id	sid	tid	token	lemma	pos
ejpam-1479	1	1	5_253356_dehghan.dvi	5_253356_dehghan.dvi	NUM
ejpam-1479	1	2	european	european	PROPN
ejpam-1479	1	3	journal	journal	PROPN
ejpam-1479	1	4	of	of	ADP
ejpam-1479	1	5	pure	pure	ADJ
ejpam-1479	1	6	and	and	CCONJ
ejpam-1479	1	7	applied	apply	VERB
ejpam-1479	1	8	mathematics	mathematic	NOUN
ejpam-1479	1	9	vol	vol	NOUN
ejpam-1479	1	10	.	.	PROPN
ejpam-1479	1	11	5	5	NUM
ejpam-1479	1	12	,	,	PUNCT
ejpam-1479	1	13	no	no	INTJ
ejpam-1479	1	14	.	.	NOUN
ejpam-1479	1	15	1	1	NUM
ejpam-1479	1	16	,	,	PUNCT
ejpam-1479	1	17	2012	2012	NUM
ejpam-1479	1	18	,	,	PUNCT
ejpam-1479	1	19	45	45	NUM
ejpam-1479	1	20	-	-	SYM
ejpam-1479	1	21	54	54	NUM
ejpam-1479	1	22	issn	issn	PROPN
ejpam-1479	1	23	1307	1307	NUM
ejpam-1479	1	24	-	-	SYM
ejpam-1479	1	25	5543	5543	NUM
ejpam-1479	1	26	–	–	PUNCT
ejpam-1479	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1479	1	28	special	special	ADJ
ejpam-1479	1	29	issue	issue	NOUN
ejpam-1479	1	30	for	for	ADP
ejpam-1479	1	31	the	the	DET
ejpam-1479	1	32	international	international	ADJ
ejpam-1479	1	33	conference	conference	NOUN
ejpam-1479	1	34	on	on	ADP
ejpam-1479	1	35	applied	apply	VERB
ejpam-1479	1	36	analysis	analysis	NOUN
ejpam-1479	1	37	and	and	CCONJ
ejpam-1479	1	38	algebra	algebra	NOUN
ejpam-1479	1	39	29	29	NUM
ejpam-1479	1	40	june	june	PROPN
ejpam-1479	1	41	02	02	NUM
ejpam-1479	1	42	july	july	PROPN
ejpam-1479	1	43	2011	2011	NUM
ejpam-1479	1	44	,	,	PUNCT
ejpam-1479	1	45	istanbul	istanbul	PROPN
ejpam-1479	1	46	turkey	turkey	PROPN
ejpam-1479	1	47	weak	weak	ADJ
ejpam-1479	1	48	and	and	CCONJ
ejpam-1479	1	49	strong	strong	ADJ
ejpam-1479	1	50	convergence	convergence	NOUN
ejpam-1479	1	51	of	of	ADP
ejpam-1479	1	52	a	a	DET
ejpam-1479	1	53	two	two	NUM
ejpam-1479	1	54	-	-	PUNCT
ejpam-1479	1	55	step	step	NOUN
ejpam-1479	1	56	iterations	iteration	NOUN
ejpam-1479	1	57	for	for	ADP
ejpam-1479	1	58	a	a	DET
ejpam-1479	1	59	finite	finite	ADJ
ejpam-1479	1	60	family	family	NOUN
ejpam-1479	1	61	of	of	ADP
ejpam-1479	1	62	generalized	generalized	ADJ
ejpam-1479	1	63	asymptotically	asymptotically	ADV
ejpam-1479	1	64	quasi	quasi	ADJ
ejpam-1479	1	65	-	-	ADJ
ejpam-1479	1	66	nonexpansive	nonexpansive	ADJ
ejpam-1479	1	67	mappings	mapping	NOUN
ejpam-1479	1	68	hossein	hossein	PROPN
ejpam-1479	1	69	dehghan	dehghan	PROPN
ejpam-1479	1	70	1,∗	1,∗	PROPN
ejpam-1479	1	71	,	,	PUNCT
ejpam-1479	1	72	amir	amir	PROPN
ejpam-1479	1	73	gharajelo	gharajelo	VERB
ejpam-1479	1	74	2	2	NUM
ejpam-1479	1	75	1	1	NUM
ejpam-1479	1	76	department	department	NOUN
ejpam-1479	1	77	of	of	ADP
ejpam-1479	1	78	mathematics	mathematics	PROPN
ejpam-1479	1	79	,	,	PUNCT
ejpam-1479	1	80	institute	institute	NOUN
ejpam-1479	1	81	for	for	ADP
ejpam-1479	1	82	advanced	advanced	ADJ
ejpam-1479	1	83	studies	study	NOUN
ejpam-1479	1	84	in	in	ADP
ejpam-1479	1	85	basic	basic	ADJ
ejpam-1479	1	86	sciences	science	NOUN
ejpam-1479	1	87	(	(	PUNCT
ejpam-1479	1	88	iasbs	iasbs	ADJ
ejpam-1479	1	89	)	)	PUNCT
ejpam-1479	1	90	,	,	PUNCT
ejpam-1479	1	91	zanjan	zanjan	PROPN
ejpam-1479	1	92	,	,	PUNCT
ejpam-1479	1	93	iran	iran	PROPN
ejpam-1479	1	94	2	2	NUM
ejpam-1479	1	95	department	department	NOUN
ejpam-1479	1	96	of	of	ADP
ejpam-1479	1	97	mathematics	mathematic	NOUN
ejpam-1479	1	98	,	,	PUNCT
ejpam-1479	1	99	roozbeh	roozbeh	NOUN
ejpam-1479	1	100	institute	institute	PROPN
ejpam-1479	1	101	of	of	ADP
ejpam-1479	1	102	higher	high	ADJ
ejpam-1479	1	103	education	education	NOUN
ejpam-1479	1	104	,	,	PUNCT
ejpam-1479	1	105	zanjan	zanjan	PROPN
ejpam-1479	1	106	,	,	PUNCT
ejpam-1479	1	107	iran	iran	PROPN
ejpam-1479	1	108	abstract	abstract	ADJ
ejpam-1479	1	109	.	.	PUNCT
ejpam-1479	2	1	in	in	ADP
ejpam-1479	2	2	this	this	DET
ejpam-1479	2	3	paper	paper	NOUN
ejpam-1479	2	4	,	,	PUNCT
ejpam-1479	2	5	we	we	PRON
ejpam-1479	2	6	introduce	introduce	VERB
ejpam-1479	2	7	and	and	CCONJ
ejpam-1479	2	8	study	study	VERB
ejpam-1479	2	9	a	a	DET
ejpam-1479	2	10	new	new	ADJ
ejpam-1479	2	11	two	two	NUM
ejpam-1479	2	12	-	-	PUNCT
ejpam-1479	2	13	step	step	NOUN
ejpam-1479	2	14	iterative	iterative	NOUN
ejpam-1479	2	15	scheme	scheme	NOUN
ejpam-1479	2	16	to	to	PART
ejpam-1479	2	17	approximate	approximate	VERB
ejpam-1479	2	18	common	common	ADJ
ejpam-1479	2	19	fixed	fix	VERB
ejpam-1479	2	20	points	point	NOUN
ejpam-1479	2	21	for	for	ADP
ejpam-1479	2	22	a	a	DET
ejpam-1479	2	23	finite	finite	ADJ
ejpam-1479	2	24	family	family	NOUN
ejpam-1479	2	25	of	of	ADP
ejpam-1479	2	26	generalized	generalized	ADJ
ejpam-1479	2	27	asymptotically	asymptotically	ADV
ejpam-1479	2	28	quasi	quasi	ADJ
ejpam-1479	2	29	-	-	ADJ
ejpam-1479	2	30	nonexpansive	nonexpansive	ADJ
ejpam-1479	2	31	mappings	mapping	NOUN
ejpam-1479	2	32	.	.	PUNCT
ejpam-1479	3	1	we	we	PRON
ejpam-1479	3	2	establish	establish	VERB
ejpam-1479	3	3	several	several	ADJ
ejpam-1479	3	4	strong	strong	ADJ
ejpam-1479	3	5	and	and	CCONJ
ejpam-1479	3	6	weak	weak	ADJ
ejpam-1479	3	7	convergence	convergence	NOUN
ejpam-1479	3	8	results	result	NOUN
ejpam-1479	3	9	of	of	ADP
ejpam-1479	3	10	the	the	DET
ejpam-1479	3	11	proposed	propose	VERB
ejpam-1479	3	12	algorithm	algorithm	NOUN
ejpam-1479	3	13	in	in	ADP
ejpam-1479	3	14	banach	banach	NOUN
ejpam-1479	3	15	spaces	space	NOUN
ejpam-1479	3	16	.	.	PUNCT
ejpam-1479	4	1	these	these	DET
ejpam-1479	4	2	results	result	NOUN
ejpam-1479	4	3	generalize	generalize	VERB
ejpam-1479	4	4	and	and	CCONJ
ejpam-1479	4	5	refine	refine	VERB
ejpam-1479	4	6	many	many	ADJ
ejpam-1479	4	7	known	know	VERB
ejpam-1479	4	8	results	result	NOUN
ejpam-1479	4	9	in	in	ADP
ejpam-1479	4	10	the	the	DET
ejpam-1479	4	11	current	current	ADJ
ejpam-1479	4	12	literature	literature	NOUN
ejpam-1479	4	13	.	.	PUNCT
ejpam-1479	5	1	2000	2000	NUM
ejpam-1479	5	2	mathematics	mathematic	NOUN
ejpam-1479	5	3	subject	subject	NOUN
ejpam-1479	5	4	classifications	classification	NOUN
ejpam-1479	5	5	:	:	PUNCT
ejpam-1479	5	6	ams	am	NOUN
ejpam-1479	5	7	47h09	47h09	NUM
ejpam-1479	5	8	,	,	PUNCT
ejpam-1479	5	9	47h10	47h10	PRON
ejpam-1479	5	10	key	key	ADJ
ejpam-1479	5	11	words	word	NOUN
ejpam-1479	5	12	and	and	CCONJ
ejpam-1479	5	13	phrases	phrase	NOUN
ejpam-1479	5	14	:	:	PUNCT
ejpam-1479	5	15	generalized	generalize	VERB
ejpam-1479	5	16	asymptotically	asymptotically	ADV
ejpam-1479	5	17	quasi	quasi	ADJ
ejpam-1479	5	18	-	-	ADJ
ejpam-1479	5	19	nonexpansive	nonexpansive	ADJ
ejpam-1479	5	20	mapping	mapping	NOUN
ejpam-1479	5	21	,	,	PUNCT
ejpam-1479	5	22	mann	mann	NOUN
ejpam-1479	5	23	-	-	PUNCT
ejpam-1479	5	24	type	type	NOUN
ejpam-1479	5	25	iteration	iteration	NOUN
ejpam-1479	5	26	,	,	PUNCT
ejpam-1479	5	27	ishikawa	ishikawa	NOUN
ejpam-1479	5	28	-	-	PUNCT
ejpam-1479	5	29	type	type	NOUN
ejpam-1479	5	30	iteration	iteration	NOUN
ejpam-1479	5	31	,	,	PUNCT
ejpam-1479	5	32	uniformly	uniformly	ADV
ejpam-1479	5	33	convex	convex	VERB
ejpam-1479	5	34	banach	banach	NOUN
ejpam-1479	5	35	space	space	NOUN
ejpam-1479	5	36	,	,	PUNCT
ejpam-1479	5	37	common	common	ADJ
ejpam-1479	5	38	fixed	fix	VERB
ejpam-1479	5	39	point	point	NOUN
ejpam-1479	5	40	.	.	PUNCT
ejpam-1479	6	1	1	1	X
ejpam-1479	6	2	.	.	X
ejpam-1479	6	3	introduction	introduction	NOUN
ejpam-1479	6	4	in	in	ADP
ejpam-1479	6	5	recent	recent	ADJ
ejpam-1479	6	6	years	year	NOUN
ejpam-1479	6	7	,	,	PUNCT
ejpam-1479	6	8	one	one	NUM
ejpam-1479	6	9	-	-	PUNCT
ejpam-1479	6	10	step	step	NOUN
ejpam-1479	6	11	and	and	CCONJ
ejpam-1479	6	12	two	two	NUM
ejpam-1479	6	13	-	-	PUNCT
ejpam-1479	6	14	step	step	NOUN
ejpam-1479	6	15	iterative	iterative	NOUN
ejpam-1479	6	16	schemes	scheme	NOUN
ejpam-1479	6	17	(	(	PUNCT
ejpam-1479	6	18	including	include	VERB
ejpam-1479	6	19	mann	mann	PROPN
ejpam-1479	6	20	iteration	iteration	NOUN
ejpam-1479	6	21	and	and	CCONJ
ejpam-1479	6	22	ishikawa	ishikawa	PROPN
ejpam-1479	6	23	iteration	iteration	NOUN
ejpam-1479	6	24	processes	process	NOUN
ejpam-1479	6	25	as	as	ADP
ejpam-1479	6	26	the	the	DET
ejpam-1479	6	27	most	most	ADV
ejpam-1479	6	28	important	important	ADJ
ejpam-1479	6	29	cases	case	NOUN
ejpam-1479	6	30	)	)	PUNCT
ejpam-1479	6	31	have	have	AUX
ejpam-1479	6	32	been	be	AUX
ejpam-1479	6	33	studied	study	VERB
ejpam-1479	6	34	extensively	extensively	ADV
ejpam-1479	6	35	by	by	ADP
ejpam-1479	6	36	many	many	ADJ
ejpam-1479	6	37	authors	author	NOUN
ejpam-1479	6	38	to	to	PART
ejpam-1479	6	39	approximate	approximate	VERB
ejpam-1479	6	40	fixed	fix	VERB
ejpam-1479	6	41	points	point	NOUN
ejpam-1479	6	42	of	of	ADP
ejpam-1479	6	43	various	various	ADJ
ejpam-1479	6	44	classes	class	NOUN
ejpam-1479	6	45	of	of	ADP
ejpam-1479	6	46	mappings	mapping	NOUN
ejpam-1479	6	47	(	(	PUNCT
ejpam-1479	6	48	see	see	VERB
ejpam-1479	6	49	for	for	ADP
ejpam-1479	6	50	example	example	NOUN
ejpam-1479	6	51	[	[	X
ejpam-1479	6	52	1	1	NUM
ejpam-1479	6	53	,	,	PUNCT
ejpam-1479	6	54	4	4	NUM
ejpam-1479	6	55	,	,	PUNCT
ejpam-1479	6	56	5	5	NUM
ejpam-1479	6	57	,	,	PUNCT
ejpam-1479	6	58	8	8	NUM
ejpam-1479	6	59	,	,	PUNCT
ejpam-1479	6	60	10	10	NUM
ejpam-1479	6	61	]	]	NUM
ejpam-1479	6	62	)	)	PUNCT
ejpam-1479	6	63	.	.	PUNCT
ejpam-1479	7	1	approximating	approximate	VERB
ejpam-1479	7	2	common	common	ADJ
ejpam-1479	7	3	fixed	fix	VERB
ejpam-1479	7	4	points	point	NOUN
ejpam-1479	7	5	of	of	ADP
ejpam-1479	7	6	a	a	DET
ejpam-1479	7	7	finite	finite	ADJ
ejpam-1479	7	8	family	family	NOUN
ejpam-1479	7	9	of	of	ADP
ejpam-1479	7	10	nonlinear	nonlinear	ADJ
ejpam-1479	7	11	mappings	mapping	NOUN
ejpam-1479	7	12	plays	play	VERB
ejpam-1479	7	13	an	an	DET
ejpam-1479	7	14	important	important	ADJ
ejpam-1479	7	15	role	role	NOUN
ejpam-1479	7	16	in	in	ADP
ejpam-1479	7	17	solving	solve	VERB
ejpam-1479	7	18	systems	system	NOUN
ejpam-1479	7	19	of	of	ADP
ejpam-1479	7	20	equations	equation	NOUN
ejpam-1479	7	21	and	and	CCONJ
ejpam-1479	7	22	inequalities	inequality	NOUN
ejpam-1479	7	23	that	that	PRON
ejpam-1479	7	24	often	often	ADV
ejpam-1479	7	25	arise	arise	VERB
ejpam-1479	7	26	in	in	ADP
ejpam-1479	7	27	applied	applied	ADJ
ejpam-1479	7	28	mathematics	mathematic	NOUN
ejpam-1479	7	29	.	.	PUNCT
ejpam-1479	8	1	for	for	ADP
ejpam-1479	8	2	a	a	DET
ejpam-1479	8	3	finite	finite	ADJ
ejpam-1479	8	4	family	family	NOUN
ejpam-1479	8	5	of	of	ADP
ejpam-1479	8	6	mappings	mapping	NOUN
ejpam-1479	8	7	{	{	PUNCT
ejpam-1479	8	8	ti	ti	NOUN
ejpam-1479	8	9	:	:	PUNCT
ejpam-1479	8	10	i	i	NOUN
ejpam-1479	8	11	=	=	SYM
ejpam-1479	8	12	1,2	1,2	NUM
ejpam-1479	8	13	,	,	PUNCT
ejpam-1479	8	14	.	.	PUNCT
ejpam-1479	8	15	.	.	PUNCT
ejpam-1479	8	16	.	.	PUNCT
ejpam-1479	9	1	,	,	PUNCT
ejpam-1479	9	2	m	m	VERB
ejpam-1479	9	3	}	}	PUNCT
ejpam-1479	9	4	,	,	PUNCT
ejpam-1479	9	5	it	it	PRON
ejpam-1479	9	6	is	be	AUX
ejpam-1479	9	7	desirable	desirable	ADJ
ejpam-1479	9	8	to	to	PART
ejpam-1479	9	9	devise	devise	VERB
ejpam-1479	9	10	a	a	DET
ejpam-1479	9	11	iteration	iteration	NOUN
ejpam-1479	9	12	scheme	scheme	NOUN
ejpam-1479	9	13	which	which	PRON
ejpam-1479	9	14	extends	extend	VERB
ejpam-1479	9	15	the	the	DET
ejpam-1479	9	16	modified	modify	VERB
ejpam-1479	9	17	mann	mann	PROPN
ejpam-1479	9	18	iteration	iteration	NOUN
ejpam-1479	9	19	and	and	CCONJ
ejpam-1479	9	20	the	the	DET
ejpam-1479	9	21	modified	modify	VERB
ejpam-1479	9	22	ishikawa	ishikawa	PROPN
ejpam-1479	9	23	∗corresponding	∗corresponde	VERB
ejpam-1479	9	24	author	author	NOUN
ejpam-1479	9	25	.	.	PUNCT
ejpam-1479	10	1	email	email	NOUN
ejpam-1479	10	2	addresses	address	NOUN
ejpam-1479	10	3	:	:	PUNCT
ejpam-1479	10	4	h_dehghan	h_dehghan	X
ejpam-1479	10	5	�	�	PROPN
ejpam-1479	10	6	iasbs.a	iasbs.a	PROPN
ejpam-1479	10	7	.ir	.ir	NUM
ejpam-1479	10	8	,	,	PUNCT
ejpam-1479	10	9	hossein.dehgan	hossein.dehgan	PROPN
ejpam-1479	10	10	�	�	NOUN
ejpam-1479	10	11	gmail	gmail	NOUN
ejpam-1479	10	12	.	.	PUNCT
ejpam-1479	11	1	om	om	PROPN
ejpam-1479	11	2	(	(	PUNCT
ejpam-1479	11	3	h.	h.	PROPN
ejpam-1479	11	4	dehghan),amirgharajelo	dehghan),amirgharajelo	PROPN
ejpam-1479	11	5	�	�	PROPN
ejpam-1479	11	6	yahoo	yahoo	PROPN
ejpam-1479	11	7	.	.	PUNCT
ejpam-1479	12	1	om	om	PROPN
ejpam-1479	12	2	(	(	PUNCT
ejpam-1479	12	3	a.	a.	NOUN
ejpam-1479	12	4	gharajelo	gharajelo	PROPN
ejpam-1479	12	5	)	)	PUNCT
ejpam-1479	12	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1479	13	1	45	45	NUM
ejpam-1479	13	2	c	c	X
ejpam-1479	13	3	©	©	PROPN
ejpam-1479	13	4	2012	2012	NUM
ejpam-1479	13	5	ejpam	ejpam	VERB
ejpam-1479	13	6	all	all	DET
ejpam-1479	13	7	rights	right	NOUN
ejpam-1479	13	8	reserved	reserve	VERB
ejpam-1479	13	9	.	.	PUNCT
ejpam-1479	14	1	h.	h.	PROPN
ejpam-1479	14	2	dehghan	dehghan	PROPN
ejpam-1479	14	3	,	,	PUNCT
ejpam-1479	14	4	a.	a.	NOUN
ejpam-1479	14	5	gharajelo	gharajelo	PROPN
ejpam-1479	14	6	/	/	SYM
ejpam-1479	14	7	eur	eur	PROPN
ejpam-1479	14	8	.	.	PUNCT
ejpam-1479	15	1	j.	j.	PROPN
ejpam-1479	15	2	pure	pure	PROPN
ejpam-1479	15	3	appl	appl	PROPN
ejpam-1479	15	4	.	.	PROPN
ejpam-1479	15	5	math	math	PROPN
ejpam-1479	15	6	,	,	PUNCT
ejpam-1479	15	7	5	5	NUM
ejpam-1479	15	8	(	(	PUNCT
ejpam-1479	15	9	2012	2012	NUM
ejpam-1479	15	10	)	)	PUNCT
ejpam-1479	15	11	,	,	PUNCT
ejpam-1479	15	12	45	45	NUM
ejpam-1479	15	13	-	-	SYM
ejpam-1479	15	14	54	54	NUM
ejpam-1479	15	15	46	46	NUM
ejpam-1479	15	16	iteration	iteration	NOUN
ejpam-1479	15	17	from	from	ADP
ejpam-1479	15	18	one	one	NUM
ejpam-1479	15	19	mapping	mapping	NOUN
ejpam-1479	15	20	to	to	ADP
ejpam-1479	15	21	a	a	DET
ejpam-1479	15	22	finite	finite	ADJ
ejpam-1479	15	23	family	family	NOUN
ejpam-1479	15	24	of	of	ADP
ejpam-1479	15	25	mappings	mapping	NOUN
ejpam-1479	15	26	.	.	PUNCT
ejpam-1479	16	1	thereby	thereby	ADV
ejpam-1479	16	2	,	,	PUNCT
ejpam-1479	16	3	to	to	PART
ejpam-1479	16	4	achieve	achieve	VERB
ejpam-1479	16	5	this	this	DET
ejpam-1479	16	6	goal	goal	NOUN
ejpam-1479	16	7	,	,	PUNCT
ejpam-1479	16	8	we	we	PRON
ejpam-1479	16	9	introduce	introduce	VERB
ejpam-1479	16	10	a	a	DET
ejpam-1479	16	11	new	new	ADJ
ejpam-1479	16	12	two	two	NUM
ejpam-1479	16	13	-	-	PUNCT
ejpam-1479	16	14	step	step	NOUN
ejpam-1479	16	15	iterative	iterative	NOUN
ejpam-1479	16	16	scheme	scheme	NOUN
ejpam-1479	16	17	for	for	ADP
ejpam-1479	16	18	a	a	DET
ejpam-1479	16	19	finite	finite	ADJ
ejpam-1479	16	20	family	family	NOUN
ejpam-1479	16	21	of	of	ADP
ejpam-1479	16	22	mappings	mapping	NOUN
ejpam-1479	16	23	as	as	SCONJ
ejpam-1479	16	24	follows	follow	VERB
ejpam-1479	16	25	:	:	PUNCT
ejpam-1479	16	26	let	let	VERB
ejpam-1479	16	27	c	c	PART
ejpam-1479	16	28	be	be	AUX
ejpam-1479	16	29	a	a	DET
ejpam-1479	16	30	nonempty	nonempty	ADJ
ejpam-1479	16	31	convex	convex	NOUN
ejpam-1479	16	32	subset	subset	NOUN
ejpam-1479	16	33	of	of	ADP
ejpam-1479	16	34	a	a	DET
ejpam-1479	16	35	real	real	ADJ
ejpam-1479	16	36	banach	banach	NOUN
ejpam-1479	16	37	space	space	NOUN
ejpam-1479	16	38	x	x	PUNCT
ejpam-1479	16	39	and	and	CCONJ
ejpam-1479	16	40	{	{	PUNCT
ejpam-1479	16	41	ti	ti	NOUN
ejpam-1479	16	42	:	:	PUNCT
ejpam-1479	16	43	i	i	NOUN
ejpam-1479	16	44	=	=	SYM
ejpam-1479	16	45	1,2	1,2	NUM
ejpam-1479	16	46	,	,	PUNCT
ejpam-1479	16	47	.	.	PUNCT
ejpam-1479	16	48	.	.	PUNCT
ejpam-1479	17	1	.	.	PUNCT
ejpam-1479	18	1	,	,	PUNCT
ejpam-1479	18	2	m	m	AUX
ejpam-1479	18	3	}	}	PUNCT
ejpam-1479	18	4	be	be	AUX
ejpam-1479	18	5	a	a	DET
ejpam-1479	18	6	family	family	NOUN
ejpam-1479	18	7	of	of	ADP
ejpam-1479	18	8	self	self	NOUN
ejpam-1479	18	9	-	-	PUNCT
ejpam-1479	18	10	mappings	mapping	NOUN
ejpam-1479	18	11	of	of	ADP
ejpam-1479	18	12	c	c	NOUN
ejpam-1479	18	13	.	.	PUNCT
ejpam-1479	19	1	for	for	ADP
ejpam-1479	19	2	a	a	DET
ejpam-1479	19	3	given	give	VERB
ejpam-1479	19	4	x1	x1	PROPN
ejpam-1479	19	5	∈	∈	PROPN
ejpam-1479	19	6	c	c	NOUN
ejpam-1479	19	7	,	,	PUNCT
ejpam-1479	19	8	compute	compute	VERB
ejpam-1479	19	9	the	the	DET
ejpam-1479	19	10	sequences	sequence	NOUN
ejpam-1479	19	11	{	{	PUNCT
ejpam-1479	19	12	xn	xn	NUM
ejpam-1479	19	13	}	}	PUNCT
ejpam-1479	19	14	and	and	CCONJ
ejpam-1479	19	15	{	{	PUNCT
ejpam-1479	19	16	yn	yn	NOUN
ejpam-1479	19	17	}	}	PUNCT
ejpam-1479	19	18	by	by	ADP
ejpam-1479	19	19	the	the	DET
ejpam-1479	19	20	iterative	iterative	NOUN
ejpam-1479	19	21	schemes	scheme	NOUN
ejpam-1479	19	22	yn	yn	X
ejpam-1479	20	1	=	=	PUNCT
ejpam-1479	20	2	m	m	VERB
ejpam-1479	20	3	∑	∑	PUNCT
ejpam-1479	20	4	i=1	i=1	PROPN
ejpam-1479	20	5	ai	be	VERB
ejpam-1479	20	6	nt	not	PART
ejpam-1479	20	7	n	n	ADV
ejpam-1479	21	1	i	i	PRON
ejpam-1479	21	2	xn+	xn+	PROPN
ejpam-1479	22	1	bn	bn	INTJ
ejpam-1479	22	2	xn	xn	PROPN
ejpam-1479	22	3	xn+1	xn+1	PROPN
ejpam-1479	23	1	=	=	PUNCT
ejpam-1479	23	2	m	m	VERB
ejpam-1479	23	3	∑	∑	VERB
ejpam-1479	23	4	i=1	i=1	PROPN
ejpam-1479	23	5	�	�	PROPN
ejpam-1479	23	6	αint	αint	PROPN
ejpam-1479	24	1	n	n	INTJ
ejpam-1479	24	2	i	i	PRON
ejpam-1479	24	3	yn	yn	PROPN
ejpam-1479	25	1	+	+	NOUN
ejpam-1479	25	2	βint	βint	NOUN
ejpam-1479	26	1	n	n	INTJ
ejpam-1479	26	2	i	i	NOUN
ejpam-1479	26	3	xn	xn	PROPN
ejpam-1479	26	4	�	�	PROPN
ejpam-1479	26	5	+	+	CCONJ
ejpam-1479	26	6	γn	γn	NOUN
ejpam-1479	26	7	xn	xn	NOUN
ejpam-1479	26	8	,	,	PUNCT
ejpam-1479	26	9	n≥	n≥	PROPN
ejpam-1479	26	10	1	1	NUM
ejpam-1479	26	11	,	,	PUNCT
ejpam-1479	26	12	(	(	PUNCT
ejpam-1479	26	13	1	1	X
ejpam-1479	26	14	)	)	PUNCT
ejpam-1479	26	15	where	where	SCONJ
ejpam-1479	26	16	{	{	PUNCT
ejpam-1479	26	17	ain	ain	NOUN
ejpam-1479	26	18	}	}	PUNCT
ejpam-1479	26	19	,	,	PUNCT
ejpam-1479	26	20	{	{	PUNCT
ejpam-1479	26	21	bn	bn	NOUN
ejpam-1479	26	22	}	}	PUNCT
ejpam-1479	26	23	,	,	PUNCT
ejpam-1479	26	24	{	{	PUNCT
ejpam-1479	26	25	αin	αin	NOUN
ejpam-1479	26	26	}	}	PUNCT
ejpam-1479	26	27	,	,	PUNCT
ejpam-1479	26	28	{	{	PUNCT
ejpam-1479	26	29	βin	βin	NOUN
ejpam-1479	26	30	}	}	PUNCT
ejpam-1479	26	31	,	,	PUNCT
ejpam-1479	26	32	and	and	CCONJ
ejpam-1479	26	33	{	{	PUNCT
ejpam-1479	26	34	γn	γn	NOUN
ejpam-1479	26	35	}	}	PUNCT
ejpam-1479	26	36	are	be	AUX
ejpam-1479	26	37	appropriate	appropriate	ADJ
ejpam-1479	26	38	sequences	sequence	NOUN
ejpam-1479	26	39	in	in	ADP
ejpam-1479	26	40	[	[	X
ejpam-1479	26	41	0,1	0,1	NUM
ejpam-1479	26	42	]	]	PUNCT
ejpam-1479	26	43	for	for	ADP
ejpam-1479	26	44	all	all	PRON
ejpam-1479	26	45	i	i	PRON
ejpam-1479	26	46	∈	∈	PROPN
ejpam-1479	26	47	{	{	PUNCT
ejpam-1479	26	48	1,2	1,2	NUM
ejpam-1479	26	49	,	,	PUNCT
ejpam-1479	26	50	.	.	PUNCT
ejpam-1479	26	51	.	.	PUNCT
ejpam-1479	27	1	.	.	PUNCT
ejpam-1479	28	1	,	,	PUNCT
ejpam-1479	28	2	m	m	VERB
ejpam-1479	28	3	}	}	PUNCT
ejpam-1479	28	4	such	such	ADJ
ejpam-1479	28	5	that	that	DET
ejpam-1479	28	6	bn+	bn+	NOUN
ejpam-1479	29	1	∑m	∑m	PROPN
ejpam-1479	29	2	i=1	i=1	PROPN
ejpam-1479	29	3	ain	ain	PROPN
ejpam-1479	29	4	=	=	SYM
ejpam-1479	29	5	γn+	γn+	ADJ
ejpam-1479	29	6	∑m	∑m	PROPN
ejpam-1479	29	7	i=1	i=1	PROPN
ejpam-1479	29	8	�	�	PROPN
ejpam-1479	29	9	αin	αin	NOUN
ejpam-1479	29	10	+	+	CCONJ
ejpam-1479	29	11	βin	βin	NOUN
ejpam-1479	29	12	�	�	NOUN
ejpam-1479	29	13	=	=	NOUN
ejpam-1479	29	14	1	1	NUM
ejpam-1479	29	15	for	for	ADP
ejpam-1479	29	16	each	each	DET
ejpam-1479	29	17	n≥	n≥	NOUN
ejpam-1479	29	18	1	1	NUM
ejpam-1479	29	19	.	.	PUNCT
ejpam-1479	30	1	if	if	SCONJ
ejpam-1479	30	2	t1	t1	NOUN
ejpam-1479	30	3	=	=	SYM
ejpam-1479	30	4	t2	t2	PROPN
ejpam-1479	30	5	=	=	SYM
ejpam-1479	30	6	·	·	PUNCT
ejpam-1479	30	7	·	·	PUNCT
ejpam-1479	30	8	·	·	PUNCT
ejpam-1479	31	1	=	=	SYM
ejpam-1479	31	2	tm	tm	PROPN
ejpam-1479	31	3	,	,	PUNCT
ejpam-1479	31	4	then	then	ADV
ejpam-1479	31	5	the	the	DET
ejpam-1479	31	6	iteration	iteration	NOUN
ejpam-1479	31	7	process	process	NOUN
ejpam-1479	31	8	(	(	PUNCT
ejpam-1479	31	9	1	1	X
ejpam-1479	31	10	)	)	PUNCT
ejpam-1479	31	11	reduces	reduce	VERB
ejpam-1479	31	12	to	to	ADP
ejpam-1479	31	13	yn	yn	NOUN
ejpam-1479	31	14	=	=	PUNCT
ejpam-1479	31	15	ant	ant	PROPN
ejpam-1479	32	1	n	n	DET
ejpam-1479	32	2	xn+	xn+	PROPN
ejpam-1479	32	3	(	(	PUNCT
ejpam-1479	32	4	1−	1−	NUM
ejpam-1479	32	5	an)xn	an)xn	PROPN
ejpam-1479	32	6	xn+1	xn+1	PUNCT
ejpam-1479	33	1	=	=	PUNCT
ejpam-1479	33	2	αnt	αnt	NOUN
ejpam-1479	33	3	n	n	X
ejpam-1479	33	4	yn	yn	X
ejpam-1479	33	5	+	+	CCONJ
ejpam-1479	33	6	βnt	βnt	ADV
ejpam-1479	33	7	n	n	PRON
ejpam-1479	33	8	xn+	xn+	VERB
ejpam-1479	33	9	γn	γn	ADP
ejpam-1479	33	10	xn	xn	PROPN
ejpam-1479	33	11	,	,	PUNCT
ejpam-1479	33	12	n≥	n≥	PROPN
ejpam-1479	33	13	1	1	NUM
ejpam-1479	33	14	,	,	PUNCT
ejpam-1479	33	15	(	(	PUNCT
ejpam-1479	33	16	2	2	X
ejpam-1479	33	17	)	)	PUNCT
ejpam-1479	33	18	where	where	SCONJ
ejpam-1479	33	19	{	{	PUNCT
ejpam-1479	33	20	an	an	X
ejpam-1479	33	21	}	}	PUNCT
ejpam-1479	33	22	,	,	PUNCT
ejpam-1479	33	23	{	{	PUNCT
ejpam-1479	33	24	αn	αn	NOUN
ejpam-1479	33	25	}	}	PUNCT
ejpam-1479	33	26	,	,	PUNCT
ejpam-1479	33	27	{	{	AUX
ejpam-1479	33	28	βn	βn	NOUN
ejpam-1479	33	29	}	}	PUNCT
ejpam-1479	33	30	,	,	PUNCT
ejpam-1479	33	31	and	and	CCONJ
ejpam-1479	33	32	{	{	PUNCT
ejpam-1479	33	33	γn	γn	NOUN
ejpam-1479	33	34	}	}	PUNCT
ejpam-1479	33	35	are	be	AUX
ejpam-1479	33	36	appropriate	appropriate	ADJ
ejpam-1479	33	37	sequences	sequence	NOUN
ejpam-1479	33	38	in	in	ADP
ejpam-1479	33	39	[	[	X
ejpam-1479	33	40	0,1	0,1	NUM
ejpam-1479	33	41	]	]	PUNCT
ejpam-1479	33	42	such	such	ADJ
ejpam-1479	33	43	that	that	SCONJ
ejpam-1479	33	44	αn+βn+γn	αn+βn+γn	PROPN
ejpam-1479	33	45	=	=	NOUN
ejpam-1479	33	46	1	1	NUM
ejpam-1479	33	47	for	for	ADP
ejpam-1479	33	48	each	each	DET
ejpam-1479	33	49	n≥	n≥	NOUN
ejpam-1479	33	50	1	1	NUM
ejpam-1479	33	51	.	.	PUNCT
ejpam-1479	34	1	clearly	clearly	ADV
ejpam-1479	34	2	,	,	PUNCT
ejpam-1479	34	3	the	the	DET
ejpam-1479	34	4	iteration	iteration	NOUN
ejpam-1479	34	5	process	process	NOUN
ejpam-1479	34	6	(	(	PUNCT
ejpam-1479	34	7	2	2	X
ejpam-1479	34	8	)	)	PUNCT
ejpam-1479	34	9	includes	include	VERB
ejpam-1479	34	10	the	the	DET
ejpam-1479	34	11	modified	modify	VERB
ejpam-1479	34	12	ishikawa	ishikawa	PROPN
ejpam-1479	34	13	iteration	iteration	NOUN
ejpam-1479	34	14	yn	yn	PROPN
ejpam-1479	34	15	=	=	PUNCT
ejpam-1479	34	16	ant	ant	PROPN
ejpam-1479	34	17	n	n	PRON
ejpam-1479	34	18	xn+	xn+	PROPN
ejpam-1479	34	19	(	(	PUNCT
ejpam-1479	34	20	1−	1−	NUM
ejpam-1479	34	21	an)xn	an)xn	PROPN
ejpam-1479	34	22	,	,	PUNCT
ejpam-1479	34	23	(	(	PUNCT
ejpam-1479	34	24	3	3	X
ejpam-1479	34	25	)	)	PUNCT
ejpam-1479	34	26	xn+1	xn+1	NOUN
ejpam-1479	35	1	=	=	SYM
ejpam-1479	35	2	αnt	αnt	NOUN
ejpam-1479	35	3	n	n	X
ejpam-1479	35	4	yn	yn	PRON
ejpam-1479	36	1	+	+	CCONJ
ejpam-1479	36	2	(	(	PUNCT
ejpam-1479	36	3	1−αn)xn	1−αn)xn	NOUN
ejpam-1479	36	4	,	,	PUNCT
ejpam-1479	36	5	n≥	n≥	NOUN
ejpam-1479	36	6	1	1	NUM
ejpam-1479	36	7	,	,	PUNCT
ejpam-1479	36	8	where	where	SCONJ
ejpam-1479	36	9	{	{	PUNCT
ejpam-1479	36	10	an	an	NOUN
ejpam-1479	36	11	}	}	PUNCT
ejpam-1479	36	12	and	and	CCONJ
ejpam-1479	36	13	{	{	PUNCT
ejpam-1479	36	14	αn	αn	NOUN
ejpam-1479	36	15	}	}	PUNCT
ejpam-1479	36	16	are	be	AUX
ejpam-1479	36	17	appropriate	appropriate	ADJ
ejpam-1479	36	18	sequences	sequence	NOUN
ejpam-1479	36	19	in	in	ADP
ejpam-1479	36	20	[	[	X
ejpam-1479	36	21	0,1	0,1	NUM
ejpam-1479	36	22	]	]	PUNCT
ejpam-1479	36	23	,	,	PUNCT
ejpam-1479	36	24	and	and	CCONJ
ejpam-1479	36	25	the	the	DET
ejpam-1479	36	26	modified	modify	VERB
ejpam-1479	36	27	mann	mann	PROPN
ejpam-1479	36	28	iteration	iteration	NOUN
ejpam-1479	36	29	xn+1	xn+1	PROPN
ejpam-1479	36	30	=	=	NOUN
ejpam-1479	36	31	ant	ant	PROPN
ejpam-1479	36	32	n	n	PRON
ejpam-1479	36	33	xn+	xn+	PROPN
ejpam-1479	36	34	(	(	PUNCT
ejpam-1479	36	35	1−	1−	NUM
ejpam-1479	36	36	an)xn	an)xn	PROPN
ejpam-1479	36	37	,	,	PUNCT
ejpam-1479	36	38	n≥	n≥	PROPN
ejpam-1479	36	39	1	1	NUM
ejpam-1479	36	40	,	,	PUNCT
ejpam-1479	36	41	(	(	PUNCT
ejpam-1479	36	42	4	4	X
ejpam-1479	36	43	)	)	PUNCT
ejpam-1479	36	44	where	where	SCONJ
ejpam-1479	36	45	{	{	PUNCT
ejpam-1479	36	46	an	an	PRON
ejpam-1479	36	47	}	}	PUNCT
ejpam-1479	36	48	is	be	AUX
ejpam-1479	36	49	appropriate	appropriate	ADJ
ejpam-1479	36	50	sequences	sequence	NOUN
ejpam-1479	36	51	in	in	ADP
ejpam-1479	36	52	[	[	X
ejpam-1479	36	53	0,1	0,1	NUM
ejpam-1479	36	54	]	]	PUNCT
ejpam-1479	36	55	.	.	PUNCT
ejpam-1479	37	1	therefore	therefore	ADV
ejpam-1479	37	2	,	,	PUNCT
ejpam-1479	37	3	(	(	PUNCT
ejpam-1479	37	4	1	1	X
ejpam-1479	37	5	)	)	PUNCT
ejpam-1479	37	6	generalizes	generalize	VERB
ejpam-1479	37	7	the	the	DET
ejpam-1479	37	8	modified	modify	VERB
ejpam-1479	37	9	ishikawa	ishikawa	PROPN
ejpam-1479	37	10	iteration	iteration	NOUN
ejpam-1479	37	11	and	and	CCONJ
ejpam-1479	37	12	the	the	DET
ejpam-1479	37	13	modified	modify	VERB
ejpam-1479	37	14	mann	mann	PROPN
ejpam-1479	37	15	iteration	iteration	NOUN
ejpam-1479	37	16	from	from	ADP
ejpam-1479	37	17	one	one	NUM
ejpam-1479	37	18	mapping	mapping	NOUN
ejpam-1479	37	19	to	to	ADP
ejpam-1479	37	20	the	the	DET
ejpam-1479	37	21	finite	finite	ADJ
ejpam-1479	37	22	family	family	NOUN
ejpam-1479	37	23	of	of	ADP
ejpam-1479	37	24	mappings	mapping	NOUN
ejpam-1479	37	25	{	{	PUNCT
ejpam-1479	37	26	t	t	PROPN
ejpam-1479	37	27	j	j	PROPN
ejpam-1479	37	28	:	:	PUNCT
ejpam-1479	37	29	j	j	X
ejpam-1479	37	30	=	=	SYM
ejpam-1479	37	31	1,2	1,2	NUM
ejpam-1479	37	32	,	,	PUNCT
ejpam-1479	37	33	.	.	PUNCT
ejpam-1479	37	34	.	.	PUNCT
ejpam-1479	38	1	.	.	PUNCT
ejpam-1479	39	1	,	,	PUNCT
ejpam-1479	39	2	m	m	VERB
ejpam-1479	39	3	}	}	PUNCT
ejpam-1479	39	4	.	.	PUNCT
ejpam-1479	40	1	the	the	DET
ejpam-1479	40	2	aim	aim	NOUN
ejpam-1479	40	3	of	of	ADP
ejpam-1479	40	4	this	this	DET
ejpam-1479	40	5	paper	paper	NOUN
ejpam-1479	40	6	is	be	AUX
ejpam-1479	40	7	to	to	PART
ejpam-1479	40	8	obtain	obtain	VERB
ejpam-1479	40	9	some	some	DET
ejpam-1479	40	10	strong	strong	ADJ
ejpam-1479	40	11	and	and	CCONJ
ejpam-1479	40	12	weak	weak	ADJ
ejpam-1479	40	13	convergence	convergence	NOUN
ejpam-1479	40	14	results	result	NOUN
ejpam-1479	40	15	for	for	ADP
ejpam-1479	40	16	the	the	DET
ejpam-1479	40	17	iterative	iterative	NOUN
ejpam-1479	40	18	process	process	NOUN
ejpam-1479	40	19	(	(	PUNCT
ejpam-1479	40	20	1	1	NUM
ejpam-1479	40	21	)	)	PUNCT
ejpam-1479	40	22	of	of	ADP
ejpam-1479	40	23	a	a	DET
ejpam-1479	40	24	finite	finite	ADJ
ejpam-1479	40	25	family	family	NOUN
ejpam-1479	40	26	of	of	ADP
ejpam-1479	40	27	generalized	generalized	ADJ
ejpam-1479	40	28	asymptotically	asymptotically	ADV
ejpam-1479	40	29	quasi	quasi	ADJ
ejpam-1479	40	30	-	-	ADJ
ejpam-1479	40	31	nonexpansive	nonexpansive	ADJ
ejpam-1479	40	32	mappings	mapping	NOUN
ejpam-1479	40	33	in	in	ADP
ejpam-1479	40	34	banach	banach	NOUN
ejpam-1479	40	35	spaces	space	NOUN
ejpam-1479	40	36	.	.	PUNCT
ejpam-1479	41	1	now	now	ADV
ejpam-1479	41	2	,	,	PUNCT
ejpam-1479	41	3	we	we	PRON
ejpam-1479	41	4	recall	recall	VERB
ejpam-1479	41	5	the	the	DET
ejpam-1479	41	6	well	well	ADV
ejpam-1479	41	7	-	-	PUNCT
ejpam-1479	41	8	known	know	VERB
ejpam-1479	41	9	concepts	concept	NOUN
ejpam-1479	41	10	and	and	CCONJ
ejpam-1479	41	11	results	result	NOUN
ejpam-1479	41	12	.	.	PUNCT
ejpam-1479	42	1	for	for	ADP
ejpam-1479	42	2	convenience	convenience	NOUN
ejpam-1479	42	3	,	,	PUNCT
ejpam-1479	42	4	we	we	PRON
ejpam-1479	42	5	use	use	VERB
ejpam-1479	42	6	the	the	DET
ejpam-1479	42	7	notations	notation	NOUN
ejpam-1479	42	8	limn	limn	PROPN
ejpam-1479	42	9	≡	≡	PROPN
ejpam-1479	42	10	limn→∞	limn→∞	PROPN
ejpam-1479	42	11	,	,	PUNCT
ejpam-1479	42	12	lim	lim	PROPN
ejpam-1479	42	13	infn	infn	PROPN
ejpam-1479	42	14	≡	≡	PROPN
ejpam-1479	42	15	lim	lim	PROPN
ejpam-1479	42	16	infn→∞	infn→∞	PROPN
ejpam-1479	42	17	and	and	CCONJ
ejpam-1479	42	18	lim	lim	PROPN
ejpam-1479	42	19	supn	supn	PROPN
ejpam-1479	42	20	≡	≡	PROPN
ejpam-1479	42	21	lim	lim	PROPN
ejpam-1479	42	22	supn→∞.	supn→∞.	PROPN
ejpam-1479	42	23	let	let	VERB
ejpam-1479	42	24	c	c	NOUN
ejpam-1479	42	25	be	be	AUX
ejpam-1479	42	26	a	a	DET
ejpam-1479	42	27	nonempty	nonempty	ADJ
ejpam-1479	42	28	subset	subset	NOUN
ejpam-1479	42	29	of	of	ADP
ejpam-1479	42	30	a	a	DET
ejpam-1479	42	31	real	real	ADJ
ejpam-1479	42	32	banach	banach	NOUN
ejpam-1479	42	33	space	space	NOUN
ejpam-1479	42	34	x	x	PUNCT
ejpam-1479	42	35	and	and	CCONJ
ejpam-1479	42	36	t	t	PROPN
ejpam-1479	42	37	be	be	AUX
ejpam-1479	42	38	a	a	DET
ejpam-1479	42	39	self	self	NOUN
ejpam-1479	42	40	-	-	PUNCT
ejpam-1479	42	41	mapping	mapping	NOUN
ejpam-1479	42	42	of	of	ADP
ejpam-1479	42	43	c	c	PROPN
ejpam-1479	42	44	.	.	PUNCT
ejpam-1479	43	1	the	the	DET
ejpam-1479	43	2	fixed	fixed	ADJ
ejpam-1479	43	3	point	point	NOUN
ejpam-1479	43	4	set	set	NOUN
ejpam-1479	43	5	of	of	ADP
ejpam-1479	43	6	t	t	PROPN
ejpam-1479	43	7	is	be	AUX
ejpam-1479	43	8	denoted	denote	VERB
ejpam-1479	43	9	by	by	ADP
ejpam-1479	43	10	f(t	f(t	NOUN
ejpam-1479	43	11	)	)	PUNCT
ejpam-1479	44	1	=	=	PUNCT
ejpam-1479	44	2	{	{	PUNCT
ejpam-1479	44	3	x	x	PUNCT
ejpam-1479	44	4	∈	∈	PROPN
ejpam-1479	44	5	c	c	NOUN
ejpam-1479	44	6	:	:	PUNCT
ejpam-1479	44	7	t	t	NOUN
ejpam-1479	44	8	x	x	PUNCT
ejpam-1479	44	9	=	=	PUNCT
ejpam-1479	44	10	x	x	X
ejpam-1479	44	11	}	}	PUNCT
ejpam-1479	44	12	.	.	PUNCT
ejpam-1479	45	1	the	the	DET
ejpam-1479	45	2	mapping	mapping	NOUN
ejpam-1479	45	3	t	t	PROPN
ejpam-1479	45	4	is	be	AUX
ejpam-1479	45	5	called	call	VERB
ejpam-1479	45	6	(	(	PUNCT
ejpam-1479	45	7	i	i	NOUN
ejpam-1479	45	8	)	)	PUNCT
ejpam-1479	45	9	asymptotically	asymptotically	ADV
ejpam-1479	45	10	nonexpansive	nonexpansive	ADJ
ejpam-1479	45	11	if	if	SCONJ
ejpam-1479	45	12	there	there	PRON
ejpam-1479	45	13	exists	exist	VERB
ejpam-1479	45	14	a	a	DET
ejpam-1479	45	15	sequence	sequence	NOUN
ejpam-1479	45	16	{	{	PUNCT
ejpam-1479	45	17	rn	rn	NOUN
ejpam-1479	45	18	}	}	PUNCT
ejpam-1479	45	19	in	in	ADP
ejpam-1479	45	20	[	[	X
ejpam-1479	45	21	0,∞	0,∞	NOUN
ejpam-1479	45	22	)	)	PUNCT
ejpam-1479	45	23	with	with	ADP
ejpam-1479	45	24	limn	limn	PROPN
ejpam-1479	45	25	rn	rn	PROPN
ejpam-1479	45	26	=	=	PROPN
ejpam-1479	45	27	0	0	PROPN
ejpam-1479	45	28	such	such	ADJ
ejpam-1479	45	29	that	that	SCONJ
ejpam-1479	45	30	‖t	‖t	NOUN
ejpam-1479	45	31	n	n	NOUN
ejpam-1479	45	32	x	x	NOUN
ejpam-1479	45	33	−	−	PROPN
ejpam-1479	45	34	t	t	PROPN
ejpam-1479	46	1	n	n	PROPN
ejpam-1479	46	2	y‖	y‖	PROPN
ejpam-1479	46	3	≤	≤	NUM
ejpam-1479	46	4	(	(	PUNCT
ejpam-1479	46	5	1	1	NUM
ejpam-1479	46	6	+	+	NUM
ejpam-1479	46	7	rn)‖x	rn)‖x	NOUN
ejpam-1479	46	8	−	−	NOUN
ejpam-1479	46	9	y‖	y‖	NOUN
ejpam-1479	46	10	for	for	ADP
ejpam-1479	46	11	all	all	DET
ejpam-1479	46	12	x	x	SYM
ejpam-1479	46	13	,	,	PUNCT
ejpam-1479	46	14	y	y	PROPN
ejpam-1479	46	15	∈	∈	PROPN
ejpam-1479	46	16	c	c	PROPN
ejpam-1479	46	17	and	and	CCONJ
ejpam-1479	46	18	each	each	DET
ejpam-1479	46	19	n≥	n≥	PROPN
ejpam-1479	46	20	1	1	NUM
ejpam-1479	46	21	;	;	PUNCT
ejpam-1479	46	22	(	(	PUNCT
ejpam-1479	46	23	ii	ii	NOUN
ejpam-1479	46	24	)	)	PUNCT
ejpam-1479	46	25	asymptotically	asymptotically	ADV
ejpam-1479	46	26	quasi	quasi	ADJ
ejpam-1479	46	27	-	-	ADJ
ejpam-1479	46	28	nonexpansive	nonexpansive	ADJ
ejpam-1479	46	29	if	if	SCONJ
ejpam-1479	46	30	f(t	f(t	PROPN
ejpam-1479	46	31	)	)	PUNCT
ejpam-1479	46	32	6=	6=	NUM
ejpam-1479	46	33	;	;	PUNCT
ejpam-1479	46	34	and	and	CCONJ
ejpam-1479	46	35	there	there	PRON
ejpam-1479	46	36	exists	exist	VERB
ejpam-1479	46	37	a	a	DET
ejpam-1479	46	38	sequence	sequence	NOUN
ejpam-1479	46	39	{	{	PUNCT
ejpam-1479	46	40	rn	rn	NOUN
ejpam-1479	46	41	}	}	PUNCT
ejpam-1479	46	42	in	in	ADP
ejpam-1479	46	43	[	[	X
ejpam-1479	46	44	0,∞	0,∞	NOUN
ejpam-1479	46	45	)	)	PUNCT
ejpam-1479	46	46	with	with	ADP
ejpam-1479	46	47	limn	limn	PROPN
ejpam-1479	46	48	rn	rn	PROPN
ejpam-1479	46	49	=	=	PROPN
ejpam-1479	46	50	0	0	PROPN
ejpam-1479	46	51	such	such	ADJ
ejpam-1479	46	52	that	that	SCONJ
ejpam-1479	46	53	‖t	‖t	PROPN
ejpam-1479	46	54	n	n	CCONJ
ejpam-1479	46	55	x−	x−	PROPN
ejpam-1479	46	56	p‖	p‖	PROPN
ejpam-1479	46	57	≤	≤	PROPN
ejpam-1479	46	58	(	(	PUNCT
ejpam-1479	46	59	1	1	NUM
ejpam-1479	46	60	+	+	NUM
ejpam-1479	46	61	rn)‖x−	rn)‖x−	NOUN
ejpam-1479	46	62	p‖	p‖	NOUN
ejpam-1479	46	63	for	for	ADP
ejpam-1479	46	64	all	all	DET
ejpam-1479	46	65	x	x	SYM
ejpam-1479	46	66	∈	∈	PROPN
ejpam-1479	46	67	c	c	NOUN
ejpam-1479	46	68	,	,	PUNCT
ejpam-1479	46	69	p	p	PROPN
ejpam-1479	46	70	∈	∈	PROPN
ejpam-1479	46	71	f(t	f(t	PROPN
ejpam-1479	46	72	)	)	PUNCT
ejpam-1479	46	73	and	and	CCONJ
ejpam-1479	46	74	each	each	DET
ejpam-1479	46	75	n≥	n≥	PROPN
ejpam-1479	46	76	1	1	NUM
ejpam-1479	46	77	;	;	PUNCT
ejpam-1479	46	78	h.	h.	PROPN
ejpam-1479	46	79	dehghan	dehghan	PROPN
ejpam-1479	46	80	,	,	PUNCT
ejpam-1479	46	81	a.	a.	NOUN
ejpam-1479	46	82	gharajelo	gharajelo	PROPN
ejpam-1479	46	83	/	/	SYM
ejpam-1479	46	84	eur	eur	PROPN
ejpam-1479	46	85	.	.	PUNCT
ejpam-1479	47	1	j.	j.	PROPN
ejpam-1479	47	2	pure	pure	PROPN
ejpam-1479	47	3	appl	appl	PROPN
ejpam-1479	47	4	.	.	PROPN
ejpam-1479	47	5	math	math	PROPN
ejpam-1479	47	6	,	,	PUNCT
ejpam-1479	47	7	5	5	NUM
ejpam-1479	47	8	(	(	PUNCT
ejpam-1479	47	9	2012	2012	NUM
ejpam-1479	47	10	)	)	PUNCT
ejpam-1479	47	11	,	,	PUNCT
ejpam-1479	47	12	45	45	NUM
ejpam-1479	47	13	-	-	SYM
ejpam-1479	47	14	54	54	NUM
ejpam-1479	47	15	47	47	NUM
ejpam-1479	47	16	(	(	PUNCT
ejpam-1479	47	17	iii	iii	NOUN
ejpam-1479	47	18	)	)	PUNCT
ejpam-1479	47	19	generalized	generalize	VERB
ejpam-1479	47	20	asymptotically	asymptotically	ADV
ejpam-1479	47	21	quasi	quasi	ADJ
ejpam-1479	47	22	-	-	ADJ
ejpam-1479	47	23	nonexpansive	nonexpansive	ADJ
ejpam-1479	48	1	[	[	X
ejpam-1479	48	2	7	7	NUM
ejpam-1479	48	3	]	]	PUNCT
ejpam-1479	48	4	if	if	SCONJ
ejpam-1479	48	5	f(t	f(t	PROPN
ejpam-1479	48	6	)	)	PUNCT
ejpam-1479	48	7	6=	6=	NUM
ejpam-1479	48	8	;	;	PUNCT
ejpam-1479	48	9	and	and	CCONJ
ejpam-1479	48	10	there	there	PRON
ejpam-1479	48	11	exist	exist	VERB
ejpam-1479	48	12	two	two	NUM
ejpam-1479	48	13	sequences	sequence	NOUN
ejpam-1479	48	14	{	{	PUNCT
ejpam-1479	48	15	rn	rn	NOUN
ejpam-1479	48	16	}	}	PUNCT
ejpam-1479	48	17	and	and	CCONJ
ejpam-1479	48	18	{	{	PUNCT
ejpam-1479	48	19	sn	sn	NOUN
ejpam-1479	48	20	}	}	PUNCT
ejpam-1479	48	21	in	in	ADP
ejpam-1479	48	22	[	[	X
ejpam-1479	48	23	0,∞	0,∞	NOUN
ejpam-1479	48	24	)	)	PUNCT
ejpam-1479	48	25	with	with	ADP
ejpam-1479	48	26	limn	limn	PROPN
ejpam-1479	48	27	rn	rn	PROPN
ejpam-1479	48	28	=	=	PROPN
ejpam-1479	48	29	limn	limn	PROPN
ejpam-1479	48	30	sn	sn	PROPN
ejpam-1479	49	1	=	=	NOUN
ejpam-1479	49	2	0	0	NUM
ejpam-1479	49	3	such	such	ADJ
ejpam-1479	49	4	that	that	SCONJ
ejpam-1479	49	5	‖t	‖t	NOUN
ejpam-1479	49	6	n	n	NOUN
ejpam-1479	49	7	x	x	SYM
ejpam-1479	49	8	−	−	PROPN
ejpam-1479	49	9	p‖	p‖	NOUN
ejpam-1479	49	10	≤	≤	NUM
ejpam-1479	49	11	(	(	PUNCT
ejpam-1479	49	12	1	1	NUM
ejpam-1479	49	13	+	+	NUM
ejpam-1479	49	14	rn)‖x	rn)‖x	NOUN
ejpam-1479	49	15	−	−	NOUN
ejpam-1479	49	16	p‖+	p‖+	PROPN
ejpam-1479	49	17	sn	sn	PROPN
ejpam-1479	49	18	for	for	ADP
ejpam-1479	49	19	all	all	DET
ejpam-1479	49	20	x	x	SYM
ejpam-1479	49	21	∈	∈	PROPN
ejpam-1479	49	22	c	c	NOUN
ejpam-1479	49	23	,	,	PUNCT
ejpam-1479	49	24	p	p	PROPN
ejpam-1479	49	25	∈	∈	PROPN
ejpam-1479	49	26	f(t	f(t	PROPN
ejpam-1479	49	27	)	)	PUNCT
ejpam-1479	49	28	and	and	CCONJ
ejpam-1479	49	29	each	each	DET
ejpam-1479	49	30	n≥	n≥	PROPN
ejpam-1479	49	31	1	1	NUM
ejpam-1479	49	32	;	;	PUNCT
ejpam-1479	49	33	(	(	PUNCT
ejpam-1479	49	34	iv	iv	X
ejpam-1479	49	35	)	)	PUNCT
ejpam-1479	49	36	uniformly	uniformly	ADV
ejpam-1479	49	37	l	l	NOUN
ejpam-1479	49	38	-	-	NOUN
ejpam-1479	49	39	lipschitz	lipschitz	NOUN
ejpam-1479	49	40	if	if	SCONJ
ejpam-1479	49	41	there	there	PRON
ejpam-1479	49	42	exists	exist	VERB
ejpam-1479	49	43	constant	constant	ADJ
ejpam-1479	49	44	l	l	NOUN
ejpam-1479	49	45	>	>	X
ejpam-1479	49	46	0	0	NUM
ejpam-1479	49	47	such	such	ADJ
ejpam-1479	49	48	that	that	SCONJ
ejpam-1479	49	49	‖t	‖t	NOUN
ejpam-1479	49	50	n	n	NOUN
ejpam-1479	49	51	x	x	NOUN
ejpam-1479	49	52	−	−	PROPN
ejpam-1479	49	53	t	t	PROPN
ejpam-1479	49	54	n	n	NOUN
ejpam-1479	49	55	y‖	y‖	PROPN
ejpam-1479	49	56	≤	≤	NUM
ejpam-1479	49	57	l‖x	l‖x	PROPN
ejpam-1479	49	58	−	−	PROPN
ejpam-1479	49	59	y‖	y‖	PROPN
ejpam-1479	49	60	for	for	ADP
ejpam-1479	49	61	all	all	DET
ejpam-1479	49	62	x	x	SYM
ejpam-1479	49	63	,	,	PUNCT
ejpam-1479	49	64	y	y	PROPN
ejpam-1479	49	65	∈	∈	PROPN
ejpam-1479	49	66	c	c	PROPN
ejpam-1479	49	67	and	and	CCONJ
ejpam-1479	49	68	each	each	DET
ejpam-1479	49	69	n≥	n≥	NOUN
ejpam-1479	49	70	1	1	X
ejpam-1479	49	71	.	.	PUNCT
ejpam-1479	50	1	it	it	PRON
ejpam-1479	50	2	is	be	AUX
ejpam-1479	50	3	clear	clear	ADJ
ejpam-1479	50	4	that	that	SCONJ
ejpam-1479	50	5	a	a	DET
ejpam-1479	50	6	generalized	generalize	VERB
ejpam-1479	50	7	asymptotically	asymptotically	ADV
ejpam-1479	50	8	quasi	quasi	ADJ
ejpam-1479	50	9	-	-	ADJ
ejpam-1479	50	10	nonexpansive	nonexpansive	ADJ
ejpam-1479	50	11	mapping	mapping	NOUN
ejpam-1479	50	12	is	be	AUX
ejpam-1479	50	13	to	to	PART
ejpam-1479	50	14	unify	unify	VERB
ejpam-1479	50	15	various	various	ADJ
ejpam-1479	50	16	classes	class	NOUN
ejpam-1479	50	17	of	of	ADP
ejpam-1479	50	18	mappings	mapping	NOUN
ejpam-1479	50	19	associated	associate	VERB
ejpam-1479	50	20	with	with	ADP
ejpam-1479	50	21	the	the	DET
ejpam-1479	50	22	class	class	NOUN
ejpam-1479	50	23	of	of	ADP
ejpam-1479	50	24	asymptotically	asymptotically	ADV
ejpam-1479	50	25	quasi	quasi	ADJ
ejpam-1479	50	26	-	-	ADJ
ejpam-1479	50	27	nonexpansive	nonexpansive	ADJ
ejpam-1479	50	28	mapping	mapping	NOUN
ejpam-1479	50	29	,	,	PUNCT
ejpam-1479	50	30	asymptotically	asymptotically	ADV
ejpam-1479	50	31	nonexpansive	nonexpansive	ADJ
ejpam-1479	50	32	mappings	mapping	NOUN
ejpam-1479	50	33	and	and	CCONJ
ejpam-1479	50	34	nonexpansive	nonexpansive	ADJ
ejpam-1479	50	35	mappings	mapping	NOUN
ejpam-1479	50	36	.	.	PUNCT
ejpam-1479	51	1	however	however	ADV
ejpam-1479	51	2	,	,	PUNCT
ejpam-1479	51	3	the	the	DET
ejpam-1479	51	4	converse	converse	NOUN
ejpam-1479	51	5	of	of	ADP
ejpam-1479	51	6	each	each	PRON
ejpam-1479	51	7	of	of	ADP
ejpam-1479	51	8	above	above	ADP
ejpam-1479	51	9	statement	statement	NOUN
ejpam-1479	51	10	may	may	AUX
ejpam-1479	51	11	be	be	AUX
ejpam-1479	51	12	not	not	PART
ejpam-1479	51	13	true	true	ADJ
ejpam-1479	51	14	.	.	PUNCT
ejpam-1479	52	1	the	the	DET
ejpam-1479	52	2	example	example	NOUN
ejpam-1479	52	3	,	,	PUNCT
ejpam-1479	52	4	shows	show	VERB
ejpam-1479	52	5	that	that	SCONJ
ejpam-1479	52	6	a	a	DET
ejpam-1479	52	7	generalized	generalize	VERB
ejpam-1479	52	8	asymptotically	asymptotically	ADV
ejpam-1479	52	9	quasi	quasi	ADJ
ejpam-1479	52	10	-	-	ADJ
ejpam-1479	52	11	nonexpansive	nonexpansive	ADJ
ejpam-1479	52	12	mapping	mapping	NOUN
ejpam-1479	52	13	is	be	AUX
ejpam-1479	52	14	not	not	PART
ejpam-1479	52	15	an	an	DET
ejpam-1479	52	16	asymptotically	asymptotically	ADV
ejpam-1479	52	17	quasi	quasi	ADJ
ejpam-1479	52	18	-	-	ADJ
ejpam-1479	52	19	nonexpansive	nonexpansive	ADJ
ejpam-1479	52	20	mapping	mapping	NOUN
ejpam-1479	52	21	,	,	PUNCT
ejpam-1479	52	22	can	can	AUX
ejpam-1479	52	23	be	be	AUX
ejpam-1479	52	24	found	find	VERB
ejpam-1479	52	25	in	in	ADP
ejpam-1479	52	26	[	[	X
ejpam-1479	52	27	7	7	NUM
ejpam-1479	52	28	]	]	PUNCT
ejpam-1479	52	29	.	.	PUNCT
ejpam-1479	53	1	a	a	DET
ejpam-1479	53	2	family	family	NOUN
ejpam-1479	53	3	of	of	ADP
ejpam-1479	53	4	self	self	NOUN
ejpam-1479	53	5	-	-	PUNCT
ejpam-1479	53	6	mappings	mapping	NOUN
ejpam-1479	53	7	{	{	PUNCT
ejpam-1479	53	8	ti	ti	NOUN
ejpam-1479	53	9	:	:	PUNCT
ejpam-1479	53	10	i	i	NOUN
ejpam-1479	53	11	=	=	SYM
ejpam-1479	53	12	1,2	1,2	NUM
ejpam-1479	53	13	,	,	PUNCT
ejpam-1479	53	14	.	.	PUNCT
ejpam-1479	53	15	.	.	PUNCT
ejpam-1479	53	16	.	.	PUNCT
ejpam-1479	54	1	,	,	PUNCT
ejpam-1479	54	2	m	m	VERB
ejpam-1479	54	3	}	}	PUNCT
ejpam-1479	54	4	of	of	ADP
ejpam-1479	54	5	c	c	PROPN
ejpam-1479	54	6	is	be	AUX
ejpam-1479	54	7	said	say	VERB
ejpam-1479	54	8	to	to	PART
ejpam-1479	54	9	satisfy	satisfy	VERB
ejpam-1479	54	10	condition	condition	NOUN
ejpam-1479	54	11	(	(	PUNCT
ejpam-1479	54	12	a′′	a′′	NOUN
ejpam-1479	54	13	)	)	PUNCT
ejpam-1479	55	1	[	[	X
ejpam-1479	55	2	3	3	X
ejpam-1479	55	3	]	]	X
ejpam-1479	55	4	if	if	SCONJ
ejpam-1479	55	5	there	there	PRON
ejpam-1479	55	6	exists	exist	VERB
ejpam-1479	55	7	a	a	DET
ejpam-1479	55	8	nondecreasing	nondecrease	VERB
ejpam-1479	55	9	function	function	NOUN
ejpam-1479	55	10	f	f	NOUN
ejpam-1479	55	11	:	:	PUNCT
ejpam-1479	56	1	[	[	X
ejpam-1479	56	2	0,∞)→	0,∞)→	NOUN
ejpam-1479	56	3	[	[	X
ejpam-1479	56	4	0,∞	0,∞	NOUN
ejpam-1479	56	5	)	)	PUNCT
ejpam-1479	56	6	with	with	ADP
ejpam-1479	56	7	f	f	PROPN
ejpam-1479	56	8	(	(	PUNCT
ejpam-1479	56	9	0	0	NUM
ejpam-1479	56	10	)	)	PUNCT
ejpam-1479	56	11	=	=	SYM
ejpam-1479	56	12	0	0	NUM
ejpam-1479	56	13	and	and	CCONJ
ejpam-1479	56	14	f	f	PROPN
ejpam-1479	56	15	(	(	PUNCT
ejpam-1479	56	16	r	r	NOUN
ejpam-1479	56	17	)	)	PUNCT
ejpam-1479	56	18	>	>	X
ejpam-1479	56	19	0	0	PUNCT
ejpam-1479	56	20	for	for	ADP
ejpam-1479	56	21	all	all	DET
ejpam-1479	56	22	r	r	NOUN
ejpam-1479	56	23	∈	∈	PROPN
ejpam-1479	56	24	(	(	PUNCT
ejpam-1479	56	25	0,∞	0,∞	NOUN
ejpam-1479	56	26	)	)	PUNCT
ejpam-1479	56	27	such	such	ADJ
ejpam-1479	56	28	that	that	SCONJ
ejpam-1479	56	29	f	f	PROPN
ejpam-1479	56	30	(	(	PUNCT
ejpam-1479	56	31	d(x	d(x	PROPN
ejpam-1479	56	32	,	,	PUNCT
ejpam-1479	56	33	f	f	X
ejpam-1479	56	34	)	)	PUNCT
ejpam-1479	56	35	)	)	PUNCT
ejpam-1479	56	36	≤	≤	NUM
ejpam-1479	57	1	‖xn	‖xn	PUNCT
ejpam-1479	57	2	−	−	NOUN
ejpam-1479	57	3	ti	ti	NOUN
ejpam-1479	57	4	xn‖	xn‖	NOUN
ejpam-1479	57	5	for	for	ADP
ejpam-1479	57	6	some	some	DET
ejpam-1479	57	7	1	1	NUM
ejpam-1479	57	8	≤	≤	NUM
ejpam-1479	57	9	i	i	PRON
ejpam-1479	57	10	≤	≤	NOUN
ejpam-1479	57	11	m	m	VERB
ejpam-1479	57	12	and	and	CCONJ
ejpam-1479	57	13	for	for	ADP
ejpam-1479	57	14	all	all	DET
ejpam-1479	57	15	x	x	SYM
ejpam-1479	57	16	∈	∈	NOUN
ejpam-1479	57	17	c	c	NOUN
ejpam-1479	58	1	where	where	SCONJ
ejpam-1479	58	2	d(x	d(x	PROPN
ejpam-1479	58	3	,	,	PUNCT
ejpam-1479	58	4	f	f	X
ejpam-1479	58	5	)	)	PUNCT
ejpam-1479	58	6	=	=	SYM
ejpam-1479	58	7	inf{‖x−	inf{‖x−	NUM
ejpam-1479	58	8	y‖	y‖	NOUN
ejpam-1479	58	9	:	:	PUNCT
ejpam-1479	58	10	y	y	PROPN
ejpam-1479	58	11	∈	∈	PROPN
ejpam-1479	58	12	f	f	PROPN
ejpam-1479	58	13	=	=	PUNCT
ejpam-1479	58	14	⋂m	⋂m	PROPN
ejpam-1479	58	15	i=1	i=1	PROPN
ejpam-1479	58	16	f(ti	f(ti	NOUN
ejpam-1479	58	17	)	)	PUNCT
ejpam-1479	58	18	}	}	PUNCT
ejpam-1479	58	19	.	.	PUNCT
ejpam-1479	59	1	we	we	PRON
ejpam-1479	59	2	recall	recall	VERB
ejpam-1479	59	3	that	that	SCONJ
ejpam-1479	59	4	a	a	DET
ejpam-1479	59	5	banach	banach	NOUN
ejpam-1479	59	6	space	space	NOUN
ejpam-1479	59	7	x	x	PRON
ejpam-1479	59	8	is	be	AUX
ejpam-1479	59	9	said	say	VERB
ejpam-1479	59	10	to	to	PART
ejpam-1479	59	11	satisfy	satisfy	VERB
ejpam-1479	59	12	opial	opial	PROPN
ejpam-1479	59	13	’s	’s	PART
ejpam-1479	59	14	condition	condition	NOUN
ejpam-1479	60	1	[	[	X
ejpam-1479	60	2	6	6	NUM
ejpam-1479	60	3	]	]	PUNCT
ejpam-1479	60	4	if	if	SCONJ
ejpam-1479	60	5	xn	xn	NOUN
ejpam-1479	60	6	converging	converge	VERB
ejpam-1479	60	7	to	to	ADP
ejpam-1479	60	8	x	x	PART
ejpam-1479	60	9	weakly	weakly	ADJ
ejpam-1479	60	10	and	and	CCONJ
ejpam-1479	60	11	x	x	SYM
ejpam-1479	60	12	6=	6=	NOUN
ejpam-1479	61	1	y	y	PRON
ejpam-1479	61	2	imply	imply	VERB
ejpam-1479	61	3	that	that	SCONJ
ejpam-1479	61	4	lim	lim	PROPN
ejpam-1479	61	5	sup	sup	NOUN
ejpam-1479	61	6	n	n	PROPN
ejpam-1479	61	7	xn−	xn−	PUNCT
ejpam-1479	61	8	x	x	PUNCT
ejpam-1479	61	9	<	<	X
ejpam-1479	61	10	lim	lim	PROPN
ejpam-1479	61	11	sup	sup	PROPN
ejpam-1479	61	12	n	n	PROPN
ejpam-1479	61	13	xn−	xn−	PROPN
ejpam-1479	61	14	y	y	PROPN
ejpam-1479	61	15	.	.	PUNCT
ejpam-1479	62	1	in	in	ADP
ejpam-1479	62	2	the	the	DET
ejpam-1479	62	3	sequel	sequel	NOUN
ejpam-1479	62	4	,	,	PUNCT
ejpam-1479	62	5	the	the	DET
ejpam-1479	62	6	following	follow	VERB
ejpam-1479	62	7	lemmas	lemma	NOUN
ejpam-1479	62	8	are	be	AUX
ejpam-1479	62	9	needed	need	VERB
ejpam-1479	62	10	to	to	PART
ejpam-1479	62	11	prove	prove	VERB
ejpam-1479	62	12	our	our	PRON
ejpam-1479	62	13	main	main	ADJ
ejpam-1479	62	14	results	result	NOUN
ejpam-1479	62	15	.	.	PUNCT
ejpam-1479	63	1	lemma	lemma	PROPN
ejpam-1479	63	2	1	1	NUM
ejpam-1479	63	3	(	(	PUNCT
ejpam-1479	63	4	[	[	X
ejpam-1479	63	5	9	9	NUM
ejpam-1479	63	6	,	,	PUNCT
ejpam-1479	63	7	lemma	lemma	PROPN
ejpam-1479	63	8	1	1	NUM
ejpam-1479	63	9	]	]	PUNCT
ejpam-1479	63	10	)	)	PUNCT
ejpam-1479	63	11	.	.	PUNCT
ejpam-1479	64	1	let	let	VERB
ejpam-1479	64	2	{	{	PUNCT
ejpam-1479	64	3	an	an	X
ejpam-1479	64	4	}	}	PUNCT
ejpam-1479	64	5	,	,	PUNCT
ejpam-1479	64	6	{	{	PUNCT
ejpam-1479	64	7	bn	bn	NOUN
ejpam-1479	64	8	}	}	PUNCT
ejpam-1479	64	9	and	and	CCONJ
ejpam-1479	64	10	{	{	PUNCT
ejpam-1479	64	11	δn	δn	NOUN
ejpam-1479	64	12	}	}	PUNCT
ejpam-1479	64	13	be	be	VERB
ejpam-1479	64	14	sequences	sequence	NOUN
ejpam-1479	64	15	of	of	ADP
ejpam-1479	64	16	nonnegative	nonnegative	ADJ
ejpam-1479	64	17	real	real	ADJ
ejpam-1479	64	18	numbers	number	NOUN
ejpam-1479	64	19	satisfying	satisfy	VERB
ejpam-1479	64	20	the	the	DET
ejpam-1479	64	21	inequality	inequality	NOUN
ejpam-1479	64	22	an+1	an+1	NOUN
ejpam-1479	64	23	≤	≤	NOUN
ejpam-1479	64	24	(	(	PUNCT
ejpam-1479	64	25	1+δn)an+	1+δn)an+	PROPN
ejpam-1479	64	26	bn	bn	NOUN
ejpam-1479	64	27	,	,	PUNCT
ejpam-1479	64	28	∀n≥	∀n≥	VERB
ejpam-1479	64	29	1	1	NUM
ejpam-1479	64	30	.	.	PUNCT
ejpam-1479	65	1	if	if	SCONJ
ejpam-1479	65	2	∑∞	∑∞	NOUN
ejpam-1479	65	3	n=1	n=1	PUNCT
ejpam-1479	65	4	δn	δn	ADP
ejpam-1479	65	5	<	<	NOUN
ejpam-1479	65	6	∞	∞	NUM
ejpam-1479	65	7	and	and	CCONJ
ejpam-1479	65	8	∑∞	∑∞	NOUN
ejpam-1479	65	9	n=1	n=1	PROPN
ejpam-1479	65	10	bn	bn	PROPN
ejpam-1479	65	11	<	<	X
ejpam-1479	65	12	∞	∞	PROPN
ejpam-1479	65	13	,	,	PUNCT
ejpam-1479	65	14	then	then	ADV
ejpam-1479	65	15	limn	limn	PROPN
ejpam-1479	65	16	an	an	DET
ejpam-1479	65	17	exists	exist	NOUN
ejpam-1479	65	18	.	.	PUNCT
ejpam-1479	66	1	lemma	lemma	PROPN
ejpam-1479	66	2	2	2	NUM
ejpam-1479	66	3	(	(	PUNCT
ejpam-1479	66	4	[	[	X
ejpam-1479	66	5	2	2	NUM
ejpam-1479	66	6	,	,	PUNCT
ejpam-1479	66	7	lemma	lemma	PROPN
ejpam-1479	66	8	1.2	1.2	NUM
ejpam-1479	66	9	]	]	PUNCT
ejpam-1479	66	10	)	)	PUNCT
ejpam-1479	66	11	.	.	PUNCT
ejpam-1479	67	1	let	let	VERB
ejpam-1479	67	2	k	k	PROPN
ejpam-1479	67	3	≥	≥	NUM
ejpam-1479	67	4	2	2	NUM
ejpam-1479	67	5	and	and	CCONJ
ejpam-1479	67	6	{	{	PUNCT
ejpam-1479	67	7	y(1)n	y(1)n	PROPN
ejpam-1479	67	8	}	}	PUNCT
ejpam-1479	67	9	,	,	PUNCT
ejpam-1479	67	10	.	.	PUNCT
ejpam-1479	67	11	.	.	PUNCT
ejpam-1479	68	1	.	.	PUNCT
ejpam-1479	69	1	,	,	PUNCT
ejpam-1479	69	2	{	{	PUNCT
ejpam-1479	69	3	y(k)n	y(k)n	PROPN
ejpam-1479	69	4	}	}	PUNCT
ejpam-1479	69	5	be	be	AUX
ejpam-1479	69	6	sequences	sequence	NOUN
ejpam-1479	69	7	in	in	ADP
ejpam-1479	69	8	a	a	DET
ejpam-1479	69	9	uniformly	uniformly	ADJ
ejpam-1479	69	10	convex	convex	NOUN
ejpam-1479	69	11	banach	banach	NOUN
ejpam-1479	69	12	space	space	NOUN
ejpam-1479	69	13	x	x	PUNCT
ejpam-1479	69	14	with	with	ADP
ejpam-1479	69	15	lim	lim	PROPN
ejpam-1479	69	16	supn	supn	PROPN
ejpam-1479	69	17	‖y	‖y	PROPN
ejpam-1479	70	1	(	(	PUNCT
ejpam-1479	70	2	i	i	NOUN
ejpam-1479	70	3	)	)	PUNCT
ejpam-1479	70	4	n	n	CCONJ
ejpam-1479	70	5	‖	‖	PROPN
ejpam-1479	70	6	≤	≤	PROPN
ejpam-1479	70	7	a	a	PRON
ejpam-1479	70	8	for	for	ADP
ejpam-1479	70	9	each	each	DET
ejpam-1479	70	10	i	i	NOUN
ejpam-1479	70	11	=	=	NOUN
ejpam-1479	70	12	1,2	1,2	NUM
ejpam-1479	70	13	,	,	PUNCT
ejpam-1479	70	14	.	.	PUNCT
ejpam-1479	70	15	.	.	PUNCT
ejpam-1479	70	16	.	.	PUNCT
ejpam-1479	71	1	,	,	PUNCT
ejpam-1479	71	2	k	k	PROPN
ejpam-1479	71	3	and	and	CCONJ
ejpam-1479	71	4	for	for	ADP
ejpam-1479	71	5	some	some	PRON
ejpam-1479	71	6	a	a	DET
ejpam-1479	71	7	≥	≥	NOUN
ejpam-1479	71	8	0	0	NUM
ejpam-1479	71	9	.	.	PUNCT
ejpam-1479	71	10	suppose	suppose	VERB
ejpam-1479	71	11	{	{	PUNCT
ejpam-1479	71	12	α(1)n	α(1)n	X
ejpam-1479	71	13	}	}	PUNCT
ejpam-1479	71	14	,	,	PUNCT
ejpam-1479	71	15	.	.	PUNCT
ejpam-1479	71	16	.	.	PUNCT
ejpam-1479	71	17	.	.	PUNCT
ejpam-1479	72	1	,	,	PUNCT
ejpam-1479	72	2	{	{	PUNCT
ejpam-1479	72	3	α(k)n	α(k)n	PROPN
ejpam-1479	72	4	}	}	PUNCT
ejpam-1479	72	5	be	be	AUX
ejpam-1479	72	6	sequences	sequence	NOUN
ejpam-1479	72	7	in	in	ADP
ejpam-1479	72	8	[	[	X
ejpam-1479	72	9	0,1	0,1	NUM
ejpam-1479	72	10	]	]	PUNCT
ejpam-1479	72	11	such	such	ADJ
ejpam-1479	72	12	that	that	SCONJ
ejpam-1479	72	13	∑k	∑k	PROPN
ejpam-1479	72	14	i=1α	i=1α	PROPN
ejpam-1479	72	15	(	(	PUNCT
ejpam-1479	72	16	i	i	NOUN
ejpam-1479	72	17	)	)	PUNCT
ejpam-1479	72	18	n	n	PROPN
ejpam-1479	72	19	=	=	SYM
ejpam-1479	72	20	1	1	NUM
ejpam-1479	72	21	and	and	CCONJ
ejpam-1479	72	22	limn	limn	PROPN
ejpam-1479	72	23	‖	‖	PROPN
ejpam-1479	73	1	∑k	∑k	PROPN
ejpam-1479	73	2	i=1α	i=1α	PROPN
ejpam-1479	73	3	(	(	PUNCT
ejpam-1479	73	4	i	i	NOUN
ejpam-1479	73	5	)	)	PUNCT
ejpam-1479	73	6	n	n	CCONJ
ejpam-1479	74	1	y(i)n	y(i)n	PROPN
ejpam-1479	74	2	‖	‖	PROPN
ejpam-1479	74	3	=	=	NOUN
ejpam-1479	74	4	a.	a.	NOUN
ejpam-1479	74	5	if	if	SCONJ
ejpam-1479	74	6	lim	lim	PROPN
ejpam-1479	74	7	infnα	infnα	PROPN
ejpam-1479	74	8	(	(	PUNCT
ejpam-1479	74	9	i	i	NOUN
ejpam-1479	74	10	)	)	PUNCT
ejpam-1479	74	11	n	n	CCONJ
ejpam-1479	74	12	>	>	PUNCT
ejpam-1479	74	13	0	0	PUNCT
ejpam-1479	75	1	and	and	CCONJ
ejpam-1479	75	2	lim	lim	PROPN
ejpam-1479	75	3	infnα	infnα	PROPN
ejpam-1479	75	4	(	(	PUNCT
ejpam-1479	75	5	j	j	PROPN
ejpam-1479	75	6	)	)	PUNCT
ejpam-1479	75	7	n	n	CCONJ
ejpam-1479	75	8	>	>	X
ejpam-1479	75	9	0	0	PUNCT
ejpam-1479	75	10	for	for	ADP
ejpam-1479	75	11	some	some	DET
ejpam-1479	75	12	i	i	PROPN
ejpam-1479	75	13	,	,	PUNCT
ejpam-1479	75	14	j	j	PROPN
ejpam-1479	75	15	∈	∈	PROPN
ejpam-1479	75	16	{	{	PUNCT
ejpam-1479	75	17	1,2	1,2	NUM
ejpam-1479	75	18	,	,	PUNCT
ejpam-1479	75	19	.	.	PUNCT
ejpam-1479	75	20	.	.	PUNCT
ejpam-1479	75	21	.	.	PUNCT
ejpam-1479	76	1	,	,	PUNCT
ejpam-1479	76	2	k	k	X
ejpam-1479	76	3	}	}	PUNCT
ejpam-1479	76	4	,	,	PUNCT
ejpam-1479	76	5	then	then	ADV
ejpam-1479	76	6	limn	limn	PROPN
ejpam-1479	76	7	‖y	‖y	PROPN
ejpam-1479	76	8	(	(	PUNCT
ejpam-1479	76	9	i	i	NOUN
ejpam-1479	76	10	)	)	PUNCT
ejpam-1479	76	11	n	n	CCONJ
ejpam-1479	76	12	−	−	PROPN
ejpam-1479	76	13	y	y	PROPN
ejpam-1479	76	14	(	(	PUNCT
ejpam-1479	76	15	j	j	PROPN
ejpam-1479	76	16	)	)	PUNCT
ejpam-1479	76	17	n	n	PROPN
ejpam-1479	76	18	‖=	‖=	NOUN
ejpam-1479	76	19	0	0	X
ejpam-1479	76	20	.	.	NOUN
ejpam-1479	76	21	2	2	NUM
ejpam-1479	76	22	.	.	X
ejpam-1479	76	23	convergence	convergence	NOUN
ejpam-1479	76	24	in	in	ADP
ejpam-1479	76	25	banach	banach	NOUN
ejpam-1479	76	26	spaces	space	NOUN
ejpam-1479	76	27	the	the	DET
ejpam-1479	76	28	aim	aim	NOUN
ejpam-1479	76	29	of	of	ADP
ejpam-1479	76	30	this	this	DET
ejpam-1479	76	31	section	section	NOUN
ejpam-1479	76	32	is	be	AUX
ejpam-1479	76	33	to	to	PART
ejpam-1479	76	34	establish	establish	VERB
ejpam-1479	76	35	the	the	DET
ejpam-1479	76	36	strong	strong	ADJ
ejpam-1479	76	37	convergence	convergence	NOUN
ejpam-1479	76	38	of	of	ADP
ejpam-1479	76	39	the	the	DET
ejpam-1479	76	40	iterative	iterative	NOUN
ejpam-1479	76	41	process	process	NOUN
ejpam-1479	76	42	(	(	PUNCT
ejpam-1479	76	43	1	1	X
ejpam-1479	76	44	)	)	PUNCT
ejpam-1479	76	45	to	to	PART
ejpam-1479	76	46	converge	converge	VERB
ejpam-1479	76	47	to	to	ADP
ejpam-1479	76	48	a	a	DET
ejpam-1479	76	49	common	common	ADJ
ejpam-1479	76	50	fixed	fix	VERB
ejpam-1479	76	51	point	point	NOUN
ejpam-1479	76	52	of	of	ADP
ejpam-1479	76	53	a	a	DET
ejpam-1479	76	54	finite	finite	ADJ
ejpam-1479	76	55	family	family	NOUN
ejpam-1479	76	56	of	of	ADP
ejpam-1479	76	57	generalized	generalized	ADJ
ejpam-1479	76	58	asymptotically	asymptotically	ADV
ejpam-1479	76	59	quasinonexpansive	quasinonexpansive	ADJ
ejpam-1479	76	60	mappings	mapping	NOUN
ejpam-1479	76	61	in	in	ADP
ejpam-1479	76	62	a	a	DET
ejpam-1479	76	63	banach	banach	NOUN
ejpam-1479	76	64	space	space	NOUN
ejpam-1479	76	65	.	.	PUNCT
ejpam-1479	77	1	to	to	PART
ejpam-1479	77	2	proceed	proceed	VERB
ejpam-1479	77	3	in	in	ADP
ejpam-1479	77	4	this	this	DET
ejpam-1479	77	5	direction	direction	NOUN
ejpam-1479	77	6	,	,	PUNCT
ejpam-1479	77	7	the	the	DET
ejpam-1479	77	8	following	follow	VERB
ejpam-1479	77	9	lemma	lemma	PROPN
ejpam-1479	77	10	is	be	AUX
ejpam-1479	77	11	needed	need	VERB
ejpam-1479	77	12	.	.	PUNCT
ejpam-1479	78	1	lemma	lemma	PROPN
ejpam-1479	78	2	3	3	X
ejpam-1479	78	3	.	.	PUNCT
ejpam-1479	79	1	let	let	VERB
ejpam-1479	79	2	x	x	PRON
ejpam-1479	79	3	be	be	AUX
ejpam-1479	79	4	a	a	DET
ejpam-1479	79	5	real	real	ADJ
ejpam-1479	79	6	banach	banach	NOUN
ejpam-1479	79	7	space	space	NOUN
ejpam-1479	79	8	,	,	PUNCT
ejpam-1479	79	9	c	c	X
ejpam-1479	79	10	be	be	AUX
ejpam-1479	79	11	a	a	DET
ejpam-1479	79	12	nonempty	nonempty	ADV
ejpam-1479	79	13	closed	close	VERB
ejpam-1479	79	14	convex	convex	NOUN
ejpam-1479	79	15	subset	subset	NOUN
ejpam-1479	79	16	of	of	ADP
ejpam-1479	79	17	x	x	PUNCT
ejpam-1479	79	18	and	and	CCONJ
ejpam-1479	79	19	{	{	PUNCT
ejpam-1479	79	20	ti	ti	NOUN
ejpam-1479	79	21	:	:	PUNCT
ejpam-1479	79	22	i	i	NOUN
ejpam-1479	79	23	=	=	SYM
ejpam-1479	79	24	1,2	1,2	NUM
ejpam-1479	79	25	,	,	PUNCT
ejpam-1479	79	26	.	.	PUNCT
ejpam-1479	79	27	.	.	PUNCT
ejpam-1479	80	1	.	.	PUNCT
ejpam-1479	81	1	,	,	PUNCT
ejpam-1479	81	2	m	m	AUX
ejpam-1479	81	3	}	}	PUNCT
ejpam-1479	81	4	be	be	AUX
ejpam-1479	81	5	a	a	DET
ejpam-1479	81	6	family	family	NOUN
ejpam-1479	81	7	of	of	ADP
ejpam-1479	81	8	generalized	generalized	ADJ
ejpam-1479	81	9	asymptotically	asymptotically	ADV
ejpam-1479	81	10	quasi	quasi	ADJ
ejpam-1479	81	11	-	-	ADJ
ejpam-1479	81	12	nonexpansive	nonexpansive	ADJ
ejpam-1479	81	13	self	self	NOUN
ejpam-1479	81	14	-	-	PUNCT
ejpam-1479	81	15	mappings	mapping	NOUN
ejpam-1479	81	16	of	of	ADP
ejpam-1479	81	17	c	c	NOUN
ejpam-1479	81	18	with	with	ADP
ejpam-1479	81	19	the	the	DET
ejpam-1479	81	20	sequences	sequence	NOUN
ejpam-1479	81	21	{	{	PUNCT
ejpam-1479	81	22	r(1)n	r(1)n	X
ejpam-1479	81	23	}	}	PUNCT
ejpam-1479	81	24	,	,	PUNCT
ejpam-1479	81	25	.	.	PUNCT
ejpam-1479	81	26	.	.	PUNCT
ejpam-1479	82	1	.	.	PUNCT
ejpam-1479	83	1	,	,	PUNCT
ejpam-1479	83	2	{	{	PUNCT
ejpam-1479	83	3	r(m)n	r(m)n	PROPN
ejpam-1479	83	4	}	}	PUNCT
ejpam-1479	83	5	and	and	CCONJ
ejpam-1479	83	6	{	{	PUNCT
ejpam-1479	83	7	s(1)n	s(1)n	PROPN
ejpam-1479	83	8	}	}	PUNCT
ejpam-1479	83	9	,	,	PUNCT
ejpam-1479	83	10	.	.	PUNCT
ejpam-1479	83	11	.	.	PUNCT
ejpam-1479	84	1	.	.	PUNCT
ejpam-1479	85	1	,	,	PUNCT
ejpam-1479	85	2	{	{	PUNCT
ejpam-1479	85	3	s(m)n	s(m)n	NOUN
ejpam-1479	85	4	}	}	PUNCT
ejpam-1479	85	5	such	such	ADJ
ejpam-1479	85	6	that	that	DET
ejpam-1479	85	7	∑∞	∑∞	NOUN
ejpam-1479	85	8	n=1	n=1	PUNCT
ejpam-1479	85	9	r(i)n	r(i)n	PROPN
ejpam-1479	85	10	<	<	X
ejpam-1479	85	11	∞	∞	PROPN
ejpam-1479	85	12	and	and	CCONJ
ejpam-1479	85	13	∑∞	∑∞	NOUN
ejpam-1479	85	14	n=1	n=1	PROPN
ejpam-1479	85	15	s(i)n	s(i)n	PROPN
ejpam-1479	85	16	<	<	X
ejpam-1479	85	17	∞	∞	PROPN
ejpam-1479	85	18	for	for	ADP
ejpam-1479	85	19	each	each	DET
ejpam-1479	85	20	i	i	NOUN
ejpam-1479	85	21	=	=	NOUN
ejpam-1479	85	22	1,2	1,2	NUM
ejpam-1479	85	23	,	,	PUNCT
ejpam-1479	85	24	.	.	PUNCT
ejpam-1479	85	25	.	.	PUNCT
ejpam-1479	86	1	.	.	PUNCT
ejpam-1479	87	1	,	,	PUNCT
ejpam-1479	87	2	m.	m.	NOUN
ejpam-1479	87	3	let	let	AUX
ejpam-1479	87	4	{	{	PUNCT
ejpam-1479	87	5	xn	xn	VERB
ejpam-1479	87	6	}	}	PUNCT
ejpam-1479	87	7	be	be	VERB
ejpam-1479	87	8	the	the	DET
ejpam-1479	87	9	sequence	sequence	NOUN
ejpam-1479	87	10	defined	define	VERB
ejpam-1479	87	11	by	by	ADP
ejpam-1479	87	12	(	(	PUNCT
ejpam-1479	87	13	1	1	NUM
ejpam-1479	87	14	)	)	PUNCT
ejpam-1479	87	15	.	.	PUNCT
ejpam-1479	88	1	if	if	SCONJ
ejpam-1479	88	2	f	f	PROPN
ejpam-1479	88	3	=	=	SYM
ejpam-1479	88	4	⋂m	⋂m	PROPN
ejpam-1479	88	5	i=1	i=1	PROPN
ejpam-1479	88	6	f(ti	f(ti	NOUN
ejpam-1479	88	7	)	)	PUNCT
ejpam-1479	88	8	6=	6=	ADP
ejpam-1479	88	9	;	;	PUNCT
ejpam-1479	88	10	,	,	PUNCT
ejpam-1479	88	11	then	then	ADV
ejpam-1479	88	12	we	we	PRON
ejpam-1479	88	13	have	have	VERB
ejpam-1479	88	14	the	the	DET
ejpam-1479	88	15	following	follow	VERB
ejpam-1479	88	16	conclusions	conclusion	NOUN
ejpam-1479	88	17	.	.	PUNCT
ejpam-1479	89	1	h.	h.	PROPN
ejpam-1479	89	2	dehghan	dehghan	PROPN
ejpam-1479	89	3	,	,	PUNCT
ejpam-1479	89	4	a.	a.	NOUN
ejpam-1479	89	5	gharajelo	gharajelo	PROPN
ejpam-1479	89	6	/	/	SYM
ejpam-1479	89	7	eur	eur	PROPN
ejpam-1479	89	8	.	.	PUNCT
ejpam-1479	90	1	j.	j.	PROPN
ejpam-1479	90	2	pure	pure	PROPN
ejpam-1479	90	3	appl	appl	PROPN
ejpam-1479	90	4	.	.	PROPN
ejpam-1479	90	5	math	math	PROPN
ejpam-1479	90	6	,	,	PUNCT
ejpam-1479	90	7	5	5	NUM
ejpam-1479	90	8	(	(	PUNCT
ejpam-1479	90	9	2012	2012	NUM
ejpam-1479	90	10	)	)	PUNCT
ejpam-1479	90	11	,	,	PUNCT
ejpam-1479	90	12	45	45	NUM
ejpam-1479	90	13	-	-	SYM
ejpam-1479	90	14	54	54	NUM
ejpam-1479	90	15	48	48	NUM
ejpam-1479	90	16	(	(	PUNCT
ejpam-1479	90	17	i	i	NOUN
ejpam-1479	90	18	)	)	PUNCT
ejpam-1479	90	19	limn	limn	PROPN
ejpam-1479	90	20	‖xn−	‖xn−	PROPN
ejpam-1479	91	1	p‖	p‖	NOUN
ejpam-1479	91	2	exists	exist	VERB
ejpam-1479	91	3	for	for	ADP
ejpam-1479	91	4	all	all	DET
ejpam-1479	91	5	p	p	PROPN
ejpam-1479	91	6	∈	∈	PROPN
ejpam-1479	91	7	f.	f.	PROPN
ejpam-1479	91	8	(	(	PUNCT
ejpam-1479	91	9	ii	ii	PROPN
ejpam-1479	91	10	)	)	PUNCT
ejpam-1479	91	11	limn	limn	PROPN
ejpam-1479	91	12	d(xn	d(xn	PROPN
ejpam-1479	91	13	,	,	PUNCT
ejpam-1479	91	14	f	f	X
ejpam-1479	91	15	)	)	PUNCT
ejpam-1479	91	16	exists	exist	VERB
ejpam-1479	91	17	.	.	PUNCT
ejpam-1479	92	1	(	(	PUNCT
ejpam-1479	92	2	iii	iii	X
ejpam-1479	92	3	)	)	PUNCT
ejpam-1479	92	4	if	if	SCONJ
ejpam-1479	92	5	lim	lim	PROPN
ejpam-1479	92	6	infnαin	infnαin	VERB
ejpam-1479	92	7	>	>	X
ejpam-1479	92	8	0	0	PUNCT
ejpam-1479	92	9	for	for	ADP
ejpam-1479	92	10	some	some	DET
ejpam-1479	92	11	i	i	PRON
ejpam-1479	92	12	∈	∈	PROPN
ejpam-1479	92	13	{	{	PUNCT
ejpam-1479	92	14	1,2	1,2	NUM
ejpam-1479	92	15	,	,	PUNCT
ejpam-1479	92	16	.	.	PUNCT
ejpam-1479	92	17	.	.	PUNCT
ejpam-1479	92	18	.	.	PUNCT
ejpam-1479	93	1	,	,	PUNCT
ejpam-1479	93	2	m	m	VERB
ejpam-1479	93	3	}	}	PUNCT
ejpam-1479	93	4	,	,	PUNCT
ejpam-1479	93	5	then	then	ADV
ejpam-1479	93	6	limn	limn	PROPN
ejpam-1479	94	1	‖yn	‖yn	PROPN
ejpam-1479	94	2	−	−	PROPN
ejpam-1479	94	3	p‖	p‖	NOUN
ejpam-1479	94	4	=	=	SYM
ejpam-1479	94	5	limn	limn	PROPN
ejpam-1479	94	6	‖xn	‖xn	PROPN
ejpam-1479	94	7	−	−	PROPN
ejpam-1479	94	8	p‖	p‖	NOUN
ejpam-1479	94	9	for	for	ADP
ejpam-1479	94	10	all	all	DET
ejpam-1479	94	11	p	p	PROPN
ejpam-1479	94	12	∈	∈	PROPN
ejpam-1479	94	13	f.	f.	NOUN
ejpam-1479	94	14	proof	proof	NOUN
ejpam-1479	94	15	.	.	PUNCT
ejpam-1479	95	1	let	let	VERB
ejpam-1479	95	2	p	p	PROPN
ejpam-1479	95	3	∈	∈	PROPN
ejpam-1479	95	4	f	f	X
ejpam-1479	95	5	,	,	PUNCT
ejpam-1479	95	6	rn	rn	PROPN
ejpam-1479	95	7	=	=	NOUN
ejpam-1479	95	8	max1≤i≤m	max1≤i≤m	PROPN
ejpam-1479	95	9	rin	rin	NOUN
ejpam-1479	95	10	and	and	CCONJ
ejpam-1479	95	11	sn	sn	NOUN
ejpam-1479	95	12	=	=	ADJ
ejpam-1479	95	13	max1≤i≤m	max1≤i≤m	ADJ
ejpam-1479	95	14	sin	sin	NOUN
ejpam-1479	95	15	.	.	PUNCT
ejpam-1479	96	1	for	for	ADP
ejpam-1479	96	2	each	each	DET
ejpam-1479	96	3	n≥	n≥	NOUN
ejpam-1479	96	4	1	1	NUM
ejpam-1479	96	5	,	,	PUNCT
ejpam-1479	96	6	we	we	PRON
ejpam-1479	96	7	note	note	VERB
ejpam-1479	96	8	that	that	SCONJ
ejpam-1479	96	9	‖yn	‖yn	PROPN
ejpam-1479	96	10	−	−	PROPN
ejpam-1479	96	11	p‖	p‖	NOUN
ejpam-1479	96	12	=	=	NOUN
ejpam-1479	96	13	m	m	VERB
ejpam-1479	96	14	∑	∑	VERB
ejpam-1479	96	15	i=1	i=1	PROPN
ejpam-1479	96	16	ai	be	VERB
ejpam-1479	96	17	nt	not	PART
ejpam-1479	96	18	n	n	ADV
ejpam-1479	97	1	i	i	PRON
ejpam-1479	97	2	xn+	xn+	PROPN
ejpam-1479	98	1	bn	bn	INTJ
ejpam-1479	98	2	xn−	xn−	PUNCT
ejpam-1479	99	1	p	p	X
ejpam-1479	99	2	≤	≤	NUM
ejpam-1479	99	3	m	m	VERB
ejpam-1479	99	4	∑	∑	PROPN
ejpam-1479	99	5	i=1	i=1	PROPN
ejpam-1479	99	6	ain	ain	PROPN
ejpam-1479	99	7	t	t	PROPN
ejpam-1479	100	1	n	n	NOUN
ejpam-1479	101	1	i	i	PRON
ejpam-1479	101	2	xn−	xn−	PUNCT
ejpam-1479	102	1	p	p	X
ejpam-1479	103	1	+	+	PROPN
ejpam-1479	103	2	bn‖xn−	bn‖xn−	PROPN
ejpam-1479	103	3	p‖	p‖	NOUN
ejpam-1479	103	4	≤	≤	NUM
ejpam-1479	103	5	m	m	VERB
ejpam-1479	103	6	∑	∑	PROPN
ejpam-1479	103	7	i=1	i=1	PROPN
ejpam-1479	103	8	ain	ain	PROPN
ejpam-1479	103	9	�	�	PROPN
ejpam-1479	103	10	(	(	PUNCT
ejpam-1479	103	11	1	1	NUM
ejpam-1479	103	12	+	+	NUM
ejpam-1479	103	13	rin)‖xn−	rin)‖xn−	PROPN
ejpam-1479	103	14	p‖+	p‖+	PROPN
ejpam-1479	103	15	sin	sin	NOUN
ejpam-1479	103	16	)	)	PUNCT
ejpam-1479	103	17	�	�	PROPN
ejpam-1479	103	18	+	+	CCONJ
ejpam-1479	103	19	bn(1	bn(1	NOUN
ejpam-1479	103	20	+	+	CCONJ
ejpam-1479	103	21	rn)‖xn−	rn)‖xn−	NUM
ejpam-1479	103	22	p‖	p‖	NOUN
ejpam-1479	103	23	≤	≤	NUM
ejpam-1479	103	24	(	(	PUNCT
ejpam-1479	103	25	1	1	NUM
ejpam-1479	103	26	+	+	CCONJ
ejpam-1479	103	27	rn)‖xn−	rn)‖xn−	NUM
ejpam-1479	103	28	p‖+	p‖+	PROPN
ejpam-1479	103	29	sn	sn	PROPN
ejpam-1479	103	30	.	.	PUNCT
ejpam-1479	104	1	(	(	PUNCT
ejpam-1479	104	2	5	5	X
ejpam-1479	104	3	)	)	PUNCT
ejpam-1479	104	4	it	it	PRON
ejpam-1479	104	5	follows	follow	VERB
ejpam-1479	104	6	from	from	ADP
ejpam-1479	104	7	(	(	PUNCT
ejpam-1479	104	8	5	5	NUM
ejpam-1479	104	9	)	)	PUNCT
ejpam-1479	104	10	that	that	PRON
ejpam-1479	104	11	‖xn+1−	‖xn+1−	PROPN
ejpam-1479	104	12	p‖	p‖	PROPN
ejpam-1479	104	13	≤	≤	ADV
ejpam-1479	105	1	m	m	VERB
ejpam-1479	105	2	∑	∑	PROPN
ejpam-1479	105	3	i=1	i=1	PROPN
ejpam-1479	105	4	�	�	PROPN
ejpam-1479	105	5	αin‖t	αin‖t	NUM
ejpam-1479	106	1	n	n	CCONJ
ejpam-1479	107	1	i	i	PRON
ejpam-1479	107	2	yn	yn	INTJ
ejpam-1479	107	3	−	−	VERB
ejpam-1479	107	4	p‖+	p‖+	NOUN
ejpam-1479	107	5	βin‖t	βin‖t	PUNCT
ejpam-1479	107	6	n	n	NOUN
ejpam-1479	108	1	i	i	PRON
ejpam-1479	108	2	xn−	xn−	PUNCT
ejpam-1479	108	3	p‖	p‖	PROPN
ejpam-1479	108	4	�	�	PROPN
ejpam-1479	108	5	+	+	CCONJ
ejpam-1479	108	6	γn‖xn−	γn‖xn−	PROPN
ejpam-1479	108	7	p‖	p‖	NOUN
ejpam-1479	108	8	≤	≤	ADV
ejpam-1479	108	9	m	m	VERB
ejpam-1479	108	10	∑	∑	PROPN
ejpam-1479	108	11	i=1	i=1	PROPN
ejpam-1479	108	12	�	�	PROPN
ejpam-1479	108	13	αin[(1	αin[(1	PROPN
ejpam-1479	108	14	+	+	PROPN
ejpam-1479	108	15	rin)‖yn−	rin)‖yn−	PROPN
ejpam-1479	108	16	p‖+	p‖+	NOUN
ejpam-1479	108	17	sin	sin	NOUN
ejpam-1479	108	18	]	]	PUNCT
ejpam-1479	109	1	+	+	CCONJ
ejpam-1479	109	2	βin[(1	βin[(1	PROPN
ejpam-1479	109	3	+	+	PROPN
ejpam-1479	109	4	rin)‖xn−	rin)‖xn−	PROPN
ejpam-1479	109	5	p‖+	p‖+	PROPN
ejpam-1479	109	6	sin	sin	PROPN
ejpam-1479	109	7	]	]	PUNCT
ejpam-1479	109	8	�	�	PROPN
ejpam-1479	110	1	+	+	NOUN
ejpam-1479	110	2	γn(1	γn(1	PROPN
ejpam-1479	110	3	+	+	SYM
ejpam-1479	110	4	rn	rn	NOUN
ejpam-1479	110	5	)	)	PUNCT
ejpam-1479	110	6	2‖xn−	2‖xn−	NUM
ejpam-1479	110	7	p‖	p‖	NOUN
ejpam-1479	110	8	≤	≤	ADV
ejpam-1479	111	1	m	m	VERB
ejpam-1479	111	2	∑	∑	PROPN
ejpam-1479	111	3	i=1	i=1	PROPN
ejpam-1479	111	4	�	�	PROPN
ejpam-1479	111	5	αin[(1	αin[(1	PROPN
ejpam-1479	112	1	+	+	PROPN
ejpam-1479	112	2	rn)[(1	rn)[(1	PROPN
ejpam-1479	112	3	+	+	CCONJ
ejpam-1479	112	4	rn)‖xn−	rn)‖xn−	NUM
ejpam-1479	112	5	p‖+	p‖+	PROPN
ejpam-1479	112	6	sn	sn	PROPN
ejpam-1479	112	7	]	]	PUNCT
ejpam-1479	112	8	+	+	CCONJ
ejpam-1479	112	9	sn	sn	X
ejpam-1479	112	10	]	]	X
ejpam-1479	112	11	+	+	ADJ
ejpam-1479	112	12	βin[(1	βin[(1	PROPN
ejpam-1479	112	13	+	+	CCONJ
ejpam-1479	112	14	rn	rn	PROPN
ejpam-1479	112	15	)	)	PUNCT
ejpam-1479	112	16	2‖xn	2‖xn	NOUN
ejpam-1479	112	17	−	−	PROPN
ejpam-1479	112	18	p‖+	p‖+	PROPN
ejpam-1479	112	19	sn	sn	PROPN
ejpam-1479	112	20	]	]	X
ejpam-1479	112	21	�	�	PROPN
ejpam-1479	112	22	+	+	CCONJ
ejpam-1479	112	23	γn(1	γn(1	PROPN
ejpam-1479	112	24	+	+	SYM
ejpam-1479	112	25	rn	rn	NOUN
ejpam-1479	112	26	)	)	PUNCT
ejpam-1479	112	27	2‖xn−	2‖xn−	NUM
ejpam-1479	112	28	p‖	p‖	NOUN
ejpam-1479	112	29	≤	≤	NUM
ejpam-1479	112	30	(	(	PUNCT
ejpam-1479	112	31	1	1	NUM
ejpam-1479	112	32	+	+	NUM
ejpam-1479	112	33	rn	rn	NOUN
ejpam-1479	112	34	)	)	PUNCT
ejpam-1479	113	1	2‖xn−	2‖xn−	NUM
ejpam-1479	113	2	p‖+	p‖+	NOUN
ejpam-1479	113	3	(	(	PUNCT
ejpam-1479	113	4	2	2	NUM
ejpam-1479	113	5	+	+	NUM
ejpam-1479	113	6	rn)sn	rn)sn	X
ejpam-1479	113	7	.	.	PUNCT
ejpam-1479	114	1	(	(	PUNCT
ejpam-1479	114	2	6	6	NUM
ejpam-1479	114	3	)	)	PUNCT
ejpam-1479	114	4	since	since	SCONJ
ejpam-1479	114	5	{	{	PUNCT
ejpam-1479	114	6	rn	rn	NOUN
ejpam-1479	114	7	}	}	PUNCT
ejpam-1479	114	8	and	and	CCONJ
ejpam-1479	114	9	{	{	PUNCT
ejpam-1479	114	10	sn	sn	NOUN
ejpam-1479	114	11	}	}	PUNCT
ejpam-1479	114	12	are	be	AUX
ejpam-1479	114	13	independent	independent	ADJ
ejpam-1479	114	14	of	of	ADP
ejpam-1479	114	15	p	p	PRON
ejpam-1479	114	16	,	,	PUNCT
ejpam-1479	114	17	by	by	ADP
ejpam-1479	114	18	taking	take	VERB
ejpam-1479	114	19	infimum	infimum	ADV
ejpam-1479	114	20	over	over	ADP
ejpam-1479	114	21	all	all	DET
ejpam-1479	114	22	p	p	NOUN
ejpam-1479	114	23	∈	∈	PROPN
ejpam-1479	114	24	f	f	NOUN
ejpam-1479	114	25	in	in	ADP
ejpam-1479	114	26	both	both	DET
ejpam-1479	114	27	sides	side	NOUN
ejpam-1479	114	28	of	of	ADP
ejpam-1479	114	29	(	(	PUNCT
ejpam-1479	114	30	6	6	NUM
ejpam-1479	114	31	)	)	PUNCT
ejpam-1479	114	32	,	,	PUNCT
ejpam-1479	114	33	we	we	PRON
ejpam-1479	114	34	obtain	obtain	VERB
ejpam-1479	114	35	d(xn+1	d(xn+1	PROPN
ejpam-1479	114	36	,	,	PUNCT
ejpam-1479	114	37	f	f	X
ejpam-1479	114	38	)	)	PUNCT
ejpam-1479	114	39	≤	≤	NOUN
ejpam-1479	114	40	(	(	PUNCT
ejpam-1479	114	41	1	1	NUM
ejpam-1479	114	42	+	+	NUM
ejpam-1479	114	43	rn	rn	NOUN
ejpam-1479	114	44	)	)	PUNCT
ejpam-1479	114	45	2d(xn	2d(xn	NUM
ejpam-1479	114	46	,	,	PUNCT
ejpam-1479	114	47	f	f	X
ejpam-1479	114	48	)	)	PUNCT
ejpam-1479	115	1	+	+	CCONJ
ejpam-1479	115	2	(	(	PUNCT
ejpam-1479	115	3	2	2	NUM
ejpam-1479	115	4	+	+	NUM
ejpam-1479	115	5	rn)sn	rn)sn	X
ejpam-1479	115	6	.	.	PUNCT
ejpam-1479	116	1	(	(	PUNCT
ejpam-1479	116	2	7	7	X
ejpam-1479	116	3	)	)	PUNCT
ejpam-1479	116	4	using	use	VERB
ejpam-1479	116	5	lemma	lemma	PROPN
ejpam-1479	116	6	1	1	NUM
ejpam-1479	116	7	,	,	PUNCT
ejpam-1479	116	8	the	the	DET
ejpam-1479	116	9	conclusions	conclusion	NOUN
ejpam-1479	116	10	(	(	PUNCT
ejpam-1479	116	11	i	i	NOUN
ejpam-1479	116	12	)	)	PUNCT
ejpam-1479	116	13	and	and	CCONJ
ejpam-1479	116	14	(	(	PUNCT
ejpam-1479	116	15	ii	ii	NOUN
ejpam-1479	116	16	)	)	PUNCT
ejpam-1479	116	17	of	of	ADP
ejpam-1479	116	18	lemma	lemma	PROPN
ejpam-1479	116	19	follow	follow	VERB
ejpam-1479	116	20	from	from	ADP
ejpam-1479	116	21	(	(	PUNCT
ejpam-1479	116	22	6	6	NUM
ejpam-1479	116	23	)	)	PUNCT
ejpam-1479	116	24	and	and	CCONJ
ejpam-1479	116	25	(	(	PUNCT
ejpam-1479	116	26	7	7	NUM
ejpam-1479	116	27	)	)	PUNCT
ejpam-1479	116	28	,	,	PUNCT
ejpam-1479	116	29	respectively	respectively	ADV
ejpam-1479	116	30	.	.	PUNCT
ejpam-1479	117	1	(	(	PUNCT
ejpam-1479	117	2	iii	iii	X
ejpam-1479	117	3	)	)	PUNCT
ejpam-1479	117	4	since	since	SCONJ
ejpam-1479	117	5	limn	limn	PROPN
ejpam-1479	117	6	‖xn−	‖xn−	PROPN
ejpam-1479	117	7	p‖	p‖	NOUN
ejpam-1479	117	8	exists	exist	VERB
ejpam-1479	117	9	,	,	PUNCT
ejpam-1479	117	10	it	it	PRON
ejpam-1479	117	11	follows	follow	VERB
ejpam-1479	117	12	from	from	ADP
ejpam-1479	117	13	(	(	PUNCT
ejpam-1479	117	14	5	5	NUM
ejpam-1479	117	15	)	)	PUNCT
ejpam-1479	118	1	that	that	PRON
ejpam-1479	118	2	lim	lim	PROPN
ejpam-1479	118	3	supn	supn	PROPN
ejpam-1479	118	4	‖yn	‖yn	PROPN
ejpam-1479	118	5	−	−	PROPN
ejpam-1479	118	6	p‖	p‖	NOUN
ejpam-1479	118	7	≤	≤	X
ejpam-1479	118	8	limn	limn	PROPN
ejpam-1479	118	9	‖xn−	‖xn−	PROPN
ejpam-1479	118	10	p‖.	p‖.	PROPN
ejpam-1479	118	11	also	also	ADV
ejpam-1479	118	12	,	,	PUNCT
ejpam-1479	118	13	by	by	ADP
ejpam-1479	118	14	(	(	PUNCT
ejpam-1479	118	15	6	6	NUM
ejpam-1479	118	16	)	)	PUNCT
ejpam-1479	118	17	‖xn+1−	‖xn+1−	PROPN
ejpam-1479	118	18	p‖	p‖	NOUN
ejpam-1479	118	19	≤	≤	ADV
ejpam-1479	118	20	m	m	VERB
ejpam-1479	118	21	∑	∑	PROPN
ejpam-1479	118	22	i=1	i=1	PROPN
ejpam-1479	118	23	�	�	PROPN
ejpam-1479	118	24	αin[(1	αin[(1	PROPN
ejpam-1479	118	25	+	+	CCONJ
ejpam-1479	118	26	rn)‖yn−	rn)‖yn−	VERB
ejpam-1479	118	27	p‖+	p‖+	PROPN
ejpam-1479	118	28	sn	sn	PROPN
ejpam-1479	118	29	]	]	PUNCT
ejpam-1479	119	1	+	+	CCONJ
ejpam-1479	119	2	βin[(1	βin[(1	PROPN
ejpam-1479	119	3	+	+	CCONJ
ejpam-1479	119	4	rn)‖xn−	rn)‖xn−	NUM
ejpam-1479	119	5	p‖+	p‖+	PROPN
ejpam-1479	119	6	sn	sn	PROPN
ejpam-1479	119	7	]	]	X
ejpam-1479	119	8	�	�	PROPN
ejpam-1479	120	1	+	+	NOUN
ejpam-1479	120	2	γn(1	γn(1	PROPN
ejpam-1479	120	3	+	+	SYM
ejpam-1479	120	4	rn	rn	NOUN
ejpam-1479	120	5	)	)	PUNCT
ejpam-1479	120	6	2‖xn−	2‖xn−	NUM
ejpam-1479	120	7	p‖	p‖	PROPN
ejpam-1479	120	8	h.	h.	PROPN
ejpam-1479	120	9	dehghan	dehghan	PROPN
ejpam-1479	120	10	,	,	PUNCT
ejpam-1479	120	11	a.	a.	NOUN
ejpam-1479	120	12	gharajelo	gharajelo	PROPN
ejpam-1479	120	13	/	/	SYM
ejpam-1479	120	14	eur	eur	PROPN
ejpam-1479	120	15	.	.	PUNCT
ejpam-1479	121	1	j.	j.	PROPN
ejpam-1479	121	2	pure	pure	PROPN
ejpam-1479	121	3	appl	appl	PROPN
ejpam-1479	121	4	.	.	PROPN
ejpam-1479	121	5	math	math	PROPN
ejpam-1479	121	6	,	,	PUNCT
ejpam-1479	121	7	5	5	NUM
ejpam-1479	121	8	(	(	PUNCT
ejpam-1479	121	9	2012	2012	NUM
ejpam-1479	121	10	)	)	PUNCT
ejpam-1479	121	11	,	,	PUNCT
ejpam-1479	121	12	45	45	NUM
ejpam-1479	121	13	-	-	SYM
ejpam-1479	121	14	54	54	NUM
ejpam-1479	121	15	49	49	NUM
ejpam-1479	121	16	≤	≤	NOUN
ejpam-1479	121	17	(	(	PUNCT
ejpam-1479	121	18	1	1	NUM
ejpam-1479	121	19	+	+	NUM
ejpam-1479	121	20	rn	rn	NOUN
ejpam-1479	121	21	)	)	PUNCT
ejpam-1479	121	22	2	2	NUM
ejpam-1479	121	23	m	m	NOUN
ejpam-1479	121	24	∑	∑	NOUN
ejpam-1479	121	25	i=1	i=1	PROPN
ejpam-1479	121	26	αin‖yn	αin‖yn	PROPN
ejpam-1479	121	27	−	−	NOUN
ejpam-1479	122	1	p‖+	p‖+	NOUN
ejpam-1479	122	2	1−	1−	NUM
ejpam-1479	122	3	m	m	VERB
ejpam-1479	122	4	∑	∑	PUNCT
ejpam-1479	122	5	i=1	i=1	PROPN
ejpam-1479	122	6	αin	αin	NOUN
ejpam-1479	122	7	!	!	PUNCT
ejpam-1479	123	1	‖xn	‖xn	NUM
ejpam-1479	123	2	−	−	PROPN
ejpam-1479	123	3	p‖	p‖	NOUN
ejpam-1479	123	4	!	!	PUNCT
ejpam-1479	124	1	+	+	ADJ
ejpam-1479	124	2	(	(	PUNCT
ejpam-1479	124	3	2	2	NUM
ejpam-1479	124	4	+	+	NUM
ejpam-1479	124	5	rn)sn	rn)sn	X
ejpam-1479	124	6	.	.	PUNCT
ejpam-1479	125	1	for	for	ADP
ejpam-1479	125	2	all	all	PRON
ejpam-1479	125	3	n≥	n≥	ADJ
ejpam-1479	125	4	1	1	NUM
ejpam-1479	125	5	.	.	PUNCT
ejpam-1479	126	1	since	since	SCONJ
ejpam-1479	126	2	lim	lim	PROPN
ejpam-1479	126	3	infn	infn	PROPN
ejpam-1479	126	4	∑m	∑m	PROPN
ejpam-1479	126	5	i=1αin	i=1αin	VERB
ejpam-1479	126	6	>	>	X
ejpam-1479	126	7	0	0	NUM
ejpam-1479	126	8	,	,	PUNCT
ejpam-1479	126	9	we	we	PRON
ejpam-1479	126	10	have	have	VERB
ejpam-1479	126	11	‖xn+1−	‖xn+1−	PROPN
ejpam-1479	126	12	p‖	p‖	NOUN
ejpam-1479	127	1	−	−	PROPN
ejpam-1479	128	1	(	(	PUNCT
ejpam-1479	128	2	1	1	NUM
ejpam-1479	128	3	+	+	NUM
ejpam-1479	128	4	rn	rn	NOUN
ejpam-1479	128	5	)	)	PUNCT
ejpam-1479	128	6	2‖xn−	2‖xn−	NUM
ejpam-1479	128	7	p‖	p‖	NOUN
ejpam-1479	128	8	(	(	PUNCT
ejpam-1479	128	9	1	1	NUM
ejpam-1479	128	10	+	+	NUM
ejpam-1479	128	11	rn	rn	NOUN
ejpam-1479	128	12	)	)	PUNCT
ejpam-1479	128	13	2	2	NUM
ejpam-1479	128	14	∑m	∑m	ADJ
ejpam-1479	128	15	i=1αin	i=1αin	NOUN
ejpam-1479	128	16	+	+	CCONJ
ejpam-1479	128	17	‖xn−	‖xn−	NUM
ejpam-1479	128	18	p‖	p‖	NOUN
ejpam-1479	128	19	≤	≤	PROPN
ejpam-1479	129	1	‖yn	‖yn	PROPN
ejpam-1479	129	2	−	−	NOUN
ejpam-1479	129	3	p‖+	p‖+	NOUN
ejpam-1479	129	4	(	(	PUNCT
ejpam-1479	129	5	2	2	NUM
ejpam-1479	129	6	+	+	NUM
ejpam-1479	129	7	rn)sn	rn)sn	PROPN
ejpam-1479	129	8	(	(	PUNCT
ejpam-1479	129	9	1	1	NUM
ejpam-1479	129	10	+	+	NUM
ejpam-1479	129	11	rn	rn	NOUN
ejpam-1479	129	12	)	)	PUNCT
ejpam-1479	129	13	2	2	NUM
ejpam-1479	129	14	∑m	∑m	ADJ
ejpam-1479	129	15	i=1αin	i=1αin	NOUN
ejpam-1479	129	16	for	for	ADP
ejpam-1479	129	17	sufficiently	sufficiently	ADV
ejpam-1479	129	18	large	large	ADJ
ejpam-1479	129	19	numbers	number	NOUN
ejpam-1479	129	20	n.	n.	VERB
ejpam-1479	129	21	by	by	ADP
ejpam-1479	129	22	taking	take	VERB
ejpam-1479	129	23	lim	lim	PROPN
ejpam-1479	129	24	infn	infn	PROPN
ejpam-1479	129	25	in	in	ADP
ejpam-1479	129	26	both	both	DET
ejpam-1479	129	27	sides	side	NOUN
ejpam-1479	129	28	,	,	PUNCT
ejpam-1479	129	29	we	we	PRON
ejpam-1479	129	30	obtain	obtain	VERB
ejpam-1479	129	31	lim	lim	PROPN
ejpam-1479	129	32	n	n	PROPN
ejpam-1479	129	33	‖xn−	‖xn−	PROPN
ejpam-1479	129	34	p‖	p‖	PROPN
ejpam-1479	129	35	≤	≤	PROPN
ejpam-1479	129	36	lim	lim	PROPN
ejpam-1479	129	37	inf	inf	PROPN
ejpam-1479	129	38	n	n	PROPN
ejpam-1479	129	39	‖yn	‖yn	PROPN
ejpam-1479	129	40	−	−	PROPN
ejpam-1479	129	41	p‖.	p‖.	NOUN
ejpam-1479	129	42	this	this	PRON
ejpam-1479	129	43	completes	complete	VERB
ejpam-1479	129	44	the	the	DET
ejpam-1479	129	45	proof	proof	NOUN
ejpam-1479	129	46	.	.	PUNCT
ejpam-1479	130	1	theorem	theorem	NOUN
ejpam-1479	130	2	1	1	NUM
ejpam-1479	130	3	.	.	PUNCT
ejpam-1479	131	1	let	let	VERB
ejpam-1479	131	2	x	x	PRON
ejpam-1479	131	3	,	,	PUNCT
ejpam-1479	131	4	c	c	X
ejpam-1479	131	5	,	,	PUNCT
ejpam-1479	131	6	t1	t1	NOUN
ejpam-1479	131	7	,	,	PUNCT
ejpam-1479	131	8	.	.	PUNCT
ejpam-1479	131	9	.	.	PUNCT
ejpam-1479	132	1	.	.	PUNCT
ejpam-1479	133	1	,	,	PUNCT
ejpam-1479	133	2	tm	tm	NOUN
ejpam-1479	133	3	and	and	CCONJ
ejpam-1479	133	4	{	{	PUNCT
ejpam-1479	133	5	xn	xn	NOUN
ejpam-1479	133	6	}	}	PUNCT
ejpam-1479	133	7	be	be	VERB
ejpam-1479	133	8	as	as	ADP
ejpam-1479	133	9	in	in	ADP
ejpam-1479	133	10	lemma	lemma	PROPN
ejpam-1479	133	11	3	3	NUM
ejpam-1479	133	12	with	with	ADP
ejpam-1479	133	13	the	the	DET
ejpam-1479	133	14	restriction	restriction	NOUN
ejpam-1479	133	15	that	that	PRON
ejpam-1479	133	16	f	f	PROPN
ejpam-1479	133	17	=	=	PUNCT
ejpam-1479	133	18	⋂m	⋂m	PROPN
ejpam-1479	133	19	i=1	i=1	PROPN
ejpam-1479	133	20	f(ti	f(ti	NOUN
ejpam-1479	133	21	)	)	PUNCT
ejpam-1479	133	22	be	be	AUX
ejpam-1479	133	23	nonempty	nonempty	ADJ
ejpam-1479	133	24	and	and	CCONJ
ejpam-1479	133	25	closed	closed	ADJ
ejpam-1479	133	26	.	.	PUNCT
ejpam-1479	134	1	then	then	ADV
ejpam-1479	134	2	{	{	PUNCT
ejpam-1479	134	3	xn	xn	X
ejpam-1479	134	4	}	}	PUNCT
ejpam-1479	134	5	converges	converge	VERB
ejpam-1479	134	6	strongly	strongly	ADV
ejpam-1479	134	7	to	to	ADP
ejpam-1479	134	8	a	a	DET
ejpam-1479	134	9	common	common	ADJ
ejpam-1479	134	10	fixed	fix	VERB
ejpam-1479	134	11	point	point	NOUN
ejpam-1479	134	12	of	of	ADP
ejpam-1479	134	13	the	the	DET
ejpam-1479	134	14	family	family	NOUN
ejpam-1479	134	15	of	of	ADP
ejpam-1479	134	16	mappings	mapping	NOUN
ejpam-1479	134	17	if	if	SCONJ
ejpam-1479	134	18	and	and	CCONJ
ejpam-1479	134	19	only	only	ADV
ejpam-1479	134	20	if	if	SCONJ
ejpam-1479	134	21	lim	lim	PROPN
ejpam-1479	134	22	infn	infn	PROPN
ejpam-1479	134	23	d(xn	d(xn	PROPN
ejpam-1479	134	24	,	,	PUNCT
ejpam-1479	134	25	f	f	X
ejpam-1479	134	26	)	)	PUNCT
ejpam-1479	134	27	=	=	SYM
ejpam-1479	135	1	0	0	X
ejpam-1479	135	2	.	.	PUNCT
ejpam-1479	136	1	proof	proof	NOUN
ejpam-1479	136	2	.	.	PUNCT
ejpam-1479	137	1	the	the	DET
ejpam-1479	137	2	necessity	necessity	NOUN
ejpam-1479	137	3	is	be	AUX
ejpam-1479	137	4	obvious	obvious	ADJ
ejpam-1479	137	5	and	and	CCONJ
ejpam-1479	137	6	then	then	ADV
ejpam-1479	137	7	we	we	PRON
ejpam-1479	137	8	prove	prove	VERB
ejpam-1479	137	9	only	only	ADV
ejpam-1479	137	10	the	the	DET
ejpam-1479	137	11	sufficiency	sufficiency	NOUN
ejpam-1479	137	12	.	.	PUNCT
ejpam-1479	138	1	let	let	VERB
ejpam-1479	138	2	p	p	PRON
ejpam-1479	138	3	∈	∈	PROPN
ejpam-1479	138	4	f	f	X
ejpam-1479	138	5	.	.	PUNCT
ejpam-1479	139	1	from	from	ADP
ejpam-1479	139	2	lemma	lemma	PROPN
ejpam-1479	139	3	3(i	3(i	NUM
ejpam-1479	139	4	)	)	PUNCT
ejpam-1479	139	5	,	,	PUNCT
ejpam-1479	139	6	we	we	PRON
ejpam-1479	139	7	know	know	VERB
ejpam-1479	139	8	that	that	SCONJ
ejpam-1479	139	9	limn	limn	PROPN
ejpam-1479	139	10	‖xn	‖xn	PROPN
ejpam-1479	139	11	−	−	PROPN
ejpam-1479	139	12	p‖	p‖	NOUN
ejpam-1479	139	13	exists	exist	VERB
ejpam-1479	139	14	and	and	CCONJ
ejpam-1479	139	15	hence	hence	ADV
ejpam-1479	139	16	{	{	PUNCT
ejpam-1479	139	17	‖xn	‖xn	PROPN
ejpam-1479	139	18	−	−	PROPN
ejpam-1479	139	19	p‖	p‖	NOUN
ejpam-1479	139	20	}	}	PUNCT
ejpam-1479	139	21	is	be	AUX
ejpam-1479	139	22	bounded	bound	VERB
ejpam-1479	139	23	.	.	PUNCT
ejpam-1479	140	1	we	we	PRON
ejpam-1479	140	2	put	put	VERB
ejpam-1479	140	3	m	m	VERB
ejpam-1479	140	4	=	=	PUNCT
ejpam-1479	140	5	supn≥1	supn≥1	ADJ
ejpam-1479	140	6	‖xn	‖xn	PROPN
ejpam-1479	140	7	−	−	PROPN
ejpam-1479	140	8	p‖.	p‖.	NOUN
ejpam-1479	140	9	it	it	PRON
ejpam-1479	140	10	follows	follow	VERB
ejpam-1479	140	11	from	from	ADP
ejpam-1479	140	12	(	(	PUNCT
ejpam-1479	140	13	6	6	NUM
ejpam-1479	140	14	)	)	PUNCT
ejpam-1479	141	1	that	that	SCONJ
ejpam-1479	141	2	‖xn+1	‖xn+1	NUM
ejpam-1479	141	3	−	−	PROPN
ejpam-1479	141	4	p‖	p‖	NOUN
ejpam-1479	141	5	≤	≤	NUM
ejpam-1479	141	6	(	(	PUNCT
ejpam-1479	141	7	1+δn)‖xn−	1+δn)‖xn−	NUM
ejpam-1479	141	8	p‖+	p‖+	NOUN
ejpam-1479	141	9	dn	dn	PROPN
ejpam-1479	141	10	,	,	PUNCT
ejpam-1479	141	11	(	(	PUNCT
ejpam-1479	141	12	8)	8)	NUM
ejpam-1479	141	13	where	where	SCONJ
ejpam-1479	141	14	δn	δn	NOUN
ejpam-1479	141	15	=	=	SYM
ejpam-1479	141	16	(	(	PUNCT
ejpam-1479	141	17	1	1	NUM
ejpam-1479	141	18	+	+	NUM
ejpam-1479	141	19	rn	rn	NOUN
ejpam-1479	141	20	)	)	PUNCT
ejpam-1479	141	21	2	2	NUM
ejpam-1479	141	22	−	−	NOUN
ejpam-1479	141	23	1	1	NUM
ejpam-1479	141	24	and	and	CCONJ
ejpam-1479	141	25	dn	dn	NOUN
ejpam-1479	141	26	=	=	PUNCT
ejpam-1479	141	27	(	(	PUNCT
ejpam-1479	141	28	2	2	NUM
ejpam-1479	141	29	+	+	NUM
ejpam-1479	141	30	rn)sn	rn)sn	PUNCT
ejpam-1479	141	31	so	so	SCONJ
ejpam-1479	141	32	that	that	SCONJ
ejpam-1479	141	33	∑∞	∑∞	NOUN
ejpam-1479	141	34	n=1	n=1	PUNCT
ejpam-1479	141	35	δn	δn	ADP
ejpam-1479	141	36	<	<	NOUN
ejpam-1479	141	37	∞	∞	NUM
ejpam-1479	141	38	and	and	CCONJ
ejpam-1479	141	39	∑∞	∑∞	NOUN
ejpam-1479	141	40	n=1	n=1	PUNCT
ejpam-1479	141	41	dn	dn	PROPN
ejpam-1479	141	42	<	<	PROPN
ejpam-1479	141	43	∞.	∞.	PROPN
ejpam-1479	141	44	thus	thus	ADV
ejpam-1479	141	45	,	,	PUNCT
ejpam-1479	141	46	for	for	ADP
ejpam-1479	141	47	positive	positive	ADJ
ejpam-1479	141	48	integers	integer	NOUN
ejpam-1479	141	49	k	k	PROPN
ejpam-1479	141	50	and	and	CCONJ
ejpam-1479	141	51	n	n	CCONJ
ejpam-1479	141	52	,	,	PUNCT
ejpam-1479	141	53	we	we	PRON
ejpam-1479	141	54	have	have	VERB
ejpam-1479	141	55	‖xn+k	‖xn+k	PROPN
ejpam-1479	142	1	−	−	PROPN
ejpam-1479	142	2	p‖	p‖	NOUN
ejpam-1479	142	3	≤	≤	NOUN
ejpam-1479	142	4	‖xn+k−1−	‖xn+k−1−	PROPN
ejpam-1479	142	5	p‖+mδn+k−1	p‖+mδn+k−1	NOUN
ejpam-1479	142	6	+	+	CCONJ
ejpam-1479	142	7	dn+k−1	dn+k−1	ADJ
ejpam-1479	142	8	≤	≤	ADJ
ejpam-1479	142	9	‖xn+k−2−	‖xn+k−2−	NOUN
ejpam-1479	142	10	p‖+m(δn+k−2	p‖+m(δn+k−2	NOUN
ejpam-1479	142	11	+	+	CCONJ
ejpam-1479	142	12	δn+k−1	δn+k−1	PROPN
ejpam-1479	142	13	)	)	PUNCT
ejpam-1479	142	14	+	+	SYM
ejpam-1479	142	15	dn+k−2	dn+k−2	NOUN
ejpam-1479	142	16	+	+	CCONJ
ejpam-1479	142	17	dn+k−1	dn+k−1	ADJ
ejpam-1479	142	18	...	...	PUNCT
ejpam-1479	142	19	≤	≤	NUM
ejpam-1479	142	20	‖xn−	‖xn−	NUM
ejpam-1479	142	21	p‖+m	p‖+m	X
ejpam-1479	143	1	n+k−1	n+k−1	PROPN
ejpam-1479	143	2	∑	∑	PUNCT
ejpam-1479	143	3	i	i	PROPN
ejpam-1479	143	4	=	=	NOUN
ejpam-1479	143	5	n	n	NOUN
ejpam-1479	143	6	δi	δi	VERB
ejpam-1479	144	1	+	+	CCONJ
ejpam-1479	144	2	n+k−1	n+k−1	PROPN
ejpam-1479	144	3	∑	∑	PROPN
ejpam-1479	144	4	i	i	PROPN
ejpam-1479	144	5	=	=	PROPN
ejpam-1479	144	6	n	n	X
ejpam-1479	144	7	di	di	NOUN
ejpam-1479	144	8	.	.	PUNCT
ejpam-1479	145	1	(	(	PUNCT
ejpam-1479	145	2	9	9	X
ejpam-1479	145	3	)	)	PUNCT
ejpam-1479	145	4	it	it	PRON
ejpam-1479	145	5	follows	follow	VERB
ejpam-1479	145	6	from	from	ADP
ejpam-1479	145	7	lemma	lemma	PROPN
ejpam-1479	145	8	3(ii	3(ii	NUM
ejpam-1479	145	9	)	)	PUNCT
ejpam-1479	145	10	that	that	SCONJ
ejpam-1479	145	11	limn	limn	PROPN
ejpam-1479	145	12	d(xn	d(xn	PROPN
ejpam-1479	145	13	,	,	PUNCT
ejpam-1479	145	14	f	f	X
ejpam-1479	145	15	)	)	PUNCT
ejpam-1479	145	16	exists	exist	VERB
ejpam-1479	145	17	.	.	PUNCT
ejpam-1479	146	1	thus	thus	ADV
ejpam-1479	146	2	limn	limn	PROPN
ejpam-1479	146	3	d(xn	d(xn	PROPN
ejpam-1479	146	4	,	,	PUNCT
ejpam-1479	146	5	f	f	X
ejpam-1479	146	6	)	)	PUNCT
ejpam-1479	146	7	=	=	SYM
ejpam-1479	147	1	0	0	X
ejpam-1479	147	2	.	.	PUNCT
ejpam-1479	148	1	now	now	ADV
ejpam-1479	148	2	,	,	PUNCT
ejpam-1479	148	3	we	we	PRON
ejpam-1479	148	4	show	show	VERB
ejpam-1479	148	5	that	that	SCONJ
ejpam-1479	148	6	{	{	PUNCT
ejpam-1479	148	7	xn	xn	X
ejpam-1479	148	8	}	}	PUNCT
ejpam-1479	148	9	is	be	AUX
ejpam-1479	148	10	a	a	DET
ejpam-1479	148	11	cauchy	cauchy	ADJ
ejpam-1479	148	12	sequence	sequence	NOUN
ejpam-1479	148	13	.	.	PUNCT
ejpam-1479	149	1	by	by	ADP
ejpam-1479	149	2	limn	limn	PROPN
ejpam-1479	149	3	d(xn	d(xn	PROPN
ejpam-1479	149	4	,	,	PUNCT
ejpam-1479	149	5	f	f	X
ejpam-1479	149	6	)	)	PUNCT
ejpam-1479	149	7	=	=	SYM
ejpam-1479	149	8	0	0	NUM
ejpam-1479	149	9	,	,	PUNCT
ejpam-1479	149	10	∑∞	∑∞	NOUN
ejpam-1479	149	11	n=1	n=1	PUNCT
ejpam-1479	149	12	δn	δn	VERB
ejpam-1479	149	13	<	<	X
ejpam-1479	149	14	∞	∞	PROPN
ejpam-1479	149	15	and	and	CCONJ
ejpam-1479	149	16	∑∞	∑∞	NOUN
ejpam-1479	149	17	n=1	n=1	PUNCT
ejpam-1479	149	18	dn	dn	ADP
ejpam-1479	149	19	<	<	X
ejpam-1479	149	20	∞	∞	PROPN
ejpam-1479	149	21	,	,	PUNCT
ejpam-1479	149	22	we	we	PRON
ejpam-1479	149	23	get	get	VERB
ejpam-1479	149	24	that	that	PRON
ejpam-1479	149	25	for	for	ADP
ejpam-1479	149	26	any	any	DET
ejpam-1479	149	27	ε	ε	PROPN
ejpam-1479	149	28	>	>	X
ejpam-1479	149	29	0	0	PROPN
ejpam-1479	149	30	,	,	PUNCT
ejpam-1479	149	31	there	there	PRON
ejpam-1479	149	32	exists	exist	VERB
ejpam-1479	149	33	a	a	DET
ejpam-1479	149	34	positive	positive	ADJ
ejpam-1479	149	35	integer	integer	NOUN
ejpam-1479	149	36	n0	n0	NOUN
ejpam-1479	149	37	such	such	ADJ
ejpam-1479	149	38	that	that	PRON
ejpam-1479	149	39	d(xn0	d(xn0	NOUN
ejpam-1479	149	40	,	,	PUNCT
ejpam-1479	149	41	f	f	X
ejpam-1479	149	42	)	)	PUNCT
ejpam-1479	149	43	<	<	X
ejpam-1479	149	44	ε	ε	PROPN
ejpam-1479	149	45	6	6	NUM
ejpam-1479	149	46	,	,	PUNCT
ejpam-1479	149	47	∞	∞	PROPN
ejpam-1479	149	48	∑	∑	PROPN
ejpam-1479	149	49	i	i	PROPN
ejpam-1479	149	50	=	=	NOUN
ejpam-1479	149	51	n0	n0	X
ejpam-1479	149	52	δi	δi	NOUN
ejpam-1479	149	53	<	<	X
ejpam-1479	149	54	ε	ε	PROPN
ejpam-1479	149	55	3	3	NUM
ejpam-1479	149	56	m	m	NOUN
ejpam-1479	149	57	and	and	CCONJ
ejpam-1479	149	58	∞	∞	NUM
ejpam-1479	149	59	∑	∑	PROPN
ejpam-1479	149	60	i	i	PROPN
ejpam-1479	149	61	=	=	PROPN
ejpam-1479	149	62	n0	n0	X
ejpam-1479	149	63	di	di	X
ejpam-1479	149	64	<	<	X
ejpam-1479	149	65	ε	ε	PROPN
ejpam-1479	149	66	3	3	NUM
ejpam-1479	149	67	.	.	PUNCT
ejpam-1479	150	1	therefore	therefore	ADV
ejpam-1479	150	2	,	,	PUNCT
ejpam-1479	150	3	there	there	PRON
ejpam-1479	150	4	exists	exist	VERB
ejpam-1479	150	5	p0	p0	NOUN
ejpam-1479	150	6	∈	∈	PROPN
ejpam-1479	150	7	f	f	PROPN
ejpam-1479	150	8	such	such	ADJ
ejpam-1479	150	9	that	that	PRON
ejpam-1479	150	10	‖xn0	‖xn0	PROPN
ejpam-1479	150	11	−	−	PROPN
ejpam-1479	150	12	p0‖	p0‖	NOUN
ejpam-1479	150	13	<	<	X
ejpam-1479	150	14	ε/6	ε/6	NUM
ejpam-1479	150	15	.	.	PUNCT
ejpam-1479	151	1	it	it	PRON
ejpam-1479	151	2	follows	follow	VERB
ejpam-1479	151	3	from	from	ADP
ejpam-1479	151	4	(	(	PUNCT
ejpam-1479	151	5	9	9	NUM
ejpam-1479	151	6	)	)	PUNCT
ejpam-1479	151	7	that	that	SCONJ
ejpam-1479	151	8	‖xn0+k	‖xn0+k	NOUN
ejpam-1479	152	1	−	−	X
ejpam-1479	152	2	xn0	xn0	PUNCT
ejpam-1479	153	1	‖	‖	PROPN
ejpam-1479	153	2	≤	≤	PROPN
ejpam-1479	153	3	‖xn0+k	‖xn0+k	NOUN
ejpam-1479	153	4	−	−	PROPN
ejpam-1479	153	5	p0‖+	p0‖+	ADP
ejpam-1479	153	6	‖xn0	‖xn0	VERB
ejpam-1479	153	7	−	−	PROPN
ejpam-1479	153	8	p0‖	p0‖	PROPN
ejpam-1479	153	9	h.	h.	NOUN
ejpam-1479	153	10	dehghan	dehghan	PROPN
ejpam-1479	153	11	,	,	PUNCT
ejpam-1479	153	12	a.	a.	NOUN
ejpam-1479	153	13	gharajelo	gharajelo	PROPN
ejpam-1479	153	14	/	/	SYM
ejpam-1479	153	15	eur	eur	PROPN
ejpam-1479	153	16	.	.	PUNCT
ejpam-1479	154	1	j.	j.	PROPN
ejpam-1479	154	2	pure	pure	PROPN
ejpam-1479	154	3	appl	appl	PROPN
ejpam-1479	154	4	.	.	PROPN
ejpam-1479	154	5	math	math	PROPN
ejpam-1479	154	6	,	,	PUNCT
ejpam-1479	154	7	5	5	NUM
ejpam-1479	154	8	(	(	PUNCT
ejpam-1479	154	9	2012	2012	NUM
ejpam-1479	154	10	)	)	PUNCT
ejpam-1479	154	11	,	,	PUNCT
ejpam-1479	154	12	45	45	NUM
ejpam-1479	154	13	-	-	SYM
ejpam-1479	154	14	54	54	NUM
ejpam-1479	154	15	50	50	NUM
ejpam-1479	154	16	≤	≤	NUM
ejpam-1479	154	17	2‖xn0	2‖xn0	NUM
ejpam-1479	155	1	−	−	NOUN
ejpam-1479	156	1	p0‖+m	p0‖+m	X
ejpam-1479	156	2	n0+k−1	n0+k−1	VERB
ejpam-1479	156	3	∑	∑	PUNCT
ejpam-1479	156	4	i	i	PROPN
ejpam-1479	156	5	=	=	NOUN
ejpam-1479	156	6	n0	n0	X
ejpam-1479	156	7	δi	δi	VERB
ejpam-1479	157	1	+	+	CCONJ
ejpam-1479	157	2	n0+k−1	n0+k−1	PROPN
ejpam-1479	157	3	∑	∑	PUNCT
ejpam-1479	158	1	i	i	PROPN
ejpam-1479	158	2	=	=	PROPN
ejpam-1479	158	3	n0	n0	X
ejpam-1479	158	4	di	di	X
ejpam-1479	158	5	<	<	PROPN
ejpam-1479	158	6	2	2	NUM
ejpam-1479	158	7	�	�	NOUN
ejpam-1479	158	8	ε	ε	PROPN
ejpam-1479	158	9	6	6	NUM
ejpam-1479	158	10	�	�	PROPN
ejpam-1479	158	11	+	+	PROPN
ejpam-1479	158	12	m	m	PROPN
ejpam-1479	158	13	�	�	PROPN
ejpam-1479	158	14	ε	ε	PROPN
ejpam-1479	158	15	3	3	NUM
ejpam-1479	158	16	m	m	PROPN
ejpam-1479	158	17	�	�	PROPN
ejpam-1479	158	18	+	+	CCONJ
ejpam-1479	158	19	ε	ε	PROPN
ejpam-1479	158	20	3	3	NUM
ejpam-1479	158	21	=	=	SYM
ejpam-1479	158	22	ε	ε	PROPN
ejpam-1479	158	23	for	for	ADP
ejpam-1479	158	24	all	all	DET
ejpam-1479	158	25	k	k	PROPN
ejpam-1479	158	26	≥	≥	NUM
ejpam-1479	158	27	1	1	NUM
ejpam-1479	158	28	.	.	PUNCT
ejpam-1479	159	1	thus	thus	ADV
ejpam-1479	159	2	{	{	PUNCT
ejpam-1479	159	3	xn	xn	X
ejpam-1479	159	4	}	}	PUNCT
ejpam-1479	159	5	is	be	AUX
ejpam-1479	159	6	a	a	DET
ejpam-1479	159	7	cauchy	cauchy	ADJ
ejpam-1479	159	8	sequence	sequence	NOUN
ejpam-1479	159	9	and	and	CCONJ
ejpam-1479	159	10	hence	hence	ADV
ejpam-1479	159	11	xn→	xn→	PRON
ejpam-1479	159	12	q	q	X
ejpam-1479	160	1	for	for	ADP
ejpam-1479	160	2	some	some	DET
ejpam-1479	160	3	q	q	NOUN
ejpam-1479	160	4	∈	∈	PROPN
ejpam-1479	160	5	c	c	NOUN
ejpam-1479	160	6	.	.	PUNCT
ejpam-1479	161	1	moreover	moreover	ADV
ejpam-1479	161	2	,	,	PUNCT
ejpam-1479	161	3	d(q	d(q	PROPN
ejpam-1479	161	4	,	,	PUNCT
ejpam-1479	161	5	f	f	NOUN
ejpam-1479	161	6	)	)	PUNCT
ejpam-1479	161	7	≤	≤	NOUN
ejpam-1479	161	8	‖xn−	‖xn−	PROPN
ejpam-1479	161	9	q‖+	q‖+	VERB
ejpam-1479	161	10	d(xn	d(xn	PROPN
ejpam-1479	161	11	,	,	PUNCT
ejpam-1479	161	12	f)→	f)→	PROPN
ejpam-1479	161	13	0	0	NUM
ejpam-1479	161	14	as	as	ADP
ejpam-1479	161	15	n→∞.	n→∞.	ADJ
ejpam-1479	161	16	since	since	SCONJ
ejpam-1479	161	17	f	f	PROPN
ejpam-1479	161	18	is	be	AUX
ejpam-1479	161	19	closed	closed	ADJ
ejpam-1479	161	20	,	,	PUNCT
ejpam-1479	161	21	then	then	ADV
ejpam-1479	161	22	q	q	PROPN
ejpam-1479	161	23	∈	∈	PROPN
ejpam-1479	161	24	f	f	X
ejpam-1479	161	25	.	.	PUNCT
ejpam-1479	162	1	this	this	PRON
ejpam-1479	162	2	completes	complete	VERB
ejpam-1479	162	3	the	the	DET
ejpam-1479	162	4	proof	proof	NOUN
ejpam-1479	162	5	.	.	PUNCT
ejpam-1479	163	1	3	3	X
ejpam-1479	163	2	.	.	X
ejpam-1479	163	3	convergence	convergence	NOUN
ejpam-1479	163	4	in	in	ADP
ejpam-1479	163	5	uniformly	uniformly	ADV
ejpam-1479	163	6	convex	convex	NOUN
ejpam-1479	163	7	banach	banach	NOUN
ejpam-1479	163	8	spaces	space	NOUN
ejpam-1479	163	9	in	in	ADP
ejpam-1479	163	10	this	this	DET
ejpam-1479	163	11	section	section	NOUN
ejpam-1479	163	12	,	,	PUNCT
ejpam-1479	163	13	some	some	DET
ejpam-1479	163	14	weak	weak	ADJ
ejpam-1479	163	15	and	and	CCONJ
ejpam-1479	163	16	strong	strong	ADJ
ejpam-1479	163	17	convergence	convergence	NOUN
ejpam-1479	163	18	results	result	NOUN
ejpam-1479	163	19	are	be	AUX
ejpam-1479	163	20	established	establish	VERB
ejpam-1479	163	21	for	for	ADP
ejpam-1479	163	22	iterative	iterative	ADJ
ejpam-1479	163	23	scheme	scheme	NOUN
ejpam-1479	163	24	(	(	PUNCT
ejpam-1479	163	25	1	1	NUM
ejpam-1479	163	26	)	)	PUNCT
ejpam-1479	163	27	in	in	ADP
ejpam-1479	163	28	uniformly	uniformly	ADV
ejpam-1479	163	29	convex	convex	VERB
ejpam-1479	163	30	banach	banach	NOUN
ejpam-1479	163	31	spaces	space	NOUN
ejpam-1479	163	32	without	without	ADP
ejpam-1479	163	33	using	use	VERB
ejpam-1479	163	34	the	the	DET
ejpam-1479	163	35	condition	condition	NOUN
ejpam-1479	163	36	lim	lim	PROPN
ejpam-1479	163	37	infn	infn	PROPN
ejpam-1479	164	1	d(xn	d(xn	PROPN
ejpam-1479	164	2	,	,	PUNCT
ejpam-1479	164	3	f	f	X
ejpam-1479	164	4	)	)	PUNCT
ejpam-1479	164	5	=	=	SYM
ejpam-1479	164	6	0	0	PUNCT
ejpam-1479	164	7	appearing	appear	VERB
ejpam-1479	164	8	in	in	ADP
ejpam-1479	164	9	the	the	DET
ejpam-1479	164	10	preceding	precede	VERB
ejpam-1479	164	11	section	section	NOUN
ejpam-1479	164	12	.	.	PUNCT
ejpam-1479	165	1	for	for	ADP
ejpam-1479	165	2	this	this	PRON
ejpam-1479	165	3	we	we	PRON
ejpam-1479	165	4	have	have	VERB
ejpam-1479	165	5	to	to	PART
ejpam-1479	165	6	consider	consider	VERB
ejpam-1479	165	7	condition	condition	NOUN
ejpam-1479	165	8	(	(	PUNCT
ejpam-1479	165	9	a′′	a′′	NOUN
ejpam-1479	165	10	)	)	PUNCT
ejpam-1479	165	11	and	and	CCONJ
ejpam-1479	165	12	opial	opial	ADJ
ejpam-1479	165	13	property	property	NOUN
ejpam-1479	165	14	.	.	PUNCT
ejpam-1479	166	1	the	the	DET
ejpam-1479	166	2	following	follow	VERB
ejpam-1479	166	3	lemma	lemma	PROPN
ejpam-1479	166	4	has	have	VERB
ejpam-1479	166	5	the	the	DET
ejpam-1479	166	6	important	important	ADJ
ejpam-1479	166	7	ingredients	ingredient	NOUN
ejpam-1479	166	8	for	for	ADP
ejpam-1479	166	9	proving	prove	VERB
ejpam-1479	166	10	our	our	PRON
ejpam-1479	166	11	main	main	ADJ
ejpam-1479	166	12	results	result	NOUN
ejpam-1479	166	13	.	.	PUNCT
ejpam-1479	167	1	lemma	lemma	PROPN
ejpam-1479	167	2	4	4	X
ejpam-1479	167	3	.	.	PUNCT
ejpam-1479	168	1	let	let	VERB
ejpam-1479	168	2	x	x	PRON
ejpam-1479	168	3	be	be	AUX
ejpam-1479	168	4	a	a	DET
ejpam-1479	168	5	uniformly	uniformly	ADV
ejpam-1479	168	6	convex	convex	NOUN
ejpam-1479	168	7	banach	banach	NOUN
ejpam-1479	168	8	space	space	NOUN
ejpam-1479	168	9	,	,	PUNCT
ejpam-1479	168	10	c	c	X
ejpam-1479	168	11	be	be	AUX
ejpam-1479	168	12	a	a	DET
ejpam-1479	168	13	nonempty	nonempty	ADV
ejpam-1479	168	14	closed	close	VERB
ejpam-1479	168	15	convex	convex	NOUN
ejpam-1479	168	16	subset	subset	NOUN
ejpam-1479	168	17	of	of	ADP
ejpam-1479	168	18	x	x	PUNCT
ejpam-1479	168	19	and	and	CCONJ
ejpam-1479	168	20	{	{	PUNCT
ejpam-1479	168	21	ti	ti	NOUN
ejpam-1479	168	22	:	:	PUNCT
ejpam-1479	168	23	i	i	NOUN
ejpam-1479	168	24	=	=	SYM
ejpam-1479	168	25	1,2	1,2	NUM
ejpam-1479	168	26	,	,	PUNCT
ejpam-1479	168	27	.	.	PUNCT
ejpam-1479	168	28	.	.	PUNCT
ejpam-1479	169	1	.	.	PUNCT
ejpam-1479	170	1	,	,	PUNCT
ejpam-1479	170	2	m	m	AUX
ejpam-1479	170	3	}	}	PUNCT
ejpam-1479	170	4	be	be	AUX
ejpam-1479	170	5	a	a	DET
ejpam-1479	170	6	family	family	NOUN
ejpam-1479	170	7	of	of	ADP
ejpam-1479	170	8	uniformly	uniformly	ADJ
ejpam-1479	170	9	l	l	NOUN
ejpam-1479	170	10	-	-	NOUN
ejpam-1479	170	11	lipschitz	lipschitz	NOUN
ejpam-1479	170	12	and	and	CCONJ
ejpam-1479	170	13	generalized	generalize	VERB
ejpam-1479	170	14	asymptotically	asymptotically	ADV
ejpam-1479	170	15	quasi	quasi	ADJ
ejpam-1479	170	16	-	-	ADJ
ejpam-1479	170	17	nonexpansive	nonexpansive	ADJ
ejpam-1479	170	18	self	self	NOUN
ejpam-1479	170	19	-	-	PUNCT
ejpam-1479	170	20	mappings	mapping	NOUN
ejpam-1479	170	21	of	of	ADP
ejpam-1479	170	22	c	c	NOUN
ejpam-1479	170	23	with	with	ADP
ejpam-1479	170	24	the	the	DET
ejpam-1479	170	25	sequences	sequence	NOUN
ejpam-1479	170	26	{	{	PUNCT
ejpam-1479	170	27	r(1)n	r(1)n	X
ejpam-1479	170	28	}	}	PUNCT
ejpam-1479	170	29	,	,	PUNCT
ejpam-1479	170	30	.	.	PUNCT
ejpam-1479	170	31	.	.	PUNCT
ejpam-1479	171	1	.	.	PUNCT
ejpam-1479	172	1	,	,	PUNCT
ejpam-1479	172	2	{	{	PUNCT
ejpam-1479	172	3	r(m)n	r(m)n	PROPN
ejpam-1479	172	4	}	}	PUNCT
ejpam-1479	172	5	and	and	CCONJ
ejpam-1479	172	6	{	{	PUNCT
ejpam-1479	172	7	s(1)n	s(1)n	PROPN
ejpam-1479	172	8	}	}	PUNCT
ejpam-1479	172	9	,	,	PUNCT
ejpam-1479	172	10	.	.	PUNCT
ejpam-1479	172	11	.	.	PUNCT
ejpam-1479	173	1	.	.	PUNCT
ejpam-1479	174	1	,	,	PUNCT
ejpam-1479	174	2	{	{	PUNCT
ejpam-1479	174	3	s(m)n	s(m)n	NOUN
ejpam-1479	174	4	}	}	PUNCT
ejpam-1479	174	5	such	such	ADJ
ejpam-1479	174	6	that	that	DET
ejpam-1479	174	7	∑∞	∑∞	NOUN
ejpam-1479	174	8	n=1	n=1	PUNCT
ejpam-1479	174	9	r(i)n	r(i)n	PROPN
ejpam-1479	174	10	<	<	X
ejpam-1479	174	11	∞	∞	NUM
ejpam-1479	174	12	and	and	CCONJ
ejpam-1479	174	13	∑∞	∑∞	NOUN
ejpam-1479	174	14	n=1	n=1	PROPN
ejpam-1479	174	15	s(i)n	s(i)n	PROPN
ejpam-1479	174	16	<	<	X
ejpam-1479	174	17	∞	∞	PROPN
ejpam-1479	174	18	for	for	ADP
ejpam-1479	174	19	each	each	DET
ejpam-1479	174	20	i	i	NOUN
ejpam-1479	174	21	=	=	NOUN
ejpam-1479	174	22	1,2	1,2	NUM
ejpam-1479	174	23	,	,	PUNCT
ejpam-1479	174	24	.	.	PUNCT
ejpam-1479	174	25	.	.	PUNCT
ejpam-1479	175	1	.	.	PUNCT
ejpam-1479	176	1	,	,	PUNCT
ejpam-1479	176	2	m.	m.	NOUN
ejpam-1479	176	3	let	let	AUX
ejpam-1479	176	4	{	{	PUNCT
ejpam-1479	176	5	xn	xn	VERB
ejpam-1479	176	6	}	}	PUNCT
ejpam-1479	176	7	be	be	VERB
ejpam-1479	176	8	the	the	DET
ejpam-1479	176	9	sequence	sequence	NOUN
ejpam-1479	176	10	defined	define	VERB
ejpam-1479	176	11	by	by	ADP
ejpam-1479	176	12	(	(	PUNCT
ejpam-1479	176	13	1	1	NUM
ejpam-1479	176	14	)	)	PUNCT
ejpam-1479	176	15	.	.	PUNCT
ejpam-1479	177	1	then	then	ADV
ejpam-1479	177	2	we	we	PRON
ejpam-1479	177	3	have	have	VERB
ejpam-1479	177	4	the	the	DET
ejpam-1479	177	5	following	follow	VERB
ejpam-1479	177	6	conclusions	conclusion	NOUN
ejpam-1479	177	7	.	.	PUNCT
ejpam-1479	178	1	(	(	PUNCT
ejpam-1479	178	2	i	i	NOUN
ejpam-1479	178	3	)	)	PUNCT
ejpam-1479	178	4	if	if	SCONJ
ejpam-1479	178	5	0	0	NUM
ejpam-1479	178	6	<	<	X
ejpam-1479	178	7	lim	lim	NOUN
ejpam-1479	178	8	infnαin	infnαin	VERB
ejpam-1479	178	9	≤	≤	NUM
ejpam-1479	178	10	lim	lim	PROPN
ejpam-1479	178	11	supn(1−	supn(1−	PROPN
ejpam-1479	178	12	γn	γn	PROPN
ejpam-1479	178	13	)	)	PUNCT
ejpam-1479	178	14	<	<	X
ejpam-1479	178	15	1	1	NUM
ejpam-1479	178	16	,	,	PUNCT
ejpam-1479	178	17	then	then	ADV
ejpam-1479	178	18	limn	limn	PROPN
ejpam-1479	178	19	‖t	‖t	PROPN
ejpam-1479	179	1	n	n	CCONJ
ejpam-1479	180	1	i	i	PRON
ejpam-1479	180	2	yn	yn	INTJ
ejpam-1479	180	3	−	−	NOUN
ejpam-1479	180	4	xn‖	xn‖	PROPN
ejpam-1479	180	5	=	=	SYM
ejpam-1479	180	6	0	0	PROPN
ejpam-1479	180	7	.	.	PUNCT
ejpam-1479	180	8	(	(	PUNCT
ejpam-1479	180	9	ii	ii	NOUN
ejpam-1479	180	10	)	)	PUNCT
ejpam-1479	180	11	if	if	SCONJ
ejpam-1479	180	12	0	0	NUM
ejpam-1479	180	13	<	<	X
ejpam-1479	180	14	lim	lim	PROPN
ejpam-1479	180	15	infnβin	infnβin	VERB
ejpam-1479	180	16	≤	≤	NUM
ejpam-1479	180	17	lim	lim	PROPN
ejpam-1479	180	18	supn(1−	supn(1−	PROPN
ejpam-1479	180	19	γn	γn	PROPN
ejpam-1479	180	20	)	)	PUNCT
ejpam-1479	180	21	<	<	X
ejpam-1479	180	22	1	1	NUM
ejpam-1479	180	23	,	,	PUNCT
ejpam-1479	180	24	then	then	ADV
ejpam-1479	180	25	limn	limn	PROPN
ejpam-1479	180	26	‖t	‖t	PROPN
ejpam-1479	181	1	n	n	CCONJ
ejpam-1479	182	1	i	i	PRON
ejpam-1479	182	2	xn−	xn−	PUNCT
ejpam-1479	182	3	xn‖=	xn‖=	PROPN
ejpam-1479	182	4	0	0	PUNCT
ejpam-1479	182	5	.	.	PUNCT
ejpam-1479	183	1	(	(	PUNCT
ejpam-1479	183	2	iii	iii	X
ejpam-1479	183	3	)	)	PUNCT
ejpam-1479	184	1	if	if	SCONJ
ejpam-1479	184	2	lim	lim	PROPN
ejpam-1479	184	3	infnα	infnα	PROPN
ejpam-1479	184	4	jn	jn	PROPN
ejpam-1479	184	5	>	>	X
ejpam-1479	184	6	0	0	PUNCT
ejpam-1479	184	7	for	for	ADP
ejpam-1479	184	8	some	some	DET
ejpam-1479	184	9	j	j	NOUN
ejpam-1479	184	10	=	=	SYM
ejpam-1479	184	11	1,2	1,2	NUM
ejpam-1479	184	12	,	,	PUNCT
ejpam-1479	184	13	.	.	PUNCT
ejpam-1479	184	14	.	.	PUNCT
ejpam-1479	185	1	.	.	PUNCT
ejpam-1479	186	1	,	,	PUNCT
ejpam-1479	186	2	m	m	VERB
ejpam-1479	186	3	and	and	CCONJ
ejpam-1479	186	4	0	0	NUM
ejpam-1479	186	5	<	<	X
ejpam-1479	186	6	lim	lim	PROPN
ejpam-1479	186	7	infn	infn	PROPN
ejpam-1479	186	8	ain	ain	PROPN
ejpam-1479	186	9	≤	≤	PROPN
ejpam-1479	186	10	lim	lim	PROPN
ejpam-1479	186	11	supn(1−	supn(1−	PROPN
ejpam-1479	186	12	bn	bn	PROPN
ejpam-1479	186	13	)	)	PUNCT
ejpam-1479	186	14	<	<	X
ejpam-1479	187	1	1	1	NUM
ejpam-1479	187	2	,	,	PUNCT
ejpam-1479	187	3	then	then	ADV
ejpam-1479	187	4	limn	limn	PROPN
ejpam-1479	187	5	‖t	‖t	PROPN
ejpam-1479	187	6	n	n	CCONJ
ejpam-1479	188	1	i	i	PRON
ejpam-1479	188	2	xn−	xn−	PROPN
ejpam-1479	188	3	xn‖	xn‖	PROPN
ejpam-1479	188	4	=	=	PUNCT
ejpam-1479	188	5	0	0	PROPN
ejpam-1479	188	6	.	.	PUNCT
ejpam-1479	189	1	(	(	PUNCT
ejpam-1479	189	2	iv	iv	X
ejpam-1479	189	3	)	)	PUNCT
ejpam-1479	190	1	if	if	SCONJ
ejpam-1479	190	2	limn	limn	PROPN
ejpam-1479	190	3	‖t	‖t	PROPN
ejpam-1479	190	4	n	n	NOUN
ejpam-1479	190	5	i	i	PRON
ejpam-1479	190	6	xn−	xn−	PROPN
ejpam-1479	190	7	xn‖	xn‖	PROPN
ejpam-1479	191	1	=	=	PUNCT
ejpam-1479	191	2	0	0	NUM
ejpam-1479	191	3	for	for	ADP
ejpam-1479	191	4	all	all	DET
ejpam-1479	191	5	i	i	NOUN
ejpam-1479	191	6	=	=	SYM
ejpam-1479	191	7	1,2	1,2	NUM
ejpam-1479	191	8	,	,	PUNCT
ejpam-1479	191	9	.	.	PUNCT
ejpam-1479	191	10	.	.	PUNCT
ejpam-1479	191	11	.	.	PUNCT
ejpam-1479	192	1	,	,	PUNCT
ejpam-1479	192	2	m	m	PROPN
ejpam-1479	192	3	,	,	PUNCT
ejpam-1479	192	4	then	then	ADV
ejpam-1479	192	5	limn	limn	PROPN
ejpam-1479	193	1	‖ti	‖ti	NUM
ejpam-1479	193	2	xn−	xn−	PUNCT
ejpam-1479	193	3	xn‖	xn‖	PROPN
ejpam-1479	193	4	=	=	PUNCT
ejpam-1479	193	5	0	0	NUM
ejpam-1479	194	1	for	for	ADP
ejpam-1479	194	2	all	all	DET
ejpam-1479	194	3	i	i	NOUN
ejpam-1479	194	4	=	=	SYM
ejpam-1479	194	5	1,2	1,2	NUM
ejpam-1479	194	6	,	,	PUNCT
ejpam-1479	194	7	.	.	PUNCT
ejpam-1479	194	8	.	.	PUNCT
ejpam-1479	194	9	.	.	PUNCT
ejpam-1479	195	1	,	,	PUNCT
ejpam-1479	195	2	m.	m.	NOUN
ejpam-1479	195	3	proof	proof	NOUN
ejpam-1479	195	4	.	.	PUNCT
ejpam-1479	196	1	(	(	PUNCT
ejpam-1479	196	2	i	i	NOUN
ejpam-1479	196	3	)	)	PUNCT
ejpam-1479	196	4	let	let	VERB
ejpam-1479	196	5	p	p	PROPN
ejpam-1479	196	6	∈	∈	PROPN
ejpam-1479	196	7	f	f	X
ejpam-1479	196	8	.	.	PUNCT
ejpam-1479	197	1	by	by	ADP
ejpam-1479	197	2	lemma	lemma	PROPN
ejpam-1479	197	3	3(i	3(i	NUM
ejpam-1479	197	4	)	)	PUNCT
ejpam-1479	197	5	,	,	PUNCT
ejpam-1479	197	6	limn	limn	PROPN
ejpam-1479	197	7	‖xn	‖xn	PROPN
ejpam-1479	197	8	−	−	PROPN
ejpam-1479	197	9	p‖	p‖	NOUN
ejpam-1479	197	10	exists	exist	VERB
ejpam-1479	197	11	.	.	PUNCT
ejpam-1479	198	1	let	let	VERB
ejpam-1479	198	2	limn	limn	PROPN
ejpam-1479	198	3	‖xn	‖xn	PROPN
ejpam-1479	198	4	−	−	PROPN
ejpam-1479	198	5	p‖	p‖	NOUN
ejpam-1479	198	6	=	=	PUNCT
ejpam-1479	198	7	a	a	PRON
ejpam-1479	198	8	for	for	ADP
ejpam-1479	198	9	some	some	PRON
ejpam-1479	198	10	a	a	DET
ejpam-1479	198	11	≥	≥	NOUN
ejpam-1479	198	12	0	0	NUM
ejpam-1479	198	13	.	.	PUNCT
ejpam-1479	199	1	then	then	ADV
ejpam-1479	199	2	,	,	PUNCT
ejpam-1479	199	3	lim	lim	PROPN
ejpam-1479	199	4	sup	sup	PROPN
ejpam-1479	199	5	n	n	PROPN
ejpam-1479	199	6	‖t	‖t	NOUN
ejpam-1479	199	7	n	n	CCONJ
ejpam-1479	200	1	i	i	PRON
ejpam-1479	200	2	xn−	xn−	PUNCT
ejpam-1479	200	3	p‖	p‖	PROPN
ejpam-1479	200	4	≤	≤	PROPN
ejpam-1479	200	5	lim	lim	PROPN
ejpam-1479	200	6	sup	sup	PROPN
ejpam-1479	200	7	n	n	PROPN
ejpam-1479	200	8	(	(	PUNCT
ejpam-1479	200	9	(	(	PUNCT
ejpam-1479	200	10	1	1	NUM
ejpam-1479	200	11	+	+	NUM
ejpam-1479	200	12	rin)‖xn−	rin)‖xn−	ADJ
ejpam-1479	200	13	p‖+	p‖+	NOUN
ejpam-1479	200	14	sin)≤	sin)≤	NOUN
ejpam-1479	200	15	a	a	PRON
ejpam-1479	200	16	(	(	PUNCT
ejpam-1479	200	17	10	10	NUM
ejpam-1479	200	18	)	)	PUNCT
ejpam-1479	200	19	for	for	ADP
ejpam-1479	200	20	all	all	DET
ejpam-1479	200	21	i	i	NOUN
ejpam-1479	200	22	=	=	SYM
ejpam-1479	200	23	1,2	1,2	NUM
ejpam-1479	200	24	,	,	PUNCT
ejpam-1479	200	25	.	.	PUNCT
ejpam-1479	200	26	.	.	PUNCT
ejpam-1479	200	27	.	.	PUNCT
ejpam-1479	201	1	,	,	PUNCT
ejpam-1479	201	2	m.	m.	NOUN
ejpam-1479	201	3	also	also	ADV
ejpam-1479	201	4	,	,	PUNCT
ejpam-1479	201	5	by	by	ADP
ejpam-1479	201	6	taking	take	VERB
ejpam-1479	201	7	lim	lim	PROPN
ejpam-1479	201	8	supn	supn	NOUN
ejpam-1479	201	9	in	in	ADP
ejpam-1479	201	10	both	both	DET
ejpam-1479	201	11	sides	side	NOUN
ejpam-1479	201	12	of	of	ADP
ejpam-1479	201	13	(	(	PUNCT
ejpam-1479	201	14	5	5	NUM
ejpam-1479	201	15	)	)	PUNCT
ejpam-1479	201	16	,	,	PUNCT
ejpam-1479	201	17	we	we	PRON
ejpam-1479	201	18	obtain	obtain	VERB
ejpam-1479	201	19	that	that	SCONJ
ejpam-1479	201	20	lim	lim	PROPN
ejpam-1479	201	21	sup	sup	NOUN
ejpam-1479	201	22	n	n	PROPN
ejpam-1479	201	23	‖yn	‖yn	PROPN
ejpam-1479	201	24	−	−	PROPN
ejpam-1479	201	25	p‖	p‖	NOUN
ejpam-1479	201	26	≤	≤	PROPN
ejpam-1479	201	27	lim	lim	PROPN
ejpam-1479	201	28	sup	sup	PROPN
ejpam-1479	201	29	n	n	PROPN
ejpam-1479	201	30	‖xn−	‖xn−	PROPN
ejpam-1479	201	31	p‖	p‖	NOUN
ejpam-1479	201	32	=	=	PUNCT
ejpam-1479	201	33	a	a	PROPN
ejpam-1479	202	1	and	and	CCONJ
ejpam-1479	202	2	so	so	ADV
ejpam-1479	202	3	lim	lim	PROPN
ejpam-1479	202	4	sup	sup	PROPN
ejpam-1479	202	5	n	n	PROPN
ejpam-1479	202	6	‖t	‖t	NOUN
ejpam-1479	203	1	n	n	CCONJ
ejpam-1479	204	1	i	i	PRON
ejpam-1479	204	2	yn	yn	INTJ
ejpam-1479	204	3	−	−	PROPN
ejpam-1479	204	4	p‖	p‖	NOUN
ejpam-1479	204	5	≤	≤	PROPN
ejpam-1479	204	6	lim	lim	PROPN
ejpam-1479	204	7	sup	sup	PROPN
ejpam-1479	204	8	n	n	PROPN
ejpam-1479	204	9	(	(	PUNCT
ejpam-1479	204	10	(	(	PUNCT
ejpam-1479	204	11	1	1	NUM
ejpam-1479	204	12	+	+	NUM
ejpam-1479	204	13	rin)‖yn	rin)‖yn	ADJ
ejpam-1479	204	14	−	−	NOUN
ejpam-1479	204	15	p‖+	p‖+	NOUN
ejpam-1479	204	16	sin	sin	NOUN
ejpam-1479	204	17	)	)	PUNCT
ejpam-1479	204	18	≤	≤	NOUN
ejpam-1479	204	19	a	a	DET
ejpam-1479	204	20	(	(	PUNCT
ejpam-1479	204	21	11	11	NUM
ejpam-1479	204	22	)	)	PUNCT
ejpam-1479	204	23	h.	h.	NOUN
ejpam-1479	204	24	dehghan	dehghan	PROPN
ejpam-1479	204	25	,	,	PUNCT
ejpam-1479	204	26	a.	a.	NOUN
ejpam-1479	204	27	gharajelo	gharajelo	PROPN
ejpam-1479	204	28	/	/	SYM
ejpam-1479	204	29	eur	eur	PROPN
ejpam-1479	204	30	.	.	PUNCT
ejpam-1479	205	1	j.	j.	PROPN
ejpam-1479	205	2	pure	pure	PROPN
ejpam-1479	205	3	appl	appl	PROPN
ejpam-1479	205	4	.	.	PROPN
ejpam-1479	205	5	math	math	PROPN
ejpam-1479	205	6	,	,	PUNCT
ejpam-1479	205	7	5	5	NUM
ejpam-1479	205	8	(	(	PUNCT
ejpam-1479	205	9	2012	2012	NUM
ejpam-1479	205	10	)	)	PUNCT
ejpam-1479	205	11	,	,	PUNCT
ejpam-1479	205	12	45	45	NUM
ejpam-1479	205	13	-	-	SYM
ejpam-1479	205	14	54	54	NUM
ejpam-1479	205	15	51	51	NUM
ejpam-1479	205	16	for	for	ADP
ejpam-1479	205	17	all	all	DET
ejpam-1479	205	18	i	i	NOUN
ejpam-1479	205	19	=	=	SYM
ejpam-1479	205	20	1,2	1,2	NUM
ejpam-1479	205	21	,	,	PUNCT
ejpam-1479	205	22	.	.	PUNCT
ejpam-1479	205	23	.	.	PUNCT
ejpam-1479	205	24	.	.	PUNCT
ejpam-1479	206	1	,	,	PUNCT
ejpam-1479	206	2	m.	m.	NOUN
ejpam-1479	206	3	moreover	moreover	ADV
ejpam-1479	206	4	,	,	PUNCT
ejpam-1479	206	5	we	we	PRON
ejpam-1479	206	6	note	note	VERB
ejpam-1479	206	7	that	that	SCONJ
ejpam-1479	206	8	a	a	PRON
ejpam-1479	206	9	=	=	X
ejpam-1479	206	10	lim	lim	PROPN
ejpam-1479	206	11	n	n	PROPN
ejpam-1479	206	12	‖xn+1	‖xn+1	PROPN
ejpam-1479	206	13	−	−	PROPN
ejpam-1479	206	14	p‖	p‖	NOUN
ejpam-1479	207	1	=	=	PROPN
ejpam-1479	207	2	lim	lim	PROPN
ejpam-1479	207	3	n	n	PROPN
ejpam-1479	207	4	m	m	PROPN
ejpam-1479	207	5	∑	∑	PROPN
ejpam-1479	207	6	i=1	i=1	PROPN
ejpam-1479	207	7	�	�	PROPN
ejpam-1479	207	8	αint	αint	PROPN
ejpam-1479	208	1	n	n	CCONJ
ejpam-1479	208	2	i	i	PRON
ejpam-1479	208	3	yn	yn	INTJ
ejpam-1479	209	1	+	+	CCONJ
ejpam-1479	209	2	βint	βint	NOUN
ejpam-1479	209	3	n	n	INTJ
ejpam-1479	210	1	i	i	NOUN
ejpam-1479	210	2	xn	xn	PROPN
ejpam-1479	210	3	�	�	PROPN
ejpam-1479	210	4	+	+	NUM
ejpam-1479	210	5	γn	γn	ADP
ejpam-1479	210	6	xn−	xn−	PUNCT
ejpam-1479	210	7	p	p	X
ejpam-1479	211	1	=	=	PUNCT
ejpam-1479	211	2	lim	lim	PROPN
ejpam-1479	211	3	n	n	PROPN
ejpam-1479	211	4	m	m	PROPN
ejpam-1479	211	5	∑	∑	PROPN
ejpam-1479	211	6	i=1	i=1	PROPN
ejpam-1479	211	7	�	�	PROPN
ejpam-1479	211	8	αin(t	αin(t	PROPN
ejpam-1479	211	9	n	n	PROPN
ejpam-1479	211	10	i	i	NOUN
ejpam-1479	211	11	yn−	yn−	PROPN
ejpam-1479	212	1	p	p	X
ejpam-1479	212	2	)	)	PUNCT
ejpam-1479	213	1	+	+	CCONJ
ejpam-1479	213	2	βin(t	βin(t	PROPN
ejpam-1479	214	1	n	n	NOUN
ejpam-1479	215	1	i	i	PRON
ejpam-1479	215	2	xn−	xn−	PUNCT
ejpam-1479	216	1	p	p	X
ejpam-1479	216	2	)	)	PUNCT
ejpam-1479	216	3	�	�	PROPN
ejpam-1479	216	4	+	+	NUM
ejpam-1479	216	5	γn(xn−	γn(xn−	PROPN
ejpam-1479	216	6	p	p	NOUN
ejpam-1479	216	7	)	)	PUNCT
ejpam-1479	216	8	.	.	PUNCT
ejpam-1479	217	1	this	this	PRON
ejpam-1479	217	2	together	together	ADV
ejpam-1479	217	3	with	with	ADP
ejpam-1479	217	4	(	(	PUNCT
ejpam-1479	217	5	10	10	NUM
ejpam-1479	217	6	)	)	PUNCT
ejpam-1479	217	7	,	,	PUNCT
ejpam-1479	217	8	(	(	PUNCT
ejpam-1479	217	9	11	11	NUM
ejpam-1479	217	10	)	)	PUNCT
ejpam-1479	217	11	and	and	CCONJ
ejpam-1479	217	12	lemma	lemma	PROPN
ejpam-1479	217	13	2	2	NUM
ejpam-1479	217	14	implies	imply	VERB
ejpam-1479	217	15	that	that	SCONJ
ejpam-1479	217	16	the	the	DET
ejpam-1479	217	17	conclusions	conclusion	NOUN
ejpam-1479	217	18	(	(	PUNCT
ejpam-1479	217	19	i	i	NOUN
ejpam-1479	217	20	)	)	PUNCT
ejpam-1479	217	21	and	and	CCONJ
ejpam-1479	217	22	(	(	PUNCT
ejpam-1479	217	23	ii	ii	NOUN
ejpam-1479	217	24	)	)	PUNCT
ejpam-1479	217	25	of	of	ADP
ejpam-1479	217	26	lemma	lemma	PROPN
ejpam-1479	217	27	are	be	AUX
ejpam-1479	217	28	satisfied	satisfied	ADJ
ejpam-1479	217	29	.	.	PUNCT
ejpam-1479	218	1	next	next	ADV
ejpam-1479	218	2	,	,	PUNCT
ejpam-1479	218	3	we	we	PRON
ejpam-1479	218	4	shall	shall	AUX
ejpam-1479	218	5	prove	prove	VERB
ejpam-1479	218	6	(	(	PUNCT
ejpam-1479	218	7	iii	iii	NOUN
ejpam-1479	218	8	)	)	PUNCT
ejpam-1479	218	9	.	.	PUNCT
ejpam-1479	219	1	since	since	SCONJ
ejpam-1479	219	2	lim	lim	PROPN
ejpam-1479	219	3	infnα	infnα	PROPN
ejpam-1479	219	4	jn	jn	PROPN
ejpam-1479	219	5	>	>	X
ejpam-1479	219	6	0	0	PROPN
ejpam-1479	219	7	,	,	PUNCT
ejpam-1479	219	8	it	it	PRON
ejpam-1479	219	9	follows	follow	VERB
ejpam-1479	219	10	from	from	ADP
ejpam-1479	219	11	lemma	lemma	PROPN
ejpam-1479	219	12	3(iii	3(iii	NUM
ejpam-1479	219	13	)	)	PUNCT
ejpam-1479	219	14	that	that	SCONJ
ejpam-1479	219	15	limn	limn	PROPN
ejpam-1479	219	16	‖yn	‖yn	PROPN
ejpam-1479	219	17	−	−	PROPN
ejpam-1479	219	18	p‖	p‖	NOUN
ejpam-1479	220	1	=	=	NOUN
ejpam-1479	220	2	a.	a.	NOUN
ejpam-1479	220	3	therefore	therefore	ADV
ejpam-1479	220	4	,	,	PUNCT
ejpam-1479	220	5	a	a	DET
ejpam-1479	220	6	=	=	X
ejpam-1479	220	7	lim	lim	PROPN
ejpam-1479	220	8	n	n	PROPN
ejpam-1479	220	9	yn	yn	NOUN
ejpam-1479	220	10	−	−	PROPN
ejpam-1479	221	1	p	p	PROPN
ejpam-1479	221	2	=	=	PROPN
ejpam-1479	221	3	lim	lim	PROPN
ejpam-1479	221	4	n	n	PROPN
ejpam-1479	221	5	m	m	VERB
ejpam-1479	221	6	∑	∑	PROPN
ejpam-1479	221	7	i=1	i=1	PROPN
ejpam-1479	221	8	ai	be	VERB
ejpam-1479	221	9	nt	not	PART
ejpam-1479	221	10	n	n	ADV
ejpam-1479	222	1	i	i	PRON
ejpam-1479	222	2	xn+	xn+	PROPN
ejpam-1479	223	1	bn	bn	INTJ
ejpam-1479	223	2	xn−	xn−	PUNCT
ejpam-1479	224	1	p	p	X
ejpam-1479	224	2	=	=	PUNCT
ejpam-1479	224	3	lim	lim	PROPN
ejpam-1479	224	4	n	n	PROPN
ejpam-1479	224	5	m	m	VERB
ejpam-1479	224	6	∑	∑	PROPN
ejpam-1479	224	7	i=1	i=1	PROPN
ejpam-1479	224	8	ain(t	ain(t	PROPN
ejpam-1479	224	9	n	n	ADV
ejpam-1479	224	10	i	i	PRON
ejpam-1479	224	11	xn−	xn−	PUNCT
ejpam-1479	225	1	p	p	X
ejpam-1479	225	2	)	)	PUNCT
ejpam-1479	225	3	+	+	CCONJ
ejpam-1479	225	4	bn(xn−	bn(xn−	ADJ
ejpam-1479	225	5	p	p	X
ejpam-1479	225	6	)	)	PUNCT
ejpam-1479	225	7	.	.	PUNCT
ejpam-1479	226	1	this	this	PRON
ejpam-1479	226	2	together	together	ADV
ejpam-1479	226	3	with	with	ADP
ejpam-1479	226	4	(	(	PUNCT
ejpam-1479	226	5	10	10	NUM
ejpam-1479	226	6	)	)	PUNCT
ejpam-1479	226	7	and	and	CCONJ
ejpam-1479	226	8	lemma	lemma	PROPN
ejpam-1479	226	9	2	2	NUM
ejpam-1479	226	10	implies	imply	VERB
ejpam-1479	226	11	that	that	SCONJ
ejpam-1479	226	12	limn	limn	PROPN
ejpam-1479	226	13	‖t	‖t	PROPN
ejpam-1479	227	1	n	n	NOUN
ejpam-1479	228	1	i	i	PRON
ejpam-1479	228	2	xn−	xn−	PUNCT
ejpam-1479	228	3	xn‖=	xn‖=	PROPN
ejpam-1479	228	4	0	0	X
ejpam-1479	228	5	.	.	PUNCT
ejpam-1479	229	1	(	(	PUNCT
ejpam-1479	229	2	v	v	NOUN
ejpam-1479	229	3	)	)	PUNCT
ejpam-1479	229	4	using	use	VERB
ejpam-1479	229	5	(	(	PUNCT
ejpam-1479	229	6	1	1	NUM
ejpam-1479	229	7	)	)	PUNCT
ejpam-1479	229	8	,	,	PUNCT
ejpam-1479	229	9	we	we	PRON
ejpam-1479	229	10	have	have	VERB
ejpam-1479	229	11	‖yn	‖yn	NUM
ejpam-1479	229	12	−	−	NOUN
ejpam-1479	229	13	xn‖	xn‖	PROPN
ejpam-1479	229	14	≤	≤	NUM
ejpam-1479	229	15	m	m	VERB
ejpam-1479	229	16	∑	∑	PROPN
ejpam-1479	229	17	i=1	i=1	PROPN
ejpam-1479	229	18	ain‖t	ain‖t	PROPN
ejpam-1479	230	1	n	n	NOUN
ejpam-1479	231	1	i	i	PRON
ejpam-1479	231	2	xn−	xn−	PROPN
ejpam-1479	231	3	xn‖	xn‖	PROPN
ejpam-1479	231	4	→	→	SYM
ejpam-1479	231	5	0	0	NUM
ejpam-1479	231	6	,	,	PUNCT
ejpam-1479	231	7	‖t	‖t	NOUN
ejpam-1479	232	1	n	n	CCONJ
ejpam-1479	233	1	i	i	PRON
ejpam-1479	233	2	yn	yn	INTJ
ejpam-1479	234	1	−	−	NOUN
ejpam-1479	234	2	xn‖	xn‖	PROPN
ejpam-1479	234	3	≤	≤	NOUN
ejpam-1479	234	4	‖t	‖t	PROPN
ejpam-1479	235	1	n	n	INTJ
ejpam-1479	236	1	i	i	PRON
ejpam-1479	236	2	yn	yn	INTJ
ejpam-1479	236	3	−	−	PROPN
ejpam-1479	236	4	t	t	PROPN
ejpam-1479	237	1	n	n	INTJ
ejpam-1479	237	2	i	i	PRON
ejpam-1479	237	3	xn‖+	xn‖+	PROPN
ejpam-1479	237	4	‖t	‖t	PUNCT
ejpam-1479	238	1	n	n	CCONJ
ejpam-1479	239	1	i	i	PRON
ejpam-1479	239	2	xn−	xn−	PROPN
ejpam-1479	239	3	xn‖	xn‖	PROPN
ejpam-1479	239	4	≤	≤	PROPN
ejpam-1479	240	1	l‖yn	l‖yn	PROPN
ejpam-1479	240	2	−	−	PROPN
ejpam-1479	240	3	xn‖+	xn‖+	PROPN
ejpam-1479	240	4	‖t	‖t	PROPN
ejpam-1479	240	5	n	n	CCONJ
ejpam-1479	240	6	i	i	PRON
ejpam-1479	240	7	xn−	xn−	PROPN
ejpam-1479	240	8	xn‖	xn‖	PROPN
ejpam-1479	240	9	→	→	SYM
ejpam-1479	240	10	0	0	X
ejpam-1479	240	11	.	.	PUNCT
ejpam-1479	241	1	then	then	ADV
ejpam-1479	241	2	,	,	PUNCT
ejpam-1479	241	3	‖xn+1	‖xn+1	NUM
ejpam-1479	241	4	−	−	NOUN
ejpam-1479	241	5	xn‖	xn‖	PROPN
ejpam-1479	241	6	≤	≤	NUM
ejpam-1479	241	7	m	m	VERB
ejpam-1479	241	8	∑	∑	PROPN
ejpam-1479	241	9	i=1	i=1	PROPN
ejpam-1479	241	10	�	�	PROPN
ejpam-1479	241	11	αin‖t	αin‖t	NUM
ejpam-1479	241	12	n	n	CCONJ
ejpam-1479	242	1	i	i	PRON
ejpam-1479	242	2	yn	yn	PROPN
ejpam-1479	243	1	−	−	PROPN
ejpam-1479	243	2	xn‖+	xn‖+	PROPN
ejpam-1479	243	3	βin‖t	βin‖t	PROPN
ejpam-1479	244	1	n	n	NOUN
ejpam-1479	244	2	i	i	PRON
ejpam-1479	244	3	xn−	xn−	PROPN
ejpam-1479	244	4	xn‖	xn‖	PROPN
ejpam-1479	244	5	)	)	PUNCT
ejpam-1479	244	6	�	�	PROPN
ejpam-1479	244	7	→	→	SYM
ejpam-1479	244	8	0	0	NUM
ejpam-1479	244	9	.	.	PUNCT
ejpam-1479	245	1	(	(	PUNCT
ejpam-1479	245	2	12	12	NUM
ejpam-1479	245	3	)	)	PUNCT
ejpam-1479	245	4	for	for	ADP
ejpam-1479	245	5	each	each	PRON
ejpam-1479	245	6	i	i	NOUN
ejpam-1479	245	7	=	=	SYM
ejpam-1479	245	8	1,2	1,2	NUM
ejpam-1479	245	9	,	,	PUNCT
ejpam-1479	245	10	·	·	PUNCT
ejpam-1479	245	11	·	·	PUNCT
ejpam-1479	245	12	·	·	PUNCT
ejpam-1479	245	13	,	,	PUNCT
ejpam-1479	245	14	m	m	X
ejpam-1479	245	15	,	,	PUNCT
ejpam-1479	245	16	we	we	PRON
ejpam-1479	245	17	have	have	VERB
ejpam-1479	245	18	‖ti	‖ti	NUM
ejpam-1479	245	19	xn−	xn−	PUNCT
ejpam-1479	245	20	xn‖	xn‖	PROPN
ejpam-1479	245	21	≤	≤	X
ejpam-1479	246	1	‖ti	‖ti	NUM
ejpam-1479	246	2	xn−	xn−	PUNCT
ejpam-1479	246	3	t	t	PROPN
ejpam-1479	246	4	n+1	n+1	PROPN
ejpam-1479	247	1	i	i	PRON
ejpam-1479	247	2	xn‖+	xn‖+	PROPN
ejpam-1479	247	3	‖t	‖t	NOUN
ejpam-1479	247	4	n+1	n+1	PUNCT
ejpam-1479	248	1	i	i	PRON
ejpam-1479	248	2	xn−	xn−	PROPN
ejpam-1479	249	1	t	t	PROPN
ejpam-1479	249	2	n+1	n+1	PROPN
ejpam-1479	249	3	i	i	PRON
ejpam-1479	249	4	xn+1‖+	xn+1‖+	PUNCT
ejpam-1479	250	1	‖t	‖t	NOUN
ejpam-1479	250	2	n+1	n+1	PUNCT
ejpam-1479	251	1	i	i	PRON
ejpam-1479	251	2	xn+1	xn+1	VERB
ejpam-1479	251	3	−	−	PROPN
ejpam-1479	252	1	xn+1‖	xn+1‖	PROPN
ejpam-1479	252	2	+	+	PROPN
ejpam-1479	252	3	‖xn+1−	‖xn+1−	PROPN
ejpam-1479	252	4	xn‖	xn‖	PROPN
ejpam-1479	252	5	≤	≤	PROPN
ejpam-1479	252	6	l‖xn−	l‖xn−	VERB
ejpam-1479	252	7	t	t	PROPN
ejpam-1479	252	8	n	n	NOUN
ejpam-1479	252	9	i	i	PRON
ejpam-1479	252	10	xn‖+	xn‖+	PUNCT
ejpam-1479	253	1	l‖xn	l‖xn	PROPN
ejpam-1479	253	2	−	−	PROPN
ejpam-1479	253	3	xn+1‖+	xn+1‖+	PUNCT
ejpam-1479	254	1	‖t	‖t	PROPN
ejpam-1479	254	2	n+1	n+1	PUNCT
ejpam-1479	255	1	i	i	PRON
ejpam-1479	255	2	xn+1−	xn+1−	PROPN
ejpam-1479	256	1	xn+1‖	xn+1‖	PROPN
ejpam-1479	257	1	+	+	PROPN
ejpam-1479	257	2	‖xn+1−	‖xn+1−	PROPN
ejpam-1479	257	3	xn‖	xn‖	PROPN
ejpam-1479	257	4	which	which	DET
ejpam-1479	257	5	together	together	ADV
ejpam-1479	257	6	with	with	ADP
ejpam-1479	257	7	(	(	PUNCT
ejpam-1479	257	8	12	12	NUM
ejpam-1479	257	9	)	)	PUNCT
ejpam-1479	257	10	implies	imply	VERB
ejpam-1479	257	11	that	that	SCONJ
ejpam-1479	257	12	lim	lim	PROPN
ejpam-1479	257	13	n	n	PROPN
ejpam-1479	257	14	‖t1	‖t1	PROPN
ejpam-1479	257	15	xn−	xn−	PROPN
ejpam-1479	257	16	xn‖	xn‖	PROPN
ejpam-1479	258	1	=	=	PROPN
ejpam-1479	258	2	lim	lim	PROPN
ejpam-1479	258	3	n	n	PRON
ejpam-1479	258	4	‖t2	‖t2	PROPN
ejpam-1479	258	5	xn−	xn−	PROPN
ejpam-1479	258	6	xn‖	xn‖	PROPN
ejpam-1479	258	7	=	=	PUNCT
ejpam-1479	258	8	·	·	PUNCT
ejpam-1479	258	9	·	·	PUNCT
ejpam-1479	259	1	·	·	PUNCT
ejpam-1479	259	2	=	=	SYM
ejpam-1479	259	3	lim	lim	PROPN
ejpam-1479	259	4	n	n	PROPN
ejpam-1479	259	5	‖tm	‖tm	PROPN
ejpam-1479	259	6	xn−	xn−	PUNCT
ejpam-1479	259	7	xn‖=	xn‖=	PROPN
ejpam-1479	259	8	0	0	X
ejpam-1479	259	9	.	.	PUNCT
ejpam-1479	260	1	this	this	PRON
ejpam-1479	260	2	completes	complete	VERB
ejpam-1479	260	3	the	the	DET
ejpam-1479	260	4	proof	proof	NOUN
ejpam-1479	260	5	of	of	ADP
ejpam-1479	260	6	lemma	lemma	PROPN
ejpam-1479	260	7	.	.	PUNCT
ejpam-1479	261	1	h.	h.	PROPN
ejpam-1479	261	2	dehghan	dehghan	PROPN
ejpam-1479	261	3	,	,	PUNCT
ejpam-1479	261	4	a.	a.	NOUN
ejpam-1479	261	5	gharajelo	gharajelo	PROPN
ejpam-1479	261	6	/	/	SYM
ejpam-1479	261	7	eur	eur	PROPN
ejpam-1479	261	8	.	.	PUNCT
ejpam-1479	262	1	j.	j.	PROPN
ejpam-1479	262	2	pure	pure	PROPN
ejpam-1479	262	3	appl	appl	PROPN
ejpam-1479	262	4	.	.	PROPN
ejpam-1479	262	5	math	math	PROPN
ejpam-1479	262	6	,	,	PUNCT
ejpam-1479	262	7	5	5	NUM
ejpam-1479	262	8	(	(	PUNCT
ejpam-1479	262	9	2012	2012	NUM
ejpam-1479	262	10	)	)	PUNCT
ejpam-1479	262	11	,	,	PUNCT
ejpam-1479	262	12	45	45	NUM
ejpam-1479	262	13	-	-	SYM
ejpam-1479	262	14	54	54	NUM
ejpam-1479	262	15	52	52	NUM
ejpam-1479	262	16	lemma	lemma	PROPN
ejpam-1479	262	17	5	5	NUM
ejpam-1479	262	18	.	.	PUNCT
ejpam-1479	263	1	let	let	VERB
ejpam-1479	263	2	x	x	PRON
ejpam-1479	263	3	,	,	PUNCT
ejpam-1479	263	4	c	c	PROPN
ejpam-1479	263	5	and	and	CCONJ
ejpam-1479	263	6	t1	t1	PROPN
ejpam-1479	263	7	,	,	PUNCT
ejpam-1479	263	8	t2	t2	NOUN
ejpam-1479	263	9	,	,	PUNCT
ejpam-1479	263	10	.	.	PUNCT
ejpam-1479	263	11	.	.	PUNCT
ejpam-1479	264	1	.	.	PUNCT
ejpam-1479	265	1	,	,	PUNCT
ejpam-1479	265	2	tm	tm	NOUN
ejpam-1479	265	3	be	be	VERB
ejpam-1479	265	4	as	as	SCONJ
ejpam-1479	265	5	in	in	ADP
ejpam-1479	265	6	lemma	lemma	PROPN
ejpam-1479	265	7	4	4	NUM
ejpam-1479	265	8	and	and	CCONJ
ejpam-1479	265	9	{	{	PUNCT
ejpam-1479	265	10	xn	xn	NOUN
ejpam-1479	265	11	}	}	PUNCT
ejpam-1479	265	12	be	be	VERB
ejpam-1479	265	13	the	the	DET
ejpam-1479	265	14	sequence	sequence	NOUN
ejpam-1479	265	15	defined	define	VERB
ejpam-1479	265	16	by	by	ADP
ejpam-1479	265	17	(	(	PUNCT
ejpam-1479	265	18	1	1	X
ejpam-1479	265	19	)	)	PUNCT
ejpam-1479	265	20	such	such	ADJ
ejpam-1479	265	21	that	that	SCONJ
ejpam-1479	265	22	the	the	DET
ejpam-1479	265	23	parameters	parameter	NOUN
ejpam-1479	265	24	satisfy	satisfy	VERB
ejpam-1479	265	25	one	one	NUM
ejpam-1479	265	26	of	of	ADP
ejpam-1479	265	27	the	the	DET
ejpam-1479	265	28	following	follow	VERB
ejpam-1479	265	29	control	control	NOUN
ejpam-1479	265	30	conditions	condition	NOUN
ejpam-1479	265	31	:	:	PUNCT
ejpam-1479	265	32	(	(	PUNCT
ejpam-1479	265	33	c1	c1	NOUN
ejpam-1479	265	34	)	)	PUNCT
ejpam-1479	265	35	0	0	PUNCT
ejpam-1479	265	36	<	<	X
ejpam-1479	265	37	lim	lim	PROPN
ejpam-1479	265	38	infnαin	infnαin	VERB
ejpam-1479	265	39	≤	≤	NUM
ejpam-1479	265	40	lim	lim	PROPN
ejpam-1479	265	41	supn(1−	supn(1−	PROPN
ejpam-1479	265	42	γn	γn	PROPN
ejpam-1479	265	43	)	)	PUNCT
ejpam-1479	265	44	<	<	X
ejpam-1479	265	45	1	1	NUM
ejpam-1479	265	46	for	for	ADP
ejpam-1479	265	47	all	all	DET
ejpam-1479	265	48	i	i	NOUN
ejpam-1479	265	49	=	=	SYM
ejpam-1479	265	50	1,2	1,2	NUM
ejpam-1479	265	51	,	,	PUNCT
ejpam-1479	265	52	.	.	PUNCT
ejpam-1479	265	53	.	.	PUNCT
ejpam-1479	266	1	.	.	PUNCT
ejpam-1479	267	1	,	,	PUNCT
ejpam-1479	267	2	m	m	PROPN
ejpam-1479	267	3	and	and	CCONJ
ejpam-1479	267	4	lim	lim	PROPN
ejpam-1479	267	5	supn(1−	supn(1−	PROPN
ejpam-1479	267	6	bn)l	bn)l	PROPN
ejpam-1479	267	7	<	<	X
ejpam-1479	267	8	1	1	NUM
ejpam-1479	267	9	;	;	PUNCT
ejpam-1479	267	10	(	(	PUNCT
ejpam-1479	267	11	c2	c2	PROPN
ejpam-1479	267	12	)	)	PUNCT
ejpam-1479	267	13	0	0	NUM
ejpam-1479	267	14	<	<	X
ejpam-1479	267	15	lim	lim	PROPN
ejpam-1479	267	16	infnβin	infnβin	VERB
ejpam-1479	267	17	≤	≤	NUM
ejpam-1479	267	18	lim	lim	PROPN
ejpam-1479	267	19	supn(1−	supn(1−	PROPN
ejpam-1479	267	20	γn	γn	PROPN
ejpam-1479	267	21	)	)	PUNCT
ejpam-1479	267	22	<	<	X
ejpam-1479	267	23	1	1	NUM
ejpam-1479	267	24	for	for	ADP
ejpam-1479	267	25	all	all	DET
ejpam-1479	267	26	i	i	NOUN
ejpam-1479	267	27	=	=	SYM
ejpam-1479	267	28	1,2	1,2	NUM
ejpam-1479	267	29	,	,	PUNCT
ejpam-1479	267	30	.	.	PUNCT
ejpam-1479	267	31	.	.	PUNCT
ejpam-1479	268	1	.	.	PUNCT
ejpam-1479	269	1	,	,	PUNCT
ejpam-1479	269	2	m	m	PROPN
ejpam-1479	269	3	;	;	PUNCT
ejpam-1479	269	4	(	(	PUNCT
ejpam-1479	269	5	c3	c3	PROPN
ejpam-1479	269	6	)	)	PUNCT
ejpam-1479	270	1	lim	lim	PROPN
ejpam-1479	270	2	infnα	infnα	PROPN
ejpam-1479	270	3	jn	jn	PROPN
ejpam-1479	270	4	>	>	X
ejpam-1479	270	5	0	0	PUNCT
ejpam-1479	271	1	for	for	ADP
ejpam-1479	271	2	some	some	DET
ejpam-1479	271	3	j	j	PROPN
ejpam-1479	271	4	∈	∈	PROPN
ejpam-1479	271	5	{	{	PUNCT
ejpam-1479	271	6	1,2	1,2	NUM
ejpam-1479	271	7	,	,	PUNCT
ejpam-1479	271	8	.	.	PUNCT
ejpam-1479	271	9	.	.	PUNCT
ejpam-1479	271	10	.	.	PUNCT
ejpam-1479	272	1	,	,	PUNCT
ejpam-1479	272	2	m	m	VERB
ejpam-1479	272	3	}	}	PUNCT
ejpam-1479	272	4	and	and	CCONJ
ejpam-1479	272	5	0	0	NUM
ejpam-1479	272	6	<	<	X
ejpam-1479	272	7	lim	lim	PROPN
ejpam-1479	272	8	infn	infn	PROPN
ejpam-1479	272	9	ain	ain	PROPN
ejpam-1479	272	10	≤	≤	PROPN
ejpam-1479	272	11	lim	lim	PROPN
ejpam-1479	272	12	supn(1−	supn(1−	PROPN
ejpam-1479	272	13	bn	bn	PROPN
ejpam-1479	272	14	)	)	PUNCT
ejpam-1479	272	15	<	<	X
ejpam-1479	272	16	1	1	NUM
ejpam-1479	272	17	for	for	ADP
ejpam-1479	272	18	all	all	DET
ejpam-1479	272	19	i	i	NOUN
ejpam-1479	272	20	=	=	SYM
ejpam-1479	272	21	1,2	1,2	NUM
ejpam-1479	272	22	,	,	PUNCT
ejpam-1479	272	23	.	.	PUNCT
ejpam-1479	272	24	.	.	PUNCT
ejpam-1479	273	1	.	.	PUNCT
ejpam-1479	274	1	,	,	PUNCT
ejpam-1479	274	2	m.	m.	NOUN
ejpam-1479	274	3	then	then	ADV
ejpam-1479	274	4	limn	limn	PROPN
ejpam-1479	274	5	‖t	‖t	PROPN
ejpam-1479	275	1	n	n	CCONJ
ejpam-1479	276	1	i	i	PRON
ejpam-1479	276	2	xn−	xn−	PUNCT
ejpam-1479	276	3	xn‖=	xn‖=	PROPN
ejpam-1479	276	4	0	0	PUNCT
ejpam-1479	277	1	for	for	ADP
ejpam-1479	277	2	all	all	DET
ejpam-1479	277	3	i	i	NOUN
ejpam-1479	277	4	=	=	SYM
ejpam-1479	277	5	1,2	1,2	NUM
ejpam-1479	277	6	,	,	PUNCT
ejpam-1479	277	7	.	.	PUNCT
ejpam-1479	277	8	.	.	PUNCT
ejpam-1479	277	9	.	.	PUNCT
ejpam-1479	278	1	,	,	PUNCT
ejpam-1479	278	2	m	m	PROPN
ejpam-1479	278	3	,	,	PUNCT
ejpam-1479	278	4	and	and	CCONJ
ejpam-1479	278	5	so	so	ADV
ejpam-1479	278	6	by	by	ADP
ejpam-1479	278	7	lemma	lemma	PROPN
ejpam-1479	278	8	4(iv	4(iv	NUM
ejpam-1479	278	9	)	)	PUNCT
ejpam-1479	278	10	,	,	PUNCT
ejpam-1479	278	11	limn	limn	PROPN
ejpam-1479	279	1	‖ti	‖ti	NUM
ejpam-1479	279	2	xn−	xn−	PUNCT
ejpam-1479	279	3	xn‖	xn‖	PROPN
ejpam-1479	279	4	=	=	PUNCT
ejpam-1479	279	5	0	0	NUM
ejpam-1479	280	1	for	for	ADP
ejpam-1479	280	2	all	all	DET
ejpam-1479	280	3	i	i	NOUN
ejpam-1479	280	4	=	=	SYM
ejpam-1479	280	5	1,2	1,2	NUM
ejpam-1479	280	6	,	,	PUNCT
ejpam-1479	280	7	.	.	PUNCT
ejpam-1479	280	8	.	.	PUNCT
ejpam-1479	280	9	.	.	PUNCT
ejpam-1479	281	1	,	,	PUNCT
ejpam-1479	281	2	m.	m.	NOUN
ejpam-1479	281	3	proof	proof	NOUN
ejpam-1479	281	4	.	.	PUNCT
ejpam-1479	282	1	(	(	PUNCT
ejpam-1479	282	2	c1	c1	PROPN
ejpam-1479	282	3	)	)	PUNCT
ejpam-1479	282	4	it	it	PRON
ejpam-1479	282	5	follows	follow	VERB
ejpam-1479	282	6	from	from	ADP
ejpam-1479	282	7	lemma	lemma	PROPN
ejpam-1479	282	8	4(i	4(i	NUM
ejpam-1479	282	9	)	)	PUNCT
ejpam-1479	283	1	that	that	SCONJ
ejpam-1479	283	2	limn	limn	PROPN
ejpam-1479	283	3	‖t	‖t	PROPN
ejpam-1479	283	4	n	n	CCONJ
ejpam-1479	284	1	i	i	PRON
ejpam-1479	284	2	yn	yn	INTJ
ejpam-1479	284	3	−	−	NOUN
ejpam-1479	284	4	xn‖	xn‖	PROPN
ejpam-1479	285	1	=	=	SYM
ejpam-1479	285	2	0	0	NUM
ejpam-1479	285	3	for	for	ADP
ejpam-1479	285	4	all	all	DET
ejpam-1479	285	5	i	i	NOUN
ejpam-1479	285	6	=	=	SYM
ejpam-1479	285	7	1,2	1,2	NUM
ejpam-1479	285	8	,	,	PUNCT
ejpam-1479	285	9	.	.	PUNCT
ejpam-1479	285	10	.	.	PUNCT
ejpam-1479	285	11	.	.	PUNCT
ejpam-1479	286	1	,	,	PUNCT
ejpam-1479	286	2	m.	m.	NOUN
ejpam-1479	286	3	using	use	VERB
ejpam-1479	286	4	(	(	PUNCT
ejpam-1479	286	5	1	1	X
ejpam-1479	286	6	)	)	PUNCT
ejpam-1479	286	7	we	we	PRON
ejpam-1479	286	8	have	have	VERB
ejpam-1479	286	9	‖yn	‖yn	NUM
ejpam-1479	286	10	−	−	NOUN
ejpam-1479	287	1	xn‖	xn‖	PROPN
ejpam-1479	287	2	≤	≤	NUM
ejpam-1479	287	3	m	m	VERB
ejpam-1479	287	4	∑	∑	PROPN
ejpam-1479	287	5	i=1	i=1	PROPN
ejpam-1479	287	6	ain‖t	ain‖t	PROPN
ejpam-1479	288	1	n	n	NOUN
ejpam-1479	289	1	i	i	PRON
ejpam-1479	289	2	xn−	xn−	PROPN
ejpam-1479	289	3	xn‖	xn‖	PROPN
ejpam-1479	289	4	≤	≤	NUM
ejpam-1479	289	5	m	m	VERB
ejpam-1479	289	6	∑	∑	PROPN
ejpam-1479	289	7	i=1	i=1	PROPN
ejpam-1479	289	8	ain(‖t	ain(‖t	PROPN
ejpam-1479	290	1	n	n	NOUN
ejpam-1479	291	1	i	i	PRON
ejpam-1479	291	2	xn−	xn−	PROPN
ejpam-1479	292	1	t	t	PROPN
ejpam-1479	292	2	n	n	CCONJ
ejpam-1479	293	1	i	i	PROPN
ejpam-1479	293	2	yn‖+	yn‖+	PROPN
ejpam-1479	293	3	‖t	‖t	PROPN
ejpam-1479	293	4	n	n	CCONJ
ejpam-1479	293	5	i	i	PRON
ejpam-1479	293	6	yn	yn	INTJ
ejpam-1479	293	7	−	−	NOUN
ejpam-1479	293	8	xn‖	xn‖	PROPN
ejpam-1479	293	9	)	)	PUNCT
ejpam-1479	293	10	≤	≤	NUM
ejpam-1479	293	11	m	m	VERB
ejpam-1479	293	12	∑	∑	NOUN
ejpam-1479	293	13	i=1	i=1	PROPN
ejpam-1479	293	14	ain(l‖yn	ain(l‖yn	ADV
ejpam-1479	293	15	−	−	PROPN
ejpam-1479	293	16	xn‖+	xn‖+	PROPN
ejpam-1479	293	17	‖t	‖t	PROPN
ejpam-1479	294	1	n	n	CCONJ
ejpam-1479	294	2	i	i	PRON
ejpam-1479	294	3	yn	yn	INTJ
ejpam-1479	294	4	−	−	NOUN
ejpam-1479	294	5	xn‖	xn‖	PROPN
ejpam-1479	294	6	)	)	PUNCT
ejpam-1479	295	1	=	=	PUNCT
ejpam-1479	295	2	(	(	PUNCT
ejpam-1479	295	3	1−	1−	NUM
ejpam-1479	295	4	bn)l‖yn	bn)l‖yn	NOUN
ejpam-1479	296	1	−	−	PROPN
ejpam-1479	296	2	xn‖+	xn‖+	PROPN
ejpam-1479	296	3	m	m	PROPN
ejpam-1479	296	4	∑	∑	PROPN
ejpam-1479	296	5	i=1	i=1	PROPN
ejpam-1479	296	6	ain‖t	ain‖t	PROPN
ejpam-1479	296	7	n	n	NOUN
ejpam-1479	297	1	i	i	PRON
ejpam-1479	297	2	yn	yn	INTJ
ejpam-1479	297	3	−	−	NOUN
ejpam-1479	297	4	xn‖.	xn‖.	PROPN
ejpam-1479	297	5	thus	thus	ADV
ejpam-1479	297	6	,	,	PUNCT
ejpam-1479	297	7	limn(1−	limn(1−	PROPN
ejpam-1479	297	8	(	(	PUNCT
ejpam-1479	297	9	1−	1−	NUM
ejpam-1479	297	10	bn)l)‖yn	bn)l)‖yn	NOUN
ejpam-1479	297	11	−	−	PROPN
ejpam-1479	297	12	xn‖=	xn‖=	PROPN
ejpam-1479	297	13	0	0	PUNCT
ejpam-1479	297	14	.	.	PUNCT
ejpam-1479	298	1	since	since	SCONJ
ejpam-1479	298	2	lim	lim	PROPN
ejpam-1479	298	3	supn(1−	supn(1−	PROPN
ejpam-1479	298	4	bn)l	bn)l	PROPN
ejpam-1479	298	5	<	<	X
ejpam-1479	298	6	1	1	NUM
ejpam-1479	298	7	,	,	PUNCT
ejpam-1479	298	8	then	then	ADV
ejpam-1479	298	9	lim	lim	PROPN
ejpam-1479	298	10	n	n	PROPN
ejpam-1479	298	11	‖yn	‖yn	PROPN
ejpam-1479	298	12	−	−	NOUN
ejpam-1479	298	13	xn‖	xn‖	PROPN
ejpam-1479	298	14	=	=	SYM
ejpam-1479	298	15	0	0	PROPN
ejpam-1479	298	16	.	.	PUNCT
ejpam-1479	299	1	(	(	PUNCT
ejpam-1479	299	2	13	13	NUM
ejpam-1479	299	3	)	)	PUNCT
ejpam-1479	299	4	next	next	ADV
ejpam-1479	299	5	,	,	PUNCT
ejpam-1479	299	6	we	we	PRON
ejpam-1479	299	7	observe	observe	VERB
ejpam-1479	299	8	that	that	SCONJ
ejpam-1479	299	9	‖t	‖t	NOUN
ejpam-1479	299	10	n	n	NOUN
ejpam-1479	300	1	i	i	PRON
ejpam-1479	300	2	xn−	xn−	PROPN
ejpam-1479	300	3	xn‖	xn‖	PROPN
ejpam-1479	300	4	≤	≤	PROPN
ejpam-1479	300	5	‖t	‖t	PROPN
ejpam-1479	300	6	n	n	NOUN
ejpam-1479	301	1	i	i	PRON
ejpam-1479	301	2	xn−	xn−	PROPN
ejpam-1479	302	1	t	t	PROPN
ejpam-1479	302	2	n	n	CCONJ
ejpam-1479	303	1	i	i	PROPN
ejpam-1479	303	2	yn‖+	yn‖+	PROPN
ejpam-1479	303	3	‖t	‖t	PROPN
ejpam-1479	303	4	n	n	CCONJ
ejpam-1479	303	5	i	i	PRON
ejpam-1479	303	6	yn	yn	INTJ
ejpam-1479	303	7	−	−	NOUN
ejpam-1479	303	8	xn‖	xn‖	PROPN
ejpam-1479	303	9	≤	≤	PROPN
ejpam-1479	304	1	l‖yn	l‖yn	PROPN
ejpam-1479	304	2	−	−	PROPN
ejpam-1479	304	3	xn‖+	xn‖+	PROPN
ejpam-1479	304	4	‖t	‖t	PROPN
ejpam-1479	305	1	n	n	INTJ
ejpam-1479	306	1	i	i	PRON
ejpam-1479	306	2	yn	yn	INTJ
ejpam-1479	306	3	−	−	VERB
ejpam-1479	306	4	xn‖.	xn‖.	PROPN
ejpam-1479	306	5	this	this	PRON
ejpam-1479	306	6	together	together	ADV
ejpam-1479	306	7	with	with	ADP
ejpam-1479	306	8	(	(	PUNCT
ejpam-1479	306	9	13	13	NUM
ejpam-1479	306	10	)	)	PUNCT
ejpam-1479	306	11	implies	imply	VERB
ejpam-1479	306	12	that	that	SCONJ
ejpam-1479	306	13	limn	limn	PROPN
ejpam-1479	306	14	‖t	‖t	PROPN
ejpam-1479	306	15	n	n	NOUN
ejpam-1479	306	16	i	i	PRON
ejpam-1479	306	17	xn−xn‖=	xn−xn‖=	PROPN
ejpam-1479	306	18	0	0	PUNCT
ejpam-1479	307	1	for	for	ADP
ejpam-1479	307	2	all	all	DET
ejpam-1479	307	3	i	i	NOUN
ejpam-1479	307	4	=	=	SYM
ejpam-1479	307	5	1,2	1,2	NUM
ejpam-1479	307	6	,	,	PUNCT
ejpam-1479	307	7	.	.	PUNCT
ejpam-1479	307	8	.	.	PUNCT
ejpam-1479	307	9	.	.	PUNCT
ejpam-1479	308	1	,	,	PUNCT
ejpam-1479	308	2	m.	m.	NOUN
ejpam-1479	308	3	this	this	PRON
ejpam-1479	308	4	completes	complete	VERB
ejpam-1479	308	5	the	the	DET
ejpam-1479	308	6	proof	proof	NOUN
ejpam-1479	308	7	of	of	ADP
ejpam-1479	308	8	(	(	PUNCT
ejpam-1479	308	9	c1	c1	PROPN
ejpam-1479	308	10	)	)	PUNCT
ejpam-1479	308	11	.	.	PUNCT
ejpam-1479	309	1	(	(	PUNCT
ejpam-1479	309	2	c2	c2	PROPN
ejpam-1479	309	3	)	)	PUNCT
ejpam-1479	309	4	and	and	CCONJ
ejpam-1479	309	5	(	(	PUNCT
ejpam-1479	309	6	c3	c3	PROPN
ejpam-1479	309	7	)	)	PUNCT
ejpam-1479	309	8	follow	follow	VERB
ejpam-1479	309	9	from	from	ADP
ejpam-1479	309	10	(	(	PUNCT
ejpam-1479	309	11	ii	ii	NOUN
ejpam-1479	309	12	)	)	PUNCT
ejpam-1479	309	13	and	and	CCONJ
ejpam-1479	309	14	(	(	PUNCT
ejpam-1479	309	15	iii	iii	NOUN
ejpam-1479	309	16	)	)	PUNCT
ejpam-1479	309	17	of	of	ADP
ejpam-1479	309	18	lemma	lemma	PROPN
ejpam-1479	309	19	4	4	NUM
ejpam-1479	309	20	,	,	PUNCT
ejpam-1479	309	21	respectively	respectively	ADV
ejpam-1479	309	22	.	.	PUNCT
ejpam-1479	310	1	now	now	ADV
ejpam-1479	310	2	,	,	PUNCT
ejpam-1479	310	3	we	we	PRON
ejpam-1479	310	4	state	state	VERB
ejpam-1479	310	5	and	and	CCONJ
ejpam-1479	310	6	prove	prove	VERB
ejpam-1479	310	7	the	the	DET
ejpam-1479	310	8	weak	weak	ADJ
ejpam-1479	310	9	and	and	CCONJ
ejpam-1479	310	10	strong	strong	ADJ
ejpam-1479	310	11	convergence	convergence	NOUN
ejpam-1479	310	12	theorems	theorem	NOUN
ejpam-1479	310	13	of	of	ADP
ejpam-1479	310	14	(	(	PUNCT
ejpam-1479	310	15	1	1	NUM
ejpam-1479	310	16	)	)	PUNCT
ejpam-1479	310	17	.	.	PUNCT
ejpam-1479	311	1	theorem	theorem	NOUN
ejpam-1479	311	2	2	2	NUM
ejpam-1479	311	3	.	.	PUNCT
ejpam-1479	312	1	let	let	VERB
ejpam-1479	312	2	x	x	PRON
ejpam-1479	312	3	,	,	PUNCT
ejpam-1479	312	4	c	c	X
ejpam-1479	312	5	,	,	PUNCT
ejpam-1479	312	6	t1	t1	NOUN
ejpam-1479	312	7	,	,	PUNCT
ejpam-1479	312	8	.	.	PUNCT
ejpam-1479	312	9	.	.	PUNCT
ejpam-1479	313	1	.	.	PUNCT
ejpam-1479	314	1	,	,	PUNCT
ejpam-1479	314	2	tm	tm	NOUN
ejpam-1479	314	3	and	and	CCONJ
ejpam-1479	314	4	{	{	PUNCT
ejpam-1479	314	5	xn	xn	NOUN
ejpam-1479	314	6	}	}	PUNCT
ejpam-1479	314	7	be	be	VERB
ejpam-1479	314	8	as	as	ADP
ejpam-1479	314	9	in	in	ADP
ejpam-1479	314	10	lemma	lemma	PROPN
ejpam-1479	314	11	5	5	NUM
ejpam-1479	314	12	.	.	PUNCT
ejpam-1479	315	1	then	then	ADV
ejpam-1479	315	2	we	we	PRON
ejpam-1479	315	3	have	have	VERB
ejpam-1479	315	4	the	the	DET
ejpam-1479	315	5	followings	following	NOUN
ejpam-1479	315	6	.	.	PUNCT
ejpam-1479	316	1	(	(	PUNCT
ejpam-1479	316	2	i	i	NOUN
ejpam-1479	316	3	)	)	PUNCT
ejpam-1479	316	4	if	if	SCONJ
ejpam-1479	316	5	{	{	PUNCT
ejpam-1479	316	6	ti	ti	X
ejpam-1479	316	7	:	:	PUNCT
ejpam-1479	316	8	i	i	NOUN
ejpam-1479	316	9	=	=	SYM
ejpam-1479	316	10	1,2	1,2	NUM
ejpam-1479	316	11	,	,	PUNCT
ejpam-1479	316	12	.	.	PUNCT
ejpam-1479	316	13	.	.	PUNCT
ejpam-1479	316	14	.	.	PUNCT
ejpam-1479	317	1	,	,	PUNCT
ejpam-1479	317	2	m	m	VERB
ejpam-1479	317	3	}	}	PUNCT
ejpam-1479	317	4	satisfies	satisfy	VERB
ejpam-1479	317	5	condition	condition	NOUN
ejpam-1479	317	6	(	(	PUNCT
ejpam-1479	317	7	a′′	a′′	NOUN
ejpam-1479	317	8	)	)	PUNCT
ejpam-1479	317	9	,	,	PUNCT
ejpam-1479	317	10	then	then	ADV
ejpam-1479	317	11	{	{	PUNCT
ejpam-1479	317	12	xn	xn	X
ejpam-1479	317	13	}	}	PUNCT
ejpam-1479	317	14	converges	converge	VERB
ejpam-1479	317	15	strongly	strongly	ADV
ejpam-1479	317	16	to	to	ADP
ejpam-1479	317	17	a	a	DET
ejpam-1479	317	18	common	common	ADJ
ejpam-1479	317	19	fixed	fix	VERB
ejpam-1479	317	20	point	point	NOUN
ejpam-1479	317	21	of	of	ADP
ejpam-1479	317	22	the	the	DET
ejpam-1479	317	23	family	family	NOUN
ejpam-1479	317	24	.	.	PUNCT
ejpam-1479	318	1	(	(	PUNCT
ejpam-1479	318	2	ii	ii	NOUN
ejpam-1479	318	3	)	)	PUNCT
ejpam-1479	318	4	if	if	SCONJ
ejpam-1479	318	5	x	x	PRON
ejpam-1479	318	6	satisfies	satisfy	VERB
ejpam-1479	318	7	opial	opial	NOUN
ejpam-1479	318	8	’s	’s	PART
ejpam-1479	318	9	condition	condition	NOUN
ejpam-1479	319	1	and	and	CCONJ
ejpam-1479	319	2	i	i	PRON
ejpam-1479	319	3	−	−	VERB
ejpam-1479	319	4	ti	ti	NOUN
ejpam-1479	319	5	is	be	AUX
ejpam-1479	319	6	demiclosed	demiclose	VERB
ejpam-1479	319	7	at	at	ADP
ejpam-1479	319	8	0	0	NUM
ejpam-1479	319	9	for	for	ADP
ejpam-1479	319	10	all	all	DET
ejpam-1479	319	11	i	i	NOUN
ejpam-1479	319	12	=	=	SYM
ejpam-1479	319	13	1,2	1,2	NUM
ejpam-1479	319	14	,	,	PUNCT
ejpam-1479	319	15	.	.	PUNCT
ejpam-1479	319	16	.	.	PUNCT
ejpam-1479	320	1	.	.	PUNCT
ejpam-1479	321	1	,	,	PUNCT
ejpam-1479	321	2	m	m	PROPN
ejpam-1479	321	3	,	,	PUNCT
ejpam-1479	321	4	then	then	ADV
ejpam-1479	321	5	{	{	PUNCT
ejpam-1479	321	6	xn	xn	X
ejpam-1479	321	7	}	}	PUNCT
ejpam-1479	321	8	converges	converge	VERB
ejpam-1479	321	9	weakly	weakly	ADV
ejpam-1479	321	10	to	to	ADP
ejpam-1479	321	11	a	a	DET
ejpam-1479	321	12	common	common	ADJ
ejpam-1479	321	13	fixed	fix	VERB
ejpam-1479	321	14	point	point	NOUN
ejpam-1479	321	15	of	of	ADP
ejpam-1479	321	16	the	the	DET
ejpam-1479	321	17	family	family	NOUN
ejpam-1479	321	18	.	.	PUNCT
ejpam-1479	322	1	references	reference	NOUN
ejpam-1479	322	2	53	53	NUM
ejpam-1479	322	3	proof	proof	NOUN
ejpam-1479	322	4	.	.	PUNCT
ejpam-1479	323	1	(	(	PUNCT
ejpam-1479	323	2	i	i	NOUN
ejpam-1479	323	3	)	)	PUNCT
ejpam-1479	323	4	it	it	PRON
ejpam-1479	323	5	follows	follow	VERB
ejpam-1479	323	6	from	from	ADP
ejpam-1479	323	7	lemma	lemma	PROPN
ejpam-1479	323	8	5	5	NUM
ejpam-1479	323	9	that	that	SCONJ
ejpam-1479	323	10	limn	limn	NOUN
ejpam-1479	323	11	‖xn	‖xn	PROPN
ejpam-1479	323	12	−	−	PROPN
ejpam-1479	323	13	ti	ti	NOUN
ejpam-1479	323	14	xn‖	xn‖	PROPN
ejpam-1479	323	15	=	=	SYM
ejpam-1479	323	16	0	0	NUM
ejpam-1479	324	1	for	for	ADP
ejpam-1479	324	2	all	all	DET
ejpam-1479	324	3	i	i	NOUN
ejpam-1479	324	4	=	=	SYM
ejpam-1479	324	5	1,2	1,2	NUM
ejpam-1479	324	6	,	,	PUNCT
ejpam-1479	324	7	.	.	PUNCT
ejpam-1479	324	8	.	.	PUNCT
ejpam-1479	324	9	.	.	PUNCT
ejpam-1479	325	1	,	,	PUNCT
ejpam-1479	325	2	m.	m.	NOUN
ejpam-1479	325	3	therefore	therefore	ADV
ejpam-1479	325	4	,	,	PUNCT
ejpam-1479	325	5	by	by	ADP
ejpam-1479	325	6	using	use	VERB
ejpam-1479	325	7	condition	condition	NOUN
ejpam-1479	325	8	(	(	PUNCT
ejpam-1479	325	9	a′′	a′′	NOUN
ejpam-1479	325	10	)	)	PUNCT
ejpam-1479	325	11	,	,	PUNCT
ejpam-1479	325	12	there	there	PRON
ejpam-1479	325	13	exists	exist	VERB
ejpam-1479	325	14	a	a	DET
ejpam-1479	325	15	nondecreasing	nondecrease	VERB
ejpam-1479	325	16	function	function	NOUN
ejpam-1479	325	17	f	f	NOUN
ejpam-1479	325	18	:	:	PUNCT
ejpam-1479	326	1	[	[	X
ejpam-1479	326	2	0,∞)→	0,∞)→	NOUN
ejpam-1479	326	3	[	[	X
ejpam-1479	326	4	0,∞	0,∞	NOUN
ejpam-1479	326	5	)	)	PUNCT
ejpam-1479	326	6	with	with	ADP
ejpam-1479	326	7	f	f	PROPN
ejpam-1479	326	8	(	(	PUNCT
ejpam-1479	326	9	0	0	NUM
ejpam-1479	326	10	)	)	PUNCT
ejpam-1479	326	11	=	=	SYM
ejpam-1479	326	12	0	0	NUM
ejpam-1479	326	13	and	and	CCONJ
ejpam-1479	326	14	f	f	PROPN
ejpam-1479	326	15	(	(	PUNCT
ejpam-1479	326	16	r	r	NOUN
ejpam-1479	326	17	)	)	PUNCT
ejpam-1479	326	18	>	>	X
ejpam-1479	326	19	0	0	PUNCT
ejpam-1479	326	20	for	for	ADP
ejpam-1479	326	21	all	all	DET
ejpam-1479	326	22	r	r	NOUN
ejpam-1479	326	23	∈	∈	PROPN
ejpam-1479	326	24	(	(	PUNCT
ejpam-1479	326	25	0,∞	0,∞	NOUN
ejpam-1479	326	26	)	)	PUNCT
ejpam-1479	326	27	such	such	ADJ
ejpam-1479	326	28	that	that	SCONJ
ejpam-1479	326	29	lim	lim	PROPN
ejpam-1479	326	30	n	n	PROPN
ejpam-1479	326	31	f	f	PROPN
ejpam-1479	326	32	(	(	PUNCT
ejpam-1479	326	33	d(xn	d(xn	PROPN
ejpam-1479	326	34	,	,	PUNCT
ejpam-1479	326	35	f	f	NOUN
ejpam-1479	326	36	)	)	PUNCT
ejpam-1479	326	37	)	)	PUNCT
ejpam-1479	326	38	≤	≤	NOUN
ejpam-1479	327	1	lim	lim	PROPN
ejpam-1479	327	2	n	n	PROPN
ejpam-1479	327	3	‖xn−	‖xn−	PROPN
ejpam-1479	327	4	ti	ti	X
ejpam-1479	327	5	xn‖	xn‖	PROPN
ejpam-1479	327	6	=	=	SYM
ejpam-1479	327	7	0	0	NUM
ejpam-1479	327	8	for	for	ADP
ejpam-1479	327	9	some	some	DET
ejpam-1479	327	10	i	i	NOUN
ejpam-1479	327	11	=	=	NOUN
ejpam-1479	327	12	1,2	1,2	NUM
ejpam-1479	327	13	,	,	PUNCT
ejpam-1479	327	14	.	.	PUNCT
ejpam-1479	327	15	.	.	PUNCT
ejpam-1479	327	16	.	.	PUNCT
ejpam-1479	328	1	,	,	PUNCT
ejpam-1479	328	2	m.	m.	NOUN
ejpam-1479	328	3	that	that	PRON
ejpam-1479	328	4	is	be	AUX
ejpam-1479	328	5	limn	limn	PROPN
ejpam-1479	328	6	d(xn	d(xn	PROPN
ejpam-1479	328	7	,	,	PUNCT
ejpam-1479	328	8	f	f	X
ejpam-1479	328	9	)	)	PUNCT
ejpam-1479	329	1	=	=	SYM
ejpam-1479	329	2	0	0	X
ejpam-1479	329	3	.	.	PUNCT
ejpam-1479	329	4	by	by	ADP
ejpam-1479	329	5	theorem	theorem	NOUN
ejpam-1479	329	6	1	1	NUM
ejpam-1479	329	7	,	,	PUNCT
ejpam-1479	329	8	we	we	PRON
ejpam-1479	329	9	conclude	conclude	VERB
ejpam-1479	329	10	that	that	SCONJ
ejpam-1479	329	11	{	{	PUNCT
ejpam-1479	329	12	xn	xn	X
ejpam-1479	329	13	}	}	PUNCT
ejpam-1479	329	14	converges	converge	VERB
ejpam-1479	329	15	strongly	strongly	ADV
ejpam-1479	329	16	to	to	ADP
ejpam-1479	329	17	a	a	DET
ejpam-1479	329	18	point	point	NOUN
ejpam-1479	330	1	p	p	X
ejpam-1479	330	2	∈	∈	PROPN
ejpam-1479	330	3	f	f	X
ejpam-1479	330	4	.	.	PUNCT
ejpam-1479	331	1	(	(	PUNCT
ejpam-1479	331	2	ii	ii	NOUN
ejpam-1479	331	3	)	)	PUNCT
ejpam-1479	331	4	let	let	VERB
ejpam-1479	331	5	p	p	PROPN
ejpam-1479	331	6	∈	∈	PROPN
ejpam-1479	331	7	f	f	X
ejpam-1479	331	8	.	.	PUNCT
ejpam-1479	332	1	it	it	PRON
ejpam-1479	332	2	follows	follow	VERB
ejpam-1479	332	3	from	from	ADP
ejpam-1479	332	4	lemma	lemma	PROPN
ejpam-1479	332	5	3	3	NUM
ejpam-1479	332	6	that	that	SCONJ
ejpam-1479	332	7	limn	limn	PROPN
ejpam-1479	332	8	‖xn	‖xn	PROPN
ejpam-1479	332	9	−	−	PROPN
ejpam-1479	332	10	p‖	p‖	NOUN
ejpam-1479	332	11	exists	exist	VERB
ejpam-1479	332	12	and	and	CCONJ
ejpam-1479	332	13	hence	hence	ADV
ejpam-1479	332	14	{	{	PUNCT
ejpam-1479	332	15	xn	xn	X
ejpam-1479	332	16	}	}	PUNCT
ejpam-1479	332	17	is	be	AUX
ejpam-1479	332	18	bounded	bound	VERB
ejpam-1479	332	19	.	.	PUNCT
ejpam-1479	333	1	since	since	SCONJ
ejpam-1479	333	2	x	x	PRON
ejpam-1479	333	3	is	be	AUX
ejpam-1479	333	4	uniformly	uniformly	ADV
ejpam-1479	333	5	convex	convex	NOUN
ejpam-1479	333	6	,	,	PUNCT
ejpam-1479	333	7	there	there	PRON
ejpam-1479	333	8	exists	exist	VERB
ejpam-1479	333	9	a	a	DET
ejpam-1479	333	10	subsequence	subsequence	NOUN
ejpam-1479	333	11	{	{	PUNCT
ejpam-1479	333	12	xnk	xnk	PROPN
ejpam-1479	333	13	}	}	PUNCT
ejpam-1479	333	14	of	of	ADP
ejpam-1479	333	15	{	{	PUNCT
ejpam-1479	333	16	xn	xn	NOUN
ejpam-1479	333	17	}	}	PUNCT
ejpam-1479	333	18	converging	converge	VERB
ejpam-1479	333	19	weakly	weakly	ADV
ejpam-1479	333	20	to	to	ADP
ejpam-1479	333	21	some	some	DET
ejpam-1479	333	22	u	u	NOUN
ejpam-1479	333	23	∈	∈	PROPN
ejpam-1479	333	24	c	c	NOUN
ejpam-1479	333	25	.	.	PUNCT
ejpam-1479	334	1	by	by	ADP
ejpam-1479	334	2	lemma	lemma	PROPN
ejpam-1479	334	3	4	4	NUM
ejpam-1479	334	4	,	,	PUNCT
ejpam-1479	334	5	limn	limn	NOUN
ejpam-1479	334	6	‖xn−	‖xn−	PROPN
ejpam-1479	334	7	ti	ti	NOUN
ejpam-1479	334	8	xn‖=	xn‖=	PROPN
ejpam-1479	334	9	0	0	PUNCT
ejpam-1479	335	1	for	for	ADP
ejpam-1479	335	2	all	all	DET
ejpam-1479	335	3	i	i	NOUN
ejpam-1479	335	4	=	=	SYM
ejpam-1479	335	5	1,2	1,2	NUM
ejpam-1479	335	6	,	,	PUNCT
ejpam-1479	335	7	.	.	PUNCT
ejpam-1479	335	8	.	.	PUNCT
ejpam-1479	335	9	.	.	PUNCT
ejpam-1479	336	1	,	,	PUNCT
ejpam-1479	336	2	m.	m.	NOUN
ejpam-1479	336	3	since	since	SCONJ
ejpam-1479	336	4	i	i	PRON
ejpam-1479	336	5	−	−	VERB
ejpam-1479	336	6	ti	ti	NOUN
ejpam-1479	336	7	is	be	AUX
ejpam-1479	336	8	demiclosed	demiclose	VERB
ejpam-1479	336	9	for	for	ADP
ejpam-1479	336	10	all	all	DET
ejpam-1479	336	11	i	i	PRON
ejpam-1479	336	12	=	=	SYM
ejpam-1479	336	13	1,2	1,2	NUM
ejpam-1479	336	14	,	,	PUNCT
ejpam-1479	336	15	.	.	PUNCT
ejpam-1479	336	16	.	.	PUNCT
ejpam-1479	337	1	.	.	PUNCT
ejpam-1479	338	1	,	,	PUNCT
ejpam-1479	338	2	m	m	X
ejpam-1479	338	3	,	,	PUNCT
ejpam-1479	338	4	we	we	PRON
ejpam-1479	338	5	obtain	obtain	VERB
ejpam-1479	338	6	u	u	NOUN
ejpam-1479	338	7	∈	∈	PROPN
ejpam-1479	338	8	f	f	X
ejpam-1479	338	9	.	.	PUNCT
ejpam-1479	339	1	suppose	suppose	VERB
ejpam-1479	339	2	that	that	SCONJ
ejpam-1479	339	3	subsequences	subsequence	VERB
ejpam-1479	339	4	{	{	PUNCT
ejpam-1479	339	5	xnk	xnk	PROPN
ejpam-1479	339	6	}	}	PUNCT
ejpam-1479	339	7	and	and	CCONJ
ejpam-1479	339	8	{	{	PUNCT
ejpam-1479	339	9	xnl	xnl	NOUN
ejpam-1479	339	10	}	}	PUNCT
ejpam-1479	339	11	of	of	ADP
ejpam-1479	339	12	{	{	PUNCT
ejpam-1479	339	13	xn	xn	NOUN
ejpam-1479	339	14	}	}	PUNCT
ejpam-1479	339	15	converge	converge	VERB
ejpam-1479	339	16	weakly	weakly	ADV
ejpam-1479	339	17	to	to	ADP
ejpam-1479	339	18	u	u	NOUN
ejpam-1479	339	19	and	and	CCONJ
ejpam-1479	339	20	v	v	NOUN
ejpam-1479	339	21	,	,	PUNCT
ejpam-1479	339	22	respectively	respectively	ADV
ejpam-1479	339	23	.	.	PUNCT
ejpam-1479	340	1	as	as	SCONJ
ejpam-1479	340	2	proved	prove	VERB
ejpam-1479	340	3	above	above	ADP
ejpam-1479	340	4	u	u	NOUN
ejpam-1479	340	5	,	,	PUNCT
ejpam-1479	340	6	v	v	PROPN
ejpam-1479	340	7	∈	∈	PROPN
ejpam-1479	340	8	f	f	X
ejpam-1479	340	9	.	.	PUNCT
ejpam-1479	341	1	again	again	ADV
ejpam-1479	341	2	by	by	ADP
ejpam-1479	341	3	lemma	lemma	PROPN
ejpam-1479	341	4	3	3	NUM
ejpam-1479	341	5	,	,	PUNCT
ejpam-1479	341	6	limn	limn	PROPN
ejpam-1479	341	7	‖xn−	‖xn−	PROPN
ejpam-1479	341	8	u‖	u‖	ADJ
ejpam-1479	341	9	and	and	CCONJ
ejpam-1479	341	10	limn	limn	PROPN
ejpam-1479	341	11	‖xn	‖xn	PROPN
ejpam-1479	341	12	−	−	PROPN
ejpam-1479	341	13	v‖	v‖	NOUN
ejpam-1479	341	14	exist	exist	VERB
ejpam-1479	341	15	.	.	PUNCT
ejpam-1479	342	1	assume	assume	VERB
ejpam-1479	342	2	that	that	SCONJ
ejpam-1479	342	3	u	u	PROPN
ejpam-1479	342	4	6=	6=	PROPN
ejpam-1479	342	5	v.	v.	CCONJ
ejpam-1479	342	6	then	then	ADV
ejpam-1479	342	7	by	by	ADP
ejpam-1479	342	8	the	the	DET
ejpam-1479	342	9	opial	opial	ADJ
ejpam-1479	342	10	property	property	NOUN
ejpam-1479	342	11	lim	lim	PROPN
ejpam-1479	342	12	n	n	PROPN
ejpam-1479	342	13	‖xn−	‖xn−	PROPN
ejpam-1479	342	14	u‖	u‖	PROPN
ejpam-1479	342	15	=	=	PROPN
ejpam-1479	342	16	lim	lim	PROPN
ejpam-1479	342	17	k	k	PROPN
ejpam-1479	342	18	‖xnk	‖xnk	PROPN
ejpam-1479	343	1	−	−	PROPN
ejpam-1479	343	2	u‖	u‖	PROPN
ejpam-1479	343	3	<	<	X
ejpam-1479	343	4	lim	lim	PROPN
ejpam-1479	343	5	k	k	PROPN
ejpam-1479	343	6	‖xnk	‖xnk	PROPN
ejpam-1479	343	7	−	−	PROPN
ejpam-1479	344	1	v‖=	v‖=	ADV
ejpam-1479	344	2	lim	lim	PROPN
ejpam-1479	344	3	n	n	PROPN
ejpam-1479	344	4	‖xn	‖xn	PROPN
ejpam-1479	344	5	−	−	PROPN
ejpam-1479	344	6	v‖	v‖	NOUN
ejpam-1479	345	1	=	=	PUNCT
ejpam-1479	345	2	lim	lim	PROPN
ejpam-1479	345	3	l	l	PROPN
ejpam-1479	345	4	‖xnl	‖xnl	PROPN
ejpam-1479	346	1	−	−	PROPN
ejpam-1479	346	2	v‖	v‖	PROPN
ejpam-1479	346	3	<	<	X
ejpam-1479	346	4	lim	lim	PROPN
ejpam-1479	346	5	l	l	PROPN
ejpam-1479	346	6	‖xnl	‖xnl	PROPN
ejpam-1479	347	1	−	−	NOUN
ejpam-1479	347	2	u‖	u‖	NOUN
ejpam-1479	347	3	=	=	PROPN
ejpam-1479	347	4	lim	lim	PROPN
ejpam-1479	347	5	n	n	PROPN
ejpam-1479	347	6	‖xn	‖xn	PROPN
ejpam-1479	347	7	−	−	PROPN
ejpam-1479	347	8	u‖	u‖	NOUN
ejpam-1479	347	9	this	this	DET
ejpam-1479	347	10	contradiction	contradiction	NOUN
ejpam-1479	347	11	proves	prove	VERB
ejpam-1479	347	12	that	that	SCONJ
ejpam-1479	347	13	{	{	PUNCT
ejpam-1479	347	14	xn	xn	X
ejpam-1479	347	15	}	}	PUNCT
ejpam-1479	347	16	converges	converge	VERB
ejpam-1479	347	17	weakly	weakly	ADV
ejpam-1479	347	18	to	to	ADP
ejpam-1479	347	19	a	a	DET
ejpam-1479	347	20	common	common	ADJ
ejpam-1479	347	21	fixed	fix	VERB
ejpam-1479	347	22	point	point	NOUN
ejpam-1479	347	23	of	of	ADP
ejpam-1479	347	24	the	the	DET
ejpam-1479	347	25	family	family	NOUN
ejpam-1479	347	26	{	{	PUNCT
ejpam-1479	347	27	ti	ti	NOUN
ejpam-1479	347	28	:	:	PUNCT
ejpam-1479	348	1	i	i	NOUN
ejpam-1479	348	2	=	=	SYM
ejpam-1479	348	3	1,2	1,2	NUM
ejpam-1479	348	4	,	,	PUNCT
ejpam-1479	348	5	.	.	PUNCT
ejpam-1479	348	6	.	.	PUNCT
ejpam-1479	348	7	.	.	PUNCT
ejpam-1479	349	1	,	,	PUNCT
ejpam-1479	349	2	m	m	VERB
ejpam-1479	349	3	}	}	PUNCT
ejpam-1479	349	4	and	and	CCONJ
ejpam-1479	349	5	the	the	DET
ejpam-1479	349	6	proof	proof	NOUN
ejpam-1479	349	7	is	be	AUX
ejpam-1479	349	8	completed	complete	VERB
ejpam-1479	349	9	.	.	PUNCT
ejpam-1479	350	1	remark	remark	NOUN
ejpam-1479	350	2	1	1	NUM
ejpam-1479	350	3	.	.	PUNCT
ejpam-1479	351	1	if	if	SCONJ
ejpam-1479	351	2	t1	t1	NOUN
ejpam-1479	351	3	=	=	SYM
ejpam-1479	351	4	t2	t2	PROPN
ejpam-1479	351	5	=	=	SYM
ejpam-1479	351	6	·	·	PUNCT
ejpam-1479	351	7	·	·	PUNCT
ejpam-1479	351	8	·	·	PUNCT
ejpam-1479	352	1	=	=	SYM
ejpam-1479	352	2	tm	tm	NOUN
ejpam-1479	352	3	in	in	ADP
ejpam-1479	352	4	theorem	theorem	NOUN
ejpam-1479	352	5	2	2	NUM
ejpam-1479	352	6	we	we	PRON
ejpam-1479	352	7	obtain	obtain	VERB
ejpam-1479	352	8	weak	weak	ADJ
ejpam-1479	352	9	and	and	CCONJ
ejpam-1479	352	10	strong	strong	ADJ
ejpam-1479	352	11	convergence	convergence	NOUN
ejpam-1479	352	12	of	of	ADP
ejpam-1479	352	13	the	the	DET
ejpam-1479	352	14	modified	modify	VERB
ejpam-1479	352	15	mann	mann	PROPN
ejpam-1479	352	16	iteration	iteration	NOUN
ejpam-1479	352	17	(	(	PUNCT
ejpam-1479	352	18	4	4	NUM
ejpam-1479	352	19	)	)	PUNCT
ejpam-1479	352	20	and	and	CCONJ
ejpam-1479	352	21	the	the	DET
ejpam-1479	352	22	modified	modify	VERB
ejpam-1479	352	23	ishikawa	ishikawa	PROPN
ejpam-1479	352	24	iteration	iteration	NOUN
ejpam-1479	352	25	.	.	PUNCT
ejpam-1479	353	1	references	reference	NOUN
ejpam-1479	353	2	[	[	X
ejpam-1479	353	3	1	1	NUM
ejpam-1479	353	4	]	]	X
ejpam-1479	353	5	s	s	PART
ejpam-1479	353	6	c	c	NOUN
ejpam-1479	353	7	bose	bose	NOUN
ejpam-1479	353	8	.	.	PUNCT
ejpam-1479	354	1	weak	weak	ADJ
ejpam-1479	354	2	convergence	convergence	NOUN
ejpam-1479	354	3	to	to	ADP
ejpam-1479	354	4	the	the	DET
ejpam-1479	354	5	fixed	fix	VERB
ejpam-1479	354	6	point	point	NOUN
ejpam-1479	354	7	of	of	ADP
ejpam-1479	354	8	an	an	DET
ejpam-1479	354	9	asymptotically	asymptotically	ADV
ejpam-1479	354	10	nonexpansive	nonexpansive	ADJ
ejpam-1479	354	11	map	map	NOUN
ejpam-1479	354	12	.	.	PUNCT
ejpam-1479	355	1	proc	proc	PROPN
ejpam-1479	355	2	.	.	PUNCT
ejpam-1479	356	1	amer	amer	PROPN
ejpam-1479	356	2	.	.	PUNCT
ejpam-1479	356	3	math	math	PROPN
ejpam-1479	356	4	.	.	PUNCT
ejpam-1479	357	1	soc	soc	PROPN
ejpam-1479	357	2	.	.	PUNCT
ejpam-1479	357	3	,	,	PUNCT
ejpam-1479	358	1	68:305–308	68:305–308	NUM
ejpam-1479	358	2	,	,	PUNCT
ejpam-1479	358	3	1978	1978	NUM
ejpam-1479	358	4	.	.	PUNCT
ejpam-1479	359	1	[	[	X
ejpam-1479	359	2	2	2	NUM
ejpam-1479	359	3	]	]	PUNCT
ejpam-1479	359	4	h	h	NOUN
ejpam-1479	359	5	dehghan	dehghan	PROPN
ejpam-1479	359	6	.	.	PUNCT
ejpam-1479	360	1	an	an	DET
ejpam-1479	360	2	ishikawa	ishikawa	NOUN
ejpam-1479	360	3	-	-	PUNCT
ejpam-1479	360	4	type	type	NOUN
ejpam-1479	360	5	iterative	iterative	NOUN
ejpam-1479	360	6	scheme	scheme	NOUN
ejpam-1479	360	7	for	for	ADP
ejpam-1479	360	8	a	a	DET
ejpam-1479	360	9	finite	finite	ADJ
ejpam-1479	360	10	family	family	NOUN
ejpam-1479	360	11	of	of	ADP
ejpam-1479	360	12	asymptotically	asymptotically	ADV
ejpam-1479	360	13	nonexpansive	nonexpansive	ADJ
ejpam-1479	360	14	mappings	mapping	NOUN
ejpam-1479	360	15	.	.	PUNCT
ejpam-1479	361	1	jp	jp	PROPN
ejpam-1479	361	2	jour	jour	X
ejpam-1479	361	3	.	.	PUNCT
ejpam-1479	362	1	fixed	fix	VERB
ejpam-1479	362	2	point	point	NOUN
ejpam-1479	362	3	theory	theory	NOUN
ejpam-1479	362	4	appl	appl	PROPN
ejpam-1479	362	5	.	.	PROPN
ejpam-1479	362	6	,	,	PUNCT
ejpam-1479	363	1	5:171–181	5:171–181	NUM
ejpam-1479	363	2	,	,	PUNCT
ejpam-1479	363	3	2010	2010	NUM
ejpam-1479	363	4	.	.	PUNCT
ejpam-1479	364	1	[	[	X
ejpam-1479	364	2	3	3	X
ejpam-1479	364	3	]	]	PUNCT
ejpam-1479	364	4	a	a	DET
ejpam-1479	364	5	kettapun	kettapun	NOUN
ejpam-1479	364	6	,	,	PUNCT
ejpam-1479	364	7	a	a	DET
ejpam-1479	364	8	kananthai	kananthai	NOUN
ejpam-1479	364	9	,	,	PUNCT
ejpam-1479	364	10	and	and	CCONJ
ejpam-1479	364	11	s	s	AUX
ejpam-1479	364	12	suantai	suantai	VERB
ejpam-1479	364	13	.	.	PUNCT
ejpam-1479	365	1	a	a	DET
ejpam-1479	365	2	new	new	ADJ
ejpam-1479	365	3	approximation	approximation	NOUN
ejpam-1479	365	4	method	method	NOUN
ejpam-1479	365	5	for	for	ADP
ejpam-1479	365	6	common	common	ADJ
ejpam-1479	365	7	fixed	fix	VERB
ejpam-1479	365	8	points	point	NOUN
ejpam-1479	365	9	of	of	ADP
ejpam-1479	365	10	a	a	DET
ejpam-1479	365	11	finite	finite	ADJ
ejpam-1479	365	12	family	family	NOUN
ejpam-1479	365	13	of	of	ADP
ejpam-1479	365	14	asymptotically	asymptotically	ADV
ejpam-1479	365	15	quasi	quasi	ADJ
ejpam-1479	365	16	-	-	ADJ
ejpam-1479	365	17	nonexpansive	nonexpansive	ADJ
ejpam-1479	365	18	mappings	mapping	NOUN
ejpam-1479	365	19	in	in	ADP
ejpam-1479	365	20	banach	banach	NOUN
ejpam-1479	365	21	spaces	space	NOUN
ejpam-1479	365	22	.	.	PUNCT
ejpam-1479	366	1	comput	comput	NOUN
ejpam-1479	366	2	.	.	PUNCT
ejpam-1479	367	1	math	math	NOUN
ejpam-1479	367	2	.	.	PUNCT
ejpam-1479	368	1	appl	appl	PROPN
ejpam-1479	368	2	.	.	PROPN
ejpam-1479	368	3	,	,	PUNCT
ejpam-1479	368	4	60:1430–1439	60:1430–1439	NUM
ejpam-1479	368	5	,	,	PUNCT
ejpam-1479	368	6	2010	2010	NUM
ejpam-1479	368	7	.	.	PUNCT
ejpam-1479	369	1	[	[	X
ejpam-1479	369	2	4	4	NUM
ejpam-1479	369	3	]	]	X
ejpam-1479	369	4	s	s	PART
ejpam-1479	369	5	khan	khan	PROPN
ejpam-1479	369	6	and	and	CCONJ
ejpam-1479	369	7	w	w	PROPN
ejpam-1479	369	8	takahasi	takahasi	PROPN
ejpam-1479	369	9	.	.	PUNCT
ejpam-1479	370	1	approximating	approximate	VERB
ejpam-1479	370	2	common	common	ADJ
ejpam-1479	370	3	fixed	fix	VERB
ejpam-1479	370	4	points	point	NOUN
ejpam-1479	370	5	of	of	ADP
ejpam-1479	370	6	two	two	NUM
ejpam-1479	370	7	asymptotically	asymptotically	ADV
ejpam-1479	370	8	nonexpanisve	nonexpanisve	ADJ
ejpam-1479	370	9	mappings	mapping	NOUN
ejpam-1479	370	10	.	.	PUNCT
ejpam-1479	371	1	sci	sci	PROPN
ejpam-1479	371	2	.	.	PROPN
ejpam-1479	371	3	math	math	PROPN
ejpam-1479	371	4	.	.	PUNCT
ejpam-1479	372	1	jpn	jpn	PROPN
ejpam-1479	372	2	.	.	PROPN
ejpam-1479	372	3	,	,	PUNCT
ejpam-1479	372	4	53:143–148	53:143–148	PROPN
ejpam-1479	372	5	,	,	PUNCT
ejpam-1479	372	6	2001	2001	NUM
ejpam-1479	372	7	.	.	PUNCT
ejpam-1479	373	1	[	[	X
ejpam-1479	373	2	5	5	NUM
ejpam-1479	373	3	]	]	PUNCT
ejpam-1479	373	4	w	w	NOUN
ejpam-1479	373	5	nilsrakoo	nilsrakoo	NOUN
ejpam-1479	373	6	and	and	CCONJ
ejpam-1479	373	7	s	s	VERB
ejpam-1479	373	8	saejung	saejung	PROPN
ejpam-1479	373	9	.	.	PUNCT
ejpam-1479	374	1	a	a	DET
ejpam-1479	374	2	new	new	ADJ
ejpam-1479	374	3	three	three	NUM
ejpam-1479	374	4	-	-	PUNCT
ejpam-1479	374	5	step	step	NOUN
ejpam-1479	374	6	fixed	fix	VERB
ejpam-1479	374	7	point	point	NOUN
ejpam-1479	374	8	iteration	iteration	NOUN
ejpam-1479	374	9	scheme	scheme	NOUN
ejpam-1479	374	10	for	for	ADP
ejpam-1479	374	11	asymptotically	asymptotically	ADV
ejpam-1479	374	12	nonexpansive	nonexpansive	ADJ
ejpam-1479	374	13	mappings	mapping	NOUN
ejpam-1479	374	14	.	.	PUNCT
ejpam-1479	375	1	appl	appl	PROPN
ejpam-1479	375	2	.	.	PROPN
ejpam-1479	375	3	math	math	PROPN
ejpam-1479	375	4	.	.	PUNCT
ejpam-1479	376	1	comput	comput	NOUN
ejpam-1479	376	2	.	.	PUNCT
ejpam-1479	376	3	,	,	PUNCT
ejpam-1479	376	4	181:1472–1478	181:1472–1478	NUM
ejpam-1479	376	5	,	,	PUNCT
ejpam-1479	376	6	2006	2006	NUM
ejpam-1479	376	7	.	.	PUNCT
ejpam-1479	377	1	[	[	X
ejpam-1479	377	2	6	6	NUM
ejpam-1479	377	3	]	]	PUNCT
ejpam-1479	377	4	z	z	NOUN
ejpam-1479	377	5	opial	opial	NOUN
ejpam-1479	377	6	.	.	PUNCT
ejpam-1479	378	1	weak	weak	ADJ
ejpam-1479	378	2	convergence	convergence	NOUN
ejpam-1479	378	3	of	of	ADP
ejpam-1479	378	4	successive	successive	ADJ
ejpam-1479	378	5	approximations	approximation	NOUN
ejpam-1479	378	6	for	for	ADP
ejpam-1479	378	7	nonexpansive	nonexpansive	ADJ
ejpam-1479	378	8	mappings	mapping	NOUN
ejpam-1479	378	9	.	.	PUNCT
ejpam-1479	379	1	bull	bull	NOUN
ejpam-1479	379	2	.	.	PUNCT
ejpam-1479	380	1	amer	amer	PROPN
ejpam-1479	380	2	.	.	PUNCT
ejpam-1479	380	3	math	math	PROPN
ejpam-1479	380	4	.	.	PUNCT
ejpam-1479	381	1	soc	soc	PROPN
ejpam-1479	381	2	.	.	PUNCT
ejpam-1479	381	3	,	,	PUNCT
ejpam-1479	382	1	73:591–597	73:591–597	NOUN
ejpam-1479	382	2	,	,	PUNCT
ejpam-1479	382	3	1967	1967	NUM
ejpam-1479	382	4	.	.	PUNCT
ejpam-1479	383	1	references	reference	NOUN
ejpam-1479	383	2	54	54	NUM
ejpam-1479	384	1	[	[	X
ejpam-1479	384	2	7	7	NUM
ejpam-1479	384	3	]	]	PUNCT
ejpam-1479	384	4	n	n	CCONJ
ejpam-1479	384	5	shahzad	shahzad	PROPN
ejpam-1479	384	6	and	and	CCONJ
ejpam-1479	384	7	h	h	PROPN
ejpam-1479	384	8	zegeye	zegeye	NOUN
ejpam-1479	384	9	.	.	PUNCT
ejpam-1479	385	1	strong	strong	ADJ
ejpam-1479	385	2	convergence	convergence	NOUN
ejpam-1479	385	3	of	of	ADP
ejpam-1479	385	4	an	an	DET
ejpam-1479	385	5	implicit	implicit	ADJ
ejpam-1479	385	6	iteration	iteration	NOUN
ejpam-1479	385	7	process	process	NOUN
ejpam-1479	385	8	for	for	ADP
ejpam-1479	385	9	a	a	DET
ejpam-1479	385	10	finite	finite	ADJ
ejpam-1479	385	11	family	family	NOUN
ejpam-1479	385	12	of	of	ADP
ejpam-1479	385	13	asymptotically	asymptotically	ADV
ejpam-1479	385	14	nonexpansive	nonexpansive	ADJ
ejpam-1479	385	15	maps	map	NOUN
ejpam-1479	385	16	.	.	PUNCT
ejpam-1479	386	1	appl	appl	PROPN
ejpam-1479	386	2	.	.	PROPN
ejpam-1479	386	3	math	math	PROPN
ejpam-1479	386	4	.	.	PUNCT
ejpam-1479	387	1	and	and	CCONJ
ejpam-1479	387	2	comput	comput	NOUN
ejpam-1479	387	3	.	.	PUNCT
ejpam-1479	387	4	,	,	PUNCT
ejpam-1479	387	5	189:1058–1065	189:1058–1065	NUM
ejpam-1479	387	6	,	,	PUNCT
ejpam-1479	387	7	2007	2007	NUM
ejpam-1479	387	8	.	.	PUNCT
ejpam-1479	388	1	[	[	X
ejpam-1479	388	2	8	8	NUM
ejpam-1479	388	3	]	]	X
ejpam-1479	388	4	s	s	AUX
ejpam-1479	388	5	suantai	suantai	VERB
ejpam-1479	388	6	.	.	PUNCT
ejpam-1479	389	1	weak	weak	ADJ
ejpam-1479	389	2	and	and	CCONJ
ejpam-1479	389	3	strong	strong	ADJ
ejpam-1479	389	4	convergence	convergence	NOUN
ejpam-1479	389	5	criteria	criterion	NOUN
ejpam-1479	389	6	of	of	ADP
ejpam-1479	389	7	noor	noor	PROPN
ejpam-1479	389	8	iterations	iteration	NOUN
ejpam-1479	389	9	for	for	ADP
ejpam-1479	389	10	asymptotically	asymptotically	ADV
ejpam-1479	389	11	nonexpansive	nonexpansive	ADJ
ejpam-1479	389	12	mappings	mapping	NOUN
ejpam-1479	389	13	.	.	PUNCT
ejpam-1479	390	1	j.	j.	PROPN
ejpam-1479	390	2	math	math	PROPN
ejpam-1479	390	3	.	.	PUNCT
ejpam-1479	391	1	anal	anal	PROPN
ejpam-1479	391	2	.	.	PUNCT
ejpam-1479	392	1	appl	appl	PROPN
ejpam-1479	392	2	.	.	PROPN
ejpam-1479	392	3	,	,	PUNCT
ejpam-1479	393	1	311:506–517	311:506–517	PROPN
ejpam-1479	393	2	,	,	PUNCT
ejpam-1479	393	3	2005	2005	NUM
ejpam-1479	393	4	.	.	PUNCT
ejpam-1479	394	1	[	[	X
ejpam-1479	394	2	9	9	NUM
ejpam-1479	394	3	]	]	SYM
ejpam-1479	394	4	k	k	PROPN
ejpam-1479	394	5	tan	tan	PROPN
ejpam-1479	394	6	and	and	CCONJ
ejpam-1479	394	7	h	h	PROPN
ejpam-1479	394	8	xu	xu	PROPN
ejpam-1479	394	9	.	.	PUNCT
ejpam-1479	395	1	approximating	approximate	VERB
ejpam-1479	395	2	fixed	fix	VERB
ejpam-1479	395	3	points	point	NOUN
ejpam-1479	395	4	of	of	ADP
ejpam-1479	395	5	nonexpansive	nonexpansive	ADJ
ejpam-1479	395	6	mappings	mapping	NOUN
ejpam-1479	395	7	by	by	ADP
ejpam-1479	395	8	the	the	DET
ejpam-1479	395	9	ishikawa	ishikawa	PROPN
ejpam-1479	395	10	iteration	iteration	NOUN
ejpam-1479	395	11	process	process	NOUN
ejpam-1479	395	12	.	.	PUNCT
ejpam-1479	396	1	j.	j.	PROPN
ejpam-1479	396	2	math	math	PROPN
ejpam-1479	396	3	.	.	PUNCT
ejpam-1479	397	1	anal	anal	PROPN
ejpam-1479	397	2	.	.	PUNCT
ejpam-1479	398	1	appl	appl	PROPN
ejpam-1479	398	2	.	.	PROPN
ejpam-1479	398	3	,	,	PUNCT
ejpam-1479	398	4	178:301–308	178:301–308	NUM
ejpam-1479	398	5	,	,	PUNCT
ejpam-1479	398	6	1993	1993	NUM
ejpam-1479	398	7	.	.	PUNCT
ejpam-1479	399	1	[	[	X
ejpam-1479	399	2	10	10	NUM
ejpam-1479	399	3	]	]	X
ejpam-1479	399	4	b	b	X
ejpam-1479	399	5	xu	xu	PROPN
ejpam-1479	399	6	and	and	CCONJ
ejpam-1479	399	7	m	m	PROPN
ejpam-1479	399	8	noor	noor	PROPN
ejpam-1479	399	9	.	.	PUNCT
ejpam-1479	400	1	fixed	fix	VERB
ejpam-1479	400	2	point	point	NOUN
ejpam-1479	400	3	iterations	iteration	NOUN
ejpam-1479	400	4	for	for	ADP
ejpam-1479	400	5	asymptotically	asymptotically	ADV
ejpam-1479	400	6	nonexpansive	nonexpansive	ADJ
ejpam-1479	400	7	mappings	mapping	NOUN
ejpam-1479	400	8	in	in	ADP
ejpam-1479	400	9	banach	banach	NOUN
ejpam-1479	400	10	spaces	space	NOUN
ejpam-1479	400	11	.	.	PUNCT
ejpam-1479	401	1	j.	j.	PROPN
ejpam-1479	401	2	math	math	PROPN
ejpam-1479	401	3	.	.	PUNCT
ejpam-1479	402	1	anal	anal	PROPN
ejpam-1479	402	2	.	.	PUNCT
ejpam-1479	402	3	appl	appl	PROPN
ejpam-1479	402	4	.	.	PROPN
ejpam-1479	402	5	,	,	PUNCT
ejpam-1479	402	6	267:444–453	267:444–453	NUM
ejpam-1479	402	7	,	,	PUNCT
ejpam-1479	402	8	2002	2002	NUM
ejpam-1479	402	9	.	.	PUNCT