id	sid	tid	token	lemma	pos
ejpam-5388	1	1	european	european	PROPN
ejpam-5388	1	2	journal	journal	PROPN
ejpam-5388	1	3	of	of	ADP
ejpam-5388	1	4	pure	pure	ADJ
ejpam-5388	1	5	and	and	CCONJ
ejpam-5388	1	6	applied	apply	VERB
ejpam-5388	1	7	mathematics	mathematic	NOUN
ejpam-5388	1	8	vol	vol	NOUN
ejpam-5388	1	9	.	.	PROPN
ejpam-5388	2	1	17	17	NUM
ejpam-5388	2	2	,	,	PUNCT
ejpam-5388	2	3	no	no	INTJ
ejpam-5388	2	4	.	.	NOUN
ejpam-5388	2	5	4	4	NUM
ejpam-5388	2	6	,	,	PUNCT
ejpam-5388	2	7	2024	2024	NUM
ejpam-5388	2	8	,	,	PUNCT
ejpam-5388	2	9	2492	2492	NUM
ejpam-5388	2	10	-	-	SYM
ejpam-5388	2	11	2504	2504	NUM
ejpam-5388	2	12	issn	issn	PROPN
ejpam-5388	2	13	1307	1307	NUM
ejpam-5388	2	14	-	-	SYM
ejpam-5388	2	15	5543	5543	NUM
ejpam-5388	2	16	–	–	PUNCT
ejpam-5388	2	17	ejpam.com	ejpam.com	X
ejpam-5388	2	18	published	publish	VERB
ejpam-5388	2	19	by	by	ADP
ejpam-5388	2	20	new	new	PROPN
ejpam-5388	2	21	york	york	PROPN
ejpam-5388	2	22	business	business	PROPN
ejpam-5388	2	23	global	global	ADJ
ejpam-5388	2	24	common	common	ADJ
ejpam-5388	2	25	fixed	fix	VERB
ejpam-5388	2	26	point	point	NOUN
ejpam-5388	2	27	of	of	ADP
ejpam-5388	2	28	generalized	generalized	ADJ
ejpam-5388	2	29	berinde	berinde	NOUN
ejpam-5388	2	30	type	type	NOUN
ejpam-5388	2	31	contraction	contraction	NOUN
ejpam-5388	2	32	and	and	CCONJ
ejpam-5388	2	33	an	an	DET
ejpam-5388	2	34	application	application	NOUN
ejpam-5388	2	35	habes	habe	NOUN
ejpam-5388	2	36	alsamir1,∗	alsamir1,∗	VERB
ejpam-5388	2	37	,	,	PUNCT
ejpam-5388	2	38	haitham	haitham	PROPN
ejpam-5388	2	39	qawaqneh2	qawaqneh2	PROPN
ejpam-5388	2	40	,	,	PUNCT
ejpam-5388	2	41	gawhara	gawhara	PROPN
ejpam-5388	2	42	al	al	PROPN
ejpam-5388	2	43	-	-	PUNCT
ejpam-5388	2	44	musannef3	musannef3	PROPN
ejpam-5388	2	45	,	,	PUNCT
ejpam-5388	2	46	roshdi	roshdi	NOUN
ejpam-5388	2	47	khalil4	khalil4	NOUN
ejpam-5388	2	48	1	1	NUM
ejpam-5388	2	49	finance	finance	NOUN
ejpam-5388	2	50	and	and	CCONJ
ejpam-5388	2	51	banking	banking	NOUN
ejpam-5388	2	52	department	department	NOUN
ejpam-5388	2	53	,	,	PUNCT
ejpam-5388	2	54	business	business	NOUN
ejpam-5388	2	55	administration	administration	PROPN
ejpam-5388	2	56	college	college	PROPN
ejpam-5388	2	57	,	,	PUNCT
ejpam-5388	2	58	dar	dar	PROPN
ejpam-5388	2	59	aluloom	aluloom	NOUN
ejpam-5388	2	60	university	university	PROPN
ejpam-5388	2	61	,	,	PUNCT
ejpam-5388	2	62	riyadh	riyadh	PROPN
ejpam-5388	2	63	,	,	PUNCT
ejpam-5388	2	64	saudi	saudi	PROPN
ejpam-5388	2	65	arabia	arabia	PROPN
ejpam-5388	2	66	2	2	NUM
ejpam-5388	2	67	department	department	NOUN
ejpam-5388	2	68	of	of	ADP
ejpam-5388	2	69	mathematics	mathematic	NOUN
ejpam-5388	2	70	,	,	PUNCT
ejpam-5388	2	71	faculty	faculty	NOUN
ejpam-5388	2	72	of	of	ADP
ejpam-5388	2	73	science	science	NOUN
ejpam-5388	2	74	and	and	CCONJ
ejpam-5388	2	75	information	information	NOUN
ejpam-5388	2	76	technology	technology	NOUN
ejpam-5388	2	77	,	,	PUNCT
ejpam-5388	2	78	al	al	PROPN
ejpam-5388	2	79	-	-	PROPN
ejpam-5388	2	80	zaytoonah	zaytoonah	PROPN
ejpam-5388	2	81	university	university	PROPN
ejpam-5388	2	82	of	of	ADP
ejpam-5388	2	83	jordan	jordan	PROPN
ejpam-5388	2	84	,	,	PUNCT
ejpam-5388	2	85	amman	amman	PROPN
ejpam-5388	2	86	11733	11733	NUM
ejpam-5388	2	87	,	,	PUNCT
ejpam-5388	2	88	jordan	jordan	PROPN
ejpam-5388	2	89	.	.	PUNCT
ejpam-5388	3	1	3	3	NUM
ejpam-5388	3	2	faculty	faculty	NOUN
ejpam-5388	3	3	of	of	ADP
ejpam-5388	3	4	business	business	NOUN
ejpam-5388	3	5	studies	study	NOUN
ejpam-5388	3	6	,	,	PUNCT
ejpam-5388	3	7	arab	arab	ADJ
ejpam-5388	3	8	open	open	PROPN
ejpam-5388	3	9	university	university	PROPN
ejpam-5388	3	10	,	,	PUNCT
ejpam-5388	3	11	jeddah	jeddah	PROPN
ejpam-5388	3	12	,	,	PUNCT
ejpam-5388	3	13	saudi	saudi	PROPN
ejpam-5388	3	14	arabia	arabia	PROPN
ejpam-5388	3	15	4	4	NUM
ejpam-5388	3	16	department	department	NOUN
ejpam-5388	3	17	of	of	ADP
ejpam-5388	3	18	mathematics	mathematic	NOUN
ejpam-5388	3	19	,	,	PUNCT
ejpam-5388	3	20	faculty	faculty	NOUN
ejpam-5388	3	21	of	of	ADP
ejpam-5388	3	22	science	science	NOUN
ejpam-5388	3	23	,	,	PUNCT
ejpam-5388	3	24	the	the	DET
ejpam-5388	3	25	university	university	PROPN
ejpam-5388	3	26	of	of	ADP
ejpam-5388	3	27	jordan	jordan	PROPN
ejpam-5388	3	28	,	,	PUNCT
ejpam-5388	3	29	amman	amman	PROPN
ejpam-5388	3	30	,	,	PUNCT
ejpam-5388	3	31	11942	11942	NUM
ejpam-5388	3	32	,	,	PUNCT
ejpam-5388	3	33	jordan	jordan	PROPN
ejpam-5388	3	34	abstract	abstract	PROPN
ejpam-5388	3	35	.	.	PUNCT
ejpam-5388	4	1	in	in	ADP
ejpam-5388	4	2	this	this	DET
ejpam-5388	4	3	paper	paper	NOUN
ejpam-5388	4	4	,	,	PUNCT
ejpam-5388	4	5	we	we	PRON
ejpam-5388	4	6	introduce	introduce	VERB
ejpam-5388	4	7	λ(s	λ(s	PROPN
ejpam-5388	4	8	,	,	PUNCT
ejpam-5388	4	9	φ	φ	NOUN
ejpam-5388	4	10	,	,	PUNCT
ejpam-5388	4	11	ψ	ψ	PROPN
ejpam-5388	4	12	,	,	PUNCT
ejpam-5388	4	13	l)-generalized	l)-generalize	VERB
ejpam-5388	4	14	berinde	berinde	NOUN
ejpam-5388	4	15	type	type	NOUN
ejpam-5388	4	16	contraction	contraction	NOUN
ejpam-5388	4	17	and	and	CCONJ
ejpam-5388	4	18	obtain	obtain	VERB
ejpam-5388	4	19	some	some	DET
ejpam-5388	4	20	common	common	ADJ
ejpam-5388	4	21	fixed	fix	VERB
ejpam-5388	4	22	point	point	NOUN
ejpam-5388	4	23	results	result	NOUN
ejpam-5388	4	24	for	for	ADP
ejpam-5388	4	25	such	such	ADJ
ejpam-5388	4	26	class	class	NOUN
ejpam-5388	4	27	of	of	ADP
ejpam-5388	4	28	contractions	contraction	NOUN
ejpam-5388	4	29	the	the	DET
ejpam-5388	4	30	setting	setting	NOUN
ejpam-5388	4	31	of	of	ADP
ejpam-5388	4	32	triangular	triangular	NOUN
ejpam-5388	4	33	α	α	NOUN
ejpam-5388	4	34	-	-	ADJ
ejpam-5388	4	35	admissible	admissible	ADJ
ejpam-5388	4	36	mappings	mapping	NOUN
ejpam-5388	4	37	with	with	ADP
ejpam-5388	4	38	respect	respect	NOUN
ejpam-5388	4	39	to	to	ADP
ejpam-5388	4	40	η	η	PROPN
ejpam-5388	4	41	in	in	ADP
ejpam-5388	4	42	the	the	DET
ejpam-5388	4	43	framework	framework	NOUN
ejpam-5388	4	44	of	of	ADP
ejpam-5388	4	45	b	b	NOUN
ejpam-5388	4	46	-	-	PUNCT
ejpam-5388	4	47	metric	metric	ADJ
ejpam-5388	4	48	spaces	space	NOUN
ejpam-5388	4	49	.	.	PUNCT
ejpam-5388	5	1	our	our	PRON
ejpam-5388	5	2	results	result	NOUN
ejpam-5388	5	3	generalize	generalize	VERB
ejpam-5388	5	4	and	and	CCONJ
ejpam-5388	5	5	extend	extend	VERB
ejpam-5388	5	6	some	some	DET
ejpam-5388	5	7	theorems	theorem	NOUN
ejpam-5388	5	8	in	in	ADP
ejpam-5388	5	9	the	the	DET
ejpam-5388	5	10	literature	literature	NOUN
ejpam-5388	5	11	.	.	PUNCT
ejpam-5388	6	1	an	an	DET
ejpam-5388	6	2	example	example	NOUN
ejpam-5388	6	3	is	be	AUX
ejpam-5388	6	4	given	give	VERB
ejpam-5388	6	5	to	to	PART
ejpam-5388	6	6	support	support	VERB
ejpam-5388	6	7	our	our	PRON
ejpam-5388	6	8	result	result	NOUN
ejpam-5388	6	9	.	.	PUNCT
ejpam-5388	7	1	2020	2020	NUM
ejpam-5388	7	2	mathematics	mathematic	NOUN
ejpam-5388	7	3	subject	subject	NOUN
ejpam-5388	7	4	classifications	classification	NOUN
ejpam-5388	7	5	:	:	PUNCT
ejpam-5388	7	6	47h10	47h10	NUM
ejpam-5388	7	7	,	,	PUNCT
ejpam-5388	7	8	54h25	54h25	NUM
ejpam-5388	7	9	key	key	ADJ
ejpam-5388	7	10	words	word	NOUN
ejpam-5388	7	11	and	and	CCONJ
ejpam-5388	7	12	phrases	phrase	NOUN
ejpam-5388	7	13	:	:	PUNCT
ejpam-5388	7	14	triangular	triangular	NOUN
ejpam-5388	7	15	α	α	NUM
ejpam-5388	7	16	-	-	ADJ
ejpam-5388	7	17	admissible	admissible	ADJ
ejpam-5388	7	18	mappings	mapping	NOUN
ejpam-5388	7	19	with	with	ADP
ejpam-5388	7	20	respect	respect	NOUN
ejpam-5388	7	21	to	to	ADP
ejpam-5388	7	22	η	η	PROPN
ejpam-5388	7	23	,	,	PUNCT
ejpam-5388	7	24	common	common	ADJ
ejpam-5388	7	25	fixed	fix	VERB
ejpam-5388	7	26	point	point	NOUN
ejpam-5388	7	27	,	,	PUNCT
ejpam-5388	7	28	b−metric	b−metric	ADJ
ejpam-5388	7	29	spaces	space	NOUN
ejpam-5388	7	30	1	1	NUM
ejpam-5388	7	31	.	.	PUNCT
ejpam-5388	7	32	introduction	introduction	NOUN
ejpam-5388	7	33	and	and	CCONJ
ejpam-5388	7	34	preliminaries	preliminary	NOUN
ejpam-5388	7	35	the	the	DET
ejpam-5388	7	36	most	most	ADV
ejpam-5388	7	37	important	important	ADJ
ejpam-5388	7	38	tools	tool	NOUN
ejpam-5388	7	39	in	in	ADP
ejpam-5388	7	40	fixed	fix	VERB
ejpam-5388	7	41	point	point	NOUN
ejpam-5388	7	42	theory	theory	NOUN
ejpam-5388	7	43	is	be	AUX
ejpam-5388	7	44	banach	banach	NOUN
ejpam-5388	7	45	contraction	contraction	NOUN
ejpam-5388	7	46	principle	principle	NOUN
ejpam-5388	7	47	.	.	PUNCT
ejpam-5388	8	1	a	a	DET
ejpam-5388	8	2	lot	lot	NOUN
ejpam-5388	8	3	of	of	ADP
ejpam-5388	8	4	authors	author	NOUN
ejpam-5388	8	5	have	have	AUX
ejpam-5388	8	6	extended	extend	VERB
ejpam-5388	8	7	or	or	CCONJ
ejpam-5388	8	8	generalized	generalize	VERB
ejpam-5388	8	9	this	this	DET
ejpam-5388	8	10	contraction	contraction	NOUN
ejpam-5388	8	11	and	and	CCONJ
ejpam-5388	8	12	proved	prove	VERB
ejpam-5388	8	13	the	the	DET
ejpam-5388	8	14	existence	existence	NOUN
ejpam-5388	8	15	of	of	ADP
ejpam-5388	8	16	fixed	fix	VERB
ejpam-5388	8	17	and	and	CCONJ
ejpam-5388	8	18	common	common	ADJ
ejpam-5388	8	19	fixed	fix	VERB
ejpam-5388	8	20	point	point	NOUN
ejpam-5388	8	21	theorems	theorem	NOUN
ejpam-5388	8	22	for	for	ADP
ejpam-5388	8	23	single	single	ADJ
ejpam-5388	8	24	valued	value	VERB
ejpam-5388	8	25	and	and	CCONJ
ejpam-5388	8	26	multi	multi	ADJ
ejpam-5388	8	27	-	-	ADJ
ejpam-5388	8	28	valued	value	VERB
ejpam-5388	8	29	mappings	mapping	NOUN
ejpam-5388	8	30	and	and	CCONJ
ejpam-5388	8	31	some	some	DET
ejpam-5388	8	32	application	application	NOUN
ejpam-5388	8	33	(	(	PUNCT
ejpam-5388	8	34	see	see	VERB
ejpam-5388	8	35	[	[	X
ejpam-5388	8	36	3–6	3–6	NUM
ejpam-5388	8	37	,	,	PUNCT
ejpam-5388	8	38	11	11	NUM
ejpam-5388	8	39	,	,	PUNCT
ejpam-5388	8	40	14–18	14–18	NUM
ejpam-5388	8	41	,	,	PUNCT
ejpam-5388	8	42	21–23	21–23	NOUN
ejpam-5388	8	43	]	]	NUM
ejpam-5388	8	44	)	)	PUNCT
ejpam-5388	8	45	.	.	PUNCT
ejpam-5388	9	1	the	the	DET
ejpam-5388	9	2	concept	concept	NOUN
ejpam-5388	9	3	of	of	ADP
ejpam-5388	9	4	the	the	DET
ejpam-5388	9	5	b	b	NOUN
ejpam-5388	9	6	-	-	PUNCT
ejpam-5388	9	7	metric	metric	ADJ
ejpam-5388	9	8	space	space	NOUN
ejpam-5388	9	9	was	be	AUX
ejpam-5388	9	10	introduced	introduce	VERB
ejpam-5388	9	11	by	by	ADP
ejpam-5388	9	12	czerwik	czerwik	PROPN
ejpam-5388	9	13	[	[	X
ejpam-5388	9	14	12	12	NUM
ejpam-5388	9	15	]	]	PUNCT
ejpam-5388	9	16	and	and	CCONJ
ejpam-5388	9	17	he	he	PRON
ejpam-5388	9	18	also	also	ADV
ejpam-5388	9	19	obtained	obtain	VERB
ejpam-5388	9	20	some	some	DET
ejpam-5388	9	21	fixed	fix	VERB
ejpam-5388	9	22	-	-	PUNCT
ejpam-5388	9	23	point	point	NOUN
ejpam-5388	9	24	theorems	theorem	NOUN
ejpam-5388	9	25	of	of	ADP
ejpam-5388	9	26	contractive	contractive	ADJ
ejpam-5388	9	27	mappings	mapping	NOUN
ejpam-5388	9	28	in	in	ADP
ejpam-5388	9	29	b	b	NOUN
ejpam-5388	9	30	-	-	PUNCT
ejpam-5388	9	31	metric	metric	ADJ
ejpam-5388	9	32	space	space	NOUN
ejpam-5388	9	33	.	.	PUNCT
ejpam-5388	10	1	since	since	SCONJ
ejpam-5388	10	2	then	then	ADV
ejpam-5388	10	3	,	,	PUNCT
ejpam-5388	10	4	this	this	DET
ejpam-5388	10	5	notion	notion	NOUN
ejpam-5388	10	6	has	have	AUX
ejpam-5388	10	7	been	be	AUX
ejpam-5388	10	8	used	use	VERB
ejpam-5388	10	9	by	by	ADP
ejpam-5388	10	10	many	many	ADJ
ejpam-5388	10	11	authors	author	NOUN
ejpam-5388	10	12	to	to	PART
ejpam-5388	10	13	obtain	obtain	VERB
ejpam-5388	10	14	various	various	ADJ
ejpam-5388	10	15	fixed	fix	VERB
ejpam-5388	10	16	point	point	NOUN
ejpam-5388	10	17	theorems	theorem	NOUN
ejpam-5388	10	18	.	.	PUNCT
ejpam-5388	11	1	roshan	roshan	PROPN
ejpam-5388	11	2	et	et	PROPN
ejpam-5388	11	3	al	al	PROPN
ejpam-5388	11	4	.	.	PUNCT
ejpam-5388	12	1	in	in	ADP
ejpam-5388	12	2	[	[	X
ejpam-5388	12	3	18	18	NUM
ejpam-5388	12	4	]	]	PUNCT
ejpam-5388	12	5	used	use	VERB
ejpam-5388	12	6	the	the	DET
ejpam-5388	12	7	notion	notion	NOUN
ejpam-5388	12	8	of	of	ADP
ejpam-5388	12	9	almost	almost	ADV
ejpam-5388	12	10	generalized	generalize	VERB
ejpam-5388	12	11	contractive	contractive	ADJ
ejpam-5388	12	12	mappings	mapping	NOUN
ejpam-5388	12	13	in	in	ADP
ejpam-5388	12	14	ordered	order	VERB
ejpam-5388	12	15	complete	complete	ADJ
ejpam-5388	12	16	b	b	X
ejpam-5388	12	17	-	-	PUNCT
ejpam-5388	12	18	metric	metric	ADJ
ejpam-5388	12	19	spaces	space	NOUN
ejpam-5388	12	20	and	and	CCONJ
ejpam-5388	12	21	established	establish	VERB
ejpam-5388	12	22	some	some	DET
ejpam-5388	12	23	fixed	fix	VERB
ejpam-5388	12	24	and	and	CCONJ
ejpam-5388	12	25	common	common	ADJ
ejpam-5388	12	26	fixed	fix	VERB
ejpam-5388	12	27	point	point	NOUN
ejpam-5388	12	28	results	result	NOUN
ejpam-5388	12	29	.	.	PUNCT
ejpam-5388	13	1	the	the	DET
ejpam-5388	13	2	main	main	ADJ
ejpam-5388	13	3	goal	goal	NOUN
ejpam-5388	13	4	of	of	ADP
ejpam-5388	13	5	this	this	DET
ejpam-5388	13	6	section	section	NOUN
ejpam-5388	13	7	is	be	AUX
ejpam-5388	13	8	to	to	PART
ejpam-5388	13	9	present	present	VERB
ejpam-5388	13	10	some	some	DET
ejpam-5388	13	11	definitions	definition	NOUN
ejpam-5388	13	12	and	and	CCONJ
ejpam-5388	13	13	properties	property	NOUN
ejpam-5388	13	14	of	of	ADP
ejpam-5388	13	15	b	b	NOUN
ejpam-5388	13	16	-	-	PUNCT
ejpam-5388	13	17	metric	metric	ADJ
ejpam-5388	13	18	spaces	space	NOUN
ejpam-5388	13	19	:	:	PUNCT
ejpam-5388	13	20	definition	definition	NOUN
ejpam-5388	13	21	1.1	1.1	NUM
ejpam-5388	13	22	.	.	PUNCT
ejpam-5388	14	1	(	(	PUNCT
ejpam-5388	14	2	[	[	X
ejpam-5388	14	3	12	12	NUM
ejpam-5388	14	4	]	]	PUNCT
ejpam-5388	14	5	)	)	PUNCT
ejpam-5388	14	6	let	let	VERB
ejpam-5388	14	7	𭟋	𭟋	PART
ejpam-5388	14	8	be	be	AUX
ejpam-5388	14	9	a	a	DET
ejpam-5388	14	10	nonempty	nonempty	ADV
ejpam-5388	14	11	set	set	VERB
ejpam-5388	14	12	.	.	PUNCT
ejpam-5388	15	1	a	a	DET
ejpam-5388	15	2	mapping	mapping	NOUN
ejpam-5388	15	3	λb	λb	ADP
ejpam-5388	15	4	:	:	PUNCT
ejpam-5388	15	5	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	15	6	→	→	SYM
ejpam-5388	16	1	[	[	X
ejpam-5388	16	2	0,+∞	0,+∞	NUM
ejpam-5388	16	3	)	)	PUNCT
ejpam-5388	16	4	is	be	AUX
ejpam-5388	16	5	said	say	VERB
ejpam-5388	16	6	to	to	PART
ejpam-5388	16	7	be	be	AUX
ejpam-5388	16	8	a	a	DET
ejpam-5388	16	9	b	b	NOUN
ejpam-5388	16	10	-	-	PUNCT
ejpam-5388	16	11	metric	metric	ADJ
ejpam-5388	16	12	if	if	SCONJ
ejpam-5388	16	13	the	the	DET
ejpam-5388	16	14	following	follow	VERB
ejpam-5388	16	15	three	three	NUM
ejpam-5388	16	16	conditions	condition	NOUN
ejpam-5388	16	17	hold	hold	VERB
ejpam-5388	16	18	for	for	ADP
ejpam-5388	16	19	all	all	DET
ejpam-5388	16	20	u	u	NOUN
ejpam-5388	16	21	,	,	PUNCT
ejpam-5388	16	22	v	v	ADP
ejpam-5388	16	23	∈	∈	NOUN
ejpam-5388	16	24	𭟋	𭟋	NOUN
ejpam-5388	16	25	:	:	PUNCT
ejpam-5388	16	26	(	(	PUNCT
ejpam-5388	16	27	λ1	λ1	ADJ
ejpam-5388	16	28	)	)	PUNCT
ejpam-5388	16	29	λ(u	λ(u	PROPN
ejpam-5388	16	30	,	,	PUNCT
ejpam-5388	16	31	v	v	NOUN
ejpam-5388	16	32	)	)	PUNCT
ejpam-5388	16	33	=	=	SYM
ejpam-5388	16	34	0	0	NUM
ejpam-5388	16	35	⇒	⇒	NOUN
ejpam-5388	16	36	u	u	NOUN
ejpam-5388	16	37	=	=	PROPN
ejpam-5388	16	38	v	v	NOUN
ejpam-5388	16	39	;	;	PUNCT
ejpam-5388	16	40	(	(	PUNCT
ejpam-5388	16	41	λ2	λ2	NOUN
ejpam-5388	16	42	)	)	PUNCT
ejpam-5388	16	43	λ(u	λ(u	PROPN
ejpam-5388	16	44	,	,	PUNCT
ejpam-5388	16	45	v	v	NOUN
ejpam-5388	16	46	)	)	PUNCT
ejpam-5388	16	47	=	=	SYM
ejpam-5388	17	1	λ(v	λ(v	PROPN
ejpam-5388	17	2	,	,	PUNCT
ejpam-5388	17	3	u	u	NOUN
ejpam-5388	17	4	)	)	PUNCT
ejpam-5388	17	5	;	;	PUNCT
ejpam-5388	17	6	(	(	PUNCT
ejpam-5388	17	7	λ3	λ3	PROPN
ejpam-5388	17	8	)	)	PUNCT
ejpam-5388	17	9	λ(u	λ(u	PROPN
ejpam-5388	17	10	,	,	PUNCT
ejpam-5388	17	11	v	v	NOUN
ejpam-5388	17	12	)	)	PUNCT
ejpam-5388	17	13	≤	≤	NOUN
ejpam-5388	17	14	s[λ(u	s[λ(u	NUM
ejpam-5388	17	15	,	,	PUNCT
ejpam-5388	17	16	w	w	NOUN
ejpam-5388	17	17	)	)	PUNCT
ejpam-5388	17	18	+	+	CCONJ
ejpam-5388	18	1	λ(w	λ(w	X
ejpam-5388	18	2	,	,	PUNCT
ejpam-5388	18	3	v	v	NOUN
ejpam-5388	18	4	)	)	PUNCT
ejpam-5388	18	5	]	]	PUNCT
ejpam-5388	18	6	.	.	PUNCT
ejpam-5388	19	1	in	in	ADP
ejpam-5388	19	2	this	this	DET
ejpam-5388	19	3	case	case	NOUN
ejpam-5388	19	4	,	,	PUNCT
ejpam-5388	19	5	the	the	DET
ejpam-5388	19	6	pair	pair	NOUN
ejpam-5388	19	7	(	(	PUNCT
ejpam-5388	19	8	𭟋	𭟋	NOUN
ejpam-5388	19	9	,	,	PUNCT
ejpam-5388	19	10	λb	λb	NOUN
ejpam-5388	19	11	)	)	PUNCT
ejpam-5388	19	12	is	be	AUX
ejpam-5388	19	13	called	call	VERB
ejpam-5388	19	14	a	a	DET
ejpam-5388	19	15	b	b	NOUN
ejpam-5388	19	16	-	-	PUNCT
ejpam-5388	19	17	metric	metric	ADJ
ejpam-5388	19	18	space	space	NOUN
ejpam-5388	19	19	.	.	PUNCT
ejpam-5388	19	20	example	example	NOUN
ejpam-5388	20	1	1.2	1.2	NUM
ejpam-5388	20	2	.	.	PUNCT
ejpam-5388	21	1	let	let	AUX
ejpam-5388	21	2	(	(	PUNCT
ejpam-5388	21	3	𭟋	𭟋	NOUN
ejpam-5388	21	4	,	,	PUNCT
ejpam-5388	21	5	λb	λb	NOUN
ejpam-5388	21	6	)	)	PUNCT
ejpam-5388	21	7	be	be	AUX
ejpam-5388	21	8	a	a	DET
ejpam-5388	21	9	metric	metric	ADJ
ejpam-5388	21	10	space	space	NOUN
ejpam-5388	21	11	and	and	CCONJ
ejpam-5388	21	12	let	let	VERB
ejpam-5388	21	13	β	β	PRON
ejpam-5388	21	14	>	>	X
ejpam-5388	21	15	1	1	NUM
ejpam-5388	21	16	,	,	PUNCT
ejpam-5388	21	17	ϱ	ϱ	ADP
ejpam-5388	21	18	≥	≥	NOUN
ejpam-5388	21	19	0	0	NUM
ejpam-5388	21	20	and	and	CCONJ
ejpam-5388	21	21	µ	µ	X
ejpam-5388	21	22	>	>	X
ejpam-5388	21	23	0	0	NUM
ejpam-5388	21	24	.	.	PUNCT
ejpam-5388	22	1	for	for	ADP
ejpam-5388	22	2	u	u	NOUN
ejpam-5388	22	3	,	,	PUNCT
ejpam-5388	22	4	v	v	PROPN
ejpam-5388	22	5	∈	∈	PROPN
ejpam-5388	22	6	𭟋	𭟋	NOUN
ejpam-5388	22	7	,	,	PUNCT
ejpam-5388	22	8	set	set	VERB
ejpam-5388	22	9	λb(u	λb(u	NOUN
ejpam-5388	22	10	,	,	PUNCT
ejpam-5388	22	11	v	v	NOUN
ejpam-5388	22	12	)	)	PUNCT
ejpam-5388	22	13	=	=	SYM
ejpam-5388	22	14	ϱλb(u	ϱλb(u	PROPN
ejpam-5388	22	15	,	,	PUNCT
ejpam-5388	22	16	v)+µλb(u	v)+µλb(u	PROPN
ejpam-5388	22	17	,	,	PUNCT
ejpam-5388	22	18	v	v	NOUN
ejpam-5388	22	19	)	)	PUNCT
ejpam-5388	22	20	β	β	NOUN
ejpam-5388	22	21	.	.	PUNCT
ejpam-5388	23	1	then	then	ADV
ejpam-5388	23	2	(	(	PUNCT
ejpam-5388	23	3	𭟋	𭟋	NOUN
ejpam-5388	23	4	,	,	PUNCT
ejpam-5388	23	5	λb	λb	NOUN
ejpam-5388	23	6	)	)	PUNCT
ejpam-5388	23	7	is	be	AUX
ejpam-5388	23	8	a	a	DET
ejpam-5388	23	9	b	b	NOUN
ejpam-5388	23	10	-	-	PUNCT
ejpam-5388	23	11	metric	metric	ADJ
ejpam-5388	23	12	space	space	NOUN
ejpam-5388	23	13	with	with	ADP
ejpam-5388	23	14	the	the	DET
ejpam-5388	23	15	parameter	parameter	NOUN
ejpam-5388	23	16	s	s	PART
ejpam-5388	23	17	=	=	NOUN
ejpam-5388	23	18	2β−1	2β−1	NUM
ejpam-5388	23	19	and	and	CCONJ
ejpam-5388	23	20	not	not	PART
ejpam-5388	23	21	a	a	DET
ejpam-5388	23	22	metric	metric	ADJ
ejpam-5388	23	23	space	space	NOUN
ejpam-5388	23	24	on	on	ADP
ejpam-5388	23	25	𭟋	𭟋	ADP
ejpam-5388	23	26	.	.	PUNCT
ejpam-5388	23	27	∗corresponding	∗corresponde	VERB
ejpam-5388	23	28	author	author	NOUN
ejpam-5388	23	29	.	.	PUNCT
ejpam-5388	24	1	doi	doi	NOUN
ejpam-5388	24	2	:	:	PUNCT
ejpam-5388	24	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5388	https://doi.org/10.29020/nybg.ejpam.v17i4.5388	ADJ
ejpam-5388	24	4	email	email	NOUN
ejpam-5388	24	5	addresses	address	NOUN
ejpam-5388	24	6	:	:	PUNCT
ejpam-5388	24	7	habes@dau.edu.sa	habes@dau.edu.sa	PROPN
ejpam-5388	24	8	(	(	PUNCT
ejpam-5388	24	9	h.	h.	PROPN
ejpam-5388	24	10	alsamir	alsamir	PROPN
ejpam-5388	24	11	)	)	PUNCT
ejpam-5388	24	12	,	,	PUNCT
ejpam-5388	24	13	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-5388	24	14	(	(	PUNCT
ejpam-5388	24	15	h.	h.	PROPN
ejpam-5388	24	16	qawaqneh	qawaqneh	PROPN
ejpam-5388	24	17	)	)	PUNCT
ejpam-5388	24	18	,	,	PUNCT
ejpam-5388	24	19	g.almusannef@arabou.edu.sa	g.almusannef@arabou.edu.sa	PROPN
ejpam-5388	24	20	(	(	PUNCT
ejpam-5388	24	21	j.m	j.m	PROPN
ejpam-5388	24	22	.	.	PROPN
ejpam-5388	24	23	al	al	PROPN
ejpam-5388	24	24	-	-	PUNCT
ejpam-5388	24	25	musannef	musannef	NOUN
ejpam-5388	24	26	)	)	PUNCT
ejpam-5388	24	27	,	,	PUNCT
ejpam-5388	25	1	roshdi@ju.edu.jo	roshdi@ju.edu.jo	PROPN
ejpam-5388	25	2	(	(	PUNCT
ejpam-5388	25	3	r.	r.	PROPN
ejpam-5388	25	4	khalil	khalil	PROPN
ejpam-5388	25	5	)	)	PUNCT
ejpam-5388	25	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5388	25	7	2492	2492	NUM
ejpam-5388	25	8	copyright	copyright	NOUN
ejpam-5388	25	9	:	:	PUNCT
ejpam-5388	25	10	©	©	PROPN
ejpam-5388	25	11	2024	2024	NUM
ejpam-5388	25	12	the	the	DET
ejpam-5388	25	13	author(s	author(s	NOUN
ejpam-5388	25	14	)	)	PUNCT
ejpam-5388	25	15	.	.	PUNCT
ejpam-5388	26	1	(	(	PUNCT
ejpam-5388	26	2	cc	cc	NOUN
ejpam-5388	26	3	by	by	ADP
ejpam-5388	26	4	-	-	PUNCT
ejpam-5388	26	5	nc	nc	PROPN
ejpam-5388	26	6	4.0	4.0	NUM
ejpam-5388	26	7	)	)	PUNCT
ejpam-5388	26	8	h.	h.	NOUN
ejpam-5388	26	9	alsamir	alsamir	VERB
ejpam-5388	27	1	et	et	PROPN
ejpam-5388	27	2	al	al	PROPN
ejpam-5388	27	3	.	.	PUNCT
ejpam-5388	27	4	/	/	SYM
ejpam-5388	27	5	eur	eur	PROPN
ejpam-5388	27	6	.	.	PUNCT
ejpam-5388	28	1	j.	j.	PROPN
ejpam-5388	28	2	pure	pure	PROPN
ejpam-5388	28	3	appl	appl	PROPN
ejpam-5388	28	4	.	.	PROPN
ejpam-5388	28	5	math	math	PROPN
ejpam-5388	28	6	,	,	PUNCT
ejpam-5388	28	7	17	17	NUM
ejpam-5388	28	8	(	(	PUNCT
ejpam-5388	28	9	4	4	NUM
ejpam-5388	28	10	)	)	PUNCT
ejpam-5388	28	11	(	(	PUNCT
ejpam-5388	28	12	2024	2024	NUM
ejpam-5388	28	13	)	)	PUNCT
ejpam-5388	28	14	,	,	PUNCT
ejpam-5388	28	15	2492	2492	NUM
ejpam-5388	28	16	-	-	SYM
ejpam-5388	28	17	2504	2504	NUM
ejpam-5388	28	18	2493	2493	NUM
ejpam-5388	28	19	example	example	NOUN
ejpam-5388	28	20	1.3	1.3	NUM
ejpam-5388	28	21	.	.	PUNCT
ejpam-5388	29	1	let	let	VERB
ejpam-5388	29	2	𭟋	𭟋	PART
ejpam-5388	29	3	be	be	AUX
ejpam-5388	29	4	the	the	DET
ejpam-5388	29	5	set	set	NOUN
ejpam-5388	29	6	of	of	ADP
ejpam-5388	29	7	lebesgue	lebesgue	ADJ
ejpam-5388	29	8	measurable	measurable	ADJ
ejpam-5388	29	9	functions	function	NOUN
ejpam-5388	29	10	on	on	ADP
ejpam-5388	29	11	[	[	X
ejpam-5388	29	12	0,1	0,1	NUM
ejpam-5388	29	13	]	]	PUNCT
ejpam-5388	29	14	such	such	ADJ
ejpam-5388	29	15	that	that	SCONJ
ejpam-5388	29	16	∫	∫	PROPN
ejpam-5388	29	17	1	1	NUM
ejpam-5388	29	18	0	0	NUM
ejpam-5388	29	19	|	|	CCONJ
ejpam-5388	29	20	p(u	p(u	NOUN
ejpam-5388	29	21	)	)	PUNCT
ejpam-5388	29	22	|2	|2	PUNCT
ejpam-5388	29	23	<	<	X
ejpam-5388	30	1	+	+	ADJ
ejpam-5388	30	2	∞.	∞.	PROPN
ejpam-5388	30	3	define	define	VERB
ejpam-5388	30	4	λb(u	λb(u	NOUN
ejpam-5388	30	5	,	,	PUNCT
ejpam-5388	30	6	v	v	NOUN
ejpam-5388	30	7	)	)	PUNCT
ejpam-5388	31	1	=	=	SYM
ejpam-5388	31	2	∫	∫	PROPN
ejpam-5388	31	3	1	1	NUM
ejpam-5388	31	4	0	0	NUM
ejpam-5388	32	1	|	|	ADV
ejpam-5388	32	2	p(u)−	p(u)−	PROPN
ejpam-5388	32	3	q(u	q(u	NOUN
ejpam-5388	32	4	)	)	PUNCT
ejpam-5388	32	5	|2	|2	NUM
ejpam-5388	32	6	d(u	d(u	PROPN
ejpam-5388	32	7	)	)	PUNCT
ejpam-5388	32	8	.	.	PUNCT
ejpam-5388	33	1	then	then	ADV
ejpam-5388	33	2	λb	λb	INTJ
ejpam-5388	33	3	satisfies	satisfy	VERB
ejpam-5388	33	4	the	the	DET
ejpam-5388	33	5	following	follow	VERB
ejpam-5388	33	6	properties	property	NOUN
ejpam-5388	33	7	:	:	PUNCT
ejpam-5388	33	8	(	(	PUNCT
ejpam-5388	33	9	i	i	NOUN
ejpam-5388	33	10	)	)	PUNCT
ejpam-5388	33	11	λb(u	λb(u	PROPN
ejpam-5388	33	12	,	,	PUNCT
ejpam-5388	33	13	v	v	NOUN
ejpam-5388	33	14	)	)	PUNCT
ejpam-5388	33	15	=	=	SYM
ejpam-5388	33	16	0	0	NUM
ejpam-5388	33	17	⇔	⇔	X
ejpam-5388	33	18	u	u	PROPN
ejpam-5388	33	19	=	=	PROPN
ejpam-5388	33	20	v	v	PROPN
ejpam-5388	33	21	(	(	PUNCT
ejpam-5388	33	22	ii	ii	NOUN
ejpam-5388	33	23	)	)	PUNCT
ejpam-5388	33	24	λb(u	λb(u	PROPN
ejpam-5388	33	25	,	,	PUNCT
ejpam-5388	33	26	v	v	NOUN
ejpam-5388	33	27	)	)	PUNCT
ejpam-5388	33	28	=	=	SYM
ejpam-5388	33	29	λb(v	λb(v	NOUN
ejpam-5388	33	30	,	,	PUNCT
ejpam-5388	33	31	u	u	NOUN
ejpam-5388	33	32	)	)	PUNCT
ejpam-5388	33	33	,	,	PUNCT
ejpam-5388	33	34	for	for	ADP
ejpam-5388	33	35	all	all	DET
ejpam-5388	33	36	u	u	NOUN
ejpam-5388	33	37	,	,	PUNCT
ejpam-5388	33	38	v	v	NOUN
ejpam-5388	33	39	∈	∈	ADJ
ejpam-5388	33	40	𭟋	𭟋	X
ejpam-5388	33	41	(	(	PUNCT
ejpam-5388	33	42	iii	iii	NOUN
ejpam-5388	33	43	)	)	PUNCT
ejpam-5388	33	44	λb(u	λb(u	NOUN
ejpam-5388	33	45	,	,	PUNCT
ejpam-5388	33	46	v	v	NOUN
ejpam-5388	33	47	)	)	PUNCT
ejpam-5388	33	48	≤	≤	NOUN
ejpam-5388	33	49	2[λb(u	2[λb(u	NUM
ejpam-5388	33	50	,	,	PUNCT
ejpam-5388	33	51	w	w	NOUN
ejpam-5388	33	52	)	)	PUNCT
ejpam-5388	33	53	+	+	CCONJ
ejpam-5388	33	54	λb(w	λb(w	NOUN
ejpam-5388	33	55	,	,	PUNCT
ejpam-5388	33	56	v	v	NOUN
ejpam-5388	33	57	)	)	PUNCT
ejpam-5388	33	58	]	]	PUNCT
ejpam-5388	33	59	,	,	PUNCT
ejpam-5388	33	60	for	for	ADP
ejpam-5388	33	61	all	all	DET
ejpam-5388	33	62	u	u	NOUN
ejpam-5388	33	63	,	,	PUNCT
ejpam-5388	33	64	w	w	PROPN
ejpam-5388	33	65	,	,	PUNCT
ejpam-5388	33	66	v	v	NOUN
ejpam-5388	33	67	∈	∈	PROPN
ejpam-5388	33	68	𭟋	𭟋	NOUN
ejpam-5388	33	69	.	.	PUNCT
ejpam-5388	33	70	definition	definition	NOUN
ejpam-5388	33	71	1.4	1.4	NUM
ejpam-5388	33	72	.	.	PUNCT
ejpam-5388	34	1	(	(	PUNCT
ejpam-5388	34	2	[	[	X
ejpam-5388	34	3	20	20	NUM
ejpam-5388	34	4	]	]	PUNCT
ejpam-5388	34	5	)	)	PUNCT
ejpam-5388	34	6	let	let	AUX
ejpam-5388	34	7	(	(	PUNCT
ejpam-5388	34	8	𭟋	𭟋	NOUN
ejpam-5388	34	9	,	,	PUNCT
ejpam-5388	34	10	λb	λb	NOUN
ejpam-5388	34	11	)	)	PUNCT
ejpam-5388	34	12	be	be	AUX
ejpam-5388	34	13	a	a	DET
ejpam-5388	34	14	b	b	NOUN
ejpam-5388	34	15	-	-	PUNCT
ejpam-5388	34	16	metric	metric	ADJ
ejpam-5388	34	17	space	space	NOUN
ejpam-5388	34	18	.	.	PUNCT
ejpam-5388	35	1	then	then	ADV
ejpam-5388	35	2	a	a	DET
ejpam-5388	35	3	sequence	sequence	NOUN
ejpam-5388	35	4	{	{	PUNCT
ejpam-5388	35	5	un	un	PROPN
ejpam-5388	35	6	}	}	PUNCT
ejpam-5388	35	7	in	in	ADP
ejpam-5388	35	8	𭟋	𭟋	PROPN
ejpam-5388	35	9	is	be	AUX
ejpam-5388	35	10	called	call	VERB
ejpam-5388	35	11	:	:	PUNCT
ejpam-5388	35	12	(	(	PUNCT
ejpam-5388	35	13	i	i	NOUN
ejpam-5388	35	14	)	)	PUNCT
ejpam-5388	35	15	b	b	X
ejpam-5388	35	16	-	-	PUNCT
ejpam-5388	35	17	convergent	convergent	NOUN
ejpam-5388	35	18	if	if	SCONJ
ejpam-5388	35	19	and	and	CCONJ
ejpam-5388	35	20	only	only	ADV
ejpam-5388	35	21	if	if	SCONJ
ejpam-5388	35	22	there	there	PRON
ejpam-5388	35	23	exists	exist	VERB
ejpam-5388	35	24	v	v	ADP
ejpam-5388	35	25	∈	∈	PROPN
ejpam-5388	35	26	𭟋	𭟋	ADP
ejpam-5388	35	27	such	such	ADJ
ejpam-5388	35	28	that	that	PRON
ejpam-5388	35	29	λb(un	λb(un	PROPN
ejpam-5388	35	30	,	,	PUNCT
ejpam-5388	35	31	u	u	NOUN
ejpam-5388	35	32	)	)	PUNCT
ejpam-5388	35	33	→	→	SYM
ejpam-5388	35	34	0	0	NUM
ejpam-5388	35	35	,	,	PUNCT
ejpam-5388	35	36	as	as	SCONJ
ejpam-5388	35	37	n	n	PROPN
ejpam-5388	35	38	→	→	PUNCT
ejpam-5388	35	39	+	+	PROPN
ejpam-5388	35	40	∞.	∞.	PROPN
ejpam-5388	35	41	in	in	ADP
ejpam-5388	35	42	this	this	DET
ejpam-5388	35	43	case	case	NOUN
ejpam-5388	35	44	,	,	PUNCT
ejpam-5388	35	45	we	we	PRON
ejpam-5388	35	46	write	write	VERB
ejpam-5388	35	47	limn→+∞	limn→+∞	ADP
ejpam-5388	35	48	un	un	PROPN
ejpam-5388	35	49	=	=	PROPN
ejpam-5388	35	50	u.	u.	PROPN
ejpam-5388	35	51	(	(	PUNCT
ejpam-5388	35	52	2	2	NUM
ejpam-5388	35	53	)	)	PUNCT
ejpam-5388	35	54	b	b	NOUN
ejpam-5388	35	55	-	-	PUNCT
ejpam-5388	35	56	cauchy	cauchy	ADJ
ejpam-5388	35	57	if	if	SCONJ
ejpam-5388	35	58	and	and	CCONJ
ejpam-5388	35	59	only	only	ADV
ejpam-5388	35	60	if	if	SCONJ
ejpam-5388	35	61	λb(un	λb(un	PROPN
ejpam-5388	35	62	,	,	PUNCT
ejpam-5388	35	63	um	um	INTJ
ejpam-5388	35	64	)	)	PUNCT
ejpam-5388	35	65	=	=	SYM
ejpam-5388	35	66	0	0	NUM
ejpam-5388	35	67	as	as	ADP
ejpam-5388	35	68	n	n	CCONJ
ejpam-5388	35	69	,	,	PUNCT
ejpam-5388	35	70	m→	m→	NOUN
ejpam-5388	35	71	∞.	∞.	PROPN
ejpam-5388	35	72	proposition	proposition	NOUN
ejpam-5388	35	73	1.5	1.5	NUM
ejpam-5388	35	74	.	.	PUNCT
ejpam-5388	36	1	(	(	PUNCT
ejpam-5388	36	2	[	[	X
ejpam-5388	36	3	11	11	NUM
ejpam-5388	36	4	]	]	PUNCT
ejpam-5388	36	5	)	)	PUNCT
ejpam-5388	36	6	in	in	ADP
ejpam-5388	36	7	b	b	X
ejpam-5388	36	8	-	-	PUNCT
ejpam-5388	36	9	metric	metric	ADJ
ejpam-5388	36	10	space	space	NOUN
ejpam-5388	36	11	(	(	PUNCT
ejpam-5388	36	12	𭟋	𭟋	NOUN
ejpam-5388	36	13	,	,	PUNCT
ejpam-5388	36	14	λb	λb	PROPN
ejpam-5388	36	15	)	)	PUNCT
ejpam-5388	36	16	the	the	DET
ejpam-5388	36	17	following	follow	VERB
ejpam-5388	36	18	assertions	assertion	NOUN
ejpam-5388	36	19	holds	hold	VERB
ejpam-5388	36	20	:	:	PUNCT
ejpam-5388	36	21	(	(	PUNCT
ejpam-5388	36	22	1	1	X
ejpam-5388	36	23	)	)	PUNCT
ejpam-5388	36	24	a	a	DET
ejpam-5388	36	25	b	b	NOUN
ejpam-5388	36	26	-	-	PUNCT
ejpam-5388	36	27	convergent	convergent	ADJ
ejpam-5388	36	28	sequence	sequence	NOUN
ejpam-5388	36	29	has	have	VERB
ejpam-5388	36	30	a	a	DET
ejpam-5388	36	31	unique	unique	ADJ
ejpam-5388	36	32	limit	limit	NOUN
ejpam-5388	36	33	,	,	PUNCT
ejpam-5388	36	34	(	(	PUNCT
ejpam-5388	36	35	2	2	X
ejpam-5388	36	36	)	)	PUNCT
ejpam-5388	36	37	each	each	DET
ejpam-5388	36	38	b	b	NOUN
ejpam-5388	36	39	-	-	PUNCT
ejpam-5388	36	40	convergent	convergent	NOUN
ejpam-5388	36	41	is	be	AUX
ejpam-5388	36	42	b	b	NOUN
ejpam-5388	36	43	-	-	PUNCT
ejpam-5388	36	44	cauchy	cauchy	ADJ
ejpam-5388	36	45	,	,	PUNCT
ejpam-5388	36	46	(	(	PUNCT
ejpam-5388	36	47	3	3	X
ejpam-5388	36	48	)	)	PUNCT
ejpam-5388	36	49	in	in	ADP
ejpam-5388	36	50	general	general	ADJ
ejpam-5388	36	51	,	,	PUNCT
ejpam-5388	36	52	a	a	DET
ejpam-5388	36	53	b	b	X
ejpam-5388	36	54	-	-	ADJ
ejpam-5388	36	55	metric	metric	ADJ
ejpam-5388	36	56	is	be	AUX
ejpam-5388	36	57	not	not	PART
ejpam-5388	36	58	continuous	continuous	ADJ
ejpam-5388	36	59	.	.	PUNCT
ejpam-5388	37	1	proposition	proposition	NOUN
ejpam-5388	37	2	1.6	1.6	NUM
ejpam-5388	37	3	.	.	PUNCT
ejpam-5388	38	1	(	(	PUNCT
ejpam-5388	38	2	[	[	X
ejpam-5388	38	3	11	11	NUM
ejpam-5388	38	4	]	]	PUNCT
ejpam-5388	38	5	)	)	PUNCT
ejpam-5388	38	6	the	the	DET
ejpam-5388	38	7	b	b	X
ejpam-5388	38	8	-	-	PUNCT
ejpam-5388	38	9	metric	metric	ADJ
ejpam-5388	38	10	space	space	NOUN
ejpam-5388	38	11	(	(	PUNCT
ejpam-5388	38	12	𭟋	𭟋	NOUN
ejpam-5388	38	13	,	,	PUNCT
ejpam-5388	38	14	λb	λb	NOUN
ejpam-5388	38	15	)	)	PUNCT
ejpam-5388	38	16	is	be	AUX
ejpam-5388	38	17	complete	complete	ADJ
ejpam-5388	38	18	if	if	SCONJ
ejpam-5388	38	19	every	every	DET
ejpam-5388	38	20	cauchy	cauchy	ADJ
ejpam-5388	38	21	sequence	sequence	NOUN
ejpam-5388	38	22	in	in	ADP
ejpam-5388	38	23	𭟋	𭟋	DET
ejpam-5388	38	24	b	b	NOUN
ejpam-5388	38	25	-	-	PUNCT
ejpam-5388	38	26	converges	converge	NOUN
ejpam-5388	38	27	.	.	PUNCT
ejpam-5388	39	1	qawagneh	qawagneh	PROPN
ejpam-5388	39	2	et	et	PROPN
ejpam-5388	39	3	al	al	PROPN
ejpam-5388	39	4	.	.	PUNCT
ejpam-5388	40	1	[	[	X
ejpam-5388	40	2	19	19	NUM
ejpam-5388	40	3	]	]	PUNCT
ejpam-5388	40	4	introduced	introduce	VERB
ejpam-5388	40	5	the	the	DET
ejpam-5388	40	6	notion	notion	NOUN
ejpam-5388	40	7	of	of	ADP
ejpam-5388	40	8	triangular	triangular	NOUN
ejpam-5388	40	9	α	α	NOUN
ejpam-5388	40	10	-	-	ADJ
ejpam-5388	40	11	admissible	admissible	ADJ
ejpam-5388	40	12	with	with	ADP
ejpam-5388	40	13	respect	respect	NOUN
ejpam-5388	40	14	to	to	ADP
ejpam-5388	40	15	η	η	PROPN
ejpam-5388	40	16	for	for	ADP
ejpam-5388	40	17	p	p	PROPN
ejpam-5388	40	18	and	and	CCONJ
ejpam-5388	40	19	q	q	NOUN
ejpam-5388	40	20	on	on	ADP
ejpam-5388	40	21	a	a	DET
ejpam-5388	40	22	set	set	NOUN
ejpam-5388	40	23	𭟋	𭟋	NOUN
ejpam-5388	40	24	as	as	ADP
ejpam-5388	40	25	the	the	DET
ejpam-5388	40	26	following	following	NOUN
ejpam-5388	40	27	:	:	PUNCT
ejpam-5388	40	28	definition	definition	NOUN
ejpam-5388	40	29	1.7	1.7	NUM
ejpam-5388	40	30	.	.	PUNCT
ejpam-5388	41	1	(	(	PUNCT
ejpam-5388	41	2	[	[	X
ejpam-5388	41	3	20])let	20])let	NUM
ejpam-5388	41	4	p	p	NOUN
ejpam-5388	41	5	,	,	PUNCT
ejpam-5388	41	6	q	q	NOUN
ejpam-5388	41	7	:	:	PUNCT
ejpam-5388	41	8	𭟋	𭟋	PROPN
ejpam-5388	41	9	→	→	PUNCT
ejpam-5388	41	10	𭟋	𭟋	X
ejpam-5388	41	11	be	be	AUX
ejpam-5388	41	12	two	two	NUM
ejpam-5388	41	13	mappings	mapping	NOUN
ejpam-5388	41	14	and	and	CCONJ
ejpam-5388	41	15	α	α	NOUN
ejpam-5388	41	16	,	,	PUNCT
ejpam-5388	41	17	η	η	PROPN
ejpam-5388	41	18	:	:	PUNCT
ejpam-5388	41	19	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	41	20	→	→	SYM
ejpam-5388	41	21	r	r	NOUN
ejpam-5388	41	22	be	be	VERB
ejpam-5388	41	23	two	two	NUM
ejpam-5388	41	24	functions	function	NOUN
ejpam-5388	41	25	such	such	ADJ
ejpam-5388	41	26	that	that	SCONJ
ejpam-5388	41	27	the	the	DET
ejpam-5388	41	28	following	follow	VERB
ejpam-5388	41	29	assertions	assertion	NOUN
ejpam-5388	41	30	hold	hold	VERB
ejpam-5388	41	31	:	:	PUNCT
ejpam-5388	41	32	(	(	PUNCT
ejpam-5388	41	33	i	i	NOUN
ejpam-5388	41	34	)	)	PUNCT
ejpam-5388	41	35	if	if	SCONJ
ejpam-5388	41	36	α(u	α(u	PROPN
ejpam-5388	41	37	,	,	PUNCT
ejpam-5388	41	38	v	v	NOUN
ejpam-5388	41	39	)	)	PUNCT
ejpam-5388	41	40	≥	≥	NOUN
ejpam-5388	41	41	η(u	η(u	NOUN
ejpam-5388	41	42	,	,	PUNCT
ejpam-5388	41	43	v	v	NOUN
ejpam-5388	41	44	)	)	PUNCT
ejpam-5388	41	45	,	,	PUNCT
ejpam-5388	41	46	then	then	ADV
ejpam-5388	41	47	α(pu	α(pu	NUM
ejpam-5388	41	48	,	,	PUNCT
ejpam-5388	41	49	qv	qv	PROPN
ejpam-5388	41	50	)	)	PUNCT
ejpam-5388	41	51	≥	≥	PROPN
ejpam-5388	41	52	η(pu	η(pu	NOUN
ejpam-5388	41	53	,	,	PUNCT
ejpam-5388	41	54	qv	qv	X
ejpam-5388	41	55	)	)	PUNCT
ejpam-5388	41	56	,	,	PUNCT
ejpam-5388	41	57	and	and	CCONJ
ejpam-5388	41	58	α(pqu	α(pqu	NOUN
ejpam-5388	41	59	,	,	PUNCT
ejpam-5388	41	60	qpv	qpv	PROPN
ejpam-5388	41	61	)	)	PUNCT
ejpam-5388	41	62	≥	≥	PROPN
ejpam-5388	41	63	η(pqu	η(pqu	NOUN
ejpam-5388	41	64	,	,	PUNCT
ejpam-5388	41	65	qpv	qpv	PROPN
ejpam-5388	41	66	)	)	PUNCT
ejpam-5388	41	67	,	,	PUNCT
ejpam-5388	41	68	(	(	PUNCT
ejpam-5388	41	69	ii	ii	NOUN
ejpam-5388	41	70	)	)	PUNCT
ejpam-5388	41	71	if	if	SCONJ
ejpam-5388	41	72	α(u	α(u	PROPN
ejpam-5388	41	73	,	,	PUNCT
ejpam-5388	41	74	h	h	NOUN
ejpam-5388	41	75	)	)	PUNCT
ejpam-5388	41	76	≥	≥	NOUN
ejpam-5388	41	77	η(u	η(u	NOUN
ejpam-5388	41	78	,	,	PUNCT
ejpam-5388	41	79	h	h	NOUN
ejpam-5388	41	80	)	)	PUNCT
ejpam-5388	41	81	,	,	PUNCT
ejpam-5388	41	82	and	and	CCONJ
ejpam-5388	41	83	α(h	α(h	NOUN
ejpam-5388	41	84	,	,	PUNCT
ejpam-5388	41	85	v	v	NOUN
ejpam-5388	41	86	)	)	PUNCT
ejpam-5388	41	87	≥	≥	NOUN
ejpam-5388	41	88	η(h	η(h	PROPN
ejpam-5388	41	89	,	,	PUNCT
ejpam-5388	41	90	v	v	NOUN
ejpam-5388	41	91	)	)	PUNCT
ejpam-5388	41	92	,	,	PUNCT
ejpam-5388	41	93	then	then	ADV
ejpam-5388	41	94	α(u	α(u	PROPN
ejpam-5388	41	95	,	,	PUNCT
ejpam-5388	41	96	v	v	NOUN
ejpam-5388	41	97	)	)	PUNCT
ejpam-5388	41	98	≥	≥	NOUN
ejpam-5388	41	99	η(u	η(u	NOUN
ejpam-5388	41	100	,	,	PUNCT
ejpam-5388	41	101	v	v	NOUN
ejpam-5388	41	102	)	)	PUNCT
ejpam-5388	41	103	,	,	PUNCT
ejpam-5388	41	104	lemma	lemma	PROPN
ejpam-5388	41	105	1.8	1.8	NUM
ejpam-5388	41	106	.	.	PUNCT
ejpam-5388	42	1	(	(	PUNCT
ejpam-5388	42	2	[	[	X
ejpam-5388	42	3	22	22	NUM
ejpam-5388	42	4	]	]	PUNCT
ejpam-5388	42	5	)	)	PUNCT
ejpam-5388	42	6	let	let	VERB
ejpam-5388	42	7	p	p	PRON
ejpam-5388	42	8	,	,	PUNCT
ejpam-5388	42	9	q	q	NOUN
ejpam-5388	42	10	:	:	PUNCT
ejpam-5388	42	11	𭟋	𭟋	PROPN
ejpam-5388	42	12	→	→	PUNCT
ejpam-5388	42	13	𭟋	𭟋	X
ejpam-5388	42	14	be	be	AUX
ejpam-5388	42	15	two	two	NUM
ejpam-5388	42	16	mappings	mapping	NOUN
ejpam-5388	42	17	and	and	CCONJ
ejpam-5388	42	18	α	α	NOUN
ejpam-5388	42	19	,	,	PUNCT
ejpam-5388	42	20	η	η	PROPN
ejpam-5388	42	21	:	:	PUNCT
ejpam-5388	42	22	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	42	23	→	→	SYM
ejpam-5388	42	24	r	r	NOUN
ejpam-5388	42	25	be	be	VERB
ejpam-5388	42	26	two	two	NUM
ejpam-5388	42	27	functions	function	NOUN
ejpam-5388	42	28	such	such	ADJ
ejpam-5388	42	29	that	that	SCONJ
ejpam-5388	42	30	the	the	DET
ejpam-5388	42	31	pair	pair	NOUN
ejpam-5388	42	32	(	(	PUNCT
ejpam-5388	42	33	p	p	X
ejpam-5388	42	34	,	,	PUNCT
ejpam-5388	42	35	q	q	NOUN
ejpam-5388	42	36	)	)	PUNCT
ejpam-5388	42	37	is	be	AUX
ejpam-5388	42	38	triangular	triangular	ADJ
ejpam-5388	42	39	α	α	NOUN
ejpam-5388	42	40	-	-	ADJ
ejpam-5388	42	41	admissible	admissible	ADJ
ejpam-5388	42	42	with	with	ADP
ejpam-5388	42	43	respect	respect	NOUN
ejpam-5388	42	44	to	to	ADP
ejpam-5388	42	45	η	η	PROPN
ejpam-5388	42	46	.	.	PROPN
ejpam-5388	42	47	assume	assume	VERB
ejpam-5388	42	48	that	that	SCONJ
ejpam-5388	42	49	there	there	PRON
ejpam-5388	42	50	exist	exist	VERB
ejpam-5388	42	51	u0	u0	ADJ
ejpam-5388	42	52	∈	∈	PROPN
ejpam-5388	42	53	𭟋	𭟋	ADP
ejpam-5388	42	54	such	such	ADJ
ejpam-5388	42	55	that	that	SCONJ
ejpam-5388	42	56	α(u0	α(u0	NOUN
ejpam-5388	42	57	,	,	PUNCT
ejpam-5388	42	58	pu0	pu0	NOUN
ejpam-5388	42	59	)	)	PUNCT
ejpam-5388	42	60	≥	≥	PROPN
ejpam-5388	42	61	η(u0	η(u0	NOUN
ejpam-5388	42	62	,	,	PUNCT
ejpam-5388	42	63	pu0	pu0	NOUN
ejpam-5388	42	64	)	)	PUNCT
ejpam-5388	42	65	.	.	PUNCT
ejpam-5388	43	1	define	define	VERB
ejpam-5388	43	2	a	a	DET
ejpam-5388	43	3	sequence	sequence	NOUN
ejpam-5388	43	4	{	{	PUNCT
ejpam-5388	43	5	un	un	PROPN
ejpam-5388	43	6	}	}	PUNCT
ejpam-5388	43	7	in	in	ADP
ejpam-5388	43	8	𭟋	𭟋	ADP
ejpam-5388	43	9	by	by	ADP
ejpam-5388	43	10	pu2n	pu2n	PROPN
ejpam-5388	43	11	=	=	SYM
ejpam-5388	43	12	u2n+1	u2n+1	PROPN
ejpam-5388	43	13	and	and	CCONJ
ejpam-5388	43	14	qu2n+1	qu2n+1	PROPN
ejpam-5388	43	15	=	=	SYM
ejpam-5388	43	16	u2n+2	u2n+2	PROPN
ejpam-5388	43	17	.	.	PUNCT
ejpam-5388	44	1	then	then	ADV
ejpam-5388	44	2	α(un	α(un	PROPN
ejpam-5388	44	3	,	,	PUNCT
ejpam-5388	44	4	um	um	INTJ
ejpam-5388	44	5	)	)	PUNCT
ejpam-5388	44	6	≥	≥	NOUN
ejpam-5388	44	7	η(un	η(un	PROPN
ejpam-5388	44	8	,	,	PUNCT
ejpam-5388	44	9	um	um	INTJ
ejpam-5388	44	10	)	)	PUNCT
ejpam-5388	44	11	for	for	ADP
ejpam-5388	44	12	all	all	DET
ejpam-5388	44	13	m	m	PROPN
ejpam-5388	44	14	,	,	PUNCT
ejpam-5388	44	15	n	n	PROPN
ejpam-5388	44	16	∈	∈	PROPN
ejpam-5388	44	17	n	n	NOUN
ejpam-5388	44	18	with	with	ADP
ejpam-5388	44	19	n	n	CCONJ
ejpam-5388	44	20	<	<	X
ejpam-5388	44	21	m.	m.	NOUN
ejpam-5388	44	22	berinde	berinde	NOUN
ejpam-5388	45	1	[	[	X
ejpam-5388	45	2	[	[	X
ejpam-5388	45	3	6],[7],[8],[9],[10	6],[7],[8],[9],[10	NUM
ejpam-5388	45	4	]	]	X
ejpam-5388	45	5	]	]	PUNCT
ejpam-5388	45	6	presented	present	VERB
ejpam-5388	45	7	many	many	ADJ
ejpam-5388	45	8	interesting	interesting	ADJ
ejpam-5388	45	9	fixed	fix	VERB
ejpam-5388	45	10	-	-	PUNCT
ejpam-5388	45	11	point	point	NOUN
ejpam-5388	45	12	results	result	NOUN
ejpam-5388	45	13	for	for	ADP
ejpam-5388	45	14	various	various	ADJ
ejpam-5388	45	15	types	type	NOUN
ejpam-5388	45	16	of	of	ADP
ejpam-5388	45	17	contraction	contraction	NOUN
ejpam-5388	45	18	mappings	mapping	NOUN
ejpam-5388	45	19	.	.	PUNCT
ejpam-5388	46	1	in	in	ADP
ejpam-5388	46	2	[	[	X
ejpam-5388	46	3	8	8	NUM
ejpam-5388	46	4	]	]	PUNCT
ejpam-5388	46	5	and	and	CCONJ
ejpam-5388	46	6	[	[	X
ejpam-5388	46	7	9	9	NUM
ejpam-5388	46	8	]	]	PUNCT
ejpam-5388	46	9	,	,	PUNCT
ejpam-5388	46	10	he	he	PRON
ejpam-5388	46	11	defined	define	VERB
ejpam-5388	46	12	the	the	DET
ejpam-5388	46	13	almost	almost	ADV
ejpam-5388	46	14	contraction	contraction	NOUN
ejpam-5388	46	15	map	map	NOUN
ejpam-5388	46	16	as	as	SCONJ
ejpam-5388	46	17	follows	follow	VERB
ejpam-5388	46	18	.	.	PUNCT
ejpam-5388	47	1	definition	definition	NOUN
ejpam-5388	47	2	1.9	1.9	NUM
ejpam-5388	47	3	.	.	PUNCT
ejpam-5388	48	1	let	let	AUX
ejpam-5388	48	2	(	(	PUNCT
ejpam-5388	48	3	𭟋	𭟋	NOUN
ejpam-5388	48	4	,	,	PUNCT
ejpam-5388	48	5	λ	λ	NOUN
ejpam-5388	48	6	)	)	PUNCT
ejpam-5388	48	7	be	be	VERB
ejpam-5388	48	8	a	a	DET
ejpam-5388	48	9	metric	metric	ADJ
ejpam-5388	48	10	space	space	NOUN
ejpam-5388	48	11	.	.	PUNCT
ejpam-5388	49	1	a	a	DET
ejpam-5388	49	2	map	map	NOUN
ejpam-5388	49	3	p	p	X
ejpam-5388	49	4	:	:	PUNCT
ejpam-5388	49	5	𭟋	𭟋	PROPN
ejpam-5388	49	6	→	→	SYM
ejpam-5388	49	7	𭟋	𭟋	X
ejpam-5388	49	8	is	be	AUX
ejpam-5388	49	9	called	call	VERB
ejpam-5388	49	10	an	an	DET
ejpam-5388	49	11	almost	almost	ADV
ejpam-5388	49	12	contraction	contraction	NOUN
ejpam-5388	49	13	if	if	SCONJ
ejpam-5388	49	14	there	there	PRON
ejpam-5388	49	15	exist	exist	VERB
ejpam-5388	49	16	a	a	DET
ejpam-5388	49	17	constant	constant	ADJ
ejpam-5388	49	18	λ	λ	X
ejpam-5388	49	19	∈	∈	PROPN
ejpam-5388	50	1	[	[	X
ejpam-5388	50	2	0	0	NUM
ejpam-5388	50	3	,	,	PUNCT
ejpam-5388	50	4	1	1	NUM
ejpam-5388	50	5	)	)	PUNCT
ejpam-5388	50	6	and	and	CCONJ
ejpam-5388	50	7	some	some	DET
ejpam-5388	50	8	l	l	NOUN
ejpam-5388	50	9	≥	≥	NOUN
ejpam-5388	50	10	0	0	NUM
ejpam-5388	51	1	such	such	ADJ
ejpam-5388	51	2	that	that	SCONJ
ejpam-5388	51	3	:	:	PUNCT
ejpam-5388	51	4	λ(pu	λ(pu	NUM
ejpam-5388	51	5	,	,	PUNCT
ejpam-5388	51	6	pv	pv	NOUN
ejpam-5388	51	7	)	)	PUNCT
ejpam-5388	51	8	≤	≤	NOUN
ejpam-5388	51	9	λλ(u	λλ(u	NUM
ejpam-5388	51	10	,	,	PUNCT
ejpam-5388	51	11	v	v	NOUN
ejpam-5388	51	12	)	)	PUNCT
ejpam-5388	51	13	+	+	CCONJ
ejpam-5388	51	14	lλ(v	lλ(v	NUM
ejpam-5388	51	15	,	,	PUNCT
ejpam-5388	51	16	pu	pu	PROPN
ejpam-5388	51	17	)	)	PUNCT
ejpam-5388	51	18	for	for	ADP
ejpam-5388	51	19	all	all	DET
ejpam-5388	51	20	u	u	NOUN
ejpam-5388	51	21	,	,	PUNCT
ejpam-5388	51	22	v	v	NOUN
ejpam-5388	51	23	∈	∈	PROPN
ejpam-5388	51	24	𭟋	𭟋	NOUN
ejpam-5388	51	25	.	.	PUNCT
ejpam-5388	51	26	let	let	VERB
ejpam-5388	51	27	φ	φ	PROPN
ejpam-5388	51	28	the	the	DET
ejpam-5388	51	29	set	set	NOUN
ejpam-5388	51	30	of	of	ADP
ejpam-5388	51	31	all	all	DET
ejpam-5388	51	32	increasing	increase	VERB
ejpam-5388	51	33	and	and	CCONJ
ejpam-5388	51	34	continuous	continuous	ADJ
ejpam-5388	51	35	functions	function	NOUN
ejpam-5388	51	36	φ	φ	X
ejpam-5388	51	37	:	:	PUNCT
ejpam-5388	52	1	[	[	X
ejpam-5388	52	2	0,+∞	0,+∞	NUM
ejpam-5388	52	3	)	)	PUNCT
ejpam-5388	52	4	→	→	PUNCT
ejpam-5388	53	1	[	[	X
ejpam-5388	53	2	0,+∞	0,+∞	NUM
ejpam-5388	53	3	)	)	PUNCT
ejpam-5388	53	4	and	and	CCONJ
ejpam-5388	53	5	let	let	VERB
ejpam-5388	53	6	∆	∆	PROPN
ejpam-5388	53	7	be	be	AUX
ejpam-5388	53	8	the	the	DET
ejpam-5388	53	9	set	set	NOUN
ejpam-5388	53	10	of	of	ADP
ejpam-5388	53	11	all	all	DET
ejpam-5388	53	12	lower	low	ADJ
ejpam-5388	53	13	semi	semi	ADJ
ejpam-5388	53	14	-	-	ADJ
ejpam-5388	53	15	continuous	continuous	ADJ
ejpam-5388	53	16	functions	function	NOUN
ejpam-5388	53	17	ψ	ψ	NOUN
ejpam-5388	53	18	:	:	PUNCT
ejpam-5388	54	1	[	[	X
ejpam-5388	54	2	0,+∞	0,+∞	NUM
ejpam-5388	54	3	)	)	PUNCT
ejpam-5388	54	4	→	→	PUNCT
ejpam-5388	55	1	[	[	X
ejpam-5388	55	2	0,+∞	0,+∞	NUM
ejpam-5388	55	3	)	)	PUNCT
ejpam-5388	55	4	with	with	ADP
ejpam-5388	55	5	ψ(b	ψ(b	NOUN
ejpam-5388	55	6	)	)	PUNCT
ejpam-5388	56	1	=	=	SYM
ejpam-5388	57	1	b	b	X
ejpam-5388	58	1	if	if	SCONJ
ejpam-5388	58	2	and	and	CCONJ
ejpam-5388	58	3	only	only	ADV
ejpam-5388	58	4	if	if	SCONJ
ejpam-5388	58	5	b	b	X
ejpam-5388	58	6	=	=	SYM
ejpam-5388	58	7	0	0	PROPN
ejpam-5388	58	8	.	.	PUNCT
ejpam-5388	58	9	h.	h.	PROPN
ejpam-5388	58	10	alsamir	alsamir	VERB
ejpam-5388	58	11	et	et	PROPN
ejpam-5388	58	12	al	al	PROPN
ejpam-5388	58	13	.	.	PUNCT
ejpam-5388	58	14	/	/	SYM
ejpam-5388	58	15	eur	eur	PROPN
ejpam-5388	58	16	.	.	PUNCT
ejpam-5388	59	1	j.	j.	PROPN
ejpam-5388	59	2	pure	pure	PROPN
ejpam-5388	59	3	appl	appl	PROPN
ejpam-5388	59	4	.	.	PROPN
ejpam-5388	59	5	math	math	PROPN
ejpam-5388	59	6	,	,	PUNCT
ejpam-5388	59	7	17	17	NUM
ejpam-5388	59	8	(	(	PUNCT
ejpam-5388	59	9	4	4	NUM
ejpam-5388	59	10	)	)	PUNCT
ejpam-5388	59	11	(	(	PUNCT
ejpam-5388	59	12	2024	2024	NUM
ejpam-5388	59	13	)	)	PUNCT
ejpam-5388	59	14	,	,	PUNCT
ejpam-5388	59	15	2492	2492	NUM
ejpam-5388	59	16	-	-	SYM
ejpam-5388	59	17	2504	2504	NUM
ejpam-5388	59	18	2494	2494	NUM
ejpam-5388	59	19	2	2	NUM
ejpam-5388	59	20	.	.	PUNCT
ejpam-5388	60	1	an	an	DET
ejpam-5388	60	2	λ(s	λ(s	PROPN
ejpam-5388	60	3	,	,	PUNCT
ejpam-5388	60	4	φ	φ	NOUN
ejpam-5388	60	5	,	,	PUNCT
ejpam-5388	60	6	ψ	ψ	SYM
ejpam-5388	60	7	,	,	PUNCT
ejpam-5388	60	8	l)generalized	l)generalize	VERB
ejpam-5388	60	9	berinde	berinde	NOUN
ejpam-5388	60	10	type	type	NOUN
ejpam-5388	60	11	contraction	contraction	NOUN
ejpam-5388	60	12	mapping	mapping	NOUN
ejpam-5388	60	13	now	now	ADV
ejpam-5388	60	14	,	,	PUNCT
ejpam-5388	60	15	we	we	PRON
ejpam-5388	60	16	will	will	AUX
ejpam-5388	60	17	present	present	VERB
ejpam-5388	60	18	λ(s	λ(s	PROPN
ejpam-5388	60	19	,	,	PUNCT
ejpam-5388	60	20	φ,ϕ,l)generalized	φ,ϕ,l)generalize	VERB
ejpam-5388	60	21	berinde	berinde	NOUN
ejpam-5388	60	22	type	type	NOUN
ejpam-5388	60	23	contraction	contraction	NOUN
ejpam-5388	60	24	mapping	mapping	NOUN
ejpam-5388	60	25	prove	prove	VERB
ejpam-5388	60	26	our	our	PRON
ejpam-5388	60	27	main	main	ADJ
ejpam-5388	60	28	result	result	NOUN
ejpam-5388	60	29	for	for	ADP
ejpam-5388	60	30	such	such	ADJ
ejpam-5388	60	31	class	class	NOUN
ejpam-5388	60	32	of	of	ADP
ejpam-5388	60	33	contractions	contraction	NOUN
ejpam-5388	60	34	in	in	ADP
ejpam-5388	60	35	the	the	DET
ejpam-5388	60	36	framework	framework	NOUN
ejpam-5388	60	37	of	of	ADP
ejpam-5388	60	38	b	b	NOUN
ejpam-5388	60	39	-	-	PUNCT
ejpam-5388	60	40	metric	metric	ADJ
ejpam-5388	60	41	spaces	space	NOUN
ejpam-5388	60	42	.	.	PUNCT
ejpam-5388	61	1	definition	definition	NOUN
ejpam-5388	61	2	2.1	2.1	NUM
ejpam-5388	61	3	.	.	PUNCT
ejpam-5388	62	1	let	let	AUX
ejpam-5388	62	2	(	(	PUNCT
ejpam-5388	62	3	𭟋	𭟋	NOUN
ejpam-5388	62	4	,	,	PUNCT
ejpam-5388	62	5	λb	λb	NOUN
ejpam-5388	62	6	)	)	PUNCT
ejpam-5388	62	7	be	be	AUX
ejpam-5388	62	8	a	a	DET
ejpam-5388	62	9	b	b	NOUN
ejpam-5388	62	10	-	-	PUNCT
ejpam-5388	62	11	metric	metric	ADJ
ejpam-5388	62	12	space	space	NOUN
ejpam-5388	62	13	with	with	ADP
ejpam-5388	62	14	parameter	parameter	PROPN
ejpam-5388	62	15	s	s	PART
ejpam-5388	62	16	≥	≥	NOUN
ejpam-5388	62	17	1	1	NUM
ejpam-5388	62	18	and	and	CCONJ
ejpam-5388	62	19	p	p	X
ejpam-5388	62	20	,	,	PUNCT
ejpam-5388	62	21	q	q	NOUN
ejpam-5388	62	22	:	:	PUNCT
ejpam-5388	62	23	𭟋	𭟋	PROPN
ejpam-5388	62	24	→	→	PUNCT
ejpam-5388	62	25	𭟋	𭟋	X
ejpam-5388	62	26	be	be	AUX
ejpam-5388	62	27	a	a	DET
ejpam-5388	62	28	two	two	NUM
ejpam-5388	62	29	mappings	mapping	NOUN
ejpam-5388	62	30	.	.	PUNCT
ejpam-5388	63	1	then	then	ADV
ejpam-5388	63	2	we	we	PRON
ejpam-5388	63	3	consider	consider	VERB
ejpam-5388	63	4	that	that	SCONJ
ejpam-5388	63	5	the	the	DET
ejpam-5388	63	6	pair	pair	NOUN
ejpam-5388	63	7	(	(	PUNCT
ejpam-5388	63	8	p	p	X
ejpam-5388	63	9	,	,	PUNCT
ejpam-5388	63	10	q	q	NOUN
ejpam-5388	63	11	)	)	PUNCT
ejpam-5388	63	12	is	be	AUX
ejpam-5388	63	13	λ(s	λ(s	PROPN
ejpam-5388	63	14	,	,	PUNCT
ejpam-5388	63	15	φ,ϕ,l)-generalized	φ,ϕ,l)-generalize	VERB
ejpam-5388	63	16	berinde	berinde	NOUN
ejpam-5388	63	17	type	type	NOUN
ejpam-5388	63	18	contraction	contraction	NOUN
ejpam-5388	63	19	mapping	mapping	NOUN
ejpam-5388	63	20	if	if	SCONJ
ejpam-5388	63	21	there	there	PRON
ejpam-5388	63	22	exists	exist	VERB
ejpam-5388	63	23	α	α	NUM
ejpam-5388	63	24	,	,	PUNCT
ejpam-5388	63	25	η	η	PROPN
ejpam-5388	63	26	:	:	PUNCT
ejpam-5388	63	27	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	63	28	→	→	SYM
ejpam-5388	63	29	r	r	NOUN
ejpam-5388	63	30	be	be	VERB
ejpam-5388	63	31	two	two	NUM
ejpam-5388	63	32	mappings	mapping	NOUN
ejpam-5388	63	33	,	,	PUNCT
ejpam-5388	63	34	φ	φ	PROPN
ejpam-5388	63	35	∈	∈	PROPN
ejpam-5388	63	36	ω	ω	PROPN
ejpam-5388	63	37	,	,	PUNCT
ejpam-5388	63	38	ϕ	ϕ	PROPN
ejpam-5388	63	39	∈	∈	PROPN
ejpam-5388	63	40	φ	φ	PROPN
ejpam-5388	63	41	,	,	PUNCT
ejpam-5388	63	42	λ	λ	PROPN
ejpam-5388	63	43	∈	∈	PROPN
ejpam-5388	64	1	[	[	X
ejpam-5388	64	2	0	0	NUM
ejpam-5388	64	3	,	,	PUNCT
ejpam-5388	64	4	1	1	NUM
ejpam-5388	64	5	)	)	PUNCT
ejpam-5388	64	6	,	,	PUNCT
ejpam-5388	65	1	l	l	X
ejpam-5388	65	2	≥	≥	X
ejpam-5388	65	3	0	0	NUM
ejpam-5388	65	4	such	such	ADJ
ejpam-5388	65	5	that	that	SCONJ
ejpam-5388	65	6	φ	φ	PROPN
ejpam-5388	65	7	(	(	PUNCT
ejpam-5388	65	8	s2λb(pu	s2λb(pu	PROPN
ejpam-5388	65	9	,	,	PUNCT
ejpam-5388	65	10	qv	qv	X
ejpam-5388	65	11	)	)	PUNCT
ejpam-5388	65	12	)	)	PUNCT
ejpam-5388	65	13	≤	≤	NUM
ejpam-5388	66	1	λ	λ	PROPN
ejpam-5388	66	2	[	[	X
ejpam-5388	66	3	φ	φ	X
ejpam-5388	66	4	(	(	PUNCT
ejpam-5388	66	5	mλb	mλb	PROPN
ejpam-5388	66	6	(	(	PUNCT
ejpam-5388	66	7	u	u	NOUN
ejpam-5388	66	8	,	,	PUNCT
ejpam-5388	66	9	v))−	v))−	NOUN
ejpam-5388	66	10	ϕ	ϕ	NOUN
ejpam-5388	66	11	(	(	PUNCT
ejpam-5388	66	12	mλb	mλb	PROPN
ejpam-5388	66	13	(	(	PUNCT
ejpam-5388	66	14	u	u	NOUN
ejpam-5388	66	15	,	,	PUNCT
ejpam-5388	66	16	v	v	NOUN
ejpam-5388	66	17	)	)	PUNCT
ejpam-5388	66	18	)	)	PUNCT
ejpam-5388	67	1	+	+	CCONJ
ejpam-5388	67	2	lnλb	lnλb	ADJ
ejpam-5388	67	3	(	(	PUNCT
ejpam-5388	67	4	u	u	NOUN
ejpam-5388	67	5	,	,	PUNCT
ejpam-5388	67	6	v	v	NOUN
ejpam-5388	67	7	)	)	PUNCT
ejpam-5388	67	8	]	]	PUNCT
ejpam-5388	67	9	,	,	PUNCT
ejpam-5388	67	10	(	(	PUNCT
ejpam-5388	67	11	2.1	2.1	NUM
ejpam-5388	67	12	)	)	PUNCT
ejpam-5388	67	13	holds	hold	VERB
ejpam-5388	67	14	for	for	ADP
ejpam-5388	67	15	all	all	DET
ejpam-5388	67	16	u	u	NOUN
ejpam-5388	67	17	,	,	PUNCT
ejpam-5388	67	18	v	v	NOUN
ejpam-5388	67	19	∈	∈	PROPN
ejpam-5388	67	20	𭟋	𭟋	NOUN
ejpam-5388	67	21	,	,	PUNCT
ejpam-5388	67	22	where	where	SCONJ
ejpam-5388	67	23	mλb	mλb	PROPN
ejpam-5388	67	24	(	(	PUNCT
ejpam-5388	67	25	u	u	NOUN
ejpam-5388	67	26	,	,	PUNCT
ejpam-5388	67	27	v	v	NOUN
ejpam-5388	67	28	)	)	PUNCT
ejpam-5388	67	29	=	=	SYM
ejpam-5388	67	30	max	max	PROPN
ejpam-5388	67	31	{	{	PUNCT
ejpam-5388	67	32	λb(u	λb(u	PROPN
ejpam-5388	67	33	,	,	PUNCT
ejpam-5388	67	34	v),λb(u	v),λb(u	PROPN
ejpam-5388	67	35	,	,	PUNCT
ejpam-5388	67	36	pu),λb(v	pu),λb(v	NOUN
ejpam-5388	67	37	,	,	PUNCT
ejpam-5388	67	38	qv	qv	X
ejpam-5388	67	39	)	)	PUNCT
ejpam-5388	67	40	,	,	PUNCT
ejpam-5388	67	41	λb(u	λb(u	NUM
ejpam-5388	67	42	,	,	PUNCT
ejpam-5388	67	43	qv	qv	X
ejpam-5388	67	44	)	)	PUNCT
ejpam-5388	68	1	+	+	CCONJ
ejpam-5388	68	2	λb(pu	λb(pu	PROPN
ejpam-5388	68	3	,	,	PUNCT
ejpam-5388	68	4	v	v	NOUN
ejpam-5388	68	5	)	)	PUNCT
ejpam-5388	68	6	2s[1	2s[1	PROPN
ejpam-5388	69	1	+	+	CCONJ
ejpam-5388	69	2	λb(pu	λb(pu	PROPN
ejpam-5388	69	3	,	,	PUNCT
ejpam-5388	69	4	v	v	NOUN
ejpam-5388	69	5	)	)	PUNCT
ejpam-5388	69	6	]	]	PUNCT
ejpam-5388	69	7	}	}	PUNCT
ejpam-5388	69	8	,	,	PUNCT
ejpam-5388	69	9	and	and	CCONJ
ejpam-5388	69	10	nλb	nλb	PROPN
ejpam-5388	69	11	(	(	PUNCT
ejpam-5388	69	12	u	u	NOUN
ejpam-5388	69	13	,	,	PUNCT
ejpam-5388	69	14	v	v	NOUN
ejpam-5388	69	15	)	)	PUNCT
ejpam-5388	69	16	=	=	SYM
ejpam-5388	69	17	min	min	NOUN
ejpam-5388	69	18	{	{	PUNCT
ejpam-5388	69	19	λb(u	λb(u	PROPN
ejpam-5388	69	20	,	,	PUNCT
ejpam-5388	69	21	v),λb(u	v),λb(u	PROPN
ejpam-5388	69	22	,	,	PUNCT
ejpam-5388	69	23	pu),λb(v	pu),λb(v	NOUN
ejpam-5388	69	24	,	,	PUNCT
ejpam-5388	69	25	qv),λb(v	qv),λb(v	NOUN
ejpam-5388	69	26	,	,	PUNCT
ejpam-5388	69	27	pu	pu	PROPN
ejpam-5388	69	28	)	)	PUNCT
ejpam-5388	69	29	}	}	PUNCT
ejpam-5388	69	30	.	.	PUNCT
ejpam-5388	70	1	now	now	ADV
ejpam-5388	70	2	we	we	PRON
ejpam-5388	70	3	begin	begin	VERB
ejpam-5388	70	4	with	with	ADP
ejpam-5388	70	5	our	our	PRON
ejpam-5388	70	6	first	first	ADJ
ejpam-5388	70	7	result	result	NOUN
ejpam-5388	70	8	.	.	PUNCT
ejpam-5388	71	1	theorem	theorem	VERB
ejpam-5388	71	2	2.2	2.2	NUM
ejpam-5388	71	3	.	.	PUNCT
ejpam-5388	72	1	let	let	AUX
ejpam-5388	72	2	(	(	PUNCT
ejpam-5388	72	3	𭟋	𭟋	NOUN
ejpam-5388	72	4	,	,	PUNCT
ejpam-5388	72	5	λb	λb	NOUN
ejpam-5388	72	6	)	)	PUNCT
ejpam-5388	72	7	be	be	AUX
ejpam-5388	72	8	a	a	DET
ejpam-5388	72	9	complete	complete	ADJ
ejpam-5388	72	10	b	b	X
ejpam-5388	72	11	-	-	PUNCT
ejpam-5388	72	12	metric	metric	ADJ
ejpam-5388	72	13	space	space	NOUN
ejpam-5388	72	14	with	with	ADP
ejpam-5388	72	15	the	the	DET
ejpam-5388	72	16	constant	constant	ADJ
ejpam-5388	72	17	s	s	PART
ejpam-5388	72	18	≥	≥	NOUN
ejpam-5388	72	19	1	1	NUM
ejpam-5388	72	20	,	,	PUNCT
ejpam-5388	72	21	and	and	CCONJ
ejpam-5388	72	22	(	(	PUNCT
ejpam-5388	72	23	p	p	X
ejpam-5388	72	24	,	,	PUNCT
ejpam-5388	72	25	q	q	NOUN
ejpam-5388	72	26	)	)	PUNCT
ejpam-5388	72	27	be	be	AUX
ejpam-5388	72	28	two	two	NUM
ejpam-5388	72	29	self	self	NOUN
ejpam-5388	72	30	-	-	PUNCT
ejpam-5388	72	31	mappings	mapping	NOUN
ejpam-5388	72	32	on	on	ADP
ejpam-5388	72	33	𭟋	𭟋	ADP
ejpam-5388	72	34	.	.	PROPN
ejpam-5388	73	1	suppose	suppose	VERB
ejpam-5388	73	2	that	that	SCONJ
ejpam-5388	73	3	α	α	PROPN
ejpam-5388	73	4	,	,	PUNCT
ejpam-5388	73	5	η	η	PROPN
ejpam-5388	73	6	:	:	PUNCT
ejpam-5388	73	7	𭟋	𭟋	PROPN
ejpam-5388	73	8	×	×	NOUN
ejpam-5388	73	9	𭟋	𭟋	PROPN
ejpam-5388	73	10	→	→	X
ejpam-5388	73	11	r	r	NOUN
ejpam-5388	73	12	are	be	AUX
ejpam-5388	73	13	two	two	NUM
ejpam-5388	73	14	functions	function	NOUN
ejpam-5388	73	15	.	.	PUNCT
ejpam-5388	74	1	assume	assume	VERB
ejpam-5388	74	2	that	that	SCONJ
ejpam-5388	74	3	the	the	DET
ejpam-5388	74	4	following	follow	VERB
ejpam-5388	74	5	conditions	condition	NOUN
ejpam-5388	74	6	hold	hold	VERB
ejpam-5388	74	7	:	:	PUNCT
ejpam-5388	74	8	(	(	PUNCT
ejpam-5388	74	9	i	i	NOUN
ejpam-5388	74	10	)	)	PUNCT
ejpam-5388	74	11	λ(s	λ(s	PROPN
ejpam-5388	74	12	,	,	PUNCT
ejpam-5388	74	13	φ,ϕ,l)-berinde	φ,ϕ,l)-berinde	NOUN
ejpam-5388	74	14	type	type	NOUN
ejpam-5388	74	15	contraction	contraction	NOUN
ejpam-5388	74	16	mapping	mapping	NOUN
ejpam-5388	74	17	;	;	PUNCT
ejpam-5388	74	18	(	(	PUNCT
ejpam-5388	74	19	ii	ii	NOUN
ejpam-5388	74	20	)	)	PUNCT
ejpam-5388	74	21	the	the	DET
ejpam-5388	74	22	pair	pair	NOUN
ejpam-5388	74	23	(	(	PUNCT
ejpam-5388	74	24	p	p	X
ejpam-5388	74	25	,	,	PUNCT
ejpam-5388	74	26	q	q	NOUN
ejpam-5388	74	27	)	)	PUNCT
ejpam-5388	74	28	is	be	AUX
ejpam-5388	74	29	triangular	triangular	ADJ
ejpam-5388	74	30	α	α	NOUN
ejpam-5388	74	31	-	-	ADJ
ejpam-5388	74	32	admissible	admissible	ADJ
ejpam-5388	74	33	with	with	ADP
ejpam-5388	74	34	respect	respect	NOUN
ejpam-5388	74	35	to	to	ADP
ejpam-5388	74	36	η	η	PROPN
ejpam-5388	74	37	;	;	PUNCT
ejpam-5388	74	38	(	(	PUNCT
ejpam-5388	74	39	iii	iii	X
ejpam-5388	74	40	)	)	PUNCT
ejpam-5388	74	41	there	there	PRON
ejpam-5388	74	42	exists	exist	VERB
ejpam-5388	74	43	u0	u0	PROPN
ejpam-5388	74	44	∈	∈	PROPN
ejpam-5388	74	45	𭟋	𭟋	ADP
ejpam-5388	74	46	such	such	ADJ
ejpam-5388	74	47	that	that	SCONJ
ejpam-5388	74	48	α(u0	α(u0	NOUN
ejpam-5388	74	49	,	,	PUNCT
ejpam-5388	74	50	pu0	pu0	NOUN
ejpam-5388	74	51	)	)	PUNCT
ejpam-5388	74	52	≥	≥	PROPN
ejpam-5388	74	53	η(u0	η(u0	NOUN
ejpam-5388	74	54	,	,	PUNCT
ejpam-5388	74	55	pu0	pu0	NOUN
ejpam-5388	74	56	)	)	PUNCT
ejpam-5388	74	57	,	,	PUNCT
ejpam-5388	74	58	(	(	PUNCT
ejpam-5388	74	59	iv	iv	X
ejpam-5388	74	60	)	)	PUNCT
ejpam-5388	74	61	p	p	NOUN
ejpam-5388	74	62	and	and	CCONJ
ejpam-5388	74	63	q	q	NOUN
ejpam-5388	74	64	are	be	AUX
ejpam-5388	74	65	continuous	continuous	ADJ
ejpam-5388	74	66	mappings	mapping	NOUN
ejpam-5388	74	67	.	.	PUNCT
ejpam-5388	75	1	then	then	ADV
ejpam-5388	75	2	,	,	PUNCT
ejpam-5388	75	3	p	p	NOUN
ejpam-5388	75	4	and	and	CCONJ
ejpam-5388	75	5	q	q	NOUN
ejpam-5388	75	6	have	have	VERB
ejpam-5388	75	7	a	a	DET
ejpam-5388	75	8	common	common	ADJ
ejpam-5388	75	9	fixed	fix	VERB
ejpam-5388	75	10	point	point	NOUN
ejpam-5388	75	11	in	in	ADP
ejpam-5388	75	12	𭟋	𭟋	PROPN
ejpam-5388	75	13	.	.	PUNCT
ejpam-5388	75	14	proof	proof	NOUN
ejpam-5388	75	15	.	.	PUNCT
ejpam-5388	76	1	let	let	VERB
ejpam-5388	76	2	u0	u0	PROPN
ejpam-5388	76	3	∈	∈	PROPN
ejpam-5388	76	4	𭟋	𭟋	ADP
ejpam-5388	76	5	such	such	ADJ
ejpam-5388	76	6	that	that	SCONJ
ejpam-5388	76	7	α(u0	α(u0	NOUN
ejpam-5388	76	8	,	,	PUNCT
ejpam-5388	76	9	pu0	pu0	NOUN
ejpam-5388	76	10	)	)	PUNCT
ejpam-5388	76	11	≥	≥	PROPN
ejpam-5388	76	12	η(u0	η(u0	NOUN
ejpam-5388	76	13	,	,	PUNCT
ejpam-5388	76	14	pu0	pu0	NOUN
ejpam-5388	76	15	)	)	PUNCT
ejpam-5388	76	16	.	.	PUNCT
ejpam-5388	77	1	we	we	PRON
ejpam-5388	77	2	define	define	VERB
ejpam-5388	77	3	a	a	DET
ejpam-5388	77	4	sequence	sequence	NOUN
ejpam-5388	77	5	{	{	PUNCT
ejpam-5388	77	6	un	un	PROPN
ejpam-5388	77	7	}	}	PUNCT
ejpam-5388	77	8	⊂	⊂	NOUN
ejpam-5388	77	9	𭟋	𭟋	ADP
ejpam-5388	77	10	such	such	ADJ
ejpam-5388	77	11	that	that	DET
ejpam-5388	77	12	u2n+1	u2n+1	PROPN
ejpam-5388	77	13	=	=	SYM
ejpam-5388	77	14	pu2n	pu2n	PROPN
ejpam-5388	77	15	and	and	CCONJ
ejpam-5388	77	16	u2n+2	u2n+2	PROPN
ejpam-5388	77	17	=	=	SYM
ejpam-5388	77	18	qu2n+1	qu2n+1	PROPN
ejpam-5388	77	19	for	for	ADP
ejpam-5388	77	20	all	all	PRON
ejpam-5388	77	21	n	n	DET
ejpam-5388	77	22	∈	∈	PROPN
ejpam-5388	77	23	n.	n.	NOUN
ejpam-5388	77	24	if	if	SCONJ
ejpam-5388	77	25	∃	∃	PROPN
ejpam-5388	77	26	an	an	DET
ejpam-5388	77	27	n∗	n∗	PROPN
ejpam-5388	77	28	such	such	ADJ
ejpam-5388	77	29	that	that	SCONJ
ejpam-5388	77	30	un∗+1	un∗+1	NOUN
ejpam-5388	77	31	=	=	SYM
ejpam-5388	77	32	un∗	un∗	ADJ
ejpam-5388	77	33	for	for	ADP
ejpam-5388	77	34	some	some	DET
ejpam-5388	77	35	n∗	n∗	PROPN
ejpam-5388	77	36	∈	∈	PROPN
ejpam-5388	77	37	n	n	CCONJ
ejpam-5388	77	38	,	,	PUNCT
ejpam-5388	77	39	then	then	ADV
ejpam-5388	77	40	it	it	PRON
ejpam-5388	77	41	is	be	AUX
ejpam-5388	77	42	very	very	ADV
ejpam-5388	77	43	easy	easy	ADJ
ejpam-5388	77	44	to	to	PART
ejpam-5388	77	45	show	show	VERB
ejpam-5388	77	46	that	that	SCONJ
ejpam-5388	77	47	p	p	PROPN
ejpam-5388	77	48	and	and	CCONJ
ejpam-5388	77	49	q	q	NOUN
ejpam-5388	77	50	have	have	VERB
ejpam-5388	77	51	a	a	DET
ejpam-5388	77	52	common	common	ADJ
ejpam-5388	77	53	fixed	fix	VERB
ejpam-5388	77	54	point	point	NOUN
ejpam-5388	77	55	,	,	PUNCT
ejpam-5388	77	56	which	which	PRON
ejpam-5388	77	57	completes	complete	VERB
ejpam-5388	77	58	the	the	DET
ejpam-5388	77	59	proof	proof	NOUN
ejpam-5388	77	60	.	.	PUNCT
ejpam-5388	78	1	since	since	SCONJ
ejpam-5388	78	2	the	the	DET
ejpam-5388	78	3	pair	pair	NOUN
ejpam-5388	78	4	(	(	PUNCT
ejpam-5388	78	5	p	p	X
ejpam-5388	78	6	,	,	PUNCT
ejpam-5388	78	7	q	q	NOUN
ejpam-5388	78	8	)	)	PUNCT
ejpam-5388	78	9	is	be	AUX
ejpam-5388	78	10	triangular	triangular	ADJ
ejpam-5388	78	11	α	α	NOUN
ejpam-5388	78	12	-	-	ADJ
ejpam-5388	78	13	admissible	admissible	ADJ
ejpam-5388	78	14	with	with	ADP
ejpam-5388	78	15	respect	respect	NOUN
ejpam-5388	78	16	to	to	ADP
ejpam-5388	78	17	η	η	PROPN
ejpam-5388	78	18	,	,	PUNCT
ejpam-5388	78	19	then	then	ADV
ejpam-5388	78	20	α(u1	α(u1	PROPN
ejpam-5388	78	21	,	,	PUNCT
ejpam-5388	78	22	u2	u2	NOUN
ejpam-5388	78	23	)	)	PUNCT
ejpam-5388	78	24	=	=	SYM
ejpam-5388	78	25	α(pu0	α(pu0	PROPN
ejpam-5388	78	26	,	,	PUNCT
ejpam-5388	78	27	qu1	qu1	PROPN
ejpam-5388	78	28	)	)	PUNCT
ejpam-5388	78	29	≥	≥	PROPN
ejpam-5388	78	30	η(pu0	η(pu0	PROPN
ejpam-5388	78	31	,	,	PUNCT
ejpam-5388	78	32	qu1	qu1	PROPN
ejpam-5388	78	33	)	)	PUNCT
ejpam-5388	78	34	=	=	SYM
ejpam-5388	78	35	η(u1	η(u1	NOUN
ejpam-5388	78	36	,	,	PUNCT
ejpam-5388	78	37	u2	u2	NOUN
ejpam-5388	78	38	)	)	PUNCT
ejpam-5388	78	39	and	and	CCONJ
ejpam-5388	78	40	α(u2	α(u2	NOUN
ejpam-5388	78	41	,	,	PUNCT
ejpam-5388	78	42	u1	u1	NOUN
ejpam-5388	78	43	)	)	PUNCT
ejpam-5388	78	44	=	=	SYM
ejpam-5388	78	45	α(pu1	α(pu1	NOUN
ejpam-5388	78	46	,	,	PUNCT
ejpam-5388	78	47	qu0	qu0	PROPN
ejpam-5388	78	48	)	)	PUNCT
ejpam-5388	78	49	≥	≥	NOUN
ejpam-5388	78	50	η(pu1	η(pu1	NOUN
ejpam-5388	78	51	,	,	PUNCT
ejpam-5388	78	52	qu0	qu0	ADJ
ejpam-5388	78	53	)	)	PUNCT
ejpam-5388	78	54	=	=	SYM
ejpam-5388	78	55	η(u2	η(u2	NOUN
ejpam-5388	78	56	,	,	PUNCT
ejpam-5388	78	57	u1	u1	NOUN
ejpam-5388	78	58	)	)	PUNCT
ejpam-5388	78	59	.	.	PUNCT
ejpam-5388	79	1	one	one	NUM
ejpam-5388	79	2	more	more	ADJ
ejpam-5388	79	3	time	time	NOUN
ejpam-5388	79	4	by	by	ADP
ejpam-5388	79	5	using	use	VERB
ejpam-5388	79	6	triangular	triangular	NOUN
ejpam-5388	79	7	α	α	NOUN
ejpam-5388	79	8	-	-	ADJ
ejpam-5388	79	9	admissible	admissible	ADJ
ejpam-5388	79	10	with	with	ADP
ejpam-5388	79	11	respect	respect	NOUN
ejpam-5388	79	12	to	to	ADP
ejpam-5388	79	13	η	η	PROPN
ejpam-5388	79	14	,	,	PUNCT
ejpam-5388	79	15	we	we	PRON
ejpam-5388	79	16	get	get	VERB
ejpam-5388	79	17	α(u2	α(u2	NOUN
ejpam-5388	79	18	,	,	PUNCT
ejpam-5388	79	19	u3	u3	NOUN
ejpam-5388	79	20	)	)	PUNCT
ejpam-5388	79	21	=	=	SYM
ejpam-5388	79	22	α(pu1	α(pu1	NOUN
ejpam-5388	79	23	,	,	PUNCT
ejpam-5388	79	24	qu2	qu2	PROPN
ejpam-5388	79	25	)	)	PUNCT
ejpam-5388	79	26	≥	≥	NOUN
ejpam-5388	79	27	η(pu1	η(pu1	NOUN
ejpam-5388	79	28	,	,	PUNCT
ejpam-5388	79	29	qu2	qu2	PROPN
ejpam-5388	79	30	)	)	PUNCT
ejpam-5388	80	1	=	=	SYM
ejpam-5388	80	2	η(u2	η(u2	NOUN
ejpam-5388	80	3	,	,	PUNCT
ejpam-5388	80	4	u3	u3	PROPN
ejpam-5388	80	5	)	)	PUNCT
ejpam-5388	80	6	and	and	CCONJ
ejpam-5388	80	7	α(u3	α(u3	PROPN
ejpam-5388	80	8	,	,	PUNCT
ejpam-5388	80	9	u2	u2	PROPN
ejpam-5388	80	10	)	)	PUNCT
ejpam-5388	80	11	=	=	SYM
ejpam-5388	80	12	α(pu2	α(pu2	PROPN
ejpam-5388	80	13	,	,	PUNCT
ejpam-5388	80	14	qu1	qu1	PROPN
ejpam-5388	80	15	)	)	PUNCT
ejpam-5388	80	16	≥	≥	NOUN
ejpam-5388	80	17	η(pu2	η(pu2	NOUN
ejpam-5388	80	18	,	,	PUNCT
ejpam-5388	80	19	qu1	qu1	PROPN
ejpam-5388	80	20	)	)	PUNCT
ejpam-5388	80	21	=	=	SYM
ejpam-5388	80	22	η(u3	η(u3	PROPN
ejpam-5388	80	23	,	,	PUNCT
ejpam-5388	80	24	u2	u2	PROPN
ejpam-5388	80	25	)	)	PUNCT
ejpam-5388	80	26	.	.	PUNCT
ejpam-5388	81	1	by	by	ADP
ejpam-5388	81	2	repeating	repeat	VERB
ejpam-5388	81	3	the	the	DET
ejpam-5388	81	4	above	above	ADJ
ejpam-5388	81	5	steps	step	NOUN
ejpam-5388	81	6	for	for	ADP
ejpam-5388	81	7	n−times	n−time	NOUN
ejpam-5388	81	8	,	,	PUNCT
ejpam-5388	81	9	we	we	PRON
ejpam-5388	81	10	obtain	obtain	VERB
ejpam-5388	81	11	the	the	DET
ejpam-5388	81	12	following	follow	VERB
ejpam-5388	81	13	α(un	α(un	PROPN
ejpam-5388	81	14	,	,	PUNCT
ejpam-5388	81	15	un+1	un+1	NOUN
ejpam-5388	81	16	)	)	PUNCT
ejpam-5388	81	17	≥	≥	NOUN
ejpam-5388	81	18	η(un	η(un	PROPN
ejpam-5388	81	19	,	,	PUNCT
ejpam-5388	81	20	un+1	un+1	NOUN
ejpam-5388	81	21	)	)	PUNCT
ejpam-5388	81	22	and	and	CCONJ
ejpam-5388	81	23	α(un+1	α(un+1	NUM
ejpam-5388	81	24	,	,	PUNCT
ejpam-5388	81	25	un	un	PROPN
ejpam-5388	81	26	)	)	PUNCT
ejpam-5388	81	27	≥	≥	PROPN
ejpam-5388	81	28	η(un+1	η(un+1	PROPN
ejpam-5388	81	29	,	,	PUNCT
ejpam-5388	81	30	un	un	PROPN
ejpam-5388	81	31	)	)	PUNCT
ejpam-5388	81	32	.	.	PUNCT
ejpam-5388	82	1	by	by	ADP
ejpam-5388	82	2	lemma	lemma	PROPN
ejpam-5388	82	3	1.8	1.8	NUM
ejpam-5388	82	4	,	,	PUNCT
ejpam-5388	82	5	we	we	PRON
ejpam-5388	82	6	have	have	VERB
ejpam-5388	82	7	α(u2n	α(u2n	ADJ
ejpam-5388	82	8	,	,	PUNCT
ejpam-5388	82	9	u2n+1	u2n+1	ADJ
ejpam-5388	82	10	)	)	PUNCT
ejpam-5388	82	11	≥	≥	NOUN
ejpam-5388	82	12	η(u2n	η(u2n	NOUN
ejpam-5388	82	13	,	,	PUNCT
ejpam-5388	82	14	u2n+1	u2n+1	ADJ
ejpam-5388	82	15	)	)	PUNCT
ejpam-5388	82	16	for	for	ADP
ejpam-5388	82	17	all	all	DET
ejpam-5388	82	18	n	n	PRON
ejpam-5388	82	19	∈	∈	NOUN
ejpam-5388	82	20	n	n	NOUN
ejpam-5388	82	21	and	and	CCONJ
ejpam-5388	82	22	since	since	SCONJ
ejpam-5388	82	23	(	(	PUNCT
ejpam-5388	82	24	p	p	X
ejpam-5388	82	25	,	,	PUNCT
ejpam-5388	82	26	q	q	NOUN
ejpam-5388	82	27	)	)	PUNCT
ejpam-5388	82	28	is	be	AUX
ejpam-5388	82	29	λ(s	λ(s	PROPN
ejpam-5388	82	30	,	,	PUNCT
ejpam-5388	82	31	φ	φ	NOUN
ejpam-5388	82	32	,	,	PUNCT
ejpam-5388	82	33	ψ	ψ	PROPN
ejpam-5388	82	34	,	,	PUNCT
ejpam-5388	82	35	l)-generalized	l)-generalize	VERB
ejpam-5388	82	36	berinde	berinde	NOUN
ejpam-5388	82	37	type	type	NOUN
ejpam-5388	82	38	contraction	contraction	NOUN
ejpam-5388	82	39	mapping	mapping	NOUN
ejpam-5388	82	40	,	,	PUNCT
ejpam-5388	82	41	we	we	PRON
ejpam-5388	82	42	get	get	VERB
ejpam-5388	82	43	φ(λb(u2n+1	φ(λb(u2n+1	ADJ
ejpam-5388	82	44	,	,	PUNCT
ejpam-5388	82	45	u2n+2	u2n+2	ADJ
ejpam-5388	82	46	)	)	PUNCT
ejpam-5388	82	47	)	)	PUNCT
ejpam-5388	83	1	≤	≤	NUM
ejpam-5388	83	2	φ(s2λb(pu2n	φ(s2λb(pu2n	PROPN
ejpam-5388	83	3	,	,	PUNCT
ejpam-5388	83	4	qu2n+1	qu2n+1	NOUN
ejpam-5388	83	5	)	)	PUNCT
ejpam-5388	83	6	≤	≤	NOUN
ejpam-5388	83	7	λ[φ(mλb	λ[φ(mλb	NOUN
ejpam-5388	83	8	(	(	PUNCT
ejpam-5388	83	9	u2n	u2n	PROPN
ejpam-5388	83	10	,	,	PUNCT
ejpam-5388	83	11	u2n+1))−	u2n+1))−	ADJ
ejpam-5388	83	12	ϕ(mλb	ϕ(mλb	PROPN
ejpam-5388	83	13	(	(	PUNCT
ejpam-5388	83	14	u2n	u2n	PROPN
ejpam-5388	83	15	,	,	PUNCT
ejpam-5388	83	16	u2n+1	u2n+1	PROPN
ejpam-5388	83	17	)	)	PUNCT
ejpam-5388	83	18	)	)	PUNCT
ejpam-5388	84	1	+	+	CCONJ
ejpam-5388	84	2	lnλb	lnλb	X
ejpam-5388	84	3	(	(	PUNCT
ejpam-5388	84	4	u2n	u2n	NOUN
ejpam-5388	84	5	,	,	PUNCT
ejpam-5388	84	6	u2n+1)](2.2	u2n+1)](2.2	PROPN
ejpam-5388	84	7	)	)	PUNCT
ejpam-5388	84	8	h.	h.	NOUN
ejpam-5388	84	9	alsamir	alsamir	VERB
ejpam-5388	84	10	et	et	PROPN
ejpam-5388	84	11	al	al	PROPN
ejpam-5388	84	12	.	.	PUNCT
ejpam-5388	84	13	/	/	SYM
ejpam-5388	84	14	eur	eur	PROPN
ejpam-5388	84	15	.	.	PUNCT
ejpam-5388	85	1	j.	j.	PROPN
ejpam-5388	85	2	pure	pure	PROPN
ejpam-5388	85	3	appl	appl	PROPN
ejpam-5388	85	4	.	.	PROPN
ejpam-5388	85	5	math	math	PROPN
ejpam-5388	85	6	,	,	PUNCT
ejpam-5388	85	7	17	17	NUM
ejpam-5388	85	8	(	(	PUNCT
ejpam-5388	85	9	4	4	NUM
ejpam-5388	85	10	)	)	PUNCT
ejpam-5388	85	11	(	(	PUNCT
ejpam-5388	85	12	2024	2024	NUM
ejpam-5388	85	13	)	)	PUNCT
ejpam-5388	85	14	,	,	PUNCT
ejpam-5388	85	15	2492	2492	NUM
ejpam-5388	85	16	-	-	SYM
ejpam-5388	85	17	2504	2504	NUM
ejpam-5388	85	18	2495	2495	NUM
ejpam-5388	85	19	for	for	ADP
ejpam-5388	85	20	all	all	PRON
ejpam-5388	85	21	n	n	PRON
ejpam-5388	85	22	∈	∈	PROPN
ejpam-5388	85	23	n	n	CCONJ
ejpam-5388	85	24	,	,	PUNCT
ejpam-5388	85	25	where	where	SCONJ
ejpam-5388	85	26	mλb	mλb	PROPN
ejpam-5388	85	27	(	(	PUNCT
ejpam-5388	85	28	u2n	u2n	PROPN
ejpam-5388	85	29	,	,	PUNCT
ejpam-5388	85	30	u2n+1	u2n+1	PROPN
ejpam-5388	85	31	)	)	PUNCT
ejpam-5388	85	32	=	=	SYM
ejpam-5388	85	33	max	max	PROPN
ejpam-5388	85	34	{	{	PUNCT
ejpam-5388	85	35	λb(u2n	λb(u2n	PROPN
ejpam-5388	85	36	,	,	PUNCT
ejpam-5388	85	37	u2n+1),λb(u2n	u2n+1),λb(u2n	PROPN
ejpam-5388	85	38	,	,	PUNCT
ejpam-5388	85	39	pu2n),λb(u2n+1	pu2n),λb(u2n+1	NOUN
ejpam-5388	85	40	,	,	PUNCT
ejpam-5388	85	41	qu2n+1	qu2n+1	NOUN
ejpam-5388	85	42	)	)	PUNCT
ejpam-5388	85	43	,	,	PUNCT
ejpam-5388	85	44	λb(u2n	λb(u2n	PROPN
ejpam-5388	85	45	,	,	PUNCT
ejpam-5388	85	46	qu2n+1	qu2n+1	PROPN
ejpam-5388	85	47	)	)	PUNCT
ejpam-5388	86	1	+	+	CCONJ
ejpam-5388	87	1	λb(pu2n	λb(pu2n	ADJ
ejpam-5388	87	2	,	,	PUNCT
ejpam-5388	87	3	u2n+1	u2n+1	ADJ
ejpam-5388	87	4	)	)	PUNCT
ejpam-5388	87	5	2s(1	2s(1	X
ejpam-5388	87	6	+	+	CCONJ
ejpam-5388	87	7	λb(pu2n	λb(pu2n	ADJ
ejpam-5388	87	8	,	,	PUNCT
ejpam-5388	87	9	u2n+1	u2n+1	NOUN
ejpam-5388	87	10	)	)	PUNCT
ejpam-5388	87	11	)	)	PUNCT
ejpam-5388	87	12	}	}	PUNCT
ejpam-5388	88	1	=	=	SYM
ejpam-5388	88	2	max	max	PROPN
ejpam-5388	88	3	{	{	PUNCT
ejpam-5388	88	4	λb(u2n	λb(u2n	PROPN
ejpam-5388	88	5	,	,	PUNCT
ejpam-5388	88	6	u2n+1),λb(u2n	u2n+1),λb(u2n	ADJ
ejpam-5388	88	7	,	,	PUNCT
ejpam-5388	88	8	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADJ
ejpam-5388	88	9	,	,	PUNCT
ejpam-5388	88	10	u2n+2	u2n+2	ADJ
ejpam-5388	88	11	)	)	PUNCT
ejpam-5388	88	12	,	,	PUNCT
ejpam-5388	88	13	λb(u2n	λb(u2n	PROPN
ejpam-5388	88	14	,	,	PUNCT
ejpam-5388	88	15	u2n+2	u2n+2	PROPN
ejpam-5388	88	16	)	)	PUNCT
ejpam-5388	89	1	+	+	SYM
ejpam-5388	89	2	λb(u2n+1	λb(u2n+1	ADJ
ejpam-5388	89	3	,	,	PUNCT
ejpam-5388	89	4	u2n+1	u2n+1	NOUN
ejpam-5388	89	5	)	)	PUNCT
ejpam-5388	89	6	2s(1	2s(1	X
ejpam-5388	89	7	+	+	SYM
ejpam-5388	89	8	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	89	9	,	,	PUNCT
ejpam-5388	89	10	u2n+1	u2n+1	NOUN
ejpam-5388	89	11	)	)	PUNCT
ejpam-5388	89	12	)	)	PUNCT
ejpam-5388	89	13	}	}	PUNCT
ejpam-5388	90	1	=	=	SYM
ejpam-5388	90	2	max	max	PROPN
ejpam-5388	90	3	{	{	PUNCT
ejpam-5388	90	4	λb(u2n	λb(u2n	NOUN
ejpam-5388	90	5	,	,	PUNCT
ejpam-5388	90	6	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADJ
ejpam-5388	90	7	,	,	PUNCT
ejpam-5388	90	8	u2n+2	u2n+2	ADJ
ejpam-5388	90	9	)	)	PUNCT
ejpam-5388	90	10	,	,	PUNCT
ejpam-5388	90	11	λb(u2n	λb(u2n	PROPN
ejpam-5388	90	12	,	,	PUNCT
ejpam-5388	90	13	u2n+2	u2n+2	ADJ
ejpam-5388	90	14	)	)	PUNCT
ejpam-5388	90	15	2s	2s	NOUN
ejpam-5388	90	16	}	}	PUNCT
ejpam-5388	90	17	and	and	CCONJ
ejpam-5388	90	18	nλb	nλb	PROPN
ejpam-5388	90	19	(	(	PUNCT
ejpam-5388	90	20	u2n	u2n	PROPN
ejpam-5388	90	21	,	,	PUNCT
ejpam-5388	90	22	u2n+1	u2n+1	PROPN
ejpam-5388	90	23	)	)	PUNCT
ejpam-5388	90	24	=	=	SYM
ejpam-5388	90	25	min{λb(u2n	min{λb(u2n	PROPN
ejpam-5388	90	26	,	,	PUNCT
ejpam-5388	90	27	u2n+1),λb(u2n	u2n+1),λb(u2n	PROPN
ejpam-5388	90	28	,	,	PUNCT
ejpam-5388	90	29	pu2n),λb(u2n+1	pu2n),λb(u2n+1	NOUN
ejpam-5388	90	30	,	,	PUNCT
ejpam-5388	90	31	qu2n+1),λb(u2n+1	qu2n+1),λb(u2n+1	PROPN
ejpam-5388	90	32	,	,	PUNCT
ejpam-5388	90	33	pu2n	pu2n	NOUN
ejpam-5388	90	34	)	)	PUNCT
ejpam-5388	90	35	}	}	PUNCT
ejpam-5388	90	36	i.e.	i.e.	X
ejpam-5388	90	37	,	,	PUNCT
ejpam-5388	90	38	nλb	nλb	PROPN
ejpam-5388	90	39	(	(	PUNCT
ejpam-5388	90	40	u2n	u2n	PROPN
ejpam-5388	90	41	,	,	PUNCT
ejpam-5388	90	42	u2n+1	u2n+1	PROPN
ejpam-5388	90	43	)	)	PUNCT
ejpam-5388	90	44	=	=	SYM
ejpam-5388	90	45	0	0	PUNCT
ejpam-5388	90	46	(	(	PUNCT
ejpam-5388	90	47	2.3	2.3	NUM
ejpam-5388	90	48	)	)	PUNCT
ejpam-5388	90	49	since	since	SCONJ
ejpam-5388	90	50	λb(u2n	λb(u2n	PROPN
ejpam-5388	90	51	,	,	PUNCT
ejpam-5388	90	52	u2n+2	u2n+2	PROPN
ejpam-5388	90	53	)	)	PUNCT
ejpam-5388	90	54	2s	2s	PROPN
ejpam-5388	90	55	≤	≤	NOUN
ejpam-5388	90	56	s[λb(u2n	s[λb(u2n	NOUN
ejpam-5388	90	57	,	,	PUNCT
ejpam-5388	90	58	u2n+1	u2n+1	ADJ
ejpam-5388	90	59	)	)	PUNCT
ejpam-5388	91	1	+	+	SYM
ejpam-5388	91	2	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	91	3	,	,	PUNCT
ejpam-5388	91	4	u2n+2	u2n+2	PROPN
ejpam-5388	91	5	)	)	PUNCT
ejpam-5388	91	6	]	]	PUNCT
ejpam-5388	92	1	2s	2s	X
ejpam-5388	92	2	≤	≤	NOUN
ejpam-5388	92	3	λb(u2n	λb(u2n	PROPN
ejpam-5388	92	4	,	,	PUNCT
ejpam-5388	92	5	u2n+1	u2n+1	ADJ
ejpam-5388	92	6	)	)	PUNCT
ejpam-5388	93	1	+	+	SYM
ejpam-5388	93	2	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	93	3	,	,	PUNCT
ejpam-5388	93	4	u2n+2	u2n+2	ADJ
ejpam-5388	93	5	)	)	PUNCT
ejpam-5388	93	6	2	2	NUM
ejpam-5388	93	7	≤	≤	NOUN
ejpam-5388	93	8	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	93	9	,	,	PUNCT
ejpam-5388	93	10	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	93	11	,	,	PUNCT
ejpam-5388	93	12	u2n+2	u2n+2	ADJ
ejpam-5388	93	13	)	)	PUNCT
ejpam-5388	93	14	}	}	PUNCT
ejpam-5388	93	15	,	,	PUNCT
ejpam-5388	93	16	we	we	PRON
ejpam-5388	93	17	get	get	VERB
ejpam-5388	93	18	mλb	mλb	PROPN
ejpam-5388	93	19	(	(	PUNCT
ejpam-5388	93	20	u2n	u2n	PROPN
ejpam-5388	93	21	,	,	PUNCT
ejpam-5388	93	22	u2n+1	u2n+1	PROPN
ejpam-5388	93	23	)	)	PUNCT
ejpam-5388	93	24	)	)	PUNCT
ejpam-5388	93	25	≤	≤	NOUN
ejpam-5388	93	26	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	93	27	,	,	PUNCT
ejpam-5388	93	28	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	93	29	,	,	PUNCT
ejpam-5388	93	30	u2n+2	u2n+2	ADJ
ejpam-5388	93	31	)	)	PUNCT
ejpam-5388	93	32	}	}	PUNCT
ejpam-5388	93	33	.	.	PUNCT
ejpam-5388	94	1	(	(	PUNCT
ejpam-5388	94	2	2.4	2.4	X
ejpam-5388	94	3	)	)	PUNCT
ejpam-5388	94	4	taking	take	VERB
ejpam-5388	94	5	(	(	PUNCT
ejpam-5388	94	6	2.3	2.3	NUM
ejpam-5388	94	7	)	)	PUNCT
ejpam-5388	94	8	and	and	CCONJ
ejpam-5388	94	9	(	(	PUNCT
ejpam-5388	94	10	2.4	2.4	NUM
ejpam-5388	94	11	)	)	PUNCT
ejpam-5388	94	12	into	into	ADP
ejpam-5388	94	13	account,(2.2	account,(2.2	NOUN
ejpam-5388	94	14	)	)	PUNCT
ejpam-5388	94	15	yields	yield	NOUN
ejpam-5388	94	16	φ(λb(u2n+1	φ(λb(u2n+1	VERB
ejpam-5388	94	17	,	,	PUNCT
ejpam-5388	94	18	u2n+2	u2n+2	ADJ
ejpam-5388	94	19	)	)	PUNCT
ejpam-5388	94	20	)	)	PUNCT
ejpam-5388	94	21	≤	≤	NUM
ejpam-5388	95	1	λ	λ	PROPN
ejpam-5388	96	1	[	[	X
ejpam-5388	96	2	φ	φ	X
ejpam-5388	96	3	(	(	PUNCT
ejpam-5388	96	4	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	96	5	,	,	PUNCT
ejpam-5388	96	6	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	96	7	,	,	PUNCT
ejpam-5388	96	8	u2n+2	u2n+2	ADJ
ejpam-5388	96	9	)	)	PUNCT
ejpam-5388	96	10	}	}	PUNCT
ejpam-5388	96	11	)	)	PUNCT
ejpam-5388	96	12	−λϕ	−λϕ	NOUN
ejpam-5388	96	13	(	(	PUNCT
ejpam-5388	96	14	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	96	15	,	,	PUNCT
ejpam-5388	96	16	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	96	17	,	,	PUNCT
ejpam-5388	96	18	u2n+2	u2n+2	ADJ
ejpam-5388	96	19	)	)	PUNCT
ejpam-5388	96	20	}	}	PUNCT
ejpam-5388	96	21	)	)	PUNCT
ejpam-5388	96	22	]	]	PUNCT
ejpam-5388	97	1	<	<	X
ejpam-5388	97	2	φ	φ	X
ejpam-5388	97	3	(	(	PUNCT
ejpam-5388	97	4	max{λb(u2n	max{λb(u2n	PROPN
ejpam-5388	97	5	,	,	PUNCT
ejpam-5388	97	6	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	97	7	,	,	PUNCT
ejpam-5388	97	8	u2n+2	u2n+2	ADJ
ejpam-5388	97	9	)	)	PUNCT
ejpam-5388	97	10	}	}	PUNCT
ejpam-5388	97	11	)	)	PUNCT
ejpam-5388	98	1	−	−	PROPN
ejpam-5388	98	2	ϕ	ϕ	NOUN
ejpam-5388	98	3	(	(	PUNCT
ejpam-5388	98	4	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	98	5	,	,	PUNCT
ejpam-5388	98	6	u2n+1),λb(u2n+1	u2n+1),λb(u2n+1	ADV
ejpam-5388	98	7	,	,	PUNCT
ejpam-5388	98	8	u2n+2	u2n+2	ADJ
ejpam-5388	98	9	)	)	PUNCT
ejpam-5388	98	10	}	}	PUNCT
ejpam-5388	98	11	)	)	PUNCT
ejpam-5388	98	12	.	.	PUNCT
ejpam-5388	99	1	now	now	ADV
ejpam-5388	99	2	,	,	PUNCT
ejpam-5388	99	3	we	we	PRON
ejpam-5388	99	4	will	will	AUX
ejpam-5388	99	5	show	show	VERB
ejpam-5388	99	6	that	that	SCONJ
ejpam-5388	99	7	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	99	8	,	,	PUNCT
ejpam-5388	99	9	u2n+2	u2n+2	ADJ
ejpam-5388	99	10	)	)	PUNCT
ejpam-5388	99	11	≤	≤	NOUN
ejpam-5388	99	12	λb(u2n	λb(u2n	PROPN
ejpam-5388	99	13	,	,	PUNCT
ejpam-5388	99	14	u2n+1	u2n+1	PROPN
ejpam-5388	99	15	)	)	PUNCT
ejpam-5388	99	16	.	.	PUNCT
ejpam-5388	100	1	arguing	argue	VERB
ejpam-5388	100	2	by	by	ADP
ejpam-5388	100	3	contradiction	contradiction	NOUN
ejpam-5388	100	4	,	,	PUNCT
ejpam-5388	100	5	we	we	PRON
ejpam-5388	100	6	assume	assume	VERB
ejpam-5388	100	7	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	100	8	,	,	PUNCT
ejpam-5388	100	9	u2n+2	u2n+2	PROPN
ejpam-5388	100	10	)	)	PUNCT
ejpam-5388	100	11	>	>	X
ejpam-5388	101	1	λb(u2n	λb(u2n	PROPN
ejpam-5388	101	2	,	,	PUNCT
ejpam-5388	101	3	u2n+1	u2n+1	PROPN
ejpam-5388	101	4	)	)	PUNCT
ejpam-5388	101	5	.	.	PUNCT
ejpam-5388	102	1	therefore	therefore	ADV
ejpam-5388	102	2	,	,	PUNCT
ejpam-5388	102	3	we	we	PRON
ejpam-5388	102	4	have	have	VERB
ejpam-5388	102	5	two	two	NUM
ejpam-5388	102	6	cases	case	NOUN
ejpam-5388	102	7	.	.	PUNCT
ejpam-5388	103	1	case	case	NOUN
ejpam-5388	103	2	1	1	NUM
ejpam-5388	103	3	:	:	PUNCT
ejpam-5388	103	4	mλb	mλb	PROPN
ejpam-5388	103	5	(	(	PUNCT
ejpam-5388	103	6	u2n	u2n	PROPN
ejpam-5388	103	7	,	,	PUNCT
ejpam-5388	103	8	u2n+1	u2n+1	PROPN
ejpam-5388	103	9	)	)	PUNCT
ejpam-5388	104	1	=	=	SYM
ejpam-5388	104	2	λb(u2n	λb(u2n	ADV
ejpam-5388	104	3	,	,	PUNCT
ejpam-5388	104	4	u2n+1	u2n+1	PROPN
ejpam-5388	104	5	)	)	PUNCT
ejpam-5388	104	6	.	.	PUNCT
ejpam-5388	105	1	then	then	ADV
ejpam-5388	105	2	φ(λb(u2n+1	φ(λb(u2n+1	VERB
ejpam-5388	105	3	,	,	PUNCT
ejpam-5388	105	4	u2n+2	u2n+2	PROPN
ejpam-5388	105	5	)	)	PUNCT
ejpam-5388	105	6	<	<	X
ejpam-5388	106	1	φ(λb(u2n	φ(λb(u2n	PROPN
ejpam-5388	106	2	,	,	PUNCT
ejpam-5388	106	3	u2n+1))−	u2n+1))−	ADJ
ejpam-5388	106	4	ϕ(λb(u2n	ϕ(λb(u2n	ADJ
ejpam-5388	106	5	,	,	PUNCT
ejpam-5388	106	6	u2n+1	u2n+1	PROPN
ejpam-5388	106	7	)	)	PUNCT
ejpam-5388	106	8	)	)	PUNCT
ejpam-5388	107	1	<	<	X
ejpam-5388	107	2	φ(λb(u2n	φ(λb(u2n	PROPN
ejpam-5388	107	3	,	,	PUNCT
ejpam-5388	107	4	u2n+1	u2n+1	PROPN
ejpam-5388	107	5	)	)	PUNCT
ejpam-5388	107	6	)	)	PUNCT
ejpam-5388	107	7	since	since	SCONJ
ejpam-5388	107	8	φ	φ	PROPN
ejpam-5388	107	9	is	be	AUX
ejpam-5388	107	10	increasing	increase	VERB
ejpam-5388	107	11	,	,	PUNCT
ejpam-5388	107	12	we	we	PRON
ejpam-5388	107	13	have	have	VERB
ejpam-5388	107	14	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	107	15	,	,	PUNCT
ejpam-5388	107	16	u2n+2	u2n+2	PROPN
ejpam-5388	107	17	)	)	PUNCT
ejpam-5388	107	18	<	<	X
ejpam-5388	107	19	λb(u2n	λb(u2n	PROPN
ejpam-5388	107	20	,	,	PUNCT
ejpam-5388	107	21	u2n+1	u2n+1	PROPN
ejpam-5388	107	22	)	)	PUNCT
ejpam-5388	107	23	.	.	PUNCT
ejpam-5388	108	1	which	which	PRON
ejpam-5388	108	2	is	be	AUX
ejpam-5388	108	3	a	a	DET
ejpam-5388	108	4	contradiction	contradiction	NOUN
ejpam-5388	108	5	.	.	PUNCT
ejpam-5388	109	1	case	case	NOUN
ejpam-5388	109	2	2	2	NUM
ejpam-5388	109	3	:	:	PUNCT
ejpam-5388	109	4	mλb	mλb	PROPN
ejpam-5388	109	5	(	(	PUNCT
ejpam-5388	109	6	u2n	u2n	PROPN
ejpam-5388	109	7	,	,	PUNCT
ejpam-5388	109	8	u2n+1	u2n+1	PROPN
ejpam-5388	109	9	)	)	PUNCT
ejpam-5388	109	10	=	=	SYM
ejpam-5388	109	11	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	109	12	,	,	PUNCT
ejpam-5388	109	13	u2n+2	u2n+2	PROPN
ejpam-5388	109	14	)	)	PUNCT
ejpam-5388	109	15	.	.	PUNCT
ejpam-5388	110	1	then	then	ADV
ejpam-5388	110	2	φ(λb(u2n+1	φ(λb(u2n+1	VERB
ejpam-5388	110	3	,	,	PUNCT
ejpam-5388	110	4	u2n+2	u2n+2	PROPN
ejpam-5388	110	5	)	)	PUNCT
ejpam-5388	110	6	<	<	X
ejpam-5388	110	7	φ(λb(u2n+1	φ(λb(u2n+1	NOUN
ejpam-5388	110	8	,	,	PUNCT
ejpam-5388	110	9	u2n+2))−	u2n+2))−	NOUN
ejpam-5388	110	10	ϕ(λb(u2n+1	ϕ(λb(u2n+1	NOUN
ejpam-5388	110	11	,	,	PUNCT
ejpam-5388	110	12	u2n+2	u2n+2	PROPN
ejpam-5388	110	13	)	)	PUNCT
ejpam-5388	110	14	)	)	PUNCT
ejpam-5388	110	15	<	<	X
ejpam-5388	110	16	φ(λb(u2n+1	φ(λb(u2n+1	X
ejpam-5388	110	17	,	,	PUNCT
ejpam-5388	110	18	u2n+2	u2n+2	PROPN
ejpam-5388	110	19	)	)	PUNCT
ejpam-5388	110	20	)	)	PUNCT
ejpam-5388	110	21	since	since	SCONJ
ejpam-5388	110	22	φ	φ	PROPN
ejpam-5388	110	23	is	be	AUX
ejpam-5388	110	24	increasing	increase	VERB
ejpam-5388	110	25	,	,	PUNCT
ejpam-5388	110	26	we	we	PRON
ejpam-5388	110	27	have	have	VERB
ejpam-5388	110	28	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	110	29	,	,	PUNCT
ejpam-5388	110	30	u2n+2	u2n+2	PROPN
ejpam-5388	110	31	)	)	PUNCT
ejpam-5388	110	32	<	<	X
ejpam-5388	111	1	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	111	2	,	,	PUNCT
ejpam-5388	111	3	u2n+2	u2n+2	PROPN
ejpam-5388	111	4	)	)	PUNCT
ejpam-5388	111	5	.	.	PUNCT
ejpam-5388	112	1	which	which	PRON
ejpam-5388	112	2	is	be	AUX
ejpam-5388	112	3	a	a	DET
ejpam-5388	112	4	impossible	impossible	ADJ
ejpam-5388	112	5	.	.	PUNCT
ejpam-5388	113	1	hence	hence	ADV
ejpam-5388	113	2	from	from	ADP
ejpam-5388	113	3	the	the	DET
ejpam-5388	113	4	above	above	ADV
ejpam-5388	113	5	we	we	PRON
ejpam-5388	113	6	have	have	AUX
ejpam-5388	113	7	λb(u2n+1	λb(u2n+1	PROPN
ejpam-5388	113	8	,	,	PUNCT
ejpam-5388	113	9	u2n+2	u2n+2	ADJ
ejpam-5388	113	10	)	)	PUNCT
ejpam-5388	113	11	≤	≤	NOUN
ejpam-5388	113	12	λb(u2n	λb(u2n	PROPN
ejpam-5388	113	13	,	,	PUNCT
ejpam-5388	113	14	u2n+1	u2n+1	VERB
ejpam-5388	113	15	)	)	PUNCT
ejpam-5388	113	16	by	by	ADP
ejpam-5388	113	17	similar	similar	ADJ
ejpam-5388	113	18	way	way	NOUN
ejpam-5388	113	19	,	,	PUNCT
ejpam-5388	113	20	we	we	PRON
ejpam-5388	113	21	can	can	AUX
ejpam-5388	113	22	prove	prove	VERB
ejpam-5388	113	23	that	that	SCONJ
ejpam-5388	113	24	λb(u2n	λb(u2n	PROPN
ejpam-5388	113	25	,	,	PUNCT
ejpam-5388	113	26	u2n+1	u2n+1	NOUN
ejpam-5388	113	27	)	)	PUNCT
ejpam-5388	113	28	≤	≤	NOUN
ejpam-5388	113	29	λb(u2n−1	λb(u2n−1	PROPN
ejpam-5388	113	30	,	,	PUNCT
ejpam-5388	113	31	u2n	u2n	PROPN
ejpam-5388	113	32	)	)	PUNCT
ejpam-5388	113	33	.	.	PUNCT
ejpam-5388	114	1	so	so	ADV
ejpam-5388	114	2	,	,	PUNCT
ejpam-5388	114	3	we	we	PRON
ejpam-5388	114	4	conclude	conclude	VERB
ejpam-5388	114	5	that	that	SCONJ
ejpam-5388	114	6	λb(un	λb(un	PROPN
ejpam-5388	114	7	,	,	PUNCT
ejpam-5388	114	8	un+1	un+1	NOUN
ejpam-5388	114	9	)	)	PUNCT
ejpam-5388	114	10	≤	≤	NOUN
ejpam-5388	114	11	λb(un−1	λb(un−1	PROPN
ejpam-5388	114	12	,	,	PUNCT
ejpam-5388	114	13	un	un	PROPN
ejpam-5388	114	14	)	)	PUNCT
ejpam-5388	114	15	.	.	PUNCT
ejpam-5388	115	1	that	that	PRON
ejpam-5388	115	2	is	be	AUX
ejpam-5388	115	3	,	,	PUNCT
ejpam-5388	115	4	the	the	DET
ejpam-5388	115	5	sequence	sequence	NOUN
ejpam-5388	115	6	λb(un+1	λb(un+1	PROPN
ejpam-5388	115	7	,	,	PUNCT
ejpam-5388	115	8	un+1	un+1	NOUN
ejpam-5388	115	9	)	)	PUNCT
ejpam-5388	115	10	is	be	AUX
ejpam-5388	115	11	a	a	DET
ejpam-5388	115	12	decreasing	decrease	VERB
ejpam-5388	115	13	sequence	sequence	NOUN
ejpam-5388	115	14	and	and	CCONJ
ejpam-5388	115	15	bounded	bound	VERB
ejpam-5388	115	16	below	below	ADV
ejpam-5388	115	17	for	for	ADP
ejpam-5388	115	18	all	all	DET
ejpam-5388	115	19	n	n	PRON
ejpam-5388	115	20	∈	∈	PROPN
ejpam-5388	115	21	n.	n.	NOUN
ejpam-5388	115	22	therefore	therefore	ADV
ejpam-5388	115	23	there	there	ADV
ejpam-5388	115	24	∃	∃	PROPN
ejpam-5388	115	25	ω	ω	PROPN
ejpam-5388	115	26	≥	≥	PROPN
ejpam-5388	115	27	0	0	NUM
ejpam-5388	115	28	such	such	ADJ
ejpam-5388	115	29	that	that	SCONJ
ejpam-5388	115	30	lim	lim	PROPN
ejpam-5388	115	31	n→∞	n→∞	X
ejpam-5388	116	1	λb(un	λb(un	PROPN
ejpam-5388	116	2	,	,	PUNCT
ejpam-5388	116	3	un+1	un+1	NOUN
ejpam-5388	116	4	)	)	PUNCT
ejpam-5388	116	5	=	=	SYM
ejpam-5388	116	6	ω	ω	PROPN
ejpam-5388	116	7	.	.	PUNCT
ejpam-5388	117	1	h.	h.	PROPN
ejpam-5388	117	2	alsamir	alsamir	VERB
ejpam-5388	117	3	et	et	PROPN
ejpam-5388	117	4	al	al	PROPN
ejpam-5388	117	5	.	.	PUNCT
ejpam-5388	117	6	/	/	SYM
ejpam-5388	117	7	eur	eur	PROPN
ejpam-5388	117	8	.	.	PUNCT
ejpam-5388	118	1	j.	j.	PROPN
ejpam-5388	118	2	pure	pure	PROPN
ejpam-5388	118	3	appl	appl	PROPN
ejpam-5388	118	4	.	.	PROPN
ejpam-5388	118	5	math	math	PROPN
ejpam-5388	118	6	,	,	PUNCT
ejpam-5388	118	7	17	17	NUM
ejpam-5388	118	8	(	(	PUNCT
ejpam-5388	118	9	4	4	NUM
ejpam-5388	118	10	)	)	PUNCT
ejpam-5388	118	11	(	(	PUNCT
ejpam-5388	118	12	2024	2024	NUM
ejpam-5388	118	13	)	)	PUNCT
ejpam-5388	118	14	,	,	PUNCT
ejpam-5388	118	15	2492	2492	NUM
ejpam-5388	118	16	-	-	SYM
ejpam-5388	118	17	2504	2504	NUM
ejpam-5388	118	18	2496	2496	NUM
ejpam-5388	118	19	we	we	PRON
ejpam-5388	118	20	want	want	VERB
ejpam-5388	118	21	to	to	PART
ejpam-5388	118	22	prove	prove	VERB
ejpam-5388	118	23	that	that	PRON
ejpam-5388	119	1	ω	ω	NOUN
ejpam-5388	119	2	=	=	SYM
ejpam-5388	119	3	0	0	PROPN
ejpam-5388	119	4	.	.	PUNCT
ejpam-5388	120	1	now	now	ADV
ejpam-5388	120	2	,	,	PUNCT
ejpam-5388	120	3	we	we	PRON
ejpam-5388	120	4	have	have	VERB
ejpam-5388	120	5	φ(ω	φ(ω	NOUN
ejpam-5388	120	6	)	)	PUNCT
ejpam-5388	120	7	≤	≤	NUM
ejpam-5388	120	8	λ[φ(ω)−	λ[φ(ω)−	ADP
ejpam-5388	120	9	ϕ(ω	ϕ(ω	NOUN
ejpam-5388	120	10	)	)	PUNCT
ejpam-5388	120	11	]	]	PUNCT
ejpam-5388	121	1	<	<	X
ejpam-5388	121	2	φ(ω)−	φ(ω)−	PROPN
ejpam-5388	121	3	ϕ(ω	ϕ(ω	PROPN
ejpam-5388	121	4	)	)	PUNCT
ejpam-5388	121	5	<	<	X
ejpam-5388	122	1	φ(ω	φ(ω	PROPN
ejpam-5388	122	2	)	)	PUNCT
ejpam-5388	122	3	which	which	PRON
ejpam-5388	122	4	is	be	AUX
ejpam-5388	122	5	a	a	DET
ejpam-5388	122	6	contradiction	contradiction	NOUN
ejpam-5388	122	7	.	.	PUNCT
ejpam-5388	123	1	hence	hence	ADV
ejpam-5388	123	2	lim	lim	PROPN
ejpam-5388	123	3	n→∞	n→∞	X
ejpam-5388	124	1	λb(un	λb(un	PROPN
ejpam-5388	124	2	,	,	PUNCT
ejpam-5388	124	3	un+1	un+1	NOUN
ejpam-5388	124	4	)	)	PUNCT
ejpam-5388	124	5	=	=	SYM
ejpam-5388	124	6	0	0	X
ejpam-5388	124	7	.	.	PUNCT
ejpam-5388	125	1	(	(	PUNCT
ejpam-5388	125	2	2.5	2.5	NUM
ejpam-5388	125	3	)	)	PUNCT
ejpam-5388	125	4	now	now	ADV
ejpam-5388	125	5	,	,	PUNCT
ejpam-5388	125	6	we	we	PRON
ejpam-5388	125	7	want	want	VERB
ejpam-5388	125	8	to	to	PART
ejpam-5388	125	9	prove	prove	VERB
ejpam-5388	125	10	that	that	SCONJ
ejpam-5388	125	11	{	{	PUNCT
ejpam-5388	125	12	un	un	PROPN
ejpam-5388	125	13	}	}	PUNCT
ejpam-5388	125	14	is	be	AUX
ejpam-5388	125	15	a	a	DET
ejpam-5388	125	16	cauchy	cauchy	ADJ
ejpam-5388	125	17	sequence	sequence	NOUN
ejpam-5388	125	18	by	by	ADP
ejpam-5388	125	19	lemma	lemma	PROPN
ejpam-5388	125	20	1.8	1.8	NUM
ejpam-5388	125	21	,	,	PUNCT
ejpam-5388	125	22	∃	∃	PROPN
ejpam-5388	125	23	ε	ε	PROPN
ejpam-5388	125	24	>	>	X
ejpam-5388	125	25	0	0	NUM
ejpam-5388	126	1	and	and	CCONJ
ejpam-5388	126	2	two	two	NUM
ejpam-5388	126	3	subsequences	subsequence	NOUN
ejpam-5388	126	4	{	{	PUNCT
ejpam-5388	126	5	umi	umi	ADJ
ejpam-5388	126	6	}	}	PUNCT
ejpam-5388	126	7	and	and	CCONJ
ejpam-5388	126	8	{	{	PUNCT
ejpam-5388	126	9	uni	uni	PROPN
ejpam-5388	126	10	}	}	PUNCT
ejpam-5388	126	11	of	of	ADP
ejpam-5388	126	12	{	{	PUNCT
ejpam-5388	126	13	un	un	PROPN
ejpam-5388	126	14	}	}	PUNCT
ejpam-5388	126	15	with	with	ADP
ejpam-5388	126	16	mi	mi	PROPN
ejpam-5388	126	17	>	>	X
ejpam-5388	126	18	ni	ni	PROPN
ejpam-5388	126	19	>	>	X
ejpam-5388	127	1	i	i	PRON
ejpam-5388	127	2	such	such	ADJ
ejpam-5388	127	3	that	that	PRON
ejpam-5388	127	4	λb(uni	λb(uni	PROPN
ejpam-5388	127	5	,	,	PUNCT
ejpam-5388	127	6	umi	umi	PROPN
ejpam-5388	127	7	)	)	PUNCT
ejpam-5388	127	8	≥	≥	PROPN
ejpam-5388	127	9	ε	ε	PROPN
ejpam-5388	127	10	λb(uni−1	λb(uni−1	PROPN
ejpam-5388	127	11	,	,	PUNCT
ejpam-5388	127	12	umi	umi	PROPN
ejpam-5388	127	13	)	)	PUNCT
ejpam-5388	127	14	<	<	X
ejpam-5388	127	15	ε	ε	PROPN
ejpam-5388	127	16	.	.	PUNCT
ejpam-5388	128	1	by	by	ADP
ejpam-5388	128	2	using	use	VERB
ejpam-5388	128	3	the	the	DET
ejpam-5388	128	4	triangular	triangular	NOUN
ejpam-5388	128	5	inequality	inequality	NOUN
ejpam-5388	128	6	,	,	PUNCT
ejpam-5388	128	7	we	we	PRON
ejpam-5388	128	8	have	have	VERB
ejpam-5388	128	9	ε	ε	PROPN
ejpam-5388	128	10	≤	≤	NOUN
ejpam-5388	128	11	λb(uni	λb(uni	PROPN
ejpam-5388	128	12	,	,	PUNCT
ejpam-5388	128	13	umi	umi	PROPN
ejpam-5388	128	14	)	)	PUNCT
ejpam-5388	128	15	≤	≤	NOUN
ejpam-5388	129	1	λb(uni	λb(uni	X
ejpam-5388	129	2	,	,	PUNCT
ejpam-5388	129	3	uni−1	uni−1	PROPN
ejpam-5388	129	4	)	)	PUNCT
ejpam-5388	129	5	+	+	CCONJ
ejpam-5388	129	6	sλb(uni−1	sλb(uni−1	PROPN
ejpam-5388	129	7	,	,	PUNCT
ejpam-5388	129	8	umi	umi	PROPN
ejpam-5388	129	9	)	)	PUNCT
ejpam-5388	129	10	<	<	X
ejpam-5388	129	11	s[λb(uni	s[λb(uni	PUNCT
ejpam-5388	129	12	,	,	PUNCT
ejpam-5388	129	13	uni−1	uni−1	PROPN
ejpam-5388	129	14	)	)	PUNCT
ejpam-5388	129	15	+	+	CCONJ
ejpam-5388	129	16	ε	ε	PROPN
ejpam-5388	129	17	]	]	X
ejpam-5388	129	18	(	(	PUNCT
ejpam-5388	129	19	2.6	2.6	NUM
ejpam-5388	129	20	)	)	PUNCT
ejpam-5388	129	21	letting	let	VERB
ejpam-5388	129	22	i→	i→	VERB
ejpam-5388	130	1	+	+	NOUN
ejpam-5388	130	2	∞	∞	NUM
ejpam-5388	130	3	on	on	ADP
ejpam-5388	130	4	both	both	DET
ejpam-5388	130	5	sides	side	NOUN
ejpam-5388	130	6	of	of	ADP
ejpam-5388	130	7	(	(	PUNCT
ejpam-5388	130	8	2.6	2.6	NUM
ejpam-5388	130	9	)	)	PUNCT
ejpam-5388	130	10	and	and	CCONJ
ejpam-5388	130	11	using	use	VERB
ejpam-5388	130	12	(	(	PUNCT
ejpam-5388	130	13	2.5	2.5	NUM
ejpam-5388	130	14	)	)	PUNCT
ejpam-5388	130	15	,	,	PUNCT
ejpam-5388	130	16	we	we	PRON
ejpam-5388	130	17	obtain	obtain	VERB
ejpam-5388	130	18	ε	ε	PROPN
ejpam-5388	130	19	≤	≤	PROPN
ejpam-5388	130	20	lim	lim	PROPN
ejpam-5388	130	21	n→+∞	n→+∞	VERB
ejpam-5388	130	22	λb(uni	λb(uni	PROPN
ejpam-5388	130	23	,	,	PUNCT
ejpam-5388	130	24	umi	umi	PROPN
ejpam-5388	130	25	)	)	PUNCT
ejpam-5388	130	26	<	<	X
ejpam-5388	130	27	sε	sε	X
ejpam-5388	130	28	.	.	PUNCT
ejpam-5388	131	1	(	(	PUNCT
ejpam-5388	131	2	2.7	2.7	NUM
ejpam-5388	131	3	)	)	PUNCT
ejpam-5388	131	4	from	from	ADP
ejpam-5388	131	5	triangular	triangular	NOUN
ejpam-5388	131	6	inequality	inequality	NOUN
ejpam-5388	131	7	,	,	PUNCT
ejpam-5388	131	8	we	we	PRON
ejpam-5388	131	9	have	have	VERB
ejpam-5388	131	10	λb(uni	λb(uni	NOUN
ejpam-5388	131	11	,	,	PUNCT
ejpam-5388	131	12	umi	umi	PROPN
ejpam-5388	131	13	)	)	PUNCT
ejpam-5388	131	14	≤	≤	NOUN
ejpam-5388	131	15	s[λb(uni	s[λb(uni	X
ejpam-5388	131	16	,	,	PUNCT
ejpam-5388	131	17	uni+1	uni+1	PROPN
ejpam-5388	131	18	)	)	PUNCT
ejpam-5388	131	19	+	+	NUM
ejpam-5388	131	20	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	131	21	,	,	PUNCT
ejpam-5388	131	22	umi	umi	PROPN
ejpam-5388	131	23	)	)	PUNCT
ejpam-5388	131	24	]	]	PUNCT
ejpam-5388	131	25	,	,	PUNCT
ejpam-5388	131	26	(	(	PUNCT
ejpam-5388	131	27	2.8	2.8	NUM
ejpam-5388	131	28	)	)	PUNCT
ejpam-5388	131	29	and	and	CCONJ
ejpam-5388	131	30	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	131	31	,	,	PUNCT
ejpam-5388	131	32	umi	umi	PROPN
ejpam-5388	131	33	)	)	PUNCT
ejpam-5388	131	34	≤	≤	NUM
ejpam-5388	131	35	s[λb(uni+1	s[λb(uni+1	PROPN
ejpam-5388	131	36	,	,	PUNCT
ejpam-5388	131	37	uni	uni	PROPN
ejpam-5388	131	38	)	)	PUNCT
ejpam-5388	132	1	+	+	CCONJ
ejpam-5388	132	2	λb(uni	λb(uni	PROPN
ejpam-5388	132	3	,	,	PUNCT
ejpam-5388	132	4	umi	umi	PROPN
ejpam-5388	132	5	)	)	PUNCT
ejpam-5388	132	6	]	]	PUNCT
ejpam-5388	132	7	.	.	PUNCT
ejpam-5388	133	1	(	(	PUNCT
ejpam-5388	133	2	2.9	2.9	NUM
ejpam-5388	133	3	)	)	PUNCT
ejpam-5388	133	4	by	by	ADP
ejpam-5388	133	5	taking	take	VERB
ejpam-5388	133	6	upper	upper	ADJ
ejpam-5388	133	7	limit	limit	NOUN
ejpam-5388	133	8	as	as	ADP
ejpam-5388	133	9	i→	i→	PROPN
ejpam-5388	133	10	+	+	NOUN
ejpam-5388	133	11	∞	∞	NUM
ejpam-5388	133	12	in	in	ADP
ejpam-5388	133	13	(	(	PUNCT
ejpam-5388	133	14	2.8	2.8	NUM
ejpam-5388	133	15	)	)	PUNCT
ejpam-5388	133	16	and	and	CCONJ
ejpam-5388	133	17	applying	apply	VERB
ejpam-5388	133	18	(	(	PUNCT
ejpam-5388	133	19	2.5	2.5	NUM
ejpam-5388	133	20	)	)	PUNCT
ejpam-5388	133	21	,	,	PUNCT
ejpam-5388	133	22	(	(	PUNCT
ejpam-5388	133	23	2.7	2.7	NUM
ejpam-5388	133	24	)	)	PUNCT
ejpam-5388	133	25	,	,	PUNCT
ejpam-5388	133	26	we	we	PRON
ejpam-5388	133	27	get	get	VERB
ejpam-5388	133	28	ε	ε	PROPN
ejpam-5388	133	29	≤	≤	PROPN
ejpam-5388	134	1	lim	lim	PROPN
ejpam-5388	134	2	sup	sup	PROPN
ejpam-5388	134	3	i→+∞	i→+∞	PROPN
ejpam-5388	134	4	λb(uni	λb(uni	PROPN
ejpam-5388	134	5	,	,	PUNCT
ejpam-5388	134	6	umi	umi	PROPN
ejpam-5388	134	7	)	)	PUNCT
ejpam-5388	134	8	≤	≤	NOUN
ejpam-5388	134	9	s	s	PART
ejpam-5388	134	10	(	(	PUNCT
ejpam-5388	134	11	lim	lim	PROPN
ejpam-5388	134	12	sup	sup	PROPN
ejpam-5388	134	13	+	+	PROPN
ejpam-5388	134	14	i→+∞	i→+∞	PROPN
ejpam-5388	134	15	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	134	16	,	,	PUNCT
ejpam-5388	134	17	umi	umi	PROPN
ejpam-5388	134	18	)	)	PUNCT
ejpam-5388	134	19	)	)	PUNCT
ejpam-5388	134	20	.	.	PUNCT
ejpam-5388	135	1	again	again	ADV
ejpam-5388	135	2	,	,	PUNCT
ejpam-5388	135	3	by	by	ADP
ejpam-5388	135	4	letting	let	VERB
ejpam-5388	135	5	the	the	DET
ejpam-5388	135	6	upper	upper	ADJ
ejpam-5388	135	7	limit	limit	NOUN
ejpam-5388	135	8	as	as	ADP
ejpam-5388	135	9	i→	i→	PROPN
ejpam-5388	135	10	+	+	NOUN
ejpam-5388	135	11	∞	∞	NUM
ejpam-5388	135	12	in	in	ADP
ejpam-5388	135	13	(	(	PUNCT
ejpam-5388	135	14	2.9	2.9	NUM
ejpam-5388	135	15	)	)	PUNCT
ejpam-5388	135	16	,	,	PUNCT
ejpam-5388	135	17	we	we	PRON
ejpam-5388	135	18	have	have	VERB
ejpam-5388	135	19	lim	lim	PROPN
ejpam-5388	135	20	sup	sup	PROPN
ejpam-5388	135	21	i→+∞	i→+∞	PROPN
ejpam-5388	135	22	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	135	23	,	,	PUNCT
ejpam-5388	135	24	umi	umi	ADJ
ejpam-5388	135	25	)	)	PUNCT
ejpam-5388	135	26	≤	≤	NOUN
ejpam-5388	136	1	s	s	PART
ejpam-5388	136	2	(	(	PUNCT
ejpam-5388	136	3	lim	lim	PROPN
ejpam-5388	136	4	sup	sup	PROPN
ejpam-5388	136	5	i→+∞	i→+∞	PROPN
ejpam-5388	136	6	λb(uni	λb(uni	PROPN
ejpam-5388	136	7	,	,	PUNCT
ejpam-5388	136	8	umi	umi	PROPN
ejpam-5388	136	9	)	)	PUNCT
ejpam-5388	136	10	)	)	PUNCT
ejpam-5388	136	11	≤	≤	PUNCT
ejpam-5388	137	1	s.sε	s.sε	ADP
ejpam-5388	137	2	=	=	SYM
ejpam-5388	137	3	s2ε	s2ε	NOUN
ejpam-5388	137	4	.	.	PUNCT
ejpam-5388	138	1	thus	thus	ADV
ejpam-5388	138	2	ε	ε	PROPN
ejpam-5388	138	3	s	s	PART
ejpam-5388	138	4	≤	≤	PROPN
ejpam-5388	138	5	lim	lim	PROPN
ejpam-5388	138	6	sup	sup	PROPN
ejpam-5388	138	7	i→+∞	i→+∞	PROPN
ejpam-5388	138	8	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	138	9	,	,	PUNCT
ejpam-5388	138	10	umi	umi	ADJ
ejpam-5388	138	11	)	)	PUNCT
ejpam-5388	138	12	≤	≤	NUM
ejpam-5388	138	13	s2ε	s2ε	NOUN
ejpam-5388	138	14	.	.	PUNCT
ejpam-5388	139	1	(	(	PUNCT
ejpam-5388	139	2	2.10	2.10	NUM
ejpam-5388	139	3	)	)	PUNCT
ejpam-5388	139	4	similarly	similarly	ADV
ejpam-5388	139	5	,	,	PUNCT
ejpam-5388	139	6	ε	ε	PROPN
ejpam-5388	139	7	s	s	PART
ejpam-5388	139	8	≤	≤	PROPN
ejpam-5388	139	9	lim	lim	PROPN
ejpam-5388	139	10	sup	sup	PROPN
ejpam-5388	139	11	i→+∞	i→+∞	PROPN
ejpam-5388	139	12	λb(uni	λb(uni	PROPN
ejpam-5388	139	13	,	,	PUNCT
ejpam-5388	139	14	umi+1	umi+1	NOUN
ejpam-5388	139	15	)	)	PUNCT
ejpam-5388	139	16	≤	≤	NUM
ejpam-5388	139	17	s2ε	s2ε	NOUN
ejpam-5388	139	18	.	.	PUNCT
ejpam-5388	140	1	(	(	PUNCT
ejpam-5388	140	2	2.11	2.11	NUM
ejpam-5388	140	3	)	)	PUNCT
ejpam-5388	140	4	by	by	ADP
ejpam-5388	140	5	using	use	VERB
ejpam-5388	140	6	the	the	DET
ejpam-5388	140	7	triangular	triangular	NOUN
ejpam-5388	140	8	inequality	inequality	NOUN
ejpam-5388	140	9	,	,	PUNCT
ejpam-5388	140	10	we	we	PRON
ejpam-5388	140	11	get	get	VERB
ejpam-5388	140	12	λb(uni+1	λb(uni+1	ADV
ejpam-5388	140	13	,	,	PUNCT
ejpam-5388	140	14	umi	umi	ADJ
ejpam-5388	140	15	)	)	PUNCT
ejpam-5388	140	16	≤	≤	NUM
ejpam-5388	140	17	s[λb(uni+1	s[λb(uni+1	NOUN
ejpam-5388	140	18	,	,	PUNCT
ejpam-5388	140	19	umi+1	umi+1	NOUN
ejpam-5388	140	20	)	)	PUNCT
ejpam-5388	140	21	+	+	NUM
ejpam-5388	140	22	λb(umi+1	λb(umi+1	PROPN
ejpam-5388	140	23	,	,	PUNCT
ejpam-5388	140	24	umi	umi	PROPN
ejpam-5388	140	25	)	)	PUNCT
ejpam-5388	140	26	]	]	PUNCT
ejpam-5388	140	27	.	.	PUNCT
ejpam-5388	141	1	(	(	PUNCT
ejpam-5388	141	2	2.12	2.12	NUM
ejpam-5388	141	3	)	)	PUNCT
ejpam-5388	141	4	on	on	ADP
ejpam-5388	141	5	letting	let	VERB
ejpam-5388	141	6	i→	i→	VERB
ejpam-5388	142	1	+	+	NOUN
ejpam-5388	142	2	∞	∞	NUM
ejpam-5388	142	3	in	in	ADP
ejpam-5388	142	4	(	(	PUNCT
ejpam-5388	142	5	2.12	2.12	NUM
ejpam-5388	142	6	)	)	PUNCT
ejpam-5388	142	7	and	and	CCONJ
ejpam-5388	142	8	using	use	VERB
ejpam-5388	142	9	the	the	DET
ejpam-5388	142	10	inequalities	inequality	NOUN
ejpam-5388	142	11	(	(	PUNCT
ejpam-5388	142	12	2.5	2.5	NUM
ejpam-5388	142	13	)	)	PUNCT
ejpam-5388	142	14	,	,	PUNCT
ejpam-5388	142	15	(	(	PUNCT
ejpam-5388	142	16	2.10	2.10	NUM
ejpam-5388	142	17	)	)	PUNCT
ejpam-5388	142	18	,	,	PUNCT
ejpam-5388	142	19	we	we	PRON
ejpam-5388	142	20	get	get	VERB
ejpam-5388	142	21	ε	ε	PROPN
ejpam-5388	142	22	s2	s2	VERB
ejpam-5388	142	23	≤	≤	NUM
ejpam-5388	142	24	lim	lim	PROPN
ejpam-5388	142	25	sup	sup	PROPN
ejpam-5388	142	26	i→+∞	i→+∞	PROPN
ejpam-5388	142	27	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	142	28	,	,	PUNCT
ejpam-5388	142	29	umi+1	umi+1	NOUN
ejpam-5388	142	30	)	)	PUNCT
ejpam-5388	142	31	.	.	PUNCT
ejpam-5388	143	1	(	(	PUNCT
ejpam-5388	143	2	2.13	2.13	NUM
ejpam-5388	143	3	)	)	PUNCT
ejpam-5388	143	4	h.	h.	NOUN
ejpam-5388	143	5	alsamir	alsamir	VERB
ejpam-5388	143	6	et	et	PROPN
ejpam-5388	143	7	al	al	PROPN
ejpam-5388	143	8	.	.	PUNCT
ejpam-5388	143	9	/	/	SYM
ejpam-5388	143	10	eur	eur	PROPN
ejpam-5388	143	11	.	.	PUNCT
ejpam-5388	144	1	j.	j.	PROPN
ejpam-5388	144	2	pure	pure	PROPN
ejpam-5388	144	3	appl	appl	PROPN
ejpam-5388	144	4	.	.	PROPN
ejpam-5388	144	5	math	math	PROPN
ejpam-5388	144	6	,	,	PUNCT
ejpam-5388	144	7	17	17	NUM
ejpam-5388	144	8	(	(	PUNCT
ejpam-5388	144	9	4	4	NUM
ejpam-5388	144	10	)	)	PUNCT
ejpam-5388	144	11	(	(	PUNCT
ejpam-5388	144	12	2024	2024	NUM
ejpam-5388	144	13	)	)	PUNCT
ejpam-5388	144	14	,	,	PUNCT
ejpam-5388	144	15	2492	2492	NUM
ejpam-5388	144	16	-	-	SYM
ejpam-5388	144	17	2504	2504	NUM
ejpam-5388	144	18	2497	2497	NUM
ejpam-5388	144	19	by	by	ADP
ejpam-5388	144	20	following	follow	VERB
ejpam-5388	144	21	the	the	DET
ejpam-5388	144	22	above	above	ADJ
ejpam-5388	144	23	methods	method	NOUN
ejpam-5388	144	24	,	,	PUNCT
ejpam-5388	144	25	we	we	PRON
ejpam-5388	144	26	find	find	VERB
ejpam-5388	144	27	lim	lim	PROPN
ejpam-5388	144	28	sup	sup	PROPN
ejpam-5388	144	29	i→+∞	i→+∞	PROPN
ejpam-5388	144	30	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	144	31	,	,	PUNCT
ejpam-5388	144	32	umi+1	umi+1	NOUN
ejpam-5388	144	33	)	)	PUNCT
ejpam-5388	144	34	≤	≤	NUM
ejpam-5388	144	35	s3ε	s3ε	NOUN
ejpam-5388	144	36	.	.	PUNCT
ejpam-5388	145	1	(	(	PUNCT
ejpam-5388	145	2	2.14	2.14	NUM
ejpam-5388	145	3	)	)	PUNCT
ejpam-5388	145	4	from	from	ADP
ejpam-5388	145	5	(	(	PUNCT
ejpam-5388	145	6	2.13	2.13	NUM
ejpam-5388	145	7	)	)	PUNCT
ejpam-5388	145	8	and	and	CCONJ
ejpam-5388	145	9	(	(	PUNCT
ejpam-5388	145	10	2.14	2.14	NUM
ejpam-5388	145	11	)	)	PUNCT
ejpam-5388	145	12	,	,	PUNCT
ejpam-5388	145	13	we	we	PRON
ejpam-5388	145	14	obtain	obtain	VERB
ejpam-5388	145	15	ε	ε	PROPN
ejpam-5388	145	16	s	s	PART
ejpam-5388	145	17	≤	≤	NOUN
ejpam-5388	145	18	lim	lim	PROPN
ejpam-5388	145	19	sup	sup	PROPN
ejpam-5388	145	20	i→+∞	i→+∞	PROPN
ejpam-5388	145	21	λb(uni+1	λb(uni+1	PROPN
ejpam-5388	145	22	,	,	PUNCT
ejpam-5388	145	23	umi+1	umi+1	NOUN
ejpam-5388	145	24	)	)	PUNCT
ejpam-5388	145	25	≤	≤	NUM
ejpam-5388	145	26	s3ε	s3ε	NOUN
ejpam-5388	145	27	.	.	PUNCT
ejpam-5388	146	1	(	(	PUNCT
ejpam-5388	146	2	2.15	2.15	NUM
ejpam-5388	146	3	)	)	PUNCT
ejpam-5388	146	4	by	by	ADP
ejpam-5388	146	5	lemma	lemma	PROPN
ejpam-5388	146	6	1.8	1.8	NUM
ejpam-5388	146	7	,	,	PUNCT
ejpam-5388	146	8	we	we	PRON
ejpam-5388	146	9	have	have	VERB
ejpam-5388	146	10	α(uni+1	α(uni+1	PROPN
ejpam-5388	146	11	,	,	PUNCT
ejpam-5388	146	12	umi+1	umi+1	NOUN
ejpam-5388	146	13	)	)	PUNCT
ejpam-5388	146	14	≥	≥	NOUN
ejpam-5388	146	15	η(uni+1	η(uni+1	NOUN
ejpam-5388	146	16	,	,	PUNCT
ejpam-5388	146	17	umi+1	umi+1	NOUN
ejpam-5388	146	18	)	)	PUNCT
ejpam-5388	146	19	.	.	PUNCT
ejpam-5388	147	1	thus	thus	ADV
ejpam-5388	147	2	,	,	PUNCT
ejpam-5388	147	3	we	we	PRON
ejpam-5388	147	4	have	have	VERB
ejpam-5388	147	5	φ(λb(uni+1	φ(λb(uni+1	NUM
ejpam-5388	147	6	,	,	PUNCT
ejpam-5388	147	7	umi+1	umi+1	NOUN
ejpam-5388	147	8	)	)	PUNCT
ejpam-5388	147	9	)	)	PUNCT
ejpam-5388	148	1	≤	≤	PROPN
ejpam-5388	149	1	φ(s2λb(uni+1	φ(s2λb(uni+1	ADP
ejpam-5388	149	2	,	,	PUNCT
ejpam-5388	149	3	umi+1	umi+1	NOUN
ejpam-5388	149	4	)	)	PUNCT
ejpam-5388	149	5	)	)	PUNCT
ejpam-5388	149	6	≤	≤	NUM
ejpam-5388	150	1	λ	λ	PROPN
ejpam-5388	151	1	[	[	X
ejpam-5388	151	2	φ	φ	X
ejpam-5388	151	3	(	(	PUNCT
ejpam-5388	151	4	mλb	mλb	PROPN
ejpam-5388	151	5	(	(	PUNCT
ejpam-5388	151	6	uni	uni	INTJ
ejpam-5388	151	7	,	,	PUNCT
ejpam-5388	151	8	umi))−	umi))−	PROPN
ejpam-5388	151	9	ϕ	ϕ	NOUN
ejpam-5388	151	10	(	(	PUNCT
ejpam-5388	151	11	mλb	mλb	PROPN
ejpam-5388	151	12	(	(	PUNCT
ejpam-5388	151	13	uni	uni	PROPN
ejpam-5388	151	14	,	,	PUNCT
ejpam-5388	151	15	umi	umi	PROPN
ejpam-5388	151	16	)	)	PUNCT
ejpam-5388	151	17	)	)	PUNCT
ejpam-5388	152	1	+	+	CCONJ
ejpam-5388	152	2	l	l	NOUN
ejpam-5388	152	3	(	(	PUNCT
ejpam-5388	152	4	nλb	nλb	PROPN
ejpam-5388	152	5	(	(	PUNCT
ejpam-5388	152	6	uni	uni	INTJ
ejpam-5388	152	7	,	,	PUNCT
ejpam-5388	152	8	umi	umi	PROPN
ejpam-5388	152	9	)	)	PUNCT
ejpam-5388	152	10	)	)	PUNCT
ejpam-5388	152	11	]	]	PUNCT
ejpam-5388	153	1	=	=	PUNCT
ejpam-5388	154	1	[	[	X
ejpam-5388	154	2	λφ	λφ	X
ejpam-5388	154	3	(	(	PUNCT
ejpam-5388	154	4	mλb	mλb	PROPN
ejpam-5388	154	5	(	(	PUNCT
ejpam-5388	154	6	uni	uni	INTJ
ejpam-5388	154	7	,	,	PUNCT
ejpam-5388	154	8	umi))−	umi))−	INTJ
ejpam-5388	154	9	λϕ	λϕ	ADV
ejpam-5388	154	10	(	(	PUNCT
ejpam-5388	154	11	mλb	mλb	PROPN
ejpam-5388	154	12	(	(	PUNCT
ejpam-5388	154	13	uni	uni	PROPN
ejpam-5388	154	14	,	,	PUNCT
ejpam-5388	154	15	umi	umi	PROPN
ejpam-5388	154	16	)	)	PUNCT
ejpam-5388	154	17	)	)	PUNCT
ejpam-5388	155	1	+	+	CCONJ
ejpam-5388	155	2	λl	λl	X
ejpam-5388	155	3	(	(	PUNCT
ejpam-5388	155	4	nλb	nλb	PROPN
ejpam-5388	155	5	(	(	PUNCT
ejpam-5388	155	6	uni	uni	INTJ
ejpam-5388	155	7	,	,	PUNCT
ejpam-5388	155	8	umi	umi	PROPN
ejpam-5388	155	9	)	)	PUNCT
ejpam-5388	155	10	)	)	PUNCT
ejpam-5388	155	11	]	]	PUNCT
ejpam-5388	155	12	,	,	PUNCT
ejpam-5388	155	13	where	where	SCONJ
ejpam-5388	155	14	mλb	mλb	PROPN
ejpam-5388	155	15	(	(	PUNCT
ejpam-5388	155	16	uni	uni	PROPN
ejpam-5388	155	17	,	,	PUNCT
ejpam-5388	155	18	umi	umi	PROPN
ejpam-5388	155	19	)	)	PUNCT
ejpam-5388	155	20	=	=	SYM
ejpam-5388	155	21	max{λb(uni	max{λb(uni	X
ejpam-5388	155	22	,	,	PUNCT
ejpam-5388	155	23	umi),λb(uni	umi),λb(uni	PROPN
ejpam-5388	155	24	,	,	PUNCT
ejpam-5388	155	25	puni),λb(umi	puni),λb(umi	NOUN
ejpam-5388	155	26	,	,	PUNCT
ejpam-5388	155	27	qumi	qumi	ADJ
ejpam-5388	155	28	)	)	PUNCT
ejpam-5388	155	29	,	,	PUNCT
ejpam-5388	155	30	λb(uni	λb(uni	NOUN
ejpam-5388	155	31	,	,	PUNCT
ejpam-5388	155	32	qumi	qumi	ADJ
ejpam-5388	155	33	)	)	PUNCT
ejpam-5388	155	34	+	+	CCONJ
ejpam-5388	155	35	λb(puni	λb(puni	NOUN
ejpam-5388	155	36	,	,	PUNCT
ejpam-5388	155	37	umi	umi	ADJ
ejpam-5388	155	38	)	)	PUNCT
ejpam-5388	155	39	2s(1	2s(1	X
ejpam-5388	155	40	+	+	CCONJ
ejpam-5388	155	41	λb(puni	λb(puni	NOUN
ejpam-5388	155	42	,	,	PUNCT
ejpam-5388	155	43	umi	umi	PROPN
ejpam-5388	155	44	)	)	PUNCT
ejpam-5388	155	45	)	)	PUNCT
ejpam-5388	155	46	}	}	PUNCT
ejpam-5388	155	47	.	.	PUNCT
ejpam-5388	156	1	nλb	nλb	PROPN
ejpam-5388	156	2	(	(	PUNCT
ejpam-5388	156	3	uni	uni	INTJ
ejpam-5388	156	4	,	,	PUNCT
ejpam-5388	156	5	umi	umi	PROPN
ejpam-5388	156	6	)	)	PUNCT
ejpam-5388	156	7	=	=	SYM
ejpam-5388	156	8	min	min	NOUN
ejpam-5388	156	9	{	{	PUNCT
ejpam-5388	156	10	λb(uni	λb(uni	X
ejpam-5388	156	11	,	,	PUNCT
ejpam-5388	156	12	umi),λb(uni	umi),λb(uni	PROPN
ejpam-5388	156	13	,	,	PUNCT
ejpam-5388	156	14	puni),λb(umi	puni),λb(umi	NOUN
ejpam-5388	156	15	,	,	PUNCT
ejpam-5388	156	16	qumi),λb(umi	qumi),λb(umi	NOUN
ejpam-5388	156	17	,	,	PUNCT
ejpam-5388	156	18	puni	puni	ADJ
ejpam-5388	156	19	)	)	PUNCT
ejpam-5388	156	20	}	}	PUNCT
ejpam-5388	156	21	=	=	SYM
ejpam-5388	156	22	min	min	NOUN
ejpam-5388	156	23	{	{	PUNCT
ejpam-5388	156	24	λb(uni	λb(uni	X
ejpam-5388	156	25	,	,	PUNCT
ejpam-5388	156	26	umi),λb(uni	umi),λb(uni	PROPN
ejpam-5388	156	27	,	,	PUNCT
ejpam-5388	156	28	uni+1),λb(umi	uni+1),λb(umi	PROPN
ejpam-5388	156	29	,	,	PUNCT
ejpam-5388	156	30	umi+1),λb(umi	umi+1),λb(umi	PROPN
ejpam-5388	156	31	,	,	PUNCT
ejpam-5388	156	32	uni+1)}(2.16	uni+1)}(2.16	PROPN
ejpam-5388	156	33	)	)	PUNCT
ejpam-5388	156	34	taking	take	VERB
ejpam-5388	156	35	the	the	DET
ejpam-5388	156	36	limit	limit	NOUN
ejpam-5388	156	37	as	as	ADP
ejpam-5388	156	38	i	i	PRON
ejpam-5388	156	39	→	→	PUNCT
ejpam-5388	157	1	+	+	ADJ
ejpam-5388	157	2	∞	∞	PROPN
ejpam-5388	157	3	in	in	ADP
ejpam-5388	157	4	the	the	DET
ejpam-5388	157	5	above	above	ADJ
ejpam-5388	157	6	two	two	NUM
ejpam-5388	157	7	expressions	expression	NOUN
ejpam-5388	157	8	and	and	CCONJ
ejpam-5388	157	9	using	use	VERB
ejpam-5388	157	10	(	(	PUNCT
ejpam-5388	157	11	2.5),(2.7	2.5),(2.7	NUM
ejpam-5388	157	12	)	)	PUNCT
ejpam-5388	157	13	,	,	PUNCT
ejpam-5388	157	14	(	(	PUNCT
ejpam-5388	157	15	2.10	2.10	NUM
ejpam-5388	157	16	)	)	PUNCT
ejpam-5388	157	17	and	and	CCONJ
ejpam-5388	157	18	(	(	PUNCT
ejpam-5388	157	19	2.11	2.11	NUM
ejpam-5388	157	20	)	)	PUNCT
ejpam-5388	157	21	,	,	PUNCT
ejpam-5388	157	22	we	we	PRON
ejpam-5388	157	23	obtain	obtain	VERB
ejpam-5388	157	24	ε	ε	X
ejpam-5388	157	25	=	=	SYM
ejpam-5388	157	26	max{ε	max{ε	PROPN
ejpam-5388	157	27	,	,	PUNCT
ejpam-5388	158	1	ε	ε	PROPN
ejpam-5388	158	2	s	s	PART
ejpam-5388	159	1	+	+	CCONJ
ejpam-5388	159	2	ε	ε	PROPN
ejpam-5388	159	3	s	s	PART
ejpam-5388	159	4	2s	2s	PROPN
ejpam-5388	159	5	}	}	PUNCT
ejpam-5388	159	6	≤	≤	PROPN
ejpam-5388	159	7	lim	lim	PROPN
ejpam-5388	159	8	sup	sup	PROPN
ejpam-5388	159	9	i→+∞	i→+∞	PROPN
ejpam-5388	159	10	λb(uni	λb(uni	PROPN
ejpam-5388	159	11	,	,	PUNCT
ejpam-5388	159	12	umi	umi	PROPN
ejpam-5388	159	13	)	)	PUNCT
ejpam-5388	159	14	≤	≤	NOUN
ejpam-5388	159	15	max{sε	max{sε	NOUN
ejpam-5388	159	16	,	,	PUNCT
ejpam-5388	159	17	s	s	PART
ejpam-5388	159	18	2ε+	2ε+	NUM
ejpam-5388	159	19	s2ε	s2ε	NOUN
ejpam-5388	159	20	2s	2s	NUM
ejpam-5388	159	21	}	}	PUNCT
ejpam-5388	159	22	=	=	SYM
ejpam-5388	159	23	sε	sε	PROPN
ejpam-5388	159	24	.	.	PUNCT
ejpam-5388	160	1	lim	lim	PROPN
ejpam-5388	160	2	sup	sup	PROPN
ejpam-5388	160	3	i→+∞	i→+∞	PROPN
ejpam-5388	160	4	nλb	nλb	PROPN
ejpam-5388	160	5	(	(	PUNCT
ejpam-5388	160	6	uni	uni	INTJ
ejpam-5388	160	7	,	,	PUNCT
ejpam-5388	160	8	umi	umi	PROPN
ejpam-5388	160	9	)	)	PUNCT
ejpam-5388	161	1	=	=	SYM
ejpam-5388	161	2	0	0	X
ejpam-5388	161	3	.	.	PUNCT
ejpam-5388	162	1	from	from	ADP
ejpam-5388	162	2	(	(	PUNCT
ejpam-5388	162	3	2.13	2.13	NUM
ejpam-5388	162	4	)	)	PUNCT
ejpam-5388	162	5	,	,	PUNCT
ejpam-5388	162	6	we	we	PRON
ejpam-5388	162	7	obtain	obtain	VERB
ejpam-5388	162	8	φ(sε	φ(sε	NOUN
ejpam-5388	162	9	)	)	PUNCT
ejpam-5388	162	10	≤	≤	NOUN
ejpam-5388	162	11	φ(s2	φ(s2	NOUN
ejpam-5388	162	12	ε	ε	PROPN
ejpam-5388	162	13	s2	s2	PROPN
ejpam-5388	162	14	)	)	PUNCT
ejpam-5388	162	15	≤	≤	NOUN
ejpam-5388	163	1	φ(s2	φ(s2	NOUN
ejpam-5388	163	2	lim	lim	PROPN
ejpam-5388	163	3	sup	sup	PROPN
ejpam-5388	163	4	i→+∞	i→+∞	PROPN
ejpam-5388	163	5	φ(λb(uni+1	φ(λb(uni+1	PROPN
ejpam-5388	163	6	,	,	PUNCT
ejpam-5388	163	7	umi+1	umi+1	NOUN
ejpam-5388	163	8	)	)	PUNCT
ejpam-5388	163	9	)	)	PUNCT
ejpam-5388	164	1	≤	≤	NUM
ejpam-5388	164	2	λ[φ(lim	λ[φ(lim	NOUN
ejpam-5388	164	3	sup	sup	PROPN
ejpam-5388	164	4	i→+∞	i→+∞	PROPN
ejpam-5388	164	5	mλb	mλb	PROPN
ejpam-5388	164	6	(	(	PUNCT
ejpam-5388	164	7	uni	uni	INTJ
ejpam-5388	164	8	,	,	PUNCT
ejpam-5388	164	9	umi)−	umi)−	PROPN
ejpam-5388	164	10	ϕ(lim	ϕ(lim	PROPN
ejpam-5388	164	11	inf	inf	NOUN
ejpam-5388	164	12	i→+∞	i→+∞	PROPN
ejpam-5388	164	13	mλb	mλb	PROPN
ejpam-5388	164	14	(	(	PUNCT
ejpam-5388	164	15	uni	uni	PROPN
ejpam-5388	164	16	,	,	PUNCT
ejpam-5388	164	17	umi	umi	ADJ
ejpam-5388	164	18	)	)	PUNCT
ejpam-5388	164	19	≤	≤	NOUN
ejpam-5388	164	20	λ[φ(sε)−	λ[φ(sε)−	PROPN
ejpam-5388	164	21	ϕ(sε	ϕ(sε	NOUN
ejpam-5388	164	22	)	)	PUNCT
ejpam-5388	164	23	]	]	PUNCT
ejpam-5388	165	1	≤	≤	NOUN
ejpam-5388	166	1	λ(φ(sε))−	λ(φ(sε))−	NUM
ejpam-5388	166	2	λ(ϕ(sε	λ(ϕ(sε	NOUN
ejpam-5388	166	3	)	)	PUNCT
ejpam-5388	166	4	)	)	PUNCT
ejpam-5388	167	1	<	<	X
ejpam-5388	167	2	λφ(sε	λφ(sε	NOUN
ejpam-5388	167	3	)	)	PUNCT
ejpam-5388	167	4	which	which	PRON
ejpam-5388	167	5	leads	lead	VERB
ejpam-5388	167	6	to	to	ADP
ejpam-5388	167	7	a	a	DET
ejpam-5388	167	8	contradiction	contradiction	NOUN
ejpam-5388	167	9	.	.	PUNCT
ejpam-5388	168	1	thus	thus	ADV
ejpam-5388	168	2	{	{	PUNCT
ejpam-5388	168	3	un	un	PROPN
ejpam-5388	168	4	}	}	PUNCT
ejpam-5388	168	5	is	be	AUX
ejpam-5388	168	6	a	a	DET
ejpam-5388	168	7	cauchy	cauchy	ADJ
ejpam-5388	168	8	sequence	sequence	NOUN
ejpam-5388	168	9	.	.	PUNCT
ejpam-5388	169	1	since	since	SCONJ
ejpam-5388	169	2	𭟋	𭟋	NOUN
ejpam-5388	169	3	is	be	AUX
ejpam-5388	169	4	an	an	DET
ejpam-5388	169	5	complete	complete	ADJ
ejpam-5388	169	6	bmetric	bmetric	ADJ
ejpam-5388	169	7	space	space	NOUN
ejpam-5388	169	8	and	and	CCONJ
ejpam-5388	169	9	α(uni+1	α(uni+1	PROPN
ejpam-5388	169	10	,	,	PUNCT
ejpam-5388	169	11	umi+1	umi+1	NOUN
ejpam-5388	169	12	)	)	PUNCT
ejpam-5388	169	13	≥	≥	NOUN
ejpam-5388	169	14	η(uni+1	η(uni+1	NOUN
ejpam-5388	169	15	,	,	PUNCT
ejpam-5388	169	16	umi+1	umi+1	NOUN
ejpam-5388	169	17	)	)	PUNCT
ejpam-5388	169	18	for	for	ADP
ejpam-5388	169	19	all	all	DET
ejpam-5388	169	20	n	n	PRON
ejpam-5388	169	21	∈	∈	PROPN
ejpam-5388	169	22	n0	n0	NOUN
ejpam-5388	169	23	,	,	PUNCT
ejpam-5388	169	24	there	there	PRON
ejpam-5388	169	25	exists	exist	VERB
ejpam-5388	169	26	θ	θ	NOUN
ejpam-5388	169	27	such	such	ADJ
ejpam-5388	169	28	that	that	PRON
ejpam-5388	169	29	limn→+∞	limn→+∞	ADP
ejpam-5388	169	30	un	un	PROPN
ejpam-5388	169	31	=	=	PROPN
ejpam-5388	169	32	θ	θ	PROPN
ejpam-5388	169	33	.	.	PUNCT
ejpam-5388	170	1	if	if	SCONJ
ejpam-5388	170	2	p	p	NOUN
ejpam-5388	170	3	is	be	AUX
ejpam-5388	170	4	continuous	continuous	ADJ
ejpam-5388	170	5	,	,	PUNCT
ejpam-5388	170	6	we	we	PRON
ejpam-5388	170	7	have	have	AUX
ejpam-5388	170	8	pθ	pθ	VERB
ejpam-5388	170	9	=	=	PUNCT
ejpam-5388	170	10	limn→+∞	limn→+∞	PROPN
ejpam-5388	170	11	pu2n	pu2n	PROPN
ejpam-5388	170	12	=	=	PUNCT
ejpam-5388	170	13	limn→+∞	limn→+∞	VERB
ejpam-5388	170	14	u2n+1	u2n+1	PROPN
ejpam-5388	170	15	=	=	SYM
ejpam-5388	170	16	θ	θ	PROPN
ejpam-5388	170	17	.	.	NOUN
ejpam-5388	170	18	from	from	ADP
ejpam-5388	170	19	condition	condition	NOUN
ejpam-5388	170	20	(	(	PUNCT
ejpam-5388	170	21	2.2	2.2	NUM
ejpam-5388	170	22	)	)	PUNCT
ejpam-5388	170	23	,	,	PUNCT
ejpam-5388	170	24	we	we	PRON
ejpam-5388	170	25	have	have	VERB
ejpam-5388	170	26	:	:	PUNCT
ejpam-5388	170	27	φ(λb(θ	φ(λb(θ	NUM
ejpam-5388	170	28	,	,	PUNCT
ejpam-5388	170	29	qθ	qθ	NOUN
ejpam-5388	170	30	)	)	PUNCT
ejpam-5388	170	31	)	)	PUNCT
ejpam-5388	171	1	≤	≤	NOUN
ejpam-5388	171	2	φ(s2λb(θ	φ(s2λb(θ	ADP
ejpam-5388	171	3	,	,	PUNCT
ejpam-5388	171	4	θ	θ	NOUN
ejpam-5388	171	5	)	)	PUNCT
ejpam-5388	171	6	)	)	PUNCT
ejpam-5388	171	7	≤	≤	NUM
ejpam-5388	171	8	λ[(φ(mλb	λ[(φ(mλb	PROPN
ejpam-5388	171	9	(	(	PUNCT
ejpam-5388	171	10	θ	θ	PROPN
ejpam-5388	171	11	,	,	PUNCT
ejpam-5388	171	12	θ))−	θ))−	NUM
ejpam-5388	171	13	ϕ(mλb	ϕ(mλb	PROPN
ejpam-5388	171	14	(	(	PUNCT
ejpam-5388	171	15	θ	θ	PROPN
ejpam-5388	171	16	,	,	PUNCT
ejpam-5388	171	17	θ	θ	NOUN
ejpam-5388	171	18	)	)	PUNCT
ejpam-5388	171	19	)	)	PUNCT
ejpam-5388	172	1	+	+	CCONJ
ejpam-5388	172	2	lnλb	lnλb	ADJ
ejpam-5388	172	3	(	(	PUNCT
ejpam-5388	172	4	θ	θ	NOUN
ejpam-5388	172	5	,	,	PUNCT
ejpam-5388	172	6	θ	θ	NOUN
ejpam-5388	172	7	)	)	PUNCT
ejpam-5388	172	8	]	]	PUNCT
ejpam-5388	172	9	h.	h.	PROPN
ejpam-5388	172	10	alsamir	alsamir	VERB
ejpam-5388	172	11	et	et	PROPN
ejpam-5388	172	12	al	al	PROPN
ejpam-5388	172	13	.	.	PUNCT
ejpam-5388	172	14	/	/	SYM
ejpam-5388	172	15	eur	eur	PROPN
ejpam-5388	172	16	.	.	PUNCT
ejpam-5388	173	1	j.	j.	PROPN
ejpam-5388	173	2	pure	pure	PROPN
ejpam-5388	173	3	appl	appl	PROPN
ejpam-5388	173	4	.	.	PROPN
ejpam-5388	173	5	math	math	PROPN
ejpam-5388	173	6	,	,	PUNCT
ejpam-5388	173	7	17	17	NUM
ejpam-5388	173	8	(	(	PUNCT
ejpam-5388	173	9	4	4	NUM
ejpam-5388	173	10	)	)	PUNCT
ejpam-5388	173	11	(	(	PUNCT
ejpam-5388	173	12	2024	2024	NUM
ejpam-5388	173	13	)	)	PUNCT
ejpam-5388	173	14	,	,	PUNCT
ejpam-5388	173	15	2492	2492	NUM
ejpam-5388	173	16	-	-	SYM
ejpam-5388	173	17	2504	2504	NUM
ejpam-5388	173	18	2498	2498	NUM
ejpam-5388	173	19	for	for	ADP
ejpam-5388	173	20	all	all	PRON
ejpam-5388	173	21	n	n	PRON
ejpam-5388	173	22	∈	∈	PROPN
ejpam-5388	173	23	n	n	CCONJ
ejpam-5388	173	24	,	,	PUNCT
ejpam-5388	173	25	where	where	SCONJ
ejpam-5388	173	26	mλb	mλb	PROPN
ejpam-5388	173	27	(	(	PUNCT
ejpam-5388	173	28	θ	θ	PROPN
ejpam-5388	173	29	,	,	PUNCT
ejpam-5388	173	30	θ	θ	NOUN
ejpam-5388	173	31	)	)	PUNCT
ejpam-5388	173	32	=	=	SYM
ejpam-5388	173	33	max{λb(θ	max{λb(θ	PROPN
ejpam-5388	173	34	,	,	PUNCT
ejpam-5388	173	35	θ),λb(θ	θ),λb(θ	PROPN
ejpam-5388	173	36	,	,	PUNCT
ejpam-5388	173	37	pθ),λb(θ	pθ),λb(θ	NOUN
ejpam-5388	173	38	,	,	PUNCT
ejpam-5388	173	39	qθ	qθ	PROPN
ejpam-5388	173	40	)	)	PUNCT
ejpam-5388	173	41	,	,	PUNCT
ejpam-5388	173	42	λb(θ	λb(θ	ADV
ejpam-5388	173	43	,	,	PUNCT
ejpam-5388	173	44	qθ	qθ	PROPN
ejpam-5388	173	45	)	)	PUNCT
ejpam-5388	174	1	+	+	CCONJ
ejpam-5388	174	2	λb(pθ	λb(pθ	PROPN
ejpam-5388	174	3	,	,	PUNCT
ejpam-5388	174	4	θ	θ	NOUN
ejpam-5388	174	5	)	)	PUNCT
ejpam-5388	174	6	2s(1	2s(1	X
ejpam-5388	174	7	+	+	CCONJ
ejpam-5388	174	8	λb(pθ	λb(pθ	PROPN
ejpam-5388	174	9	,	,	PUNCT
ejpam-5388	174	10	θ	θ	NOUN
ejpam-5388	174	11	)	)	PUNCT
ejpam-5388	174	12	)	)	PUNCT
ejpam-5388	174	13	}	}	PUNCT
ejpam-5388	175	1	=	=	PUNCT
ejpam-5388	175	2	λb(θ	λb(θ	ADV
ejpam-5388	175	3	,	,	PUNCT
ejpam-5388	175	4	qθ	qθ	PROPN
ejpam-5388	175	5	)	)	PUNCT
ejpam-5388	175	6	and	and	CCONJ
ejpam-5388	175	7	nλb	nλb	INTJ
ejpam-5388	175	8	(	(	PUNCT
ejpam-5388	175	9	θ	θ	NOUN
ejpam-5388	175	10	,	,	PUNCT
ejpam-5388	175	11	θ	θ	NOUN
ejpam-5388	175	12	)	)	PUNCT
ejpam-5388	175	13	=	=	SYM
ejpam-5388	175	14	min{λb(θ	min{λb(θ	PROPN
ejpam-5388	175	15	,	,	PUNCT
ejpam-5388	175	16	θ),λb(θ	θ),λb(θ	PROPN
ejpam-5388	175	17	,	,	PUNCT
ejpam-5388	175	18	pθ),λb(θ	pθ),λb(θ	NOUN
ejpam-5388	175	19	,	,	PUNCT
ejpam-5388	175	20	qθ),λb(θ	qθ),λb(θ	PROPN
ejpam-5388	175	21	,	,	PUNCT
ejpam-5388	175	22	qθ	qθ	NOUN
ejpam-5388	175	23	)	)	PUNCT
ejpam-5388	175	24	}	}	PUNCT
ejpam-5388	175	25	=	=	SYM
ejpam-5388	176	1	0	0	X
ejpam-5388	176	2	.	.	PUNCT
ejpam-5388	176	3	by	by	ADP
ejpam-5388	176	4	using	use	VERB
ejpam-5388	176	5	the	the	DET
ejpam-5388	176	6	properties	property	NOUN
ejpam-5388	176	7	of	of	ADP
ejpam-5388	176	8	φ	φ	PROPN
ejpam-5388	176	9	and	and	CCONJ
ejpam-5388	176	10	ϕ	ϕ	PROPN
ejpam-5388	176	11	,	,	PUNCT
ejpam-5388	176	12	we	we	PRON
ejpam-5388	176	13	have	have	VERB
ejpam-5388	176	14	φ(λb(θ	φ(λb(θ	NUM
ejpam-5388	176	15	,	,	PUNCT
ejpam-5388	176	16	qθ	qθ	NOUN
ejpam-5388	176	17	)	)	PUNCT
ejpam-5388	176	18	)	)	PUNCT
ejpam-5388	177	1	=	=	SYM
ejpam-5388	177	2	φ(s2λb(pθ	φ(s2λb(pθ	PROPN
ejpam-5388	177	3	,	,	PUNCT
ejpam-5388	177	4	qθ	qθ	NOUN
ejpam-5388	177	5	)	)	PUNCT
ejpam-5388	177	6	)	)	PUNCT
ejpam-5388	177	7	≤	≤	NUM
ejpam-5388	177	8	λ[(φ(mλb	λ[(φ(mλb	PROPN
ejpam-5388	177	9	(	(	PUNCT
ejpam-5388	177	10	θ	θ	NOUN
ejpam-5388	177	11	,	,	PUNCT
ejpam-5388	177	12	qθ))−	qθ))−	NOUN
ejpam-5388	177	13	ϕ(mλb	ϕ(mλb	PROPN
ejpam-5388	177	14	(	(	PUNCT
ejpam-5388	177	15	θ	θ	PROPN
ejpam-5388	177	16	,	,	PUNCT
ejpam-5388	177	17	θ	θ	NOUN
ejpam-5388	177	18	)	)	PUNCT
ejpam-5388	177	19	)	)	PUNCT
ejpam-5388	177	20	]	]	PUNCT
ejpam-5388	178	1	=	=	PUNCT
ejpam-5388	178	2	λ[(φ(λb(θ	λ[(φ(λb(θ	ADJ
ejpam-5388	178	3	,	,	PUNCT
ejpam-5388	178	4	qθ))−	qθ))−	ADV
ejpam-5388	178	5	ϕ(λb(θ	ϕ(λb(θ	NOUN
ejpam-5388	178	6	,	,	PUNCT
ejpam-5388	178	7	qθ	qθ	NOUN
ejpam-5388	178	8	)	)	PUNCT
ejpam-5388	178	9	)	)	PUNCT
ejpam-5388	178	10	]	]	PUNCT
ejpam-5388	178	11	<	<	X
ejpam-5388	178	12	λ(φ(λb(θ	λ(φ(λb(θ	PROPN
ejpam-5388	178	13	,	,	PUNCT
ejpam-5388	178	14	qθ	qθ	PROPN
ejpam-5388	178	15	)	)	PUNCT
ejpam-5388	178	16	)	)	PUNCT
ejpam-5388	178	17	)	)	PUNCT
ejpam-5388	178	18	.	.	PUNCT
ejpam-5388	179	1	hence	hence	ADV
ejpam-5388	179	2	,	,	PUNCT
ejpam-5388	179	3	θ	θ	PROPN
ejpam-5388	179	4	=	=	PUNCT
ejpam-5388	179	5	qθ	qθ	PROPN
ejpam-5388	179	6	is	be	AUX
ejpam-5388	179	7	θ	θ	PROPN
ejpam-5388	179	8	is	be	AUX
ejpam-5388	179	9	the	the	DET
ejpam-5388	179	10	common	common	ADJ
ejpam-5388	179	11	fixed	fix	VERB
ejpam-5388	179	12	of	of	ADP
ejpam-5388	179	13	p	p	NOUN
ejpam-5388	179	14	and	and	CCONJ
ejpam-5388	179	15	q.	q.	NOUN
ejpam-5388	179	16	if	if	SCONJ
ejpam-5388	179	17	q	q	NOUN
ejpam-5388	179	18	is	be	AUX
ejpam-5388	179	19	continuous	continuous	ADJ
ejpam-5388	179	20	,	,	PUNCT
ejpam-5388	179	21	then	then	ADV
ejpam-5388	179	22	,	,	PUNCT
ejpam-5388	179	23	by	by	ADP
ejpam-5388	179	24	a	a	DET
ejpam-5388	179	25	similar	similar	ADJ
ejpam-5388	179	26	way	way	NOUN
ejpam-5388	179	27	of	of	ADP
ejpam-5388	179	28	the	the	DET
ejpam-5388	179	29	above	above	NOUN
ejpam-5388	179	30	,	,	PUNCT
ejpam-5388	179	31	we	we	PRON
ejpam-5388	179	32	can	can	AUX
ejpam-5388	179	33	prove	prove	VERB
ejpam-5388	179	34	that	that	SCONJ
ejpam-5388	179	35	p	p	PROPN
ejpam-5388	179	36	and	and	CCONJ
ejpam-5388	179	37	q	q	NOUN
ejpam-5388	179	38	have	have	VERB
ejpam-5388	179	39	a	a	DET
ejpam-5388	179	40	common	common	ADJ
ejpam-5388	179	41	fixed	fix	VERB
ejpam-5388	179	42	point	point	NOUN
ejpam-5388	179	43	.	.	PUNCT
ejpam-5388	180	1	theorem	theorem	VERB
ejpam-5388	180	2	2.3	2.3	NUM
ejpam-5388	180	3	.	.	PUNCT
ejpam-5388	181	1	let	let	AUX
ejpam-5388	181	2	(	(	PUNCT
ejpam-5388	181	3	𭟋	𭟋	NOUN
ejpam-5388	181	4	,	,	PUNCT
ejpam-5388	181	5	λb	λb	NOUN
ejpam-5388	181	6	)	)	PUNCT
ejpam-5388	181	7	be	be	AUX
ejpam-5388	181	8	a	a	DET
ejpam-5388	181	9	complete	complete	ADJ
ejpam-5388	181	10	b	b	X
ejpam-5388	181	11	-	-	PUNCT
ejpam-5388	181	12	metric	metric	ADJ
ejpam-5388	181	13	space	space	NOUN
ejpam-5388	181	14	with	with	ADP
ejpam-5388	181	15	the	the	DET
ejpam-5388	181	16	constant	constant	ADJ
ejpam-5388	181	17	s	s	PART
ejpam-5388	181	18	≥	≥	NOUN
ejpam-5388	181	19	1	1	NUM
ejpam-5388	181	20	,	,	PUNCT
ejpam-5388	181	21	and	and	CCONJ
ejpam-5388	181	22	(	(	PUNCT
ejpam-5388	181	23	p	p	X
ejpam-5388	181	24	,	,	PUNCT
ejpam-5388	181	25	q	q	NOUN
ejpam-5388	181	26	)	)	PUNCT
ejpam-5388	181	27	be	be	AUX
ejpam-5388	181	28	two	two	NUM
ejpam-5388	181	29	self	self	NOUN
ejpam-5388	181	30	-	-	PUNCT
ejpam-5388	181	31	mappings	mapping	NOUN
ejpam-5388	181	32	on	on	ADP
ejpam-5388	181	33	𭟋	𭟋	ADP
ejpam-5388	181	34	.	.	PROPN
ejpam-5388	182	1	suppose	suppose	VERB
ejpam-5388	182	2	that	that	SCONJ
ejpam-5388	182	3	α	α	PROPN
ejpam-5388	182	4	,	,	PUNCT
ejpam-5388	182	5	η	η	PROPN
ejpam-5388	182	6	:	:	PUNCT
ejpam-5388	182	7	𭟋	𭟋	PROPN
ejpam-5388	182	8	×	×	NOUN
ejpam-5388	182	9	𭟋	𭟋	PROPN
ejpam-5388	182	10	→	→	X
ejpam-5388	182	11	r	r	NOUN
ejpam-5388	182	12	are	be	AUX
ejpam-5388	182	13	two	two	NUM
ejpam-5388	182	14	functions	function	NOUN
ejpam-5388	182	15	.	.	PUNCT
ejpam-5388	183	1	assume	assume	VERB
ejpam-5388	183	2	that	that	SCONJ
ejpam-5388	183	3	the	the	DET
ejpam-5388	183	4	following	follow	VERB
ejpam-5388	183	5	conditions	condition	NOUN
ejpam-5388	183	6	hold	hold	VERB
ejpam-5388	183	7	:	:	PUNCT
ejpam-5388	183	8	(	(	PUNCT
ejpam-5388	183	9	i	i	NOUN
ejpam-5388	183	10	)	)	PUNCT
ejpam-5388	183	11	λ(s	λ(s	PROPN
ejpam-5388	183	12	,	,	PUNCT
ejpam-5388	183	13	φ,ϕ,l)-berinde	φ,ϕ,l)-berinde	NOUN
ejpam-5388	183	14	type	type	NOUN
ejpam-5388	183	15	contraction	contraction	NOUN
ejpam-5388	183	16	mapping	mapping	NOUN
ejpam-5388	183	17	;	;	PUNCT
ejpam-5388	183	18	(	(	PUNCT
ejpam-5388	183	19	ii	ii	NOUN
ejpam-5388	183	20	)	)	PUNCT
ejpam-5388	183	21	the	the	DET
ejpam-5388	183	22	pair	pair	NOUN
ejpam-5388	183	23	(	(	PUNCT
ejpam-5388	183	24	p	p	X
ejpam-5388	183	25	,	,	PUNCT
ejpam-5388	183	26	q	q	NOUN
ejpam-5388	183	27	)	)	PUNCT
ejpam-5388	183	28	is	be	AUX
ejpam-5388	183	29	triangular	triangular	ADJ
ejpam-5388	183	30	α	α	NOUN
ejpam-5388	183	31	-	-	ADJ
ejpam-5388	183	32	admissible	admissible	ADJ
ejpam-5388	183	33	with	with	ADP
ejpam-5388	183	34	respect	respect	NOUN
ejpam-5388	183	35	to	to	ADP
ejpam-5388	183	36	η	η	PROPN
ejpam-5388	183	37	;	;	PUNCT
ejpam-5388	183	38	(	(	PUNCT
ejpam-5388	183	39	iii	iii	X
ejpam-5388	183	40	)	)	PUNCT
ejpam-5388	183	41	if	if	SCONJ
ejpam-5388	183	42	∃	∃	PROPN
ejpam-5388	183	43	u0	u0	PROPN
ejpam-5388	183	44	∈	∈	PROPN
ejpam-5388	183	45	𭟋	𭟋	ADP
ejpam-5388	183	46	such	such	ADJ
ejpam-5388	183	47	that	that	SCONJ
ejpam-5388	183	48	α(u0	α(u0	NOUN
ejpam-5388	183	49	,	,	PUNCT
ejpam-5388	183	50	pu0	pu0	NOUN
ejpam-5388	183	51	)	)	PUNCT
ejpam-5388	183	52	≥	≥	PROPN
ejpam-5388	183	53	η(u0	η(u0	NOUN
ejpam-5388	183	54	,	,	PUNCT
ejpam-5388	183	55	pu0	pu0	NOUN
ejpam-5388	183	56	)	)	PUNCT
ejpam-5388	183	57	,	,	PUNCT
ejpam-5388	183	58	(	(	PUNCT
ejpam-5388	183	59	iv	iv	X
ejpam-5388	183	60	)	)	PUNCT
ejpam-5388	183	61	if	if	SCONJ
ejpam-5388	183	62	{	{	PUNCT
ejpam-5388	183	63	un	un	ADJ
ejpam-5388	183	64	}	}	PUNCT
ejpam-5388	183	65	is	be	AUX
ejpam-5388	183	66	a	a	DET
ejpam-5388	183	67	sequence	sequence	NOUN
ejpam-5388	183	68	in	in	ADP
ejpam-5388	183	69	𭟋	𭟋	ADP
ejpam-5388	183	70	such	such	ADJ
ejpam-5388	183	71	that	that	SCONJ
ejpam-5388	183	72	α(un	α(un	PROPN
ejpam-5388	183	73	,	,	PUNCT
ejpam-5388	183	74	un+1	un+1	NOUN
ejpam-5388	183	75	)	)	PUNCT
ejpam-5388	183	76	≥	≥	NOUN
ejpam-5388	183	77	η(un	η(un	PROPN
ejpam-5388	183	78	,	,	PUNCT
ejpam-5388	183	79	un+1	un+1	NOUN
ejpam-5388	183	80	)	)	PUNCT
ejpam-5388	183	81	,	,	PUNCT
ejpam-5388	183	82	for	for	ADP
ejpam-5388	183	83	all	all	PRON
ejpam-5388	183	84	n	n	PRON
ejpam-5388	183	85	∈	∈	PROPN
ejpam-5388	183	86	n	n	NOUN
ejpam-5388	183	87	and	and	CCONJ
ejpam-5388	183	88	un	un	PROPN
ejpam-5388	183	89	→	→	SYM
ejpam-5388	183	90	θ	θ	PROPN
ejpam-5388	183	91	as	as	ADP
ejpam-5388	183	92	n→	n→	PROPN
ejpam-5388	183	93	∞	∞	PROPN
ejpam-5388	183	94	,	,	PUNCT
ejpam-5388	183	95	then	then	ADV
ejpam-5388	183	96	∃	∃	PROPN
ejpam-5388	183	97	a	a	DET
ejpam-5388	183	98	subsequence	subsequence	NOUN
ejpam-5388	183	99	{	{	PUNCT
ejpam-5388	183	100	uni	uni	PROPN
ejpam-5388	183	101	}	}	PUNCT
ejpam-5388	183	102	of	of	ADP
ejpam-5388	183	103	{	{	PUNCT
ejpam-5388	183	104	un	un	PROPN
ejpam-5388	183	105	}	}	PUNCT
ejpam-5388	183	106	such	such	ADJ
ejpam-5388	183	107	that	that	SCONJ
ejpam-5388	183	108	α(uni	α(uni	PROPN
ejpam-5388	183	109	,	,	PUNCT
ejpam-5388	183	110	u∗	u∗	PROPN
ejpam-5388	183	111	)	)	PUNCT
ejpam-5388	183	112	≥	≥	NOUN
ejpam-5388	183	113	η(uni	η(uni	PROPN
ejpam-5388	183	114	,	,	PUNCT
ejpam-5388	183	115	u∗	u∗	PROPN
ejpam-5388	183	116	)	)	PUNCT
ejpam-5388	183	117	,	,	PUNCT
ejpam-5388	183	118	for	for	ADP
ejpam-5388	183	119	all	all	DET
ejpam-5388	183	120	i	i	PRON
ejpam-5388	183	121	∈	∈	PROPN
ejpam-5388	183	122	n.	n.	NOUN
ejpam-5388	183	123	then	then	ADV
ejpam-5388	183	124	,	,	PUNCT
ejpam-5388	183	125	p	p	NOUN
ejpam-5388	183	126	and	and	CCONJ
ejpam-5388	183	127	q	q	NOUN
ejpam-5388	183	128	have	have	VERB
ejpam-5388	183	129	a	a	DET
ejpam-5388	183	130	common	common	ADJ
ejpam-5388	183	131	fixed	fix	VERB
ejpam-5388	183	132	point	point	NOUN
ejpam-5388	183	133	in	in	ADP
ejpam-5388	183	134	𭟋	𭟋	PROPN
ejpam-5388	183	135	.	.	PUNCT
ejpam-5388	183	136	proof	proof	NOUN
ejpam-5388	183	137	.	.	PUNCT
ejpam-5388	184	1	following	follow	VERB
ejpam-5388	184	2	similar	similar	ADJ
ejpam-5388	184	3	arguments	argument	NOUN
ejpam-5388	184	4	as	as	ADP
ejpam-5388	184	5	in	in	ADP
ejpam-5388	184	6	the	the	DET
ejpam-5388	184	7	proof	proof	NOUN
ejpam-5388	184	8	of	of	ADP
ejpam-5388	184	9	theorem	theorem	ADJ
ejpam-5388	184	10	2.2	2.2	NUM
ejpam-5388	184	11	,	,	PUNCT
ejpam-5388	184	12	we	we	PRON
ejpam-5388	184	13	obtain	obtain	VERB
ejpam-5388	184	14	a	a	DET
ejpam-5388	184	15	sequence	sequence	NOUN
ejpam-5388	184	16	{	{	PUNCT
ejpam-5388	184	17	un	un	PROPN
ejpam-5388	184	18	}	}	PUNCT
ejpam-5388	184	19	is	be	AUX
ejpam-5388	184	20	defined	define	VERB
ejpam-5388	184	21	by	by	ADP
ejpam-5388	184	22	u2n+1	u2n+1	PROPN
ejpam-5388	184	23	=	=	SYM
ejpam-5388	184	24	pu2n	pu2n	PROPN
ejpam-5388	184	25	and	and	CCONJ
ejpam-5388	184	26	u2n+2	u2n+2	PROPN
ejpam-5388	184	27	=	=	SYM
ejpam-5388	184	28	pu2n+1	pu2n+1	PROPN
ejpam-5388	184	29	for	for	ADP
ejpam-5388	184	30	all	all	PRON
ejpam-5388	185	1	n	n	DET
ejpam-5388	185	2	∈	∈	PRON
ejpam-5388	185	3	n	n	ADV
ejpam-5388	185	4	converging	converge	VERB
ejpam-5388	185	5	to	to	ADP
ejpam-5388	185	6	u∗	u∗	VERB
ejpam-5388	185	7	∈	∈	PROPN
ejpam-5388	185	8	𭟋	𭟋	ADP
ejpam-5388	185	9	such	such	ADJ
ejpam-5388	185	10	that	that	SCONJ
ejpam-5388	185	11	α(u2n	α(u2n	ADJ
ejpam-5388	185	12	,	,	PUNCT
ejpam-5388	185	13	u2n+1	u2n+1	ADJ
ejpam-5388	185	14	)	)	PUNCT
ejpam-5388	185	15	≥	≥	NOUN
ejpam-5388	185	16	η(u2n	η(u2n	NOUN
ejpam-5388	185	17	,	,	PUNCT
ejpam-5388	185	18	u2n+1	u2n+1	ADJ
ejpam-5388	185	19	)	)	PUNCT
ejpam-5388	185	20	for	for	ADP
ejpam-5388	185	21	all	all	PRON
ejpam-5388	185	22	n	n	DET
ejpam-5388	185	23	∈	∈	NOUN
ejpam-5388	185	24	n.	n.	NOUN
ejpam-5388	185	25	by	by	ADP
ejpam-5388	185	26	(	(	PUNCT
ejpam-5388	185	27	iv	iv	X
ejpam-5388	185	28	)	)	PUNCT
ejpam-5388	185	29	,	,	PUNCT
ejpam-5388	185	30	there	there	PRON
ejpam-5388	185	31	exist	exist	VERB
ejpam-5388	185	32	a	a	DET
ejpam-5388	185	33	subsequence	subsequence	NOUN
ejpam-5388	185	34	{	{	PUNCT
ejpam-5388	185	35	uni	uni	PROPN
ejpam-5388	185	36	}	}	PUNCT
ejpam-5388	185	37	of	of	ADP
ejpam-5388	185	38	{	{	PUNCT
ejpam-5388	185	39	un	un	PROPN
ejpam-5388	185	40	}	}	PUNCT
ejpam-5388	185	41	such	such	ADJ
ejpam-5388	185	42	that	that	SCONJ
ejpam-5388	185	43	α(uni	α(uni	PROPN
ejpam-5388	185	44	,	,	PUNCT
ejpam-5388	185	45	u∗	u∗	PROPN
ejpam-5388	185	46	)	)	PUNCT
ejpam-5388	185	47	≥	≥	NOUN
ejpam-5388	185	48	η(uni	η(uni	PROPN
ejpam-5388	185	49	,	,	PUNCT
ejpam-5388	185	50	u∗	u∗	PROPN
ejpam-5388	185	51	)	)	PUNCT
ejpam-5388	185	52	,	,	PUNCT
ejpam-5388	185	53	for	for	ADP
ejpam-5388	185	54	all	all	PRON
ejpam-5388	185	55	i	i	PRON
ejpam-5388	185	56	∈	∈	PROPN
ejpam-5388	185	57	n.	n.	NOUN
ejpam-5388	185	58	therefore	therefore	ADV
ejpam-5388	185	59	φ(λb(u2ni+1	φ(λb(u2ni+1	ADV
ejpam-5388	185	60	,	,	PUNCT
ejpam-5388	185	61	qu∗	qu∗	NOUN
ejpam-5388	185	62	)	)	PUNCT
ejpam-5388	185	63	)	)	PUNCT
ejpam-5388	186	1	≤	≤	NUM
ejpam-5388	186	2	φ(s2λb(pu2ni	φ(s2λb(pu2ni	PROPN
ejpam-5388	186	3	,	,	PUNCT
ejpam-5388	186	4	qu∗	qu∗	ADJ
ejpam-5388	186	5	)	)	PUNCT
ejpam-5388	186	6	≤	≤	NUM
ejpam-5388	186	7	λ[(φ(mλb	λ[(φ(mλb	PROPN
ejpam-5388	186	8	(	(	PUNCT
ejpam-5388	186	9	u2ni	u2ni	X
ejpam-5388	186	10	,	,	PUNCT
ejpam-5388	186	11	u∗))−	u∗))−	PROPN
ejpam-5388	186	12	ϕ(mλb	ϕ(mλb	PROPN
ejpam-5388	186	13	(	(	PUNCT
ejpam-5388	186	14	u2ni	u2ni	X
ejpam-5388	186	15	,	,	PUNCT
ejpam-5388	186	16	u∗	u∗	PROPN
ejpam-5388	186	17	)	)	PUNCT
ejpam-5388	186	18	)	)	PUNCT
ejpam-5388	187	1	+	+	CCONJ
ejpam-5388	187	2	lnλb	lnλb	X
ejpam-5388	187	3	(	(	PUNCT
ejpam-5388	187	4	u2ni	u2ni	X
ejpam-5388	187	5	,	,	PUNCT
ejpam-5388	187	6	u∗	u∗	PROPN
ejpam-5388	187	7	)	)	PUNCT
ejpam-5388	187	8	]	]	PUNCT
ejpam-5388	187	9	(	(	PUNCT
ejpam-5388	187	10	2.17	2.17	NUM
ejpam-5388	187	11	)	)	PUNCT
ejpam-5388	187	12	for	for	ADP
ejpam-5388	187	13	all	all	PRON
ejpam-5388	187	14	n	n	PRON
ejpam-5388	187	15	∈	∈	PROPN
ejpam-5388	187	16	n	n	CCONJ
ejpam-5388	187	17	,	,	PUNCT
ejpam-5388	187	18	where	where	SCONJ
ejpam-5388	187	19	mλb	mλb	PROPN
ejpam-5388	187	20	(	(	PUNCT
ejpam-5388	187	21	u2ni	u2ni	PROPN
ejpam-5388	187	22	,	,	PUNCT
ejpam-5388	187	23	u∗	u∗	PROPN
ejpam-5388	187	24	)	)	PUNCT
ejpam-5388	187	25	)	)	PUNCT
ejpam-5388	188	1	=	=	SYM
ejpam-5388	188	2	max{λb(u2ni	max{λb(u2ni	PROPN
ejpam-5388	188	3	,	,	PUNCT
ejpam-5388	188	4	u∗),λb(u2ni	u∗),λb(u2ni	PROPN
ejpam-5388	188	5	,	,	PUNCT
ejpam-5388	188	6	pu2ni),λb(u∗	pu2ni),λb(u∗	NOUN
ejpam-5388	188	7	,	,	PUNCT
ejpam-5388	188	8	qu∗	qu∗	NOUN
ejpam-5388	188	9	)	)	PUNCT
ejpam-5388	188	10	,	,	PUNCT
ejpam-5388	188	11	λb(u2ni	λb(u2ni	X
ejpam-5388	188	12	,	,	PUNCT
ejpam-5388	188	13	qu∗	qu∗	ADJ
ejpam-5388	188	14	)	)	PUNCT
ejpam-5388	189	1	+	+	CCONJ
ejpam-5388	189	2	λb(pu2ni	λb(pu2ni	X
ejpam-5388	189	3	,	,	PUNCT
ejpam-5388	189	4	u∗	u∗	ADJ
ejpam-5388	189	5	)	)	PUNCT
ejpam-5388	189	6	2s(1	2s(1	X
ejpam-5388	189	7	+	+	CCONJ
ejpam-5388	189	8	λb(pu2ni	λb(pu2ni	X
ejpam-5388	189	9	,	,	PUNCT
ejpam-5388	189	10	u∗	u∗	PROPN
ejpam-5388	189	11	)	)	PUNCT
ejpam-5388	189	12	)	)	PUNCT
ejpam-5388	189	13	}	}	PUNCT
ejpam-5388	190	1	=	=	PUNCT
ejpam-5388	190	2	max{λb(u2n	max{λb(u2n	NOUN
ejpam-5388	190	3	,	,	PUNCT
ejpam-5388	190	4	u∗),λb(u2n	u∗),λb(u2n	INTJ
ejpam-5388	190	5	,	,	PUNCT
ejpam-5388	190	6	u2ni+1),λb(u∗	u2ni+1),λb(u∗	NOUN
ejpam-5388	190	7	,	,	PUNCT
ejpam-5388	190	8	qu∗	qu∗	NOUN
ejpam-5388	190	9	)	)	PUNCT
ejpam-5388	190	10	,	,	PUNCT
ejpam-5388	190	11	λb(u2ni	λb(u2ni	X
ejpam-5388	190	12	,	,	PUNCT
ejpam-5388	190	13	qu∗	qu∗	ADJ
ejpam-5388	190	14	)	)	PUNCT
ejpam-5388	190	15	+	+	CCONJ
ejpam-5388	191	1	λb(u2ni+1	λb(u2ni+1	ADJ
ejpam-5388	191	2	,	,	PUNCT
ejpam-5388	191	3	u∗	u∗	PROPN
ejpam-5388	191	4	)	)	PUNCT
ejpam-5388	191	5	2s(1	2s(1	X
ejpam-5388	191	6	+	+	SYM
ejpam-5388	192	1	λb(u2ni+1	λb(u2ni+1	PROPN
ejpam-5388	192	2	,	,	PUNCT
ejpam-5388	192	3	u∗	u∗	PROPN
ejpam-5388	192	4	)	)	PUNCT
ejpam-5388	192	5	)	)	PUNCT
ejpam-5388	192	6	}	}	PUNCT
ejpam-5388	192	7	and	and	CCONJ
ejpam-5388	192	8	nλb	nλb	PROPN
ejpam-5388	192	9	(	(	PUNCT
ejpam-5388	192	10	u2ni	u2ni	X
ejpam-5388	192	11	,	,	PUNCT
ejpam-5388	192	12	u∗	u∗	ADJ
ejpam-5388	192	13	)	)	PUNCT
ejpam-5388	192	14	=	=	SYM
ejpam-5388	193	1	min{λb(u2ni	min{λb(u2ni	PROPN
ejpam-5388	193	2	,	,	PUNCT
ejpam-5388	193	3	u∗),λb(u2ni	u∗),λb(u2ni	PROPN
ejpam-5388	193	4	,	,	PUNCT
ejpam-5388	193	5	pu2ni),λb(u∗	pu2ni),λb(u∗	NOUN
ejpam-5388	193	6	,	,	PUNCT
ejpam-5388	193	7	qu∗),λb(u∗	qu∗),λb(u∗	PROPN
ejpam-5388	193	8	,	,	PUNCT
ejpam-5388	193	9	pu2ni	pu2ni	ADJ
ejpam-5388	193	10	)	)	PUNCT
ejpam-5388	193	11	}	}	PUNCT
ejpam-5388	193	12	=	=	SYM
ejpam-5388	193	13	min{λb(u2ni	min{λb(u2ni	PROPN
ejpam-5388	193	14	,	,	PUNCT
ejpam-5388	193	15	u∗),λb(u2ni	u∗),λb(u2ni	PROPN
ejpam-5388	193	16	,	,	PUNCT
ejpam-5388	193	17	u2ni+1),λb(u∗	u2ni+1),λb(u∗	PROPN
ejpam-5388	193	18	,	,	PUNCT
ejpam-5388	193	19	qu∗),λb(u∗	qu∗),λb(u∗	PROPN
ejpam-5388	193	20	,	,	PUNCT
ejpam-5388	193	21	u2ni+1	u2ni+1	NOUN
ejpam-5388	193	22	)	)	PUNCT
ejpam-5388	193	23	}	}	PUNCT
ejpam-5388	193	24	.	.	PUNCT
ejpam-5388	194	1	since	since	SCONJ
ejpam-5388	194	2	lim	lim	PROPN
ejpam-5388	194	3	sup	sup	VERB
ejpam-5388	194	4	i→∞	i→∞	NUM
ejpam-5388	194	5	λb(u2ni	λb(u2ni	ADJ
ejpam-5388	194	6	,	,	PUNCT
ejpam-5388	194	7	qu∗	qu∗	ADJ
ejpam-5388	194	8	)	)	PUNCT
ejpam-5388	195	1	+	+	CCONJ
ejpam-5388	196	1	λb(u2ni+1	λb(u2ni+1	ADJ
ejpam-5388	196	2	,	,	PUNCT
ejpam-5388	196	3	u∗	u∗	PROPN
ejpam-5388	196	4	)	)	PUNCT
ejpam-5388	196	5	2s(1	2s(1	X
ejpam-5388	196	6	+	+	SYM
ejpam-5388	197	1	λb(u2ni+1	λb(u2ni+1	PROPN
ejpam-5388	197	2	,	,	PUNCT
ejpam-5388	197	3	u∗	u∗	PROPN
ejpam-5388	197	4	)	)	PUNCT
ejpam-5388	197	5	)	)	PUNCT
ejpam-5388	198	1	≤	≤	NUM
ejpam-5388	198	2	λb(u∗	λb(u∗	NOUN
ejpam-5388	198	3	,	,	PUNCT
ejpam-5388	198	4	qu∗	qu∗	ADJ
ejpam-5388	198	5	)	)	PUNCT
ejpam-5388	198	6	2	2	NUM
ejpam-5388	198	7	.	.	PUNCT
ejpam-5388	199	1	h.	h.	PROPN
ejpam-5388	199	2	alsamir	alsamir	VERB
ejpam-5388	199	3	et	et	PROPN
ejpam-5388	199	4	al	al	PROPN
ejpam-5388	199	5	.	.	PUNCT
ejpam-5388	199	6	/	/	SYM
ejpam-5388	199	7	eur	eur	PROPN
ejpam-5388	199	8	.	.	PUNCT
ejpam-5388	200	1	j.	j.	PROPN
ejpam-5388	200	2	pure	pure	PROPN
ejpam-5388	200	3	appl	appl	PROPN
ejpam-5388	200	4	.	.	PROPN
ejpam-5388	200	5	math	math	PROPN
ejpam-5388	200	6	,	,	PUNCT
ejpam-5388	200	7	17	17	NUM
ejpam-5388	200	8	(	(	PUNCT
ejpam-5388	200	9	4	4	NUM
ejpam-5388	200	10	)	)	PUNCT
ejpam-5388	200	11	(	(	PUNCT
ejpam-5388	200	12	2024	2024	NUM
ejpam-5388	200	13	)	)	PUNCT
ejpam-5388	200	14	,	,	PUNCT
ejpam-5388	200	15	2492	2492	NUM
ejpam-5388	200	16	-	-	SYM
ejpam-5388	200	17	2504	2504	NUM
ejpam-5388	200	18	2499	2499	NUM
ejpam-5388	200	19	by	by	ADP
ejpam-5388	200	20	taking	take	VERB
ejpam-5388	200	21	i→	i→	PROPN
ejpam-5388	200	22	∞	∞	PROPN
ejpam-5388	200	23	in	in	ADP
ejpam-5388	200	24	(	(	PUNCT
ejpam-5388	200	25	2.18	2.18	NUM
ejpam-5388	200	26	)	)	PUNCT
ejpam-5388	200	27	and	and	CCONJ
ejpam-5388	200	28	(	(	PUNCT
ejpam-5388	200	29	2.18	2.18	NUM
ejpam-5388	200	30	)	)	PUNCT
ejpam-5388	200	31	using	use	VERB
ejpam-5388	200	32	(	(	PUNCT
ejpam-5388	200	33	2.5	2.5	NUM
ejpam-5388	200	34	)	)	PUNCT
ejpam-5388	200	35	,	,	PUNCT
ejpam-5388	200	36	we	we	PRON
ejpam-5388	200	37	deduce	deduce	VERB
ejpam-5388	200	38	that	that	SCONJ
ejpam-5388	200	39	lim	lim	PROPN
ejpam-5388	200	40	sup	sup	PROPN
ejpam-5388	200	41	i→∞	i→∞	NUM
ejpam-5388	200	42	mλb	mλb	PROPN
ejpam-5388	200	43	(	(	PUNCT
ejpam-5388	200	44	u2ni	u2ni	X
ejpam-5388	200	45	,	,	PUNCT
ejpam-5388	200	46	u∗	u∗	PROPN
ejpam-5388	200	47	)	)	PUNCT
ejpam-5388	200	48	)	)	PUNCT
ejpam-5388	201	1	=	=	SYM
ejpam-5388	201	2	λb(u∗	λb(u∗	NOUN
ejpam-5388	201	3	,	,	PUNCT
ejpam-5388	201	4	qu∗	qu∗	ADJ
ejpam-5388	201	5	)	)	PUNCT
ejpam-5388	201	6	and	and	CCONJ
ejpam-5388	201	7	lim	lim	PROPN
ejpam-5388	201	8	sup	sup	PROPN
ejpam-5388	201	9	i→∞	i→∞	NUM
ejpam-5388	201	10	nλb	nλb	PROPN
ejpam-5388	201	11	(	(	PUNCT
ejpam-5388	201	12	u2ni	u2ni	X
ejpam-5388	201	13	,	,	PUNCT
ejpam-5388	201	14	u∗	u∗	PROPN
ejpam-5388	201	15	)	)	PUNCT
ejpam-5388	201	16	)	)	PUNCT
ejpam-5388	202	1	=	=	PUNCT
ejpam-5388	202	2	0	0	X
ejpam-5388	202	3	.	.	PUNCT
ejpam-5388	203	1	from	from	ADP
ejpam-5388	203	2	(	(	PUNCT
ejpam-5388	203	3	2.17)and	2.17)and	NUM
ejpam-5388	203	4	taking	take	VERB
ejpam-5388	203	5	in	in	ADP
ejpam-5388	203	6	account	account	NOUN
ejpam-5388	203	7	(	(	PUNCT
ejpam-5388	203	8	)	)	PUNCT
ejpam-5388	203	9	and	and	CCONJ
ejpam-5388	203	10	(	(	PUNCT
ejpam-5388	203	11	)	)	PUNCT
ejpam-5388	203	12	,	,	PUNCT
ejpam-5388	203	13	we	we	PRON
ejpam-5388	203	14	have	have	VERB
ejpam-5388	203	15	φ(λb(u∗	φ(λb(u∗	VERB
ejpam-5388	203	16	,	,	PUNCT
ejpam-5388	203	17	qu∗	qu∗	NOUN
ejpam-5388	203	18	)	)	PUNCT
ejpam-5388	203	19	)	)	PUNCT
ejpam-5388	203	20	≤	≤	NUM
ejpam-5388	204	1	λ[φ(λb(u∗	λ[φ(λb(u∗	ADV
ejpam-5388	204	2	,	,	PUNCT
ejpam-5388	204	3	qu∗))−	qu∗))−	VERB
ejpam-5388	204	4	ϕ(λb(u∗	ϕ(λb(u∗	NOUN
ejpam-5388	204	5	,	,	PUNCT
ejpam-5388	204	6	qu∗	qu∗	NOUN
ejpam-5388	204	7	)	)	PUNCT
ejpam-5388	204	8	)	)	PUNCT
ejpam-5388	204	9	)	)	PUNCT
ejpam-5388	204	10	]	]	PUNCT
ejpam-5388	204	11	(	(	PUNCT
ejpam-5388	204	12	2.18	2.18	NUM
ejpam-5388	204	13	)	)	PUNCT
ejpam-5388	204	14	<	<	X
ejpam-5388	205	1	λφ(λb(u∗	λφ(λb(u∗	PROPN
ejpam-5388	205	2	,	,	PUNCT
ejpam-5388	205	3	qu∗))−	qu∗))−	NOUN
ejpam-5388	205	4	λϕ(λb(u∗	λϕ(λb(u∗	PROPN
ejpam-5388	205	5	,	,	PUNCT
ejpam-5388	205	6	qu∗	qu∗	NOUN
ejpam-5388	205	7	)	)	PUNCT
ejpam-5388	205	8	)	)	PUNCT
ejpam-5388	205	9	.	.	PUNCT
ejpam-5388	206	1	(	(	PUNCT
ejpam-5388	206	2	2.19	2.19	NUM
ejpam-5388	206	3	)	)	PUNCT
ejpam-5388	206	4	by	by	ADP
ejpam-5388	206	5	definition	definition	NOUN
ejpam-5388	206	6	of	of	ADP
ejpam-5388	206	7	φ	φ	PROPN
ejpam-5388	206	8	and	and	CCONJ
ejpam-5388	206	9	ϕ	ϕ	PROPN
ejpam-5388	206	10	,	,	PUNCT
ejpam-5388	206	11	we	we	PRON
ejpam-5388	206	12	have	have	VERB
ejpam-5388	206	13	a	a	DET
ejpam-5388	206	14	contradiction	contradiction	NOUN
ejpam-5388	206	15	.	.	PUNCT
ejpam-5388	207	1	hence	hence	ADV
ejpam-5388	207	2	λb(u∗	λb(u∗	NOUN
ejpam-5388	207	3	,	,	PUNCT
ejpam-5388	207	4	qu∗	qu∗	ADJ
ejpam-5388	207	5	)	)	PUNCT
ejpam-5388	207	6	=	=	SYM
ejpam-5388	207	7	0	0	NUM
ejpam-5388	207	8	,	,	PUNCT
ejpam-5388	207	9	i.e.	i.e.	X
ejpam-5388	207	10	,	,	PUNCT
ejpam-5388	207	11	qu∗	qu∗	NOUN
ejpam-5388	207	12	=	=	SYM
ejpam-5388	207	13	u∗.	u∗.	PROPN
ejpam-5388	207	14	by	by	ADP
ejpam-5388	207	15	the	the	DET
ejpam-5388	207	16	same	same	ADJ
ejpam-5388	207	17	way	way	NOUN
ejpam-5388	207	18	we	we	PRON
ejpam-5388	207	19	can	can	AUX
ejpam-5388	207	20	prove	prove	VERB
ejpam-5388	207	21	that	that	DET
ejpam-5388	207	22	pu∗	pu∗	PROPN
ejpam-5388	207	23	=	=	PRON
ejpam-5388	207	24	u∗.	u∗.	PROPN
ejpam-5388	207	25	definition	definition	NOUN
ejpam-5388	207	26	2.4	2.4	NUM
ejpam-5388	207	27	.	.	PUNCT
ejpam-5388	208	1	let	let	AUX
ejpam-5388	208	2	(	(	PUNCT
ejpam-5388	208	3	𭟋	𭟋	NOUN
ejpam-5388	208	4	,	,	PUNCT
ejpam-5388	208	5	λb	λb	NOUN
ejpam-5388	208	6	)	)	PUNCT
ejpam-5388	208	7	be	be	AUX
ejpam-5388	208	8	a	a	DET
ejpam-5388	208	9	b	b	NOUN
ejpam-5388	208	10	-	-	PUNCT
ejpam-5388	208	11	metric	metric	ADJ
ejpam-5388	208	12	space	space	NOUN
ejpam-5388	208	13	with	with	ADP
ejpam-5388	208	14	parameter	parameter	PROPN
ejpam-5388	208	15	s	s	PART
ejpam-5388	208	16	≥	≥	NOUN
ejpam-5388	208	17	1	1	NUM
ejpam-5388	208	18	,	,	PUNCT
ejpam-5388	208	19	p	p	X
ejpam-5388	208	20	,	,	PUNCT
ejpam-5388	208	21	q	q	NOUN
ejpam-5388	208	22	:	:	PUNCT
ejpam-5388	208	23	𭟋	𭟋	PROPN
ejpam-5388	208	24	→	→	SYM
ejpam-5388	208	25	𭟋	𭟋	PROPN
ejpam-5388	208	26	and	and	CCONJ
ejpam-5388	208	27	α	α	NOUN
ejpam-5388	208	28	,	,	PUNCT
ejpam-5388	208	29	η	η	PROPN
ejpam-5388	208	30	:	:	PUNCT
ejpam-5388	208	31	𭟋	𭟋	PROPN
ejpam-5388	208	32	×	×	NOUN
ejpam-5388	208	33	𭟋	𭟋	PROPN
ejpam-5388	208	34	→	→	PUNCT
ejpam-5388	208	35	r	r	NOUN
ejpam-5388	208	36	be	be	AUX
ejpam-5388	208	37	two	two	NUM
ejpam-5388	208	38	functions	function	NOUN
ejpam-5388	208	39	.	.	PUNCT
ejpam-5388	209	1	let	let	VERB
ejpam-5388	209	2	φ	φ	PROPN
ejpam-5388	209	3	∈	∈	PROPN
ejpam-5388	209	4	ω	ω	PROPN
ejpam-5388	209	5	,	,	PUNCT
ejpam-5388	209	6	ϕ	ϕ	PROPN
ejpam-5388	209	7	∈	∈	PROPN
ejpam-5388	209	8	φ	φ	NOUN
ejpam-5388	209	9	and	and	CCONJ
ejpam-5388	209	10	λ	λ	X
ejpam-5388	209	11	∈	∈	PROPN
ejpam-5388	210	1	[	[	X
ejpam-5388	210	2	0	0	NUM
ejpam-5388	210	3	,	,	PUNCT
ejpam-5388	210	4	1	1	NUM
ejpam-5388	210	5	)	)	PUNCT
ejpam-5388	210	6	.	.	PUNCT
ejpam-5388	211	1	then	then	ADV
ejpam-5388	211	2	the	the	DET
ejpam-5388	211	3	pair	pair	NOUN
ejpam-5388	211	4	(	(	PUNCT
ejpam-5388	211	5	p	p	X
ejpam-5388	211	6	,	,	PUNCT
ejpam-5388	211	7	q	q	NOUN
ejpam-5388	211	8	)	)	PUNCT
ejpam-5388	211	9	is	be	AUX
ejpam-5388	211	10	called	call	VERB
ejpam-5388	211	11	λ(s	λ(s	PROPN
ejpam-5388	211	12	,	,	PUNCT
ejpam-5388	211	13	φ	φ	NOUN
ejpam-5388	211	14	,	,	PUNCT
ejpam-5388	211	15	ϕ)-contraction	ϕ)-contraction	PUNCT
ejpam-5388	211	16	mapping	mapping	NOUN
ejpam-5388	211	17	of	of	ADP
ejpam-5388	211	18	type	type	NOUN
ejpam-5388	211	19	(	(	PUNCT
ejpam-5388	211	20	b	b	NOUN
ejpam-5388	211	21	)	)	PUNCT
ejpam-5388	211	22	if	if	SCONJ
ejpam-5388	211	23	α(u	α(u	PROPN
ejpam-5388	211	24	,	,	PUNCT
ejpam-5388	211	25	v	v	NOUN
ejpam-5388	211	26	)	)	PUNCT
ejpam-5388	211	27	≥	≥	NOUN
ejpam-5388	211	28	η(u	η(u	NOUN
ejpam-5388	211	29	,	,	PUNCT
ejpam-5388	211	30	v	v	NOUN
ejpam-5388	211	31	)	)	PUNCT
ejpam-5388	211	32	,	,	PUNCT
ejpam-5388	211	33	then	then	ADV
ejpam-5388	211	34	φ	φ	PROPN
ejpam-5388	211	35	(	(	PUNCT
ejpam-5388	211	36	s2λb(pu	s2λb(pu	PROPN
ejpam-5388	211	37	,	,	PUNCT
ejpam-5388	211	38	qv	qv	X
ejpam-5388	211	39	)	)	PUNCT
ejpam-5388	211	40	)	)	PUNCT
ejpam-5388	211	41	≤	≤	NUM
ejpam-5388	212	1	λ	λ	PROPN
ejpam-5388	212	2	[	[	X
ejpam-5388	212	3	φ	φ	X
ejpam-5388	212	4	(	(	PUNCT
ejpam-5388	212	5	mλb	mλb	PROPN
ejpam-5388	212	6	(	(	PUNCT
ejpam-5388	212	7	u	u	NOUN
ejpam-5388	212	8	,	,	PUNCT
ejpam-5388	212	9	v))−	v))−	NOUN
ejpam-5388	212	10	ϕ	ϕ	NOUN
ejpam-5388	212	11	(	(	PUNCT
ejpam-5388	212	12	mλb	mλb	PROPN
ejpam-5388	212	13	(	(	PUNCT
ejpam-5388	212	14	u	u	NOUN
ejpam-5388	212	15	,	,	PUNCT
ejpam-5388	212	16	v	v	NOUN
ejpam-5388	212	17	)	)	PUNCT
ejpam-5388	212	18	)	)	PUNCT
ejpam-5388	212	19	]	]	PUNCT
ejpam-5388	212	20	,	,	PUNCT
ejpam-5388	212	21	(	(	PUNCT
ejpam-5388	212	22	2.20	2.20	NUM
ejpam-5388	212	23	)	)	PUNCT
ejpam-5388	212	24	where	where	SCONJ
ejpam-5388	212	25	λ	λ	PROPN
ejpam-5388	212	26	∈	∈	PROPN
ejpam-5388	213	1	[	[	X
ejpam-5388	213	2	0	0	NUM
ejpam-5388	213	3	,	,	PUNCT
ejpam-5388	213	4	1	1	NUM
ejpam-5388	213	5	)	)	PUNCT
ejpam-5388	213	6	φ	φ	PROPN
ejpam-5388	213	7	∈	∈	PROPN
ejpam-5388	213	8	ω	ω	PROPN
ejpam-5388	213	9	,	,	PUNCT
ejpam-5388	213	10	ϕ	ϕ	PROPN
ejpam-5388	213	11	∈	∈	PROPN
ejpam-5388	213	12	φ	φ	PROPN
ejpam-5388	213	13	and	and	CCONJ
ejpam-5388	213	14	mλb	mλb	PROPN
ejpam-5388	213	15	(	(	PUNCT
ejpam-5388	213	16	u	u	NOUN
ejpam-5388	213	17	,	,	PUNCT
ejpam-5388	213	18	v	v	NOUN
ejpam-5388	213	19	)	)	PUNCT
ejpam-5388	213	20	=	=	SYM
ejpam-5388	213	21	max	max	PROPN
ejpam-5388	213	22	{	{	PUNCT
ejpam-5388	213	23	λb(u	λb(u	PROPN
ejpam-5388	213	24	,	,	PUNCT
ejpam-5388	213	25	v),λb(u	v),λb(u	PROPN
ejpam-5388	213	26	,	,	PUNCT
ejpam-5388	213	27	pu),λb(v	pu),λb(v	NOUN
ejpam-5388	213	28	,	,	PUNCT
ejpam-5388	213	29	qv	qv	X
ejpam-5388	213	30	)	)	PUNCT
ejpam-5388	213	31	,	,	PUNCT
ejpam-5388	213	32	λb(u	λb(u	NUM
ejpam-5388	213	33	,	,	PUNCT
ejpam-5388	213	34	qv	qv	X
ejpam-5388	213	35	)	)	PUNCT
ejpam-5388	214	1	+	+	CCONJ
ejpam-5388	214	2	λb(pu	λb(pu	PROPN
ejpam-5388	214	3	,	,	PUNCT
ejpam-5388	214	4	v	v	NOUN
ejpam-5388	214	5	)	)	PUNCT
ejpam-5388	214	6	2s[1	2s[1	PROPN
ejpam-5388	215	1	+	+	CCONJ
ejpam-5388	215	2	λb(pu	λb(pu	PROPN
ejpam-5388	215	3	,	,	PUNCT
ejpam-5388	215	4	v	v	NOUN
ejpam-5388	215	5	)	)	PUNCT
ejpam-5388	215	6	]	]	PUNCT
ejpam-5388	215	7	}	}	PUNCT
ejpam-5388	215	8	.	.	PUNCT
ejpam-5388	215	9	.	.	PUNCT
ejpam-5388	216	1	the	the	DET
ejpam-5388	216	2	proof	proof	NOUN
ejpam-5388	216	3	of	of	ADP
ejpam-5388	216	4	the	the	DET
ejpam-5388	216	5	followings	following	NOUN
ejpam-5388	216	6	two	two	NUM
ejpam-5388	216	7	theorems	theorem	NOUN
ejpam-5388	216	8	follows	follow	VERB
ejpam-5388	216	9	from	from	ADP
ejpam-5388	216	10	theorem	theorem	ADJ
ejpam-5388	216	11	2.2	2.2	NUM
ejpam-5388	216	12	and	and	CCONJ
ejpam-5388	216	13	theorem	theorem	VERB
ejpam-5388	216	14	2.3	2.3	NUM
ejpam-5388	216	15	by	by	ADP
ejpam-5388	216	16	putting	put	VERB
ejpam-5388	216	17	l	l	NOUN
ejpam-5388	216	18	=	=	SYM
ejpam-5388	216	19	0	0	X
ejpam-5388	216	20	.	.	PUNCT
ejpam-5388	216	21	theorem	theorem	VERB
ejpam-5388	216	22	2.5	2.5	NUM
ejpam-5388	216	23	.	.	PUNCT
ejpam-5388	217	1	let	let	AUX
ejpam-5388	217	2	(	(	PUNCT
ejpam-5388	217	3	𭟋	𭟋	NOUN
ejpam-5388	217	4	,	,	PUNCT
ejpam-5388	217	5	λb	λb	NOUN
ejpam-5388	217	6	)	)	PUNCT
ejpam-5388	217	7	be	be	AUX
ejpam-5388	217	8	a	a	DET
ejpam-5388	217	9	complete	complete	ADJ
ejpam-5388	217	10	b	b	X
ejpam-5388	217	11	-	-	PUNCT
ejpam-5388	217	12	metric	metric	ADJ
ejpam-5388	217	13	space	space	NOUN
ejpam-5388	217	14	with	with	ADP
ejpam-5388	217	15	the	the	DET
ejpam-5388	217	16	constant	constant	ADJ
ejpam-5388	217	17	s	s	PART
ejpam-5388	217	18	≥	≥	NOUN
ejpam-5388	217	19	1	1	NUM
ejpam-5388	217	20	,	,	PUNCT
ejpam-5388	217	21	and	and	CCONJ
ejpam-5388	217	22	(	(	PUNCT
ejpam-5388	217	23	p	p	X
ejpam-5388	217	24	,	,	PUNCT
ejpam-5388	217	25	q	q	NOUN
ejpam-5388	217	26	)	)	PUNCT
ejpam-5388	217	27	be	be	AUX
ejpam-5388	217	28	two	two	NUM
ejpam-5388	217	29	self	self	NOUN
ejpam-5388	217	30	-	-	PUNCT
ejpam-5388	217	31	mappings	mapping	NOUN
ejpam-5388	217	32	on	on	ADP
ejpam-5388	217	33	𭟋	𭟋	ADP
ejpam-5388	217	34	.	.	PROPN
ejpam-5388	218	1	suppose	suppose	VERB
ejpam-5388	218	2	that	that	SCONJ
ejpam-5388	218	3	α	α	PROPN
ejpam-5388	218	4	,	,	PUNCT
ejpam-5388	218	5	η	η	PROPN
ejpam-5388	218	6	:	:	PUNCT
ejpam-5388	218	7	𭟋	𭟋	PROPN
ejpam-5388	218	8	×	×	NOUN
ejpam-5388	218	9	𭟋	𭟋	PROPN
ejpam-5388	218	10	→	→	X
ejpam-5388	218	11	r	r	NOUN
ejpam-5388	218	12	are	be	AUX
ejpam-5388	218	13	two	two	NUM
ejpam-5388	218	14	functions	function	NOUN
ejpam-5388	218	15	.	.	PUNCT
ejpam-5388	219	1	assume	assume	VERB
ejpam-5388	219	2	that	that	SCONJ
ejpam-5388	219	3	the	the	DET
ejpam-5388	219	4	following	follow	VERB
ejpam-5388	219	5	conditions	condition	NOUN
ejpam-5388	219	6	hold	hold	VERB
ejpam-5388	219	7	:	:	PUNCT
ejpam-5388	219	8	(	(	PUNCT
ejpam-5388	219	9	i	i	NOUN
ejpam-5388	219	10	)	)	PUNCT
ejpam-5388	219	11	λ(s	λ(s	PROPN
ejpam-5388	219	12	,	,	PUNCT
ejpam-5388	219	13	φ	φ	PROPN
ejpam-5388	219	14	,	,	PUNCT
ejpam-5388	219	15	ϕ)contraction	ϕ)contraction	PROPN
ejpam-5388	219	16	type	type	NOUN
ejpam-5388	219	17	(	(	PUNCT
ejpam-5388	219	18	b	b	NOUN
ejpam-5388	219	19	)	)	PUNCT
ejpam-5388	219	20	mapping	mapping	NOUN
ejpam-5388	219	21	;	;	PUNCT
ejpam-5388	219	22	(	(	PUNCT
ejpam-5388	219	23	ii	ii	NOUN
ejpam-5388	219	24	)	)	PUNCT
ejpam-5388	219	25	the	the	DET
ejpam-5388	219	26	pair	pair	NOUN
ejpam-5388	219	27	(	(	PUNCT
ejpam-5388	219	28	p	p	X
ejpam-5388	219	29	,	,	PUNCT
ejpam-5388	219	30	q	q	NOUN
ejpam-5388	219	31	)	)	PUNCT
ejpam-5388	219	32	is	be	AUX
ejpam-5388	219	33	triangular	triangular	ADJ
ejpam-5388	219	34	α	α	NOUN
ejpam-5388	219	35	-	-	ADJ
ejpam-5388	219	36	admissible	admissible	ADJ
ejpam-5388	219	37	with	with	ADP
ejpam-5388	219	38	respect	respect	NOUN
ejpam-5388	219	39	to	to	ADP
ejpam-5388	219	40	η	η	PROPN
ejpam-5388	219	41	;	;	PUNCT
ejpam-5388	219	42	(	(	PUNCT
ejpam-5388	219	43	iii	iii	X
ejpam-5388	219	44	)	)	PUNCT
ejpam-5388	219	45	there	there	PRON
ejpam-5388	219	46	exists	exist	VERB
ejpam-5388	219	47	u0	u0	PROPN
ejpam-5388	219	48	∈	∈	PROPN
ejpam-5388	219	49	𭟋	𭟋	ADP
ejpam-5388	219	50	such	such	ADJ
ejpam-5388	219	51	that	that	SCONJ
ejpam-5388	219	52	α(u0	α(u0	NOUN
ejpam-5388	219	53	,	,	PUNCT
ejpam-5388	219	54	pu0	pu0	NOUN
ejpam-5388	219	55	)	)	PUNCT
ejpam-5388	219	56	≥	≥	PROPN
ejpam-5388	219	57	η(u0	η(u0	NOUN
ejpam-5388	219	58	,	,	PUNCT
ejpam-5388	219	59	pu0	pu0	NOUN
ejpam-5388	219	60	)	)	PUNCT
ejpam-5388	219	61	,	,	PUNCT
ejpam-5388	219	62	(	(	PUNCT
ejpam-5388	219	63	iv	iv	X
ejpam-5388	219	64	)	)	PUNCT
ejpam-5388	219	65	p	p	NOUN
ejpam-5388	219	66	and	and	CCONJ
ejpam-5388	219	67	q	q	NOUN
ejpam-5388	219	68	are	be	AUX
ejpam-5388	219	69	continuous	continuous	ADJ
ejpam-5388	219	70	mappings	mapping	NOUN
ejpam-5388	219	71	.	.	PUNCT
ejpam-5388	220	1	then	then	ADV
ejpam-5388	220	2	,	,	PUNCT
ejpam-5388	220	3	p	p	NOUN
ejpam-5388	220	4	and	and	CCONJ
ejpam-5388	220	5	q	q	NOUN
ejpam-5388	220	6	have	have	VERB
ejpam-5388	220	7	a	a	DET
ejpam-5388	220	8	common	common	ADJ
ejpam-5388	220	9	fixed	fix	VERB
ejpam-5388	220	10	point	point	NOUN
ejpam-5388	220	11	in	in	ADP
ejpam-5388	220	12	𭟋	𭟋	PROPN
ejpam-5388	220	13	.	.	PUNCT
ejpam-5388	220	14	theorem	theorem	VERB
ejpam-5388	220	15	2.6	2.6	NUM
ejpam-5388	220	16	.	.	PUNCT
ejpam-5388	221	1	let	let	AUX
ejpam-5388	221	2	(	(	PUNCT
ejpam-5388	221	3	𭟋	𭟋	NOUN
ejpam-5388	221	4	,	,	PUNCT
ejpam-5388	221	5	λb	λb	NOUN
ejpam-5388	221	6	)	)	PUNCT
ejpam-5388	221	7	be	be	AUX
ejpam-5388	221	8	a	a	DET
ejpam-5388	221	9	complete	complete	ADJ
ejpam-5388	221	10	b	b	X
ejpam-5388	221	11	-	-	PUNCT
ejpam-5388	221	12	metric	metric	ADJ
ejpam-5388	221	13	space	space	NOUN
ejpam-5388	221	14	with	with	ADP
ejpam-5388	221	15	the	the	DET
ejpam-5388	221	16	constant	constant	ADJ
ejpam-5388	221	17	s	s	PART
ejpam-5388	221	18	≥	≥	NOUN
ejpam-5388	221	19	1	1	NUM
ejpam-5388	221	20	,	,	PUNCT
ejpam-5388	221	21	and	and	CCONJ
ejpam-5388	221	22	(	(	PUNCT
ejpam-5388	221	23	p	p	X
ejpam-5388	221	24	,	,	PUNCT
ejpam-5388	221	25	q	q	NOUN
ejpam-5388	221	26	)	)	PUNCT
ejpam-5388	221	27	be	be	AUX
ejpam-5388	221	28	two	two	NUM
ejpam-5388	221	29	self	self	NOUN
ejpam-5388	221	30	-	-	PUNCT
ejpam-5388	221	31	mappings	mapping	NOUN
ejpam-5388	221	32	on	on	ADP
ejpam-5388	221	33	𭟋	𭟋	ADP
ejpam-5388	221	34	.	.	PROPN
ejpam-5388	222	1	suppose	suppose	VERB
ejpam-5388	222	2	that	that	SCONJ
ejpam-5388	222	3	α	α	PROPN
ejpam-5388	222	4	,	,	PUNCT
ejpam-5388	222	5	η	η	PROPN
ejpam-5388	222	6	:	:	PUNCT
ejpam-5388	222	7	𭟋	𭟋	PROPN
ejpam-5388	222	8	×	×	NOUN
ejpam-5388	222	9	𭟋	𭟋	PROPN
ejpam-5388	222	10	→	→	X
ejpam-5388	222	11	r	r	NOUN
ejpam-5388	222	12	are	be	AUX
ejpam-5388	222	13	two	two	NUM
ejpam-5388	222	14	functions	function	NOUN
ejpam-5388	222	15	.	.	PUNCT
ejpam-5388	223	1	assume	assume	VERB
ejpam-5388	223	2	that	that	SCONJ
ejpam-5388	223	3	the	the	DET
ejpam-5388	223	4	following	follow	VERB
ejpam-5388	223	5	conditions	condition	NOUN
ejpam-5388	223	6	hold	hold	VERB
ejpam-5388	223	7	:	:	PUNCT
ejpam-5388	223	8	(	(	PUNCT
ejpam-5388	223	9	i	i	NOUN
ejpam-5388	223	10	)	)	PUNCT
ejpam-5388	223	11	λ(s	λ(s	PROPN
ejpam-5388	223	12	,	,	PUNCT
ejpam-5388	223	13	φ	φ	NOUN
ejpam-5388	223	14	,	,	PUNCT
ejpam-5388	223	15	ϕ)-contraction	ϕ)-contraction	PUNCT
ejpam-5388	223	16	mapping	mapping	NOUN
ejpam-5388	223	17	type	type	NOUN
ejpam-5388	223	18	(	(	PUNCT
ejpam-5388	223	19	b	b	NOUN
ejpam-5388	223	20	)	)	PUNCT
ejpam-5388	223	21	;	;	PUNCT
ejpam-5388	223	22	(	(	PUNCT
ejpam-5388	223	23	ii	ii	NOUN
ejpam-5388	223	24	)	)	PUNCT
ejpam-5388	223	25	the	the	DET
ejpam-5388	223	26	pair	pair	NOUN
ejpam-5388	223	27	(	(	PUNCT
ejpam-5388	223	28	p	p	X
ejpam-5388	223	29	,	,	PUNCT
ejpam-5388	223	30	q	q	NOUN
ejpam-5388	223	31	)	)	PUNCT
ejpam-5388	223	32	is	be	AUX
ejpam-5388	223	33	triangular	triangular	ADJ
ejpam-5388	223	34	α	α	NOUN
ejpam-5388	223	35	-	-	ADJ
ejpam-5388	223	36	admissible	admissible	ADJ
ejpam-5388	223	37	with	with	ADP
ejpam-5388	223	38	respect	respect	NOUN
ejpam-5388	223	39	to	to	ADP
ejpam-5388	223	40	η	η	PROPN
ejpam-5388	223	41	;	;	PUNCT
ejpam-5388	223	42	(	(	PUNCT
ejpam-5388	223	43	iii	iii	X
ejpam-5388	223	44	)	)	PUNCT
ejpam-5388	223	45	if	if	SCONJ
ejpam-5388	223	46	∃	∃	PROPN
ejpam-5388	223	47	u0	u0	PROPN
ejpam-5388	223	48	∈	∈	PROPN
ejpam-5388	223	49	𭟋	𭟋	ADP
ejpam-5388	223	50	such	such	ADJ
ejpam-5388	223	51	that	that	SCONJ
ejpam-5388	223	52	α(u0	α(u0	NOUN
ejpam-5388	223	53	,	,	PUNCT
ejpam-5388	223	54	pu0	pu0	NOUN
ejpam-5388	223	55	)	)	PUNCT
ejpam-5388	223	56	≥	≥	PROPN
ejpam-5388	223	57	η(u0	η(u0	NOUN
ejpam-5388	223	58	,	,	PUNCT
ejpam-5388	223	59	pu0	pu0	NOUN
ejpam-5388	223	60	)	)	PUNCT
ejpam-5388	223	61	,	,	PUNCT
ejpam-5388	223	62	(	(	PUNCT
ejpam-5388	223	63	iv	iv	X
ejpam-5388	223	64	)	)	PUNCT
ejpam-5388	223	65	if	if	SCONJ
ejpam-5388	223	66	{	{	PUNCT
ejpam-5388	223	67	un	un	ADJ
ejpam-5388	223	68	}	}	PUNCT
ejpam-5388	223	69	is	be	AUX
ejpam-5388	223	70	a	a	DET
ejpam-5388	223	71	sequence	sequence	NOUN
ejpam-5388	223	72	in	in	ADP
ejpam-5388	223	73	𭟋	𭟋	ADP
ejpam-5388	223	74	such	such	ADJ
ejpam-5388	223	75	that	that	SCONJ
ejpam-5388	223	76	α(un	α(un	PROPN
ejpam-5388	223	77	,	,	PUNCT
ejpam-5388	223	78	un+1	un+1	NOUN
ejpam-5388	223	79	)	)	PUNCT
ejpam-5388	223	80	≥	≥	NOUN
ejpam-5388	223	81	η(un	η(un	PROPN
ejpam-5388	223	82	,	,	PUNCT
ejpam-5388	223	83	un+1	un+1	NOUN
ejpam-5388	223	84	)	)	PUNCT
ejpam-5388	223	85	,	,	PUNCT
ejpam-5388	223	86	for	for	ADP
ejpam-5388	223	87	all	all	DET
ejpam-5388	223	88	n	n	PRON
ejpam-5388	223	89	∈	∈	PROPN
ejpam-5388	223	90	n	n	NOUN
ejpam-5388	223	91	and	and	CCONJ
ejpam-5388	223	92	un	un	PROPN
ejpam-5388	223	93	→	→	SYM
ejpam-5388	223	94	θ	θ	PROPN
ejpam-5388	223	95	as	as	ADP
ejpam-5388	223	96	n→	n→	PROPN
ejpam-5388	223	97	∞	∞	PROPN
ejpam-5388	223	98	,	,	PUNCT
ejpam-5388	223	99	then	then	ADV
ejpam-5388	223	100	there	there	PRON
ejpam-5388	223	101	exist	exist	VERB
ejpam-5388	223	102	a	a	DET
ejpam-5388	223	103	subsequence	subsequence	NOUN
ejpam-5388	223	104	{	{	PUNCT
ejpam-5388	223	105	uni	uni	NOUN
ejpam-5388	223	106	of	of	ADP
ejpam-5388	223	107	{	{	PUNCT
ejpam-5388	223	108	un	un	PROPN
ejpam-5388	223	109	}	}	PUNCT
ejpam-5388	223	110	such	such	ADJ
ejpam-5388	223	111	that	that	SCONJ
ejpam-5388	223	112	α(uni	α(uni	PROPN
ejpam-5388	223	113	,	,	PUNCT
ejpam-5388	223	114	u∗	u∗	PROPN
ejpam-5388	223	115	)	)	PUNCT
ejpam-5388	223	116	≥	≥	NOUN
ejpam-5388	223	117	η(uni	η(uni	PROPN
ejpam-5388	223	118	,	,	PUNCT
ejpam-5388	223	119	u∗	u∗	PROPN
ejpam-5388	223	120	)	)	PUNCT
ejpam-5388	223	121	,	,	PUNCT
ejpam-5388	223	122	for	for	ADP
ejpam-5388	223	123	all	all	DET
ejpam-5388	223	124	i	i	PRON
ejpam-5388	223	125	∈	∈	PROPN
ejpam-5388	223	126	n.	n.	NOUN
ejpam-5388	223	127	then	then	ADV
ejpam-5388	223	128	,	,	PUNCT
ejpam-5388	223	129	p	p	NOUN
ejpam-5388	223	130	and	and	CCONJ
ejpam-5388	223	131	q	q	NOUN
ejpam-5388	223	132	have	have	VERB
ejpam-5388	223	133	a	a	DET
ejpam-5388	223	134	common	common	ADJ
ejpam-5388	223	135	fixed	fix	VERB
ejpam-5388	223	136	point	point	NOUN
ejpam-5388	223	137	in	in	ADP
ejpam-5388	223	138	𭟋	𭟋	PROPN
ejpam-5388	223	139	.	.	PUNCT
ejpam-5388	224	1	the	the	DET
ejpam-5388	224	2	following	follow	VERB
ejpam-5388	224	3	corollaries	corollary	NOUN
ejpam-5388	224	4	are	be	AUX
ejpam-5388	224	5	consequences	consequence	NOUN
ejpam-5388	224	6	of	of	ADP
ejpam-5388	224	7	theorem	theorem	ADJ
ejpam-5388	224	8	2.2	2.2	NUM
ejpam-5388	224	9	and	and	CCONJ
ejpam-5388	224	10	theorem	theorem	VERB
ejpam-5388	224	11	2.3	2.3	NUM
ejpam-5388	224	12	.	.	PUNCT
ejpam-5388	225	1	h.	h.	PROPN
ejpam-5388	225	2	alsamir	alsamir	VERB
ejpam-5388	225	3	et	et	PROPN
ejpam-5388	225	4	al	al	PROPN
ejpam-5388	225	5	.	.	PUNCT
ejpam-5388	225	6	/	/	SYM
ejpam-5388	225	7	eur	eur	PROPN
ejpam-5388	225	8	.	.	PUNCT
ejpam-5388	226	1	j.	j.	PROPN
ejpam-5388	226	2	pure	pure	PROPN
ejpam-5388	226	3	appl	appl	PROPN
ejpam-5388	226	4	.	.	PROPN
ejpam-5388	226	5	math	math	PROPN
ejpam-5388	226	6	,	,	PUNCT
ejpam-5388	226	7	17	17	NUM
ejpam-5388	226	8	(	(	PUNCT
ejpam-5388	226	9	4	4	NUM
ejpam-5388	226	10	)	)	PUNCT
ejpam-5388	226	11	(	(	PUNCT
ejpam-5388	226	12	2024	2024	NUM
ejpam-5388	226	13	)	)	PUNCT
ejpam-5388	226	14	,	,	PUNCT
ejpam-5388	226	15	2492	2492	NUM
ejpam-5388	226	16	-	-	SYM
ejpam-5388	226	17	2504	2504	NUM
ejpam-5388	226	18	2500	2500	NUM
ejpam-5388	226	19	corollary	corollary	ADJ
ejpam-5388	226	20	2.7	2.7	NUM
ejpam-5388	226	21	.	.	PUNCT
ejpam-5388	227	1	let	let	AUX
ejpam-5388	227	2	(	(	PUNCT
ejpam-5388	227	3	𭟋	𭟋	NOUN
ejpam-5388	227	4	,	,	PUNCT
ejpam-5388	227	5	λb	λb	NOUN
ejpam-5388	227	6	)	)	PUNCT
ejpam-5388	227	7	be	be	AUX
ejpam-5388	227	8	a	a	DET
ejpam-5388	227	9	complete	complete	ADJ
ejpam-5388	227	10	b	b	X
ejpam-5388	227	11	-	-	PUNCT
ejpam-5388	227	12	metric	metric	ADJ
ejpam-5388	227	13	space	space	NOUN
ejpam-5388	227	14	with	with	ADP
ejpam-5388	227	15	the	the	DET
ejpam-5388	227	16	constant	constant	ADJ
ejpam-5388	227	17	s	s	PART
ejpam-5388	227	18	≥	≥	NOUN
ejpam-5388	227	19	1	1	NUM
ejpam-5388	227	20	,	,	PUNCT
ejpam-5388	227	21	and	and	CCONJ
ejpam-5388	227	22	p	p	NOUN
ejpam-5388	227	23	be	be	AUX
ejpam-5388	227	24	a	a	DET
ejpam-5388	227	25	self	self	NOUN
ejpam-5388	227	26	-	-	PUNCT
ejpam-5388	227	27	mapping	mapping	NOUN
ejpam-5388	227	28	on	on	ADP
ejpam-5388	227	29	𭟋	𭟋	PROPN
ejpam-5388	227	30	.	.	PROPN
ejpam-5388	227	31	suppose	suppose	VERB
ejpam-5388	227	32	that	that	SCONJ
ejpam-5388	227	33	α	α	PROPN
ejpam-5388	227	34	,	,	PUNCT
ejpam-5388	227	35	η	η	PROPN
ejpam-5388	227	36	:	:	PUNCT
ejpam-5388	227	37	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	227	38	→	→	SYM
ejpam-5388	227	39	r	r	NOUN
ejpam-5388	227	40	are	be	AUX
ejpam-5388	227	41	two	two	NUM
ejpam-5388	227	42	functions	function	NOUN
ejpam-5388	227	43	.	.	PUNCT
ejpam-5388	228	1	suppose	suppose	VERB
ejpam-5388	228	2	that	that	SCONJ
ejpam-5388	228	3	the	the	DET
ejpam-5388	228	4	following	follow	VERB
ejpam-5388	228	5	conditions	condition	NOUN
ejpam-5388	228	6	hold	hold	VERB
ejpam-5388	228	7	:	:	PUNCT
ejpam-5388	228	8	(	(	PUNCT
ejpam-5388	228	9	i	i	NOUN
ejpam-5388	228	10	)	)	PUNCT
ejpam-5388	228	11	if	if	SCONJ
ejpam-5388	228	12	α(u	α(u	PROPN
ejpam-5388	228	13	,	,	PUNCT
ejpam-5388	228	14	v	v	NOUN
ejpam-5388	228	15	)	)	PUNCT
ejpam-5388	228	16	≥	≥	NOUN
ejpam-5388	228	17	η(u	η(u	NOUN
ejpam-5388	228	18	,	,	PUNCT
ejpam-5388	228	19	v	v	NOUN
ejpam-5388	228	20	)	)	PUNCT
ejpam-5388	228	21	⇒	⇒	NOUN
ejpam-5388	228	22	φ	φ	PROPN
ejpam-5388	228	23	(	(	PUNCT
ejpam-5388	228	24	s2λb(pu	s2λb(pu	PROPN
ejpam-5388	228	25	,	,	PUNCT
ejpam-5388	228	26	pv	pv	NOUN
ejpam-5388	228	27	)	)	PUNCT
ejpam-5388	228	28	)	)	PUNCT
ejpam-5388	228	29	≤	≤	NUM
ejpam-5388	229	1	λ	λ	PROPN
ejpam-5388	229	2	[	[	X
ejpam-5388	229	3	φ	φ	X
ejpam-5388	229	4	(	(	PUNCT
ejpam-5388	229	5	mλb	mλb	PROPN
ejpam-5388	229	6	(	(	PUNCT
ejpam-5388	229	7	u	u	NOUN
ejpam-5388	229	8	,	,	PUNCT
ejpam-5388	229	9	v))−	v))−	NOUN
ejpam-5388	229	10	ϕ	ϕ	NOUN
ejpam-5388	229	11	(	(	PUNCT
ejpam-5388	229	12	mλb	mλb	PROPN
ejpam-5388	229	13	(	(	PUNCT
ejpam-5388	229	14	u	u	NOUN
ejpam-5388	229	15	,	,	PUNCT
ejpam-5388	229	16	v	v	NOUN
ejpam-5388	229	17	)	)	PUNCT
ejpam-5388	229	18	)	)	PUNCT
ejpam-5388	230	1	+	+	CCONJ
ejpam-5388	230	2	(	(	PUNCT
ejpam-5388	230	3	nλb	nλb	INTJ
ejpam-5388	230	4	(	(	PUNCT
ejpam-5388	230	5	u	u	NOUN
ejpam-5388	230	6	,	,	PUNCT
ejpam-5388	230	7	v	v	NOUN
ejpam-5388	230	8	)	)	PUNCT
ejpam-5388	230	9	)	)	PUNCT
ejpam-5388	230	10	]	]	PUNCT
ejpam-5388	231	1	,	,	PUNCT
ejpam-5388	231	2	(	(	PUNCT
ejpam-5388	231	3	2.21	2.21	NUM
ejpam-5388	231	4	)	)	PUNCT
ejpam-5388	231	5	(	(	PUNCT
ejpam-5388	231	6	ii)p	ii)p	PROPN
ejpam-5388	231	7	is	be	AUX
ejpam-5388	231	8	triangular	triangular	ADJ
ejpam-5388	231	9	α	α	NOUN
ejpam-5388	231	10	-	-	ADJ
ejpam-5388	231	11	admissible	admissible	ADJ
ejpam-5388	231	12	with	with	ADP
ejpam-5388	231	13	respect	respect	NOUN
ejpam-5388	231	14	to	to	ADP
ejpam-5388	231	15	η	η	PROPN
ejpam-5388	231	16	;	;	PUNCT
ejpam-5388	231	17	(	(	PUNCT
ejpam-5388	231	18	iii	iii	X
ejpam-5388	231	19	)	)	PUNCT
ejpam-5388	231	20	if	if	SCONJ
ejpam-5388	231	21	∃	∃	PROPN
ejpam-5388	231	22	u0	u0	PROPN
ejpam-5388	231	23	∈	∈	PROPN
ejpam-5388	231	24	𭟋	𭟋	ADP
ejpam-5388	231	25	such	such	ADJ
ejpam-5388	231	26	that	that	SCONJ
ejpam-5388	231	27	α(u0	α(u0	NOUN
ejpam-5388	231	28	,	,	PUNCT
ejpam-5388	231	29	pu0	pu0	NOUN
ejpam-5388	231	30	)	)	PUNCT
ejpam-5388	231	31	≥	≥	PROPN
ejpam-5388	231	32	η(u0	η(u0	NOUN
ejpam-5388	231	33	,	,	PUNCT
ejpam-5388	231	34	pu0	pu0	NOUN
ejpam-5388	231	35	)	)	PUNCT
ejpam-5388	231	36	,	,	PUNCT
ejpam-5388	231	37	(	(	PUNCT
ejpam-5388	231	38	iv	iv	X
ejpam-5388	231	39	)	)	PUNCT
ejpam-5388	231	40	p	p	NOUN
ejpam-5388	231	41	is	be	AUX
ejpam-5388	231	42	a	a	DET
ejpam-5388	231	43	continuous	continuous	ADJ
ejpam-5388	231	44	mappings	mapping	NOUN
ejpam-5388	231	45	.	.	PUNCT
ejpam-5388	232	1	then	then	ADV
ejpam-5388	232	2	,	,	PUNCT
ejpam-5388	232	3	p	p	PROPN
ejpam-5388	232	4	has	have	VERB
ejpam-5388	232	5	a	a	DET
ejpam-5388	232	6	fixed	fix	VERB
ejpam-5388	232	7	point	point	NOUN
ejpam-5388	232	8	in	in	ADP
ejpam-5388	232	9	𭟋	𭟋	PROPN
ejpam-5388	232	10	.	.	PUNCT
ejpam-5388	232	11	proof	proof	NOUN
ejpam-5388	232	12	.	.	PUNCT
ejpam-5388	233	1	the	the	DET
ejpam-5388	233	2	conclusion	conclusion	NOUN
ejpam-5388	233	3	follows	follow	VERB
ejpam-5388	233	4	from	from	ADP
ejpam-5388	233	5	theorem	theorem	ADJ
ejpam-5388	233	6	2.2	2.2	NUM
ejpam-5388	233	7	by	by	ADP
ejpam-5388	233	8	taking	take	VERB
ejpam-5388	233	9	q	q	NOUN
ejpam-5388	234	1	=	=	PUNCT
ejpam-5388	235	1	p.	p.	NOUN
ejpam-5388	235	2	corollary	corollary	NOUN
ejpam-5388	235	3	2.8	2.8	NUM
ejpam-5388	235	4	.	.	PUNCT
ejpam-5388	236	1	let	let	AUX
ejpam-5388	236	2	(	(	PUNCT
ejpam-5388	236	3	𭟋	𭟋	NOUN
ejpam-5388	236	4	,	,	PUNCT
ejpam-5388	236	5	λb	λb	NOUN
ejpam-5388	236	6	)	)	PUNCT
ejpam-5388	236	7	be	be	AUX
ejpam-5388	236	8	a	a	DET
ejpam-5388	236	9	complete	complete	ADJ
ejpam-5388	236	10	b	b	X
ejpam-5388	236	11	-	-	PUNCT
ejpam-5388	236	12	metric	metric	ADJ
ejpam-5388	236	13	space	space	NOUN
ejpam-5388	236	14	with	with	ADP
ejpam-5388	236	15	the	the	DET
ejpam-5388	236	16	constant	constant	ADJ
ejpam-5388	236	17	s	s	PART
ejpam-5388	236	18	≥	≥	NOUN
ejpam-5388	236	19	1	1	NUM
ejpam-5388	236	20	,	,	PUNCT
ejpam-5388	236	21	and	and	CCONJ
ejpam-5388	236	22	p	p	NOUN
ejpam-5388	236	23	be	be	AUX
ejpam-5388	236	24	a	a	DET
ejpam-5388	236	25	self	self	NOUN
ejpam-5388	236	26	-	-	PUNCT
ejpam-5388	236	27	mapping	mapping	NOUN
ejpam-5388	236	28	on	on	ADP
ejpam-5388	236	29	𭟋	𭟋	PROPN
ejpam-5388	236	30	.	.	PROPN
ejpam-5388	237	1	suppose	suppose	VERB
ejpam-5388	237	2	that	that	SCONJ
ejpam-5388	237	3	α	α	X
ejpam-5388	237	4	:	:	PUNCT
ejpam-5388	237	5	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	237	6	→	→	SYM
ejpam-5388	237	7	r	r	NOUN
ejpam-5388	237	8	are	be	AUX
ejpam-5388	237	9	two	two	NUM
ejpam-5388	237	10	functions	function	NOUN
ejpam-5388	237	11	.	.	PUNCT
ejpam-5388	238	1	assume	assume	VERB
ejpam-5388	238	2	that	that	SCONJ
ejpam-5388	238	3	the	the	DET
ejpam-5388	238	4	following	follow	VERB
ejpam-5388	238	5	conditions	condition	NOUN
ejpam-5388	238	6	hold	hold	VERB
ejpam-5388	238	7	:	:	PUNCT
ejpam-5388	238	8	(	(	PUNCT
ejpam-5388	238	9	i	i	NOUN
ejpam-5388	238	10	)	)	PUNCT
ejpam-5388	238	11	if	if	SCONJ
ejpam-5388	238	12	α(u	α(u	PROPN
ejpam-5388	238	13	,	,	PUNCT
ejpam-5388	238	14	v	v	NOUN
ejpam-5388	238	15	)	)	PUNCT
ejpam-5388	238	16	≥	≥	NOUN
ejpam-5388	238	17	1	1	NUM
ejpam-5388	238	18	⇒	⇒	PROPN
ejpam-5388	238	19	φ	φ	PROPN
ejpam-5388	238	20	(	(	PUNCT
ejpam-5388	238	21	s2λb(pu	s2λb(pu	PROPN
ejpam-5388	238	22	,	,	PUNCT
ejpam-5388	238	23	pv	pv	NOUN
ejpam-5388	238	24	)	)	PUNCT
ejpam-5388	238	25	)	)	PUNCT
ejpam-5388	238	26	≤	≤	NUM
ejpam-5388	239	1	λ	λ	PROPN
ejpam-5388	239	2	[	[	X
ejpam-5388	239	3	φ	φ	X
ejpam-5388	239	4	(	(	PUNCT
ejpam-5388	239	5	mλb	mλb	PROPN
ejpam-5388	239	6	(	(	PUNCT
ejpam-5388	239	7	u	u	NOUN
ejpam-5388	239	8	,	,	PUNCT
ejpam-5388	239	9	v))−	v))−	NOUN
ejpam-5388	239	10	ϕ	ϕ	NOUN
ejpam-5388	239	11	(	(	PUNCT
ejpam-5388	239	12	mλb	mλb	PROPN
ejpam-5388	239	13	(	(	PUNCT
ejpam-5388	239	14	u	u	NOUN
ejpam-5388	239	15	,	,	PUNCT
ejpam-5388	239	16	v	v	NOUN
ejpam-5388	239	17	)	)	PUNCT
ejpam-5388	239	18	)	)	PUNCT
ejpam-5388	240	1	+	+	CCONJ
ejpam-5388	240	2	(	(	PUNCT
ejpam-5388	240	3	nλb	nλb	INTJ
ejpam-5388	240	4	(	(	PUNCT
ejpam-5388	240	5	u	u	NOUN
ejpam-5388	240	6	,	,	PUNCT
ejpam-5388	240	7	v	v	NOUN
ejpam-5388	240	8	)	)	PUNCT
ejpam-5388	240	9	)	)	PUNCT
ejpam-5388	240	10	]	]	PUNCT
ejpam-5388	240	11	,	,	PUNCT
ejpam-5388	240	12	(	(	PUNCT
ejpam-5388	240	13	2.22	2.22	NUM
ejpam-5388	240	14	)	)	PUNCT
ejpam-5388	240	15	(	(	PUNCT
ejpam-5388	240	16	ii)p	ii)p	PROPN
ejpam-5388	240	17	is	be	AUX
ejpam-5388	240	18	triangular	triangular	ADJ
ejpam-5388	240	19	α	α	NOUN
ejpam-5388	240	20	-	-	ADJ
ejpam-5388	240	21	admissible	admissible	ADJ
ejpam-5388	240	22	with	with	ADP
ejpam-5388	240	23	respect	respect	NOUN
ejpam-5388	240	24	to	to	ADP
ejpam-5388	240	25	η	η	PROPN
ejpam-5388	240	26	;	;	PUNCT
ejpam-5388	240	27	(	(	PUNCT
ejpam-5388	240	28	iii	iii	X
ejpam-5388	240	29	)	)	PUNCT
ejpam-5388	240	30	there	there	PRON
ejpam-5388	240	31	exists	exist	VERB
ejpam-5388	240	32	u0	u0	PROPN
ejpam-5388	240	33	∈	∈	PROPN
ejpam-5388	240	34	𭟋	𭟋	ADP
ejpam-5388	240	35	such	such	ADJ
ejpam-5388	240	36	that	that	SCONJ
ejpam-5388	240	37	α(u0	α(u0	NOUN
ejpam-5388	240	38	,	,	PUNCT
ejpam-5388	240	39	pu0	pu0	NOUN
ejpam-5388	240	40	)	)	PUNCT
ejpam-5388	240	41	≥	≥	NOUN
ejpam-5388	240	42	1	1	NUM
ejpam-5388	240	43	,	,	PUNCT
ejpam-5388	240	44	(	(	PUNCT
ejpam-5388	240	45	iv	iv	X
ejpam-5388	240	46	)	)	PUNCT
ejpam-5388	240	47	p	p	NOUN
ejpam-5388	240	48	is	be	AUX
ejpam-5388	240	49	a	a	DET
ejpam-5388	240	50	continuous	continuous	ADJ
ejpam-5388	240	51	mappings	mapping	NOUN
ejpam-5388	240	52	.	.	PUNCT
ejpam-5388	241	1	then	then	ADV
ejpam-5388	241	2	,	,	PUNCT
ejpam-5388	241	3	p	p	PROPN
ejpam-5388	241	4	has	have	VERB
ejpam-5388	241	5	a	a	DET
ejpam-5388	241	6	fixed	fix	VERB
ejpam-5388	241	7	point	point	NOUN
ejpam-5388	241	8	in	in	ADP
ejpam-5388	241	9	𭟋	𭟋	PROPN
ejpam-5388	241	10	.	.	PUNCT
ejpam-5388	241	11	proof	proof	NOUN
ejpam-5388	241	12	.	.	PUNCT
ejpam-5388	242	1	the	the	DET
ejpam-5388	242	2	proof	proof	NOUN
ejpam-5388	242	3	follows	follow	VERB
ejpam-5388	242	4	corollary	corollary	ADJ
ejpam-5388	242	5	2.7	2.7	NUM
ejpam-5388	242	6	by	by	ADP
ejpam-5388	242	7	defining	define	VERB
ejpam-5388	242	8	η	η	PROPN
ejpam-5388	242	9	:	:	PUNCT
ejpam-5388	242	10	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	242	11	→	→	SYM
ejpam-5388	242	12	r	r	NOUN
ejpam-5388	242	13	via	via	ADP
ejpam-5388	242	14	η(u	η(u	NOUN
ejpam-5388	242	15	,	,	PUNCT
ejpam-5388	242	16	v	v	NOUN
ejpam-5388	242	17	)	)	PUNCT
ejpam-5388	242	18	=	=	SYM
ejpam-5388	242	19	1	1	X
ejpam-5388	242	20	.	.	NOUN
ejpam-5388	242	21	remark	remark	NOUN
ejpam-5388	242	22	2.9	2.9	NUM
ejpam-5388	242	23	.	.	PUNCT
ejpam-5388	243	1	since	since	SCONJ
ejpam-5388	243	2	a	a	DET
ejpam-5388	243	3	b	b	NOUN
ejpam-5388	243	4	-	-	PUNCT
ejpam-5388	243	5	metric	metric	ADJ
ejpam-5388	243	6	space	space	NOUN
ejpam-5388	243	7	is	be	AUX
ejpam-5388	243	8	a	a	DET
ejpam-5388	243	9	metric	metric	ADJ
ejpam-5388	243	10	space	space	NOUN
ejpam-5388	243	11	when	when	SCONJ
ejpam-5388	243	12	s	s	VERB
ejpam-5388	243	13	=	=	SYM
ejpam-5388	243	14	1	1	NUM
ejpam-5388	243	15	,	,	PUNCT
ejpam-5388	243	16	so	so	SCONJ
ejpam-5388	243	17	our	our	PRON
ejpam-5388	243	18	theorems	theorem	NOUN
ejpam-5388	243	19	can	can	AUX
ejpam-5388	243	20	be	be	AUX
ejpam-5388	243	21	seen	see	VERB
ejpam-5388	243	22	as	as	ADP
ejpam-5388	243	23	a	a	DET
ejpam-5388	243	24	generalizations	generalization	NOUN
ejpam-5388	243	25	and	and	CCONJ
ejpam-5388	243	26	extensions	extension	NOUN
ejpam-5388	243	27	of	of	ADP
ejpam-5388	243	28	several	several	ADJ
ejpam-5388	243	29	comparable	comparable	ADJ
ejpam-5388	243	30	results	result	NOUN
ejpam-5388	243	31	in	in	ADP
ejpam-5388	243	32	metric	metric	ADJ
ejpam-5388	243	33	spaces	space	NOUN
ejpam-5388	243	34	and	and	CCONJ
ejpam-5388	243	35	b	b	X
ejpam-5388	243	36	-	-	PUNCT
ejpam-5388	243	37	metric	metric	ADJ
ejpam-5388	243	38	spaces	space	NOUN
ejpam-5388	243	39	.	.	PUNCT
ejpam-5388	244	1	the	the	DET
ejpam-5388	244	2	following	follow	VERB
ejpam-5388	244	3	example	example	NOUN
ejpam-5388	244	4	illustrates	illustrate	VERB
ejpam-5388	244	5	the	the	DET
ejpam-5388	244	6	above	above	ADJ
ejpam-5388	244	7	result	result	NOUN
ejpam-5388	244	8	.	.	PUNCT
ejpam-5388	245	1	example	example	NOUN
ejpam-5388	245	2	2.10	2.10	NUM
ejpam-5388	245	3	.	.	PUNCT
ejpam-5388	246	1	let	let	VERB
ejpam-5388	246	2	𭟋	𭟋	VERB
ejpam-5388	246	3	=	=	PUNCT
ejpam-5388	246	4	{	{	PUNCT
ejpam-5388	246	5	1	1	NUM
ejpam-5388	246	6	,	,	PUNCT
ejpam-5388	246	7	2	2	NUM
ejpam-5388	246	8	,	,	PUNCT
ejpam-5388	246	9	3	3	NUM
ejpam-5388	246	10	,	,	PUNCT
ejpam-5388	246	11	4	4	NUM
ejpam-5388	246	12	}	}	PUNCT
ejpam-5388	246	13	.	.	PUNCT
ejpam-5388	247	1	define	define	VERB
ejpam-5388	247	2	λb	λb	ADP
ejpam-5388	247	3	:	:	PUNCT
ejpam-5388	247	4	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	247	5	→	→	SYM
ejpam-5388	248	1	[	[	X
ejpam-5388	248	2	0,+∞	0,+∞	NUM
ejpam-5388	248	3	)	)	PUNCT
ejpam-5388	248	4	as	as	SCONJ
ejpam-5388	248	5	follows	follow	VERB
ejpam-5388	248	6	:	:	PUNCT
ejpam-5388	248	7	λb(u	λb(u	NUM
ejpam-5388	248	8	,	,	PUNCT
ejpam-5388	248	9	v	v	NOUN
ejpam-5388	248	10	)	)	PUNCT
ejpam-5388	248	11	=	=	SYM
ejpam-5388	249	1	λb(v	λb(v	NOUN
ejpam-5388	249	2	,	,	PUNCT
ejpam-5388	249	3	u	u	NOUN
ejpam-5388	249	4	)	)	PUNCT
ejpam-5388	249	5	=	=	SYM
ejpam-5388	249	6	0	0	PUNCT
ejpam-5388	250	1	if	if	SCONJ
ejpam-5388	250	2	u	u	PROPN
ejpam-5388	250	3	̸=	̸=	PROPN
ejpam-5388	250	4	v	v	NOUN
ejpam-5388	250	5	,	,	PUNCT
ejpam-5388	250	6	u	u	NOUN
ejpam-5388	250	7	=	=	PROPN
ejpam-5388	250	8	v	v	NUM
ejpam-5388	250	9	λb(u	λb(u	NUM
ejpam-5388	250	10	,	,	PUNCT
ejpam-5388	250	11	v	v	NOUN
ejpam-5388	250	12	)	)	PUNCT
ejpam-5388	250	13	=	=	SYM
ejpam-5388	250	14	λb(v	λb(v	NOUN
ejpam-5388	250	15	,	,	PUNCT
ejpam-5388	250	16	u	u	NOUN
ejpam-5388	250	17	)	)	PUNCT
ejpam-5388	250	18	=	=	SYM
ejpam-5388	250	19	2	2	NUM
ejpam-5388	250	20	if	if	SCONJ
ejpam-5388	250	21	u	u	NOUN
ejpam-5388	250	22	=	=	NOUN
ejpam-5388	250	23	1	1	NUM
ejpam-5388	250	24	,	,	PUNCT
ejpam-5388	250	25	v	v	NOUN
ejpam-5388	250	26	=	=	SYM
ejpam-5388	250	27	2	2	NUM
ejpam-5388	250	28	λb(u	λb(u	NOUN
ejpam-5388	250	29	,	,	PUNCT
ejpam-5388	250	30	v	v	NOUN
ejpam-5388	250	31	)	)	PUNCT
ejpam-5388	250	32	=	=	SYM
ejpam-5388	251	1	λb(v	λb(v	NOUN
ejpam-5388	251	2	,	,	PUNCT
ejpam-5388	251	3	u	u	NOUN
ejpam-5388	251	4	)	)	PUNCT
ejpam-5388	251	5	=	=	SYM
ejpam-5388	251	6	1	1	NUM
ejpam-5388	251	7	if	if	SCONJ
ejpam-5388	251	8	u	u	NOUN
ejpam-5388	251	9	=	=	NOUN
ejpam-5388	251	10	1	1	NUM
ejpam-5388	251	11	,	,	PUNCT
ejpam-5388	251	12	v	v	NOUN
ejpam-5388	251	13	=	=	SYM
ejpam-5388	251	14	3	3	NUM
ejpam-5388	251	15	λb(u	λb(u	NOUN
ejpam-5388	251	16	,	,	PUNCT
ejpam-5388	251	17	v	v	NOUN
ejpam-5388	251	18	)	)	PUNCT
ejpam-5388	251	19	=	=	SYM
ejpam-5388	252	1	λb(v	λb(v	NOUN
ejpam-5388	252	2	,	,	PUNCT
ejpam-5388	252	3	u	u	NOUN
ejpam-5388	252	4	)	)	PUNCT
ejpam-5388	252	5	=	=	SYM
ejpam-5388	252	6	10	10	NUM
ejpam-5388	252	7	if	if	SCONJ
ejpam-5388	252	8	u	u	NOUN
ejpam-5388	252	9	,	,	PUNCT
ejpam-5388	252	10	v	v	NOUN
ejpam-5388	252	11	=	=	SYM
ejpam-5388	252	12	1	1	NUM
ejpam-5388	252	13	,	,	PUNCT
ejpam-5388	252	14	2	2	NUM
ejpam-5388	252	15	,	,	PUNCT
ejpam-5388	252	16	3	3	NUM
ejpam-5388	252	17	,	,	PUNCT
ejpam-5388	252	18	v	v	NOUN
ejpam-5388	252	19	=	=	SYM
ejpam-5388	252	20	4	4	NUM
ejpam-5388	252	21	define	define	VERB
ejpam-5388	252	22	φ(t	φ(t	NUM
ejpam-5388	252	23	)	)	PUNCT
ejpam-5388	252	24	=	=	SYM
ejpam-5388	252	25	et	et	NOUN
ejpam-5388	252	26	,	,	PUNCT
ejpam-5388	252	27	ϕ(t	ϕ(t	NUM
ejpam-5388	252	28	)	)	PUNCT
ejpam-5388	253	1	=	=	SYM
ejpam-5388	253	2	et	et	NOUN
ejpam-5388	253	3	2+et	2+et	NUM
ejpam-5388	253	4	,	,	PUNCT
ejpam-5388	253	5	λ	λ	X
ejpam-5388	253	6	=	=	NOUN
ejpam-5388	253	7	1	1	NUM
ejpam-5388	253	8	2	2	NUM
ejpam-5388	253	9	,	,	PUNCT
ejpam-5388	253	10	l	l	NOUN
ejpam-5388	253	11	=	=	SYM
ejpam-5388	253	12	2	2	NUM
ejpam-5388	253	13	and	and	CCONJ
ejpam-5388	253	14	define	define	VERB
ejpam-5388	253	15	the	the	DET
ejpam-5388	253	16	mappings	mapping	NOUN
ejpam-5388	253	17	p	p	NOUN
ejpam-5388	253	18	,	,	PUNCT
ejpam-5388	253	19	q	q	NOUN
ejpam-5388	253	20	:	:	PUNCT
ejpam-5388	253	21	𭟋	𭟋	PROPN
ejpam-5388	253	22	→	→	SYM
ejpam-5388	253	23	𭟋	𭟋	NOUN
ejpam-5388	253	24	by	by	ADP
ejpam-5388	253	25	p1	p1	NOUN
ejpam-5388	253	26	=	=	SYM
ejpam-5388	253	27	p2	p2	PROPN
ejpam-5388	253	28	=	=	SYM
ejpam-5388	253	29	p3	p3	PROPN
ejpam-5388	253	30	=	=	SYM
ejpam-5388	253	31	1	1	NUM
ejpam-5388	253	32	,	,	PUNCT
ejpam-5388	253	33	p4	p4	ADJ
ejpam-5388	253	34	=	=	SYM
ejpam-5388	253	35	3	3	NUM
ejpam-5388	253	36	q1	q1	NOUN
ejpam-5388	253	37	=	=	SYM
ejpam-5388	253	38	2	2	NUM
ejpam-5388	253	39	,	,	PUNCT
ejpam-5388	253	40	q2	q2	NOUN
ejpam-5388	253	41	=	=	SYM
ejpam-5388	253	42	q3	q3	PROPN
ejpam-5388	253	43	=	=	PROPN
ejpam-5388	253	44	q4	q4	PROPN
ejpam-5388	253	45	=	=	NOUN
ejpam-5388	253	46	1	1	X
ejpam-5388	253	47	.	.	PUNCT
ejpam-5388	254	1	it	it	PRON
ejpam-5388	254	2	is	be	AUX
ejpam-5388	254	3	obvious	obvious	ADJ
ejpam-5388	254	4	that	that	SCONJ
ejpam-5388	254	5	(	(	PUNCT
ejpam-5388	254	6	𭟋	𭟋	NOUN
ejpam-5388	254	7	,	,	PUNCT
ejpam-5388	254	8	λb	λb	NOUN
ejpam-5388	254	9	)	)	PUNCT
ejpam-5388	254	10	is	be	AUX
ejpam-5388	254	11	a	a	DET
ejpam-5388	254	12	complete	complete	ADJ
ejpam-5388	254	13	b	b	X
ejpam-5388	254	14	-	-	PUNCT
ejpam-5388	254	15	metric	metric	ADJ
ejpam-5388	254	16	space	space	NOUN
ejpam-5388	254	17	with	with	ADP
ejpam-5388	254	18	the	the	DET
ejpam-5388	254	19	constant	constant	ADJ
ejpam-5388	254	20	s	s	PART
ejpam-5388	254	21	=	=	ADJ
ejpam-5388	254	22	2	2	X
ejpam-5388	254	23	.	.	PUNCT
ejpam-5388	255	1	we	we	PRON
ejpam-5388	255	2	show	show	VERB
ejpam-5388	255	3	that	that	SCONJ
ejpam-5388	255	4	the	the	DET
ejpam-5388	255	5	condition	condition	NOUN
ejpam-5388	255	6	(	(	PUNCT
ejpam-5388	255	7	2.1	2.1	NUM
ejpam-5388	255	8	)	)	PUNCT
ejpam-5388	255	9	is	be	AUX
ejpam-5388	255	10	true	true	ADJ
ejpam-5388	255	11	.	.	PUNCT
ejpam-5388	256	1	we	we	PRON
ejpam-5388	256	2	put	put	VERB
ejpam-5388	256	3	φ	φ	PROPN
ejpam-5388	256	4	(	(	PUNCT
ejpam-5388	256	5	s2λb(pu	s2λb(pu	PROPN
ejpam-5388	256	6	,	,	PUNCT
ejpam-5388	256	7	qv	qv	PROPN
ejpam-5388	256	8	)	)	PUNCT
ejpam-5388	256	9	)	)	PUNCT
ejpam-5388	257	1	=	=	SYM
ejpam-5388	257	2	a	a	PRON
ejpam-5388	257	3	,	,	PUNCT
ejpam-5388	257	4	φ(mλb	φ(mλb	PROPN
ejpam-5388	257	5	(	(	PUNCT
ejpam-5388	257	6	u	u	NOUN
ejpam-5388	257	7	,	,	PUNCT
ejpam-5388	257	8	v	v	NOUN
ejpam-5388	257	9	)	)	PUNCT
ejpam-5388	257	10	)	)	PUNCT
ejpam-5388	258	1	=	=	SYM
ejpam-5388	258	2	b,ϕ(mλb	b,ϕ(mλb	PROPN
ejpam-5388	258	3	(	(	PUNCT
ejpam-5388	258	4	u	u	NOUN
ejpam-5388	258	5	,	,	PUNCT
ejpam-5388	258	6	v	v	NOUN
ejpam-5388	258	7	)	)	PUNCT
ejpam-5388	258	8	)	)	PUNCT
ejpam-5388	259	1	=	=	SYM
ejpam-5388	259	2	c	c	PROPN
ejpam-5388	259	3	and	and	CCONJ
ejpam-5388	259	4	nλb	nλb	PROPN
ejpam-5388	259	5	(	(	PUNCT
ejpam-5388	259	6	u	u	NOUN
ejpam-5388	259	7	,	,	PUNCT
ejpam-5388	259	8	v	v	NOUN
ejpam-5388	259	9	)	)	PUNCT
ejpam-5388	259	10	=	=	SYM
ejpam-5388	260	1	d.	d.	PROPN
ejpam-5388	260	2	then	then	ADV
ejpam-5388	260	3	we	we	PRON
ejpam-5388	260	4	have	have	VERB
ejpam-5388	260	5	the	the	DET
ejpam-5388	260	6	following	follow	VERB
ejpam-5388	260	7	cases	case	NOUN
ejpam-5388	260	8	:	:	PUNCT
ejpam-5388	260	9	h.	h.	PROPN
ejpam-5388	260	10	alsamir	alsamir	VERB
ejpam-5388	260	11	et	et	PROPN
ejpam-5388	260	12	al	al	PROPN
ejpam-5388	260	13	.	.	PUNCT
ejpam-5388	260	14	/	/	SYM
ejpam-5388	260	15	eur	eur	PROPN
ejpam-5388	260	16	.	.	PUNCT
ejpam-5388	261	1	j.	j.	PROPN
ejpam-5388	261	2	pure	pure	PROPN
ejpam-5388	261	3	appl	appl	PROPN
ejpam-5388	261	4	.	.	PROPN
ejpam-5388	261	5	math	math	PROPN
ejpam-5388	261	6	,	,	PUNCT
ejpam-5388	261	7	17	17	NUM
ejpam-5388	261	8	(	(	PUNCT
ejpam-5388	261	9	4	4	NUM
ejpam-5388	261	10	)	)	PUNCT
ejpam-5388	261	11	(	(	PUNCT
ejpam-5388	261	12	2024	2024	NUM
ejpam-5388	261	13	)	)	PUNCT
ejpam-5388	261	14	,	,	PUNCT
ejpam-5388	261	15	2492	2492	NUM
ejpam-5388	261	16	-	-	SYM
ejpam-5388	261	17	2504	2504	NUM
ejpam-5388	261	18	2501	2501	NUM
ejpam-5388	261	19	table	table	NOUN
ejpam-5388	261	20	1	1	NUM
ejpam-5388	261	21	:	:	PUNCT
ejpam-5388	261	22	the	the	DET
ejpam-5388	261	23	possible	possible	ADJ
ejpam-5388	261	24	values	value	NOUN
ejpam-5388	261	25	of	of	ADP
ejpam-5388	261	26	u	u	NOUN
ejpam-5388	261	27	,	,	PUNCT
ejpam-5388	261	28	v	v	ADP
ejpam-5388	261	29	λb(u	λb(u	NUM
ejpam-5388	261	30	,	,	PUNCT
ejpam-5388	261	31	v	v	NOUN
ejpam-5388	261	32	)	)	PUNCT
ejpam-5388	261	33	a	a	DET
ejpam-5388	261	34	λ[b	λ[b	NOUN
ejpam-5388	261	35	−	−	NOUN
ejpam-5388	261	36	c	c	NOUN
ejpam-5388	262	1	+	+	PROPN
ejpam-5388	262	2	d	d	X
ejpam-5388	262	3	]	]	X
ejpam-5388	262	4	a	a	DET
ejpam-5388	262	5	≤	≤	NUM
ejpam-5388	262	6	λ[b	λ[b	NUM
ejpam-5388	262	7	−	−	NOUN
ejpam-5388	263	1	c	c	NOUN
ejpam-5388	264	1	+	+	NOUN
ejpam-5388	264	2	d	d	X
ejpam-5388	264	3	]	]	X
ejpam-5388	264	4	✓	✓	ADJ
ejpam-5388	264	5	λb(1	λb(1	NOUN
ejpam-5388	264	6	,	,	PUNCT
ejpam-5388	264	7	1	1	NUM
ejpam-5388	264	8	)	)	PUNCT
ejpam-5388	264	9	≈	≈	PROPN
ejpam-5388	264	10	2.72	2.72	NUM
ejpam-5388	265	1	≈	≈	PROPN
ejpam-5388	265	2	3.30	3.30	NUM
ejpam-5388	265	3	2.72	2.72	NUM
ejpam-5388	265	4	<	<	SYM
ejpam-5388	265	5	3.30	3.30	NUM
ejpam-5388	265	6	✓	✓	ADJ
ejpam-5388	265	7	λb(2	λb(2	NOUN
ejpam-5388	265	8	,	,	PUNCT
ejpam-5388	265	9	2	2	NUM
ejpam-5388	265	10	)	)	PUNCT
ejpam-5388	265	11	1	1	NUM
ejpam-5388	266	1	≈	≈	PROPN
ejpam-5388	266	2	3.30	3.30	NUM
ejpam-5388	266	3	1	1	NUM
ejpam-5388	266	4	<	<	X
ejpam-5388	266	5	3.30	3.30	NUM
ejpam-5388	266	6	✓	✓	ADJ
ejpam-5388	266	7	λb(3	λb(3	NOUN
ejpam-5388	266	8	,	,	PUNCT
ejpam-5388	266	9	3	3	X
ejpam-5388	266	10	)	)	PUNCT
ejpam-5388	266	11	1	1	NUM
ejpam-5388	267	1	≈	≈	NUM
ejpam-5388	267	2	1.07	1.07	NUM
ejpam-5388	267	3	1	1	NUM
ejpam-5388	267	4	<	<	X
ejpam-5388	267	5	1.07	1.07	NUM
ejpam-5388	267	6	✓	✓	PROPN
ejpam-5388	267	7	λb(4	λb(4	PROPN
ejpam-5388	267	8	,	,	PUNCT
ejpam-5388	267	9	4	4	NUM
ejpam-5388	267	10	)	)	PUNCT
ejpam-5388	267	11	≈	≈	PROPN
ejpam-5388	267	12	54.60	54.60	NUM
ejpam-5388	267	13	≈	≈	PROPN
ejpam-5388	267	14	11012.73	11012.73	NUM
ejpam-5388	267	15	54.60	54.60	NUM
ejpam-5388	267	16	<	<	X
ejpam-5388	267	17	11012.73	11012.73	NUM
ejpam-5388	267	18	✓	✓	ADJ
ejpam-5388	267	19	λb(1	λb(1	NOUN
ejpam-5388	267	20	,	,	PUNCT
ejpam-5388	267	21	2	2	NUM
ejpam-5388	267	22	)	)	PUNCT
ejpam-5388	267	23	1	1	NUM
ejpam-5388	268	1	≈	≈	PROPN
ejpam-5388	268	2	3.30	3.30	NUM
ejpam-5388	268	3	1	1	NUM
ejpam-5388	268	4	<	<	X
ejpam-5388	268	5	3.30	3.30	NUM
ejpam-5388	268	6	✓	✓	ADJ
ejpam-5388	268	7	λb(1	λb(1	NOUN
ejpam-5388	268	8	,	,	PUNCT
ejpam-5388	268	9	3	3	X
ejpam-5388	268	10	)	)	PUNCT
ejpam-5388	268	11	1	1	NUM
ejpam-5388	269	1	≈	≈	NUM
ejpam-5388	269	2	1.07	1.07	NUM
ejpam-5388	269	3	1	1	NUM
ejpam-5388	269	4	<	<	X
ejpam-5388	269	5	1.07	1.07	NUM
ejpam-5388	269	6	✓	✓	ADJ
ejpam-5388	269	7	λb(1	λb(1	NOUN
ejpam-5388	269	8	,	,	PUNCT
ejpam-5388	269	9	4	4	NUM
ejpam-5388	269	10	)	)	PUNCT
ejpam-5388	269	11	1	1	NUM
ejpam-5388	270	1	≈	≈	PROPN
ejpam-5388	270	2	11012.73	11012.73	NUM
ejpam-5388	270	3	1	1	NUM
ejpam-5388	270	4	<	<	X
ejpam-5388	270	5	11012.73	11012.73	NUM
ejpam-5388	270	6	✓	✓	PROPN
ejpam-5388	270	7	λb(2	λb(2	NOUN
ejpam-5388	270	8	,	,	PUNCT
ejpam-5388	270	9	3	3	X
ejpam-5388	270	10	)	)	PUNCT
ejpam-5388	270	11	1	1	NUM
ejpam-5388	271	1	≈	≈	PROPN
ejpam-5388	271	2	3.30	3.30	NUM
ejpam-5388	271	3	1	1	NUM
ejpam-5388	271	4	<	<	SYM
ejpam-5388	271	5	3.30	3.30	NUM
ejpam-5388	271	6	✓	✓	ADJ
ejpam-5388	271	7	λb(2	λb(2	NOUN
ejpam-5388	271	8	,	,	PUNCT
ejpam-5388	271	9	4	4	NUM
ejpam-5388	271	10	)	)	PUNCT
ejpam-5388	271	11	1	1	NUM
ejpam-5388	272	1	≈	≈	PROPN
ejpam-5388	272	2	11012.73	11012.73	NUM
ejpam-5388	272	3	1	1	NUM
ejpam-5388	272	4	<	<	X
ejpam-5388	272	5	11012.73	11012.73	NUM
ejpam-5388	272	6	✓	✓	ADJ
ejpam-5388	272	7	λb(3	λb(3	NOUN
ejpam-5388	272	8	,	,	PUNCT
ejpam-5388	272	9	4	4	NUM
ejpam-5388	272	10	)	)	PUNCT
ejpam-5388	272	11	1	1	NUM
ejpam-5388	273	1	≈	≈	PROPN
ejpam-5388	273	2	11012.73	11012.73	NUM
ejpam-5388	273	3	1	1	NUM
ejpam-5388	273	4	<	<	X
ejpam-5388	273	5	11012.73	11012.73	NUM
ejpam-5388	273	6	✓	✓	ADJ
ejpam-5388	273	7	λ[b	λ[b	NUM
ejpam-5388	273	8	−	−	NOUN
ejpam-5388	273	9	c	c	NOUN
ejpam-5388	274	1	+	+	PROPN
ejpam-5388	274	2	d	d	X
ejpam-5388	274	3	]	]	X
ejpam-5388	274	4	a	a	PRON
ejpam-5388	274	5	a	a	PRON
ejpam-5388	274	6	=	=	SYM
ejpam-5388	274	7	λ[b	λ[b	NUM
ejpam-5388	274	8	−	−	NOUN
ejpam-5388	275	1	c	c	NOUN
ejpam-5388	276	1	+	+	PROPN
ejpam-5388	276	2	d	d	X
ejpam-5388	276	3	]	]	X
ejpam-5388	276	4	a	a	DET
ejpam-5388	276	5	≤	≤	NUM
ejpam-5388	276	6	λ[b	λ[b	NUM
ejpam-5388	276	7	−	−	NOUN
ejpam-5388	277	1	c	c	NOUN
ejpam-5388	278	1	+	+	PROPN
ejpam-5388	278	2	d	d	X
ejpam-5388	278	3	]	]	X
ejpam-5388	278	4	λb(1	λb(1	NOUN
ejpam-5388	278	5	,	,	PUNCT
ejpam-5388	278	6	1	1	X
ejpam-5388	278	7	)	)	PUNCT
ejpam-5388	278	8	λb(2	λb(2	NOUN
ejpam-5388	278	9	,	,	PUNCT
ejpam-5388	278	10	2)λb(3	2)λb(3	NUM
ejpam-5388	278	11	,	,	PUNCT
ejpam-5388	278	12	3	3	X
ejpam-5388	278	13	)	)	PUNCT
ejpam-5388	278	14	λb(4	λb(4	PROPN
ejpam-5388	278	15	,	,	PUNCT
ejpam-5388	278	16	4	4	X
ejpam-5388	278	17	)	)	PUNCT
ejpam-5388	278	18	figure	figure	NOUN
ejpam-5388	278	19	1	1	NUM
ejpam-5388	278	20	.	.	PUNCT
ejpam-5388	279	1	satisfing	satisfe	VERB
ejpam-5388	279	2	the	the	DET
ejpam-5388	279	3	enquality	enquality	NOUN
ejpam-5388	279	4	a	a	DET
ejpam-5388	279	5	≤	≤	NUM
ejpam-5388	279	6	λ[b	λ[b	NUM
ejpam-5388	279	7	−	−	NOUN
ejpam-5388	279	8	c	c	NOUN
ejpam-5388	280	1	+	+	PROPN
ejpam-5388	280	2	d	d	X
ejpam-5388	280	3	]	]	X
ejpam-5388	280	4	thus	thus	ADV
ejpam-5388	280	5	,	,	PUNCT
ejpam-5388	280	6	all	all	DET
ejpam-5388	280	7	the	the	DET
ejpam-5388	280	8	conditions	condition	NOUN
ejpam-5388	280	9	of	of	ADP
ejpam-5388	280	10	theorem	theorem	ADJ
ejpam-5388	280	11	2.1	2.1	NUM
ejpam-5388	280	12	are	be	AUX
ejpam-5388	280	13	satisfied	satisfied	ADJ
ejpam-5388	280	14	and	and	CCONJ
ejpam-5388	280	15	hence	hence	ADV
ejpam-5388	280	16	p	p	NOUN
ejpam-5388	280	17	and	and	CCONJ
ejpam-5388	280	18	q	q	AUX
ejpam-5388	280	19	have	have	VERB
ejpam-5388	280	20	a	a	DET
ejpam-5388	280	21	common	common	ADJ
ejpam-5388	280	22	fixed	fix	VERB
ejpam-5388	280	23	point	point	NOUN
ejpam-5388	280	24	.	.	PUNCT
ejpam-5388	281	1	indeed	indeed	ADV
ejpam-5388	281	2	,	,	PUNCT
ejpam-5388	281	3	1	1	NUM
ejpam-5388	281	4	is	be	AUX
ejpam-5388	281	5	a	a	DET
ejpam-5388	281	6	common	common	ADJ
ejpam-5388	281	7	fixed	fix	VERB
ejpam-5388	281	8	point	point	NOUN
ejpam-5388	281	9	of	of	ADP
ejpam-5388	281	10	p	p	NOUN
ejpam-5388	281	11	and	and	CCONJ
ejpam-5388	281	12	q.	q.	PROPN
ejpam-5388	281	13	3	3	NUM
ejpam-5388	281	14	.	.	PUNCT
ejpam-5388	281	15	application	application	NOUN
ejpam-5388	281	16	fixed	fix	VERB
ejpam-5388	281	17	point	point	NOUN
ejpam-5388	281	18	theorem	theorem	NOUN
ejpam-5388	281	19	has	have	VERB
ejpam-5388	281	20	numerous	numerous	ADJ
ejpam-5388	281	21	applications	application	NOUN
ejpam-5388	281	22	,	,	PUNCT
ejpam-5388	281	23	such	such	ADJ
ejpam-5388	281	24	as	as	ADP
ejpam-5388	281	25	fractional	fractional	ADJ
ejpam-5388	281	26	differential	differential	ADJ
ejpam-5388	281	27	equations	equation	NOUN
ejpam-5388	281	28	(	(	PUNCT
ejpam-5388	281	29	[	[	X
ejpam-5388	281	30	1	1	NUM
ejpam-5388	281	31	]	]	PUNCT
ejpam-5388	281	32	,	,	PUNCT
ejpam-5388	281	33	[	[	X
ejpam-5388	281	34	2	2	NUM
ejpam-5388	281	35	]	]	PUNCT
ejpam-5388	281	36	,	,	PUNCT
ejpam-5388	281	37	[	[	X
ejpam-5388	281	38	13	13	NUM
ejpam-5388	281	39	]	]	NUM
ejpam-5388	281	40	)	)	PUNCT
ejpam-5388	281	41	,	,	PUNCT
ejpam-5388	281	42	the	the	DET
ejpam-5388	281	43	significance	significance	NOUN
ejpam-5388	281	44	of	of	ADP
ejpam-5388	281	45	these	these	DET
ejpam-5388	281	46	types	type	NOUN
ejpam-5388	281	47	of	of	ADP
ejpam-5388	281	48	equations	equation	NOUN
ejpam-5388	281	49	is	be	AUX
ejpam-5388	281	50	their	their	PRON
ejpam-5388	281	51	utilization	utilization	NOUN
ejpam-5388	281	52	in	in	ADP
ejpam-5388	281	53	modeling	modeling	NOUN
ejpam-5388	281	54	in	in	ADP
ejpam-5388	281	55	many	many	ADJ
ejpam-5388	281	56	subjects	subject	NOUN
ejpam-5388	281	57	.	.	PUNCT
ejpam-5388	282	1	in	in	ADP
ejpam-5388	282	2	this	this	DET
ejpam-5388	282	3	section	section	NOUN
ejpam-5388	282	4	,	,	PUNCT
ejpam-5388	282	5	we	we	PRON
ejpam-5388	282	6	utilize	utilize	VERB
ejpam-5388	282	7	our	our	PRON
ejpam-5388	282	8	results	result	NOUN
ejpam-5388	282	9	to	to	PART
ejpam-5388	282	10	demonstrate	demonstrate	VERB
ejpam-5388	282	11	the	the	DET
ejpam-5388	282	12	existence	existence	NOUN
ejpam-5388	282	13	and	and	CCONJ
ejpam-5388	282	14	uniqueness	uniqueness	NOUN
ejpam-5388	282	15	of	of	ADP
ejpam-5388	282	16	the	the	DET
ejpam-5388	282	17	fredholm	fredholm	NOUN
ejpam-5388	282	18	type	type	NOUN
ejpam-5388	282	19	integral	integral	ADJ
ejpam-5388	282	20	equation	equation	NOUN
ejpam-5388	282	21	.	.	PUNCT
ejpam-5388	283	1	now	now	ADV
ejpam-5388	283	2	,	,	PUNCT
ejpam-5388	283	3	consider	consider	VERB
ejpam-5388	283	4	the	the	DET
ejpam-5388	283	5	set	set	NOUN
ejpam-5388	283	6	𭟋	𭟋	PROPN
ejpam-5388	283	7	=	=	SYM
ejpam-5388	283	8	c([0	c([0	PROPN
ejpam-5388	283	9	,	,	PUNCT
ejpam-5388	283	10	1	1	NUM
ejpam-5388	283	11	]	]	PUNCT
ejpam-5388	283	12	,	,	PUNCT
ejpam-5388	283	13	(	(	PUNCT
ejpam-5388	283	14	−∞,∞	−∞,∞	NOUN
ejpam-5388	283	15	)	)	PUNCT
ejpam-5388	283	16	)	)	PUNCT
ejpam-5388	283	17	and	and	CCONJ
ejpam-5388	283	18	the	the	DET
ejpam-5388	283	19	following	follow	VERB
ejpam-5388	283	20	fredholm	fredholm	NOUN
ejpam-5388	283	21	type	type	NOUN
ejpam-5388	283	22	integral	integral	ADJ
ejpam-5388	283	23	equation	equation	NOUN
ejpam-5388	283	24	:	:	PUNCT
ejpam-5388	283	25	ṕ(t	ṕ(t	PROPN
ejpam-5388	283	26	)	)	PUNCT
ejpam-5388	284	1	=	=	SYM
ejpam-5388	284	2	∫	∫	PROPN
ejpam-5388	284	3	1	1	NUM
ejpam-5388	284	4	0	0	NUM
ejpam-5388	284	5	s(t	s(t	PROPN
ejpam-5388	284	6	,	,	PUNCT
ejpam-5388	284	7	s	s	PRON
ejpam-5388	284	8	,	,	PUNCT
ejpam-5388	284	9	ṕ(t	ṕ(t	PROPN
ejpam-5388	284	10	)	)	PUNCT
ejpam-5388	284	11	)	)	PUNCT
ejpam-5388	284	12	ds	ds	PROPN
ejpam-5388	284	13	,	,	PUNCT
ejpam-5388	284	14	for	for	ADP
ejpam-5388	284	15	t	t	PROPN
ejpam-5388	284	16	,	,	PUNCT
ejpam-5388	284	17	s	s	PART
ejpam-5388	284	18	∈	∈	PROPN
ejpam-5388	285	1	[	[	X
ejpam-5388	285	2	0	0	NUM
ejpam-5388	285	3	,	,	PUNCT
ejpam-5388	285	4	1	1	NUM
ejpam-5388	285	5	]	]	PUNCT
ejpam-5388	285	6	,	,	PUNCT
ejpam-5388	285	7	(	(	PUNCT
ejpam-5388	285	8	3.1	3.1	NUM
ejpam-5388	285	9	)	)	PUNCT
ejpam-5388	285	10	where	where	SCONJ
ejpam-5388	285	11	s(t	s(t	PROPN
ejpam-5388	285	12	,	,	PUNCT
ejpam-5388	285	13	s	s	PART
ejpam-5388	285	14	,	,	PUNCT
ejpam-5388	285	15	ṕ(t	ṕ(t	PROPN
ejpam-5388	285	16	)	)	PUNCT
ejpam-5388	285	17	)	)	PUNCT
ejpam-5388	285	18	is	be	AUX
ejpam-5388	285	19	a	a	DET
ejpam-5388	285	20	continuous	continuous	ADJ
ejpam-5388	285	21	function	function	NOUN
ejpam-5388	285	22	on	on	ADP
ejpam-5388	285	23	[	[	X
ejpam-5388	285	24	0	0	NUM
ejpam-5388	285	25	,	,	PUNCT
ejpam-5388	285	26	1]×	1]×	NUM
ejpam-5388	285	27	[	[	X
ejpam-5388	285	28	0	0	NUM
ejpam-5388	285	29	,	,	PUNCT
ejpam-5388	285	30	1	1	NUM
ejpam-5388	285	31	]	]	PUNCT
ejpam-5388	285	32	→	→	PUNCT
ejpam-5388	285	33	(	(	PUNCT
ejpam-5388	285	34	−∞,∞	−∞,∞	NOUN
ejpam-5388	285	35	)	)	PUNCT
ejpam-5388	285	36	.	.	PUNCT
ejpam-5388	286	1	now	now	ADV
ejpam-5388	286	2	,	,	PUNCT
ejpam-5388	286	3	define	define	VERB
ejpam-5388	286	4	λb	λb	ADP
ejpam-5388	286	5	:	:	PUNCT
ejpam-5388	286	6	𭟋×𭟋	𭟋×𭟋	PROPN
ejpam-5388	286	7	→	→	SYM
ejpam-5388	286	8	c	c	PROPN
ejpam-5388	286	9	and	and	CCONJ
ejpam-5388	286	10	(	(	PUNCT
ejpam-5388	286	11	p	p	X
ejpam-5388	286	12	,	,	PUNCT
ejpam-5388	286	13	q	q	NOUN
ejpam-5388	286	14	)	)	PUNCT
ejpam-5388	286	15	7→|	7→|	NUM
ejpam-5388	286	16	ṕ(t)−	ṕ(t)−	PROPN
ejpam-5388	286	17	q(t	q(t	PROPN
ejpam-5388	286	18	)	)	PUNCT
ejpam-5388	286	19	|	|	ADV
ejpam-5388	286	20	.	.	PUNCT
ejpam-5388	287	1	note	note	VERB
ejpam-5388	287	2	that	that	SCONJ
ejpam-5388	287	3	(	(	PUNCT
ejpam-5388	287	4	𭟋	𭟋	NOUN
ejpam-5388	287	5	,	,	PUNCT
ejpam-5388	287	6	λb	λb	NOUN
ejpam-5388	287	7	)	)	PUNCT
ejpam-5388	287	8	is	be	AUX
ejpam-5388	287	9	a	a	DET
ejpam-5388	287	10	complete	complete	ADJ
ejpam-5388	287	11	b	b	NOUN
ejpam-5388	287	12	-	-	PUNCT
ejpam-5388	287	13	metric	metric	ADJ
ejpam-5388	287	14	space	space	NOUN
ejpam-5388	287	15	,	,	PUNCT
ejpam-5388	287	16	where	where	SCONJ
ejpam-5388	287	17	the	the	DET
ejpam-5388	287	18	parameter	parameter	NOUN
ejpam-5388	287	19	s	s	PART
ejpam-5388	287	20	=	=	SYM
ejpam-5388	287	21	2	2	X
ejpam-5388	287	22	.	.	PUNCT
ejpam-5388	287	23	theorem	theorem	NOUN
ejpam-5388	287	24	3.1	3.1	NUM
ejpam-5388	287	25	.	.	PUNCT
ejpam-5388	287	26	suppose	suppose	VERB
ejpam-5388	288	1	that	that	SCONJ
ejpam-5388	288	2	for	for	ADP
ejpam-5388	288	3	all	all	DET
ejpam-5388	288	4	p	p	NOUN
ejpam-5388	288	5	,	,	PUNCT
ejpam-5388	288	6	q	q	NOUN
ejpam-5388	288	7	∈	∈	PROPN
ejpam-5388	288	8	𭟋	𭟋	X
ejpam-5388	288	9	(	(	PUNCT
ejpam-5388	288	10	1	1	NUM
ejpam-5388	288	11	)	)	PUNCT
ejpam-5388	288	12	|	|	ADV
ejpam-5388	288	13	s(t	s(t	PROPN
ejpam-5388	288	14	,	,	PUNCT
ejpam-5388	288	15	s	s	PROPN
ejpam-5388	288	16	,	,	PUNCT
ejpam-5388	288	17	ṕ(t))−	ṕ(t))−	PROPN
ejpam-5388	288	18	s(t	s(t	PROPN
ejpam-5388	288	19	,	,	PUNCT
ejpam-5388	288	20	s	s	NOUN
ejpam-5388	288	21	,	,	PUNCT
ejpam-5388	288	22	q(t	q(t	ADJ
ejpam-5388	288	23	)	)	PUNCT
ejpam-5388	288	24	)	)	PUNCT
ejpam-5388	288	25	|≤	|≤	PROPN
ejpam-5388	288	26	|ṕ(t)−q(t)|	|ṕ(t)−q(t)|	PROPN
ejpam-5388	288	27	2	2	NUM
ejpam-5388	288	28	.	.	PUNCT
ejpam-5388	288	29	references	reference	NOUN
ejpam-5388	288	30	2502	2502	NUM
ejpam-5388	288	31	(	(	PUNCT
ejpam-5388	288	32	2	2	NUM
ejpam-5388	288	33	)	)	PUNCT
ejpam-5388	288	34	|	|	ADV
ejpam-5388	288	35	s(t	s(t	PROPN
ejpam-5388	288	36	,	,	PUNCT
ejpam-5388	288	37	s	s	PROPN
ejpam-5388	288	38	,	,	PUNCT
ejpam-5388	288	39	∫	∫	PROPN
ejpam-5388	288	40	1	1	NUM
ejpam-5388	288	41	0	0	NUM
ejpam-5388	288	42	s(t	s(t	PROPN
ejpam-5388	288	43	,	,	PUNCT
ejpam-5388	288	44	s	s	PRON
ejpam-5388	288	45	,	,	PUNCT
ejpam-5388	288	46	ṕ(t	ṕ(t	PROPN
ejpam-5388	288	47	)	)	PUNCT
ejpam-5388	288	48	)	)	PUNCT
ejpam-5388	288	49	ds	ds	ADJ
ejpam-5388	288	50	)	)	PUNCT
ejpam-5388	288	51	−	−	NOUN
ejpam-5388	288	52	s(t	s(t	PROPN
ejpam-5388	288	53	,	,	PUNCT
ejpam-5388	288	54	s	s	AUX
ejpam-5388	288	55	,	,	PUNCT
ejpam-5388	288	56	q	q	PROPN
ejpam-5388	288	57	∫	∫	PROPN
ejpam-5388	288	58	1	1	NUM
ejpam-5388	288	59	0	0	NUM
ejpam-5388	288	60	s(t	s(t	PROPN
ejpam-5388	288	61	,	,	PUNCT
ejpam-5388	288	62	s	s	NOUN
ejpam-5388	288	63	,	,	PUNCT
ejpam-5388	288	64	q(t	q(t	ADJ
ejpam-5388	288	65	)	)	PUNCT
ejpam-5388	288	66	)	)	PUNCT
ejpam-5388	288	67	ds	ds	ADJ
ejpam-5388	288	68	)	)	PUNCT
ejpam-5388	288	69	|≤|	|≤|	NOUN
ejpam-5388	288	70	s(t	s(t	PROPN
ejpam-5388	288	71	,	,	PUNCT
ejpam-5388	288	72	s	s	PART
ejpam-5388	288	73	,	,	PUNCT
ejpam-5388	288	74	ṕ(t	ṕ(t	PROPN
ejpam-5388	288	75	)	)	PUNCT
ejpam-5388	288	76	)	)	PUNCT
ejpam-5388	289	1	−	−	PROPN
ejpam-5388	289	2	s(t	s(t	PROPN
ejpam-5388	289	3	,	,	PUNCT
ejpam-5388	289	4	s	s	NOUN
ejpam-5388	289	5	,	,	PUNCT
ejpam-5388	289	6	q(t	q(t	ADJ
ejpam-5388	289	7	)	)	PUNCT
ejpam-5388	289	8	)	)	PUNCT
ejpam-5388	290	1	|	|	ADV
ejpam-5388	290	2	for	for	ADP
ejpam-5388	290	3	all	all	DET
ejpam-5388	290	4	t	t	PROPN
ejpam-5388	290	5	,	,	PUNCT
ejpam-5388	290	6	s.	s.	PROPN
ejpam-5388	290	7	then	then	ADV
ejpam-5388	290	8	the	the	DET
ejpam-5388	290	9	integral	integral	ADJ
ejpam-5388	290	10	equation	equation	NOUN
ejpam-5388	290	11	3.1	3.1	NUM
ejpam-5388	290	12	has	have	VERB
ejpam-5388	290	13	a	a	DET
ejpam-5388	290	14	unique	unique	ADJ
ejpam-5388	290	15	solution	solution	NOUN
ejpam-5388	290	16	.	.	PUNCT
ejpam-5388	291	1	proof	proof	NOUN
ejpam-5388	291	2	.	.	PUNCT
ejpam-5388	292	1	let	let	VERB
ejpam-5388	292	2	ṕ(t	ṕ(t	ADV
ejpam-5388	292	3	)	)	PUNCT
ejpam-5388	292	4	:	:	PUNCT
ejpam-5388	293	1	𭟋	𭟋	X
ejpam-5388	293	2	→	→	SYM
ejpam-5388	293	3	𭟋	𭟋	PRON
ejpam-5388	293	4	defined	define	VERB
ejpam-5388	293	5	by	by	ADP
ejpam-5388	293	6	ṕ(t	ṕ(t	NOUN
ejpam-5388	293	7	)	)	PUNCT
ejpam-5388	293	8	=	=	SYM
ejpam-5388	294	1	∫	∫	PROPN
ejpam-5388	294	2	1	1	NUM
ejpam-5388	294	3	0	0	NUM
ejpam-5388	294	4	s(t	s(t	PROPN
ejpam-5388	294	5	,	,	PUNCT
ejpam-5388	294	6	s	s	PRON
ejpam-5388	294	7	,	,	PUNCT
ejpam-5388	294	8	ṕ(t	ṕ(t	PROPN
ejpam-5388	294	9	)	)	PUNCT
ejpam-5388	294	10	)	)	PUNCT
ejpam-5388	294	11	ds	ds	PROPN
ejpam-5388	294	12	,	,	PUNCT
ejpam-5388	294	13	then	then	ADV
ejpam-5388	294	14	λb(ṕ	λb(ṕ	PROPN
ejpam-5388	294	15	,	,	PUNCT
ejpam-5388	294	16	q	q	X
ejpam-5388	294	17	)	)	PUNCT
ejpam-5388	294	18	=|	=|	X
ejpam-5388	294	19	ṕ(t)−	ṕ(t)−	PROPN
ejpam-5388	294	20	q(t	q(t	PROPN
ejpam-5388	294	21	)	)	PUNCT
ejpam-5388	294	22	|	|	ADV
ejpam-5388	294	23	.	.	PUNCT
ejpam-5388	295	1	now	now	ADV
ejpam-5388	295	2	we	we	PRON
ejpam-5388	295	3	have	have	VERB
ejpam-5388	295	4	λb(ṕ(t	λb(ṕ(t	NUM
ejpam-5388	295	5	)	)	PUNCT
ejpam-5388	295	6	,	,	PUNCT
ejpam-5388	295	7	q(t	q(t	NOUN
ejpam-5388	295	8	)	)	PUNCT
ejpam-5388	295	9	)	)	PUNCT
ejpam-5388	296	1	=	=	PUNCT
ejpam-5388	297	1	|	|	ADV
ejpam-5388	297	2	ṕ(t)−	ṕ(t)−	PROPN
ejpam-5388	297	3	q(t	q(t	PROPN
ejpam-5388	297	4	)	)	PUNCT
ejpam-5388	297	5	|	|	NOUN
ejpam-5388	297	6	=	=	SYM
ejpam-5388	297	7	|	|	ADV
ejpam-5388	297	8	s(t	s(t	PROPN
ejpam-5388	297	9	,	,	PUNCT
ejpam-5388	297	10	s	s	PROPN
ejpam-5388	297	11	,	,	PUNCT
ejpam-5388	297	12	∫	∫	PROPN
ejpam-5388	297	13	1	1	NUM
ejpam-5388	297	14	0	0	NUM
ejpam-5388	297	15	s(t	s(t	PROPN
ejpam-5388	297	16	,	,	PUNCT
ejpam-5388	297	17	s	s	PRON
ejpam-5388	297	18	,	,	PUNCT
ejpam-5388	297	19	ṕ(t	ṕ(t	PROPN
ejpam-5388	297	20	)	)	PUNCT
ejpam-5388	297	21	)	)	PUNCT
ejpam-5388	297	22	ds)−	ds)−	PROPN
ejpam-5388	298	1	s(t	s(t	PROPN
ejpam-5388	298	2	,	,	PUNCT
ejpam-5388	298	3	s	s	AUX
ejpam-5388	298	4	,	,	PUNCT
ejpam-5388	298	5	q	q	PROPN
ejpam-5388	298	6	∫	∫	PROPN
ejpam-5388	298	7	1	1	NUM
ejpam-5388	298	8	0	0	NUM
ejpam-5388	298	9	s(t	s(t	PROPN
ejpam-5388	298	10	,	,	PUNCT
ejpam-5388	298	11	s	s	NOUN
ejpam-5388	298	12	,	,	PUNCT
ejpam-5388	298	13	q(t	q(t	ADJ
ejpam-5388	298	14	)	)	PUNCT
ejpam-5388	298	15	)	)	PUNCT
ejpam-5388	298	16	ds	ds	ADJ
ejpam-5388	298	17	)	)	PUNCT
ejpam-5388	298	18	|	|	ADV
ejpam-5388	298	19	≤	≤	PUNCT
ejpam-5388	298	20	|	|	ADV
ejpam-5388	298	21	s(t	s(t	PROPN
ejpam-5388	298	22	,	,	PUNCT
ejpam-5388	298	23	s	s	PROPN
ejpam-5388	298	24	,	,	PUNCT
ejpam-5388	298	25	ṕ(t))−	ṕ(t))−	PROPN
ejpam-5388	298	26	s(t	s(t	PROPN
ejpam-5388	298	27	,	,	PUNCT
ejpam-5388	298	28	s	s	NOUN
ejpam-5388	298	29	,	,	PUNCT
ejpam-5388	298	30	q(t	q(t	ADJ
ejpam-5388	298	31	)	)	PUNCT
ejpam-5388	298	32	)	)	PUNCT
ejpam-5388	299	1	|	|	ADV
ejpam-5388	299	2	≤	≤	PUNCT
ejpam-5388	299	3	|	|	ADV
ejpam-5388	299	4	ṕ(t)−	ṕ(t)−	PROPN
ejpam-5388	299	5	q(t	q(t	PROPN
ejpam-5388	299	6	)	)	PUNCT
ejpam-5388	299	7	|	|	ADV
ejpam-5388	299	8	2	2	NUM
ejpam-5388	299	9	≤	≤	NUM
ejpam-5388	299	10	1	1	NUM
ejpam-5388	299	11	2	2	NUM
ejpam-5388	299	12	λb(ṕ(t	λb(ṕ(t	NUM
ejpam-5388	299	13	)	)	PUNCT
ejpam-5388	299	14	,	,	PUNCT
ejpam-5388	299	15	q(t	q(t	NOUN
ejpam-5388	299	16	)	)	PUNCT
ejpam-5388	299	17	)	)	PUNCT
ejpam-5388	300	1	=	=	PUNCT
ejpam-5388	300	2	λ	λ	X
ejpam-5388	301	1	[	[	X
ejpam-5388	301	2	φ	φ	X
ejpam-5388	301	3	(	(	PUNCT
ejpam-5388	301	4	mλb	mλb	PROPN
ejpam-5388	301	5	(	(	PUNCT
ejpam-5388	301	6	ṕ(t	ṕ(t	PROPN
ejpam-5388	301	7	)	)	PUNCT
ejpam-5388	301	8	,	,	PUNCT
ejpam-5388	301	9	q(t)))−	q(t)))−	PROPN
ejpam-5388	301	10	ϕ	ϕ	X
ejpam-5388	301	11	(	(	PUNCT
ejpam-5388	301	12	mλb	mλb	PROPN
ejpam-5388	301	13	(	(	PUNCT
ejpam-5388	301	14	ṕ(t	ṕ(t	PROPN
ejpam-5388	301	15	)	)	PUNCT
ejpam-5388	301	16	,	,	PUNCT
ejpam-5388	301	17	q(t	q(t	NOUN
ejpam-5388	301	18	)	)	PUNCT
ejpam-5388	301	19	)	)	PUNCT
ejpam-5388	301	20	)	)	PUNCT
ejpam-5388	301	21	]	]	PUNCT
ejpam-5388	301	22	,	,	PUNCT
ejpam-5388	301	23	where	where	SCONJ
ejpam-5388	301	24	φ(t	φ(t	VERB
ejpam-5388	301	25	)	)	PUNCT
ejpam-5388	301	26	=	=	SYM
ejpam-5388	301	27	t	t	PROPN
ejpam-5388	301	28	and	and	CCONJ
ejpam-5388	301	29	ϕ(t	ϕ(t	NUM
ejpam-5388	301	30	)	)	PUNCT
ejpam-5388	302	1	=	=	SYM
ejpam-5388	302	2	t	t	PROPN
ejpam-5388	302	3	2	2	NUM
ejpam-5388	302	4	.	.	PUNCT
ejpam-5388	303	1	also	also	ADV
ejpam-5388	303	2	the	the	DET
ejpam-5388	303	3	parameter	parameter	NOUN
ejpam-5388	303	4	s	s	PART
ejpam-5388	303	5	<	<	X
ejpam-5388	303	6	3	3	NUM
ejpam-5388	303	7	.	.	PUNCT
ejpam-5388	304	1	hence	hence	ADV
ejpam-5388	304	2	,	,	PUNCT
ejpam-5388	304	3	all	all	DET
ejpam-5388	304	4	the	the	DET
ejpam-5388	304	5	hypotheses	hypothesis	NOUN
ejpam-5388	304	6	of	of	ADP
ejpam-5388	304	7	theorem	theorem	NOUN
ejpam-5388	304	8	2.2	2.2	NUM
ejpam-5388	304	9	,	,	PUNCT
ejpam-5388	304	10	are	be	AUX
ejpam-5388	304	11	fulfilled	fulfil	VERB
ejpam-5388	304	12	and	and	CCONJ
ejpam-5388	304	13	then	then	ADV
ejpam-5388	304	14	the	the	DET
ejpam-5388	304	15	equation	equation	NOUN
ejpam-5388	304	16	3.1	3.1	NUM
ejpam-5388	304	17	has	have	VERB
ejpam-5388	304	18	a	a	DET
ejpam-5388	304	19	unique	unique	ADJ
ejpam-5388	304	20	solution	solution	NOUN
ejpam-5388	304	21	.	.	PUNCT
ejpam-5388	305	1	4	4	X
ejpam-5388	305	2	.	.	X
ejpam-5388	305	3	conclusion	conclusion	NOUN
ejpam-5388	305	4	we	we	PRON
ejpam-5388	305	5	have	have	AUX
ejpam-5388	305	6	demonstrated	demonstrate	VERB
ejpam-5388	305	7	the	the	DET
ejpam-5388	305	8	existence	existence	NOUN
ejpam-5388	305	9	and	and	CCONJ
ejpam-5388	305	10	uniqueness	uniqueness	NOUN
ejpam-5388	305	11	of	of	ADP
ejpam-5388	305	12	a	a	DET
ejpam-5388	305	13	fixed	fix	VERB
ejpam-5388	305	14	point	point	NOUN
ejpam-5388	305	15	for	for	ADP
ejpam-5388	305	16	self	self	NOUN
ejpam-5388	305	17	-	-	PUNCT
ejpam-5388	305	18	mapping	mapping	NOUN
ejpam-5388	305	19	in	in	ADP
ejpam-5388	305	20	bmetric	bmetric	ADJ
ejpam-5388	305	21	spaces	space	NOUN
ejpam-5388	305	22	under	under	ADP
ejpam-5388	305	23	diverse	diverse	ADJ
ejpam-5388	305	24	nonlinear	nonlinear	ADJ
ejpam-5388	305	25	mappings	mapping	NOUN
ejpam-5388	305	26	with	with	ADP
ejpam-5388	305	27	continuous	continuous	ADJ
ejpam-5388	305	28	control	control	NOUN
ejpam-5388	305	29	functions	function	NOUN
ejpam-5388	305	30	.	.	PUNCT
ejpam-5388	306	1	also	also	ADV
ejpam-5388	306	2	,	,	PUNCT
ejpam-5388	306	3	we	we	PRON
ejpam-5388	306	4	show	show	VERB
ejpam-5388	306	5	an	an	DET
ejpam-5388	306	6	application	application	NOUN
ejpam-5388	306	7	of	of	ADP
ejpam-5388	306	8	our	our	PRON
ejpam-5388	306	9	results	result	NOUN
ejpam-5388	306	10	to	to	ADP
ejpam-5388	306	11	fredholm	fredholm	NOUN
ejpam-5388	306	12	-	-	PUNCT
ejpam-5388	306	13	type	type	NOUN
ejpam-5388	306	14	integral	integral	ADJ
ejpam-5388	306	15	equations	equation	NOUN
ejpam-5388	306	16	.	.	PUNCT
ejpam-5388	307	1	additionally	additionally	ADV
ejpam-5388	307	2	,	,	PUNCT
ejpam-5388	307	3	we	we	PRON
ejpam-5388	307	4	would	would	AUX
ejpam-5388	307	5	like	like	VERB
ejpam-5388	307	6	to	to	PART
ejpam-5388	307	7	bring	bring	VERB
ejpam-5388	307	8	the	the	DET
ejpam-5388	307	9	researchers	researcher	NOUN
ejpam-5388	307	10	consideration	consideration	NOUN
ejpam-5388	307	11	to	to	ADP
ejpam-5388	307	12	the	the	DET
ejpam-5388	307	13	following	following	ADJ
ejpam-5388	307	14	question	question	NOUN
ejpam-5388	307	15	.	.	PUNCT
ejpam-5388	308	1	4.1	4.1	NUM
ejpam-5388	308	2	.	.	PUNCT
ejpam-5388	308	3	question	question	NOUN
ejpam-5388	308	4	under	under	ADP
ejpam-5388	308	5	what	what	DET
ejpam-5388	308	6	conditions	condition	NOUN
ejpam-5388	308	7	we	we	PRON
ejpam-5388	308	8	will	will	AUX
ejpam-5388	308	9	get	get	VERB
ejpam-5388	308	10	the	the	DET
ejpam-5388	308	11	same	same	ADJ
ejpam-5388	308	12	results	result	NOUN
ejpam-5388	308	13	for	for	ADP
ejpam-5388	308	14	self	self	NOUN
ejpam-5388	308	15	-	-	PUNCT
ejpam-5388	308	16	mapping	mapping	NOUN
ejpam-5388	308	17	in	in	ADP
ejpam-5388	308	18	partial	partial	ADJ
ejpam-5388	308	19	b	b	NOUN
ejpam-5388	308	20	-	-	PUNCT
ejpam-5388	308	21	metric	metric	ADJ
ejpam-5388	308	22	spaces	space	NOUN
ejpam-5388	308	23	?	?	PUNCT
ejpam-5388	309	1	acknowledgements	acknowledgement	NOUN
ejpam-5388	309	2	we	we	PRON
ejpam-5388	309	3	extend	extend	VERB
ejpam-5388	309	4	their	their	PRON
ejpam-5388	309	5	appreciation	appreciation	NOUN
ejpam-5388	309	6	to	to	ADP
ejpam-5388	309	7	the	the	DET
ejpam-5388	309	8	deanship	deanship	NOUN
ejpam-5388	309	9	of	of	ADP
ejpam-5388	309	10	post	post	NOUN
ejpam-5388	309	11	graduate	graduate	ADJ
ejpam-5388	309	12	and	and	CCONJ
ejpam-5388	309	13	scientific	scientific	ADJ
ejpam-5388	309	14	research	research	NOUN
ejpam-5388	309	15	at	at	ADP
ejpam-5388	309	16	dar	dar	PROPN
ejpam-5388	309	17	al	al	PROPN
ejpam-5388	309	18	uloom	uloom	PROPN
ejpam-5388	309	19	university	university	PROPN
ejpam-5388	309	20	for	for	ADP
ejpam-5388	309	21	funding	fund	VERB
ejpam-5388	309	22	this	this	DET
ejpam-5388	309	23	work	work	NOUN
ejpam-5388	309	24	.	.	PUNCT
ejpam-5388	310	1	references	reference	NOUN
ejpam-5388	310	2	[	[	X
ejpam-5388	310	3	1	1	X
ejpam-5388	310	4	]	]	X
ejpam-5388	310	5	i	i	PRON
ejpam-5388	310	6	m	m	AUX
ejpam-5388	310	7	batiha	batiha	VERB
ejpam-5388	310	8	;	;	PUNCT
ejpam-5388	310	9	j	j	PROPN
ejpam-5388	310	10	oudetallah	oudetallah	PROPN
ejpam-5388	310	11	;	;	PUNCT
ejpam-5388	310	12	a	a	DET
ejpam-5388	310	13	ouannas	ouanna	NOUN
ejpam-5388	310	14	;	;	PUNCT
ejpam-5388	310	15	a	a	DET
ejpam-5388	310	16	a	a	DET
ejpam-5388	310	17	al	al	PROPN
ejpam-5388	310	18	-	-	PUNCT
ejpam-5388	310	19	nana	nana	PROPN
ejpam-5388	310	20	and	and	CCONJ
ejpam-5388	310	21	i	i	PRON
ejpam-5388	311	1	h	h	NOUN
ejpam-5388	311	2	jebril	jebril	VERB
ejpam-5388	311	3	.	.	PUNCT
ejpam-5388	312	1	tuning	tune	VERB
ejpam-5388	312	2	the	the	DET
ejpam-5388	312	3	fractionalorder	fractionalorder	ADJ
ejpam-5388	312	4	pid	pid	NOUN
ejpam-5388	312	5	-	-	NOUN
ejpam-5388	312	6	controller	controller	NOUN
ejpam-5388	312	7	for	for	ADP
ejpam-5388	312	8	blood	blood	NOUN
ejpam-5388	312	9	glucose	glucose	NOUN
ejpam-5388	312	10	level	level	NOUN
ejpam-5388	312	11	of	of	ADP
ejpam-5388	312	12	diabetic	diabetic	ADJ
ejpam-5388	312	13	patients	patient	NOUN
ejpam-5388	312	14	.	.	PUNCT
ejpam-5388	313	1	international	international	ADJ
ejpam-5388	313	2	journal	journal	NOUN
ejpam-5388	313	3	of	of	ADP
ejpam-5388	313	4	advances	advance	NOUN
ejpam-5388	313	5	in	in	ADP
ejpam-5388	313	6	soft	soft	ADJ
ejpam-5388	313	7	computing	computing	NOUN
ejpam-5388	313	8	and	and	CCONJ
ejpam-5388	313	9	its	its	PRON
ejpam-5388	313	10	applications	application	NOUN
ejpam-5388	313	11	,	,	PUNCT
ejpam-5388	313	12	13(2):1–10	13(2):1–10	NOUN
ejpam-5388	313	13	,	,	PUNCT
ejpam-5388	313	14	2021	2021	NUM
ejpam-5388	313	15	.	.	PUNCT
ejpam-5388	314	1	[	[	X
ejpam-5388	314	2	2	2	NUM
ejpam-5388	314	3	]	]	X
ejpam-5388	314	4	h	h	NOUN
ejpam-5388	314	5	qawaqneh	qawaqneh	NOUN
ejpam-5388	314	6	;	;	PUNCT
ejpam-5388	314	7	j	j	PROPN
ejpam-5388	314	8	manafian	manafian	NOUN
ejpam-5388	314	9	;	;	PUNCT
ejpam-5388	315	1	m	m	VERB
ejpam-5388	315	2	alharthi	alharthi	PROPN
ejpam-5388	315	3	and	and	CCONJ
ejpam-5388	315	4	y	y	PROPN
ejpam-5388	315	5	alrashed	alrashe	VERB
ejpam-5388	315	6	.	.	PUNCT
ejpam-5388	316	1	stability	stability	NOUN
ejpam-5388	316	2	analysis	analysis	NOUN
ejpam-5388	316	3	,	,	PUNCT
ejpam-5388	316	4	modulation	modulation	NOUN
ejpam-5388	316	5	instability	instability	NOUN
ejpam-5388	316	6	,	,	PUNCT
ejpam-5388	316	7	and	and	CCONJ
ejpam-5388	316	8	beta	beta	NOUN
ejpam-5388	316	9	-	-	PUNCT
ejpam-5388	316	10	time	time	NOUN
ejpam-5388	316	11	fractional	fractional	ADJ
ejpam-5388	316	12	exact	exact	ADJ
ejpam-5388	316	13	soliton	soliton	NOUN
ejpam-5388	316	14	solutions	solution	NOUN
ejpam-5388	316	15	to	to	ADP
ejpam-5388	316	16	the	the	DET
ejpam-5388	316	17	van	van	PROPN
ejpam-5388	316	18	der	der	NOUN
ejpam-5388	316	19	waals	waal	NOUN
ejpam-5388	316	20	equation	equation	NOUN
ejpam-5388	316	21	.	.	PUNCT
ejpam-5388	317	1	mathematics	mathematic	NOUN
ejpam-5388	317	2	,	,	PUNCT
ejpam-5388	317	3	12(14	12(14	NUM
ejpam-5388	317	4	:	:	PUNCT
ejpam-5388	317	5	2257	2257	NUM
ejpam-5388	317	6	)	)	PUNCT
ejpam-5388	317	7	,	,	PUNCT
ejpam-5388	317	8	2024	2024	NUM
ejpam-5388	317	9	.	.	PUNCT
ejpam-5388	318	1	[	[	X
ejpam-5388	318	2	3	3	X
ejpam-5388	318	3	]	]	X
ejpam-5388	318	4	h	h	NOUN
ejpam-5388	318	5	akhadkulov	akhadkulov	NOUN
ejpam-5388	318	6	;	;	PUNCT
ejpam-5388	319	1	m	m	PROPN
ejpam-5388	319	2	s	s	X
ejpam-5388	319	3	m	m	VERB
ejpam-5388	319	4	noorani	noorani	ADJ
ejpam-5388	319	5	;	;	PUNCT
ejpam-5388	319	6	a	a	DET
ejpam-5388	319	7	b	b	NOUN
ejpam-5388	319	8	saaban	saaban	NOUN
ejpam-5388	319	9	;	;	PUNCT
ejpam-5388	319	10	f	f	PROPN
ejpam-5388	319	11	m	m	VERB
ejpam-5388	319	12	alipiah	alipiah	NOUN
ejpam-5388	319	13	and	and	CCONJ
ejpam-5388	319	14	h	h	PROPN
ejpam-5388	319	15	alsamir	alsamir	PROPN
ejpam-5388	319	16	.	.	PUNCT
ejpam-5388	320	1	notes	note	NOUN
ejpam-5388	320	2	on	on	ADP
ejpam-5388	320	3	multidimensional	multidimensional	ADJ
ejpam-5388	320	4	fixed	fix	VERB
ejpam-5388	320	5	-	-	PUNCT
ejpam-5388	320	6	point	point	NOUN
ejpam-5388	320	7	theorems	theorem	NOUN
ejpam-5388	320	8	.	.	PROPN
ejpam-5388	320	9	demonstratio	demonstratio	PROPN
ejpam-5388	320	10	mathematica	mathematica	PROPN
ejpam-5388	320	11	,	,	PUNCT
ejpam-5388	320	12	50(1):360–374	50(1):360–374	NOUN
ejpam-5388	320	13	,	,	PUNCT
ejpam-5388	320	14	2017	2017	NUM
ejpam-5388	320	15	.	.	PUNCT
ejpam-5388	321	1	references	reference	NOUN
ejpam-5388	321	2	2503	2503	NUM
ejpam-5388	322	1	[	[	X
ejpam-5388	322	2	4	4	NUM
ejpam-5388	322	3	]	]	X
ejpam-5388	322	4	w	w	NOUN
ejpam-5388	322	5	shatanawi	shatanawi	ADJ
ejpam-5388	322	6	;	;	PUNCT
ejpam-5388	322	7	m	m	PROPN
ejpam-5388	322	8	s	s	VERB
ejpam-5388	322	9	m	m	VERB
ejpam-5388	322	10	noorani	noorani	ADJ
ejpam-5388	322	11	;	;	PUNCT
ejpam-5388	322	12	j	j	PROPN
ejpam-5388	322	13	ahmad	ahmad	PROPN
ejpam-5388	322	14	;	;	PUNCT
ejpam-5388	322	15	h	h	NOUN
ejpam-5388	322	16	alsamir	alsamir	NOUN
ejpam-5388	322	17	and	and	CCONJ
ejpam-5388	322	18	m	m	PROPN
ejpam-5388	322	19	kutbi	kutbi	NOUN
ejpam-5388	322	20	.	.	PUNCT
ejpam-5388	323	1	some	some	DET
ejpam-5388	323	2	common	common	ADJ
ejpam-5388	323	3	fixed	fix	VERB
ejpam-5388	323	4	points	point	NOUN
ejpam-5388	323	5	of	of	ADP
ejpam-5388	323	6	multivalued	multivalued	ADJ
ejpam-5388	323	7	mappings	mapping	NOUN
ejpam-5388	323	8	on	on	ADP
ejpam-5388	323	9	complex	complex	ADV
ejpam-5388	323	10	-	-	PUNCT
ejpam-5388	323	11	valued	value	VERB
ejpam-5388	323	12	metric	metric	ADJ
ejpam-5388	323	13	spaces	space	NOUN
ejpam-5388	323	14	with	with	ADP
ejpam-5388	323	15	homotopy	homotopy	NOUN
ejpam-5388	323	16	result	result	NOUN
ejpam-5388	323	17	.	.	PUNCT
ejpam-5388	324	1	j.	j.	PROPN
ejpam-5388	324	2	nonlinear	nonlinear	PROPN
ejpam-5388	324	3	sci	sci	PROPN
ejpam-5388	324	4	.	.	PUNCT
ejpam-5388	324	5	appl	appl	PROPN
ejpam-5388	324	6	.	.	PROPN
ejpam-5388	324	7	,	,	PUNCT
ejpam-5388	324	8	10:3381–796	10:3381–796	PROPN
ejpam-5388	324	9	,	,	PUNCT
ejpam-5388	324	10	2017	2017	NUM
ejpam-5388	324	11	.	.	PUNCT
ejpam-5388	325	1	[	[	X
ejpam-5388	325	2	5	5	NUM
ejpam-5388	325	3	]	]	X
ejpam-5388	325	4	h	h	NOUN
ejpam-5388	325	5	aydi	aydi	VERB
ejpam-5388	325	6	and	and	CCONJ
ejpam-5388	325	7	a	a	DET
ejpam-5388	325	8	felhi	felhi	NOUN
ejpam-5388	325	9	.	.	PUNCT
ejpam-5388	326	1	best	good	ADJ
ejpam-5388	326	2	proximity	proximity	NOUN
ejpam-5388	326	3	points	point	NOUN
ejpam-5388	326	4	for	for	ADP
ejpam-5388	326	5	cyclic	cyclic	PROPN
ejpam-5388	326	6	kannan	kannan	PROPN
ejpam-5388	326	7	-	-	PUNCT
ejpam-5388	326	8	chatterjeaciric	chatterjeaciric	PROPN
ejpam-5388	326	9	type	type	NOUN
ejpam-5388	326	10	contractions	contraction	NOUN
ejpam-5388	326	11	on	on	ADP
ejpam-5388	326	12	metric	metric	ADJ
ejpam-5388	326	13	-	-	PUNCT
ejpam-5388	326	14	like	like	ADJ
ejpam-5388	326	15	spaces	space	NOUN
ejpam-5388	326	16	.	.	PUNCT
ejpam-5388	327	1	j.	j.	PROPN
ejpam-5388	327	2	nonlinear	nonlinear	PROPN
ejpam-5388	327	3	sci	sci	PROPN
ejpam-5388	327	4	.	.	PUNCT
ejpam-5388	327	5	appl	appl	PROPN
ejpam-5388	327	6	.	.	PROPN
ejpam-5388	327	7	,	,	PUNCT
ejpam-5388	327	8	9:5202–5218	9:5202–5218	NUM
ejpam-5388	327	9	,	,	PUNCT
ejpam-5388	327	10	2016	2016	NUM
ejpam-5388	327	11	.	.	PUNCT
ejpam-5388	328	1	[	[	X
ejpam-5388	328	2	6	6	NUM
ejpam-5388	328	3	]	]	SYM
ejpam-5388	328	4	v	v	NOUN
ejpam-5388	328	5	berinde	berinde	NOUN
ejpam-5388	328	6	.	.	PUNCT
ejpam-5388	329	1	approximating	approximate	VERB
ejpam-5388	329	2	fixed	fix	VERB
ejpam-5388	329	3	points	point	NOUN
ejpam-5388	329	4	of	of	ADP
ejpam-5388	329	5	weak	weak	ADJ
ejpam-5388	329	6	contractions	contraction	NOUN
ejpam-5388	329	7	using	use	VERB
ejpam-5388	329	8	the	the	DET
ejpam-5388	329	9	picard	picard	NOUN
ejpam-5388	329	10	iteration	iteration	NOUN
ejpam-5388	329	11	.	.	PUNCT
ejpam-5388	330	1	carpathian	carpathian	ADJ
ejpam-5388	330	2	journal	journal	PROPN
ejpam-5388	330	3	of	of	ADP
ejpam-5388	330	4	mathematics	mathematic	NOUN
ejpam-5388	330	5	,	,	PUNCT
ejpam-5388	330	6	pages	page	NOUN
ejpam-5388	330	7	7–22	7–22	PROPN
ejpam-5388	330	8	,	,	PUNCT
ejpam-5388	330	9	2003	2003	NUM
ejpam-5388	330	10	.	.	PUNCT
ejpam-5388	331	1	[	[	X
ejpam-5388	331	2	7	7	NUM
ejpam-5388	331	3	]	]	SYM
ejpam-5388	331	4	v	v	NOUN
ejpam-5388	331	5	berinde	berinde	NOUN
ejpam-5388	331	6	.	.	PUNCT
ejpam-5388	332	1	approximating	approximate	VERB
ejpam-5388	332	2	fixed	fix	VERB
ejpam-5388	332	3	points	point	NOUN
ejpam-5388	332	4	of	of	ADP
ejpam-5388	332	5	weak	weak	ADJ
ejpam-5388	332	6	φ	φ	NOUN
ejpam-5388	332	7	-	-	PUNCT
ejpam-5388	332	8	contractions	contraction	NOUN
ejpam-5388	332	9	using	use	VERB
ejpam-5388	332	10	the	the	DET
ejpam-5388	332	11	picard	picard	NOUN
ejpam-5388	332	12	iteration	iteration	NOUN
ejpam-5388	332	13	.	.	PUNCT
ejpam-5388	333	1	fixed	fix	VERB
ejpam-5388	333	2	point	point	NOUN
ejpam-5388	333	3	theory	theory	NOUN
ejpam-5388	333	4	,	,	PUNCT
ejpam-5388	333	5	2(2):7–22	2(2):7–22	PROPN
ejpam-5388	333	6	,	,	PUNCT
ejpam-5388	333	7	2003	2003	NUM
ejpam-5388	333	8	.	.	PUNCT
ejpam-5388	334	1	[	[	X
ejpam-5388	334	2	8	8	NUM
ejpam-5388	334	3	]	]	SYM
ejpam-5388	334	4	v	v	NOUN
ejpam-5388	334	5	berinde	berinde	NOUN
ejpam-5388	334	6	.	.	PUNCT
ejpam-5388	335	1	approximating	approximate	VERB
ejpam-5388	335	2	fixed	fix	VERB
ejpam-5388	335	3	points	point	NOUN
ejpam-5388	335	4	of	of	ADP
ejpam-5388	335	5	weak	weak	ADJ
ejpam-5388	335	6	contractions	contraction	NOUN
ejpam-5388	335	7	using	use	VERB
ejpam-5388	335	8	the	the	DET
ejpam-5388	335	9	picard	picard	NOUN
ejpam-5388	335	10	iteration	iteration	NOUN
ejpam-5388	335	11	.	.	PUNCT
ejpam-5388	336	1	nonlinear	nonlinear	ADJ
ejpam-5388	336	2	anal	anal	PROPN
ejpam-5388	336	3	.	.	PUNCT
ejpam-5388	337	1	forum	forum	PROPN
ejpam-5388	337	2	,	,	PUNCT
ejpam-5388	337	3	9:43–53	9:43–53	NOUN
ejpam-5388	337	4	,	,	PUNCT
ejpam-5388	337	5	2004	2004	NUM
ejpam-5388	337	6	.	.	PUNCT
ejpam-5388	338	1	[	[	X
ejpam-5388	338	2	9	9	NUM
ejpam-5388	338	3	]	]	SYM
ejpam-5388	338	4	v	v	NOUN
ejpam-5388	338	5	berinde	berinde	NOUN
ejpam-5388	338	6	.	.	PUNCT
ejpam-5388	339	1	general	general	ADJ
ejpam-5388	339	2	constructive	constructive	ADJ
ejpam-5388	339	3	fixed	fix	VERB
ejpam-5388	339	4	point	point	NOUN
ejpam-5388	339	5	theorems	theorem	NOUN
ejpam-5388	339	6	for	for	ADP
ejpam-5388	339	7	c̀iric̀-type	c̀iric̀-type	NOUN
ejpam-5388	339	8	almost	almost	ADV
ejpam-5388	339	9	contractions	contraction	NOUN
ejpam-5388	339	10	in	in	ADP
ejpam-5388	339	11	metric	metric	ADJ
ejpam-5388	339	12	spaces	space	NOUN
ejpam-5388	339	13	.	.	PUNCT
ejpam-5388	340	1	carpathian	carpathian	ADJ
ejpam-5388	340	2	journal	journal	PROPN
ejpam-5388	340	3	of	of	ADP
ejpam-5388	340	4	mathematics	mathematic	NOUN
ejpam-5388	340	5	,	,	PUNCT
ejpam-5388	340	6	pages	page	NOUN
ejpam-5388	340	7	10–19	10–19	NUM
ejpam-5388	340	8	,	,	PUNCT
ejpam-5388	340	9	2008	2008	NUM
ejpam-5388	340	10	.	.	PUNCT
ejpam-5388	341	1	[	[	X
ejpam-5388	341	2	10	10	NUM
ejpam-5388	341	3	]	]	SYM
ejpam-5388	341	4	v	v	NOUN
ejpam-5388	341	5	berinde	berinde	NOUN
ejpam-5388	341	6	.	.	PUNCT
ejpam-5388	342	1	some	some	DET
ejpam-5388	342	2	remarks	remark	NOUN
ejpam-5388	342	3	on	on	ADP
ejpam-5388	342	4	a	a	DET
ejpam-5388	342	5	fixed	fix	VERB
ejpam-5388	342	6	point	point	NOUN
ejpam-5388	342	7	theorem	theorem	NOUN
ejpam-5388	342	8	for	for	ADP
ejpam-5388	342	9	c̀iric̀-type	c̀iric̀-type	NOUN
ejpam-5388	342	10	almost	almost	ADV
ejpam-5388	342	11	contractions	contraction	NOUN
ejpam-5388	342	12	.	.	PUNCT
ejpam-5388	343	1	carpathian	carpathian	ADJ
ejpam-5388	343	2	journal	journal	PROPN
ejpam-5388	343	3	of	of	ADP
ejpam-5388	343	4	mathematics	mathematic	NOUN
ejpam-5388	343	5	.	.	PUNCT
ejpam-5388	344	1	carpathian	carpathian	ADJ
ejpam-5388	344	2	journal	journal	PROPN
ejpam-5388	344	3	of	of	ADP
ejpam-5388	344	4	mathematics	mathematic	NOUN
ejpam-5388	344	5	,	,	PUNCT
ejpam-5388	344	6	pages	page	NOUN
ejpam-5388	344	7	157–162	157–162	NUM
ejpam-5388	344	8	,	,	PUNCT
ejpam-5388	344	9	2009	2009	NUM
ejpam-5388	344	10	.	.	PUNCT
ejpam-5388	345	1	[	[	X
ejpam-5388	345	2	11	11	NUM
ejpam-5388	345	3	]	]	X
ejpam-5388	345	4	m	m	VERB
ejpam-5388	345	5	boriceanu	boriceanu	PROPN
ejpam-5388	345	6	;	;	PUNCT
ejpam-5388	345	7	m	m	VERB
ejpam-5388	345	8	bota	bota	ADJ
ejpam-5388	345	9	and	and	CCONJ
ejpam-5388	345	10	a	a	DET
ejpam-5388	345	11	petrusel	petrusel	NOUN
ejpam-5388	345	12	.	.	PUNCT
ejpam-5388	346	1	multivalued	multivalue	VERB
ejpam-5388	346	2	fractals	fractal	NOUN
ejpam-5388	346	3	in	in	ADP
ejpam-5388	346	4	b	b	NOUN
ejpam-5388	346	5	-	-	PUNCT
ejpam-5388	346	6	metric	metric	ADJ
ejpam-5388	346	7	spaces	space	NOUN
ejpam-5388	346	8	.	.	PUNCT
ejpam-5388	347	1	cent	cent	NOUN
ejpam-5388	347	2	.	.	PUNCT
ejpam-5388	348	1	eur	eur	PROPN
ejpam-5388	348	2	.	.	PUNCT
ejpam-5388	349	1	j.	j.	PROPN
ejpam-5388	349	2	math	math	PROPN
ejpam-5388	349	3	.	.	PUNCT
ejpam-5388	349	4	,	,	PUNCT
ejpam-5388	349	5	8(2):367–377	8(2):367–377	NOUN
ejpam-5388	349	6	,	,	PUNCT
ejpam-5388	349	7	2010	2010	NUM
ejpam-5388	349	8	.	.	PUNCT
ejpam-5388	350	1	[	[	X
ejpam-5388	350	2	12	12	NUM
ejpam-5388	350	3	]	]	X
ejpam-5388	350	4	s	s	PART
ejpam-5388	350	5	czerwik	czerwik	PROPN
ejpam-5388	350	6	.	.	PUNCT
ejpam-5388	351	1	nonlinear	nonlinear	ADJ
ejpam-5388	351	2	set	set	NOUN
ejpam-5388	351	3	-	-	PUNCT
ejpam-5388	351	4	valued	value	VERB
ejpam-5388	351	5	contraction	contraction	NOUN
ejpam-5388	351	6	mappings	mapping	NOUN
ejpam-5388	351	7	in	in	ADP
ejpam-5388	351	8	b	b	NOUN
ejpam-5388	351	9	-	-	ADJ
ejpam-5388	351	10	metric	metric	ADJ
ejpam-5388	351	11	spaces	space	NOUN
ejpam-5388	351	12	.	.	PUNCT
ejpam-5388	352	1	atti	atti	PROPN
ejpam-5388	352	2	semin	semin	PROPN
ejpam-5388	352	3	.	.	PUNCT
ejpam-5388	353	1	international	international	ADJ
ejpam-5388	353	2	journal	journal	PROPN
ejpam-5388	353	3	of	of	ADP
ejpam-5388	353	4	advances	advance	NOUN
ejpam-5388	353	5	in	in	ADP
ejpam-5388	353	6	soft	soft	ADJ
ejpam-5388	353	7	computing	computing	NOUN
ejpam-5388	353	8	and	and	CCONJ
ejpam-5388	353	9	its	its	PRON
ejpam-5388	353	10	applications	application	NOUN
ejpam-5388	353	11	,	,	PUNCT
ejpam-5388	353	12	46(2):263–276	46(2):263–276	NUM
ejpam-5388	353	13	,	,	PUNCT
ejpam-5388	353	14	1998	1998	NUM
ejpam-5388	353	15	.	.	PUNCT
ejpam-5388	354	1	[	[	X
ejpam-5388	354	2	13	13	NUM
ejpam-5388	354	3	]	]	X
ejpam-5388	354	4	i	i	PRON
ejpam-5388	354	5	m	m	AUX
ejpam-5388	354	6	batiha	batiha	VERB
ejpam-5388	354	7	;	;	PUNCT
ejpam-5388	354	8	s	s	VERB
ejpam-5388	354	9	a	a	DET
ejpam-5388	354	10	njadat	njadat	NOUN
ejpam-5388	354	11	;	;	PUNCT
ejpam-5388	354	12	r	r	NOUN
ejpam-5388	354	13	m	m	PROPN
ejpam-5388	354	14	batyha	batyha	NOUN
ejpam-5388	354	15	;	;	PUNCT
ejpam-5388	354	16	a	a	DET
ejpam-5388	354	17	zraiqat	zraiqat	NOUN
ejpam-5388	354	18	;	;	PUNCT
ejpam-5388	354	19	a	a	DET
ejpam-5388	354	20	dababneh	dababneh	NOUN
ejpam-5388	354	21	and	and	CCONJ
ejpam-5388	354	22	sh	sh	PROPN
ejpam-5388	354	23	momani	momani	PROPN
ejpam-5388	354	24	.	.	PUNCT
ejpam-5388	355	1	design	design	NOUN
ejpam-5388	355	2	fractional	fractional	ADJ
ejpam-5388	355	3	-	-	PUNCT
ejpam-5388	355	4	order	order	NOUN
ejpam-5388	355	5	pid	pid	NOUN
ejpam-5388	355	6	controllers	controller	NOUN
ejpam-5388	355	7	for	for	ADP
ejpam-5388	355	8	single	single	ADJ
ejpam-5388	355	9	-	-	PUNCT
ejpam-5388	355	10	joint	joint	ADJ
ejpam-5388	355	11	robot	robot	NOUN
ejpam-5388	355	12	arm	arm	NOUN
ejpam-5388	355	13	model	model	NOUN
ejpam-5388	355	14	.	.	PUNCT
ejpam-5388	356	1	international	international	ADJ
ejpam-5388	356	2	journal	journal	NOUN
ejpam-5388	356	3	of	of	ADP
ejpam-5388	356	4	advances	advance	NOUN
ejpam-5388	356	5	in	in	ADP
ejpam-5388	356	6	soft	soft	ADJ
ejpam-5388	356	7	computing	computing	NOUN
ejpam-5388	356	8	and	and	CCONJ
ejpam-5388	356	9	its	its	PRON
ejpam-5388	356	10	applications	application	NOUN
ejpam-5388	356	11	,	,	PUNCT
ejpam-5388	356	12	14(2):96–114	14(2):96–114	NUM
ejpam-5388	356	13	,	,	PUNCT
ejpam-5388	356	14	2022	2022	NUM
ejpam-5388	356	15	.	.	PUNCT
ejpam-5388	357	1	[	[	X
ejpam-5388	357	2	14	14	NUM
ejpam-5388	357	3	]	]	X
ejpam-5388	357	4	a	a	DET
ejpam-5388	357	5	f	f	PROPN
ejpam-5388	357	6	roldan	roldan	PROPN
ejpam-5388	357	7	-	-	PUNCT
ejpam-5388	357	8	lópez	lópez	PROPN
ejpam-5388	357	9	de	de	PROPN
ejpam-5388	357	10	-	-	NOUN
ejpam-5388	357	11	hierro	hierro	ADJ
ejpam-5388	357	12	;	;	PUNCT
ejpam-5388	357	13	e	e	X
ejpam-5388	357	14	karapinar	karapinar	NOUN
ejpam-5388	357	15	;	;	PUNCT
ejpam-5388	357	16	c	c	NOUN
ejpam-5388	357	17	roldán	roldán	NOUN
ejpam-5388	357	18	-	-	PUNCT
ejpam-5388	357	19	lópez	lópez	ADV
ejpam-5388	357	20	-	-	PUNCT
ejpam-5388	357	21	de	de	X
ejpam-5388	357	22	hierro	hierro	PROPN
ejpam-5388	357	23	and	and	CCONJ
ejpam-5388	357	24	j	j	PROPN
ejpam-5388	357	25	mart́ıinezmoreno	mart́ıinezmoreno	PROPN
ejpam-5388	357	26	.	.	PUNCT
ejpam-5388	358	1	coincidence	coincidence	NOUN
ejpam-5388	358	2	point	point	NOUN
ejpam-5388	358	3	theorems	theorem	NOUN
ejpam-5388	358	4	on	on	ADP
ejpam-5388	358	5	metric	metric	ADJ
ejpam-5388	358	6	spaces	space	NOUN
ejpam-5388	358	7	via	via	ADP
ejpam-5388	358	8	simulation	simulation	NOUN
ejpam-5388	358	9	functions	function	NOUN
ejpam-5388	358	10	.	.	PUNCT
ejpam-5388	359	1	j.	j.	PROPN
ejpam-5388	359	2	comput	comput	PROPN
ejpam-5388	359	3	.	.	PUNCT
ejpam-5388	360	1	appl	appl	PROPN
ejpam-5388	360	2	.	.	PROPN
ejpam-5388	360	3	math	math	PROPN
ejpam-5388	360	4	.	.	PUNCT
ejpam-5388	360	5	,	,	PUNCT
ejpam-5388	360	6	275:345–75	275:345–75	NUM
ejpam-5388	360	7	,	,	PUNCT
ejpam-5388	360	8	2015	2015	NUM
ejpam-5388	360	9	.	.	PUNCT
ejpam-5388	361	1	[	[	X
ejpam-5388	361	2	15	15	NUM
ejpam-5388	361	3	]	]	X
ejpam-5388	361	4	m	m	VERB
ejpam-5388	361	5	a	a	DET
ejpam-5388	361	6	khamsi	khamsi	NOUN
ejpam-5388	361	7	and	and	CCONJ
ejpam-5388	361	8	n	n	PRON
ejpam-5388	361	9	hussain	hussain	PROPN
ejpam-5388	361	10	.	.	PUNCT
ejpam-5388	362	1	kkm	kkm	PROPN
ejpam-5388	362	2	mappings	mapping	NOUN
ejpam-5388	362	3	in	in	ADP
ejpam-5388	362	4	metric	metric	ADJ
ejpam-5388	362	5	type	type	NOUN
ejpam-5388	362	6	spaces	space	NOUN
ejpam-5388	362	7	.	.	PUNCT
ejpam-5388	363	1	nonlinear	nonlinear	ADJ
ejpam-5388	363	2	anal	anal	PROPN
ejpam-5388	363	3	.	.	PUNCT
ejpam-5388	363	4	,	,	PUNCT
ejpam-5388	364	1	73(9):3123–3129	73(9):3123–3129	NUM
ejpam-5388	364	2	,	,	PUNCT
ejpam-5388	364	3	2010	2010	NUM
ejpam-5388	364	4	.	.	PUNCT
ejpam-5388	365	1	[	[	X
ejpam-5388	365	2	16	16	NUM
ejpam-5388	365	3	]	]	X
ejpam-5388	365	4	h	h	PROPN
ejpam-5388	365	5	alsamir	alsamir	NOUN
ejpam-5388	365	6	;	;	PUNCT
ejpam-5388	365	7	m	m	VERB
ejpam-5388	365	8	s	s	VERB
ejpam-5388	365	9	m	m	NOUN
ejpam-5388	365	10	noorani	noorani	ADJ
ejpam-5388	365	11	and	and	CCONJ
ejpam-5388	365	12	w	w	PROPN
ejpam-5388	365	13	shatanawi	shatanawi	ADJ
ejpam-5388	365	14	.	.	PUNCT
ejpam-5388	366	1	on	on	ADP
ejpam-5388	366	2	new	new	ADJ
ejpam-5388	366	3	fixed	fix	VERB
ejpam-5388	366	4	point	point	NOUN
ejpam-5388	366	5	theorems	theorem	NOUN
ejpam-5388	366	6	for	for	ADP
ejpam-5388	366	7	three	three	NUM
ejpam-5388	366	8	types	type	NOUN
ejpam-5388	366	9	of	of	ADP
ejpam-5388	366	10	(	(	PUNCT
ejpam-5388	366	11	α	α	NOUN
ejpam-5388	366	12	,	,	PUNCT
ejpam-5388	366	13	β)−(ψ	β)−(ψ	PRON
ejpam-5388	366	14	,	,	PUNCT
ejpam-5388	366	15	θ	θ	PROPN
ejpam-5388	366	16	,	,	PUNCT
ejpam-5388	366	17	ϕ)-multivalued	ϕ)-multivalue	VERB
ejpam-5388	366	18	contractive	contractive	ADJ
ejpam-5388	366	19	mappings	mapping	NOUN
ejpam-5388	366	20	in	in	ADP
ejpam-5388	366	21	metric	metric	ADJ
ejpam-5388	366	22	spaces	space	NOUN
ejpam-5388	366	23	.	.	PUNCT
ejpam-5388	367	1	cogent	cogent	NOUN
ejpam-5388	367	2	mathematics	mathematic	NOUN
ejpam-5388	367	3	,	,	PUNCT
ejpam-5388	367	4	3(1):1257473	3(1):1257473	NUM
ejpam-5388	367	5	,	,	PUNCT
ejpam-5388	367	6	2016	2016	NUM
ejpam-5388	367	7	.	.	PUNCT
ejpam-5388	368	1	[	[	X
ejpam-5388	368	2	17	17	NUM
ejpam-5388	368	3	]	]	X
ejpam-5388	368	4	h	h	NOUN
ejpam-5388	368	5	qawagneh	qawagneh	PROPN
ejpam-5388	368	6	;	;	PUNCT
ejpam-5388	368	7	m	m	PROPN
ejpam-5388	368	8	s	s	VERB
ejpam-5388	368	9	m	m	NOUN
ejpam-5388	368	10	noorani	noorani	ADJ
ejpam-5388	368	11	and	and	CCONJ
ejpam-5388	368	12	w	w	PROPN
ejpam-5388	368	13	shatanawi	shatanawi	PROPN
ejpam-5388	368	14	.	.	PUNCT
ejpam-5388	369	1	fixed	fix	VERB
ejpam-5388	369	2	point	point	NOUN
ejpam-5388	369	3	theorems	theorem	NOUN
ejpam-5388	369	4	for	for	ADP
ejpam-5388	369	5	(	(	PUNCT
ejpam-5388	369	6	α	α	X
ejpam-5388	369	7	,	,	PUNCT
ejpam-5388	369	8	k	k	PROPN
ejpam-5388	369	9	,	,	PUNCT
ejpam-5388	369	10	θ)contractive	θ)contractive	ADJ
ejpam-5388	369	11	multi	multi	ADJ
ejpam-5388	369	12	-	-	ADJ
ejpam-5388	369	13	valued	value	VERB
ejpam-5388	369	14	mapping	mapping	NOUN
ejpam-5388	369	15	in	in	ADP
ejpam-5388	369	16	b	b	NOUN
ejpam-5388	369	17	-	-	PUNCT
ejpam-5388	369	18	metric	metric	ADJ
ejpam-5388	369	19	space	space	NOUN
ejpam-5388	369	20	and	and	CCONJ
ejpam-5388	369	21	applications	application	NOUN
ejpam-5388	369	22	.	.	PUNCT
ejpam-5388	370	1	international	international	ADJ
ejpam-5388	370	2	journal	journal	PROPN
ejpam-5388	370	3	of	of	ADP
ejpam-5388	370	4	mathematics	mathematic	NOUN
ejpam-5388	370	5	and	and	CCONJ
ejpam-5388	370	6	computer	computer	NOUN
ejpam-5388	370	7	science	science	NOUN
ejpam-5388	370	8	,	,	PUNCT
ejpam-5388	370	9	14(1):263–283	14(1):263–283	NUM
ejpam-5388	370	10	,	,	PUNCT
ejpam-5388	370	11	2019	2019	NUM
ejpam-5388	370	12	.	.	PUNCT
ejpam-5388	371	1	[	[	X
ejpam-5388	371	2	18	18	NUM
ejpam-5388	371	3	]	]	X
ejpam-5388	371	4	j	j	PROPN
ejpam-5388	371	5	roshan	roshan	PROPN
ejpam-5388	371	6	;	;	PUNCT
ejpam-5388	371	7	v	v	NUM
ejpam-5388	371	8	parvaneh	parvaneh	NOUN
ejpam-5388	371	9	and	and	CCONJ
ejpam-5388	371	10	i	i	PRON
ejpam-5388	371	11	altun	altun	NOUN
ejpam-5388	371	12	.	.	PUNCT
ejpam-5388	372	1	some	some	DET
ejpam-5388	372	2	coincidence	coincidence	NOUN
ejpam-5388	372	3	point	point	NOUN
ejpam-5388	372	4	results	result	NOUN
ejpam-5388	372	5	in	in	ADP
ejpam-5388	372	6	ordered	order	VERB
ejpam-5388	372	7	b	b	X
ejpam-5388	372	8	-	-	ADJ
ejpam-5388	372	9	metric	metric	ADJ
ejpam-5388	372	10	spaces	space	NOUN
ejpam-5388	372	11	and	and	CCONJ
ejpam-5388	372	12	applications	application	NOUN
ejpam-5388	372	13	in	in	ADP
ejpam-5388	372	14	a	a	DET
ejpam-5388	372	15	system	system	NOUN
ejpam-5388	372	16	of	of	ADP
ejpam-5388	372	17	integral	integral	ADJ
ejpam-5388	372	18	equations	equation	NOUN
ejpam-5388	372	19	.	.	PUNCT
ejpam-5388	373	1	appl	appl	PROPN
ejpam-5388	373	2	.	.	PROPN
ejpam-5388	373	3	math	math	PROPN
ejpam-5388	373	4	.	.	PUNCT
ejpam-5388	374	1	comput	comput	NOUN
ejpam-5388	374	2	.	.	PUNCT
ejpam-5388	374	3	,	,	PUNCT
ejpam-5388	374	4	226:725	226:725	PROPN
ejpam-5388	374	5	–	–	PUNCT
ejpam-5388	374	6	737	737	NUM
ejpam-5388	374	7	,	,	PUNCT
ejpam-5388	374	8	2014	2014	NUM
ejpam-5388	374	9	.	.	PUNCT
ejpam-5388	375	1	[	[	X
ejpam-5388	375	2	19	19	NUM
ejpam-5388	375	3	]	]	X
ejpam-5388	375	4	h	h	NOUN
ejpam-5388	375	5	qawaqneh	qawaqneh	PROPN
ejpam-5388	375	6	.	.	PUNCT
ejpam-5388	376	1	new	new	ADJ
ejpam-5388	376	2	contraction	contraction	NOUN
ejpam-5388	376	3	embedded	embed	VERB
ejpam-5388	376	4	with	with	ADP
ejpam-5388	376	5	simulation	simulation	NOUN
ejpam-5388	376	6	function	function	NOUN
ejpam-5388	376	7	and	and	CCONJ
ejpam-5388	376	8	cyclic	cyclic	ADJ
ejpam-5388	376	9	(	(	PUNCT
ejpam-5388	376	10	α	α	NOUN
ejpam-5388	376	11	,	,	PUNCT
ejpam-5388	376	12	β)−admissible	β)−admissible	ADJ
ejpam-5388	376	13	in	in	ADP
ejpam-5388	376	14	metric	metric	ADJ
ejpam-5388	376	15	-	-	PUNCT
ejpam-5388	376	16	like	like	ADJ
ejpam-5388	376	17	spaces	space	NOUN
ejpam-5388	376	18	.	.	PUNCT
ejpam-5388	377	1	international	international	ADJ
ejpam-5388	377	2	journal	journal	PROPN
ejpam-5388	377	3	of	of	ADP
ejpam-5388	377	4	mathematics	mathematic	NOUN
ejpam-5388	377	5	and	and	CCONJ
ejpam-5388	377	6	computer	computer	NOUN
ejpam-5388	377	7	science	science	NOUN
ejpam-5388	377	8	,	,	PUNCT
ejpam-5388	377	9	15(1):1029–1044	15(1):1029–1044	PROPN
ejpam-5388	377	10	,	,	PUNCT
ejpam-5388	377	11	2020	2020	NUM
ejpam-5388	377	12	.	.	PUNCT
ejpam-5388	378	1	references	reference	NOUN
ejpam-5388	378	2	2504	2504	NUM
ejpam-5388	378	3	[	[	X
ejpam-5388	378	4	20	20	NUM
ejpam-5388	378	5	]	]	PUNCT
ejpam-5388	378	6	h	h	NOUN
ejpam-5388	378	7	qawaqneh	qawaqneh	PROPN
ejpam-5388	378	8	.	.	PUNCT
ejpam-5388	379	1	fractional	fractional	ADJ
ejpam-5388	379	2	analytic	analytic	ADJ
ejpam-5388	379	3	solutions	solution	NOUN
ejpam-5388	379	4	and	and	CCONJ
ejpam-5388	379	5	fixed	fix	VERB
ejpam-5388	379	6	point	point	NOUN
ejpam-5388	379	7	results	result	NOUN
ejpam-5388	379	8	with	with	ADP
ejpam-5388	379	9	some	some	DET
ejpam-5388	379	10	applications	application	NOUN
ejpam-5388	379	11	.	.	PUNCT
ejpam-5388	380	1	adv	adv	PROPN
ejpam-5388	380	2	.	.	PUNCT
ejpam-5388	380	3	fixed	fix	VERB
ejpam-5388	380	4	point	point	NOUN
ejpam-5388	380	5	theory	theory	NOUN
ejpam-5388	380	6	,	,	PUNCT
ejpam-5388	380	7	14(1	14(1	NUM
ejpam-5388	380	8	)	)	PUNCT
ejpam-5388	380	9	,	,	PUNCT
ejpam-5388	380	10	2024	2024	NUM
ejpam-5388	380	11	.	.	PUNCT
ejpam-5388	381	1	[	[	X
ejpam-5388	381	2	21	21	NUM
ejpam-5388	381	3	]	]	X
ejpam-5388	381	4	h	h	PROPN
ejpam-5388	381	5	alsamir	alsamir	NOUN
ejpam-5388	381	6	;	;	PUNCT
ejpam-5388	381	7	h	h	NOUN
ejpam-5388	381	8	aydi	aydi	VERB
ejpam-5388	381	9	;	;	PUNCT
ejpam-5388	381	10	m	m	PROPN
ejpam-5388	381	11	s	s	PART
ejpam-5388	381	12	m	m	VERB
ejpam-5388	381	13	noorani	noorani	ADJ
ejpam-5388	381	14	;	;	PUNCT
ejpam-5388	381	15	w	w	NOUN
ejpam-5388	381	16	shatanawi	shatanawi	ADJ
ejpam-5388	381	17	;	;	PUNCT
ejpam-5388	381	18	h	h	NOUN
ejpam-5388	381	19	akhadkulov	akhadkulov	NOUN
ejpam-5388	381	20	;	;	PUNCT
ejpam-5388	381	21	h	h	NOUN
ejpam-5388	381	22	qawaqneh	qawaqneh	PROPN
ejpam-5388	381	23	and	and	CCONJ
ejpam-5388	381	24	k	k	PROPN
ejpam-5388	381	25	alanazi	alanazi	PROPN
ejpam-5388	381	26	.	.	PUNCT
ejpam-5388	382	1	fixed	fix	VERB
ejpam-5388	382	2	point	point	NOUN
ejpam-5388	382	3	results	result	NOUN
ejpam-5388	382	4	in	in	ADP
ejpam-5388	382	5	metric	metric	ADJ
ejpam-5388	382	6	-	-	PUNCT
ejpam-5388	382	7	like	like	ADJ
ejpam-5388	382	8	spaces	space	NOUN
ejpam-5388	382	9	via	via	ADP
ejpam-5388	382	10	σ	σ	PROPN
ejpam-5388	382	11	-	-	PUNCT
ejpam-5388	382	12	simulation	simulation	NOUN
ejpam-5388	382	13	functions	function	NOUN
ejpam-5388	382	14	.	.	PUNCT
ejpam-5388	383	1	european	european	ADJ
ejpam-5388	383	2	journal	journal	PROPN
ejpam-5388	383	3	of	of	ADP
ejpam-5388	383	4	pure	pure	ADJ
ejpam-5388	383	5	and	and	CCONJ
ejpam-5388	383	6	applied	applied	ADJ
ejpam-5388	383	7	mathematics	mathematic	NOUN
ejpam-5388	383	8	,	,	PUNCT
ejpam-5388	383	9	12(1):88–100	12(1):88–100	NUM
ejpam-5388	383	10	,	,	PUNCT
ejpam-5388	383	11	2019	2019	NUM
ejpam-5388	383	12	.	.	PUNCT
ejpam-5388	384	1	[	[	X
ejpam-5388	384	2	22	22	NUM
ejpam-5388	384	3	]	]	PUNCT
ejpam-5388	384	4	a	a	DET
ejpam-5388	384	5	h	h	NOUN
ejpam-5388	384	6	ansari	ansari	X
ejpam-5388	384	7	;	;	PUNCT
ejpam-5388	384	8	s	s	VERB
ejpam-5388	384	9	chandok	chandok	NOUN
ejpam-5388	384	10	x	x	X
ejpam-5388	384	11	l	l	X
ejpam-5388	384	12	liu	liu	PROPN
ejpam-5388	384	13	and	and	CCONJ
ejpam-5388	384	14	s	s	PROPN
ejpam-5388	384	15	radenovicl	radenovicl	NOUN
ejpam-5388	384	16	.	.	PUNCT
ejpam-5388	385	1	on	on	ADP
ejpam-5388	385	2	some	some	DET
ejpam-5388	385	3	results	result	NOUN
ejpam-5388	385	4	in	in	ADP
ejpam-5388	385	5	metric	metric	ADJ
ejpam-5388	385	6	spaces	space	NOUN
ejpam-5388	385	7	using	use	VERB
ejpam-5388	385	8	auxiliary	auxiliary	ADJ
ejpam-5388	385	9	simulation	simulation	NOUN
ejpam-5388	385	10	functions	function	NOUN
ejpam-5388	385	11	via	via	ADP
ejpam-5388	385	12	new	new	ADJ
ejpam-5388	385	13	functions	function	NOUN
ejpam-5388	385	14	.	.	PUNCT
ejpam-5388	386	1	j.	j.	PROPN
ejpam-5388	386	2	comput	comput	PROPN
ejpam-5388	386	3	.	.	PUNCT
ejpam-5388	387	1	anal	anal	PROPN
ejpam-5388	387	2	.	.	PUNCT
ejpam-5388	387	3	appl	appl	PROPN
ejpam-5388	387	4	.	.	PROPN
ejpam-5388	387	5	,	,	PUNCT
ejpam-5388	388	1	24(6):1103–1114	24(6):1103–1114	NUM
ejpam-5388	388	2	,	,	PUNCT
ejpam-5388	388	3	2018	2018	NUM
ejpam-5388	388	4	.	.	PUNCT
ejpam-5388	389	1	[	[	X
ejpam-5388	389	2	23	23	NUM
ejpam-5388	389	3	]	]	X
ejpam-5388	389	4	h	h	NOUN
ejpam-5388	389	5	qawaqneh	qawaqneh	NOUN
ejpam-5388	389	6	;	;	PUNCT
ejpam-5388	389	7	m	m	PROPN
ejpam-5388	389	8	s	s	PART
ejpam-5388	389	9	m	m	VERB
ejpam-5388	389	10	noorani	noorani	ADJ
ejpam-5388	389	11	;	;	PUNCT
ejpam-5388	389	12	h	h	NOUN
ejpam-5388	389	13	aydi	aydi	VERB
ejpam-5388	389	14	;	;	PUNCT
ejpam-5388	389	15	a	a	DET
ejpam-5388	389	16	zraiqat	zraiqat	NOUN
ejpam-5388	389	17	and	and	CCONJ
ejpam-5388	389	18	a	a	DET
ejpam-5388	389	19	h	h	NOUN
ejpam-5388	389	20	ansari	ansari	ADJ
ejpam-5388	389	21	.	.	PUNCT
ejpam-5388	390	1	on	on	ADP
ejpam-5388	390	2	fixed	fix	VERB
ejpam-5388	390	3	pointresults	pointresult	NOUN
ejpam-5388	390	4	in	in	ADP
ejpam-5388	390	5	partial	partial	ADJ
ejpam-5388	390	6	b	b	NOUN
ejpam-5388	390	7	-	-	PUNCT
ejpam-5388	390	8	metric	metric	ADJ
ejpam-5388	390	9	spaces	space	NOUN
ejpam-5388	390	10	.	.	PUNCT
ejpam-5388	391	1	journal	journal	NOUN
ejpam-5388	391	2	of	of	ADP
ejpam-5388	391	3	function	function	NOUN
ejpam-5388	391	4	spaces	space	NOUN
ejpam-5388	391	5	,	,	PUNCT
ejpam-5388	391	6	2021	2021	NUM
ejpam-5388	391	7	,	,	PUNCT
ejpam-5388	391	8	2021	2021	NUM
ejpam-5388	391	9	.	.	PUNCT