	0	NUM
ejpam-6173	385	35	such	such	ADJ
ejpam-6173	385	36	that	that	DET
ejpam-6173	385	37	df	df	PROPN
ejpam-6173	385	38	(	(	PUNCT
ejpam-6173	385	39	xn−1	xn−1	PROPN
ejpam-6173	385	40	,	,	PUNCT
ejpam-6173	385	41	xn	xn	PROPN
ejpam-6173	385	42	)	)	PUNCT
ejpam-6173	385	43	≤	≤	NOUN
ejpam-6173	386	1	l∥xn−1	l∥xn−1	ADP
ejpam-6173	386	2	−	−	PROPN
ejpam-6173	386	3	xn∥.	xn∥.	PROPN
ejpam-6173	386	4	thus	thus	ADV
ejpam-6173	386	5	,	,	PUNCT
ejpam-6173	386	6	θndf	θndf	NOUN
ejpam-6173	386	7	(	(	PUNCT
ejpam-6173	386	8	xn−1	xn−1	PROPN
ejpam-6173	386	9	,	,	PUNCT
ejpam-6173	386	10	xn	xn	PROPN
ejpam-6173	386	11	)	)	PUNCT
ejpam-6173	386	12	≤	≤	NOUN
ejpam-6173	386	13	lθn∥xn−1	lθn∥xn−1	ADJ
ejpam-6173	386	14	−	−	PROPN
ejpam-6173	386	15	xn∥	xn∥	PROPN
ejpam-6173	386	16	→	→	SYM
ejpam-6173	386	17	0	0	X
ejpam-6173	386	18	.	.	PUNCT
ejpam-6173	386	19	by	by	ADP
ejpam-6173	386	20	cauchy	cauchy	PROPN
ejpam-6173	386	21	-	-	PUNCT
ejpam-6173	386	22	schwarz	schwarz	PROPN
ejpam-6173	386	23	and	and	CCONJ
ejpam-6173	386	24	boundedness	boundedness	NOUN
ejpam-6173	386	25	of	of	ADP
ejpam-6173	386	26	{	{	PUNCT
ejpam-6173	386	27	xn	xn	PROPN
ejpam-6173	386	28	}	}	PUNCT
ejpam-6173	386	29	,	,	PUNCT
ejpam-6173	386	30	we	we	PRON
ejpam-6173	386	31	have	have	VERB
ejpam-6173	386	32	|θn⟨∇f(xn)−∇f(xn−1	|θn⟨∇f(xn)−∇f(xn−1	NOUN
ejpam-6173	386	33	)	)	PUNCT
ejpam-6173	386	34	,	,	PUNCT
ejpam-6173	386	35	xn−1	xn−1	PROPN
ejpam-6173	386	36	−	−	PROPN
ejpam-6173	386	37	p⟩|	p⟩|	VERB
ejpam-6173	386	38	≤	≤	NOUN
ejpam-6173	386	39	θn∥∇f(xn)−∇f(xn−1)∥	θn∥∇f(xn)−∇f(xn−1)∥	PUNCT
ejpam-6173	386	40	·	·	PUNCT
ejpam-6173	387	1	∥xn−1	∥xn−1	ADJ
ejpam-6173	387	2	−	−	NOUN
ejpam-6173	387	3	p∥	p∥	NOUN
ejpam-6173	387	4	→	→	SYM
ejpam-6173	387	5	0	0	NUM
ejpam-6173	387	6	.	.	PUNCT
ejpam-6173	388	1	hence	hence	ADV
ejpam-6173	388	2	,	,	PUNCT
ejpam-6173	388	3	lim	lim	PROPN
ejpam-6173	388	4	n→∞	n→∞	NUM
ejpam-6173	388	5	θn[df	θn[df	PROPN
ejpam-6173	388	6	(	(	PUNCT
ejpam-6173	388	7	p	p	NOUN
ejpam-6173	388	8	,	,	PUNCT
ejpam-6173	388	9	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	389	1	(	(	PUNCT
ejpam-6173	389	2	p	p	X
ejpam-6173	389	3	,	,	PUNCT
ejpam-6173	389	4	xn	xn	PROPN
ejpam-6173	389	5	)	)	PUNCT
ejpam-6173	389	6	]	]	PUNCT
ejpam-6173	390	1	=	=	PUNCT
ejpam-6173	390	2	0	0	X
ejpam-6173	390	3	.	.	PUNCT
ejpam-6173	391	1	v.	v.	ADP
ejpam-6173	391	2	darvish	darvish	PROPN
ejpam-6173	391	3	et	et	PROPN
ejpam-6173	391	4	al	al	PROPN
ejpam-6173	391	5	.	.	PUNCT
ejpam-6173	391	6	/	/	SYM
ejpam-6173	391	7	eur	eur	PROPN
ejpam-6173	391	8	.	.	PUNCT
ejpam-6173	392	1	j.	j.	PROPN
ejpam-6173	392	2	pure	pure	PROPN
ejpam-6173	392	3	appl	appl	PROPN
ejpam-6173	392	4	.	.	PROPN
ejpam-6173	392	5	math	math	PROPN
ejpam-6173	392	6	,	,	PUNCT
ejpam-6173	392	7	18	18	NUM
ejpam-6173	392	8	(	(	PUNCT
ejpam-6173	392	9	3	3	NUM
ejpam-6173	392	10	)	)	PUNCT
ejpam-6173	392	11	(	(	PUNCT
ejpam-6173	392	12	2025	2025	NUM
ejpam-6173	392	13	)	)	PUNCT
ejpam-6173	392	14	,	,	PUNCT
ejpam-6173	392	15	6173	6173	NUM
ejpam-6173	392	16	16	16	NUM
ejpam-6173	392	17	of	of	ADP
ejpam-6173	392	18	32	32	NUM
ejpam-6173	392	19	(	(	PUNCT
ejpam-6173	392	20	ii	ii	NOUN
ejpam-6173	392	21	)	)	PUNCT
ejpam-6173	392	22	also	also	ADV
ejpam-6173	392	23	,	,	PUNCT
ejpam-6173	392	24	since	since	SCONJ
ejpam-6173	392	25	lim	lim	PROPN
ejpam-6173	392	26	n→+∞	n→+∞	VERB
ejpam-6173	392	27	ξn	ξn	PROPN
ejpam-6173	392	28	βn	βn	NOUN
ejpam-6173	392	29	=	=	SYM
ejpam-6173	392	30	0	0	NUM
ejpam-6173	392	31	,	,	PUNCT
ejpam-6173	392	32	we	we	PRON
ejpam-6173	392	33	obtain	obtain	VERB
ejpam-6173	392	34	from	from	ADP
ejpam-6173	392	35	(	(	PUNCT
ejpam-6173	392	36	4.8	4.8	NUM
ejpam-6173	392	37	)	)	PUNCT
ejpam-6173	392	38	that	that	PRON
ejpam-6173	392	39	lim	lim	PROPN
ejpam-6173	392	40	n→+∞	n→+∞	VERB
ejpam-6173	392	41	θn	θn	PROPN
ejpam-6173	392	42	βn	βn	ADP
ejpam-6173	392	43	∥xn	∥xn	PROPN
ejpam-6173	392	44	−	−	PROPN
ejpam-6173	392	45	xn−1∥	xn−1∥	PROPN
ejpam-6173	392	46	≤	≤	PROPN
ejpam-6173	392	47	lim	lim	PROPN
ejpam-6173	392	48	n→+∞	n→+∞	VERB
ejpam-6173	392	49	ξn	ξn	NOUN
ejpam-6173	392	50	βn	βn	NOUN
ejpam-6173	392	51	=	=	NOUN
ejpam-6173	392	52	0	0	PROPN
ejpam-6173	392	53	.	.	PUNCT
ejpam-6173	393	1	(	(	PUNCT
ejpam-6173	393	2	4.13	4.13	NUM
ejpam-6173	393	3	)	)	PUNCT
ejpam-6173	393	4	since	since	SCONJ
ejpam-6173	393	5	∇f	∇f	PROPN
ejpam-6173	393	6	is	be	AUX
ejpam-6173	393	7	norm	norm	NOUN
ejpam-6173	393	8	-	-	PUNCT
ejpam-6173	393	9	to	to	ADP
ejpam-6173	393	10	-	-	PUNCT
ejpam-6173	393	11	norm	norm	NOUN
ejpam-6173	393	12	continuous	continuous	ADJ
ejpam-6173	393	13	on	on	ADP
ejpam-6173	393	14	subsets	subset	NOUN
ejpam-6173	393	15	of	of	ADP
ejpam-6173	393	16	e	e	NOUN
ejpam-6173	393	17	,	,	PUNCT
ejpam-6173	393	18	we	we	PRON
ejpam-6173	393	19	obtain	obtain	VERB
ejpam-6173	393	20	lim	lim	PROPN
ejpam-6173	393	21	n→+∞	n→+∞	PROPN
ejpam-6173	394	1	θn	θn	ADP
ejpam-6173	394	2	βn	βn	NOUN
ejpam-6173	394	3	∥∇f	∥∇f	NOUN
ejpam-6173	394	4	(	(	PUNCT
ejpam-6173	394	5	xn)−∇f	xn)−∇f	X
ejpam-6173	394	6	(	(	PUNCT
ejpam-6173	394	7	xn−1)∥	xn−1)∥	PROPN
ejpam-6173	394	8	=	=	SYM
ejpam-6173	394	9	0	0	PROPN
ejpam-6173	394	10	.	.	PUNCT
ejpam-6173	395	1	(	(	PUNCT
ejpam-6173	395	2	4.14	4.14	NUM
ejpam-6173	395	3	)	)	PUNCT
ejpam-6173	395	4	multiplying	multiplying	NOUN
ejpam-6173	395	5	(	(	PUNCT
ejpam-6173	395	6	4.11	4.11	NUM
ejpam-6173	395	7	)	)	PUNCT
ejpam-6173	395	8	by	by	ADP
ejpam-6173	395	9	θn	θn	INTJ
ejpam-6173	395	10	βn	βn	PROPN
ejpam-6173	395	11	,	,	PUNCT
ejpam-6173	395	12	we	we	PRON
ejpam-6173	395	13	have	have	VERB
ejpam-6173	395	14	θn	θn	INTJ
ejpam-6173	395	15	βn	βn	NOUN
ejpam-6173	396	1	[	[	X
ejpam-6173	396	2	df	df	X
ejpam-6173	396	3	(	(	PUNCT
ejpam-6173	396	4	p	p	NOUN
ejpam-6173	396	5	,	,	PUNCT
ejpam-6173	396	6	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	397	1	(	(	PUNCT
ejpam-6173	397	2	p	p	X
ejpam-6173	397	3	,	,	PUNCT
ejpam-6173	397	4	xn	xn	PROPN
ejpam-6173	397	5	)	)	PUNCT
ejpam-6173	397	6	]	]	PUNCT
ejpam-6173	398	1	=	=	PUNCT
ejpam-6173	398	2	−	−	PUNCT
ejpam-6173	398	3	θn	θn	INTJ
ejpam-6173	398	4	βn	βn	PROPN
ejpam-6173	398	5	df	df	PROPN
ejpam-6173	398	6	(	(	PUNCT
ejpam-6173	398	7	xn−1	xn−1	PROPN
ejpam-6173	398	8	,	,	PUNCT
ejpam-6173	398	9	xn	xn	PUNCT
ejpam-6173	398	10	)	)	PUNCT
ejpam-6173	398	11	+	+	CCONJ
ejpam-6173	398	12	θn	θn	ADP
ejpam-6173	398	13	βn	βn	ADJ
ejpam-6173	398	14	⟨∇f(xn)−∇f(xn−1	⟨∇f(xn)−∇f(xn−1	X
ejpam-6173	398	15	)	)	PUNCT
ejpam-6173	398	16	,	,	PUNCT
ejpam-6173	398	17	xn−1	xn−1	PROPN
ejpam-6173	398	18	−	−	PROPN
ejpam-6173	398	19	p⟩.	p⟩.	INTJ
ejpam-6173	398	20	from	from	ADP
ejpam-6173	398	21	(	(	PUNCT
ejpam-6173	398	22	4.11	4.11	NUM
ejpam-6173	398	23	)	)	PUNCT
ejpam-6173	398	24	,	,	PUNCT
ejpam-6173	398	25	(	(	PUNCT
ejpam-6173	398	26	4.13	4.13	NUM
ejpam-6173	398	27	)	)	PUNCT
ejpam-6173	398	28	,	,	PUNCT
ejpam-6173	398	29	and	and	CCONJ
ejpam-6173	398	30	(	(	PUNCT
ejpam-6173	398	31	4.14	4.14	NUM
ejpam-6173	398	32	)	)	PUNCT
ejpam-6173	398	33	,	,	PUNCT
ejpam-6173	398	34	we	we	PRON
ejpam-6173	398	35	have	have	VERB
ejpam-6173	398	36	limn→∞	limn→∞	PRON
ejpam-6173	398	37	θn	θn	ADP
ejpam-6173	398	38	βn	βn	NOUN
ejpam-6173	398	39	[	[	X
ejpam-6173	398	40	df	df	X
ejpam-6173	398	41	(	(	PUNCT
ejpam-6173	398	42	p	p	X
ejpam-6173	398	43	,	,	PUNCT
ejpam-6173	398	44	xn−1	xn−1	PROPN
ejpam-6173	398	45	)	)	PUNCT
ejpam-6173	398	46	−	−	PROPN
ejpam-6173	399	1	df	df	NOUN
ejpam-6173	399	2	(	(	PUNCT
ejpam-6173	399	3	p	p	X
ejpam-6173	399	4	,	,	PUNCT
ejpam-6173	399	5	xn	xn	PROPN
ejpam-6173	399	6	)	)	PUNCT
ejpam-6173	399	7	]	]	PUNCT
ejpam-6173	400	1	=	=	PUNCT
ejpam-6173	400	2	0	0	NUM
ejpam-6173	400	3	,	,	PUNCT
ejpam-6173	400	4	which	which	PRON
ejpam-6173	400	5	completes	complete	VERB
ejpam-6173	400	6	the	the	DET
ejpam-6173	400	7	proof	proof	NOUN
ejpam-6173	400	8	.	.	PUNCT
ejpam-6173	401	1	lemma	lemma	PROPN
ejpam-6173	401	2	16	16	NUM
ejpam-6173	401	3	.	.	PUNCT
ejpam-6173	402	1	let	let	VERB
ejpam-6173	402	2	{	{	PUNCT
ejpam-6173	402	3	xn	xn	VERB
ejpam-6173	402	4	}	}	PUNCT
ejpam-6173	402	5	be	be	AUX
ejpam-6173	402	6	a	a	DET
ejpam-6173	402	7	sequence	sequence	NOUN
ejpam-6173	402	8	generated	generate	VERB
ejpam-6173	402	9	by	by	ADP
ejpam-6173	402	10	algorithm	algorithm	NOUN
ejpam-6173	402	11	3.2	3.2	NUM
ejpam-6173	402	12	satisfying	satisfy	VERB
ejpam-6173	402	13	assumption	assumption	NOUN
ejpam-6173	402	14	3.1(a	3.1(a	NUM
ejpam-6173	402	15	and	and	CCONJ
ejpam-6173	402	16	b	b	NOUN
ejpam-6173	402	17	)	)	PUNCT
ejpam-6173	402	18	.	.	PUNCT
ejpam-6173	403	1	suppose	suppose	VERB
ejpam-6173	403	2	that	that	SCONJ
ejpam-6173	403	3	p	p	PROPN
ejpam-6173	403	4	∈	∈	PROPN
ejpam-6173	403	5	ω	ω	PROPN
ejpam-6173	403	6	.	.	PUNCT
ejpam-6173	404	1	then	then	ADV
ejpam-6173	404	2	,	,	PUNCT
ejpam-6173	404	3	the	the	DET
ejpam-6173	404	4	following	follow	VERB
ejpam-6173	404	5	holds	hold	VERB
ejpam-6173	404	6	:	:	PUNCT
ejpam-6173	404	7	df	df	PROPN
ejpam-6173	404	8	(	(	PUNCT
ejpam-6173	404	9	p	p	X
ejpam-6173	404	10	,	,	PUNCT
ejpam-6173	404	11	xn+1	xn+1	NUM
ejpam-6173	404	12	)	)	PUNCT
ejpam-6173	404	13	≤	≤	NOUN
ejpam-6173	405	1	[	[	X
ejpam-6173	405	2	1−	1−	NUM
ejpam-6173	405	3	βn(1−	βn(1−	ADJ
ejpam-6173	405	4	αn)]df	αn)]df	PROPN
ejpam-6173	405	5	(	(	PUNCT
ejpam-6173	405	6	p	p	X
ejpam-6173	405	7	,	,	PUNCT
ejpam-6173	405	8	xn	xn	PUNCT
ejpam-6173	405	9	)	)	PUNCT
ejpam-6173	405	10	+	+	NUM
ejpam-6173	405	11	β(1−	β(1−	NOUN
ejpam-6173	405	12	αn)bn	αn)bn	NUM
ejpam-6173	405	13	,	,	PUNCT
ejpam-6173	405	14	where	where	SCONJ
ejpam-6173	405	15	bn	bn	NOUN
ejpam-6173	405	16	=	=	SYM
ejpam-6173	405	17	1−βn(1−αn	1−βn(1−αn	NOUN
ejpam-6173	405	18	)	)	PUNCT
ejpam-6173	405	19	1−αn	1−αn	NUM
ejpam-6173	405	20	·	·	PUNCT
ejpam-6173	405	21	θn	θn	X
ejpam-6173	405	22	βn	βn	NOUN
ejpam-6173	405	23	[	[	X
ejpam-6173	405	24	df	df	X
ejpam-6173	405	25	(	(	PUNCT
ejpam-6173	405	26	p	p	NOUN
ejpam-6173	405	27	,	,	PUNCT
ejpam-6173	405	28	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	405	29	(	(	PUNCT
ejpam-6173	405	30	p	p	X
ejpam-6173	405	31	,	,	PUNCT
ejpam-6173	405	32	xn	xn	PROPN
ejpam-6173	405	33	)	)	PUNCT
ejpam-6173	405	34	]	]	PUNCT
ejpam-6173	406	1	+	+	CCONJ
ejpam-6173	406	2	⟨yn	⟨yn	ADJ
ejpam-6173	406	3	−	−	NOUN
ejpam-6173	407	1	p,∇f	p,∇f	NOUN
ejpam-6173	407	2	(	(	PUNCT
ejpam-6173	407	3	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	407	4	.	.	PUNCT
ejpam-6173	408	1	v.	v.	ADP
ejpam-6173	408	2	darvish	darvish	PROPN
ejpam-6173	408	3	et	et	PROPN
ejpam-6173	408	4	al	al	PROPN
ejpam-6173	408	5	.	.	PUNCT
ejpam-6173	408	6	/	/	SYM
ejpam-6173	408	7	eur	eur	PROPN
ejpam-6173	408	8	.	.	PUNCT
ejpam-6173	409	1	j.	j.	PROPN
ejpam-6173	409	2	pure	pure	PROPN
ejpam-6173	409	3	appl	appl	PROPN
ejpam-6173	409	4	.	.	PROPN
ejpam-6173	409	5	math	math	PROPN
ejpam-6173	409	6	,	,	PUNCT
ejpam-6173	409	7	18	18	NUM
ejpam-6173	409	8	(	(	PUNCT
ejpam-6173	409	9	3	3	NUM
ejpam-6173	409	10	)	)	PUNCT
ejpam-6173	409	11	(	(	PUNCT
ejpam-6173	409	12	2025	2025	NUM
ejpam-6173	409	13	)	)	PUNCT
ejpam-6173	409	14	,	,	PUNCT
ejpam-6173	409	15	6173	6173	NUM
ejpam-6173	409	16	17	17	NUM
ejpam-6173	409	17	of	of	ADP
ejpam-6173	409	18	32	32	NUM
ejpam-6173	409	19	proof	proof	NOUN
ejpam-6173	409	20	.	.	PUNCT
ejpam-6173	410	1	let	let	VERB
ejpam-6173	410	2	p	p	PROPN
ejpam-6173	410	3	∈	∈	PROPN
ejpam-6173	410	4	ω	ω	PROPN
ejpam-6173	410	5	.	.	PUNCT
ejpam-6173	411	1	from	from	ADP
ejpam-6173	411	2	(	(	PUNCT
ejpam-6173	411	3	2.7	2.7	NUM
ejpam-6173	411	4	)	)	PUNCT
ejpam-6173	411	5	,	,	PUNCT
ejpam-6173	411	6	(	(	PUNCT
ejpam-6173	411	7	4.4	4.4	NUM
ejpam-6173	411	8	)	)	PUNCT
ejpam-6173	411	9	,	,	PUNCT
ejpam-6173	411	10	(	(	PUNCT
ejpam-6173	411	11	4.5	4.5	NUM
ejpam-6173	411	12	)	)	PUNCT
ejpam-6173	411	13	,	,	PUNCT
ejpam-6173	411	14	we	we	PRON
ejpam-6173	411	15	have	have	VERB
ejpam-6173	411	16	df	df	NOUN
ejpam-6173	411	17	(	(	PUNCT
ejpam-6173	411	18	p	p	X
ejpam-6173	411	19	,	,	PUNCT
ejpam-6173	411	20	xn+1	xn+1	NUM
ejpam-6173	411	21	)	)	PUNCT
ejpam-6173	412	1	=	=	SYM
ejpam-6173	412	2	∇f	∇f	NOUN
ejpam-6173	412	3	(	(	PUNCT
ejpam-6173	412	4	p,∇f∗	p,∇f∗	X
ejpam-6173	412	5	(	(	PUNCT
ejpam-6173	412	6	αn∇f	αn∇f	NOUN
ejpam-6173	412	7	(	(	PUNCT
ejpam-6173	412	8	wn	wn	PROPN
ejpam-6173	412	9	)	)	PUNCT
ejpam-6173	412	10	+	+	CCONJ
ejpam-6173	412	11	(	(	PUNCT
ejpam-6173	412	12	1−	1−	NUM
ejpam-6173	412	13	αn)∇f	αn)∇f	NOUN
ejpam-6173	412	14	(	(	PUNCT
ejpam-6173	412	15	t	t	PROPN
ejpam-6173	412	16	(	(	PUNCT
ejpam-6173	412	17	yn	yn	PROPN
ejpam-6173	412	18	)	)	PUNCT
ejpam-6173	412	19	)	)	PUNCT
ejpam-6173	412	20	)	)	PUNCT
ejpam-6173	412	21	)	)	PUNCT
ejpam-6173	413	1	≤	≤	NUM
ejpam-6173	413	2	αndf	αndf	ADJ
ejpam-6173	413	3	(	(	PUNCT
ejpam-6173	413	4	p	p	X
ejpam-6173	413	5	,	,	PUNCT
ejpam-6173	413	6	wn	wn	PROPN
ejpam-6173	413	7	)	)	PUNCT
ejpam-6173	413	8	+	+	CCONJ
ejpam-6173	413	9	(	(	PUNCT
ejpam-6173	413	10	1−	1−	NUM
ejpam-6173	413	11	αn)df	αn)df	NUM
ejpam-6173	413	12	(	(	PUNCT
ejpam-6173	413	13	p	p	X
ejpam-6173	413	14	,	,	PUNCT
ejpam-6173	413	15	t	t	PROPN
ejpam-6173	413	16	(	(	PUNCT
ejpam-6173	413	17	yn	yn	PROPN
ejpam-6173	413	18	)	)	PUNCT
ejpam-6173	413	19	)	)	PUNCT
ejpam-6173	413	20	≤	≤	NUM
ejpam-6173	413	21	αndf	αndf	ADJ
ejpam-6173	413	22	(	(	PUNCT
ejpam-6173	413	23	p	p	X
ejpam-6173	413	24	,	,	PUNCT
ejpam-6173	413	25	wn	wn	PROPN
ejpam-6173	413	26	)	)	PUNCT
ejpam-6173	413	27	+	+	CCONJ
ejpam-6173	413	28	(	(	PUNCT
ejpam-6173	413	29	1−	1−	NUM
ejpam-6173	413	30	αn	αn	NOUN
ejpam-6173	413	31	)	)	PUNCT
ejpam-6173	414	1	[	[	X
ejpam-6173	414	2	df	df	NOUN
ejpam-6173	414	3	(	(	PUNCT
ejpam-6173	414	4	p,∇∗βn∇f	p,∇∗βn∇f	VERB
ejpam-6173	414	5	(	(	PUNCT
ejpam-6173	414	6	qn	qn	NOUN
ejpam-6173	414	7	)	)	PUNCT
ejpam-6173	414	8	+	+	CCONJ
ejpam-6173	414	9	(	(	PUNCT
ejpam-6173	414	10	1−	1−	NUM
ejpam-6173	414	11	βn)∇f	βn)∇f	X
ejpam-6173	414	12	(	(	PUNCT
ejpam-6173	414	13	t	t	PROPN
ejpam-6173	414	14	(	(	PUNCT
ejpam-6173	414	15	zn	zn	NOUN
ejpam-6173	414	16	)	)	PUNCT
ejpam-6173	414	17	)	)	PUNCT
ejpam-6173	414	18	]	]	PUNCT
ejpam-6173	415	1	=	=	SYM
ejpam-6173	415	2	αndf	αndf	ADJ
ejpam-6173	415	3	(	(	PUNCT
ejpam-6173	415	4	p	p	X
ejpam-6173	415	5	,	,	PUNCT
ejpam-6173	415	6	wn	wn	PROPN
ejpam-6173	415	7	)	)	PUNCT
ejpam-6173	415	8	+	+	CCONJ
ejpam-6173	415	9	(	(	PUNCT
ejpam-6173	415	10	1−	1−	NUM
ejpam-6173	415	11	αn	αn	NOUN
ejpam-6173	415	12	)	)	PUNCT
ejpam-6173	416	1	[	[	X
ejpam-6173	416	2	vf	vf	X
ejpam-6173	416	3	(	(	PUNCT
ejpam-6173	416	4	p	p	NOUN
ejpam-6173	416	5	,	,	PUNCT
ejpam-6173	416	6	βn∇f	βn∇f	NOUN
ejpam-6173	416	7	(	(	PUNCT
ejpam-6173	416	8	qn	qn	NOUN
ejpam-6173	416	9	)	)	PUNCT
ejpam-6173	416	10	+	+	CCONJ
ejpam-6173	416	11	(	(	PUNCT
ejpam-6173	416	12	1−	1−	NUM
ejpam-6173	416	13	βn)∇f	βn)∇f	X
ejpam-6173	416	14	(	(	PUNCT
ejpam-6173	416	15	t	t	PROPN
ejpam-6173	416	16	(	(	PUNCT
ejpam-6173	416	17	zn	zn	NOUN
ejpam-6173	416	18	)	)	PUNCT
ejpam-6173	416	19	)	)	PUNCT
ejpam-6173	416	20	)	)	PUNCT
ejpam-6173	416	21	]	]	PUNCT
ejpam-6173	417	1	≤	≤	NUM
ejpam-6173	417	2	αndf	αndf	ADJ
ejpam-6173	417	3	(	(	PUNCT
ejpam-6173	417	4	p	p	X
ejpam-6173	417	5	,	,	PUNCT
ejpam-6173	417	6	wn	wn	PROPN
ejpam-6173	417	7	)	)	PUNCT
ejpam-6173	417	8	+	+	CCONJ
ejpam-6173	417	9	(	(	PUNCT
ejpam-6173	417	10	1−	1−	NUM
ejpam-6173	417	11	αn	αn	NOUN
ejpam-6173	417	12	)	)	PUNCT
ejpam-6173	418	1	[	[	X
ejpam-6173	418	2	vf	vf	X
ejpam-6173	418	3	(	(	PUNCT
ejpam-6173	418	4	p	p	NOUN
ejpam-6173	418	5	,	,	PUNCT
ejpam-6173	418	6	βn∇f	βn∇f	NOUN
ejpam-6173	418	7	(	(	PUNCT
ejpam-6173	418	8	qn	qn	NOUN
ejpam-6173	418	9	)	)	PUNCT
ejpam-6173	418	10	+	+	CCONJ
ejpam-6173	418	11	(	(	PUNCT
ejpam-6173	418	12	1−	1−	NUM
ejpam-6173	418	13	βn)∇f	βn)∇f	X
ejpam-6173	418	14	(	(	PUNCT
ejpam-6173	418	15	t	t	PROPN
ejpam-6173	418	16	(	(	PUNCT
ejpam-6173	418	17	zn	zn	NOUN
ejpam-6173	418	18	)	)	PUNCT
ejpam-6173	418	19	)	)	PUNCT
ejpam-6173	419	1	−	−	PROPN
ejpam-6173	420	1	βn	βn	INTJ
ejpam-6173	420	2	(	(	PUNCT
ejpam-6173	420	3	∇f	∇f	NOUN
ejpam-6173	420	4	(	(	PUNCT
ejpam-6173	420	5	qn)−∇f(p))−	qn)−∇f(p))−	NUM
ejpam-6173	420	6	⟨yn	⟨yn	NUM
ejpam-6173	420	7	−	−	NOUN
ejpam-6173	420	8	p,−βn	p,−βn	NOUN
ejpam-6173	420	9	(	(	PUNCT
ejpam-6173	420	10	∇f	∇f	NOUN
ejpam-6173	420	11	(	(	PUNCT
ejpam-6173	420	12	qn)−∇f(p)⟩	qn)−∇f(p)⟩	PROPN
ejpam-6173	420	13	]	]	X
ejpam-6173	420	14	=	=	SYM
ejpam-6173	420	15	αndf	αndf	ADJ
ejpam-6173	420	16	(	(	PUNCT
ejpam-6173	420	17	p	p	X
ejpam-6173	420	18	,	,	PUNCT
ejpam-6173	420	19	wn	wn	PROPN
ejpam-6173	420	20	)	)	PUNCT
ejpam-6173	420	21	+	+	CCONJ
ejpam-6173	420	22	(	(	PUNCT
ejpam-6173	420	23	1−	1−	NUM
ejpam-6173	420	24	αn	αn	NOUN
ejpam-6173	420	25	)	)	PUNCT
ejpam-6173	421	1	[	[	X
ejpam-6173	421	2	vf	vf	X
ejpam-6173	421	3	(	(	PUNCT
ejpam-6173	421	4	p	p	NOUN
ejpam-6173	421	5	,	,	PUNCT
ejpam-6173	421	6	βn∇f(p	βn∇f(p	NUM
ejpam-6173	421	7	)	)	PUNCT
ejpam-6173	422	1	+	+	CCONJ
ejpam-6173	422	2	(	(	PUNCT
ejpam-6173	422	3	1−	1−	NUM
ejpam-6173	422	4	βn)∇f	βn)∇f	X
ejpam-6173	422	5	(	(	PUNCT
ejpam-6173	422	6	t	t	PROPN
ejpam-6173	422	7	(	(	PUNCT
ejpam-6173	422	8	zn	zn	NOUN
ejpam-6173	422	9	)	)	PUNCT
ejpam-6173	422	10	)	)	PUNCT
ejpam-6173	422	11	)	)	PUNCT
ejpam-6173	423	1	+	+	CCONJ
ejpam-6173	423	2	βn	βn	VERB
ejpam-6173	423	3	⟨yn	⟨yn	ADJ
ejpam-6173	423	4	−	−	PROPN
ejpam-6173	423	5	p,∇f	p,∇f	NOUN
ejpam-6173	423	6	(	(	PUNCT
ejpam-6173	423	7	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	423	8	≤	≤	ADV
ejpam-6173	423	9	αndf	αndf	ADJ
ejpam-6173	423	10	(	(	PUNCT
ejpam-6173	423	11	p	p	X
ejpam-6173	423	12	,	,	PUNCT
ejpam-6173	423	13	wn	wn	PROPN
ejpam-6173	423	14	)	)	PUNCT
ejpam-6173	423	15	+	+	CCONJ
ejpam-6173	423	16	(	(	PUNCT
ejpam-6173	423	17	1−	1−	NUM
ejpam-6173	423	18	αn	αn	NOUN
ejpam-6173	423	19	)	)	PUNCT
ejpam-6173	424	1	[	[	X
ejpam-6173	424	2	βndf	βndf	NOUN
ejpam-6173	424	3	(	(	PUNCT
ejpam-6173	424	4	p	p	X
ejpam-6173	424	5	,	,	PUNCT
ejpam-6173	424	6	p	p	NOUN
ejpam-6173	424	7	)	)	PUNCT
ejpam-6173	424	8	+	+	CCONJ
ejpam-6173	424	9	(	(	PUNCT
ejpam-6173	424	10	1−	1−	NUM
ejpam-6173	424	11	βn)df	βn)df	PUNCT
ejpam-6173	424	12	(	(	PUNCT
ejpam-6173	424	13	p	p	X
ejpam-6173	424	14	,	,	PUNCT
ejpam-6173	424	15	t	t	PROPN
ejpam-6173	424	16	(	(	PUNCT
ejpam-6173	424	17	zn	zn	NOUN
ejpam-6173	424	18	)	)	PUNCT
ejpam-6173	424	19	)	)	PUNCT
ejpam-6173	425	1	+	+	CCONJ
ejpam-6173	425	2	βn	βn	VERB
ejpam-6173	425	3	⟨yn	⟨yn	ADJ
ejpam-6173	425	4	−	−	PROPN
ejpam-6173	425	5	p,∇f	p,∇f	NOUN
ejpam-6173	425	6	(	(	PUNCT
ejpam-6173	425	7	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	425	8	=	=	SYM
ejpam-6173	425	9	αndf	αndf	ADJ
ejpam-6173	425	10	(	(	PUNCT
ejpam-6173	425	11	p	p	X
ejpam-6173	425	12	,	,	PUNCT
ejpam-6173	425	13	wn	wn	PROPN
ejpam-6173	425	14	)	)	PUNCT
ejpam-6173	426	1	+	+	CCONJ
ejpam-6173	426	2	(	(	PUNCT
ejpam-6173	426	3	1−	1−	NUM
ejpam-6173	426	4	αn	αn	NOUN
ejpam-6173	426	5	)	)	PUNCT
ejpam-6173	427	1	[	[	X
ejpam-6173	427	2	(	(	PUNCT
ejpam-6173	427	3	1−	1−	NUM
ejpam-6173	427	4	βn)df	βn)df	PUNCT
ejpam-6173	427	5	(	(	PUNCT
ejpam-6173	427	6	p	p	X
ejpam-6173	427	7	,	,	PUNCT
ejpam-6173	427	8	t	t	PROPN
ejpam-6173	427	9	(	(	PUNCT
ejpam-6173	427	10	zn	zn	NOUN
ejpam-6173	427	11	)	)	PUNCT
ejpam-6173	427	12	)	)	PUNCT
ejpam-6173	428	1	+	+	CCONJ
ejpam-6173	428	2	βn	βn	VERB
ejpam-6173	428	3	⟨yn	⟨yn	ADJ
ejpam-6173	428	4	−	−	PROPN
ejpam-6173	428	5	p,∇f	p,∇f	NOUN
ejpam-6173	428	6	(	(	PUNCT
ejpam-6173	428	7	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	428	8	≤	≤	ADV
ejpam-6173	428	9	αndf	αndf	ADJ
ejpam-6173	428	10	(	(	PUNCT
ejpam-6173	428	11	p	p	X
ejpam-6173	428	12	,	,	PUNCT
ejpam-6173	428	13	wn	wn	PROPN
ejpam-6173	428	14	)	)	PUNCT
ejpam-6173	428	15	+	+	CCONJ
ejpam-6173	428	16	(	(	PUNCT
ejpam-6173	428	17	1−	1−	NUM
ejpam-6173	428	18	αn	αn	NOUN
ejpam-6173	428	19	)	)	PUNCT
ejpam-6173	429	1	[	[	X
ejpam-6173	429	2	(	(	PUNCT
ejpam-6173	429	3	1−	1−	NUM
ejpam-6173	429	4	βn)df	βn)df	PUNCT
ejpam-6173	429	5	(	(	PUNCT
ejpam-6173	429	6	p	p	X
ejpam-6173	429	7	,	,	PUNCT
ejpam-6173	429	8	zn	zn	PROPN
ejpam-6173	429	9	)	)	PUNCT
ejpam-6173	430	1	+	+	CCONJ
ejpam-6173	430	2	βn	βn	VERB
ejpam-6173	430	3	⟨yn	⟨yn	ADJ
ejpam-6173	430	4	−	−	PROPN
ejpam-6173	430	5	p,∇f	p,∇f	NOUN
ejpam-6173	430	6	(	(	PUNCT
ejpam-6173	430	7	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	430	8	≤	≤	NOUN
ejpam-6173	431	1	[	[	X
ejpam-6173	431	2	αn	αn	NOUN
ejpam-6173	431	3	+	+	CCONJ
ejpam-6173	431	4	(	(	PUNCT
ejpam-6173	431	5	1−	1−	NUM
ejpam-6173	431	6	αn	αn	NOUN
ejpam-6173	431	7	)	)	PUNCT
ejpam-6173	431	8	(	(	PUNCT
ejpam-6173	431	9	1−	1−	NUM
ejpam-6173	431	10	βn)]df	βn)]df	PUNCT
ejpam-6173	431	11	(	(	PUNCT
ejpam-6173	431	12	p	p	X
ejpam-6173	431	13	,	,	PUNCT
ejpam-6173	431	14	wn	wn	PROPN
ejpam-6173	431	15	)	)	PUNCT
ejpam-6173	431	16	+	+	CCONJ
ejpam-6173	431	17	(	(	PUNCT
ejpam-6173	431	18	1−	1−	NUM
ejpam-6173	431	19	αn)βn	αn)βn	NUM
ejpam-6173	431	20	⟨yn	⟨yn	NUM
ejpam-6173	431	21	−	−	PROPN
ejpam-6173	431	22	p,∇f	p,∇f	NOUN
ejpam-6173	431	23	(	(	PUNCT
ejpam-6173	431	24	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	431	25	=	=	PUNCT
ejpam-6173	432	1	[	[	X
ejpam-6173	432	2	1−	1−	NUM
ejpam-6173	432	3	βn	βn	NOUN
ejpam-6173	432	4	(	(	PUNCT
ejpam-6173	432	5	1−	1−	NUM
ejpam-6173	432	6	αn)]df	αn)]df	PROPN
ejpam-6173	432	7	(	(	PUNCT
ejpam-6173	432	8	p	p	X
ejpam-6173	432	9	,	,	PUNCT
ejpam-6173	432	10	wn	wn	PROPN
ejpam-6173	432	11	)	)	PUNCT
ejpam-6173	432	12	+	+	CCONJ
ejpam-6173	432	13	(	(	PUNCT
ejpam-6173	432	14	1−	1−	NUM
ejpam-6173	432	15	αn)βn	αn)βn	NUM
ejpam-6173	432	16	⟨yn	⟨yn	NUM
ejpam-6173	432	17	−	−	PROPN
ejpam-6173	433	1	p,∇f	p,∇f	NOUN
ejpam-6173	433	2	(	(	PUNCT
ejpam-6173	433	3	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	433	4	≤	≤	NOUN
ejpam-6173	434	1	[	[	X
ejpam-6173	434	2	1−	1−	NUM
ejpam-6173	434	3	βn	βn	NOUN
ejpam-6173	434	4	(	(	PUNCT
ejpam-6173	434	5	1−	1−	NUM
ejpam-6173	434	6	αn	αn	NOUN
ejpam-6173	434	7	)	)	PUNCT
ejpam-6173	434	8	]	]	PUNCT
ejpam-6173	435	1	[	[	X
ejpam-6173	435	2	(	(	PUNCT
ejpam-6173	435	3	1−	1−	NUM
ejpam-6173	435	4	θn)df	θn)df	X
ejpam-6173	435	5	(	(	PUNCT
ejpam-6173	435	6	p	p	X
ejpam-6173	435	7	,	,	PUNCT
ejpam-6173	435	8	xn	xn	PUNCT
ejpam-6173	435	9	)	)	PUNCT
ejpam-6173	436	1	+	+	CCONJ
ejpam-6173	436	2	θndf	θndf	NOUN
ejpam-6173	436	3	(	(	PUNCT
ejpam-6173	436	4	p	p	X
ejpam-6173	436	5	,	,	PUNCT
ejpam-6173	436	6	xn−1	xn−1	PROPN
ejpam-6173	436	7	)	)	PUNCT
ejpam-6173	436	8	]	]	PUNCT
ejpam-6173	437	1	+	+	CCONJ
ejpam-6173	437	2	(	(	PUNCT
ejpam-6173	437	3	1−	1−	NUM
ejpam-6173	437	4	αn)βn	αn)βn	NUM
ejpam-6173	437	5	⟨yn	⟨yn	NUM
ejpam-6173	437	6	−	−	PROPN
ejpam-6173	437	7	p,∇f	p,∇f	NOUN
ejpam-6173	437	8	(	(	PUNCT
ejpam-6173	437	9	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	437	10	=	=	PUNCT
ejpam-6173	438	1	[	[	X
ejpam-6173	438	2	1−	1−	NUM
ejpam-6173	438	3	βn	βn	NOUN
ejpam-6173	438	4	(	(	PUNCT
ejpam-6173	438	5	1−	1−	NUM
ejpam-6173	438	6	αn)]df	αn)]df	PROPN
ejpam-6173	438	7	(	(	PUNCT
ejpam-6173	438	8	p	p	X
ejpam-6173	438	9	,	,	PUNCT
ejpam-6173	438	10	xn	xn	PUNCT
ejpam-6173	438	11	)	)	PUNCT
ejpam-6173	439	1	+	+	CCONJ
ejpam-6173	440	1	[	[	X
ejpam-6173	440	2	1−	1−	NUM
ejpam-6173	440	3	βn	βn	NOUN
ejpam-6173	440	4	(	(	PUNCT
ejpam-6173	440	5	1−	1−	NUM
ejpam-6173	440	6	αn	αn	NOUN
ejpam-6173	440	7	)	)	PUNCT
ejpam-6173	440	8	]	]	PUNCT
ejpam-6173	440	9	θn	θn	X
ejpam-6173	441	1	[	[	X
ejpam-6173	441	2	df	df	X
ejpam-6173	441	3	(	(	PUNCT
ejpam-6173	441	4	p	p	NOUN
ejpam-6173	441	5	,	,	PUNCT
ejpam-6173	441	6	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	441	7	(	(	PUNCT
ejpam-6173	441	8	p	p	X
ejpam-6173	441	9	,	,	PUNCT
ejpam-6173	441	10	xn	xn	PROPN
ejpam-6173	441	11	)	)	PUNCT
ejpam-6173	441	12	]	]	PUNCT
ejpam-6173	442	1	+	+	CCONJ
ejpam-6173	442	2	βn	βn	ADJ
ejpam-6173	442	3	(	(	PUNCT
ejpam-6173	442	4	1−	1−	NUM
ejpam-6173	442	5	αn	αn	NOUN
ejpam-6173	442	6	)	)	PUNCT
ejpam-6173	442	7	⟨yn	⟨yn	NUM
ejpam-6173	442	8	−	−	PROPN
ejpam-6173	442	9	p,∇f	p,∇f	NOUN
ejpam-6173	442	10	(	(	PUNCT
ejpam-6173	442	11	qn)−∇f(p)⟩	qn)−∇f(p)⟩	NOUN
ejpam-6173	442	12	=	=	PUNCT
ejpam-6173	443	1	[	[	X
ejpam-6173	443	2	1−	1−	NUM
ejpam-6173	443	3	βn	βn	NOUN
ejpam-6173	443	4	(	(	PUNCT
ejpam-6173	443	5	1−	1−	NUM
ejpam-6173	443	6	αn)]df	αn)]df	PROPN
ejpam-6173	443	7	(	(	PUNCT
ejpam-6173	443	8	p	p	X
ejpam-6173	443	9	,	,	PUNCT
ejpam-6173	443	10	xn	xn	PUNCT
ejpam-6173	443	11	)	)	PUNCT
ejpam-6173	444	1	+	+	CCONJ
ejpam-6173	444	2	βn	βn	ADJ
ejpam-6173	444	3	(	(	PUNCT
ejpam-6173	444	4	1−	1−	NUM
ejpam-6173	444	5	αn	αn	NOUN
ejpam-6173	444	6	)	)	PUNCT
ejpam-6173	445	1	[	[	X
ejpam-6173	445	2	1−	1−	NUM
ejpam-6173	445	3	βn	βn	NOUN
ejpam-6173	445	4	(	(	PUNCT
ejpam-6173	445	5	1−	1−	NUM
ejpam-6173	445	6	αn	αn	NOUN
ejpam-6173	445	7	)	)	PUNCT
ejpam-6173	445	8	(	(	PUNCT
ejpam-6173	445	9	1−	1−	NUM
ejpam-6173	445	10	αn	αn	NOUN
ejpam-6173	445	11	)	)	PUNCT
ejpam-6173	445	12	·	·	PUNCT
ejpam-6173	446	1	θn	θn	X
ejpam-6173	446	2	βn	βn	X
ejpam-6173	446	3	(	(	PUNCT
ejpam-6173	446	4	df	df	PROPN
ejpam-6173	446	5	(	(	PUNCT
ejpam-6173	446	6	p	p	NOUN
ejpam-6173	446	7	,	,	PUNCT
ejpam-6173	446	8	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	447	1	(	(	PUNCT
ejpam-6173	447	2	p	p	X
ejpam-6173	447	3	,	,	PUNCT
ejpam-6173	447	4	xn	xn	PUNCT
ejpam-6173	447	5	)	)	PUNCT
ejpam-6173	448	1	+	+	CCONJ
ejpam-6173	448	2	⟨yn	⟨yn	NUM
ejpam-6173	448	3	−	−	PUNCT
ejpam-6173	448	4	p,∇f(qn)−∇f	p,∇f(qn)−∇f	PROPN
ejpam-6173	448	5	(	(	PUNCT
ejpam-6173	448	6	p)⟩	p)⟩	NOUN
ejpam-6173	448	7	]	]	PUNCT
ejpam-6173	448	8	,	,	PUNCT
ejpam-6173	448	9	which	which	PRON
ejpam-6173	448	10	completes	complete	VERB
ejpam-6173	448	11	the	the	DET
ejpam-6173	448	12	proof	proof	NOUN
ejpam-6173	448	13	.	.	PUNCT
ejpam-6173	449	1	theorem	theorem	NOUN
ejpam-6173	449	2	1	1	X
ejpam-6173	449	3	.	.	PUNCT
ejpam-6173	450	1	let	let	AUX
ejpam-6173	450	2	{	{	PUNCT
ejpam-6173	450	3	xn	xn	VERB
ejpam-6173	450	4	}	}	PUNCT
ejpam-6173	450	5	be	be	AUX
ejpam-6173	450	6	a	a	DET
ejpam-6173	450	7	sequence	sequence	NOUN
ejpam-6173	450	8	generated	generate	VERB
ejpam-6173	450	9	by	by	ADP
ejpam-6173	450	10	algorithm	algorithm	NOUN
ejpam-6173	450	11	3.2	3.2	NUM
ejpam-6173	450	12	satisfying	satisfy	VERB
ejpam-6173	450	13	assumption	assumption	NOUN
ejpam-6173	450	14	3.1	3.1	NUM
ejpam-6173	450	15	(	(	PUNCT
ejpam-6173	450	16	a	a	PRON
ejpam-6173	450	17	and	and	CCONJ
ejpam-6173	450	18	b	b	NOUN
ejpam-6173	450	19	)	)	PUNCT
ejpam-6173	450	20	.	.	PUNCT
ejpam-6173	451	1	then	then	ADV
ejpam-6173	451	2	,	,	PUNCT
ejpam-6173	451	3	{	{	PUNCT
ejpam-6173	451	4	xn	xn	X
ejpam-6173	451	5	}	}	PUNCT
ejpam-6173	451	6	converges	converge	VERB
ejpam-6173	451	7	strongly	strongly	ADV
ejpam-6173	451	8	to	to	PART
ejpam-6173	451	9	p∗	p∗	VERB
ejpam-6173	451	10	in	in	ADP
ejpam-6173	451	11	ω	ω	PROPN
ejpam-6173	451	12	.	.	PUNCT
ejpam-6173	452	1	proof	proof	NOUN
ejpam-6173	452	2	.	.	PUNCT
ejpam-6173	453	1	let	let	VERB
ejpam-6173	453	2	p∗	p∗	PROPN
ejpam-6173	453	3	∈	∈	PROPN
ejpam-6173	453	4	ω	ω	PROPN
ejpam-6173	453	5	.	.	PUNCT
ejpam-6173	454	1	then	then	ADV
ejpam-6173	454	2	,	,	PUNCT
ejpam-6173	454	3	from	from	ADP
ejpam-6173	454	4	lemma	lemma	PROPN
ejpam-6173	454	5	16	16	NUM
ejpam-6173	454	6	,	,	PUNCT
ejpam-6173	454	7	we	we	PRON
ejpam-6173	454	8	have	have	VERB
ejpam-6173	454	9	df	df	NOUN
ejpam-6173	454	10	(	(	PUNCT
ejpam-6173	454	11	p	p	X
ejpam-6173	454	12	,	,	PUNCT
ejpam-6173	454	13	xn+1	xn+1	NUM
ejpam-6173	454	14	)	)	PUNCT
ejpam-6173	454	15	≤	≤	NOUN
ejpam-6173	455	1	[	[	X
ejpam-6173	455	2	1−	1−	NUM
ejpam-6173	455	3	βn	βn	NOUN
ejpam-6173	455	4	(	(	PUNCT
ejpam-6173	455	5	1−	1−	NUM
ejpam-6173	455	6	αn)]df	αn)]df	PROPN
ejpam-6173	455	7	(	(	PUNCT
ejpam-6173	455	8	p	p	X
ejpam-6173	455	9	,	,	PUNCT
ejpam-6173	455	10	xn	xn	PUNCT
ejpam-6173	455	11	)	)	PUNCT
ejpam-6173	456	1	+	+	ADJ
ejpam-6173	456	2	βn	βn	NOUN
ejpam-6173	456	3	(	(	PUNCT
ejpam-6173	456	4	1−	1−	NUM
ejpam-6173	456	5	αn	αn	NOUN
ejpam-6173	456	6	)	)	PUNCT
ejpam-6173	457	1	[	[	X
ejpam-6173	457	2	1−	1−	NUM
ejpam-6173	457	3	βn(1−	βn(1−	ADJ
ejpam-6173	457	4	αn	αn	NOUN
ejpam-6173	457	5	)	)	PUNCT
ejpam-6173	457	6	(	(	PUNCT
ejpam-6173	457	7	1−	1−	NUM
ejpam-6173	457	8	αn	αn	NOUN
ejpam-6173	457	9	)	)	PUNCT
ejpam-6173	457	10	·	·	PUNCT
ejpam-6173	458	1	θn	θn	X
ejpam-6173	458	2	βn	βn	NOUN
ejpam-6173	458	3	[	[	X
ejpam-6173	458	4	df	df	X
ejpam-6173	458	5	(	(	PUNCT
ejpam-6173	458	6	p	p	NOUN
ejpam-6173	458	7	,	,	PUNCT
ejpam-6173	458	8	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	458	9	(	(	PUNCT
ejpam-6173	458	10	p	p	X
ejpam-6173	458	11	,	,	PUNCT
ejpam-6173	458	12	xn)](4.15	xn)](4.15	NUM
ejpam-6173	458	13	)	)	PUNCT
ejpam-6173	458	14	v.	v.	CCONJ
ejpam-6173	458	15	darvish	darvish	PROPN
ejpam-6173	458	16	et	et	PROPN
ejpam-6173	458	17	al	al	PROPN
ejpam-6173	458	18	.	.	PUNCT
ejpam-6173	458	19	/	/	SYM
ejpam-6173	458	20	eur	eur	PROPN
ejpam-6173	458	21	.	.	PUNCT
ejpam-6173	459	1	j.	j.	PROPN
ejpam-6173	459	2	pure	pure	PROPN
ejpam-6173	459	3	appl	appl	PROPN
ejpam-6173	459	4	.	.	PROPN
ejpam-6173	459	5	math	math	PROPN
ejpam-6173	459	6	,	,	PUNCT
ejpam-6173	459	7	18	18	NUM
ejpam-6173	459	8	(	(	PUNCT
ejpam-6173	459	9	3	3	NUM
ejpam-6173	459	10	)	)	PUNCT
ejpam-6173	459	11	(	(	PUNCT
ejpam-6173	459	12	2025	2025	NUM
ejpam-6173	459	13	)	)	PUNCT
ejpam-6173	459	14	,	,	PUNCT
ejpam-6173	459	15	6173	6173	NUM
ejpam-6173	459	16	18	18	NUM
ejpam-6173	459	17	of	of	ADP
ejpam-6173	459	18	32	32	NUM
ejpam-6173	459	19	+	+	CCONJ
ejpam-6173	459	20	⟨yn	⟨yn	NUM
ejpam-6173	459	21	−	−	PUNCT
ejpam-6173	460	1	p,∇f(qn)−∇f	p,∇f(qn)−∇f	PROPN
ejpam-6173	460	2	(	(	PUNCT
ejpam-6173	460	3	p)⟩	p)⟩	NOUN
ejpam-6173	460	4	]	]	PUNCT
ejpam-6173	460	5	=	=	PUNCT
ejpam-6173	461	1	[	[	X
ejpam-6173	461	2	1−	1−	NUM
ejpam-6173	461	3	βn	βn	NOUN
ejpam-6173	461	4	(	(	PUNCT
ejpam-6173	461	5	1−	1−	NUM
ejpam-6173	461	6	αn)]df	αn)]df	PROPN
ejpam-6173	461	7	(	(	PUNCT
ejpam-6173	461	8	p	p	X
ejpam-6173	461	9	,	,	PUNCT
ejpam-6173	461	10	xn	xn	PUNCT
ejpam-6173	461	11	)	)	PUNCT
ejpam-6173	462	1	+	+	CCONJ
ejpam-6173	462	2	βn	βn	ADJ
ejpam-6173	462	3	(	(	PUNCT
ejpam-6173	462	4	1−	1−	NUM
ejpam-6173	462	5	αn	αn	NOUN
ejpam-6173	462	6	)	)	PUNCT
ejpam-6173	462	7	bn	bn	NOUN
ejpam-6173	462	8	,	,	PUNCT
ejpam-6173	462	9	(	(	PUNCT
ejpam-6173	462	10	4.16	4.16	NUM
ejpam-6173	462	11	)	)	PUNCT
ejpam-6173	462	12	where	where	SCONJ
ejpam-6173	462	13	bn	bn	NOUN
ejpam-6173	462	14	=	=	SYM
ejpam-6173	462	15	1−βn(1−αn	1−βn(1−αn	NOUN
ejpam-6173	462	16	)	)	PUNCT
ejpam-6173	462	17	1−αn	1−αn	NUM
ejpam-6173	462	18	·	·	PUNCT
ejpam-6173	462	19	θn	θn	X
ejpam-6173	462	20	βn	βn	NOUN
ejpam-6173	462	21	[	[	X
ejpam-6173	462	22	df	df	X
ejpam-6173	462	23	(	(	PUNCT
ejpam-6173	462	24	p	p	NOUN
ejpam-6173	462	25	,	,	PUNCT
ejpam-6173	462	26	xn−1)−df	xn−1)−df	PROPN
ejpam-6173	462	27	(	(	PUNCT
ejpam-6173	462	28	p	p	X
ejpam-6173	462	29	,	,	PUNCT
ejpam-6173	462	30	xn	xn	PROPN
ejpam-6173	462	31	)	)	PUNCT
ejpam-6173	462	32	]	]	PUNCT
ejpam-6173	463	1	+	+	CCONJ
ejpam-6173	463	2	⟨yn	⟨yn	ADJ
ejpam-6173	463	3	−	−	NOUN
ejpam-6173	464	1	p,∇f	p,∇f	NOUN
ejpam-6173	464	2	(	(	PUNCT
ejpam-6173	464	3	qn)−∇f(p)⟩	qn)−∇f(p)⟩	PROPN
ejpam-6173	464	4	.	.	PUNCT
ejpam-6173	465	1	next	next	ADV
ejpam-6173	465	2	,	,	PUNCT
ejpam-6173	465	3	we	we	PRON
ejpam-6173	465	4	show	show	VERB
ejpam-6173	465	5	that	that	SCONJ
ejpam-6173	465	6	{	{	PUNCT
ejpam-6173	465	7	df	df	PROPN
ejpam-6173	465	8	(	(	PUNCT
ejpam-6173	465	9	p	p	NOUN
ejpam-6173	465	10	∗	∗	NOUN
ejpam-6173	465	11	,	,	PUNCT
ejpam-6173	465	12	xn	xn	PROPN
ejpam-6173	465	13	)	)	PUNCT
ejpam-6173	465	14	}	}	PUNCT
ejpam-6173	465	15	converges	converge	VERB
ejpam-6173	465	16	to	to	ADP
ejpam-6173	465	17	zero	zero	NUM
ejpam-6173	465	18	.	.	PUNCT
ejpam-6173	466	1	to	to	PART
ejpam-6173	466	2	show	show	VERB
ejpam-6173	466	3	this	this	PRON
ejpam-6173	466	4	,	,	PUNCT
ejpam-6173	466	5	by	by	ADP
ejpam-6173	466	6	lemma	lemma	PROPN
ejpam-6173	466	7	12	12	NUM
ejpam-6173	466	8	,	,	PUNCT
ejpam-6173	466	9	we	we	PRON
ejpam-6173	466	10	need	need	VERB
ejpam-6173	466	11	to	to	PART
ejpam-6173	466	12	show	show	VERB
ejpam-6173	466	13	that	that	SCONJ
ejpam-6173	466	14	lim	lim	PROPN
ejpam-6173	466	15	sup	sup	NOUN
ejpam-6173	466	16	k→+∞	k→+∞	PROPN
ejpam-6173	466	17	bnk	bnk	PROPN
ejpam-6173	466	18	≤	≤	NOUN
ejpam-6173	466	19	0	0	NUM
ejpam-6173	466	20	for	for	SCONJ
ejpam-6173	466	21	every	every	DET
ejpam-6173	466	22	subsequence	subsequence	NOUN
ejpam-6173	466	23	{	{	PUNCT
ejpam-6173	466	24	df	df	NOUN
ejpam-6173	466	25	(	(	PUNCT
ejpam-6173	466	26	p	p	NOUN
ejpam-6173	466	27	∗	∗	NOUN
ejpam-6173	466	28	,	,	PUNCT
ejpam-6173	466	29	xnk	xnk	PROPN
ejpam-6173	466	30	)	)	PUNCT
ejpam-6173	466	31	}	}	PUNCT
ejpam-6173	466	32	of	of	ADP
ejpam-6173	466	33	{	{	PUNCT
ejpam-6173	466	34	df	df	PROPN
ejpam-6173	466	35	(	(	PUNCT
ejpam-6173	466	36	p	p	NOUN
ejpam-6173	466	37	∗	∗	NOUN
ejpam-6173	466	38	,	,	PUNCT
ejpam-6173	466	39	xn	xn	PROPN
ejpam-6173	466	40	)	)	PUNCT
ejpam-6173	466	41	}	}	PUNCT
ejpam-6173	466	42	satisfying	satisfy	VERB
ejpam-6173	466	43	lim	lim	PROPN
ejpam-6173	466	44	inf	inf	PROPN
ejpam-6173	466	45	k→+∞	k→+∞	PROPN
ejpam-6173	466	46	(	(	PUNCT
ejpam-6173	466	47	df	df	PROPN
ejpam-6173	466	48	(	(	PUNCT
ejpam-6173	466	49	p	p	NOUN
ejpam-6173	466	50	∗	∗	NOUN
ejpam-6173	466	51	,	,	PUNCT
ejpam-6173	466	52	xnk+1	xnk+1	NUM
ejpam-6173	466	53	)	)	PUNCT
ejpam-6173	466	54	−df	−df	PROPN
ejpam-6173	466	55	(	(	PUNCT
ejpam-6173	466	56	p	p	NOUN
ejpam-6173	466	57	∗	∗	NOUN
ejpam-6173	466	58	,	,	PUNCT
ejpam-6173	466	59	xnk	xnk	PROPN
ejpam-6173	466	60	)	)	PUNCT
ejpam-6173	466	61	)	)	PUNCT
ejpam-6173	466	62	≥	≥	NOUN
ejpam-6173	466	63	0	0	NUM
ejpam-6173	466	64	.	.	PUNCT
ejpam-6173	467	1	(	(	PUNCT
ejpam-6173	467	2	4.17	4.17	NUM
ejpam-6173	467	3	)	)	PUNCT
ejpam-6173	467	4	suppose	suppose	VERB
ejpam-6173	467	5	{	{	PUNCT
ejpam-6173	467	6	df	df	X
ejpam-6173	467	7	(	(	PUNCT
ejpam-6173	467	8	p	p	NOUN
ejpam-6173	467	9	∗	∗	NOUN
ejpam-6173	467	10	,	,	PUNCT
ejpam-6173	467	11	xnk	xnk	PROPN
ejpam-6173	467	12	)	)	PUNCT
ejpam-6173	467	13	}	}	PUNCT
ejpam-6173	467	14	is	be	AUX
ejpam-6173	467	15	a	a	DET
ejpam-6173	467	16	subsequence	subsequence	NOUN
ejpam-6173	467	17	of	of	ADP
ejpam-6173	467	18	{	{	PUNCT
ejpam-6173	467	19	df	df	PROPN
ejpam-6173	467	20	(	(	PUNCT
ejpam-6173	467	21	p	p	NOUN
ejpam-6173	467	22	∗	∗	NOUN
ejpam-6173	467	23	,	,	PUNCT
ejpam-6173	467	24	xn	xn	PROPN
ejpam-6173	467	25	)	)	PUNCT
ejpam-6173	467	26	}	}	PUNCT
ejpam-6173	467	27	such	such	ADJ
ejpam-6173	467	28	that	that	SCONJ
ejpam-6173	467	29	(	(	PUNCT
ejpam-6173	467	30	4.17	4.17	NUM
ejpam-6173	467	31	)	)	PUNCT
ejpam-6173	467	32	holds	hold	VERB
ejpam-6173	467	33	.	.	PUNCT
ejpam-6173	468	1	from	from	ADP
ejpam-6173	468	2	lemma	lemma	PROPN
ejpam-6173	468	3	7	7	NUM
ejpam-6173	468	4	,	,	PUNCT
ejpam-6173	468	5	lemma	lemma	PROPN
ejpam-6173	468	6	15	15	NUM
ejpam-6173	468	7	and	and	CCONJ
ejpam-6173	468	8	the	the	DET
ejpam-6173	468	9	definition	definition	NOUN
ejpam-6173	468	10	of	of	ADP
ejpam-6173	468	11	znk	znk	PROPN
ejpam-6173	468	12	,	,	PUNCT
ejpam-6173	468	13	we	we	PRON
ejpam-6173	468	14	have	have	VERB
ejpam-6173	468	15	lim	lim	PROPN
ejpam-6173	468	16	k→+∞	k→+∞	PROPN
ejpam-6173	468	17	df	df	PROPN
ejpam-6173	468	18	(	(	PUNCT
ejpam-6173	468	19	xnk	xnk	PROPN
ejpam-6173	468	20	,	,	PUNCT
ejpam-6173	468	21	znk	znk	PROPN
ejpam-6173	468	22	)	)	PUNCT
ejpam-6173	469	1	=	=	SYM
ejpam-6173	469	2	lim	lim	PROPN
ejpam-6173	469	3	k→+∞	k→+∞	PROPN
ejpam-6173	469	4	df	df	PROPN
ejpam-6173	469	5	(	(	PUNCT
ejpam-6173	469	6	xnk	xnk	PROPN
ejpam-6173	469	7	,	,	PUNCT
ejpam-6173	469	8	resfbθn	resfbθn	NOUN
ejpam-6173	469	9	◦	◦	NOUN
ejpam-6173	469	10	.	.	PUNCT
ejpam-6173	469	11	.	.	PUNCT
ejpam-6173	469	12	.	.	PUNCT
ejpam-6173	470	1	◦	◦	NOUN
ejpam-6173	470	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	470	3	(	(	PUNCT
ejpam-6173	470	4	wnk	wnk	PROPN
ejpam-6173	470	5	)	)	PUNCT
ejpam-6173	470	6	)	)	PUNCT
ejpam-6173	471	1	≤	≤	PROPN
ejpam-6173	471	2	lim	lim	PROPN
ejpam-6173	471	3	k→+∞	k→+∞	PROPN
ejpam-6173	471	4	df	df	PROPN
ejpam-6173	471	5	(	(	PUNCT
ejpam-6173	471	6	xnk	xnk	INTJ
ejpam-6173	471	7	,	,	PUNCT
ejpam-6173	471	8	resfbθn−1	resfbθn−1	VERB
ejpam-6173	471	9	◦	◦	NOUN
ejpam-6173	471	10	·	·	PUNCT
ejpam-6173	471	11	·	·	PUNCT
ejpam-6173	471	12	·	·	PUNCT
ejpam-6173	471	13	◦	◦	NOUN
ejpam-6173	471	14	resfbθ1	resfbθ1	NOUN
ejpam-6173	471	15	(	(	PUNCT
ejpam-6173	471	16	wnk	wnk	PROPN
ejpam-6173	471	17	)	)	PUNCT
ejpam-6173	471	18	)	)	PUNCT
ejpam-6173	471	19	≤	≤	PROPN
ejpam-6173	472	1	lim	lim	PROPN
ejpam-6173	472	2	k→+∞	k→+∞	PROPN
ejpam-6173	472	3	df	df	PROPN
ejpam-6173	472	4	(	(	PUNCT
ejpam-6173	472	5	xnk	xnk	PROPN
ejpam-6173	472	6	,	,	PUNCT
ejpam-6173	472	7	resfbθ1	resfbθ1	PROPN
ejpam-6173	472	8	(	(	PUNCT
ejpam-6173	472	9	wnk	wnk	PROPN
ejpam-6173	472	10	)	)	PUNCT
ejpam-6173	472	11	)	)	PUNCT
ejpam-6173	472	12	(	(	PUNCT
ejpam-6173	472	13	4.18	4.18	NUM
ejpam-6173	472	14	)	)	PUNCT
ejpam-6173	472	15	≤	≤	NOUN
ejpam-6173	473	1	lim	lim	PROPN
ejpam-6173	473	2	k→+∞	k→+∞	PROPN
ejpam-6173	473	3	[	[	PUNCT
ejpam-6173	473	4	df	df	PROPN
ejpam-6173	473	5	(	(	PUNCT
ejpam-6173	473	6	p∗	p∗	PROPN
ejpam-6173	473	7	,	,	PUNCT
ejpam-6173	473	8	resfbθ1	resfbθ1	PROPN
ejpam-6173	473	9	(	(	PUNCT
ejpam-6173	473	10	wnk	wnk	PROPN
ejpam-6173	473	11	)	)	PUNCT
ejpam-6173	473	12	)	)	PUNCT
ejpam-6173	474	1	−df	−df	PROPN
ejpam-6173	474	2	(	(	PUNCT
ejpam-6173	474	3	p	p	NOUN
ejpam-6173	474	4	∗	∗	NOUN
ejpam-6173	474	5	,	,	PUNCT
ejpam-6173	474	6	xnk	xnk	PROPN
ejpam-6173	474	7	)	)	PUNCT
ejpam-6173	474	8	]	]	PUNCT
ejpam-6173	475	1	≤	≤	NUM
ejpam-6173	475	2	lim	lim	PROPN
ejpam-6173	475	3	k→+∞	k→+∞	PROPN
ejpam-6173	476	1	[	[	X
ejpam-6173	476	2	df	df	X
ejpam-6173	476	3	(	(	PUNCT
ejpam-6173	476	4	p	p	NOUN
ejpam-6173	476	5	∗	∗	NOUN
ejpam-6173	476	6	,	,	PUNCT
ejpam-6173	476	7	wnk	wnk	X
ejpam-6173	476	8	)	)	PUNCT
ejpam-6173	476	9	−df	−df	PROPN
ejpam-6173	476	10	(	(	PUNCT
ejpam-6173	476	11	p	p	NOUN
ejpam-6173	476	12	∗	∗	NOUN
ejpam-6173	476	13	,	,	PUNCT
ejpam-6173	476	14	xnk	xnk	PROPN
ejpam-6173	476	15	)	)	PUNCT
ejpam-6173	476	16	]	]	PUNCT
ejpam-6173	476	17	(	(	PUNCT
ejpam-6173	476	18	4.19	4.19	NUM
ejpam-6173	476	19	)	)	PUNCT
ejpam-6173	476	20	≤	≤	NOUN
ejpam-6173	476	21	lim	lim	PROPN
ejpam-6173	476	22	k→+∞	k→+∞	PROPN
ejpam-6173	476	23	[	[	PUNCT
ejpam-6173	476	24	(	(	PUNCT
ejpam-6173	476	25	1−	1−	NUM
ejpam-6173	476	26	θnk	θnk	NOUN
ejpam-6173	476	27	)	)	PUNCT
ejpam-6173	476	28	df	df	NOUN
ejpam-6173	476	29	(	(	PUNCT
ejpam-6173	476	30	p	p	NOUN
ejpam-6173	476	31	∗	∗	NOUN
ejpam-6173	476	32	,	,	PUNCT
ejpam-6173	476	33	xnk	xnk	PROPN
ejpam-6173	476	34	)	)	PUNCT
ejpam-6173	477	1	+	+	CCONJ
ejpam-6173	477	2	θnk	θnk	PROPN
ejpam-6173	477	3	df	df	PROPN
ejpam-6173	477	4	(	(	PUNCT
ejpam-6173	477	5	p∗	p∗	PROPN
ejpam-6173	477	6	,	,	PUNCT
ejpam-6173	477	7	xnk−1	xnk−1	PROPN
ejpam-6173	477	8	)	)	PUNCT
ejpam-6173	477	9	−df	−df	PROPN
ejpam-6173	477	10	(	(	PUNCT
ejpam-6173	477	11	p	p	NOUN
ejpam-6173	477	12	∗	∗	NOUN
ejpam-6173	477	13	,	,	PUNCT
ejpam-6173	477	14	xnk	xnk	PROPN
ejpam-6173	477	15	)	)	PUNCT
ejpam-6173	477	16	]	]	PUNCT
ejpam-6173	478	1	=	=	PUNCT
ejpam-6173	478	2	lim	lim	PROPN
ejpam-6173	478	3	k→+∞	k→+∞	PROPN
ejpam-6173	478	4	[	[	PUNCT
ejpam-6173	478	5	θnk	θnk	NOUN
ejpam-6173	478	6	df	df	PROPN
ejpam-6173	478	7	(	(	PUNCT
ejpam-6173	478	8	p∗	p∗	PROPN
ejpam-6173	478	9	,	,	PUNCT
ejpam-6173	478	10	xnk−1	xnk−1	PROPN
ejpam-6173	478	11	)	)	PUNCT
ejpam-6173	479	1	−	−	DET
ejpam-6173	479	2	θnk	θnk	NOUN
ejpam-6173	479	3	df	df	NOUN
ejpam-6173	479	4	(	(	PUNCT
ejpam-6173	479	5	p	p	NOUN
ejpam-6173	479	6	∗	∗	NOUN
ejpam-6173	479	7	,	,	PUNCT
ejpam-6173	479	8	xnk	xnk	PROPN
ejpam-6173	479	9	)	)	PUNCT
ejpam-6173	479	10	]	]	PUNCT
ejpam-6173	480	1	=	=	PUNCT
ejpam-6173	480	2	lim	lim	PROPN
ejpam-6173	480	3	k→+∞	k→+∞	PROPN
ejpam-6173	480	4	θnk	θnk	PROPN
ejpam-6173	480	5	[	[	PUNCT
ejpam-6173	480	6	df	df	NOUN
ejpam-6173	480	7	(	(	PUNCT
ejpam-6173	480	8	p∗	p∗	PROPN
ejpam-6173	480	9	,	,	PUNCT
ejpam-6173	480	10	xnk−1	xnk−1	PROPN
ejpam-6173	480	11	)	)	PUNCT
ejpam-6173	480	12	−df	−df	PROPN
ejpam-6173	480	13	(	(	PUNCT
ejpam-6173	480	14	p	p	NOUN
ejpam-6173	480	15	∗	∗	NOUN
ejpam-6173	480	16	,	,	PUNCT
ejpam-6173	480	17	xnk	xnk	PROPN
ejpam-6173	480	18	)	)	PUNCT
ejpam-6173	480	19	]	]	PUNCT
ejpam-6173	481	1	=	=	PUNCT
ejpam-6173	481	2	0	0	X
ejpam-6173	481	3	.	.	PUNCT
ejpam-6173	481	4	(	(	PUNCT
ejpam-6173	481	5	4.20	4.20	NUM
ejpam-6173	481	6	)	)	PUNCT
ejpam-6173	481	7	from	from	ADP
ejpam-6173	481	8	lemma	lemma	PROPN
ejpam-6173	481	9	1	1	NUM
ejpam-6173	481	10	,	,	PUNCT
ejpam-6173	481	11	we	we	PRON
ejpam-6173	481	12	obtain	obtain	VERB
ejpam-6173	481	13	lim	lim	PROPN
ejpam-6173	481	14	k→+∞	k→+∞	PROPN
ejpam-6173	481	15	∥xnk	∥xnk	PROPN
ejpam-6173	481	16	−	−	PROPN
ejpam-6173	482	1	znk	znk	NOUN
ejpam-6173	482	2	∥	∥	NUM
ejpam-6173	482	3	=	=	SYM
ejpam-6173	482	4	0	0	X
ejpam-6173	482	5	.	.	PUNCT
ejpam-6173	483	1	(	(	PUNCT
ejpam-6173	483	2	4.21	4.21	NUM
ejpam-6173	483	3	)	)	PUNCT
ejpam-6173	483	4	since	since	SCONJ
ejpam-6173	483	5	f	f	PROPN
ejpam-6173	483	6	is	be	AUX
ejpam-6173	483	7	uniformly	uniformly	ADV
ejpam-6173	483	8	fréchet	fréchet	VERB
ejpam-6173	483	9	differentiable	differentiable	ADJ
ejpam-6173	483	10	on	on	ADP
ejpam-6173	483	11	bounded	bounded	ADJ
ejpam-6173	483	12	subsets	subset	NOUN
ejpam-6173	483	13	of	of	ADP
ejpam-6173	483	14	e	e	PROPN
ejpam-6173	483	15	,	,	PUNCT
ejpam-6173	483	16	by	by	ADP
ejpam-6173	483	17	lemma	lemma	PROPN
ejpam-6173	483	18	5	5	NUM
ejpam-6173	483	19	,	,	PUNCT
ejpam-6173	483	20	∇f	∇f	PROPN
ejpam-6173	483	21	is	be	AUX
ejpam-6173	483	22	norm	norm	NOUN
ejpam-6173	483	23	-	-	PUNCT
ejpam-6173	483	24	to	to	ADP
ejpam-6173	483	25	-	-	PUNCT
ejpam-6173	483	26	norm	norm	NOUN
ejpam-6173	483	27	uniformly	uniformly	ADV
ejpam-6173	483	28	continuous	continuous	ADJ
ejpam-6173	483	29	on	on	ADP
ejpam-6173	483	30	bounded	bounded	ADJ
ejpam-6173	483	31	subsets	subset	NOUN
ejpam-6173	483	32	of	of	ADP
ejpam-6173	483	33	e.	e.	PROPN
ejpam-6173	483	34	hence	hence	PROPN
ejpam-6173	483	35	,	,	PUNCT
ejpam-6173	483	36	lim	lim	PROPN
ejpam-6173	483	37	k→+∞	k→+∞	PROPN
ejpam-6173	483	38	∥∇f	∥∇f	NOUN
ejpam-6173	483	39	(	(	PUNCT
ejpam-6173	483	40	xnk	xnk	NOUN
ejpam-6173	483	41	)	)	PUNCT
ejpam-6173	483	42	−∇f	−∇f	NOUN
ejpam-6173	483	43	(	(	PUNCT
ejpam-6173	483	44	znk	znk	NOUN
ejpam-6173	483	45	)	)	PUNCT
ejpam-6173	483	46	∥⋆	∥⋆	NOUN
ejpam-6173	483	47	=	=	SYM
ejpam-6173	483	48	0	0	NUM
ejpam-6173	483	49	.	.	PUNCT
ejpam-6173	484	1	(	(	PUNCT
ejpam-6173	484	2	4.22	4.22	NUM
ejpam-6173	484	3	)	)	PUNCT
ejpam-6173	484	4	also	also	ADV
ejpam-6173	484	5	,	,	PUNCT
ejpam-6173	484	6	since	since	SCONJ
ejpam-6173	484	7	f	f	PROPN
ejpam-6173	484	8	is	be	AUX
ejpam-6173	484	9	uniformly	uniformly	ADV
ejpam-6173	484	10	fréchet	fréchet	VERB
ejpam-6173	484	11	differentiable	differentiable	ADJ
ejpam-6173	484	12	,	,	PUNCT
ejpam-6173	484	13	it	it	PRON
ejpam-6173	484	14	is	be	AUX
ejpam-6173	484	15	also	also	ADV
ejpam-6173	484	16	uniformly	uniformly	ADV
ejpam-6173	484	17	continuous	continuous	ADJ
ejpam-6173	484	18	,	,	PUNCT
ejpam-6173	484	19	hence	hence	ADV
ejpam-6173	484	20	we	we	PRON
ejpam-6173	484	21	obtain	obtain	VERB
ejpam-6173	485	1	that	that	SCONJ
ejpam-6173	485	2	lim	lim	PROPN
ejpam-6173	485	3	k→+∞	k→+∞	PROPN
ejpam-6173	485	4	∥f	∥f	PROPN
ejpam-6173	485	5	(	(	PUNCT
ejpam-6173	485	6	xnk	xnk	PROPN
ejpam-6173	485	7	)	)	PUNCT
ejpam-6173	485	8	−	−	PROPN
ejpam-6173	485	9	f	f	NOUN
ejpam-6173	485	10	(	(	PUNCT
ejpam-6173	485	11	znk	znk	PROPN
ejpam-6173	485	12	)	)	PUNCT
ejpam-6173	485	13	∥	∥	X
ejpam-6173	485	14	=	=	SYM
ejpam-6173	485	15	0	0	X
ejpam-6173	485	16	.	.	PUNCT
ejpam-6173	485	17	(	(	PUNCT
ejpam-6173	485	18	4.23	4.23	NUM
ejpam-6173	485	19	)	)	PUNCT
ejpam-6173	485	20	using	use	VERB
ejpam-6173	485	21	the	the	DET
ejpam-6173	485	22	bregman	bregman	NOUN
ejpam-6173	485	23	distance	distance	NOUN
ejpam-6173	485	24	,	,	PUNCT
ejpam-6173	485	25	we	we	PRON
ejpam-6173	485	26	obtain	obtain	VERB
ejpam-6173	485	27	df	df	NOUN
ejpam-6173	485	28	(	(	PUNCT
ejpam-6173	485	29	p	p	NOUN
ejpam-6173	485	30	∗	∗	NOUN
ejpam-6173	485	31	,	,	PUNCT
ejpam-6173	486	1	xnk	xnk	PROPN
ejpam-6173	486	2	)	)	PUNCT
ejpam-6173	486	3	−df	−df	PROPN
ejpam-6173	486	4	(	(	PUNCT
ejpam-6173	486	5	p	p	NOUN
ejpam-6173	486	6	∗	∗	NOUN
ejpam-6173	486	7	,	,	PUNCT
ejpam-6173	486	8	znk	znk	PROPN
ejpam-6173	486	9	)	)	PUNCT
ejpam-6173	487	1	v.	v.	ADP
ejpam-6173	487	2	darvish	darvish	PROPN
ejpam-6173	487	3	et	et	PROPN
ejpam-6173	487	4	al	al	PROPN
ejpam-6173	487	5	.	.	PUNCT
ejpam-6173	487	6	/	/	SYM
ejpam-6173	487	7	eur	eur	PROPN
ejpam-6173	487	8	.	.	PUNCT
ejpam-6173	488	1	j.	j.	PROPN
ejpam-6173	488	2	pure	pure	PROPN
ejpam-6173	488	3	appl	appl	PROPN
ejpam-6173	488	4	.	.	PROPN
ejpam-6173	488	5	math	math	PROPN
ejpam-6173	488	6	,	,	PUNCT
ejpam-6173	488	7	18	18	NUM
ejpam-6173	488	8	(	(	PUNCT
ejpam-6173	488	9	3	3	NUM
ejpam-6173	488	10	)	)	PUNCT
ejpam-6173	488	11	(	(	PUNCT
ejpam-6173	488	12	2025	2025	NUM
ejpam-6173	488	13	)	)	PUNCT
ejpam-6173	488	14	,	,	PUNCT
ejpam-6173	488	15	6173	6173	NUM
ejpam-6173	488	16	19	19	NUM
ejpam-6173	488	17	of	of	ADP
ejpam-6173	488	18	32	32	NUM
ejpam-6173	488	19	=	=	SYM
ejpam-6173	488	20	f(p∗)−	f(p∗)−	PROPN
ejpam-6173	488	21	f	f	PROPN
ejpam-6173	488	22	(	(	PUNCT
ejpam-6173	488	23	xnk	xnk	PROPN
ejpam-6173	488	24	)	)	PUNCT
ejpam-6173	488	25	−	−	NOUN
ejpam-6173	488	26	⟨∇f	⟨∇f	NOUN
ejpam-6173	488	27	(	(	PUNCT
ejpam-6173	488	28	xnk	xnk	PROPN
ejpam-6173	488	29	)	)	PUNCT
ejpam-6173	489	1	,	,	PUNCT
ejpam-6173	489	2	p∗	p∗	VERB
ejpam-6173	489	3	−	−	PROPN
ejpam-6173	489	4	xnk	xnk	PROPN
ejpam-6173	489	5	⟩	⟩	PROPN
ejpam-6173	489	6	−	−	PROPN
ejpam-6173	489	7	f(p∗	f(p∗	NUM
ejpam-6173	489	8	)	)	PUNCT
ejpam-6173	490	1	+	+	NUM
ejpam-6173	490	2	f	f	X
ejpam-6173	490	3	(	(	PUNCT
ejpam-6173	490	4	znk	znk	PROPN
ejpam-6173	490	5	)	)	PUNCT
ejpam-6173	490	6	+	+	NUM
ejpam-6173	490	7	⟨∇f	⟨∇f	NOUN
ejpam-6173	490	8	(	(	PUNCT
ejpam-6173	490	9	znk	znk	NOUN
ejpam-6173	490	10	)	)	PUNCT
ejpam-6173	490	11	,	,	PUNCT
ejpam-6173	490	12	p∗	p∗	VERB
ejpam-6173	490	13	−	−	NOUN
ejpam-6173	490	14	znk	znk	NOUN
ejpam-6173	490	15	⟩	⟩	NOUN
ejpam-6173	490	16	=	=	SYM
ejpam-6173	490	17	f	f	PROPN
ejpam-6173	490	18	(	(	PUNCT
ejpam-6173	490	19	znk	znk	PROPN
ejpam-6173	490	20	)	)	PUNCT
ejpam-6173	490	21	−	−	PROPN
ejpam-6173	491	1	f	f	PROPN
ejpam-6173	491	2	(	(	PUNCT
ejpam-6173	491	3	xnk	xnk	PROPN
ejpam-6173	491	4	)	)	PUNCT
ejpam-6173	492	1	+	+	NUM
ejpam-6173	492	2	⟨∇f	⟨∇f	NOUN
ejpam-6173	492	3	(	(	PUNCT
ejpam-6173	492	4	znk	znk	NOUN
ejpam-6173	492	5	)	)	PUNCT
ejpam-6173	492	6	,	,	PUNCT
ejpam-6173	492	7	p∗	p∗	VERB
ejpam-6173	492	8	−	−	NOUN
ejpam-6173	492	9	znk	znk	NOUN
ejpam-6173	492	10	⟩	⟩	NOUN
ejpam-6173	492	11	−	−	NOUN
ejpam-6173	492	12	⟨∇f	⟨∇f	NOUN
ejpam-6173	492	13	(	(	PUNCT
ejpam-6173	492	14	xnk	xnk	PROPN
ejpam-6173	492	15	)	)	PUNCT
ejpam-6173	492	16	,	,	PUNCT
ejpam-6173	492	17	p∗	p∗	VERB
ejpam-6173	492	18	−	−	PROPN
ejpam-6173	492	19	xnk	xnk	PROPN
ejpam-6173	492	20	⟩	⟩	PROPN
ejpam-6173	493	1	=	=	SYM
ejpam-6173	493	2	f	f	PROPN
ejpam-6173	493	3	(	(	PUNCT
ejpam-6173	493	4	znk	znk	PROPN
ejpam-6173	493	5	)	)	PUNCT
ejpam-6173	493	6	−	−	PROPN
ejpam-6173	494	1	f	f	PROPN
ejpam-6173	494	2	(	(	PUNCT
ejpam-6173	494	3	xnk	xnk	PROPN
ejpam-6173	494	4	)	)	PUNCT
ejpam-6173	495	1	+	+	NUM
ejpam-6173	495	2	⟨∇f	⟨∇f	NOUN
ejpam-6173	495	3	(	(	PUNCT
ejpam-6173	495	4	znk	znk	NOUN
ejpam-6173	495	5	)	)	PUNCT
ejpam-6173	495	6	,	,	PUNCT
ejpam-6173	495	7	xnk	xnk	PROPN
ejpam-6173	495	8	−	−	PROPN
ejpam-6173	495	9	znk	znk	NOUN
ejpam-6173	495	10	⟩	⟩	NOUN
ejpam-6173	495	11	−	−	NOUN
ejpam-6173	495	12	⟨∇f	⟨∇f	NOUN
ejpam-6173	495	13	(	(	PUNCT
ejpam-6173	495	14	znk	znk	NOUN
ejpam-6173	495	15	)	)	PUNCT
ejpam-6173	495	16	−∇f	−∇f	NOUN
ejpam-6173	495	17	(	(	PUNCT
ejpam-6173	495	18	xnk	xnk	PROPN
ejpam-6173	495	19	)	)	PUNCT
ejpam-6173	495	20	,	,	PUNCT
ejpam-6173	495	21	p∗	p∗	VERB
ejpam-6173	495	22	−	−	PROPN
ejpam-6173	495	23	xnk	xnk	PROPN
ejpam-6173	495	24	⟩	⟩	PROPN
ejpam-6173	495	25	,	,	PUNCT
ejpam-6173	495	26	for	for	ADP
ejpam-6173	495	27	p∗	p∗	PROPN
ejpam-6173	495	28	∈	∈	PROPN
ejpam-6173	495	29	f	f	X
ejpam-6173	495	30	(	(	PUNCT
ejpam-6173	495	31	t	t	PROPN
ejpam-6173	495	32	)	)	PUNCT
ejpam-6173	495	33	.	.	PUNCT
ejpam-6173	496	1	from	from	ADP
ejpam-6173	496	2	(	(	PUNCT
ejpam-6173	496	3	4.21	4.21	NUM
ejpam-6173	496	4	)	)	PUNCT
ejpam-6173	496	5	and	and	CCONJ
ejpam-6173	496	6	(	(	PUNCT
ejpam-6173	496	7	4.23	4.23	NUM
ejpam-6173	496	8	)	)	PUNCT
ejpam-6173	496	9	,	,	PUNCT
ejpam-6173	496	10	we	we	PRON
ejpam-6173	496	11	obtain	obtain	VERB
ejpam-6173	496	12	lim	lim	PROPN
ejpam-6173	496	13	k→+∞	k→+∞	PROPN
ejpam-6173	497	1	[	[	X
ejpam-6173	497	2	df	df	X
ejpam-6173	497	3	(	(	PUNCT
ejpam-6173	497	4	p	p	X
ejpam-6173	497	5	,	,	PUNCT
ejpam-6173	497	6	xnk	xnk	PROPN
ejpam-6173	497	7	)	)	PUNCT
ejpam-6173	497	8	−df	−df	PROPN
ejpam-6173	497	9	(	(	PUNCT
ejpam-6173	497	10	p	p	X
ejpam-6173	497	11	,	,	PUNCT
ejpam-6173	497	12	znk	znk	PROPN
ejpam-6173	497	13	)	)	PUNCT
ejpam-6173	497	14	]	]	PUNCT
ejpam-6173	497	15	=	=	PUNCT
ejpam-6173	497	16	0	0	X
ejpam-6173	497	17	.	.	PUNCT
ejpam-6173	498	1	(	(	PUNCT
ejpam-6173	498	2	4.24	4.24	NUM
ejpam-6173	498	3	)	)	PUNCT
ejpam-6173	498	4	also	also	ADV
ejpam-6173	498	5	,	,	PUNCT
ejpam-6173	498	6	since	since	SCONJ
ejpam-6173	498	7	βnk	βnk	PROPN
ejpam-6173	498	8	→	→	SYM
ejpam-6173	498	9	0	0	PUNCT
ejpam-6173	498	10	as	as	ADP
ejpam-6173	498	11	k	k	PROPN
ejpam-6173	498	12	→	→	SYM
ejpam-6173	498	13	+	+	PROPN
ejpam-6173	498	14	∞	∞	PROPN
ejpam-6173	498	15	,	,	PUNCT
ejpam-6173	498	16	we	we	PRON
ejpam-6173	498	17	obtain	obtain	VERB
ejpam-6173	498	18	df	df	NOUN
ejpam-6173	498	19	(	(	PUNCT
ejpam-6173	498	20	znk	znk	X
ejpam-6173	498	21	,	,	PUNCT
ejpam-6173	498	22	ynk	ynk	NOUN
ejpam-6173	498	23	)	)	PUNCT
ejpam-6173	499	1	=	=	SYM
ejpam-6173	499	2	df	df	NOUN
ejpam-6173	499	3	(	(	PUNCT
ejpam-6173	499	4	p	p	NOUN
ejpam-6173	499	5	∗	∗	NOUN
ejpam-6173	499	6	,	,	PUNCT
ejpam-6173	499	7	ynk	ynk	NOUN
ejpam-6173	499	8	)	)	PUNCT
ejpam-6173	499	9	−df	−df	PROPN
ejpam-6173	499	10	(	(	PUNCT
ejpam-6173	499	11	p	p	NOUN
ejpam-6173	499	12	∗	∗	NOUN
ejpam-6173	499	13	,	,	PUNCT
ejpam-6173	499	14	znk	znk	NOUN
ejpam-6173	499	15	)	)	PUNCT
ejpam-6173	500	1	=	=	SYM
ejpam-6173	500	2	df	df	NOUN
ejpam-6173	500	3	(	(	PUNCT
ejpam-6173	500	4	p	p	PROPN
ejpam-6173	500	5	∗,∇f∗	∗,∇f∗	PROPN
ejpam-6173	500	6	(	(	PUNCT
ejpam-6173	500	7	βnk	βnk	NOUN
ejpam-6173	500	8	∇f	∇f	PROPN
ejpam-6173	500	9	(	(	PUNCT
ejpam-6173	500	10	qnk	qnk	PROPN
ejpam-6173	500	11	)	)	PUNCT
ejpam-6173	501	1	+	+	CCONJ
ejpam-6173	501	2	(	(	PUNCT
ejpam-6173	501	3	1−	1−	NUM
ejpam-6173	501	4	βnk	βnk	NOUN
ejpam-6173	501	5	)	)	PUNCT
ejpam-6173	501	6	∇f	∇f	NOUN
ejpam-6173	501	7	(	(	PUNCT
ejpam-6173	501	8	t	t	PROPN
ejpam-6173	501	9	(	(	PUNCT
ejpam-6173	501	10	znk	znk	PROPN
ejpam-6173	501	11	)	)	PUNCT
ejpam-6173	501	12	)	)	PUNCT
ejpam-6173	501	13	)	)	PUNCT
ejpam-6173	501	14	)	)	PUNCT
ejpam-6173	502	1	−df	−df	PROPN
ejpam-6173	502	2	(	(	PUNCT
ejpam-6173	502	3	p	p	NOUN
ejpam-6173	502	4	∗	∗	NOUN
ejpam-6173	502	5	,	,	PUNCT
ejpam-6173	502	6	znk	znk	NOUN
ejpam-6173	502	7	)	)	PUNCT
ejpam-6173	502	8	≤	≤	NUM
ejpam-6173	502	9	βnk	βnk	NOUN
ejpam-6173	502	10	df	df	NOUN
ejpam-6173	502	11	(	(	PUNCT
ejpam-6173	502	12	p	p	NOUN
ejpam-6173	502	13	∗	∗	NOUN
ejpam-6173	502	14	,	,	PUNCT
ejpam-6173	502	15	qnk	qnk	NOUN
ejpam-6173	502	16	)	)	PUNCT
ejpam-6173	503	1	+	+	CCONJ
ejpam-6173	503	2	(	(	PUNCT
ejpam-6173	503	3	1−	1−	NUM
ejpam-6173	503	4	βnk	βnk	NOUN
ejpam-6173	503	5	)	)	PUNCT
ejpam-6173	503	6	df	df	NOUN
ejpam-6173	503	7	(	(	PUNCT
ejpam-6173	503	8	p	p	NOUN
ejpam-6173	503	9	∗	∗	NOUN
ejpam-6173	503	10	,	,	PUNCT
ejpam-6173	503	11	t	t	PROPN
ejpam-6173	503	12	(	(	PUNCT
ejpam-6173	503	13	znk	znk	PROPN
ejpam-6173	503	14	)	)	PUNCT
ejpam-6173	503	15	)	)	PUNCT
ejpam-6173	503	16	−df	−df	PROPN
ejpam-6173	503	17	(	(	PUNCT
ejpam-6173	503	18	p	p	NOUN
ejpam-6173	503	19	∗	∗	NOUN
ejpam-6173	503	20	,	,	PUNCT
ejpam-6173	503	21	znk	znk	NOUN
ejpam-6173	503	22	)	)	PUNCT
ejpam-6173	503	23	≤	≤	NUM
ejpam-6173	503	24	βnk	βnk	NOUN
ejpam-6173	503	25	df	df	NOUN
ejpam-6173	503	26	(	(	PUNCT
ejpam-6173	503	27	p	p	NOUN
ejpam-6173	503	28	∗	∗	NOUN
ejpam-6173	503	29	,	,	PUNCT
ejpam-6173	503	30	qnk	qnk	NOUN
ejpam-6173	503	31	)	)	PUNCT
ejpam-6173	504	1	+	+	CCONJ
ejpam-6173	504	2	(	(	PUNCT
ejpam-6173	504	3	1−	1−	NUM
ejpam-6173	504	4	βnk)df	βnk)df	NOUN
ejpam-6173	504	5	(	(	PUNCT
ejpam-6173	504	6	p	p	NOUN
ejpam-6173	504	7	∗	∗	NOUN
ejpam-6173	504	8	,	,	PUNCT
ejpam-6173	504	9	znk	znk	NOUN
ejpam-6173	504	10	)	)	PUNCT
ejpam-6173	504	11	−df	−df	PROPN
ejpam-6173	504	12	(	(	PUNCT
ejpam-6173	504	13	p	p	NOUN
ejpam-6173	504	14	∗	∗	NOUN
ejpam-6173	504	15	,	,	PUNCT
ejpam-6173	504	16	znk	znk	NOUN
ejpam-6173	504	17	)	)	PUNCT
ejpam-6173	504	18	=	=	PUNCT
ejpam-6173	504	19	βnk	βnk	NOUN
ejpam-6173	505	1	[	[	X
ejpam-6173	505	2	df	df	X
ejpam-6173	505	3	(	(	PUNCT
ejpam-6173	505	4	p	p	NOUN
ejpam-6173	505	5	∗	∗	NOUN
ejpam-6173	505	6	,	,	PUNCT
ejpam-6173	505	7	qnk	qnk	NOUN
ejpam-6173	505	8	)	)	PUNCT
ejpam-6173	505	9	−df	−df	PROPN
ejpam-6173	505	10	(	(	PUNCT
ejpam-6173	505	11	p	p	NOUN
ejpam-6173	505	12	∗	∗	NOUN
ejpam-6173	505	13	,	,	PUNCT
ejpam-6173	505	14	znk	znk	PROPN
ejpam-6173	505	15	)	)	PUNCT
ejpam-6173	505	16	]	]	PUNCT
ejpam-6173	505	17	→	→	PUNCT
ejpam-6173	505	18	0	0	NUM
ejpam-6173	505	19	,	,	PUNCT
ejpam-6173	505	20	as	as	ADP
ejpam-6173	505	21	k	k	PROPN
ejpam-6173	505	22	→	→	PROPN
ejpam-6173	505	23	+	+	PROPN
ejpam-6173	505	24	∞.	∞.	PROPN
ejpam-6173	505	25	(	(	PUNCT
ejpam-6173	505	26	4.25	4.25	NUM
ejpam-6173	505	27	)	)	PUNCT
ejpam-6173	505	28	hence	hence	ADV
ejpam-6173	505	29	,	,	PUNCT
ejpam-6173	505	30	lim	lim	PROPN
ejpam-6173	505	31	k→+∞	k→+∞	PROPN
ejpam-6173	505	32	df	df	PROPN
ejpam-6173	505	33	(	(	PUNCT
ejpam-6173	505	34	znk	znk	PROPN
ejpam-6173	505	35	,	,	PUNCT
ejpam-6173	505	36	ynk	ynk	NOUN
ejpam-6173	505	37	)	)	PUNCT
ejpam-6173	505	38	=	=	PUNCT
ejpam-6173	506	1	0	0	X
ejpam-6173	506	2	.	.	PUNCT
ejpam-6173	506	3	from	from	ADP
ejpam-6173	506	4	2.4	2.4	NUM
ejpam-6173	506	5	,	,	PUNCT
ejpam-6173	506	6	we	we	PRON
ejpam-6173	506	7	obtain	obtain	VERB
ejpam-6173	506	8	lim	lim	PROPN
ejpam-6173	506	9	k→+∞	k→+∞	PROPN
ejpam-6173	506	10	∥znk	∥znk	PROPN
ejpam-6173	506	11	−	−	PROPN
ejpam-6173	506	12	ynk	ynk	NOUN
ejpam-6173	506	13	∥	∥	PUNCT
ejpam-6173	506	14	=	=	SYM
ejpam-6173	506	15	0	0	X
ejpam-6173	506	16	.	.	PUNCT
ejpam-6173	507	1	(	(	PUNCT
ejpam-6173	507	2	4.26	4.26	NUM
ejpam-6173	507	3	)	)	PUNCT
ejpam-6173	507	4	consequently	consequently	ADV
ejpam-6173	507	5	,	,	PUNCT
ejpam-6173	507	6	we	we	PRON
ejpam-6173	507	7	have	have	VERB
ejpam-6173	507	8	lim	lim	PROPN
ejpam-6173	507	9	k→+∞	k→+∞	PROPN
ejpam-6173	507	10	∥∇f(znk	∥∇f(znk	NUM
ejpam-6173	507	11	)	)	PUNCT
ejpam-6173	507	12	−∇f(ynk	−∇f(ynk	NOUN
ejpam-6173	507	13	)	)	PUNCT
ejpam-6173	507	14	∥	∥	X
ejpam-6173	507	15	=	=	SYM
ejpam-6173	508	1	lim	lim	PROPN
ejpam-6173	508	2	k→+∞	k→+∞	PROPN
ejpam-6173	508	3	∥f(znk	∥f(znk	PROPN
ejpam-6173	508	4	)	)	PUNCT
ejpam-6173	508	5	−	−	PROPN
ejpam-6173	508	6	f(ynk	f(ynk	NOUN
ejpam-6173	508	7	)	)	PUNCT
ejpam-6173	508	8	∥	∥	PUNCT
ejpam-6173	508	9	=	=	SYM
ejpam-6173	509	1	0	0	X
ejpam-6173	509	2	.	.	PUNCT
ejpam-6173	510	1	from	from	ADP
ejpam-6173	510	2	(	(	PUNCT
ejpam-6173	510	3	4.21	4.21	NUM
ejpam-6173	510	4	)	)	PUNCT
ejpam-6173	510	5	and	and	CCONJ
ejpam-6173	510	6	(	(	PUNCT
ejpam-6173	510	7	4.26	4.26	NUM
ejpam-6173	510	8	)	)	PUNCT
ejpam-6173	510	9	,	,	PUNCT
ejpam-6173	510	10	we	we	PRON
ejpam-6173	510	11	obtain	obtain	VERB
ejpam-6173	510	12	∥xnk	∥xnk	PROPN
ejpam-6173	510	13	−	−	NOUN
ejpam-6173	511	1	ynk	ynk	NOUN
ejpam-6173	511	2	∥	∥	NOUN
ejpam-6173	511	3	=	=	SYM
ejpam-6173	511	4	∥xnk	∥xnk	PROPN
ejpam-6173	511	5	−	−	NOUN
ejpam-6173	511	6	znk	znk	NOUN
ejpam-6173	511	7	+	+	CCONJ
ejpam-6173	512	1	znk	znk	NOUN
ejpam-6173	512	2	−	−	NOUN
ejpam-6173	512	3	ynk	ynk	NOUN
ejpam-6173	512	4	∥	∥	PUNCT
ejpam-6173	512	5	≤	≤	PUNCT
ejpam-6173	512	6	∥xnk	∥xnk	PROPN
ejpam-6173	512	7	−	−	PROPN
ejpam-6173	512	8	znk	znk	PROPN
ejpam-6173	512	9	∥+	∥+	NOUN
ejpam-6173	512	10	∥znk	∥znk	PROPN
ejpam-6173	512	11	−	−	PROPN
ejpam-6173	512	12	ynk	ynk	NOUN
ejpam-6173	512	13	∥	∥	PROPN
ejpam-6173	512	14	=	=	SYM
ejpam-6173	512	15	0	0	NUM
ejpam-6173	512	16	,	,	PUNCT
ejpam-6173	512	17	as	as	ADP
ejpam-6173	512	18	k	k	PROPN
ejpam-6173	512	19	→	→	PROPN
ejpam-6173	512	20	+	+	PROPN
ejpam-6173	512	21	∞.	∞.	PROPN
ejpam-6173	512	22	therefore	therefore	ADV
ejpam-6173	512	23	,	,	PUNCT
ejpam-6173	512	24	lim	lim	PROPN
ejpam-6173	512	25	k→+∞	k→+∞	PROPN
ejpam-6173	512	26	∥xnk	∥xnk	PROPN
ejpam-6173	512	27	−	−	PROPN
ejpam-6173	512	28	ynk	ynk	NOUN
ejpam-6173	512	29	∥	∥	PUNCT
ejpam-6173	512	30	=	=	SYM
ejpam-6173	512	31	0	0	NUM
ejpam-6173	512	32	.	.	PUNCT
ejpam-6173	513	1	(	(	PUNCT
ejpam-6173	513	2	4.27	4.27	NUM
ejpam-6173	513	3	)	)	PUNCT
ejpam-6173	513	4	since	since	SCONJ
ejpam-6173	513	5	f	f	PROPN
ejpam-6173	513	6	is	be	AUX
ejpam-6173	513	7	uniformly	uniformly	ADV
ejpam-6173	513	8	fréchet	fréchet	VERB
ejpam-6173	513	9	differentiable	differentiable	ADJ
ejpam-6173	513	10	on	on	ADP
ejpam-6173	513	11	bounded	bounded	ADJ
ejpam-6173	513	12	subsets	subset	NOUN
ejpam-6173	513	13	of	of	ADP
ejpam-6173	513	14	e	e	PROPN
ejpam-6173	513	15	,	,	PUNCT
ejpam-6173	513	16	by	by	ADP
ejpam-6173	513	17	lemma	lemma	PROPN
ejpam-6173	513	18	5	5	NUM
ejpam-6173	513	19	,	,	PUNCT
ejpam-6173	513	20	∇f	∇f	PROPN
ejpam-6173	513	21	is	be	AUX
ejpam-6173	513	22	norm	norm	NOUN
ejpam-6173	513	23	-	-	PUNCT
ejpam-6173	513	24	to	to	ADP
ejpam-6173	513	25	-	-	PUNCT
ejpam-6173	513	26	norm	norm	NOUN
ejpam-6173	513	27	uniformly	uniformly	ADV
ejpam-6173	513	28	continuous	continuous	ADJ
ejpam-6173	513	29	on	on	ADP
ejpam-6173	513	30	bounded	bounded	ADJ
ejpam-6173	513	31	subsets	subset	NOUN
ejpam-6173	513	32	of	of	ADP
ejpam-6173	513	33	e.	e.	PROPN
ejpam-6173	514	1	hence	hence	ADV
ejpam-6173	514	2	lim	lim	PROPN
ejpam-6173	515	1	k→+∞	k→+∞	PROPN
ejpam-6173	515	2	∥∇f	∥∇f	NOUN
ejpam-6173	515	3	(	(	PUNCT
ejpam-6173	515	4	xnk	xnk	NOUN
ejpam-6173	515	5	)	)	PUNCT
ejpam-6173	515	6	−∇f	−∇f	PROPN
ejpam-6173	515	7	(	(	PUNCT
ejpam-6173	515	8	ynk	ynk	NOUN
ejpam-6173	515	9	)	)	PUNCT
ejpam-6173	515	10	∥∗	∥∗	PROPN
ejpam-6173	515	11	=	=	SYM
ejpam-6173	515	12	0	0	X
ejpam-6173	515	13	.	.	PUNCT
ejpam-6173	515	14	(	(	PUNCT
ejpam-6173	515	15	4.28	4.28	NUM
ejpam-6173	515	16	)	)	PUNCT
ejpam-6173	515	17	on	on	ADP
ejpam-6173	515	18	the	the	DET
ejpam-6173	515	19	other	other	ADJ
ejpam-6173	515	20	hand	hand	NOUN
ejpam-6173	515	21	,	,	PUNCT
ejpam-6173	515	22	since	since	SCONJ
ejpam-6173	515	23	f	f	PROPN
ejpam-6173	515	24	is	be	AUX
ejpam-6173	515	25	uniformly	uniformly	ADV
ejpam-6173	515	26	fréchet	fréchet	VERB
ejpam-6173	515	27	differentiable	differentiable	ADJ
ejpam-6173	515	28	,	,	PUNCT
ejpam-6173	515	29	we	we	PRON
ejpam-6173	515	30	have	have	VERB
ejpam-6173	515	31	that	that	SCONJ
ejpam-6173	515	32	f	f	PROPN
ejpam-6173	515	33	is	be	AUX
ejpam-6173	515	34	also	also	ADV
ejpam-6173	515	35	uniformly	uniformly	ADV
ejpam-6173	515	36	continuous	continuous	ADJ
ejpam-6173	515	37	.	.	PUNCT
ejpam-6173	516	1	hence	hence	ADV
ejpam-6173	516	2	,	,	PUNCT
ejpam-6173	516	3	lim	lim	PROPN
ejpam-6173	516	4	k→+∞	k→+∞	PROPN
ejpam-6173	516	5	∥f	∥f	PROPN
ejpam-6173	516	6	(	(	PUNCT
ejpam-6173	516	7	xnk	xnk	PROPN
ejpam-6173	516	8	)	)	PUNCT
ejpam-6173	517	1	−	−	PROPN
ejpam-6173	517	2	f	f	PROPN
ejpam-6173	517	3	(	(	PUNCT
ejpam-6173	517	4	ynk	ynk	PROPN
ejpam-6173	517	5	)	)	PUNCT
ejpam-6173	517	6	∥	∥	X
ejpam-6173	517	7	=	=	SYM
ejpam-6173	517	8	0	0	X
ejpam-6173	517	9	.	.	PUNCT
ejpam-6173	517	10	(	(	PUNCT
ejpam-6173	517	11	4.29	4.29	NUM
ejpam-6173	517	12	)	)	PUNCT
ejpam-6173	517	13	v.	v.	ADP
ejpam-6173	517	14	darvish	darvish	PROPN
ejpam-6173	517	15	et	et	PROPN
ejpam-6173	517	16	al	al	PROPN
ejpam-6173	517	17	.	.	PUNCT
ejpam-6173	517	18	/	/	SYM
ejpam-6173	517	19	eur	eur	PROPN
ejpam-6173	517	20	.	.	PUNCT
ejpam-6173	518	1	j.	j.	PROPN
ejpam-6173	518	2	pure	pure	PROPN
ejpam-6173	518	3	appl	appl	PROPN
ejpam-6173	518	4	.	.	PROPN
ejpam-6173	518	5	math	math	PROPN
ejpam-6173	518	6	,	,	PUNCT
ejpam-6173	518	7	18	18	NUM
ejpam-6173	518	8	(	(	PUNCT
ejpam-6173	518	9	3	3	NUM
ejpam-6173	518	10	)	)	PUNCT
ejpam-6173	518	11	(	(	PUNCT
ejpam-6173	518	12	2025	2025	NUM
ejpam-6173	518	13	)	)	PUNCT
ejpam-6173	518	14	,	,	PUNCT
ejpam-6173	518	15	6173	6173	NUM
ejpam-6173	518	16	20	20	NUM
ejpam-6173	518	17	of	of	ADP
ejpam-6173	518	18	32	32	NUM
ejpam-6173	518	19	applying	apply	VERB
ejpam-6173	518	20	the	the	DET
ejpam-6173	518	21	bregman	bregman	NOUN
ejpam-6173	518	22	distance	distance	NOUN
ejpam-6173	518	23	,	,	PUNCT
ejpam-6173	518	24	we	we	PRON
ejpam-6173	518	25	obtain	obtain	VERB
ejpam-6173	518	26	df	df	NOUN
ejpam-6173	518	27	(	(	PUNCT
ejpam-6173	518	28	p	p	NOUN
ejpam-6173	518	29	∗	∗	NOUN
ejpam-6173	518	30	,	,	PUNCT
ejpam-6173	518	31	wnk	wnk	X
ejpam-6173	518	32	)	)	PUNCT
ejpam-6173	518	33	−df	−df	PROPN
ejpam-6173	518	34	(	(	PUNCT
ejpam-6173	518	35	p	p	NOUN
ejpam-6173	518	36	∗	∗	NOUN
ejpam-6173	518	37	,	,	PUNCT
ejpam-6173	518	38	ynk	ynk	NOUN
ejpam-6173	518	39	)	)	PUNCT
ejpam-6173	519	1	=	=	PUNCT
ejpam-6173	520	1	f(p∗)−	f(p∗)−	PROPN
ejpam-6173	520	2	f	f	PROPN
ejpam-6173	520	3	(	(	PUNCT
ejpam-6173	520	4	wnk	wnk	X
ejpam-6173	520	5	)	)	PUNCT
ejpam-6173	520	6	−	−	NOUN
ejpam-6173	520	7	⟨∇f	⟨∇f	NOUN
ejpam-6173	520	8	(	(	PUNCT
ejpam-6173	520	9	wnk	wnk	PROPN
ejpam-6173	520	10	)	)	PUNCT
ejpam-6173	520	11	,	,	PUNCT
ejpam-6173	520	12	p∗	p∗	PROPN
ejpam-6173	520	13	−	−	PROPN
ejpam-6173	520	14	wnk	wnk	NOUN
ejpam-6173	520	15	⟩	⟩	NOUN
ejpam-6173	520	16	−	−	PROPN
ejpam-6173	520	17	f(p∗	f(p∗	NUM
ejpam-6173	520	18	)	)	PUNCT
ejpam-6173	521	1	+	+	NUM
ejpam-6173	521	2	f	f	X
ejpam-6173	521	3	(	(	PUNCT
ejpam-6173	521	4	ynk	ynk	PROPN
ejpam-6173	521	5	)	)	PUNCT
ejpam-6173	521	6	+	+	NUM
ejpam-6173	521	7	⟨∇f	⟨∇f	NOUN
ejpam-6173	521	8	(	(	PUNCT
ejpam-6173	521	9	ynk	ynk	NOUN
ejpam-6173	521	10	)	)	PUNCT
ejpam-6173	521	11	,	,	PUNCT
ejpam-6173	521	12	p∗	p∗	VERB
ejpam-6173	521	13	−	−	PROPN
ejpam-6173	521	14	ynk	ynk	NOUN
ejpam-6173	521	15	⟩	⟩	NOUN
ejpam-6173	522	1	=	=	SYM
ejpam-6173	522	2	f	f	PROPN
ejpam-6173	522	3	(	(	PUNCT
ejpam-6173	522	4	ynk	ynk	PROPN
ejpam-6173	522	5	)	)	PUNCT
ejpam-6173	522	6	−	−	PROPN
ejpam-6173	522	7	f	f	PROPN
ejpam-6173	522	8	(	(	PUNCT
ejpam-6173	522	9	wnk	wnk	PROPN
ejpam-6173	522	10	)	)	PUNCT
ejpam-6173	523	1	+	+	NUM
ejpam-6173	523	2	⟨∇f	⟨∇f	NOUN
ejpam-6173	523	3	(	(	PUNCT
ejpam-6173	523	4	ynk	ynk	NOUN
ejpam-6173	523	5	)	)	PUNCT
ejpam-6173	523	6	,	,	PUNCT
ejpam-6173	523	7	p∗	p∗	VERB
ejpam-6173	523	8	−	−	PROPN
ejpam-6173	523	9	ynk	ynk	NOUN
ejpam-6173	523	10	⟩	⟩	NOUN
ejpam-6173	523	11	−	−	NOUN
ejpam-6173	523	12	⟨∇f	⟨∇f	NOUN
ejpam-6173	523	13	(	(	PUNCT
ejpam-6173	523	14	wnk	wnk	PROPN
ejpam-6173	523	15	)	)	PUNCT
ejpam-6173	523	16	,	,	PUNCT
ejpam-6173	523	17	p∗	p∗	PROPN
ejpam-6173	523	18	−	−	PROPN
ejpam-6173	523	19	wnk	wnk	NOUN
ejpam-6173	524	1	⟩	⟩	NOUN
ejpam-6173	524	2	=	=	SYM
ejpam-6173	524	3	f	f	PROPN
ejpam-6173	524	4	(	(	PUNCT
ejpam-6173	524	5	ynk	ynk	PROPN
ejpam-6173	524	6	)	)	PUNCT
ejpam-6173	524	7	−	−	PROPN
ejpam-6173	524	8	f	f	PROPN
ejpam-6173	524	9	(	(	PUNCT
ejpam-6173	524	10	wnk	wnk	PROPN
ejpam-6173	524	11	)	)	PUNCT
ejpam-6173	525	1	+	+	NUM
ejpam-6173	525	2	⟨∇f	⟨∇f	NOUN
ejpam-6173	525	3	(	(	PUNCT
ejpam-6173	525	4	ynk	ynk	NOUN
ejpam-6173	525	5	)	)	PUNCT
ejpam-6173	525	6	,	,	PUNCT
ejpam-6173	525	7	wnk	wnk	INTJ
ejpam-6173	525	8	−	−	NOUN
ejpam-6173	525	9	ynk	ynk	NOUN
ejpam-6173	526	1	⟩+	⟩+	ADJ
ejpam-6173	526	2	⟨∇f	⟨∇f	NOUN
ejpam-6173	526	3	(	(	PUNCT
ejpam-6173	526	4	ynk	ynk	NOUN
ejpam-6173	526	5	)	)	PUNCT
ejpam-6173	526	6	−∇f	−∇f	PROPN
ejpam-6173	526	7	(	(	PUNCT
ejpam-6173	526	8	wnk	wnk	PROPN
ejpam-6173	526	9	)	)	PUNCT
ejpam-6173	526	10	,	,	PUNCT
ejpam-6173	526	11	p∗	p∗	PROPN
ejpam-6173	526	12	−	−	PROPN
ejpam-6173	526	13	wnk	wnk	NOUN
ejpam-6173	526	14	⟩	⟩	NOUN
ejpam-6173	526	15	,	,	PUNCT
ejpam-6173	526	16	(	(	PUNCT
ejpam-6173	526	17	4.30	4.30	NUM
ejpam-6173	526	18	)	)	PUNCT
ejpam-6173	526	19	for	for	ADP
ejpam-6173	526	20	p∗	p∗	PROPN
ejpam-6173	526	21	∈	∈	PROPN
ejpam-6173	526	22	f	f	X
ejpam-6173	526	23	(	(	PUNCT
ejpam-6173	526	24	t	t	PROPN
ejpam-6173	526	25	)	)	PUNCT
ejpam-6173	526	26	.	.	PUNCT
ejpam-6173	527	1	from	from	ADP
ejpam-6173	527	2	the	the	DET
ejpam-6173	527	3	definition	definition	NOUN
ejpam-6173	527	4	of	of	ADP
ejpam-6173	527	5	wnk	wnk	PROPN
ejpam-6173	527	6	and	and	CCONJ
ejpam-6173	527	7	(	(	PUNCT
ejpam-6173	527	8	4.10	4.10	NUM
ejpam-6173	527	9	)	)	PUNCT
ejpam-6173	527	10	,	,	PUNCT
ejpam-6173	527	11	we	we	PRON
ejpam-6173	527	12	have	have	VERB
ejpam-6173	527	13	∥∇f	∥∇f	NOUN
ejpam-6173	527	14	(	(	PUNCT
ejpam-6173	527	15	wnk	wnk	X
ejpam-6173	527	16	)	)	PUNCT
ejpam-6173	527	17	−∇f	−∇f	PROPN
ejpam-6173	527	18	(	(	PUNCT
ejpam-6173	527	19	xnk	xnk	PROPN
ejpam-6173	527	20	)	)	PUNCT
ejpam-6173	527	21	∥	∥	X
ejpam-6173	528	1	=	=	PUNCT
ejpam-6173	528	2	∥∥∇f	∥∥∇f	PROPN
ejpam-6173	528	3	(	(	PUNCT
ejpam-6173	528	4	xnk	xnk	PROPN
ejpam-6173	528	5	)	)	PUNCT
ejpam-6173	529	1	+	+	NUM
ejpam-6173	529	2	θnk	θnk	NOUN
ejpam-6173	529	3	(	(	PUNCT
ejpam-6173	529	4	∇f	∇f	PROPN
ejpam-6173	529	5	(	(	PUNCT
ejpam-6173	529	6	xnk−1	xnk−1	PROPN
ejpam-6173	529	7	)	)	PUNCT
ejpam-6173	529	8	−∇f	−∇f	NOUN
ejpam-6173	529	9	(	(	PUNCT
ejpam-6173	529	10	xnk	xnk	PROPN
ejpam-6173	529	11	)	)	PUNCT
ejpam-6173	529	12	)	)	PUNCT
ejpam-6173	530	1	−∇f	−∇f	NOUN
ejpam-6173	530	2	(	(	PUNCT
ejpam-6173	530	3	xnk	xnk	PROPN
ejpam-6173	530	4	)	)	PUNCT
ejpam-6173	530	5	∥∥	∥∥	X
ejpam-6173	530	6	=	=	PUNCT
ejpam-6173	530	7	θnk	θnk	PROPN
ejpam-6173	530	8	∥∥∇f	∥∥∇f	PROPN
ejpam-6173	530	9	(	(	PUNCT
ejpam-6173	530	10	xnk−1	xnk−1	PROPN
ejpam-6173	530	11	)	)	PUNCT
ejpam-6173	530	12	−∇f	−∇f	NOUN
ejpam-6173	530	13	(	(	PUNCT
ejpam-6173	530	14	xnk	xnk	PROPN
ejpam-6173	530	15	)	)	PUNCT
ejpam-6173	530	16	∥∥→	∥∥→	PROPN
ejpam-6173	530	17	0	0	PUNCT
ejpam-6173	531	1	as	as	SCONJ
ejpam-6173	531	2	k	k	PROPN
ejpam-6173	531	3	→	→	PROPN
ejpam-6173	531	4	+	+	PROPN
ejpam-6173	531	5	∞.	∞.	PROPN
ejpam-6173	531	6	(	(	PUNCT
ejpam-6173	531	7	4.31	4.31	NUM
ejpam-6173	531	8	)	)	PUNCT
ejpam-6173	531	9	from	from	ADP
ejpam-6173	531	10	(	(	PUNCT
ejpam-6173	531	11	4.28	4.28	NUM
ejpam-6173	531	12	)	)	PUNCT
ejpam-6173	531	13	and	and	CCONJ
ejpam-6173	531	14	(	(	PUNCT
ejpam-6173	531	15	4.31	4.31	NUM
ejpam-6173	531	16	)	)	PUNCT
ejpam-6173	531	17	,	,	PUNCT
ejpam-6173	531	18	we	we	PRON
ejpam-6173	531	19	can	can	AUX
ejpam-6173	531	20	write	write	VERB
ejpam-6173	531	21	lim	lim	PROPN
ejpam-6173	531	22	k→+∞	k→+∞	PROPN
ejpam-6173	531	23	∥∇f	∥∇f	NOUN
ejpam-6173	531	24	(	(	PUNCT
ejpam-6173	531	25	wnk	wnk	X
ejpam-6173	531	26	)	)	PUNCT
ejpam-6173	531	27	−∇f	−∇f	PROPN
ejpam-6173	531	28	(	(	PUNCT
ejpam-6173	531	29	ynk	ynk	NOUN
ejpam-6173	531	30	)	)	PUNCT
ejpam-6173	531	31	∥	∥	PUNCT
ejpam-6173	531	32	≤	≤	NUM
ejpam-6173	532	1	lim	lim	NOUN
ejpam-6173	532	2	k→+∞	k→+∞	PROPN
ejpam-6173	533	1	[	[	X
ejpam-6173	533	2	∥∇f	∥∇f	X
ejpam-6173	533	3	(	(	PUNCT
ejpam-6173	533	4	wnk	wnk	X
ejpam-6173	533	5	)	)	PUNCT
ejpam-6173	533	6	−∇f	−∇f	PROPN
ejpam-6173	533	7	(	(	PUNCT
ejpam-6173	533	8	xnk	xnk	PROPN
ejpam-6173	533	9	)	)	PUNCT
ejpam-6173	533	10	∥+	∥+	PROPN
ejpam-6173	533	11	∥∇f(xnk	∥∇f(xnk	PUNCT
ejpam-6173	533	12	)	)	PUNCT
ejpam-6173	533	13	−∇f(ynk	−∇f(ynk	NOUN
ejpam-6173	533	14	)	)	PUNCT
ejpam-6173	533	15	]	]	PUNCT
ejpam-6173	534	1	=	=	SYM
ejpam-6173	534	2	0	0	PUNCT
ejpam-6173	534	3	(	(	PUNCT
ejpam-6173	534	4	4.32	4.32	NUM
ejpam-6173	534	5	)	)	PUNCT
ejpam-6173	534	6	combining	combine	VERB
ejpam-6173	534	7	(	(	PUNCT
ejpam-6173	534	8	4.30	4.30	NUM
ejpam-6173	534	9	)	)	PUNCT
ejpam-6173	534	10	and	and	CCONJ
ejpam-6173	534	11	(	(	PUNCT
ejpam-6173	534	12	4.32	4.32	NUM
ejpam-6173	534	13	)	)	PUNCT
ejpam-6173	534	14	,	,	PUNCT
ejpam-6173	534	15	we	we	PRON
ejpam-6173	534	16	have	have	VERB
ejpam-6173	534	17	lim	lim	PROPN
ejpam-6173	534	18	k→+∞	k→+∞	PROPN
ejpam-6173	534	19	(	(	PUNCT
ejpam-6173	534	20	df	df	PROPN
ejpam-6173	534	21	(	(	PUNCT
ejpam-6173	534	22	p	p	NOUN
ejpam-6173	534	23	∗	∗	NOUN
ejpam-6173	534	24	,	,	PUNCT
ejpam-6173	534	25	wnk	wnk	X
ejpam-6173	534	26	)	)	PUNCT
ejpam-6173	534	27	−df	−df	PROPN
ejpam-6173	534	28	(	(	PUNCT
ejpam-6173	534	29	p	p	NOUN
ejpam-6173	534	30	∗	∗	NOUN
ejpam-6173	534	31	,	,	PUNCT
ejpam-6173	534	32	ynk	ynk	NOUN
ejpam-6173	534	33	)	)	PUNCT
ejpam-6173	534	34	)	)	PUNCT
ejpam-6173	535	1	=	=	PUNCT
ejpam-6173	535	2	0	0	X
ejpam-6173	535	3	.	.	PUNCT
ejpam-6173	535	4	(	(	PUNCT
ejpam-6173	535	5	4.33	4.33	NUM
ejpam-6173	535	6	)	)	PUNCT
ejpam-6173	535	7	also	also	ADV
ejpam-6173	535	8	,	,	PUNCT
ejpam-6173	535	9	from	from	ADP
ejpam-6173	535	10	(	(	PUNCT
ejpam-6173	535	11	4.27	4.27	NUM
ejpam-6173	535	12	)	)	PUNCT
ejpam-6173	535	13	and	and	CCONJ
ejpam-6173	535	14	(	(	PUNCT
ejpam-6173	535	15	4.32	4.32	NUM
ejpam-6173	535	16	)	)	PUNCT
ejpam-6173	535	17	,	,	PUNCT
ejpam-6173	535	18	we	we	PRON
ejpam-6173	535	19	have	have	VERB
ejpam-6173	535	20	that	that	DET
ejpam-6173	535	21	lim	lim	PROPN
ejpam-6173	535	22	k→+∞	k→+∞	PROPN
ejpam-6173	535	23	∥wnk	∥wnk	PROPN
ejpam-6173	536	1	−	−	NOUN
ejpam-6173	536	2	xnk	xnk	NOUN
ejpam-6173	536	3	∥	∥	X
ejpam-6173	536	4	=	=	PUNCT
ejpam-6173	537	1	0	0	X
ejpam-6173	537	2	.	.	PUNCT
ejpam-6173	538	1	(	(	PUNCT
ejpam-6173	538	2	4.34	4.34	NUM
ejpam-6173	538	3	)	)	PUNCT
ejpam-6173	538	4	from	from	ADP
ejpam-6173	538	5	(	(	PUNCT
ejpam-6173	538	6	4.33	4.33	NUM
ejpam-6173	538	7	)	)	PUNCT
ejpam-6173	538	8	and	and	CCONJ
ejpam-6173	538	9	the	the	DET
ejpam-6173	538	10	definition	definition	NOUN
ejpam-6173	538	11	of	of	ADP
ejpam-6173	538	12	xnk+1	xnk+1	PROPN
ejpam-6173	538	13	,	,	PUNCT
ejpam-6173	538	14	we	we	PRON
ejpam-6173	538	15	have	have	VERB
ejpam-6173	538	16	df	df	PROPN
ejpam-6173	538	17	(	(	PUNCT
ejpam-6173	538	18	ynk	ynk	PROPN
ejpam-6173	538	19	,	,	PUNCT
ejpam-6173	538	20	xnk+1	xnk+1	PROPN
ejpam-6173	538	21	)	)	PUNCT
ejpam-6173	539	1	=	=	SYM
ejpam-6173	539	2	df	df	PROPN
ejpam-6173	539	3	(	(	PUNCT
ejpam-6173	539	4	p∗	p∗	PROPN
ejpam-6173	539	5	,	,	PUNCT
ejpam-6173	539	6	xnk+1	xnk+1	NUM
ejpam-6173	539	7	)	)	PUNCT
ejpam-6173	539	8	−df	−df	PROPN
ejpam-6173	539	9	(	(	PUNCT
ejpam-6173	539	10	p	p	NOUN
ejpam-6173	539	11	∗	∗	NOUN
ejpam-6173	539	12	,	,	PUNCT
ejpam-6173	539	13	ynk	ynk	NOUN
ejpam-6173	539	14	)	)	PUNCT
ejpam-6173	540	1	=	=	SYM
ejpam-6173	540	2	df	df	NOUN
ejpam-6173	540	3	(	(	PUNCT
ejpam-6173	540	4	p	p	PROPN
ejpam-6173	540	5	∗,∇f∗	∗,∇f∗	PROPN
ejpam-6173	540	6	(	(	PUNCT
ejpam-6173	540	7	αnk	αnk	INTJ
ejpam-6173	540	8	∇f	∇f	PROPN
ejpam-6173	540	9	(	(	PUNCT
ejpam-6173	540	10	wnk	wnk	PROPN
ejpam-6173	540	11	)	)	PUNCT
ejpam-6173	541	1	+	+	CCONJ
ejpam-6173	541	2	(	(	PUNCT
ejpam-6173	541	3	1−	1−	NUM
ejpam-6173	541	4	αnk	αnk	NOUN
ejpam-6173	541	5	)	)	PUNCT
ejpam-6173	541	6	∇f	∇f	NOUN
ejpam-6173	541	7	(	(	PUNCT
ejpam-6173	541	8	t	t	PROPN
ejpam-6173	541	9	(	(	PUNCT
ejpam-6173	541	10	ynk	ynk	NOUN
ejpam-6173	541	11	)	)	PUNCT
ejpam-6173	541	12	)	)	PUNCT
ejpam-6173	541	13	)	)	PUNCT
ejpam-6173	541	14	)	)	PUNCT
ejpam-6173	541	15	−df	−df	PROPN
ejpam-6173	541	16	(	(	PUNCT
ejpam-6173	541	17	p	p	NOUN
ejpam-6173	541	18	∗	∗	NOUN
ejpam-6173	541	19	,	,	PUNCT
ejpam-6173	541	20	ynk	ynk	NOUN
ejpam-6173	541	21	)	)	PUNCT
ejpam-6173	541	22	≤	≤	NOUN
ejpam-6173	542	1	df	df	NOUN
ejpam-6173	542	2	(	(	PUNCT
ejpam-6173	542	3	p	p	PROPN
ejpam-6173	542	4	∗,∇f∗	∗,∇f∗	PROPN
ejpam-6173	542	5	(	(	PUNCT
ejpam-6173	542	6	αnk	αnk	INTJ
ejpam-6173	542	7	∇f	∇f	PROPN
ejpam-6173	542	8	(	(	PUNCT
ejpam-6173	542	9	wnk	wnk	PROPN
ejpam-6173	542	10	)	)	PUNCT
ejpam-6173	542	11	+	+	CCONJ
ejpam-6173	542	12	(	(	PUNCT
ejpam-6173	542	13	1−	1−	NUM
ejpam-6173	542	14	αnk	αnk	NOUN
ejpam-6173	542	15	)	)	PUNCT
ejpam-6173	542	16	∇f	∇f	NOUN
ejpam-6173	542	17	(	(	PUNCT
ejpam-6173	542	18	t	t	PROPN
ejpam-6173	542	19	(	(	PUNCT
ejpam-6173	542	20	ynk	ynk	NOUN
ejpam-6173	542	21	)	)	PUNCT
ejpam-6173	542	22	)	)	PUNCT
ejpam-6173	542	23	−df	−df	PROPN
ejpam-6173	542	24	(	(	PUNCT
ejpam-6173	542	25	p	p	NOUN
ejpam-6173	542	26	,	,	PUNCT
ejpam-6173	542	27	ynk	ynk	NOUN
ejpam-6173	542	28	)	)	PUNCT
ejpam-6173	542	29	)	)	PUNCT
ejpam-6173	542	30	)	)	PUNCT
ejpam-6173	542	31	≤	≤	NUM
ejpam-6173	543	1	αnk	αnk	INTJ
ejpam-6173	543	2	df	df	NOUN
ejpam-6173	543	3	(	(	PUNCT
ejpam-6173	543	4	p	p	NOUN
ejpam-6173	543	5	∗	∗	NOUN
ejpam-6173	543	6	,	,	PUNCT
ejpam-6173	543	7	wnk	wnk	X
ejpam-6173	543	8	)	)	PUNCT
ejpam-6173	543	9	+	+	CCONJ
ejpam-6173	543	10	(	(	PUNCT
ejpam-6173	543	11	1−	1−	NUM
ejpam-6173	543	12	αnk	αnk	INTJ
ejpam-6173	543	13	)	)	PUNCT
ejpam-6173	543	14	df	df	NOUN
ejpam-6173	543	15	(	(	PUNCT
ejpam-6173	543	16	p	p	NOUN
ejpam-6173	543	17	∗	∗	NOUN
ejpam-6173	543	18	,	,	PUNCT
ejpam-6173	543	19	t	t	PROPN
ejpam-6173	543	20	(	(	PUNCT
ejpam-6173	543	21	ynk	ynk	PROPN
ejpam-6173	543	22	)	)	PUNCT
ejpam-6173	543	23	)	)	PUNCT
ejpam-6173	543	24	−df	−df	PROPN
ejpam-6173	543	25	(	(	PUNCT
ejpam-6173	543	26	p	p	NOUN
ejpam-6173	543	27	∗	∗	NOUN
ejpam-6173	543	28	,	,	PUNCT
ejpam-6173	543	29	ynk	ynk	NOUN
ejpam-6173	543	30	)	)	PUNCT
ejpam-6173	543	31	≤	≤	NUM
ejpam-6173	543	32	αnk	αnk	INTJ
ejpam-6173	543	33	df	df	NOUN
ejpam-6173	543	34	(	(	PUNCT
ejpam-6173	543	35	p	p	NOUN
ejpam-6173	543	36	∗	∗	NOUN
ejpam-6173	543	37	,	,	PUNCT
ejpam-6173	543	38	wnk	wnk	X
ejpam-6173	543	39	)	)	PUNCT
ejpam-6173	544	1	+	+	CCONJ
ejpam-6173	544	2	(	(	PUNCT
ejpam-6173	544	3	1−	1−	NUM
ejpam-6173	544	4	αnk	αnk	INTJ
ejpam-6173	544	5	)	)	PUNCT
ejpam-6173	544	6	df	df	NOUN
ejpam-6173	544	7	(	(	PUNCT
ejpam-6173	544	8	p	p	NOUN
ejpam-6173	544	9	∗	∗	NOUN
ejpam-6173	544	10	,	,	PUNCT
ejpam-6173	544	11	ynk	ynk	NOUN
ejpam-6173	544	12	)	)	PUNCT
ejpam-6173	544	13	−df	−df	PROPN
ejpam-6173	544	14	(	(	PUNCT
ejpam-6173	544	15	p	p	NOUN
ejpam-6173	544	16	∗	∗	NOUN
ejpam-6173	544	17	,	,	PUNCT
ejpam-6173	544	18	ynk	ynk	NOUN
ejpam-6173	544	19	)	)	PUNCT
ejpam-6173	544	20	=	=	PUNCT
ejpam-6173	545	1	αnk	αnk	INTJ
ejpam-6173	546	1	[	[	X
ejpam-6173	546	2	df	df	X
ejpam-6173	546	3	(	(	PUNCT
ejpam-6173	546	4	p	p	NOUN
ejpam-6173	546	5	∗	∗	NOUN
ejpam-6173	546	6	,	,	PUNCT
ejpam-6173	546	7	wnk	wnk	X
ejpam-6173	546	8	)	)	PUNCT
ejpam-6173	546	9	−df	−df	PROPN
ejpam-6173	546	10	(	(	PUNCT
ejpam-6173	546	11	p	p	NOUN
ejpam-6173	546	12	∗	∗	NOUN
ejpam-6173	546	13	,	,	PUNCT
ejpam-6173	546	14	ynk	ynk	NOUN
ejpam-6173	546	15	)	)	PUNCT
ejpam-6173	546	16	]	]	PUNCT
ejpam-6173	546	17	→	→	SYM
ejpam-6173	546	18	0	0	PUNCT
ejpam-6173	546	19	as	as	SCONJ
ejpam-6173	546	20	k	k	PROPN
ejpam-6173	546	21	→	→	PROPN
ejpam-6173	546	22	+	+	PROPN
ejpam-6173	546	23	∞.	∞.	PROPN
ejpam-6173	546	24	from	from	ADP
ejpam-6173	546	25	lemma	lemma	PROPN
ejpam-6173	546	26	1	1	NUM
ejpam-6173	546	27	,	,	PUNCT
ejpam-6173	546	28	he	he	PRON
ejpam-6173	546	29	have	have	VERB
ejpam-6173	546	30	lim	lim	PROPN
ejpam-6173	546	31	k→+∞	k→+∞	PROPN
ejpam-6173	546	32	∥∥ynk	∥∥ynk	PROPN
ejpam-6173	547	1	−	−	PROPN
ejpam-6173	547	2	xnk+1	xnk+1	VERB
ejpam-6173	547	3	∥∥	∥∥	X
ejpam-6173	547	4	=	=	SYM
ejpam-6173	547	5	0	0	PROPN
ejpam-6173	547	6	.	.	PUNCT
ejpam-6173	548	1	(	(	PUNCT
ejpam-6173	548	2	4.35	4.35	NUM
ejpam-6173	548	3	)	)	PUNCT
ejpam-6173	548	4	from	from	ADP
ejpam-6173	548	5	(	(	PUNCT
ejpam-6173	548	6	4.25	4.25	NUM
ejpam-6173	548	7	)	)	PUNCT
ejpam-6173	548	8	,	,	PUNCT
ejpam-6173	548	9	and	and	CCONJ
ejpam-6173	548	10	the	the	DET
ejpam-6173	548	11	fact	fact	NOUN
ejpam-6173	548	12	that	that	SCONJ
ejpam-6173	548	13	βnk	βnk	PRON
ejpam-6173	548	14	→	→	SYM
ejpam-6173	548	15	0	0	PUNCT
ejpam-6173	548	16	as	as	ADP
ejpam-6173	548	17	k	k	PROPN
ejpam-6173	548	18	→	→	SYM
ejpam-6173	548	19	+	+	PROPN
ejpam-6173	548	20	∞	∞	PROPN
ejpam-6173	548	21	,	,	PUNCT
ejpam-6173	548	22	we	we	PRON
ejpam-6173	548	23	have	have	VERB
ejpam-6173	548	24	df	df	NOUN
ejpam-6173	548	25	(	(	PUNCT
ejpam-6173	548	26	tynk	tynk	NOUN
ejpam-6173	548	27	,	,	PUNCT
ejpam-6173	548	28	ynk	ynk	NOUN
ejpam-6173	548	29	)	)	PUNCT
ejpam-6173	549	1	=	=	SYM
ejpam-6173	549	2	df	df	NOUN
ejpam-6173	549	3	(	(	PUNCT
ejpam-6173	549	4	p	p	NOUN
ejpam-6173	549	5	∗	∗	NOUN
ejpam-6173	549	6	,	,	PUNCT
ejpam-6173	549	7	ynk	ynk	NOUN
ejpam-6173	549	8	)	)	PUNCT
ejpam-6173	549	9	−df	−df	PROPN
ejpam-6173	549	10	(	(	PUNCT
ejpam-6173	549	11	p	p	NOUN
ejpam-6173	549	12	∗	∗	NOUN
ejpam-6173	549	13	,	,	PUNCT
ejpam-6173	549	14	t	t	PROPN
ejpam-6173	549	15	ynk	ynk	PROPN
ejpam-6173	549	16	)	)	PUNCT
ejpam-6173	549	17	≤	≤	NUM
ejpam-6173	550	1	βnk	βnk	NOUN
ejpam-6173	551	1	df	df	NOUN
ejpam-6173	552	1	(	(	PUNCT
ejpam-6173	552	2	p	p	NOUN
ejpam-6173	552	3	∗	∗	NOUN
ejpam-6173	552	4	,	,	PUNCT
ejpam-6173	552	5	qnk	qnk	NOUN
ejpam-6173	552	6	)	)	PUNCT
ejpam-6173	553	1	+	+	CCONJ
ejpam-6173	553	2	(	(	PUNCT
ejpam-6173	553	3	1−	1−	NUM
ejpam-6173	553	4	βnk	βnk	NOUN
ejpam-6173	553	5	)	)	PUNCT
ejpam-6173	553	6	df	df	NOUN
ejpam-6173	553	7	(	(	PUNCT
ejpam-6173	553	8	p	p	NOUN
ejpam-6173	553	9	∗	∗	NOUN
ejpam-6173	553	10	,	,	PUNCT
ejpam-6173	553	11	t	t	PROPN
ejpam-6173	553	12	(	(	PUNCT
ejpam-6173	553	13	znk	znk	PROPN
ejpam-6173	553	14	)	)	PUNCT
ejpam-6173	553	15	)	)	PUNCT
ejpam-6173	553	16	−df	−df	PROPN
ejpam-6173	553	17	(	(	PUNCT
ejpam-6173	553	18	p	p	NOUN
ejpam-6173	553	19	∗	∗	NOUN
ejpam-6173	553	20	,	,	PUNCT
ejpam-6173	553	21	t	t	PROPN
ejpam-6173	553	22	ynk	ynk	PROPN
ejpam-6173	553	23	)	)	PUNCT
ejpam-6173	553	24	≤	≤	NUM
ejpam-6173	553	25	βnk	βnk	NOUN
ejpam-6173	553	26	df	df	NOUN
ejpam-6173	553	27	(	(	PUNCT
ejpam-6173	553	28	p	p	NOUN
ejpam-6173	553	29	∗	∗	NOUN
ejpam-6173	553	30	,	,	PUNCT
ejpam-6173	553	31	qnk	qnk	NOUN
ejpam-6173	553	32	)	)	PUNCT
ejpam-6173	554	1	+	+	CCONJ
ejpam-6173	554	2	(	(	PUNCT
ejpam-6173	554	3	1−	1−	NUM
ejpam-6173	554	4	βnk	βnk	NOUN
ejpam-6173	554	5	)	)	PUNCT
ejpam-6173	554	6	df	df	NOUN
ejpam-6173	554	7	(	(	PUNCT
ejpam-6173	554	8	p	p	NOUN
ejpam-6173	554	9	∗	∗	NOUN
ejpam-6173	554	10	,	,	PUNCT
ejpam-6173	554	11	znk	znk	NOUN
ejpam-6173	554	12	)	)	PUNCT
ejpam-6173	554	13	−df	−df	PROPN
ejpam-6173	554	14	(	(	PUNCT
ejpam-6173	554	15	p	p	NOUN
ejpam-6173	554	16	∗	∗	NOUN
ejpam-6173	554	17	,	,	PUNCT
ejpam-6173	554	18	ynk	ynk	NOUN
ejpam-6173	554	19	)	)	PUNCT
ejpam-6173	554	20	=	=	PUNCT
ejpam-6173	555	1	βnk	βnk	NOUN
ejpam-6173	556	1	[	[	X
ejpam-6173	556	2	df	df	X
ejpam-6173	556	3	(	(	PUNCT
ejpam-6173	556	4	p	p	NOUN
ejpam-6173	556	5	∗	∗	NOUN
ejpam-6173	556	6	,	,	PUNCT
ejpam-6173	556	7	qnk	qnk	NOUN
ejpam-6173	556	8	)	)	PUNCT
ejpam-6173	556	9	−df	−df	PROPN
ejpam-6173	556	10	(	(	PUNCT
ejpam-6173	556	11	p	p	NOUN
ejpam-6173	556	12	∗	∗	NOUN
ejpam-6173	556	13	,	,	PUNCT
ejpam-6173	556	14	znk	znk	NOUN
ejpam-6173	556	15	)	)	PUNCT
ejpam-6173	556	16	]	]	PUNCT
ejpam-6173	557	1	+	+	CCONJ
ejpam-6173	557	2	[	[	X
ejpam-6173	557	3	df	df	X
ejpam-6173	557	4	(	(	PUNCT
ejpam-6173	557	5	p	p	NOUN
ejpam-6173	557	6	∗	∗	NOUN
ejpam-6173	557	7	,	,	PUNCT
ejpam-6173	557	8	znk	znk	NOUN
ejpam-6173	557	9	)	)	PUNCT
ejpam-6173	557	10	−df	−df	PROPN
ejpam-6173	557	11	(	(	PUNCT
ejpam-6173	557	12	p	p	NOUN
ejpam-6173	557	13	∗	∗	NOUN
ejpam-6173	557	14	,	,	PUNCT
ejpam-6173	557	15	ynk	ynk	NOUN
ejpam-6173	557	16	)	)	PUNCT
ejpam-6173	557	17	]	]	PUNCT
ejpam-6173	557	18	→	→	SYM
ejpam-6173	557	19	0	0	PUNCT
ejpam-6173	557	20	as	as	ADP
ejpam-6173	557	21	k	k	PROPN
ejpam-6173	557	22	→	→	PROPN
ejpam-6173	557	23	+	+	PROPN
ejpam-6173	557	24	∞.	∞.	PROPN
ejpam-6173	557	25	v.	v.	ADP
ejpam-6173	557	26	darvish	darvish	PROPN
ejpam-6173	557	27	et	et	PROPN
ejpam-6173	557	28	al	al	PROPN
ejpam-6173	557	29	.	.	PUNCT
ejpam-6173	557	30	/	/	SYM
ejpam-6173	557	31	eur	eur	PROPN
ejpam-6173	557	32	.	.	PUNCT
ejpam-6173	558	1	j.	j.	PROPN
ejpam-6173	558	2	pure	pure	PROPN
ejpam-6173	558	3	appl	appl	PROPN
ejpam-6173	558	4	.	.	PROPN
ejpam-6173	558	5	math	math	PROPN
ejpam-6173	558	6	,	,	PUNCT
ejpam-6173	558	7	18	18	NUM
ejpam-6173	558	8	(	(	PUNCT
ejpam-6173	558	9	3	3	NUM
ejpam-6173	558	10	)	)	PUNCT
ejpam-6173	558	11	(	(	PUNCT
ejpam-6173	558	12	2025	2025	NUM
ejpam-6173	558	13	)	)	PUNCT
ejpam-6173	558	14	,	,	PUNCT
ejpam-6173	558	15	6173	6173	NUM
ejpam-6173	558	16	21	21	NUM
ejpam-6173	558	17	of	of	ADP
ejpam-6173	558	18	32	32	NUM
ejpam-6173	558	19	therefore	therefore	ADV
ejpam-6173	558	20	,	,	PUNCT
ejpam-6173	558	21	lim	lim	PROPN
ejpam-6173	558	22	k→+∞	k→+∞	PROPN
ejpam-6173	558	23	df	df	PROPN
ejpam-6173	558	24	(	(	PUNCT
ejpam-6173	558	25	tynk	tynk	NOUN
ejpam-6173	558	26	,	,	PUNCT
ejpam-6173	558	27	ynk	ynk	NOUN
ejpam-6173	558	28	)	)	PUNCT
ejpam-6173	559	1	=	=	PUNCT
ejpam-6173	559	2	0	0	X
ejpam-6173	559	3	.	.	PUNCT
ejpam-6173	559	4	from	from	ADP
ejpam-6173	559	5	lemma	lemma	PROPN
ejpam-6173	559	6	1	1	NUM
ejpam-6173	559	7	,	,	PUNCT
ejpam-6173	559	8	we	we	PRON
ejpam-6173	559	9	obtain	obtain	VERB
ejpam-6173	559	10	lim	lim	PROPN
ejpam-6173	559	11	k→+∞	k→+∞	PROPN
ejpam-6173	559	12	∥tynk	∥tynk	NOUN
ejpam-6173	559	13	−	−	PROPN
ejpam-6173	559	14	ynk	ynk	NOUN
ejpam-6173	559	15	∥	∥	PROPN
ejpam-6173	559	16	=	=	SYM
ejpam-6173	560	1	0	0	NUM
ejpam-6173	560	2	.	.	PUNCT
ejpam-6173	561	1	(	(	PUNCT
ejpam-6173	561	2	4.36	4.36	NUM
ejpam-6173	561	3	)	)	PUNCT
ejpam-6173	561	4	from	from	ADP
ejpam-6173	561	5	(	(	PUNCT
ejpam-6173	561	6	4.35	4.35	NUM
ejpam-6173	561	7	)	)	PUNCT
ejpam-6173	561	8	and	and	CCONJ
ejpam-6173	561	9	(	(	PUNCT
ejpam-6173	561	10	4.36	4.36	NUM
ejpam-6173	561	11	)	)	PUNCT
ejpam-6173	561	12	,	,	PUNCT
ejpam-6173	561	13	we	we	PRON
ejpam-6173	561	14	have∥∥xnk+1	have∥∥xnk+1	VERB
ejpam-6173	561	15	−	−	PROPN
ejpam-6173	561	16	tynk	tynk	NOUN
ejpam-6173	561	17	∥∥	∥∥	PRON
ejpam-6173	561	18	≤	≤	PROPN
ejpam-6173	561	19	∥∥xnk+1	∥∥xnk+1	VERB
ejpam-6173	562	1	−	−	PROPN
ejpam-6173	562	2	ynk	ynk	NOUN
ejpam-6173	562	3	∥∥+	∥∥+	SYM
ejpam-6173	562	4	∥ynk	∥ynk	PROPN
ejpam-6173	562	5	−	−	PROPN
ejpam-6173	562	6	tynk	tynk	NOUN
ejpam-6173	562	7	∥	∥	PUNCT
ejpam-6173	562	8	→	→	SYM
ejpam-6173	562	9	0	0	NUM
ejpam-6173	562	10	,	,	PUNCT
ejpam-6173	562	11	as	as	ADP
ejpam-6173	562	12	k	k	PROPN
ejpam-6173	562	13	→	→	PROPN
ejpam-6173	562	14	+	+	PROPN
ejpam-6173	562	15	∞.	∞.	PROPN
ejpam-6173	562	16	in	in	ADP
ejpam-6173	562	17	other	other	ADJ
ejpam-6173	562	18	words	word	NOUN
ejpam-6173	562	19	,	,	PUNCT
ejpam-6173	562	20	lim	lim	PROPN
ejpam-6173	562	21	k→+∞	k→+∞	PROPN
ejpam-6173	562	22	∥∥xnk+1	∥∥xnk+1	VERB
ejpam-6173	562	23	−	−	PROPN
ejpam-6173	562	24	tynk	tynk	NOUN
ejpam-6173	562	25	∥∥	∥∥	NOUN
ejpam-6173	562	26	=	=	SYM
ejpam-6173	562	27	0	0	PROPN
ejpam-6173	562	28	.	.	PUNCT
ejpam-6173	563	1	(	(	PUNCT
ejpam-6173	563	2	4.37	4.37	NUM
ejpam-6173	563	3	)	)	PUNCT
ejpam-6173	563	4	from	from	ADP
ejpam-6173	563	5	(	(	PUNCT
ejpam-6173	563	6	4.27	4.27	NUM
ejpam-6173	563	7	)	)	PUNCT
ejpam-6173	563	8	and	and	CCONJ
ejpam-6173	563	9	(	(	PUNCT
ejpam-6173	563	10	4.36	4.36	NUM
ejpam-6173	563	11	)	)	PUNCT
ejpam-6173	563	12	we	we	PRON
ejpam-6173	563	13	have	have	VERB
ejpam-6173	563	14	∥xnk	∥xnk	PROPN
ejpam-6173	563	15	−	−	PUNCT
ejpam-6173	563	16	txnk	txnk	VERB
ejpam-6173	563	17	∥	∥	PUNCT
ejpam-6173	563	18	≤	≤	PUNCT
ejpam-6173	564	1	∥xnk	∥xnk	PROPN
ejpam-6173	564	2	−	−	PROPN
ejpam-6173	564	3	ynk	ynk	PROPN
ejpam-6173	564	4	∥+	∥+	PROPN
ejpam-6173	564	5	∥ynk	∥ynk	PROPN
ejpam-6173	564	6	−	−	NOUN
ejpam-6173	564	7	tynk	tynk	NOUN
ejpam-6173	564	8	∥+	∥+	NOUN
ejpam-6173	564	9	∥tynk	∥tynk	NOUN
ejpam-6173	564	10	−	−	NOUN
ejpam-6173	564	11	txnk	txnk	X
ejpam-6173	564	12	∥	∥	X
ejpam-6173	564	13	→	→	SYM
ejpam-6173	564	14	0	0	PUNCT
ejpam-6173	564	15	as	as	SCONJ
ejpam-6173	564	16	k	k	PROPN
ejpam-6173	564	17	→	→	PROPN
ejpam-6173	564	18	+	+	PROPN
ejpam-6173	564	19	∞.	∞.	PROPN
ejpam-6173	564	20	hence	hence	ADV
ejpam-6173	564	21	,	,	PUNCT
ejpam-6173	564	22	lim	lim	PROPN
ejpam-6173	564	23	k→+∞	k→+∞	PROPN
ejpam-6173	564	24	∥xnk	∥xnk	PROPN
ejpam-6173	564	25	−	−	PUNCT
ejpam-6173	564	26	txnk	txnk	VERB
ejpam-6173	564	27	∥	∥	PUNCT
ejpam-6173	564	28	=	=	SYM
ejpam-6173	564	29	0	0	X
ejpam-6173	564	30	.	.	PUNCT
ejpam-6173	564	31	(	(	PUNCT
ejpam-6173	564	32	4.38	4.38	NUM
ejpam-6173	564	33	)	)	PUNCT
ejpam-6173	564	34	from	from	ADP
ejpam-6173	564	35	(	(	PUNCT
ejpam-6173	564	36	4.27)-(4.38	4.27)-(4.38	NUM
ejpam-6173	564	37	)	)	PUNCT
ejpam-6173	564	38	we	we	PRON
ejpam-6173	564	39	have	have	VERB
ejpam-6173	564	40	lim	lim	PROPN
ejpam-6173	564	41	n→+∞	n→+∞	PROPN
ejpam-6173	564	42	∥xnk+1	∥xnk+1	VERB
ejpam-6173	564	43	−	−	PROPN
ejpam-6173	564	44	xnk	xnk	PROPN
ejpam-6173	564	45	∥	∥	X
ejpam-6173	565	1	=	=	PUNCT
ejpam-6173	566	1	0	0	X
ejpam-6173	566	2	.	.	PUNCT
ejpam-6173	567	1	(	(	PUNCT
ejpam-6173	567	2	4.39	4.39	NUM
ejpam-6173	567	3	)	)	PUNCT
ejpam-6173	567	4	since	since	SCONJ
ejpam-6173	567	5	{	{	PUNCT
ejpam-6173	567	6	xn	xn	X
ejpam-6173	567	7	}	}	PUNCT
ejpam-6173	567	8	is	be	AUX
ejpam-6173	567	9	bounded	bound	VERB
ejpam-6173	567	10	,	,	PUNCT
ejpam-6173	567	11	there	there	PRON
ejpam-6173	567	12	exists	exist	VERB
ejpam-6173	567	13	a	a	DET
ejpam-6173	567	14	subsequence	subsequence	NOUN
ejpam-6173	567	15	{	{	PUNCT
ejpam-6173	567	16	xnk	xnk	PROPN
ejpam-6173	567	17	}	}	PUNCT
ejpam-6173	567	18	of	of	ADP
ejpam-6173	567	19	{	{	PUNCT
ejpam-6173	567	20	xn	xn	NOUN
ejpam-6173	567	21	}	}	PUNCT
ejpam-6173	567	22	such	such	ADJ
ejpam-6173	567	23	that	that	SCONJ
ejpam-6173	567	24	{	{	PUNCT
ejpam-6173	567	25	xnk	xnk	NOUN
ejpam-6173	567	26	}	}	PUNCT
ejpam-6173	567	27	⇀	⇀	PROPN
ejpam-6173	567	28	p∗.	p∗.	NOUN
ejpam-6173	567	29	from	from	ADP
ejpam-6173	567	30	(	(	PUNCT
ejpam-6173	567	31	4.38	4.38	NUM
ejpam-6173	567	32	)	)	PUNCT
ejpam-6173	567	33	,	,	PUNCT
ejpam-6173	567	34	we	we	PRON
ejpam-6173	567	35	have	have	VERB
ejpam-6173	567	36	∥xnk	∥xnk	PROPN
ejpam-6173	567	37	−	−	PROPN
ejpam-6173	567	38	t	t	PROPN
ejpam-6173	567	39	(	(	PUNCT
ejpam-6173	567	40	xnk	xnk	PROPN
ejpam-6173	567	41	)	)	PUNCT
ejpam-6173	567	42	∥	∥	PUNCT
ejpam-6173	567	43	→	→	SYM
ejpam-6173	567	44	0	0	PUNCT
ejpam-6173	567	45	as	as	ADP
ejpam-6173	567	46	k	k	PROPN
ejpam-6173	567	47	→	→	PROPN
ejpam-6173	567	48	+	+	PROPN
ejpam-6173	567	49	∞.	∞.	PROPN
ejpam-6173	567	50	hence	hence	ADV
ejpam-6173	567	51	,	,	PUNCT
ejpam-6173	567	52	p∗	p∗	PROPN
ejpam-6173	567	53	∈	∈	PROPN
ejpam-6173	567	54	f	f	X
ejpam-6173	567	55	(	(	PUNCT
ejpam-6173	567	56	t	t	PROPN
ejpam-6173	567	57	)	)	PUNCT
ejpam-6173	567	58	.	.	PUNCT
ejpam-6173	568	1	for	for	ADP
ejpam-6173	568	2	any	any	DET
ejpam-6173	568	3	w	w	PROPN
ejpam-6173	568	4	∈	∈	PROPN
ejpam-6173	568	5	(	(	PUNCT
ejpam-6173	568	6	f	f	X
ejpam-6173	568	7	(	(	PUNCT
ejpam-6173	568	8	t	t	PROPN
ejpam-6173	568	9	)	)	PUNCT
ejpam-6173	568	10	∩	∩	NOUN
ejpam-6173	568	11	(	(	PUNCT
ejpam-6173	568	12	⋂n	⋂n	PROPN
ejpam-6173	568	13	j=1b	j=1b	PROPN
ejpam-6173	568	14	−1	−1	PROPN
ejpam-6173	568	15	θj	θj	NOUN
ejpam-6173	568	16	(	(	PUNCT
ejpam-6173	568	17	0∗	0∗	NOUN
ejpam-6173	568	18	)	)	PUNCT
ejpam-6173	568	19	)	)	PUNCT
ejpam-6173	568	20	)	)	PUNCT
ejpam-6173	568	21	,	,	PUNCT
ejpam-6173	568	22	it	it	PRON
ejpam-6173	568	23	follows	follow	VERB
ejpam-6173	568	24	from	from	ADP
ejpam-6173	568	25	the	the	DET
ejpam-6173	568	26	there	there	NOUN
ejpam-6173	568	27	point	point	VERB
ejpam-6173	568	28	identity	identity	NOUN
ejpam-6173	568	29	that	that	PRON
ejpam-6173	568	30	|df	|df	PRON
ejpam-6173	568	31	(	(	PUNCT
ejpam-6173	568	32	w	w	PROPN
ejpam-6173	568	33	,	,	PUNCT
ejpam-6173	568	34	wnk	wnk	X
ejpam-6173	568	35	)	)	PUNCT
ejpam-6173	568	36	−df	−df	PROPN
ejpam-6173	568	37	(	(	PUNCT
ejpam-6173	568	38	w	w	PROPN
ejpam-6173	568	39	,	,	PUNCT
ejpam-6173	568	40	ynk	ynk	NOUN
ejpam-6173	568	41	)	)	PUNCT
ejpam-6173	568	42	|	|	ADV
ejpam-6173	568	43	=	=	SYM
ejpam-6173	568	44	|df	|df	PROPN
ejpam-6173	568	45	(	(	PUNCT
ejpam-6173	568	46	w	w	PROPN
ejpam-6173	568	47	,	,	PUNCT
ejpam-6173	568	48	ynk	ynk	NOUN
ejpam-6173	568	49	)	)	PUNCT
ejpam-6173	569	1	+	+	ADP
ejpam-6173	569	2	df	df	PROPN
ejpam-6173	569	3	(	(	PUNCT
ejpam-6173	569	4	ynk	ynk	PROPN
ejpam-6173	569	5	,	,	PUNCT
ejpam-6173	569	6	wnk	wnk	X
ejpam-6173	569	7	)	)	PUNCT
ejpam-6173	570	1	+	+	CCONJ
ejpam-6173	570	2	⟨w	⟨w	X
ejpam-6173	570	3	−	−	PROPN
ejpam-6173	570	4	ynk	ynk	NOUN
ejpam-6173	570	5	,	,	PUNCT
ejpam-6173	570	6	∇f	∇f	PROPN
ejpam-6173	570	7	(	(	PUNCT
ejpam-6173	570	8	ynk	ynk	NOUN
ejpam-6173	570	9	)	)	PUNCT
ejpam-6173	570	10	−∇f	−∇f	PROPN
ejpam-6173	570	11	(	(	PUNCT
ejpam-6173	570	12	wnk	wnk	X
ejpam-6173	570	13	)	)	PUNCT
ejpam-6173	570	14	⟩	⟩	NOUN
ejpam-6173	570	15	−df	−df	PROPN
ejpam-6173	570	16	(	(	PUNCT
ejpam-6173	570	17	w	w	PROPN
ejpam-6173	570	18	,	,	PUNCT
ejpam-6173	570	19	ynk	ynk	NOUN
ejpam-6173	570	20	)	)	PUNCT
ejpam-6173	571	1	|	|	ADV
ejpam-6173	571	2	=	=	SYM
ejpam-6173	571	3	|df	|df	PROPN
ejpam-6173	571	4	(	(	PUNCT
ejpam-6173	571	5	ynk	ynk	NOUN
ejpam-6173	571	6	,	,	PUNCT
ejpam-6173	571	7	wnk	wnk	X
ejpam-6173	571	8	)	)	PUNCT
ejpam-6173	572	1	+	+	CCONJ
ejpam-6173	572	2	⟨w	⟨w	X
ejpam-6173	572	3	−	−	PROPN
ejpam-6173	572	4	ynk	ynk	NOUN
ejpam-6173	572	5	,	,	PUNCT
ejpam-6173	572	6	∇f	∇f	PROPN
ejpam-6173	572	7	(	(	PUNCT
ejpam-6173	572	8	ynk	ynk	NOUN
ejpam-6173	572	9	)	)	PUNCT
ejpam-6173	572	10	−∇f	−∇f	PROPN
ejpam-6173	572	11	(	(	PUNCT
ejpam-6173	572	12	wnk	wnk	X
ejpam-6173	572	13	)	)	PUNCT
ejpam-6173	572	14	⟩|	⟩|	PROPN
ejpam-6173	572	15	≤	≤	PROPN
ejpam-6173	572	16	df	df	PROPN
ejpam-6173	572	17	(	(	PUNCT
ejpam-6173	572	18	ynk	ynk	PROPN
ejpam-6173	572	19	,	,	PUNCT
ejpam-6173	572	20	wnk	wnk	X
ejpam-6173	572	21	)	)	PUNCT
ejpam-6173	573	1	+	+	CCONJ
ejpam-6173	573	2	∥w	∥w	PROPN
ejpam-6173	573	3	−	−	PROPN
ejpam-6173	573	4	ynk	ynk	NOUN
ejpam-6173	573	5	∥	∥	NOUN
ejpam-6173	573	6	∥∇f	∥∇f	NOUN
ejpam-6173	573	7	(	(	PUNCT
ejpam-6173	573	8	ynk	ynk	NOUN
ejpam-6173	573	9	)	)	PUNCT
ejpam-6173	573	10	−∇f	−∇f	PROPN
ejpam-6173	573	11	(	(	PUNCT
ejpam-6173	573	12	wnk	wnk	X
ejpam-6173	573	13	)	)	PUNCT
ejpam-6173	573	14	∥	∥	NOUN
ejpam-6173	573	15	≤	≤	NUM
ejpam-6173	574	1	∥ynk	∥ynk	NOUN
ejpam-6173	574	2	−	−	PROPN
ejpam-6173	574	3	wnk	wnk	NOUN
ejpam-6173	574	4	∥+	∥+	PROPN
ejpam-6173	575	1	∥w	∥w	PROPN
ejpam-6173	575	2	−	−	PROPN
ejpam-6173	575	3	ynk	ynk	NOUN
ejpam-6173	575	4	∥	∥	NOUN
ejpam-6173	575	5	∥∇f	∥∇f	NOUN
ejpam-6173	575	6	(	(	PUNCT
ejpam-6173	575	7	ynk	ynk	NOUN
ejpam-6173	575	8	)	)	PUNCT
ejpam-6173	575	9	−∇f	−∇f	PROPN
ejpam-6173	575	10	(	(	PUNCT
ejpam-6173	575	11	wnk	wnk	X
ejpam-6173	575	12	)	)	PUNCT
ejpam-6173	575	13	∥	∥	PUNCT
ejpam-6173	575	14	→	→	SYM
ejpam-6173	575	15	0	0	PUNCT
ejpam-6173	575	16	as	as	ADP
ejpam-6173	575	17	k	k	PROPN
ejpam-6173	575	18	→	→	PROPN
ejpam-6173	575	19	+	+	ADJ
ejpam-6173	575	20	∞	∞	NUM
ejpam-6173	575	21	by	by	ADP
ejpam-6173	575	22	(	(	PUNCT
ejpam-6173	575	23	4.32	4.32	NUM
ejpam-6173	575	24	)	)	PUNCT
ejpam-6173	575	25	.	.	PUNCT
ejpam-6173	576	1	hence	hence	ADV
ejpam-6173	576	2	,	,	PUNCT
ejpam-6173	576	3	lim	lim	PROPN
ejpam-6173	576	4	k→+∞	k→+∞	PROPN
ejpam-6173	576	5	|df	|df	PROPN
ejpam-6173	576	6	(	(	PUNCT
ejpam-6173	576	7	w	w	PROPN
ejpam-6173	576	8	,	,	PUNCT
ejpam-6173	576	9	wnk	wnk	X
ejpam-6173	576	10	)	)	PUNCT
ejpam-6173	576	11	−df	−df	PROPN
ejpam-6173	576	12	(	(	PUNCT
ejpam-6173	576	13	w	w	PROPN
ejpam-6173	576	14	,	,	PUNCT
ejpam-6173	576	15	ynk	ynk	NOUN
ejpam-6173	576	16	)	)	PUNCT
ejpam-6173	576	17	|	|	ADV
ejpam-6173	576	18	=	=	SYM
ejpam-6173	576	19	0	0	X
ejpam-6173	576	20	.	.	PUNCT
ejpam-6173	577	1	since	since	SCONJ
ejpam-6173	577	2	resfbθ	resfbθ	NOUN
ejpam-6173	577	3	is	be	AUX
ejpam-6173	577	4	bqfne	bqfne	NOUN
ejpam-6173	577	5	,	,	PUNCT
ejpam-6173	577	6	we	we	PRON
ejpam-6173	577	7	have	have	VERB
ejpam-6173	577	8	df	df	NOUN
ejpam-6173	577	9	(	(	PUNCT
ejpam-6173	577	10	resfbθj	resfbθj	VERB
ejpam-6173	577	11	◦	◦	NOUN
ejpam-6173	577	12	·	·	PUNCT
ejpam-6173	577	13	·	·	PUNCT
ejpam-6173	577	14	·	·	PUNCT
ejpam-6173	578	1	◦	◦	NOUN
ejpam-6173	578	2	resfbθ1	resfbθ1	NOUN
ejpam-6173	578	3	(	(	PUNCT
ejpam-6173	578	4	wnk	wnk	PROPN
ejpam-6173	578	5	)	)	PUNCT
ejpam-6173	578	6	,	,	PUNCT
ejpam-6173	578	7	resfbθj−1	resfbθj−1	PROPN
ejpam-6173	578	8	◦	◦	NOUN
ejpam-6173	578	9	.	.	PUNCT
ejpam-6173	578	10	.	.	PUNCT
ejpam-6173	578	11	.	.	PUNCT
ejpam-6173	579	1	◦	◦	NOUN
ejpam-6173	579	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	579	3	(	(	PUNCT
ejpam-6173	579	4	wnk	wnk	PROPN
ejpam-6173	579	5	)	)	PUNCT
ejpam-6173	579	6	)	)	PUNCT
ejpam-6173	580	1	=	=	SYM
ejpam-6173	580	2	df	df	PROPN
ejpam-6173	580	3	(	(	PUNCT
ejpam-6173	580	4	resfbθj	resfbθj	VERB
ejpam-6173	580	5	◦	◦	NOUN
ejpam-6173	580	6	resfbθj−1	resfbθj−1	NOUN
ejpam-6173	580	7	◦	◦	NOUN
ejpam-6173	580	8	.	.	PUNCT
ejpam-6173	580	9	.	.	PUNCT
ejpam-6173	580	10	.	.	PUNCT
ejpam-6173	581	1	◦	◦	NOUN
ejpam-6173	581	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	581	3	(	(	PUNCT
ejpam-6173	581	4	wnk	wnk	PROPN
ejpam-6173	581	5	)	)	PUNCT
ejpam-6173	581	6	,	,	PUNCT
ejpam-6173	581	7	resfbθj−1	resfbθj−1	PROPN
ejpam-6173	581	8	◦	◦	NOUN
ejpam-6173	581	9	.	.	PUNCT
ejpam-6173	581	10	.	.	PUNCT
ejpam-6173	581	11	.	.	PUNCT
ejpam-6173	582	1	◦	◦	NOUN
ejpam-6173	582	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	582	3	(	(	PUNCT
ejpam-6173	582	4	wnk	wnk	PROPN
ejpam-6173	582	5	)	)	PUNCT
ejpam-6173	582	6	)	)	PUNCT
ejpam-6173	582	7	≤	≤	NUM
ejpam-6173	583	1	df	df	NOUN
ejpam-6173	583	2	(	(	PUNCT
ejpam-6173	583	3	w	w	PROPN
ejpam-6173	583	4	,	,	PUNCT
ejpam-6173	583	5	wnk	wnk	X
ejpam-6173	583	6	)	)	PUNCT
ejpam-6173	583	7	−df	−df	PROPN
ejpam-6173	583	8	(	(	PUNCT
ejpam-6173	583	9	w	w	PROPN
ejpam-6173	583	10	,	,	PUNCT
ejpam-6173	583	11	wnk	wnk	NOUN
ejpam-6173	583	12	)	)	PUNCT
ejpam-6173	583	13	→	→	SYM
ejpam-6173	583	14	0	0	NUM
ejpam-6173	583	15	v.	v.	ADP
ejpam-6173	583	16	darvish	darvish	PROPN
ejpam-6173	583	17	et	et	PROPN
ejpam-6173	583	18	al	al	PROPN
ejpam-6173	583	19	.	.	PUNCT
ejpam-6173	583	20	/	/	SYM
ejpam-6173	583	21	eur	eur	PROPN
ejpam-6173	583	22	.	.	PUNCT
ejpam-6173	584	1	j.	j.	PROPN
ejpam-6173	584	2	pure	pure	PROPN
ejpam-6173	584	3	appl	appl	PROPN
ejpam-6173	584	4	.	.	PROPN
ejpam-6173	584	5	math	math	PROPN
ejpam-6173	584	6	,	,	PUNCT
ejpam-6173	584	7	18	18	NUM
ejpam-6173	584	8	(	(	PUNCT
ejpam-6173	584	9	3	3	NUM
ejpam-6173	584	10	)	)	PUNCT
ejpam-6173	584	11	(	(	PUNCT
ejpam-6173	584	12	2025	2025	NUM
ejpam-6173	584	13	)	)	PUNCT
ejpam-6173	584	14	,	,	PUNCT
ejpam-6173	584	15	6173	6173	NUM
ejpam-6173	584	16	22	22	NUM
ejpam-6173	584	17	of	of	ADP
ejpam-6173	584	18	32	32	NUM
ejpam-6173	584	19	as	as	ADP
ejpam-6173	584	20	k	k	PROPN
ejpam-6173	584	21	→	→	PROPN
ejpam-6173	585	1	+	+	ADJ
ejpam-6173	585	2	∞	∞	PROPN
ejpam-6173	585	3	for	for	ADP
ejpam-6173	585	4	all	all	DET
ejpam-6173	585	5	j	j	PROPN
ejpam-6173	585	6	∈	∈	PROPN
ejpam-6173	585	7	{	{	PUNCT
ejpam-6173	585	8	1	1	NUM
ejpam-6173	585	9	,	,	PUNCT
ejpam-6173	585	10	2	2	NUM
ejpam-6173	585	11	,	,	PUNCT
ejpam-6173	585	12	.	.	PUNCT
ejpam-6173	585	13	.	.	PUNCT
ejpam-6173	586	1	.	.	PUNCT
ejpam-6173	586	2	,	,	PUNCT
ejpam-6173	587	1	n	n	CCONJ
ejpam-6173	587	2	}	}	PUNCT
ejpam-6173	587	3	.	.	PUNCT
ejpam-6173	588	1	it	it	PRON
ejpam-6173	588	2	then	then	ADV
ejpam-6173	588	3	follows	follow	VERB
ejpam-6173	588	4	that	that	SCONJ
ejpam-6173	588	5	lim	lim	PROPN
ejpam-6173	588	6	k→+∞	k→+∞	PROPN
ejpam-6173	588	7	df	df	PROPN
ejpam-6173	588	8	(	(	PUNCT
ejpam-6173	588	9	(	(	PUNCT
ejpam-6173	588	10	resfbθj	resfbθj	NOUN
ejpam-6173	588	11	◦	◦	NOUN
ejpam-6173	588	12	.	.	PUNCT
ejpam-6173	588	13	.	.	PUNCT
ejpam-6173	588	14	.	.	PUNCT
ejpam-6173	589	1	◦	◦	NOUN
ejpam-6173	589	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	589	3	(	(	PUNCT
ejpam-6173	589	4	wnk	wnk	PROPN
ejpam-6173	589	5	)	)	PUNCT
ejpam-6173	589	6	,	,	PUNCT
ejpam-6173	589	7	wnk	wnk	X
ejpam-6173	589	8	)	)	PUNCT
ejpam-6173	589	9	)	)	PUNCT
ejpam-6173	590	1	=	=	SYM
ejpam-6173	590	2	0	0	NUM
ejpam-6173	590	3	for	for	ADP
ejpam-6173	590	4	all	all	DET
ejpam-6173	590	5	j	j	PROPN
ejpam-6173	590	6	∈	∈	PROPN
ejpam-6173	590	7	{	{	PUNCT
ejpam-6173	590	8	1	1	NUM
ejpam-6173	590	9	,	,	PUNCT
ejpam-6173	590	10	2	2	NUM
ejpam-6173	590	11	,	,	PUNCT
ejpam-6173	590	12	.	.	PUNCT
ejpam-6173	590	13	.	.	PUNCT
ejpam-6173	591	1	.	.	PUNCT
ejpam-6173	591	2	,	,	PUNCT
ejpam-6173	591	3	n	n	CCONJ
ejpam-6173	591	4	}	}	PUNCT
ejpam-6173	591	5	.	.	PUNCT
ejpam-6173	592	1	so	so	ADV
ejpam-6173	592	2	,	,	PUNCT
ejpam-6173	592	3	lim	lim	PROPN
ejpam-6173	592	4	k→+∞	k→+∞	PROPN
ejpam-6173	592	5	∥resfbθj	∥resfbθj	PROPN
ejpam-6173	592	6	◦	◦	PROPN
ejpam-6173	592	7	.	.	PUNCT
ejpam-6173	592	8	.	.	PUNCT
ejpam-6173	592	9	.	.	PUNCT
ejpam-6173	593	1	◦	◦	NOUN
ejpam-6173	593	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	593	3	(	(	PUNCT
ejpam-6173	593	4	wnk	wnk	INTJ
ejpam-6173	593	5	)	)	PUNCT
ejpam-6173	593	6	−	−	PROPN
ejpam-6173	593	7	wnk	wnk	X
ejpam-6173	593	8	∥	∥	X
ejpam-6173	593	9	=	=	SYM
ejpam-6173	593	10	0	0	NUM
ejpam-6173	593	11	(	(	PUNCT
ejpam-6173	593	12	4.40	4.40	NUM
ejpam-6173	593	13	)	)	PUNCT
ejpam-6173	593	14	for	for	ADP
ejpam-6173	593	15	all	all	DET
ejpam-6173	593	16	j	j	PROPN
ejpam-6173	593	17	∈	∈	PROPN
ejpam-6173	593	18	{	{	PUNCT
ejpam-6173	593	19	1	1	NUM
ejpam-6173	593	20	,	,	PUNCT
ejpam-6173	593	21	2	2	NUM
ejpam-6173	593	22	,	,	PUNCT
ejpam-6173	593	23	.	.	PUNCT
ejpam-6173	593	24	.	.	PUNCT
ejpam-6173	594	1	.	.	PUNCT
ejpam-6173	594	2	,	,	PUNCT
ejpam-6173	594	3	n	n	CCONJ
ejpam-6173	594	4	}	}	PUNCT
ejpam-6173	594	5	.	.	PUNCT
ejpam-6173	595	1	from	from	ADP
ejpam-6173	595	2	the	the	DET
ejpam-6173	595	3	definition	definition	NOUN
ejpam-6173	595	4	of	of	ADP
ejpam-6173	595	5	the	the	DET
ejpam-6173	595	6	f	f	PROPN
ejpam-6173	595	7	-resolvent	-resolvent	PROPN
ejpam-6173	595	8	,	,	PUNCT
ejpam-6173	595	9	we	we	PRON
ejpam-6173	595	10	have	have	VERB
ejpam-6173	595	11	∇f	∇f	NOUN
ejpam-6173	595	12	(	(	PUNCT
ejpam-6173	595	13	resfbθj−1	resfbθj−1	NOUN
ejpam-6173	595	14	◦	◦	NOUN
ejpam-6173	595	15	.	.	PUNCT
ejpam-6173	595	16	.	.	PUNCT
ejpam-6173	595	17	.	.	PUNCT
ejpam-6173	596	1	◦	◦	NOUN
ejpam-6173	596	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	596	3	(	(	PUNCT
ejpam-6173	596	4	wnk	wnk	PROPN
ejpam-6173	596	5	)	)	PUNCT
ejpam-6173	596	6	)	)	PUNCT
ejpam-6173	597	1	∈	∈	PROPN
ejpam-6173	597	2	(	(	PUNCT
ejpam-6173	597	3	∇f	∇f	NOUN
ejpam-6173	597	4	+	+	CCONJ
ejpam-6173	597	5	λj	λj	PROPN
ejpam-6173	597	6	nk	nk	PROPN
ejpam-6173	597	7	bθj	bθj	PROPN
ejpam-6173	597	8	)	)	PUNCT
ejpam-6173	597	9	(	(	PUNCT
ejpam-6173	597	10	resfbθj	resfbθj	NOUN
ejpam-6173	597	11	◦	◦	NOUN
ejpam-6173	597	12	.	.	PUNCT
ejpam-6173	597	13	.	.	PUNCT
ejpam-6173	597	14	.	.	PUNCT
ejpam-6173	598	1	◦	◦	NOUN
ejpam-6173	598	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	598	3	(	(	PUNCT
ejpam-6173	598	4	wnk	wnk	PROPN
ejpam-6173	598	5	)	)	PUNCT
ejpam-6173	598	6	)	)	PUNCT
ejpam-6173	598	7	.	.	PUNCT
ejpam-6173	599	1	hence	hence	ADV
ejpam-6173	599	2	ζjnk	ζjnk	VERB
ejpam-6173	599	3	:	:	PUNCT
ejpam-6173	599	4	=	=	SYM
ejpam-6173	599	5	1	1	NUM
ejpam-6173	599	6	λj	λj	PROPN
ejpam-6173	599	7	nk	nk	PROPN
ejpam-6173	599	8	(	(	PUNCT
ejpam-6173	599	9	∇f(resfbθj−1	∇f(resfbθj−1	NOUN
ejpam-6173	599	10	◦	◦	NOUN
ejpam-6173	599	11	.	.	PUNCT
ejpam-6173	599	12	.	.	PUNCT
ejpam-6173	599	13	.	.	PUNCT
ejpam-6173	600	1	◦	◦	NOUN
ejpam-6173	600	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	600	3	(	(	PUNCT
ejpam-6173	600	4	wnk	wnk	PROPN
ejpam-6173	600	5	)	)	PUNCT
ejpam-6173	600	6	)	)	PUNCT
ejpam-6173	601	1	−∇f(resfbθj	−∇f(resfbθj	PROPN
ejpam-6173	601	2	◦	◦	NOUN
ejpam-6173	601	3	.	.	PUNCT
ejpam-6173	601	4	.	.	PUNCT
ejpam-6173	601	5	.	.	PUNCT
ejpam-6173	602	1	◦	◦	NOUN
ejpam-6173	602	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	602	3	(	(	PUNCT
ejpam-6173	602	4	wnk	wnk	PROPN
ejpam-6173	602	5	)	)	PUNCT
ejpam-6173	602	6	)	)	PUNCT
ejpam-6173	602	7	)	)	PUNCT
ejpam-6173	603	1	for	for	ADP
ejpam-6173	603	2	all	all	DET
ejpam-6173	603	3	j	j	PROPN
ejpam-6173	603	4	∈	∈	PROPN
ejpam-6173	603	5	{	{	PUNCT
ejpam-6173	603	6	1	1	NUM
ejpam-6173	603	7	,	,	PUNCT
ejpam-6173	603	8	2	2	NUM
ejpam-6173	603	9	,	,	PUNCT
ejpam-6173	603	10	.	.	PUNCT
ejpam-6173	603	11	.	.	PUNCT
ejpam-6173	603	12	.	.	PUNCT
ejpam-6173	603	13	,	,	PUNCT
ejpam-6173	603	14	n	n	CCONJ
ejpam-6173	603	15	}	}	PUNCT
ejpam-6173	603	16	.	.	PUNCT
ejpam-6173	604	1	it	it	PRON
ejpam-6173	604	2	follows	follow	VERB
ejpam-6173	604	3	from	from	ADP
ejpam-6173	604	4	the	the	DET
ejpam-6173	604	5	above	above	ADJ
ejpam-6173	604	6	equations	equation	NOUN
ejpam-6173	604	7	that	that	PRON
ejpam-6173	604	8	lim	lim	PROPN
ejpam-6173	604	9	k→+∞	k→+∞	PROPN
ejpam-6173	604	10	∥ζjnk∥	∥ζjnk∥	PROPN
ejpam-6173	604	11	=	=	X
ejpam-6173	604	12	0	0	NUM
ejpam-6173	604	13	for	for	ADP
ejpam-6173	604	14	any	any	DET
ejpam-6173	604	15	j	j	PROPN
ejpam-6173	604	16	∈	∈	PROPN
ejpam-6173	604	17	{	{	PUNCT
ejpam-6173	604	18	1	1	NUM
ejpam-6173	604	19	,	,	PUNCT
ejpam-6173	604	20	2	2	NUM
ejpam-6173	604	21	,	,	PUNCT
ejpam-6173	604	22	.	.	PUNCT
ejpam-6173	604	23	.	.	PUNCT
ejpam-6173	605	1	.	.	PUNCT
ejpam-6173	605	2	,	,	PUNCT
ejpam-6173	605	3	n	n	CCONJ
ejpam-6173	605	4	}	}	PUNCT
ejpam-6173	605	5	.	.	PUNCT
ejpam-6173	606	1	since	since	SCONJ
ejpam-6173	606	2	xnk	xnk	PROPN
ejpam-6173	606	3	⇀	⇀	PROPN
ejpam-6173	606	4	p∗	p∗	PROPN
ejpam-6173	606	5	,	,	PUNCT
ejpam-6173	606	6	we	we	PRON
ejpam-6173	606	7	obtain	obtain	VERB
ejpam-6173	606	8	from	from	ADP
ejpam-6173	606	9	(	(	PUNCT
ejpam-6173	606	10	4.34	4.34	NUM
ejpam-6173	606	11	)	)	PUNCT
ejpam-6173	606	12	that	that	PRON
ejpam-6173	606	13	wnk	wnk	VERB
ejpam-6173	606	14	⇀	⇀	NUM
ejpam-6173	606	15	p∗.	p∗.	NOUN
ejpam-6173	606	16	from	from	ADP
ejpam-6173	606	17	(	(	PUNCT
ejpam-6173	606	18	4.40	4.40	NUM
ejpam-6173	606	19	)	)	PUNCT
ejpam-6173	606	20	and	and	CCONJ
ejpam-6173	606	21	the	the	DET
ejpam-6173	606	22	fact	fact	NOUN
ejpam-6173	606	23	that	that	SCONJ
ejpam-6173	606	24	wnk	wnk	PROPN
ejpam-6173	607	1	⇀	⇀	X
ejpam-6173	608	1	p∗	p∗	PROPN
ejpam-6173	608	2	,	,	PUNCT
ejpam-6173	608	3	we	we	PRON
ejpam-6173	608	4	obtain	obtain	VERB
ejpam-6173	608	5	resfbθj	resfbθj	NOUN
ejpam-6173	608	6	◦	◦	NOUN
ejpam-6173	608	7	.	.	PUNCT
ejpam-6173	608	8	.	.	PUNCT
ejpam-6173	608	9	.	.	PUNCT
ejpam-6173	609	1	◦	◦	NOUN
ejpam-6173	609	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	609	3	(	(	PUNCT
ejpam-6173	609	4	wnk	wnk	INTJ
ejpam-6173	609	5	)	)	PUNCT
ejpam-6173	610	1	⇀	⇀	PRON
ejpam-6173	610	2	p∗	p∗	ADJ
ejpam-6173	610	3	for	for	ADP
ejpam-6173	610	4	any	any	DET
ejpam-6173	610	5	j	j	PROPN
ejpam-6173	610	6	∈	∈	PROPN
ejpam-6173	610	7	{	{	PUNCT
ejpam-6173	610	8	1	1	NUM
ejpam-6173	610	9	,	,	PUNCT
ejpam-6173	610	10	2	2	NUM
ejpam-6173	610	11	,	,	PUNCT
ejpam-6173	610	12	.	.	PUNCT
ejpam-6173	610	13	.	.	PUNCT
ejpam-6173	611	1	.	.	PUNCT
ejpam-6173	611	2	,	,	PUNCT
ejpam-6173	611	3	n	n	CCONJ
ejpam-6173	611	4	}	}	PUNCT
ejpam-6173	611	5	.	.	PUNCT
ejpam-6173	612	1	consequently	consequently	ADV
ejpam-6173	612	2	,	,	PUNCT
ejpam-6173	612	3	we	we	PRON
ejpam-6173	612	4	have	have	VERB
ejpam-6173	612	5	resfbθj	resfbθj	NOUN
ejpam-6173	612	6	◦	◦	NOUN
ejpam-6173	612	7	.	.	PUNCT
ejpam-6173	612	8	.	.	PUNCT
ejpam-6173	612	9	.	.	PUNCT
ejpam-6173	613	1	◦	◦	NOUN
ejpam-6173	613	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	613	3	(	(	PUNCT
ejpam-6173	613	4	xnk	xnk	PROPN
ejpam-6173	613	5	)	)	PUNCT
ejpam-6173	614	1	⇀	⇀	PRON
ejpam-6173	614	2	p∗	p∗	ADJ
ejpam-6173	614	3	for	for	ADP
ejpam-6173	614	4	any	any	DET
ejpam-6173	614	5	j	j	PROPN
ejpam-6173	614	6	∈	∈	PROPN
ejpam-6173	614	7	{	{	PUNCT
ejpam-6173	614	8	1	1	NUM
ejpam-6173	614	9	,	,	PUNCT
ejpam-6173	614	10	2	2	NUM
ejpam-6173	614	11	,	,	PUNCT
ejpam-6173	614	12	.	.	PUNCT
ejpam-6173	614	13	.	.	PUNCT
ejpam-6173	615	1	.	.	PUNCT
ejpam-6173	615	2	,	,	PUNCT
ejpam-6173	615	3	n	n	CCONJ
ejpam-6173	615	4	}	}	PUNCT
ejpam-6173	615	5	.	.	PUNCT
ejpam-6173	616	1	from	from	ADP
ejpam-6173	616	2	the	the	DET
ejpam-6173	616	3	monotonicity	monotonicity	NOUN
ejpam-6173	616	4	of	of	ADP
ejpam-6173	616	5	bθ	bθ	PROPN
ejpam-6173	616	6	,	,	PUNCT
ejpam-6173	616	7	we	we	PRON
ejpam-6173	616	8	have	have	VERB
ejpam-6173	616	9	⟨η	⟨η	NOUN
ejpam-6173	616	10	−	−	PROPN
ejpam-6173	616	11	ζjnk	ζjnk	PROPN
ejpam-6173	616	12	,	,	PUNCT
ejpam-6173	616	13	x−resfbθj	x−resfbθj	X
ejpam-6173	617	1	◦	◦	NOUN
ejpam-6173	617	2	.	.	PUNCT
ejpam-6173	617	3	.	.	PUNCT
ejpam-6173	617	4	.	.	PUNCT
ejpam-6173	618	1	◦	◦	NOUN
ejpam-6173	619	1	resfbθ1	resfbθ1	PROPN
ejpam-6173	619	2	(	(	PUNCT
ejpam-6173	619	3	xnk	xnk	PROPN
ejpam-6173	619	4	)	)	PUNCT
ejpam-6173	619	5	⟩	⟩	NOUN
ejpam-6173	619	6	≥	≥	NOUN
ejpam-6173	619	7	0	0	NUM
ejpam-6173	619	8	.	.	PUNCT
ejpam-6173	620	1	for	for	ADP
ejpam-6173	620	2	all	all	DET
ejpam-6173	620	3	(	(	PUNCT
ejpam-6173	620	4	x	x	NOUN
ejpam-6173	620	5	,	,	PUNCT
ejpam-6173	620	6	η	η	NOUN
ejpam-6173	620	7	)	)	PUNCT
ejpam-6173	620	8	∈	∈	PROPN
ejpam-6173	620	9	graph(bθj	graph(bθj	NOUN
ejpam-6173	620	10	)	)	PUNCT
ejpam-6173	620	11	.	.	PUNCT
ejpam-6173	621	1	this	this	PRON
ejpam-6173	621	2	implies	imply	VERB
ejpam-6173	621	3	that	that	PRON
ejpam-6173	621	4	⟨η	⟨η	ADP
ejpam-6173	621	5	,	,	PUNCT
ejpam-6173	621	6	x	x	PUNCT
ejpam-6173	621	7	−	−	PROPN
ejpam-6173	621	8	p∗⟩	p∗⟩	PROPN
ejpam-6173	621	9	≥	≥	NOUN
ejpam-6173	621	10	0	0	NUM
ejpam-6173	621	11	for	for	ADP
ejpam-6173	621	12	all	all	DET
ejpam-6173	621	13	(	(	PUNCT
ejpam-6173	621	14	x	x	NOUN
ejpam-6173	621	15	,	,	PUNCT
ejpam-6173	621	16	η	η	NOUN
ejpam-6173	621	17	)	)	PUNCT
ejpam-6173	621	18	∈	∈	PROPN
ejpam-6173	621	19	graph(bθj	graph(bθj	NOUN
ejpam-6173	621	20	)	)	PUNCT
ejpam-6173	621	21	and	and	CCONJ
ejpam-6173	621	22	for	for	ADP
ejpam-6173	621	23	all	all	DET
ejpam-6173	621	24	j	j	PROPN
ejpam-6173	621	25	∈	∈	PROPN
ejpam-6173	621	26	{	{	PUNCT
ejpam-6173	621	27	1	1	NUM
ejpam-6173	621	28	,	,	PUNCT
ejpam-6173	621	29	2	2	NUM
ejpam-6173	621	30	,	,	PUNCT
ejpam-6173	621	31	.	.	PUNCT
ejpam-6173	621	32	.	.	PUNCT
ejpam-6173	622	1	.	.	PUNCT
ejpam-6173	622	2	,	,	PUNCT
ejpam-6173	622	3	n	n	CCONJ
ejpam-6173	622	4	}	}	PUNCT
ejpam-6173	622	5	.	.	PUNCT
ejpam-6173	623	1	so	so	ADV
ejpam-6173	623	2	,	,	PUNCT
ejpam-6173	623	3	by	by	ADP
ejpam-6173	623	4	the	the	DET
ejpam-6173	623	5	maximal	maximal	ADJ
ejpam-6173	623	6	monotonicity	monotonicity	NOUN
ejpam-6173	623	7	of	of	ADP
ejpam-6173	623	8	bθj	bθj	NOUN
ejpam-6173	623	9	we	we	PRON
ejpam-6173	623	10	have	have	VERB
ejpam-6173	623	11	p	p	NOUN
ejpam-6173	623	12	∗	∗	NOUN
ejpam-6173	623	13	∈	∈	PROPN
ejpam-6173	624	1	b−1	b−1	PROPN
ejpam-6173	624	2	θj	θj	NOUN
ejpam-6173	624	3	(	(	PUNCT
ejpam-6173	624	4	0	0	NUM
ejpam-6173	624	5	)	)	PUNCT
ejpam-6173	624	6	for	for	ADP
ejpam-6173	624	7	all	all	DET
ejpam-6173	624	8	j	j	PROPN
ejpam-6173	624	9	∈	∈	PROPN
ejpam-6173	624	10	{	{	PUNCT
ejpam-6173	624	11	1	1	NUM
ejpam-6173	624	12	,	,	PUNCT
ejpam-6173	624	13	2	2	NUM
ejpam-6173	624	14	,	,	PUNCT
ejpam-6173	624	15	.	.	PUNCT
ejpam-6173	624	16	.	.	PUNCT
ejpam-6173	625	1	.	.	PUNCT
ejpam-6173	625	2	,	,	PUNCT
ejpam-6173	625	3	n	n	CCONJ
ejpam-6173	625	4	}	}	PUNCT
ejpam-6173	625	5	.	.	PUNCT
ejpam-6173	626	1	therefore	therefore	ADV
ejpam-6173	626	2	p∗	p∗	PROPN
ejpam-6173	626	3	∈	∈	PROPN
ejpam-6173	626	4	∩n	∩n	PROPN
ejpam-6173	626	5	j=1b	j=1b	PROPN
ejpam-6173	626	6	−1	−1	ADV
ejpam-6173	626	7	θj	θj	ADV
ejpam-6173	626	8	(	(	PUNCT
ejpam-6173	626	9	0	0	NUM
ejpam-6173	626	10	)	)	PUNCT
ejpam-6173	626	11	.	.	PUNCT
ejpam-6173	627	1	hence	hence	ADV
ejpam-6173	627	2	,	,	PUNCT
ejpam-6173	627	3	we	we	PRON
ejpam-6173	627	4	have	have	AUX
ejpam-6173	627	5	shown	show	VERB
ejpam-6173	627	6	that	that	SCONJ
ejpam-6173	627	7	p∗	p∗	PROPN
ejpam-6173	627	8	∈	∈	PROPN
ejpam-6173	627	9	(	(	PUNCT
ejpam-6173	627	10	f	f	X
ejpam-6173	627	11	(	(	PUNCT
ejpam-6173	627	12	t	t	PROPN
ejpam-6173	627	13	)	)	PUNCT
ejpam-6173	627	14	∩	∩	NOUN
ejpam-6173	627	15	(	(	PUNCT
ejpam-6173	627	16	∩n	∩n	PROPN
ejpam-6173	627	17	j=1b	j=1b	PROPN
ejpam-6173	627	18	−1	−1	ADV
ejpam-6173	627	19	θj	θj	ADV
ejpam-6173	627	20	(	(	PUNCT
ejpam-6173	627	21	0∗	0∗	NOUN
ejpam-6173	627	22	)	)	PUNCT
ejpam-6173	627	23	)	)	PUNCT
ejpam-6173	627	24	)	)	PUNCT
ejpam-6173	627	25	.	.	PUNCT
ejpam-6173	628	1	since	since	SCONJ
ejpam-6173	628	2	e	e	PROPN
ejpam-6173	628	3	is	be	AUX
ejpam-6173	628	4	reflexive	reflexive	ADJ
ejpam-6173	628	5	and	and	CCONJ
ejpam-6173	628	6	{	{	PUNCT
ejpam-6173	628	7	xnk	xnk	PROPN
ejpam-6173	628	8	}	}	PUNCT
ejpam-6173	628	9	is	be	AUX
ejpam-6173	628	10	bounded	bound	VERB
ejpam-6173	628	11	,	,	PUNCT
ejpam-6173	628	12	there	there	PRON
ejpam-6173	628	13	exists	exist	VERB
ejpam-6173	628	14	a	a	DET
ejpam-6173	628	15	subsequence	subsequence	NOUN
ejpam-6173	628	16	{	{	PUNCT
ejpam-6173	628	17	xnkj	xnkj	PROPN
ejpam-6173	628	18	}	}	PUNCT
ejpam-6173	628	19	of	of	ADP
ejpam-6173	628	20	{	{	PUNCT
ejpam-6173	628	21	xnk	xnk	PROPN
ejpam-6173	628	22	}	}	PUNCT
ejpam-6173	628	23	such	such	ADJ
ejpam-6173	628	24	that	that	SCONJ
ejpam-6173	628	25	{	{	PUNCT
ejpam-6173	628	26	xnkj	xnkj	PROPN
ejpam-6173	628	27	}	}	PUNCT
ejpam-6173	628	28	⇀	⇀	PUNCT
ejpam-6173	628	29	u	u	NOUN
ejpam-6173	628	30	∈	∈	PROPN
ejpam-6173	628	31	c	c	PROPN
ejpam-6173	628	32	and	and	CCONJ
ejpam-6173	628	33	lim	lim	PROPN
ejpam-6173	628	34	j→+∞	j→+∞	PROPN
ejpam-6173	628	35	〈	〈	PROPN
ejpam-6173	628	36	∇f(qnk	∇f(qnk	NOUN
ejpam-6173	628	37	)	)	PUNCT
ejpam-6173	628	38	−∇f(p̂	−∇f(p̂	NOUN
ejpam-6173	628	39	)	)	PUNCT
ejpam-6173	628	40	,	,	PUNCT
ejpam-6173	628	41	xnkj	xnkj	PROPN
ejpam-6173	628	42	−	−	PROPN
ejpam-6173	628	43	p̂	p̂	X
ejpam-6173	628	44	〉	〉	NOUN
ejpam-6173	628	45	=	=	SYM
ejpam-6173	628	46	lim	lim	PROPN
ejpam-6173	628	47	sup	sup	PROPN
ejpam-6173	628	48	k→+∞	k→+∞	PROPN
ejpam-6173	628	49	⟨∇f(qnk	⟨∇f(qnk	X
ejpam-6173	628	50	)	)	PUNCT
ejpam-6173	628	51	−∇f(p̂	−∇f(p̂	NOUN
ejpam-6173	628	52	)	)	PUNCT
ejpam-6173	628	53	,	,	PUNCT
ejpam-6173	629	1	xnk	xnk	PROPN
ejpam-6173	629	2	−	−	PROPN
ejpam-6173	629	3	p̂⟩	p̂⟩	NOUN
ejpam-6173	629	4	=	=	PROPN
ejpam-6173	629	5	lim	lim	PROPN
ejpam-6173	629	6	sup	sup	PROPN
ejpam-6173	629	7	k→+∞	k→+∞	PROPN
ejpam-6173	629	8	⟨∇f(qnk	⟨∇f(qnk	X
ejpam-6173	629	9	)	)	PUNCT
ejpam-6173	629	10	−∇f(p̂	−∇f(p̂	NOUN
ejpam-6173	629	11	)	)	PUNCT
ejpam-6173	629	12	,	,	PUNCT
ejpam-6173	629	13	ynk	ynk	VERB
ejpam-6173	629	14	−	−	PROPN
ejpam-6173	629	15	p̂⟩.	p̂⟩.	ADV
ejpam-6173	629	16	v.	v.	CCONJ
ejpam-6173	629	17	darvish	darvish	X
ejpam-6173	629	18	et	et	PROPN
ejpam-6173	629	19	al	al	PROPN
ejpam-6173	629	20	.	.	PUNCT
ejpam-6173	629	21	/	/	SYM
ejpam-6173	629	22	eur	eur	PROPN
ejpam-6173	629	23	.	.	PUNCT
ejpam-6173	630	1	j.	j.	PROPN
ejpam-6173	630	2	pure	pure	PROPN
ejpam-6173	630	3	appl	appl	PROPN
ejpam-6173	630	4	.	.	PROPN
ejpam-6173	630	5	math	math	PROPN
ejpam-6173	630	6	,	,	PUNCT
ejpam-6173	630	7	18	18	NUM
ejpam-6173	630	8	(	(	PUNCT
ejpam-6173	630	9	3	3	NUM
ejpam-6173	630	10	)	)	PUNCT
ejpam-6173	630	11	(	(	PUNCT
ejpam-6173	630	12	2025	2025	NUM
ejpam-6173	630	13	)	)	PUNCT
ejpam-6173	630	14	,	,	PUNCT
ejpam-6173	630	15	6173	6173	NUM
ejpam-6173	630	16	23	23	NUM
ejpam-6173	630	17	of	of	ADP
ejpam-6173	630	18	32	32	NUM
ejpam-6173	630	19	it	it	PRON
ejpam-6173	630	20	follows	follow	VERB
ejpam-6173	630	21	from	from	ADP
ejpam-6173	630	22	the	the	DET
ejpam-6173	630	23	definition	definition	NOUN
ejpam-6173	630	24	of	of	ADP
ejpam-6173	630	25	the	the	DET
ejpam-6173	630	26	bregman	bregman	NOUN
ejpam-6173	630	27	projection	projection	NOUN
ejpam-6173	631	1	that	that	SCONJ
ejpam-6173	631	2	lim	lim	PROPN
ejpam-6173	631	3	sup	sup	PROPN
ejpam-6173	631	4	k→+∞	k→+∞	PROPN
ejpam-6173	631	5	⟨∇f(qnk	⟨∇f(qnk	X
ejpam-6173	631	6	)	)	PUNCT
ejpam-6173	631	7	−∇f(p̂	−∇f(p̂	NOUN
ejpam-6173	631	8	)	)	PUNCT
ejpam-6173	631	9	,	,	PUNCT
ejpam-6173	631	10	ynk	ynk	NOUN
ejpam-6173	631	11	−	−	PROPN
ejpam-6173	631	12	p̂⟩	p̂⟩	NOUN
ejpam-6173	631	13	=	=	PROPN
ejpam-6173	631	14	lim	lim	PROPN
ejpam-6173	631	15	j→+∞	j→+∞	PROPN
ejpam-6173	631	16	〈	〈	PROPN
ejpam-6173	631	17	∇f(qnk	∇f(qnk	NOUN
ejpam-6173	631	18	)	)	PUNCT
ejpam-6173	631	19	−∇f(p̂	−∇f(p̂	NOUN
ejpam-6173	631	20	)	)	PUNCT
ejpam-6173	631	21	,	,	PUNCT
ejpam-6173	631	22	xnkj	xnkj	PROPN
ejpam-6173	631	23	−	−	PROPN
ejpam-6173	631	24	p̂	p̂	X
ejpam-6173	631	25	〉	〉	NOUN
ejpam-6173	631	26	(	(	PUNCT
ejpam-6173	631	27	4.41	4.41	NUM
ejpam-6173	631	28	)	)	PUNCT
ejpam-6173	631	29	=	=	SYM
ejpam-6173	631	30	⟨∇f(q)−∇f(p̂	⟨∇f(q)−∇f(p̂	PROPN
ejpam-6173	631	31	)	)	PUNCT
ejpam-6173	631	32	,	,	PUNCT
ejpam-6173	631	33	u−	u−	PROPN
ejpam-6173	631	34	p̂⟩	p̂⟩	VERB
ejpam-6173	631	35	≤	≤	ADJ
ejpam-6173	631	36	0	0	NUM
ejpam-6173	631	37	.	.	PUNCT
ejpam-6173	632	1	(	(	PUNCT
ejpam-6173	632	2	4.42	4.42	NUM
ejpam-6173	632	3	)	)	PUNCT
ejpam-6173	632	4	by	by	ADP
ejpam-6173	632	5	lemma	lemma	PROPN
ejpam-6173	632	6	15	15	NUM
ejpam-6173	632	7	,	,	PUNCT
ejpam-6173	632	8	(	(	PUNCT
ejpam-6173	632	9	4.41	4.41	NUM
ejpam-6173	632	10	)	)	PUNCT
ejpam-6173	632	11	and	and	CCONJ
ejpam-6173	632	12	the	the	DET
ejpam-6173	632	13	condition	condition	NOUN
ejpam-6173	632	14	on	on	ADP
ejpam-6173	632	15	α	α	NOUN
ejpam-6173	632	16	,	,	PUNCT
ejpam-6173	632	17	we	we	PRON
ejpam-6173	632	18	can	can	AUX
ejpam-6173	632	19	conclude	conclude	VERB
ejpam-6173	632	20	that	that	PRON
ejpam-6173	632	21	lim	lim	PROPN
ejpam-6173	632	22	sup	sup	PROPN
ejpam-6173	632	23	k→+∞	k→+∞	PROPN
ejpam-6173	632	24	bnk	bnk	PROPN
ejpam-6173	632	25	≤	≤	NUM
ejpam-6173	632	26	0	0	NUM
ejpam-6173	632	27	.	.	PUNCT
ejpam-6173	633	1	from	from	ADP
ejpam-6173	633	2	lemma	lemma	PROPN
ejpam-6173	633	3	4.17	4.17	NUM
ejpam-6173	633	4	and	and	CCONJ
ejpam-6173	633	5	(	(	PUNCT
ejpam-6173	633	6	4.15	4.15	NUM
ejpam-6173	633	7	)	)	PUNCT
ejpam-6173	633	8	we	we	PRON
ejpam-6173	633	9	have	have	VERB
ejpam-6173	633	10	limn→+∞df	limn→+∞df	NOUN
ejpam-6173	633	11	(	(	PUNCT
ejpam-6173	633	12	p̂	p̂	X
ejpam-6173	633	13	,	,	PUNCT
ejpam-6173	633	14	xn	xn	PROPN
ejpam-6173	633	15	)	)	PUNCT
ejpam-6173	633	16	=	=	SYM
ejpam-6173	634	1	0	0	X
ejpam-6173	634	2	.	.	PUNCT
ejpam-6173	634	3	therefore	therefore	ADV
ejpam-6173	634	4	,	,	PUNCT
ejpam-6173	634	5	by	by	ADP
ejpam-6173	634	6	lemma	lemma	PROPN
ejpam-6173	634	7	11	11	NUM
ejpam-6173	634	8	,	,	PUNCT
ejpam-6173	634	9	we	we	PRON
ejpam-6173	634	10	have	have	VERB
ejpam-6173	634	11	lim	lim	PROPN
ejpam-6173	634	12	n→+∞	n→+∞	PROPN
ejpam-6173	634	13	xn	xn	PUNCT
ejpam-6173	635	1	=	=	SYM
ejpam-6173	635	2	p̂.	p̂.	NOUN
ejpam-6173	636	1	this	this	PRON
ejpam-6173	636	2	completes	complete	VERB
ejpam-6173	636	3	the	the	DET
ejpam-6173	636	4	proof	proof	NOUN
ejpam-6173	636	5	.	.	PUNCT
ejpam-6173	637	1	using	use	VERB
ejpam-6173	637	2	theorem	theorem	NOUN
ejpam-6173	637	3	1	1	NUM
ejpam-6173	637	4	and	and	CCONJ
ejpam-6173	637	5	lemma	lemma	PROPN
ejpam-6173	637	6	13	13	NUM
ejpam-6173	637	7	,	,	PUNCT
ejpam-6173	637	8	we	we	PRON
ejpam-6173	637	9	have	have	VERB
ejpam-6173	637	10	the	the	DET
ejpam-6173	637	11	following	follow	VERB
ejpam-6173	637	12	result	result	NOUN
ejpam-6173	637	13	.	.	PUNCT
ejpam-6173	638	1	let	let	VERB
ejpam-6173	638	2	φ	φ	PROPN
ejpam-6173	638	3	=	=	SYM
ejpam-6173	638	4	ψ	ψ	PROPN
ejpam-6173	638	5	=	=	X
ejpam-6173	638	6	θn	θn	NOUN
ejpam-6173	638	7	=	=	PROPN
ejpam-6173	638	8	0	0	PROPN
ejpam-6173	638	9	and	and	CCONJ
ejpam-6173	638	10	t	t	NOUN
ejpam-6173	639	1	=	=	SYM
ejpam-6173	639	2	i	i	PRON
ejpam-6173	639	3	then	then	ADV
ejpam-6173	639	4	we	we	PRON
ejpam-6173	639	5	have	have	VERB
ejpam-6173	639	6	the	the	DET
ejpam-6173	639	7	following	follow	VERB
ejpam-6173	639	8	corollary	corollary	NOUN
ejpam-6173	639	9	which	which	PRON
ejpam-6173	639	10	was	be	AUX
ejpam-6173	639	11	obtained	obtain	VERB
ejpam-6173	639	12	in	in	ADP
ejpam-6173	639	13	[	[	X
ejpam-6173	639	14	56	56	NUM
ejpam-6173	639	15	]	]	PUNCT
ejpam-6173	639	16	.	.	PUNCT
ejpam-6173	640	1	corollary	corollary	ADJ
ejpam-6173	640	2	1	1	NUM
ejpam-6173	640	3	.	.	PUNCT
ejpam-6173	641	1	let	let	VERB
ejpam-6173	641	2	e	e	PRON
ejpam-6173	641	3	be	be	AUX
ejpam-6173	641	4	a	a	DET
ejpam-6173	641	5	real	real	ADJ
ejpam-6173	641	6	reflexive	reflexive	ADJ
ejpam-6173	641	7	banach	banach	NOUN
ejpam-6173	641	8	space	space	NOUN
ejpam-6173	641	9	,	,	PUNCT
ejpam-6173	641	10	c	c	X
ejpam-6173	641	11	be	be	AUX
ejpam-6173	641	12	a	a	DET
ejpam-6173	641	13	nonempty	nonempty	ADJ
ejpam-6173	641	14	,	,	PUNCT
ejpam-6173	641	15	closed	closed	ADJ
ejpam-6173	641	16	and	and	CCONJ
ejpam-6173	641	17	convex	convex	NOUN
ejpam-6173	641	18	subset	subset	NOUN
ejpam-6173	641	19	of	of	ADP
ejpam-6173	641	20	int(domf	int(domf	NOUN
ejpam-6173	641	21	)	)	PUNCT
ejpam-6173	641	22	.	.	PUNCT
ejpam-6173	642	1	let	let	VERB
ejpam-6173	642	2	f	f	NOUN
ejpam-6173	642	3	:	:	PUNCT
ejpam-6173	642	4	e	e	X
ejpam-6173	642	5	→	→	SYM
ejpam-6173	642	6	r	r	NOUN
ejpam-6173	642	7	be	be	AUX
ejpam-6173	642	8	a	a	DET
ejpam-6173	642	9	super	super	ADV
ejpam-6173	642	10	coercive	coercive	ADJ
ejpam-6173	642	11	legendre	legendre	PROPN
ejpam-6173	642	12	function	function	NOUN
ejpam-6173	642	13	which	which	PRON
ejpam-6173	642	14	is	be	AUX
ejpam-6173	642	15	bounded	bound	VERB
ejpam-6173	642	16	,	,	PUNCT
ejpam-6173	642	17	uniformly	uniformly	ADV
ejpam-6173	642	18	fréchet	fréchet	VERB
ejpam-6173	642	19	differentiable	differentiable	ADJ
ejpam-6173	642	20	and	and	CCONJ
ejpam-6173	642	21	totally	totally	ADV
ejpam-6173	642	22	convex	convex	VERB
ejpam-6173	642	23	on	on	ADP
ejpam-6173	642	24	bounded	bounded	ADJ
ejpam-6173	642	25	subsets	subset	NOUN
ejpam-6173	642	26	of	of	ADP
ejpam-6173	642	27	e.	e.	PROPN
ejpam-6173	642	28	let	let	VERB
ejpam-6173	642	29	bθj	bθj	VERB
ejpam-6173	642	30	:	:	PUNCT
ejpam-6173	642	31	e	e	X
ejpam-6173	642	32	→	→	SYM
ejpam-6173	642	33	2e	2e	NUM
ejpam-6173	642	34	∗	∗	NOUN
ejpam-6173	642	35	,	,	PUNCT
ejpam-6173	642	36	j	j	PROPN
ejpam-6173	642	37	=	=	SYM
ejpam-6173	642	38	1	1	NUM
ejpam-6173	642	39	,	,	PUNCT
ejpam-6173	642	40	2	2	NUM
ejpam-6173	642	41	,	,	PUNCT
ejpam-6173	642	42	.	.	PUNCT
ejpam-6173	642	43	.	.	PUNCT
ejpam-6173	643	1	.	.	PUNCT
ejpam-6173	644	1	,	,	PUNCT
ejpam-6173	644	2	n	n	PRON
ejpam-6173	644	3	be	be	VERB
ejpam-6173	644	4	n	n	PRON
ejpam-6173	644	5	maximal	maximal	ADJ
ejpam-6173	644	6	monotone	monotone	ADJ
ejpam-6173	644	7	mapping	mapping	NOUN
ejpam-6173	644	8	with	with	ADP
ejpam-6173	644	9	dom(b	dom(b	PROPN
ejpam-6173	644	10	)	)	PUNCT
ejpam-6173	644	11	⊂	⊂	PROPN
ejpam-6173	644	12	c.	c.	PROPN
ejpam-6173	644	13	assume	assume	VERB
ejpam-6173	644	14	that	that	SCONJ
ejpam-6173	644	15	(	(	PUNCT
ejpam-6173	644	16	∩n	∩n	PROPN
ejpam-6173	644	17	j=1b	j=1b	PROPN
ejpam-6173	644	18	−1	−1	ADV
ejpam-6173	644	19	θj	θj	ADV
ejpam-6173	644	20	(	(	PUNCT
ejpam-6173	644	21	0∗	0∗	NOUN
ejpam-6173	644	22	)	)	PUNCT
ejpam-6173	644	23	)	)	PUNCT
ejpam-6173	645	1	̸=	̸=	NOUN
ejpam-6173	645	2	∅	∅	NOUN
ejpam-6173	645	3	,	,	PUNCT
ejpam-6173	645	4	{	{	PUNCT
ejpam-6173	645	5	αn	αn	VERB
ejpam-6173	645	6	}	}	PUNCT
ejpam-6173	645	7	and	and	CCONJ
ejpam-6173	645	8	{	{	PUNCT
ejpam-6173	645	9	βn	βn	NOUN
ejpam-6173	645	10	}	}	PUNCT
ejpam-6173	645	11	be	be	AUX
ejpam-6173	645	12	sequences	sequence	NOUN
ejpam-6173	645	13	in	in	ADP
ejpam-6173	645	14	[	[	X
ejpam-6173	645	15	0	0	NUM
ejpam-6173	645	16	,	,	PUNCT
ejpam-6173	645	17	1	1	NUM
ejpam-6173	645	18	]	]	PUNCT
ejpam-6173	645	19	satisfying	satisfy	VERB
ejpam-6173	645	20	the	the	DET
ejpam-6173	645	21	following	follow	VERB
ejpam-6173	645	22	conditions	condition	NOUN
ejpam-6173	645	23	:	:	PUNCT
ejpam-6173	645	24	(	(	PUNCT
ejpam-6173	645	25	i	i	NOUN
ejpam-6173	645	26	)	)	PUNCT
ejpam-6173	645	27	lim	lim	PROPN
ejpam-6173	645	28	n→+∞	n→+∞	VERB
ejpam-6173	645	29	βn	βn	NOUN
ejpam-6173	645	30	=	=	SYM
ejpam-6173	645	31	0	0	NUM
ejpam-6173	645	32	;	;	PUNCT
ejpam-6173	645	33	(	(	PUNCT
ejpam-6173	645	34	ii	ii	X
ejpam-6173	645	35	)	)	PUNCT
ejpam-6173	646	1	+	+	ADP
ejpam-6173	646	2	∞∑	∞∑	NOUN
ejpam-6173	646	3	n=1	n=1	ADP
ejpam-6173	646	4	βn	βn	NOUN
ejpam-6173	646	5	=	=	PUNCT
ejpam-6173	647	1	+	+	NOUN
ejpam-6173	647	2	∞	∞	NUM
ejpam-6173	647	3	;	;	PUNCT
ejpam-6173	647	4	(	(	PUNCT
ejpam-6173	647	5	iii	iii	NOUN
ejpam-6173	647	6	)	)	PUNCT
ejpam-6173	647	7	0	0	PUNCT
ejpam-6173	648	1	<	<	X
ejpam-6173	648	2	lim	lim	PROPN
ejpam-6173	648	3	inf	inf	PROPN
ejpam-6173	648	4	n→+∞	n→+∞	VERB
ejpam-6173	648	5	αn	αn	NOUN
ejpam-6173	648	6	≤	≤	PROPN
ejpam-6173	649	1	lim	lim	PROPN
ejpam-6173	649	2	supn→+∞	supn→+∞	VERB
ejpam-6173	649	3	αn	αn	INTJ
ejpam-6173	649	4	<	<	X
ejpam-6173	650	1	1	1	X
ejpam-6173	650	2	.	.	PUNCT
ejpam-6173	651	1	let	let	VERB
ejpam-6173	651	2	{	{	PUNCT
ejpam-6173	651	3	xn	xn	VERB
ejpam-6173	651	4	}	}	PUNCT
ejpam-6173	651	5	be	be	AUX
ejpam-6173	651	6	a	a	DET
ejpam-6173	651	7	sequence	sequence	NOUN
ejpam-6173	651	8	generated	generate	VERB
ejpam-6173	651	9	by	by	ADP
ejpam-6173	651	10	u	u	PROPN
ejpam-6173	651	11	∈	∈	PROPN
ejpam-6173	651	12	e	e	PROPN
ejpam-6173	651	13	,	,	PUNCT
ejpam-6173	651	14	x1	x1	PROPN
ejpam-6173	651	15	∈	∈	PROPN
ejpam-6173	651	16	e	e	NOUN
ejpam-6173	651	17	chosen	choose	VERB
ejpam-6173	651	18	arbitrarily	arbitrarily	ADV
ejpam-6173	651	19	,	,	PUNCT
ejpam-6173	651	20	zn	zn	PROPN
ejpam-6173	651	21	=	=	SYM
ejpam-6173	651	22	resfbθn	resfbθn	PROPN
ejpam-6173	651	23	◦	◦	NOUN
ejpam-6173	651	24	.	.	PUNCT
ejpam-6173	651	25	.	.	PUNCT
ejpam-6173	651	26	.	.	PUNCT
ejpam-6173	652	1	◦	◦	NOUN
ejpam-6173	652	2	resfbθ1	resfbθ1	PROPN
ejpam-6173	652	3	(	(	PUNCT
ejpam-6173	652	4	xn	xn	PROPN
ejpam-6173	652	5	)	)	PUNCT
ejpam-6173	652	6	,	,	PUNCT
ejpam-6173	652	7	yn	yn	PROPN
ejpam-6173	653	1	=	=	PUNCT
ejpam-6173	653	2	∇f∗	∇f∗	PROPN
ejpam-6173	653	3	(	(	PUNCT
ejpam-6173	653	4	βn∇f(qn	βn∇f(qn	PROPN
ejpam-6173	653	5	)	)	PUNCT
ejpam-6173	654	1	+	+	CCONJ
ejpam-6173	654	2	(	(	PUNCT
ejpam-6173	654	3	1−	1−	NUM
ejpam-6173	654	4	βn)∇f(zn	βn)∇f(zn	NOUN
ejpam-6173	654	5	)	)	PUNCT
ejpam-6173	654	6	)	)	PUNCT
ejpam-6173	655	1	xn+1	xn+1	PROPN
ejpam-6173	656	1	=	=	SYM
ejpam-6173	656	2	∇f∗	∇f∗	PROPN
ejpam-6173	656	3	(	(	PUNCT
ejpam-6173	656	4	αn∇f(xn	αn∇f(xn	PROPN
ejpam-6173	656	5	)	)	PUNCT
ejpam-6173	656	6	+	+	CCONJ
ejpam-6173	656	7	(	(	PUNCT
ejpam-6173	656	8	1−	1−	NUM
ejpam-6173	656	9	αn)∇f(yn	αn)∇f(yn	NOUN
ejpam-6173	656	10	)	)	PUNCT
ejpam-6173	656	11	)	)	PUNCT
ejpam-6173	656	12	,	,	PUNCT
ejpam-6173	656	13	(	(	PUNCT
ejpam-6173	656	14	4.43	4.43	NUM
ejpam-6173	656	15	)	)	PUNCT
ejpam-6173	656	16	where	where	SCONJ
ejpam-6173	656	17	∇f	∇f	PROPN
ejpam-6173	656	18	is	be	AUX
ejpam-6173	656	19	the	the	DET
ejpam-6173	656	20	gradient	gradient	NOUN
ejpam-6173	656	21	of	of	ADP
ejpam-6173	656	22	f	f	PROPN
ejpam-6173	656	23	.	.	PUNCT
ejpam-6173	657	1	then	then	ADV
ejpam-6173	657	2	the	the	DET
ejpam-6173	657	3	sequence	sequence	NOUN
ejpam-6173	657	4	{	{	PUNCT
ejpam-6173	657	5	xn	xn	PROPN
ejpam-6173	657	6	}	}	PUNCT
ejpam-6173	657	7	generated	generate	VERB
ejpam-6173	657	8	by	by	ADP
ejpam-6173	657	9	(	(	PUNCT
ejpam-6173	657	10	4.43	4.43	NUM
ejpam-6173	657	11	)	)	PUNCT
ejpam-6173	657	12	converges	converge	NOUN
ejpam-6173	657	13	to	to	ADP
ejpam-6173	657	14	projf∩n	projf∩n	NOUN
ejpam-6173	657	15	j=1b	j=1b	ADV
ejpam-6173	657	16	−1	−1	ADV
ejpam-6173	657	17	θj	θj	NOUN
ejpam-6173	657	18	(	(	PUNCT
ejpam-6173	657	19	0∗	0∗	NOUN
ejpam-6173	657	20	)	)	PUNCT
ejpam-6173	657	21	x	x	PUNCT
ejpam-6173	657	22	as	as	ADP
ejpam-6173	657	23	n	n	PROPN
ejpam-6173	657	24	→	→	PUNCT
ejpam-6173	657	25	+	+	PROPN
ejpam-6173	657	26	∞.	∞.	PROPN
ejpam-6173	657	27	5	5	NUM
ejpam-6173	657	28	.	.	PUNCT
ejpam-6173	657	29	numerical	numerical	ADJ
ejpam-6173	657	30	experiment	experiment	NOUN
ejpam-6173	657	31	in	in	ADP
ejpam-6173	657	32	this	this	DET
ejpam-6173	657	33	section	section	NOUN
ejpam-6173	657	34	,	,	PUNCT
ejpam-6173	657	35	we	we	PRON
ejpam-6173	657	36	present	present	VERB
ejpam-6173	657	37	numerical	numerical	ADJ
ejpam-6173	657	38	experiments	experiment	NOUN
ejpam-6173	657	39	to	to	PART
ejpam-6173	657	40	illustrate	illustrate	VERB
ejpam-6173	657	41	the	the	DET
ejpam-6173	657	42	performance	performance	NOUN
ejpam-6173	657	43	of	of	ADP
ejpam-6173	657	44	our	our	PRON
ejpam-6173	657	45	proposed	propose	VERB
ejpam-6173	657	46	method	method	NOUN
ejpam-6173	657	47	.	.	PUNCT
ejpam-6173	658	1	in	in	ADP
ejpam-6173	658	2	all	all	DET
ejpam-6173	658	3	our	our	PRON
ejpam-6173	658	4	experiments	experiment	NOUN
ejpam-6173	658	5	,	,	PUNCT
ejpam-6173	658	6	we	we	PRON
ejpam-6173	658	7	use	use	VERB
ejpam-6173	658	8	∥xn+1	∥xn+1	NOUN
ejpam-6173	658	9	−	−	PROPN
ejpam-6173	659	1	xn∥	xn∥	PROPN
ejpam-6173	659	2	<	<	X
ejpam-6173	659	3	10−4	10−4	PROPN
ejpam-6173	659	4	as	as	ADP
ejpam-6173	659	5	our	our	PRON
ejpam-6173	659	6	stopping	stopping	NOUN
ejpam-6173	659	7	criterion	criterion	NOUN
ejpam-6173	659	8	.	.	PUNCT
ejpam-6173	660	1	all	all	DET
ejpam-6173	660	2	the	the	DET
ejpam-6173	660	3	numerical	numerical	ADJ
ejpam-6173	660	4	computations	computation	NOUN
ejpam-6173	660	5	were	be	AUX
ejpam-6173	660	6	carried	carry	VERB
ejpam-6173	660	7	out	out	ADP
ejpam-6173	660	8	using	use	VERB
ejpam-6173	660	9	using	use	VERB
ejpam-6173	660	10	matlab	matlab	PROPN
ejpam-6173	660	11	version	version	NOUN
ejpam-6173	660	12	r2024(b	r2024(b	NOUN
ejpam-6173	660	13	)	)	PUNCT
ejpam-6173	660	14	.	.	PUNCT
ejpam-6173	661	1	being	be	AUX
ejpam-6173	661	2	a	a	DET
ejpam-6173	661	3	non	non	ADJ
ejpam-6173	661	4	-	-	ADJ
ejpam-6173	661	5	accelerated	accelerated	ADJ
ejpam-6173	661	6	version	version	NOUN
ejpam-6173	661	7	of	of	ADP
ejpam-6173	661	8	our	our	PRON
ejpam-6173	661	9	method	method	NOUN
ejpam-6173	661	10	,	,	PUNCT
ejpam-6173	661	11	we	we	PRON
ejpam-6173	661	12	made	make	VERB
ejpam-6173	661	13	a	a	DET
ejpam-6173	661	14	comparison	comparison	NOUN
ejpam-6173	661	15	with	with	ADP
ejpam-6173	661	16	algorithm	algorithm	NOUN
ejpam-6173	661	17	(	(	PUNCT
ejpam-6173	661	18	1.5	1.5	NUM
ejpam-6173	661	19	)	)	PUNCT
ejpam-6173	661	20	in	in	ADP
ejpam-6173	661	21	[	[	X
ejpam-6173	661	22	23	23	NUM
ejpam-6173	661	23	]	]	PUNCT
ejpam-6173	661	24	with	with	ADP
ejpam-6173	661	25	a	a	DET
ejpam-6173	661	26	short	short	ADJ
ejpam-6173	661	27	name	name	NOUN
ejpam-6173	661	28	”	"	PUNCT
ejpam-6173	661	29	esra	esra	PROPN
ejpam-6173	661	30	”	"	PUNCT
ejpam-6173	661	31	.	.	PUNCT
ejpam-6173	662	1	v.	v.	ADP
ejpam-6173	662	2	darvish	darvish	PROPN
ejpam-6173	662	3	et	et	PROPN
ejpam-6173	662	4	al	al	PROPN
ejpam-6173	662	5	.	.	PUNCT
ejpam-6173	662	6	/	/	SYM
ejpam-6173	662	7	eur	eur	PROPN
ejpam-6173	662	8	.	.	PUNCT
ejpam-6173	663	1	j.	j.	PROPN
ejpam-6173	663	2	pure	pure	PROPN
ejpam-6173	663	3	appl	appl	PROPN
ejpam-6173	663	4	.	.	PROPN
ejpam-6173	663	5	math	math	PROPN
ejpam-6173	663	6	,	,	PUNCT
ejpam-6173	663	7	18	18	NUM
ejpam-6173	663	8	(	(	PUNCT
ejpam-6173	663	9	3	3	NUM
ejpam-6173	663	10	)	)	PUNCT
ejpam-6173	663	11	(	(	PUNCT
ejpam-6173	663	12	2025	2025	NUM
ejpam-6173	663	13	)	)	PUNCT
ejpam-6173	663	14	,	,	PUNCT
ejpam-6173	663	15	6173	6173	NUM
ejpam-6173	663	16	24	24	NUM
ejpam-6173	663	17	of	of	ADP
ejpam-6173	663	18	32	32	NUM
ejpam-6173	663	19	example	example	NOUN
ejpam-6173	663	20	1	1	NUM
ejpam-6173	663	21	.	.	PUNCT
ejpam-6173	664	1	let	let	VERB
ejpam-6173	664	2	e	e	NOUN
ejpam-6173	664	3	=	=	SYM
ejpam-6173	664	4	r	r	NOUN
ejpam-6173	664	5	and	and	CCONJ
ejpam-6173	664	6	c	c	NOUN
ejpam-6173	664	7	=	=	PUNCT
ejpam-6173	665	1	[	[	X
ejpam-6173	665	2	−1	−1	NOUN
ejpam-6173	665	3	,	,	PUNCT
ejpam-6173	665	4	1	1	NUM
ejpam-6173	665	5	]	]	PUNCT
ejpam-6173	665	6	.	.	PUNCT
ejpam-6173	666	1	let	let	VERB
ejpam-6173	666	2	θi(x	θi(x	VERB
ejpam-6173	666	3	,	,	PUNCT
ejpam-6173	666	4	y	y	NOUN
ejpam-6173	666	5	)	)	PUNCT
ejpam-6173	667	1	=	=	SYM
ejpam-6173	667	2	−9ix2+xy+(9i−1)y2,ψi(x	−9ix2+xy+(9i−1)y2,ψi(x	NOUN
ejpam-6173	667	3	,	,	PUNCT
ejpam-6173	667	4	y	y	NOUN
ejpam-6173	667	5	)	)	PUNCT
ejpam-6173	667	6	=	=	SYM
ejpam-6173	667	7	(	(	PUNCT
ejpam-6173	667	8	9i−3)x	9i−3)x	NUM
ejpam-6173	667	9	,	,	PUNCT
ejpam-6173	667	10	φi(x	φi(x	NUM
ejpam-6173	667	11	,	,	PUNCT
ejpam-6173	667	12	y	y	NOUN
ejpam-6173	667	13	)	)	PUNCT
ejpam-6173	667	14	=	=	PUNCT
ejpam-6173	668	1	(	(	PUNCT
ejpam-6173	668	2	9i−6)x	9i−6)x	NUM
ejpam-6173	668	3	,	,	PUNCT
ejpam-6173	668	4	i	i	PRON
ejpam-6173	668	5	=	=	NOUN
ejpam-6173	668	6	1	1	NUM
ejpam-6173	668	7	,	,	PUNCT
ejpam-6173	668	8	2	2	NUM
ejpam-6173	668	9	,	,	PUNCT
ejpam-6173	668	10	3	3	NUM
ejpam-6173	668	11	,	,	PUNCT
ejpam-6173	668	12	·	·	PUNCT
ejpam-6173	668	13	·	·	PUNCT
ejpam-6173	668	14	·	·	PUNCT
ejpam-6173	668	15	,	,	PUNCT
ejpam-6173	668	16	n	n	CCONJ
ejpam-6173	668	17	,	,	PUNCT
ejpam-6173	668	18	we	we	PRON
ejpam-6173	668	19	have	have	AUX
ejpam-6173	668	20	resfbθi	resfbθi	VERB
ejpam-6173	668	21	(	(	PUNCT
ejpam-6173	668	22	x	x	NOUN
ejpam-6173	668	23	)	)	PUNCT
ejpam-6173	669	1	=	=	SYM
ejpam-6173	669	2	x	x	SYM
ejpam-6173	669	3	5(9i−3	5(9i−3	NUM
ejpam-6173	669	4	)	)	PUNCT
ejpam-6173	669	5	.	.	PUNCT
ejpam-6173	670	1	let	let	VERB
ejpam-6173	670	2	f	f	NOUN
ejpam-6173	670	3	=	=	PUNCT
ejpam-6173	670	4	∥x∥2	∥x∥2	PROPN
ejpam-6173	670	5	and	and	CCONJ
ejpam-6173	670	6	t	t	PROPN
ejpam-6173	670	7	(	(	PUNCT
ejpam-6173	670	8	x	x	X
ejpam-6173	670	9	)	)	PUNCT
ejpam-6173	670	10	=	=	SYM
ejpam-6173	670	11	pc(x	pc(x	NOUN
ejpam-6173	670	12	)	)	PUNCT
ejpam-6173	670	13	where	where	SCONJ
ejpam-6173	670	14	pc(x	pc(x	NOUN
ejpam-6173	670	15	)	)	PUNCT
ejpam-6173	670	16	=	=	SYM
ejpam-6173	671	1			PRON
ejpam-6173	671	2	−1	−1	ADV
ejpam-6173	671	3	,	,	PUNCT
ejpam-6173	671	4	x	x	X
ejpam-6173	671	5	<	<	X
ejpam-6173	671	6	−1	−1	NOUN
ejpam-6173	671	7	x	x	NOUN
ejpam-6173	671	8	,	,	PUNCT
ejpam-6173	671	9	x	x	SYM
ejpam-6173	671	10	∈	∈	PROPN
ejpam-6173	672	1	[	[	X
ejpam-6173	672	2	−1	−1	NOUN
ejpam-6173	672	3	,	,	PUNCT
ejpam-6173	672	4	1	1	NUM
ejpam-6173	672	5	]	]	SYM
ejpam-6173	672	6	1	1	NUM
ejpam-6173	672	7	,	,	PUNCT
ejpam-6173	672	8	x	x	X
ejpam-6173	672	9	>	>	X
ejpam-6173	672	10	1	1	X
ejpam-6173	672	11	.	.	PUNCT
ejpam-6173	672	12	clearly	clearly	ADV
ejpam-6173	672	13	,	,	PUNCT
ejpam-6173	672	14	we	we	PRON
ejpam-6173	672	15	observe	observe	VERB
ejpam-6173	672	16	that	that	SCONJ
ejpam-6173	672	17	the	the	DET
ejpam-6173	672	18	bifunction	bifunction	NOUN
ejpam-6173	672	19	θ	θ	NOUN
ejpam-6173	672	20	satisfies	satisfie	NOUN
ejpam-6173	672	21	(	(	PUNCT
ejpam-6173	672	22	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	672	23	)	)	PUNCT
ejpam-6173	672	24	,	,	PUNCT
ejpam-6173	672	25	ψ	ψ	NOUN
ejpam-6173	672	26	is	be	AUX
ejpam-6173	672	27	monotone	monotone	ADJ
ejpam-6173	672	28	and	and	CCONJ
ejpam-6173	672	29	t	t	PROPN
ejpam-6173	672	30	is	be	AUX
ejpam-6173	672	31	bregman	bregman	NOUN
ejpam-6173	672	32	strongly	strongly	ADV
ejpam-6173	672	33	nonexpansive	nonexpansive	ADJ
ejpam-6173	672	34	mapping	mapping	NOUN
ejpam-6173	672	35	.	.	PUNCT
ejpam-6173	673	1	in	in	ADP
ejpam-6173	673	2	this	this	DET
ejpam-6173	673	3	example	example	NOUN
ejpam-6173	673	4	,	,	PUNCT
ejpam-6173	673	5	we	we	PRON
ejpam-6173	673	6	select	select	VERB
ejpam-6173	673	7	αn	αn	NOUN
ejpam-6173	673	8	=	=	SYM
ejpam-6173	673	9	1	1	NUM
ejpam-6173	673	10	2n+3	2n+3	NOUN
ejpam-6173	673	11	,	,	PUNCT
ejpam-6173	673	12	βn	βn	NOUN
ejpam-6173	673	13	=	=	SYM
ejpam-6173	674	1	n	n	SYM
ejpam-6173	674	2	n+1	n+1	PROPN
ejpam-6173	674	3	,	,	PUNCT
ejpam-6173	674	4	qn	qn	NOUN
ejpam-6173	674	5	=	=	NOUN
ejpam-6173	674	6	1	1	NUM
ejpam-6173	674	7	n+1	n+1	PROPN
ejpam-6173	674	8	,	,	PUNCT
ejpam-6173	674	9	ϵ	ϵ	X
ejpam-6173	674	10	=	=	SYM
ejpam-6173	674	11	1	1	NUM
ejpam-6173	674	12	n3.1	n3.1	ADJ
ejpam-6173	674	13	,	,	PUNCT
ejpam-6173	674	14	θ	θ	X
ejpam-6173	674	15	=	=	SYM
ejpam-6173	674	16	0.1	0.1	NUM
ejpam-6173	674	17	and	and	CCONJ
ejpam-6173	674	18	set	set	VERB
ejpam-6173	674	19	n	n	NOUN
ejpam-6173	674	20	=	=	SYM
ejpam-6173	674	21	100	100	NUM
ejpam-6173	674	22	.	.	PUNCT
ejpam-6173	675	1	as	as	ADP
ejpam-6173	675	2	a	a	DET
ejpam-6173	675	3	stopping	stopping	NOUN
ejpam-6173	675	4	criterion	criterion	NOUN
ejpam-6173	675	5	,	,	PUNCT
ejpam-6173	675	6	we	we	PRON
ejpam-6173	675	7	use	use	VERB
ejpam-6173	675	8	∥xn+1	∥xn+1	NOUN
ejpam-6173	675	9	−	−	PROPN
ejpam-6173	675	10	xn∥	xn∥	PROPN
ejpam-6173	675	11	≤	≤	PROPN
ejpam-6173	675	12	ϵ	ϵ	ADP
ejpam-6173	675	13	where	where	SCONJ
ejpam-6173	675	14	ϵ	ϵ	PROPN
ejpam-6173	675	15	=	=	SYM
ejpam-6173	675	16	10−4	10−4	PROPN
ejpam-6173	675	17	.	.	PUNCT
ejpam-6173	676	1	the	the	DET
ejpam-6173	676	2	experiment	experiment	NOUN
ejpam-6173	676	3	was	be	AUX
ejpam-6173	676	4	conducted	conduct	VERB
ejpam-6173	676	5	for	for	ADP
ejpam-6173	676	6	the	the	DET
ejpam-6173	676	7	following	following	ADJ
ejpam-6173	676	8	initial	initial	ADJ
ejpam-6173	676	9	values	value	NOUN
ejpam-6173	676	10	of	of	ADP
ejpam-6173	676	11	x0	x0	PROPN
ejpam-6173	676	12	and	and	CCONJ
ejpam-6173	676	13	x1	x1	PROPN
ejpam-6173	676	14	given	give	VERB
ejpam-6173	676	15	as	as	ADP
ejpam-6173	676	16	cases	case	NOUN
ejpam-6173	676	17	i	i	PRON
ejpam-6173	676	18	-	-	PUNCT
ejpam-6173	676	19	iv	iv	VERB
ejpam-6173	676	20	:	:	PUNCT
ejpam-6173	676	21	(	(	PUNCT
ejpam-6173	676	22	case	case	NOUN
ejpam-6173	676	23	i	i	X
ejpam-6173	676	24	)	)	PUNCT
ejpam-6173	676	25	:	:	PUNCT
ejpam-6173	677	1	x0	x0	PROPN
ejpam-6173	677	2	=	=	PUNCT
ejpam-6173	677	3	0.96	0.96	NUM
ejpam-6173	677	4	and	and	CCONJ
ejpam-6173	677	5	x1	x1	NUM
ejpam-6173	677	6	=	=	SYM
ejpam-6173	677	7	0.59	0.59	NUM
ejpam-6173	677	8	;	;	PUNCT
ejpam-6173	677	9	(	(	PUNCT
ejpam-6173	677	10	case	case	NOUN
ejpam-6173	677	11	ii	ii	X
ejpam-6173	677	12	)	)	PUNCT
ejpam-6173	677	13	:	:	PUNCT
ejpam-6173	678	1	x0	x0	PROPN
ejpam-6173	678	2	=	=	PUNCT
ejpam-6173	678	3	1.1	1.1	NUM
ejpam-6173	678	4	and	and	CCONJ
ejpam-6173	678	5	x1	x1	NOUN
ejpam-6173	678	6	=	=	NOUN
ejpam-6173	678	7	1.3	1.3	NUM
ejpam-6173	678	8	;	;	PUNCT
ejpam-6173	678	9	(	(	PUNCT
ejpam-6173	678	10	case	case	NOUN
ejpam-6173	678	11	iii	iii	X
ejpam-6173	678	12	)	)	PUNCT
ejpam-6173	678	13	:	:	PUNCT
ejpam-6173	679	1	x0	x0	PROPN
ejpam-6173	679	2	=	=	PUNCT
ejpam-6173	679	3	2.1	2.1	NUM
ejpam-6173	679	4	and	and	CCONJ
ejpam-6173	679	5	x1	x1	NOUN
ejpam-6173	679	6	=	=	SYM
ejpam-6173	679	7	1.7	1.7	NUM
ejpam-6173	679	8	;	;	PUNCT
ejpam-6173	679	9	(	(	PUNCT
ejpam-6173	679	10	case	case	NOUN
ejpam-6173	679	11	iv	iv	X
ejpam-6173	679	12	)	)	PUNCT
ejpam-6173	679	13	:	:	PUNCT
ejpam-6173	680	1	x0	x0	PROPN
ejpam-6173	680	2	=	=	PUNCT
ejpam-6173	681	1	0.69	0.69	NUM
ejpam-6173	681	2	and	and	CCONJ
ejpam-6173	681	3	x1	x1	NOUN
ejpam-6173	681	4	=	=	SYM
ejpam-6173	681	5	0.09	0.09	NUM
ejpam-6173	681	6	.	.	PUNCT
ejpam-6173	682	1	the	the	DET
ejpam-6173	682	2	report	report	NOUN
ejpam-6173	682	3	appears	appear	VERB
ejpam-6173	682	4	in	in	ADP
ejpam-6173	682	5	the	the	DET
ejpam-6173	682	6	form	form	NOUN
ejpam-6173	682	7	of	of	ADP
ejpam-6173	682	8	figures	figure	NOUN
ejpam-6173	682	9	14	14	NUM
ejpam-6173	682	10	showing	show	VERB
ejpam-6173	682	11	that	that	SCONJ
ejpam-6173	682	12	our	our	PRON
ejpam-6173	682	13	method	method	NOUN
ejpam-6173	682	14	converges	converge	VERB
ejpam-6173	682	15	faster	fast	ADV
ejpam-6173	682	16	in	in	ADP
ejpam-6173	682	17	terms	term	NOUN
ejpam-6173	682	18	of	of	ADP
ejpam-6173	682	19	number	number	NOUN
ejpam-6173	682	20	iteration	iteration	NOUN
ejpam-6173	682	21	than	than	ADP
ejpam-6173	682	22	the	the	DET
ejpam-6173	682	23	non	non	ADJ
ejpam-6173	682	24	-	-	ADJ
ejpam-6173	682	25	accelerated	accelerated	ADJ
ejpam-6173	682	26	version	version	NOUN
ejpam-6173	682	27	.	.	PUNCT
ejpam-6173	683	1	0	0	NUM
ejpam-6173	683	2	2	2	NUM
ejpam-6173	683	3	4	4	NUM
ejpam-6173	683	4	6	6	NUM
ejpam-6173	683	5	8	8	NUM
ejpam-6173	683	6	10	10	NUM
ejpam-6173	683	7	12	12	NUM
ejpam-6173	683	8	14	14	NUM
ejpam-6173	683	9	number	number	NOUN
ejpam-6173	683	10	of	of	ADP
ejpam-6173	683	11	iterations	iteration	NOUN
ejpam-6173	683	12	10	10	NUM
ejpam-6173	683	13	-	-	SYM
ejpam-6173	683	14	4	4	NUM
ejpam-6173	683	15	10	10	NUM
ejpam-6173	683	16	-	-	SYM
ejpam-6173	683	17	3	3	NUM
ejpam-6173	683	18	10	10	NUM
ejpam-6173	683	19	-	-	SYM
ejpam-6173	683	20	2	2	NUM
ejpam-6173	683	21	10	10	NUM
ejpam-6173	683	22	-	-	SYM
ejpam-6173	683	23	1	1	NUM
ejpam-6173	683	24	100	100	NUM
ejpam-6173	683	25	t	t	NOUN
ejpam-6173	683	26	o	o	NOUN
ejpam-6173	683	27	l	l	NOUN
ejpam-6173	683	28	case	case	NOUN
ejpam-6173	683	29	i	i	PRON
ejpam-6173	683	30	our	our	PRON
ejpam-6173	683	31	algorithm	algorithm	PROPN
ejpam-6173	683	32	esra	esra	PROPN
ejpam-6173	683	33	figure	figure	NOUN
ejpam-6173	683	34	1	1	NUM
ejpam-6173	683	35	:	:	PUNCT
ejpam-6173	683	36	example	example	NOUN
ejpam-6173	683	37	1	1	NUM
ejpam-6173	683	38	.	.	PUNCT
ejpam-6173	683	39	case	case	NOUN
ejpam-6173	683	40	i.	i.	PROPN
ejpam-6173	683	41	v.	v.	ADP
ejpam-6173	683	42	darvish	darvish	PROPN
ejpam-6173	683	43	et	et	PROPN
ejpam-6173	683	44	al	al	PROPN
ejpam-6173	683	45	.	.	PUNCT
ejpam-6173	683	46	/	/	SYM
ejpam-6173	683	47	eur	eur	PROPN
ejpam-6173	683	48	.	.	PUNCT
ejpam-6173	684	1	j.	j.	PROPN
ejpam-6173	684	2	pure	pure	PROPN
ejpam-6173	684	3	appl	appl	PROPN
ejpam-6173	684	4	.	.	PROPN
ejpam-6173	684	5	math	math	PROPN
ejpam-6173	684	6	,	,	PUNCT
ejpam-6173	684	7	18	18	NUM
ejpam-6173	684	8	(	(	PUNCT
ejpam-6173	684	9	3	3	NUM
ejpam-6173	684	10	)	)	PUNCT
ejpam-6173	684	11	(	(	PUNCT
ejpam-6173	684	12	2025	2025	NUM
ejpam-6173	684	13	)	)	PUNCT
ejpam-6173	684	14	,	,	PUNCT
ejpam-6173	684	15	6173	6173	NUM
ejpam-6173	684	16	25	25	NUM
ejpam-6173	684	17	of	of	ADP
ejpam-6173	684	18	32	32	NUM
ejpam-6173	684	19	0	0	NUM
ejpam-6173	684	20	2	2	NUM
ejpam-6173	684	21	4	4	NUM
ejpam-6173	684	22	6	6	NUM
ejpam-6173	684	23	8	8	NUM
ejpam-6173	684	24	10	10	NUM
ejpam-6173	684	25	12	12	NUM
ejpam-6173	684	26	14	14	NUM
ejpam-6173	684	27	number	number	NOUN
ejpam-6173	684	28	of	of	ADP
ejpam-6173	684	29	iterations	iteration	NOUN
ejpam-6173	684	30	10	10	NUM
ejpam-6173	684	31	-	-	SYM
ejpam-6173	684	32	4	4	NUM
ejpam-6173	684	33	10	10	NUM
ejpam-6173	684	34	-	-	SYM
ejpam-6173	684	35	3	3	NUM
ejpam-6173	684	36	10	10	NUM
ejpam-6173	684	37	-	-	SYM
ejpam-6173	684	38	2	2	NUM
ejpam-6173	684	39	10	10	NUM
ejpam-6173	684	40	-	-	SYM
ejpam-6173	684	41	1	1	NUM
ejpam-6173	684	42	100	100	NUM
ejpam-6173	684	43	101	101	NUM
ejpam-6173	684	44	t	t	NOUN
ejpam-6173	684	45	o	o	NOUN
ejpam-6173	684	46	l	l	NOUN
ejpam-6173	684	47	case	case	NOUN
ejpam-6173	684	48	ii	ii	VERB
ejpam-6173	684	49	our	our	PRON
ejpam-6173	684	50	algorithm	algorithm	PROPN
ejpam-6173	684	51	esra	esra	PROPN
ejpam-6173	684	52	figure	figure	NOUN
ejpam-6173	684	53	2	2	NUM
ejpam-6173	684	54	:	:	PUNCT
ejpam-6173	684	55	example	example	NOUN
ejpam-6173	684	56	1	1	NUM
ejpam-6173	684	57	.	.	PUNCT
ejpam-6173	684	58	case	case	NOUN
ejpam-6173	684	59	ii	ii	PROPN
ejpam-6173	684	60	.	.	PROPN
ejpam-6173	684	61	0	0	NUM
ejpam-6173	684	62	2	2	NUM
ejpam-6173	684	63	4	4	NUM
ejpam-6173	684	64	6	6	NUM
ejpam-6173	684	65	8	8	NUM
ejpam-6173	684	66	10	10	NUM
ejpam-6173	684	67	12	12	NUM
ejpam-6173	684	68	14	14	NUM
ejpam-6173	684	69	number	number	NOUN
ejpam-6173	684	70	of	of	ADP
ejpam-6173	684	71	iterations	iteration	NOUN
ejpam-6173	684	72	10	10	NUM
ejpam-6173	684	73	-	-	SYM
ejpam-6173	684	74	4	4	NUM
ejpam-6173	684	75	10	10	NUM
ejpam-6173	684	76	-	-	SYM
ejpam-6173	684	77	3	3	NUM
ejpam-6173	684	78	10	10	NUM
ejpam-6173	684	79	-	-	SYM
ejpam-6173	684	80	2	2	NUM
ejpam-6173	684	81	10	10	NUM
ejpam-6173	684	82	-	-	SYM
ejpam-6173	684	83	1	1	NUM
ejpam-6173	684	84	100	100	NUM
ejpam-6173	684	85	101	101	NUM
ejpam-6173	684	86	t	t	NOUN
ejpam-6173	684	87	o	o	NOUN
ejpam-6173	684	88	l	l	NOUN
ejpam-6173	684	89	case	case	NOUN
ejpam-6173	684	90	iii	iii	VERB
ejpam-6173	684	91	our	our	PRON
ejpam-6173	684	92	algorithm	algorithm	NOUN
ejpam-6173	684	93	esra	esra	PROPN
ejpam-6173	684	94	figure	figure	NOUN
ejpam-6173	684	95	3	3	NUM
ejpam-6173	684	96	:	:	PUNCT
ejpam-6173	684	97	example	example	NOUN
ejpam-6173	684	98	1	1	NUM
ejpam-6173	684	99	.	.	PUNCT
ejpam-6173	684	100	case	case	NOUN
ejpam-6173	684	101	iii	iii	PROPN
ejpam-6173	684	102	.	.	PROPN
ejpam-6173	684	103	example	example	NOUN
ejpam-6173	685	1	2	2	NUM
ejpam-6173	685	2	.	.	PUNCT
ejpam-6173	685	3	let	let	VERB
ejpam-6173	685	4	e	e	NOUN
ejpam-6173	685	5	=	=	PUNCT
ejpam-6173	685	6	(	(	PUNCT
ejpam-6173	685	7	ℓ2(r	ℓ2(r	NOUN
ejpam-6173	685	8	)	)	PUNCT
ejpam-6173	685	9	,	,	PUNCT
ejpam-6173	685	10	∥	∥	X
ejpam-6173	685	11	·	·	PUNCT
ejpam-6173	685	12	∥	∥	NUM
ejpam-6173	685	13	)	)	PUNCT
ejpam-6173	685	14	,	,	PUNCT
ejpam-6173	685	15	where	where	SCONJ
ejpam-6173	685	16	ℓ2(r	ℓ2(r	NOUN
ejpam-6173	685	17	)	)	PUNCT
ejpam-6173	685	18	:	:	PUNCT
ejpam-6173	685	19	=	=	X
ejpam-6173	685	20	{	{	PUNCT
ejpam-6173	685	21	x	x	X
ejpam-6173	685	22	:	:	PUNCT
ejpam-6173	685	23	x	x	SYM
ejpam-6173	685	24	=	=	SYM
ejpam-6173	685	25	{	{	PUNCT
ejpam-6173	685	26	xi}+∞	xi}+∞	PROPN
ejpam-6173	685	27	i=1	i=1	PROPN
ejpam-6173	685	28	,	,	PUNCT
ejpam-6173	686	1	+	+	PUNCT
ejpam-6173	686	2	∞∑	∞∑	NUM
ejpam-6173	686	3	i=1	i=1	ADP
ejpam-6173	686	4	|xi|2	|xi|2	PUNCT
ejpam-6173	686	5	<	<	X
ejpam-6173	686	6	+	+	NOUN
ejpam-6173	686	7	∞	∞	NUM
ejpam-6173	686	8	}	}	PUNCT
ejpam-6173	686	9	,	,	PUNCT
ejpam-6173	686	10	with	with	SCONJ
ejpam-6173	686	11	an	an	DET
ejpam-6173	686	12	inner	inner	ADJ
ejpam-6173	686	13	product	product	NOUN
ejpam-6173	686	14	⟨	⟨	VERB
ejpam-6173	686	15	·	·	PUNCT
ejpam-6173	686	16	,	,	PUNCT
ejpam-6173	686	17	·	·	PUNCT
ejpam-6173	686	18	⟩	⟩	NOUN
ejpam-6173	686	19	:	:	PUNCT
ejpam-6173	686	20	ℓ2	ℓ2	NOUN
ejpam-6173	686	21	×	×	NOUN
ejpam-6173	686	22	ℓ2	ℓ2	NOUN
ejpam-6173	686	23	→	→	SYM
ejpam-6173	686	24	r	r	NOUN
ejpam-6173	686	25	given	give	VERB
ejpam-6173	686	26	by	by	ADP
ejpam-6173	686	27	⟨x	⟨x	NUM
ejpam-6173	686	28	,	,	PUNCT
ejpam-6173	686	29	y⟩	y⟩	NOUN
ejpam-6173	686	30	=	=	PUNCT
ejpam-6173	687	1	+	+	ADP
ejpam-6173	687	2	∞∑	∞∑	NOUN
ejpam-6173	687	3	i=1	i=1	ADP
ejpam-6173	687	4	xiyi	xiyi	ADJ
ejpam-6173	688	1	where	where	SCONJ
ejpam-6173	688	2	x	x	X
ejpam-6173	688	3	=	=	PRON
ejpam-6173	688	4	{	{	PUNCT
ejpam-6173	688	5	xi}+∞	xi}+∞	PROPN
ejpam-6173	688	6	i=1	i=1	PROPN
ejpam-6173	688	7	,	,	PUNCT
ejpam-6173	688	8	y	y	PROPN
ejpam-6173	688	9	=	=	PUNCT
ejpam-6173	688	10	{	{	PUNCT
ejpam-6173	688	11	yi}+∞	yi}+∞	NUM
ejpam-6173	688	12	i=1	i=1	PROPN
ejpam-6173	688	13	and	and	CCONJ
ejpam-6173	688	14	the	the	DET
ejpam-6173	688	15	norm	norm	NOUN
ejpam-6173	688	16	∥	∥	X
ejpam-6173	688	17	·	·	PUNCT
ejpam-6173	688	18	∥	∥	NUM
ejpam-6173	688	19	:	:	PUNCT
ejpam-6173	688	20	ℓ2	ℓ2	NOUN
ejpam-6173	688	21	→	→	SYM
ejpam-6173	688	22	r	r	NOUN
ejpam-6173	688	23	is	be	AUX
ejpam-6173	688	24	given	give	VERB
ejpam-6173	688	25	by	by	ADP
ejpam-6173	688	26	∥x∥2	∥x∥2	NOUN
ejpam-6173	688	27	=	=	SYM
ejpam-6173	688	28	√	√	PROPN
ejpam-6173	688	29	(	(	PUNCT
ejpam-6173	688	30	+	+	PROPN
ejpam-6173	688	31	∞∑	∞∑	NUM
ejpam-6173	688	32	i=1	i=1	PRON
ejpam-6173	688	33	|xi|2	|xi|2	PUNCT
ejpam-6173	688	34	)	)	PUNCT
ejpam-6173	688	35	.	.	PUNCT
ejpam-6173	689	1	let	let	VERB
ejpam-6173	689	2	f(x	f(x	PROPN
ejpam-6173	689	3	)	)	PUNCT
ejpam-6173	690	1	=	=	SYM
ejpam-6173	691	1	x2	x2	NOUN
ejpam-6173	691	2	2	2	NUM
ejpam-6173	691	3	,	,	PUNCT
ejpam-6173	691	4	then	then	ADV
ejpam-6173	691	5	f	f	PROPN
ejpam-6173	691	6	satisfies	satisfy	VERB
ejpam-6173	691	7	assumption	assumption	NOUN
ejpam-6173	691	8	3.1	3.1	NUM
ejpam-6173	691	9	let	let	VERB
ejpam-6173	691	10	c	c	NOUN
ejpam-6173	691	11	:	:	PUNCT
ejpam-6173	691	12	=	=	SYM
ejpam-6173	691	13	{	{	PUNCT
ejpam-6173	691	14	x	x	PUNCT
ejpam-6173	691	15	∈	∈	PROPN
ejpam-6173	691	16	ℓ2(r	ℓ2(r	NUM
ejpam-6173	691	17	)	)	PUNCT
ejpam-6173	691	18	:	:	PUNCT
ejpam-6173	691	19	∥x∥2	∥x∥2	NOUN
ejpam-6173	691	20	≤	≤	NOUN
ejpam-6173	691	21	1	1	NUM
ejpam-6173	691	22	}	}	PUNCT
ejpam-6173	691	23	and	and	CCONJ
ejpam-6173	691	24	θi	θi	X
ejpam-6173	691	25	:	:	PUNCT
ejpam-6173	691	26	e	e	X
ejpam-6173	691	27	×	×	NOUN
ejpam-6173	691	28	e	e	X
ejpam-6173	691	29	→	→	PUNCT
ejpam-6173	691	30	r	r	NOUN
ejpam-6173	691	31	be	be	AUX
ejpam-6173	691	32	defined	define	VERB
ejpam-6173	691	33	by	by	ADP
ejpam-6173	691	34	θi(x	θi(x	ADJ
ejpam-6173	691	35	,	,	PUNCT
ejpam-6173	691	36	y	y	NOUN
ejpam-6173	691	37	)	)	PUNCT
ejpam-6173	691	38	=	=	PUNCT
ejpam-6173	691	39	−3ix2	−3ix2	NOUN
ejpam-6173	691	40	+	+	X
ejpam-6173	691	41	2ixy	2ixy	NUM
ejpam-6173	691	42	+	+	CCONJ
ejpam-6173	691	43	iy2	iy2	NOUN
ejpam-6173	691	44	for	for	ADP
ejpam-6173	691	45	all	all	DET
ejpam-6173	691	46	i	i	PRON
ejpam-6173	691	47	and	and	CCONJ
ejpam-6173	691	48	x	x	X
ejpam-6173	691	49	,	,	PUNCT
ejpam-6173	691	50	y	y	PROPN
ejpam-6173	691	51	∈	∈	PROPN
ejpam-6173	691	52	ℓ2	ℓ2	PROPN
ejpam-6173	691	53	.	.	PUNCT
ejpam-6173	692	1	let	let	VERB
ejpam-6173	692	2	ψi	ψi	NOUN
ejpam-6173	692	3	:	:	PUNCT
ejpam-6173	692	4	ℓ2	ℓ2	NOUN
ejpam-6173	692	5	→	→	SYM
ejpam-6173	692	6	r	r	NOUN
ejpam-6173	692	7	and	and	CCONJ
ejpam-6173	692	8	φi	φi	ADV
ejpam-6173	692	9	:	:	PUNCT
ejpam-6173	692	10	ℓ2	ℓ2	NOUN
ejpam-6173	692	11	→	→	SYM
ejpam-6173	692	12	r	r	NOUN
ejpam-6173	692	13	for	for	ADP
ejpam-6173	692	14	all	all	DET
ejpam-6173	692	15	i	i	PRON
ejpam-6173	692	16	and	and	CCONJ
ejpam-6173	692	17	x	x	PROPN
ejpam-6173	692	18	∈	∈	PROPN
ejpam-6173	692	19	ℓ2	ℓ2	NOUN
ejpam-6173	692	20	be	be	AUX
ejpam-6173	692	21	given	give	VERB
ejpam-6173	692	22	by	by	ADP
ejpam-6173	692	23	ψi	ψi	ADJ
ejpam-6173	692	24	=	=	SYM
ejpam-6173	692	25	ix2	ix2	PROPN
ejpam-6173	692	26	and	and	CCONJ
ejpam-6173	692	27	φi	φi	PROPN
ejpam-6173	692	28	=	=	PUNCT
ejpam-6173	692	29	ix	ix	ADJ
ejpam-6173	692	30	,	,	PUNCT
ejpam-6173	692	31	respectively	respectively	ADV
ejpam-6173	692	32	.	.	PUNCT
ejpam-6173	693	1	we	we	PRON
ejpam-6173	693	2	have	have	VERB
ejpam-6173	693	3	that	that	DET
ejpam-6173	693	4	resfbθi	resfbθi	NOUN
ejpam-6173	693	5	(	(	PUNCT
ejpam-6173	693	6	x	x	NOUN
ejpam-6173	693	7	)	)	PUNCT
ejpam-6173	693	8	=	=	NOUN
ejpam-6173	693	9	x	x	SYM
ejpam-6173	693	10	1	1	NUM
ejpam-6173	693	11	+	+	NOUN
ejpam-6173	693	12	7j	7j	NOUN
ejpam-6173	693	13	.	.	PUNCT
ejpam-6173	694	1	let	let	VERB
ejpam-6173	694	2	t	t	NOUN
ejpam-6173	694	3	=	=	PUNCT
ejpam-6173	694	4	x+2	x+2	SYM
ejpam-6173	694	5	2	2	NUM
ejpam-6173	694	6	.	.	PUNCT
ejpam-6173	695	1	clearly	clearly	ADV
ejpam-6173	695	2	,	,	PUNCT
ejpam-6173	695	3	we	we	PRON
ejpam-6173	695	4	observe	observe	VERB
ejpam-6173	695	5	that	that	SCONJ
ejpam-6173	695	6	the	the	DET
ejpam-6173	695	7	bifunction	bifunction	NOUN
ejpam-6173	695	8	θ	θ	PROPN
ejpam-6173	695	9	satisfies	satisfy	VERB
ejpam-6173	695	10	v.	v.	ADP
ejpam-6173	695	11	darvish	darvish	X
ejpam-6173	695	12	et	et	PROPN
ejpam-6173	695	13	al	al	PROPN
ejpam-6173	695	14	.	.	PUNCT
ejpam-6173	695	15	/	/	SYM
ejpam-6173	695	16	eur	eur	PROPN
ejpam-6173	695	17	.	.	PUNCT
ejpam-6173	696	1	j.	j.	PROPN
ejpam-6173	696	2	pure	pure	PROPN
ejpam-6173	696	3	appl	appl	PROPN
ejpam-6173	696	4	.	.	PROPN
ejpam-6173	696	5	math	math	PROPN
ejpam-6173	696	6	,	,	PUNCT
ejpam-6173	696	7	18	18	NUM
ejpam-6173	696	8	(	(	PUNCT
ejpam-6173	696	9	3	3	NUM
ejpam-6173	696	10	)	)	PUNCT
ejpam-6173	696	11	(	(	PUNCT
ejpam-6173	696	12	2025	2025	NUM
ejpam-6173	696	13	)	)	PUNCT
ejpam-6173	696	14	,	,	PUNCT
ejpam-6173	696	15	6173	6173	NUM
ejpam-6173	696	16	26	26	NUM
ejpam-6173	696	17	of	of	ADP
ejpam-6173	696	18	32	32	NUM
ejpam-6173	696	19	0	0	NUM
ejpam-6173	696	20	2	2	NUM
ejpam-6173	696	21	4	4	NUM
ejpam-6173	696	22	6	6	NUM
ejpam-6173	696	23	8	8	NUM
ejpam-6173	696	24	10	10	NUM
ejpam-6173	696	25	12	12	NUM
ejpam-6173	696	26	14	14	NUM
ejpam-6173	696	27	number	number	NOUN
ejpam-6173	696	28	of	of	ADP
ejpam-6173	696	29	iterations	iteration	NOUN
ejpam-6173	696	30	10	10	NUM
ejpam-6173	696	31	-	-	SYM
ejpam-6173	696	32	4	4	NUM
ejpam-6173	696	33	10	10	NUM
ejpam-6173	696	34	-	-	SYM
ejpam-6173	696	35	3	3	NUM
ejpam-6173	696	36	10	10	NUM
ejpam-6173	696	37	-	-	SYM
ejpam-6173	696	38	2	2	NUM
ejpam-6173	696	39	10	10	NUM
ejpam-6173	696	40	-	-	SYM
ejpam-6173	696	41	1	1	NUM
ejpam-6173	696	42	t	t	NOUN
ejpam-6173	696	43	o	o	NOUN
ejpam-6173	696	44	l	l	NOUN
ejpam-6173	696	45	case	case	NOUN
ejpam-6173	696	46	iv	iv	VERB
ejpam-6173	696	47	our	our	PRON
ejpam-6173	696	48	algorithm	algorithm	PROPN
ejpam-6173	696	49	esra	esra	PROPN
ejpam-6173	696	50	figure	figure	NOUN
ejpam-6173	696	51	4	4	NUM
ejpam-6173	696	52	:	:	PUNCT
ejpam-6173	696	53	example	example	NOUN
ejpam-6173	696	54	1	1	NUM
ejpam-6173	696	55	.	.	X
ejpam-6173	696	56	case	case	NOUN
ejpam-6173	696	57	iv	iv	NUM
ejpam-6173	696	58	.	.	PUNCT
ejpam-6173	696	59	(	(	PUNCT
ejpam-6173	696	60	a1)-(a4	a1)-(a4	PROPN
ejpam-6173	696	61	)	)	PUNCT
ejpam-6173	696	62	,	,	PUNCT
ejpam-6173	696	63	ψ	ψ	NOUN
ejpam-6173	696	64	is	be	AUX
ejpam-6173	696	65	monotone	monotone	ADJ
ejpam-6173	696	66	and	and	CCONJ
ejpam-6173	696	67	t	t	PROPN
ejpam-6173	696	68	is	be	AUX
ejpam-6173	696	69	bregman	bregman	NOUN
ejpam-6173	696	70	strongly	strongly	ADV
ejpam-6173	696	71	nonexpansive	nonexpansive	ADJ
ejpam-6173	696	72	mapping	mapping	NOUN
ejpam-6173	696	73	.	.	PUNCT
ejpam-6173	697	1	for	for	ADP
ejpam-6173	697	2	example	example	NOUN
ejpam-6173	697	3	2	2	NUM
ejpam-6173	697	4	,	,	PUNCT
ejpam-6173	697	5	we	we	PRON
ejpam-6173	697	6	choose	choose	VERB
ejpam-6173	697	7	αn	αn	NOUN
ejpam-6173	697	8	=	=	SYM
ejpam-6173	697	9	1	1	NUM
ejpam-6173	697	10	2n+3	2n+3	NOUN
ejpam-6173	697	11	,	,	PUNCT
ejpam-6173	697	12	βn	βn	NOUN
ejpam-6173	697	13	=	=	SYM
ejpam-6173	697	14	1	1	X
ejpam-6173	697	15	n+1	n+1	PRON
ejpam-6173	697	16	,	,	PUNCT
ejpam-6173	697	17	qn	qn	NOUN
ejpam-6173	697	18	=	=	NOUN
ejpam-6173	697	19	1	1	NUM
ejpam-6173	697	20	5	5	NUM
ejpam-6173	697	21	,	,	PUNCT
ejpam-6173	697	22	ϵ	ϵ	X
ejpam-6173	697	23	=	=	SYM
ejpam-6173	697	24	1	1	NUM
ejpam-6173	697	25	n3.1	n3.1	ADJ
ejpam-6173	697	26	,	,	PUNCT
ejpam-6173	697	27	θ	θ	X
ejpam-6173	697	28	=	=	SYM
ejpam-6173	697	29	0.1	0.1	NUM
ejpam-6173	697	30	and	and	CCONJ
ejpam-6173	697	31	set	set	VERB
ejpam-6173	697	32	n	n	NOUN
ejpam-6173	697	33	=	=	SYM
ejpam-6173	697	34	100	100	NUM
ejpam-6173	697	35	.	.	PUNCT
ejpam-6173	698	1	as	as	ADP
ejpam-6173	698	2	a	a	DET
ejpam-6173	698	3	stopping	stopping	NOUN
ejpam-6173	698	4	criterion	criterion	NOUN
ejpam-6173	698	5	,	,	PUNCT
ejpam-6173	698	6	we	we	PRON
ejpam-6173	698	7	use	use	VERB
ejpam-6173	698	8	∥xn+1−xn∥	∥xn+1−xn∥	PUNCT
ejpam-6173	698	9	≤	≤	NUM
ejpam-6173	698	10	ϵ	ϵ	ADP
ejpam-6173	698	11	where	where	SCONJ
ejpam-6173	698	12	ϵ	ϵ	PROPN
ejpam-6173	698	13	=	=	SYM
ejpam-6173	698	14	10−4	10−4	PROPN
ejpam-6173	698	15	.	.	PUNCT
ejpam-6173	699	1	the	the	DET
ejpam-6173	699	2	experiment	experiment	NOUN
ejpam-6173	699	3	was	be	AUX
ejpam-6173	699	4	conducted	conduct	VERB
ejpam-6173	699	5	for	for	ADP
ejpam-6173	699	6	the	the	DET
ejpam-6173	699	7	following	following	ADJ
ejpam-6173	699	8	initial	initial	ADJ
ejpam-6173	699	9	values	value	NOUN
ejpam-6173	699	10	of	of	ADP
ejpam-6173	699	11	x0	x0	PROPN
ejpam-6173	699	12	and	and	CCONJ
ejpam-6173	699	13	x1	x1	PROPN
ejpam-6173	699	14	given	give	VERB
ejpam-6173	699	15	as	as	ADP
ejpam-6173	699	16	cases	case	NOUN
ejpam-6173	699	17	a	a	DET
ejpam-6173	699	18	-	-	PUNCT
ejpam-6173	699	19	d	d	NOUN
ejpam-6173	699	20	:	:	PUNCT
ejpam-6173	699	21	(	(	PUNCT
ejpam-6173	699	22	case	case	NOUN
ejpam-6173	699	23	a	a	X
ejpam-6173	699	24	)	)	PUNCT
ejpam-6173	699	25	:	:	PUNCT
ejpam-6173	700	1	x0	x0	PROPN
ejpam-6173	700	2	=	=	PUNCT
ejpam-6173	701	1	[	[	X
ejpam-6173	701	2	0.25	0.25	NUM
ejpam-6173	701	3	,	,	PUNCT
ejpam-6173	701	4	0.25	0.25	NUM
ejpam-6173	701	5	,	,	PUNCT
ejpam-6173	701	6	0.33	0.33	NUM
ejpam-6173	701	7	,	,	PUNCT
ejpam-6173	701	8	·	·	PUNCT
ejpam-6173	701	9	·	·	PUNCT
ejpam-6173	701	10	·	·	PUNCT
ejpam-6173	701	11	,	,	PUNCT
ejpam-6173	701	12	0	0	NUM
ejpam-6173	701	13	,	,	PUNCT
ejpam-6173	701	14	0	0	NUM
ejpam-6173	701	15	,	,	PUNCT
ejpam-6173	701	16	·	·	PUNCT
ejpam-6173	701	17	·	·	PUNCT
ejpam-6173	701	18	·	·	PUNCT
ejpam-6173	701	19	]	]	PUNCT
ejpam-6173	702	1	and	and	CCONJ
ejpam-6173	702	2	x1	x1	NOUN
ejpam-6173	702	3	=	=	PUNCT
ejpam-6173	703	1	[	[	X
ejpam-6173	703	2	0.2	0.2	NUM
ejpam-6173	703	3	,	,	PUNCT
ejpam-6173	703	4	0.2	0.2	NUM
ejpam-6173	703	5	,	,	PUNCT
ejpam-6173	703	6	0.3	0.3	NUM
ejpam-6173	703	7	,	,	PUNCT
ejpam-6173	703	8	·	·	PUNCT
ejpam-6173	703	9	·	·	PUNCT
ejpam-6173	703	10	·	·	PUNCT
ejpam-6173	703	11	,	,	PUNCT
ejpam-6173	703	12	0	0	NUM
ejpam-6173	703	13	,	,	PUNCT
ejpam-6173	703	14	0	0	NUM
ejpam-6173	703	15	,	,	PUNCT
ejpam-6173	703	16	·	·	PUNCT
ejpam-6173	703	17	·	·	PUNCT
ejpam-6173	703	18	·	·	PUNCT
ejpam-6173	703	19	]	]	X
ejpam-6173	703	20	;	;	PUNCT
ejpam-6173	703	21	(	(	PUNCT
ejpam-6173	703	22	case	case	NOUN
ejpam-6173	703	23	b	b	X
ejpam-6173	703	24	)	)	PUNCT
ejpam-6173	703	25	:	:	PUNCT
ejpam-6173	703	26	x0	x0	PROPN
ejpam-6173	703	27	=	=	PUNCT
ejpam-6173	704	1	[	[	X
ejpam-6173	704	2	1	1	NUM
ejpam-6173	704	3	,	,	PUNCT
ejpam-6173	704	4	0.5	0.5	NUM
ejpam-6173	704	5	,	,	PUNCT
ejpam-6173	704	6	0.25	0.25	NUM
ejpam-6173	704	7	,	,	PUNCT
ejpam-6173	704	8	·	·	PUNCT
ejpam-6173	704	9	·	·	PUNCT
ejpam-6173	704	10	·	·	PUNCT
ejpam-6173	704	11	,	,	PUNCT
ejpam-6173	704	12	0	0	NUM
ejpam-6173	704	13	,	,	PUNCT
ejpam-6173	704	14	0	0	NUM
ejpam-6173	704	15	,	,	PUNCT
ejpam-6173	704	16	·	·	PUNCT
ejpam-6173	704	17	·	·	PUNCT
ejpam-6173	704	18	·	·	PUNCT
ejpam-6173	704	19	]	]	PUNCT
ejpam-6173	705	1	and	and	CCONJ
ejpam-6173	705	2	x1	x1	NOUN
ejpam-6173	705	3	=	=	PUNCT
ejpam-6173	706	1	[	[	X
ejpam-6173	706	2	0.2	0.2	NUM
ejpam-6173	706	3	,	,	PUNCT
ejpam-6173	706	4	0.25	0.25	NUM
ejpam-6173	706	5	,	,	PUNCT
ejpam-6173	706	6	0.125	0.125	NUM
ejpam-6173	706	7	,	,	PUNCT
ejpam-6173	706	8	·	·	PUNCT
ejpam-6173	706	9	·	·	PUNCT
ejpam-6173	706	10	·	·	PUNCT
ejpam-6173	706	11	,	,	PUNCT
ejpam-6173	706	12	0	0	NUM
ejpam-6173	706	13	,	,	PUNCT
ejpam-6173	706	14	0	0	NUM
ejpam-6173	706	15	,	,	PUNCT
ejpam-6173	706	16	·	·	PUNCT
ejpam-6173	706	17	·	·	PUNCT
ejpam-6173	706	18	·	·	PUNCT
ejpam-6173	706	19	]	]	X
ejpam-6173	706	20	;	;	PUNCT
ejpam-6173	706	21	(	(	PUNCT
ejpam-6173	706	22	case	case	NOUN
ejpam-6173	706	23	c	c	X
ejpam-6173	706	24	)	)	PUNCT
ejpam-6173	706	25	:	:	PUNCT
ejpam-6173	706	26	x0	x0	PROPN
ejpam-6173	707	1	=	=	PUNCT
ejpam-6173	708	1	[	[	X
ejpam-6173	708	2	0.91	0.91	NUM
ejpam-6173	708	3	,	,	PUNCT
ejpam-6173	708	4	0.55	0.55	NUM
ejpam-6173	708	5	,	,	PUNCT
ejpam-6173	708	6	0.53	0.53	NUM
ejpam-6173	708	7	,	,	PUNCT
ejpam-6173	708	8	·	·	PUNCT
ejpam-6173	708	9	·	·	PUNCT
ejpam-6173	708	10	·	·	PUNCT
ejpam-6173	708	11	,	,	PUNCT
ejpam-6173	708	12	0	0	NUM
ejpam-6173	708	13	,	,	PUNCT
ejpam-6173	708	14	0	0	NUM
ejpam-6173	708	15	,	,	PUNCT
ejpam-6173	708	16	·	·	PUNCT
ejpam-6173	708	17	·	·	PUNCT
ejpam-6173	708	18	·	·	PUNCT
ejpam-6173	708	19	]	]	PUNCT
ejpam-6173	708	20	and	and	CCONJ
ejpam-6173	708	21	x1	x1	NOUN
ejpam-6173	708	22	=	=	PUNCT
ejpam-6173	709	1	[	[	X
ejpam-6173	709	2	0.85	0.85	NUM
ejpam-6173	709	3	,	,	PUNCT
ejpam-6173	709	4	0.65	0.65	NUM
ejpam-6173	709	5	,	,	PUNCT
ejpam-6173	709	6	0.65	0.65	NUM
ejpam-6173	709	7	,	,	PUNCT
ejpam-6173	709	8	·	·	PUNCT
ejpam-6173	709	9	·	·	PUNCT
ejpam-6173	709	10	·	·	PUNCT
ejpam-6173	709	11	,	,	PUNCT
ejpam-6173	709	12	0	0	NUM
ejpam-6173	709	13	,	,	PUNCT
ejpam-6173	709	14	0	0	NUM
ejpam-6173	709	15	,	,	PUNCT
ejpam-6173	709	16	·	·	PUNCT
ejpam-6173	709	17	·	·	PUNCT
ejpam-6173	709	18	·	·	PUNCT
ejpam-6173	709	19	]	]	X
ejpam-6173	709	20	;	;	PUNCT
ejpam-6173	709	21	(	(	PUNCT
ejpam-6173	709	22	case	case	NOUN
ejpam-6173	709	23	d	d	X
ejpam-6173	709	24	)	)	PUNCT
ejpam-6173	709	25	:	:	PUNCT
ejpam-6173	710	1	x0	x0	PROPN
ejpam-6173	710	2	=	=	PUNCT
ejpam-6173	711	1	[	[	X
ejpam-6173	711	2	1.2	1.2	NUM
ejpam-6173	711	3	,	,	PUNCT
ejpam-6173	711	4	0	0	NUM
ejpam-6173	711	5	,	,	PUNCT
ejpam-6173	711	6	0.38	0.38	NUM
ejpam-6173	711	7	,	,	PUNCT
ejpam-6173	711	8	·	·	PUNCT
ejpam-6173	711	9	·	·	PUNCT
ejpam-6173	711	10	·	·	PUNCT
ejpam-6173	711	11	,	,	PUNCT
ejpam-6173	711	12	0	0	NUM
ejpam-6173	711	13	,	,	PUNCT
ejpam-6173	711	14	0	0	NUM
ejpam-6173	711	15	,	,	PUNCT
ejpam-6173	711	16	·	·	PUNCT
ejpam-6173	711	17	·	·	PUNCT
ejpam-6173	711	18	·	·	PUNCT
ejpam-6173	711	19	]	]	PUNCT
ejpam-6173	711	20	and	and	CCONJ
ejpam-6173	711	21	x1	x1	NUM
ejpam-6173	711	22	=	=	PUNCT
ejpam-6173	712	1	[	[	X
ejpam-6173	712	2	0.8	0.8	NUM
ejpam-6173	712	3	,	,	PUNCT
ejpam-6173	712	4	0	0	NUM
ejpam-6173	712	5	,	,	PUNCT
ejpam-6173	712	6	1.2	1.2	NUM
ejpam-6173	712	7	,	,	PUNCT
ejpam-6173	712	8	·	·	PUNCT
ejpam-6173	712	9	·	·	PUNCT
ejpam-6173	712	10	·	·	PUNCT
ejpam-6173	712	11	,	,	PUNCT
ejpam-6173	712	12	0	0	NUM
ejpam-6173	712	13	,	,	PUNCT
ejpam-6173	712	14	0	0	NUM
ejpam-6173	712	15	,	,	PUNCT
ejpam-6173	712	16	·	·	PUNCT
ejpam-6173	712	17	·	·	PUNCT
ejpam-6173	712	18	·	·	PUNCT
ejpam-6173	713	1	]	]	PUNCT
ejpam-6173	713	2	.	.	PUNCT
ejpam-6173	714	1	the	the	DET
ejpam-6173	714	2	report	report	NOUN
ejpam-6173	714	3	of	of	ADP
ejpam-6173	714	4	this	this	DET
ejpam-6173	714	5	experiment	experiment	NOUN
ejpam-6173	714	6	is	be	AUX
ejpam-6173	714	7	displayed	display	VERB
ejpam-6173	714	8	figures	figure	NOUN
ejpam-6173	714	9	58	58	NUM
ejpam-6173	714	10	showing	show	VERB
ejpam-6173	714	11	that	that	SCONJ
ejpam-6173	714	12	our	our	PRON
ejpam-6173	714	13	method	method	NOUN
ejpam-6173	714	14	converges	converge	VERB
ejpam-6173	714	15	faster	fast	ADV
ejpam-6173	714	16	in	in	ADP
ejpam-6173	714	17	terms	term	NOUN
ejpam-6173	714	18	of	of	ADP
ejpam-6173	714	19	number	number	NOUN
ejpam-6173	714	20	iteration	iteration	NOUN
ejpam-6173	714	21	than	than	ADP
ejpam-6173	714	22	the	the	DET
ejpam-6173	714	23	non	non	ADJ
ejpam-6173	714	24	-	-	ADJ
ejpam-6173	714	25	accelerated	accelerated	ADJ
ejpam-6173	714	26	version	version	NOUN
ejpam-6173	714	27	presented	present	VERB
ejpam-6173	714	28	in	in	ADP
ejpam-6173	714	29	[	[	X
ejpam-6173	714	30	23	23	NUM
ejpam-6173	714	31	]	]	PUNCT
ejpam-6173	714	32	.	.	PUNCT
ejpam-6173	715	1	6	6	X
ejpam-6173	715	2	.	.	X
ejpam-6173	715	3	conclusion	conclusion	NOUN
ejpam-6173	715	4	in	in	ADP
ejpam-6173	715	5	this	this	DET
ejpam-6173	715	6	paper	paper	NOUN
ejpam-6173	715	7	,	,	PUNCT
ejpam-6173	715	8	we	we	PRON
ejpam-6173	715	9	studied	study	VERB
ejpam-6173	715	10	the	the	DET
ejpam-6173	715	11	generalized	generalize	VERB
ejpam-6173	715	12	mixed	mixed	ADJ
ejpam-6173	715	13	equilibrium	equilibrium	NOUN
ejpam-6173	715	14	problem	problem	NOUN
ejpam-6173	715	15	and	and	CCONJ
ejpam-6173	715	16	the	the	DET
ejpam-6173	715	17	fixed	fix	VERB
ejpam-6173	715	18	point	point	NOUN
ejpam-6173	715	19	problem	problem	NOUN
ejpam-6173	715	20	in	in	ADP
ejpam-6173	715	21	the	the	DET
ejpam-6173	715	22	framework	framework	NOUN
ejpam-6173	715	23	of	of	ADP
ejpam-6173	715	24	real	real	ADJ
ejpam-6173	715	25	reflexive	reflexive	ADJ
ejpam-6173	715	26	banach	banach	NOUN
ejpam-6173	715	27	spaces	space	VERB
ejpam-6173	715	28	.	.	PUNCT
ejpam-6173	716	1	we	we	PRON
ejpam-6173	716	2	introduce	introduce	VERB
ejpam-6173	716	3	an	an	DET
ejpam-6173	716	4	inertial	inertial	ADJ
ejpam-6173	716	5	method	method	NOUN
ejpam-6173	716	6	for	for	ADP
ejpam-6173	716	7	approximating	approximate	VERB
ejpam-6173	716	8	the	the	DET
ejpam-6173	716	9	common	common	ADJ
ejpam-6173	716	10	solution	solution	NOUN
ejpam-6173	716	11	of	of	ADP
ejpam-6173	716	12	the	the	DET
ejpam-6173	716	13	above	above	ADJ
ejpam-6173	716	14	mentioned	mention	VERB
ejpam-6173	716	15	problems	problem	NOUN
ejpam-6173	716	16	.	.	PUNCT
ejpam-6173	717	1	under	under	ADP
ejpam-6173	717	2	mild	mild	ADJ
ejpam-6173	717	3	conditions	condition	NOUN
ejpam-6173	717	4	,	,	PUNCT
ejpam-6173	717	5	we	we	PRON
ejpam-6173	717	6	obtained	obtain	VERB
ejpam-6173	717	7	the	the	DET
ejpam-6173	717	8	strong	strong	ADJ
ejpam-6173	717	9	convergence	convergence	NOUN
ejpam-6173	717	10	of	of	ADP
ejpam-6173	717	11	our	our	PRON
ejpam-6173	717	12	proposed	propose	VERB
ejpam-6173	717	13	method	method	NOUN
ejpam-6173	717	14	.	.	PUNCT
ejpam-6173	718	1	finally	finally	ADV
ejpam-6173	718	2	,	,	PUNCT
ejpam-6173	718	3	we	we	PRON
ejpam-6173	718	4	present	present	VERB
ejpam-6173	718	5	numerical	numerical	ADJ
ejpam-6173	718	6	experiments	experiment	NOUN
ejpam-6173	718	7	in	in	ADP
ejpam-6173	718	8	comparison	comparison	NOUN
ejpam-6173	718	9	with	with	ADP
ejpam-6173	718	10	an	an	DET
ejpam-6173	718	11	algorithm	algorithm	NOUN
ejpam-6173	718	12	in	in	ADP
ejpam-6173	718	13	the	the	DET
ejpam-6173	718	14	literature	literature	NOUN
ejpam-6173	718	15	to	to	PART
ejpam-6173	718	16	illustrate	illustrate	VERB
ejpam-6173	718	17	the	the	DET
ejpam-6173	718	18	applicability	applicability	NOUN
ejpam-6173	718	19	of	of	ADP
ejpam-6173	718	20	our	our	PRON
ejpam-6173	718	21	proposed	propose	VERB
ejpam-6173	718	22	method	method	NOUN
ejpam-6173	718	23	.	.	PUNCT
ejpam-6173	719	1	v.	v.	ADP
ejpam-6173	719	2	darvish	darvish	PROPN
ejpam-6173	719	3	et	et	PROPN
ejpam-6173	719	4	al	al	PROPN
ejpam-6173	719	5	.	.	PUNCT
ejpam-6173	719	6	/	/	SYM
ejpam-6173	719	7	eur	eur	PROPN
ejpam-6173	719	8	.	.	PUNCT
ejpam-6173	720	1	j.	j.	PROPN
ejpam-6173	720	2	pure	pure	PROPN
ejpam-6173	720	3	appl	appl	PROPN
ejpam-6173	720	4	.	.	PROPN
ejpam-6173	720	5	math	math	PROPN
ejpam-6173	720	6	,	,	PUNCT
ejpam-6173	720	7	18	18	NUM
ejpam-6173	720	8	(	(	PUNCT
ejpam-6173	720	9	3	3	NUM
ejpam-6173	720	10	)	)	PUNCT
ejpam-6173	720	11	(	(	PUNCT
ejpam-6173	720	12	2025	2025	NUM
ejpam-6173	720	13	)	)	PUNCT
ejpam-6173	720	14	,	,	PUNCT
ejpam-6173	720	15	6173	6173	NUM
ejpam-6173	720	16	27	27	NUM
ejpam-6173	720	17	of	of	ADP
ejpam-6173	720	18	32	32	NUM
ejpam-6173	720	19	0	0	NUM
ejpam-6173	720	20	2	2	NUM
ejpam-6173	720	21	4	4	NUM
ejpam-6173	720	22	6	6	NUM
ejpam-6173	720	23	8	8	NUM
ejpam-6173	720	24	10	10	NUM
ejpam-6173	720	25	12	12	NUM
ejpam-6173	720	26	14	14	NUM
ejpam-6173	720	27	16	16	NUM
ejpam-6173	720	28	18	18	NUM
ejpam-6173	720	29	number	number	NOUN
ejpam-6173	720	30	of	of	ADP
ejpam-6173	720	31	iterations	iteration	NOUN
ejpam-6173	720	32	10	10	NUM
ejpam-6173	720	33	-	-	SYM
ejpam-6173	720	34	4	4	NUM
ejpam-6173	720	35	10	10	NUM
ejpam-6173	720	36	-	-	SYM
ejpam-6173	720	37	3	3	NUM
ejpam-6173	720	38	10	10	NUM
ejpam-6173	720	39	-	-	SYM
ejpam-6173	720	40	2	2	NUM
ejpam-6173	720	41	10	10	NUM
ejpam-6173	720	42	-	-	SYM
ejpam-6173	720	43	1	1	NUM
ejpam-6173	720	44	100	100	NUM
ejpam-6173	720	45	101	101	NUM
ejpam-6173	720	46	t	t	NOUN
ejpam-6173	720	47	o	o	NOUN
ejpam-6173	720	48	l	l	NOUN
ejpam-6173	720	49	case	case	NOUN
ejpam-6173	720	50	a	a	DET
ejpam-6173	720	51	our	our	PRON
ejpam-6173	720	52	algorithm	algorithm	NOUN
ejpam-6173	720	53	esra	esra	PROPN
ejpam-6173	720	54	figure	figure	NOUN
ejpam-6173	720	55	5	5	NUM
ejpam-6173	720	56	:	:	PUNCT
ejpam-6173	720	57	example	example	NOUN
ejpam-6173	721	1	2	2	NUM
ejpam-6173	721	2	.	.	PUNCT
ejpam-6173	721	3	case	case	NOUN
ejpam-6173	721	4	a.	a.	NOUN
ejpam-6173	721	5	0	0	NUM
ejpam-6173	721	6	2	2	NUM
ejpam-6173	721	7	4	4	NUM
ejpam-6173	721	8	6	6	NUM
ejpam-6173	721	9	8	8	NUM
ejpam-6173	721	10	10	10	NUM
ejpam-6173	721	11	12	12	NUM
ejpam-6173	721	12	14	14	NUM
ejpam-6173	721	13	16	16	NUM
ejpam-6173	721	14	18	18	NUM
ejpam-6173	721	15	number	number	NOUN
ejpam-6173	721	16	of	of	ADP
ejpam-6173	721	17	iterations	iteration	NOUN
ejpam-6173	721	18	10	10	NUM
ejpam-6173	721	19	-	-	SYM
ejpam-6173	721	20	4	4	NUM
ejpam-6173	721	21	10	10	NUM
ejpam-6173	721	22	-	-	SYM
ejpam-6173	721	23	3	3	NUM
ejpam-6173	721	24	10	10	NUM
ejpam-6173	721	25	-	-	SYM
ejpam-6173	721	26	2	2	NUM
ejpam-6173	721	27	10	10	NUM
ejpam-6173	721	28	-	-	SYM
ejpam-6173	721	29	1	1	NUM
ejpam-6173	721	30	100	100	NUM
ejpam-6173	721	31	101	101	NUM
ejpam-6173	721	32	t	t	NOUN
ejpam-6173	721	33	o	o	NOUN
ejpam-6173	721	34	l	l	NOUN
ejpam-6173	721	35	case	case	NOUN
ejpam-6173	721	36	b	b	ADP
ejpam-6173	721	37	our	our	PRON
ejpam-6173	721	38	algorithm	algorithm	PROPN
ejpam-6173	721	39	esra	esra	PROPN
ejpam-6173	721	40	figure	figure	NOUN
ejpam-6173	721	41	6	6	NUM
ejpam-6173	721	42	:	:	PUNCT
ejpam-6173	721	43	example	example	NOUN
ejpam-6173	721	44	2	2	NUM
ejpam-6173	721	45	.	.	X
ejpam-6173	721	46	case	case	NOUN
ejpam-6173	721	47	b.	b.	PROPN
ejpam-6173	721	48	references	reference	NOUN
ejpam-6173	721	49	[	[	X
ejpam-6173	721	50	1	1	NUM
ejpam-6173	721	51	]	]	PUNCT
ejpam-6173	721	52	l.	l.	PROPN
ejpam-6173	721	53	c.	c.	PROPN
ejpam-6173	721	54	ceng	ceng	PROPN
ejpam-6173	721	55	and	and	CCONJ
ejpam-6173	721	56	j.	j.	PROPN
ejpam-6173	721	57	c.	c.	PROPN
ejpam-6173	721	58	yao	yao	PROPN
ejpam-6173	721	59	.	.	PUNCT
ejpam-6173	722	1	a	a	DET
ejpam-6173	722	2	hybrid	hybrid	ADJ
ejpam-6173	722	3	iterative	iterative	NOUN
ejpam-6173	722	4	scheme	scheme	NOUN
ejpam-6173	722	5	for	for	ADP
ejpam-6173	722	6	mixed	mixed	ADJ
ejpam-6173	722	7	equilibrium	equilibrium	NOUN
ejpam-6173	722	8	problems	problem	NOUN
ejpam-6173	722	9	and	and	CCONJ
ejpam-6173	722	10	fixed	fix	VERB
ejpam-6173	722	11	point	point	NOUN
ejpam-6173	722	12	problems	problem	NOUN
ejpam-6173	722	13	.	.	PUNCT
ejpam-6173	723	1	journal	journal	NOUN
ejpam-6173	723	2	of	of	ADP
ejpam-6173	723	3	computational	computational	ADJ
ejpam-6173	723	4	and	and	CCONJ
ejpam-6173	723	5	applied	applied	ADJ
ejpam-6173	723	6	mathematics	mathematic	NOUN
ejpam-6173	723	7	,	,	PUNCT
ejpam-6173	723	8	214:186–201	214:186–201	NUM
ejpam-6173	723	9	,	,	PUNCT
ejpam-6173	723	10	2008	2008	NUM
ejpam-6173	723	11	.	.	PUNCT
ejpam-6173	724	1	[	[	X
ejpam-6173	724	2	2	2	X
ejpam-6173	724	3	]	]	PUNCT
ejpam-6173	724	4	w.	w.	PROPN
ejpam-6173	724	5	takahashi	takahashi	PROPN
ejpam-6173	724	6	and	and	CCONJ
ejpam-6173	724	7	m.	m.	PROPN
ejpam-6173	724	8	toyoda	toyoda	PROPN
ejpam-6173	724	9	.	.	PUNCT
ejpam-6173	725	1	weak	weak	ADJ
ejpam-6173	725	2	convergence	convergence	NOUN
ejpam-6173	725	3	theorems	theorem	NOUN
ejpam-6173	725	4	for	for	ADP
ejpam-6173	725	5	nonexpansive	nonexpansive	ADJ
ejpam-6173	725	6	mappings	mapping	NOUN
ejpam-6173	725	7	and	and	CCONJ
ejpam-6173	725	8	monotone	monotone	ADJ
ejpam-6173	725	9	mappings	mapping	NOUN
ejpam-6173	725	10	.	.	PUNCT
ejpam-6173	726	1	journal	journal	NOUN
ejpam-6173	726	2	of	of	ADP
ejpam-6173	726	3	optimization	optimization	NOUN
ejpam-6173	726	4	theory	theory	NOUN
ejpam-6173	726	5	and	and	CCONJ
ejpam-6173	726	6	applications	application	NOUN
ejpam-6173	726	7	,	,	PUNCT
ejpam-6173	726	8	118:417–428	118:417–428	NUM
ejpam-6173	726	9	,	,	PUNCT
ejpam-6173	726	10	2003	2003	NUM
ejpam-6173	726	11	.	.	PUNCT
ejpam-6173	727	1	[	[	X
ejpam-6173	727	2	3	3	X
ejpam-6173	727	3	]	]	X
ejpam-6173	727	4	f.	f.	PROPN
ejpam-6173	727	5	e.	e.	PROPN
ejpam-6173	727	6	browder	browder	PROPN
ejpam-6173	727	7	.	.	PUNCT
ejpam-6173	728	1	existence	existence	NOUN
ejpam-6173	728	2	and	and	CCONJ
ejpam-6173	728	3	approximation	approximation	NOUN
ejpam-6173	728	4	of	of	ADP
ejpam-6173	728	5	solutions	solution	NOUN
ejpam-6173	728	6	of	of	ADP
ejpam-6173	728	7	nonlinear	nonlinear	ADJ
ejpam-6173	728	8	variational	variational	ADJ
ejpam-6173	728	9	inequalities	inequality	NOUN
ejpam-6173	728	10	.	.	PUNCT
ejpam-6173	729	1	proceedings	proceeding	NOUN
ejpam-6173	729	2	of	of	ADP
ejpam-6173	729	3	the	the	DET
ejpam-6173	729	4	national	national	PROPN
ejpam-6173	729	5	academy	academy	PROPN
ejpam-6173	729	6	of	of	ADP
ejpam-6173	729	7	sciences	sciences	PROPN
ejpam-6173	729	8	of	of	ADP
ejpam-6173	729	9	the	the	DET
ejpam-6173	729	10	united	united	PROPN
ejpam-6173	729	11	states	states	PROPN
ejpam-6173	729	12	of	of	ADP
ejpam-6173	729	13	v.	v.	ADP
ejpam-6173	729	14	darvish	darvish	PROPN
ejpam-6173	729	15	et	et	PROPN
ejpam-6173	729	16	al	al	PROPN
ejpam-6173	729	17	.	.	PUNCT
ejpam-6173	729	18	/	/	SYM
ejpam-6173	729	19	eur	eur	PROPN
ejpam-6173	729	20	.	.	PUNCT
ejpam-6173	730	1	j.	j.	PROPN
ejpam-6173	730	2	pure	pure	PROPN
ejpam-6173	730	3	appl	appl	PROPN
ejpam-6173	730	4	.	.	PROPN
ejpam-6173	730	5	math	math	PROPN
ejpam-6173	730	6	,	,	PUNCT
ejpam-6173	730	7	18	18	NUM
ejpam-6173	730	8	(	(	PUNCT
ejpam-6173	730	9	3	3	NUM
ejpam-6173	730	10	)	)	PUNCT
ejpam-6173	730	11	(	(	PUNCT
ejpam-6173	730	12	2025	2025	NUM
ejpam-6173	730	13	)	)	PUNCT
ejpam-6173	730	14	,	,	PUNCT
ejpam-6173	730	15	6173	6173	NUM
ejpam-6173	730	16	28	28	NUM
ejpam-6173	730	17	of	of	ADP
ejpam-6173	730	18	32	32	NUM
ejpam-6173	730	19	0	0	NUM
ejpam-6173	730	20	2	2	NUM
ejpam-6173	730	21	4	4	NUM
ejpam-6173	730	22	6	6	NUM
ejpam-6173	730	23	8	8	NUM
ejpam-6173	730	24	10	10	NUM
ejpam-6173	730	25	12	12	NUM
ejpam-6173	730	26	14	14	NUM
ejpam-6173	730	27	16	16	NUM
ejpam-6173	730	28	number	number	NOUN
ejpam-6173	730	29	of	of	ADP
ejpam-6173	730	30	iterations	iteration	NOUN
ejpam-6173	730	31	10	10	NUM
ejpam-6173	730	32	-	-	SYM
ejpam-6173	730	33	4	4	NUM
ejpam-6173	730	34	10	10	NUM
ejpam-6173	730	35	-	-	SYM
ejpam-6173	730	36	3	3	NUM
ejpam-6173	730	37	10	10	NUM
ejpam-6173	730	38	-	-	SYM
ejpam-6173	730	39	2	2	NUM
ejpam-6173	730	40	10	10	NUM
ejpam-6173	730	41	-	-	SYM
ejpam-6173	730	42	1	1	NUM
ejpam-6173	730	43	100	100	NUM
ejpam-6173	730	44	101	101	NUM
ejpam-6173	730	45	t	t	NOUN
ejpam-6173	730	46	o	o	NOUN
ejpam-6173	730	47	l	l	NOUN
ejpam-6173	730	48	case	case	NOUN
ejpam-6173	730	49	c	c	X
ejpam-6173	730	50	our	our	PRON
ejpam-6173	730	51	algorithm	algorithm	PROPN
ejpam-6173	730	52	esra	esra	PROPN
ejpam-6173	730	53	figure	figure	NOUN
ejpam-6173	730	54	7	7	NUM
ejpam-6173	730	55	:	:	PUNCT
ejpam-6173	730	56	example	example	NOUN
ejpam-6173	730	57	2	2	NUM
ejpam-6173	730	58	.	.	PUNCT
ejpam-6173	730	59	case	case	NOUN
ejpam-6173	730	60	c.	c.	NOUN
ejpam-6173	730	61	0	0	NUM
ejpam-6173	730	62	5	5	NUM
ejpam-6173	730	63	10	10	NUM
ejpam-6173	730	64	15	15	NUM
ejpam-6173	730	65	number	number	NOUN
ejpam-6173	730	66	of	of	ADP
ejpam-6173	730	67	iterations	iteration	NOUN
ejpam-6173	730	68	10	10	NUM
ejpam-6173	730	69	-	-	SYM
ejpam-6173	730	70	4	4	NUM
ejpam-6173	730	71	10	10	NUM
ejpam-6173	730	72	-	-	SYM
ejpam-6173	730	73	3	3	NUM
ejpam-6173	730	74	10	10	NUM
ejpam-6173	730	75	-	-	SYM
ejpam-6173	730	76	2	2	NUM
ejpam-6173	730	77	10	10	NUM
ejpam-6173	730	78	-	-	SYM
ejpam-6173	730	79	1	1	NUM
ejpam-6173	730	80	100	100	NUM
ejpam-6173	730	81	101	101	NUM
ejpam-6173	730	82	t	t	NOUN
ejpam-6173	730	83	o	o	NOUN
ejpam-6173	730	84	l	l	NOUN
ejpam-6173	730	85	case	case	NOUN
ejpam-6173	731	1	d	d	X
ejpam-6173	731	2	our	our	PRON
ejpam-6173	731	3	algorithm	algorithm	PROPN
ejpam-6173	731	4	esra	esra	PROPN
ejpam-6173	731	5	figure	figure	NOUN
ejpam-6173	731	6	8	8	NUM
ejpam-6173	731	7	:	:	PUNCT
ejpam-6173	731	8	example	example	NOUN
ejpam-6173	732	1	2	2	NUM
ejpam-6173	732	2	.	.	X
ejpam-6173	732	3	case	case	NOUN
ejpam-6173	732	4	d.	d.	PROPN
ejpam-6173	732	5	america	america	PROPN
ejpam-6173	732	6	,	,	PUNCT
ejpam-6173	732	7	56:1080–1086	56:1080–1086	NUM
ejpam-6173	732	8	,	,	PUNCT
ejpam-6173	732	9	1966	1966	NUM
ejpam-6173	732	10	.	.	PUNCT
ejpam-6173	733	1	[	[	X
ejpam-6173	733	2	4	4	X
ejpam-6173	733	3	]	]	X
ejpam-6173	733	4	e.	e.	PROPN
ejpam-6173	733	5	blum	blum	PROPN
ejpam-6173	733	6	and	and	CCONJ
ejpam-6173	733	7	w.	w.	PROPN
ejpam-6173	733	8	oettli	oettli	PROPN
ejpam-6173	733	9	.	.	PUNCT
ejpam-6173	734	1	from	from	ADP
ejpam-6173	734	2	optimization	optimization	NOUN
ejpam-6173	734	3	and	and	CCONJ
ejpam-6173	734	4	variational	variational	ADJ
ejpam-6173	734	5	inequalities	inequality	NOUN
ejpam-6173	734	6	to	to	ADP
ejpam-6173	734	7	equilibrium	equilibrium	NOUN
ejpam-6173	734	8	problems	problem	NOUN
ejpam-6173	734	9	.	.	PUNCT
ejpam-6173	735	1	mathematical	mathematical	ADJ
ejpam-6173	735	2	student	student	NOUN
ejpam-6173	735	3	,	,	PUNCT
ejpam-6173	735	4	63:123–145	63:123–145	PROPN
ejpam-6173	735	5	,	,	PUNCT
ejpam-6173	735	6	1994	1994	NUM
ejpam-6173	735	7	.	.	PUNCT
ejpam-6173	736	1	[	[	X
ejpam-6173	736	2	5	5	X
ejpam-6173	736	3	]	]	PUNCT
ejpam-6173	736	4	m.	m.	NOUN
ejpam-6173	736	5	aslam	aslam	PROPN
ejpam-6173	736	6	noor	noor	PROPN
ejpam-6173	736	7	and	and	CCONJ
ejpam-6173	736	8	w.	w.	PROPN
ejpam-6173	736	9	oettli	oettli	PROPN
ejpam-6173	736	10	.	.	PUNCT
ejpam-6173	737	1	on	on	ADP
ejpam-6173	737	2	general	general	ADJ
ejpam-6173	737	3	nonlinear	nonlinear	ADJ
ejpam-6173	737	4	complementarity	complementarity	NOUN
ejpam-6173	737	5	problems	problem	NOUN
ejpam-6173	737	6	and	and	CCONJ
ejpam-6173	737	7	quasi	quasi	ADJ
ejpam-6173	737	8	equilibria	equilibria	PROPN
ejpam-6173	737	9	.	.	PUNCT
ejpam-6173	737	10	matematiche	matematiche	PROPN
ejpam-6173	737	11	(	(	PUNCT
ejpam-6173	737	12	catania	catania	PROPN
ejpam-6173	737	13	)	)	PUNCT
ejpam-6173	737	14	,	,	PUNCT
ejpam-6173	737	15	49:313–331	49:313–331	PROPN
ejpam-6173	737	16	,	,	PUNCT
ejpam-6173	737	17	1994	1994	NUM
ejpam-6173	737	18	.	.	PUNCT
ejpam-6173	738	1	[	[	X
ejpam-6173	738	2	6	6	NUM
ejpam-6173	738	3	]	]	PUNCT
ejpam-6173	738	4	p.	p.	NOUN
ejpam-6173	738	5	l.	l.	PROPN
ejpam-6173	738	6	combettes	combettes	PROPN
ejpam-6173	738	7	and	and	CCONJ
ejpam-6173	738	8	s.	s.	PROPN
ejpam-6173	738	9	a.	a.	PROPN
ejpam-6173	738	10	hirstoaga	hirstoaga	PROPN
ejpam-6173	738	11	.	.	PUNCT
ejpam-6173	739	1	equilibrium	equilibrium	NOUN
ejpam-6173	739	2	programming	programming	NOUN
ejpam-6173	739	3	in	in	ADP
ejpam-6173	739	4	hilbert	hilbert	PROPN
ejpam-6173	739	5	spaces	space	NOUN
ejpam-6173	739	6	.	.	PUNCT
ejpam-6173	740	1	journal	journal	PROPN
ejpam-6173	740	2	of	of	ADP
ejpam-6173	740	3	nonlinear	nonlinear	ADJ
ejpam-6173	740	4	and	and	CCONJ
ejpam-6173	740	5	convex	convex	ADJ
ejpam-6173	740	6	analysis	analysis	NOUN
ejpam-6173	740	7	,	,	PUNCT
ejpam-6173	740	8	6:117–136	6:117–136	NOUN
ejpam-6173	740	9	,	,	PUNCT
ejpam-6173	740	10	2005	2005	NUM
ejpam-6173	740	11	.	.	PUNCT
ejpam-6173	741	1	[	[	X
ejpam-6173	741	2	7	7	X
ejpam-6173	741	3	]	]	PUNCT
ejpam-6173	741	4	s.	s.	PROPN
ejpam-6173	741	5	d.	d.	PROPN
ejpam-6173	741	6	flam	flam	PROPN
ejpam-6173	741	7	and	and	CCONJ
ejpam-6173	741	8	a.	a.	PROPN
ejpam-6173	741	9	s.	s.	PROPN
ejpam-6173	741	10	antipin	antipin	PROPN
ejpam-6173	741	11	.	.	PUNCT
ejpam-6173	742	1	equilibrium	equilibrium	NOUN
ejpam-6173	742	2	programming	programming	NOUN
ejpam-6173	742	3	using	use	VERB
ejpam-6173	742	4	proximal	proximal	ADJ
ejpam-6173	742	5	-	-	PUNCT
ejpam-6173	742	6	link	link	NOUN
ejpam-6173	742	7	algorithms	algorithm	NOUN
ejpam-6173	742	8	.	.	PUNCT
ejpam-6173	743	1	mathematical	mathematical	ADJ
ejpam-6173	743	2	programming	programming	NOUN
ejpam-6173	743	3	,	,	PUNCT
ejpam-6173	743	4	78:29–41	78:29–41	NOUN
ejpam-6173	743	5	,	,	PUNCT
ejpam-6173	743	6	1997	1997	NUM
ejpam-6173	743	7	.	.	PUNCT
ejpam-6173	744	1	[	[	X
ejpam-6173	744	2	8	8	NUM
ejpam-6173	744	3	]	]	X
ejpam-6173	744	4	g.	g.	PROPN
ejpam-6173	744	5	kassay	kassay	PROPN
ejpam-6173	744	6	,	,	PUNCT
ejpam-6173	744	7	s.	s.	PROPN
ejpam-6173	744	8	reich	reich	PROPN
ejpam-6173	744	9	,	,	PUNCT
ejpam-6173	744	10	and	and	CCONJ
ejpam-6173	744	11	s.	s.	PROPN
ejpam-6173	744	12	sabach	sabach	PROPN
ejpam-6173	744	13	.	.	PUNCT
ejpam-6173	745	1	iterative	iterative	NOUN
ejpam-6173	745	2	methods	method	NOUN
ejpam-6173	745	3	for	for	ADP
ejpam-6173	745	4	solving	solve	VERB
ejpam-6173	745	5	systems	system	NOUN
ejpam-6173	745	6	of	of	ADP
ejpam-6173	745	7	variational	variational	ADJ
ejpam-6173	745	8	inequalities	inequality	NOUN
ejpam-6173	745	9	in	in	ADP
ejpam-6173	745	10	reflexive	reflexive	ADJ
ejpam-6173	745	11	banach	banach	NOUN
ejpam-6173	745	12	spaces	space	NOUN
ejpam-6173	745	13	.	.	PUNCT
ejpam-6173	746	1	siam	siam	PROPN
ejpam-6173	746	2	journal	journal	PROPN
ejpam-6173	746	3	on	on	ADP
ejpam-6173	746	4	optimization	optimization	NOUN
ejpam-6173	746	5	,	,	PUNCT
ejpam-6173	746	6	v.	v.	CCONJ
ejpam-6173	747	1	darvish	darvish	PROPN
ejpam-6173	747	2	et	et	PROPN
ejpam-6173	747	3	al	al	PROPN
ejpam-6173	747	4	.	.	PUNCT
ejpam-6173	747	5	/	/	SYM
ejpam-6173	747	6	eur	eur	PROPN
ejpam-6173	747	7	.	.	PUNCT
ejpam-6173	748	1	j.	j.	PROPN
ejpam-6173	748	2	pure	pure	PROPN
ejpam-6173	748	3	appl	appl	PROPN
ejpam-6173	748	4	.	.	PROPN
ejpam-6173	748	5	math	math	PROPN
ejpam-6173	748	6	,	,	PUNCT
ejpam-6173	748	7	18	18	NUM
ejpam-6173	748	8	(	(	PUNCT
ejpam-6173	748	9	3	3	NUM
ejpam-6173	748	10	)	)	PUNCT
ejpam-6173	748	11	(	(	PUNCT
ejpam-6173	748	12	2025	2025	NUM
ejpam-6173	748	13	)	)	PUNCT
ejpam-6173	748	14	,	,	PUNCT
ejpam-6173	748	15	6173	6173	NUM
ejpam-6173	748	16	29	29	NUM
ejpam-6173	748	17	of	of	ADP
ejpam-6173	748	18	32	32	NUM
ejpam-6173	748	19	21:1319–1344	21:1319–1344	NUM
ejpam-6173	748	20	,	,	PUNCT
ejpam-6173	748	21	2011	2011	NUM
ejpam-6173	748	22	.	.	PUNCT
ejpam-6173	749	1	[	[	X
ejpam-6173	749	2	9	9	NUM
ejpam-6173	749	3	]	]	PUNCT
ejpam-6173	749	4	s.	s.	PROPN
ejpam-6173	749	5	reich	reich	PROPN
ejpam-6173	749	6	and	and	CCONJ
ejpam-6173	749	7	s.	s.	PROPN
ejpam-6173	749	8	sabach	sabach	PROPN
ejpam-6173	749	9	.	.	PUNCT
ejpam-6173	750	1	three	three	NUM
ejpam-6173	750	2	strong	strong	ADJ
ejpam-6173	750	3	convergence	convergence	NOUN
ejpam-6173	750	4	theorems	theorem	NOUN
ejpam-6173	750	5	regarding	regard	VERB
ejpam-6173	750	6	iterative	iterative	NOUN
ejpam-6173	750	7	methods	method	NOUN
ejpam-6173	750	8	for	for	ADP
ejpam-6173	750	9	solving	solve	VERB
ejpam-6173	750	10	equilibrium	equilibrium	NOUN
ejpam-6173	750	11	problems	problem	NOUN
ejpam-6173	750	12	in	in	ADP
ejpam-6173	750	13	reflexive	reflexive	ADJ
ejpam-6173	750	14	banach	banach	NOUN
ejpam-6173	750	15	spaces	space	VERB
ejpam-6173	750	16	.	.	PUNCT
ejpam-6173	751	1	contemporary	contemporary	ADJ
ejpam-6173	751	2	mathematics	mathematics	PROPN
ejpam-6173	751	3	,	,	PUNCT
ejpam-6173	751	4	568:225–240	568:225–240	NUM
ejpam-6173	751	5	,	,	PUNCT
ejpam-6173	751	6	2012	2012	NUM
ejpam-6173	751	7	.	.	PUNCT
ejpam-6173	752	1	[	[	X
ejpam-6173	752	2	10	10	NUM
ejpam-6173	752	3	]	]	PUNCT
ejpam-6173	752	4	s.	s.	PROPN
ejpam-6173	752	5	takahashi	takahashi	PROPN
ejpam-6173	752	6	and	and	CCONJ
ejpam-6173	752	7	w.	w.	PROPN
ejpam-6173	752	8	takahashi	takahashi	PROPN
ejpam-6173	752	9	.	.	PUNCT
ejpam-6173	753	1	viscosity	viscosity	NOUN
ejpam-6173	753	2	approximation	approximation	NOUN
ejpam-6173	753	3	methods	method	NOUN
ejpam-6173	753	4	for	for	ADP
ejpam-6173	753	5	equilibrium	equilibrium	NOUN
ejpam-6173	753	6	problems	problem	NOUN
ejpam-6173	753	7	and	and	CCONJ
ejpam-6173	753	8	fixed	fix	VERB
ejpam-6173	753	9	point	point	NOUN
ejpam-6173	753	10	problems	problem	NOUN
ejpam-6173	753	11	in	in	ADP
ejpam-6173	753	12	hilbert	hilbert	PROPN
ejpam-6173	753	13	spaces	space	NOUN
ejpam-6173	753	14	.	.	PUNCT
ejpam-6173	754	1	journal	journal	PROPN
ejpam-6173	754	2	of	of	ADP
ejpam-6173	754	3	mathematical	mathematical	ADJ
ejpam-6173	754	4	analysis	analysis	NOUN
ejpam-6173	754	5	and	and	CCONJ
ejpam-6173	754	6	applications	application	NOUN
ejpam-6173	754	7	,	,	PUNCT
ejpam-6173	754	8	331:506–515	331:506–515	NUM
ejpam-6173	754	9	,	,	PUNCT
ejpam-6173	754	10	2007	2007	NUM
ejpam-6173	754	11	.	.	PUNCT
ejpam-6173	755	1	[	[	X
ejpam-6173	755	2	11	11	NUM
ejpam-6173	755	3	]	]	PUNCT
ejpam-6173	755	4	j.	j.	PROPN
ejpam-6173	755	5	w.	w.	PROPN
ejpam-6173	755	6	peng	peng	PROPN
ejpam-6173	755	7	and	and	CCONJ
ejpam-6173	755	8	j.	j.	PROPN
ejpam-6173	755	9	c.	c.	PROPN
ejpam-6173	755	10	yao	yao	PROPN
ejpam-6173	755	11	.	.	PUNCT
ejpam-6173	756	1	strong	strong	ADJ
ejpam-6173	756	2	convergence	convergence	NOUN
ejpam-6173	756	3	theorems	theorem	NOUN
ejpam-6173	756	4	of	of	ADP
ejpam-6173	756	5	iterative	iterative	ADJ
ejpam-6173	756	6	scheme	scheme	NOUN
ejpam-6173	756	7	based	base	VERB
ejpam-6173	756	8	on	on	ADP
ejpam-6173	756	9	the	the	DET
ejpam-6173	756	10	extragradient	extragradient	NOUN
ejpam-6173	756	11	method	method	NOUN
ejpam-6173	756	12	for	for	ADP
ejpam-6173	756	13	mixed	mixed	ADJ
ejpam-6173	756	14	equilibrium	equilibrium	NOUN
ejpam-6173	756	15	problems	problem	NOUN
ejpam-6173	756	16	and	and	CCONJ
ejpam-6173	756	17	fixed	fix	VERB
ejpam-6173	756	18	point	point	NOUN
ejpam-6173	756	19	problems	problem	NOUN
ejpam-6173	756	20	.	.	PUNCT
ejpam-6173	757	1	mathematical	mathematical	ADJ
ejpam-6173	757	2	and	and	CCONJ
ejpam-6173	757	3	computer	computer	NOUN
ejpam-6173	757	4	modelling	modelling	NOUN
ejpam-6173	757	5	,	,	PUNCT
ejpam-6173	757	6	49:1816–1828	49:1816–1828	NUM
ejpam-6173	757	7	,	,	PUNCT
ejpam-6173	757	8	2009	2009	NUM
ejpam-6173	757	9	.	.	PUNCT
ejpam-6173	758	1	[	[	X
ejpam-6173	758	2	12	12	NUM
ejpam-6173	758	3	]	]	PUNCT
ejpam-6173	758	4	t.	t.	NOUN
ejpam-6173	758	5	m.	m.	NOUN
ejpam-6173	758	6	tuyen	tuyen	PROPN
ejpam-6173	758	7	.	.	PUNCT
ejpam-6173	759	1	parallel	parallel	ADJ
ejpam-6173	759	2	iterative	iterative	NOUN
ejpam-6173	759	3	methods	method	NOUN
ejpam-6173	759	4	for	for	ADP
ejpam-6173	759	5	solving	solve	VERB
ejpam-6173	759	6	systems	system	NOUN
ejpam-6173	759	7	of	of	ADP
ejpam-6173	759	8	generalized	generalized	ADJ
ejpam-6173	759	9	mixed	mixed	ADJ
ejpam-6173	759	10	equilibrium	equilibrium	NOUN
ejpam-6173	759	11	problems	problem	NOUN
ejpam-6173	759	12	in	in	ADP
ejpam-6173	759	13	reflexive	reflexive	ADJ
ejpam-6173	759	14	banach	banach	NOUN
ejpam-6173	759	15	spaces	space	NOUN
ejpam-6173	759	16	.	.	PUNCT
ejpam-6173	760	1	optimization	optimization	NOUN
ejpam-6173	760	2	,	,	PUNCT
ejpam-6173	760	3	66(4):623–637	66(4):623–637	PROPN
ejpam-6173	760	4	,	,	PUNCT
ejpam-6173	760	5	2017	2017	NUM
ejpam-6173	760	6	.	.	PUNCT
ejpam-6173	761	1	[	[	X
ejpam-6173	761	2	13	13	NUM
ejpam-6173	761	3	]	]	PUNCT
ejpam-6173	761	4	i.	i.	NOUN
ejpam-6173	761	5	beg	beg	PROPN
ejpam-6173	761	6	,	,	PUNCT
ejpam-6173	761	7	m.	m.	NOUN
ejpam-6173	761	8	gunaseelan	gunaseelan	PROPN
ejpam-6173	761	9	,	,	PUNCT
ejpam-6173	761	10	and	and	CCONJ
ejpam-6173	761	11	g.	g.	PROPN
ejpam-6173	761	12	a.	a.	PROPN
ejpam-6173	761	13	joseph	joseph	PROPN
ejpam-6173	761	14	.	.	PUNCT
ejpam-6173	762	1	best	good	ADJ
ejpam-6173	762	2	proximity	proximity	NOUN
ejpam-6173	762	3	point	point	NOUN
ejpam-6173	762	4	of	of	ADP
ejpam-6173	762	5	generalized	generalized	ADJ
ejpam-6173	762	6	fproximal	fproximal	ADJ
ejpam-6173	762	7	non	non	ADJ
ejpam-6173	762	8	-	-	ADJ
ejpam-6173	762	9	self	self	ADJ
ejpam-6173	762	10	contraction	contraction	NOUN
ejpam-6173	762	11	.	.	PUNCT
ejpam-6173	763	1	journal	journal	NOUN
ejpam-6173	763	2	of	of	ADP
ejpam-6173	763	3	fixed	fix	VERB
ejpam-6173	763	4	point	point	NOUN
ejpam-6173	763	5	theory	theory	NOUN
ejpam-6173	763	6	and	and	CCONJ
ejpam-6173	763	7	applications	application	NOUN
ejpam-6173	763	8	,	,	PUNCT
ejpam-6173	763	9	23:49	23:49	NUM
ejpam-6173	763	10	,	,	PUNCT
ejpam-6173	763	11	2021	2021	NUM
ejpam-6173	763	12	.	.	PUNCT
ejpam-6173	764	1	[	[	X
ejpam-6173	764	2	14	14	NUM
ejpam-6173	764	3	]	]	PUNCT
ejpam-6173	764	4	a.	a.	NOUN
ejpam-6173	764	5	j.	j.	PROPN
ejpam-6173	764	6	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6173	764	7	,	,	PUNCT
ejpam-6173	764	8	g.	g.	PROPN
ejpam-6173	764	9	nallaselli	nallaselli	PROPN
ejpam-6173	764	10	,	,	PUNCT
ejpam-6173	764	11	a.	a.	PROPN
ejpam-6173	764	12	u.	u.	PROPN
ejpam-6173	764	13	haq	haq	PROPN
ejpam-6173	764	14	,	,	PUNCT
ejpam-6173	764	15	g.	g.	PROPN
ejpam-6173	764	16	mani	mani	PROPN
ejpam-6173	764	17	,	,	PUNCT
ejpam-6173	764	18	i.	i.	PROPN
ejpam-6173	764	19	a.	a.	PROPN
ejpam-6173	764	20	baloch	baloch	PROPN
ejpam-6173	764	21	,	,	PUNCT
ejpam-6173	764	22	and	and	CCONJ
ejpam-6173	764	23	k.	k.	X
ejpam-6173	764	24	nonlaopon	nonlaopon	PROPN
ejpam-6173	764	25	.	.	PUNCT
ejpam-6173	765	1	common	common	ADJ
ejpam-6173	765	2	fixed	fix	VERB
ejpam-6173	765	3	-	-	PUNCT
ejpam-6173	765	4	points	point	NOUN
ejpam-6173	765	5	technique	technique	NOUN
ejpam-6173	765	6	for	for	ADP
ejpam-6173	765	7	the	the	DET
ejpam-6173	765	8	existence	existence	NOUN
ejpam-6173	765	9	of	of	ADP
ejpam-6173	765	10	a	a	DET
ejpam-6173	765	11	solution	solution	NOUN
ejpam-6173	765	12	to	to	ADP
ejpam-6173	765	13	fractional	fractional	ADJ
ejpam-6173	765	14	integro	integro	ADJ
ejpam-6173	765	15	-	-	PUNCT
ejpam-6173	765	16	differential	differential	NOUN
ejpam-6173	765	17	equations	equation	NOUN
ejpam-6173	765	18	via	via	ADP
ejpam-6173	765	19	orthogonal	orthogonal	ADJ
ejpam-6173	765	20	branciari	branciari	NOUN
ejpam-6173	765	21	metric	metric	ADJ
ejpam-6173	765	22	spaces	space	NOUN
ejpam-6173	765	23	.	.	PUNCT
ejpam-6173	766	1	symmetry	symmetry	NOUN
ejpam-6173	766	2	,	,	PUNCT
ejpam-6173	766	3	14:1859	14:1859	NUM
ejpam-6173	766	4	,	,	PUNCT
ejpam-6173	766	5	2022	2022	NUM
ejpam-6173	766	6	.	.	PUNCT
ejpam-6173	767	1	[	[	X
ejpam-6173	767	2	15	15	NUM
ejpam-6173	767	3	]	]	X
ejpam-6173	767	4	z.	z.	PROPN
ejpam-6173	767	5	gu	gu	PROPN
ejpam-6173	767	6	,	,	PUNCT
ejpam-6173	767	7	g.	g.	PROPN
ejpam-6173	767	8	mani	mani	PROPN
ejpam-6173	767	9	,	,	PUNCT
ejpam-6173	767	10	a.	a.	PROPN
ejpam-6173	767	11	j.	j.	PROPN
ejpam-6173	767	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6173	767	13	,	,	PUNCT
ejpam-6173	767	14	and	and	CCONJ
ejpam-6173	767	15	y.	y.	PROPN
ejpam-6173	767	16	li	li	PROPN
ejpam-6173	767	17	.	.	PUNCT
ejpam-6173	768	1	solving	solve	VERB
ejpam-6173	768	2	a	a	DET
ejpam-6173	768	3	system	system	NOUN
ejpam-6173	768	4	of	of	ADP
ejpam-6173	768	5	nonlinear	nonlinear	ADJ
ejpam-6173	768	6	integral	integral	ADJ
ejpam-6173	768	7	equations	equation	NOUN
ejpam-6173	768	8	via	via	ADP
ejpam-6173	768	9	common	common	ADJ
ejpam-6173	768	10	fixed	fix	VERB
ejpam-6173	768	11	point	point	NOUN
ejpam-6173	768	12	theorems	theorem	NOUN
ejpam-6173	768	13	on	on	ADP
ejpam-6173	768	14	bicomplex	bicomplex	NOUN
ejpam-6173	768	15	partial	partial	ADJ
ejpam-6173	768	16	metric	metric	ADJ
ejpam-6173	768	17	space	space	NOUN
ejpam-6173	768	18	.	.	PUNCT
ejpam-6173	769	1	mathematics	mathematic	NOUN
ejpam-6173	769	2	,	,	PUNCT
ejpam-6173	769	3	9:1584	9:1584	NUM
ejpam-6173	769	4	,	,	PUNCT
ejpam-6173	769	5	2021	2021	NUM
ejpam-6173	769	6	.	.	PUNCT
ejpam-6173	770	1	[	[	X
ejpam-6173	770	2	16	16	NUM
ejpam-6173	770	3	]	]	X
ejpam-6173	770	4	g.	g.	PROPN
ejpam-6173	770	5	nallaselli	nallaselli	PROPN
ejpam-6173	770	6	,	,	PUNCT
ejpam-6173	770	7	a.	a.	PROPN
ejpam-6173	770	8	s.	s.	PROPN
ejpam-6173	770	9	baazeem	baazeem	PROPN
ejpam-6173	770	10	,	,	PUNCT
ejpam-6173	770	11	a.	a.	PROPN
ejpam-6173	770	12	j.	j.	PROPN
ejpam-6173	770	13	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6173	770	14	,	,	PUNCT
ejpam-6173	770	15	g.	g.	PROPN
ejpam-6173	770	16	mani	mani	PROPN
ejpam-6173	770	17	,	,	PUNCT
ejpam-6173	770	18	k.	k.	PROPN
ejpam-6173	770	19	javed	javed	PROPN
ejpam-6173	770	20	,	,	PUNCT
ejpam-6173	770	21	e.	e.	PROPN
ejpam-6173	770	22	ameer	ameer	PROPN
ejpam-6173	770	23	,	,	PUNCT
ejpam-6173	770	24	and	and	CCONJ
ejpam-6173	770	25	n.	n.	PROPN
ejpam-6173	770	26	mlaiki	mlaiki	PROPN
ejpam-6173	770	27	.	.	PUNCT
ejpam-6173	771	1	fixed	fix	VERB
ejpam-6173	771	2	point	point	NOUN
ejpam-6173	771	3	theorems	theorem	NOUN
ejpam-6173	771	4	via	via	ADP
ejpam-6173	771	5	orthogonal	orthogonal	ADJ
ejpam-6173	771	6	convex	convex	NOUN
ejpam-6173	771	7	contraction	contraction	NOUN
ejpam-6173	771	8	in	in	ADP
ejpam-6173	771	9	orthogonal	orthogonal	ADJ
ejpam-6173	771	10	b	b	NOUN
ejpam-6173	771	11	-	-	PUNCT
ejpam-6173	771	12	metric	metric	ADJ
ejpam-6173	771	13	spaces	space	NOUN
ejpam-6173	771	14	and	and	CCONJ
ejpam-6173	771	15	applications	application	NOUN
ejpam-6173	771	16	.	.	PUNCT
ejpam-6173	772	1	axioms	axiom	NOUN
ejpam-6173	772	2	,	,	PUNCT
ejpam-6173	772	3	12:143	12:143	NUM
ejpam-6173	772	4	,	,	PUNCT
ejpam-6173	772	5	2023	2023	NUM
ejpam-6173	772	6	.	.	PUNCT
ejpam-6173	773	1	[	[	X
ejpam-6173	773	2	17	17	NUM
ejpam-6173	773	3	]	]	X
ejpam-6173	773	4	r.	r.	PROPN
ejpam-6173	773	5	ramaswamy	ramaswamy	PROPN
ejpam-6173	773	6	,	,	PUNCT
ejpam-6173	773	7	g.	g.	PROPN
ejpam-6173	773	8	mani	mani	PROPN
ejpam-6173	773	9	,	,	PUNCT
ejpam-6173	773	10	a.	a.	PROPN
ejpam-6173	773	11	j.	j.	PROPN
ejpam-6173	773	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6173	773	13	,	,	PUNCT
ejpam-6173	773	14	o.	o.	PROPN
ejpam-6173	773	15	a.	a.	PROPN
ejpam-6173	773	16	a.	a.	PROPN
ejpam-6173	773	17	abdelnaby	abdelnaby	PROPN
ejpam-6173	773	18	,	,	PUNCT
ejpam-6173	773	19	v.	v.	ADP
ejpam-6173	773	20	stojiljković	stojiljković	PROPN
ejpam-6173	773	21	,	,	PUNCT
ejpam-6173	773	22	s.	s.	PROPN
ejpam-6173	773	23	radojevic	radojevic	PROPN
ejpam-6173	773	24	,	,	PUNCT
ejpam-6173	773	25	and	and	CCONJ
ejpam-6173	773	26	s.	s.	PROPN
ejpam-6173	774	1	radenović.	radenović.	PROPN
ejpam-6173	774	2	fixed	fix	VERB
ejpam-6173	774	3	points	point	NOUN
ejpam-6173	774	4	on	on	ADP
ejpam-6173	774	5	covariant	covariant	NOUN
ejpam-6173	774	6	and	and	CCONJ
ejpam-6173	774	7	contravariant	contravariant	PROPN
ejpam-6173	774	8	maps	map	NOUN
ejpam-6173	774	9	with	with	ADP
ejpam-6173	774	10	an	an	DET
ejpam-6173	774	11	application	application	NOUN
ejpam-6173	774	12	.	.	PUNCT
ejpam-6173	775	1	mathematics	mathematic	NOUN
ejpam-6173	775	2	,	,	PUNCT
ejpam-6173	775	3	10:4385	10:4385	NUM
ejpam-6173	775	4	,	,	PUNCT
ejpam-6173	775	5	2022	2022	NUM
ejpam-6173	775	6	.	.	PUNCT
ejpam-6173	776	1	[	[	X
ejpam-6173	776	2	18	18	NUM
ejpam-6173	776	3	]	]	PUNCT
ejpam-6173	776	4	a.	a.	NOUN
ejpam-6173	776	5	moudafi	moudafi	PROPN
ejpam-6173	776	6	.	.	PUNCT
ejpam-6173	776	7	viscosity	viscosity	NOUN
ejpam-6173	776	8	approximation	approximation	NOUN
ejpam-6173	776	9	methods	method	NOUN
ejpam-6173	776	10	for	for	ADP
ejpam-6173	776	11	fixed	fix	VERB
ejpam-6173	776	12	points	point	NOUN
ejpam-6173	776	13	.	.	PUNCT
ejpam-6173	777	1	journal	journal	PROPN
ejpam-6173	777	2	of	of	ADP
ejpam-6173	777	3	mathematical	mathematical	ADJ
ejpam-6173	777	4	analysis	analysis	NOUN
ejpam-6173	777	5	and	and	CCONJ
ejpam-6173	777	6	applications	application	NOUN
ejpam-6173	777	7	,	,	PUNCT
ejpam-6173	777	8	204(1):45–56	204(1):45–56	NUM
ejpam-6173	777	9	,	,	PUNCT
ejpam-6173	777	10	1997	1997	NUM
ejpam-6173	777	11	.	.	PUNCT
ejpam-6173	778	1	[	[	X
ejpam-6173	778	2	19	19	NUM
ejpam-6173	778	3	]	]	PUNCT
ejpam-6173	778	4	h.	h.	PROPN
ejpam-6173	778	5	a.	a.	PROPN
ejpam-6173	778	6	abass	abass	PROPN
ejpam-6173	778	7	,	,	PUNCT
ejpam-6173	778	8	m.	m.	NOUN
ejpam-6173	778	9	aphane	aphane	PROPN
ejpam-6173	778	10	,	,	PUNCT
ejpam-6173	778	11	and	and	CCONJ
ejpam-6173	778	12	m.	m.	NOUN
ejpam-6173	778	13	o.	o.	PROPN
ejpam-6173	778	14	olayiwola	olayiwola	PROPN
ejpam-6173	778	15	.	.	PUNCT
ejpam-6173	779	1	an	an	DET
ejpam-6173	779	2	inertial	inertial	ADJ
ejpam-6173	779	3	method	method	NOUN
ejpam-6173	779	4	for	for	ADP
ejpam-6173	779	5	solving	solve	VERB
ejpam-6173	779	6	systems	system	NOUN
ejpam-6173	779	7	of	of	ADP
ejpam-6173	779	8	generalized	generalized	ADJ
ejpam-6173	779	9	mixed	mixed	ADJ
ejpam-6173	779	10	equilibrium	equilibrium	NOUN
ejpam-6173	779	11	and	and	CCONJ
ejpam-6173	779	12	fixed	fix	VERB
ejpam-6173	779	13	point	point	NOUN
ejpam-6173	779	14	problems	problem	NOUN
ejpam-6173	779	15	in	in	ADP
ejpam-6173	779	16	reflexive	reflexive	ADJ
ejpam-6173	779	17	banach	banach	NOUN
ejpam-6173	779	18	spaces	space	NOUN
ejpam-6173	779	19	.	.	PUNCT
ejpam-6173	780	1	asian	asian	ADJ
ejpam-6173	780	2	-	-	PUNCT
ejpam-6173	780	3	european	european	ADJ
ejpam-6173	780	4	journal	journal	NOUN
ejpam-6173	780	5	of	of	ADP
ejpam-6173	780	6	mathematics	mathematic	NOUN
ejpam-6173	780	7	,	,	PUNCT
ejpam-6173	780	8	16(11):2350207	16(11):2350207	NUM
ejpam-6173	780	9	,	,	PUNCT
ejpam-6173	780	10	2023	2023	NUM
ejpam-6173	780	11	.	.	PUNCT
ejpam-6173	781	1	[	[	X
ejpam-6173	781	2	20	20	NUM
ejpam-6173	781	3	]	]	PUNCT
ejpam-6173	781	4	o.	o.	PROPN
ejpam-6173	781	5	k.	k.	PROPN
ejpam-6173	781	6	oyewole	oyewole	PROPN
ejpam-6173	781	7	and	and	CCONJ
ejpam-6173	781	8	o.	o.	NOUN
ejpam-6173	781	9	t.	t.	PROPN
ejpam-6173	781	10	mewomo	mewomo	PROPN
ejpam-6173	781	11	.	.	PUNCT
ejpam-6173	782	1	existence	existence	NOUN
ejpam-6173	782	2	results	result	VERB
ejpam-6173	782	3	for	for	ADP
ejpam-6173	782	4	new	new	ADJ
ejpam-6173	782	5	generalized	generalize	VERB
ejpam-6173	782	6	mixed	mixed	ADJ
ejpam-6173	782	7	equilibrium	equilibrium	NOUN
ejpam-6173	782	8	and	and	CCONJ
ejpam-6173	782	9	fixed	fix	VERB
ejpam-6173	782	10	point	point	NOUN
ejpam-6173	782	11	problems	problem	NOUN
ejpam-6173	782	12	in	in	ADP
ejpam-6173	782	13	banach	banach	NOUN
ejpam-6173	782	14	spaces	space	NOUN
ejpam-6173	782	15	.	.	PUNCT
ejpam-6173	783	1	nonlinear	nonlinear	ADJ
ejpam-6173	783	2	functional	functional	ADJ
ejpam-6173	783	3	analysis	analysis	NOUN
ejpam-6173	783	4	and	and	CCONJ
ejpam-6173	783	5	applications	application	NOUN
ejpam-6173	783	6	,	,	PUNCT
ejpam-6173	783	7	pages	page	NOUN
ejpam-6173	783	8	273–301	273–301	NUM
ejpam-6173	783	9	,	,	PUNCT
ejpam-6173	783	10	2020	2020	NUM
ejpam-6173	783	11	.	.	PUNCT
ejpam-6173	784	1	[	[	X
ejpam-6173	784	2	21	21	NUM
ejpam-6173	784	3	]	]	X
ejpam-6173	784	4	n.	n.	NOUN
ejpam-6173	784	5	petrot	petrot	PROPN
ejpam-6173	784	6	,	,	PUNCT
ejpam-6173	784	7	k.	k.	PROPN
ejpam-6173	784	8	wattanawitoon	wattanawitoon	PROPN
ejpam-6173	784	9	,	,	PUNCT
ejpam-6173	784	10	and	and	CCONJ
ejpam-6173	784	11	p.	p.	PROPN
ejpam-6173	784	12	kumam	kumam	PROPN
ejpam-6173	784	13	.	.	PUNCT
ejpam-6173	785	1	a	a	DET
ejpam-6173	785	2	hybrid	hybrid	ADJ
ejpam-6173	785	3	projection	projection	NOUN
ejpam-6173	785	4	method	method	NOUN
ejpam-6173	785	5	for	for	ADP
ejpam-6173	785	6	generalized	generalized	ADJ
ejpam-6173	785	7	mixed	mixed	ADJ
ejpam-6173	785	8	equilibrium	equilibrium	NOUN
ejpam-6173	785	9	problems	problem	NOUN
ejpam-6173	785	10	and	and	CCONJ
ejpam-6173	785	11	fixed	fix	VERB
ejpam-6173	785	12	point	point	NOUN
ejpam-6173	785	13	problems	problem	NOUN
ejpam-6173	785	14	in	in	ADP
ejpam-6173	785	15	banach	banach	NOUN
ejpam-6173	785	16	spaces	space	NOUN
ejpam-6173	785	17	.	.	PUNCT
ejpam-6173	786	1	nonlinear	nonlinear	ADJ
ejpam-6173	786	2	analysis	analysis	NOUN
ejpam-6173	786	3	:	:	PUNCT
ejpam-6173	786	4	hybrid	hybrid	ADJ
ejpam-6173	786	5	systems	system	NOUN
ejpam-6173	786	6	,	,	PUNCT
ejpam-6173	786	7	4(4):631–643	4(4):631–643	NOUN
ejpam-6173	786	8	,	,	PUNCT
ejpam-6173	786	9	2010	2010	NUM
ejpam-6173	786	10	.	.	PUNCT
ejpam-6173	787	1	[	[	X
ejpam-6173	787	2	22	22	NUM
ejpam-6173	787	3	]	]	PUNCT
ejpam-6173	787	4	s.	s.	PROPN
ejpam-6173	787	5	takahashi	takahashi	PROPN
ejpam-6173	787	6	and	and	CCONJ
ejpam-6173	787	7	w.	w.	PROPN
ejpam-6173	787	8	takahashi	takahashi	PROPN
ejpam-6173	787	9	.	.	PUNCT
ejpam-6173	788	1	strong	strong	ADJ
ejpam-6173	788	2	convergence	convergence	NOUN
ejpam-6173	788	3	theorem	theorem	VERB
ejpam-6173	788	4	for	for	ADP
ejpam-6173	788	5	a	a	DET
ejpam-6173	788	6	generalized	generalized	ADJ
ejpam-6173	788	7	equilibrium	equilibrium	NOUN
ejpam-6173	788	8	problem	problem	NOUN
ejpam-6173	788	9	and	and	CCONJ
ejpam-6173	788	10	a	a	DET
ejpam-6173	788	11	nonexpansive	nonexpansive	ADJ
ejpam-6173	788	12	mapping	mapping	NOUN
ejpam-6173	788	13	in	in	ADP
ejpam-6173	788	14	a	a	DET
ejpam-6173	788	15	hilbert	hilbert	NOUN
ejpam-6173	788	16	space	space	NOUN
ejpam-6173	788	17	.	.	PUNCT
ejpam-6173	789	1	nonlinear	nonlinear	ADJ
ejpam-6173	789	2	analysis	analysis	NOUN
ejpam-6173	789	3	,	,	PUNCT
ejpam-6173	789	4	69:1025–1033	69:1025–1033	NUM
ejpam-6173	789	5	,	,	PUNCT
ejpam-6173	789	6	2008	2008	NUM
ejpam-6173	789	7	.	.	PUNCT
ejpam-6173	790	1	[	[	X
ejpam-6173	790	2	23	23	NUM
ejpam-6173	790	3	]	]	X
ejpam-6173	790	4	g.	g.	PROPN
ejpam-6173	790	5	z.	z.	PROPN
ejpam-6173	790	6	eskandani	eskandani	PROPN
ejpam-6173	790	7	and	and	CCONJ
ejpam-6173	790	8	m.	m.	NOUN
ejpam-6173	790	9	raeisi	raeisi	VERB
ejpam-6173	790	10	.	.	PUNCT
ejpam-6173	791	1	a	a	DET
ejpam-6173	791	2	new	new	ADJ
ejpam-6173	791	3	algorithm	algorithm	NOUN
ejpam-6173	791	4	for	for	ADP
ejpam-6173	791	5	finding	find	VERB
ejpam-6173	791	6	fixed	fix	VERB
ejpam-6173	791	7	points	point	NOUN
ejpam-6173	791	8	of	of	ADP
ejpam-6173	791	9	bregman	bregman	NOUN
ejpam-6173	791	10	v.	v.	ADP
ejpam-6173	791	11	darvish	darvish	PROPN
ejpam-6173	791	12	et	et	PROPN
ejpam-6173	791	13	al	al	PROPN
ejpam-6173	791	14	.	.	PUNCT
ejpam-6173	791	15	/	/	SYM
ejpam-6173	791	16	eur	eur	PROPN
ejpam-6173	791	17	.	.	PUNCT
ejpam-6173	792	1	j.	j.	PROPN
ejpam-6173	792	2	pure	pure	PROPN
ejpam-6173	792	3	appl	appl	PROPN
ejpam-6173	792	4	.	.	PROPN
ejpam-6173	792	5	math	math	PROPN
ejpam-6173	792	6	,	,	PUNCT
ejpam-6173	792	7	18	18	NUM
ejpam-6173	792	8	(	(	PUNCT
ejpam-6173	792	9	3	3	NUM
ejpam-6173	792	10	)	)	PUNCT
ejpam-6173	792	11	(	(	PUNCT
ejpam-6173	792	12	2025	2025	NUM
ejpam-6173	792	13	)	)	PUNCT
ejpam-6173	792	14	,	,	PUNCT
ejpam-6173	792	15	6173	6173	NUM
ejpam-6173	792	16	30	30	NUM
ejpam-6173	792	17	of	of	ADP
ejpam-6173	792	18	32	32	NUM
ejpam-6173	792	19	quasi	quasi	ADJ
ejpam-6173	792	20	-	-	ADJ
ejpam-6173	792	21	nonexpansive	nonexpansive	ADJ
ejpam-6173	792	22	mappings	mapping	NOUN
ejpam-6173	792	23	and	and	CCONJ
ejpam-6173	792	24	zeros	zero	NOUN
ejpam-6173	792	25	of	of	ADP
ejpam-6173	792	26	maximal	maximal	ADJ
ejpam-6173	792	27	monotone	monotone	ADJ
ejpam-6173	792	28	operators	operator	NOUN
ejpam-6173	792	29	by	by	ADP
ejpam-6173	792	30	using	use	VERB
ejpam-6173	792	31	products	product	NOUN
ejpam-6173	792	32	of	of	ADP
ejpam-6173	792	33	resolvents	resolvent	NOUN
ejpam-6173	792	34	.	.	PUNCT
ejpam-6173	793	1	results	result	NOUN
ejpam-6173	793	2	in	in	ADP
ejpam-6173	793	3	mathematics	mathematic	NOUN
ejpam-6173	793	4	,	,	PUNCT
ejpam-6173	793	5	71:1307–1326	71:1307–1326	NUM
ejpam-6173	793	6	,	,	PUNCT
ejpam-6173	793	7	2017	2017	NUM
ejpam-6173	793	8	.	.	PUNCT
ejpam-6173	794	1	[	[	X
ejpam-6173	794	2	24	24	NUM
ejpam-6173	794	3	]	]	PUNCT
ejpam-6173	794	4	b.	b.	PROPN
ejpam-6173	794	5	t.	t.	PROPN
ejpam-6173	794	6	polyak	polyak	PROPN
ejpam-6173	794	7	.	.	PUNCT
ejpam-6173	795	1	some	some	DET
ejpam-6173	795	2	methods	method	NOUN
ejpam-6173	795	3	of	of	ADP
ejpam-6173	795	4	speeding	speed	VERB
ejpam-6173	795	5	up	up	ADP
ejpam-6173	795	6	the	the	DET
ejpam-6173	795	7	convergence	convergence	NOUN
ejpam-6173	795	8	of	of	ADP
ejpam-6173	795	9	iteration	iteration	NOUN
ejpam-6173	795	10	methods	method	NOUN
ejpam-6173	795	11	.	.	PUNCT
ejpam-6173	796	1	ussr	ussr	ADJ
ejpam-6173	796	2	computational	computational	ADJ
ejpam-6173	796	3	mathematics	mathematic	NOUN
ejpam-6173	796	4	and	and	CCONJ
ejpam-6173	796	5	mathematical	mathematical	ADJ
ejpam-6173	796	6	physics	physics	NOUN
ejpam-6173	796	7	,	,	PUNCT
ejpam-6173	796	8	4(5):1–17	4(5):1–17	NUM
ejpam-6173	796	9	,	,	PUNCT
ejpam-6173	796	10	1964	1964	NUM
ejpam-6173	796	11	.	.	PUNCT
ejpam-6173	797	1	[	[	X
ejpam-6173	797	2	25	25	NUM
ejpam-6173	797	3	]	]	X
ejpam-6173	797	4	d.	d.	PROPN
ejpam-6173	797	5	v.	v.	PROPN
ejpam-6173	797	6	hieu	hieu	PROPN
ejpam-6173	797	7	.	.	PUNCT
ejpam-6173	798	1	new	new	ADJ
ejpam-6173	798	2	inertial	inertial	ADJ
ejpam-6173	798	3	algorithm	algorithm	NOUN
ejpam-6173	798	4	for	for	ADP
ejpam-6173	798	5	a	a	DET
ejpam-6173	798	6	class	class	NOUN
ejpam-6173	798	7	of	of	ADP
ejpam-6173	798	8	equilibrium	equilibrium	NOUN
ejpam-6173	798	9	problems	problem	NOUN
ejpam-6173	798	10	.	.	PUNCT
ejpam-6173	799	1	numerical	numerical	ADJ
ejpam-6173	799	2	algorithms	algorithms	PROPN
ejpam-6173	799	3	,	,	PUNCT
ejpam-6173	799	4	80:1413–1436	80:1413–1436	NUM
ejpam-6173	799	5	,	,	PUNCT
ejpam-6173	799	6	2019	2019	NUM
ejpam-6173	799	7	.	.	PUNCT
ejpam-6173	800	1	[	[	X
ejpam-6173	800	2	26	26	NUM
ejpam-6173	800	3	]	]	X
ejpam-6173	800	4	d.	d.	PROPN
ejpam-6173	800	5	v.	v.	PROPN
ejpam-6173	800	6	hieu	hieu	PROPN
ejpam-6173	800	7	.	.	PUNCT
ejpam-6173	801	1	an	an	DET
ejpam-6173	801	2	inertial	inertial	NOUN
ejpam-6173	801	3	-	-	PUNCT
ejpam-6173	801	4	like	like	ADJ
ejpam-6173	801	5	proximal	proximal	ADJ
ejpam-6173	801	6	algorithm	algorithm	NOUN
ejpam-6173	801	7	for	for	ADP
ejpam-6173	801	8	equilibrium	equilibrium	NOUN
ejpam-6173	801	9	problems	problem	NOUN
ejpam-6173	801	10	.	.	PUNCT
ejpam-6173	802	1	mathematical	mathematical	ADJ
ejpam-6173	802	2	methods	method	NOUN
ejpam-6173	802	3	of	of	ADP
ejpam-6173	802	4	operations	operation	NOUN
ejpam-6173	802	5	research	research	NOUN
ejpam-6173	802	6	,	,	PUNCT
ejpam-6173	802	7	88:399–415	88:399–415	PROPN
ejpam-6173	802	8	,	,	PUNCT
ejpam-6173	802	9	2018	2018	NUM
ejpam-6173	802	10	.	.	PUNCT
ejpam-6173	803	1	[	[	X
ejpam-6173	803	2	27	27	NUM
ejpam-6173	803	3	]	]	X
ejpam-6173	803	4	n.	n.	NOUN
ejpam-6173	803	5	t.	t.	PROPN
ejpam-6173	803	6	vinh	vinh	PROPN
ejpam-6173	803	7	and	and	CCONJ
ejpam-6173	803	8	l.	l.	PROPN
ejpam-6173	803	9	d.	d.	PROPN
ejpam-6173	803	10	muu	muu	PROPN
ejpam-6173	803	11	.	.	PUNCT
ejpam-6173	804	1	inertial	inertial	ADJ
ejpam-6173	804	2	extragradient	extragradient	NOUN
ejpam-6173	804	3	algorithms	algorithm	NOUN
ejpam-6173	804	4	for	for	ADP
ejpam-6173	804	5	solving	solve	VERB
ejpam-6173	804	6	equilibrium	equilibrium	NOUN
ejpam-6173	804	7	problems	problem	NOUN
ejpam-6173	804	8	.	.	PUNCT
ejpam-6173	805	1	acta	acta	PROPN
ejpam-6173	805	2	mathematica	mathematica	PROPN
ejpam-6173	805	3	vietnamica	vietnamica	PROPN
ejpam-6173	805	4	,	,	PUNCT
ejpam-6173	805	5	44:639–663	44:639–663	PROPN
ejpam-6173	805	6	,	,	PUNCT
ejpam-6173	805	7	2019	2019	NUM
ejpam-6173	805	8	.	.	PUNCT
ejpam-6173	806	1	[	[	X
ejpam-6173	806	2	28	28	NUM
ejpam-6173	806	3	]	]	PUNCT
ejpam-6173	806	4	j.	j.	PROPN
ejpam-6173	806	5	f.	f.	PROPN
ejpam-6173	806	6	bonnans	bonnans	PROPN
ejpam-6173	806	7	and	and	CCONJ
ejpam-6173	806	8	a.	a.	NOUN
ejpam-6173	806	9	shapiro	shapiro	PROPN
ejpam-6173	806	10	.	.	PUNCT
ejpam-6173	807	1	perturbation	perturbation	NOUN
ejpam-6173	807	2	analysis	analysis	NOUN
ejpam-6173	807	3	of	of	ADP
ejpam-6173	807	4	optimization	optimization	NOUN
ejpam-6173	807	5	problems	problem	NOUN
ejpam-6173	807	6	.	.	PUNCT
ejpam-6173	808	1	springer	springer	NOUN
ejpam-6173	808	2	,	,	PUNCT
ejpam-6173	808	3	new	new	PROPN
ejpam-6173	808	4	york	york	PROPN
ejpam-6173	808	5	,	,	PUNCT
ejpam-6173	808	6	ny	ny	PROPN
ejpam-6173	808	7	,	,	PUNCT
ejpam-6173	808	8	2000	2000	NUM
ejpam-6173	808	9	.	.	PUNCT
ejpam-6173	809	1	[	[	X
ejpam-6173	809	2	29	29	NUM
ejpam-6173	809	3	]	]	X
ejpam-6173	809	4	y.	y.	NOUN
ejpam-6173	809	5	censor	censor	PROPN
ejpam-6173	809	6	and	and	CCONJ
ejpam-6173	809	7	a.	a.	NOUN
ejpam-6173	809	8	lent	lent	NOUN
ejpam-6173	809	9	.	.	PUNCT
ejpam-6173	810	1	an	an	DET
ejpam-6173	810	2	iterative	iterative	NOUN
ejpam-6173	810	3	row	row	NOUN
ejpam-6173	810	4	-	-	PUNCT
ejpam-6173	810	5	action	action	NOUN
ejpam-6173	810	6	method	method	NOUN
ejpam-6173	810	7	for	for	ADP
ejpam-6173	810	8	interval	interval	NOUN
ejpam-6173	810	9	convex	convex	NOUN
ejpam-6173	810	10	programming	programming	NOUN
ejpam-6173	810	11	.	.	PUNCT
ejpam-6173	811	1	journal	journal	PROPN
ejpam-6173	811	2	of	of	ADP
ejpam-6173	811	3	optimization	optimization	NOUN
ejpam-6173	811	4	theory	theory	NOUN
ejpam-6173	811	5	and	and	CCONJ
ejpam-6173	811	6	applications	application	NOUN
ejpam-6173	811	7	,	,	PUNCT
ejpam-6173	811	8	34:321–353	34:321–353	NUM
ejpam-6173	811	9	,	,	PUNCT
ejpam-6173	811	10	1981	1981	NUM
ejpam-6173	811	11	.	.	PUNCT
ejpam-6173	812	1	[	[	X
ejpam-6173	812	2	30	30	NUM
ejpam-6173	812	3	]	]	PUNCT
ejpam-6173	812	4	m.	m.	NOUN
ejpam-6173	812	5	teboulle	teboulle	PROPN
ejpam-6173	812	6	.	.	PUNCT
ejpam-6173	813	1	a	a	DET
ejpam-6173	813	2	simplified	simplified	ADJ
ejpam-6173	813	3	view	view	NOUN
ejpam-6173	813	4	of	of	ADP
ejpam-6173	813	5	first	first	ADJ
ejpam-6173	813	6	order	order	NOUN
ejpam-6173	813	7	methods	method	NOUN
ejpam-6173	813	8	for	for	ADP
ejpam-6173	813	9	optimization	optimization	NOUN
ejpam-6173	813	10	.	.	PUNCT
ejpam-6173	814	1	mathematical	mathematical	ADJ
ejpam-6173	814	2	programming	programming	NOUN
ejpam-6173	814	3	,	,	PUNCT
ejpam-6173	814	4	170(1):67–96	170(1):67–96	NUM
ejpam-6173	814	5	,	,	PUNCT
ejpam-6173	814	6	2018	2018	NUM
ejpam-6173	814	7	.	.	PUNCT
ejpam-6173	815	1	[	[	X
ejpam-6173	815	2	31	31	NUM
ejpam-6173	815	3	]	]	PUNCT
ejpam-6173	815	4	g.	g.	PROPN
ejpam-6173	815	5	b.	b.	PROPN
ejpam-6173	815	6	wega	wega	PROPN
ejpam-6173	815	7	and	and	CCONJ
ejpam-6173	815	8	h.	h.	PROPN
ejpam-6173	815	9	zegeye	zegeye	PROPN
ejpam-6173	815	10	.	.	PUNCT
ejpam-6173	816	1	convergence	convergence	NOUN
ejpam-6173	816	2	results	result	NOUN
ejpam-6173	816	3	of	of	ADP
ejpam-6173	816	4	forward	forward	ADV
ejpam-6173	816	5	-	-	PUNCT
ejpam-6173	816	6	backward	backward	ADJ
ejpam-6173	816	7	method	method	NOUN
ejpam-6173	816	8	for	for	ADP
ejpam-6173	816	9	a	a	DET
ejpam-6173	816	10	zero	zero	NUM
ejpam-6173	816	11	of	of	ADP
ejpam-6173	816	12	the	the	DET
ejpam-6173	816	13	sum	sum	NOUN
ejpam-6173	816	14	of	of	ADP
ejpam-6173	816	15	maximally	maximally	ADV
ejpam-6173	816	16	monotone	monotone	ADJ
ejpam-6173	816	17	mappings	mapping	NOUN
ejpam-6173	816	18	in	in	ADP
ejpam-6173	816	19	banach	banach	NOUN
ejpam-6173	816	20	spaces	space	NOUN
ejpam-6173	816	21	.	.	PUNCT
ejpam-6173	817	1	computational	computational	ADJ
ejpam-6173	817	2	and	and	CCONJ
ejpam-6173	817	3	applied	applied	ADJ
ejpam-6173	817	4	mathematics	mathematic	NOUN
ejpam-6173	817	5	,	,	PUNCT
ejpam-6173	817	6	39(3):223	39(3):223	NUM
ejpam-6173	817	7	,	,	PUNCT
ejpam-6173	817	8	2020	2020	NUM
ejpam-6173	817	9	.	.	PUNCT
ejpam-6173	818	1	[	[	X
ejpam-6173	818	2	32	32	NUM
ejpam-6173	818	3	]	]	PUNCT
ejpam-6173	818	4	h.	h.	PROPN
ejpam-6173	818	5	h.	h.	PROPN
ejpam-6173	818	6	bauschke	bauschke	PROPN
ejpam-6173	818	7	,	,	PUNCT
ejpam-6173	818	8	j.	j.	PROPN
ejpam-6173	818	9	m.	m.	PROPN
ejpam-6173	818	10	borwein	borwein	PROPN
ejpam-6173	818	11	,	,	PUNCT
ejpam-6173	818	12	and	and	CCONJ
ejpam-6173	818	13	p.	p.	NOUN
ejpam-6173	818	14	l.	l.	PROPN
ejpam-6173	818	15	combettes	combettes	PROPN
ejpam-6173	818	16	.	.	PUNCT
ejpam-6173	819	1	essential	essential	ADJ
ejpam-6173	819	2	smoothness	smoothness	NOUN
ejpam-6173	819	3	,	,	PUNCT
ejpam-6173	819	4	essential	essential	ADJ
ejpam-6173	819	5	strict	strict	ADJ
ejpam-6173	819	6	convexity	convexity	NOUN
ejpam-6173	819	7	,	,	PUNCT
ejpam-6173	819	8	and	and	CCONJ
ejpam-6173	819	9	legendre	legendre	PROPN
ejpam-6173	819	10	functions	function	NOUN
ejpam-6173	819	11	in	in	ADP
ejpam-6173	819	12	banach	banach	NOUN
ejpam-6173	819	13	spaces	space	NOUN
ejpam-6173	819	14	.	.	PUNCT
ejpam-6173	820	1	communications	communication	NOUN
ejpam-6173	820	2	in	in	ADP
ejpam-6173	820	3	contemporary	contemporary	ADJ
ejpam-6173	820	4	mathematics	mathematic	NOUN
ejpam-6173	820	5	,	,	PUNCT
ejpam-6173	820	6	3:615–647	3:615–647	NUM
ejpam-6173	820	7	,	,	PUNCT
ejpam-6173	820	8	2001	2001	NUM
ejpam-6173	820	9	.	.	PUNCT
ejpam-6173	821	1	[	[	X
ejpam-6173	821	2	33	33	NUM
ejpam-6173	821	3	]	]	PUNCT
ejpam-6173	821	4	r.	r.	PROPN
ejpam-6173	821	5	r.	r.	PROPN
ejpam-6173	821	6	phelps	phelps	PROPN
ejpam-6173	821	7	.	.	PUNCT
ejpam-6173	822	1	convex	convex	NOUN
ejpam-6173	822	2	functions	function	NOUN
ejpam-6173	822	3	,	,	PUNCT
ejpam-6173	822	4	monotone	monotone	ADJ
ejpam-6173	822	5	operators	operator	NOUN
ejpam-6173	822	6	,	,	PUNCT
ejpam-6173	822	7	and	and	CCONJ
ejpam-6173	822	8	differentiability	differentiability	NOUN
ejpam-6173	822	9	,	,	PUNCT
ejpam-6173	822	10	volume	volume	NOUN
ejpam-6173	822	11	1364	1364	NUM
ejpam-6173	822	12	of	of	ADP
ejpam-6173	822	13	lecture	lecture	NOUN
ejpam-6173	822	14	notes	note	NOUN
ejpam-6173	822	15	in	in	ADP
ejpam-6173	822	16	mathematics	mathematic	NOUN
ejpam-6173	822	17	.	.	PUNCT
ejpam-6173	823	1	springer	springer	NOUN
ejpam-6173	823	2	-	-	PUNCT
ejpam-6173	823	3	verlag	verlag	PROPN
ejpam-6173	823	4	,	,	PUNCT
ejpam-6173	823	5	berlin	berlin	PROPN
ejpam-6173	823	6	,	,	PUNCT
ejpam-6173	823	7	second	second	ADJ
ejpam-6173	823	8	edition	edition	NOUN
ejpam-6173	823	9	,	,	PUNCT
ejpam-6173	823	10	1993	1993	NUM
ejpam-6173	823	11	.	.	PUNCT
ejpam-6173	824	1	[	[	X
ejpam-6173	824	2	34	34	NUM
ejpam-6173	824	3	]	]	X
ejpam-6173	824	4	d.	d.	PROPN
ejpam-6173	824	5	reem	reem	PROPN
ejpam-6173	824	6	and	and	CCONJ
ejpam-6173	824	7	s.	s.	PROPN
ejpam-6173	824	8	reich	reich	PROPN
ejpam-6173	824	9	.	.	PUNCT
ejpam-6173	825	1	solutions	solution	NOUN
ejpam-6173	825	2	to	to	PART
ejpam-6173	825	3	inexact	inexact	VERB
ejpam-6173	825	4	resolvent	resolvent	ADJ
ejpam-6173	825	5	inclusion	inclusion	NOUN
ejpam-6173	825	6	problems	problem	NOUN
ejpam-6173	825	7	with	with	ADP
ejpam-6173	825	8	applications	application	NOUN
ejpam-6173	825	9	to	to	PART
ejpam-6173	825	10	nonlinear	nonlinear	VERB
ejpam-6173	825	11	analysis	analysis	NOUN
ejpam-6173	825	12	and	and	CCONJ
ejpam-6173	825	13	optimization	optimization	NOUN
ejpam-6173	825	14	.	.	PUNCT
ejpam-6173	826	1	rendiconti	rendiconti	ADJ
ejpam-6173	826	2	del	del	PROPN
ejpam-6173	826	3	circolo	circolo	PROPN
ejpam-6173	826	4	matematico	matematico	NOUN
ejpam-6173	826	5	di	di	NOUN
ejpam-6173	826	6	palermo	palermo	NOUN
ejpam-6173	826	7	,	,	PUNCT
ejpam-6173	826	8	67:337–371	67:337–371	PROPN
ejpam-6173	826	9	,	,	PUNCT
ejpam-6173	826	10	2018	2018	NUM
ejpam-6173	826	11	.	.	PUNCT
ejpam-6173	827	1	[	[	X
ejpam-6173	827	2	35	35	NUM
ejpam-6173	827	3	]	]	X
ejpam-6173	827	4	y.	y.	PROPN
ejpam-6173	827	5	i.	i.	PROPN
ejpam-6173	827	6	alber	alber	PROPN
ejpam-6173	827	7	.	.	PUNCT
ejpam-6173	828	1	metric	metric	ADJ
ejpam-6173	828	2	and	and	CCONJ
ejpam-6173	828	3	generalized	generalized	ADJ
ejpam-6173	828	4	projection	projection	NOUN
ejpam-6173	828	5	operators	operator	NOUN
ejpam-6173	828	6	in	in	ADP
ejpam-6173	828	7	banach	banach	NOUN
ejpam-6173	828	8	spaces	space	NOUN
ejpam-6173	828	9	:	:	PUNCT
ejpam-6173	828	10	properties	property	NOUN
ejpam-6173	828	11	and	and	CCONJ
ejpam-6173	828	12	applications	application	NOUN
ejpam-6173	828	13	.	.	PUNCT
ejpam-6173	829	1	in	in	ADP
ejpam-6173	829	2	a.	a.	PROPN
ejpam-6173	829	3	g.	g.	PROPN
ejpam-6173	829	4	kartsatos	kartsatos	PROPN
ejpam-6173	829	5	,	,	PUNCT
ejpam-6173	829	6	editor	editor	NOUN
ejpam-6173	829	7	,	,	PUNCT
ejpam-6173	829	8	theory	theory	NOUN
ejpam-6173	829	9	and	and	CCONJ
ejpam-6173	829	10	applications	application	NOUN
ejpam-6173	829	11	of	of	ADP
ejpam-6173	829	12	nonlinear	nonlinear	ADJ
ejpam-6173	829	13	operators	operator	NOUN
ejpam-6173	829	14	of	of	ADP
ejpam-6173	829	15	accretive	accretive	ADJ
ejpam-6173	829	16	and	and	CCONJ
ejpam-6173	829	17	monotone	monotone	ADJ
ejpam-6173	829	18	type	type	NOUN
ejpam-6173	829	19	,	,	PUNCT
ejpam-6173	829	20	pages	page	NOUN
ejpam-6173	829	21	15–50	15–50	NUM
ejpam-6173	829	22	.	.	PUNCT
ejpam-6173	830	1	marcel	marcel	PROPN
ejpam-6173	830	2	dekker	dekker	PROPN
ejpam-6173	830	3	,	,	PUNCT
ejpam-6173	830	4	new	new	PROPN
ejpam-6173	830	5	york	york	PROPN
ejpam-6173	830	6	,	,	PUNCT
ejpam-6173	830	7	1996	1996	NUM
ejpam-6173	830	8	.	.	PUNCT
ejpam-6173	831	1	[	[	X
ejpam-6173	831	2	36	36	NUM
ejpam-6173	831	3	]	]	X
ejpam-6173	831	4	d.	d.	PROPN
ejpam-6173	831	5	butnariu	butnariu	PROPN
ejpam-6173	831	6	,	,	PUNCT
ejpam-6173	831	7	s.	s.	PROPN
ejpam-6173	831	8	reich	reich	PROPN
ejpam-6173	831	9	,	,	PUNCT
ejpam-6173	831	10	and	and	CCONJ
ejpam-6173	831	11	a.	a.	PROPN
ejpam-6173	831	12	j.	j.	PROPN
ejpam-6173	831	13	zaslavski	zaslavski	PROPN
ejpam-6173	831	14	.	.	PUNCT
ejpam-6173	832	1	there	there	PRON
ejpam-6173	832	2	are	be	VERB
ejpam-6173	832	3	many	many	ADJ
ejpam-6173	832	4	totally	totally	ADV
ejpam-6173	832	5	convex	convex	NOUN
ejpam-6173	832	6	functions	function	NOUN
ejpam-6173	832	7	.	.	PUNCT
ejpam-6173	833	1	journal	journal	NOUN
ejpam-6173	833	2	of	of	ADP
ejpam-6173	833	3	convex	convex	PROPN
ejpam-6173	833	4	analysis	analysis	NOUN
ejpam-6173	833	5	,	,	PUNCT
ejpam-6173	833	6	13:623–632	13:623–632	NUM
ejpam-6173	833	7	,	,	PUNCT
ejpam-6173	833	8	2006	2006	NUM
ejpam-6173	833	9	.	.	PUNCT
ejpam-6173	834	1	[	[	X
ejpam-6173	834	2	37	37	NUM
ejpam-6173	834	3	]	]	X
ejpam-6173	834	4	d.	d.	PROPN
ejpam-6173	834	5	butnariu	butnariu	PROPN
ejpam-6173	834	6	and	and	CCONJ
ejpam-6173	834	7	a.	a.	NOUN
ejpam-6173	834	8	n.	n.	PROPN
ejpam-6173	834	9	iusem	iusem	PROPN
ejpam-6173	834	10	.	.	PUNCT
ejpam-6173	835	1	totally	totally	ADV
ejpam-6173	835	2	convex	convex	VERB
ejpam-6173	835	3	functions	function	NOUN
ejpam-6173	835	4	for	for	ADP
ejpam-6173	835	5	fixed	fix	VERB
ejpam-6173	835	6	points	point	NOUN
ejpam-6173	835	7	computation	computation	NOUN
ejpam-6173	835	8	and	and	CCONJ
ejpam-6173	835	9	infinite	infinite	ADJ
ejpam-6173	835	10	dimensional	dimensional	ADJ
ejpam-6173	835	11	optimization	optimization	NOUN
ejpam-6173	835	12	,	,	PUNCT
ejpam-6173	835	13	volume	volume	NOUN
ejpam-6173	835	14	40	40	NUM
ejpam-6173	835	15	of	of	ADP
ejpam-6173	835	16	applied	applied	ADJ
ejpam-6173	835	17	optimization	optimization	NOUN
ejpam-6173	835	18	.	.	PUNCT
ejpam-6173	836	1	kluwer	kluwer	PROPN
ejpam-6173	836	2	academic	academic	PROPN
ejpam-6173	836	3	,	,	PUNCT
ejpam-6173	836	4	dordrecht	dordrecht	PROPN
ejpam-6173	836	5	,	,	PUNCT
ejpam-6173	836	6	2000	2000	NUM
ejpam-6173	836	7	.	.	PUNCT
ejpam-6173	837	1	[	[	X
ejpam-6173	837	2	38	38	NUM
ejpam-6173	837	3	]	]	PUNCT
ejpam-6173	837	4	s.	s.	PROPN
ejpam-6173	837	5	reich	reich	PROPN
ejpam-6173	837	6	and	and	CCONJ
ejpam-6173	837	7	s.	s.	PROPN
ejpam-6173	837	8	sabach	sabach	PROPN
ejpam-6173	837	9	.	.	PUNCT
ejpam-6173	838	1	two	two	NUM
ejpam-6173	838	2	strong	strong	ADJ
ejpam-6173	838	3	convergence	convergence	NOUN
ejpam-6173	838	4	theorems	theorem	NOUN
ejpam-6173	838	5	for	for	ADP
ejpam-6173	838	6	a	a	DET
ejpam-6173	838	7	proximal	proximal	ADJ
ejpam-6173	838	8	method	method	NOUN
ejpam-6173	838	9	in	in	ADP
ejpam-6173	838	10	reflexive	reflexive	ADJ
ejpam-6173	838	11	banach	banach	NOUN
ejpam-6173	838	12	spaces	space	NOUN
ejpam-6173	838	13	.	.	PUNCT
ejpam-6173	839	1	numerical	numerical	ADJ
ejpam-6173	839	2	functional	functional	ADJ
ejpam-6173	839	3	analysis	analysis	NOUN
ejpam-6173	839	4	and	and	CCONJ
ejpam-6173	839	5	optimization	optimization	NOUN
ejpam-6173	839	6	,	,	PUNCT
ejpam-6173	839	7	31:22–44	31:22–44	NUM
ejpam-6173	839	8	,	,	PUNCT
ejpam-6173	839	9	2010	2010	NUM
ejpam-6173	839	10	.	.	PUNCT
ejpam-6173	840	1	[	[	X
ejpam-6173	840	2	39	39	NUM
ejpam-6173	840	3	]	]	PUNCT
ejpam-6173	840	4	j.	j.	PROPN
ejpam-6173	840	5	b.	b.	PROPN
ejpam-6173	840	6	hiriart	hiriart	PROPN
ejpam-6173	840	7	-	-	PUNCT
ejpam-6173	840	8	urruty	urruty	NOUN
ejpam-6173	840	9	and	and	CCONJ
ejpam-6173	840	10	c.	c.	PROPN
ejpam-6173	840	11	lemaréchal	lemaréchal	PROPN
ejpam-6173	840	12	.	.	PUNCT
ejpam-6173	841	1	convex	convex	VERB
ejpam-6173	841	2	analysis	analysis	NOUN
ejpam-6173	841	3	and	and	CCONJ
ejpam-6173	841	4	minimization	minimization	NOUN
ejpam-6173	841	5	algorithms	algorithms	PROPN
ejpam-6173	841	6	ii	ii	PROPN
ejpam-6173	841	7	,	,	PUNCT
ejpam-6173	841	8	volume	volume	NOUN
ejpam-6173	841	9	306	306	NUM
ejpam-6173	841	10	of	of	ADP
ejpam-6173	841	11	grundlehren	grundlehren	PROPN
ejpam-6173	841	12	der	der	PROPN
ejpam-6173	841	13	mathematischen	mathematischen	PROPN
ejpam-6173	841	14	wissenschaften	wissenschaften	PROPN
ejpam-6173	841	15	.	.	PUNCT
ejpam-6173	842	1	springerverlag	springerverlag	PROPN
ejpam-6173	842	2	,	,	PUNCT
ejpam-6173	842	3	1993	1993	NUM
ejpam-6173	842	4	.	.	PUNCT
ejpam-6173	843	1	[	[	X
ejpam-6173	843	2	40	40	NUM
ejpam-6173	843	3	]	]	PUNCT
ejpam-6173	843	4	d.	d.	PROPN
ejpam-6173	843	5	butnariu	butnariu	PROPN
ejpam-6173	843	6	and	and	CCONJ
ejpam-6173	843	7	e.	e.	PROPN
ejpam-6173	843	8	resmerita	resmerita	PROPN
ejpam-6173	843	9	.	.	PUNCT
ejpam-6173	844	1	bregman	bregman	NOUN
ejpam-6173	844	2	distances	distance	NOUN
ejpam-6173	844	3	,	,	PUNCT
ejpam-6173	844	4	totally	totally	ADV
ejpam-6173	844	5	convex	convex	NOUN
ejpam-6173	844	6	functions	function	NOUN
ejpam-6173	844	7	and	and	CCONJ
ejpam-6173	844	8	v.	v.	ADP
ejpam-6173	844	9	darvish	darvish	NOUN
ejpam-6173	844	10	et	et	PROPN
ejpam-6173	844	11	al	al	PROPN
ejpam-6173	844	12	.	.	PUNCT
ejpam-6173	844	13	/	/	SYM
ejpam-6173	844	14	eur	eur	PROPN
ejpam-6173	844	15	.	.	PUNCT
ejpam-6173	845	1	j.	j.	PROPN
ejpam-6173	845	2	pure	pure	PROPN
ejpam-6173	845	3	appl	appl	PROPN
ejpam-6173	845	4	.	.	PROPN
ejpam-6173	845	5	math	math	PROPN
ejpam-6173	845	6	,	,	PUNCT
ejpam-6173	845	7	18	18	NUM
ejpam-6173	845	8	(	(	PUNCT
ejpam-6173	845	9	3	3	NUM
ejpam-6173	845	10	)	)	PUNCT
ejpam-6173	845	11	(	(	PUNCT
ejpam-6173	845	12	2025	2025	NUM
ejpam-6173	845	13	)	)	PUNCT
ejpam-6173	845	14	,	,	PUNCT
ejpam-6173	845	15	6173	6173	NUM
ejpam-6173	845	16	31	31	NUM
ejpam-6173	845	17	of	of	ADP
ejpam-6173	845	18	32	32	NUM
ejpam-6173	845	19	a	a	DET
ejpam-6173	845	20	method	method	NOUN
ejpam-6173	845	21	for	for	ADP
ejpam-6173	845	22	solving	solve	VERB
ejpam-6173	845	23	operator	operator	NOUN
ejpam-6173	845	24	equations	equation	NOUN
ejpam-6173	845	25	in	in	ADP
ejpam-6173	845	26	banach	banach	NOUN
ejpam-6173	845	27	spaces	space	NOUN
ejpam-6173	845	28	.	.	PUNCT
ejpam-6173	846	1	abstract	abstract	ADJ
ejpam-6173	846	2	and	and	CCONJ
ejpam-6173	846	3	applied	apply	VERB
ejpam-6173	846	4	analysis	analysis	NOUN
ejpam-6173	846	5	,	,	PUNCT
ejpam-6173	846	6	2006:1–39	2006:1–39	NUM
ejpam-6173	846	7	,	,	PUNCT
ejpam-6173	846	8	2006	2006	NUM
ejpam-6173	846	9	.	.	PUNCT
ejpam-6173	847	1	article	article	NOUN
ejpam-6173	847	2	i	i	PROPN
ejpam-6173	847	3	d	d	PROPN
ejpam-6173	847	4	84919	84919	NUM
ejpam-6173	847	5	.	.	PUNCT
ejpam-6173	848	1	[	[	X
ejpam-6173	848	2	41	41	NUM
ejpam-6173	848	3	]	]	X
ejpam-6173	848	4	s.	s.	PROPN
ejpam-6173	848	5	reich	reich	PROPN
ejpam-6173	848	6	and	and	CCONJ
ejpam-6173	848	7	s.	s.	PROPN
ejpam-6173	848	8	sabach	sabach	PROPN
ejpam-6173	848	9	.	.	PUNCT
ejpam-6173	849	1	a	a	DET
ejpam-6173	849	2	strong	strong	ADJ
ejpam-6173	849	3	convergence	convergence	NOUN
ejpam-6173	849	4	theorem	theorem	NOUN
ejpam-6173	849	5	for	for	ADP
ejpam-6173	849	6	a	a	DET
ejpam-6173	849	7	proximal	proximal	ADJ
ejpam-6173	849	8	-	-	PUNCT
ejpam-6173	849	9	type	type	NOUN
ejpam-6173	849	10	algorithm	algorithm	NOUN
ejpam-6173	849	11	in	in	ADP
ejpam-6173	849	12	reflexive	reflexive	ADJ
ejpam-6173	849	13	banach	banach	NOUN
ejpam-6173	849	14	spaces	space	NOUN
ejpam-6173	849	15	.	.	PUNCT
ejpam-6173	850	1	journal	journal	PROPN
ejpam-6173	850	2	of	of	ADP
ejpam-6173	850	3	nonlinear	nonlinear	ADJ
ejpam-6173	850	4	and	and	CCONJ
ejpam-6173	850	5	convex	convex	ADJ
ejpam-6173	850	6	analysis	analysis	NOUN
ejpam-6173	850	7	,	,	PUNCT
ejpam-6173	850	8	10:471–485	10:471–485	NUM
ejpam-6173	850	9	,	,	PUNCT
ejpam-6173	850	10	2009	2009	NUM
ejpam-6173	850	11	.	.	PUNCT
ejpam-6173	851	1	[	[	X
ejpam-6173	851	2	42	42	NUM
ejpam-6173	851	3	]	]	PUNCT
ejpam-6173	851	4	s.	s.	PROPN
ejpam-6173	851	5	reich	reich	PROPN
ejpam-6173	851	6	.	.	PUNCT
ejpam-6173	852	1	a	a	DET
ejpam-6173	852	2	weak	weak	ADJ
ejpam-6173	852	3	convergence	convergence	NOUN
ejpam-6173	852	4	theorem	theorem	NOUN
ejpam-6173	852	5	for	for	ADP
ejpam-6173	852	6	the	the	DET
ejpam-6173	852	7	alternating	alternating	NOUN
ejpam-6173	852	8	method	method	NOUN
ejpam-6173	852	9	with	with	ADP
ejpam-6173	852	10	bregman	bregman	NOUN
ejpam-6173	852	11	distances	distance	NOUN
ejpam-6173	852	12	.	.	PUNCT
ejpam-6173	853	1	in	in	ADP
ejpam-6173	853	2	a.	a.	PROPN
ejpam-6173	853	3	g.	g.	PROPN
ejpam-6173	853	4	kartsatos	kartsatos	PROPN
ejpam-6173	853	5	,	,	PUNCT
ejpam-6173	853	6	editor	editor	NOUN
ejpam-6173	853	7	,	,	PUNCT
ejpam-6173	853	8	theory	theory	NOUN
ejpam-6173	853	9	and	and	CCONJ
ejpam-6173	853	10	applications	application	NOUN
ejpam-6173	853	11	of	of	ADP
ejpam-6173	853	12	nonlinear	nonlinear	ADJ
ejpam-6173	853	13	operators	operator	NOUN
ejpam-6173	853	14	of	of	ADP
ejpam-6173	853	15	accretive	accretive	ADJ
ejpam-6173	853	16	and	and	CCONJ
ejpam-6173	853	17	monotone	monotone	ADJ
ejpam-6173	853	18	type	type	NOUN
ejpam-6173	853	19	,	,	PUNCT
ejpam-6173	853	20	pages	page	NOUN
ejpam-6173	853	21	313–318	313–318	NUM
ejpam-6173	853	22	.	.	PUNCT
ejpam-6173	853	23	marcel	marcel	PROPN
ejpam-6173	853	24	dekker	dekker	PROPN
ejpam-6173	853	25	,	,	PUNCT
ejpam-6173	853	26	new	new	PROPN
ejpam-6173	853	27	york	york	PROPN
ejpam-6173	853	28	,	,	PUNCT
ejpam-6173	853	29	1996	1996	NUM
ejpam-6173	853	30	.	.	PUNCT
ejpam-6173	854	1	[	[	X
ejpam-6173	854	2	43	43	NUM
ejpam-6173	854	3	]	]	X
ejpam-6173	854	4	d.	d.	PROPN
ejpam-6173	854	5	butnariu	butnariu	PROPN
ejpam-6173	854	6	,	,	PUNCT
ejpam-6173	854	7	s.	s.	PROPN
ejpam-6173	854	8	reich	reich	PROPN
ejpam-6173	854	9	,	,	PUNCT
ejpam-6173	854	10	and	and	CCONJ
ejpam-6173	854	11	a.	a.	PROPN
ejpam-6173	854	12	j.	j.	PROPN
ejpam-6173	854	13	zaslavski	zaslavski	PROPN
ejpam-6173	854	14	.	.	PUNCT
ejpam-6173	855	1	asymptotic	asymptotic	ADJ
ejpam-6173	855	2	behavior	behavior	NOUN
ejpam-6173	855	3	of	of	ADP
ejpam-6173	855	4	relatively	relatively	ADV
ejpam-6173	855	5	nonexpansive	nonexpansive	ADJ
ejpam-6173	855	6	operators	operator	NOUN
ejpam-6173	855	7	in	in	ADP
ejpam-6173	855	8	banach	banach	NOUN
ejpam-6173	855	9	spaces	space	NOUN
ejpam-6173	855	10	.	.	PUNCT
ejpam-6173	856	1	journal	journal	NOUN
ejpam-6173	856	2	of	of	ADP
ejpam-6173	856	3	applied	apply	VERB
ejpam-6173	856	4	analysis	analysis	NOUN
ejpam-6173	856	5	,	,	PUNCT
ejpam-6173	856	6	7:151–174	7:151–174	NUM
ejpam-6173	856	7	,	,	PUNCT
ejpam-6173	856	8	2001	2001	NUM
ejpam-6173	856	9	.	.	PUNCT
ejpam-6173	857	1	[	[	X
ejpam-6173	857	2	44	44	NUM
ejpam-6173	857	3	]	]	PUNCT
ejpam-6173	857	4	r.	r.	PROPN
ejpam-6173	857	5	e.	e.	PROPN
ejpam-6173	857	6	bruck	bruck	PROPN
ejpam-6173	857	7	and	and	CCONJ
ejpam-6173	857	8	s.	s.	PROPN
ejpam-6173	857	9	reich	reich	PROPN
ejpam-6173	857	10	.	.	PROPN
ejpam-6173	858	1	nonexpansive	nonexpansive	ADJ
ejpam-6173	858	2	projections	projection	NOUN
ejpam-6173	858	3	and	and	CCONJ
ejpam-6173	858	4	resolvents	resolvent	NOUN
ejpam-6173	858	5	of	of	ADP
ejpam-6173	858	6	accretive	accretive	ADJ
ejpam-6173	858	7	operators	operator	NOUN
ejpam-6173	858	8	in	in	ADP
ejpam-6173	858	9	banach	banach	NOUN
ejpam-6173	858	10	spaces	space	NOUN
ejpam-6173	858	11	.	.	PUNCT
ejpam-6173	859	1	houston	houston	PROPN
ejpam-6173	859	2	journal	journal	PROPN
ejpam-6173	859	3	of	of	ADP
ejpam-6173	859	4	mathematics	mathematic	NOUN
ejpam-6173	859	5	,	,	PUNCT
ejpam-6173	859	6	3:459–470	3:459–470	NUM
ejpam-6173	859	7	,	,	PUNCT
ejpam-6173	859	8	1977	1977	NUM
ejpam-6173	859	9	.	.	PUNCT
ejpam-6173	860	1	[	[	X
ejpam-6173	860	2	45	45	NUM
ejpam-6173	860	3	]	]	PUNCT
ejpam-6173	860	4	s.	s.	PROPN
ejpam-6173	860	5	reich	reich	PROPN
ejpam-6173	860	6	and	and	CCONJ
ejpam-6173	860	7	s.	s.	PROPN
ejpam-6173	860	8	sabach	sabach	PROPN
ejpam-6173	860	9	.	.	PUNCT
ejpam-6173	861	1	two	two	NUM
ejpam-6173	861	2	strong	strong	ADJ
ejpam-6173	861	3	convergence	convergence	NOUN
ejpam-6173	861	4	theorems	theorem	NOUN
ejpam-6173	861	5	for	for	ADP
ejpam-6173	861	6	bregman	bregman	NOUN
ejpam-6173	861	7	strongly	strongly	ADV
ejpam-6173	861	8	nonexpansive	nonexpansive	ADJ
ejpam-6173	861	9	operators	operator	NOUN
ejpam-6173	861	10	in	in	ADP
ejpam-6173	861	11	reflexive	reflexive	ADJ
ejpam-6173	861	12	banach	banach	NOUN
ejpam-6173	861	13	spaces	space	VERB
ejpam-6173	861	14	.	.	PUNCT
ejpam-6173	862	1	nonlinear	nonlinear	ADJ
ejpam-6173	862	2	analysis	analysis	NOUN
ejpam-6173	862	3	,	,	PUNCT
ejpam-6173	862	4	73:122–135	73:122–135	NUM
ejpam-6173	862	5	,	,	PUNCT
ejpam-6173	862	6	2010	2010	NUM
ejpam-6173	862	7	.	.	PUNCT
ejpam-6173	863	1	[	[	X
ejpam-6173	863	2	46	46	NUM
ejpam-6173	863	3	]	]	X
ejpam-6173	863	4	f.	f.	PROPN
ejpam-6173	863	5	kohsaka	kohsaka	PROPN
ejpam-6173	863	6	and	and	CCONJ
ejpam-6173	863	7	w.	w.	PROPN
ejpam-6173	863	8	takahashi	takahashi	PROPN
ejpam-6173	863	9	.	.	PUNCT
ejpam-6173	864	1	proximal	proximal	ADJ
ejpam-6173	864	2	point	point	NOUN
ejpam-6173	864	3	algorithms	algorithm	NOUN
ejpam-6173	864	4	with	with	ADP
ejpam-6173	864	5	bregman	bregman	NOUN
ejpam-6173	864	6	functions	function	NOUN
ejpam-6173	864	7	in	in	ADP
ejpam-6173	864	8	banach	banach	NOUN
ejpam-6173	864	9	spaces	space	NOUN
ejpam-6173	864	10	.	.	PUNCT
ejpam-6173	865	1	journal	journal	PROPN
ejpam-6173	865	2	of	of	ADP
ejpam-6173	865	3	nonlinear	nonlinear	ADJ
ejpam-6173	865	4	and	and	CCONJ
ejpam-6173	865	5	convex	convex	ADJ
ejpam-6173	865	6	analysis	analysis	NOUN
ejpam-6173	865	7	,	,	PUNCT
ejpam-6173	865	8	6:505–523	6:505–523	NOUN
ejpam-6173	865	9	,	,	PUNCT
ejpam-6173	865	10	2005	2005	NUM
ejpam-6173	865	11	.	.	PUNCT
ejpam-6173	866	1	[	[	X
ejpam-6173	866	2	47	47	NUM
ejpam-6173	866	3	]	]	X
ejpam-6173	866	4	v.	v.	ADP
ejpam-6173	866	5	mart́ın	mart́ın	NOUN
ejpam-6173	866	6	-	-	PUNCT
ejpam-6173	866	7	márquez	márquez	PROPN
ejpam-6173	866	8	,	,	PUNCT
ejpam-6173	866	9	s.	s.	PROPN
ejpam-6173	866	10	reich	reich	PROPN
ejpam-6173	866	11	,	,	PUNCT
ejpam-6173	866	12	and	and	CCONJ
ejpam-6173	866	13	s.	s.	PROPN
ejpam-6173	866	14	sabach	sabach	PROPN
ejpam-6173	866	15	.	.	PUNCT
ejpam-6173	867	1	iterative	iterative	NOUN
ejpam-6173	867	2	methods	method	NOUN
ejpam-6173	867	3	for	for	ADP
ejpam-6173	867	4	approximating	approximate	VERB
ejpam-6173	867	5	fixed	fix	VERB
ejpam-6173	867	6	points	point	NOUN
ejpam-6173	867	7	of	of	ADP
ejpam-6173	867	8	bregman	bregman	PROPN
ejpam-6173	867	9	nonexpansive	nonexpansive	PROPN
ejpam-6173	867	10	operators	operator	NOUN
ejpam-6173	867	11	.	.	PUNCT
ejpam-6173	868	1	discrete	discrete	ADJ
ejpam-6173	868	2	and	and	CCONJ
ejpam-6173	868	3	continuous	continuous	ADJ
ejpam-6173	868	4	dynamical	dynamical	ADJ
ejpam-6173	868	5	systems	system	NOUN
ejpam-6173	868	6	series	series	NOUN
ejpam-6173	868	7	s	s	PART
ejpam-6173	868	8	,	,	PUNCT
ejpam-6173	868	9	6:1043–1063	6:1043–1063	NUM
ejpam-6173	868	10	,	,	PUNCT
ejpam-6173	868	11	2013	2013	NUM
ejpam-6173	868	12	.	.	PUNCT
ejpam-6173	869	1	[	[	X
ejpam-6173	869	2	48	48	NUM
ejpam-6173	869	3	]	]	PUNCT
ejpam-6173	869	4	c.	c.	PROPN
ejpam-6173	869	5	zălinescu	zălinescu	PROPN
ejpam-6173	869	6	.	.	PUNCT
ejpam-6173	870	1	convex	convex	VERB
ejpam-6173	870	2	analysis	analysis	NOUN
ejpam-6173	870	3	in	in	ADP
ejpam-6173	870	4	general	general	ADJ
ejpam-6173	870	5	vector	vector	NOUN
ejpam-6173	870	6	spaces	space	NOUN
ejpam-6173	870	7	.	.	PUNCT
ejpam-6173	871	1	world	world	NOUN
ejpam-6173	871	2	scientific	scientific	ADJ
ejpam-6173	871	3	,	,	PUNCT
ejpam-6173	871	4	river	river	NOUN
ejpam-6173	871	5	edge	edge	NOUN
ejpam-6173	871	6	,	,	PUNCT
ejpam-6173	871	7	nj	nj	PROPN
ejpam-6173	871	8	,	,	PUNCT
ejpam-6173	871	9	2002	2002	NUM
ejpam-6173	871	10	.	.	PUNCT
ejpam-6173	872	1	[	[	X
ejpam-6173	872	2	49	49	NUM
ejpam-6173	872	3	]	]	PUNCT
ejpam-6173	872	4	s.	s.	PROPN
ejpam-6173	872	5	reich	reich	PROPN
ejpam-6173	872	6	and	and	CCONJ
ejpam-6173	872	7	s.	s.	PROPN
ejpam-6173	872	8	sabach	sabach	PROPN
ejpam-6173	872	9	.	.	PUNCT
ejpam-6173	873	1	existence	existence	NOUN
ejpam-6173	873	2	and	and	CCONJ
ejpam-6173	873	3	approximation	approximation	NOUN
ejpam-6173	873	4	of	of	ADP
ejpam-6173	873	5	fixed	fix	VERB
ejpam-6173	873	6	points	point	NOUN
ejpam-6173	873	7	of	of	ADP
ejpam-6173	873	8	bregman	bregman	NOUN
ejpam-6173	873	9	firmly	firmly	ADV
ejpam-6173	873	10	nonexpansive	nonexpansive	ADJ
ejpam-6173	873	11	mappings	mapping	NOUN
ejpam-6173	873	12	in	in	ADP
ejpam-6173	873	13	reflexive	reflexive	ADJ
ejpam-6173	873	14	banach	banach	NOUN
ejpam-6173	873	15	spaces	space	VERB
ejpam-6173	873	16	.	.	PUNCT
ejpam-6173	874	1	in	in	ADP
ejpam-6173	874	2	fixed	fix	VERB
ejpam-6173	874	3	-	-	PUNCT
ejpam-6173	874	4	point	point	NOUN
ejpam-6173	874	5	algorithms	algorithm	NOUN
ejpam-6173	874	6	for	for	ADP
ejpam-6173	874	7	inverse	inverse	NOUN
ejpam-6173	874	8	problems	problem	NOUN
ejpam-6173	874	9	in	in	ADP
ejpam-6173	874	10	science	science	NOUN
ejpam-6173	874	11	and	and	CCONJ
ejpam-6173	874	12	engineering	engineering	NOUN
ejpam-6173	874	13	,	,	PUNCT
ejpam-6173	874	14	volume	volume	NOUN
ejpam-6173	874	15	49	49	NUM
ejpam-6173	874	16	of	of	ADP
ejpam-6173	874	17	optimization	optimization	NOUN
ejpam-6173	874	18	and	and	CCONJ
ejpam-6173	874	19	its	its	PRON
ejpam-6173	874	20	applications	application	NOUN
ejpam-6173	874	21	,	,	PUNCT
ejpam-6173	874	22	pages	page	NOUN
ejpam-6173	874	23	301–316	301–316	NUM
ejpam-6173	874	24	.	.	NOUN
ejpam-6173	874	25	2011	2011	NUM
ejpam-6173	874	26	.	.	PUNCT
ejpam-6173	875	1	[	[	X
ejpam-6173	875	2	50	50	NUM
ejpam-6173	875	3	]	]	X
ejpam-6173	875	4	v.	v.	X
ejpam-6173	875	5	darvish	darvish	PROPN
ejpam-6173	875	6	.	.	PUNCT
ejpam-6173	876	1	strong	strong	ADJ
ejpam-6173	876	2	convergence	convergence	NOUN
ejpam-6173	876	3	theorem	theorem	VERB
ejpam-6173	876	4	for	for	ADP
ejpam-6173	876	5	generalized	generalized	ADJ
ejpam-6173	876	6	mixed	mixed	ADJ
ejpam-6173	876	7	equilibrium	equilibrium	NOUN
ejpam-6173	876	8	problems	problem	NOUN
ejpam-6173	876	9	and	and	CCONJ
ejpam-6173	876	10	bregman	bregman	NOUN
ejpam-6173	876	11	nonexpansive	nonexpansive	ADJ
ejpam-6173	876	12	mapping	mapping	NOUN
ejpam-6173	876	13	in	in	ADP
ejpam-6173	876	14	banach	banach	NOUN
ejpam-6173	876	15	spaces	space	NOUN
ejpam-6173	876	16	.	.	PUNCT
ejpam-6173	877	1	mathematica	mathematica	PROPN
ejpam-6173	877	2	moravica	moravica	PROPN
ejpam-6173	877	3	,	,	PUNCT
ejpam-6173	877	4	20(1):69–87	20(1):69–87	NUM
ejpam-6173	877	5	,	,	PUNCT
ejpam-6173	877	6	2016	2016	NUM
ejpam-6173	877	7	.	.	PUNCT
ejpam-6173	878	1	[	[	X
ejpam-6173	878	2	51	51	NUM
ejpam-6173	878	3	]	]	PUNCT
ejpam-6173	878	4	e.	e.	PROPN
ejpam-6173	878	5	naraghirad	naraghirad	PROPN
ejpam-6173	878	6	and	and	CCONJ
ejpam-6173	878	7	j.	j.	PROPN
ejpam-6173	878	8	c.	c.	PROPN
ejpam-6173	878	9	yao	yao	PROPN
ejpam-6173	878	10	.	.	PUNCT
ejpam-6173	879	1	bregman	bregman	PROPN
ejpam-6173	879	2	weak	weak	ADJ
ejpam-6173	879	3	relatively	relatively	ADV
ejpam-6173	879	4	nonexpansive	nonexpansive	ADJ
ejpam-6173	879	5	mappings	mapping	NOUN
ejpam-6173	879	6	in	in	ADP
ejpam-6173	879	7	banach	banach	NOUN
ejpam-6173	879	8	space	space	NOUN
ejpam-6173	879	9	.	.	PUNCT
ejpam-6173	880	1	fixed	fix	VERB
ejpam-6173	880	2	point	point	NOUN
ejpam-6173	880	3	theory	theory	NOUN
ejpam-6173	880	4	and	and	CCONJ
ejpam-6173	880	5	applications	application	NOUN
ejpam-6173	880	6	,	,	PUNCT
ejpam-6173	880	7	2013(43):141	2013(43):141	NUM
ejpam-6173	880	8	,	,	PUNCT
ejpam-6173	880	9	2013	2013	NUM
ejpam-6173	880	10	.	.	PUNCT
ejpam-6173	881	1	[	[	X
ejpam-6173	881	2	52	52	NUM
ejpam-6173	881	3	]	]	PUNCT
ejpam-6173	881	4	s.	s.	PROPN
ejpam-6173	881	5	saejung	saejung	PROPN
ejpam-6173	881	6	and	and	CCONJ
ejpam-6173	881	7	p.	p.	PROPN
ejpam-6173	881	8	yotkaew	yotkaew	PROPN
ejpam-6173	881	9	.	.	PUNCT
ejpam-6173	882	1	approximation	approximation	NOUN
ejpam-6173	882	2	of	of	ADP
ejpam-6173	882	3	zeros	zero	NOUN
ejpam-6173	882	4	of	of	ADP
ejpam-6173	882	5	inverse	inverse	NOUN
ejpam-6173	882	6	strongly	strongly	ADV
ejpam-6173	882	7	monotone	monotone	ADJ
ejpam-6173	882	8	operators	operator	NOUN
ejpam-6173	882	9	in	in	ADP
ejpam-6173	882	10	banach	banach	NOUN
ejpam-6173	882	11	spaces	space	NOUN
ejpam-6173	882	12	.	.	PUNCT
ejpam-6173	883	1	nonlinear	nonlinear	ADJ
ejpam-6173	883	2	analysis	analysis	NOUN
ejpam-6173	883	3	,	,	PUNCT
ejpam-6173	883	4	75:742–750	75:742–750	NOUN
ejpam-6173	883	5	,	,	PUNCT
ejpam-6173	883	6	2012	2012	NUM
ejpam-6173	883	7	.	.	PUNCT
ejpam-6173	884	1	[	[	X
ejpam-6173	884	2	53	53	NUM
ejpam-6173	884	3	]	]	PUNCT
ejpam-6173	884	4	s.	s.	PROPN
ejpam-6173	884	5	sabach	sabach	PROPN
ejpam-6173	884	6	.	.	PUNCT
ejpam-6173	885	1	products	product	NOUN
ejpam-6173	885	2	of	of	ADP
ejpam-6173	885	3	finitely	finitely	ADV
ejpam-6173	885	4	many	many	ADJ
ejpam-6173	885	5	resolvents	resolvent	NOUN
ejpam-6173	885	6	of	of	ADP
ejpam-6173	885	7	maximal	maximal	ADJ
ejpam-6173	885	8	monotone	monotone	ADJ
ejpam-6173	885	9	mappings	mapping	NOUN
ejpam-6173	885	10	in	in	ADP
ejpam-6173	885	11	reflexive	reflexive	ADJ
ejpam-6173	885	12	banach	banach	NOUN
ejpam-6173	885	13	spaces	space	NOUN
ejpam-6173	885	14	.	.	PUNCT
ejpam-6173	886	1	siam	siam	PROPN
ejpam-6173	886	2	journal	journal	PROPN
ejpam-6173	886	3	on	on	ADP
ejpam-6173	886	4	optimization	optimization	NOUN
ejpam-6173	886	5	,	,	PUNCT
ejpam-6173	886	6	21:1289–1308	21:1289–1308	NUM
ejpam-6173	886	7	,	,	PUNCT
ejpam-6173	886	8	2011	2011	NUM
ejpam-6173	886	9	.	.	PUNCT
ejpam-6173	887	1	[	[	X
ejpam-6173	887	2	54	54	NUM
ejpam-6173	887	3	]	]	PUNCT
ejpam-6173	887	4	h.	h.	PROPN
ejpam-6173	887	5	h.	h.	PROPN
ejpam-6173	887	6	bauschke	bauschke	PROPN
ejpam-6173	887	7	,	,	PUNCT
ejpam-6173	887	8	x.	x.	PROPN
ejpam-6173	887	9	wang	wang	PROPN
ejpam-6173	887	10	,	,	PUNCT
ejpam-6173	887	11	and	and	CCONJ
ejpam-6173	887	12	l.	l.	PROPN
ejpam-6173	887	13	yao	yao	PROPN
ejpam-6173	887	14	.	.	PUNCT
ejpam-6173	888	1	general	general	ADJ
ejpam-6173	888	2	resolvents	resolvent	NOUN
ejpam-6173	888	3	for	for	ADP
ejpam-6173	888	4	monotone	monotone	ADJ
ejpam-6173	888	5	operators	operator	NOUN
ejpam-6173	888	6	:	:	PUNCT
ejpam-6173	888	7	characterization	characterization	NOUN
ejpam-6173	888	8	and	and	CCONJ
ejpam-6173	888	9	extension	extension	NOUN
ejpam-6173	888	10	.	.	PUNCT
ejpam-6173	889	1	in	in	ADP
ejpam-6173	889	2	biomedical	biomedical	ADJ
ejpam-6173	889	3	mathematics	mathematic	NOUN
ejpam-6173	889	4	:	:	PUNCT
ejpam-6173	889	5	promising	promise	VERB
ejpam-6173	889	6	directions	direction	NOUN
ejpam-6173	889	7	in	in	ADP
ejpam-6173	889	8	imaging	imaging	NOUN
ejpam-6173	889	9	,	,	PUNCT
ejpam-6173	889	10	therapy	therapy	NOUN
ejpam-6173	889	11	planning	planning	NOUN
ejpam-6173	889	12	and	and	CCONJ
ejpam-6173	889	13	inverse	inverse	NOUN
ejpam-6173	889	14	problems	problem	NOUN
ejpam-6173	889	15	,	,	PUNCT
ejpam-6173	889	16	pages	page	NOUN
ejpam-6173	889	17	57–74	57–74	NUM
ejpam-6173	889	18	.	.	PUNCT
ejpam-6173	890	1	medical	medical	ADJ
ejpam-6173	890	2	physics	physics	PROPN
ejpam-6173	890	3	publishing	publishing	NOUN
ejpam-6173	890	4	,	,	PUNCT
ejpam-6173	890	5	madison	madison	PROPN
ejpam-6173	890	6	,	,	PUNCT
ejpam-6173	890	7	wi	wi	PROPN
ejpam-6173	890	8	,	,	PUNCT
ejpam-6173	890	9	usa	usa	PROPN
ejpam-6173	890	10	,	,	PUNCT
ejpam-6173	890	11	2010	2010	NUM
ejpam-6173	890	12	.	.	PUNCT
ejpam-6173	891	1	[	[	X
ejpam-6173	891	2	55	55	NUM
ejpam-6173	891	3	]	]	X
ejpam-6173	891	4	d.	d.	PROPN
ejpam-6173	891	5	butnariu	butnariu	PROPN
ejpam-6173	891	6	,	,	PUNCT
ejpam-6173	891	7	a.	a.	PROPN
ejpam-6173	891	8	n.	n.	PROPN
ejpam-6173	891	9	iusem	iusem	PROPN
ejpam-6173	891	10	,	,	PUNCT
ejpam-6173	891	11	and	and	CCONJ
ejpam-6173	891	12	c.	c.	PROPN
ejpam-6173	891	13	zălinescu	zălinescu	PROPN
ejpam-6173	891	14	.	.	PUNCT
ejpam-6173	892	1	on	on	ADP
ejpam-6173	892	2	uniform	uniform	ADJ
ejpam-6173	892	3	convexity	convexity	NOUN
ejpam-6173	892	4	,	,	PUNCT
ejpam-6173	892	5	total	total	ADJ
ejpam-6173	892	6	convexity	convexity	NOUN
ejpam-6173	892	7	and	and	CCONJ
ejpam-6173	892	8	convergence	convergence	NOUN
ejpam-6173	892	9	of	of	ADP
ejpam-6173	892	10	the	the	DET
ejpam-6173	892	11	proximal	proximal	ADJ
ejpam-6173	892	12	point	point	NOUN
ejpam-6173	892	13	and	and	CCONJ
ejpam-6173	892	14	outer	outer	ADJ
ejpam-6173	892	15	bregman	bregman	NOUN
ejpam-6173	892	16	projection	projection	NOUN
ejpam-6173	892	17	algorithms	algorithm	NOUN
ejpam-6173	892	18	in	in	ADP
ejpam-6173	892	19	banach	banach	NOUN
ejpam-6173	892	20	spaces	space	NOUN
ejpam-6173	892	21	.	.	PUNCT
ejpam-6173	893	1	journal	journal	NOUN
ejpam-6173	893	2	of	of	ADP
ejpam-6173	893	3	convex	convex	PROPN
ejpam-6173	893	4	analysis	analysis	NOUN
ejpam-6173	893	5	,	,	PUNCT
ejpam-6173	893	6	10:35–61	10:35–61	NUM
ejpam-6173	893	7	,	,	PUNCT
ejpam-6173	893	8	2003	2003	NUM
ejpam-6173	893	9	.	.	PUNCT
ejpam-6173	894	1	[	[	X
ejpam-6173	894	2	56	56	NUM
ejpam-6173	894	3	]	]	X
ejpam-6173	894	4	s.	s.	PROPN
ejpam-6173	894	5	timnaka	timnaka	PROPN
ejpam-6173	894	6	,	,	PUNCT
ejpam-6173	894	7	e.	e.	PROPN
ejpam-6173	894	8	naraghirad	naraghirad	PROPN
ejpam-6173	894	9	,	,	PUNCT
ejpam-6173	894	10	and	and	CCONJ
ejpam-6173	894	11	n.	n.	PROPN
ejpam-6173	894	12	hussain	hussain	PROPN
ejpam-6173	894	13	.	.	PUNCT
ejpam-6173	895	1	strong	strong	ADJ
ejpam-6173	895	2	convergence	convergence	NOUN
ejpam-6173	895	3	of	of	ADP
ejpam-6173	895	4	halpern	halpern	ADJ
ejpam-6173	895	5	iteration	iteration	NOUN
ejpam-6173	895	6	v.	v.	ADP
ejpam-6173	895	7	darvish	darvish	PROPN
ejpam-6173	895	8	et	et	PROPN
ejpam-6173	895	9	al	al	PROPN
ejpam-6173	895	10	.	.	PUNCT
ejpam-6173	895	11	/	/	SYM
ejpam-6173	895	12	eur	eur	PROPN
ejpam-6173	895	13	.	.	PUNCT
ejpam-6173	896	1	j.	j.	PROPN
ejpam-6173	896	2	pure	pure	PROPN
ejpam-6173	896	3	appl	appl	PROPN
ejpam-6173	896	4	.	.	PROPN
ejpam-6173	896	5	math	math	PROPN
ejpam-6173	896	6	,	,	PUNCT
ejpam-6173	896	7	18	18	NUM
ejpam-6173	896	8	(	(	PUNCT
ejpam-6173	896	9	3	3	NUM
ejpam-6173	896	10	)	)	PUNCT
ejpam-6173	896	11	(	(	PUNCT
ejpam-6173	896	12	2025	2025	NUM
ejpam-6173	896	13	)	)	PUNCT
ejpam-6173	896	14	,	,	PUNCT
ejpam-6173	896	15	6173	6173	NUM
ejpam-6173	896	16	32	32	NUM
ejpam-6173	896	17	of	of	ADP
ejpam-6173	896	18	32	32	NUM
ejpam-6173	896	19	for	for	ADP
ejpam-6173	896	20	products	product	NOUN
ejpam-6173	896	21	of	of	ADP
ejpam-6173	896	22	finitely	finitely	ADV
ejpam-6173	896	23	many	many	ADJ
ejpam-6173	896	24	resolvents	resolvent	NOUN
ejpam-6173	896	25	of	of	ADP
ejpam-6173	896	26	maximal	maximal	ADJ
ejpam-6173	896	27	monotone	monotone	ADJ
ejpam-6173	896	28	operators	operator	NOUN
ejpam-6173	896	29	in	in	ADP
ejpam-6173	896	30	banach	banach	NOUN
ejpam-6173	896	31	spaces	space	NOUN
ejpam-6173	896	32	.	.	PUNCT
ejpam-6173	897	1	filomat	filomat	NOUN
ejpam-6173	897	2	,	,	PUNCT
ejpam-6173	897	3	31(15):4673–4693	31(15):4673–4693	PROPN
ejpam-6173	897	4	,	,	PUNCT
ejpam-6173	897	5	2017	2017	NUM
ejpam-6173	897	6	.	.	PUNCT