id	sid	tid	token	lemma	pos
ejpam-6062	1	1	european	european	PROPN
ejpam-6062	1	2	journal	journal	PROPN
ejpam-6062	1	3	of	of	ADP
ejpam-6062	1	4	pure	pure	ADJ
ejpam-6062	1	5	and	and	CCONJ
ejpam-6062	1	6	applied	applied	ADJ
ejpam-6062	1	7	mathematics	mathematic	NOUN
ejpam-6062	1	8	2025	2025	NUM
ejpam-6062	1	9	,	,	PUNCT
ejpam-6062	1	10	vol	vol	NOUN
ejpam-6062	1	11	.	.	PROPN
ejpam-6062	1	12	18	18	NUM
ejpam-6062	1	13	,	,	PUNCT
ejpam-6062	1	14	issue	issue	NOUN
ejpam-6062	1	15	2	2	NUM
ejpam-6062	1	16	,	,	PUNCT
ejpam-6062	1	17	article	article	NOUN
ejpam-6062	1	18	number	number	NOUN
ejpam-6062	1	19	6062	6062	NUM
ejpam-6062	1	20	issn	issn	VERB
ejpam-6062	1	21	1307	1307	NUM
ejpam-6062	1	22	-	-	SYM
ejpam-6062	1	23	5543	5543	NUM
ejpam-6062	1	24	–	–	PUNCT
ejpam-6062	1	25	ejpam.com	ejpam.com	X
ejpam-6062	1	26	published	publish	VERB
ejpam-6062	1	27	by	by	ADP
ejpam-6062	1	28	new	new	PROPN
ejpam-6062	1	29	york	york	PROPN
ejpam-6062	1	30	business	business	PROPN
ejpam-6062	1	31	global	global	ADJ
ejpam-6062	1	32	solving	solving	NOUN
ejpam-6062	1	33	system	system	NOUN
ejpam-6062	1	34	of	of	ADP
ejpam-6062	1	35	monotone	monotone	ADJ
ejpam-6062	1	36	variational	variational	ADJ
ejpam-6062	1	37	inclusion	inclusion	NOUN
ejpam-6062	1	38	problems	problem	NOUN
ejpam-6062	1	39	with	with	ADP
ejpam-6062	1	40	multiple	multiple	ADJ
ejpam-6062	1	41	output	output	NOUN
ejpam-6062	1	42	sets	set	NOUN
ejpam-6062	1	43	in	in	ADP
ejpam-6062	1	44	banach	banach	NOUN
ejpam-6062	1	45	spaces	space	NOUN
ejpam-6062	1	46	h.	h.	PROPN
ejpam-6062	1	47	a.	a.	PROPN
ejpam-6062	1	48	abass1,4,∗	abass1,4,∗	PROPN
ejpam-6062	1	49	,	,	PUNCT
ejpam-6062	1	50	m.	m.	PROPN
ejpam-6062	1	51	aphane1	aphane1	PROPN
ejpam-6062	1	52	,	,	PUNCT
ejpam-6062	1	53	o.	o.	PROPN
ejpam-6062	1	54	k.	k.	PROPN
ejpam-6062	1	55	oyewole2	oyewole2	PROPN
ejpam-6062	1	56	,	,	PUNCT
ejpam-6062	1	57	o.	o.	PROPN
ejpam-6062	1	58	k.	k.	PROPN
ejpam-6062	1	59	narain3	narain3	PROPN
ejpam-6062	1	60	,	,	PUNCT
ejpam-6062	1	61	k.	k.	PROPN
ejpam-6062	1	62	i.	i.	PROPN
ejpam-6062	1	63	mustafoyev4	mustafoyev4	PROPN
ejpam-6062	2	1	1	1	NUM
ejpam-6062	2	2	department	department	NOUN
ejpam-6062	2	3	of	of	ADP
ejpam-6062	2	4	mathematics	mathematic	NOUN
ejpam-6062	2	5	and	and	CCONJ
ejpam-6062	2	6	applied	apply	VERB
ejpam-6062	2	7	mathematics	mathematic	NOUN
ejpam-6062	2	8	,	,	PUNCT
ejpam-6062	2	9	sefako	sefako	VERB
ejpam-6062	2	10	makgatho	makgatho	PROPN
ejpam-6062	2	11	health	health	PROPN
ejpam-6062	2	12	sciences	sciences	PROPN
ejpam-6062	2	13	university	university	PROPN
ejpam-6062	2	14	,	,	PUNCT
ejpam-6062	2	15	p.o	p.o	PROPN
ejpam-6062	2	16	.	.	PROPN
ejpam-6062	2	17	box	box	PROPN
ejpam-6062	2	18	94	94	NUM
ejpam-6062	2	19	medunsa	medunsa	ADJ
ejpam-6062	2	20	0204	0204	NUM
ejpam-6062	2	21	,	,	PUNCT
ejpam-6062	2	22	pretoria	pretoria	PROPN
ejpam-6062	2	23	,	,	PUNCT
ejpam-6062	2	24	south	south	PROPN
ejpam-6062	2	25	africa	africa	PROPN
ejpam-6062	2	26	2	2	NUM
ejpam-6062	2	27	department	department	NOUN
ejpam-6062	2	28	of	of	ADP
ejpam-6062	2	29	mathematics	mathematic	NOUN
ejpam-6062	2	30	,	,	PUNCT
ejpam-6062	2	31	tshwane	tshwane	NOUN
ejpam-6062	2	32	university	university	NOUN
ejpam-6062	2	33	of	of	ADP
ejpam-6062	2	34	technology	technology	PROPN
ejpam-6062	2	35	,	,	PUNCT
ejpam-6062	2	36	arcadia	arcadia	PROPN
ejpam-6062	2	37	,	,	PUNCT
ejpam-6062	2	38	pmb	pmb	PROPN
ejpam-6062	2	39	0007	0007	NUM
ejpam-6062	2	40	,	,	PUNCT
ejpam-6062	2	41	pretoria	pretoria	PROPN
ejpam-6062	2	42	,	,	PUNCT
ejpam-6062	2	43	south	south	PROPN
ejpam-6062	2	44	africa	africa	PROPN
ejpam-6062	2	45	3	3	NUM
ejpam-6062	2	46	school	school	NOUN
ejpam-6062	2	47	of	of	ADP
ejpam-6062	2	48	mathematics	mathematic	NOUN
ejpam-6062	2	49	,	,	PUNCT
ejpam-6062	2	50	statistics	statistic	NOUN
ejpam-6062	2	51	and	and	CCONJ
ejpam-6062	2	52	computer	computer	NOUN
ejpam-6062	2	53	science	science	NOUN
ejpam-6062	2	54	,	,	PUNCT
ejpam-6062	2	55	university	university	NOUN
ejpam-6062	2	56	of	of	ADP
ejpam-6062	2	57	kwazulu	kwazulu	PROPN
ejpam-6062	2	58	-	-	PUNCT
ejpam-6062	2	59	natal	natal	ADJ
ejpam-6062	2	60	,	,	PUNCT
ejpam-6062	2	61	durban	durban	PROPN
ejpam-6062	2	62	,	,	PUNCT
ejpam-6062	2	63	south	south	PROPN
ejpam-6062	2	64	africa	africa	PROPN
ejpam-6062	2	65	4	4	NUM
ejpam-6062	2	66	center	center	NOUN
ejpam-6062	2	67	of	of	ADP
ejpam-6062	2	68	research	research	NOUN
ejpam-6062	2	69	and	and	CCONJ
ejpam-6062	2	70	innovation	innovation	NOUN
ejpam-6062	2	71	,	,	PUNCT
ejpam-6062	2	72	asia	asia	PROPN
ejpam-6062	2	73	international	international	PROPN
ejpam-6062	2	74	university	university	PROPN
ejpam-6062	2	75	,	,	PUNCT
ejpam-6062	2	76	yangiobod	yangiobod	ADJ
ejpam-6062	2	77	mfy	mfy	NOUN
ejpam-6062	2	78	,	,	PUNCT
ejpam-6062	2	79	g‘ijduvon	g‘ijduvon	PROPN
ejpam-6062	2	80	street	street	PROPN
ejpam-6062	2	81	,	,	PUNCT
ejpam-6062	2	82	house	house	NOUN
ejpam-6062	2	83	74	74	NUM
ejpam-6062	2	84	,	,	PUNCT
ejpam-6062	2	85	bukhara	bukhara	PROPN
ejpam-6062	2	86	,	,	PUNCT
ejpam-6062	2	87	uzbekistan	uzbekistan	PROPN
ejpam-6062	2	88	abstract	abstract	NOUN
ejpam-6062	2	89	.	.	PUNCT
ejpam-6062	3	1	in	in	ADP
ejpam-6062	3	2	this	this	DET
ejpam-6062	3	3	article	article	NOUN
ejpam-6062	3	4	,	,	PUNCT
ejpam-6062	3	5	we	we	PRON
ejpam-6062	3	6	introduce	introduce	VERB
ejpam-6062	3	7	a	a	DET
ejpam-6062	3	8	self	self	NOUN
ejpam-6062	3	9	-	-	PUNCT
ejpam-6062	3	10	adaptive	adaptive	ADJ
ejpam-6062	3	11	method	method	NOUN
ejpam-6062	3	12	for	for	ADP
ejpam-6062	3	13	approximating	approximate	VERB
ejpam-6062	3	14	solutions	solution	NOUN
ejpam-6062	3	15	of	of	ADP
ejpam-6062	3	16	split	split	ADJ
ejpam-6062	3	17	common	common	ADJ
ejpam-6062	3	18	fixed	fix	VERB
ejpam-6062	3	19	point	point	NOUN
ejpam-6062	3	20	problem	problem	NOUN
ejpam-6062	3	21	of	of	ADP
ejpam-6062	3	22	bregman	bregman	NOUN
ejpam-6062	3	23	demigeneralized	demigeneralize	VERB
ejpam-6062	3	24	mappings	mapping	NOUN
ejpam-6062	3	25	and	and	CCONJ
ejpam-6062	3	26	system	system	NOUN
ejpam-6062	3	27	of	of	ADP
ejpam-6062	3	28	monotone	monotone	ADJ
ejpam-6062	3	29	variational	variational	ADJ
ejpam-6062	3	30	inclusion	inclusion	NOUN
ejpam-6062	3	31	problem	problem	NOUN
ejpam-6062	3	32	with	with	ADP
ejpam-6062	3	33	multiple	multiple	ADJ
ejpam-6062	3	34	output	output	NOUN
ejpam-6062	3	35	sets	set	NOUN
ejpam-6062	3	36	in	in	ADP
ejpam-6062	3	37	reflexive	reflexive	ADJ
ejpam-6062	3	38	banach	banach	NOUN
ejpam-6062	3	39	spaces	space	VERB
ejpam-6062	3	40	.	.	PUNCT
ejpam-6062	4	1	by	by	ADP
ejpam-6062	4	2	employing	employ	VERB
ejpam-6062	4	3	our	our	PRON
ejpam-6062	4	4	iterative	iterative	NOUN
ejpam-6062	4	5	method	method	NOUN
ejpam-6062	4	6	,	,	PUNCT
ejpam-6062	4	7	we	we	PRON
ejpam-6062	4	8	prove	prove	VERB
ejpam-6062	4	9	a	a	DET
ejpam-6062	4	10	strong	strong	ADJ
ejpam-6062	4	11	convergence	convergence	NOUN
ejpam-6062	4	12	theorem	theorem	NOUN
ejpam-6062	4	13	for	for	ADP
ejpam-6062	4	14	approximating	approximate	VERB
ejpam-6062	4	15	solutions	solution	NOUN
ejpam-6062	4	16	of	of	ADP
ejpam-6062	4	17	the	the	DET
ejpam-6062	4	18	aforementioned	aforementioned	ADJ
ejpam-6062	4	19	problems	problem	NOUN
ejpam-6062	4	20	.	.	PUNCT
ejpam-6062	5	1	in	in	ADP
ejpam-6062	5	2	summary	summary	NOUN
ejpam-6062	5	3	,	,	PUNCT
ejpam-6062	5	4	we	we	PRON
ejpam-6062	5	5	state	state	VERB
ejpam-6062	5	6	some	some	DET
ejpam-6062	5	7	consequences	consequence	NOUN
ejpam-6062	5	8	of	of	ADP
ejpam-6062	5	9	our	our	PRON
ejpam-6062	5	10	main	main	ADJ
ejpam-6062	5	11	result	result	NOUN
ejpam-6062	5	12	.	.	PUNCT
ejpam-6062	6	1	the	the	DET
ejpam-6062	6	2	result	result	NOUN
ejpam-6062	6	3	discuss	discuss	NOUN
ejpam-6062	6	4	in	in	ADP
ejpam-6062	6	5	this	this	DET
ejpam-6062	6	6	paper	paper	NOUN
ejpam-6062	6	7	extends	extend	VERB
ejpam-6062	6	8	and	and	CCONJ
ejpam-6062	6	9	complements	complement	VERB
ejpam-6062	6	10	many	many	ADJ
ejpam-6062	6	11	related	related	ADJ
ejpam-6062	6	12	results	result	NOUN
ejpam-6062	6	13	in	in	ADP
ejpam-6062	6	14	literature	literature	NOUN
ejpam-6062	6	15	.	.	PUNCT
ejpam-6062	7	1	2020	2020	NUM
ejpam-6062	7	2	mathematics	mathematic	NOUN
ejpam-6062	7	3	subject	subject	NOUN
ejpam-6062	7	4	classifications	classification	NOUN
ejpam-6062	7	5	:	:	PUNCT
ejpam-6062	7	6	47h06	47h06	NUM
ejpam-6062	7	7	,	,	PUNCT
ejpam-6062	7	8	47h09	47h09	NUM
ejpam-6062	7	9	,	,	PUNCT
ejpam-6062	7	10	47j05	47j05	NUM
ejpam-6062	7	11	,	,	PUNCT
ejpam-6062	7	12	47j25	47j25	NUM
ejpam-6062	7	13	key	key	ADJ
ejpam-6062	7	14	words	word	NOUN
ejpam-6062	7	15	and	and	CCONJ
ejpam-6062	7	16	phrases	phrase	NOUN
ejpam-6062	7	17	:	:	PUNCT
ejpam-6062	7	18	bregman	bregman	NOUN
ejpam-6062	7	19	demigeneralized	demigeneralize	VERB
ejpam-6062	7	20	mapping	mapping	NOUN
ejpam-6062	7	21	,	,	PUNCT
ejpam-6062	7	22	monotone	monotone	ADJ
ejpam-6062	7	23	operators	operator	NOUN
ejpam-6062	7	24	,	,	PUNCT
ejpam-6062	7	25	self	self	NOUN
ejpam-6062	7	26	-	-	PUNCT
ejpam-6062	7	27	adapative	adapative	NOUN
ejpam-6062	7	28	method	method	NOUN
ejpam-6062	7	29	,	,	PUNCT
ejpam-6062	7	30	split	split	VERB
ejpam-6062	7	31	common	common	ADJ
ejpam-6062	7	32	fixed	fix	VERB
ejpam-6062	7	33	point	point	NOUN
ejpam-6062	7	34	problem	problem	NOUN
ejpam-6062	7	35	1	1	NUM
ejpam-6062	7	36	.	.	PUNCT
ejpam-6062	7	37	introduction	introduction	NOUN
ejpam-6062	7	38	for	for	ADP
ejpam-6062	7	39	modelling	model	VERB
ejpam-6062	7	40	inverse	inverse	NOUN
ejpam-6062	7	41	problems	problem	NOUN
ejpam-6062	7	42	which	which	PRON
ejpam-6062	7	43	arise	arise	VERB
ejpam-6062	7	44	from	from	ADP
ejpam-6062	7	45	phase	phase	NOUN
ejpam-6062	7	46	retrievals	retrieval	NOUN
ejpam-6062	7	47	and	and	CCONJ
ejpam-6062	7	48	medical	medical	ADJ
ejpam-6062	7	49	image	image	NOUN
ejpam-6062	7	50	reconstruction	reconstruction	NOUN
ejpam-6062	7	51	,	,	PUNCT
ejpam-6062	7	52	(	(	PUNCT
ejpam-6062	7	53	see	see	VERB
ejpam-6062	7	54	[	[	X
ejpam-6062	7	55	1	1	NUM
ejpam-6062	7	56	]	]	NUM
ejpam-6062	7	57	)	)	PUNCT
ejpam-6062	7	58	,	,	PUNCT
ejpam-6062	7	59	censor	censor	VERB
ejpam-6062	7	60	and	and	CCONJ
ejpam-6062	7	61	elfving	elfve	VERB
ejpam-6062	7	62	[	[	X
ejpam-6062	7	63	2	2	NUM
ejpam-6062	7	64	]	]	PUNCT
ejpam-6062	7	65	introduced	introduce	VERB
ejpam-6062	7	66	the	the	DET
ejpam-6062	7	67	split	split	NOUN
ejpam-6062	7	68	feasibility	feasibility	NOUN
ejpam-6062	7	69	problem	problem	NOUN
ejpam-6062	7	70	(	(	PUNCT
ejpam-6062	7	71	sfp	sfp	NOUN
ejpam-6062	7	72	)	)	PUNCT
ejpam-6062	7	73	in	in	ADP
ejpam-6062	7	74	1994	1994	NUM
ejpam-6062	7	75	,	,	PUNCT
ejpam-6062	7	76	which	which	PRON
ejpam-6062	7	77	is	be	AUX
ejpam-6062	7	78	to	to	PART
ejpam-6062	7	79	find	find	VERB
ejpam-6062	7	80	u∗	u∗	ADJ
ejpam-6062	7	81	∈	∈	PROPN
ejpam-6062	7	82	c	c	NOUN
ejpam-6062	7	83	such	such	ADJ
ejpam-6062	7	84	that	that	SCONJ
ejpam-6062	7	85	fu∗	fu∗	VERB
ejpam-6062	7	86	∈	∈	PROPN
ejpam-6062	7	87	q	q	NOUN
ejpam-6062	7	88	,	,	PUNCT
ejpam-6062	7	89	(	(	PUNCT
ejpam-6062	7	90	1	1	X
ejpam-6062	7	91	)	)	PUNCT
ejpam-6062	7	92	∗corresponding	∗corresponde	VERB
ejpam-6062	7	93	author	author	NOUN
ejpam-6062	7	94	.	.	PUNCT
ejpam-6062	8	1	doi	doi	NOUN
ejpam-6062	8	2	:	:	PUNCT
ejpam-6062	8	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6062	https://doi.org/10.29020/nybg.ejpam.v18i2.6062	PRON
ejpam-6062	8	4	email	email	NOUN
ejpam-6062	8	5	addresses	address	NOUN
ejpam-6062	8	6	:	:	PUNCT
ejpam-6062	8	7	hammed.abass@smu.ac.za	hammed.abass@smu.ac.za	NOUN
ejpam-6062	8	8	,	,	PUNCT
ejpam-6062	8	9	hammedabass548@gmail.com	hammedabass548@gmail.com	PROPN
ejpam-6062	8	10	(	(	PUNCT
ejpam-6062	8	11	h.	h.	PROPN
ejpam-6062	8	12	a.	a.	PROPN
ejpam-6062	8	13	abass	abass	PROPN
ejpam-6062	8	14	)	)	PUNCT
ejpam-6062	8	15	,	,	PUNCT
ejpam-6062	8	16	maggie.aphane@smu.ac.za	maggie.aphane@smu.ac.za	PROPN
ejpam-6062	8	17	(	(	PUNCT
ejpam-6062	8	18	m.	m.	NOUN
ejpam-6062	8	19	aphane	aphane	PROPN
ejpam-6062	8	20	)	)	PUNCT
ejpam-6062	8	21	,	,	PUNCT
ejpam-6062	8	22	oyewoleolawalekazeem@gmail.com	oyewoleolawalekazeem@gmail.com	X
ejpam-6062	8	23	(	(	PUNCT
ejpam-6062	8	24	o.	o.	PROPN
ejpam-6062	8	25	k.	k.	PROPN
ejpam-6062	8	26	oyewole	oyewole	PROPN
ejpam-6062	8	27	)	)	PUNCT
ejpam-6062	8	28	,	,	PUNCT
ejpam-6062	8	29	naraino@ukzn.ac.za	naraino@ukzn.ac.za	NOUN
ejpam-6062	8	30	,	,	PUNCT
ejpam-6062	8	31	(	(	PUNCT
ejpam-6062	8	32	o.	o.	PROPN
ejpam-6062	8	33	k.	k.	PROPN
ejpam-6062	8	34	narain	narain	PROPN
ejpam-6062	8	35	)	)	PUNCT
ejpam-6062	8	36	,	,	PUNCT
ejpam-6062	8	37	k.mustafoyev@oxu.uz	k.mustafoyev@oxu.uz	PROPN
ejpam-6062	8	38	(	(	PUNCT
ejpam-6062	8	39	k.	k.	PROPN
ejpam-6062	8	40	i.	i.	PROPN
ejpam-6062	8	41	mustafoyev	mustafoyev	PROPN
ejpam-6062	8	42	)	)	PUNCT
ejpam-6062	8	43	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6062	8	44	1	1	NUM
ejpam-6062	8	45	copyright	copyright	NOUN
ejpam-6062	8	46	:	:	PUNCT
ejpam-6062	8	47	©	©	PROPN
ejpam-6062	8	48	2025	2025	NUM
ejpam-6062	8	49	the	the	DET
ejpam-6062	8	50	author(s	author(s	NOUN
ejpam-6062	8	51	)	)	PUNCT
ejpam-6062	8	52	.	.	PUNCT
ejpam-6062	9	1	(	(	PUNCT
ejpam-6062	9	2	cc	cc	NOUN
ejpam-6062	9	3	by	by	ADP
ejpam-6062	9	4	-	-	PUNCT
ejpam-6062	9	5	nc	nc	PROPN
ejpam-6062	9	6	4.0	4.0	NUM
ejpam-6062	9	7	)	)	PUNCT
ejpam-6062	9	8	h.	h.	PROPN
ejpam-6062	9	9	a.	a.	PROPN
ejpam-6062	9	10	abass	abass	PROPN
ejpam-6062	9	11	et	et	PROPN
ejpam-6062	9	12	al	al	PROPN
ejpam-6062	9	13	.	.	PUNCT
ejpam-6062	9	14	/	/	SYM
ejpam-6062	9	15	eur	eur	PROPN
ejpam-6062	9	16	.	.	PUNCT
ejpam-6062	10	1	j.	j.	PROPN
ejpam-6062	10	2	pure	pure	PROPN
ejpam-6062	10	3	appl	appl	PROPN
ejpam-6062	10	4	.	.	PROPN
ejpam-6062	10	5	math	math	PROPN
ejpam-6062	10	6	,	,	PUNCT
ejpam-6062	10	7	18	18	NUM
ejpam-6062	10	8	(	(	PUNCT
ejpam-6062	10	9	2	2	NUM
ejpam-6062	10	10	)	)	PUNCT
ejpam-6062	10	11	(	(	PUNCT
ejpam-6062	10	12	2025	2025	NUM
ejpam-6062	10	13	)	)	PUNCT
ejpam-6062	10	14	,	,	PUNCT
ejpam-6062	10	15	6062	6062	NUM
ejpam-6062	10	16	2	2	NUM
ejpam-6062	10	17	of	of	ADP
ejpam-6062	10	18	22	22	NUM
ejpam-6062	10	19	where	where	SCONJ
ejpam-6062	10	20	c	c	PROPN
ejpam-6062	10	21	and	and	CCONJ
ejpam-6062	10	22	q	q	PROPN
ejpam-6062	10	23	are	be	AUX
ejpam-6062	10	24	nonempty	nonempty	ADJ
ejpam-6062	10	25	,	,	PUNCT
ejpam-6062	10	26	closed	closed	ADJ
ejpam-6062	10	27	and	and	CCONJ
ejpam-6062	10	28	convex	convex	ADJ
ejpam-6062	10	29	subsets	subset	NOUN
ejpam-6062	10	30	of	of	ADP
ejpam-6062	10	31	real	real	ADJ
ejpam-6062	10	32	banach	banach	NOUN
ejpam-6062	10	33	spaces	space	NOUN
ejpam-6062	10	34	e1	e1	PROPN
ejpam-6062	10	35	and	and	CCONJ
ejpam-6062	10	36	e2	e2	NOUN
ejpam-6062	10	37	respectively	respectively	ADV
ejpam-6062	10	38	,	,	PUNCT
ejpam-6062	10	39	and	and	CCONJ
ejpam-6062	10	40	f	f	NOUN
ejpam-6062	10	41	:	:	PUNCT
ejpam-6062	10	42	e1	e1	PROPN
ejpam-6062	10	43	→	→	SYM
ejpam-6062	10	44	e2	e2	PROPN
ejpam-6062	10	45	is	be	AUX
ejpam-6062	10	46	a	a	DET
ejpam-6062	10	47	bounded	bounded	ADJ
ejpam-6062	10	48	linear	linear	ADJ
ejpam-6062	10	49	operator	operator	NOUN
ejpam-6062	10	50	.	.	PUNCT
ejpam-6062	11	1	the	the	DET
ejpam-6062	11	2	sfp	sfp	NOUN
ejpam-6062	11	3	have	have	AUX
ejpam-6062	11	4	been	be	AUX
ejpam-6062	11	5	well	well	ADV
ejpam-6062	11	6	studied	study	VERB
ejpam-6062	11	7	in	in	ADP
ejpam-6062	11	8	the	the	DET
ejpam-6062	11	9	framework	framework	NOUN
ejpam-6062	11	10	of	of	ADP
ejpam-6062	11	11	real	real	ADJ
ejpam-6062	11	12	hilbert	hilbert	NOUN
ejpam-6062	11	13	spaces	space	NOUN
ejpam-6062	11	14	,	,	PUNCT
ejpam-6062	11	15	uniformly	uniformly	ADV
ejpam-6062	11	16	convex	convex	VERB
ejpam-6062	11	17	and	and	CCONJ
ejpam-6062	11	18	uniformly	uniformly	ADV
ejpam-6062	11	19	smooth	smooth	ADJ
ejpam-6062	11	20	banach	banach	NOUN
ejpam-6062	11	21	spaces	space	NOUN
ejpam-6062	11	22	,	,	PUNCT
ejpam-6062	11	23	see	see	VERB
ejpam-6062	11	24	(	(	PUNCT
ejpam-6062	11	25	[	[	X
ejpam-6062	11	26	3–5	3–5	NOUN
ejpam-6062	11	27	]	]	PUNCT
ejpam-6062	11	28	and	and	CCONJ
ejpam-6062	11	29	other	other	ADJ
ejpam-6062	11	30	references	reference	NOUN
ejpam-6062	11	31	contained	contain	VERB
ejpam-6062	11	32	in	in	ADP
ejpam-6062	11	33	)	)	PUNCT
ejpam-6062	11	34	.	.	PUNCT
ejpam-6062	12	1	different	different	ADJ
ejpam-6062	12	2	optimization	optimization	NOUN
ejpam-6062	12	3	problems	problem	NOUN
ejpam-6062	12	4	have	have	AUX
ejpam-6062	12	5	been	be	AUX
ejpam-6062	12	6	formulated	formulate	VERB
ejpam-6062	12	7	in	in	ADP
ejpam-6062	12	8	terms	term	NOUN
ejpam-6062	12	9	of	of	ADP
ejpam-6062	12	10	sfp	sfp	NOUN
ejpam-6062	12	11	(	(	PUNCT
ejpam-6062	12	12	1	1	NUM
ejpam-6062	12	13	)	)	PUNCT
ejpam-6062	12	14	,	,	PUNCT
ejpam-6062	12	15	for	for	ADP
ejpam-6062	12	16	instance	instance	NOUN
ejpam-6062	12	17	,	,	PUNCT
ejpam-6062	12	18	if	if	SCONJ
ejpam-6062	12	19	q	q	X
ejpam-6062	12	20	=	=	PUNCT
ejpam-6062	12	21	{	{	PUNCT
ejpam-6062	12	22	b	b	NOUN
ejpam-6062	12	23	}	}	PUNCT
ejpam-6062	12	24	in	in	ADP
ejpam-6062	12	25	sfp	sfp	PROPN
ejpam-6062	12	26	(	(	PUNCT
ejpam-6062	12	27	1	1	NUM
ejpam-6062	12	28	)	)	PUNCT
ejpam-6062	12	29	is	be	AUX
ejpam-6062	12	30	a	a	DET
ejpam-6062	12	31	singleton	singleton	NOUN
ejpam-6062	12	32	,	,	PUNCT
ejpam-6062	12	33	then	then	ADV
ejpam-6062	12	34	we	we	PRON
ejpam-6062	12	35	have	have	VERB
ejpam-6062	12	36	the	the	DET
ejpam-6062	12	37	following	follow	VERB
ejpam-6062	12	38	convexly	convexly	ADV
ejpam-6062	12	39	constrained	constrain	VERB
ejpam-6062	12	40	linear	linear	ADJ
ejpam-6062	12	41	inverse	inverse	NOUN
ejpam-6062	12	42	problem	problem	NOUN
ejpam-6062	12	43	(	(	PUNCT
ejpam-6062	12	44	cclip	cclip	NOUN
ejpam-6062	12	45	)	)	PUNCT
ejpam-6062	12	46	defined	define	VERB
ejpam-6062	12	47	as	as	SCONJ
ejpam-6062	12	48	follows	follow	VERB
ejpam-6062	12	49	:	:	PUNCT
ejpam-6062	12	50	find	find	VERB
ejpam-6062	12	51	a	a	DET
ejpam-6062	12	52	point	point	NOUN
ejpam-6062	12	53	u∗	u∗	NOUN
ejpam-6062	12	54	∈	∈	PROPN
ejpam-6062	12	55	c	c	NOUN
ejpam-6062	12	56	such	such	ADJ
ejpam-6062	12	57	that	that	DET
ejpam-6062	12	58	fu∗	fu∗	PROPN
ejpam-6062	12	59	=	=	PUNCT
ejpam-6062	12	60	b.	b.	PROPN
ejpam-6062	13	1	also	also	ADV
ejpam-6062	13	2	,	,	PUNCT
ejpam-6062	13	3	if	if	SCONJ
ejpam-6062	13	4	c	c	NOUN
ejpam-6062	13	5	=	=	SYM
ejpam-6062	13	6	fix(t	fix(t	PROPN
ejpam-6062	13	7	)	)	PUNCT
ejpam-6062	14	1	=	=	PRON
ejpam-6062	15	1	{	{	PUNCT
ejpam-6062	15	2	x	x	PUNCT
ejpam-6062	15	3	∈	∈	PROPN
ejpam-6062	15	4	e	e	NOUN
ejpam-6062	15	5	:	:	PUNCT
ejpam-6062	15	6	x	x	SYM
ejpam-6062	15	7	=	=	SYM
ejpam-6062	15	8	tx	tx	PROPN
ejpam-6062	15	9	}	}	PUNCT
ejpam-6062	15	10	and	and	CCONJ
ejpam-6062	15	11	q	q	ADJ
ejpam-6062	15	12	=	=	SYM
ejpam-6062	15	13	fix(s	fix(s	PROPN
ejpam-6062	15	14	)	)	PUNCT
ejpam-6062	15	15	,	,	PUNCT
ejpam-6062	15	16	then	then	ADV
ejpam-6062	15	17	sfp	sfp	VERB
ejpam-6062	15	18	(	(	PUNCT
ejpam-6062	15	19	1	1	X
ejpam-6062	15	20	)	)	PUNCT
ejpam-6062	15	21	becomes	become	VERB
ejpam-6062	15	22	split	split	ADJ
ejpam-6062	15	23	common	common	ADJ
ejpam-6062	15	24	fixed	fix	VERB
ejpam-6062	15	25	point	point	NOUN
ejpam-6062	15	26	problem	problem	NOUN
ejpam-6062	15	27	(	(	PUNCT
ejpam-6062	15	28	scfpp	scfpp	PROPN
ejpam-6062	15	29	)	)	PUNCT
ejpam-6062	15	30	which	which	PRON
ejpam-6062	15	31	is	be	AUX
ejpam-6062	15	32	to	to	PART
ejpam-6062	15	33	find	find	VERB
ejpam-6062	15	34	a	a	DET
ejpam-6062	15	35	point	point	NOUN
ejpam-6062	15	36	u∗	u∗	NOUN
ejpam-6062	15	37	∈	∈	PROPN
ejpam-6062	15	38	fix(t	fix(t	PROPN
ejpam-6062	15	39	)	)	PUNCT
ejpam-6062	15	40	such	such	ADJ
ejpam-6062	15	41	that	that	SCONJ
ejpam-6062	15	42	fu∗	fu∗	VERB
ejpam-6062	15	43	∈	∈	PROPN
ejpam-6062	15	44	fix(s	fix(s	PROPN
ejpam-6062	15	45	)	)	PUNCT
ejpam-6062	15	46	.	.	PUNCT
ejpam-6062	16	1	(	(	PUNCT
ejpam-6062	16	2	2	2	X
ejpam-6062	16	3	)	)	PUNCT
ejpam-6062	16	4	since	since	SCONJ
ejpam-6062	16	5	the	the	DET
ejpam-6062	16	6	introduction	introduction	NOUN
ejpam-6062	16	7	of	of	ADP
ejpam-6062	16	8	the	the	DET
ejpam-6062	16	9	scfpp	scfpp	NOUN
ejpam-6062	16	10	(	(	PUNCT
ejpam-6062	16	11	2	2	NUM
ejpam-6062	16	12	)	)	PUNCT
ejpam-6062	16	13	,	,	PUNCT
ejpam-6062	16	14	authors	author	NOUN
ejpam-6062	16	15	have	have	AUX
ejpam-6062	16	16	considered	consider	VERB
ejpam-6062	16	17	several	several	ADJ
ejpam-6062	16	18	schematic	schematic	ADJ
ejpam-6062	16	19	methods	method	NOUN
ejpam-6062	16	20	for	for	ADP
ejpam-6062	16	21	approximating	approximate	VERB
ejpam-6062	16	22	its	its	PRON
ejpam-6062	16	23	solution	solution	NOUN
ejpam-6062	16	24	.	.	PUNCT
ejpam-6062	17	1	for	for	ADP
ejpam-6062	17	2	instance	instance	NOUN
ejpam-6062	17	3	,	,	PUNCT
ejpam-6062	17	4	censor	censor	NOUN
ejpam-6062	17	5	and	and	CCONJ
ejpam-6062	17	6	segal	segal	PROPN
ejpam-6062	18	1	[	[	X
ejpam-6062	18	2	6	6	NUM
ejpam-6062	18	3	]	]	PUNCT
ejpam-6062	18	4	introduced	introduce	VERB
ejpam-6062	18	5	the	the	DET
ejpam-6062	18	6	following	following	ADJ
ejpam-6062	18	7	iterative	iterative	NOUN
ejpam-6062	18	8	algorithm	algorithm	NOUN
ejpam-6062	18	9	for	for	ADP
ejpam-6062	18	10	solving	solve	VERB
ejpam-6062	18	11	the	the	DET
ejpam-6062	18	12	scfpp	scfpp	NOUN
ejpam-6062	18	13	(	(	PUNCT
ejpam-6062	18	14	2	2	NUM
ejpam-6062	18	15	)	)	PUNCT
ejpam-6062	18	16	in	in	ADP
ejpam-6062	18	17	finite	finite	ADJ
ejpam-6062	18	18	dimensional	dimensional	ADJ
ejpam-6062	18	19	spaces	space	NOUN
ejpam-6062	18	20	.	.	PUNCT
ejpam-6062	19	1	they	they	PRON
ejpam-6062	19	2	defined	define	VERB
ejpam-6062	19	3	the	the	DET
ejpam-6062	19	4	algorithm	algorithm	NOUN
ejpam-6062	19	5	as	as	SCONJ
ejpam-6062	19	6	follows	follow	VERB
ejpam-6062	19	7	:	:	PUNCT
ejpam-6062	19	8	xn+1	xn+1	PROPN
ejpam-6062	19	9	=	=	SYM
ejpam-6062	19	10	t	t	PROPN
ejpam-6062	19	11	(	(	PUNCT
ejpam-6062	19	12	xn	xn	PROPN
ejpam-6062	20	1	+	+	CCONJ
ejpam-6062	20	2	τf	τf	ADP
ejpam-6062	20	3	t(s	t(s	PROPN
ejpam-6062	20	4	−	−	PROPN
ejpam-6062	20	5	i)fxn	i)fxn	PROPN
ejpam-6062	20	6	)	)	PUNCT
ejpam-6062	20	7	,	,	PUNCT
ejpam-6062	20	8	for	for	ADP
ejpam-6062	20	9	each	each	DET
ejpam-6062	20	10	n	n	PRON
ejpam-6062	20	11	≥	≥	NOUN
ejpam-6062	20	12	1	1	NUM
ejpam-6062	20	13	,	,	PUNCT
ejpam-6062	20	14	where	where	SCONJ
ejpam-6062	20	15	τ	τ	PROPN
ejpam-6062	20	16	∈	∈	PROPN
ejpam-6062	20	17	(	(	PUNCT
ejpam-6062	20	18	0	0	NUM
ejpam-6062	20	19	,	,	PUNCT
ejpam-6062	20	20	0γ	0γ	NUM
ejpam-6062	20	21	)	)	PUNCT
ejpam-6062	20	22	with	with	ADP
ejpam-6062	20	23	γ	γ	NOUN
ejpam-6062	20	24	being	be	AUX
ejpam-6062	20	25	the	the	DET
ejpam-6062	20	26	largest	large	ADJ
ejpam-6062	20	27	eigenvalue	eigenvalue	NOUN
ejpam-6062	20	28	of	of	ADP
ejpam-6062	20	29	the	the	DET
ejpam-6062	20	30	matrix	matrix	NOUN
ejpam-6062	21	1	f	f	X
ejpam-6062	21	2	tf	tf	INTJ
ejpam-6062	21	3	(	(	PUNCT
ejpam-6062	21	4	f	f	PROPN
ejpam-6062	21	5	t	t	PROPN
ejpam-6062	21	6	being	be	AUX
ejpam-6062	21	7	the	the	DET
ejpam-6062	21	8	matrix	matrix	NOUN
ejpam-6062	21	9	transposition	transposition	NOUN
ejpam-6062	21	10	)	)	PUNCT
ejpam-6062	21	11	.	.	PUNCT
ejpam-6062	22	1	also	also	ADV
ejpam-6062	22	2	,	,	PUNCT
ejpam-6062	22	3	moudafi	moudafi	PROPN
ejpam-6062	23	1	[	[	X
ejpam-6062	23	2	7	7	X
ejpam-6062	23	3	]	]	PUNCT
ejpam-6062	23	4	introduced	introduce	VERB
ejpam-6062	23	5	a	a	DET
ejpam-6062	23	6	relaxed	relaxed	ADJ
ejpam-6062	23	7	algorithm	algorithm	NOUN
ejpam-6062	23	8	for	for	ADP
ejpam-6062	23	9	approximating	approximate	VERB
ejpam-6062	23	10	a	a	DET
ejpam-6062	23	11	solution	solution	NOUN
ejpam-6062	23	12	of	of	ADP
ejpam-6062	23	13	scfpp	scfpp	NOUN
ejpam-6062	23	14	(	(	PUNCT
ejpam-6062	23	15	2	2	NUM
ejpam-6062	23	16	)	)	PUNCT
ejpam-6062	23	17	and	and	CCONJ
ejpam-6062	23	18	proved	prove	VERB
ejpam-6062	23	19	some	some	DET
ejpam-6062	23	20	weak	weak	ADJ
ejpam-6062	23	21	convergence	convergence	NOUN
ejpam-6062	23	22	results	result	NOUN
ejpam-6062	23	23	in	in	ADP
ejpam-6062	23	24	hilbert	hilbert	NOUN
ejpam-6062	23	25	spaces	space	NOUN
ejpam-6062	23	26	with	with	ADP
ejpam-6062	23	27	the	the	DET
ejpam-6062	23	28	mappings	mapping	NOUN
ejpam-6062	23	29	t	t	NOUN
ejpam-6062	23	30	and	and	CCONJ
ejpam-6062	23	31	s	s	AUX
ejpam-6062	23	32	being	be	AUX
ejpam-6062	23	33	quasi	quasi	ADJ
ejpam-6062	23	34	-	-	ADJ
ejpam-6062	23	35	nonexpansive	nonexpansive	ADJ
ejpam-6062	23	36	mappings	mapping	NOUN
ejpam-6062	23	37	.	.	PUNCT
ejpam-6062	24	1	the	the	DET
ejpam-6062	24	2	variational	variational	ADJ
ejpam-6062	24	3	inclusion	inclusion	NOUN
ejpam-6062	24	4	problem	problem	NOUN
ejpam-6062	24	5	consists	consist	VERB
ejpam-6062	24	6	of	of	ADP
ejpam-6062	24	7	finding	find	VERB
ejpam-6062	24	8	a	a	DET
ejpam-6062	24	9	point	point	NOUN
ejpam-6062	24	10	x∗	x∗	PROPN
ejpam-6062	24	11	∈	∈	PROPN
ejpam-6062	24	12	e	e	NOUN
ejpam-6062	24	13	such	such	ADJ
ejpam-6062	24	14	that	that	PRON
ejpam-6062	24	15	0	0	NUM
ejpam-6062	24	16	∈	∈	NOUN
ejpam-6062	24	17	(	(	PUNCT
ejpam-6062	24	18	a+b)x∗	a+b)x∗	PROPN
ejpam-6062	24	19	,	,	PUNCT
ejpam-6062	24	20	(	(	PUNCT
ejpam-6062	24	21	3	3	X
ejpam-6062	24	22	)	)	PUNCT
ejpam-6062	24	23	where	where	SCONJ
ejpam-6062	24	24	a	a	DET
ejpam-6062	24	25	:	:	PUNCT
ejpam-6062	24	26	e	e	NOUN
ejpam-6062	24	27	→	→	SYM
ejpam-6062	24	28	e∗	e∗	PROPN
ejpam-6062	24	29	is	be	AUX
ejpam-6062	24	30	a	a	DET
ejpam-6062	24	31	single	single	ADV
ejpam-6062	24	32	-	-	PUNCT
ejpam-6062	24	33	valued	value	VERB
ejpam-6062	24	34	mapping	mapping	NOUN
ejpam-6062	24	35	and	and	CCONJ
ejpam-6062	24	36	b	b	NOUN
ejpam-6062	24	37	:	:	PUNCT
ejpam-6062	24	38	e	e	X
ejpam-6062	24	39	→	→	SYM
ejpam-6062	24	40	2e	2e	PROPN
ejpam-6062	24	41	∗	∗	NOUN
ejpam-6062	24	42	is	be	AUX
ejpam-6062	24	43	a	a	DET
ejpam-6062	24	44	multi	multi	ADJ
ejpam-6062	24	45	-	-	ADJ
ejpam-6062	24	46	valued	value	VERB
ejpam-6062	24	47	mapping	mapping	NOUN
ejpam-6062	24	48	on	on	ADP
ejpam-6062	24	49	a	a	DET
ejpam-6062	24	50	real	real	ADJ
ejpam-6062	24	51	banach	banach	NOUN
ejpam-6062	24	52	space	space	NOUN
ejpam-6062	24	53	e	e	NOUN
ejpam-6062	24	54	with	with	ADP
ejpam-6062	24	55	dual	dual	ADJ
ejpam-6062	24	56	space	space	NOUN
ejpam-6062	24	57	e∗.	e∗.	NOUN
ejpam-6062	24	58	combining	combine	VERB
ejpam-6062	24	59	the	the	DET
ejpam-6062	24	60	notions	notion	NOUN
ejpam-6062	24	61	of	of	ADP
ejpam-6062	24	62	sfp	sfp	NOUN
ejpam-6062	24	63	and	and	CCONJ
ejpam-6062	24	64	vip	vip	NOUN
ejpam-6062	24	65	,	,	PUNCT
ejpam-6062	25	1	moudafi	moudafi	NOUN
ejpam-6062	26	1	[	[	X
ejpam-6062	26	2	8	8	NUM
ejpam-6062	26	3	]	]	PUNCT
ejpam-6062	26	4	introduced	introduce	VERB
ejpam-6062	26	5	the	the	DET
ejpam-6062	26	6	following	following	ADJ
ejpam-6062	26	7	split	split	ADJ
ejpam-6062	26	8	variational	variational	ADJ
ejpam-6062	26	9	inclusion	inclusion	NOUN
ejpam-6062	26	10	problem	problem	NOUN
ejpam-6062	26	11	(	(	PUNCT
ejpam-6062	26	12	svip	svip	PROPN
ejpam-6062	26	13	):	):	PUNCT
ejpam-6062	26	14	let	let	VERB
ejpam-6062	26	15	h1	h1	NOUN
ejpam-6062	26	16	and	and	CCONJ
ejpam-6062	26	17	h2	h2	NOUN
ejpam-6062	26	18	be	be	AUX
ejpam-6062	26	19	real	real	ADJ
ejpam-6062	26	20	hilbert	hilbert	NOUN
ejpam-6062	26	21	spaces	space	NOUN
ejpam-6062	26	22	,	,	PUNCT
ejpam-6062	26	23	ai	ai	VERB
ejpam-6062	26	24	:	:	PUNCT
ejpam-6062	26	25	hi	hi	INTJ
ejpam-6062	26	26	→	→	SYM
ejpam-6062	26	27	hi	hi	INTJ
ejpam-6062	26	28	,	,	PUNCT
ejpam-6062	26	29	i	i	PRON
ejpam-6062	26	30	=	=	NOUN
ejpam-6062	26	31	1	1	NUM
ejpam-6062	26	32	,	,	PUNCT
ejpam-6062	26	33	2	2	NUM
ejpam-6062	26	34	be	be	VERB
ejpam-6062	26	35	single	single	ADJ
ejpam-6062	26	36	-	-	PUNCT
ejpam-6062	26	37	valued	value	VERB
ejpam-6062	26	38	mappings	mapping	NOUN
ejpam-6062	26	39	,	,	PUNCT
ejpam-6062	26	40	bi	bi	NOUN
ejpam-6062	26	41	:	:	PUNCT
ejpam-6062	26	42	hi	hi	INTJ
ejpam-6062	26	43	→	→	SYM
ejpam-6062	26	44	2hi	2hi	NOUN
ejpam-6062	26	45	be	be	AUX
ejpam-6062	26	46	multi	multi	ADJ
ejpam-6062	26	47	-	-	ADJ
ejpam-6062	26	48	valued	value	VERB
ejpam-6062	26	49	mappings	mapping	NOUN
ejpam-6062	26	50	and	and	CCONJ
ejpam-6062	26	51	f	f	NOUN
ejpam-6062	26	52	:	:	PUNCT
ejpam-6062	26	53	h1	h1	PROPN
ejpam-6062	26	54	→	→	SYM
ejpam-6062	26	55	h2	h2	PROPN
ejpam-6062	26	56	be	be	AUX
ejpam-6062	26	57	a	a	DET
ejpam-6062	26	58	bounded	bounded	ADJ
ejpam-6062	26	59	linear	linear	ADJ
ejpam-6062	26	60	operator	operator	NOUN
ejpam-6062	26	61	.	.	PUNCT
ejpam-6062	27	1	the	the	DET
ejpam-6062	27	2	svip	svip	PROPN
ejpam-6062	27	3	consists	consist	VERB
ejpam-6062	27	4	of	of	ADP
ejpam-6062	27	5	finding	find	VERB
ejpam-6062	27	6	x∗	x∗	PROPN
ejpam-6062	27	7	∈	∈	PROPN
ejpam-6062	27	8	h1	h1	VERB
ejpam-6062	27	9	such	such	ADJ
ejpam-6062	27	10	that	that	SCONJ
ejpam-6062	27	11	0	0	NUM
ejpam-6062	27	12	∈	∈	NOUN
ejpam-6062	27	13	(	(	PUNCT
ejpam-6062	27	14	a+b)x∗	a+b)x∗	PROPN
ejpam-6062	27	15	(	(	PUNCT
ejpam-6062	27	16	4	4	NUM
ejpam-6062	27	17	)	)	PUNCT
ejpam-6062	27	18	and	and	CCONJ
ejpam-6062	27	19	such	such	ADJ
ejpam-6062	27	20	that	that	DET
ejpam-6062	27	21	y∗	y∗	PROPN
ejpam-6062	27	22	=	=	SYM
ejpam-6062	27	23	fx∗	fx∗	PROPN
ejpam-6062	27	24	solves	solve	NOUN
ejpam-6062	27	25	0	0	NUM
ejpam-6062	27	26	∈	∈	NOUN
ejpam-6062	27	27	(	(	PUNCT
ejpam-6062	27	28	a+b)fx∗.	a+b)fx∗.	NOUN
ejpam-6062	27	29	(	(	PUNCT
ejpam-6062	27	30	5	5	NUM
ejpam-6062	27	31	)	)	PUNCT
ejpam-6062	27	32	we	we	PRON
ejpam-6062	27	33	note	note	VERB
ejpam-6062	27	34	that	that	SCONJ
ejpam-6062	27	35	since	since	SCONJ
ejpam-6062	27	36	its	its	PRON
ejpam-6062	27	37	introduction	introduction	NOUN
ejpam-6062	27	38	,	,	PUNCT
ejpam-6062	27	39	the	the	DET
ejpam-6062	27	40	svip	svip	NOUN
ejpam-6062	27	41	has	have	AUX
ejpam-6062	27	42	been	be	AUX
ejpam-6062	27	43	considered	consider	VERB
ejpam-6062	27	44	in	in	ADP
ejpam-6062	27	45	other	other	ADJ
ejpam-6062	27	46	more	more	ADV
ejpam-6062	27	47	general	general	ADJ
ejpam-6062	27	48	frameworks	framework	NOUN
ejpam-6062	27	49	than	than	ADP
ejpam-6062	27	50	the	the	DET
ejpam-6062	27	51	hilbert	hilbert	NOUN
ejpam-6062	27	52	spaces	space	NOUN
ejpam-6062	27	53	(	(	PUNCT
ejpam-6062	27	54	see	see	VERB
ejpam-6062	27	55	[	[	X
ejpam-6062	27	56	9–19	9–19	NOUN
ejpam-6062	27	57	]	]	PUNCT
ejpam-6062	27	58	and	and	CCONJ
ejpam-6062	27	59	the	the	DET
ejpam-6062	27	60	references	reference	NOUN
ejpam-6062	27	61	therein	therein	ADV
ejpam-6062	27	62	)	)	PUNCT
ejpam-6062	27	63	.	.	PUNCT
ejpam-6062	28	1	h.	h.	PROPN
ejpam-6062	28	2	a.	a.	PROPN
ejpam-6062	28	3	abass	abass	PROPN
ejpam-6062	28	4	et	et	PROPN
ejpam-6062	28	5	al	al	PROPN
ejpam-6062	28	6	.	.	PUNCT
ejpam-6062	28	7	/	/	SYM
ejpam-6062	28	8	eur	eur	PROPN
ejpam-6062	28	9	.	.	PUNCT
ejpam-6062	29	1	j.	j.	PROPN
ejpam-6062	29	2	pure	pure	PROPN
ejpam-6062	29	3	appl	appl	PROPN
ejpam-6062	29	4	.	.	PROPN
ejpam-6062	29	5	math	math	PROPN
ejpam-6062	29	6	,	,	PUNCT
ejpam-6062	29	7	18	18	NUM
ejpam-6062	29	8	(	(	PUNCT
ejpam-6062	29	9	2	2	NUM
ejpam-6062	29	10	)	)	PUNCT
ejpam-6062	29	11	(	(	PUNCT
ejpam-6062	29	12	2025	2025	NUM
ejpam-6062	29	13	)	)	PUNCT
ejpam-6062	29	14	,	,	PUNCT
ejpam-6062	29	15	6062	6062	NUM
ejpam-6062	29	16	3	3	NUM
ejpam-6062	29	17	of	of	ADP
ejpam-6062	29	18	22	22	NUM
ejpam-6062	29	19	the	the	DET
ejpam-6062	29	20	several	several	ADJ
ejpam-6062	29	21	variants	variant	NOUN
ejpam-6062	29	22	of	of	ADP
ejpam-6062	29	23	the	the	DET
ejpam-6062	29	24	sfp	sfp	NOUN
ejpam-6062	29	25	continue	continue	VERB
ejpam-6062	29	26	to	to	PART
ejpam-6062	29	27	recieve	recieve	VERB
ejpam-6062	29	28	attention	attention	NOUN
ejpam-6062	29	29	of	of	ADP
ejpam-6062	29	30	various	various	ADJ
ejpam-6062	29	31	authors	author	NOUN
ejpam-6062	29	32	,	,	PUNCT
ejpam-6062	29	33	notably	notably	ADV
ejpam-6062	29	34	because	because	SCONJ
ejpam-6062	29	35	of	of	ADP
ejpam-6062	29	36	the	the	DET
ejpam-6062	29	37	many	many	ADJ
ejpam-6062	29	38	rich	rich	ADJ
ejpam-6062	29	39	applications	application	NOUN
ejpam-6062	29	40	,	,	PUNCT
ejpam-6062	29	41	(	(	PUNCT
ejpam-6062	29	42	see	see	VERB
ejpam-6062	29	43	[	[	X
ejpam-6062	29	44	6	6	NUM
ejpam-6062	29	45	,	,	PUNCT
ejpam-6062	29	46	20	20	NUM
ejpam-6062	29	47	]	]	PUNCT
ejpam-6062	29	48	)	)	PUNCT
ejpam-6062	29	49	.	.	PUNCT
ejpam-6062	30	1	there	there	PRON
ejpam-6062	30	2	have	have	AUX
ejpam-6062	30	3	been	be	AUX
ejpam-6062	30	4	attempts	attempt	NOUN
ejpam-6062	30	5	at	at	ADP
ejpam-6062	30	6	extending	extend	VERB
ejpam-6062	30	7	the	the	DET
ejpam-6062	30	8	sfp	sfp	NOUN
ejpam-6062	30	9	for	for	SCONJ
ejpam-6062	30	10	more	more	ADJ
ejpam-6062	30	11	operators	operator	NOUN
ejpam-6062	30	12	to	to	PART
ejpam-6062	30	13	cover	cover	VERB
ejpam-6062	30	14	the	the	DET
ejpam-6062	30	15	previous	previous	ADJ
ejpam-6062	30	16	studies	study	NOUN
ejpam-6062	30	17	in	in	ADP
ejpam-6062	30	18	the	the	DET
ejpam-6062	30	19	literature	literature	NOUN
ejpam-6062	30	20	.	.	PUNCT
ejpam-6062	31	1	for	for	ADP
ejpam-6062	31	2	instance	instance	NOUN
ejpam-6062	31	3	,	,	PUNCT
ejpam-6062	31	4	reich	reich	PROPN
ejpam-6062	31	5	and	and	CCONJ
ejpam-6062	31	6	tuyen	tuyen	NOUN
ejpam-6062	31	7	[	[	X
ejpam-6062	31	8	21	21	NUM
ejpam-6062	31	9	]	]	PUNCT
ejpam-6062	31	10	introduced	introduce	VERB
ejpam-6062	31	11	the	the	DET
ejpam-6062	31	12	generalized	generalize	VERB
ejpam-6062	31	13	split	split	VERB
ejpam-6062	31	14	common	common	ADJ
ejpam-6062	31	15	monotone	monotone	ADJ
ejpam-6062	31	16	inclusion	inclusion	NOUN
ejpam-6062	31	17	problem	problem	NOUN
ejpam-6062	31	18	(	(	PUNCT
ejpam-6062	31	19	gscmip	gscmip	ADJ
ejpam-6062	31	20	):	):	PUNCT
ejpam-6062	31	21	let	let	VERB
ejpam-6062	31	22	i	i	PRON
ejpam-6062	31	23	=	=	NOUN
ejpam-6062	31	24	1	1	NUM
ejpam-6062	31	25	,	,	PUNCT
ejpam-6062	31	26	2	2	NUM
ejpam-6062	31	27	,	,	PUNCT
ejpam-6062	31	28	·	·	PUNCT
ejpam-6062	31	29	·	·	PUNCT
ejpam-6062	31	30	·	·	PUNCT
ejpam-6062	31	31	,	,	PUNCT
ejpam-6062	31	32	n	n	CCONJ
ejpam-6062	31	33	,	,	PUNCT
ejpam-6062	31	34	hi	hi	INTJ
ejpam-6062	31	35	be	be	AUX
ejpam-6062	31	36	real	real	ADJ
ejpam-6062	31	37	hilbert	hilbert	NOUN
ejpam-6062	31	38	spaces	space	NOUN
ejpam-6062	31	39	,	,	PUNCT
ejpam-6062	31	40	ai	ai	VERB
ejpam-6062	31	41	:	:	PUNCT
ejpam-6062	31	42	hi	hi	INTJ
ejpam-6062	31	43	→	→	SYM
ejpam-6062	31	44	2hi	2hi	NOUN
ejpam-6062	31	45	be	be	AUX
ejpam-6062	31	46	maximal	maximal	ADJ
ejpam-6062	31	47	monotone	monotone	ADJ
ejpam-6062	31	48	operators	operator	NOUN
ejpam-6062	31	49	.	.	PUNCT
ejpam-6062	32	1	let	let	VERB
ejpam-6062	32	2	fi	fi	NOUN
ejpam-6062	32	3	:	:	PUNCT
ejpam-6062	32	4	hi	hi	INTJ
ejpam-6062	32	5	→	→	SYM
ejpam-6062	32	6	hi+1	hi+1	AUX
ejpam-6062	32	7	be	be	AUX
ejpam-6062	32	8	bounded	bound	VERB
ejpam-6062	32	9	linear	linear	ADJ
ejpam-6062	32	10	opertors	opertor	NOUN
ejpam-6062	32	11	for	for	ADP
ejpam-6062	32	12	i	i	PRON
ejpam-6062	32	13	=	=	SYM
ejpam-6062	32	14	1	1	NUM
ejpam-6062	32	15	,	,	PUNCT
ejpam-6062	32	16	2	2	NUM
ejpam-6062	32	17	,	,	PUNCT
ejpam-6062	32	18	·	·	PUNCT
ejpam-6062	32	19	·	·	PUNCT
ejpam-6062	32	20	·	·	PUNCT
ejpam-6062	32	21	,	,	PUNCT
ejpam-6062	32	22	n	n	CCONJ
ejpam-6062	32	23	−	−	PROPN
ejpam-6062	32	24	1	1	NUM
ejpam-6062	32	25	such	such	ADJ
ejpam-6062	32	26	that	that	SCONJ
ejpam-6062	32	27	ti	ti	X
ejpam-6062	32	28	̸=	̸=	PROPN
ejpam-6062	32	29	0	0	NUM
ejpam-6062	32	30	.	.	PUNCT
ejpam-6062	33	1	then	then	ADV
ejpam-6062	33	2	the	the	DET
ejpam-6062	33	3	gscmip	gscmip	NOUN
ejpam-6062	33	4	is	be	AUX
ejpam-6062	33	5	to	to	PART
ejpam-6062	33	6	find	find	VERB
ejpam-6062	33	7	x∗	x∗	PROPN
ejpam-6062	33	8	∈	∈	PROPN
ejpam-6062	33	9	h1	h1	VERB
ejpam-6062	33	10	such	such	ADJ
ejpam-6062	33	11	that	that	DET
ejpam-6062	33	12	0	0	NUM
ejpam-6062	33	13	∈	∈	NOUN
ejpam-6062	33	14	a1(x	a1(x	DET
ejpam-6062	33	15	∗	∗	NOUN
ejpam-6062	33	16	)	)	PUNCT
ejpam-6062	33	17	,	,	PUNCT
ejpam-6062	33	18	0	0	NUM
ejpam-6062	33	19	∈	∈	NOUN
ejpam-6062	33	20	a2(f1(x	a2(f1(x	NOUN
ejpam-6062	33	21	∗	∗	NOUN
ejpam-6062	33	22	)	)	PUNCT
ejpam-6062	33	23	)	)	PUNCT
ejpam-6062	33	24	,	,	PUNCT
ejpam-6062	33	25	·	·	PUNCT
ejpam-6062	33	26	·	·	PUNCT
ejpam-6062	33	27	·	·	PUNCT
ejpam-6062	33	28	,	,	PUNCT
ejpam-6062	33	29	0	0	NUM
ejpam-6062	33	30	∈	∈	PROPN
ejpam-6062	33	31	an	an	DET
ejpam-6062	33	32	(	(	PUNCT
ejpam-6062	33	33	tn−1tn−2	tn−1tn−2	X
ejpam-6062	33	34	·	·	PUNCT
ejpam-6062	33	35	·	·	PUNCT
ejpam-6062	33	36	·	·	PUNCT
ejpam-6062	33	37	t1(x	t1(x	NOUN
ejpam-6062	33	38	∗	∗	NOUN
ejpam-6062	33	39	)	)	PUNCT
ejpam-6062	33	40	)	)	PUNCT
ejpam-6062	33	41	.	.	PUNCT
ejpam-6062	34	1	(	(	PUNCT
ejpam-6062	34	2	6	6	NUM
ejpam-6062	34	3	)	)	PUNCT
ejpam-6062	34	4	very	very	ADV
ejpam-6062	34	5	recently	recently	ADV
ejpam-6062	34	6	,	,	PUNCT
ejpam-6062	34	7	the	the	DET
ejpam-6062	34	8	same	same	ADJ
ejpam-6062	34	9	authors	author	NOUN
ejpam-6062	34	10	in	in	ADP
ejpam-6062	34	11	[	[	X
ejpam-6062	34	12	16	16	NUM
ejpam-6062	34	13	]	]	PUNCT
ejpam-6062	34	14	introduced	introduce	VERB
ejpam-6062	34	15	and	and	CCONJ
ejpam-6062	34	16	studied	study	VERB
ejpam-6062	34	17	a	a	DET
ejpam-6062	34	18	split	split	ADJ
ejpam-6062	34	19	common	common	ADJ
ejpam-6062	34	20	monotone	monotone	ADJ
ejpam-6062	34	21	inclusion	inclusion	NOUN
ejpam-6062	34	22	problem	problem	NOUN
ejpam-6062	34	23	with	with	ADP
ejpam-6062	34	24	multiple	multiple	ADJ
ejpam-6062	34	25	output	output	NOUN
ejpam-6062	34	26	sets	set	NOUN
ejpam-6062	34	27	(	(	PUNCT
ejpam-6062	34	28	scmipos	scmipos	NOUN
ejpam-6062	34	29	)	)	PUNCT
ejpam-6062	34	30	in	in	ADP
ejpam-6062	34	31	hilbert	hilbert	PROPN
ejpam-6062	34	32	spaces	space	NOUN
ejpam-6062	34	33	.	.	PUNCT
ejpam-6062	35	1	let	let	VERB
ejpam-6062	35	2	h	h	NOUN
ejpam-6062	35	3	,	,	PUNCT
ejpam-6062	35	4	h1	h1	NOUN
ejpam-6062	35	5	,	,	PUNCT
ejpam-6062	35	6	·	·	PUNCT
ejpam-6062	35	7	·	·	PUNCT
ejpam-6062	35	8	·	·	PUNCT
ejpam-6062	35	9	,	,	PUNCT
ejpam-6062	35	10	hn	hn	PROPN
ejpam-6062	35	11	be	be	VERB
ejpam-6062	35	12	real	real	ADJ
ejpam-6062	35	13	hilbert	hilbert	NOUN
ejpam-6062	35	14	spaces	space	NOUN
ejpam-6062	35	15	,	,	PUNCT
ejpam-6062	35	16	fi	fi	NOUN
ejpam-6062	35	17	:	:	PUNCT
ejpam-6062	36	1	h	h	PROPN
ejpam-6062	36	2	→	→	SYM
ejpam-6062	36	3	hi	hi	INTJ
ejpam-6062	36	4	,	,	PUNCT
ejpam-6062	36	5	i	i	PRON
ejpam-6062	36	6	=	=	NOUN
ejpam-6062	36	7	1	1	NUM
ejpam-6062	36	8	,	,	PUNCT
ejpam-6062	36	9	2	2	NUM
ejpam-6062	36	10	,	,	PUNCT
ejpam-6062	36	11	·	·	PUNCT
ejpam-6062	36	12	·	·	PUNCT
ejpam-6062	36	13	·	·	PUNCT
ejpam-6062	36	14	,	,	PUNCT
ejpam-6062	36	15	n	n	CCONJ
ejpam-6062	36	16	be	be	AUX
ejpam-6062	36	17	bounded	bound	VERB
ejpam-6062	36	18	linear	linear	PROPN
ejpam-6062	36	19	operators	operator	NOUN
ejpam-6062	36	20	.	.	PUNCT
ejpam-6062	37	1	let	let	VERB
ejpam-6062	37	2	b	b	X
ejpam-6062	37	3	:	:	PUNCT
ejpam-6062	37	4	h	h	NOUN
ejpam-6062	37	5	→	→	SYM
ejpam-6062	37	6	2h	2h	NUM
ejpam-6062	37	7	,	,	PUNCT
ejpam-6062	37	8	bi	bi	NOUN
ejpam-6062	37	9	:	:	PUNCT
ejpam-6062	37	10	hi	hi	INTJ
ejpam-6062	37	11	→	→	SYM
ejpam-6062	37	12	2hi	2hi	NOUN
ejpam-6062	38	1	,	,	PUNCT
ejpam-6062	38	2	i	i	PRON
ejpam-6062	38	3	=	=	VERB
ejpam-6062	38	4	i	i	PROPN
ejpam-6062	38	5	,	,	PUNCT
ejpam-6062	38	6	2	2	NUM
ejpam-6062	38	7	,	,	PUNCT
ejpam-6062	38	8	·	·	PUNCT
ejpam-6062	38	9	·	·	PUNCT
ejpam-6062	38	10	·	·	PUNCT
ejpam-6062	38	11	,	,	PUNCT
ejpam-6062	38	12	n	n	PRON
ejpam-6062	38	13	be	be	AUX
ejpam-6062	38	14	maximal	maximal	ADJ
ejpam-6062	38	15	monotone	monotone	ADJ
ejpam-6062	38	16	operators	operator	NOUN
ejpam-6062	38	17	,	,	PUNCT
ejpam-6062	38	18	then	then	ADV
ejpam-6062	38	19	scmipos	scmipos	NOUN
ejpam-6062	38	20	consists	consist	VERB
ejpam-6062	38	21	of	of	ADP
ejpam-6062	38	22	finding	find	VERB
ejpam-6062	38	23	a	a	DET
ejpam-6062	38	24	point	point	NOUN
ejpam-6062	38	25	x∗	x∗	PROPN
ejpam-6062	38	26	∈	∈	PROPN
ejpam-6062	38	27	h	h	NOUN
ejpam-6062	38	28	such	such	ADJ
ejpam-6062	38	29	that	that	SCONJ
ejpam-6062	38	30	x∗	x∗	PROPN
ejpam-6062	38	31	∈	∈	PROPN
ejpam-6062	38	32	b−1(0	b−1(0	X
ejpam-6062	38	33	)	)	PUNCT
ejpam-6062	38	34	∩	∩	NOUN
ejpam-6062	38	35	(	(	PUNCT
ejpam-6062	38	36	n⋂	n⋂	NOUN
ejpam-6062	38	37	i=1	i=1	PROPN
ejpam-6062	39	1	f−1	f−1	INTJ
ejpam-6062	39	2	i	i	PRON
ejpam-6062	39	3	(	(	PUNCT
ejpam-6062	39	4	b−1	b−1	PROPN
ejpam-6062	39	5	i	i	PRON
ejpam-6062	39	6	(	(	PUNCT
ejpam-6062	39	7	0	0	NUM
ejpam-6062	39	8	)	)	PUNCT
ejpam-6062	39	9	)	)	PUNCT
ejpam-6062	39	10	)	)	PUNCT
ejpam-6062	39	11	.	.	PUNCT
ejpam-6062	40	1	(	(	PUNCT
ejpam-6062	40	2	7	7	X
ejpam-6062	40	3	)	)	PUNCT
ejpam-6062	40	4	in	in	ADP
ejpam-6062	40	5	this	this	DET
ejpam-6062	40	6	paper	paper	NOUN
ejpam-6062	40	7	,	,	PUNCT
ejpam-6062	40	8	our	our	PRON
ejpam-6062	40	9	motivation	motivation	NOUN
ejpam-6062	40	10	is	be	AUX
ejpam-6062	40	11	in	in	ADP
ejpam-6062	40	12	two	two	NUM
ejpam-6062	40	13	folds	fold	NOUN
ejpam-6062	40	14	.	.	PUNCT
ejpam-6062	41	1	first	first	ADV
ejpam-6062	41	2	,	,	PUNCT
ejpam-6062	41	3	we	we	PRON
ejpam-6062	41	4	combine	combine	VERB
ejpam-6062	41	5	the	the	DET
ejpam-6062	41	6	notions	notion	NOUN
ejpam-6062	41	7	of	of	ADP
ejpam-6062	41	8	svip	svip	NOUN
ejpam-6062	41	9	and	and	CCONJ
ejpam-6062	41	10	the	the	DET
ejpam-6062	41	11	scmipos	scmipos	NOUN
ejpam-6062	41	12	to	to	PART
ejpam-6062	41	13	introduce	introduce	VERB
ejpam-6062	41	14	a	a	DET
ejpam-6062	41	15	split	split	ADJ
ejpam-6062	41	16	variational	variational	ADJ
ejpam-6062	41	17	inclusion	inclusion	NOUN
ejpam-6062	41	18	problem	problem	NOUN
ejpam-6062	41	19	with	with	ADP
ejpam-6062	41	20	multiple	multiple	ADJ
ejpam-6062	41	21	output	output	NOUN
ejpam-6062	41	22	sets	set	NOUN
ejpam-6062	41	23	(	(	PUNCT
ejpam-6062	41	24	svipos	svipos	NOUN
ejpam-6062	41	25	)	)	PUNCT
ejpam-6062	41	26	in	in	ADP
ejpam-6062	41	27	the	the	DET
ejpam-6062	41	28	framework	framework	NOUN
ejpam-6062	41	29	of	of	ADP
ejpam-6062	41	30	real	real	ADJ
ejpam-6062	41	31	banach	banach	NOUN
ejpam-6062	41	32	spaces	space	VERB
ejpam-6062	41	33	.	.	PUNCT
ejpam-6062	42	1	let	let	VERB
ejpam-6062	42	2	e	e	NOUN
ejpam-6062	42	3	=	=	SYM
ejpam-6062	42	4	e0	e0	PROPN
ejpam-6062	42	5	,	,	PUNCT
ejpam-6062	42	6	e1	e1	PROPN
ejpam-6062	42	7	,	,	PUNCT
ejpam-6062	42	8	e2	e2	PROPN
ejpam-6062	42	9	,	,	PUNCT
ejpam-6062	42	10	·	·	PUNCT
ejpam-6062	42	11	·	·	PUNCT
ejpam-6062	42	12	·	·	PUNCT
ejpam-6062	42	13	,	,	PUNCT
ejpam-6062	42	14	en	en	X
ejpam-6062	42	15	be	be	AUX
ejpam-6062	42	16	real	real	ADJ
ejpam-6062	42	17	banach	banach	NOUN
ejpam-6062	42	18	spaces	space	NOUN
ejpam-6062	42	19	and	and	CCONJ
ejpam-6062	42	20	fi	fi	NOUN
ejpam-6062	42	21	:	:	PUNCT
ejpam-6062	43	1	e	e	X
ejpam-6062	43	2	→	→	SYM
ejpam-6062	43	3	ei	ei	PROPN
ejpam-6062	43	4	,	,	PUNCT
ejpam-6062	43	5	i	i	PRON
ejpam-6062	43	6	=	=	NOUN
ejpam-6062	43	7	0	0	NUM
ejpam-6062	43	8	,	,	PUNCT
ejpam-6062	43	9	1	1	NUM
ejpam-6062	43	10	,	,	PUNCT
ejpam-6062	43	11	·	·	PUNCT
ejpam-6062	43	12	·	·	PUNCT
ejpam-6062	43	13	·	·	PUNCT
ejpam-6062	43	14	,	,	PUNCT
ejpam-6062	43	15	n	n	CCONJ
ejpam-6062	43	16	with	with	ADP
ejpam-6062	43	17	f0	f0	PROPN
ejpam-6062	43	18	=	=	PUNCT
ejpam-6062	43	19	ie	ie	X
ejpam-6062	43	20	be	be	AUX
ejpam-6062	43	21	bounded	bound	VERB
ejpam-6062	43	22	linear	linear	PROPN
ejpam-6062	43	23	operators	operator	NOUN
ejpam-6062	43	24	.	.	PUNCT
ejpam-6062	44	1	for	for	ADP
ejpam-6062	44	2	i	i	PRON
ejpam-6062	44	3	=	=	SYM
ejpam-6062	44	4	0	0	NUM
ejpam-6062	44	5	,	,	PUNCT
ejpam-6062	44	6	1	1	NUM
ejpam-6062	44	7	,	,	PUNCT
ejpam-6062	44	8	·	·	PUNCT
ejpam-6062	44	9	·	·	PUNCT
ejpam-6062	44	10	·	·	PUNCT
ejpam-6062	44	11	,	,	PUNCT
ejpam-6062	44	12	n	n	CCONJ
ejpam-6062	44	13	,	,	PUNCT
ejpam-6062	44	14	let	let	VERB
ejpam-6062	44	15	ai	ai	VERB
ejpam-6062	44	16	:	:	PUNCT
ejpam-6062	44	17	hi	hi	INTJ
ejpam-6062	44	18	→	→	SYM
ejpam-6062	44	19	hi	hi	INTJ
ejpam-6062	44	20	with	with	ADP
ejpam-6062	44	21	a	a	DET
ejpam-6062	44	22	=	=	X
ejpam-6062	44	23	a0	a0	PROPN
ejpam-6062	44	24	be	be	VERB
ejpam-6062	44	25	single	single	ADV
ejpam-6062	44	26	-	-	PUNCT
ejpam-6062	44	27	valued	value	VERB
ejpam-6062	44	28	mappings	mapping	NOUN
ejpam-6062	44	29	and	and	CCONJ
ejpam-6062	44	30	bi	bi	NOUN
ejpam-6062	44	31	:	:	PUNCT
ejpam-6062	44	32	hi	hi	INTJ
ejpam-6062	44	33	→	→	SYM
ejpam-6062	44	34	2hi	2hi	NOUN
ejpam-6062	44	35	with	with	ADP
ejpam-6062	44	36	b	b	NOUN
ejpam-6062	44	37	=	=	SYM
ejpam-6062	44	38	b0	b0	NOUN
ejpam-6062	44	39	be	be	AUX
ejpam-6062	44	40	multi	multi	ADJ
ejpam-6062	44	41	-	-	ADJ
ejpam-6062	44	42	valued	value	VERB
ejpam-6062	44	43	mappings	mapping	NOUN
ejpam-6062	44	44	.	.	PUNCT
ejpam-6062	45	1	then	then	ADV
ejpam-6062	45	2	the	the	DET
ejpam-6062	45	3	svipos	svipos	NOUN
ejpam-6062	45	4	is	be	AUX
ejpam-6062	45	5	the	the	DET
ejpam-6062	45	6	problem	problem	NOUN
ejpam-6062	45	7	of	of	ADP
ejpam-6062	45	8	finding	find	VERB
ejpam-6062	45	9	a	a	DET
ejpam-6062	45	10	point	point	NOUN
ejpam-6062	45	11	x∗	x∗	PROPN
ejpam-6062	45	12	∈	∈	PROPN
ejpam-6062	45	13	e	e	NOUN
ejpam-6062	45	14	such	such	ADJ
ejpam-6062	45	15	that	that	SCONJ
ejpam-6062	45	16	x∗	x∗	PROPN
ejpam-6062	45	17	∈	∈	PROPN
ejpam-6062	45	18	(	(	PUNCT
ejpam-6062	45	19	a+b)−1(0	a+b)−1(0	PROPN
ejpam-6062	45	20	)	)	PUNCT
ejpam-6062	45	21	⋂	⋂	PROPN
ejpam-6062	45	22	(	(	PUNCT
ejpam-6062	45	23	n⋂	n⋂	NOUN
ejpam-6062	45	24	i=1	i=1	PROPN
ejpam-6062	46	1	f−1	f−1	INTJ
ejpam-6062	46	2	i	i	PRON
ejpam-6062	46	3	(	(	PUNCT
ejpam-6062	46	4	(	(	PUNCT
ejpam-6062	46	5	ai	ai	VERB
ejpam-6062	46	6	+	+	PROPN
ejpam-6062	46	7	bi	bi	ADJ
ejpam-6062	46	8	)	)	PUNCT
ejpam-6062	46	9	−1(0	−1(0	NOUN
ejpam-6062	46	10	)	)	PUNCT
ejpam-6062	46	11	)	)	PUNCT
ejpam-6062	46	12	)	)	PUNCT
ejpam-6062	46	13	.	.	PUNCT
ejpam-6062	47	1	(	(	PUNCT
ejpam-6062	47	2	8)	8)	NUM
ejpam-6062	47	3	on	on	ADP
ejpam-6062	47	4	the	the	DET
ejpam-6062	47	5	other	other	ADJ
ejpam-6062	47	6	hand	hand	NOUN
ejpam-6062	47	7	,	,	PUNCT
ejpam-6062	47	8	the	the	DET
ejpam-6062	47	9	fixed	fix	VERB
ejpam-6062	47	10	point	point	NOUN
ejpam-6062	47	11	problem	problem	NOUN
ejpam-6062	47	12	(	(	PUNCT
ejpam-6062	47	13	fpp	fpp	PROPN
ejpam-6062	47	14	)	)	PUNCT
ejpam-6062	47	15	for	for	ADP
ejpam-6062	47	16	a	a	DET
ejpam-6062	47	17	multi	multi	ADJ
ejpam-6062	47	18	-	-	ADJ
ejpam-6062	47	19	valued	value	VERB
ejpam-6062	47	20	mapping	mapping	NOUN
ejpam-6062	47	21	have	have	AUX
ejpam-6062	47	22	been	be	AUX
ejpam-6062	47	23	well	well	ADV
ejpam-6062	47	24	discussed	discuss	VERB
ejpam-6062	47	25	due	due	ADP
ejpam-6062	47	26	to	to	ADP
ejpam-6062	47	27	its	its	PRON
ejpam-6062	47	28	many	many	ADJ
ejpam-6062	47	29	applications	application	NOUN
ejpam-6062	47	30	.	.	PUNCT
ejpam-6062	48	1	for	for	ADP
ejpam-6062	48	2	instance	instance	NOUN
ejpam-6062	48	3	,	,	PUNCT
ejpam-6062	48	4	the	the	DET
ejpam-6062	48	5	fpp	fpp	NOUN
ejpam-6062	48	6	is	be	AUX
ejpam-6062	48	7	used	use	VERB
ejpam-6062	48	8	in	in	ADP
ejpam-6062	48	9	game	game	NOUN
ejpam-6062	48	10	theory	theory	NOUN
ejpam-6062	48	11	,	,	PUNCT
ejpam-6062	48	12	control	control	PROPN
ejpam-6062	48	13	theory	theory	NOUN
ejpam-6062	48	14	,	,	PUNCT
ejpam-6062	48	15	convex	convex	ADJ
ejpam-6062	48	16	optimization	optimization	NOUN
ejpam-6062	48	17	differential	differential	NOUN
ejpam-6062	48	18	inclusion	inclusion	NOUN
ejpam-6062	48	19	and	and	CCONJ
ejpam-6062	48	20	so	so	ADV
ejpam-6062	48	21	on	on	ADP
ejpam-6062	48	22	[	[	PUNCT
ejpam-6062	48	23	22–26	22–26	NOUN
ejpam-6062	48	24	]	]	PUNCT
ejpam-6062	48	25	.	.	PUNCT
ejpam-6062	49	1	the	the	DET
ejpam-6062	49	2	problem	problem	NOUN
ejpam-6062	49	3	of	of	ADP
ejpam-6062	49	4	obtaining	obtain	VERB
ejpam-6062	49	5	a	a	DET
ejpam-6062	49	6	common	common	ADJ
ejpam-6062	49	7	solution	solution	NOUN
ejpam-6062	49	8	of	of	ADP
ejpam-6062	49	9	a	a	DET
ejpam-6062	49	10	fixed	fix	VERB
ejpam-6062	49	11	point	point	NOUN
ejpam-6062	49	12	problem	problem	NOUN
ejpam-6062	49	13	(	(	PUNCT
ejpam-6062	49	14	in	in	ADP
ejpam-6062	49	15	short	short	ADJ
ejpam-6062	49	16	,	,	PUNCT
ejpam-6062	49	17	fpp	fpp	PROPN
ejpam-6062	49	18	)	)	PUNCT
ejpam-6062	49	19	and	and	CCONJ
ejpam-6062	49	20	other	other	ADJ
ejpam-6062	49	21	optimization	optimization	NOUN
ejpam-6062	49	22	problems	problem	NOUN
ejpam-6062	49	23	have	have	AUX
ejpam-6062	49	24	been	be	AUX
ejpam-6062	49	25	considered	consider	VERB
ejpam-6062	49	26	in	in	ADP
ejpam-6062	49	27	recent	recent	ADJ
ejpam-6062	49	28	articles	article	NOUN
ejpam-6062	49	29	.	.	PUNCT
ejpam-6062	50	1	we	we	PRON
ejpam-6062	50	2	note	note	VERB
ejpam-6062	50	3	that	that	SCONJ
ejpam-6062	50	4	these	these	DET
ejpam-6062	50	5	type	type	NOUN
ejpam-6062	50	6	of	of	ADP
ejpam-6062	50	7	problems	problem	NOUN
ejpam-6062	50	8	become	become	VERB
ejpam-6062	50	9	more	more	ADV
ejpam-6062	50	10	applicable	applicable	ADJ
ejpam-6062	50	11	in	in	ADP
ejpam-6062	50	12	real	real	ADJ
ejpam-6062	50	13	life	life	NOUN
ejpam-6062	50	14	problems	problem	NOUN
ejpam-6062	50	15	whose	whose	DET
ejpam-6062	50	16	constraints	constraint	NOUN
ejpam-6062	50	17	can	can	AUX
ejpam-6062	50	18	be	be	AUX
ejpam-6062	50	19	modelled	model	VERB
ejpam-6062	50	20	as	as	ADP
ejpam-6062	50	21	fixed	fix	VERB
ejpam-6062	50	22	point	point	NOUN
ejpam-6062	50	23	and	and	CCONJ
ejpam-6062	50	24	optimization	optimization	NOUN
ejpam-6062	50	25	problems	problem	NOUN
ejpam-6062	50	26	.	.	PUNCT
ejpam-6062	51	1	in	in	ADP
ejpam-6062	51	2	this	this	DET
ejpam-6062	51	3	direction	direction	NOUN
ejpam-6062	51	4	,	,	PUNCT
ejpam-6062	51	5	izuchukwu	izuchukwu	PROPN
ejpam-6062	51	6	et	et	PROPN
ejpam-6062	51	7	al	al	PROPN
ejpam-6062	51	8	.	.	PUNCT
ejpam-6062	52	1	[	[	X
ejpam-6062	52	2	15	15	NUM
ejpam-6062	52	3	]	]	PUNCT
ejpam-6062	52	4	studied	study	VERB
ejpam-6062	52	5	the	the	DET
ejpam-6062	52	6	following	follow	VERB
ejpam-6062	52	7	split	split	VERB
ejpam-6062	52	8	monotone	monotone	ADJ
ejpam-6062	52	9	variational	variational	ADJ
ejpam-6062	52	10	inclusion	inclusion	NOUN
ejpam-6062	52	11	and	and	CCONJ
ejpam-6062	52	12	fixed	fix	VERB
ejpam-6062	52	13	point	point	NOUN
ejpam-6062	52	14	problem	problem	NOUN
ejpam-6062	52	15	between	between	ADP
ejpam-6062	52	16	hilbert	hilbert	NOUN
ejpam-6062	52	17	space	space	NOUN
ejpam-6062	52	18	and	and	CCONJ
ejpam-6062	52	19	a	a	DET
ejpam-6062	52	20	banach	banach	NOUN
ejpam-6062	52	21	space	space	NOUN
ejpam-6062	52	22	which	which	PRON
ejpam-6062	52	23	is	be	AUX
ejpam-6062	52	24	defined	define	VERB
ejpam-6062	52	25	as	as	ADP
ejpam-6062	52	26	follows	follow	VERB
ejpam-6062	52	27	:	:	PUNCT
ejpam-6062	52	28	find	find	VERB
ejpam-6062	52	29	x∗	x∗	PROPN
ejpam-6062	52	30	∈	∈	PROPN
ejpam-6062	52	31	fix(t	fix(t	PROPN
ejpam-6062	52	32	)	)	PUNCT
ejpam-6062	52	33	∩	∩	NOUN
ejpam-6062	52	34	(	(	PUNCT
ejpam-6062	52	35	a+b)−1(0	a+b)−1(0	PROPN
ejpam-6062	52	36	)	)	PUNCT
ejpam-6062	52	37	such	such	ADJ
ejpam-6062	52	38	that	that	SCONJ
ejpam-6062	52	39	fu∗	fu∗	VERB
ejpam-6062	52	40	∈	∈	PROPN
ejpam-6062	52	41	g−1(0	g−1(0	NOUN
ejpam-6062	52	42	)	)	PUNCT
ejpam-6062	52	43	,	,	PUNCT
ejpam-6062	52	44	where	where	SCONJ
ejpam-6062	52	45	h	h	NOUN
ejpam-6062	52	46	is	be	AUX
ejpam-6062	52	47	a	a	DET
ejpam-6062	52	48	hilbert	hilbert	NOUN
ejpam-6062	52	49	space	space	NOUN
ejpam-6062	52	50	,	,	PUNCT
ejpam-6062	52	51	e	e	X
ejpam-6062	52	52	is	be	AUX
ejpam-6062	52	53	a	a	DET
ejpam-6062	52	54	uniformly	uniformly	ADV
ejpam-6062	52	55	convex	convex	NOUN
ejpam-6062	52	56	and	and	CCONJ
ejpam-6062	52	57	uniformly	uniformly	ADV
ejpam-6062	52	58	smooth	smooth	ADJ
ejpam-6062	52	59	banach	banach	NOUN
ejpam-6062	52	60	space	space	NOUN
ejpam-6062	52	61	,	,	PUNCT
ejpam-6062	52	62	t	t	PROPN
ejpam-6062	52	63	a	a	DET
ejpam-6062	52	64	multivalued	multivalued	ADJ
ejpam-6062	52	65	quasi	quasi	ADJ
ejpam-6062	52	66	-	-	ADJ
ejpam-6062	52	67	nonexpansive	nonexpansive	ADJ
ejpam-6062	52	68	mapping	mapping	NOUN
ejpam-6062	52	69	,	,	PUNCT
ejpam-6062	52	70	b	b	NOUN
ejpam-6062	52	71	:	:	PUNCT
ejpam-6062	52	72	h	h	NOUN
ejpam-6062	52	73	→	→	SYM
ejpam-6062	52	74	2h	2h	NUM
ejpam-6062	52	75	and	and	CCONJ
ejpam-6062	52	76	g	g	NOUN
ejpam-6062	52	77	:	:	PUNCT
ejpam-6062	52	78	e	e	X
ejpam-6062	52	79	→	→	SYM
ejpam-6062	52	80	2e	2e	PROPN
ejpam-6062	52	81	are	be	AUX
ejpam-6062	52	82	maximal	maximal	ADJ
ejpam-6062	52	83	monotone	monotone	ADJ
ejpam-6062	52	84	operators	operator	NOUN
ejpam-6062	52	85	,	,	PUNCT
ejpam-6062	52	86	f	f	X
ejpam-6062	52	87	:	:	PUNCT
ejpam-6062	52	88	h	h	NOUN
ejpam-6062	52	89	→	→	PUNCT
ejpam-6062	52	90	e	e	NOUN
ejpam-6062	52	91	is	be	AUX
ejpam-6062	52	92	a	a	DET
ejpam-6062	52	93	bounded	bounded	ADJ
ejpam-6062	52	94	linear	linear	ADJ
ejpam-6062	52	95	operator	operator	NOUN
ejpam-6062	52	96	.	.	PUNCT
ejpam-6062	53	1	they	they	PRON
ejpam-6062	53	2	proposed	propose	VERB
ejpam-6062	53	3	a	a	DET
ejpam-6062	53	4	viscosity	viscosity	NOUN
ejpam-6062	53	5	iterative	iterative	NOUN
ejpam-6062	53	6	scheme	scheme	NOUN
ejpam-6062	53	7	and	and	CCONJ
ejpam-6062	53	8	under	under	ADP
ejpam-6062	53	9	mild	mild	ADJ
ejpam-6062	53	10	conditions	condition	NOUN
ejpam-6062	53	11	and	and	CCONJ
ejpam-6062	53	12	proved	prove	VERB
ejpam-6062	53	13	a	a	DET
ejpam-6062	53	14	strong	strong	ADJ
ejpam-6062	53	15	convergence	convergence	NOUN
ejpam-6062	53	16	theorem	theorem	VERB
ejpam-6062	53	17	.	.	PUNCT
ejpam-6062	54	1	h.	h.	PROPN
ejpam-6062	54	2	a.	a.	PROPN
ejpam-6062	54	3	abass	abass	PROPN
ejpam-6062	54	4	et	et	PROPN
ejpam-6062	54	5	al	al	PROPN
ejpam-6062	54	6	.	.	PUNCT
ejpam-6062	54	7	/	/	SYM
ejpam-6062	54	8	eur	eur	PROPN
ejpam-6062	54	9	.	.	PUNCT
ejpam-6062	55	1	j.	j.	PROPN
ejpam-6062	55	2	pure	pure	PROPN
ejpam-6062	55	3	appl	appl	PROPN
ejpam-6062	55	4	.	.	PROPN
ejpam-6062	55	5	math	math	PROPN
ejpam-6062	55	6	,	,	PUNCT
ejpam-6062	55	7	18	18	NUM
ejpam-6062	55	8	(	(	PUNCT
ejpam-6062	55	9	2	2	NUM
ejpam-6062	55	10	)	)	PUNCT
ejpam-6062	55	11	(	(	PUNCT
ejpam-6062	55	12	2025	2025	NUM
ejpam-6062	55	13	)	)	PUNCT
ejpam-6062	55	14	,	,	PUNCT
ejpam-6062	55	15	6062	6062	NUM
ejpam-6062	55	16	4	4	NUM
ejpam-6062	55	17	of	of	ADP
ejpam-6062	55	18	22	22	NUM
ejpam-6062	55	19	inspired	inspire	VERB
ejpam-6062	55	20	by	by	ADP
ejpam-6062	55	21	the	the	DET
ejpam-6062	55	22	results	result	NOUN
ejpam-6062	55	23	discussed	discuss	VERB
ejpam-6062	55	24	above	above	ADV
ejpam-6062	55	25	,	,	PUNCT
ejpam-6062	55	26	our	our	PRON
ejpam-6062	55	27	second	second	ADJ
ejpam-6062	55	28	motivation	motivation	NOUN
ejpam-6062	55	29	is	be	AUX
ejpam-6062	55	30	to	to	PART
ejpam-6062	55	31	propose	propose	VERB
ejpam-6062	55	32	an	an	DET
ejpam-6062	55	33	iterative	iterative	NOUN
ejpam-6062	55	34	algorithm	algorithm	NOUN
ejpam-6062	55	35	for	for	ADP
ejpam-6062	55	36	approximating	approximate	VERB
ejpam-6062	55	37	a	a	DET
ejpam-6062	55	38	common	common	ADJ
ejpam-6062	55	39	solution	solution	NOUN
ejpam-6062	55	40	of	of	ADP
ejpam-6062	55	41	a	a	DET
ejpam-6062	55	42	fixed	fix	VERB
ejpam-6062	55	43	point	point	NOUN
ejpam-6062	55	44	problem	problem	NOUN
ejpam-6062	55	45	and	and	CCONJ
ejpam-6062	55	46	split	split	VERB
ejpam-6062	55	47	variational	variational	ADJ
ejpam-6062	55	48	inclusion	inclusion	NOUN
ejpam-6062	55	49	problem	problem	NOUN
ejpam-6062	55	50	with	with	ADP
ejpam-6062	55	51	multiple	multiple	ADJ
ejpam-6062	55	52	output	output	NOUN
ejpam-6062	55	53	sets	set	NOUN
ejpam-6062	55	54	.	.	PUNCT
ejpam-6062	56	1	the	the	DET
ejpam-6062	56	2	proposed	propose	VERB
ejpam-6062	56	3	method	method	NOUN
ejpam-6062	56	4	combines	combine	VERB
ejpam-6062	56	5	the	the	DET
ejpam-6062	56	6	mann	mann	PROPN
ejpam-6062	56	7	iterative	iterative	NOUN
ejpam-6062	56	8	,	,	PUNCT
ejpam-6062	56	9	the	the	DET
ejpam-6062	56	10	halpern	halpern	ADJ
ejpam-6062	56	11	technique	technique	NOUN
ejpam-6062	56	12	and	and	CCONJ
ejpam-6062	56	13	a	a	DET
ejpam-6062	56	14	carefully	carefully	ADV
ejpam-6062	56	15	selected	select	VERB
ejpam-6062	56	16	step	step	NOUN
ejpam-6062	56	17	size	size	NOUN
ejpam-6062	56	18	to	to	PART
ejpam-6062	56	19	avoid	avoid	VERB
ejpam-6062	56	20	the	the	DET
ejpam-6062	56	21	dependence	dependence	NOUN
ejpam-6062	56	22	of	of	ADP
ejpam-6062	56	23	the	the	DET
ejpam-6062	56	24	method	method	NOUN
ejpam-6062	56	25	on	on	ADP
ejpam-6062	56	26	prior	prior	ADJ
ejpam-6062	56	27	knowledge	knowledge	NOUN
ejpam-6062	56	28	of	of	ADP
ejpam-6062	56	29	the	the	DET
ejpam-6062	56	30	operator	operator	NOUN
ejpam-6062	56	31	norms	norm	NOUN
ejpam-6062	56	32	.	.	PUNCT
ejpam-6062	57	1	using	use	VERB
ejpam-6062	57	2	this	this	DET
ejpam-6062	57	3	method	method	NOUN
ejpam-6062	57	4	,	,	PUNCT
ejpam-6062	57	5	we	we	PRON
ejpam-6062	57	6	prove	prove	VERB
ejpam-6062	57	7	a	a	DET
ejpam-6062	57	8	strong	strong	ADJ
ejpam-6062	57	9	convergence	convergence	NOUN
ejpam-6062	57	10	method	method	NOUN
ejpam-6062	57	11	for	for	ADP
ejpam-6062	57	12	approximating	approximate	VERB
ejpam-6062	57	13	a	a	DET
ejpam-6062	57	14	common	common	ADJ
ejpam-6062	57	15	solution	solution	NOUN
ejpam-6062	57	16	of	of	ADP
ejpam-6062	57	17	an	an	DET
ejpam-6062	57	18	svipos	svipos	NOUN
ejpam-6062	57	19	and	and	CCONJ
ejpam-6062	57	20	a	a	DET
ejpam-6062	57	21	fixed	fix	VERB
ejpam-6062	57	22	point	point	NOUN
ejpam-6062	57	23	problem	problem	NOUN
ejpam-6062	57	24	for	for	ADP
ejpam-6062	57	25	a	a	DET
ejpam-6062	57	26	bregman	bregman	NOUN
ejpam-6062	57	27	multi	multi	ADJ
ejpam-6062	57	28	-	-	ADJ
ejpam-6062	57	29	valued	value	VERB
ejpam-6062	57	30	mapping	mapping	NOUN
ejpam-6062	57	31	in	in	ADP
ejpam-6062	57	32	the	the	DET
ejpam-6062	57	33	framework	framework	NOUN
ejpam-6062	57	34	of	of	ADP
ejpam-6062	57	35	real	real	ADJ
ejpam-6062	57	36	reflexive	reflexive	ADJ
ejpam-6062	57	37	banach	banach	NOUN
ejpam-6062	57	38	spaces	space	VERB
ejpam-6062	57	39	.	.	PUNCT
ejpam-6062	58	1	in	in	ADP
ejpam-6062	58	2	particular	particular	ADJ
ejpam-6062	58	3	,	,	PUNCT
ejpam-6062	58	4	the	the	DET
ejpam-6062	58	5	following	follow	VERB
ejpam-6062	58	6	are	be	AUX
ejpam-6062	58	7	some	some	PRON
ejpam-6062	58	8	of	of	ADP
ejpam-6062	58	9	the	the	DET
ejpam-6062	58	10	highlights	highlight	NOUN
ejpam-6062	58	11	of	of	ADP
ejpam-6062	58	12	the	the	DET
ejpam-6062	58	13	present	present	ADJ
ejpam-6062	58	14	study	study	NOUN
ejpam-6062	58	15	:	:	PUNCT
ejpam-6062	58	16	(	(	PUNCT
ejpam-6062	58	17	i	i	NOUN
ejpam-6062	58	18	)	)	PUNCT
ejpam-6062	58	19	the	the	DET
ejpam-6062	58	20	main	main	ADJ
ejpam-6062	58	21	result	result	NOUN
ejpam-6062	58	22	in	in	ADP
ejpam-6062	58	23	this	this	DET
ejpam-6062	58	24	article	article	NOUN
ejpam-6062	58	25	generalizes	generalize	VERB
ejpam-6062	58	26	the	the	DET
ejpam-6062	58	27	results	result	NOUN
ejpam-6062	58	28	in	in	ADP
ejpam-6062	58	29	[	[	X
ejpam-6062	58	30	27	27	NUM
ejpam-6062	58	31	]	]	PUNCT
ejpam-6062	58	32	and	and	CCONJ
ejpam-6062	58	33	[	[	X
ejpam-6062	58	34	14	14	NUM
ejpam-6062	58	35	]	]	PUNCT
ejpam-6062	58	36	from	from	ADP
ejpam-6062	58	37	p	p	ADJ
ejpam-6062	58	38	-	-	PUNCT
ejpam-6062	58	39	uniformly	uniformly	ADJ
ejpam-6062	58	40	banach	banach	NOUN
ejpam-6062	58	41	spaces	space	NOUN
ejpam-6062	58	42	which	which	PRON
ejpam-6062	58	43	are	be	AUX
ejpam-6062	58	44	also	also	ADV
ejpam-6062	58	45	uniformly	uniformly	ADV
ejpam-6062	58	46	smooth	smooth	ADJ
ejpam-6062	58	47	to	to	PART
ejpam-6062	58	48	reflexive	reflexive	VERB
ejpam-6062	58	49	banach	banach	NOUN
ejpam-6062	58	50	spaces	space	NOUN
ejpam-6062	58	51	.	.	PUNCT
ejpam-6062	59	1	(	(	PUNCT
ejpam-6062	59	2	ii	ii	X
ejpam-6062	59	3	)	)	PUNCT
ejpam-6062	59	4	the	the	DET
ejpam-6062	59	5	problem	problem	NOUN
ejpam-6062	59	6	considered	consider	VERB
ejpam-6062	59	7	in	in	ADP
ejpam-6062	59	8	[	[	X
ejpam-6062	59	9	19	19	NUM
ejpam-6062	59	10	]	]	PUNCT
ejpam-6062	59	11	is	be	AUX
ejpam-6062	59	12	a	a	DET
ejpam-6062	59	13	special	special	ADJ
ejpam-6062	59	14	case	case	NOUN
ejpam-6062	59	15	of	of	ADP
ejpam-6062	59	16	the	the	DET
ejpam-6062	59	17	one	one	NOUN
ejpam-6062	59	18	considered	consider	VERB
ejpam-6062	59	19	in	in	ADP
ejpam-6062	59	20	this	this	DET
ejpam-6062	59	21	article	article	NOUN
ejpam-6062	59	22	and	and	CCONJ
ejpam-6062	59	23	generalizes	generalize	VERB
ejpam-6062	59	24	the	the	DET
ejpam-6062	59	25	results	result	NOUN
ejpam-6062	59	26	in	in	ADP
ejpam-6062	59	27	[	[	X
ejpam-6062	59	28	6	6	NUM
ejpam-6062	59	29	,	,	PUNCT
ejpam-6062	59	30	7	7	NUM
ejpam-6062	59	31	,	,	PUNCT
ejpam-6062	59	32	11	11	NUM
ejpam-6062	59	33	,	,	PUNCT
ejpam-6062	59	34	19	19	NUM
ejpam-6062	59	35	,	,	PUNCT
ejpam-6062	59	36	28	28	NUM
ejpam-6062	59	37	,	,	PUNCT
ejpam-6062	59	38	29	29	NUM
ejpam-6062	59	39	]	]	PUNCT
ejpam-6062	59	40	from	from	ADP
ejpam-6062	59	41	real	real	ADJ
ejpam-6062	59	42	hilbert	hilbert	NOUN
ejpam-6062	59	43	spaces	space	NOUN
ejpam-6062	59	44	to	to	ADP
ejpam-6062	59	45	a	a	DET
ejpam-6062	59	46	reflexive	reflexive	ADJ
ejpam-6062	59	47	banach	banach	NOUN
ejpam-6062	59	48	spaces	space	VERB
ejpam-6062	59	49	.	.	PUNCT
ejpam-6062	60	1	(	(	PUNCT
ejpam-6062	60	2	iii	iii	X
ejpam-6062	60	3	)	)	PUNCT
ejpam-6062	60	4	it	it	PRON
ejpam-6062	60	5	is	be	AUX
ejpam-6062	60	6	worth	worth	ADJ
ejpam-6062	60	7	mentioning	mention	VERB
ejpam-6062	60	8	that	that	SCONJ
ejpam-6062	60	9	the	the	DET
ejpam-6062	60	10	proof	proof	NOUN
ejpam-6062	60	11	of	of	ADP
ejpam-6062	60	12	convergence	convergence	NOUN
ejpam-6062	60	13	proposed	propose	VERB
ejpam-6062	60	14	in	in	ADP
ejpam-6062	60	15	this	this	DET
ejpam-6062	60	16	paper	paper	NOUN
ejpam-6062	60	17	is	be	AUX
ejpam-6062	60	18	different	different	ADJ
ejpam-6062	60	19	from	from	ADP
ejpam-6062	60	20	the	the	DET
ejpam-6062	60	21	ones	one	NOUN
ejpam-6062	60	22	in	in	ADP
ejpam-6062	60	23	[	[	X
ejpam-6062	60	24	6	6	NUM
ejpam-6062	60	25	,	,	PUNCT
ejpam-6062	60	26	14	14	NUM
ejpam-6062	60	27	,	,	PUNCT
ejpam-6062	60	28	27	27	NUM
ejpam-6062	60	29	,	,	PUNCT
ejpam-6062	60	30	29	29	NUM
ejpam-6062	60	31	]	]	PUNCT
ejpam-6062	60	32	in	in	ADP
ejpam-6062	60	33	the	the	DET
ejpam-6062	60	34	sense	sense	NOUN
ejpam-6062	60	35	that	that	SCONJ
ejpam-6062	60	36	our	our	PRON
ejpam-6062	60	37	approach	approach	NOUN
ejpam-6062	60	38	does	do	AUX
ejpam-6062	60	39	not	not	PART
ejpam-6062	60	40	distinguish	distinguish	VERB
ejpam-6062	60	41	between	between	ADP
ejpam-6062	60	42	whether	whether	SCONJ
ejpam-6062	60	43	the	the	DET
ejpam-6062	60	44	sequence	sequence	NOUN
ejpam-6062	60	45	generated	generate	VERB
ejpam-6062	60	46	by	by	ADP
ejpam-6062	60	47	our	our	PRON
ejpam-6062	60	48	algorithm	algorithm	NOUN
ejpam-6062	60	49	is	be	AUX
ejpam-6062	60	50	fejer	fejer	ADJ
ejpam-6062	60	51	-	-	PUNCT
ejpam-6062	60	52	monotone	monotone	NOUN
ejpam-6062	60	53	or	or	CCONJ
ejpam-6062	60	54	not	not	PART
ejpam-6062	60	55	.	.	PUNCT
ejpam-6062	61	1	our	our	PRON
ejpam-6062	61	2	approach	approach	NOUN
ejpam-6062	61	3	is	be	AUX
ejpam-6062	61	4	simple	simple	ADJ
ejpam-6062	61	5	and	and	CCONJ
ejpam-6062	61	6	more	more	ADV
ejpam-6062	61	7	elegant	elegant	ADJ
ejpam-6062	61	8	.	.	PUNCT
ejpam-6062	62	1	(	(	PUNCT
ejpam-6062	62	2	iv	iv	X
ejpam-6062	62	3	)	)	PUNCT
ejpam-6062	62	4	we	we	PRON
ejpam-6062	62	5	dispensed	dispense	VERB
ejpam-6062	62	6	the	the	DET
ejpam-6062	62	7	sets	set	NOUN
ejpam-6062	62	8	{	{	PUNCT
ejpam-6062	62	9	cn	cn	INTJ
ejpam-6062	62	10	,	,	PUNCT
ejpam-6062	62	11	dn	dn	PROPN
ejpam-6062	62	12	,	,	PUNCT
ejpam-6062	62	13	qn}n∈n	qn}n∈n	NOUN
ejpam-6062	62	14	in	in	ADP
ejpam-6062	62	15	our	our	PRON
ejpam-6062	62	16	algorithm	algorithm	NOUN
ejpam-6062	62	17	as	as	SCONJ
ejpam-6062	62	18	this	this	PRON
ejpam-6062	62	19	gives	give	VERB
ejpam-6062	62	20	difficulties	difficulty	NOUN
ejpam-6062	62	21	in	in	ADP
ejpam-6062	62	22	computation	computation	NOUN
ejpam-6062	62	23	.	.	PUNCT
ejpam-6062	63	1	lastly	lastly	ADV
ejpam-6062	63	2	,	,	PUNCT
ejpam-6062	63	3	our	our	PRON
ejpam-6062	63	4	iterative	iterative	NOUN
ejpam-6062	63	5	algorithm	algorithm	NOUN
ejpam-6062	63	6	is	be	AUX
ejpam-6062	63	7	designed	design	VERB
ejpam-6062	63	8	in	in	ADP
ejpam-6062	63	9	such	such	DET
ejpam-6062	63	10	a	a	DET
ejpam-6062	63	11	way	way	NOUN
ejpam-6062	63	12	that	that	PRON
ejpam-6062	63	13	it	it	PRON
ejpam-6062	63	14	does	do	AUX
ejpam-6062	63	15	not	not	PART
ejpam-6062	63	16	require	require	VERB
ejpam-6062	63	17	prior	prior	ADJ
ejpam-6062	63	18	knowledge	knowledge	NOUN
ejpam-6062	63	19	of	of	ADP
ejpam-6062	63	20	operator	operator	NOUN
ejpam-6062	63	21	norm	norm	NOUN
ejpam-6062	63	22	as	as	SCONJ
ejpam-6062	63	23	this	this	PRON
ejpam-6062	63	24	also	also	ADV
ejpam-6062	63	25	gives	give	VERB
ejpam-6062	63	26	difficulties	difficulty	NOUN
ejpam-6062	63	27	in	in	ADP
ejpam-6062	63	28	computation	computation	NOUN
ejpam-6062	63	29	.	.	PUNCT
ejpam-6062	64	1	2	2	X
ejpam-6062	64	2	.	.	X
ejpam-6062	64	3	preliminaries	preliminary	NOUN
ejpam-6062	64	4	we	we	PRON
ejpam-6062	64	5	state	state	VERB
ejpam-6062	64	6	some	some	DET
ejpam-6062	64	7	known	know	VERB
ejpam-6062	64	8	and	and	CCONJ
ejpam-6062	64	9	useful	useful	ADJ
ejpam-6062	64	10	results	result	NOUN
ejpam-6062	64	11	which	which	PRON
ejpam-6062	64	12	will	will	AUX
ejpam-6062	64	13	be	be	AUX
ejpam-6062	64	14	needed	need	VERB
ejpam-6062	64	15	in	in	ADP
ejpam-6062	64	16	the	the	DET
ejpam-6062	64	17	proof	proof	NOUN
ejpam-6062	64	18	of	of	ADP
ejpam-6062	64	19	our	our	PRON
ejpam-6062	64	20	main	main	ADJ
ejpam-6062	64	21	theorem	theorem	NOUN
ejpam-6062	64	22	.	.	PUNCT
ejpam-6062	65	1	in	in	ADP
ejpam-6062	65	2	the	the	DET
ejpam-6062	65	3	sequel	sequel	NOUN
ejpam-6062	65	4	,	,	PUNCT
ejpam-6062	65	5	we	we	PRON
ejpam-6062	65	6	denote	denote	VERB
ejpam-6062	65	7	strong	strong	ADJ
ejpam-6062	65	8	and	and	CCONJ
ejpam-6062	65	9	weak	weak	ADJ
ejpam-6062	65	10	convergence	convergence	NOUN
ejpam-6062	65	11	by	by	ADP
ejpam-6062	65	12	”	"	PUNCT
ejpam-6062	65	13	→	→	PUNCT
ejpam-6062	65	14	”	"	PUNCT
ejpam-6062	65	15	and	and	CCONJ
ejpam-6062	65	16	”	"	PUNCT
ejpam-6062	65	17	⇀	⇀	PROPN
ejpam-6062	65	18	”	"	PUNCT
ejpam-6062	65	19	,	,	PUNCT
ejpam-6062	65	20	respectively	respectively	ADV
ejpam-6062	65	21	.	.	PUNCT
ejpam-6062	66	1	for	for	ADP
ejpam-6062	66	2	any	any	DET
ejpam-6062	66	3	x	x	SYM
ejpam-6062	66	4	∈	∈	PROPN
ejpam-6062	66	5	e	e	NOUN
ejpam-6062	66	6	,	,	PUNCT
ejpam-6062	66	7	we	we	PRON
ejpam-6062	66	8	denote	denote	VERB
ejpam-6062	66	9	the	the	DET
ejpam-6062	66	10	value	value	NOUN
ejpam-6062	66	11	of	of	ADP
ejpam-6062	66	12	x∗	x∗	PROPN
ejpam-6062	66	13	∈	∈	PROPN
ejpam-6062	66	14	e	e	X
ejpam-6062	66	15	at	at	ADP
ejpam-6062	66	16	x	x	SYM
ejpam-6062	66	17	by	by	ADP
ejpam-6062	66	18	⟨x	⟨x	NUM
ejpam-6062	66	19	,	,	PUNCT
ejpam-6062	66	20	x∗⟩	x∗⟩	PROPN
ejpam-6062	66	21	.	.	PUNCT
ejpam-6062	67	1	let	let	VERB
ejpam-6062	67	2	e	e	PRON
ejpam-6062	67	3	be	be	AUX
ejpam-6062	67	4	a	a	DET
ejpam-6062	67	5	reflexive	reflexive	ADJ
ejpam-6062	67	6	banach	banach	NOUN
ejpam-6062	67	7	space	space	NOUN
ejpam-6062	67	8	with	with	ADP
ejpam-6062	67	9	e∗	e∗	PROPN
ejpam-6062	67	10	its	its	PRON
ejpam-6062	67	11	dual	dual	ADJ
ejpam-6062	67	12	and	and	CCONJ
ejpam-6062	67	13	q	q	AUX
ejpam-6062	67	14	be	be	AUX
ejpam-6062	67	15	a	a	DET
ejpam-6062	67	16	nonempty	nonempty	ADV
ejpam-6062	67	17	closed	close	VERB
ejpam-6062	67	18	and	and	CCONJ
ejpam-6062	67	19	convex	convex	PROPN
ejpam-6062	67	20	subset	subset	NOUN
ejpam-6062	67	21	of	of	ADP
ejpam-6062	67	22	e.	e.	PROPN
ejpam-6062	67	23	let	let	VERB
ejpam-6062	67	24	g	g	NOUN
ejpam-6062	67	25	:	:	PUNCT
ejpam-6062	67	26	e	e	X
ejpam-6062	67	27	→	→	PUNCT
ejpam-6062	67	28	(	(	PUNCT
ejpam-6062	67	29	−∞,+∞	−∞,+∞	ADV
ejpam-6062	67	30	]	]	PUNCT
ejpam-6062	67	31	be	be	AUX
ejpam-6062	67	32	a	a	DET
ejpam-6062	67	33	proper	proper	ADJ
ejpam-6062	67	34	,	,	PUNCT
ejpam-6062	67	35	lower	lower	ADV
ejpam-6062	67	36	semicontinuous	semicontinuous	ADJ
ejpam-6062	67	37	and	and	CCONJ
ejpam-6062	67	38	convex	convex	ADJ
ejpam-6062	67	39	function	function	NOUN
ejpam-6062	67	40	,	,	PUNCT
ejpam-6062	67	41	then	then	ADV
ejpam-6062	67	42	the	the	DET
ejpam-6062	67	43	fenchel	fenchel	PROPN
ejpam-6062	67	44	conjugate	conjugate	NOUN
ejpam-6062	67	45	of	of	ADP
ejpam-6062	67	46	g	g	PROPN
ejpam-6062	67	47	is	be	AUX
ejpam-6062	67	48	the	the	DET
ejpam-6062	67	49	map	map	NOUN
ejpam-6062	67	50	g∗	g∗	NOUN
ejpam-6062	67	51	:	:	PUNCT
ejpam-6062	67	52	e∗	e∗	PROPN
ejpam-6062	67	53	→	→	SYM
ejpam-6062	67	54	(	(	PUNCT
ejpam-6062	67	55	−∞,+∞	−∞,+∞	ADV
ejpam-6062	67	56	]	]	PUNCT
ejpam-6062	67	57	defined	define	VERB
ejpam-6062	67	58	by	by	ADP
ejpam-6062	67	59	g∗(x∗	g∗(x∗	NOUN
ejpam-6062	67	60	)	)	PUNCT
ejpam-6062	67	61	=	=	PUNCT
ejpam-6062	68	1	sup{⟨x	sup{⟨x	NOUN
ejpam-6062	68	2	,	,	PUNCT
ejpam-6062	68	3	x∗⟩	x∗⟩	PROPN
ejpam-6062	68	4	−	−	PROPN
ejpam-6062	68	5	g(x	g(x	NOUN
ejpam-6062	68	6	)	)	PUNCT
ejpam-6062	68	7	:	:	PUNCT
ejpam-6062	69	1	x	x	X
ejpam-6062	69	2	∈	∈	NOUN
ejpam-6062	69	3	e	e	NOUN
ejpam-6062	69	4	}	}	PUNCT
ejpam-6062	69	5	,	,	PUNCT
ejpam-6062	69	6	x∗	x∗	PROPN
ejpam-6062	69	7	∈	∈	PROPN
ejpam-6062	69	8	e∗.	e∗.	NOUN
ejpam-6062	69	9	let	let	VERB
ejpam-6062	69	10	the	the	DET
ejpam-6062	69	11	domain	domain	NOUN
ejpam-6062	69	12	of	of	ADP
ejpam-6062	69	13	g	g	PROPN
ejpam-6062	69	14	be	be	AUX
ejpam-6062	69	15	denoted	denote	VERB
ejpam-6062	69	16	by	by	ADP
ejpam-6062	69	17	domg	domg	NOUN
ejpam-6062	69	18	=	=	SYM
ejpam-6062	69	19	{	{	PUNCT
ejpam-6062	69	20	x	x	PUNCT
ejpam-6062	69	21	∈	∈	PROPN
ejpam-6062	69	22	e	e	NOUN
ejpam-6062	69	23	:	:	PUNCT
ejpam-6062	69	24	g(x	g(x	NOUN
ejpam-6062	69	25	)	)	PUNCT
ejpam-6062	69	26	<	<	X
ejpam-6062	70	1	+	+	PUNCT
ejpam-6062	70	2	∞	∞	NOUN
ejpam-6062	70	3	}	}	PUNCT
ejpam-6062	70	4	,	,	PUNCT
ejpam-6062	70	5	hence	hence	ADV
ejpam-6062	70	6	for	for	ADP
ejpam-6062	70	7	any	any	DET
ejpam-6062	70	8	y	y	PROPN
ejpam-6062	70	9	∈	∈	PROPN
ejpam-6062	70	10	e	e	NOUN
ejpam-6062	70	11	,	,	PUNCT
ejpam-6062	70	12	we	we	PRON
ejpam-6062	70	13	define	define	VERB
ejpam-6062	70	14	the	the	DET
ejpam-6062	70	15	directional	directional	ADJ
ejpam-6062	70	16	derivative	derivative	NOUN
ejpam-6062	70	17	of	of	ADP
ejpam-6062	70	18	g	g	PROPN
ejpam-6062	70	19	at	at	ADP
ejpam-6062	70	20	x	x	X
ejpam-6062	70	21	in	in	ADP
ejpam-6062	70	22	the	the	DET
ejpam-6062	70	23	direction	direction	NOUN
ejpam-6062	70	24	of	of	ADP
ejpam-6062	70	25	y	y	PROPN
ejpam-6062	70	26	by	by	ADP
ejpam-6062	70	27	g0(x	g0(x	PROPN
ejpam-6062	70	28	,	,	PUNCT
ejpam-6062	70	29	y	y	NOUN
ejpam-6062	70	30	)	)	PUNCT
ejpam-6062	70	31	=	=	SYM
ejpam-6062	70	32	lim	lim	PROPN
ejpam-6062	70	33	t→0	t→0	PROPN
ejpam-6062	70	34	+	+	CCONJ
ejpam-6062	70	35	g(x+	g(x+	CCONJ
ejpam-6062	70	36	ty)−	ty)−	PRON
ejpam-6062	70	37	g(x	g(x	NOUN
ejpam-6062	70	38	)	)	PUNCT
ejpam-6062	70	39	t	t	NOUN
ejpam-6062	70	40	.	.	PUNCT
ejpam-6062	71	1	h.	h.	PROPN
ejpam-6062	71	2	a.	a.	PROPN
ejpam-6062	71	3	abass	abass	PROPN
ejpam-6062	71	4	et	et	PROPN
ejpam-6062	71	5	al	al	PROPN
ejpam-6062	71	6	.	.	PUNCT
ejpam-6062	71	7	/	/	SYM
ejpam-6062	71	8	eur	eur	PROPN
ejpam-6062	71	9	.	.	PUNCT
ejpam-6062	72	1	j.	j.	PROPN
ejpam-6062	72	2	pure	pure	PROPN
ejpam-6062	72	3	appl	appl	PROPN
ejpam-6062	72	4	.	.	PROPN
ejpam-6062	72	5	math	math	PROPN
ejpam-6062	72	6	,	,	PUNCT
ejpam-6062	72	7	18	18	NUM
ejpam-6062	72	8	(	(	PUNCT
ejpam-6062	72	9	2	2	NUM
ejpam-6062	72	10	)	)	PUNCT
ejpam-6062	72	11	(	(	PUNCT
ejpam-6062	72	12	2025	2025	NUM
ejpam-6062	72	13	)	)	PUNCT
ejpam-6062	72	14	,	,	PUNCT
ejpam-6062	72	15	6062	6062	NUM
ejpam-6062	72	16	5	5	NUM
ejpam-6062	72	17	of	of	ADP
ejpam-6062	72	18	22	22	NUM
ejpam-6062	72	19	the	the	DET
ejpam-6062	72	20	function	function	NOUN
ejpam-6062	72	21	g	g	PROPN
ejpam-6062	72	22	is	be	AUX
ejpam-6062	72	23	said	say	VERB
ejpam-6062	72	24	to	to	PART
ejpam-6062	72	25	be	be	AUX
ejpam-6062	72	26	(	(	PUNCT
ejpam-6062	72	27	i	i	NOUN
ejpam-6062	72	28	)	)	PUNCT
ejpam-6062	72	29	gâteaux	gâteaux	PROPN
ejpam-6062	72	30	differentiable	differentiable	ADJ
ejpam-6062	72	31	at	at	ADP
ejpam-6062	72	32	x	x	X
ejpam-6062	72	33	if	if	SCONJ
ejpam-6062	72	34	limt→0	limt→0	NOUN
ejpam-6062	72	35	+	+	CCONJ
ejpam-6062	72	36	g(x+ty)−g(x	g(x+ty)−g(x	PROPN
ejpam-6062	72	37	)	)	PUNCT
ejpam-6062	72	38	t	t	NOUN
ejpam-6062	72	39	exists	exist	VERB
ejpam-6062	72	40	for	for	ADP
ejpam-6062	72	41	any	any	DET
ejpam-6062	72	42	y.	y.	NOUN
ejpam-6062	72	43	at	at	ADP
ejpam-6062	72	44	this	this	DET
ejpam-6062	72	45	time	time	NOUN
ejpam-6062	72	46	,	,	PUNCT
ejpam-6062	72	47	the	the	DET
ejpam-6062	72	48	gradient	gradient	NOUN
ejpam-6062	72	49	of	of	ADP
ejpam-6062	72	50	g	g	PROPN
ejpam-6062	72	51	at	at	ADP
ejpam-6062	72	52	x	x	PROPN
ejpam-6062	72	53	is	be	AUX
ejpam-6062	72	54	the	the	DET
ejpam-6062	72	55	linear	linear	ADJ
ejpam-6062	72	56	function	function	NOUN
ejpam-6062	72	57	∇g	∇g	ADJ
ejpam-6062	72	58	e(x	e(x	NUM
ejpam-6062	72	59	)	)	PUNCT
ejpam-6062	72	60	satisfying	satisfy	VERB
ejpam-6062	72	61	⟨∇g	⟨∇g	NOUN
ejpam-6062	72	62	e(x	e(x	NUM
ejpam-6062	72	63	)	)	PUNCT
ejpam-6062	72	64	,	,	PUNCT
ejpam-6062	72	65	y⟩	y⟩	NOUN
ejpam-6062	72	66	:	:	PUNCT
ejpam-6062	72	67	=	=	SYM
ejpam-6062	72	68	g0(x	g0(x	PROPN
ejpam-6062	72	69	,	,	PUNCT
ejpam-6062	72	70	y	y	PROPN
ejpam-6062	72	71	)	)	PUNCT
ejpam-6062	72	72	,	,	PUNCT
ejpam-6062	72	73	∀	∀	PUNCT
ejpam-6062	72	74	y	y	PROPN
ejpam-6062	72	75	∈	∈	PROPN
ejpam-6062	72	76	e.	e.	PROPN
ejpam-6062	72	77	(	(	PUNCT
ejpam-6062	72	78	ii	ii	PROPN
ejpam-6062	72	79	)	)	PUNCT
ejpam-6062	72	80	gâteaux	gâteaux	NOUN
ejpam-6062	72	81	differentiable	differentiable	ADJ
ejpam-6062	72	82	,	,	PUNCT
ejpam-6062	72	83	if	if	SCONJ
ejpam-6062	72	84	it	it	PRON
ejpam-6062	72	85	is	be	AUX
ejpam-6062	72	86	gâteaux	gâteaux	ADV
ejpam-6062	72	87	differentiable	differentiable	ADJ
ejpam-6062	72	88	for	for	ADP
ejpam-6062	72	89	any	any	DET
ejpam-6062	72	90	x	x	SYM
ejpam-6062	72	91	∈	∈	PROPN
ejpam-6062	72	92	int(domg	int(domg	NOUN
ejpam-6062	72	93	)	)	PUNCT
ejpam-6062	72	94	;	;	PUNCT
ejpam-6062	72	95	where	where	SCONJ
ejpam-6062	72	96	int(domg	int(domg	NOUN
ejpam-6062	72	97	)	)	PUNCT
ejpam-6062	72	98	stands	stand	VERB
ejpam-6062	72	99	for	for	ADP
ejpam-6062	72	100	the	the	DET
ejpam-6062	72	101	interior	interior	NOUN
ejpam-6062	72	102	of	of	ADP
ejpam-6062	72	103	domain	domain	NOUN
ejpam-6062	72	104	of	of	ADP
ejpam-6062	72	105	g.	g.	PROPN
ejpam-6062	72	106	(	(	PUNCT
ejpam-6062	72	107	iii	iii	NOUN
ejpam-6062	72	108	)	)	PUNCT
ejpam-6062	72	109	fréchet	fréchet	NOUN
ejpam-6062	72	110	differentiable	differentiable	ADJ
ejpam-6062	72	111	at	at	ADP
ejpam-6062	72	112	x	x	X
ejpam-6062	72	113	,	,	PUNCT
ejpam-6062	72	114	if	if	SCONJ
ejpam-6062	72	115	its	its	PRON
ejpam-6062	72	116	limit	limit	NOUN
ejpam-6062	72	117	is	be	AUX
ejpam-6062	72	118	attained	attain	VERB
ejpam-6062	72	119	uniformly	uniformly	ADV
ejpam-6062	72	120	in	in	ADP
ejpam-6062	72	121	||y||	||y||	NOUN
ejpam-6062	72	122	=	=	SYM
ejpam-6062	72	123	1	1	NUM
ejpam-6062	72	124	;	;	PUNCT
ejpam-6062	72	125	(	(	PUNCT
ejpam-6062	72	126	iv	iv	X
ejpam-6062	72	127	)	)	PUNCT
ejpam-6062	72	128	uniformly	uniformly	ADV
ejpam-6062	72	129	fréchet	fréchet	VERB
ejpam-6062	72	130	differentiable	differentiable	ADJ
ejpam-6062	72	131	on	on	ADP
ejpam-6062	72	132	a	a	DET
ejpam-6062	72	133	subset	subset	NOUN
ejpam-6062	72	134	q	q	NOUN
ejpam-6062	72	135	of	of	ADP
ejpam-6062	72	136	e	e	NOUN
ejpam-6062	72	137	,	,	PUNCT
ejpam-6062	72	138	if	if	SCONJ
ejpam-6062	72	139	the	the	DET
ejpam-6062	72	140	above	above	ADJ
ejpam-6062	72	141	limit	limit	NOUN
ejpam-6062	72	142	is	be	AUX
ejpam-6062	72	143	attained	attain	VERB
ejpam-6062	72	144	uniformly	uniformly	ADV
ejpam-6062	72	145	for	for	ADP
ejpam-6062	72	146	x	x	SYM
ejpam-6062	72	147	∈	∈	PROPN
ejpam-6062	72	148	q	q	NOUN
ejpam-6062	72	149	and	and	CCONJ
ejpam-6062	72	150	||y||	||y||	X
ejpam-6062	72	151	=	=	SYM
ejpam-6062	72	152	1	1	X
ejpam-6062	72	153	.	.	PUNCT
ejpam-6062	73	1	let	let	VERB
ejpam-6062	73	2	g	g	NOUN
ejpam-6062	73	3	:	:	PUNCT
ejpam-6062	73	4	e	e	X
ejpam-6062	73	5	→	→	PUNCT
ejpam-6062	73	6	(	(	PUNCT
ejpam-6062	73	7	−∞,+∞	−∞,+∞	ADV
ejpam-6062	73	8	]	]	PUNCT
ejpam-6062	73	9	be	be	VERB
ejpam-6062	73	10	a	a	DET
ejpam-6062	73	11	function	function	NOUN
ejpam-6062	73	12	,	,	PUNCT
ejpam-6062	73	13	then	then	ADV
ejpam-6062	73	14	g	g	PROPN
ejpam-6062	73	15	is	be	AUX
ejpam-6062	73	16	said	say	VERB
ejpam-6062	73	17	to	to	PART
ejpam-6062	73	18	be	be	AUX
ejpam-6062	73	19	:	:	PUNCT
ejpam-6062	73	20	(	(	PUNCT
ejpam-6062	73	21	i	i	NOUN
ejpam-6062	73	22	)	)	PUNCT
ejpam-6062	73	23	essentially	essentially	ADV
ejpam-6062	73	24	smooth	smooth	ADJ
ejpam-6062	73	25	,	,	PUNCT
ejpam-6062	73	26	if	if	SCONJ
ejpam-6062	73	27	the	the	DET
ejpam-6062	73	28	subdifferential	subdifferential	NOUN
ejpam-6062	73	29	of	of	ADP
ejpam-6062	73	30	g	g	NOUN
ejpam-6062	73	31	denoted	denote	VERB
ejpam-6062	73	32	by	by	ADP
ejpam-6062	73	33	∂g	∂g	PROPN
ejpam-6062	73	34	is	be	AUX
ejpam-6062	73	35	both	both	PRON
ejpam-6062	73	36	locally	locally	ADV
ejpam-6062	73	37	bounded	bounded	ADJ
ejpam-6062	73	38	and	and	CCONJ
ejpam-6062	73	39	single	single	ADV
ejpam-6062	73	40	-	-	PUNCT
ejpam-6062	73	41	valued	value	VERB
ejpam-6062	73	42	on	on	ADP
ejpam-6062	73	43	its	its	PRON
ejpam-6062	73	44	domain	domain	NOUN
ejpam-6062	73	45	,	,	PUNCT
ejpam-6062	73	46	where	where	SCONJ
ejpam-6062	73	47	∂g(x	∂g(x	NOUN
ejpam-6062	73	48	)	)	PUNCT
ejpam-6062	74	1	=	=	PRON
ejpam-6062	74	2	{	{	PUNCT
ejpam-6062	74	3	x∗	x∗	PROPN
ejpam-6062	74	4	∈	∈	PROPN
ejpam-6062	74	5	e∗	e∗	NOUN
ejpam-6062	74	6	:	:	PUNCT
ejpam-6062	74	7	g(x	g(x	NOUN
ejpam-6062	74	8	)	)	PUNCT
ejpam-6062	75	1	+	+	CCONJ
ejpam-6062	75	2	⟨y	⟨y	X
ejpam-6062	76	1	−	−	NOUN
ejpam-6062	76	2	x	x	SYM
ejpam-6062	76	3	,	,	PUNCT
ejpam-6062	76	4	x∗⟩	x∗⟩	PROPN
ejpam-6062	76	5	≤	≤	NUM
ejpam-6062	76	6	g(y	g(y	NOUN
ejpam-6062	76	7	)	)	PUNCT
ejpam-6062	76	8	,	,	PUNCT
ejpam-6062	76	9	y	y	PROPN
ejpam-6062	76	10	∈	∈	PROPN
ejpam-6062	76	11	e	e	X
ejpam-6062	76	12	}	}	PUNCT
ejpam-6062	76	13	;	;	PUNCT
ejpam-6062	76	14	(	(	PUNCT
ejpam-6062	76	15	ii	ii	NOUN
ejpam-6062	76	16	)	)	PUNCT
ejpam-6062	76	17	essentially	essentially	ADV
ejpam-6062	76	18	strictly	strictly	ADV
ejpam-6062	76	19	convex	convex	VERB
ejpam-6062	76	20	,	,	PUNCT
ejpam-6062	76	21	if	if	SCONJ
ejpam-6062	76	22	(	(	PUNCT
ejpam-6062	76	23	∂g)−1	∂g)−1	INTJ
ejpam-6062	76	24	is	be	AUX
ejpam-6062	76	25	locally	locally	ADV
ejpam-6062	76	26	bounded	bound	VERB
ejpam-6062	76	27	on	on	ADP
ejpam-6062	76	28	its	its	PRON
ejpam-6062	76	29	domain	domain	NOUN
ejpam-6062	76	30	and	and	CCONJ
ejpam-6062	76	31	g	g	NOUN
ejpam-6062	76	32	is	be	AUX
ejpam-6062	76	33	strictly	strictly	ADV
ejpam-6062	76	34	convex	convex	ADJ
ejpam-6062	76	35	on	on	ADP
ejpam-6062	76	36	every	every	DET
ejpam-6062	76	37	convex	convex	NOUN
ejpam-6062	76	38	subset	subset	NOUN
ejpam-6062	76	39	of	of	ADP
ejpam-6062	76	40	dom	dom	NOUN
ejpam-6062	76	41	∂g	∂g	PROPN
ejpam-6062	76	42	;	;	PUNCT
ejpam-6062	76	43	(	(	PUNCT
ejpam-6062	76	44	iii	iii	X
ejpam-6062	76	45	)	)	PUNCT
ejpam-6062	76	46	legendre	legendre	PROPN
ejpam-6062	76	47	,	,	PUNCT
ejpam-6062	76	48	if	if	SCONJ
ejpam-6062	76	49	it	it	PRON
ejpam-6062	76	50	is	be	AUX
ejpam-6062	76	51	both	both	PRON
ejpam-6062	76	52	essentially	essentially	ADV
ejpam-6062	76	53	smooth	smooth	ADJ
ejpam-6062	76	54	and	and	CCONJ
ejpam-6062	76	55	essentially	essentially	ADV
ejpam-6062	76	56	strictly	strictly	ADV
ejpam-6062	76	57	convex	convex	VERB
ejpam-6062	76	58	.	.	PUNCT
ejpam-6062	77	1	see	see	VERB
ejpam-6062	77	2	[	[	X
ejpam-6062	77	3	30	30	NUM
ejpam-6062	77	4	,	,	PUNCT
ejpam-6062	77	5	31	31	NUM
ejpam-6062	77	6	]	]	PUNCT
ejpam-6062	77	7	for	for	ADP
ejpam-6062	77	8	more	more	ADJ
ejpam-6062	77	9	details	detail	NOUN
ejpam-6062	77	10	on	on	ADP
ejpam-6062	77	11	legendre	legendre	PROPN
ejpam-6062	77	12	functions	function	NOUN
ejpam-6062	77	13	.	.	PUNCT
ejpam-6062	78	1	alternatively	alternatively	ADV
ejpam-6062	78	2	,	,	PUNCT
ejpam-6062	78	3	a	a	DET
ejpam-6062	78	4	function	function	NOUN
ejpam-6062	78	5	g	g	NOUN
ejpam-6062	78	6	is	be	AUX
ejpam-6062	78	7	said	say	VERB
ejpam-6062	78	8	to	to	PART
ejpam-6062	78	9	be	be	AUX
ejpam-6062	78	10	legendre	legendre	PROPN
ejpam-6062	78	11	if	if	SCONJ
ejpam-6062	78	12	it	it	PRON
ejpam-6062	78	13	satisfies	satisfy	VERB
ejpam-6062	78	14	the	the	DET
ejpam-6062	78	15	following	follow	VERB
ejpam-6062	78	16	conditions	condition	NOUN
ejpam-6062	78	17	:	:	PUNCT
ejpam-6062	78	18	(	(	PUNCT
ejpam-6062	78	19	i	i	NOUN
ejpam-6062	78	20	)	)	PUNCT
ejpam-6062	78	21	the	the	DET
ejpam-6062	78	22	int(domg	int(domg	NOUN
ejpam-6062	78	23	)	)	PUNCT
ejpam-6062	78	24	is	be	AUX
ejpam-6062	78	25	nonempty	nonempty	ADJ
ejpam-6062	78	26	,	,	PUNCT
ejpam-6062	78	27	g	g	PROPN
ejpam-6062	78	28	is	be	AUX
ejpam-6062	78	29	gâteaux	gâteaux	ADV
ejpam-6062	78	30	differentiable	differentiable	ADJ
ejpam-6062	78	31	on	on	ADP
ejpam-6062	78	32	int(dom)g	int(dom)g	PROPN
ejpam-6062	78	33	and	and	CCONJ
ejpam-6062	78	34	dom∇g	dom∇g	NOUN
ejpam-6062	78	35	=	=	SYM
ejpam-6062	78	36	int(domg	int(domg	NOUN
ejpam-6062	78	37	)	)	PUNCT
ejpam-6062	78	38	;	;	PUNCT
ejpam-6062	78	39	(	(	PUNCT
ejpam-6062	78	40	ii	ii	X
ejpam-6062	78	41	)	)	PUNCT
ejpam-6062	78	42	the	the	DET
ejpam-6062	78	43	int(domg∗	int(domg∗	NOUN
ejpam-6062	78	44	)	)	PUNCT
ejpam-6062	78	45	is	be	AUX
ejpam-6062	78	46	nonempty	nonempty	ADJ
ejpam-6062	78	47	,	,	PUNCT
ejpam-6062	78	48	g∗	g∗	PROPN
ejpam-6062	78	49	is	be	AUX
ejpam-6062	78	50	gâteaux	gâteaux	VERB
ejpam-6062	78	51	differentiable	differentiable	ADJ
ejpam-6062	78	52	on	on	ADP
ejpam-6062	78	53	int(domg∗	int(domg∗	NOUN
ejpam-6062	78	54	)	)	PUNCT
ejpam-6062	78	55	and	and	CCONJ
ejpam-6062	78	56	dom∇g∗	dom∇g∗	VERB
ejpam-6062	78	57	e∗	e∗	NOUN
ejpam-6062	78	58	=	=	SYM
ejpam-6062	78	59	int(domg∗	int(domg∗	PROPN
ejpam-6062	78	60	)	)	PUNCT
ejpam-6062	78	61	.	.	PUNCT
ejpam-6062	79	1	definition	definition	NOUN
ejpam-6062	79	2	1	1	NUM
ejpam-6062	79	3	.	.	PUNCT
ejpam-6062	80	1	[	[	X
ejpam-6062	80	2	32	32	NUM
ejpam-6062	80	3	]	]	PUNCT
ejpam-6062	80	4	let	let	VERB
ejpam-6062	80	5	e	e	PRON
ejpam-6062	80	6	be	be	AUX
ejpam-6062	80	7	a	a	DET
ejpam-6062	80	8	banach	banach	NOUN
ejpam-6062	80	9	space	space	NOUN
ejpam-6062	80	10	.	.	PUNCT
ejpam-6062	81	1	a	a	DET
ejpam-6062	81	2	function	function	NOUN
ejpam-6062	81	3	g	g	NOUN
ejpam-6062	81	4	:	:	PUNCT
ejpam-6062	81	5	e	e	X
ejpam-6062	81	6	→	→	PUNCT
ejpam-6062	81	7	(	(	PUNCT
ejpam-6062	81	8	−∞,∞	−∞,∞	NOUN
ejpam-6062	81	9	]	]	X
ejpam-6062	81	10	is	be	AUX
ejpam-6062	81	11	said	say	VERB
ejpam-6062	81	12	to	to	PART
ejpam-6062	81	13	be	be	AUX
ejpam-6062	81	14	proper	proper	ADJ
ejpam-6062	81	15	if	if	SCONJ
ejpam-6062	81	16	the	the	DET
ejpam-6062	81	17	interior	interior	NOUN
ejpam-6062	81	18	of	of	ADP
ejpam-6062	81	19	its	its	PRON
ejpam-6062	81	20	domain	domain	NOUN
ejpam-6062	81	21	dom(g	dom(g	NOUN
ejpam-6062	81	22	)	)	PUNCT
ejpam-6062	82	1	is	be	AUX
ejpam-6062	82	2	nonempty	nonempty	ADJ
ejpam-6062	82	3	.	.	PUNCT
ejpam-6062	83	1	let	let	VERB
ejpam-6062	83	2	g	g	NOUN
ejpam-6062	83	3	:	:	PUNCT
ejpam-6062	83	4	e	e	X
ejpam-6062	83	5	→	→	PUNCT
ejpam-6062	83	6	(	(	PUNCT
ejpam-6062	83	7	−∞,∞	−∞,∞	VERB
ejpam-6062	83	8	]	]	X
ejpam-6062	83	9	be	be	AUX
ejpam-6062	83	10	a	a	DET
ejpam-6062	83	11	convex	convex	NOUN
ejpam-6062	83	12	and	and	CCONJ
ejpam-6062	83	13	gâteaux	gâteaux	ADJ
ejpam-6062	83	14	differentiable	differentiable	ADJ
ejpam-6062	83	15	function	function	NOUN
ejpam-6062	83	16	.	.	PUNCT
ejpam-6062	84	1	then	then	ADV
ejpam-6062	84	2	the	the	DET
ejpam-6062	84	3	bregman	bregman	NOUN
ejpam-6062	84	4	distance	distance	NOUN
ejpam-6062	84	5	corresponding	correspond	VERB
ejpam-6062	84	6	to	to	ADP
ejpam-6062	84	7	g	g	PROPN
ejpam-6062	84	8	is	be	AUX
ejpam-6062	84	9	the	the	DET
ejpam-6062	84	10	function	function	NOUN
ejpam-6062	84	11	dg	dg	NOUN
ejpam-6062	84	12	:	:	PUNCT
ejpam-6062	84	13	dom(g)×	dom(g)×	NOUN
ejpam-6062	84	14	intdom(g	intdom(g	PROPN
ejpam-6062	84	15	)	)	PUNCT
ejpam-6062	84	16	→	→	SYM
ejpam-6062	85	1	r	r	NOUN
ejpam-6062	85	2	defined	define	VERB
ejpam-6062	85	3	by	by	ADP
ejpam-6062	85	4	dg(x	dg(x	NUM
ejpam-6062	85	5	,	,	PUNCT
ejpam-6062	85	6	y	y	PROPN
ejpam-6062	85	7	)	)	PUNCT
ejpam-6062	85	8	:	:	PUNCT
ejpam-6062	86	1	=	=	PUNCT
ejpam-6062	86	2	g(x)−	g(x)−	PROPN
ejpam-6062	86	3	g(y)−	g(y)−	PROPN
ejpam-6062	86	4	⟨x−	⟨x−	PROPN
ejpam-6062	86	5	y,∇g	y,∇g	NUM
ejpam-6062	86	6	e(y)⟩	e(y)⟩	NOUN
ejpam-6062	86	7	,	,	PUNCT
ejpam-6062	86	8	∀	∀	X
ejpam-6062	86	9	x	x	NOUN
ejpam-6062	86	10	,	,	PUNCT
ejpam-6062	86	11	y	y	PROPN
ejpam-6062	86	12	∈	∈	PROPN
ejpam-6062	86	13	e.	e.	PROPN
ejpam-6062	86	14	(	(	PUNCT
ejpam-6062	86	15	9	9	NUM
ejpam-6062	86	16	)	)	PUNCT
ejpam-6062	86	17	is	be	AUX
ejpam-6062	86	18	called	call	VERB
ejpam-6062	86	19	the	the	DET
ejpam-6062	86	20	bregman	bregman	NOUN
ejpam-6062	86	21	distance	distance	NOUN
ejpam-6062	86	22	with	with	ADP
ejpam-6062	86	23	respect	respect	NOUN
ejpam-6062	86	24	to	to	ADP
ejpam-6062	86	25	g.	g.	NOUN
ejpam-6062	86	26	it	it	PRON
ejpam-6062	86	27	is	be	AUX
ejpam-6062	86	28	clear	clear	ADJ
ejpam-6062	86	29	that	that	SCONJ
ejpam-6062	86	30	dg(x	dg(x	PROPN
ejpam-6062	86	31	,	,	PUNCT
ejpam-6062	86	32	y	y	PROPN
ejpam-6062	86	33	)	)	PUNCT
ejpam-6062	86	34	≥	≥	NOUN
ejpam-6062	86	35	0	0	NUM
ejpam-6062	86	36	for	for	ADP
ejpam-6062	86	37	all	all	DET
ejpam-6062	86	38	x	x	NOUN
ejpam-6062	86	39	,	,	PUNCT
ejpam-6062	86	40	y	y	PROPN
ejpam-6062	86	41	∈	∈	PROPN
ejpam-6062	86	42	e.	e.	PROPN
ejpam-6062	86	43	h.	h.	PROPN
ejpam-6062	86	44	a.	a.	PROPN
ejpam-6062	86	45	abass	abass	PROPN
ejpam-6062	86	46	et	et	PROPN
ejpam-6062	86	47	al	al	PROPN
ejpam-6062	86	48	.	.	PUNCT
ejpam-6062	86	49	/	/	SYM
ejpam-6062	86	50	eur	eur	PROPN
ejpam-6062	86	51	.	.	PUNCT
ejpam-6062	87	1	j.	j.	PROPN
ejpam-6062	87	2	pure	pure	PROPN
ejpam-6062	87	3	appl	appl	PROPN
ejpam-6062	87	4	.	.	PROPN
ejpam-6062	87	5	math	math	PROPN
ejpam-6062	87	6	,	,	PUNCT
ejpam-6062	87	7	18	18	NUM
ejpam-6062	87	8	(	(	PUNCT
ejpam-6062	87	9	2	2	NUM
ejpam-6062	87	10	)	)	PUNCT
ejpam-6062	87	11	(	(	PUNCT
ejpam-6062	87	12	2025	2025	NUM
ejpam-6062	87	13	)	)	PUNCT
ejpam-6062	87	14	,	,	PUNCT
ejpam-6062	87	15	6062	6062	NUM
ejpam-6062	87	16	6	6	NUM
ejpam-6062	87	17	of	of	ADP
ejpam-6062	87	18	22	22	NUM
ejpam-6062	87	19	it	it	PRON
ejpam-6062	87	20	is	be	AUX
ejpam-6062	87	21	well	well	ADV
ejpam-6062	87	22	-	-	PUNCT
ejpam-6062	87	23	known	know	VERB
ejpam-6062	87	24	that	that	PRON
ejpam-6062	87	25	bregman	bregman	NOUN
ejpam-6062	87	26	distance	distance	NOUN
ejpam-6062	87	27	dg	dg	PROPN
ejpam-6062	87	28	does	do	AUX
ejpam-6062	87	29	not	not	PART
ejpam-6062	87	30	satisfy	satisfy	VERB
ejpam-6062	87	31	the	the	DET
ejpam-6062	87	32	properties	property	NOUN
ejpam-6062	87	33	of	of	ADP
ejpam-6062	87	34	a	a	DET
ejpam-6062	87	35	metric	metric	NOUN
ejpam-6062	87	36	because	because	SCONJ
ejpam-6062	87	37	dg	dg	NOUN
ejpam-6062	87	38	fail	fail	VERB
ejpam-6062	87	39	to	to	PART
ejpam-6062	87	40	satisfy	satisfy	VERB
ejpam-6062	87	41	the	the	DET
ejpam-6062	87	42	symmetric	symmetric	ADJ
ejpam-6062	87	43	and	and	CCONJ
ejpam-6062	87	44	triangular	triangular	NOUN
ejpam-6062	87	45	inequality	inequality	NOUN
ejpam-6062	87	46	property	property	NOUN
ejpam-6062	87	47	.	.	PUNCT
ejpam-6062	88	1	however	however	ADV
ejpam-6062	88	2	,	,	PUNCT
ejpam-6062	88	3	the	the	DET
ejpam-6062	88	4	bregman	bregman	NOUN
ejpam-6062	88	5	distance	distance	NOUN
ejpam-6062	88	6	satisfies	satisfy	VERB
ejpam-6062	88	7	the	the	DET
ejpam-6062	88	8	following	follow	VERB
ejpam-6062	88	9	so	so	ADV
ejpam-6062	88	10	-	-	PUNCT
ejpam-6062	88	11	called	call	VERB
ejpam-6062	88	12	three	three	NUM
ejpam-6062	88	13	point	point	NOUN
ejpam-6062	88	14	identity	identity	NOUN
ejpam-6062	88	15	:	:	PUNCT
ejpam-6062	88	16	for	for	ADP
ejpam-6062	88	17	any	any	DET
ejpam-6062	88	18	x	x	SYM
ejpam-6062	88	19	∈	∈	PROPN
ejpam-6062	88	20	domg	domg	NOUN
ejpam-6062	88	21	and	and	CCONJ
ejpam-6062	88	22	y	y	PROPN
ejpam-6062	88	23	,	,	PUNCT
ejpam-6062	88	24	z	z	PROPN
ejpam-6062	88	25	∈	∈	PROPN
ejpam-6062	88	26	int(domg	int(domg	NOUN
ejpam-6062	88	27	)	)	PUNCT
ejpam-6062	88	28	,	,	PUNCT
ejpam-6062	88	29	dg(x	dg(x	X
ejpam-6062	88	30	,	,	PUNCT
ejpam-6062	88	31	z	z	X
ejpam-6062	88	32	)	)	PUNCT
ejpam-6062	88	33	=	=	SYM
ejpam-6062	88	34	dg(x	dg(x	X
ejpam-6062	88	35	,	,	PUNCT
ejpam-6062	88	36	y	y	NOUN
ejpam-6062	88	37	)	)	PUNCT
ejpam-6062	89	1	+	+	NOUN
ejpam-6062	89	2	dg(y	dg(y	ADJ
ejpam-6062	89	3	,	,	PUNCT
ejpam-6062	89	4	z	z	NOUN
ejpam-6062	89	5	)	)	PUNCT
ejpam-6062	89	6	+	+	CCONJ
ejpam-6062	89	7	⟨x−	⟨x−	PROPN
ejpam-6062	89	8	y,∇g	y,∇g	NUM
ejpam-6062	89	9	e(y)−∇g	e(y)−∇g	NOUN
ejpam-6062	89	10	e(z)⟩.	e(z)⟩.	NOUN
ejpam-6062	89	11	(	(	PUNCT
ejpam-6062	89	12	10	10	NUM
ejpam-6062	89	13	)	)	PUNCT
ejpam-6062	89	14	in	in	ADP
ejpam-6062	89	15	particular	particular	ADJ
ejpam-6062	89	16	,	,	PUNCT
ejpam-6062	89	17	dg(x	dg(x	X
ejpam-6062	89	18	,	,	PUNCT
ejpam-6062	89	19	y	y	NOUN
ejpam-6062	89	20	)	)	PUNCT
ejpam-6062	89	21	=	=	PUNCT
ejpam-6062	89	22	−dg(y	−dg(y	PROPN
ejpam-6062	89	23	,	,	PUNCT
ejpam-6062	89	24	x	x	PUNCT
ejpam-6062	89	25	)	)	PUNCT
ejpam-6062	89	26	+	+	CCONJ
ejpam-6062	89	27	⟨y	⟨y	X
ejpam-6062	89	28	−	−	X
ejpam-6062	89	29	x,∇g	x,∇g	NUM
ejpam-6062	89	30	e(y)−∇g	e(y)−∇g	PROPN
ejpam-6062	89	31	e(x)⟩	e(x)⟩	PROPN
ejpam-6062	89	32	,	,	PUNCT
ejpam-6062	89	33	∀	∀	X
ejpam-6062	89	34	x	x	NOUN
ejpam-6062	89	35	,	,	PUNCT
ejpam-6062	89	36	y	y	PROPN
ejpam-6062	89	37	∈	∈	PROPN
ejpam-6062	89	38	e.	e.	PROPN
ejpam-6062	89	39	let	let	VERB
ejpam-6062	89	40	b	b	NOUN
ejpam-6062	89	41	:	:	PUNCT
ejpam-6062	89	42	e	e	X
ejpam-6062	89	43	→	→	SYM
ejpam-6062	89	44	2e	2e	PROPN
ejpam-6062	89	45	∗	∗	NOUN
ejpam-6062	89	46	be	be	VERB
ejpam-6062	89	47	a	a	DET
ejpam-6062	89	48	set	set	NOUN
ejpam-6062	89	49	-	-	PUNCT
ejpam-6062	89	50	valued	value	VERB
ejpam-6062	89	51	mapping	mapping	NOUN
ejpam-6062	89	52	.	.	PUNCT
ejpam-6062	90	1	we	we	PRON
ejpam-6062	90	2	define	define	VERB
ejpam-6062	90	3	the	the	DET
ejpam-6062	90	4	domain	domain	NOUN
ejpam-6062	90	5	and	and	CCONJ
ejpam-6062	90	6	range	range	NOUN
ejpam-6062	90	7	of	of	ADP
ejpam-6062	90	8	b	b	NOUN
ejpam-6062	90	9	by	by	ADP
ejpam-6062	90	10	domb	domb	NOUN
ejpam-6062	90	11	=	=	SYM
ejpam-6062	90	12	{	{	PUNCT
ejpam-6062	90	13	x	x	PUNCT
ejpam-6062	90	14	∈	∈	PROPN
ejpam-6062	90	15	e	e	NOUN
ejpam-6062	90	16	:	:	PUNCT
ejpam-6062	90	17	bx	bx	PROPN
ejpam-6062	90	18	̸=	̸=	PROPN
ejpam-6062	90	19	∅	∅	NOUN
ejpam-6062	90	20	}	}	PUNCT
ejpam-6062	90	21	and	and	CCONJ
ejpam-6062	90	22	ranb	ranb	X
ejpam-6062	90	23	=	=	PUNCT
ejpam-6062	90	24	⋃	⋃	PROPN
ejpam-6062	90	25	x∈e	x∈e	X
ejpam-6062	90	26	bx	bx	PROPN
ejpam-6062	90	27	,	,	PUNCT
ejpam-6062	90	28	respectively	respectively	ADV
ejpam-6062	90	29	.	.	PUNCT
ejpam-6062	91	1	the	the	DET
ejpam-6062	91	2	graph	graph	NOUN
ejpam-6062	91	3	of	of	ADP
ejpam-6062	91	4	b	b	NOUN
ejpam-6062	91	5	denoted	denote	VERB
ejpam-6062	91	6	by	by	ADP
ejpam-6062	91	7	g(b	g(b	PROPN
ejpam-6062	91	8	)	)	PUNCT
ejpam-6062	91	9	=	=	PRON
ejpam-6062	91	10	{	{	PUNCT
ejpam-6062	91	11	(	(	PUNCT
ejpam-6062	91	12	x	x	NOUN
ejpam-6062	91	13	,	,	PUNCT
ejpam-6062	91	14	x∗	x∗	PROPN
ejpam-6062	91	15	)	)	PUNCT
ejpam-6062	91	16	∈	∈	PROPN
ejpam-6062	91	17	e	e	X
ejpam-6062	91	18	×	×	NOUN
ejpam-6062	91	19	e∗	e∗	PROPN
ejpam-6062	91	20	:	:	PUNCT
ejpam-6062	91	21	x∗	x∗	PROPN
ejpam-6062	91	22	∈	∈	PROPN
ejpam-6062	91	23	bx	bx	PROPN
ejpam-6062	91	24	}	}	PUNCT
ejpam-6062	91	25	.	.	PUNCT
ejpam-6062	92	1	the	the	DET
ejpam-6062	92	2	mapping	mapping	PROPN
ejpam-6062	92	3	b	b	X
ejpam-6062	92	4	⊂	⊂	PROPN
ejpam-6062	92	5	e	e	PROPN
ejpam-6062	92	6	×	×	PROPN
ejpam-6062	92	7	e∗	e∗	PROPN
ejpam-6062	92	8	is	be	AUX
ejpam-6062	92	9	said	say	VERB
ejpam-6062	92	10	to	to	PART
ejpam-6062	92	11	be	be	AUX
ejpam-6062	92	12	monotone	monotone	ADJ
ejpam-6062	93	1	[	[	X
ejpam-6062	93	2	33	33	NUM
ejpam-6062	93	3	]	]	PUNCT
ejpam-6062	93	4	if	if	SCONJ
ejpam-6062	93	5	⟨x	⟨x	VERB
ejpam-6062	93	6	−	−	PROPN
ejpam-6062	93	7	y	y	PROPN
ejpam-6062	93	8	,	,	PUNCT
ejpam-6062	93	9	x∗	x∗	PROPN
ejpam-6062	93	10	−	−	PROPN
ejpam-6062	93	11	y∗⟩	y∗⟩	NOUN
ejpam-6062	93	12	≥	≥	VERB
ejpam-6062	93	13	0	0	PUNCT
ejpam-6062	94	1	whenever	whenever	SCONJ
ejpam-6062	94	2	(	(	PUNCT
ejpam-6062	94	3	x	x	NOUN
ejpam-6062	94	4	,	,	PUNCT
ejpam-6062	94	5	x∗	x∗	PROPN
ejpam-6062	94	6	)	)	PUNCT
ejpam-6062	94	7	,	,	PUNCT
ejpam-6062	94	8	(	(	PUNCT
ejpam-6062	94	9	y	y	NOUN
ejpam-6062	94	10	,	,	PUNCT
ejpam-6062	94	11	y∗	y∗	PROPN
ejpam-6062	94	12	)	)	PUNCT
ejpam-6062	94	13	∈	∈	PROPN
ejpam-6062	94	14	b.	b.	PROPN
ejpam-6062	94	15	it	it	PRON
ejpam-6062	94	16	is	be	AUX
ejpam-6062	94	17	also	also	ADV
ejpam-6062	94	18	said	say	VERB
ejpam-6062	94	19	to	to	PART
ejpam-6062	94	20	be	be	AUX
ejpam-6062	94	21	maximal	maximal	ADJ
ejpam-6062	94	22	monotone	monotone	ADJ
ejpam-6062	94	23	[	[	X
ejpam-6062	94	24	34	34	NUM
ejpam-6062	94	25	]	]	PUNCT
ejpam-6062	94	26	if	if	SCONJ
ejpam-6062	94	27	its	its	PRON
ejpam-6062	94	28	graph	graph	NOUN
ejpam-6062	94	29	is	be	AUX
ejpam-6062	94	30	not	not	PART
ejpam-6062	94	31	contained	contain	VERB
ejpam-6062	94	32	in	in	ADP
ejpam-6062	94	33	the	the	DET
ejpam-6062	94	34	graph	graph	NOUN
ejpam-6062	94	35	of	of	ADP
ejpam-6062	94	36	any	any	DET
ejpam-6062	94	37	other	other	ADJ
ejpam-6062	94	38	monotone	monotone	ADJ
ejpam-6062	94	39	operator	operator	NOUN
ejpam-6062	94	40	on	on	ADP
ejpam-6062	94	41	e.	e.	PROPN
ejpam-6062	94	42	if	if	SCONJ
ejpam-6062	94	43	b	b	PROPN
ejpam-6062	94	44	⊂	⊂	PROPN
ejpam-6062	94	45	e	e	PROPN
ejpam-6062	94	46	×	×	PROPN
ejpam-6062	94	47	e∗	e∗	PROPN
ejpam-6062	94	48	is	be	AUX
ejpam-6062	94	49	maximal	maximal	ADJ
ejpam-6062	94	50	monotone	monotone	ADJ
ejpam-6062	94	51	,	,	PUNCT
ejpam-6062	94	52	then	then	ADV
ejpam-6062	94	53	we	we	PRON
ejpam-6062	94	54	can	can	AUX
ejpam-6062	94	55	represent	represent	VERB
ejpam-6062	94	56	the	the	DET
ejpam-6062	94	57	set	set	NOUN
ejpam-6062	94	58	b−1(0	b−1(0	NOUN
ejpam-6062	94	59	)	)	PUNCT
ejpam-6062	94	60	=	=	PRON
ejpam-6062	95	1	{	{	PUNCT
ejpam-6062	95	2	z	z	NOUN
ejpam-6062	95	3	∈	∈	PROPN
ejpam-6062	95	4	e	e	NOUN
ejpam-6062	95	5	:	:	PUNCT
ejpam-6062	95	6	0	0	NUM
ejpam-6062	95	7	∈	∈	PROPN
ejpam-6062	95	8	bz	bz	PROPN
ejpam-6062	95	9	}	}	PUNCT
ejpam-6062	95	10	is	be	AUX
ejpam-6062	95	11	closed	close	VERB
ejpam-6062	95	12	and	and	CCONJ
ejpam-6062	95	13	convex	convex	NOUN
ejpam-6062	95	14	.	.	PUNCT
ejpam-6062	96	1	let	let	VERB
ejpam-6062	96	2	a	a	PRON
ejpam-6062	96	3	:	:	PUNCT
ejpam-6062	96	4	e	e	X
ejpam-6062	96	5	→	→	SYM
ejpam-6062	96	6	2e	2e	PROPN
ejpam-6062	96	7	∗	∗	NOUN
ejpam-6062	96	8	be	be	VERB
ejpam-6062	96	9	a	a	DET
ejpam-6062	96	10	mapping	mapping	NOUN
ejpam-6062	96	11	,	,	PUNCT
ejpam-6062	96	12	then	then	ADV
ejpam-6062	96	13	the	the	DET
ejpam-6062	96	14	resolvent	resolvent	NOUN
ejpam-6062	96	15	associated	associate	VERB
ejpam-6062	96	16	with	with	ADP
ejpam-6062	96	17	a	a	PRON
ejpam-6062	96	18	and	and	CCONJ
ejpam-6062	96	19	λ	λ	NOUN
ejpam-6062	96	20	for	for	ADP
ejpam-6062	96	21	any	any	DET
ejpam-6062	96	22	λ	λ	PROPN
ejpam-6062	96	23	>	>	X
ejpam-6062	96	24	0	0	NUM
ejpam-6062	96	25	is	be	AUX
ejpam-6062	96	26	the	the	DET
ejpam-6062	96	27	mapping	mapping	NOUN
ejpam-6062	96	28	resgλa	resgλa	ADV
ejpam-6062	96	29	:	:	PUNCT
ejpam-6062	96	30	e	e	X
ejpam-6062	96	31	→	→	SYM
ejpam-6062	96	32	2e	2e	PROPN
ejpam-6062	96	33	defined	define	VERB
ejpam-6062	96	34	by	by	ADP
ejpam-6062	96	35	resgλa	resgλa	NOUN
ejpam-6062	96	36	:	:	PUNCT
ejpam-6062	96	37	=	=	SYM
ejpam-6062	96	38	(	(	PUNCT
ejpam-6062	96	39	∇g	∇g	NOUN
ejpam-6062	96	40	e	e	NOUN
ejpam-6062	96	41	+	+	NOUN
ejpam-6062	96	42	λa)−1	λa)−1	ADP
ejpam-6062	96	43	◦	◦	NOUN
ejpam-6062	96	44	∇g	∇g	ADJ
ejpam-6062	96	45	e	e	NOUN
ejpam-6062	96	46	.	.	PUNCT
ejpam-6062	97	1	it	it	PRON
ejpam-6062	97	2	is	be	AUX
ejpam-6062	97	3	worth	worth	ADJ
ejpam-6062	97	4	mentioning	mention	VERB
ejpam-6062	97	5	that	that	SCONJ
ejpam-6062	97	6	a	a	DET
ejpam-6062	97	7	mapping	mapping	NOUN
ejpam-6062	97	8	a	a	PRON
ejpam-6062	97	9	:	:	PUNCT
ejpam-6062	97	10	e	e	X
ejpam-6062	97	11	→	→	SYM
ejpam-6062	97	12	2e	2e	PROPN
ejpam-6062	97	13	∗	∗	NOUN
ejpam-6062	97	14	is	be	AUX
ejpam-6062	97	15	called	call	VERB
ejpam-6062	97	16	bregman	bregman	NOUN
ejpam-6062	97	17	inverse	inverse	NOUN
ejpam-6062	97	18	strongly	strongly	ADV
ejpam-6062	97	19	monotone	monotone	ADJ
ejpam-6062	97	20	(	(	PUNCT
ejpam-6062	97	21	bism	bism	NOUN
ejpam-6062	97	22	)	)	PUNCT
ejpam-6062	97	23	on	on	ADP
ejpam-6062	97	24	the	the	DET
ejpam-6062	97	25	set	set	NOUN
ejpam-6062	97	26	c	c	NOUN
ejpam-6062	98	1	if	if	SCONJ
ejpam-6062	98	2	c	c	PROPN
ejpam-6062	98	3	∩	∩	X
ejpam-6062	98	4	(	(	PUNCT
ejpam-6062	98	5	domg	domg	NOUN
ejpam-6062	98	6	)	)	PUNCT
ejpam-6062	98	7	∩	∩	NOUN
ejpam-6062	98	8	(	(	PUNCT
ejpam-6062	98	9	int	int	NOUN
ejpam-6062	98	10	dom	dom	NOUN
ejpam-6062	98	11	g	g	NOUN
ejpam-6062	98	12	)	)	PUNCT
ejpam-6062	98	13	̸=	̸=	PROPN
ejpam-6062	98	14	∅	∅	NOUN
ejpam-6062	98	15	,	,	PUNCT
ejpam-6062	98	16	and	and	CCONJ
ejpam-6062	98	17	for	for	ADP
ejpam-6062	98	18	any	any	DET
ejpam-6062	98	19	x	x	NOUN
ejpam-6062	98	20	,	,	PUNCT
ejpam-6062	98	21	y	y	PROPN
ejpam-6062	98	22	∈	∈	PROPN
ejpam-6062	98	23	c	c	NOUN
ejpam-6062	98	24	∩	∩	X
ejpam-6062	98	25	(	(	PUNCT
ejpam-6062	98	26	int	int	NOUN
ejpam-6062	98	27	dom	dom	NOUN
ejpam-6062	98	28	g	g	NOUN
ejpam-6062	98	29	)	)	PUNCT
ejpam-6062	98	30	,	,	PUNCT
ejpam-6062	98	31	η	η	PROPN
ejpam-6062	98	32	∈	∈	PROPN
ejpam-6062	98	33	ax	ax	NOUN
ejpam-6062	98	34	and	and	CCONJ
ejpam-6062	98	35	ξ	ξ	PROPN
ejpam-6062	98	36	∈	∈	PROPN
ejpam-6062	98	37	ay	ay	NOUN
ejpam-6062	98	38	,	,	PUNCT
ejpam-6062	98	39	we	we	PRON
ejpam-6062	98	40	have	have	VERB
ejpam-6062	98	41	⟨η	⟨η	NOUN
ejpam-6062	98	42	−	−	PROPN
ejpam-6062	98	43	ξ	ξ	PROPN
ejpam-6062	98	44	,	,	PUNCT
ejpam-6062	98	45	(	(	PUNCT
ejpam-6062	98	46	∇g∗	∇g∗	NUM
ejpam-6062	98	47	e∗(x)−	e∗(x)−	VERB
ejpam-6062	98	48	η)−∇g∗	η)−∇g∗	PROPN
ejpam-6062	98	49	e∗(∇g	e∗(∇g	PROPN
ejpam-6062	98	50	e(y)−	e(y)−	PROPN
ejpam-6062	98	51	ξ)⟩	ξ)⟩	PROPN
ejpam-6062	98	52	≥	≥	NOUN
ejpam-6062	98	53	0	0	NUM
ejpam-6062	98	54	.	.	PUNCT
ejpam-6062	99	1	the	the	DET
ejpam-6062	99	2	anti	anti	ADJ
ejpam-6062	99	3	-	-	ADJ
ejpam-6062	99	4	resolvent	resolvent	ADJ
ejpam-6062	99	5	ag	ag	PROPN
ejpam-6062	99	6	λ	λ	PROPN
ejpam-6062	99	7	:	:	PUNCT
ejpam-6062	99	8	e	e	X
ejpam-6062	99	9	→	→	SYM
ejpam-6062	99	10	2e	2e	PROPN
ejpam-6062	99	11	associated	associate	VERB
ejpam-6062	99	12	with	with	ADP
ejpam-6062	99	13	the	the	DET
ejpam-6062	99	14	mapping	mapping	NOUN
ejpam-6062	99	15	a	a	PRON
ejpam-6062	99	16	:	:	PUNCT
ejpam-6062	99	17	e	e	X
ejpam-6062	99	18	→	→	SYM
ejpam-6062	99	19	2e	2e	NUM
ejpam-6062	99	20	∗	∗	NOUN
ejpam-6062	99	21	and	and	CCONJ
ejpam-6062	99	22	λ	λ	X
ejpam-6062	99	23	>	>	X
ejpam-6062	99	24	0	0	NUM
ejpam-6062	99	25	is	be	AUX
ejpam-6062	99	26	defined	define	VERB
ejpam-6062	99	27	by	by	ADP
ejpam-6062	99	28	ag	ag	PROPN
ejpam-6062	99	29	λ	λ	PROPN
ejpam-6062	99	30	:	:	PUNCT
ejpam-6062	99	31	=	=	SYM
ejpam-6062	99	32	(	(	PUNCT
ejpam-6062	99	33	∇g	∇g	PROPN
ejpam-6062	99	34	e	e	NOUN
ejpam-6062	99	35	)	)	PUNCT
ejpam-6062	99	36	−1	−1	NOUN
ejpam-6062	99	37	◦	◦	NOUN
ejpam-6062	99	38	(	(	PUNCT
ejpam-6062	99	39	∇g	∇g	NOUN
ejpam-6062	99	40	e	e	NOUN
ejpam-6062	99	41	−	−	NOUN
ejpam-6062	99	42	λa	λa	NOUN
ejpam-6062	99	43	)	)	PUNCT
ejpam-6062	99	44	.	.	PUNCT
ejpam-6062	100	1	(	(	PUNCT
ejpam-6062	100	2	11	11	NUM
ejpam-6062	100	3	)	)	PUNCT
ejpam-6062	100	4	a	a	DET
ejpam-6062	100	5	point	point	NOUN
ejpam-6062	100	6	p	p	X
ejpam-6062	100	7	∈	∈	PROPN
ejpam-6062	100	8	q	q	NOUN
ejpam-6062	100	9	is	be	AUX
ejpam-6062	100	10	called	call	VERB
ejpam-6062	100	11	an	an	DET
ejpam-6062	100	12	asymptotic	asymptotic	ADJ
ejpam-6062	100	13	fixed	fix	VERB
ejpam-6062	100	14	point	point	NOUN
ejpam-6062	100	15	of	of	ADP
ejpam-6062	100	16	t	t	PROPN
ejpam-6062	100	17	if	if	SCONJ
ejpam-6062	100	18	q	q	PROPN
ejpam-6062	100	19	contains	contain	VERB
ejpam-6062	100	20	a	a	DET
ejpam-6062	100	21	sequence	sequence	NOUN
ejpam-6062	100	22	{	{	PUNCT
ejpam-6062	100	23	xn	xn	NOUN
ejpam-6062	100	24	}	}	PUNCT
ejpam-6062	100	25	which	which	PRON
ejpam-6062	100	26	converges	converge	VERB
ejpam-6062	100	27	weakly	weakly	ADV
ejpam-6062	100	28	to	to	ADP
ejpam-6062	100	29	p	p	NOUN
ejpam-6062	100	30	such	such	ADJ
ejpam-6062	100	31	that	that	SCONJ
ejpam-6062	100	32	lim	lim	PROPN
ejpam-6062	100	33	n→∞	n→∞	PRON
ejpam-6062	100	34	||txn	||txn	ADJ
ejpam-6062	100	35	−	−	PROPN
ejpam-6062	100	36	xn||	xn||	PUNCT
ejpam-6062	101	1	=	=	PUNCT
ejpam-6062	101	2	0	0	X
ejpam-6062	101	3	.	.	PUNCT
ejpam-6062	102	1	we	we	PRON
ejpam-6062	102	2	denote	denote	VERB
ejpam-6062	102	3	by	by	ADP
ejpam-6062	102	4	ˆfix(t	ˆfix(t	PROPN
ejpam-6062	102	5	)	)	PUNCT
ejpam-6062	102	6	the	the	DET
ejpam-6062	102	7	set	set	NOUN
ejpam-6062	102	8	of	of	ADP
ejpam-6062	102	9	asymptotic	asymptotic	ADJ
ejpam-6062	102	10	fixed	fix	VERB
ejpam-6062	102	11	points	point	NOUN
ejpam-6062	102	12	of	of	ADP
ejpam-6062	102	13	t	t	PROPN
ejpam-6062	102	14	.	.	PUNCT
ejpam-6062	103	1	let	let	VERB
ejpam-6062	103	2	q	q	PRON
ejpam-6062	103	3	be	be	AUX
ejpam-6062	103	4	a	a	DET
ejpam-6062	103	5	nonempty	nonempty	ADV
ejpam-6062	103	6	closed	close	VERB
ejpam-6062	103	7	and	and	CCONJ
ejpam-6062	103	8	convex	convex	NOUN
ejpam-6062	103	9	subset	subset	NOUN
ejpam-6062	103	10	of	of	ADP
ejpam-6062	103	11	int(dom	int(dom	PROPN
ejpam-6062	103	12	g	g	PROPN
ejpam-6062	103	13	)	)	PUNCT
ejpam-6062	103	14	,	,	PUNCT
ejpam-6062	103	15	then	then	ADV
ejpam-6062	103	16	we	we	PRON
ejpam-6062	103	17	define	define	VERB
ejpam-6062	103	18	an	an	DET
ejpam-6062	103	19	operator	operator	NOUN
ejpam-6062	103	20	t	t	NOUN
ejpam-6062	103	21	:	:	PUNCT
ejpam-6062	103	22	q	q	X
ejpam-6062	103	23	→	→	SYM
ejpam-6062	103	24	int(domg	int(domg	NOUN
ejpam-6062	103	25	)	)	PUNCT
ejpam-6062	103	26	to	to	PART
ejpam-6062	103	27	be	be	AUX
ejpam-6062	103	28	:	:	PUNCT
ejpam-6062	103	29	(	(	PUNCT
ejpam-6062	103	30	i	i	NOUN
ejpam-6062	103	31	)	)	PUNCT
ejpam-6062	103	32	bregman	bregman	NOUN
ejpam-6062	103	33	relatively	relatively	ADV
ejpam-6062	103	34	nonexpansive	nonexpansive	ADJ
ejpam-6062	103	35	(	(	PUNCT
ejpam-6062	103	36	brne	brne	PROPN
ejpam-6062	103	37	)	)	PUNCT
ejpam-6062	103	38	,	,	PUNCT
ejpam-6062	103	39	if	if	SCONJ
ejpam-6062	103	40	fix(t	fix(t	PROPN
ejpam-6062	103	41	)	)	PUNCT
ejpam-6062	103	42	̸=	̸=	PROPN
ejpam-6062	103	43	∅	∅	NOUN
ejpam-6062	103	44	,	,	PUNCT
ejpam-6062	103	45	and	and	CCONJ
ejpam-6062	103	46	dg(p	dg(p	NOUN
ejpam-6062	103	47	,	,	PUNCT
ejpam-6062	103	48	tx	tx	PROPN
ejpam-6062	103	49	)	)	PUNCT
ejpam-6062	103	50	≤	≤	NOUN
ejpam-6062	103	51	dg(p	dg(p	NOUN
ejpam-6062	103	52	,	,	PUNCT
ejpam-6062	103	53	x	x	NOUN
ejpam-6062	103	54	)	)	PUNCT
ejpam-6062	103	55	,	,	PUNCT
ejpam-6062	103	56	∀	∀	PUNCT
ejpam-6062	103	57	p	p	NOUN
ejpam-6062	103	58	∈	∈	NOUN
ejpam-6062	103	59	fix(t	fix(t	PROPN
ejpam-6062	103	60	)	)	PUNCT
ejpam-6062	103	61	,	,	PUNCT
ejpam-6062	103	62	x	x	PUNCT
ejpam-6062	103	63	∈	∈	PROPN
ejpam-6062	103	64	q	q	NOUN
ejpam-6062	103	65	and	and	CCONJ
ejpam-6062	103	66	ˆfix(t	ˆfix(t	NOUN
ejpam-6062	103	67	)	)	PUNCT
ejpam-6062	104	1	=	=	SYM
ejpam-6062	104	2	fix(t	fix(t	PROPN
ejpam-6062	104	3	)	)	PUNCT
ejpam-6062	104	4	.	.	PUNCT
ejpam-6062	105	1	h.	h.	PROPN
ejpam-6062	105	2	a.	a.	PROPN
ejpam-6062	105	3	abass	abass	PROPN
ejpam-6062	105	4	et	et	PROPN
ejpam-6062	105	5	al	al	PROPN
ejpam-6062	105	6	.	.	PUNCT
ejpam-6062	105	7	/	/	SYM
ejpam-6062	105	8	eur	eur	PROPN
ejpam-6062	105	9	.	.	PUNCT
ejpam-6062	106	1	j.	j.	PROPN
ejpam-6062	106	2	pure	pure	PROPN
ejpam-6062	106	3	appl	appl	PROPN
ejpam-6062	106	4	.	.	PROPN
ejpam-6062	106	5	math	math	PROPN
ejpam-6062	106	6	,	,	PUNCT
ejpam-6062	106	7	18	18	NUM
ejpam-6062	106	8	(	(	PUNCT
ejpam-6062	106	9	2	2	NUM
ejpam-6062	106	10	)	)	PUNCT
ejpam-6062	106	11	(	(	PUNCT
ejpam-6062	106	12	2025	2025	NUM
ejpam-6062	106	13	)	)	PUNCT
ejpam-6062	106	14	,	,	PUNCT
ejpam-6062	106	15	6062	6062	NUM
ejpam-6062	106	16	7	7	NUM
ejpam-6062	106	17	of	of	ADP
ejpam-6062	106	18	22	22	NUM
ejpam-6062	106	19	(	(	PUNCT
ejpam-6062	106	20	ii	ii	NOUN
ejpam-6062	106	21	)	)	PUNCT
ejpam-6062	106	22	bregman	bregman	NOUN
ejpam-6062	106	23	quasi	quasi	ADJ
ejpam-6062	106	24	-	-	ADJ
ejpam-6062	106	25	nonexpansive	nonexpansive	ADJ
ejpam-6062	106	26	mapping	mapping	NOUN
ejpam-6062	106	27	(	(	PUNCT
ejpam-6062	106	28	bqne	bqne	PROPN
ejpam-6062	106	29	)	)	PUNCT
ejpam-6062	106	30	,	,	PUNCT
ejpam-6062	106	31	if	if	SCONJ
ejpam-6062	106	32	fix(t	fix(t	PROPN
ejpam-6062	106	33	)	)	PUNCT
ejpam-6062	106	34	̸=	̸=	PROPN
ejpam-6062	106	35	∅	∅	NOUN
ejpam-6062	106	36	and	and	CCONJ
ejpam-6062	106	37	df	df	PROPN
ejpam-6062	106	38	(	(	PUNCT
ejpam-6062	106	39	p	p	X
ejpam-6062	106	40	,	,	PUNCT
ejpam-6062	106	41	tx	tx	PROPN
ejpam-6062	106	42	)	)	PUNCT
ejpam-6062	106	43	≤	≤	NOUN
ejpam-6062	106	44	df	df	NOUN
ejpam-6062	106	45	(	(	PUNCT
ejpam-6062	106	46	p	p	X
ejpam-6062	106	47	,	,	PUNCT
ejpam-6062	106	48	x),∀	x),∀	PROPN
ejpam-6062	106	49	x	x	X
ejpam-6062	107	1	∈	∈	PROPN
ejpam-6062	107	2	q	q	X
ejpam-6062	107	3	and	and	CCONJ
ejpam-6062	107	4	p	p	NOUN
ejpam-6062	107	5	∈	∈	PROPN
ejpam-6062	107	6	fix(t	fix(t	PROPN
ejpam-6062	107	7	)	)	PUNCT
ejpam-6062	107	8	.	.	PUNCT
ejpam-6062	108	1	(	(	PUNCT
ejpam-6062	108	2	iii	iii	X
ejpam-6062	108	3	)	)	PUNCT
ejpam-6062	108	4	bregman	bregman	NOUN
ejpam-6062	108	5	firmly	firmly	ADV
ejpam-6062	108	6	nonexpansive	nonexpansive	ADJ
ejpam-6062	108	7	(	(	PUNCT
ejpam-6062	108	8	bfne	bfne	ADJ
ejpam-6062	108	9	)	)	PUNCT
ejpam-6062	108	10	,	,	PUNCT
ejpam-6062	108	11	if	if	SCONJ
ejpam-6062	108	12	⟨∇g	⟨∇g	NUM
ejpam-6062	108	13	e(tx)−∇g	e(tx)−∇g	NOUN
ejpam-6062	108	14	e(ty	e(ty	PROPN
ejpam-6062	108	15	)	)	PUNCT
ejpam-6062	108	16	,	,	PUNCT
ejpam-6062	108	17	tx−	tx−	X
ejpam-6062	108	18	ty⟩	ty⟩	NOUN
ejpam-6062	108	19	≤	≤	PROPN
ejpam-6062	108	20	⟨∇g	⟨∇g	PUNCT
ejpam-6062	108	21	e(x)−∇g	e(x)−∇g	PROPN
ejpam-6062	108	22	e(y	e(y	NUM
ejpam-6062	108	23	)	)	PUNCT
ejpam-6062	108	24	,	,	PUNCT
ejpam-6062	108	25	tx−	tx−	PROPN
ejpam-6062	108	26	ty⟩	ty⟩	PROPN
ejpam-6062	108	27	,	,	PUNCT
ejpam-6062	108	28	∀	∀	X
ejpam-6062	108	29	x	x	NOUN
ejpam-6062	108	30	,	,	PUNCT
ejpam-6062	108	31	y	y	PROPN
ejpam-6062	108	32	∈	∈	PROPN
ejpam-6062	108	33	e.	e.	PROPN
ejpam-6062	108	34	definition	definition	NOUN
ejpam-6062	108	35	2	2	NUM
ejpam-6062	108	36	.	.	PUNCT
ejpam-6062	109	1	[	[	X
ejpam-6062	109	2	35	35	NUM
ejpam-6062	109	3	]	]	PUNCT
ejpam-6062	109	4	let	let	VERB
ejpam-6062	109	5	c	c	PRON
ejpam-6062	109	6	be	be	AUX
ejpam-6062	109	7	a	a	DET
ejpam-6062	109	8	nonempty	nonempty	ADJ
ejpam-6062	109	9	,	,	PUNCT
ejpam-6062	109	10	closed	closed	ADJ
ejpam-6062	109	11	and	and	CCONJ
ejpam-6062	109	12	convex	convex	NOUN
ejpam-6062	109	13	subset	subset	NOUN
ejpam-6062	109	14	of	of	ADP
ejpam-6062	109	15	a	a	DET
ejpam-6062	109	16	reflexive	reflexive	ADJ
ejpam-6062	109	17	banach	banach	NOUN
ejpam-6062	109	18	space	space	NOUN
ejpam-6062	109	19	e	e	NOUN
ejpam-6062	109	20	and	and	CCONJ
ejpam-6062	109	21	g	g	NOUN
ejpam-6062	109	22	:	:	PUNCT
ejpam-6062	109	23	e	e	X
ejpam-6062	109	24	→	→	PUNCT
ejpam-6062	109	25	(	(	PUNCT
ejpam-6062	109	26	−∞,+∞	−∞,+∞	ADV
ejpam-6062	109	27	]	]	PUNCT
ejpam-6062	109	28	be	be	AUX
ejpam-6062	109	29	a	a	DET
ejpam-6062	109	30	strongly	strongly	ADV
ejpam-6062	109	31	coercive	coercive	ADJ
ejpam-6062	109	32	bregman	bregman	NOUN
ejpam-6062	109	33	function	function	NOUN
ejpam-6062	109	34	.	.	PUNCT
ejpam-6062	110	1	let	let	VERB
ejpam-6062	110	2	β	β	PRON
ejpam-6062	110	3	and	and	CCONJ
ejpam-6062	110	4	γ	γ	PROPN
ejpam-6062	110	5	be	be	AUX
ejpam-6062	110	6	real	real	ADJ
ejpam-6062	110	7	numbers	number	NOUN
ejpam-6062	110	8	with	with	ADP
ejpam-6062	110	9	β	β	X
ejpam-6062	110	10	∈	∈	PROPN
ejpam-6062	110	11	(	(	PUNCT
ejpam-6062	110	12	−∞	−∞	NOUN
ejpam-6062	110	13	,	,	PUNCT
ejpam-6062	110	14	1	1	NUM
ejpam-6062	110	15	)	)	PUNCT
ejpam-6062	110	16	and	and	CCONJ
ejpam-6062	110	17	γ	γ	PRON
ejpam-6062	110	18	∈	∈	PROPN
ejpam-6062	111	1	[	[	X
ejpam-6062	111	2	0,∞	0,∞	NOUN
ejpam-6062	111	3	)	)	PUNCT
ejpam-6062	111	4	,	,	PUNCT
ejpam-6062	111	5	respectively	respectively	ADV
ejpam-6062	111	6	.	.	PUNCT
ejpam-6062	112	1	then	then	ADV
ejpam-6062	112	2	a	a	DET
ejpam-6062	112	3	mapping	mapping	NOUN
ejpam-6062	112	4	t	t	NOUN
ejpam-6062	112	5	:	:	PUNCT
ejpam-6062	112	6	c	c	X
ejpam-6062	112	7	→	→	SYM
ejpam-6062	112	8	e	e	NOUN
ejpam-6062	112	9	with	with	ADP
ejpam-6062	112	10	fix(t	fix(t	PROPN
ejpam-6062	112	11	)	)	PUNCT
ejpam-6062	112	12	̸=	̸=	PROPN
ejpam-6062	112	13	∅	∅	NOUN
ejpam-6062	112	14	is	be	AUX
ejpam-6062	112	15	called	call	VERB
ejpam-6062	112	16	bregman	bregman	NOUN
ejpam-6062	112	17	(	(	PUNCT
ejpam-6062	112	18	β	β	X
ejpam-6062	112	19	,	,	PUNCT
ejpam-6062	112	20	γ)-demigeneralized	γ)-demigeneralize	VERB
ejpam-6062	112	21	if	if	SCONJ
ejpam-6062	112	22	for	for	ADP
ejpam-6062	112	23	any	any	DET
ejpam-6062	112	24	x	x	SYM
ejpam-6062	112	25	∈	∈	PROPN
ejpam-6062	112	26	c	c	NOUN
ejpam-6062	112	27	and	and	CCONJ
ejpam-6062	112	28	p	p	NOUN
ejpam-6062	112	29	∈	∈	PROPN
ejpam-6062	112	30	fix(t	fix(t	PROPN
ejpam-6062	112	31	)	)	PUNCT
ejpam-6062	112	32	,	,	PUNCT
ejpam-6062	112	33	⟨x−	⟨x−	PROPN
ejpam-6062	112	34	p,∇g	p,∇g	PROPN
ejpam-6062	112	35	e(x)−∇g	e(x)−∇g	NOUN
ejpam-6062	112	36	e(tx)⟩	e(tx)⟩	X
ejpam-6062	112	37	≥	≥	X
ejpam-6062	112	38	(	(	PUNCT
ejpam-6062	112	39	1−	1−	NUM
ejpam-6062	112	40	β)dg(x	β)dg(x	NUM
ejpam-6062	112	41	,	,	PUNCT
ejpam-6062	112	42	tx	tx	PROPN
ejpam-6062	112	43	)	)	PUNCT
ejpam-6062	113	1	+	+	CCONJ
ejpam-6062	113	2	γdg(tx	γdg(tx	NUM
ejpam-6062	113	3	,	,	PUNCT
ejpam-6062	113	4	x	x	NOUN
ejpam-6062	113	5	)	)	PUNCT
ejpam-6062	113	6	,	,	PUNCT
ejpam-6062	113	7	∀	∀	PUNCT
ejpam-6062	113	8	x	x	SYM
ejpam-6062	113	9	∈	∈	NOUN
ejpam-6062	113	10	e	e	NOUN
ejpam-6062	113	11	and	and	CCONJ
ejpam-6062	113	12	p	p	NOUN
ejpam-6062	113	13	∈	∈	PROPN
ejpam-6062	113	14	f	f	X
ejpam-6062	113	15	(	(	PUNCT
ejpam-6062	113	16	t	t	PROPN
ejpam-6062	113	17	)	)	PUNCT
ejpam-6062	113	18	.	.	PUNCT
ejpam-6062	114	1	definition	definition	NOUN
ejpam-6062	114	2	3	3	NUM
ejpam-6062	114	3	.	.	PUNCT
ejpam-6062	115	1	a	a	DET
ejpam-6062	115	2	function	function	NOUN
ejpam-6062	115	3	g	g	NOUN
ejpam-6062	115	4	:	:	PUNCT
ejpam-6062	115	5	e	e	X
ejpam-6062	115	6	→	→	SYM
ejpam-6062	115	7	r	r	NOUN
ejpam-6062	115	8	is	be	AUX
ejpam-6062	115	9	said	say	VERB
ejpam-6062	115	10	to	to	PART
ejpam-6062	115	11	be	be	AUX
ejpam-6062	115	12	strongly	strongly	ADV
ejpam-6062	115	13	coercive	coercive	ADJ
ejpam-6062	115	14	if	if	SCONJ
ejpam-6062	115	15	lim	lim	PROPN
ejpam-6062	115	16	||xn||→∞	||xn||→∞	PROPN
ejpam-6062	115	17	g(xn	g(xn	AUX
ejpam-6062	115	18	)	)	PUNCT
ejpam-6062	115	19	||xn||	||xn||	PROPN
ejpam-6062	116	1	=	=	SYM
ejpam-6062	116	2	∞.	∞.	PROPN
ejpam-6062	116	3	lemma	lemma	PROPN
ejpam-6062	116	4	1	1	NUM
ejpam-6062	116	5	.	.	PUNCT
ejpam-6062	117	1	[	[	X
ejpam-6062	117	2	19	19	NUM
ejpam-6062	117	3	]	]	PUNCT
ejpam-6062	117	4	let	let	VERB
ejpam-6062	117	5	e	e	PRON
ejpam-6062	117	6	be	be	AUX
ejpam-6062	117	7	a	a	DET
ejpam-6062	117	8	banach	banach	NOUN
ejpam-6062	117	9	space	space	NOUN
ejpam-6062	117	10	,	,	PUNCT
ejpam-6062	117	11	s	s	VERB
ejpam-6062	117	12	>	>	X
ejpam-6062	117	13	0	0	PUNCT
ejpam-6062	117	14	be	be	AUX
ejpam-6062	117	15	a	a	DET
ejpam-6062	117	16	constant	constant	ADJ
ejpam-6062	117	17	,	,	PUNCT
ejpam-6062	117	18	ρs	ρs	ADV
ejpam-6062	117	19	be	be	AUX
ejpam-6062	117	20	the	the	DET
ejpam-6062	117	21	gauge	gauge	NOUN
ejpam-6062	117	22	of	of	ADP
ejpam-6062	117	23	uniform	uniform	ADJ
ejpam-6062	117	24	convexity	convexity	NOUN
ejpam-6062	117	25	of	of	ADP
ejpam-6062	117	26	g	g	PROPN
ejpam-6062	117	27	and	and	CCONJ
ejpam-6062	117	28	g	g	NOUN
ejpam-6062	117	29	:	:	PUNCT
ejpam-6062	117	30	e	e	X
ejpam-6062	117	31	→	→	SYM
ejpam-6062	117	32	r	r	NOUN
ejpam-6062	117	33	be	be	AUX
ejpam-6062	117	34	a	a	DET
ejpam-6062	117	35	strongly	strongly	ADV
ejpam-6062	117	36	coercive	coercive	ADJ
ejpam-6062	117	37	bregman	bregman	NOUN
ejpam-6062	117	38	function	function	NOUN
ejpam-6062	117	39	.	.	PUNCT
ejpam-6062	118	1	then	then	ADV
ejpam-6062	118	2	,	,	PUNCT
ejpam-6062	118	3	(	(	PUNCT
ejpam-6062	118	4	i	i	NOUN
ejpam-6062	118	5	)	)	PUNCT
ejpam-6062	118	6	for	for	ADP
ejpam-6062	118	7	any	any	DET
ejpam-6062	118	8	x	x	NOUN
ejpam-6062	118	9	,	,	PUNCT
ejpam-6062	118	10	y	y	PROPN
ejpam-6062	118	11	∈	∈	PROPN
ejpam-6062	118	12	bs	bs	NOUN
ejpam-6062	118	13	and	and	CCONJ
ejpam-6062	118	14	α	α	PRON
ejpam-6062	118	15	∈	∈	PROPN
ejpam-6062	118	16	(	(	PUNCT
ejpam-6062	118	17	0	0	NUM
ejpam-6062	118	18	,	,	PUNCT
ejpam-6062	118	19	1	1	NUM
ejpam-6062	118	20	)	)	PUNCT
ejpam-6062	118	21	,	,	PUNCT
ejpam-6062	118	22	we	we	PRON
ejpam-6062	118	23	have	have	VERB
ejpam-6062	118	24	dg	dg	NOUN
ejpam-6062	118	25	(	(	PUNCT
ejpam-6062	118	26	x,∇g∗	x,∇g∗	NUM
ejpam-6062	118	27	e∗	e∗	PROPN
ejpam-6062	119	1	[	[	X
ejpam-6062	119	2	α∇g	α∇g	NOUN
ejpam-6062	119	3	e∇	e∇	PROPN
ejpam-6062	119	4	g	g	NOUN
ejpam-6062	119	5	e(y	e(y	NUM
ejpam-6062	119	6	)	)	PUNCT
ejpam-6062	119	7	+	+	CCONJ
ejpam-6062	119	8	(	(	PUNCT
ejpam-6062	119	9	1−	1−	NUM
ejpam-6062	119	10	α)∇g	α)∇g	NOUN
ejpam-6062	119	11	e(z	e(z	PROPN
ejpam-6062	119	12	)	)	PUNCT
ejpam-6062	119	13	]	]	PUNCT
ejpam-6062	119	14	)	)	PUNCT
ejpam-6062	119	15	≤	≤	PUNCT
ejpam-6062	120	1	αdg(x	αdg(x	PROPN
ejpam-6062	120	2	,	,	PUNCT
ejpam-6062	120	3	y	y	NOUN
ejpam-6062	120	4	)	)	PUNCT
ejpam-6062	121	1	+	+	CCONJ
ejpam-6062	121	2	(	(	PUNCT
ejpam-6062	121	3	1−	1−	NUM
ejpam-6062	121	4	α)dg(x	α)dg(x	NUM
ejpam-6062	121	5	,	,	PUNCT
ejpam-6062	121	6	z)−	z)−	PROPN
ejpam-6062	121	7	α(1−	α(1−	PROPN
ejpam-6062	121	8	α)ρs(||∇g	α)ρs(||∇g	NUM
ejpam-6062	121	9	e(y)−∇g	e(y)−∇g	PROPN
ejpam-6062	121	10	e(z)||	e(z)||	NOUN
ejpam-6062	121	11	)	)	PUNCT
ejpam-6062	121	12	,	,	PUNCT
ejpam-6062	121	13	(	(	PUNCT
ejpam-6062	121	14	ii	ii	NOUN
ejpam-6062	121	15	)	)	PUNCT
ejpam-6062	121	16	for	for	ADP
ejpam-6062	121	17	any	any	DET
ejpam-6062	121	18	x	x	NOUN
ejpam-6062	121	19	,	,	PUNCT
ejpam-6062	121	20	y	y	PROPN
ejpam-6062	121	21	∈	∈	PROPN
ejpam-6062	121	22	bs	bs	PROPN
ejpam-6062	121	23	,	,	PUNCT
ejpam-6062	121	24	ρs(||x−	ρs(||x−	NOUN
ejpam-6062	121	25	y||	y||	PROPN
ejpam-6062	121	26	)	)	PUNCT
ejpam-6062	121	27	≤	≤	NOUN
ejpam-6062	121	28	dg(x	dg(x	PUNCT
ejpam-6062	121	29	,	,	PUNCT
ejpam-6062	121	30	y	y	PROPN
ejpam-6062	121	31	)	)	PUNCT
ejpam-6062	121	32	.	.	PUNCT
ejpam-6062	122	1	lemma	lemma	PROPN
ejpam-6062	122	2	2	2	NUM
ejpam-6062	122	3	.	.	PUNCT
ejpam-6062	123	1	[	[	X
ejpam-6062	123	2	36	36	NUM
ejpam-6062	123	3	]	]	PUNCT
ejpam-6062	123	4	let	let	VERB
ejpam-6062	123	5	e	e	PRON
ejpam-6062	123	6	be	be	AUX
ejpam-6062	123	7	a	a	DET
ejpam-6062	123	8	reflexive	reflexive	ADJ
ejpam-6062	123	9	banach	banach	NOUN
ejpam-6062	123	10	space	space	NOUN
ejpam-6062	123	11	,	,	PUNCT
ejpam-6062	123	12	g	g	NOUN
ejpam-6062	123	13	:	:	PUNCT
ejpam-6062	123	14	e	e	X
ejpam-6062	123	15	→	→	SYM
ejpam-6062	123	16	r	r	NOUN
ejpam-6062	123	17	be	be	AUX
ejpam-6062	123	18	a	a	DET
ejpam-6062	123	19	strongly	strongly	ADV
ejpam-6062	123	20	coercive	coercive	ADJ
ejpam-6062	123	21	bregman	bregman	NOUN
ejpam-6062	123	22	function	function	NOUN
ejpam-6062	123	23	and	and	CCONJ
ejpam-6062	123	24	v	v	AUX
ejpam-6062	123	25	be	be	AUX
ejpam-6062	123	26	a	a	DET
ejpam-6062	123	27	function	function	NOUN
ejpam-6062	123	28	defined	define	VERB
ejpam-6062	123	29	by	by	ADP
ejpam-6062	123	30	v	v	NUM
ejpam-6062	123	31	(	(	PUNCT
ejpam-6062	123	32	x	x	NOUN
ejpam-6062	123	33	,	,	PUNCT
ejpam-6062	123	34	x∗	x∗	PROPN
ejpam-6062	123	35	)	)	PUNCT
ejpam-6062	124	1	=	=	VERB
ejpam-6062	124	2	g(x)−	g(x)−	PROPN
ejpam-6062	124	3	⟨x	⟨x	VERB
ejpam-6062	124	4	,	,	PUNCT
ejpam-6062	124	5	x∗⟩+	x∗⟩+	PROPN
ejpam-6062	124	6	g∗(x∗	g∗(x∗	PROPN
ejpam-6062	124	7	)	)	PUNCT
ejpam-6062	124	8	,	,	PUNCT
ejpam-6062	124	9	x	x	PUNCT
ejpam-6062	124	10	∈	∈	PROPN
ejpam-6062	124	11	e	e	NOUN
ejpam-6062	124	12	,	,	PUNCT
ejpam-6062	124	13	x∗	x∗	PROPN
ejpam-6062	124	14	∈	∈	PROPN
ejpam-6062	124	15	e∗.	e∗.	NOUN
ejpam-6062	124	16	the	the	DET
ejpam-6062	124	17	following	follow	VERB
ejpam-6062	124	18	assertions	assertion	NOUN
ejpam-6062	124	19	also	also	ADV
ejpam-6062	124	20	hold	hold	VERB
ejpam-6062	124	21	:	:	PUNCT
ejpam-6062	124	22	dg(x,∇g∗	dg(x,∇g∗	PROPN
ejpam-6062	124	23	e∗(x	e∗(x	NOUN
ejpam-6062	124	24	∗	∗	NOUN
ejpam-6062	124	25	)	)	PUNCT
ejpam-6062	124	26	)	)	PUNCT
ejpam-6062	125	1	=	=	SYM
ejpam-6062	125	2	v	v	X
ejpam-6062	125	3	(	(	PUNCT
ejpam-6062	125	4	x	x	NOUN
ejpam-6062	125	5	,	,	PUNCT
ejpam-6062	125	6	x∗	x∗	PROPN
ejpam-6062	125	7	)	)	PUNCT
ejpam-6062	125	8	,	,	PUNCT
ejpam-6062	125	9	for	for	ADP
ejpam-6062	125	10	all	all	DET
ejpam-6062	125	11	x	x	SYM
ejpam-6062	125	12	∈	∈	PROPN
ejpam-6062	125	13	e	e	NOUN
ejpam-6062	125	14	and	and	CCONJ
ejpam-6062	125	15	x∗	x∗	PROPN
ejpam-6062	125	16	∈	∈	PROPN
ejpam-6062	125	17	e∗.	e∗.	X
ejpam-6062	125	18	v	v	PROPN
ejpam-6062	125	19	(	(	PUNCT
ejpam-6062	125	20	x	x	NOUN
ejpam-6062	125	21	,	,	PUNCT
ejpam-6062	125	22	x∗	x∗	PROPN
ejpam-6062	125	23	)	)	PUNCT
ejpam-6062	125	24	+	+	CCONJ
ejpam-6062	125	25	⟨∇g∗	⟨∇g∗	PUNCT
ejpam-6062	125	26	e∗(x	e∗(x	NOUN
ejpam-6062	125	27	∗)−	∗)−	NOUN
ejpam-6062	125	28	x	x	NOUN
ejpam-6062	125	29	,	,	PUNCT
ejpam-6062	125	30	y∗⟩	y∗⟩	PROPN
ejpam-6062	125	31	≤	≤	NUM
ejpam-6062	125	32	v	v	NOUN
ejpam-6062	125	33	(	(	PUNCT
ejpam-6062	125	34	x	x	NOUN
ejpam-6062	125	35	,	,	PUNCT
ejpam-6062	125	36	x∗	x∗	PROPN
ejpam-6062	125	37	+	+	CCONJ
ejpam-6062	125	38	y∗	y∗	ADV
ejpam-6062	125	39	)	)	PUNCT
ejpam-6062	125	40	for	for	ADP
ejpam-6062	125	41	all	all	PRON
ejpam-6062	125	42	x	x	SYM
ejpam-6062	125	43	∈	∈	PROPN
ejpam-6062	125	44	eand	eand	NOUN
ejpam-6062	125	45	x∗	x∗	PROPN
ejpam-6062	125	46	,	,	PUNCT
ejpam-6062	125	47	y∗	y∗	PROPN
ejpam-6062	125	48	∈	∈	PROPN
ejpam-6062	125	49	e∗.	e∗.	NOUN
ejpam-6062	125	50	h.	h.	PROPN
ejpam-6062	125	51	a.	a.	PROPN
ejpam-6062	125	52	abass	abass	PROPN
ejpam-6062	125	53	et	et	PROPN
ejpam-6062	125	54	al	al	PROPN
ejpam-6062	125	55	.	.	PUNCT
ejpam-6062	125	56	/	/	SYM
ejpam-6062	125	57	eur	eur	PROPN
ejpam-6062	125	58	.	.	PUNCT
ejpam-6062	126	1	j.	j.	PROPN
ejpam-6062	126	2	pure	pure	PROPN
ejpam-6062	126	3	appl	appl	PROPN
ejpam-6062	126	4	.	.	PROPN
ejpam-6062	126	5	math	math	PROPN
ejpam-6062	126	6	,	,	PUNCT
ejpam-6062	126	7	18	18	NUM
ejpam-6062	126	8	(	(	PUNCT
ejpam-6062	126	9	2	2	NUM
ejpam-6062	126	10	)	)	PUNCT
ejpam-6062	126	11	(	(	PUNCT
ejpam-6062	126	12	2025	2025	NUM
ejpam-6062	126	13	)	)	PUNCT
ejpam-6062	126	14	,	,	PUNCT
ejpam-6062	126	15	6062	6062	NUM
ejpam-6062	126	16	8	8	NUM
ejpam-6062	126	17	of	of	ADP
ejpam-6062	126	18	22	22	NUM
ejpam-6062	126	19	lemma	lemma	PROPN
ejpam-6062	126	20	3	3	NUM
ejpam-6062	126	21	.	.	PUNCT
ejpam-6062	127	1	[	[	X
ejpam-6062	127	2	35	35	NUM
ejpam-6062	127	3	]	]	PUNCT
ejpam-6062	127	4	let	let	VERB
ejpam-6062	127	5	e1	e1	PROPN
ejpam-6062	127	6	and	and	CCONJ
ejpam-6062	127	7	e2	e2	PROPN
ejpam-6062	127	8	be	be	VERB
ejpam-6062	127	9	two	two	NUM
ejpam-6062	127	10	banach	banach	NOUN
ejpam-6062	127	11	spaces	space	NOUN
ejpam-6062	127	12	.	.	PUNCT
ejpam-6062	128	1	let	let	VERB
ejpam-6062	128	2	f	f	NOUN
ejpam-6062	128	3	:	:	PUNCT
ejpam-6062	128	4	e1	e1	PROPN
ejpam-6062	128	5	→	→	SYM
ejpam-6062	128	6	e2	e2	PROPN
ejpam-6062	128	7	be	be	AUX
ejpam-6062	128	8	a	a	DET
ejpam-6062	128	9	bounded	bounded	ADJ
ejpam-6062	128	10	linear	linear	ADJ
ejpam-6062	128	11	operator	operator	NOUN
ejpam-6062	128	12	and	and	CCONJ
ejpam-6062	128	13	t	t	PROPN
ejpam-6062	128	14	:	:	PUNCT
ejpam-6062	128	15	e2	e2	PROPN
ejpam-6062	128	16	→	→	SYM
ejpam-6062	128	17	e2	e2	PROPN
ejpam-6062	128	18	be	be	AUX
ejpam-6062	128	19	a	a	DET
ejpam-6062	128	20	bregman	bregman	NOUN
ejpam-6062	128	21	(	(	PUNCT
ejpam-6062	128	22	ϕ	ϕ	NOUN
ejpam-6062	128	23	,	,	PUNCT
ejpam-6062	128	24	σ)-demigeneralized	σ)-demigeneralize	VERB
ejpam-6062	128	25	for	for	ADP
ejpam-6062	128	26	some	some	DET
ejpam-6062	128	27	ϕ	ϕ	PROPN
ejpam-6062	128	28	∈	∈	PROPN
ejpam-6062	128	29	(	(	PUNCT
ejpam-6062	128	30	−∞	−∞	NOUN
ejpam-6062	128	31	,	,	PUNCT
ejpam-6062	128	32	1	1	NUM
ejpam-6062	128	33	)	)	PUNCT
ejpam-6062	128	34	and	and	CCONJ
ejpam-6062	128	35	σ	σ	NUM
ejpam-6062	128	36	∈	∈	PROPN
ejpam-6062	129	1	[	[	X
ejpam-6062	129	2	0,∞	0,∞	NOUN
ejpam-6062	129	3	)	)	PUNCT
ejpam-6062	129	4	.	.	PUNCT
ejpam-6062	129	5	suppose	suppose	VERB
ejpam-6062	129	6	that	that	SCONJ
ejpam-6062	129	7	k	k	PROPN
ejpam-6062	129	8	=	=	PUNCT
ejpam-6062	129	9	ran(a	ran(a	PROPN
ejpam-6062	129	10	)	)	PUNCT
ejpam-6062	129	11	∩	∩	NOUN
ejpam-6062	129	12	fix(t	fix(t	PROPN
ejpam-6062	129	13	)	)	PUNCT
ejpam-6062	129	14	̸=	̸=	PROPN
ejpam-6062	129	15	∅	∅	NOUN
ejpam-6062	129	16	(	(	PUNCT
ejpam-6062	129	17	where	where	SCONJ
ejpam-6062	129	18	ran(b	ran(b	NOUN
ejpam-6062	129	19	)	)	PUNCT
ejpam-6062	129	20	denotes	denote	VERB
ejpam-6062	129	21	the	the	DET
ejpam-6062	129	22	range	range	NOUN
ejpam-6062	129	23	of	of	ADP
ejpam-6062	129	24	b	b	NOUN
ejpam-6062	129	25	)	)	PUNCT
ejpam-6062	129	26	.	.	PUNCT
ejpam-6062	130	1	then	then	ADV
ejpam-6062	130	2	for	for	ADP
ejpam-6062	130	3	any	any	DET
ejpam-6062	130	4	(	(	PUNCT
ejpam-6062	130	5	x	x	NOUN
ejpam-6062	130	6	,	,	PUNCT
ejpam-6062	130	7	q	q	ADJ
ejpam-6062	130	8	)	)	PUNCT
ejpam-6062	130	9	∈	∈	PROPN
ejpam-6062	130	10	e1	e1	NOUN
ejpam-6062	130	11	×k	×k	NOUN
ejpam-6062	130	12	,	,	PUNCT
ejpam-6062	130	13	⟨x−	⟨x−	PROPN
ejpam-6062	130	14	q	q	PROPN
ejpam-6062	130	15	,	,	PUNCT
ejpam-6062	130	16	f	f	PROPN
ejpam-6062	130	17	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	130	18	e2	e2	PROPN
ejpam-6062	130	19	(	(	PUNCT
ejpam-6062	130	20	t	t	PROPN
ejpam-6062	130	21	(	(	PUNCT
ejpam-6062	130	22	fx)))⟩	fx)))⟩	NOUN
ejpam-6062	130	23	≥	≥	X
ejpam-6062	130	24	(	(	PUNCT
ejpam-6062	130	25	1−	1−	NUM
ejpam-6062	130	26	ϕ)dg2(fx	ϕ)dg2(fx	NOUN
ejpam-6062	130	27	,	,	PUNCT
ejpam-6062	130	28	t	t	PROPN
ejpam-6062	130	29	(	(	PUNCT
ejpam-6062	130	30	fx	fx	PROPN
ejpam-6062	130	31	)	)	PUNCT
ejpam-6062	130	32	)	)	PUNCT
ejpam-6062	131	1	+	+	CCONJ
ejpam-6062	131	2	σdg2(t	σdg2(t	X
ejpam-6062	131	3	(	(	PUNCT
ejpam-6062	131	4	fx	fx	PROPN
ejpam-6062	131	5	)	)	PUNCT
ejpam-6062	131	6	,	,	PUNCT
ejpam-6062	131	7	fx	fx	PROPN
ejpam-6062	131	8	)	)	PUNCT
ejpam-6062	131	9	≥	≥	NOUN
ejpam-6062	131	10	(	(	PUNCT
ejpam-6062	131	11	1−	1−	NUM
ejpam-6062	131	12	ϕ)dg2(fx	ϕ)dg2(fx	NOUN
ejpam-6062	131	13	,	,	PUNCT
ejpam-6062	131	14	t	t	PROPN
ejpam-6062	131	15	(	(	PUNCT
ejpam-6062	131	16	fx	fx	PROPN
ejpam-6062	131	17	)	)	PUNCT
ejpam-6062	131	18	)	)	PUNCT
ejpam-6062	131	19	.	.	PUNCT
ejpam-6062	132	1	(	(	PUNCT
ejpam-6062	132	2	12	12	NUM
ejpam-6062	132	3	)	)	PUNCT
ejpam-6062	132	4	so	so	ADV
ejpam-6062	132	5	,	,	PUNCT
ejpam-6062	132	6	given	give	VERB
ejpam-6062	132	7	any	any	DET
ejpam-6062	132	8	real	real	ADJ
ejpam-6062	132	9	numbers	number	NOUN
ejpam-6062	132	10	ξ1	ξ1	NOUN
ejpam-6062	132	11	and	and	CCONJ
ejpam-6062	132	12	ξ2	ξ2	NOUN
ejpam-6062	132	13	,	,	PUNCT
ejpam-6062	132	14	the	the	DET
ejpam-6062	132	15	mapping	mapping	NOUN
ejpam-6062	132	16	l1	l1	PROPN
ejpam-6062	132	17	:	:	PUNCT
ejpam-6062	132	18	e1	e1	PROPN
ejpam-6062	132	19	→	→	PUNCT
ejpam-6062	133	1	[	[	X
ejpam-6062	133	2	0,∞	0,∞	NUM
ejpam-6062	133	3	)	)	PUNCT
ejpam-6062	133	4	and	and	CCONJ
ejpam-6062	133	5	l2	l2	NOUN
ejpam-6062	133	6	:	:	PUNCT
ejpam-6062	133	7	e2	e2	PROPN
ejpam-6062	133	8	→	→	PUNCT
ejpam-6062	134	1	[	[	X
ejpam-6062	134	2	0.∞	0.∞	NOUN
ejpam-6062	134	3	)	)	PUNCT
ejpam-6062	134	4	formulated	formulate	VERB
ejpam-6062	134	5	for	for	ADP
ejpam-6062	134	6	x	x	PROPN
ejpam-6062	134	7	∈	∈	PROPN
ejpam-6062	134	8	e1	e1	PROPN
ejpam-6062	134	9	as	as	ADP
ejpam-6062	134	10	l1(x	l1(x	NOUN
ejpam-6062	134	11	)	)	PUNCT
ejpam-6062	134	12	=	=	PUNCT
ejpam-6062	134	13			PROPN
ejpam-6062	134	14	dg2	dg2	PROPN
ejpam-6062	134	15	(	(	PUNCT
ejpam-6062	134	16	fx	fx	PROPN
ejpam-6062	134	17	,	,	PUNCT
ejpam-6062	134	18	tfx	tfx	PROPN
ejpam-6062	134	19	)	)	PUNCT
ejpam-6062	134	20	d∗	d∗	PROPN
ejpam-6062	134	21	g1	g1	PROPN
ejpam-6062	134	22	(	(	PUNCT
ejpam-6062	134	23	f	f	PROPN
ejpam-6062	134	24	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	134	25	e2	e2	PROPN
ejpam-6062	134	26	(	(	PUNCT
ejpam-6062	134	27	fx)),f	fx)),f	PROPN
ejpam-6062	134	28	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	134	29	e2	e2	PROPN
ejpam-6062	134	30	(	(	PUNCT
ejpam-6062	134	31	tfx	tfx	PROPN
ejpam-6062	134	32	)	)	PUNCT
ejpam-6062	134	33	)	)	PUNCT
ejpam-6062	134	34	,	,	PUNCT
ejpam-6062	134	35	if	if	SCONJ
ejpam-6062	134	36	,	,	PUNCT
ejpam-6062	134	37	(	(	PUNCT
ejpam-6062	134	38	i	i	PRON
ejpam-6062	134	39	−	−	PROPN
ejpam-6062	134	40	t	t	NOUN
ejpam-6062	134	41	)	)	PUNCT
ejpam-6062	134	42	fx	fx	PROPN
ejpam-6062	134	43	̸=	̸=	PROPN
ejpam-6062	134	44	0	0	NUM
ejpam-6062	134	45	,	,	PUNCT
ejpam-6062	134	46	ξ1	ξ1	NOUN
ejpam-6062	134	47	,	,	PUNCT
ejpam-6062	134	48	otherwise	otherwise	ADV
ejpam-6062	134	49	,	,	PUNCT
ejpam-6062	134	50	(	(	PUNCT
ejpam-6062	134	51	13	13	NUM
ejpam-6062	134	52	)	)	PUNCT
ejpam-6062	134	53	and	and	CCONJ
ejpam-6062	134	54	l2(x	l2(x	PROPN
ejpam-6062	134	55	)	)	PUNCT
ejpam-6062	134	56	=	=	PUNCT
ejpam-6062	134	57			PUNCT
ejpam-6062	134	58	d∗	d∗	PROPN
ejpam-6062	134	59	g1	g1	PROPN
ejpam-6062	134	60	(	(	PUNCT
ejpam-6062	134	61	∇g1	∇g1	PROPN
ejpam-6062	134	62	e1	e1	PROPN
ejpam-6062	134	63	(	(	PUNCT
ejpam-6062	134	64	x)−γf	x)−γf	PROPN
ejpam-6062	134	65	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	134	66	e2	e2	PROPN
ejpam-6062	134	67	(	(	PUNCT
ejpam-6062	134	68	fx)−∇g2	fx)−∇g2	PROPN
ejpam-6062	134	69	e2	e2	PROPN
ejpam-6062	134	70	(	(	PUNCT
ejpam-6062	134	71	tfx)),∇g1	tfx)),∇g1	PROPN
ejpam-6062	134	72	e1	e1	PROPN
ejpam-6062	134	73	(	(	PUNCT
ejpam-6062	134	74	x	x	NOUN
ejpam-6062	134	75	)	)	PUNCT
ejpam-6062	134	76	)	)	PUNCT
ejpam-6062	134	77	d∗	d∗	PROPN
ejpam-6062	134	78	g1	g1	PROPN
ejpam-6062	134	79	(	(	PUNCT
ejpam-6062	134	80	f	f	PROPN
ejpam-6062	134	81	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	134	82	e2	e2	PROPN
ejpam-6062	134	83	(	(	PUNCT
ejpam-6062	134	84	fx)),f	fx)),f	PROPN
ejpam-6062	134	85	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	134	86	e2	e2	PROPN
ejpam-6062	134	87	(	(	PUNCT
ejpam-6062	134	88	tfx	tfx	PROPN
ejpam-6062	134	89	)	)	PUNCT
ejpam-6062	134	90	)	)	PUNCT
ejpam-6062	134	91	,	,	PUNCT
ejpam-6062	134	92	if	if	SCONJ
ejpam-6062	134	93	,	,	PUNCT
ejpam-6062	134	94	(	(	PUNCT
ejpam-6062	134	95	i	i	PRON
ejpam-6062	134	96	−	−	PROPN
ejpam-6062	134	97	t	t	NOUN
ejpam-6062	134	98	)	)	PUNCT
ejpam-6062	134	99	fx	fx	PROPN
ejpam-6062	134	100	̸=	̸=	PROPN
ejpam-6062	134	101	0	0	NUM
ejpam-6062	134	102	,	,	PUNCT
ejpam-6062	134	103	ξ2	ξ2	ADJ
ejpam-6062	134	104	,	,	PUNCT
ejpam-6062	134	105	otherwise	otherwise	ADV
ejpam-6062	134	106	,	,	PUNCT
ejpam-6062	134	107	(	(	PUNCT
ejpam-6062	134	108	14	14	NUM
ejpam-6062	134	109	)	)	PUNCT
ejpam-6062	134	110	are	be	AUX
ejpam-6062	134	111	well	well	ADV
ejpam-6062	134	112	-	-	PUNCT
ejpam-6062	134	113	defined	define	VERB
ejpam-6062	134	114	,	,	PUNCT
ejpam-6062	134	115	where	where	SCONJ
ejpam-6062	134	116	γ	γ	PROPN
ejpam-6062	134	117	is	be	AUX
ejpam-6062	134	118	any	any	DET
ejpam-6062	134	119	nonnegative	nonnegative	ADJ
ejpam-6062	134	120	real	real	ADJ
ejpam-6062	134	121	number	number	NOUN
ejpam-6062	134	122	.	.	PUNCT
ejpam-6062	135	1	moreover	moreover	ADV
ejpam-6062	135	2	,	,	PUNCT
ejpam-6062	135	3	for	for	ADP
ejpam-6062	135	4	any	any	DET
ejpam-6062	135	5	(	(	PUNCT
ejpam-6062	135	6	x	x	NOUN
ejpam-6062	135	7	,	,	PUNCT
ejpam-6062	135	8	p	p	NOUN
ejpam-6062	135	9	)	)	PUNCT
ejpam-6062	135	10	∈	∈	PROPN
ejpam-6062	135	11	e1	e1	NOUN
ejpam-6062	135	12	×k	×k	NOUN
ejpam-6062	135	13	,	,	PUNCT
ejpam-6062	135	14	we	we	PRON
ejpam-6062	135	15	have	have	VERB
ejpam-6062	135	16	dg1(q	dg1(q	PROPN
ejpam-6062	135	17	,	,	PUNCT
ejpam-6062	135	18	y	y	NOUN
ejpam-6062	135	19	)	)	PUNCT
ejpam-6062	135	20	≤	≤	PUNCT
ejpam-6062	136	1	dg1(q	dg1(q	PROPN
ejpam-6062	136	2	,	,	PUNCT
ejpam-6062	136	3	x)−	x)−	PROPN
ejpam-6062	136	4	(	(	PUNCT
ejpam-6062	136	5	γ(1−	γ(1−	PROPN
ejpam-6062	136	6	ϕ)l1(x)−	ϕ)l1(x)−	PROPN
ejpam-6062	136	7	l2(x))dg∗1	l2(x))dg∗1	PROPN
ejpam-6062	136	8	(	(	PUNCT
ejpam-6062	136	9	f	f	PROPN
ejpam-6062	136	10	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	136	11	e2	e2	PROPN
ejpam-6062	136	12	(	(	PUNCT
ejpam-6062	136	13	fx	fx	PROPN
ejpam-6062	136	14	)	)	PUNCT
ejpam-6062	136	15	)	)	PUNCT
ejpam-6062	136	16	,	,	PUNCT
ejpam-6062	136	17	f	f	PROPN
ejpam-6062	136	18	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	136	19	e2	e2	PROPN
ejpam-6062	136	20	(	(	PUNCT
ejpam-6062	136	21	tfx	tfx	PROPN
ejpam-6062	136	22	)	)	PUNCT
ejpam-6062	136	23	)	)	PUNCT
ejpam-6062	136	24	,	,	PUNCT
ejpam-6062	136	25	(	(	PUNCT
ejpam-6062	136	26	15	15	NUM
ejpam-6062	136	27	)	)	PUNCT
ejpam-6062	136	28	where	where	SCONJ
ejpam-6062	136	29	y	y	PROPN
ejpam-6062	136	30	=	=	PRON
ejpam-6062	136	31	(	(	PUNCT
ejpam-6062	136	32	∇g1	∇g1	PROPN
ejpam-6062	136	33	e1	e1	PROPN
ejpam-6062	136	34	)	)	PUNCT
ejpam-6062	136	35	−1[∇g1	−1[∇g1	X
ejpam-6062	137	1	e1	e1	PROPN
ejpam-6062	137	2	(	(	PUNCT
ejpam-6062	137	3	x)−	x)−	PROPN
ejpam-6062	137	4	γf	γf	PROPN
ejpam-6062	137	5	∗(∇g2	∗(∇g2	PROPN
ejpam-6062	137	6	e2	e2	PROPN
ejpam-6062	137	7	(	(	PUNCT
ejpam-6062	137	8	fx)−∇g2	fx)−∇g2	PROPN
ejpam-6062	137	9	e2	e2	PROPN
ejpam-6062	137	10	(	(	PUNCT
ejpam-6062	137	11	tfx	tfx	PROPN
ejpam-6062	137	12	)	)	PUNCT
ejpam-6062	137	13	)	)	PUNCT
ejpam-6062	137	14	]	]	PUNCT
ejpam-6062	137	15	.	.	PUNCT
ejpam-6062	138	1	lemma	lemma	PROPN
ejpam-6062	138	2	4	4	NUM
ejpam-6062	138	3	.	.	PUNCT
ejpam-6062	139	1	[	[	X
ejpam-6062	139	2	36	36	NUM
ejpam-6062	139	3	]	]	PUNCT
ejpam-6062	139	4	let	let	VERB
ejpam-6062	139	5	e	e	PRON
ejpam-6062	139	6	be	be	AUX
ejpam-6062	139	7	a	a	DET
ejpam-6062	139	8	banach	banach	NOUN
ejpam-6062	139	9	space	space	NOUN
ejpam-6062	139	10	and	and	CCONJ
ejpam-6062	139	11	g	g	NOUN
ejpam-6062	139	12	:	:	PUNCT
ejpam-6062	139	13	e	e	X
ejpam-6062	139	14	→	→	SYM
ejpam-6062	139	15	r	r	NOUN
ejpam-6062	139	16	a	a	DET
ejpam-6062	139	17	gâteaux	gâteaux	ADV
ejpam-6062	139	18	differentiable	differentiable	ADJ
ejpam-6062	139	19	function	function	NOUN
ejpam-6062	139	20	which	which	PRON
ejpam-6062	139	21	is	be	AUX
ejpam-6062	139	22	uniformly	uniformly	ADV
ejpam-6062	139	23	convex	convex	ADJ
ejpam-6062	139	24	on	on	ADP
ejpam-6062	139	25	bounded	bounded	ADJ
ejpam-6062	139	26	subsets	subset	NOUN
ejpam-6062	139	27	of	of	ADP
ejpam-6062	139	28	e.	e.	PROPN
ejpam-6062	139	29	let	let	VERB
ejpam-6062	139	30	{	{	PUNCT
ejpam-6062	139	31	x}n∈n	x}n∈n	PROPN
ejpam-6062	139	32	and	and	CCONJ
ejpam-6062	139	33	{	{	PUNCT
ejpam-6062	139	34	yn}n∈n	yn}n∈n	NOUN
ejpam-6062	139	35	be	be	AUX
ejpam-6062	139	36	bounded	bound	VERB
ejpam-6062	139	37	sequences	sequence	NOUN
ejpam-6062	139	38	in	in	ADP
ejpam-6062	139	39	e.	e.	PROPN
ejpam-6062	139	40	then	then	ADV
ejpam-6062	139	41	,	,	PUNCT
ejpam-6062	139	42	lim	lim	PROPN
ejpam-6062	139	43	n→∞	n→∞	NUM
ejpam-6062	139	44	dg(yn	dg(yn	PROPN
ejpam-6062	139	45	,	,	PUNCT
ejpam-6062	139	46	xn	xn	X
ejpam-6062	139	47	)	)	PUNCT
ejpam-6062	139	48	=	=	SYM
ejpam-6062	139	49	0	0	NUM
ejpam-6062	139	50	⇒	⇒	PROPN
ejpam-6062	139	51	lim	lim	PROPN
ejpam-6062	139	52	n→∞	n→∞	X
ejpam-6062	140	1	||yn	||yn	NUM
ejpam-6062	140	2	−	−	NOUN
ejpam-6062	140	3	xn||	xn||	PUNCT
ejpam-6062	141	1	=	=	PUNCT
ejpam-6062	141	2	0	0	X
ejpam-6062	141	3	.	.	PUNCT
ejpam-6062	142	1	lemma	lemma	PROPN
ejpam-6062	142	2	5	5	NUM
ejpam-6062	142	3	.	.	PUNCT
ejpam-6062	143	1	[	[	X
ejpam-6062	143	2	37	37	NUM
ejpam-6062	143	3	]	]	PUNCT
ejpam-6062	143	4	let	let	VERB
ejpam-6062	143	5	g	g	NOUN
ejpam-6062	143	6	:	:	PUNCT
ejpam-6062	143	7	e	e	X
ejpam-6062	143	8	→	→	PUNCT
ejpam-6062	143	9	(	(	PUNCT
ejpam-6062	143	10	−∞,+∞	−∞,+∞	ADV
ejpam-6062	143	11	]	]	PUNCT
ejpam-6062	143	12	be	be	VERB
ejpam-6062	143	13	a	a	DET
ejpam-6062	143	14	legendre	legendre	NOUN
ejpam-6062	143	15	function	function	NOUN
ejpam-6062	143	16	.	.	PUNCT
ejpam-6062	144	1	let	let	VERB
ejpam-6062	144	2	{	{	PUNCT
ejpam-6062	144	3	ti}ni=1	ti}ni=1	ADV
ejpam-6062	144	4	:	:	PUNCT
ejpam-6062	144	5	e	e	X
ejpam-6062	144	6	→	→	PUNCT
ejpam-6062	144	7	e	e	X
ejpam-6062	144	8	be	be	AUX
ejpam-6062	144	9	a	a	DET
ejpam-6062	144	10	bqne	bqne	NOUN
ejpam-6062	144	11	such	such	ADJ
ejpam-6062	144	12	that	that	DET
ejpam-6062	144	13	n⋂	n⋂	NOUN
ejpam-6062	144	14	i=1	i=1	PROPN
ejpam-6062	144	15	fix(ti	fix(ti	NOUN
ejpam-6062	144	16	)	)	PUNCT
ejpam-6062	144	17	̸=	̸=	NOUN
ejpam-6062	144	18	∅	∅	NOUN
ejpam-6062	144	19	and	and	CCONJ
ejpam-6062	144	20	{	{	PUNCT
ejpam-6062	144	21	βi}ni=0	βi}ni=0	PROPN
ejpam-6062	144	22	⊂	⊂	PROPN
ejpam-6062	144	23	(	(	PUNCT
ejpam-6062	144	24	0	0	NUM
ejpam-6062	144	25	,	,	PUNCT
ejpam-6062	144	26	1	1	X
ejpam-6062	144	27	)	)	PUNCT
ejpam-6062	144	28	satisfy	satisfy	NOUN
ejpam-6062	144	29	n∑	n∑	PROPN
ejpam-6062	144	30	i=0	i=0	PROPN
ejpam-6062	144	31	βi	βi	X
ejpam-6062	145	1	=	=	SYM
ejpam-6062	145	2	1	1	X
ejpam-6062	145	3	.	.	X
ejpam-6062	145	4	define	define	VERB
ejpam-6062	145	5	a	a	DET
ejpam-6062	145	6	mapping	mapping	NOUN
ejpam-6062	145	7	s	s	PART
ejpam-6062	145	8	:	:	PUNCT
ejpam-6062	145	9	e	e	X
ejpam-6062	145	10	→	→	SYM
ejpam-6062	145	11	e	e	X
ejpam-6062	145	12	by	by	ADP
ejpam-6062	145	13	sx	sx	PROPN
ejpam-6062	145	14	:	:	PUNCT
ejpam-6062	145	15	=	=	SYM
ejpam-6062	145	16	(	(	PUNCT
ejpam-6062	145	17	∇g	∇g	PROPN
ejpam-6062	145	18	e	e	NOUN
ejpam-6062	145	19	)	)	PUNCT
ejpam-6062	145	20	−1(β0∇g	−1(β0∇g	X
ejpam-6062	145	21	e(x	e(x	NUM
ejpam-6062	145	22	)	)	PUNCT
ejpam-6062	146	1	+	+	CCONJ
ejpam-6062	146	2	n∑	n∑	X
ejpam-6062	146	3	i=1	i=1	X
ejpam-6062	146	4	βi∇g	βi∇g	PROPN
ejpam-6062	146	5	e(tix	e(tix	PROPN
ejpam-6062	146	6	)	)	PUNCT
ejpam-6062	146	7	)	)	PUNCT
ejpam-6062	146	8	for	for	ADP
ejpam-6062	146	9	all	all	DET
ejpam-6062	146	10	x	x	SYM
ejpam-6062	146	11	∈	∈	PROPN
ejpam-6062	146	12	e.	e.	PROPN
ejpam-6062	146	13	then	then	ADV
ejpam-6062	146	14	s	s	VERB
ejpam-6062	146	15	is	be	AUX
ejpam-6062	146	16	bqne	bqne	ADV
ejpam-6062	146	17	such	such	ADJ
ejpam-6062	146	18	that	that	DET
ejpam-6062	146	19	fix(s	fix(s	PROPN
ejpam-6062	146	20	)	)	PUNCT
ejpam-6062	146	21	=	=	PRON
ejpam-6062	147	1	n⋂	n⋂	VERB
ejpam-6062	147	2	i=1	i=1	PROPN
ejpam-6062	147	3	fix(ti	fix(ti	NOUN
ejpam-6062	147	4	)	)	PUNCT
ejpam-6062	147	5	.	.	PUNCT
ejpam-6062	148	1	h.	h.	PROPN
ejpam-6062	148	2	a.	a.	PROPN
ejpam-6062	148	3	abass	abass	PROPN
ejpam-6062	148	4	et	et	PROPN
ejpam-6062	148	5	al	al	PROPN
ejpam-6062	148	6	.	.	PUNCT
ejpam-6062	148	7	/	/	SYM
ejpam-6062	148	8	eur	eur	PROPN
ejpam-6062	148	9	.	.	PUNCT
ejpam-6062	149	1	j.	j.	PROPN
ejpam-6062	149	2	pure	pure	PROPN
ejpam-6062	149	3	appl	appl	PROPN
ejpam-6062	149	4	.	.	PROPN
ejpam-6062	149	5	math	math	PROPN
ejpam-6062	149	6	,	,	PUNCT
ejpam-6062	149	7	18	18	NUM
ejpam-6062	149	8	(	(	PUNCT
ejpam-6062	149	9	2	2	NUM
ejpam-6062	149	10	)	)	PUNCT
ejpam-6062	149	11	(	(	PUNCT
ejpam-6062	149	12	2025	2025	NUM
ejpam-6062	149	13	)	)	PUNCT
ejpam-6062	149	14	,	,	PUNCT
ejpam-6062	149	15	6062	6062	NUM
ejpam-6062	149	16	9	9	NUM
ejpam-6062	149	17	of	of	ADP
ejpam-6062	149	18	22	22	NUM
ejpam-6062	149	19	lemma	lemma	PROPN
ejpam-6062	149	20	6	6	NUM
ejpam-6062	149	21	.	.	PUNCT
ejpam-6062	150	1	[	[	X
ejpam-6062	150	2	38	38	NUM
ejpam-6062	150	3	]	]	PUNCT
ejpam-6062	150	4	let	let	VERB
ejpam-6062	150	5	b	b	NOUN
ejpam-6062	150	6	:	:	PUNCT
ejpam-6062	150	7	e	e	X
ejpam-6062	150	8	→	→	SYM
ejpam-6062	150	9	2e	2e	PROPN
ejpam-6062	150	10	∗	∗	NOUN
ejpam-6062	150	11	be	be	VERB
ejpam-6062	150	12	a	a	DET
ejpam-6062	150	13	maximal	maximal	ADJ
ejpam-6062	150	14	monotone	monotone	NOUN
ejpam-6062	150	15	operator	operator	NOUN
ejpam-6062	150	16	and	and	CCONJ
ejpam-6062	150	17	a	a	DET
ejpam-6062	150	18	:	:	PUNCT
ejpam-6062	150	19	e	e	X
ejpam-6062	150	20	→	→	SYM
ejpam-6062	150	21	e∗	e∗	PROPN
ejpam-6062	150	22	be	be	AUX
ejpam-6062	150	23	a	a	DET
ejpam-6062	150	24	bism	bism	NOUN
ejpam-6062	150	25	mapping	mapping	NOUN
ejpam-6062	150	26	such	such	ADJ
ejpam-6062	150	27	that	that	SCONJ
ejpam-6062	150	28	(	(	PUNCT
ejpam-6062	150	29	a	a	DET
ejpam-6062	150	30	+	+	X
ejpam-6062	150	31	b)−1(0∗	b)−1(0∗	PROPN
ejpam-6062	150	32	)	)	PUNCT
ejpam-6062	151	1	̸=	̸=	PROPN
ejpam-6062	151	2	∅.	∅.	ADV
ejpam-6062	151	3	let	let	VERB
ejpam-6062	151	4	g	g	NOUN
ejpam-6062	151	5	:	:	PUNCT
ejpam-6062	151	6	e	e	X
ejpam-6062	151	7	→	→	SYM
ejpam-6062	151	8	r	r	NOUN
ejpam-6062	151	9	be	be	AUX
ejpam-6062	151	10	a	a	DET
ejpam-6062	151	11	legendre	legendre	NOUN
ejpam-6062	151	12	function	function	NOUN
ejpam-6062	151	13	,	,	PUNCT
ejpam-6062	151	14	which	which	PRON
ejpam-6062	151	15	is	be	AUX
ejpam-6062	151	16	uniformly	uniformly	ADV
ejpam-6062	151	17	fréchet	fréchet	VERB
ejpam-6062	151	18	differentiable	differentiable	ADJ
ejpam-6062	151	19	and	and	CCONJ
ejpam-6062	151	20	bounded	bound	VERB
ejpam-6062	151	21	on	on	ADP
ejpam-6062	151	22	bounded	bounded	PROPN
ejpam-6062	151	23	subset	subset	PROPN
ejpam-6062	151	24	of	of	ADP
ejpam-6062	151	25	e.	e.	PROPN
ejpam-6062	151	26	then	then	ADV
ejpam-6062	151	27	,	,	PUNCT
ejpam-6062	151	28	dg(u	dg(u	X
ejpam-6062	151	29	,	,	PUNCT
ejpam-6062	151	30	resgλb	resgλb	NOUN
ejpam-6062	151	31	◦	◦	NOUN
ejpam-6062	151	32	ag(x	ag(x	X
ejpam-6062	151	33	)	)	PUNCT
ejpam-6062	151	34	)	)	PUNCT
ejpam-6062	152	1	+	+	PUNCT
ejpam-6062	152	2	dg(resgλb(x	dg(resgλb(x	PROPN
ejpam-6062	152	3	)	)	PUNCT
ejpam-6062	152	4	,	,	PUNCT
ejpam-6062	152	5	x	x	X
ejpam-6062	152	6	)	)	PUNCT
ejpam-6062	152	7	≤	≤	NOUN
ejpam-6062	152	8	dg(u	dg(u	NOUN
ejpam-6062	152	9	,	,	PUNCT
ejpam-6062	152	10	x	x	X
ejpam-6062	152	11	)	)	PUNCT
ejpam-6062	152	12	,	,	PUNCT
ejpam-6062	152	13	for	for	ADP
ejpam-6062	152	14	any	any	DET
ejpam-6062	152	15	u	u	PROPN
ejpam-6062	152	16	∈	∈	PROPN
ejpam-6062	152	17	(	(	PUNCT
ejpam-6062	152	18	a+b)−1(0∗	a+b)−1(0∗	NOUN
ejpam-6062	152	19	)	)	PUNCT
ejpam-6062	152	20	,	,	PUNCT
ejpam-6062	152	21	x	x	PUNCT
ejpam-6062	152	22	∈	∈	PROPN
ejpam-6062	152	23	e	e	NOUN
ejpam-6062	152	24	and	and	CCONJ
ejpam-6062	152	25	λ	λ	X
ejpam-6062	152	26	>	>	X
ejpam-6062	152	27	0	0	X
ejpam-6062	152	28	.	.	PUNCT
ejpam-6062	153	1	lemma	lemma	PROPN
ejpam-6062	153	2	7	7	NUM
ejpam-6062	153	3	.	.	PUNCT
ejpam-6062	154	1	[	[	X
ejpam-6062	154	2	38	38	NUM
ejpam-6062	154	3	]	]	PUNCT
ejpam-6062	154	4	let	let	VERB
ejpam-6062	154	5	b	b	NOUN
ejpam-6062	154	6	:	:	PUNCT
ejpam-6062	154	7	e	e	X
ejpam-6062	154	8	→	→	SYM
ejpam-6062	154	9	2e	2e	PROPN
ejpam-6062	154	10	∗	∗	NOUN
ejpam-6062	154	11	be	be	VERB
ejpam-6062	154	12	a	a	DET
ejpam-6062	154	13	maximal	maximal	ADJ
ejpam-6062	154	14	monotone	monotone	NOUN
ejpam-6062	154	15	operator	operator	NOUN
ejpam-6062	154	16	and	and	CCONJ
ejpam-6062	154	17	a	a	DET
ejpam-6062	154	18	:	:	PUNCT
ejpam-6062	154	19	e	e	X
ejpam-6062	154	20	→	→	SYM
ejpam-6062	154	21	e∗	e∗	PROPN
ejpam-6062	154	22	be	be	AUX
ejpam-6062	154	23	a	a	DET
ejpam-6062	154	24	bism	bism	NOUN
ejpam-6062	154	25	mapping	mapping	NOUN
ejpam-6062	154	26	such	such	ADJ
ejpam-6062	154	27	that	that	SCONJ
ejpam-6062	154	28	(	(	PUNCT
ejpam-6062	154	29	a	a	DET
ejpam-6062	154	30	+	+	X
ejpam-6062	154	31	b)−1(0∗	b)−1(0∗	PROPN
ejpam-6062	154	32	)	)	PUNCT
ejpam-6062	155	1	̸=	̸=	PROPN
ejpam-6062	155	2	∅.	∅.	ADV
ejpam-6062	155	3	let	let	VERB
ejpam-6062	155	4	g	g	NOUN
ejpam-6062	155	5	:	:	PUNCT
ejpam-6062	155	6	e	e	X
ejpam-6062	155	7	→	→	SYM
ejpam-6062	155	8	r	r	NOUN
ejpam-6062	155	9	be	be	AUX
ejpam-6062	155	10	a	a	DET
ejpam-6062	155	11	legendre	legendre	NOUN
ejpam-6062	155	12	function	function	NOUN
ejpam-6062	155	13	,	,	PUNCT
ejpam-6062	155	14	which	which	PRON
ejpam-6062	155	15	is	be	AUX
ejpam-6062	155	16	uniformly	uniformly	ADV
ejpam-6062	155	17	fréchet	fréchet	VERB
ejpam-6062	155	18	differentiable	differentiable	ADJ
ejpam-6062	155	19	and	and	CCONJ
ejpam-6062	155	20	bounded	bound	VERB
ejpam-6062	155	21	on	on	ADP
ejpam-6062	155	22	bounded	bounded	PROPN
ejpam-6062	155	23	subset	subset	PROPN
ejpam-6062	155	24	of	of	ADP
ejpam-6062	155	25	e.	e.	PROPN
ejpam-6062	155	26	then	then	ADV
ejpam-6062	155	27	,	,	PUNCT
ejpam-6062	155	28	(	(	PUNCT
ejpam-6062	155	29	i	i	NOUN
ejpam-6062	155	30	)	)	PUNCT
ejpam-6062	155	31	(	(	PUNCT
ejpam-6062	155	32	a+b)−1(0∗	a+b)−1(0∗	NOUN
ejpam-6062	155	33	)	)	PUNCT
ejpam-6062	155	34	=	=	SYM
ejpam-6062	155	35	fix(resgλb	fix(resgλb	SYM
ejpam-6062	155	36	◦	◦	NOUN
ejpam-6062	155	37	ag	ag	PROPN
ejpam-6062	155	38	λ	λ	PROPN
ejpam-6062	155	39	)	)	PUNCT
ejpam-6062	155	40	;	;	PUNCT
ejpam-6062	155	41	(	(	PUNCT
ejpam-6062	155	42	ii	ii	NOUN
ejpam-6062	155	43	)	)	PUNCT
ejpam-6062	155	44	resgλb	resgλb	PROPN
ejpam-6062	155	45	◦	◦	PROPN
ejpam-6062	155	46	ag	ag	PROPN
ejpam-6062	155	47	λ	λ	PROPN
ejpam-6062	155	48	is	be	AUX
ejpam-6062	155	49	a	a	DET
ejpam-6062	155	50	bsne	bsne	NOUN
ejpam-6062	155	51	operator	operator	NOUN
ejpam-6062	155	52	with	with	ADP
ejpam-6062	155	53	fix(resgλb	fix(resgλb	NOUN
ejpam-6062	155	54	◦	◦	NOUN
ejpam-6062	155	55	ag	ag	PROPN
ejpam-6062	155	56	λ	λ	PROPN
ejpam-6062	155	57	)	)	PUNCT
ejpam-6062	155	58	=	=	SYM
ejpam-6062	155	59	ˆfix(resgλb	ˆfix(resgλb	PROPN
ejpam-6062	155	60	◦	◦	NOUN
ejpam-6062	155	61	ag	ag	PROPN
ejpam-6062	155	62	λ	λ	PROPN
ejpam-6062	155	63	)	)	PUNCT
ejpam-6062	155	64	.	.	PUNCT
ejpam-6062	156	1	lemma	lemma	PROPN
ejpam-6062	156	2	8	8	NUM
ejpam-6062	156	3	.	.	PUNCT
ejpam-6062	157	1	[	[	X
ejpam-6062	157	2	39	39	NUM
ejpam-6062	157	3	]	]	PUNCT
ejpam-6062	157	4	let	let	VERB
ejpam-6062	157	5	g	g	NOUN
ejpam-6062	157	6	:	:	PUNCT
ejpam-6062	157	7	e	e	X
ejpam-6062	157	8	→	→	SYM
ejpam-6062	157	9	r	r	NOUN
ejpam-6062	157	10	be	be	AUX
ejpam-6062	157	11	a	a	DET
ejpam-6062	157	12	gâteaux	gâteaux	ADV
ejpam-6062	157	13	differentiable	differentiable	ADJ
ejpam-6062	157	14	and	and	CCONJ
ejpam-6062	157	15	totally	totally	ADV
ejpam-6062	157	16	convex	convex	ADJ
ejpam-6062	157	17	function	function	NOUN
ejpam-6062	157	18	.	.	PUNCT
ejpam-6062	158	1	if	if	SCONJ
ejpam-6062	158	2	x0	x0	PROPN
ejpam-6062	158	3	∈	∈	PROPN
ejpam-6062	158	4	e	e	NOUN
ejpam-6062	158	5	and	and	CCONJ
ejpam-6062	158	6	the	the	DET
ejpam-6062	158	7	sequence	sequence	NOUN
ejpam-6062	158	8	{	{	PUNCT
ejpam-6062	158	9	dg(xn	dg(xn	PROPN
ejpam-6062	158	10	,	,	PUNCT
ejpam-6062	158	11	x0	x0	PROPN
ejpam-6062	158	12	)	)	PUNCT
ejpam-6062	158	13	}	}	PUNCT
ejpam-6062	158	14	is	be	AUX
ejpam-6062	158	15	bounded	bound	VERB
ejpam-6062	158	16	,	,	PUNCT
ejpam-6062	158	17	then	then	ADV
ejpam-6062	158	18	the	the	DET
ejpam-6062	158	19	sequence	sequence	NOUN
ejpam-6062	158	20	{	{	PUNCT
ejpam-6062	158	21	xn	xn	NOUN
ejpam-6062	158	22	}	}	PUNCT
ejpam-6062	158	23	is	be	AUX
ejpam-6062	158	24	also	also	ADV
ejpam-6062	158	25	bounded	bound	VERB
ejpam-6062	158	26	.	.	PUNCT
ejpam-6062	159	1	definition	definition	NOUN
ejpam-6062	159	2	4	4	NUM
ejpam-6062	159	3	.	.	PUNCT
ejpam-6062	160	1	let	let	VERB
ejpam-6062	160	2	c	c	PRON
ejpam-6062	160	3	be	be	AUX
ejpam-6062	160	4	a	a	DET
ejpam-6062	160	5	nonempty	nonempty	ADV
ejpam-6062	160	6	closed	close	VERB
ejpam-6062	160	7	and	and	CCONJ
ejpam-6062	160	8	convex	convex	NOUN
ejpam-6062	160	9	subset	subset	NOUN
ejpam-6062	160	10	of	of	ADP
ejpam-6062	160	11	a	a	DET
ejpam-6062	160	12	reflexive	reflexive	ADJ
ejpam-6062	160	13	banach	banach	NOUN
ejpam-6062	160	14	space	space	NOUN
ejpam-6062	160	15	e	e	NOUN
ejpam-6062	160	16	and	and	CCONJ
ejpam-6062	160	17	g	g	NOUN
ejpam-6062	160	18	:	:	PUNCT
ejpam-6062	160	19	e	e	X
ejpam-6062	160	20	→	→	PUNCT
ejpam-6062	160	21	(	(	PUNCT
ejpam-6062	160	22	−∞,+∞	−∞,+∞	ADV
ejpam-6062	160	23	]	]	PUNCT
ejpam-6062	160	24	be	be	AUX
ejpam-6062	160	25	a	a	DET
ejpam-6062	160	26	strongly	strongly	ADV
ejpam-6062	160	27	coercive	coercive	ADJ
ejpam-6062	160	28	bregman	bregman	NOUN
ejpam-6062	160	29	function	function	NOUN
ejpam-6062	160	30	.	.	PUNCT
ejpam-6062	161	1	a	a	DET
ejpam-6062	161	2	bregman	bregman	NOUN
ejpam-6062	161	3	projection	projection	NOUN
ejpam-6062	161	4	of	of	ADP
ejpam-6062	161	5	x	x	PROPN
ejpam-6062	161	6	∈	∈	PROPN
ejpam-6062	161	7	int(domg	int(domg	NOUN
ejpam-6062	161	8	)	)	PUNCT
ejpam-6062	161	9	onto	onto	ADP
ejpam-6062	161	10	c	c	PROPN
ejpam-6062	161	11	⊂	⊂	PROPN
ejpam-6062	161	12	int(domg	int(domg	NOUN
ejpam-6062	161	13	)	)	PUNCT
ejpam-6062	161	14	is	be	AUX
ejpam-6062	161	15	the	the	DET
ejpam-6062	161	16	unique	unique	ADJ
ejpam-6062	161	17	vector	vector	NOUN
ejpam-6062	161	18	projgc(x	projgc(x	NOUN
ejpam-6062	161	19	)	)	PUNCT
ejpam-6062	161	20	∈	∈	PROPN
ejpam-6062	161	21	c	c	NOUN
ejpam-6062	161	22	satisfying	satisfy	VERB
ejpam-6062	161	23	dg(projgc(x	dg(projgc(x	PROPN
ejpam-6062	161	24	)	)	PUNCT
ejpam-6062	161	25	,	,	PUNCT
ejpam-6062	161	26	x	x	X
ejpam-6062	161	27	)	)	PUNCT
ejpam-6062	161	28	=	=	SYM
ejpam-6062	161	29	int{dg(y	int{dg(y	PROPN
ejpam-6062	161	30	,	,	PUNCT
ejpam-6062	161	31	x	x	X
ejpam-6062	161	32	)	)	PUNCT
ejpam-6062	161	33	:	:	PUNCT
ejpam-6062	161	34	y	y	PROPN
ejpam-6062	161	35	∈	∈	PROPN
ejpam-6062	161	36	c	c	X
ejpam-6062	161	37	}	}	PUNCT
ejpam-6062	161	38	.	.	PUNCT
ejpam-6062	162	1	lemma	lemma	PROPN
ejpam-6062	162	2	9	9	NUM
ejpam-6062	162	3	.	.	PUNCT
ejpam-6062	163	1	[	[	X
ejpam-6062	163	2	40	40	NUM
ejpam-6062	163	3	]	]	PUNCT
ejpam-6062	163	4	let	let	VERB
ejpam-6062	163	5	c	c	PRON
ejpam-6062	163	6	be	be	AUX
ejpam-6062	163	7	a	a	DET
ejpam-6062	163	8	nonempty	nonempty	ADV
ejpam-6062	163	9	closed	close	VERB
ejpam-6062	163	10	and	and	CCONJ
ejpam-6062	163	11	convex	convex	NOUN
ejpam-6062	163	12	subset	subset	NOUN
ejpam-6062	163	13	of	of	ADP
ejpam-6062	163	14	a	a	DET
ejpam-6062	163	15	reflexive	reflexive	ADJ
ejpam-6062	163	16	banach	banach	NOUN
ejpam-6062	163	17	space	space	NOUN
ejpam-6062	163	18	e	e	NOUN
ejpam-6062	163	19	and	and	CCONJ
ejpam-6062	163	20	x	x	PROPN
ejpam-6062	163	21	∈	∈	PROPN
ejpam-6062	163	22	e.	e.	PROPN
ejpam-6062	163	23	let	let	VERB
ejpam-6062	163	24	g	g	NOUN
ejpam-6062	163	25	:	:	PUNCT
ejpam-6062	163	26	e	e	X
ejpam-6062	163	27	→	→	SYM
ejpam-6062	163	28	r	r	NOUN
ejpam-6062	163	29	be	be	AUX
ejpam-6062	163	30	a	a	DET
ejpam-6062	163	31	strongly	strongly	ADV
ejpam-6062	163	32	coercive	coercive	ADJ
ejpam-6062	163	33	bregman	bregman	NOUN
ejpam-6062	163	34	function	function	NOUN
ejpam-6062	163	35	.	.	PUNCT
ejpam-6062	164	1	then	then	ADV
ejpam-6062	164	2	,	,	PUNCT
ejpam-6062	164	3	(	(	PUNCT
ejpam-6062	164	4	i	i	NOUN
ejpam-6062	164	5	)	)	PUNCT
ejpam-6062	164	6	z	z	NOUN
ejpam-6062	164	7	=	=	SYM
ejpam-6062	164	8	projgc(x	projgc(x	PROPN
ejpam-6062	164	9	)	)	PUNCT
ejpam-6062	165	1	if	if	SCONJ
ejpam-6062	165	2	and	and	CCONJ
ejpam-6062	165	3	only	only	ADV
ejpam-6062	165	4	if	if	SCONJ
ejpam-6062	165	5	⟨∇g	⟨∇g	PRON
ejpam-6062	165	6	e(x)−∇g	e(x)−∇g	VERB
ejpam-6062	165	7	e(z	e(z	PROPN
ejpam-6062	165	8	)	)	PUNCT
ejpam-6062	165	9	,	,	PUNCT
ejpam-6062	165	10	y	y	PROPN
ejpam-6062	165	11	−	−	PROPN
ejpam-6062	165	12	z⟩	z⟩	NOUN
ejpam-6062	165	13	≤	≤	NUM
ejpam-6062	165	14	0	0	NUM
ejpam-6062	165	15	,	,	PUNCT
ejpam-6062	165	16	∀	∀	PUNCT
ejpam-6062	165	17	y	y	PROPN
ejpam-6062	165	18	∈	∈	PROPN
ejpam-6062	165	19	c.	c.	PROPN
ejpam-6062	165	20	(	(	PUNCT
ejpam-6062	165	21	ii	ii	PROPN
ejpam-6062	165	22	)	)	PUNCT
ejpam-6062	165	23	dg(y	dg(y	PROPN
ejpam-6062	165	24	,	,	PUNCT
ejpam-6062	165	25	projgc(x	projgc(x	NOUN
ejpam-6062	165	26	)	)	PUNCT
ejpam-6062	165	27	)	)	PUNCT
ejpam-6062	166	1	+	+	PROPN
ejpam-6062	166	2	dg(projgc(x	dg(projgc(x	NOUN
ejpam-6062	166	3	)	)	PUNCT
ejpam-6062	166	4	,	,	PUNCT
ejpam-6062	166	5	x	x	X
ejpam-6062	166	6	)	)	PUNCT
ejpam-6062	166	7	≤	≤	NOUN
ejpam-6062	166	8	dg(y	dg(y	NOUN
ejpam-6062	166	9	,	,	PUNCT
ejpam-6062	166	10	x	x	NOUN
ejpam-6062	166	11	)	)	PUNCT
ejpam-6062	166	12	,	,	PUNCT
ejpam-6062	166	13	∀	∀	PUNCT
ejpam-6062	166	14	y	y	PROPN
ejpam-6062	166	15	∈	∈	PROPN
ejpam-6062	166	16	c.	c.	PROPN
ejpam-6062	166	17	lemma	lemma	PROPN
ejpam-6062	166	18	10	10	NUM
ejpam-6062	166	19	.	.	PUNCT
ejpam-6062	167	1	[	[	X
ejpam-6062	167	2	41	41	NUM
ejpam-6062	167	3	]	]	PUNCT
ejpam-6062	167	4	let	let	VERB
ejpam-6062	167	5	{	{	PUNCT
ejpam-6062	167	6	an	an	NOUN
ejpam-6062	167	7	}	}	PUNCT
ejpam-6062	167	8	and	and	CCONJ
ejpam-6062	167	9	{	{	PUNCT
ejpam-6062	167	10	dn	dn	AUX
ejpam-6062	167	11	}	}	PUNCT
ejpam-6062	167	12	be	be	VERB
ejpam-6062	167	13	sequences	sequence	NOUN
ejpam-6062	167	14	of	of	ADP
ejpam-6062	167	15	nonnegative	nonnegative	ADJ
ejpam-6062	167	16	real	real	ADJ
ejpam-6062	167	17	numbers	number	NOUN
ejpam-6062	167	18	such	such	ADJ
ejpam-6062	167	19	that	that	PRON
ejpam-6062	167	20	an+1	an+1	ADJ
ejpam-6062	167	21	≤	≤	X
ejpam-6062	167	22	(	(	PUNCT
ejpam-6062	167	23	1−	1−	NUM
ejpam-6062	167	24	δn)an	δn)an	PUNCT
ejpam-6062	167	25	+	+	PUNCT
ejpam-6062	167	26	bn	bn	PUNCT
ejpam-6062	167	27	+	+	NUM
ejpam-6062	167	28	dn	dn	PROPN
ejpam-6062	167	29	,	,	PUNCT
ejpam-6062	167	30	n	n	PRON
ejpam-6062	167	31	≥	≥	NOUN
ejpam-6062	167	32	1	1	NUM
ejpam-6062	167	33	,	,	PUNCT
ejpam-6062	167	34	where	where	SCONJ
ejpam-6062	167	35	{	{	PUNCT
ejpam-6062	167	36	δn	δn	NOUN
ejpam-6062	167	37	}	}	PUNCT
ejpam-6062	167	38	is	be	AUX
ejpam-6062	167	39	a	a	DET
ejpam-6062	167	40	sequence	sequence	NOUN
ejpam-6062	167	41	in	in	ADP
ejpam-6062	167	42	(	(	PUNCT
ejpam-6062	167	43	0	0	NUM
ejpam-6062	167	44	,	,	PUNCT
ejpam-6062	167	45	1	1	NUM
ejpam-6062	167	46	)	)	PUNCT
ejpam-6062	167	47	and	and	CCONJ
ejpam-6062	167	48	{	{	PUNCT
ejpam-6062	167	49	bn	bn	X
ejpam-6062	167	50	}	}	PUNCT
ejpam-6062	167	51	is	be	AUX
ejpam-6062	167	52	a	a	DET
ejpam-6062	167	53	real	real	ADJ
ejpam-6062	167	54	sequence	sequence	NOUN
ejpam-6062	167	55	.	.	PUNCT
ejpam-6062	168	1	assume	assume	VERB
ejpam-6062	168	2	that	that	SCONJ
ejpam-6062	168	3	∞∑	∞∑	NUM
ejpam-6062	168	4	n=1	n=1	PART
ejpam-6062	168	5	dn	dn	ADP
ejpam-6062	168	6	<	<	X
ejpam-6062	168	7	∞	∞	PROPN
ejpam-6062	168	8	,	,	PUNCT
ejpam-6062	168	9	∞∑	∞∑	NUM
ejpam-6062	168	10	n=1	n=1	ADJ
ejpam-6062	168	11	δn	δn	NOUN
ejpam-6062	168	12	=	=	SYM
ejpam-6062	168	13	∞	∞	PROPN
ejpam-6062	168	14	and	and	CCONJ
ejpam-6062	168	15	lim	lim	PROPN
ejpam-6062	168	16	sup	sup	VERB
ejpam-6062	168	17	n→∞	n→∞	NUM
ejpam-6062	168	18	bn	bn	NUM
ejpam-6062	168	19	δn	δn	ADJ
ejpam-6062	168	20	≤	≤	NUM
ejpam-6062	168	21	0	0	NUM
ejpam-6062	168	22	,	,	PUNCT
ejpam-6062	168	23	then	then	ADV
ejpam-6062	168	24	lim	lim	PROPN
ejpam-6062	168	25	n→∞	n→∞	NUM
ejpam-6062	168	26	an	an	DET
ejpam-6062	168	27	=	=	NOUN
ejpam-6062	168	28	0	0	X
ejpam-6062	168	29	.	.	PUNCT
ejpam-6062	169	1	lemma	lemma	PROPN
ejpam-6062	169	2	11	11	NUM
ejpam-6062	169	3	.	.	PUNCT
ejpam-6062	170	1	[	[	X
ejpam-6062	170	2	42	42	NUM
ejpam-6062	170	3	]	]	PUNCT
ejpam-6062	170	4	let	let	AUX
ejpam-6062	170	5	{	{	PUNCT
ejpam-6062	170	6	γn	γn	PART
ejpam-6062	170	7	}	}	PUNCT
ejpam-6062	170	8	be	be	AUX
ejpam-6062	170	9	a	a	DET
ejpam-6062	170	10	sequence	sequence	NOUN
ejpam-6062	170	11	of	of	ADP
ejpam-6062	170	12	real	real	ADJ
ejpam-6062	170	13	numbers	number	NOUN
ejpam-6062	170	14	that	that	PRON
ejpam-6062	170	15	does	do	AUX
ejpam-6062	170	16	not	not	PART
ejpam-6062	170	17	decrease	decrease	VERB
ejpam-6062	170	18	at	at	ADP
ejpam-6062	170	19	infinity	infinity	NOUN
ejpam-6062	170	20	in	in	ADP
ejpam-6062	170	21	the	the	DET
ejpam-6062	170	22	sense	sense	NOUN
ejpam-6062	170	23	that	that	SCONJ
ejpam-6062	170	24	there	there	PRON
ejpam-6062	170	25	exists	exist	VERB
ejpam-6062	170	26	a	a	DET
ejpam-6062	170	27	subsequence	subsequence	NOUN
ejpam-6062	170	28	{	{	PUNCT
ejpam-6062	170	29	γnj	γnj	PROPN
ejpam-6062	170	30	}	}	PUNCT
ejpam-6062	170	31	of	of	ADP
ejpam-6062	170	32	{	{	PUNCT
ejpam-6062	170	33	γn	γn	NOUN
ejpam-6062	170	34	}	}	PUNCT
ejpam-6062	170	35	which	which	PRON
ejpam-6062	170	36	satisfies	satisfy	VERB
ejpam-6062	170	37	γnj	γnj	PROPN
ejpam-6062	170	38	<	<	X
ejpam-6062	170	39	γnj+1	γnj+1	X
ejpam-6062	170	40	for	for	ADP
ejpam-6062	170	41	all	all	DET
ejpam-6062	170	42	j	j	PROPN
ejpam-6062	170	43	∈	∈	PROPN
ejpam-6062	170	44	n.	n.	NOUN
ejpam-6062	170	45	define	define	VERB
ejpam-6062	170	46	the	the	DET
ejpam-6062	170	47	sequence	sequence	NOUN
ejpam-6062	170	48	{	{	PUNCT
ejpam-6062	170	49	τ(n)}n≥n0	τ(n)}n≥n0	ADP
ejpam-6062	170	50	of	of	ADP
ejpam-6062	170	51	integers	integer	NOUN
ejpam-6062	170	52	as	as	SCONJ
ejpam-6062	170	53	follows	follow	VERB
ejpam-6062	170	54	:	:	PUNCT
ejpam-6062	170	55	τ(n	τ(n	NOUN
ejpam-6062	170	56	)	)	PUNCT
ejpam-6062	170	57	:	:	PUNCT
ejpam-6062	170	58	=	=	SYM
ejpam-6062	170	59	max{k	max{k	PROPN
ejpam-6062	170	60	≤	≤	PUNCT
ejpam-6062	170	61	n	n	CCONJ
ejpam-6062	170	62	:	:	PUNCT
ejpam-6062	170	63	γk	γk	X
ejpam-6062	170	64	<	<	X
ejpam-6062	170	65	γk+1	γk+1	X
ejpam-6062	170	66	}	}	PUNCT
ejpam-6062	170	67	,	,	PUNCT
ejpam-6062	170	68	where	where	SCONJ
ejpam-6062	170	69	n0	n0	X
ejpam-6062	170	70	∈	∈	PROPN
ejpam-6062	170	71	n	n	PRON
ejpam-6062	170	72	such	such	ADJ
ejpam-6062	170	73	that	that	SCONJ
ejpam-6062	170	74	{	{	PUNCT
ejpam-6062	170	75	k	k	PROPN
ejpam-6062	170	76	≤	≤	PROPN
ejpam-6062	170	77	n0	n0	NUM
ejpam-6062	170	78	:	:	PUNCT
ejpam-6062	170	79	γk	γk	PROPN
ejpam-6062	170	80	<	<	X
ejpam-6062	170	81	γk+1	γk+1	NOUN
ejpam-6062	170	82	}	}	PUNCT
ejpam-6062	170	83	=	=	NOUN
ejpam-6062	170	84	̸	̸	X
ejpam-6062	170	85	∅.	∅.	ADV
ejpam-6062	170	86	then	then	ADV
ejpam-6062	170	87	,	,	PUNCT
ejpam-6062	170	88	the	the	DET
ejpam-6062	170	89	following	follow	VERB
ejpam-6062	170	90	hold	hold	NOUN
ejpam-6062	170	91	:	:	PUNCT
ejpam-6062	170	92	(	(	PUNCT
ejpam-6062	170	93	i	i	NOUN
ejpam-6062	170	94	)	)	PUNCT
ejpam-6062	170	95	τ(n0	τ(n0	NOUN
ejpam-6062	170	96	)	)	PUNCT
ejpam-6062	170	97	≤	≤	NOUN
ejpam-6062	170	98	τ(n0	τ(n0	VERB
ejpam-6062	170	99	+	+	CCONJ
ejpam-6062	170	100	1	1	X
ejpam-6062	170	101	)	)	PUNCT
ejpam-6062	170	102	≤	≤	NOUN
ejpam-6062	170	103	·	·	PUNCT
ejpam-6062	170	104	·	·	PUNCT
ejpam-6062	170	105	·	·	PUNCT
ejpam-6062	170	106	and	and	CCONJ
ejpam-6062	170	107	τ(n	τ(n	PROPN
ejpam-6062	170	108	)	)	PUNCT
ejpam-6062	170	109	→	→	SYM
ejpam-6062	170	110	∞	∞	PROPN
ejpam-6062	170	111	,	,	PUNCT
ejpam-6062	170	112	(	(	PUNCT
ejpam-6062	170	113	ii	ii	NOUN
ejpam-6062	170	114	)	)	PUNCT
ejpam-6062	170	115	γτ(n	γτ(n	NOUN
ejpam-6062	170	116	)	)	PUNCT
ejpam-6062	170	117	≤	≤	NOUN
ejpam-6062	170	118	γτ(n)+1	γτ(n)+1	NOUN
ejpam-6062	170	119	and	and	CCONJ
ejpam-6062	170	120	γτ(n	γτ(n	NOUN
ejpam-6062	170	121	)	)	PUNCT
ejpam-6062	170	122	≤	≤	NOUN
ejpam-6062	170	123	γτ(n)+1	γτ(n)+1	NOUN
ejpam-6062	170	124	,	,	PUNCT
ejpam-6062	170	125	∀	∀	X
ejpam-6062	170	126	n	n	PRON
ejpam-6062	170	127	≥	≥	NOUN
ejpam-6062	170	128	n0	n0	NUM
ejpam-6062	170	129	.	.	PUNCT
ejpam-6062	171	1	h.	h.	PROPN
ejpam-6062	171	2	a.	a.	PROPN
ejpam-6062	171	3	abass	abass	PROPN
ejpam-6062	171	4	et	et	PROPN
ejpam-6062	171	5	al	al	PROPN
ejpam-6062	171	6	.	.	PUNCT
ejpam-6062	171	7	/	/	SYM
ejpam-6062	171	8	eur	eur	PROPN
ejpam-6062	171	9	.	.	PUNCT
ejpam-6062	172	1	j.	j.	PROPN
ejpam-6062	172	2	pure	pure	PROPN
ejpam-6062	172	3	appl	appl	PROPN
ejpam-6062	172	4	.	.	PROPN
ejpam-6062	172	5	math	math	PROPN
ejpam-6062	172	6	,	,	PUNCT
ejpam-6062	172	7	18	18	NUM
ejpam-6062	172	8	(	(	PUNCT
ejpam-6062	172	9	2	2	NUM
ejpam-6062	172	10	)	)	PUNCT
ejpam-6062	172	11	(	(	PUNCT
ejpam-6062	172	12	2025	2025	NUM
ejpam-6062	172	13	)	)	PUNCT
ejpam-6062	172	14	,	,	PUNCT
ejpam-6062	172	15	6062	6062	NUM
ejpam-6062	172	16	10	10	NUM
ejpam-6062	172	17	of	of	ADP
ejpam-6062	172	18	22	22	NUM
ejpam-6062	172	19	3	3	NUM
ejpam-6062	172	20	.	.	PUNCT
ejpam-6062	172	21	main	main	ADJ
ejpam-6062	172	22	result	result	NOUN
ejpam-6062	172	23	throughout	throughout	ADP
ejpam-6062	172	24	this	this	DET
ejpam-6062	172	25	section	section	NOUN
ejpam-6062	173	1	,	,	PUNCT
ejpam-6062	173	2	we	we	PRON
ejpam-6062	173	3	assume	assume	VERB
ejpam-6062	173	4	that	that	SCONJ
ejpam-6062	173	5	assumption	assumption	NOUN
ejpam-6062	173	6	1	1	X
ejpam-6062	173	7	.	.	PUNCT
ejpam-6062	174	1	(	(	PUNCT
ejpam-6062	174	2	i	i	NOUN
ejpam-6062	174	3	)	)	PUNCT
ejpam-6062	174	4	let	let	VERB
ejpam-6062	174	5	ei	ei	INTJ
ejpam-6062	174	6	for	for	ADP
ejpam-6062	174	7	i	i	PROPN
ejpam-6062	174	8	=	=	SYM
ejpam-6062	174	9	0	0	NUM
ejpam-6062	174	10	,	,	PUNCT
ejpam-6062	174	11	1	1	NUM
ejpam-6062	174	12	,	,	PUNCT
ejpam-6062	174	13	2	2	NUM
ejpam-6062	174	14	,	,	PUNCT
ejpam-6062	174	15	·	·	PUNCT
ejpam-6062	174	16	·	·	PUNCT
ejpam-6062	174	17	·	·	PUNCT
ejpam-6062	174	18	,	,	PUNCT
ejpam-6062	174	19	n	n	PRON
ejpam-6062	174	20	be	be	AUX
ejpam-6062	174	21	reflexive	reflexive	ADJ
ejpam-6062	174	22	banach	banach	NOUN
ejpam-6062	174	23	spaces	space	NOUN
ejpam-6062	175	1	where	where	SCONJ
ejpam-6062	175	2	e0	e0	PROPN
ejpam-6062	175	3	=	=	SYM
ejpam-6062	175	4	e	e	PROPN
ejpam-6062	175	5	,	,	PUNCT
ejpam-6062	175	6	g	g	NOUN
ejpam-6062	175	7	:	:	PUNCT
ejpam-6062	175	8	e	e	X
ejpam-6062	175	9	→	→	PUNCT
ejpam-6062	175	10	(	(	PUNCT
ejpam-6062	175	11	−∞,+∞	−∞,+∞	ADV
ejpam-6062	175	12	]	]	PUNCT
ejpam-6062	175	13	and	and	CCONJ
ejpam-6062	175	14	gi	gi	INTJ
ejpam-6062	175	15	:	:	PUNCT
ejpam-6062	175	16	ei	ei	X
ejpam-6062	175	17	→	→	PUNCT
ejpam-6062	175	18	(	(	PUNCT
ejpam-6062	175	19	−∞,+∞	−∞,+∞	ADV
ejpam-6062	175	20	]	]	PUNCT
ejpam-6062	175	21	be	be	AUX
ejpam-6062	175	22	strongly	strongly	ADV
ejpam-6062	175	23	coercive	coercive	ADJ
ejpam-6062	175	24	legendre	legendre	PROPN
ejpam-6062	175	25	functions	function	NOUN
ejpam-6062	175	26	which	which	PRON
ejpam-6062	175	27	are	be	AUX
ejpam-6062	175	28	bounded	bound	VERB
ejpam-6062	175	29	,	,	PUNCT
ejpam-6062	175	30	uniformly	uniformly	ADV
ejpam-6062	175	31	fréchet	fréchet	VERB
ejpam-6062	175	32	differentiable	differentiable	ADJ
ejpam-6062	175	33	and	and	CCONJ
ejpam-6062	175	34	totally	totally	ADV
ejpam-6062	175	35	convex	convex	VERB
ejpam-6062	175	36	on	on	ADP
ejpam-6062	175	37	bounded	bounded	ADJ
ejpam-6062	175	38	subsets	subset	NOUN
ejpam-6062	175	39	of	of	ADP
ejpam-6062	175	40	e	e	PROPN
ejpam-6062	175	41	and	and	CCONJ
ejpam-6062	175	42	ei	ei	NOUN
ejpam-6062	175	43	,	,	PUNCT
ejpam-6062	175	44	i	i	PRON
ejpam-6062	175	45	=	=	NOUN
ejpam-6062	175	46	1	1	NUM
ejpam-6062	175	47	,	,	PUNCT
ejpam-6062	175	48	2	2	NUM
ejpam-6062	175	49	,	,	PUNCT
ejpam-6062	175	50	·	·	PUNCT
ejpam-6062	175	51	·	·	PUNCT
ejpam-6062	175	52	·	·	PUNCT
ejpam-6062	175	53	,	,	PUNCT
ejpam-6062	175	54	n	n	CCONJ
ejpam-6062	175	55	,	,	PUNCT
ejpam-6062	175	56	respectively	respectively	ADV
ejpam-6062	175	57	.	.	PUNCT
ejpam-6062	176	1	let	let	VERB
ejpam-6062	176	2	∇g	∇g	ADJ
ejpam-6062	176	3	e	e	NOUN
ejpam-6062	176	4	and	and	CCONJ
ejpam-6062	176	5	∇gi	∇gi	ADJ
ejpam-6062	176	6	ei	ei	AUX
ejpam-6062	176	7	be	be	AUX
ejpam-6062	176	8	the	the	DET
ejpam-6062	176	9	gradients	gradient	NOUN
ejpam-6062	176	10	of	of	ADP
ejpam-6062	176	11	e	e	NOUN
ejpam-6062	176	12	dependent	dependent	ADJ
ejpam-6062	176	13	on	on	ADP
ejpam-6062	176	14	g	g	PROPN
ejpam-6062	176	15	and	and	CCONJ
ejpam-6062	176	16	ei	ei	X
ejpam-6062	176	17	dependent	dependent	ADJ
ejpam-6062	176	18	on	on	ADP
ejpam-6062	176	19	gi	gi	NOUN
ejpam-6062	176	20	respectively	respectively	ADV
ejpam-6062	176	21	.	.	PUNCT
ejpam-6062	177	1	(	(	PUNCT
ejpam-6062	177	2	ii	ii	NOUN
ejpam-6062	177	3	)	)	PUNCT
ejpam-6062	177	4	let	let	VERB
ejpam-6062	177	5	fj	fj	X
ejpam-6062	177	6	:	:	PUNCT
ejpam-6062	177	7	e	e	PROPN
ejpam-6062	177	8	→	→	SYM
ejpam-6062	177	9	e∗	e∗	PROPN
ejpam-6062	177	10	,	,	PUNCT
ejpam-6062	177	11	j	j	PROPN
ejpam-6062	177	12	=	=	SYM
ejpam-6062	177	13	1	1	NUM
ejpam-6062	177	14	,	,	PUNCT
ejpam-6062	177	15	2	2	NUM
ejpam-6062	177	16	,	,	PUNCT
ejpam-6062	177	17	·	·	PUNCT
ejpam-6062	177	18	·	·	PUNCT
ejpam-6062	177	19	·	·	PUNCT
ejpam-6062	177	20	,	,	PUNCT
ejpam-6062	177	21	m	m	VERB
ejpam-6062	177	22	be	be	VERB
ejpam-6062	177	23	bism	bism	NOUN
ejpam-6062	177	24	mappings	mapping	NOUN
ejpam-6062	177	25	and	and	CCONJ
ejpam-6062	177	26	gj	gj	NOUN
ejpam-6062	177	27	:	:	PUNCT
ejpam-6062	177	28	e	e	PROPN
ejpam-6062	177	29	→	→	SYM
ejpam-6062	177	30	e∗	e∗	PROPN
ejpam-6062	177	31	,	,	PUNCT
ejpam-6062	177	32	j	j	PROPN
ejpam-6062	177	33	=	=	SYM
ejpam-6062	177	34	1	1	NUM
ejpam-6062	177	35	,	,	PUNCT
ejpam-6062	177	36	2	2	NUM
ejpam-6062	177	37	,	,	PUNCT
ejpam-6062	177	38	·	·	PUNCT
ejpam-6062	177	39	·	·	PUNCT
ejpam-6062	177	40	·	·	PUNCT
ejpam-6062	177	41	,	,	PUNCT
ejpam-6062	177	42	m	m	VERB
ejpam-6062	177	43	be	be	VERB
ejpam-6062	177	44	maximal	maximal	ADJ
ejpam-6062	177	45	monotone	monotone	ADJ
ejpam-6062	177	46	mappings	mapping	NOUN
ejpam-6062	177	47	respectively	respectively	ADV
ejpam-6062	177	48	.	.	PUNCT
ejpam-6062	178	1	suppose	suppose	VERB
ejpam-6062	178	2	ai	ai	INTJ
ejpam-6062	178	3	:	:	PUNCT
ejpam-6062	178	4	e	e	X
ejpam-6062	178	5	→	→	SYM
ejpam-6062	178	6	ei	ei	PROPN
ejpam-6062	178	7	,	,	PUNCT
ejpam-6062	178	8	i	i	PRON
ejpam-6062	178	9	=	=	NOUN
ejpam-6062	178	10	1	1	NUM
ejpam-6062	178	11	,	,	PUNCT
ejpam-6062	178	12	2	2	NUM
ejpam-6062	178	13	,	,	PUNCT
ejpam-6062	178	14	·	·	PUNCT
ejpam-6062	178	15	·	·	PUNCT
ejpam-6062	178	16	·	·	PUNCT
ejpam-6062	178	17	,	,	PUNCT
ejpam-6062	178	18	n	n	CCONJ
ejpam-6062	178	19	be	be	AUX
ejpam-6062	178	20	bounded	bound	VERB
ejpam-6062	178	21	linear	linear	ADJ
ejpam-6062	178	22	operator	operator	NOUN
ejpam-6062	178	23	such	such	ADJ
ejpam-6062	178	24	that	that	SCONJ
ejpam-6062	178	25	ai	ai	VERB
ejpam-6062	178	26	̸=	̸=	PROPN
ejpam-6062	178	27	0	0	NUM
ejpam-6062	178	28	and	and	CCONJ
ejpam-6062	178	29	a∗	a∗	PROPN
ejpam-6062	178	30	i	i	PRON
ejpam-6062	178	31	be	be	VERB
ejpam-6062	178	32	the	the	DET
ejpam-6062	178	33	adjoint	adjoint	NOUN
ejpam-6062	178	34	of	of	ADP
ejpam-6062	178	35	ai	ai	PROPN
ejpam-6062	178	36	.	.	PUNCT
ejpam-6062	179	1	(	(	PUNCT
ejpam-6062	179	2	iii	iii	X
ejpam-6062	179	3	)	)	PUNCT
ejpam-6062	179	4	si	si	NOUN
ejpam-6062	179	5	:	:	PUNCT
ejpam-6062	179	6	ei	ei	X
ejpam-6062	179	7	→	→	SYM
ejpam-6062	179	8	ei	ei	PROPN
ejpam-6062	179	9	,	,	PUNCT
ejpam-6062	179	10	i	i	PRON
ejpam-6062	179	11	=	=	NOUN
ejpam-6062	179	12	0	0	NUM
ejpam-6062	179	13	,	,	PUNCT
ejpam-6062	179	14	1	1	NUM
ejpam-6062	179	15	,	,	PUNCT
ejpam-6062	179	16	2	2	NUM
ejpam-6062	179	17	,	,	PUNCT
ejpam-6062	179	18	·	·	PUNCT
ejpam-6062	179	19	·	·	PUNCT
ejpam-6062	179	20	·	·	PUNCT
ejpam-6062	179	21	,	,	PUNCT
ejpam-6062	179	22	n	n	CCONJ
ejpam-6062	179	23	be	be	AUX
ejpam-6062	179	24	bregman	bregman	NOUN
ejpam-6062	179	25	(	(	PUNCT
ejpam-6062	179	26	ρs	ρs	INTJ
ejpam-6062	179	27	,	,	PUNCT
ejpam-6062	179	28	µs)−	µs)−	PROPN
ejpam-6062	179	29	demigeneralized	demigeneralize	VERB
ejpam-6062	179	30	mapping	mapping	NOUN
ejpam-6062	179	31	such	such	ADJ
ejpam-6062	179	32	that	that	DET
ejpam-6062	179	33	ρs	ρs	NOUN
ejpam-6062	179	34	∈	∈	PROPN
ejpam-6062	179	35	(	(	PUNCT
ejpam-6062	179	36	−∞	−∞	NOUN
ejpam-6062	179	37	,	,	PUNCT
ejpam-6062	179	38	1	1	NUM
ejpam-6062	179	39	)	)	PUNCT
ejpam-6062	179	40	and	and	CCONJ
ejpam-6062	179	41	µs	µs	ADP
ejpam-6062	179	42	∈	∈	PROPN
ejpam-6062	179	43	[	[	X
ejpam-6062	179	44	0,∞	0,∞	NOUN
ejpam-6062	179	45	)	)	PUNCT
ejpam-6062	179	46	.	.	PUNCT
ejpam-6062	180	1	assume	assume	VERB
ejpam-6062	180	2	that	that	SCONJ
ejpam-6062	180	3	ω	ω	X
ejpam-6062	180	4	:	:	PUNCT
ejpam-6062	180	5	=	=	X
ejpam-6062	180	6	{	{	PUNCT
ejpam-6062	180	7	x∗	x∗	PROPN
ejpam-6062	180	8	∈	∈	PROPN
ejpam-6062	180	9	m⋂	m⋂	NOUN
ejpam-6062	180	10	j=1	j=1	PROPN
ejpam-6062	180	11	fix(t	fix(t	PROPN
ejpam-6062	180	12	j	j	PROPN
ejpam-6062	180	13	σ)∩fix(s	σ)∩fix(s	PROPN
ejpam-6062	180	14	)	)	PUNCT
ejpam-6062	180	15	:	:	PUNCT
ejpam-6062	180	16	aix	aix	NOUN
ejpam-6062	180	17	∗	∗	NOUN
ejpam-6062	180	18	∈	∈	PROPN
ejpam-6062	180	19	n⋂	n⋂	NOUN
ejpam-6062	180	20	i=1	i=1	PROPN
ejpam-6062	180	21	fix(si	fix(si	PROPN
ejpam-6062	180	22	)	)	PUNCT
ejpam-6062	180	23	}	}	PUNCT
ejpam-6062	181	1	=	=	NOUN
ejpam-6062	181	2	̸	̸	ADJ
ejpam-6062	181	3	∅	∅	NOUN
ejpam-6062	181	4	,	,	PUNCT
ejpam-6062	181	5	(	(	PUNCT
ejpam-6062	181	6	iv	iv	X
ejpam-6062	181	7	)	)	PUNCT
ejpam-6062	181	8	let	let	VERB
ejpam-6062	181	9	γ	γ	X
ejpam-6062	181	10	>	>	X
ejpam-6062	181	11	0	0	NUM
ejpam-6062	181	12	be	be	AUX
ejpam-6062	181	13	a	a	DET
ejpam-6062	181	14	real	real	ADJ
ejpam-6062	181	15	number	number	NOUN
ejpam-6062	181	16	and	and	CCONJ
ejpam-6062	181	17	{	{	PUNCT
ejpam-6062	181	18	αn}n∈n	αn}n∈n	NOUN
ejpam-6062	181	19	,	,	PUNCT
ejpam-6062	181	20	{	{	PUNCT
ejpam-6062	181	21	βj}mj=0	βj}mj=0	VERB
ejpam-6062	181	22	and	and	CCONJ
ejpam-6062	181	23	{	{	PUNCT
ejpam-6062	181	24	λi	λi	PROPN
ejpam-6062	181	25	,	,	PUNCT
ejpam-6062	181	26	n}n∈n	n}n∈n	X
ejpam-6062	181	27	be	be	VERB
ejpam-6062	181	28	sequences	sequence	NOUN
ejpam-6062	181	29	in	in	ADP
ejpam-6062	181	30	(	(	PUNCT
ejpam-6062	181	31	0,1	0,1	NUM
ejpam-6062	181	32	)	)	PUNCT
ejpam-6062	181	33	with	with	ADP
ejpam-6062	181	34	m∑	m∑	PUNCT
ejpam-6062	181	35	j=0	j=0	PROPN
ejpam-6062	181	36	βj	βj	SYM
ejpam-6062	181	37	=	=	SYM
ejpam-6062	181	38	1	1	NUM
ejpam-6062	181	39	and	and	CCONJ
ejpam-6062	181	40	n∑	n∑	PROPN
ejpam-6062	181	41	i=0	i=0	PROPN
ejpam-6062	182	1	λi	λi	SYM
ejpam-6062	182	2	,	,	PUNCT
ejpam-6062	182	3	n	n	NOUN
ejpam-6062	182	4	=	=	SYM
ejpam-6062	182	5	1	1	NUM
ejpam-6062	182	6	respectively	respectively	ADV
ejpam-6062	182	7	,	,	PUNCT
ejpam-6062	182	8	satisfying	satisfy	VERB
ejpam-6062	182	9	the	the	DET
ejpam-6062	182	10	following	follow	VERB
ejpam-6062	182	11	control	control	NOUN
ejpam-6062	182	12	condition	condition	NOUN
ejpam-6062	182	13	:	:	PUNCT
ejpam-6062	182	14	(	(	PUNCT
ejpam-6062	182	15	i	i	NOUN
ejpam-6062	182	16	)	)	PUNCT
ejpam-6062	182	17	lim	lim	PROPN
ejpam-6062	182	18	n→∞	n→∞	NUM
ejpam-6062	182	19	αn	αn	NOUN
ejpam-6062	182	20	=	=	SYM
ejpam-6062	182	21	0	0	NUM
ejpam-6062	182	22	,	,	PUNCT
ejpam-6062	182	23	∞∑	∞∑	NUM
ejpam-6062	182	24	n=1	n=1	NOUN
ejpam-6062	182	25	αn	αn	NOUN
ejpam-6062	182	26	=	=	SYM
ejpam-6062	182	27	∞.	∞.	PROPN
ejpam-6062	182	28	let	let	VERB
ejpam-6062	182	29	t	t	PROPN
ejpam-6062	182	30	j	j	PROPN
ejpam-6062	182	31	σ	σ	X
ejpam-6062	182	32	:	:	PUNCT
ejpam-6062	182	33	=	=	SYM
ejpam-6062	182	34	resgσgj	resgσgj	NOUN
ejpam-6062	183	1	◦	◦	NOUN
ejpam-6062	183	2	f	f	PROPN
ejpam-6062	183	3	g	g	PROPN
ejpam-6062	183	4	j	j	PROPN
ejpam-6062	183	5	for	for	ADP
ejpam-6062	183	6	j	j	PROPN
ejpam-6062	183	7	=	=	SYM
ejpam-6062	183	8	1	1	NUM
ejpam-6062	183	9	,	,	PUNCT
ejpam-6062	183	10	2	2	NUM
ejpam-6062	183	11	,	,	PUNCT
ejpam-6062	183	12	·	·	PUNCT
ejpam-6062	183	13	·	·	PUNCT
ejpam-6062	183	14	·	·	PUNCT
ejpam-6062	183	15	,	,	PUNCT
ejpam-6062	183	16	m	m	PROPN
ejpam-6062	183	17	,	,	PUNCT
ejpam-6062	183	18	clearly	clearly	ADV
ejpam-6062	183	19	fix(t	fix(t	PROPN
ejpam-6062	183	20	j	j	PROPN
ejpam-6062	183	21	σ	σ	PROPN
ejpam-6062	183	22	)	)	PUNCT
ejpam-6062	183	23	=	=	PUNCT
ejpam-6062	184	1	(	(	PUNCT
ejpam-6062	184	2	fj	fj	PROPN
ejpam-6062	184	3	+	+	CCONJ
ejpam-6062	184	4	gj	gj	NOUN
ejpam-6062	184	5	)	)	PUNCT
ejpam-6062	184	6	−1(0	−1(0	NOUN
ejpam-6062	184	7	)	)	PUNCT
ejpam-6062	184	8	for	for	ADP
ejpam-6062	184	9	each	each	PRON
ejpam-6062	184	10	j	j	PROPN
ejpam-6062	184	11	=	=	SYM
ejpam-6062	184	12	1	1	NUM
ejpam-6062	184	13	,	,	PUNCT
ejpam-6062	184	14	2	2	NUM
ejpam-6062	184	15	,	,	PUNCT
ejpam-6062	184	16	·	·	PUNCT
ejpam-6062	184	17	·	·	PUNCT
ejpam-6062	184	18	·	·	PUNCT
ejpam-6062	184	19	,	,	PUNCT
ejpam-6062	184	20	m	m	PROPN
ejpam-6062	184	21	and	and	CCONJ
ejpam-6062	184	22	σ	σ	NOUN
ejpam-6062	184	23	>	>	X
ejpam-6062	184	24	0	0	X
ejpam-6062	184	25	.	.	PUNCT
ejpam-6062	185	1	define	define	VERB
ejpam-6062	185	2	the	the	DET
ejpam-6062	185	3	sequence	sequence	NOUN
ejpam-6062	185	4	{	{	PUNCT
ejpam-6062	185	5	xn	xn	PUNCT
ejpam-6062	185	6	}	}	PUNCT
ejpam-6062	185	7	by	by	ADP
ejpam-6062	185	8	the	the	DET
ejpam-6062	185	9	following	follow	VERB
ejpam-6062	185	10	recursive	recursive	ADJ
ejpam-6062	185	11	formula	formula	NOUN
ejpam-6062	185	12	:	:	PUNCT
ejpam-6062	185	13	algorithm	algorithm	NOUN
ejpam-6062	185	14	1	1	NUM
ejpam-6062	185	15	.	.	PUNCT
ejpam-6062	186	1	for	for	ADP
ejpam-6062	186	2	fixed	fix	VERB
ejpam-6062	186	3	u	u	PROPN
ejpam-6062	186	4	∈	∈	PROPN
ejpam-6062	186	5	e	e	NOUN
ejpam-6062	186	6	,	,	PUNCT
ejpam-6062	186	7	let	let	VERB
ejpam-6062	186	8	{	{	PUNCT
ejpam-6062	186	9	xn}∞n=1	xn}∞n=1	PART
ejpam-6062	186	10	be	be	AUX
ejpam-6062	186	11	a	a	DET
ejpam-6062	186	12	sequence	sequence	NOUN
ejpam-6062	186	13	generated	generate	VERB
ejpam-6062	186	14	by	by	ADP
ejpam-6062	186	15	x1	x1	PROPN
ejpam-6062	186	16	∈	∈	PROPN
ejpam-6062	186	17	e	e	NOUN
ejpam-6062	186	18	such	such	ADJ
ejpam-6062	186	19	that	that	PROPN
ejpam-6062	186	20	zn	zn	NOUN
ejpam-6062	186	21	=	=	SYM
ejpam-6062	186	22	(	(	PUNCT
ejpam-6062	186	23	∇g	∇g	PROPN
ejpam-6062	186	24	e	e	NOUN
ejpam-6062	186	25	)	)	PUNCT
ejpam-6062	186	26	−1	−1	NOUN
ejpam-6062	186	27	[	[	PUNCT
ejpam-6062	186	28	n∑	n∑	PROPN
ejpam-6062	186	29	i=0	i=0	PROPN
ejpam-6062	186	30	λi	λi	SYM
ejpam-6062	186	31	,	,	PUNCT
ejpam-6062	186	32	n	n	CCONJ
ejpam-6062	186	33	(	(	PUNCT
ejpam-6062	186	34	∇g	∇g	ADJ
ejpam-6062	186	35	e(xn)−	e(xn)−	NOUN
ejpam-6062	186	36	γa∗	γa∗	NOUN
ejpam-6062	187	1	i	i	PRON
ejpam-6062	187	2	(	(	PUNCT
ejpam-6062	187	3	∇	∇	X
ejpam-6062	187	4	gi	gi	INTJ
ejpam-6062	187	5	ei	ei	X
ejpam-6062	187	6	(	(	PUNCT
ejpam-6062	187	7	aixn)−∇gi	aixn)−∇gi	ADJ
ejpam-6062	187	8	ei	ei	X
ejpam-6062	187	9	(	(	PUNCT
ejpam-6062	187	10	siaixn	siaixn	NOUN
ejpam-6062	187	11	)	)	PUNCT
ejpam-6062	187	12	)	)	PUNCT
ejpam-6062	187	13	)	)	PUNCT
ejpam-6062	187	14	]	]	PUNCT
ejpam-6062	187	15	yn	yn	X
ejpam-6062	187	16	=	=	PUNCT
ejpam-6062	187	17	(	(	PUNCT
ejpam-6062	187	18	∇g	∇g	PROPN
ejpam-6062	187	19	e	e	NOUN
ejpam-6062	187	20	)	)	PUNCT
ejpam-6062	187	21	−1	−1	NOUN
ejpam-6062	187	22	[	[	PUNCT
ejpam-6062	187	23	(	(	PUNCT
ejpam-6062	187	24	β0∇g	β0∇g	X
ejpam-6062	187	25	e(zn	e(zn	PROPN
ejpam-6062	187	26	)	)	PUNCT
ejpam-6062	187	27	+	+	CCONJ
ejpam-6062	187	28	m∑	m∑	SCONJ
ejpam-6062	187	29	j=1	j=1	PROPN
ejpam-6062	187	30	βj∇g	βj∇g	PROPN
ejpam-6062	187	31	e(t	e(t	PROPN
ejpam-6062	187	32	j	j	PROPN
ejpam-6062	187	33	σzn	σzn	PROPN
ejpam-6062	187	34	)	)	PUNCT
ejpam-6062	187	35	]	]	PUNCT
ejpam-6062	187	36	xn+1	xn+1	PUNCT
ejpam-6062	187	37	=	=	SYM
ejpam-6062	187	38	(	(	PUNCT
ejpam-6062	187	39	∇g	∇g	PROPN
ejpam-6062	187	40	e	e	NOUN
ejpam-6062	187	41	)	)	PUNCT
ejpam-6062	187	42	−1	−1	NOUN
ejpam-6062	187	43	[	[	PUNCT
ejpam-6062	187	44	αn∇g	αn∇g	NOUN
ejpam-6062	187	45	e(u	e(u	PROPN
ejpam-6062	187	46	)	)	PUNCT
ejpam-6062	188	1	+	+	CCONJ
ejpam-6062	188	2	(	(	PUNCT
ejpam-6062	188	3	1−	1−	NUM
ejpam-6062	188	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	188	5	e(yn	e(yn	NOUN
ejpam-6062	188	6	)	)	PUNCT
ejpam-6062	188	7	]	]	PUNCT
ejpam-6062	188	8	.	.	PUNCT
ejpam-6062	189	1	(	(	PUNCT
ejpam-6062	189	2	16	16	X
ejpam-6062	189	3	)	)	PUNCT
ejpam-6062	189	4	suppose	suppose	VERB
ejpam-6062	189	5	{	{	PUNCT
ejpam-6062	189	6	ξ1,n}n∈n	ξ1,n}n∈n	NUM
ejpam-6062	189	7	and	and	CCONJ
ejpam-6062	189	8	{	{	PUNCT
ejpam-6062	189	9	ξ2,n}n∈n	ξ2,n}n∈n	NOUN
ejpam-6062	189	10	are	be	AUX
ejpam-6062	189	11	two	two	NUM
ejpam-6062	189	12	sequences	sequence	NOUN
ejpam-6062	189	13	,	,	PUNCT
ejpam-6062	189	14	where	where	SCONJ
ejpam-6062	189	15	ξ1,n	ξ1,n	PROPN
ejpam-6062	189	16	=	=	SYM
ejpam-6062	189	17			PROPN
ejpam-6062	189	18	dgi	dgi	PROPN
ejpam-6062	189	19	(	(	PUNCT
ejpam-6062	189	20	aixn	aixn	NOUN
ejpam-6062	189	21	,	,	PUNCT
ejpam-6062	189	22	siaixn	siaixn	ADJ
ejpam-6062	189	23	)	)	PUNCT
ejpam-6062	189	24	d∗	d∗	PROPN
ejpam-6062	189	25	g(a	g(a	PROPN
ejpam-6062	189	26	∗	∗	NOUN
ejpam-6062	189	27	i	i	PRON
ejpam-6062	189	28	(	(	PUNCT
ejpam-6062	189	29	∇	∇	X
ejpam-6062	189	30	gi	gi	INTJ
ejpam-6062	189	31	ei	ei	X
ejpam-6062	189	32	(	(	PUNCT
ejpam-6062	189	33	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	189	34	i	i	PRON
ejpam-6062	189	35	(	(	PUNCT
ejpam-6062	189	36	∇	∇	X
ejpam-6062	189	37	gi	gi	PART
ejpam-6062	189	38	ei	ei	X
ejpam-6062	189	39	(	(	PUNCT
ejpam-6062	189	40	siaixn	siaixn	NOUN
ejpam-6062	189	41	)	)	PUNCT
ejpam-6062	189	42	)	)	PUNCT
ejpam-6062	189	43	,	,	PUNCT
ejpam-6062	190	1	if	if	SCONJ
ejpam-6062	190	2	,	,	PUNCT
ejpam-6062	190	3	(	(	PUNCT
ejpam-6062	190	4	i	i	PRON
ejpam-6062	190	5	−	−	PROPN
ejpam-6062	190	6	si)aixn	si)aixn	ADJ
ejpam-6062	190	7	̸=	̸=	PROPN
ejpam-6062	190	8	0	0	NUM
ejpam-6062	190	9	,	,	PUNCT
ejpam-6062	190	10	ξ1	ξ1	NOUN
ejpam-6062	190	11	,	,	PUNCT
ejpam-6062	190	12	otherwise	otherwise	ADV
ejpam-6062	190	13	,	,	PUNCT
ejpam-6062	190	14	h.	h.	PROPN
ejpam-6062	190	15	a.	a.	PROPN
ejpam-6062	190	16	abass	abass	PROPN
ejpam-6062	190	17	et	et	PROPN
ejpam-6062	190	18	al	al	PROPN
ejpam-6062	190	19	.	.	PUNCT
ejpam-6062	190	20	/	/	SYM
ejpam-6062	190	21	eur	eur	PROPN
ejpam-6062	190	22	.	.	PUNCT
ejpam-6062	191	1	j.	j.	PROPN
ejpam-6062	191	2	pure	pure	PROPN
ejpam-6062	191	3	appl	appl	PROPN
ejpam-6062	191	4	.	.	PROPN
ejpam-6062	191	5	math	math	PROPN
ejpam-6062	191	6	,	,	PUNCT
ejpam-6062	191	7	18	18	NUM
ejpam-6062	191	8	(	(	PUNCT
ejpam-6062	191	9	2	2	NUM
ejpam-6062	191	10	)	)	PUNCT
ejpam-6062	191	11	(	(	PUNCT
ejpam-6062	191	12	2025	2025	NUM
ejpam-6062	191	13	)	)	PUNCT
ejpam-6062	191	14	,	,	PUNCT
ejpam-6062	191	15	6062	6062	NUM
ejpam-6062	191	16	11	11	NUM
ejpam-6062	191	17	of	of	ADP
ejpam-6062	191	18	22	22	NUM
ejpam-6062	191	19	and	and	CCONJ
ejpam-6062	191	20	ξ2,n	ξ2,n	NOUN
ejpam-6062	191	21	=	=	PUNCT
ejpam-6062	191	22			PUNCT
ejpam-6062	191	23	d∗	d∗	NOUN
ejpam-6062	191	24	g(∇	g(∇	VERB
ejpam-6062	191	25	g	g	PROPN
ejpam-6062	191	26	e(xn)−γa∗	e(xn)−γa∗	NOUN
ejpam-6062	191	27	i	i	PRON
ejpam-6062	191	28	(	(	PUNCT
ejpam-6062	191	29	∇	∇	X
ejpam-6062	191	30	gi	gi	INTJ
ejpam-6062	191	31	ei	ei	X
ejpam-6062	191	32	(	(	PUNCT
ejpam-6062	191	33	aixn)−∇gi	aixn)−∇gi	ADV
ejpam-6062	191	34	ei	ei	X
ejpam-6062	191	35	(	(	PUNCT
ejpam-6062	191	36	siaixn)),∇g	siaixn)),∇g	VERB
ejpam-6062	191	37	e(xn	e(xn	NOUN
ejpam-6062	191	38	)	)	PUNCT
ejpam-6062	191	39	)	)	PUNCT
ejpam-6062	192	1	d∗	d∗	PROPN
ejpam-6062	192	2	g(a	g(a	PROPN
ejpam-6062	192	3	∗	∗	NOUN
ejpam-6062	192	4	i	i	PRON
ejpam-6062	192	5	(	(	PUNCT
ejpam-6062	192	6	∇	∇	X
ejpam-6062	192	7	gi	gi	INTJ
ejpam-6062	192	8	ei	ei	X
ejpam-6062	192	9	(	(	PUNCT
ejpam-6062	192	10	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	192	11	i	i	PRON
ejpam-6062	192	12	(	(	PUNCT
ejpam-6062	192	13	∇	∇	X
ejpam-6062	192	14	gi	gi	PART
ejpam-6062	192	15	ei	ei	X
ejpam-6062	192	16	(	(	PUNCT
ejpam-6062	192	17	siaixn	siaixn	NOUN
ejpam-6062	192	18	)	)	PUNCT
ejpam-6062	192	19	)	)	PUNCT
ejpam-6062	192	20	,	,	PUNCT
ejpam-6062	192	21	if	if	SCONJ
ejpam-6062	192	22	,	,	PUNCT
ejpam-6062	192	23	(	(	PUNCT
ejpam-6062	192	24	i	i	PRON
ejpam-6062	192	25	−	−	PROPN
ejpam-6062	192	26	si)aixn	si)aixn	ADJ
ejpam-6062	192	27	̸=	̸=	PROPN
ejpam-6062	192	28	0	0	NUM
ejpam-6062	192	29	,	,	PUNCT
ejpam-6062	192	30	ξ2	ξ2	ADJ
ejpam-6062	192	31	,	,	PUNCT
ejpam-6062	192	32	otherwise	otherwise	ADV
ejpam-6062	192	33	.	.	PUNCT
ejpam-6062	193	1	then	then	ADV
ejpam-6062	193	2	,	,	PUNCT
ejpam-6062	193	3	the	the	DET
ejpam-6062	193	4	sequence	sequence	NOUN
ejpam-6062	193	5	{	{	PUNCT
ejpam-6062	193	6	xn	xn	NOUN
ejpam-6062	193	7	}	}	PUNCT
ejpam-6062	193	8	defined	define	VERB
ejpam-6062	193	9	in	in	ADP
ejpam-6062	193	10	(	(	PUNCT
ejpam-6062	193	11	16	16	NUM
ejpam-6062	193	12	)	)	PUNCT
ejpam-6062	193	13	converges	converge	VERB
ejpam-6062	193	14	strongly	strongly	ADV
ejpam-6062	193	15	to	to	ADP
ejpam-6062	193	16	v	v	NOUN
ejpam-6062	193	17	=	=	SYM
ejpam-6062	193	18	projgωu	projgωu	NOUN
ejpam-6062	193	19	,	,	PUNCT
ejpam-6062	193	20	where	where	SCONJ
ejpam-6062	193	21	projgω	projgω	NOUN
ejpam-6062	193	22	is	be	AUX
ejpam-6062	193	23	the	the	DET
ejpam-6062	193	24	bregman	bregman	NOUN
ejpam-6062	193	25	projection	projection	NOUN
ejpam-6062	193	26	of	of	ADP
ejpam-6062	193	27	e	e	PROPN
ejpam-6062	193	28	onto	onto	ADP
ejpam-6062	193	29	ω	ω	NUM
ejpam-6062	193	30	.	.	PUNCT
ejpam-6062	194	1	proof	proof	NOUN
ejpam-6062	194	2	.	.	PUNCT
ejpam-6062	195	1	let	let	VERB
ejpam-6062	195	2	vσ	vσ	VERB
ejpam-6062	195	3	=	=	VERB
ejpam-6062	195	4	β0∇g	β0∇g	NOUN
ejpam-6062	195	5	e+β1∇g	e+β1∇g	ADP
ejpam-6062	195	6	e(resgσg1	e(resgσg1	PROPN
ejpam-6062	195	7	◦	◦	NOUN
ejpam-6062	195	8	f	f	PROPN
ejpam-6062	195	9	g	g	PROPN
ejpam-6062	195	10	1	1	NUM
ejpam-6062	195	11	)	)	PUNCT
ejpam-6062	196	1	+	+	X
ejpam-6062	196	2	β2∇g	β2∇g	X
ejpam-6062	196	3	e(resgσg2	e(resgσg2	NOUN
ejpam-6062	196	4	◦	◦	NOUN
ejpam-6062	196	5	f	f	NOUN
ejpam-6062	196	6	g	g	PROPN
ejpam-6062	196	7	2	2	NUM
ejpam-6062	196	8	)	)	PUNCT
ejpam-6062	196	9	+	+	PROPN
ejpam-6062	196	10	·	·	PUNCT
ejpam-6062	196	11	·	·	PUNCT
ejpam-6062	196	12	·	·	PUNCT
ejpam-6062	196	13	+	+	ADJ
ejpam-6062	196	14	βj∇g	βj∇g	NOUN
ejpam-6062	196	15	e(resgσgm	e(resgσgm	NOUN
ejpam-6062	197	1	◦	◦	NOUN
ejpam-6062	197	2	f	f	X
ejpam-6062	197	3	g	g	PROPN
ejpam-6062	197	4	m	m	PROPN
ejpam-6062	197	5	)	)	PUNCT
ejpam-6062	197	6	,	,	PUNCT
ejpam-6062	197	7	then	then	ADV
ejpam-6062	197	8	yn	yn	X
ejpam-6062	197	9	=	=	PUNCT
ejpam-6062	197	10	vσzn	vσzn	PROPN
ejpam-6062	197	11	.	.	PUNCT
ejpam-6062	198	1	by	by	ADP
ejpam-6062	198	2	applying	apply	VERB
ejpam-6062	198	3	lemma	lemma	PROPN
ejpam-6062	198	4	5	5	NUM
ejpam-6062	198	5	and	and	CCONJ
ejpam-6062	198	6	using	use	VERB
ejpam-6062	198	7	the	the	DET
ejpam-6062	198	8	fact	fact	NOUN
ejpam-6062	198	9	that	that	SCONJ
ejpam-6062	198	10	t	t	PROPN
ejpam-6062	198	11	j	j	PROPN
ejpam-6062	198	12	σ	σ	PROPN
ejpam-6062	198	13	is	be	AUX
ejpam-6062	198	14	bqne	bqne	ADV
ejpam-6062	198	15	then	then	ADV
ejpam-6062	198	16	we	we	PRON
ejpam-6062	198	17	have	have	VERB
ejpam-6062	198	18	that	that	PRON
ejpam-6062	198	19	fix(vσ	fix(vσ	VERB
ejpam-6062	198	20	)	)	PUNCT
ejpam-6062	198	21	=	=	SYM
ejpam-6062	199	1	m⋂	m⋂	NOUN
ejpam-6062	199	2	j=1	j=1	PROPN
ejpam-6062	199	3	fix(t	fix(t	PROPN
ejpam-6062	199	4	j	j	PROPN
ejpam-6062	199	5	σ	σ	PROPN
ejpam-6062	199	6	)	)	PUNCT
ejpam-6062	199	7	=	=	SYM
ejpam-6062	200	1	m⋂	m⋂	NOUN
ejpam-6062	200	2	j=1	j=1	NOUN
ejpam-6062	200	3	(	(	PUNCT
ejpam-6062	200	4	fj	fj	PROPN
ejpam-6062	200	5	+	+	CCONJ
ejpam-6062	200	6	gj	gj	NOUN
ejpam-6062	200	7	)	)	PUNCT
ejpam-6062	200	8	−1(0	−1(0	NOUN
ejpam-6062	200	9	)	)	PUNCT
ejpam-6062	200	10	.	.	PUNCT
ejpam-6062	201	1	let	let	VERB
ejpam-6062	201	2	v	v	X
ejpam-6062	201	3	∈	∈	PROPN
ejpam-6062	201	4	ω	ω	PROPN
ejpam-6062	201	5	,	,	PUNCT
ejpam-6062	201	6	then	then	ADV
ejpam-6062	201	7	we	we	PRON
ejpam-6062	201	8	obtain	obtain	VERB
ejpam-6062	201	9	from	from	ADP
ejpam-6062	201	10	lemma	lemma	PROPN
ejpam-6062	201	11	3	3	NUM
ejpam-6062	201	12	that	that	PRON
ejpam-6062	201	13	dg(v	dg(v	NOUN
ejpam-6062	201	14	,	,	PUNCT
ejpam-6062	201	15	zn	zn	NOUN
ejpam-6062	201	16	)	)	PUNCT
ejpam-6062	201	17	=	=	PUNCT
ejpam-6062	202	1	dg(v	dg(v	X
ejpam-6062	202	2	,	,	PUNCT
ejpam-6062	202	3	(	(	PUNCT
ejpam-6062	202	4	∇g	∇g	NOUN
ejpam-6062	202	5	e	e	NOUN
ejpam-6062	202	6	)	)	PUNCT
ejpam-6062	202	7	−1	−1	NOUN
ejpam-6062	202	8	[	[	PUNCT
ejpam-6062	202	9	n∑	n∑	PROPN
ejpam-6062	202	10	i=0	i=0	PROPN
ejpam-6062	202	11	λi	λi	SYM
ejpam-6062	202	12	,	,	PUNCT
ejpam-6062	202	13	n(∇g	n(∇g	NUM
ejpam-6062	202	14	e(xn)−	e(xn)−	NOUN
ejpam-6062	202	15	γa∗	γa∗	VERB
ejpam-6062	203	1	i	i	PRON
ejpam-6062	203	2	(	(	PUNCT
ejpam-6062	203	3	∇	∇	X
ejpam-6062	203	4	gi	gi	INTJ
ejpam-6062	203	5	ei	ei	X
ejpam-6062	203	6	(	(	PUNCT
ejpam-6062	203	7	aixn)−∇gi	aixn)−∇gi	ADJ
ejpam-6062	203	8	ei	ei	X
ejpam-6062	203	9	(	(	PUNCT
ejpam-6062	203	10	siaixn	siaixn	NOUN
ejpam-6062	203	11	)	)	PUNCT
ejpam-6062	203	12	)	)	PUNCT
ejpam-6062	203	13	)	)	PUNCT
ejpam-6062	203	14	]	]	PUNCT
ejpam-6062	204	1	≤	≤	X
ejpam-6062	204	2	dg(v	dg(v	NOUN
ejpam-6062	204	3	,	,	PUNCT
ejpam-6062	204	4	xn)−	xn)−	PUNCT
ejpam-6062	205	1	n∑	n∑	PROPN
ejpam-6062	205	2	i=0	i=0	PROPN
ejpam-6062	205	3	λi	λi	SYM
ejpam-6062	205	4	,	,	PUNCT
ejpam-6062	205	5	n(γ(1−	n(γ(1−	PROPN
ejpam-6062	205	6	ρs)ξ1,n	ρs)ξ1,n	PART
ejpam-6062	205	7	−	−	NOUN
ejpam-6062	205	8	ξ2,n)d	ξ2,n)d	NOUN
ejpam-6062	205	9	∗	∗	PROPN
ejpam-6062	205	10	g(a	g(a	PROPN
ejpam-6062	205	11	∗	∗	NOUN
ejpam-6062	205	12	i	i	PRON
ejpam-6062	205	13	(	(	PUNCT
ejpam-6062	205	14	∇	∇	X
ejpam-6062	205	15	gi	gi	INTJ
ejpam-6062	205	16	ei	ei	NOUN
ejpam-6062	205	17	(	(	PUNCT
ejpam-6062	205	18	aixn	aixn	NOUN
ejpam-6062	205	19	)	)	PUNCT
ejpam-6062	205	20	)	)	PUNCT
ejpam-6062	205	21	,	,	PUNCT
ejpam-6062	205	22	a	a	DET
ejpam-6062	205	23	∗	∗	X
ejpam-6062	205	24	i	i	PRON
ejpam-6062	205	25	(	(	PUNCT
ejpam-6062	205	26	∇	∇	X
ejpam-6062	205	27	gi	gi	PART
ejpam-6062	205	28	ei	ei	X
ejpam-6062	205	29	(	(	PUNCT
ejpam-6062	205	30	siaixn	siaixn	NOUN
ejpam-6062	205	31	)	)	PUNCT
ejpam-6062	205	32	)	)	PUNCT
ejpam-6062	205	33	(	(	PUNCT
ejpam-6062	205	34	17	17	NUM
ejpam-6062	205	35	)	)	PUNCT
ejpam-6062	205	36	≤	≤	NOUN
ejpam-6062	205	37	dg(v	dg(v	NOUN
ejpam-6062	205	38	,	,	PUNCT
ejpam-6062	205	39	xn	xn	PROPN
ejpam-6062	205	40	)	)	PUNCT
ejpam-6062	205	41	.	.	PUNCT
ejpam-6062	206	1	(	(	PUNCT
ejpam-6062	206	2	18	18	NUM
ejpam-6062	206	3	)	)	PUNCT
ejpam-6062	206	4	it	it	PRON
ejpam-6062	206	5	follows	follow	VERB
ejpam-6062	206	6	from	from	ADP
ejpam-6062	206	7	(	(	PUNCT
ejpam-6062	206	8	16	16	NUM
ejpam-6062	206	9	)	)	PUNCT
ejpam-6062	206	10	and	and	CCONJ
ejpam-6062	206	11	(	(	PUNCT
ejpam-6062	206	12	18	18	NUM
ejpam-6062	206	13	)	)	PUNCT
ejpam-6062	206	14	that	that	PRON
ejpam-6062	206	15	dg(v	dg(v	ADV
ejpam-6062	206	16	,	,	PUNCT
ejpam-6062	206	17	yn	yn	PROPN
ejpam-6062	206	18	)	)	PUNCT
ejpam-6062	206	19	=	=	PUNCT
ejpam-6062	206	20	dg(v	dg(v	X
ejpam-6062	206	21	,	,	PUNCT
ejpam-6062	206	22	(	(	PUNCT
ejpam-6062	206	23	∇g	∇g	NOUN
ejpam-6062	206	24	e	e	NOUN
ejpam-6062	206	25	)	)	PUNCT
ejpam-6062	206	26	−1	−1	NOUN
ejpam-6062	206	27	[	[	PUNCT
ejpam-6062	206	28	β0∇g	β0∇g	PROPN
ejpam-6062	206	29	e(zn	e(zn	PROPN
ejpam-6062	206	30	)	)	PUNCT
ejpam-6062	207	1	+	+	CCONJ
ejpam-6062	207	2	m∑	m∑	SCONJ
ejpam-6062	207	3	j=1	j=1	PROPN
ejpam-6062	207	4	βj∇g	βj∇g	PROPN
ejpam-6062	207	5	e(t	e(t	PROPN
ejpam-6062	207	6	j	j	PROPN
ejpam-6062	207	7	σzn	σzn	PROPN
ejpam-6062	207	8	)	)	PUNCT
ejpam-6062	207	9	]	]	PUNCT
ejpam-6062	207	10	)	)	PUNCT
ejpam-6062	208	1	≤	≤	NOUN
ejpam-6062	209	1	β0dg(v	β0dg(v	PUNCT
ejpam-6062	209	2	,	,	PUNCT
ejpam-6062	209	3	zn	zn	X
ejpam-6062	209	4	)	)	PUNCT
ejpam-6062	209	5	+	+	CCONJ
ejpam-6062	209	6	m∑	m∑	PROPN
ejpam-6062	209	7	j=1	j=1	PROPN
ejpam-6062	209	8	βjdg(v	βjdg(v	PROPN
ejpam-6062	209	9	,	,	PUNCT
ejpam-6062	209	10	t	t	PROPN
ejpam-6062	209	11	j	j	PROPN
ejpam-6062	209	12	σzn	σzn	PROPN
ejpam-6062	209	13	)	)	PUNCT
ejpam-6062	209	14	≤	≤	NOUN
ejpam-6062	210	1	β0dg(v	β0dg(v	PUNCT
ejpam-6062	210	2	,	,	PUNCT
ejpam-6062	210	3	zn	zn	X
ejpam-6062	210	4	)	)	PUNCT
ejpam-6062	210	5	+	+	CCONJ
ejpam-6062	210	6	m∑	m∑	PROPN
ejpam-6062	210	7	j=1	j=1	PROPN
ejpam-6062	210	8	βjdg(v	βjdg(v	PROPN
ejpam-6062	210	9	,	,	PUNCT
ejpam-6062	210	10	zn	zn	NOUN
ejpam-6062	210	11	)	)	PUNCT
ejpam-6062	210	12	=	=	PUNCT
ejpam-6062	210	13	dg(v	dg(v	X
ejpam-6062	210	14	,	,	PUNCT
ejpam-6062	210	15	zn	zn	NOUN
ejpam-6062	210	16	)	)	PUNCT
ejpam-6062	210	17	(	(	PUNCT
ejpam-6062	210	18	19	19	NUM
ejpam-6062	210	19	)	)	PUNCT
ejpam-6062	210	20	≤	≤	NOUN
ejpam-6062	210	21	dg(v	dg(v	NOUN
ejpam-6062	210	22	,	,	PUNCT
ejpam-6062	210	23	xn	xn	PROPN
ejpam-6062	210	24	)	)	PUNCT
ejpam-6062	210	25	.	.	PUNCT
ejpam-6062	211	1	(	(	PUNCT
ejpam-6062	211	2	20	20	X
ejpam-6062	211	3	)	)	PUNCT
ejpam-6062	211	4	using	use	VERB
ejpam-6062	211	5	(	(	PUNCT
ejpam-6062	211	6	16	16	NUM
ejpam-6062	211	7	)	)	PUNCT
ejpam-6062	211	8	,	,	PUNCT
ejpam-6062	211	9	(	(	PUNCT
ejpam-6062	211	10	18	18	NUM
ejpam-6062	211	11	)	)	PUNCT
ejpam-6062	211	12	and	and	CCONJ
ejpam-6062	211	13	(	(	PUNCT
ejpam-6062	211	14	19	19	NUM
ejpam-6062	211	15	)	)	PUNCT
ejpam-6062	211	16	,	,	PUNCT
ejpam-6062	211	17	we	we	PRON
ejpam-6062	211	18	get	get	VERB
ejpam-6062	211	19	dg(v	dg(v	NOUN
ejpam-6062	211	20	,	,	PUNCT
ejpam-6062	211	21	xn+1	xn+1	NUM
ejpam-6062	211	22	)	)	PUNCT
ejpam-6062	211	23	=	=	SYM
ejpam-6062	212	1	dg(v	dg(v	X
ejpam-6062	212	2	,	,	PUNCT
ejpam-6062	212	3	(	(	PUNCT
ejpam-6062	212	4	∇g	∇g	NOUN
ejpam-6062	212	5	e	e	NOUN
ejpam-6062	212	6	)	)	PUNCT
ejpam-6062	212	7	−1	−1	NOUN
ejpam-6062	212	8	[	[	PUNCT
ejpam-6062	212	9	αn∇g	αn∇g	NOUN
ejpam-6062	212	10	e(u	e(u	PROPN
ejpam-6062	212	11	)	)	PUNCT
ejpam-6062	213	1	+	+	CCONJ
ejpam-6062	213	2	(	(	PUNCT
ejpam-6062	213	3	1−	1−	NUM
ejpam-6062	213	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	213	5	e(yn	e(yn	NOUN
ejpam-6062	213	6	)	)	PUNCT
ejpam-6062	213	7	]	]	PUNCT
ejpam-6062	213	8	)	)	PUNCT
ejpam-6062	214	1	≤	≤	NUM
ejpam-6062	214	2	αndg(v	αndg(v	ADP
ejpam-6062	214	3	,	,	PUNCT
ejpam-6062	214	4	u	u	NOUN
ejpam-6062	214	5	)	)	PUNCT
ejpam-6062	214	6	+	+	CCONJ
ejpam-6062	214	7	(	(	PUNCT
ejpam-6062	214	8	1−	1−	NUM
ejpam-6062	214	9	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	214	10	,	,	PUNCT
ejpam-6062	214	11	yn	yn	PROPN
ejpam-6062	214	12	)	)	PUNCT
ejpam-6062	214	13	(	(	PUNCT
ejpam-6062	214	14	21	21	NUM
ejpam-6062	214	15	)	)	PUNCT
ejpam-6062	214	16	≤	≤	NOUN
ejpam-6062	214	17	αndg(v	αndg(v	NUM
ejpam-6062	214	18	,	,	PUNCT
ejpam-6062	214	19	u	u	NOUN
ejpam-6062	214	20	)	)	PUNCT
ejpam-6062	214	21	+	+	CCONJ
ejpam-6062	214	22	(	(	PUNCT
ejpam-6062	214	23	1−	1−	NUM
ejpam-6062	214	24	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	214	25	,	,	PUNCT
ejpam-6062	214	26	zn	zn	NOUN
ejpam-6062	214	27	)	)	PUNCT
ejpam-6062	214	28	≤	≤	NOUN
ejpam-6062	215	1	αndg(v	αndg(v	NUM
ejpam-6062	215	2	,	,	PUNCT
ejpam-6062	215	3	u	u	NOUN
ejpam-6062	215	4	)	)	PUNCT
ejpam-6062	215	5	+	+	CCONJ
ejpam-6062	215	6	(	(	PUNCT
ejpam-6062	215	7	1−	1−	NUM
ejpam-6062	215	8	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	215	9	,	,	PUNCT
ejpam-6062	215	10	xn	xn	NUM
ejpam-6062	215	11	)	)	PUNCT
ejpam-6062	215	12	≤	≤	NUM
ejpam-6062	215	13	max{dg(v	max{dg(v	PROPN
ejpam-6062	215	14	,	,	PUNCT
ejpam-6062	215	15	u	u	NOUN
ejpam-6062	215	16	)	)	PUNCT
ejpam-6062	215	17	,	,	PUNCT
ejpam-6062	215	18	dg(v	dg(v	X
ejpam-6062	215	19	,	,	PUNCT
ejpam-6062	215	20	xn	xn	PROPN
ejpam-6062	215	21	)	)	PUNCT
ejpam-6062	215	22	}	}	PUNCT
ejpam-6062	215	23	h.	h.	PROPN
ejpam-6062	215	24	a.	a.	PROPN
ejpam-6062	215	25	abass	abass	PROPN
ejpam-6062	215	26	et	et	PROPN
ejpam-6062	215	27	al	al	PROPN
ejpam-6062	215	28	.	.	PUNCT
ejpam-6062	215	29	/	/	SYM
ejpam-6062	215	30	eur	eur	PROPN
ejpam-6062	215	31	.	.	PUNCT
ejpam-6062	216	1	j.	j.	PROPN
ejpam-6062	216	2	pure	pure	PROPN
ejpam-6062	216	3	appl	appl	PROPN
ejpam-6062	216	4	.	.	PROPN
ejpam-6062	216	5	math	math	PROPN
ejpam-6062	216	6	,	,	PUNCT
ejpam-6062	216	7	18	18	NUM
ejpam-6062	216	8	(	(	PUNCT
ejpam-6062	216	9	2	2	NUM
ejpam-6062	216	10	)	)	PUNCT
ejpam-6062	216	11	(	(	PUNCT
ejpam-6062	216	12	2025	2025	NUM
ejpam-6062	216	13	)	)	PUNCT
ejpam-6062	216	14	,	,	PUNCT
ejpam-6062	216	15	6062	6062	NUM
ejpam-6062	216	16	12	12	NUM
ejpam-6062	216	17	of	of	ADP
ejpam-6062	216	18	22	22	NUM
ejpam-6062	216	19	...	...	PUNCT
ejpam-6062	216	20	≤	≤	NUM
ejpam-6062	216	21	max{dg(v	max{dg(v	PROPN
ejpam-6062	216	22	,	,	PUNCT
ejpam-6062	216	23	u	u	NOUN
ejpam-6062	216	24	)	)	PUNCT
ejpam-6062	216	25	,	,	PUNCT
ejpam-6062	216	26	dg(v	dg(v	X
ejpam-6062	216	27	,	,	PUNCT
ejpam-6062	216	28	x1	x1	PROPN
ejpam-6062	216	29	)	)	PUNCT
ejpam-6062	216	30	}	}	PUNCT
ejpam-6062	216	31	.	.	PUNCT
ejpam-6062	217	1	∀	∀	X
ejpam-6062	218	1	n	n	PRON
ejpam-6062	218	2	≥	≥	NOUN
ejpam-6062	218	3	1	1	NUM
ejpam-6062	218	4	.	.	PUNCT
ejpam-6062	219	1	thus	thus	ADV
ejpam-6062	219	2	,	,	PUNCT
ejpam-6062	219	3	we	we	PRON
ejpam-6062	219	4	obtain	obtain	VERB
ejpam-6062	219	5	that	that	SCONJ
ejpam-6062	219	6	the	the	DET
ejpam-6062	219	7	sequence	sequence	NOUN
ejpam-6062	219	8	{	{	PUNCT
ejpam-6062	219	9	dg(v	dg(v	X
ejpam-6062	219	10	,	,	PUNCT
ejpam-6062	219	11	xn)}n∈n	xn)}n∈n	PROPN
ejpam-6062	219	12	is	be	AUX
ejpam-6062	219	13	bounded	bound	VERB
ejpam-6062	219	14	.	.	PUNCT
ejpam-6062	220	1	using	use	VERB
ejpam-6062	220	2	lemma	lemma	PROPN
ejpam-6062	220	3	8	8	NUM
ejpam-6062	220	4	,	,	PUNCT
ejpam-6062	220	5	then	then	ADV
ejpam-6062	220	6	we	we	PRON
ejpam-6062	220	7	conclude	conclude	VERB
ejpam-6062	220	8	that	that	SCONJ
ejpam-6062	220	9	{	{	PUNCT
ejpam-6062	220	10	xn}n∈n	xn}n∈n	X
ejpam-6062	220	11	is	be	AUX
ejpam-6062	220	12	bounded	bound	VERB
ejpam-6062	220	13	.	.	PUNCT
ejpam-6062	221	1	consequently	consequently	ADV
ejpam-6062	221	2	,	,	PUNCT
ejpam-6062	221	3	{	{	PUNCT
ejpam-6062	221	4	yn}n∈n	yn}n∈n	NOUN
ejpam-6062	221	5	and	and	CCONJ
ejpam-6062	221	6	{	{	PUNCT
ejpam-6062	221	7	zn}n∈n	zn}n∈n	NOUN
ejpam-6062	221	8	are	be	AUX
ejpam-6062	221	9	bounded	bound	VERB
ejpam-6062	221	10	.	.	PUNCT
ejpam-6062	222	1	by	by	ADP
ejpam-6062	222	2	lemma	lemma	PROPN
ejpam-6062	222	3	6	6	NUM
ejpam-6062	222	4	,	,	PUNCT
ejpam-6062	222	5	(	(	PUNCT
ejpam-6062	222	6	16	16	NUM
ejpam-6062	222	7	)	)	PUNCT
ejpam-6062	222	8	and	and	CCONJ
ejpam-6062	222	9	(	(	PUNCT
ejpam-6062	222	10	20	20	NUM
ejpam-6062	222	11	)	)	PUNCT
ejpam-6062	222	12	,	,	PUNCT
ejpam-6062	222	13	we	we	PRON
ejpam-6062	222	14	obtain	obtain	VERB
ejpam-6062	222	15	that	that	DET
ejpam-6062	222	16	dg(v	dg(v	PUNCT
ejpam-6062	222	17	,	,	PUNCT
ejpam-6062	222	18	yn	yn	PROPN
ejpam-6062	222	19	)	)	PUNCT
ejpam-6062	222	20	=	=	PUNCT
ejpam-6062	222	21	dg(v	dg(v	X
ejpam-6062	222	22	,	,	PUNCT
ejpam-6062	222	23	(	(	PUNCT
ejpam-6062	222	24	∇g	∇g	PROPN
ejpam-6062	222	25	e	e	NOUN
ejpam-6062	222	26	)	)	PUNCT
ejpam-6062	222	27	−1[β0∇g	−1[β0∇g	PROPN
ejpam-6062	222	28	e(zn	e(zn	PROPN
ejpam-6062	222	29	)	)	PUNCT
ejpam-6062	223	1	+	+	CCONJ
ejpam-6062	223	2	m∑	m∑	SCONJ
ejpam-6062	223	3	j=1	j=1	PROPN
ejpam-6062	223	4	βj∇g	βj∇g	PROPN
ejpam-6062	223	5	e(t	e(t	PROPN
ejpam-6062	223	6	j	j	PROPN
ejpam-6062	223	7	σzn	σzn	PROPN
ejpam-6062	223	8	)	)	PUNCT
ejpam-6062	223	9	]	]	PUNCT
ejpam-6062	223	10	)	)	PUNCT
ejpam-6062	223	11	≤	≤	NOUN
ejpam-6062	224	1	β0dg(v	β0dg(v	PUNCT
ejpam-6062	224	2	,	,	PUNCT
ejpam-6062	224	3	zn	zn	X
ejpam-6062	224	4	)	)	PUNCT
ejpam-6062	224	5	+	+	CCONJ
ejpam-6062	224	6	m∑	m∑	PROPN
ejpam-6062	224	7	j=1	j=1	PROPN
ejpam-6062	224	8	βjdg(v	βjdg(v	PROPN
ejpam-6062	224	9	,	,	PUNCT
ejpam-6062	224	10	t	t	PROPN
ejpam-6062	224	11	j	j	PROPN
ejpam-6062	224	12	σzn	σzn	PROPN
ejpam-6062	224	13	)	)	PUNCT
ejpam-6062	224	14	≤	≤	NOUN
ejpam-6062	225	1	β0dg(v	β0dg(v	PUNCT
ejpam-6062	225	2	,	,	PUNCT
ejpam-6062	225	3	zn	zn	X
ejpam-6062	225	4	)	)	PUNCT
ejpam-6062	226	1	+	+	CCONJ
ejpam-6062	226	2	m∑	m∑	ADV
ejpam-6062	226	3	j=1	j=1	ADJ
ejpam-6062	226	4	βj	βj	X
ejpam-6062	226	5	(	(	PUNCT
ejpam-6062	226	6	dg(v	dg(v	X
ejpam-6062	226	7	,	,	PUNCT
ejpam-6062	226	8	zn)−dg(t	zn)−dg(t	NOUN
ejpam-6062	226	9	j	j	PROPN
ejpam-6062	226	10	σzn	σzn	PROPN
ejpam-6062	226	11	,	,	PUNCT
ejpam-6062	226	12	zn	zn	PROPN
ejpam-6062	226	13	)	)	PUNCT
ejpam-6062	226	14	)	)	PUNCT
ejpam-6062	227	1	=	=	PUNCT
ejpam-6062	227	2	dg(v	dg(v	X
ejpam-6062	227	3	,	,	PUNCT
ejpam-6062	227	4	zn)−	zn)−	NOUN
ejpam-6062	227	5	m∑	m∑	ADP
ejpam-6062	227	6	j=1	j=1	PROPN
ejpam-6062	227	7	βjdg(t	βjdg(t	NOUN
ejpam-6062	227	8	j	j	PROPN
ejpam-6062	227	9	σzn	σzn	PROPN
ejpam-6062	227	10	,	,	PUNCT
ejpam-6062	227	11	zn	zn	PROPN
ejpam-6062	227	12	)	)	PUNCT
ejpam-6062	227	13	(	(	PUNCT
ejpam-6062	227	14	22	22	NUM
ejpam-6062	227	15	)	)	PUNCT
ejpam-6062	227	16	≤	≤	NOUN
ejpam-6062	227	17	dg(v	dg(v	NOUN
ejpam-6062	227	18	,	,	PUNCT
ejpam-6062	227	19	xn)−	xn)−	PUNCT
ejpam-6062	228	1	m∑	m∑	CCONJ
ejpam-6062	229	1	j=1	j=1	ADJ
ejpam-6062	229	2	βjdg(t	βjdg(t	NOUN
ejpam-6062	229	3	j	j	PROPN
ejpam-6062	229	4	σzn	σzn	PROPN
ejpam-6062	229	5	,	,	PUNCT
ejpam-6062	229	6	zn	zn	PROPN
ejpam-6062	229	7	)	)	PUNCT
ejpam-6062	229	8	(	(	PUNCT
ejpam-6062	229	9	23	23	NUM
ejpam-6062	229	10	)	)	PUNCT
ejpam-6062	229	11	from	from	ADP
ejpam-6062	229	12	(	(	PUNCT
ejpam-6062	229	13	17	17	NUM
ejpam-6062	229	14	)	)	PUNCT
ejpam-6062	229	15	,	,	PUNCT
ejpam-6062	229	16	(	(	PUNCT
ejpam-6062	229	17	21	21	NUM
ejpam-6062	229	18	)	)	PUNCT
ejpam-6062	229	19	and	and	CCONJ
ejpam-6062	229	20	(	(	PUNCT
ejpam-6062	229	21	22	22	NUM
ejpam-6062	229	22	)	)	PUNCT
ejpam-6062	229	23	,	,	PUNCT
ejpam-6062	229	24	we	we	PRON
ejpam-6062	229	25	get	get	VERB
ejpam-6062	229	26	dg(v	dg(v	NOUN
ejpam-6062	229	27	,	,	PUNCT
ejpam-6062	229	28	xn+1	xn+1	NUM
ejpam-6062	229	29	)	)	PUNCT
ejpam-6062	229	30	≤	≤	NOUN
ejpam-6062	230	1	αndg(v	αndg(v	NUM
ejpam-6062	230	2	,	,	PUNCT
ejpam-6062	230	3	u	u	NOUN
ejpam-6062	230	4	)	)	PUNCT
ejpam-6062	230	5	+	+	CCONJ
ejpam-6062	230	6	(	(	PUNCT
ejpam-6062	230	7	1−	1−	NUM
ejpam-6062	230	8	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	230	9	,	,	PUNCT
ejpam-6062	230	10	yn	yn	NOUN
ejpam-6062	230	11	)	)	PUNCT
ejpam-6062	230	12	≤	≤	NOUN
ejpam-6062	230	13	αndg(v	αndg(v	NUM
ejpam-6062	230	14	,	,	PUNCT
ejpam-6062	230	15	u	u	NOUN
ejpam-6062	230	16	)	)	PUNCT
ejpam-6062	230	17	+	+	CCONJ
ejpam-6062	230	18	(	(	PUNCT
ejpam-6062	230	19	1−	1−	NUM
ejpam-6062	230	20	αn	αn	NOUN
ejpam-6062	230	21	)	)	PUNCT
ejpam-6062	230	22	(	(	PUNCT
ejpam-6062	230	23	dg(v	dg(v	X
ejpam-6062	230	24	,	,	PUNCT
ejpam-6062	230	25	zn)−	zn)−	NOUN
ejpam-6062	230	26	m∑	m∑	ADP
ejpam-6062	230	27	j=1	j=1	PROPN
ejpam-6062	230	28	βjdg(t	βjdg(t	NOUN
ejpam-6062	230	29	j	j	PROPN
ejpam-6062	230	30	σzn	σzn	PROPN
ejpam-6062	230	31	,	,	PUNCT
ejpam-6062	230	32	zn	zn	PROPN
ejpam-6062	230	33	)	)	PUNCT
ejpam-6062	230	34	)	)	PUNCT
ejpam-6062	231	1	=	=	SYM
ejpam-6062	231	2	αndg(v	αndg(v	NUM
ejpam-6062	231	3	,	,	PUNCT
ejpam-6062	231	4	u	u	NOUN
ejpam-6062	231	5	)	)	PUNCT
ejpam-6062	231	6	+	+	CCONJ
ejpam-6062	231	7	(	(	PUNCT
ejpam-6062	231	8	1−	1−	NUM
ejpam-6062	231	9	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	231	10	,	,	PUNCT
ejpam-6062	231	11	xn)−	xn)−	X
ejpam-6062	231	12	(	(	PUNCT
ejpam-6062	231	13	1−	1−	NUM
ejpam-6062	231	14	αn	αn	NOUN
ejpam-6062	231	15	)	)	PUNCT
ejpam-6062	231	16	m∑	m∑	VERB
ejpam-6062	231	17	j=1	j=1	PROPN
ejpam-6062	231	18	βjdg(t	βjdg(t	NOUN
ejpam-6062	231	19	j	j	PROPN
ejpam-6062	231	20	σzn	σzn	PROPN
ejpam-6062	231	21	,	,	PUNCT
ejpam-6062	231	22	zn	zn	PROPN
ejpam-6062	231	23	)	)	PUNCT
ejpam-6062	231	24	−	−	PROPN
ejpam-6062	232	1	(	(	PUNCT
ejpam-6062	232	2	1−	1−	NUM
ejpam-6062	232	3	αn	αn	NOUN
ejpam-6062	232	4	)	)	PUNCT
ejpam-6062	233	1	n∑	n∑	PROPN
ejpam-6062	233	2	i=0	i=0	PROPN
ejpam-6062	233	3	λi	λi	X
ejpam-6062	233	4	,	,	PUNCT
ejpam-6062	233	5	n(γ(1−	n(γ(1−	PROPN
ejpam-6062	233	6	ρs)ξ1,n	ρs)ξ1,n	PART
ejpam-6062	234	1	−	−	NOUN
ejpam-6062	234	2	ξ2,n)d	ξ2,n)d	NOUN
ejpam-6062	234	3	∗	∗	PROPN
ejpam-6062	234	4	g(a	g(a	PROPN
ejpam-6062	234	5	∗	∗	NOUN
ejpam-6062	234	6	i	i	PRON
ejpam-6062	234	7	(	(	PUNCT
ejpam-6062	234	8	∇	∇	X
ejpam-6062	234	9	gi	gi	INTJ
ejpam-6062	234	10	ei	ei	NOUN
ejpam-6062	234	11	(	(	PUNCT
ejpam-6062	234	12	aixn	aixn	NOUN
ejpam-6062	234	13	)	)	PUNCT
ejpam-6062	234	14	)	)	PUNCT
ejpam-6062	234	15	,	,	PUNCT
ejpam-6062	234	16	a	a	DET
ejpam-6062	234	17	∗	∗	X
ejpam-6062	234	18	i	i	PRON
ejpam-6062	234	19	(	(	PUNCT
ejpam-6062	234	20	∇	∇	X
ejpam-6062	234	21	gi	gi	PART
ejpam-6062	234	22	ei	ei	X
ejpam-6062	234	23	(	(	PUNCT
ejpam-6062	234	24	siaixn	siaixn	NOUN
ejpam-6062	234	25	)	)	PUNCT
ejpam-6062	234	26	)	)	PUNCT
ejpam-6062	234	27	.	.	PUNCT
ejpam-6062	235	1	(	(	PUNCT
ejpam-6062	235	2	24	24	NUM
ejpam-6062	235	3	)	)	PUNCT
ejpam-6062	235	4	we	we	PRON
ejpam-6062	235	5	now	now	ADV
ejpam-6062	235	6	divide	divide	VERB
ejpam-6062	235	7	the	the	DET
ejpam-6062	235	8	remaining	remain	VERB
ejpam-6062	235	9	proof	proof	NOUN
ejpam-6062	235	10	into	into	ADP
ejpam-6062	235	11	two	two	NUM
ejpam-6062	235	12	cases	case	NOUN
ejpam-6062	235	13	.	.	PUNCT
ejpam-6062	236	1	case	case	NOUN
ejpam-6062	236	2	1	1	NUM
ejpam-6062	236	3	:	:	PUNCT
ejpam-6062	236	4	suppose	suppose	VERB
ejpam-6062	236	5	that	that	SCONJ
ejpam-6062	236	6	there	there	PRON
ejpam-6062	236	7	exists	exist	VERB
ejpam-6062	236	8	n0	n0	PROPN
ejpam-6062	236	9	∈	∈	PROPN
ejpam-6062	236	10	n	n	PRON
ejpam-6062	236	11	such	such	ADJ
ejpam-6062	236	12	that	that	SCONJ
ejpam-6062	236	13	{	{	PUNCT
ejpam-6062	236	14	dg(v	dg(v	X
ejpam-6062	236	15	,	,	PUNCT
ejpam-6062	236	16	xn	xn	PROPN
ejpam-6062	236	17	)	)	PUNCT
ejpam-6062	236	18	}	}	PUNCT
ejpam-6062	236	19	is	be	AUX
ejpam-6062	236	20	non	non	ADJ
ejpam-6062	236	21	-	-	ADJ
ejpam-6062	236	22	increasing	increase	VERB
ejpam-6062	236	23	,	,	PUNCT
ejpam-6062	236	24	then	then	ADV
ejpam-6062	236	25	we	we	PRON
ejpam-6062	236	26	obtain	obtain	VERB
ejpam-6062	236	27	that	that	SCONJ
ejpam-6062	236	28	lim	lim	PROPN
ejpam-6062	236	29	n→∞	n→∞	PRON
ejpam-6062	236	30	dg(v	dg(v	PROPN
ejpam-6062	236	31	,	,	PUNCT
ejpam-6062	236	32	xn	xn	PRON
ejpam-6062	236	33	)	)	PUNCT
ejpam-6062	236	34	exists	exist	VERB
ejpam-6062	236	35	.	.	PUNCT
ejpam-6062	237	1	thus	thus	ADV
ejpam-6062	237	2	,	,	PUNCT
ejpam-6062	237	3	dg(v	dg(v	X
ejpam-6062	237	4	,	,	PUNCT
ejpam-6062	237	5	xn)−dg(v	xn)−dg(v	NOUN
ejpam-6062	237	6	,	,	PUNCT
ejpam-6062	237	7	xn+1	xn+1	NUM
ejpam-6062	237	8	)	)	PUNCT
ejpam-6062	237	9	→	→	SYM
ejpam-6062	237	10	0	0	NUM
ejpam-6062	237	11	,	,	PUNCT
ejpam-6062	237	12	n	n	PROPN
ejpam-6062	237	13	→	→	SYM
ejpam-6062	237	14	∞.	∞.	PROPN
ejpam-6062	237	15	(	(	PUNCT
ejpam-6062	237	16	25	25	NUM
ejpam-6062	237	17	)	)	PUNCT
ejpam-6062	237	18	from	from	ADP
ejpam-6062	237	19	(	(	PUNCT
ejpam-6062	237	20	24	24	NUM
ejpam-6062	237	21	)	)	PUNCT
ejpam-6062	237	22	,	,	PUNCT
ejpam-6062	237	23	25	25	NUM
ejpam-6062	237	24	and	and	CCONJ
ejpam-6062	237	25	condition	condition	NOUN
ejpam-6062	237	26	(	(	PUNCT
ejpam-6062	237	27	i	i	NOUN
ejpam-6062	237	28	)	)	PUNCT
ejpam-6062	237	29	of	of	ADP
ejpam-6062	237	30	assumption	assumption	NOUN
ejpam-6062	237	31	(	(	PUNCT
ejpam-6062	237	32	1	1	NUM
ejpam-6062	237	33	)	)	PUNCT
ejpam-6062	237	34	,	,	PUNCT
ejpam-6062	237	35	we	we	PRON
ejpam-6062	237	36	have	have	VERB
ejpam-6062	237	37	that	that	PRON
ejpam-6062	237	38	(	(	PUNCT
ejpam-6062	237	39	1−	1−	NUM
ejpam-6062	237	40	αn	αn	NOUN
ejpam-6062	237	41	)	)	PUNCT
ejpam-6062	238	1	[	[	PUNCT
ejpam-6062	238	2	n∑	n∑	PROPN
ejpam-6062	238	3	i=0	i=0	PROPN
ejpam-6062	238	4	λi	λi	PROPN
ejpam-6062	238	5	,	,	PUNCT
ejpam-6062	238	6	n(γ(1−	n(γ(1−	PROPN
ejpam-6062	238	7	ρs)ξ1,n	ρs)ξ1,n	PART
ejpam-6062	238	8	−	−	NOUN
ejpam-6062	238	9	ξ2,n)d	ξ2,n)d	NOUN
ejpam-6062	238	10	∗	∗	PROPN
ejpam-6062	238	11	g(a	g(a	PROPN
ejpam-6062	238	12	∗	∗	NOUN
ejpam-6062	238	13	i	i	PRON
ejpam-6062	238	14	(	(	PUNCT
ejpam-6062	238	15	∇	∇	X
ejpam-6062	238	16	gi	gi	INTJ
ejpam-6062	238	17	ei	ei	NOUN
ejpam-6062	238	18	(	(	PUNCT
ejpam-6062	238	19	aixn	aixn	NOUN
ejpam-6062	238	20	)	)	PUNCT
ejpam-6062	238	21	)	)	PUNCT
ejpam-6062	238	22	,	,	PUNCT
ejpam-6062	238	23	a	a	DET
ejpam-6062	238	24	∗	∗	X
ejpam-6062	238	25	i	i	PRON
ejpam-6062	238	26	(	(	PUNCT
ejpam-6062	238	27	∇	∇	X
ejpam-6062	238	28	gi	gi	PART
ejpam-6062	238	29	ei	ei	X
ejpam-6062	238	30	(	(	PUNCT
ejpam-6062	238	31	siaixn	siaixn	ADJ
ejpam-6062	238	32	)	)	PUNCT
ejpam-6062	238	33	)	)	PUNCT
ejpam-6062	238	34	h.	h.	PROPN
ejpam-6062	238	35	a.	a.	PROPN
ejpam-6062	238	36	abass	abass	PROPN
ejpam-6062	238	37	et	et	PROPN
ejpam-6062	238	38	al	al	PROPN
ejpam-6062	238	39	.	.	PUNCT
ejpam-6062	238	40	/	/	SYM
ejpam-6062	238	41	eur	eur	PROPN
ejpam-6062	238	42	.	.	PUNCT
ejpam-6062	239	1	j.	j.	PROPN
ejpam-6062	239	2	pure	pure	PROPN
ejpam-6062	239	3	appl	appl	PROPN
ejpam-6062	239	4	.	.	PROPN
ejpam-6062	239	5	math	math	PROPN
ejpam-6062	239	6	,	,	PUNCT
ejpam-6062	239	7	18	18	NUM
ejpam-6062	239	8	(	(	PUNCT
ejpam-6062	239	9	2	2	NUM
ejpam-6062	239	10	)	)	PUNCT
ejpam-6062	239	11	(	(	PUNCT
ejpam-6062	239	12	2025	2025	NUM
ejpam-6062	239	13	)	)	PUNCT
ejpam-6062	239	14	,	,	PUNCT
ejpam-6062	239	15	6062	6062	NUM
ejpam-6062	239	16	13	13	NUM
ejpam-6062	239	17	of	of	ADP
ejpam-6062	239	18	22	22	NUM
ejpam-6062	239	19	+	+	CCONJ
ejpam-6062	239	20	m∑	m∑	ADV
ejpam-6062	239	21	j=1	j=1	ADJ
ejpam-6062	239	22	βjdg(t	βjdg(t	NOUN
ejpam-6062	239	23	j	j	PROPN
ejpam-6062	239	24	σzn	σzn	PROPN
ejpam-6062	239	25	,	,	PUNCT
ejpam-6062	239	26	zn	zn	PROPN
ejpam-6062	239	27	)	)	PUNCT
ejpam-6062	239	28	)	)	PUNCT
ejpam-6062	239	29	]	]	PUNCT
ejpam-6062	240	1	≤	≤	NUM
ejpam-6062	240	2	αndg(v	αndg(v	ADP
ejpam-6062	240	3	,	,	PUNCT
ejpam-6062	240	4	u	u	NOUN
ejpam-6062	240	5	)	)	PUNCT
ejpam-6062	240	6	+	+	CCONJ
ejpam-6062	240	7	(	(	PUNCT
ejpam-6062	240	8	1−	1−	NUM
ejpam-6062	240	9	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	240	10	,	,	PUNCT
ejpam-6062	240	11	xn)−dg(v	xn)−dg(v	NOUN
ejpam-6062	240	12	,	,	PUNCT
ejpam-6062	240	13	xn+1	xn+1	NUM
ejpam-6062	240	14	)	)	PUNCT
ejpam-6062	240	15	,	,	PUNCT
ejpam-6062	240	16	which	which	PRON
ejpam-6062	240	17	implies	imply	VERB
ejpam-6062	240	18	from	from	ADP
ejpam-6062	240	19	lemma	lemma	PROPN
ejpam-6062	240	20	4	4	NUM
ejpam-6062	240	21	that	that	PRON
ejpam-6062	240	22	lim	lim	PROPN
ejpam-6062	240	23	n→∞	n→∞	PRON
ejpam-6062	240	24	dg(t	dg(t	PROPN
ejpam-6062	240	25	j	j	PROPN
ejpam-6062	240	26	σzn	σzn	PROPN
ejpam-6062	240	27	,	,	PUNCT
ejpam-6062	240	28	zn	zn	PROPN
ejpam-6062	240	29	)	)	PUNCT
ejpam-6062	240	30	=	=	SYM
ejpam-6062	240	31	0	0	PUNCT
ejpam-6062	241	1	=	=	SYM
ejpam-6062	241	2	lim	lim	PROPN
ejpam-6062	241	3	n→∞	n→∞	NUM
ejpam-6062	241	4	||t	||t	PROPN
ejpam-6062	241	5	j	j	PROPN
ejpam-6062	241	6	σzn	σzn	PROPN
ejpam-6062	241	7	−	−	PROPN
ejpam-6062	241	8	zn||	zn||	PROPN
ejpam-6062	241	9	.	.	PUNCT
ejpam-6062	242	1	(	(	PUNCT
ejpam-6062	242	2	26	26	NUM
ejpam-6062	242	3	)	)	PUNCT
ejpam-6062	242	4	also	also	ADV
ejpam-6062	242	5	,	,	PUNCT
ejpam-6062	242	6	lim	lim	PROPN
ejpam-6062	242	7	n→∞	n→∞	NUM
ejpam-6062	242	8	n∑	n∑	PROPN
ejpam-6062	242	9	i=0	i=0	PROPN
ejpam-6062	242	10	λi	λi	SYM
ejpam-6062	242	11	,	,	PUNCT
ejpam-6062	242	12	n(γ(1−	n(γ(1−	PROPN
ejpam-6062	242	13	ρs)ξ1,n	ρs)ξ1,n	PART
ejpam-6062	242	14	−	−	NOUN
ejpam-6062	242	15	ξ2,n)d	ξ2,n)d	NOUN
ejpam-6062	242	16	∗	∗	PROPN
ejpam-6062	242	17	g(a	g(a	PROPN
ejpam-6062	242	18	∗	∗	NOUN
ejpam-6062	242	19	i	i	PRON
ejpam-6062	242	20	(	(	PUNCT
ejpam-6062	242	21	∇	∇	X
ejpam-6062	242	22	gi	gi	INTJ
ejpam-6062	242	23	ei	ei	NOUN
ejpam-6062	242	24	(	(	PUNCT
ejpam-6062	242	25	aixn	aixn	NOUN
ejpam-6062	242	26	)	)	PUNCT
ejpam-6062	242	27	)	)	PUNCT
ejpam-6062	242	28	,	,	PUNCT
ejpam-6062	242	29	a	a	DET
ejpam-6062	242	30	∗	∗	X
ejpam-6062	242	31	i	i	PRON
ejpam-6062	242	32	(	(	PUNCT
ejpam-6062	242	33	∇	∇	X
ejpam-6062	242	34	gi	gi	PART
ejpam-6062	242	35	ei	ei	X
ejpam-6062	242	36	(	(	PUNCT
ejpam-6062	242	37	siaixn	siaixn	ADJ
ejpam-6062	242	38	)	)	PUNCT
ejpam-6062	242	39	)	)	PUNCT
ejpam-6062	243	1	=	=	PUNCT
ejpam-6062	243	2	0	0	X
ejpam-6062	243	3	.	.	PUNCT
ejpam-6062	244	1	(	(	PUNCT
ejpam-6062	244	2	27	27	NUM
ejpam-6062	244	3	)	)	PUNCT
ejpam-6062	244	4	therefore	therefore	ADV
ejpam-6062	244	5	,	,	PUNCT
ejpam-6062	244	6	we	we	PRON
ejpam-6062	244	7	have	have	VERB
ejpam-6062	244	8	lim	lim	PROPN
ejpam-6062	244	9	n→∞	n→∞	NUM
ejpam-6062	244	10	d∗	d∗	PROPN
ejpam-6062	244	11	g(a	g(a	PROPN
ejpam-6062	244	12	∗	∗	NOUN
ejpam-6062	244	13	i	i	PRON
ejpam-6062	244	14	(	(	PUNCT
ejpam-6062	244	15	∇	∇	X
ejpam-6062	244	16	gi	gi	INTJ
ejpam-6062	244	17	ei	ei	NOUN
ejpam-6062	244	18	(	(	PUNCT
ejpam-6062	244	19	aixn	aixn	NOUN
ejpam-6062	244	20	)	)	PUNCT
ejpam-6062	244	21	)	)	PUNCT
ejpam-6062	244	22	,	,	PUNCT
ejpam-6062	244	23	a	a	DET
ejpam-6062	244	24	∗	∗	X
ejpam-6062	244	25	i	i	PRON
ejpam-6062	244	26	(	(	PUNCT
ejpam-6062	244	27	∇	∇	X
ejpam-6062	244	28	gi	gi	PART
ejpam-6062	244	29	ei	ei	X
ejpam-6062	244	30	(	(	PUNCT
ejpam-6062	244	31	siaixn	siaixn	ADJ
ejpam-6062	244	32	)	)	PUNCT
ejpam-6062	244	33	)	)	PUNCT
ejpam-6062	245	1	=	=	PUNCT
ejpam-6062	245	2	0	0	X
ejpam-6062	245	3	.	.	PUNCT
ejpam-6062	246	1	(	(	PUNCT
ejpam-6062	246	2	28	28	NUM
ejpam-6062	246	3	)	)	PUNCT
ejpam-6062	246	4	hence	hence	ADV
ejpam-6062	246	5	,	,	PUNCT
ejpam-6062	246	6	by	by	ADP
ejpam-6062	246	7	applying	apply	VERB
ejpam-6062	246	8	lemma	lemma	PROPN
ejpam-6062	246	9	4	4	NUM
ejpam-6062	246	10	,	,	PUNCT
ejpam-6062	246	11	(	(	PUNCT
ejpam-6062	246	12	12	12	NUM
ejpam-6062	246	13	)	)	PUNCT
ejpam-6062	246	14	and	and	CCONJ
ejpam-6062	246	15	the	the	DET
ejpam-6062	246	16	properties	property	NOUN
ejpam-6062	246	17	of	of	ADP
ejpam-6062	246	18	d∗	d∗	PROPN
ejpam-6062	246	19	g	g	PROPN
ejpam-6062	246	20	and	and	CCONJ
ejpam-6062	246	21	a	a	PRON
ejpam-6062	246	22	,	,	PUNCT
ejpam-6062	246	23	we	we	PRON
ejpam-6062	246	24	get	get	VERB
ejpam-6062	246	25	lim	lim	PROPN
ejpam-6062	246	26	n→∞	n→∞	X
ejpam-6062	246	27	||aixn	||aixn	ADJ
ejpam-6062	246	28	−	−	NOUN
ejpam-6062	246	29	siaixn||	siaixn||	VERB
ejpam-6062	246	30	=	=	SYM
ejpam-6062	246	31	0	0	PROPN
ejpam-6062	246	32	,	,	PUNCT
ejpam-6062	246	33	i	i	PRON
ejpam-6062	246	34	=	=	NOUN
ejpam-6062	246	35	0	0	NUM
ejpam-6062	246	36	,	,	PUNCT
ejpam-6062	246	37	1	1	NUM
ejpam-6062	246	38	,	,	PUNCT
ejpam-6062	246	39	2	2	NUM
ejpam-6062	246	40	,	,	PUNCT
ejpam-6062	246	41	·	·	PUNCT
ejpam-6062	246	42	·	·	PUNCT
ejpam-6062	246	43	·	·	PUNCT
ejpam-6062	246	44	,	,	PUNCT
ejpam-6062	246	45	n.	n.	NOUN
ejpam-6062	246	46	(	(	PUNCT
ejpam-6062	246	47	29	29	NUM
ejpam-6062	246	48	)	)	PUNCT
ejpam-6062	246	49	in	in	ADP
ejpam-6062	246	50	view	view	NOUN
ejpam-6062	246	51	of	of	ADP
ejpam-6062	246	52	(	(	PUNCT
ejpam-6062	246	53	16	16	NUM
ejpam-6062	246	54	)	)	PUNCT
ejpam-6062	246	55	,	,	PUNCT
ejpam-6062	246	56	(	(	PUNCT
ejpam-6062	246	57	26	26	NUM
ejpam-6062	246	58	)	)	PUNCT
ejpam-6062	246	59	,	,	PUNCT
ejpam-6062	246	60	(	(	PUNCT
ejpam-6062	246	61	28	28	NUM
ejpam-6062	246	62	)	)	PUNCT
ejpam-6062	246	63	and	and	CCONJ
ejpam-6062	246	64	lemma	lemma	PROPN
ejpam-6062	246	65	4	4	NUM
ejpam-6062	246	66	,	,	PUNCT
ejpam-6062	246	67	we	we	PRON
ejpam-6062	246	68	obtain	obtain	VERB
ejpam-6062	246	69	that	that	SCONJ
ejpam-6062	246	70	lim	lim	PROPN
ejpam-6062	246	71	n→∞	n→∞	PRON
ejpam-6062	246	72	dg(zn	dg(zn	PROPN
ejpam-6062	246	73	,	,	PUNCT
ejpam-6062	246	74	xn	xn	PUNCT
ejpam-6062	246	75	)	)	PUNCT
ejpam-6062	246	76	=	=	SYM
ejpam-6062	246	77	0	0	PUNCT
ejpam-6062	247	1	=	=	SYM
ejpam-6062	247	2	lim	lim	PROPN
ejpam-6062	247	3	n→∞	n→∞	NUM
ejpam-6062	247	4	||zn	||zn	NOUN
ejpam-6062	247	5	−	−	PROPN
ejpam-6062	247	6	xn||	xn||	PROPN
ejpam-6062	247	7	,	,	PUNCT
ejpam-6062	247	8	(	(	PUNCT
ejpam-6062	247	9	30	30	NUM
ejpam-6062	247	10	)	)	PUNCT
ejpam-6062	247	11	and	and	CCONJ
ejpam-6062	247	12	lim	lim	PROPN
ejpam-6062	247	13	n→∞	n→∞	NUM
ejpam-6062	247	14	dg(yn	dg(yn	PROPN
ejpam-6062	247	15	,	,	PUNCT
ejpam-6062	247	16	zn	zn	X
ejpam-6062	247	17	)	)	PUNCT
ejpam-6062	247	18	=	=	SYM
ejpam-6062	247	19	0	0	PUNCT
ejpam-6062	248	1	=	=	SYM
ejpam-6062	248	2	lim	lim	PROPN
ejpam-6062	248	3	n→∞	n→∞	X
ejpam-6062	249	1	||yn	||yn	NUM
ejpam-6062	249	2	−	−	PROPN
ejpam-6062	249	3	zn||	zn||	PROPN
ejpam-6062	249	4	=	=	PUNCT
ejpam-6062	250	1	0	0	X
ejpam-6062	250	2	.	.	PUNCT
ejpam-6062	251	1	(	(	PUNCT
ejpam-6062	251	2	31	31	NUM
ejpam-6062	251	3	)	)	PUNCT
ejpam-6062	251	4	by	by	ADP
ejpam-6062	251	5	applying	apply	VERB
ejpam-6062	251	6	(	(	PUNCT
ejpam-6062	251	7	30	30	NUM
ejpam-6062	251	8	)	)	PUNCT
ejpam-6062	251	9	and	and	CCONJ
ejpam-6062	251	10	(	(	PUNCT
ejpam-6062	251	11	31	31	NUM
ejpam-6062	251	12	)	)	PUNCT
ejpam-6062	251	13	we	we	PRON
ejpam-6062	251	14	obtain	obtain	VERB
ejpam-6062	251	15	lim	lim	PROPN
ejpam-6062	251	16	n→∞	n→∞	X
ejpam-6062	251	17	dg(yn	dg(yn	PROPN
ejpam-6062	251	18	,	,	PUNCT
ejpam-6062	251	19	xn	xn	X
ejpam-6062	251	20	)	)	PUNCT
ejpam-6062	252	1	=	=	SYM
ejpam-6062	252	2	0	0	PUNCT
ejpam-6062	253	1	=	=	SYM
ejpam-6062	253	2	lim	lim	PROPN
ejpam-6062	253	3	n→∞	n→∞	X
ejpam-6062	253	4	||yn	||yn	NUM
ejpam-6062	253	5	−	−	NOUN
ejpam-6062	253	6	xn||	xn||	PRON
ejpam-6062	253	7	.	.	PUNCT
ejpam-6062	254	1	(	(	PUNCT
ejpam-6062	254	2	32	32	NUM
ejpam-6062	254	3	)	)	PUNCT
ejpam-6062	254	4	more	more	ADV
ejpam-6062	254	5	so	so	ADV
ejpam-6062	254	6	,	,	PUNCT
ejpam-6062	254	7	employing	employ	VERB
ejpam-6062	254	8	condition	condition	NOUN
ejpam-6062	254	9	(	(	PUNCT
ejpam-6062	254	10	i	i	NOUN
ejpam-6062	254	11	)	)	PUNCT
ejpam-6062	254	12	of	of	ADP
ejpam-6062	254	13	assumption	assumption	NOUN
ejpam-6062	254	14	1	1	NUM
ejpam-6062	254	15	and	and	CCONJ
ejpam-6062	254	16	lemma	lemma	PROPN
ejpam-6062	254	17	4	4	NUM
ejpam-6062	254	18	,	,	PUNCT
ejpam-6062	254	19	we	we	PRON
ejpam-6062	254	20	arrive	arrive	VERB
ejpam-6062	254	21	at	at	ADP
ejpam-6062	254	22	lim	lim	PROPN
ejpam-6062	254	23	n→∞	n→∞	NUM
ejpam-6062	254	24	dg(xn+1	dg(xn+1	PROPN
ejpam-6062	254	25	,	,	PUNCT
ejpam-6062	254	26	yn	yn	PROPN
ejpam-6062	254	27	)	)	PUNCT
ejpam-6062	254	28	=	=	SYM
ejpam-6062	254	29	0	0	X
ejpam-6062	255	1	=	=	SYM
ejpam-6062	255	2	lim	lim	PROPN
ejpam-6062	255	3	n→∞	n→∞	NUM
ejpam-6062	255	4	||xn+1	||xn+1	PROPN
ejpam-6062	255	5	−	−	PROPN
ejpam-6062	255	6	yn||	yn||	PROPN
ejpam-6062	255	7	.	.	PUNCT
ejpam-6062	256	1	(	(	PUNCT
ejpam-6062	256	2	33	33	NUM
ejpam-6062	256	3	)	)	PUNCT
ejpam-6062	256	4	we	we	PRON
ejpam-6062	256	5	therefore	therefore	ADV
ejpam-6062	256	6	conclude	conclude	VERB
ejpam-6062	256	7	from	from	ADP
ejpam-6062	256	8	(	(	PUNCT
ejpam-6062	256	9	32	32	NUM
ejpam-6062	256	10	)	)	PUNCT
ejpam-6062	256	11	and	and	CCONJ
ejpam-6062	256	12	(	(	PUNCT
ejpam-6062	256	13	33	33	NUM
ejpam-6062	256	14	)	)	PUNCT
ejpam-6062	256	15	that	that	PRON
ejpam-6062	256	16	lim	lim	PROPN
ejpam-6062	256	17	n→∞	n→∞	NUM
ejpam-6062	256	18	dg(xn+1	dg(xn+1	PROPN
ejpam-6062	256	19	,	,	PUNCT
ejpam-6062	256	20	xn	xn	PROPN
ejpam-6062	256	21	)	)	PUNCT
ejpam-6062	256	22	=	=	SYM
ejpam-6062	256	23	0	0	X
ejpam-6062	257	1	=	=	SYM
ejpam-6062	257	2	lim	lim	PROPN
ejpam-6062	257	3	n→∞	n→∞	X
ejpam-6062	257	4	||xn+1	||xn+1	PROPN
ejpam-6062	257	5	−	−	PROPN
ejpam-6062	257	6	xn||	xn||	PROPN
ejpam-6062	257	7	.	.	PUNCT
ejpam-6062	258	1	(	(	PUNCT
ejpam-6062	258	2	34	34	NUM
ejpam-6062	258	3	)	)	PUNCT
ejpam-6062	258	4	since	since	SCONJ
ejpam-6062	258	5	{	{	PUNCT
ejpam-6062	258	6	xn	xn	X
ejpam-6062	258	7	}	}	PUNCT
ejpam-6062	258	8	is	be	AUX
ejpam-6062	258	9	bounded	bound	VERB
ejpam-6062	258	10	and	and	CCONJ
ejpam-6062	258	11	e	e	NOUN
ejpam-6062	258	12	is	be	AUX
ejpam-6062	258	13	reflexive	reflexive	ADJ
ejpam-6062	258	14	,	,	PUNCT
ejpam-6062	258	15	there	there	PRON
ejpam-6062	258	16	exists	exist	VERB
ejpam-6062	258	17	a	a	DET
ejpam-6062	258	18	subsequence	subsequence	NOUN
ejpam-6062	258	19	{	{	PUNCT
ejpam-6062	258	20	xnk	xnk	PROPN
ejpam-6062	258	21	}	}	PUNCT
ejpam-6062	258	22	of	of	ADP
ejpam-6062	258	23	{	{	PUNCT
ejpam-6062	258	24	xn	xn	NOUN
ejpam-6062	258	25	}	}	PUNCT
ejpam-6062	258	26	such	such	ADJ
ejpam-6062	258	27	that	that	SCONJ
ejpam-6062	258	28	{	{	PUNCT
ejpam-6062	258	29	xnk	xnk	NOUN
ejpam-6062	258	30	}	}	PUNCT
ejpam-6062	258	31	⇀	⇀	PROPN
ejpam-6062	258	32	x∗.	x∗.	PUNCT
ejpam-6062	259	1	also	also	ADV
ejpam-6062	259	2	,	,	PUNCT
ejpam-6062	259	3	from	from	ADP
ejpam-6062	259	4	(	(	PUNCT
ejpam-6062	259	5	30	30	NUM
ejpam-6062	259	6	)	)	PUNCT
ejpam-6062	259	7	and	and	CCONJ
ejpam-6062	259	8	(	(	PUNCT
ejpam-6062	259	9	32	32	NUM
ejpam-6062	259	10	)	)	PUNCT
ejpam-6062	259	11	,	,	PUNCT
ejpam-6062	259	12	there	there	PRON
ejpam-6062	259	13	exist	exist	VERB
ejpam-6062	259	14	subsequences	subsequence	NOUN
ejpam-6062	259	15	{	{	PUNCT
ejpam-6062	259	16	znk	znk	NOUN
ejpam-6062	259	17	}	}	PUNCT
ejpam-6062	259	18	of	of	ADP
ejpam-6062	259	19	{	{	PUNCT
ejpam-6062	259	20	zn	zn	NOUN
ejpam-6062	259	21	}	}	PUNCT
ejpam-6062	259	22	and	and	CCONJ
ejpam-6062	259	23	{	{	PUNCT
ejpam-6062	259	24	ynk	ynk	NOUN
ejpam-6062	259	25	}	}	PUNCT
ejpam-6062	259	26	of	of	ADP
ejpam-6062	259	27	{	{	PUNCT
ejpam-6062	259	28	yn	yn	PROPN
ejpam-6062	259	29	}	}	PUNCT
ejpam-6062	259	30	which	which	PRON
ejpam-6062	259	31	converge	converge	VERB
ejpam-6062	259	32	weakly	weakly	ADV
ejpam-6062	259	33	to	to	ADP
ejpam-6062	259	34	x∗	x∗	PROPN
ejpam-6062	259	35	respectively	respectively	ADV
ejpam-6062	259	36	.	.	PUNCT
ejpam-6062	260	1	thus	thus	ADV
ejpam-6062	260	2	,	,	PUNCT
ejpam-6062	260	3	for	for	ADP
ejpam-6062	260	4	each	each	DET
ejpam-6062	260	5	i	i	NOUN
ejpam-6062	260	6	=	=	NOUN
ejpam-6062	260	7	0	0	NUM
ejpam-6062	260	8	,	,	PUNCT
ejpam-6062	260	9	1	1	NUM
ejpam-6062	260	10	,	,	PUNCT
ejpam-6062	260	11	2	2	NUM
ejpam-6062	260	12	,	,	PUNCT
ejpam-6062	260	13	·	·	PUNCT
ejpam-6062	260	14	·	·	PUNCT
ejpam-6062	260	15	·	·	PUNCT
ejpam-6062	260	16	n	n	CCONJ
ejpam-6062	260	17	,	,	PUNCT
ejpam-6062	260	18	ai	ai	VERB
ejpam-6062	260	19	is	be	AUX
ejpam-6062	260	20	a	a	DET
ejpam-6062	260	21	bounded	bounded	ADJ
ejpam-6062	260	22	linear	linear	ADJ
ejpam-6062	260	23	operator	operator	NOUN
ejpam-6062	260	24	,	,	PUNCT
ejpam-6062	260	25	then	then	ADV
ejpam-6062	260	26	it	it	PRON
ejpam-6062	260	27	follows	follow	VERB
ejpam-6062	260	28	that	that	PRON
ejpam-6062	260	29	aixnk	aixnk	NOUN
ejpam-6062	260	30	⇀	⇀	PROPN
ejpam-6062	260	31	aix	aix	NOUN
ejpam-6062	260	32	∗.	∗.	PROPN
ejpam-6062	260	33	hence	hence	ADV
ejpam-6062	260	34	,	,	PUNCT
ejpam-6062	260	35	using	use	VERB
ejpam-6062	260	36	the	the	DET
ejpam-6062	260	37	demiclosedness	demiclosedness	NOUN
ejpam-6062	260	38	principle	principle	NOUN
ejpam-6062	260	39	and	and	CCONJ
ejpam-6062	260	40	(	(	PUNCT
ejpam-6062	260	41	29	29	NUM
ejpam-6062	260	42	)	)	PUNCT
ejpam-6062	260	43	,	,	PUNCT
ejpam-6062	260	44	we	we	PRON
ejpam-6062	260	45	arrive	arrive	VERB
ejpam-6062	260	46	at	at	ADP
ejpam-6062	260	47	aix	aix	PROPN
ejpam-6062	260	48	∗	∗	PROPN
ejpam-6062	260	49	∈	∈	PROPN
ejpam-6062	260	50	fix(si	fix(si	PROPN
ejpam-6062	260	51	)	)	PUNCT
ejpam-6062	260	52	for	for	ADP
ejpam-6062	260	53	all	all	DET
ejpam-6062	260	54	i	i	PRON
ejpam-6062	260	55	=	=	NOUN
ejpam-6062	260	56	0	0	NUM
ejpam-6062	260	57	,	,	PUNCT
ejpam-6062	260	58	1	1	NUM
ejpam-6062	260	59	,	,	PUNCT
ejpam-6062	260	60	2	2	NUM
ejpam-6062	260	61	,	,	PUNCT
ejpam-6062	260	62	·	·	PUNCT
ejpam-6062	260	63	·	·	PUNCT
ejpam-6062	261	1	·	·	PUNCT
ejpam-6062	261	2	n.	n.	PROPN
ejpam-6062	261	3	also	also	ADV
ejpam-6062	261	4	,	,	PUNCT
ejpam-6062	261	5	h.	h.	PROPN
ejpam-6062	261	6	a.	a.	PROPN
ejpam-6062	261	7	abass	abass	PROPN
ejpam-6062	261	8	et	et	PROPN
ejpam-6062	261	9	al	al	PROPN
ejpam-6062	261	10	.	.	PUNCT
ejpam-6062	261	11	/	/	SYM
ejpam-6062	261	12	eur	eur	PROPN
ejpam-6062	261	13	.	.	PUNCT
ejpam-6062	262	1	j.	j.	PROPN
ejpam-6062	262	2	pure	pure	PROPN
ejpam-6062	262	3	appl	appl	PROPN
ejpam-6062	262	4	.	.	PROPN
ejpam-6062	262	5	math	math	PROPN
ejpam-6062	262	6	,	,	PUNCT
ejpam-6062	262	7	18	18	NUM
ejpam-6062	262	8	(	(	PUNCT
ejpam-6062	262	9	2	2	NUM
ejpam-6062	262	10	)	)	PUNCT
ejpam-6062	262	11	(	(	PUNCT
ejpam-6062	262	12	2025	2025	NUM
ejpam-6062	262	13	)	)	PUNCT
ejpam-6062	262	14	,	,	PUNCT
ejpam-6062	262	15	6062	6062	NUM
ejpam-6062	262	16	14	14	NUM
ejpam-6062	262	17	of	of	ADP
ejpam-6062	262	18	22	22	NUM
ejpam-6062	262	19	from	from	ADP
ejpam-6062	262	20	(	(	PUNCT
ejpam-6062	262	21	26	26	NUM
ejpam-6062	262	22	)	)	PUNCT
ejpam-6062	262	23	,	,	PUNCT
ejpam-6062	262	24	we	we	PRON
ejpam-6062	262	25	obtain	obtain	VERB
ejpam-6062	262	26	that	that	SCONJ
ejpam-6062	262	27	x∗	x∗	PROPN
ejpam-6062	262	28	∈	∈	PROPN
ejpam-6062	262	29	ˆfix(t	ˆfix(t	PROPN
ejpam-6062	262	30	j	j	PROPN
ejpam-6062	262	31	σ	σ	PROPN
ejpam-6062	262	32	)	)	PUNCT
ejpam-6062	262	33	=	=	SYM
ejpam-6062	263	1	fix(t	fix(t	PROPN
ejpam-6062	263	2	j	j	PROPN
ejpam-6062	263	3	σ	σ	PROPN
ejpam-6062	263	4	)	)	PUNCT
ejpam-6062	263	5	for	for	ADP
ejpam-6062	263	6	each	each	PRON
ejpam-6062	263	7	j	j	PROPN
ejpam-6062	263	8	=	=	SYM
ejpam-6062	263	9	1	1	NUM
ejpam-6062	263	10	,	,	PUNCT
ejpam-6062	263	11	2	2	NUM
ejpam-6062	263	12	,	,	PUNCT
ejpam-6062	263	13	·	·	PUNCT
ejpam-6062	263	14	·	·	PUNCT
ejpam-6062	263	15	·	·	PUNCT
ejpam-6062	263	16	m.	m.	NOUN
ejpam-6062	263	17	this	this	PRON
ejpam-6062	263	18	implies	imply	VERB
ejpam-6062	263	19	from	from	ADP
ejpam-6062	263	20	lemma	lemma	PROPN
ejpam-6062	263	21	7	7	NUM
ejpam-6062	263	22	that	that	PRON
ejpam-6062	263	23	x∗	x∗	PROPN
ejpam-6062	263	24	∈	∈	PROPN
ejpam-6062	263	25	m⋂	m⋂	NOUN
ejpam-6062	264	1	j=1	j=1	PROPN
ejpam-6062	264	2	fix(t	fix(t	PROPN
ejpam-6062	264	3	j	j	PROPN
ejpam-6062	264	4	σ	σ	PROPN
ejpam-6062	264	5	)	)	PUNCT
ejpam-6062	264	6	=	=	SYM
ejpam-6062	265	1	m⋂	m⋂	NOUN
ejpam-6062	265	2	j=1	j=1	NOUN
ejpam-6062	265	3	(	(	PUNCT
ejpam-6062	265	4	fj	fj	PROPN
ejpam-6062	265	5	+	+	CCONJ
ejpam-6062	265	6	gj	gj	NOUN
ejpam-6062	265	7	)	)	PUNCT
ejpam-6062	265	8	−1(0	−1(0	NOUN
ejpam-6062	265	9	)	)	PUNCT
ejpam-6062	265	10	.	.	PUNCT
ejpam-6062	266	1	therefore	therefore	ADV
ejpam-6062	266	2	,	,	PUNCT
ejpam-6062	266	3	we	we	PRON
ejpam-6062	266	4	conclude	conclude	VERB
ejpam-6062	266	5	that	that	SCONJ
ejpam-6062	266	6	x∗	x∗	PROPN
ejpam-6062	266	7	∈	∈	PROPN
ejpam-6062	266	8	ω	ω	PROPN
ejpam-6062	266	9	.	.	PUNCT
ejpam-6062	267	1	next	next	ADJ
ejpam-6062	267	2	is	be	AUX
ejpam-6062	267	3	to	to	PART
ejpam-6062	267	4	show	show	VERB
ejpam-6062	267	5	that	that	SCONJ
ejpam-6062	267	6	⟨∇g	⟨∇g	PROPN
ejpam-6062	267	7	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	267	8	e(z	e(z	PROPN
ejpam-6062	267	9	)	)	PUNCT
ejpam-6062	267	10	,	,	PUNCT
ejpam-6062	267	11	xn+1	xn+1	PROPN
ejpam-6062	267	12	−	−	PROPN
ejpam-6062	267	13	z⟩	z⟩	NOUN
ejpam-6062	267	14	≤	≤	NUM
ejpam-6062	267	15	0	0	NUM
ejpam-6062	267	16	.	.	PUNCT
ejpam-6062	268	1	now	now	ADV
ejpam-6062	268	2	,	,	PUNCT
ejpam-6062	268	3	from	from	ADP
ejpam-6062	268	4	(	(	PUNCT
ejpam-6062	268	5	34	34	NUM
ejpam-6062	268	6	)	)	PUNCT
ejpam-6062	268	7	,	,	PUNCT
ejpam-6062	268	8	we	we	PRON
ejpam-6062	268	9	have	have	VERB
ejpam-6062	268	10	lim	lim	PROPN
ejpam-6062	268	11	sup	sup	PROPN
ejpam-6062	268	12	n→∞	n→∞	NUM
ejpam-6062	268	13	⟨∇g	⟨∇g	NOUN
ejpam-6062	269	1	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	269	2	e(z	e(z	PROPN
ejpam-6062	269	3	)	)	PUNCT
ejpam-6062	269	4	,	,	PUNCT
ejpam-6062	270	1	xn+1	xn+1	PROPN
ejpam-6062	270	2	−	−	NOUN
ejpam-6062	270	3	z⟩	z⟩	X
ejpam-6062	271	1	=	=	PROPN
ejpam-6062	271	2	lim	lim	PROPN
ejpam-6062	271	3	k→∞	k→∞	PROPN
ejpam-6062	271	4	⟨∇g	⟨∇g	PROPN
ejpam-6062	271	5	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	271	6	e(z	e(z	PROPN
ejpam-6062	271	7	)	)	PUNCT
ejpam-6062	271	8	,	,	PUNCT
ejpam-6062	271	9	xnk+1	xnk+1	PUNCT
ejpam-6062	271	10	−	−	PROPN
ejpam-6062	271	11	z⟩	z⟩	NOUN
ejpam-6062	271	12	≤	≤	PROPN
ejpam-6062	271	13	⟨∇g	⟨∇g	PUNCT
ejpam-6062	271	14	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	271	15	e(z	e(z	PROPN
ejpam-6062	271	16	)	)	PUNCT
ejpam-6062	271	17	,	,	PUNCT
ejpam-6062	271	18	x	x	X
ejpam-6062	271	19	∗	∗	NOUN
ejpam-6062	271	20	−	−	PROPN
ejpam-6062	271	21	z⟩.	z⟩.	NOUN
ejpam-6062	271	22	hence	hence	ADV
ejpam-6062	271	23	,	,	PUNCT
ejpam-6062	271	24	we	we	PRON
ejpam-6062	271	25	obtain	obtain	VERB
ejpam-6062	271	26	that	that	SCONJ
ejpam-6062	271	27	lim	lim	PROPN
ejpam-6062	271	28	sup	sup	PROPN
ejpam-6062	271	29	k→∞	k→∞	NOUN
ejpam-6062	271	30	⟨∇g	⟨∇g	NOUN
ejpam-6062	272	1	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	272	2	e(z	e(z	PROPN
ejpam-6062	272	3	)	)	PUNCT
ejpam-6062	273	1	,	,	PUNCT
ejpam-6062	273	2	xn+1	xn+1	PROPN
ejpam-6062	273	3	−	−	PROPN
ejpam-6062	273	4	z⟩	z⟩	NOUN
ejpam-6062	273	5	≤	≤	PROPN
ejpam-6062	273	6	⟨∇g	⟨∇g	PUNCT
ejpam-6062	274	1	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	274	2	e(z	e(z	PROPN
ejpam-6062	274	3	)	)	PUNCT
ejpam-6062	274	4	,	,	PUNCT
ejpam-6062	274	5	x	x	X
ejpam-6062	274	6	∗	∗	NOUN
ejpam-6062	274	7	−	−	PROPN
ejpam-6062	274	8	z⟩	z⟩	NOUN
ejpam-6062	274	9	≤	≤	NUM
ejpam-6062	274	10	0	0	NUM
ejpam-6062	274	11	.	.	PUNCT
ejpam-6062	275	1	(	(	PUNCT
ejpam-6062	275	2	35	35	NUM
ejpam-6062	275	3	)	)	PUNCT
ejpam-6062	275	4	next	next	ADV
ejpam-6062	275	5	is	be	AUX
ejpam-6062	275	6	to	to	PART
ejpam-6062	275	7	prove	prove	VERB
ejpam-6062	275	8	that	that	SCONJ
ejpam-6062	275	9	{	{	PUNCT
ejpam-6062	275	10	xn	xn	X
ejpam-6062	275	11	}	}	PUNCT
ejpam-6062	275	12	converges	converge	VERB
ejpam-6062	275	13	strongly	strongly	ADV
ejpam-6062	275	14	to	to	ADP
ejpam-6062	275	15	v	v	PROPN
ejpam-6062	275	16	∈	∈	PROPN
ejpam-6062	275	17	ω	ω	NOUN
ejpam-6062	275	18	.	.	PUNCT
ejpam-6062	276	1	using	use	VERB
ejpam-6062	276	2	lemma	lemma	PROPN
ejpam-6062	276	3	2	2	NUM
ejpam-6062	276	4	,	,	PUNCT
ejpam-6062	276	5	(	(	PUNCT
ejpam-6062	276	6	18	18	NUM
ejpam-6062	276	7	)	)	PUNCT
ejpam-6062	276	8	and	and	CCONJ
ejpam-6062	276	9	(	(	PUNCT
ejpam-6062	276	10	20	20	NUM
ejpam-6062	276	11	)	)	PUNCT
ejpam-6062	276	12	,	,	PUNCT
ejpam-6062	276	13	dg(v	dg(v	X
ejpam-6062	276	14	,	,	PUNCT
ejpam-6062	276	15	xn+1	xn+1	NUM
ejpam-6062	276	16	)	)	PUNCT
ejpam-6062	276	17	=	=	SYM
ejpam-6062	277	1	dg(v	dg(v	X
ejpam-6062	277	2	,	,	PUNCT
ejpam-6062	277	3	(	(	PUNCT
ejpam-6062	277	4	∇g	∇g	NOUN
ejpam-6062	277	5	e	e	NOUN
ejpam-6062	277	6	)	)	PUNCT
ejpam-6062	277	7	−1	−1	NOUN
ejpam-6062	277	8	[	[	PUNCT
ejpam-6062	277	9	αn∇g	αn∇g	NOUN
ejpam-6062	277	10	e(u	e(u	PROPN
ejpam-6062	277	11	)	)	PUNCT
ejpam-6062	278	1	+	+	CCONJ
ejpam-6062	278	2	(	(	PUNCT
ejpam-6062	278	3	1−	1−	NUM
ejpam-6062	278	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	278	5	e(yn	e(yn	NOUN
ejpam-6062	278	6	)	)	PUNCT
ejpam-6062	278	7	]	]	PUNCT
ejpam-6062	278	8	)	)	PUNCT
ejpam-6062	279	1	=	=	SYM
ejpam-6062	279	2	vg(v	vg(v	X
ejpam-6062	279	3	,	,	PUNCT
ejpam-6062	279	4	αn∇g	αn∇g	PROPN
ejpam-6062	279	5	e(u	e(u	PROPN
ejpam-6062	279	6	)	)	PUNCT
ejpam-6062	280	1	+	+	CCONJ
ejpam-6062	280	2	(	(	PUNCT
ejpam-6062	280	3	1−	1−	NUM
ejpam-6062	280	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	280	5	e(yn	e(yn	NOUN
ejpam-6062	280	6	)	)	PUNCT
ejpam-6062	280	7	)	)	PUNCT
ejpam-6062	281	1	≤	≤	NOUN
ejpam-6062	281	2	vg(v	vg(v	NOUN
ejpam-6062	281	3	,	,	PUNCT
ejpam-6062	281	4	αn∇g	αn∇g	PROPN
ejpam-6062	281	5	e(u	e(u	PROPN
ejpam-6062	281	6	)	)	PUNCT
ejpam-6062	282	1	+	+	CCONJ
ejpam-6062	282	2	(	(	PUNCT
ejpam-6062	282	3	1−	1−	NUM
ejpam-6062	282	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	282	5	e(yn)−	e(yn)−	ADP
ejpam-6062	282	6	αn(∇g	αn(∇g	PROPN
ejpam-6062	282	7	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	282	8	e(v	e(v	NOUN
ejpam-6062	282	9	)	)	PUNCT
ejpam-6062	282	10	)	)	PUNCT
ejpam-6062	283	1	+	+	CCONJ
ejpam-6062	283	2	⟨αn(∇g	⟨αn(∇g	PROPN
ejpam-6062	283	3	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	283	4	e(v	e(v	NOUN
ejpam-6062	283	5	)	)	PUNCT
ejpam-6062	283	6	)	)	PUNCT
ejpam-6062	283	7	,	,	PUNCT
ejpam-6062	283	8	xn+1	xn+1	PROPN
ejpam-6062	283	9	−	−	NOUN
ejpam-6062	283	10	v)⟩	v)⟩	NOUN
ejpam-6062	283	11	=	=	SYM
ejpam-6062	283	12	vg(v	vg(v	X
ejpam-6062	283	13	,	,	PUNCT
ejpam-6062	283	14	αn∇g	αn∇g	NOUN
ejpam-6062	283	15	e(v	e(v	NOUN
ejpam-6062	283	16	)	)	PUNCT
ejpam-6062	284	1	+	+	CCONJ
ejpam-6062	284	2	(	(	PUNCT
ejpam-6062	284	3	1−	1−	NUM
ejpam-6062	284	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	284	5	e(yn	e(yn	NOUN
ejpam-6062	284	6	)	)	PUNCT
ejpam-6062	284	7	)	)	PUNCT
ejpam-6062	285	1	+	+	CCONJ
ejpam-6062	285	2	αn⟨∇g	αn⟨∇g	NOUN
ejpam-6062	285	3	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	285	4	e(v	e(v	NOUN
ejpam-6062	285	5	)	)	PUNCT
ejpam-6062	285	6	,	,	PUNCT
ejpam-6062	285	7	xn+1	xn+1	PROPN
ejpam-6062	285	8	−	−	NOUN
ejpam-6062	285	9	v⟩	v⟩	VERB
ejpam-6062	285	10	≤	≤	NOUN
ejpam-6062	285	11	αnvg(v,∇g	αnvg(v,∇g	NUM
ejpam-6062	285	12	e(v	e(v	NOUN
ejpam-6062	285	13	)	)	PUNCT
ejpam-6062	285	14	)	)	PUNCT
ejpam-6062	286	1	+	+	CCONJ
ejpam-6062	286	2	(	(	PUNCT
ejpam-6062	286	3	1−	1−	NUM
ejpam-6062	286	4	αn)vg(v,∇g	αn)vg(v,∇g	ADJ
ejpam-6062	286	5	e(yn	e(yn	X
ejpam-6062	286	6	)	)	PUNCT
ejpam-6062	286	7	)	)	PUNCT
ejpam-6062	287	1	+	+	CCONJ
ejpam-6062	287	2	αn⟨∇g	αn⟨∇g	NOUN
ejpam-6062	287	3	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	287	4	e(v	e(v	NOUN
ejpam-6062	287	5	)	)	PUNCT
ejpam-6062	287	6	,	,	PUNCT
ejpam-6062	287	7	xn+1	xn+1	PROPN
ejpam-6062	287	8	−	−	NOUN
ejpam-6062	287	9	v⟩	v⟩	PUNCT
ejpam-6062	287	10	=	=	SYM
ejpam-6062	287	11	αndg(v	αndg(v	NUM
ejpam-6062	287	12	,	,	PUNCT
ejpam-6062	287	13	v	v	NOUN
ejpam-6062	287	14	)	)	PUNCT
ejpam-6062	287	15	+	+	CCONJ
ejpam-6062	287	16	(	(	PUNCT
ejpam-6062	287	17	1−	1−	NUM
ejpam-6062	287	18	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	287	19	,	,	PUNCT
ejpam-6062	287	20	yn	yn	PROPN
ejpam-6062	287	21	)	)	PUNCT
ejpam-6062	287	22	+	+	NUM
ejpam-6062	287	23	αn⟨∇g	αn⟨∇g	NOUN
ejpam-6062	287	24	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	287	25	e(v	e(v	NOUN
ejpam-6062	287	26	)	)	PUNCT
ejpam-6062	287	27	,	,	PUNCT
ejpam-6062	287	28	xn+1	xn+1	PROPN
ejpam-6062	287	29	−	−	NOUN
ejpam-6062	287	30	v⟩	v⟩	ADJ
ejpam-6062	287	31	≤	≤	NOUN
ejpam-6062	287	32	(	(	PUNCT
ejpam-6062	287	33	1−	1−	NUM
ejpam-6062	287	34	αn)dg(v	αn)dg(v	PROPN
ejpam-6062	287	35	,	,	PUNCT
ejpam-6062	287	36	xn	xn	PUNCT
ejpam-6062	287	37	)	)	PUNCT
ejpam-6062	288	1	+	+	NUM
ejpam-6062	288	2	αn⟨∇g	αn⟨∇g	NOUN
ejpam-6062	288	3	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	288	4	e(v	e(v	NOUN
ejpam-6062	288	5	)	)	PUNCT
ejpam-6062	288	6	,	,	PUNCT
ejpam-6062	288	7	xn+1	xn+1	PROPN
ejpam-6062	288	8	−	−	PROPN
ejpam-6062	288	9	v⟩.	v⟩.	X
ejpam-6062	288	10	(	(	PUNCT
ejpam-6062	288	11	36	36	NUM
ejpam-6062	288	12	)	)	PUNCT
ejpam-6062	288	13	in	in	ADP
ejpam-6062	288	14	view	view	NOUN
ejpam-6062	288	15	of	of	ADP
ejpam-6062	288	16	lemma	lemma	PROPN
ejpam-6062	288	17	10	10	NUM
ejpam-6062	288	18	and	and	CCONJ
ejpam-6062	288	19	(	(	PUNCT
ejpam-6062	288	20	35	35	NUM
ejpam-6062	288	21	)	)	PUNCT
ejpam-6062	288	22	,	,	PUNCT
ejpam-6062	288	23	we	we	PRON
ejpam-6062	288	24	conclude	conclude	VERB
ejpam-6062	288	25	that	that	SCONJ
ejpam-6062	288	26	lim	lim	PROPN
ejpam-6062	288	27	n→∞	n→∞	NUM
ejpam-6062	288	28	dg(v	dg(v	PROPN
ejpam-6062	288	29	,	,	PUNCT
ejpam-6062	288	30	xn	xn	PUNCT
ejpam-6062	288	31	)	)	PUNCT
ejpam-6062	288	32	=	=	SYM
ejpam-6062	289	1	0	0	X
ejpam-6062	289	2	.	.	PUNCT
ejpam-6062	289	3	therefore	therefore	ADV
ejpam-6062	289	4	{	{	PUNCT
ejpam-6062	289	5	xn	xn	X
ejpam-6062	289	6	}	}	PUNCT
ejpam-6062	289	7	converges	converge	VERB
ejpam-6062	289	8	strongly	strongly	ADV
ejpam-6062	289	9	to	to	ADP
ejpam-6062	289	10	v.	v.	NOUN
ejpam-6062	289	11	case	case	NOUN
ejpam-6062	289	12	2	2	NUM
ejpam-6062	289	13	:	:	PUNCT
ejpam-6062	289	14	suppose	suppose	VERB
ejpam-6062	289	15	that	that	SCONJ
ejpam-6062	289	16	there	there	PRON
ejpam-6062	289	17	exists	exist	VERB
ejpam-6062	289	18	a	a	DET
ejpam-6062	289	19	subsequence	subsequence	NOUN
ejpam-6062	289	20	{	{	PUNCT
ejpam-6062	289	21	nk	nk	NOUN
ejpam-6062	289	22	}	}	PUNCT
ejpam-6062	289	23	of	of	ADP
ejpam-6062	289	24	{	{	PUNCT
ejpam-6062	289	25	n	n	CCONJ
ejpam-6062	289	26	}	}	PUNCT
ejpam-6062	289	27	such	such	ADJ
ejpam-6062	289	28	that	that	PRON
ejpam-6062	289	29	dg(v	dg(v	NOUN
ejpam-6062	289	30	,	,	PUNCT
ejpam-6062	289	31	xnk	xnk	PROPN
ejpam-6062	289	32	)	)	PUNCT
ejpam-6062	289	33	<	<	X
ejpam-6062	289	34	dg(v	dg(v	X
ejpam-6062	289	35	,	,	PUNCT
ejpam-6062	289	36	xnk+1	xnk+1	X
ejpam-6062	289	37	)	)	PUNCT
ejpam-6062	289	38	for	for	ADP
ejpam-6062	289	39	all	all	DET
ejpam-6062	289	40	k	k	PROPN
ejpam-6062	289	41	∈	∈	PROPN
ejpam-6062	289	42	n.	n.	NOUN
ejpam-6062	289	43	we	we	PRON
ejpam-6062	289	44	define	define	VERB
ejpam-6062	289	45	a	a	DET
ejpam-6062	289	46	positive	positive	ADJ
ejpam-6062	289	47	integer	integer	NOUN
ejpam-6062	289	48	sequence	sequence	NOUN
ejpam-6062	289	49	{	{	PUNCT
ejpam-6062	289	50	τ(n	τ(n	PROPN
ejpam-6062	289	51	)	)	PUNCT
ejpam-6062	289	52	}	}	PUNCT
ejpam-6062	289	53	by	by	ADP
ejpam-6062	289	54	τ(n	τ(n	NOUN
ejpam-6062	289	55	)	)	PUNCT
ejpam-6062	289	56	:	:	PUNCT
ejpam-6062	289	57	=	=	PUNCT
ejpam-6062	289	58	max{k	max{k	PROPN
ejpam-6062	289	59	∈	∈	PROPN
ejpam-6062	289	60	n	n	CCONJ
ejpam-6062	289	61	:	:	PUNCT
ejpam-6062	289	62	dg(v	dg(v	X
ejpam-6062	289	63	,	,	PUNCT
ejpam-6062	289	64	xk	xk	X
ejpam-6062	289	65	)	)	PUNCT
ejpam-6062	289	66	<	<	X
ejpam-6062	289	67	dg(v	dg(v	X
ejpam-6062	289	68	,	,	PUNCT
ejpam-6062	289	69	xk+1	xk+1	NUM
ejpam-6062	289	70	)	)	PUNCT
ejpam-6062	289	71	}	}	PUNCT
ejpam-6062	289	72	for	for	ADP
ejpam-6062	289	73	all	all	PRON
ejpam-6062	289	74	n	n	DET
ejpam-6062	289	75	≥	≥	NOUN
ejpam-6062	289	76	n0	n0	NUM
ejpam-6062	289	77	(	(	PUNCT
ejpam-6062	289	78	for	for	ADP
ejpam-6062	289	79	some	some	DET
ejpam-6062	289	80	n0	n0	NOUN
ejpam-6062	289	81	large	large	ADJ
ejpam-6062	289	82	enough	enough	ADV
ejpam-6062	289	83	)	)	PUNCT
ejpam-6062	289	84	.	.	PUNCT
ejpam-6062	290	1	applying	apply	VERB
ejpam-6062	290	2	lemma	lemma	PROPN
ejpam-6062	290	3	11	11	NUM
ejpam-6062	290	4	,	,	PUNCT
ejpam-6062	290	5	we	we	PRON
ejpam-6062	290	6	have	have	VERB
ejpam-6062	290	7	{	{	PUNCT
ejpam-6062	290	8	τ(n	τ(n	NOUN
ejpam-6062	290	9	)	)	PUNCT
ejpam-6062	290	10	}	}	PUNCT
ejpam-6062	290	11	to	to	PART
ejpam-6062	290	12	be	be	AUX
ejpam-6062	290	13	non	non	ADJ
ejpam-6062	290	14	-	-	ADJ
ejpam-6062	290	15	decreasing	decrease	VERB
ejpam-6062	290	16	sequence	sequence	NOUN
ejpam-6062	290	17	such	such	ADJ
ejpam-6062	290	18	that	that	DET
ejpam-6062	290	19	τ(n	τ(n	NOUN
ejpam-6062	290	20	)	)	PUNCT
ejpam-6062	290	21	→	→	SYM
ejpam-6062	290	22	∞	∞	PROPN
ejpam-6062	290	23	as	as	ADP
ejpam-6062	290	24	n	n	PROPN
ejpam-6062	290	25	→	→	SYM
ejpam-6062	290	26	∞	∞	PROPN
ejpam-6062	290	27	and	and	CCONJ
ejpam-6062	290	28	dg(v	dg(v	PUNCT
ejpam-6062	290	29	,	,	PUNCT
ejpam-6062	290	30	xτ(n))−dg(v	xτ(n))−dg(v	NOUN
ejpam-6062	290	31	,	,	PUNCT
ejpam-6062	290	32	xτ(n)+1	xτ(n)+1	PROPN
ejpam-6062	290	33	)	)	PUNCT
ejpam-6062	290	34	≤	≤	NOUN
ejpam-6062	290	35	0	0	NUM
ejpam-6062	290	36	.	.	PUNCT
ejpam-6062	291	1	h.	h.	PROPN
ejpam-6062	291	2	a.	a.	PROPN
ejpam-6062	291	3	abass	abass	PROPN
ejpam-6062	291	4	et	et	PROPN
ejpam-6062	291	5	al	al	PROPN
ejpam-6062	291	6	.	.	PUNCT
ejpam-6062	291	7	/	/	SYM
ejpam-6062	291	8	eur	eur	PROPN
ejpam-6062	291	9	.	.	PUNCT
ejpam-6062	292	1	j.	j.	PROPN
ejpam-6062	292	2	pure	pure	PROPN
ejpam-6062	292	3	appl	appl	PROPN
ejpam-6062	292	4	.	.	PROPN
ejpam-6062	292	5	math	math	PROPN
ejpam-6062	292	6	,	,	PUNCT
ejpam-6062	292	7	18	18	NUM
ejpam-6062	292	8	(	(	PUNCT
ejpam-6062	292	9	2	2	NUM
ejpam-6062	292	10	)	)	PUNCT
ejpam-6062	292	11	(	(	PUNCT
ejpam-6062	292	12	2025	2025	NUM
ejpam-6062	292	13	)	)	PUNCT
ejpam-6062	292	14	,	,	PUNCT
ejpam-6062	292	15	6062	6062	NUM
ejpam-6062	292	16	15	15	NUM
ejpam-6062	292	17	of	of	ADP
ejpam-6062	292	18	22	22	NUM
ejpam-6062	292	19	following	follow	VERB
ejpam-6062	292	20	the	the	DET
ejpam-6062	292	21	same	same	ADJ
ejpam-6062	292	22	argument	argument	NOUN
ejpam-6062	292	23	to	to	ADP
ejpam-6062	292	24	the	the	DET
ejpam-6062	292	25	one	one	NOUN
ejpam-6062	292	26	used	use	VERB
ejpam-6062	292	27	in	in	ADP
ejpam-6062	292	28	case	case	NOUN
ejpam-6062	292	29	1	1	NUM
ejpam-6062	292	30	of	of	ADP
ejpam-6062	292	31	the	the	DET
ejpam-6062	292	32	proof	proof	NOUN
ejpam-6062	292	33	of	of	ADP
ejpam-6062	292	34	(	(	PUNCT
ejpam-6062	292	35	16	16	NUM
ejpam-6062	292	36	)	)	PUNCT
ejpam-6062	292	37	,	,	PUNCT
ejpam-6062	292	38	we	we	PRON
ejpam-6062	292	39	obtain	obtain	VERB
ejpam-6062	292	40	that	that	SCONJ
ejpam-6062	292	41			PROPN
ejpam-6062	292	42	lim	lim	PROPN
ejpam-6062	292	43	τ(n)→∞	τ(n)→∞	PROPN
ejpam-6062	292	44	dg(t	dg(t	PROPN
ejpam-6062	292	45	j	j	PROPN
ejpam-6062	292	46	σzτ(n	σzτ(n	PROPN
ejpam-6062	292	47	)	)	PUNCT
ejpam-6062	292	48	,	,	PUNCT
ejpam-6062	292	49	zτ(n	zτ(n	NOUN
ejpam-6062	292	50	)	)	PUNCT
ejpam-6062	292	51	)	)	PUNCT
ejpam-6062	293	1	=	=	PUNCT
ejpam-6062	293	2	0	0	NUM
ejpam-6062	293	3	,	,	PUNCT
ejpam-6062	293	4	for	for	ADP
ejpam-6062	293	5	j	j	PROPN
ejpam-6062	293	6	=	=	SYM
ejpam-6062	293	7	1	1	NUM
ejpam-6062	293	8	,	,	PUNCT
ejpam-6062	293	9	2	2	NUM
ejpam-6062	293	10	,	,	PUNCT
ejpam-6062	293	11	·	·	PUNCT
ejpam-6062	293	12	·	·	PUNCT
ejpam-6062	293	13	·	·	PUNCT
ejpam-6062	293	14	,	,	PUNCT
ejpam-6062	293	15	m	m	PROPN
ejpam-6062	293	16	,	,	PUNCT
ejpam-6062	293	17	lim	lim	PROPN
ejpam-6062	293	18	τ(n)→∞	τ(n)→∞	PROPN
ejpam-6062	293	19	||aixτ(n	||aixτ(n	NUM
ejpam-6062	293	20	)	)	PUNCT
ejpam-6062	293	21	−	−	NOUN
ejpam-6062	293	22	siaixτ(n)||	siaixτ(n)||	NOUN
ejpam-6062	293	23	=	=	NOUN
ejpam-6062	293	24	0	0	NUM
ejpam-6062	293	25	,	,	PUNCT
ejpam-6062	293	26	for	for	ADP
ejpam-6062	293	27	i	i	PROPN
ejpam-6062	293	28	=	=	SYM
ejpam-6062	293	29	0	0	NUM
ejpam-6062	293	30	,	,	PUNCT
ejpam-6062	293	31	1	1	NUM
ejpam-6062	293	32	,	,	PUNCT
ejpam-6062	293	33	2	2	NUM
ejpam-6062	293	34	,	,	PUNCT
ejpam-6062	293	35	·	·	PUNCT
ejpam-6062	293	36	·	·	PUNCT
ejpam-6062	293	37	·	·	PUNCT
ejpam-6062	293	38	,	,	PUNCT
ejpam-6062	293	39	n	n	CCONJ
ejpam-6062	293	40	,	,	PUNCT
ejpam-6062	293	41	r	r	NOUN
ejpam-6062	293	42	lim	lim	PROPN
ejpam-6062	293	43	τ(n)→∞	τ(n)→∞	PROPN
ejpam-6062	293	44	dg(zτ(n	dg(zτ(n	PROPN
ejpam-6062	293	45	)	)	PUNCT
ejpam-6062	293	46	,	,	PUNCT
ejpam-6062	293	47	xτ(n	xτ(n	NUM
ejpam-6062	293	48	)	)	PUNCT
ejpam-6062	293	49	)	)	PUNCT
ejpam-6062	294	1	=	=	SYM
ejpam-6062	294	2	0	0	NUM
ejpam-6062	294	3	,	,	PUNCT
ejpam-6062	294	4	lim	lim	PROPN
ejpam-6062	294	5	τ(n)→∞	τ(n)→∞	VERB
ejpam-6062	294	6	dg(yτ(n	dg(yτ(n	PROPN
ejpam-6062	294	7	)	)	PUNCT
ejpam-6062	294	8	,	,	PUNCT
ejpam-6062	294	9	xτ(n	xτ(n	NUM
ejpam-6062	294	10	)	)	PUNCT
ejpam-6062	294	11	)	)	PUNCT
ejpam-6062	295	1	=	=	SYM
ejpam-6062	295	2	0	0	NUM
ejpam-6062	295	3	,	,	PUNCT
ejpam-6062	295	4	lim	lim	PROPN
ejpam-6062	295	5	τ(n)→∞	τ(n)→∞	VERB
ejpam-6062	295	6	⟨∇g	⟨∇g	PROPN
ejpam-6062	295	7	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	295	8	e(v	e(v	NOUN
ejpam-6062	295	9	)	)	PUNCT
ejpam-6062	295	10	,	,	PUNCT
ejpam-6062	295	11	xτ(n)+1	xτ(n)+1	PROPN
ejpam-6062	296	1	−	−	PROPN
ejpam-6062	296	2	v⟩	v⟩	VERB
ejpam-6062	296	3	≤	≤	ADJ
ejpam-6062	296	4	0	0	NUM
ejpam-6062	296	5	.	.	PUNCT
ejpam-6062	297	1	(	(	PUNCT
ejpam-6062	297	2	37	37	NUM
ejpam-6062	297	3	)	)	PUNCT
ejpam-6062	297	4	and	and	CCONJ
ejpam-6062	297	5	dg(v	dg(v	X
ejpam-6062	297	6	,	,	PUNCT
ejpam-6062	297	7	xτ(n)+1	xτ(n)+1	PROPN
ejpam-6062	297	8	)	)	PUNCT
ejpam-6062	297	9	≤	≤	NOUN
ejpam-6062	297	10	(	(	PUNCT
ejpam-6062	297	11	1−	1−	NUM
ejpam-6062	297	12	ατ(n))dg(v	ατ(n))dg(v	NOUN
ejpam-6062	297	13	,	,	PUNCT
ejpam-6062	297	14	xτ(n	xτ(n	NUM
ejpam-6062	297	15	)	)	PUNCT
ejpam-6062	297	16	)	)	PUNCT
ejpam-6062	298	1	+	+	CCONJ
ejpam-6062	298	2	ατ(n)⟨∇	ατ(n)⟨∇	PROPN
ejpam-6062	298	3	g	g	PROPN
ejpam-6062	298	4	e(u)−∇g	e(u)−∇g	PROPN
ejpam-6062	298	5	e(v	e(v	NOUN
ejpam-6062	298	6	)	)	PUNCT
ejpam-6062	298	7	,	,	PUNCT
ejpam-6062	298	8	xτ(n)+1	xτ(n)+1	PROPN
ejpam-6062	299	1	−	−	PROPN
ejpam-6062	299	2	v⟩.	v⟩.	AUX
ejpam-6062	299	3	using	use	VERB
ejpam-6062	299	4	lemma	lemma	PROPN
ejpam-6062	299	5	11	11	NUM
ejpam-6062	299	6	,	,	PUNCT
ejpam-6062	299	7	we	we	PRON
ejpam-6062	299	8	arrive	arrive	VERB
ejpam-6062	299	9	at	at	ADP
ejpam-6062	299	10	dg(v	dg(v	NOUN
ejpam-6062	299	11	,	,	PUNCT
ejpam-6062	299	12	xτ(n	xτ(n	NUM
ejpam-6062	299	13	)	)	PUNCT
ejpam-6062	299	14	)	)	PUNCT
ejpam-6062	299	15	≤	≤	NOUN
ejpam-6062	299	16	dg(v	dg(v	PROPN
ejpam-6062	299	17	,	,	PUNCT
ejpam-6062	299	18	xτ(n)+1	xτ(n)+1	PROPN
ejpam-6062	299	19	)	)	PUNCT
ejpam-6062	299	20	.	.	PUNCT
ejpam-6062	300	1	hence	hence	ADV
ejpam-6062	300	2	,	,	PUNCT
ejpam-6062	300	3	we	we	PRON
ejpam-6062	300	4	conclude	conclude	VERB
ejpam-6062	300	5	that	that	SCONJ
ejpam-6062	300	6	lim	lim	PROPN
ejpam-6062	300	7	n→∞	n→∞	NUM
ejpam-6062	300	8	dg(v	dg(v	PROPN
ejpam-6062	300	9	,	,	PUNCT
ejpam-6062	300	10	xn	xn	PUNCT
ejpam-6062	300	11	)	)	PUNCT
ejpam-6062	300	12	=	=	SYM
ejpam-6062	301	1	0	0	X
ejpam-6062	301	2	.	.	PUNCT
ejpam-6062	302	1	therefore	therefore	ADV
ejpam-6062	302	2	,	,	PUNCT
ejpam-6062	302	3	{	{	PUNCT
ejpam-6062	302	4	xn	xn	X
ejpam-6062	302	5	}	}	PUNCT
ejpam-6062	302	6	converges	converge	VERB
ejpam-6062	302	7	strongly	strongly	ADV
ejpam-6062	302	8	to	to	ADP
ejpam-6062	302	9	v.	v.	ADP
ejpam-6062	302	10	this	this	PRON
ejpam-6062	302	11	completes	complete	VERB
ejpam-6062	302	12	the	the	DET
ejpam-6062	302	13	proof	proof	NOUN
ejpam-6062	302	14	of	of	ADP
ejpam-6062	302	15	our	our	PRON
ejpam-6062	302	16	theorem	theorem	NOUN
ejpam-6062	302	17	.	.	PUNCT
ejpam-6062	303	1	h.	h.	PROPN
ejpam-6062	303	2	a.	a.	PROPN
ejpam-6062	303	3	abass	abass	PROPN
ejpam-6062	303	4	et	et	PROPN
ejpam-6062	303	5	al	al	PROPN
ejpam-6062	303	6	.	.	PUNCT
ejpam-6062	303	7	/	/	SYM
ejpam-6062	303	8	eur	eur	PROPN
ejpam-6062	303	9	.	.	PUNCT
ejpam-6062	304	1	j.	j.	PROPN
ejpam-6062	304	2	pure	pure	PROPN
ejpam-6062	304	3	appl	appl	PROPN
ejpam-6062	304	4	.	.	PROPN
ejpam-6062	304	5	math	math	PROPN
ejpam-6062	304	6	,	,	PUNCT
ejpam-6062	304	7	18	18	NUM
ejpam-6062	304	8	(	(	PUNCT
ejpam-6062	304	9	2	2	NUM
ejpam-6062	304	10	)	)	PUNCT
ejpam-6062	304	11	(	(	PUNCT
ejpam-6062	304	12	2025	2025	NUM
ejpam-6062	304	13	)	)	PUNCT
ejpam-6062	304	14	,	,	PUNCT
ejpam-6062	304	15	6062	6062	NUM
ejpam-6062	304	16	16	16	NUM
ejpam-6062	304	17	of	of	ADP
ejpam-6062	304	18	22	22	NUM
ejpam-6062	304	19	if	if	SCONJ
ejpam-6062	304	20	we	we	PRON
ejpam-6062	304	21	put	put	VERB
ejpam-6062	304	22	m	m	NOUN
ejpam-6062	304	23	=	=	NOUN
ejpam-6062	304	24	1	1	NUM
ejpam-6062	304	25	,	,	PUNCT
ejpam-6062	304	26	then	then	ADV
ejpam-6062	304	27	we	we	PRON
ejpam-6062	304	28	have	have	VERB
ejpam-6062	304	29	the	the	DET
ejpam-6062	304	30	following	following	ADJ
ejpam-6062	304	31	iterative	iterative	NOUN
ejpam-6062	304	32	method	method	NOUN
ejpam-6062	304	33	which	which	PRON
ejpam-6062	304	34	solves	solve	VERB
ejpam-6062	304	35	ω	ω	NOUN
ejpam-6062	304	36	:	:	PUNCT
ejpam-6062	304	37	=	=	SYM
ejpam-6062	304	38	{	{	PUNCT
ejpam-6062	304	39	x∗	x∗	PROPN
ejpam-6062	304	40	∈	∈	PROPN
ejpam-6062	304	41	(	(	PUNCT
ejpam-6062	304	42	f	f	PROPN
ejpam-6062	304	43	+	+	PROPN
ejpam-6062	304	44	g)−1(0	g)−1(0	NOUN
ejpam-6062	304	45	)	)	PUNCT
ejpam-6062	304	46	∩	∩	ADJ
ejpam-6062	304	47	fix(s	fix(s	PROPN
ejpam-6062	304	48	)	)	PUNCT
ejpam-6062	304	49	:	:	PUNCT
ejpam-6062	304	50	aix	aix	NOUN
ejpam-6062	304	51	∗	∗	NOUN
ejpam-6062	304	52	∈	∈	PROPN
ejpam-6062	304	53	n⋂	n⋂	NOUN
ejpam-6062	304	54	i=1	i=1	PROPN
ejpam-6062	304	55	fix(si	fix(si	PROPN
ejpam-6062	304	56	)	)	PUNCT
ejpam-6062	304	57	}	}	PUNCT
ejpam-6062	305	1	=	=	SYM
ejpam-6062	305	2	̸	̸	ADV
ejpam-6062	305	3	∅.	∅.	VERB
ejpam-6062	305	4	corollary	corollary	ADJ
ejpam-6062	305	5	1	1	NUM
ejpam-6062	305	6	.	.	PUNCT
ejpam-6062	305	7	algorithm	algorithm	NOUN
ejpam-6062	305	8	2	2	NUM
ejpam-6062	305	9	.	.	PUNCT
ejpam-6062	305	10	for	for	ADP
ejpam-6062	305	11	fixed	fix	VERB
ejpam-6062	305	12	u	u	PROPN
ejpam-6062	305	13	∈	∈	PROPN
ejpam-6062	305	14	e	e	NOUN
ejpam-6062	305	15	,	,	PUNCT
ejpam-6062	305	16	let	let	VERB
ejpam-6062	305	17	{	{	PUNCT
ejpam-6062	305	18	xn}∞n=1	xn}∞n=1	PART
ejpam-6062	305	19	be	be	AUX
ejpam-6062	305	20	a	a	DET
ejpam-6062	305	21	sequence	sequence	NOUN
ejpam-6062	305	22	generated	generate	VERB
ejpam-6062	305	23	by	by	ADP
ejpam-6062	305	24	x1	x1	PROPN
ejpam-6062	305	25	∈	∈	PROPN
ejpam-6062	305	26	e	e	NOUN
ejpam-6062	305	27	such	such	ADJ
ejpam-6062	305	28	that	that	PROPN
ejpam-6062	305	29	zn	zn	NOUN
ejpam-6062	305	30	=	=	SYM
ejpam-6062	306	1	(	(	PUNCT
ejpam-6062	306	2	∇g	∇g	PROPN
ejpam-6062	306	3	e	e	NOUN
ejpam-6062	306	4	)	)	PUNCT
ejpam-6062	306	5	−1	−1	NOUN
ejpam-6062	306	6	[	[	PUNCT
ejpam-6062	306	7	n∑	n∑	PROPN
ejpam-6062	306	8	i=0	i=0	PROPN
ejpam-6062	306	9	λi	λi	SYM
ejpam-6062	306	10	,	,	PUNCT
ejpam-6062	306	11	n	n	CCONJ
ejpam-6062	306	12	(	(	PUNCT
ejpam-6062	306	13	∇g	∇g	ADJ
ejpam-6062	306	14	e(xn)−	e(xn)−	NOUN
ejpam-6062	306	15	γa∗	γa∗	NOUN
ejpam-6062	307	1	i	i	PRON
ejpam-6062	307	2	(	(	PUNCT
ejpam-6062	307	3	∇	∇	X
ejpam-6062	307	4	gi	gi	INTJ
ejpam-6062	307	5	ei	ei	X
ejpam-6062	307	6	(	(	PUNCT
ejpam-6062	307	7	aixn)−∇gi	aixn)−∇gi	ADJ
ejpam-6062	307	8	ei	ei	X
ejpam-6062	307	9	(	(	PUNCT
ejpam-6062	307	10	siaixn	siaixn	NOUN
ejpam-6062	307	11	)	)	PUNCT
ejpam-6062	307	12	)	)	PUNCT
ejpam-6062	307	13	)	)	PUNCT
ejpam-6062	307	14	]	]	PUNCT
ejpam-6062	307	15	yn	yn	X
ejpam-6062	307	16	=	=	PUNCT
ejpam-6062	307	17	(	(	PUNCT
ejpam-6062	307	18	∇g	∇g	PROPN
ejpam-6062	307	19	e	e	NOUN
ejpam-6062	307	20	)	)	PUNCT
ejpam-6062	307	21	−1	−1	NOUN
ejpam-6062	307	22	[	[	PUNCT
ejpam-6062	307	23	(	(	PUNCT
ejpam-6062	307	24	βn∇g	βn∇g	PROPN
ejpam-6062	307	25	e(zn	e(zn	PROPN
ejpam-6062	307	26	)	)	PUNCT
ejpam-6062	308	1	+	+	CCONJ
ejpam-6062	308	2	(	(	PUNCT
ejpam-6062	308	3	1−	1−	NUM
ejpam-6062	308	4	βn)∇g	βn)∇g	NOUN
ejpam-6062	308	5	e(resgσg	e(resgσg	NOUN
ejpam-6062	308	6	◦	◦	NOUN
ejpam-6062	308	7	f	f	PROPN
ejpam-6062	308	8	g	g	NOUN
ejpam-6062	308	9	)	)	PUNCT
ejpam-6062	308	10	]	]	PUNCT
ejpam-6062	308	11	xn+1	xn+1	PUNCT
ejpam-6062	308	12	=	=	SYM
ejpam-6062	308	13	(	(	PUNCT
ejpam-6062	308	14	∇g	∇g	PROPN
ejpam-6062	308	15	e	e	NOUN
ejpam-6062	308	16	)	)	PUNCT
ejpam-6062	308	17	−1	−1	NOUN
ejpam-6062	308	18	[	[	PUNCT
ejpam-6062	308	19	αn∇g	αn∇g	NOUN
ejpam-6062	308	20	e(u	e(u	PROPN
ejpam-6062	308	21	)	)	PUNCT
ejpam-6062	309	1	+	+	CCONJ
ejpam-6062	309	2	(	(	PUNCT
ejpam-6062	309	3	1−	1−	NUM
ejpam-6062	309	4	αn)∇g	αn)∇g	NOUN
ejpam-6062	309	5	e(yn	e(yn	NOUN
ejpam-6062	309	6	)	)	PUNCT
ejpam-6062	309	7	]	]	PUNCT
ejpam-6062	309	8	.	.	PUNCT
ejpam-6062	310	1	(	(	PUNCT
ejpam-6062	310	2	38	38	NUM
ejpam-6062	310	3	)	)	PUNCT
ejpam-6062	310	4	where	where	SCONJ
ejpam-6062	310	5	0	0	PUNCT
ejpam-6062	310	6	<	<	X
ejpam-6062	310	7	a	a	DET
ejpam-6062	310	8	≤	≤	NUM
ejpam-6062	310	9	βn	βn	ADJ
ejpam-6062	310	10	≤	≤	PROPN
ejpam-6062	310	11	b	b	NOUN
ejpam-6062	310	12	<	<	X
ejpam-6062	310	13	1	1	NUM
ejpam-6062	310	14	.	.	PUNCT
ejpam-6062	310	15	suppose	suppose	VERB
ejpam-6062	310	16	{	{	PUNCT
ejpam-6062	310	17	ξ1,n}n∈n	ξ1,n}n∈n	NUM
ejpam-6062	310	18	and	and	CCONJ
ejpam-6062	310	19	{	{	PUNCT
ejpam-6062	310	20	ξ2,n}n∈n	ξ2,n}n∈n	NOUN
ejpam-6062	310	21	are	be	AUX
ejpam-6062	310	22	two	two	NUM
ejpam-6062	310	23	sequences	sequence	NOUN
ejpam-6062	310	24	,	,	PUNCT
ejpam-6062	310	25	where	where	SCONJ
ejpam-6062	310	26	ξ1,n	ξ1,n	PROPN
ejpam-6062	310	27	=	=	SYM
ejpam-6062	310	28			PROPN
ejpam-6062	310	29	dgi	dgi	PROPN
ejpam-6062	310	30	(	(	PUNCT
ejpam-6062	310	31	aixn	aixn	NOUN
ejpam-6062	310	32	,	,	PUNCT
ejpam-6062	310	33	siaixn	siaixn	ADJ
ejpam-6062	310	34	)	)	PUNCT
ejpam-6062	310	35	d∗	d∗	PROPN
ejpam-6062	310	36	g(a	g(a	PROPN
ejpam-6062	310	37	∗	∗	NOUN
ejpam-6062	310	38	i	i	PRON
ejpam-6062	310	39	(	(	PUNCT
ejpam-6062	310	40	∇	∇	X
ejpam-6062	310	41	gi	gi	INTJ
ejpam-6062	310	42	ei	ei	X
ejpam-6062	310	43	(	(	PUNCT
ejpam-6062	310	44	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	310	45	i	i	PRON
ejpam-6062	310	46	(	(	PUNCT
ejpam-6062	310	47	∇	∇	X
ejpam-6062	310	48	gi	gi	PART
ejpam-6062	310	49	ei	ei	X
ejpam-6062	310	50	(	(	PUNCT
ejpam-6062	310	51	siaixn	siaixn	NOUN
ejpam-6062	310	52	)	)	PUNCT
ejpam-6062	310	53	)	)	PUNCT
ejpam-6062	310	54	,	,	PUNCT
ejpam-6062	310	55	if	if	SCONJ
ejpam-6062	310	56	,	,	PUNCT
ejpam-6062	310	57	(	(	PUNCT
ejpam-6062	310	58	i	i	PRON
ejpam-6062	310	59	−	−	PROPN
ejpam-6062	310	60	si)aixn	si)aixn	ADJ
ejpam-6062	310	61	̸=	̸=	PROPN
ejpam-6062	310	62	0	0	NUM
ejpam-6062	310	63	,	,	PUNCT
ejpam-6062	310	64	ξ1	ξ1	NOUN
ejpam-6062	310	65	,	,	PUNCT
ejpam-6062	310	66	otherwise	otherwise	ADV
ejpam-6062	310	67	,	,	PUNCT
ejpam-6062	310	68	and	and	CCONJ
ejpam-6062	310	69	ξ2,n	ξ2,n	PROPN
ejpam-6062	310	70	=	=	PUNCT
ejpam-6062	310	71			PUNCT
ejpam-6062	310	72	d∗	d∗	NOUN
ejpam-6062	310	73	g(∇	g(∇	VERB
ejpam-6062	310	74	g	g	PROPN
ejpam-6062	310	75	e(xn)−γa∗	e(xn)−γa∗	NOUN
ejpam-6062	310	76	i	i	PRON
ejpam-6062	310	77	(	(	PUNCT
ejpam-6062	310	78	∇	∇	X
ejpam-6062	310	79	gi	gi	INTJ
ejpam-6062	310	80	ei	ei	X
ejpam-6062	310	81	(	(	PUNCT
ejpam-6062	310	82	aixn)−∇gi	aixn)−∇gi	ADV
ejpam-6062	310	83	ei	ei	X
ejpam-6062	310	84	(	(	PUNCT
ejpam-6062	310	85	siaixn)),∇g	siaixn)),∇g	VERB
ejpam-6062	310	86	e(xn	e(xn	NOUN
ejpam-6062	310	87	)	)	PUNCT
ejpam-6062	310	88	)	)	PUNCT
ejpam-6062	310	89	d∗	d∗	PROPN
ejpam-6062	310	90	g(a	g(a	PROPN
ejpam-6062	310	91	∗	∗	NOUN
ejpam-6062	310	92	i	i	PRON
ejpam-6062	310	93	(	(	PUNCT
ejpam-6062	310	94	∇	∇	X
ejpam-6062	310	95	gi	gi	INTJ
ejpam-6062	310	96	ei	ei	X
ejpam-6062	310	97	(	(	PUNCT
ejpam-6062	310	98	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	310	99	i	i	PRON
ejpam-6062	310	100	(	(	PUNCT
ejpam-6062	310	101	∇	∇	X
ejpam-6062	310	102	gi	gi	PART
ejpam-6062	310	103	ei	ei	X
ejpam-6062	310	104	(	(	PUNCT
ejpam-6062	310	105	siaixn	siaixn	NOUN
ejpam-6062	310	106	)	)	PUNCT
ejpam-6062	310	107	)	)	PUNCT
ejpam-6062	310	108	,	,	PUNCT
ejpam-6062	310	109	if	if	SCONJ
ejpam-6062	310	110	,	,	PUNCT
ejpam-6062	310	111	(	(	PUNCT
ejpam-6062	310	112	i	i	PRON
ejpam-6062	310	113	−	−	PROPN
ejpam-6062	310	114	si)aixn	si)aixn	ADJ
ejpam-6062	310	115	̸=	̸=	PROPN
ejpam-6062	310	116	0	0	NUM
ejpam-6062	310	117	,	,	PUNCT
ejpam-6062	310	118	ξ2	ξ2	ADJ
ejpam-6062	310	119	,	,	PUNCT
ejpam-6062	310	120	otherwise	otherwise	ADV
ejpam-6062	310	121	.	.	PUNCT
ejpam-6062	311	1	then	then	ADV
ejpam-6062	311	2	,	,	PUNCT
ejpam-6062	311	3	the	the	DET
ejpam-6062	311	4	sequence	sequence	NOUN
ejpam-6062	311	5	{	{	PUNCT
ejpam-6062	311	6	xn	xn	NOUN
ejpam-6062	311	7	}	}	PUNCT
ejpam-6062	311	8	defined	define	VERB
ejpam-6062	311	9	in	in	ADP
ejpam-6062	311	10	(	(	PUNCT
ejpam-6062	311	11	38	38	NUM
ejpam-6062	311	12	)	)	PUNCT
ejpam-6062	311	13	converges	converge	VERB
ejpam-6062	311	14	strongly	strongly	ADV
ejpam-6062	311	15	to	to	ADP
ejpam-6062	311	16	v	v	NOUN
ejpam-6062	311	17	=	=	SYM
ejpam-6062	311	18	projgωu	projgωu	NOUN
ejpam-6062	311	19	,	,	PUNCT
ejpam-6062	311	20	where	where	SCONJ
ejpam-6062	311	21	projgω	projgω	NOUN
ejpam-6062	311	22	is	be	AUX
ejpam-6062	311	23	the	the	DET
ejpam-6062	311	24	bregman	bregman	NOUN
ejpam-6062	311	25	projection	projection	NOUN
ejpam-6062	311	26	of	of	ADP
ejpam-6062	311	27	e	e	PROPN
ejpam-6062	311	28	onto	onto	ADP
ejpam-6062	311	29	ω	ω	NUM
ejpam-6062	311	30	.	.	PUNCT
ejpam-6062	312	1	here	here	ADV
ejpam-6062	312	2	we	we	PRON
ejpam-6062	312	3	consider	consider	VERB
ejpam-6062	312	4	the	the	DET
ejpam-6062	312	5	split	split	ADJ
ejpam-6062	312	6	common	common	ADJ
ejpam-6062	312	7	fixed	fix	VERB
ejpam-6062	312	8	point	point	NOUN
ejpam-6062	312	9	problem	problem	NOUN
ejpam-6062	312	10	of	of	ADP
ejpam-6062	312	11	bregman	bregman	NOUN
ejpam-6062	312	12	demigeneralized	demigeneralize	VERB
ejpam-6062	312	13	mapping	mapping	NOUN
ejpam-6062	312	14	which	which	PRON
ejpam-6062	312	15	is	be	AUX
ejpam-6062	312	16	defined	define	VERB
ejpam-6062	312	17	as	as	ADP
ejpam-6062	312	18	ω	ω	NUM
ejpam-6062	312	19	:	:	PUNCT
ejpam-6062	312	20	=	=	SYM
ejpam-6062	312	21	{	{	PUNCT
ejpam-6062	312	22	x∗	x∗	PROPN
ejpam-6062	312	23	∈	∈	PROPN
ejpam-6062	312	24	fix(s	fix(s	PROPN
ejpam-6062	312	25	)	)	PUNCT
ejpam-6062	312	26	:	:	PUNCT
ejpam-6062	312	27	aix	aix	NOUN
ejpam-6062	312	28	∗	∗	NOUN
ejpam-6062	312	29	∈	∈	PROPN
ejpam-6062	312	30	n⋂	n⋂	NOUN
ejpam-6062	312	31	i=1	i=1	PROPN
ejpam-6062	312	32	fix(si	fix(si	PROPN
ejpam-6062	312	33	)	)	PUNCT
ejpam-6062	312	34	}	}	PUNCT
ejpam-6062	313	1	=	=	SYM
ejpam-6062	313	2	̸	̸	ADV
ejpam-6062	313	3	∅.	∅.	VERB
ejpam-6062	313	4	corollary	corollary	ADJ
ejpam-6062	313	5	2	2	NUM
ejpam-6062	313	6	.	.	PUNCT
ejpam-6062	313	7	algorithm	algorithm	NOUN
ejpam-6062	313	8	3	3	NUM
ejpam-6062	313	9	.	.	PUNCT
ejpam-6062	314	1	for	for	ADP
ejpam-6062	314	2	fixed	fix	VERB
ejpam-6062	314	3	u	u	PROPN
ejpam-6062	314	4	∈	∈	PROPN
ejpam-6062	314	5	e	e	NOUN
ejpam-6062	314	6	,	,	PUNCT
ejpam-6062	314	7	let	let	VERB
ejpam-6062	314	8	{	{	PUNCT
ejpam-6062	314	9	xn}∞n=1	xn}∞n=1	PART
ejpam-6062	314	10	be	be	AUX
ejpam-6062	314	11	a	a	DET
ejpam-6062	314	12	sequence	sequence	NOUN
ejpam-6062	314	13	generated	generate	VERB
ejpam-6062	314	14	by	by	ADP
ejpam-6062	314	15	x1	x1	PROPN
ejpam-6062	314	16	∈	∈	PROPN
ejpam-6062	314	17	e	e	NOUN
ejpam-6062	314	18	such	such	ADJ
ejpam-6062	314	19	thatzn	thatzn	PROPN
ejpam-6062	314	20	=	=	SYM
ejpam-6062	314	21	(	(	PUNCT
ejpam-6062	314	22	∇g	∇g	PROPN
ejpam-6062	314	23	e	e	NOUN
ejpam-6062	314	24	)	)	PUNCT
ejpam-6062	314	25	−1	−1	NOUN
ejpam-6062	314	26	[	[	PUNCT
ejpam-6062	314	27	n∑	n∑	PROPN
ejpam-6062	314	28	i=0	i=0	PROPN
ejpam-6062	314	29	λi	λi	SYM
ejpam-6062	314	30	,	,	PUNCT
ejpam-6062	314	31	n	n	CCONJ
ejpam-6062	314	32	(	(	PUNCT
ejpam-6062	314	33	∇g	∇g	ADJ
ejpam-6062	314	34	e(xn)−	e(xn)−	NOUN
ejpam-6062	314	35	γa∗	γa∗	NOUN
ejpam-6062	315	1	i	i	PRON
ejpam-6062	315	2	(	(	PUNCT
ejpam-6062	315	3	∇	∇	X
ejpam-6062	315	4	gi	gi	INTJ
ejpam-6062	315	5	ei	ei	X
ejpam-6062	315	6	(	(	PUNCT
ejpam-6062	315	7	aixn)−∇gi	aixn)−∇gi	ADJ
ejpam-6062	315	8	ei	ei	X
ejpam-6062	315	9	(	(	PUNCT
ejpam-6062	315	10	siaixn	siaixn	NOUN
ejpam-6062	315	11	)	)	PUNCT
ejpam-6062	315	12	)	)	PUNCT
ejpam-6062	315	13	)	)	PUNCT
ejpam-6062	315	14	]	]	PUNCT
ejpam-6062	315	15	xn+1	xn+1	PUNCT
ejpam-6062	315	16	=	=	SYM
ejpam-6062	316	1	(	(	PUNCT
ejpam-6062	316	2	∇g	∇g	PROPN
ejpam-6062	316	3	e	e	NOUN
ejpam-6062	316	4	)	)	PUNCT
ejpam-6062	316	5	−1	−1	NOUN
ejpam-6062	316	6	[	[	PUNCT
ejpam-6062	316	7	αn∇g	αn∇g	NOUN
ejpam-6062	316	8	e(u	e(u	PROPN
ejpam-6062	316	9	)	)	PUNCT
ejpam-6062	317	1	+	+	CCONJ
ejpam-6062	317	2	(	(	PUNCT
ejpam-6062	317	3	1−	1−	NUM
ejpam-6062	317	4	αn)∇g	αn)∇g	NUM
ejpam-6062	317	5	e(zn	e(zn	PROPN
ejpam-6062	317	6	)	)	PUNCT
ejpam-6062	317	7	]	]	PUNCT
ejpam-6062	317	8	.	.	PUNCT
ejpam-6062	318	1	(	(	PUNCT
ejpam-6062	318	2	39	39	NUM
ejpam-6062	318	3	)	)	PUNCT
ejpam-6062	318	4	suppose	suppose	VERB
ejpam-6062	318	5	{	{	PUNCT
ejpam-6062	318	6	ξ1,n}n∈n	ξ1,n}n∈n	NUM
ejpam-6062	318	7	and	and	CCONJ
ejpam-6062	318	8	{	{	PUNCT
ejpam-6062	318	9	ξ2,n}n∈n	ξ2,n}n∈n	NOUN
ejpam-6062	318	10	are	be	AUX
ejpam-6062	318	11	two	two	NUM
ejpam-6062	318	12	sequences	sequence	NOUN
ejpam-6062	318	13	,	,	PUNCT
ejpam-6062	318	14	where	where	SCONJ
ejpam-6062	318	15	ξ1,n	ξ1,n	PROPN
ejpam-6062	318	16	=	=	SYM
ejpam-6062	318	17			PROPN
ejpam-6062	318	18	dgi	dgi	PROPN
ejpam-6062	318	19	(	(	PUNCT
ejpam-6062	318	20	aixn	aixn	NOUN
ejpam-6062	318	21	,	,	PUNCT
ejpam-6062	318	22	siaixn	siaixn	ADJ
ejpam-6062	318	23	)	)	PUNCT
ejpam-6062	318	24	d∗	d∗	PROPN
ejpam-6062	318	25	g(a	g(a	PROPN
ejpam-6062	318	26	∗	∗	NOUN
ejpam-6062	318	27	i	i	PRON
ejpam-6062	318	28	(	(	PUNCT
ejpam-6062	318	29	∇	∇	X
ejpam-6062	318	30	gi	gi	INTJ
ejpam-6062	318	31	ei	ei	X
ejpam-6062	318	32	(	(	PUNCT
ejpam-6062	318	33	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	318	34	i	i	PRON
ejpam-6062	318	35	(	(	PUNCT
ejpam-6062	318	36	∇	∇	X
ejpam-6062	318	37	gi	gi	PART
ejpam-6062	318	38	ei	ei	X
ejpam-6062	318	39	(	(	PUNCT
ejpam-6062	318	40	siaixn	siaixn	NOUN
ejpam-6062	318	41	)	)	PUNCT
ejpam-6062	318	42	)	)	PUNCT
ejpam-6062	318	43	,	,	PUNCT
ejpam-6062	319	1	if	if	SCONJ
ejpam-6062	319	2	,	,	PUNCT
ejpam-6062	319	3	(	(	PUNCT
ejpam-6062	319	4	i	i	PRON
ejpam-6062	319	5	−	−	PROPN
ejpam-6062	319	6	si)aixn	si)aixn	ADJ
ejpam-6062	319	7	̸=	̸=	PROPN
ejpam-6062	319	8	0	0	NUM
ejpam-6062	319	9	,	,	PUNCT
ejpam-6062	319	10	ξ1	ξ1	NOUN
ejpam-6062	319	11	,	,	PUNCT
ejpam-6062	319	12	otherwise	otherwise	ADV
ejpam-6062	319	13	,	,	PUNCT
ejpam-6062	319	14	and	and	CCONJ
ejpam-6062	319	15	ξ2,n	ξ2,n	PROPN
ejpam-6062	319	16	=	=	PUNCT
ejpam-6062	319	17			PUNCT
ejpam-6062	319	18	d∗	d∗	NOUN
ejpam-6062	319	19	g(∇	g(∇	VERB
ejpam-6062	319	20	g	g	PROPN
ejpam-6062	319	21	e(xn)−γa∗	e(xn)−γa∗	NOUN
ejpam-6062	319	22	i	i	PRON
ejpam-6062	319	23	(	(	PUNCT
ejpam-6062	319	24	∇	∇	X
ejpam-6062	319	25	gi	gi	INTJ
ejpam-6062	319	26	ei	ei	X
ejpam-6062	319	27	(	(	PUNCT
ejpam-6062	319	28	aixn)−∇gi	aixn)−∇gi	ADV
ejpam-6062	319	29	ei	ei	X
ejpam-6062	319	30	(	(	PUNCT
ejpam-6062	319	31	siaixn)),∇g	siaixn)),∇g	VERB
ejpam-6062	319	32	e(xn	e(xn	NOUN
ejpam-6062	319	33	)	)	PUNCT
ejpam-6062	319	34	)	)	PUNCT
ejpam-6062	319	35	d∗	d∗	PROPN
ejpam-6062	319	36	g(a	g(a	PROPN
ejpam-6062	319	37	∗	∗	NOUN
ejpam-6062	319	38	i	i	PRON
ejpam-6062	319	39	(	(	PUNCT
ejpam-6062	319	40	∇	∇	X
ejpam-6062	319	41	gi	gi	INTJ
ejpam-6062	319	42	ei	ei	X
ejpam-6062	319	43	(	(	PUNCT
ejpam-6062	319	44	aixn)),a∗	aixn)),a∗	INTJ
ejpam-6062	319	45	i	i	PRON
ejpam-6062	319	46	(	(	PUNCT
ejpam-6062	319	47	∇	∇	X
ejpam-6062	319	48	gi	gi	PART
ejpam-6062	319	49	ei	ei	X
ejpam-6062	319	50	(	(	PUNCT
ejpam-6062	319	51	siaixn	siaixn	NOUN
ejpam-6062	319	52	)	)	PUNCT
ejpam-6062	319	53	)	)	PUNCT
ejpam-6062	319	54	,	,	PUNCT
ejpam-6062	319	55	if	if	SCONJ
ejpam-6062	319	56	,	,	PUNCT
ejpam-6062	319	57	(	(	PUNCT
ejpam-6062	319	58	i	i	PRON
ejpam-6062	319	59	−	−	PROPN
ejpam-6062	319	60	si)aixn	si)aixn	ADJ
ejpam-6062	319	61	̸=	̸=	PROPN
ejpam-6062	319	62	0	0	NUM
ejpam-6062	319	63	,	,	PUNCT
ejpam-6062	319	64	ξ2	ξ2	ADJ
ejpam-6062	319	65	,	,	PUNCT
ejpam-6062	319	66	otherwise	otherwise	ADV
ejpam-6062	319	67	.	.	PUNCT
ejpam-6062	320	1	then	then	ADV
ejpam-6062	320	2	,	,	PUNCT
ejpam-6062	320	3	the	the	DET
ejpam-6062	320	4	sequence	sequence	NOUN
ejpam-6062	320	5	{	{	PUNCT
ejpam-6062	320	6	xn	xn	NOUN
ejpam-6062	320	7	}	}	PUNCT
ejpam-6062	320	8	defined	define	VERB
ejpam-6062	320	9	in	in	ADP
ejpam-6062	320	10	(	(	PUNCT
ejpam-6062	320	11	39	39	NUM
ejpam-6062	320	12	)	)	PUNCT
ejpam-6062	320	13	converges	converge	VERB
ejpam-6062	320	14	strongly	strongly	ADV
ejpam-6062	320	15	to	to	ADP
ejpam-6062	320	16	v	v	NOUN
ejpam-6062	320	17	=	=	SYM
ejpam-6062	320	18	projgωu	projgωu	NOUN
ejpam-6062	320	19	,	,	PUNCT
ejpam-6062	320	20	where	where	SCONJ
ejpam-6062	320	21	projgω	projgω	NOUN
ejpam-6062	320	22	is	be	AUX
ejpam-6062	320	23	the	the	DET
ejpam-6062	320	24	bregman	bregman	NOUN
ejpam-6062	320	25	projection	projection	NOUN
ejpam-6062	320	26	of	of	ADP
ejpam-6062	320	27	e	e	PROPN
ejpam-6062	320	28	onto	onto	ADP
ejpam-6062	320	29	ω	ω	PROPN
ejpam-6062	320	30	.	.	PUNCT
ejpam-6062	321	1	h.	h.	PROPN
ejpam-6062	321	2	a.	a.	PROPN
ejpam-6062	321	3	abass	abass	PROPN
ejpam-6062	321	4	et	et	PROPN
ejpam-6062	321	5	al	al	PROPN
ejpam-6062	321	6	.	.	PUNCT
ejpam-6062	321	7	/	/	SYM
ejpam-6062	321	8	eur	eur	PROPN
ejpam-6062	321	9	.	.	PUNCT
ejpam-6062	322	1	j.	j.	PROPN
ejpam-6062	322	2	pure	pure	PROPN
ejpam-6062	322	3	appl	appl	PROPN
ejpam-6062	322	4	.	.	PROPN
ejpam-6062	322	5	math	math	PROPN
ejpam-6062	322	6	,	,	PUNCT
ejpam-6062	322	7	18	18	NUM
ejpam-6062	322	8	(	(	PUNCT
ejpam-6062	322	9	2	2	NUM
ejpam-6062	322	10	)	)	PUNCT
ejpam-6062	322	11	(	(	PUNCT
ejpam-6062	322	12	2025	2025	NUM
ejpam-6062	322	13	)	)	PUNCT
ejpam-6062	322	14	,	,	PUNCT
ejpam-6062	322	15	6062	6062	NUM
ejpam-6062	322	16	17	17	NUM
ejpam-6062	322	17	of	of	ADP
ejpam-6062	322	18	22	22	NUM
ejpam-6062	322	19	4	4	NUM
ejpam-6062	322	20	.	.	PUNCT
ejpam-6062	322	21	numerical	numerical	ADJ
ejpam-6062	322	22	example	example	NOUN
ejpam-6062	322	23	in	in	ADP
ejpam-6062	322	24	this	this	DET
ejpam-6062	322	25	section	section	NOUN
ejpam-6062	322	26	,	,	PUNCT
ejpam-6062	322	27	we	we	PRON
ejpam-6062	322	28	give	give	VERB
ejpam-6062	322	29	a	a	DET
ejpam-6062	322	30	numerical	numerical	ADJ
ejpam-6062	322	31	example	example	NOUN
ejpam-6062	322	32	to	to	PART
ejpam-6062	322	33	illustrate	illustrate	VERB
ejpam-6062	322	34	the	the	DET
ejpam-6062	322	35	performance	performance	NOUN
ejpam-6062	322	36	of	of	ADP
ejpam-6062	322	37	our	our	PRON
ejpam-6062	322	38	method	method	NOUN
ejpam-6062	322	39	.	.	PUNCT
ejpam-6062	322	40	example	example	NOUN
ejpam-6062	323	1	1	1	NUM
ejpam-6062	323	2	:	:	PUNCT
ejpam-6062	323	3	let	let	VERB
ejpam-6062	323	4	e	e	NOUN
ejpam-6062	323	5	=	=	NOUN
ejpam-6062	323	6	ei	ei	X
ejpam-6062	323	7	=	=	PUNCT
ejpam-6062	323	8	r4	r4	PROPN
ejpam-6062	323	9	for	for	ADP
ejpam-6062	323	10	i	i	PRON
ejpam-6062	323	11	=	=	NOUN
ejpam-6062	323	12	1	1	NUM
ejpam-6062	323	13	,	,	PUNCT
ejpam-6062	323	14	2	2	NUM
ejpam-6062	323	15	.	.	X
ejpam-6062	324	1	we	we	PRON
ejpam-6062	324	2	define	define	VERB
ejpam-6062	324	3	hm	hm	INTJ
ejpam-6062	324	4	:	:	PUNCT
ejpam-6062	324	5	r	r	NOUN
ejpam-6062	324	6	→	→	SYM
ejpam-6062	324	7	(	(	PUNCT
ejpam-6062	324	8	−∞,+∞	−∞,+∞	ADV
ejpam-6062	324	9	]	]	PUNCT
ejpam-6062	324	10	by	by	ADP
ejpam-6062	324	11	hm(x	hm(x	NOUN
ejpam-6062	324	12	)	)	PUNCT
ejpam-6062	324	13	=	=	SYM
ejpam-6062	325	1	1	1	NUM
ejpam-6062	325	2	2x	2x	NUM
ejpam-6062	325	3	2	2	NUM
ejpam-6062	325	4	,	,	PUNCT
ejpam-6062	325	5	m	m	VERB
ejpam-6062	325	6	=	=	NOUN
ejpam-6062	325	7	1	1	NUM
ejpam-6062	325	8	,	,	PUNCT
ejpam-6062	325	9	2	2	NUM
ejpam-6062	325	10	,	,	PUNCT
ejpam-6062	325	11	3	3	NUM
ejpam-6062	325	12	,	,	PUNCT
ejpam-6062	325	13	4	4	NUM
ejpam-6062	325	14	.	.	PUNCT
ejpam-6062	325	15	also	also	ADV
ejpam-6062	325	16	,	,	PUNCT
ejpam-6062	325	17	let	let	VERB
ejpam-6062	325	18	g	g	NOUN
ejpam-6062	325	19	=	=	VERB
ejpam-6062	325	20	gi	gi	VERB
ejpam-6062	325	21	for	for	ADP
ejpam-6062	325	22	i	i	PROPN
ejpam-6062	325	23	=	=	SYM
ejpam-6062	325	24	1	1	NUM
ejpam-6062	325	25	,	,	PUNCT
ejpam-6062	325	26	2	2	NUM
ejpam-6062	325	27	be	be	AUX
ejpam-6062	325	28	defined	define	VERB
ejpam-6062	325	29	by	by	ADP
ejpam-6062	325	30	g	g	NOUN
ejpam-6062	325	31	:	:	PUNCT
ejpam-6062	325	32	r2	r2	PROPN
ejpam-6062	325	33	→	→	SYM
ejpam-6062	325	34	(	(	PUNCT
ejpam-6062	325	35	−∞,+∞	−∞,+∞	NUM
ejpam-6062	325	36	]	]	X
ejpam-6062	325	37	,	,	PUNCT
ejpam-6062	325	38	g(x	g(x	NOUN
ejpam-6062	325	39	)	)	PUNCT
ejpam-6062	325	40	=	=	SYM
ejpam-6062	326	1	h1(x	h1(x	NOUN
ejpam-6062	326	2	)	)	PUNCT
ejpam-6062	326	3	+	+	NUM
ejpam-6062	326	4	h2(x	h2(x	NUM
ejpam-6062	326	5	)	)	PUNCT
ejpam-6062	326	6	+	+	NUM
ejpam-6062	326	7	h3(x	h3(x	NOUN
ejpam-6062	326	8	)	)	PUNCT
ejpam-6062	326	9	+	+	NUM
ejpam-6062	326	10	h4(x	h4(x	X
ejpam-6062	326	11	)	)	PUNCT
ejpam-6062	326	12	=	=	SYM
ejpam-6062	327	1	1	1	NUM
ejpam-6062	327	2	2x	2x	NUM
ejpam-6062	327	3	2	2	NUM
ejpam-6062	327	4	1	1	NUM
ejpam-6062	327	5	+	+	NUM
ejpam-6062	327	6	1	1	NUM
ejpam-6062	327	7	2x	2x	NUM
ejpam-6062	327	8	2	2	NUM
ejpam-6062	327	9	2	2	NUM
ejpam-6062	327	10	+	+	CCONJ
ejpam-6062	327	11	1	1	NUM
ejpam-6062	327	12	2x	2x	NUM
ejpam-6062	327	13	2	2	NUM
ejpam-6062	327	14	3	3	NUM
ejpam-6062	327	15	+	+	CCONJ
ejpam-6062	327	16	1	1	NUM
ejpam-6062	327	17	2x	2x	NUM
ejpam-6062	327	18	2	2	NUM
ejpam-6062	327	19	4	4	NUM
ejpam-6062	327	20	.	.	PUNCT
ejpam-6062	328	1	then	then	ADV
ejpam-6062	328	2	,	,	PUNCT
ejpam-6062	328	3	we	we	PRON
ejpam-6062	328	4	have	have	VERB
ejpam-6062	328	5	∇g(x	∇g(x	VERB
ejpam-6062	328	6	)	)	PUNCT
ejpam-6062	329	1	=	=	SYM
ejpam-6062	329	2	(	(	PUNCT
ejpam-6062	329	3	∇h(x1)),∇h(x2),∇h(x3),∇h(x4	∇h(x1)),∇h(x2),∇h(x3),∇h(x4	NOUN
ejpam-6062	329	4	)	)	PUNCT
ejpam-6062	329	5	=	=	SYM
ejpam-6062	329	6	(	(	PUNCT
ejpam-6062	329	7	x1	x1	PROPN
ejpam-6062	329	8	,	,	PUNCT
ejpam-6062	329	9	x2	x2	PROPN
ejpam-6062	329	10	,	,	PUNCT
ejpam-6062	329	11	x3	x3	ADJ
ejpam-6062	329	12	,	,	PUNCT
ejpam-6062	329	13	x4	x4	PROPN
ejpam-6062	329	14	)	)	PUNCT
ejpam-6062	329	15	=	=	SYM
ejpam-6062	329	16			ADJ
ejpam-6062	329	17	1	1	NUM
ejpam-6062	329	18	0	0	NUM
ejpam-6062	329	19	0	0	NUM
ejpam-6062	329	20	0	0	NUM
ejpam-6062	329	21	0	0	NUM
ejpam-6062	329	22	1	1	NUM
ejpam-6062	329	23	0	0	NUM
ejpam-6062	329	24	0	0	NUM
ejpam-6062	329	25	0	0	NUM
ejpam-6062	329	26	0	0	NUM
ejpam-6062	329	27	1	1	NUM
ejpam-6062	329	28	0	0	NUM
ejpam-6062	329	29	0	0	NUM
ejpam-6062	329	30	0	0	NUM
ejpam-6062	329	31	0	0	NUM
ejpam-6062	329	32	1	1	NUM
ejpam-6062	329	33			NOUN
ejpam-6062	329	34			NOUN
ejpam-6062	330	1	x1	x1	NOUN
ejpam-6062	330	2	x2	x2	PROPN
ejpam-6062	330	3	x3	x3	PROPN
ejpam-6062	330	4	x4	x4	PROPN
ejpam-6062	330	5			NOUN
ejpam-6062	330	6	.	.	PUNCT
ejpam-6062	331	1	for	for	ADP
ejpam-6062	331	2	i	i	PRON
ejpam-6062	331	3	=	=	SYM
ejpam-6062	331	4	0	0	NUM
ejpam-6062	331	5	,	,	PUNCT
ejpam-6062	331	6	1	1	NUM
ejpam-6062	331	7	,	,	PUNCT
ejpam-6062	331	8	2	2	NUM
ejpam-6062	331	9	,	,	PUNCT
ejpam-6062	331	10	let	let	VERB
ejpam-6062	331	11	ai	ai	VERB
ejpam-6062	331	12	:	:	PUNCT
ejpam-6062	331	13	r	r	NOUN
ejpam-6062	331	14	→	→	SYM
ejpam-6062	331	15	r	r	NOUN
ejpam-6062	331	16	be	be	AUX
ejpam-6062	331	17	defined	define	VERB
ejpam-6062	331	18	by	by	ADP
ejpam-6062	331	19	ai(x	ai(x	ADJ
ejpam-6062	331	20	)	)	PUNCT
ejpam-6062	332	1	=	=	SYM
ejpam-6062	332	2	x	x	X
ejpam-6062	332	3	(	(	PUNCT
ejpam-6062	332	4	i+1	i+1	NOUN
ejpam-6062	332	5	)	)	PUNCT
ejpam-6062	332	6	for	for	ADP
ejpam-6062	332	7	x	x	SYM
ejpam-6062	332	8	=	=	SYM
ejpam-6062	332	9	(	(	PUNCT
ejpam-6062	332	10	x1	x1	PROPN
ejpam-6062	332	11	,	,	PUNCT
ejpam-6062	332	12	x2	x2	PROPN
ejpam-6062	332	13	,	,	PUNCT
ejpam-6062	332	14	x3	x3	ADJ
ejpam-6062	332	15	,	,	PUNCT
ejpam-6062	332	16	x4	x4	ADJ
ejpam-6062	332	17	)	)	PUNCT
ejpam-6062	332	18	∈	∈	PROPN
ejpam-6062	332	19	r4	r4	NOUN
ejpam-6062	332	20	.	.	PUNCT
ejpam-6062	333	1	we	we	PRON
ejpam-6062	333	2	also	also	ADV
ejpam-6062	333	3	define	define	VERB
ejpam-6062	333	4	the	the	DET
ejpam-6062	333	5	mapping	mapping	NOUN
ejpam-6062	333	6	si	si	NOUN
ejpam-6062	333	7	:	:	PUNCT
ejpam-6062	333	8	r	r	NOUN
ejpam-6062	333	9	→	→	SYM
ejpam-6062	333	10	r	r	NOUN
ejpam-6062	333	11	by	by	ADP
ejpam-6062	333	12	si(x	si(x	NOUN
ejpam-6062	333	13	)	)	PUNCT
ejpam-6062	334	1	=	=	SYM
ejpam-6062	334	2	−(i	−(i	NOUN
ejpam-6062	334	3	+	+	CCONJ
ejpam-6062	334	4	1)x	1)x	NUM
ejpam-6062	334	5	for	for	ADP
ejpam-6062	334	6	each	each	DET
ejpam-6062	334	7	i	i	NOUN
ejpam-6062	334	8	=	=	NOUN
ejpam-6062	334	9	0	0	NUM
ejpam-6062	334	10	,	,	PUNCT
ejpam-6062	334	11	1	1	NUM
ejpam-6062	334	12	,	,	PUNCT
ejpam-6062	334	13	2	2	NUM
ejpam-6062	334	14	.	.	PUNCT
ejpam-6062	335	1	then	then	ADV
ejpam-6062	335	2	the	the	DET
ejpam-6062	335	3	mappings	mapping	NOUN
ejpam-6062	335	4	si	si	X
ejpam-6062	335	5	are	be	AUX
ejpam-6062	335	6	(	(	PUNCT
ejpam-6062	335	7	−	−	PROPN
ejpam-6062	335	8	1	1	NUM
ejpam-6062	335	9	i+1	i+1	NUM
ejpam-6062	335	10	,	,	PUNCT
ejpam-6062	335	11	0	0	NUM
ejpam-6062	335	12	)	)	PUNCT
ejpam-6062	335	13	-bregman	-bregman	NOUN
ejpam-6062	335	14	demigeneralized	demigeneralize	VERB
ejpam-6062	335	15	.	.	PUNCT
ejpam-6062	336	1	now	now	ADV
ejpam-6062	336	2	,	,	PUNCT
ejpam-6062	336	3	define	define	VERB
ejpam-6062	336	4	the	the	DET
ejpam-6062	336	5	mappings	mapping	NOUN
ejpam-6062	336	6	f1	f1	NOUN
ejpam-6062	336	7	,	,	PUNCT
ejpam-6062	336	8	f2	f2	PROPN
ejpam-6062	336	9	,	,	PUNCT
ejpam-6062	336	10	f3	f3	PROPN
ejpam-6062	336	11	:	:	PUNCT
ejpam-6062	336	12	r	r	NOUN
ejpam-6062	336	13	→	→	SYM
ejpam-6062	336	14	r	r	NOUN
ejpam-6062	336	15	respectively	respectively	ADV
ejpam-6062	336	16	by	by	ADP
ejpam-6062	336	17	f1	f1	NOUN
ejpam-6062	336	18	=	=	SYM
ejpam-6062	336	19			ADJ
ejpam-6062	336	20	1	1	NUM
ejpam-6062	336	21	0	0	SYM
ejpam-6062	336	22	0	0	NUM
ejpam-6062	336	23	2	2	NUM
ejpam-6062	336	24	1	1	NUM
ejpam-6062	336	25	0	0	NUM
ejpam-6062	336	26	0	0	NUM
ejpam-6062	336	27	1	1	NUM
ejpam-6062	336	28	1	1	NUM
ejpam-6062	336	29	0	0	NUM
ejpam-6062	336	30	1	1	NUM
ejpam-6062	336	31	1	1	NUM
ejpam-6062	336	32	1	1	NUM
ejpam-6062	336	33	0	0	NUM
ejpam-6062	336	34	0	0	NUM
ejpam-6062	336	35	−1	−1	NOUN
ejpam-6062	336	36			NOUN
ejpam-6062	336	37	,	,	PUNCT
ejpam-6062	336	38	f2	f2	PROPN
ejpam-6062	336	39	=	=	SYM
ejpam-6062	336	40			ADJ
ejpam-6062	336	41	1	1	NUM
ejpam-6062	336	42	1	1	NUM
ejpam-6062	336	43	0	0	NUM
ejpam-6062	336	44	2	2	NUM
ejpam-6062	336	45	1	1	NUM
ejpam-6062	336	46	2	2	NUM
ejpam-6062	336	47	0	0	NUM
ejpam-6062	336	48	1	1	NUM
ejpam-6062	336	49	1	1	NUM
ejpam-6062	336	50	2	2	NUM
ejpam-6062	336	51	1	1	NUM
ejpam-6062	336	52	2	2	NUM
ejpam-6062	336	53	1	1	NUM
ejpam-6062	336	54	2	2	NUM
ejpam-6062	336	55	0	0	NUM
ejpam-6062	336	56	3	3	NUM
ejpam-6062	336	57			NOUN
ejpam-6062	336	58	,	,	PUNCT
ejpam-6062	336	59	f3	f3	NOUN
ejpam-6062	336	60	=	=	SYM
ejpam-6062	336	61			ADJ
ejpam-6062	336	62	1	1	NUM
ejpam-6062	336	63	1	1	NUM
ejpam-6062	336	64	0	0	NUM
ejpam-6062	336	65	2	2	NUM
ejpam-6062	336	66	1	1	NUM
ejpam-6062	336	67	2	2	NUM
ejpam-6062	336	68	0	0	NUM
ejpam-6062	336	69	1	1	NUM
ejpam-6062	336	70	1	1	NUM
ejpam-6062	336	71	0	0	NUM
ejpam-6062	336	72	5	5	NUM
ejpam-6062	336	73	1	1	NUM
ejpam-6062	336	74	1	1	NUM
ejpam-6062	336	75	2	2	NUM
ejpam-6062	336	76	0	0	NUM
ejpam-6062	336	77	3	3	NUM
ejpam-6062	336	78			NOUN
ejpam-6062	336	79	and	and	CCONJ
ejpam-6062	336	80	the	the	DET
ejpam-6062	336	81	mappings	mapping	NOUN
ejpam-6062	336	82	g1	g1	NOUN
ejpam-6062	336	83	,	,	PUNCT
ejpam-6062	336	84	g2	g2	PROPN
ejpam-6062	336	85	,	,	PUNCT
ejpam-6062	336	86	g3	g3	PROPN
ejpam-6062	336	87	:	:	PUNCT
ejpam-6062	336	88	r	r	NOUN
ejpam-6062	336	89	→	→	SYM
ejpam-6062	336	90	r	r	NOUN
ejpam-6062	336	91	respectively	respectively	ADV
ejpam-6062	336	92	by	by	ADP
ejpam-6062	336	93	g1	g1	NOUN
ejpam-6062	336	94	=	=	SYM
ejpam-6062	336	95			ADJ
ejpam-6062	336	96	1	1	NUM
ejpam-6062	336	97	1	1	NUM
ejpam-6062	336	98	0	0	NUM
ejpam-6062	336	99	−2	−2	NOUN
ejpam-6062	336	100	1	1	NUM
ejpam-6062	336	101	2	2	NUM
ejpam-6062	336	102	−2	−2	NOUN
ejpam-6062	336	103	1	1	NUM
ejpam-6062	336	104	−1	−1	NOUN
ejpam-6062	336	105	0	0	NUM
ejpam-6062	336	106	0	0	NUM
ejpam-6062	336	107	1	1	NUM
ejpam-6062	336	108	0	0	NUM
ejpam-6062	336	109	2	2	NUM
ejpam-6062	336	110	0	0	NUM
ejpam-6062	336	111	3	3	NUM
ejpam-6062	336	112			NOUN
ejpam-6062	336	113	,	,	PUNCT
ejpam-6062	336	114	g2	g2	PROPN
ejpam-6062	336	115	=	=	PUNCT
ejpam-6062	336	116			ADJ
ejpam-6062	336	117	1	1	NUM
ejpam-6062	336	118	−2	−2	NOUN
ejpam-6062	336	119	−1	−1	NOUN
ejpam-6062	336	120	2	2	NUM
ejpam-6062	336	121	0	0	NUM
ejpam-6062	336	122	0	0	NUM
ejpam-6062	336	123	1	1	NUM
ejpam-6062	336	124	3	3	NUM
ejpam-6062	336	125	−1	−1	NOUN
ejpam-6062	336	126	2	2	NUM
ejpam-6062	336	127	−3	−3	NOUN
ejpam-6062	336	128	4	4	NUM
ejpam-6062	336	129	0	0	NUM
ejpam-6062	336	130	3	3	NUM
ejpam-6062	336	131	0	0	NUM
ejpam-6062	336	132	5	5	NUM
ejpam-6062	336	133			NOUN
ejpam-6062	336	134	,	,	PUNCT
ejpam-6062	336	135	g3	g3	NOUN
ejpam-6062	336	136	=	=	SYM
ejpam-6062	336	137			ADJ
ejpam-6062	336	138	0	0	NUM
ejpam-6062	336	139	2	2	NUM
ejpam-6062	336	140	0	0	NUM
ejpam-6062	336	141	−2	−2	NOUN
ejpam-6062	336	142	0	0	NUM
ejpam-6062	336	143	0	0	NUM
ejpam-6062	336	144	1	1	NUM
ejpam-6062	336	145	−3	−3	NOUN
ejpam-6062	336	146	1	1	NUM
ejpam-6062	336	147	2	2	NUM
ejpam-6062	336	148	0	0	NUM
ejpam-6062	336	149	1	1	NUM
ejpam-6062	336	150	1	1	NUM
ejpam-6062	336	151	3	3	NUM
ejpam-6062	336	152	0	0	NUM
ejpam-6062	336	153	2	2	NUM
ejpam-6062	336	154			NOUN
ejpam-6062	336	155	.	.	PUNCT
ejpam-6062	337	1	it	it	PRON
ejpam-6062	337	2	is	be	AUX
ejpam-6062	337	3	easy	easy	ADJ
ejpam-6062	337	4	to	to	PART
ejpam-6062	337	5	see	see	VERB
ejpam-6062	337	6	for	for	ADP
ejpam-6062	337	7	any	any	DET
ejpam-6062	337	8	λ	λ	PROPN
ejpam-6062	337	9	>	>	X
ejpam-6062	337	10	0	0	NUM
ejpam-6062	337	11	,	,	PUNCT
ejpam-6062	337	12	that	that	PRON
ejpam-6062	337	13	t1(x	t1(x	NOUN
ejpam-6062	337	14	)	)	PUNCT
ejpam-6062	337	15	=	=	NOUN
ejpam-6062	337	16	(	(	PUNCT
ejpam-6062	338	1	∇g	∇g	NOUN
ejpam-6062	338	2	e	e	NOUN
ejpam-6062	338	3	+	+	CCONJ
ejpam-6062	338	4	λg1	λg1	NOUN
ejpam-6062	338	5	)	)	PUNCT
ejpam-6062	338	6	◦	◦	VERB
ejpam-6062	338	7	∇g	∇g	ADJ
ejpam-6062	338	8	e	e	NOUN
ejpam-6062	338	9	◦	◦	NOUN
ejpam-6062	338	10	(	(	PUNCT
ejpam-6062	338	11	∇g	∇g	PROPN
ejpam-6062	338	12	e	e	NOUN
ejpam-6062	338	13	)	)	PUNCT
ejpam-6062	338	14	−1(∇g	−1(∇g	NOUN
ejpam-6062	338	15	e	e	PROPN
ejpam-6062	339	1	−	−	PROPN
ejpam-6062	339	2	λf1)(x	λf1)(x	PROPN
ejpam-6062	339	3	)	)	PUNCT
ejpam-6062	339	4	=	=	SYM
ejpam-6062	339	5			NOUN
ejpam-6062	339	6			ADJ
ejpam-6062	339	7	1	1	NUM
ejpam-6062	339	8	0	0	NUM
ejpam-6062	339	9	0	0	NUM
ejpam-6062	339	10	0	0	NUM
ejpam-6062	339	11	0	0	NUM
ejpam-6062	339	12	1	1	NUM
ejpam-6062	339	13	0	0	NUM
ejpam-6062	339	14	0	0	NUM
ejpam-6062	339	15	0	0	NUM
ejpam-6062	339	16	0	0	NUM
ejpam-6062	339	17	1	1	NUM
ejpam-6062	339	18	0	0	NUM
ejpam-6062	339	19	0	0	NUM
ejpam-6062	339	20	0	0	NUM
ejpam-6062	339	21	0	0	NUM
ejpam-6062	339	22	1	1	NUM
ejpam-6062	339	23	+	+	NOUN
ejpam-6062	340	1	λ×	λ×	PROPN
ejpam-6062	340	2			ADJ
ejpam-6062	340	3	1	1	NUM
ejpam-6062	340	4	1	1	NUM
ejpam-6062	340	5	0	0	NUM
ejpam-6062	340	6	−2	−2	NOUN
ejpam-6062	340	7	1	1	NUM
ejpam-6062	340	8	2	2	NUM
ejpam-6062	340	9	−2	−2	NOUN
ejpam-6062	340	10	1	1	NUM
ejpam-6062	340	11	−1	−1	NOUN
ejpam-6062	340	12	0	0	NUM
ejpam-6062	340	13	0	0	NUM
ejpam-6062	340	14	1	1	NUM
ejpam-6062	340	15	0	0	NUM
ejpam-6062	340	16	2	2	NUM
ejpam-6062	340	17	0	0	NUM
ejpam-6062	340	18	3	3	NUM
ejpam-6062	340	19			NOUN
ejpam-6062	340	20			NOUN
ejpam-6062	340	21	−1	−1	NOUN
ejpam-6062	340	22			NOUN
ejpam-6062	340	23			ADJ
ejpam-6062	340	24	1	1	NUM
ejpam-6062	340	25	0	0	NUM
ejpam-6062	340	26	0	0	NUM
ejpam-6062	340	27	0	0	NUM
ejpam-6062	340	28	0	0	NUM
ejpam-6062	340	29	1	1	NUM
ejpam-6062	340	30	0	0	NUM
ejpam-6062	340	31	0	0	NUM
ejpam-6062	340	32	0	0	NUM
ejpam-6062	340	33	0	0	NUM
ejpam-6062	340	34	1	1	NUM
ejpam-6062	340	35	0	0	NUM
ejpam-6062	340	36	0	0	NUM
ejpam-6062	340	37	0	0	NUM
ejpam-6062	340	38	0	0	NUM
ejpam-6062	340	39	1	1	NUM
ejpam-6062	340	40	−	−	NOUN
ejpam-6062	341	1	λ×	λ×	X
ejpam-6062	341	2			VERB
ejpam-6062	341	3	1	1	NUM
ejpam-6062	341	4	0	0	SYM
ejpam-6062	341	5	0	0	NUM
ejpam-6062	341	6	2	2	NUM
ejpam-6062	341	7	1	1	NUM
ejpam-6062	341	8	0	0	NUM
ejpam-6062	341	9	0	0	NUM
ejpam-6062	341	10	1	1	NUM
ejpam-6062	341	11	1	1	NUM
ejpam-6062	341	12	0	0	NUM
ejpam-6062	341	13	1	1	NUM
ejpam-6062	341	14	1	1	NUM
ejpam-6062	341	15	1	1	NUM
ejpam-6062	341	16	0	0	NUM
ejpam-6062	341	17	0	0	NUM
ejpam-6062	341	18	−1	−1	NOUN
ejpam-6062	341	19			NOUN
ejpam-6062	341	20			PROPN
ejpam-6062	341	21			NOUN
ejpam-6062	341	22	x1	x1	NUM
ejpam-6062	341	23	x2	x2	PROPN
ejpam-6062	341	24	x3	x3	PROPN
ejpam-6062	341	25	x4	x4	PROPN
ejpam-6062	341	26			NOUN
ejpam-6062	341	27	=	=	SYM
ejpam-6062	341	28			NOUN
ejpam-6062	341	29			ADJ
ejpam-6062	341	30	1	1	NUM
ejpam-6062	342	1	+	+	NUM
ejpam-6062	342	2	λ	λ	PROPN
ejpam-6062	342	3	λ	λ	X
ejpam-6062	342	4	0	0	PUNCT
ejpam-6062	342	5	−2λ	−2λ	PROPN
ejpam-6062	342	6	λ	λ	PROPN
ejpam-6062	342	7	1	1	NUM
ejpam-6062	342	8	+	+	NUM
ejpam-6062	342	9	2λ	2λ	NUM
ejpam-6062	342	10	−2λ	−2λ	PROPN
ejpam-6062	342	11	λ	λ	PROPN
ejpam-6062	342	12	−λ	−λ	NOUN
ejpam-6062	342	13	0	0	NUM
ejpam-6062	342	14	1	1	NUM
ejpam-6062	342	15	λ	λ	SYM
ejpam-6062	342	16	0	0	PROPN
ejpam-6062	342	17	2λ	2λ	NOUN
ejpam-6062	342	18	0	0	NUM
ejpam-6062	342	19	1	1	NUM
ejpam-6062	342	20	+	+	NUM
ejpam-6062	342	21	3λ	3λ	NUM
ejpam-6062	342	22			NOUN
ejpam-6062	342	23			PROPN
ejpam-6062	342	24	−1	−1	NOUN
ejpam-6062	342	25			NOUN
ejpam-6062	342	26			ADJ
ejpam-6062	342	27	1−	1−	NUM
ejpam-6062	342	28	λ	λ	NOUN
ejpam-6062	342	29	0	0	NUM
ejpam-6062	342	30	0	0	NUM
ejpam-6062	342	31	2λ	2λ	NOUN
ejpam-6062	342	32	−λ	−λ	NOUN
ejpam-6062	342	33	1	1	NUM
ejpam-6062	342	34	0	0	NUM
ejpam-6062	342	35	−λ	−λ	NOUN
ejpam-6062	342	36	−λ	−λ	PROPN
ejpam-6062	342	37	0	0	NUM
ejpam-6062	342	38	1−	1−	NUM
ejpam-6062	343	1	λ	λ	NOUN
ejpam-6062	343	2	−λ	−λ	NOUN
ejpam-6062	343	3	−λ	−λ	PROPN
ejpam-6062	343	4	0	0	NUM
ejpam-6062	343	5	0	0	NUM
ejpam-6062	343	6	1	1	NUM
ejpam-6062	343	7	+	+	NUM
ejpam-6062	343	8	λ	λ	PROPN
ejpam-6062	343	9			NOUN
ejpam-6062	343	10			PROPN
ejpam-6062	343	11			NOUN
ejpam-6062	343	12	x1	x1	NUM
ejpam-6062	343	13	x2	x2	PROPN
ejpam-6062	343	14	x3	x3	PROPN
ejpam-6062	343	15	x4	x4	PROPN
ejpam-6062	343	16			PROPN
ejpam-6062	343	17	.	.	PUNCT
ejpam-6062	344	1	suppose	suppose	VERB
ejpam-6062	344	2	λ	λ	X
ejpam-6062	344	3	=	=	SYM
ejpam-6062	344	4	1	1	NUM
ejpam-6062	344	5	,	,	PUNCT
ejpam-6062	344	6	we	we	PRON
ejpam-6062	344	7	obtain	obtain	VERB
ejpam-6062	344	8	t1(x	t1(x	NOUN
ejpam-6062	344	9	)	)	PUNCT
ejpam-6062	344	10	=	=	SYM
ejpam-6062	344	11			NOUN
ejpam-6062	344	12			ADJ
ejpam-6062	344	13	2	2	NUM
ejpam-6062	344	14	1	1	NUM
ejpam-6062	344	15	0	0	NUM
ejpam-6062	344	16	−2	−2	NOUN
ejpam-6062	344	17	1	1	NUM
ejpam-6062	344	18	3	3	NUM
ejpam-6062	344	19	−2	−2	NOUN
ejpam-6062	344	20	1	1	NUM
ejpam-6062	344	21	−1	−1	NOUN
ejpam-6062	344	22	0	0	NUM
ejpam-6062	344	23	1	1	NUM
ejpam-6062	344	24	1	1	NUM
ejpam-6062	344	25	0	0	NUM
ejpam-6062	344	26	2	2	NUM
ejpam-6062	344	27	0	0	NUM
ejpam-6062	344	28	4	4	NUM
ejpam-6062	344	29			NOUN
ejpam-6062	344	30			NOUN
ejpam-6062	344	31	−1	−1	NOUN
ejpam-6062	344	32			NOUN
ejpam-6062	344	33			ADJ
ejpam-6062	344	34	0	0	NUM
ejpam-6062	344	35	0	0	SYM
ejpam-6062	344	36	0	0	NUM
ejpam-6062	344	37	2	2	NUM
ejpam-6062	344	38	−1	−1	NOUN
ejpam-6062	344	39	1	1	NUM
ejpam-6062	344	40	0	0	NUM
ejpam-6062	344	41	−1	−1	NOUN
ejpam-6062	344	42	−1	−1	NOUN
ejpam-6062	344	43	0	0	NUM
ejpam-6062	344	44	0	0	NUM
ejpam-6062	344	45	−1	−1	NOUN
ejpam-6062	344	46	−1	−1	NOUN
ejpam-6062	344	47	0	0	NUM
ejpam-6062	344	48	0	0	NUM
ejpam-6062	344	49	2	2	NUM
ejpam-6062	344	50			NOUN
ejpam-6062	344	51			NOUN
ejpam-6062	344	52			NOUN
ejpam-6062	345	1	x1	x1	NUM
ejpam-6062	345	2	x2	x2	PROPN
ejpam-6062	345	3	x3	x3	PROPN
ejpam-6062	345	4	x4	x4	PROPN
ejpam-6062	345	5			PROPN
ejpam-6062	345	6	h.	h.	PROPN
ejpam-6062	345	7	a.	a.	PROPN
ejpam-6062	345	8	abass	abass	PROPN
ejpam-6062	345	9	et	et	PROPN
ejpam-6062	345	10	al	al	PROPN
ejpam-6062	345	11	.	.	PUNCT
ejpam-6062	345	12	/	/	SYM
ejpam-6062	345	13	eur	eur	PROPN
ejpam-6062	345	14	.	.	PUNCT
ejpam-6062	346	1	j.	j.	PROPN
ejpam-6062	346	2	pure	pure	PROPN
ejpam-6062	346	3	appl	appl	PROPN
ejpam-6062	346	4	.	.	PROPN
ejpam-6062	346	5	math	math	PROPN
ejpam-6062	346	6	,	,	PUNCT
ejpam-6062	346	7	18	18	NUM
ejpam-6062	346	8	(	(	PUNCT
ejpam-6062	346	9	2	2	NUM
ejpam-6062	346	10	)	)	PUNCT
ejpam-6062	346	11	(	(	PUNCT
ejpam-6062	346	12	2025	2025	NUM
ejpam-6062	346	13	)	)	PUNCT
ejpam-6062	346	14	,	,	PUNCT
ejpam-6062	346	15	6062	6062	NUM
ejpam-6062	346	16	18	18	NUM
ejpam-6062	346	17	of	of	ADP
ejpam-6062	346	18	22	22	NUM
ejpam-6062	346	19	=	=	SYM
ejpam-6062	346	20			NOUN
ejpam-6062	346	21			ADJ
ejpam-6062	346	22	1	1	NUM
ejpam-6062	346	23	0	0	NUM
ejpam-6062	346	24	0	0	NUM
ejpam-6062	346	25	0	0	NUM
ejpam-6062	346	26	0	0	NUM
ejpam-6062	346	27	1	1	NUM
ejpam-6062	346	28	0	0	NUM
ejpam-6062	346	29	0	0	NUM
ejpam-6062	346	30	0	0	NUM
ejpam-6062	346	31	0	0	NUM
ejpam-6062	346	32	1	1	NUM
ejpam-6062	346	33	0	0	NUM
ejpam-6062	346	34	0	0	NUM
ejpam-6062	346	35	0	0	NUM
ejpam-6062	346	36	0	0	NUM
ejpam-6062	346	37	1	1	NUM
ejpam-6062	346	38			NOUN
ejpam-6062	346	39			NOUN
ejpam-6062	346	40			NOUN
ejpam-6062	346	41	x1	x1	NUM
ejpam-6062	346	42	x2	x2	PROPN
ejpam-6062	346	43	x3	x3	PROPN
ejpam-6062	346	44	x4	x4	PROPN
ejpam-6062	346	45			NOUN
ejpam-6062	346	46	.	.	PUNCT
ejpam-6062	347	1	proceeding	proceed	VERB
ejpam-6062	347	2	same	same	ADJ
ejpam-6062	347	3	way	way	NOUN
ejpam-6062	347	4	,	,	PUNCT
ejpam-6062	347	5	we	we	PRON
ejpam-6062	347	6	obtain	obtain	VERB
ejpam-6062	347	7	t2(x	t2(x	NOUN
ejpam-6062	347	8	)	)	PUNCT
ejpam-6062	348	1	=	=	SYM
ejpam-6062	348	2			NOUN
ejpam-6062	349	1			ADJ
ejpam-6062	349	2	1	1	NUM
ejpam-6062	349	3	0	0	NUM
ejpam-6062	349	4	0	0	NUM
ejpam-6062	349	5	0	0	NUM
ejpam-6062	349	6	0	0	NUM
ejpam-6062	349	7	1	1	NUM
ejpam-6062	349	8	0	0	NUM
ejpam-6062	349	9	0	0	NUM
ejpam-6062	349	10	0	0	NUM
ejpam-6062	349	11	0	0	NUM
ejpam-6062	349	12	1	1	NUM
ejpam-6062	349	13	0	0	NUM
ejpam-6062	349	14	0	0	NUM
ejpam-6062	349	15	0	0	NUM
ejpam-6062	349	16	0	0	NUM
ejpam-6062	349	17	1	1	NUM
ejpam-6062	349	18			NOUN
ejpam-6062	349	19			NOUN
ejpam-6062	349	20			NOUN
ejpam-6062	349	21	x1	x1	NUM
ejpam-6062	349	22	x2	x2	PROPN
ejpam-6062	349	23	x3	x3	PROPN
ejpam-6062	349	24	x4	x4	PROPN
ejpam-6062	349	25			NOUN
ejpam-6062	349	26	and	and	CCONJ
ejpam-6062	349	27	t3(x	t3(x	NUM
ejpam-6062	349	28	)	)	PUNCT
ejpam-6062	349	29	=	=	SYM
ejpam-6062	349	30	1	1	NUM
ejpam-6062	349	31	9999	9999	NUM
ejpam-6062	349	32			NOUN
ejpam-6062	349	33			ADJ
ejpam-6062	349	34	15554	15554	NUM
ejpam-6062	349	35	14443	14443	NUM
ejpam-6062	349	36	17776	17776	NUM
ejpam-6062	349	37	−2222	−2222	ADJ
ejpam-6062	349	38	−8148	−8148	NOUN
ejpam-6062	349	39	11851	11851	NUM
ejpam-6062	349	40	7407	7407	NUM
ejpam-6062	349	41	−7407	−7407	PROPN
ejpam-6062	349	42	−2963	−2963	NOUN
ejpam-6062	349	43	2963	2963	NUM
ejpam-6062	349	44	11851	11851	NUM
ejpam-6062	349	45	1852	1852	NUM
ejpam-6062	349	46	−370	−370	ADP
ejpam-6062	350	1	370	370	NUM
ejpam-6062	350	2	−1481	−1481	NUM
ejpam-6062	350	3	1481	1481	NUM
ejpam-6062	350	4			NOUN
ejpam-6062	350	5			PROPN
ejpam-6062	350	6			NOUN
ejpam-6062	350	7	x1	x1	NUM
ejpam-6062	350	8	x2	x2	PROPN
ejpam-6062	350	9	x3	x3	PROPN
ejpam-6062	350	10	x4	x4	PROPN
ejpam-6062	350	11			NOUN
ejpam-6062	350	12	.	.	PUNCT
ejpam-6062	351	1	for	for	ADP
ejpam-6062	351	2	this	this	DET
ejpam-6062	351	3	example	example	NOUN
ejpam-6062	351	4	,	,	PUNCT
ejpam-6062	351	5	we	we	PRON
ejpam-6062	351	6	choose	choose	VERB
ejpam-6062	351	7	αn	αn	NOUN
ejpam-6062	351	8	=	=	SYM
ejpam-6062	351	9	1	1	NUM
ejpam-6062	351	10	n+1	n+1	NUM
ejpam-6062	351	11	,	,	PUNCT
ejpam-6062	351	12	β0	β0	NOUN
ejpam-6062	351	13	=	=	SYM
ejpam-6062	351	14	2	2	NUM
ejpam-6062	351	15	n+15	n+15	NOUN
ejpam-6062	351	16	,	,	PUNCT
ejpam-6062	351	17	β1	β1	PROPN
ejpam-6062	351	18	=	=	PUNCT
ejpam-6062	351	19	6	6	NUM
ejpam-6062	351	20	n+15	n+15	PROPN
ejpam-6062	351	21	,	,	PUNCT
ejpam-6062	351	22	β2	β2	NOUN
ejpam-6062	351	23	=	=	PROPN
ejpam-6062	351	24	3+n	3+n	NUM
ejpam-6062	351	25	n+15	n+15	NOUN
ejpam-6062	351	26	and	and	CCONJ
ejpam-6062	351	27	β3	β3	ADJ
ejpam-6062	351	28	=	=	SYM
ejpam-6062	351	29	4	4	NUM
ejpam-6062	351	30	n+15	n+15	PROPN
ejpam-6062	351	31	.	.	PUNCT
ejpam-6062	352	1	we	we	PRON
ejpam-6062	352	2	also	also	ADV
ejpam-6062	352	3	choose	choose	VERB
ejpam-6062	352	4	γ	γ	X
ejpam-6062	352	5	=	=	NOUN
ejpam-6062	352	6	0.75	0.75	NUM
ejpam-6062	352	7	,	,	PUNCT
ejpam-6062	352	8	λ0,n	λ0,n	ADJ
ejpam-6062	352	9	=	=	SYM
ejpam-6062	352	10	5n	5n	NUM
ejpam-6062	352	11	10n+17	10n+17	NUM
ejpam-6062	352	12	,	,	PUNCT
ejpam-6062	352	13	λ1,n	λ1,n	PROPN
ejpam-6062	352	14	=	=	PUNCT
ejpam-6062	352	15	3n+10	3n+10	NUM
ejpam-6062	352	16	10n+17	10n+17	NUM
ejpam-6062	352	17	and	and	CCONJ
ejpam-6062	352	18	λ2,n	λ2,n	PROPN
ejpam-6062	352	19	=	=	SYM
ejpam-6062	352	20	2n+7	2n+7	PROPN
ejpam-6062	352	21	10n+17	10n+17	NUM
ejpam-6062	352	22	.	.	PUNCT
ejpam-6062	353	1	let	let	VERB
ejpam-6062	353	2	en	en	X
ejpam-6062	353	3	=	=	PUNCT
ejpam-6062	353	4	∥xn+1	∥xn+1	PROPN
ejpam-6062	353	5	−	−	PROPN
ejpam-6062	353	6	xn∥2	xn∥2	NOUN
ejpam-6062	353	7	<	<	X
ejpam-6062	353	8	10−4	10−4	PROPN
ejpam-6062	353	9	be	be	AUX
ejpam-6062	353	10	the	the	DET
ejpam-6062	353	11	stopping	stopping	NOUN
ejpam-6062	353	12	criterion	criterion	NOUN
ejpam-6062	353	13	.	.	PUNCT
ejpam-6062	354	1	we	we	PRON
ejpam-6062	354	2	illustrate	illustrate	VERB
ejpam-6062	354	3	this	this	DET
ejpam-6062	354	4	example	example	NOUN
ejpam-6062	354	5	with	with	ADP
ejpam-6062	354	6	different	different	ADJ
ejpam-6062	354	7	initial	initial	ADJ
ejpam-6062	354	8	values	value	NOUN
ejpam-6062	354	9	of	of	ADP
ejpam-6062	354	10	x1	x1	PROPN
ejpam-6062	354	11	.	.	PUNCT
ejpam-6062	355	1	(	(	PUNCT
ejpam-6062	355	2	case	case	NOUN
ejpam-6062	355	3	1	1	NUM
ejpam-6062	355	4	)	)	PUNCT
ejpam-6062	355	5	x1	x1	NOUN
ejpam-6062	355	6	=	=	PUNCT
ejpam-6062	355	7	(	(	PUNCT
ejpam-6062	355	8	1	1	NUM
ejpam-6062	355	9	,	,	PUNCT
ejpam-6062	355	10	1	1	NUM
ejpam-6062	355	11	,	,	PUNCT
ejpam-6062	355	12	2	2	NUM
ejpam-6062	355	13	,	,	PUNCT
ejpam-6062	355	14	2)′	2)′	NUM
ejpam-6062	355	15	;	;	PUNCT
ejpam-6062	355	16	(	(	PUNCT
ejpam-6062	355	17	case	case	NOUN
ejpam-6062	355	18	2	2	NUM
ejpam-6062	355	19	)	)	PUNCT
ejpam-6062	355	20	x1	x1	NOUN
ejpam-6062	355	21	=	=	SYM
ejpam-6062	355	22	(	(	PUNCT
ejpam-6062	355	23	5	5	NUM
ejpam-6062	355	24	,	,	PUNCT
ejpam-6062	355	25	5	5	NUM
ejpam-6062	355	26	,	,	PUNCT
ejpam-6062	355	27	5	5	NUM
ejpam-6062	355	28	,	,	PUNCT
ejpam-6062	355	29	5)′	5)′	NUM
ejpam-6062	355	30	;	;	PUNCT
ejpam-6062	355	31	(	(	PUNCT
ejpam-6062	355	32	case	case	NOUN
ejpam-6062	355	33	3	3	NUM
ejpam-6062	355	34	)	)	PUNCT
ejpam-6062	355	35	x1	x1	NOUN
ejpam-6062	355	36	=	=	PUNCT
ejpam-6062	355	37	(	(	PUNCT
ejpam-6062	355	38	0.25	0.25	NUM
ejpam-6062	355	39	,	,	PUNCT
ejpam-6062	355	40	0.5	0.5	NUM
ejpam-6062	355	41	,	,	PUNCT
ejpam-6062	355	42	0.25	0.25	NUM
ejpam-6062	355	43	,	,	PUNCT
ejpam-6062	355	44	0.25)′	0.25)′	NOUN
ejpam-6062	355	45	;	;	PUNCT
ejpam-6062	355	46	(	(	PUNCT
ejpam-6062	355	47	case	case	NOUN
ejpam-6062	355	48	4	4	NUM
ejpam-6062	355	49	)	)	PUNCT
ejpam-6062	355	50	x1	x1	NOUN
ejpam-6062	355	51	=	=	PUNCT
ejpam-6062	355	52	(	(	PUNCT
ejpam-6062	355	53	10	10	NUM
ejpam-6062	355	54	,	,	PUNCT
ejpam-6062	355	55	5,−5,−20)′.	5,−5,−20)′.	NUM
ejpam-6062	355	56	the	the	DET
ejpam-6062	355	57	results	result	NOUN
ejpam-6062	355	58	of	of	ADP
ejpam-6062	355	59	this	this	DET
ejpam-6062	355	60	experiment	experiment	NOUN
ejpam-6062	355	61	are	be	AUX
ejpam-6062	355	62	presented	present	VERB
ejpam-6062	355	63	in	in	ADP
ejpam-6062	355	64	figure	figure	NOUN
ejpam-6062	355	65	1	1	NUM
ejpam-6062	355	66	.	.	PUNCT
ejpam-6062	356	1	h.	h.	PROPN
ejpam-6062	356	2	a.	a.	PROPN
ejpam-6062	356	3	abass	abass	PROPN
ejpam-6062	356	4	et	et	PROPN
ejpam-6062	356	5	al	al	PROPN
ejpam-6062	356	6	.	.	PUNCT
ejpam-6062	356	7	/	/	SYM
ejpam-6062	356	8	eur	eur	PROPN
ejpam-6062	356	9	.	.	PUNCT
ejpam-6062	357	1	j.	j.	PROPN
ejpam-6062	357	2	pure	pure	PROPN
ejpam-6062	357	3	appl	appl	PROPN
ejpam-6062	357	4	.	.	PROPN
ejpam-6062	357	5	math	math	PROPN
ejpam-6062	357	6	,	,	PUNCT
ejpam-6062	357	7	18	18	NUM
ejpam-6062	357	8	(	(	PUNCT
ejpam-6062	357	9	2	2	NUM
ejpam-6062	357	10	)	)	PUNCT
ejpam-6062	357	11	(	(	PUNCT
ejpam-6062	357	12	2025	2025	NUM
ejpam-6062	357	13	)	)	PUNCT
ejpam-6062	357	14	,	,	PUNCT
ejpam-6062	357	15	6062	6062	NUM
ejpam-6062	357	16	19	19	NUM
ejpam-6062	357	17	of	of	ADP
ejpam-6062	357	18	22	22	NUM
ejpam-6062	357	19	0	0	NUM
ejpam-6062	357	20	2	2	NUM
ejpam-6062	357	21	4	4	NUM
ejpam-6062	357	22	6	6	NUM
ejpam-6062	357	23	8	8	NUM
ejpam-6062	357	24	10	10	NUM
ejpam-6062	357	25	12	12	NUM
ejpam-6062	357	26	14	14	NUM
ejpam-6062	357	27	16	16	NUM
ejpam-6062	357	28	18	18	NUM
ejpam-6062	357	29	number	number	NOUN
ejpam-6062	357	30	of	of	ADP
ejpam-6062	357	31	iterations	iteration	NOUN
ejpam-6062	357	32	0	0	NUM
ejpam-6062	357	33	2	2	NUM
ejpam-6062	357	34	4	4	NUM
ejpam-6062	357	35	6	6	NUM
ejpam-6062	357	36	8	8	NUM
ejpam-6062	357	37	10	10	NUM
ejpam-6062	357	38	12	12	NUM
ejpam-6062	357	39	14	14	NUM
ejpam-6062	357	40	16	16	NUM
ejpam-6062	357	41	18	18	NUM
ejpam-6062	357	42	20	20	NUM
ejpam-6062	357	43	e	e	NOUN
ejpam-6062	357	44	n	n	NOUN
ejpam-6062	357	45	algorithm	algorithm	NOUN
ejpam-6062	357	46	3.2	3.2	NUM
ejpam-6062	357	47	0	0	NUM
ejpam-6062	357	48	2	2	NUM
ejpam-6062	357	49	4	4	NUM
ejpam-6062	357	50	6	6	NUM
ejpam-6062	357	51	8	8	NUM
ejpam-6062	357	52	10	10	NUM
ejpam-6062	357	53	12	12	NUM
ejpam-6062	357	54	14	14	NUM
ejpam-6062	357	55	16	16	NUM
ejpam-6062	357	56	18	18	NUM
ejpam-6062	357	57	number	number	NOUN
ejpam-6062	357	58	of	of	ADP
ejpam-6062	357	59	iterations	iteration	NOUN
ejpam-6062	357	60	0	0	NUM
ejpam-6062	358	1	50	50	NUM
ejpam-6062	358	2	100	100	NUM
ejpam-6062	358	3	150	150	NUM
ejpam-6062	358	4	200	200	NUM
ejpam-6062	358	5	250	250	NUM
ejpam-6062	358	6	e	e	NOUN
ejpam-6062	358	7	n	n	NUM
ejpam-6062	358	8	algorithm	algorithm	NOUN
ejpam-6062	358	9	3.2	3.2	NUM
ejpam-6062	358	10	0	0	NUM
ejpam-6062	358	11	2	2	NUM
ejpam-6062	358	12	4	4	NUM
ejpam-6062	358	13	6	6	NUM
ejpam-6062	358	14	8	8	NUM
ejpam-6062	358	15	10	10	NUM
ejpam-6062	358	16	12	12	NUM
ejpam-6062	358	17	14	14	NUM
ejpam-6062	358	18	16	16	NUM
ejpam-6062	358	19	18	18	NUM
ejpam-6062	358	20	number	number	NOUN
ejpam-6062	358	21	of	of	ADP
ejpam-6062	358	22	iterations	iteration	NOUN
ejpam-6062	358	23	0	0	NUM
ejpam-6062	358	24	0.05	0.05	NUM
ejpam-6062	358	25	0.1	0.1	NUM
ejpam-6062	358	26	0.15	0.15	NUM
ejpam-6062	358	27	0.2	0.2	NUM
ejpam-6062	358	28	0.25	0.25	NUM
ejpam-6062	358	29	0.3	0.3	NUM
ejpam-6062	358	30	e	e	NOUN
ejpam-6062	358	31	n	n	DET
ejpam-6062	358	32	algorithm	algorithm	NOUN
ejpam-6062	358	33	3.2	3.2	NUM
ejpam-6062	358	34	0	0	NUM
ejpam-6062	358	35	2	2	NUM
ejpam-6062	358	36	4	4	NUM
ejpam-6062	358	37	6	6	NUM
ejpam-6062	358	38	8	8	NUM
ejpam-6062	358	39	10	10	NUM
ejpam-6062	358	40	12	12	NUM
ejpam-6062	358	41	14	14	NUM
ejpam-6062	358	42	16	16	NUM
ejpam-6062	358	43	18	18	NUM
ejpam-6062	358	44	number	number	NOUN
ejpam-6062	358	45	of	of	ADP
ejpam-6062	358	46	iterations	iteration	NOUN
ejpam-6062	358	47	0	0	NUM
ejpam-6062	358	48	500	500	NUM
ejpam-6062	358	49	1000	1000	NUM
ejpam-6062	358	50	1500	1500	NUM
ejpam-6062	358	51	2000	2000	NUM
ejpam-6062	358	52	2500	2500	NUM
ejpam-6062	358	53	e	e	NOUN
ejpam-6062	358	54	n	n	NOUN
ejpam-6062	358	55	algorithm	algorithm	NOUN
ejpam-6062	358	56	3.2	3.2	NUM
ejpam-6062	358	57	figure	figure	NOUN
ejpam-6062	358	58	1	1	NUM
ejpam-6062	358	59	:	:	PUNCT
ejpam-6062	358	60	example	example	NOUN
ejpam-6062	358	61	4	4	NUM
ejpam-6062	358	62	.	.	X
ejpam-6062	358	63	top	top	NOUN
ejpam-6062	358	64	left	left	ADJ
ejpam-6062	358	65	:	:	PUNCT
ejpam-6062	358	66	case	case	NOUN
ejpam-6062	358	67	1	1	NUM
ejpam-6062	358	68	,	,	PUNCT
ejpam-6062	358	69	top	top	ADJ
ejpam-6062	358	70	right	right	NOUN
ejpam-6062	358	71	:	:	PUNCT
ejpam-6062	358	72	case	case	NOUN
ejpam-6062	358	73	2	2	NUM
ejpam-6062	358	74	,	,	PUNCT
ejpam-6062	358	75	bottom	bottom	NOUN
ejpam-6062	358	76	left	left	ADJ
ejpam-6062	358	77	:	:	PUNCT
ejpam-6062	358	78	case	case	NOUN
ejpam-6062	358	79	3	3	NUM
ejpam-6062	358	80	,	,	PUNCT
ejpam-6062	358	81	bottom	bottom	ADJ
ejpam-6062	358	82	right	right	NOUN
ejpam-6062	358	83	:	:	PUNCT
ejpam-6062	358	84	case	case	NOUN
ejpam-6062	358	85	4	4	NUM
ejpam-6062	358	86	.	.	PUNCT
ejpam-6062	358	87	references	reference	NOUN
ejpam-6062	358	88	[	[	X
ejpam-6062	358	89	1	1	NUM
ejpam-6062	358	90	]	]	PUNCT
ejpam-6062	358	91	c.	c.	PROPN
ejpam-6062	358	92	bryne	bryne	PROPN
ejpam-6062	358	93	.	.	PUNCT
ejpam-6062	359	1	iterative	iterative	ADJ
ejpam-6062	359	2	oblique	oblique	ADJ
ejpam-6062	359	3	projection	projection	NOUN
ejpam-6062	359	4	onto	onto	ADP
ejpam-6062	359	5	convex	convex	NOUN
ejpam-6062	359	6	subsets	subset	NOUN
ejpam-6062	359	7	and	and	CCONJ
ejpam-6062	359	8	the	the	DET
ejpam-6062	359	9	split	split	NOUN
ejpam-6062	359	10	feasibility	feasibility	NOUN
ejpam-6062	359	11	problems	problem	NOUN
ejpam-6062	359	12	.	.	PUNCT
ejpam-6062	360	1	inverse	inverse	PROPN
ejpam-6062	360	2	probl	probl	PROPN
ejpam-6062	360	3	.	.	PUNCT
ejpam-6062	360	4	,	,	PUNCT
ejpam-6062	360	5	18:441–453	18:441–453	NUM
ejpam-6062	360	6	,	,	PUNCT
ejpam-6062	360	7	2002	2002	NUM
ejpam-6062	360	8	.	.	PUNCT
ejpam-6062	361	1	[	[	X
ejpam-6062	361	2	2	2	X
ejpam-6062	361	3	]	]	X
ejpam-6062	361	4	y.	y.	NOUN
ejpam-6062	361	5	censor	censor	NOUN
ejpam-6062	361	6	and	and	CCONJ
ejpam-6062	361	7	t.	t.	PROPN
ejpam-6062	361	8	elfving	elfving	NOUN
ejpam-6062	361	9	.	.	PUNCT
ejpam-6062	362	1	a	a	DET
ejpam-6062	362	2	multi	multi	ADJ
ejpam-6062	362	3	projection	projection	NOUN
ejpam-6062	362	4	algorithms	algorithm	NOUN
ejpam-6062	362	5	using	use	VERB
ejpam-6062	362	6	bregman	bregman	NOUN
ejpam-6062	362	7	projections	projection	NOUN
ejpam-6062	362	8	in	in	ADP
ejpam-6062	362	9	a	a	DET
ejpam-6062	362	10	product	product	NOUN
ejpam-6062	362	11	space	space	NOUN
ejpam-6062	362	12	.	.	PUNCT
ejpam-6062	363	1	numer	numer	PROPN
ejpam-6062	363	2	.	.	PROPN
ejpam-6062	364	1	algor	algor	PROPN
ejpam-6062	364	2	.	.	PUNCT
ejpam-6062	364	3	,	,	PUNCT
ejpam-6062	364	4	8:221–239	8:221–239	NUM
ejpam-6062	364	5	,	,	PUNCT
ejpam-6062	364	6	1994	1994	NUM
ejpam-6062	364	7	.	.	PUNCT
ejpam-6062	365	1	[	[	X
ejpam-6062	365	2	3	3	X
ejpam-6062	365	3	]	]	PUNCT
ejpam-6062	365	4	p.	p.	NOUN
ejpam-6062	365	5	sunthrayuth	sunthrayuth	PROPN
ejpam-6062	365	6	p.	p.	PROPN
ejpam-6062	365	7	cholamjiak	cholamjiak	PROPN
ejpam-6062	365	8	.	.	PUNCT
ejpam-6062	366	1	a	a	DET
ejpam-6062	366	2	halpern	halpern	ADJ
ejpam-6062	366	3	-	-	PUNCT
ejpam-6062	366	4	type	type	NOUN
ejpam-6062	366	5	iteration	iteration	NOUN
ejpam-6062	366	6	for	for	ADP
ejpam-6062	366	7	solving	solve	VERB
ejpam-6062	366	8	the	the	DET
ejpam-6062	366	9	split	split	NOUN
ejpam-6062	366	10	feasibility	feasibility	NOUN
ejpam-6062	366	11	problem	problem	NOUN
ejpam-6062	366	12	and	and	CCONJ
ejpam-6062	366	13	fixed	fix	VERB
ejpam-6062	366	14	point	point	NOUN
ejpam-6062	366	15	problem	problem	NOUN
ejpam-6062	366	16	of	of	ADP
ejpam-6062	366	17	bregman	bregman	NOUN
ejpam-6062	366	18	relatively	relatively	ADV
ejpam-6062	366	19	nonexpansive	nonexpansive	ADJ
ejpam-6062	366	20	semigroup	semigroup	NOUN
ejpam-6062	366	21	in	in	ADP
ejpam-6062	366	22	banach	banach	NOUN
ejpam-6062	366	23	spaces	space	NOUN
ejpam-6062	366	24	.	.	PUNCT
ejpam-6062	367	1	filomat	filomat	NOUN
ejpam-6062	367	2	,	,	PUNCT
ejpam-6062	367	3	32(9):3211–3227	32(9):3211–3227	NUM
ejpam-6062	367	4	,	,	PUNCT
ejpam-6062	367	5	2018	2018	NUM
ejpam-6062	367	6	.	.	PUNCT
ejpam-6062	368	1	[	[	X
ejpam-6062	368	2	4	4	X
ejpam-6062	368	3	]	]	PUNCT
ejpam-6062	368	4	k.	k.	PROPN
ejpam-6062	368	5	r.	r.	PROPN
ejpam-6062	368	6	kazmi	kazmi	PROPN
ejpam-6062	368	7	,	,	PUNCT
ejpam-6062	368	8	r.	r.	PROPN
ejpam-6062	368	9	ali	ali	PROPN
ejpam-6062	368	10	,	,	PUNCT
ejpam-6062	368	11	and	and	CCONJ
ejpam-6062	368	12	s.	s.	PROPN
ejpam-6062	368	13	yousuf	yousuf	PROPN
ejpam-6062	368	14	.	.	PUNCT
ejpam-6062	369	1	generalized	generalize	VERB
ejpam-6062	369	2	equilibrium	equilibrium	NOUN
ejpam-6062	369	3	and	and	CCONJ
ejpam-6062	369	4	fixed	fix	VERB
ejpam-6062	369	5	point	point	NOUN
ejpam-6062	369	6	problems	problem	NOUN
ejpam-6062	369	7	for	for	ADP
ejpam-6062	369	8	bregman	bregman	NOUN
ejpam-6062	369	9	relatively	relatively	ADV
ejpam-6062	369	10	nonexpansive	nonexpansive	ADJ
ejpam-6062	369	11	mappings	mapping	NOUN
ejpam-6062	369	12	in	in	ADP
ejpam-6062	369	13	banach	banach	NOUN
ejpam-6062	369	14	spaces	space	NOUN
ejpam-6062	369	15	.	.	PUNCT
ejpam-6062	370	1	j.	j.	PROPN
ejpam-6062	370	2	fixed	fix	VERB
ejpam-6062	370	3	poibt	poibt	PROPN
ejpam-6062	370	4	theory	theory	NOUN
ejpam-6062	370	5	appl	appl	PROPN
ejpam-6062	370	6	.	.	PROPN
ejpam-6062	370	7	,	,	PUNCT
ejpam-6062	370	8	20(151	20(151	NOUN
ejpam-6062	370	9	)	)	PUNCT
ejpam-6062	370	10	,	,	PUNCT
ejpam-6062	370	11	2018	2018	NUM
ejpam-6062	370	12	.	.	PUNCT
ejpam-6062	371	1	[	[	X
ejpam-6062	371	2	5	5	X
ejpam-6062	371	3	]	]	X
ejpam-6062	371	4	y.	y.	PROPN
ejpam-6062	371	5	shehu	shehu	PROPN
ejpam-6062	371	6	,	,	PUNCT
ejpam-6062	371	7	f.	f.	PROPN
ejpam-6062	371	8	u.	u.	PROPN
ejpam-6062	371	9	ogbuisi	ogbuisi	PROPN
ejpam-6062	371	10	,	,	PUNCT
ejpam-6062	371	11	and	and	CCONJ
ejpam-6062	371	12	o.	o.	PROPN
ejpam-6062	371	13	s.	s.	PROPN
ejpam-6062	371	14	iyiola	iyiola	PROPN
ejpam-6062	371	15	.	.	PUNCT
ejpam-6062	372	1	convergence	convergence	NOUN
ejpam-6062	372	2	analysis	analysis	NOUN
ejpam-6062	372	3	of	of	ADP
ejpam-6062	372	4	an	an	DET
ejpam-6062	372	5	iterative	iterative	NOUN
ejpam-6062	372	6	h.	h.	PROPN
ejpam-6062	372	7	a.	a.	PROPN
ejpam-6062	372	8	abass	abass	PROPN
ejpam-6062	372	9	et	et	PROPN
ejpam-6062	372	10	al	al	PROPN
ejpam-6062	372	11	.	.	PUNCT
ejpam-6062	372	12	/	/	SYM
ejpam-6062	372	13	eur	eur	PROPN
ejpam-6062	372	14	.	.	PUNCT
ejpam-6062	373	1	j.	j.	PROPN
ejpam-6062	373	2	pure	pure	PROPN
ejpam-6062	373	3	appl	appl	PROPN
ejpam-6062	373	4	.	.	PROPN
ejpam-6062	373	5	math	math	PROPN
ejpam-6062	373	6	,	,	PUNCT
ejpam-6062	373	7	18	18	NUM
ejpam-6062	373	8	(	(	PUNCT
ejpam-6062	373	9	2	2	NUM
ejpam-6062	373	10	)	)	PUNCT
ejpam-6062	373	11	(	(	PUNCT
ejpam-6062	373	12	2025	2025	NUM
ejpam-6062	373	13	)	)	PUNCT
ejpam-6062	373	14	,	,	PUNCT
ejpam-6062	373	15	6062	6062	NUM
ejpam-6062	373	16	20	20	NUM
ejpam-6062	373	17	of	of	ADP
ejpam-6062	373	18	22	22	NUM
ejpam-6062	373	19	algorithm	algorithm	NOUN
ejpam-6062	373	20	for	for	ADP
ejpam-6062	373	21	fixed	fix	VERB
ejpam-6062	373	22	point	point	NOUN
ejpam-6062	373	23	problems	problem	NOUN
ejpam-6062	373	24	and	and	CCONJ
ejpam-6062	373	25	split	split	VERB
ejpam-6062	373	26	feasibility	feasibility	NOUN
ejpam-6062	373	27	problems	problem	NOUN
ejpam-6062	373	28	in	in	ADP
ejpam-6062	373	29	certain	certain	ADJ
ejpam-6062	373	30	banach	banach	NOUN
ejpam-6062	373	31	spaces	space	NOUN
ejpam-6062	373	32	.	.	PUNCT
ejpam-6062	374	1	optimization	optimization	NOUN
ejpam-6062	374	2	,	,	PUNCT
ejpam-6062	374	3	65:299–323	65:299–323	PROPN
ejpam-6062	374	4	,	,	PUNCT
ejpam-6062	374	5	2016	2016	NUM
ejpam-6062	374	6	.	.	PUNCT
ejpam-6062	375	1	[	[	X
ejpam-6062	375	2	6	6	NUM
ejpam-6062	375	3	]	]	X
ejpam-6062	375	4	y.	y.	NOUN
ejpam-6062	375	5	censor	censor	NOUN
ejpam-6062	375	6	and	and	CCONJ
ejpam-6062	375	7	a.	a.	NOUN
ejpam-6062	375	8	segal	segal	PROPN
ejpam-6062	375	9	.	.	PUNCT
ejpam-6062	376	1	the	the	DET
ejpam-6062	376	2	split	split	ADJ
ejpam-6062	376	3	common	common	ADJ
ejpam-6062	376	4	fixed	fix	VERB
ejpam-6062	376	5	point	point	NOUN
ejpam-6062	376	6	problem	problem	NOUN
ejpam-6062	376	7	for	for	ADP
ejpam-6062	376	8	directed	direct	VERB
ejpam-6062	376	9	operators	operator	NOUN
ejpam-6062	376	10	.	.	PUNCT
ejpam-6062	377	1	j.	j.	PROPN
ejpam-6062	377	2	convex	convex	PROPN
ejpam-6062	377	3	anal	anal	PROPN
ejpam-6062	377	4	.	.	PUNCT
ejpam-6062	377	5	,	,	PUNCT
ejpam-6062	377	6	16(2):587–600	16(2):587–600	PROPN
ejpam-6062	377	7	,	,	PUNCT
ejpam-6062	377	8	2009	2009	NUM
ejpam-6062	377	9	.	.	PUNCT
ejpam-6062	378	1	[	[	X
ejpam-6062	378	2	7	7	X
ejpam-6062	378	3	]	]	PUNCT
ejpam-6062	378	4	a.	a.	NOUN
ejpam-6062	378	5	moudafi	moudafi	PROPN
ejpam-6062	378	6	.	.	PUNCT
ejpam-6062	379	1	a	a	DET
ejpam-6062	379	2	note	note	NOUN
ejpam-6062	379	3	on	on	ADP
ejpam-6062	379	4	the	the	DET
ejpam-6062	379	5	split	split	ADJ
ejpam-6062	379	6	common	common	ADJ
ejpam-6062	379	7	fixed	fix	VERB
ejpam-6062	379	8	point	point	NOUN
ejpam-6062	379	9	problem	problem	NOUN
ejpam-6062	379	10	for	for	ADP
ejpam-6062	379	11	quasi	quasi	ADJ
ejpam-6062	379	12	-	-	ADJ
ejpam-6062	379	13	nonexpansive	nonexpansive	ADJ
ejpam-6062	379	14	operator	operator	NOUN
ejpam-6062	379	15	.	.	PUNCT
ejpam-6062	380	1	nonlinear	nonlinear	ADJ
ejpam-6062	380	2	anal	anal	PROPN
ejpam-6062	380	3	.	.	PUNCT
ejpam-6062	380	4	,	,	PUNCT
ejpam-6062	380	5	74:4083–4087	74:4083–4087	NUM
ejpam-6062	380	6	,	,	PUNCT
ejpam-6062	380	7	2011	2011	NUM
ejpam-6062	380	8	.	.	PUNCT
ejpam-6062	381	1	[	[	X
ejpam-6062	381	2	8	8	NUM
ejpam-6062	381	3	]	]	PUNCT
ejpam-6062	381	4	a.	a.	NOUN
ejpam-6062	381	5	moudafi	moudafi	PROPN
ejpam-6062	381	6	.	.	PUNCT
ejpam-6062	382	1	split	split	VERB
ejpam-6062	382	2	monotone	monotone	ADJ
ejpam-6062	382	3	variational	variational	ADJ
ejpam-6062	382	4	inclusions	inclusion	NOUN
ejpam-6062	382	5	.	.	PUNCT
ejpam-6062	383	1	j.	j.	PROPN
ejpam-6062	383	2	optim	optim	PROPN
ejpam-6062	383	3	.	.	PUNCT
ejpam-6062	384	1	theory	theory	NOUN
ejpam-6062	384	2	appl	appl	PROPN
ejpam-6062	384	3	.	.	PROPN
ejpam-6062	384	4	,	,	PUNCT
ejpam-6062	384	5	150:275	150:275	NUM
ejpam-6062	384	6	–	–	PUNCT
ejpam-6062	384	7	283	283	NUM
ejpam-6062	384	8	,	,	PUNCT
ejpam-6062	384	9	2011	2011	NUM
ejpam-6062	384	10	.	.	PUNCT
ejpam-6062	385	1	[	[	X
ejpam-6062	385	2	9	9	NUM
ejpam-6062	385	3	]	]	PUNCT
ejpam-6062	385	4	h.	h.	PROPN
ejpam-6062	385	5	a.	a.	PROPN
ejpam-6062	385	6	abass	abass	PROPN
ejpam-6062	385	7	,	,	PUNCT
ejpam-6062	385	8	c.	c.	PROPN
ejpam-6062	385	9	izuchukwu	izuchukwu	NOUN
ejpam-6062	385	10	,	,	PUNCT
ejpam-6062	385	11	o.	o.	NOUN
ejpam-6062	385	12	t.	t.	PROPN
ejpam-6062	385	13	mewomo	mewomo	PROPN
ejpam-6062	385	14	,	,	PUNCT
ejpam-6062	385	15	and	and	CCONJ
ejpam-6062	385	16	q.	q.	PROPN
ejpam-6062	385	17	l.	l.	PROPN
ejpam-6062	385	18	dong	dong	PROPN
ejpam-6062	385	19	.	.	PUNCT
ejpam-6062	386	1	strong	strong	ADJ
ejpam-6062	386	2	convergence	convergence	NOUN
ejpam-6062	386	3	of	of	ADP
ejpam-6062	386	4	an	an	DET
ejpam-6062	386	5	inertial	inertial	ADJ
ejpam-6062	386	6	forward	forward	ADJ
ejpam-6062	386	7	-	-	PUNCT
ejpam-6062	386	8	backward	backward	ADJ
ejpam-6062	386	9	splitting	splitting	NOUN
ejpam-6062	386	10	method	method	NOUN
ejpam-6062	386	11	for	for	ADP
ejpam-6062	386	12	accretive	accretive	ADJ
ejpam-6062	386	13	operators	operator	NOUN
ejpam-6062	386	14	in	in	ADP
ejpam-6062	386	15	real	real	ADJ
ejpam-6062	386	16	banach	banach	NOUN
ejpam-6062	386	17	space	space	NOUN
ejpam-6062	386	18	.	.	PUNCT
ejpam-6062	387	1	fixed	fix	VERB
ejpam-6062	387	2	point	point	NOUN
ejpam-6062	387	3	theory	theory	NOUN
ejpam-6062	387	4	,	,	PUNCT
ejpam-6062	387	5	20(2):397–412	20(2):397–412	PROPN
ejpam-6062	387	6	,	,	PUNCT
ejpam-6062	387	7	2020	2020	NUM
ejpam-6062	387	8	.	.	PUNCT
ejpam-6062	388	1	[	[	X
ejpam-6062	388	2	10	10	NUM
ejpam-6062	388	3	]	]	X
ejpam-6062	388	4	h.	h.	PROPN
ejpam-6062	388	5	a.	a.	PROPN
ejpam-6062	388	6	abass	abass	PROPN
ejpam-6062	388	7	,	,	PUNCT
ejpam-6062	388	8	k.	k.	PROPN
ejpam-6062	388	9	o.	o.	PROPN
ejpam-6062	388	10	aremu	aremu	PROPN
ejpam-6062	388	11	,	,	PUNCT
ejpam-6062	388	12	l.	l.	PROPN
ejpam-6062	388	13	o.	o.	PROPN
ejpam-6062	388	14	jolaoso	jolaoso	PROPN
ejpam-6062	388	15	,	,	PUNCT
ejpam-6062	388	16	and	and	CCONJ
ejpam-6062	388	17	o.t	o.t	PROPN
ejpam-6062	388	18	.	.	PROPN
ejpam-6062	388	19	mewomo	mewomo	PROPN
ejpam-6062	388	20	.	.	PUNCT
ejpam-6062	389	1	an	an	DET
ejpam-6062	389	2	inertial	inertial	ADJ
ejpam-6062	389	3	forwardbackward	forwardbackward	NOUN
ejpam-6062	389	4	splitting	splitting	NOUN
ejpam-6062	389	5	method	method	NOUN
ejpam-6062	389	6	for	for	ADP
ejpam-6062	389	7	approximating	approximate	VERB
ejpam-6062	389	8	solutions	solution	NOUN
ejpam-6062	389	9	of	of	ADP
ejpam-6062	389	10	certain	certain	ADJ
ejpam-6062	389	11	optimization	optimization	NOUN
ejpam-6062	389	12	problem	problem	NOUN
ejpam-6062	389	13	.	.	PUNCT
ejpam-6062	390	1	j.	j.	PROPN
ejpam-6062	390	2	nonlinear	nonlinear	PROPN
ejpam-6062	390	3	funct	funct	PROPN
ejpam-6062	390	4	.	.	PUNCT
ejpam-6062	391	1	anal	anal	PROPN
ejpam-6062	391	2	.	.	PROPN
ejpam-6062	391	3	,	,	PUNCT
ejpam-6062	391	4	2020	2020	NUM
ejpam-6062	391	5	:	:	PUNCT
ejpam-6062	391	6	article	article	NOUN
ejpam-6062	391	7	i	i	PROPN
ejpam-6062	391	8	d	d	PROPN
ejpam-6062	391	9	6	6	NUM
ejpam-6062	391	10	,	,	PUNCT
ejpam-6062	391	11	2020	2020	NUM
ejpam-6062	391	12	.	.	PUNCT
ejpam-6062	392	1	[	[	X
ejpam-6062	392	2	11	11	NUM
ejpam-6062	392	3	]	]	X
ejpam-6062	392	4	l.	l.	PROPN
ejpam-6062	392	5	mokaba	mokaba	PROPN
ejpam-6062	392	6	,	,	PUNCT
ejpam-6062	392	7	h.	h.	PROPN
ejpam-6062	392	8	a.	a.	PROPN
ejpam-6062	392	9	abass	abass	PROPN
ejpam-6062	392	10	,	,	PUNCT
ejpam-6062	392	11	and	and	CCONJ
ejpam-6062	392	12	a.	a.	PROPN
ejpam-6062	392	13	adamu	adamu	PROPN
ejpam-6062	392	14	.	.	PUNCT
ejpam-6062	393	1	two	two	NUM
ejpam-6062	393	2	step	step	NOUN
ejpam-6062	393	3	inertial	inertial	NOUN
ejpam-6062	393	4	tseng	tseng	PROPN
ejpam-6062	393	5	method	method	NOUN
ejpam-6062	393	6	for	for	ADP
ejpam-6062	393	7	solving	solve	VERB
ejpam-6062	393	8	monotone	monotone	ADJ
ejpam-6062	393	9	variational	variational	ADJ
ejpam-6062	393	10	inclusion	inclusion	NOUN
ejpam-6062	393	11	problem	problem	NOUN
ejpam-6062	393	12	.	.	PUNCT
ejpam-6062	394	1	results	result	NOUN
ejpam-6062	394	2	in	in	ADP
ejpam-6062	394	3	applied	applied	ADJ
ejpam-6062	394	4	mathematics	mathematic	NOUN
ejpam-6062	394	5	,	,	PUNCT
ejpam-6062	394	6	25:100545	25:100545	NUM
ejpam-6062	394	7	,	,	PUNCT
ejpam-6062	394	8	2025	2025	NUM
ejpam-6062	394	9	.	.	PUNCT
ejpam-6062	395	1	[	[	X
ejpam-6062	395	2	12	12	NUM
ejpam-6062	395	3	]	]	PUNCT
ejpam-6062	395	4	a.	a.	NOUN
ejpam-6062	395	5	akbar	akbar	NOUN
ejpam-6062	395	6	and	and	CCONJ
ejpam-6062	395	7	e.	e.	PROPN
ejpam-6062	395	8	shahrosvand	shahrosvand	PROPN
ejpam-6062	395	9	.	.	PUNCT
ejpam-6062	396	1	split	split	VERB
ejpam-6062	396	2	equality	equality	NOUN
ejpam-6062	396	3	common	common	ADJ
ejpam-6062	396	4	null	null	ADJ
ejpam-6062	396	5	point	point	NOUN
ejpam-6062	396	6	problem	problem	NOUN
ejpam-6062	396	7	for	for	ADP
ejpam-6062	396	8	bregman	bregman	NOUN
ejpam-6062	396	9	quasi	quasi	ADJ
ejpam-6062	396	10	-	-	ADJ
ejpam-6062	396	11	nonexpansive	nonexpansive	ADJ
ejpam-6062	396	12	mappings	mapping	NOUN
ejpam-6062	396	13	.	.	PUNCT
ejpam-6062	397	1	filomat	filomat	NOUN
ejpam-6062	397	2	,	,	PUNCT
ejpam-6062	397	3	32(11):3917–3932	32(11):3917–3932	NUM
ejpam-6062	397	4	,	,	PUNCT
ejpam-6062	397	5	2018	2018	NUM
ejpam-6062	397	6	.	.	PUNCT
ejpam-6062	398	1	[	[	X
ejpam-6062	398	2	13	13	NUM
ejpam-6062	398	3	]	]	PUNCT
ejpam-6062	398	4	p.	p.	PROPN
ejpam-6062	398	5	cholamjiak	cholamjiak	PROPN
ejpam-6062	398	6	,	,	PUNCT
ejpam-6062	398	7	d.	d.	PROPN
ejpam-6062	398	8	v.	v.	PROPN
ejpam-6062	398	9	hieu	hieu	PROPN
ejpam-6062	398	10	,	,	PUNCT
ejpam-6062	398	11	and	and	CCONJ
ejpam-6062	398	12	y.	y.	PROPN
ejpam-6062	398	13	j.	j.	PROPN
ejpam-6062	398	14	cho	cho	PROPN
ejpam-6062	398	15	.	.	PUNCT
ejpam-6062	399	1	relaxed	relax	VERB
ejpam-6062	399	2	forward	forward	ADJ
ejpam-6062	399	3	-	-	PUNCT
ejpam-6062	399	4	backward	backward	ADJ
ejpam-6062	399	5	splitting	splitting	NOUN
ejpam-6062	399	6	methods	method	NOUN
ejpam-6062	399	7	for	for	ADP
ejpam-6062	399	8	solving	solve	VERB
ejpam-6062	399	9	variational	variational	ADJ
ejpam-6062	399	10	inclusions	inclusion	NOUN
ejpam-6062	399	11	and	and	CCONJ
ejpam-6062	399	12	applications	application	NOUN
ejpam-6062	399	13	.	.	PUNCT
ejpam-6062	400	1	j.	j.	PROPN
ejpam-6062	400	2	sci	sci	PROPN
ejpam-6062	400	3	.	.	PUNCT
ejpam-6062	401	1	comput	comput	PROPN
ejpam-6062	401	2	.	.	PUNCT
ejpam-6062	401	3	,	,	PUNCT
ejpam-6062	401	4	88(3):1	88(3):1	NUM
ejpam-6062	401	5	–	–	PUNCT
ejpam-6062	401	6	23	23	NUM
ejpam-6062	401	7	,	,	PUNCT
ejpam-6062	401	8	2021	2021	NUM
ejpam-6062	401	9	.	.	PUNCT
ejpam-6062	402	1	[	[	X
ejpam-6062	402	2	14	14	NUM
ejpam-6062	402	3	]	]	X
ejpam-6062	402	4	f.	f.	PROPN
ejpam-6062	402	5	u.	u.	PROPN
ejpam-6062	402	6	ogbuisi	ogbuisi	PROPN
ejpam-6062	402	7	and	and	CCONJ
ejpam-6062	402	8	o.	o.	NOUN
ejpam-6062	402	9	t.	t.	PROPN
ejpam-6062	402	10	mewomo	mewomo	PROPN
ejpam-6062	402	11	.	.	PUNCT
ejpam-6062	403	1	iterative	iterative	NOUN
ejpam-6062	403	2	solution	solution	NOUN
ejpam-6062	403	3	of	of	ADP
ejpam-6062	403	4	split	split	ADJ
ejpam-6062	403	5	variational	variational	ADJ
ejpam-6062	403	6	inclusion	inclusion	NOUN
ejpam-6062	403	7	problem	problem	NOUN
ejpam-6062	403	8	in	in	ADP
ejpam-6062	403	9	a	a	DET
ejpam-6062	403	10	real	real	ADJ
ejpam-6062	403	11	banach	banach	NOUN
ejpam-6062	403	12	spaces	space	VERB
ejpam-6062	403	13	.	.	PUNCT
ejpam-6062	404	1	afr	afr	PROPN
ejpam-6062	404	2	.	.	PUNCT
ejpam-6062	405	1	mat	mat	PROPN
ejpam-6062	405	2	.	.	PROPN
ejpam-6062	405	3	,	,	PUNCT
ejpam-6062	405	4	28:295–309	28:295–309	NUM
ejpam-6062	405	5	,	,	PUNCT
ejpam-6062	405	6	2017	2017	NUM
ejpam-6062	405	7	.	.	PUNCT
ejpam-6062	406	1	[	[	X
ejpam-6062	406	2	15	15	NUM
ejpam-6062	406	3	]	]	X
ejpam-6062	406	4	c.	c.	PROPN
ejpam-6062	406	5	izuchukwu	izuchukwu	PROPN
ejpam-6062	406	6	,	,	PUNCT
ejpam-6062	406	7	c.	c.	PROPN
ejpam-6062	406	8	c.	c.	PROPN
ejpam-6062	406	9	okeke	okeke	PROPN
ejpam-6062	406	10	,	,	PUNCT
ejpam-6062	406	11	and	and	CCONJ
ejpam-6062	406	12	f.	f.	PROPN
ejpam-6062	406	13	o.	o.	PROPN
ejpam-6062	406	14	isiogugu	isiogugu	PROPN
ejpam-6062	406	15	.	.	PUNCT
ejpam-6062	407	1	a	a	DET
ejpam-6062	407	2	viscosity	viscosity	NOUN
ejpam-6062	407	3	iterative	iterative	NOUN
ejpam-6062	407	4	technique	technique	NOUN
ejpam-6062	407	5	for	for	ADP
ejpam-6062	407	6	split	split	ADJ
ejpam-6062	407	7	variational	variational	ADJ
ejpam-6062	407	8	inclusion	inclusion	NOUN
ejpam-6062	407	9	and	and	CCONJ
ejpam-6062	407	10	fixed	fix	VERB
ejpam-6062	407	11	point	point	NOUN
ejpam-6062	407	12	problems	problem	NOUN
ejpam-6062	407	13	between	between	ADP
ejpam-6062	407	14	a	a	DET
ejpam-6062	407	15	hilbert	hilbert	NOUN
ejpam-6062	407	16	and	and	CCONJ
ejpam-6062	407	17	a	a	DET
ejpam-6062	407	18	banach	banach	NOUN
ejpam-6062	407	19	space	space	NOUN
ejpam-6062	407	20	.	.	PUNCT
ejpam-6062	408	1	j.	j.	PROPN
ejpam-6062	408	2	fixed	fix	VERB
ejpam-6062	408	3	point	point	PROPN
ejpam-6062	408	4	theory	theory	NOUN
ejpam-6062	408	5	appl	appl	PROPN
ejpam-6062	408	6	.	.	PROPN
ejpam-6062	408	7	,	,	PUNCT
ejpam-6062	408	8	20(157	20(157	NUM
ejpam-6062	408	9	)	)	PUNCT
ejpam-6062	408	10	,	,	PUNCT
ejpam-6062	408	11	2018	2018	NUM
ejpam-6062	408	12	.	.	PUNCT
ejpam-6062	409	1	[	[	X
ejpam-6062	409	2	16	16	NUM
ejpam-6062	409	3	]	]	PUNCT
ejpam-6062	409	4	s.	s.	PROPN
ejpam-6062	409	5	reich	reich	PROPN
ejpam-6062	409	6	and	and	CCONJ
ejpam-6062	409	7	t.m	t.m	PROPN
ejpam-6062	409	8	.	.	PROPN
ejpam-6062	409	9	tuyen	tuyen	PROPN
ejpam-6062	409	10	.	.	PUNCT
ejpam-6062	410	1	two	two	NUM
ejpam-6062	410	2	new	new	ADJ
ejpam-6062	410	3	self	self	NOUN
ejpam-6062	410	4	-	-	PUNCT
ejpam-6062	410	5	adaptive	adaptive	ADJ
ejpam-6062	410	6	algorithms	algorithm	NOUN
ejpam-6062	410	7	for	for	ADP
ejpam-6062	410	8	solving	solve	VERB
ejpam-6062	410	9	the	the	DET
ejpam-6062	410	10	split	split	ADJ
ejpam-6062	410	11	common	common	ADJ
ejpam-6062	410	12	null	null	ADJ
ejpam-6062	410	13	point	point	NOUN
ejpam-6062	410	14	problem	problem	NOUN
ejpam-6062	410	15	with	with	ADP
ejpam-6062	410	16	multiple	multiple	ADJ
ejpam-6062	410	17	output	output	NOUN
ejpam-6062	410	18	sets	set	NOUN
ejpam-6062	410	19	in	in	ADP
ejpam-6062	410	20	hilbert	hilbert	PROPN
ejpam-6062	410	21	spaces	space	NOUN
ejpam-6062	410	22	.	.	PUNCT
ejpam-6062	411	1	j.	j.	PROPN
ejpam-6062	411	2	fixed	fix	VERB
ejpam-6062	411	3	point	point	PROPN
ejpam-6062	411	4	theory	theory	NOUN
ejpam-6062	411	5	appl	appl	PROPN
ejpam-6062	411	6	.	.	PROPN
ejpam-6062	411	7	,	,	PUNCT
ejpam-6062	411	8	23(16	23(16	NUM
ejpam-6062	411	9	)	)	PUNCT
ejpam-6062	411	10	,	,	PUNCT
ejpam-6062	411	11	2021	2021	NUM
ejpam-6062	411	12	.	.	PUNCT
ejpam-6062	412	1	[	[	X
ejpam-6062	412	2	17	17	NUM
ejpam-6062	412	3	]	]	X
ejpam-6062	412	4	y.	y.	NOUN
ejpam-6062	412	5	shehu	shehu	PROPN
ejpam-6062	412	6	and	and	CCONJ
ejpam-6062	412	7	f.	f.	PROPN
ejpam-6062	412	8	u.	u.	PROPN
ejpam-6062	412	9	ogbuisi	ogbuisi	PROPN
ejpam-6062	412	10	.	.	PUNCT
ejpam-6062	413	1	an	an	DET
ejpam-6062	413	2	iterative	iterative	NOUN
ejpam-6062	413	3	method	method	NOUN
ejpam-6062	413	4	for	for	ADP
ejpam-6062	413	5	solving	solve	VERB
ejpam-6062	413	6	split	split	VERB
ejpam-6062	413	7	monotone	monotone	ADJ
ejpam-6062	413	8	variational	variational	ADJ
ejpam-6062	413	9	inclusion	inclusion	NOUN
ejpam-6062	413	10	and	and	CCONJ
ejpam-6062	413	11	fixed	fix	VERB
ejpam-6062	413	12	point	point	NOUN
ejpam-6062	413	13	problem	problem	NOUN
ejpam-6062	413	14	.	.	PUNCT
ejpam-6062	414	1	racsam	racsam	PROPN
ejpam-6062	414	2	,	,	PUNCT
ejpam-6062	414	3	110:503–518	110:503–518	NUM
ejpam-6062	414	4	,	,	PUNCT
ejpam-6062	414	5	2016	2016	NUM
ejpam-6062	414	6	.	.	PUNCT
ejpam-6062	415	1	[	[	X
ejpam-6062	415	2	18	18	NUM
ejpam-6062	415	3	]	]	PUNCT
ejpam-6062	415	4	a.	a.	NOUN
ejpam-6062	415	5	taiwo	taiwo	PROPN
ejpam-6062	415	6	,	,	PUNCT
ejpam-6062	415	7	t.	t.	PROPN
ejpam-6062	415	8	o.	o.	PROPN
ejpam-6062	415	9	alakoya	alakoya	PROPN
ejpam-6062	415	10	,	,	PUNCT
ejpam-6062	415	11	and	and	CCONJ
ejpam-6062	415	12	o.	o.	NOUN
ejpam-6062	415	13	t.	t.	PROPN
ejpam-6062	415	14	mewomo	mewomo	PROPN
ejpam-6062	415	15	.	.	PUNCT
ejpam-6062	416	1	halpern	halpern	PROPN
ejpam-6062	416	2	type	type	NOUN
ejpam-6062	416	3	iterative	iterative	NOUN
ejpam-6062	416	4	process	process	NOUN
ejpam-6062	416	5	for	for	ADP
ejpam-6062	416	6	solving	solve	VERB
ejpam-6062	416	7	split	split	VERB
ejpam-6062	416	8	common	common	ADJ
ejpam-6062	416	9	fixed	fix	VERB
ejpam-6062	416	10	point	point	NOUN
ejpam-6062	416	11	and	and	CCONJ
ejpam-6062	416	12	monotone	monotone	ADJ
ejpam-6062	416	13	variational	variational	ADJ
ejpam-6062	416	14	inclusion	inclusion	NOUN
ejpam-6062	416	15	problem	problem	NOUN
ejpam-6062	416	16	between	between	ADP
ejpam-6062	416	17	banach	banach	NOUN
ejpam-6062	416	18	spaces	space	NOUN
ejpam-6062	416	19	.	.	PUNCT
ejpam-6062	417	1	numer	numer	PROPN
ejpam-6062	417	2	.	.	PROPN
ejpam-6062	418	1	algor	algor	PROPN
ejpam-6062	418	2	.	.	PUNCT
ejpam-6062	418	3	,	,	PUNCT
ejpam-6062	418	4	86:1359–1389	86:1359–1389	PROPN
ejpam-6062	418	5	,	,	PUNCT
ejpam-6062	418	6	2021	2021	NUM
ejpam-6062	418	7	.	.	PUNCT
ejpam-6062	419	1	[	[	X
ejpam-6062	419	2	19	19	NUM
ejpam-6062	419	3	]	]	X
ejpam-6062	419	4	s.	s.	PROPN
ejpam-6062	419	5	timnak	timnak	PROPN
ejpam-6062	419	6	,	,	PUNCT
ejpam-6062	419	7	e.	e.	PROPN
ejpam-6062	419	8	naraghirad	naraghirad	PROPN
ejpam-6062	419	9	,	,	PUNCT
ejpam-6062	419	10	and	and	CCONJ
ejpam-6062	419	11	n.	n.	PROPN
ejpam-6062	419	12	hussain	hussain	PROPN
ejpam-6062	419	13	.	.	PUNCT
ejpam-6062	420	1	strong	strong	ADJ
ejpam-6062	420	2	convergence	convergence	NOUN
ejpam-6062	420	3	of	of	ADP
ejpam-6062	420	4	halpern	halpern	ADJ
ejpam-6062	420	5	iteration	iteration	NOUN
ejpam-6062	420	6	for	for	ADP
ejpam-6062	420	7	products	product	NOUN
ejpam-6062	420	8	of	of	ADP
ejpam-6062	420	9	finitely	finitely	ADV
ejpam-6062	420	10	many	many	ADJ
ejpam-6062	420	11	resolvents	resolvent	NOUN
ejpam-6062	420	12	of	of	ADP
ejpam-6062	420	13	maximal	maximal	ADJ
ejpam-6062	420	14	monotone	monotone	ADJ
ejpam-6062	420	15	operators	operator	NOUN
ejpam-6062	420	16	in	in	ADP
ejpam-6062	420	17	banach	banach	NOUN
ejpam-6062	420	18	spaces	space	NOUN
ejpam-6062	420	19	.	.	PUNCT
ejpam-6062	421	1	filomat	filomat	NOUN
ejpam-6062	421	2	,	,	PUNCT
ejpam-6062	421	3	31(15):4673–4693	31(15):4673–4693	PROPN
ejpam-6062	421	4	,	,	PUNCT
ejpam-6062	421	5	2017	2017	NUM
ejpam-6062	421	6	.	.	PUNCT
ejpam-6062	422	1	[	[	X
ejpam-6062	422	2	20	20	NUM
ejpam-6062	422	3	]	]	PUNCT
ejpam-6062	422	4	b.	b.	PROPN
ejpam-6062	422	5	tan	tan	PROPN
ejpam-6062	422	6	,	,	PUNCT
ejpam-6062	422	7	h.	h.	PROPN
ejpam-6062	422	8	a.	a.	PROPN
ejpam-6062	422	9	abass	abass	PROPN
ejpam-6062	422	10	,	,	PUNCT
ejpam-6062	422	11	s.	s.	PROPN
ejpam-6062	422	12	li	li	PROPN
ejpam-6062	422	13	,	,	PUNCT
ejpam-6062	422	14	and	and	CCONJ
ejpam-6062	422	15	o.	o.	PROPN
ejpam-6062	422	16	k.	k.	PROPN
ejpam-6062	422	17	oyewole	oyewole	PROPN
ejpam-6062	422	18	.	.	PUNCT
ejpam-6062	423	1	two	two	NUM
ejpam-6062	423	2	accelerated	accelerate	VERB
ejpam-6062	423	3	double	double	ADJ
ejpam-6062	423	4	inertial	inertial	ADJ
ejpam-6062	423	5	algorithms	algorithm	NOUN
ejpam-6062	423	6	for	for	ADP
ejpam-6062	423	7	variational	variational	ADJ
ejpam-6062	423	8	inequalities	inequality	NOUN
ejpam-6062	423	9	on	on	ADP
ejpam-6062	423	10	hadamard	hadamard	ADJ
ejpam-6062	423	11	manifolds	manifold	NOUN
ejpam-6062	423	12	.	.	PUNCT
ejpam-6062	424	1	commun	commun	PROPN
ejpam-6062	424	2	.	.	PUNCT
ejpam-6062	425	1	nonlinear	nonlinear	PROPN
ejpam-6062	425	2	sci	sci	PROPN
ejpam-6062	425	3	.	.	PUNCT
ejpam-6062	425	4	numer	numer	PROPN
ejpam-6062	425	5	.	.	PUNCT
ejpam-6062	426	1	simulat	simulat	NOUN
ejpam-6062	426	2	.	.	PUNCT
ejpam-6062	426	3	,	,	PUNCT
ejpam-6062	426	4	145:108734	145:108734	NUM
ejpam-6062	426	5	,	,	PUNCT
ejpam-6062	426	6	2025	2025	NUM
ejpam-6062	426	7	.	.	PUNCT
ejpam-6062	427	1	[	[	X
ejpam-6062	427	2	21	21	NUM
ejpam-6062	427	3	]	]	X
ejpam-6062	427	4	s.	s.	PROPN
ejpam-6062	427	5	reich	reich	PROPN
ejpam-6062	427	6	and	and	CCONJ
ejpam-6062	427	7	t.m	t.m	PROPN
ejpam-6062	427	8	.	.	PROPN
ejpam-6062	427	9	tuyen	tuyen	PROPN
ejpam-6062	427	10	.	.	PUNCT
ejpam-6062	428	1	iterative	iterative	NOUN
ejpam-6062	428	2	methods	method	NOUN
ejpam-6062	428	3	for	for	ADP
ejpam-6062	428	4	solving	solve	VERB
ejpam-6062	428	5	the	the	DET
ejpam-6062	428	6	generalized	generalize	VERB
ejpam-6062	428	7	split	split	VERB
ejpam-6062	428	8	common	common	ADJ
ejpam-6062	428	9	null	null	ADJ
ejpam-6062	428	10	point	point	NOUN
ejpam-6062	428	11	problem	problem	NOUN
ejpam-6062	428	12	in	in	ADP
ejpam-6062	428	13	hilbert	hilbert	PROPN
ejpam-6062	428	14	spaces	space	NOUN
ejpam-6062	428	15	.	.	PUNCT
ejpam-6062	429	1	optimization	optimization	NOUN
ejpam-6062	429	2	,	,	PUNCT
ejpam-6062	429	3	69:1013–1038	69:1013–1038	PROPN
ejpam-6062	429	4	,	,	PUNCT
ejpam-6062	429	5	2020	2020	NUM
ejpam-6062	429	6	.	.	PUNCT
ejpam-6062	430	1	h.	h.	PROPN
ejpam-6062	430	2	a.	a.	PROPN
ejpam-6062	430	3	abass	abass	PROPN
ejpam-6062	430	4	et	et	PROPN
ejpam-6062	430	5	al	al	PROPN
ejpam-6062	430	6	.	.	PUNCT
ejpam-6062	430	7	/	/	SYM
ejpam-6062	430	8	eur	eur	PROPN
ejpam-6062	430	9	.	.	PUNCT
ejpam-6062	431	1	j.	j.	PROPN
ejpam-6062	431	2	pure	pure	PROPN
ejpam-6062	431	3	appl	appl	PROPN
ejpam-6062	431	4	.	.	PROPN
ejpam-6062	431	5	math	math	PROPN
ejpam-6062	431	6	,	,	PUNCT
ejpam-6062	431	7	18	18	NUM
ejpam-6062	431	8	(	(	PUNCT
ejpam-6062	431	9	2	2	NUM
ejpam-6062	431	10	)	)	PUNCT
ejpam-6062	431	11	(	(	PUNCT
ejpam-6062	431	12	2025	2025	NUM
ejpam-6062	431	13	)	)	PUNCT
ejpam-6062	431	14	,	,	PUNCT
ejpam-6062	431	15	6062	6062	NUM
ejpam-6062	431	16	21	21	NUM
ejpam-6062	431	17	of	of	ADP
ejpam-6062	431	18	22	22	NUM
ejpam-6062	432	1	[	[	X
ejpam-6062	432	2	22	22	NUM
ejpam-6062	432	3	]	]	PUNCT
ejpam-6062	432	4	a.	a.	NOUN
ejpam-6062	432	5	a.	a.	PROPN
ejpam-6062	432	6	mebawondu	mebawondu	PROPN
ejpam-6062	432	7	,	,	PUNCT
ejpam-6062	432	8	h.	h.	PROPN
ejpam-6062	432	9	a.	a.	PROPN
ejpam-6062	432	10	abass	abass	PROPN
ejpam-6062	432	11	,	,	PUNCT
ejpam-6062	432	12	and	and	CCONJ
ejpam-6062	432	13	o.	o.	PROPN
ejpam-6062	432	14	k.	k.	PROPN
ejpam-6062	432	15	oyewole	oyewole	PROPN
ejpam-6062	432	16	.	.	PUNCT
ejpam-6062	433	1	an	an	DET
ejpam-6062	433	2	accelerated	accelerate	VERB
ejpam-6062	433	3	tseng	tseng	PROPN
ejpam-6062	433	4	type	type	NOUN
ejpam-6062	433	5	method	method	NOUN
ejpam-6062	433	6	for	for	ADP
ejpam-6062	433	7	solving	solve	VERB
ejpam-6062	433	8	zero	zero	NUM
ejpam-6062	433	9	point	point	NOUN
ejpam-6062	433	10	problems	problem	NOUN
ejpam-6062	433	11	and	and	CCONJ
ejpam-6062	433	12	certain	certain	ADJ
ejpam-6062	433	13	optimization	optimization	NOUN
ejpam-6062	433	14	problems	problem	NOUN
ejpam-6062	433	15	.	.	PUNCT
ejpam-6062	434	1	,	,	PUNCT
ejpam-6062	434	2	volume	volume	NOUN
ejpam-6062	434	3	36	36	NUM
ejpam-6062	434	4	.	.	PUNCT
ejpam-6062	435	1	https://doi.org/10.1007/s13370-024-01217-1	https://doi.org/10.1007/s13370-024-01217-1	VERB
ejpam-6062	435	2	,	,	PUNCT
ejpam-6062	435	3	2025	2025	NUM
ejpam-6062	435	4	.	.	PUNCT
ejpam-6062	436	1	[	[	X
ejpam-6062	436	2	23	23	NUM
ejpam-6062	436	3	]	]	X
ejpam-6062	436	4	i.	i.	NOUN
ejpam-6062	436	5	bartolini	bartolini	PROPN
ejpam-6062	436	6	,	,	PUNCT
ejpam-6062	436	7	p.	p.	NOUN
ejpam-6062	436	8	ciaccia	ciaccia	NOUN
ejpam-6062	436	9	,	,	PUNCT
ejpam-6062	436	10	and	and	CCONJ
ejpam-6062	436	11	m.	m.	NOUN
ejpam-6062	436	12	pattela	pattela	PROPN
ejpam-6062	436	13	.	.	PUNCT
ejpam-6062	436	14	string	string	PROPN
ejpam-6062	436	15	matching	match	VERB
ejpam-6062	436	16	with	with	ADP
ejpam-6062	436	17	trees	tree	NOUN
ejpam-6062	436	18	using	use	VERB
ejpam-6062	436	19	an	an	DET
ejpam-6062	436	20	approximate	approximate	ADJ
ejpam-6062	436	21	distance	distance	NOUN
ejpam-6062	436	22	.	.	PUNCT
ejpam-6062	437	1	spir	spir	PROPN
ejpam-6062	437	2	lecture	lecture	PROPN
ejpam-6062	437	3	notes	note	NOUN
ejpam-6062	437	4	in	in	ADP
ejpam-6062	437	5	computer	computer	NOUN
ejpam-6062	437	6	science	science	NOUN
ejpam-6062	437	7	,	,	PUNCT
ejpam-6062	437	8	vol	vol	NOUN
ejpam-6062	437	9	.	.	PROPN
ejpam-6062	437	10	2476	2476	NUM
ejpam-6062	437	11	.	.	PUNCT
ejpam-6062	438	1	spring	spring	PROPN
ejpam-6062	438	2	,	,	PUNCT
ejpam-6062	438	3	berlin	berlin	PROPN
ejpam-6062	438	4	,	,	PUNCT
ejpam-6062	438	5	1999	1999	NUM
ejpam-6062	438	6	.	.	PUNCT
ejpam-6062	439	1	[	[	X
ejpam-6062	439	2	24	24	NUM
ejpam-6062	439	3	]	]	PUNCT
ejpam-6062	439	4	s.	s.	PROPN
ejpam-6062	439	5	s.	s.	PROPN
ejpam-6062	439	6	chang	chang	PROPN
ejpam-6062	439	7	,	,	PUNCT
ejpam-6062	439	8	y.	y.	PROPN
ejpam-6062	439	9	j.	j.	PROPN
ejpam-6062	439	10	cho	cho	PROPN
ejpam-6062	439	11	,	,	PUNCT
ejpam-6062	439	12	b.	b.	PROPN
ejpam-6062	439	13	s.	s.	PROPN
ejpam-6062	439	14	lee	lee	PROPN
ejpam-6062	439	15	,	,	PUNCT
ejpam-6062	439	16	and	and	CCONJ
ejpam-6062	439	17	i.	i.	PROPN
ejpam-6062	439	18	h.	h.	PROPN
ejpam-6062	439	19	jung	jung	PROPN
ejpam-6062	439	20	.	.	PUNCT
ejpam-6062	440	1	generalized	generalize	VERB
ejpam-6062	440	2	set	set	NOUN
ejpam-6062	440	3	-	-	PUNCT
ejpam-6062	440	4	valued	value	VERB
ejpam-6062	440	5	variational	variational	ADJ
ejpam-6062	440	6	inclusions	inclusion	NOUN
ejpam-6062	440	7	in	in	ADP
ejpam-6062	440	8	banach	banach	NOUN
ejpam-6062	440	9	spaces	space	NOUN
ejpam-6062	440	10	.	.	PUNCT
ejpam-6062	441	1	j.	j.	PROPN
ejpam-6062	441	2	mathematica	mathematica	PROPN
ejpam-6062	441	3	;	;	PUNCT
ejpam-6062	441	4	anal	anal	PROPN
ejpam-6062	441	5	.	.	PUNCT
ejpam-6062	442	1	appl	appl	PROPN
ejpam-6062	442	2	.	.	PROPN
ejpam-6062	442	3	,	,	PUNCT
ejpam-6062	442	4	246(2):409–422	246(2):409–422	NUM
ejpam-6062	442	5	,	,	PUNCT
ejpam-6062	442	6	2000	2000	NUM
ejpam-6062	442	7	.	.	PUNCT
ejpam-6062	443	1	[	[	X
ejpam-6062	443	2	25	25	NUM
ejpam-6062	443	3	]	]	X
ejpam-6062	443	4	c.	c.	PROPN
ejpam-6062	443	5	izuchukwu	izuchukwu	PROPN
ejpam-6062	443	6	,	,	PUNCT
ejpam-6062	443	7	h.	h.	PROPN
ejpam-6062	443	8	a.	a.	PROPN
ejpam-6062	443	9	abass	abass	PROPN
ejpam-6062	443	10	,	,	PUNCT
ejpam-6062	443	11	and	and	CCONJ
ejpam-6062	443	12	o.	o.	NOUN
ejpam-6062	443	13	t.	t.	PROPN
ejpam-6062	443	14	mewomo	mewomo	PROPN
ejpam-6062	443	15	.	.	PUNCT
ejpam-6062	444	1	viscosity	viscosity	NOUN
ejpam-6062	444	2	approximation	approximation	NOUN
ejpam-6062	444	3	method	method	NOUN
ejpam-6062	444	4	for	for	ADP
ejpam-6062	444	5	solving	solve	VERB
ejpam-6062	444	6	minimization	minimization	NOUN
ejpam-6062	444	7	problem	problem	NOUN
ejpam-6062	444	8	and	and	CCONJ
ejpam-6062	444	9	fixed	fix	VERB
ejpam-6062	444	10	point	point	NOUN
ejpam-6062	444	11	problem	problem	NOUN
ejpam-6062	444	12	for	for	ADP
ejpam-6062	444	13	nonexpansive	nonexpansive	ADJ
ejpam-6062	444	14	multi	multi	ADJ
ejpam-6062	444	15	-	-	ADJ
ejpam-6062	444	16	valued	value	VERB
ejpam-6062	444	17	mappings	mapping	NOUN
ejpam-6062	444	18	in	in	ADP
ejpam-6062	444	19	cat(0	cat(0	ADJ
ejpam-6062	444	20	)	)	PUNCT
ejpam-6062	444	21	spaces	space	NOUN
ejpam-6062	444	22	.	.	PUNCT
ejpam-6062	445	1	ann	ann	PROPN
ejpam-6062	445	2	.	.	PUNCT
ejpam-6062	445	3	acad	acad	PROPN
ejpam-6062	445	4	.	.	PUNCT
ejpam-6062	446	1	rom	rom	PROPN
ejpam-6062	446	2	.	.	PUNCT
ejpam-6062	447	1	sci	sci	PROPN
ejpam-6062	447	2	.	.	PUNCT
ejpam-6062	447	3	ser	ser	PROPN
ejpam-6062	447	4	.	.	PROPN
ejpam-6062	447	5	math	math	PROPN
ejpam-6062	447	6	.	.	PUNCT
ejpam-6062	448	1	appl	appl	PROPN
ejpam-6062	448	2	.	.	PROPN
ejpam-6062	448	3	,	,	PUNCT
ejpam-6062	448	4	11(1	11(1	NUM
ejpam-6062	448	5	)	)	PUNCT
ejpam-6062	448	6	,	,	PUNCT
ejpam-6062	448	7	2019	2019	NUM
ejpam-6062	448	8	.	.	PUNCT
ejpam-6062	449	1	[	[	X
ejpam-6062	449	2	26	26	NUM
ejpam-6062	449	3	]	]	X
ejpam-6062	449	4	k.o	k.o	PROPN
ejpam-6062	449	5	.	.	PROPN
ejpam-6062	449	6	aremu	aremu	PROPN
ejpam-6062	449	7	l.o	l.o	PROPN
ejpam-6062	449	8	.	.	PROPN
ejpam-6062	449	9	jolaoso	jolaoso	PROPN
ejpam-6062	449	10	,	,	PUNCT
ejpam-6062	449	11	o.k	o.k	PROPN
ejpam-6062	449	12	.	.	PROPN
ejpam-6062	449	13	oyewole	oyewole	PROPN
ejpam-6062	449	14	and	and	CCONJ
ejpam-6062	449	15	o.t	o.t	PROPN
ejpam-6062	449	16	.	.	PROPN
ejpam-6062	449	17	mewomo	mewomo	PROPN
ejpam-6062	449	18	.	.	PUNCT
ejpam-6062	450	1	a	a	DET
ejpam-6062	450	2	new	new	ADJ
ejpam-6062	450	3	efficient	efficient	ADJ
ejpam-6062	450	4	algorithm	algorithm	NOUN
ejpam-6062	450	5	for	for	ADP
ejpam-6062	450	6	finding	find	VERB
ejpam-6062	450	7	common	common	ADJ
ejpam-6062	450	8	fixed	fix	VERB
ejpam-6062	450	9	points	point	NOUN
ejpam-6062	450	10	of	of	ADP
ejpam-6062	450	11	multi	multi	ADJ
ejpam-6062	450	12	-	-	ADJ
ejpam-6062	450	13	valued	value	VERB
ejpam-6062	450	14	demicontractive	demicontractive	ADJ
ejpam-6062	450	15	mappings	mapping	NOUN
ejpam-6062	450	16	and	and	CCONJ
ejpam-6062	450	17	solutions	solution	NOUN
ejpam-6062	450	18	of	of	ADP
ejpam-6062	450	19	split	split	ADJ
ejpam-6062	450	20	generalized	generalized	ADJ
ejpam-6062	450	21	equilibrium	equilibrium	NOUN
ejpam-6062	450	22	problems	problem	NOUN
ejpam-6062	450	23	in	in	ADP
ejpam-6062	450	24	hilbert	hilbert	PROPN
ejpam-6062	450	25	spaces	space	NOUN
ejpam-6062	450	26	.	.	PUNCT
ejpam-6062	451	1	intl	intl	PROPN
ejpam-6062	451	2	.	.	PUNCT
ejpam-6062	452	1	j.	j.	PROPN
ejpam-6062	452	2	comp	comp	PROPN
ejpam-6062	452	3	.	.	PUNCT
ejpam-6062	453	1	mat	mat	PROPN
ejpam-6062	453	2	.	.	PROPN
ejpam-6062	453	3	,	,	PUNCT
ejpam-6062	453	4	98(9):1892–1919	98(9):1892–1919	NUM
ejpam-6062	453	5	,	,	PUNCT
ejpam-6062	453	6	2020	2020	NUM
ejpam-6062	453	7	.	.	PUNCT
ejpam-6062	454	1	[	[	X
ejpam-6062	454	2	27	27	NUM
ejpam-6062	454	3	]	]	PUNCT
ejpam-6062	454	4	j.	j.	PROPN
ejpam-6062	454	5	y.	y.	PROPN
ejpam-6062	454	6	bello	bello	PROPN
ejpam-6062	454	7	and	and	CCONJ
ejpam-6062	454	8	y.	y.	PROPN
ejpam-6062	454	9	shehu	shehu	PROPN
ejpam-6062	454	10	.	.	PUNCT
ejpam-6062	455	1	an	an	DET
ejpam-6062	455	2	iterative	iterative	NOUN
ejpam-6062	455	3	method	method	NOUN
ejpam-6062	455	4	for	for	ADP
ejpam-6062	455	5	split	split	ADJ
ejpam-6062	455	6	inclusion	inclusion	NOUN
ejpam-6062	455	7	problem	problem	NOUN
ejpam-6062	455	8	without	without	ADP
ejpam-6062	455	9	prior	prior	ADJ
ejpam-6062	455	10	knowledge	knowledge	NOUN
ejpam-6062	455	11	of	of	ADP
ejpam-6062	455	12	operator	operator	NOUN
ejpam-6062	455	13	norm	norm	NOUN
ejpam-6062	455	14	.	.	PUNCT
ejpam-6062	456	1	j.	j.	PROPN
ejpam-6062	456	2	fixed	fix	VERB
ejpam-6062	456	3	point	point	PROPN
ejpam-6062	456	4	theory	theory	NOUN
ejpam-6062	456	5	appl	appl	PROPN
ejpam-6062	456	6	.	.	PROPN
ejpam-6062	456	7	,	,	PUNCT
ejpam-6062	457	1	19(3):2017–2036	19(3):2017–2036	NUM
ejpam-6062	457	2	,	,	PUNCT
ejpam-6062	457	3	2017	2017	NUM
ejpam-6062	457	4	.	.	PUNCT
ejpam-6062	458	1	[	[	X
ejpam-6062	458	2	28	28	NUM
ejpam-6062	458	3	]	]	X
ejpam-6062	458	4	o.	o.	PROPN
ejpam-6062	458	5	k.	k.	PROPN
ejpam-6062	458	6	oyewole	oyewole	PROPN
ejpam-6062	458	7	,	,	PUNCT
ejpam-6062	458	8	h.	h.	PROPN
ejpam-6062	458	9	a.	a.	PROPN
ejpam-6062	458	10	abass	abass	PROPN
ejpam-6062	458	11	,	,	PUNCT
ejpam-6062	458	12	and	and	CCONJ
ejpam-6062	458	13	o.	o.	PROPN
ejpam-6062	458	14	j.	j.	PROPN
ejpam-6062	458	15	ogunsola	ogunsola	PROPN
ejpam-6062	458	16	.	.	PUNCT
ejpam-6062	459	1	an	an	DET
ejpam-6062	459	2	improved	improve	VERB
ejpam-6062	459	3	subgradient	subgradient	NOUN
ejpam-6062	459	4	extragradient	extragradient	NOUN
ejpam-6062	459	5	self	self	NOUN
ejpam-6062	459	6	-	-	PUNCT
ejpam-6062	459	7	adaptive	adaptive	ADJ
ejpam-6062	459	8	algorithm	algorithm	NOUN
ejpam-6062	459	9	based	base	VERB
ejpam-6062	459	10	on	on	ADP
ejpam-6062	459	11	the	the	DET
ejpam-6062	459	12	golden	golden	ADJ
ejpam-6062	459	13	ratio	ratio	NOUN
ejpam-6062	459	14	technique	technique	NOUN
ejpam-6062	459	15	for	for	ADP
ejpam-6062	459	16	variational	variational	ADJ
ejpam-6062	459	17	inequality	inequality	NOUN
ejpam-6062	459	18	problems	problem	NOUN
ejpam-6062	459	19	in	in	ADP
ejpam-6062	459	20	banach	banach	NOUN
ejpam-6062	459	21	spaces	space	NOUN
ejpam-6062	459	22	.	.	PUNCT
ejpam-6062	460	1	j.	j.	PROPN
ejpam-6062	460	2	comput	comput	PROPN
ejpam-6062	460	3	.	.	PUNCT
ejpam-6062	461	1	appl	appl	PROPN
ejpam-6062	461	2	.	.	PROPN
ejpam-6062	461	3	math	math	PROPN
ejpam-6062	461	4	.	.	PUNCT
ejpam-6062	461	5	,	,	PUNCT
ejpam-6062	461	6	460(116420	460(116420	NUM
ejpam-6062	461	7	)	)	PUNCT
ejpam-6062	461	8	,	,	PUNCT
ejpam-6062	461	9	2025	2025	NUM
ejpam-6062	461	10	.	.	PUNCT
ejpam-6062	462	1	[	[	X
ejpam-6062	462	2	29	29	NUM
ejpam-6062	462	3	]	]	X
ejpam-6062	462	4	q.	q.	PROPN
ejpam-6062	462	5	h.	h.	PROPN
ejpam-6062	462	6	ansari	ansari	PROPN
ejpam-6062	462	7	and	and	CCONJ
ejpam-6062	462	8	a.	a.	NOUN
ejpam-6062	462	9	rehan	rehan	PROPN
ejpam-6062	462	10	.	.	PUNCT
ejpam-6062	463	1	iterative	iterative	NOUN
ejpam-6062	463	2	methods	method	NOUN
ejpam-6062	463	3	for	for	ADP
ejpam-6062	463	4	generalized	generalized	ADJ
ejpam-6062	463	5	split	split	NOUN
ejpam-6062	463	6	feasibility	feasibility	NOUN
ejpam-6062	463	7	problems	problem	NOUN
ejpam-6062	463	8	in	in	ADP
ejpam-6062	463	9	banach	banach	NOUN
ejpam-6062	463	10	spaces	space	NOUN
ejpam-6062	463	11	.	.	PUNCT
ejpam-6062	464	1	carapathian	carapathian	ADJ
ejpam-6062	464	2	j.	j.	PROPN
ejpam-6062	464	3	math	math	PROPN
ejpam-6062	464	4	.	.	PUNCT
ejpam-6062	464	5	,	,	PUNCT
ejpam-6062	464	6	33(1	33(1	NUM
ejpam-6062	464	7	)	)	PUNCT
ejpam-6062	464	8	,	,	PUNCT
ejpam-6062	464	9	2017	2017	NUM
ejpam-6062	464	10	.	.	PUNCT
ejpam-6062	465	1	[	[	X
ejpam-6062	465	2	30	30	NUM
ejpam-6062	465	3	]	]	X
ejpam-6062	465	4	h.	h.	PROPN
ejpam-6062	465	5	h.	h.	PROPN
ejpam-6062	465	6	bauschke	bauschke	PROPN
ejpam-6062	465	7	and	and	CCONJ
ejpam-6062	465	8	j.	j.	PROPN
ejpam-6062	465	9	m.	m.	PROPN
ejpam-6062	465	10	borwein	borwein	PROPN
ejpam-6062	465	11	.	.	PUNCT
ejpam-6062	466	1	legendre	legendre	PROPN
ejpam-6062	466	2	functions	function	NOUN
ejpam-6062	466	3	and	and	CCONJ
ejpam-6062	466	4	method	method	NOUN
ejpam-6062	466	5	of	of	ADP
ejpam-6062	466	6	random	random	ADJ
ejpam-6062	466	7	bregman	bregman	NOUN
ejpam-6062	466	8	functions	function	NOUN
ejpam-6062	466	9	.	.	PUNCT
ejpam-6062	467	1	j.	j.	PROPN
ejpam-6062	467	2	convex	convex	PROPN
ejpam-6062	467	3	anal	anal	PROPN
ejpam-6062	467	4	.	.	PUNCT
ejpam-6062	467	5	,	,	PUNCT
ejpam-6062	467	6	4:27–67	4:27–67	NUM
ejpam-6062	467	7	,	,	PUNCT
ejpam-6062	467	8	1997	1997	NUM
ejpam-6062	467	9	.	.	PUNCT
ejpam-6062	468	1	[	[	X
ejpam-6062	468	2	31	31	NUM
ejpam-6062	468	3	]	]	PUNCT
ejpam-6062	468	4	h.	h.	PROPN
ejpam-6062	468	5	h.	h.	PROPN
ejpam-6062	468	6	bauschke	bauschke	PROPN
ejpam-6062	468	7	,	,	PUNCT
ejpam-6062	468	8	j.	j.	PROPN
ejpam-6062	468	9	m.	m.	PROPN
ejpam-6062	468	10	borwein	borwein	PROPN
ejpam-6062	468	11	,	,	PUNCT
ejpam-6062	468	12	and	and	CCONJ
ejpam-6062	468	13	p.	p.	NOUN
ejpam-6062	468	14	l.	l.	PROPN
ejpam-6062	468	15	combettes	combettes	PROPN
ejpam-6062	468	16	.	.	PUNCT
ejpam-6062	469	1	essentially	essentially	ADV
ejpam-6062	469	2	smoothness	smoothness	ADJ
ejpam-6062	469	3	,	,	PUNCT
ejpam-6062	469	4	essentially	essentially	ADV
ejpam-6062	469	5	strict	strict	ADJ
ejpam-6062	469	6	convexity	convexity	NOUN
ejpam-6062	469	7	and	and	CCONJ
ejpam-6062	469	8	legendre	legendre	PROPN
ejpam-6062	469	9	functions	function	NOUN
ejpam-6062	469	10	in	in	ADP
ejpam-6062	469	11	banach	banach	NOUN
ejpam-6062	469	12	spaces	space	NOUN
ejpam-6062	469	13	.	.	PUNCT
ejpam-6062	470	1	commun	commun	PROPN
ejpam-6062	470	2	.	.	PUNCT
ejpam-6062	471	1	contemp	contemp	PROPN
ejpam-6062	471	2	.	.	PUNCT
ejpam-6062	472	1	math	math	NOUN
ejpam-6062	472	2	.	.	PUNCT
ejpam-6062	472	3	,	,	PUNCT
ejpam-6062	472	4	3:615–647	3:615–647	NUM
ejpam-6062	472	5	,	,	PUNCT
ejpam-6062	472	6	2001	2001	NUM
ejpam-6062	472	7	.	.	PUNCT
ejpam-6062	473	1	[	[	X
ejpam-6062	473	2	32	32	NUM
ejpam-6062	473	3	]	]	PUNCT
ejpam-6062	473	4	l.	l.	PROPN
ejpam-6062	473	5	m.	m.	PROPN
ejpam-6062	473	6	bregman	bregman	PROPN
ejpam-6062	473	7	.	.	PUNCT
ejpam-6062	474	1	the	the	DET
ejpam-6062	474	2	relaxation	relaxation	NOUN
ejpam-6062	474	3	method	method	NOUN
ejpam-6062	474	4	for	for	ADP
ejpam-6062	474	5	finding	find	VERB
ejpam-6062	474	6	the	the	DET
ejpam-6062	474	7	common	common	ADJ
ejpam-6062	474	8	point	point	NOUN
ejpam-6062	474	9	of	of	ADP
ejpam-6062	474	10	convex	convex	NOUN
ejpam-6062	474	11	sets	set	NOUN
ejpam-6062	474	12	and	and	CCONJ
ejpam-6062	474	13	its	its	PRON
ejpam-6062	474	14	application	application	NOUN
ejpam-6062	474	15	to	to	ADP
ejpam-6062	474	16	solution	solution	NOUN
ejpam-6062	474	17	of	of	ADP
ejpam-6062	474	18	problems	problem	NOUN
ejpam-6062	474	19	in	in	ADP
ejpam-6062	474	20	convex	convex	NOUN
ejpam-6062	474	21	programming	programming	NOUN
ejpam-6062	474	22	.	.	PUNCT
ejpam-6062	475	1	u.s.s.r	u.s.s.r	ADJ
ejpam-6062	475	2	comput	comput	NOUN
ejpam-6062	475	3	.	.	PUNCT
ejpam-6062	476	1	math	math	NOUN
ejpam-6062	476	2	.	.	PUNCT
ejpam-6062	477	1	phys	phy	NOUN
ejpam-6062	477	2	.	.	PUNCT
ejpam-6062	477	3	,	,	PUNCT
ejpam-6062	477	4	7:200–217	7:200–217	NOUN
ejpam-6062	477	5	,	,	PUNCT
ejpam-6062	477	6	1967	1967	NUM
ejpam-6062	477	7	.	.	PUNCT
ejpam-6062	478	1	[	[	X
ejpam-6062	478	2	33	33	NUM
ejpam-6062	478	3	]	]	X
ejpam-6062	478	4	r.t	r.t	PROPN
ejpam-6062	478	5	.	.	PROPN
ejpam-6062	478	6	rockafellar	rockafellar	PROPN
ejpam-6062	478	7	.	.	PUNCT
ejpam-6062	479	1	on	on	ADP
ejpam-6062	479	2	the	the	DET
ejpam-6062	479	3	maximality	maximality	NOUN
ejpam-6062	479	4	of	of	ADP
ejpam-6062	479	5	sums	sum	NOUN
ejpam-6062	479	6	of	of	ADP
ejpam-6062	479	7	nonlinear	nonlinear	ADJ
ejpam-6062	479	8	monotone	monotone	ADJ
ejpam-6062	479	9	operators	operator	NOUN
ejpam-6062	479	10	.	.	PUNCT
ejpam-6062	480	1	trans	trans	PROPN
ejpam-6062	480	2	.	.	PUNCT
ejpam-6062	481	1	amer	amer	PROPN
ejpam-6062	481	2	.	.	PUNCT
ejpam-6062	481	3	math	math	PROPN
ejpam-6062	481	4	.	.	PUNCT
ejpam-6062	482	1	soc	soc	PROPN
ejpam-6062	482	2	.	.	PUNCT
ejpam-6062	482	3	,	,	PUNCT
ejpam-6062	482	4	149:75–88	149:75–88	NUM
ejpam-6062	482	5	,	,	PUNCT
ejpam-6062	482	6	1970	1970	NUM
ejpam-6062	482	7	.	.	PUNCT
ejpam-6062	483	1	[	[	X
ejpam-6062	483	2	34	34	NUM
ejpam-6062	483	3	]	]	X
ejpam-6062	483	4	r.	r.	PROPN
ejpam-6062	483	5	t.	t.	PROPN
ejpam-6062	483	6	rockafellar	rockafellar	PROPN
ejpam-6062	483	7	.	.	PUNCT
ejpam-6062	484	1	characterization	characterization	NOUN
ejpam-6062	484	2	of	of	ADP
ejpam-6062	484	3	the	the	DET
ejpam-6062	484	4	subdifferentials	subdifferential	NOUN
ejpam-6062	484	5	of	of	ADP
ejpam-6062	484	6	convex	convex	NOUN
ejpam-6062	484	7	functions	function	NOUN
ejpam-6062	484	8	.	.	PUNCT
ejpam-6062	485	1	pac	pac	PROPN
ejpam-6062	485	2	.	.	PUNCT
ejpam-6062	486	1	j.	j.	PROPN
ejpam-6062	486	2	math	math	PROPN
ejpam-6062	486	3	.	.	PUNCT
ejpam-6062	486	4	,	,	PUNCT
ejpam-6062	486	5	17:497–510	17:497–510	NUM
ejpam-6062	486	6	,	,	PUNCT
ejpam-6062	486	7	1966	1966	NUM
ejpam-6062	486	8	.	.	PUNCT
ejpam-6062	487	1	[	[	X
ejpam-6062	487	2	35	35	NUM
ejpam-6062	487	3	]	]	X
ejpam-6062	487	4	h.	h.	PROPN
ejpam-6062	487	5	gazmeh	gazmeh	PROPN
ejpam-6062	487	6	and	and	CCONJ
ejpam-6062	487	7	e.	e.	PROPN
ejpam-6062	487	8	naraghirad	naraghirad	PROPN
ejpam-6062	487	9	.	.	PUNCT
ejpam-6062	488	1	the	the	DET
ejpam-6062	488	2	split	split	ADJ
ejpam-6062	488	3	common	common	ADJ
ejpam-6062	488	4	null	null	ADJ
ejpam-6062	488	5	point	point	NOUN
ejpam-6062	488	6	problem	problem	NOUN
ejpam-6062	488	7	for	for	ADP
ejpam-6062	488	8	bregman	bregman	NOUN
ejpam-6062	488	9	generalized	generalize	VERB
ejpam-6062	488	10	resolvents	resolvent	NOUN
ejpam-6062	488	11	in	in	ADP
ejpam-6062	488	12	two	two	NUM
ejpam-6062	488	13	banach	banach	NOUN
ejpam-6062	488	14	spaces	space	NOUN
ejpam-6062	488	15	.	.	PUNCT
ejpam-6062	489	1	optimization	optimization	NOUN
ejpam-6062	489	2	,	,	PUNCT
ejpam-6062	489	3	70(8):1725–1758	70(8):1725–1758	NUM
ejpam-6062	489	4	,	,	PUNCT
ejpam-6062	489	5	2020	2020	NUM
ejpam-6062	489	6	.	.	PUNCT
ejpam-6062	490	1	[	[	X
ejpam-6062	490	2	36	36	NUM
ejpam-6062	490	3	]	]	X
ejpam-6062	490	4	d.	d.	PROPN
ejpam-6062	490	5	butnairu	butnairu	PROPN
ejpam-6062	490	6	and	and	CCONJ
ejpam-6062	490	7	e.	e.	PROPN
ejpam-6062	490	8	resmerita	resmerita	PROPN
ejpam-6062	490	9	.	.	PUNCT
ejpam-6062	491	1	bregman	bregman	NOUN
ejpam-6062	491	2	distances	distance	NOUN
ejpam-6062	491	3	,	,	PUNCT
ejpam-6062	491	4	totally	totally	ADV
ejpam-6062	491	5	convex	convex	NOUN
ejpam-6062	491	6	functions	function	NOUN
ejpam-6062	491	7	and	and	CCONJ
ejpam-6062	491	8	a	a	DET
ejpam-6062	491	9	method	method	NOUN
ejpam-6062	491	10	for	for	ADP
ejpam-6062	491	11	solving	solve	VERB
ejpam-6062	491	12	operator	operator	NOUN
ejpam-6062	491	13	equations	equation	NOUN
ejpam-6062	491	14	in	in	ADP
ejpam-6062	491	15	banach	banach	NOUN
ejpam-6062	491	16	spaces	space	NOUN
ejpam-6062	491	17	.	.	PUNCT
ejpam-6062	492	1	abstract	abstract	ADJ
ejpam-6062	492	2	and	and	CCONJ
ejpam-6062	492	3	applied	apply	VERB
ejpam-6062	492	4	analysis	analysis	NOUN
ejpam-6062	492	5	,	,	PUNCT
ejpam-6062	492	6	art	art	NOUN
ejpam-6062	492	7	.	.	PUNCT
ejpam-6062	493	1	i	i	PRON
ejpam-6062	493	2	d	d	PROPN
ejpam-6062	493	3	84919:1–39	84919:1–39	NUM
ejpam-6062	493	4	,	,	PUNCT
ejpam-6062	493	5	2006	2006	NUM
ejpam-6062	493	6	.	.	PUNCT
ejpam-6062	494	1	[	[	X
ejpam-6062	494	2	37	37	NUM
ejpam-6062	494	3	]	]	PUNCT
ejpam-6062	494	4	t.	t.	PROPN
ejpam-6062	494	5	m.	m.	NOUN
ejpam-6062	494	6	tuyen	tuyen	PROPN
ejpam-6062	494	7	,	,	PUNCT
ejpam-6062	494	8	r.	r.	PROPN
ejpam-6062	494	9	promkan	promkan	PROPN
ejpam-6062	494	10	,	,	PUNCT
ejpam-6062	494	11	and	and	CCONJ
ejpam-6062	494	12	p.	p.	PROPN
ejpam-6062	494	13	sunthrayuth	sunthrayuth	PROPN
ejpam-6062	494	14	.	.	PUNCT
ejpam-6062	495	1	strong	strong	ADJ
ejpam-6062	495	2	convergence	convergence	NOUN
ejpam-6062	495	3	of	of	ADP
ejpam-6062	495	4	a	a	DET
ejpam-6062	495	5	generalized	generalized	ADJ
ejpam-6062	495	6	forward	forward	ADJ
ejpam-6062	495	7	-	-	PUNCT
ejpam-6062	495	8	backward	backward	ADJ
ejpam-6062	495	9	splitting	splitting	NOUN
ejpam-6062	495	10	method	method	NOUN
ejpam-6062	495	11	in	in	ADP
ejpam-6062	495	12	reflexive	reflexive	ADJ
ejpam-6062	495	13	banach	banach	NOUN
ejpam-6062	495	14	spaces	space	NOUN
ejpam-6062	495	15	.	.	PUNCT
ejpam-6062	496	1	optimization	optimization	NOUN
ejpam-6062	496	2	,	,	PUNCT
ejpam-6062	496	3	pages	page	NOUN
ejpam-6062	496	4	1–26	1–26	PROPN
ejpam-6062	496	5	,	,	PUNCT
ejpam-6062	496	6	2020	2020	NUM
ejpam-6062	496	7	.	.	PUNCT
ejpam-6062	497	1	h.	h.	PROPN
ejpam-6062	497	2	a.	a.	PROPN
ejpam-6062	497	3	abass	abass	PROPN
ejpam-6062	497	4	et	et	PROPN
ejpam-6062	497	5	al	al	PROPN
ejpam-6062	497	6	.	.	PUNCT
ejpam-6062	497	7	/	/	SYM
ejpam-6062	497	8	eur	eur	PROPN
ejpam-6062	497	9	.	.	PUNCT
ejpam-6062	498	1	j.	j.	PROPN
ejpam-6062	498	2	pure	pure	PROPN
ejpam-6062	498	3	appl	appl	PROPN
ejpam-6062	498	4	.	.	PROPN
ejpam-6062	498	5	math	math	PROPN
ejpam-6062	498	6	,	,	PUNCT
ejpam-6062	498	7	18	18	NUM
ejpam-6062	498	8	(	(	PUNCT
ejpam-6062	498	9	2	2	NUM
ejpam-6062	498	10	)	)	PUNCT
ejpam-6062	498	11	(	(	PUNCT
ejpam-6062	498	12	2025	2025	NUM
ejpam-6062	498	13	)	)	PUNCT
ejpam-6062	498	14	,	,	PUNCT
ejpam-6062	498	15	6062	6062	NUM
ejpam-6062	498	16	22	22	NUM
ejpam-6062	498	17	of	of	ADP
ejpam-6062	498	18	22	22	NUM
ejpam-6062	499	1	[	[	X
ejpam-6062	499	2	38	38	NUM
ejpam-6062	499	3	]	]	PUNCT
ejpam-6062	499	4	f.	f.	PROPN
ejpam-6062	499	5	u.	u.	PROPN
ejpam-6062	499	6	ogbuisi	ogbuisi	PROPN
ejpam-6062	499	7	and	and	CCONJ
ejpam-6062	499	8	c.	c.	PROPN
ejpam-6062	499	9	izuchukwu	izuchukwu	PROPN
ejpam-6062	499	10	.	.	PUNCT
ejpam-6062	500	1	approximating	approximate	VERB
ejpam-6062	500	2	a	a	DET
ejpam-6062	500	3	zero	zero	NUM
ejpam-6062	500	4	of	of	ADP
ejpam-6062	500	5	sum	sum	NOUN
ejpam-6062	500	6	of	of	ADP
ejpam-6062	500	7	two	two	NUM
ejpam-6062	500	8	monotone	monotone	ADJ
ejpam-6062	500	9	operators	operator	NOUN
ejpam-6062	500	10	which	which	PRON
ejpam-6062	500	11	solves	solve	VERB
ejpam-6062	500	12	a	a	DET
ejpam-6062	500	13	fixed	fix	VERB
ejpam-6062	500	14	point	point	NOUN
ejpam-6062	500	15	problem	problem	NOUN
ejpam-6062	500	16	in	in	ADP
ejpam-6062	500	17	reflexive	reflexive	ADJ
ejpam-6062	500	18	banach	banach	NOUN
ejpam-6062	500	19	spaces	space	VERB
ejpam-6062	500	20	.	.	PUNCT
ejpam-6062	501	1	numer	numer	PROPN
ejpam-6062	501	2	.	.	PUNCT
ejpam-6062	502	1	funct	funct	PROPN
ejpam-6062	502	2	.	.	PUNCT
ejpam-6062	503	1	anal	anal	PROPN
ejpam-6062	503	2	.	.	PUNCT
ejpam-6062	503	3	,	,	PUNCT
ejpam-6062	503	4	41(3):322–343	41(3):322–343	PROPN
ejpam-6062	503	5	,	,	PUNCT
ejpam-6062	503	6	2019	2019	NUM
ejpam-6062	503	7	.	.	PUNCT
ejpam-6062	504	1	[	[	X
ejpam-6062	504	2	39	39	NUM
ejpam-6062	504	3	]	]	PUNCT
ejpam-6062	504	4	s.	s.	PROPN
ejpam-6062	504	5	reich	reich	PROPN
ejpam-6062	504	6	and	and	CCONJ
ejpam-6062	504	7	s.	s.	PROPN
ejpam-6062	504	8	sabach	sabach	PROPN
ejpam-6062	504	9	.	.	PUNCT
ejpam-6062	505	1	two	two	NUM
ejpam-6062	505	2	strong	strong	ADJ
ejpam-6062	505	3	convergence	convergence	NOUN
ejpam-6062	505	4	theorems	theorem	NOUN
ejpam-6062	505	5	for	for	ADP
ejpam-6062	505	6	a	a	DET
ejpam-6062	505	7	proximal	proximal	ADJ
ejpam-6062	505	8	method	method	NOUN
ejpam-6062	505	9	in	in	ADP
ejpam-6062	505	10	reflexive	reflexive	ADJ
ejpam-6062	505	11	banach	banach	NOUN
ejpam-6062	505	12	spaces	space	VERB
ejpam-6062	505	13	.	.	PUNCT
ejpam-6062	506	1	numer	numer	PROPN
ejpam-6062	506	2	.	.	PUNCT
ejpam-6062	507	1	funct	funct	PROPN
ejpam-6062	507	2	.	.	PUNCT
ejpam-6062	508	1	anal	anal	PROPN
ejpam-6062	508	2	.	.	PUNCT
ejpam-6062	509	1	optim	optim	PROPN
ejpam-6062	509	2	.	.	PROPN
ejpam-6062	509	3	,	,	PUNCT
ejpam-6062	509	4	31:24–44	31:24–44	PROPN
ejpam-6062	509	5	,	,	PUNCT
ejpam-6062	509	6	2010	2010	NUM
ejpam-6062	509	7	.	.	PUNCT
ejpam-6062	510	1	[	[	X
ejpam-6062	510	2	40	40	NUM
ejpam-6062	510	3	]	]	PUNCT
ejpam-6062	510	4	s.	s.	PROPN
ejpam-6062	510	5	reich	reich	PROPN
ejpam-6062	510	6	and	and	CCONJ
ejpam-6062	510	7	s.	s.	PROPN
ejpam-6062	510	8	sabach	sabach	PROPN
ejpam-6062	510	9	.	.	PUNCT
ejpam-6062	511	1	a	a	DET
ejpam-6062	511	2	strong	strong	ADJ
ejpam-6062	511	3	convergence	convergence	NOUN
ejpam-6062	511	4	theorem	theorem	NOUN
ejpam-6062	511	5	for	for	ADP
ejpam-6062	511	6	a	a	DET
ejpam-6062	511	7	proximal	proximal	ADJ
ejpam-6062	511	8	-	-	PUNCT
ejpam-6062	511	9	type	type	NOUN
ejpam-6062	511	10	algorithm	algorithm	NOUN
ejpam-6062	511	11	in	in	ADP
ejpam-6062	511	12	reflexive	reflexive	ADJ
ejpam-6062	511	13	banach	banach	NOUN
ejpam-6062	511	14	spaces	space	VERB
ejpam-6062	511	15	.	.	PUNCT
ejpam-6062	512	1	j.	j.	PROPN
ejpam-6062	512	2	nonlinear	nonlinear	PROPN
ejpam-6062	512	3	convex	convex	PROPN
ejpam-6062	512	4	anal	anal	NOUN
ejpam-6062	512	5	.	.	PUNCT
ejpam-6062	512	6	,	,	PUNCT
ejpam-6062	512	7	10:471–485	10:471–485	NUM
ejpam-6062	512	8	,	,	PUNCT
ejpam-6062	512	9	2009	2009	NUM
ejpam-6062	512	10	.	.	PUNCT
ejpam-6062	513	1	[	[	X
ejpam-6062	513	2	41	41	NUM
ejpam-6062	513	3	]	]	X
ejpam-6062	513	4	p.	p.	PROPN
ejpam-6062	513	5	e.	e.	PROPN
ejpam-6062	513	6	mainge	mainge	PROPN
ejpam-6062	513	7	.	.	PUNCT
ejpam-6062	514	1	approximation	approximation	NOUN
ejpam-6062	514	2	methods	method	NOUN
ejpam-6062	514	3	from	from	ADP
ejpam-6062	514	4	common	common	ADJ
ejpam-6062	514	5	fixed	fix	VERB
ejpam-6062	514	6	points	point	NOUN
ejpam-6062	514	7	of	of	ADP
ejpam-6062	514	8	nonexpansive	nonexpansive	ADJ
ejpam-6062	514	9	mappings	mapping	NOUN
ejpam-6062	514	10	in	in	ADP
ejpam-6062	514	11	hilbert	hilbert	PROPN
ejpam-6062	514	12	spaces	space	NOUN
ejpam-6062	514	13	.	.	PUNCT
ejpam-6062	515	1	j.	j.	PROPN
ejpam-6062	515	2	math	math	PROPN
ejpam-6062	515	3	.	.	PUNCT
ejpam-6062	516	1	anal	anal	PROPN
ejpam-6062	516	2	.	.	PUNCT
ejpam-6062	517	1	appl	appl	PROPN
ejpam-6062	517	2	,	,	PUNCT
ejpam-6062	517	3	325:469–479	325:469–479	NUM
ejpam-6062	517	4	,	,	PUNCT
ejpam-6062	517	5	2007	2007	NUM
ejpam-6062	517	6	.	.	PUNCT
ejpam-6062	518	1	[	[	X
ejpam-6062	518	2	42	42	NUM
ejpam-6062	518	3	]	]	PUNCT
ejpam-6062	518	4	p.	p.	PROPN
ejpam-6062	518	5	e.	e.	PROPN
ejpam-6062	518	6	mainge	mainge	PROPN
ejpam-6062	518	7	.	.	PUNCT
ejpam-6062	519	1	strong	strong	ADJ
ejpam-6062	519	2	convergence	convergence	NOUN
ejpam-6062	519	3	of	of	ADP
ejpam-6062	519	4	projected	project	VERB
ejpam-6062	519	5	subgradient	subgradient	ADJ
ejpam-6062	519	6	methods	method	NOUN
ejpam-6062	519	7	for	for	ADP
ejpam-6062	519	8	nonsmooth	nonsmooth	NOUN
ejpam-6062	519	9	and	and	CCONJ
ejpam-6062	519	10	non	non	ADJ
ejpam-6062	519	11	strictly	strictly	ADV
ejpam-6062	519	12	convex	convex	VERB
ejpam-6062	519	13	minimization	minimization	NOUN
ejpam-6062	519	14	.	.	PUNCT
ejpam-6062	520	1	set	set	NOUN
ejpam-6062	520	2	-	-	PUNCT
ejpam-6062	520	3	valued	value	VERB
ejpam-6062	520	4	anal	anal	NOUN
ejpam-6062	520	5	.	.	PUNCT
ejpam-6062	520	6	,	,	PUNCT
ejpam-6062	520	7	16:899–912	16:899–912	NUM
ejpam-6062	520	8	,	,	PUNCT
ejpam-6062	520	9	2008	2008	NUM
ejpam-6062	520	10	.	.	PUNCT