id	sid	tid	token	lemma	pos
ejpam-3286	1	1	european	european	PROPN
ejpam-3286	1	2	journal	journal	PROPN
ejpam-3286	1	3	of	of	ADP
ejpam-3286	1	4	pure	pure	ADJ
ejpam-3286	1	5	and	and	CCONJ
ejpam-3286	1	6	applied	apply	VERB
ejpam-3286	1	7	mathematics	mathematic	NOUN
ejpam-3286	1	8	vol	vol	NOUN
ejpam-3286	1	9	.	.	PUNCT
ejpam-3286	2	1	11	11	NUM
ejpam-3286	2	2	,	,	PUNCT
ejpam-3286	2	3	no	no	INTJ
ejpam-3286	2	4	.	.	NOUN
ejpam-3286	2	5	3	3	NUM
ejpam-3286	2	6	,	,	PUNCT
ejpam-3286	2	7	2018	2018	NUM
ejpam-3286	2	8	,	,	PUNCT
ejpam-3286	2	9	869	869	NUM
ejpam-3286	2	10	-	-	SYM
ejpam-3286	2	11	875	875	NUM
ejpam-3286	2	12	issn	issn	PROPN
ejpam-3286	2	13	1307	1307	NUM
ejpam-3286	2	14	-	-	SYM
ejpam-3286	2	15	5543	5543	NUM
ejpam-3286	2	16	–	–	PUNCT
ejpam-3286	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3286	2	18	published	publish	VERB
ejpam-3286	2	19	by	by	ADP
ejpam-3286	2	20	new	new	PROPN
ejpam-3286	2	21	york	york	PROPN
ejpam-3286	2	22	business	business	PROPN
ejpam-3286	3	1	global	global	PROPN
ejpam-3286	3	2	a	a	DET
ejpam-3286	3	3	common	common	ADJ
ejpam-3286	3	4	best	good	ADJ
ejpam-3286	3	5	proximity	proximity	NOUN
ejpam-3286	3	6	point	point	NOUN
ejpam-3286	3	7	theorem	theorem	NOUN
ejpam-3286	3	8	for	for	ADP
ejpam-3286	3	9	φ	φ	VERB
ejpam-3286	3	10	-	-	PUNCT
ejpam-3286	3	11	dominated	dominate	VERB
ejpam-3286	3	12	pair	pair	NOUN
ejpam-3286	3	13	mahdi	mahdi	PROPN
ejpam-3286	3	14	iranmanesh1	iranmanesh1	PROPN
ejpam-3286	3	15	,	,	PUNCT
ejpam-3286	3	16	ali	ali	PROPN
ejpam-3286	3	17	ganjbakhsh	ganjbakhsh	PROPN
ejpam-3286	3	18	sanatee1,∗	sanatee1,∗	NOUN
ejpam-3286	3	19	1	1	NUM
ejpam-3286	3	20	department	department	NOUN
ejpam-3286	3	21	of	of	ADP
ejpam-3286	3	22	pure	pure	ADJ
ejpam-3286	3	23	mathematics	mathematic	NOUN
ejpam-3286	3	24	,	,	PUNCT
ejpam-3286	3	25	shahrood	shahrood	NOUN
ejpam-3286	3	26	university	university	PROPN
ejpam-3286	3	27	of	of	ADP
ejpam-3286	3	28	technology	technology	NOUN
ejpam-3286	3	29	,	,	PUNCT
ejpam-3286	3	30	shahrood	shahrood	NOUN
ejpam-3286	3	31	,	,	PUNCT
ejpam-3286	3	32	iran	iran	PROPN
ejpam-3286	3	33	abstract	abstract	ADJ
ejpam-3286	3	34	.	.	PUNCT
ejpam-3286	4	1	in	in	ADP
ejpam-3286	4	2	the	the	DET
ejpam-3286	4	3	present	present	ADJ
ejpam-3286	4	4	research	research	NOUN
ejpam-3286	4	5	,	,	PUNCT
ejpam-3286	4	6	an	an	DET
ejpam-3286	4	7	interesting	interesting	ADJ
ejpam-3286	4	8	common	common	ADJ
ejpam-3286	4	9	best	good	ADJ
ejpam-3286	4	10	proximity	proximity	NOUN
ejpam-3286	4	11	point	point	NOUN
ejpam-3286	4	12	theorem	theorem	NOUN
ejpam-3286	4	13	for	for	ADP
ejpam-3286	4	14	pairs	pair	NOUN
ejpam-3286	4	15	of	of	ADP
ejpam-3286	4	16	non	non	ADJ
ejpam-3286	4	17	-	-	ADJ
ejpam-3286	4	18	self	self	NOUN
ejpam-3286	4	19	-	-	PUNCT
ejpam-3286	4	20	mappings	mapping	NOUN
ejpam-3286	4	21	is	be	AUX
ejpam-3286	4	22	presented	present	VERB
ejpam-3286	4	23	.	.	PUNCT
ejpam-3286	5	1	it	it	PRON
ejpam-3286	5	2	satisfies	satisfy	VERB
ejpam-3286	5	3	a	a	DET
ejpam-3286	5	4	weakly	weakly	ADJ
ejpam-3286	5	5	contraction	contraction	NOUN
ejpam-3286	5	6	-	-	PUNCT
ejpam-3286	5	7	like	like	ADJ
ejpam-3286	5	8	condition	condition	NOUN
ejpam-3286	5	9	,	,	PUNCT
ejpam-3286	5	10	thereby	thereby	ADV
ejpam-3286	5	11	producing	produce	VERB
ejpam-3286	5	12	common	common	ADJ
ejpam-3286	5	13	optimal	optimal	ADJ
ejpam-3286	5	14	approximate	approximate	ADJ
ejpam-3286	5	15	solutions	solution	NOUN
ejpam-3286	5	16	of	of	ADP
ejpam-3286	5	17	certain	certain	ADJ
ejpam-3286	5	18	simultaneous	simultaneous	ADJ
ejpam-3286	5	19	fixed	fix	VERB
ejpam-3286	5	20	point	point	NOUN
ejpam-3286	5	21	equations	equation	NOUN
ejpam-3286	5	22	.	.	PUNCT
ejpam-3286	6	1	2010	2010	NUM
ejpam-3286	6	2	mathematics	mathematic	NOUN
ejpam-3286	6	3	subject	subject	NOUN
ejpam-3286	6	4	classifications	classification	NOUN
ejpam-3286	6	5	:	:	PUNCT
ejpam-3286	6	6	47h09	47h09	NUM
ejpam-3286	6	7	,	,	PUNCT
ejpam-3286	6	8	47h10	47h10	PRON
ejpam-3286	6	9	key	key	ADJ
ejpam-3286	6	10	words	word	NOUN
ejpam-3286	6	11	and	and	CCONJ
ejpam-3286	6	12	phrases	phrase	NOUN
ejpam-3286	6	13	:	:	PUNCT
ejpam-3286	6	14	common	common	ADJ
ejpam-3286	6	15	best	good	ADJ
ejpam-3286	6	16	proximity	proximity	NOUN
ejpam-3286	6	17	point	point	NOUN
ejpam-3286	6	18	,	,	PUNCT
ejpam-3286	6	19	φ	φ	PROPN
ejpam-3286	6	20	-	-	PUNCT
ejpam-3286	6	21	dominated	dominate	VERB
ejpam-3286	6	22	pair	pair	NOUN
ejpam-3286	6	23	,	,	PUNCT
ejpam-3286	6	24	φ	φ	PROPN
ejpam-3286	6	25	-	-	NOUN
ejpam-3286	6	26	contraction	contraction	NOUN
ejpam-3286	6	27	,	,	PUNCT
ejpam-3286	6	28	fixed	fix	VERB
ejpam-3286	6	29	point	point	NOUN
ejpam-3286	6	30	1	1	NUM
ejpam-3286	6	31	.	.	PUNCT
ejpam-3286	7	1	introduction	introduction	NOUN
ejpam-3286	7	2	fixed	fix	VERB
ejpam-3286	7	3	point	point	NOUN
ejpam-3286	7	4	theory	theory	NOUN
ejpam-3286	7	5	is	be	AUX
ejpam-3286	7	6	indispensable	indispensable	ADJ
ejpam-3286	7	7	tx	tx	PROPN
ejpam-3286	8	1	=	=	PUNCT
ejpam-3286	8	2	x	x	PROPN
ejpam-3286	8	3	for	for	ADP
ejpam-3286	8	4	self	self	NOUN
ejpam-3286	8	5	-	-	PUNCT
ejpam-3286	8	6	mappings	mapping	NOUN
ejpam-3286	8	7	t	t	NOUN
ejpam-3286	8	8	on	on	ADP
ejpam-3286	8	9	subsets	subset	NOUN
ejpam-3286	8	10	of	of	ADP
ejpam-3286	8	11	metric	metric	ADJ
ejpam-3286	8	12	space	space	NOUN
ejpam-3286	8	13	or	or	CCONJ
ejpam-3286	8	14	normed	normed	ADJ
ejpam-3286	8	15	space	space	NOUN
ejpam-3286	8	16	.	.	PUNCT
ejpam-3286	9	1	let	let	VERB
ejpam-3286	9	2	a	a	PRON
ejpam-3286	9	3	and	and	CCONJ
ejpam-3286	9	4	b	b	NOUN
ejpam-3286	9	5	be	be	AUX
ejpam-3286	9	6	non	non	ADJ
ejpam-3286	9	7	-	-	ADJ
ejpam-3286	9	8	empty	empty	ADJ
ejpam-3286	9	9	subsets	subset	NOUN
ejpam-3286	9	10	of	of	ADP
ejpam-3286	9	11	metric	metric	ADJ
ejpam-3286	9	12	space	space	NOUN
ejpam-3286	9	13	(	(	PUNCT
ejpam-3286	9	14	x	x	X
ejpam-3286	9	15	,	,	PUNCT
ejpam-3286	9	16	d	d	NOUN
ejpam-3286	9	17	)	)	PUNCT
ejpam-3286	9	18	and	and	CCONJ
ejpam-3286	9	19	let	let	VERB
ejpam-3286	9	20	t	t	NOUN
ejpam-3286	9	21	:	:	PUNCT
ejpam-3286	9	22	a	a	DET
ejpam-3286	9	23	−→	−→	NOUN
ejpam-3286	9	24	b	b	AUX
ejpam-3286	9	25	be	be	AUX
ejpam-3286	9	26	non	non	ADJ
ejpam-3286	9	27	-	-	ADJ
ejpam-3286	9	28	self	self	ADJ
ejpam-3286	9	29	mapping	mapping	NOUN
ejpam-3286	9	30	.	.	PUNCT
ejpam-3286	10	1	if	if	SCONJ
ejpam-3286	10	2	the	the	DET
ejpam-3286	10	3	equation	equation	NOUN
ejpam-3286	10	4	tx	tx	VERB
ejpam-3286	10	5	=	=	PUNCT
ejpam-3286	10	6	x	x	X
ejpam-3286	10	7	does	do	AUX
ejpam-3286	10	8	not	not	PART
ejpam-3286	10	9	possess	possess	VERB
ejpam-3286	10	10	solution	solution	NOUN
ejpam-3286	10	11	,	,	PUNCT
ejpam-3286	10	12	then	then	ADV
ejpam-3286	10	13	d(x	d(x	PROPN
ejpam-3286	10	14	,	,	PUNCT
ejpam-3286	10	15	tx	tx	PROPN
ejpam-3286	10	16	)	)	PUNCT
ejpam-3286	10	17	>	>	X
ejpam-3286	11	1	0	0	X
ejpam-3286	11	2	.	.	PUNCT
ejpam-3286	12	1	in	in	ADP
ejpam-3286	12	2	this	this	DET
ejpam-3286	12	3	case	case	NOUN
ejpam-3286	12	4	,	,	PUNCT
ejpam-3286	12	5	it	it	PRON
ejpam-3286	12	6	is	be	AUX
ejpam-3286	12	7	important	important	ADJ
ejpam-3286	12	8	that	that	SCONJ
ejpam-3286	12	9	we	we	PRON
ejpam-3286	12	10	find	find	VERB
ejpam-3286	12	11	an	an	DET
ejpam-3286	12	12	element	element	NOUN
ejpam-3286	12	13	x	x	SYM
ejpam-3286	12	14	∈	∈	PROPN
ejpam-3286	12	15	a	a	DET
ejpam-3286	12	16	such	such	ADJ
ejpam-3286	12	17	that	that	DET
ejpam-3286	12	18	d(x	d(x	PROPN
ejpam-3286	12	19	,	,	PUNCT
ejpam-3286	12	20	tx	tx	PROPN
ejpam-3286	12	21	)	)	PUNCT
ejpam-3286	12	22	is	be	AUX
ejpam-3286	12	23	minimum	minimum	ADJ
ejpam-3286	12	24	in	in	ADP
ejpam-3286	12	25	some	some	DET
ejpam-3286	12	26	sense	sense	NOUN
ejpam-3286	12	27	.	.	PUNCT
ejpam-3286	13	1	for	for	ADP
ejpam-3286	13	2	example	example	NOUN
ejpam-3286	13	3	,	,	PUNCT
ejpam-3286	13	4	the	the	DET
ejpam-3286	13	5	best	good	ADJ
ejpam-3286	13	6	approximation	approximation	NOUN
ejpam-3286	13	7	problem	problem	NOUN
ejpam-3286	13	8	and	and	CCONJ
ejpam-3286	13	9	best	good	ADJ
ejpam-3286	13	10	proximity	proximity	NOUN
ejpam-3286	13	11	problem	problem	NOUN
ejpam-3286	13	12	are	be	AUX
ejpam-3286	13	13	investigated	investigate	VERB
ejpam-3286	13	14	in	in	ADP
ejpam-3286	13	15	this	this	DET
ejpam-3286	13	16	regard	regard	NOUN
ejpam-3286	13	17	(	(	PUNCT
ejpam-3286	13	18	see	see	VERB
ejpam-3286	13	19	[	[	X
ejpam-3286	13	20	2	2	NUM
ejpam-3286	13	21	]	]	PUNCT
ejpam-3286	13	22	and	and	CCONJ
ejpam-3286	13	23	[	[	X
ejpam-3286	13	24	5	5	NUM
ejpam-3286	13	25	]	]	NUM
ejpam-3286	13	26	)	)	PUNCT
ejpam-3286	13	27	.	.	PUNCT
ejpam-3286	14	1	an	an	DET
ejpam-3286	14	2	element	element	NOUN
ejpam-3286	14	3	x	x	SYM
ejpam-3286	14	4	∈	∈	PROPN
ejpam-3286	14	5	a	a	PRON
ejpam-3286	14	6	is	be	AUX
ejpam-3286	14	7	said	say	VERB
ejpam-3286	14	8	to	to	PART
ejpam-3286	14	9	be	be	AUX
ejpam-3286	14	10	a	a	DET
ejpam-3286	14	11	best	good	ADJ
ejpam-3286	14	12	proximity	proximity	NOUN
ejpam-3286	14	13	point	point	NOUN
ejpam-3286	14	14	of	of	ADP
ejpam-3286	14	15	t	t	PROPN
ejpam-3286	14	16	if	if	SCONJ
ejpam-3286	14	17	d(x	d(x	PROPN
ejpam-3286	14	18	,	,	PUNCT
ejpam-3286	14	19	tx	tx	PROPN
ejpam-3286	14	20	)	)	PUNCT
ejpam-3286	14	21	=	=	SYM
ejpam-3286	15	1	d(a	d(a	PROPN
ejpam-3286	15	2	,	,	PUNCT
ejpam-3286	15	3	b	b	NOUN
ejpam-3286	15	4	)	)	PUNCT
ejpam-3286	15	5	where	where	SCONJ
ejpam-3286	15	6	d(a	d(a	PROPN
ejpam-3286	15	7	,	,	PUNCT
ejpam-3286	15	8	b	b	NOUN
ejpam-3286	15	9	)	)	PUNCT
ejpam-3286	15	10	=	=	PUNCT
ejpam-3286	15	11	inf{d(x	inf{d(x	PROPN
ejpam-3286	15	12	,	,	PUNCT
ejpam-3286	15	13	y	y	PROPN
ejpam-3286	15	14	)	)	PUNCT
ejpam-3286	15	15	:	:	PUNCT
ejpam-3286	16	1	x	x	X
ejpam-3286	16	2	∈	∈	PROPN
ejpam-3286	16	3	a	a	X
ejpam-3286	16	4	,	,	PUNCT
ejpam-3286	16	5	y	y	PROPN
ejpam-3286	16	6	∈	∈	PROPN
ejpam-3286	16	7	b	b	PROPN
ejpam-3286	16	8	}	}	PUNCT
ejpam-3286	16	9	.	.	PUNCT
ejpam-3286	17	1	it	it	PRON
ejpam-3286	17	2	is	be	AUX
ejpam-3286	17	3	easy	easy	ADJ
ejpam-3286	17	4	to	to	PART
ejpam-3286	17	5	check	check	VERB
ejpam-3286	17	6	that	that	SCONJ
ejpam-3286	17	7	if	if	SCONJ
ejpam-3286	17	8	t	t	PROPN
ejpam-3286	17	9	is	be	AUX
ejpam-3286	17	10	self	self	NOUN
ejpam-3286	17	11	-	-	PUNCT
ejpam-3286	17	12	mapping	mapping	NOUN
ejpam-3286	17	13	the	the	DET
ejpam-3286	17	14	best	good	ADJ
ejpam-3286	17	15	proximity	proximity	NOUN
ejpam-3286	17	16	problem	problem	NOUN
ejpam-3286	17	17	reduces	reduce	VERB
ejpam-3286	17	18	to	to	ADP
ejpam-3286	17	19	fixed	fix	VERB
ejpam-3286	17	20	point	point	NOUN
ejpam-3286	17	21	problem	problem	NOUN
ejpam-3286	17	22	.	.	PUNCT
ejpam-3286	18	1	there	there	PRON
ejpam-3286	18	2	are	be	VERB
ejpam-3286	18	3	several	several	ADJ
ejpam-3286	18	4	various	various	ADJ
ejpam-3286	18	5	of	of	ADP
ejpam-3286	18	6	contractions	contraction	NOUN
ejpam-3286	18	7	that	that	PRON
ejpam-3286	18	8	guarantee	guarantee	VERB
ejpam-3286	18	9	the	the	DET
ejpam-3286	18	10	existence	existence	NOUN
ejpam-3286	18	11	of	of	ADP
ejpam-3286	18	12	a	a	DET
ejpam-3286	18	13	best	good	ADJ
ejpam-3286	18	14	proximity	proximity	NOUN
ejpam-3286	18	15	point	point	NOUN
ejpam-3286	18	16	(	(	PUNCT
ejpam-3286	18	17	see	see	VERB
ejpam-3286	18	18	[	[	X
ejpam-3286	18	19	2	2	NUM
ejpam-3286	18	20	]	]	PUNCT
ejpam-3286	18	21	,	,	PUNCT
ejpam-3286	18	22	[	[	X
ejpam-3286	18	23	5	5	NUM
ejpam-3286	18	24	]	]	PUNCT
ejpam-3286	18	25	,	,	PUNCT
ejpam-3286	18	26	and	and	CCONJ
ejpam-3286	18	27	[	[	X
ejpam-3286	18	28	11	11	NUM
ejpam-3286	18	29	]	]	PUNCT
ejpam-3286	18	30	)	)	PUNCT
ejpam-3286	18	31	.	.	PUNCT
ejpam-3286	19	1	suppose	suppose	VERB
ejpam-3286	19	2	that	that	SCONJ
ejpam-3286	19	3	a	a	PRON
ejpam-3286	19	4	and	and	CCONJ
ejpam-3286	19	5	b	b	NOUN
ejpam-3286	19	6	be	be	AUX
ejpam-3286	19	7	nonempty	nonempty	X
ejpam-3286	19	8	subsets	subset	NOUN
ejpam-3286	19	9	of	of	ADP
ejpam-3286	19	10	metric	metric	ADJ
ejpam-3286	19	11	space	space	NOUN
ejpam-3286	19	12	(	(	PUNCT
ejpam-3286	19	13	x	x	X
ejpam-3286	19	14	,	,	PUNCT
ejpam-3286	19	15	d	d	NOUN
ejpam-3286	19	16	)	)	PUNCT
ejpam-3286	19	17	.	.	PUNCT
ejpam-3286	20	1	let	let	VERB
ejpam-3286	20	2	t	t	NOUN
ejpam-3286	20	3	:	:	PUNCT
ejpam-3286	20	4	a	a	DET
ejpam-3286	20	5	−→	−→	NOUN
ejpam-3286	20	6	b	b	PROPN
ejpam-3286	20	7	and	and	CCONJ
ejpam-3286	20	8	s	s	VERB
ejpam-3286	20	9	:	:	PUNCT
ejpam-3286	20	10	a	a	DET
ejpam-3286	20	11	−→	−→	NOUN
ejpam-3286	20	12	b	b	NOUN
ejpam-3286	20	13	be	be	AUX
ejpam-3286	20	14	nonself	nonself	PROPN
ejpam-3286	20	15	mapping	mapping	NOUN
ejpam-3286	20	16	.	.	PUNCT
ejpam-3286	21	1	let	let	VERB
ejpam-3286	21	2	considering	consider	VERB
ejpam-3286	21	3	the	the	DET
ejpam-3286	21	4	fact	fact	NOUN
ejpam-3286	21	5	s	s	NOUN
ejpam-3286	21	6	and	and	CCONJ
ejpam-3286	21	7	t	t	PROPN
ejpam-3286	21	8	are	be	AUX
ejpam-3286	21	9	nonselfmappings	nonselfmapping	NOUN
ejpam-3286	21	10	,	,	PUNCT
ejpam-3286	21	11	it	it	PRON
ejpam-3286	21	12	is	be	AUX
ejpam-3286	21	13	possible	possible	ADJ
ejpam-3286	21	14	that	that	SCONJ
ejpam-3286	21	15	the	the	DET
ejpam-3286	21	16	equations	equation	NOUN
ejpam-3286	21	17	tx	tx	VERB
ejpam-3286	21	18	=	=	PUNCT
ejpam-3286	22	1	x	x	PROPN
ejpam-3286	22	2	and	and	CCONJ
ejpam-3286	22	3	sx	sx	PROPN
ejpam-3286	22	4	=	=	PUNCT
ejpam-3286	22	5	x	x	AUX
ejpam-3286	22	6	have	have	VERB
ejpam-3286	22	7	a	a	DET
ejpam-3286	22	8	common	common	ADJ
ejpam-3286	22	9	solution	solution	NOUN
ejpam-3286	22	10	,	,	PUNCT
ejpam-3286	22	11	considered	consider	VERB
ejpam-3286	22	12	as	as	ADP
ejpam-3286	22	13	a	a	DET
ejpam-3286	22	14	common	common	ADJ
ejpam-3286	22	15	fixed	fix	VERB
ejpam-3286	22	16	point	point	NOUN
ejpam-3286	22	17	of	of	ADP
ejpam-3286	22	18	the	the	DET
ejpam-3286	22	19	mappings	mapping	NOUN
ejpam-3286	22	20	t	t	NOUN
ejpam-3286	22	21	and	and	CCONJ
ejpam-3286	22	22	s	s	X
ejpam-3286	22	23	.	.	PUNCT
ejpam-3286	23	1	when	when	SCONJ
ejpam-3286	23	2	the	the	DET
ejpam-3286	23	3	equations	equation	NOUN
ejpam-3286	23	4	have	have	VERB
ejpam-3286	23	5	no	no	DET
ejpam-3286	23	6	common	common	ADJ
ejpam-3286	23	7	solution	solution	NOUN
ejpam-3286	23	8	,	,	PUNCT
ejpam-3286	23	9	one	one	PRON
ejpam-3286	23	10	thinks	think	VERB
ejpam-3286	23	11	to	to	PART
ejpam-3286	23	12	find	find	VERB
ejpam-3286	23	13	an	an	DET
ejpam-3286	23	14	element	element	NOUN
ejpam-3286	23	15	x	x	PUNCT
ejpam-3286	23	16	that	that	PRON
ejpam-3286	23	17	is	be	AUX
ejpam-3286	23	18	in	in	ADP
ejpam-3286	23	19	near	near	ADJ
ejpam-3286	23	20	proximity	proximity	NOUN
ejpam-3286	23	21	to	to	ADP
ejpam-3286	23	22	∗corresponding	∗corresponde	VERB
ejpam-3286	23	23	author	author	NOUN
ejpam-3286	23	24	.	.	PUNCT
ejpam-3286	24	1	doi	doi	NOUN
ejpam-3286	24	2	:	:	PUNCT
ejpam-3286	24	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3286	https://doi.org/10.29020/nybg.ejpam.v11i3.3286	ADJ
ejpam-3286	24	4	email	email	NOUN
ejpam-3286	24	5	addresses	address	NOUN
ejpam-3286	24	6	:	:	PUNCT
ejpam-3286	24	7	m.iranmanesh2012@gmail.com	m.iranmanesh2012@gmail.com	X
ejpam-3286	24	8	(	(	PUNCT
ejpam-3286	24	9	m.	m.	NOUN
ejpam-3286	24	10	iranmanesh	iranmanesh	PROPN
ejpam-3286	24	11	)	)	PUNCT
ejpam-3286	24	12	,	,	PUNCT
ejpam-3286	24	13	alisanatee62@gmail.com	alisanatee62@gmail.com	PROPN
ejpam-3286	24	14	(	(	PUNCT
ejpam-3286	24	15	a.	a.	NOUN
ejpam-3286	24	16	ganjbakhsh	ganjbakhsh	NOUN
ejpam-3286	24	17	sanatee	sanatee	NOUN
ejpam-3286	24	18	)	)	PUNCT
ejpam-3286	24	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3286	25	1	869	869	NUM
ejpam-3286	25	2	c	c	NOUN
ejpam-3286	25	3	©	©	PROPN
ejpam-3286	25	4	2018	2018	NUM
ejpam-3286	25	5	ejpam	ejpam	VERB
ejpam-3286	25	6	all	all	DET
ejpam-3286	25	7	rights	right	NOUN
ejpam-3286	25	8	reserved	reserve	VERB
ejpam-3286	25	9	.	.	PUNCT
ejpam-3286	26	1	m.	m.	PROPN
ejpam-3286	26	2	iranmanesh	iranmanesh	PROPN
ejpam-3286	26	3	,	,	PUNCT
ejpam-3286	26	4	a.	a.	NOUN
ejpam-3286	26	5	g.	g.	PROPN
ejpam-3286	26	6	sanatee	sanatee	PROPN
ejpam-3286	26	7	/	/	SYM
ejpam-3286	26	8	eur	eur	PROPN
ejpam-3286	26	9	.	.	PUNCT
ejpam-3286	27	1	j.	j.	PROPN
ejpam-3286	27	2	pure	pure	PROPN
ejpam-3286	27	3	appl	appl	PROPN
ejpam-3286	27	4	.	.	PROPN
ejpam-3286	27	5	math	math	PROPN
ejpam-3286	27	6	,	,	PUNCT
ejpam-3286	27	7	11	11	NUM
ejpam-3286	27	8	(	(	PUNCT
ejpam-3286	27	9	3	3	NUM
ejpam-3286	27	10	)	)	PUNCT
ejpam-3286	27	11	(	(	PUNCT
ejpam-3286	27	12	2018	2018	NUM
ejpam-3286	27	13	)	)	PUNCT
ejpam-3286	27	14	,	,	PUNCT
ejpam-3286	27	15	869	869	NUM
ejpam-3286	27	16	-	-	SYM
ejpam-3286	27	17	875	875	NUM
ejpam-3286	27	18	870	870	NUM
ejpam-3286	27	19	tx	tx	NOUN
ejpam-3286	27	20	and	and	CCONJ
ejpam-3286	27	21	sx	sx	PROPN
ejpam-3286	27	22	in	in	ADP
ejpam-3286	27	23	the	the	DET
ejpam-3286	27	24	sense	sense	NOUN
ejpam-3286	27	25	that	that	SCONJ
ejpam-3286	27	26	d(x	d(x	NOUN
ejpam-3286	27	27	,	,	PUNCT
ejpam-3286	27	28	tx	tx	PROPN
ejpam-3286	27	29	)	)	PUNCT
ejpam-3286	27	30	and	and	CCONJ
ejpam-3286	27	31	d(x	d(x	PROPN
ejpam-3286	27	32	,	,	PUNCT
ejpam-3286	27	33	sx	sx	PROPN
ejpam-3286	27	34	)	)	PUNCT
ejpam-3286	27	35	are	be	AUX
ejpam-3286	27	36	minimal	minimal	ADJ
ejpam-3286	27	37	.	.	PUNCT
ejpam-3286	28	1	in	in	ADP
ejpam-3286	28	2	fact	fact	NOUN
ejpam-3286	28	3	,	,	PUNCT
ejpam-3286	28	4	one	one	PRON
ejpam-3286	28	5	investigates	investigate	VERB
ejpam-3286	28	6	the	the	DET
ejpam-3286	28	7	existence	existence	NOUN
ejpam-3286	28	8	of	of	ADP
ejpam-3286	28	9	such	such	ADJ
ejpam-3286	28	10	optimal	optimal	ADJ
ejpam-3286	28	11	approximate	approximate	ADJ
ejpam-3286	28	12	solutions	solution	NOUN
ejpam-3286	28	13	,	,	PUNCT
ejpam-3286	28	14	known	know	VERB
ejpam-3286	28	15	as	as	ADP
ejpam-3286	28	16	common	common	ADJ
ejpam-3286	28	17	best	good	ADJ
ejpam-3286	28	18	proximity	proximity	NOUN
ejpam-3286	28	19	points	point	NOUN
ejpam-3286	28	20	,	,	PUNCT
ejpam-3286	28	21	to	to	ADP
ejpam-3286	28	22	the	the	DET
ejpam-3286	28	23	equations	equation	NOUN
ejpam-3286	28	24	sx	sx	NOUN
ejpam-3286	28	25	=	=	PUNCT
ejpam-3286	28	26	x	x	PROPN
ejpam-3286	28	27	and	and	CCONJ
ejpam-3286	28	28	tx	tx	PROPN
ejpam-3286	28	29	=	=	PUNCT
ejpam-3286	28	30	x.	x.	NOUN
ejpam-3286	28	31	further	far	ADV
ejpam-3286	28	32	,	,	PUNCT
ejpam-3286	28	33	one	one	PRON
ejpam-3286	28	34	can	can	AUX
ejpam-3286	28	35	comprehend	comprehend	VERB
ejpam-3286	28	36	that	that	SCONJ
ejpam-3286	28	37	the	the	DET
ejpam-3286	28	38	real	real	ADV
ejpam-3286	28	39	valued	value	VERB
ejpam-3286	28	40	functions	function	NOUN
ejpam-3286	28	41	x	x	X
ejpam-3286	28	42	−→	−→	ADJ
ejpam-3286	28	43	d(x	d(x	PROPN
ejpam-3286	28	44	,	,	PUNCT
ejpam-3286	28	45	tx	tx	PROPN
ejpam-3286	28	46	)	)	PUNCT
ejpam-3286	28	47	and	and	CCONJ
ejpam-3286	28	48	x	x	ADJ
ejpam-3286	28	49	−→	−→	ADJ
ejpam-3286	28	50	d(x	d(x	PROPN
ejpam-3286	28	51	,	,	PUNCT
ejpam-3286	28	52	sx	sx	PROPN
ejpam-3286	28	53	)	)	PUNCT
ejpam-3286	28	54	approximate	approximate	VERB
ejpam-3286	28	55	the	the	DET
ejpam-3286	28	56	value	value	NOUN
ejpam-3286	28	57	of	of	ADP
ejpam-3286	28	58	the	the	DET
ejpam-3286	28	59	error	error	NOUN
ejpam-3286	28	60	of	of	ADP
ejpam-3286	28	61	proximate	proximate	NOUN
ejpam-3286	28	62	solution	solution	NOUN
ejpam-3286	28	63	of	of	ADP
ejpam-3286	28	64	the	the	DET
ejpam-3286	28	65	equations	equation	NOUN
ejpam-3286	28	66	tx	tx	VERB
ejpam-3286	28	67	=	=	PUNCT
ejpam-3286	29	1	x	x	PROPN
ejpam-3286	29	2	and	and	CCONJ
ejpam-3286	29	3	sx	sx	PROPN
ejpam-3286	29	4	=	=	PUNCT
ejpam-3286	29	5	x.	x.	NOUN
ejpam-3286	30	1	in	in	ADP
ejpam-3286	30	2	view	view	NOUN
ejpam-3286	30	3	of	of	ADP
ejpam-3286	30	4	the	the	DET
ejpam-3286	30	5	fact	fact	NOUN
ejpam-3286	30	6	that	that	SCONJ
ejpam-3286	30	7	d(a	d(a	PROPN
ejpam-3286	30	8	,	,	PUNCT
ejpam-3286	30	9	b	b	NOUN
ejpam-3286	30	10	)	)	PUNCT
ejpam-3286	30	11	≤	≤	NOUN
ejpam-3286	30	12	d(x	d(x	NOUN
ejpam-3286	30	13	,	,	PUNCT
ejpam-3286	30	14	tx	tx	PROPN
ejpam-3286	30	15	)	)	PUNCT
ejpam-3286	30	16	and	and	CCONJ
ejpam-3286	30	17	d(a	d(a	PROPN
ejpam-3286	30	18	,	,	PUNCT
ejpam-3286	30	19	b	b	NOUN
ejpam-3286	30	20	)	)	PUNCT
ejpam-3286	30	21	≤	≤	NOUN
ejpam-3286	30	22	d(x	d(x	NOUN
ejpam-3286	30	23	,	,	PUNCT
ejpam-3286	30	24	sx	sx	PROPN
ejpam-3286	30	25	)	)	PUNCT
ejpam-3286	30	26	,	,	PUNCT
ejpam-3286	30	27	a	a	DET
ejpam-3286	30	28	common	common	ADJ
ejpam-3286	30	29	best	good	ADJ
ejpam-3286	30	30	proximity	proximity	NOUN
ejpam-3286	30	31	point	point	NOUN
ejpam-3286	30	32	theorem	theorem	VERB
ejpam-3286	30	33	determines	determine	VERB
ejpam-3286	30	34	global	global	ADJ
ejpam-3286	30	35	minimum	minimum	NOUN
ejpam-3286	30	36	of	of	ADP
ejpam-3286	30	37	both	both	DET
ejpam-3286	30	38	functions	function	NOUN
ejpam-3286	30	39	x	x	X
ejpam-3286	30	40	−→	−→	ADJ
ejpam-3286	30	41	d(x	d(x	NOUN
ejpam-3286	30	42	,	,	PUNCT
ejpam-3286	30	43	tx	tx	PROPN
ejpam-3286	30	44	)	)	PUNCT
ejpam-3286	30	45	and	and	CCONJ
ejpam-3286	30	46	x	x	ADJ
ejpam-3286	30	47	−→	−→	ADJ
ejpam-3286	30	48	d(x	d(x	PROPN
ejpam-3286	30	49	,	,	PUNCT
ejpam-3286	30	50	sx	sx	PROPN
ejpam-3286	30	51	)	)	PUNCT
ejpam-3286	30	52	by	by	ADP
ejpam-3286	30	53	limiting	limit	VERB
ejpam-3286	30	54	a	a	DET
ejpam-3286	30	55	common	common	ADJ
ejpam-3286	30	56	approximate	approximate	ADJ
ejpam-3286	30	57	solution	solution	NOUN
ejpam-3286	30	58	of	of	ADP
ejpam-3286	30	59	the	the	DET
ejpam-3286	30	60	equations	equation	NOUN
ejpam-3286	30	61	tx	tx	VERB
ejpam-3286	30	62	=	=	PUNCT
ejpam-3286	31	1	x	x	PROPN
ejpam-3286	31	2	and	and	CCONJ
ejpam-3286	31	3	sx	sx	X
ejpam-3286	31	4	=	=	NOUN
ejpam-3286	31	5	x	x	VERB
ejpam-3286	31	6	to	to	PART
ejpam-3286	31	7	attain	attain	VERB
ejpam-3286	31	8	the	the	DET
ejpam-3286	31	9	requirement	requirement	NOUN
ejpam-3286	31	10	that	that	SCONJ
ejpam-3286	31	11	d(x	d(x	NOUN
ejpam-3286	31	12	,	,	PUNCT
ejpam-3286	31	13	sx	sx	PROPN
ejpam-3286	31	14	)	)	PUNCT
ejpam-3286	31	15	=	=	SYM
ejpam-3286	32	1	d(a	d(a	PROPN
ejpam-3286	32	2	,	,	PUNCT
ejpam-3286	32	3	b	b	NOUN
ejpam-3286	32	4	)	)	PUNCT
ejpam-3286	32	5	and	and	CCONJ
ejpam-3286	32	6	d(x	d(x	PROPN
ejpam-3286	32	7	,	,	PUNCT
ejpam-3286	32	8	tx	tx	PROPN
ejpam-3286	32	9	)	)	PUNCT
ejpam-3286	32	10	=	=	SYM
ejpam-3286	33	1	d(a	d(a	PROPN
ejpam-3286	33	2	,	,	PUNCT
ejpam-3286	33	3	b	b	NOUN
ejpam-3286	33	4	)	)	PUNCT
ejpam-3286	33	5	.	.	PUNCT
ejpam-3286	34	1	common	common	ADJ
ejpam-3286	34	2	best	good	ADJ
ejpam-3286	34	3	proximity	proximity	NOUN
ejpam-3286	34	4	point	point	NOUN
ejpam-3286	34	5	problem	problem	NOUN
ejpam-3286	34	6	was	be	AUX
ejpam-3286	34	7	studied	study	VERB
ejpam-3286	34	8	by	by	ADP
ejpam-3286	34	9	many	many	ADJ
ejpam-3286	34	10	mathematicians	mathematician	NOUN
ejpam-3286	34	11	(	(	PUNCT
ejpam-3286	34	12	see	see	VERB
ejpam-3286	34	13	[	[	X
ejpam-3286	34	14	7	7	NUM
ejpam-3286	34	15	]	]	PUNCT
ejpam-3286	34	16	,	,	PUNCT
ejpam-3286	34	17	[	[	X
ejpam-3286	34	18	8	8	NUM
ejpam-3286	34	19	]	]	PUNCT
ejpam-3286	34	20	and	and	CCONJ
ejpam-3286	34	21	[	[	X
ejpam-3286	34	22	11	11	NUM
ejpam-3286	34	23	]	]	NUM
ejpam-3286	34	24	)	)	PUNCT
ejpam-3286	34	25	.	.	PUNCT
ejpam-3286	35	1	2	2	X
ejpam-3286	35	2	.	.	X
ejpam-3286	35	3	preliminary	preliminary	ADJ
ejpam-3286	35	4	concepts	concept	NOUN
ejpam-3286	35	5	definition	definition	NOUN
ejpam-3286	35	6	1	1	NUM
ejpam-3286	35	7	.	.	PUNCT
ejpam-3286	36	1	an	an	DET
ejpam-3286	36	2	element	element	NOUN
ejpam-3286	36	3	x	x	SYM
ejpam-3286	36	4	∈	∈	PROPN
ejpam-3286	36	5	x	x	PUNCT
ejpam-3286	36	6	is	be	AUX
ejpam-3286	36	7	said	say	VERB
ejpam-3286	36	8	to	to	PART
ejpam-3286	36	9	be	be	AUX
ejpam-3286	36	10	common	common	ADJ
ejpam-3286	36	11	best	good	ADJ
ejpam-3286	36	12	proximity	proximity	NOUN
ejpam-3286	36	13	point	point	NOUN
ejpam-3286	36	14	of	of	ADP
ejpam-3286	36	15	the	the	DET
ejpam-3286	36	16	nonself	nonself	NOUN
ejpam-3286	36	17	-	-	PUNCT
ejpam-3286	36	18	mappings	mapping	NOUN
ejpam-3286	36	19	s	s	PART
ejpam-3286	36	20	:	:	PUNCT
ejpam-3286	36	21	a	a	DET
ejpam-3286	36	22	−→	−→	NOUN
ejpam-3286	36	23	b	b	NOUN
ejpam-3286	36	24	and	and	CCONJ
ejpam-3286	36	25	t	t	PROPN
ejpam-3286	36	26	:	:	PUNCT
ejpam-3286	36	27	a	a	DET
ejpam-3286	36	28	−→	−→	NOUN
ejpam-3286	36	29	b	b	NOUN
ejpam-3286	36	30	if	if	SCONJ
ejpam-3286	36	31	it	it	PRON
ejpam-3286	36	32	satisfies	satisfy	VERB
ejpam-3286	36	33	the	the	DET
ejpam-3286	36	34	condition	condition	NOUN
ejpam-3286	36	35	that	that	SCONJ
ejpam-3286	36	36	d(x	d(x	NOUN
ejpam-3286	36	37	,	,	PUNCT
ejpam-3286	36	38	sx	sx	PROPN
ejpam-3286	36	39	)	)	PUNCT
ejpam-3286	36	40	=	=	SYM
ejpam-3286	36	41	d(x	d(x	PROPN
ejpam-3286	36	42	,	,	PUNCT
ejpam-3286	36	43	tx	tx	PROPN
ejpam-3286	36	44	)	)	PUNCT
ejpam-3286	37	1	=	=	SYM
ejpam-3286	37	2	d(a	d(a	PROPN
ejpam-3286	37	3	,	,	PUNCT
ejpam-3286	37	4	b	b	NOUN
ejpam-3286	37	5	)	)	PUNCT
ejpam-3286	37	6	.	.	PUNCT
ejpam-3286	38	1	definition	definition	NOUN
ejpam-3286	38	2	2	2	NUM
ejpam-3286	38	3	.	.	PUNCT
ejpam-3286	39	1	[	[	X
ejpam-3286	39	2	4	4	X
ejpam-3286	39	3	]	]	X
ejpam-3286	39	4	a	a	DET
ejpam-3286	39	5	function	function	NOUN
ejpam-3286	39	6	φ	φ	NOUN
ejpam-3286	39	7	:	:	PUNCT
ejpam-3286	40	1	[	[	X
ejpam-3286	40	2	0,+∞	0,+∞	NUM
ejpam-3286	40	3	)	)	PUNCT
ejpam-3286	40	4	−→	−→	NOUN
ejpam-3286	40	5	[	[	X
ejpam-3286	40	6	0,+∞	0,+∞	NUM
ejpam-3286	40	7	)	)	PUNCT
ejpam-3286	40	8	is	be	AUX
ejpam-3286	40	9	called	call	VERB
ejpam-3286	40	10	a	a	DET
ejpam-3286	40	11	comparison	comparison	NOUN
ejpam-3286	40	12	if	if	SCONJ
ejpam-3286	40	13	it	it	PRON
ejpam-3286	40	14	satisfies	satisfy	VERB
ejpam-3286	40	15	the	the	DET
ejpam-3286	40	16	following	follow	VERB
ejpam-3286	40	17	conditions	condition	NOUN
ejpam-3286	40	18	:	:	PUNCT
ejpam-3286	40	19	•	•	NUM
ejpam-3286	40	20	φ	φ	PROPN
ejpam-3286	40	21	is	be	AUX
ejpam-3286	40	22	increasing	increase	VERB
ejpam-3286	40	23	,	,	PUNCT
ejpam-3286	40	24	•	•	ADP
ejpam-3286	40	25	the	the	DET
ejpam-3286	40	26	sequence	sequence	NOUN
ejpam-3286	40	27	(	(	PUNCT
ejpam-3286	40	28	φn(t))n∈n	φn(t))n∈n	SCONJ
ejpam-3286	40	29	converges	converge	NOUN
ejpam-3286	40	30	to	to	ADP
ejpam-3286	40	31	0	0	NUM
ejpam-3286	40	32	as	as	ADP
ejpam-3286	40	33	n→	n→	ADV
ejpam-3286	40	34	+	+	PROPN
ejpam-3286	40	35	∞	∞	PROPN
ejpam-3286	40	36	,	,	PUNCT
ejpam-3286	40	37	for	for	ADP
ejpam-3286	40	38	all	all	DET
ejpam-3286	40	39	t	t	NOUN
ejpam-3286	40	40	∈	∈	PROPN
ejpam-3286	41	1	[	[	X
ejpam-3286	41	2	0,+∞	0,+∞	NUM
ejpam-3286	41	3	)	)	PUNCT
ejpam-3286	41	4	.	.	PUNCT
ejpam-3286	42	1	we	we	PRON
ejpam-3286	42	2	recall	recall	VERB
ejpam-3286	42	3	that	that	SCONJ
ejpam-3286	42	4	a	a	DET
ejpam-3286	42	5	self	self	NOUN
ejpam-3286	42	6	-	-	PUNCT
ejpam-3286	42	7	mapping	mapping	NOUN
ejpam-3286	42	8	t	t	NOUN
ejpam-3286	42	9	on	on	ADP
ejpam-3286	42	10	a	a	DET
ejpam-3286	42	11	metric	metric	ADJ
ejpam-3286	42	12	space	space	NOUN
ejpam-3286	42	13	(	(	PUNCT
ejpam-3286	42	14	x	x	X
ejpam-3286	42	15	,	,	PUNCT
ejpam-3286	42	16	d	d	NOUN
ejpam-3286	42	17	)	)	PUNCT
ejpam-3286	42	18	is	be	AUX
ejpam-3286	42	19	said	say	VERB
ejpam-3286	42	20	to	to	PART
ejpam-3286	42	21	be	be	AUX
ejpam-3286	42	22	φ−contraction	φ−contraction	NOUN
ejpam-3286	42	23	if	if	SCONJ
ejpam-3286	42	24	d(t	d(t	PROPN
ejpam-3286	42	25	(	(	PUNCT
ejpam-3286	42	26	x	x	NOUN
ejpam-3286	42	27	)	)	PUNCT
ejpam-3286	42	28	,	,	PUNCT
ejpam-3286	42	29	t	t	PROPN
ejpam-3286	42	30	(	(	PUNCT
ejpam-3286	42	31	y	y	NOUN
ejpam-3286	42	32	)	)	PUNCT
ejpam-3286	42	33	)	)	PUNCT
ejpam-3286	42	34	≤	≤	ADV
ejpam-3286	43	1	φ(d(x	φ(d(x	PROPN
ejpam-3286	43	2	,	,	PUNCT
ejpam-3286	43	3	y	y	NOUN
ejpam-3286	43	4	)	)	PUNCT
ejpam-3286	43	5	)	)	PUNCT
ejpam-3286	44	1	for	for	ADP
ejpam-3286	44	2	any	any	DET
ejpam-3286	44	3	x	x	NOUN
ejpam-3286	44	4	,	,	PUNCT
ejpam-3286	44	5	y	y	PROPN
ejpam-3286	44	6	∈	∈	PROPN
ejpam-3286	44	7	x	x	X
ejpam-3286	44	8	;	;	PUNCT
ejpam-3286	44	9	where	where	SCONJ
ejpam-3286	44	10	φ	φ	PROPN
ejpam-3286	44	11	is	be	AUX
ejpam-3286	44	12	comparison	comparison	NOUN
ejpam-3286	44	13	function	function	NOUN
ejpam-3286	44	14	.	.	PUNCT
ejpam-3286	45	1	remark	remark	PROPN
ejpam-3286	45	2	1	1	NUM
ejpam-3286	45	3	.	.	PUNCT
ejpam-3286	46	1	if	if	SCONJ
ejpam-3286	46	2	φ	φ	PROPN
ejpam-3286	46	3	is	be	AUX
ejpam-3286	46	4	comparison	comparison	NOUN
ejpam-3286	46	5	function	function	NOUN
ejpam-3286	46	6	then	then	ADV
ejpam-3286	46	7	•	•	NUM
ejpam-3286	46	8	φ(t	φ(t	PROPN
ejpam-3286	46	9	)	)	PUNCT
ejpam-3286	46	10	<	<	X
ejpam-3286	46	11	t	t	PROPN
ejpam-3286	46	12	for	for	ADP
ejpam-3286	46	13	any	any	DET
ejpam-3286	46	14	t	t	NOUN
ejpam-3286	46	15	∈	∈	PROPN
ejpam-3286	46	16	(	(	PUNCT
ejpam-3286	46	17	0,+∞	0,+∞	NUM
ejpam-3286	46	18	)	)	PUNCT
ejpam-3286	46	19	,	,	PUNCT
ejpam-3286	46	20	•	•	X
ejpam-3286	46	21	φ(t	φ(t	PROPN
ejpam-3286	46	22	)	)	PUNCT
ejpam-3286	46	23	=	=	SYM
ejpam-3286	46	24	0	0	PUNCT
ejpam-3286	47	1	if	if	SCONJ
ejpam-3286	47	2	and	and	CCONJ
ejpam-3286	47	3	only	only	ADV
ejpam-3286	47	4	if	if	SCONJ
ejpam-3286	47	5	t	t	PROPN
ejpam-3286	47	6	=	=	SYM
ejpam-3286	47	7	0	0	X
ejpam-3286	47	8	.	.	PUNCT
ejpam-3286	47	9	lemma	lemma	PROPN
ejpam-3286	47	10	1	1	NUM
ejpam-3286	47	11	.	.	PUNCT
ejpam-3286	48	1	[	[	X
ejpam-3286	48	2	4	4	X
ejpam-3286	48	3	]	]	X
ejpam-3286	48	4	let	let	VERB
ejpam-3286	48	5	(	(	PUNCT
ejpam-3286	48	6	x	x	NOUN
ejpam-3286	48	7	,	,	PUNCT
ejpam-3286	48	8	d	d	NOUN
ejpam-3286	48	9	)	)	PUNCT
ejpam-3286	48	10	be	be	AUX
ejpam-3286	48	11	a	a	DET
ejpam-3286	48	12	metric	metric	ADJ
ejpam-3286	48	13	space	space	NOUN
ejpam-3286	48	14	and	and	CCONJ
ejpam-3286	48	15	let	let	VERB
ejpam-3286	48	16	(	(	PUNCT
ejpam-3286	48	17	xn)n∈n	xn)n∈n	NUM
ejpam-3286	48	18	be	be	AUX
ejpam-3286	48	19	a	a	DET
ejpam-3286	48	20	sequence	sequence	NOUN
ejpam-3286	48	21	in	in	ADP
ejpam-3286	48	22	x	x	INTJ
ejpam-3286	48	23	such	such	ADJ
ejpam-3286	48	24	that	that	DET
ejpam-3286	48	25	d(xn+1	d(xn+1	PROPN
ejpam-3286	48	26	,	,	PUNCT
ejpam-3286	48	27	xn	xn	PROPN
ejpam-3286	48	28	)	)	PUNCT
ejpam-3286	48	29	→	→	SYM
ejpam-3286	48	30	0	0	X
ejpam-3286	48	31	.	.	PUNCT
ejpam-3286	49	1	if	if	SCONJ
ejpam-3286	49	2	(	(	PUNCT
ejpam-3286	49	3	xn)n∈n	xn)n∈n	PROPN
ejpam-3286	49	4	is	be	AUX
ejpam-3286	49	5	not	not	PART
ejpam-3286	49	6	cauchy	cauchy	ADJ
ejpam-3286	49	7	sequence	sequence	NOUN
ejpam-3286	49	8	then	then	ADV
ejpam-3286	49	9	there	there	PRON
ejpam-3286	49	10	exists	exist	VERB
ejpam-3286	49	11	ε	ε	PROPN
ejpam-3286	49	12	>	>	PUNCT
ejpam-3286	49	13	0	0	PUNCT
ejpam-3286	50	1	and	and	CCONJ
ejpam-3286	50	2	sequences	sequence	NOUN
ejpam-3286	50	3	(	(	PUNCT
ejpam-3286	50	4	n(k	n(k	PROPN
ejpam-3286	50	5	)	)	PUNCT
ejpam-3286	50	6	)	)	PUNCT
ejpam-3286	51	1	and	and	CCONJ
ejpam-3286	51	2	(	(	PUNCT
ejpam-3286	51	3	m(k	m(k	PROPN
ejpam-3286	51	4	)	)	PUNCT
ejpam-3286	51	5	)	)	PUNCT
ejpam-3286	51	6	of	of	ADP
ejpam-3286	51	7	positive	positive	ADJ
ejpam-3286	51	8	integers	integer	NOUN
ejpam-3286	51	9	such	such	ADJ
ejpam-3286	51	10	that	that	SCONJ
ejpam-3286	51	11	the	the	DET
ejpam-3286	51	12	following	follow	VERB
ejpam-3286	51	13	sequences	sequence	NOUN
ejpam-3286	51	14	tend	tend	VERB
ejpam-3286	51	15	to	to	PART
ejpam-3286	51	16	ε	ε	VERB
ejpam-3286	51	17	as	as	ADP
ejpam-3286	51	18	k	k	PROPN
ejpam-3286	51	19	→	→	PROPN
ejpam-3286	51	20	+	+	ADJ
ejpam-3286	51	21	∞	∞	NOUN
ejpam-3286	51	22	:	:	PUNCT
ejpam-3286	51	23	d(xm(k	d(xm(k	ADJ
ejpam-3286	51	24	)	)	PUNCT
ejpam-3286	51	25	,	,	PUNCT
ejpam-3286	51	26	xn(k	xn(k	NUM
ejpam-3286	51	27	)	)	PUNCT
ejpam-3286	51	28	)	)	PUNCT
ejpam-3286	51	29	,	,	PUNCT
ejpam-3286	51	30	d(xm(k	d(xm(k	PROPN
ejpam-3286	51	31	)	)	PUNCT
ejpam-3286	51	32	,	,	PUNCT
ejpam-3286	51	33	xn(k)+1	xn(k)+1	PROPN
ejpam-3286	51	34	)	)	PUNCT
ejpam-3286	51	35	,	,	PUNCT
ejpam-3286	51	36	d(xm(k)−1	d(xm(k)−1	PROPN
ejpam-3286	51	37	,	,	PUNCT
ejpam-3286	51	38	xn(k	xn(k	NUM
ejpam-3286	51	39	)	)	PUNCT
ejpam-3286	51	40	)	)	PUNCT
ejpam-3286	51	41	,	,	PUNCT
ejpam-3286	51	42	d(xm(k)−1	d(xm(k)−1	PROPN
ejpam-3286	51	43	,	,	PUNCT
ejpam-3286	51	44	xn(k)+1	xn(k)+1	PROPN
ejpam-3286	51	45	)	)	PUNCT
ejpam-3286	51	46	,	,	PUNCT
ejpam-3286	51	47	d(xm(k)+1	d(xm(k)+1	NOUN
ejpam-3286	51	48	,	,	PUNCT
ejpam-3286	51	49	xn(k)+1	xn(k)+1	PROPN
ejpam-3286	51	50	)	)	PUNCT
ejpam-3286	51	51	,	,	PUNCT
ejpam-3286	51	52	d(xm(k)+1	d(xm(k)+1	NOUN
ejpam-3286	51	53	,	,	PUNCT
ejpam-3286	51	54	xn(k	xn(k	NUM
ejpam-3286	51	55	)	)	PUNCT
ejpam-3286	51	56	)	)	PUNCT
ejpam-3286	51	57	.	.	PUNCT
ejpam-3286	52	1	definition	definition	NOUN
ejpam-3286	52	2	3	3	X
ejpam-3286	52	3	.	.	PUNCT
ejpam-3286	53	1	let	let	VERB
ejpam-3286	53	2	s	s	PRON
ejpam-3286	53	3	:	:	PUNCT
ejpam-3286	53	4	a	a	DET
ejpam-3286	53	5	−→	−→	NOUN
ejpam-3286	53	6	b	b	NOUN
ejpam-3286	53	7	,	,	PUNCT
ejpam-3286	53	8	t	t	X
ejpam-3286	53	9	:	:	PUNCT
ejpam-3286	53	10	a	a	DET
ejpam-3286	53	11	−→	−→	NOUN
ejpam-3286	53	12	b	b	PROPN
ejpam-3286	53	13	and	and	CCONJ
ejpam-3286	53	14	f	f	NOUN
ejpam-3286	53	15	:	:	PUNCT
ejpam-3286	53	16	b	b	X
ejpam-3286	53	17	−→	−→	NOUN
ejpam-3286	53	18	a	a	PRON
ejpam-3286	53	19	be	be	AUX
ejpam-3286	53	20	given	give	VERB
ejpam-3286	53	21	.	.	PUNCT
ejpam-3286	54	1	f	f	PROPN
ejpam-3286	54	2	is	be	AUX
ejpam-3286	54	3	said	say	VERB
ejpam-3286	54	4	to	to	PART
ejpam-3286	54	5	commute	commute	VERB
ejpam-3286	54	6	with	with	ADP
ejpam-3286	54	7	the	the	DET
ejpam-3286	54	8	pair	pair	NOUN
ejpam-3286	54	9	(	(	PUNCT
ejpam-3286	54	10	s	s	PROPN
ejpam-3286	54	11	,	,	PUNCT
ejpam-3286	54	12	t	t	PROPN
ejpam-3286	54	13	)	)	PUNCT
ejpam-3286	55	1	if	if	SCONJ
ejpam-3286	55	2	sft	sft	NOUN
ejpam-3286	55	3	=	=	SYM
ejpam-3286	55	4	tfs	tfs	PROPN
ejpam-3286	55	5	.	.	PUNCT
ejpam-3286	55	6	m.	m.	PROPN
ejpam-3286	55	7	iranmanesh	iranmanesh	PROPN
ejpam-3286	55	8	,	,	PUNCT
ejpam-3286	55	9	a.	a.	NOUN
ejpam-3286	55	10	g.	g.	PROPN
ejpam-3286	55	11	sanatee	sanatee	PROPN
ejpam-3286	55	12	/	/	SYM
ejpam-3286	55	13	eur	eur	PROPN
ejpam-3286	55	14	.	.	PUNCT
ejpam-3286	56	1	j.	j.	PROPN
ejpam-3286	56	2	pure	pure	PROPN
ejpam-3286	56	3	appl	appl	PROPN
ejpam-3286	56	4	.	.	PROPN
ejpam-3286	56	5	math	math	PROPN
ejpam-3286	56	6	,	,	PUNCT
ejpam-3286	56	7	11	11	NUM
ejpam-3286	56	8	(	(	PUNCT
ejpam-3286	56	9	3	3	NUM
ejpam-3286	56	10	)	)	PUNCT
ejpam-3286	56	11	(	(	PUNCT
ejpam-3286	56	12	2018	2018	NUM
ejpam-3286	56	13	)	)	PUNCT
ejpam-3286	56	14	,	,	PUNCT
ejpam-3286	56	15	869	869	NUM
ejpam-3286	56	16	-	-	SYM
ejpam-3286	56	17	875	875	NUM
ejpam-3286	56	18	871	871	NUM
ejpam-3286	56	19	definition	definition	NOUN
ejpam-3286	56	20	4	4	NUM
ejpam-3286	56	21	.	.	PUNCT
ejpam-3286	57	1	let	let	VERB
ejpam-3286	57	2	s	s	PRON
ejpam-3286	57	3	:	:	PUNCT
ejpam-3286	57	4	a	a	DET
ejpam-3286	57	5	−→	−→	NOUN
ejpam-3286	57	6	b	b	NOUN
ejpam-3286	57	7	,	,	PUNCT
ejpam-3286	57	8	t	t	X
ejpam-3286	57	9	:	:	PUNCT
ejpam-3286	57	10	a	a	DET
ejpam-3286	57	11	−→	−→	NOUN
ejpam-3286	57	12	b	b	NOUN
ejpam-3286	57	13	,	,	PUNCT
ejpam-3286	57	14	f	f	X
ejpam-3286	57	15	:	:	PUNCT
ejpam-3286	58	1	b	b	X
ejpam-3286	58	2	−→	−→	NOUN
ejpam-3286	58	3	a	a	PRON
ejpam-3286	58	4	and	and	CCONJ
ejpam-3286	58	5	g	g	NOUN
ejpam-3286	58	6	:	:	PUNCT
ejpam-3286	58	7	b	b	X
ejpam-3286	58	8	−→	−→	NOUN
ejpam-3286	58	9	a	a	DET
ejpam-3286	58	10	be	be	NOUN
ejpam-3286	58	11	mappings	mapping	NOUN
ejpam-3286	58	12	.	.	PUNCT
ejpam-3286	59	1	the	the	DET
ejpam-3286	59	2	pair	pair	NOUN
ejpam-3286	59	3	(	(	PUNCT
ejpam-3286	59	4	f	f	X
ejpam-3286	59	5	,	,	PUNCT
ejpam-3286	59	6	s	s	PART
ejpam-3286	59	7	)	)	PUNCT
ejpam-3286	59	8	is	be	AUX
ejpam-3286	59	9	said	say	VERB
ejpam-3286	59	10	to	to	PART
ejpam-3286	59	11	be	be	AUX
ejpam-3286	59	12	φ−dominated	φ−dominate	VERB
ejpam-3286	59	13	by	by	ADP
ejpam-3286	59	14	the	the	DET
ejpam-3286	59	15	pair	pair	NOUN
ejpam-3286	59	16	(	(	PUNCT
ejpam-3286	59	17	g	g	NOUN
ejpam-3286	59	18	,	,	PUNCT
ejpam-3286	59	19	t	t	PROPN
ejpam-3286	59	20	)	)	PUNCT
ejpam-3286	59	21	if	if	SCONJ
ejpam-3286	59	22	for	for	ADP
ejpam-3286	59	23	any	any	DET
ejpam-3286	59	24	x	x	SYM
ejpam-3286	59	25	∈	∈	PROPN
ejpam-3286	59	26	a	a	PRON
ejpam-3286	59	27	and	and	CCONJ
ejpam-3286	59	28	y	y	PROPN
ejpam-3286	59	29	∈	∈	PROPN
ejpam-3286	60	1	b	b	NOUN
ejpam-3286	61	1	it	it	PRON
ejpam-3286	61	2	satisfies	satisfy	VERB
ejpam-3286	61	3	the	the	DET
ejpam-3286	61	4	condition	condition	NOUN
ejpam-3286	61	5	that	that	SCONJ
ejpam-3286	61	6	d(fsx	d(fsx	NOUN
ejpam-3286	61	7	,	,	PUNCT
ejpam-3286	61	8	fsy	fsy	ADJ
ejpam-3286	61	9	)	)	PUNCT
ejpam-3286	61	10	≤	≤	NOUN
ejpam-3286	61	11	φ(d(gtx	φ(d(gtx	PROPN
ejpam-3286	61	12	,	,	PUNCT
ejpam-3286	61	13	gty	gty	NOUN
ejpam-3286	61	14	)	)	PUNCT
ejpam-3286	61	15	)	)	PUNCT
ejpam-3286	61	16	where	where	SCONJ
ejpam-3286	61	17	φ	φ	PROPN
ejpam-3286	61	18	is	be	AUX
ejpam-3286	61	19	comparison	comparison	NOUN
ejpam-3286	61	20	function	function	NOUN
ejpam-3286	61	21	.	.	PUNCT
ejpam-3286	62	1	3	3	X
ejpam-3286	62	2	.	.	X
ejpam-3286	62	3	main	main	ADJ
ejpam-3286	62	4	results	result	NOUN
ejpam-3286	62	5	from	from	ADP
ejpam-3286	62	6	here	here	ADV
ejpam-3286	62	7	throughout	throughout	ADP
ejpam-3286	62	8	this	this	DET
ejpam-3286	62	9	paper	paper	NOUN
ejpam-3286	62	10	,	,	PUNCT
ejpam-3286	62	11	x	x	PRON
ejpam-3286	62	12	denotes	denote	VERB
ejpam-3286	62	13	a	a	DET
ejpam-3286	62	14	complete	complete	ADJ
ejpam-3286	62	15	metric	metric	ADJ
ejpam-3286	62	16	space	space	NOUN
ejpam-3286	62	17	and	and	CCONJ
ejpam-3286	62	18	a	a	PRON
ejpam-3286	62	19	and	and	CCONJ
ejpam-3286	62	20	b	b	NOUN
ejpam-3286	62	21	are	be	AUX
ejpam-3286	62	22	its	its	PRON
ejpam-3286	62	23	nonempty	nonempty	ADJ
ejpam-3286	62	24	subsets	subset	NOUN
ejpam-3286	62	25	.	.	PUNCT
ejpam-3286	63	1	now	now	ADV
ejpam-3286	63	2	,	,	PUNCT
ejpam-3286	63	3	we	we	PRON
ejpam-3286	63	4	are	be	AUX
ejpam-3286	63	5	ready	ready	ADJ
ejpam-3286	63	6	to	to	PART
ejpam-3286	63	7	present	present	VERB
ejpam-3286	63	8	our	our	PRON
ejpam-3286	63	9	main	main	ADJ
ejpam-3286	63	10	result	result	NOUN
ejpam-3286	63	11	.	.	PUNCT
ejpam-3286	64	1	theorem	theorem	NOUN
ejpam-3286	64	2	1	1	X
ejpam-3286	64	3	.	.	PUNCT
ejpam-3286	65	1	let	let	VERB
ejpam-3286	65	2	a	a	PRON
ejpam-3286	65	3	and	and	CCONJ
ejpam-3286	65	4	b	b	NOUN
ejpam-3286	65	5	be	be	AUX
ejpam-3286	65	6	closed	close	VERB
ejpam-3286	65	7	.	.	PUNCT
ejpam-3286	66	1	moreover	moreover	ADV
ejpam-3286	66	2	,	,	PUNCT
ejpam-3286	66	3	assume	assume	VERB
ejpam-3286	66	4	that	that	SCONJ
ejpam-3286	66	5	s	s	VERB
ejpam-3286	66	6	:	:	PUNCT
ejpam-3286	66	7	a	a	DET
ejpam-3286	66	8	−→	−→	NOUN
ejpam-3286	66	9	b	b	NOUN
ejpam-3286	66	10	,	,	PUNCT
ejpam-3286	66	11	t	t	X
ejpam-3286	66	12	:	:	PUNCT
ejpam-3286	66	13	a	a	DET
ejpam-3286	66	14	−→	−→	NOUN
ejpam-3286	66	15	b	b	NOUN
ejpam-3286	66	16	,	,	PUNCT
ejpam-3286	66	17	f	f	X
ejpam-3286	66	18	:	:	PUNCT
ejpam-3286	67	1	b	b	X
ejpam-3286	67	2	−→	−→	NOUN
ejpam-3286	67	3	a	a	PRON
ejpam-3286	67	4	and	and	CCONJ
ejpam-3286	67	5	g	g	NOUN
ejpam-3286	67	6	:	:	PUNCT
ejpam-3286	67	7	b	b	X
ejpam-3286	67	8	−→	−→	NOUN
ejpam-3286	67	9	a	a	PRON
ejpam-3286	67	10	are	be	AUX
ejpam-3286	67	11	continuous	continuous	ADJ
ejpam-3286	67	12	functions	function	NOUN
ejpam-3286	67	13	satisfying	satisfy	VERB
ejpam-3286	67	14	the	the	DET
ejpam-3286	67	15	following	follow	VERB
ejpam-3286	67	16	conditions	condition	NOUN
ejpam-3286	67	17	:	:	PUNCT
ejpam-3286	67	18	(	(	PUNCT
ejpam-3286	67	19	1	1	X
ejpam-3286	67	20	)	)	PUNCT
ejpam-3286	67	21	fs	fs	ADP
ejpam-3286	67	22	commutes	commute	NOUN
ejpam-3286	67	23	with	with	ADP
ejpam-3286	67	24	gt	gt	PROPN
ejpam-3286	67	25	and	and	CCONJ
ejpam-3286	67	26	sf	sf	ADJ
ejpam-3286	67	27	commutes	commute	NOUN
ejpam-3286	67	28	with	with	ADP
ejpam-3286	67	29	tg	tg	PROPN
ejpam-3286	67	30	.	.	PUNCT
ejpam-3286	68	1	(	(	PUNCT
ejpam-3286	68	2	2	2	NUM
ejpam-3286	68	3	)	)	PUNCT
ejpam-3286	68	4	(	(	PUNCT
ejpam-3286	68	5	f	f	X
ejpam-3286	68	6	,	,	PUNCT
ejpam-3286	68	7	s	s	PART
ejpam-3286	68	8	)	)	PUNCT
ejpam-3286	68	9	is	be	AUX
ejpam-3286	68	10	φ−dominated	φ−dominate	VERB
ejpam-3286	68	11	by	by	ADP
ejpam-3286	68	12	(	(	PUNCT
ejpam-3286	68	13	g	g	PROPN
ejpam-3286	68	14	,	,	PUNCT
ejpam-3286	68	15	t	t	PROPN
ejpam-3286	68	16	)	)	PUNCT
ejpam-3286	68	17	and	and	CCONJ
ejpam-3286	68	18	(	(	PUNCT
ejpam-3286	68	19	s	s	X
ejpam-3286	68	20	,	,	PUNCT
ejpam-3286	68	21	f	f	PROPN
ejpam-3286	68	22	)	)	PUNCT
ejpam-3286	68	23	is	be	AUX
ejpam-3286	68	24	ψ−dominated	ψ−dominate	VERB
ejpam-3286	68	25	by	by	ADP
ejpam-3286	68	26	(	(	PUNCT
ejpam-3286	68	27	t	t	PROPN
ejpam-3286	68	28	,	,	PUNCT
ejpam-3286	68	29	g	g	NOUN
ejpam-3286	68	30	)	)	PUNCT
ejpam-3286	68	31	,	,	PUNCT
ejpam-3286	68	32	where	where	SCONJ
ejpam-3286	68	33	φ	φ	PROPN
ejpam-3286	68	34	and	and	CCONJ
ejpam-3286	68	35	ψ	ψ	PROPN
ejpam-3286	68	36	are	be	AUX
ejpam-3286	68	37	comparison	comparison	NOUN
ejpam-3286	68	38	functions	function	NOUN
ejpam-3286	68	39	.	.	PUNCT
ejpam-3286	69	1	(	(	PUNCT
ejpam-3286	69	2	3	3	X
ejpam-3286	69	3	)	)	PUNCT
ejpam-3286	69	4	fs(a	fs(a	NOUN
ejpam-3286	69	5	)	)	PUNCT
ejpam-3286	70	1	⊂	⊂	PROPN
ejpam-3286	70	2	gt	gt	PROPN
ejpam-3286	70	3	(	(	PUNCT
ejpam-3286	70	4	a	a	NOUN
ejpam-3286	70	5	)	)	PUNCT
ejpam-3286	70	6	and	and	CCONJ
ejpam-3286	70	7	sf	sf	INTJ
ejpam-3286	70	8	(	(	PUNCT
ejpam-3286	70	9	b	b	NOUN
ejpam-3286	70	10	)	)	PUNCT
ejpam-3286	70	11	⊂	⊂	PROPN
ejpam-3286	70	12	tg(b	tg(b	NOUN
ejpam-3286	70	13	)	)	PUNCT
ejpam-3286	70	14	.	.	PUNCT
ejpam-3286	71	1	(	(	PUNCT
ejpam-3286	71	2	4	4	X
ejpam-3286	71	3	)	)	PUNCT
ejpam-3286	71	4	s	s	PART
ejpam-3286	71	5	and	and	CCONJ
ejpam-3286	71	6	t	t	PROPN
ejpam-3286	71	7	commute	commute	NOUN
ejpam-3286	71	8	with	with	ADP
ejpam-3286	71	9	the	the	DET
ejpam-3286	71	10	pair	pair	NOUN
ejpam-3286	71	11	(	(	PUNCT
ejpam-3286	71	12	f	f	X
ejpam-3286	71	13	,	,	PUNCT
ejpam-3286	71	14	g	g	NOUN
ejpam-3286	71	15	)	)	PUNCT
ejpam-3286	71	16	,	,	PUNCT
ejpam-3286	71	17	and	and	CCONJ
ejpam-3286	71	18	f	f	PROPN
ejpam-3286	71	19	and	and	CCONJ
ejpam-3286	71	20	g	g	PROPN
ejpam-3286	71	21	commute	commute	NOUN
ejpam-3286	71	22	with	with	ADP
ejpam-3286	71	23	the	the	DET
ejpam-3286	71	24	pair	pair	NOUN
ejpam-3286	71	25	(	(	PUNCT
ejpam-3286	71	26	s	s	PROPN
ejpam-3286	71	27	,	,	PUNCT
ejpam-3286	71	28	t	t	PROPN
ejpam-3286	71	29	)	)	PUNCT
ejpam-3286	71	30	.	.	PUNCT
ejpam-3286	72	1	(	(	PUNCT
ejpam-3286	72	2	5	5	X
ejpam-3286	72	3	)	)	PUNCT
ejpam-3286	72	4	there	there	PRON
ejpam-3286	72	5	is	be	VERB
ejpam-3286	72	6	a	a	DET
ejpam-3286	72	7	non	non	ADJ
ejpam-3286	72	8	-	-	ADJ
ejpam-3286	72	9	negative	negative	ADJ
ejpam-3286	72	10	number	number	NOUN
ejpam-3286	72	11	α	α	NOUN
ejpam-3286	72	12	<	<	X
ejpam-3286	72	13	1	1	NUM
ejpam-3286	72	14	such	such	ADJ
ejpam-3286	72	15	that	that	PRON
ejpam-3286	72	16	for	for	ADP
ejpam-3286	72	17	all	all	PRON
ejpam-3286	72	18	x	x	SYM
ejpam-3286	72	19	∈	∈	PROPN
ejpam-3286	72	20	a	a	DET
ejpam-3286	72	21	d(sx	d(sx	NOUN
ejpam-3286	72	22	,	,	PUNCT
ejpam-3286	72	23	fsx	fsx	NOUN
ejpam-3286	72	24	)	)	PUNCT
ejpam-3286	72	25	≤	≤	NOUN
ejpam-3286	72	26	αd(tx	αd(tx	PROPN
ejpam-3286	72	27	,	,	PUNCT
ejpam-3286	72	28	gtx	gtx	ADJ
ejpam-3286	72	29	)	)	PUNCT
ejpam-3286	73	1	+	+	CCONJ
ejpam-3286	73	2	(	(	PUNCT
ejpam-3286	73	3	1−	1−	NUM
ejpam-3286	73	4	α)d(a	α)d(a	PROPN
ejpam-3286	73	5	,	,	PUNCT
ejpam-3286	73	6	b	b	NOUN
ejpam-3286	73	7	)	)	PUNCT
ejpam-3286	73	8	.	.	PUNCT
ejpam-3286	74	1	then	then	ADV
ejpam-3286	74	2	,	,	PUNCT
ejpam-3286	74	3	there	there	PRON
ejpam-3286	74	4	exists	exist	VERB
ejpam-3286	74	5	u	u	PROPN
ejpam-3286	74	6	∈	∈	PROPN
ejpam-3286	74	7	a	a	PRON
ejpam-3286	74	8	and	and	CCONJ
ejpam-3286	74	9	v	v	ADP
ejpam-3286	74	10	∈	∈	PROPN
ejpam-3286	74	11	b	b	NOUN
ejpam-3286	74	12	such	such	ADJ
ejpam-3286	74	13	that	that	SCONJ
ejpam-3286	74	14	d(u	d(u	PROPN
ejpam-3286	74	15	,	,	PUNCT
ejpam-3286	74	16	su	su	NOUN
ejpam-3286	74	17	)	)	PUNCT
ejpam-3286	74	18	=	=	SYM
ejpam-3286	74	19	d(u	d(u	PROPN
ejpam-3286	74	20	,	,	PUNCT
ejpam-3286	74	21	tu	tu	PROPN
ejpam-3286	74	22	)	)	PUNCT
ejpam-3286	74	23	=	=	SYM
ejpam-3286	75	1	d(a	d(a	PROPN
ejpam-3286	75	2	,	,	PUNCT
ejpam-3286	75	3	b	b	NOUN
ejpam-3286	75	4	)	)	PUNCT
ejpam-3286	75	5	d(v	d(v	PROPN
ejpam-3286	75	6	,	,	PUNCT
ejpam-3286	75	7	fv	fv	NOUN
ejpam-3286	75	8	)	)	PUNCT
ejpam-3286	75	9	=	=	SYM
ejpam-3286	75	10	d(v	d(v	PROPN
ejpam-3286	75	11	,	,	PUNCT
ejpam-3286	75	12	gv	gv	X
ejpam-3286	75	13	)	)	PUNCT
ejpam-3286	75	14	=	=	SYM
ejpam-3286	76	1	d(a	d(a	PROPN
ejpam-3286	76	2	,	,	PUNCT
ejpam-3286	76	3	b	b	NOUN
ejpam-3286	76	4	)	)	PUNCT
ejpam-3286	76	5	d(u	d(u	PROPN
ejpam-3286	76	6	,	,	PUNCT
ejpam-3286	76	7	v	v	NOUN
ejpam-3286	76	8	)	)	PUNCT
ejpam-3286	76	9	=	=	SYM
ejpam-3286	77	1	d(a	d(a	PROPN
ejpam-3286	77	2	,	,	PUNCT
ejpam-3286	77	3	b	b	NOUN
ejpam-3286	77	4	)	)	PUNCT
ejpam-3286	77	5	.	.	PUNCT
ejpam-3286	78	1	if	if	SCONJ
ejpam-3286	78	2	(	(	PUNCT
ejpam-3286	78	3	i	i	PRON
ejpam-3286	78	4	,	,	PUNCT
ejpam-3286	78	5	s	s	AUX
ejpam-3286	78	6	)	)	PUNCT
ejpam-3286	78	7	is	be	AUX
ejpam-3286	78	8	φ−dominated	φ−dominate	VERB
ejpam-3286	78	9	by	by	ADP
ejpam-3286	78	10	(	(	PUNCT
ejpam-3286	78	11	i	i	PROPN
ejpam-3286	78	12	,	,	PUNCT
ejpam-3286	78	13	t	t	PROPN
ejpam-3286	78	14	)	)	PUNCT
ejpam-3286	78	15	,	,	PUNCT
ejpam-3286	78	16	where	where	SCONJ
ejpam-3286	78	17	i	i	PRON
ejpam-3286	78	18	is	be	AUX
ejpam-3286	78	19	the	the	DET
ejpam-3286	78	20	identity	identity	NOUN
ejpam-3286	78	21	mapping	mapping	NOUN
ejpam-3286	78	22	on	on	ADP
ejpam-3286	78	23	b	b	NOUN
ejpam-3286	78	24	,	,	PUNCT
ejpam-3286	78	25	then	then	ADV
ejpam-3286	78	26	2d(a	2d(a	NUM
ejpam-3286	78	27	,	,	PUNCT
ejpam-3286	78	28	b	b	NOUN
ejpam-3286	78	29	)	)	PUNCT
ejpam-3286	79	1	+	+	CCONJ
ejpam-3286	79	2	φ(2d(a	φ(2d(a	PROPN
ejpam-3286	79	3	,	,	PUNCT
ejpam-3286	79	4	b	b	NOUN
ejpam-3286	79	5	)	)	PUNCT
ejpam-3286	79	6	+	+	CCONJ
ejpam-3286	79	7	d(a	d(a	PROPN
ejpam-3286	79	8	,	,	PUNCT
ejpam-3286	79	9	a′))−	a′))−	PRON
ejpam-3286	79	10	d(a	d(a	PROPN
ejpam-3286	79	11	,	,	PUNCT
ejpam-3286	79	12	a′	a′	PROPN
ejpam-3286	79	13	)	)	PUNCT
ejpam-3286	79	14	≥	≥	NOUN
ejpam-3286	79	15	0	0	PUNCT
ejpam-3286	80	1	whevever	whevever	SCONJ
ejpam-3286	80	2	a′	a′	PROPN
ejpam-3286	80	3	is	be	AUX
ejpam-3286	80	4	another	another	DET
ejpam-3286	80	5	common	common	ADJ
ejpam-3286	80	6	best	good	ADJ
ejpam-3286	80	7	proximity	proximity	NOUN
ejpam-3286	80	8	point	point	NOUN
ejpam-3286	80	9	of	of	ADP
ejpam-3286	80	10	s	s	PRON
ejpam-3286	80	11	and	and	CCONJ
ejpam-3286	80	12	t	t	PROPN
ejpam-3286	80	13	.	.	PUNCT
ejpam-3286	81	1	proof	proof	NOUN
ejpam-3286	81	2	.	.	PUNCT
ejpam-3286	82	1	let	let	VERB
ejpam-3286	82	2	x0	x0	PROPN
ejpam-3286	82	3	be	be	AUX
ejpam-3286	82	4	an	an	DET
ejpam-3286	82	5	element	element	NOUN
ejpam-3286	82	6	in	in	ADP
ejpam-3286	82	7	a.	a.	NOUN
ejpam-3286	82	8	since	since	SCONJ
ejpam-3286	82	9	fs(a	fs(a	NOUN
ejpam-3286	82	10	)	)	PUNCT
ejpam-3286	83	1	⊂	⊂	PROPN
ejpam-3286	83	2	gt	gt	PROPN
ejpam-3286	83	3	(	(	PUNCT
ejpam-3286	83	4	a	a	X
ejpam-3286	83	5	)	)	PUNCT
ejpam-3286	83	6	,	,	PUNCT
ejpam-3286	83	7	there	there	PRON
ejpam-3286	83	8	exists	exist	VERB
ejpam-3286	83	9	an	an	DET
ejpam-3286	83	10	element	element	NOUN
ejpam-3286	83	11	x1	x1	PROPN
ejpam-3286	83	12	∈	∈	PROPN
ejpam-3286	83	13	a	a	DET
ejpam-3286	83	14	such	such	ADJ
ejpam-3286	83	15	that	that	DET
ejpam-3286	83	16	fs(x0	fs(x0	NOUN
ejpam-3286	83	17	)	)	PUNCT
ejpam-3286	84	1	=	=	SYM
ejpam-3286	84	2	gt	gt	INTJ
ejpam-3286	84	3	(	(	PUNCT
ejpam-3286	84	4	x1	x1	PROPN
ejpam-3286	84	5	)	)	PUNCT
ejpam-3286	84	6	.	.	PUNCT
ejpam-3286	85	1	again	again	ADV
ejpam-3286	85	2	by	by	ADP
ejpam-3286	85	3	fs(a	fs(a	NOUN
ejpam-3286	85	4	)	)	PUNCT
ejpam-3286	86	1	⊂	⊂	PROPN
ejpam-3286	86	2	gt	gt	PROPN
ejpam-3286	86	3	(	(	PUNCT
ejpam-3286	86	4	a	a	X
ejpam-3286	86	5	)	)	PUNCT
ejpam-3286	86	6	,	,	PUNCT
ejpam-3286	86	7	we	we	PRON
ejpam-3286	86	8	can	can	AUX
ejpam-3286	86	9	choose	choose	VERB
ejpam-3286	86	10	an	an	DET
ejpam-3286	86	11	element	element	NOUN
ejpam-3286	86	12	x2	x2	PROPN
ejpam-3286	86	13	∈	∈	PROPN
ejpam-3286	86	14	a	a	DET
ejpam-3286	86	15	such	such	ADJ
ejpam-3286	86	16	that	that	DET
ejpam-3286	86	17	fs(x1	fs(x1	NOUN
ejpam-3286	86	18	)	)	PUNCT
ejpam-3286	86	19	=	=	SYM
ejpam-3286	86	20	gt	gt	INTJ
ejpam-3286	86	21	(	(	PUNCT
ejpam-3286	86	22	x2	x2	PROPN
ejpam-3286	86	23	)	)	PUNCT
ejpam-3286	86	24	.	.	PUNCT
ejpam-3286	87	1	by	by	ADP
ejpam-3286	87	2	continuing	continue	VERB
ejpam-3286	87	3	this	this	DET
ejpam-3286	87	4	process	process	NOUN
ejpam-3286	87	5	,	,	PUNCT
ejpam-3286	87	6	we	we	PRON
ejpam-3286	87	7	can	can	AUX
ejpam-3286	87	8	construct	construct	VERB
ejpam-3286	87	9	a	a	DET
ejpam-3286	87	10	sequence	sequence	NOUN
ejpam-3286	87	11	(	(	PUNCT
ejpam-3286	87	12	xn	xn	X
ejpam-3286	87	13	)	)	PUNCT
ejpam-3286	87	14	such	such	ADJ
ejpam-3286	87	15	that	that	SCONJ
ejpam-3286	87	16	fs(xn	fs(xn	NOUN
ejpam-3286	87	17	)	)	PUNCT
ejpam-3286	87	18	=	=	SYM
ejpam-3286	87	19	gt	gt	PROPN
ejpam-3286	87	20	(	(	PUNCT
ejpam-3286	87	21	xn+1	xn+1	NUM
ejpam-3286	87	22	)	)	PUNCT
ejpam-3286	87	23	.	.	PUNCT
ejpam-3286	88	1	by	by	ADP
ejpam-3286	88	2	condition	condition	NOUN
ejpam-3286	88	3	(	(	PUNCT
ejpam-3286	88	4	2	2	X
ejpam-3286	88	5	)	)	PUNCT
ejpam-3286	88	6	there	there	PRON
ejpam-3286	88	7	exists	exist	VERB
ejpam-3286	88	8	continuous	continuous	ADJ
ejpam-3286	88	9	non	non	ADJ
ejpam-3286	88	10	-	-	ADJ
ejpam-3286	88	11	decreasing	decrease	VERB
ejpam-3286	88	12	function	function	NOUN
ejpam-3286	88	13	φ	φ	NOUN
ejpam-3286	88	14	:	:	PUNCT
ejpam-3286	89	1	[	[	X
ejpam-3286	89	2	0,+∞	0,+∞	NUM
ejpam-3286	89	3	)	)	PUNCT
ejpam-3286	89	4	−→	−→	NOUN
ejpam-3286	89	5	[	[	X
ejpam-3286	89	6	0,+∞	0,+∞	NUM
ejpam-3286	89	7	)	)	PUNCT
ejpam-3286	89	8	,	,	PUNCT
ejpam-3286	89	9	with	with	ADP
ejpam-3286	89	10	limn⇒∞	limn⇒∞	PROPN
ejpam-3286	89	11	φn(t	φn(t	PUNCT
ejpam-3286	89	12	)	)	PUNCT
ejpam-3286	90	1	=	=	SYM
ejpam-3286	90	2	0	0	NUM
ejpam-3286	91	1	for	for	ADP
ejpam-3286	91	2	all	all	DET
ejpam-3286	91	3	t	t	NOUN
ejpam-3286	91	4	∈	∈	PROPN
ejpam-3286	92	1	[	[	X
ejpam-3286	92	2	0,+∞	0,+∞	NUM
ejpam-3286	92	3	)	)	PUNCT
ejpam-3286	92	4	,	,	PUNCT
ejpam-3286	92	5	such	such	ADJ
ejpam-3286	92	6	that	that	DET
ejpam-3286	92	7	d(fsxn	d(fsxn	NOUN
ejpam-3286	92	8	,	,	PUNCT
ejpam-3286	92	9	fsxn+1	fsxn+1	PROPN
ejpam-3286	92	10	)	)	PUNCT
ejpam-3286	92	11	≤	≤	NOUN
ejpam-3286	92	12	φ(d(gtxn	φ(d(gtxn	NOUN
ejpam-3286	92	13	,	,	PUNCT
ejpam-3286	92	14	gtxn+1	gtxn+1	PROPN
ejpam-3286	92	15	)	)	PUNCT
ejpam-3286	92	16	)	)	PUNCT
ejpam-3286	92	17	.	.	PUNCT
ejpam-3286	93	1	m.	m.	PROPN
ejpam-3286	93	2	iranmanesh	iranmanesh	PROPN
ejpam-3286	93	3	,	,	PUNCT
ejpam-3286	93	4	a.	a.	NOUN
ejpam-3286	93	5	g.	g.	PROPN
ejpam-3286	93	6	sanatee	sanatee	PROPN
ejpam-3286	93	7	/	/	SYM
ejpam-3286	93	8	eur	eur	PROPN
ejpam-3286	93	9	.	.	PUNCT
ejpam-3286	94	1	j.	j.	PROPN
ejpam-3286	94	2	pure	pure	PROPN
ejpam-3286	94	3	appl	appl	PROPN
ejpam-3286	94	4	.	.	PROPN
ejpam-3286	94	5	math	math	PROPN
ejpam-3286	94	6	,	,	PUNCT
ejpam-3286	94	7	11	11	NUM
ejpam-3286	94	8	(	(	PUNCT
ejpam-3286	94	9	3	3	NUM
ejpam-3286	94	10	)	)	PUNCT
ejpam-3286	94	11	(	(	PUNCT
ejpam-3286	94	12	2018	2018	NUM
ejpam-3286	94	13	)	)	PUNCT
ejpam-3286	94	14	,	,	PUNCT
ejpam-3286	94	15	869	869	NUM
ejpam-3286	94	16	-	-	SYM
ejpam-3286	94	17	875	875	NUM
ejpam-3286	94	18	872	872	NUM
ejpam-3286	94	19	since	since	SCONJ
ejpam-3286	94	20	fs(xn	fs(xn	NUM
ejpam-3286	94	21	)	)	PUNCT
ejpam-3286	95	1	=	=	SYM
ejpam-3286	95	2	gt	gt	PROPN
ejpam-3286	95	3	(	(	PUNCT
ejpam-3286	95	4	xn+1	xn+1	X
ejpam-3286	95	5	)	)	PUNCT
ejpam-3286	95	6	so	so	ADV
ejpam-3286	95	7	,	,	PUNCT
ejpam-3286	95	8	d(fsxn	d(fsxn	PROPN
ejpam-3286	95	9	,	,	PUNCT
ejpam-3286	95	10	fsxn+1	fsxn+1	PROPN
ejpam-3286	95	11	)	)	PUNCT
ejpam-3286	95	12	≤	≤	NOUN
ejpam-3286	95	13	φ(d(gtxn	φ(d(gtxn	NOUN
ejpam-3286	95	14	,	,	PUNCT
ejpam-3286	95	15	gtxn+1	gtxn+1	PROPN
ejpam-3286	95	16	)	)	PUNCT
ejpam-3286	95	17	)	)	PUNCT
ejpam-3286	96	1	=	=	PUNCT
ejpam-3286	96	2	φ(d(fsxn−1	φ(d(fsxn−1	ADJ
ejpam-3286	96	3	,	,	PUNCT
ejpam-3286	96	4	fsxn	fsxn	NOUN
ejpam-3286	96	5	)	)	PUNCT
ejpam-3286	96	6	)	)	PUNCT
ejpam-3286	97	1	≤	≤	ADV
ejpam-3286	97	2	φ2(d(gtxn−1	φ2(d(gtxn−1	X
ejpam-3286	97	3	,	,	PUNCT
ejpam-3286	97	4	gtxn	gtxn	NOUN
ejpam-3286	97	5	)	)	PUNCT
ejpam-3286	97	6	)	)	PUNCT
ejpam-3286	98	1	=	=	SYM
ejpam-3286	98	2	φ2(d(fsxn−2	φ2(d(fsxn−2	X
ejpam-3286	98	3	,	,	PUNCT
ejpam-3286	98	4	gtxn−1	gtxn−1	NOUN
ejpam-3286	98	5	)	)	PUNCT
ejpam-3286	98	6	)	)	PUNCT
ejpam-3286	98	7	≤	≤	NOUN
ejpam-3286	98	8	φ3(d(fsxn−3	φ3(d(fsxn−3	NUM
ejpam-3286	98	9	,	,	PUNCT
ejpam-3286	98	10	fsxn−2	fsxn−2	ADJ
ejpam-3286	98	11	)	)	PUNCT
ejpam-3286	98	12	)	)	PUNCT
ejpam-3286	98	13	≤	≤	NOUN
ejpam-3286	98	14	.	.	PUNCT
ejpam-3286	98	15	.	.	PUNCT
ejpam-3286	98	16	.	.	PUNCT
ejpam-3286	99	1	≤	≤	ADJ
ejpam-3286	99	2	φn(d(fsx0	φn(d(fsx0	PROPN
ejpam-3286	99	3	,	,	PUNCT
ejpam-3286	99	4	fsx1	fsx1	PROPN
ejpam-3286	99	5	)	)	PUNCT
ejpam-3286	99	6	)	)	PUNCT
ejpam-3286	99	7	.	.	PUNCT
ejpam-3286	100	1	hence	hence	ADV
ejpam-3286	100	2	,	,	PUNCT
ejpam-3286	100	3	d(fsxn	d(fsxn	PROPN
ejpam-3286	100	4	,	,	PUNCT
ejpam-3286	100	5	fsxn+1	fsxn+1	PROPN
ejpam-3286	100	6	)	)	PUNCT
ejpam-3286	100	7	≤	≤	PROPN
ejpam-3286	100	8	φn(d(fsx0	φn(d(fsx0	PROPN
ejpam-3286	100	9	,	,	PUNCT
ejpam-3286	100	10	fsx1	fsx1	PROPN
ejpam-3286	100	11	)	)	PUNCT
ejpam-3286	100	12	)	)	PUNCT
ejpam-3286	101	1	taking	take	VERB
ejpam-3286	101	2	n	n	ADV
ejpam-3286	101	3	−→	−→	NOUN
ejpam-3286	101	4	+	+	ADV
ejpam-3286	101	5	∞	∞	NOUN
ejpam-3286	101	6	we	we	PRON
ejpam-3286	101	7	have	have	VERB
ejpam-3286	101	8	lim	lim	PROPN
ejpam-3286	101	9	n→+∞	n→+∞	VERB
ejpam-3286	101	10	d(fsxn	d(fsxn	PROPN
ejpam-3286	101	11	,	,	PUNCT
ejpam-3286	101	12	fsxn+1	fsxn+1	PROPN
ejpam-3286	101	13	)	)	PUNCT
ejpam-3286	102	1	=	=	SYM
ejpam-3286	102	2	0	0	X
ejpam-3286	102	3	.	.	PUNCT
ejpam-3286	102	4	clime	clime	NOUN
ejpam-3286	102	5	:	:	PUNCT
ejpam-3286	102	6	(	(	PUNCT
ejpam-3286	102	7	fsxn	fsxn	NOUN
ejpam-3286	102	8	)	)	PUNCT
ejpam-3286	102	9	is	be	AUX
ejpam-3286	102	10	a	a	DET
ejpam-3286	102	11	cauchy	cauchy	ADJ
ejpam-3286	102	12	sequence	sequence	NOUN
ejpam-3286	102	13	.	.	PUNCT
ejpam-3286	103	1	let	let	VERB
ejpam-3286	103	2	(	(	PUNCT
ejpam-3286	103	3	fsxn	fsxn	NOUN
ejpam-3286	103	4	)	)	PUNCT
ejpam-3286	103	5	is	be	AUX
ejpam-3286	103	6	not	not	PART
ejpam-3286	103	7	cauchy	cauchy	ADJ
ejpam-3286	103	8	.	.	PUNCT
ejpam-3286	104	1	then	then	ADV
ejpam-3286	104	2	there	there	PRON
ejpam-3286	104	3	exists	exist	VERB
ejpam-3286	104	4	ε	ε	PROPN
ejpam-3286	104	5	>	>	PUNCT
ejpam-3286	104	6	0	0	NUM
ejpam-3286	105	1	and	and	CCONJ
ejpam-3286	105	2	two	two	NUM
ejpam-3286	105	3	sequences	sequence	NOUN
ejpam-3286	105	4	(	(	PUNCT
ejpam-3286	105	5	n(k	n(k	PROPN
ejpam-3286	105	6	)	)	PUNCT
ejpam-3286	105	7	)	)	PUNCT
ejpam-3286	106	1	and	and	CCONJ
ejpam-3286	106	2	(	(	PUNCT
ejpam-3286	106	3	m(k	m(k	PROPN
ejpam-3286	106	4	)	)	PUNCT
ejpam-3286	106	5	)	)	PUNCT
ejpam-3286	106	6	of	of	ADP
ejpam-3286	106	7	positive	positive	ADJ
ejpam-3286	106	8	integers	integer	NOUN
ejpam-3286	106	9	such	such	ADJ
ejpam-3286	106	10	that	that	SCONJ
ejpam-3286	106	11	n(k	n(k	PROPN
ejpam-3286	106	12	)	)	PUNCT
ejpam-3286	106	13	>	>	X
ejpam-3286	107	1	m(k	m(k	PROPN
ejpam-3286	107	2	)	)	PUNCT
ejpam-3286	107	3	>	>	X
ejpam-3286	108	1	k	k	PROPN
ejpam-3286	108	2	,	,	PUNCT
ejpam-3286	108	3	d(fsxm(k	d(fsxm(k	ADJ
ejpam-3286	108	4	)	)	PUNCT
ejpam-3286	108	5	,	,	PUNCT
ejpam-3286	108	6	fsxn(k)−1	fsxn(k)−1	NOUN
ejpam-3286	108	7	)	)	PUNCT
ejpam-3286	108	8	<	<	X
ejpam-3286	108	9	ε	ε	PROPN
ejpam-3286	108	10	and	and	CCONJ
ejpam-3286	108	11	d(fsxm(k	d(fsxm(k	PROPN
ejpam-3286	108	12	)	)	PUNCT
ejpam-3286	108	13	,	,	PUNCT
ejpam-3286	108	14	fsxn(k	fsxn(k	NOUN
ejpam-3286	108	15	)	)	PUNCT
ejpam-3286	108	16	)	)	PUNCT
ejpam-3286	108	17	≥	≥	X
ejpam-3286	108	18	ε	ε	PROPN
ejpam-3286	108	19	.	.	PUNCT
ejpam-3286	109	1	(	(	PUNCT
ejpam-3286	109	2	1	1	X
ejpam-3286	109	3	)	)	PUNCT
ejpam-3286	109	4	using	use	VERB
ejpam-3286	109	5	condition	condition	NOUN
ejpam-3286	109	6	(	(	PUNCT
ejpam-3286	109	7	2	2	NUM
ejpam-3286	109	8	)	)	PUNCT
ejpam-3286	109	9	and	and	CCONJ
ejpam-3286	109	10	the	the	DET
ejpam-3286	109	11	fact	fact	NOUN
ejpam-3286	109	12	that	that	SCONJ
ejpam-3286	109	13	φ	φ	PROPN
ejpam-3286	109	14	is	be	AUX
ejpam-3286	109	15	a	a	DET
ejpam-3286	109	16	comparison	comparison	NOUN
ejpam-3286	109	17	function	function	NOUN
ejpam-3286	109	18	we	we	PRON
ejpam-3286	109	19	obtain	obtain	VERB
ejpam-3286	109	20	that	that	DET
ejpam-3286	109	21	d(fsxm(k)+1	d(fsxm(k)+1	NOUN
ejpam-3286	109	22	,	,	PUNCT
ejpam-3286	109	23	fsxn(k	fsxn(k	NOUN
ejpam-3286	109	24	)	)	PUNCT
ejpam-3286	109	25	)	)	PUNCT
ejpam-3286	110	1	≤	≤	PROPN
ejpam-3286	110	2	φ	φ	PROPN
ejpam-3286	110	3	(	(	PUNCT
ejpam-3286	110	4	d(gtxm(k)+1	d(gtxm(k)+1	PROPN
ejpam-3286	110	5	,	,	PUNCT
ejpam-3286	110	6	gtxn(k	gtxn(k	PROPN
ejpam-3286	110	7	)	)	PUNCT
ejpam-3286	110	8	)	)	PUNCT
ejpam-3286	110	9	)	)	PUNCT
ejpam-3286	111	1	=	=	SYM
ejpam-3286	111	2	φ	φ	PROPN
ejpam-3286	111	3	(	(	PUNCT
ejpam-3286	111	4	d(fsxm(k	d(fsxm(k	PROPN
ejpam-3286	111	5	)	)	PUNCT
ejpam-3286	111	6	,	,	PUNCT
ejpam-3286	111	7	fsxn(k)−1	fsxn(k)−1	NOUN
ejpam-3286	111	8	)	)	PUNCT
ejpam-3286	111	9	)	)	PUNCT
ejpam-3286	111	10	≤	≤	PROPN
ejpam-3286	112	1	φ(ε	φ(ε	ADV
ejpam-3286	112	2	)	)	PUNCT
ejpam-3286	112	3	<	<	X
ejpam-3286	112	4	ε	ε	PROPN
ejpam-3286	112	5	.	.	PUNCT
ejpam-3286	112	6	(	(	PUNCT
ejpam-3286	112	7	2	2	X
ejpam-3286	112	8	)	)	PUNCT
ejpam-3286	112	9	taking	take	VERB
ejpam-3286	112	10	n	n	PRON
ejpam-3286	112	11	−→	−→	NOUN
ejpam-3286	112	12	+	+	NOUN
ejpam-3286	112	13	∞	∞	NUM
ejpam-3286	112	14	in	in	ADP
ejpam-3286	112	15	(	(	PUNCT
ejpam-3286	112	16	2	2	X
ejpam-3286	112	17	)	)	PUNCT
ejpam-3286	112	18	we	we	PRON
ejpam-3286	112	19	get	get	VERB
ejpam-3286	113	1	ε	ε	PROPN
ejpam-3286	113	2	=	=	SYM
ejpam-3286	113	3	lim	lim	PROPN
ejpam-3286	113	4	k→+∞	k→+∞	PROPN
ejpam-3286	113	5	d(fsxm(k)+1	d(fsxm(k)+1	PROPN
ejpam-3286	113	6	,	,	PUNCT
ejpam-3286	113	7	fsxn(k	fsxn(k	NOUN
ejpam-3286	113	8	)	)	PUNCT
ejpam-3286	113	9	)	)	PUNCT
ejpam-3286	113	10	≤	≤	PROPN
ejpam-3286	114	1	φ(ε	φ(ε	ADV
ejpam-3286	114	2	)	)	PUNCT
ejpam-3286	114	3	<	<	X
ejpam-3286	114	4	ε	ε	PROPN
ejpam-3286	114	5	.	.	PUNCT
ejpam-3286	115	1	this	this	PRON
ejpam-3286	115	2	is	be	AUX
ejpam-3286	115	3	a	a	DET
ejpam-3286	115	4	contradiction	contradiction	NOUN
ejpam-3286	115	5	.	.	PUNCT
ejpam-3286	116	1	hence	hence	ADV
ejpam-3286	116	2	(	(	PUNCT
ejpam-3286	116	3	fsxn	fsxn	PROPN
ejpam-3286	116	4	)	)	PUNCT
ejpam-3286	116	5	is	be	AUX
ejpam-3286	116	6	cauchy	cauchy	ADJ
ejpam-3286	116	7	sequence	sequence	NOUN
ejpam-3286	116	8	.	.	PUNCT
ejpam-3286	117	1	obviosly	obviosly	ADV
ejpam-3286	117	2	,	,	PUNCT
ejpam-3286	117	3	(	(	PUNCT
ejpam-3286	117	4	gtxn	gtxn	NOUN
ejpam-3286	117	5	)	)	PUNCT
ejpam-3286	117	6	is	be	AUX
ejpam-3286	117	7	also	also	ADV
ejpam-3286	117	8	cauchy	cauchy	ADJ
ejpam-3286	117	9	.	.	PUNCT
ejpam-3286	118	1	because	because	SCONJ
ejpam-3286	118	2	of	of	ADP
ejpam-3286	118	3	the	the	DET
ejpam-3286	118	4	completeness	completeness	NOUN
ejpam-3286	118	5	of	of	ADP
ejpam-3286	118	6	the	the	DET
ejpam-3286	118	7	space	space	NOUN
ejpam-3286	118	8	,	,	PUNCT
ejpam-3286	118	9	there	there	PRON
ejpam-3286	118	10	exists	exist	VERB
ejpam-3286	118	11	an	an	DET
ejpam-3286	118	12	element	element	NOUN
ejpam-3286	118	13	x	x	SYM
ejpam-3286	118	14	∈	∈	PROPN
ejpam-3286	118	15	a	a	DET
ejpam-3286	118	16	such	such	ADJ
ejpam-3286	118	17	that	that	DET
ejpam-3286	118	18	fsxn	fsxn	NOUN
ejpam-3286	118	19	−→	−→	ADV
ejpam-3286	118	20	x.	x.	NOUN
ejpam-3286	118	21	by	by	ADP
ejpam-3286	118	22	continuity	continuity	NOUN
ejpam-3286	118	23	of	of	ADP
ejpam-3286	118	24	fs	f	NOUN
ejpam-3286	118	25	and	and	CCONJ
ejpam-3286	118	26	gt	gt	INTJ
ejpam-3286	118	27	;	;	PUNCT
ejpam-3286	118	28	(	(	PUNCT
ejpam-3286	118	29	gt	gt	INTJ
ejpam-3286	118	30	)	)	PUNCT
ejpam-3286	118	31	(	(	PUNCT
ejpam-3286	118	32	fs)xn	fs)xn	AUX
ejpam-3286	118	33	−→	−→	ADJ
ejpam-3286	118	34	gtx	gtx	PROPN
ejpam-3286	118	35	(	(	PUNCT
ejpam-3286	118	36	fs)(gt	fs)(gt	PROPN
ejpam-3286	118	37	)	)	PUNCT
ejpam-3286	118	38	xn	xn	PROPN
ejpam-3286	118	39	−→	−→	PROPN
ejpam-3286	118	40	fsx	fsx	NOUN
ejpam-3286	118	41	.	.	PUNCT
ejpam-3286	119	1	by	by	ADP
ejpam-3286	119	2	condition	condition	NOUN
ejpam-3286	119	3	(	(	PUNCT
ejpam-3286	119	4	1	1	NUM
ejpam-3286	119	5	)	)	PUNCT
ejpam-3286	119	6	,	,	PUNCT
ejpam-3286	119	7	it	it	PRON
ejpam-3286	119	8	follows	follow	VERB
ejpam-3286	119	9	that	that	DET
ejpam-3286	119	10	gtx	gtx	PROPN
ejpam-3286	119	11	=	=	SYM
ejpam-3286	119	12	fsx	fsx	PROPN
ejpam-3286	119	13	.	.	PUNCT
ejpam-3286	120	1	put	put	VERB
ejpam-3286	120	2	a	a	DET
ejpam-3286	120	3	=	=	X
ejpam-3286	120	4	gtx	gtx	NOUN
ejpam-3286	120	5	=	=	SYM
ejpam-3286	120	6	fsx	fsx	NOUN
ejpam-3286	120	7	.	.	PUNCT
ejpam-3286	121	1	then	then	ADV
ejpam-3286	121	2	,	,	PUNCT
ejpam-3286	121	3	by	by	ADP
ejpam-3286	121	4	condition	condition	NOUN
ejpam-3286	121	5	(	(	PUNCT
ejpam-3286	121	6	1	1	NUM
ejpam-3286	121	7	)	)	PUNCT
ejpam-3286	121	8	and	and	CCONJ
ejpam-3286	121	9	(	(	PUNCT
ejpam-3286	121	10	2	2	NUM
ejpam-3286	121	11	)	)	PUNCT
ejpam-3286	121	12	,	,	PUNCT
ejpam-3286	121	13	d(fsa	d(fsa	PROPN
ejpam-3286	121	14	,	,	PUNCT
ejpam-3286	121	15	a	a	PRON
ejpam-3286	121	16	)	)	PUNCT
ejpam-3286	121	17	=	=	SYM
ejpam-3286	121	18	d(fsa	d(fsa	PROPN
ejpam-3286	121	19	,	,	PUNCT
ejpam-3286	121	20	fsx	fsx	NOUN
ejpam-3286	121	21	)	)	PUNCT
ejpam-3286	121	22	≤	≤	NOUN
ejpam-3286	121	23	φ(d(gta	φ(d(gta	NUM
ejpam-3286	121	24	,	,	PUNCT
ejpam-3286	121	25	gtx	gtx	PROPN
ejpam-3286	121	26	)	)	PUNCT
ejpam-3286	121	27	)	)	PUNCT
ejpam-3286	122	1	=	=	SYM
ejpam-3286	122	2	φ(d(gt	φ(d(gt	X
ejpam-3286	122	3	(	(	PUNCT
ejpam-3286	122	4	fsx	fsx	NOUN
ejpam-3286	122	5	)	)	PUNCT
ejpam-3286	122	6	,	,	PUNCT
ejpam-3286	122	7	a	a	PRON
ejpam-3286	122	8	)	)	PUNCT
ejpam-3286	122	9	)	)	PUNCT
ejpam-3286	123	1	=	=	SYM
ejpam-3286	123	2	φ(d(fs(gtx	φ(d(fs(gtx	NOUN
ejpam-3286	123	3	)	)	PUNCT
ejpam-3286	123	4	,	,	PUNCT
ejpam-3286	123	5	a	a	PRON
ejpam-3286	123	6	)	)	PUNCT
ejpam-3286	123	7	)	)	PUNCT
ejpam-3286	124	1	=	=	SYM
ejpam-3286	124	2	φ(d(fsa	φ(d(fsa	PROPN
ejpam-3286	124	3	,	,	PUNCT
ejpam-3286	124	4	a	a	PRON
ejpam-3286	124	5	)	)	PUNCT
ejpam-3286	124	6	)	)	PUNCT
ejpam-3286	124	7	.	.	PUNCT
ejpam-3286	125	1	since	since	SCONJ
ejpam-3286	125	2	φ	φ	PROPN
ejpam-3286	125	3	is	be	AUX
ejpam-3286	125	4	comparison	comparison	NOUN
ejpam-3286	125	5	by	by	ADP
ejpam-3286	125	6	remark	remark	NOUN
ejpam-3286	125	7	1	1	NUM
ejpam-3286	125	8	we	we	PRON
ejpam-3286	125	9	get	get	VERB
ejpam-3286	125	10	d(fsa	d(fsa	PROPN
ejpam-3286	125	11	,	,	PUNCT
ejpam-3286	125	12	a	a	PRON
ejpam-3286	125	13	)	)	PUNCT
ejpam-3286	125	14	=	=	SYM
ejpam-3286	125	15	0	0	PUNCT
ejpam-3286	126	1	=	=	AUX
ejpam-3286	126	2	⇒	⇒	PROPN
ejpam-3286	126	3	fsa	fsa	PROPN
ejpam-3286	126	4	=	=	SYM
ejpam-3286	126	5	a.	a.	PROPN
ejpam-3286	126	6	m.	m.	PROPN
ejpam-3286	126	7	iranmanesh	iranmanesh	PROPN
ejpam-3286	126	8	,	,	PUNCT
ejpam-3286	126	9	a.	a.	NOUN
ejpam-3286	126	10	g.	g.	PROPN
ejpam-3286	126	11	sanatee	sanatee	PROPN
ejpam-3286	126	12	/	/	SYM
ejpam-3286	126	13	eur	eur	PROPN
ejpam-3286	126	14	.	.	PUNCT
ejpam-3286	127	1	j.	j.	PROPN
ejpam-3286	127	2	pure	pure	PROPN
ejpam-3286	127	3	appl	appl	PROPN
ejpam-3286	127	4	.	.	PROPN
ejpam-3286	127	5	math	math	PROPN
ejpam-3286	127	6	,	,	PUNCT
ejpam-3286	127	7	11	11	NUM
ejpam-3286	127	8	(	(	PUNCT
ejpam-3286	127	9	3	3	NUM
ejpam-3286	127	10	)	)	PUNCT
ejpam-3286	127	11	(	(	PUNCT
ejpam-3286	127	12	2018	2018	NUM
ejpam-3286	127	13	)	)	PUNCT
ejpam-3286	127	14	,	,	PUNCT
ejpam-3286	127	15	869	869	NUM
ejpam-3286	127	16	-	-	SYM
ejpam-3286	127	17	875	875	NUM
ejpam-3286	127	18	873	873	NUM
ejpam-3286	127	19	further	far	ADV
ejpam-3286	127	20	,	,	PUNCT
ejpam-3286	127	21	gta	gta	X
ejpam-3286	128	1	=	=	SYM
ejpam-3286	128	2	(	(	PUNCT
ejpam-3286	128	3	gt	gt	INTJ
ejpam-3286	128	4	)	)	PUNCT
ejpam-3286	128	5	(	(	PUNCT
ejpam-3286	128	6	fsx	fsx	NOUN
ejpam-3286	128	7	)	)	PUNCT
ejpam-3286	128	8	=	=	SYM
ejpam-3286	128	9	(	(	PUNCT
ejpam-3286	128	10	fs)(gtx	fs)(gtx	X
ejpam-3286	128	11	)	)	PUNCT
ejpam-3286	128	12	=	=	SYM
ejpam-3286	128	13	fsa	fsa	PROPN
ejpam-3286	128	14	=	=	PUNCT
ejpam-3286	128	15	a.	a.	NOUN
ejpam-3286	128	16	a	a	DET
ejpam-3286	128	17	similar	similar	ADJ
ejpam-3286	128	18	argument	argument	NOUN
ejpam-3286	128	19	can	can	AUX
ejpam-3286	128	20	be	be	AUX
ejpam-3286	128	21	given	give	VERB
ejpam-3286	128	22	to	to	PART
ejpam-3286	128	23	assert	assert	VERB
ejpam-3286	128	24	that	that	SCONJ
ejpam-3286	128	25	there	there	PRON
ejpam-3286	128	26	exists	exist	VERB
ejpam-3286	128	27	an	an	DET
ejpam-3286	128	28	element	element	NOUN
ejpam-3286	128	29	b	b	PROPN
ejpam-3286	128	30	∈	∈	PROPN
ejpam-3286	128	31	b	b	NOUN
ejpam-3286	128	32	such	such	ADJ
ejpam-3286	128	33	that	that	SCONJ
ejpam-3286	128	34	sfb	sfb	PROPN
ejpam-3286	128	35	=	=	PROPN
ejpam-3286	128	36	tgb	tgb	PROPN
ejpam-3286	128	37	=	=	PROPN
ejpam-3286	128	38	b.	b.	PROPN
ejpam-3286	128	39	also	also	ADV
ejpam-3286	128	40	,	,	PUNCT
ejpam-3286	128	41	since	since	SCONJ
ejpam-3286	128	42	t	t	NOUN
ejpam-3286	128	43	commutes	commute	NOUN
ejpam-3286	128	44	with	with	ADP
ejpam-3286	128	45	the	the	DET
ejpam-3286	128	46	pair	pair	NOUN
ejpam-3286	128	47	(	(	PUNCT
ejpam-3286	128	48	f	f	X
ejpam-3286	128	49	,	,	PUNCT
ejpam-3286	128	50	g	g	PROPN
ejpam-3286	128	51	)	)	PUNCT
ejpam-3286	128	52	,	,	PUNCT
ejpam-3286	128	53	gtfb	gtfb	NOUN
ejpam-3286	128	54	=	=	SYM
ejpam-3286	128	55	ftgb	ftgb	NOUN
ejpam-3286	129	1	=	=	NOUN
ejpam-3286	129	2	fb	fb	INTJ
ejpam-3286	129	3	.	.	PUNCT
ejpam-3286	130	1	so	so	ADV
ejpam-3286	130	2	,	,	PUNCT
ejpam-3286	130	3	d(a	d(a	PROPN
ejpam-3286	130	4	,	,	PUNCT
ejpam-3286	130	5	fb	fb	INTJ
ejpam-3286	130	6	)	)	PUNCT
ejpam-3286	130	7	=	=	SYM
ejpam-3286	130	8	d(fsa	d(fsa	PROPN
ejpam-3286	130	9	,	,	PUNCT
ejpam-3286	130	10	fs(fb	fs(fb	PROPN
ejpam-3286	130	11	)	)	PUNCT
ejpam-3286	130	12	)	)	PUNCT
ejpam-3286	131	1	≤	≤	NUM
ejpam-3286	131	2	φ(d(gta	φ(d(gta	NUM
ejpam-3286	131	3	,	,	PUNCT
ejpam-3286	131	4	gt	gt	PROPN
ejpam-3286	131	5	(	(	PUNCT
ejpam-3286	131	6	fb	fb	INTJ
ejpam-3286	131	7	)	)	PUNCT
ejpam-3286	131	8	)	)	PUNCT
ejpam-3286	131	9	)	)	PUNCT
ejpam-3286	132	1	=	=	SYM
ejpam-3286	132	2	φ(d(a	φ(d(a	PROPN
ejpam-3286	132	3	,	,	PUNCT
ejpam-3286	132	4	fb	fb	NOUN
ejpam-3286	132	5	)	)	PUNCT
ejpam-3286	132	6	)	)	PUNCT
ejpam-3286	132	7	.	.	PUNCT
ejpam-3286	133	1	since	since	SCONJ
ejpam-3286	133	2	φ	φ	PROPN
ejpam-3286	133	3	is	be	AUX
ejpam-3286	133	4	a	a	DET
ejpam-3286	133	5	comparison	comparison	NOUN
ejpam-3286	133	6	by	by	ADP
ejpam-3286	133	7	remark	remark	NOUN
ejpam-3286	133	8	1	1	NUM
ejpam-3286	133	9	,	,	PUNCT
ejpam-3286	133	10	it	it	PRON
ejpam-3286	133	11	follows	follow	VERB
ejpam-3286	133	12	that	that	PRON
ejpam-3286	133	13	fb	fb	INTJ
ejpam-3286	133	14	=	=	NOUN
ejpam-3286	133	15	a.	a.	NOUN
ejpam-3286	133	16	by	by	ADP
ejpam-3286	133	17	the	the	DET
ejpam-3286	133	18	same	same	ADJ
ejpam-3286	133	19	argument	argument	NOUN
ejpam-3286	133	20	we	we	PRON
ejpam-3286	133	21	can	can	AUX
ejpam-3286	133	22	show	show	VERB
ejpam-3286	133	23	that	that	DET
ejpam-3286	133	24	gb	gb	NOUN
ejpam-3286	133	25	=	=	PUNCT
ejpam-3286	133	26	a	a	NOUN
ejpam-3286	133	27	,	,	PUNCT
ejpam-3286	133	28	sa	sa	PROPN
ejpam-3286	133	29	=	=	SYM
ejpam-3286	133	30	b	b	PROPN
ejpam-3286	133	31	and	and	CCONJ
ejpam-3286	133	32	ta	ta	PROPN
ejpam-3286	133	33	=	=	PROPN
ejpam-3286	133	34	b.	b.	PROPN
ejpam-3286	133	35	consequently	consequently	ADV
ejpam-3286	133	36	,	,	PUNCT
ejpam-3286	133	37	by	by	ADP
ejpam-3286	133	38	condition	condition	NOUN
ejpam-3286	133	39	(	(	PUNCT
ejpam-3286	133	40	5	5	X
ejpam-3286	133	41	)	)	PUNCT
ejpam-3286	133	42	there	there	PRON
ejpam-3286	133	43	exists	exist	VERB
ejpam-3286	133	44	α	α	PRON
ejpam-3286	133	45	∈	∈	PROPN
ejpam-3286	134	1	[	[	X
ejpam-3286	134	2	0	0	NUM
ejpam-3286	134	3	,	,	PUNCT
ejpam-3286	134	4	1	1	NUM
ejpam-3286	134	5	)	)	PUNCT
ejpam-3286	134	6	such	such	ADJ
ejpam-3286	134	7	that	that	SCONJ
ejpam-3286	134	8	d(a	d(a	PROPN
ejpam-3286	134	9	,	,	PUNCT
ejpam-3286	134	10	b	b	NOUN
ejpam-3286	134	11	)	)	PUNCT
ejpam-3286	134	12	=	=	SYM
ejpam-3286	134	13	d(sa	d(sa	PROPN
ejpam-3286	134	14	,	,	PUNCT
ejpam-3286	134	15	fsa	fsa	PROPN
ejpam-3286	134	16	)	)	PUNCT
ejpam-3286	134	17	≤	≤	NOUN
ejpam-3286	134	18	αd(ta	αd(ta	PROPN
ejpam-3286	134	19	,	,	PUNCT
ejpam-3286	134	20	gta	gta	PROPN
ejpam-3286	134	21	)	)	PUNCT
ejpam-3286	134	22	+	+	CCONJ
ejpam-3286	134	23	(	(	PUNCT
ejpam-3286	134	24	1−	1−	NUM
ejpam-3286	134	25	α)d(a	α)d(a	PROPN
ejpam-3286	134	26	,	,	PUNCT
ejpam-3286	134	27	b	b	NOUN
ejpam-3286	134	28	)	)	PUNCT
ejpam-3286	134	29	=	=	SYM
ejpam-3286	134	30	αd(a	αd(a	X
ejpam-3286	134	31	,	,	PUNCT
ejpam-3286	134	32	b	b	NOUN
ejpam-3286	134	33	)	)	PUNCT
ejpam-3286	134	34	+	+	CCONJ
ejpam-3286	134	35	(	(	PUNCT
ejpam-3286	134	36	1−	1−	NUM
ejpam-3286	134	37	α)d(a	α)d(a	PROPN
ejpam-3286	134	38	,	,	PUNCT
ejpam-3286	134	39	b	b	NOUN
ejpam-3286	134	40	)	)	PUNCT
ejpam-3286	134	41	.	.	PUNCT
ejpam-3286	135	1	so	so	ADV
ejpam-3286	135	2	d(a	d(a	PROPN
ejpam-3286	135	3	,	,	PUNCT
ejpam-3286	135	4	b	b	NOUN
ejpam-3286	135	5	)	)	PUNCT
ejpam-3286	135	6	≤	≤	NOUN
ejpam-3286	136	1	d(a	d(a	PROPN
ejpam-3286	136	2	,	,	PUNCT
ejpam-3286	136	3	b	b	NOUN
ejpam-3286	136	4	)	)	PUNCT
ejpam-3286	136	5	and	and	CCONJ
ejpam-3286	136	6	hence	hence	ADV
ejpam-3286	136	7	d(a	d(a	PROPN
ejpam-3286	136	8	,	,	PUNCT
ejpam-3286	136	9	b	b	NOUN
ejpam-3286	136	10	)	)	PUNCT
ejpam-3286	136	11	=	=	SYM
ejpam-3286	137	1	d(a	d(a	PROPN
ejpam-3286	137	2	,	,	PUNCT
ejpam-3286	137	3	b	b	NOUN
ejpam-3286	137	4	)	)	PUNCT
ejpam-3286	137	5	.	.	PUNCT
ejpam-3286	138	1	therefore	therefore	ADV
ejpam-3286	138	2	,	,	PUNCT
ejpam-3286	138	3	d(a	d(a	PROPN
ejpam-3286	138	4	,	,	PUNCT
ejpam-3286	138	5	sa	sa	PROPN
ejpam-3286	138	6	)	)	PUNCT
ejpam-3286	138	7	=	=	SYM
ejpam-3286	139	1	d(a	d(a	PROPN
ejpam-3286	139	2	,	,	PUNCT
ejpam-3286	139	3	ta	ta	PROPN
ejpam-3286	139	4	)	)	PUNCT
ejpam-3286	139	5	=	=	SYM
ejpam-3286	140	1	d(a	d(a	PROPN
ejpam-3286	140	2	,	,	PUNCT
ejpam-3286	140	3	b	b	NOUN
ejpam-3286	140	4	)	)	PUNCT
ejpam-3286	140	5	=	=	SYM
ejpam-3286	141	1	d(a	d(a	PROPN
ejpam-3286	141	2	,	,	PUNCT
ejpam-3286	141	3	b	b	NOUN
ejpam-3286	141	4	)	)	PUNCT
ejpam-3286	141	5	d(b	d(b	PROPN
ejpam-3286	141	6	,	,	PUNCT
ejpam-3286	141	7	fb	fb	INTJ
ejpam-3286	141	8	)	)	PUNCT
ejpam-3286	141	9	=	=	PUNCT
ejpam-3286	141	10	d(b	d(b	PROPN
ejpam-3286	141	11	,	,	PUNCT
ejpam-3286	141	12	gb	gb	NOUN
ejpam-3286	141	13	)	)	PUNCT
ejpam-3286	141	14	=	=	SYM
ejpam-3286	142	1	d(a	d(a	PROPN
ejpam-3286	142	2	,	,	PUNCT
ejpam-3286	142	3	b	b	NOUN
ejpam-3286	142	4	)	)	PUNCT
ejpam-3286	142	5	=	=	SYM
ejpam-3286	143	1	d(a	d(a	PROPN
ejpam-3286	143	2	,	,	PUNCT
ejpam-3286	143	3	b	b	NOUN
ejpam-3286	143	4	)	)	PUNCT
ejpam-3286	143	5	.	.	PUNCT
ejpam-3286	144	1	if	if	SCONJ
ejpam-3286	144	2	(	(	PUNCT
ejpam-3286	144	3	i	i	PRON
ejpam-3286	144	4	,	,	PUNCT
ejpam-3286	144	5	s	s	AUX
ejpam-3286	144	6	)	)	PUNCT
ejpam-3286	144	7	is	be	AUX
ejpam-3286	144	8	φ−dominated	φ−dominate	VERB
ejpam-3286	144	9	by	by	ADP
ejpam-3286	144	10	(	(	PUNCT
ejpam-3286	144	11	i	i	PROPN
ejpam-3286	144	12	,	,	PUNCT
ejpam-3286	144	13	t	t	PROPN
ejpam-3286	144	14	)	)	PUNCT
ejpam-3286	144	15	and	and	CCONJ
ejpam-3286	144	16	a′	a′	PROPN
ejpam-3286	144	17	is	be	AUX
ejpam-3286	144	18	another	another	DET
ejpam-3286	144	19	common	common	ADJ
ejpam-3286	144	20	best	good	ADJ
ejpam-3286	144	21	proximity	proximity	NOUN
ejpam-3286	144	22	point	point	NOUN
ejpam-3286	144	23	of	of	ADP
ejpam-3286	144	24	s	s	PRON
ejpam-3286	144	25	and	and	CCONJ
ejpam-3286	144	26	t	t	PROPN
ejpam-3286	144	27	,	,	PUNCT
ejpam-3286	144	28	then	then	ADV
ejpam-3286	144	29	d(a	d(a	PROPN
ejpam-3286	144	30	,	,	PUNCT
ejpam-3286	144	31	a′	a′	PROPN
ejpam-3286	144	32	)	)	PUNCT
ejpam-3286	144	33	≤	≤	NOUN
ejpam-3286	145	1	d(a	d(a	PROPN
ejpam-3286	145	2	,	,	PUNCT
ejpam-3286	145	3	sa	sa	PROPN
ejpam-3286	145	4	)	)	PUNCT
ejpam-3286	146	1	+	+	NUM
ejpam-3286	146	2	d(sa	d(sa	ADJ
ejpam-3286	146	3	,	,	PUNCT
ejpam-3286	146	4	sa′	sa′	NUM
ejpam-3286	146	5	)	)	PUNCT
ejpam-3286	146	6	+	+	CCONJ
ejpam-3286	146	7	d(a′	d(a′	ADJ
ejpam-3286	146	8	,	,	PUNCT
ejpam-3286	146	9	sa′	sa′	NUM
ejpam-3286	146	10	)	)	PUNCT
ejpam-3286	146	11	≤	≤	NOUN
ejpam-3286	146	12	2d(a	2d(a	NUM
ejpam-3286	146	13	,	,	PUNCT
ejpam-3286	146	14	b	b	NOUN
ejpam-3286	146	15	)	)	PUNCT
ejpam-3286	146	16	+	+	PROPN
ejpam-3286	146	17	φ(d(ta	φ(d(ta	ADJ
ejpam-3286	146	18	,	,	PUNCT
ejpam-3286	146	19	ta′	ta′	ADJ
ejpam-3286	146	20	)	)	PUNCT
ejpam-3286	146	21	)	)	PUNCT
ejpam-3286	146	22	≤	≤	NUM
ejpam-3286	147	1	2d(a	2d(a	NUM
ejpam-3286	147	2	,	,	PUNCT
ejpam-3286	147	3	b	b	NOUN
ejpam-3286	147	4	)	)	PUNCT
ejpam-3286	147	5	+	+	CCONJ
ejpam-3286	148	1	φ(2d(a	φ(2d(a	PROPN
ejpam-3286	148	2	,	,	PUNCT
ejpam-3286	148	3	b	b	NOUN
ejpam-3286	148	4	)	)	PUNCT
ejpam-3286	148	5	+	+	CCONJ
ejpam-3286	148	6	d(a	d(a	PROPN
ejpam-3286	148	7	,	,	PUNCT
ejpam-3286	148	8	a′	a′	PROPN
ejpam-3286	148	9	)	)	PUNCT
ejpam-3286	148	10	)	)	PUNCT
ejpam-3286	148	11	and	and	CCONJ
ejpam-3286	148	12	hence	hence	ADV
ejpam-3286	148	13	2d(a	2d(a	NUM
ejpam-3286	148	14	,	,	PUNCT
ejpam-3286	148	15	b	b	NOUN
ejpam-3286	148	16	)	)	PUNCT
ejpam-3286	148	17	+	+	CCONJ
ejpam-3286	149	1	φ(2d(a	φ(2d(a	PROPN
ejpam-3286	149	2	,	,	PUNCT
ejpam-3286	149	3	b	b	NOUN
ejpam-3286	149	4	)	)	PUNCT
ejpam-3286	149	5	+	+	CCONJ
ejpam-3286	149	6	d(a	d(a	PROPN
ejpam-3286	149	7	,	,	PUNCT
ejpam-3286	149	8	a′))−	a′))−	PRON
ejpam-3286	149	9	d(a	d(a	PROPN
ejpam-3286	149	10	,	,	PUNCT
ejpam-3286	149	11	a′	a′	PROPN
ejpam-3286	149	12	)	)	PUNCT
ejpam-3286	149	13	≥	≥	NOUN
ejpam-3286	149	14	0	0	NUM
ejpam-3286	149	15	.	.	PUNCT
ejpam-3286	149	16	example	example	NOUN
ejpam-3286	150	1	1	1	X
ejpam-3286	150	2	.	.	X
ejpam-3286	150	3	consider	consider	VERB
ejpam-3286	150	4	the	the	DET
ejpam-3286	150	5	space	space	NOUN
ejpam-3286	150	6	of	of	ADP
ejpam-3286	150	7	real	real	ADJ
ejpam-3286	150	8	numbers	number	NOUN
ejpam-3286	150	9	with	with	ADP
ejpam-3286	150	10	the	the	DET
ejpam-3286	150	11	euclidean	euclidean	ADJ
ejpam-3286	150	12	meteric	meteric	NOUN
ejpam-3286	150	13	.	.	PUNCT
ejpam-3286	151	1	let	let	VERB
ejpam-3286	151	2	a	a	PRON
ejpam-3286	151	3	=	=	SYM
ejpam-3286	152	1	[	[	X
ejpam-3286	152	2	3,+∞	3,+∞	NUM
ejpam-3286	152	3	)	)	PUNCT
ejpam-3286	152	4	and	and	CCONJ
ejpam-3286	152	5	b	b	X
ejpam-3286	152	6	=	=	SYM
ejpam-3286	152	7	(	(	PUNCT
ejpam-3286	152	8	−∞,−3	−∞,−3	PROPN
ejpam-3286	152	9	]	]	PUNCT
ejpam-3286	152	10	suppose	suppose	VERB
ejpam-3286	152	11	that	that	SCONJ
ejpam-3286	152	12	s	s	PROPN
ejpam-3286	152	13	,	,	PUNCT
ejpam-3286	152	14	t	t	X
ejpam-3286	152	15	:	:	PUNCT
ejpam-3286	152	16	a	a	DET
ejpam-3286	152	17	→	→	SYM
ejpam-3286	152	18	b	b	PROPN
ejpam-3286	152	19	,	,	PUNCT
ejpam-3286	152	20	f	f	PROPN
ejpam-3286	152	21	,	,	PUNCT
ejpam-3286	152	22	g	g	NOUN
ejpam-3286	152	23	:	:	PUNCT
ejpam-3286	152	24	b	b	X
ejpam-3286	152	25	→	→	SYM
ejpam-3286	152	26	a	a	PROPN
ejpam-3286	152	27	and	and	CCONJ
ejpam-3286	152	28	φ	φ	NUM
ejpam-3286	152	29	,	,	PUNCT
ejpam-3286	152	30	ψ	ψ	X
ejpam-3286	152	31	:	:	PUNCT
ejpam-3286	153	1	[	[	X
ejpam-3286	153	2	0,+∞)→	0,+∞)→	X
ejpam-3286	153	3	[	[	X
ejpam-3286	153	4	0,+∞	0,+∞	NUM
ejpam-3286	153	5	)	)	PUNCT
ejpam-3286	153	6	are	be	AUX
ejpam-3286	153	7	defined	define	VERB
ejpam-3286	153	8	by	by	ADP
ejpam-3286	153	9	s(x	s(x	NOUN
ejpam-3286	153	10	)	)	PUNCT
ejpam-3286	153	11	=	=	PUNCT
ejpam-3286	154	1	−3	−3	ADV
ejpam-3286	154	2	;	;	PUNCT
ejpam-3286	154	3	t	t	PROPN
ejpam-3286	154	4	(	(	PUNCT
ejpam-3286	154	5	x	x	NOUN
ejpam-3286	154	6	)	)	PUNCT
ejpam-3286	154	7	=	=	SYM
ejpam-3286	154	8	−x	−x	NOUN
ejpam-3286	154	9	;	;	PUNCT
ejpam-3286	154	10	f	f	PROPN
ejpam-3286	154	11	(	(	PUNCT
ejpam-3286	154	12	y	y	NOUN
ejpam-3286	154	13	)	)	PUNCT
ejpam-3286	154	14	=	=	PRON
ejpam-3286	154	15	{	{	PUNCT
ejpam-3286	154	16	3	3	NUM
ejpam-3286	154	17	y	y	PROPN
ejpam-3286	154	18	∈	∈	PROPN
ejpam-3286	154	19	z	z	NOUN
ejpam-3286	154	20	4	4	NUM
ejpam-3286	154	21	y	y	NOUN
ejpam-3286	154	22	∈	∈	PROPN
ejpam-3286	154	23	r	r	NOUN
ejpam-3286	154	24	\	\	PROPN
ejpam-3286	154	25	z	z	NOUN
ejpam-3286	154	26	;	;	PUNCT
ejpam-3286	155	1	g(y	g(y	X
ejpam-3286	155	2	)	)	PUNCT
ejpam-3286	155	3	=	=	VERB
ejpam-3286	155	4	−y	−y	NOUN
ejpam-3286	155	5	and	and	CCONJ
ejpam-3286	155	6	φ(x	φ(x	NOUN
ejpam-3286	155	7	)	)	PUNCT
ejpam-3286	155	8	=	=	SYM
ejpam-3286	155	9	ψ(x	ψ(x	NOUN
ejpam-3286	155	10	)	)	PUNCT
ejpam-3286	156	1	=	=	PUNCT
ejpam-3286	156	2	x	x	SYM
ejpam-3286	156	3	1	1	NUM
ejpam-3286	156	4	+	+	NOUN
ejpam-3286	156	5	x	x	X
ejpam-3286	156	6	.	.	PUNCT
ejpam-3286	157	1	it	it	PRON
ejpam-3286	157	2	is	be	AUX
ejpam-3286	157	3	easy	easy	ADJ
ejpam-3286	157	4	to	to	PART
ejpam-3286	157	5	check	check	VERB
ejpam-3286	157	6	that	that	SCONJ
ejpam-3286	157	7	d(a	d(a	PROPN
ejpam-3286	157	8	,	,	PUNCT
ejpam-3286	157	9	b	b	NOUN
ejpam-3286	157	10	)	)	PUNCT
ejpam-3286	157	11	=	=	SYM
ejpam-3286	157	12	6	6	NUM
ejpam-3286	157	13	and	and	CCONJ
ejpam-3286	157	14	the	the	DET
ejpam-3286	157	15	mapping	mapping	NOUN
ejpam-3286	157	16	s	s	PROPN
ejpam-3286	157	17	,	,	PUNCT
ejpam-3286	157	18	t	t	PROPN
ejpam-3286	157	19	,	,	PUNCT
ejpam-3286	157	20	f	f	PROPN
ejpam-3286	157	21	and	and	CCONJ
ejpam-3286	157	22	g	g	PROPN
ejpam-3286	157	23	are	be	AUX
ejpam-3286	157	24	satisfied	satisfied	ADJ
ejpam-3286	157	25	the	the	DET
ejpam-3286	157	26	conditions	condition	NOUN
ejpam-3286	157	27	in	in	ADP
ejpam-3286	157	28	theorem	theorem	ADJ
ejpam-3286	157	29	1	1	NUM
ejpam-3286	157	30	and	and	CCONJ
ejpam-3286	157	31	d(3	d(3	PROPN
ejpam-3286	157	32	,	,	PUNCT
ejpam-3286	157	33	s(3	s(3	PROPN
ejpam-3286	157	34	)	)	PUNCT
ejpam-3286	157	35	)	)	PUNCT
ejpam-3286	158	1	=	=	SYM
ejpam-3286	158	2	d(3	d(3	PROPN
ejpam-3286	158	3	,	,	PUNCT
ejpam-3286	158	4	t	t	PROPN
ejpam-3286	158	5	(	(	PUNCT
ejpam-3286	158	6	3	3	NUM
ejpam-3286	158	7	)	)	PUNCT
ejpam-3286	158	8	)	)	PUNCT
ejpam-3286	159	1	=	=	SYM
ejpam-3286	159	2	d(a	d(a	PROPN
ejpam-3286	159	3	,	,	PUNCT
ejpam-3286	159	4	b	b	NOUN
ejpam-3286	159	5	)	)	PUNCT
ejpam-3286	159	6	d(−3	d(−3	NOUN
ejpam-3286	159	7	,	,	PUNCT
ejpam-3286	159	8	f	f	PROPN
ejpam-3286	159	9	(	(	PUNCT
ejpam-3286	159	10	−3	−3	NOUN
ejpam-3286	159	11	)	)	PUNCT
ejpam-3286	159	12	)	)	PUNCT
ejpam-3286	160	1	=	=	SYM
ejpam-3286	160	2	d(−3	d(−3	NOUN
ejpam-3286	160	3	,	,	PUNCT
ejpam-3286	160	4	g(−3	g(−3	NOUN
ejpam-3286	160	5	)	)	PUNCT
ejpam-3286	160	6	)	)	PUNCT
ejpam-3286	161	1	=	=	SYM
ejpam-3286	161	2	d(a	d(a	PROPN
ejpam-3286	161	3	,	,	PUNCT
ejpam-3286	161	4	b	b	NOUN
ejpam-3286	161	5	)	)	PUNCT
ejpam-3286	161	6	d(3,−3	d(3,−3	PROPN
ejpam-3286	161	7	)	)	PUNCT
ejpam-3286	161	8	=	=	SYM
ejpam-3286	162	1	d(a	d(a	PROPN
ejpam-3286	162	2	,	,	PUNCT
ejpam-3286	162	3	b	b	NOUN
ejpam-3286	162	4	)	)	PUNCT
ejpam-3286	162	5	.	.	PUNCT
ejpam-3286	163	1	references	reference	NOUN
ejpam-3286	163	2	874	874	NUM
ejpam-3286	164	1	if	if	SCONJ
ejpam-3286	164	2	s	s	PRON
ejpam-3286	164	3	and	and	CCONJ
ejpam-3286	164	4	t	t	PROPN
ejpam-3286	164	5	are	be	AUX
ejpam-3286	164	6	self	self	NOUN
ejpam-3286	164	7	-	-	PUNCT
ejpam-3286	164	8	mappings	mapping	NOUN
ejpam-3286	164	9	on	on	ADP
ejpam-3286	164	10	x	x	PUNCT
ejpam-3286	164	11	and	and	CCONJ
ejpam-3286	164	12	f	f	PROPN
ejpam-3286	164	13	and	and	CCONJ
ejpam-3286	164	14	g	g	PROPN
ejpam-3286	164	15	are	be	AUX
ejpam-3286	164	16	identity	identity	NOUN
ejpam-3286	164	17	mappings	mapping	NOUN
ejpam-3286	164	18	on	on	ADP
ejpam-3286	164	19	x	x	NOUN
ejpam-3286	164	20	,	,	PUNCT
ejpam-3286	164	21	then	then	ADV
ejpam-3286	164	22	theorem	theorem	VERB
ejpam-3286	164	23	1	1	NUM
ejpam-3286	164	24	yields	yield	NOUN
ejpam-3286	164	25	the	the	DET
ejpam-3286	164	26	following	follow	VERB
ejpam-3286	164	27	common	common	ADJ
ejpam-3286	164	28	fixed	fix	VERB
ejpam-3286	164	29	point	point	NOUN
ejpam-3286	164	30	theorem	theorem	NOUN
ejpam-3286	164	31	for	for	ADP
ejpam-3286	164	32	pairs	pair	NOUN
ejpam-3286	164	33	of	of	ADP
ejpam-3286	164	34	commuting	commuting	NOUN
ejpam-3286	164	35	selfmappings	selfmapping	NOUN
ejpam-3286	164	36	.	.	PUNCT
ejpam-3286	165	1	corollary	corollary	ADJ
ejpam-3286	165	2	1	1	NUM
ejpam-3286	165	3	.	.	PUNCT
ejpam-3286	166	1	let	let	VERB
ejpam-3286	166	2	x	x	PRON
ejpam-3286	166	3	be	be	AUX
ejpam-3286	166	4	a	a	DET
ejpam-3286	166	5	complete	complete	ADJ
ejpam-3286	166	6	metric	metric	ADJ
ejpam-3286	166	7	space	space	NOUN
ejpam-3286	166	8	.	.	PUNCT
ejpam-3286	167	1	moreover	moreover	ADV
ejpam-3286	167	2	,	,	PUNCT
ejpam-3286	167	3	assume	assume	VERB
ejpam-3286	167	4	that	that	SCONJ
ejpam-3286	167	5	s	s	VERB
ejpam-3286	167	6	:	:	PUNCT
ejpam-3286	167	7	x	x	PUNCT
ejpam-3286	167	8	−→	−→	NOUN
ejpam-3286	167	9	x	x	NOUN
ejpam-3286	167	10	,	,	PUNCT
ejpam-3286	167	11	t	t	PROPN
ejpam-3286	167	12	:	:	PUNCT
ejpam-3286	167	13	x	x	PUNCT
ejpam-3286	167	14	−→	−→	NOUN
ejpam-3286	167	15	x	x	NOUN
ejpam-3286	167	16	are	be	AUX
ejpam-3286	167	17	continuous	continuous	ADJ
ejpam-3286	167	18	functions	function	NOUN
ejpam-3286	167	19	satisfying	satisfy	VERB
ejpam-3286	167	20	the	the	DET
ejpam-3286	167	21	following	follow	VERB
ejpam-3286	167	22	conditions	condition	NOUN
ejpam-3286	167	23	:	:	PUNCT
ejpam-3286	167	24	(	(	PUNCT
ejpam-3286	167	25	1	1	X
ejpam-3286	167	26	)	)	PUNCT
ejpam-3286	167	27	s	s	VERB
ejpam-3286	167	28	commutes	commute	NOUN
ejpam-3286	167	29	with	with	ADP
ejpam-3286	167	30	t	t	PROPN
ejpam-3286	167	31	.	.	PUNCT
ejpam-3286	168	1	(	(	PUNCT
ejpam-3286	168	2	2	2	X
ejpam-3286	168	3	)	)	PUNCT
ejpam-3286	168	4	there	there	PRON
ejpam-3286	168	5	exists	exist	VERB
ejpam-3286	168	6	comparison	comparison	NOUN
ejpam-3286	168	7	function	function	NOUN
ejpam-3286	168	8	φ	φ	PROPN
ejpam-3286	168	9	such	such	ADJ
ejpam-3286	168	10	that	that	SCONJ
ejpam-3286	168	11	d(sx	d(sx	PROPN
ejpam-3286	168	12	,	,	PUNCT
ejpam-3286	168	13	sy	sy	NOUN
ejpam-3286	168	14	)	)	PUNCT
ejpam-3286	168	15	≤	≤	NOUN
ejpam-3286	169	1	φ(d(tx	φ(d(tx	VERB
ejpam-3286	169	2	,	,	PUNCT
ejpam-3286	169	3	ty	ty	NOUN
ejpam-3286	169	4	)	)	PUNCT
ejpam-3286	169	5	)	)	PUNCT
ejpam-3286	169	6	for	for	ADP
ejpam-3286	169	7	all	all	DET
ejpam-3286	169	8	x	x	NOUN
ejpam-3286	169	9	,	,	PUNCT
ejpam-3286	169	10	y	y	PROPN
ejpam-3286	169	11	∈	∈	PROPN
ejpam-3286	169	12	x.	x.	NOUN
ejpam-3286	169	13	(	(	PUNCT
ejpam-3286	169	14	3	3	NUM
ejpam-3286	169	15	)	)	PUNCT
ejpam-3286	169	16	s(x	s(x	PROPN
ejpam-3286	169	17	)	)	PUNCT
ejpam-3286	170	1	⊂	⊂	PROPN
ejpam-3286	170	2	t	t	PROPN
ejpam-3286	170	3	(	(	PUNCT
ejpam-3286	170	4	x	x	NOUN
ejpam-3286	170	5	)	)	PUNCT
ejpam-3286	170	6	.	.	PUNCT
ejpam-3286	171	1	then	then	ADV
ejpam-3286	171	2	the	the	DET
ejpam-3286	171	3	pair	pair	NOUN
ejpam-3286	171	4	(	(	PUNCT
ejpam-3286	171	5	s	s	PROPN
ejpam-3286	171	6	,	,	PUNCT
ejpam-3286	171	7	t	t	PROPN
ejpam-3286	171	8	)	)	PUNCT
ejpam-3286	171	9	has	have	VERB
ejpam-3286	171	10	a	a	DET
ejpam-3286	171	11	unique	unique	ADJ
ejpam-3286	171	12	common	common	ADJ
ejpam-3286	171	13	fixed	fix	VERB
ejpam-3286	171	14	point	point	NOUN
ejpam-3286	171	15	.	.	PUNCT
ejpam-3286	172	1	references	reference	NOUN
ejpam-3286	172	2	[	[	X
ejpam-3286	172	3	1	1	NUM
ejpam-3286	172	4	]	]	PUNCT
ejpam-3286	172	5	m.	m.	NOUN
ejpam-3286	172	6	a.	a.	PROPN
ejpam-3286	172	7	al	al	PROPN
ejpam-3286	172	8	-	-	PUNCT
ejpam-3286	172	9	thagafi	thagafi	PROPN
ejpam-3286	172	10	,	,	PUNCT
ejpam-3286	172	11	n.	n.	PROPN
ejpam-3286	172	12	shahzad	shahzad	PROPN
ejpam-3286	172	13	,	,	PUNCT
ejpam-3286	172	14	convergence	convergence	NOUN
ejpam-3286	172	15	and	and	CCONJ
ejpam-3286	172	16	existence	existence	NOUN
ejpam-3286	172	17	results	result	VERB
ejpam-3286	172	18	for	for	ADP
ejpam-3286	172	19	best	good	ADJ
ejpam-3286	172	20	proximity	proximity	NOUN
ejpam-3286	172	21	points	point	NOUN
ejpam-3286	172	22	,	,	PUNCT
ejpam-3286	172	23	nonlinear	nonlinear	ADJ
ejpam-3286	172	24	analysis	analysis	NOUN
ejpam-3286	172	25	:	:	PUNCT
ejpam-3286	172	26	theory	theory	NOUN
ejpam-3286	172	27	,	,	PUNCT
ejpam-3286	172	28	methods	method	NOUN
ejpam-3286	172	29	&	&	CCONJ
ejpam-3286	172	30	applications	application	NOUN
ejpam-3286	172	31	,	,	PUNCT
ejpam-3286	172	32	70	70	NUM
ejpam-3286	172	33	(	(	PUNCT
ejpam-3286	172	34	10	10	NUM
ejpam-3286	172	35	)	)	PUNCT
ejpam-3286	172	36	,	,	PUNCT
ejpam-3286	172	37	3665	3665	NUM
ejpam-3286	172	38	-	-	SYM
ejpam-3286	172	39	3671	3671	NUM
ejpam-3286	172	40	,	,	PUNCT
ejpam-3286	172	41	2009	2009	NUM
ejpam-3286	172	42	.	.	PUNCT
ejpam-3286	173	1	[	[	X
ejpam-3286	173	2	2	2	NUM
ejpam-3286	173	3	]	]	PUNCT
ejpam-3286	173	4	a.	a.	NOUN
ejpam-3286	173	5	abkar	abkar	PROPN
ejpam-3286	173	6	,	,	PUNCT
ejpam-3286	173	7	m.	m.	NOUN
ejpam-3286	173	8	gabeleh	gabeleh	NOUN
ejpam-3286	173	9	,	,	PUNCT
ejpam-3286	173	10	best	good	ADJ
ejpam-3286	173	11	proximity	proximity	NOUN
ejpam-3286	173	12	points	point	NOUN
ejpam-3286	173	13	for	for	ADP
ejpam-3286	173	14	asymptotic	asymptotic	ADJ
ejpam-3286	173	15	cyclic	cyclic	ADJ
ejpam-3286	173	16	contraction	contraction	NOUN
ejpam-3286	173	17	mappings	mapping	NOUN
ejpam-3286	173	18	,	,	PUNCT
ejpam-3286	173	19	nonlinear	nonlinear	ADJ
ejpam-3286	173	20	analysis	analysis	NOUN
ejpam-3286	173	21	:	:	PUNCT
ejpam-3286	173	22	theory	theory	NOUN
ejpam-3286	173	23	,	,	PUNCT
ejpam-3286	173	24	methods	method	NOUN
ejpam-3286	173	25	&	&	CCONJ
ejpam-3286	173	26	applications	application	NOUN
ejpam-3286	173	27	,	,	PUNCT
ejpam-3286	173	28	74	74	NUM
ejpam-3286	173	29	,	,	PUNCT
ejpam-3286	173	30	7261	7261	NUM
ejpam-3286	173	31	-	-	SYM
ejpam-3286	173	32	7268	7268	NUM
ejpam-3286	173	33	,	,	PUNCT
ejpam-3286	173	34	2011	2011	NUM
ejpam-3286	173	35	.	.	PUNCT
ejpam-3286	174	1	[	[	X
ejpam-3286	174	2	3	3	X
ejpam-3286	174	3	]	]	PUNCT
ejpam-3286	174	4	a.	a.	NOUN
ejpam-3286	174	5	ninsri	ninsri	PROPN
ejpam-3286	174	6	,	,	PUNCT
ejpam-3286	174	7	w.	w.	PROPN
ejpam-3286	174	8	sintunavarat	sintunavarat	PROPN
ejpam-3286	174	9	,	,	PUNCT
ejpam-3286	174	10	toward	toward	ADP
ejpam-3286	174	11	a	a	DET
ejpam-3286	174	12	generalized	generalize	VERB
ejpam-3286	174	13	contractive	contractive	ADJ
ejpam-3286	174	14	condition	condition	NOUN
ejpam-3286	174	15	in	in	ADP
ejpam-3286	174	16	partial	partial	ADJ
ejpam-3286	174	17	metric	metric	ADJ
ejpam-3286	174	18	spaces	space	NOUN
ejpam-3286	174	19	with	with	ADP
ejpam-3286	174	20	the	the	DET
ejpam-3286	174	21	existence	existence	NOUN
ejpam-3286	174	22	results	result	NOUN
ejpam-3286	174	23	of	of	ADP
ejpam-3286	174	24	fixed	fix	VERB
ejpam-3286	174	25	points	point	NOUN
ejpam-3286	174	26	and	and	CCONJ
ejpam-3286	174	27	best	good	ADJ
ejpam-3286	174	28	proximity	proximity	NOUN
ejpam-3286	174	29	points	point	NOUN
ejpam-3286	174	30	,	,	PUNCT
ejpam-3286	174	31	journal	journal	NOUN
ejpam-3286	174	32	of	of	ADP
ejpam-3286	174	33	fixed	fix	VERB
ejpam-3286	174	34	point	point	NOUN
ejpam-3286	174	35	theory	theory	NOUN
ejpam-3286	174	36	and	and	CCONJ
ejpam-3286	174	37	applications	application	NOUN
ejpam-3286	174	38	,	,	PUNCT
ejpam-3286	174	39	20	20	NUM
ejpam-3286	174	40	,	,	PUNCT
ejpam-3286	174	41	2018	2018	NUM
ejpam-3286	174	42	.	.	PUNCT
ejpam-3286	175	1	[	[	X
ejpam-3286	175	2	4	4	X
ejpam-3286	175	3	]	]	X
ejpam-3286	175	4	s.	s.	PROPN
ejpam-3286	175	5	radenović	radenović	PROPN
ejpam-3286	175	6	,	,	PUNCT
ejpam-3286	175	7	a	a	DET
ejpam-3286	175	8	note	note	NOUN
ejpam-3286	175	9	on	on	ADP
ejpam-3286	175	10	fixed	fix	VERB
ejpam-3286	175	11	point	point	NOUN
ejpam-3286	175	12	theory	theory	NOUN
ejpam-3286	175	13	for	for	ADP
ejpam-3286	175	14	cyclic	cyclic	ADJ
ejpam-3286	175	15	φ	φ	PROPN
ejpam-3286	175	16	-	-	NOUN
ejpam-3286	175	17	contractions	contraction	NOUN
ejpam-3286	175	18	,	,	PUNCT
ejpam-3286	175	19	fixed	fix	VERB
ejpam-3286	175	20	point	point	NOUN
ejpam-3286	175	21	theory	theory	NOUN
ejpam-3286	175	22	and	and	CCONJ
ejpam-3286	175	23	applications	application	NOUN
ejpam-3286	175	24	,	,	PUNCT
ejpam-3286	175	25	2015	2015	NUM
ejpam-3286	175	26	.	.	PUNCT
ejpam-3286	176	1	[	[	X
ejpam-3286	176	2	5	5	X
ejpam-3286	176	3	]	]	PUNCT
ejpam-3286	176	4	s.	s.	PROPN
ejpam-3286	176	5	sadiq	sadiq	PROPN
ejpam-3286	176	6	basha	basha	PROPN
ejpam-3286	176	7	,	,	PUNCT
ejpam-3286	176	8	best	good	ADJ
ejpam-3286	176	9	proximity	proximity	NOUN
ejpam-3286	176	10	point	point	NOUN
ejpam-3286	176	11	theorems	theorem	NOUN
ejpam-3286	176	12	,	,	PUNCT
ejpam-3286	176	13	journal	journal	NOUN
ejpam-3286	176	14	of	of	ADP
ejpam-3286	176	15	approximation	approximation	NOUN
ejpam-3286	176	16	theory	theory	NOUN
ejpam-3286	176	17	,	,	PUNCT
ejpam-3286	176	18	163	163	NUM
ejpam-3286	176	19	,	,	PUNCT
ejpam-3286	176	20	1772	1772	NUM
ejpam-3286	176	21	-	-	SYM
ejpam-3286	176	22	1781	1781	NUM
ejpam-3286	176	23	,	,	PUNCT
ejpam-3286	176	24	2011	2011	NUM
ejpam-3286	176	25	.	.	PUNCT
ejpam-3286	177	1	[	[	X
ejpam-3286	177	2	6	6	NUM
ejpam-3286	177	3	]	]	PUNCT
ejpam-3286	177	4	h.	h.	NOUN
ejpam-3286	177	5	isik	isik	PROPN
ejpam-3286	177	6	,	,	PUNCT
ejpam-3286	177	7	m.	m.	NOUN
ejpam-3286	177	8	s.	s.	PROPN
ejpam-3286	177	9	sezen	sezen	PROPN
ejpam-3286	177	10	,	,	PUNCT
ejpam-3286	177	11	c.	c.	PROPN
ejpam-3286	177	12	vetro	vetro	PROPN
ejpam-3286	177	13	,	,	PUNCT
ejpam-3286	177	14	ϕ-best	ϕ-best	NOUN
ejpam-3286	177	15	proximity	proximity	NOUN
ejpam-3286	177	16	point	point	NOUN
ejpam-3286	177	17	theorems	theorem	NOUN
ejpam-3286	177	18	and	and	CCONJ
ejpam-3286	177	19	applications	application	NOUN
ejpam-3286	177	20	to	to	ADP
ejpam-3286	177	21	variational	variational	ADJ
ejpam-3286	177	22	inequality	inequality	NOUN
ejpam-3286	177	23	problems	problem	NOUN
ejpam-3286	177	24	,	,	PUNCT
ejpam-3286	177	25	journal	journal	NOUN
ejpam-3286	177	26	of	of	ADP
ejpam-3286	177	27	fixed	fix	VERB
ejpam-3286	177	28	point	point	NOUN
ejpam-3286	177	29	theory	theory	NOUN
ejpam-3286	177	30	and	and	CCONJ
ejpam-3286	177	31	applications	application	NOUN
ejpam-3286	177	32	,	,	PUNCT
ejpam-3286	177	33	19	19	NUM
ejpam-3286	177	34	,	,	PUNCT
ejpam-3286	177	35	3177	3177	NUM
ejpam-3286	177	36	-	-	SYM
ejpam-3286	177	37	3189	3189	NUM
ejpam-3286	177	38	,	,	PUNCT
ejpam-3286	177	39	2017	2017	NUM
ejpam-3286	177	40	.	.	PUNCT
ejpam-3286	178	1	[	[	X
ejpam-3286	178	2	7	7	X
ejpam-3286	178	3	]	]	PUNCT
ejpam-3286	178	4	s.	s.	PROPN
ejpam-3286	178	5	sadiq	sadiq	PROPN
ejpam-3286	178	6	basha	basha	PROPN
ejpam-3286	178	7	,	,	PUNCT
ejpam-3286	178	8	n.	n.	PROPN
ejpam-3286	178	9	shahzad	shahzad	PROPN
ejpam-3286	178	10	,	,	PUNCT
ejpam-3286	178	11	common	common	ADJ
ejpam-3286	178	12	best	good	ADJ
ejpam-3286	178	13	proximity	proximity	NOUN
ejpam-3286	178	14	point	point	NOUN
ejpam-3286	178	15	theorems	theorem	NOUN
ejpam-3286	178	16	:	:	PUNCT
ejpam-3286	178	17	global	global	ADJ
ejpam-3286	178	18	minimization	minimization	NOUN
ejpam-3286	178	19	of	of	ADP
ejpam-3286	178	20	some	some	DET
ejpam-3286	178	21	real	real	ADV
ejpam-3286	178	22	-	-	PUNCT
ejpam-3286	178	23	valued	value	VERB
ejpam-3286	178	24	multi	multi	ADJ
ejpam-3286	178	25	-	-	ADJ
ejpam-3286	178	26	objective	objective	ADJ
ejpam-3286	178	27	functions	function	NOUN
ejpam-3286	178	28	,	,	PUNCT
ejpam-3286	178	29	journal	journal	NOUN
ejpam-3286	178	30	of	of	ADP
ejpam-3286	178	31	fixed	fix	VERB
ejpam-3286	178	32	point	point	NOUN
ejpam-3286	178	33	theory	theory	NOUN
ejpam-3286	178	34	and	and	CCONJ
ejpam-3286	178	35	applications	application	NOUN
ejpam-3286	178	36	,	,	PUNCT
ejpam-3286	178	37	18	18	NUM
ejpam-3286	178	38	(	(	PUNCT
ejpam-3286	178	39	3	3	NUM
ejpam-3286	178	40	)	)	PUNCT
ejpam-3286	178	41	,	,	PUNCT
ejpam-3286	178	42	587	587	NUM
ejpam-3286	178	43	-	-	SYM
ejpam-3286	178	44	600	600	NUM
ejpam-3286	178	45	,	,	PUNCT
ejpam-3286	178	46	2016	2016	NUM
ejpam-3286	178	47	.	.	PUNCT
ejpam-3286	179	1	[	[	X
ejpam-3286	179	2	8	8	X
ejpam-3286	179	3	]	]	PUNCT
ejpam-3286	179	4	s.	s.	PROPN
ejpam-3286	179	5	sadiq	sadiq	PROPN
ejpam-3286	179	6	basha	basha	PROPN
ejpam-3286	179	7	,	,	PUNCT
ejpam-3286	179	8	n.	n.	PROPN
ejpam-3286	179	9	shazad	shazad	PROPN
ejpam-3286	179	10	,	,	PUNCT
ejpam-3286	179	11	r.	r.	PROPN
ejpam-3286	179	12	jeyaraj	jeyaraj	PROPN
ejpam-3286	179	13	,	,	PUNCT
ejpam-3286	179	14	common	common	ADJ
ejpam-3286	179	15	best	good	ADJ
ejpam-3286	179	16	proximity	proximity	NOUN
ejpam-3286	179	17	point	point	NOUN
ejpam-3286	179	18	:	:	PUNCT
ejpam-3286	179	19	global	global	ADJ
ejpam-3286	179	20	optimizations	optimization	NOUN
ejpam-3286	179	21	of	of	ADP
ejpam-3286	179	22	multi	multi	ADJ
ejpam-3286	179	23	-	-	ADJ
ejpam-3286	179	24	objective	objective	ADJ
ejpam-3286	179	25	functions	function	NOUN
ejpam-3286	179	26	,	,	PUNCT
ejpam-3286	179	27	applied	apply	VERB
ejpam-3286	179	28	mathematics	mathematics	NOUN
ejpam-3286	179	29	letters	letter	NOUN
ejpam-3286	179	30	,	,	PUNCT
ejpam-3286	179	31	24	24	NUM
ejpam-3286	179	32	,	,	PUNCT
ejpam-3286	179	33	883	883	NUM
ejpam-3286	179	34	-	-	SYM
ejpam-3286	179	35	886	886	NUM
ejpam-3286	179	36	,	,	PUNCT
ejpam-3286	179	37	2011	2011	NUM
ejpam-3286	179	38	.	.	PUNCT
ejpam-3286	180	1	references	reference	NOUN
ejpam-3286	180	2	875	875	NUM
ejpam-3286	180	3	[	[	X
ejpam-3286	180	4	9	9	NUM
ejpam-3286	180	5	]	]	PUNCT
ejpam-3286	180	6	s.	s.	PROPN
ejpam-3286	180	7	sadiq	sadiq	PROPN
ejpam-3286	180	8	basha	basha	PROPN
ejpam-3286	180	9	,	,	PUNCT
ejpam-3286	180	10	p.	p.	PROPN
ejpam-3286	180	11	veeramani	veeramani	PROPN
ejpam-3286	180	12	,	,	PUNCT
ejpam-3286	180	13	best	good	ADJ
ejpam-3286	180	14	proximity	proximity	NOUN
ejpam-3286	180	15	pair	pair	NOUN
ejpam-3286	180	16	theorems	theorem	NOUN
ejpam-3286	180	17	for	for	ADP
ejpam-3286	180	18	multi	multi	NOUN
ejpam-3286	180	19	functions	function	NOUN
ejpam-3286	180	20	with	with	ADP
ejpam-3286	180	21	open	open	ADJ
ejpam-3286	180	22	fibres	fibre	NOUN
ejpam-3286	180	23	,	,	PUNCT
ejpam-3286	180	24	journal	journal	NOUN
ejpam-3286	180	25	of	of	ADP
ejpam-3286	180	26	approximation	approximation	NOUN
ejpam-3286	180	27	theory	theory	NOUN
ejpam-3286	180	28	,	,	PUNCT
ejpam-3286	180	29	103	103	NUM
ejpam-3286	180	30	,	,	PUNCT
ejpam-3286	180	31	119	119	NUM
ejpam-3286	180	32	-	-	SYM
ejpam-3286	180	33	129	129	NUM
ejpam-3286	180	34	,	,	PUNCT
ejpam-3286	180	35	2000	2000	NUM
ejpam-3286	180	36	.	.	PUNCT
ejpam-3286	181	1	[	[	X
ejpam-3286	181	2	10	10	NUM
ejpam-3286	181	3	]	]	X
ejpam-3286	181	4	v.	v.	ADP
ejpam-3286	181	5	sankar	sankar	PROPN
ejpam-3286	181	6	raj	raj	PROPN
ejpam-3286	181	7	,	,	PUNCT
ejpam-3286	181	8	p.	p.	PROPN
ejpam-3286	181	9	veeramani	veeramani	PROPN
ejpam-3286	181	10	,	,	PUNCT
ejpam-3286	181	11	best	good	ADJ
ejpam-3286	181	12	proximity	proximity	NOUN
ejpam-3286	181	13	pair	pair	NOUN
ejpam-3286	181	14	theorems	theorem	NOUN
ejpam-3286	181	15	for	for	ADP
ejpam-3286	181	16	relatively	relatively	ADV
ejpam-3286	181	17	nonexpansive	nonexpansive	ADJ
ejpam-3286	181	18	mappings	mapping	NOUN
ejpam-3286	181	19	,	,	PUNCT
ejpam-3286	181	20	applied	apply	VERB
ejpam-3286	181	21	general	general	ADJ
ejpam-3286	181	22	topology	topology	NOUN
ejpam-3286	181	23	,	,	PUNCT
ejpam-3286	181	24	10	10	NUM
ejpam-3286	181	25	(	(	PUNCT
ejpam-3286	181	26	1	1	NUM
ejpam-3286	181	27	)	)	PUNCT
ejpam-3286	181	28	,	,	PUNCT
ejpam-3286	181	29	21	21	NUM
ejpam-3286	181	30	-	-	SYM
ejpam-3286	181	31	28	28	NUM
ejpam-3286	181	32	,	,	PUNCT
ejpam-3286	181	33	2009	2009	NUM
ejpam-3286	181	34	.	.	PUNCT
ejpam-3286	182	1	[	[	X
ejpam-3286	182	2	11	11	NUM
ejpam-3286	182	3	]	]	X
ejpam-3286	182	4	n.	n.	PROPN
ejpam-3286	182	5	shahzad	shahzad	PROPN
ejpam-3286	182	6	,	,	PUNCT
ejpam-3286	182	7	s.	s.	PROPN
ejpam-3286	182	8	sadiq	sadiq	PROPN
ejpam-3286	182	9	basha	basha	PROPN
ejpam-3286	182	10	and	and	CCONJ
ejpam-3286	182	11	r.	r.	PROPN
ejpam-3286	182	12	jeyaraj	jeyaraj	PROPN
ejpam-3286	182	13	,	,	PUNCT
ejpam-3286	182	14	common	common	ADJ
ejpam-3286	182	15	best	good	ADJ
ejpam-3286	182	16	proximity	proximity	NOUN
ejpam-3286	182	17	points	point	NOUN
ejpam-3286	182	18	:	:	PUNCT
ejpam-3286	182	19	global	global	ADJ
ejpam-3286	182	20	optimal	optimal	ADJ
ejpam-3286	182	21	solutions	solution	NOUN
ejpam-3286	182	22	,	,	PUNCT
ejpam-3286	182	23	journal	journal	NOUN
ejpam-3286	182	24	of	of	ADP
ejpam-3286	182	25	optimization	optimization	NOUN
ejpam-3286	182	26	theory	theory	NOUN
ejpam-3286	182	27	and	and	CCONJ
ejpam-3286	182	28	applications	application	NOUN
ejpam-3286	182	29	,	,	PUNCT
ejpam-3286	182	30	148	148	NUM
ejpam-3286	182	31	,	,	PUNCT
ejpam-3286	182	32	69	69	NUM
ejpam-3286	182	33	-	-	SYM
ejpam-3286	182	34	78	78	NUM
ejpam-3286	182	35	,	,	PUNCT
ejpam-3286	182	36	2011	2011	NUM
ejpam-3286	182	37	.	.	PUNCT