id	sid	tid	token	lemma	pos
ejpam-4005	1	1	european	european	PROPN
ejpam-4005	1	2	journal	journal	PROPN
ejpam-4005	1	3	of	of	ADP
ejpam-4005	1	4	pure	pure	ADJ
ejpam-4005	1	5	and	and	CCONJ
ejpam-4005	1	6	applied	apply	VERB
ejpam-4005	1	7	mathematics	mathematic	NOUN
ejpam-4005	1	8	vol	vol	NOUN
ejpam-4005	1	9	.	.	PUNCT
ejpam-4005	2	1	14	14	NUM
ejpam-4005	2	2	,	,	PUNCT
ejpam-4005	2	3	no	no	INTJ
ejpam-4005	2	4	.	.	NOUN
ejpam-4005	2	5	3	3	NUM
ejpam-4005	2	6	,	,	PUNCT
ejpam-4005	2	7	2021	2021	NUM
ejpam-4005	2	8	,	,	PUNCT
ejpam-4005	2	9	650	650	NUM
ejpam-4005	2	10	-	-	SYM
ejpam-4005	2	11	665	665	NUM
ejpam-4005	2	12	issn	issn	PROPN
ejpam-4005	2	13	1307	1307	NUM
ejpam-4005	2	14	-	-	SYM
ejpam-4005	2	15	5543	5543	NUM
ejpam-4005	2	16	–	–	PUNCT
ejpam-4005	2	17	ejpam.com	ejpam.com	X
ejpam-4005	2	18	published	publish	VERB
ejpam-4005	2	19	by	by	ADP
ejpam-4005	2	20	new	new	PROPN
ejpam-4005	2	21	york	york	PROPN
ejpam-4005	2	22	business	business	PROPN
ejpam-4005	2	23	global	global	ADJ
ejpam-4005	2	24	mixed	mixed	ADJ
ejpam-4005	2	25	type	type	NOUN
ejpam-4005	2	26	algorithms	algorithm	NOUN
ejpam-4005	2	27	for	for	ADP
ejpam-4005	2	28	asymptotically	asymptotically	ADV
ejpam-4005	2	29	nonexpansive	nonexpansive	ADJ
ejpam-4005	2	30	mappings	mapping	NOUN
ejpam-4005	2	31	in	in	ADP
ejpam-4005	2	32	hyperbolic	hyperbolic	ADJ
ejpam-4005	2	33	spaces	space	NOUN
ejpam-4005	2	34	tanakit	tanakit	PROPN
ejpam-4005	2	35	thianwan	thianwan	PROPN
ejpam-4005	2	36	department	department	PROPN
ejpam-4005	2	37	of	of	ADP
ejpam-4005	2	38	mathematics	mathematics	PROPN
ejpam-4005	2	39	,	,	PUNCT
ejpam-4005	2	40	school	school	NOUN
ejpam-4005	2	41	of	of	ADP
ejpam-4005	2	42	science	science	NOUN
ejpam-4005	2	43	,	,	PUNCT
ejpam-4005	2	44	university	university	NOUN
ejpam-4005	2	45	of	of	ADP
ejpam-4005	2	46	phayao	phayao	NOUN
ejpam-4005	2	47	,	,	PUNCT
ejpam-4005	2	48	phayao	phayao	NOUN
ejpam-4005	2	49	,	,	PUNCT
ejpam-4005	2	50	56000	56000	NUM
ejpam-4005	2	51	,	,	PUNCT
ejpam-4005	2	52	thailand	thailand	PROPN
ejpam-4005	2	53	abstract	abstract	NOUN
ejpam-4005	2	54	.	.	PUNCT
ejpam-4005	3	1	in	in	ADP
ejpam-4005	3	2	this	this	DET
ejpam-4005	3	3	paper	paper	NOUN
ejpam-4005	3	4	,	,	PUNCT
ejpam-4005	3	5	a	a	DET
ejpam-4005	3	6	new	new	ADJ
ejpam-4005	3	7	mixed	mixed	ADJ
ejpam-4005	3	8	type	type	NOUN
ejpam-4005	3	9	iteration	iteration	NOUN
ejpam-4005	3	10	process	process	NOUN
ejpam-4005	3	11	for	for	ADP
ejpam-4005	3	12	approximating	approximate	VERB
ejpam-4005	3	13	a	a	DET
ejpam-4005	3	14	common	common	ADJ
ejpam-4005	3	15	fixed	fix	VERB
ejpam-4005	3	16	point	point	NOUN
ejpam-4005	3	17	of	of	ADP
ejpam-4005	3	18	two	two	NUM
ejpam-4005	3	19	asymptotically	asymptotically	ADV
ejpam-4005	3	20	nonexpansive	nonexpansive	ADJ
ejpam-4005	3	21	self	self	NOUN
ejpam-4005	3	22	-	-	PUNCT
ejpam-4005	3	23	mappings	mapping	NOUN
ejpam-4005	3	24	and	and	CCONJ
ejpam-4005	3	25	two	two	NUM
ejpam-4005	3	26	asymptotically	asymptotically	ADV
ejpam-4005	3	27	nonexpansive	nonexpansive	ADJ
ejpam-4005	3	28	nonself	nonself	NOUN
ejpam-4005	3	29	-	-	PUNCT
ejpam-4005	3	30	mappings	mapping	NOUN
ejpam-4005	3	31	is	be	AUX
ejpam-4005	3	32	constructed	construct	VERB
ejpam-4005	3	33	.	.	PUNCT
ejpam-4005	4	1	we	we	PRON
ejpam-4005	4	2	then	then	ADV
ejpam-4005	4	3	establish	establish	VERB
ejpam-4005	4	4	a	a	DET
ejpam-4005	4	5	strong	strong	ADJ
ejpam-4005	4	6	convergence	convergence	NOUN
ejpam-4005	4	7	theorem	theorem	VERB
ejpam-4005	4	8	under	under	ADP
ejpam-4005	4	9	mild	mild	ADJ
ejpam-4005	4	10	conditions	condition	NOUN
ejpam-4005	4	11	in	in	ADP
ejpam-4005	4	12	a	a	DET
ejpam-4005	4	13	uniformly	uniformly	ADV
ejpam-4005	4	14	convex	convex	ADJ
ejpam-4005	4	15	hyperbolic	hyperbolic	ADJ
ejpam-4005	4	16	space	space	NOUN
ejpam-4005	4	17	.	.	PUNCT
ejpam-4005	5	1	the	the	DET
ejpam-4005	5	2	results	result	NOUN
ejpam-4005	5	3	presented	present	VERB
ejpam-4005	5	4	here	here	ADV
ejpam-4005	5	5	extend	extend	VERB
ejpam-4005	5	6	and	and	CCONJ
ejpam-4005	5	7	improve	improve	VERB
ejpam-4005	5	8	some	some	DET
ejpam-4005	5	9	related	relate	VERB
ejpam-4005	5	10	results	result	NOUN
ejpam-4005	5	11	in	in	ADP
ejpam-4005	5	12	the	the	DET
ejpam-4005	5	13	literature	literature	NOUN
ejpam-4005	5	14	.	.	PUNCT
ejpam-4005	6	1	2020	2020	NUM
ejpam-4005	6	2	mathematics	mathematics	PROPN
ejpam-4005	6	3	subject	subject	NOUN
ejpam-4005	6	4	classifications	classification	NOUN
ejpam-4005	6	5	:	:	PUNCT
ejpam-4005	6	6	47h10	47h10	NUM
ejpam-4005	6	7	,	,	PUNCT
ejpam-4005	6	8	47h09	47h09	NUM
ejpam-4005	6	9	,	,	PUNCT
ejpam-4005	6	10	46b20	46b20	NUM
ejpam-4005	6	11	key	key	ADJ
ejpam-4005	6	12	words	word	NOUN
ejpam-4005	6	13	and	and	CCONJ
ejpam-4005	6	14	phrases	phrase	NOUN
ejpam-4005	6	15	:	:	PUNCT
ejpam-4005	6	16	uniformly	uniformly	ADV
ejpam-4005	6	17	convex	convex	VERB
ejpam-4005	6	18	hyperbolic	hyperbolic	ADJ
ejpam-4005	6	19	space	space	NOUN
ejpam-4005	6	20	,	,	PUNCT
ejpam-4005	6	21	strong	strong	ADJ
ejpam-4005	6	22	convergence	convergence	NOUN
ejpam-4005	6	23	,	,	PUNCT
ejpam-4005	6	24	common	common	ADJ
ejpam-4005	6	25	fixed	fix	VERB
ejpam-4005	6	26	points	point	NOUN
ejpam-4005	6	27	,	,	PUNCT
ejpam-4005	6	28	mixed	mixed	ADJ
ejpam-4005	6	29	type	type	NOUN
ejpam-4005	6	30	algorithm	algorithm	NOUN
ejpam-4005	6	31	,	,	PUNCT
ejpam-4005	6	32	asymptotically	asymptotically	ADV
ejpam-4005	6	33	nonexpansive	nonexpansive	ADJ
ejpam-4005	6	34	mapping	mapping	NOUN
ejpam-4005	6	35	1	1	NUM
ejpam-4005	6	36	.	.	PUNCT
ejpam-4005	7	1	introduction	introduction	NOUN
ejpam-4005	7	2	and	and	CCONJ
ejpam-4005	7	3	preliminaries	preliminary	NOUN
ejpam-4005	7	4	iterative	iterative	NOUN
ejpam-4005	7	5	schemes	scheme	NOUN
ejpam-4005	7	6	play	play	VERB
ejpam-4005	7	7	a	a	DET
ejpam-4005	7	8	prominent	prominent	ADJ
ejpam-4005	7	9	role	role	NOUN
ejpam-4005	7	10	in	in	ADP
ejpam-4005	7	11	approximating	approximate	VERB
ejpam-4005	7	12	fixed	fix	VERB
ejpam-4005	7	13	points	point	NOUN
ejpam-4005	7	14	of	of	ADP
ejpam-4005	7	15	nonlinear	nonlinear	ADJ
ejpam-4005	7	16	mappings	mapping	NOUN
ejpam-4005	7	17	.	.	PUNCT
ejpam-4005	8	1	structural	structural	ADJ
ejpam-4005	8	2	properties	property	NOUN
ejpam-4005	8	3	of	of	ADP
ejpam-4005	8	4	the	the	DET
ejpam-4005	8	5	underlying	underlying	ADJ
ejpam-4005	8	6	space	space	NOUN
ejpam-4005	8	7	,	,	PUNCT
ejpam-4005	8	8	such	such	ADJ
ejpam-4005	8	9	as	as	ADP
ejpam-4005	8	10	strict	strict	ADJ
ejpam-4005	8	11	convexity	convexity	NOUN
ejpam-4005	8	12	and	and	CCONJ
ejpam-4005	8	13	uniform	uniform	ADJ
ejpam-4005	8	14	convexity	convexity	NOUN
ejpam-4005	8	15	,	,	PUNCT
ejpam-4005	8	16	are	be	AUX
ejpam-4005	8	17	very	very	ADV
ejpam-4005	8	18	much	much	ADV
ejpam-4005	8	19	needed	need	VERB
ejpam-4005	8	20	for	for	ADP
ejpam-4005	8	21	the	the	DET
ejpam-4005	8	22	development	development	NOUN
ejpam-4005	8	23	of	of	ADP
ejpam-4005	8	24	iterative	iterative	ADJ
ejpam-4005	8	25	fixed	fix	VERB
ejpam-4005	8	26	point	point	NOUN
ejpam-4005	8	27	theory	theory	NOUN
ejpam-4005	8	28	in	in	ADP
ejpam-4005	8	29	it	it	PRON
ejpam-4005	8	30	.	.	PUNCT
ejpam-4005	9	1	hyperbolic	hyperbolic	ADJ
ejpam-4005	9	2	spaces	space	NOUN
ejpam-4005	9	3	are	be	AUX
ejpam-4005	9	4	general	general	ADJ
ejpam-4005	9	5	in	in	ADP
ejpam-4005	9	6	nature	nature	NOUN
ejpam-4005	9	7	and	and	CCONJ
ejpam-4005	9	8	inherit	inherit	VERB
ejpam-4005	9	9	rich	rich	ADJ
ejpam-4005	9	10	geometrical	geometrical	ADJ
ejpam-4005	9	11	structure	structure	NOUN
ejpam-4005	9	12	suitable	suitable	ADJ
ejpam-4005	9	13	to	to	PART
ejpam-4005	9	14	obtain	obtain	VERB
ejpam-4005	9	15	new	new	ADJ
ejpam-4005	9	16	results	result	NOUN
ejpam-4005	9	17	in	in	ADP
ejpam-4005	9	18	topology	topology	NOUN
ejpam-4005	9	19	,	,	PUNCT
ejpam-4005	9	20	graph	graph	NOUN
ejpam-4005	9	21	theory	theory	NOUN
ejpam-4005	9	22	,	,	PUNCT
ejpam-4005	9	23	multi	multi	ADJ
ejpam-4005	9	24	-	-	ADJ
ejpam-4005	9	25	valued	value	VERB
ejpam-4005	9	26	analysis	analysis	NOUN
ejpam-4005	9	27	and	and	CCONJ
ejpam-4005	9	28	metric	metric	ADJ
ejpam-4005	9	29	fixed	fix	VERB
ejpam-4005	9	30	point	point	NOUN
ejpam-4005	9	31	theory	theory	NOUN
ejpam-4005	9	32	.	.	PUNCT
ejpam-4005	10	1	fixed	fix	VERB
ejpam-4005	10	2	-	-	PUNCT
ejpam-4005	10	3	point	point	NOUN
ejpam-4005	10	4	iteration	iteration	NOUN
ejpam-4005	10	5	processes	process	NOUN
ejpam-4005	10	6	for	for	ADP
ejpam-4005	10	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	10	8	self	self	NOUN
ejpam-4005	10	9	and	and	CCONJ
ejpam-4005	10	10	nonself	nonself	NOUN
ejpam-4005	10	11	mappings	mapping	NOUN
ejpam-4005	10	12	have	have	AUX
ejpam-4005	10	13	been	be	AUX
ejpam-4005	10	14	studied	study	VERB
ejpam-4005	10	15	extensively	extensively	ADV
ejpam-4005	10	16	by	by	ADP
ejpam-4005	10	17	various	various	ADJ
ejpam-4005	10	18	authors	author	NOUN
ejpam-4005	10	19	to	to	PART
ejpam-4005	10	20	solve	solve	VERB
ejpam-4005	10	21	the	the	DET
ejpam-4005	10	22	nonlinear	nonlinear	ADJ
ejpam-4005	10	23	operator	operator	NOUN
ejpam-4005	10	24	equations	equation	NOUN
ejpam-4005	10	25	in	in	ADP
ejpam-4005	10	26	hilbert	hilbert	NOUN
ejpam-4005	10	27	spaces	space	NOUN
ejpam-4005	10	28	and	and	CCONJ
ejpam-4005	10	29	banach	banach	NOUN
ejpam-4005	10	30	spaces	space	NOUN
ejpam-4005	10	31	(	(	PUNCT
ejpam-4005	10	32	see	see	VERB
ejpam-4005	10	33	[	[	X
ejpam-4005	10	34	10	10	NUM
ejpam-4005	10	35	,	,	PUNCT
ejpam-4005	10	36	11	11	NUM
ejpam-4005	10	37	,	,	PUNCT
ejpam-4005	10	38	17–19	17–19	NUM
ejpam-4005	10	39	,	,	PUNCT
ejpam-4005	10	40	21	21	NUM
ejpam-4005	10	41	,	,	PUNCT
ejpam-4005	10	42	28	28	NUM
ejpam-4005	10	43	,	,	PUNCT
ejpam-4005	10	44	30	30	NUM
ejpam-4005	10	45	,	,	PUNCT
ejpam-4005	10	46	33	33	NUM
ejpam-4005	10	47	,	,	PUNCT
ejpam-4005	10	48	37	37	NUM
ejpam-4005	10	49	]	]	PUNCT
ejpam-4005	10	50	and	and	CCONJ
ejpam-4005	10	51	the	the	DET
ejpam-4005	10	52	references	reference	NOUN
ejpam-4005	10	53	cited	cite	VERB
ejpam-4005	10	54	therein	therein	ADV
ejpam-4005	10	55	)	)	PUNCT
ejpam-4005	10	56	.	.	PUNCT
ejpam-4005	11	1	goebel	goebel	NOUN
ejpam-4005	11	2	and	and	CCONJ
ejpam-4005	11	3	kirk	kirk	NOUN
ejpam-4005	12	1	[	[	X
ejpam-4005	12	2	6	6	NUM
ejpam-4005	12	3	]	]	PUNCT
ejpam-4005	12	4	,	,	PUNCT
ejpam-4005	12	5	in	in	ADP
ejpam-4005	12	6	1972	1972	NUM
ejpam-4005	12	7	,	,	PUNCT
ejpam-4005	12	8	introduced	introduce	VERB
ejpam-4005	12	9	the	the	DET
ejpam-4005	12	10	class	class	NOUN
ejpam-4005	12	11	of	of	ADP
ejpam-4005	12	12	asymptotically	asymptotically	ADV
ejpam-4005	12	13	nonexpansive	nonexpansive	ADJ
ejpam-4005	12	14	self	self	NOUN
ejpam-4005	12	15	-	-	PUNCT
ejpam-4005	12	16	mappings	mapping	NOUN
ejpam-4005	12	17	,	,	PUNCT
ejpam-4005	12	18	which	which	PRON
ejpam-4005	12	19	is	be	AUX
ejpam-4005	12	20	an	an	DET
ejpam-4005	12	21	important	important	ADJ
ejpam-4005	12	22	generalization	generalization	NOUN
ejpam-4005	12	23	of	of	ADP
ejpam-4005	12	24	the	the	DET
ejpam-4005	12	25	class	class	NOUN
ejpam-4005	12	26	of	of	ADP
ejpam-4005	12	27	nonexpansive	nonexpansive	ADJ
ejpam-4005	12	28	selfmappings	selfmapping	NOUN
ejpam-4005	12	29	.	.	PUNCT
ejpam-4005	13	1	in	in	ADP
ejpam-4005	13	2	the	the	DET
ejpam-4005	13	3	last	last	ADJ
ejpam-4005	13	4	few	few	ADJ
ejpam-4005	13	5	decades	decade	NOUN
ejpam-4005	13	6	investigations	investigation	NOUN
ejpam-4005	13	7	of	of	ADP
ejpam-4005	13	8	fixed	fix	VERB
ejpam-4005	13	9	points	point	NOUN
ejpam-4005	13	10	by	by	ADP
ejpam-4005	13	11	some	some	DET
ejpam-4005	13	12	iterative	iterative	ADJ
ejpam-4005	13	13	schemes	scheme	NOUN
ejpam-4005	13	14	for	for	ADP
ejpam-4005	13	15	asymptotically	asymptotically	ADV
ejpam-4005	13	16	nonexpansive	nonexpansive	ADJ
ejpam-4005	13	17	mappings	mapping	NOUN
ejpam-4005	13	18	have	have	AUX
ejpam-4005	13	19	attracted	attract	VERB
ejpam-4005	13	20	many	many	ADJ
ejpam-4005	13	21	mathematicians	mathematician	NOUN
ejpam-4005	13	22	.	.	PUNCT
ejpam-4005	14	1	in	in	ADP
ejpam-4005	14	2	1991	1991	NUM
ejpam-4005	14	3	,	,	PUNCT
ejpam-4005	14	4	schu	schu	PROPN
ejpam-4005	15	1	[	[	X
ejpam-4005	15	2	28	28	NUM
ejpam-4005	15	3	]	]	PUNCT
ejpam-4005	15	4	introduced	introduce	VERB
ejpam-4005	15	5	the	the	DET
ejpam-4005	15	6	following	follow	VERB
ejpam-4005	15	7	modified	modify	VERB
ejpam-4005	15	8	mann	mann	PROPN
ejpam-4005	15	9	iteration	iteration	NOUN
ejpam-4005	15	10	process	process	NOUN
ejpam-4005	15	11	un+1	un+1	ADV
ejpam-4005	15	12	=	=	SYM
ejpam-4005	15	13	(	(	PUNCT
ejpam-4005	15	14	1−	1−	NUM
ejpam-4005	15	15	ϑn)un	ϑn)un	PUNCT
ejpam-4005	16	1	+	+	NUM
ejpam-4005	16	2	ϑnt	ϑnt	ADJ
ejpam-4005	16	3	nun	nun	PROPN
ejpam-4005	16	4	,	,	PUNCT
ejpam-4005	16	5	n	n	PRON
ejpam-4005	16	6	≥	≥	NOUN
ejpam-4005	16	7	1	1	NUM
ejpam-4005	16	8	,	,	PUNCT
ejpam-4005	16	9	(	(	PUNCT
ejpam-4005	16	10	1	1	X
ejpam-4005	16	11	)	)	PUNCT
ejpam-4005	16	12	doi	doi	NOUN
ejpam-4005	16	13	:	:	PUNCT
ejpam-4005	16	14	https://doi.org/10.29020/nybg.ejpam.v14i3.4005	https://doi.org/10.29020/nybg.ejpam.v14i3.4005	PROPN
ejpam-4005	16	15	email	email	NOUN
ejpam-4005	16	16	address	address	NOUN
ejpam-4005	16	17	:	:	PUNCT
ejpam-4005	16	18	tanakit.th@up.ac.th	tanakit.th@up.ac.th	PROPN
ejpam-4005	16	19	(	(	PUNCT
ejpam-4005	16	20	t.	t.	PROPN
ejpam-4005	16	21	thianwan	thianwan	PROPN
ejpam-4005	16	22	)	)	PUNCT
ejpam-4005	16	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4005	17	1	650	650	NUM
ejpam-4005	17	2	©	©	PROPN
ejpam-4005	17	3	2021	2021	NUM
ejpam-4005	17	4	ejpam	ejpam	VERB
ejpam-4005	17	5	all	all	DET
ejpam-4005	17	6	rights	right	NOUN
ejpam-4005	17	7	reserved	reserve	VERB
ejpam-4005	17	8	.	.	PUNCT
ejpam-4005	18	1	t.	t.	PROPN
ejpam-4005	18	2	thianwan	thianwan	PROPN
ejpam-4005	18	3	/	/	SYM
ejpam-4005	18	4	eur	eur	PROPN
ejpam-4005	18	5	.	.	PUNCT
ejpam-4005	19	1	j.	j.	PROPN
ejpam-4005	19	2	pure	pure	PROPN
ejpam-4005	19	3	appl	appl	PROPN
ejpam-4005	19	4	.	.	PROPN
ejpam-4005	19	5	math	math	PROPN
ejpam-4005	19	6	,	,	PUNCT
ejpam-4005	19	7	14	14	NUM
ejpam-4005	19	8	(	(	PUNCT
ejpam-4005	19	9	3	3	NUM
ejpam-4005	19	10	)	)	PUNCT
ejpam-4005	19	11	(	(	PUNCT
ejpam-4005	19	12	2021	2021	NUM
ejpam-4005	19	13	)	)	PUNCT
ejpam-4005	19	14	,	,	PUNCT
ejpam-4005	19	15	650	650	NUM
ejpam-4005	19	16	-	-	SYM
ejpam-4005	19	17	665	665	NUM
ejpam-4005	19	18	651	651	NUM
ejpam-4005	19	19	to	to	PART
ejpam-4005	19	20	approximate	approximate	VERB
ejpam-4005	19	21	fixed	fix	VERB
ejpam-4005	19	22	points	point	NOUN
ejpam-4005	19	23	of	of	ADP
ejpam-4005	19	24	asymptotically	asymptotically	ADV
ejpam-4005	19	25	nonexpansive	nonexpansive	ADJ
ejpam-4005	19	26	self	self	NOUN
ejpam-4005	19	27	-	-	PUNCT
ejpam-4005	19	28	mappings	mapping	NOUN
ejpam-4005	19	29	in	in	ADP
ejpam-4005	19	30	a	a	DET
ejpam-4005	19	31	hilbert	hilbert	NOUN
ejpam-4005	19	32	space	space	NOUN
ejpam-4005	19	33	.	.	PUNCT
ejpam-4005	20	1	since	since	SCONJ
ejpam-4005	20	2	then	then	ADV
ejpam-4005	20	3	,	,	PUNCT
ejpam-4005	20	4	schu	schu	PROPN
ejpam-4005	20	5	’s	’s	PART
ejpam-4005	20	6	iteration	iteration	NOUN
ejpam-4005	20	7	process	process	NOUN
ejpam-4005	20	8	(	(	PUNCT
ejpam-4005	20	9	1	1	X
ejpam-4005	20	10	)	)	PUNCT
ejpam-4005	20	11	has	have	AUX
ejpam-4005	20	12	been	be	AUX
ejpam-4005	20	13	widely	widely	ADV
ejpam-4005	20	14	used	use	VERB
ejpam-4005	20	15	to	to	PART
ejpam-4005	20	16	approximate	approximate	VERB
ejpam-4005	20	17	fixed	fix	VERB
ejpam-4005	20	18	points	point	NOUN
ejpam-4005	20	19	of	of	ADP
ejpam-4005	20	20	asymptotically	asymptotically	ADV
ejpam-4005	20	21	nonexpansive	nonexpansive	ADJ
ejpam-4005	20	22	self	self	NOUN
ejpam-4005	20	23	-	-	PUNCT
ejpam-4005	20	24	mappings	mapping	NOUN
ejpam-4005	20	25	in	in	ADP
ejpam-4005	20	26	hilbert	hilbert	NOUN
ejpam-4005	20	27	spaces	space	NOUN
ejpam-4005	20	28	or	or	CCONJ
ejpam-4005	20	29	banach	banach	NOUN
ejpam-4005	20	30	spaces	space	NOUN
ejpam-4005	20	31	(	(	PUNCT
ejpam-4005	20	32	[	[	X
ejpam-4005	20	33	4	4	NUM
ejpam-4005	20	34	,	,	PUNCT
ejpam-4005	20	35	18	18	NUM
ejpam-4005	20	36	,	,	PUNCT
ejpam-4005	20	37	22	22	NUM
ejpam-4005	20	38	,	,	PUNCT
ejpam-4005	20	39	24	24	NUM
ejpam-4005	20	40	,	,	PUNCT
ejpam-4005	20	41	28	28	NUM
ejpam-4005	20	42	,	,	PUNCT
ejpam-4005	20	43	29	29	NUM
ejpam-4005	20	44	,	,	PUNCT
ejpam-4005	20	45	34	34	NUM
ejpam-4005	20	46	]	]	PUNCT
ejpam-4005	20	47	)	)	PUNCT
ejpam-4005	20	48	.	.	PUNCT
ejpam-4005	21	1	in	in	ADP
ejpam-4005	21	2	2003	2003	NUM
ejpam-4005	21	3	,	,	PUNCT
ejpam-4005	21	4	chidume	chidume	NOUN
ejpam-4005	21	5	,	,	PUNCT
ejpam-4005	21	6	ofoedu	ofoedu	NOUN
ejpam-4005	21	7	,	,	PUNCT
ejpam-4005	21	8	and	and	CCONJ
ejpam-4005	21	9	zegeye	zegeye	NOUN
ejpam-4005	22	1	[	[	X
ejpam-4005	22	2	5	5	X
ejpam-4005	22	3	]	]	PUNCT
ejpam-4005	22	4	introduced	introduce	VERB
ejpam-4005	22	5	the	the	DET
ejpam-4005	22	6	concept	concept	NOUN
ejpam-4005	22	7	of	of	ADP
ejpam-4005	22	8	asymptotically	asymptotically	ADV
ejpam-4005	22	9	nonexpansive	nonexpansive	ADJ
ejpam-4005	22	10	nonself	nonself	NOUN
ejpam-4005	22	11	-	-	PUNCT
ejpam-4005	22	12	mappings	mapping	NOUN
ejpam-4005	22	13	.	.	PUNCT
ejpam-4005	23	1	also	also	ADV
ejpam-4005	23	2	,	,	PUNCT
ejpam-4005	23	3	they	they	PRON
ejpam-4005	23	4	studied	study	VERB
ejpam-4005	23	5	the	the	DET
ejpam-4005	23	6	following	follow	VERB
ejpam-4005	23	7	iterative	iterative	NOUN
ejpam-4005	23	8	sequence	sequence	NOUN
ejpam-4005	23	9	un+1	un+1	NOUN
ejpam-4005	23	10	=	=	SYM
ejpam-4005	23	11	p((1−	p((1−	X
ejpam-4005	23	12	ϑn)un	ϑn)un	PUNCT
ejpam-4005	24	1	+	+	CCONJ
ejpam-4005	24	2	ϑnt	ϑnt	PROPN
ejpam-4005	24	3	(	(	PUNCT
ejpam-4005	24	4	pt	pt	INTJ
ejpam-4005	24	5	)	)	PUNCT
ejpam-4005	24	6	n−1un	n−1un	NOUN
ejpam-4005	24	7	)	)	PUNCT
ejpam-4005	24	8	(	(	PUNCT
ejpam-4005	24	9	2	2	X
ejpam-4005	24	10	)	)	PUNCT
ejpam-4005	24	11	to	to	PART
ejpam-4005	24	12	approximate	approximate	VERB
ejpam-4005	24	13	some	some	DET
ejpam-4005	24	14	fixed	fix	VERB
ejpam-4005	24	15	point	point	NOUN
ejpam-4005	24	16	of	of	ADP
ejpam-4005	24	17	t	t	PROPN
ejpam-4005	24	18	under	under	ADP
ejpam-4005	24	19	suitable	suitable	ADJ
ejpam-4005	24	20	conditions	condition	NOUN
ejpam-4005	24	21	.	.	PUNCT
ejpam-4005	25	1	if	if	SCONJ
ejpam-4005	25	2	t	t	PROPN
ejpam-4005	25	3	is	be	AUX
ejpam-4005	25	4	a	a	DET
ejpam-4005	25	5	self	self	NOUN
ejpam-4005	25	6	-	-	PUNCT
ejpam-4005	25	7	mapping	mapping	NOUN
ejpam-4005	25	8	,	,	PUNCT
ejpam-4005	25	9	then	then	ADV
ejpam-4005	25	10	p	p	NOUN
ejpam-4005	25	11	becomes	become	VERB
ejpam-4005	25	12	the	the	DET
ejpam-4005	25	13	identity	identity	NOUN
ejpam-4005	25	14	mapping	mapping	NOUN
ejpam-4005	25	15	so	so	SCONJ
ejpam-4005	25	16	that	that	SCONJ
ejpam-4005	25	17	(	(	PUNCT
ejpam-4005	25	18	2	2	X
ejpam-4005	25	19	)	)	PUNCT
ejpam-4005	25	20	reduces	reduce	VERB
ejpam-4005	25	21	to	to	ADP
ejpam-4005	25	22	(	(	PUNCT
ejpam-4005	25	23	1	1	NUM
ejpam-4005	25	24	)	)	PUNCT
ejpam-4005	25	25	.	.	PUNCT
ejpam-4005	26	1	in	in	ADP
ejpam-4005	26	2	2006	2006	NUM
ejpam-4005	26	3	,	,	PUNCT
ejpam-4005	26	4	wang	wang	PROPN
ejpam-4005	27	1	[	[	X
ejpam-4005	27	2	36	36	NUM
ejpam-4005	27	3	]	]	PUNCT
ejpam-4005	27	4	considered	consider	VERB
ejpam-4005	27	5	the	the	DET
ejpam-4005	27	6	following	follow	VERB
ejpam-4005	27	7	iteration	iteration	NOUN
ejpam-4005	27	8	process	process	NOUN
ejpam-4005	27	9	which	which	PRON
ejpam-4005	27	10	is	be	AUX
ejpam-4005	27	11	a	a	DET
ejpam-4005	27	12	generalization	generalization	NOUN
ejpam-4005	27	13	of	of	ADP
ejpam-4005	27	14	(	(	PUNCT
ejpam-4005	27	15	2	2	NUM
ejpam-4005	27	16	)	)	PUNCT
ejpam-4005	27	17	,	,	PUNCT
ejpam-4005	27	18	vn	vn	NOUN
ejpam-4005	27	19	=	=	SYM
ejpam-4005	27	20	p((1−	p((1−	X
ejpam-4005	27	21	ζn)un	ζn)un	PUNCT
ejpam-4005	28	1	+	+	CCONJ
ejpam-4005	28	2	ζnt2(pt	ζnt2(pt	PROPN
ejpam-4005	28	3	2)n−1un	2)n−1un	NUM
ejpam-4005	28	4	)	)	PUNCT
ejpam-4005	28	5	,	,	PUNCT
ejpam-4005	28	6	un+1	un+1	NOUN
ejpam-4005	28	7	=	=	SYM
ejpam-4005	28	8	p((1−	p((1−	X
ejpam-4005	28	9	ϑn)un	ϑn)un	PUNCT
ejpam-4005	29	1	+	+	CCONJ
ejpam-4005	29	2	ϑnt1(pt	ϑnt1(pt	PROPN
ejpam-4005	29	3	1)n−1vn	1)n−1vn	NUM
ejpam-4005	29	4	)	)	PUNCT
ejpam-4005	29	5	,	,	PUNCT
ejpam-4005	29	6	n	n	PRON
ejpam-4005	29	7	≥	≥	NOUN
ejpam-4005	29	8	1	1	NUM
ejpam-4005	29	9	,	,	PUNCT
ejpam-4005	29	10	(	(	PUNCT
ejpam-4005	29	11	3	3	X
ejpam-4005	29	12	)	)	PUNCT
ejpam-4005	29	13	where	where	SCONJ
ejpam-4005	29	14	t1	t1	NOUN
ejpam-4005	29	15	,	,	PUNCT
ejpam-4005	29	16	t2	t2	NOUN
ejpam-4005	29	17	:	:	PUNCT
ejpam-4005	29	18	k	k	X
ejpam-4005	29	19	→	→	PUNCT
ejpam-4005	29	20	x	x	NOUN
ejpam-4005	29	21	are	be	AUX
ejpam-4005	29	22	asymptotically	asymptotically	ADV
ejpam-4005	29	23	nonexpansive	nonexpansive	ADJ
ejpam-4005	29	24	nonself	nonself	NOUN
ejpam-4005	29	25	-	-	PUNCT
ejpam-4005	29	26	mappings	mapping	NOUN
ejpam-4005	29	27	and	and	CCONJ
ejpam-4005	29	28	{	{	PUNCT
ejpam-4005	29	29	ϑn	ϑn	NOUN
ejpam-4005	29	30	}	}	PUNCT
ejpam-4005	29	31	and	and	CCONJ
ejpam-4005	29	32	{	{	PUNCT
ejpam-4005	29	33	ζn	ζn	X
ejpam-4005	29	34	}	}	PUNCT
ejpam-4005	29	35	are	be	AUX
ejpam-4005	29	36	real	real	ADJ
ejpam-4005	29	37	sequences	sequence	NOUN
ejpam-4005	29	38	in	in	ADP
ejpam-4005	29	39	[	[	NOUN
ejpam-4005	29	40	0,1	0,1	NUM
ejpam-4005	29	41	)	)	PUNCT
ejpam-4005	29	42	.	.	PUNCT
ejpam-4005	30	1	meanwhile	meanwhile	ADV
ejpam-4005	30	2	,	,	PUNCT
ejpam-4005	30	3	the	the	DET
ejpam-4005	30	4	results	result	NOUN
ejpam-4005	30	5	of	of	ADP
ejpam-4005	30	6	[	[	X
ejpam-4005	30	7	36	36	NUM
ejpam-4005	30	8	]	]	PUNCT
ejpam-4005	30	9	generalized	generalize	VERB
ejpam-4005	30	10	the	the	DET
ejpam-4005	30	11	results	result	NOUN
ejpam-4005	30	12	of	of	ADP
ejpam-4005	30	13	[	[	X
ejpam-4005	30	14	5	5	NUM
ejpam-4005	30	15	]	]	PUNCT
ejpam-4005	30	16	.	.	PUNCT
ejpam-4005	31	1	the	the	DET
ejpam-4005	31	2	projection	projection	NOUN
ejpam-4005	31	3	type	type	NOUN
ejpam-4005	31	4	ishikawa	ishikawa	PROPN
ejpam-4005	31	5	iteration	iteration	NOUN
ejpam-4005	31	6	process	process	NOUN
ejpam-4005	31	7	for	for	ADP
ejpam-4005	31	8	approximating	approximate	VERB
ejpam-4005	31	9	common	common	ADJ
ejpam-4005	31	10	fixed	fix	VERB
ejpam-4005	31	11	points	point	NOUN
ejpam-4005	31	12	of	of	ADP
ejpam-4005	31	13	two	two	NUM
ejpam-4005	31	14	asymptotically	asymptotically	ADV
ejpam-4005	31	15	nonexpansive	nonexpansive	ADJ
ejpam-4005	31	16	nonself	nonself	NOUN
ejpam-4005	31	17	-	-	PUNCT
ejpam-4005	31	18	mappings	mapping	NOUN
ejpam-4005	31	19	was	be	AUX
ejpam-4005	31	20	defined	define	VERB
ejpam-4005	31	21	and	and	CCONJ
ejpam-4005	31	22	constructed	construct	VERB
ejpam-4005	31	23	by	by	ADP
ejpam-4005	31	24	thianwan	thianwan	PROPN
ejpam-4005	32	1	[	[	X
ejpam-4005	32	2	35	35	NUM
ejpam-4005	32	3	]	]	PUNCT
ejpam-4005	32	4	in	in	ADP
ejpam-4005	32	5	a	a	DET
ejpam-4005	32	6	uniformly	uniformly	ADJ
ejpam-4005	32	7	convex	convex	NOUN
ejpam-4005	32	8	banach	banach	NOUN
ejpam-4005	32	9	space	space	NOUN
ejpam-4005	32	10	as	as	SCONJ
ejpam-4005	32	11	follows	follow	VERB
ejpam-4005	32	12	:	:	PUNCT
ejpam-4005	32	13	vn	vn	NUM
ejpam-4005	32	14	=	=	SYM
ejpam-4005	32	15	p((1−	p((1−	X
ejpam-4005	32	16	ζn)un	ζn)un	PUNCT
ejpam-4005	33	1	+	+	CCONJ
ejpam-4005	33	2	ζnt2(pt	ζnt2(pt	PROPN
ejpam-4005	33	3	2)n−1un	2)n−1un	NUM
ejpam-4005	33	4	)	)	PUNCT
ejpam-4005	33	5	,	,	PUNCT
ejpam-4005	33	6	un+1	un+1	NOUN
ejpam-4005	33	7	=	=	SYM
ejpam-4005	33	8	p((1−	p((1−	NOUN
ejpam-4005	33	9	ϑn)vn	ϑn)vn	PUNCT
ejpam-4005	34	1	+	+	CCONJ
ejpam-4005	34	2	ϑnt1(pt	ϑnt1(pt	PROPN
ejpam-4005	34	3	1)n−1vn	1)n−1vn	NUM
ejpam-4005	34	4	)	)	PUNCT
ejpam-4005	34	5	,	,	PUNCT
ejpam-4005	34	6	n	n	PRON
ejpam-4005	34	7	≥	≥	NOUN
ejpam-4005	34	8	1	1	NUM
ejpam-4005	34	9	,	,	PUNCT
ejpam-4005	34	10	(	(	PUNCT
ejpam-4005	34	11	4	4	X
ejpam-4005	34	12	)	)	PUNCT
ejpam-4005	34	13	where	where	SCONJ
ejpam-4005	34	14	{	{	PUNCT
ejpam-4005	34	15	ϑn	ϑn	NOUN
ejpam-4005	34	16	}	}	PUNCT
ejpam-4005	34	17	and	and	CCONJ
ejpam-4005	34	18	{	{	PUNCT
ejpam-4005	34	19	ζn	ζn	X
ejpam-4005	34	20	}	}	PUNCT
ejpam-4005	34	21	are	be	AUX
ejpam-4005	34	22	appropriate	appropriate	ADJ
ejpam-4005	34	23	real	real	ADJ
ejpam-4005	34	24	sequences	sequence	NOUN
ejpam-4005	34	25	in	in	ADP
ejpam-4005	34	26	[	[	NOUN
ejpam-4005	34	27	0,1	0,1	NUM
ejpam-4005	34	28	)	)	PUNCT
ejpam-4005	34	29	.	.	PUNCT
ejpam-4005	35	1	note	note	VERB
ejpam-4005	35	2	that	that	SCONJ
ejpam-4005	35	3	thianwan	thianwan	PROPN
ejpam-4005	35	4	process	process	NOUN
ejpam-4005	35	5	(	(	PUNCT
ejpam-4005	35	6	4	4	NUM
ejpam-4005	35	7	)	)	PUNCT
ejpam-4005	35	8	and	and	CCONJ
ejpam-4005	35	9	wang	wang	PROPN
ejpam-4005	35	10	process	process	NOUN
ejpam-4005	35	11	(	(	PUNCT
ejpam-4005	35	12	3	3	X
ejpam-4005	35	13	)	)	PUNCT
ejpam-4005	35	14	are	be	AUX
ejpam-4005	35	15	independent	independent	ADJ
ejpam-4005	35	16	neither	neither	CCONJ
ejpam-4005	35	17	reduces	reduce	VERB
ejpam-4005	35	18	to	to	ADP
ejpam-4005	35	19	the	the	DET
ejpam-4005	35	20	other	other	ADJ
ejpam-4005	35	21	.	.	PUNCT
ejpam-4005	36	1	in	in	ADP
ejpam-4005	36	2	2012	2012	NUM
ejpam-4005	36	3	,	,	PUNCT
ejpam-4005	36	4	guo	guo	PROPN
ejpam-4005	36	5	,	,	PUNCT
ejpam-4005	36	6	cho	cho	NOUN
ejpam-4005	36	7	and	and	CCONJ
ejpam-4005	36	8	guo	guo	PROPN
ejpam-4005	37	1	[	[	X
ejpam-4005	37	2	9	9	NUM
ejpam-4005	37	3	]	]	PUNCT
ejpam-4005	37	4	studied	study	VERB
ejpam-4005	37	5	the	the	DET
ejpam-4005	37	6	following	follow	VERB
ejpam-4005	37	7	iteration	iteration	NOUN
ejpam-4005	37	8	scheme	scheme	NOUN
ejpam-4005	37	9	:	:	PUNCT
ejpam-4005	37	10	vn	vn	NOUN
ejpam-4005	37	11	=	=	SYM
ejpam-4005	37	12	p((1−	p((1−	PROPN
ejpam-4005	37	13	ζn)sn2	ζn)sn2	VERB
ejpam-4005	37	14	un	un	PROPN
ejpam-4005	37	15	+	+	CCONJ
ejpam-4005	37	16	ζnt2(pt	ζnt2(pt	PROPN
ejpam-4005	37	17	2)n−1un	2)n−1un	NUM
ejpam-4005	37	18	)	)	PUNCT
ejpam-4005	37	19	,	,	PUNCT
ejpam-4005	37	20	un+1	un+1	NOUN
ejpam-4005	37	21	=	=	SYM
ejpam-4005	37	22	p((1−	p((1−	X
ejpam-4005	37	23	ϑn)sn1	ϑn)sn1	NOUN
ejpam-4005	37	24	un	un	VERB
ejpam-4005	37	25	+	+	CCONJ
ejpam-4005	37	26	ϑnt1(pt	ϑnt1(pt	PROPN
ejpam-4005	37	27	1)n−1vn	1)n−1vn	NUM
ejpam-4005	37	28	)	)	PUNCT
ejpam-4005	37	29	,	,	PUNCT
ejpam-4005	38	1	n	n	PRON
ejpam-4005	38	2	≥	≥	NOUN
ejpam-4005	38	3	1	1	NUM
ejpam-4005	38	4	,	,	PUNCT
ejpam-4005	38	5	(	(	PUNCT
ejpam-4005	38	6	5	5	NUM
ejpam-4005	38	7	)	)	PUNCT
ejpam-4005	38	8	where	where	SCONJ
ejpam-4005	38	9	s1,s2	s1,s2	PROPN
ejpam-4005	38	10	:	:	PUNCT
ejpam-4005	39	1	k	k	PROPN
ejpam-4005	39	2	→	→	PUNCT
ejpam-4005	39	3	k	k	X
ejpam-4005	39	4	are	be	AUX
ejpam-4005	39	5	asymptotically	asymptotically	ADV
ejpam-4005	39	6	nonexpansive	nonexpansive	ADJ
ejpam-4005	39	7	self	self	NOUN
ejpam-4005	39	8	-	-	PUNCT
ejpam-4005	39	9	mappings	mapping	NOUN
ejpam-4005	39	10	,	,	PUNCT
ejpam-4005	39	11	t1	t1	NOUN
ejpam-4005	39	12	,	,	PUNCT
ejpam-4005	39	13	t2	t2	NOUN
ejpam-4005	39	14	:	:	PUNCT
ejpam-4005	39	15	k	k	X
ejpam-4005	39	16	→	→	PUNCT
ejpam-4005	39	17	x	x	NOUN
ejpam-4005	39	18	are	be	AUX
ejpam-4005	39	19	asymptotically	asymptotically	ADV
ejpam-4005	39	20	nonexpansive	nonexpansive	ADJ
ejpam-4005	39	21	nonself	nonself	NOUN
ejpam-4005	39	22	-	-	PUNCT
ejpam-4005	39	23	mappings	mapping	NOUN
ejpam-4005	39	24	and	and	CCONJ
ejpam-4005	39	25	{	{	PUNCT
ejpam-4005	39	26	ϑn	ϑn	NOUN
ejpam-4005	39	27	}	}	PUNCT
ejpam-4005	39	28	,	,	PUNCT
ejpam-4005	39	29	{	{	PUNCT
ejpam-4005	39	30	ζn	ζn	NOUN
ejpam-4005	39	31	}	}	PUNCT
ejpam-4005	39	32	are	be	AUX
ejpam-4005	39	33	two	two	NUM
ejpam-4005	39	34	sequences	sequence	NOUN
ejpam-4005	39	35	in	in	ADP
ejpam-4005	39	36	[	[	NOUN
ejpam-4005	39	37	0,1	0,1	NUM
ejpam-4005	39	38	)	)	PUNCT
ejpam-4005	39	39	to	to	PART
ejpam-4005	39	40	approximate	approximate	VERB
ejpam-4005	39	41	common	common	ADJ
ejpam-4005	39	42	fixed	fix	VERB
ejpam-4005	39	43	points	point	NOUN
ejpam-4005	39	44	of	of	ADP
ejpam-4005	39	45	s1,s2	s1,s2	PROPN
ejpam-4005	39	46	,	,	PUNCT
ejpam-4005	39	47	t1	t1	NOUN
ejpam-4005	39	48	and	and	CCONJ
ejpam-4005	39	49	t2	t2	NOUN
ejpam-4005	39	50	under	under	ADP
ejpam-4005	39	51	proper	proper	ADJ
ejpam-4005	39	52	conditions	condition	NOUN
ejpam-4005	39	53	.	.	PUNCT
ejpam-4005	40	1	the	the	DET
ejpam-4005	40	2	class	class	NOUN
ejpam-4005	40	3	of	of	ADP
ejpam-4005	40	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	40	5	spaces	space	NOUN
ejpam-4005	40	6	,	,	PUNCT
ejpam-4005	40	7	nonlinear	nonlinear	NOUN
ejpam-4005	40	8	in	in	ADP
ejpam-4005	40	9	nature	nature	NOUN
ejpam-4005	40	10	,	,	PUNCT
ejpam-4005	40	11	is	be	AUX
ejpam-4005	40	12	a	a	DET
ejpam-4005	40	13	general	general	ADJ
ejpam-4005	40	14	abstract	abstract	ADJ
ejpam-4005	40	15	theoretic	theoretic	NOUN
ejpam-4005	40	16	setting	setting	NOUN
ejpam-4005	40	17	with	with	ADP
ejpam-4005	40	18	rich	rich	ADJ
ejpam-4005	40	19	geometrical	geometrical	ADJ
ejpam-4005	40	20	structure	structure	NOUN
ejpam-4005	40	21	for	for	ADP
ejpam-4005	40	22	metric	metric	ADJ
ejpam-4005	40	23	fixed	fix	VERB
ejpam-4005	40	24	point	point	NOUN
ejpam-4005	40	25	theory	theory	NOUN
ejpam-4005	40	26	.	.	PUNCT
ejpam-4005	41	1	the	the	DET
ejpam-4005	41	2	study	study	NOUN
ejpam-4005	41	3	of	of	ADP
ejpam-4005	41	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	41	5	spaces	space	NOUN
ejpam-4005	41	6	has	have	AUX
ejpam-4005	41	7	been	be	AUX
ejpam-4005	41	8	largely	largely	ADV
ejpam-4005	41	9	motivated	motivated	ADJ
ejpam-4005	41	10	and	and	CCONJ
ejpam-4005	41	11	dominated	dominate	VERB
ejpam-4005	41	12	by	by	ADP
ejpam-4005	41	13	questions	question	NOUN
ejpam-4005	41	14	about	about	ADP
ejpam-4005	41	15	hyperbolic	hyperbolic	ADJ
ejpam-4005	41	16	groups	group	NOUN
ejpam-4005	41	17	,	,	PUNCT
ejpam-4005	41	18	one	one	NUM
ejpam-4005	41	19	of	of	ADP
ejpam-4005	41	20	the	the	DET
ejpam-4005	41	21	main	main	ADJ
ejpam-4005	41	22	objects	object	NOUN
ejpam-4005	41	23	of	of	ADP
ejpam-4005	41	24	study	study	NOUN
ejpam-4005	41	25	in	in	ADP
ejpam-4005	41	26	geometric	geometric	ADJ
ejpam-4005	41	27	group	group	NOUN
ejpam-4005	41	28	theory	theory	NOUN
ejpam-4005	41	29	.	.	PUNCT
ejpam-4005	42	1	fixed	fix	VERB
ejpam-4005	42	2	point	point	NOUN
ejpam-4005	42	3	theory	theory	NOUN
ejpam-4005	42	4	and	and	CCONJ
ejpam-4005	42	5	hence	hence	ADV
ejpam-4005	42	6	approximation	approximation	NOUN
ejpam-4005	42	7	techniques	technique	NOUN
ejpam-4005	42	8	have	have	AUX
ejpam-4005	42	9	been	be	AUX
ejpam-4005	42	10	extended	extend	VERB
ejpam-4005	42	11	to	to	ADP
ejpam-4005	42	12	hyperbolic	hyperbolic	ADJ
ejpam-4005	42	13	spaces	space	NOUN
ejpam-4005	42	14	(	(	PUNCT
ejpam-4005	42	15	see	see	VERB
ejpam-4005	42	16	[	[	X
ejpam-4005	42	17	1–3	1–3	NOUN
ejpam-4005	42	18	,	,	PUNCT
ejpam-4005	42	19	25–27	25–27	NUM
ejpam-4005	42	20	]	]	PUNCT
ejpam-4005	42	21	and	and	CCONJ
ejpam-4005	42	22	references	reference	NOUN
ejpam-4005	42	23	therein	therein	ADV
ejpam-4005	42	24	)	)	PUNCT
ejpam-4005	42	25	.	.	PUNCT
ejpam-4005	43	1	t.	t.	PROPN
ejpam-4005	43	2	thianwan	thianwan	PROPN
ejpam-4005	43	3	/	/	SYM
ejpam-4005	43	4	eur	eur	PROPN
ejpam-4005	43	5	.	.	PUNCT
ejpam-4005	44	1	j.	j.	PROPN
ejpam-4005	44	2	pure	pure	PROPN
ejpam-4005	44	3	appl	appl	PROPN
ejpam-4005	44	4	.	.	PROPN
ejpam-4005	44	5	math	math	PROPN
ejpam-4005	44	6	,	,	PUNCT
ejpam-4005	44	7	14	14	NUM
ejpam-4005	44	8	(	(	PUNCT
ejpam-4005	44	9	3	3	NUM
ejpam-4005	44	10	)	)	PUNCT
ejpam-4005	44	11	(	(	PUNCT
ejpam-4005	44	12	2021	2021	NUM
ejpam-4005	44	13	)	)	PUNCT
ejpam-4005	44	14	,	,	PUNCT
ejpam-4005	44	15	650	650	NUM
ejpam-4005	44	16	-	-	SYM
ejpam-4005	44	17	665	665	NUM
ejpam-4005	44	18	652	652	NUM
ejpam-4005	44	19	throughout	throughout	ADP
ejpam-4005	44	20	this	this	DET
ejpam-4005	44	21	paper	paper	NOUN
ejpam-4005	44	22	,	,	PUNCT
ejpam-4005	44	23	we	we	PRON
ejpam-4005	44	24	work	work	VERB
ejpam-4005	44	25	in	in	ADP
ejpam-4005	44	26	the	the	DET
ejpam-4005	44	27	setting	setting	NOUN
ejpam-4005	44	28	of	of	ADP
ejpam-4005	44	29	hyperbolic	hyperbolic	ADJ
ejpam-4005	44	30	spaces	space	NOUN
ejpam-4005	44	31	introduced	introduce	VERB
ejpam-4005	44	32	by	by	ADP
ejpam-4005	44	33	kohlenbach	kohlenbach	NOUN
ejpam-4005	44	34	[	[	X
ejpam-4005	44	35	13	13	NUM
ejpam-4005	44	36	]	]	PUNCT
ejpam-4005	44	37	,	,	PUNCT
ejpam-4005	44	38	defined	define	VERB
ejpam-4005	44	39	below	below	ADP
ejpam-4005	44	40	,	,	PUNCT
ejpam-4005	44	41	which	which	PRON
ejpam-4005	44	42	play	play	VERB
ejpam-4005	44	43	a	a	DET
ejpam-4005	44	44	significant	significant	ADJ
ejpam-4005	44	45	role	role	NOUN
ejpam-4005	44	46	in	in	ADP
ejpam-4005	44	47	many	many	ADJ
ejpam-4005	44	48	branches	branch	NOUN
ejpam-4005	44	49	of	of	ADP
ejpam-4005	44	50	mathematics	mathematic	NOUN
ejpam-4005	44	51	.	.	PUNCT
ejpam-4005	45	1	a	a	DET
ejpam-4005	45	2	hyperbolic	hyperbolic	ADJ
ejpam-4005	45	3	space	space	NOUN
ejpam-4005	45	4	(	(	PUNCT
ejpam-4005	45	5	x	x	X
ejpam-4005	45	6	,	,	PUNCT
ejpam-4005	45	7	d	d	NOUN
ejpam-4005	45	8	,	,	PUNCT
ejpam-4005	45	9	h	h	NOUN
ejpam-4005	45	10	)	)	PUNCT
ejpam-4005	45	11	is	be	AUX
ejpam-4005	45	12	a	a	DET
ejpam-4005	45	13	metric	metric	ADJ
ejpam-4005	45	14	space	space	NOUN
ejpam-4005	45	15	(	(	PUNCT
ejpam-4005	45	16	x	x	NOUN
ejpam-4005	45	17	,	,	PUNCT
ejpam-4005	45	18	d	d	NOUN
ejpam-4005	45	19	)	)	PUNCT
ejpam-4005	45	20	together	together	ADV
ejpam-4005	45	21	with	with	ADP
ejpam-4005	45	22	a	a	DET
ejpam-4005	45	23	mapping	mapping	NOUN
ejpam-4005	45	24	h	h	NOUN
ejpam-4005	45	25	:	:	PUNCT
ejpam-4005	46	1	x	x	PUNCT
ejpam-4005	46	2	×	×	NOUN
ejpam-4005	46	3	x	x	SYM
ejpam-4005	46	4	×	×	NOUN
ejpam-4005	47	1	[	[	X
ejpam-4005	47	2	0	0	NUM
ejpam-4005	47	3	,	,	PUNCT
ejpam-4005	47	4	1]→	1]→	NOUN
ejpam-4005	47	5	x	x	SYM
ejpam-4005	47	6	satisfying	satisfy	VERB
ejpam-4005	47	7	(	(	PUNCT
ejpam-4005	47	8	h1	h1	PROPN
ejpam-4005	47	9	)	)	PUNCT
ejpam-4005	47	10	:	:	PUNCT
ejpam-4005	48	1	d(z	d(z	PROPN
ejpam-4005	48	2	,	,	PUNCT
ejpam-4005	48	3	h(u	h(u	PROPN
ejpam-4005	48	4	,	,	PUNCT
ejpam-4005	48	5	v	v	NOUN
ejpam-4005	48	6	,	,	PUNCT
ejpam-4005	48	7	ψ	ψ	NOUN
ejpam-4005	48	8	)	)	PUNCT
ejpam-4005	48	9	)	)	PUNCT
ejpam-4005	48	10	≤	≤	NOUN
ejpam-4005	48	11	(	(	PUNCT
ejpam-4005	48	12	1−	1−	NUM
ejpam-4005	48	13	ψ	ψ	NOUN
ejpam-4005	48	14	)	)	PUNCT
ejpam-4005	48	15	d(z	d(z	PROPN
ejpam-4005	48	16	,	,	PUNCT
ejpam-4005	48	17	u	u	NOUN
ejpam-4005	48	18	)	)	PUNCT
ejpam-4005	48	19	+	+	CCONJ
ejpam-4005	48	20	ψd(z	ψd(z	NOUN
ejpam-4005	48	21	,	,	PUNCT
ejpam-4005	48	22	v	v	NOUN
ejpam-4005	48	23	)	)	PUNCT
ejpam-4005	48	24	,	,	PUNCT
ejpam-4005	48	25	(	(	PUNCT
ejpam-4005	48	26	h2	h2	NOUN
ejpam-4005	48	27	)	)	PUNCT
ejpam-4005	48	28	:	:	PUNCT
ejpam-4005	49	1	d(h(u	d(h(u	PROPN
ejpam-4005	49	2	,	,	PUNCT
ejpam-4005	49	3	v	v	NOUN
ejpam-4005	49	4	,	,	PUNCT
ejpam-4005	49	5	ψ)),h(u	ψ)),h(u	NOUN
ejpam-4005	49	6	,	,	PUNCT
ejpam-4005	49	7	v	v	NOUN
ejpam-4005	49	8	,	,	PUNCT
ejpam-4005	49	9	µ	µ	NOUN
ejpam-4005	49	10	)	)	PUNCT
ejpam-4005	49	11	=	=	SYM
ejpam-4005	49	12	|ψ	|ψ	ADP
ejpam-4005	49	13	−	−	PROPN
ejpam-4005	49	14	µ|	µ|	PROPN
ejpam-4005	49	15	d(u	d(u	PROPN
ejpam-4005	49	16	,	,	PUNCT
ejpam-4005	49	17	v	v	NOUN
ejpam-4005	49	18	)	)	PUNCT
ejpam-4005	49	19	,	,	PUNCT
ejpam-4005	49	20	(	(	PUNCT
ejpam-4005	49	21	h3	h3	NOUN
ejpam-4005	49	22	)	)	PUNCT
ejpam-4005	49	23	:	:	PUNCT
ejpam-4005	49	24	h(u	h(u	PROPN
ejpam-4005	49	25	,	,	PUNCT
ejpam-4005	49	26	v	v	NOUN
ejpam-4005	49	27	,	,	PUNCT
ejpam-4005	49	28	ψ	ψ	NOUN
ejpam-4005	49	29	)	)	PUNCT
ejpam-4005	49	30	=	=	SYM
ejpam-4005	50	1	h(v	h(v	PROPN
ejpam-4005	50	2	,	,	PUNCT
ejpam-4005	50	3	u	u	NOUN
ejpam-4005	50	4	,	,	PUNCT
ejpam-4005	50	5	1−	1−	NUM
ejpam-4005	50	6	ψ	ψ	NOUN
ejpam-4005	50	7	)	)	PUNCT
ejpam-4005	50	8	,	,	PUNCT
ejpam-4005	50	9	(	(	PUNCT
ejpam-4005	50	10	h4	h4	PROPN
ejpam-4005	50	11	)	)	PUNCT
ejpam-4005	50	12	:	:	PUNCT
ejpam-4005	51	1	d(h(u	d(h(u	PROPN
ejpam-4005	51	2	,	,	PUNCT
ejpam-4005	51	3	z	z	NOUN
ejpam-4005	51	4	,	,	PUNCT
ejpam-4005	51	5	ψ),h(v	ψ),h(v	PROPN
ejpam-4005	51	6	,	,	PUNCT
ejpam-4005	51	7	w	w	NOUN
ejpam-4005	51	8	,	,	PUNCT
ejpam-4005	51	9	ψ	ψ	NOUN
ejpam-4005	51	10	)	)	PUNCT
ejpam-4005	51	11	)	)	PUNCT
ejpam-4005	51	12	≤	≤	NOUN
ejpam-4005	51	13	(	(	PUNCT
ejpam-4005	51	14	1−	1−	NUM
ejpam-4005	51	15	ψ	ψ	NOUN
ejpam-4005	51	16	)	)	PUNCT
ejpam-4005	51	17	d(u	d(u	PROPN
ejpam-4005	51	18	,	,	PUNCT
ejpam-4005	51	19	v	v	NOUN
ejpam-4005	51	20	)	)	PUNCT
ejpam-4005	52	1	+	+	CCONJ
ejpam-4005	52	2	ψd(z	ψd(z	NOUN
ejpam-4005	52	3	,	,	PUNCT
ejpam-4005	52	4	w	w	NOUN
ejpam-4005	52	5	)	)	PUNCT
ejpam-4005	52	6	for	for	ADP
ejpam-4005	52	7	all	all	DET
ejpam-4005	52	8	u	u	NOUN
ejpam-4005	52	9	,	,	PUNCT
ejpam-4005	52	10	v	v	NOUN
ejpam-4005	52	11	,	,	PUNCT
ejpam-4005	52	12	w	w	PROPN
ejpam-4005	52	13	,	,	PUNCT
ejpam-4005	52	14	z	z	NOUN
ejpam-4005	52	15	∈	∈	PROPN
ejpam-4005	52	16	x	x	X
ejpam-4005	52	17	and	and	CCONJ
ejpam-4005	52	18	ψ	ψ	PROPN
ejpam-4005	52	19	,	,	PUNCT
ejpam-4005	52	20	µ	µ	PRON
ejpam-4005	52	21	∈	∈	NOUN
ejpam-4005	53	1	[	[	X
ejpam-4005	53	2	0	0	NUM
ejpam-4005	53	3	,	,	PUNCT
ejpam-4005	53	4	1	1	NUM
ejpam-4005	53	5	]	]	PUNCT
ejpam-4005	53	6	.	.	PUNCT
ejpam-4005	54	1	a	a	DET
ejpam-4005	54	2	subset	subset	NOUN
ejpam-4005	54	3	k	k	NOUN
ejpam-4005	54	4	of	of	ADP
ejpam-4005	54	5	a	a	DET
ejpam-4005	54	6	hyperbolic	hyperbolic	ADJ
ejpam-4005	54	7	space	space	NOUN
ejpam-4005	54	8	x	x	PUNCT
ejpam-4005	54	9	is	be	AUX
ejpam-4005	54	10	convex	convex	ADJ
ejpam-4005	54	11	if	if	SCONJ
ejpam-4005	54	12	h(u	h(u	PROPN
ejpam-4005	54	13	,	,	PUNCT
ejpam-4005	54	14	v	v	NOUN
ejpam-4005	54	15	,	,	PUNCT
ejpam-4005	54	16	ψ	ψ	NOUN
ejpam-4005	54	17	)	)	PUNCT
ejpam-4005	54	18	∈	∈	PROPN
ejpam-4005	54	19	k	k	PROPN
ejpam-4005	54	20	for	for	ADP
ejpam-4005	54	21	all	all	DET
ejpam-4005	54	22	u	u	NOUN
ejpam-4005	54	23	,	,	PUNCT
ejpam-4005	54	24	v	v	ADP
ejpam-4005	54	25	∈	∈	PROPN
ejpam-4005	54	26	k	k	NOUN
ejpam-4005	54	27	and	and	CCONJ
ejpam-4005	54	28	ψ	ψ	X
ejpam-4005	54	29	∈	∈	PROPN
ejpam-4005	55	1	[	[	X
ejpam-4005	55	2	0	0	NUM
ejpam-4005	55	3	,	,	PUNCT
ejpam-4005	55	4	1	1	NUM
ejpam-4005	55	5	]	]	PUNCT
ejpam-4005	55	6	.	.	PUNCT
ejpam-4005	56	1	if	if	SCONJ
ejpam-4005	56	2	a	a	DET
ejpam-4005	56	3	space	space	NOUN
ejpam-4005	56	4	satisfies	satisfie	NOUN
ejpam-4005	56	5	only	only	ADV
ejpam-4005	56	6	(	(	PUNCT
ejpam-4005	56	7	h1	h1	PROPN
ejpam-4005	56	8	)	)	PUNCT
ejpam-4005	56	9	,	,	PUNCT
ejpam-4005	56	10	it	it	PRON
ejpam-4005	56	11	coincides	coincide	VERB
ejpam-4005	56	12	with	with	ADP
ejpam-4005	56	13	the	the	DET
ejpam-4005	56	14	convex	convex	ADJ
ejpam-4005	56	15	metric	metric	ADJ
ejpam-4005	56	16	space	space	NOUN
ejpam-4005	56	17	introduced	introduce	VERB
ejpam-4005	56	18	by	by	ADP
ejpam-4005	56	19	takahashi	takahashi	PROPN
ejpam-4005	56	20	[	[	X
ejpam-4005	56	21	32	32	NUM
ejpam-4005	56	22	]	]	PUNCT
ejpam-4005	56	23	.	.	PUNCT
ejpam-4005	57	1	the	the	DET
ejpam-4005	57	2	concept	concept	NOUN
ejpam-4005	57	3	of	of	ADP
ejpam-4005	57	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	57	5	spaces	space	NOUN
ejpam-4005	57	6	in	in	ADP
ejpam-4005	57	7	[	[	X
ejpam-4005	57	8	13	13	NUM
ejpam-4005	57	9	]	]	PUNCT
ejpam-4005	57	10	is	be	AUX
ejpam-4005	57	11	more	more	ADV
ejpam-4005	57	12	restrictive	restrictive	ADJ
ejpam-4005	57	13	than	than	ADP
ejpam-4005	57	14	the	the	DET
ejpam-4005	57	15	hyperbolic	hyperbolic	ADJ
ejpam-4005	57	16	type	type	NOUN
ejpam-4005	57	17	introduced	introduce	VERB
ejpam-4005	57	18	by	by	ADP
ejpam-4005	57	19	goebel	goebel	NOUN
ejpam-4005	57	20	et	et	PROPN
ejpam-4005	57	21	al	al	PROPN
ejpam-4005	57	22	.	.	PUNCT
ejpam-4005	58	1	[	[	X
ejpam-4005	58	2	7	7	X
ejpam-4005	58	3	]	]	PUNCT
ejpam-4005	58	4	since	since	SCONJ
ejpam-4005	58	5	(	(	PUNCT
ejpam-4005	58	6	h1	h1	PROPN
ejpam-4005	58	7	)	)	PUNCT
ejpam-4005	58	8	−	−	PROPN
ejpam-4005	58	9	(	(	PUNCT
ejpam-4005	58	10	h3	h3	NOUN
ejpam-4005	58	11	)	)	PUNCT
ejpam-4005	58	12	together	together	ADV
ejpam-4005	58	13	are	be	AUX
ejpam-4005	58	14	equivalent	equivalent	ADJ
ejpam-4005	58	15	to	to	ADP
ejpam-4005	58	16	(	(	PUNCT
ejpam-4005	58	17	x	x	X
ejpam-4005	58	18	,	,	PUNCT
ejpam-4005	58	19	d	d	NOUN
ejpam-4005	58	20	,	,	PUNCT
ejpam-4005	58	21	h	h	NOUN
ejpam-4005	58	22	)	)	PUNCT
ejpam-4005	58	23	being	be	AUX
ejpam-4005	58	24	a	a	DET
ejpam-4005	58	25	space	space	NOUN
ejpam-4005	58	26	of	of	ADP
ejpam-4005	58	27	hyperbolic	hyperbolic	ADJ
ejpam-4005	58	28	type	type	NOUN
ejpam-4005	58	29	in	in	ADP
ejpam-4005	58	30	[	[	X
ejpam-4005	58	31	7	7	NUM
ejpam-4005	58	32	]	]	PUNCT
ejpam-4005	58	33	.	.	PUNCT
ejpam-4005	59	1	also	also	ADV
ejpam-4005	59	2	it	it	PRON
ejpam-4005	59	3	is	be	AUX
ejpam-4005	59	4	slightly	slightly	ADV
ejpam-4005	59	5	more	more	ADV
ejpam-4005	59	6	general	general	ADJ
ejpam-4005	59	7	than	than	ADP
ejpam-4005	59	8	the	the	DET
ejpam-4005	59	9	hyperbolic	hyperbolic	ADJ
ejpam-4005	59	10	space	space	NOUN
ejpam-4005	59	11	defined	define	VERB
ejpam-4005	59	12	by	by	ADP
ejpam-4005	59	13	reich	reich	PROPN
ejpam-4005	59	14	et	et	PROPN
ejpam-4005	59	15	al	al	PROPN
ejpam-4005	59	16	.	.	PUNCT
ejpam-4005	60	1	[	[	X
ejpam-4005	60	2	23	23	NUM
ejpam-4005	60	3	]	]	PUNCT
ejpam-4005	60	4	.	.	PUNCT
ejpam-4005	61	1	a	a	DET
ejpam-4005	61	2	hyperbolic	hyperbolic	ADJ
ejpam-4005	61	3	space	space	NOUN
ejpam-4005	61	4	(	(	PUNCT
ejpam-4005	61	5	x	x	X
ejpam-4005	61	6	,	,	PUNCT
ejpam-4005	61	7	d	d	NOUN
ejpam-4005	61	8	,	,	PUNCT
ejpam-4005	61	9	h	h	NOUN
ejpam-4005	61	10	)	)	PUNCT
ejpam-4005	61	11	is	be	AUX
ejpam-4005	61	12	said	say	VERB
ejpam-4005	61	13	to	to	PART
ejpam-4005	61	14	be	be	AUX
ejpam-4005	61	15	(	(	PUNCT
ejpam-4005	61	16	i	i	NOUN
ejpam-4005	61	17	)	)	PUNCT
ejpam-4005	61	18	strictly	strictly	ADV
ejpam-4005	61	19	convex	convex	VERB
ejpam-4005	62	1	[	[	X
ejpam-4005	62	2	32	32	NUM
ejpam-4005	62	3	]	]	PUNCT
ejpam-4005	62	4	if	if	SCONJ
ejpam-4005	62	5	for	for	ADP
ejpam-4005	62	6	any	any	DET
ejpam-4005	62	7	u	u	NOUN
ejpam-4005	62	8	,	,	PUNCT
ejpam-4005	62	9	v	v	NOUN
ejpam-4005	62	10	∈	∈	NOUN
ejpam-4005	62	11	x	x	X
ejpam-4005	62	12	and	and	CCONJ
ejpam-4005	62	13	ψ	ψ	X
ejpam-4005	62	14	∈	∈	PROPN
ejpam-4005	63	1	[	[	X
ejpam-4005	63	2	0	0	NUM
ejpam-4005	63	3	,	,	PUNCT
ejpam-4005	63	4	1	1	NUM
ejpam-4005	63	5	]	]	PUNCT
ejpam-4005	63	6	,	,	PUNCT
ejpam-4005	63	7	there	there	PRON
ejpam-4005	63	8	exists	exist	VERB
ejpam-4005	63	9	a	a	DET
ejpam-4005	63	10	unique	unique	ADJ
ejpam-4005	63	11	element	element	NOUN
ejpam-4005	63	12	z	z	NOUN
ejpam-4005	63	13	∈	∈	PROPN
ejpam-4005	63	14	x	x	PUNCT
ejpam-4005	63	15	such	such	ADJ
ejpam-4005	63	16	that	that	SCONJ
ejpam-4005	63	17	d(z	d(z	PROPN
ejpam-4005	63	18	,	,	PUNCT
ejpam-4005	63	19	u	u	NOUN
ejpam-4005	63	20	)	)	PUNCT
ejpam-4005	63	21	=	=	SYM
ejpam-4005	63	22	ψd(u	ψd(u	X
ejpam-4005	63	23	,	,	PUNCT
ejpam-4005	63	24	v	v	NOUN
ejpam-4005	63	25	)	)	PUNCT
ejpam-4005	63	26	and	and	CCONJ
ejpam-4005	63	27	d(z	d(z	PROPN
ejpam-4005	63	28	,	,	PUNCT
ejpam-4005	63	29	v	v	NOUN
ejpam-4005	63	30	)	)	PUNCT
ejpam-4005	63	31	=	=	PUNCT
ejpam-4005	63	32	(	(	PUNCT
ejpam-4005	63	33	1−	1−	NUM
ejpam-4005	63	34	ψ)d(u	ψ)d(u	ADJ
ejpam-4005	63	35	,	,	PUNCT
ejpam-4005	63	36	v	v	NOUN
ejpam-4005	63	37	)	)	PUNCT
ejpam-4005	63	38	;	;	PUNCT
ejpam-4005	63	39	(	(	PUNCT
ejpam-4005	63	40	ii	ii	NOUN
ejpam-4005	63	41	)	)	PUNCT
ejpam-4005	63	42	uniformly	uniformly	ADV
ejpam-4005	63	43	convex	convex	VERB
ejpam-4005	64	1	[	[	X
ejpam-4005	64	2	31	31	NUM
ejpam-4005	64	3	]	]	X
ejpam-4005	64	4	if	if	SCONJ
ejpam-4005	64	5	for	for	ADP
ejpam-4005	64	6	all	all	DET
ejpam-4005	64	7	u	u	NOUN
ejpam-4005	64	8	,	,	PUNCT
ejpam-4005	64	9	v	v	NOUN
ejpam-4005	64	10	,	,	PUNCT
ejpam-4005	64	11	w	w	PROPN
ejpam-4005	64	12	∈	∈	PROPN
ejpam-4005	64	13	x	x	X
ejpam-4005	64	14	,	,	PUNCT
ejpam-4005	64	15	r	r	NOUN
ejpam-4005	64	16	>	>	X
ejpam-4005	64	17	0	0	NUM
ejpam-4005	65	1	and	and	CCONJ
ejpam-4005	65	2	ε	ε	PROPN
ejpam-4005	65	3	∈	∈	PROPN
ejpam-4005	65	4	(	(	PUNCT
ejpam-4005	65	5	0	0	NUM
ejpam-4005	65	6	,	,	PUNCT
ejpam-4005	65	7	2	2	NUM
ejpam-4005	65	8	]	]	PUNCT
ejpam-4005	65	9	,	,	PUNCT
ejpam-4005	65	10	there	there	PRON
ejpam-4005	65	11	exists	exist	VERB
ejpam-4005	65	12	δ	δ	PROPN
ejpam-4005	65	13	∈	∈	PROPN
ejpam-4005	65	14	(	(	PUNCT
ejpam-4005	65	15	0	0	NUM
ejpam-4005	65	16	,	,	PUNCT
ejpam-4005	65	17	1	1	NUM
ejpam-4005	65	18	]	]	PUNCT
ejpam-4005	65	19	such	such	ADJ
ejpam-4005	65	20	that	that	SCONJ
ejpam-4005	65	21	d(h(u	d(h(u	PROPN
ejpam-4005	65	22	,	,	PUNCT
ejpam-4005	65	23	v	v	NOUN
ejpam-4005	65	24	,	,	PUNCT
ejpam-4005	65	25	1	1	NUM
ejpam-4005	65	26	2	2	NUM
ejpam-4005	65	27	)	)	PUNCT
ejpam-4005	65	28	,	,	PUNCT
ejpam-4005	65	29	u	u	NOUN
ejpam-4005	65	30	)	)	PUNCT
ejpam-4005	65	31	≤	≤	NOUN
ejpam-4005	65	32	(	(	PUNCT
ejpam-4005	65	33	1−	1−	NUM
ejpam-4005	65	34	δ)r	δ)r	NOUN
ejpam-4005	65	35	whenever	whenever	SCONJ
ejpam-4005	65	36	d(u	d(u	PROPN
ejpam-4005	65	37	,	,	PUNCT
ejpam-4005	65	38	w	w	NOUN
ejpam-4005	65	39	)	)	PUNCT
ejpam-4005	65	40	≤	≤	NOUN
ejpam-4005	65	41	r	r	NOUN
ejpam-4005	65	42	,	,	PUNCT
ejpam-4005	65	43	d(v	d(v	PROPN
ejpam-4005	65	44	,	,	PUNCT
ejpam-4005	65	45	w	w	NOUN
ejpam-4005	65	46	)	)	PUNCT
ejpam-4005	65	47	≤	≤	NOUN
ejpam-4005	65	48	r	r	NOUN
ejpam-4005	65	49	and	and	CCONJ
ejpam-4005	65	50	d(u	d(u	PROPN
ejpam-4005	65	51	,	,	PUNCT
ejpam-4005	65	52	v	v	NOUN
ejpam-4005	65	53	)	)	PUNCT
ejpam-4005	65	54	≥	≥	NOUN
ejpam-4005	65	55	εr	εr	VERB
ejpam-4005	65	56	.	.	PUNCT
ejpam-4005	66	1	a	a	DET
ejpam-4005	66	2	mapping	mapping	NOUN
ejpam-4005	66	3	η	η	NOUN
ejpam-4005	66	4	:	:	PUNCT
ejpam-4005	66	5	(	(	PUNCT
ejpam-4005	66	6	0,∞	0,∞	NUM
ejpam-4005	66	7	)	)	PUNCT
ejpam-4005	66	8	×	×	NOUN
ejpam-4005	66	9	(	(	PUNCT
ejpam-4005	66	10	0	0	NUM
ejpam-4005	66	11	,	,	PUNCT
ejpam-4005	66	12	2	2	NUM
ejpam-4005	66	13	]	]	PUNCT
ejpam-4005	66	14	→	→	X
ejpam-4005	66	15	(	(	PUNCT
ejpam-4005	66	16	0	0	NUM
ejpam-4005	66	17	,	,	PUNCT
ejpam-4005	66	18	1	1	NUM
ejpam-4005	66	19	]	]	PUNCT
ejpam-4005	66	20	providing	provide	VERB
ejpam-4005	66	21	such	such	ADJ
ejpam-4005	66	22	δ	δ	NOUN
ejpam-4005	66	23	=	=	PUNCT
ejpam-4005	66	24	η(r	η(r	PROPN
ejpam-4005	66	25	,	,	PUNCT
ejpam-4005	66	26	ε	ε	PROPN
ejpam-4005	66	27	)	)	PUNCT
ejpam-4005	66	28	for	for	ADP
ejpam-4005	66	29	given	give	VERB
ejpam-4005	66	30	r	r	NOUN
ejpam-4005	66	31	>	>	PUNCT
ejpam-4005	66	32	0	0	PUNCT
ejpam-4005	66	33	and	and	CCONJ
ejpam-4005	66	34	ε	ε	PROPN
ejpam-4005	66	35	∈	∈	PROPN
ejpam-4005	66	36	(	(	PUNCT
ejpam-4005	66	37	0	0	NUM
ejpam-4005	66	38	,	,	PUNCT
ejpam-4005	66	39	2	2	NUM
ejpam-4005	66	40	]	]	PUNCT
ejpam-4005	66	41	is	be	AUX
ejpam-4005	66	42	called	call	VERB
ejpam-4005	66	43	modulus	modulus	NOUN
ejpam-4005	66	44	of	of	ADP
ejpam-4005	66	45	uniform	uniform	ADJ
ejpam-4005	66	46	convexity	convexity	NOUN
ejpam-4005	66	47	.	.	PUNCT
ejpam-4005	67	1	we	we	PRON
ejpam-4005	67	2	call	call	VERB
ejpam-4005	67	3	η	η	NOUN
ejpam-4005	67	4	monotone	monotone	NOUN
ejpam-4005	67	5	if	if	SCONJ
ejpam-4005	67	6	it	it	PRON
ejpam-4005	67	7	decreases	decrease	VERB
ejpam-4005	67	8	with	with	ADP
ejpam-4005	67	9	r	r	NOUN
ejpam-4005	67	10	(	(	PUNCT
ejpam-4005	67	11	for	for	ADP
ejpam-4005	67	12	a	a	DET
ejpam-4005	67	13	fixed	fix	VERB
ejpam-4005	67	14	ε	ε	PROPN
ejpam-4005	67	15	)	)	PUNCT
ejpam-4005	67	16	.	.	PUNCT
ejpam-4005	68	1	a	a	DET
ejpam-4005	68	2	uniformly	uniformly	ADV
ejpam-4005	68	3	convex	convex	ADJ
ejpam-4005	68	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	68	5	space	space	NOUN
ejpam-4005	68	6	is	be	AUX
ejpam-4005	68	7	strictly	strictly	ADV
ejpam-4005	68	8	convex	convex	ADJ
ejpam-4005	68	9	(	(	PUNCT
ejpam-4005	68	10	see	see	VERB
ejpam-4005	68	11	[	[	X
ejpam-4005	68	12	15	15	NUM
ejpam-4005	68	13	]	]	NUM
ejpam-4005	68	14	)	)	PUNCT
ejpam-4005	68	15	.	.	PUNCT
ejpam-4005	69	1	in	in	ADP
ejpam-4005	69	2	the	the	DET
ejpam-4005	69	3	sequel	sequel	NOUN
ejpam-4005	69	4	,	,	PUNCT
ejpam-4005	69	5	let	let	VERB
ejpam-4005	69	6	(	(	PUNCT
ejpam-4005	69	7	x	x	X
ejpam-4005	69	8	,	,	PUNCT
ejpam-4005	69	9	d	d	X
ejpam-4005	69	10	)	)	PUNCT
ejpam-4005	69	11	be	be	AUX
ejpam-4005	69	12	a	a	DET
ejpam-4005	69	13	metric	metric	ADJ
ejpam-4005	69	14	space	space	NOUN
ejpam-4005	69	15	,	,	PUNCT
ejpam-4005	69	16	and	and	CCONJ
ejpam-4005	69	17	let	let	VERB
ejpam-4005	69	18	k	k	PRON
ejpam-4005	69	19	be	be	AUX
ejpam-4005	69	20	a	a	DET
ejpam-4005	69	21	nonempty	nonempty	ADJ
ejpam-4005	69	22	subset	subset	NOUN
ejpam-4005	69	23	of	of	ADP
ejpam-4005	69	24	x	x	X
ejpam-4005	69	25	.	.	PUNCT
ejpam-4005	70	1	we	we	PRON
ejpam-4005	70	2	shall	shall	AUX
ejpam-4005	70	3	denote	denote	VERB
ejpam-4005	70	4	the	the	DET
ejpam-4005	70	5	fixed	fix	VERB
ejpam-4005	70	6	point	point	NOUN
ejpam-4005	70	7	set	set	NOUN
ejpam-4005	70	8	of	of	ADP
ejpam-4005	70	9	a	a	DET
ejpam-4005	70	10	mapping	mapping	NOUN
ejpam-4005	70	11	t	t	NOUN
ejpam-4005	70	12	by	by	ADP
ejpam-4005	70	13	f(t	f(t	NOUN
ejpam-4005	70	14	)	)	PUNCT
ejpam-4005	71	1	=	=	PUNCT
ejpam-4005	71	2	{	{	PUNCT
ejpam-4005	71	3	u	u	NOUN
ejpam-4005	71	4	∈	∈	PROPN
ejpam-4005	71	5	k	k	NOUN
ejpam-4005	71	6	:	:	PUNCT
ejpam-4005	71	7	t	t	PROPN
ejpam-4005	71	8	u	u	X
ejpam-4005	71	9	=	=	SYM
ejpam-4005	71	10	u	u	NOUN
ejpam-4005	71	11	}	}	PUNCT
ejpam-4005	71	12	and	and	CCONJ
ejpam-4005	71	13	d(u	d(u	PROPN
ejpam-4005	71	14	,	,	PUNCT
ejpam-4005	71	15	f(t	f(t	PROPN
ejpam-4005	71	16	)	)	PUNCT
ejpam-4005	71	17	)	)	PUNCT
ejpam-4005	72	1	=	=	PRON
ejpam-4005	72	2	inf	inf	PROPN
ejpam-4005	72	3	{	{	PUNCT
ejpam-4005	72	4	d(u	d(u	PROPN
ejpam-4005	72	5	,	,	PUNCT
ejpam-4005	72	6	p	p	NOUN
ejpam-4005	72	7	)	)	PUNCT
ejpam-4005	72	8	:	:	PUNCT
ejpam-4005	72	9	p	p	X
ejpam-4005	72	10	∈	∈	PROPN
ejpam-4005	72	11	f(t	f(t	PROPN
ejpam-4005	72	12	)	)	PUNCT
ejpam-4005	72	13	}	}	PUNCT
ejpam-4005	72	14	.	.	PUNCT
ejpam-4005	73	1	a	a	DET
ejpam-4005	73	2	self	self	NOUN
ejpam-4005	73	3	-	-	PUNCT
ejpam-4005	73	4	mapping	mapping	NOUN
ejpam-4005	73	5	t	t	NOUN
ejpam-4005	73	6	is	be	AUX
ejpam-4005	73	7	said	say	VERB
ejpam-4005	73	8	to	to	PART
ejpam-4005	73	9	be	be	AUX
ejpam-4005	73	10	nonexpansive	nonexpansive	ADJ
ejpam-4005	74	1	if	if	SCONJ
ejpam-4005	74	2	d(t	d(t	PROPN
ejpam-4005	74	3	u	u	PROPN
ejpam-4005	74	4	,	,	PUNCT
ejpam-4005	74	5	t	t	PROPN
ejpam-4005	74	6	v	v	NOUN
ejpam-4005	74	7	)	)	PUNCT
ejpam-4005	74	8	≤	≤	PUNCT
ejpam-4005	74	9	d(u	d(u	PROPN
ejpam-4005	74	10	,	,	PUNCT
ejpam-4005	74	11	v	v	NOUN
ejpam-4005	74	12	)	)	PUNCT
ejpam-4005	74	13	for	for	ADP
ejpam-4005	74	14	all	all	DET
ejpam-4005	74	15	u	u	NOUN
ejpam-4005	74	16	,	,	PUNCT
ejpam-4005	74	17	v	v	PROPN
ejpam-4005	74	18	∈	∈	PROPN
ejpam-4005	74	19	k.	k.	PROPN
ejpam-4005	74	20	t	t	PROPN
ejpam-4005	74	21	:	:	PUNCT
ejpam-4005	74	22	k	k	PROPN
ejpam-4005	74	23	→	→	PUNCT
ejpam-4005	74	24	k	k	PROPN
ejpam-4005	74	25	is	be	AUX
ejpam-4005	74	26	called	call	VERB
ejpam-4005	74	27	asymptotically	asymptotically	ADV
ejpam-4005	74	28	nonexpansive	nonexpansive	ADJ
ejpam-4005	74	29	if	if	SCONJ
ejpam-4005	74	30	there	there	PRON
ejpam-4005	74	31	exists	exist	VERB
ejpam-4005	74	32	a	a	DET
ejpam-4005	74	33	sequence	sequence	NOUN
ejpam-4005	74	34	{	{	PUNCT
ejpam-4005	74	35	kn	kn	PROPN
ejpam-4005	74	36	}	}	PUNCT
ejpam-4005	74	37	⊂	⊂	PROPN
ejpam-4005	74	38	[	[	X
ejpam-4005	74	39	1,∞	1,∞	NUM
ejpam-4005	74	40	)	)	PUNCT
ejpam-4005	74	41	with	with	ADP
ejpam-4005	74	42	kn	kn	PROPN
ejpam-4005	74	43	→	→	SYM
ejpam-4005	74	44	1	1	NUM
ejpam-4005	74	45	such	such	ADJ
ejpam-4005	74	46	that	that	SCONJ
ejpam-4005	74	47	d(t	d(t	PROPN
ejpam-4005	74	48	nu	nu	PROPN
ejpam-4005	74	49	,	,	PUNCT
ejpam-4005	74	50	t	t	PROPN
ejpam-4005	74	51	nv	nv	PROPN
ejpam-4005	74	52	)	)	PUNCT
ejpam-4005	74	53	≤	≤	PROPN
ejpam-4005	75	1	knd(u	knd(u	PROPN
ejpam-4005	75	2	,	,	PUNCT
ejpam-4005	75	3	v	v	NOUN
ejpam-4005	75	4	)	)	PUNCT
ejpam-4005	75	5	(	(	PUNCT
ejpam-4005	75	6	6	6	NUM
ejpam-4005	75	7	)	)	PUNCT
ejpam-4005	75	8	for	for	ADP
ejpam-4005	75	9	all	all	DET
ejpam-4005	75	10	u	u	NOUN
ejpam-4005	75	11	,	,	PUNCT
ejpam-4005	75	12	v	v	ADP
ejpam-4005	75	13	∈	∈	PROPN
ejpam-4005	75	14	k	k	NOUN
ejpam-4005	75	15	and	and	CCONJ
ejpam-4005	75	16	n	n	PRON
ejpam-4005	75	17	≥	≥	NUM
ejpam-4005	75	18	1	1	NUM
ejpam-4005	75	19	.	.	PUNCT
ejpam-4005	76	1	t	t	NOUN
ejpam-4005	76	2	:	:	PUNCT
ejpam-4005	77	1	k	k	PROPN
ejpam-4005	77	2	→	→	PUNCT
ejpam-4005	77	3	k	k	PROPN
ejpam-4005	77	4	is	be	AUX
ejpam-4005	77	5	said	say	VERB
ejpam-4005	77	6	to	to	PART
ejpam-4005	77	7	be	be	AUX
ejpam-4005	77	8	uniformly	uniformly	ADV
ejpam-4005	77	9	l	l	NOUN
ejpam-4005	77	10	-	-	NOUN
ejpam-4005	77	11	lipschitzian	lipschitzian	ADJ
ejpam-4005	77	12	if	if	SCONJ
ejpam-4005	77	13	there	there	PRON
ejpam-4005	77	14	exists	exist	VERB
ejpam-4005	77	15	a	a	DET
ejpam-4005	77	16	constant	constant	ADJ
ejpam-4005	77	17	l	l	NOUN
ejpam-4005	77	18	>	>	X
ejpam-4005	77	19	0	0	NUM
ejpam-4005	77	20	such	such	ADJ
ejpam-4005	77	21	that	that	SCONJ
ejpam-4005	77	22	d(t	d(t	PROPN
ejpam-4005	77	23	nu	nu	PROPN
ejpam-4005	77	24	,	,	PUNCT
ejpam-4005	77	25	t	t	PROPN
ejpam-4005	77	26	nv	nv	PROPN
ejpam-4005	77	27	)	)	PUNCT
ejpam-4005	77	28	≤	≤	NOUN
ejpam-4005	77	29	ld(u	ld(u	X
ejpam-4005	77	30	,	,	PUNCT
ejpam-4005	77	31	v	v	NOUN
ejpam-4005	77	32	)	)	PUNCT
ejpam-4005	77	33	for	for	ADP
ejpam-4005	77	34	all	all	DET
ejpam-4005	77	35	u	u	NOUN
ejpam-4005	77	36	,	,	PUNCT
ejpam-4005	77	37	v	v	ADP
ejpam-4005	77	38	∈	∈	PROPN
ejpam-4005	77	39	k	k	NOUN
ejpam-4005	77	40	and	and	CCONJ
ejpam-4005	77	41	n	n	PRON
ejpam-4005	77	42	≥	≥	NOUN
ejpam-4005	77	43	1	1	NUM
ejpam-4005	77	44	.	.	PUNCT
ejpam-4005	78	1	it	it	PRON
ejpam-4005	78	2	follows	follow	VERB
ejpam-4005	78	3	that	that	SCONJ
ejpam-4005	78	4	each	each	DET
ejpam-4005	78	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	78	6	mapping	mapping	NOUN
ejpam-4005	78	7	is	be	AUX
ejpam-4005	78	8	an	an	DET
ejpam-4005	78	9	asymptotically	asymptotically	ADV
ejpam-4005	78	10	nonexpansive	nonexpansive	ADJ
ejpam-4005	78	11	mapping	mapping	NOUN
ejpam-4005	78	12	with	with	ADP
ejpam-4005	78	13	kn	kn	PROPN
ejpam-4005	78	14	=	=	PROPN
ejpam-4005	78	15	1	1	NUM
ejpam-4005	78	16	,	,	PUNCT
ejpam-4005	78	17	∀n	∀n	NUM
ejpam-4005	78	18	≥	≥	NOUN
ejpam-4005	78	19	1	1	NUM
ejpam-4005	78	20	.	.	PUNCT
ejpam-4005	79	1	moreover	moreover	ADV
ejpam-4005	79	2	,	,	PUNCT
ejpam-4005	79	3	each	each	DET
ejpam-4005	79	4	asymptotically	asymptotically	ADV
ejpam-4005	79	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	79	6	mapping	mapping	NOUN
ejpam-4005	79	7	is	be	AUX
ejpam-4005	79	8	a	a	DET
ejpam-4005	79	9	uniformly	uniformly	ADJ
ejpam-4005	79	10	l	l	NOUN
ejpam-4005	79	11	-lipschitzian	-lipschitzian	ADJ
ejpam-4005	79	12	mapping	mapping	NOUN
ejpam-4005	79	13	with	with	ADP
ejpam-4005	79	14	l	l	NOUN
ejpam-4005	79	15	=	=	SYM
ejpam-4005	79	16	supn∈ℵ	supn∈ℵ	PROPN
ejpam-4005	79	17	{	{	PUNCT
ejpam-4005	79	18	kn	kn	PROPN
ejpam-4005	79	19	}	}	PUNCT
ejpam-4005	79	20	.	.	PUNCT
ejpam-4005	80	1	however	however	ADV
ejpam-4005	80	2	,	,	PUNCT
ejpam-4005	80	3	the	the	DET
ejpam-4005	80	4	converse	converse	NOUN
ejpam-4005	80	5	of	of	ADP
ejpam-4005	80	6	these	these	DET
ejpam-4005	80	7	statements	statement	NOUN
ejpam-4005	80	8	is	be	AUX
ejpam-4005	80	9	not	not	PART
ejpam-4005	80	10	true	true	ADJ
ejpam-4005	80	11	,	,	PUNCT
ejpam-4005	80	12	in	in	ADP
ejpam-4005	80	13	general	general	ADJ
ejpam-4005	80	14	.	.	PUNCT
ejpam-4005	81	1	note	note	VERB
ejpam-4005	81	2	that	that	SCONJ
ejpam-4005	81	3	,	,	PUNCT
ejpam-4005	81	4	a	a	DET
ejpam-4005	81	5	subset	subset	NOUN
ejpam-4005	81	6	k	k	PROPN
ejpam-4005	81	7	of	of	ADP
ejpam-4005	81	8	x	x	PROPN
ejpam-4005	81	9	is	be	AUX
ejpam-4005	81	10	said	say	VERB
ejpam-4005	81	11	to	to	PART
ejpam-4005	81	12	be	be	AUX
ejpam-4005	81	13	a	a	DET
ejpam-4005	81	14	retract	retract	NOUN
ejpam-4005	81	15	if	if	SCONJ
ejpam-4005	81	16	there	there	PRON
ejpam-4005	81	17	exists	exist	VERB
ejpam-4005	81	18	a	a	DET
ejpam-4005	81	19	continuous	continuous	ADJ
ejpam-4005	81	20	mapping	mapping	NOUN
ejpam-4005	81	21	p	p	NOUN
ejpam-4005	81	22	:	:	PUNCT
ejpam-4005	81	23	x	x	X
ejpam-4005	81	24	→	→	SYM
ejpam-4005	81	25	k	k	X
ejpam-4005	81	26	such	such	ADJ
ejpam-4005	81	27	that	that	SCONJ
ejpam-4005	81	28	pu	pu	PROPN
ejpam-4005	81	29	=	=	SYM
ejpam-4005	81	30	u	u	PROPN
ejpam-4005	81	31	for	for	ADP
ejpam-4005	81	32	all	all	DET
ejpam-4005	81	33	u	u	PROPN
ejpam-4005	81	34	∈	∈	PROPN
ejpam-4005	81	35	k.	k.	NOUN
ejpam-4005	81	36	for	for	ADP
ejpam-4005	81	37	more	more	ADJ
ejpam-4005	81	38	information	information	NOUN
ejpam-4005	81	39	on	on	ADP
ejpam-4005	81	40	nonexpansive	nonexpansive	ADJ
ejpam-4005	81	41	retracts	retract	NOUN
ejpam-4005	81	42	and	and	CCONJ
ejpam-4005	81	43	retractions	retraction	NOUN
ejpam-4005	81	44	,	,	PUNCT
ejpam-4005	81	45	we	we	PRON
ejpam-4005	81	46	refer	refer	VERB
ejpam-4005	81	47	the	the	DET
ejpam-4005	81	48	reader	reader	NOUN
ejpam-4005	81	49	to	to	ADP
ejpam-4005	81	50	(	(	PUNCT
ejpam-4005	81	51	[	[	X
ejpam-4005	81	52	8	8	NUM
ejpam-4005	81	53	,	,	PUNCT
ejpam-4005	81	54	14	14	NUM
ejpam-4005	81	55	]	]	PUNCT
ejpam-4005	81	56	)	)	PUNCT
ejpam-4005	81	57	.	.	PUNCT
ejpam-4005	82	1	for	for	ADP
ejpam-4005	82	2	any	any	DET
ejpam-4005	82	3	nonempty	nonempty	NOUN
ejpam-4005	82	4	subset	subset	VERB
ejpam-4005	82	5	k	k	PROPN
ejpam-4005	82	6	of	of	ADP
ejpam-4005	82	7	a	a	DET
ejpam-4005	82	8	real	real	ADJ
ejpam-4005	82	9	metric	metric	ADJ
ejpam-4005	82	10	space	space	NOUN
ejpam-4005	82	11	(	(	PUNCT
ejpam-4005	82	12	x	x	NOUN
ejpam-4005	82	13	,	,	PUNCT
ejpam-4005	82	14	d	d	PROPN
ejpam-4005	82	15	)	)	PUNCT
ejpam-4005	82	16	,	,	PUNCT
ejpam-4005	82	17	let	let	VERB
ejpam-4005	82	18	p	p	PRON
ejpam-4005	82	19	:	:	PUNCT
ejpam-4005	82	20	x	x	SYM
ejpam-4005	82	21	→	→	SYM
ejpam-4005	82	22	k	k	X
ejpam-4005	82	23	be	be	AUX
ejpam-4005	82	24	a	a	DET
ejpam-4005	82	25	nonexpansive	nonexpansive	ADJ
ejpam-4005	82	26	retraction	retraction	NOUN
ejpam-4005	82	27	of	of	ADP
ejpam-4005	82	28	x	x	PUNCT
ejpam-4005	82	29	onto	onto	ADP
ejpam-4005	82	30	k.	k.	PROPN
ejpam-4005	82	31	then	then	ADV
ejpam-4005	82	32	,	,	PUNCT
ejpam-4005	82	33	t	t	PROPN
ejpam-4005	82	34	:	:	PUNCT
ejpam-4005	82	35	k	k	X
ejpam-4005	82	36	→	→	PUNCT
ejpam-4005	82	37	x	x	X
ejpam-4005	82	38	is	be	AUX
ejpam-4005	82	39	said	say	VERB
ejpam-4005	82	40	to	to	PART
ejpam-4005	82	41	be	be	AUX
ejpam-4005	82	42	an	an	DET
ejpam-4005	82	43	asymptotically	asymptotically	ADV
ejpam-4005	82	44	nonexpansive	nonexpansive	ADJ
ejpam-4005	82	45	t.	t.	PROPN
ejpam-4005	82	46	thianwan	thianwan	PROPN
ejpam-4005	82	47	/	/	SYM
ejpam-4005	82	48	eur	eur	PROPN
ejpam-4005	82	49	.	.	PUNCT
ejpam-4005	83	1	j.	j.	PROPN
ejpam-4005	83	2	pure	pure	PROPN
ejpam-4005	83	3	appl	appl	PROPN
ejpam-4005	83	4	.	.	PROPN
ejpam-4005	83	5	math	math	PROPN
ejpam-4005	83	6	,	,	PUNCT
ejpam-4005	83	7	14	14	NUM
ejpam-4005	83	8	(	(	PUNCT
ejpam-4005	83	9	3	3	NUM
ejpam-4005	83	10	)	)	PUNCT
ejpam-4005	83	11	(	(	PUNCT
ejpam-4005	83	12	2021	2021	NUM
ejpam-4005	83	13	)	)	PUNCT
ejpam-4005	83	14	,	,	PUNCT
ejpam-4005	83	15	650	650	NUM
ejpam-4005	83	16	-	-	SYM
ejpam-4005	83	17	665	665	NUM
ejpam-4005	83	18	653	653	NUM
ejpam-4005	83	19	nonself	nonself	NOUN
ejpam-4005	83	20	-	-	PUNCT
ejpam-4005	83	21	mapping	mapping	NOUN
ejpam-4005	83	22	(	(	PUNCT
ejpam-4005	83	23	see	see	VERB
ejpam-4005	83	24	[	[	X
ejpam-4005	83	25	5	5	NUM
ejpam-4005	83	26	]	]	PUNCT
ejpam-4005	83	27	)	)	PUNCT
ejpam-4005	83	28	if	if	SCONJ
ejpam-4005	83	29	there	there	PRON
ejpam-4005	83	30	exists	exist	VERB
ejpam-4005	83	31	a	a	DET
ejpam-4005	83	32	sequence	sequence	NOUN
ejpam-4005	83	33	{	{	PUNCT
ejpam-4005	83	34	kn	kn	PROPN
ejpam-4005	83	35	}	}	PUNCT
ejpam-4005	83	36	⊂	⊂	PROPN
ejpam-4005	84	1	[	[	X
ejpam-4005	84	2	1,∞	1,∞	NUM
ejpam-4005	84	3	)	)	PUNCT
ejpam-4005	84	4	with	with	ADP
ejpam-4005	84	5	kn	kn	PROPN
ejpam-4005	84	6	→	→	SYM
ejpam-4005	84	7	1	1	NUM
ejpam-4005	84	8	as	as	ADP
ejpam-4005	84	9	n→∞	n→∞	NUM
ejpam-4005	84	10	such	such	ADJ
ejpam-4005	84	11	that	that	SCONJ
ejpam-4005	84	12	d(t	d(t	PROPN
ejpam-4005	84	13	(	(	PUNCT
ejpam-4005	84	14	pt	pt	PROPN
ejpam-4005	84	15	)	)	PUNCT
ejpam-4005	84	16	n−1	n−1	PROPN
ejpam-4005	84	17	u	u	PROPN
ejpam-4005	84	18	,	,	PUNCT
ejpam-4005	84	19	t	t	PROPN
ejpam-4005	84	20	(	(	PUNCT
ejpam-4005	84	21	pt	pt	PROPN
ejpam-4005	84	22	)	)	PUNCT
ejpam-4005	84	23	n−1	n−1	PROPN
ejpam-4005	84	24	v	v	NOUN
ejpam-4005	84	25	)	)	PUNCT
ejpam-4005	84	26	≤	≤	PROPN
ejpam-4005	84	27	knd	knd	X
ejpam-4005	84	28	(	(	PUNCT
ejpam-4005	84	29	u	u	PROPN
ejpam-4005	84	30	,	,	PUNCT
ejpam-4005	84	31	v	v	NOUN
ejpam-4005	84	32	)	)	PUNCT
ejpam-4005	84	33	(	(	PUNCT
ejpam-4005	84	34	7	7	X
ejpam-4005	84	35	)	)	PUNCT
ejpam-4005	84	36	for	for	ADP
ejpam-4005	84	37	all	all	DET
ejpam-4005	84	38	u	u	NOUN
ejpam-4005	84	39	,	,	PUNCT
ejpam-4005	84	40	v	v	ADP
ejpam-4005	84	41	∈	∈	PROPN
ejpam-4005	84	42	k	k	NOUN
ejpam-4005	84	43	and	and	CCONJ
ejpam-4005	84	44	n	n	PRON
ejpam-4005	84	45	≥	≥	NUM
ejpam-4005	84	46	1	1	NUM
ejpam-4005	84	47	.	.	PUNCT
ejpam-4005	85	1	we	we	PRON
ejpam-4005	85	2	denote	denote	VERB
ejpam-4005	85	3	by	by	ADP
ejpam-4005	85	4	(	(	PUNCT
ejpam-4005	85	5	pt	pt	INTJ
ejpam-4005	85	6	)	)	PUNCT
ejpam-4005	85	7	0	0	PROPN
ejpam-4005	86	1	the	the	DET
ejpam-4005	86	2	identity	identity	NOUN
ejpam-4005	86	3	map	map	NOUN
ejpam-4005	86	4	from	from	ADP
ejpam-4005	86	5	k	k	PROPN
ejpam-4005	86	6	onto	onto	ADP
ejpam-4005	86	7	itself	itself	PRON
ejpam-4005	86	8	.	.	PUNCT
ejpam-4005	87	1	we	we	PRON
ejpam-4005	87	2	see	see	VERB
ejpam-4005	87	3	that	that	SCONJ
ejpam-4005	87	4	if	if	SCONJ
ejpam-4005	87	5	t	t	PROPN
ejpam-4005	87	6	is	be	AUX
ejpam-4005	87	7	a	a	DET
ejpam-4005	87	8	self	self	NOUN
ejpam-4005	87	9	-	-	PUNCT
ejpam-4005	87	10	mapping	mapping	NOUN
ejpam-4005	87	11	,	,	PUNCT
ejpam-4005	87	12	then	then	ADV
ejpam-4005	87	13	p	p	NOUN
ejpam-4005	87	14	becomes	become	VERB
ejpam-4005	87	15	the	the	DET
ejpam-4005	87	16	identity	identity	NOUN
ejpam-4005	87	17	mapping	mapping	NOUN
ejpam-4005	87	18	,	,	PUNCT
ejpam-4005	87	19	so	so	SCONJ
ejpam-4005	87	20	that	that	SCONJ
ejpam-4005	87	21	(	(	PUNCT
ejpam-4005	87	22	7	7	X
ejpam-4005	87	23	)	)	PUNCT
ejpam-4005	87	24	reduces	reduce	VERB
ejpam-4005	87	25	to	to	ADP
ejpam-4005	87	26	(	(	PUNCT
ejpam-4005	87	27	6	6	NUM
ejpam-4005	87	28	)	)	PUNCT
ejpam-4005	87	29	.	.	PUNCT
ejpam-4005	88	1	in	in	ADP
ejpam-4005	88	2	addition	addition	NOUN
ejpam-4005	88	3	,	,	PUNCT
ejpam-4005	88	4	if	if	SCONJ
ejpam-4005	88	5	t	t	NOUN
ejpam-4005	88	6	:	:	PUNCT
ejpam-4005	88	7	k	k	X
ejpam-4005	88	8	→	→	PUNCT
ejpam-4005	88	9	x	x	X
ejpam-4005	88	10	is	be	AUX
ejpam-4005	88	11	asymtotically	asymtotically	ADV
ejpam-4005	88	12	nonexpansive	nonexpansive	ADJ
ejpam-4005	88	13	in	in	ADP
ejpam-4005	88	14	light	light	NOUN
ejpam-4005	88	15	of	of	ADP
ejpam-4005	88	16	(	(	PUNCT
ejpam-4005	88	17	7	7	NUM
ejpam-4005	88	18	)	)	PUNCT
ejpam-4005	88	19	and	and	CCONJ
ejpam-4005	88	20	p	p	X
ejpam-4005	88	21	:	:	PUNCT
ejpam-4005	88	22	x	x	X
ejpam-4005	88	23	→	→	SYM
ejpam-4005	88	24	k	k	X
ejpam-4005	88	25	is	be	AUX
ejpam-4005	88	26	a	a	DET
ejpam-4005	88	27	nonexpansive	nonexpansive	ADJ
ejpam-4005	88	28	retraction	retraction	NOUN
ejpam-4005	88	29	,	,	PUNCT
ejpam-4005	88	30	then	then	ADV
ejpam-4005	88	31	pt	pt	X
ejpam-4005	88	32	:	:	PUNCT
ejpam-4005	88	33	k	k	PROPN
ejpam-4005	88	34	→	→	PUNCT
ejpam-4005	88	35	k	k	PROPN
ejpam-4005	88	36	is	be	AUX
ejpam-4005	88	37	asymtotically	asymtotically	ADV
ejpam-4005	88	38	nonexpansive	nonexpansive	ADJ
ejpam-4005	88	39	in	in	ADP
ejpam-4005	88	40	light	light	NOUN
ejpam-4005	88	41	of	of	ADP
ejpam-4005	88	42	(	(	PUNCT
ejpam-4005	88	43	6	6	NUM
ejpam-4005	88	44	)	)	PUNCT
ejpam-4005	88	45	(	(	PUNCT
ejpam-4005	88	46	see	see	VERB
ejpam-4005	88	47	also	also	ADV
ejpam-4005	88	48	(	(	PUNCT
ejpam-4005	88	49	8)	8)	NUM
ejpam-4005	88	50	)	)	PUNCT
ejpam-4005	88	51	.	.	PUNCT
ejpam-4005	89	1	indeed	indeed	ADV
ejpam-4005	89	2	,	,	PUNCT
ejpam-4005	89	3	for	for	ADP
ejpam-4005	89	4	all	all	DET
ejpam-4005	89	5	u	u	NOUN
ejpam-4005	89	6	,	,	PUNCT
ejpam-4005	89	7	v	v	ADP
ejpam-4005	89	8	∈	∈	PROPN
ejpam-4005	89	9	k	k	NOUN
ejpam-4005	89	10	and	and	CCONJ
ejpam-4005	89	11	n	n	PRON
ejpam-4005	89	12	≥	≥	NUM
ejpam-4005	89	13	1	1	NUM
ejpam-4005	89	14	,	,	PUNCT
ejpam-4005	89	15	by	by	ADP
ejpam-4005	89	16	(	(	PUNCT
ejpam-4005	89	17	7	7	NUM
ejpam-4005	89	18	)	)	PUNCT
ejpam-4005	89	19	,	,	PUNCT
ejpam-4005	89	20	it	it	PRON
ejpam-4005	89	21	follows	follow	VERB
ejpam-4005	89	22	that	that	SCONJ
ejpam-4005	89	23	d((pt	d((pt	PROPN
ejpam-4005	89	24	)	)	PUNCT
ejpam-4005	89	25	nu	nu	PROPN
ejpam-4005	89	26	,	,	PUNCT
ejpam-4005	89	27	(	(	PUNCT
ejpam-4005	89	28	pt	pt	INTJ
ejpam-4005	89	29	)	)	PUNCT
ejpam-4005	89	30	nv	nv	PROPN
ejpam-4005	89	31	)	)	PUNCT
ejpam-4005	90	1	=	=	SYM
ejpam-4005	90	2	d(pt	d(pt	PROPN
ejpam-4005	90	3	(	(	PUNCT
ejpam-4005	90	4	pt	pt	INTJ
ejpam-4005	90	5	)	)	PUNCT
ejpam-4005	90	6	n−1u	n−1u	PROPN
ejpam-4005	90	7	,	,	PUNCT
ejpam-4005	90	8	pt	pt	X
ejpam-4005	90	9	(	(	PUNCT
ejpam-4005	90	10	pt	pt	INTJ
ejpam-4005	90	11	)	)	PUNCT
ejpam-4005	90	12	n−1v	n−1v	NOUN
ejpam-4005	90	13	)	)	PUNCT
ejpam-4005	90	14	≤	≤	NOUN
ejpam-4005	90	15	d(t	d(t	PROPN
ejpam-4005	90	16	(	(	PUNCT
ejpam-4005	90	17	pt	pt	PROPN
ejpam-4005	90	18	)	)	PUNCT
ejpam-4005	90	19	n−1u	n−1u	PROPN
ejpam-4005	90	20	,	,	PUNCT
ejpam-4005	90	21	t	t	PROPN
ejpam-4005	90	22	(	(	PUNCT
ejpam-4005	90	23	pt	pt	INTJ
ejpam-4005	90	24	)	)	PUNCT
ejpam-4005	90	25	n−1v	n−1v	NOUN
ejpam-4005	90	26	)	)	PUNCT
ejpam-4005	90	27	≤	≤	PUNCT
ejpam-4005	91	1	knd(u	knd(u	PROPN
ejpam-4005	91	2	,	,	PUNCT
ejpam-4005	91	3	v	v	NOUN
ejpam-4005	91	4	)	)	PUNCT
ejpam-4005	91	5	.	.	PUNCT
ejpam-4005	92	1	therefore	therefore	ADV
ejpam-4005	92	2	,	,	PUNCT
ejpam-4005	92	3	we	we	PRON
ejpam-4005	92	4	now	now	ADV
ejpam-4005	92	5	introduce	introduce	VERB
ejpam-4005	92	6	the	the	DET
ejpam-4005	92	7	following	follow	VERB
ejpam-4005	92	8	definition	definition	NOUN
ejpam-4005	92	9	.	.	PUNCT
ejpam-4005	93	1	definition	definition	NOUN
ejpam-4005	93	2	1	1	NUM
ejpam-4005	93	3	.	.	PUNCT
ejpam-4005	94	1	for	for	ADP
ejpam-4005	94	2	any	any	DET
ejpam-4005	94	3	nonempty	nonempty	NOUN
ejpam-4005	94	4	subset	subset	VERB
ejpam-4005	94	5	k	k	PROPN
ejpam-4005	94	6	of	of	ADP
ejpam-4005	94	7	a	a	DET
ejpam-4005	94	8	metric	metric	ADJ
ejpam-4005	94	9	space	space	NOUN
ejpam-4005	94	10	(	(	PUNCT
ejpam-4005	94	11	x	x	NOUN
ejpam-4005	94	12	,	,	PUNCT
ejpam-4005	94	13	d	d	NOUN
ejpam-4005	94	14	)	)	PUNCT
ejpam-4005	94	15	.	.	PUNCT
ejpam-4005	95	1	let	let	VERB
ejpam-4005	95	2	p	p	PRON
ejpam-4005	95	3	:	:	PUNCT
ejpam-4005	95	4	x	x	SYM
ejpam-4005	95	5	→	→	SYM
ejpam-4005	95	6	k	k	X
ejpam-4005	95	7	be	be	AUX
ejpam-4005	95	8	a	a	DET
ejpam-4005	95	9	nonexpansive	nonexpansive	ADJ
ejpam-4005	95	10	retraction	retraction	NOUN
ejpam-4005	95	11	of	of	ADP
ejpam-4005	95	12	x	x	PUNCT
ejpam-4005	95	13	onto	onto	ADP
ejpam-4005	95	14	k.	k.	PROPN
ejpam-4005	95	15	a	a	DET
ejpam-4005	95	16	nonself	nonself	NOUN
ejpam-4005	95	17	-	-	PUNCT
ejpam-4005	95	18	mapping	mapping	NOUN
ejpam-4005	95	19	t	t	NOUN
ejpam-4005	95	20	:	:	PUNCT
ejpam-4005	96	1	k	k	X
ejpam-4005	96	2	→	→	PUNCT
ejpam-4005	96	3	x	x	X
ejpam-4005	96	4	is	be	AUX
ejpam-4005	96	5	called	call	VERB
ejpam-4005	96	6	asymptotically	asymptotically	ADV
ejpam-4005	96	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	96	8	with	with	ADP
ejpam-4005	96	9	respect	respect	NOUN
ejpam-4005	96	10	to	to	ADP
ejpam-4005	96	11	p	p	NOUN
ejpam-4005	96	12	if	if	SCONJ
ejpam-4005	96	13	there	there	PRON
ejpam-4005	96	14	exists	exist	VERB
ejpam-4005	96	15	a	a	DET
ejpam-4005	96	16	sequence	sequence	NOUN
ejpam-4005	96	17	{	{	PUNCT
ejpam-4005	96	18	kn	kn	PROPN
ejpam-4005	96	19	}	}	PUNCT
ejpam-4005	96	20	⊂	⊂	PROPN
ejpam-4005	96	21	[	[	X
ejpam-4005	96	22	1,∞	1,∞	NUM
ejpam-4005	96	23	)	)	PUNCT
ejpam-4005	96	24	with	with	ADP
ejpam-4005	96	25	kn	kn	PROPN
ejpam-4005	96	26	→	→	SYM
ejpam-4005	96	27	1	1	NUM
ejpam-4005	96	28	as	as	ADP
ejpam-4005	96	29	n→∞	n→∞	PRON
ejpam-4005	96	30	such	such	ADJ
ejpam-4005	96	31	that	that	SCONJ
ejpam-4005	96	32	d((pt	d((pt	PROPN
ejpam-4005	96	33	)	)	PUNCT
ejpam-4005	96	34	n	n	PRON
ejpam-4005	96	35	u	u	NOUN
ejpam-4005	96	36	,	,	PUNCT
ejpam-4005	96	37	(	(	PUNCT
ejpam-4005	96	38	pt	pt	X
ejpam-4005	96	39	)	)	PUNCT
ejpam-4005	96	40	n	n	PRON
ejpam-4005	96	41	v	v	NOUN
ejpam-4005	96	42	)	)	PUNCT
ejpam-4005	96	43	≤	≤	PROPN
ejpam-4005	96	44	knd	knd	X
ejpam-4005	96	45	(	(	PUNCT
ejpam-4005	96	46	u	u	PROPN
ejpam-4005	96	47	,	,	PUNCT
ejpam-4005	96	48	v	v	NOUN
ejpam-4005	96	49	)	)	PUNCT
ejpam-4005	96	50	(	(	PUNCT
ejpam-4005	96	51	8)	8)	NUM
ejpam-4005	96	52	for	for	ADP
ejpam-4005	96	53	all	all	DET
ejpam-4005	96	54	u	u	NOUN
ejpam-4005	96	55	,	,	PUNCT
ejpam-4005	96	56	v	v	ADP
ejpam-4005	96	57	∈	∈	PROPN
ejpam-4005	96	58	k	k	NOUN
ejpam-4005	96	59	and	and	CCONJ
ejpam-4005	96	60	n	n	PRON
ejpam-4005	96	61	≥	≥	NOUN
ejpam-4005	96	62	1	1	NUM
ejpam-4005	96	63	.	.	PUNCT
ejpam-4005	97	1	in	in	ADP
ejpam-4005	97	2	the	the	DET
ejpam-4005	97	3	sequel	sequel	NOUN
ejpam-4005	97	4	,	,	PUNCT
ejpam-4005	97	5	we	we	PRON
ejpam-4005	97	6	shall	shall	AUX
ejpam-4005	97	7	need	need	VERB
ejpam-4005	97	8	the	the	DET
ejpam-4005	97	9	following	follow	VERB
ejpam-4005	97	10	lemmas	lemmas	NOUN
ejpam-4005	97	11	.	.	PUNCT
ejpam-4005	98	1	lemma	lemma	PROPN
ejpam-4005	98	2	1	1	NUM
ejpam-4005	98	3	.	.	PUNCT
ejpam-4005	99	1	(	(	PUNCT
ejpam-4005	99	2	[	[	X
ejpam-4005	99	3	20	20	NUM
ejpam-4005	99	4	]	]	PUNCT
ejpam-4005	99	5	)	)	PUNCT
ejpam-4005	99	6	let	let	VERB
ejpam-4005	99	7	{	{	PUNCT
ejpam-4005	99	8	ηn	ηn	VERB
ejpam-4005	99	9	}	}	PUNCT
ejpam-4005	99	10	,	,	PUNCT
ejpam-4005	99	11	{	{	PUNCT
ejpam-4005	99	12	ϑn	ϑn	NOUN
ejpam-4005	99	13	}	}	PUNCT
ejpam-4005	99	14	and	and	CCONJ
ejpam-4005	99	15	{	{	PUNCT
ejpam-4005	99	16	ζn	ζn	PART
ejpam-4005	99	17	}	}	PUNCT
ejpam-4005	99	18	be	be	AUX
ejpam-4005	99	19	sequences	sequence	NOUN
ejpam-4005	99	20	of	of	ADP
ejpam-4005	99	21	non	non	ADJ
ejpam-4005	99	22	-	-	ADJ
ejpam-4005	99	23	negative	negative	ADJ
ejpam-4005	99	24	real	real	ADJ
ejpam-4005	99	25	numbers	number	NOUN
ejpam-4005	99	26	such	such	ADJ
ejpam-4005	99	27	that	that	SCONJ
ejpam-4005	99	28	ηn+1	ηn+1	ADV
ejpam-4005	99	29	≤	≤	NUM
ejpam-4005	99	30	(	(	PUNCT
ejpam-4005	99	31	1	1	NUM
ejpam-4005	99	32	+	+	CCONJ
ejpam-4005	99	33	ϑn)ηn	ϑn)ηn	X
ejpam-4005	100	1	+	+	NOUN
ejpam-4005	100	2	ζn	ζn	PROPN
ejpam-4005	100	3	,	,	PUNCT
ejpam-4005	100	4	∀n	∀n	NUM
ejpam-4005	100	5	≥	≥	NOUN
ejpam-4005	100	6	1	1	NUM
ejpam-4005	100	7	.	.	PUNCT
ejpam-4005	101	1	if	if	SCONJ
ejpam-4005	101	2	∞∑	∞∑	NUM
ejpam-4005	101	3	n=1	n=1	PUNCT
ejpam-4005	101	4	ϑn	ϑn	ADP
ejpam-4005	101	5	<	<	X
ejpam-4005	101	6	∞	∞	NUM
ejpam-4005	101	7	and	and	CCONJ
ejpam-4005	101	8	∞∑	∞∑	NUM
ejpam-4005	101	9	n=1	n=1	PROPN
ejpam-4005	101	10	ζn	ζn	ADP
ejpam-4005	101	11	<	<	X
ejpam-4005	101	12	∞	∞	PROPN
ejpam-4005	101	13	,	,	PUNCT
ejpam-4005	101	14	then	then	ADV
ejpam-4005	101	15	lim	lim	PROPN
ejpam-4005	101	16	n→∞	n→∞	PROPN
ejpam-4005	101	17	ηn	ηn	PROPN
ejpam-4005	101	18	exists	exist	VERB
ejpam-4005	101	19	.	.	PUNCT
ejpam-4005	102	1	lemma	lemma	PROPN
ejpam-4005	102	2	2	2	NUM
ejpam-4005	102	3	.	.	PUNCT
ejpam-4005	103	1	(	(	PUNCT
ejpam-4005	103	2	[	[	X
ejpam-4005	103	3	12	12	NUM
ejpam-4005	103	4	]	]	PUNCT
ejpam-4005	103	5	)	)	PUNCT
ejpam-4005	103	6	let	let	VERB
ejpam-4005	103	7	{	{	PUNCT
ejpam-4005	103	8	un	un	VERB
ejpam-4005	103	9	}	}	PUNCT
ejpam-4005	103	10	and	and	CCONJ
ejpam-4005	103	11	{	{	PUNCT
ejpam-4005	103	12	vn	vn	NOUN
ejpam-4005	103	13	}	}	PUNCT
ejpam-4005	103	14	be	be	AUX
ejpam-4005	103	15	two	two	NUM
ejpam-4005	103	16	sequences	sequence	NOUN
ejpam-4005	103	17	of	of	ADP
ejpam-4005	103	18	a	a	DET
ejpam-4005	103	19	uniformly	uniformly	ADV
ejpam-4005	103	20	convex	convex	ADJ
ejpam-4005	103	21	hyperbolic	hyperbolic	ADJ
ejpam-4005	103	22	space	space	NOUN
ejpam-4005	103	23	(	(	PUNCT
ejpam-4005	103	24	x	x	X
ejpam-4005	103	25	,	,	PUNCT
ejpam-4005	103	26	d	d	NOUN
ejpam-4005	103	27	,	,	PUNCT
ejpam-4005	103	28	h	h	NOUN
ejpam-4005	103	29	)	)	PUNCT
ejpam-4005	103	30	such	such	ADJ
ejpam-4005	103	31	that	that	SCONJ
ejpam-4005	103	32	,	,	PUNCT
ejpam-4005	103	33	for	for	ADP
ejpam-4005	103	34	r	r	PROPN
ejpam-4005	103	35	∈	∈	PROPN
ejpam-4005	104	1	[	[	X
ejpam-4005	104	2	0,∞	0,∞	NOUN
ejpam-4005	104	3	)	)	PUNCT
ejpam-4005	104	4	,	,	PUNCT
ejpam-4005	104	5	lim	lim	PROPN
ejpam-4005	104	6	n→∞	n→∞	NUM
ejpam-4005	104	7	sup	sup	PROPN
ejpam-4005	104	8	d(un	d(un	PROPN
ejpam-4005	104	9	,	,	PUNCT
ejpam-4005	104	10	a	a	PRON
ejpam-4005	104	11	)	)	PUNCT
ejpam-4005	104	12	≤	≤	NOUN
ejpam-4005	104	13	r	r	NOUN
ejpam-4005	104	14	,	,	PUNCT
ejpam-4005	104	15	lim	lim	PROPN
ejpam-4005	104	16	n→∞	n→∞	NUM
ejpam-4005	104	17	sup	sup	PROPN
ejpam-4005	104	18	d(vn	d(vn	PROPN
ejpam-4005	104	19	,	,	PUNCT
ejpam-4005	104	20	a	a	PRON
ejpam-4005	104	21	)	)	PUNCT
ejpam-4005	104	22	≤	≤	NOUN
ejpam-4005	104	23	r	r	NOUN
ejpam-4005	104	24	,	,	PUNCT
ejpam-4005	104	25	and	and	CCONJ
ejpam-4005	104	26	lim	lim	PROPN
ejpam-4005	104	27	n→∞	n→∞	NUM
ejpam-4005	104	28	d(h(un	d(h(un	PROPN
ejpam-4005	104	29	,	,	PUNCT
ejpam-4005	104	30	vn	vn	NOUN
ejpam-4005	104	31	,	,	PUNCT
ejpam-4005	104	32	ςn	ςn	PROPN
ejpam-4005	104	33	)	)	PUNCT
ejpam-4005	104	34	,	,	PUNCT
ejpam-4005	105	1	a	a	X
ejpam-4005	105	2	)	)	PUNCT
ejpam-4005	105	3	=	=	SYM
ejpam-4005	105	4	r	r	NOUN
ejpam-4005	105	5	,	,	PUNCT
ejpam-4005	105	6	where	where	SCONJ
ejpam-4005	105	7	ςn	ςn	PROPN
ejpam-4005	105	8	∈	∈	PROPN
ejpam-4005	105	9	[	[	X
ejpam-4005	105	10	a	a	X
ejpam-4005	105	11	,	,	PUNCT
ejpam-4005	105	12	b	b	NOUN
ejpam-4005	105	13	]	]	X
ejpam-4005	105	14	with	with	ADP
ejpam-4005	105	15	0	0	NUM
ejpam-4005	105	16	<	<	X
ejpam-4005	105	17	a	a	DET
ejpam-4005	105	18	≤	≤	NUM
ejpam-4005	105	19	b	b	NOUN
ejpam-4005	105	20	<	<	X
ejpam-4005	105	21	1	1	NUM
ejpam-4005	105	22	,	,	PUNCT
ejpam-4005	105	23	then	then	ADV
ejpam-4005	105	24	we	we	PRON
ejpam-4005	105	25	have	have	VERB
ejpam-4005	105	26	,	,	PUNCT
ejpam-4005	105	27	lim	lim	PROPN
ejpam-4005	105	28	n→∞	n→∞	NUM
ejpam-4005	105	29	d(un	d(un	PROPN
ejpam-4005	105	30	,	,	PUNCT
ejpam-4005	105	31	vn	vn	NOUN
ejpam-4005	105	32	)	)	PUNCT
ejpam-4005	105	33	=	=	SYM
ejpam-4005	106	1	0	0	X
ejpam-4005	106	2	.	.	PUNCT
ejpam-4005	107	1	t.	t.	PROPN
ejpam-4005	107	2	thianwan	thianwan	PROPN
ejpam-4005	107	3	/	/	SYM
ejpam-4005	107	4	eur	eur	PROPN
ejpam-4005	107	5	.	.	PUNCT
ejpam-4005	108	1	j.	j.	PROPN
ejpam-4005	108	2	pure	pure	PROPN
ejpam-4005	108	3	appl	appl	PROPN
ejpam-4005	108	4	.	.	PROPN
ejpam-4005	108	5	math	math	PROPN
ejpam-4005	108	6	,	,	PUNCT
ejpam-4005	108	7	14	14	NUM
ejpam-4005	108	8	(	(	PUNCT
ejpam-4005	108	9	3	3	NUM
ejpam-4005	108	10	)	)	PUNCT
ejpam-4005	108	11	(	(	PUNCT
ejpam-4005	108	12	2021	2021	NUM
ejpam-4005	108	13	)	)	PUNCT
ejpam-4005	108	14	,	,	PUNCT
ejpam-4005	108	15	650	650	NUM
ejpam-4005	108	16	-	-	SYM
ejpam-4005	108	17	665	665	NUM
ejpam-4005	108	18	654	654	NUM
ejpam-4005	108	19	2	2	NUM
ejpam-4005	108	20	.	.	PUNCT
ejpam-4005	108	21	main	main	ADJ
ejpam-4005	108	22	results	result	NOUN
ejpam-4005	108	23	in	in	ADP
ejpam-4005	108	24	this	this	DET
ejpam-4005	108	25	section	section	NOUN
ejpam-4005	108	26	,	,	PUNCT
ejpam-4005	108	27	we	we	PRON
ejpam-4005	108	28	suggest	suggest	VERB
ejpam-4005	108	29	a	a	DET
ejpam-4005	108	30	new	new	ADJ
ejpam-4005	108	31	iterative	iterative	NOUN
ejpam-4005	108	32	algorithm	algorithm	NOUN
ejpam-4005	108	33	for	for	ADP
ejpam-4005	108	34	mixed	mixed	ADJ
ejpam-4005	108	35	type	type	NOUN
ejpam-4005	108	36	asypmtotically	asypmtotically	ADV
ejpam-4005	108	37	nonexpansive	nonexpansive	ADJ
ejpam-4005	108	38	mappings	mapping	NOUN
ejpam-4005	108	39	and	and	CCONJ
ejpam-4005	108	40	establish	establish	VERB
ejpam-4005	108	41	the	the	DET
ejpam-4005	108	42	strong	strong	ADJ
ejpam-4005	108	43	convergence	convergence	NOUN
ejpam-4005	108	44	theorem	theorem	VERB
ejpam-4005	108	45	in	in	ADP
ejpam-4005	108	46	a	a	DET
ejpam-4005	108	47	uniformly	uniformly	ADV
ejpam-4005	108	48	convex	convex	ADJ
ejpam-4005	108	49	hyperbolic	hyperbolic	ADJ
ejpam-4005	108	50	space	space	NOUN
ejpam-4005	108	51	.	.	PUNCT
ejpam-4005	109	1	let	let	VERB
ejpam-4005	109	2	k	k	PRON
ejpam-4005	109	3	be	be	AUX
ejpam-4005	109	4	a	a	DET
ejpam-4005	109	5	nonempty	nonempty	ADV
ejpam-4005	109	6	closed	close	VERB
ejpam-4005	109	7	convex	convex	NOUN
ejpam-4005	109	8	subset	subset	NOUN
ejpam-4005	109	9	of	of	ADP
ejpam-4005	109	10	a	a	DET
ejpam-4005	109	11	uniformly	uniformly	ADV
ejpam-4005	109	12	convex	convex	ADJ
ejpam-4005	109	13	hyperbolic	hyperbolic	ADJ
ejpam-4005	109	14	space	space	NOUN
ejpam-4005	109	15	(	(	PUNCT
ejpam-4005	109	16	x	x	X
ejpam-4005	109	17	,	,	PUNCT
ejpam-4005	109	18	d	d	NOUN
ejpam-4005	109	19	,	,	PUNCT
ejpam-4005	109	20	h	h	NOUN
ejpam-4005	109	21	)	)	PUNCT
ejpam-4005	109	22	and	and	CCONJ
ejpam-4005	109	23	p	p	X
ejpam-4005	109	24	:	:	PUNCT
ejpam-4005	109	25	x	x	X
ejpam-4005	109	26	→	→	SYM
ejpam-4005	109	27	k	k	X
ejpam-4005	109	28	be	be	AUX
ejpam-4005	109	29	a	a	DET
ejpam-4005	109	30	nonexpansive	nonexpansive	ADJ
ejpam-4005	109	31	retraction	retraction	NOUN
ejpam-4005	109	32	of	of	ADP
ejpam-4005	109	33	x	x	PUNCT
ejpam-4005	109	34	onto	onto	ADP
ejpam-4005	109	35	k.	k.	NOUN
ejpam-4005	109	36	let	let	VERB
ejpam-4005	109	37	s1,s2	s1,s2	PROPN
ejpam-4005	109	38	:	:	PUNCT
ejpam-4005	109	39	k	k	X
ejpam-4005	109	40	→	→	PUNCT
ejpam-4005	109	41	k	k	X
ejpam-4005	109	42	be	be	AUX
ejpam-4005	109	43	two	two	NUM
ejpam-4005	109	44	asymptotically	asymptotically	ADV
ejpam-4005	109	45	nonexpasive	nonexpasive	ADJ
ejpam-4005	109	46	self	self	NOUN
ejpam-4005	109	47	-	-	PUNCT
ejpam-4005	109	48	mappings	mapping	NOUN
ejpam-4005	109	49	and	and	CCONJ
ejpam-4005	109	50	t1	t1	NOUN
ejpam-4005	109	51	,	,	PUNCT
ejpam-4005	109	52	t2	t2	NOUN
ejpam-4005	109	53	:	:	PUNCT
ejpam-4005	109	54	k	k	X
ejpam-4005	109	55	→	→	PUNCT
ejpam-4005	109	56	x	x	PUNCT
ejpam-4005	109	57	be	be	AUX
ejpam-4005	109	58	two	two	NUM
ejpam-4005	109	59	asymptotically	asymptotically	ADV
ejpam-4005	109	60	nonexpasive	nonexpasive	ADJ
ejpam-4005	109	61	nonself	nonself	NOUN
ejpam-4005	109	62	-	-	PUNCT
ejpam-4005	109	63	mappings	mapping	NOUN
ejpam-4005	109	64	.	.	PUNCT
ejpam-4005	110	1	we	we	PRON
ejpam-4005	110	2	will	will	AUX
ejpam-4005	110	3	denote	denote	VERB
ejpam-4005	110	4	the	the	DET
ejpam-4005	110	5	set	set	NOUN
ejpam-4005	110	6	of	of	ADP
ejpam-4005	110	7	common	common	ADJ
ejpam-4005	110	8	fixed	fix	VERB
ejpam-4005	110	9	points	point	NOUN
ejpam-4005	110	10	of	of	ADP
ejpam-4005	110	11	s1	s1	NOUN
ejpam-4005	110	12	,	,	PUNCT
ejpam-4005	110	13	s2	s2	PROPN
ejpam-4005	110	14	,	,	PUNCT
ejpam-4005	110	15	t1	t1	NOUN
ejpam-4005	110	16	and	and	CCONJ
ejpam-4005	110	17	t2	t2	NOUN
ejpam-4005	110	18	by	by	ADP
ejpam-4005	110	19	f	f	PROPN
ejpam-4005	110	20	,	,	PUNCT
ejpam-4005	110	21	that	that	ADV
ejpam-4005	110	22	is	is	ADV
ejpam-4005	110	23	,	,	PUNCT
ejpam-4005	110	24	f	f	X
ejpam-4005	110	25	:	:	PUNCT
ejpam-4005	110	26	=	=	NOUN
ejpam-4005	110	27	f(s1)∩f(s2)∩f(t1)∩f(t2	f(s1)∩f(s2)∩f(t1)∩f(t2	NOUN
ejpam-4005	110	28	)	)	PUNCT
ejpam-4005	110	29	.	.	PUNCT
ejpam-4005	111	1	the	the	DET
ejpam-4005	111	2	algorithm	algorithm	NOUN
ejpam-4005	111	3	is	be	AUX
ejpam-4005	111	4	defined	define	VERB
ejpam-4005	111	5	as	as	SCONJ
ejpam-4005	111	6	follows	follow	VERB
ejpam-4005	111	7	:	:	PUNCT
ejpam-4005	112	1	u1	u1	PROPN
ejpam-4005	112	2	∈	∈	PROPN
ejpam-4005	112	3	k	k	PROPN
ejpam-4005	112	4	,	,	PUNCT
ejpam-4005	112	5	vn	vn	PROPN
ejpam-4005	112	6	=	=	PROPN
ejpam-4005	112	7	h(sn2	h(sn2	PROPN
ejpam-4005	112	8	un	un	PROPN
ejpam-4005	112	9	,	,	PUNCT
ejpam-4005	112	10	(	(	PUNCT
ejpam-4005	112	11	pt	pt	X
ejpam-4005	112	12	2)nun	2)nun	NUM
ejpam-4005	112	13	,	,	PUNCT
ejpam-4005	112	14	ζn	ζn	NOUN
ejpam-4005	112	15	)	)	PUNCT
ejpam-4005	112	16	,	,	PUNCT
ejpam-4005	112	17	un+1	un+1	X
ejpam-4005	112	18	=	=	X
ejpam-4005	112	19	h(sn1	h(sn1	X
ejpam-4005	112	20	vn	vn	X
ejpam-4005	112	21	,	,	PUNCT
ejpam-4005	112	22	(	(	PUNCT
ejpam-4005	112	23	pt	pt	X
ejpam-4005	112	24	1)nvn	1)nvn	NUM
ejpam-4005	112	25	,	,	PUNCT
ejpam-4005	112	26	ϑn	ϑn	NOUN
ejpam-4005	112	27	)	)	PUNCT
ejpam-4005	112	28	,	,	PUNCT
ejpam-4005	112	29	(	(	PUNCT
ejpam-4005	112	30	9	9	X
ejpam-4005	112	31	)	)	PUNCT
ejpam-4005	112	32	where	where	SCONJ
ejpam-4005	112	33	{	{	PUNCT
ejpam-4005	112	34	ϑn	ϑn	NOUN
ejpam-4005	112	35	}	}	PUNCT
ejpam-4005	112	36	and	and	CCONJ
ejpam-4005	112	37	{	{	PUNCT
ejpam-4005	112	38	ζn	ζn	X
ejpam-4005	112	39	}	}	PUNCT
ejpam-4005	112	40	are	be	AUX
ejpam-4005	112	41	two	two	NUM
ejpam-4005	112	42	sequences	sequence	NOUN
ejpam-4005	112	43	in	in	ADP
ejpam-4005	112	44	[	[	X
ejpam-4005	112	45	0	0	NUM
ejpam-4005	112	46	,	,	PUNCT
ejpam-4005	112	47	1	1	NUM
ejpam-4005	112	48	)	)	PUNCT
ejpam-4005	112	49	.	.	PUNCT
ejpam-4005	113	1	the	the	DET
ejpam-4005	113	2	following	follow	VERB
ejpam-4005	113	3	lemmas	lemma	NOUN
ejpam-4005	113	4	are	be	AUX
ejpam-4005	113	5	needed	need	VERB
ejpam-4005	113	6	.	.	PUNCT
ejpam-4005	114	1	lemma	lemma	PROPN
ejpam-4005	114	2	3	3	X
ejpam-4005	114	3	.	.	PUNCT
ejpam-4005	115	1	let	let	VERB
ejpam-4005	115	2	(	(	PUNCT
ejpam-4005	115	3	x	x	X
ejpam-4005	115	4	,	,	PUNCT
ejpam-4005	115	5	d	d	NOUN
ejpam-4005	115	6	,	,	PUNCT
ejpam-4005	115	7	h	h	NOUN
ejpam-4005	115	8	)	)	PUNCT
ejpam-4005	115	9	be	be	VERB
ejpam-4005	115	10	a	a	DET
ejpam-4005	115	11	uniformly	uniformly	ADV
ejpam-4005	115	12	convex	convex	ADJ
ejpam-4005	115	13	hyperbolic	hyperbolic	ADJ
ejpam-4005	115	14	space	space	NOUN
ejpam-4005	115	15	and	and	CCONJ
ejpam-4005	115	16	k	k	PROPN
ejpam-4005	115	17	be	be	AUX
ejpam-4005	115	18	a	a	DET
ejpam-4005	115	19	nonempty	nonempty	ADV
ejpam-4005	115	20	closed	close	VERB
ejpam-4005	115	21	convex	convex	NOUN
ejpam-4005	115	22	subset	subset	NOUN
ejpam-4005	115	23	of	of	ADP
ejpam-4005	115	24	x	x	X
ejpam-4005	115	25	.	.	PUNCT
ejpam-4005	116	1	let	let	VERB
ejpam-4005	116	2	s1,s2	s1,s2	PROPN
ejpam-4005	116	3	:	:	PUNCT
ejpam-4005	117	1	k	k	X
ejpam-4005	117	2	→	→	PUNCT
ejpam-4005	117	3	k	k	X
ejpam-4005	117	4	be	be	AUX
ejpam-4005	117	5	two	two	NUM
ejpam-4005	117	6	asymptotically	asymptotically	ADV
ejpam-4005	117	7	nonexpasive	nonexpasive	ADJ
ejpam-4005	117	8	selfmappings	selfmapping	NOUN
ejpam-4005	117	9	with	with	ADP
ejpam-4005	117	10	{	{	PUNCT
ejpam-4005	117	11	k(1	k(1	NOUN
ejpam-4005	117	12	)	)	PUNCT
ejpam-4005	117	13	n	n	CCONJ
ejpam-4005	117	14	}	}	PUNCT
ejpam-4005	117	15	,	,	PUNCT
ejpam-4005	117	16	{	{	PUNCT
ejpam-4005	117	17	k(2	k(2	NOUN
ejpam-4005	117	18	)	)	PUNCT
ejpam-4005	117	19	n	n	CCONJ
ejpam-4005	117	20	}	}	PUNCT
ejpam-4005	117	21	⊂	⊂	PROPN
ejpam-4005	118	1	[	[	X
ejpam-4005	118	2	1,∞	1,∞	NUM
ejpam-4005	118	3	)	)	PUNCT
ejpam-4005	118	4	and	and	CCONJ
ejpam-4005	118	5	t1	t1	NOUN
ejpam-4005	118	6	,	,	PUNCT
ejpam-4005	118	7	t2	t2	NOUN
ejpam-4005	118	8	:	:	PUNCT
ejpam-4005	118	9	k	k	X
ejpam-4005	118	10	→	→	PUNCT
ejpam-4005	118	11	x	x	PUNCT
ejpam-4005	118	12	be	be	AUX
ejpam-4005	118	13	two	two	NUM
ejpam-4005	118	14	asymptotically	asymptotically	ADV
ejpam-4005	118	15	nonexpasive	nonexpasive	ADJ
ejpam-4005	118	16	nonself	nonself	NOUN
ejpam-4005	118	17	-	-	PUNCT
ejpam-4005	118	18	mappings	mapping	NOUN
ejpam-4005	118	19	with	with	ADP
ejpam-4005	118	20	{	{	PUNCT
ejpam-4005	118	21	l(1	l(1	PROPN
ejpam-4005	118	22	)	)	PUNCT
ejpam-4005	118	23	n	n	CCONJ
ejpam-4005	118	24	}	}	PUNCT
ejpam-4005	118	25	,	,	PUNCT
ejpam-4005	118	26	{	{	PUNCT
ejpam-4005	118	27	l(2	l(2	NOUN
ejpam-4005	118	28	)	)	PUNCT
ejpam-4005	118	29	n	n	CCONJ
ejpam-4005	118	30	}	}	PUNCT
ejpam-4005	118	31	⊂	⊂	PROPN
ejpam-4005	119	1	[	[	X
ejpam-4005	119	2	1,∞	1,∞	NUM
ejpam-4005	119	3	)	)	PUNCT
ejpam-4005	119	4	such	such	ADJ
ejpam-4005	119	5	that	that	SCONJ
ejpam-4005	119	6	∞∑	∞∑	NUM
ejpam-4005	119	7	n=1	n=1	PROPN
ejpam-4005	119	8	(	(	PUNCT
ejpam-4005	119	9	k(i	k(i	PROPN
ejpam-4005	119	10	)	)	PUNCT
ejpam-4005	119	11	n	n	CCONJ
ejpam-4005	119	12	−	−	PROPN
ejpam-4005	119	13	1	1	NUM
ejpam-4005	119	14	)	)	PUNCT
ejpam-4005	119	15	<	<	X
ejpam-4005	119	16	∞	∞	PROPN
ejpam-4005	119	17	and	and	CCONJ
ejpam-4005	119	18	∞∑	∞∑	NUM
ejpam-4005	119	19	n=1	n=1	PROPN
ejpam-4005	119	20	(	(	PUNCT
ejpam-4005	119	21	l(i)n	l(i)n	PROPN
ejpam-4005	119	22	−1	−1	NOUN
ejpam-4005	119	23	)	)	PUNCT
ejpam-4005	120	1	<	<	X
ejpam-4005	120	2	∞	∞	NUM
ejpam-4005	120	3	for	for	ADP
ejpam-4005	120	4	i	i	PRON
ejpam-4005	120	5	=	=	NOUN
ejpam-4005	120	6	1	1	NUM
ejpam-4005	120	7	,	,	PUNCT
ejpam-4005	120	8	2	2	NUM
ejpam-4005	120	9	,	,	PUNCT
ejpam-4005	120	10	respectively	respectively	ADV
ejpam-4005	120	11	and	and	CCONJ
ejpam-4005	120	12	f	f	PROPN
ejpam-4005	120	13	6=	6=	PROPN
ejpam-4005	120	14	∅.	∅.	PROPN
ejpam-4005	120	15	suppose	suppose	VERB
ejpam-4005	120	16	that	that	SCONJ
ejpam-4005	120	17	{	{	PUNCT
ejpam-4005	120	18	ϑn	ϑn	NOUN
ejpam-4005	120	19	}	}	PUNCT
ejpam-4005	120	20	and	and	CCONJ
ejpam-4005	120	21	{	{	PUNCT
ejpam-4005	120	22	ζn	ζn	X
ejpam-4005	120	23	}	}	PUNCT
ejpam-4005	120	24	are	be	AUX
ejpam-4005	120	25	real	real	ADJ
ejpam-4005	120	26	sequences	sequence	NOUN
ejpam-4005	120	27	in	in	ADP
ejpam-4005	120	28	[	[	X
ejpam-4005	120	29	0	0	NUM
ejpam-4005	120	30	,	,	PUNCT
ejpam-4005	120	31	1	1	NUM
ejpam-4005	120	32	)	)	PUNCT
ejpam-4005	120	33	.	.	PUNCT
ejpam-4005	121	1	from	from	ADP
ejpam-4005	121	2	an	an	DET
ejpam-4005	121	3	arbitrary	arbitrary	ADJ
ejpam-4005	121	4	u1	u1	NOUN
ejpam-4005	121	5	∈	∈	PROPN
ejpam-4005	121	6	k	k	NOUN
ejpam-4005	121	7	,	,	PUNCT
ejpam-4005	121	8	define	define	VERB
ejpam-4005	121	9	the	the	DET
ejpam-4005	121	10	sequence	sequence	NOUN
ejpam-4005	121	11	{	{	PUNCT
ejpam-4005	121	12	un	un	PROPN
ejpam-4005	121	13	}	}	PUNCT
ejpam-4005	121	14	using	use	VERB
ejpam-4005	121	15	algorithm	algorithm	NOUN
ejpam-4005	121	16	(	(	PUNCT
ejpam-4005	121	17	9	9	NUM
ejpam-4005	121	18	)	)	PUNCT
ejpam-4005	121	19	.	.	PUNCT
ejpam-4005	122	1	then	then	ADV
ejpam-4005	122	2	lim	lim	PROPN
ejpam-4005	122	3	n→∞	n→∞	PROPN
ejpam-4005	123	1	d	d	PROPN
ejpam-4005	123	2	(	(	PUNCT
ejpam-4005	123	3	un	un	PROPN
ejpam-4005	123	4	,	,	PUNCT
ejpam-4005	123	5	q	q	NOUN
ejpam-4005	123	6	)	)	PUNCT
ejpam-4005	123	7	exists	exist	VERB
ejpam-4005	123	8	for	for	ADP
ejpam-4005	123	9	any	any	DET
ejpam-4005	123	10	q	q	NOUN
ejpam-4005	123	11	∈	∈	PROPN
ejpam-4005	123	12	f	f	X
ejpam-4005	123	13	.	.	PUNCT
ejpam-4005	124	1	proof	proof	NOUN
ejpam-4005	124	2	.	.	PUNCT
ejpam-4005	125	1	let	let	VERB
ejpam-4005	125	2	q	q	PROPN
ejpam-4005	125	3	∈	∈	PROPN
ejpam-4005	125	4	f	f	X
ejpam-4005	125	5	.	.	PUNCT
ejpam-4005	126	1	setting	set	VERB
ejpam-4005	126	2	hn	hn	PRON
ejpam-4005	126	3	=	=	SYM
ejpam-4005	126	4	max{k(1	max{k(1	NOUN
ejpam-4005	126	5	)	)	PUNCT
ejpam-4005	126	6	n	n	NOUN
ejpam-4005	126	7	,	,	PUNCT
ejpam-4005	126	8	k	k	X
ejpam-4005	126	9	(	(	PUNCT
ejpam-4005	126	10	2	2	NUM
ejpam-4005	126	11	)	)	PUNCT
ejpam-4005	126	12	n	n	NOUN
ejpam-4005	126	13	,	,	PUNCT
ejpam-4005	126	14	l	l	X
ejpam-4005	126	15	(	(	PUNCT
ejpam-4005	126	16	1	1	NUM
ejpam-4005	126	17	)	)	PUNCT
ejpam-4005	126	18	n	n	NOUN
ejpam-4005	126	19	,	,	PUNCT
ejpam-4005	126	20	l	l	X
ejpam-4005	126	21	(	(	PUNCT
ejpam-4005	126	22	2	2	NUM
ejpam-4005	126	23	)	)	PUNCT
ejpam-4005	126	24	n	n	CCONJ
ejpam-4005	126	25	}	}	PUNCT
ejpam-4005	126	26	.	.	PUNCT
ejpam-4005	127	1	using	use	VERB
ejpam-4005	127	2	algorithm	algorithm	NOUN
ejpam-4005	127	3	(	(	PUNCT
ejpam-4005	127	4	9	9	NUM
ejpam-4005	127	5	)	)	PUNCT
ejpam-4005	127	6	,	,	PUNCT
ejpam-4005	127	7	we	we	PRON
ejpam-4005	127	8	have	have	VERB
ejpam-4005	127	9	d	d	X
ejpam-4005	127	10	(	(	PUNCT
ejpam-4005	127	11	vn	vn	X
ejpam-4005	127	12	,	,	PUNCT
ejpam-4005	127	13	q	q	NOUN
ejpam-4005	127	14	)	)	PUNCT
ejpam-4005	127	15	=	=	SYM
ejpam-4005	128	1	d	d	PROPN
ejpam-4005	128	2	(	(	PUNCT
ejpam-4005	128	3	h	h	PROPN
ejpam-4005	128	4	(	(	PUNCT
ejpam-4005	128	5	sn2	sn2	PROPN
ejpam-4005	128	6	un	un	PROPN
ejpam-4005	128	7	,	,	PUNCT
ejpam-4005	128	8	(	(	PUNCT
ejpam-4005	128	9	pt	pt	PROPN
ejpam-4005	128	10	2)n	2)n	NUM
ejpam-4005	128	11	un	un	PROPN
ejpam-4005	128	12	,	,	PUNCT
ejpam-4005	128	13	ζn	ζn	NOUN
ejpam-4005	128	14	)	)	PUNCT
ejpam-4005	128	15	,	,	PUNCT
ejpam-4005	128	16	q	q	X
ejpam-4005	128	17	)	)	PUNCT
ejpam-4005	128	18	≤	≤	NOUN
ejpam-4005	128	19	(	(	PUNCT
ejpam-4005	128	20	1−	1−	NUM
ejpam-4005	128	21	ζn	ζn	NOUN
ejpam-4005	128	22	)	)	PUNCT
ejpam-4005	128	23	d	d	PROPN
ejpam-4005	128	24	(	(	PUNCT
ejpam-4005	128	25	sn2	sn2	PROPN
ejpam-4005	128	26	un	un	PROPN
ejpam-4005	128	27	,	,	PUNCT
ejpam-4005	128	28	q	q	X
ejpam-4005	128	29	)	)	PUNCT
ejpam-4005	128	30	+	+	CCONJ
ejpam-4005	128	31	ζnd	ζnd	PROPN
ejpam-4005	128	32	(	(	PUNCT
ejpam-4005	128	33	(	(	PUNCT
ejpam-4005	128	34	pt	pt	PROPN
ejpam-4005	128	35	2)n	2)n	NUM
ejpam-4005	128	36	un	un	PROPN
ejpam-4005	128	37	,	,	PUNCT
ejpam-4005	128	38	q	q	NOUN
ejpam-4005	128	39	)	)	PUNCT
ejpam-4005	128	40	≤	≤	NOUN
ejpam-4005	128	41	(	(	PUNCT
ejpam-4005	128	42	1−	1−	NUM
ejpam-4005	128	43	ζn)hnd	ζn)hnd	PROPN
ejpam-4005	128	44	(	(	PUNCT
ejpam-4005	128	45	un	un	PROPN
ejpam-4005	128	46	,	,	PUNCT
ejpam-4005	128	47	q	q	NOUN
ejpam-4005	128	48	)	)	PUNCT
ejpam-4005	128	49	+	+	CCONJ
ejpam-4005	128	50	ζnhnd	ζnhnd	NOUN
ejpam-4005	128	51	(	(	PUNCT
ejpam-4005	128	52	un	un	PROPN
ejpam-4005	128	53	,	,	PUNCT
ejpam-4005	128	54	q	q	NOUN
ejpam-4005	128	55	)	)	PUNCT
ejpam-4005	128	56	=	=	SYM
ejpam-4005	128	57	hnd	hnd	X
ejpam-4005	128	58	(	(	PUNCT
ejpam-4005	128	59	un	un	PROPN
ejpam-4005	128	60	,	,	PUNCT
ejpam-4005	128	61	q	q	NOUN
ejpam-4005	128	62	)	)	PUNCT
ejpam-4005	128	63	,	,	PUNCT
ejpam-4005	128	64	(	(	PUNCT
ejpam-4005	128	65	10	10	NUM
ejpam-4005	128	66	)	)	PUNCT
ejpam-4005	128	67	and	and	CCONJ
ejpam-4005	128	68	so	so	ADV
ejpam-4005	128	69	d	d	X
ejpam-4005	128	70	(	(	PUNCT
ejpam-4005	128	71	un+1	un+1	PROPN
ejpam-4005	128	72	,	,	PUNCT
ejpam-4005	128	73	q	q	NOUN
ejpam-4005	128	74	)	)	PUNCT
ejpam-4005	128	75	=	=	SYM
ejpam-4005	129	1	d	d	PROPN
ejpam-4005	129	2	(	(	PUNCT
ejpam-4005	129	3	h	h	PROPN
ejpam-4005	129	4	(	(	PUNCT
ejpam-4005	129	5	sn1	sn1	PROPN
ejpam-4005	129	6	vn	vn	PROPN
ejpam-4005	129	7	,	,	PUNCT
ejpam-4005	129	8	(	(	PUNCT
ejpam-4005	129	9	pt	pt	X
ejpam-4005	129	10	1)n	1)n	NUM
ejpam-4005	129	11	vn	vn	NOUN
ejpam-4005	129	12	,	,	PUNCT
ejpam-4005	129	13	ϑn	ϑn	NOUN
ejpam-4005	129	14	)	)	PUNCT
ejpam-4005	129	15	,	,	PUNCT
ejpam-4005	129	16	q	q	X
ejpam-4005	129	17	)	)	PUNCT
ejpam-4005	129	18	≤	≤	NOUN
ejpam-4005	129	19	(	(	PUNCT
ejpam-4005	129	20	1−	1−	NUM
ejpam-4005	129	21	ϑn	ϑn	NOUN
ejpam-4005	129	22	)	)	PUNCT
ejpam-4005	129	23	d	d	PROPN
ejpam-4005	129	24	(	(	PUNCT
ejpam-4005	129	25	sn1	sn1	PROPN
ejpam-4005	129	26	vn	vn	PROPN
ejpam-4005	129	27	,	,	PUNCT
ejpam-4005	129	28	q	q	X
ejpam-4005	129	29	)	)	PUNCT
ejpam-4005	130	1	+	+	CCONJ
ejpam-4005	130	2	ϑnd	ϑnd	X
ejpam-4005	130	3	(	(	PUNCT
ejpam-4005	130	4	(	(	PUNCT
ejpam-4005	130	5	pt	pt	X
ejpam-4005	130	6	1)n	1)n	NUM
ejpam-4005	130	7	vn	vn	PROPN
ejpam-4005	130	8	,	,	PUNCT
ejpam-4005	130	9	q	q	NOUN
ejpam-4005	130	10	)	)	PUNCT
ejpam-4005	130	11	≤	≤	NOUN
ejpam-4005	130	12	(	(	PUNCT
ejpam-4005	130	13	1−	1−	NUM
ejpam-4005	130	14	ϑn)hnd	ϑn)hnd	NOUN
ejpam-4005	130	15	(	(	PUNCT
ejpam-4005	130	16	vn	vn	NOUN
ejpam-4005	130	17	,	,	PUNCT
ejpam-4005	130	18	q	q	NOUN
ejpam-4005	130	19	)	)	PUNCT
ejpam-4005	131	1	+	+	CCONJ
ejpam-4005	131	2	ϑnhnd	ϑnhnd	VERB
ejpam-4005	131	3	(	(	PUNCT
ejpam-4005	131	4	vn	vn	NOUN
ejpam-4005	131	5	,	,	PUNCT
ejpam-4005	131	6	q	q	NOUN
ejpam-4005	131	7	)	)	PUNCT
ejpam-4005	131	8	=	=	SYM
ejpam-4005	132	1	hnd	hnd	X
ejpam-4005	132	2	(	(	PUNCT
ejpam-4005	132	3	vn	vn	PROPN
ejpam-4005	132	4	,	,	PUNCT
ejpam-4005	132	5	q	q	NOUN
ejpam-4005	132	6	)	)	PUNCT
ejpam-4005	132	7	≤	≤	NUM
ejpam-4005	132	8	h2	h2	PROPN
ejpam-4005	132	9	nd	nd	ADP
ejpam-4005	132	10	(	(	PUNCT
ejpam-4005	132	11	un	un	PROPN
ejpam-4005	132	12	,	,	PUNCT
ejpam-4005	132	13	q	q	NOUN
ejpam-4005	132	14	)	)	PUNCT
ejpam-4005	132	15	t.	t.	PROPN
ejpam-4005	132	16	thianwan	thianwan	PROPN
ejpam-4005	132	17	/	/	SYM
ejpam-4005	132	18	eur	eur	PROPN
ejpam-4005	132	19	.	.	PUNCT
ejpam-4005	133	1	j.	j.	PROPN
ejpam-4005	133	2	pure	pure	PROPN
ejpam-4005	133	3	appl	appl	PROPN
ejpam-4005	133	4	.	.	PROPN
ejpam-4005	133	5	math	math	PROPN
ejpam-4005	133	6	,	,	PUNCT
ejpam-4005	133	7	14	14	NUM
ejpam-4005	133	8	(	(	PUNCT
ejpam-4005	133	9	3	3	NUM
ejpam-4005	133	10	)	)	PUNCT
ejpam-4005	133	11	(	(	PUNCT
ejpam-4005	133	12	2021	2021	NUM
ejpam-4005	133	13	)	)	PUNCT
ejpam-4005	133	14	,	,	PUNCT
ejpam-4005	133	15	650	650	NUM
ejpam-4005	133	16	-	-	SYM
ejpam-4005	133	17	665	665	NUM
ejpam-4005	133	18	655	655	NUM
ejpam-4005	133	19	=	=	SYM
ejpam-4005	133	20	(	(	PUNCT
ejpam-4005	133	21	1	1	NUM
ejpam-4005	133	22	+	+	CCONJ
ejpam-4005	133	23	(	(	PUNCT
ejpam-4005	133	24	h2	h2	PROPN
ejpam-4005	133	25	n	n	CCONJ
ejpam-4005	133	26	−	−	PROPN
ejpam-4005	133	27	1	1	NUM
ejpam-4005	133	28	)	)	PUNCT
ejpam-4005	133	29	)	)	PUNCT
ejpam-4005	134	1	d	d	X
ejpam-4005	134	2	(	(	PUNCT
ejpam-4005	134	3	un	un	PROPN
ejpam-4005	134	4	,	,	PUNCT
ejpam-4005	134	5	q	q	NOUN
ejpam-4005	134	6	)	)	PUNCT
ejpam-4005	134	7	.	.	PUNCT
ejpam-4005	135	1	(	(	PUNCT
ejpam-4005	135	2	11	11	NUM
ejpam-4005	135	3	)	)	PUNCT
ejpam-4005	135	4	since	since	SCONJ
ejpam-4005	135	5	∞∑	∞∑	NUM
ejpam-4005	135	6	n=1	n=1	PROPN
ejpam-4005	135	7	(	(	PUNCT
ejpam-4005	135	8	k(i	k(i	PROPN
ejpam-4005	135	9	)	)	PUNCT
ejpam-4005	135	10	n	n	CCONJ
ejpam-4005	135	11	−	−	PROPN
ejpam-4005	135	12	1	1	NUM
ejpam-4005	135	13	)	)	PUNCT
ejpam-4005	135	14	<	<	X
ejpam-4005	135	15	∞	∞	PROPN
ejpam-4005	135	16	and	and	CCONJ
ejpam-4005	135	17	∞∑	∞∑	NUM
ejpam-4005	135	18	n=1	n=1	PROPN
ejpam-4005	135	19	(	(	PUNCT
ejpam-4005	135	20	l(i)n	l(i)n	PROPN
ejpam-4005	135	21	−	−	PROPN
ejpam-4005	135	22	1	1	NUM
ejpam-4005	135	23	)	)	PUNCT
ejpam-4005	135	24	<	<	X
ejpam-4005	135	25	∞	∞	PROPN
ejpam-4005	135	26	for	for	ADP
ejpam-4005	135	27	i	i	PRON
ejpam-4005	135	28	=	=	NOUN
ejpam-4005	135	29	1	1	NUM
ejpam-4005	135	30	,	,	PUNCT
ejpam-4005	135	31	2	2	NUM
ejpam-4005	135	32	,	,	PUNCT
ejpam-4005	135	33	we	we	PRON
ejpam-4005	135	34	have	have	VERB
ejpam-4005	135	35	∞∑	∞∑	NUM
ejpam-4005	135	36	n=1	n=1	PROPN
ejpam-4005	135	37	(	(	PUNCT
ejpam-4005	135	38	h2	h2	PROPN
ejpam-4005	135	39	n	n	CCONJ
ejpam-4005	135	40	−	−	PROPN
ejpam-4005	135	41	1	1	NUM
ejpam-4005	135	42	)	)	PUNCT
ejpam-4005	136	1	<	<	X
ejpam-4005	136	2	∞.	∞.	PROPN
ejpam-4005	136	3	it	it	PRON
ejpam-4005	136	4	follows	follow	VERB
ejpam-4005	136	5	from	from	ADP
ejpam-4005	136	6	lemma	lemma	PROPN
ejpam-4005	136	7	1	1	NUM
ejpam-4005	136	8	that	that	SCONJ
ejpam-4005	136	9	limn→∞	limn→∞	PROPN
ejpam-4005	136	10	d	d	X
ejpam-4005	136	11	(	(	PUNCT
ejpam-4005	136	12	un	un	PROPN
ejpam-4005	136	13	,	,	PUNCT
ejpam-4005	136	14	q	q	NOUN
ejpam-4005	136	15	)	)	PUNCT
ejpam-4005	136	16	exists	exist	VERB
ejpam-4005	136	17	.	.	PUNCT
ejpam-4005	137	1	lemma	lemma	PROPN
ejpam-4005	137	2	4	4	X
ejpam-4005	137	3	.	.	PUNCT
ejpam-4005	138	1	let	let	VERB
ejpam-4005	138	2	(	(	PUNCT
ejpam-4005	138	3	x	x	X
ejpam-4005	138	4	,	,	PUNCT
ejpam-4005	138	5	d	d	X
ejpam-4005	138	6	,	,	PUNCT
ejpam-4005	138	7	w	w	NOUN
ejpam-4005	138	8	)	)	PUNCT
ejpam-4005	138	9	be	be	AUX
ejpam-4005	138	10	a	a	DET
ejpam-4005	138	11	uniformly	uniformly	ADV
ejpam-4005	138	12	convex	convex	ADJ
ejpam-4005	138	13	hyperbolic	hyperbolic	ADJ
ejpam-4005	138	14	space	space	NOUN
ejpam-4005	138	15	and	and	CCONJ
ejpam-4005	138	16	k	k	PROPN
ejpam-4005	138	17	be	be	AUX
ejpam-4005	138	18	a	a	DET
ejpam-4005	138	19	nonempty	nonempty	ADV
ejpam-4005	138	20	closed	close	VERB
ejpam-4005	138	21	convex	convex	NOUN
ejpam-4005	138	22	subset	subset	NOUN
ejpam-4005	138	23	of	of	ADP
ejpam-4005	138	24	x	x	X
ejpam-4005	138	25	.	.	PUNCT
ejpam-4005	139	1	let	let	VERB
ejpam-4005	139	2	s1,s2	s1,s2	PROPN
ejpam-4005	139	3	:	:	PUNCT
ejpam-4005	140	1	k	k	X
ejpam-4005	140	2	→	→	PUNCT
ejpam-4005	140	3	k	k	X
ejpam-4005	140	4	be	be	AUX
ejpam-4005	140	5	two	two	NUM
ejpam-4005	140	6	asymptotically	asymptotically	ADV
ejpam-4005	140	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	140	8	selfmappings	selfmapping	NOUN
ejpam-4005	140	9	with	with	ADP
ejpam-4005	140	10	{	{	PUNCT
ejpam-4005	140	11	k(1	k(1	NOUN
ejpam-4005	140	12	)	)	PUNCT
ejpam-4005	140	13	n	n	CCONJ
ejpam-4005	140	14	}	}	PUNCT
ejpam-4005	140	15	,	,	PUNCT
ejpam-4005	140	16	{	{	PUNCT
ejpam-4005	140	17	k(2	k(2	NOUN
ejpam-4005	140	18	)	)	PUNCT
ejpam-4005	140	19	n	n	CCONJ
ejpam-4005	140	20	}	}	PUNCT
ejpam-4005	140	21	⊂	⊂	PROPN
ejpam-4005	141	1	[	[	X
ejpam-4005	141	2	1,∞	1,∞	NUM
ejpam-4005	141	3	)	)	PUNCT
ejpam-4005	141	4	and	and	CCONJ
ejpam-4005	141	5	t1	t1	NOUN
ejpam-4005	141	6	,	,	PUNCT
ejpam-4005	141	7	t2	t2	NOUN
ejpam-4005	141	8	:	:	PUNCT
ejpam-4005	141	9	k	k	X
ejpam-4005	141	10	→	→	PUNCT
ejpam-4005	141	11	x	x	PUNCT
ejpam-4005	141	12	be	be	AUX
ejpam-4005	141	13	two	two	NUM
ejpam-4005	141	14	asymptotically	asymptotically	ADV
ejpam-4005	141	15	nonexpansive	nonexpansive	ADJ
ejpam-4005	141	16	nonself	nonself	NOUN
ejpam-4005	141	17	-	-	PUNCT
ejpam-4005	141	18	mappings	mapping	NOUN
ejpam-4005	141	19	with	with	ADP
ejpam-4005	141	20	{	{	PUNCT
ejpam-4005	141	21	l(1	l(1	PROPN
ejpam-4005	141	22	)	)	PUNCT
ejpam-4005	141	23	n	n	CCONJ
ejpam-4005	141	24	}	}	PUNCT
ejpam-4005	141	25	,	,	PUNCT
ejpam-4005	141	26	{	{	PUNCT
ejpam-4005	141	27	l(2	l(2	NOUN
ejpam-4005	141	28	)	)	PUNCT
ejpam-4005	141	29	n	n	CCONJ
ejpam-4005	141	30	}	}	PUNCT
ejpam-4005	141	31	⊂	⊂	PROPN
ejpam-4005	142	1	[	[	X
ejpam-4005	142	2	1,∞	1,∞	NUM
ejpam-4005	142	3	)	)	PUNCT
ejpam-4005	142	4	such	such	ADJ
ejpam-4005	142	5	that	that	SCONJ
ejpam-4005	142	6	∞∑	∞∑	NUM
ejpam-4005	142	7	n=1	n=1	PROPN
ejpam-4005	142	8	(	(	PUNCT
ejpam-4005	142	9	k(i	k(i	PROPN
ejpam-4005	142	10	)	)	PUNCT
ejpam-4005	142	11	n	n	CCONJ
ejpam-4005	142	12	−	−	PROPN
ejpam-4005	142	13	1	1	NUM
ejpam-4005	142	14	)	)	PUNCT
ejpam-4005	142	15	<	<	X
ejpam-4005	142	16	∞	∞	PROPN
ejpam-4005	142	17	and	and	CCONJ
ejpam-4005	142	18	∞∑	∞∑	NUM
ejpam-4005	142	19	n=1	n=1	PROPN
ejpam-4005	142	20	(	(	PUNCT
ejpam-4005	142	21	l(i)n	l(i)n	PROPN
ejpam-4005	142	22	−	−	PROPN
ejpam-4005	142	23	1	1	NUM
ejpam-4005	142	24	)	)	PUNCT
ejpam-4005	142	25	<	<	X
ejpam-4005	142	26	∞	∞	PROPN
ejpam-4005	142	27	for	for	ADP
ejpam-4005	142	28	i	i	PRON
ejpam-4005	142	29	=	=	NOUN
ejpam-4005	142	30	1	1	NUM
ejpam-4005	142	31	,	,	PUNCT
ejpam-4005	142	32	2	2	NUM
ejpam-4005	142	33	,	,	PUNCT
ejpam-4005	142	34	respectively	respectively	ADV
ejpam-4005	142	35	,	,	PUNCT
ejpam-4005	142	36	and	and	CCONJ
ejpam-4005	142	37	f	f	PROPN
ejpam-4005	142	38	6=	6=	ADP
ejpam-4005	142	39	∅.	∅.	ADV
ejpam-4005	142	40	from	from	ADP
ejpam-4005	142	41	an	an	DET
ejpam-4005	142	42	arbitrary	arbitrary	ADJ
ejpam-4005	142	43	u1	u1	NOUN
ejpam-4005	142	44	∈	∈	PROPN
ejpam-4005	142	45	k	k	NOUN
ejpam-4005	142	46	,	,	PUNCT
ejpam-4005	142	47	define	define	VERB
ejpam-4005	142	48	the	the	DET
ejpam-4005	142	49	sequence	sequence	NOUN
ejpam-4005	142	50	{	{	PUNCT
ejpam-4005	142	51	un	un	PROPN
ejpam-4005	142	52	}	}	PUNCT
ejpam-4005	142	53	using	use	VERB
ejpam-4005	142	54	algorithm	algorithm	NOUN
ejpam-4005	142	55	(	(	PUNCT
ejpam-4005	142	56	9	9	NUM
ejpam-4005	142	57	)	)	PUNCT
ejpam-4005	142	58	and	and	CCONJ
ejpam-4005	142	59	the	the	DET
ejpam-4005	142	60	following	follow	VERB
ejpam-4005	142	61	conditions	condition	NOUN
ejpam-4005	142	62	hold	hold	VERB
ejpam-4005	142	63	:	:	PUNCT
ejpam-4005	142	64	(	(	PUNCT
ejpam-4005	142	65	i	i	NOUN
ejpam-4005	142	66	)	)	PUNCT
ejpam-4005	142	67	{	{	PUNCT
ejpam-4005	142	68	ϑn	ϑn	NOUN
ejpam-4005	142	69	}	}	PUNCT
ejpam-4005	142	70	and	and	CCONJ
ejpam-4005	142	71	{	{	PUNCT
ejpam-4005	142	72	ζn	ζn	X
ejpam-4005	142	73	}	}	PUNCT
ejpam-4005	142	74	are	be	AUX
ejpam-4005	142	75	real	real	ADJ
ejpam-4005	142	76	sequences	sequence	NOUN
ejpam-4005	142	77	in	in	ADP
ejpam-4005	142	78	[	[	X
ejpam-4005	142	79	ε	ε	PROPN
ejpam-4005	142	80	,	,	PUNCT
ejpam-4005	142	81	1−	1−	NUM
ejpam-4005	142	82	ε	ε	X
ejpam-4005	142	83	]	]	PUNCT
ejpam-4005	142	84	for	for	ADP
ejpam-4005	142	85	some	some	DET
ejpam-4005	142	86	ε	ε	PROPN
ejpam-4005	142	87	∈	∈	PROPN
ejpam-4005	142	88	(	(	PUNCT
ejpam-4005	142	89	0	0	NUM
ejpam-4005	142	90	,	,	PUNCT
ejpam-4005	142	91	1	1	NUM
ejpam-4005	142	92	)	)	PUNCT
ejpam-4005	142	93	;	;	PUNCT
ejpam-4005	142	94	(	(	PUNCT
ejpam-4005	142	95	ii	ii	X
ejpam-4005	142	96	)	)	PUNCT
ejpam-4005	142	97	d(u	d(u	PROPN
ejpam-4005	142	98	,	,	PUNCT
ejpam-4005	142	99	tiv	tiv	PROPN
ejpam-4005	142	100	)	)	PUNCT
ejpam-4005	142	101	≤	≤	PROPN
ejpam-4005	143	1	d(siu	d(siu	PROPN
ejpam-4005	143	2	,	,	PUNCT
ejpam-4005	143	3	tiv	tiv	PROPN
ejpam-4005	143	4	)	)	PUNCT
ejpam-4005	143	5	for	for	ADP
ejpam-4005	143	6	all	all	DET
ejpam-4005	143	7	u	u	NOUN
ejpam-4005	143	8	,	,	PUNCT
ejpam-4005	143	9	v	v	ADP
ejpam-4005	143	10	∈	∈	PROPN
ejpam-4005	143	11	k	k	NOUN
ejpam-4005	143	12	and	and	CCONJ
ejpam-4005	143	13	i	i	NOUN
ejpam-4005	143	14	=	=	NOUN
ejpam-4005	143	15	1	1	NUM
ejpam-4005	143	16	,	,	PUNCT
ejpam-4005	143	17	2	2	NUM
ejpam-4005	143	18	.	.	PUNCT
ejpam-4005	144	1	then	then	ADV
ejpam-4005	144	2	,	,	PUNCT
ejpam-4005	144	3	lim	lim	PROPN
ejpam-4005	144	4	n→∞	n→∞	NUM
ejpam-4005	144	5	d(un	d(un	PROPN
ejpam-4005	144	6	,	,	PUNCT
ejpam-4005	144	7	siun	siun	ADJ
ejpam-4005	144	8	)	)	PUNCT
ejpam-4005	145	1	=	=	VERB
ejpam-4005	145	2	lim	lim	PROPN
ejpam-4005	145	3	n→∞	n→∞	NUM
ejpam-4005	145	4	d(un	d(un	PROPN
ejpam-4005	145	5	,	,	PUNCT
ejpam-4005	145	6	(	(	PUNCT
ejpam-4005	145	7	pt	pt	X
ejpam-4005	145	8	i)un	i)un	PROPN
ejpam-4005	145	9	)	)	PUNCT
ejpam-4005	145	10	=	=	SYM
ejpam-4005	145	11	0	0	PUNCT
ejpam-4005	146	1	for	for	ADP
ejpam-4005	146	2	i	i	PRON
ejpam-4005	146	3	=	=	NOUN
ejpam-4005	146	4	1	1	NUM
ejpam-4005	146	5	,	,	PUNCT
ejpam-4005	146	6	2	2	NUM
ejpam-4005	146	7	.	.	PUNCT
ejpam-4005	146	8	proof	proof	NOUN
ejpam-4005	146	9	.	.	PUNCT
ejpam-4005	147	1	let	let	VERB
ejpam-4005	147	2	q	q	PROPN
ejpam-4005	147	3	∈	∈	PROPN
ejpam-4005	147	4	f	f	X
ejpam-4005	147	5	.	.	PUNCT
ejpam-4005	148	1	set	set	VERB
ejpam-4005	148	2	hn	hn	NOUN
ejpam-4005	148	3	=	=	SYM
ejpam-4005	148	4	max{k(1	max{k(1	NOUN
ejpam-4005	148	5	)	)	PUNCT
ejpam-4005	148	6	n	n	NOUN
ejpam-4005	148	7	,	,	PUNCT
ejpam-4005	148	8	k	k	X
ejpam-4005	148	9	(	(	PUNCT
ejpam-4005	148	10	2	2	NUM
ejpam-4005	148	11	)	)	PUNCT
ejpam-4005	148	12	n	n	NOUN
ejpam-4005	148	13	,	,	PUNCT
ejpam-4005	148	14	l	l	X
ejpam-4005	148	15	(	(	PUNCT
ejpam-4005	148	16	1	1	NUM
ejpam-4005	148	17	)	)	PUNCT
ejpam-4005	148	18	n	n	NOUN
ejpam-4005	148	19	,	,	PUNCT
ejpam-4005	148	20	l	l	X
ejpam-4005	148	21	(	(	PUNCT
ejpam-4005	148	22	2	2	NUM
ejpam-4005	148	23	)	)	PUNCT
ejpam-4005	148	24	n	n	CCONJ
ejpam-4005	148	25	}	}	PUNCT
ejpam-4005	148	26	.	.	PUNCT
ejpam-4005	149	1	by	by	ADP
ejpam-4005	149	2	lemma	lemma	PROPN
ejpam-4005	149	3	3	3	NUM
ejpam-4005	149	4	,	,	PUNCT
ejpam-4005	149	5	we	we	PRON
ejpam-4005	149	6	have	have	VERB
ejpam-4005	149	7	lim	lim	PROPN
ejpam-4005	149	8	n→∞	n→∞	NUM
ejpam-4005	149	9	d(un	d(un	PROPN
ejpam-4005	149	10	,	,	PUNCT
ejpam-4005	149	11	q	q	NOUN
ejpam-4005	149	12	)	)	PUNCT
ejpam-4005	149	13	exists	exist	VERB
ejpam-4005	149	14	.	.	PUNCT
ejpam-4005	150	1	assume	assume	VERB
ejpam-4005	150	2	that	that	SCONJ
ejpam-4005	150	3	lim	lim	PROPN
ejpam-4005	150	4	n→∞	n→∞	NUM
ejpam-4005	150	5	d(un	d(un	PROPN
ejpam-4005	150	6	,	,	PUNCT
ejpam-4005	150	7	q	q	NOUN
ejpam-4005	150	8	)	)	PUNCT
ejpam-4005	150	9	=	=	SYM
ejpam-4005	150	10	c	c	X
ejpam-4005	150	11	,	,	PUNCT
ejpam-4005	150	12	letting	let	VERB
ejpam-4005	150	13	n→∞	n→∞	PRON
ejpam-4005	150	14	in	in	ADP
ejpam-4005	150	15	the	the	DET
ejpam-4005	150	16	inequality	inequality	NOUN
ejpam-4005	150	17	(	(	PUNCT
ejpam-4005	150	18	11	11	NUM
ejpam-4005	150	19	)	)	PUNCT
ejpam-4005	150	20	,	,	PUNCT
ejpam-4005	150	21	we	we	PRON
ejpam-4005	150	22	have	have	VERB
ejpam-4005	150	23	lim	lim	PROPN
ejpam-4005	150	24	n→∞	n→∞	NUM
ejpam-4005	150	25	d(h(sn1	d(h(sn1	PROPN
ejpam-4005	150	26	vn	vn	PROPN
ejpam-4005	150	27	,	,	PUNCT
ejpam-4005	150	28	(	(	PUNCT
ejpam-4005	150	29	pt	pt	X
ejpam-4005	150	30	1)nvn	1)nvn	NUM
ejpam-4005	150	31	,	,	PUNCT
ejpam-4005	150	32	ϑn	ϑn	NOUN
ejpam-4005	150	33	)	)	PUNCT
ejpam-4005	150	34	,	,	PUNCT
ejpam-4005	150	35	q	q	X
ejpam-4005	150	36	)	)	PUNCT
ejpam-4005	151	1	=	=	SYM
ejpam-4005	151	2	c.	c.	NOUN
ejpam-4005	151	3	(	(	PUNCT
ejpam-4005	151	4	12	12	NUM
ejpam-4005	151	5	)	)	PUNCT
ejpam-4005	151	6	in	in	ADP
ejpam-4005	151	7	addition	addition	NOUN
ejpam-4005	151	8	,	,	PUNCT
ejpam-4005	151	9	using	use	VERB
ejpam-4005	151	10	(	(	PUNCT
ejpam-4005	151	11	10	10	NUM
ejpam-4005	151	12	)	)	PUNCT
ejpam-4005	151	13	,	,	PUNCT
ejpam-4005	151	14	we	we	PRON
ejpam-4005	151	15	have	have	VERB
ejpam-4005	151	16	d(sn1	d(sn1	NOUN
ejpam-4005	151	17	vn	vn	PROPN
ejpam-4005	151	18	,	,	PUNCT
ejpam-4005	151	19	q	q	NOUN
ejpam-4005	151	20	)	)	PUNCT
ejpam-4005	151	21	≤	≤	NUM
ejpam-4005	151	22	h2	h2	PROPN
ejpam-4005	151	23	nd(un	nd(un	PROPN
ejpam-4005	151	24	,	,	PUNCT
ejpam-4005	151	25	q	q	NOUN
ejpam-4005	151	26	)	)	PUNCT
ejpam-4005	151	27	.	.	PUNCT
ejpam-4005	152	1	taking	take	VERB
ejpam-4005	152	2	the	the	DET
ejpam-4005	152	3	lim	lim	NOUN
ejpam-4005	152	4	sup	sup	NOUN
ejpam-4005	152	5	on	on	ADP
ejpam-4005	152	6	both	both	DET
ejpam-4005	152	7	sides	side	NOUN
ejpam-4005	152	8	in	in	ADP
ejpam-4005	152	9	this	this	DET
ejpam-4005	152	10	inequality	inequality	NOUN
ejpam-4005	152	11	,	,	PUNCT
ejpam-4005	152	12	we	we	PRON
ejpam-4005	152	13	have	have	VERB
ejpam-4005	152	14	lim	lim	PROPN
ejpam-4005	152	15	sup	sup	PROPN
ejpam-4005	152	16	n→∞	n→∞	NUM
ejpam-4005	152	17	d(sn1	d(sn1	NOUN
ejpam-4005	152	18	vn	vn	PROPN
ejpam-4005	152	19	,	,	PUNCT
ejpam-4005	152	20	q	q	NOUN
ejpam-4005	152	21	)	)	PUNCT
ejpam-4005	152	22	≤	≤	ADJ
ejpam-4005	152	23	c.	c.	NOUN
ejpam-4005	152	24	(	(	PUNCT
ejpam-4005	152	25	13	13	NUM
ejpam-4005	152	26	)	)	PUNCT
ejpam-4005	152	27	taking	take	VERB
ejpam-4005	152	28	the	the	DET
ejpam-4005	152	29	lim	lim	NOUN
ejpam-4005	152	30	sup	sup	NOUN
ejpam-4005	152	31	on	on	ADP
ejpam-4005	152	32	both	both	DET
ejpam-4005	152	33	sides	side	NOUN
ejpam-4005	152	34	in	in	ADP
ejpam-4005	152	35	the	the	DET
ejpam-4005	152	36	inequality	inequality	NOUN
ejpam-4005	152	37	(	(	PUNCT
ejpam-4005	152	38	10	10	NUM
ejpam-4005	152	39	)	)	PUNCT
ejpam-4005	152	40	,	,	PUNCT
ejpam-4005	152	41	we	we	PRON
ejpam-4005	152	42	obtain	obtain	VERB
ejpam-4005	152	43	lim	lim	PROPN
ejpam-4005	152	44	sup	sup	X
ejpam-4005	152	45	n→∞	n→∞	NUM
ejpam-4005	152	46	d(vn	d(vn	PROPN
ejpam-4005	152	47	,	,	PUNCT
ejpam-4005	152	48	q	q	NOUN
ejpam-4005	152	49	)	)	PUNCT
ejpam-4005	152	50	≤	≤	NUM
ejpam-4005	153	1	c	c	NOUN
ejpam-4005	153	2	,	,	PUNCT
ejpam-4005	153	3	and	and	CCONJ
ejpam-4005	153	4	so	so	ADV
ejpam-4005	153	5	lim	lim	PROPN
ejpam-4005	153	6	sup	sup	PROPN
ejpam-4005	153	7	n→∞	n→∞	NUM
ejpam-4005	153	8	d((pt	d((pt	PROPN
ejpam-4005	153	9	1)nvn	1)nvn	NUM
ejpam-4005	153	10	,	,	PUNCT
ejpam-4005	153	11	q	q	NOUN
ejpam-4005	153	12	)	)	PUNCT
ejpam-4005	153	13	≤	≤	NOUN
ejpam-4005	153	14	lim	lim	PROPN
ejpam-4005	153	15	sup	sup	VERB
ejpam-4005	153	16	n→∞	n→∞	NUM
ejpam-4005	153	17	hnd(vn	hnd(vn	ADJ
ejpam-4005	153	18	,	,	PUNCT
ejpam-4005	153	19	q	q	ADJ
ejpam-4005	153	20	)	)	PUNCT
ejpam-4005	153	21	=	=	SYM
ejpam-4005	153	22	c.	c.	NOUN
ejpam-4005	153	23	(	(	PUNCT
ejpam-4005	153	24	14	14	NUM
ejpam-4005	153	25	)	)	PUNCT
ejpam-4005	153	26	using	use	VERB
ejpam-4005	153	27	(	(	PUNCT
ejpam-4005	153	28	12	12	NUM
ejpam-4005	153	29	)	)	PUNCT
ejpam-4005	153	30	,	,	PUNCT
ejpam-4005	153	31	(	(	PUNCT
ejpam-4005	153	32	13	13	NUM
ejpam-4005	153	33	)	)	PUNCT
ejpam-4005	153	34	,	,	PUNCT
ejpam-4005	153	35	(	(	PUNCT
ejpam-4005	153	36	14	14	NUM
ejpam-4005	153	37	)	)	PUNCT
ejpam-4005	153	38	,	,	PUNCT
ejpam-4005	153	39	and	and	CCONJ
ejpam-4005	153	40	lemma	lemma	PROPN
ejpam-4005	153	41	2	2	NUM
ejpam-4005	153	42	,	,	PUNCT
ejpam-4005	153	43	we	we	PRON
ejpam-4005	153	44	have	have	VERB
ejpam-4005	153	45	lim	lim	PROPN
ejpam-4005	153	46	n→∞	n→∞	NUM
ejpam-4005	153	47	d(sn1	d(sn1	PROPN
ejpam-4005	153	48	vn	vn	PROPN
ejpam-4005	153	49	,	,	PUNCT
ejpam-4005	153	50	(	(	PUNCT
ejpam-4005	153	51	pt	pt	X
ejpam-4005	153	52	1)nvn	1)nvn	NUM
ejpam-4005	153	53	)	)	PUNCT
ejpam-4005	153	54	=	=	SYM
ejpam-4005	154	1	0	0	X
ejpam-4005	154	2	.	.	PUNCT
ejpam-4005	155	1	(	(	PUNCT
ejpam-4005	155	2	15	15	NUM
ejpam-4005	155	3	)	)	PUNCT
ejpam-4005	155	4	by	by	ADP
ejpam-4005	155	5	the	the	DET
ejpam-4005	155	6	condition	condition	NOUN
ejpam-4005	155	7	(	(	PUNCT
ejpam-4005	155	8	ii	ii	NOUN
ejpam-4005	155	9	)	)	PUNCT
ejpam-4005	155	10	,	,	PUNCT
ejpam-4005	155	11	we	we	PRON
ejpam-4005	155	12	have	have	VERB
ejpam-4005	155	13	t.	t.	PROPN
ejpam-4005	155	14	thianwan	thianwan	PROPN
ejpam-4005	155	15	/	/	PUNCT
ejpam-4005	155	16	eur	eur	PROPN
ejpam-4005	155	17	.	.	PUNCT
ejpam-4005	156	1	j.	j.	PROPN
ejpam-4005	156	2	pure	pure	PROPN
ejpam-4005	156	3	appl	appl	PROPN
ejpam-4005	156	4	.	.	PROPN
ejpam-4005	156	5	math	math	PROPN
ejpam-4005	156	6	,	,	PUNCT
ejpam-4005	156	7	14	14	NUM
ejpam-4005	156	8	(	(	PUNCT
ejpam-4005	156	9	3	3	NUM
ejpam-4005	156	10	)	)	PUNCT
ejpam-4005	156	11	(	(	PUNCT
ejpam-4005	156	12	2021	2021	NUM
ejpam-4005	156	13	)	)	PUNCT
ejpam-4005	156	14	,	,	PUNCT
ejpam-4005	156	15	650	650	NUM
ejpam-4005	156	16	-	-	SYM
ejpam-4005	156	17	665	665	NUM
ejpam-4005	156	18	656	656	NUM
ejpam-4005	156	19	d(vn	d(vn	PROPN
ejpam-4005	156	20	,	,	PUNCT
ejpam-4005	156	21	(	(	PUNCT
ejpam-4005	156	22	pt	pt	X
ejpam-4005	156	23	1)nvn	1)nvn	NUM
ejpam-4005	156	24	)	)	PUNCT
ejpam-4005	156	25	≤	≤	NOUN
ejpam-4005	157	1	d(sn1	d(sn1	NOUN
ejpam-4005	157	2	vn	vn	PROPN
ejpam-4005	157	3	,	,	PUNCT
ejpam-4005	157	4	(	(	PUNCT
ejpam-4005	157	5	pt	pt	PROPN
ejpam-4005	157	6	1)nvn	1)nvn	NUM
ejpam-4005	157	7	)	)	PUNCT
ejpam-4005	157	8	.	.	PUNCT
ejpam-4005	158	1	(	(	PUNCT
ejpam-4005	158	2	16	16	X
ejpam-4005	158	3	)	)	PUNCT
ejpam-4005	158	4	letting	let	VERB
ejpam-4005	158	5	n→∞	n→∞	PRON
ejpam-4005	158	6	in	in	ADP
ejpam-4005	158	7	the	the	DET
ejpam-4005	158	8	inequality	inequality	NOUN
ejpam-4005	158	9	(	(	PUNCT
ejpam-4005	158	10	16	16	NUM
ejpam-4005	158	11	)	)	PUNCT
ejpam-4005	158	12	,	,	PUNCT
ejpam-4005	158	13	by	by	ADP
ejpam-4005	158	14	(	(	PUNCT
ejpam-4005	158	15	15	15	NUM
ejpam-4005	158	16	)	)	PUNCT
ejpam-4005	158	17	,	,	PUNCT
ejpam-4005	158	18	we	we	PRON
ejpam-4005	158	19	have	have	VERB
ejpam-4005	158	20	lim	lim	PROPN
ejpam-4005	158	21	n→∞	n→∞	NUM
ejpam-4005	158	22	d(vn	d(vn	PROPN
ejpam-4005	158	23	,	,	PUNCT
ejpam-4005	158	24	(	(	PUNCT
ejpam-4005	158	25	pt	pt	X
ejpam-4005	158	26	1)nvn	1)nvn	NUM
ejpam-4005	158	27	)	)	PUNCT
ejpam-4005	159	1	=	=	SYM
ejpam-4005	159	2	0	0	X
ejpam-4005	159	3	.	.	PUNCT
ejpam-4005	160	1	(	(	PUNCT
ejpam-4005	160	2	17	17	NUM
ejpam-4005	160	3	)	)	PUNCT
ejpam-4005	160	4	using	use	VERB
ejpam-4005	160	5	(	(	PUNCT
ejpam-4005	160	6	11	11	NUM
ejpam-4005	160	7	)	)	PUNCT
ejpam-4005	160	8	,	,	PUNCT
ejpam-4005	160	9	we	we	PRON
ejpam-4005	160	10	have	have	VERB
ejpam-4005	160	11	d(un+1	d(un+1	NUM
ejpam-4005	160	12	,	,	PUNCT
ejpam-4005	160	13	q	q	NOUN
ejpam-4005	160	14	)	)	PUNCT
ejpam-4005	160	15	≤	≤	NOUN
ejpam-4005	160	16	(	(	PUNCT
ejpam-4005	160	17	1−	1−	NUM
ejpam-4005	160	18	ϑn)d(sn1	ϑn)d(sn1	PROPN
ejpam-4005	160	19	vn	vn	PROPN
ejpam-4005	160	20	,	,	PUNCT
ejpam-4005	160	21	q	q	NOUN
ejpam-4005	160	22	)	)	PUNCT
ejpam-4005	161	1	+	+	CCONJ
ejpam-4005	161	2	ϑnd((pt	ϑnd((pt	PROPN
ejpam-4005	161	3	1)nvn	1)nvn	NUM
ejpam-4005	161	4	,	,	PUNCT
ejpam-4005	161	5	q	q	NOUN
ejpam-4005	161	6	)	)	PUNCT
ejpam-4005	161	7	≤	≤	NOUN
ejpam-4005	161	8	(	(	PUNCT
ejpam-4005	161	9	1−	1−	NUM
ejpam-4005	161	10	ϑn)d(sn1	ϑn)d(sn1	PROPN
ejpam-4005	161	11	vn	vn	PROPN
ejpam-4005	161	12	,	,	PUNCT
ejpam-4005	161	13	q	q	NOUN
ejpam-4005	161	14	)	)	PUNCT
ejpam-4005	161	15	+	+	CCONJ
ejpam-4005	161	16	ϑnd(sn1	ϑnd(sn1	NOUN
ejpam-4005	161	17	vn	vn	NOUN
ejpam-4005	161	18	,	,	PUNCT
ejpam-4005	161	19	(	(	PUNCT
ejpam-4005	161	20	pt	pt	X
ejpam-4005	161	21	1)nvn	1)nvn	NUM
ejpam-4005	161	22	)	)	PUNCT
ejpam-4005	161	23	+	+	CCONJ
ejpam-4005	161	24	ϑnd(sn1	ϑnd(sn1	NOUN
ejpam-4005	161	25	vn	vn	NOUN
ejpam-4005	161	26	,	,	PUNCT
ejpam-4005	161	27	q	q	NOUN
ejpam-4005	161	28	)	)	PUNCT
ejpam-4005	161	29	=	=	NOUN
ejpam-4005	162	1	d(sn1	d(sn1	NOUN
ejpam-4005	162	2	vn	vn	PROPN
ejpam-4005	162	3	,	,	PUNCT
ejpam-4005	162	4	q	q	NOUN
ejpam-4005	162	5	)	)	PUNCT
ejpam-4005	162	6	+	+	CCONJ
ejpam-4005	162	7	ϑnd(sn1	ϑnd(sn1	NOUN
ejpam-4005	162	8	vn	vn	NOUN
ejpam-4005	162	9	,	,	PUNCT
ejpam-4005	162	10	(	(	PUNCT
ejpam-4005	162	11	pt	pt	X
ejpam-4005	162	12	1)nvn	1)nvn	NUM
ejpam-4005	162	13	)	)	PUNCT
ejpam-4005	162	14	≤	≤	NOUN
ejpam-4005	162	15	hnd(vn	hnd(vn	NOUN
ejpam-4005	162	16	,	,	PUNCT
ejpam-4005	162	17	q	q	NOUN
ejpam-4005	162	18	)	)	PUNCT
ejpam-4005	162	19	+	+	CCONJ
ejpam-4005	162	20	ϑnd(sn1	ϑnd(sn1	NOUN
ejpam-4005	162	21	vn	vn	NOUN
ejpam-4005	162	22	,	,	PUNCT
ejpam-4005	162	23	(	(	PUNCT
ejpam-4005	162	24	pt	pt	PROPN
ejpam-4005	162	25	1)nvn	1)nvn	NUM
ejpam-4005	162	26	)	)	PUNCT
ejpam-4005	162	27	.	.	PUNCT
ejpam-4005	163	1	(	(	PUNCT
ejpam-4005	163	2	18	18	NUM
ejpam-4005	163	3	)	)	PUNCT
ejpam-4005	163	4	taking	take	VERB
ejpam-4005	163	5	the	the	DET
ejpam-4005	163	6	lim	lim	PROPN
ejpam-4005	163	7	inf	inf	PROPN
ejpam-4005	163	8	on	on	ADP
ejpam-4005	163	9	both	both	DET
ejpam-4005	163	10	sides	side	NOUN
ejpam-4005	163	11	in	in	ADP
ejpam-4005	163	12	the	the	DET
ejpam-4005	163	13	inequality	inequality	NOUN
ejpam-4005	163	14	(	(	PUNCT
ejpam-4005	163	15	18	18	NUM
ejpam-4005	163	16	)	)	PUNCT
ejpam-4005	163	17	,	,	PUNCT
ejpam-4005	163	18	using	use	VERB
ejpam-4005	163	19	(	(	PUNCT
ejpam-4005	163	20	15	15	NUM
ejpam-4005	163	21	)	)	PUNCT
ejpam-4005	163	22	,	,	PUNCT
ejpam-4005	163	23	∞∑	∞∑	NUM
ejpam-4005	163	24	n=1	n=1	PUNCT
ejpam-4005	163	25	(	(	PUNCT
ejpam-4005	163	26	hn	hn	NOUN
ejpam-4005	163	27	−	−	PROPN
ejpam-4005	163	28	1	1	NUM
ejpam-4005	163	29	)	)	PUNCT
ejpam-4005	163	30	<	<	X
ejpam-4005	163	31	∞	∞	PROPN
ejpam-4005	163	32	and	and	CCONJ
ejpam-4005	163	33	lim	lim	PROPN
ejpam-4005	163	34	n→∞	n→∞	X
ejpam-4005	163	35	d(un+1	d(un+1	PROPN
ejpam-4005	163	36	,	,	PUNCT
ejpam-4005	163	37	q	q	NOUN
ejpam-4005	163	38	)	)	PUNCT
ejpam-4005	164	1	=	=	SYM
ejpam-4005	164	2	c	c	X
ejpam-4005	164	3	,	,	PUNCT
ejpam-4005	164	4	we	we	PRON
ejpam-4005	164	5	have	have	VERB
ejpam-4005	164	6	lim	lim	PROPN
ejpam-4005	164	7	inf	inf	PROPN
ejpam-4005	164	8	n→∞	n→∞	X
ejpam-4005	164	9	d(vn	d(vn	PROPN
ejpam-4005	164	10	,	,	PUNCT
ejpam-4005	164	11	q	q	NOUN
ejpam-4005	164	12	)	)	PUNCT
ejpam-4005	164	13	≥	≥	PROPN
ejpam-4005	164	14	c.	c.	NOUN
ejpam-4005	164	15	(	(	PUNCT
ejpam-4005	164	16	19	19	NUM
ejpam-4005	164	17	)	)	PUNCT
ejpam-4005	164	18	since	since	SCONJ
ejpam-4005	164	19	lim	lim	PROPN
ejpam-4005	164	20	sup	sup	VERB
ejpam-4005	164	21	n→∞	n→∞	NUM
ejpam-4005	164	22	d(vn	d(vn	PROPN
ejpam-4005	164	23	,	,	PUNCT
ejpam-4005	164	24	q	q	NOUN
ejpam-4005	164	25	)	)	PUNCT
ejpam-4005	164	26	≤	≤	NOUN
ejpam-4005	165	1	c	c	X
ejpam-4005	165	2	,	,	PUNCT
ejpam-4005	165	3	by	by	ADP
ejpam-4005	165	4	(	(	PUNCT
ejpam-4005	165	5	19	19	NUM
ejpam-4005	165	6	)	)	PUNCT
ejpam-4005	165	7	,	,	PUNCT
ejpam-4005	165	8	we	we	PRON
ejpam-4005	165	9	have	have	VERB
ejpam-4005	165	10	lim	lim	PROPN
ejpam-4005	165	11	n→∞	n→∞	NUM
ejpam-4005	165	12	d(vn	d(vn	PROPN
ejpam-4005	165	13	,	,	PUNCT
ejpam-4005	165	14	q	q	X
ejpam-4005	165	15	)	)	PUNCT
ejpam-4005	165	16	=	=	SYM
ejpam-4005	166	1	c.	c.	NOUN
ejpam-4005	166	2	this	this	PRON
ejpam-4005	166	3	implies	imply	VERB
ejpam-4005	166	4	that	that	SCONJ
ejpam-4005	166	5	c	c	PROPN
ejpam-4005	166	6	=	=	SYM
ejpam-4005	166	7	lim	lim	PROPN
ejpam-4005	166	8	n→∞	n→∞	X
ejpam-4005	166	9	d(vn	d(vn	PROPN
ejpam-4005	166	10	,	,	PUNCT
ejpam-4005	166	11	q	q	NOUN
ejpam-4005	166	12	)	)	PUNCT
ejpam-4005	166	13	≤	≤	NOUN
ejpam-4005	166	14	lim	lim	PROPN
ejpam-4005	166	15	n→∞	n→∞	NUM
ejpam-4005	167	1	d(h(sn2	d(h(sn2	PROPN
ejpam-4005	167	2	un	un	PROPN
ejpam-4005	167	3	,	,	PUNCT
ejpam-4005	167	4	(	(	PUNCT
ejpam-4005	167	5	pt	pt	X
ejpam-4005	167	6	2)nun	2)nun	NUM
ejpam-4005	167	7	,	,	PUNCT
ejpam-4005	167	8	ζn	ζn	NOUN
ejpam-4005	167	9	)	)	PUNCT
ejpam-4005	167	10	,	,	PUNCT
ejpam-4005	167	11	q	q	X
ejpam-4005	167	12	)	)	PUNCT
ejpam-4005	167	13	≤	≤	PROPN
ejpam-4005	167	14	lim	lim	PROPN
ejpam-4005	167	15	n→∞	n→∞	NUM
ejpam-4005	168	1	d(un	d(un	PROPN
ejpam-4005	168	2	,	,	PUNCT
ejpam-4005	168	3	q	q	NOUN
ejpam-4005	168	4	)	)	PUNCT
ejpam-4005	168	5	=	=	SYM
ejpam-4005	168	6	c	c	NOUN
ejpam-4005	168	7	,	,	PUNCT
ejpam-4005	168	8	and	and	CCONJ
ejpam-4005	169	1	so	so	ADV
ejpam-4005	169	2	lim	lim	PROPN
ejpam-4005	169	3	n→∞	n→∞	PRON
ejpam-4005	170	1	d(h(sn2	d(h(sn2	PROPN
ejpam-4005	170	2	un	un	PROPN
ejpam-4005	170	3	,	,	PUNCT
ejpam-4005	170	4	(	(	PUNCT
ejpam-4005	170	5	pt	pt	X
ejpam-4005	170	6	2)nun	2)nun	NUM
ejpam-4005	170	7	,	,	PUNCT
ejpam-4005	170	8	ζn	ζn	NOUN
ejpam-4005	170	9	)	)	PUNCT
ejpam-4005	170	10	,	,	PUNCT
ejpam-4005	170	11	q	q	X
ejpam-4005	170	12	)	)	PUNCT
ejpam-4005	170	13	=	=	SYM
ejpam-4005	170	14	c.	c.	NOUN
ejpam-4005	170	15	(	(	PUNCT
ejpam-4005	170	16	20	20	NUM
ejpam-4005	170	17	)	)	PUNCT
ejpam-4005	170	18	in	in	ADP
ejpam-4005	170	19	addition	addition	NOUN
ejpam-4005	170	20	,	,	PUNCT
ejpam-4005	170	21	we	we	PRON
ejpam-4005	170	22	have	have	VERB
ejpam-4005	170	23	lim	lim	PROPN
ejpam-4005	170	24	sup	sup	X
ejpam-4005	170	25	n→∞	n→∞	NUM
ejpam-4005	170	26	d(sn2	d(sn2	NOUN
ejpam-4005	170	27	un	un	PROPN
ejpam-4005	170	28	,	,	PUNCT
ejpam-4005	170	29	q	q	NOUN
ejpam-4005	170	30	)	)	PUNCT
ejpam-4005	170	31	≤	≤	NOUN
ejpam-4005	170	32	lim	lim	PROPN
ejpam-4005	170	33	sup	sup	PROPN
ejpam-4005	170	34	n→∞	n→∞	NUM
ejpam-4005	170	35	hnd(un	hnd(un	NOUN
ejpam-4005	170	36	,	,	PUNCT
ejpam-4005	170	37	q	q	X
ejpam-4005	170	38	)	)	PUNCT
ejpam-4005	170	39	=	=	SYM
ejpam-4005	170	40	c	c	X
ejpam-4005	170	41	(	(	PUNCT
ejpam-4005	170	42	21	21	NUM
ejpam-4005	170	43	)	)	PUNCT
ejpam-4005	170	44	and	and	CCONJ
ejpam-4005	170	45	lim	lim	PROPN
ejpam-4005	170	46	sup	sup	PROPN
ejpam-4005	170	47	n→∞	n→∞	X
ejpam-4005	170	48	d((pt	d((pt	PROPN
ejpam-4005	170	49	2)nun	2)nun	NUM
ejpam-4005	170	50	,	,	PUNCT
ejpam-4005	170	51	q	q	NOUN
ejpam-4005	170	52	)	)	PUNCT
ejpam-4005	170	53	≤	≤	NOUN
ejpam-4005	170	54	lim	lim	PROPN
ejpam-4005	170	55	sup	sup	PROPN
ejpam-4005	170	56	n→∞	n→∞	NUM
ejpam-4005	170	57	hnd(un	hnd(un	NOUN
ejpam-4005	170	58	,	,	PUNCT
ejpam-4005	170	59	q	q	NOUN
ejpam-4005	170	60	)	)	PUNCT
ejpam-4005	170	61	=	=	SYM
ejpam-4005	170	62	c.	c.	NOUN
ejpam-4005	170	63	(	(	PUNCT
ejpam-4005	170	64	22	22	NUM
ejpam-4005	170	65	)	)	PUNCT
ejpam-4005	170	66	it	it	PRON
ejpam-4005	170	67	follows	follow	VERB
ejpam-4005	170	68	from	from	ADP
ejpam-4005	170	69	(	(	PUNCT
ejpam-4005	170	70	20	20	NUM
ejpam-4005	170	71	)	)	PUNCT
ejpam-4005	170	72	,	,	PUNCT
ejpam-4005	170	73	(	(	PUNCT
ejpam-4005	170	74	21	21	NUM
ejpam-4005	170	75	)	)	PUNCT
ejpam-4005	170	76	,	,	PUNCT
ejpam-4005	170	77	(	(	PUNCT
ejpam-4005	170	78	22	22	NUM
ejpam-4005	170	79	)	)	PUNCT
ejpam-4005	170	80	,	,	PUNCT
ejpam-4005	170	81	and	and	CCONJ
ejpam-4005	170	82	lemma	lemma	PROPN
ejpam-4005	170	83	2	2	NUM
ejpam-4005	170	84	that	that	PRON
ejpam-4005	170	85	lim	lim	PROPN
ejpam-4005	170	86	n→∞	n→∞	PRON
ejpam-4005	170	87	d(sn2	d(sn2	PROPN
ejpam-4005	170	88	un	un	PROPN
ejpam-4005	170	89	,	,	PUNCT
ejpam-4005	170	90	(	(	PUNCT
ejpam-4005	170	91	pt	pt	NOUN
ejpam-4005	170	92	2)nun	2)nun	NUM
ejpam-4005	170	93	)	)	PUNCT
ejpam-4005	170	94	=	=	SYM
ejpam-4005	171	1	0	0	X
ejpam-4005	171	2	.	.	PUNCT
ejpam-4005	172	1	(	(	PUNCT
ejpam-4005	172	2	23	23	NUM
ejpam-4005	172	3	)	)	PUNCT
ejpam-4005	172	4	t.	t.	PROPN
ejpam-4005	172	5	thianwan	thianwan	PROPN
ejpam-4005	172	6	/	/	SYM
ejpam-4005	172	7	eur	eur	PROPN
ejpam-4005	172	8	.	.	PUNCT
ejpam-4005	173	1	j.	j.	PROPN
ejpam-4005	173	2	pure	pure	PROPN
ejpam-4005	173	3	appl	appl	PROPN
ejpam-4005	173	4	.	.	PROPN
ejpam-4005	173	5	math	math	PROPN
ejpam-4005	173	6	,	,	PUNCT
ejpam-4005	173	7	14	14	NUM
ejpam-4005	173	8	(	(	PUNCT
ejpam-4005	173	9	3	3	NUM
ejpam-4005	173	10	)	)	PUNCT
ejpam-4005	173	11	(	(	PUNCT
ejpam-4005	173	12	2021	2021	NUM
ejpam-4005	173	13	)	)	PUNCT
ejpam-4005	173	14	,	,	PUNCT
ejpam-4005	173	15	650	650	NUM
ejpam-4005	173	16	-	-	SYM
ejpam-4005	173	17	665	665	NUM
ejpam-4005	173	18	657	657	NUM
ejpam-4005	173	19	now	now	ADV
ejpam-4005	173	20	,	,	PUNCT
ejpam-4005	173	21	we	we	PRON
ejpam-4005	173	22	prove	prove	VERB
ejpam-4005	173	23	that	that	SCONJ
ejpam-4005	173	24	lim	lim	PROPN
ejpam-4005	173	25	n→∞	n→∞	NUM
ejpam-4005	173	26	d(un	d(un	PROPN
ejpam-4005	173	27	,	,	PUNCT
ejpam-4005	173	28	(	(	PUNCT
ejpam-4005	173	29	pt	pt	X
ejpam-4005	173	30	1)un	1)un	NUM
ejpam-4005	173	31	)	)	PUNCT
ejpam-4005	173	32	=	=	SYM
ejpam-4005	173	33	0	0	PUNCT
ejpam-4005	174	1	=	=	SYM
ejpam-4005	174	2	lim	lim	PROPN
ejpam-4005	174	3	n→∞	n→∞	NUM
ejpam-4005	174	4	d(un	d(un	PROPN
ejpam-4005	174	5	,	,	PUNCT
ejpam-4005	174	6	(	(	PUNCT
ejpam-4005	174	7	pt	pt	NOUN
ejpam-4005	174	8	2)un	2)un	NUM
ejpam-4005	174	9	)	)	PUNCT
ejpam-4005	174	10	.	.	PUNCT
ejpam-4005	175	1	indeed	indeed	ADV
ejpam-4005	175	2	,	,	PUNCT
ejpam-4005	175	3	by	by	ADP
ejpam-4005	175	4	the	the	DET
ejpam-4005	175	5	condition	condition	NOUN
ejpam-4005	175	6	(	(	PUNCT
ejpam-4005	175	7	ii	ii	NOUN
ejpam-4005	175	8	)	)	PUNCT
ejpam-4005	175	9	,	,	PUNCT
ejpam-4005	175	10	we	we	PRON
ejpam-4005	175	11	have	have	VERB
ejpam-4005	175	12	d(un	d(un	PROPN
ejpam-4005	175	13	,	,	PUNCT
ejpam-4005	175	14	(	(	PUNCT
ejpam-4005	175	15	pt	pt	X
ejpam-4005	175	16	2)nun	2)nun	NUM
ejpam-4005	175	17	)	)	PUNCT
ejpam-4005	175	18	≤	≤	NUM
ejpam-4005	176	1	d(sn2	d(sn2	NOUN
ejpam-4005	176	2	un	un	PROPN
ejpam-4005	176	3	,	,	PUNCT
ejpam-4005	176	4	(	(	PUNCT
ejpam-4005	176	5	pt	pt	NOUN
ejpam-4005	176	6	2)nun	2)nun	NUM
ejpam-4005	176	7	)	)	PUNCT
ejpam-4005	176	8	.	.	PUNCT
ejpam-4005	177	1	(	(	PUNCT
ejpam-4005	177	2	24	24	NUM
ejpam-4005	177	3	)	)	PUNCT
ejpam-4005	177	4	using	use	VERB
ejpam-4005	177	5	(	(	PUNCT
ejpam-4005	177	6	23	23	NUM
ejpam-4005	177	7	)	)	PUNCT
ejpam-4005	177	8	and	and	CCONJ
ejpam-4005	177	9	(	(	PUNCT
ejpam-4005	177	10	24	24	NUM
ejpam-4005	177	11	)	)	PUNCT
ejpam-4005	177	12	,	,	PUNCT
ejpam-4005	177	13	we	we	PRON
ejpam-4005	177	14	have	have	VERB
ejpam-4005	177	15	lim	lim	PROPN
ejpam-4005	177	16	n→∞	n→∞	NUM
ejpam-4005	177	17	d(un	d(un	PROPN
ejpam-4005	177	18	,	,	PUNCT
ejpam-4005	177	19	(	(	PUNCT
ejpam-4005	177	20	pt	pt	X
ejpam-4005	177	21	2)nun	2)nun	NUM
ejpam-4005	177	22	)	)	PUNCT
ejpam-4005	177	23	=	=	SYM
ejpam-4005	178	1	0	0	X
ejpam-4005	178	2	.	.	PUNCT
ejpam-4005	179	1	(	(	PUNCT
ejpam-4005	179	2	25	25	NUM
ejpam-4005	179	3	)	)	PUNCT
ejpam-4005	179	4	using	use	VERB
ejpam-4005	179	5	algorithm	algorithm	NOUN
ejpam-4005	179	6	(	(	PUNCT
ejpam-4005	179	7	9	9	NUM
ejpam-4005	179	8	)	)	PUNCT
ejpam-4005	179	9	,	,	PUNCT
ejpam-4005	179	10	we	we	PRON
ejpam-4005	179	11	have	have	VERB
ejpam-4005	179	12	d(vn	d(vn	PROPN
ejpam-4005	179	13	,	,	PUNCT
ejpam-4005	179	14	sn2	sn2	PROPN
ejpam-4005	179	15	un	un	PROPN
ejpam-4005	179	16	)	)	PUNCT
ejpam-4005	179	17	≤	≤	NOUN
ejpam-4005	179	18	(	(	PUNCT
ejpam-4005	179	19	1−	1−	NUM
ejpam-4005	179	20	ζn)d(sn2	ζn)d(sn2	PROPN
ejpam-4005	179	21	un	un	PROPN
ejpam-4005	179	22	,	,	PUNCT
ejpam-4005	179	23	sn2	sn2	PROPN
ejpam-4005	179	24	un	un	PROPN
ejpam-4005	179	25	)	)	PUNCT
ejpam-4005	180	1	+	+	PROPN
ejpam-4005	180	2	ζnd(sn2	ζnd(sn2	PROPN
ejpam-4005	180	3	un	un	PROPN
ejpam-4005	180	4	,	,	PUNCT
ejpam-4005	180	5	(	(	PUNCT
ejpam-4005	180	6	pt	pt	NOUN
ejpam-4005	180	7	2)nun	2)nun	NUM
ejpam-4005	180	8	)	)	PUNCT
ejpam-4005	180	9	=	=	SYM
ejpam-4005	180	10	ζnd(sn2	ζnd(sn2	PROPN
ejpam-4005	180	11	un	un	PROPN
ejpam-4005	180	12	,	,	PUNCT
ejpam-4005	180	13	(	(	PUNCT
ejpam-4005	180	14	pt	pt	NOUN
ejpam-4005	180	15	2)nun	2)nun	NUM
ejpam-4005	180	16	)	)	PUNCT
ejpam-4005	180	17	.	.	PUNCT
ejpam-4005	181	1	it	it	PRON
ejpam-4005	181	2	follows	follow	VERB
ejpam-4005	181	3	from	from	ADP
ejpam-4005	181	4	(	(	PUNCT
ejpam-4005	181	5	23	23	NUM
ejpam-4005	181	6	)	)	PUNCT
ejpam-4005	182	1	that	that	PRON
ejpam-4005	182	2	lim	lim	PROPN
ejpam-4005	182	3	n→∞	n→∞	PROPN
ejpam-4005	182	4	d(vn	d(vn	PROPN
ejpam-4005	182	5	,	,	PUNCT
ejpam-4005	182	6	sn2	sn2	PROPN
ejpam-4005	182	7	un	un	PROPN
ejpam-4005	182	8	)	)	PUNCT
ejpam-4005	182	9	=	=	SYM
ejpam-4005	182	10	0	0	X
ejpam-4005	182	11	.	.	PUNCT
ejpam-4005	182	12	(	(	PUNCT
ejpam-4005	182	13	26	26	NUM
ejpam-4005	182	14	)	)	PUNCT
ejpam-4005	182	15	furthermore	furthermore	ADV
ejpam-4005	182	16	,	,	PUNCT
ejpam-4005	182	17	we	we	PRON
ejpam-4005	182	18	have	have	VERB
ejpam-4005	182	19	d(vn	d(vn	PROPN
ejpam-4005	182	20	,	,	PUNCT
ejpam-4005	182	21	un	un	PROPN
ejpam-4005	182	22	)	)	PUNCT
ejpam-4005	182	23	≤	≤	NUM
ejpam-4005	182	24	d(vn	d(vn	PROPN
ejpam-4005	182	25	,	,	PUNCT
ejpam-4005	182	26	sn2	sn2	PROPN
ejpam-4005	182	27	un	un	PROPN
ejpam-4005	182	28	)	)	PUNCT
ejpam-4005	182	29	+	+	NUM
ejpam-4005	182	30	d(sn2	d(sn2	NOUN
ejpam-4005	182	31	un	un	PROPN
ejpam-4005	182	32	,	,	PUNCT
ejpam-4005	182	33	(	(	PUNCT
ejpam-4005	182	34	pt	pt	X
ejpam-4005	182	35	2)nun	2)nun	NUM
ejpam-4005	182	36	)	)	PUNCT
ejpam-4005	182	37	+	+	CCONJ
ejpam-4005	182	38	d((pt	d((pt	PROPN
ejpam-4005	182	39	2)nun	2)nun	NUM
ejpam-4005	182	40	,	,	PUNCT
ejpam-4005	182	41	un	un	PROPN
ejpam-4005	182	42	)	)	PUNCT
ejpam-4005	182	43	.	.	PUNCT
ejpam-4005	183	1	(	(	PUNCT
ejpam-4005	183	2	27	27	NUM
ejpam-4005	183	3	)	)	PUNCT
ejpam-4005	183	4	it	it	PRON
ejpam-4005	183	5	follows	follow	VERB
ejpam-4005	183	6	from	from	ADP
ejpam-4005	183	7	(	(	PUNCT
ejpam-4005	183	8	23	23	NUM
ejpam-4005	183	9	)	)	PUNCT
ejpam-4005	183	10	,	,	PUNCT
ejpam-4005	183	11	(	(	PUNCT
ejpam-4005	183	12	25	25	NUM
ejpam-4005	183	13	)	)	PUNCT
ejpam-4005	183	14	,	,	PUNCT
ejpam-4005	183	15	(	(	PUNCT
ejpam-4005	183	16	26	26	NUM
ejpam-4005	183	17	)	)	PUNCT
ejpam-4005	183	18	,	,	PUNCT
ejpam-4005	183	19	and	and	CCONJ
ejpam-4005	183	20	(	(	PUNCT
ejpam-4005	183	21	27	27	NUM
ejpam-4005	183	22	)	)	PUNCT
ejpam-4005	183	23	that	that	PRON
ejpam-4005	183	24	lim	lim	PROPN
ejpam-4005	183	25	n→∞	n→∞	NUM
ejpam-4005	183	26	d(un	d(un	PROPN
ejpam-4005	183	27	,	,	PUNCT
ejpam-4005	183	28	vn	vn	NOUN
ejpam-4005	183	29	)	)	PUNCT
ejpam-4005	183	30	=	=	SYM
ejpam-4005	184	1	0	0	X
ejpam-4005	184	2	.	.	PUNCT
ejpam-4005	185	1	(	(	PUNCT
ejpam-4005	185	2	28	28	NUM
ejpam-4005	185	3	)	)	PUNCT
ejpam-4005	185	4	by	by	ADP
ejpam-4005	185	5	the	the	DET
ejpam-4005	185	6	condition	condition	NOUN
ejpam-4005	185	7	(	(	PUNCT
ejpam-4005	185	8	ii	ii	NOUN
ejpam-4005	185	9	)	)	PUNCT
ejpam-4005	185	10	,	,	PUNCT
ejpam-4005	185	11	we	we	PRON
ejpam-4005	185	12	have	have	VERB
ejpam-4005	185	13	d(un	d(un	PROPN
ejpam-4005	185	14	,	,	PUNCT
ejpam-4005	185	15	(	(	PUNCT
ejpam-4005	185	16	pt	pt	PROPN
ejpam-4005	185	17	1)nun	1)nun	NUM
ejpam-4005	185	18	)	)	PUNCT
ejpam-4005	185	19	≤	≤	NOUN
ejpam-4005	185	20	d(sn1	d(sn1	NOUN
ejpam-4005	185	21	un	un	PROPN
ejpam-4005	185	22	,	,	PUNCT
ejpam-4005	185	23	(	(	PUNCT
ejpam-4005	185	24	pt	pt	NOUN
ejpam-4005	185	25	1)nun	1)nun	NUM
ejpam-4005	185	26	)	)	PUNCT
ejpam-4005	185	27	.	.	PUNCT
ejpam-4005	186	1	since	since	SCONJ
ejpam-4005	186	2	d(sn1	d(sn1	PROPN
ejpam-4005	186	3	un	un	PROPN
ejpam-4005	186	4	,	,	PUNCT
ejpam-4005	186	5	(	(	PUNCT
ejpam-4005	186	6	pt	pt	PROPN
ejpam-4005	186	7	1)nun	1)nun	NUM
ejpam-4005	186	8	)	)	PUNCT
ejpam-4005	186	9	≤	≤	NOUN
ejpam-4005	186	10	d(sn1	d(sn1	NOUN
ejpam-4005	186	11	un	un	PROPN
ejpam-4005	186	12	,	,	PUNCT
ejpam-4005	186	13	sn1	sn1	PROPN
ejpam-4005	186	14	vn	vn	PROPN
ejpam-4005	186	15	)	)	PUNCT
ejpam-4005	186	16	+	+	NUM
ejpam-4005	186	17	d(sn1	d(sn1	PROPN
ejpam-4005	186	18	vn	vn	PROPN
ejpam-4005	186	19	,	,	PUNCT
ejpam-4005	186	20	(	(	PUNCT
ejpam-4005	186	21	pt	pt	X
ejpam-4005	186	22	1)nvn	1)nvn	NUM
ejpam-4005	186	23	)	)	PUNCT
ejpam-4005	186	24	+	+	CCONJ
ejpam-4005	186	25	d((pt	d((pt	PROPN
ejpam-4005	186	26	1)nvn	1)nvn	NUM
ejpam-4005	186	27	,	,	PUNCT
ejpam-4005	186	28	(	(	PUNCT
ejpam-4005	186	29	pt	pt	PROPN
ejpam-4005	186	30	1)nun	1)nun	NUM
ejpam-4005	186	31	)	)	PUNCT
ejpam-4005	186	32	≤	≤	NUM
ejpam-4005	186	33	hnd(un	hnd(un	NOUN
ejpam-4005	186	34	,	,	PUNCT
ejpam-4005	186	35	vn	vn	NOUN
ejpam-4005	186	36	)	)	PUNCT
ejpam-4005	187	1	+	+	NUM
ejpam-4005	187	2	d(sn1	d(sn1	PROPN
ejpam-4005	187	3	vn	vn	PROPN
ejpam-4005	187	4	,	,	PUNCT
ejpam-4005	187	5	(	(	PUNCT
ejpam-4005	187	6	pt	pt	X
ejpam-4005	187	7	1)nvn	1)nvn	NUM
ejpam-4005	187	8	)	)	PUNCT
ejpam-4005	187	9	+	+	CCONJ
ejpam-4005	187	10	hnd(vn	hnd(vn	ADJ
ejpam-4005	187	11	,	,	PUNCT
ejpam-4005	187	12	un	un	PROPN
ejpam-4005	187	13	)	)	PUNCT
ejpam-4005	187	14	,	,	PUNCT
ejpam-4005	187	15	(	(	PUNCT
ejpam-4005	187	16	29	29	NUM
ejpam-4005	187	17	)	)	PUNCT
ejpam-4005	187	18	using	use	VERB
ejpam-4005	187	19	(	(	PUNCT
ejpam-4005	187	20	15	15	NUM
ejpam-4005	187	21	)	)	PUNCT
ejpam-4005	187	22	,	,	PUNCT
ejpam-4005	187	23	(	(	PUNCT
ejpam-4005	187	24	28	28	NUM
ejpam-4005	187	25	)	)	PUNCT
ejpam-4005	187	26	and	and	CCONJ
ejpam-4005	187	27	(	(	PUNCT
ejpam-4005	187	28	29	29	NUM
ejpam-4005	187	29	)	)	PUNCT
ejpam-4005	187	30	,	,	PUNCT
ejpam-4005	187	31	we	we	PRON
ejpam-4005	187	32	have	have	VERB
ejpam-4005	187	33	lim	lim	PROPN
ejpam-4005	187	34	n→∞	n→∞	NUM
ejpam-4005	187	35	d(sn1	d(sn1	PROPN
ejpam-4005	187	36	un	un	PROPN
ejpam-4005	187	37	,	,	PUNCT
ejpam-4005	187	38	(	(	PUNCT
ejpam-4005	187	39	pt	pt	NOUN
ejpam-4005	187	40	1)nun	1)nun	NUM
ejpam-4005	187	41	)	)	PUNCT
ejpam-4005	187	42	=	=	SYM
ejpam-4005	187	43	0	0	NUM
ejpam-4005	187	44	,	,	PUNCT
ejpam-4005	187	45	(	(	PUNCT
ejpam-4005	187	46	30	30	NUM
ejpam-4005	187	47	)	)	PUNCT
ejpam-4005	187	48	t.	t.	PROPN
ejpam-4005	187	49	thianwan	thianwan	PROPN
ejpam-4005	187	50	/	/	SYM
ejpam-4005	187	51	eur	eur	PROPN
ejpam-4005	187	52	.	.	PUNCT
ejpam-4005	188	1	j.	j.	PROPN
ejpam-4005	188	2	pure	pure	PROPN
ejpam-4005	188	3	appl	appl	PROPN
ejpam-4005	188	4	.	.	PROPN
ejpam-4005	188	5	math	math	PROPN
ejpam-4005	188	6	,	,	PUNCT
ejpam-4005	188	7	14	14	NUM
ejpam-4005	188	8	(	(	PUNCT
ejpam-4005	188	9	3	3	NUM
ejpam-4005	188	10	)	)	PUNCT
ejpam-4005	188	11	(	(	PUNCT
ejpam-4005	188	12	2021	2021	NUM
ejpam-4005	188	13	)	)	PUNCT
ejpam-4005	188	14	,	,	PUNCT
ejpam-4005	188	15	650	650	NUM
ejpam-4005	188	16	-	-	SYM
ejpam-4005	188	17	665	665	NUM
ejpam-4005	188	18	658	658	NUM
ejpam-4005	188	19	and	and	CCONJ
ejpam-4005	188	20	so	so	ADV
ejpam-4005	188	21	lim	lim	PROPN
ejpam-4005	188	22	n→∞	n→∞	NUM
ejpam-4005	189	1	d(un	d(un	PROPN
ejpam-4005	189	2	,	,	PUNCT
ejpam-4005	189	3	(	(	PUNCT
ejpam-4005	189	4	pt	pt	NOUN
ejpam-4005	189	5	1)nun	1)nun	NUM
ejpam-4005	189	6	)	)	PUNCT
ejpam-4005	189	7	=	=	SYM
ejpam-4005	189	8	0	0	X
ejpam-4005	189	9	.	.	PUNCT
ejpam-4005	190	1	(	(	PUNCT
ejpam-4005	190	2	31	31	NUM
ejpam-4005	190	3	)	)	PUNCT
ejpam-4005	190	4	in	in	ADP
ejpam-4005	190	5	addition	addition	NOUN
ejpam-4005	190	6	,	,	PUNCT
ejpam-4005	190	7	d(un+1,sn1	d(un+1,sn1	NOUN
ejpam-4005	190	8	vn	vn	VERB
ejpam-4005	190	9	)	)	PUNCT
ejpam-4005	191	1	=	=	VERB
ejpam-4005	191	2	d((h(sn1	d((h(sn1	NOUN
ejpam-4005	191	3	vn	vn	VERB
ejpam-4005	191	4	,	,	PUNCT
ejpam-4005	191	5	(	(	PUNCT
ejpam-4005	191	6	pt	pt	PROPN
ejpam-4005	191	7	1)nvn	1)nvn	NUM
ejpam-4005	191	8	,	,	PUNCT
ejpam-4005	191	9	αn)),sn1	αn)),sn1	PROPN
ejpam-4005	191	10	vn	vn	PROPN
ejpam-4005	191	11	)	)	PUNCT
ejpam-4005	191	12	≤	≤	NOUN
ejpam-4005	191	13	(	(	PUNCT
ejpam-4005	191	14	1−	1−	NUM
ejpam-4005	191	15	ϑn)d(sn1	ϑn)d(sn1	PROPN
ejpam-4005	191	16	vn	vn	PROPN
ejpam-4005	191	17	,	,	PUNCT
ejpam-4005	191	18	sn1	sn1	PROPN
ejpam-4005	191	19	vn	vn	PROPN
ejpam-4005	191	20	)	)	PUNCT
ejpam-4005	192	1	+	+	CCONJ
ejpam-4005	192	2	ϑnd((pt	ϑnd((pt	PROPN
ejpam-4005	192	3	1)nvn	1)nvn	NUM
ejpam-4005	192	4	,	,	PUNCT
ejpam-4005	192	5	sn1	sn1	PROPN
ejpam-4005	192	6	vn	vn	PROPN
ejpam-4005	192	7	)	)	PUNCT
ejpam-4005	193	1	=	=	SYM
ejpam-4005	193	2	ϑnd((pt	ϑnd((pt	PROPN
ejpam-4005	193	3	1)nvn	1)nvn	NUM
ejpam-4005	193	4	,	,	PUNCT
ejpam-4005	193	5	sn1	sn1	PROPN
ejpam-4005	193	6	vn	vn	PROPN
ejpam-4005	193	7	)	)	PUNCT
ejpam-4005	193	8	.	.	PUNCT
ejpam-4005	194	1	thus	thus	ADV
ejpam-4005	194	2	,	,	PUNCT
ejpam-4005	194	3	it	it	PRON
ejpam-4005	194	4	follows	follow	VERB
ejpam-4005	194	5	from	from	ADP
ejpam-4005	194	6	(	(	PUNCT
ejpam-4005	194	7	15	15	NUM
ejpam-4005	194	8	)	)	PUNCT
ejpam-4005	194	9	that	that	PRON
ejpam-4005	194	10	lim	lim	PROPN
ejpam-4005	194	11	n→∞	n→∞	NUM
ejpam-4005	194	12	d(un+1,sn1	d(un+1,sn1	NOUN
ejpam-4005	194	13	vn	vn	VERB
ejpam-4005	194	14	)	)	PUNCT
ejpam-4005	194	15	=	=	SYM
ejpam-4005	195	1	0	0	X
ejpam-4005	195	2	.	.	PUNCT
ejpam-4005	196	1	(	(	PUNCT
ejpam-4005	196	2	32	32	NUM
ejpam-4005	196	3	)	)	PUNCT
ejpam-4005	196	4	in	in	ADP
ejpam-4005	196	5	addition	addition	NOUN
ejpam-4005	196	6	d(un+1	d(un+1	PROPN
ejpam-4005	196	7	,	,	PUNCT
ejpam-4005	196	8	(	(	PUNCT
ejpam-4005	196	9	pt	pt	X
ejpam-4005	196	10	1)nvn	1)nvn	NUM
ejpam-4005	196	11	)	)	PUNCT
ejpam-4005	196	12	≤	≤	NOUN
ejpam-4005	196	13	d(un+1,sn1	d(un+1,sn1	NOUN
ejpam-4005	196	14	vn	vn	VERB
ejpam-4005	196	15	)	)	PUNCT
ejpam-4005	197	1	+	+	NUM
ejpam-4005	197	2	d(sn1	d(sn1	PROPN
ejpam-4005	197	3	vn	vn	PROPN
ejpam-4005	197	4	,	,	PUNCT
ejpam-4005	197	5	(	(	PUNCT
ejpam-4005	197	6	pt	pt	PROPN
ejpam-4005	197	7	1)nvn	1)nvn	NUM
ejpam-4005	197	8	)	)	PUNCT
ejpam-4005	197	9	.	.	PUNCT
ejpam-4005	198	1	using	use	VERB
ejpam-4005	198	2	(	(	PUNCT
ejpam-4005	198	3	15	15	NUM
ejpam-4005	198	4	)	)	PUNCT
ejpam-4005	198	5	and	and	CCONJ
ejpam-4005	198	6	(	(	PUNCT
ejpam-4005	198	7	32	32	NUM
ejpam-4005	198	8	)	)	PUNCT
ejpam-4005	198	9	,	,	PUNCT
ejpam-4005	198	10	we	we	PRON
ejpam-4005	198	11	have	have	VERB
ejpam-4005	198	12	lim	lim	PROPN
ejpam-4005	198	13	n→∞	n→∞	X
ejpam-4005	198	14	d(un+1	d(un+1	PROPN
ejpam-4005	198	15	,	,	PUNCT
ejpam-4005	198	16	(	(	PUNCT
ejpam-4005	198	17	pt	pt	X
ejpam-4005	198	18	1)nvn	1)nvn	NUM
ejpam-4005	198	19	)	)	PUNCT
ejpam-4005	198	20	=	=	SYM
ejpam-4005	199	1	0	0	X
ejpam-4005	199	2	.	.	PUNCT
ejpam-4005	200	1	(	(	PUNCT
ejpam-4005	200	2	33	33	NUM
ejpam-4005	200	3	)	)	PUNCT
ejpam-4005	200	4	it	it	PRON
ejpam-4005	200	5	follows	follow	VERB
ejpam-4005	200	6	from	from	ADP
ejpam-4005	200	7	(	(	PUNCT
ejpam-4005	200	8	30	30	NUM
ejpam-4005	200	9	)	)	PUNCT
ejpam-4005	200	10	and	and	CCONJ
ejpam-4005	200	11	(	(	PUNCT
ejpam-4005	200	12	31	31	NUM
ejpam-4005	200	13	)	)	PUNCT
ejpam-4005	200	14	that	that	PRON
ejpam-4005	200	15	d(sn1	d(sn1	PROPN
ejpam-4005	200	16	un	un	PROPN
ejpam-4005	200	17	,	,	PUNCT
ejpam-4005	200	18	un	un	ADJ
ejpam-4005	200	19	)	)	PUNCT
ejpam-4005	200	20	≤	≤	NOUN
ejpam-4005	201	1	d(sn1	d(sn1	NOUN
ejpam-4005	201	2	un	un	PROPN
ejpam-4005	201	3	,	,	PUNCT
ejpam-4005	201	4	(	(	PUNCT
ejpam-4005	201	5	pt	pt	NOUN
ejpam-4005	201	6	1)nun	1)nun	NUM
ejpam-4005	201	7	)	)	PUNCT
ejpam-4005	202	1	+	+	CCONJ
ejpam-4005	202	2	d((pt	d((pt	PROPN
ejpam-4005	202	3	1)nun	1)nun	NUM
ejpam-4005	202	4	,	,	PUNCT
ejpam-4005	202	5	un	un	PROPN
ejpam-4005	202	6	)	)	PUNCT
ejpam-4005	202	7	→	→	SYM
ejpam-4005	202	8	0	0	NUM
ejpam-4005	202	9	(	(	PUNCT
ejpam-4005	202	10	as	as	ADP
ejpam-4005	202	11	n→∞	n→∞	NUM
ejpam-4005	202	12	)	)	PUNCT
ejpam-4005	202	13	.	.	PUNCT
ejpam-4005	203	1	(	(	PUNCT
ejpam-4005	203	2	34	34	NUM
ejpam-4005	203	3	)	)	PUNCT
ejpam-4005	203	4	in	in	ADP
ejpam-4005	203	5	addition	addition	NOUN
ejpam-4005	203	6	,	,	PUNCT
ejpam-4005	203	7	d(sn1	d(sn1	PROPN
ejpam-4005	203	8	un	un	PROPN
ejpam-4005	203	9	,	,	PUNCT
ejpam-4005	203	10	(	(	PUNCT
ejpam-4005	203	11	pt	pt	X
ejpam-4005	203	12	2)nun	2)nun	NUM
ejpam-4005	203	13	)	)	PUNCT
ejpam-4005	203	14	≤	≤	NUM
ejpam-4005	204	1	d(sn1	d(sn1	PROPN
ejpam-4005	204	2	un	un	PROPN
ejpam-4005	204	3	,	,	PUNCT
ejpam-4005	204	4	un	un	ADJ
ejpam-4005	204	5	)	)	PUNCT
ejpam-4005	205	1	+	+	CCONJ
ejpam-4005	205	2	d(un	d(un	PROPN
ejpam-4005	205	3	,	,	PUNCT
ejpam-4005	205	4	(	(	PUNCT
ejpam-4005	205	5	pt	pt	NOUN
ejpam-4005	205	6	2)nun	2)nun	NUM
ejpam-4005	205	7	)	)	PUNCT
ejpam-4005	205	8	.	.	PUNCT
ejpam-4005	206	1	thus	thus	ADV
ejpam-4005	206	2	,	,	PUNCT
ejpam-4005	206	3	it	it	PRON
ejpam-4005	206	4	follows	follow	VERB
ejpam-4005	206	5	from	from	ADP
ejpam-4005	206	6	(	(	PUNCT
ejpam-4005	206	7	25	25	NUM
ejpam-4005	206	8	)	)	PUNCT
ejpam-4005	206	9	and	and	CCONJ
ejpam-4005	206	10	(	(	PUNCT
ejpam-4005	206	11	34	34	NUM
ejpam-4005	206	12	)	)	PUNCT
ejpam-4005	206	13	that	that	PRON
ejpam-4005	206	14	lim	lim	PROPN
ejpam-4005	206	15	n→∞	n→∞	PRON
ejpam-4005	206	16	d(sn1	d(sn1	PROPN
ejpam-4005	206	17	un	un	PROPN
ejpam-4005	206	18	,	,	PUNCT
ejpam-4005	206	19	(	(	PUNCT
ejpam-4005	206	20	pt	pt	NOUN
ejpam-4005	206	21	2)nun	2)nun	NUM
ejpam-4005	206	22	)	)	PUNCT
ejpam-4005	206	23	=	=	SYM
ejpam-4005	207	1	0	0	X
ejpam-4005	207	2	.	.	PUNCT
ejpam-4005	208	1	(	(	PUNCT
ejpam-4005	208	2	35	35	NUM
ejpam-4005	208	3	)	)	PUNCT
ejpam-4005	208	4	in	in	ADP
ejpam-4005	208	5	addition	addition	NOUN
ejpam-4005	208	6	,	,	PUNCT
ejpam-4005	208	7	d(sn1	d(sn1	PROPN
ejpam-4005	208	8	vn	vn	PROPN
ejpam-4005	208	9	,	,	PUNCT
ejpam-4005	208	10	(	(	PUNCT
ejpam-4005	208	11	pt	pt	X
ejpam-4005	208	12	2)nun	2)nun	NUM
ejpam-4005	208	13	)	)	PUNCT
ejpam-4005	208	14	≤	≤	PART
ejpam-4005	209	1	d(sn1	d(sn1	NOUN
ejpam-4005	209	2	vn	vn	PROPN
ejpam-4005	209	3	,	,	PUNCT
ejpam-4005	209	4	sn1	sn1	PROPN
ejpam-4005	209	5	un	un	PROPN
ejpam-4005	209	6	)	)	PUNCT
ejpam-4005	210	1	+	+	NUM
ejpam-4005	210	2	d(sn1	d(sn1	PROPN
ejpam-4005	210	3	un	un	PROPN
ejpam-4005	210	4	,	,	PUNCT
ejpam-4005	210	5	(	(	PUNCT
ejpam-4005	210	6	pt	pt	X
ejpam-4005	210	7	2)nun	2)nun	NUM
ejpam-4005	210	8	)	)	PUNCT
ejpam-4005	210	9	≤	≤	NUM
ejpam-4005	210	10	hnd(vn	hnd(vn	NOUN
ejpam-4005	210	11	,	,	PUNCT
ejpam-4005	210	12	un	un	ADJ
ejpam-4005	210	13	)	)	PUNCT
ejpam-4005	210	14	+	+	NUM
ejpam-4005	210	15	d(sn1	d(sn1	PROPN
ejpam-4005	210	16	un	un	PROPN
ejpam-4005	210	17	,	,	PUNCT
ejpam-4005	210	18	(	(	PUNCT
ejpam-4005	210	19	pt	pt	NOUN
ejpam-4005	210	20	2)nun	2)nun	NUM
ejpam-4005	210	21	)	)	PUNCT
ejpam-4005	210	22	.	.	PUNCT
ejpam-4005	211	1	using	use	VERB
ejpam-4005	211	2	(	(	PUNCT
ejpam-4005	211	3	28	28	NUM
ejpam-4005	211	4	)	)	PUNCT
ejpam-4005	211	5	and	and	CCONJ
ejpam-4005	211	6	(	(	PUNCT
ejpam-4005	211	7	35	35	NUM
ejpam-4005	211	8	)	)	PUNCT
ejpam-4005	211	9	,	,	PUNCT
ejpam-4005	211	10	we	we	PRON
ejpam-4005	211	11	have	have	VERB
ejpam-4005	211	12	t.	t.	PROPN
ejpam-4005	211	13	thianwan	thianwan	PROPN
ejpam-4005	211	14	/	/	PUNCT
ejpam-4005	211	15	eur	eur	PROPN
ejpam-4005	211	16	.	.	PUNCT
ejpam-4005	212	1	j.	j.	PROPN
ejpam-4005	212	2	pure	pure	PROPN
ejpam-4005	212	3	appl	appl	PROPN
ejpam-4005	212	4	.	.	PROPN
ejpam-4005	212	5	math	math	PROPN
ejpam-4005	212	6	,	,	PUNCT
ejpam-4005	212	7	14	14	NUM
ejpam-4005	212	8	(	(	PUNCT
ejpam-4005	212	9	3	3	NUM
ejpam-4005	212	10	)	)	PUNCT
ejpam-4005	212	11	(	(	PUNCT
ejpam-4005	212	12	2021	2021	NUM
ejpam-4005	212	13	)	)	PUNCT
ejpam-4005	212	14	,	,	PUNCT
ejpam-4005	212	15	650	650	NUM
ejpam-4005	212	16	-	-	SYM
ejpam-4005	212	17	665	665	NUM
ejpam-4005	212	18	659	659	NUM
ejpam-4005	212	19	lim	lim	PROPN
ejpam-4005	212	20	n→∞	n→∞	NUM
ejpam-4005	212	21	d(sn1	d(sn1	PROPN
ejpam-4005	212	22	vn	vn	PROPN
ejpam-4005	212	23	,	,	PUNCT
ejpam-4005	212	24	(	(	PUNCT
ejpam-4005	212	25	pt	pt	NOUN
ejpam-4005	212	26	2)nun	2)nun	NUM
ejpam-4005	212	27	)	)	PUNCT
ejpam-4005	212	28	=	=	SYM
ejpam-4005	213	1	0	0	X
ejpam-4005	213	2	.	.	PUNCT
ejpam-4005	214	1	(	(	PUNCT
ejpam-4005	214	2	36	36	NUM
ejpam-4005	214	3	)	)	PUNCT
ejpam-4005	214	4	it	it	PRON
ejpam-4005	214	5	follows	follow	VERB
ejpam-4005	214	6	from	from	ADP
ejpam-4005	214	7	(	(	PUNCT
ejpam-4005	214	8	28	28	NUM
ejpam-4005	214	9	)	)	PUNCT
ejpam-4005	214	10	,	,	PUNCT
ejpam-4005	214	11	(	(	PUNCT
ejpam-4005	214	12	32	32	NUM
ejpam-4005	214	13	)	)	PUNCT
ejpam-4005	214	14	and	and	CCONJ
ejpam-4005	214	15	(	(	PUNCT
ejpam-4005	214	16	36	36	NUM
ejpam-4005	214	17	)	)	PUNCT
ejpam-4005	214	18	that	that	PRON
ejpam-4005	214	19	d(un+1	d(un+1	PROPN
ejpam-4005	214	20	,	,	PUNCT
ejpam-4005	214	21	(	(	PUNCT
ejpam-4005	214	22	pt	pt	X
ejpam-4005	214	23	2)nvn	2)nvn	NUM
ejpam-4005	214	24	)	)	PUNCT
ejpam-4005	214	25	≤	≤	NUM
ejpam-4005	214	26	d(un+1,sn1	d(un+1,sn1	NOUN
ejpam-4005	214	27	vn	vn	VERB
ejpam-4005	214	28	)	)	PUNCT
ejpam-4005	215	1	+	+	NUM
ejpam-4005	215	2	d(sn1	d(sn1	PROPN
ejpam-4005	215	3	vn	vn	PROPN
ejpam-4005	215	4	,	,	PUNCT
ejpam-4005	215	5	(	(	PUNCT
ejpam-4005	215	6	pt	pt	NOUN
ejpam-4005	215	7	2)nun	2)nun	NUM
ejpam-4005	215	8	)	)	PUNCT
ejpam-4005	215	9	+	+	CCONJ
ejpam-4005	215	10	d((pt	d((pt	PROPN
ejpam-4005	215	11	2)nun	2)nun	NUM
ejpam-4005	215	12	,	,	PUNCT
ejpam-4005	215	13	(	(	PUNCT
ejpam-4005	215	14	pt	pt	X
ejpam-4005	215	15	2)nvn	2)nvn	NUM
ejpam-4005	215	16	)	)	PUNCT
ejpam-4005	215	17	≤	≤	NUM
ejpam-4005	215	18	d(un+1,sn1	d(un+1,sn1	NOUN
ejpam-4005	215	19	vn	vn	VERB
ejpam-4005	215	20	)	)	PUNCT
ejpam-4005	216	1	+	+	NUM
ejpam-4005	216	2	d(sn1	d(sn1	PROPN
ejpam-4005	216	3	vn	vn	PROPN
ejpam-4005	216	4	,	,	PUNCT
ejpam-4005	216	5	(	(	PUNCT
ejpam-4005	216	6	pt	pt	X
ejpam-4005	216	7	2)nun	2)nun	NUM
ejpam-4005	216	8	)	)	PUNCT
ejpam-4005	216	9	+	+	CCONJ
ejpam-4005	216	10	hnd(un	hnd(un	NOUN
ejpam-4005	216	11	,	,	PUNCT
ejpam-4005	216	12	vn	vn	NOUN
ejpam-4005	216	13	)	)	PUNCT
ejpam-4005	216	14	→	→	SYM
ejpam-4005	216	15	0	0	NUM
ejpam-4005	216	16	(	(	PUNCT
ejpam-4005	216	17	as	as	ADP
ejpam-4005	216	18	n→∞	n→∞	NUM
ejpam-4005	216	19	)	)	PUNCT
ejpam-4005	216	20	.	.	PUNCT
ejpam-4005	217	1	(	(	PUNCT
ejpam-4005	217	2	37	37	NUM
ejpam-4005	217	3	)	)	PUNCT
ejpam-4005	217	4	again	again	ADV
ejpam-4005	217	5	,	,	PUNCT
ejpam-4005	217	6	since	since	SCONJ
ejpam-4005	217	7	(	(	PUNCT
ejpam-4005	217	8	pt	pt	X
ejpam-4005	217	9	i)(pt	i)(pt	PROPN
ejpam-4005	217	10	i	i	PROPN
ejpam-4005	217	11	)	)	PUNCT
ejpam-4005	217	12	n−1vn−1	n−1vn−1	PROPN
ejpam-4005	217	13	,	,	PUNCT
ejpam-4005	217	14	un	un	PROPN
ejpam-4005	217	15	∈	∈	PROPN
ejpam-4005	217	16	k	k	PROPN
ejpam-4005	217	17	for	for	ADP
ejpam-4005	217	18	i	i	PRON
ejpam-4005	217	19	=	=	NOUN
ejpam-4005	217	20	1	1	NUM
ejpam-4005	217	21	,	,	PUNCT
ejpam-4005	217	22	2	2	NUM
ejpam-4005	217	23	and	and	CCONJ
ejpam-4005	217	24	t1	t1	NOUN
ejpam-4005	217	25	,	,	PUNCT
ejpam-4005	217	26	t2	t2	PROPN
ejpam-4005	217	27	are	be	AUX
ejpam-4005	217	28	two	two	NUM
ejpam-4005	217	29	asymptotically	asymptotically	ADV
ejpam-4005	217	30	nonexpansive	nonexpansive	ADJ
ejpam-4005	217	31	nonself	nonself	NOUN
ejpam-4005	217	32	-	-	PUNCT
ejpam-4005	217	33	mappings	mapping	NOUN
ejpam-4005	217	34	,	,	PUNCT
ejpam-4005	217	35	we	we	PRON
ejpam-4005	217	36	have	have	VERB
ejpam-4005	217	37	d((pt	d((pt	PROPN
ejpam-4005	217	38	i	i	PRON
ejpam-4005	217	39	)	)	PUNCT
ejpam-4005	217	40	nvn−1	nvn−1	PROPN
ejpam-4005	217	41	,	,	PUNCT
ejpam-4005	217	42	(	(	PUNCT
ejpam-4005	217	43	pt	pt	X
ejpam-4005	217	44	i)un	i)un	PROPN
ejpam-4005	217	45	)	)	PUNCT
ejpam-4005	218	1	=	=	SYM
ejpam-4005	218	2	d(((pt	d(((pt	PROPN
ejpam-4005	218	3	i)(pt	i)(pt	PROPN
ejpam-4005	218	4	i	i	PROPN
ejpam-4005	218	5	)	)	PUNCT
ejpam-4005	218	6	n−1vn−1	n−1vn−1	PROPN
ejpam-4005	218	7	)	)	PUNCT
ejpam-4005	218	8	,	,	PUNCT
ejpam-4005	218	9	(	(	PUNCT
ejpam-4005	218	10	pt	pt	PROPN
ejpam-4005	218	11	i)un	i)un	PROPN
ejpam-4005	218	12	)	)	PUNCT
ejpam-4005	218	13	≤	≤	NUM
ejpam-4005	218	14	max{l(1	max{l(1	NOUN
ejpam-4005	218	15	)	)	PUNCT
ejpam-4005	218	16	1	1	NUM
ejpam-4005	218	17	,	,	PUNCT
ejpam-4005	218	18	l	l	NOUN
ejpam-4005	218	19	(	(	PUNCT
ejpam-4005	218	20	2	2	NUM
ejpam-4005	218	21	)	)	PUNCT
ejpam-4005	218	22	1	1	NUM
ejpam-4005	218	23	}	}	PUNCT
ejpam-4005	218	24	d((pt	d((pt	PROPN
ejpam-4005	218	25	i	i	PRON
ejpam-4005	218	26	)	)	PUNCT
ejpam-4005	218	27	n−1vn−1	n−1vn−1	PROPN
ejpam-4005	218	28	,	,	PUNCT
ejpam-4005	218	29	un	un	PROPN
ejpam-4005	218	30	)	)	PUNCT
ejpam-4005	218	31	.	.	PUNCT
ejpam-4005	219	1	(	(	PUNCT
ejpam-4005	219	2	38	38	NUM
ejpam-4005	219	3	)	)	PUNCT
ejpam-4005	219	4	using	use	VERB
ejpam-4005	219	5	(	(	PUNCT
ejpam-4005	219	6	33	33	NUM
ejpam-4005	219	7	)	)	PUNCT
ejpam-4005	219	8	,	,	PUNCT
ejpam-4005	219	9	(	(	PUNCT
ejpam-4005	219	10	37	37	NUM
ejpam-4005	219	11	)	)	PUNCT
ejpam-4005	219	12	,	,	PUNCT
ejpam-4005	219	13	and	and	CCONJ
ejpam-4005	219	14	(	(	PUNCT
ejpam-4005	219	15	38	38	NUM
ejpam-4005	219	16	)	)	PUNCT
ejpam-4005	219	17	,	,	PUNCT
ejpam-4005	219	18	for	for	ADP
ejpam-4005	219	19	i	i	PROPN
ejpam-4005	219	20	=	=	SYM
ejpam-4005	219	21	1	1	NUM
ejpam-4005	219	22	,	,	PUNCT
ejpam-4005	219	23	2	2	NUM
ejpam-4005	219	24	,	,	PUNCT
ejpam-4005	219	25	we	we	PRON
ejpam-4005	219	26	have	have	VERB
ejpam-4005	219	27	lim	lim	PROPN
ejpam-4005	219	28	n→∞	n→∞	X
ejpam-4005	219	29	d((pt	d((pt	PROPN
ejpam-4005	219	30	i	i	PROPN
ejpam-4005	219	31	)	)	PUNCT
ejpam-4005	219	32	nvn−1	nvn−1	PROPN
ejpam-4005	219	33	,	,	PUNCT
ejpam-4005	219	34	(	(	PUNCT
ejpam-4005	219	35	pt	pt	X
ejpam-4005	219	36	i)un	i)un	PROPN
ejpam-4005	219	37	)	)	PUNCT
ejpam-4005	219	38	=	=	NOUN
ejpam-4005	220	1	0	0	X
ejpam-4005	220	2	.	.	PUNCT
ejpam-4005	221	1	(	(	PUNCT
ejpam-4005	221	2	39	39	NUM
ejpam-4005	221	3	)	)	PUNCT
ejpam-4005	221	4	moreover	moreover	ADV
ejpam-4005	221	5	,	,	PUNCT
ejpam-4005	221	6	we	we	PRON
ejpam-4005	221	7	have	have	VERB
ejpam-4005	221	8	d(un+1	d(un+1	NUM
ejpam-4005	221	9	,	,	PUNCT
ejpam-4005	221	10	vn	vn	NOUN
ejpam-4005	221	11	)	)	PUNCT
ejpam-4005	221	12	≤	≤	NOUN
ejpam-4005	221	13	d(un+1	d(un+1	PROPN
ejpam-4005	221	14	,	,	PUNCT
ejpam-4005	221	15	(	(	PUNCT
ejpam-4005	221	16	pt	pt	X
ejpam-4005	221	17	1)nvn	1)nvn	NUM
ejpam-4005	221	18	)	)	PUNCT
ejpam-4005	221	19	+	+	CCONJ
ejpam-4005	221	20	d((pt	d((pt	PROPN
ejpam-4005	221	21	1)nvn	1)nvn	NUM
ejpam-4005	221	22	,	,	PUNCT
ejpam-4005	221	23	vn	vn	PROPN
ejpam-4005	221	24	)	)	PUNCT
ejpam-4005	221	25	.	.	PUNCT
ejpam-4005	222	1	using	use	VERB
ejpam-4005	222	2	(	(	PUNCT
ejpam-4005	222	3	17	17	NUM
ejpam-4005	222	4	)	)	PUNCT
ejpam-4005	222	5	and	and	CCONJ
ejpam-4005	222	6	(	(	PUNCT
ejpam-4005	222	7	33	33	NUM
ejpam-4005	222	8	)	)	PUNCT
ejpam-4005	222	9	,	,	PUNCT
ejpam-4005	222	10	we	we	PRON
ejpam-4005	222	11	have	have	VERB
ejpam-4005	222	12	lim	lim	PROPN
ejpam-4005	222	13	n→∞	n→∞	X
ejpam-4005	222	14	d(un+1	d(un+1	PROPN
ejpam-4005	222	15	,	,	PUNCT
ejpam-4005	222	16	vn	vn	NOUN
ejpam-4005	222	17	)	)	PUNCT
ejpam-4005	222	18	=	=	SYM
ejpam-4005	223	1	0	0	X
ejpam-4005	223	2	.	.	PUNCT
ejpam-4005	224	1	(	(	PUNCT
ejpam-4005	224	2	40	40	NUM
ejpam-4005	224	3	)	)	PUNCT
ejpam-4005	224	4	in	in	ADP
ejpam-4005	224	5	addition	addition	NOUN
ejpam-4005	224	6	,	,	PUNCT
ejpam-4005	224	7	for	for	ADP
ejpam-4005	224	8	i	i	PROPN
ejpam-4005	224	9	=	=	SYM
ejpam-4005	224	10	1	1	NUM
ejpam-4005	224	11	,	,	PUNCT
ejpam-4005	224	12	2	2	NUM
ejpam-4005	224	13	,	,	PUNCT
ejpam-4005	224	14	we	we	PRON
ejpam-4005	224	15	have	have	VERB
ejpam-4005	224	16	d(un	d(un	PROPN
ejpam-4005	224	17	,	,	PUNCT
ejpam-4005	224	18	(	(	PUNCT
ejpam-4005	224	19	pt	pt	X
ejpam-4005	224	20	i)un	i)un	PROPN
ejpam-4005	224	21	)	)	PUNCT
ejpam-4005	224	22	≤	≤	PUNCT
ejpam-4005	225	1	d(un	d(un	PROPN
ejpam-4005	225	2	,	,	PUNCT
ejpam-4005	225	3	(	(	PUNCT
ejpam-4005	225	4	pt	pt	X
ejpam-4005	225	5	i	i	NOUN
ejpam-4005	225	6	)	)	PUNCT
ejpam-4005	225	7	nun	nun	PROPN
ejpam-4005	225	8	)	)	PUNCT
ejpam-4005	225	9	+	+	CCONJ
ejpam-4005	225	10	d((pt	d((pt	PROPN
ejpam-4005	225	11	i	i	NOUN
ejpam-4005	225	12	)	)	PUNCT
ejpam-4005	225	13	nun	nun	PROPN
ejpam-4005	225	14	,	,	PUNCT
ejpam-4005	225	15	(	(	PUNCT
ejpam-4005	225	16	pt	pt	X
ejpam-4005	225	17	i	i	NOUN
ejpam-4005	225	18	)	)	PUNCT
ejpam-4005	225	19	nvn−1	nvn−1	PROPN
ejpam-4005	225	20	)	)	PUNCT
ejpam-4005	225	21	+	+	CCONJ
ejpam-4005	225	22	d((pt	d((pt	PROPN
ejpam-4005	225	23	i	i	NOUN
ejpam-4005	225	24	)	)	PUNCT
ejpam-4005	225	25	nvn−1	nvn−1	PROPN
ejpam-4005	225	26	,	,	PUNCT
ejpam-4005	225	27	(	(	PUNCT
ejpam-4005	225	28	pt	pt	X
ejpam-4005	225	29	i)un	i)un	PROPN
ejpam-4005	225	30	)	)	PUNCT
ejpam-4005	225	31	≤	≤	PUNCT
ejpam-4005	225	32	d(un	d(un	PROPN
ejpam-4005	225	33	,	,	PUNCT
ejpam-4005	225	34	(	(	PUNCT
ejpam-4005	225	35	pt	pt	X
ejpam-4005	225	36	i	i	NOUN
ejpam-4005	225	37	)	)	PUNCT
ejpam-4005	225	38	nun	nun	PROPN
ejpam-4005	225	39	)	)	PUNCT
ejpam-4005	226	1	+	+	NOUN
ejpam-4005	226	2	max{supn≥1l	max{supn≥1l	NOUN
ejpam-4005	226	3	(	(	PUNCT
ejpam-4005	226	4	1	1	NUM
ejpam-4005	226	5	)	)	PUNCT
ejpam-4005	226	6	n	n	CCONJ
ejpam-4005	226	7	,	,	PUNCT
ejpam-4005	226	8	supn≥1l	supn≥1l	NOUN
ejpam-4005	226	9	(	(	PUNCT
ejpam-4005	226	10	2	2	NUM
ejpam-4005	226	11	)	)	PUNCT
ejpam-4005	226	12	n	n	CCONJ
ejpam-4005	226	13	}	}	PUNCT
ejpam-4005	226	14	d(un	d(un	PROPN
ejpam-4005	226	15	,	,	PUNCT
ejpam-4005	226	16	vn−1	vn−1	ADJ
ejpam-4005	226	17	)	)	PUNCT
ejpam-4005	226	18	+	+	CCONJ
ejpam-4005	226	19	d((pt	d((pt	PROPN
ejpam-4005	226	20	i	i	NOUN
ejpam-4005	226	21	)	)	PUNCT
ejpam-4005	226	22	nvn−1	nvn−1	PROPN
ejpam-4005	226	23	,	,	PUNCT
ejpam-4005	226	24	(	(	PUNCT
ejpam-4005	226	25	pt	pt	X
ejpam-4005	226	26	i)un	i)un	PROPN
ejpam-4005	226	27	)	)	PUNCT
ejpam-4005	226	28	.	.	PUNCT
ejpam-4005	227	1	thus	thus	ADV
ejpam-4005	227	2	,	,	PUNCT
ejpam-4005	227	3	it	it	PRON
ejpam-4005	227	4	follows	follow	VERB
ejpam-4005	227	5	from	from	ADP
ejpam-4005	227	6	(	(	PUNCT
ejpam-4005	227	7	25	25	NUM
ejpam-4005	227	8	)	)	PUNCT
ejpam-4005	227	9	,	,	PUNCT
ejpam-4005	227	10	(	(	PUNCT
ejpam-4005	227	11	31	31	NUM
ejpam-4005	227	12	)	)	PUNCT
ejpam-4005	227	13	,	,	PUNCT
ejpam-4005	227	14	(	(	PUNCT
ejpam-4005	227	15	39	39	NUM
ejpam-4005	227	16	)	)	PUNCT
ejpam-4005	227	17	,	,	PUNCT
ejpam-4005	227	18	and	and	CCONJ
ejpam-4005	227	19	(	(	PUNCT
ejpam-4005	227	20	40	40	NUM
ejpam-4005	227	21	)	)	PUNCT
ejpam-4005	227	22	that	that	PRON
ejpam-4005	227	23	lim	lim	PROPN
ejpam-4005	227	24	n→∞	n→∞	NUM
ejpam-4005	227	25	d(un	d(un	PROPN
ejpam-4005	227	26	,	,	PUNCT
ejpam-4005	227	27	(	(	PUNCT
ejpam-4005	227	28	pt	pt	X
ejpam-4005	227	29	1)un	1)un	NUM
ejpam-4005	227	30	)	)	PUNCT
ejpam-4005	227	31	=	=	SYM
ejpam-4005	227	32	lim	lim	PROPN
ejpam-4005	227	33	n→∞	n→∞	NUM
ejpam-4005	227	34	d(un	d(un	PROPN
ejpam-4005	227	35	,	,	PUNCT
ejpam-4005	227	36	(	(	PUNCT
ejpam-4005	227	37	pt	pt	NOUN
ejpam-4005	227	38	2)un	2)un	NUM
ejpam-4005	227	39	)	)	PUNCT
ejpam-4005	227	40	=	=	SYM
ejpam-4005	228	1	0	0	X
ejpam-4005	228	2	.	.	PUNCT
ejpam-4005	229	1	finally	finally	ADV
ejpam-4005	229	2	,	,	PUNCT
ejpam-4005	229	3	we	we	PRON
ejpam-4005	229	4	prove	prove	VERB
ejpam-4005	229	5	that	that	SCONJ
ejpam-4005	229	6	t.	t.	PROPN
ejpam-4005	229	7	thianwan	thianwan	PROPN
ejpam-4005	229	8	/	/	PUNCT
ejpam-4005	229	9	eur	eur	PROPN
ejpam-4005	229	10	.	.	PUNCT
ejpam-4005	230	1	j.	j.	PROPN
ejpam-4005	230	2	pure	pure	PROPN
ejpam-4005	230	3	appl	appl	PROPN
ejpam-4005	230	4	.	.	PROPN
ejpam-4005	230	5	math	math	PROPN
ejpam-4005	230	6	,	,	PUNCT
ejpam-4005	230	7	14	14	NUM
ejpam-4005	230	8	(	(	PUNCT
ejpam-4005	230	9	3	3	NUM
ejpam-4005	230	10	)	)	PUNCT
ejpam-4005	230	11	(	(	PUNCT
ejpam-4005	230	12	2021	2021	NUM
ejpam-4005	230	13	)	)	PUNCT
ejpam-4005	230	14	,	,	PUNCT
ejpam-4005	230	15	650	650	NUM
ejpam-4005	230	16	-	-	SYM
ejpam-4005	230	17	665	665	NUM
ejpam-4005	230	18	660	660	NUM
ejpam-4005	230	19	lim	lim	PROPN
ejpam-4005	230	20	n→∞	n→∞	X
ejpam-4005	230	21	d(un	d(un	PROPN
ejpam-4005	230	22	,	,	PUNCT
ejpam-4005	230	23	s1un	s1un	PUNCT
ejpam-4005	230	24	)	)	PUNCT
ejpam-4005	231	1	=	=	VERB
ejpam-4005	231	2	lim	lim	PROPN
ejpam-4005	231	3	n→∞	n→∞	NUM
ejpam-4005	231	4	d(un	d(un	PROPN
ejpam-4005	231	5	,	,	PUNCT
ejpam-4005	231	6	s2un	s2un	X
ejpam-4005	231	7	)	)	PUNCT
ejpam-4005	232	1	=	=	SYM
ejpam-4005	232	2	0	0	X
ejpam-4005	232	3	.	.	PUNCT
ejpam-4005	233	1	in	in	ADP
ejpam-4005	233	2	fact	fact	NOUN
ejpam-4005	233	3	,	,	PUNCT
ejpam-4005	233	4	for	for	ADP
ejpam-4005	233	5	i	i	PROPN
ejpam-4005	233	6	=	=	SYM
ejpam-4005	233	7	1	1	NUM
ejpam-4005	233	8	,	,	PUNCT
ejpam-4005	233	9	2	2	NUM
ejpam-4005	233	10	,	,	PUNCT
ejpam-4005	233	11	we	we	PRON
ejpam-4005	233	12	have	have	VERB
ejpam-4005	233	13	d(un	d(un	PROPN
ejpam-4005	233	14	,	,	PUNCT
ejpam-4005	233	15	siun	siun	ADJ
ejpam-4005	233	16	)	)	PUNCT
ejpam-4005	233	17	≤	≤	PUNCT
ejpam-4005	234	1	d(un	d(un	PROPN
ejpam-4005	234	2	,	,	PUNCT
ejpam-4005	234	3	(	(	PUNCT
ejpam-4005	234	4	pt	pt	X
ejpam-4005	234	5	i	i	NOUN
ejpam-4005	234	6	)	)	PUNCT
ejpam-4005	234	7	nun	nun	PROPN
ejpam-4005	234	8	)	)	PUNCT
ejpam-4005	234	9	+	+	CCONJ
ejpam-4005	234	10	d(siun	d(siun	NOUN
ejpam-4005	234	11	,	,	PUNCT
ejpam-4005	234	12	(	(	PUNCT
ejpam-4005	234	13	pt	pt	X
ejpam-4005	234	14	i	i	NOUN
ejpam-4005	234	15	)	)	PUNCT
ejpam-4005	234	16	nun	nun	PROPN
ejpam-4005	234	17	)	)	PUNCT
ejpam-4005	234	18	≤	≤	PUNCT
ejpam-4005	234	19	d(un	d(un	PROPN
ejpam-4005	234	20	,	,	PUNCT
ejpam-4005	234	21	(	(	PUNCT
ejpam-4005	234	22	pt	pt	X
ejpam-4005	234	23	i	i	NOUN
ejpam-4005	234	24	)	)	PUNCT
ejpam-4005	234	25	nun	nun	PROPN
ejpam-4005	234	26	)	)	PUNCT
ejpam-4005	234	27	+	+	CCONJ
ejpam-4005	234	28	d(sni	d(sni	ADJ
ejpam-4005	234	29	un	un	NOUN
ejpam-4005	234	30	,	,	PUNCT
ejpam-4005	234	31	(	(	PUNCT
ejpam-4005	234	32	pt	pt	X
ejpam-4005	234	33	i	i	NOUN
ejpam-4005	234	34	)	)	PUNCT
ejpam-4005	234	35	nun	nun	PROPN
ejpam-4005	234	36	)	)	PUNCT
ejpam-4005	234	37	.	.	PUNCT
ejpam-4005	235	1	thus	thus	ADV
ejpam-4005	235	2	,	,	PUNCT
ejpam-4005	235	3	it	it	PRON
ejpam-4005	235	4	follows	follow	VERB
ejpam-4005	235	5	from	from	ADP
ejpam-4005	235	6	(	(	PUNCT
ejpam-4005	235	7	23	23	NUM
ejpam-4005	235	8	)	)	PUNCT
ejpam-4005	235	9	,	,	PUNCT
ejpam-4005	235	10	(	(	PUNCT
ejpam-4005	235	11	25	25	NUM
ejpam-4005	235	12	)	)	PUNCT
ejpam-4005	235	13	,	,	PUNCT
ejpam-4005	235	14	(	(	PUNCT
ejpam-4005	235	15	30	30	NUM
ejpam-4005	235	16	)	)	PUNCT
ejpam-4005	235	17	,	,	PUNCT
ejpam-4005	235	18	and	and	CCONJ
ejpam-4005	235	19	(	(	PUNCT
ejpam-4005	235	20	31	31	NUM
ejpam-4005	235	21	)	)	PUNCT
ejpam-4005	236	1	that	that	PRON
ejpam-4005	236	2	lim	lim	PROPN
ejpam-4005	236	3	n→∞	n→∞	NUM
ejpam-4005	236	4	d(un	d(un	PROPN
ejpam-4005	236	5	,	,	PUNCT
ejpam-4005	236	6	s1un	s1un	PUNCT
ejpam-4005	236	7	)	)	PUNCT
ejpam-4005	237	1	=	=	VERB
ejpam-4005	237	2	lim	lim	PROPN
ejpam-4005	237	3	n→∞	n→∞	NUM
ejpam-4005	237	4	d(un	d(un	PROPN
ejpam-4005	237	5	,	,	PUNCT
ejpam-4005	237	6	s2un	s2un	X
ejpam-4005	237	7	)	)	PUNCT
ejpam-4005	238	1	=	=	SYM
ejpam-4005	238	2	0	0	X
ejpam-4005	238	3	.	.	PUNCT
ejpam-4005	239	1	the	the	DET
ejpam-4005	239	2	proof	proof	NOUN
ejpam-4005	239	3	is	be	AUX
ejpam-4005	239	4	completed	complete	VERB
ejpam-4005	239	5	.	.	PUNCT
ejpam-4005	240	1	the	the	DET
ejpam-4005	240	2	following	follow	VERB
ejpam-4005	240	3	example	example	NOUN
ejpam-4005	240	4	presents	present	VERB
ejpam-4005	240	5	the	the	DET
ejpam-4005	240	6	condition	condition	NOUN
ejpam-4005	240	7	(	(	PUNCT
ejpam-4005	240	8	ii	ii	NOUN
ejpam-4005	240	9	)	)	PUNCT
ejpam-4005	240	10	in	in	ADP
ejpam-4005	240	11	lemma	lemma	PROPN
ejpam-4005	240	12	4	4	NUM
ejpam-4005	240	13	which	which	PRON
ejpam-4005	240	14	is	be	AUX
ejpam-4005	240	15	satisfied	satisfied	ADJ
ejpam-4005	240	16	by	by	ADP
ejpam-4005	240	17	the	the	DET
ejpam-4005	240	18	mappings	mapping	NOUN
ejpam-4005	240	19	si	si	X
ejpam-4005	240	20	and	and	CCONJ
ejpam-4005	240	21	ti	ti	PROPN
ejpam-4005	240	22	,	,	PUNCT
ejpam-4005	240	23	i	i	NOUN
ejpam-4005	240	24	=	=	NOUN
ejpam-4005	240	25	1	1	NUM
ejpam-4005	240	26	,	,	PUNCT
ejpam-4005	240	27	2	2	NUM
ejpam-4005	240	28	,	,	PUNCT
ejpam-4005	240	29	when	when	SCONJ
ejpam-4005	240	30	s1	s1	PROPN
ejpam-4005	240	31	=	=	SYM
ejpam-4005	240	32	s2	s2	PROPN
ejpam-4005	240	33	=	=	SYM
ejpam-4005	240	34	s	s	PROPN
ejpam-4005	240	35	and	and	CCONJ
ejpam-4005	240	36	t1	t1	NOUN
ejpam-4005	240	37	=	=	SYM
ejpam-4005	240	38	t2	t2	PROPN
ejpam-4005	240	39	=	=	SYM
ejpam-4005	240	40	t	t	PROPN
ejpam-4005	240	41	,	,	PUNCT
ejpam-4005	240	42	where	where	SCONJ
ejpam-4005	240	43	s	s	PRON
ejpam-4005	240	44	and	and	CCONJ
ejpam-4005	240	45	t	t	PROPN
ejpam-4005	240	46	are	be	AUX
ejpam-4005	240	47	given	give	VERB
ejpam-4005	240	48	in	in	ADP
ejpam-4005	240	49	the	the	DET
ejpam-4005	240	50	next	next	ADJ
ejpam-4005	240	51	example	example	NOUN
ejpam-4005	240	52	.	.	PUNCT
ejpam-4005	241	1	example	example	NOUN
ejpam-4005	242	1	1	1	NUM
ejpam-4005	242	2	.	.	PUNCT
ejpam-4005	243	1	(	(	PUNCT
ejpam-4005	243	2	[	[	X
ejpam-4005	243	3	16	16	NUM
ejpam-4005	243	4	]	]	PUNCT
ejpam-4005	243	5	)	)	PUNCT
ejpam-4005	243	6	let	let	VERB
ejpam-4005	243	7	x	x	PRON
ejpam-4005	243	8	be	be	AUX
ejpam-4005	243	9	the	the	DET
ejpam-4005	243	10	real	real	ADJ
ejpam-4005	243	11	line	line	NOUN
ejpam-4005	243	12	with	with	ADP
ejpam-4005	243	13	metric	metric	ADJ
ejpam-4005	243	14	d(u	d(u	PROPN
ejpam-4005	243	15	,	,	PUNCT
ejpam-4005	243	16	v	v	NOUN
ejpam-4005	243	17	)	)	PUNCT
ejpam-4005	243	18	=	=	PUNCT
ejpam-4005	243	19	|u	|u	ADP
ejpam-4005	243	20	−	−	PROPN
ejpam-4005	243	21	v|	v|	NOUN
ejpam-4005	243	22	and	and	CCONJ
ejpam-4005	243	23	k	k	NOUN
ejpam-4005	243	24	=	=	PUNCT
ejpam-4005	244	1	[	[	X
ejpam-4005	244	2	−1	−1	NOUN
ejpam-4005	244	3	,	,	PUNCT
ejpam-4005	244	4	1	1	NUM
ejpam-4005	244	5	]	]	PUNCT
ejpam-4005	244	6	.	.	PUNCT
ejpam-4005	245	1	define	define	VERB
ejpam-4005	245	2	h	h	NOUN
ejpam-4005	245	3	:	:	PUNCT
ejpam-4005	245	4	x	x	SYM
ejpam-4005	245	5	×	×	NOUN
ejpam-4005	245	6	x	x	SYM
ejpam-4005	245	7	×	×	NOUN
ejpam-4005	246	1	[	[	X
ejpam-4005	246	2	0	0	NUM
ejpam-4005	246	3	,	,	PUNCT
ejpam-4005	246	4	1	1	NUM
ejpam-4005	246	5	]	]	PUNCT
ejpam-4005	246	6	→	→	PUNCT
ejpam-4005	246	7	x	x	SYM
ejpam-4005	246	8	by	by	ADP
ejpam-4005	246	9	h(u	h(u	PROPN
ejpam-4005	246	10	,	,	PUNCT
ejpam-4005	246	11	v	v	NOUN
ejpam-4005	246	12	,	,	PUNCT
ejpam-4005	246	13	ψ	ψ	NOUN
ejpam-4005	246	14	)	)	PUNCT
ejpam-4005	246	15	:	:	PUNCT
ejpam-4005	247	1	=	=	SYM
ejpam-4005	247	2	ψu	ψu	PROPN
ejpam-4005	247	3	+	+	CCONJ
ejpam-4005	247	4	(	(	PUNCT
ejpam-4005	247	5	1	1	NUM
ejpam-4005	247	6	−	−	NOUN
ejpam-4005	247	7	ψ)v	ψ)v	PUNCT
ejpam-4005	247	8	for	for	ADP
ejpam-4005	247	9	all	all	DET
ejpam-4005	247	10	u	u	NOUN
ejpam-4005	247	11	,	,	PUNCT
ejpam-4005	247	12	v	v	NOUN
ejpam-4005	247	13	∈	∈	NOUN
ejpam-4005	247	14	x	x	X
ejpam-4005	247	15	and	and	CCONJ
ejpam-4005	247	16	ψ	ψ	X
ejpam-4005	247	17	∈	∈	PROPN
ejpam-4005	248	1	[	[	X
ejpam-4005	248	2	0	0	NUM
ejpam-4005	248	3	,	,	PUNCT
ejpam-4005	248	4	1	1	NUM
ejpam-4005	248	5	]	]	PUNCT
ejpam-4005	248	6	.	.	PUNCT
ejpam-4005	249	1	then	then	ADV
ejpam-4005	249	2	(	(	PUNCT
ejpam-4005	249	3	x	x	X
ejpam-4005	249	4	,	,	PUNCT
ejpam-4005	249	5	d	d	NOUN
ejpam-4005	249	6	,	,	PUNCT
ejpam-4005	249	7	h	h	NOUN
ejpam-4005	249	8	)	)	PUNCT
ejpam-4005	249	9	is	be	AUX
ejpam-4005	249	10	a	a	DET
ejpam-4005	249	11	complete	complete	ADJ
ejpam-4005	249	12	uniformly	uniformly	ADV
ejpam-4005	249	13	hyperbolic	hyperbolic	ADJ
ejpam-4005	249	14	space	space	NOUN
ejpam-4005	249	15	with	with	ADP
ejpam-4005	249	16	a	a	DET
ejpam-4005	249	17	monotone	monotone	ADJ
ejpam-4005	249	18	modulus	modulus	NOUN
ejpam-4005	249	19	of	of	ADP
ejpam-4005	249	20	uniform	uniform	ADJ
ejpam-4005	249	21	convexity	convexity	NOUN
ejpam-4005	249	22	and	and	CCONJ
ejpam-4005	249	23	k	k	PROPN
ejpam-4005	249	24	is	be	AUX
ejpam-4005	249	25	a	a	DET
ejpam-4005	249	26	nonempty	nonempty	ADV
ejpam-4005	249	27	closed	close	VERB
ejpam-4005	249	28	convex	convex	NOUN
ejpam-4005	249	29	subset	subset	NOUN
ejpam-4005	249	30	of	of	ADP
ejpam-4005	249	31	x	x	X
ejpam-4005	249	32	.	.	PUNCT
ejpam-4005	250	1	define	define	VERB
ejpam-4005	250	2	two	two	NUM
ejpam-4005	250	3	mappings	mapping	NOUN
ejpam-4005	250	4	s	s	PART
ejpam-4005	250	5	,	,	PUNCT
ejpam-4005	250	6	t	t	PROPN
ejpam-4005	250	7	:	:	PUNCT
ejpam-4005	250	8	k	k	PROPN
ejpam-4005	250	9	→	→	PUNCT
ejpam-4005	250	10	k	k	PROPN
ejpam-4005	250	11	by	by	ADP
ejpam-4005	250	12	t	t	PROPN
ejpam-4005	250	13	u	u	NOUN
ejpam-4005	250	14	=	=	PUNCT
ejpam-4005	250	15	{	{	PUNCT
ejpam-4005	250	16	−2	−2	PROPN
ejpam-4005	250	17	sin	sin	NOUN
ejpam-4005	250	18	u	u	NOUN
ejpam-4005	250	19	2	2	NUM
ejpam-4005	250	20	,	,	PUNCT
ejpam-4005	250	21	if	if	SCONJ
ejpam-4005	250	22	u	u	PROPN
ejpam-4005	250	23	∈	∈	PROPN
ejpam-4005	251	1	[	[	X
ejpam-4005	251	2	0	0	NUM
ejpam-4005	251	3	,	,	PUNCT
ejpam-4005	251	4	1	1	NUM
ejpam-4005	251	5	]	]	PUNCT
ejpam-4005	251	6	,	,	PUNCT
ejpam-4005	251	7	2	2	NUM
ejpam-4005	251	8	sin	sin	NOUN
ejpam-4005	251	9	u	u	NOUN
ejpam-4005	251	10	2	2	NUM
ejpam-4005	251	11	,	,	PUNCT
ejpam-4005	251	12	if	if	SCONJ
ejpam-4005	251	13	u	u	PROPN
ejpam-4005	251	14	∈	∈	PROPN
ejpam-4005	252	1	[	[	X
ejpam-4005	252	2	−1	−1	NOUN
ejpam-4005	252	3	,	,	PUNCT
ejpam-4005	252	4	0	0	NUM
ejpam-4005	252	5	)	)	PUNCT
ejpam-4005	252	6	and	and	CCONJ
ejpam-4005	252	7	su	su	NOUN
ejpam-4005	253	1	=	=	NOUN
ejpam-4005	253	2	{	{	PUNCT
ejpam-4005	253	3	u	u	NOUN
ejpam-4005	253	4	,	,	PUNCT
ejpam-4005	253	5	if	if	SCONJ
ejpam-4005	253	6	u	u	PROPN
ejpam-4005	253	7	∈	∈	PROPN
ejpam-4005	254	1	[	[	X
ejpam-4005	254	2	0	0	NUM
ejpam-4005	254	3	,	,	PUNCT
ejpam-4005	254	4	1	1	NUM
ejpam-4005	254	5	]	]	PUNCT
ejpam-4005	254	6	,	,	PUNCT
ejpam-4005	254	7	−u	−u	PROPN
ejpam-4005	254	8	,	,	PUNCT
ejpam-4005	254	9	if	if	SCONJ
ejpam-4005	254	10	u	u	PROPN
ejpam-4005	254	11	∈	∈	PROPN
ejpam-4005	255	1	[	[	X
ejpam-4005	255	2	−1	−1	NOUN
ejpam-4005	255	3	,	,	PUNCT
ejpam-4005	255	4	0	0	NUM
ejpam-4005	255	5	)	)	PUNCT
ejpam-4005	255	6	.	.	PUNCT
ejpam-4005	256	1	clearly	clearly	ADV
ejpam-4005	256	2	,	,	PUNCT
ejpam-4005	256	3	f(t	f(t	PROPN
ejpam-4005	256	4	)	)	PUNCT
ejpam-4005	257	1	=	=	PUNCT
ejpam-4005	257	2	{	{	PUNCT
ejpam-4005	257	3	0	0	NUM
ejpam-4005	257	4	}	}	PUNCT
ejpam-4005	257	5	and	and	CCONJ
ejpam-4005	257	6	f(s	f(	NOUN
ejpam-4005	257	7	)	)	PUNCT
ejpam-4005	258	1	=	=	SYM
ejpam-4005	258	2	{	{	PUNCT
ejpam-4005	258	3	u	u	NOUN
ejpam-4005	258	4	∈	∈	PROPN
ejpam-4005	258	5	k	k	NOUN
ejpam-4005	258	6	;	;	PUNCT
ejpam-4005	258	7	0	0	NUM
ejpam-4005	258	8	≤	≤	NUM
ejpam-4005	258	9	u	u	NOUN
ejpam-4005	258	10	≤	≤	NOUN
ejpam-4005	258	11	1	1	NUM
ejpam-4005	258	12	}	}	PUNCT
ejpam-4005	258	13	.	.	PUNCT
ejpam-4005	259	1	now	now	ADV
ejpam-4005	259	2	,	,	PUNCT
ejpam-4005	259	3	we	we	PRON
ejpam-4005	259	4	show	show	VERB
ejpam-4005	259	5	that	that	SCONJ
ejpam-4005	259	6	t	t	PROPN
ejpam-4005	259	7	is	be	AUX
ejpam-4005	259	8	nonexpansive	nonexpansive	ADJ
ejpam-4005	259	9	.	.	PUNCT
ejpam-4005	260	1	in	in	ADP
ejpam-4005	260	2	fact	fact	NOUN
ejpam-4005	260	3	,	,	PUNCT
ejpam-4005	260	4	if	if	SCONJ
ejpam-4005	260	5	u	u	NOUN
ejpam-4005	260	6	,	,	PUNCT
ejpam-4005	260	7	v	v	NOUN
ejpam-4005	260	8	∈	∈	PROPN
ejpam-4005	260	9	[	[	X
ejpam-4005	260	10	0	0	NUM
ejpam-4005	260	11	,	,	PUNCT
ejpam-4005	260	12	1	1	NUM
ejpam-4005	260	13	]	]	PUNCT
ejpam-4005	260	14	or	or	CCONJ
ejpam-4005	260	15	u	u	NOUN
ejpam-4005	260	16	,	,	PUNCT
ejpam-4005	260	17	v	v	NOUN
ejpam-4005	260	18	∈	∈	PROPN
ejpam-4005	260	19	[	[	X
ejpam-4005	260	20	−1	−1	NOUN
ejpam-4005	260	21	,	,	PUNCT
ejpam-4005	260	22	0	0	NUM
ejpam-4005	260	23	)	)	PUNCT
ejpam-4005	260	24	,	,	PUNCT
ejpam-4005	260	25	then	then	ADV
ejpam-4005	260	26	d(t	d(t	PROPN
ejpam-4005	260	27	u	u	PROPN
ejpam-4005	260	28	,	,	PUNCT
ejpam-4005	260	29	t	t	PROPN
ejpam-4005	260	30	v	v	NOUN
ejpam-4005	260	31	)	)	PUNCT
ejpam-4005	260	32	=	=	PUNCT
ejpam-4005	260	33	|t	|t	VERB
ejpam-4005	260	34	u−	u−	PROPN
ejpam-4005	260	35	t	t	NOUN
ejpam-4005	260	36	v|	v|	PROPN
ejpam-4005	260	37	=	=	SYM
ejpam-4005	260	38	2|	2|	NUM
ejpam-4005	260	39	sin	sin	VERB
ejpam-4005	260	40	u	u	NOUN
ejpam-4005	260	41	2	2	NUM
ejpam-4005	260	42	−	−	NOUN
ejpam-4005	260	43	sin	sin	NOUN
ejpam-4005	260	44	v	v	ADP
ejpam-4005	260	45	2	2	NUM
ejpam-4005	260	46	|	|	ADV
ejpam-4005	260	47	≤	≤	NOUN
ejpam-4005	260	48	|u−	|u−	NOUN
ejpam-4005	260	49	v|	v|	NOUN
ejpam-4005	260	50	=	=	SYM
ejpam-4005	260	51	d(u	d(u	PROPN
ejpam-4005	260	52	,	,	PUNCT
ejpam-4005	260	53	v	v	NOUN
ejpam-4005	260	54	)	)	PUNCT
ejpam-4005	260	55	.	.	PUNCT
ejpam-4005	261	1	if	if	SCONJ
ejpam-4005	261	2	u	u	PROPN
ejpam-4005	261	3	∈	∈	PROPN
ejpam-4005	262	1	[	[	X
ejpam-4005	262	2	0	0	NUM
ejpam-4005	262	3	,	,	PUNCT
ejpam-4005	262	4	1	1	NUM
ejpam-4005	262	5	]	]	PUNCT
ejpam-4005	262	6	and	and	CCONJ
ejpam-4005	262	7	v	v	ADP
ejpam-4005	262	8	∈	∈	PROPN
ejpam-4005	263	1	[	[	X
ejpam-4005	263	2	−1	−1	NOUN
ejpam-4005	263	3	,	,	PUNCT
ejpam-4005	263	4	0	0	NUM
ejpam-4005	263	5	)	)	PUNCT
ejpam-4005	263	6	or	or	CCONJ
ejpam-4005	263	7	u	u	PROPN
ejpam-4005	263	8	∈	∈	PROPN
ejpam-4005	264	1	[	[	X
ejpam-4005	264	2	−1	−1	NOUN
ejpam-4005	264	3	,	,	PUNCT
ejpam-4005	264	4	0	0	NUM
ejpam-4005	264	5	)	)	PUNCT
ejpam-4005	264	6	and	and	CCONJ
ejpam-4005	264	7	v	v	ADP
ejpam-4005	264	8	∈	∈	PROPN
ejpam-4005	265	1	[	[	X
ejpam-4005	265	2	0	0	NUM
ejpam-4005	265	3	,	,	PUNCT
ejpam-4005	265	4	1	1	NUM
ejpam-4005	265	5	]	]	PUNCT
ejpam-4005	265	6	,	,	PUNCT
ejpam-4005	265	7	then	then	ADV
ejpam-4005	265	8	d(t	d(t	PROPN
ejpam-4005	265	9	u	u	PROPN
ejpam-4005	265	10	,	,	PUNCT
ejpam-4005	265	11	t	t	PROPN
ejpam-4005	265	12	v	v	NOUN
ejpam-4005	265	13	)	)	PUNCT
ejpam-4005	265	14	=	=	PUNCT
ejpam-4005	265	15	|t	|t	VERB
ejpam-4005	265	16	u−	u−	PROPN
ejpam-4005	265	17	t	t	NOUN
ejpam-4005	265	18	v|	v|	PROPN
ejpam-4005	265	19	=	=	SYM
ejpam-4005	265	20	2|	2|	NUM
ejpam-4005	265	21	sin	sin	VERB
ejpam-4005	265	22	u	u	NOUN
ejpam-4005	265	23	2	2	NUM
ejpam-4005	265	24	+	+	NUM
ejpam-4005	265	25	sin	sin	NOUN
ejpam-4005	265	26	v	v	ADP
ejpam-4005	265	27	2	2	NUM
ejpam-4005	265	28	|	|	NOUN
ejpam-4005	265	29	=	=	SYM
ejpam-4005	265	30	4|	4|	NUM
ejpam-4005	265	31	sin	sin	NOUN
ejpam-4005	265	32	u+	u+	NOUN
ejpam-4005	265	33	v	v	ADP
ejpam-4005	265	34	4	4	NUM
ejpam-4005	265	35	cos	cos	PROPN
ejpam-4005	265	36	u−	u−	PROPN
ejpam-4005	266	1	v	v	ADP
ejpam-4005	266	2	4	4	NUM
ejpam-4005	266	3	|	|	ADV
ejpam-4005	266	4	≤	≤	NUM
ejpam-4005	266	5	|u+	|u+	NOUN
ejpam-4005	266	6	v|	v|	ADV
ejpam-4005	266	7	≤	≤	ADJ
ejpam-4005	266	8	|u−	|u−	NOUN
ejpam-4005	266	9	v|	v|	NOUN
ejpam-4005	266	10	t.	t.	PROPN
ejpam-4005	266	11	thianwan	thianwan	PROPN
ejpam-4005	266	12	/	/	SYM
ejpam-4005	266	13	eur	eur	PROPN
ejpam-4005	266	14	.	.	PUNCT
ejpam-4005	267	1	j.	j.	PROPN
ejpam-4005	267	2	pure	pure	PROPN
ejpam-4005	267	3	appl	appl	PROPN
ejpam-4005	267	4	.	.	PROPN
ejpam-4005	267	5	math	math	PROPN
ejpam-4005	267	6	,	,	PUNCT
ejpam-4005	267	7	14	14	NUM
ejpam-4005	267	8	(	(	PUNCT
ejpam-4005	267	9	3	3	NUM
ejpam-4005	267	10	)	)	PUNCT
ejpam-4005	267	11	(	(	PUNCT
ejpam-4005	267	12	2021	2021	NUM
ejpam-4005	267	13	)	)	PUNCT
ejpam-4005	267	14	,	,	PUNCT
ejpam-4005	267	15	650	650	NUM
ejpam-4005	267	16	-	-	SYM
ejpam-4005	267	17	665	665	NUM
ejpam-4005	267	18	661	661	NUM
ejpam-4005	267	19	=	=	SYM
ejpam-4005	267	20	d(u	d(u	PROPN
ejpam-4005	267	21	,	,	PUNCT
ejpam-4005	267	22	v	v	NOUN
ejpam-4005	267	23	)	)	PUNCT
ejpam-4005	267	24	.	.	PUNCT
ejpam-4005	268	1	that	that	PRON
ejpam-4005	268	2	is	is	ADV
ejpam-4005	268	3	,	,	PUNCT
ejpam-4005	268	4	t	t	PROPN
ejpam-4005	268	5	is	be	AUX
ejpam-4005	268	6	nonexpansive	nonexpansive	ADJ
ejpam-4005	268	7	.	.	PUNCT
ejpam-4005	269	1	it	it	PRON
ejpam-4005	269	2	follows	follow	VERB
ejpam-4005	269	3	that	that	SCONJ
ejpam-4005	269	4	t	t	PROPN
ejpam-4005	269	5	is	be	AUX
ejpam-4005	269	6	an	an	DET
ejpam-4005	269	7	asymptotically	asymptotically	ADV
ejpam-4005	269	8	nonexpansive	nonexpansive	ADJ
ejpam-4005	269	9	mapping	mapping	NOUN
ejpam-4005	269	10	with	with	ADP
ejpam-4005	269	11	kn	kn	PROPN
ejpam-4005	269	12	=	=	PROPN
ejpam-4005	269	13	1	1	NUM
ejpam-4005	269	14	for	for	ADP
ejpam-4005	269	15	each	each	DET
ejpam-4005	269	16	n	n	PRON
ejpam-4005	269	17	≥	≥	NOUN
ejpam-4005	269	18	1	1	NUM
ejpam-4005	269	19	.	.	PUNCT
ejpam-4005	270	1	similarly	similarly	ADV
ejpam-4005	270	2	,	,	PUNCT
ejpam-4005	270	3	we	we	PRON
ejpam-4005	270	4	can	can	AUX
ejpam-4005	270	5	show	show	VERB
ejpam-4005	270	6	that	that	SCONJ
ejpam-4005	270	7	s	s	VERB
ejpam-4005	270	8	is	be	AUX
ejpam-4005	270	9	an	an	DET
ejpam-4005	270	10	asymptotically	asymptotically	ADV
ejpam-4005	270	11	nonexpansive	nonexpansive	ADJ
ejpam-4005	270	12	mapping	mapping	NOUN
ejpam-4005	270	13	with	with	ADP
ejpam-4005	270	14	ln	ln	ADJ
ejpam-4005	270	15	=	=	NOUN
ejpam-4005	270	16	1	1	NUM
ejpam-4005	270	17	for	for	ADP
ejpam-4005	270	18	each	each	DET
ejpam-4005	270	19	n	n	PRON
ejpam-4005	270	20	≥	≥	NOUN
ejpam-4005	270	21	1	1	NUM
ejpam-4005	270	22	.	.	PUNCT
ejpam-4005	271	1	next	next	ADV
ejpam-4005	271	2	,	,	PUNCT
ejpam-4005	271	3	to	to	PART
ejpam-4005	271	4	show	show	VERB
ejpam-4005	271	5	that	that	PRON
ejpam-4005	271	6	s	s	VERB
ejpam-4005	271	7	and	and	CCONJ
ejpam-4005	271	8	t	t	PROPN
ejpam-4005	271	9	satisfy	satisfy	VERB
ejpam-4005	271	10	the	the	DET
ejpam-4005	271	11	condition	condition	NOUN
ejpam-4005	271	12	(	(	PUNCT
ejpam-4005	271	13	ii	ii	NOUN
ejpam-4005	271	14	)	)	PUNCT
ejpam-4005	271	15	in	in	ADP
ejpam-4005	271	16	lemma	lemma	PROPN
ejpam-4005	271	17	4	4	NUM
ejpam-4005	271	18	,	,	PUNCT
ejpam-4005	271	19	we	we	PRON
ejpam-4005	271	20	have	have	VERB
ejpam-4005	271	21	to	to	PART
ejpam-4005	271	22	consider	consider	VERB
ejpam-4005	271	23	the	the	DET
ejpam-4005	271	24	following	follow	VERB
ejpam-4005	271	25	cases	case	NOUN
ejpam-4005	271	26	:	:	PUNCT
ejpam-4005	271	27	case	case	NOUN
ejpam-4005	271	28	1	1	X
ejpam-4005	271	29	.	.	PUNCT
ejpam-4005	272	1	let	let	VERB
ejpam-4005	272	2	u	u	NOUN
ejpam-4005	272	3	,	,	PUNCT
ejpam-4005	272	4	v	v	NOUN
ejpam-4005	272	5	∈	∈	PROPN
ejpam-4005	273	1	[	[	X
ejpam-4005	273	2	0	0	NUM
ejpam-4005	273	3	,	,	PUNCT
ejpam-4005	273	4	1	1	NUM
ejpam-4005	273	5	]	]	PUNCT
ejpam-4005	273	6	.	.	PUNCT
ejpam-4005	274	1	it	it	PRON
ejpam-4005	274	2	follows	follow	VERB
ejpam-4005	274	3	that	that	SCONJ
ejpam-4005	274	4	d(u	d(u	PROPN
ejpam-4005	274	5	,	,	PUNCT
ejpam-4005	274	6	t	t	PROPN
ejpam-4005	274	7	v	v	NOUN
ejpam-4005	274	8	)	)	PUNCT
ejpam-4005	274	9	=	=	PUNCT
ejpam-4005	274	10	|u−	|u−	PROPN
ejpam-4005	274	11	t	t	NOUN
ejpam-4005	274	12	v|	v|	NOUN
ejpam-4005	274	13	=	=	PUNCT
ejpam-4005	274	14	|u+	|u+	NUM
ejpam-4005	274	15	2	2	NUM
ejpam-4005	274	16	sin	sin	NOUN
ejpam-4005	274	17	v	v	ADP
ejpam-4005	274	18	2	2	NUM
ejpam-4005	274	19	|	|	ADV
ejpam-4005	274	20	=	=	SYM
ejpam-4005	274	21	|su−	|su−	VERB
ejpam-4005	274	22	t	t	PROPN
ejpam-4005	274	23	v|	v|	NOUN
ejpam-4005	274	24	=	=	PUNCT
ejpam-4005	274	25	d(su	d(su	PROPN
ejpam-4005	274	26	,	,	PUNCT
ejpam-4005	274	27	t	t	NOUN
ejpam-4005	274	28	v	v	NOUN
ejpam-4005	274	29	)	)	PUNCT
ejpam-4005	274	30	.	.	PUNCT
ejpam-4005	275	1	case	case	NOUN
ejpam-4005	275	2	2	2	X
ejpam-4005	275	3	.	.	PUNCT
ejpam-4005	276	1	let	let	VERB
ejpam-4005	276	2	u	u	NOUN
ejpam-4005	276	3	,	,	PUNCT
ejpam-4005	276	4	v	v	NOUN
ejpam-4005	276	5	∈	∈	PROPN
ejpam-4005	277	1	[	[	X
ejpam-4005	277	2	−1	−1	NOUN
ejpam-4005	277	3	,	,	PUNCT
ejpam-4005	277	4	0	0	NUM
ejpam-4005	277	5	)	)	PUNCT
ejpam-4005	277	6	.	.	PUNCT
ejpam-4005	278	1	it	it	PRON
ejpam-4005	278	2	follows	follow	VERB
ejpam-4005	278	3	that	that	SCONJ
ejpam-4005	278	4	d(u	d(u	PROPN
ejpam-4005	278	5	,	,	PUNCT
ejpam-4005	278	6	t	t	PROPN
ejpam-4005	278	7	v	v	NOUN
ejpam-4005	278	8	)	)	PUNCT
ejpam-4005	278	9	=	=	PUNCT
ejpam-4005	278	10	|u−	|u−	PROPN
ejpam-4005	278	11	t	t	NOUN
ejpam-4005	278	12	v|	v|	NOUN
ejpam-4005	278	13	=	=	PUNCT
ejpam-4005	278	14	|u−	|u−	ADJ
ejpam-4005	278	15	2	2	NUM
ejpam-4005	278	16	sin	sin	NOUN
ejpam-4005	278	17	v	v	ADP
ejpam-4005	278	18	2	2	NUM
ejpam-4005	279	1	|	|	ADV
ejpam-4005	279	2	≤	≤	PUNCT
ejpam-4005	280	1	|	|	ADV
ejpam-4005	280	2	−	−	PUNCT
ejpam-4005	280	3	u−	u−	PROPN
ejpam-4005	280	4	2	2	NUM
ejpam-4005	280	5	sin	sin	NOUN
ejpam-4005	280	6	v	v	ADP
ejpam-4005	280	7	2	2	NUM
ejpam-4005	280	8	|	|	ADV
ejpam-4005	280	9	=	=	SYM
ejpam-4005	280	10	|su−	|su−	VERB
ejpam-4005	280	11	t	t	PROPN
ejpam-4005	280	12	v|	v|	NOUN
ejpam-4005	280	13	=	=	PUNCT
ejpam-4005	281	1	d(su	d(su	PROPN
ejpam-4005	281	2	,	,	PUNCT
ejpam-4005	281	3	t	t	NOUN
ejpam-4005	281	4	v	v	NOUN
ejpam-4005	281	5	)	)	PUNCT
ejpam-4005	281	6	.	.	PUNCT
ejpam-4005	282	1	case	case	NOUN
ejpam-4005	282	2	3	3	X
ejpam-4005	282	3	.	.	PUNCT
ejpam-4005	283	1	let	let	VERB
ejpam-4005	283	2	u	u	PRON
ejpam-4005	283	3	∈	∈	PROPN
ejpam-4005	283	4	[	[	X
ejpam-4005	283	5	−1	−1	NOUN
ejpam-4005	283	6	,	,	PUNCT
ejpam-4005	283	7	0	0	NUM
ejpam-4005	283	8	)	)	PUNCT
ejpam-4005	283	9	and	and	CCONJ
ejpam-4005	283	10	v	v	ADP
ejpam-4005	283	11	∈	∈	PROPN
ejpam-4005	284	1	[	[	X
ejpam-4005	284	2	0	0	NUM
ejpam-4005	284	3	,	,	PUNCT
ejpam-4005	284	4	1	1	NUM
ejpam-4005	284	5	]	]	PUNCT
ejpam-4005	284	6	.	.	PUNCT
ejpam-4005	285	1	it	it	PRON
ejpam-4005	285	2	follows	follow	VERB
ejpam-4005	285	3	that	that	SCONJ
ejpam-4005	285	4	d(u	d(u	PROPN
ejpam-4005	285	5	,	,	PUNCT
ejpam-4005	285	6	t	t	PROPN
ejpam-4005	285	7	v	v	NOUN
ejpam-4005	285	8	)	)	PUNCT
ejpam-4005	285	9	=	=	PUNCT
ejpam-4005	285	10	|u−	|u−	PROPN
ejpam-4005	285	11	t	t	NOUN
ejpam-4005	285	12	v|	v|	NOUN
ejpam-4005	285	13	=	=	PUNCT
ejpam-4005	285	14	|u+	|u+	NUM
ejpam-4005	285	15	2	2	NUM
ejpam-4005	285	16	sin	sin	NOUN
ejpam-4005	285	17	v	v	ADP
ejpam-4005	285	18	2	2	NUM
ejpam-4005	285	19	|	|	ADV
ejpam-4005	285	20	≤	≤	PUNCT
ejpam-4005	285	21	|	|	ADV
ejpam-4005	285	22	−	−	NOUN
ejpam-4005	285	23	u+	u+	NOUN
ejpam-4005	285	24	2	2	NUM
ejpam-4005	285	25	sin	sin	NOUN
ejpam-4005	285	26	v	v	ADP
ejpam-4005	285	27	2	2	NUM
ejpam-4005	285	28	|	|	ADV
ejpam-4005	285	29	=	=	SYM
ejpam-4005	285	30	|su−	|su−	VERB
ejpam-4005	285	31	t	t	PROPN
ejpam-4005	285	32	v|	v|	NOUN
ejpam-4005	285	33	=	=	PUNCT
ejpam-4005	285	34	d(su	d(su	PROPN
ejpam-4005	285	35	,	,	PUNCT
ejpam-4005	285	36	t	t	NOUN
ejpam-4005	285	37	v	v	NOUN
ejpam-4005	285	38	)	)	PUNCT
ejpam-4005	285	39	.	.	PUNCT
ejpam-4005	286	1	case	case	NOUN
ejpam-4005	286	2	4	4	X
ejpam-4005	286	3	.	.	PUNCT
ejpam-4005	287	1	let	let	VERB
ejpam-4005	287	2	u	u	PRON
ejpam-4005	287	3	∈	∈	PROPN
ejpam-4005	287	4	[	[	X
ejpam-4005	287	5	0	0	NUM
ejpam-4005	287	6	,	,	PUNCT
ejpam-4005	287	7	1	1	NUM
ejpam-4005	287	8	]	]	PUNCT
ejpam-4005	287	9	and	and	CCONJ
ejpam-4005	287	10	v	v	ADP
ejpam-4005	287	11	∈	∈	PROPN
ejpam-4005	288	1	[	[	X
ejpam-4005	288	2	−1	−1	NOUN
ejpam-4005	288	3	,	,	PUNCT
ejpam-4005	288	4	0	0	NUM
ejpam-4005	288	5	]	]	PUNCT
ejpam-4005	288	6	.	.	PUNCT
ejpam-4005	289	1	it	it	PRON
ejpam-4005	289	2	follows	follow	VERB
ejpam-4005	289	3	that	that	SCONJ
ejpam-4005	289	4	d(u	d(u	PROPN
ejpam-4005	289	5	,	,	PUNCT
ejpam-4005	289	6	t	t	PROPN
ejpam-4005	289	7	v	v	NOUN
ejpam-4005	289	8	)	)	PUNCT
ejpam-4005	289	9	=	=	PUNCT
ejpam-4005	289	10	|u−	|u−	PROPN
ejpam-4005	289	11	t	t	NOUN
ejpam-4005	289	12	v|	v|	NOUN
ejpam-4005	289	13	=	=	PUNCT
ejpam-4005	289	14	|u−	|u−	ADJ
ejpam-4005	289	15	2	2	NUM
ejpam-4005	289	16	sin	sin	NOUN
ejpam-4005	289	17	v	v	ADP
ejpam-4005	289	18	2	2	NUM
ejpam-4005	289	19	|	|	ADV
ejpam-4005	289	20	=	=	SYM
ejpam-4005	289	21	|su−	|su−	VERB
ejpam-4005	289	22	t	t	PROPN
ejpam-4005	289	23	v|	v|	NOUN
ejpam-4005	289	24	=	=	PUNCT
ejpam-4005	289	25	d(su	d(su	PROPN
ejpam-4005	289	26	,	,	PUNCT
ejpam-4005	289	27	t	t	NOUN
ejpam-4005	289	28	v	v	NOUN
ejpam-4005	289	29	)	)	PUNCT
ejpam-4005	289	30	.	.	PUNCT
ejpam-4005	290	1	hence	hence	ADV
ejpam-4005	290	2	the	the	DET
ejpam-4005	290	3	condition	condition	NOUN
ejpam-4005	290	4	(	(	PUNCT
ejpam-4005	290	5	ii	ii	NOUN
ejpam-4005	290	6	)	)	PUNCT
ejpam-4005	290	7	in	in	ADP
ejpam-4005	290	8	lemma	lemma	PROPN
ejpam-4005	290	9	4	4	NUM
ejpam-4005	290	10	is	be	AUX
ejpam-4005	290	11	satisfied	satisfied	ADJ
ejpam-4005	290	12	.	.	PUNCT
ejpam-4005	291	1	now	now	ADV
ejpam-4005	291	2	,	,	PUNCT
ejpam-4005	291	3	we	we	PRON
ejpam-4005	291	4	can	can	AUX
ejpam-4005	291	5	prove	prove	VERB
ejpam-4005	291	6	a	a	DET
ejpam-4005	291	7	strong	strong	ADJ
ejpam-4005	291	8	convergence	convergence	NOUN
ejpam-4005	291	9	theorem	theorem	NOUN
ejpam-4005	291	10	.	.	PUNCT
ejpam-4005	291	11	theorem	theorem	NOUN
ejpam-4005	291	12	1	1	NUM
ejpam-4005	291	13	.	.	PUNCT
ejpam-4005	292	1	let	let	VERB
ejpam-4005	292	2	k	k	NOUN
ejpam-4005	292	3	,	,	PUNCT
ejpam-4005	292	4	x	x	INTJ
ejpam-4005	292	5	,	,	PUNCT
ejpam-4005	292	6	s1,s2	s1,s2	PROPN
ejpam-4005	292	7	,	,	PUNCT
ejpam-4005	292	8	t1	t1	NOUN
ejpam-4005	292	9	and	and	CCONJ
ejpam-4005	292	10	t2	t2	NOUN
ejpam-4005	292	11	satisfy	satisfy	VERB
ejpam-4005	292	12	the	the	DET
ejpam-4005	292	13	hypotheses	hypothesis	NOUN
ejpam-4005	292	14	of	of	ADP
ejpam-4005	292	15	lemma	lemma	PROPN
ejpam-4005	292	16	4	4	NUM
ejpam-4005	292	17	.	.	PUNCT
ejpam-4005	292	18	suppose	suppose	VERB
ejpam-4005	292	19	that	that	SCONJ
ejpam-4005	292	20	{	{	PUNCT
ejpam-4005	292	21	ϑn	ϑn	NOUN
ejpam-4005	292	22	}	}	PUNCT
ejpam-4005	292	23	,	,	PUNCT
ejpam-4005	292	24	{	{	PUNCT
ejpam-4005	292	25	ζn	ζn	NOUN
ejpam-4005	292	26	}	}	PUNCT
ejpam-4005	292	27	are	be	AUX
ejpam-4005	292	28	real	real	ADJ
ejpam-4005	292	29	sequences	sequence	NOUN
ejpam-4005	292	30	in	in	ADP
ejpam-4005	292	31	[	[	X
ejpam-4005	292	32	ε	ε	PROPN
ejpam-4005	292	33	,	,	PUNCT
ejpam-4005	292	34	1−ε	1−ε	NUM
ejpam-4005	292	35	]	]	PUNCT
ejpam-4005	292	36	for	for	ADP
ejpam-4005	292	37	some	some	DET
ejpam-4005	292	38	ε	ε	PROPN
ejpam-4005	292	39	∈	∈	PROPN
ejpam-4005	292	40	(	(	PUNCT
ejpam-4005	292	41	0	0	NUM
ejpam-4005	292	42	,	,	PUNCT
ejpam-4005	292	43	1	1	NUM
ejpam-4005	292	44	)	)	PUNCT
ejpam-4005	292	45	and	and	CCONJ
ejpam-4005	292	46	si	si	INTJ
ejpam-4005	292	47	,	,	PUNCT
ejpam-4005	292	48	ti	ti	NOUN
ejpam-4005	292	49	for	for	ADP
ejpam-4005	292	50	all	all	DET
ejpam-4005	292	51	i	i	PRON
ejpam-4005	292	52	=	=	NOUN
ejpam-4005	292	53	1	1	NUM
ejpam-4005	292	54	,	,	PUNCT
ejpam-4005	292	55	2	2	NUM
ejpam-4005	292	56	satisfy	satisfy	VERB
ejpam-4005	292	57	the	the	DET
ejpam-4005	292	58	condition	condition	NOUN
ejpam-4005	292	59	(	(	PUNCT
ejpam-4005	292	60	ii	ii	NOUN
ejpam-4005	292	61	)	)	PUNCT
ejpam-4005	292	62	in	in	ADP
ejpam-4005	292	63	lemma	lemma	PROPN
ejpam-4005	292	64	4	4	NUM
ejpam-4005	292	65	.	.	PUNCT
ejpam-4005	293	1	if	if	SCONJ
ejpam-4005	293	2	there	there	PRON
ejpam-4005	293	3	is	be	VERB
ejpam-4005	293	4	a	a	DET
ejpam-4005	293	5	nondecreasing	nondecrease	VERB
ejpam-4005	293	6	function	function	NOUN
ejpam-4005	293	7	f	f	NOUN
ejpam-4005	293	8	:	:	PUNCT
ejpam-4005	294	1	[	[	X
ejpam-4005	294	2	0,∞	0,∞	NOUN
ejpam-4005	294	3	)	)	PUNCT
ejpam-4005	294	4	→	→	PUNCT
ejpam-4005	295	1	[	[	X
ejpam-4005	295	2	0,∞	0,∞	NOUN
ejpam-4005	295	3	)	)	PUNCT
ejpam-4005	295	4	with	with	ADP
ejpam-4005	295	5	f(0	f(0	NOUN
ejpam-4005	295	6	)	)	PUNCT
ejpam-4005	295	7	=	=	SYM
ejpam-4005	295	8	0	0	NUM
ejpam-4005	295	9	and	and	CCONJ
ejpam-4005	295	10	f(r	f(r	NOUN
ejpam-4005	295	11	)	)	PUNCT
ejpam-4005	295	12	>	>	X
ejpam-4005	295	13	0	0	PUNCT
ejpam-4005	295	14	for	for	ADP
ejpam-4005	295	15	all	all	DET
ejpam-4005	295	16	r	r	NOUN
ejpam-4005	295	17	∈	∈	PROPN
ejpam-4005	295	18	(	(	PUNCT
ejpam-4005	295	19	0,∞	0,∞	NOUN
ejpam-4005	295	20	)	)	PUNCT
ejpam-4005	295	21	such	such	ADJ
ejpam-4005	295	22	that	that	SCONJ
ejpam-4005	295	23	f(d(u	f(d(u	PROPN
ejpam-4005	295	24	,	,	PUNCT
ejpam-4005	295	25	f	f	NOUN
ejpam-4005	295	26	)	)	PUNCT
ejpam-4005	295	27	)	)	PUNCT
ejpam-4005	295	28	≤	≤	PUNCT
ejpam-4005	296	1	d(u	d(u	PROPN
ejpam-4005	296	2	,	,	PUNCT
ejpam-4005	296	3	s1u	s1u	NOUN
ejpam-4005	296	4	)	)	PUNCT
ejpam-4005	296	5	+	+	CCONJ
ejpam-4005	296	6	d(u	d(u	PROPN
ejpam-4005	296	7	,	,	PUNCT
ejpam-4005	296	8	s2u	s2u	NOUN
ejpam-4005	296	9	)	)	PUNCT
ejpam-4005	296	10	+	+	CCONJ
ejpam-4005	296	11	d(u	d(u	PROPN
ejpam-4005	296	12	,	,	PUNCT
ejpam-4005	296	13	(	(	PUNCT
ejpam-4005	296	14	pt	pt	X
ejpam-4005	296	15	1)u	1)u	NUM
ejpam-4005	296	16	)	)	PUNCT
ejpam-4005	296	17	+	+	CCONJ
ejpam-4005	296	18	d(u	d(u	PROPN
ejpam-4005	296	19	,	,	PUNCT
ejpam-4005	296	20	(	(	PUNCT
ejpam-4005	296	21	pt	pt	NOUN
ejpam-4005	296	22	2)u	2)u	NUM
ejpam-4005	296	23	)	)	PUNCT
ejpam-4005	296	24	for	for	ADP
ejpam-4005	296	25	all	all	DET
ejpam-4005	296	26	u	u	PROPN
ejpam-4005	296	27	∈	∈	PROPN
ejpam-4005	296	28	k	k	NOUN
ejpam-4005	296	29	,	,	PUNCT
ejpam-4005	296	30	where	where	SCONJ
ejpam-4005	296	31	d(u	d(u	PROPN
ejpam-4005	296	32	,	,	PUNCT
ejpam-4005	296	33	f	f	NOUN
ejpam-4005	296	34	)	)	PUNCT
ejpam-4005	296	35	=	=	SYM
ejpam-4005	296	36	inf{d(u	inf{d(u	PROPN
ejpam-4005	296	37	,	,	PUNCT
ejpam-4005	296	38	q	q	NOUN
ejpam-4005	296	39	)	)	PUNCT
ejpam-4005	296	40	:	:	PUNCT
ejpam-4005	296	41	q	q	PUNCT
ejpam-4005	296	42	∈	∈	NOUN
ejpam-4005	296	43	f	f	X
ejpam-4005	296	44	}	}	PUNCT
ejpam-4005	296	45	.	.	PUNCT
ejpam-4005	297	1	then	then	ADV
ejpam-4005	297	2	the	the	DET
ejpam-4005	297	3	sequence	sequence	NOUN
ejpam-4005	297	4	{	{	PUNCT
ejpam-4005	297	5	un	un	PROPN
ejpam-4005	297	6	}	}	PUNCT
ejpam-4005	297	7	defined	define	VERB
ejpam-4005	297	8	by	by	ADP
ejpam-4005	297	9	algorithm	algorithm	NOUN
ejpam-4005	297	10	(	(	PUNCT
ejpam-4005	297	11	9	9	X
ejpam-4005	297	12	)	)	PUNCT
ejpam-4005	297	13	converges	converge	VERB
ejpam-4005	297	14	strongly	strongly	ADV
ejpam-4005	297	15	to	to	ADP
ejpam-4005	297	16	a	a	DET
ejpam-4005	297	17	common	common	ADJ
ejpam-4005	297	18	fixed	fix	VERB
ejpam-4005	297	19	point	point	NOUN
ejpam-4005	297	20	of	of	ADP
ejpam-4005	297	21	s1,s2	s1,s2	PROPN
ejpam-4005	297	22	,	,	PUNCT
ejpam-4005	297	23	t1	t1	NOUN
ejpam-4005	297	24	and	and	CCONJ
ejpam-4005	297	25	t2	t2	NOUN
ejpam-4005	297	26	.	.	PUNCT
ejpam-4005	298	1	proof	proof	NOUN
ejpam-4005	298	2	.	.	PUNCT
ejpam-4005	299	1	by	by	ADP
ejpam-4005	299	2	lemma	lemma	PROPN
ejpam-4005	299	3	4	4	NUM
ejpam-4005	299	4	,	,	PUNCT
ejpam-4005	299	5	we	we	PRON
ejpam-4005	299	6	have	have	VERB
ejpam-4005	299	7	lim	lim	PROPN
ejpam-4005	299	8	n→∞	n→∞	NUM
ejpam-4005	299	9	d(un	d(un	PROPN
ejpam-4005	299	10	,	,	PUNCT
ejpam-4005	299	11	siun	siun	ADJ
ejpam-4005	299	12	)	)	PUNCT
ejpam-4005	300	1	=	=	VERB
ejpam-4005	300	2	lim	lim	PROPN
ejpam-4005	300	3	n→∞	n→∞	NUM
ejpam-4005	300	4	d(un	d(un	PROPN
ejpam-4005	300	5	,	,	PUNCT
ejpam-4005	300	6	(	(	PUNCT
ejpam-4005	300	7	pt	pt	X
ejpam-4005	300	8	i)un	i)un	PROPN
ejpam-4005	300	9	)	)	PUNCT
ejpam-4005	300	10	=	=	SYM
ejpam-4005	300	11	0	0	PUNCT
ejpam-4005	301	1	for	for	ADP
ejpam-4005	301	2	i	i	PRON
ejpam-4005	301	3	=	=	NOUN
ejpam-4005	301	4	1	1	NUM
ejpam-4005	301	5	,	,	PUNCT
ejpam-4005	301	6	2	2	NUM
ejpam-4005	301	7	.	.	PUNCT
ejpam-4005	301	8	it	it	PRON
ejpam-4005	301	9	follows	follow	VERB
ejpam-4005	301	10	from	from	ADP
ejpam-4005	301	11	hypothesis	hypothesis	NOUN
ejpam-4005	301	12	that	that	PRON
ejpam-4005	301	13	lim	lim	PROPN
ejpam-4005	301	14	n→∞	n→∞	NUM
ejpam-4005	301	15	f(d(un	f(d(un	NOUN
ejpam-4005	301	16	,	,	PUNCT
ejpam-4005	301	17	f	f	NOUN
ejpam-4005	301	18	)	)	PUNCT
ejpam-4005	301	19	)	)	PUNCT
ejpam-4005	301	20	≤	≤	PROPN
ejpam-4005	301	21	lim	lim	PROPN
ejpam-4005	301	22	n→∞	n→∞	X
ejpam-4005	301	23	(	(	PUNCT
ejpam-4005	301	24	d(un	d(un	PROPN
ejpam-4005	301	25	,	,	PUNCT
ejpam-4005	301	26	s1un	s1un	PUNCT
ejpam-4005	301	27	)	)	PUNCT
ejpam-4005	302	1	+	+	CCONJ
ejpam-4005	302	2	d(un	d(un	PROPN
ejpam-4005	302	3	,	,	PUNCT
ejpam-4005	302	4	s2un	s2un	PUNCT
ejpam-4005	302	5	)	)	PUNCT
ejpam-4005	303	1	+	+	CCONJ
ejpam-4005	303	2	d(un	d(un	PROPN
ejpam-4005	303	3	,	,	PUNCT
ejpam-4005	303	4	(	(	PUNCT
ejpam-4005	303	5	pt	pt	X
ejpam-4005	303	6	1)un	1)un	NUM
ejpam-4005	303	7	)	)	PUNCT
ejpam-4005	303	8	+	+	CCONJ
ejpam-4005	303	9	d(un	d(un	PROPN
ejpam-4005	303	10	,	,	PUNCT
ejpam-4005	303	11	(	(	PUNCT
ejpam-4005	303	12	pt	pt	NOUN
ejpam-4005	303	13	2)un	2)un	NUM
ejpam-4005	303	14	)	)	PUNCT
ejpam-4005	303	15	)	)	PUNCT
ejpam-4005	304	1	=	=	PUNCT
ejpam-4005	304	2	0	0	X
ejpam-4005	304	3	.	.	PUNCT
ejpam-4005	305	1	thus	thus	ADV
ejpam-4005	305	2	lim	lim	PROPN
ejpam-4005	305	3	n→∞	n→∞	NUM
ejpam-4005	305	4	f(d(un	f(d(un	NOUN
ejpam-4005	305	5	,	,	PUNCT
ejpam-4005	305	6	f	f	NOUN
ejpam-4005	305	7	)	)	PUNCT
ejpam-4005	305	8	)	)	PUNCT
ejpam-4005	306	1	=	=	PUNCT
ejpam-4005	306	2	0	0	X
ejpam-4005	306	3	.	.	PUNCT
ejpam-4005	307	1	since	since	SCONJ
ejpam-4005	307	2	f	f	PROPN
ejpam-4005	307	3	:	:	PUNCT
ejpam-4005	307	4	[	[	X
ejpam-4005	307	5	0,∞)→	0,∞)→	NOUN
ejpam-4005	307	6	[	[	X
ejpam-4005	307	7	0,∞	0,∞	NOUN
ejpam-4005	307	8	)	)	PUNCT
ejpam-4005	307	9	is	be	AUX
ejpam-4005	307	10	a	a	DET
ejpam-4005	307	11	nondecreasing	nondecrease	VERB
ejpam-4005	307	12	function	function	NOUN
ejpam-4005	307	13	satisfying	satisfy	VERB
ejpam-4005	307	14	f(0	f(0	NOUN
ejpam-4005	307	15	)	)	PUNCT
ejpam-4005	308	1	=	=	SYM
ejpam-4005	308	2	0	0	NUM
ejpam-4005	308	3	,	,	PUNCT
ejpam-4005	308	4	f(r	f(r	NOUN
ejpam-4005	308	5	)	)	PUNCT
ejpam-4005	308	6	>	>	X
ejpam-4005	308	7	0	0	PUNCT
ejpam-4005	309	1	for	for	ADP
ejpam-4005	309	2	all	all	DET
ejpam-4005	309	3	r	r	NOUN
ejpam-4005	309	4	∈	∈	PROPN
ejpam-4005	309	5	(	(	PUNCT
ejpam-4005	309	6	0,∞	0,∞	NOUN
ejpam-4005	309	7	)	)	PUNCT
ejpam-4005	309	8	.	.	PUNCT
ejpam-4005	310	1	using	use	VERB
ejpam-4005	310	2	lemma	lemma	PROPN
ejpam-4005	310	3	11	11	NUM
ejpam-4005	310	4	,	,	PUNCT
ejpam-4005	310	5	we	we	PRON
ejpam-4005	310	6	have	have	VERB
ejpam-4005	310	7	lim	lim	PROPN
ejpam-4005	310	8	n→∞	n→∞	NUM
ejpam-4005	310	9	d(un	d(un	PROPN
ejpam-4005	310	10	,	,	PUNCT
ejpam-4005	310	11	f	f	NUM
ejpam-4005	310	12	)	)	PUNCT
ejpam-4005	310	13	exists	exist	VERB
ejpam-4005	310	14	.	.	PUNCT
ejpam-4005	311	1	it	it	PRON
ejpam-4005	311	2	implies	imply	VERB
ejpam-4005	311	3	that	that	SCONJ
ejpam-4005	311	4	lim	lim	PROPN
ejpam-4005	311	5	n→∞	n→∞	NUM
ejpam-4005	311	6	d(un	d(un	PROPN
ejpam-4005	311	7	,	,	PUNCT
ejpam-4005	311	8	f	f	X
ejpam-4005	311	9	)	)	PUNCT
ejpam-4005	311	10	=	=	SYM
ejpam-4005	312	1	0	0	X
ejpam-4005	312	2	.	.	PUNCT
ejpam-4005	313	1	now	now	ADV
ejpam-4005	313	2	,	,	PUNCT
ejpam-4005	313	3	we	we	PRON
ejpam-4005	313	4	show	show	VERB
ejpam-4005	313	5	that	that	SCONJ
ejpam-4005	313	6	{	{	PUNCT
ejpam-4005	313	7	un	un	PROPN
ejpam-4005	313	8	}	}	PUNCT
ejpam-4005	313	9	is	be	AUX
ejpam-4005	313	10	a	a	DET
ejpam-4005	313	11	cauchy	cauchy	ADJ
ejpam-4005	313	12	sequence	sequence	NOUN
ejpam-4005	313	13	in	in	ADP
ejpam-4005	313	14	k.	k.	PROPN
ejpam-4005	313	15	in	in	ADP
ejpam-4005	313	16	fact	fact	NOUN
ejpam-4005	313	17	,	,	PUNCT
ejpam-4005	313	18	from	from	ADP
ejpam-4005	313	19	(	(	PUNCT
ejpam-4005	313	20	11	11	NUM
ejpam-4005	313	21	)	)	PUNCT
ejpam-4005	313	22	,	,	PUNCT
ejpam-4005	313	23	we	we	PRON
ejpam-4005	313	24	have	have	VERB
ejpam-4005	313	25	d(un+1	d(un+1	NUM
ejpam-4005	313	26	,	,	PUNCT
ejpam-4005	313	27	q	q	NOUN
ejpam-4005	313	28	)	)	PUNCT
ejpam-4005	313	29	≤	≤	NOUN
ejpam-4005	313	30	(	(	PUNCT
ejpam-4005	313	31	1	1	NUM
ejpam-4005	313	32	+	+	CCONJ
ejpam-4005	313	33	(	(	PUNCT
ejpam-4005	313	34	h2	h2	PROPN
ejpam-4005	313	35	n	n	CCONJ
ejpam-4005	313	36	−	−	PROPN
ejpam-4005	313	37	1))d(un	1))d(un	NUM
ejpam-4005	313	38	,	,	PUNCT
ejpam-4005	313	39	q	q	NOUN
ejpam-4005	313	40	)	)	PUNCT
ejpam-4005	313	41	for	for	ADP
ejpam-4005	313	42	each	each	DET
ejpam-4005	313	43	n	n	PRON
ejpam-4005	313	44	≥	≥	NOUN
ejpam-4005	313	45	1	1	NUM
ejpam-4005	313	46	,	,	PUNCT
ejpam-4005	313	47	where	where	SCONJ
ejpam-4005	313	48	hn	hn	PROPN
ejpam-4005	313	49	=	=	PUNCT
ejpam-4005	313	50	max{k(1	max{k(1	PROPN
ejpam-4005	313	51	)	)	PUNCT
ejpam-4005	313	52	n	n	NOUN
ejpam-4005	313	53	,	,	PUNCT
ejpam-4005	313	54	k	k	X
ejpam-4005	313	55	(	(	PUNCT
ejpam-4005	313	56	2	2	NUM
ejpam-4005	313	57	)	)	PUNCT
ejpam-4005	313	58	n	n	NOUN
ejpam-4005	313	59	,	,	PUNCT
ejpam-4005	313	60	l	l	X
ejpam-4005	313	61	(	(	PUNCT
ejpam-4005	313	62	1	1	NUM
ejpam-4005	313	63	)	)	PUNCT
ejpam-4005	313	64	n	n	NOUN
ejpam-4005	313	65	,	,	PUNCT
ejpam-4005	313	66	l	l	X
ejpam-4005	313	67	(	(	PUNCT
ejpam-4005	313	68	2	2	NUM
ejpam-4005	313	69	)	)	PUNCT
ejpam-4005	313	70	n	n	CCONJ
ejpam-4005	313	71	}	}	PUNCT
ejpam-4005	313	72	and	and	CCONJ
ejpam-4005	313	73	q	q	PROPN
ejpam-4005	313	74	∈	∈	PROPN
ejpam-4005	313	75	f	f	X
ejpam-4005	313	76	.	.	PUNCT
ejpam-4005	314	1	for	for	ADP
ejpam-4005	314	2	any	any	DET
ejpam-4005	314	3	m	m	NOUN
ejpam-4005	314	4	,	,	PUNCT
ejpam-4005	314	5	n	n	CCONJ
ejpam-4005	314	6	,	,	PUNCT
ejpam-4005	314	7	m	m	VERB
ejpam-4005	314	8	>	>	X
ejpam-4005	314	9	n	n	X
ejpam-4005	314	10	≥	≥	NUM
ejpam-4005	314	11	1	1	NUM
ejpam-4005	314	12	,	,	PUNCT
ejpam-4005	314	13	we	we	PRON
ejpam-4005	314	14	have	have	VERB
ejpam-4005	314	15	d(um	d(um	NOUN
ejpam-4005	314	16	,	,	PUNCT
ejpam-4005	314	17	q	q	NOUN
ejpam-4005	314	18	)	)	PUNCT
ejpam-4005	314	19	≤	≤	NOUN
ejpam-4005	314	20	(	(	PUNCT
ejpam-4005	314	21	1	1	NUM
ejpam-4005	314	22	+	+	CCONJ
ejpam-4005	314	23	(	(	PUNCT
ejpam-4005	314	24	h2	h2	NOUN
ejpam-4005	314	25	m−1	m−1	PROPN
ejpam-4005	314	26	−	−	PROPN
ejpam-4005	315	1	1))d(um−1	1))d(um−1	NOUN
ejpam-4005	315	2	,	,	PUNCT
ejpam-4005	315	3	q	q	X
ejpam-4005	315	4	)	)	PUNCT
ejpam-4005	315	5	t.	t.	PROPN
ejpam-4005	315	6	thianwan	thianwan	PROPN
ejpam-4005	315	7	/	/	SYM
ejpam-4005	315	8	eur	eur	PROPN
ejpam-4005	315	9	.	.	PUNCT
ejpam-4005	316	1	j.	j.	PROPN
ejpam-4005	316	2	pure	pure	PROPN
ejpam-4005	316	3	appl	appl	PROPN
ejpam-4005	316	4	.	.	PROPN
ejpam-4005	316	5	math	math	PROPN
ejpam-4005	316	6	,	,	PUNCT
ejpam-4005	316	7	14	14	NUM
ejpam-4005	316	8	(	(	PUNCT
ejpam-4005	316	9	3	3	NUM
ejpam-4005	316	10	)	)	PUNCT
ejpam-4005	316	11	(	(	PUNCT
ejpam-4005	316	12	2021	2021	NUM
ejpam-4005	316	13	)	)	PUNCT
ejpam-4005	316	14	,	,	PUNCT
ejpam-4005	316	15	650	650	NUM
ejpam-4005	316	16	-	-	SYM
ejpam-4005	316	17	665	665	NUM
ejpam-4005	316	18	662	662	NUM
ejpam-4005	316	19	≤	≤	NUM
ejpam-4005	316	20	eh	eh	INTJ
ejpam-4005	316	21	2	2	NUM
ejpam-4005	316	22	m−1−1d(um−1	m−1−1d(um−1	PROPN
ejpam-4005	316	23	,	,	PUNCT
ejpam-4005	316	24	q	q	NOUN
ejpam-4005	316	25	)	)	PUNCT
ejpam-4005	316	26	≤	≤	NOUN
ejpam-4005	316	27	eh	eh	INTJ
ejpam-4005	316	28	2	2	NUM
ejpam-4005	316	29	m−1−1e	m−1−1e	NUM
ejpam-4005	316	30	h2	h2	NOUN
ejpam-4005	316	31	m−2−1d(um−2	m−2−1d(um−2	PROPN
ejpam-4005	316	32	,	,	PUNCT
ejpam-4005	316	33	q	q	NOUN
ejpam-4005	316	34	)	)	PUNCT
ejpam-4005	316	35	...	...	PUNCT
ejpam-4005	317	1	≤	≤	NUM
ejpam-4005	317	2	e	e	X
ejpam-4005	317	3	∑m−1	∑m−1	PROPN
ejpam-4005	317	4	i	i	PRON
ejpam-4005	317	5	=	=	NOUN
ejpam-4005	317	6	n	n	PRON
ejpam-4005	317	7	(	(	PUNCT
ejpam-4005	317	8	h2	h2	PROPN
ejpam-4005	317	9	i−1)d(un	i−1)d(un	PROPN
ejpam-4005	317	10	,	,	PUNCT
ejpam-4005	317	11	q	q	NOUN
ejpam-4005	317	12	)	)	PUNCT
ejpam-4005	317	13	≤md(un	≤md(un	PROPN
ejpam-4005	317	14	,	,	PUNCT
ejpam-4005	317	15	q	q	NOUN
ejpam-4005	317	16	)	)	PUNCT
ejpam-4005	317	17	,	,	PUNCT
ejpam-4005	317	18	where	where	SCONJ
ejpam-4005	317	19	m	m	VERB
ejpam-4005	317	20	=	=	VERB
ejpam-4005	317	21	eς∞i=1(h2	eς∞i=1(h2	NOUN
ejpam-4005	317	22	i−1	i−1	PROPN
ejpam-4005	317	23	)	)	PUNCT
ejpam-4005	317	24	.	.	PUNCT
ejpam-4005	318	1	thus	thus	ADV
ejpam-4005	318	2	,	,	PUNCT
ejpam-4005	318	3	for	for	ADP
ejpam-4005	318	4	any	any	DET
ejpam-4005	318	5	q	q	NOUN
ejpam-4005	318	6	∈	∈	PROPN
ejpam-4005	318	7	f	f	NOUN
ejpam-4005	318	8	,	,	PUNCT
ejpam-4005	318	9	we	we	PRON
ejpam-4005	318	10	have	have	VERB
ejpam-4005	318	11	d(un	d(un	PROPN
ejpam-4005	318	12	,	,	PUNCT
ejpam-4005	318	13	um	um	INTJ
ejpam-4005	318	14	)	)	PUNCT
ejpam-4005	318	15	≤	≤	PUNCT
ejpam-4005	319	1	d(un	d(un	PROPN
ejpam-4005	319	2	,	,	PUNCT
ejpam-4005	319	3	q	q	NOUN
ejpam-4005	319	4	)	)	PUNCT
ejpam-4005	319	5	+	+	CCONJ
ejpam-4005	319	6	d(um	d(um	NOUN
ejpam-4005	319	7	,	,	PUNCT
ejpam-4005	319	8	q	q	NOUN
ejpam-4005	319	9	)	)	PUNCT
ejpam-4005	319	10	≤	≤	NOUN
ejpam-4005	319	11	(	(	PUNCT
ejpam-4005	319	12	1	1	NUM
ejpam-4005	319	13	+	+	NOUN
ejpam-4005	319	14	m)d(un	m)d(un	NOUN
ejpam-4005	319	15	,	,	PUNCT
ejpam-4005	319	16	q	q	NOUN
ejpam-4005	319	17	)	)	PUNCT
ejpam-4005	319	18	.	.	PUNCT
ejpam-4005	320	1	taking	take	VERB
ejpam-4005	320	2	the	the	DET
ejpam-4005	320	3	infimum	infimum	NOUN
ejpam-4005	320	4	over	over	ADP
ejpam-4005	320	5	all	all	DET
ejpam-4005	320	6	q	q	PROPN
ejpam-4005	320	7	∈	∈	PROPN
ejpam-4005	320	8	f	f	NOUN
ejpam-4005	320	9	,	,	PUNCT
ejpam-4005	320	10	we	we	PRON
ejpam-4005	320	11	have	have	VERB
ejpam-4005	320	12	d(un	d(un	PROPN
ejpam-4005	320	13	,	,	PUNCT
ejpam-4005	320	14	um	um	INTJ
ejpam-4005	320	15	)	)	PUNCT
ejpam-4005	320	16	≤	≤	NOUN
ejpam-4005	320	17	(	(	PUNCT
ejpam-4005	320	18	1	1	NUM
ejpam-4005	320	19	+	+	NOUN
ejpam-4005	320	20	m)d(un	m)d(un	NUM
ejpam-4005	320	21	,	,	PUNCT
ejpam-4005	320	22	f	f	NOUN
ejpam-4005	320	23	)	)	PUNCT
ejpam-4005	320	24	.	.	PUNCT
ejpam-4005	321	1	thus	thus	ADV
ejpam-4005	321	2	it	it	PRON
ejpam-4005	321	3	follows	follow	VERB
ejpam-4005	321	4	from	from	ADP
ejpam-4005	321	5	lim	lim	PROPN
ejpam-4005	321	6	n→∞	n→∞	X
ejpam-4005	321	7	d(un	d(un	PROPN
ejpam-4005	321	8	,	,	PUNCT
ejpam-4005	321	9	f	f	X
ejpam-4005	321	10	)	)	PUNCT
ejpam-4005	321	11	=	=	SYM
ejpam-4005	321	12	0	0	NUM
ejpam-4005	321	13	that	that	SCONJ
ejpam-4005	321	14	{	{	PUNCT
ejpam-4005	321	15	un	un	PROPN
ejpam-4005	321	16	}	}	PUNCT
ejpam-4005	321	17	is	be	AUX
ejpam-4005	321	18	a	a	DET
ejpam-4005	321	19	cauchy	cauchy	ADJ
ejpam-4005	321	20	sequence	sequence	NOUN
ejpam-4005	321	21	.	.	PUNCT
ejpam-4005	322	1	since	since	SCONJ
ejpam-4005	322	2	k	k	PROPN
ejpam-4005	322	3	is	be	AUX
ejpam-4005	322	4	a	a	DET
ejpam-4005	322	5	closed	closed	ADJ
ejpam-4005	322	6	subset	subset	NOUN
ejpam-4005	322	7	in	in	ADP
ejpam-4005	322	8	a	a	DET
ejpam-4005	322	9	complete	complete	ADJ
ejpam-4005	322	10	hyperbolic	hyperbolic	ADJ
ejpam-4005	322	11	space	space	NOUN
ejpam-4005	322	12	x	x	SYM
ejpam-4005	322	13	,	,	PUNCT
ejpam-4005	322	14	the	the	DET
ejpam-4005	322	15	sequence	sequence	NOUN
ejpam-4005	322	16	{	{	PUNCT
ejpam-4005	322	17	un	un	PROPN
ejpam-4005	322	18	}	}	PUNCT
ejpam-4005	322	19	converges	converge	VERB
ejpam-4005	322	20	strongly	strongly	ADV
ejpam-4005	322	21	to	to	ADP
ejpam-4005	322	22	some	some	DET
ejpam-4005	322	23	q∗	q∗	NOUN
ejpam-4005	322	24	∈	∈	PROPN
ejpam-4005	322	25	k.	k.	NOUN
ejpam-4005	323	1	it	it	PRON
ejpam-4005	323	2	is	be	AUX
ejpam-4005	323	3	easy	easy	ADJ
ejpam-4005	323	4	to	to	PART
ejpam-4005	323	5	prove	prove	VERB
ejpam-4005	323	6	that	that	SCONJ
ejpam-4005	323	7	f(s1),f(s2),f(t1	f(s1),f(s2),f(t1	PROPN
ejpam-4005	323	8	)	)	PUNCT
ejpam-4005	323	9	and	and	CCONJ
ejpam-4005	323	10	f(t2	f(t2	ADJ
ejpam-4005	323	11	)	)	PUNCT
ejpam-4005	323	12	are	be	AUX
ejpam-4005	323	13	all	all	PRON
ejpam-4005	323	14	closed	closed	ADJ
ejpam-4005	323	15	and	and	CCONJ
ejpam-4005	323	16	so	so	ADV
ejpam-4005	323	17	f	f	PROPN
ejpam-4005	323	18	is	be	AUX
ejpam-4005	323	19	a	a	DET
ejpam-4005	323	20	closed	closed	ADJ
ejpam-4005	323	21	subset	subset	NOUN
ejpam-4005	323	22	of	of	ADP
ejpam-4005	323	23	k.	k.	PROPN
ejpam-4005	323	24	since	since	SCONJ
ejpam-4005	323	25	lim	lim	PROPN
ejpam-4005	323	26	n→∞	n→∞	X
ejpam-4005	323	27	d(un	d(un	PROPN
ejpam-4005	323	28	,	,	PUNCT
ejpam-4005	323	29	f	f	X
ejpam-4005	323	30	)	)	PUNCT
ejpam-4005	323	31	=	=	SYM
ejpam-4005	323	32	0	0	PROPN
ejpam-4005	323	33	gives	give	VERB
ejpam-4005	323	34	that	that	PRON
ejpam-4005	323	35	d(q∗,f	d(q∗,f	NOUN
ejpam-4005	323	36	)	)	PUNCT
ejpam-4005	324	1	=	=	SYM
ejpam-4005	324	2	0	0	X
ejpam-4005	324	3	.	.	PUNCT
ejpam-4005	324	4	therefore	therefore	ADV
ejpam-4005	324	5	q∗	q∗	PROPN
ejpam-4005	324	6	∈	∈	PROPN
ejpam-4005	324	7	f	f	PROPN
ejpam-4005	324	8	.	.	PUNCT
ejpam-4005	325	1	this	this	PRON
ejpam-4005	325	2	completes	complete	VERB
ejpam-4005	325	3	the	the	DET
ejpam-4005	325	4	proof	proof	NOUN
ejpam-4005	325	5	.	.	PUNCT
ejpam-4005	326	1	if	if	SCONJ
ejpam-4005	326	2	t1	t1	NOUN
ejpam-4005	326	3	and	and	CCONJ
ejpam-4005	326	4	t2	t2	NOUN
ejpam-4005	326	5	are	be	AUX
ejpam-4005	326	6	self	self	NOUN
ejpam-4005	326	7	-	-	PUNCT
ejpam-4005	326	8	mappings	mapping	NOUN
ejpam-4005	326	9	,	,	PUNCT
ejpam-4005	326	10	then	then	ADV
ejpam-4005	326	11	p	p	NOUN
ejpam-4005	326	12	becomes	become	VERB
ejpam-4005	326	13	the	the	DET
ejpam-4005	326	14	identity	identity	NOUN
ejpam-4005	326	15	mapping	mapping	NOUN
ejpam-4005	326	16	.	.	PUNCT
ejpam-4005	327	1	by	by	ADP
ejpam-4005	327	2	using	use	VERB
ejpam-4005	327	3	to	to	ADP
ejpam-4005	327	4	the	the	DET
ejpam-4005	327	5	same	same	ADJ
ejpam-4005	327	6	ideas	idea	NOUN
ejpam-4005	327	7	and	and	CCONJ
ejpam-4005	327	8	techniques	technique	NOUN
ejpam-4005	327	9	as	as	ADP
ejpam-4005	327	10	in	in	ADP
ejpam-4005	327	11	lemma	lemma	PROPN
ejpam-4005	327	12	3	3	NUM
ejpam-4005	327	13	,	,	PUNCT
ejpam-4005	327	14	lemma	lemma	PROPN
ejpam-4005	327	15	4	4	NUM
ejpam-4005	327	16	and	and	CCONJ
ejpam-4005	327	17	theorem	theorem	VERB
ejpam-4005	327	18	1	1	NUM
ejpam-4005	327	19	,	,	PUNCT
ejpam-4005	327	20	we	we	PRON
ejpam-4005	327	21	can	can	AUX
ejpam-4005	327	22	also	also	ADV
ejpam-4005	327	23	obtain	obtain	VERB
ejpam-4005	327	24	a	a	DET
ejpam-4005	327	25	strong	strong	ADJ
ejpam-4005	327	26	convergence	convergence	NOUN
ejpam-4005	327	27	theorem	theorem	NOUN
ejpam-4005	327	28	for	for	ADP
ejpam-4005	327	29	asymptotically	asymptotically	ADV
ejpam-4005	327	30	nonexpansive	nonexpansive	ADJ
ejpam-4005	327	31	mappings	mapping	NOUN
ejpam-4005	327	32	in	in	ADP
ejpam-4005	327	33	a	a	DET
ejpam-4005	327	34	uniformly	uniformly	ADV
ejpam-4005	327	35	convex	convex	ADJ
ejpam-4005	327	36	hyperbolic	hyperbolic	ADJ
ejpam-4005	327	37	space	space	NOUN
ejpam-4005	327	38	.	.	PUNCT
ejpam-4005	328	1	therefore	therefore	ADV
ejpam-4005	328	2	we	we	PRON
ejpam-4005	328	3	can	can	AUX
ejpam-4005	328	4	state	state	VERB
ejpam-4005	328	5	the	the	DET
ejpam-4005	328	6	following	following	ADJ
ejpam-4005	328	7	result	result	NOUN
ejpam-4005	328	8	without	without	ADP
ejpam-4005	328	9	proofs	proof	NOUN
ejpam-4005	328	10	.	.	PUNCT
ejpam-4005	329	1	theorem	theorem	NOUN
ejpam-4005	329	2	2	2	NUM
ejpam-4005	329	3	.	.	X
ejpam-4005	330	1	let	let	VERB
ejpam-4005	330	2	(	(	PUNCT
ejpam-4005	330	3	x	x	X
ejpam-4005	330	4	,	,	PUNCT
ejpam-4005	330	5	d	d	X
ejpam-4005	330	6	,	,	PUNCT
ejpam-4005	330	7	w	w	NOUN
ejpam-4005	330	8	)	)	PUNCT
ejpam-4005	330	9	be	be	AUX
ejpam-4005	330	10	a	a	DET
ejpam-4005	330	11	uniformly	uniformly	ADV
ejpam-4005	330	12	convex	convex	ADJ
ejpam-4005	330	13	hyperbolic	hyperbolic	ADJ
ejpam-4005	330	14	space	space	NOUN
ejpam-4005	330	15	and	and	CCONJ
ejpam-4005	330	16	k	k	PROPN
ejpam-4005	330	17	be	be	AUX
ejpam-4005	330	18	a	a	DET
ejpam-4005	330	19	nonempty	nonempty	ADV
ejpam-4005	330	20	closed	close	VERB
ejpam-4005	330	21	convex	convex	NOUN
ejpam-4005	330	22	subset	subset	NOUN
ejpam-4005	330	23	of	of	ADP
ejpam-4005	330	24	x	x	X
ejpam-4005	330	25	.	.	PUNCT
ejpam-4005	331	1	let	let	VERB
ejpam-4005	331	2	s1,s2	s1,s2	PROPN
ejpam-4005	331	3	:	:	PUNCT
ejpam-4005	332	1	k	k	X
ejpam-4005	332	2	→	→	PUNCT
ejpam-4005	332	3	k	k	X
ejpam-4005	332	4	be	be	AUX
ejpam-4005	332	5	two	two	NUM
ejpam-4005	332	6	asymptotically	asymptotically	ADV
ejpam-4005	332	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	332	8	mappings	mapping	NOUN
ejpam-4005	332	9	with	with	ADP
ejpam-4005	332	10	{	{	PUNCT
ejpam-4005	332	11	k(1	k(1	NOUN
ejpam-4005	332	12	)	)	PUNCT
ejpam-4005	332	13	n	n	CCONJ
ejpam-4005	332	14	}	}	PUNCT
ejpam-4005	332	15	,	,	PUNCT
ejpam-4005	332	16	{	{	PUNCT
ejpam-4005	332	17	k(2	k(2	NOUN
ejpam-4005	332	18	)	)	PUNCT
ejpam-4005	332	19	n	n	CCONJ
ejpam-4005	332	20	}	}	PUNCT
ejpam-4005	332	21	⊂	⊂	PROPN
ejpam-4005	333	1	[	[	X
ejpam-4005	333	2	1,∞	1,∞	NUM
ejpam-4005	333	3	)	)	PUNCT
ejpam-4005	333	4	and	and	CCONJ
ejpam-4005	333	5	t1	t1	NOUN
ejpam-4005	333	6	,	,	PUNCT
ejpam-4005	333	7	t2	t2	NOUN
ejpam-4005	333	8	:	:	PUNCT
ejpam-4005	333	9	k	k	PROPN
ejpam-4005	333	10	→	→	PUNCT
ejpam-4005	333	11	k	k	X
ejpam-4005	333	12	be	be	AUX
ejpam-4005	333	13	two	two	NUM
ejpam-4005	333	14	asymptotically	asymptotically	ADV
ejpam-4005	333	15	nonexpansive	nonexpansive	ADJ
ejpam-4005	333	16	mappings	mapping	NOUN
ejpam-4005	333	17	with	with	ADP
ejpam-4005	333	18	{	{	PUNCT
ejpam-4005	333	19	l(1	l(1	PROPN
ejpam-4005	333	20	)	)	PUNCT
ejpam-4005	333	21	n	n	CCONJ
ejpam-4005	333	22	}	}	PUNCT
ejpam-4005	333	23	,	,	PUNCT
ejpam-4005	333	24	{	{	PUNCT
ejpam-4005	333	25	l(2	l(2	NOUN
ejpam-4005	333	26	)	)	PUNCT
ejpam-4005	333	27	n	n	CCONJ
ejpam-4005	333	28	}	}	PUNCT
ejpam-4005	333	29	⊂	⊂	PROPN
ejpam-4005	334	1	[	[	X
ejpam-4005	334	2	1,∞	1,∞	NUM
ejpam-4005	334	3	)	)	PUNCT
ejpam-4005	334	4	such	such	ADJ
ejpam-4005	334	5	that	that	SCONJ
ejpam-4005	334	6	∞∑	∞∑	NUM
ejpam-4005	334	7	n=1	n=1	PROPN
ejpam-4005	334	8	(	(	PUNCT
ejpam-4005	334	9	k(i	k(i	PROPN
ejpam-4005	334	10	)	)	PUNCT
ejpam-4005	334	11	n	n	PRON
ejpam-4005	334	12	−1	−1	NOUN
ejpam-4005	334	13	)	)	PUNCT
ejpam-4005	335	1	<	<	X
ejpam-4005	335	2	∞	∞	NUM
ejpam-4005	335	3	and	and	CCONJ
ejpam-4005	335	4	∞∑	∞∑	NUM
ejpam-4005	335	5	n=1	n=1	PROPN
ejpam-4005	335	6	(	(	PUNCT
ejpam-4005	335	7	l(i)n	l(i)n	PROPN
ejpam-4005	335	8	−1	−1	NOUN
ejpam-4005	335	9	)	)	PUNCT
ejpam-4005	336	1	<	<	X
ejpam-4005	336	2	∞	∞	NUM
ejpam-4005	336	3	for	for	ADP
ejpam-4005	336	4	i	i	PRON
ejpam-4005	336	5	=	=	NOUN
ejpam-4005	336	6	1	1	NUM
ejpam-4005	336	7	,	,	PUNCT
ejpam-4005	336	8	2	2	NUM
ejpam-4005	336	9	,	,	PUNCT
ejpam-4005	336	10	respectively	respectively	ADV
ejpam-4005	336	11	,	,	PUNCT
ejpam-4005	336	12	and	and	CCONJ
ejpam-4005	336	13	f	f	PROPN
ejpam-4005	337	1	6=	6=	PROPN
ejpam-4005	337	2	∅.	∅.	PROPN
ejpam-4005	337	3	suppose	suppose	VERB
ejpam-4005	337	4	that	that	SCONJ
ejpam-4005	337	5	{	{	PUNCT
ejpam-4005	337	6	ϑn	ϑn	NOUN
ejpam-4005	337	7	}	}	PUNCT
ejpam-4005	337	8	,	,	PUNCT
ejpam-4005	337	9	{	{	PUNCT
ejpam-4005	337	10	ζn	ζn	NOUN
ejpam-4005	337	11	}	}	PUNCT
ejpam-4005	337	12	are	be	AUX
ejpam-4005	337	13	real	real	ADJ
ejpam-4005	337	14	sequences	sequence	NOUN
ejpam-4005	337	15	in	in	ADP
ejpam-4005	337	16	[	[	X
ejpam-4005	337	17	ε	ε	PROPN
ejpam-4005	337	18	,	,	PUNCT
ejpam-4005	337	19	1	1	NUM
ejpam-4005	337	20	−	−	NOUN
ejpam-4005	337	21	ε	ε	PROPN
ejpam-4005	337	22	]	]	PUNCT
ejpam-4005	337	23	for	for	ADP
ejpam-4005	337	24	some	some	DET
ejpam-4005	337	25	ε	ε	PROPN
ejpam-4005	337	26	∈	∈	PROPN
ejpam-4005	337	27	(	(	PUNCT
ejpam-4005	337	28	0	0	NUM
ejpam-4005	337	29	,	,	PUNCT
ejpam-4005	337	30	1	1	NUM
ejpam-4005	337	31	)	)	PUNCT
ejpam-4005	337	32	and	and	CCONJ
ejpam-4005	337	33	si	si	INTJ
ejpam-4005	337	34	,	,	PUNCT
ejpam-4005	337	35	ti	ti	NOUN
ejpam-4005	337	36	for	for	ADP
ejpam-4005	337	37	all	all	DET
ejpam-4005	337	38	i	i	PRON
ejpam-4005	337	39	=	=	NOUN
ejpam-4005	337	40	1	1	NUM
ejpam-4005	337	41	,	,	PUNCT
ejpam-4005	337	42	2	2	NUM
ejpam-4005	337	43	satisfy	satisfy	VERB
ejpam-4005	337	44	the	the	DET
ejpam-4005	337	45	condition	condition	NOUN
ejpam-4005	337	46	(	(	PUNCT
ejpam-4005	337	47	ii	ii	NOUN
ejpam-4005	337	48	)	)	PUNCT
ejpam-4005	337	49	in	in	ADP
ejpam-4005	337	50	lemma	lemma	PROPN
ejpam-4005	337	51	4	4	NUM
ejpam-4005	337	52	.	.	PUNCT
ejpam-4005	338	1	if	if	SCONJ
ejpam-4005	338	2	there	there	PRON
ejpam-4005	338	3	is	be	VERB
ejpam-4005	338	4	a	a	DET
ejpam-4005	338	5	nondecreasing	nondecrease	VERB
ejpam-4005	338	6	function	function	NOUN
ejpam-4005	338	7	f	f	NOUN
ejpam-4005	338	8	:	:	PUNCT
ejpam-4005	339	1	[	[	X
ejpam-4005	339	2	0,∞	0,∞	NOUN
ejpam-4005	339	3	)	)	PUNCT
ejpam-4005	339	4	→	→	PUNCT
ejpam-4005	340	1	[	[	X
ejpam-4005	340	2	0,∞	0,∞	NOUN
ejpam-4005	340	3	)	)	PUNCT
ejpam-4005	340	4	with	with	ADP
ejpam-4005	340	5	f(0	f(0	NOUN
ejpam-4005	340	6	)	)	PUNCT
ejpam-4005	340	7	=	=	SYM
ejpam-4005	340	8	0	0	NUM
ejpam-4005	340	9	and	and	CCONJ
ejpam-4005	340	10	f(r	f(r	NOUN
ejpam-4005	340	11	)	)	PUNCT
ejpam-4005	340	12	>	>	X
ejpam-4005	340	13	0	0	PUNCT
ejpam-4005	340	14	for	for	ADP
ejpam-4005	340	15	all	all	DET
ejpam-4005	340	16	r	r	NOUN
ejpam-4005	340	17	∈	∈	PROPN
ejpam-4005	340	18	(	(	PUNCT
ejpam-4005	340	19	0,∞	0,∞	NOUN
ejpam-4005	340	20	)	)	PUNCT
ejpam-4005	340	21	such	such	ADJ
ejpam-4005	340	22	that	that	SCONJ
ejpam-4005	340	23	f(d(u	f(d(u	PROPN
ejpam-4005	340	24	,	,	PUNCT
ejpam-4005	340	25	f	f	NOUN
ejpam-4005	340	26	)	)	PUNCT
ejpam-4005	340	27	)	)	PUNCT
ejpam-4005	340	28	≤	≤	PUNCT
ejpam-4005	341	1	d(u	d(u	PROPN
ejpam-4005	341	2	,	,	PUNCT
ejpam-4005	341	3	s1u	s1u	NOUN
ejpam-4005	341	4	)	)	PUNCT
ejpam-4005	341	5	+	+	CCONJ
ejpam-4005	341	6	d(u	d(u	PROPN
ejpam-4005	341	7	,	,	PUNCT
ejpam-4005	341	8	s2u	s2u	NOUN
ejpam-4005	341	9	)	)	PUNCT
ejpam-4005	341	10	+	+	CCONJ
ejpam-4005	341	11	d(u	d(u	PROPN
ejpam-4005	341	12	,	,	PUNCT
ejpam-4005	341	13	t1u	t1u	NOUN
ejpam-4005	341	14	)	)	PUNCT
ejpam-4005	342	1	+	+	CCONJ
ejpam-4005	342	2	d(u	d(u	PROPN
ejpam-4005	342	3	,	,	PUNCT
ejpam-4005	342	4	t2u	t2u	NUM
ejpam-4005	342	5	)	)	PUNCT
ejpam-4005	342	6	for	for	ADP
ejpam-4005	342	7	all	all	DET
ejpam-4005	342	8	u	u	PROPN
ejpam-4005	342	9	∈	∈	PROPN
ejpam-4005	342	10	k	k	NOUN
ejpam-4005	342	11	,	,	PUNCT
ejpam-4005	342	12	where	where	SCONJ
ejpam-4005	342	13	d(u	d(u	PROPN
ejpam-4005	342	14	,	,	PUNCT
ejpam-4005	342	15	f	f	NOUN
ejpam-4005	342	16	)	)	PUNCT
ejpam-4005	342	17	=	=	SYM
ejpam-4005	342	18	inf{d(u	inf{d(u	PROPN
ejpam-4005	342	19	,	,	PUNCT
ejpam-4005	342	20	q	q	NOUN
ejpam-4005	342	21	)	)	PUNCT
ejpam-4005	342	22	:	:	PUNCT
ejpam-4005	342	23	q	q	PUNCT
ejpam-4005	342	24	∈	∈	NOUN
ejpam-4005	342	25	f	f	X
ejpam-4005	342	26	}	}	PUNCT
ejpam-4005	342	27	.	.	PUNCT
ejpam-4005	343	1	then	then	ADV
ejpam-4005	343	2	the	the	DET
ejpam-4005	343	3	sequence	sequence	NOUN
ejpam-4005	343	4	{	{	PUNCT
ejpam-4005	343	5	un	un	PROPN
ejpam-4005	343	6	}	}	PUNCT
ejpam-4005	343	7	defined	define	VERB
ejpam-4005	343	8	by	by	ADP
ejpam-4005	343	9	vn	vn	PROPN
ejpam-4005	343	10	=	=	PROPN
ejpam-4005	343	11	h(sn2	h(sn2	PROPN
ejpam-4005	343	12	un	un	PROPN
ejpam-4005	343	13	,	,	PUNCT
ejpam-4005	343	14	t	t	PROPN
ejpam-4005	343	15	n	n	PROPN
ejpam-4005	343	16	2	2	NUM
ejpam-4005	343	17	un	un	PROPN
ejpam-4005	343	18	,	,	PUNCT
ejpam-4005	343	19	ζn	ζn	NOUN
ejpam-4005	343	20	)	)	PUNCT
ejpam-4005	343	21	,	,	PUNCT
ejpam-4005	343	22	un+1	un+1	X
ejpam-4005	343	23	=	=	X
ejpam-4005	343	24	h(sn1	h(sn1	NOUN
ejpam-4005	343	25	vn	vn	X
ejpam-4005	343	26	,	,	PUNCT
ejpam-4005	343	27	t	t	PROPN
ejpam-4005	343	28	n	n	PROPN
ejpam-4005	343	29	1	1	NUM
ejpam-4005	343	30	vn	vn	NOUN
ejpam-4005	343	31	,	,	PUNCT
ejpam-4005	343	32	ϑn	ϑn	NOUN
ejpam-4005	343	33	)	)	PUNCT
ejpam-4005	343	34	converges	converge	VERB
ejpam-4005	343	35	strongly	strongly	ADV
ejpam-4005	343	36	to	to	ADP
ejpam-4005	343	37	a	a	DET
ejpam-4005	343	38	common	common	ADJ
ejpam-4005	343	39	fixed	fix	VERB
ejpam-4005	343	40	point	point	NOUN
ejpam-4005	343	41	of	of	ADP
ejpam-4005	343	42	s1,s2	s1,s2	PROPN
ejpam-4005	343	43	,	,	PUNCT
ejpam-4005	343	44	t1	t1	NOUN
ejpam-4005	343	45	and	and	CCONJ
ejpam-4005	343	46	t2	t2	NOUN
ejpam-4005	343	47	.	.	PUNCT
ejpam-4005	344	1	references	reference	NOUN
ejpam-4005	344	2	663	663	NUM
ejpam-4005	344	3	3	3	NUM
ejpam-4005	344	4	.	.	PUNCT
ejpam-4005	344	5	conclusions	conclusion	NOUN
ejpam-4005	344	6	author	author	NOUN
ejpam-4005	344	7	constructed	construct	VERB
ejpam-4005	344	8	a	a	DET
ejpam-4005	344	9	new	new	ADJ
ejpam-4005	344	10	mixed	mixed	ADJ
ejpam-4005	344	11	type	type	NOUN
ejpam-4005	344	12	iterative	iterative	NOUN
ejpam-4005	344	13	method	method	NOUN
ejpam-4005	344	14	to	to	PART
ejpam-4005	344	15	approximate	approximate	VERB
ejpam-4005	344	16	a	a	DET
ejpam-4005	344	17	common	common	ADJ
ejpam-4005	344	18	fixed	fix	VERB
ejpam-4005	344	19	point	point	NOUN
ejpam-4005	344	20	for	for	ADP
ejpam-4005	344	21	two	two	NUM
ejpam-4005	344	22	asymptotically	asymptotically	ADV
ejpam-4005	344	23	nonexpansive	nonexpansive	ADJ
ejpam-4005	344	24	self	self	NOUN
ejpam-4005	344	25	-	-	PUNCT
ejpam-4005	344	26	mappings	mapping	NOUN
ejpam-4005	344	27	and	and	CCONJ
ejpam-4005	344	28	two	two	NUM
ejpam-4005	344	29	asymptotically	asymptotically	ADV
ejpam-4005	344	30	nonexpansive	nonexpansive	ADJ
ejpam-4005	344	31	nonself	nonself	NOUN
ejpam-4005	344	32	-	-	PUNCT
ejpam-4005	344	33	mappings	mapping	NOUN
ejpam-4005	344	34	in	in	ADP
ejpam-4005	344	35	a	a	DET
ejpam-4005	344	36	uniformly	uniformly	ADV
ejpam-4005	344	37	convex	convex	ADJ
ejpam-4005	344	38	hyperbolic	hyperbolic	ADJ
ejpam-4005	344	39	space	space	NOUN
ejpam-4005	344	40	.	.	PUNCT
ejpam-4005	345	1	an	an	DET
ejpam-4005	345	2	asymptotically	asymptotically	ADV
ejpam-4005	345	3	nonexpansive	nonexpansive	ADJ
ejpam-4005	345	4	nonself	nonself	NOUN
ejpam-4005	345	5	-	-	PUNCT
ejpam-4005	345	6	mapping	mapping	NOUN
ejpam-4005	345	7	with	with	ADP
ejpam-4005	345	8	respect	respect	NOUN
ejpam-4005	345	9	to	to	ADP
ejpam-4005	345	10	a	a	DET
ejpam-4005	345	11	nonexpansive	nonexpansive	ADJ
ejpam-4005	345	12	retraction	retraction	NOUN
ejpam-4005	345	13	is	be	AUX
ejpam-4005	345	14	defined	define	VERB
ejpam-4005	345	15	in	in	ADP
ejpam-4005	345	16	definition	definition	NOUN
ejpam-4005	345	17	1	1	NUM
ejpam-4005	345	18	.	.	PUNCT
ejpam-4005	346	1	an	an	DET
ejpam-4005	346	2	illustrative	illustrative	ADJ
ejpam-4005	346	3	example	example	NOUN
ejpam-4005	346	4	is	be	AUX
ejpam-4005	346	5	also	also	ADV
ejpam-4005	346	6	provided	provide	VERB
ejpam-4005	346	7	as	as	ADP
ejpam-4005	346	8	example	example	NOUN
ejpam-4005	346	9	1	1	NUM
ejpam-4005	346	10	.	.	PUNCT
ejpam-4005	347	1	author	author	NOUN
ejpam-4005	347	2	proved	prove	VERB
ejpam-4005	347	3	strong	strong	ADJ
ejpam-4005	347	4	convergence	convergence	NOUN
ejpam-4005	347	5	result	result	NOUN
ejpam-4005	347	6	which	which	PRON
ejpam-4005	347	7	is	be	AUX
ejpam-4005	347	8	stronger	strong	ADJ
ejpam-4005	347	9	than	than	ADP
ejpam-4005	347	10	that	that	PRON
ejpam-4005	347	11	of	of	ADP
ejpam-4005	347	12	delta	delta	NOUN
ejpam-4005	347	13	and	and	CCONJ
ejpam-4005	347	14	weak	weak	ADJ
ejpam-4005	347	15	convergence	convergence	NOUN
ejpam-4005	347	16	results	result	NOUN
ejpam-4005	347	17	.	.	PUNCT
ejpam-4005	348	1	acknowledgements	acknowledgement	VERB
ejpam-4005	348	2	the	the	DET
ejpam-4005	348	3	author	author	NOUN
ejpam-4005	348	4	would	would	AUX
ejpam-4005	348	5	like	like	VERB
ejpam-4005	348	6	to	to	PART
ejpam-4005	348	7	thank	thank	VERB
ejpam-4005	348	8	the	the	DET
ejpam-4005	348	9	anonymous	anonymous	ADJ
ejpam-4005	348	10	referee	referee	NOUN
ejpam-4005	348	11	for	for	ADP
ejpam-4005	348	12	giving	give	VERB
ejpam-4005	348	13	many	many	ADJ
ejpam-4005	348	14	helpful	helpful	ADJ
ejpam-4005	348	15	suggestion	suggestion	NOUN
ejpam-4005	348	16	on	on	ADP
ejpam-4005	348	17	the	the	DET
ejpam-4005	348	18	revision	revision	NOUN
ejpam-4005	348	19	of	of	ADP
ejpam-4005	348	20	present	present	ADJ
ejpam-4005	348	21	paper	paper	NOUN
ejpam-4005	348	22	.	.	PUNCT
ejpam-4005	349	1	the	the	DET
ejpam-4005	349	2	author	author	NOUN
ejpam-4005	349	3	acknowledge	acknowledge	VERB
ejpam-4005	349	4	the	the	DET
ejpam-4005	349	5	financial	financial	ADJ
ejpam-4005	349	6	support	support	NOUN
ejpam-4005	349	7	provided	provide	VERB
ejpam-4005	349	8	by	by	ADP
ejpam-4005	349	9	university	university	NOUN
ejpam-4005	349	10	of	of	ADP
ejpam-4005	349	11	phayao	phayao	NOUN
ejpam-4005	349	12	,	,	PUNCT
ejpam-4005	349	13	phayao	phayao	NOUN
ejpam-4005	349	14	,	,	PUNCT
ejpam-4005	349	15	thailand	thailand	PROPN
ejpam-4005	349	16	(	(	PUNCT
ejpam-4005	349	17	grant	grant	VERB
ejpam-4005	349	18	no	no	DET
ejpam-4005	349	19	ff64	ff64	PROPN
ejpam-4005	349	20	-	-	PUNCT
ejpam-4005	349	21	rib001	rib001	NOUN
ejpam-4005	349	22	)	)	PUNCT
ejpam-4005	349	23	.	.	PUNCT
ejpam-4005	350	1	references	reference	NOUN
ejpam-4005	350	2	[	[	X
ejpam-4005	350	3	1	1	NUM
ejpam-4005	350	4	]	]	PUNCT
ejpam-4005	350	5	s.	s.	PROPN
ejpam-4005	350	6	aggarwal	aggarwal	PROPN
ejpam-4005	350	7	,	,	PUNCT
ejpam-4005	350	8	s.h	s.h	PROPN
ejpam-4005	350	9	.	.	PROPN
ejpam-4005	350	10	khan	khan	PROPN
ejpam-4005	350	11	,	,	PUNCT
ejpam-4005	350	12	and	and	CCONJ
ejpam-4005	350	13	i.	i.	PROPN
ejpam-4005	350	14	uddin	uddin	PROPN
ejpam-4005	350	15	.	.	PUNCT
ejpam-4005	351	1	semi	semi	ADJ
ejpam-4005	351	2	-	-	ADJ
ejpam-4005	351	3	implicit	implicit	ADJ
ejpam-4005	351	4	midpoint	midpoint	NOUN
ejpam-4005	351	5	rule	rule	NOUN
ejpam-4005	351	6	for	for	ADP
ejpam-4005	351	7	convergence	convergence	NOUN
ejpam-4005	351	8	in	in	ADP
ejpam-4005	351	9	hyperbolic	hyperbolic	ADJ
ejpam-4005	351	10	metric	metric	ADJ
ejpam-4005	351	11	space	space	NOUN
ejpam-4005	351	12	.	.	PUNCT
ejpam-4005	352	1	mathematics	mathematic	NOUN
ejpam-4005	352	2	in	in	ADP
ejpam-4005	352	3	engineering	engineering	NOUN
ejpam-4005	352	4	,	,	PUNCT
ejpam-4005	352	5	science	science	NOUN
ejpam-4005	352	6	and	and	CCONJ
ejpam-4005	352	7	aerospace	aerospace	NOUN
ejpam-4005	352	8	,	,	PUNCT
ejpam-4005	352	9	12:413–420	12:413–420	NUM
ejpam-4005	352	10	,	,	PUNCT
ejpam-4005	352	11	2021	2021	NUM
ejpam-4005	352	12	.	.	PUNCT
ejpam-4005	353	1	[	[	X
ejpam-4005	353	2	2	2	X
ejpam-4005	353	3	]	]	PUNCT
ejpam-4005	353	4	s.	s.	PROPN
ejpam-4005	353	5	aggarwal	aggarwal	PROPN
ejpam-4005	353	6	and	and	CCONJ
ejpam-4005	353	7	i.	i.	PROPN
ejpam-4005	353	8	uddin	uddin	PROPN
ejpam-4005	353	9	.	.	PUNCT
ejpam-4005	354	1	convergence	convergence	NOUN
ejpam-4005	354	2	and	and	CCONJ
ejpam-4005	354	3	stability	stability	NOUN
ejpam-4005	354	4	of	of	ADP
ejpam-4005	354	5	fibonacci	fibonacci	NOUN
ejpam-4005	354	6	-	-	PUNCT
ejpam-4005	354	7	mann	mann	PROPN
ejpam-4005	354	8	iteration	iteration	NOUN
ejpam-4005	354	9	for	for	ADP
ejpam-4005	354	10	a	a	DET
ejpam-4005	354	11	monotone	monotone	ADJ
ejpam-4005	354	12	non	non	ADJ
ejpam-4005	354	13	-	-	ADJ
ejpam-4005	354	14	lipschitzian	lipschitzian	ADJ
ejpam-4005	354	15	mapping	mapping	NOUN
ejpam-4005	354	16	.	.	PUNCT
ejpam-4005	355	1	demonstr	demonstr	PROPN
ejpam-4005	355	2	.	.	PUNCT
ejpam-4005	356	1	math	math	NOUN
ejpam-4005	356	2	.	.	PUNCT
ejpam-4005	356	3	,	,	PUNCT
ejpam-4005	357	1	52:388–396	52:388–396	NUM
ejpam-4005	357	2	,	,	PUNCT
ejpam-4005	357	3	2019	2019	NUM
ejpam-4005	357	4	.	.	PUNCT
ejpam-4005	358	1	[	[	X
ejpam-4005	358	2	3	3	X
ejpam-4005	358	3	]	]	X
ejpam-4005	358	4	s.	s.	PROPN
ejpam-4005	358	5	aggarwal	aggarwal	PROPN
ejpam-4005	358	6	,	,	PUNCT
ejpam-4005	358	7	i.	i.	PROPN
ejpam-4005	358	8	uddin	uddin	PROPN
ejpam-4005	358	9	,	,	PUNCT
ejpam-4005	358	10	and	and	CCONJ
ejpam-4005	358	11	j.j	j.j	PROPN
ejpam-4005	358	12	.	.	PROPN
ejpam-4005	358	13	nieto	nieto	PROPN
ejpam-4005	358	14	.	.	PUNCT
ejpam-4005	359	1	a	a	DET
ejpam-4005	359	2	fixed	fix	VERB
ejpam-4005	359	3	-	-	PUNCT
ejpam-4005	359	4	point	point	NOUN
ejpam-4005	359	5	theorem	theorem	NOUN
ejpam-4005	359	6	for	for	ADP
ejpam-4005	359	7	monotone	monotone	NOUN
ejpam-4005	359	8	nearly	nearly	ADV
ejpam-4005	359	9	asymptotically	asymptotically	ADV
ejpam-4005	359	10	nonexpansive	nonexpansive	ADJ
ejpam-4005	359	11	mappings	mapping	NOUN
ejpam-4005	359	12	.	.	PUNCT
ejpam-4005	360	1	j.	j.	PROPN
ejpam-4005	360	2	fixed	fix	VERB
ejpam-4005	360	3	point	point	PROPN
ejpam-4005	360	4	theory	theory	NOUN
ejpam-4005	360	5	appl	appl	PROPN
ejpam-4005	360	6	.	.	PROPN
ejpam-4005	360	7	,	,	PUNCT
ejpam-4005	360	8	21:91	21:91	NUM
ejpam-4005	360	9	,	,	PUNCT
ejpam-4005	360	10	2019	2019	NUM
ejpam-4005	360	11	.	.	PUNCT
ejpam-4005	361	1	[	[	X
ejpam-4005	361	2	4	4	NUM
ejpam-4005	361	3	]	]	X
ejpam-4005	361	4	r.e	r.e	PROPN
ejpam-4005	361	5	.	.	PROPN
ejpam-4005	361	6	bruck	bruck	PROPN
ejpam-4005	361	7	,	,	PUNCT
ejpam-4005	361	8	t.	t.	PROPN
ejpam-4005	361	9	kuczumow	kuczumow	PROPN
ejpam-4005	361	10	,	,	PUNCT
ejpam-4005	361	11	and	and	CCONJ
ejpam-4005	361	12	s.	s.	PROPN
ejpam-4005	361	13	reich	reich	PROPN
ejpam-4005	361	14	.	.	PUNCT
ejpam-4005	362	1	convergence	convergence	NOUN
ejpam-4005	362	2	of	of	ADP
ejpam-4005	362	3	iterates	iterate	NOUN
ejpam-4005	362	4	of	of	ADP
ejpam-4005	362	5	asymptotically	asymptotically	ADV
ejpam-4005	362	6	nonexpansive	nonexpansive	ADJ
ejpam-4005	362	7	mappings	mapping	NOUN
ejpam-4005	362	8	in	in	ADP
ejpam-4005	362	9	banach	banach	NOUN
ejpam-4005	362	10	spaces	space	NOUN
ejpam-4005	362	11	with	with	ADP
ejpam-4005	362	12	the	the	DET
ejpam-4005	362	13	uniform	uniform	ADJ
ejpam-4005	362	14	opial	opial	ADJ
ejpam-4005	362	15	property	property	NOUN
ejpam-4005	362	16	.	.	PUNCT
ejpam-4005	363	1	colloquium	colloquium	NOUN
ejpam-4005	363	2	math	math	NOUN
ejpam-4005	363	3	.	.	PUNCT
ejpam-4005	363	4	,	,	PUNCT
ejpam-4005	363	5	65:169–179	65:169–179	PROPN
ejpam-4005	363	6	,	,	PUNCT
ejpam-4005	363	7	1993	1993	NUM
ejpam-4005	363	8	.	.	PUNCT
ejpam-4005	364	1	[	[	X
ejpam-4005	364	2	5	5	NUM
ejpam-4005	364	3	]	]	X
ejpam-4005	364	4	c.e	c.e	PROPN
ejpam-4005	364	5	.	.	PROPN
ejpam-4005	364	6	chidume	chidume	PROPN
ejpam-4005	364	7	,	,	PUNCT
ejpam-4005	364	8	e.u	e.u	PROPN
ejpam-4005	364	9	.	.	PROPN
ejpam-4005	364	10	ofoedu	ofoedu	PROPN
ejpam-4005	364	11	,	,	PUNCT
ejpam-4005	364	12	and	and	CCONJ
ejpam-4005	364	13	h.	h.	PROPN
ejpam-4005	364	14	zegeye	zegeye	PROPN
ejpam-4005	364	15	.	.	PUNCT
ejpam-4005	365	1	strong	strong	ADJ
ejpam-4005	365	2	and	and	CCONJ
ejpam-4005	365	3	weak	weak	ADJ
ejpam-4005	365	4	convergence	convergence	NOUN
ejpam-4005	365	5	theorems	theorem	NOUN
ejpam-4005	365	6	for	for	ADP
ejpam-4005	365	7	asymptotically	asymptotically	ADV
ejpam-4005	365	8	nonexpansive	nonexpansive	ADJ
ejpam-4005	365	9	mappings	mapping	NOUN
ejpam-4005	365	10	.	.	PUNCT
ejpam-4005	366	1	j.	j.	PROPN
ejpam-4005	366	2	math	math	PROPN
ejpam-4005	366	3	.	.	PUNCT
ejpam-4005	367	1	anal	anal	PROPN
ejpam-4005	367	2	.	.	PUNCT
ejpam-4005	367	3	appl	appl	PROPN
ejpam-4005	367	4	.	.	PROPN
ejpam-4005	367	5	,	,	PUNCT
ejpam-4005	367	6	280:364–374	280:364–374	NUM
ejpam-4005	367	7	,	,	PUNCT
ejpam-4005	367	8	2003	2003	NUM
ejpam-4005	367	9	.	.	PUNCT
ejpam-4005	368	1	[	[	X
ejpam-4005	368	2	6	6	NUM
ejpam-4005	368	3	]	]	PUNCT
ejpam-4005	368	4	k.	k.	PROPN
ejpam-4005	368	5	goebel	goebel	PROPN
ejpam-4005	368	6	and	and	CCONJ
ejpam-4005	368	7	w.a	w.a	PROPN
ejpam-4005	368	8	.	.	PROPN
ejpam-4005	368	9	kirk	kirk	PROPN
ejpam-4005	368	10	.	.	PUNCT
ejpam-4005	369	1	a	a	DET
ejpam-4005	369	2	fixed	fix	VERB
ejpam-4005	369	3	point	point	NOUN
ejpam-4005	369	4	theorem	theorem	NOUN
ejpam-4005	369	5	for	for	ADP
ejpam-4005	369	6	asymptotically	asymptotically	ADV
ejpam-4005	369	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	369	8	mappings	mapping	NOUN
ejpam-4005	369	9	.	.	PUNCT
ejpam-4005	370	1	proc	proc	NOUN
ejpam-4005	370	2	.	.	PUNCT
ejpam-4005	371	1	am	be	AUX
ejpam-4005	371	2	.	.	PUNCT
ejpam-4005	372	1	math	math	NOUN
ejpam-4005	372	2	.	.	PUNCT
ejpam-4005	373	1	soc	soc	PROPN
ejpam-4005	373	2	.	.	PUNCT
ejpam-4005	373	3	,	,	PUNCT
ejpam-4005	373	4	35:171–174	35:171–174	NUM
ejpam-4005	373	5	,	,	PUNCT
ejpam-4005	373	6	1972	1972	NUM
ejpam-4005	373	7	.	.	PUNCT
ejpam-4005	374	1	[	[	X
ejpam-4005	374	2	7	7	X
ejpam-4005	374	3	]	]	PUNCT
ejpam-4005	374	4	k.	k.	PROPN
ejpam-4005	374	5	goebel	goebel	PROPN
ejpam-4005	374	6	and	and	CCONJ
ejpam-4005	374	7	w.a	w.a	PROPN
ejpam-4005	374	8	.	.	PROPN
ejpam-4005	374	9	kirk	kirk	PROPN
ejpam-4005	374	10	.	.	PUNCT
ejpam-4005	375	1	iteration	iteration	NOUN
ejpam-4005	375	2	processes	process	NOUN
ejpam-4005	375	3	for	for	ADP
ejpam-4005	375	4	nonexpansive	nonexpansive	ADJ
ejpam-4005	375	5	mappings	mapping	NOUN
ejpam-4005	375	6	.	.	PUNCT
ejpam-4005	376	1	in	in	ADP
ejpam-4005	376	2	s.p	s.p	PROPN
ejpam-4005	376	3	.	.	PROPN
ejpam-4005	376	4	singh	singh	PROPN
ejpam-4005	376	5	,	,	PUNCT
ejpam-4005	376	6	s.	s.	PROPN
ejpam-4005	376	7	thomeier	thomeier	PROPN
ejpam-4005	376	8	,	,	PUNCT
ejpam-4005	376	9	and	and	CCONJ
ejpam-4005	376	10	b.	b.	PROPN
ejpam-4005	376	11	watson	watson	PROPN
ejpam-4005	376	12	,	,	PUNCT
ejpam-4005	376	13	editors	editor	NOUN
ejpam-4005	376	14	,	,	PUNCT
ejpam-4005	376	15	topological	topological	ADJ
ejpam-4005	376	16	methods	method	NOUN
ejpam-4005	376	17	in	in	ADP
ejpam-4005	376	18	nonlinear	nonlinear	ADJ
ejpam-4005	376	19	functional	functional	ADJ
ejpam-4005	376	20	analysis	analysis	NOUN
ejpam-4005	376	21	.	.	PUNCT
ejpam-4005	377	1	contemp	contemp	NOUN
ejpam-4005	377	2	.	.	PUNCT
ejpam-4005	378	1	math	math	NOUN
ejpam-4005	378	2	.	.	PUNCT
ejpam-4005	379	1	,	,	PUNCT
ejpam-4005	379	2	volume	volume	NOUN
ejpam-4005	379	3	21	21	NUM
ejpam-4005	379	4	,	,	PUNCT
ejpam-4005	379	5	pp	pp	ADJ
ejpam-4005	379	6	.	.	PUNCT
ejpam-4005	380	1	115	115	NUM
ejpam-4005	380	2	-	-	SYM
ejpam-4005	380	3	123	123	NUM
ejpam-4005	380	4	.	.	PUNCT
ejpam-4005	381	1	am	be	AUX
ejpam-4005	381	2	.	.	PUNCT
ejpam-4005	382	1	math	math	NOUN
ejpam-4005	382	2	.	.	PUNCT
ejpam-4005	383	1	soc	soc	PROPN
ejpam-4005	383	2	.	.	PUNCT
ejpam-4005	383	3	,	,	PUNCT
ejpam-4005	383	4	providence	providence	NOUN
ejpam-4005	383	5	,	,	PUNCT
ejpam-4005	383	6	1983	1983	NUM
ejpam-4005	383	7	.	.	PUNCT
ejpam-4005	384	1	[	[	X
ejpam-4005	384	2	8	8	NUM
ejpam-4005	384	3	]	]	PUNCT
ejpam-4005	384	4	k.	k.	PROPN
ejpam-4005	384	5	goebel	goebel	PROPN
ejpam-4005	384	6	and	and	CCONJ
ejpam-4005	384	7	s.	s.	PROPN
ejpam-4005	384	8	reich	reich	PROPN
ejpam-4005	384	9	.	.	PROPN
ejpam-4005	385	1	uniform	uniform	PROPN
ejpam-4005	385	2	convexity	convexity	NOUN
ejpam-4005	385	3	,	,	PUNCT
ejpam-4005	385	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	385	5	geometry	geometry	NOUN
ejpam-4005	385	6	,	,	PUNCT
ejpam-4005	385	7	and	and	CCONJ
ejpam-4005	385	8	nonexpansive	nonexpansive	ADJ
ejpam-4005	385	9	mappings	mapping	NOUN
ejpam-4005	385	10	.	.	PUNCT
ejpam-4005	386	1	marcel	marcel	PROPN
ejpam-4005	386	2	dekker	dekker	PROPN
ejpam-4005	386	3	,	,	PUNCT
ejpam-4005	386	4	new	new	PROPN
ejpam-4005	386	5	york	york	PROPN
ejpam-4005	386	6	,	,	PUNCT
ejpam-4005	386	7	1984	1984	NUM
ejpam-4005	386	8	.	.	PUNCT
ejpam-4005	387	1	references	reference	NOUN
ejpam-4005	387	2	664	664	NUM
ejpam-4005	387	3	[	[	X
ejpam-4005	387	4	9	9	NUM
ejpam-4005	387	5	]	]	PUNCT
ejpam-4005	387	6	w.	w.	PROPN
ejpam-4005	387	7	guo	guo	PROPN
ejpam-4005	387	8	,	,	PUNCT
ejpam-4005	387	9	y.j	y.j	PROPN
ejpam-4005	387	10	.	.	PUNCT
ejpam-4005	387	11	cho	cho	PROPN
ejpam-4005	387	12	,	,	PUNCT
ejpam-4005	387	13	and	and	CCONJ
ejpam-4005	387	14	w.	w.	PROPN
ejpam-4005	387	15	guo	guo	PROPN
ejpam-4005	387	16	.	.	PUNCT
ejpam-4005	388	1	convergence	convergence	NOUN
ejpam-4005	388	2	theorems	theorem	NOUN
ejpam-4005	388	3	for	for	ADP
ejpam-4005	388	4	mixed	mixed	ADJ
ejpam-4005	388	5	type	type	NOUN
ejpam-4005	388	6	asymptotically	asymptotically	ADV
ejpam-4005	388	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	388	8	mappings	mapping	NOUN
ejpam-4005	388	9	.	.	PUNCT
ejpam-4005	389	1	fixed	fix	VERB
ejpam-4005	389	2	point	point	NOUN
ejpam-4005	389	3	theory	theory	NOUN
ejpam-4005	389	4	appl	appl	PROPN
ejpam-4005	389	5	.	.	PROPN
ejpam-4005	389	6	,	,	PUNCT
ejpam-4005	389	7	2012:224	2012:224	NUM
ejpam-4005	389	8	,	,	PUNCT
ejpam-4005	389	9	2012	2012	NUM
ejpam-4005	389	10	.	.	PUNCT
ejpam-4005	390	1	[	[	X
ejpam-4005	390	2	10	10	NUM
ejpam-4005	390	3	]	]	X
ejpam-4005	390	4	s.	s.	PROPN
ejpam-4005	390	5	ishikawa	ishikawa	PROPN
ejpam-4005	390	6	.	.	PUNCT
ejpam-4005	390	7	fixed	fix	VERB
ejpam-4005	390	8	points	point	NOUN
ejpam-4005	390	9	by	by	ADP
ejpam-4005	390	10	a	a	DET
ejpam-4005	390	11	new	new	ADJ
ejpam-4005	390	12	iteration	iteration	NOUN
ejpam-4005	390	13	method	method	NOUN
ejpam-4005	390	14	.	.	PUNCT
ejpam-4005	391	1	proc	proc	NOUN
ejpam-4005	391	2	.	.	PUNCT
ejpam-4005	392	1	am	be	AUX
ejpam-4005	392	2	.	.	PUNCT
ejpam-4005	393	1	math	math	NOUN
ejpam-4005	393	2	.	.	PUNCT
ejpam-4005	394	1	soc	soc	PROPN
ejpam-4005	394	2	.	.	PUNCT
ejpam-4005	394	3	,	,	PUNCT
ejpam-4005	394	4	44:147	44:147	NOUN
ejpam-4005	394	5	–	–	PUNCT
ejpam-4005	394	6	150	150	NUM
ejpam-4005	394	7	,	,	PUNCT
ejpam-4005	394	8	1974	1974	NUM
ejpam-4005	394	9	.	.	PUNCT
ejpam-4005	395	1	[	[	X
ejpam-4005	395	2	11	11	NUM
ejpam-4005	395	3	]	]	X
ejpam-4005	395	4	j.s	j.s	PROPN
ejpam-4005	395	5	.	.	PROPN
ejpam-4005	395	6	jung	jung	PROPN
ejpam-4005	395	7	and	and	CCONJ
ejpam-4005	395	8	s.s	s.s	PROPN
ejpam-4005	395	9	.	.	PROPN
ejpam-4005	395	10	kim	kim	PROPN
ejpam-4005	395	11	.	.	PUNCT
ejpam-4005	396	1	strong	strong	ADJ
ejpam-4005	396	2	convergence	convergence	NOUN
ejpam-4005	396	3	theorems	theorem	NOUN
ejpam-4005	396	4	for	for	ADP
ejpam-4005	396	5	nonexpansive	nonexpansive	PROPN
ejpam-4005	396	6	nonself	nonself	PROPN
ejpam-4005	396	7	mappings	mapping	NOUN
ejpam-4005	396	8	in	in	ADP
ejpam-4005	396	9	banach	banach	NOUN
ejpam-4005	396	10	spaces	space	NOUN
ejpam-4005	396	11	.	.	PUNCT
ejpam-4005	397	1	nonlinear	nonlinear	ADJ
ejpam-4005	397	2	anal	anal	PROPN
ejpam-4005	397	3	.	.	PUNCT
ejpam-4005	397	4	,	,	PUNCT
ejpam-4005	397	5	33:321–329	33:321–329	PROPN
ejpam-4005	397	6	,	,	PUNCT
ejpam-4005	397	7	1998	1998	NUM
ejpam-4005	397	8	.	.	PUNCT
ejpam-4005	398	1	[	[	X
ejpam-4005	398	2	12	12	NUM
ejpam-4005	398	3	]	]	X
ejpam-4005	398	4	a.r	a.r	PROPN
ejpam-4005	398	5	.	.	PROPN
ejpam-4005	398	6	khan	khan	PROPN
ejpam-4005	398	7	,	,	PUNCT
ejpam-4005	398	8	h.	h.	PROPN
ejpam-4005	398	9	fukhar	fukhar	PROPN
ejpam-4005	398	10	-	-	PUNCT
ejpam-4005	398	11	ud	ud	ADP
ejpam-4005	398	12	-	-	PUNCT
ejpam-4005	398	13	din	din	NOUN
ejpam-4005	398	14	,	,	PUNCT
ejpam-4005	398	15	and	and	CCONJ
ejpam-4005	398	16	m.a.a	m.a.a	PROPN
ejpam-4005	398	17	.	.	PUNCT
ejpam-4005	399	1	khan	khan	PROPN
ejpam-4005	399	2	.	.	PUNCT
ejpam-4005	400	1	an	an	DET
ejpam-4005	400	2	implicit	implicit	ADJ
ejpam-4005	400	3	algorithm	algorithm	NOUN
ejpam-4005	400	4	for	for	ADP
ejpam-4005	400	5	two	two	NUM
ejpam-4005	400	6	finite	finite	ADJ
ejpam-4005	400	7	families	family	NOUN
ejpam-4005	400	8	of	of	ADP
ejpam-4005	400	9	nonexpansive	nonexpansive	ADJ
ejpam-4005	400	10	maps	map	NOUN
ejpam-4005	400	11	in	in	ADP
ejpam-4005	400	12	hyperbolic	hyperbolic	ADJ
ejpam-4005	400	13	spaces	space	NOUN
ejpam-4005	400	14	.	.	PUNCT
ejpam-4005	401	1	fixed	fix	VERB
ejpam-4005	401	2	point	point	NOUN
ejpam-4005	401	3	theory	theory	NOUN
ejpam-4005	401	4	appl	appl	PROPN
ejpam-4005	401	5	.	.	PROPN
ejpam-4005	401	6	,	,	PUNCT
ejpam-4005	401	7	54	54	NUM
ejpam-4005	401	8	:	:	PUNCT
ejpam-4005	401	9	doi:10.1186/1687–1812–2012–54	doi:10.1186/1687–1812–2012–54	PROPN
ejpam-4005	401	10	,	,	PUNCT
ejpam-4005	401	11	2012	2012	NUM
ejpam-4005	401	12	.	.	PUNCT
ejpam-4005	402	1	[	[	X
ejpam-4005	402	2	13	13	NUM
ejpam-4005	402	3	]	]	X
ejpam-4005	402	4	u.	u.	NOUN
ejpam-4005	402	5	kohlenbach	kohlenbach	PROPN
ejpam-4005	402	6	.	.	PUNCT
ejpam-4005	403	1	some	some	DET
ejpam-4005	403	2	logical	logical	ADJ
ejpam-4005	403	3	metatheorems	metatheorem	NOUN
ejpam-4005	403	4	with	with	ADP
ejpam-4005	403	5	applications	application	NOUN
ejpam-4005	403	6	in	in	ADP
ejpam-4005	403	7	functional	functional	ADJ
ejpam-4005	403	8	analysis	analysis	NOUN
ejpam-4005	403	9	.	.	PUNCT
ejpam-4005	404	1	trans	trans	PROPN
ejpam-4005	404	2	.	.	PUNCT
ejpam-4005	405	1	amer	amer	PROPN
ejpam-4005	405	2	.	.	PUNCT
ejpam-4005	405	3	math	math	PROPN
ejpam-4005	405	4	.	.	PUNCT
ejpam-4005	406	1	soc	soc	PROPN
ejpam-4005	406	2	.	.	PUNCT
ejpam-4005	406	3	,	,	PUNCT
ejpam-4005	406	4	357(1):89–128	357(1):89–128	PROPN
ejpam-4005	406	5	,	,	PUNCT
ejpam-4005	406	6	2004	2004	NUM
ejpam-4005	406	7	.	.	PUNCT
ejpam-4005	407	1	[	[	X
ejpam-4005	407	2	14	14	NUM
ejpam-4005	407	3	]	]	X
ejpam-4005	407	4	e.	e.	PROPN
ejpam-4005	407	5	kopecká	kopecká	PROPN
ejpam-4005	407	6	and	and	CCONJ
ejpam-4005	407	7	s.	s.	PROPN
ejpam-4005	407	8	reich	reich	PROPN
ejpam-4005	407	9	.	.	PROPN
ejpam-4005	408	1	nonexpansive	nonexpansive	PROPN
ejpam-4005	408	2	retracts	retract	VERB
ejpam-4005	408	3	in	in	ADP
ejpam-4005	408	4	banach	banach	NOUN
ejpam-4005	408	5	spaces	space	NOUN
ejpam-4005	408	6	.	.	PUNCT
ejpam-4005	409	1	banach	banach	NOUN
ejpam-4005	409	2	center	center	NOUN
ejpam-4005	409	3	publ	publ	NOUN
ejpam-4005	409	4	.	.	PUNCT
ejpam-4005	409	5	,	,	PUNCT
ejpam-4005	409	6	77:161–174	77:161–174	NUM
ejpam-4005	409	7	,	,	PUNCT
ejpam-4005	409	8	2007	2007	NUM
ejpam-4005	409	9	.	.	PUNCT
ejpam-4005	410	1	[	[	X
ejpam-4005	410	2	15	15	NUM
ejpam-4005	410	3	]	]	X
ejpam-4005	410	4	l.	l.	PROPN
ejpam-4005	410	5	leustean	leustean	PROPN
ejpam-4005	410	6	.	.	PUNCT
ejpam-4005	411	1	a	a	DET
ejpam-4005	411	2	quadratic	quadratic	ADJ
ejpam-4005	411	3	rate	rate	NOUN
ejpam-4005	411	4	of	of	ADP
ejpam-4005	411	5	asymptotic	asymptotic	ADJ
ejpam-4005	411	6	regularity	regularity	NOUN
ejpam-4005	411	7	for	for	ADP
ejpam-4005	411	8	cat(0)-spaces	cat(0)-space	NOUN
ejpam-4005	411	9	.	.	PUNCT
ejpam-4005	412	1	j.	j.	PROPN
ejpam-4005	412	2	math	math	PROPN
ejpam-4005	412	3	.	.	PUNCT
ejpam-4005	413	1	anal	anal	PROPN
ejpam-4005	413	2	.	.	PUNCT
ejpam-4005	414	1	appl	appl	PROPN
ejpam-4005	414	2	.	.	PROPN
ejpam-4005	414	3	,	,	PUNCT
ejpam-4005	414	4	325:386–399	325:386–399	PROPN
ejpam-4005	414	5	,	,	PUNCT
ejpam-4005	414	6	2007	2007	NUM
ejpam-4005	414	7	.	.	PUNCT
ejpam-4005	415	1	[	[	X
ejpam-4005	415	2	16	16	NUM
ejpam-4005	415	3	]	]	PUNCT
ejpam-4005	415	4	z.	z.	PROPN
ejpam-4005	415	5	liu	liu	PROPN
ejpam-4005	415	6	,	,	PUNCT
ejpam-4005	415	7	c.	c.	PROPN
ejpam-4005	415	8	feng	feng	PROPN
ejpam-4005	415	9	,	,	PUNCT
ejpam-4005	415	10	j.s	j.s	PROPN
ejpam-4005	415	11	.	.	PROPN
ejpam-4005	415	12	ume	ume	PROPN
ejpam-4005	415	13	,	,	PUNCT
ejpam-4005	415	14	and	and	CCONJ
ejpam-4005	415	15	s.m	s.m	PROPN
ejpam-4005	415	16	.	.	PROPN
ejpam-4005	415	17	kang	kang	PROPN
ejpam-4005	415	18	.	.	PUNCT
ejpam-4005	416	1	weak	weak	ADJ
ejpam-4005	416	2	and	and	CCONJ
ejpam-4005	416	3	strong	strong	ADJ
ejpam-4005	416	4	convergence	convergence	NOUN
ejpam-4005	416	5	for	for	ADP
ejpam-4005	416	6	common	common	ADJ
ejpam-4005	416	7	fixed	fix	VERB
ejpam-4005	416	8	points	point	NOUN
ejpam-4005	416	9	of	of	ADP
ejpam-4005	416	10	a	a	DET
ejpam-4005	416	11	pair	pair	NOUN
ejpam-4005	416	12	of	of	ADP
ejpam-4005	416	13	nonexpansive	nonexpansive	ADJ
ejpam-4005	416	14	and	and	CCONJ
ejpam-4005	416	15	asymptotically	asymptotically	ADV
ejpam-4005	416	16	nonexpansive	nonexpansive	ADJ
ejpam-4005	416	17	mappings	mapping	NOUN
ejpam-4005	416	18	.	.	PUNCT
ejpam-4005	417	1	taiwan	taiwan	PROPN
ejpam-4005	417	2	.	.	PUNCT
ejpam-4005	418	1	j.	j.	PROPN
ejpam-4005	418	2	math	math	PROPN
ejpam-4005	418	3	.	.	PROPN
ejpam-4005	418	4	,	,	PUNCT
ejpam-4005	418	5	11:27–42	11:27–42	NUM
ejpam-4005	418	6	,	,	PUNCT
ejpam-4005	418	7	2007	2007	NUM
ejpam-4005	418	8	.	.	PUNCT
ejpam-4005	419	1	[	[	X
ejpam-4005	419	2	17	17	NUM
ejpam-4005	419	3	]	]	SYM
ejpam-4005	419	4	s.y	s.y	PROPN
ejpam-4005	419	5	.	.	PROPN
ejpam-4005	419	6	matsushita	matsushita	PROPN
ejpam-4005	419	7	and	and	CCONJ
ejpam-4005	419	8	d.	d.	PROPN
ejpam-4005	419	9	kuroiwa	kuroiwa	PROPN
ejpam-4005	419	10	.	.	PUNCT
ejpam-4005	420	1	strong	strong	ADJ
ejpam-4005	420	2	convergence	convergence	NOUN
ejpam-4005	420	3	of	of	ADP
ejpam-4005	420	4	averaging	average	VERB
ejpam-4005	420	5	iteration	iteration	NOUN
ejpam-4005	420	6	of	of	ADP
ejpam-4005	420	7	nonexpansive	nonexpansive	PROPN
ejpam-4005	420	8	nonself	nonself	PROPN
ejpam-4005	420	9	-	-	PUNCT
ejpam-4005	420	10	mappings	mapping	NOUN
ejpam-4005	420	11	.	.	PUNCT
ejpam-4005	421	1	j.	j.	PROPN
ejpam-4005	421	2	math	math	PROPN
ejpam-4005	421	3	.	.	PUNCT
ejpam-4005	422	1	anal	anal	PROPN
ejpam-4005	422	2	.	.	PUNCT
ejpam-4005	422	3	appl	appl	PROPN
ejpam-4005	422	4	.	.	PROPN
ejpam-4005	422	5	,	,	PUNCT
ejpam-4005	422	6	294:206–214	294:206–214	NUM
ejpam-4005	422	7	,	,	PUNCT
ejpam-4005	422	8	2004	2004	NUM
ejpam-4005	422	9	.	.	PUNCT
ejpam-4005	423	1	[	[	X
ejpam-4005	423	2	18	18	NUM
ejpam-4005	423	3	]	]	X
ejpam-4005	423	4	m.o	m.o	PROPN
ejpam-4005	423	5	.	.	PROPN
ejpam-4005	423	6	osilike	osilike	PROPN
ejpam-4005	423	7	and	and	CCONJ
ejpam-4005	423	8	a.	a.	NOUN
ejpam-4005	423	9	udomene	udomene	PROPN
ejpam-4005	423	10	.	.	PUNCT
ejpam-4005	424	1	weak	weak	ADJ
ejpam-4005	424	2	and	and	CCONJ
ejpam-4005	424	3	strong	strong	ADJ
ejpam-4005	424	4	convergence	convergence	NOUN
ejpam-4005	424	5	theorems	theorem	NOUN
ejpam-4005	424	6	for	for	ADP
ejpam-4005	424	7	fixed	fix	VERB
ejpam-4005	424	8	points	point	NOUN
ejpam-4005	424	9	of	of	ADP
ejpam-4005	424	10	asymptotically	asymptotically	ADV
ejpam-4005	424	11	nonexpansive	nonexpansive	ADJ
ejpam-4005	424	12	mappings	mapping	NOUN
ejpam-4005	424	13	.	.	PUNCT
ejpam-4005	425	1	math	math	NOUN
ejpam-4005	425	2	.	.	PUNCT
ejpam-4005	426	1	comput	comput	NOUN
ejpam-4005	426	2	.	.	PUNCT
ejpam-4005	427	1	model	model	PROPN
ejpam-4005	427	2	.	.	PROPN
ejpam-4005	427	3	,	,	PUNCT
ejpam-4005	427	4	32:1181	32:1181	NUM
ejpam-4005	427	5	–	–	PUNCT
ejpam-4005	427	6	1191	1191	NUM
ejpam-4005	427	7	,	,	PUNCT
ejpam-4005	427	8	2000	2000	NUM
ejpam-4005	427	9	.	.	PUNCT
ejpam-4005	428	1	[	[	X
ejpam-4005	428	2	19	19	NUM
ejpam-4005	428	3	]	]	X
ejpam-4005	428	4	m.o	m.o	PROPN
ejpam-4005	428	5	.	.	PROPN
ejpam-4005	428	6	osilike	osilike	PROPN
ejpam-4005	428	7	and	and	CCONJ
ejpam-4005	428	8	a.	a.	NOUN
ejpam-4005	428	9	udomene	udomene	PROPN
ejpam-4005	428	10	.	.	PUNCT
ejpam-4005	429	1	demiclosedness	demiclosedness	NOUN
ejpam-4005	429	2	principle	principle	NOUN
ejpam-4005	429	3	and	and	CCONJ
ejpam-4005	429	4	convergence	convergence	NOUN
ejpam-4005	429	5	theorems	theorem	NOUN
ejpam-4005	429	6	for	for	ADP
ejpam-4005	429	7	strictly	strictly	ADV
ejpam-4005	429	8	pseudocontractive	pseudocontractive	ADJ
ejpam-4005	429	9	mappings	mapping	NOUN
ejpam-4005	429	10	of	of	ADP
ejpam-4005	429	11	browder	browder	NOUN
ejpam-4005	429	12	-	-	PUNCT
ejpam-4005	429	13	petryshyn	petryshyn	ADJ
ejpam-4005	429	14	type	type	NOUN
ejpam-4005	429	15	.	.	PUNCT
ejpam-4005	430	1	j.	j.	PROPN
ejpam-4005	430	2	math	math	PROPN
ejpam-4005	430	3	.	.	PUNCT
ejpam-4005	431	1	anal	anal	PROPN
ejpam-4005	431	2	.	.	PUNCT
ejpam-4005	432	1	appl	appl	PROPN
ejpam-4005	432	2	.	.	PROPN
ejpam-4005	432	3	,	,	PUNCT
ejpam-4005	432	4	256:431–445	256:431–445	NUM
ejpam-4005	432	5	,	,	PUNCT
ejpam-4005	432	6	2001	2001	NUM
ejpam-4005	432	7	.	.	PUNCT
ejpam-4005	433	1	[	[	X
ejpam-4005	433	2	20	20	NUM
ejpam-4005	433	3	]	]	PUNCT
ejpam-4005	433	4	l.	l.	PROPN
ejpam-4005	433	5	qihou	qihou	PROPN
ejpam-4005	433	6	.	.	PUNCT
ejpam-4005	434	1	iterative	iterative	NOUN
ejpam-4005	434	2	sequences	sequence	NOUN
ejpam-4005	434	3	for	for	ADP
ejpam-4005	434	4	asymptotically	asymptotically	ADV
ejpam-4005	434	5	quasi	quasi	ADJ
ejpam-4005	434	6	-	-	ADJ
ejpam-4005	434	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	434	8	mappings	mapping	NOUN
ejpam-4005	434	9	with	with	ADP
ejpam-4005	434	10	error	error	NOUN
ejpam-4005	434	11	member	member	NOUN
ejpam-4005	434	12	.	.	PUNCT
ejpam-4005	435	1	j.	j.	PROPN
ejpam-4005	435	2	math	math	PROPN
ejpam-4005	435	3	.	.	PUNCT
ejpam-4005	436	1	anal	anal	PROPN
ejpam-4005	436	2	.	.	PUNCT
ejpam-4005	437	1	appl	appl	PROPN
ejpam-4005	437	2	.	.	PROPN
ejpam-4005	438	1	,	,	PUNCT
ejpam-4005	438	2	259:18–24	259:18–24	NUM
ejpam-4005	438	3	,	,	PUNCT
ejpam-4005	438	4	2001	2001	NUM
ejpam-4005	438	5	.	.	PUNCT
ejpam-4005	439	1	[	[	X
ejpam-4005	439	2	21	21	NUM
ejpam-4005	439	3	]	]	X
ejpam-4005	439	4	s.	s.	PROPN
ejpam-4005	439	5	reich	reich	PROPN
ejpam-4005	439	6	.	.	PUNCT
ejpam-4005	440	1	fixed	fix	VERB
ejpam-4005	440	2	point	point	NOUN
ejpam-4005	440	3	iterations	iteration	NOUN
ejpam-4005	440	4	of	of	ADP
ejpam-4005	440	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	440	6	mappings	mapping	NOUN
ejpam-4005	440	7	.	.	PUNCT
ejpam-4005	441	1	pac	pac	PROPN
ejpam-4005	441	2	.	.	PUNCT
ejpam-4005	442	1	j.	j.	PROPN
ejpam-4005	442	2	math	math	PROPN
ejpam-4005	442	3	.	.	PUNCT
ejpam-4005	442	4	,	,	PUNCT
ejpam-4005	442	5	60(2):195	60(2):195	X
ejpam-4005	442	6	–	–	PUNCT
ejpam-4005	442	7	198	198	NUM
ejpam-4005	442	8	,	,	PUNCT
ejpam-4005	442	9	1975	1975	NUM
ejpam-4005	442	10	.	.	PUNCT
ejpam-4005	443	1	[	[	X
ejpam-4005	443	2	22	22	NUM
ejpam-4005	443	3	]	]	PUNCT
ejpam-4005	443	4	s.	s.	PROPN
ejpam-4005	443	5	reich	reich	PROPN
ejpam-4005	443	6	.	.	PUNCT
ejpam-4005	444	1	weak	weak	ADJ
ejpam-4005	444	2	convergence	convergence	NOUN
ejpam-4005	444	3	theorems	theorem	NOUN
ejpam-4005	444	4	for	for	ADP
ejpam-4005	444	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	444	6	mappings	mapping	NOUN
ejpam-4005	444	7	in	in	ADP
ejpam-4005	444	8	banach	banach	NOUN
ejpam-4005	444	9	spaces	space	NOUN
ejpam-4005	444	10	.	.	PUNCT
ejpam-4005	445	1	j.	j.	PROPN
ejpam-4005	445	2	math	math	PROPN
ejpam-4005	445	3	.	.	PUNCT
ejpam-4005	446	1	anal	anal	PROPN
ejpam-4005	446	2	.	.	PUNCT
ejpam-4005	447	1	appl	appl	PROPN
ejpam-4005	447	2	.	.	PROPN
ejpam-4005	447	3	,	,	PUNCT
ejpam-4005	447	4	67:274–276	67:274–276	PROPN
ejpam-4005	447	5	,	,	PUNCT
ejpam-4005	447	6	1979	1979	NUM
ejpam-4005	447	7	.	.	PUNCT
ejpam-4005	448	1	[	[	X
ejpam-4005	448	2	23	23	NUM
ejpam-4005	448	3	]	]	PUNCT
ejpam-4005	448	4	s.	s.	PROPN
ejpam-4005	448	5	reich	reich	PROPN
ejpam-4005	448	6	and	and	CCONJ
ejpam-4005	448	7	i.	i.	PROPN
ejpam-4005	448	8	shafrir	shafrir	PROPN
ejpam-4005	448	9	.	.	PUNCT
ejpam-4005	449	1	nonexpansive	nonexpansive	ADJ
ejpam-4005	449	2	iterations	iteration	NOUN
ejpam-4005	449	3	in	in	ADP
ejpam-4005	449	4	hyperbolic	hyperbolic	ADJ
ejpam-4005	449	5	spaces	space	NOUN
ejpam-4005	449	6	.	.	PUNCT
ejpam-4005	450	1	nonlinear	nonlinear	ADJ
ejpam-4005	450	2	anal	anal	PROPN
ejpam-4005	450	3	.	.	PUNCT
ejpam-4005	450	4	,	,	PUNCT
ejpam-4005	450	5	theory	theory	NOUN
ejpam-4005	450	6	methods	method	NOUN
ejpam-4005	450	7	appl	appl	PROPN
ejpam-4005	450	8	.	.	PUNCT
ejpam-4005	450	9	,	,	PUNCT
ejpam-4005	450	10	15:537–558	15:537–558	NUM
ejpam-4005	450	11	,	,	PUNCT
ejpam-4005	450	12	1990	1990	NUM
ejpam-4005	450	13	.	.	PUNCT
ejpam-4005	451	1	references	reference	NOUN
ejpam-4005	451	2	665	665	NUM
ejpam-4005	451	3	[	[	X
ejpam-4005	451	4	24	24	NUM
ejpam-4005	451	5	]	]	X
ejpam-4005	451	6	b.e	b.e	PROPN
ejpam-4005	451	7	.	.	PROPN
ejpam-4005	451	8	rhoades	rhoades	PROPN
ejpam-4005	451	9	.	.	PUNCT
ejpam-4005	452	1	fixed	fix	VERB
ejpam-4005	452	2	point	point	NOUN
ejpam-4005	452	3	iterations	iteration	NOUN
ejpam-4005	452	4	for	for	ADP
ejpam-4005	452	5	certain	certain	ADJ
ejpam-4005	452	6	nonlinear	nonlinear	ADJ
ejpam-4005	452	7	mappings	mapping	NOUN
ejpam-4005	452	8	.	.	PUNCT
ejpam-4005	453	1	j.	j.	PROPN
ejpam-4005	453	2	math	math	PROPN
ejpam-4005	453	3	.	.	PUNCT
ejpam-4005	454	1	anal	anal	PROPN
ejpam-4005	454	2	.	.	PUNCT
ejpam-4005	455	1	appl	appl	PROPN
ejpam-4005	455	2	.	.	PROPN
ejpam-4005	455	3	,	,	PUNCT
ejpam-4005	455	4	183:118–120	183:118–120	NUM
ejpam-4005	455	5	,	,	PUNCT
ejpam-4005	455	6	1994	1994	NUM
ejpam-4005	455	7	.	.	PUNCT
ejpam-4005	456	1	[	[	X
ejpam-4005	456	2	25	25	NUM
ejpam-4005	456	3	]	]	PUNCT
ejpam-4005	456	4	a.	a.	NOUN
ejpam-4005	456	5	sahin	sahin	PROPN
ejpam-4005	456	6	.	.	PUNCT
ejpam-4005	457	1	some	some	DET
ejpam-4005	457	2	new	new	ADJ
ejpam-4005	457	3	results	result	NOUN
ejpam-4005	457	4	of	of	ADP
ejpam-4005	457	5	m	m	NOUN
ejpam-4005	457	6	-	-	PUNCT
ejpam-4005	457	7	iteration	iteration	NOUN
ejpam-4005	457	8	process	process	NOUN
ejpam-4005	457	9	in	in	ADP
ejpam-4005	457	10	hyperbolic	hyperbolic	ADJ
ejpam-4005	457	11	spaces	space	NOUN
ejpam-4005	457	12	.	.	PUNCT
ejpam-4005	458	1	carpathian	carpathian	PROPN
ejpam-4005	458	2	j.	j.	PROPN
ejpam-4005	458	3	math	math	PROPN
ejpam-4005	458	4	.	.	PUNCT
ejpam-4005	458	5	,	,	PUNCT
ejpam-4005	459	1	35:221–232	35:221–232	PROPN
ejpam-4005	459	2	,	,	PUNCT
ejpam-4005	459	3	2019	2019	NUM
ejpam-4005	459	4	.	.	PUNCT
ejpam-4005	460	1	[	[	X
ejpam-4005	460	2	26	26	NUM
ejpam-4005	460	3	]	]	PUNCT
ejpam-4005	460	4	a.	a.	NOUN
ejpam-4005	460	5	sahin	sahin	PROPN
ejpam-4005	460	6	.	.	PUNCT
ejpam-4005	461	1	some	some	DET
ejpam-4005	461	2	results	result	NOUN
ejpam-4005	461	3	of	of	ADP
ejpam-4005	461	4	the	the	DET
ejpam-4005	461	5	picard	picard	NOUN
ejpam-4005	461	6	-	-	PUNCT
ejpam-4005	461	7	krasnoselskii	krasnoselskii	PROPN
ejpam-4005	461	8	hybrid	hybrid	ADJ
ejpam-4005	461	9	iterative	iterative	NOUN
ejpam-4005	461	10	process	process	NOUN
ejpam-4005	461	11	.	.	PUNCT
ejpam-4005	462	1	filomat	filomat	NOUN
ejpam-4005	462	2	,	,	PUNCT
ejpam-4005	462	3	33:359–365	33:359–365	PROPN
ejpam-4005	462	4	,	,	PUNCT
ejpam-4005	462	5	2019	2019	NUM
ejpam-4005	462	6	.	.	PUNCT
ejpam-4005	463	1	[	[	X
ejpam-4005	463	2	27	27	NUM
ejpam-4005	463	3	]	]	PUNCT
ejpam-4005	463	4	a.	a.	NOUN
ejpam-4005	463	5	sahin	sahin	PROPN
ejpam-4005	463	6	and	and	CCONJ
ejpam-4005	463	7	m.	m.	NOUN
ejpam-4005	463	8	basarir	basarir	NOUN
ejpam-4005	463	9	.	.	PUNCT
ejpam-4005	464	1	some	some	DET
ejpam-4005	464	2	convergence	convergence	NOUN
ejpam-4005	464	3	results	result	VERB
ejpam-4005	464	4	for	for	ADP
ejpam-4005	464	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	464	6	mappings	mapping	NOUN
ejpam-4005	464	7	in	in	ADP
ejpam-4005	464	8	uniformly	uniformly	ADV
ejpam-4005	464	9	convex	convex	VERB
ejpam-4005	464	10	hyperbolic	hyperbolic	ADJ
ejpam-4005	464	11	spaces	space	NOUN
ejpam-4005	464	12	.	.	PUNCT
ejpam-4005	465	1	creat	creat	PROPN
ejpam-4005	465	2	.	.	PUNCT
ejpam-4005	465	3	math	math	PROPN
ejpam-4005	465	4	.	.	PUNCT
ejpam-4005	466	1	inform	inform	NOUN
ejpam-4005	466	2	.	.	PUNCT
ejpam-4005	466	3	,	,	PUNCT
ejpam-4005	466	4	26:331–338	26:331–338	NUM
ejpam-4005	466	5	,	,	PUNCT
ejpam-4005	466	6	2017	2017	NUM
ejpam-4005	466	7	.	.	PUNCT
ejpam-4005	467	1	[	[	X
ejpam-4005	467	2	28	28	NUM
ejpam-4005	467	3	]	]	X
ejpam-4005	467	4	j.	j.	PROPN
ejpam-4005	467	5	schu	schu	PROPN
ejpam-4005	467	6	.	.	PROPN
ejpam-4005	467	7	iterative	iterative	PROPN
ejpam-4005	467	8	construction	construction	NOUN
ejpam-4005	467	9	of	of	ADP
ejpam-4005	467	10	a	a	DET
ejpam-4005	467	11	fixed	fix	VERB
ejpam-4005	467	12	points	point	NOUN
ejpam-4005	467	13	of	of	ADP
ejpam-4005	467	14	asymptotically	asymptotically	ADV
ejpam-4005	467	15	nonexpansive	nonexpansive	ADJ
ejpam-4005	467	16	mappings	mapping	NOUN
ejpam-4005	467	17	.	.	PUNCT
ejpam-4005	468	1	j.	j.	PROPN
ejpam-4005	468	2	math	math	PROPN
ejpam-4005	468	3	.	.	PUNCT
ejpam-4005	469	1	anal	anal	PROPN
ejpam-4005	469	2	.	.	PUNCT
ejpam-4005	470	1	appl	appl	PROPN
ejpam-4005	470	2	.	.	PROPN
ejpam-4005	470	3	,	,	PUNCT
ejpam-4005	470	4	158:407–413	158:407–413	NUM
ejpam-4005	470	5	,	,	PUNCT
ejpam-4005	470	6	1991	1991	NUM
ejpam-4005	470	7	.	.	PUNCT
ejpam-4005	471	1	[	[	X
ejpam-4005	471	2	29	29	NUM
ejpam-4005	471	3	]	]	X
ejpam-4005	471	4	j.	j.	PROPN
ejpam-4005	471	5	schu	schu	PROPN
ejpam-4005	471	6	.	.	PUNCT
ejpam-4005	472	1	weak	weak	ADJ
ejpam-4005	472	2	and	and	CCONJ
ejpam-4005	472	3	strong	strong	ADJ
ejpam-4005	472	4	convergence	convergence	NOUN
ejpam-4005	472	5	to	to	ADP
ejpam-4005	472	6	fixed	fix	VERB
ejpam-4005	472	7	points	point	NOUN
ejpam-4005	472	8	of	of	ADP
ejpam-4005	472	9	asymptotically	asymptotically	ADV
ejpam-4005	472	10	nonexpansive	nonexpansive	ADJ
ejpam-4005	472	11	mappings	mapping	NOUN
ejpam-4005	472	12	.	.	PUNCT
ejpam-4005	473	1	bull	bull	NOUN
ejpam-4005	473	2	.	.	PUNCT
ejpam-4005	474	1	aust	aust	PROPN
ejpam-4005	474	2	.	.	PUNCT
ejpam-4005	474	3	math	math	PROPN
ejpam-4005	474	4	.	.	PUNCT
ejpam-4005	475	1	soc	soc	PROPN
ejpam-4005	475	2	.	.	PUNCT
ejpam-4005	475	3	,	,	PUNCT
ejpam-4005	475	4	43:153–159	43:153–159	PROPN
ejpam-4005	475	5	,	,	PUNCT
ejpam-4005	475	6	1991	1991	NUM
ejpam-4005	475	7	.	.	PUNCT
ejpam-4005	476	1	[	[	X
ejpam-4005	476	2	30	30	NUM
ejpam-4005	476	3	]	]	X
ejpam-4005	476	4	n.	n.	PROPN
ejpam-4005	476	5	shahzad	shahzad	PROPN
ejpam-4005	476	6	.	.	PUNCT
ejpam-4005	477	1	approximating	approximate	VERB
ejpam-4005	477	2	fixed	fix	VERB
ejpam-4005	477	3	points	point	NOUN
ejpam-4005	477	4	of	of	ADP
ejpam-4005	477	5	non	non	ADJ
ejpam-4005	477	6	-	-	ADJ
ejpam-4005	477	7	self	self	ADJ
ejpam-4005	477	8	nonexpansive	nonexpansive	ADJ
ejpam-4005	477	9	mappings	mapping	NOUN
ejpam-4005	477	10	in	in	ADP
ejpam-4005	477	11	banach	banach	NOUN
ejpam-4005	477	12	spaces	space	NOUN
ejpam-4005	477	13	.	.	PUNCT
ejpam-4005	478	1	nonlinear	nonlinear	ADJ
ejpam-4005	478	2	anal	anal	PROPN
ejpam-4005	478	3	.	.	PUNCT
ejpam-4005	478	4	,	,	PUNCT
ejpam-4005	478	5	61:1031–1039	61:1031–1039	NUM
ejpam-4005	478	6	,	,	PUNCT
ejpam-4005	478	7	2005	2005	NUM
ejpam-4005	478	8	.	.	PUNCT
ejpam-4005	479	1	[	[	X
ejpam-4005	479	2	31	31	NUM
ejpam-4005	479	3	]	]	PUNCT
ejpam-4005	479	4	t.	t.	PROPN
ejpam-4005	479	5	shimizu	shimizu	PROPN
ejpam-4005	479	6	and	and	CCONJ
ejpam-4005	479	7	w.	w.	PROPN
ejpam-4005	479	8	takahashi	takahashi	PROPN
ejpam-4005	479	9	.	.	PUNCT
ejpam-4005	480	1	fixed	fix	VERB
ejpam-4005	480	2	points	point	NOUN
ejpam-4005	480	3	of	of	ADP
ejpam-4005	480	4	multivalued	multivalue	VERB
ejpam-4005	480	5	mappings	mapping	NOUN
ejpam-4005	480	6	in	in	ADP
ejpam-4005	480	7	certain	certain	ADJ
ejpam-4005	480	8	convex	convex	NOUN
ejpam-4005	480	9	metric	metric	ADJ
ejpam-4005	480	10	spaces	space	NOUN
ejpam-4005	480	11	.	.	PUNCT
ejpam-4005	481	1	topol	topol	NOUN
ejpam-4005	481	2	.	.	PUNCT
ejpam-4005	482	1	methods	method	NOUN
ejpam-4005	482	2	nonlinear	nonlinear	PROPN
ejpam-4005	482	3	anal	anal	PROPN
ejpam-4005	482	4	.	.	PUNCT
ejpam-4005	482	5	,	,	PUNCT
ejpam-4005	482	6	8:197–203	8:197–203	NOUN
ejpam-4005	482	7	,	,	PUNCT
ejpam-4005	482	8	1996	1996	NUM
ejpam-4005	482	9	.	.	PUNCT
ejpam-4005	483	1	[	[	X
ejpam-4005	483	2	32	32	NUM
ejpam-4005	483	3	]	]	PUNCT
ejpam-4005	483	4	w.	w.	PROPN
ejpam-4005	483	5	takahashi	takahashi	PROPN
ejpam-4005	483	6	.	.	PUNCT
ejpam-4005	484	1	a	a	DET
ejpam-4005	484	2	convexity	convexity	NOUN
ejpam-4005	484	3	in	in	ADP
ejpam-4005	484	4	metric	metric	ADJ
ejpam-4005	484	5	spaces	space	NOUN
ejpam-4005	484	6	and	and	CCONJ
ejpam-4005	484	7	nonexpansive	nonexpansive	ADJ
ejpam-4005	484	8	mappings	mapping	NOUN
ejpam-4005	484	9	.	.	PUNCT
ejpam-4005	485	1	kodai	kodai	PROPN
ejpam-4005	485	2	math	math	PROPN
ejpam-4005	485	3	.	.	PUNCT
ejpam-4005	486	1	semin	semin	PROPN
ejpam-4005	486	2	.	.	PUNCT
ejpam-4005	487	1	rep	rep	PROPN
ejpam-4005	487	2	.	.	PROPN
ejpam-4005	487	3	,	,	PUNCT
ejpam-4005	487	4	22:142–149	22:142–149	PROPN
ejpam-4005	487	5	,	,	PUNCT
ejpam-4005	487	6	1970	1970	NUM
ejpam-4005	487	7	.	.	PUNCT
ejpam-4005	488	1	[	[	X
ejpam-4005	488	2	33	33	NUM
ejpam-4005	488	3	]	]	PUNCT
ejpam-4005	488	4	w.	w.	PROPN
ejpam-4005	488	5	takahashi	takahashi	PROPN
ejpam-4005	488	6	and	and	CCONJ
ejpam-4005	488	7	g.e	g.e	PROPN
ejpam-4005	488	8	.	.	PUNCT
ejpam-4005	489	1	kim	kim	PROPN
ejpam-4005	489	2	.	.	PUNCT
ejpam-4005	490	1	strong	strong	ADJ
ejpam-4005	490	2	convergence	convergence	NOUN
ejpam-4005	490	3	of	of	ADP
ejpam-4005	490	4	approximants	approximant	NOUN
ejpam-4005	490	5	to	to	ADP
ejpam-4005	490	6	fixed	fix	VERB
ejpam-4005	490	7	points	point	NOUN
ejpam-4005	490	8	of	of	ADP
ejpam-4005	490	9	nonexpansive	nonexpansive	PROPN
ejpam-4005	490	10	nonself	nonself	PROPN
ejpam-4005	490	11	-	-	PUNCT
ejpam-4005	490	12	mappings	mapping	NOUN
ejpam-4005	490	13	.	.	PUNCT
ejpam-4005	491	1	nonlinear	nonlinear	ADJ
ejpam-4005	491	2	anal	anal	PROPN
ejpam-4005	491	3	.	.	PUNCT
ejpam-4005	491	4	,	,	PUNCT
ejpam-4005	492	1	32:447–454	32:447–454	PROPN
ejpam-4005	492	2	,	,	PUNCT
ejpam-4005	492	3	1998	1998	NUM
ejpam-4005	492	4	.	.	PUNCT
ejpam-4005	493	1	[	[	X
ejpam-4005	493	2	34	34	NUM
ejpam-4005	493	3	]	]	X
ejpam-4005	493	4	k.k	k.k	PROPN
ejpam-4005	493	5	.	.	PROPN
ejpam-4005	493	6	tan	tan	PROPN
ejpam-4005	493	7	and	and	CCONJ
ejpam-4005	493	8	h.k	h.k	PROPN
ejpam-4005	493	9	.	.	PROPN
ejpam-4005	493	10	xu	xu	PROPN
ejpam-4005	493	11	.	.	PUNCT
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ejpam-4005	494	2	fixed	fix	VERB
ejpam-4005	494	3	points	point	NOUN
ejpam-4005	494	4	of	of	ADP
ejpam-4005	494	5	nonexpansive	nonexpansive	ADJ
ejpam-4005	494	6	mapping	mapping	NOUN
ejpam-4005	494	7	by	by	ADP
ejpam-4005	494	8	the	the	DET
ejpam-4005	494	9	ishikawa	ishikawa	PROPN
ejpam-4005	494	10	iteration	iteration	NOUN
ejpam-4005	494	11	process	process	NOUN
ejpam-4005	494	12	.	.	PUNCT
ejpam-4005	495	1	j.	j.	PROPN
ejpam-4005	495	2	math	math	PROPN
ejpam-4005	495	3	.	.	PUNCT
ejpam-4005	496	1	anal	anal	PROPN
ejpam-4005	496	2	.	.	PUNCT
ejpam-4005	497	1	appl	appl	PROPN
ejpam-4005	497	2	.	.	PROPN
ejpam-4005	497	3	,	,	PUNCT
ejpam-4005	497	4	178:301–308	178:301–308	NUM
ejpam-4005	497	5	,	,	PUNCT
ejpam-4005	497	6	1993	1993	NUM
ejpam-4005	497	7	.	.	PUNCT
ejpam-4005	498	1	[	[	X
ejpam-4005	498	2	35	35	NUM
ejpam-4005	498	3	]	]	X
ejpam-4005	498	4	s.	s.	PROPN
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ejpam-4005	498	6	.	.	PUNCT
ejpam-4005	499	1	common	common	ADJ
ejpam-4005	499	2	fixed	fix	VERB
ejpam-4005	499	3	points	point	NOUN
ejpam-4005	499	4	of	of	ADP
ejpam-4005	499	5	new	new	ADJ
ejpam-4005	499	6	iterations	iteration	NOUN
ejpam-4005	499	7	for	for	ADP
ejpam-4005	499	8	two	two	NUM
ejpam-4005	499	9	asymptotically	asymptotically	ADV
ejpam-4005	499	10	nonexpansive	nonexpansive	ADJ
ejpam-4005	499	11	nonself	nonself	NOUN
ejpam-4005	499	12	-	-	PUNCT
ejpam-4005	499	13	mappings	mapping	NOUN
ejpam-4005	499	14	in	in	ADP
ejpam-4005	499	15	a	a	DET
ejpam-4005	499	16	banach	banach	NOUN
ejpam-4005	499	17	space	space	NOUN
ejpam-4005	499	18	.	.	PUNCT
ejpam-4005	500	1	j.	j.	PROPN
ejpam-4005	500	2	comput	comput	PROPN
ejpam-4005	500	3	.	.	PUNCT
ejpam-4005	501	1	appl	appl	PROPN
ejpam-4005	501	2	.	.	PROPN
ejpam-4005	501	3	math	math	PROPN
ejpam-4005	501	4	.	.	PUNCT
ejpam-4005	501	5	,	,	PUNCT
ejpam-4005	501	6	224:688–695	224:688–695	NUM
ejpam-4005	501	7	,	,	PUNCT
ejpam-4005	501	8	2009	2009	NUM
ejpam-4005	501	9	.	.	PUNCT
ejpam-4005	502	1	[	[	X
ejpam-4005	502	2	36	36	NUM
ejpam-4005	502	3	]	]	PUNCT
ejpam-4005	502	4	l.	l.	PROPN
ejpam-4005	502	5	wang	wang	PROPN
ejpam-4005	502	6	.	.	PUNCT
ejpam-4005	503	1	strong	strong	ADJ
ejpam-4005	503	2	and	and	CCONJ
ejpam-4005	503	3	weak	weak	ADJ
ejpam-4005	503	4	convergence	convergence	NOUN
ejpam-4005	503	5	theorems	theorem	NOUN
ejpam-4005	503	6	for	for	ADP
ejpam-4005	503	7	common	common	ADJ
ejpam-4005	503	8	fixed	fix	VERB
ejpam-4005	503	9	points	point	NOUN
ejpam-4005	503	10	of	of	ADP
ejpam-4005	503	11	nonself	nonself	PROPN
ejpam-4005	503	12	asymptotically	asymptotically	ADV
ejpam-4005	503	13	nonexpansive	nonexpansive	ADJ
ejpam-4005	503	14	mappings	mapping	NOUN
ejpam-4005	503	15	.	.	PUNCT
ejpam-4005	504	1	j.	j.	PROPN
ejpam-4005	504	2	math	math	PROPN
ejpam-4005	504	3	.	.	PUNCT
ejpam-4005	505	1	anal	anal	PROPN
ejpam-4005	505	2	.	.	PUNCT
ejpam-4005	506	1	appl	appl	PROPN
ejpam-4005	506	2	.	.	PROPN
ejpam-4005	506	3	,	,	PUNCT
ejpam-4005	506	4	323:550–557	323:550–557	NUM
ejpam-4005	506	5	,	,	PUNCT
ejpam-4005	506	6	2006	2006	NUM
ejpam-4005	506	7	.	.	PUNCT
ejpam-4005	507	1	[	[	X
ejpam-4005	507	2	37	37	NUM
ejpam-4005	507	3	]	]	SYM
ejpam-4005	507	4	h.k	h.k	PROPN
ejpam-4005	507	5	.	.	PROPN
ejpam-4005	507	6	xu	xu	PROPN
ejpam-4005	507	7	and	and	CCONJ
ejpam-4005	507	8	x.m	x.m	PROPN
ejpam-4005	507	9	.	.	PROPN
ejpam-4005	507	10	yin	yin	PROPN
ejpam-4005	507	11	.	.	PUNCT
ejpam-4005	508	1	strong	strong	ADJ
ejpam-4005	508	2	convergence	convergence	NOUN
ejpam-4005	508	3	theorems	theorem	NOUN
ejpam-4005	508	4	for	for	ADP
ejpam-4005	508	5	nonexpansive	nonexpansive	PROPN
ejpam-4005	508	6	nonself	nonself	PROPN
ejpam-4005	508	7	mappings	mapping	NOUN
ejpam-4005	508	8	.	.	PUNCT
ejpam-4005	509	1	nonlinear	nonlinear	ADJ
ejpam-4005	509	2	anal	anal	PROPN
ejpam-4005	509	3	.	.	PROPN
ejpam-4005	509	4	,	,	PUNCT
ejpam-4005	509	5	242:223–228	242:223–228	NUM
ejpam-4005	509	6	,	,	PUNCT
ejpam-4005	509	7	1995	1995	NUM
ejpam-4005	509	8	.	.	PUNCT