id	sid	tid	token	lemma	pos
ejpam-5792	1	1	european	european	PROPN
ejpam-5792	1	2	journal	journal	PROPN
ejpam-5792	1	3	of	of	ADP
ejpam-5792	1	4	pure	pure	ADJ
ejpam-5792	1	5	and	and	CCONJ
ejpam-5792	1	6	applied	applied	ADJ
ejpam-5792	1	7	mathematics	mathematic	NOUN
ejpam-5792	1	8	2025	2025	NUM
ejpam-5792	1	9	,	,	PUNCT
ejpam-5792	1	10	vol	vol	NOUN
ejpam-5792	1	11	.	.	PROPN
ejpam-5792	1	12	18	18	NUM
ejpam-5792	1	13	,	,	PUNCT
ejpam-5792	1	14	issue	issue	NOUN
ejpam-5792	1	15	2	2	NUM
ejpam-5792	1	16	,	,	PUNCT
ejpam-5792	1	17	article	article	NOUN
ejpam-5792	1	18	number	number	NOUN
ejpam-5792	1	19	5792	5792	NUM
ejpam-5792	1	20	issn	issn	PROPN
ejpam-5792	1	21	1307	1307	NUM
ejpam-5792	1	22	-	-	SYM
ejpam-5792	1	23	5543	5543	NUM
ejpam-5792	1	24	–	–	PUNCT
ejpam-5792	1	25	ejpam.com	ejpam.com	X
ejpam-5792	1	26	published	publish	VERB
ejpam-5792	1	27	by	by	ADP
ejpam-5792	1	28	new	new	PROPN
ejpam-5792	1	29	york	york	PROPN
ejpam-5792	1	30	business	business	PROPN
ejpam-5792	1	31	global	global	ADJ
ejpam-5792	1	32	fixed	fix	VERB
ejpam-5792	1	33	point	point	NOUN
ejpam-5792	1	34	results	result	NOUN
ejpam-5792	1	35	for	for	ADP
ejpam-5792	1	36	enriched	enriched	ADJ
ejpam-5792	1	37	interpolative	interpolative	ADJ
ejpam-5792	1	38	type	type	NOUN
ejpam-5792	1	39	multivalued	multivalue	VERB
ejpam-5792	1	40	contractions	contraction	NOUN
ejpam-5792	1	41	via	via	ADP
ejpam-5792	1	42	a	a	DET
ejpam-5792	1	43	simulation	simulation	NOUN
ejpam-5792	1	44	function	function	PROPN
ejpam-5792	1	45	amit	amit	PROPN
ejpam-5792	1	46	gangwar1	gangwar1	PROPN
ejpam-5792	1	47	,	,	PUNCT
ejpam-5792	1	48	shivam	shivam	PROPN
ejpam-5792	1	49	rawat2	rawat2	PROPN
ejpam-5792	1	50	,	,	PUNCT
ejpam-5792	1	51	hassen	hassen	PROPN
ejpam-5792	1	52	aydi3,4	aydi3,4	PROPN
ejpam-5792	1	53	,	,	PUNCT
ejpam-5792	1	54	sarah	sarah	PROPN
ejpam-5792	1	55	aljohani5,∗	aljohani5,∗	PROPN
ejpam-5792	1	56	,	,	PUNCT
ejpam-5792	1	57	nabil	nabil	PROPN
ejpam-5792	1	58	mlaiki5	mlaiki5	PROPN
ejpam-5792	2	1	1	1	NUM
ejpam-5792	2	2	h.n.b	h.n.b	NOUN
ejpam-5792	2	3	.	.	PUNCT
ejpam-5792	2	4	garhwal	garhwal	PROPN
ejpam-5792	2	5	university	university	PROPN
ejpam-5792	2	6	,	,	PUNCT
ejpam-5792	2	7	srinagar	srinagar	PROPN
ejpam-5792	2	8	garhwal	garhwal	PROPN
ejpam-5792	2	9	,	,	PUNCT
ejpam-5792	2	10	uttarakhand	uttarakhand	NOUN
ejpam-5792	2	11	246174	246174	NUM
ejpam-5792	2	12	,	,	PUNCT
ejpam-5792	2	13	india	india	PROPN
ejpam-5792	2	14	.	.	PROPN
ejpam-5792	2	15	2	2	NUM
ejpam-5792	2	16	department	department	NOUN
ejpam-5792	2	17	of	of	ADP
ejpam-5792	2	18	mathematics	mathematic	NOUN
ejpam-5792	2	19	,	,	PUNCT
ejpam-5792	2	20	graphic	graphic	ADJ
ejpam-5792	2	21	era	era	NOUN
ejpam-5792	2	22	(	(	PUNCT
ejpam-5792	2	23	deemed	deem	VERB
ejpam-5792	2	24	to	to	PART
ejpam-5792	2	25	be	be	AUX
ejpam-5792	2	26	)	)	PUNCT
ejpam-5792	2	27	university	university	NOUN
ejpam-5792	2	28	,	,	PUNCT
ejpam-5792	2	29	dehradun	dehradun	PROPN
ejpam-5792	2	30	,	,	PUNCT
ejpam-5792	2	31	uttarakhand	uttarakhand	PROPN
ejpam-5792	2	32	,	,	PUNCT
ejpam-5792	2	33	248002	248002	NUM
ejpam-5792	2	34	,	,	PUNCT
ejpam-5792	2	35	india	india	PROPN
ejpam-5792	2	36	.	.	PROPN
ejpam-5792	3	1	3	3	NUM
ejpam-5792	3	2	institut	institut	PROPN
ejpam-5792	3	3	supérieur	supérieur	PROPN
ejpam-5792	3	4	d’informatique	d’informatique	PROPN
ejpam-5792	3	5	et	et	NOUN
ejpam-5792	3	6	des	des	X
ejpam-5792	3	7	techniques	techniques	X
ejpam-5792	3	8	de	de	X
ejpam-5792	3	9	communication	communication	NOUN
ejpam-5792	3	10	,	,	PUNCT
ejpam-5792	3	11	université	université	ADJ
ejpam-5792	3	12	de	de	X
ejpam-5792	3	13	sousse	sousse	PROPN
ejpam-5792	3	14	,	,	PUNCT
ejpam-5792	3	15	h.	h.	PROPN
ejpam-5792	3	16	sousse	sousse	PROPN
ejpam-5792	3	17	4000	4000	NUM
ejpam-5792	3	18	,	,	PUNCT
ejpam-5792	3	19	tunisia	tunisia	PROPN
ejpam-5792	3	20	4	4	NUM
ejpam-5792	3	21	department	department	NOUN
ejpam-5792	3	22	of	of	ADP
ejpam-5792	3	23	mathematics	mathematic	NOUN
ejpam-5792	3	24	and	and	CCONJ
ejpam-5792	3	25	applied	apply	VERB
ejpam-5792	3	26	mathematics	mathematic	NOUN
ejpam-5792	3	27	,	,	PUNCT
ejpam-5792	3	28	sefako	sefako	VERB
ejpam-5792	3	29	makgatho	makgatho	PROPN
ejpam-5792	3	30	health	health	PROPN
ejpam-5792	3	31	sciences	sciences	PROPN
ejpam-5792	3	32	university	university	PROPN
ejpam-5792	3	33	,	,	PUNCT
ejpam-5792	3	34	ga	ga	PROPN
ejpam-5792	3	35	-	-	NOUN
ejpam-5792	3	36	rankuwa	rankuwa	PROPN
ejpam-5792	3	37	,	,	PUNCT
ejpam-5792	3	38	south	south	PROPN
ejpam-5792	3	39	africa	africa	PROPN
ejpam-5792	3	40	5	5	NUM
ejpam-5792	3	41	department	department	NOUN
ejpam-5792	3	42	of	of	ADP
ejpam-5792	3	43	mathematics	mathematic	NOUN
ejpam-5792	3	44	and	and	CCONJ
ejpam-5792	3	45	sciences	science	NOUN
ejpam-5792	3	46	,	,	PUNCT
ejpam-5792	3	47	prince	prince	PROPN
ejpam-5792	3	48	sultan	sultan	PROPN
ejpam-5792	3	49	university	university	PROPN
ejpam-5792	3	50	,	,	PUNCT
ejpam-5792	3	51	riyadh	riyadh	PROPN
ejpam-5792	3	52	11586	11586	NUM
ejpam-5792	3	53	,	,	PUNCT
ejpam-5792	3	54	saudi	saudi	PROPN
ejpam-5792	3	55	arabia	arabia	PROPN
ejpam-5792	3	56	abstract	abstract	NOUN
ejpam-5792	3	57	.	.	PUNCT
ejpam-5792	4	1	in	in	ADP
ejpam-5792	4	2	this	this	DET
ejpam-5792	4	3	paper	paper	NOUN
ejpam-5792	4	4	,	,	PUNCT
ejpam-5792	4	5	using	use	VERB
ejpam-5792	4	6	a	a	DET
ejpam-5792	4	7	simulation	simulation	NOUN
ejpam-5792	4	8	function	function	NOUN
ejpam-5792	4	9	in	in	ADP
ejpam-5792	4	10	the	the	DET
ejpam-5792	4	11	sense	sense	NOUN
ejpam-5792	4	12	of	of	ADP
ejpam-5792	4	13	khojasteh	khojasteh	NOUN
ejpam-5792	4	14	,	,	PUNCT
ejpam-5792	4	15	we	we	PRON
ejpam-5792	4	16	define	define	VERB
ejpam-5792	4	17	multivalued	multivalued	ADJ
ejpam-5792	4	18	enriched	enrich	VERB
ejpam-5792	4	19	interpolative	interpolative	ADJ
ejpam-5792	4	20	kannan	kannan	PROPN
ejpam-5792	4	21	-	-	PUNCT
ejpam-5792	4	22	type	type	NOUN
ejpam-5792	4	23	and	and	CCONJ
ejpam-5792	4	24	hardy	hardy	ADJ
ejpam-5792	4	25	-	-	PUNCT
ejpam-5792	4	26	rogers	rogers	NOUN
ejpam-5792	4	27	-	-	PUNCT
ejpam-5792	4	28	type	type	NOUN
ejpam-5792	4	29	contractions	contraction	NOUN
ejpam-5792	4	30	from	from	ADP
ejpam-5792	4	31	a	a	DET
ejpam-5792	4	32	convex	convex	ADJ
ejpam-5792	4	33	metric	metric	ADJ
ejpam-5792	4	34	space	space	NOUN
ejpam-5792	4	35	u	u	NOUN
ejpam-5792	4	36	to	to	ADP
ejpam-5792	4	37	the	the	DET
ejpam-5792	4	38	collection	collection	NOUN
ejpam-5792	4	39	of	of	ADP
ejpam-5792	4	40	closed	closed	ADJ
ejpam-5792	4	41	and	and	CCONJ
ejpam-5792	4	42	bounded	bound	VERB
ejpam-5792	4	43	subsets	subset	NOUN
ejpam-5792	4	44	of	of	ADP
ejpam-5792	4	45	u	u	PROPN
ejpam-5792	4	46	.	.	PUNCT
ejpam-5792	5	1	we	we	PRON
ejpam-5792	5	2	establish	establish	VERB
ejpam-5792	5	3	two	two	NUM
ejpam-5792	5	4	fixed	fix	VERB
ejpam-5792	5	5	points	point	NOUN
ejpam-5792	5	6	for	for	ADP
ejpam-5792	5	7	these	these	DET
ejpam-5792	5	8	types	type	NOUN
ejpam-5792	5	9	of	of	ADP
ejpam-5792	5	10	multivalued	multivalued	ADJ
ejpam-5792	5	11	contractions	contraction	NOUN
ejpam-5792	5	12	.	.	PUNCT
ejpam-5792	6	1	our	our	PRON
ejpam-5792	6	2	results	result	NOUN
ejpam-5792	6	3	are	be	AUX
ejpam-5792	6	4	illustrated	illustrate	VERB
ejpam-5792	6	5	by	by	ADP
ejpam-5792	6	6	examples	example	NOUN
ejpam-5792	6	7	and	and	CCONJ
ejpam-5792	6	8	followed	follow	VERB
ejpam-5792	6	9	by	by	ADP
ejpam-5792	6	10	some	some	DET
ejpam-5792	6	11	corollaries	corollary	NOUN
ejpam-5792	6	12	.	.	PUNCT
ejpam-5792	7	1	as	as	ADP
ejpam-5792	7	2	a	a	DET
ejpam-5792	7	3	consequence	consequence	NOUN
ejpam-5792	7	4	of	of	ADP
ejpam-5792	7	5	each	each	DET
ejpam-5792	7	6	main	main	ADJ
ejpam-5792	7	7	result	result	NOUN
ejpam-5792	7	8	,	,	PUNCT
ejpam-5792	7	9	a	a	DET
ejpam-5792	7	10	theorem	theorem	NOUN
ejpam-5792	7	11	on	on	ADP
ejpam-5792	7	12	data	datum	NOUN
ejpam-5792	7	13	dependence	dependence	NOUN
ejpam-5792	7	14	of	of	ADP
ejpam-5792	7	15	fixed	fix	VERB
ejpam-5792	7	16	point	point	NOUN
ejpam-5792	7	17	is	be	AUX
ejpam-5792	7	18	proved	prove	VERB
ejpam-5792	7	19	.	.	PUNCT
ejpam-5792	8	1	2020	2020	NUM
ejpam-5792	8	2	mathematics	mathematic	NOUN
ejpam-5792	8	3	subject	subject	NOUN
ejpam-5792	8	4	classifications	classification	NOUN
ejpam-5792	8	5	:	:	PUNCT
ejpam-5792	8	6	47h09	47h09	NUM
ejpam-5792	8	7	,	,	PUNCT
ejpam-5792	8	8	47h10	47h10	NUM
ejpam-5792	8	9	,	,	PUNCT
ejpam-5792	8	10	54h25	54h25	NUM
ejpam-5792	8	11	key	key	ADJ
ejpam-5792	8	12	words	word	NOUN
ejpam-5792	8	13	and	and	CCONJ
ejpam-5792	8	14	phrases	phrase	NOUN
ejpam-5792	8	15	:	:	PUNCT
ejpam-5792	8	16	convex	convex	VERB
ejpam-5792	8	17	metric	metric	ADJ
ejpam-5792	8	18	space	space	NOUN
ejpam-5792	8	19	,	,	PUNCT
ejpam-5792	8	20	simulation	simulation	NOUN
ejpam-5792	8	21	function	function	NOUN
ejpam-5792	8	22	,	,	PUNCT
ejpam-5792	8	23	fixed	fix	VERB
ejpam-5792	8	24	point	point	NOUN
ejpam-5792	8	25	1	1	NUM
ejpam-5792	8	26	.	.	PUNCT
ejpam-5792	8	27	introduction	introduction	NOUN
ejpam-5792	8	28	the	the	DET
ejpam-5792	8	29	banach	banach	NOUN
ejpam-5792	8	30	contraction	contraction	NOUN
ejpam-5792	8	31	principle	principle	NOUN
ejpam-5792	9	1	[	[	X
ejpam-5792	9	2	1	1	X
ejpam-5792	9	3	]	]	PUNCT
ejpam-5792	9	4	stands	stand	VERB
ejpam-5792	9	5	as	as	ADP
ejpam-5792	9	6	a	a	DET
ejpam-5792	9	7	pivotal	pivotal	ADJ
ejpam-5792	9	8	result	result	NOUN
ejpam-5792	9	9	in	in	ADP
ejpam-5792	9	10	the	the	DET
ejpam-5792	9	11	field	field	NOUN
ejpam-5792	9	12	of	of	ADP
ejpam-5792	9	13	fixed	fix	VERB
ejpam-5792	9	14	point	point	NOUN
ejpam-5792	9	15	theory	theory	NOUN
ejpam-5792	9	16	,	,	PUNCT
ejpam-5792	9	17	furnishing	furnish	VERB
ejpam-5792	9	18	a	a	DET
ejpam-5792	9	19	robust	robust	ADJ
ejpam-5792	9	20	framework	framework	NOUN
ejpam-5792	9	21	for	for	ADP
ejpam-5792	9	22	comprehending	comprehend	VERB
ejpam-5792	9	23	the	the	DET
ejpam-5792	9	24	existence	existence	NOUN
ejpam-5792	9	25	and	and	CCONJ
ejpam-5792	9	26	uniqueness	uniqueness	NOUN
ejpam-5792	9	27	of	of	ADP
ejpam-5792	9	28	fixed	fix	VERB
ejpam-5792	9	29	points	point	NOUN
ejpam-5792	9	30	of	of	ADP
ejpam-5792	9	31	mappings	mapping	NOUN
ejpam-5792	9	32	which	which	PRON
ejpam-5792	9	33	are	be	AUX
ejpam-5792	9	34	defined	define	VERB
ejpam-5792	9	35	on	on	ADP
ejpam-5792	9	36	a	a	DET
ejpam-5792	9	37	complete	complete	ADJ
ejpam-5792	9	38	metric	metric	ADJ
ejpam-5792	9	39	space	space	NOUN
ejpam-5792	9	40	.	.	PUNCT
ejpam-5792	10	1	due	due	ADP
ejpam-5792	10	2	to	to	ADP
ejpam-5792	10	3	various	various	ADJ
ejpam-5792	10	4	applications	application	NOUN
ejpam-5792	10	5	,	,	PUNCT
ejpam-5792	10	6	this	this	DET
ejpam-5792	10	7	result	result	NOUN
ejpam-5792	10	8	was	be	AUX
ejpam-5792	10	9	generalized	generalize	VERB
ejpam-5792	10	10	and	and	CCONJ
ejpam-5792	10	11	extended	extend	VERB
ejpam-5792	10	12	in	in	ADP
ejpam-5792	10	13	numerous	numerous	ADJ
ejpam-5792	10	14	ways	way	NOUN
ejpam-5792	10	15	(	(	PUNCT
ejpam-5792	10	16	see	see	VERB
ejpam-5792	10	17	,	,	PUNCT
ejpam-5792	10	18	for	for	ADP
ejpam-5792	10	19	instance	instance	NOUN
ejpam-5792	10	20	,	,	PUNCT
ejpam-5792	10	21	[	[	X
ejpam-5792	10	22	2–5	2–5	X
ejpam-5792	10	23	]	]	PUNCT
ejpam-5792	10	24	and	and	CCONJ
ejpam-5792	10	25	references	reference	NOUN
ejpam-5792	10	26	therein	therein	ADV
ejpam-5792	10	27	)	)	PUNCT
ejpam-5792	10	28	.	.	PUNCT
ejpam-5792	11	1	given	give	VERB
ejpam-5792	11	2	the	the	DET
ejpam-5792	11	3	continuity	continuity	NOUN
ejpam-5792	11	4	of	of	ADP
ejpam-5792	11	5	mappings	mapping	NOUN
ejpam-5792	11	6	satisfying	satisfy	VERB
ejpam-5792	11	7	the	the	DET
ejpam-5792	11	8	banach	banach	NOUN
ejpam-5792	11	9	contraction	contraction	NOUN
ejpam-5792	11	10	principle	principle	NOUN
ejpam-5792	11	11	,	,	PUNCT
ejpam-5792	11	12	a	a	DET
ejpam-5792	11	13	natural	natural	ADJ
ejpam-5792	11	14	question	question	NOUN
ejpam-5792	11	15	arose	arise	VERB
ejpam-5792	11	16	regarding	regard	VERB
ejpam-5792	11	17	the	the	DET
ejpam-5792	11	18	existence	existence	NOUN
ejpam-5792	11	19	of	of	ADP
ejpam-5792	11	20	fixed	fix	VERB
ejpam-5792	11	21	∗corresponding	∗corresponde	VERB
ejpam-5792	11	22	author	author	NOUN
ejpam-5792	11	23	.	.	PUNCT
ejpam-5792	12	1	doi	doi	NOUN
ejpam-5792	12	2	:	:	PUNCT
ejpam-5792	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5792	https://doi.org/10.29020/nybg.ejpam.v18i2.5792	ADJ
ejpam-5792	12	4	email	email	NOUN
ejpam-5792	12	5	addresses	address	NOUN
ejpam-5792	12	6	:	:	PUNCT
ejpam-5792	12	7	amitgangwar069@gmail.com	amitgangwar069@gmail.com	X
ejpam-5792	12	8	(	(	PUNCT
ejpam-5792	12	9	a.	a.	NOUN
ejpam-5792	12	10	gangwar	gangwar	PROPN
ejpam-5792	12	11	)	)	PUNCT
ejpam-5792	12	12	,	,	PUNCT
ejpam-5792	12	13	rawat.shivam09@gmail.com	rawat.shivam09@gmail.com	X
ejpam-5792	12	14	(	(	PUNCT
ejpam-5792	12	15	s.	s.	PROPN
ejpam-5792	12	16	rawat	rawat	PROPN
ejpam-5792	12	17	)	)	PUNCT
ejpam-5792	12	18	,	,	PUNCT
ejpam-5792	13	1	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-5792	13	2	(	(	PUNCT
ejpam-5792	13	3	h.	h.	PROPN
ejpam-5792	13	4	aydi	aydi	ADV
ejpam-5792	13	5	)	)	PUNCT
ejpam-5792	13	6	,	,	PUNCT
ejpam-5792	13	7	sjohani@psu.edu.sa	sjohani@psu.edu.sa	PROPN
ejpam-5792	13	8	(	(	PUNCT
ejpam-5792	13	9	s.	s.	PROPN
ejpam-5792	13	10	aljohani	aljohani	PROPN
ejpam-5792	13	11	)	)	PUNCT
ejpam-5792	13	12	,	,	PUNCT
ejpam-5792	13	13	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-5792	13	14	;	;	PUNCT
ejpam-5792	13	15	nmlaiki2012@gmail.com	nmlaiki2012@gmail.com	X
ejpam-5792	14	1	(	(	PUNCT
ejpam-5792	14	2	n.	n.	PROPN
ejpam-5792	14	3	mlaiki	mlaiki	PROPN
ejpam-5792	14	4	)	)	PUNCT
ejpam-5792	14	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5792	15	1	1	1	NUM
ejpam-5792	15	2	copyright	copyright	NOUN
ejpam-5792	15	3	:	:	PUNCT
ejpam-5792	15	4	©	©	PROPN
ejpam-5792	15	5	2025	2025	NUM
ejpam-5792	15	6	the	the	DET
ejpam-5792	15	7	author(s	author(s	NOUN
ejpam-5792	15	8	)	)	PUNCT
ejpam-5792	15	9	.	.	PUNCT
ejpam-5792	16	1	(	(	PUNCT
ejpam-5792	16	2	cc	cc	NOUN
ejpam-5792	16	3	by	by	ADP
ejpam-5792	16	4	-	-	PUNCT
ejpam-5792	16	5	nc	nc	PROPN
ejpam-5792	16	6	4.0	4.0	NUM
ejpam-5792	16	7	)	)	PUNCT
ejpam-5792	16	8	a.	a.	NOUN
ejpam-5792	16	9	gangwar	gangwar	NOUN
ejpam-5792	16	10	et	et	PROPN
ejpam-5792	16	11	al	al	PROPN
ejpam-5792	16	12	.	.	PUNCT
ejpam-5792	16	13	/	/	SYM
ejpam-5792	16	14	eur	eur	PROPN
ejpam-5792	16	15	.	.	PUNCT
ejpam-5792	17	1	j.	j.	PROPN
ejpam-5792	17	2	pure	pure	PROPN
ejpam-5792	17	3	appl	appl	PROPN
ejpam-5792	17	4	.	.	PROPN
ejpam-5792	17	5	math	math	PROPN
ejpam-5792	17	6	,	,	PUNCT
ejpam-5792	17	7	18	18	NUM
ejpam-5792	17	8	(	(	PUNCT
ejpam-5792	17	9	2	2	NUM
ejpam-5792	17	10	)	)	PUNCT
ejpam-5792	17	11	(	(	PUNCT
ejpam-5792	17	12	2025	2025	NUM
ejpam-5792	17	13	)	)	PUNCT
ejpam-5792	17	14	,	,	PUNCT
ejpam-5792	17	15	5792	5792	NUM
ejpam-5792	17	16	2	2	NUM
ejpam-5792	17	17	of	of	ADP
ejpam-5792	17	18	16	16	NUM
ejpam-5792	17	19	points	point	NOUN
ejpam-5792	17	20	of	of	ADP
ejpam-5792	17	21	discontinuous	discontinuous	ADJ
ejpam-5792	17	22	mappings	mapping	NOUN
ejpam-5792	17	23	that	that	PRON
ejpam-5792	17	24	satisfy	satisfy	VERB
ejpam-5792	17	25	similar	similar	ADJ
ejpam-5792	17	26	contractive	contractive	ADJ
ejpam-5792	17	27	criteria	criterion	NOUN
ejpam-5792	17	28	.	.	PUNCT
ejpam-5792	18	1	kannan	kannan	PROPN
ejpam-5792	18	2	[	[	X
ejpam-5792	18	3	6	6	NUM
ejpam-5792	18	4	]	]	PUNCT
ejpam-5792	18	5	provided	provide	VERB
ejpam-5792	18	6	an	an	DET
ejpam-5792	18	7	affirmative	affirmative	ADJ
ejpam-5792	18	8	response	response	NOUN
ejpam-5792	18	9	to	to	ADP
ejpam-5792	18	10	this	this	DET
ejpam-5792	18	11	inquiry	inquiry	NOUN
ejpam-5792	18	12	by	by	ADP
ejpam-5792	18	13	establishing	establish	VERB
ejpam-5792	18	14	a	a	DET
ejpam-5792	18	15	contractive	contractive	ADJ
ejpam-5792	18	16	condition	condition	NOUN
ejpam-5792	18	17	for	for	ADP
ejpam-5792	18	18	a	a	DET
ejpam-5792	18	19	discontinuous	discontinuous	ADJ
ejpam-5792	18	20	map	map	NOUN
ejpam-5792	18	21	t	t	NOUN
ejpam-5792	18	22	,	,	PUNCT
ejpam-5792	18	23	demonstrating	demonstrate	VERB
ejpam-5792	18	24	the	the	DET
ejpam-5792	18	25	existence	existence	NOUN
ejpam-5792	18	26	and	and	CCONJ
ejpam-5792	18	27	uniqueness	uniqueness	NOUN
ejpam-5792	18	28	of	of	ADP
ejpam-5792	18	29	fixed	fix	VERB
ejpam-5792	18	30	points	point	NOUN
ejpam-5792	18	31	within	within	ADP
ejpam-5792	18	32	the	the	DET
ejpam-5792	18	33	context	context	NOUN
ejpam-5792	18	34	of	of	ADP
ejpam-5792	18	35	complete	complete	ADJ
ejpam-5792	18	36	metric	metric	ADJ
ejpam-5792	18	37	spaces	space	NOUN
ejpam-5792	18	38	.	.	PUNCT
ejpam-5792	19	1	in	in	ADP
ejpam-5792	19	2	2018	2018	NUM
ejpam-5792	19	3	,	,	PUNCT
ejpam-5792	19	4	karapinar	karapinar	VERB
ejpam-5792	19	5	[	[	X
ejpam-5792	19	6	7	7	NUM
ejpam-5792	19	7	]	]	X
ejpam-5792	19	8	utilized	utilize	VERB
ejpam-5792	19	9	the	the	DET
ejpam-5792	19	10	interpolation	interpolation	NOUN
ejpam-5792	19	11	technique	technique	NOUN
ejpam-5792	19	12	to	to	PART
ejpam-5792	19	13	revisit	revisit	VERB
ejpam-5792	19	14	kannan	kannan	PROPN
ejpam-5792	19	15	type	type	NOUN
ejpam-5792	19	16	contractions	contraction	NOUN
ejpam-5792	19	17	.	.	PUNCT
ejpam-5792	20	1	prior	prior	ADV
ejpam-5792	20	2	to	to	ADP
ejpam-5792	20	3	[	[	X
ejpam-5792	20	4	7	7	NUM
ejpam-5792	20	5	]	]	PUNCT
ejpam-5792	20	6	,	,	PUNCT
ejpam-5792	20	7	interpolative	interpolative	ADJ
ejpam-5792	20	8	techniques	technique	NOUN
ejpam-5792	20	9	are	be	AUX
ejpam-5792	20	10	used	use	VERB
ejpam-5792	20	11	in	in	ADP
ejpam-5792	20	12	interpolation	interpolation	NOUN
ejpam-5792	20	13	theory	theory	NOUN
ejpam-5792	20	14	,	,	PUNCT
ejpam-5792	20	15	a	a	DET
ejpam-5792	20	16	field	field	NOUN
ejpam-5792	20	17	of	of	ADP
ejpam-5792	20	18	functional	functional	ADJ
ejpam-5792	20	19	analysis	analysis	NOUN
ejpam-5792	20	20	.	.	PUNCT
ejpam-5792	21	1	karapinar	karapinar	NOUN
ejpam-5792	22	1	[	[	X
ejpam-5792	22	2	7	7	NUM
ejpam-5792	22	3	]	]	PUNCT
ejpam-5792	22	4	formulated	formulate	VERB
ejpam-5792	22	5	the	the	DET
ejpam-5792	22	6	interpolative	interpolative	ADJ
ejpam-5792	22	7	kannan	kannan	PROPN
ejpam-5792	22	8	-	-	PUNCT
ejpam-5792	22	9	type	type	NOUN
ejpam-5792	22	10	contraction	contraction	NOUN
ejpam-5792	22	11	on	on	ADP
ejpam-5792	22	12	a	a	DET
ejpam-5792	22	13	complete	complete	ADJ
ejpam-5792	22	14	metric	metric	ADJ
ejpam-5792	22	15	space	space	NOUN
ejpam-5792	22	16	(	(	PUNCT
ejpam-5792	22	17	u	u	NOUN
ejpam-5792	22	18	,	,	PUNCT
ejpam-5792	22	19	ρ	ρ	PROPN
ejpam-5792	22	20	)	)	PUNCT
ejpam-5792	22	21	as	as	SCONJ
ejpam-5792	22	22	follows	follow	VERB
ejpam-5792	22	23	:	:	PUNCT
ejpam-5792	22	24	ρ(tx	ρ(tx	NUM
ejpam-5792	22	25	,	,	PUNCT
ejpam-5792	22	26	ty	ty	INTJ
ejpam-5792	22	27	)	)	PUNCT
ejpam-5792	22	28	≤	≤	NOUN
ejpam-5792	22	29	λ([ρ(x	λ([ρ(x	ADP
ejpam-5792	22	30	,	,	PUNCT
ejpam-5792	22	31	tx)]α.[ρ(y	tx)]α.[ρ(y	ADP
ejpam-5792	22	32	,	,	PUNCT
ejpam-5792	22	33	ty)]1−α	ty)]1−α	NOUN
ejpam-5792	22	34	)	)	PUNCT
ejpam-5792	22	35	,	,	PUNCT
ejpam-5792	22	36	for	for	ADP
ejpam-5792	22	37	each	each	DET
ejpam-5792	22	38	x	x	NOUN
ejpam-5792	22	39	,	,	PUNCT
ejpam-5792	22	40	y	y	PROPN
ejpam-5792	22	41	∈	∈	PROPN
ejpam-5792	22	42	u	u	NOUN
ejpam-5792	22	43	\fix(t	\fix(t	PROPN
ejpam-5792	22	44	)	)	PUNCT
ejpam-5792	22	45	,	,	PUNCT
ejpam-5792	22	46	where	where	SCONJ
ejpam-5792	22	47	fix(t	fix(t	PROPN
ejpam-5792	22	48	)	)	PUNCT
ejpam-5792	23	1	=	=	PRON
ejpam-5792	23	2	{	{	PUNCT
ejpam-5792	23	3	x	x	PUNCT
ejpam-5792	23	4	∈	∈	PROPN
ejpam-5792	23	5	u	u	NOUN
ejpam-5792	23	6	,	,	PUNCT
ejpam-5792	23	7	tx	tx	PROPN
ejpam-5792	23	8	=	=	PUNCT
ejpam-5792	23	9	x	x	X
ejpam-5792	23	10	}	}	PUNCT
ejpam-5792	23	11	and	and	CCONJ
ejpam-5792	23	12	λ	λ	X
ejpam-5792	23	13	∈	∈	PROPN
ejpam-5792	24	1	[	[	X
ejpam-5792	24	2	0	0	NUM
ejpam-5792	24	3	,	,	PUNCT
ejpam-5792	24	4	1	1	NUM
ejpam-5792	24	5	)	)	PUNCT
ejpam-5792	24	6	.	.	PUNCT
ejpam-5792	25	1	recent	recent	ADJ
ejpam-5792	25	2	studies	study	NOUN
ejpam-5792	25	3	in	in	ADP
ejpam-5792	25	4	the	the	DET
ejpam-5792	25	5	field	field	NOUN
ejpam-5792	25	6	of	of	ADP
ejpam-5792	25	7	interpolative	interpolative	ADJ
ejpam-5792	25	8	ćirić-reich	ćirić-reich	NOUN
ejpam-5792	25	9	-	-	PUNCT
ejpam-5792	25	10	rus	rus	NOUN
ejpam-5792	25	11	type	type	NOUN
ejpam-5792	25	12	contractions	contraction	NOUN
ejpam-5792	25	13	[	[	X
ejpam-5792	25	14	8–10	8–10	NOUN
ejpam-5792	25	15	]	]	PUNCT
ejpam-5792	25	16	and	and	CCONJ
ejpam-5792	25	17	meirkeeler	meirkeeler	NOUN
ejpam-5792	25	18	type	type	NOUN
ejpam-5792	25	19	contractions	contraction	NOUN
ejpam-5792	26	1	[	[	X
ejpam-5792	26	2	11	11	NUM
ejpam-5792	26	3	,	,	PUNCT
ejpam-5792	26	4	12	12	NUM
ejpam-5792	26	5	]	]	PUNCT
ejpam-5792	26	6	can	can	AUX
ejpam-5792	26	7	be	be	AUX
ejpam-5792	26	8	also	also	ADV
ejpam-5792	26	9	referred	refer	VERB
ejpam-5792	26	10	to	to	ADP
ejpam-5792	26	11	[	[	X
ejpam-5792	26	12	13	13	NUM
ejpam-5792	26	13	,	,	PUNCT
ejpam-5792	26	14	14	14	NUM
ejpam-5792	26	15	]	]	PUNCT
ejpam-5792	26	16	.	.	PUNCT
ejpam-5792	27	1	recently	recently	ADV
ejpam-5792	27	2	,	,	PUNCT
ejpam-5792	27	3	berinde	berinde	VERB
ejpam-5792	27	4	[	[	X
ejpam-5792	27	5	15	15	NUM
ejpam-5792	27	6	,	,	PUNCT
ejpam-5792	27	7	16	16	NUM
ejpam-5792	27	8	]	]	PUNCT
ejpam-5792	27	9	has	have	AUX
ejpam-5792	27	10	extended	extend	VERB
ejpam-5792	27	11	the	the	DET
ejpam-5792	27	12	literature	literature	NOUN
ejpam-5792	27	13	related	relate	VERB
ejpam-5792	27	14	to	to	ADP
ejpam-5792	27	15	banach	banach	NOUN
ejpam-5792	27	16	contraction	contraction	NOUN
ejpam-5792	27	17	principle	principle	NOUN
ejpam-5792	27	18	[	[	X
ejpam-5792	27	19	1	1	X
ejpam-5792	27	20	]	]	PUNCT
ejpam-5792	27	21	in	in	ADP
ejpam-5792	27	22	banach	banach	NOUN
ejpam-5792	27	23	spaces	space	NOUN
ejpam-5792	27	24	by	by	ADP
ejpam-5792	27	25	introducing	introduce	VERB
ejpam-5792	27	26	enriched	enriched	ADJ
ejpam-5792	27	27	contractions	contraction	NOUN
ejpam-5792	27	28	.	.	PUNCT
ejpam-5792	28	1	enriched	enrich	VERB
ejpam-5792	28	2	contractions	contraction	NOUN
ejpam-5792	28	3	[	[	X
ejpam-5792	28	4	17	17	NUM
ejpam-5792	28	5	]	]	PUNCT
ejpam-5792	28	6	refer	refer	VERB
ejpam-5792	28	7	to	to	ADP
ejpam-5792	28	8	self	self	NOUN
ejpam-5792	28	9	-	-	PUNCT
ejpam-5792	28	10	mappings	mapping	NOUN
ejpam-5792	28	11	t	t	NOUN
ejpam-5792	28	12	on	on	ADP
ejpam-5792	28	13	the	the	DET
ejpam-5792	28	14	structure	structure	NOUN
ejpam-5792	28	15	u	u	NOUN
ejpam-5792	28	16	of	of	ADP
ejpam-5792	28	17	a	a	DET
ejpam-5792	28	18	normed	normed	ADJ
ejpam-5792	28	19	linear	linear	ADJ
ejpam-5792	28	20	space	space	NOUN
ejpam-5792	28	21	(	(	PUNCT
ejpam-5792	28	22	u	u	NOUN
ejpam-5792	28	23	,	,	PUNCT
ejpam-5792	28	24	∥	∥	PROPN
ejpam-5792	28	25	.	.	PUNCT
ejpam-5792	29	1	∥	∥	NUM
ejpam-5792	29	2	)	)	PUNCT
ejpam-5792	29	3	.	.	PUNCT
ejpam-5792	30	1	these	these	DET
ejpam-5792	30	2	mappings	mapping	NOUN
ejpam-5792	30	3	adhere	adhere	VERB
ejpam-5792	30	4	to	to	ADP
ejpam-5792	30	5	a	a	DET
ejpam-5792	30	6	symmetric	symmetric	ADJ
ejpam-5792	30	7	contraction	contraction	NOUN
ejpam-5792	30	8	condition	condition	NOUN
ejpam-5792	30	9	,	,	PUNCT
ejpam-5792	30	10	expressed	express	VERB
ejpam-5792	30	11	as	as	ADP
ejpam-5792	30	12	∥	∥	PUNCT
ejpam-5792	30	13	b(x	b(x	NOUN
ejpam-5792	30	14	−	−	PROPN
ejpam-5792	30	15	y	y	PROPN
ejpam-5792	30	16	)	)	PUNCT
ejpam-5792	31	1	+	+	CCONJ
ejpam-5792	31	2	tx	tx	PROPN
ejpam-5792	31	3	−	−	PROPN
ejpam-5792	31	4	ty	ty	INTJ
ejpam-5792	31	5	∥≤	∥≤	PROPN
ejpam-5792	31	6	θ	θ	X
ejpam-5792	31	7	∥	∥	PUNCT
ejpam-5792	31	8	x	x	PUNCT
ejpam-5792	31	9	−	−	PROPN
ejpam-5792	31	10	y	y	PROPN
ejpam-5792	31	11	∥	∥	PROPN
ejpam-5792	31	12	,	,	PUNCT
ejpam-5792	31	13	where	where	SCONJ
ejpam-5792	31	14	b	b	X
ejpam-5792	31	15	∈	∈	PROPN
ejpam-5792	32	1	[	[	X
ejpam-5792	32	2	0,∞	0,∞	NOUN
ejpam-5792	32	3	)	)	PUNCT
ejpam-5792	32	4	and	and	CCONJ
ejpam-5792	32	5	θ	θ	PROPN
ejpam-5792	32	6	∈	∈	PROPN
ejpam-5792	33	1	[	[	X
ejpam-5792	33	2	0	0	NUM
ejpam-5792	33	3	,	,	PUNCT
ejpam-5792	33	4	b	b	NOUN
ejpam-5792	33	5	+	+	NOUN
ejpam-5792	33	6	1	1	NUM
ejpam-5792	33	7	)	)	PUNCT
ejpam-5792	33	8	,	,	PUNCT
ejpam-5792	33	9	for	for	ADP
ejpam-5792	33	10	each	each	DET
ejpam-5792	33	11	x	x	NOUN
ejpam-5792	33	12	,	,	PUNCT
ejpam-5792	33	13	y	y	PROPN
ejpam-5792	33	14	∈	∈	PROPN
ejpam-5792	33	15	u	u	PROPN
ejpam-5792	33	16	.	.	PUNCT
ejpam-5792	34	1	undoubtedly	undoubtedly	ADV
ejpam-5792	34	2	,	,	PUNCT
ejpam-5792	34	3	the	the	DET
ejpam-5792	34	4	category	category	NOUN
ejpam-5792	34	5	of	of	ADP
ejpam-5792	34	6	enriched	enriched	ADJ
ejpam-5792	34	7	contractions	contraction	NOUN
ejpam-5792	34	8	is	be	AUX
ejpam-5792	34	9	more	more	ADV
ejpam-5792	34	10	extensive	extensive	ADJ
ejpam-5792	34	11	,	,	PUNCT
ejpam-5792	34	12	encompassing	encompass	VERB
ejpam-5792	34	13	not	not	PART
ejpam-5792	34	14	only	only	ADV
ejpam-5792	34	15	the	the	DET
ejpam-5792	34	16	conventional	conventional	ADJ
ejpam-5792	34	17	banach	banach	NOUN
ejpam-5792	34	18	contractions	contraction	NOUN
ejpam-5792	34	19	(	(	PUNCT
ejpam-5792	34	20	where	where	SCONJ
ejpam-5792	34	21	b	b	NOUN
ejpam-5792	34	22	=	=	NOUN
ejpam-5792	34	23	0	0	NUM
ejpam-5792	34	24	)	)	PUNCT
ejpam-5792	34	25	but	but	CCONJ
ejpam-5792	34	26	also	also	ADV
ejpam-5792	34	27	incorporating	incorporate	VERB
ejpam-5792	34	28	lipschitztype	lipschitztype	ADJ
ejpam-5792	34	29	and	and	CCONJ
ejpam-5792	34	30	non	non	ADJ
ejpam-5792	34	31	-	-	ADJ
ejpam-5792	34	32	expansive	expansive	ADJ
ejpam-5792	34	33	mappings	mapping	NOUN
ejpam-5792	34	34	.	.	PUNCT
ejpam-5792	35	1	the	the	DET
ejpam-5792	35	2	broader	broad	ADJ
ejpam-5792	35	3	scope	scope	NOUN
ejpam-5792	35	4	of	of	ADP
ejpam-5792	35	5	the	the	DET
ejpam-5792	35	6	enriched	enriched	ADJ
ejpam-5792	35	7	contraction	contraction	NOUN
ejpam-5792	35	8	,	,	PUNCT
ejpam-5792	35	9	which	which	PRON
ejpam-5792	35	10	is	be	AUX
ejpam-5792	35	11	an	an	DET
ejpam-5792	35	12	extension	extension	NOUN
ejpam-5792	35	13	of	of	ADP
ejpam-5792	35	14	banach	banach	NOUN
ejpam-5792	35	15	contractions	contraction	NOUN
ejpam-5792	35	16	,	,	PUNCT
ejpam-5792	35	17	reinforces	reinforce	VERB
ejpam-5792	35	18	the	the	DET
ejpam-5792	35	19	assertion	assertion	NOUN
ejpam-5792	35	20	that	that	SCONJ
ejpam-5792	35	21	within	within	ADP
ejpam-5792	35	22	the	the	DET
ejpam-5792	35	23	banach	banach	NOUN
ejpam-5792	35	24	space	space	NOUN
ejpam-5792	35	25	context	context	NOUN
ejpam-5792	35	26	,	,	PUNCT
ejpam-5792	35	27	a	a	DET
ejpam-5792	35	28	fixed	fix	VERB
ejpam-5792	35	29	point	point	NOUN
ejpam-5792	35	30	x∗	x∗	PROPN
ejpam-5792	35	31	is	be	AUX
ejpam-5792	35	32	guaranteed	guarantee	VERB
ejpam-5792	35	33	to	to	PART
ejpam-5792	35	34	exist	exist	VERB
ejpam-5792	35	35	,	,	PUNCT
ejpam-5792	35	36	and	and	CCONJ
ejpam-5792	35	37	the	the	DET
ejpam-5792	35	38	krasnoselskij	krasnoselskij	PROPN
ejpam-5792	35	39	iteration	iteration	NOUN
ejpam-5792	35	40	offers	offer	VERB
ejpam-5792	35	41	an	an	DET
ejpam-5792	35	42	approach	approach	NOUN
ejpam-5792	35	43	to	to	PART
ejpam-5792	35	44	approximate	approximate	VERB
ejpam-5792	35	45	the	the	DET
ejpam-5792	35	46	fixed	fix	VERB
ejpam-5792	35	47	point	point	NOUN
ejpam-5792	35	48	.	.	PUNCT
ejpam-5792	36	1	this	this	DET
ejpam-5792	36	2	assertion	assertion	NOUN
ejpam-5792	36	3	has	have	AUX
ejpam-5792	36	4	been	be	AUX
ejpam-5792	36	5	substantiated	substantiate	VERB
ejpam-5792	36	6	by	by	ADP
ejpam-5792	36	7	berinde	berinde	NOUN
ejpam-5792	36	8	and	and	CCONJ
ejpam-5792	36	9	păcurar	păcurar	NOUN
ejpam-5792	36	10	[	[	NOUN
ejpam-5792	36	11	17	17	NUM
ejpam-5792	36	12	]	]	PUNCT
ejpam-5792	36	13	.	.	PUNCT
ejpam-5792	37	1	additionally	additionally	ADV
ejpam-5792	37	2	,	,	PUNCT
ejpam-5792	37	3	it	it	PRON
ejpam-5792	37	4	’s	’	VERB
ejpam-5792	37	5	worth	worth	ADJ
ejpam-5792	37	6	noting	note	VERB
ejpam-5792	37	7	that	that	SCONJ
ejpam-5792	37	8	contractive	contractive	ADJ
ejpam-5792	37	9	mappings	mapping	NOUN
ejpam-5792	37	10	of	of	ADP
ejpam-5792	37	11	kannan	kannan	PROPN
ejpam-5792	37	12	type	type	NOUN
ejpam-5792	37	13	and	and	CCONJ
ejpam-5792	37	14	of	of	ADP
ejpam-5792	37	15	chatterjea	chatterjea	ADJ
ejpam-5792	37	16	type	type	NOUN
ejpam-5792	37	17	,	,	PUNCT
ejpam-5792	37	18	can	can	AUX
ejpam-5792	37	19	similarly	similarly	ADV
ejpam-5792	37	20	be	be	AUX
ejpam-5792	37	21	enriched	enrich	VERB
ejpam-5792	37	22	,	,	PUNCT
ejpam-5792	37	23	as	as	SCONJ
ejpam-5792	37	24	discussed	discuss	VERB
ejpam-5792	37	25	in	in	ADP
ejpam-5792	37	26	[	[	X
ejpam-5792	37	27	18	18	NUM
ejpam-5792	37	28	,	,	PUNCT
ejpam-5792	37	29	19	19	NUM
ejpam-5792	37	30	]	]	PUNCT
ejpam-5792	37	31	.	.	PUNCT
ejpam-5792	38	1	in	in	ADP
ejpam-5792	38	2	2022	2022	NUM
ejpam-5792	38	3	,	,	PUNCT
ejpam-5792	38	4	rawat	rawat	PROPN
ejpam-5792	38	5	et	et	PROPN
ejpam-5792	38	6	al	al	PROPN
ejpam-5792	38	7	.	.	PUNCT
ejpam-5792	39	1	[	[	X
ejpam-5792	39	2	20	20	NUM
ejpam-5792	39	3	]	]	PUNCT
ejpam-5792	39	4	introduced	introduce	VERB
ejpam-5792	39	5	the	the	DET
ejpam-5792	39	6	notion	notion	NOUN
ejpam-5792	39	7	of	of	ADP
ejpam-5792	39	8	an	an	DET
ejpam-5792	39	9	enriched	enrich	VERB
ejpam-5792	39	10	ordered	order	VERB
ejpam-5792	39	11	contraction	contraction	NOUN
ejpam-5792	39	12	to	to	PART
ejpam-5792	39	13	prove	prove	VERB
ejpam-5792	39	14	some	some	DET
ejpam-5792	39	15	novel	novel	ADJ
ejpam-5792	39	16	fixed	fix	VERB
ejpam-5792	39	17	point	point	NOUN
ejpam-5792	39	18	theorems	theorem	NOUN
ejpam-5792	39	19	in	in	ADP
ejpam-5792	39	20	a	a	DET
ejpam-5792	39	21	convex	convex	ADJ
ejpam-5792	39	22	noncommutative	noncommutative	ADJ
ejpam-5792	39	23	banach	banach	NOUN
ejpam-5792	39	24	space	space	NOUN
ejpam-5792	39	25	.	.	PUNCT
ejpam-5792	40	1	recently	recently	ADV
ejpam-5792	40	2	,	,	PUNCT
ejpam-5792	40	3	gangwar	gangwar	VERB
ejpam-5792	40	4	et	et	PROPN
ejpam-5792	40	5	al	al	PROPN
ejpam-5792	40	6	.	.	PUNCT
ejpam-5792	41	1	[	[	X
ejpam-5792	41	2	21	21	NUM
ejpam-5792	41	3	]	]	X
ejpam-5792	41	4	defined	define	VERB
ejpam-5792	41	5	λ	λ	ADJ
ejpam-5792	41	6	-	-	ADJ
ejpam-5792	41	7	enriched	enrich	VERB
ejpam-5792	41	8	multivalued	multivalue	VERB
ejpam-5792	41	9	nonexpansive	nonexpansive	ADJ
ejpam-5792	41	10	mappings	mapping	NOUN
ejpam-5792	41	11	and	and	CCONJ
ejpam-5792	41	12	(	(	PUNCT
ejpam-5792	41	13	λ	λ	PROPN
ejpam-5792	41	14	,	,	PUNCT
ejpam-5792	41	15	θ)enriched	θ)enriche	VERB
ejpam-5792	41	16	multivalued	multivalued	ADJ
ejpam-5792	41	17	contractions	contraction	NOUN
ejpam-5792	41	18	on	on	ADP
ejpam-5792	41	19	a	a	DET
ejpam-5792	41	20	double	double	ADJ
ejpam-5792	41	21	controlled	control	VERB
ejpam-5792	41	22	metric	metric	ADJ
ejpam-5792	41	23	type	type	NOUN
ejpam-5792	41	24	space	space	NOUN
ejpam-5792	41	25	and	and	CCONJ
ejpam-5792	41	26	deduced	deduce	VERB
ejpam-5792	41	27	some	some	DET
ejpam-5792	41	28	novel	novel	ADJ
ejpam-5792	41	29	fixed	fix	VERB
ejpam-5792	41	30	point	point	NOUN
ejpam-5792	41	31	results	result	NOUN
ejpam-5792	41	32	along	along	ADP
ejpam-5792	41	33	with	with	ADP
ejpam-5792	41	34	an	an	DET
ejpam-5792	41	35	application	application	NOUN
ejpam-5792	41	36	to	to	ADP
ejpam-5792	41	37	differential	differential	ADJ
ejpam-5792	41	38	inclusions	inclusion	NOUN
ejpam-5792	41	39	.	.	PUNCT
ejpam-5792	42	1	nadler	nadler	NOUN
ejpam-5792	43	1	[	[	X
ejpam-5792	43	2	22	22	NUM
ejpam-5792	43	3	]	]	PUNCT
ejpam-5792	43	4	presented	present	VERB
ejpam-5792	43	5	a	a	DET
ejpam-5792	43	6	notable	notable	ADJ
ejpam-5792	43	7	and	and	CCONJ
ejpam-5792	43	8	widely	widely	ADV
ejpam-5792	43	9	acknowledged	acknowledge	VERB
ejpam-5792	43	10	extension	extension	NOUN
ejpam-5792	43	11	by	by	ADP
ejpam-5792	43	12	introducing	introduce	VERB
ejpam-5792	43	13	the	the	DET
ejpam-5792	43	14	notion	notion	NOUN
ejpam-5792	43	15	of	of	ADP
ejpam-5792	43	16	hausdorff	hausdorff	PROPN
ejpam-5792	43	17	metric	metric	PROPN
ejpam-5792	43	18	,	,	PUNCT
ejpam-5792	43	19	which	which	PRON
ejpam-5792	43	20	is	be	AUX
ejpam-5792	43	21	defined	define	VERB
ejpam-5792	43	22	over	over	ADP
ejpam-5792	43	23	a	a	DET
ejpam-5792	43	24	collection	collection	NOUN
ejpam-5792	43	25	of	of	ADP
ejpam-5792	43	26	bounded	bounded	ADJ
ejpam-5792	43	27	and	and	CCONJ
ejpam-5792	43	28	closed	closed	ADJ
ejpam-5792	43	29	subsets	subset	NOUN
ejpam-5792	43	30	on	on	ADP
ejpam-5792	43	31	a	a	DET
ejpam-5792	43	32	complete	complete	ADJ
ejpam-5792	43	33	metric	metric	ADJ
ejpam-5792	43	34	space	space	NOUN
ejpam-5792	43	35	.	.	PUNCT
ejpam-5792	44	1	he	he	PRON
ejpam-5792	44	2	laid	lay	VERB
ejpam-5792	44	3	the	the	DET
ejpam-5792	44	4	groundwork	groundwork	NOUN
ejpam-5792	44	5	for	for	ADP
ejpam-5792	44	6	multivalued	multivalued	ADJ
ejpam-5792	44	7	contraction	contraction	NOUN
ejpam-5792	44	8	mappings	mapping	NOUN
ejpam-5792	44	9	.	.	PUNCT
ejpam-5792	45	1	to	to	PART
ejpam-5792	45	2	facilitate	facilitate	VERB
ejpam-5792	45	3	understanding	understanding	NOUN
ejpam-5792	45	4	,	,	PUNCT
ejpam-5792	45	5	we	we	PRON
ejpam-5792	45	6	revisit	revisit	VERB
ejpam-5792	45	7	several	several	ADJ
ejpam-5792	45	8	standard	standard	ADJ
ejpam-5792	45	9	notations	notation	NOUN
ejpam-5792	45	10	and	and	CCONJ
ejpam-5792	45	11	terms	term	NOUN
ejpam-5792	45	12	.	.	PUNCT
ejpam-5792	46	1	consider	consider	VERB
ejpam-5792	46	2	a	a	DET
ejpam-5792	46	3	metric	metric	ADJ
ejpam-5792	46	4	space	space	NOUN
ejpam-5792	46	5	(	(	PUNCT
ejpam-5792	46	6	u	u	NOUN
ejpam-5792	46	7	,	,	PUNCT
ejpam-5792	46	8	ρ	ρ	PROPN
ejpam-5792	46	9	)	)	PUNCT
ejpam-5792	46	10	.	.	PUNCT
ejpam-5792	47	1	the	the	DET
ejpam-5792	47	2	set	set	NOUN
ejpam-5792	47	3	cb(u	cb(u	X
ejpam-5792	47	4	)	)	PUNCT
ejpam-5792	47	5	(	(	PUNCT
ejpam-5792	47	6	resp	resp	NOUN
ejpam-5792	47	7	.	.	PUNCT
ejpam-5792	48	1	c(u	c(u	NOUN
ejpam-5792	48	2	)	)	PUNCT
ejpam-5792	48	3	)	)	PUNCT
ejpam-5792	48	4	denotes	denote	VERB
ejpam-5792	48	5	the	the	DET
ejpam-5792	48	6	collection	collection	NOUN
ejpam-5792	48	7	of	of	ADP
ejpam-5792	48	8	those	those	DET
ejpam-5792	48	9	subsets	subset	NOUN
ejpam-5792	48	10	of	of	ADP
ejpam-5792	48	11	u	u	PRON
ejpam-5792	48	12	which	which	PRON
ejpam-5792	48	13	are	be	AUX
ejpam-5792	48	14	nonempty	nonempty	ADV
ejpam-5792	48	15	bounded	bound	VERB
ejpam-5792	48	16	and	and	CCONJ
ejpam-5792	48	17	closed	closed	ADJ
ejpam-5792	48	18	(	(	PUNCT
ejpam-5792	48	19	resp	resp	NOUN
ejpam-5792	48	20	.	.	PUNCT
ejpam-5792	49	1	compact	compact	ADJ
ejpam-5792	49	2	)	)	PUNCT
ejpam-5792	49	3	subsets	subset	NOUN
ejpam-5792	49	4	.	.	PUNCT
ejpam-5792	50	1	for	for	ADP
ejpam-5792	50	2	a	a	DET
ejpam-5792	50	3	,	,	PUNCT
ejpam-5792	50	4	b	b	PROPN
ejpam-5792	50	5	∈	∈	PROPN
ejpam-5792	50	6	cb(u	cb(u	PUNCT
ejpam-5792	50	7	)	)	PUNCT
ejpam-5792	50	8	,	,	PUNCT
ejpam-5792	50	9	h	h	NOUN
ejpam-5792	50	10	:	:	PUNCT
ejpam-5792	50	11	cb(u	cb(u	X
ejpam-5792	50	12	)	)	PUNCT
ejpam-5792	50	13	×	×	NOUN
ejpam-5792	50	14	cb(u	cb(u	X
ejpam-5792	50	15	)	)	PUNCT
ejpam-5792	50	16	→	→	PUNCT
ejpam-5792	51	1	[	[	X
ejpam-5792	51	2	0,+∞	0,+∞	NUM
ejpam-5792	51	3	)	)	PUNCT
ejpam-5792	51	4	defined	define	VERB
ejpam-5792	51	5	as	as	ADP
ejpam-5792	51	6	h(a	h(a	PROPN
ejpam-5792	51	7	,	,	PUNCT
ejpam-5792	51	8	b	b	NOUN
ejpam-5792	51	9	)	)	PUNCT
ejpam-5792	51	10	=	=	SYM
ejpam-5792	51	11	max{d∗(a	max{d∗(a	PROPN
ejpam-5792	51	12	,	,	PUNCT
ejpam-5792	51	13	b),d∗(b	b),d∗(b	PROPN
ejpam-5792	51	14	,	,	PUNCT
ejpam-5792	51	15	a	a	PRON
ejpam-5792	51	16	)	)	PUNCT
ejpam-5792	51	17	}	}	PUNCT
ejpam-5792	51	18	,	,	PUNCT
ejpam-5792	51	19	where	where	SCONJ
ejpam-5792	51	20	d∗(a	d∗(a	PROPN
ejpam-5792	51	21	,	,	PUNCT
ejpam-5792	51	22	b	b	NOUN
ejpam-5792	51	23	)	)	PUNCT
ejpam-5792	51	24	=	=	SYM
ejpam-5792	51	25	sup	sup	NOUN
ejpam-5792	51	26	a∈a	a∈a	VERB
ejpam-5792	51	27	inf	inf	PROPN
ejpam-5792	51	28	b∈b	b∈b	NOUN
ejpam-5792	51	29	ρ(a	ρ(a	PROPN
ejpam-5792	51	30	,	,	PUNCT
ejpam-5792	51	31	b	b	NOUN
ejpam-5792	51	32	)	)	PUNCT
ejpam-5792	51	33	,	,	PUNCT
ejpam-5792	51	34	is	be	AUX
ejpam-5792	51	35	known	know	VERB
ejpam-5792	51	36	as	as	ADP
ejpam-5792	51	37	the	the	DET
ejpam-5792	51	38	hausdorff	hausdorff	PROPN
ejpam-5792	51	39	metric	metric	PROPN
ejpam-5792	51	40	.	.	PUNCT
ejpam-5792	52	1	nadler	nadler	PROPN
ejpam-5792	52	2	formulated	formulate	VERB
ejpam-5792	52	3	a	a	DET
ejpam-5792	52	4	theorem	theorem	NOUN
ejpam-5792	52	5	for	for	ADP
ejpam-5792	52	6	fixed	fix	VERB
ejpam-5792	52	7	points	point	NOUN
ejpam-5792	52	8	applicable	applicable	ADJ
ejpam-5792	52	9	to	to	PART
ejpam-5792	52	10	set	set	VERB
ejpam-5792	52	11	-	-	PUNCT
ejpam-5792	52	12	valued	value	VERB
ejpam-5792	52	13	mappings	mapping	NOUN
ejpam-5792	52	14	satisfying	satisfy	VERB
ejpam-5792	52	15	a	a	DET
ejpam-5792	52	16	symmetric	symmetric	ADJ
ejpam-5792	52	17	contraction	contraction	NOUN
ejpam-5792	52	18	condition	condition	NOUN
ejpam-5792	52	19	.	.	PUNCT
ejpam-5792	53	1	takahashi	takahashi	PROPN
ejpam-5792	54	1	[	[	X
ejpam-5792	54	2	23	23	NUM
ejpam-5792	54	3	]	]	PUNCT
ejpam-5792	54	4	defined	define	VERB
ejpam-5792	54	5	a	a	DET
ejpam-5792	54	6	convex	convex	NOUN
ejpam-5792	54	7	structure	structure	NOUN
ejpam-5792	54	8	in	in	ADP
ejpam-5792	54	9	a	a	DET
ejpam-5792	54	10	metric	metric	ADJ
ejpam-5792	54	11	space	space	NOUN
ejpam-5792	54	12	and	and	CCONJ
ejpam-5792	54	13	referred	refer	VERB
ejpam-5792	54	14	to	to	ADP
ejpam-5792	54	15	it	it	PRON
ejpam-5792	54	16	as	as	ADP
ejpam-5792	54	17	a	a	DET
ejpam-5792	54	18	convex	convex	ADJ
ejpam-5792	54	19	metric	metric	ADJ
ejpam-5792	54	20	space	space	NOUN
ejpam-5792	54	21	.	.	PUNCT
ejpam-5792	55	1	takahashi	takahashi	PROPN
ejpam-5792	55	2	also	also	ADV
ejpam-5792	55	3	a.	a.	PROPN
ejpam-5792	55	4	gangwar	gangwar	PROPN
ejpam-5792	55	5	et	et	PROPN
ejpam-5792	55	6	al	al	PROPN
ejpam-5792	55	7	.	.	PUNCT
ejpam-5792	55	8	/	/	SYM
ejpam-5792	55	9	eur	eur	PROPN
ejpam-5792	55	10	.	.	PUNCT
ejpam-5792	56	1	j.	j.	PROPN
ejpam-5792	56	2	pure	pure	PROPN
ejpam-5792	56	3	appl	appl	PROPN
ejpam-5792	56	4	.	.	PROPN
ejpam-5792	56	5	math	math	PROPN
ejpam-5792	56	6	,	,	PUNCT
ejpam-5792	56	7	18	18	NUM
ejpam-5792	56	8	(	(	PUNCT
ejpam-5792	56	9	2	2	NUM
ejpam-5792	56	10	)	)	PUNCT
ejpam-5792	56	11	(	(	PUNCT
ejpam-5792	56	12	2025	2025	NUM
ejpam-5792	56	13	)	)	PUNCT
ejpam-5792	56	14	,	,	PUNCT
ejpam-5792	56	15	5792	5792	NUM
ejpam-5792	56	16	3	3	NUM
ejpam-5792	56	17	of	of	ADP
ejpam-5792	56	18	16	16	NUM
ejpam-5792	56	19	studied	study	VERB
ejpam-5792	56	20	various	various	ADJ
ejpam-5792	56	21	characteristics	characteristic	NOUN
ejpam-5792	56	22	of	of	ADP
ejpam-5792	56	23	this	this	DET
ejpam-5792	56	24	metric	metric	ADJ
ejpam-5792	56	25	space	space	NOUN
ejpam-5792	56	26	to	to	PART
ejpam-5792	56	27	conclude	conclude	VERB
ejpam-5792	56	28	the	the	PRON
ejpam-5792	56	29	that	that	SCONJ
ejpam-5792	56	30	a	a	DET
ejpam-5792	56	31	fixed	fix	VERB
ejpam-5792	56	32	point	point	NOUN
ejpam-5792	56	33	exists	exist	VERB
ejpam-5792	56	34	for	for	ADP
ejpam-5792	56	35	nonexpansive	nonexpansive	ADJ
ejpam-5792	56	36	mappings	mapping	NOUN
ejpam-5792	56	37	in	in	ADP
ejpam-5792	56	38	the	the	DET
ejpam-5792	56	39	framework	framework	NOUN
ejpam-5792	56	40	of	of	ADP
ejpam-5792	56	41	a	a	DET
ejpam-5792	56	42	convex	convex	ADJ
ejpam-5792	56	43	metric	metric	ADJ
ejpam-5792	56	44	space	space	NOUN
ejpam-5792	56	45	.	.	PUNCT
ejpam-5792	57	1	very	very	ADV
ejpam-5792	57	2	recently	recently	ADV
ejpam-5792	57	3	,	,	PUNCT
ejpam-5792	57	4	rawat	rawat	PROPN
ejpam-5792	57	5	et	et	PROPN
ejpam-5792	57	6	al	al	PROPN
ejpam-5792	57	7	.	.	PUNCT
ejpam-5792	58	1	[	[	X
ejpam-5792	58	2	24	24	NUM
ejpam-5792	58	3	]	]	PUNCT
ejpam-5792	58	4	enriched	enrich	VERB
ejpam-5792	58	5	three	three	NUM
ejpam-5792	58	6	types	type	NOUN
ejpam-5792	58	7	of	of	ADP
ejpam-5792	58	8	existing	exist	VERB
ejpam-5792	58	9	interpolative	interpolative	ADJ
ejpam-5792	58	10	contractions	contraction	NOUN
ejpam-5792	58	11	(	(	PUNCT
ejpam-5792	58	12	kannan	kannan	PROPN
ejpam-5792	58	13	,	,	PUNCT
ejpam-5792	58	14	hardy	hardy	ADJ
ejpam-5792	58	15	-	-	PUNCT
ejpam-5792	58	16	rogers	roger	NOUN
ejpam-5792	58	17	and	and	CCONJ
ejpam-5792	58	18	matkowski	matkowski	PROPN
ejpam-5792	58	19	)	)	PUNCT
ejpam-5792	58	20	in	in	ADP
ejpam-5792	58	21	the	the	DET
ejpam-5792	58	22	context	context	NOUN
ejpam-5792	58	23	of	of	ADP
ejpam-5792	58	24	a	a	DET
ejpam-5792	58	25	convex	convex	ADJ
ejpam-5792	58	26	metric	metric	ADJ
ejpam-5792	58	27	space	space	NOUN
ejpam-5792	58	28	.	.	PUNCT
ejpam-5792	59	1	in	in	ADP
ejpam-5792	59	2	2015	2015	NUM
ejpam-5792	59	3	,	,	PUNCT
ejpam-5792	59	4	khojasteh	khojasteh	PROPN
ejpam-5792	59	5	et	et	PROPN
ejpam-5792	59	6	al	al	PROPN
ejpam-5792	59	7	.	.	PUNCT
ejpam-5792	60	1	[	[	X
ejpam-5792	60	2	25	25	NUM
ejpam-5792	60	3	]	]	PUNCT
ejpam-5792	60	4	presented	present	VERB
ejpam-5792	60	5	a	a	DET
ejpam-5792	60	6	novel	novel	ADJ
ejpam-5792	60	7	approach	approach	NOUN
ejpam-5792	60	8	to	to	ADP
ejpam-5792	60	9	examining	examine	VERB
ejpam-5792	60	10	fixed	fix	VERB
ejpam-5792	60	11	points	point	NOUN
ejpam-5792	60	12	by	by	ADP
ejpam-5792	60	13	introducing	introduce	VERB
ejpam-5792	60	14	a	a	DET
ejpam-5792	60	15	simulation	simulation	NOUN
ejpam-5792	60	16	function	function	NOUN
ejpam-5792	60	17	.	.	PUNCT
ejpam-5792	61	1	they	they	PRON
ejpam-5792	61	2	introduced	introduce	VERB
ejpam-5792	61	3	a	a	DET
ejpam-5792	61	4	new	new	ADJ
ejpam-5792	61	5	type	type	NOUN
ejpam-5792	61	6	of	of	ADP
ejpam-5792	61	7	contraction	contraction	NOUN
ejpam-5792	61	8	mappings	mapping	NOUN
ejpam-5792	61	9	known	know	VERB
ejpam-5792	61	10	as	as	ADP
ejpam-5792	61	11	z	z	NOUN
ejpam-5792	61	12	-	-	PUNCT
ejpam-5792	61	13	contractions	contraction	NOUN
ejpam-5792	61	14	.	.	PUNCT
ejpam-5792	62	1	subsequently	subsequently	ADV
ejpam-5792	62	2	,	,	PUNCT
ejpam-5792	62	3	other	other	ADJ
ejpam-5792	62	4	prominent	prominent	ADJ
ejpam-5792	62	5	researchers	researcher	NOUN
ejpam-5792	62	6	utilized	utilize	VERB
ejpam-5792	62	7	the	the	DET
ejpam-5792	62	8	concept	concept	NOUN
ejpam-5792	62	9	of	of	ADP
ejpam-5792	62	10	z	z	NOUN
ejpam-5792	62	11	-	-	PUNCT
ejpam-5792	62	12	contractions	contraction	NOUN
ejpam-5792	62	13	to	to	PART
ejpam-5792	62	14	explore	explore	VERB
ejpam-5792	62	15	common	common	ADJ
ejpam-5792	62	16	fixed	fix	VERB
ejpam-5792	62	17	points	point	NOUN
ejpam-5792	62	18	and	and	CCONJ
ejpam-5792	62	19	coincidence	coincidence	NOUN
ejpam-5792	62	20	points	point	NOUN
ejpam-5792	62	21	in	in	ADP
ejpam-5792	62	22	various	various	ADJ
ejpam-5792	62	23	metric	metric	ADJ
ejpam-5792	62	24	space	space	NOUN
ejpam-5792	62	25	settings	setting	NOUN
ejpam-5792	62	26	.	.	PUNCT
ejpam-5792	63	1	de	de	PROPN
ejpam-5792	63	2	hierro	hierro	PROPN
ejpam-5792	63	3	et	et	PROPN
ejpam-5792	63	4	al	al	PROPN
ejpam-5792	63	5	.	.	PUNCT
ejpam-5792	64	1	[	[	X
ejpam-5792	64	2	26	26	NUM
ejpam-5792	64	3	]	]	PUNCT
ejpam-5792	64	4	incorporated	incorporate	VERB
ejpam-5792	64	5	the	the	DET
ejpam-5792	64	6	notion	notion	NOUN
ejpam-5792	64	7	of	of	ADP
ejpam-5792	64	8	z	z	NOUN
ejpam-5792	64	9	-	-	PUNCT
ejpam-5792	64	10	contractions	contraction	NOUN
ejpam-5792	64	11	to	to	PART
ejpam-5792	64	12	establish	establish	VERB
ejpam-5792	64	13	results	result	NOUN
ejpam-5792	64	14	on	on	ADP
ejpam-5792	64	15	coincidence	coincidence	NOUN
ejpam-5792	64	16	points	point	NOUN
ejpam-5792	64	17	in	in	ADP
ejpam-5792	64	18	metric	metric	ADJ
ejpam-5792	64	19	spaces	space	NOUN
ejpam-5792	64	20	.	.	PUNCT
ejpam-5792	65	1	additionally	additionally	ADV
ejpam-5792	65	2	,	,	PUNCT
ejpam-5792	65	3	argoubi	argoubi	ADV
ejpam-5792	65	4	et	et	NOUN
ejpam-5792	65	5	al	al	PROPN
ejpam-5792	65	6	.	.	PUNCT
ejpam-5792	66	1	[	[	X
ejpam-5792	66	2	27	27	NUM
ejpam-5792	66	3	]	]	PUNCT
ejpam-5792	66	4	demonstrated	demonstrate	VERB
ejpam-5792	66	5	results	result	NOUN
ejpam-5792	66	6	within	within	ADP
ejpam-5792	66	7	the	the	DET
ejpam-5792	66	8	framework	framework	NOUN
ejpam-5792	66	9	of	of	ADP
ejpam-5792	66	10	partially	partially	ADV
ejpam-5792	66	11	ordered	order	VERB
ejpam-5792	66	12	metric	metric	ADJ
ejpam-5792	66	13	spaces	space	NOUN
ejpam-5792	66	14	by	by	ADP
ejpam-5792	66	15	employing	employ	VERB
ejpam-5792	66	16	some	some	DET
ejpam-5792	66	17	non	non	ADJ
ejpam-5792	66	18	-	-	ADJ
ejpam-5792	66	19	linear	linear	ADJ
ejpam-5792	66	20	contractions	contraction	NOUN
ejpam-5792	66	21	based	base	VERB
ejpam-5792	66	22	on	on	ADP
ejpam-5792	66	23	simulation	simulation	NOUN
ejpam-5792	66	24	functions	function	NOUN
ejpam-5792	66	25	.	.	PUNCT
ejpam-5792	67	1	inspired	inspire	VERB
ejpam-5792	67	2	by	by	ADP
ejpam-5792	67	3	the	the	DET
ejpam-5792	67	4	results	result	NOUN
ejpam-5792	67	5	mentioned	mention	VERB
ejpam-5792	67	6	earlier	early	ADV
ejpam-5792	67	7	,	,	PUNCT
ejpam-5792	67	8	this	this	DET
ejpam-5792	67	9	study	study	NOUN
ejpam-5792	67	10	introduces	introduce	VERB
ejpam-5792	67	11	enriched	enrich	VERB
ejpam-5792	67	12	interpolative	interpolative	ADJ
ejpam-5792	67	13	kannan	kannan	PROPN
ejpam-5792	67	14	type	type	NOUN
ejpam-5792	67	15	contractions	contraction	NOUN
ejpam-5792	67	16	(	(	PUNCT
ejpam-5792	67	17	eik	eik	NOUN
ejpam-5792	67	18	-	-	PUNCT
ejpam-5792	67	19	contractions	contraction	NOUN
ejpam-5792	67	20	)	)	PUNCT
ejpam-5792	67	21	and	and	CCONJ
ejpam-5792	67	22	enriched	enrich	VERB
ejpam-5792	67	23	interpolative	interpolative	ADJ
ejpam-5792	67	24	hardy	hardy	ADJ
ejpam-5792	67	25	-	-	PUNCT
ejpam-5792	67	26	rogers	rogers	NOUN
ejpam-5792	67	27	type	type	NOUN
ejpam-5792	67	28	contractions	contraction	NOUN
ejpam-5792	67	29	(	(	PUNCT
ejpam-5792	67	30	eihr	eihr	NOUN
ejpam-5792	67	31	-	-	PUNCT
ejpam-5792	67	32	contractions	contraction	NOUN
ejpam-5792	67	33	)	)	PUNCT
ejpam-5792	67	34	for	for	ADP
ejpam-5792	67	35	multivalued	multivalued	ADJ
ejpam-5792	67	36	mappings	mapping	NOUN
ejpam-5792	67	37	via	via	ADP
ejpam-5792	67	38	a	a	DET
ejpam-5792	67	39	simulation	simulation	NOUN
ejpam-5792	67	40	function	function	NOUN
ejpam-5792	67	41	.	.	PUNCT
ejpam-5792	68	1	the	the	DET
ejpam-5792	68	2	research	research	NOUN
ejpam-5792	68	3	also	also	ADV
ejpam-5792	68	4	establishes	establish	VERB
ejpam-5792	68	5	several	several	ADJ
ejpam-5792	68	6	fixed	fix	VERB
ejpam-5792	68	7	-	-	PUNCT
ejpam-5792	68	8	point	point	NOUN
ejpam-5792	68	9	theorems	theorem	NOUN
ejpam-5792	68	10	utilizing	utilize	VERB
ejpam-5792	68	11	multivalued	multivalued	ADJ
ejpam-5792	68	12	mappings	mapping	NOUN
ejpam-5792	68	13	by	by	ADP
ejpam-5792	68	14	employing	employ	VERB
ejpam-5792	68	15	these	these	DET
ejpam-5792	68	16	contractions	contraction	NOUN
ejpam-5792	68	17	.	.	PUNCT
ejpam-5792	69	1	to	to	PART
ejpam-5792	69	2	support	support	VERB
ejpam-5792	69	3	our	our	PRON
ejpam-5792	69	4	findings	finding	NOUN
ejpam-5792	69	5	,	,	PUNCT
ejpam-5792	69	6	illustrative	illustrative	ADJ
ejpam-5792	69	7	examples	example	NOUN
ejpam-5792	69	8	are	be	AUX
ejpam-5792	69	9	also	also	ADV
ejpam-5792	69	10	provided	provide	VERB
ejpam-5792	69	11	.	.	PUNCT
ejpam-5792	70	1	as	as	ADP
ejpam-5792	70	2	a	a	DET
ejpam-5792	70	3	consequence	consequence	NOUN
ejpam-5792	70	4	of	of	ADP
ejpam-5792	70	5	each	each	DET
ejpam-5792	70	6	main	main	ADJ
ejpam-5792	70	7	result	result	NOUN
ejpam-5792	70	8	,	,	PUNCT
ejpam-5792	70	9	a	a	DET
ejpam-5792	70	10	theorem	theorem	NOUN
ejpam-5792	70	11	on	on	ADP
ejpam-5792	70	12	data	datum	NOUN
ejpam-5792	70	13	dependence	dependence	NOUN
ejpam-5792	70	14	of	of	ADP
ejpam-5792	70	15	fixed	fix	VERB
ejpam-5792	70	16	point	point	NOUN
ejpam-5792	70	17	is	be	AUX
ejpam-5792	70	18	proved	prove	VERB
ejpam-5792	70	19	.	.	PUNCT
ejpam-5792	71	1	2	2	X
ejpam-5792	71	2	.	.	X
ejpam-5792	71	3	preliminaries	preliminary	NOUN
ejpam-5792	71	4	khojasteh	khojasteh	PROPN
ejpam-5792	71	5	et	et	PROPN
ejpam-5792	71	6	.	.	PUNCT
ejpam-5792	72	1	al	al	PROPN
ejpam-5792	72	2	.	.	PUNCT
ejpam-5792	73	1	[	[	X
ejpam-5792	73	2	25	25	NUM
ejpam-5792	73	3	]	]	PUNCT
ejpam-5792	73	4	introduced	introduce	VERB
ejpam-5792	73	5	a	a	DET
ejpam-5792	73	6	new	new	ADJ
ejpam-5792	73	7	approach	approach	NOUN
ejpam-5792	73	8	in	in	ADP
ejpam-5792	73	9	fixed	fix	VERB
ejpam-5792	73	10	point	point	NOUN
ejpam-5792	73	11	theory	theory	NOUN
ejpam-5792	73	12	by	by	ADP
ejpam-5792	73	13	using	use	VERB
ejpam-5792	73	14	the	the	DET
ejpam-5792	73	15	concept	concept	NOUN
ejpam-5792	73	16	of	of	ADP
ejpam-5792	73	17	a	a	DET
ejpam-5792	73	18	simulation	simulation	NOUN
ejpam-5792	73	19	function	function	NOUN
ejpam-5792	73	20	and	and	CCONJ
ejpam-5792	73	21	thus	thus	ADV
ejpam-5792	73	22	generalized	generalize	VERB
ejpam-5792	73	23	many	many	ADJ
ejpam-5792	73	24	known	know	VERB
ejpam-5792	73	25	results	result	NOUN
ejpam-5792	73	26	,	,	PUNCT
ejpam-5792	73	27	starting	start	VERB
ejpam-5792	73	28	with	with	ADP
ejpam-5792	73	29	banach	banach	NOUN
ejpam-5792	73	30	contraction	contraction	NOUN
ejpam-5792	73	31	principle	principle	NOUN
ejpam-5792	73	32	.	.	PUNCT
ejpam-5792	74	1	a	a	DET
ejpam-5792	74	2	simulation	simulation	NOUN
ejpam-5792	74	3	function	function	NOUN
ejpam-5792	74	4	is	be	AUX
ejpam-5792	74	5	a	a	DET
ejpam-5792	74	6	function	function	NOUN
ejpam-5792	74	7	ζ	ζ	NOUN
ejpam-5792	74	8	:	:	PUNCT
ejpam-5792	75	1	[	[	X
ejpam-5792	75	2	0,∞)×	0,∞)×	NUM
ejpam-5792	75	3	[	[	X
ejpam-5792	75	4	0,∞	0,∞	NUM
ejpam-5792	75	5	)	)	PUNCT
ejpam-5792	75	6	→	→	SYM
ejpam-5792	75	7	r	r	NOUN
ejpam-5792	75	8	satisfying	satisfy	VERB
ejpam-5792	75	9	the	the	DET
ejpam-5792	75	10	following	follow	VERB
ejpam-5792	75	11	three	three	NUM
ejpam-5792	75	12	conditions	condition	NOUN
ejpam-5792	75	13	:	:	PUNCT
ejpam-5792	75	14	(	(	PUNCT
ejpam-5792	75	15	ζ1	ζ1	NOUN
ejpam-5792	75	16	)	)	PUNCT
ejpam-5792	75	17	ζ(0	ζ(0	NOUN
ejpam-5792	75	18	,	,	PUNCT
ejpam-5792	75	19	0	0	NUM
ejpam-5792	75	20	)	)	PUNCT
ejpam-5792	75	21	=	=	SYM
ejpam-5792	75	22	0	0	NUM
ejpam-5792	75	23	;	;	PUNCT
ejpam-5792	75	24	(	(	PUNCT
ejpam-5792	75	25	ζ2	ζ2	NOUN
ejpam-5792	75	26	)	)	PUNCT
ejpam-5792	75	27	ζ(x	ζ(x	NOUN
ejpam-5792	75	28	,	,	PUNCT
ejpam-5792	75	29	y	y	NOUN
ejpam-5792	75	30	)	)	PUNCT
ejpam-5792	75	31	<	<	X
ejpam-5792	75	32	y	y	PROPN
ejpam-5792	75	33	−	−	PROPN
ejpam-5792	75	34	x	x	NOUN
ejpam-5792	75	35	,	,	PUNCT
ejpam-5792	75	36	∀	∀	X
ejpam-5792	75	37	x	x	NOUN
ejpam-5792	75	38	,	,	PUNCT
ejpam-5792	75	39	y	y	PROPN
ejpam-5792	75	40	>	>	X
ejpam-5792	75	41	0	0	NUM
ejpam-5792	75	42	;	;	PUNCT
ejpam-5792	75	43	(	(	PUNCT
ejpam-5792	75	44	ζ3	ζ3	NOUN
ejpam-5792	75	45	)	)	PUNCT
ejpam-5792	75	46	if	if	SCONJ
ejpam-5792	75	47	sequences	sequence	NOUN
ejpam-5792	75	48	{	{	PUNCT
ejpam-5792	75	49	xn	xn	NUM
ejpam-5792	75	50	}	}	PUNCT
ejpam-5792	75	51	and	and	CCONJ
ejpam-5792	75	52	{	{	PUNCT
ejpam-5792	75	53	yn	yn	NOUN
ejpam-5792	75	54	}	}	PUNCT
ejpam-5792	75	55	in	in	ADP
ejpam-5792	75	56	the	the	DET
ejpam-5792	75	57	interval	interval	NOUN
ejpam-5792	75	58	[	[	X
ejpam-5792	75	59	0,∞	0,∞	X
ejpam-5792	75	60	)	)	PUNCT
ejpam-5792	75	61	satisfy	satisfy	NOUN
ejpam-5792	75	62	limn→∞	limn→∞	PROPN
ejpam-5792	75	63	xn	xn	PUNCT
ejpam-5792	76	1	=	=	SYM
ejpam-5792	76	2	limn→∞	limn→∞	PROPN
ejpam-5792	76	3	yn	yn	X
ejpam-5792	76	4	>	>	X
ejpam-5792	76	5	0	0	PROPN
ejpam-5792	76	6	,	,	PUNCT
ejpam-5792	76	7	then	then	ADV
ejpam-5792	76	8	lim	lim	PROPN
ejpam-5792	76	9	n→∞	n→∞	NUM
ejpam-5792	76	10	sup	sup	NOUN
ejpam-5792	76	11	ζ(xn	ζ(xn	NOUN
ejpam-5792	76	12	,	,	PUNCT
ejpam-5792	76	13	yn	yn	PROPN
ejpam-5792	76	14	)	)	PUNCT
ejpam-5792	76	15	<	<	X
ejpam-5792	76	16	0	0	X
ejpam-5792	76	17	.	.	PUNCT
ejpam-5792	77	1	the	the	DET
ejpam-5792	77	2	collection	collection	NOUN
ejpam-5792	77	3	of	of	ADP
ejpam-5792	77	4	all	all	DET
ejpam-5792	77	5	simulation	simulation	NOUN
ejpam-5792	77	6	functions	function	NOUN
ejpam-5792	77	7	will	will	AUX
ejpam-5792	77	8	be	be	AUX
ejpam-5792	77	9	denoted	denote	VERB
ejpam-5792	77	10	by	by	ADP
ejpam-5792	77	11	z.	z.	PROPN
ejpam-5792	77	12	definition	definition	NOUN
ejpam-5792	77	13	1	1	NUM
ejpam-5792	77	14	.	.	PUNCT
ejpam-5792	77	15	consider	consider	VERB
ejpam-5792	77	16	a	a	DET
ejpam-5792	77	17	self	self	NOUN
ejpam-5792	77	18	-	-	PUNCT
ejpam-5792	77	19	mapping	mapping	NOUN
ejpam-5792	77	20	t	t	NOUN
ejpam-5792	77	21	on	on	ADP
ejpam-5792	77	22	a	a	DET
ejpam-5792	77	23	metric	metric	ADJ
ejpam-5792	77	24	space	space	NOUN
ejpam-5792	77	25	(	(	PUNCT
ejpam-5792	77	26	u	u	NOUN
ejpam-5792	77	27	,	,	PUNCT
ejpam-5792	77	28	ρ	ρ	PROPN
ejpam-5792	77	29	)	)	PUNCT
ejpam-5792	77	30	.	.	PUNCT
ejpam-5792	78	1	if	if	SCONJ
ejpam-5792	78	2	for	for	ADP
ejpam-5792	78	3	each	each	DET
ejpam-5792	78	4	x	x	NOUN
ejpam-5792	78	5	,	,	PUNCT
ejpam-5792	78	6	y	y	PROPN
ejpam-5792	78	7	∈	∈	PROPN
ejpam-5792	78	8	u	u	X
ejpam-5792	78	9	ζ(ρ(tx	ζ(ρ(tx	NOUN
ejpam-5792	78	10	,	,	PUNCT
ejpam-5792	78	11	ty	ty	NOUN
ejpam-5792	78	12	)	)	PUNCT
ejpam-5792	78	13	,	,	PUNCT
ejpam-5792	78	14	ρ(x	ρ(x	PROPN
ejpam-5792	78	15	,	,	PUNCT
ejpam-5792	78	16	y	y	NOUN
ejpam-5792	78	17	)	)	PUNCT
ejpam-5792	78	18	)	)	PUNCT
ejpam-5792	78	19	≥	≥	NOUN
ejpam-5792	78	20	0	0	NUM
ejpam-5792	78	21	,	,	PUNCT
ejpam-5792	78	22	then	then	ADV
ejpam-5792	78	23	t	t	PROPN
ejpam-5792	78	24	is	be	AUX
ejpam-5792	78	25	known	know	VERB
ejpam-5792	78	26	as	as	ADP
ejpam-5792	78	27	a	a	DET
ejpam-5792	78	28	z	z	NOUN
ejpam-5792	78	29	-	-	PUNCT
ejpam-5792	78	30	contraction	contraction	NOUN
ejpam-5792	78	31	with	with	ADP
ejpam-5792	78	32	respect	respect	NOUN
ejpam-5792	78	33	to	to	ADP
ejpam-5792	78	34	ζ	ζ	NOUN
ejpam-5792	78	35	.	.	PUNCT
ejpam-5792	79	1	the	the	DET
ejpam-5792	79	2	concept	concept	NOUN
ejpam-5792	79	3	of	of	ADP
ejpam-5792	79	4	a	a	DET
ejpam-5792	79	5	simulation	simulation	NOUN
ejpam-5792	79	6	function	function	NOUN
ejpam-5792	79	7	was	be	AUX
ejpam-5792	79	8	broadened	broaden	VERB
ejpam-5792	79	9	by	by	ADP
ejpam-5792	79	10	roldán	roldán	PROPN
ejpam-5792	79	11	et	et	PROPN
ejpam-5792	79	12	al	al	PROPN
ejpam-5792	79	13	.	.	PUNCT
ejpam-5792	80	1	[	[	X
ejpam-5792	80	2	28	28	NUM
ejpam-5792	80	3	]	]	PUNCT
ejpam-5792	80	4	by	by	ADP
ejpam-5792	80	5	just	just	ADV
ejpam-5792	80	6	replacing	replace	VERB
ejpam-5792	80	7	the	the	DET
ejpam-5792	80	8	property	property	NOUN
ejpam-5792	80	9	(	(	PUNCT
ejpam-5792	80	10	ζ3	ζ3	NOUN
ejpam-5792	80	11	)	)	PUNCT
ejpam-5792	80	12	with	with	ADP
ejpam-5792	80	13	(	(	PUNCT
ejpam-5792	80	14	ζ	ζ	NOUN
ejpam-5792	80	15	′3	′3	NOUN
ejpam-5792	80	16	):	):	PUNCT
ejpam-5792	80	17	a.	a.	NOUN
ejpam-5792	80	18	gangwar	gangwar	NOUN
ejpam-5792	80	19	et	et	PROPN
ejpam-5792	80	20	al	al	PROPN
ejpam-5792	80	21	.	.	PUNCT
ejpam-5792	80	22	/	/	SYM
ejpam-5792	80	23	eur	eur	PROPN
ejpam-5792	80	24	.	.	PUNCT
ejpam-5792	81	1	j.	j.	PROPN
ejpam-5792	81	2	pure	pure	PROPN
ejpam-5792	81	3	appl	appl	PROPN
ejpam-5792	81	4	.	.	PROPN
ejpam-5792	81	5	math	math	PROPN
ejpam-5792	81	6	,	,	PUNCT
ejpam-5792	81	7	18	18	NUM
ejpam-5792	81	8	(	(	PUNCT
ejpam-5792	81	9	2	2	NUM
ejpam-5792	81	10	)	)	PUNCT
ejpam-5792	81	11	(	(	PUNCT
ejpam-5792	81	12	2025	2025	NUM
ejpam-5792	81	13	)	)	PUNCT
ejpam-5792	81	14	,	,	PUNCT
ejpam-5792	81	15	5792	5792	NUM
ejpam-5792	81	16	4	4	NUM
ejpam-5792	81	17	of	of	ADP
ejpam-5792	81	18	16	16	NUM
ejpam-5792	81	19	(	(	PUNCT
ejpam-5792	81	20	ζ	ζ	NOUN
ejpam-5792	81	21	′3	′3	NOUN
ejpam-5792	81	22	)	)	PUNCT
ejpam-5792	81	23	if	if	SCONJ
ejpam-5792	81	24	{	{	PUNCT
ejpam-5792	81	25	xn	xn	X
ejpam-5792	81	26	}	}	PUNCT
ejpam-5792	81	27	and	and	CCONJ
ejpam-5792	81	28	{	{	PUNCT
ejpam-5792	81	29	yn	yn	NOUN
ejpam-5792	81	30	}	}	PUNCT
ejpam-5792	81	31	are	be	AUX
ejpam-5792	81	32	sequences	sequence	NOUN
ejpam-5792	81	33	in	in	ADP
ejpam-5792	81	34	[	[	X
ejpam-5792	81	35	0,∞	0,∞	NOUN
ejpam-5792	81	36	)	)	PUNCT
ejpam-5792	81	37	such	such	ADJ
ejpam-5792	81	38	that	that	SCONJ
ejpam-5792	81	39	limn→∞	limn→∞	PROPN
ejpam-5792	81	40	xn	xn	PUNCT
ejpam-5792	81	41	=	=	SYM
ejpam-5792	81	42	limn→∞	limn→∞	PROPN
ejpam-5792	81	43	yn	yn	X
ejpam-5792	81	44	>	>	X
ejpam-5792	81	45	0	0	PUNCT
ejpam-5792	82	1	and	and	CCONJ
ejpam-5792	82	2	xn	xn	PROPN
ejpam-5792	82	3	<	<	X
ejpam-5792	82	4	yn	yn	PROPN
ejpam-5792	82	5	for	for	ADP
ejpam-5792	82	6	all	all	PRON
ejpam-5792	82	7	n	n	PRON
ejpam-5792	82	8	∈	∈	PROPN
ejpam-5792	82	9	n	n	CCONJ
ejpam-5792	82	10	,	,	PUNCT
ejpam-5792	82	11	then	then	ADV
ejpam-5792	82	12	lim	lim	PROPN
ejpam-5792	82	13	n→∞	n→∞	NUM
ejpam-5792	82	14	sup	sup	NOUN
ejpam-5792	82	15	ζ(xn	ζ(xn	NOUN
ejpam-5792	82	16	,	,	PUNCT
ejpam-5792	82	17	yn	yn	PROPN
ejpam-5792	82	18	)	)	PUNCT
ejpam-5792	82	19	<	<	X
ejpam-5792	82	20	0	0	X
ejpam-5792	82	21	.	.	PUNCT
ejpam-5792	83	1	a	a	DET
ejpam-5792	83	2	c	c	NOUN
ejpam-5792	83	3	-	-	PUNCT
ejpam-5792	83	4	class	class	NOUN
ejpam-5792	83	5	function	function	NOUN
ejpam-5792	83	6	[	[	X
ejpam-5792	83	7	29	29	NUM
ejpam-5792	83	8	]	]	X
ejpam-5792	83	9	g	g	NOUN
ejpam-5792	83	10	:	:	PUNCT
ejpam-5792	84	1	[	[	X
ejpam-5792	84	2	0,∞)×	0,∞)×	NUM
ejpam-5792	84	3	[	[	X
ejpam-5792	84	4	0,∞	0,∞	NUM
ejpam-5792	84	5	)	)	PUNCT
ejpam-5792	84	6	→	→	PUNCT
ejpam-5792	84	7	r	r	NOUN
ejpam-5792	84	8	fulfills	fulfill	VERB
ejpam-5792	84	9	the	the	DET
ejpam-5792	84	10	following	following	NOUN
ejpam-5792	84	11	for	for	ADP
ejpam-5792	84	12	each	each	DET
ejpam-5792	84	13	x	x	NOUN
ejpam-5792	84	14	,	,	PUNCT
ejpam-5792	84	15	y	y	PROPN
ejpam-5792	84	16	∈	∈	PROPN
ejpam-5792	85	1	[	[	X
ejpam-5792	85	2	0,∞	0,∞	NOUN
ejpam-5792	85	3	)	)	PUNCT
ejpam-5792	85	4	:	:	PUNCT
ejpam-5792	85	5	(	(	PUNCT
ejpam-5792	85	6	i	i	NOUN
ejpam-5792	85	7	)	)	PUNCT
ejpam-5792	85	8	g(x	g(x	PROPN
ejpam-5792	85	9	,	,	PUNCT
ejpam-5792	85	10	y	y	NOUN
ejpam-5792	85	11	)	)	PUNCT
ejpam-5792	85	12	≤	≤	NOUN
ejpam-5792	86	1	x	x	X
ejpam-5792	86	2	;	;	PUNCT
ejpam-5792	86	3	(	(	PUNCT
ejpam-5792	86	4	ii	ii	NOUN
ejpam-5792	86	5	)	)	PUNCT
ejpam-5792	86	6	g(x	g(x	PROPN
ejpam-5792	86	7	,	,	PUNCT
ejpam-5792	86	8	y	y	NOUN
ejpam-5792	86	9	)	)	PUNCT
ejpam-5792	86	10	=	=	NOUN
ejpam-5792	86	11	x	x	NOUN
ejpam-5792	86	12	implies	imply	VERB
ejpam-5792	86	13	either	either	CCONJ
ejpam-5792	86	14	y	y	PROPN
ejpam-5792	86	15	=	=	SYM
ejpam-5792	86	16	0	0	NUM
ejpam-5792	86	17	or	or	CCONJ
ejpam-5792	86	18	x	x	SYM
ejpam-5792	86	19	=	=	SYM
ejpam-5792	86	20	0	0	PROPN
ejpam-5792	86	21	.	.	PUNCT
ejpam-5792	86	22	definition	definition	NOUN
ejpam-5792	86	23	2	2	NUM
ejpam-5792	86	24	.	.	PUNCT
ejpam-5792	87	1	[	[	X
ejpam-5792	87	2	30	30	NUM
ejpam-5792	87	3	]	]	PUNCT
ejpam-5792	87	4	consider	consider	VERB
ejpam-5792	87	5	a	a	DET
ejpam-5792	87	6	mapping	mapping	NOUN
ejpam-5792	87	7	g	g	NOUN
ejpam-5792	87	8	:	:	PUNCT
ejpam-5792	88	1	[	[	X
ejpam-5792	88	2	0,∞	0,∞	NUM
ejpam-5792	88	3	)	)	PUNCT
ejpam-5792	88	4	×	×	NOUN
ejpam-5792	89	1	[	[	X
ejpam-5792	89	2	0,∞	0,∞	NOUN
ejpam-5792	89	3	)	)	PUNCT
ejpam-5792	89	4	→	→	PUNCT
ejpam-5792	89	5	r.	r.	PROPN
ejpam-5792	89	6	it	it	PRON
ejpam-5792	89	7	is	be	AUX
ejpam-5792	89	8	said	say	VERB
ejpam-5792	89	9	to	to	PART
ejpam-5792	89	10	fulfill	fulfill	VERB
ejpam-5792	89	11	property	property	NOUN
ejpam-5792	89	12	cg	cg	NOUN
ejpam-5792	89	13	if	if	SCONJ
ejpam-5792	89	14	for	for	ADP
ejpam-5792	89	15	each	each	DET
ejpam-5792	89	16	x	x	NOUN
ejpam-5792	89	17	,	,	PUNCT
ejpam-5792	89	18	y	y	PROPN
ejpam-5792	89	19	∈	∈	PROPN
ejpam-5792	90	1	[	[	X
ejpam-5792	90	2	0,∞	0,∞	NOUN
ejpam-5792	90	3	)	)	PUNCT
ejpam-5792	90	4	,	,	PUNCT
ejpam-5792	90	5	there	there	PRON
ejpam-5792	90	6	is	be	VERB
ejpam-5792	90	7	some	some	DET
ejpam-5792	90	8	constant	constant	ADJ
ejpam-5792	90	9	cg	cg	NOUN
ejpam-5792	90	10	≥	≥	NOUN
ejpam-5792	90	11	0	0	NUM
ejpam-5792	90	12	for	for	ADP
ejpam-5792	90	13	which	which	PRON
ejpam-5792	90	14	:	:	PUNCT
ejpam-5792	90	15	(	(	PUNCT
ejpam-5792	90	16	i	i	NOUN
ejpam-5792	90	17	)	)	PUNCT
ejpam-5792	90	18	g(x	g(x	PROPN
ejpam-5792	90	19	,	,	PUNCT
ejpam-5792	90	20	y	y	PROPN
ejpam-5792	90	21	)	)	PUNCT
ejpam-5792	90	22	>	>	X
ejpam-5792	91	1	cg	cg	NOUN
ejpam-5792	91	2	implies	imply	VERB
ejpam-5792	91	3	x	x	PUNCT
ejpam-5792	91	4	>	>	PUNCT
ejpam-5792	91	5	y	y	PROPN
ejpam-5792	91	6	;	;	PUNCT
ejpam-5792	91	7	(	(	PUNCT
ejpam-5792	91	8	ii	ii	NOUN
ejpam-5792	91	9	)	)	PUNCT
ejpam-5792	91	10	g(y	g(y	PROPN
ejpam-5792	91	11	,	,	PUNCT
ejpam-5792	91	12	y	y	NOUN
ejpam-5792	91	13	)	)	PUNCT
ejpam-5792	91	14	≤	≤	NOUN
ejpam-5792	91	15	cg	cg	NOUN
ejpam-5792	91	16	,	,	PUNCT
ejpam-5792	91	17	for	for	ADP
ejpam-5792	91	18	each	each	DET
ejpam-5792	91	19	y.	y.	NOUN
ejpam-5792	91	20	definition	definition	NOUN
ejpam-5792	91	21	3	3	NUM
ejpam-5792	91	22	.	.	PUNCT
ejpam-5792	92	1	[	[	X
ejpam-5792	92	2	30	30	NUM
ejpam-5792	92	3	]	]	X
ejpam-5792	92	4	a	a	DET
ejpam-5792	92	5	zg	zg	PROPN
ejpam-5792	92	6	simulation	simulation	NOUN
ejpam-5792	92	7	function	function	NOUN
ejpam-5792	92	8	is	be	AUX
ejpam-5792	92	9	any	any	DET
ejpam-5792	92	10	mapping	mapping	NOUN
ejpam-5792	92	11	ζ	ζ	NOUN
ejpam-5792	92	12	:	:	PUNCT
ejpam-5792	93	1	[	[	X
ejpam-5792	93	2	0,∞	0,∞	NUM
ejpam-5792	93	3	)	)	PUNCT
ejpam-5792	93	4	×	×	NOUN
ejpam-5792	94	1	[	[	X
ejpam-5792	94	2	0,∞	0,∞	NOUN
ejpam-5792	94	3	)	)	PUNCT
ejpam-5792	95	1	→	→	SYM
ejpam-5792	95	2	r	r	NOUN
ejpam-5792	95	3	which	which	PRON
ejpam-5792	95	4	fulfills	fulfill	VERB
ejpam-5792	95	5	the	the	DET
ejpam-5792	95	6	following	following	NOUN
ejpam-5792	95	7	:	:	PUNCT
ejpam-5792	95	8	(	(	PUNCT
ejpam-5792	95	9	i	i	NOUN
ejpam-5792	95	10	)	)	PUNCT
ejpam-5792	95	11	ζ(0	ζ(0	NOUN
ejpam-5792	95	12	,	,	PUNCT
ejpam-5792	95	13	0	0	NUM
ejpam-5792	95	14	)	)	PUNCT
ejpam-5792	95	15	=	=	SYM
ejpam-5792	95	16	0	0	NUM
ejpam-5792	95	17	;	;	PUNCT
ejpam-5792	95	18	(	(	PUNCT
ejpam-5792	95	19	ii	ii	NOUN
ejpam-5792	95	20	)	)	PUNCT
ejpam-5792	95	21	ζ(x	ζ(x	PROPN
ejpam-5792	95	22	,	,	PUNCT
ejpam-5792	95	23	y	y	NOUN
ejpam-5792	95	24	)	)	PUNCT
ejpam-5792	95	25	<	<	X
ejpam-5792	96	1	g(y	g(y	PROPN
ejpam-5792	96	2	,	,	PUNCT
ejpam-5792	96	3	x	x	NOUN
ejpam-5792	96	4	)	)	PUNCT
ejpam-5792	96	5	,	,	PUNCT
ejpam-5792	96	6	∀	∀	X
ejpam-5792	96	7	x	x	NOUN
ejpam-5792	96	8	,	,	PUNCT
ejpam-5792	96	9	y	y	PROPN
ejpam-5792	96	10	>	>	X
ejpam-5792	96	11	0	0	PROPN
ejpam-5792	96	12	,	,	PUNCT
ejpam-5792	96	13	where	where	SCONJ
ejpam-5792	96	14	g	g	PROPN
ejpam-5792	96	15	is	be	AUX
ejpam-5792	96	16	a	a	DET
ejpam-5792	96	17	c	c	NOUN
ejpam-5792	96	18	-	-	PUNCT
ejpam-5792	96	19	class	class	NOUN
ejpam-5792	96	20	function	function	NOUN
ejpam-5792	96	21	;	;	PUNCT
ejpam-5792	96	22	(	(	PUNCT
ejpam-5792	96	23	iii	iii	X
ejpam-5792	96	24	)	)	PUNCT
ejpam-5792	96	25	if	if	SCONJ
ejpam-5792	96	26	sequences	sequence	NOUN
ejpam-5792	96	27	{	{	PUNCT
ejpam-5792	96	28	xn	xn	NUM
ejpam-5792	96	29	}	}	PUNCT
ejpam-5792	96	30	and	and	CCONJ
ejpam-5792	96	31	{	{	PUNCT
ejpam-5792	96	32	yn	yn	NOUN
ejpam-5792	96	33	}	}	PUNCT
ejpam-5792	96	34	in	in	ADP
ejpam-5792	96	35	the	the	DET
ejpam-5792	96	36	interval	interval	NOUN
ejpam-5792	96	37	[	[	X
ejpam-5792	96	38	0,∞	0,∞	X
ejpam-5792	96	39	)	)	PUNCT
ejpam-5792	96	40	satisfy	satisfy	NOUN
ejpam-5792	96	41	limn→∞	limn→∞	PROPN
ejpam-5792	96	42	xn	xn	PUNCT
ejpam-5792	96	43	=	=	SYM
ejpam-5792	96	44	limn→∞	limn→∞	PROPN
ejpam-5792	96	45	yn	yn	X
ejpam-5792	96	46	>	>	X
ejpam-5792	96	47	0	0	PROPN
ejpam-5792	96	48	,	,	PUNCT
ejpam-5792	96	49	then	then	ADV
ejpam-5792	96	50	lim	lim	PROPN
ejpam-5792	96	51	n→∞	n→∞	NUM
ejpam-5792	96	52	sup	sup	NOUN
ejpam-5792	96	53	ζ(xn	ζ(xn	NOUN
ejpam-5792	96	54	,	,	PUNCT
ejpam-5792	96	55	yn	yn	PROPN
ejpam-5792	96	56	)	)	PUNCT
ejpam-5792	96	57	<	<	X
ejpam-5792	96	58	cg	cg	INTJ
ejpam-5792	96	59	.	.	PUNCT
ejpam-5792	97	1	lemma	lemma	PROPN
ejpam-5792	97	2	1	1	NUM
ejpam-5792	97	3	.	.	PUNCT
ejpam-5792	98	1	[	[	X
ejpam-5792	98	2	31	31	NUM
ejpam-5792	98	3	]	]	PUNCT
ejpam-5792	98	4	consider	consider	VERB
ejpam-5792	98	5	a	a	DET
ejpam-5792	98	6	metric	metric	ADJ
ejpam-5792	98	7	space	space	NOUN
ejpam-5792	98	8	(	(	PUNCT
ejpam-5792	98	9	u	u	NOUN
ejpam-5792	98	10	,	,	PUNCT
ejpam-5792	98	11	ρ	ρ	PROPN
ejpam-5792	98	12	)	)	PUNCT
ejpam-5792	98	13	and	and	CCONJ
ejpam-5792	98	14	a	a	PRON
ejpam-5792	98	15	,	,	PUNCT
ejpam-5792	98	16	b	b	PROPN
ejpam-5792	98	17	⊆	⊆	NUM
ejpam-5792	98	18	u	u	NOUN
ejpam-5792	98	19	.	.	PUNCT
ejpam-5792	99	1	then	then	ADV
ejpam-5792	99	2	,	,	PUNCT
ejpam-5792	99	3	for	for	ADP
ejpam-5792	99	4	every	every	DET
ejpam-5792	99	5	a	a	DET
ejpam-5792	99	6	∈	∈	PROPN
ejpam-5792	99	7	a	a	PRON
ejpam-5792	99	8	,	,	PUNCT
ejpam-5792	99	9	there	there	PRON
ejpam-5792	99	10	is	be	VERB
ejpam-5792	99	11	some	some	DET
ejpam-5792	99	12	b	b	NOUN
ejpam-5792	99	13	∈	∈	NOUN
ejpam-5792	99	14	b	b	NOUN
ejpam-5792	99	15	so	so	SCONJ
ejpam-5792	99	16	that	that	SCONJ
ejpam-5792	99	17	for	for	ADP
ejpam-5792	99	18	q	q	PROPN
ejpam-5792	99	19	>	>	X
ejpam-5792	99	20	1	1	NUM
ejpam-5792	99	21	,	,	PUNCT
ejpam-5792	99	22	we	we	PRON
ejpam-5792	99	23	obtain	obtain	VERB
ejpam-5792	99	24	ρ(a	ρ(a	PROPN
ejpam-5792	99	25	,	,	PUNCT
ejpam-5792	99	26	b	b	NOUN
ejpam-5792	99	27	)	)	PUNCT
ejpam-5792	99	28	≤	≤	NOUN
ejpam-5792	100	1	q	q	PROPN
ejpam-5792	100	2	h(a	h(a	PROPN
ejpam-5792	100	3	,	,	PUNCT
ejpam-5792	100	4	b	b	NOUN
ejpam-5792	100	5	)	)	PUNCT
ejpam-5792	100	6	.	.	PUNCT
ejpam-5792	101	1	rawat	rawat	PROPN
ejpam-5792	101	2	et	et	PROPN
ejpam-5792	101	3	al	al	PROPN
ejpam-5792	101	4	.	.	PUNCT
ejpam-5792	102	1	[	[	X
ejpam-5792	102	2	24	24	NUM
ejpam-5792	102	3	]	]	PUNCT
ejpam-5792	102	4	defined	define	VERB
ejpam-5792	102	5	an	an	DET
ejpam-5792	102	6	enriched	enriched	ADJ
ejpam-5792	102	7	interpolative	interpolative	ADJ
ejpam-5792	102	8	kannan	kannan	PROPN
ejpam-5792	102	9	type	type	NOUN
ejpam-5792	102	10	contraction	contraction	NOUN
ejpam-5792	102	11	(	(	PUNCT
ejpam-5792	102	12	eik	eik	NOUN
ejpam-5792	102	13	-	-	PUNCT
ejpam-5792	102	14	contraction	contraction	NOUN
ejpam-5792	102	15	)	)	PUNCT
ejpam-5792	102	16	for	for	ADP
ejpam-5792	102	17	single	single	ADJ
ejpam-5792	102	18	valued	value	VERB
ejpam-5792	102	19	mappings	mapping	NOUN
ejpam-5792	102	20	as	as	SCONJ
ejpam-5792	102	21	follows	follow	VERB
ejpam-5792	102	22	.	.	PUNCT
ejpam-5792	103	1	definition	definition	NOUN
ejpam-5792	103	2	4	4	NUM
ejpam-5792	103	3	.	.	PUNCT
ejpam-5792	104	1	let	let	VERB
ejpam-5792	104	2	(	(	PUNCT
ejpam-5792	104	3	u	u	NOUN
ejpam-5792	104	4	,	,	PUNCT
ejpam-5792	104	5	d	d	PROPN
ejpam-5792	104	6	,	,	PUNCT
ejpam-5792	104	7	w	w	PROPN
ejpam-5792	104	8	)	)	PUNCT
ejpam-5792	104	9	be	be	AUX
ejpam-5792	104	10	a	a	DET
ejpam-5792	104	11	convex	convex	ADJ
ejpam-5792	104	12	metric	metric	ADJ
ejpam-5792	104	13	space	space	NOUN
ejpam-5792	104	14	.	.	PUNCT
ejpam-5792	105	1	a	a	DET
ejpam-5792	105	2	self	self	NOUN
ejpam-5792	105	3	-	-	PUNCT
ejpam-5792	105	4	mapping	mapping	NOUN
ejpam-5792	105	5	t	t	NOUN
ejpam-5792	105	6	:	:	PUNCT
ejpam-5792	105	7	u	u	NOUN
ejpam-5792	105	8	→	→	SYM
ejpam-5792	105	9	u	u	PROPN
ejpam-5792	105	10	is	be	AUX
ejpam-5792	105	11	an	an	DET
ejpam-5792	105	12	eik	eik	NOUN
ejpam-5792	105	13	-	-	PUNCT
ejpam-5792	105	14	contraction	contraction	NOUN
ejpam-5792	105	15	if	if	SCONJ
ejpam-5792	105	16	there	there	PRON
ejpam-5792	105	17	exist	exist	VERB
ejpam-5792	105	18	λ	λ	PROPN
ejpam-5792	105	19	∈	∈	PROPN
ejpam-5792	106	1	[	[	X
ejpam-5792	106	2	0	0	NUM
ejpam-5792	106	3	,	,	PUNCT
ejpam-5792	106	4	1	1	NUM
ejpam-5792	106	5	)	)	PUNCT
ejpam-5792	106	6	,	,	PUNCT
ejpam-5792	106	7	c	c	PROPN
ejpam-5792	106	8	∈	∈	PROPN
ejpam-5792	107	1	[	[	X
ejpam-5792	107	2	0	0	NUM
ejpam-5792	107	3	,	,	PUNCT
ejpam-5792	107	4	1	1	NUM
ejpam-5792	107	5	)	)	PUNCT
ejpam-5792	107	6	and	and	CCONJ
ejpam-5792	107	7	α	α	PRON
ejpam-5792	107	8	∈	∈	PROPN
ejpam-5792	107	9	(	(	PUNCT
ejpam-5792	107	10	0	0	NUM
ejpam-5792	107	11	,	,	PUNCT
ejpam-5792	107	12	1	1	NUM
ejpam-5792	107	13	)	)	PUNCT
ejpam-5792	107	14	,	,	PUNCT
ejpam-5792	107	15	such	such	ADJ
ejpam-5792	107	16	that	that	SCONJ
ejpam-5792	107	17	d(w	d(w	PROPN
ejpam-5792	107	18	(	(	PUNCT
ejpam-5792	107	19	x	x	X
ejpam-5792	107	20	,	,	PUNCT
ejpam-5792	107	21	tx;λ),w	tx;λ),w	PROPN
ejpam-5792	107	22	(	(	PUNCT
ejpam-5792	107	23	y	y	NOUN
ejpam-5792	107	24	,	,	PUNCT
ejpam-5792	107	25	ty;λ	ty;λ	NUM
ejpam-5792	107	26	)	)	PUNCT
ejpam-5792	107	27	)	)	PUNCT
ejpam-5792	107	28	≤	≤	NUM
ejpam-5792	107	29	c[d(x	c[d(x	NOUN
ejpam-5792	107	30	,	,	PUNCT
ejpam-5792	107	31	w	w	NOUN
ejpam-5792	107	32	(	(	PUNCT
ejpam-5792	107	33	x	x	X
ejpam-5792	107	34	,	,	PUNCT
ejpam-5792	107	35	tx;λ))]α.[d(y	tx;λ))]α.[d(y	NUM
ejpam-5792	107	36	,	,	PUNCT
ejpam-5792	107	37	w	w	PROPN
ejpam-5792	107	38	(	(	PUNCT
ejpam-5792	107	39	y	y	PROPN
ejpam-5792	107	40	,	,	PUNCT
ejpam-5792	107	41	ty;λ))]1−α	ty;λ))]1−α	PROPN
ejpam-5792	107	42	,	,	PUNCT
ejpam-5792	107	43	for	for	ADP
ejpam-5792	107	44	all	all	DET
ejpam-5792	107	45	x	x	NOUN
ejpam-5792	107	46	,	,	PUNCT
ejpam-5792	107	47	y	y	PROPN
ejpam-5792	107	48	∈	∈	PROPN
ejpam-5792	107	49	x\fix(t	x\fix(t	PUNCT
ejpam-5792	107	50	)	)	PUNCT
ejpam-5792	107	51	.	.	PUNCT
ejpam-5792	108	1	they	they	PRON
ejpam-5792	108	2	further	far	ADV
ejpam-5792	108	3	demonstrated	demonstrate	VERB
ejpam-5792	108	4	the	the	DET
ejpam-5792	108	5	next	next	ADJ
ejpam-5792	108	6	result	result	NOUN
ejpam-5792	108	7	.	.	PUNCT
ejpam-5792	109	1	theorem	theorem	NOUN
ejpam-5792	109	2	1	1	NUM
ejpam-5792	109	3	.	.	PUNCT
ejpam-5792	110	1	[	[	X
ejpam-5792	110	2	24	24	NUM
ejpam-5792	110	3	]	]	X
ejpam-5792	110	4	let	let	VERB
ejpam-5792	110	5	(	(	PUNCT
ejpam-5792	110	6	u	u	NOUN
ejpam-5792	110	7	,	,	PUNCT
ejpam-5792	110	8	ρ	ρ	PROPN
ejpam-5792	110	9	)	)	PUNCT
ejpam-5792	110	10	be	be	VERB
ejpam-5792	110	11	a	a	DET
ejpam-5792	110	12	convex	convex	NOUN
ejpam-5792	110	13	complete	complete	ADJ
ejpam-5792	110	14	metric	metric	ADJ
ejpam-5792	110	15	space	space	NOUN
ejpam-5792	110	16	and	and	CCONJ
ejpam-5792	110	17	t	t	NOUN
ejpam-5792	110	18	:	:	PUNCT
ejpam-5792	110	19	u	u	X
ejpam-5792	110	20	→	→	SYM
ejpam-5792	110	21	u	u	X
ejpam-5792	110	22	be	be	VERB
ejpam-5792	110	23	an	an	DET
ejpam-5792	110	24	eik	eik	NOUN
ejpam-5792	110	25	-	-	PUNCT
ejpam-5792	110	26	contraction	contraction	NOUN
ejpam-5792	110	27	mapping	mapping	NOUN
ejpam-5792	110	28	.	.	PUNCT
ejpam-5792	111	1	then	then	ADV
ejpam-5792	111	2	t	t	PROPN
ejpam-5792	111	3	admits	admit	VERB
ejpam-5792	111	4	a	a	DET
ejpam-5792	111	5	fixed	fixed	ADJ
ejpam-5792	111	6	point	point	NOUN
ejpam-5792	111	7	.	.	PUNCT
ejpam-5792	112	1	a.	a.	NOUN
ejpam-5792	112	2	gangwar	gangwar	PROPN
ejpam-5792	112	3	et	et	PROPN
ejpam-5792	112	4	al	al	PROPN
ejpam-5792	112	5	.	.	PUNCT
ejpam-5792	112	6	/	/	SYM
ejpam-5792	112	7	eur	eur	PROPN
ejpam-5792	112	8	.	.	PUNCT
ejpam-5792	113	1	j.	j.	PROPN
ejpam-5792	113	2	pure	pure	PROPN
ejpam-5792	113	3	appl	appl	PROPN
ejpam-5792	113	4	.	.	PROPN
ejpam-5792	113	5	math	math	PROPN
ejpam-5792	113	6	,	,	PUNCT
ejpam-5792	113	7	18	18	NUM
ejpam-5792	113	8	(	(	PUNCT
ejpam-5792	113	9	2	2	NUM
ejpam-5792	113	10	)	)	PUNCT
ejpam-5792	113	11	(	(	PUNCT
ejpam-5792	113	12	2025	2025	NUM
ejpam-5792	113	13	)	)	PUNCT
ejpam-5792	113	14	,	,	PUNCT
ejpam-5792	113	15	5792	5792	NUM
ejpam-5792	113	16	5	5	NUM
ejpam-5792	113	17	of	of	ADP
ejpam-5792	113	18	16	16	NUM
ejpam-5792	113	19	karapinar	karapinar	NOUN
ejpam-5792	113	20	et	et	PROPN
ejpam-5792	113	21	al	al	PROPN
ejpam-5792	113	22	.	.	PUNCT
ejpam-5792	114	1	[	[	X
ejpam-5792	114	2	32	32	NUM
ejpam-5792	114	3	]	]	PUNCT
ejpam-5792	114	4	defined	define	VERB
ejpam-5792	114	5	a	a	DET
ejpam-5792	114	6	multivalued	multivalued	ADJ
ejpam-5792	114	7	interpolative	interpolative	ADJ
ejpam-5792	114	8	hardy	hardy	ADJ
ejpam-5792	114	9	-	-	PUNCT
ejpam-5792	114	10	rogers	rogers	NOUN
ejpam-5792	114	11	type	type	NOUN
ejpam-5792	114	12	contraction	contraction	NOUN
ejpam-5792	114	13	(	(	PUNCT
ejpam-5792	114	14	ihr	ihr	NOUN
ejpam-5792	114	15	-	-	PUNCT
ejpam-5792	114	16	contraction	contraction	NOUN
ejpam-5792	114	17	)	)	PUNCT
ejpam-5792	114	18	as	as	SCONJ
ejpam-5792	114	19	follows	follow	VERB
ejpam-5792	114	20	.	.	PUNCT
ejpam-5792	115	1	definition	definition	NOUN
ejpam-5792	115	2	5	5	NUM
ejpam-5792	115	3	.	.	PUNCT
ejpam-5792	116	1	let	let	VERB
ejpam-5792	116	2	(	(	PUNCT
ejpam-5792	116	3	u	u	NOUN
ejpam-5792	116	4	,	,	PUNCT
ejpam-5792	116	5	d	d	PROPN
ejpam-5792	116	6	)	)	PUNCT
ejpam-5792	116	7	be	be	AUX
ejpam-5792	116	8	a	a	DET
ejpam-5792	116	9	metric	metric	ADJ
ejpam-5792	116	10	space	space	NOUN
ejpam-5792	116	11	.	.	PUNCT
ejpam-5792	117	1	we	we	PRON
ejpam-5792	117	2	say	say	VERB
ejpam-5792	117	3	that	that	PRON
ejpam-5792	117	4	t	t	NOUN
ejpam-5792	117	5	:	:	PUNCT
ejpam-5792	117	6	u	u	PROPN
ejpam-5792	117	7	→	→	SYM
ejpam-5792	117	8	cb(u	cb(u	X
ejpam-5792	117	9	)	)	PUNCT
ejpam-5792	117	10	is	be	AUX
ejpam-5792	117	11	a	a	DET
ejpam-5792	117	12	multivalued	multivalue	VERB
ejpam-5792	117	13	interpolative	interpolative	ADJ
ejpam-5792	117	14	hr	hr	NOUN
ejpam-5792	117	15	-	-	NOUN
ejpam-5792	117	16	contraction	contraction	NOUN
ejpam-5792	117	17	via	via	ADP
ejpam-5792	117	18	a	a	DET
ejpam-5792	117	19	simulation	simulation	NOUN
ejpam-5792	117	20	function	function	NOUN
ejpam-5792	117	21	zg	zg	PROPN
ejpam-5792	117	22	,	,	PUNCT
ejpam-5792	117	23	if	if	SCONJ
ejpam-5792	117	24	there	there	PRON
ejpam-5792	117	25	exist	exist	VERB
ejpam-5792	117	26	k	k	PROPN
ejpam-5792	117	27	∈	∈	PROPN
ejpam-5792	118	1	[	[	X
ejpam-5792	118	2	0	0	NUM
ejpam-5792	118	3	,	,	PUNCT
ejpam-5792	118	4	1	1	NUM
ejpam-5792	118	5	)	)	PUNCT
ejpam-5792	118	6	and	and	CCONJ
ejpam-5792	118	7	α	α	NOUN
ejpam-5792	118	8	,	,	PUNCT
ejpam-5792	118	9	β	β	X
ejpam-5792	118	10	,	,	PUNCT
ejpam-5792	118	11	γ	γ	X
ejpam-5792	118	12	≥≥	≥≥	X
ejpam-5792	118	13	0	0	NUM
ejpam-5792	118	14	with	with	ADP
ejpam-5792	118	15	α+	α+	X
ejpam-5792	118	16	β	β	NOUN
ejpam-5792	118	17	+	+	X
ejpam-5792	118	18	γ	γ	X
ejpam-5792	118	19	<	<	X
ejpam-5792	118	20	1	1	NUM
ejpam-5792	118	21	such	such	ADJ
ejpam-5792	118	22	that	that	PRON
ejpam-5792	118	23	ζ(h(tx	ζ(h(tx	NOUN
ejpam-5792	118	24	,	,	PUNCT
ejpam-5792	118	25	ty	ty	NOUN
ejpam-5792	118	26	)	)	PUNCT
ejpam-5792	118	27	,	,	PUNCT
ejpam-5792	118	28	r(x	r(x	PROPN
ejpam-5792	118	29	,	,	PUNCT
ejpam-5792	118	30	y	y	NOUN
ejpam-5792	118	31	)	)	PUNCT
ejpam-5792	118	32	)	)	PUNCT
ejpam-5792	118	33	≥	≥	X
ejpam-5792	118	34	cg	cg	NOUN
ejpam-5792	118	35	,	,	PUNCT
ejpam-5792	118	36	where	where	SCONJ
ejpam-5792	118	37	r(x	r(x	PROPN
ejpam-5792	118	38	,	,	PUNCT
ejpam-5792	118	39	y	y	NOUN
ejpam-5792	118	40	)	)	PUNCT
ejpam-5792	118	41	=	=	SYM
ejpam-5792	118	42	k[d(x	k[d(x	NOUN
ejpam-5792	118	43	,	,	PUNCT
ejpam-5792	118	44	y)]α[d(x	y)]α[d(x	NOUN
ejpam-5792	118	45	,	,	PUNCT
ejpam-5792	118	46	tx)]β[d(y	tx)]β[d(y	NOUN
ejpam-5792	118	47	,	,	PUNCT
ejpam-5792	118	48	ty)]γ	ty)]γ	NOUN
ejpam-5792	118	49	[	[	X
ejpam-5792	118	50	12(d(x	12(d(x	NUM
ejpam-5792	118	51	,	,	PUNCT
ejpam-5792	118	52	ty	ty	INTJ
ejpam-5792	118	53	)	)	PUNCT
ejpam-5792	118	54	+	+	NOUN
ejpam-5792	118	55	d(x	d(x	PROPN
ejpam-5792	118	56	,	,	PUNCT
ejpam-5792	118	57	tx))]1−α−β−γ	tx))]1−α−β−γ	NOUN
ejpam-5792	118	58	,	,	PUNCT
ejpam-5792	118	59	for	for	ADP
ejpam-5792	118	60	all	all	DET
ejpam-5792	118	61	x	x	NOUN
ejpam-5792	118	62	,	,	PUNCT
ejpam-5792	118	63	y	y	PROPN
ejpam-5792	118	64	∈	∈	PROPN
ejpam-5792	118	65	u	u	NOUN
ejpam-5792	118	66	\fix(t	\fix(t	PROPN
ejpam-5792	118	67	)	)	PUNCT
ejpam-5792	118	68	.	.	PUNCT
ejpam-5792	119	1	they	they	PRON
ejpam-5792	119	2	further	far	ADV
ejpam-5792	119	3	demonstrated	demonstrate	VERB
ejpam-5792	119	4	the	the	DET
ejpam-5792	119	5	next	next	ADJ
ejpam-5792	119	6	result	result	NOUN
ejpam-5792	119	7	.	.	PUNCT
ejpam-5792	120	1	theorem	theorem	NOUN
ejpam-5792	120	2	2	2	NUM
ejpam-5792	120	3	.	.	PUNCT
ejpam-5792	121	1	[	[	X
ejpam-5792	121	2	32	32	NUM
ejpam-5792	121	3	]	]	PUNCT
ejpam-5792	121	4	let	let	VERB
ejpam-5792	121	5	(	(	PUNCT
ejpam-5792	121	6	u	u	NOUN
ejpam-5792	121	7	,	,	PUNCT
ejpam-5792	121	8	ρ	ρ	PROPN
ejpam-5792	121	9	)	)	PUNCT
ejpam-5792	121	10	be	be	VERB
ejpam-5792	121	11	a	a	DET
ejpam-5792	121	12	complete	complete	ADJ
ejpam-5792	121	13	metric	metric	ADJ
ejpam-5792	121	14	space	space	NOUN
ejpam-5792	121	15	and	and	CCONJ
ejpam-5792	121	16	t	t	PROPN
ejpam-5792	121	17	be	be	AUX
ejpam-5792	121	18	a	a	DET
ejpam-5792	121	19	multivalued	multivalued	ADJ
ejpam-5792	121	20	ihrcontraction	ihrcontraction	NOUN
ejpam-5792	121	21	via	via	ADP
ejpam-5792	121	22	a	a	DET
ejpam-5792	121	23	simulation	simulation	NOUN
ejpam-5792	121	24	function	function	PROPN
ejpam-5792	121	25	zg	zg	PROPN
ejpam-5792	121	26	.	.	PUNCT
ejpam-5792	122	1	then	then	ADV
ejpam-5792	122	2	fix(t	fix(t	PROPN
ejpam-5792	122	3	)	)	PUNCT
ejpam-5792	122	4	̸=	̸=	PROPN
ejpam-5792	122	5	ϕ.	ϕ.	VERB
ejpam-5792	122	6	now	now	ADV
ejpam-5792	122	7	,	,	PUNCT
ejpam-5792	122	8	we	we	PRON
ejpam-5792	122	9	define	define	VERB
ejpam-5792	122	10	some	some	DET
ejpam-5792	122	11	basic	basic	ADJ
ejpam-5792	122	12	preliminaries	preliminary	NOUN
ejpam-5792	122	13	related	relate	VERB
ejpam-5792	122	14	to	to	PART
ejpam-5792	122	15	convex	convex	VERB
ejpam-5792	122	16	metric	metric	ADJ
ejpam-5792	122	17	spaces	space	NOUN
ejpam-5792	122	18	.	.	PUNCT
ejpam-5792	123	1	definition	definition	NOUN
ejpam-5792	123	2	6	6	NUM
ejpam-5792	123	3	.	.	PUNCT
ejpam-5792	124	1	[	[	X
ejpam-5792	124	2	23	23	NUM
ejpam-5792	124	3	]	]	PUNCT
ejpam-5792	124	4	let	let	VERB
ejpam-5792	124	5	u	u	PRON
ejpam-5792	124	6	be	be	AUX
ejpam-5792	124	7	a	a	DET
ejpam-5792	124	8	metric	metric	ADJ
ejpam-5792	124	9	space	space	NOUN
ejpam-5792	124	10	.	.	PUNCT
ejpam-5792	125	1	a	a	DET
ejpam-5792	125	2	continuous	continuous	ADJ
ejpam-5792	125	3	function	function	NOUN
ejpam-5792	125	4	w	w	NOUN
ejpam-5792	125	5	:	:	PUNCT
ejpam-5792	125	6	u	u	NOUN
ejpam-5792	125	7	×u	×u	PRON
ejpam-5792	125	8	×	×	NOUN
ejpam-5792	125	9	[	[	X
ejpam-5792	125	10	0	0	NUM
ejpam-5792	125	11	,	,	PUNCT
ejpam-5792	125	12	1	1	NUM
ejpam-5792	125	13	]	]	PUNCT
ejpam-5792	125	14	→	→	SYM
ejpam-5792	125	15	u	u	NOUN
ejpam-5792	125	16	is	be	AUX
ejpam-5792	125	17	known	know	VERB
ejpam-5792	125	18	as	as	ADP
ejpam-5792	125	19	a	a	DET
ejpam-5792	125	20	convex	convex	NOUN
ejpam-5792	125	21	structure	structure	NOUN
ejpam-5792	125	22	on	on	ADP
ejpam-5792	125	23	u	u	PROPN
ejpam-5792	125	24	,	,	PUNCT
ejpam-5792	125	25	if	if	SCONJ
ejpam-5792	125	26	for	for	ADP
ejpam-5792	125	27	every	every	DET
ejpam-5792	125	28	λ	λ	PROPN
ejpam-5792	125	29	∈	∈	PROPN
ejpam-5792	126	1	[	[	X
ejpam-5792	126	2	0	0	NUM
ejpam-5792	126	3	,	,	PUNCT
ejpam-5792	126	4	1	1	NUM
ejpam-5792	126	5	]	]	PUNCT
ejpam-5792	126	6	and	and	CCONJ
ejpam-5792	126	7	x	x	X
ejpam-5792	126	8	,	,	PUNCT
ejpam-5792	126	9	y	y	PROPN
ejpam-5792	126	10	∈	∈	PROPN
ejpam-5792	126	11	u	u	PROPN
ejpam-5792	126	12	,	,	PUNCT
ejpam-5792	126	13	the	the	DET
ejpam-5792	126	14	next	next	ADJ
ejpam-5792	126	15	inequality	inequality	NOUN
ejpam-5792	126	16	holds	hold	VERB
ejpam-5792	126	17	:	:	PUNCT
ejpam-5792	126	18	ρ(u	ρ(u	PROPN
ejpam-5792	126	19	,	,	PUNCT
ejpam-5792	126	20	w	w	PROPN
ejpam-5792	126	21	(	(	PUNCT
ejpam-5792	126	22	x	x	NOUN
ejpam-5792	126	23	,	,	PUNCT
ejpam-5792	126	24	y;λ	y;λ	PROPN
ejpam-5792	126	25	)	)	PUNCT
ejpam-5792	126	26	)	)	PUNCT
ejpam-5792	126	27	≤	≤	NOUN
ejpam-5792	126	28	λρ(u	λρ(u	PUNCT
ejpam-5792	126	29	,	,	PUNCT
ejpam-5792	126	30	x	x	X
ejpam-5792	126	31	)	)	PUNCT
ejpam-5792	127	1	+	+	CCONJ
ejpam-5792	127	2	(	(	PUNCT
ejpam-5792	127	3	1−	1−	NUM
ejpam-5792	127	4	λ)ρ(u	λ)ρ(u	PROPN
ejpam-5792	127	5	,	,	PUNCT
ejpam-5792	127	6	y	y	NOUN
ejpam-5792	127	7	)	)	PUNCT
ejpam-5792	127	8	,	,	PUNCT
ejpam-5792	127	9	for	for	ADP
ejpam-5792	127	10	each	each	DET
ejpam-5792	127	11	x	x	SYM
ejpam-5792	127	12	∈	∈	PROPN
ejpam-5792	127	13	u	u	NOUN
ejpam-5792	127	14	.	.	PUNCT
ejpam-5792	128	1	(	(	PUNCT
ejpam-5792	128	2	1	1	X
ejpam-5792	128	3	)	)	PUNCT
ejpam-5792	128	4	a	a	DET
ejpam-5792	128	5	metric	metric	ADJ
ejpam-5792	128	6	space	space	NOUN
ejpam-5792	128	7	u	u	NOUN
ejpam-5792	128	8	with	with	ADP
ejpam-5792	128	9	a	a	DET
ejpam-5792	128	10	convex	convex	ADJ
ejpam-5792	128	11	structure	structure	NOUN
ejpam-5792	128	12	w	w	NOUN
ejpam-5792	128	13	on	on	ADP
ejpam-5792	128	14	u	u	PROPN
ejpam-5792	128	15	is	be	AUX
ejpam-5792	128	16	called	call	VERB
ejpam-5792	128	17	a	a	DET
ejpam-5792	128	18	takahashi	takahashi	PROPN
ejpam-5792	128	19	convex	convex	PROPN
ejpam-5792	128	20	metric	metric	ADJ
ejpam-5792	128	21	structure	structure	NOUN
ejpam-5792	128	22	,	,	PUNCT
ejpam-5792	128	23	or	or	CCONJ
ejpam-5792	128	24	simply	simply	ADV
ejpam-5792	128	25	with	with	ADP
ejpam-5792	128	26	a	a	DET
ejpam-5792	128	27	convex	convex	ADJ
ejpam-5792	128	28	metric	metric	ADJ
ejpam-5792	128	29	structure	structure	NOUN
ejpam-5792	128	30	and	and	CCONJ
ejpam-5792	128	31	will	will	AUX
ejpam-5792	128	32	be	be	AUX
ejpam-5792	128	33	denoted	denote	VERB
ejpam-5792	128	34	as	as	ADP
ejpam-5792	128	35	(	(	PUNCT
ejpam-5792	128	36	u	u	PROPN
ejpam-5792	128	37	,	,	PUNCT
ejpam-5792	128	38	ρ	ρ	PROPN
ejpam-5792	128	39	,	,	PUNCT
ejpam-5792	128	40	w	w	NOUN
ejpam-5792	128	41	)	)	PUNCT
ejpam-5792	128	42	.	.	PUNCT
ejpam-5792	129	1	the	the	DET
ejpam-5792	129	2	lemmas	lemma	NOUN
ejpam-5792	129	3	below	below	ADP
ejpam-5792	129	4	outline	outline	NOUN
ejpam-5792	129	5	some	some	DET
ejpam-5792	129	6	fundamental	fundamental	ADJ
ejpam-5792	129	7	properties	property	NOUN
ejpam-5792	129	8	of	of	ADP
ejpam-5792	129	9	a	a	DET
ejpam-5792	129	10	convex	convex	ADJ
ejpam-5792	129	11	metric	metric	ADJ
ejpam-5792	129	12	space	space	NOUN
ejpam-5792	129	13	.	.	PUNCT
ejpam-5792	130	1	lemma	lemma	PROPN
ejpam-5792	130	2	2	2	NUM
ejpam-5792	130	3	.	.	PUNCT
ejpam-5792	131	1	[	[	X
ejpam-5792	131	2	23	23	NUM
ejpam-5792	131	3	]	]	X
ejpam-5792	131	4	let	let	VERB
ejpam-5792	131	5	(	(	PUNCT
ejpam-5792	131	6	u	u	NOUN
ejpam-5792	131	7	,	,	PUNCT
ejpam-5792	131	8	ρ	ρ	PROPN
ejpam-5792	131	9	,	,	PUNCT
ejpam-5792	131	10	w	w	NOUN
ejpam-5792	131	11	)	)	PUNCT
ejpam-5792	131	12	be	be	AUX
ejpam-5792	131	13	a	a	DET
ejpam-5792	131	14	convex	convex	ADJ
ejpam-5792	131	15	metric	metric	ADJ
ejpam-5792	131	16	space	space	NOUN
ejpam-5792	131	17	.	.	PUNCT
ejpam-5792	132	1	for	for	ADP
ejpam-5792	132	2	any	any	DET
ejpam-5792	132	3	x	x	NOUN
ejpam-5792	132	4	,	,	PUNCT
ejpam-5792	132	5	y	y	PROPN
ejpam-5792	132	6	∈	∈	PROPN
ejpam-5792	132	7	u	u	NOUN
ejpam-5792	132	8	and	and	CCONJ
ejpam-5792	132	9	any	any	DET
ejpam-5792	132	10	λ	λ	X
ejpam-5792	132	11	∈	∈	PROPN
ejpam-5792	132	12	[	[	X
ejpam-5792	132	13	0	0	NUM
ejpam-5792	132	14	,	,	PUNCT
ejpam-5792	132	15	1	1	NUM
ejpam-5792	132	16	]	]	PUNCT
ejpam-5792	132	17	,	,	PUNCT
ejpam-5792	132	18	the	the	DET
ejpam-5792	132	19	following	follow	VERB
ejpam-5792	132	20	holds	hold	NOUN
ejpam-5792	132	21	:	:	PUNCT
ejpam-5792	132	22	ρ(x	ρ(x	NOUN
ejpam-5792	132	23	,	,	PUNCT
ejpam-5792	132	24	y	y	NOUN
ejpam-5792	132	25	)	)	PUNCT
ejpam-5792	132	26	=	=	SYM
ejpam-5792	132	27	ρ(x	ρ(x	NOUN
ejpam-5792	132	28	,	,	PUNCT
ejpam-5792	132	29	w	w	NOUN
ejpam-5792	132	30	(	(	PUNCT
ejpam-5792	132	31	x	x	NOUN
ejpam-5792	132	32	,	,	PUNCT
ejpam-5792	132	33	y;λ	y;λ	PROPN
ejpam-5792	132	34	)	)	PUNCT
ejpam-5792	132	35	)	)	PUNCT
ejpam-5792	133	1	+	+	CCONJ
ejpam-5792	133	2	ρ(w	ρ(w	PROPN
ejpam-5792	133	3	(	(	PUNCT
ejpam-5792	133	4	x	x	X
ejpam-5792	133	5	,	,	PUNCT
ejpam-5792	133	6	y;λ	y;λ	PROPN
ejpam-5792	133	7	)	)	PUNCT
ejpam-5792	133	8	,	,	PUNCT
ejpam-5792	133	9	y	y	PROPN
ejpam-5792	133	10	)	)	PUNCT
ejpam-5792	133	11	.	.	PUNCT
ejpam-5792	134	1	lemma	lemma	PROPN
ejpam-5792	134	2	3	3	X
ejpam-5792	134	3	.	.	PUNCT
ejpam-5792	135	1	[	[	X
ejpam-5792	135	2	33	33	NUM
ejpam-5792	135	3	]	]	PUNCT
ejpam-5792	135	4	let	let	VERB
ejpam-5792	135	5	(	(	PUNCT
ejpam-5792	135	6	u	u	NOUN
ejpam-5792	135	7	,	,	PUNCT
ejpam-5792	135	8	ρ	ρ	PROPN
ejpam-5792	135	9	,	,	PUNCT
ejpam-5792	135	10	w	w	NOUN
ejpam-5792	135	11	)	)	PUNCT
ejpam-5792	135	12	be	be	AUX
ejpam-5792	135	13	a	a	DET
ejpam-5792	135	14	convex	convex	ADJ
ejpam-5792	135	15	metric	metric	ADJ
ejpam-5792	135	16	space	space	NOUN
ejpam-5792	135	17	.	.	PUNCT
ejpam-5792	136	1	for	for	ADP
ejpam-5792	136	2	any	any	DET
ejpam-5792	136	3	x	x	NOUN
ejpam-5792	136	4	,	,	PUNCT
ejpam-5792	136	5	y	y	PROPN
ejpam-5792	136	6	∈	∈	PROPN
ejpam-5792	136	7	u	u	NOUN
ejpam-5792	136	8	and	and	CCONJ
ejpam-5792	136	9	any	any	DET
ejpam-5792	136	10	λ	λ	PROPN
ejpam-5792	136	11	,	,	PUNCT
ejpam-5792	136	12	λ1	λ1	ADJ
ejpam-5792	136	13	,	,	PUNCT
ejpam-5792	136	14	λ2	λ2	PROPN
ejpam-5792	136	15	∈	∈	PROPN
ejpam-5792	136	16	[	[	X
ejpam-5792	136	17	0	0	NUM
ejpam-5792	136	18	,	,	PUNCT
ejpam-5792	136	19	1	1	NUM
ejpam-5792	136	20	]	]	PUNCT
ejpam-5792	136	21	,	,	PUNCT
ejpam-5792	136	22	the	the	DET
ejpam-5792	136	23	following	follow	VERB
ejpam-5792	136	24	holds	hold	VERB
ejpam-5792	136	25	:	:	PUNCT
ejpam-5792	136	26	(	(	PUNCT
ejpam-5792	136	27	i	i	NOUN
ejpam-5792	136	28	)	)	PUNCT
ejpam-5792	136	29	w	w	PROPN
ejpam-5792	136	30	(	(	PUNCT
ejpam-5792	136	31	x	x	X
ejpam-5792	136	32	,	,	PUNCT
ejpam-5792	136	33	x;λ	x;λ	PUNCT
ejpam-5792	136	34	)	)	PUNCT
ejpam-5792	137	1	=	=	PUNCT
ejpam-5792	137	2	x;w	x;w	PUNCT
ejpam-5792	138	1	(	(	PUNCT
ejpam-5792	138	2	x	x	X
ejpam-5792	138	3	,	,	PUNCT
ejpam-5792	138	4	y	y	PROPN
ejpam-5792	138	5	;	;	PUNCT
ejpam-5792	138	6	0	0	NUM
ejpam-5792	138	7	)	)	PUNCT
ejpam-5792	138	8	=	=	SYM
ejpam-5792	138	9	y	y	PROPN
ejpam-5792	138	10	and	and	CCONJ
ejpam-5792	138	11	w	w	PROPN
ejpam-5792	138	12	(	(	PUNCT
ejpam-5792	138	13	x	x	PROPN
ejpam-5792	138	14	,	,	PUNCT
ejpam-5792	138	15	y	y	PROPN
ejpam-5792	138	16	;	;	PUNCT
ejpam-5792	138	17	1	1	X
ejpam-5792	138	18	)	)	PUNCT
ejpam-5792	138	19	=	=	PUNCT
ejpam-5792	139	1	x.	x.	NOUN
ejpam-5792	139	2	(	(	PUNCT
ejpam-5792	139	3	ii	ii	NOUN
ejpam-5792	139	4	)	)	PUNCT
ejpam-5792	139	5	|λ1	|λ1	NOUN
ejpam-5792	140	1	−	−	PROPN
ejpam-5792	140	2	λ2|ρ(x	λ2|ρ(x	PROPN
ejpam-5792	140	3	,	,	PUNCT
ejpam-5792	140	4	y	y	NOUN
ejpam-5792	140	5	)	)	PUNCT
ejpam-5792	140	6	≤	≤	NUM
ejpam-5792	140	7	ρ(w	ρ(w	PROPN
ejpam-5792	140	8	(	(	PUNCT
ejpam-5792	140	9	x	x	X
ejpam-5792	140	10	,	,	PUNCT
ejpam-5792	140	11	y;λ1),w	y;λ1),w	PROPN
ejpam-5792	140	12	(	(	PUNCT
ejpam-5792	140	13	x	x	NOUN
ejpam-5792	140	14	,	,	PUNCT
ejpam-5792	140	15	y;λ2	y;λ2	NUM
ejpam-5792	140	16	)	)	PUNCT
ejpam-5792	140	17	)	)	PUNCT
ejpam-5792	140	18	.	.	PUNCT
ejpam-5792	141	1	lemma	lemma	PROPN
ejpam-5792	141	2	4	4	NUM
ejpam-5792	141	3	.	.	PUNCT
ejpam-5792	142	1	[	[	X
ejpam-5792	142	2	23	23	NUM
ejpam-5792	142	3	]	]	X
ejpam-5792	142	4	let	let	VERB
ejpam-5792	142	5	(	(	PUNCT
ejpam-5792	142	6	u	u	NOUN
ejpam-5792	142	7	,	,	PUNCT
ejpam-5792	142	8	ρ	ρ	PROPN
ejpam-5792	142	9	,	,	PUNCT
ejpam-5792	142	10	w	w	NOUN
ejpam-5792	142	11	)	)	PUNCT
ejpam-5792	142	12	be	be	AUX
ejpam-5792	142	13	a	a	DET
ejpam-5792	142	14	convex	convex	ADJ
ejpam-5792	142	15	metric	metric	ADJ
ejpam-5792	142	16	space	space	NOUN
ejpam-5792	142	17	.	.	PUNCT
ejpam-5792	143	1	for	for	ADP
ejpam-5792	143	2	any	any	DET
ejpam-5792	143	3	x	x	NOUN
ejpam-5792	143	4	,	,	PUNCT
ejpam-5792	143	5	y	y	PROPN
ejpam-5792	143	6	∈	∈	PROPN
ejpam-5792	143	7	u	u	NOUN
ejpam-5792	143	8	and	and	CCONJ
ejpam-5792	143	9	any	any	DET
ejpam-5792	143	10	λ	λ	X
ejpam-5792	143	11	∈	∈	PROPN
ejpam-5792	143	12	[	[	X
ejpam-5792	143	13	0	0	NUM
ejpam-5792	143	14	,	,	PUNCT
ejpam-5792	143	15	1	1	NUM
ejpam-5792	143	16	]	]	PUNCT
ejpam-5792	143	17	,	,	PUNCT
ejpam-5792	143	18	the	the	DET
ejpam-5792	143	19	following	follow	VERB
ejpam-5792	143	20	holds	hold	NOUN
ejpam-5792	143	21	:	:	PUNCT
ejpam-5792	143	22	ρ(x	ρ(x	NOUN
ejpam-5792	143	23	,	,	PUNCT
ejpam-5792	143	24	w	w	NOUN
ejpam-5792	143	25	(	(	PUNCT
ejpam-5792	143	26	x	x	NOUN
ejpam-5792	143	27	,	,	PUNCT
ejpam-5792	143	28	y;λ	y;λ	PROPN
ejpam-5792	143	29	)	)	PUNCT
ejpam-5792	143	30	)	)	PUNCT
ejpam-5792	144	1	=	=	SYM
ejpam-5792	144	2	(	(	PUNCT
ejpam-5792	144	3	1−	1−	NUM
ejpam-5792	144	4	λ)ρ(x	λ)ρ(x	NOUN
ejpam-5792	144	5	,	,	PUNCT
ejpam-5792	144	6	y	y	PROPN
ejpam-5792	144	7	)	)	PUNCT
ejpam-5792	144	8	and	and	CCONJ
ejpam-5792	144	9	ρ(w	ρ(w	PROPN
ejpam-5792	144	10	(	(	PUNCT
ejpam-5792	144	11	x	x	X
ejpam-5792	144	12	,	,	PUNCT
ejpam-5792	144	13	y;λ	y;λ	PROPN
ejpam-5792	144	14	)	)	PUNCT
ejpam-5792	144	15	,	,	PUNCT
ejpam-5792	144	16	y	y	PROPN
ejpam-5792	144	17	)	)	PUNCT
ejpam-5792	144	18	=	=	SYM
ejpam-5792	145	1	λρ(x	λρ(x	X
ejpam-5792	145	2	,	,	PUNCT
ejpam-5792	145	3	y	y	NOUN
ejpam-5792	145	4	)	)	PUNCT
ejpam-5792	145	5	.	.	PUNCT
ejpam-5792	146	1	lemma	lemma	PROPN
ejpam-5792	146	2	5	5	NUM
ejpam-5792	146	3	.	.	PUNCT
ejpam-5792	147	1	[	[	X
ejpam-5792	147	2	33	33	NUM
ejpam-5792	147	3	]	]	PUNCT
ejpam-5792	147	4	let	let	VERB
ejpam-5792	147	5	(	(	PUNCT
ejpam-5792	147	6	u	u	NOUN
ejpam-5792	147	7	,	,	PUNCT
ejpam-5792	147	8	ρ	ρ	PROPN
ejpam-5792	147	9	,	,	PUNCT
ejpam-5792	147	10	w	w	NOUN
ejpam-5792	147	11	)	)	PUNCT
ejpam-5792	147	12	be	be	AUX
ejpam-5792	147	13	a	a	DET
ejpam-5792	147	14	convex	convex	ADJ
ejpam-5792	147	15	metric	metric	ADJ
ejpam-5792	147	16	space	space	NOUN
ejpam-5792	147	17	and	and	CCONJ
ejpam-5792	147	18	t	t	NOUN
ejpam-5792	147	19	:	:	PUNCT
ejpam-5792	147	20	u	u	X
ejpam-5792	147	21	→	→	SYM
ejpam-5792	147	22	u	u	X
ejpam-5792	147	23	be	be	VERB
ejpam-5792	147	24	a	a	DET
ejpam-5792	147	25	mapping	mapping	NOUN
ejpam-5792	147	26	.	.	PUNCT
ejpam-5792	148	1	for	for	ADP
ejpam-5792	148	2	each	each	DET
ejpam-5792	148	3	λ	λ	PROPN
ejpam-5792	148	4	∈	∈	PROPN
ejpam-5792	148	5	[	[	X
ejpam-5792	148	6	0	0	NUM
ejpam-5792	148	7	,	,	PUNCT
ejpam-5792	148	8	1	1	NUM
ejpam-5792	148	9	)	)	PUNCT
ejpam-5792	148	10	,	,	PUNCT
ejpam-5792	148	11	,	,	PUNCT
ejpam-5792	148	12	define	define	VERB
ejpam-5792	148	13	the	the	DET
ejpam-5792	148	14	mapping	mapping	NOUN
ejpam-5792	148	15	tλ	tλ	ADP
ejpam-5792	148	16	:	:	PUNCT
ejpam-5792	148	17	u	u	X
ejpam-5792	148	18	→	→	SYM
ejpam-5792	148	19	u	u	NOUN
ejpam-5792	148	20	as	as	SCONJ
ejpam-5792	148	21	follows	follow	VERB
ejpam-5792	148	22	:	:	PUNCT
ejpam-5792	148	23	tλx	tλx	PROPN
ejpam-5792	149	1	=	=	SYM
ejpam-5792	149	2	w	w	PROPN
ejpam-5792	149	3	(	(	PUNCT
ejpam-5792	149	4	x	x	NOUN
ejpam-5792	149	5	,	,	PUNCT
ejpam-5792	149	6	tx;λ	tx;λ	NUM
ejpam-5792	149	7	)	)	PUNCT
ejpam-5792	149	8	,	,	PUNCT
ejpam-5792	149	9	x	x	PUNCT
ejpam-5792	149	10	∈	∈	PROPN
ejpam-5792	149	11	u	u	NOUN
ejpam-5792	149	12	.	.	PUNCT
ejpam-5792	150	1	(	(	PUNCT
ejpam-5792	150	2	2	2	NUM
ejpam-5792	150	3	)	)	PUNCT
ejpam-5792	150	4	then	then	ADV
ejpam-5792	150	5	,	,	PUNCT
ejpam-5792	150	6	fix(t	fix(t	PROPN
ejpam-5792	150	7	)	)	PUNCT
ejpam-5792	150	8	=	=	SYM
ejpam-5792	150	9	fix(tλ	fix(tλ	PROPN
ejpam-5792	150	10	)	)	PUNCT
ejpam-5792	150	11	.	.	PUNCT
ejpam-5792	151	1	a.	a.	PROPN
ejpam-5792	151	2	gangwar	gangwar	PROPN
ejpam-5792	151	3	et	et	PROPN
ejpam-5792	151	4	al	al	PROPN
ejpam-5792	151	5	.	.	PUNCT
ejpam-5792	151	6	/	/	SYM
ejpam-5792	151	7	eur	eur	PROPN
ejpam-5792	151	8	.	.	PUNCT
ejpam-5792	152	1	j.	j.	PROPN
ejpam-5792	152	2	pure	pure	PROPN
ejpam-5792	152	3	appl	appl	PROPN
ejpam-5792	152	4	.	.	PROPN
ejpam-5792	152	5	math	math	PROPN
ejpam-5792	152	6	,	,	PUNCT
ejpam-5792	152	7	18	18	NUM
ejpam-5792	152	8	(	(	PUNCT
ejpam-5792	152	9	2	2	NUM
ejpam-5792	152	10	)	)	PUNCT
ejpam-5792	152	11	(	(	PUNCT
ejpam-5792	152	12	2025	2025	NUM
ejpam-5792	152	13	)	)	PUNCT
ejpam-5792	152	14	,	,	PUNCT
ejpam-5792	152	15	5792	5792	NUM
ejpam-5792	152	16	6	6	NUM
ejpam-5792	152	17	of	of	ADP
ejpam-5792	152	18	16	16	NUM
ejpam-5792	152	19	3	3	NUM
ejpam-5792	152	20	.	.	PUNCT
ejpam-5792	152	21	main	main	ADJ
ejpam-5792	152	22	results	result	NOUN
ejpam-5792	152	23	definition	definition	NOUN
ejpam-5792	152	24	7	7	NUM
ejpam-5792	152	25	.	.	PUNCT
ejpam-5792	153	1	let	let	VERB
ejpam-5792	153	2	(	(	PUNCT
ejpam-5792	153	3	u	u	NOUN
ejpam-5792	153	4	,	,	PUNCT
ejpam-5792	153	5	ρ	ρ	PROPN
ejpam-5792	153	6	,	,	PUNCT
ejpam-5792	153	7	w	w	NOUN
ejpam-5792	153	8	)	)	PUNCT
ejpam-5792	153	9	be	be	AUX
ejpam-5792	153	10	a	a	DET
ejpam-5792	153	11	convex	convex	ADJ
ejpam-5792	153	12	metric	metric	ADJ
ejpam-5792	153	13	space	space	NOUN
ejpam-5792	153	14	.	.	PUNCT
ejpam-5792	154	1	a	a	DET
ejpam-5792	154	2	multivalued	multivalue	VERB
ejpam-5792	154	3	mapping	mapping	NOUN
ejpam-5792	154	4	t	t	NOUN
ejpam-5792	154	5	:	:	PUNCT
ejpam-5792	154	6	u	u	SYM
ejpam-5792	154	7	→	→	SYM
ejpam-5792	154	8	cb(u	cb(u	X
ejpam-5792	154	9	)	)	PUNCT
ejpam-5792	154	10	is	be	AUX
ejpam-5792	154	11	an	an	DET
ejpam-5792	154	12	eik	eik	NOUN
ejpam-5792	154	13	-	-	PUNCT
ejpam-5792	154	14	contraction	contraction	NOUN
ejpam-5792	154	15	via	via	ADP
ejpam-5792	154	16	a	a	DET
ejpam-5792	154	17	simulation	simulation	NOUN
ejpam-5792	154	18	function	function	PROPN
ejpam-5792	154	19	zg	zg	PROPN
ejpam-5792	154	20	,	,	PUNCT
ejpam-5792	154	21	if	if	SCONJ
ejpam-5792	154	22	there	there	PRON
ejpam-5792	154	23	are	be	VERB
ejpam-5792	154	24	α	α	PRON
ejpam-5792	154	25	∈	∈	PROPN
ejpam-5792	155	1	[	[	X
ejpam-5792	155	2	0	0	NUM
ejpam-5792	155	3	,	,	PUNCT
ejpam-5792	155	4	1	1	NUM
ejpam-5792	155	5	)	)	PUNCT
ejpam-5792	155	6	and	and	CCONJ
ejpam-5792	155	7	λ	λ	PROPN
ejpam-5792	155	8	,	,	PUNCT
ejpam-5792	155	9	p	p	PROPN
ejpam-5792	155	10	∈	∈	PROPN
ejpam-5792	155	11	(	(	PUNCT
ejpam-5792	155	12	0	0	NUM
ejpam-5792	155	13	,	,	PUNCT
ejpam-5792	155	14	1	1	NUM
ejpam-5792	155	15	)	)	PUNCT
ejpam-5792	156	1	so	so	SCONJ
ejpam-5792	156	2	that	that	PRON
ejpam-5792	156	3	ζ(h(w	ζ(h(w	PROPN
ejpam-5792	156	4	(	(	PUNCT
ejpam-5792	156	5	x	x	X
ejpam-5792	156	6	,	,	PUNCT
ejpam-5792	156	7	tx;λ),w	tx;λ),w	PROPN
ejpam-5792	156	8	(	(	PUNCT
ejpam-5792	156	9	y	y	NOUN
ejpam-5792	156	10	,	,	PUNCT
ejpam-5792	156	11	ty;λ	ty;λ	NUM
ejpam-5792	156	12	)	)	PUNCT
ejpam-5792	156	13	)	)	PUNCT
ejpam-5792	156	14	,	,	PUNCT
ejpam-5792	156	15	q(x	q(x	PROPN
ejpam-5792	156	16	,	,	PUNCT
ejpam-5792	156	17	y	y	NOUN
ejpam-5792	156	18	)	)	PUNCT
ejpam-5792	156	19	)	)	PUNCT
ejpam-5792	156	20	≥	≥	X
ejpam-5792	156	21	cg	cg	INTJ
ejpam-5792	156	22	.	.	PUNCT
ejpam-5792	157	1	(	(	PUNCT
ejpam-5792	157	2	3	3	X
ejpam-5792	157	3	)	)	PUNCT
ejpam-5792	157	4	here	here	ADV
ejpam-5792	157	5	,	,	PUNCT
ejpam-5792	157	6	q(x	q(x	PROPN
ejpam-5792	157	7	,	,	PUNCT
ejpam-5792	157	8	y	y	NOUN
ejpam-5792	157	9	)	)	PUNCT
ejpam-5792	157	10	=	=	SYM
ejpam-5792	157	11	p[d∗(x	p[d∗(x	NOUN
ejpam-5792	157	12	,	,	PUNCT
ejpam-5792	157	13	w	w	PROPN
ejpam-5792	157	14	(	(	PUNCT
ejpam-5792	157	15	x	x	PROPN
ejpam-5792	157	16	,	,	PUNCT
ejpam-5792	157	17	tx;λ)]α[d∗(y	tx;λ)]α[d∗(y	PROPN
ejpam-5792	157	18	,	,	PUNCT
ejpam-5792	157	19	w	w	PROPN
ejpam-5792	157	20	(	(	PUNCT
ejpam-5792	157	21	y	y	PROPN
ejpam-5792	157	22	,	,	PUNCT
ejpam-5792	157	23	ty;λ)]1−α	ty;λ)]1−α	ADJ
ejpam-5792	157	24	for	for	ADP
ejpam-5792	157	25	each	each	DET
ejpam-5792	157	26	x	x	NOUN
ejpam-5792	157	27	,	,	PUNCT
ejpam-5792	157	28	y	y	PROPN
ejpam-5792	157	29	∈	∈	PROPN
ejpam-5792	157	30	u	u	PROPN
ejpam-5792	157	31	/f	/f	NOUN
ejpam-5792	157	32	ix(t	ix(t	PROPN
ejpam-5792	157	33	)	)	PUNCT
ejpam-5792	157	34	.	.	PUNCT
ejpam-5792	158	1	theorem	theorem	NOUN
ejpam-5792	158	2	3	3	X
ejpam-5792	158	3	.	.	PUNCT
ejpam-5792	159	1	let	let	VERB
ejpam-5792	159	2	(	(	PUNCT
ejpam-5792	159	3	u	u	NOUN
ejpam-5792	159	4	,	,	PUNCT
ejpam-5792	159	5	ρ	ρ	PROPN
ejpam-5792	159	6	,	,	PUNCT
ejpam-5792	159	7	w	w	NOUN
ejpam-5792	159	8	)	)	PUNCT
ejpam-5792	159	9	be	be	AUX
ejpam-5792	159	10	a	a	DET
ejpam-5792	159	11	convex	convex	NOUN
ejpam-5792	159	12	complete	complete	ADJ
ejpam-5792	159	13	metric	metric	ADJ
ejpam-5792	159	14	space	space	NOUN
ejpam-5792	159	15	and	and	CCONJ
ejpam-5792	159	16	t	t	NOUN
ejpam-5792	159	17	:	:	PUNCT
ejpam-5792	159	18	u	u	PROPN
ejpam-5792	159	19	→	→	SYM
ejpam-5792	159	20	cb(u	cb(u	PUNCT
ejpam-5792	159	21	)	)	PUNCT
ejpam-5792	159	22	be	be	AUX
ejpam-5792	159	23	a	a	DET
ejpam-5792	159	24	multivalued	multivalue	VERB
ejpam-5792	159	25	eik	eik	NOUN
ejpam-5792	159	26	-	-	PUNCT
ejpam-5792	159	27	contraction	contraction	NOUN
ejpam-5792	159	28	via	via	ADP
ejpam-5792	159	29	a	a	DET
ejpam-5792	159	30	simulation	simulation	NOUN
ejpam-5792	159	31	function	function	PROPN
ejpam-5792	159	32	zg	zg	PROPN
ejpam-5792	159	33	.	.	PUNCT
ejpam-5792	160	1	then	then	ADV
ejpam-5792	160	2	fix(t	fix(t	PROPN
ejpam-5792	160	3	)	)	PUNCT
ejpam-5792	160	4	̸=	̸=	PROPN
ejpam-5792	160	5	ϕ.	ϕ.	NOUN
ejpam-5792	160	6	proof	proof	NOUN
ejpam-5792	160	7	.	.	PUNCT
ejpam-5792	161	1	using	use	VERB
ejpam-5792	161	2	the	the	DET
ejpam-5792	161	3	multivalued	multivalue	VERB
ejpam-5792	161	4	eik	eik	PROPN
ejpam-5792	161	5	-	-	PUNCT
ejpam-5792	161	6	contraction	contraction	NOUN
ejpam-5792	161	7	condition	condition	NOUN
ejpam-5792	161	8	(	(	PUNCT
ejpam-5792	161	9	3	3	NUM
ejpam-5792	161	10	)	)	PUNCT
ejpam-5792	161	11	,	,	PUNCT
ejpam-5792	161	12	the	the	DET
ejpam-5792	161	13	mapping	mapping	NOUN
ejpam-5792	161	14	tλ	tλ	ADP
ejpam-5792	161	15	:	:	PUNCT
ejpam-5792	161	16	u	u	PROPN
ejpam-5792	161	17	→	→	SYM
ejpam-5792	161	18	cb(u	cb(u	X
ejpam-5792	161	19	)	)	PUNCT
ejpam-5792	161	20	given	give	VERB
ejpam-5792	161	21	by	by	ADP
ejpam-5792	161	22	(	(	PUNCT
ejpam-5792	161	23	2	2	X
ejpam-5792	161	24	)	)	PUNCT
ejpam-5792	161	25	satisfies	satisfie	NOUN
ejpam-5792	161	26	ζ(h(tλx	ζ(h(tλx	ADP
ejpam-5792	161	27	,	,	PUNCT
ejpam-5792	161	28	tλy	tλy	NOUN
ejpam-5792	161	29	)	)	PUNCT
ejpam-5792	161	30	,	,	PUNCT
ejpam-5792	161	31	q(x	q(x	PROPN
ejpam-5792	161	32	,	,	PUNCT
ejpam-5792	161	33	y	y	NOUN
ejpam-5792	161	34	)	)	PUNCT
ejpam-5792	161	35	)	)	PUNCT
ejpam-5792	161	36	≥	≥	X
ejpam-5792	161	37	cg	cg	INTJ
ejpam-5792	161	38	,	,	PUNCT
ejpam-5792	161	39	(	(	PUNCT
ejpam-5792	161	40	4	4	X
ejpam-5792	161	41	)	)	PUNCT
ejpam-5792	161	42	where	where	SCONJ
ejpam-5792	161	43	q(x	q(x	PROPN
ejpam-5792	161	44	,	,	PUNCT
ejpam-5792	161	45	y	y	NOUN
ejpam-5792	161	46	)	)	PUNCT
ejpam-5792	161	47	=	=	SYM
ejpam-5792	161	48	p[d∗(x	p[d∗(x	NOUN
ejpam-5792	161	49	,	,	PUNCT
ejpam-5792	161	50	tλx	tλx	NOUN
ejpam-5792	161	51	)	)	PUNCT
ejpam-5792	161	52	]	]	PUNCT
ejpam-5792	162	1	α[d∗(y	α[d∗(y	PROPN
ejpam-5792	162	2	,	,	PUNCT
ejpam-5792	162	3	tλy	tλy	NOUN
ejpam-5792	162	4	)	)	PUNCT
ejpam-5792	162	5	]	]	PUNCT
ejpam-5792	162	6	1−α	1−α	NUM
ejpam-5792	162	7	for	for	ADP
ejpam-5792	162	8	each	each	DET
ejpam-5792	162	9	x	x	NOUN
ejpam-5792	162	10	,	,	PUNCT
ejpam-5792	162	11	y	y	PROPN
ejpam-5792	162	12	∈	∈	PROPN
ejpam-5792	162	13	u	u	PROPN
ejpam-5792	162	14	/f	/f	NOUN
ejpam-5792	162	15	ix(t	ix(t	PROPN
ejpam-5792	162	16	)	)	PUNCT
ejpam-5792	162	17	,	,	PUNCT
ejpam-5792	162	18	that	that	ADV
ejpam-5792	162	19	is	is	ADV
ejpam-5792	162	20	,	,	PUNCT
ejpam-5792	162	21	tλ	tλ	NOUN
ejpam-5792	162	22	is	be	AUX
ejpam-5792	162	23	an	an	DET
ejpam-5792	162	24	interpolative	interpolative	ADJ
ejpam-5792	162	25	kannan	kannan	PROPN
ejpam-5792	162	26	type	type	NOUN
ejpam-5792	162	27	contraction	contraction	NOUN
ejpam-5792	162	28	.	.	PUNCT
ejpam-5792	163	1	let	let	VERB
ejpam-5792	163	2	y0	y0	PRON
ejpam-5792	163	3	∈	∈	PROPN
ejpam-5792	163	4	u	u	NOUN
ejpam-5792	163	5	and	and	CCONJ
ejpam-5792	163	6	define	define	VERB
ejpam-5792	163	7	a	a	DET
ejpam-5792	163	8	sequence	sequence	NOUN
ejpam-5792	163	9	yn	yn	INTJ
ejpam-5792	163	10	∈	∈	PROPN
ejpam-5792	163	11	tλyn−1	tλyn−1	PROPN
ejpam-5792	163	12	,	,	PUNCT
ejpam-5792	163	13	for	for	ADP
ejpam-5792	163	14	each	each	DET
ejpam-5792	163	15	n	n	DET
ejpam-5792	163	16	≥	≥	NOUN
ejpam-5792	163	17	1	1	NUM
ejpam-5792	163	18	.	.	PUNCT
ejpam-5792	164	1	if	if	SCONJ
ejpam-5792	164	2	we	we	PRON
ejpam-5792	164	3	have	have	VERB
ejpam-5792	164	4	yn0	yn0	NOUN
ejpam-5792	164	5	=	=	PUNCT
ejpam-5792	164	6	yn0	yn0	ADJ
ejpam-5792	164	7	+	+	ADJ
ejpam-5792	164	8	1	1	NUM
ejpam-5792	164	9	for	for	ADP
ejpam-5792	164	10	some	some	DET
ejpam-5792	164	11	n0	n0	PROPN
ejpam-5792	164	12	∈	∈	PROPN
ejpam-5792	164	13	n	n	CCONJ
ejpam-5792	164	14	,	,	PUNCT
ejpam-5792	164	15	then	then	ADV
ejpam-5792	164	16	yn0	yn0	PROPN
ejpam-5792	164	17	is	be	AUX
ejpam-5792	164	18	fixed	fix	VERB
ejpam-5792	164	19	point	point	NOUN
ejpam-5792	164	20	of	of	ADP
ejpam-5792	164	21	tλ	tλ	ADP
ejpam-5792	164	22	and	and	CCONJ
ejpam-5792	164	23	thus	thus	ADV
ejpam-5792	164	24	a	a	DET
ejpam-5792	164	25	fixed	fix	VERB
ejpam-5792	164	26	point	point	NOUN
ejpam-5792	164	27	of	of	ADP
ejpam-5792	164	28	t	t	PROPN
ejpam-5792	164	29	.	.	PUNCT
ejpam-5792	165	1	so	so	ADV
ejpam-5792	165	2	there	there	PRON
ejpam-5792	165	3	is	be	VERB
ejpam-5792	165	4	nothing	nothing	PRON
ejpam-5792	165	5	to	to	PART
ejpam-5792	165	6	prove	prove	VERB
ejpam-5792	165	7	.	.	PUNCT
ejpam-5792	166	1	let	let	VERB
ejpam-5792	166	2	yn	yn	PRON
ejpam-5792	166	3	̸=	̸=	PROPN
ejpam-5792	166	4	yn+1	yn+1	NUM
ejpam-5792	166	5	for	for	ADP
ejpam-5792	166	6	each	each	DET
ejpam-5792	166	7	n	n	PRON
ejpam-5792	166	8	≥	≥	NOUN
ejpam-5792	166	9	0	0	NUM
ejpam-5792	166	10	.	.	PUNCT
ejpam-5792	167	1	since	since	SCONJ
ejpam-5792	167	2	0	0	NUM
ejpam-5792	167	3	<	<	X
ejpam-5792	167	4	p	p	X
ejpam-5792	167	5	<	<	X
ejpam-5792	167	6	1	1	NUM
ejpam-5792	167	7	and	and	CCONJ
ejpam-5792	167	8	yn	yn	PRON
ejpam-5792	167	9	∈	∈	PROPN
ejpam-5792	167	10	tλyn−1	tλyn−1	PROPN
ejpam-5792	167	11	for	for	ADP
ejpam-5792	167	12	each	each	DET
ejpam-5792	167	13	n	n	PRON
ejpam-5792	167	14	≥	≥	NOUN
ejpam-5792	167	15	1	1	NUM
ejpam-5792	167	16	,	,	PUNCT
ejpam-5792	167	17	we	we	PRON
ejpam-5792	167	18	can	can	AUX
ejpam-5792	167	19	choose	choose	VERB
ejpam-5792	167	20	q	q	PROPN
ejpam-5792	167	21	>	>	PUNCT
ejpam-5792	167	22	1	1	NUM
ejpam-5792	167	23	so	so	SCONJ
ejpam-5792	167	24	that	that	SCONJ
ejpam-5792	167	25	qp	qp	ADP
ejpam-5792	167	26	<	<	X
ejpam-5792	167	27	1	1	NUM
ejpam-5792	167	28	,	,	PUNCT
ejpam-5792	167	29	then	then	ADV
ejpam-5792	167	30	from	from	ADP
ejpam-5792	167	31	lemma	lemma	PROPN
ejpam-5792	167	32	1	1	NUM
ejpam-5792	167	33	there	there	PRON
ejpam-5792	167	34	is	be	VERB
ejpam-5792	167	35	yn+1	yn+1	PROPN
ejpam-5792	167	36	∈	∈	PROPN
ejpam-5792	167	37	tλyn	tλyn	NOUN
ejpam-5792	167	38	,	,	PUNCT
ejpam-5792	167	39	for	for	ADP
ejpam-5792	167	40	each	each	DET
ejpam-5792	167	41	n	n	PRON
ejpam-5792	167	42	≥	≥	NOUN
ejpam-5792	167	43	1	1	NUM
ejpam-5792	167	44	so	so	SCONJ
ejpam-5792	167	45	that	that	SCONJ
ejpam-5792	167	46	ρ(yn	ρ(yn	NUM
ejpam-5792	167	47	,	,	PUNCT
ejpam-5792	167	48	yn+1	yn+1	NUM
ejpam-5792	167	49	)	)	PUNCT
ejpam-5792	167	50	≤	≤	NOUN
ejpam-5792	167	51	qh(tλyn−1	qh(tλyn−1	ADV
ejpam-5792	167	52	,	,	PUNCT
ejpam-5792	167	53	tλyn	tλyn	VERB
ejpam-5792	167	54	)	)	PUNCT
ejpam-5792	167	55	.	.	PUNCT
ejpam-5792	168	1	(	(	PUNCT
ejpam-5792	168	2	5	5	X
ejpam-5792	168	3	)	)	PUNCT
ejpam-5792	168	4	taking	take	VERB
ejpam-5792	168	5	x	x	PUNCT
ejpam-5792	168	6	=	=	PUNCT
ejpam-5792	168	7	yn	yn	PROPN
ejpam-5792	168	8	and	and	CCONJ
ejpam-5792	168	9	y	y	PROPN
ejpam-5792	168	10	=	=	SYM
ejpam-5792	168	11	yn−1	yn−1	PROPN
ejpam-5792	168	12	,	,	PUNCT
ejpam-5792	168	13	from	from	ADP
ejpam-5792	168	14	equation	equation	NOUN
ejpam-5792	168	15	(	(	PUNCT
ejpam-5792	168	16	3	3	NUM
ejpam-5792	168	17	)	)	PUNCT
ejpam-5792	168	18	,	,	PUNCT
ejpam-5792	168	19	we	we	PRON
ejpam-5792	168	20	obtain	obtain	VERB
ejpam-5792	168	21	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	168	22	,	,	PUNCT
ejpam-5792	168	23	tλyn−1	tλyn−1	PROPN
ejpam-5792	168	24	)	)	PUNCT
ejpam-5792	168	25	,	,	PUNCT
ejpam-5792	168	26	q(yn	q(yn	PROPN
ejpam-5792	168	27	,	,	PUNCT
ejpam-5792	168	28	yn−1	yn−1	PROPN
ejpam-5792	168	29	)	)	PUNCT
ejpam-5792	168	30	≥	≥	NOUN
ejpam-5792	169	1	cg	cg	NOUN
ejpam-5792	169	2	.	.	PUNCT
ejpam-5792	170	1	(	(	PUNCT
ejpam-5792	170	2	6	6	NUM
ejpam-5792	170	3	)	)	PUNCT
ejpam-5792	170	4	by	by	ADP
ejpam-5792	170	5	definition	definition	NOUN
ejpam-5792	170	6	3	3	NUM
ejpam-5792	170	7	,	,	PUNCT
ejpam-5792	170	8	we	we	PRON
ejpam-5792	170	9	obtain	obtain	VERB
ejpam-5792	170	10	cg	cg	NOUN
ejpam-5792	170	11	≤	≤	NOUN
ejpam-5792	170	12	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	170	13	,	,	PUNCT
ejpam-5792	170	14	tλyn−1	tλyn−1	PROPN
ejpam-5792	170	15	)	)	PUNCT
ejpam-5792	170	16	,	,	PUNCT
ejpam-5792	170	17	q(yn	q(yn	PROPN
ejpam-5792	170	18	,	,	PUNCT
ejpam-5792	170	19	yn−1	yn−1	NOUN
ejpam-5792	170	20	)	)	PUNCT
ejpam-5792	170	21	)	)	PUNCT
ejpam-5792	171	1	<	<	X
ejpam-5792	171	2	g(q(yn	g(q(yn	X
ejpam-5792	171	3	,	,	PUNCT
ejpam-5792	171	4	yn−1	yn−1	NOUN
ejpam-5792	171	5	)	)	PUNCT
ejpam-5792	171	6	,	,	PUNCT
ejpam-5792	171	7	h(tλyn	h(tλyn	VERB
ejpam-5792	171	8	,	,	PUNCT
ejpam-5792	171	9	tλyn−1	tλyn−1	PROPN
ejpam-5792	171	10	)	)	PUNCT
ejpam-5792	171	11	.	.	PUNCT
ejpam-5792	172	1	from	from	ADP
ejpam-5792	172	2	definition	definition	NOUN
ejpam-5792	172	3	2	2	NUM
ejpam-5792	172	4	,	,	PUNCT
ejpam-5792	172	5	we	we	PRON
ejpam-5792	172	6	obtain	obtain	VERB
ejpam-5792	172	7	h(tλyn	h(tλyn	ADJ
ejpam-5792	172	8	,	,	PUNCT
ejpam-5792	172	9	tλyn−1	tλyn−1	NUM
ejpam-5792	172	10	)	)	PUNCT
ejpam-5792	173	1	<	<	X
ejpam-5792	173	2	q(yn	q(yn	PROPN
ejpam-5792	173	3	,	,	PUNCT
ejpam-5792	173	4	yn−1	yn−1	NOUN
ejpam-5792	173	5	)	)	PUNCT
ejpam-5792	173	6	=	=	SYM
ejpam-5792	173	7	p[d∗(yn	p[d∗(yn	NOUN
ejpam-5792	173	8	,	,	PUNCT
ejpam-5792	173	9	tλyn	tλyn	VERB
ejpam-5792	173	10	]	]	PUNCT
ejpam-5792	173	11	α.[d∗(yn−1	α.[d∗(yn−1	PROPN
ejpam-5792	173	12	,	,	PUNCT
ejpam-5792	173	13	tλyn−1	tλyn−1	PROPN
ejpam-5792	173	14	]	]	X
ejpam-5792	173	15	1−α	1−α	NUM
ejpam-5792	173	16	.	.	PUNCT
ejpam-5792	174	1	a.	a.	NOUN
ejpam-5792	174	2	gangwar	gangwar	PROPN
ejpam-5792	174	3	et	et	PROPN
ejpam-5792	174	4	al	al	PROPN
ejpam-5792	174	5	.	.	PUNCT
ejpam-5792	174	6	/	/	SYM
ejpam-5792	174	7	eur	eur	PROPN
ejpam-5792	174	8	.	.	PUNCT
ejpam-5792	175	1	j.	j.	PROPN
ejpam-5792	175	2	pure	pure	PROPN
ejpam-5792	175	3	appl	appl	PROPN
ejpam-5792	175	4	.	.	PROPN
ejpam-5792	175	5	math	math	PROPN
ejpam-5792	175	6	,	,	PUNCT
ejpam-5792	175	7	18	18	NUM
ejpam-5792	175	8	(	(	PUNCT
ejpam-5792	175	9	2	2	NUM
ejpam-5792	175	10	)	)	PUNCT
ejpam-5792	175	11	(	(	PUNCT
ejpam-5792	175	12	2025	2025	NUM
ejpam-5792	175	13	)	)	PUNCT
ejpam-5792	175	14	,	,	PUNCT
ejpam-5792	175	15	5792	5792	NUM
ejpam-5792	175	16	7	7	NUM
ejpam-5792	175	17	of	of	ADP
ejpam-5792	175	18	16	16	NUM
ejpam-5792	175	19	using	use	VERB
ejpam-5792	175	20	equation	equation	NOUN
ejpam-5792	175	21	(	(	PUNCT
ejpam-5792	175	22	5	5	NUM
ejpam-5792	175	23	)	)	PUNCT
ejpam-5792	175	24	and	and	CCONJ
ejpam-5792	175	25	substituting	substitute	VERB
ejpam-5792	175	26	pq	pq	PROPN
ejpam-5792	175	27	=	=	SYM
ejpam-5792	175	28	θ	θ	X
ejpam-5792	175	29	<	<	X
ejpam-5792	175	30	1	1	NUM
ejpam-5792	175	31	,	,	PUNCT
ejpam-5792	175	32	we	we	PRON
ejpam-5792	175	33	obtain	obtain	VERB
ejpam-5792	175	34	ρ(yn	ρ(yn	NUM
ejpam-5792	175	35	,	,	PUNCT
ejpam-5792	175	36	yn+1	yn+1	NUM
ejpam-5792	175	37	)	)	PUNCT
ejpam-5792	175	38	<	<	X
ejpam-5792	175	39	pq	pq	PROPN
ejpam-5792	176	1	[	[	X
ejpam-5792	176	2	d∗(yn	d∗(yn	NOUN
ejpam-5792	176	3	,	,	PUNCT
ejpam-5792	176	4	tλyn	tλyn	VERB
ejpam-5792	176	5	]	]	PUNCT
ejpam-5792	176	6	α.[d∗(yn−1	α.[d∗(yn−1	PROPN
ejpam-5792	176	7	,	,	PUNCT
ejpam-5792	176	8	tλyn−1	tλyn−1	PROPN
ejpam-5792	176	9	]	]	X
ejpam-5792	176	10	1−α	1−α	NUM
ejpam-5792	177	1	=	=	SYM
ejpam-5792	177	2	θ[d∗(yn	θ[d∗(yn	ADJ
ejpam-5792	177	3	,	,	PUNCT
ejpam-5792	177	4	tλyn	tλyn	VERB
ejpam-5792	177	5	]	]	PUNCT
ejpam-5792	177	6	α.[d∗(yn−1	α.[d∗(yn−1	PROPN
ejpam-5792	177	7	,	,	PUNCT
ejpam-5792	177	8	tλyn−1	tλyn−1	PROPN
ejpam-5792	177	9	]	]	X
ejpam-5792	177	10	1−α	1−α	NUM
ejpam-5792	177	11	.	.	PUNCT
ejpam-5792	178	1	since	since	SCONJ
ejpam-5792	178	2	we	we	PRON
ejpam-5792	178	3	know	know	VERB
ejpam-5792	178	4	yn	yn	PRON
ejpam-5792	178	5	∈	∈	PROPN
ejpam-5792	178	6	tλyn−1	tλyn−1	PROPN
ejpam-5792	178	7	,	,	PUNCT
ejpam-5792	178	8	one	one	PRON
ejpam-5792	178	9	gets	get	VERB
ejpam-5792	178	10	d∗(yn−1	d∗(yn−1	ADJ
ejpam-5792	178	11	,	,	PUNCT
ejpam-5792	178	12	tyn−1	tyn−1	PROPN
ejpam-5792	178	13	)	)	PUNCT
ejpam-5792	178	14	≤	≤	NOUN
ejpam-5792	178	15	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	178	16	,	,	PUNCT
ejpam-5792	178	17	yn	yn	PROPN
ejpam-5792	178	18	)	)	PUNCT
ejpam-5792	178	19	,	,	PUNCT
ejpam-5792	178	20	∀	∀	X
ejpam-5792	178	21	n	n	PRON
ejpam-5792	178	22	≥	≥	NOUN
ejpam-5792	178	23	1	1	NUM
ejpam-5792	178	24	.	.	PUNCT
ejpam-5792	179	1	therefore	therefore	ADV
ejpam-5792	179	2	,	,	PUNCT
ejpam-5792	179	3	we	we	PRON
ejpam-5792	179	4	obtain	obtain	VERB
ejpam-5792	179	5	ρ(yn	ρ(yn	NUM
ejpam-5792	179	6	,	,	PUNCT
ejpam-5792	179	7	yn+1	yn+1	X
ejpam-5792	179	8	)	)	PUNCT
ejpam-5792	179	9	<	<	X
ejpam-5792	179	10	θ[ρ(yn	θ[ρ(yn	NOUN
ejpam-5792	179	11	,	,	PUNCT
ejpam-5792	179	12	yn+1	yn+1	X
ejpam-5792	179	13	)	)	PUNCT
ejpam-5792	179	14	]	]	PUNCT
ejpam-5792	179	15	α[ρ(yn−1	α[ρ(yn−1	PROPN
ejpam-5792	179	16	,	,	PUNCT
ejpam-5792	179	17	yn	yn	X
ejpam-5792	179	18	]	]	X
ejpam-5792	179	19	1−α	1−α	NUM
ejpam-5792	179	20	.	.	PUNCT
ejpam-5792	180	1	(	(	PUNCT
ejpam-5792	180	2	7	7	X
ejpam-5792	180	3	)	)	PUNCT
ejpam-5792	180	4	suppose	suppose	VERB
ejpam-5792	180	5	if	if	SCONJ
ejpam-5792	180	6	possible	possible	ADJ
ejpam-5792	180	7	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	180	8	,	,	PUNCT
ejpam-5792	180	9	yn	yn	PROPN
ejpam-5792	180	10	)	)	PUNCT
ejpam-5792	180	11	<	<	X
ejpam-5792	180	12	ρ(yn	ρ(yn	NUM
ejpam-5792	180	13	,	,	PUNCT
ejpam-5792	180	14	yn+1	yn+1	NUM
ejpam-5792	180	15	)	)	PUNCT
ejpam-5792	180	16	for	for	ADP
ejpam-5792	180	17	some	some	DET
ejpam-5792	180	18	n	n	PRON
ejpam-5792	180	19	≥	≥	NOUN
ejpam-5792	180	20	1	1	NUM
ejpam-5792	180	21	,	,	PUNCT
ejpam-5792	180	22	then	then	ADV
ejpam-5792	180	23	ρ(yn	ρ(yn	NUM
ejpam-5792	180	24	,	,	PUNCT
ejpam-5792	180	25	yn+1	yn+1	X
ejpam-5792	180	26	)	)	PUNCT
ejpam-5792	180	27	<	<	X
ejpam-5792	180	28	θ[ρ(yn	θ[ρ(yn	NOUN
ejpam-5792	180	29	,	,	PUNCT
ejpam-5792	180	30	yn+1	yn+1	X
ejpam-5792	180	31	)	)	PUNCT
ejpam-5792	180	32	]	]	X
ejpam-5792	181	1	α[ρ(yn	α[ρ(yn	PROPN
ejpam-5792	181	2	,	,	PUNCT
ejpam-5792	181	3	yn+1	yn+1	NUM
ejpam-5792	181	4	)	)	PUNCT
ejpam-5792	181	5	]	]	PUNCT
ejpam-5792	182	1	1−α	1−α	NUM
ejpam-5792	182	2	=	=	SYM
ejpam-5792	182	3	θρ(yn	θρ(yn	NOUN
ejpam-5792	182	4	,	,	PUNCT
ejpam-5792	182	5	yn+1	yn+1	NUM
ejpam-5792	182	6	)	)	PUNCT
ejpam-5792	182	7	.	.	PUNCT
ejpam-5792	183	1	this	this	PRON
ejpam-5792	183	2	leads	lead	VERB
ejpam-5792	183	3	to	to	ADP
ejpam-5792	183	4	a	a	DET
ejpam-5792	183	5	contradiction	contradiction	NOUN
ejpam-5792	183	6	as	as	ADP
ejpam-5792	183	7	θ	θ	PROPN
ejpam-5792	183	8	<	<	X
ejpam-5792	183	9	1	1	NUM
ejpam-5792	183	10	.	.	PUNCT
ejpam-5792	183	11	therefore	therefore	ADV
ejpam-5792	183	12	,	,	PUNCT
ejpam-5792	183	13	ρ(yn	ρ(yn	PROPN
ejpam-5792	183	14	,	,	PUNCT
ejpam-5792	183	15	yn+1	yn+1	NUM
ejpam-5792	183	16	)	)	PUNCT
ejpam-5792	183	17	≤	≤	NOUN
ejpam-5792	183	18	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	183	19	,	,	PUNCT
ejpam-5792	183	20	yn	yn	PROPN
ejpam-5792	183	21	)	)	PUNCT
ejpam-5792	183	22	.	.	PUNCT
ejpam-5792	184	1	from	from	ADP
ejpam-5792	184	2	equation	equation	NOUN
ejpam-5792	184	3	(	(	PUNCT
ejpam-5792	184	4	7	7	NUM
ejpam-5792	184	5	)	)	PUNCT
ejpam-5792	184	6	,	,	PUNCT
ejpam-5792	184	7	we	we	PRON
ejpam-5792	184	8	obtain	obtain	VERB
ejpam-5792	184	9	ρ(yn	ρ(yn	NUM
ejpam-5792	184	10	,	,	PUNCT
ejpam-5792	184	11	yn+1	yn+1	NUM
ejpam-5792	184	12	)	)	PUNCT
ejpam-5792	184	13	≤	≤	NOUN
ejpam-5792	184	14	θρ(yn−1	θρ(yn−1	PROPN
ejpam-5792	184	15	,	,	PUNCT
ejpam-5792	184	16	yn	yn	PROPN
ejpam-5792	184	17	)	)	PUNCT
ejpam-5792	184	18	,	,	PUNCT
ejpam-5792	184	19	(	(	PUNCT
ejpam-5792	184	20	8)	8)	NUM
ejpam-5792	184	21	which	which	PRON
ejpam-5792	184	22	further	far	ADV
ejpam-5792	184	23	implies	imply	VERB
ejpam-5792	184	24	ρ(yn	ρ(yn	NUM
ejpam-5792	184	25	,	,	PUNCT
ejpam-5792	184	26	yn+1	yn+1	NUM
ejpam-5792	184	27	)	)	PUNCT
ejpam-5792	184	28	<	<	X
ejpam-5792	184	29	θρ(yn−1	θρ(yn−1	PROPN
ejpam-5792	184	30	,	,	PUNCT
ejpam-5792	184	31	yn	yn	PROPN
ejpam-5792	184	32	)	)	PUNCT
ejpam-5792	184	33	<	<	X
ejpam-5792	185	1	θ2ρ(yn−2	θ2ρ(yn−2	PROPN
ejpam-5792	185	2	,	,	PUNCT
ejpam-5792	185	3	yn−1	yn−1	NOUN
ejpam-5792	185	4	)	)	PUNCT
ejpam-5792	185	5	<	<	X
ejpam-5792	185	6	.	.	PUNCT
ejpam-5792	185	7	.	.	PUNCT
ejpam-5792	185	8	.	.	PUNCT
ejpam-5792	186	1	<	<	X
ejpam-5792	186	2	θnρ(y0	θnρ(y0	PROPN
ejpam-5792	186	3	,	,	PUNCT
ejpam-5792	186	4	y1	y1	PROPN
ejpam-5792	186	5	)	)	PUNCT
ejpam-5792	186	6	.	.	PUNCT
ejpam-5792	187	1	taking	take	VERB
ejpam-5792	187	2	n→	n→	ADV
ejpam-5792	187	3	∞	∞	PROPN
ejpam-5792	187	4	,	,	PUNCT
ejpam-5792	187	5	we	we	PRON
ejpam-5792	187	6	get	get	VERB
ejpam-5792	187	7	ρ(yn	ρ(yn	NUM
ejpam-5792	187	8	,	,	PUNCT
ejpam-5792	187	9	yn+1	yn+1	NUM
ejpam-5792	187	10	)	)	PUNCT
ejpam-5792	187	11	→	→	SYM
ejpam-5792	188	1	0	0	X
ejpam-5792	188	2	.	.	PUNCT
ejpam-5792	189	1	let	let	VERB
ejpam-5792	189	2	m	m	PRON
ejpam-5792	189	3	,	,	PUNCT
ejpam-5792	189	4	n	n	PROPN
ejpam-5792	189	5	∈	∈	PROPN
ejpam-5792	189	6	n	n	CCONJ
ejpam-5792	189	7	,	,	PUNCT
ejpam-5792	189	8	m	m	VERB
ejpam-5792	189	9	>	>	X
ejpam-5792	189	10	n	n	CCONJ
ejpam-5792	189	11	,	,	PUNCT
ejpam-5792	189	12	then	then	ADV
ejpam-5792	189	13	ρ(yn	ρ(yn	NUM
ejpam-5792	189	14	,	,	PUNCT
ejpam-5792	189	15	ym	ym	NOUN
ejpam-5792	189	16	)	)	PUNCT
ejpam-5792	189	17	≤	≤	NOUN
ejpam-5792	189	18	ρ(yn	ρ(yn	NUM
ejpam-5792	189	19	,	,	PUNCT
ejpam-5792	189	20	yn+1	yn+1	NUM
ejpam-5792	189	21	)	)	PUNCT
ejpam-5792	189	22	+	+	X
ejpam-5792	189	23	ρ(yn+1	ρ(yn+1	PROPN
ejpam-5792	189	24	,	,	PUNCT
ejpam-5792	189	25	yn+2	yn+2	NUM
ejpam-5792	189	26	)	)	PUNCT
ejpam-5792	189	27	+	+	CCONJ
ejpam-5792	189	28	·	·	PUNCT
ejpam-5792	189	29	·	·	PUNCT
ejpam-5792	189	30	·	·	PUNCT
ejpam-5792	189	31	+	+	NUM
ejpam-5792	189	32	d(ym−1	d(ym−1	NUM
ejpam-5792	189	33	,	,	PUNCT
ejpam-5792	189	34	ym	ym	NOUN
ejpam-5792	189	35	)	)	PUNCT
ejpam-5792	189	36	≤	≤	NUM
ejpam-5792	190	1	θn	θn	ADP
ejpam-5792	190	2	1−	1−	NUM
ejpam-5792	190	3	θ	θ	PROPN
ejpam-5792	190	4	ρ(y0	ρ(y0	NOUN
ejpam-5792	190	5	,	,	PUNCT
ejpam-5792	190	6	y1	y1	NOUN
ejpam-5792	190	7	)	)	PUNCT
ejpam-5792	190	8	.	.	PUNCT
ejpam-5792	191	1	as	as	ADP
ejpam-5792	191	2	n	n	NUM
ejpam-5792	191	3	→	→	SYM
ejpam-5792	191	4	∞	∞	PROPN
ejpam-5792	191	5	,	,	PUNCT
ejpam-5792	191	6	we	we	PRON
ejpam-5792	191	7	obtain	obtain	VERB
ejpam-5792	191	8	ρ(yn	ρ(yn	NUM
ejpam-5792	191	9	,	,	PUNCT
ejpam-5792	191	10	ym	ym	NOUN
ejpam-5792	191	11	)	)	PUNCT
ejpam-5792	191	12	→	→	SYM
ejpam-5792	192	1	0	0	X
ejpam-5792	192	2	.	.	PUNCT
ejpam-5792	193	1	this	this	PRON
ejpam-5792	193	2	implies	imply	VERB
ejpam-5792	193	3	{	{	PUNCT
ejpam-5792	193	4	yn	yn	PRON
ejpam-5792	193	5	}	}	PUNCT
ejpam-5792	193	6	is	be	AUX
ejpam-5792	193	7	a	a	DET
ejpam-5792	193	8	cauchy	cauchy	ADJ
ejpam-5792	193	9	sequence	sequence	NOUN
ejpam-5792	193	10	and	and	CCONJ
ejpam-5792	193	11	using	use	VERB
ejpam-5792	193	12	the	the	DET
ejpam-5792	193	13	completeness	completeness	NOUN
ejpam-5792	193	14	of	of	ADP
ejpam-5792	193	15	u	u	NOUN
ejpam-5792	193	16	,	,	PUNCT
ejpam-5792	193	17	there	there	PRON
ejpam-5792	193	18	is	be	VERB
ejpam-5792	193	19	y∗	y∗	PROPN
ejpam-5792	193	20	∈	∈	NOUN
ejpam-5792	193	21	u	u	NOUN
ejpam-5792	193	22	so	so	SCONJ
ejpam-5792	193	23	that	that	SCONJ
ejpam-5792	193	24	lim	lim	PROPN
ejpam-5792	193	25	n→∞	n→∞	X
ejpam-5792	193	26	yn	yn	X
ejpam-5792	193	27	=	=	PUNCT
ejpam-5792	193	28	y∗.	y∗.	PRON
ejpam-5792	193	29	suppose	suppose	VERB
ejpam-5792	193	30	y	y	PROPN
ejpam-5792	193	31	/∈	/∈	PUNCT
ejpam-5792	194	1	ty	ty	INTJ
ejpam-5792	194	2	,	,	PUNCT
ejpam-5792	194	3	then	then	ADV
ejpam-5792	194	4	y	y	PROPN
ejpam-5792	194	5	/∈	/∈	PUNCT
ejpam-5792	195	1	tλy	tλy	INTJ
ejpam-5792	195	2	.	.	PUNCT
ejpam-5792	196	1	since	since	SCONJ
ejpam-5792	196	2	tλyn	tλyn	PROPN
ejpam-5792	196	3	is	be	AUX
ejpam-5792	196	4	closed	close	VERB
ejpam-5792	196	5	for	for	ADP
ejpam-5792	196	6	each	each	DET
ejpam-5792	196	7	n	n	PRON
ejpam-5792	196	8	≥	≥	NOUN
ejpam-5792	196	9	0	0	NUM
ejpam-5792	196	10	,	,	PUNCT
ejpam-5792	196	11	therefore	therefore	ADV
ejpam-5792	196	12	yn	yn	PROPN
ejpam-5792	196	13	/∈	/∈	PROPN
ejpam-5792	196	14	tλyn	tλyn	PROPN
ejpam-5792	196	15	.	.	PUNCT
ejpam-5792	197	1	from	from	ADP
ejpam-5792	197	2	equation	equation	NOUN
ejpam-5792	197	3	(	(	PUNCT
ejpam-5792	197	4	4	4	NUM
ejpam-5792	197	5	)	)	PUNCT
ejpam-5792	197	6	,	,	PUNCT
ejpam-5792	197	7	we	we	PRON
ejpam-5792	197	8	get	get	VERB
ejpam-5792	197	9	cg	cg	NOUN
ejpam-5792	197	10	≤	≤	NOUN
ejpam-5792	197	11	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	197	12	,	,	PUNCT
ejpam-5792	197	13	tλyn−1	tλyn−1	PROPN
ejpam-5792	197	14	)	)	PUNCT
ejpam-5792	197	15	,	,	PUNCT
ejpam-5792	197	16	q(yn	q(yn	PROPN
ejpam-5792	197	17	,	,	PUNCT
ejpam-5792	197	18	yn−1	yn−1	PROPN
ejpam-5792	197	19	)	)	PUNCT
ejpam-5792	197	20	<	<	X
ejpam-5792	197	21	cg	cg	NOUN
ejpam-5792	197	22	,	,	PUNCT
ejpam-5792	197	23	which	which	PRON
ejpam-5792	197	24	leads	lead	VERB
ejpam-5792	197	25	to	to	ADP
ejpam-5792	197	26	a	a	DET
ejpam-5792	197	27	contradiction	contradiction	NOUN
ejpam-5792	197	28	.	.	PUNCT
ejpam-5792	198	1	hence	hence	ADV
ejpam-5792	198	2	,	,	PUNCT
ejpam-5792	198	3	y	y	PROPN
ejpam-5792	198	4	∈	∈	PROPN
ejpam-5792	198	5	ty	ty	NOUN
ejpam-5792	198	6	,	,	PUNCT
ejpam-5792	198	7	which	which	PRON
ejpam-5792	198	8	implies	imply	VERB
ejpam-5792	198	9	fix(t	fix(t	PROPN
ejpam-5792	198	10	)	)	PUNCT
ejpam-5792	198	11	̸=	̸=	PROPN
ejpam-5792	198	12	ϕ.	ϕ.	VERB
ejpam-5792	198	13	now	now	ADV
ejpam-5792	198	14	,	,	PUNCT
ejpam-5792	198	15	we	we	PRON
ejpam-5792	198	16	present	present	VERB
ejpam-5792	198	17	an	an	DET
ejpam-5792	198	18	example	example	NOUN
ejpam-5792	198	19	in	in	ADP
ejpam-5792	198	20	support	support	NOUN
ejpam-5792	198	21	of	of	ADP
ejpam-5792	198	22	our	our	PRON
ejpam-5792	198	23	first	first	ADJ
ejpam-5792	198	24	theorem	theorem	NOUN
ejpam-5792	198	25	.	.	PUNCT
ejpam-5792	199	1	a.	a.	PROPN
ejpam-5792	199	2	gangwar	gangwar	PROPN
ejpam-5792	199	3	et	et	PROPN
ejpam-5792	199	4	al	al	PROPN
ejpam-5792	199	5	.	.	PUNCT
ejpam-5792	199	6	/	/	SYM
ejpam-5792	199	7	eur	eur	PROPN
ejpam-5792	199	8	.	.	PUNCT
ejpam-5792	200	1	j.	j.	PROPN
ejpam-5792	200	2	pure	pure	PROPN
ejpam-5792	200	3	appl	appl	PROPN
ejpam-5792	200	4	.	.	PROPN
ejpam-5792	200	5	math	math	PROPN
ejpam-5792	200	6	,	,	PUNCT
ejpam-5792	200	7	18	18	NUM
ejpam-5792	200	8	(	(	PUNCT
ejpam-5792	200	9	2	2	NUM
ejpam-5792	200	10	)	)	PUNCT
ejpam-5792	200	11	(	(	PUNCT
ejpam-5792	200	12	2025	2025	NUM
ejpam-5792	200	13	)	)	PUNCT
ejpam-5792	200	14	,	,	PUNCT
ejpam-5792	200	15	5792	5792	NUM
ejpam-5792	200	16	8	8	NUM
ejpam-5792	200	17	of	of	ADP
ejpam-5792	200	18	16	16	NUM
ejpam-5792	200	19	example	example	NOUN
ejpam-5792	200	20	1	1	NUM
ejpam-5792	200	21	.	.	PUNCT
ejpam-5792	201	1	let	let	VERB
ejpam-5792	201	2	u	u	NOUN
ejpam-5792	201	3	=	=	NOUN
ejpam-5792	201	4	r	r	NOUN
ejpam-5792	201	5	be	be	AUX
ejpam-5792	201	6	equipped	equip	VERB
ejpam-5792	201	7	with	with	ADP
ejpam-5792	201	8	the	the	DET
ejpam-5792	201	9	euclidean	euclidean	ADJ
ejpam-5792	201	10	metric	metric	ADJ
ejpam-5792	201	11	ρ(x	ρ(x	PROPN
ejpam-5792	201	12	,	,	PUNCT
ejpam-5792	201	13	y	y	NOUN
ejpam-5792	201	14	)	)	PUNCT
ejpam-5792	201	15	=	=	PUNCT
ejpam-5792	201	16	|x−	|x−	NOUN
ejpam-5792	201	17	y|	y|	NOUN
ejpam-5792	201	18	,	,	PUNCT
ejpam-5792	201	19	∀	∀	X
ejpam-5792	201	20	x	x	NOUN
ejpam-5792	201	21	,	,	PUNCT
ejpam-5792	201	22	y	y	PROPN
ejpam-5792	201	23	∈	∈	PROPN
ejpam-5792	201	24	u	u	PROPN
ejpam-5792	201	25	,	,	PUNCT
ejpam-5792	201	26	and	and	CCONJ
ejpam-5792	201	27	t	t	PROPN
ejpam-5792	201	28	:	:	PUNCT
ejpam-5792	201	29	u	u	PROPN
ejpam-5792	201	30	→	→	SYM
ejpam-5792	201	31	cb(u	cb(u	PUNCT
ejpam-5792	201	32	)	)	PUNCT
ejpam-5792	201	33	be	be	AUX
ejpam-5792	201	34	given	give	VERB
ejpam-5792	201	35	as	as	ADP
ejpam-5792	201	36	t	t	PROPN
ejpam-5792	201	37	(	(	PUNCT
ejpam-5792	201	38	x	x	NOUN
ejpam-5792	201	39	)	)	PUNCT
ejpam-5792	202	1	=	=	SYM
ejpam-5792	202	2	{	{	PUNCT
ejpam-5792	202	3	−x	−x	NOUN
ejpam-5792	202	4	,	,	PUNCT
ejpam-5792	202	5	1−	1−	NUM
ejpam-5792	202	6	x	x	NOUN
ejpam-5792	202	7	}	}	PUNCT
ejpam-5792	202	8	.	.	PUNCT
ejpam-5792	203	1	also	also	ADV
ejpam-5792	203	2	,	,	PUNCT
ejpam-5792	203	3	let	let	VERB
ejpam-5792	203	4	ζ(t	ζ(t	VERB
ejpam-5792	203	5	,	,	PUNCT
ejpam-5792	203	6	r	r	NOUN
ejpam-5792	203	7	)	)	PUNCT
ejpam-5792	203	8	=	=	SYM
ejpam-5792	203	9	1	1	NUM
ejpam-5792	203	10	2r	2r	NUM
ejpam-5792	203	11	−	−	PROPN
ejpam-5792	203	12	t	t	PROPN
ejpam-5792	203	13	,	,	PUNCT
ejpam-5792	203	14	g(r	g(r	PROPN
ejpam-5792	203	15	,	,	PUNCT
ejpam-5792	203	16	t	t	PROPN
ejpam-5792	203	17	)	)	PUNCT
ejpam-5792	204	1	=	=	SYM
ejpam-5792	204	2	r	r	NOUN
ejpam-5792	204	3	−	−	PROPN
ejpam-5792	204	4	t	t	NOUN
ejpam-5792	204	5	for	for	ADP
ejpam-5792	204	6	each	each	DET
ejpam-5792	204	7	r	r	NOUN
ejpam-5792	204	8	,	,	PUNCT
ejpam-5792	204	9	t	t	PROPN
ejpam-5792	204	10	∈	∈	PROPN
ejpam-5792	205	1	[	[	X
ejpam-5792	205	2	0,∞	0,∞	NUM
ejpam-5792	205	3	)	)	PUNCT
ejpam-5792	205	4	and	and	CCONJ
ejpam-5792	205	5	cg	cg	NOUN
ejpam-5792	205	6	=	=	NOUN
ejpam-5792	205	7	0	0	X
ejpam-5792	205	8	.	.	PUNCT
ejpam-5792	206	1	taking	take	VERB
ejpam-5792	206	2	λ	λ	NOUN
ejpam-5792	206	3	=	=	NOUN
ejpam-5792	206	4	1	1	NUM
ejpam-5792	206	5	2	2	NUM
ejpam-5792	206	6	,	,	PUNCT
ejpam-5792	206	7	we	we	PRON
ejpam-5792	206	8	obtain	obtain	VERB
ejpam-5792	206	9	t	t	PROPN
ejpam-5792	206	10	1	1	NUM
ejpam-5792	206	11	2	2	NUM
ejpam-5792	206	12	(	(	PUNCT
ejpam-5792	206	13	x	x	NOUN
ejpam-5792	206	14	)	)	PUNCT
ejpam-5792	206	15	=	=	SYM
ejpam-5792	206	16	{	{	PUNCT
ejpam-5792	206	17	0	0	NUM
ejpam-5792	206	18	,	,	PUNCT
ejpam-5792	206	19	1	1	NUM
ejpam-5792	206	20	2	2	NUM
ejpam-5792	206	21	}	}	PUNCT
ejpam-5792	206	22	.	.	PUNCT
ejpam-5792	207	1	since	since	SCONJ
ejpam-5792	207	2	fix(t	fix(t	PROPN
ejpam-5792	207	3	)	)	PUNCT
ejpam-5792	207	4	=	=	PUNCT
ejpam-5792	207	5	{	{	PUNCT
ejpam-5792	207	6	0	0	NUM
ejpam-5792	207	7	,	,	PUNCT
ejpam-5792	207	8	12	12	NUM
ejpam-5792	207	9	}	}	PUNCT
ejpam-5792	207	10	,	,	PUNCT
ejpam-5792	207	11	we	we	PRON
ejpam-5792	207	12	get	get	VERB
ejpam-5792	207	13	for	for	ADP
ejpam-5792	207	14	each	each	DET
ejpam-5792	207	15	x	x	NOUN
ejpam-5792	207	16	,	,	PUNCT
ejpam-5792	207	17	y	y	PROPN
ejpam-5792	207	18	∈	∈	PROPN
ejpam-5792	207	19	u	u	NOUN
ejpam-5792	207	20	/{0	/{0	X
ejpam-5792	207	21	,	,	PUNCT
ejpam-5792	207	22	12	12	NUM
ejpam-5792	207	23	}	}	PUNCT
ejpam-5792	207	24	,	,	PUNCT
ejpam-5792	207	25	h(tλx	h(tλx	PROPN
ejpam-5792	207	26	,	,	PUNCT
ejpam-5792	207	27	tλy	tλy	NOUN
ejpam-5792	207	28	)	)	PUNCT
ejpam-5792	207	29	=	=	SYM
ejpam-5792	207	30	0	0	NUM
ejpam-5792	208	1	and	and	CCONJ
ejpam-5792	208	2	for	for	ADP
ejpam-5792	208	3	α	α	DET
ejpam-5792	208	4	∈	∈	PROPN
ejpam-5792	208	5	(	(	PUNCT
ejpam-5792	208	6	0	0	NUM
ejpam-5792	208	7	,	,	PUNCT
ejpam-5792	208	8	1	1	NUM
ejpam-5792	208	9	)	)	PUNCT
ejpam-5792	208	10	,	,	PUNCT
ejpam-5792	208	11	q(x	q(x	PROPN
ejpam-5792	208	12	,	,	PUNCT
ejpam-5792	208	13	y	y	NOUN
ejpam-5792	208	14	)	)	PUNCT
ejpam-5792	208	15	=	=	SYM
ejpam-5792	208	16	c[d∗(x	c[d∗(x	NOUN
ejpam-5792	208	17	,	,	PUNCT
ejpam-5792	208	18	{	{	PUNCT
ejpam-5792	208	19	0	0	NUM
ejpam-5792	208	20	,	,	PUNCT
ejpam-5792	208	21	12	12	NUM
ejpam-5792	208	22	}	}	PUNCT
ejpam-5792	208	23	)	)	PUNCT
ejpam-5792	208	24	]	]	PUNCT
ejpam-5792	209	1	α[d∗(y	α[d∗(y	NOUN
ejpam-5792	209	2	,	,	PUNCT
ejpam-5792	209	3	{	{	PUNCT
ejpam-5792	209	4	0	0	NUM
ejpam-5792	209	5	,	,	PUNCT
ejpam-5792	209	6	12	12	NUM
ejpam-5792	209	7	}	}	PUNCT
ejpam-5792	209	8	)	)	PUNCT
ejpam-5792	209	9	]	]	PUNCT
ejpam-5792	210	1	1−α	1−α	NUM
ejpam-5792	210	2	>	>	X
ejpam-5792	210	3	0	0	NUM
ejpam-5792	210	4	,	,	PUNCT
ejpam-5792	210	5	which	which	PRON
ejpam-5792	210	6	implies	imply	VERB
ejpam-5792	210	7	ζ(h(tλx	ζ(h(tλx	NUM
ejpam-5792	210	8	,	,	PUNCT
ejpam-5792	210	9	tλy	tλy	NOUN
ejpam-5792	210	10	)	)	PUNCT
ejpam-5792	210	11	,	,	PUNCT
ejpam-5792	210	12	q(x	q(x	PROPN
ejpam-5792	210	13	,	,	PUNCT
ejpam-5792	210	14	y	y	NOUN
ejpam-5792	210	15	)	)	PUNCT
ejpam-5792	210	16	=	=	SYM
ejpam-5792	210	17	1	1	NUM
ejpam-5792	210	18	2	2	NUM
ejpam-5792	210	19	q(x	q(x	PROPN
ejpam-5792	210	20	,	,	PUNCT
ejpam-5792	210	21	y	y	NOUN
ejpam-5792	210	22	)	)	PUNCT
ejpam-5792	210	23	≥	≥	PROPN
ejpam-5792	210	24	cg	cg	NOUN
ejpam-5792	210	25	.	.	PUNCT
ejpam-5792	211	1	also	also	ADV
ejpam-5792	211	2	,	,	PUNCT
ejpam-5792	211	3	g(q(x	g(q(x	PROPN
ejpam-5792	211	4	,	,	PUNCT
ejpam-5792	211	5	y	y	PROPN
ejpam-5792	211	6	)	)	PUNCT
ejpam-5792	211	7	,	,	PUNCT
ejpam-5792	211	8	h(tλx	h(tλx	PROPN
ejpam-5792	211	9	,	,	PUNCT
ejpam-5792	211	10	tλy	tλy	NOUN
ejpam-5792	211	11	)	)	PUNCT
ejpam-5792	211	12	)	)	PUNCT
ejpam-5792	212	1	=	=	SYM
ejpam-5792	212	2	q(x	q(x	PROPN
ejpam-5792	212	3	,	,	PUNCT
ejpam-5792	212	4	y	y	NOUN
ejpam-5792	212	5	)	)	PUNCT
ejpam-5792	212	6	,	,	PUNCT
ejpam-5792	212	7	and	and	CCONJ
ejpam-5792	212	8	cg	cg	X
ejpam-5792	212	9	≤	≤	NOUN
ejpam-5792	212	10	ζ(h(tλx	ζ(h(tλx	ADP
ejpam-5792	212	11	,	,	PUNCT
ejpam-5792	212	12	tλy	tλy	NOUN
ejpam-5792	212	13	)	)	PUNCT
ejpam-5792	212	14	,	,	PUNCT
ejpam-5792	212	15	q(x	q(x	PROPN
ejpam-5792	212	16	,	,	PUNCT
ejpam-5792	212	17	y	y	NOUN
ejpam-5792	212	18	)	)	PUNCT
ejpam-5792	212	19	<	<	X
ejpam-5792	212	20	g(q(x	g(q(x	PROPN
ejpam-5792	212	21	,	,	PUNCT
ejpam-5792	212	22	y	y	PROPN
ejpam-5792	212	23	)	)	PUNCT
ejpam-5792	212	24	,	,	PUNCT
ejpam-5792	212	25	h(tλx	h(tλx	PROPN
ejpam-5792	212	26	,	,	PUNCT
ejpam-5792	212	27	tλy	tλy	NOUN
ejpam-5792	212	28	)	)	PUNCT
ejpam-5792	212	29	)	)	PUNCT
ejpam-5792	212	30	.	.	PUNCT
ejpam-5792	213	1	thus	thus	ADV
ejpam-5792	213	2	,	,	PUNCT
ejpam-5792	213	3	t	t	PROPN
ejpam-5792	213	4	is	be	AUX
ejpam-5792	213	5	a	a	DET
ejpam-5792	213	6	multivalued	multivalue	VERB
ejpam-5792	213	7	eik	eik	NOUN
ejpam-5792	213	8	-	-	PUNCT
ejpam-5792	213	9	contraction	contraction	NOUN
ejpam-5792	213	10	via	via	ADP
ejpam-5792	213	11	a	a	DET
ejpam-5792	213	12	simulation	simulation	NOUN
ejpam-5792	213	13	function	function	NOUN
ejpam-5792	213	14	zg	zg	PROPN
ejpam-5792	213	15	and	and	CCONJ
ejpam-5792	213	16	all	all	DET
ejpam-5792	213	17	requirements	requirement	NOUN
ejpam-5792	213	18	outlined	outline	VERB
ejpam-5792	213	19	in	in	ADP
ejpam-5792	213	20	theorem	theorem	ADJ
ejpam-5792	213	21	3.1	3.1	NUM
ejpam-5792	213	22	are	be	AUX
ejpam-5792	213	23	met	meet	VERB
ejpam-5792	213	24	.	.	PUNCT
ejpam-5792	214	1	here	here	ADV
ejpam-5792	214	2	,	,	PUNCT
ejpam-5792	214	3	fix(t	fix(t	PROPN
ejpam-5792	214	4	)	)	PUNCT
ejpam-5792	214	5	=	=	PUNCT
ejpam-5792	214	6	{	{	PUNCT
ejpam-5792	214	7	0	0	NUM
ejpam-5792	214	8	,	,	PUNCT
ejpam-5792	214	9	12	12	NUM
ejpam-5792	214	10	}	}	PUNCT
ejpam-5792	214	11	.	.	PUNCT
ejpam-5792	215	1	corollary	corollary	ADJ
ejpam-5792	215	2	4	4	NUM
ejpam-5792	215	3	.	.	PUNCT
ejpam-5792	216	1	let	let	AUX
ejpam-5792	216	2	(	(	PUNCT
ejpam-5792	216	3	u	u	NOUN
ejpam-5792	216	4	,	,	PUNCT
ejpam-5792	216	5	ρ	ρ	PROPN
ejpam-5792	216	6	)	)	PUNCT
ejpam-5792	216	7	be	be	VERB
ejpam-5792	216	8	a	a	DET
ejpam-5792	216	9	complete	complete	ADJ
ejpam-5792	216	10	metric	metric	ADJ
ejpam-5792	216	11	space	space	NOUN
ejpam-5792	216	12	which	which	PRON
ejpam-5792	216	13	.	.	PUNCT
ejpam-5792	217	1	if	if	SCONJ
ejpam-5792	217	2	t	t	PROPN
ejpam-5792	217	3	is	be	AUX
ejpam-5792	217	4	a	a	DET
ejpam-5792	217	5	multivalued	multivalue	VERB
ejpam-5792	217	6	interpolative	interpolative	ADJ
ejpam-5792	217	7	kannan	kannan	PROPN
ejpam-5792	217	8	type	type	NOUN
ejpam-5792	217	9	contraction	contraction	NOUN
ejpam-5792	217	10	via	via	ADP
ejpam-5792	217	11	a	a	DET
ejpam-5792	217	12	simulation	simulation	NOUN
ejpam-5792	217	13	function	function	PROPN
ejpam-5792	217	14	zg	zg	PROPN
ejpam-5792	217	15	,	,	PUNCT
ejpam-5792	217	16	then	then	ADV
ejpam-5792	217	17	fix(t	fix(t	PROPN
ejpam-5792	217	18	)	)	PUNCT
ejpam-5792	217	19	̸=	̸=	PROPN
ejpam-5792	217	20	ϕ.	ϕ.	NOUN
ejpam-5792	217	21	proof	proof	NOUN
ejpam-5792	217	22	.	.	PUNCT
ejpam-5792	218	1	taking	take	VERB
ejpam-5792	218	2	λ	λ	PROPN
ejpam-5792	218	3	=	=	SYM
ejpam-5792	218	4	0	0	PUNCT
ejpam-5792	218	5	and	and	CCONJ
ejpam-5792	218	6	using	use	VERB
ejpam-5792	218	7	the	the	DET
ejpam-5792	218	8	same	same	ADJ
ejpam-5792	218	9	method	method	NOUN
ejpam-5792	218	10	of	of	ADP
ejpam-5792	218	11	proof	proof	NOUN
ejpam-5792	218	12	as	as	ADP
ejpam-5792	218	13	in	in	ADP
ejpam-5792	218	14	theorem	theorem	NOUN
ejpam-5792	218	15	3.1	3.1	NUM
ejpam-5792	218	16	,	,	PUNCT
ejpam-5792	218	17	we	we	PRON
ejpam-5792	218	18	achieve	achieve	VERB
ejpam-5792	218	19	the	the	DET
ejpam-5792	218	20	intended	intend	VERB
ejpam-5792	218	21	result	result	NOUN
ejpam-5792	218	22	.	.	PUNCT
ejpam-5792	219	1	corollary	corollary	ADJ
ejpam-5792	219	2	5	5	NUM
ejpam-5792	219	3	.	.	PUNCT
ejpam-5792	220	1	let	let	VERB
ejpam-5792	220	2	(	(	PUNCT
ejpam-5792	220	3	u	u	NOUN
ejpam-5792	220	4	,	,	PUNCT
ejpam-5792	220	5	ρ	ρ	PROPN
ejpam-5792	220	6	)	)	PUNCT
ejpam-5792	220	7	be	be	VERB
ejpam-5792	220	8	a	a	DET
ejpam-5792	220	9	convex	convex	NOUN
ejpam-5792	220	10	complete	complete	ADJ
ejpam-5792	220	11	metric	metric	ADJ
ejpam-5792	220	12	space	space	NOUN
ejpam-5792	220	13	.	.	PUNCT
ejpam-5792	221	1	if	if	SCONJ
ejpam-5792	221	2	a	a	DET
ejpam-5792	221	3	self	self	NOUN
ejpam-5792	221	4	mapping	mapping	NOUN
ejpam-5792	221	5	t	t	NOUN
ejpam-5792	221	6	is	be	AUX
ejpam-5792	221	7	an	an	DET
ejpam-5792	221	8	eik	eik	NOUN
ejpam-5792	221	9	-	-	PUNCT
ejpam-5792	221	10	contraction	contraction	NOUN
ejpam-5792	221	11	via	via	ADP
ejpam-5792	221	12	a	a	DET
ejpam-5792	221	13	simulation	simulation	NOUN
ejpam-5792	221	14	function	function	PROPN
ejpam-5792	221	15	zg	zg	PROPN
ejpam-5792	221	16	,	,	PUNCT
ejpam-5792	221	17	then	then	ADV
ejpam-5792	221	18	t	t	PROPN
ejpam-5792	221	19	possesses	possess	VERB
ejpam-5792	221	20	a	a	DET
ejpam-5792	221	21	fixed	fix	VERB
ejpam-5792	221	22	point	point	NOUN
ejpam-5792	221	23	.	.	PUNCT
ejpam-5792	222	1	definition	definition	NOUN
ejpam-5792	222	2	8	8	NUM
ejpam-5792	222	3	.	.	PUNCT
ejpam-5792	223	1	let	let	VERB
ejpam-5792	223	2	(	(	PUNCT
ejpam-5792	223	3	u	u	NOUN
ejpam-5792	223	4	,	,	PUNCT
ejpam-5792	223	5	ρ	ρ	PROPN
ejpam-5792	223	6	,	,	PUNCT
ejpam-5792	223	7	w	w	NOUN
ejpam-5792	223	8	)	)	PUNCT
ejpam-5792	223	9	be	be	AUX
ejpam-5792	223	10	a	a	DET
ejpam-5792	223	11	convex	convex	ADJ
ejpam-5792	223	12	metric	metric	ADJ
ejpam-5792	223	13	space	space	NOUN
ejpam-5792	223	14	.	.	PUNCT
ejpam-5792	224	1	then	then	ADV
ejpam-5792	224	2	t	t	X
ejpam-5792	224	3	:	:	PUNCT
ejpam-5792	224	4	u	u	PROPN
ejpam-5792	224	5	→	→	SYM
ejpam-5792	224	6	cb(u	cb(u	X
ejpam-5792	224	7	)	)	PUNCT
ejpam-5792	224	8	is	be	AUX
ejpam-5792	224	9	a	a	DET
ejpam-5792	224	10	multivalued	multivalue	VERB
ejpam-5792	224	11	eihr	eihr	NOUN
ejpam-5792	224	12	-	-	PUNCT
ejpam-5792	224	13	contraction	contraction	NOUN
ejpam-5792	224	14	via	via	ADP
ejpam-5792	224	15	a	a	DET
ejpam-5792	224	16	simulation	simulation	NOUN
ejpam-5792	224	17	function	function	PROPN
ejpam-5792	224	18	zg	zg	PROPN
ejpam-5792	224	19	,	,	PUNCT
ejpam-5792	224	20	if	if	SCONJ
ejpam-5792	224	21	there	there	PRON
ejpam-5792	224	22	is	be	VERB
ejpam-5792	224	23	some	some	DET
ejpam-5792	224	24	p	p	NOUN
ejpam-5792	224	25	∈	∈	PROPN
ejpam-5792	224	26	(	(	PUNCT
ejpam-5792	224	27	0	0	NUM
ejpam-5792	224	28	,	,	PUNCT
ejpam-5792	224	29	1	1	NUM
ejpam-5792	224	30	)	)	PUNCT
ejpam-5792	224	31	and	and	CCONJ
ejpam-5792	224	32	α	α	NOUN
ejpam-5792	224	33	,	,	PUNCT
ejpam-5792	224	34	β	β	X
ejpam-5792	224	35	,	,	PUNCT
ejpam-5792	224	36	γ	γ	PROPN
ejpam-5792	224	37	∈	∈	PROPN
ejpam-5792	225	1	[	[	X
ejpam-5792	225	2	0	0	NUM
ejpam-5792	225	3	,	,	PUNCT
ejpam-5792	225	4	1	1	NUM
ejpam-5792	225	5	)	)	PUNCT
ejpam-5792	225	6	with	with	ADP
ejpam-5792	225	7	α+	α+	PRON
ejpam-5792	225	8	β	β	NOUN
ejpam-5792	225	9	+	+	X
ejpam-5792	225	10	γ	γ	X
ejpam-5792	225	11	<	<	X
ejpam-5792	225	12	1	1	NUM
ejpam-5792	225	13	so	so	SCONJ
ejpam-5792	225	14	that	that	DET
ejpam-5792	225	15	ζ(h(w	ζ(h(w	PROPN
ejpam-5792	225	16	(	(	PUNCT
ejpam-5792	225	17	x	x	X
ejpam-5792	225	18	,	,	PUNCT
ejpam-5792	225	19	tx;λ),w	tx;λ),w	PROPN
ejpam-5792	225	20	(	(	PUNCT
ejpam-5792	225	21	y	y	NOUN
ejpam-5792	225	22	,	,	PUNCT
ejpam-5792	225	23	ty;λ	ty;λ	NUM
ejpam-5792	225	24	)	)	PUNCT
ejpam-5792	225	25	)	)	PUNCT
ejpam-5792	225	26	,	,	PUNCT
ejpam-5792	225	27	q(x	q(x	PROPN
ejpam-5792	225	28	,	,	PUNCT
ejpam-5792	225	29	y	y	PROPN
ejpam-5792	225	30	)	)	PUNCT
ejpam-5792	225	31	≥	≥	PROPN
ejpam-5792	225	32	cg	cg	NOUN
ejpam-5792	225	33	.	.	PUNCT
ejpam-5792	226	1	(	(	PUNCT
ejpam-5792	226	2	9	9	NUM
ejpam-5792	226	3	)	)	PUNCT
ejpam-5792	226	4	here	here	ADV
ejpam-5792	226	5	,	,	PUNCT
ejpam-5792	226	6	cg	cg	NOUN
ejpam-5792	226	7	≥	≥	NOUN
ejpam-5792	226	8	0	0	NUM
ejpam-5792	226	9	and	and	CCONJ
ejpam-5792	226	10	q(x	q(x	PROPN
ejpam-5792	226	11	,	,	PUNCT
ejpam-5792	226	12	y	y	NOUN
ejpam-5792	226	13	)	)	PUNCT
ejpam-5792	226	14	=	=	SYM
ejpam-5792	226	15	p.ρ(x	p.ρ(x	NOUN
ejpam-5792	226	16	,	,	PUNCT
ejpam-5792	226	17	y)α.[d∗(x	y)α.[d∗(x	NOUN
ejpam-5792	226	18	,	,	PUNCT
ejpam-5792	226	19	w	w	PROPN
ejpam-5792	226	20	(	(	PUNCT
ejpam-5792	226	21	x	x	NOUN
ejpam-5792	226	22	,	,	PUNCT
ejpam-5792	226	23	tx;λ))]β.[d∗(y	tx;λ))]β.[d∗(y	PROPN
ejpam-5792	226	24	,	,	PUNCT
ejpam-5792	226	25	w	w	PROPN
ejpam-5792	226	26	(	(	PUNCT
ejpam-5792	226	27	y	y	NOUN
ejpam-5792	226	28	,	,	PUNCT
ejpam-5792	226	29	ty;λ)))]γ	ty;λ)))]γ	NOUN
ejpam-5792	226	30	.	.	PUNCT
ejpam-5792	227	1	[	[	PUNCT
ejpam-5792	227	2	1	1	NUM
ejpam-5792	227	3	2	2	NUM
ejpam-5792	227	4	(	(	PUNCT
ejpam-5792	227	5	d∗(x	d∗(x	PROPN
ejpam-5792	227	6	,	,	PUNCT
ejpam-5792	227	7	w	w	PROPN
ejpam-5792	227	8	(	(	PUNCT
ejpam-5792	227	9	y	y	PROPN
ejpam-5792	227	10	,	,	PUNCT
ejpam-5792	227	11	ty;λ	ty;λ	NUM
ejpam-5792	227	12	)	)	PUNCT
ejpam-5792	227	13	)	)	PUNCT
ejpam-5792	228	1	+	+	PROPN
ejpam-5792	228	2	d∗(y	d∗(y	PROPN
ejpam-5792	228	3	,	,	PUNCT
ejpam-5792	228	4	w	w	PROPN
ejpam-5792	228	5	(	(	PUNCT
ejpam-5792	228	6	x	x	NOUN
ejpam-5792	228	7	,	,	PUNCT
ejpam-5792	228	8	tx;λ	tx;λ	NUM
ejpam-5792	228	9	)	)	PUNCT
ejpam-5792	228	10	)	)	PUNCT
ejpam-5792	228	11	)	)	PUNCT
ejpam-5792	229	1	]	]	X
ejpam-5792	229	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-5792	229	3	for	for	ADP
ejpam-5792	229	4	each	each	DET
ejpam-5792	229	5	x	x	NOUN
ejpam-5792	229	6	,	,	PUNCT
ejpam-5792	229	7	y	y	PROPN
ejpam-5792	229	8	∈	∈	PROPN
ejpam-5792	229	9	u	u	PROPN
ejpam-5792	229	10	/f	/f	NOUN
ejpam-5792	229	11	ix(t	ix(t	PROPN
ejpam-5792	229	12	)	)	PUNCT
ejpam-5792	229	13	.	.	PUNCT
ejpam-5792	230	1	a.	a.	PROPN
ejpam-5792	230	2	gangwar	gangwar	PROPN
ejpam-5792	230	3	et	et	PROPN
ejpam-5792	230	4	al	al	PROPN
ejpam-5792	230	5	.	.	PUNCT
ejpam-5792	230	6	/	/	SYM
ejpam-5792	230	7	eur	eur	PROPN
ejpam-5792	230	8	.	.	PUNCT
ejpam-5792	231	1	j.	j.	PROPN
ejpam-5792	231	2	pure	pure	PROPN
ejpam-5792	231	3	appl	appl	PROPN
ejpam-5792	231	4	.	.	PROPN
ejpam-5792	231	5	math	math	PROPN
ejpam-5792	231	6	,	,	PUNCT
ejpam-5792	231	7	18	18	NUM
ejpam-5792	231	8	(	(	PUNCT
ejpam-5792	231	9	2	2	NUM
ejpam-5792	231	10	)	)	PUNCT
ejpam-5792	231	11	(	(	PUNCT
ejpam-5792	231	12	2025	2025	NUM
ejpam-5792	231	13	)	)	PUNCT
ejpam-5792	231	14	,	,	PUNCT
ejpam-5792	231	15	5792	5792	NUM
ejpam-5792	231	16	9	9	NUM
ejpam-5792	231	17	of	of	ADP
ejpam-5792	231	18	16	16	NUM
ejpam-5792	231	19	theorem	theorem	NOUN
ejpam-5792	231	20	6	6	NUM
ejpam-5792	231	21	.	.	PUNCT
ejpam-5792	232	1	let	let	VERB
ejpam-5792	232	2	(	(	PUNCT
ejpam-5792	232	3	u	u	NOUN
ejpam-5792	232	4	,	,	PUNCT
ejpam-5792	232	5	ρ	ρ	PROPN
ejpam-5792	232	6	,	,	PUNCT
ejpam-5792	232	7	w	w	NOUN
ejpam-5792	232	8	)	)	PUNCT
ejpam-5792	232	9	be	be	AUX
ejpam-5792	232	10	a	a	DET
ejpam-5792	232	11	convex	convex	NOUN
ejpam-5792	232	12	complete	complete	ADJ
ejpam-5792	232	13	metric	metric	ADJ
ejpam-5792	232	14	space	space	NOUN
ejpam-5792	232	15	.	.	PUNCT
ejpam-5792	233	1	if	if	SCONJ
ejpam-5792	233	2	t	t	NOUN
ejpam-5792	233	3	:	:	PUNCT
ejpam-5792	233	4	u	u	PROPN
ejpam-5792	233	5	→	→	SYM
ejpam-5792	233	6	cb(u	cb(u	X
ejpam-5792	233	7	)	)	PUNCT
ejpam-5792	233	8	is	be	AUX
ejpam-5792	233	9	a	a	DET
ejpam-5792	233	10	multivalued	multivalue	VERB
ejpam-5792	233	11	eihr	eihr	NOUN
ejpam-5792	233	12	-	-	PUNCT
ejpam-5792	233	13	contraction	contraction	NOUN
ejpam-5792	233	14	via	via	ADP
ejpam-5792	233	15	a	a	DET
ejpam-5792	233	16	simulation	simulation	NOUN
ejpam-5792	233	17	function	function	PROPN
ejpam-5792	233	18	zg	zg	PROPN
ejpam-5792	233	19	,	,	PUNCT
ejpam-5792	233	20	then	then	ADV
ejpam-5792	233	21	fix(t	fix(t	PROPN
ejpam-5792	233	22	)	)	PUNCT
ejpam-5792	233	23	̸=	̸=	PROPN
ejpam-5792	233	24	ϕ.	ϕ.	NOUN
ejpam-5792	233	25	proof	proof	NOUN
ejpam-5792	233	26	.	.	PUNCT
ejpam-5792	234	1	using	use	VERB
ejpam-5792	234	2	the	the	DET
ejpam-5792	234	3	multivalued	multivalue	VERB
ejpam-5792	234	4	eihr	eihr	PROPN
ejpam-5792	234	5	-	-	PUNCT
ejpam-5792	234	6	contraction	contraction	NOUN
ejpam-5792	234	7	condition	condition	NOUN
ejpam-5792	234	8	(	(	PUNCT
ejpam-5792	234	9	9	9	NUM
ejpam-5792	234	10	)	)	PUNCT
ejpam-5792	234	11	,	,	PUNCT
ejpam-5792	234	12	the	the	DET
ejpam-5792	234	13	mapping	mapping	NOUN
ejpam-5792	234	14	tλ	tλ	ADP
ejpam-5792	234	15	:	:	PUNCT
ejpam-5792	234	16	u	u	PROPN
ejpam-5792	234	17	→	→	SYM
ejpam-5792	234	18	cb(u	cb(u	X
ejpam-5792	234	19	)	)	PUNCT
ejpam-5792	234	20	given	give	VERB
ejpam-5792	234	21	by	by	ADP
ejpam-5792	234	22	(	(	PUNCT
ejpam-5792	234	23	2	2	X
ejpam-5792	234	24	)	)	PUNCT
ejpam-5792	234	25	satisfies	satisfie	NOUN
ejpam-5792	234	26	ζ(h(tλx	ζ(h(tλx	ADP
ejpam-5792	234	27	,	,	PUNCT
ejpam-5792	234	28	tλy	tλy	NOUN
ejpam-5792	234	29	)	)	PUNCT
ejpam-5792	234	30	,	,	PUNCT
ejpam-5792	234	31	q(x	q(x	PROPN
ejpam-5792	234	32	,	,	PUNCT
ejpam-5792	234	33	y	y	NOUN
ejpam-5792	234	34	)	)	PUNCT
ejpam-5792	234	35	)	)	PUNCT
ejpam-5792	234	36	≥	≥	X
ejpam-5792	234	37	cg	cg	INTJ
ejpam-5792	234	38	,	,	PUNCT
ejpam-5792	234	39	(	(	PUNCT
ejpam-5792	234	40	10	10	NUM
ejpam-5792	234	41	)	)	PUNCT
ejpam-5792	235	1	where	where	SCONJ
ejpam-5792	235	2	cg	cg	NOUN
ejpam-5792	235	3	≥	≥	NOUN
ejpam-5792	235	4	0	0	NUM
ejpam-5792	235	5	and	and	CCONJ
ejpam-5792	235	6	q(x	q(x	PROPN
ejpam-5792	235	7	,	,	PUNCT
ejpam-5792	235	8	y	y	NOUN
ejpam-5792	235	9	)	)	PUNCT
ejpam-5792	235	10	=	=	SYM
ejpam-5792	235	11	p.ρ(x	p.ρ(x	NOUN
ejpam-5792	235	12	,	,	PUNCT
ejpam-5792	235	13	y)α.[d∗(x	y)α.[d∗(x	NOUN
ejpam-5792	235	14	,	,	PUNCT
ejpam-5792	235	15	tλx	tλx	NOUN
ejpam-5792	235	16	)	)	PUNCT
ejpam-5792	235	17	]	]	PUNCT
ejpam-5792	235	18	β.[d∗(y	β.[d∗(y	PROPN
ejpam-5792	235	19	,	,	PUNCT
ejpam-5792	235	20	tλy	tλy	NOUN
ejpam-5792	235	21	)	)	PUNCT
ejpam-5792	235	22	]	]	PUNCT
ejpam-5792	235	23	γ	γ	X
ejpam-5792	235	24	.	.	PUNCT
ejpam-5792	236	1	[	[	PUNCT
ejpam-5792	236	2	1	1	NUM
ejpam-5792	236	3	2	2	NUM
ejpam-5792	236	4	(	(	PUNCT
ejpam-5792	236	5	d∗(x	d∗(x	PROPN
ejpam-5792	236	6	,	,	PUNCT
ejpam-5792	236	7	tλy	tλy	NOUN
ejpam-5792	236	8	)	)	PUNCT
ejpam-5792	237	1	+	+	PROPN
ejpam-5792	237	2	d∗(y	d∗(y	PROPN
ejpam-5792	237	3	,	,	PUNCT
ejpam-5792	237	4	tλx	tλx	PROPN
ejpam-5792	237	5	)	)	PUNCT
ejpam-5792	237	6	]	]	X
ejpam-5792	237	7	1−α−β−γ	1−α−β−γ	NUM
ejpam-5792	237	8	for	for	ADP
ejpam-5792	237	9	each	each	DET
ejpam-5792	237	10	x	x	NOUN
ejpam-5792	237	11	,	,	PUNCT
ejpam-5792	237	12	y	y	PROPN
ejpam-5792	237	13	∈	∈	PROPN
ejpam-5792	237	14	u	u	PROPN
ejpam-5792	237	15	/f	/f	NOUN
ejpam-5792	237	16	ix(t	ix(t	PROPN
ejpam-5792	237	17	)	)	PUNCT
ejpam-5792	237	18	,	,	PUNCT
ejpam-5792	237	19	that	that	ADV
ejpam-5792	237	20	is	is	ADV
ejpam-5792	237	21	,	,	PUNCT
ejpam-5792	237	22	tλ	tλ	NOUN
ejpam-5792	237	23	is	be	AUX
ejpam-5792	237	24	an	an	DET
ejpam-5792	237	25	ihr	ihr	NOUN
ejpam-5792	237	26	-	-	PUNCT
ejpam-5792	237	27	contraction	contraction	NOUN
ejpam-5792	237	28	.	.	PUNCT
ejpam-5792	238	1	let	let	VERB
ejpam-5792	238	2	y0	y0	PRON
ejpam-5792	238	3	∈	∈	PROPN
ejpam-5792	238	4	u	u	NOUN
ejpam-5792	238	5	and	and	CCONJ
ejpam-5792	238	6	define	define	VERB
ejpam-5792	238	7	a	a	DET
ejpam-5792	238	8	sequence	sequence	NOUN
ejpam-5792	238	9	yn	yn	INTJ
ejpam-5792	238	10	∈	∈	PROPN
ejpam-5792	238	11	tλyn−1	tλyn−1	PROPN
ejpam-5792	238	12	,	,	PUNCT
ejpam-5792	238	13	for	for	ADP
ejpam-5792	238	14	each	each	DET
ejpam-5792	238	15	n	n	DET
ejpam-5792	238	16	≥	≥	NOUN
ejpam-5792	238	17	1	1	NUM
ejpam-5792	238	18	.	.	PUNCT
ejpam-5792	239	1	if	if	SCONJ
ejpam-5792	239	2	we	we	PRON
ejpam-5792	239	3	have	have	VERB
ejpam-5792	239	4	yn0	yn0	NOUN
ejpam-5792	239	5	=	=	PUNCT
ejpam-5792	239	6	yn0	yn0	ADJ
ejpam-5792	239	7	+	+	ADJ
ejpam-5792	239	8	1	1	NUM
ejpam-5792	239	9	for	for	ADP
ejpam-5792	239	10	a	a	DET
ejpam-5792	239	11	particular	particular	ADJ
ejpam-5792	239	12	n0	n0	X
ejpam-5792	239	13	∈	∈	PROPN
ejpam-5792	239	14	n	n	CCONJ
ejpam-5792	239	15	,	,	PUNCT
ejpam-5792	239	16	then	then	ADV
ejpam-5792	239	17	yn0	yn0	PROPN
ejpam-5792	239	18	is	be	AUX
ejpam-5792	239	19	a	a	DET
ejpam-5792	239	20	fixed	fix	VERB
ejpam-5792	239	21	point	point	NOUN
ejpam-5792	239	22	of	of	ADP
ejpam-5792	239	23	tλ	tλ	ADP
ejpam-5792	239	24	and	and	CCONJ
ejpam-5792	239	25	thus	thus	ADV
ejpam-5792	239	26	a	a	DET
ejpam-5792	239	27	fixed	fix	VERB
ejpam-5792	239	28	point	point	NOUN
ejpam-5792	239	29	of	of	ADP
ejpam-5792	239	30	t	t	PROPN
ejpam-5792	239	31	.	.	PUNCT
ejpam-5792	240	1	so	so	ADV
ejpam-5792	240	2	there	there	PRON
ejpam-5792	240	3	is	be	VERB
ejpam-5792	240	4	nothing	nothing	PRON
ejpam-5792	240	5	to	to	PART
ejpam-5792	240	6	prove	prove	VERB
ejpam-5792	240	7	.	.	PUNCT
ejpam-5792	241	1	let	let	VERB
ejpam-5792	241	2	yn	yn	PRON
ejpam-5792	241	3	̸=	̸=	PROPN
ejpam-5792	241	4	yn+1	yn+1	NUM
ejpam-5792	241	5	for	for	ADP
ejpam-5792	241	6	each	each	DET
ejpam-5792	241	7	n	n	PRON
ejpam-5792	241	8	≥	≥	NOUN
ejpam-5792	241	9	0	0	NUM
ejpam-5792	241	10	.	.	PUNCT
ejpam-5792	242	1	since	since	SCONJ
ejpam-5792	242	2	0	0	NUM
ejpam-5792	242	3	<	<	X
ejpam-5792	242	4	p	p	X
ejpam-5792	242	5	<	<	X
ejpam-5792	242	6	1	1	NUM
ejpam-5792	242	7	and	and	CCONJ
ejpam-5792	242	8	yn	yn	PRON
ejpam-5792	242	9	∈	∈	PROPN
ejpam-5792	242	10	tλyn−1	tλyn−1	PROPN
ejpam-5792	242	11	for	for	ADP
ejpam-5792	242	12	each	each	DET
ejpam-5792	242	13	n	n	PRON
ejpam-5792	242	14	≥	≥	NOUN
ejpam-5792	242	15	1	1	NUM
ejpam-5792	242	16	,	,	PUNCT
ejpam-5792	242	17	we	we	PRON
ejpam-5792	242	18	can	can	AUX
ejpam-5792	242	19	choose	choose	VERB
ejpam-5792	242	20	q	q	PROPN
ejpam-5792	242	21	>	>	PUNCT
ejpam-5792	242	22	1	1	NUM
ejpam-5792	242	23	so	so	SCONJ
ejpam-5792	242	24	that	that	SCONJ
ejpam-5792	242	25	qp	qp	ADP
ejpam-5792	242	26	<	<	X
ejpam-5792	242	27	1	1	NUM
ejpam-5792	242	28	,	,	PUNCT
ejpam-5792	242	29	then	then	ADV
ejpam-5792	242	30	from	from	ADP
ejpam-5792	242	31	lemma	lemma	PROPN
ejpam-5792	242	32	1	1	NUM
ejpam-5792	242	33	there	there	PRON
ejpam-5792	242	34	is	be	VERB
ejpam-5792	242	35	some	some	DET
ejpam-5792	242	36	yn+1	yn+1	PROPN
ejpam-5792	242	37	∈	∈	PROPN
ejpam-5792	242	38	tλyn	tλyn	NOUN
ejpam-5792	242	39	,	,	PUNCT
ejpam-5792	242	40	for	for	ADP
ejpam-5792	242	41	each	each	DET
ejpam-5792	242	42	n	n	PRON
ejpam-5792	242	43	≥	≥	NOUN
ejpam-5792	242	44	1	1	NUM
ejpam-5792	242	45	so	so	SCONJ
ejpam-5792	242	46	that	that	SCONJ
ejpam-5792	242	47	ρ(yn	ρ(yn	NUM
ejpam-5792	242	48	,	,	PUNCT
ejpam-5792	242	49	yn+1	yn+1	NUM
ejpam-5792	242	50	)	)	PUNCT
ejpam-5792	242	51	≤	≤	NOUN
ejpam-5792	242	52	qh(tλyn−1	qh(tλyn−1	ADV
ejpam-5792	242	53	,	,	PUNCT
ejpam-5792	242	54	tλyn	tλyn	VERB
ejpam-5792	242	55	)	)	PUNCT
ejpam-5792	242	56	.	.	PUNCT
ejpam-5792	243	1	(	(	PUNCT
ejpam-5792	243	2	11	11	X
ejpam-5792	243	3	)	)	PUNCT
ejpam-5792	243	4	taking	take	VERB
ejpam-5792	243	5	x	x	PUNCT
ejpam-5792	243	6	=	=	PUNCT
ejpam-5792	243	7	yn	yn	PROPN
ejpam-5792	243	8	and	and	CCONJ
ejpam-5792	243	9	y	y	PROPN
ejpam-5792	243	10	=	=	SYM
ejpam-5792	243	11	yn−1	yn−1	PROPN
ejpam-5792	243	12	,	,	PUNCT
ejpam-5792	243	13	from	from	ADP
ejpam-5792	243	14	equation	equation	NOUN
ejpam-5792	243	15	(	(	PUNCT
ejpam-5792	243	16	3	3	NUM
ejpam-5792	243	17	)	)	PUNCT
ejpam-5792	243	18	,	,	PUNCT
ejpam-5792	243	19	we	we	PRON
ejpam-5792	243	20	obtain	obtain	VERB
ejpam-5792	243	21	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	243	22	,	,	PUNCT
ejpam-5792	243	23	tλyn−1	tλyn−1	PROPN
ejpam-5792	243	24	)	)	PUNCT
ejpam-5792	243	25	,	,	PUNCT
ejpam-5792	243	26	q(yn	q(yn	PROPN
ejpam-5792	243	27	,	,	PUNCT
ejpam-5792	243	28	yn−1	yn−1	PROPN
ejpam-5792	243	29	)	)	PUNCT
ejpam-5792	243	30	≥	≥	NOUN
ejpam-5792	244	1	cg	cg	NOUN
ejpam-5792	244	2	.	.	PUNCT
ejpam-5792	245	1	(	(	PUNCT
ejpam-5792	245	2	12	12	NUM
ejpam-5792	245	3	)	)	PUNCT
ejpam-5792	245	4	by	by	ADP
ejpam-5792	245	5	definition	definition	NOUN
ejpam-5792	245	6	3	3	NUM
ejpam-5792	245	7	,	,	PUNCT
ejpam-5792	245	8	we	we	PRON
ejpam-5792	245	9	obtain	obtain	VERB
ejpam-5792	245	10	cg	cg	NOUN
ejpam-5792	245	11	≤	≤	NOUN
ejpam-5792	245	12	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	245	13	,	,	PUNCT
ejpam-5792	245	14	tλyn−1	tλyn−1	PROPN
ejpam-5792	245	15	)	)	PUNCT
ejpam-5792	245	16	,	,	PUNCT
ejpam-5792	245	17	q(yn	q(yn	PROPN
ejpam-5792	245	18	,	,	PUNCT
ejpam-5792	245	19	yn−1	yn−1	NOUN
ejpam-5792	245	20	)	)	PUNCT
ejpam-5792	245	21	)	)	PUNCT
ejpam-5792	246	1	<	<	X
ejpam-5792	246	2	g(q(yn	g(q(yn	X
ejpam-5792	246	3	,	,	PUNCT
ejpam-5792	246	4	yn−1	yn−1	NOUN
ejpam-5792	246	5	)	)	PUNCT
ejpam-5792	246	6	,	,	PUNCT
ejpam-5792	246	7	h(tλyn	h(tλyn	VERB
ejpam-5792	246	8	,	,	PUNCT
ejpam-5792	246	9	tλyn−1	tλyn−1	PROPN
ejpam-5792	246	10	)	)	PUNCT
ejpam-5792	246	11	.	.	PUNCT
ejpam-5792	247	1	from	from	ADP
ejpam-5792	247	2	definition	definition	NOUN
ejpam-5792	247	3	2	2	NUM
ejpam-5792	247	4	,	,	PUNCT
ejpam-5792	247	5	we	we	PRON
ejpam-5792	247	6	obtain	obtain	VERB
ejpam-5792	247	7	h(tλyn	h(tλyn	ADJ
ejpam-5792	247	8	,	,	PUNCT
ejpam-5792	247	9	tλyn−1	tλyn−1	NUM
ejpam-5792	247	10	)	)	PUNCT
ejpam-5792	247	11	<	<	X
ejpam-5792	247	12	q(yn	q(yn	PROPN
ejpam-5792	247	13	,	,	PUNCT
ejpam-5792	247	14	yn−1	yn−1	NOUN
ejpam-5792	247	15	)	)	PUNCT
ejpam-5792	247	16	,	,	PUNCT
ejpam-5792	247	17	(	(	PUNCT
ejpam-5792	247	18	13	13	NUM
ejpam-5792	247	19	)	)	PUNCT
ejpam-5792	247	20	where	where	SCONJ
ejpam-5792	247	21	q(yn	q(yn	NOUN
ejpam-5792	247	22	,	,	PUNCT
ejpam-5792	247	23	yn−1	yn−1	NOUN
ejpam-5792	247	24	)	)	PUNCT
ejpam-5792	247	25	=	=	SYM
ejpam-5792	247	26	p[ρ(yn−1	p[ρ(yn−1	NOUN
ejpam-5792	247	27	,	,	PUNCT
ejpam-5792	247	28	yn	yn	PROPN
ejpam-5792	247	29	)	)	PUNCT
ejpam-5792	247	30	α[d∗(yn−1	α[d∗(yn−1	PROPN
ejpam-5792	247	31	,	,	PUNCT
ejpam-5792	247	32	tλyn−1	tλyn−1	NUM
ejpam-5792	247	33	)	)	PUNCT
ejpam-5792	247	34	]	]	PUNCT
ejpam-5792	248	1	β[d∗(yn	β[d∗(yn	PROPN
ejpam-5792	248	2	,	,	PUNCT
ejpam-5792	248	3	tλyn	tλyn	VERB
ejpam-5792	248	4	)	)	PUNCT
ejpam-5792	248	5	)	)	PUNCT
ejpam-5792	248	6	]	]	PUNCT
ejpam-5792	248	7	γ	γ	X
ejpam-5792	248	8	×	×	NOUN
ejpam-5792	248	9	[	[	PUNCT
ejpam-5792	248	10	1	1	NUM
ejpam-5792	248	11	2	2	NUM
ejpam-5792	248	12	(	(	PUNCT
ejpam-5792	248	13	d∗(yn−1	d∗(yn−1	ADJ
ejpam-5792	248	14	,	,	PUNCT
ejpam-5792	248	15	tλyn	tλyn	VERB
ejpam-5792	248	16	)	)	PUNCT
ejpam-5792	248	17	+	+	SYM
ejpam-5792	248	18	d∗(yn	d∗(yn	NOUN
ejpam-5792	248	19	,	,	PUNCT
ejpam-5792	248	20	tλyn−1	tλyn−1	NUM
ejpam-5792	248	21	)	)	PUNCT
ejpam-5792	248	22	)	)	PUNCT
ejpam-5792	248	23	]	]	PUNCT
ejpam-5792	249	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-5792	249	2	≤	≤	NUM
ejpam-5792	249	3	p[ρ(yn−1	p[ρ(yn−1	NOUN
ejpam-5792	249	4	,	,	PUNCT
ejpam-5792	249	5	yn	yn	PROPN
ejpam-5792	249	6	)	)	PUNCT
ejpam-5792	249	7	α[ρ(yn−1	α[ρ(yn−1	PROPN
ejpam-5792	249	8	,	,	PUNCT
ejpam-5792	249	9	yn	yn	PROPN
ejpam-5792	249	10	)	)	PUNCT
ejpam-5792	249	11	]	]	PUNCT
ejpam-5792	249	12	β[ρ(yn	β[ρ(yn	NUM
ejpam-5792	249	13	,	,	PUNCT
ejpam-5792	249	14	yn+1	yn+1	NUM
ejpam-5792	249	15	)	)	PUNCT
ejpam-5792	249	16	)	)	PUNCT
ejpam-5792	249	17	]	]	PUNCT
ejpam-5792	250	1	γ	γ	X
ejpam-5792	250	2	×	×	NOUN
ejpam-5792	250	3	[	[	PUNCT
ejpam-5792	250	4	1	1	NUM
ejpam-5792	250	5	2	2	NUM
ejpam-5792	250	6	(	(	PUNCT
ejpam-5792	250	7	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	250	8	,	,	PUNCT
ejpam-5792	250	9	yn+1	yn+1	NUM
ejpam-5792	250	10	)	)	PUNCT
ejpam-5792	250	11	+	+	CCONJ
ejpam-5792	250	12	ρ(yn	ρ(yn	NUM
ejpam-5792	250	13	,	,	PUNCT
ejpam-5792	250	14	yn	yn	NOUN
ejpam-5792	250	15	)	)	PUNCT
ejpam-5792	250	16	)	)	PUNCT
ejpam-5792	250	17	]	]	PUNCT
ejpam-5792	251	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-5792	251	2	≤	≤	NUM
ejpam-5792	251	3	p[ρ(yn−1	p[ρ(yn−1	NOUN
ejpam-5792	251	4	,	,	PUNCT
ejpam-5792	251	5	yn	yn	PROPN
ejpam-5792	251	6	)	)	PUNCT
ejpam-5792	251	7	α[ρ(yn−1	α[ρ(yn−1	PROPN
ejpam-5792	251	8	,	,	PUNCT
ejpam-5792	251	9	yn	yn	PROPN
ejpam-5792	251	10	)	)	PUNCT
ejpam-5792	251	11	]	]	PUNCT
ejpam-5792	251	12	β[ρ(yn	β[ρ(yn	NUM
ejpam-5792	251	13	,	,	PUNCT
ejpam-5792	251	14	yn+1	yn+1	NUM
ejpam-5792	251	15	)	)	PUNCT
ejpam-5792	251	16	)	)	PUNCT
ejpam-5792	251	17	]	]	PUNCT
ejpam-5792	252	1	γ	γ	X
ejpam-5792	252	2	×	×	NOUN
ejpam-5792	252	3	[	[	PUNCT
ejpam-5792	252	4	1	1	NUM
ejpam-5792	252	5	2	2	NUM
ejpam-5792	252	6	(	(	PUNCT
ejpam-5792	252	7	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	252	8	,	,	PUNCT
ejpam-5792	252	9	yn	yn	PROPN
ejpam-5792	252	10	)	)	PUNCT
ejpam-5792	252	11	+	+	CCONJ
ejpam-5792	252	12	ρ(yn	ρ(yn	NUM
ejpam-5792	252	13	,	,	PUNCT
ejpam-5792	252	14	yn+1	yn+1	NUM
ejpam-5792	252	15	)	)	PUNCT
ejpam-5792	252	16	+	+	X
ejpam-5792	252	17	d(yn	d(yn	PROPN
ejpam-5792	252	18	,	,	PUNCT
ejpam-5792	252	19	yn	yn	NOUN
ejpam-5792	252	20	)	)	PUNCT
ejpam-5792	252	21	)	)	PUNCT
ejpam-5792	252	22	]	]	PUNCT
ejpam-5792	253	1	1−α−β−γ	1−α−β−γ	X
ejpam-5792	253	2	.	.	PUNCT
ejpam-5792	254	1	a.	a.	PROPN
ejpam-5792	254	2	gangwar	gangwar	PROPN
ejpam-5792	254	3	et	et	PROPN
ejpam-5792	254	4	al	al	PROPN
ejpam-5792	254	5	.	.	PUNCT
ejpam-5792	254	6	/	/	SYM
ejpam-5792	254	7	eur	eur	PROPN
ejpam-5792	254	8	.	.	PUNCT
ejpam-5792	255	1	j.	j.	PROPN
ejpam-5792	255	2	pure	pure	PROPN
ejpam-5792	255	3	appl	appl	PROPN
ejpam-5792	255	4	.	.	PROPN
ejpam-5792	255	5	math	math	PROPN
ejpam-5792	255	6	,	,	PUNCT
ejpam-5792	255	7	18	18	NUM
ejpam-5792	255	8	(	(	PUNCT
ejpam-5792	255	9	2	2	NUM
ejpam-5792	255	10	)	)	PUNCT
ejpam-5792	255	11	(	(	PUNCT
ejpam-5792	255	12	2025	2025	NUM
ejpam-5792	255	13	)	)	PUNCT
ejpam-5792	255	14	,	,	PUNCT
ejpam-5792	255	15	5792	5792	NUM
ejpam-5792	255	16	10	10	NUM
ejpam-5792	255	17	of	of	ADP
ejpam-5792	255	18	16	16	NUM
ejpam-5792	255	19	suppose	suppose	VERB
ejpam-5792	255	20	if	if	SCONJ
ejpam-5792	255	21	possible	possible	ADJ
ejpam-5792	255	22	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	255	23	,	,	PUNCT
ejpam-5792	255	24	yn	yn	PROPN
ejpam-5792	255	25	)	)	PUNCT
ejpam-5792	255	26	<	<	X
ejpam-5792	255	27	ρ(yn	ρ(yn	NUM
ejpam-5792	255	28	,	,	PUNCT
ejpam-5792	255	29	yn+1	yn+1	NUM
ejpam-5792	255	30	)	)	PUNCT
ejpam-5792	255	31	for	for	ADP
ejpam-5792	255	32	some	some	DET
ejpam-5792	255	33	n	n	PRON
ejpam-5792	255	34	≥	≥	NOUN
ejpam-5792	255	35	1	1	NUM
ejpam-5792	255	36	,	,	PUNCT
ejpam-5792	255	37	then	then	ADV
ejpam-5792	255	38	1	1	NUM
ejpam-5792	255	39	2	2	NUM
ejpam-5792	255	40	(	(	PUNCT
ejpam-5792	255	41	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	255	42	,	,	PUNCT
ejpam-5792	255	43	yn	yn	PROPN
ejpam-5792	255	44	)	)	PUNCT
ejpam-5792	255	45	+	+	CCONJ
ejpam-5792	256	1	ρ(yn	ρ(yn	NUM
ejpam-5792	256	2	,	,	PUNCT
ejpam-5792	256	3	yn+1	yn+1	NUM
ejpam-5792	256	4	)	)	PUNCT
ejpam-5792	256	5	+	+	CCONJ
ejpam-5792	256	6	ρ(yn	ρ(yn	NUM
ejpam-5792	256	7	,	,	PUNCT
ejpam-5792	256	8	yn	yn	NOUN
ejpam-5792	256	9	)	)	PUNCT
ejpam-5792	256	10	)	)	PUNCT
ejpam-5792	256	11	≤	≤	NUM
ejpam-5792	256	12	d(yn	d(yn	NOUN
ejpam-5792	256	13	,	,	PUNCT
ejpam-5792	256	14	yn+1	yn+1	NUM
ejpam-5792	256	15	)	)	PUNCT
ejpam-5792	256	16	,	,	PUNCT
ejpam-5792	256	17	which	which	PRON
ejpam-5792	256	18	further	far	ADV
ejpam-5792	256	19	implies	imply	VERB
ejpam-5792	256	20	p[ρ(yn−1	p[ρ(yn−1	NOUN
ejpam-5792	256	21	,	,	PUNCT
ejpam-5792	256	22	yn	yn	PROPN
ejpam-5792	256	23	)	)	PUNCT
ejpam-5792	256	24	α[ρ(yn−1	α[ρ(yn−1	PROPN
ejpam-5792	256	25	,	,	PUNCT
ejpam-5792	256	26	yn	yn	PROPN
ejpam-5792	256	27	)	)	PUNCT
ejpam-5792	256	28	]	]	PUNCT
ejpam-5792	256	29	β[ρ(yn	β[ρ(yn	NUM
ejpam-5792	256	30	,	,	PUNCT
ejpam-5792	256	31	yn+1	yn+1	NUM
ejpam-5792	256	32	)	)	PUNCT
ejpam-5792	256	33	)	)	PUNCT
ejpam-5792	256	34	]	]	PUNCT
ejpam-5792	257	1	γ	γ	X
ejpam-5792	257	2	.	.	PUNCT
ejpam-5792	258	1	[	[	PUNCT
ejpam-5792	258	2	1	1	NUM
ejpam-5792	258	3	2	2	NUM
ejpam-5792	258	4	(	(	PUNCT
ejpam-5792	258	5	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	258	6	,	,	PUNCT
ejpam-5792	258	7	yn	yn	PROPN
ejpam-5792	258	8	)	)	PUNCT
ejpam-5792	258	9	+	+	CCONJ
ejpam-5792	258	10	ρ(yn	ρ(yn	NUM
ejpam-5792	258	11	,	,	PUNCT
ejpam-5792	258	12	yn+1	yn+1	NUM
ejpam-5792	258	13	)	)	PUNCT
ejpam-5792	258	14	+	+	CCONJ
ejpam-5792	258	15	ρ(yn	ρ(yn	NUM
ejpam-5792	258	16	,	,	PUNCT
ejpam-5792	258	17	yn	yn	NOUN
ejpam-5792	258	18	)	)	PUNCT
ejpam-5792	258	19	)	)	PUNCT
ejpam-5792	258	20	]	]	PUNCT
ejpam-5792	259	1	1−α−β−γ	1−α−β−γ	X
ejpam-5792	259	2	<	<	X
ejpam-5792	259	3	p[ρ(yn	p[ρ(yn	PROPN
ejpam-5792	259	4	,	,	PUNCT
ejpam-5792	259	5	yn+1	yn+1	NUM
ejpam-5792	259	6	)	)	PUNCT
ejpam-5792	259	7	]	]	PUNCT
ejpam-5792	259	8	α+β+γ	α+β+γ	X
ejpam-5792	259	9	.[ρ(yn	.[ρ(yn	PROPN
ejpam-5792	259	10	,	,	PUNCT
ejpam-5792	259	11	yn+1	yn+1	X
ejpam-5792	259	12	)	)	PUNCT
ejpam-5792	259	13	]	]	PUNCT
ejpam-5792	260	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-5792	260	2	=	=	SYM
ejpam-5792	260	3	pd(yn	pd(yn	PROPN
ejpam-5792	260	4	,	,	PUNCT
ejpam-5792	260	5	yn+1	yn+1	X
ejpam-5792	260	6	)	)	PUNCT
ejpam-5792	260	7	i.e.	i.e.	X
ejpam-5792	260	8	,	,	PUNCT
ejpam-5792	260	9	r(yn	r(yn	X
ejpam-5792	260	10	,	,	PUNCT
ejpam-5792	260	11	yn−1	yn−1	NOUN
ejpam-5792	260	12	)	)	PUNCT
ejpam-5792	260	13	<	<	X
ejpam-5792	260	14	pd(yn	pd(yn	NOUN
ejpam-5792	260	15	,	,	PUNCT
ejpam-5792	260	16	yn+1	yn+1	NUM
ejpam-5792	260	17	)	)	PUNCT
ejpam-5792	260	18	.	.	PUNCT
ejpam-5792	261	1	from	from	ADP
ejpam-5792	261	2	equation	equation	NOUN
ejpam-5792	261	3	(	(	PUNCT
ejpam-5792	261	4	9	9	NUM
ejpam-5792	261	5	)	)	PUNCT
ejpam-5792	261	6	and	and	CCONJ
ejpam-5792	261	7	(	(	PUNCT
ejpam-5792	261	8	11	11	NUM
ejpam-5792	261	9	)	)	PUNCT
ejpam-5792	261	10	,	,	PUNCT
ejpam-5792	261	11	we	we	PRON
ejpam-5792	261	12	get	get	VERB
ejpam-5792	261	13	ρ(yn	ρ(yn	NUM
ejpam-5792	261	14	,	,	PUNCT
ejpam-5792	261	15	yn+1	yn+1	NUM
ejpam-5792	261	16	)	)	PUNCT
ejpam-5792	261	17	≤	≤	NOUN
ejpam-5792	261	18	pqρ(yn	pqρ(yn	NOUN
ejpam-5792	261	19	,	,	PUNCT
ejpam-5792	261	20	yn+1	yn+1	X
ejpam-5792	261	21	)	)	PUNCT
ejpam-5792	261	22	=	=	SYM
ejpam-5792	261	23	θρ(yn	θρ(yn	NOUN
ejpam-5792	261	24	,	,	PUNCT
ejpam-5792	261	25	yn+1	yn+1	NUM
ejpam-5792	261	26	)	)	PUNCT
ejpam-5792	261	27	.	.	PUNCT
ejpam-5792	262	1	this	this	PRON
ejpam-5792	262	2	leads	lead	VERB
ejpam-5792	262	3	to	to	ADP
ejpam-5792	262	4	a	a	DET
ejpam-5792	262	5	contradiction	contradiction	NOUN
ejpam-5792	262	6	as	as	ADP
ejpam-5792	262	7	θ	θ	PROPN
ejpam-5792	262	8	<	<	X
ejpam-5792	262	9	1	1	NUM
ejpam-5792	262	10	.	.	PUNCT
ejpam-5792	263	1	therefore	therefore	ADV
ejpam-5792	263	2	,	,	PUNCT
ejpam-5792	263	3	we	we	PRON
ejpam-5792	263	4	obtain	obtain	VERB
ejpam-5792	263	5	ρ(yn	ρ(yn	NUM
ejpam-5792	263	6	,	,	PUNCT
ejpam-5792	263	7	yn+1	yn+1	NUM
ejpam-5792	263	8	)	)	PUNCT
ejpam-5792	263	9	≤	≤	NOUN
ejpam-5792	263	10	ρ(yn−1	ρ(yn−1	PROPN
ejpam-5792	263	11	,	,	PUNCT
ejpam-5792	263	12	yn	yn	PROPN
ejpam-5792	263	13	)	)	PUNCT
ejpam-5792	263	14	.	.	PUNCT
ejpam-5792	264	1	from	from	ADP
ejpam-5792	264	2	equations	equation	NOUN
ejpam-5792	264	3	(	(	PUNCT
ejpam-5792	264	4	11	11	NUM
ejpam-5792	264	5	)	)	PUNCT
ejpam-5792	264	6	and	and	CCONJ
ejpam-5792	264	7	(	(	PUNCT
ejpam-5792	264	8	13	13	NUM
ejpam-5792	264	9	)	)	PUNCT
ejpam-5792	264	10	,	,	PUNCT
ejpam-5792	264	11	one	one	PRON
ejpam-5792	264	12	writes	write	VERB
ejpam-5792	264	13	ρ(yn	ρ(yn	NUM
ejpam-5792	264	14	,	,	PUNCT
ejpam-5792	264	15	yn+1	yn+1	NUM
ejpam-5792	264	16	)	)	PUNCT
ejpam-5792	264	17	≤	≤	NOUN
ejpam-5792	264	18	qh(tλyn−1	qh(tλyn−1	ADV
ejpam-5792	264	19	,	,	PUNCT
ejpam-5792	264	20	tλyn	tλyn	VERB
ejpam-5792	264	21	)	)	PUNCT
ejpam-5792	265	1	<	<	X
ejpam-5792	266	1	pqρ(yn−1	pqρ(yn−1	PROPN
ejpam-5792	266	2	,	,	PUNCT
ejpam-5792	266	3	yn	yn	PROPN
ejpam-5792	266	4	)	)	PUNCT
ejpam-5792	266	5	.	.	PUNCT
ejpam-5792	267	1	(	(	PUNCT
ejpam-5792	267	2	14	14	NUM
ejpam-5792	267	3	)	)	PUNCT
ejpam-5792	267	4	this	this	PRON
ejpam-5792	267	5	implies	imply	VERB
ejpam-5792	267	6	that	that	SCONJ
ejpam-5792	267	7	ρ(yn	ρ(yn	NUM
ejpam-5792	267	8	,	,	PUNCT
ejpam-5792	267	9	yn+1	yn+1	X
ejpam-5792	267	10	)	)	PUNCT
ejpam-5792	267	11	<	<	X
ejpam-5792	267	12	θρ(yn−1	θρ(yn−1	PROPN
ejpam-5792	267	13	,	,	PUNCT
ejpam-5792	267	14	yn	yn	PROPN
ejpam-5792	267	15	)	)	PUNCT
ejpam-5792	267	16	<	<	X
ejpam-5792	268	1	θ2ρ(yn−2	θ2ρ(yn−2	PROPN
ejpam-5792	268	2	,	,	PUNCT
ejpam-5792	268	3	yn−1	yn−1	NOUN
ejpam-5792	268	4	)	)	PUNCT
ejpam-5792	268	5	<	<	X
ejpam-5792	268	6	.	.	PUNCT
ejpam-5792	268	7	.	.	PUNCT
ejpam-5792	268	8	.	.	PUNCT
ejpam-5792	269	1	<	<	X
ejpam-5792	269	2	θnρ(y0	θnρ(y0	PROPN
ejpam-5792	269	3	,	,	PUNCT
ejpam-5792	269	4	y1	y1	PROPN
ejpam-5792	269	5	)	)	PUNCT
ejpam-5792	269	6	.	.	PUNCT
ejpam-5792	270	1	taking	take	VERB
ejpam-5792	270	2	n→	n→	ADV
ejpam-5792	270	3	∞	∞	PROPN
ejpam-5792	270	4	,	,	PUNCT
ejpam-5792	270	5	we	we	PRON
ejpam-5792	270	6	obtain	obtain	VERB
ejpam-5792	270	7	ρ(yn	ρ(yn	NUM
ejpam-5792	270	8	,	,	PUNCT
ejpam-5792	270	9	yn+1	yn+1	NUM
ejpam-5792	270	10	)	)	PUNCT
ejpam-5792	270	11	→	→	SYM
ejpam-5792	271	1	0	0	X
ejpam-5792	271	2	.	.	PUNCT
ejpam-5792	272	1	let	let	VERB
ejpam-5792	272	2	m	m	PRON
ejpam-5792	272	3	,	,	PUNCT
ejpam-5792	272	4	n	n	PROPN
ejpam-5792	272	5	∈	∈	PROPN
ejpam-5792	272	6	n	n	NOUN
ejpam-5792	272	7	and	and	CCONJ
ejpam-5792	272	8	m	m	PROPN
ejpam-5792	272	9	>	>	X
ejpam-5792	272	10	n	n	CCONJ
ejpam-5792	272	11	,	,	PUNCT
ejpam-5792	272	12	then	then	ADV
ejpam-5792	272	13	ρ(yn	ρ(yn	NUM
ejpam-5792	272	14	,	,	PUNCT
ejpam-5792	272	15	ym	ym	NOUN
ejpam-5792	272	16	)	)	PUNCT
ejpam-5792	272	17	≤	≤	NOUN
ejpam-5792	272	18	ρ(yn	ρ(yn	NUM
ejpam-5792	272	19	,	,	PUNCT
ejpam-5792	272	20	yn+1	yn+1	NUM
ejpam-5792	272	21	)	)	PUNCT
ejpam-5792	272	22	+	+	X
ejpam-5792	272	23	ρ(yn+1	ρ(yn+1	PROPN
ejpam-5792	272	24	,	,	PUNCT
ejpam-5792	272	25	yn+2	yn+2	NUM
ejpam-5792	272	26	)	)	PUNCT
ejpam-5792	272	27	+	+	CCONJ
ejpam-5792	272	28	·	·	PUNCT
ejpam-5792	272	29	·	·	PUNCT
ejpam-5792	272	30	·	·	PUNCT
ejpam-5792	272	31	+	+	NUM
ejpam-5792	272	32	d(ym−1	d(ym−1	NUM
ejpam-5792	272	33	,	,	PUNCT
ejpam-5792	272	34	ym	ym	NOUN
ejpam-5792	272	35	)	)	PUNCT
ejpam-5792	272	36	≤	≤	NUM
ejpam-5792	273	1	θn	θn	ADP
ejpam-5792	273	2	1−	1−	NUM
ejpam-5792	273	3	θ	θ	PROPN
ejpam-5792	273	4	ρ(y0	ρ(y0	NOUN
ejpam-5792	273	5	,	,	PUNCT
ejpam-5792	273	6	y1	y1	NOUN
ejpam-5792	273	7	)	)	PUNCT
ejpam-5792	273	8	.	.	PUNCT
ejpam-5792	274	1	as	as	ADP
ejpam-5792	274	2	n	n	NUM
ejpam-5792	274	3	→	→	SYM
ejpam-5792	274	4	∞	∞	PROPN
ejpam-5792	274	5	,	,	PUNCT
ejpam-5792	274	6	we	we	PRON
ejpam-5792	274	7	get	get	VERB
ejpam-5792	274	8	ρ(yn	ρ(yn	NUM
ejpam-5792	274	9	,	,	PUNCT
ejpam-5792	274	10	ym	ym	NOUN
ejpam-5792	274	11	)	)	PUNCT
ejpam-5792	274	12	→	→	SYM
ejpam-5792	275	1	0	0	X
ejpam-5792	275	2	.	.	PUNCT
ejpam-5792	276	1	this	this	PRON
ejpam-5792	276	2	implies	imply	VERB
ejpam-5792	276	3	{	{	PUNCT
ejpam-5792	276	4	yn	yn	PRON
ejpam-5792	276	5	}	}	PUNCT
ejpam-5792	276	6	is	be	AUX
ejpam-5792	276	7	a	a	DET
ejpam-5792	276	8	cauchy	cauchy	ADJ
ejpam-5792	276	9	sequence	sequence	NOUN
ejpam-5792	276	10	and	and	CCONJ
ejpam-5792	276	11	using	use	VERB
ejpam-5792	276	12	the	the	DET
ejpam-5792	276	13	completeness	completeness	NOUN
ejpam-5792	276	14	of	of	ADP
ejpam-5792	276	15	u	u	NOUN
ejpam-5792	276	16	there	there	PRON
ejpam-5792	276	17	is	be	VERB
ejpam-5792	276	18	some	some	DET
ejpam-5792	276	19	v∗	v∗	PROPN
ejpam-5792	276	20	∈	∈	PROPN
ejpam-5792	276	21	u	u	NOUN
ejpam-5792	276	22	so	so	SCONJ
ejpam-5792	276	23	that	that	SCONJ
ejpam-5792	276	24	lim	lim	PROPN
ejpam-5792	276	25	n→∞	n→∞	X
ejpam-5792	276	26	yn	yn	X
ejpam-5792	276	27	=	=	PUNCT
ejpam-5792	276	28	y∗.	y∗.	PRON
ejpam-5792	276	29	suppose	suppose	VERB
ejpam-5792	276	30	y	y	PROPN
ejpam-5792	276	31	/∈	/∈	PUNCT
ejpam-5792	277	1	ty	ty	INTJ
ejpam-5792	277	2	,	,	PUNCT
ejpam-5792	277	3	then	then	ADV
ejpam-5792	277	4	y	y	PROPN
ejpam-5792	277	5	/∈	/∈	PUNCT
ejpam-5792	278	1	tλy	tλy	INTJ
ejpam-5792	278	2	.	.	PUNCT
ejpam-5792	279	1	since	since	SCONJ
ejpam-5792	279	2	tλyn	tλyn	PROPN
ejpam-5792	279	3	is	be	AUX
ejpam-5792	279	4	closed	close	VERB
ejpam-5792	279	5	for	for	ADP
ejpam-5792	279	6	each	each	DET
ejpam-5792	279	7	n	n	PRON
ejpam-5792	279	8	≥	≥	NOUN
ejpam-5792	279	9	0	0	NUM
ejpam-5792	279	10	,	,	PUNCT
ejpam-5792	279	11	yn	yn	PROPN
ejpam-5792	279	12	/∈	/∈	PROPN
ejpam-5792	279	13	tλyn	tλyn	PROPN
ejpam-5792	279	14	.	.	PUNCT
ejpam-5792	280	1	from	from	ADP
ejpam-5792	280	2	equation	equation	NOUN
ejpam-5792	280	3	(	(	PUNCT
ejpam-5792	280	4	10	10	NUM
ejpam-5792	280	5	)	)	PUNCT
ejpam-5792	280	6	,	,	PUNCT
ejpam-5792	280	7	we	we	PRON
ejpam-5792	280	8	obtain	obtain	VERB
ejpam-5792	280	9	cg	cg	NOUN
ejpam-5792	280	10	≤	≤	NOUN
ejpam-5792	280	11	ζ(h(tλyn	ζ(h(tλyn	ADJ
ejpam-5792	280	12	,	,	PUNCT
ejpam-5792	280	13	tλyn−1	tλyn−1	NOUN
ejpam-5792	280	14	)	)	PUNCT
ejpam-5792	280	15	,	,	PUNCT
ejpam-5792	280	16	r(yn	r(yn	PROPN
ejpam-5792	280	17	,	,	PUNCT
ejpam-5792	280	18	yn−1	yn−1	NOUN
ejpam-5792	280	19	)	)	PUNCT
ejpam-5792	280	20	<	<	X
ejpam-5792	280	21	cg	cg	NOUN
ejpam-5792	280	22	,	,	PUNCT
ejpam-5792	280	23	which	which	PRON
ejpam-5792	280	24	leads	lead	VERB
ejpam-5792	280	25	to	to	ADP
ejpam-5792	280	26	a	a	DET
ejpam-5792	280	27	contradiction	contradiction	NOUN
ejpam-5792	280	28	.	.	PUNCT
ejpam-5792	281	1	hence	hence	ADV
ejpam-5792	281	2	,	,	PUNCT
ejpam-5792	281	3	y	y	PROPN
ejpam-5792	281	4	∈	∈	PROPN
ejpam-5792	281	5	ty	ty	NOUN
ejpam-5792	281	6	,	,	PUNCT
ejpam-5792	281	7	which	which	PRON
ejpam-5792	281	8	implies	imply	VERB
ejpam-5792	281	9	fix(t	fix(t	PROPN
ejpam-5792	281	10	)	)	PUNCT
ejpam-5792	282	1	̸=	̸=	PROPN
ejpam-5792	282	2	ϕ.	ϕ.	VERB
ejpam-5792	282	3	the	the	DET
ejpam-5792	282	4	next	next	ADJ
ejpam-5792	282	5	example	example	NOUN
ejpam-5792	282	6	justifies	justify	VERB
ejpam-5792	282	7	the	the	DET
ejpam-5792	282	8	previous	previous	ADJ
ejpam-5792	282	9	theorem	theorem	NOUN
ejpam-5792	282	10	.	.	PUNCT
ejpam-5792	282	11	a.	a.	PROPN
ejpam-5792	282	12	gangwar	gangwar	PROPN
ejpam-5792	282	13	et	et	PROPN
ejpam-5792	282	14	al	al	PROPN
ejpam-5792	282	15	.	.	PUNCT
ejpam-5792	282	16	/	/	SYM
ejpam-5792	282	17	eur	eur	PROPN
ejpam-5792	282	18	.	.	PUNCT
ejpam-5792	283	1	j.	j.	PROPN
ejpam-5792	283	2	pure	pure	PROPN
ejpam-5792	283	3	appl	appl	PROPN
ejpam-5792	283	4	.	.	PROPN
ejpam-5792	283	5	math	math	PROPN
ejpam-5792	283	6	,	,	PUNCT
ejpam-5792	283	7	18	18	NUM
ejpam-5792	283	8	(	(	PUNCT
ejpam-5792	283	9	2	2	NUM
ejpam-5792	283	10	)	)	PUNCT
ejpam-5792	283	11	(	(	PUNCT
ejpam-5792	283	12	2025	2025	NUM
ejpam-5792	283	13	)	)	PUNCT
ejpam-5792	283	14	,	,	PUNCT
ejpam-5792	283	15	5792	5792	NUM
ejpam-5792	283	16	11	11	NUM
ejpam-5792	283	17	of	of	ADP
ejpam-5792	283	18	16	16	NUM
ejpam-5792	283	19	example	example	NOUN
ejpam-5792	283	20	2	2	NUM
ejpam-5792	283	21	.	.	PUNCT
ejpam-5792	284	1	let	let	VERB
ejpam-5792	284	2	u	u	PRON
ejpam-5792	284	3	=	=	PUNCT
ejpam-5792	285	1	[	[	X
ejpam-5792	285	2	0	0	NUM
ejpam-5792	285	3	,	,	PUNCT
ejpam-5792	285	4	1	1	NUM
ejpam-5792	285	5	]	]	PUNCT
ejpam-5792	285	6	be	be	AUX
ejpam-5792	285	7	equipped	equip	VERB
ejpam-5792	285	8	with	with	ADP
ejpam-5792	285	9	the	the	DET
ejpam-5792	285	10	euclidean	euclidean	ADJ
ejpam-5792	285	11	metric	metric	ADJ
ejpam-5792	285	12	ρ(x	ρ(x	NOUN
ejpam-5792	285	13	,	,	PUNCT
ejpam-5792	285	14	v	v	NOUN
ejpam-5792	285	15	)	)	PUNCT
ejpam-5792	285	16	=	=	SYM
ejpam-5792	285	17	|x	|x	NOUN
ejpam-5792	285	18	−	−	PROPN
ejpam-5792	285	19	v|	v|	NOUN
ejpam-5792	285	20	,	,	PUNCT
ejpam-5792	285	21	for	for	ADP
ejpam-5792	285	22	each	each	DET
ejpam-5792	285	23	x	x	NOUN
ejpam-5792	285	24	,	,	PUNCT
ejpam-5792	285	25	y	y	PROPN
ejpam-5792	285	26	∈	∈	PROPN
ejpam-5792	285	27	u	u	PROPN
ejpam-5792	285	28	,	,	PUNCT
ejpam-5792	285	29	and	and	CCONJ
ejpam-5792	285	30	t	t	PROPN
ejpam-5792	285	31	:	:	PUNCT
ejpam-5792	285	32	u	u	PROPN
ejpam-5792	285	33	→	→	SYM
ejpam-5792	285	34	cb(u	cb(u	PUNCT
ejpam-5792	285	35	)	)	PUNCT
ejpam-5792	285	36	be	be	AUX
ejpam-5792	285	37	given	give	VERB
ejpam-5792	285	38	as	as	ADP
ejpam-5792	285	39	t	t	PROPN
ejpam-5792	285	40	(	(	PUNCT
ejpam-5792	285	41	x	x	NOUN
ejpam-5792	285	42	)	)	PUNCT
ejpam-5792	285	43	=	=	PRON
ejpam-5792	285	44	{	{	PUNCT
ejpam-5792	285	45	1−	1−	NUM
ejpam-5792	285	46	x	x	SYM
ejpam-5792	285	47	2	2	NUM
ejpam-5792	285	48	,	,	PUNCT
ejpam-5792	285	49	−x	−x	NOUN
ejpam-5792	285	50	2	2	NUM
ejpam-5792	285	51	}	}	PUNCT
ejpam-5792	285	52	.	.	PUNCT
ejpam-5792	286	1	also	also	ADV
ejpam-5792	286	2	,	,	PUNCT
ejpam-5792	286	3	let	let	VERB
ejpam-5792	286	4	ζ(t	ζ(t	VERB
ejpam-5792	286	5	,	,	PUNCT
ejpam-5792	286	6	r	r	NOUN
ejpam-5792	286	7	)	)	PUNCT
ejpam-5792	286	8	=	=	SYM
ejpam-5792	286	9	1	1	NUM
ejpam-5792	286	10	2r	2r	NUM
ejpam-5792	286	11	−	−	PROPN
ejpam-5792	286	12	t	t	PROPN
ejpam-5792	286	13	,	,	PUNCT
ejpam-5792	286	14	g(r	g(r	PROPN
ejpam-5792	286	15	,	,	PUNCT
ejpam-5792	286	16	t	t	PROPN
ejpam-5792	286	17	)	)	PUNCT
ejpam-5792	287	1	=	=	SYM
ejpam-5792	287	2	r	r	NOUN
ejpam-5792	287	3	−	−	PROPN
ejpam-5792	287	4	t	t	NOUN
ejpam-5792	287	5	for	for	ADP
ejpam-5792	287	6	each	each	DET
ejpam-5792	287	7	r	r	NOUN
ejpam-5792	287	8	,	,	PUNCT
ejpam-5792	287	9	t	t	PROPN
ejpam-5792	287	10	∈	∈	PROPN
ejpam-5792	288	1	[	[	X
ejpam-5792	288	2	0,∞	0,∞	NUM
ejpam-5792	288	3	)	)	PUNCT
ejpam-5792	288	4	and	and	CCONJ
ejpam-5792	288	5	cg	cg	NOUN
ejpam-5792	288	6	=	=	NOUN
ejpam-5792	288	7	0	0	X
ejpam-5792	288	8	.	.	PUNCT
ejpam-5792	289	1	taking	take	VERB
ejpam-5792	289	2	λ	λ	NOUN
ejpam-5792	289	3	=	=	NOUN
ejpam-5792	289	4	1	1	NUM
ejpam-5792	289	5	3	3	NUM
ejpam-5792	289	6	,	,	PUNCT
ejpam-5792	289	7	we	we	PRON
ejpam-5792	289	8	obtain	obtain	VERB
ejpam-5792	289	9	t	t	PROPN
ejpam-5792	289	10	1	1	NUM
ejpam-5792	289	11	3	3	NUM
ejpam-5792	289	12	(	(	PUNCT
ejpam-5792	289	13	x	x	NOUN
ejpam-5792	289	14	)	)	PUNCT
ejpam-5792	289	15	=	=	SYM
ejpam-5792	289	16	{	{	PUNCT
ejpam-5792	289	17	0	0	NUM
ejpam-5792	289	18	,	,	PUNCT
ejpam-5792	289	19	1	1	NUM
ejpam-5792	289	20	3	3	NUM
ejpam-5792	289	21	}	}	PUNCT
ejpam-5792	289	22	.	.	PUNCT
ejpam-5792	290	1	since	since	SCONJ
ejpam-5792	290	2	fix(t	fix(t	PROPN
ejpam-5792	290	3	)	)	PUNCT
ejpam-5792	290	4	=	=	PUNCT
ejpam-5792	290	5	{	{	PUNCT
ejpam-5792	290	6	0	0	NUM
ejpam-5792	290	7	,	,	PUNCT
ejpam-5792	290	8	12	12	NUM
ejpam-5792	290	9	}	}	PUNCT
ejpam-5792	290	10	,	,	PUNCT
ejpam-5792	290	11	we	we	PRON
ejpam-5792	290	12	get	get	VERB
ejpam-5792	290	13	for	for	ADP
ejpam-5792	290	14	each	each	DET
ejpam-5792	290	15	x	x	NOUN
ejpam-5792	290	16	,	,	PUNCT
ejpam-5792	290	17	y	y	PROPN
ejpam-5792	290	18	∈	∈	PROPN
ejpam-5792	290	19	u	u	NOUN
ejpam-5792	290	20	/{0	/{0	X
ejpam-5792	290	21	,	,	PUNCT
ejpam-5792	290	22	12	12	NUM
ejpam-5792	290	23	}	}	PUNCT
ejpam-5792	290	24	,	,	PUNCT
ejpam-5792	290	25	h(tλx	h(tλx	PROPN
ejpam-5792	290	26	,	,	PUNCT
ejpam-5792	290	27	tλy	tλy	NOUN
ejpam-5792	290	28	)	)	PUNCT
ejpam-5792	290	29	=	=	SYM
ejpam-5792	290	30	0	0	NUM
ejpam-5792	291	1	and	and	CCONJ
ejpam-5792	291	2	for	for	ADP
ejpam-5792	291	3	α	α	DET
ejpam-5792	291	4	∈	∈	PROPN
ejpam-5792	291	5	(	(	PUNCT
ejpam-5792	291	6	0	0	NUM
ejpam-5792	291	7	,	,	PUNCT
ejpam-5792	291	8	1	1	NUM
ejpam-5792	291	9	)	)	PUNCT
ejpam-5792	291	10	,	,	PUNCT
ejpam-5792	291	11	q(x	q(x	PROPN
ejpam-5792	291	12	,	,	PUNCT
ejpam-5792	291	13	y	y	NOUN
ejpam-5792	291	14	)	)	PUNCT
ejpam-5792	291	15	=	=	SYM
ejpam-5792	291	16	c[d∗(x	c[d∗(x	NOUN
ejpam-5792	291	17	,	,	PUNCT
ejpam-5792	291	18	{	{	PUNCT
ejpam-5792	291	19	0	0	NUM
ejpam-5792	291	20	,	,	PUNCT
ejpam-5792	291	21	12	12	NUM
ejpam-5792	291	22	}	}	PUNCT
ejpam-5792	291	23	)	)	PUNCT
ejpam-5792	291	24	]	]	PUNCT
ejpam-5792	292	1	α[d∗(y	α[d∗(y	NOUN
ejpam-5792	292	2	,	,	PUNCT
ejpam-5792	292	3	{	{	PUNCT
ejpam-5792	292	4	0	0	NUM
ejpam-5792	292	5	,	,	PUNCT
ejpam-5792	292	6	12	12	NUM
ejpam-5792	292	7	}	}	PUNCT
ejpam-5792	292	8	)	)	PUNCT
ejpam-5792	292	9	]	]	PUNCT
ejpam-5792	293	1	1−α	1−α	NUM
ejpam-5792	293	2	>	>	X
ejpam-5792	293	3	0	0	NUM
ejpam-5792	293	4	,	,	PUNCT
ejpam-5792	293	5	which	which	PRON
ejpam-5792	293	6	implies	imply	VERB
ejpam-5792	293	7	ζ(h(tλx	ζ(h(tλx	NUM
ejpam-5792	293	8	,	,	PUNCT
ejpam-5792	293	9	tλy	tλy	NOUN
ejpam-5792	293	10	)	)	PUNCT
ejpam-5792	293	11	,	,	PUNCT
ejpam-5792	293	12	q(x	q(x	PROPN
ejpam-5792	293	13	,	,	PUNCT
ejpam-5792	293	14	y	y	NOUN
ejpam-5792	293	15	)	)	PUNCT
ejpam-5792	293	16	=	=	SYM
ejpam-5792	293	17	1	1	NUM
ejpam-5792	293	18	2	2	NUM
ejpam-5792	293	19	q(x	q(x	PROPN
ejpam-5792	293	20	,	,	PUNCT
ejpam-5792	293	21	y	y	NOUN
ejpam-5792	293	22	)	)	PUNCT
ejpam-5792	293	23	≥	≥	PROPN
ejpam-5792	293	24	cg	cg	NOUN
ejpam-5792	293	25	.	.	PUNCT
ejpam-5792	294	1	also	also	ADV
ejpam-5792	294	2	,	,	PUNCT
ejpam-5792	294	3	g(r(x	g(r(x	PROPN
ejpam-5792	294	4	,	,	PUNCT
ejpam-5792	294	5	y	y	PROPN
ejpam-5792	294	6	)	)	PUNCT
ejpam-5792	294	7	,	,	PUNCT
ejpam-5792	294	8	h(tλx	h(tλx	PROPN
ejpam-5792	294	9	,	,	PUNCT
ejpam-5792	294	10	tλy	tλy	NOUN
ejpam-5792	294	11	)	)	PUNCT
ejpam-5792	294	12	)	)	PUNCT
ejpam-5792	295	1	=	=	SYM
ejpam-5792	295	2	q(x	q(x	PROPN
ejpam-5792	295	3	,	,	PUNCT
ejpam-5792	295	4	y	y	NOUN
ejpam-5792	295	5	)	)	PUNCT
ejpam-5792	295	6	.	.	PUNCT
ejpam-5792	296	1	one	one	NUM
ejpam-5792	296	2	writes	write	VERB
ejpam-5792	296	3	cg	cg	NOUN
ejpam-5792	296	4	≤	≤	NOUN
ejpam-5792	296	5	ζ(h(tλx	ζ(h(tλx	ADP
ejpam-5792	296	6	,	,	PUNCT
ejpam-5792	296	7	tλy	tλy	NOUN
ejpam-5792	296	8	)	)	PUNCT
ejpam-5792	296	9	,	,	PUNCT
ejpam-5792	296	10	q(x	q(x	PROPN
ejpam-5792	296	11	,	,	PUNCT
ejpam-5792	296	12	y	y	NOUN
ejpam-5792	296	13	)	)	PUNCT
ejpam-5792	296	14	<	<	X
ejpam-5792	297	1	g(q(x	g(q(x	PROPN
ejpam-5792	297	2	,	,	PUNCT
ejpam-5792	297	3	y	y	PROPN
ejpam-5792	297	4	)	)	PUNCT
ejpam-5792	297	5	,	,	PUNCT
ejpam-5792	297	6	h(tλx	h(tλx	PROPN
ejpam-5792	297	7	,	,	PUNCT
ejpam-5792	297	8	tλy	tλy	NOUN
ejpam-5792	297	9	)	)	PUNCT
ejpam-5792	297	10	)	)	PUNCT
ejpam-5792	297	11	.	.	PUNCT
ejpam-5792	298	1	thus	thus	ADV
ejpam-5792	298	2	,	,	PUNCT
ejpam-5792	298	3	t	t	PROPN
ejpam-5792	298	4	is	be	AUX
ejpam-5792	298	5	a	a	DET
ejpam-5792	298	6	multivalued	multivalue	VERB
ejpam-5792	298	7	eihr	eihr	NOUN
ejpam-5792	298	8	-	-	PUNCT
ejpam-5792	298	9	contraction	contraction	NOUN
ejpam-5792	298	10	via	via	ADP
ejpam-5792	298	11	a	a	DET
ejpam-5792	298	12	simulation	simulation	NOUN
ejpam-5792	298	13	function	function	NOUN
ejpam-5792	298	14	zg	zg	PROPN
ejpam-5792	298	15	and	and	CCONJ
ejpam-5792	298	16	all	all	DET
ejpam-5792	298	17	requirements	requirement	NOUN
ejpam-5792	298	18	outlined	outline	VERB
ejpam-5792	298	19	in	in	ADP
ejpam-5792	298	20	theorem	theorem	ADJ
ejpam-5792	298	21	3.5	3.5	NUM
ejpam-5792	298	22	are	be	AUX
ejpam-5792	298	23	met	meet	VERB
ejpam-5792	298	24	.	.	PUNCT
ejpam-5792	299	1	here	here	ADV
ejpam-5792	299	2	,	,	PUNCT
ejpam-5792	299	3	fix(t	fix(t	PROPN
ejpam-5792	299	4	)	)	PUNCT
ejpam-5792	299	5	=	=	PUNCT
ejpam-5792	299	6	{	{	PUNCT
ejpam-5792	299	7	0	0	NUM
ejpam-5792	299	8	,	,	PUNCT
ejpam-5792	299	9	13	13	NUM
ejpam-5792	299	10	}	}	PUNCT
ejpam-5792	299	11	.	.	PUNCT
ejpam-5792	300	1	corollary	corollary	ADJ
ejpam-5792	300	2	7	7	NUM
ejpam-5792	300	3	.	.	PUNCT
ejpam-5792	301	1	let	let	AUX
ejpam-5792	301	2	(	(	PUNCT
ejpam-5792	301	3	u	u	NOUN
ejpam-5792	301	4	,	,	PUNCT
ejpam-5792	301	5	ρ	ρ	PROPN
ejpam-5792	301	6	)	)	PUNCT
ejpam-5792	301	7	be	be	VERB
ejpam-5792	301	8	a	a	DET
ejpam-5792	301	9	complete	complete	ADJ
ejpam-5792	301	10	metric	metric	ADJ
ejpam-5792	301	11	space	space	NOUN
ejpam-5792	301	12	.	.	PUNCT
ejpam-5792	302	1	if	if	SCONJ
ejpam-5792	302	2	t	t	PROPN
ejpam-5792	302	3	is	be	AUX
ejpam-5792	302	4	a	a	DET
ejpam-5792	302	5	multivalued	multivalue	VERB
ejpam-5792	302	6	ihr	ihr	NOUN
ejpam-5792	302	7	-	-	PUNCT
ejpam-5792	302	8	contraction	contraction	NOUN
ejpam-5792	302	9	via	via	ADP
ejpam-5792	302	10	simulation	simulation	PROPN
ejpam-5792	302	11	function	function	PROPN
ejpam-5792	302	12	zg	zg	PROPN
ejpam-5792	302	13	,	,	PUNCT
ejpam-5792	302	14	then	then	ADV
ejpam-5792	302	15	fix(t	fix(t	PROPN
ejpam-5792	302	16	)	)	PUNCT
ejpam-5792	302	17	̸=	̸=	PROPN
ejpam-5792	302	18	ϕ.	ϕ.	NOUN
ejpam-5792	302	19	proof	proof	NOUN
ejpam-5792	302	20	.	.	PUNCT
ejpam-5792	303	1	taking	take	VERB
ejpam-5792	303	2	λ	λ	PROPN
ejpam-5792	303	3	=	=	SYM
ejpam-5792	303	4	0	0	NUM
ejpam-5792	303	5	,	,	PUNCT
ejpam-5792	303	6	and	and	CCONJ
ejpam-5792	303	7	using	use	VERB
ejpam-5792	303	8	the	the	DET
ejpam-5792	303	9	same	same	ADJ
ejpam-5792	303	10	method	method	NOUN
ejpam-5792	303	11	of	of	ADP
ejpam-5792	303	12	proof	proof	NOUN
ejpam-5792	303	13	as	as	ADP
ejpam-5792	303	14	in	in	ADP
ejpam-5792	303	15	theorem	theorem	NOUN
ejpam-5792	303	16	3.5	3.5	NUM
ejpam-5792	303	17	,	,	PUNCT
ejpam-5792	303	18	we	we	PRON
ejpam-5792	303	19	achieve	achieve	VERB
ejpam-5792	303	20	the	the	DET
ejpam-5792	303	21	intended	intend	VERB
ejpam-5792	303	22	result	result	NOUN
ejpam-5792	303	23	.	.	PUNCT
ejpam-5792	304	1	corollary	corollary	ADJ
ejpam-5792	304	2	8	8	NUM
ejpam-5792	304	3	.	.	PUNCT
ejpam-5792	305	1	let	let	AUX
ejpam-5792	305	2	(	(	PUNCT
ejpam-5792	305	3	u	u	NOUN
ejpam-5792	305	4	,	,	PUNCT
ejpam-5792	305	5	ρ	ρ	PROPN
ejpam-5792	305	6	)	)	PUNCT
ejpam-5792	305	7	be	be	VERB
ejpam-5792	305	8	a	a	DET
ejpam-5792	305	9	complete	complete	ADJ
ejpam-5792	305	10	metric	metric	ADJ
ejpam-5792	305	11	space	space	NOUN
ejpam-5792	305	12	.	.	PUNCT
ejpam-5792	306	1	if	if	SCONJ
ejpam-5792	306	2	a	a	DET
ejpam-5792	306	3	self	self	NOUN
ejpam-5792	306	4	mapping	mapping	NOUN
ejpam-5792	306	5	t	t	NOUN
ejpam-5792	306	6	:	:	PUNCT
ejpam-5792	306	7	u	u	SYM
ejpam-5792	306	8	→	→	SYM
ejpam-5792	306	9	u	u	PROPN
ejpam-5792	306	10	is	be	AUX
ejpam-5792	306	11	an	an	DET
ejpam-5792	306	12	ihr	ihr	NOUN
ejpam-5792	306	13	-	-	PUNCT
ejpam-5792	306	14	contraction	contraction	NOUN
ejpam-5792	306	15	via	via	ADP
ejpam-5792	306	16	a	a	DET
ejpam-5792	306	17	simulation	simulation	NOUN
ejpam-5792	306	18	function	function	PROPN
ejpam-5792	306	19	zg	zg	PROPN
ejpam-5792	306	20	,	,	PUNCT
ejpam-5792	306	21	then	then	ADV
ejpam-5792	306	22	t	t	PROPN
ejpam-5792	306	23	possesses	possess	VERB
ejpam-5792	306	24	a	a	DET
ejpam-5792	306	25	fixed	fix	VERB
ejpam-5792	306	26	point	point	NOUN
ejpam-5792	306	27	.	.	PUNCT
ejpam-5792	307	1	4	4	X
ejpam-5792	307	2	.	.	X
ejpam-5792	307	3	data	datum	NOUN
ejpam-5792	307	4	dependence	dependence	NOUN
ejpam-5792	307	5	results	result	NOUN
ejpam-5792	307	6	we	we	PRON
ejpam-5792	307	7	propose	propose	VERB
ejpam-5792	307	8	data	datum	NOUN
ejpam-5792	307	9	dependence	dependence	NOUN
ejpam-5792	307	10	results	result	NOUN
ejpam-5792	307	11	for	for	ADP
ejpam-5792	307	12	multivalued	multivalued	ADJ
ejpam-5792	307	13	eik	eik	PROPN
ejpam-5792	307	14	-	-	PUNCT
ejpam-5792	307	15	contractions	contraction	NOUN
ejpam-5792	307	16	and	and	CCONJ
ejpam-5792	307	17	multivalued	multivalue	VERB
ejpam-5792	307	18	eihr	eihr	PROPN
ejpam-5792	307	19	-	-	PUNCT
ejpam-5792	307	20	contractions	contraction	NOUN
ejpam-5792	307	21	via	via	ADP
ejpam-5792	307	22	a	a	DET
ejpam-5792	307	23	simulation	simulation	NOUN
ejpam-5792	307	24	function	function	NOUN
ejpam-5792	307	25	zg	zg	PROPN
ejpam-5792	307	26	.	.	PUNCT
ejpam-5792	308	1	here	here	ADV
ejpam-5792	308	2	p1	p1	PROPN
ejpam-5792	308	3	,	,	PUNCT
ejpam-5792	308	4	p2	p2	PROPN
ejpam-5792	308	5	∈	∈	PROPN
ejpam-5792	308	6	(	(	PUNCT
ejpam-5792	308	7	0	0	NUM
ejpam-5792	308	8	,	,	PUNCT
ejpam-5792	308	9	1	1	NUM
ejpam-5792	308	10	)	)	PUNCT
ejpam-5792	308	11	are	be	AUX
ejpam-5792	308	12	the	the	DET
ejpam-5792	308	13	constants	constant	NOUN
ejpam-5792	308	14	for	for	ADP
ejpam-5792	308	15	t1	t1	NOUN
ejpam-5792	308	16	and	and	CCONJ
ejpam-5792	308	17	t2	t2	NOUN
ejpam-5792	308	18	,	,	PUNCT
ejpam-5792	308	19	respectively	respectively	ADV
ejpam-5792	308	20	as	as	SCONJ
ejpam-5792	308	21	given	give	VERB
ejpam-5792	308	22	in	in	ADP
ejpam-5792	308	23	definition	definition	NOUN
ejpam-5792	308	24	7	7	NUM
ejpam-5792	308	25	and	and	CCONJ
ejpam-5792	308	26	definition	definition	NOUN
ejpam-5792	308	27	8	8	NUM
ejpam-5792	308	28	.	.	PUNCT
ejpam-5792	309	1	a.	a.	NOUN
ejpam-5792	309	2	gangwar	gangwar	PROPN
ejpam-5792	309	3	et	et	PROPN
ejpam-5792	309	4	al	al	PROPN
ejpam-5792	309	5	.	.	PUNCT
ejpam-5792	309	6	/	/	SYM
ejpam-5792	309	7	eur	eur	PROPN
ejpam-5792	309	8	.	.	PUNCT
ejpam-5792	310	1	j.	j.	PROPN
ejpam-5792	310	2	pure	pure	PROPN
ejpam-5792	310	3	appl	appl	PROPN
ejpam-5792	310	4	.	.	PROPN
ejpam-5792	310	5	math	math	PROPN
ejpam-5792	310	6	,	,	PUNCT
ejpam-5792	310	7	18	18	NUM
ejpam-5792	310	8	(	(	PUNCT
ejpam-5792	310	9	2	2	NUM
ejpam-5792	310	10	)	)	PUNCT
ejpam-5792	310	11	(	(	PUNCT
ejpam-5792	310	12	2025	2025	NUM
ejpam-5792	310	13	)	)	PUNCT
ejpam-5792	310	14	,	,	PUNCT
ejpam-5792	310	15	5792	5792	NUM
ejpam-5792	310	16	12	12	NUM
ejpam-5792	310	17	of	of	ADP
ejpam-5792	310	18	16	16	NUM
ejpam-5792	310	19	theorem	theorem	NOUN
ejpam-5792	310	20	9	9	NUM
ejpam-5792	310	21	.	.	PUNCT
ejpam-5792	311	1	let	let	VERB
ejpam-5792	311	2	(	(	PUNCT
ejpam-5792	311	3	u	u	NOUN
ejpam-5792	311	4	,	,	PUNCT
ejpam-5792	311	5	ρ	ρ	PROPN
ejpam-5792	311	6	)	)	PUNCT
ejpam-5792	311	7	be	be	VERB
ejpam-5792	311	8	a	a	DET
ejpam-5792	311	9	convex	convex	ADJ
ejpam-5792	311	10	metric	metric	ADJ
ejpam-5792	311	11	space	space	NOUN
ejpam-5792	311	12	and	and	CCONJ
ejpam-5792	311	13	ti	ti	NOUN
ejpam-5792	311	14	:	:	PUNCT
ejpam-5792	311	15	u	u	PROPN
ejpam-5792	311	16	→	→	SYM
ejpam-5792	311	17	cb(u	cb(u	PUNCT
ejpam-5792	311	18	)	)	PUNCT
ejpam-5792	311	19	be	be	AUX
ejpam-5792	311	20	two	two	NUM
ejpam-5792	311	21	multivalued	multivalued	ADJ
ejpam-5792	311	22	eik	eik	NOUN
ejpam-5792	311	23	-	-	PUNCT
ejpam-5792	311	24	contraction	contraction	NOUN
ejpam-5792	311	25	operators	operator	NOUN
ejpam-5792	311	26	via	via	ADP
ejpam-5792	311	27	a	a	DET
ejpam-5792	311	28	simulation	simulation	NOUN
ejpam-5792	311	29	function	function	PROPN
ejpam-5792	311	30	zg	zg	PROPN
ejpam-5792	311	31	.	.	PUNCT
ejpam-5792	311	32	suppose	suppose	VERB
ejpam-5792	311	33	that	that	SCONJ
ejpam-5792	311	34	there	there	PRON
ejpam-5792	311	35	is	be	VERB
ejpam-5792	311	36	some	some	DET
ejpam-5792	311	37	α	α	NOUN
ejpam-5792	311	38	>	>	X
ejpam-5792	311	39	0	0	PUNCT
ejpam-5792	312	1	so	so	SCONJ
ejpam-5792	312	2	that	that	SCONJ
ejpam-5792	312	3	h(t1y	h(t1y	NOUN
ejpam-5792	312	4	,	,	PUNCT
ejpam-5792	312	5	t2y	t2y	NOUN
ejpam-5792	312	6	)	)	PUNCT
ejpam-5792	312	7	≤	≤	NUM
ejpam-5792	312	8	α	α	NOUN
ejpam-5792	312	9	for	for	ADP
ejpam-5792	312	10	each	each	DET
ejpam-5792	312	11	y	y	PROPN
ejpam-5792	312	12	∈	∈	PROPN
ejpam-5792	312	13	u	u	PROPN
ejpam-5792	312	14	.	.	PUNCT
ejpam-5792	313	1	then	then	ADV
ejpam-5792	313	2	(	(	PUNCT
ejpam-5792	313	3	i)fix(ti	i)fix(ti	NOUN
ejpam-5792	313	4	)	)	PUNCT
ejpam-5792	313	5	is	be	AUX
ejpam-5792	313	6	a	a	DET
ejpam-5792	313	7	closed	closed	ADJ
ejpam-5792	313	8	subset	subset	NOUN
ejpam-5792	313	9	of	of	ADP
ejpam-5792	313	10	u	u	NOUN
ejpam-5792	313	11	for	for	ADP
ejpam-5792	313	12	i	i	PRON
ejpam-5792	313	13	∈	∈	PROPN
ejpam-5792	313	14	{	{	PUNCT
ejpam-5792	313	15	1	1	NUM
ejpam-5792	313	16	,	,	PUNCT
ejpam-5792	313	17	2	2	NUM
ejpam-5792	313	18	}	}	PUNCT
ejpam-5792	313	19	.	.	PUNCT
ejpam-5792	314	1	(	(	PUNCT
ejpam-5792	314	2	ii	ii	NOUN
ejpam-5792	314	3	)	)	PUNCT
ejpam-5792	314	4	h(fix(t1	h(fix(t1	NOUN
ejpam-5792	314	5	,	,	PUNCT
ejpam-5792	314	6	)	)	PUNCT
ejpam-5792	314	7	,	,	PUNCT
ejpam-5792	314	8	f	f	PROPN
ejpam-5792	314	9	ix(t2	ix(t2	PROPN
ejpam-5792	314	10	)	)	PUNCT
ejpam-5792	314	11	)	)	PUNCT
ejpam-5792	315	1	≤	≤	NUM
ejpam-5792	316	1	α	α	PRON
ejpam-5792	316	2	1−max{p1,p2	1−max{p1,p2	NUM
ejpam-5792	316	3	}	}	PUNCT
ejpam-5792	316	4	.	.	PUNCT
ejpam-5792	317	1	proof	proof	NOUN
ejpam-5792	317	2	.	.	PUNCT
ejpam-5792	318	1	from	from	ADP
ejpam-5792	318	2	theorem	theorem	ADJ
ejpam-5792	318	3	3.1	3.1	NUM
ejpam-5792	318	4	,	,	PUNCT
ejpam-5792	318	5	fix(ti	fix(ti	NOUN
ejpam-5792	318	6	)	)	PUNCT
ejpam-5792	318	7	̸=	̸=	PROPN
ejpam-5792	318	8	ϕ	ϕ	NOUN
ejpam-5792	318	9	for	for	ADP
ejpam-5792	318	10	i	i	PRON
ejpam-5792	318	11	∈	∈	PROPN
ejpam-5792	318	12	{	{	PUNCT
ejpam-5792	318	13	1	1	NUM
ejpam-5792	318	14	,	,	PUNCT
ejpam-5792	318	15	2	2	NUM
ejpam-5792	318	16	}	}	PUNCT
ejpam-5792	318	17	.	.	PUNCT
ejpam-5792	319	1	let	let	VERB
ejpam-5792	319	2	{	{	PUNCT
ejpam-5792	319	3	yn	yn	NOUN
ejpam-5792	319	4	}	}	PUNCT
ejpam-5792	319	5	be	be	AUX
ejpam-5792	319	6	a	a	DET
ejpam-5792	319	7	sequence	sequence	NOUN
ejpam-5792	319	8	in	in	ADP
ejpam-5792	319	9	fix(ti	fix(ti	NOUN
ejpam-5792	319	10	)	)	PUNCT
ejpam-5792	320	1	=	=	SYM
ejpam-5792	320	2	fix(tiλ	fix(tiλ	NOUN
ejpam-5792	320	3	)	)	PUNCT
ejpam-5792	320	4	for	for	ADP
ejpam-5792	320	5	i	i	PROPN
ejpam-5792	320	6	∈	∈	PROPN
ejpam-5792	320	7	{	{	PUNCT
ejpam-5792	320	8	1	1	NUM
ejpam-5792	320	9	,	,	PUNCT
ejpam-5792	320	10	2	2	NUM
ejpam-5792	320	11	}	}	PUNCT
ejpam-5792	320	12	so	so	SCONJ
ejpam-5792	320	13	that	that	SCONJ
ejpam-5792	320	14	yn	yn	PRON
ejpam-5792	320	15	→	→	PUNCT
ejpam-5792	320	16	y∗	y∗	ADV
ejpam-5792	320	17	as	as	ADP
ejpam-5792	320	18	n→	n→	PROPN
ejpam-5792	320	19	∞	∞	PROPN
ejpam-5792	320	20	,	,	PUNCT
ejpam-5792	320	21	then	then	ADV
ejpam-5792	320	22	for	for	ADP
ejpam-5792	320	23	i	i	PROPN
ejpam-5792	320	24	∈	∈	PROPN
ejpam-5792	320	25	{	{	PUNCT
ejpam-5792	320	26	1	1	NUM
ejpam-5792	320	27	,	,	PUNCT
ejpam-5792	320	28	2	2	NUM
ejpam-5792	320	29	}	}	PUNCT
ejpam-5792	320	30	ζ(h(tiλyn	ζ(h(tiλyn	PROPN
ejpam-5792	320	31	,	,	PUNCT
ejpam-5792	320	32	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	320	33	)	)	PUNCT
ejpam-5792	320	34	,	,	PUNCT
ejpam-5792	320	35	q(yn	q(yn	PROPN
ejpam-5792	320	36	,	,	PUNCT
ejpam-5792	320	37	yn−1	yn−1	PROPN
ejpam-5792	320	38	)	)	PUNCT
ejpam-5792	320	39	≥	≥	NOUN
ejpam-5792	320	40	cg	cg	NOUN
ejpam-5792	320	41	.	.	PUNCT
ejpam-5792	321	1	by	by	ADP
ejpam-5792	321	2	definition	definition	NOUN
ejpam-5792	321	3	3	3	NUM
ejpam-5792	321	4	,	,	PUNCT
ejpam-5792	321	5	we	we	PRON
ejpam-5792	321	6	obtain	obtain	VERB
ejpam-5792	321	7	cg	cg	NOUN
ejpam-5792	321	8	≤	≤	PROPN
ejpam-5792	321	9	ζ(h(tiλyn	ζ(h(tiλyn	PROPN
ejpam-5792	321	10	,	,	PUNCT
ejpam-5792	321	11	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	321	12	)	)	PUNCT
ejpam-5792	321	13	,	,	PUNCT
ejpam-5792	321	14	q(yn	q(yn	PROPN
ejpam-5792	321	15	,	,	PUNCT
ejpam-5792	321	16	yn−1	yn−1	PROPN
ejpam-5792	321	17	)	)	PUNCT
ejpam-5792	321	18	<	<	X
ejpam-5792	322	1	g(q(yn	g(q(yn	X
ejpam-5792	322	2	,	,	PUNCT
ejpam-5792	322	3	yn−1	yn−1	NOUN
ejpam-5792	322	4	)	)	PUNCT
ejpam-5792	322	5	,	,	PUNCT
ejpam-5792	322	6	h(tiλyn	h(tiλyn	VERB
ejpam-5792	322	7	,	,	PUNCT
ejpam-5792	322	8	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	322	9	)	)	PUNCT
ejpam-5792	322	10	)	)	PUNCT
ejpam-5792	322	11	.	.	PUNCT
ejpam-5792	323	1	from	from	ADP
ejpam-5792	323	2	definition	definition	NOUN
ejpam-5792	323	3	2	2	NUM
ejpam-5792	323	4	,	,	PUNCT
ejpam-5792	323	5	we	we	PRON
ejpam-5792	323	6	obtain	obtain	VERB
ejpam-5792	323	7	h(tiλyn	h(tiλyn	VERB
ejpam-5792	323	8	,	,	PUNCT
ejpam-5792	323	9	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	323	10	)	)	PUNCT
ejpam-5792	323	11	<	<	X
ejpam-5792	323	12	q(yn	q(yn	PROPN
ejpam-5792	323	13	,	,	PUNCT
ejpam-5792	323	14	yn−1	yn−1	NOUN
ejpam-5792	323	15	)	)	PUNCT
ejpam-5792	323	16	,	,	PUNCT
ejpam-5792	323	17	which	which	PRON
ejpam-5792	323	18	implies	imply	VERB
ejpam-5792	323	19	d∗(yn	d∗(yn	NOUN
ejpam-5792	323	20	,	,	PUNCT
ejpam-5792	323	21	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	323	22	)	)	PUNCT
ejpam-5792	323	23	<	<	X
ejpam-5792	323	24	q(yn	q(yn	PROPN
ejpam-5792	323	25	,	,	PUNCT
ejpam-5792	323	26	yn−1	yn−1	NOUN
ejpam-5792	323	27	)	)	PUNCT
ejpam-5792	323	28	=	=	SYM
ejpam-5792	323	29	pi[d	pi[d	PROPN
ejpam-5792	323	30	∗(yn	∗(yn	PROPN
ejpam-5792	323	31	,	,	PUNCT
ejpam-5792	323	32	tiλyn	tiλyn	VERB
ejpam-5792	323	33	]	]	PUNCT
ejpam-5792	323	34	α.[d∗(yn−1	α.[d∗(yn−1	PROPN
ejpam-5792	323	35	,	,	PUNCT
ejpam-5792	323	36	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	323	37	]	]	X
ejpam-5792	323	38	1−α	1−α	NUM
ejpam-5792	324	1	=	=	SYM
ejpam-5792	324	2	0	0	X
ejpam-5792	324	3	.	.	PUNCT
ejpam-5792	325	1	as	as	ADP
ejpam-5792	325	2	n→	n→	PROPN
ejpam-5792	325	3	∞	∞	PROPN
ejpam-5792	325	4	,	,	PUNCT
ejpam-5792	325	5	we	we	PRON
ejpam-5792	325	6	get	get	VERB
ejpam-5792	325	7	that	that	DET
ejpam-5792	325	8	d∗(x	d∗(x	PROPN
ejpam-5792	325	9	,	,	PUNCT
ejpam-5792	325	10	tiλx	tiλx	PROPN
ejpam-5792	325	11	)	)	PUNCT
ejpam-5792	325	12	=	=	SYM
ejpam-5792	326	1	0	0	X
ejpam-5792	326	2	.	.	PUNCT
ejpam-5792	327	1	since	since	SCONJ
ejpam-5792	327	2	tiλx	tiλx	PROPN
ejpam-5792	327	3	∈	∈	PROPN
ejpam-5792	327	4	cb(u	cb(u	X
ejpam-5792	327	5	)	)	PUNCT
ejpam-5792	327	6	,	,	PUNCT
ejpam-5792	327	7	we	we	PRON
ejpam-5792	327	8	have	have	VERB
ejpam-5792	327	9	x	x	PROPN
ejpam-5792	327	10	∈	∈	PROPN
ejpam-5792	327	11	tiλx	tiλx	PROPN
ejpam-5792	327	12	.	.	PUNCT
ejpam-5792	328	1	hence	hence	ADV
ejpam-5792	328	2	,	,	PUNCT
ejpam-5792	328	3	x	x	X
ejpam-5792	328	4	∈	∈	NOUN
ejpam-5792	328	5	fix(tiλ	fix(tiλ	NOUN
ejpam-5792	328	6	)	)	PUNCT
ejpam-5792	328	7	=	=	SYM
ejpam-5792	328	8	fix(ti	fix(ti	NOUN
ejpam-5792	328	9	)	)	PUNCT
ejpam-5792	328	10	for	for	ADP
ejpam-5792	328	11	i	i	PROPN
ejpam-5792	328	12	∈	∈	PROPN
ejpam-5792	328	13	{	{	PUNCT
ejpam-5792	328	14	1	1	NUM
ejpam-5792	328	15	,	,	PUNCT
ejpam-5792	328	16	2	2	NUM
ejpam-5792	328	17	}	}	PUNCT
ejpam-5792	328	18	.	.	PUNCT
ejpam-5792	329	1	let	let	VERB
ejpam-5792	329	2	y0	y0	PRON
ejpam-5792	329	3	∈	∈	NOUN
ejpam-5792	329	4	fix(t1	fix(t1	X
ejpam-5792	329	5	)	)	PUNCT
ejpam-5792	329	6	=	=	SYM
ejpam-5792	329	7	fix(t1λ	fix(t1λ	PROPN
ejpam-5792	329	8	)	)	PUNCT
ejpam-5792	329	9	be	be	AUX
ejpam-5792	329	10	arbitrary	arbitrary	ADJ
ejpam-5792	329	11	.	.	PUNCT
ejpam-5792	330	1	then	then	ADV
ejpam-5792	330	2	for	for	ADP
ejpam-5792	330	3	q	q	PROPN
ejpam-5792	330	4	>	>	X
ejpam-5792	330	5	1	1	NUM
ejpam-5792	330	6	,	,	PUNCT
ejpam-5792	330	7	there	there	PRON
ejpam-5792	330	8	is	be	VERB
ejpam-5792	330	9	some	some	DET
ejpam-5792	330	10	y1	y1	PROPN
ejpam-5792	330	11	∈	∈	PROPN
ejpam-5792	330	12	t2λy0	t2λy0	NOUN
ejpam-5792	330	13	so	so	SCONJ
ejpam-5792	330	14	that	that	SCONJ
ejpam-5792	330	15	ρ(y0	ρ(y0	NOUN
ejpam-5792	330	16	,	,	PUNCT
ejpam-5792	330	17	y1	y1	NOUN
ejpam-5792	330	18	)	)	PUNCT
ejpam-5792	330	19	≤	≤	PROPN
ejpam-5792	330	20	qh(t1λy0	qh(t1λy0	PROPN
ejpam-5792	330	21	,	,	PUNCT
ejpam-5792	330	22	t2λy0	t2λy0	NOUN
ejpam-5792	330	23	)	)	PUNCT
ejpam-5792	330	24	.	.	PUNCT
ejpam-5792	331	1	next	next	ADV
ejpam-5792	331	2	,	,	PUNCT
ejpam-5792	331	3	for	for	ADP
ejpam-5792	331	4	y1	y1	PROPN
ejpam-5792	331	5	∈	∈	PROPN
ejpam-5792	331	6	t2λy0	t2λy0	NOUN
ejpam-5792	331	7	there	there	PRON
ejpam-5792	331	8	is	be	VERB
ejpam-5792	331	9	some	some	DET
ejpam-5792	331	10	y2	y2	NOUN
ejpam-5792	331	11	∈	∈	PROPN
ejpam-5792	331	12	t2λy1	t2λy1	NOUN
ejpam-5792	331	13	so	so	SCONJ
ejpam-5792	331	14	that	that	SCONJ
ejpam-5792	331	15	ρ(y1	ρ(y1	NOUN
ejpam-5792	331	16	,	,	PUNCT
ejpam-5792	331	17	y2	y2	PROPN
ejpam-5792	331	18	)	)	PUNCT
ejpam-5792	331	19	≤	≤	PROPN
ejpam-5792	331	20	qh(t2λy0	qh(t2λy0	NOUN
ejpam-5792	331	21	,	,	PUNCT
ejpam-5792	331	22	t2λy1	t2λy1	NOUN
ejpam-5792	331	23	)	)	PUNCT
ejpam-5792	331	24	.	.	PUNCT
ejpam-5792	332	1	similarly	similarly	ADV
ejpam-5792	332	2	,	,	PUNCT
ejpam-5792	332	3	we	we	PRON
ejpam-5792	332	4	derive	derive	VERB
ejpam-5792	332	5	the	the	DET
ejpam-5792	332	6	sequence	sequence	NOUN
ejpam-5792	332	7	of	of	ADP
ejpam-5792	332	8	successive	successive	ADJ
ejpam-5792	332	9	approximations	approximation	NOUN
ejpam-5792	332	10	for	for	ADP
ejpam-5792	332	11	t2λ	t2λ	NOUN
ejpam-5792	332	12	beginning	begin	VERB
ejpam-5792	332	13	from	from	ADP
ejpam-5792	332	14	y0	y0	NOUN
ejpam-5792	332	15	,	,	PUNCT
ejpam-5792	332	16	such	such	ADJ
ejpam-5792	332	17	that	that	SCONJ
ejpam-5792	332	18	yn+1	yn+1	PROPN
ejpam-5792	332	19	∈	∈	PROPN
ejpam-5792	332	20	t2λyn	t2λyn	VERB
ejpam-5792	332	21	for	for	ADP
ejpam-5792	332	22	each	each	DET
ejpam-5792	332	23	n	n	PRON
ejpam-5792	332	24	≥	≥	NOUN
ejpam-5792	332	25	1	1	NUM
ejpam-5792	332	26	and	and	CCONJ
ejpam-5792	332	27	ρ(yn	ρ(yn	NUM
ejpam-5792	332	28	,	,	PUNCT
ejpam-5792	332	29	yn+1	yn+1	NUM
ejpam-5792	332	30	)	)	PUNCT
ejpam-5792	332	31	≤	≤	NUM
ejpam-5792	332	32	qh(t2λyn−1	qh(t2λyn−1	NUM
ejpam-5792	332	33	,	,	PUNCT
ejpam-5792	332	34	t2λyn	t2λyn	PROPN
ejpam-5792	332	35	)	)	PUNCT
ejpam-5792	332	36	.	.	PUNCT
ejpam-5792	333	1	from	from	ADP
ejpam-5792	333	2	equation	equation	NOUN
ejpam-5792	333	3	(	(	PUNCT
ejpam-5792	333	4	8)	8)	NUM
ejpam-5792	333	5	(	(	PUNCT
ejpam-5792	333	6	taking	take	VERB
ejpam-5792	333	7	p2	p2	NOUN
ejpam-5792	333	8	in	in	ADP
ejpam-5792	333	9	place	place	NOUN
ejpam-5792	333	10	of	of	ADP
ejpam-5792	333	11	θ	θ	PROPN
ejpam-5792	333	12	)	)	PUNCT
ejpam-5792	333	13	,	,	PUNCT
ejpam-5792	333	14	we	we	PRON
ejpam-5792	333	15	obtain	obtain	VERB
ejpam-5792	333	16	ρ(yn	ρ(yn	NUM
ejpam-5792	333	17	,	,	PUNCT
ejpam-5792	333	18	yn+1	yn+1	NUM
ejpam-5792	333	19	)	)	PUNCT
ejpam-5792	333	20	≤	≤	NOUN
ejpam-5792	333	21	qp2ρ(yn−1	qp2ρ(yn−1	PROPN
ejpam-5792	333	22	,	,	PUNCT
ejpam-5792	333	23	yn	yn	PROPN
ejpam-5792	333	24	)	)	PUNCT
ejpam-5792	333	25	for	for	ADP
ejpam-5792	333	26	each	each	DET
ejpam-5792	333	27	n	n	PRON
ejpam-5792	333	28	≥	≥	NOUN
ejpam-5792	333	29	1	1	NUM
ejpam-5792	333	30	.	.	PUNCT
ejpam-5792	334	1	hence	hence	ADV
ejpam-5792	334	2	,	,	PUNCT
ejpam-5792	334	3	for	for	ADP
ejpam-5792	334	4	m	m	PROPN
ejpam-5792	334	5	≥	≥	NOUN
ejpam-5792	334	6	1	1	NUM
ejpam-5792	334	7	and	and	CCONJ
ejpam-5792	334	8	n	n	PRON
ejpam-5792	334	9	∈	∈	PROPN
ejpam-5792	334	10	n	n	CCONJ
ejpam-5792	334	11	,	,	PUNCT
ejpam-5792	334	12	we	we	PRON
ejpam-5792	334	13	obtain	obtain	VERB
ejpam-5792	334	14	ρ(yn+m	ρ(yn+m	PROPN
ejpam-5792	334	15	,	,	PUNCT
ejpam-5792	334	16	yn	yn	PROPN
ejpam-5792	334	17	)	)	PUNCT
ejpam-5792	334	18	≤	≤	NOUN
ejpam-5792	334	19	ρ(yn	ρ(yn	NUM
ejpam-5792	334	20	,	,	PUNCT
ejpam-5792	334	21	yn+1	yn+1	NUM
ejpam-5792	334	22	)	)	PUNCT
ejpam-5792	334	23	+	+	X
ejpam-5792	334	24	ρ(yn+1	ρ(yn+1	PROPN
ejpam-5792	334	25	,	,	PUNCT
ejpam-5792	334	26	yn+2	yn+2	NUM
ejpam-5792	334	27	)	)	PUNCT
ejpam-5792	334	28	+	+	CCONJ
ejpam-5792	334	29	·	·	PUNCT
ejpam-5792	334	30	·	·	PUNCT
ejpam-5792	334	31	·	·	PUNCT
ejpam-5792	334	32	+	+	NUM
ejpam-5792	334	33	ρ(vn+m−1	ρ(vn+m−1	NUM
ejpam-5792	334	34	,	,	PUNCT
ejpam-5792	334	35	yn+m	yn+m	PROPN
ejpam-5792	334	36	)	)	PUNCT
ejpam-5792	334	37	a.	a.	NOUN
ejpam-5792	334	38	gangwar	gangwar	NOUN
ejpam-5792	335	1	et	et	PROPN
ejpam-5792	335	2	al	al	PROPN
ejpam-5792	335	3	.	.	PUNCT
ejpam-5792	335	4	/	/	SYM
ejpam-5792	335	5	eur	eur	PROPN
ejpam-5792	335	6	.	.	PUNCT
ejpam-5792	336	1	j.	j.	PROPN
ejpam-5792	336	2	pure	pure	PROPN
ejpam-5792	336	3	appl	appl	PROPN
ejpam-5792	336	4	.	.	PROPN
ejpam-5792	336	5	math	math	PROPN
ejpam-5792	336	6	,	,	PUNCT
ejpam-5792	336	7	18	18	NUM
ejpam-5792	336	8	(	(	PUNCT
ejpam-5792	336	9	2	2	NUM
ejpam-5792	336	10	)	)	PUNCT
ejpam-5792	336	11	(	(	PUNCT
ejpam-5792	336	12	2025	2025	NUM
ejpam-5792	336	13	)	)	PUNCT
ejpam-5792	336	14	,	,	PUNCT
ejpam-5792	336	15	5792	5792	NUM
ejpam-5792	336	16	13	13	NUM
ejpam-5792	336	17	of	of	ADP
ejpam-5792	336	18	16	16	NUM
ejpam-5792	336	19	≤	≤	NOUN
ejpam-5792	336	20	(	(	PUNCT
ejpam-5792	336	21	qp2	qp2	NOUN
ejpam-5792	336	22	)	)	PUNCT
ejpam-5792	336	23	nρ(y0	nρ(y0	NOUN
ejpam-5792	336	24	,	,	PUNCT
ejpam-5792	336	25	y1	y1	NOUN
ejpam-5792	336	26	)	)	PUNCT
ejpam-5792	336	27	+	+	CCONJ
ejpam-5792	336	28	(	(	PUNCT
ejpam-5792	336	29	qp2	qp2	NOUN
ejpam-5792	336	30	)	)	PUNCT
ejpam-5792	336	31	n+1ρ(y0	n+1ρ(y0	NOUN
ejpam-5792	336	32	,	,	PUNCT
ejpam-5792	336	33	y1	y1	PROPN
ejpam-5792	336	34	)	)	PUNCT
ejpam-5792	336	35	+	+	CCONJ
ejpam-5792	336	36	·	·	PUNCT
ejpam-5792	336	37	·	·	PUNCT
ejpam-5792	336	38	·	·	PUNCT
ejpam-5792	337	1	+	+	CCONJ
ejpam-5792	337	2	(	(	PUNCT
ejpam-5792	337	3	qp2	qp2	NOUN
ejpam-5792	337	4	)	)	PUNCT
ejpam-5792	337	5	n+m−1ρ(y0	n+m−1ρ(y0	PROPN
ejpam-5792	337	6	,	,	PUNCT
ejpam-5792	337	7	y1	y1	NOUN
ejpam-5792	337	8	)	)	PUNCT
ejpam-5792	337	9	≤	≤	NOUN
ejpam-5792	337	10	(	(	PUNCT
ejpam-5792	337	11	qp2	qp2	NOUN
ejpam-5792	337	12	)	)	PUNCT
ejpam-5792	337	13	n	n	PROPN
ejpam-5792	337	14	1−	1−	NUM
ejpam-5792	337	15	qp2	qp2	NOUN
ejpam-5792	337	16	ρ(y0	ρ(y0	NOUN
ejpam-5792	337	17	,	,	PUNCT
ejpam-5792	337	18	y1	y1	PROPN
ejpam-5792	337	19	)	)	PUNCT
ejpam-5792	337	20	.	.	PUNCT
ejpam-5792	338	1	taking	take	VERB
ejpam-5792	338	2	1	1	NUM
ejpam-5792	338	3	<	<	X
ejpam-5792	338	4	q	q	X
ejpam-5792	338	5	<	<	X
ejpam-5792	338	6	min	min	X
ejpam-5792	338	7	{	{	PUNCT
ejpam-5792	338	8	1	1	NUM
ejpam-5792	338	9	p1	p1	NOUN
ejpam-5792	338	10	,	,	PUNCT
ejpam-5792	338	11	1	1	NUM
ejpam-5792	338	12	p2	p2	PROPN
ejpam-5792	338	13	}	}	PUNCT
ejpam-5792	338	14	and	and	CCONJ
ejpam-5792	338	15	as	as	ADP
ejpam-5792	338	16	n	n	NUM
ejpam-5792	338	17	→	→	SYM
ejpam-5792	338	18	∞	∞	PROPN
ejpam-5792	338	19	,	,	PUNCT
ejpam-5792	338	20	we	we	PRON
ejpam-5792	338	21	conclude	conclude	VERB
ejpam-5792	338	22	that	that	SCONJ
ejpam-5792	338	23	the	the	PRON
ejpam-5792	338	24	{	{	PUNCT
ejpam-5792	338	25	yn	yn	NOUN
ejpam-5792	338	26	}	}	PUNCT
ejpam-5792	338	27	is	be	AUX
ejpam-5792	338	28	a	a	DET
ejpam-5792	338	29	cauchy	cauchy	ADJ
ejpam-5792	338	30	sequence	sequence	NOUN
ejpam-5792	338	31	in	in	ADP
ejpam-5792	338	32	(	(	PUNCT
ejpam-5792	338	33	u	u	NOUN
ejpam-5792	338	34	,	,	PUNCT
ejpam-5792	338	35	ρ	ρ	PROPN
ejpam-5792	338	36	)	)	PUNCT
ejpam-5792	338	37	.	.	PUNCT
ejpam-5792	339	1	therefore	therefore	ADV
ejpam-5792	339	2	,	,	PUNCT
ejpam-5792	339	3	there	there	PRON
ejpam-5792	339	4	is	be	VERB
ejpam-5792	339	5	some	some	DET
ejpam-5792	339	6	y∗	y∗	ADV
ejpam-5792	339	7	∈	∈	NOUN
ejpam-5792	339	8	u	u	NOUN
ejpam-5792	339	9	so	so	SCONJ
ejpam-5792	339	10	that	that	SCONJ
ejpam-5792	339	11	yn	yn	PRON
ejpam-5792	339	12	→	→	SYM
ejpam-5792	339	13	y∗	y∗	ADV
ejpam-5792	339	14	as	as	ADP
ejpam-5792	339	15	n→	n→	PUNCT
ejpam-5792	339	16	∞.	∞.	PROPN
ejpam-5792	339	17	claim	claim	NOUN
ejpam-5792	339	18	:	:	PUNCT
ejpam-5792	339	19	y∗	y∗	ADV
ejpam-5792	339	20	is	be	AUX
ejpam-5792	339	21	a	a	DET
ejpam-5792	339	22	fixed	fix	VERB
ejpam-5792	339	23	point	point	NOUN
ejpam-5792	339	24	of	of	ADP
ejpam-5792	339	25	t2	t2	NOUN
ejpam-5792	339	26	.	.	PUNCT
ejpam-5792	340	1	suppose	suppose	VERB
ejpam-5792	340	2	if	if	SCONJ
ejpam-5792	340	3	possible	possible	ADJ
ejpam-5792	340	4	y∗	y∗	ADV
ejpam-5792	340	5	/∈	/∈	PUNCT
ejpam-5792	341	1	t2y	t2y	ADJ
ejpam-5792	341	2	∗	∗	NOUN
ejpam-5792	341	3	,	,	PUNCT
ejpam-5792	341	4	which	which	PRON
ejpam-5792	341	5	implies	imply	VERB
ejpam-5792	341	6	y∗	y∗	ADV
ejpam-5792	341	7	/∈	/∈	PUNCT
ejpam-5792	341	8	t2λy	t2λy	NUM
ejpam-5792	341	9	∗	∗	NOUN
ejpam-5792	341	10	,	,	PUNCT
ejpam-5792	341	11	then	then	ADV
ejpam-5792	341	12	ynk	ynk	PROPN
ejpam-5792	341	13	/∈	/∈	PROPN
ejpam-5792	341	14	t2λynk	t2λynk	PROPN
ejpam-5792	341	15	.	.	PUNCT
ejpam-5792	342	1	from	from	ADP
ejpam-5792	342	2	definition	definition	NOUN
ejpam-5792	342	3	3	3	NUM
ejpam-5792	342	4	and	and	CCONJ
ejpam-5792	342	5	the	the	DET
ejpam-5792	342	6	contraction	contraction	NOUN
ejpam-5792	342	7	condition	condition	NOUN
ejpam-5792	342	8	,	,	PUNCT
ejpam-5792	342	9	we	we	PRON
ejpam-5792	342	10	obtain	obtain	VERB
ejpam-5792	342	11	cg	cg	NOUN
ejpam-5792	342	12	≤	≤	PROPN
ejpam-5792	342	13	lim	lim	PROPN
ejpam-5792	342	14	n→∞	n→∞	NUM
ejpam-5792	342	15	sup	sup	NOUN
ejpam-5792	342	16	ζ(h(t2λy	ζ(h(t2λy	PROPN
ejpam-5792	342	17	∗	∗	NOUN
ejpam-5792	342	18	,	,	PUNCT
ejpam-5792	342	19	t2λynk	t2λynk	NOUN
ejpam-5792	342	20	)	)	PUNCT
ejpam-5792	342	21	,	,	PUNCT
ejpam-5792	342	22	q(y∗	q(y∗	ADV
ejpam-5792	342	23	,	,	PUNCT
ejpam-5792	342	24	ynk	ynk	NOUN
ejpam-5792	342	25	)	)	PUNCT
ejpam-5792	342	26	)	)	PUNCT
ejpam-5792	343	1	<	<	X
ejpam-5792	343	2	cg	cg	INTJ
ejpam-5792	343	3	.	.	PUNCT
ejpam-5792	344	1	this	this	PRON
ejpam-5792	344	2	leads	lead	VERB
ejpam-5792	344	3	to	to	ADP
ejpam-5792	344	4	a	a	DET
ejpam-5792	344	5	contradiction	contradiction	NOUN
ejpam-5792	344	6	.	.	PUNCT
ejpam-5792	345	1	hence	hence	ADV
ejpam-5792	345	2	,	,	PUNCT
ejpam-5792	345	3	y∗	y∗	ADV
ejpam-5792	345	4	is	be	AUX
ejpam-5792	345	5	a	a	DET
ejpam-5792	345	6	fixed	fix	VERB
ejpam-5792	345	7	point	point	NOUN
ejpam-5792	345	8	of	of	ADP
ejpam-5792	345	9	t2	t2	NOUN
ejpam-5792	345	10	.	.	PUNCT
ejpam-5792	346	1	taking	take	VERB
ejpam-5792	346	2	m→	m→	PROPN
ejpam-5792	346	3	∞	∞	PROPN
ejpam-5792	346	4	,	,	PUNCT
ejpam-5792	346	5	then	then	ADV
ejpam-5792	346	6	for	for	ADP
ejpam-5792	346	7	each	each	DET
ejpam-5792	346	8	n	n	PRON
ejpam-5792	346	9	∈	∈	NOUN
ejpam-5792	347	1	n	n	CCONJ
ejpam-5792	347	2	we	we	PRON
ejpam-5792	347	3	obtain	obtain	VERB
ejpam-5792	347	4	ρ(y∗	ρ(y∗	NUM
ejpam-5792	347	5	,	,	PUNCT
ejpam-5792	347	6	yn	yn	NOUN
ejpam-5792	347	7	)	)	PUNCT
ejpam-5792	347	8	≤	≤	NOUN
ejpam-5792	347	9	(	(	PUNCT
ejpam-5792	347	10	qp2	qp2	NOUN
ejpam-5792	347	11	)	)	PUNCT
ejpam-5792	347	12	n	n	PROPN
ejpam-5792	348	1	1−	1−	NUM
ejpam-5792	348	2	qp2	qp2	NOUN
ejpam-5792	348	3	ρ(y0	ρ(y0	NOUN
ejpam-5792	348	4	,	,	PUNCT
ejpam-5792	348	5	y1	y1	PROPN
ejpam-5792	348	6	)	)	PUNCT
ejpam-5792	348	7	,	,	PUNCT
ejpam-5792	348	8	which	which	PRON
ejpam-5792	348	9	implies	imply	VERB
ejpam-5792	348	10	ρ(y0	ρ(y0	NOUN
ejpam-5792	348	11	,	,	PUNCT
ejpam-5792	348	12	y	y	PROPN
ejpam-5792	348	13	∗	∗	NOUN
ejpam-5792	348	14	)	)	PUNCT
ejpam-5792	348	15	≤	≤	NUM
ejpam-5792	348	16	1	1	NUM
ejpam-5792	348	17	1−	1−	NUM
ejpam-5792	348	18	qp2	qp2	NOUN
ejpam-5792	348	19	d(y0	d(y0	NOUN
ejpam-5792	348	20	,	,	PUNCT
ejpam-5792	348	21	y1	y1	NOUN
ejpam-5792	348	22	)	)	PUNCT
ejpam-5792	348	23	≤	≤	NUM
ejpam-5792	349	1	qk′	qk′	NOUN
ejpam-5792	349	2	1−	1−	NUM
ejpam-5792	349	3	qp2	qp2	NOUN
ejpam-5792	349	4	.	.	PUNCT
ejpam-5792	350	1	similarly	similarly	ADV
ejpam-5792	350	2	,	,	PUNCT
ejpam-5792	350	3	for	for	ADP
ejpam-5792	350	4	every	every	DET
ejpam-5792	350	5	x0	x0	PROPN
ejpam-5792	350	6	∈	∈	PROPN
ejpam-5792	350	7	fix(t2	fix(t2	NOUN
ejpam-5792	350	8	)	)	PUNCT
ejpam-5792	350	9	,	,	PUNCT
ejpam-5792	350	10	there	there	PRON
ejpam-5792	350	11	is	be	VERB
ejpam-5792	350	12	some	some	DET
ejpam-5792	350	13	x∗	x∗	PROPN
ejpam-5792	350	14	∈	∈	PROPN
ejpam-5792	350	15	fix(t1	fix(t1	NOUN
ejpam-5792	350	16	)	)	PUNCT
ejpam-5792	350	17	,	,	PUNCT
ejpam-5792	350	18	for	for	ADP
ejpam-5792	350	19	which	which	PRON
ejpam-5792	350	20	ρ(x0	ρ(x0	NOUN
ejpam-5792	350	21	,	,	PUNCT
ejpam-5792	350	22	x	x	NOUN
ejpam-5792	350	23	∗	∗	NOUN
ejpam-5792	350	24	)	)	PUNCT
ejpam-5792	350	25	≤	≤	NUM
ejpam-5792	350	26	1	1	NUM
ejpam-5792	350	27	1−	1−	NUM
ejpam-5792	350	28	qp2	qp2	NOUN
ejpam-5792	350	29	d(x0	d(x0	NOUN
ejpam-5792	350	30	,	,	PUNCT
ejpam-5792	350	31	x1	x1	PROPN
ejpam-5792	350	32	)	)	PUNCT
ejpam-5792	350	33	≤	≤	NUM
ejpam-5792	350	34	qk′	qk′	NOUN
ejpam-5792	350	35	1−	1−	NUM
ejpam-5792	350	36	qp2	qp2	NOUN
ejpam-5792	350	37	.	.	PUNCT
ejpam-5792	351	1	hence	hence	ADV
ejpam-5792	351	2	,	,	PUNCT
ejpam-5792	351	3	h(fix(t1	h(fix(t1	NOUN
ejpam-5792	351	4	)	)	PUNCT
ejpam-5792	351	5	,	,	PUNCT
ejpam-5792	351	6	f	f	PROPN
ejpam-5792	351	7	ix(t2	ix(t2	PROPN
ejpam-5792	351	8	)	)	PUNCT
ejpam-5792	351	9	)	)	PUNCT
ejpam-5792	352	1	≤	≤	NUM
ejpam-5792	353	1	qk′	qk′	PROPN
ejpam-5792	353	2	1−max{qp1	1−max{qp1	NUM
ejpam-5792	353	3	,	,	PUNCT
ejpam-5792	353	4	qp2	qp2	PROPN
ejpam-5792	353	5	}	}	PUNCT
ejpam-5792	353	6	letting	let	VERB
ejpam-5792	353	7	q	q	NOUN
ejpam-5792	353	8	→	→	SYM
ejpam-5792	353	9	1	1	NUM
ejpam-5792	353	10	,	,	PUNCT
ejpam-5792	353	11	we	we	PRON
ejpam-5792	353	12	achieve	achieve	VERB
ejpam-5792	353	13	the	the	DET
ejpam-5792	353	14	intended	intend	VERB
ejpam-5792	353	15	result	result	NOUN
ejpam-5792	353	16	.	.	PUNCT
ejpam-5792	354	1	theorem	theorem	ADJ
ejpam-5792	354	2	10	10	NUM
ejpam-5792	354	3	.	.	PUNCT
ejpam-5792	355	1	let	let	VERB
ejpam-5792	355	2	(	(	PUNCT
ejpam-5792	355	3	u	u	NOUN
ejpam-5792	355	4	,	,	PUNCT
ejpam-5792	355	5	ρ	ρ	PROPN
ejpam-5792	355	6	)	)	PUNCT
ejpam-5792	355	7	be	be	VERB
ejpam-5792	355	8	a	a	DET
ejpam-5792	355	9	metric	metric	ADJ
ejpam-5792	355	10	space	space	NOUN
ejpam-5792	355	11	and	and	CCONJ
ejpam-5792	355	12	ti	ti	NOUN
ejpam-5792	355	13	:	:	PUNCT
ejpam-5792	355	14	u	u	PROPN
ejpam-5792	355	15	→	→	SYM
ejpam-5792	355	16	cb(u	cb(u	PUNCT
ejpam-5792	355	17	)	)	PUNCT
ejpam-5792	355	18	be	be	AUX
ejpam-5792	355	19	two	two	NUM
ejpam-5792	355	20	multivalued	multivalued	ADJ
ejpam-5792	355	21	eihr	eihr	PROPN
ejpam-5792	355	22	-	-	PUNCT
ejpam-5792	355	23	contractions	contraction	NOUN
ejpam-5792	355	24	via	via	ADP
ejpam-5792	355	25	a	a	DET
ejpam-5792	355	26	simulation	simulation	NOUN
ejpam-5792	355	27	function	function	PROPN
ejpam-5792	355	28	zg	zg	PROPN
ejpam-5792	355	29	.	.	PUNCT
ejpam-5792	355	30	suppose	suppose	VERB
ejpam-5792	355	31	that	that	SCONJ
ejpam-5792	355	32	there	there	PRON
ejpam-5792	355	33	is	be	VERB
ejpam-5792	355	34	some	some	DET
ejpam-5792	355	35	α	α	NOUN
ejpam-5792	355	36	>	>	X
ejpam-5792	355	37	0	0	PUNCT
ejpam-5792	356	1	so	so	SCONJ
ejpam-5792	356	2	that	that	SCONJ
ejpam-5792	356	3	h(t1y	h(t1y	NOUN
ejpam-5792	356	4	,	,	PUNCT
ejpam-5792	356	5	t2y	t2y	NOUN
ejpam-5792	356	6	)	)	PUNCT
ejpam-5792	356	7	≤	≤	NUM
ejpam-5792	356	8	α	α	NOUN
ejpam-5792	356	9	for	for	ADP
ejpam-5792	356	10	each	each	DET
ejpam-5792	356	11	y	y	PROPN
ejpam-5792	356	12	∈	∈	PROPN
ejpam-5792	356	13	u	u	PROPN
ejpam-5792	356	14	.	.	PUNCT
ejpam-5792	357	1	then	then	ADV
ejpam-5792	357	2	(	(	PUNCT
ejpam-5792	357	3	i)fix(ti	i)fix(ti	NOUN
ejpam-5792	357	4	)	)	PUNCT
ejpam-5792	357	5	is	be	AUX
ejpam-5792	357	6	a	a	DET
ejpam-5792	357	7	closed	closed	ADJ
ejpam-5792	357	8	subset	subset	NOUN
ejpam-5792	357	9	of	of	ADP
ejpam-5792	357	10	u	u	NOUN
ejpam-5792	357	11	for	for	ADP
ejpam-5792	357	12	i	i	PRON
ejpam-5792	357	13	∈	∈	PROPN
ejpam-5792	357	14	{	{	PUNCT
ejpam-5792	357	15	1	1	NUM
ejpam-5792	357	16	,	,	PUNCT
ejpam-5792	357	17	2	2	NUM
ejpam-5792	357	18	}	}	PUNCT
ejpam-5792	357	19	.	.	PUNCT
ejpam-5792	358	1	(	(	PUNCT
ejpam-5792	358	2	ii	ii	NOUN
ejpam-5792	358	3	)	)	PUNCT
ejpam-5792	358	4	h(fix(t1	h(fix(t1	NOUN
ejpam-5792	358	5	,	,	PUNCT
ejpam-5792	358	6	)	)	PUNCT
ejpam-5792	358	7	,	,	PUNCT
ejpam-5792	358	8	f	f	PROPN
ejpam-5792	358	9	ix(t2	ix(t2	PROPN
ejpam-5792	358	10	)	)	PUNCT
ejpam-5792	358	11	)	)	PUNCT
ejpam-5792	359	1	≤	≤	NUM
ejpam-5792	360	1	α	α	PRON
ejpam-5792	360	2	1−max{p1,p2	1−max{p1,p2	NUM
ejpam-5792	360	3	}	}	PUNCT
ejpam-5792	360	4	.	.	PUNCT
ejpam-5792	361	1	a.	a.	NOUN
ejpam-5792	361	2	gangwar	gangwar	PROPN
ejpam-5792	361	3	et	et	PROPN
ejpam-5792	361	4	al	al	PROPN
ejpam-5792	361	5	.	.	PUNCT
ejpam-5792	361	6	/	/	SYM
ejpam-5792	361	7	eur	eur	PROPN
ejpam-5792	361	8	.	.	PUNCT
ejpam-5792	362	1	j.	j.	PROPN
ejpam-5792	362	2	pure	pure	PROPN
ejpam-5792	362	3	appl	appl	PROPN
ejpam-5792	362	4	.	.	PROPN
ejpam-5792	362	5	math	math	PROPN
ejpam-5792	362	6	,	,	PUNCT
ejpam-5792	362	7	18	18	NUM
ejpam-5792	362	8	(	(	PUNCT
ejpam-5792	362	9	2	2	NUM
ejpam-5792	362	10	)	)	PUNCT
ejpam-5792	362	11	(	(	PUNCT
ejpam-5792	362	12	2025	2025	NUM
ejpam-5792	362	13	)	)	PUNCT
ejpam-5792	362	14	,	,	PUNCT
ejpam-5792	362	15	5792	5792	NUM
ejpam-5792	362	16	14	14	NUM
ejpam-5792	362	17	of	of	ADP
ejpam-5792	362	18	16	16	NUM
ejpam-5792	362	19	proof	proof	NOUN
ejpam-5792	362	20	.	.	PUNCT
ejpam-5792	363	1	from	from	ADP
ejpam-5792	363	2	theorem	theorem	ADJ
ejpam-5792	363	3	3.5	3.5	NUM
ejpam-5792	363	4	,	,	PUNCT
ejpam-5792	363	5	fix(ti	fix(ti	NOUN
ejpam-5792	363	6	)	)	PUNCT
ejpam-5792	363	7	̸=	̸=	PROPN
ejpam-5792	363	8	ϕ	ϕ	NOUN
ejpam-5792	363	9	for	for	ADP
ejpam-5792	363	10	i	i	PRON
ejpam-5792	363	11	∈	∈	PROPN
ejpam-5792	363	12	{	{	PUNCT
ejpam-5792	363	13	1	1	NUM
ejpam-5792	363	14	,	,	PUNCT
ejpam-5792	363	15	2	2	NUM
ejpam-5792	363	16	}	}	PUNCT
ejpam-5792	363	17	.	.	PUNCT
ejpam-5792	364	1	let	let	VERB
ejpam-5792	364	2	{	{	PUNCT
ejpam-5792	364	3	yn	yn	NOUN
ejpam-5792	364	4	}	}	PUNCT
ejpam-5792	364	5	be	be	AUX
ejpam-5792	364	6	a	a	DET
ejpam-5792	364	7	sequence	sequence	NOUN
ejpam-5792	364	8	in	in	ADP
ejpam-5792	364	9	fix(ti	fix(ti	NOUN
ejpam-5792	364	10	)	)	PUNCT
ejpam-5792	365	1	=	=	SYM
ejpam-5792	365	2	fix(tiλ	fix(tiλ	NOUN
ejpam-5792	365	3	)	)	PUNCT
ejpam-5792	365	4	for	for	ADP
ejpam-5792	365	5	i	i	PROPN
ejpam-5792	365	6	∈	∈	PROPN
ejpam-5792	365	7	{	{	PUNCT
ejpam-5792	365	8	1	1	NUM
ejpam-5792	365	9	,	,	PUNCT
ejpam-5792	365	10	2	2	NUM
ejpam-5792	365	11	}	}	PUNCT
ejpam-5792	365	12	so	so	SCONJ
ejpam-5792	365	13	that	that	SCONJ
ejpam-5792	365	14	yn	yn	PRON
ejpam-5792	365	15	→	→	PUNCT
ejpam-5792	365	16	y∗	y∗	ADV
ejpam-5792	365	17	as	as	ADP
ejpam-5792	365	18	n→	n→	PROPN
ejpam-5792	365	19	∞	∞	PROPN
ejpam-5792	365	20	,	,	PUNCT
ejpam-5792	365	21	then	then	ADV
ejpam-5792	365	22	for	for	ADP
ejpam-5792	365	23	i	i	PROPN
ejpam-5792	365	24	∈	∈	PROPN
ejpam-5792	365	25	{	{	PUNCT
ejpam-5792	365	26	1	1	NUM
ejpam-5792	365	27	,	,	PUNCT
ejpam-5792	365	28	2	2	NUM
ejpam-5792	365	29	}	}	PUNCT
ejpam-5792	365	30	ζ(h(tiλyn	ζ(h(tiλyn	PROPN
ejpam-5792	365	31	,	,	PUNCT
ejpam-5792	365	32	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	365	33	)	)	PUNCT
ejpam-5792	365	34	,	,	PUNCT
ejpam-5792	365	35	q(yn	q(yn	PROPN
ejpam-5792	365	36	,	,	PUNCT
ejpam-5792	365	37	yn−1	yn−1	NOUN
ejpam-5792	365	38	)	)	PUNCT
ejpam-5792	365	39	)	)	PUNCT
ejpam-5792	365	40	≥	≥	X
ejpam-5792	365	41	cg	cg	NOUN
ejpam-5792	365	42	by	by	ADP
ejpam-5792	365	43	definition	definition	NOUN
ejpam-5792	365	44	3	3	NUM
ejpam-5792	365	45	,	,	PUNCT
ejpam-5792	365	46	we	we	PRON
ejpam-5792	365	47	obtain	obtain	VERB
ejpam-5792	365	48	cg	cg	NOUN
ejpam-5792	365	49	≤	≤	PROPN
ejpam-5792	365	50	ζ(h(tiλyn	ζ(h(tiλyn	PROPN
ejpam-5792	365	51	,	,	PUNCT
ejpam-5792	365	52	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	365	53	)	)	PUNCT
ejpam-5792	365	54	,	,	PUNCT
ejpam-5792	365	55	q(yn	q(yn	PROPN
ejpam-5792	365	56	,	,	PUNCT
ejpam-5792	365	57	yn−1	yn−1	NOUN
ejpam-5792	365	58	)	)	PUNCT
ejpam-5792	365	59	)	)	PUNCT
ejpam-5792	366	1	<	<	X
ejpam-5792	367	1	g(q(yn	g(q(yn	X
ejpam-5792	367	2	,	,	PUNCT
ejpam-5792	367	3	yn−1	yn−1	NOUN
ejpam-5792	367	4	)	)	PUNCT
ejpam-5792	367	5	,	,	PUNCT
ejpam-5792	367	6	h(tiλyn	h(tiλyn	VERB
ejpam-5792	367	7	,	,	PUNCT
ejpam-5792	367	8	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	367	9	)	)	PUNCT
ejpam-5792	367	10	)	)	PUNCT
ejpam-5792	367	11	.	.	PUNCT
ejpam-5792	368	1	using	use	VERB
ejpam-5792	368	2	definition	definition	NOUN
ejpam-5792	368	3	2	2	NUM
ejpam-5792	368	4	,	,	PUNCT
ejpam-5792	368	5	one	one	NUM
ejpam-5792	368	6	writes	write	VERB
ejpam-5792	368	7	h(tiλyn	h(tiλyn	VERB
ejpam-5792	368	8	,	,	PUNCT
ejpam-5792	368	9	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	368	10	)	)	PUNCT
ejpam-5792	368	11	<	<	X
ejpam-5792	368	12	q(yn	q(yn	PROPN
ejpam-5792	368	13	,	,	PUNCT
ejpam-5792	368	14	yn−1	yn−1	PROPN
ejpam-5792	368	15	)	)	PUNCT
ejpam-5792	368	16	which	which	PRON
ejpam-5792	368	17	implies	imply	VERB
ejpam-5792	368	18	d∗(yn	d∗(yn	NOUN
ejpam-5792	368	19	,	,	PUNCT
ejpam-5792	368	20	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	368	21	)	)	PUNCT
ejpam-5792	368	22	<	<	X
ejpam-5792	368	23	q(yn	q(yn	PROPN
ejpam-5792	368	24	,	,	PUNCT
ejpam-5792	368	25	yn−1	yn−1	NOUN
ejpam-5792	368	26	)	)	PUNCT
ejpam-5792	368	27	=	=	SYM
ejpam-5792	368	28	pi[d	pi[d	ADJ
ejpam-5792	368	29	∗(yn−1	∗(yn−1	PROPN
ejpam-5792	368	30	,	,	PUNCT
ejpam-5792	368	31	yn	yn	PROPN
ejpam-5792	368	32	)	)	PUNCT
ejpam-5792	368	33	α[d∗(yn−1	α[d∗(yn−1	PROPN
ejpam-5792	368	34	,	,	PUNCT
ejpam-5792	368	35	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	368	36	)	)	PUNCT
ejpam-5792	368	37	]	]	PUNCT
ejpam-5792	369	1	β[d∗(yn	β[d∗(yn	PROPN
ejpam-5792	369	2	,	,	PUNCT
ejpam-5792	369	3	tiλyn	tiλyn	PROPN
ejpam-5792	369	4	)	)	PUNCT
ejpam-5792	369	5	)	)	PUNCT
ejpam-5792	369	6	]	]	PUNCT
ejpam-5792	369	7	γ	γ	X
ejpam-5792	369	8	×	×	NOUN
ejpam-5792	369	9	[	[	PUNCT
ejpam-5792	369	10	1	1	NUM
ejpam-5792	369	11	2	2	NUM
ejpam-5792	369	12	(	(	PUNCT
ejpam-5792	369	13	d∗(yn−1	d∗(yn−1	ADJ
ejpam-5792	369	14	,	,	PUNCT
ejpam-5792	369	15	tiλyn	tiλyn	ADJ
ejpam-5792	369	16	)	)	PUNCT
ejpam-5792	369	17	+	+	SYM
ejpam-5792	369	18	d∗(yn	d∗(yn	NOUN
ejpam-5792	369	19	,	,	PUNCT
ejpam-5792	369	20	tiλyn−1	tiλyn−1	PROPN
ejpam-5792	369	21	)	)	PUNCT
ejpam-5792	369	22	)	)	PUNCT
ejpam-5792	369	23	]	]	PUNCT
ejpam-5792	370	1	1−α−β−γ	1−α−β−γ	X
ejpam-5792	370	2	.	.	PUNCT
ejpam-5792	371	1	now	now	ADV
ejpam-5792	371	2	,	,	PUNCT
ejpam-5792	371	3	using	use	VERB
ejpam-5792	371	4	the	the	DET
ejpam-5792	371	5	same	same	ADJ
ejpam-5792	371	6	method	method	NOUN
ejpam-5792	371	7	of	of	ADP
ejpam-5792	371	8	proof	proof	NOUN
ejpam-5792	371	9	as	as	ADP
ejpam-5792	371	10	in	in	ADP
ejpam-5792	371	11	theorem	theorem	NOUN
ejpam-5792	371	12	4.1	4.1	NUM
ejpam-5792	371	13	,	,	PUNCT
ejpam-5792	371	14	we	we	PRON
ejpam-5792	371	15	achieve	achieve	VERB
ejpam-5792	371	16	the	the	DET
ejpam-5792	371	17	intended	intend	VERB
ejpam-5792	371	18	result	result	NOUN
ejpam-5792	371	19	.	.	PUNCT
ejpam-5792	372	1	acknowledgements	acknowledgement	VERB
ejpam-5792	372	2	the	the	DET
ejpam-5792	372	3	authors	author	NOUN
ejpam-5792	372	4	s.	s.	PROPN
ejpam-5792	372	5	aljohani	aljohani	PROPN
ejpam-5792	372	6	and	and	CCONJ
ejpam-5792	372	7	n.	n.	PROPN
ejpam-5792	372	8	mlaiki	mlaiki	PROPN
ejpam-5792	372	9	would	would	AUX
ejpam-5792	372	10	like	like	VERB
ejpam-5792	372	11	to	to	PART
ejpam-5792	372	12	thank	thank	VERB
ejpam-5792	372	13	prince	prince	PROPN
ejpam-5792	372	14	sultan	sultan	PROPN
ejpam-5792	372	15	university	university	PROPN
ejpam-5792	372	16	for	for	ADP
ejpam-5792	372	17	the	the	DET
ejpam-5792	372	18	support	support	NOUN
ejpam-5792	372	19	through	through	ADP
ejpam-5792	372	20	the	the	DET
ejpam-5792	372	21	tas	tas	NOUN
ejpam-5792	372	22	research	research	NOUN
ejpam-5792	372	23	lab	lab	NOUN
ejpam-5792	372	24	and	and	CCONJ
ejpam-5792	372	25	for	for	ADP
ejpam-5792	372	26	paying	pay	VERB
ejpam-5792	372	27	the	the	DET
ejpam-5792	372	28	apc	apc	NOUN
ejpam-5792	372	29	.	.	PUNCT
ejpam-5792	373	1	the	the	DET
ejpam-5792	373	2	authors	author	NOUN
ejpam-5792	373	3	are	be	AUX
ejpam-5792	373	4	thankful	thankful	ADJ
ejpam-5792	373	5	to	to	ADP
ejpam-5792	373	6	the	the	DET
ejpam-5792	373	7	reviewers	reviewer	NOUN
ejpam-5792	373	8	for	for	ADP
ejpam-5792	373	9	their	their	PRON
ejpam-5792	373	10	fruitful	fruitful	ADJ
ejpam-5792	373	11	comments	comment	NOUN
ejpam-5792	373	12	,	,	PUNCT
ejpam-5792	373	13	which	which	PRON
ejpam-5792	373	14	helped	help	VERB
ejpam-5792	373	15	in	in	ADP
ejpam-5792	373	16	improving	improve	VERB
ejpam-5792	373	17	the	the	DET
ejpam-5792	373	18	manuscript	manuscript	NOUN
ejpam-5792	373	19	.	.	PUNCT
ejpam-5792	374	1	authors	author	NOUN
ejpam-5792	374	2	’	’	PART
ejpam-5792	374	3	contributions	contribution	NOUN
ejpam-5792	374	4	a.g	a.g	PROPN
ejpam-5792	374	5	.	.	PROPN
ejpam-5792	374	6	,	,	PUNCT
ejpam-5792	374	7	s.r	s.r	PROPN
ejpam-5792	374	8	.	.	PROPN
ejpam-5792	374	9	,	,	PUNCT
ejpam-5792	374	10	h.a	h.a	PROPN
ejpam-5792	374	11	.	.	PROPN
ejpam-5792	374	12	,	,	PUNCT
ejpam-5792	374	13	s.a	s.a	PROPN
ejpam-5792	374	14	.	.	PROPN
ejpam-5792	374	15	and	and	CCONJ
ejpam-5792	374	16	n.m	n.m	PROPN
ejpam-5792	374	17	.	.	PROPN
ejpam-5792	374	18	wrote	write	VERB
ejpam-5792	374	19	the	the	DET
ejpam-5792	374	20	main	main	ADJ
ejpam-5792	374	21	manuscript	manuscript	NOUN
ejpam-5792	374	22	text	text	NOUN
ejpam-5792	374	23	.	.	PUNCT
ejpam-5792	375	1	all	all	DET
ejpam-5792	375	2	authors	author	NOUN
ejpam-5792	375	3	reviewed	review	VERB
ejpam-5792	375	4	the	the	DET
ejpam-5792	375	5	manuscript	manuscript	NOUN
ejpam-5792	375	6	.	.	PUNCT
ejpam-5792	376	1	competing	compete	VERB
ejpam-5792	376	2	interests	interest	NOUN
ejpam-5792	376	3	the	the	DET
ejpam-5792	376	4	authors	author	NOUN
ejpam-5792	376	5	declare	declare	VERB
ejpam-5792	376	6	that	that	SCONJ
ejpam-5792	376	7	they	they	PRON
ejpam-5792	376	8	have	have	VERB
ejpam-5792	376	9	no	no	DET
ejpam-5792	376	10	conflicts	conflict	NOUN
ejpam-5792	376	11	of	of	ADP
ejpam-5792	376	12	interest	interest	NOUN
ejpam-5792	376	13	.	.	PUNCT
ejpam-5792	377	1	references	reference	NOUN
ejpam-5792	377	2	[	[	X
ejpam-5792	377	3	1	1	X
ejpam-5792	377	4	]	]	PUNCT
ejpam-5792	377	5	s.	s.	PROPN
ejpam-5792	377	6	banach	banach	PROPN
ejpam-5792	377	7	.	.	PUNCT
ejpam-5792	378	1	sur	sur	PROPN
ejpam-5792	378	2	les	les	X
ejpam-5792	378	3	opérations	opération	NOUN
ejpam-5792	378	4	dans	dan	NOUN
ejpam-5792	378	5	les	les	X
ejpam-5792	378	6	ensembles	ensemble	NOUN
ejpam-5792	378	7	abstraits	abstrait	NOUN
ejpam-5792	378	8	et	et	PROPN
ejpam-5792	378	9	leur	leur	X
ejpam-5792	378	10	application	application	PROPN
ejpam-5792	378	11	aux	aux	PROPN
ejpam-5792	378	12	équations	équations	PROPN
ejpam-5792	378	13	intégrales	intégrale	NOUN
ejpam-5792	378	14	.	.	PUNCT
ejpam-5792	379	1	fund	fund	PROPN
ejpam-5792	379	2	.	.	PUNCT
ejpam-5792	380	1	math	math	NOUN
ejpam-5792	380	2	.	.	PUNCT
ejpam-5792	380	3	,	,	PUNCT
ejpam-5792	380	4	3(1):133–181	3(1):133–181	NUM
ejpam-5792	380	5	,	,	PUNCT
ejpam-5792	380	6	1922	1922	NUM
ejpam-5792	380	7	.	.	PUNCT
ejpam-5792	381	1	[	[	X
ejpam-5792	381	2	2	2	NUM
ejpam-5792	381	3	]	]	PUNCT
ejpam-5792	381	4	a.	a.	NOUN
ejpam-5792	381	5	gangwar	gangwar	PROPN
ejpam-5792	381	6	,	,	PUNCT
ejpam-5792	381	7	s.	s.	PROPN
ejpam-5792	381	8	rawat	rawat	PROPN
ejpam-5792	381	9	,	,	PUNCT
ejpam-5792	381	10	and	and	CCONJ
ejpam-5792	381	11	r.c	r.c	PROPN
ejpam-5792	381	12	.	.	PROPN
ejpam-5792	381	13	dimri	dimri	PROPN
ejpam-5792	381	14	.	.	PUNCT
ejpam-5792	382	1	solution	solution	NOUN
ejpam-5792	382	2	of	of	ADP
ejpam-5792	382	3	differential	differential	ADJ
ejpam-5792	382	4	inclusion	inclusion	NOUN
ejpam-5792	382	5	problem	problem	NOUN
ejpam-5792	382	6	in	in	ADP
ejpam-5792	382	7	controlled	control	VERB
ejpam-5792	382	8	s	s	ADJ
ejpam-5792	382	9	-	-	ADJ
ejpam-5792	382	10	metric	metric	ADJ
ejpam-5792	382	11	spaces	space	NOUN
ejpam-5792	382	12	via	via	ADP
ejpam-5792	382	13	new	new	ADJ
ejpam-5792	382	14	multivalued	multivalue	VERB
ejpam-5792	382	15	fixed	fix	VERB
ejpam-5792	382	16	point	point	NOUN
ejpam-5792	382	17	theorem	theorem	VERB
ejpam-5792	382	18	.	.	PUNCT
ejpam-5792	383	1	j.	j.	PROPN
ejpam-5792	383	2	anal	anal	PROPN
ejpam-5792	383	3	.	.	PROPN
ejpam-5792	383	4	,	,	PUNCT
ejpam-5792	383	5	31:2459–2472	31:2459–2472	NUM
ejpam-5792	383	6	,	,	PUNCT
ejpam-5792	383	7	2023	2023	NUM
ejpam-5792	383	8	.	.	PUNCT
ejpam-5792	384	1	[	[	X
ejpam-5792	384	2	3	3	X
ejpam-5792	384	3	]	]	X
ejpam-5792	384	4	s.	s.	PROPN
ejpam-5792	384	5	rawat	rawat	PROPN
ejpam-5792	384	6	,	,	PUNCT
ejpam-5792	384	7	r.c	r.c	PROPN
ejpam-5792	384	8	.	.	PROPN
ejpam-5792	384	9	dimri	dimri	PROPN
ejpam-5792	384	10	,	,	PUNCT
ejpam-5792	384	11	and	and	CCONJ
ejpam-5792	384	12	a.	a.	NOUN
ejpam-5792	384	13	bartwal	bartwal	NOUN
ejpam-5792	384	14	.	.	PUNCT
ejpam-5792	385	1	f	f	X
ejpam-5792	385	2	-	-	PUNCT
ejpam-5792	385	3	bipolar	bipolar	ADJ
ejpam-5792	385	4	metric	metric	ADJ
ejpam-5792	385	5	spaces	space	NOUN
ejpam-5792	385	6	and	and	CCONJ
ejpam-5792	385	7	fixed	fix	VERB
ejpam-5792	385	8	point	point	NOUN
ejpam-5792	385	9	theorems	theorem	NOUN
ejpam-5792	385	10	with	with	ADP
ejpam-5792	385	11	applications	application	NOUN
ejpam-5792	385	12	.	.	PUNCT
ejpam-5792	386	1	j.	j.	PROPN
ejpam-5792	386	2	math	math	PROPN
ejpam-5792	386	3	.	.	PUNCT
ejpam-5792	387	1	comput	comput	NOUN
ejpam-5792	387	2	.	.	PUNCT
ejpam-5792	388	1	sci.-jm	sci.-jm	PROPN
ejpam-5792	388	2	,	,	PUNCT
ejpam-5792	388	3	26(2):184–195	26(2):184–195	NUM
ejpam-5792	388	4	,	,	PUNCT
ejpam-5792	388	5	2022	2022	NUM
ejpam-5792	388	6	.	.	PUNCT
ejpam-5792	389	1	a.	a.	NOUN
ejpam-5792	389	2	gangwar	gangwar	PROPN
ejpam-5792	389	3	et	et	PROPN
ejpam-5792	389	4	al	al	PROPN
ejpam-5792	389	5	.	.	PUNCT
ejpam-5792	389	6	/	/	SYM
ejpam-5792	389	7	eur	eur	PROPN
ejpam-5792	389	8	.	.	PUNCT
ejpam-5792	390	1	j.	j.	PROPN
ejpam-5792	390	2	pure	pure	PROPN
ejpam-5792	390	3	appl	appl	PROPN
ejpam-5792	390	4	.	.	PROPN
ejpam-5792	390	5	math	math	PROPN
ejpam-5792	390	6	,	,	PUNCT
ejpam-5792	390	7	18	18	NUM
ejpam-5792	390	8	(	(	PUNCT
ejpam-5792	390	9	2	2	NUM
ejpam-5792	390	10	)	)	PUNCT
ejpam-5792	390	11	(	(	PUNCT
ejpam-5792	390	12	2025	2025	NUM
ejpam-5792	390	13	)	)	PUNCT
ejpam-5792	390	14	,	,	PUNCT
ejpam-5792	390	15	5792	5792	NUM
ejpam-5792	390	16	15	15	NUM
ejpam-5792	390	17	of	of	ADP
ejpam-5792	390	18	16	16	NUM
ejpam-5792	390	19	[	[	X
ejpam-5792	390	20	4	4	NUM
ejpam-5792	390	21	]	]	X
ejpam-5792	390	22	a.z	a.z	PROPN
ejpam-5792	390	23	.	.	PROPN
ejpam-5792	390	24	rezazgui	rezazgui	PROPN
ejpam-5792	390	25	,	,	PUNCT
ejpam-5792	390	26	a.a	a.a	PROPN
ejpam-5792	390	27	.	.	PROPN
ejpam-5792	390	28	tallafha	tallafha	PROPN
ejpam-5792	390	29	,	,	PUNCT
ejpam-5792	390	30	and	and	CCONJ
ejpam-5792	390	31	w.	w.	PROPN
ejpam-5792	390	32	shatanawi	shatanawi	PROPN
ejpam-5792	390	33	.	.	PUNCT
ejpam-5792	391	1	common	common	ADJ
ejpam-5792	391	2	fixed	fix	VERB
ejpam-5792	391	3	point	point	NOUN
ejpam-5792	391	4	results	result	NOUN
ejpam-5792	391	5	via	via	ADP
ejpam-5792	391	6	aν	aν	NOUN
ejpam-5792	391	7	−	−	X
ejpam-5792	391	8	α−contractions	α−contraction	NOUN
ejpam-5792	391	9	with	with	ADP
ejpam-5792	391	10	a	a	DET
ejpam-5792	391	11	pair	pair	NOUN
ejpam-5792	391	12	and	and	CCONJ
ejpam-5792	391	13	two	two	NUM
ejpam-5792	391	14	pairs	pair	NOUN
ejpam-5792	391	15	of	of	ADP
ejpam-5792	391	16	self	self	NOUN
ejpam-5792	391	17	-	-	PUNCT
ejpam-5792	391	18	mappings	mapping	NOUN
ejpam-5792	391	19	in	in	ADP
ejpam-5792	391	20	the	the	DET
ejpam-5792	391	21	frame	frame	NOUN
ejpam-5792	391	22	of	of	ADP
ejpam-5792	391	23	an	an	DET
ejpam-5792	391	24	extended	extend	VERB
ejpam-5792	391	25	quasi	quasi	ADJ
ejpam-5792	391	26	b	b	NOUN
ejpam-5792	391	27	-	-	PUNCT
ejpam-5792	391	28	metric	metric	ADJ
ejpam-5792	391	29	space	space	NOUN
ejpam-5792	391	30	.	.	PUNCT
ejpam-5792	392	1	aims	aim	VERB
ejpam-5792	392	2	mathematics	mathematic	NOUN
ejpam-5792	392	3	,	,	PUNCT
ejpam-5792	392	4	8(3):7225–7241	8(3):7225–7241	NUM
ejpam-5792	392	5	,	,	PUNCT
ejpam-5792	392	6	2023	2023	NUM
ejpam-5792	392	7	.	.	PUNCT
ejpam-5792	393	1	[	[	X
ejpam-5792	393	2	5	5	X
ejpam-5792	393	3	]	]	PUNCT
ejpam-5792	393	4	w.	w.	PROPN
ejpam-5792	393	5	shatanawi	shatanawi	PROPN
ejpam-5792	393	6	and	and	CCONJ
ejpam-5792	393	7	t.a.m	t.a.m	PROPN
ejpam-5792	393	8	.	.	PROPN
ejpam-5792	393	9	shatnawi	shatnawi	PROPN
ejpam-5792	393	10	.	.	PUNCT
ejpam-5792	394	1	new	new	ADJ
ejpam-5792	394	2	fixed	fix	VERB
ejpam-5792	394	3	point	point	NOUN
ejpam-5792	394	4	results	result	NOUN
ejpam-5792	394	5	in	in	ADP
ejpam-5792	394	6	controlled	control	VERB
ejpam-5792	394	7	metric	metric	ADJ
ejpam-5792	394	8	type	type	NOUN
ejpam-5792	394	9	spaces	space	NOUN
ejpam-5792	394	10	based	base	VERB
ejpam-5792	394	11	on	on	ADP
ejpam-5792	394	12	new	new	ADJ
ejpam-5792	394	13	contractive	contractive	ADJ
ejpam-5792	394	14	conditions	condition	NOUN
ejpam-5792	394	15	.	.	PUNCT
ejpam-5792	395	1	aimetric	aimetric	ADJ
ejpam-5792	395	2	space	space	NOUN
ejpam-5792	395	3	mathematics	mathematic	NOUN
ejpam-5792	395	4	,	,	PUNCT
ejpam-5792	395	5	8(4):9314	8(4):9314	NUM
ejpam-5792	395	6	–	–	PUNCT
ejpam-5792	395	7	9330	9330	NUM
ejpam-5792	395	8	,	,	PUNCT
ejpam-5792	395	9	2023	2023	NUM
ejpam-5792	395	10	.	.	PUNCT
ejpam-5792	396	1	[	[	X
ejpam-5792	396	2	6	6	NUM
ejpam-5792	396	3	]	]	PUNCT
ejpam-5792	396	4	r.	r.	PROPN
ejpam-5792	396	5	kannan	kannan	PROPN
ejpam-5792	396	6	.	.	PUNCT
ejpam-5792	397	1	some	some	DET
ejpam-5792	397	2	results	result	NOUN
ejpam-5792	397	3	on	on	ADP
ejpam-5792	397	4	fixed	fix	VERB
ejpam-5792	397	5	points	point	NOUN
ejpam-5792	397	6	.	.	PUNCT
ejpam-5792	398	1	bull	bull	NOUN
ejpam-5792	398	2	.	.	PUNCT
ejpam-5792	399	1	calcutta	calcutta	PROPN
ejpam-5792	399	2	math	math	PROPN
ejpam-5792	399	3	.	.	PUNCT
ejpam-5792	400	1	soc	soc	PROPN
ejpam-5792	400	2	.	.	PUNCT
ejpam-5792	400	3	,	,	PUNCT
ejpam-5792	400	4	60:71–76	60:71–76	NUM
ejpam-5792	400	5	,	,	PUNCT
ejpam-5792	400	6	1968	1968	NUM
ejpam-5792	400	7	.	.	PUNCT
ejpam-5792	401	1	[	[	X
ejpam-5792	401	2	7	7	X
ejpam-5792	401	3	]	]	X
ejpam-5792	401	4	e.	e.	PROPN
ejpam-5792	401	5	karapinar	karapinar	PROPN
ejpam-5792	401	6	.	.	PUNCT
ejpam-5792	402	1	revisiting	revisit	VERB
ejpam-5792	402	2	the	the	DET
ejpam-5792	402	3	kannan	kannan	PROPN
ejpam-5792	402	4	type	type	NOUN
ejpam-5792	402	5	contractions	contraction	NOUN
ejpam-5792	402	6	via	via	ADP
ejpam-5792	402	7	interpolation	interpolation	NOUN
ejpam-5792	402	8	.	.	PUNCT
ejpam-5792	403	1	adv	adv	PROPN
ejpam-5792	403	2	.	.	PUNCT
ejpam-5792	403	3	theory	theory	PROPN
ejpam-5792	403	4	nonlinear	nonlinear	PROPN
ejpam-5792	403	5	anal	anal	PROPN
ejpam-5792	403	6	.	.	PUNCT
ejpam-5792	404	1	appl	appl	PROPN
ejpam-5792	404	2	.	.	PROPN
ejpam-5792	404	3	,	,	PUNCT
ejpam-5792	404	4	2(2):85–87	2(2):85–87	NUM
ejpam-5792	404	5	,	,	PUNCT
ejpam-5792	404	6	2018	2018	NUM
ejpam-5792	404	7	.	.	PUNCT
ejpam-5792	405	1	[	[	X
ejpam-5792	405	2	8	8	NUM
ejpam-5792	405	3	]	]	X
ejpam-5792	405	4	h.	h.	PROPN
ejpam-5792	405	5	aydi	aydi	PROPN
ejpam-5792	405	6	,	,	PUNCT
ejpam-5792	405	7	c.m	c.m	PROPN
ejpam-5792	405	8	.	.	PROPN
ejpam-5792	405	9	chen	chen	PROPN
ejpam-5792	405	10	,	,	PUNCT
ejpam-5792	405	11	and	and	CCONJ
ejpam-5792	405	12	e.	e.	PROPN
ejpam-5792	405	13	karapinar	karapinar	PROPN
ejpam-5792	405	14	.	.	PUNCT
ejpam-5792	406	1	interpolative	interpolative	ADJ
ejpam-5792	406	2	ćirić-reich	ćirić-reich	NOUN
ejpam-5792	406	3	-	-	PUNCT
ejpam-5792	406	4	rus	rus	NOUN
ejpam-5792	406	5	type	type	NOUN
ejpam-5792	406	6	contractions	contraction	NOUN
ejpam-5792	406	7	via	via	ADP
ejpam-5792	406	8	the	the	DET
ejpam-5792	406	9	branciari	branciari	ADJ
ejpam-5792	406	10	distance	distance	NOUN
ejpam-5792	406	11	.	.	PUNCT
ejpam-5792	407	1	mathematics	mathematic	NOUN
ejpam-5792	407	2	,	,	PUNCT
ejpam-5792	407	3	7(1):84	7(1):84	NOUN
ejpam-5792	407	4	,	,	PUNCT
ejpam-5792	407	5	2019	2019	NUM
ejpam-5792	407	6	.	.	PUNCT
ejpam-5792	408	1	[	[	X
ejpam-5792	408	2	9	9	NUM
ejpam-5792	408	3	]	]	X
ejpam-5792	408	4	h.	h.	PROPN
ejpam-5792	408	5	aydi	aydi	PROPN
ejpam-5792	408	6	,	,	PUNCT
ejpam-5792	408	7	e.	e.	PROPN
ejpam-5792	408	8	karapinar	karapinar	PROPN
ejpam-5792	408	9	,	,	PUNCT
ejpam-5792	408	10	and	and	CCONJ
ejpam-5792	408	11	a.f	a.f	PROPN
ejpam-5792	408	12	.	.	PUNCT
ejpam-5792	409	1	roldán	roldán	PROPN
ejpam-5792	409	2	lópez	lópez	PROPN
ejpam-5792	409	3	de	de	PROPN
ejpam-5792	409	4	hierro	hierro	PROPN
ejpam-5792	409	5	.	.	PUNCT
ejpam-5792	410	1	ω	ω	VERB
ejpam-5792	410	2	-	-	ADJ
ejpam-5792	410	3	interpolative	interpolative	ADJ
ejpam-5792	410	4	ćirić-reichrus	ćirić-reichrus	NOUN
ejpam-5792	410	5	-	-	PUNCT
ejpam-5792	410	6	type	type	NOUN
ejpam-5792	410	7	contractions	contraction	NOUN
ejpam-5792	410	8	.	.	PUNCT
ejpam-5792	411	1	mathematics	mathematic	NOUN
ejpam-5792	411	2	,	,	PUNCT
ejpam-5792	411	3	7(1):57	7(1):57	NUM
ejpam-5792	411	4	,	,	PUNCT
ejpam-5792	411	5	2019	2019	NUM
ejpam-5792	411	6	.	.	PUNCT
ejpam-5792	412	1	[	[	X
ejpam-5792	412	2	10	10	NUM
ejpam-5792	412	3	]	]	X
ejpam-5792	412	4	b.	b.	NOUN
ejpam-5792	412	5	mohammadi	mohammadi	PROPN
ejpam-5792	412	6	,	,	PUNCT
ejpam-5792	412	7	v.	v.	CCONJ
ejpam-5792	412	8	parvaneh	parvaneh	NOUN
ejpam-5792	412	9	,	,	PUNCT
ejpam-5792	412	10	and	and	CCONJ
ejpam-5792	412	11	h.	h.	PROPN
ejpam-5792	412	12	aydi	aydi	VERB
ejpam-5792	412	13	.	.	PUNCT
ejpam-5792	413	1	on	on	ADP
ejpam-5792	413	2	extended	extend	VERB
ejpam-5792	413	3	interpolative	interpolative	ADJ
ejpam-5792	413	4	ćirić–reich	ćirić–reich	PROPN
ejpam-5792	413	5	–	–	PUNCT
ejpam-5792	413	6	rus	rus	NOUN
ejpam-5792	413	7	type	type	NOUN
ejpam-5792	413	8	f	f	NOUN
ejpam-5792	413	9	-	-	PUNCT
ejpam-5792	413	10	contractions	contraction	NOUN
ejpam-5792	413	11	and	and	CCONJ
ejpam-5792	413	12	an	an	DET
ejpam-5792	413	13	application	application	NOUN
ejpam-5792	413	14	.	.	PUNCT
ejpam-5792	414	1	j.	j.	PROPN
ejpam-5792	414	2	inequal	inequal	PROPN
ejpam-5792	414	3	.	.	PUNCT
ejpam-5792	415	1	appl	appl	PROPN
ejpam-5792	415	2	.	.	PROPN
ejpam-5792	415	3	,	,	PUNCT
ejpam-5792	415	4	page	page	NOUN
ejpam-5792	415	5	290	290	NUM
ejpam-5792	415	6	,	,	PUNCT
ejpam-5792	415	7	2019	2019	NUM
ejpam-5792	415	8	.	.	PUNCT
ejpam-5792	416	1	[	[	X
ejpam-5792	416	2	11	11	NUM
ejpam-5792	416	3	]	]	PUNCT
ejpam-5792	416	4	e.	e.	PROPN
ejpam-5792	416	5	karapınar	karapınar	PROPN
ejpam-5792	416	6	.	.	PUNCT
ejpam-5792	417	1	interpolative	interpolative	PROPN
ejpam-5792	417	2	kannan	kannan	PROPN
ejpam-5792	417	3	-	-	PUNCT
ejpam-5792	417	4	meir	meir	PROPN
ejpam-5792	417	5	-	-	PUNCT
ejpam-5792	417	6	keeler	keeler	PROPN
ejpam-5792	417	7	type	type	NOUN
ejpam-5792	417	8	contraction	contraction	NOUN
ejpam-5792	417	9	.	.	PUNCT
ejpam-5792	418	1	adv	adv	PROPN
ejpam-5792	418	2	.	.	PUNCT
ejpam-5792	418	3	theory	theory	PROPN
ejpam-5792	418	4	nonlinear	nonlinear	PROPN
ejpam-5792	418	5	anal	anal	PROPN
ejpam-5792	418	6	.	.	PUNCT
ejpam-5792	419	1	appl	appl	PROPN
ejpam-5792	419	2	.	.	PROPN
ejpam-5792	419	3	,	,	PUNCT
ejpam-5792	419	4	5(4):611–614	5(4):611–614	NUM
ejpam-5792	419	5	,	,	PUNCT
ejpam-5792	419	6	2021	2021	NUM
ejpam-5792	419	7	.	.	PUNCT
ejpam-5792	420	1	[	[	X
ejpam-5792	420	2	12	12	NUM
ejpam-5792	420	3	]	]	PUNCT
ejpam-5792	420	4	e.	e.	PROPN
ejpam-5792	420	5	karapınar	karapınar	PROPN
ejpam-5792	420	6	,	,	PUNCT
ejpam-5792	420	7	a.	a.	NOUN
ejpam-5792	420	8	fulga	fulga	NOUN
ejpam-5792	420	9	,	,	PUNCT
ejpam-5792	420	10	and	and	CCONJ
ejpam-5792	420	11	s.s	s.s	PROPN
ejpam-5792	420	12	.	.	PROPN
ejpam-5792	420	13	yesilkaya	yesilkaya	PROPN
ejpam-5792	420	14	.	.	PUNCT
ejpam-5792	421	1	interpolative	interpolative	PROPN
ejpam-5792	421	2	meir	meir	PROPN
ejpam-5792	421	3	–	–	PUNCT
ejpam-5792	421	4	keeler	keeler	NOUN
ejpam-5792	421	5	mappings	mapping	NOUN
ejpam-5792	421	6	in	in	ADP
ejpam-5792	421	7	modular	modular	ADJ
ejpam-5792	421	8	metric	metric	ADJ
ejpam-5792	421	9	spaces	space	NOUN
ejpam-5792	421	10	.	.	PUNCT
ejpam-5792	422	1	mathematics	mathematic	NOUN
ejpam-5792	422	2	,	,	PUNCT
ejpam-5792	422	3	10(16):2986	10(16):2986	NUM
ejpam-5792	422	4	,	,	PUNCT
ejpam-5792	422	5	2022	2022	NUM
ejpam-5792	422	6	.	.	PUNCT
ejpam-5792	423	1	[	[	X
ejpam-5792	423	2	13	13	NUM
ejpam-5792	423	3	]	]	PUNCT
ejpam-5792	423	4	e.	e.	PROPN
ejpam-5792	423	5	karapınar	karapınar	PROPN
ejpam-5792	423	6	,	,	PUNCT
ejpam-5792	423	7	a.	a.	NOUN
ejpam-5792	423	8	fulga	fulga	NOUN
ejpam-5792	423	9	,	,	PUNCT
ejpam-5792	423	10	and	and	CCONJ
ejpam-5792	423	11	a.	a.	PROPN
ejpam-5792	423	12	f.	f.	PROPN
ejpam-5792	423	13	roldán	roldán	PROPN
ejpam-5792	423	14	lópez	lópez	PROPN
ejpam-5792	423	15	de	de	PROPN
ejpam-5792	423	16	hierro	hierro	PROPN
ejpam-5792	423	17	.	.	PROPN
ejpam-5792	423	18	fixed	fix	VERB
ejpam-5792	423	19	point	point	NOUN
ejpam-5792	423	20	theory	theory	NOUN
ejpam-5792	423	21	in	in	ADP
ejpam-5792	423	22	the	the	DET
ejpam-5792	423	23	setting	setting	NOUN
ejpam-5792	423	24	of	of	ADP
ejpam-5792	423	25	(	(	PUNCT
ejpam-5792	423	26	α	α	PROPN
ejpam-5792	423	27	,	,	PUNCT
ejpam-5792	423	28	β	β	X
ejpam-5792	423	29	,	,	PUNCT
ejpam-5792	423	30	ψ	ψ	ADP
ejpam-5792	423	31	,	,	PUNCT
ejpam-5792	423	32	ϕ)-interpolative	ϕ)-interpolative	ADJ
ejpam-5792	423	33	contractions	contraction	NOUN
ejpam-5792	423	34	.	.	PUNCT
ejpam-5792	424	1	advances	advance	NOUN
ejpam-5792	424	2	in	in	ADP
ejpam-5792	424	3	difference	difference	NOUN
ejpam-5792	424	4	equations	equation	NOUN
ejpam-5792	424	5	,	,	PUNCT
ejpam-5792	424	6	2021(1):339	2021(1):339	NUM
ejpam-5792	424	7	,	,	PUNCT
ejpam-5792	424	8	2021	2021	NUM
ejpam-5792	424	9	.	.	PUNCT
ejpam-5792	425	1	[	[	X
ejpam-5792	425	2	14	14	NUM
ejpam-5792	425	3	]	]	PUNCT
ejpam-5792	425	4	m.	m.	PROPN
ejpam-5792	425	5	s.	s.	PROPN
ejpam-5792	425	6	khan	khan	PROPN
ejpam-5792	425	7	,	,	PUNCT
ejpam-5792	425	8	y.	y.	PROPN
ejpam-5792	425	9	m.	m.	PROPN
ejpam-5792	425	10	singh	singh	PROPN
ejpam-5792	425	11	,	,	PUNCT
ejpam-5792	425	12	and	and	CCONJ
ejpam-5792	425	13	e.	e.	PROPN
ejpam-5792	425	14	karapınar	karapınar	PROPN
ejpam-5792	425	15	.	.	PUNCT
ejpam-5792	426	1	on	on	ADP
ejpam-5792	426	2	the	the	DET
ejpam-5792	426	3	interpolative	interpolative	ADJ
ejpam-5792	426	4	(	(	PUNCT
ejpam-5792	426	5	ϕ	ϕ	NOUN
ejpam-5792	426	6	,	,	PUNCT
ejpam-5792	426	7	ψ)-type	ψ)-type	PUNCT
ejpam-5792	426	8	zcontraction	zcontraction	NOUN
ejpam-5792	426	9	.	.	PUNCT
ejpam-5792	427	1	upb	upb	PROPN
ejpam-5792	427	2	sci	sci	PROPN
ejpam-5792	427	3	.	.	PUNCT
ejpam-5792	427	4	bull	bull	PROPN
ejpam-5792	427	5	.	.	PUNCT
ejpam-5792	428	1	ser	ser	PROPN
ejpam-5792	428	2	.	.	PUNCT
ejpam-5792	429	1	a	a	DET
ejpam-5792	429	2	,	,	PUNCT
ejpam-5792	429	3	83:25–38	83:25–38	PROPN
ejpam-5792	429	4	,	,	PUNCT
ejpam-5792	429	5	2021	2021	NUM
ejpam-5792	429	6	.	.	PUNCT
ejpam-5792	430	1	[	[	X
ejpam-5792	430	2	15	15	NUM
ejpam-5792	430	3	]	]	X
ejpam-5792	430	4	v.	v.	ADP
ejpam-5792	430	5	berinde	berinde	NOUN
ejpam-5792	430	6	.	.	PUNCT
ejpam-5792	431	1	approximating	approximate	VERB
ejpam-5792	431	2	fixed	fix	VERB
ejpam-5792	431	3	points	point	NOUN
ejpam-5792	431	4	of	of	ADP
ejpam-5792	431	5	enriched	enrich	VERB
ejpam-5792	431	6	nonexpansive	nonexpansive	ADJ
ejpam-5792	431	7	mappings	mapping	NOUN
ejpam-5792	431	8	by	by	ADP
ejpam-5792	431	9	krasnoselskij	krasnoselskij	ADJ
ejpam-5792	431	10	iteration	iteration	NOUN
ejpam-5792	431	11	in	in	ADP
ejpam-5792	431	12	hilbert	hilbert	PROPN
ejpam-5792	431	13	spaces	space	NOUN
ejpam-5792	431	14	.	.	PUNCT
ejpam-5792	432	1	carpathian	carpathian	PROPN
ejpam-5792	432	2	j.	j.	PROPN
ejpam-5792	432	3	math	math	PROPN
ejpam-5792	432	4	.	.	PROPN
ejpam-5792	432	5	,	,	PUNCT
ejpam-5792	432	6	35:293–304	35:293–304	PROPN
ejpam-5792	432	7	,	,	PUNCT
ejpam-5792	432	8	2019	2019	NUM
ejpam-5792	432	9	.	.	PUNCT
ejpam-5792	433	1	[	[	X
ejpam-5792	433	2	16	16	X
ejpam-5792	433	3	]	]	PUNCT
ejpam-5792	433	4	v.	v.	CCONJ
ejpam-5792	433	5	berinde	berinde	NOUN
ejpam-5792	433	6	.	.	PUNCT
ejpam-5792	434	1	approximating	approximate	VERB
ejpam-5792	434	2	fixed	fix	VERB
ejpam-5792	434	3	points	point	NOUN
ejpam-5792	434	4	of	of	ADP
ejpam-5792	434	5	enriched	enrich	VERB
ejpam-5792	434	6	nonexpansive	nonexpansive	ADJ
ejpam-5792	434	7	mappings	mapping	NOUN
ejpam-5792	434	8	in	in	ADP
ejpam-5792	434	9	banach	banach	NOUN
ejpam-5792	434	10	spaces	space	NOUN
ejpam-5792	434	11	by	by	ADP
ejpam-5792	434	12	using	use	VERB
ejpam-5792	434	13	a	a	DET
ejpam-5792	434	14	retraction	retraction	NOUN
ejpam-5792	434	15	-	-	PUNCT
ejpam-5792	434	16	displacement	displacement	NOUN
ejpam-5792	434	17	condition	condition	NOUN
ejpam-5792	434	18	.	.	PUNCT
ejpam-5792	435	1	carpathian	carpathian	PROPN
ejpam-5792	435	2	j.	j.	PROPN
ejpam-5792	435	3	math	math	PROPN
ejpam-5792	435	4	.	.	PUNCT
ejpam-5792	435	5	,	,	PUNCT
ejpam-5792	436	1	36:27–34	36:27–34	NUM
ejpam-5792	436	2	,	,	PUNCT
ejpam-5792	436	3	2020	2020	NUM
ejpam-5792	436	4	.	.	PUNCT
ejpam-5792	437	1	[	[	X
ejpam-5792	437	2	17	17	NUM
ejpam-5792	437	3	]	]	X
ejpam-5792	437	4	v.	v.	ADP
ejpam-5792	437	5	berinde	berinde	NOUN
ejpam-5792	437	6	and	and	CCONJ
ejpam-5792	437	7	m.	m.	NOUN
ejpam-5792	437	8	pacurar	pacurar	NOUN
ejpam-5792	437	9	.	.	PUNCT
ejpam-5792	438	1	approximating	approximate	VERB
ejpam-5792	438	2	fixed	fix	VERB
ejpam-5792	438	3	points	point	NOUN
ejpam-5792	438	4	of	of	ADP
ejpam-5792	438	5	enriched	enrich	VERB
ejpam-5792	438	6	contractions	contraction	NOUN
ejpam-5792	438	7	in	in	ADP
ejpam-5792	438	8	banach	banach	NOUN
ejpam-5792	438	9	spaces	space	NOUN
ejpam-5792	438	10	.	.	PUNCT
ejpam-5792	439	1	j.	j.	PROPN
ejpam-5792	439	2	fixed	fix	VERB
ejpam-5792	439	3	point	point	PROPN
ejpam-5792	439	4	theory	theory	NOUN
ejpam-5792	439	5	appl	appl	PROPN
ejpam-5792	439	6	.	.	PROPN
ejpam-5792	439	7	,	,	PUNCT
ejpam-5792	439	8	22:10	22:10	NUM
ejpam-5792	439	9	,	,	PUNCT
ejpam-5792	439	10	2020	2020	NUM
ejpam-5792	439	11	.	.	PUNCT
ejpam-5792	440	1	[	[	X
ejpam-5792	440	2	18	18	NUM
ejpam-5792	440	3	]	]	PUNCT
ejpam-5792	440	4	v.	v.	ADP
ejpam-5792	440	5	berinde	berinde	NOUN
ejpam-5792	440	6	and	and	CCONJ
ejpam-5792	440	7	m.	m.	NOUN
ejpam-5792	440	8	păcurar	păcurar	NOUN
ejpam-5792	440	9	.	.	PUNCT
ejpam-5792	441	1	approximating	approximate	VERB
ejpam-5792	441	2	fixed	fix	VERB
ejpam-5792	441	3	points	point	NOUN
ejpam-5792	441	4	of	of	ADP
ejpam-5792	441	5	enriched	enrich	VERB
ejpam-5792	441	6	chatterjea	chatterjea	ADJ
ejpam-5792	441	7	contractions	contraction	NOUN
ejpam-5792	441	8	by	by	ADP
ejpam-5792	441	9	krasnoselskij	krasnoselskij	PROPN
ejpam-5792	441	10	iterative	iterative	NOUN
ejpam-5792	441	11	algorithm	algorithm	NOUN
ejpam-5792	441	12	in	in	ADP
ejpam-5792	441	13	banach	banach	NOUN
ejpam-5792	441	14	spaces	space	NOUN
ejpam-5792	441	15	.	.	PUNCT
ejpam-5792	442	1	j.	j.	PROPN
ejpam-5792	442	2	fixed	fix	VERB
ejpam-5792	442	3	point	point	PROPN
ejpam-5792	442	4	theory	theory	NOUN
ejpam-5792	442	5	appl	appl	PROPN
ejpam-5792	442	6	.	.	PROPN
ejpam-5792	442	7	,	,	PUNCT
ejpam-5792	442	8	2020	2020	NUM
ejpam-5792	442	9	.	.	PUNCT
ejpam-5792	443	1	[	[	X
ejpam-5792	443	2	19	19	NUM
ejpam-5792	443	3	]	]	X
ejpam-5792	443	4	v.	v.	ADP
ejpam-5792	443	5	berinde	berinde	NOUN
ejpam-5792	443	6	and	and	CCONJ
ejpam-5792	443	7	m.	m.	NOUN
ejpam-5792	443	8	păcurar	păcurar	PROPN
ejpam-5792	443	9	.	.	PUNCT
ejpam-5792	444	1	kannan	kannan	PROPN
ejpam-5792	444	2	’s	’s	PART
ejpam-5792	444	3	fixed	fix	VERB
ejpam-5792	444	4	point	point	NOUN
ejpam-5792	444	5	approximation	approximation	NOUN
ejpam-5792	444	6	for	for	ADP
ejpam-5792	444	7	solving	solve	VERB
ejpam-5792	444	8	split	split	VERB
ejpam-5792	444	9	feasibility	feasibility	NOUN
ejpam-5792	444	10	and	and	CCONJ
ejpam-5792	444	11	variational	variational	ADJ
ejpam-5792	444	12	inequality	inequality	NOUN
ejpam-5792	444	13	problems	problem	NOUN
ejpam-5792	444	14	.	.	PUNCT
ejpam-5792	445	1	j.	j.	PROPN
ejpam-5792	445	2	comput	comput	PROPN
ejpam-5792	445	3	.	.	PUNCT
ejpam-5792	446	1	appl	appl	PROPN
ejpam-5792	446	2	.	.	PROPN
ejpam-5792	446	3	math	math	PROPN
ejpam-5792	446	4	.	.	PUNCT
ejpam-5792	446	5	,	,	PUNCT
ejpam-5792	446	6	386	386	NUM
ejpam-5792	446	7	,	,	PUNCT
ejpam-5792	446	8	2021	2021	NUM
ejpam-5792	446	9	.	.	PUNCT
ejpam-5792	447	1	[	[	X
ejpam-5792	447	2	20	20	NUM
ejpam-5792	447	3	]	]	PUNCT
ejpam-5792	447	4	s.	s.	PROPN
ejpam-5792	447	5	rawat	rawat	PROPN
ejpam-5792	447	6	,	,	PUNCT
ejpam-5792	447	7	s.	s.	PROPN
ejpam-5792	447	8	kukreti	kukreti	PROPN
ejpam-5792	447	9	,	,	PUNCT
ejpam-5792	447	10	and	and	CCONJ
ejpam-5792	447	11	r.c	r.c	PROPN
ejpam-5792	447	12	.	.	PROPN
ejpam-5792	447	13	dimri	dimri	PROPN
ejpam-5792	447	14	.	.	PUNCT
ejpam-5792	448	1	fixed	fix	VERB
ejpam-5792	448	2	point	point	NOUN
ejpam-5792	448	3	results	result	NOUN
ejpam-5792	448	4	for	for	ADP
ejpam-5792	448	5	enriched	enriched	ADJ
ejpam-5792	448	6	ordered	order	VERB
ejpam-5792	448	7	contractions	contraction	NOUN
ejpam-5792	448	8	in	in	ADP
ejpam-5792	448	9	noncommutative	noncommutative	ADJ
ejpam-5792	448	10	banach	banach	NOUN
ejpam-5792	448	11	spaces	space	VERB
ejpam-5792	448	12	.	.	PUNCT
ejpam-5792	449	1	j.	j.	PROPN
ejpam-5792	449	2	anal	anal	PROPN
ejpam-5792	449	3	.	.	PROPN
ejpam-5792	449	4	,	,	PUNCT
ejpam-5792	449	5	30:1555–1566	30:1555–1566	PROPN
ejpam-5792	449	6	,	,	PUNCT
ejpam-5792	449	7	2022	2022	NUM
ejpam-5792	449	8	.	.	PUNCT
ejpam-5792	450	1	[	[	X
ejpam-5792	450	2	21	21	NUM
ejpam-5792	450	3	]	]	PUNCT
ejpam-5792	450	4	a.	a.	NOUN
ejpam-5792	450	5	gangwar	gangwar	PROPN
ejpam-5792	450	6	,	,	PUNCT
ejpam-5792	450	7	s.	s.	PROPN
ejpam-5792	450	8	rawat	rawat	PROPN
ejpam-5792	450	9	,	,	PUNCT
ejpam-5792	450	10	h.	h.	PROPN
ejpam-5792	450	11	isik	isik	PROPN
ejpam-5792	450	12	,	,	PUNCT
ejpam-5792	450	13	and	and	CCONJ
ejpam-5792	450	14	r.c	r.c	PROPN
ejpam-5792	450	15	.	.	PROPN
ejpam-5792	450	16	dimri	dimri	PROPN
ejpam-5792	450	17	.	.	PUNCT
ejpam-5792	451	1	enriched	enrich	VERB
ejpam-5792	451	2	multivalued	multivalued	ADJ
ejpam-5792	451	3	contractions	contraction	NOUN
ejpam-5792	451	4	on	on	ADP
ejpam-5792	451	5	double	double	ADJ
ejpam-5792	451	6	controlled	control	VERB
ejpam-5792	451	7	metric	metric	ADJ
ejpam-5792	451	8	type	type	NOUN
ejpam-5792	451	9	spaces	space	NOUN
ejpam-5792	451	10	with	with	ADP
ejpam-5792	451	11	an	an	DET
ejpam-5792	451	12	application	application	NOUN
ejpam-5792	451	13	.	.	PUNCT
ejpam-5792	452	1	adv	adv	PROPN
ejpam-5792	452	2	.	.	PUNCT
ejpam-5792	452	3	fixed	fix	VERB
ejpam-5792	452	4	point	point	NOUN
ejpam-5792	452	5	theory	theory	NOUN
ejpam-5792	452	6	,	,	PUNCT
ejpam-5792	452	7	14	14	NUM
ejpam-5792	452	8	,	,	PUNCT
ejpam-5792	452	9	2024	2024	NUM
ejpam-5792	452	10	.	.	PUNCT
ejpam-5792	453	1	[	[	X
ejpam-5792	453	2	22	22	NUM
ejpam-5792	453	3	]	]	X
ejpam-5792	453	4	s.b	s.b	PROPN
ejpam-5792	453	5	.	.	PROPN
ejpam-5792	453	6	nadler	nadler	PROPN
ejpam-5792	453	7	.	.	PUNCT
ejpam-5792	454	1	multi	multi	ADJ
ejpam-5792	454	2	-	-	ADJ
ejpam-5792	454	3	valued	value	VERB
ejpam-5792	454	4	contraction	contraction	NOUN
ejpam-5792	454	5	mappings	mapping	NOUN
ejpam-5792	454	6	.	.	PUNCT
ejpam-5792	455	1	pac	pac	PROPN
ejpam-5792	455	2	.	.	PUNCT
ejpam-5792	456	1	j.	j.	PROPN
ejpam-5792	456	2	math	math	PROPN
ejpam-5792	456	3	.	.	PUNCT
ejpam-5792	456	4	,	,	PUNCT
ejpam-5792	457	1	30:475–488	30:475–488	NUM
ejpam-5792	457	2	,	,	PUNCT
ejpam-5792	457	3	1969	1969	NUM
ejpam-5792	457	4	.	.	PUNCT
ejpam-5792	458	1	[	[	X
ejpam-5792	458	2	23	23	NUM
ejpam-5792	458	3	]	]	X
ejpam-5792	458	4	w.	w.	PROPN
ejpam-5792	458	5	takahashi	takahashi	PROPN
ejpam-5792	458	6	.	.	PUNCT
ejpam-5792	459	1	a	a	DET
ejpam-5792	459	2	convexity	convexity	NOUN
ejpam-5792	459	3	in	in	ADP
ejpam-5792	459	4	metric	metric	ADJ
ejpam-5792	459	5	space	space	NOUN
ejpam-5792	459	6	and	and	CCONJ
ejpam-5792	459	7	nonexpansive	nonexpansive	ADJ
ejpam-5792	459	8	mappings	mapping	NOUN
ejpam-5792	459	9	,	,	PUNCT
ejpam-5792	459	10	i.	i.	PROPN
ejpam-5792	459	11	kodai	kodai	PROPN
ejpam-5792	459	12	a.	a.	PROPN
ejpam-5792	459	13	gangwar	gangwar	VERB
ejpam-5792	459	14	et	et	PROPN
ejpam-5792	459	15	al	al	PROPN
ejpam-5792	459	16	.	.	PUNCT
ejpam-5792	459	17	/	/	SYM
ejpam-5792	459	18	eur	eur	PROPN
ejpam-5792	459	19	.	.	PUNCT
ejpam-5792	460	1	j.	j.	PROPN
ejpam-5792	460	2	pure	pure	PROPN
ejpam-5792	460	3	appl	appl	PROPN
ejpam-5792	460	4	.	.	PROPN
ejpam-5792	460	5	math	math	PROPN
ejpam-5792	460	6	,	,	PUNCT
ejpam-5792	460	7	18	18	NUM
ejpam-5792	460	8	(	(	PUNCT
ejpam-5792	460	9	2	2	NUM
ejpam-5792	460	10	)	)	PUNCT
ejpam-5792	460	11	(	(	PUNCT
ejpam-5792	460	12	2025	2025	NUM
ejpam-5792	460	13	)	)	PUNCT
ejpam-5792	460	14	,	,	PUNCT
ejpam-5792	460	15	5792	5792	NUM
ejpam-5792	460	16	16	16	NUM
ejpam-5792	460	17	of	of	ADP
ejpam-5792	460	18	16	16	NUM
ejpam-5792	460	19	math	math	NOUN
ejpam-5792	460	20	.	.	PUNCT
ejpam-5792	461	1	sem	sem	PROPN
ejpam-5792	461	2	.	.	PUNCT
ejpam-5792	461	3	rep	rep	PROPN
ejpam-5792	461	4	.	.	PROPN
ejpam-5792	461	5	,	,	PUNCT
ejpam-5792	461	6	22(2):142–149	22(2):142–149	PROPN
ejpam-5792	461	7	,	,	PUNCT
ejpam-5792	461	8	1970	1970	NUM
ejpam-5792	461	9	.	.	PUNCT
ejpam-5792	462	1	[	[	X
ejpam-5792	462	2	24	24	NUM
ejpam-5792	462	3	]	]	X
ejpam-5792	462	4	s.	s.	PROPN
ejpam-5792	462	5	rawat	rawat	PROPN
ejpam-5792	462	6	,	,	PUNCT
ejpam-5792	462	7	a.	a.	NOUN
ejpam-5792	462	8	bartwal	bartwal	PROPN
ejpam-5792	462	9	,	,	PUNCT
ejpam-5792	462	10	and	and	CCONJ
ejpam-5792	462	11	r.c	r.c	PROPN
ejpam-5792	462	12	.	.	PROPN
ejpam-5792	462	13	dimri	dimri	PROPN
ejpam-5792	462	14	.	.	PUNCT
ejpam-5792	463	1	approximation	approximation	NOUN
ejpam-5792	463	2	and	and	CCONJ
ejpam-5792	463	3	existence	existence	NOUN
ejpam-5792	463	4	of	of	ADP
ejpam-5792	463	5	fixed	fix	VERB
ejpam-5792	463	6	points	point	NOUN
ejpam-5792	463	7	via	via	ADP
ejpam-5792	463	8	interpolative	interpolative	ADJ
ejpam-5792	463	9	enriched	enrich	VERB
ejpam-5792	463	10	contractions	contraction	NOUN
ejpam-5792	463	11	.	.	PUNCT
ejpam-5792	464	1	filomat	filomat	NOUN
ejpam-5792	464	2	,	,	PUNCT
ejpam-5792	464	3	37(16):5455–5467	37(16):5455–5467	NUM
ejpam-5792	464	4	,	,	PUNCT
ejpam-5792	464	5	2023	2023	NUM
ejpam-5792	464	6	.	.	PUNCT
ejpam-5792	465	1	[	[	X
ejpam-5792	465	2	25	25	NUM
ejpam-5792	465	3	]	]	PUNCT
ejpam-5792	465	4	f.	f.	PROPN
ejpam-5792	465	5	khojasteh	khojasteh	PROPN
ejpam-5792	465	6	,	,	PUNCT
ejpam-5792	465	7	s.	s.	PROPN
ejpam-5792	465	8	shukla	shukla	PROPN
ejpam-5792	465	9	,	,	PUNCT
ejpam-5792	465	10	and	and	CCONJ
ejpam-5792	465	11	s.	s.	PROPN
ejpam-5792	466	1	radenović.	radenović.	PROPN
ejpam-5792	466	2	a	a	DET
ejpam-5792	466	3	new	new	ADJ
ejpam-5792	466	4	approach	approach	NOUN
ejpam-5792	466	5	to	to	ADP
ejpam-5792	466	6	the	the	DET
ejpam-5792	466	7	study	study	NOUN
ejpam-5792	466	8	of	of	ADP
ejpam-5792	466	9	fixed	fix	VERB
ejpam-5792	466	10	point	point	NOUN
ejpam-5792	466	11	theorems	theorem	NOUN
ejpam-5792	466	12	via	via	ADP
ejpam-5792	466	13	simulation	simulation	NOUN
ejpam-5792	466	14	functions	function	NOUN
ejpam-5792	466	15	.	.	PUNCT
ejpam-5792	467	1	filomat	filomat	NOUN
ejpam-5792	467	2	,	,	PUNCT
ejpam-5792	467	3	29(6):1189–1194	29(6):1189–1194	PROPN
ejpam-5792	467	4	,	,	PUNCT
ejpam-5792	467	5	2015	2015	NUM
ejpam-5792	467	6	.	.	PUNCT
ejpam-5792	468	1	[	[	X
ejpam-5792	468	2	26	26	NUM
ejpam-5792	468	3	]	]	X
ejpam-5792	468	4	a.f	a.f	PROPN
ejpam-5792	468	5	.	.	PUNCT
ejpam-5792	468	6	roldán	roldán	PROPN
ejpam-5792	468	7	lópez	lópez	PROPN
ejpam-5792	468	8	de	de	PROPN
ejpam-5792	468	9	hierro	hierro	PROPN
ejpam-5792	468	10	,	,	PUNCT
ejpam-5792	468	11	e.	e.	PROPN
ejpam-5792	468	12	karapınar	karapınar	PROPN
ejpam-5792	468	13	,	,	PUNCT
ejpam-5792	468	14	and	and	CCONJ
ejpam-5792	468	15	j.	j.	PROPN
ejpam-5792	468	16	mart́ınez	mart́ınez	PROPN
ejpam-5792	468	17	-	-	PUNCT
ejpam-5792	468	18	moreno	moreno	PROPN
ejpam-5792	468	19	.	.	PUNCT
ejpam-5792	469	1	coincidence	coincidence	NOUN
ejpam-5792	469	2	point	point	NOUN
ejpam-5792	469	3	theorems	theorem	NOUN
ejpam-5792	469	4	on	on	ADP
ejpam-5792	469	5	metric	metric	ADJ
ejpam-5792	469	6	spaces	space	NOUN
ejpam-5792	469	7	via	via	ADP
ejpam-5792	469	8	simulation	simulation	NOUN
ejpam-5792	469	9	functions	function	NOUN
ejpam-5792	469	10	.	.	PUNCT
ejpam-5792	470	1	j.	j.	PROPN
ejpam-5792	470	2	comput	comput	PROPN
ejpam-5792	470	3	.	.	PUNCT
ejpam-5792	471	1	appl	appl	PROPN
ejpam-5792	471	2	.	.	PROPN
ejpam-5792	471	3	math	math	PROPN
ejpam-5792	471	4	.	.	PUNCT
ejpam-5792	471	5	,	,	PUNCT
ejpam-5792	471	6	275:345–355	275:345–355	NUM
ejpam-5792	471	7	,	,	PUNCT
ejpam-5792	471	8	2015	2015	NUM
ejpam-5792	471	9	.	.	PUNCT
ejpam-5792	472	1	[	[	X
ejpam-5792	472	2	27	27	NUM
ejpam-5792	472	3	]	]	X
ejpam-5792	472	4	h.	h.	PROPN
ejpam-5792	472	5	argoubi	argoubi	PROPN
ejpam-5792	472	6	,	,	PUNCT
ejpam-5792	472	7	b.	b.	PROPN
ejpam-5792	472	8	samet	samet	PROPN
ejpam-5792	472	9	,	,	PUNCT
ejpam-5792	472	10	and	and	CCONJ
ejpam-5792	472	11	c.	c.	PROPN
ejpam-5792	472	12	vetro	vetro	PROPN
ejpam-5792	472	13	.	.	PUNCT
ejpam-5792	473	1	nonlinear	nonlinear	ADJ
ejpam-5792	473	2	contractions	contraction	NOUN
ejpam-5792	473	3	involving	involve	VERB
ejpam-5792	473	4	simulation	simulation	NOUN
ejpam-5792	473	5	functions	function	NOUN
ejpam-5792	473	6	in	in	ADP
ejpam-5792	473	7	a	a	DET
ejpam-5792	473	8	metric	metric	ADJ
ejpam-5792	473	9	space	space	NOUN
ejpam-5792	473	10	with	with	ADP
ejpam-5792	473	11	a	a	DET
ejpam-5792	473	12	partial	partial	ADJ
ejpam-5792	473	13	order	order	NOUN
ejpam-5792	473	14	.	.	PUNCT
ejpam-5792	474	1	j.	j.	PROPN
ejpam-5792	474	2	nonlinear	nonlinear	PROPN
ejpam-5792	474	3	sci	sci	PROPN
ejpam-5792	474	4	.	.	PUNCT
ejpam-5792	474	5	appl	appl	PROPN
ejpam-5792	474	6	.	.	PROPN
ejpam-5792	474	7	,	,	PUNCT
ejpam-5792	474	8	8:1082	8:1082	NUM
ejpam-5792	474	9	–	–	PUNCT
ejpam-5792	474	10	1094	1094	NUM
ejpam-5792	474	11	,	,	PUNCT
ejpam-5792	474	12	2015	2015	NUM
ejpam-5792	474	13	.	.	PUNCT
ejpam-5792	475	1	[	[	X
ejpam-5792	475	2	28	28	NUM
ejpam-5792	475	3	]	]	X
ejpam-5792	475	4	a.f	a.f	PROPN
ejpam-5792	475	5	.	.	PUNCT
ejpam-5792	475	6	roldán	roldán	NOUN
ejpam-5792	475	7	-	-	PUNCT
ejpam-5792	475	8	lópez	lópez	ADV
ejpam-5792	475	9	-	-	PUNCT
ejpam-5792	475	10	de	de	X
ejpam-5792	475	11	hierro	hierro	PROPN
ejpam-5792	475	12	,	,	PUNCT
ejpam-5792	475	13	e.	e.	PROPN
ejpam-5792	475	14	karapinar	karapinar	PROPN
ejpam-5792	475	15	,	,	PUNCT
ejpam-5792	475	16	c.	c.	PROPN
ejpam-5792	475	17	roldan	roldan	PROPN
ejpam-5792	475	18	,	,	PUNCT
ejpam-5792	475	19	and	and	CCONJ
ejpam-5792	475	20	j.	j.	PROPN
ejpam-5792	475	21	martinez	martinez	PROPN
ejpam-5792	475	22	.	.	PUNCT
ejpam-5792	476	1	coincidence	coincidence	NOUN
ejpam-5792	476	2	point	point	NOUN
ejpam-5792	476	3	theorems	theorem	NOUN
ejpam-5792	476	4	on	on	ADP
ejpam-5792	476	5	metric	metric	ADJ
ejpam-5792	476	6	spaces	space	NOUN
ejpam-5792	476	7	via	via	ADP
ejpam-5792	476	8	simulation	simulation	NOUN
ejpam-5792	476	9	function	function	NOUN
ejpam-5792	476	10	.	.	PUNCT
ejpam-5792	477	1	j.	j.	PROPN
ejpam-5792	477	2	comput	comput	PROPN
ejpam-5792	477	3	.	.	PUNCT
ejpam-5792	478	1	appl	appl	PROPN
ejpam-5792	478	2	.	.	PROPN
ejpam-5792	478	3	math	math	PROPN
ejpam-5792	478	4	.	.	PUNCT
ejpam-5792	478	5	,	,	PUNCT
ejpam-5792	478	6	275:345–355	275:345–355	NUM
ejpam-5792	478	7	,	,	PUNCT
ejpam-5792	478	8	2015	2015	NUM
ejpam-5792	478	9	.	.	PUNCT
ejpam-5792	479	1	[	[	X
ejpam-5792	479	2	29	29	NUM
ejpam-5792	479	3	]	]	X
ejpam-5792	479	4	a.h	a.h	PROPN
ejpam-5792	479	5	.	.	PROPN
ejpam-5792	479	6	ansari	ansari	PROPN
ejpam-5792	479	7	.	.	PUNCT
ejpam-5792	480	1	note	note	NOUN
ejpam-5792	480	2	on	on	ADP
ejpam-5792	480	3	ϕ	ϕ	PROPN
ejpam-5792	480	4	−	−	PROPN
ejpam-5792	480	5	ψ	ψ	NOUN
ejpam-5792	480	6	-	-	ADJ
ejpam-5792	480	7	contractive	contractive	ADJ
ejpam-5792	480	8	type	type	NOUN
ejpam-5792	480	9	mappings	mapping	NOUN
ejpam-5792	480	10	and	and	CCONJ
ejpam-5792	480	11	related	relate	VERB
ejpam-5792	480	12	fixed	fix	VERB
ejpam-5792	480	13	point	point	NOUN
ejpam-5792	480	14	.	.	PUNCT
ejpam-5792	481	1	in	in	ADP
ejpam-5792	481	2	the	the	DET
ejpam-5792	481	3	2nd	2nd	ADJ
ejpam-5792	481	4	regional	regional	ADJ
ejpam-5792	481	5	conference	conference	NOUN
ejpam-5792	481	6	on	on	ADP
ejpam-5792	481	7	math	math	NOUN
ejpam-5792	481	8	.	.	PUNCT
ejpam-5792	482	1	appl	appl	PROPN
ejpam-5792	482	2	.	.	PUNCT
ejpam-5792	483	1	pnu	pnu	PROPN
ejpam-5792	483	2	,	,	PUNCT
ejpam-5792	483	3	pages	page	NOUN
ejpam-5792	483	4	377–380	377–380	NUM
ejpam-5792	483	5	,	,	PUNCT
ejpam-5792	483	6	2014	2014	NUM
ejpam-5792	483	7	.	.	PUNCT
ejpam-5792	484	1	[	[	X
ejpam-5792	484	2	30	30	NUM
ejpam-5792	484	3	]	]	X
ejpam-5792	484	4	x.l	x.l	PROPN
ejpam-5792	484	5	.	.	PUNCT
ejpam-5792	485	1	liu	liu	PROPN
ejpam-5792	485	2	,	,	PUNCT
ejpam-5792	485	3	a.h	a.h	PROPN
ejpam-5792	485	4	.	.	PROPN
ejpam-5792	485	5	ansari	ansari	PROPN
ejpam-5792	485	6	,	,	PUNCT
ejpam-5792	485	7	s.	s.	PROPN
ejpam-5792	485	8	chandok	chandok	PROPN
ejpam-5792	485	9	,	,	PUNCT
ejpam-5792	485	10	and	and	CCONJ
ejpam-5792	485	11	s.	s.	PROPN
ejpam-5792	486	1	radenović.	radenović.	PROPN
ejpam-5792	486	2	on	on	ADP
ejpam-5792	486	3	some	some	DET
ejpam-5792	486	4	results	result	NOUN
ejpam-5792	486	5	in	in	ADP
ejpam-5792	486	6	metric	metric	ADJ
ejpam-5792	486	7	spaces	space	NOUN
ejpam-5792	486	8	using	use	VERB
ejpam-5792	486	9	auxiliary	auxiliary	ADJ
ejpam-5792	486	10	simulation	simulation	NOUN
ejpam-5792	486	11	functions	function	NOUN
ejpam-5792	486	12	via	via	ADP
ejpam-5792	486	13	new	new	ADJ
ejpam-5792	486	14	functions	function	NOUN
ejpam-5792	486	15	.	.	PUNCT
ejpam-5792	487	1	j.	j.	PROPN
ejpam-5792	487	2	comput	comput	PROPN
ejpam-5792	487	3	.	.	PUNCT
ejpam-5792	488	1	anal	anal	PROPN
ejpam-5792	488	2	.	.	PUNCT
ejpam-5792	488	3	appl	appl	PROPN
ejpam-5792	488	4	.	.	PROPN
ejpam-5792	488	5	,	,	PUNCT
ejpam-5792	489	1	24(6):1103–1114	24(6):1103–1114	NUM
ejpam-5792	489	2	,	,	PUNCT
ejpam-5792	489	3	2018	2018	NUM
ejpam-5792	489	4	.	.	PUNCT
ejpam-5792	490	1	[	[	X
ejpam-5792	490	2	31	31	NUM
ejpam-5792	490	3	]	]	X
ejpam-5792	490	4	l.b	l.b	PROPN
ejpam-5792	490	5	.	.	PUNCT
ejpam-5792	490	6	ćirić.	ćirić.	ADJ
ejpam-5792	490	7	fixed	fix	VERB
ejpam-5792	490	8	point	point	NOUN
ejpam-5792	490	9	theory	theory	NOUN
ejpam-5792	490	10	.	.	PUNCT
ejpam-5792	491	1	contraction	contraction	NOUN
ejpam-5792	491	2	mapping	mapping	NOUN
ejpam-5792	491	3	principle	principle	NOUN
ejpam-5792	491	4	.	.	PUNCT
ejpam-5792	492	1	fme	fme	PROPN
ejpam-5792	492	2	press	press	PROPN
ejpam-5792	492	3	,	,	PUNCT
ejpam-5792	492	4	beograd	beograd	PROPN
ejpam-5792	492	5	,	,	PUNCT
ejpam-5792	492	6	serbia	serbia	PROPN
ejpam-5792	492	7	,	,	PUNCT
ejpam-5792	492	8	2003	2003	NUM
ejpam-5792	492	9	.	.	PUNCT
ejpam-5792	493	1	[	[	X
ejpam-5792	493	2	32	32	NUM
ejpam-5792	493	3	]	]	PUNCT
ejpam-5792	493	4	e.	e.	PROPN
ejpam-5792	493	5	karapinar	karapinar	PROPN
ejpam-5792	493	6	,	,	PUNCT
ejpam-5792	493	7	a.	a.	PROPN
ejpam-5792	493	8	ali	ali	PROPN
ejpam-5792	493	9	,	,	PUNCT
ejpam-5792	493	10	a.	a.	NOUN
ejpam-5792	493	11	hussain	hussain	PROPN
ejpam-5792	493	12	,	,	PUNCT
ejpam-5792	493	13	and	and	CCONJ
ejpam-5792	493	14	h.	h.	PROPN
ejpam-5792	493	15	aydi	aydi	VERB
ejpam-5792	493	16	.	.	PUNCT
ejpam-5792	494	1	on	on	ADP
ejpam-5792	494	2	interpolative	interpolative	ADJ
ejpam-5792	494	3	hardy	hardy	ADJ
ejpam-5792	494	4	-	-	PUNCT
ejpam-5792	494	5	rogers	rogers	NOUN
ejpam-5792	494	6	type	type	NOUN
ejpam-5792	494	7	multivalued	multivalue	VERB
ejpam-5792	494	8	contractions	contraction	NOUN
ejpam-5792	494	9	via	via	ADP
ejpam-5792	494	10	a	a	DET
ejpam-5792	494	11	simulation	simulation	NOUN
ejpam-5792	494	12	function	function	NOUN
ejpam-5792	494	13	.	.	PUNCT
ejpam-5792	495	1	filomat	filomat	PROPN
ejpam-5792	495	2	,	,	PUNCT
ejpam-5792	495	3	36(8):2847–2856	36(8):2847–2856	PROPN
ejpam-5792	495	4	,	,	PUNCT
ejpam-5792	495	5	2022	2022	NUM
ejpam-5792	495	6	.	.	PUNCT
ejpam-5792	496	1	[	[	X
ejpam-5792	496	2	33	33	NUM
ejpam-5792	496	3	]	]	X
ejpam-5792	496	4	r.p	r.p	PROPN
ejpam-5792	496	5	.	.	PROPN
ejpam-5792	496	6	agarwal	agarwal	PROPN
ejpam-5792	496	7	,	,	PUNCT
ejpam-5792	496	8	d.	d.	PROPN
ejpam-5792	496	9	o’regan	o’regan	PROPN
ejpam-5792	496	10	,	,	PUNCT
ejpam-5792	496	11	and	and	CCONJ
ejpam-5792	496	12	d.r	d.r	PROPN
ejpam-5792	496	13	.	.	PROPN
ejpam-5792	496	14	sahu	sahu	PROPN
ejpam-5792	496	15	.	.	PUNCT
ejpam-5792	497	1	fixed	fix	VERB
ejpam-5792	497	2	point	point	NOUN
ejpam-5792	497	3	theory	theory	NOUN
ejpam-5792	497	4	for	for	ADP
ejpam-5792	497	5	lipschitzian	lipschitzian	ADJ
ejpam-5792	497	6	-	-	PUNCT
ejpam-5792	497	7	type	type	NOUN
ejpam-5792	497	8	mappings	mapping	NOUN
ejpam-5792	497	9	with	with	ADP
ejpam-5792	497	10	application	application	NOUN
ejpam-5792	497	11	.	.	PUNCT
ejpam-5792	498	1	springer	springer	NOUN
ejpam-5792	498	2	,	,	PUNCT
ejpam-5792	498	3	new	new	PROPN
ejpam-5792	498	4	york	york	PROPN
ejpam-5792	498	5	,	,	PUNCT
ejpam-5792	498	6	usa	usa	PROPN
ejpam-5792	498	7	,	,	PUNCT
ejpam-5792	498	8	2009	2009	NUM
ejpam-5792	498	9	.	.	PUNCT