id	sid	tid	token	lemma	pos
ejpam-3331	1	1	protect	protect	VERB
ejpam-3331	1	2	elax	elax	NOUN
ejpam-3331	1	3	protect	protect	NOUN
ejpam-3331	1	4	�	�	PROPN
ejpam-3331	1	5	egingroup	egingroup	NOUN
ejpam-3331	1	6	immediate	immediate	ADJ
ejpam-3331	1	7	write	write	NOUN
ejpam-3331	1	8	@unused	@unuse	VERB
ejpam-3331	1	9	def	def	ADJ
ejpam-3331	1	10	messagebreak	messagebreak	NOUN
ejpam-3331	1	11	let	let	AUX
ejpam-3331	1	12	protect	protect	VERB
ejpam-3331	1	13	edef	edef	NOUN
ejpam-3331	1	14	you	you	PRON
ejpam-3331	1	15	're	be	AUX
ejpam-3331	1	16	in	in	ADP
ejpam-3331	1	17	trouble	trouble	NOUN
ejpam-3331	1	18	here	here	ADV
ejpam-3331	1	19	.	.	PUNCT
ejpam-3331	2	1	try	try	VERB
ejpam-3331	2	2	typing	type	VERB
ejpam-3331	2	3	<	<	X
ejpam-3331	2	4	return	return	NOUN
ejpam-3331	2	5	>	>	X
ejpam-3331	2	6	to	to	ADP
ejpam-3331	2	7	proceed.messagebreak	proceed.messagebreak	NOUN
ejpam-3331	2	8	if	if	SCONJ
ejpam-3331	2	9	that	that	PRON
ejpam-3331	2	10	does	do	AUX
ejpam-3331	2	11	n't	not	PART
ejpam-3331	2	12	work	work	VERB
ejpam-3331	2	13	,	,	PUNCT
ejpam-3331	2	14	type	type	NOUN
ejpam-3331	2	15	x	x	PART
ejpam-3331	2	16	<	<	X
ejpam-3331	2	17	return	return	NOUN
ejpam-3331	2	18	>	>	X
ejpam-3331	2	19	to	to	PART
ejpam-3331	2	20	quit	quit	VERB
ejpam-3331	2	21	.	.	PUNCT
ejpam-3331	3	1	errhelp	errhelp	VERB
ejpam-3331	3	2	let	let	VERB
ejpam-3331	3	3	def	def	ADJ
ejpam-3331	3	4	messagebreak	messagebreak	PROPN
ejpam-3331	3	5	def	def	PROPN
ejpam-3331	3	6	errmessage	errmessage	PROPN
ejpam-3331	3	7	latex	latex	NOUN
ejpam-3331	3	8	error	error	NOUN
ejpam-3331	3	9	:	:	PUNCT
ejpam-3331	3	10	mathcal	mathcal	ADJ
ejpam-3331	3	11	allowed	allow	VERB
ejpam-3331	3	12	only	only	ADV
ejpam-3331	3	13	in	in	ADP
ejpam-3331	3	14	math	math	NOUN
ejpam-3331	3	15	mode	mode	NOUN
ejpam-3331	3	16	.	.	PUNCT
ejpam-3331	4	1	see	see	VERB
ejpam-3331	4	2	the	the	DET
ejpam-3331	4	3	latex	latex	NOUN
ejpam-3331	4	4	manual	manual	NOUN
ejpam-3331	4	5	or	or	CCONJ
ejpam-3331	4	6	latex	latex	NOUN
ejpam-3331	4	7	companion	companion	NOUN
ejpam-3331	4	8	for	for	ADP
ejpam-3331	4	9	explanation	explanation	NOUN
ejpam-3331	4	10	.	.	PUNCT
ejpam-3331	5	1	type	type	NOUN
ejpam-3331	5	2	h	h	NOUN
ejpam-3331	5	3	<	<	X
ejpam-3331	5	4	return	return	VERB
ejpam-3331	5	5	>	>	X
ejpam-3331	5	6	for	for	ADP
ejpam-3331	5	7	immediate	immediate	ADJ
ejpam-3331	5	8	help	help	NOUN
ejpam-3331	5	9	endgroup	endgroup	PROPN
ejpam-3331	5	10	elax	elax	VERB
ejpam-3331	5	11	n}$-soft	n}$-soft	ADV
ejpam-3331	5	12	$	$	SYM
ejpam-3331	5	13	p$-ideals	p$-ideal	NOUN
ejpam-3331	5	14	of	of	ADP
ejpam-3331	5	15	$	$	SYM
ejpam-3331	5	16	bci$-algebras	bci$-algebras	PROPN
ejpam-3331	5	17	european	european	ADJ
ejpam-3331	5	18	journal	journal	NOUN
ejpam-3331	5	19	of	of	ADP
ejpam-3331	5	20	pure	pure	ADJ
ejpam-3331	5	21	and	and	CCONJ
ejpam-3331	5	22	applied	apply	VERB
ejpam-3331	5	23	mathematics	mathematic	NOUN
ejpam-3331	5	24	vol	vol	NOUN
ejpam-3331	5	25	.	.	PROPN
ejpam-3331	6	1	12	12	NUM
ejpam-3331	6	2	,	,	PUNCT
ejpam-3331	6	3	no	no	INTJ
ejpam-3331	6	4	.	.	NOUN
ejpam-3331	6	5	1	1	NUM
ejpam-3331	6	6	,	,	PUNCT
ejpam-3331	6	7	2019	2019	NUM
ejpam-3331	6	8	,	,	PUNCT
ejpam-3331	6	9	88	88	NUM
ejpam-3331	6	10	-	-	SYM
ejpam-3331	6	11	100	100	NUM
ejpam-3331	6	12	issn	issn	PROPN
ejpam-3331	6	13	1307	1307	NUM
ejpam-3331	6	14	-	-	SYM
ejpam-3331	6	15	5543	5543	NUM
ejpam-3331	6	16	–	–	PUNCT
ejpam-3331	6	17	www.ejpam.com	www.ejpam.com	X
ejpam-3331	6	18	published	publish	VERB
ejpam-3331	6	19	by	by	ADP
ejpam-3331	6	20	new	new	PROPN
ejpam-3331	6	21	york	york	PROPN
ejpam-3331	6	22	business	business	PROPN
ejpam-3331	6	23	global	global	ADJ
ejpam-3331	6	24	fixed	fix	VERB
ejpam-3331	6	25	point	point	NOUN
ejpam-3331	6	26	results	result	NOUN
ejpam-3331	6	27	in	in	ADP
ejpam-3331	6	28	metric	metric	ADJ
ejpam-3331	6	29	-	-	PUNCT
ejpam-3331	6	30	like	like	ADJ
ejpam-3331	6	31	spaces	space	NOUN
ejpam-3331	6	32	via	via	ADP
ejpam-3331	6	33	σ	σ	PROPN
ejpam-3331	6	34	-	-	PUNCT
ejpam-3331	6	35	simulation	simulation	NOUN
ejpam-3331	6	36	functions	function	NOUN
ejpam-3331	6	37	habes	habe	NOUN
ejpam-3331	6	38	alsamir1,∗	alsamir1,∗	VERB
ejpam-3331	6	39	,	,	PUNCT
ejpam-3331	6	40	mohd	mohd	PROPN
ejpam-3331	6	41	selmi	selmi	PROPN
ejpam-3331	6	42	noorani1	noorani1	PROPN
ejpam-3331	6	43	,	,	PUNCT
ejpam-3331	6	44	wasfi	wasfi	PROPN
ejpam-3331	6	45	shatanawi2,3	shatanawi2,3	PROPN
ejpam-3331	6	46	,	,	PUNCT
ejpam-3331	6	47	hassen	hassen	PROPN
ejpam-3331	6	48	aydi4	aydi4	PROPN
ejpam-3331	6	49	,	,	PUNCT
ejpam-3331	6	50	habibulla	habibulla	PROPN
ejpam-3331	6	51	akhadkulov5	akhadkulov5	PROPN
ejpam-3331	6	52	,	,	PUNCT
ejpam-3331	6	53	haitham	haitham	PROPN
ejpam-3331	6	54	qawaqneh1	qawaqneh1	PROPN
ejpam-3331	6	55	,	,	PUNCT
ejpam-3331	6	56	kareem	kareem	PROPN
ejpam-3331	6	57	alanazi6	alanazi6	PROPN
ejpam-3331	6	58	1	1	NUM
ejpam-3331	6	59	school	school	NOUN
ejpam-3331	6	60	of	of	ADP
ejpam-3331	6	61	mathematical	mathematical	ADJ
ejpam-3331	6	62	sciences	science	NOUN
ejpam-3331	6	63	,	,	PUNCT
ejpam-3331	6	64	faculty	faculty	NOUN
ejpam-3331	6	65	of	of	ADP
ejpam-3331	6	66	science	science	NOUN
ejpam-3331	6	67	and	and	CCONJ
ejpam-3331	6	68	technology	technology	NOUN
ejpam-3331	6	69	,	,	PUNCT
ejpam-3331	6	70	universiti	universiti	PROPN
ejpam-3331	6	71	kebangsaan	kebangsaan	PROPN
ejpam-3331	6	72	malaysia	malaysia	PROPN
ejpam-3331	6	73	,	,	PUNCT
ejpam-3331	6	74	43600	43600	NUM
ejpam-3331	6	75	ukm	ukm	PROPN
ejpam-3331	6	76	,	,	PUNCT
ejpam-3331	6	77	selangor	selangor	PROPN
ejpam-3331	6	78	darul	darul	PROPN
ejpam-3331	6	79	ehsan	ehsan	PROPN
ejpam-3331	6	80	,	,	PUNCT
ejpam-3331	6	81	malaysia	malaysia	PROPN
ejpam-3331	6	82	2	2	NUM
ejpam-3331	6	83	department	department	NOUN
ejpam-3331	6	84	of	of	ADP
ejpam-3331	6	85	mathematics	mathematic	NOUN
ejpam-3331	6	86	,	,	PUNCT
ejpam-3331	6	87	hashemite	hashemite	PROPN
ejpam-3331	6	88	university	university	NOUN
ejpam-3331	6	89	,	,	PUNCT
ejpam-3331	6	90	zarqa	zarqa	PROPN
ejpam-3331	6	91	1315	1315	NUM
ejpam-3331	6	92	,	,	PUNCT
ejpam-3331	6	93	jordan	jordan	PROPN
ejpam-3331	6	94	3	3	NUM
ejpam-3331	6	95	department	department	PROPN
ejpam-3331	6	96	of	of	ADP
ejpam-3331	6	97	mathematics	mathematics	PROPN
ejpam-3331	6	98	and	and	CCONJ
ejpam-3331	6	99	general	general	ADJ
ejpam-3331	6	100	courses	course	NOUN
ejpam-3331	6	101	prince	prince	PROPN
ejpam-3331	6	102	sultan	sultan	PROPN
ejpam-3331	6	103	university	university	PROPN
ejpam-3331	6	104	,	,	PUNCT
ejpam-3331	6	105	riyadh	riyadh	PROPN
ejpam-3331	6	106	,	,	PUNCT
ejpam-3331	6	107	saudi	saudi	PROPN
ejpam-3331	6	108	arabia	arabia	PROPN
ejpam-3331	6	109	4	4	NUM
ejpam-3331	6	110	imam	imam	PROPN
ejpam-3331	6	111	abdulrahman	abdulrahman	PROPN
ejpam-3331	6	112	bin	bin	PROPN
ejpam-3331	6	113	faisal	faisal	PROPN
ejpam-3331	6	114	university	university	PROPN
ejpam-3331	6	115	,	,	PUNCT
ejpam-3331	6	116	department	department	NOUN
ejpam-3331	6	117	of	of	ADP
ejpam-3331	6	118	mathematics	mathematics	PROPN
ejpam-3331	6	119	,	,	PUNCT
ejpam-3331	6	120	college	college	NOUN
ejpam-3331	6	121	of	of	ADP
ejpam-3331	6	122	education	education	NOUN
ejpam-3331	6	123	of	of	ADP
ejpam-3331	6	124	jubail	jubail	PROPN
ejpam-3331	6	125	,	,	PUNCT
ejpam-3331	6	126	p.o	p.o	PROPN
ejpam-3331	6	127	:	:	PUNCT
ejpam-3331	6	128	12020	12020	NUM
ejpam-3331	6	129	,	,	PUNCT
ejpam-3331	6	130	industrial	industrial	ADJ
ejpam-3331	6	131	jubail	jubail	PROPN
ejpam-3331	6	132	31961	31961	NUM
ejpam-3331	6	133	.	.	PUNCT
ejpam-3331	7	1	saudi	saudi	PROPN
ejpam-3331	7	2	arabia	arabia	PROPN
ejpam-3331	7	3	5	5	NUM
ejpam-3331	7	4	school	school	NOUN
ejpam-3331	7	5	of	of	ADP
ejpam-3331	7	6	quantitative	quantitative	ADJ
ejpam-3331	7	7	sciences	science	NOUN
ejpam-3331	7	8	,	,	PUNCT
ejpam-3331	7	9	university	university	NOUN
ejpam-3331	7	10	utara	utara	NOUN
ejpam-3331	7	11	malaysia	malaysia	PROPN
ejpam-3331	7	12	,	,	PUNCT
ejpam-3331	7	13	cas	cas	PROPN
ejpam-3331	7	14	06010	06010	NUM
ejpam-3331	7	15	,	,	PUNCT
ejpam-3331	7	16	uum	uum	PROPN
ejpam-3331	7	17	sintok	sintok	ADJ
ejpam-3331	7	18	,	,	PUNCT
ejpam-3331	7	19	kedah	kedah	PROPN
ejpam-3331	7	20	darul	darul	PROPN
ejpam-3331	7	21	aman	aman	PROPN
ejpam-3331	7	22	,	,	PUNCT
ejpam-3331	7	23	malaysia	malaysia	PROPN
ejpam-3331	7	24	6	6	NUM
ejpam-3331	7	25	mathematics	mathematic	NOUN
ejpam-3331	7	26	department	department	NOUN
ejpam-3331	7	27	,	,	PUNCT
ejpam-3331	7	28	science	science	NOUN
ejpam-3331	7	29	and	and	CCONJ
ejpam-3331	7	30	arts	arts	PROPN
ejpam-3331	7	31	college	college	PROPN
ejpam-3331	7	32	,	,	PUNCT
ejpam-3331	7	33	aljouf	aljouf	PROPN
ejpam-3331	7	34	university	university	NOUN
ejpam-3331	7	35	,	,	PUNCT
ejpam-3331	7	36	saudi	saudi	PROPN
ejpam-3331	7	37	arabia	arabia	PROPN
ejpam-3331	7	38	abstract	abstract	NOUN
ejpam-3331	7	39	.	.	PUNCT
ejpam-3331	8	1	the	the	DET
ejpam-3331	8	2	purpose	purpose	NOUN
ejpam-3331	8	3	of	of	ADP
ejpam-3331	8	4	this	this	DET
ejpam-3331	8	5	paper	paper	NOUN
ejpam-3331	8	6	is	be	AUX
ejpam-3331	8	7	to	to	PART
ejpam-3331	8	8	establish	establish	VERB
ejpam-3331	8	9	some	some	DET
ejpam-3331	8	10	fixed	fix	VERB
ejpam-3331	8	11	point	point	NOUN
ejpam-3331	8	12	results	result	NOUN
ejpam-3331	8	13	for	for	ADP
ejpam-3331	8	14	(	(	PUNCT
ejpam-3331	8	15	α	α	X
ejpam-3331	8	16	,	,	PUNCT
ejpam-3331	8	17	β)-admissible	β)-admissible	PUNCT
ejpam-3331	8	18	z	z	NOUN
ejpam-3331	8	19	-	-	PUNCT
ejpam-3331	8	20	contraction	contraction	NOUN
ejpam-3331	8	21	mappings	mapping	NOUN
ejpam-3331	8	22	in	in	ADP
ejpam-3331	8	23	complete	complete	ADJ
ejpam-3331	8	24	metric	metric	ADJ
ejpam-3331	8	25	-	-	PUNCT
ejpam-3331	8	26	like	like	ADJ
ejpam-3331	8	27	spaces	space	NOUN
ejpam-3331	8	28	.	.	PUNCT
ejpam-3331	9	1	our	our	PRON
ejpam-3331	9	2	results	result	NOUN
ejpam-3331	9	3	generalize	generalize	VERB
ejpam-3331	9	4	and	and	CCONJ
ejpam-3331	9	5	extend	extend	VERB
ejpam-3331	9	6	several	several	ADJ
ejpam-3331	9	7	known	know	VERB
ejpam-3331	9	8	results	result	NOUN
ejpam-3331	9	9	on	on	ADP
ejpam-3331	9	10	literature	literature	NOUN
ejpam-3331	9	11	.	.	PUNCT
ejpam-3331	10	1	two	two	NUM
ejpam-3331	10	2	illustrated	illustrated	ADJ
ejpam-3331	10	3	examples	example	NOUN
ejpam-3331	10	4	are	be	AUX
ejpam-3331	10	5	also	also	ADV
ejpam-3331	10	6	presented	present	VERB
ejpam-3331	10	7	.	.	PUNCT
ejpam-3331	11	1	2010	2010	NUM
ejpam-3331	11	2	mathematics	mathematic	NOUN
ejpam-3331	11	3	subject	subject	NOUN
ejpam-3331	11	4	classifications	classification	NOUN
ejpam-3331	11	5	:	:	PUNCT
ejpam-3331	11	6	47h10	47h10	NUM
ejpam-3331	11	7	,	,	PUNCT
ejpam-3331	11	8	54h25	54h25	NUM
ejpam-3331	11	9	key	key	ADJ
ejpam-3331	11	10	words	word	NOUN
ejpam-3331	11	11	and	and	CCONJ
ejpam-3331	11	12	phrases	phrase	NOUN
ejpam-3331	11	13	:	:	PUNCT
ejpam-3331	11	14	fixed	fix	VERB
ejpam-3331	11	15	point	point	NOUN
ejpam-3331	11	16	,	,	PUNCT
ejpam-3331	11	17	metric	metric	ADJ
ejpam-3331	11	18	-	-	PUNCT
ejpam-3331	11	19	like	like	ADJ
ejpam-3331	11	20	space	space	NOUN
ejpam-3331	11	21	,	,	PUNCT
ejpam-3331	11	22	simulation	simulation	NOUN
ejpam-3331	11	23	function	function	NOUN
ejpam-3331	11	24	,	,	PUNCT
ejpam-3331	11	25	(	(	PUNCT
ejpam-3331	11	26	α	α	X
ejpam-3331	11	27	,	,	PUNCT
ejpam-3331	11	28	β)-admissible	β)-admissible	PUNCT
ejpam-3331	11	29	mapping	mapping	NOUN
ejpam-3331	11	30	1	1	NUM
ejpam-3331	11	31	.	.	PUNCT
ejpam-3331	12	1	introduction	introduction	NOUN
ejpam-3331	12	2	and	and	CCONJ
ejpam-3331	12	3	preliminaries	preliminary	NOUN
ejpam-3331	12	4	fixed	fix	VERB
ejpam-3331	12	5	point	point	NOUN
ejpam-3331	12	6	theory	theory	NOUN
ejpam-3331	12	7	is	be	AUX
ejpam-3331	12	8	an	an	DET
ejpam-3331	12	9	essential	essential	ADJ
ejpam-3331	12	10	tool	tool	NOUN
ejpam-3331	12	11	to	to	PART
ejpam-3331	12	12	resolve	resolve	VERB
ejpam-3331	12	13	many	many	ADJ
ejpam-3331	12	14	equations	equation	NOUN
ejpam-3331	12	15	appeared	appear	VERB
ejpam-3331	12	16	in	in	ADP
ejpam-3331	12	17	applied	apply	VERB
ejpam-3331	12	18	science	science	NOUN
ejpam-3331	12	19	such	such	ADJ
ejpam-3331	12	20	as	as	ADP
ejpam-3331	12	21	biology	biology	NOUN
ejpam-3331	12	22	,	,	PUNCT
ejpam-3331	12	23	physics	physics	NOUN
ejpam-3331	12	24	,	,	PUNCT
ejpam-3331	12	25	economics	economic	NOUN
ejpam-3331	12	26	,	,	PUNCT
ejpam-3331	12	27	engineering	engineering	NOUN
ejpam-3331	12	28	and	and	CCONJ
ejpam-3331	12	29	game	game	NOUN
ejpam-3331	12	30	theory	theory	NOUN
ejpam-3331	12	31	.	.	PUNCT
ejpam-3331	13	1	banach	banach	NOUN
ejpam-3331	13	2	contraction	contraction	NOUN
ejpam-3331	13	3	principle	principle	NOUN
ejpam-3331	13	4	[	[	X
ejpam-3331	13	5	12	12	NUM
ejpam-3331	13	6	]	]	PUNCT
ejpam-3331	13	7	is	be	AUX
ejpam-3331	13	8	considered	consider	VERB
ejpam-3331	13	9	the	the	DET
ejpam-3331	13	10	most	most	ADV
ejpam-3331	13	11	important	important	ADJ
ejpam-3331	13	12	tool	tool	NOUN
ejpam-3331	13	13	in	in	ADP
ejpam-3331	13	14	fixed	fix	VERB
ejpam-3331	13	15	point	point	NOUN
ejpam-3331	13	16	theory	theory	NOUN
ejpam-3331	13	17	.	.	PUNCT
ejpam-3331	14	1	it	it	PRON
ejpam-3331	14	2	was	be	AUX
ejpam-3331	14	3	extended	extend	VERB
ejpam-3331	14	4	in	in	ADP
ejpam-3331	14	5	several	several	ADJ
ejpam-3331	14	6	directions	direction	NOUN
ejpam-3331	14	7	.	.	PUNCT
ejpam-3331	15	1	for	for	ADP
ejpam-3331	15	2	more	more	ADJ
ejpam-3331	15	3	details	detail	NOUN
ejpam-3331	15	4	,	,	PUNCT
ejpam-3331	15	5	see	see	VERB
ejpam-3331	15	6	[	[	X
ejpam-3331	15	7	13	13	NUM
ejpam-3331	15	8	,	,	PUNCT
ejpam-3331	15	9	17	17	NUM
ejpam-3331	15	10	,	,	PUNCT
ejpam-3331	15	11	18	18	NUM
ejpam-3331	15	12	,	,	PUNCT
ejpam-3331	15	13	20–25	20–25	NUM
ejpam-3331	15	14	]	]	PUNCT
ejpam-3331	15	15	.	.	PUNCT
ejpam-3331	16	1	going	go	VERB
ejpam-3331	16	2	in	in	ADP
ejpam-3331	16	3	this	this	DET
ejpam-3331	16	4	direction	direction	NOUN
ejpam-3331	16	5	,	,	PUNCT
ejpam-3331	16	6	harandi	harandi	NOUN
ejpam-3331	17	1	[	[	X
ejpam-3331	17	2	16	16	NUM
ejpam-3331	17	3	]	]	PUNCT
ejpam-3331	17	4	reintroduced	reintroduce	VERB
ejpam-3331	17	5	the	the	DET
ejpam-3331	17	6	concept	concept	NOUN
ejpam-3331	17	7	of	of	ADP
ejpam-3331	17	8	metric	metric	ADJ
ejpam-3331	17	9	-	-	PUNCT
ejpam-3331	17	10	like	like	ADJ
ejpam-3331	17	11	spaces	space	NOUN
ejpam-3331	17	12	.	.	PUNCT
ejpam-3331	18	1	∗corresponding	∗corresponde	VERB
ejpam-3331	18	2	author	author	NOUN
ejpam-3331	18	3	.	.	PUNCT
ejpam-3331	19	1	doi	doi	NOUN
ejpam-3331	19	2	:	:	PUNCT
ejpam-3331	19	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3331	https://doi.org/10.29020/nybg.ejpam.v12i1.3331	NUM
ejpam-3331	19	4	email	email	NOUN
ejpam-3331	19	5	addresses	address	NOUN
ejpam-3331	19	6	:	:	PUNCT
ejpam-3331	19	7	h.alsamer@gmail.com	h.alsamer@gmail.com	X
ejpam-3331	19	8	(	(	PUNCT
ejpam-3331	19	9	h.	h.	PROPN
ejpam-3331	19	10	alsamir	alsamir	PROPN
ejpam-3331	19	11	)	)	PUNCT
ejpam-3331	19	12	,	,	PUNCT
ejpam-3331	19	13	msn@ukm.my	msn@ukm.my	X
ejpam-3331	19	14	(	(	PUNCT
ejpam-3331	19	15	m.s	m.s	PROPN
ejpam-3331	19	16	.	.	PROPN
ejpam-3331	19	17	noorani	noorani	PROPN
ejpam-3331	19	18	)	)	PUNCT
ejpam-3331	19	19	,	,	PUNCT
ejpam-3331	19	20	swasfi@hu.edu.jo	swasfi@hu.edu.jo	PROPN
ejpam-3331	19	21	(	(	PUNCT
ejpam-3331	19	22	w.	w.	PROPN
ejpam-3331	19	23	shatanawi	shatanawi	PROPN
ejpam-3331	19	24	)	)	PUNCT
ejpam-3331	19	25	,	,	PUNCT
ejpam-3331	19	26	wshatanawi@psu.edu.sa	wshatanawi@psu.edu.sa	PROPN
ejpam-3331	19	27	(	(	PUNCT
ejpam-3331	19	28	w.	w.	PROPN
ejpam-3331	19	29	shatanawi	shatanawi	PROPN
ejpam-3331	19	30	)	)	PUNCT
ejpam-3331	19	31	,	,	PUNCT
ejpam-3331	19	32	hmaydi@iau.edu.sa	hmaydi@iau.edu.sa	PROPN
ejpam-3331	19	33	(	(	PUNCT
ejpam-3331	19	34	h.	h.	PROPN
ejpam-3331	19	35	aydi	aydi	VERB
ejpam-3331	19	36	)	)	PUNCT
ejpam-3331	19	37	,	,	PUNCT
ejpam-3331	19	38	habibulla@uum.edu.my	habibulla@uum.edu.my	INTJ
ejpam-3331	19	39	(	(	PUNCT
ejpam-3331	19	40	h.	h.	PROPN
ejpam-3331	19	41	akhadkulov	akhadkulov	PROPN
ejpam-3331	19	42	)	)	PUNCT
ejpam-3331	19	43	,	,	PUNCT
ejpam-3331	19	44	haitham.math77@gmail.com	haitham.math77@gmail.com	X
ejpam-3331	19	45	(	(	PUNCT
ejpam-3331	19	46	h.	h.	PROPN
ejpam-3331	19	47	qawaqneh	qawaqneh	PROPN
ejpam-3331	19	48	)	)	PUNCT
ejpam-3331	19	49	,	,	PUNCT
ejpam-3331	19	50	sunshine-w@hotmail.com	sunshine-w@hotmail.com	NUM
ejpam-3331	19	51	(	(	PUNCT
ejpam-3331	19	52	k.	k.	PROPN
ejpam-3331	19	53	alanazi	alanazi	PROPN
ejpam-3331	19	54	)	)	PUNCT
ejpam-3331	19	55	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3331	20	1	88	88	NUM
ejpam-3331	20	2	c	c	X
ejpam-3331	20	3	©	©	NOUN
ejpam-3331	20	4	2019	2019	NUM
ejpam-3331	20	5	ejpam	ejpam	NOUN
ejpam-3331	20	6	all	all	DET
ejpam-3331	20	7	rights	right	NOUN
ejpam-3331	20	8	reserved	reserve	VERB
ejpam-3331	20	9	.	.	PUNCT
ejpam-3331	21	1	h.	h.	PROPN
ejpam-3331	21	2	alsamir	alsamir	VERB
ejpam-3331	21	3	et	et	PROPN
ejpam-3331	21	4	al	al	PROPN
ejpam-3331	21	5	.	.	PUNCT
ejpam-3331	21	6	/	/	SYM
ejpam-3331	21	7	eur	eur	PROPN
ejpam-3331	21	8	.	.	PUNCT
ejpam-3331	22	1	j.	j.	PROPN
ejpam-3331	22	2	pure	pure	PROPN
ejpam-3331	22	3	appl	appl	PROPN
ejpam-3331	22	4	.	.	PROPN
ejpam-3331	22	5	math	math	PROPN
ejpam-3331	22	6	,	,	PUNCT
ejpam-3331	22	7	12	12	NUM
ejpam-3331	22	8	(	(	PUNCT
ejpam-3331	22	9	1	1	NUM
ejpam-3331	22	10	)	)	PUNCT
ejpam-3331	22	11	(	(	PUNCT
ejpam-3331	22	12	2019	2019	NUM
ejpam-3331	22	13	)	)	PUNCT
ejpam-3331	22	14	,	,	PUNCT
ejpam-3331	22	15	88	88	NUM
ejpam-3331	22	16	-	-	SYM
ejpam-3331	22	17	100	100	NUM
ejpam-3331	22	18	89	89	NUM
ejpam-3331	22	19	definition	definition	NOUN
ejpam-3331	22	20	1	1	NUM
ejpam-3331	22	21	.	.	PUNCT
ejpam-3331	23	1	[	[	X
ejpam-3331	23	2	16	16	NUM
ejpam-3331	23	3	]	]	PUNCT
ejpam-3331	23	4	let	let	VERB
ejpam-3331	23	5	x	x	PRON
ejpam-3331	23	6	is	be	AUX
ejpam-3331	23	7	a	a	DET
ejpam-3331	23	8	nonempty	nonempty	ADV
ejpam-3331	23	9	set	set	VERB
ejpam-3331	23	10	.	.	PUNCT
ejpam-3331	24	1	a	a	DET
ejpam-3331	24	2	function	function	NOUN
ejpam-3331	24	3	σ	σ	NOUN
ejpam-3331	24	4	:	:	PUNCT
ejpam-3331	24	5	x	x	X
ejpam-3331	24	6	×x	×x	X
ejpam-3331	24	7	→	→	X
ejpam-3331	24	8	[	[	X
ejpam-3331	24	9	0,∞	0,∞	NOUN
ejpam-3331	24	10	)	)	PUNCT
ejpam-3331	24	11	is	be	AUX
ejpam-3331	24	12	said	say	VERB
ejpam-3331	24	13	to	to	PART
ejpam-3331	24	14	be	be	AUX
ejpam-3331	24	15	a	a	DET
ejpam-3331	24	16	metric	metric	ADJ
ejpam-3331	24	17	-	-	PUNCT
ejpam-3331	24	18	like	like	ADJ
ejpam-3331	24	19	space	space	NOUN
ejpam-3331	24	20	(	(	PUNCT
ejpam-3331	24	21	or	or	CCONJ
ejpam-3331	24	22	a	a	DET
ejpam-3331	24	23	dislocated	dislocated	ADJ
ejpam-3331	24	24	metric	metric	NOUN
ejpam-3331	24	25	)	)	PUNCT
ejpam-3331	24	26	on	on	ADP
ejpam-3331	24	27	x	x	SYM
ejpam-3331	24	28	if	if	SCONJ
ejpam-3331	24	29	for	for	ADP
ejpam-3331	24	30	any	any	DET
ejpam-3331	24	31	x	x	NOUN
ejpam-3331	24	32	,	,	PUNCT
ejpam-3331	24	33	w	w	PROPN
ejpam-3331	24	34	,	,	PUNCT
ejpam-3331	24	35	y	y	PROPN
ejpam-3331	24	36	∈	∈	PROPN
ejpam-3331	24	37	x	x	PRON
ejpam-3331	24	38	,	,	PUNCT
ejpam-3331	24	39	the	the	DET
ejpam-3331	24	40	following	follow	VERB
ejpam-3331	24	41	conditions	condition	NOUN
ejpam-3331	24	42	hold	hold	VERB
ejpam-3331	24	43	:	:	PUNCT
ejpam-3331	24	44	(	(	PUNCT
ejpam-3331	24	45	σ1	σ1	NOUN
ejpam-3331	24	46	)	)	PUNCT
ejpam-3331	24	47	σ(x	σ(x	PROPN
ejpam-3331	24	48	,	,	PUNCT
ejpam-3331	24	49	y	y	NOUN
ejpam-3331	24	50	)	)	PUNCT
ejpam-3331	24	51	=	=	SYM
ejpam-3331	24	52	0	0	NUM
ejpam-3331	24	53	implies	imply	VERB
ejpam-3331	24	54	that	that	SCONJ
ejpam-3331	24	55	x	x	X
ejpam-3331	24	56	=	=	SYM
ejpam-3331	24	57	y	y	PROPN
ejpam-3331	24	58	;	;	PUNCT
ejpam-3331	24	59	(	(	PUNCT
ejpam-3331	24	60	σ2	σ2	NOUN
ejpam-3331	24	61	)	)	PUNCT
ejpam-3331	24	62	σ(x	σ(x	PROPN
ejpam-3331	24	63	,	,	PUNCT
ejpam-3331	24	64	y	y	NOUN
ejpam-3331	24	65	)	)	PUNCT
ejpam-3331	24	66	=	=	SYM
ejpam-3331	24	67	σ(y	σ(y	NOUN
ejpam-3331	24	68	,	,	PUNCT
ejpam-3331	24	69	x	x	NOUN
ejpam-3331	24	70	)	)	PUNCT
ejpam-3331	24	71	;	;	PUNCT
ejpam-3331	24	72	(	(	PUNCT
ejpam-3331	24	73	σ3	σ3	PROPN
ejpam-3331	24	74	)	)	PUNCT
ejpam-3331	24	75	σ(x	σ(x	PROPN
ejpam-3331	24	76	,	,	PUNCT
ejpam-3331	24	77	y	y	NOUN
ejpam-3331	24	78	)	)	PUNCT
ejpam-3331	24	79	≤	≤	NOUN
ejpam-3331	25	1	σ(x	σ(x	PROPN
ejpam-3331	25	2	,	,	PUNCT
ejpam-3331	25	3	z	z	NOUN
ejpam-3331	25	4	)	)	PUNCT
ejpam-3331	25	5	+	+	CCONJ
ejpam-3331	25	6	σ(z	σ(z	PROPN
ejpam-3331	25	7	,	,	PUNCT
ejpam-3331	25	8	y	y	NOUN
ejpam-3331	25	9	)	)	PUNCT
ejpam-3331	25	10	.	.	PUNCT
ejpam-3331	26	1	the	the	DET
ejpam-3331	26	2	pair	pair	NOUN
ejpam-3331	26	3	(	(	PUNCT
ejpam-3331	26	4	x	x	NOUN
ejpam-3331	26	5	,	,	PUNCT
ejpam-3331	26	6	σ	σ	PROPN
ejpam-3331	26	7	)	)	PUNCT
ejpam-3331	26	8	is	be	AUX
ejpam-3331	26	9	called	call	VERB
ejpam-3331	26	10	a	a	DET
ejpam-3331	26	11	metric	metric	ADJ
ejpam-3331	26	12	-	-	PUNCT
ejpam-3331	26	13	like	like	ADJ
ejpam-3331	26	14	space	space	NOUN
ejpam-3331	26	15	.	.	PUNCT
ejpam-3331	27	1	it	it	PRON
ejpam-3331	27	2	is	be	AUX
ejpam-3331	27	3	clear	clear	ADJ
ejpam-3331	27	4	that	that	SCONJ
ejpam-3331	27	5	every	every	DET
ejpam-3331	27	6	metric	metric	ADJ
ejpam-3331	27	7	space	space	NOUN
ejpam-3331	27	8	and	and	CCONJ
ejpam-3331	27	9	partial	partial	ADJ
ejpam-3331	27	10	metric	metric	ADJ
ejpam-3331	27	11	space	space	NOUN
ejpam-3331	27	12	is	be	AUX
ejpam-3331	27	13	a	a	DET
ejpam-3331	27	14	metric	metric	ADJ
ejpam-3331	27	15	-	-	PUNCT
ejpam-3331	27	16	like	like	ADJ
ejpam-3331	27	17	space	space	NOUN
ejpam-3331	27	18	,	,	PUNCT
ejpam-3331	27	19	but	but	CCONJ
ejpam-3331	27	20	the	the	DET
ejpam-3331	27	21	converse	converse	NOUN
ejpam-3331	27	22	is	be	AUX
ejpam-3331	27	23	not	not	PART
ejpam-3331	27	24	true	true	ADJ
ejpam-3331	27	25	.	.	PUNCT
ejpam-3331	28	1	example	example	NOUN
ejpam-3331	29	1	1	1	NUM
ejpam-3331	29	2	.	.	PUNCT
ejpam-3331	29	3	let	let	VERB
ejpam-3331	29	4	x	x	PUNCT
ejpam-3331	29	5	=	=	PUNCT
ejpam-3331	29	6	{	{	PUNCT
ejpam-3331	29	7	0	0	NUM
ejpam-3331	29	8	,	,	PUNCT
ejpam-3331	29	9	1	1	NUM
ejpam-3331	29	10	}	}	PUNCT
ejpam-3331	29	11	and	and	CCONJ
ejpam-3331	29	12	σ(x	σ(x	PROPN
ejpam-3331	29	13	,	,	PUNCT
ejpam-3331	29	14	y	y	NOUN
ejpam-3331	29	15	)	)	PUNCT
ejpam-3331	29	16	=	=	PUNCT
ejpam-3331	30	1			PROPN
ejpam-3331	30	2	2	2	NUM
ejpam-3331	30	3	,	,	PUNCT
ejpam-3331	30	4	if	if	SCONJ
ejpam-3331	30	5	x	x	ADP
ejpam-3331	30	6	=	=	PUNCT
ejpam-3331	30	7	y	y	PROPN
ejpam-3331	30	8	=	=	SYM
ejpam-3331	30	9	0	0	NUM
ejpam-3331	30	10	;	;	PUNCT
ejpam-3331	30	11	1	1	NUM
ejpam-3331	30	12	,	,	PUNCT
ejpam-3331	30	13	otherwise	otherwise	ADV
ejpam-3331	30	14	.	.	PUNCT
ejpam-3331	31	1	then	then	ADV
ejpam-3331	31	2	(	(	PUNCT
ejpam-3331	31	3	x	x	X
ejpam-3331	31	4	,	,	PUNCT
ejpam-3331	31	5	σ	σ	PROPN
ejpam-3331	31	6	)	)	PUNCT
ejpam-3331	31	7	is	be	AUX
ejpam-3331	31	8	a	a	DET
ejpam-3331	31	9	metric	metric	ADJ
ejpam-3331	31	10	-	-	PUNCT
ejpam-3331	31	11	like	like	ADJ
ejpam-3331	31	12	space	space	NOUN
ejpam-3331	31	13	.	.	PUNCT
ejpam-3331	32	1	it	it	PRON
ejpam-3331	32	2	is	be	AUX
ejpam-3331	32	3	neither	neither	CCONJ
ejpam-3331	32	4	a	a	DET
ejpam-3331	32	5	partial	partial	ADJ
ejpam-3331	32	6	metric	metric	ADJ
ejpam-3331	32	7	space	space	NOUN
ejpam-3331	32	8	(	(	PUNCT
ejpam-3331	32	9	σ(0	σ(0	PROPN
ejpam-3331	32	10	,	,	PUNCT
ejpam-3331	32	11	0	0	NUM
ejpam-3331	32	12	)	)	PUNCT
ejpam-3331	32	13	6≤	6≤	NUM
ejpam-3331	33	1	σ(0	σ(0	PROPN
ejpam-3331	33	2	,	,	PUNCT
ejpam-3331	33	3	1	1	NUM
ejpam-3331	33	4	)	)	PUNCT
ejpam-3331	33	5	)	)	PUNCT
ejpam-3331	33	6	,	,	PUNCT
ejpam-3331	33	7	nor	nor	CCONJ
ejpam-3331	33	8	a	a	DET
ejpam-3331	33	9	metric	metric	ADJ
ejpam-3331	33	10	space	space	NOUN
ejpam-3331	33	11	(	(	PUNCT
ejpam-3331	33	12	σ(0	σ(0	PROPN
ejpam-3331	33	13	,	,	PUNCT
ejpam-3331	33	14	0	0	NUM
ejpam-3331	33	15	)	)	PUNCT
ejpam-3331	33	16	=	=	SYM
ejpam-3331	33	17	2	2	NUM
ejpam-3331	33	18	6=	6=	NUM
ejpam-3331	33	19	0	0	NUM
ejpam-3331	33	20	)	)	PUNCT
ejpam-3331	33	21	.	.	PUNCT
ejpam-3331	34	1	following	follow	VERB
ejpam-3331	34	2	[	[	X
ejpam-3331	34	3	16	16	NUM
ejpam-3331	34	4	]	]	PUNCT
ejpam-3331	34	5	,	,	PUNCT
ejpam-3331	34	6	we	we	PRON
ejpam-3331	34	7	have	have	VERB
ejpam-3331	34	8	the	the	DET
ejpam-3331	34	9	following	follow	VERB
ejpam-3331	34	10	topological	topological	ADJ
ejpam-3331	34	11	concepts	concept	NOUN
ejpam-3331	34	12	.	.	PUNCT
ejpam-3331	35	1	each	each	DET
ejpam-3331	35	2	metric	metric	ADJ
ejpam-3331	35	3	-	-	PUNCT
ejpam-3331	35	4	like	like	ADJ
ejpam-3331	35	5	σ	σ	NOUN
ejpam-3331	35	6	on	on	ADP
ejpam-3331	35	7	x	x	PUNCT
ejpam-3331	35	8	generates	generate	VERB
ejpam-3331	35	9	a	a	DET
ejpam-3331	35	10	topology	topology	NOUN
ejpam-3331	35	11	τσ	τσ	NOUN
ejpam-3331	35	12	on	on	ADP
ejpam-3331	35	13	x	x	PUNCT
ejpam-3331	35	14	whose	whose	DET
ejpam-3331	35	15	base	base	NOUN
ejpam-3331	35	16	is	be	AUX
ejpam-3331	35	17	the	the	DET
ejpam-3331	35	18	family	family	NOUN
ejpam-3331	35	19	of	of	ADP
ejpam-3331	35	20	open	open	ADJ
ejpam-3331	35	21	σ	σ	NOUN
ejpam-3331	35	22	-	-	PUNCT
ejpam-3331	35	23	balls	ball	NOUN
ejpam-3331	35	24	bσ(x	bσ(x	VERB
ejpam-3331	35	25	,	,	PUNCT
ejpam-3331	35	26	ε	ε	PROPN
ejpam-3331	35	27	)	)	PUNCT
ejpam-3331	35	28	=	=	PRON
ejpam-3331	35	29	{	{	PUNCT
ejpam-3331	35	30	y	y	PROPN
ejpam-3331	35	31	∈	∈	PROPN
ejpam-3331	36	1	x	x	X
ejpam-3331	36	2	:|	:|	PUNCT
ejpam-3331	36	3	σ(x	σ(x	PROPN
ejpam-3331	36	4	,	,	PUNCT
ejpam-3331	36	5	y)−	y)−	PROPN
ejpam-3331	36	6	σ(x	σ(x	PROPN
ejpam-3331	36	7	,	,	PUNCT
ejpam-3331	36	8	x	x	X
ejpam-3331	36	9	)	)	PUNCT
ejpam-3331	36	10	|	|	ADV
ejpam-3331	36	11	<	<	X
ejpam-3331	36	12	ε	ε	PROPN
ejpam-3331	36	13	}	}	PUNCT
ejpam-3331	36	14	,	,	PUNCT
ejpam-3331	36	15	for	for	ADP
ejpam-3331	36	16	all	all	PRON
ejpam-3331	36	17	x	x	SYM
ejpam-3331	36	18	∈	∈	PROPN
ejpam-3331	36	19	x	x	X
ejpam-3331	36	20	and	and	CCONJ
ejpam-3331	36	21	ε	ε	PROPN
ejpam-3331	36	22	>	>	X
ejpam-3331	36	23	0	0	X
ejpam-3331	36	24	.	.	PUNCT
ejpam-3331	37	1	now	now	ADV
ejpam-3331	37	2	,	,	PUNCT
ejpam-3331	37	3	let	let	VERB
ejpam-3331	37	4	(	(	PUNCT
ejpam-3331	37	5	x	x	NOUN
ejpam-3331	37	6	,	,	PUNCT
ejpam-3331	37	7	σ	σ	PROPN
ejpam-3331	37	8	)	)	PUNCT
ejpam-3331	37	9	be	be	AUX
ejpam-3331	37	10	a	a	DET
ejpam-3331	37	11	metric	metric	ADJ
ejpam-3331	37	12	-	-	PUNCT
ejpam-3331	37	13	like	like	ADJ
ejpam-3331	37	14	space	space	NOUN
ejpam-3331	37	15	.	.	PUNCT
ejpam-3331	38	1	the	the	DET
ejpam-3331	38	2	mapping	mapping	NOUN
ejpam-3331	38	3	t	t	NOUN
ejpam-3331	38	4	:	:	PUNCT
ejpam-3331	38	5	x	x	X
ejpam-3331	38	6	→	→	PUNCT
ejpam-3331	38	7	x	x	X
ejpam-3331	38	8	is	be	AUX
ejpam-3331	38	9	said	say	VERB
ejpam-3331	38	10	σ	σ	X
ejpam-3331	38	11	-	-	ADJ
ejpam-3331	38	12	continuous	continuous	ADJ
ejpam-3331	38	13	at	at	ADP
ejpam-3331	38	14	x	x	X
ejpam-3331	38	15	∈	∈	PROPN
ejpam-3331	38	16	x	x	SYM
ejpam-3331	38	17	if	if	SCONJ
ejpam-3331	38	18	for	for	ADP
ejpam-3331	38	19	all	all	DET
ejpam-3331	38	20	ε	ε	PROPN
ejpam-3331	38	21	>	>	X
ejpam-3331	38	22	0	0	PROPN
ejpam-3331	38	23	,	,	PUNCT
ejpam-3331	38	24	there	there	PRON
ejpam-3331	38	25	exists	exist	VERB
ejpam-3331	38	26	δ	δ	PROPN
ejpam-3331	38	27	>	>	X
ejpam-3331	38	28	0	0	NUM
ejpam-3331	39	1	such	such	ADJ
ejpam-3331	39	2	that	that	SCONJ
ejpam-3331	39	3	t	t	PROPN
ejpam-3331	39	4	(	(	PUNCT
ejpam-3331	39	5	bσ(x	bσ(x	PROPN
ejpam-3331	39	6	,	,	PUNCT
ejpam-3331	39	7	δ	δ	NOUN
ejpam-3331	39	8	)	)	PUNCT
ejpam-3331	39	9	)	)	PUNCT
ejpam-3331	40	1	⊆	⊆	NUM
ejpam-3331	40	2	bσ(tx	bσ(tx	PROPN
ejpam-3331	40	3	,	,	PUNCT
ejpam-3331	40	4	ε	ε	PROPN
ejpam-3331	40	5	)	)	PUNCT
ejpam-3331	40	6	.	.	PUNCT
ejpam-3331	41	1	consequently	consequently	ADV
ejpam-3331	41	2	,	,	PUNCT
ejpam-3331	41	3	if	if	SCONJ
ejpam-3331	41	4	t	t	NOUN
ejpam-3331	41	5	:	:	PUNCT
ejpam-3331	41	6	x	x	X
ejpam-3331	41	7	→	→	PUNCT
ejpam-3331	41	8	x	x	X
ejpam-3331	41	9	is	be	AUX
ejpam-3331	41	10	σ	σ	NOUN
ejpam-3331	41	11	-	-	ADJ
ejpam-3331	41	12	continuous	continuous	ADJ
ejpam-3331	41	13	,	,	PUNCT
ejpam-3331	41	14	then	then	ADV
ejpam-3331	41	15	if	if	SCONJ
ejpam-3331	41	16	limn→∞	limn→∞	PROPN
ejpam-3331	41	17	xn	xn	PROPN
ejpam-3331	42	1	=	=	SYM
ejpam-3331	42	2	x	x	NOUN
ejpam-3331	42	3	,	,	PUNCT
ejpam-3331	42	4	we	we	PRON
ejpam-3331	42	5	have	have	VERB
ejpam-3331	42	6	limn→∞	limn→∞	PROPN
ejpam-3331	42	7	txn	txn	NOUN
ejpam-3331	42	8	=	=	SYM
ejpam-3331	42	9	tx	tx	PROPN
ejpam-3331	42	10	.	.	PUNCT
ejpam-3331	43	1	a	a	DET
ejpam-3331	43	2	sequence	sequence	NOUN
ejpam-3331	43	3	{	{	PUNCT
ejpam-3331	43	4	xn}n=0	xn}n=0	NOUN
ejpam-3331	43	5	∞	∞	PROPN
ejpam-3331	43	6	of	of	ADP
ejpam-3331	43	7	elements	element	NOUN
ejpam-3331	43	8	of	of	ADP
ejpam-3331	43	9	x	x	SYM
ejpam-3331	43	10	is	be	AUX
ejpam-3331	43	11	called	call	VERB
ejpam-3331	43	12	σ	σ	PROPN
ejpam-3331	43	13	-	-	PUNCT
ejpam-3331	43	14	cauchy	cauchy	NOUN
ejpam-3331	43	15	if	if	SCONJ
ejpam-3331	43	16	the	the	DET
ejpam-3331	43	17	limit	limit	NOUN
ejpam-3331	43	18	limn	limn	NOUN
ejpam-3331	43	19	,	,	PUNCT
ejpam-3331	43	20	m→∞	m→∞	NOUN
ejpam-3331	43	21	σ(xn	σ(xn	NOUN
ejpam-3331	43	22	,	,	PUNCT
ejpam-3331	43	23	ym	ym	NOUN
ejpam-3331	43	24	)	)	PUNCT
ejpam-3331	43	25	exists	exist	VERB
ejpam-3331	43	26	and	and	CCONJ
ejpam-3331	43	27	is	be	AUX
ejpam-3331	43	28	a	a	DET
ejpam-3331	43	29	finite	finite	ADJ
ejpam-3331	43	30	number	number	NOUN
ejpam-3331	43	31	.	.	PUNCT
ejpam-3331	44	1	the	the	DET
ejpam-3331	44	2	metric	metric	ADJ
ejpam-3331	44	3	-	-	PUNCT
ejpam-3331	44	4	like	like	ADJ
ejpam-3331	44	5	space	space	NOUN
ejpam-3331	44	6	(	(	PUNCT
ejpam-3331	44	7	x	x	X
ejpam-3331	44	8	,	,	PUNCT
ejpam-3331	44	9	σ	σ	PROPN
ejpam-3331	44	10	)	)	PUNCT
ejpam-3331	44	11	is	be	AUX
ejpam-3331	44	12	called	call	VERB
ejpam-3331	44	13	complete	complete	ADJ
ejpam-3331	44	14	if	if	SCONJ
ejpam-3331	44	15	for	for	ADP
ejpam-3331	44	16	each	each	DET
ejpam-3331	44	17	σ	σ	PROPN
ejpam-3331	44	18	-	-	PUNCT
ejpam-3331	44	19	cauchy	cauchy	ADJ
ejpam-3331	44	20	sequence	sequence	NOUN
ejpam-3331	44	21	{	{	PUNCT
ejpam-3331	44	22	xn}n∞	xn}n∞	PROPN
ejpam-3331	44	23	,	,	PUNCT
ejpam-3331	44	24	there	there	PRON
ejpam-3331	44	25	is	be	VERB
ejpam-3331	44	26	some	some	DET
ejpam-3331	44	27	y	y	PROPN
ejpam-3331	44	28	∈	∈	PROPN
ejpam-3331	44	29	y	y	PROPN
ejpam-3331	44	30	such	such	ADJ
ejpam-3331	44	31	that	that	SCONJ
ejpam-3331	44	32	lim	lim	PROPN
ejpam-3331	44	33	n→∞	n→∞	NUM
ejpam-3331	44	34	σ(xn	σ(xn	NOUN
ejpam-3331	44	35	,	,	PUNCT
ejpam-3331	44	36	x	x	NOUN
ejpam-3331	44	37	)	)	PUNCT
ejpam-3331	45	1	=	=	SYM
ejpam-3331	45	2	σ(x	σ(x	PROPN
ejpam-3331	45	3	,	,	PUNCT
ejpam-3331	45	4	x	x	X
ejpam-3331	45	5	)	)	PUNCT
ejpam-3331	45	6	=	=	SYM
ejpam-3331	45	7	lim	lim	PROPN
ejpam-3331	45	8	n	n	CCONJ
ejpam-3331	45	9	,	,	PUNCT
ejpam-3331	45	10	m→∞	m→∞	NOUN
ejpam-3331	45	11	σ(xn	σ(xn	NOUN
ejpam-3331	45	12	,	,	PUNCT
ejpam-3331	45	13	xm	xm	PROPN
ejpam-3331	45	14	)	)	PUNCT
ejpam-3331	45	15	.	.	PUNCT
ejpam-3331	46	1	a	a	DET
ejpam-3331	46	2	subset	subset	NOUN
ejpam-3331	46	3	a	a	PRON
ejpam-3331	46	4	of	of	ADP
ejpam-3331	46	5	a	a	DET
ejpam-3331	46	6	metric	metric	ADJ
ejpam-3331	46	7	-	-	PUNCT
ejpam-3331	46	8	like	like	ADJ
ejpam-3331	46	9	space	space	NOUN
ejpam-3331	46	10	(	(	PUNCT
ejpam-3331	46	11	x	x	X
ejpam-3331	46	12	,	,	PUNCT
ejpam-3331	46	13	σ	σ	PROPN
ejpam-3331	46	14	)	)	PUNCT
ejpam-3331	46	15	is	be	AUX
ejpam-3331	46	16	bounded	bound	VERB
ejpam-3331	46	17	if	if	SCONJ
ejpam-3331	46	18	there	there	PRON
ejpam-3331	46	19	is	be	VERB
ejpam-3331	46	20	a	a	DET
ejpam-3331	46	21	point	point	NOUN
ejpam-3331	46	22	b	b	NOUN
ejpam-3331	46	23	∈	∈	NOUN
ejpam-3331	46	24	x	x	X
ejpam-3331	46	25	and	and	CCONJ
ejpam-3331	46	26	a	a	DET
ejpam-3331	46	27	positive	positive	ADJ
ejpam-3331	46	28	constant	constant	ADJ
ejpam-3331	46	29	k	k	NOUN
ejpam-3331	46	30	such	such	ADJ
ejpam-3331	46	31	that	that	SCONJ
ejpam-3331	46	32	σ(a	σ(a	PROPN
ejpam-3331	46	33	,	,	PUNCT
ejpam-3331	46	34	b	b	NOUN
ejpam-3331	46	35	)	)	PUNCT
ejpam-3331	46	36	≤	≤	NOUN
ejpam-3331	46	37	k	k	NOUN
ejpam-3331	46	38	for	for	ADP
ejpam-3331	46	39	all	all	DET
ejpam-3331	46	40	a	a	DET
ejpam-3331	46	41	∈	∈	PROPN
ejpam-3331	46	42	a.	a.	NOUN
ejpam-3331	46	43	remark	remark	NOUN
ejpam-3331	46	44	1	1	NUM
ejpam-3331	46	45	.	.	PUNCT
ejpam-3331	47	1	let	let	VERB
ejpam-3331	47	2	x	x	PUNCT
ejpam-3331	47	3	=	=	PUNCT
ejpam-3331	47	4	{	{	PUNCT
ejpam-3331	47	5	0	0	NUM
ejpam-3331	47	6	,	,	PUNCT
ejpam-3331	47	7	1	1	NUM
ejpam-3331	47	8	}	}	PUNCT
ejpam-3331	47	9	be	be	AUX
ejpam-3331	47	10	endowed	endow	VERB
ejpam-3331	47	11	with	with	ADP
ejpam-3331	47	12	σ(x	σ(x	PROPN
ejpam-3331	47	13	,	,	PUNCT
ejpam-3331	47	14	y	y	NOUN
ejpam-3331	47	15	)	)	PUNCT
ejpam-3331	47	16	=	=	SYM
ejpam-3331	47	17	1	1	NUM
ejpam-3331	47	18	for	for	ADP
ejpam-3331	47	19	each	each	DET
ejpam-3331	47	20	x	x	NOUN
ejpam-3331	47	21	,	,	PUNCT
ejpam-3331	47	22	y	y	PROPN
ejpam-3331	47	23	∈	∈	PROPN
ejpam-3331	47	24	x.	x.	NOUN
ejpam-3331	47	25	take	take	VERB
ejpam-3331	47	26	xn	xn	NOUN
ejpam-3331	48	1	=	=	SYM
ejpam-3331	48	2	1	1	NUM
ejpam-3331	48	3	for	for	ADP
ejpam-3331	48	4	each	each	DET
ejpam-3331	48	5	n	n	PRON
ejpam-3331	48	6	∈	∈	PROPN
ejpam-3331	48	7	n.	n.	NOUN
ejpam-3331	48	8	using	use	VERB
ejpam-3331	48	9	the	the	DET
ejpam-3331	48	10	convergence	convergence	NOUN
ejpam-3331	48	11	definition	definition	NOUN
ejpam-3331	48	12	,	,	PUNCT
ejpam-3331	48	13	it	it	PRON
ejpam-3331	48	14	is	be	AUX
ejpam-3331	48	15	is	be	AUX
ejpam-3331	48	16	easy	easy	ADJ
ejpam-3331	48	17	to	to	PART
ejpam-3331	48	18	see	see	VERB
ejpam-3331	48	19	that	that	PRON
ejpam-3331	48	20	xn	xn	PUNCT
ejpam-3331	49	1	→	→	SYM
ejpam-3331	49	2	0	0	NUM
ejpam-3331	49	3	and	and	CCONJ
ejpam-3331	49	4	xn	xn	PROPN
ejpam-3331	50	1	→	→	SYM
ejpam-3331	50	2	1	1	X
ejpam-3331	50	3	.	.	PUNCT
ejpam-3331	51	1	in	in	ADP
ejpam-3331	51	2	metric	metric	ADJ
ejpam-3331	51	3	-	-	PUNCT
ejpam-3331	51	4	like	like	ADJ
ejpam-3331	51	5	spaces	space	NOUN
ejpam-3331	51	6	,	,	PUNCT
ejpam-3331	51	7	the	the	DET
ejpam-3331	51	8	limit	limit	NOUN
ejpam-3331	51	9	of	of	ADP
ejpam-3331	51	10	a	a	DET
ejpam-3331	51	11	convergent	convergent	NOUN
ejpam-3331	51	12	sequence	sequence	NOUN
ejpam-3331	51	13	is	be	AUX
ejpam-3331	51	14	not	not	PART
ejpam-3331	51	15	necessarily	necessarily	ADV
ejpam-3331	51	16	unique	unique	ADJ
ejpam-3331	51	17	.	.	PUNCT
ejpam-3331	52	1	the	the	DET
ejpam-3331	52	2	following	follow	VERB
ejpam-3331	52	3	lemma	lemma	PROPN
ejpam-3331	52	4	is	be	AUX
ejpam-3331	52	5	known	know	VERB
ejpam-3331	52	6	and	and	CCONJ
ejpam-3331	52	7	useful	useful	ADJ
ejpam-3331	52	8	for	for	ADP
ejpam-3331	52	9	the	the	DET
ejpam-3331	52	10	rest	rest	NOUN
ejpam-3331	52	11	of	of	ADP
ejpam-3331	52	12	paper	paper	NOUN
ejpam-3331	52	13	.	.	PUNCT
ejpam-3331	53	1	h.	h.	PROPN
ejpam-3331	53	2	alsamir	alsamir	VERB
ejpam-3331	53	3	et	et	PROPN
ejpam-3331	53	4	al	al	PROPN
ejpam-3331	53	5	.	.	PUNCT
ejpam-3331	53	6	/	/	SYM
ejpam-3331	53	7	eur	eur	PROPN
ejpam-3331	53	8	.	.	PUNCT
ejpam-3331	54	1	j.	j.	PROPN
ejpam-3331	54	2	pure	pure	PROPN
ejpam-3331	54	3	appl	appl	PROPN
ejpam-3331	54	4	.	.	PROPN
ejpam-3331	54	5	math	math	PROPN
ejpam-3331	54	6	,	,	PUNCT
ejpam-3331	54	7	12	12	NUM
ejpam-3331	54	8	(	(	PUNCT
ejpam-3331	54	9	1	1	NUM
ejpam-3331	54	10	)	)	PUNCT
ejpam-3331	54	11	(	(	PUNCT
ejpam-3331	54	12	2019	2019	NUM
ejpam-3331	54	13	)	)	PUNCT
ejpam-3331	54	14	,	,	PUNCT
ejpam-3331	54	15	88	88	NUM
ejpam-3331	54	16	-	-	SYM
ejpam-3331	54	17	100	100	NUM
ejpam-3331	54	18	90	90	NUM
ejpam-3331	54	19	lemma	lemma	PROPN
ejpam-3331	54	20	1	1	NUM
ejpam-3331	54	21	.	.	PUNCT
ejpam-3331	55	1	[	[	X
ejpam-3331	55	2	5	5	NUM
ejpam-3331	55	3	,	,	PUNCT
ejpam-3331	55	4	16	16	NUM
ejpam-3331	55	5	]	]	PUNCT
ejpam-3331	55	6	let	let	VERB
ejpam-3331	55	7	(	(	PUNCT
ejpam-3331	55	8	x	x	NOUN
ejpam-3331	55	9	,	,	PUNCT
ejpam-3331	55	10	σ	σ	PROPN
ejpam-3331	55	11	)	)	PUNCT
ejpam-3331	55	12	be	be	AUX
ejpam-3331	55	13	a	a	DET
ejpam-3331	55	14	metric	metric	ADJ
ejpam-3331	55	15	-	-	PUNCT
ejpam-3331	55	16	like	like	ADJ
ejpam-3331	55	17	space	space	NOUN
ejpam-3331	55	18	.	.	PUNCT
ejpam-3331	56	1	let	let	VERB
ejpam-3331	56	2	{	{	PUNCT
ejpam-3331	56	3	xn	xn	VERB
ejpam-3331	56	4	}	}	PUNCT
ejpam-3331	56	5	be	be	AUX
ejpam-3331	56	6	a	a	DET
ejpam-3331	56	7	sequence	sequence	NOUN
ejpam-3331	56	8	in	in	ADP
ejpam-3331	56	9	x	x	INTJ
ejpam-3331	56	10	such	such	ADJ
ejpam-3331	56	11	that	that	PRON
ejpam-3331	56	12	xn	xn	PUNCT
ejpam-3331	57	1	→	→	PUNCT
ejpam-3331	57	2	x	x	X
ejpam-3331	57	3	where	where	SCONJ
ejpam-3331	57	4	x	x	SYM
ejpam-3331	57	5	∈	∈	PROPN
ejpam-3331	57	6	x	x	X
ejpam-3331	57	7	and	and	CCONJ
ejpam-3331	57	8	σ(x	σ(x	PROPN
ejpam-3331	57	9	,	,	PUNCT
ejpam-3331	57	10	y	y	NOUN
ejpam-3331	57	11	)	)	PUNCT
ejpam-3331	57	12	=	=	SYM
ejpam-3331	57	13	0	0	X
ejpam-3331	57	14	.	.	PUNCT
ejpam-3331	58	1	then	then	ADV
ejpam-3331	58	2	for	for	ADP
ejpam-3331	58	3	all	all	DET
ejpam-3331	58	4	y	y	PROPN
ejpam-3331	58	5	∈	∈	PROPN
ejpam-3331	58	6	x	x	PRON
ejpam-3331	58	7	,	,	PUNCT
ejpam-3331	58	8	we	we	PRON
ejpam-3331	58	9	have	have	VERB
ejpam-3331	58	10	limn→∞	limn→∞	ADP
ejpam-3331	58	11	σ(xn	σ(xn	NOUN
ejpam-3331	58	12	,	,	PUNCT
ejpam-3331	58	13	y	y	NOUN
ejpam-3331	58	14	)	)	PUNCT
ejpam-3331	59	1	=	=	SYM
ejpam-3331	59	2	σ(x	σ(x	PROPN
ejpam-3331	59	3	,	,	PUNCT
ejpam-3331	59	4	y	y	NOUN
ejpam-3331	59	5	)	)	PUNCT
ejpam-3331	59	6	.	.	PUNCT
ejpam-3331	60	1	in	in	ADP
ejpam-3331	60	2	literature	literature	NOUN
ejpam-3331	60	3	,	,	PUNCT
ejpam-3331	60	4	there	there	PRON
ejpam-3331	60	5	are	be	VERB
ejpam-3331	60	6	several	several	ADJ
ejpam-3331	60	7	(	(	PUNCT
ejpam-3331	60	8	common	common	ADJ
ejpam-3331	60	9	)	)	PUNCT
ejpam-3331	60	10	fixed	fix	VERB
ejpam-3331	60	11	point	point	NOUN
ejpam-3331	60	12	works	work	VERB
ejpam-3331	60	13	in	in	ADP
ejpam-3331	60	14	the	the	DET
ejpam-3331	60	15	setting	setting	NOUN
ejpam-3331	60	16	of	of	ADP
ejpam-3331	60	17	metric	metric	ADJ
ejpam-3331	60	18	-	-	PUNCT
ejpam-3331	60	19	like	like	ADJ
ejpam-3331	60	20	spaces	space	NOUN
ejpam-3331	60	21	.	.	PUNCT
ejpam-3331	61	1	for	for	ADP
ejpam-3331	61	2	instance	instance	NOUN
ejpam-3331	61	3	,	,	PUNCT
ejpam-3331	61	4	see	see	VERB
ejpam-3331	61	5	[	[	X
ejpam-3331	61	6	6	6	NUM
ejpam-3331	61	7	,	,	PUNCT
ejpam-3331	61	8	8	8	NUM
ejpam-3331	61	9	,	,	PUNCT
ejpam-3331	61	10	10	10	NUM
ejpam-3331	61	11	]	]	PUNCT
ejpam-3331	61	12	.	.	PUNCT
ejpam-3331	62	1	on	on	ADP
ejpam-3331	62	2	the	the	DET
ejpam-3331	62	3	one	one	NUM
ejpam-3331	62	4	hand	hand	NOUN
ejpam-3331	62	5	,	,	PUNCT
ejpam-3331	62	6	samet	samet	VERB
ejpam-3331	63	1	[	[	X
ejpam-3331	63	2	26	26	NUM
ejpam-3331	63	3	]	]	PUNCT
ejpam-3331	63	4	presented	present	VERB
ejpam-3331	63	5	the	the	DET
ejpam-3331	63	6	concept	concept	NOUN
ejpam-3331	63	7	of	of	ADP
ejpam-3331	63	8	α	α	NOUN
ejpam-3331	63	9	-	-	PUNCT
ejpam-3331	63	10	admissible	admissible	ADJ
ejpam-3331	63	11	mappings	mapping	NOUN
ejpam-3331	63	12	and	and	CCONJ
ejpam-3331	63	13	proved	prove	VERB
ejpam-3331	63	14	some	some	DET
ejpam-3331	63	15	fixed	fix	VERB
ejpam-3331	63	16	point	point	NOUN
ejpam-3331	63	17	theorems	theorem	NOUN
ejpam-3331	63	18	in	in	ADP
ejpam-3331	63	19	metric	metric	ADJ
ejpam-3331	63	20	spaces	space	NOUN
ejpam-3331	63	21	.	.	PUNCT
ejpam-3331	64	1	recently	recently	ADV
ejpam-3331	64	2	,	,	PUNCT
ejpam-3331	64	3	chandok	chandok	NOUN
ejpam-3331	64	4	[	[	X
ejpam-3331	64	5	14	14	NUM
ejpam-3331	64	6	]	]	PUNCT
ejpam-3331	64	7	introduced	introduce	VERB
ejpam-3331	64	8	the	the	DET
ejpam-3331	64	9	notion	notion	NOUN
ejpam-3331	64	10	of	of	ADP
ejpam-3331	64	11	(	(	PUNCT
ejpam-3331	64	12	α	α	X
ejpam-3331	64	13	,	,	PUNCT
ejpam-3331	64	14	β)-admissible	β)-admissible	PUNCT
ejpam-3331	64	15	mappings	mapping	NOUN
ejpam-3331	64	16	and	and	CCONJ
ejpam-3331	64	17	obtained	obtain	VERB
ejpam-3331	64	18	some	some	DET
ejpam-3331	64	19	fixed	fix	VERB
ejpam-3331	64	20	point	point	NOUN
ejpam-3331	64	21	theorems	theorem	NOUN
ejpam-3331	64	22	.	.	PUNCT
ejpam-3331	65	1	definition	definition	NOUN
ejpam-3331	65	2	2	2	NUM
ejpam-3331	65	3	.	.	PUNCT
ejpam-3331	66	1	[	[	X
ejpam-3331	66	2	14	14	NUM
ejpam-3331	66	3	]	]	PUNCT
ejpam-3331	66	4	let	let	VERB
ejpam-3331	66	5	x	x	PRON
ejpam-3331	66	6	be	be	AUX
ejpam-3331	66	7	a	a	DET
ejpam-3331	66	8	nonempty	nonempty	ADJ
ejpam-3331	66	9	set	set	VERB
ejpam-3331	66	10	,	,	PUNCT
ejpam-3331	66	11	f	f	X
ejpam-3331	66	12	:	:	PUNCT
ejpam-3331	66	13	x	x	X
ejpam-3331	66	14	→	→	SYM
ejpam-3331	66	15	x	x	X
ejpam-3331	66	16	and	and	CCONJ
ejpam-3331	66	17	α	α	NOUN
ejpam-3331	66	18	,	,	PUNCT
ejpam-3331	66	19	β	β	X
ejpam-3331	66	20	:	:	PUNCT
ejpam-3331	66	21	x	x	SYM
ejpam-3331	66	22	×	×	NOUN
ejpam-3331	66	23	x	x	INTJ
ejpam-3331	66	24	→	→	SYM
ejpam-3331	66	25	r+	r+	X
ejpam-3331	66	26	.	.	PUNCT
ejpam-3331	67	1	we	we	PRON
ejpam-3331	67	2	say	say	VERB
ejpam-3331	67	3	that	that	SCONJ
ejpam-3331	67	4	f	f	PROPN
ejpam-3331	67	5	is	be	AUX
ejpam-3331	67	6	an	an	DET
ejpam-3331	67	7	(	(	PUNCT
ejpam-3331	67	8	α	α	NOUN
ejpam-3331	67	9	,	,	PUNCT
ejpam-3331	67	10	β)-admissible	β)-admissible	PUNCT
ejpam-3331	67	11	mapping	mapping	NOUN
ejpam-3331	67	12	if	if	SCONJ
ejpam-3331	67	13	α(x	α(x	PROPN
ejpam-3331	67	14	,	,	PUNCT
ejpam-3331	67	15	y	y	PROPN
ejpam-3331	67	16	)	)	PUNCT
ejpam-3331	67	17	≥	≥	NOUN
ejpam-3331	67	18	1	1	NUM
ejpam-3331	67	19	and	and	CCONJ
ejpam-3331	67	20	β(x	β(x	PROPN
ejpam-3331	67	21	,	,	PUNCT
ejpam-3331	67	22	y	y	NOUN
ejpam-3331	67	23	)	)	PUNCT
ejpam-3331	67	24	≥	≥	NOUN
ejpam-3331	67	25	1	1	NUM
ejpam-3331	67	26	imply	imply	VERB
ejpam-3331	67	27	that	that	SCONJ
ejpam-3331	67	28	α(fx	α(fx	PROPN
ejpam-3331	67	29	,	,	PUNCT
ejpam-3331	67	30	fy	fy	PROPN
ejpam-3331	67	31	)	)	PUNCT
ejpam-3331	67	32	≥	≥	NOUN
ejpam-3331	67	33	1	1	NUM
ejpam-3331	67	34	and	and	CCONJ
ejpam-3331	67	35	β(fx	β(fx	PROPN
ejpam-3331	67	36	,	,	PUNCT
ejpam-3331	67	37	fy	fy	PROPN
ejpam-3331	67	38	)	)	PUNCT
ejpam-3331	67	39	≥	≥	NOUN
ejpam-3331	67	40	1	1	NUM
ejpam-3331	67	41	for	for	ADP
ejpam-3331	67	42	all	all	DET
ejpam-3331	67	43	x	x	NOUN
ejpam-3331	67	44	,	,	PUNCT
ejpam-3331	67	45	y	y	PROPN
ejpam-3331	67	46	∈	∈	PROPN
ejpam-3331	67	47	x.	x.	NOUN
ejpam-3331	67	48	for	for	ADP
ejpam-3331	67	49	other	other	ADJ
ejpam-3331	67	50	results	result	NOUN
ejpam-3331	67	51	using	use	VERB
ejpam-3331	67	52	different	different	ADJ
ejpam-3331	67	53	concepts	concept	NOUN
ejpam-3331	67	54	of	of	ADP
ejpam-3331	67	55	α	α	NOUN
ejpam-3331	67	56	-	-	PUNCT
ejpam-3331	67	57	admissible	admissible	ADJ
ejpam-3331	67	58	mappings	mapping	NOUN
ejpam-3331	67	59	,	,	PUNCT
ejpam-3331	67	60	see	see	VERB
ejpam-3331	67	61	[	[	X
ejpam-3331	67	62	1	1	NUM
ejpam-3331	67	63	,	,	PUNCT
ejpam-3331	67	64	2	2	NUM
ejpam-3331	67	65	,	,	PUNCT
ejpam-3331	67	66	7	7	NUM
ejpam-3331	67	67	,	,	PUNCT
ejpam-3331	67	68	9	9	NUM
ejpam-3331	67	69	,	,	PUNCT
ejpam-3331	67	70	11	11	NUM
ejpam-3331	67	71	,	,	PUNCT
ejpam-3331	67	72	15	15	NUM
ejpam-3331	67	73	,	,	PUNCT
ejpam-3331	67	74	27–29	27–29	NUM
ejpam-3331	67	75	]	]	PUNCT
ejpam-3331	67	76	.	.	PUNCT
ejpam-3331	68	1	on	on	ADP
ejpam-3331	68	2	the	the	DET
ejpam-3331	68	3	other	other	ADJ
ejpam-3331	68	4	hand	hand	NOUN
ejpam-3331	68	5	,	,	PUNCT
ejpam-3331	68	6	khojasteh	khojasteh	PROPN
ejpam-3331	68	7	et	et	PROPN
ejpam-3331	68	8	al	al	PROPN
ejpam-3331	68	9	.	.	PUNCT
ejpam-3331	69	1	[	[	X
ejpam-3331	69	2	19	19	NUM
ejpam-3331	69	3	]	]	PUNCT
ejpam-3331	69	4	introduced	introduce	VERB
ejpam-3331	69	5	a	a	DET
ejpam-3331	69	6	new	new	ADJ
ejpam-3331	69	7	class	class	NOUN
ejpam-3331	69	8	of	of	ADP
ejpam-3331	69	9	mappings	mapping	NOUN
ejpam-3331	69	10	called	call	VERB
ejpam-3331	69	11	simulation	simulation	NOUN
ejpam-3331	69	12	functions	function	NOUN
ejpam-3331	69	13	.	.	PUNCT
ejpam-3331	70	1	they	they	PRON
ejpam-3331	70	2	[	[	X
ejpam-3331	70	3	19	19	NUM
ejpam-3331	70	4	]	]	PUNCT
ejpam-3331	70	5	proved	prove	VERB
ejpam-3331	70	6	several	several	ADJ
ejpam-3331	70	7	fixed	fix	VERB
ejpam-3331	70	8	point	point	NOUN
ejpam-3331	70	9	theorems	theorem	NOUN
ejpam-3331	70	10	and	and	CCONJ
ejpam-3331	70	11	showed	show	VERB
ejpam-3331	70	12	that	that	SCONJ
ejpam-3331	70	13	many	many	ADJ
ejpam-3331	70	14	results	result	NOUN
ejpam-3331	70	15	in	in	ADP
ejpam-3331	70	16	the	the	DET
ejpam-3331	70	17	literature	literature	NOUN
ejpam-3331	70	18	are	be	AUX
ejpam-3331	70	19	simple	simple	ADJ
ejpam-3331	70	20	consequences	consequence	NOUN
ejpam-3331	70	21	of	of	ADP
ejpam-3331	70	22	their	their	PRON
ejpam-3331	70	23	obtained	obtain	VERB
ejpam-3331	70	24	results	result	NOUN
ejpam-3331	70	25	.	.	PUNCT
ejpam-3331	71	1	definition	definition	NOUN
ejpam-3331	71	2	3	3	NUM
ejpam-3331	71	3	.	.	PUNCT
ejpam-3331	72	1	[	[	X
ejpam-3331	72	2	19	19	NUM
ejpam-3331	72	3	]	]	PUNCT
ejpam-3331	72	4	a	a	DET
ejpam-3331	72	5	function	function	NOUN
ejpam-3331	72	6	ζ	ζ	NOUN
ejpam-3331	72	7	:	:	PUNCT
ejpam-3331	73	1	[	[	X
ejpam-3331	73	2	0,∞)×	0,∞)×	NUM
ejpam-3331	73	3	[	[	X
ejpam-3331	73	4	0,∞)→	0,∞)→	NOUN
ejpam-3331	73	5	r	r	NOUN
ejpam-3331	73	6	is	be	AUX
ejpam-3331	73	7	called	call	VERB
ejpam-3331	73	8	a	a	DET
ejpam-3331	73	9	simulation	simulation	NOUN
ejpam-3331	73	10	function	function	NOUN
ejpam-3331	73	11	if	if	SCONJ
ejpam-3331	73	12	ζ	ζ	NOUN
ejpam-3331	73	13	satisfies	satisfy	VERB
ejpam-3331	73	14	the	the	DET
ejpam-3331	73	15	following	follow	VERB
ejpam-3331	73	16	conditions	condition	NOUN
ejpam-3331	73	17	:	:	PUNCT
ejpam-3331	73	18	(	(	PUNCT
ejpam-3331	73	19	ζ1	ζ1	NOUN
ejpam-3331	73	20	)	)	PUNCT
ejpam-3331	73	21	ζ(0	ζ(0	NOUN
ejpam-3331	73	22	,	,	PUNCT
ejpam-3331	73	23	0	0	NUM
ejpam-3331	73	24	)	)	PUNCT
ejpam-3331	73	25	=	=	SYM
ejpam-3331	73	26	0	0	NUM
ejpam-3331	73	27	;	;	PUNCT
ejpam-3331	73	28	(	(	PUNCT
ejpam-3331	73	29	ζ2	ζ2	NOUN
ejpam-3331	73	30	)	)	PUNCT
ejpam-3331	73	31	ζ(t	ζ(t	PROPN
ejpam-3331	73	32	,	,	PUNCT
ejpam-3331	73	33	s	s	PART
ejpam-3331	73	34	)	)	PUNCT
ejpam-3331	73	35	<	<	X
ejpam-3331	73	36	s−	s−	PROPN
ejpam-3331	73	37	t	t	PROPN
ejpam-3331	73	38	for	for	ADP
ejpam-3331	73	39	all	all	DET
ejpam-3331	73	40	t	t	PROPN
ejpam-3331	73	41	,	,	PUNCT
ejpam-3331	73	42	s	s	PART
ejpam-3331	73	43	>	>	X
ejpam-3331	73	44	0	0	NUM
ejpam-3331	73	45	;	;	PUNCT
ejpam-3331	73	46	(	(	PUNCT
ejpam-3331	73	47	ζ3	ζ3	NOUN
ejpam-3331	73	48	)	)	PUNCT
ejpam-3331	73	49	if	if	SCONJ
ejpam-3331	73	50	{	{	PUNCT
ejpam-3331	73	51	tn	tn	NOUN
ejpam-3331	73	52	}	}	PUNCT
ejpam-3331	73	53	and	and	CCONJ
ejpam-3331	73	54	{	{	PUNCT
ejpam-3331	73	55	sn	sn	NOUN
ejpam-3331	73	56	}	}	PUNCT
ejpam-3331	73	57	are	be	AUX
ejpam-3331	73	58	sequences	sequence	NOUN
ejpam-3331	73	59	in	in	ADP
ejpam-3331	73	60	(	(	PUNCT
ejpam-3331	73	61	0,∞	0,∞	NOUN
ejpam-3331	73	62	)	)	PUNCT
ejpam-3331	73	63	such	such	ADJ
ejpam-3331	73	64	that	that	SCONJ
ejpam-3331	73	65	limn→∞	limn→∞	PROPN
ejpam-3331	73	66	tn	tn	NOUN
ejpam-3331	73	67	=	=	SYM
ejpam-3331	73	68	limn→∞	limn→∞	X
ejpam-3331	73	69	sn	sn	NOUN
ejpam-3331	73	70	=	=	PUNCT
ejpam-3331	73	71	`	`	PUNCT
ejpam-3331	73	72	∈	∈	PROPN
ejpam-3331	73	73	(	(	PUNCT
ejpam-3331	73	74	0,∞	0,∞	NOUN
ejpam-3331	73	75	)	)	PUNCT
ejpam-3331	73	76	,	,	PUNCT
ejpam-3331	73	77	then	then	ADV
ejpam-3331	73	78	lim	lim	PROPN
ejpam-3331	73	79	n→∞	n→∞	NUM
ejpam-3331	73	80	sup	sup	PROPN
ejpam-3331	73	81	ζ(tn	ζ(tn	PROPN
ejpam-3331	73	82	,	,	PUNCT
ejpam-3331	73	83	sn	sn	PROPN
ejpam-3331	73	84	)	)	PUNCT
ejpam-3331	73	85	<	<	X
ejpam-3331	73	86	0	0	X
ejpam-3331	73	87	.	.	PUNCT
ejpam-3331	74	1	in	in	ADP
ejpam-3331	74	2	[	[	X
ejpam-3331	74	3	19	19	NUM
ejpam-3331	74	4	]	]	PUNCT
ejpam-3331	74	5	,	,	PUNCT
ejpam-3331	74	6	the	the	DET
ejpam-3331	74	7	following	follow	VERB
ejpam-3331	74	8	unique	unique	ADJ
ejpam-3331	74	9	fixed	fix	VERB
ejpam-3331	74	10	point	point	NOUN
ejpam-3331	74	11	theorem	theorem	NOUN
ejpam-3331	74	12	is	be	AUX
ejpam-3331	74	13	established	establish	VERB
ejpam-3331	74	14	.	.	PUNCT
ejpam-3331	75	1	theorem	theorem	NOUN
ejpam-3331	75	2	1	1	NUM
ejpam-3331	75	3	.	.	PUNCT
ejpam-3331	76	1	[	[	X
ejpam-3331	76	2	19	19	NUM
ejpam-3331	76	3	]	]	X
ejpam-3331	76	4	let	let	VERB
ejpam-3331	76	5	(	(	PUNCT
ejpam-3331	76	6	x	x	NOUN
ejpam-3331	76	7	,	,	PUNCT
ejpam-3331	76	8	d	d	NOUN
ejpam-3331	76	9	)	)	PUNCT
ejpam-3331	76	10	be	be	AUX
ejpam-3331	76	11	a	a	DET
ejpam-3331	76	12	metric	metric	ADJ
ejpam-3331	76	13	space	space	NOUN
ejpam-3331	76	14	and	and	CCONJ
ejpam-3331	76	15	f	f	NOUN
ejpam-3331	76	16	:	:	PUNCT
ejpam-3331	76	17	x	x	X
ejpam-3331	76	18	→	→	PUNCT
ejpam-3331	76	19	x	x	PUNCT
ejpam-3331	76	20	be	be	AUX
ejpam-3331	76	21	a	a	DET
ejpam-3331	76	22	z	z	NOUN
ejpam-3331	76	23	-	-	PUNCT
ejpam-3331	76	24	contraction	contraction	NOUN
ejpam-3331	76	25	with	with	ADP
ejpam-3331	76	26	respect	respect	NOUN
ejpam-3331	76	27	to	to	ADP
ejpam-3331	76	28	a	a	DET
ejpam-3331	76	29	simulation	simulation	NOUN
ejpam-3331	76	30	function	function	NOUN
ejpam-3331	76	31	ζ	ζ	NOUN
ejpam-3331	76	32	,	,	PUNCT
ejpam-3331	76	33	that	that	ADV
ejpam-3331	76	34	is	is	ADV
ejpam-3331	76	35	,	,	PUNCT
ejpam-3331	76	36	ζ(d(fx	ζ(d(fx	ADP
ejpam-3331	76	37	,	,	PUNCT
ejpam-3331	76	38	fy	fy	PROPN
ejpam-3331	76	39	)	)	PUNCT
ejpam-3331	76	40	,	,	PUNCT
ejpam-3331	76	41	d(x	d(x	PROPN
ejpam-3331	76	42	,	,	PUNCT
ejpam-3331	76	43	y	y	NOUN
ejpam-3331	76	44	)	)	PUNCT
ejpam-3331	76	45	)	)	PUNCT
ejpam-3331	76	46	≥	≥	NOUN
ejpam-3331	76	47	0	0	NUM
ejpam-3331	76	48	,	,	PUNCT
ejpam-3331	76	49	forall	forall	NOUN
ejpam-3331	76	50	x	x	X
ejpam-3331	76	51	,	,	PUNCT
ejpam-3331	76	52	y	y	PROPN
ejpam-3331	76	53	∈	∈	PROPN
ejpam-3331	77	1	x.	x.	NOUN
ejpam-3331	77	2	then	then	ADV
ejpam-3331	77	3	t	t	PROPN
ejpam-3331	77	4	has	have	VERB
ejpam-3331	77	5	a	a	DET
ejpam-3331	77	6	unique	unique	ADJ
ejpam-3331	77	7	fixed	fix	VERB
ejpam-3331	77	8	point	point	NOUN
ejpam-3331	77	9	.	.	PUNCT
ejpam-3331	78	1	it	it	PRON
ejpam-3331	78	2	is	be	AUX
ejpam-3331	78	3	worth	worth	ADJ
ejpam-3331	78	4	mentioning	mention	VERB
ejpam-3331	78	5	that	that	SCONJ
ejpam-3331	78	6	the	the	DET
ejpam-3331	78	7	banach	banach	NOUN
ejpam-3331	78	8	contraction	contraction	NOUN
ejpam-3331	78	9	is	be	AUX
ejpam-3331	78	10	an	an	DET
ejpam-3331	78	11	example	example	NOUN
ejpam-3331	78	12	of	of	ADP
ejpam-3331	78	13	z	z	NOUN
ejpam-3331	78	14	-	-	PUNCT
ejpam-3331	78	15	contractions	contraction	NOUN
ejpam-3331	78	16	by	by	ADP
ejpam-3331	78	17	defining	define	VERB
ejpam-3331	78	18	ζ	ζ	NOUN
ejpam-3331	78	19	:	:	PUNCT
ejpam-3331	79	1	[	[	X
ejpam-3331	79	2	0,∞)×	0,∞)×	NUM
ejpam-3331	79	3	[	[	X
ejpam-3331	79	4	0,∞)→	0,∞)→	NOUN
ejpam-3331	79	5	r	r	NOUN
ejpam-3331	79	6	via	via	ADP
ejpam-3331	79	7	ζ(t	ζ(t	PROPN
ejpam-3331	79	8	,	,	PUNCT
ejpam-3331	79	9	s	s	NOUN
ejpam-3331	79	10	)	)	PUNCT
ejpam-3331	79	11	=	=	SYM
ejpam-3331	79	12	γs−	γs−	NUM
ejpam-3331	79	13	t	t	PROPN
ejpam-3331	79	14	,	,	PUNCT
ejpam-3331	79	15	∀	∀	X
ejpam-3331	79	16	s	s	NOUN
ejpam-3331	79	17	,	,	PUNCT
ejpam-3331	79	18	t	t	PROPN
ejpam-3331	79	19	∈	∈	PROPN
ejpam-3331	80	1	[	[	X
ejpam-3331	80	2	0,∞	0,∞	NOUN
ejpam-3331	80	3	)	)	PUNCT
ejpam-3331	80	4	,	,	PUNCT
ejpam-3331	80	5	where	where	SCONJ
ejpam-3331	80	6	γ	γ	X
ejpam-3331	80	7	∈	∈	PROPN
ejpam-3331	80	8	[	[	X
ejpam-3331	80	9	0	0	NUM
ejpam-3331	80	10	,	,	PUNCT
ejpam-3331	80	11	1	1	NUM
ejpam-3331	80	12	)	)	PUNCT
ejpam-3331	80	13	.	.	PUNCT
ejpam-3331	81	1	argoubi	argoubi	INTJ
ejpam-3331	81	2	et	et	PROPN
ejpam-3331	81	3	al	al	PROPN
ejpam-3331	81	4	.	.	PUNCT
ejpam-3331	82	1	[	[	X
ejpam-3331	82	2	4	4	NUM
ejpam-3331	82	3	]	]	X
ejpam-3331	82	4	modified	modified	ADJ
ejpam-3331	82	5	definition	definition	NOUN
ejpam-3331	82	6	3	3	NUM
ejpam-3331	82	7	as	as	SCONJ
ejpam-3331	82	8	follows	follow	VERB
ejpam-3331	82	9	.	.	PUNCT
ejpam-3331	83	1	h.	h.	PROPN
ejpam-3331	83	2	alsamir	alsamir	VERB
ejpam-3331	83	3	et	et	PROPN
ejpam-3331	83	4	al	al	PROPN
ejpam-3331	83	5	.	.	PUNCT
ejpam-3331	83	6	/	/	SYM
ejpam-3331	83	7	eur	eur	PROPN
ejpam-3331	83	8	.	.	PUNCT
ejpam-3331	84	1	j.	j.	PROPN
ejpam-3331	84	2	pure	pure	PROPN
ejpam-3331	84	3	appl	appl	PROPN
ejpam-3331	84	4	.	.	PROPN
ejpam-3331	84	5	math	math	PROPN
ejpam-3331	84	6	,	,	PUNCT
ejpam-3331	84	7	12	12	NUM
ejpam-3331	84	8	(	(	PUNCT
ejpam-3331	84	9	1	1	NUM
ejpam-3331	84	10	)	)	PUNCT
ejpam-3331	84	11	(	(	PUNCT
ejpam-3331	84	12	2019	2019	NUM
ejpam-3331	84	13	)	)	PUNCT
ejpam-3331	84	14	,	,	PUNCT
ejpam-3331	84	15	88	88	NUM
ejpam-3331	84	16	-	-	SYM
ejpam-3331	84	17	100	100	NUM
ejpam-3331	84	18	91	91	NUM
ejpam-3331	84	19	definition	definition	NOUN
ejpam-3331	84	20	4	4	NUM
ejpam-3331	84	21	.	.	PUNCT
ejpam-3331	85	1	[	[	X
ejpam-3331	85	2	4	4	X
ejpam-3331	85	3	]	]	X
ejpam-3331	85	4	a	a	DET
ejpam-3331	85	5	simulation	simulation	NOUN
ejpam-3331	85	6	function	function	NOUN
ejpam-3331	85	7	is	be	AUX
ejpam-3331	85	8	a	a	DET
ejpam-3331	85	9	function	function	NOUN
ejpam-3331	85	10	ζ	ζ	NOUN
ejpam-3331	85	11	:	:	PUNCT
ejpam-3331	86	1	[	[	X
ejpam-3331	86	2	0,∞)×	0,∞)×	NUM
ejpam-3331	86	3	[	[	X
ejpam-3331	86	4	0,∞)→	0,∞)→	NOUN
ejpam-3331	86	5	r	r	NOUN
ejpam-3331	86	6	that	that	PRON
ejpam-3331	86	7	satisfies	satisfy	VERB
ejpam-3331	86	8	the	the	DET
ejpam-3331	86	9	following	follow	VERB
ejpam-3331	86	10	conditions	condition	NOUN
ejpam-3331	86	11	:	:	PUNCT
ejpam-3331	86	12	(	(	PUNCT
ejpam-3331	86	13	i	i	NOUN
ejpam-3331	86	14	)	)	PUNCT
ejpam-3331	86	15	ζ(t	ζ(t	PROPN
ejpam-3331	86	16	,	,	PUNCT
ejpam-3331	86	17	s	s	PART
ejpam-3331	86	18	)	)	PUNCT
ejpam-3331	86	19	<	<	X
ejpam-3331	86	20	s−	s−	PROPN
ejpam-3331	86	21	t	t	PROPN
ejpam-3331	86	22	for	for	ADP
ejpam-3331	86	23	all	all	DET
ejpam-3331	86	24	t	t	PROPN
ejpam-3331	86	25	,	,	PUNCT
ejpam-3331	86	26	s	s	PART
ejpam-3331	86	27	>	>	X
ejpam-3331	86	28	0	0	NUM
ejpam-3331	86	29	;	;	PUNCT
ejpam-3331	86	30	(	(	PUNCT
ejpam-3331	86	31	ii	ii	NOUN
ejpam-3331	86	32	)	)	PUNCT
ejpam-3331	86	33	if	if	SCONJ
ejpam-3331	86	34	{	{	PUNCT
ejpam-3331	86	35	tn	tn	NOUN
ejpam-3331	86	36	}	}	PUNCT
ejpam-3331	86	37	and	and	CCONJ
ejpam-3331	86	38	{	{	PUNCT
ejpam-3331	86	39	sn	sn	NOUN
ejpam-3331	86	40	}	}	PUNCT
ejpam-3331	86	41	are	be	AUX
ejpam-3331	86	42	sequences	sequence	NOUN
ejpam-3331	86	43	in	in	ADP
ejpam-3331	86	44	(	(	PUNCT
ejpam-3331	86	45	0,∞	0,∞	NOUN
ejpam-3331	86	46	)	)	PUNCT
ejpam-3331	87	1	such	such	ADJ
ejpam-3331	87	2	that	that	SCONJ
ejpam-3331	87	3	limn→∞	limn→∞	PROPN
ejpam-3331	87	4	tn	tn	NOUN
ejpam-3331	87	5	=	=	SYM
ejpam-3331	87	6	limn→∞	limn→∞	X
ejpam-3331	87	7	sn	sn	NOUN
ejpam-3331	87	8	=	=	PUNCT
ejpam-3331	87	9	`	`	PUNCT
ejpam-3331	87	10	∈	∈	PROPN
ejpam-3331	87	11	(	(	PUNCT
ejpam-3331	87	12	0,∞	0,∞	NOUN
ejpam-3331	87	13	)	)	PUNCT
ejpam-3331	87	14	,	,	PUNCT
ejpam-3331	87	15	then	then	ADV
ejpam-3331	87	16	lim	lim	PROPN
ejpam-3331	87	17	n→∞	n→∞	NUM
ejpam-3331	87	18	sup	sup	PROPN
ejpam-3331	87	19	ζ(tn	ζ(tn	PROPN
ejpam-3331	87	20	,	,	PUNCT
ejpam-3331	87	21	sn	sn	PROPN
ejpam-3331	87	22	)	)	PUNCT
ejpam-3331	87	23	<	<	X
ejpam-3331	87	24	0	0	X
ejpam-3331	87	25	.	.	PUNCT
ejpam-3331	88	1	it	it	PRON
ejpam-3331	88	2	is	be	AUX
ejpam-3331	88	3	clear	clear	ADJ
ejpam-3331	88	4	that	that	SCONJ
ejpam-3331	88	5	any	any	DET
ejpam-3331	88	6	simulation	simulation	NOUN
ejpam-3331	88	7	function	function	NOUN
ejpam-3331	88	8	in	in	ADP
ejpam-3331	88	9	the	the	DET
ejpam-3331	88	10	sense	sense	NOUN
ejpam-3331	88	11	of	of	ADP
ejpam-3331	88	12	khojasteh	khojasteh	NOUN
ejpam-3331	88	13	et	et	PROPN
ejpam-3331	88	14	al	al	PROPN
ejpam-3331	88	15	.	.	PUNCT
ejpam-3331	89	1	(	(	PUNCT
ejpam-3331	89	2	definition	definition	NOUN
ejpam-3331	89	3	3	3	NUM
ejpam-3331	89	4	)	)	PUNCT
ejpam-3331	89	5	is	be	AUX
ejpam-3331	89	6	also	also	ADV
ejpam-3331	89	7	a	a	DET
ejpam-3331	89	8	simulation	simulation	NOUN
ejpam-3331	89	9	function	function	NOUN
ejpam-3331	89	10	in	in	ADP
ejpam-3331	89	11	the	the	DET
ejpam-3331	89	12	sense	sense	NOUN
ejpam-3331	89	13	of	of	ADP
ejpam-3331	89	14	argoubi	argoubi	NOUN
ejpam-3331	89	15	et	et	PROPN
ejpam-3331	89	16	al	al	PROPN
ejpam-3331	89	17	.	.	PUNCT
ejpam-3331	90	1	(	(	PUNCT
ejpam-3331	90	2	definition	definition	NOUN
ejpam-3331	90	3	4	4	NUM
ejpam-3331	90	4	)	)	PUNCT
ejpam-3331	90	5	.	.	PUNCT
ejpam-3331	91	1	the	the	DET
ejpam-3331	91	2	converse	converse	NOUN
ejpam-3331	91	3	is	be	AUX
ejpam-3331	91	4	not	not	PART
ejpam-3331	91	5	true	true	ADJ
ejpam-3331	91	6	.	.	PUNCT
ejpam-3331	92	1	for	for	ADP
ejpam-3331	92	2	more	more	ADJ
ejpam-3331	92	3	details	detail	NOUN
ejpam-3331	92	4	,	,	PUNCT
ejpam-3331	92	5	see	see	VERB
ejpam-3331	92	6	[	[	X
ejpam-3331	92	7	4	4	NUM
ejpam-3331	92	8	]	]	PUNCT
ejpam-3331	92	9	.	.	PUNCT
ejpam-3331	93	1	example	example	NOUN
ejpam-3331	94	1	2	2	NUM
ejpam-3331	94	2	.	.	PUNCT
ejpam-3331	95	1	[	[	X
ejpam-3331	95	2	4	4	X
ejpam-3331	95	3	]	]	PUNCT
ejpam-3331	95	4	define	define	VERB
ejpam-3331	95	5	a	a	DET
ejpam-3331	95	6	function	function	NOUN
ejpam-3331	95	7	ζ	ζ	NOUN
ejpam-3331	95	8	:	:	PUNCT
ejpam-3331	96	1	[	[	X
ejpam-3331	96	2	0,∞)×	0,∞)×	NUM
ejpam-3331	96	3	[	[	X
ejpam-3331	96	4	0,∞)→	0,∞)→	NOUN
ejpam-3331	96	5	r	r	NOUN
ejpam-3331	96	6	by	by	ADP
ejpam-3331	96	7	ζ(t	ζ(t	PROPN
ejpam-3331	96	8	,	,	PUNCT
ejpam-3331	96	9	s	s	NOUN
ejpam-3331	96	10	)	)	PUNCT
ejpam-3331	96	11	=	=	SYM
ejpam-3331	96	12	{	{	PUNCT
ejpam-3331	96	13	1	1	NUM
ejpam-3331	96	14	if	if	SCONJ
ejpam-3331	96	15	(	(	PUNCT
ejpam-3331	96	16	s	s	X
ejpam-3331	96	17	,	,	PUNCT
ejpam-3331	96	18	t	t	PROPN
ejpam-3331	96	19	)	)	PUNCT
ejpam-3331	96	20	=	=	SYM
ejpam-3331	96	21	(	(	PUNCT
ejpam-3331	96	22	0	0	NUM
ejpam-3331	96	23	,	,	PUNCT
ejpam-3331	96	24	0	0	NUM
ejpam-3331	96	25	)	)	PUNCT
ejpam-3331	96	26	,	,	PUNCT
ejpam-3331	96	27	λs−	λs−	PUNCT
ejpam-3331	96	28	t	t	NOUN
ejpam-3331	96	29	otherwise	otherwise	ADV
ejpam-3331	96	30	,	,	PUNCT
ejpam-3331	96	31	where	where	SCONJ
ejpam-3331	96	32	λ	λ	PROPN
ejpam-3331	96	33	∈	∈	PROPN
ejpam-3331	96	34	(	(	PUNCT
ejpam-3331	96	35	0	0	NUM
ejpam-3331	96	36	,	,	PUNCT
ejpam-3331	96	37	1	1	NUM
ejpam-3331	96	38	)	)	PUNCT
ejpam-3331	96	39	.	.	PUNCT
ejpam-3331	97	1	then	then	ADV
ejpam-3331	97	2	ζ	ζ	NOUN
ejpam-3331	97	3	is	be	AUX
ejpam-3331	97	4	a	a	DET
ejpam-3331	97	5	simulation	simulation	NOUN
ejpam-3331	97	6	function	function	NOUN
ejpam-3331	97	7	in	in	ADP
ejpam-3331	97	8	the	the	DET
ejpam-3331	97	9	sense	sense	NOUN
ejpam-3331	97	10	of	of	ADP
ejpam-3331	97	11	argoubi	argoubi	NOUN
ejpam-3331	97	12	et	et	PROPN
ejpam-3331	97	13	al	al	PROPN
ejpam-3331	97	14	.	.	PROPN
ejpam-3331	98	1	in	in	ADP
ejpam-3331	98	2	the	the	DET
ejpam-3331	98	3	following	following	NOUN
ejpam-3331	98	4	,	,	PUNCT
ejpam-3331	98	5	some	some	DET
ejpam-3331	98	6	other	other	ADJ
ejpam-3331	98	7	examples	example	NOUN
ejpam-3331	98	8	of	of	ADP
ejpam-3331	98	9	simulation	simulation	NOUN
ejpam-3331	98	10	functions	function	NOUN
ejpam-3331	98	11	in	in	ADP
ejpam-3331	98	12	the	the	DET
ejpam-3331	98	13	sense	sense	NOUN
ejpam-3331	98	14	of	of	ADP
ejpam-3331	98	15	definition	definition	NOUN
ejpam-3331	98	16	3	3	NUM
ejpam-3331	98	17	(	(	PUNCT
ejpam-3331	98	18	see	see	VERB
ejpam-3331	98	19	[	[	X
ejpam-3331	98	20	3	3	NUM
ejpam-3331	98	21	,	,	PUNCT
ejpam-3331	98	22	19	19	NUM
ejpam-3331	98	23	,	,	PUNCT
ejpam-3331	98	24	31	31	NUM
ejpam-3331	98	25	]	]	PUNCT
ejpam-3331	98	26	)	)	PUNCT
ejpam-3331	98	27	.	.	PUNCT
ejpam-3331	99	1	(	(	PUNCT
ejpam-3331	99	2	i	i	NOUN
ejpam-3331	99	3	)	)	PUNCT
ejpam-3331	99	4	ζ(t	ζ(t	PROPN
ejpam-3331	99	5	,	,	PUNCT
ejpam-3331	99	6	s	s	PART
ejpam-3331	99	7	)	)	PUNCT
ejpam-3331	99	8	=	=	SYM
ejpam-3331	100	1	cs−	cs−	NUM
ejpam-3331	100	2	t	t	NOUN
ejpam-3331	100	3	for	for	ADP
ejpam-3331	100	4	all	all	DET
ejpam-3331	100	5	t	t	PROPN
ejpam-3331	100	6	,	,	PUNCT
ejpam-3331	100	7	s	s	PART
ejpam-3331	100	8	∈	∈	PROPN
ejpam-3331	101	1	[	[	X
ejpam-3331	101	2	0,∞	0,∞	NOUN
ejpam-3331	101	3	)	)	PUNCT
ejpam-3331	101	4	where	where	SCONJ
ejpam-3331	101	5	c	c	PROPN
ejpam-3331	101	6	∈	∈	PROPN
ejpam-3331	102	1	[	[	X
ejpam-3331	102	2	0	0	NUM
ejpam-3331	102	3	,	,	PUNCT
ejpam-3331	102	4	1	1	NUM
ejpam-3331	102	5	)	)	PUNCT
ejpam-3331	102	6	.	.	PUNCT
ejpam-3331	103	1	(	(	PUNCT
ejpam-3331	103	2	ii	ii	NOUN
ejpam-3331	103	3	)	)	PUNCT
ejpam-3331	103	4	ζ(t	ζ(t	PROPN
ejpam-3331	103	5	,	,	PUNCT
ejpam-3331	103	6	s	s	X
ejpam-3331	103	7	)	)	PUNCT
ejpam-3331	103	8	=	=	SYM
ejpam-3331	103	9	s	s	PART
ejpam-3331	103	10	−	−	NOUN
ejpam-3331	103	11	φ(s	φ(s	NOUN
ejpam-3331	103	12	)	)	PUNCT
ejpam-3331	103	13	−	−	PROPN
ejpam-3331	103	14	t	t	PROPN
ejpam-3331	103	15	for	for	ADP
ejpam-3331	103	16	all	all	DET
ejpam-3331	103	17	t	t	PROPN
ejpam-3331	103	18	,	,	PUNCT
ejpam-3331	103	19	s	s	PART
ejpam-3331	103	20	∈	∈	PROPN
ejpam-3331	104	1	[	[	X
ejpam-3331	104	2	0,∞	0,∞	NOUN
ejpam-3331	104	3	)	)	PUNCT
ejpam-3331	104	4	,	,	PUNCT
ejpam-3331	104	5	where	where	SCONJ
ejpam-3331	104	6	φ	φ	PROPN
ejpam-3331	104	7	:	:	PUNCT
ejpam-3331	104	8	r+	r+	X
ejpam-3331	104	9	→	→	SYM
ejpam-3331	104	10	r+	r+	PRON
ejpam-3331	104	11	is	be	AUX
ejpam-3331	104	12	a	a	DET
ejpam-3331	104	13	lower	low	ADJ
ejpam-3331	104	14	semicontinuous	semicontinuous	ADJ
ejpam-3331	104	15	function	function	NOUN
ejpam-3331	104	16	such	such	ADJ
ejpam-3331	104	17	that	that	SCONJ
ejpam-3331	104	18	φ(t	φ(t	NOUN
ejpam-3331	104	19	)	)	PUNCT
ejpam-3331	104	20	=	=	SYM
ejpam-3331	104	21	0	0	PUNCT
ejpam-3331	105	1	if	if	SCONJ
ejpam-3331	105	2	and	and	CCONJ
ejpam-3331	105	3	only	only	ADV
ejpam-3331	105	4	if	if	SCONJ
ejpam-3331	105	5	t	t	PROPN
ejpam-3331	105	6	=	=	SYM
ejpam-3331	105	7	0	0	X
ejpam-3331	105	8	.	.	PUNCT
ejpam-3331	106	1	in	in	ADP
ejpam-3331	106	2	this	this	DET
ejpam-3331	106	3	paper	paper	NOUN
ejpam-3331	106	4	,	,	PUNCT
ejpam-3331	106	5	we	we	PRON
ejpam-3331	106	6	introduce	introduce	VERB
ejpam-3331	106	7	the	the	DET
ejpam-3331	106	8	concept	concept	NOUN
ejpam-3331	106	9	of	of	ADP
ejpam-3331	106	10	(	(	PUNCT
ejpam-3331	106	11	α	α	X
ejpam-3331	106	12	,	,	PUNCT
ejpam-3331	106	13	β)-admissible	β)-admissible	PUNCT
ejpam-3331	106	14	z	z	NOUN
ejpam-3331	106	15	-	-	PUNCT
ejpam-3331	106	16	contractions	contraction	NOUN
ejpam-3331	106	17	with	with	ADP
ejpam-3331	106	18	respect	respect	NOUN
ejpam-3331	106	19	to	to	ADP
ejpam-3331	106	20	ζ	ζ	NOUN
ejpam-3331	106	21	.	.	PUNCT
ejpam-3331	107	1	we	we	PRON
ejpam-3331	107	2	also	also	ADV
ejpam-3331	107	3	establish	establish	VERB
ejpam-3331	107	4	the	the	DET
ejpam-3331	107	5	existence	existence	NOUN
ejpam-3331	107	6	of	of	ADP
ejpam-3331	107	7	fixed	fix	VERB
ejpam-3331	107	8	points	point	NOUN
ejpam-3331	107	9	for	for	ADP
ejpam-3331	107	10	this	this	DET
ejpam-3331	107	11	class	class	NOUN
ejpam-3331	107	12	of	of	ADP
ejpam-3331	107	13	mappings	mapping	NOUN
ejpam-3331	107	14	in	in	ADP
ejpam-3331	107	15	metric	metric	ADJ
ejpam-3331	107	16	-	-	PUNCT
ejpam-3331	107	17	like	like	ADJ
ejpam-3331	107	18	spaces	space	NOUN
ejpam-3331	107	19	.	.	PUNCT
ejpam-3331	108	1	our	our	PRON
ejpam-3331	108	2	work	work	NOUN
ejpam-3331	108	3	generalizes	generalize	VERB
ejpam-3331	108	4	and	and	CCONJ
ejpam-3331	108	5	extends	extend	VERB
ejpam-3331	108	6	some	some	DET
ejpam-3331	108	7	theorems	theorem	NOUN
ejpam-3331	108	8	in	in	ADP
ejpam-3331	108	9	the	the	DET
ejpam-3331	108	10	literature	literature	NOUN
ejpam-3331	108	11	.	.	PUNCT
ejpam-3331	109	1	two	two	NUM
ejpam-3331	109	2	illustrated	illustrated	ADJ
ejpam-3331	109	3	examples	example	NOUN
ejpam-3331	109	4	are	be	AUX
ejpam-3331	109	5	given	give	VERB
ejpam-3331	109	6	to	to	PART
ejpam-3331	109	7	support	support	VERB
ejpam-3331	109	8	the	the	DET
ejpam-3331	109	9	obtained	obtain	VERB
ejpam-3331	109	10	results	result	NOUN
ejpam-3331	109	11	.	.	PUNCT
ejpam-3331	110	1	2	2	X
ejpam-3331	110	2	.	.	X
ejpam-3331	110	3	main	main	ADJ
ejpam-3331	110	4	results	result	NOUN
ejpam-3331	110	5	first	first	ADV
ejpam-3331	110	6	,	,	PUNCT
ejpam-3331	110	7	we	we	PRON
ejpam-3331	110	8	introduce	introduce	VERB
ejpam-3331	110	9	the	the	DET
ejpam-3331	110	10	following	following	NOUN
ejpam-3331	110	11	.	.	PUNCT
ejpam-3331	111	1	definition	definition	NOUN
ejpam-3331	111	2	5	5	NUM
ejpam-3331	111	3	.	.	PUNCT
ejpam-3331	112	1	let	let	VERB
ejpam-3331	112	2	(	(	PUNCT
ejpam-3331	112	3	x	x	NOUN
ejpam-3331	112	4	,	,	PUNCT
ejpam-3331	112	5	σ	σ	PROPN
ejpam-3331	112	6	)	)	PUNCT
ejpam-3331	112	7	be	be	AUX
ejpam-3331	112	8	a	a	DET
ejpam-3331	112	9	metric	metric	ADJ
ejpam-3331	112	10	-	-	PUNCT
ejpam-3331	112	11	like	like	ADJ
ejpam-3331	112	12	space	space	NOUN
ejpam-3331	112	13	.	.	PUNCT
ejpam-3331	113	1	given	give	VERB
ejpam-3331	113	2	f	f	PROPN
ejpam-3331	113	3	:	:	PUNCT
ejpam-3331	113	4	x	x	SYM
ejpam-3331	113	5	→	→	SYM
ejpam-3331	113	6	x	x	X
ejpam-3331	113	7	and	and	CCONJ
ejpam-3331	113	8	α	α	NOUN
ejpam-3331	113	9	,	,	PUNCT
ejpam-3331	113	10	β	β	X
ejpam-3331	113	11	:	:	PUNCT
ejpam-3331	113	12	x×x	x×x	PROPN
ejpam-3331	113	13	→	→	SYM
ejpam-3331	113	14	r+	r+	X
ejpam-3331	113	15	.	.	PUNCT
ejpam-3331	114	1	such	such	ADJ
ejpam-3331	114	2	f	f	PROPN
ejpam-3331	114	3	is	be	AUX
ejpam-3331	114	4	said	say	VERB
ejpam-3331	114	5	an	an	DET
ejpam-3331	114	6	(	(	PUNCT
ejpam-3331	114	7	α	α	NOUN
ejpam-3331	114	8	,	,	PUNCT
ejpam-3331	114	9	β)-admissible	β)-admissible	PUNCT
ejpam-3331	114	10	z	z	NOUN
ejpam-3331	114	11	-	-	PUNCT
ejpam-3331	114	12	contraction	contraction	NOUN
ejpam-3331	114	13	with	with	ADP
ejpam-3331	114	14	respect	respect	NOUN
ejpam-3331	114	15	to	to	ADP
ejpam-3331	114	16	ζ	ζ	PRON
ejpam-3331	114	17	if	if	SCONJ
ejpam-3331	114	18	ζ(α(x	ζ(α(x	NOUN
ejpam-3331	114	19	,	,	PUNCT
ejpam-3331	114	20	y)β(x	y)β(x	NOUN
ejpam-3331	114	21	,	,	PUNCT
ejpam-3331	114	22	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	114	23	,	,	PUNCT
ejpam-3331	114	24	fy	fy	PROPN
ejpam-3331	114	25	)	)	PUNCT
ejpam-3331	114	26	,	,	PUNCT
ejpam-3331	114	27	σ(x	σ(x	PROPN
ejpam-3331	114	28	,	,	PUNCT
ejpam-3331	114	29	y	y	NOUN
ejpam-3331	114	30	)	)	PUNCT
ejpam-3331	114	31	)	)	PUNCT
ejpam-3331	115	1	≥	≥	NOUN
ejpam-3331	115	2	0	0	NUM
ejpam-3331	115	3	(	(	PUNCT
ejpam-3331	115	4	1	1	NUM
ejpam-3331	115	5	)	)	PUNCT
ejpam-3331	115	6	for	for	ADP
ejpam-3331	115	7	all	all	DET
ejpam-3331	115	8	x	x	NOUN
ejpam-3331	115	9	,	,	PUNCT
ejpam-3331	115	10	y	y	PROPN
ejpam-3331	115	11	∈	∈	PROPN
ejpam-3331	116	1	x	x	NOUN
ejpam-3331	116	2	,	,	PUNCT
ejpam-3331	116	3	where	where	SCONJ
ejpam-3331	116	4	ζ	ζ	NOUN
ejpam-3331	116	5	is	be	AUX
ejpam-3331	116	6	a	a	DET
ejpam-3331	116	7	simulation	simulation	NOUN
ejpam-3331	116	8	function	function	NOUN
ejpam-3331	116	9	in	in	ADP
ejpam-3331	116	10	the	the	DET
ejpam-3331	116	11	sense	sense	NOUN
ejpam-3331	116	12	of	of	ADP
ejpam-3331	116	13	definition	definition	NOUN
ejpam-3331	116	14	3	3	NUM
ejpam-3331	116	15	.	.	PUNCT
ejpam-3331	117	1	now	now	ADV
ejpam-3331	117	2	,	,	PUNCT
ejpam-3331	117	3	we	we	PRON
ejpam-3331	117	4	introduce	introduce	VERB
ejpam-3331	117	5	our	our	PRON
ejpam-3331	117	6	main	main	ADJ
ejpam-3331	117	7	theorem	theorem	NOUN
ejpam-3331	117	8	.	.	PUNCT
ejpam-3331	118	1	h.	h.	PROPN
ejpam-3331	118	2	alsamir	alsamir	VERB
ejpam-3331	118	3	et	et	PROPN
ejpam-3331	118	4	al	al	PROPN
ejpam-3331	118	5	.	.	PUNCT
ejpam-3331	118	6	/	/	SYM
ejpam-3331	118	7	eur	eur	PROPN
ejpam-3331	118	8	.	.	PUNCT
ejpam-3331	119	1	j.	j.	PROPN
ejpam-3331	119	2	pure	pure	PROPN
ejpam-3331	119	3	appl	appl	PROPN
ejpam-3331	119	4	.	.	PROPN
ejpam-3331	119	5	math	math	PROPN
ejpam-3331	119	6	,	,	PUNCT
ejpam-3331	119	7	12	12	NUM
ejpam-3331	119	8	(	(	PUNCT
ejpam-3331	119	9	1	1	NUM
ejpam-3331	119	10	)	)	PUNCT
ejpam-3331	119	11	(	(	PUNCT
ejpam-3331	119	12	2019	2019	NUM
ejpam-3331	119	13	)	)	PUNCT
ejpam-3331	119	14	,	,	PUNCT
ejpam-3331	119	15	88	88	NUM
ejpam-3331	119	16	-	-	SYM
ejpam-3331	119	17	100	100	NUM
ejpam-3331	119	18	92	92	NUM
ejpam-3331	119	19	theorem	theorem	NOUN
ejpam-3331	119	20	2	2	NUM
ejpam-3331	119	21	.	.	X
ejpam-3331	120	1	let	let	AUX
ejpam-3331	120	2	(	(	PUNCT
ejpam-3331	120	3	x	x	NOUN
ejpam-3331	120	4	,	,	PUNCT
ejpam-3331	120	5	σ	σ	PROPN
ejpam-3331	120	6	)	)	PUNCT
ejpam-3331	120	7	be	be	AUX
ejpam-3331	120	8	a	a	DET
ejpam-3331	120	9	complete	complete	ADJ
ejpam-3331	120	10	metric	metric	ADJ
ejpam-3331	120	11	-	-	PUNCT
ejpam-3331	120	12	like	like	ADJ
ejpam-3331	120	13	space	space	NOUN
ejpam-3331	120	14	and	and	CCONJ
ejpam-3331	120	15	let	let	VERB
ejpam-3331	120	16	f	f	PRON
ejpam-3331	120	17	be	be	AUX
ejpam-3331	120	18	a	a	DET
ejpam-3331	120	19	self	self	NOUN
ejpam-3331	120	20	-	-	PUNCT
ejpam-3331	120	21	mapping	mapping	NOUN
ejpam-3331	120	22	on	on	ADP
ejpam-3331	120	23	x	x	PUNCT
ejpam-3331	120	24	satisfying	satisfy	VERB
ejpam-3331	120	25	the	the	DET
ejpam-3331	120	26	following	follow	VERB
ejpam-3331	120	27	conditions	condition	NOUN
ejpam-3331	120	28	:	:	PUNCT
ejpam-3331	120	29	(	(	PUNCT
ejpam-3331	120	30	i	i	NOUN
ejpam-3331	120	31	)	)	PUNCT
ejpam-3331	120	32	f	f	PROPN
ejpam-3331	120	33	is	be	AUX
ejpam-3331	120	34	(	(	PUNCT
ejpam-3331	120	35	α	α	NOUN
ejpam-3331	120	36	,	,	PUNCT
ejpam-3331	120	37	β)-admissible	β)-admissible	PUNCT
ejpam-3331	120	38	;	;	PUNCT
ejpam-3331	120	39	(	(	PUNCT
ejpam-3331	120	40	ii	ii	NOUN
ejpam-3331	120	41	)	)	PUNCT
ejpam-3331	120	42	there	there	PRON
ejpam-3331	120	43	exists	exist	VERB
ejpam-3331	120	44	x0	x0	PROPN
ejpam-3331	120	45	∈	∈	PROPN
ejpam-3331	120	46	x	x	PUNCT
ejpam-3331	120	47	such	such	ADJ
ejpam-3331	120	48	that	that	DET
ejpam-3331	120	49	α(x0	α(x0	ADJ
ejpam-3331	120	50	,	,	PUNCT
ejpam-3331	120	51	fx0	fx0	PROPN
ejpam-3331	120	52	)	)	PUNCT
ejpam-3331	120	53	≥	≥	NOUN
ejpam-3331	120	54	1	1	NUM
ejpam-3331	120	55	and	and	CCONJ
ejpam-3331	120	56	β(x0	β(x0	ADJ
ejpam-3331	120	57	,	,	PUNCT
ejpam-3331	120	58	fx0	fx0	PROPN
ejpam-3331	120	59	)	)	PUNCT
ejpam-3331	120	60	≥	≥	NOUN
ejpam-3331	120	61	1	1	NUM
ejpam-3331	120	62	;	;	PUNCT
ejpam-3331	120	63	(	(	PUNCT
ejpam-3331	120	64	iii	iii	X
ejpam-3331	120	65	)	)	PUNCT
ejpam-3331	120	66	f	f	PROPN
ejpam-3331	120	67	is	be	AUX
ejpam-3331	120	68	an	an	DET
ejpam-3331	120	69	(	(	PUNCT
ejpam-3331	120	70	α	α	NOUN
ejpam-3331	120	71	,	,	PUNCT
ejpam-3331	120	72	β)-admissible	β)-admissible	PUNCT
ejpam-3331	120	73	z	z	NOUN
ejpam-3331	120	74	-	-	PUNCT
ejpam-3331	120	75	contraction	contraction	NOUN
ejpam-3331	120	76	on	on	ADP
ejpam-3331	120	77	(	(	PUNCT
ejpam-3331	120	78	x	x	X
ejpam-3331	120	79	,	,	PUNCT
ejpam-3331	120	80	σ	σ	PROPN
ejpam-3331	120	81	)	)	PUNCT
ejpam-3331	120	82	;	;	PUNCT
ejpam-3331	120	83	(	(	PUNCT
ejpam-3331	120	84	iv	iv	X
ejpam-3331	120	85	)	)	PUNCT
ejpam-3331	120	86	f	f	PROPN
ejpam-3331	120	87	is	be	AUX
ejpam-3331	120	88	σ−continuous	σ−continuous	PROPN
ejpam-3331	120	89	.	.	PUNCT
ejpam-3331	121	1	then	then	ADV
ejpam-3331	121	2	f	f	PROPN
ejpam-3331	121	3	has	have	VERB
ejpam-3331	121	4	a	a	DET
ejpam-3331	121	5	unique	unique	ADJ
ejpam-3331	121	6	fixed	fix	VERB
ejpam-3331	121	7	point	point	NOUN
ejpam-3331	121	8	u	u	NOUN
ejpam-3331	121	9	∈	∈	PROPN
ejpam-3331	121	10	x	x	PUNCT
ejpam-3331	121	11	with	with	ADP
ejpam-3331	121	12	σ(u	σ(u	NOUN
ejpam-3331	121	13	,	,	PUNCT
ejpam-3331	121	14	u	u	NOUN
ejpam-3331	121	15	)	)	PUNCT
ejpam-3331	121	16	=	=	SYM
ejpam-3331	121	17	0	0	X
ejpam-3331	121	18	.	.	PUNCT
ejpam-3331	122	1	proof	proof	NOUN
ejpam-3331	122	2	.	.	PUNCT
ejpam-3331	123	1	by	by	ADP
ejpam-3331	123	2	(	(	PUNCT
ejpam-3331	123	3	2	2	NUM
ejpam-3331	123	4	)	)	PUNCT
ejpam-3331	123	5	,	,	PUNCT
ejpam-3331	123	6	there	there	PRON
ejpam-3331	123	7	exists	exist	VERB
ejpam-3331	123	8	x0	x0	PROPN
ejpam-3331	123	9	∈	∈	PROPN
ejpam-3331	123	10	x	x	PUNCT
ejpam-3331	123	11	such	such	ADJ
ejpam-3331	123	12	that	that	DET
ejpam-3331	123	13	α(x0	α(x0	ADJ
ejpam-3331	123	14	,	,	PUNCT
ejpam-3331	123	15	fx0	fx0	PROPN
ejpam-3331	123	16	)	)	PUNCT
ejpam-3331	123	17	≥	≥	NOUN
ejpam-3331	123	18	1	1	NUM
ejpam-3331	123	19	and	and	CCONJ
ejpam-3331	123	20	β(x0	β(x0	ADJ
ejpam-3331	123	21	,	,	PUNCT
ejpam-3331	123	22	fx0	fx0	PROPN
ejpam-3331	123	23	)	)	PUNCT
ejpam-3331	123	24	≥	≥	NOUN
ejpam-3331	124	1	1	1	NUM
ejpam-3331	124	2	.	.	PUNCT
ejpam-3331	124	3	define	define	VERB
ejpam-3331	124	4	the	the	DET
ejpam-3331	124	5	sequence	sequence	NOUN
ejpam-3331	124	6	{	{	PUNCT
ejpam-3331	124	7	xn	xn	VERB
ejpam-3331	124	8	}	}	PUNCT
ejpam-3331	124	9	by	by	ADP
ejpam-3331	124	10	xn+1	xn+1	PROPN
ejpam-3331	124	11	=	=	SYM
ejpam-3331	124	12	fxn	fxn	NOUN
ejpam-3331	124	13	for	for	ADP
ejpam-3331	124	14	all	all	DET
ejpam-3331	124	15	n	n	NOUN
ejpam-3331	124	16	=	=	SYM
ejpam-3331	124	17	0	0	NUM
ejpam-3331	124	18	,	,	PUNCT
ejpam-3331	124	19	1	1	NUM
ejpam-3331	124	20	,	,	PUNCT
ejpam-3331	124	21	2	2	NUM
ejpam-3331	124	22	,	,	PUNCT
ejpam-3331	124	23	·	·	PUNCT
ejpam-3331	124	24	·	·	PUNCT
ejpam-3331	124	25	·	·	PUNCT
ejpam-3331	124	26	.	.	PUNCT
ejpam-3331	125	1	if	if	SCONJ
ejpam-3331	125	2	xn	xn	PROPN
ejpam-3331	125	3	=	=	SYM
ejpam-3331	125	4	xn+1	xn+1	PROPN
ejpam-3331	125	5	for	for	ADP
ejpam-3331	125	6	some	some	DET
ejpam-3331	125	7	n	n	CCONJ
ejpam-3331	125	8	,	,	PUNCT
ejpam-3331	125	9	then	then	ADV
ejpam-3331	125	10	xn	xn	PUNCT
ejpam-3331	125	11	=	=	SYM
ejpam-3331	125	12	xn+1	xn+1	PROPN
ejpam-3331	125	13	=	=	SYM
ejpam-3331	125	14	fxn	fxn	NOUN
ejpam-3331	125	15	.	.	PUNCT
ejpam-3331	126	1	so	so	ADV
ejpam-3331	126	2	xn	xn	PROPN
ejpam-3331	126	3	is	be	AUX
ejpam-3331	126	4	a	a	DET
ejpam-3331	126	5	fixed	fix	VERB
ejpam-3331	126	6	point	point	NOUN
ejpam-3331	126	7	of	of	ADP
ejpam-3331	126	8	f	f	PROPN
ejpam-3331	126	9	,	,	PUNCT
ejpam-3331	126	10	and	and	CCONJ
ejpam-3331	126	11	the	the	DET
ejpam-3331	126	12	proof	proof	NOUN
ejpam-3331	126	13	is	be	AUX
ejpam-3331	126	14	completed	complete	VERB
ejpam-3331	126	15	.	.	PUNCT
ejpam-3331	127	1	from	from	ADP
ejpam-3331	127	2	now	now	ADV
ejpam-3331	127	3	on	on	ADV
ejpam-3331	127	4	,	,	PUNCT
ejpam-3331	127	5	assume	assume	VERB
ejpam-3331	127	6	that	that	SCONJ
ejpam-3331	127	7	xn	xn	PROPN
ejpam-3331	128	1	6=	6=	NUM
ejpam-3331	128	2	xn+1	xn+1	NUM
ejpam-3331	128	3	for	for	ADP
ejpam-3331	128	4	all	all	PRON
ejpam-3331	128	5	n	n	PRON
ejpam-3331	128	6	∈	∈	NOUN
ejpam-3331	128	7	n	n	NOUN
ejpam-3331	128	8	∪	∪	X
ejpam-3331	128	9	{	{	PUNCT
ejpam-3331	128	10	0	0	NUM
ejpam-3331	128	11	}	}	PUNCT
ejpam-3331	128	12	.	.	PUNCT
ejpam-3331	129	1	since	since	SCONJ
ejpam-3331	129	2	f	f	PROPN
ejpam-3331	129	3	is	be	AUX
ejpam-3331	129	4	an	an	DET
ejpam-3331	129	5	(	(	PUNCT
ejpam-3331	129	6	α	α	NOUN
ejpam-3331	129	7	,	,	PUNCT
ejpam-3331	129	8	β)-admissible	β)-admissible	PUNCT
ejpam-3331	129	9	mapping	mapping	NOUN
ejpam-3331	129	10	,	,	PUNCT
ejpam-3331	129	11	we	we	PRON
ejpam-3331	129	12	derive	derive	VERB
ejpam-3331	129	13	α(x0	α(x0	ADJ
ejpam-3331	129	14	,	,	PUNCT
ejpam-3331	129	15	fx0	fx0	NOUN
ejpam-3331	129	16	)	)	PUNCT
ejpam-3331	129	17	=	=	SYM
ejpam-3331	129	18	α(x0	α(x0	NOUN
ejpam-3331	129	19	,	,	PUNCT
ejpam-3331	129	20	x1	x1	PROPN
ejpam-3331	129	21	)	)	PUNCT
ejpam-3331	129	22	≥	≥	NOUN
ejpam-3331	129	23	1⇒	1⇒	NUM
ejpam-3331	129	24	α(fx0	α(fx0	ADV
ejpam-3331	129	25	,	,	PUNCT
ejpam-3331	129	26	fx1	fx1	NOUN
ejpam-3331	129	27	)	)	PUNCT
ejpam-3331	129	28	=	=	SYM
ejpam-3331	129	29	α(x1	α(x1	ADJ
ejpam-3331	129	30	,	,	PUNCT
ejpam-3331	129	31	x2	x2	PROPN
ejpam-3331	129	32	)	)	PUNCT
ejpam-3331	129	33	≥	≥	NOUN
ejpam-3331	129	34	1	1	NUM
ejpam-3331	129	35	.	.	PUNCT
ejpam-3331	129	36	continuing	continue	VERB
ejpam-3331	129	37	in	in	ADP
ejpam-3331	129	38	this	this	DET
ejpam-3331	129	39	process	process	NOUN
ejpam-3331	129	40	,	,	PUNCT
ejpam-3331	129	41	we	we	PRON
ejpam-3331	129	42	get	get	VERB
ejpam-3331	129	43	α(xn	α(xn	NOUN
ejpam-3331	129	44	,	,	PUNCT
ejpam-3331	129	45	xn+1	xn+1	NUM
ejpam-3331	129	46	)	)	PUNCT
ejpam-3331	129	47	≥	≥	NOUN
ejpam-3331	129	48	1	1	NUM
ejpam-3331	129	49	,	,	PUNCT
ejpam-3331	129	50	for	for	ADP
ejpam-3331	129	51	all	all	DET
ejpam-3331	129	52	n	n	PRON
ejpam-3331	129	53	≥	≥	NOUN
ejpam-3331	129	54	0	0	NUM
ejpam-3331	129	55	.	.	PUNCT
ejpam-3331	130	1	(	(	PUNCT
ejpam-3331	130	2	2	2	X
ejpam-3331	130	3	)	)	PUNCT
ejpam-3331	130	4	similarly	similarly	ADV
ejpam-3331	130	5	,	,	PUNCT
ejpam-3331	130	6	β(xn	β(xn	X
ejpam-3331	130	7	,	,	PUNCT
ejpam-3331	130	8	xn+1	xn+1	NUM
ejpam-3331	130	9	)	)	PUNCT
ejpam-3331	130	10	≥	≥	NOUN
ejpam-3331	130	11	1	1	NUM
ejpam-3331	130	12	,	,	PUNCT
ejpam-3331	130	13	for	for	ADP
ejpam-3331	130	14	all	all	DET
ejpam-3331	130	15	n	n	PRON
ejpam-3331	130	16	≥	≥	NOUN
ejpam-3331	130	17	0	0	NUM
ejpam-3331	130	18	.	.	PUNCT
ejpam-3331	131	1	(	(	PUNCT
ejpam-3331	131	2	3	3	X
ejpam-3331	131	3	)	)	PUNCT
ejpam-3331	131	4	from	from	ADP
ejpam-3331	131	5	(	(	PUNCT
ejpam-3331	131	6	1	1	NUM
ejpam-3331	131	7	)	)	PUNCT
ejpam-3331	131	8	,	,	PUNCT
ejpam-3331	131	9	(	(	PUNCT
ejpam-3331	131	10	2	2	X
ejpam-3331	131	11	)	)	PUNCT
ejpam-3331	131	12	and	and	CCONJ
ejpam-3331	131	13	(	(	PUNCT
ejpam-3331	131	14	3	3	NUM
ejpam-3331	131	15	)	)	PUNCT
ejpam-3331	131	16	,	,	PUNCT
ejpam-3331	131	17	we	we	PRON
ejpam-3331	131	18	have	have	VERB
ejpam-3331	131	19	0	0	NUM
ejpam-3331	131	20	≤	≤	NOUN
ejpam-3331	131	21	ζ(α(xn	ζ(α(xn	NOUN
ejpam-3331	131	22	,	,	PUNCT
ejpam-3331	131	23	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	131	24	,	,	PUNCT
ejpam-3331	131	25	xn−1)σ(fxn	xn−1)σ(fxn	PROPN
ejpam-3331	131	26	,	,	PUNCT
ejpam-3331	131	27	fxn−1	fxn−1	PROPN
ejpam-3331	131	28	)	)	PUNCT
ejpam-3331	131	29	,	,	PUNCT
ejpam-3331	131	30	σ(xn	σ(xn	NUM
ejpam-3331	131	31	,	,	PUNCT
ejpam-3331	131	32	xn−1	xn−1	PROPN
ejpam-3331	131	33	)	)	PUNCT
ejpam-3331	131	34	)	)	PUNCT
ejpam-3331	132	1	=	=	PUNCT
ejpam-3331	132	2	ζ(α(xn	ζ(α(xn	X
ejpam-3331	132	3	,	,	PUNCT
ejpam-3331	132	4	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	132	5	,	,	PUNCT
ejpam-3331	132	6	xn−1)σ(xn+1	xn−1)σ(xn+1	PROPN
ejpam-3331	132	7	,	,	PUNCT
ejpam-3331	132	8	xn	xn	PROPN
ejpam-3331	132	9	)	)	PUNCT
ejpam-3331	132	10	,	,	PUNCT
ejpam-3331	132	11	σ(xn	σ(xn	X
ejpam-3331	132	12	,	,	PUNCT
ejpam-3331	132	13	xn−1	xn−1	PROPN
ejpam-3331	132	14	)	)	PUNCT
ejpam-3331	132	15	)	)	PUNCT
ejpam-3331	132	16	<	<	X
ejpam-3331	132	17	σ(xn	σ(xn	PROPN
ejpam-3331	132	18	,	,	PUNCT
ejpam-3331	132	19	xn−1)−	xn−1)−	PROPN
ejpam-3331	132	20	α(xn	α(xn	PROPN
ejpam-3331	132	21	,	,	PUNCT
ejpam-3331	132	22	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	132	23	,	,	PUNCT
ejpam-3331	132	24	xn−1)σ(xn+1	xn−1)σ(xn+1	PROPN
ejpam-3331	132	25	,	,	PUNCT
ejpam-3331	132	26	xn	xn	PROPN
ejpam-3331	132	27	)	)	PUNCT
ejpam-3331	132	28	.	.	PUNCT
ejpam-3331	133	1	(	(	PUNCT
ejpam-3331	133	2	4	4	X
ejpam-3331	133	3	)	)	PUNCT
ejpam-3331	133	4	consequently	consequently	ADV
ejpam-3331	133	5	,	,	PUNCT
ejpam-3331	133	6	we	we	PRON
ejpam-3331	133	7	derive	derive	VERB
ejpam-3331	133	8	that	that	SCONJ
ejpam-3331	133	9	σ(xn+1	σ(xn+1	NOUN
ejpam-3331	133	10	,	,	PUNCT
ejpam-3331	133	11	xn	xn	NUM
ejpam-3331	133	12	)	)	PUNCT
ejpam-3331	133	13	≤	≤	NOUN
ejpam-3331	133	14	α(xn	α(xn	NUM
ejpam-3331	133	15	,	,	PUNCT
ejpam-3331	133	16	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	133	17	,	,	PUNCT
ejpam-3331	133	18	xn−1)σ(xn+1	xn−1)σ(xn+1	PROPN
ejpam-3331	133	19	,	,	PUNCT
ejpam-3331	133	20	xn	xn	PUNCT
ejpam-3331	133	21	)	)	PUNCT
ejpam-3331	133	22	<	<	X
ejpam-3331	133	23	σ(xn	σ(xn	PROPN
ejpam-3331	133	24	,	,	PUNCT
ejpam-3331	133	25	xn−1	xn−1	PROPN
ejpam-3331	133	26	)	)	PUNCT
ejpam-3331	133	27	for	for	ADP
ejpam-3331	133	28	all	all	DET
ejpam-3331	133	29	n	n	PRON
ejpam-3331	133	30	≥	≥	NOUN
ejpam-3331	133	31	0	0	NUM
ejpam-3331	133	32	.	.	PUNCT
ejpam-3331	134	1	(	(	PUNCT
ejpam-3331	134	2	5	5	X
ejpam-3331	134	3	)	)	PUNCT
ejpam-3331	134	4	the	the	DET
ejpam-3331	134	5	sequence	sequence	NOUN
ejpam-3331	134	6	{	{	PUNCT
ejpam-3331	134	7	σ(xn	σ(xn	NUM
ejpam-3331	134	8	,	,	PUNCT
ejpam-3331	134	9	xn−1	xn−1	PROPN
ejpam-3331	134	10	)	)	PUNCT
ejpam-3331	134	11	}	}	PUNCT
ejpam-3331	134	12	is	be	AUX
ejpam-3331	134	13	nondecreasing	nondecrease	VERB
ejpam-3331	134	14	,	,	PUNCT
ejpam-3331	134	15	so	so	SCONJ
ejpam-3331	134	16	there	there	PRON
ejpam-3331	134	17	exists	exist	VERB
ejpam-3331	134	18	r	r	NOUN
ejpam-3331	134	19	≥	≥	NOUN
ejpam-3331	134	20	0	0	NUM
ejpam-3331	134	21	such	such	ADJ
ejpam-3331	134	22	that	that	SCONJ
ejpam-3331	134	23	limn→∞	limn→∞	PROPN
ejpam-3331	134	24	σ(xn	σ(xn	NOUN
ejpam-3331	134	25	,	,	PUNCT
ejpam-3331	134	26	xn−1	xn−1	PROPN
ejpam-3331	134	27	)	)	PUNCT
ejpam-3331	134	28	=	=	PUNCT
ejpam-3331	135	1	r.	r.	NOUN
ejpam-3331	135	2	we	we	PRON
ejpam-3331	135	3	prove	prove	VERB
ejpam-3331	135	4	that	that	SCONJ
ejpam-3331	135	5	lim	lim	PROPN
ejpam-3331	135	6	n→∞	n→∞	NUM
ejpam-3331	135	7	σ(xn	σ(xn	NOUN
ejpam-3331	135	8	,	,	PUNCT
ejpam-3331	135	9	xn−1	xn−1	PROPN
ejpam-3331	135	10	)	)	PUNCT
ejpam-3331	136	1	=	=	SYM
ejpam-3331	136	2	0	0	X
ejpam-3331	136	3	.	.	PUNCT
ejpam-3331	137	1	(	(	PUNCT
ejpam-3331	137	2	6	6	X
ejpam-3331	137	3	)	)	PUNCT
ejpam-3331	137	4	suppose	suppose	VERB
ejpam-3331	137	5	that	that	SCONJ
ejpam-3331	137	6	r	r	NOUN
ejpam-3331	137	7	>	>	X
ejpam-3331	137	8	0	0	NUM
ejpam-3331	137	9	.	.	PUNCT
ejpam-3331	138	1	by	by	ADP
ejpam-3331	138	2	(	(	PUNCT
ejpam-3331	138	3	5	5	NUM
ejpam-3331	138	4	)	)	PUNCT
ejpam-3331	138	5	,	,	PUNCT
ejpam-3331	138	6	we	we	PRON
ejpam-3331	138	7	derive	derive	VERB
ejpam-3331	138	8	that	that	SCONJ
ejpam-3331	138	9	lim	lim	PROPN
ejpam-3331	138	10	n→∞	n→∞	X
ejpam-3331	138	11	α(xn	α(xn	PROPN
ejpam-3331	138	12	,	,	PUNCT
ejpam-3331	138	13	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	138	14	,	,	PUNCT
ejpam-3331	138	15	xn+1)σ(xn	xn+1)σ(xn	PROPN
ejpam-3331	138	16	,	,	PUNCT
ejpam-3331	138	17	xn−1	xn−1	PROPN
ejpam-3331	138	18	)	)	PUNCT
ejpam-3331	138	19	=	=	SYM
ejpam-3331	138	20	r.	r.	NOUN
ejpam-3331	138	21	(	(	PUNCT
ejpam-3331	138	22	7	7	X
ejpam-3331	138	23	)	)	PUNCT
ejpam-3331	138	24	letting	let	VERB
ejpam-3331	138	25	sn	sn	NOUN
ejpam-3331	138	26	=	=	SYM
ejpam-3331	138	27	α(xn	α(xn	PROPN
ejpam-3331	138	28	,	,	PUNCT
ejpam-3331	138	29	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	138	30	,	,	PUNCT
ejpam-3331	138	31	xn−1)σ(xn	xn−1)σ(xn	X
ejpam-3331	138	32	,	,	PUNCT
ejpam-3331	138	33	xn+1	xn+1	NUM
ejpam-3331	138	34	)	)	PUNCT
ejpam-3331	138	35	and	and	CCONJ
ejpam-3331	138	36	sn	sn	NOUN
ejpam-3331	138	37	=	=	SYM
ejpam-3331	138	38	σ(xn	σ(xn	NOUN
ejpam-3331	138	39	,	,	PUNCT
ejpam-3331	138	40	xn−1	xn−1	PROPN
ejpam-3331	138	41	)	)	PUNCT
ejpam-3331	138	42	and	and	CCONJ
ejpam-3331	138	43	taking	take	VERB
ejpam-3331	138	44	(	(	PUNCT
ejpam-3331	138	45	ζ3	ζ3	NOUN
ejpam-3331	138	46	)	)	PUNCT
ejpam-3331	138	47	into	into	ADP
ejpam-3331	138	48	account	account	NOUN
ejpam-3331	138	49	,	,	PUNCT
ejpam-3331	138	50	we	we	PRON
ejpam-3331	138	51	have	have	VERB
ejpam-3331	138	52	0	0	NUM
ejpam-3331	138	53	≤	≤	NOUN
ejpam-3331	138	54	lim	lim	PROPN
ejpam-3331	138	55	sup	sup	VERB
ejpam-3331	138	56	n→∞	n→∞	NUM
ejpam-3331	138	57	ζ(α(xn	ζ(α(xn	NOUN
ejpam-3331	138	58	,	,	PUNCT
ejpam-3331	138	59	xn−1)β(xn	xn−1)β(xn	NUM
ejpam-3331	138	60	,	,	PUNCT
ejpam-3331	138	61	xn+1)σ(xn	xn+1)σ(xn	PROPN
ejpam-3331	138	62	,	,	PUNCT
ejpam-3331	138	63	xn−1	xn−1	PROPN
ejpam-3331	138	64	)	)	PUNCT
ejpam-3331	138	65	)	)	PUNCT
ejpam-3331	139	1	<	<	X
ejpam-3331	139	2	0	0	NUM
ejpam-3331	139	3	,	,	PUNCT
ejpam-3331	139	4	(	(	PUNCT
ejpam-3331	139	5	8)	8)	NUM
ejpam-3331	139	6	h.	h.	PROPN
ejpam-3331	139	7	alsamir	alsamir	NOUN
ejpam-3331	139	8	et	et	PROPN
ejpam-3331	139	9	al	al	PROPN
ejpam-3331	139	10	.	.	PUNCT
ejpam-3331	139	11	/	/	SYM
ejpam-3331	139	12	eur	eur	PROPN
ejpam-3331	139	13	.	.	PUNCT
ejpam-3331	140	1	j.	j.	PROPN
ejpam-3331	140	2	pure	pure	PROPN
ejpam-3331	140	3	appl	appl	PROPN
ejpam-3331	140	4	.	.	PROPN
ejpam-3331	140	5	math	math	PROPN
ejpam-3331	140	6	,	,	PUNCT
ejpam-3331	140	7	12	12	NUM
ejpam-3331	140	8	(	(	PUNCT
ejpam-3331	140	9	1	1	NUM
ejpam-3331	140	10	)	)	PUNCT
ejpam-3331	140	11	(	(	PUNCT
ejpam-3331	140	12	2019	2019	NUM
ejpam-3331	140	13	)	)	PUNCT
ejpam-3331	140	14	,	,	PUNCT
ejpam-3331	140	15	88	88	NUM
ejpam-3331	140	16	-	-	SYM
ejpam-3331	140	17	100	100	NUM
ejpam-3331	140	18	93	93	NUM
ejpam-3331	140	19	which	which	PRON
ejpam-3331	140	20	is	be	AUX
ejpam-3331	140	21	a	a	DET
ejpam-3331	140	22	contradiction	contradiction	NOUN
ejpam-3331	140	23	.	.	PUNCT
ejpam-3331	141	1	thus	thus	ADV
ejpam-3331	141	2	,	,	PUNCT
ejpam-3331	141	3	r	r	NOUN
ejpam-3331	141	4	=	=	SYM
ejpam-3331	141	5	0	0	NUM
ejpam-3331	141	6	.	.	PUNCT
ejpam-3331	142	1	now	now	ADV
ejpam-3331	142	2	,	,	PUNCT
ejpam-3331	142	3	we	we	PRON
ejpam-3331	142	4	will	will	AUX
ejpam-3331	142	5	show	show	VERB
ejpam-3331	142	6	that	that	SCONJ
ejpam-3331	142	7	{	{	PUNCT
ejpam-3331	142	8	xn	xn	X
ejpam-3331	142	9	}	}	PUNCT
ejpam-3331	142	10	is	be	AUX
ejpam-3331	142	11	a	a	DET
ejpam-3331	142	12	cauchy	cauchy	ADJ
ejpam-3331	142	13	sequence	sequence	NOUN
ejpam-3331	142	14	.	.	PUNCT
ejpam-3331	143	1	suppose	suppose	VERB
ejpam-3331	143	2	on	on	ADP
ejpam-3331	143	3	the	the	DET
ejpam-3331	143	4	contrary	contrary	NOUN
ejpam-3331	143	5	that	that	SCONJ
ejpam-3331	143	6	{	{	PUNCT
ejpam-3331	143	7	xn	xn	X
ejpam-3331	143	8	}	}	PUNCT
ejpam-3331	143	9	is	be	AUX
ejpam-3331	143	10	not	not	PART
ejpam-3331	143	11	a	a	DET
ejpam-3331	143	12	cauchy	cauchy	ADJ
ejpam-3331	143	13	sequence	sequence	NOUN
ejpam-3331	143	14	.	.	PUNCT
ejpam-3331	144	1	then	then	ADV
ejpam-3331	144	2	,	,	PUNCT
ejpam-3331	144	3	there	there	PRON
ejpam-3331	144	4	exists	exist	VERB
ejpam-3331	144	5	ε	ε	PROPN
ejpam-3331	144	6	for	for	ADP
ejpam-3331	144	7	which	which	PRON
ejpam-3331	144	8	we	we	PRON
ejpam-3331	144	9	can	can	AUX
ejpam-3331	144	10	find	find	VERB
ejpam-3331	144	11	subsequences	subsequence	NOUN
ejpam-3331	144	12	{	{	PUNCT
ejpam-3331	144	13	xnl	xnl	NOUN
ejpam-3331	144	14	}	}	PUNCT
ejpam-3331	144	15	and	and	CCONJ
ejpam-3331	144	16	{	{	PUNCT
ejpam-3331	144	17	xml	xml	NOUN
ejpam-3331	144	18	}	}	PUNCT
ejpam-3331	144	19	of	of	ADP
ejpam-3331	144	20	{	{	PUNCT
ejpam-3331	144	21	xn	xn	NOUN
ejpam-3331	144	22	}	}	PUNCT
ejpam-3331	144	23	with	with	ADP
ejpam-3331	144	24	nl	nl	PROPN
ejpam-3331	144	25	>	>	X
ejpam-3331	144	26	ml	ml	X
ejpam-3331	144	27	>	>	X
ejpam-3331	144	28	l	l	NOUN
ejpam-3331	144	29	such	such	ADJ
ejpam-3331	144	30	that	that	PRON
ejpam-3331	144	31	for	for	ADP
ejpam-3331	144	32	every	every	DET
ejpam-3331	144	33	l	l	NOUN
ejpam-3331	144	34	,	,	PUNCT
ejpam-3331	144	35	σ(xnl	σ(xnl	NOUN
ejpam-3331	144	36	,	,	PUNCT
ejpam-3331	144	37	xml	xml	NOUN
ejpam-3331	144	38	)	)	PUNCT
ejpam-3331	144	39	≥	≥	X
ejpam-3331	144	40	ε	ε	PROPN
ejpam-3331	144	41	(	(	PUNCT
ejpam-3331	144	42	9	9	NUM
ejpam-3331	144	43	)	)	PUNCT
ejpam-3331	144	44	and	and	CCONJ
ejpam-3331	144	45	nl	nl	PROPN
ejpam-3331	144	46	is	be	AUX
ejpam-3331	144	47	the	the	DET
ejpam-3331	144	48	smallest	small	ADJ
ejpam-3331	144	49	number	number	NOUN
ejpam-3331	144	50	such	such	ADJ
ejpam-3331	144	51	that	that	SCONJ
ejpam-3331	144	52	(	(	PUNCT
ejpam-3331	144	53	9	9	X
ejpam-3331	144	54	)	)	PUNCT
ejpam-3331	144	55	holds	hold	NOUN
ejpam-3331	144	56	.	.	PUNCT
ejpam-3331	145	1	from	from	ADP
ejpam-3331	145	2	(	(	PUNCT
ejpam-3331	145	3	9	9	NUM
ejpam-3331	145	4	)	)	PUNCT
ejpam-3331	145	5	,	,	PUNCT
ejpam-3331	145	6	we	we	PRON
ejpam-3331	145	7	get	get	VERB
ejpam-3331	145	8	σ(xnl−1	σ(xnl−1	NOUN
ejpam-3331	145	9	,	,	PUNCT
ejpam-3331	145	10	xml	xml	NOUN
ejpam-3331	145	11	)	)	PUNCT
ejpam-3331	145	12	<	<	X
ejpam-3331	145	13	ε	ε	PROPN
ejpam-3331	145	14	.	.	PUNCT
ejpam-3331	146	1	(	(	PUNCT
ejpam-3331	146	2	10	10	NUM
ejpam-3331	146	3	)	)	PUNCT
ejpam-3331	146	4	using	use	VERB
ejpam-3331	146	5	the	the	DET
ejpam-3331	146	6	triangular	triangular	NOUN
ejpam-3331	146	7	inequality	inequality	NOUN
ejpam-3331	146	8	and	and	CCONJ
ejpam-3331	146	9	(	(	PUNCT
ejpam-3331	146	10	10	10	NUM
ejpam-3331	146	11	)	)	PUNCT
ejpam-3331	146	12	,	,	PUNCT
ejpam-3331	146	13	ε	ε	PROPN
ejpam-3331	146	14	≤	≤	PROPN
ejpam-3331	146	15	σ(xnl	σ(xnl	NOUN
ejpam-3331	146	16	,	,	PUNCT
ejpam-3331	146	17	xml	xml	NOUN
ejpam-3331	146	18	)	)	PUNCT
ejpam-3331	146	19	≤	≤	NUM
ejpam-3331	146	20	σ(xnl	σ(xnl	NOUN
ejpam-3331	146	21	,	,	PUNCT
ejpam-3331	146	22	xnl−1	xnl−1	PROPN
ejpam-3331	146	23	)	)	PUNCT
ejpam-3331	146	24	+	+	NUM
ejpam-3331	146	25	σ(xnl−1	σ(xnl−1	NOUN
ejpam-3331	146	26	,	,	PUNCT
ejpam-3331	146	27	xml	xml	NOUN
ejpam-3331	146	28	)	)	PUNCT
ejpam-3331	146	29	<	<	X
ejpam-3331	146	30	σ(xnl	σ(xnl	PROPN
ejpam-3331	146	31	,	,	PUNCT
ejpam-3331	146	32	xnl−1	xnl−1	PROPN
ejpam-3331	146	33	)	)	PUNCT
ejpam-3331	147	1	+	+	CCONJ
ejpam-3331	147	2	ε	ε	AUX
ejpam-3331	147	3	.	.	PUNCT
ejpam-3331	147	4	letting	let	VERB
ejpam-3331	147	5	n→∞	n→∞	PRON
ejpam-3331	147	6	in	in	ADP
ejpam-3331	147	7	the	the	DET
ejpam-3331	147	8	above	above	ADJ
ejpam-3331	147	9	inequality	inequality	NOUN
ejpam-3331	147	10	and	and	CCONJ
ejpam-3331	147	11	using	use	VERB
ejpam-3331	147	12	(	(	PUNCT
ejpam-3331	147	13	6	6	NUM
ejpam-3331	147	14	)	)	PUNCT
ejpam-3331	147	15	,	,	PUNCT
ejpam-3331	147	16	we	we	PRON
ejpam-3331	147	17	obtain	obtain	VERB
ejpam-3331	147	18	lim	lim	PROPN
ejpam-3331	147	19	n→∞	n→∞	NUM
ejpam-3331	147	20	σ(xnl	σ(xnl	PROPN
ejpam-3331	147	21	,	,	PUNCT
ejpam-3331	147	22	xml	xml	NOUN
ejpam-3331	147	23	)	)	PUNCT
ejpam-3331	148	1	=	=	SYM
ejpam-3331	148	2	ε	ε	AUX
ejpam-3331	148	3	.	.	PUNCT
ejpam-3331	148	4	(	(	PUNCT
ejpam-3331	148	5	11	11	NUM
ejpam-3331	148	6	)	)	PUNCT
ejpam-3331	148	7	also	also	ADV
ejpam-3331	148	8	,	,	PUNCT
ejpam-3331	148	9	from	from	ADP
ejpam-3331	148	10	the	the	DET
ejpam-3331	148	11	triangular	triangular	NOUN
ejpam-3331	148	12	inequality	inequality	NOUN
ejpam-3331	148	13	,	,	PUNCT
ejpam-3331	148	14	we	we	PRON
ejpam-3331	148	15	have	have	VERB
ejpam-3331	148	16	|	|	ADV
ejpam-3331	148	17	σ(xnl+1	σ(xnl+1	PROPN
ejpam-3331	148	18	,	,	PUNCT
ejpam-3331	148	19	xml	xml	NOUN
ejpam-3331	148	20	)	)	PUNCT
ejpam-3331	148	21	−	−	PROPN
ejpam-3331	148	22	σ(xnl	σ(xnl	NOUN
ejpam-3331	148	23	,	,	PUNCT
ejpam-3331	148	24	xml	xml	NOUN
ejpam-3331	148	25	)	)	PUNCT
ejpam-3331	148	26	|≤	|≤	PROPN
ejpam-3331	148	27	σ(xnl	σ(xnl	NOUN
ejpam-3331	148	28	,	,	PUNCT
ejpam-3331	148	29	xnl+1	xnl+1	PROPN
ejpam-3331	148	30	)	)	PUNCT
ejpam-3331	148	31	.	.	PUNCT
ejpam-3331	149	1	on	on	ADP
ejpam-3331	149	2	taking	take	VERB
ejpam-3331	149	3	limit	limit	NOUN
ejpam-3331	149	4	as	as	ADP
ejpam-3331	149	5	l→∞	l→∞	NUM
ejpam-3331	149	6	on	on	ADP
ejpam-3331	149	7	both	both	DET
ejpam-3331	149	8	sides	side	NOUN
ejpam-3331	149	9	of	of	ADP
ejpam-3331	149	10	above	above	ADP
ejpam-3331	149	11	inequality	inequality	NOUN
ejpam-3331	149	12	and	and	CCONJ
ejpam-3331	149	13	using	use	VERB
ejpam-3331	149	14	(	(	PUNCT
ejpam-3331	149	15	6	6	NUM
ejpam-3331	149	16	)	)	PUNCT
ejpam-3331	149	17	and	and	CCONJ
ejpam-3331	149	18	(	(	PUNCT
ejpam-3331	149	19	11	11	NUM
ejpam-3331	149	20	)	)	PUNCT
ejpam-3331	149	21	,	,	PUNCT
ejpam-3331	149	22	we	we	PRON
ejpam-3331	149	23	get	get	VERB
ejpam-3331	149	24	lim	lim	PROPN
ejpam-3331	149	25	l→∞	l→∞	NUM
ejpam-3331	149	26	σ(xnl+1	σ(xnl+1	PROPN
ejpam-3331	149	27	,	,	PUNCT
ejpam-3331	149	28	xml	xml	NOUN
ejpam-3331	149	29	)	)	PUNCT
ejpam-3331	150	1	=	=	SYM
ejpam-3331	150	2	ε	ε	PROPN
ejpam-3331	150	3	.	.	PUNCT
ejpam-3331	150	4	(	(	PUNCT
ejpam-3331	150	5	12	12	NUM
ejpam-3331	150	6	)	)	PUNCT
ejpam-3331	150	7	similarly	similarly	ADV
ejpam-3331	150	8	,	,	PUNCT
ejpam-3331	150	9	it	it	PRON
ejpam-3331	150	10	is	be	AUX
ejpam-3331	150	11	easy	easy	ADJ
ejpam-3331	150	12	to	to	PART
ejpam-3331	150	13	show	show	VERB
ejpam-3331	150	14	that	that	SCONJ
ejpam-3331	150	15	lim	lim	PROPN
ejpam-3331	150	16	l→∞	l→∞	NUM
ejpam-3331	150	17	σ(xnl+1	σ(xnl+1	PROPN
ejpam-3331	150	18	,	,	PUNCT
ejpam-3331	150	19	xml+1	xml+1	PROPN
ejpam-3331	150	20	)	)	PUNCT
ejpam-3331	150	21	=	=	PUNCT
ejpam-3331	150	22	ε	ε	PROPN
ejpam-3331	150	23	.	.	PUNCT
ejpam-3331	151	1	(	(	PUNCT
ejpam-3331	151	2	13	13	NUM
ejpam-3331	151	3	)	)	PUNCT
ejpam-3331	151	4	moreover	moreover	ADV
ejpam-3331	151	5	,	,	PUNCT
ejpam-3331	151	6	since	since	SCONJ
ejpam-3331	151	7	f	f	PROPN
ejpam-3331	151	8	is	be	AUX
ejpam-3331	151	9	an	an	DET
ejpam-3331	151	10	(	(	PUNCT
ejpam-3331	151	11	α	α	NOUN
ejpam-3331	151	12	,	,	PUNCT
ejpam-3331	151	13	β)-admissible	β)-admissible	PUNCT
ejpam-3331	151	14	mapping	mapping	NOUN
ejpam-3331	151	15	,	,	PUNCT
ejpam-3331	151	16	we	we	PRON
ejpam-3331	151	17	have	have	VERB
ejpam-3331	151	18	α(xnl	α(xnl	PUNCT
ejpam-3331	151	19	,	,	PUNCT
ejpam-3331	151	20	xml	xml	NOUN
ejpam-3331	151	21	)	)	PUNCT
ejpam-3331	151	22	≥	≥	NOUN
ejpam-3331	151	23	1	1	NUM
ejpam-3331	151	24	andβ(xnl	andβ(xnl	NOUN
ejpam-3331	151	25	,	,	PUNCT
ejpam-3331	151	26	xml	xml	PROPN
ejpam-3331	151	27	)	)	PUNCT
ejpam-3331	151	28	≥	≥	NOUN
ejpam-3331	152	1	1	1	NUM
ejpam-3331	152	2	.	.	PUNCT
ejpam-3331	153	1	(	(	PUNCT
ejpam-3331	153	2	14	14	NUM
ejpam-3331	153	3	)	)	PUNCT
ejpam-3331	153	4	by	by	ADP
ejpam-3331	153	5	the	the	DET
ejpam-3331	153	6	fact	fact	NOUN
ejpam-3331	153	7	f	f	NOUN
ejpam-3331	153	8	is	be	AUX
ejpam-3331	153	9	an	an	DET
ejpam-3331	153	10	(	(	PUNCT
ejpam-3331	153	11	α	α	NOUN
ejpam-3331	153	12	,	,	PUNCT
ejpam-3331	153	13	β)-admissible	β)-admissible	PUNCT
ejpam-3331	153	14	z	z	NOUN
ejpam-3331	153	15	-	-	PUNCT
ejpam-3331	153	16	contraction	contraction	NOUN
ejpam-3331	153	17	with	with	ADP
ejpam-3331	153	18	respect	respect	NOUN
ejpam-3331	153	19	to	to	ADP
ejpam-3331	153	20	ζ	ζ	NOUN
ejpam-3331	153	21	,	,	PUNCT
ejpam-3331	153	22	together	together	ADV
ejpam-3331	153	23	with	with	ADP
ejpam-3331	153	24	(	(	PUNCT
ejpam-3331	153	25	11	11	NUM
ejpam-3331	153	26	)	)	PUNCT
ejpam-3331	153	27	,	,	PUNCT
ejpam-3331	153	28	(	(	PUNCT
ejpam-3331	153	29	14	14	NUM
ejpam-3331	153	30	)	)	PUNCT
ejpam-3331	153	31	and	and	CCONJ
ejpam-3331	153	32	(	(	PUNCT
ejpam-3331	153	33	ζ3	ζ3	NOUN
ejpam-3331	153	34	)	)	PUNCT
ejpam-3331	153	35	,	,	PUNCT
ejpam-3331	153	36	we	we	PRON
ejpam-3331	153	37	get	get	VERB
ejpam-3331	153	38	0	0	NUM
ejpam-3331	153	39	≤	≤	NOUN
ejpam-3331	153	40	lim	lim	PROPN
ejpam-3331	153	41	sup	sup	PROPN
ejpam-3331	153	42	l→∞	l→∞	NUM
ejpam-3331	153	43	ζ(α(xnl	ζ(α(xnl	PRON
ejpam-3331	153	44	,	,	PUNCT
ejpam-3331	153	45	xml	xml	NOUN
ejpam-3331	153	46	)	)	PUNCT
ejpam-3331	153	47	β(xnl	β(xnl	PROPN
ejpam-3331	153	48	,	,	PUNCT
ejpam-3331	153	49	xml	xml	NOUN
ejpam-3331	153	50	)	)	PUNCT
ejpam-3331	153	51	σ(xnl+1	σ(xnl+1	PROPN
ejpam-3331	153	52	,	,	PUNCT
ejpam-3331	153	53	xml+1	xml+1	PROPN
ejpam-3331	153	54	)	)	PUNCT
ejpam-3331	153	55	,	,	PUNCT
ejpam-3331	153	56	σ(xnl	σ(xnl	NOUN
ejpam-3331	153	57	,	,	PUNCT
ejpam-3331	153	58	xml	xml	NOUN
ejpam-3331	153	59	)	)	PUNCT
ejpam-3331	153	60	)	)	PUNCT
ejpam-3331	154	1	<	<	X
ejpam-3331	154	2	0	0	NUM
ejpam-3331	154	3	,	,	PUNCT
ejpam-3331	154	4	which	which	PRON
ejpam-3331	154	5	is	be	AUX
ejpam-3331	154	6	a	a	DET
ejpam-3331	154	7	contradiction	contradiction	NOUN
ejpam-3331	154	8	.	.	PUNCT
ejpam-3331	155	1	hence	hence	ADV
ejpam-3331	155	2	{	{	PUNCT
ejpam-3331	155	3	xn	xn	X
ejpam-3331	155	4	}	}	PUNCT
ejpam-3331	155	5	is	be	AUX
ejpam-3331	155	6	a	a	DET
ejpam-3331	155	7	cauchy	cauchy	ADJ
ejpam-3331	155	8	sequence	sequence	NOUN
ejpam-3331	155	9	.	.	PUNCT
ejpam-3331	156	1	owing	owe	VERB
ejpam-3331	156	2	to	to	ADP
ejpam-3331	156	3	the	the	DET
ejpam-3331	156	4	fact	fact	NOUN
ejpam-3331	156	5	that	that	SCONJ
ejpam-3331	156	6	(	(	PUNCT
ejpam-3331	156	7	x	x	X
ejpam-3331	156	8	,	,	PUNCT
ejpam-3331	156	9	σ	σ	PROPN
ejpam-3331	156	10	)	)	PUNCT
ejpam-3331	156	11	is	be	AUX
ejpam-3331	156	12	a	a	DET
ejpam-3331	156	13	complete	complete	ADJ
ejpam-3331	156	14	metric	metric	ADJ
ejpam-3331	156	15	-	-	PUNCT
ejpam-3331	156	16	like	like	ADJ
ejpam-3331	156	17	space	space	NOUN
ejpam-3331	156	18	,	,	PUNCT
ejpam-3331	156	19	there	there	PRON
ejpam-3331	156	20	exists	exist	VERB
ejpam-3331	156	21	some	some	DET
ejpam-3331	156	22	u	u	NOUN
ejpam-3331	156	23	∈	∈	PROPN
ejpam-3331	156	24	x	x	PUNCT
ejpam-3331	157	1	such	such	ADJ
ejpam-3331	157	2	that	that	SCONJ
ejpam-3331	157	3	lim	lim	PROPN
ejpam-3331	157	4	n→∞	n→∞	NUM
ejpam-3331	157	5	σ(xn	σ(xn	NUM
ejpam-3331	157	6	,	,	PUNCT
ejpam-3331	157	7	u	u	NOUN
ejpam-3331	157	8	)	)	PUNCT
ejpam-3331	157	9	=	=	SYM
ejpam-3331	157	10	σ(u	σ(u	NOUN
ejpam-3331	157	11	,	,	PUNCT
ejpam-3331	157	12	u	u	NOUN
ejpam-3331	157	13	)	)	PUNCT
ejpam-3331	157	14	=	=	SYM
ejpam-3331	157	15	lim	lim	PROPN
ejpam-3331	157	16	n→∞	n→∞	NUM
ejpam-3331	157	17	σ(xn	σ(xn	NOUN
ejpam-3331	157	18	,	,	PUNCT
ejpam-3331	157	19	xm	xm	PROPN
ejpam-3331	157	20	)	)	PUNCT
ejpam-3331	158	1	=	=	SYM
ejpam-3331	158	2	0	0	NUM
ejpam-3331	158	3	,	,	PUNCT
ejpam-3331	158	4	(	(	PUNCT
ejpam-3331	158	5	15	15	X
ejpam-3331	158	6	)	)	PUNCT
ejpam-3331	158	7	h.	h.	NOUN
ejpam-3331	158	8	alsamir	alsamir	VERB
ejpam-3331	158	9	et	et	PROPN
ejpam-3331	158	10	al	al	PROPN
ejpam-3331	158	11	.	.	PUNCT
ejpam-3331	158	12	/	/	SYM
ejpam-3331	158	13	eur	eur	PROPN
ejpam-3331	158	14	.	.	PUNCT
ejpam-3331	159	1	j.	j.	PROPN
ejpam-3331	159	2	pure	pure	PROPN
ejpam-3331	159	3	appl	appl	PROPN
ejpam-3331	159	4	.	.	PROPN
ejpam-3331	159	5	math	math	PROPN
ejpam-3331	159	6	,	,	PUNCT
ejpam-3331	159	7	12	12	NUM
ejpam-3331	159	8	(	(	PUNCT
ejpam-3331	159	9	1	1	NUM
ejpam-3331	159	10	)	)	PUNCT
ejpam-3331	159	11	(	(	PUNCT
ejpam-3331	159	12	2019	2019	NUM
ejpam-3331	159	13	)	)	PUNCT
ejpam-3331	159	14	,	,	PUNCT
ejpam-3331	159	15	88	88	NUM
ejpam-3331	159	16	-	-	SYM
ejpam-3331	159	17	100	100	NUM
ejpam-3331	159	18	94	94	NUM
ejpam-3331	159	19	which	which	PRON
ejpam-3331	159	20	implies	imply	VERB
ejpam-3331	159	21	that	that	SCONJ
ejpam-3331	159	22	σ(u	σ(u	NOUN
ejpam-3331	159	23	,	,	PUNCT
ejpam-3331	159	24	u	u	NOUN
ejpam-3331	159	25	)	)	PUNCT
ejpam-3331	159	26	=	=	SYM
ejpam-3331	159	27	0	0	X
ejpam-3331	159	28	.	.	PUNCT
ejpam-3331	160	1	moreover	moreover	ADV
ejpam-3331	160	2	,	,	PUNCT
ejpam-3331	160	3	the	the	DET
ejpam-3331	160	4	continuity	continuity	NOUN
ejpam-3331	160	5	of	of	ADP
ejpam-3331	160	6	f	f	PROPN
ejpam-3331	160	7	implies	imply	VERB
ejpam-3331	160	8	that	that	SCONJ
ejpam-3331	160	9	lim	lim	PROPN
ejpam-3331	160	10	n→∞	n→∞	NUM
ejpam-3331	160	11	σ(xn+1	σ(xn+1	PROPN
ejpam-3331	160	12	,	,	PUNCT
ejpam-3331	160	13	fu	fu	NOUN
ejpam-3331	160	14	)	)	PUNCT
ejpam-3331	160	15	=	=	SYM
ejpam-3331	160	16	σ(fxn	σ(fxn	PROPN
ejpam-3331	160	17	,	,	PUNCT
ejpam-3331	160	18	fu	fu	NOUN
ejpam-3331	160	19	)	)	PUNCT
ejpam-3331	160	20	=	=	SYM
ejpam-3331	160	21	σ(fu	σ(fu	PROPN
ejpam-3331	160	22	,	,	PUNCT
ejpam-3331	160	23	fu	fu	NOUN
ejpam-3331	160	24	)	)	PUNCT
ejpam-3331	160	25	.	.	PUNCT
ejpam-3331	161	1	by	by	ADP
ejpam-3331	161	2	lemma	lemma	PROPN
ejpam-3331	161	3	1	1	NUM
ejpam-3331	161	4	and	and	CCONJ
ejpam-3331	161	5	(	(	PUNCT
ejpam-3331	161	6	15	15	NUM
ejpam-3331	161	7	)	)	PUNCT
ejpam-3331	161	8	,	,	PUNCT
ejpam-3331	161	9	we	we	PRON
ejpam-3331	161	10	obtain	obtain	VERB
ejpam-3331	161	11	lim	lim	PROPN
ejpam-3331	161	12	n→∞	n→∞	NUM
ejpam-3331	161	13	σ(xn+1	σ(xn+1	PROPN
ejpam-3331	161	14	,	,	PUNCT
ejpam-3331	161	15	fu	fu	NOUN
ejpam-3331	161	16	)	)	PUNCT
ejpam-3331	161	17	=	=	SYM
ejpam-3331	161	18	σ(u	σ(u	NOUN
ejpam-3331	161	19	,	,	PUNCT
ejpam-3331	161	20	fu	fu	NOUN
ejpam-3331	161	21	)	)	PUNCT
ejpam-3331	161	22	.	.	PUNCT
ejpam-3331	162	1	(	(	PUNCT
ejpam-3331	162	2	16	16	X
ejpam-3331	162	3	)	)	PUNCT
ejpam-3331	162	4	combining	combine	VERB
ejpam-3331	162	5	(	(	PUNCT
ejpam-3331	162	6	15	15	NUM
ejpam-3331	162	7	)	)	PUNCT
ejpam-3331	162	8	and	and	CCONJ
ejpam-3331	162	9	(	(	PUNCT
ejpam-3331	162	10	16	16	NUM
ejpam-3331	162	11	)	)	PUNCT
ejpam-3331	162	12	,	,	PUNCT
ejpam-3331	162	13	we	we	PRON
ejpam-3331	162	14	have	have	AUX
ejpam-3331	162	15	σ(fu	σ(fu	PROPN
ejpam-3331	162	16	,	,	PUNCT
ejpam-3331	162	17	fu	fu	NOUN
ejpam-3331	162	18	)	)	PUNCT
ejpam-3331	162	19	=	=	SYM
ejpam-3331	162	20	σ(u	σ(u	NOUN
ejpam-3331	162	21	,	,	PUNCT
ejpam-3331	162	22	fu	fu	NOUN
ejpam-3331	162	23	)	)	PUNCT
ejpam-3331	162	24	,	,	PUNCT
ejpam-3331	162	25	that	that	ADV
ejpam-3331	162	26	is	is	ADV
ejpam-3331	162	27	,	,	PUNCT
ejpam-3331	162	28	fu	fu	NOUN
ejpam-3331	162	29	=	=	SYM
ejpam-3331	162	30	u	u	PROPN
ejpam-3331	162	31	..	..	PUNCT
ejpam-3331	162	32	to	to	PART
ejpam-3331	162	33	prove	prove	VERB
ejpam-3331	162	34	the	the	DET
ejpam-3331	162	35	uniqueness	uniqueness	NOUN
ejpam-3331	162	36	of	of	ADP
ejpam-3331	162	37	the	the	DET
ejpam-3331	162	38	fixed	fix	VERB
ejpam-3331	162	39	point	point	NOUN
ejpam-3331	162	40	,	,	PUNCT
ejpam-3331	162	41	suppose	suppose	VERB
ejpam-3331	162	42	that	that	SCONJ
ejpam-3331	162	43	there	there	PRON
ejpam-3331	162	44	exists	exist	VERB
ejpam-3331	162	45	w	w	PROPN
ejpam-3331	162	46	∈	∈	PROPN
ejpam-3331	162	47	x	x	PUNCT
ejpam-3331	162	48	such	such	ADJ
ejpam-3331	162	49	that	that	SCONJ
ejpam-3331	162	50	fw	fw	PROPN
ejpam-3331	162	51	=	=	SYM
ejpam-3331	162	52	w	w	PROPN
ejpam-3331	162	53	and	and	CCONJ
ejpam-3331	162	54	w	w	PROPN
ejpam-3331	162	55	6=	6=	PROPN
ejpam-3331	162	56	u.	u.	NOUN
ejpam-3331	162	57	then	then	ADV
ejpam-3331	162	58	0	0	NUM
ejpam-3331	162	59	≤	≤	NUM
ejpam-3331	162	60	ζ(α(u	ζ(α(u	PROPN
ejpam-3331	162	61	,	,	PUNCT
ejpam-3331	162	62	w)β(u	w)β(u	PROPN
ejpam-3331	162	63	,	,	PUNCT
ejpam-3331	162	64	w)σ(fu	w)σ(fu	NOUN
ejpam-3331	162	65	,	,	PUNCT
ejpam-3331	162	66	fw	fw	ADJ
ejpam-3331	162	67	)	)	PUNCT
ejpam-3331	162	68	,	,	PUNCT
ejpam-3331	162	69	σ(u	σ(u	NOUN
ejpam-3331	162	70	,	,	PUNCT
ejpam-3331	162	71	w	w	NOUN
ejpam-3331	162	72	)	)	PUNCT
ejpam-3331	162	73	)	)	PUNCT
ejpam-3331	162	74	<	<	X
ejpam-3331	162	75	σ(u	σ(u	NOUN
ejpam-3331	162	76	,	,	PUNCT
ejpam-3331	162	77	w)−	w)−	PROPN
ejpam-3331	162	78	α(u	α(u	NOUN
ejpam-3331	162	79	,	,	PUNCT
ejpam-3331	162	80	w)β(u	w)β(u	PROPN
ejpam-3331	162	81	,	,	PUNCT
ejpam-3331	162	82	w)σ(fu	w)σ(fu	NOUN
ejpam-3331	162	83	,	,	PUNCT
ejpam-3331	162	84	fw	fw	ADJ
ejpam-3331	162	85	)	)	PUNCT
ejpam-3331	162	86	≤	≤	NOUN
ejpam-3331	162	87	0	0	NUM
ejpam-3331	162	88	,	,	PUNCT
ejpam-3331	162	89	which	which	PRON
ejpam-3331	162	90	is	be	AUX
ejpam-3331	162	91	a	a	DET
ejpam-3331	162	92	contradiction	contradiction	NOUN
ejpam-3331	162	93	,	,	PUNCT
ejpam-3331	162	94	so	so	CCONJ
ejpam-3331	162	95	u	u	NOUN
ejpam-3331	162	96	=	=	NOUN
ejpam-3331	162	97	w.	w.	PROPN
ejpam-3331	162	98	theorem	theorem	VERB
ejpam-3331	162	99	2	2	NUM
ejpam-3331	162	100	remains	remain	VERB
ejpam-3331	162	101	true	true	ADJ
ejpam-3331	162	102	if	if	SCONJ
ejpam-3331	162	103	we	we	PRON
ejpam-3331	162	104	drop	drop	VERB
ejpam-3331	162	105	the	the	DET
ejpam-3331	162	106	continuity	continuity	NOUN
ejpam-3331	162	107	hypothesis	hypothesis	NOUN
ejpam-3331	162	108	by	by	ADP
ejpam-3331	162	109	the	the	DET
ejpam-3331	162	110	following	follow	VERB
ejpam-3331	162	111	property	property	NOUN
ejpam-3331	162	112	:	:	PUNCT
ejpam-3331	162	113	(	(	PUNCT
ejpam-3331	162	114	h	h	NOUN
ejpam-3331	162	115	):	):	PUNCT
ejpam-3331	162	116	if	if	SCONJ
ejpam-3331	162	117	{	{	PUNCT
ejpam-3331	162	118	xn	xn	X
ejpam-3331	162	119	}	}	PUNCT
ejpam-3331	162	120	is	be	AUX
ejpam-3331	162	121	a	a	DET
ejpam-3331	162	122	sequence	sequence	NOUN
ejpam-3331	162	123	in	in	ADP
ejpam-3331	162	124	x	x	INTJ
ejpam-3331	162	125	such	such	ADJ
ejpam-3331	162	126	that	that	SCONJ
ejpam-3331	162	127	α(xn	α(xn	NOUN
ejpam-3331	162	128	,	,	PUNCT
ejpam-3331	162	129	xn+1	xn+1	NUM
ejpam-3331	162	130	)	)	PUNCT
ejpam-3331	162	131	≥	≥	NOUN
ejpam-3331	162	132	1	1	NUM
ejpam-3331	162	133	and	and	CCONJ
ejpam-3331	162	134	β(xn	β(xn	NOUN
ejpam-3331	162	135	,	,	PUNCT
ejpam-3331	162	136	xn+1	xn+1	NUM
ejpam-3331	162	137	)	)	PUNCT
ejpam-3331	162	138	≥	≥	NOUN
ejpam-3331	162	139	1	1	NUM
ejpam-3331	162	140	for	for	ADP
ejpam-3331	162	141	all	all	DET
ejpam-3331	162	142	n	n	CCONJ
ejpam-3331	162	143	,	,	PUNCT
ejpam-3331	162	144	then	then	ADV
ejpam-3331	162	145	there	there	PRON
ejpam-3331	162	146	exists	exist	VERB
ejpam-3331	162	147	a	a	DET
ejpam-3331	162	148	subsequence	subsequence	NOUN
ejpam-3331	162	149	{	{	PUNCT
ejpam-3331	162	150	xnl	xnl	NOUN
ejpam-3331	162	151	}	}	PUNCT
ejpam-3331	162	152	of	of	ADP
ejpam-3331	162	153	{	{	PUNCT
ejpam-3331	162	154	xn	xn	NOUN
ejpam-3331	162	155	}	}	PUNCT
ejpam-3331	162	156	such	such	ADJ
ejpam-3331	162	157	that	that	PRON
ejpam-3331	162	158	α(xnl	α(xnl	PROPN
ejpam-3331	162	159	,	,	PUNCT
ejpam-3331	162	160	xnl+1	xnl+1	PROPN
ejpam-3331	162	161	)	)	PUNCT
ejpam-3331	162	162	≥	≥	NOUN
ejpam-3331	162	163	1	1	NUM
ejpam-3331	162	164	and	and	CCONJ
ejpam-3331	162	165	β(xnl	β(xnl	PROPN
ejpam-3331	162	166	,	,	PUNCT
ejpam-3331	162	167	xnl+1	xnl+1	PROPN
ejpam-3331	162	168	)	)	PUNCT
ejpam-3331	162	169	≥	≥	NOUN
ejpam-3331	162	170	1	1	NUM
ejpam-3331	162	171	for	for	ADP
ejpam-3331	162	172	all	all	DET
ejpam-3331	162	173	l	l	NOUN
ejpam-3331	162	174	∈	∈	NOUN
ejpam-3331	162	175	n	n	NOUN
ejpam-3331	162	176	and	and	CCONJ
ejpam-3331	162	177	α(x	α(x	NOUN
ejpam-3331	162	178	,	,	PUNCT
ejpam-3331	162	179	fx	fx	PROPN
ejpam-3331	162	180	)	)	PUNCT
ejpam-3331	162	181	≥	≥	NOUN
ejpam-3331	162	182	1	1	NUM
ejpam-3331	162	183	and	and	CCONJ
ejpam-3331	162	184	β(x	β(x	PROPN
ejpam-3331	162	185	,	,	PUNCT
ejpam-3331	162	186	fx	fx	PROPN
ejpam-3331	162	187	)	)	PUNCT
ejpam-3331	162	188	≥	≥	NOUN
ejpam-3331	162	189	1	1	NUM
ejpam-3331	162	190	.	.	PUNCT
ejpam-3331	162	191	theorem	theorem	NOUN
ejpam-3331	162	192	3	3	X
ejpam-3331	162	193	.	.	PUNCT
ejpam-3331	163	1	let	let	AUX
ejpam-3331	163	2	(	(	PUNCT
ejpam-3331	163	3	x	x	NOUN
ejpam-3331	163	4	,	,	PUNCT
ejpam-3331	163	5	σ	σ	PROPN
ejpam-3331	163	6	)	)	PUNCT
ejpam-3331	163	7	be	be	AUX
ejpam-3331	163	8	a	a	DET
ejpam-3331	163	9	complete	complete	ADJ
ejpam-3331	163	10	metric	metric	ADJ
ejpam-3331	163	11	-	-	PUNCT
ejpam-3331	163	12	like	like	ADJ
ejpam-3331	163	13	space	space	NOUN
ejpam-3331	163	14	and	and	CCONJ
ejpam-3331	163	15	let	let	VERB
ejpam-3331	163	16	f	f	PRON
ejpam-3331	163	17	be	be	AUX
ejpam-3331	163	18	a	a	DET
ejpam-3331	163	19	self	self	NOUN
ejpam-3331	163	20	-	-	PUNCT
ejpam-3331	163	21	mapping	mapping	NOUN
ejpam-3331	163	22	on	on	ADP
ejpam-3331	163	23	x	x	PUNCT
ejpam-3331	163	24	satisfying	satisfy	VERB
ejpam-3331	163	25	the	the	DET
ejpam-3331	163	26	following	follow	VERB
ejpam-3331	163	27	conditions	condition	NOUN
ejpam-3331	163	28	:	:	PUNCT
ejpam-3331	163	29	(	(	PUNCT
ejpam-3331	163	30	i	i	NOUN
ejpam-3331	163	31	)	)	PUNCT
ejpam-3331	163	32	f	f	PROPN
ejpam-3331	163	33	is	be	AUX
ejpam-3331	163	34	(	(	PUNCT
ejpam-3331	163	35	α	α	NOUN
ejpam-3331	163	36	,	,	PUNCT
ejpam-3331	163	37	β)-admissible	β)-admissible	PUNCT
ejpam-3331	163	38	;	;	PUNCT
ejpam-3331	163	39	(	(	PUNCT
ejpam-3331	163	40	ii	ii	NOUN
ejpam-3331	163	41	)	)	PUNCT
ejpam-3331	163	42	there	there	PRON
ejpam-3331	163	43	exists	exist	VERB
ejpam-3331	163	44	x0	x0	PROPN
ejpam-3331	163	45	∈	∈	PROPN
ejpam-3331	163	46	x	x	PUNCT
ejpam-3331	163	47	such	such	ADJ
ejpam-3331	163	48	that	that	DET
ejpam-3331	163	49	α(x0	α(x0	ADJ
ejpam-3331	163	50	,	,	PUNCT
ejpam-3331	163	51	fx0	fx0	PROPN
ejpam-3331	163	52	)	)	PUNCT
ejpam-3331	163	53	≥	≥	NOUN
ejpam-3331	163	54	1	1	NUM
ejpam-3331	163	55	and	and	CCONJ
ejpam-3331	163	56	β(x0	β(x0	ADJ
ejpam-3331	163	57	,	,	PUNCT
ejpam-3331	163	58	fx0	fx0	PROPN
ejpam-3331	163	59	)	)	PUNCT
ejpam-3331	163	60	≥	≥	NOUN
ejpam-3331	163	61	1	1	NUM
ejpam-3331	163	62	;	;	PUNCT
ejpam-3331	163	63	(	(	PUNCT
ejpam-3331	163	64	iii	iii	X
ejpam-3331	163	65	)	)	PUNCT
ejpam-3331	163	66	f	f	PROPN
ejpam-3331	163	67	is	be	AUX
ejpam-3331	163	68	an	an	DET
ejpam-3331	163	69	(	(	PUNCT
ejpam-3331	163	70	α	α	NOUN
ejpam-3331	163	71	,	,	PUNCT
ejpam-3331	163	72	β)-admissible	β)-admissible	PUNCT
ejpam-3331	163	73	z	z	NOUN
ejpam-3331	163	74	-	-	PUNCT
ejpam-3331	163	75	contraction	contraction	NOUN
ejpam-3331	163	76	on	on	ADP
ejpam-3331	163	77	(	(	PUNCT
ejpam-3331	163	78	x	x	X
ejpam-3331	163	79	,	,	PUNCT
ejpam-3331	163	80	σ	σ	PROPN
ejpam-3331	163	81	)	)	PUNCT
ejpam-3331	163	82	;	;	PUNCT
ejpam-3331	163	83	(	(	PUNCT
ejpam-3331	163	84	iv	iv	X
ejpam-3331	163	85	)	)	PUNCT
ejpam-3331	163	86	(	(	PUNCT
ejpam-3331	163	87	h	h	NOUN
ejpam-3331	163	88	)	)	PUNCT
ejpam-3331	163	89	holds	hold	VERB
ejpam-3331	163	90	.	.	PUNCT
ejpam-3331	164	1	then	then	ADV
ejpam-3331	164	2	f	f	PROPN
ejpam-3331	164	3	has	have	VERB
ejpam-3331	164	4	a	a	DET
ejpam-3331	164	5	unique	unique	ADJ
ejpam-3331	164	6	fixed	fix	VERB
ejpam-3331	164	7	point	point	NOUN
ejpam-3331	164	8	u	u	NOUN
ejpam-3331	164	9	∈	∈	PROPN
ejpam-3331	164	10	x	x	PUNCT
ejpam-3331	164	11	with	with	ADP
ejpam-3331	164	12	σ(u	σ(u	NOUN
ejpam-3331	164	13	,	,	PUNCT
ejpam-3331	164	14	u	u	NOUN
ejpam-3331	164	15	)	)	PUNCT
ejpam-3331	164	16	=	=	SYM
ejpam-3331	164	17	0	0	X
ejpam-3331	164	18	.	.	PUNCT
ejpam-3331	165	1	proof	proof	NOUN
ejpam-3331	165	2	.	.	PUNCT
ejpam-3331	166	1	following	follow	VERB
ejpam-3331	166	2	the	the	DET
ejpam-3331	166	3	proof	proof	NOUN
ejpam-3331	166	4	of	of	ADP
ejpam-3331	166	5	theorem	theorem	NOUN
ejpam-3331	166	6	2	2	NUM
ejpam-3331	166	7	,	,	PUNCT
ejpam-3331	166	8	we	we	PRON
ejpam-3331	166	9	construct	construct	VERB
ejpam-3331	166	10	a	a	DET
ejpam-3331	166	11	sequence	sequence	NOUN
ejpam-3331	166	12	{	{	PUNCT
ejpam-3331	166	13	xn	xn	NOUN
ejpam-3331	166	14	}	}	PUNCT
ejpam-3331	166	15	in	in	ADP
ejpam-3331	166	16	x	x	PUNCT
ejpam-3331	166	17	defined	define	VERB
ejpam-3331	166	18	by	by	ADP
ejpam-3331	166	19	xn+1	xn+1	PROPN
ejpam-3331	166	20	=	=	SYM
ejpam-3331	166	21	fxn	fxn	NOUN
ejpam-3331	166	22	,	,	PUNCT
ejpam-3331	166	23	which	which	PRON
ejpam-3331	166	24	converges	converge	VERB
ejpam-3331	166	25	to	to	ADP
ejpam-3331	166	26	some	some	DET
ejpam-3331	166	27	u	u	NOUN
ejpam-3331	166	28	∈	∈	NOUN
ejpam-3331	166	29	x.	x.	NOUN
ejpam-3331	166	30	from	from	ADP
ejpam-3331	166	31	definition	definition	NOUN
ejpam-3331	166	32	(	(	PUNCT
ejpam-3331	166	33	2	2	NUM
ejpam-3331	166	34	)	)	PUNCT
ejpam-3331	166	35	and	and	CCONJ
ejpam-3331	166	36	(	(	PUNCT
ejpam-3331	166	37	h	h	NOUN
ejpam-3331	166	38	)	)	PUNCT
ejpam-3331	166	39	,	,	PUNCT
ejpam-3331	166	40	there	there	PRON
ejpam-3331	166	41	exists	exist	VERB
ejpam-3331	166	42	a	a	DET
ejpam-3331	166	43	subsequence	subsequence	NOUN
ejpam-3331	166	44	{	{	PUNCT
ejpam-3331	166	45	xnl	xnl	NOUN
ejpam-3331	166	46	}	}	PUNCT
ejpam-3331	166	47	of	of	ADP
ejpam-3331	166	48	{	{	PUNCT
ejpam-3331	166	49	xn	xn	NOUN
ejpam-3331	166	50	}	}	PUNCT
ejpam-3331	166	51	such	such	ADJ
ejpam-3331	166	52	that	that	DET
ejpam-3331	166	53	α(xnl	α(xnl	NOUN
ejpam-3331	166	54	,	,	PUNCT
ejpam-3331	166	55	xnl	xnl	PROPN
ejpam-3331	166	56	)	)	PUNCT
ejpam-3331	166	57	≥	≥	NOUN
ejpam-3331	166	58	1	1	NUM
ejpam-3331	166	59	and	and	CCONJ
ejpam-3331	166	60	β(xnl	β(xnl	INTJ
ejpam-3331	166	61	,	,	PUNCT
ejpam-3331	166	62	xnl	xnl	PROPN
ejpam-3331	166	63	)	)	PUNCT
ejpam-3331	167	1	≥	≥	NOUN
ejpam-3331	167	2	1	1	NUM
ejpam-3331	167	3	for	for	ADP
ejpam-3331	167	4	all	all	DET
ejpam-3331	167	5	l	l	NOUN
ejpam-3331	167	6	∈	∈	PROPN
ejpam-3331	167	7	n.	n.	NOUN
ejpam-3331	167	8	thus	thus	ADV
ejpam-3331	167	9	applying	apply	VERB
ejpam-3331	167	10	(	(	PUNCT
ejpam-3331	167	11	1	1	NUM
ejpam-3331	167	12	)	)	PUNCT
ejpam-3331	167	13	for	for	ADP
ejpam-3331	167	14	all	all	DET
ejpam-3331	167	15	l	l	NOUN
ejpam-3331	167	16	,	,	PUNCT
ejpam-3331	167	17	we	we	PRON
ejpam-3331	167	18	have	have	VERB
ejpam-3331	167	19	0	0	NUM
ejpam-3331	167	20	≤	≤	NUM
ejpam-3331	167	21	ζ(α(xnl	ζ(α(xnl	ADJ
ejpam-3331	167	22	,	,	PUNCT
ejpam-3331	167	23	u)β(xnl	u)β(xnl	NUM
ejpam-3331	167	24	,	,	PUNCT
ejpam-3331	167	25	u)σ(fxn	u)σ(fxn	PROPN
ejpam-3331	167	26	,	,	PUNCT
ejpam-3331	167	27	fu	fu	NOUN
ejpam-3331	167	28	)	)	PUNCT
ejpam-3331	167	29	,	,	PUNCT
ejpam-3331	167	30	σ(xnl	σ(xnl	NOUN
ejpam-3331	167	31	,	,	PUNCT
ejpam-3331	167	32	u	u	NOUN
ejpam-3331	167	33	)	)	PUNCT
ejpam-3331	167	34	)	)	PUNCT
ejpam-3331	168	1	=	=	PUNCT
ejpam-3331	169	1	ζ(α(xnl	ζ(α(xnl	NUM
ejpam-3331	169	2	,	,	PUNCT
ejpam-3331	169	3	u)β(xnl	u)β(xnl	PUNCT
ejpam-3331	169	4	,	,	PUNCT
ejpam-3331	169	5	u)σ(xn+1	u)σ(xn+1	ADJ
ejpam-3331	169	6	,	,	PUNCT
ejpam-3331	169	7	fu	fu	NOUN
ejpam-3331	169	8	)	)	PUNCT
ejpam-3331	169	9	,	,	PUNCT
ejpam-3331	169	10	σ(xnl	σ(xnl	NOUN
ejpam-3331	169	11	,	,	PUNCT
ejpam-3331	169	12	u	u	NOUN
ejpam-3331	169	13	)	)	PUNCT
ejpam-3331	169	14	)	)	PUNCT
ejpam-3331	169	15	<	<	X
ejpam-3331	169	16	σ(xnl	σ(xnl	NOUN
ejpam-3331	169	17	,	,	PUNCT
ejpam-3331	169	18	u)−	u)−	PROPN
ejpam-3331	169	19	α(xnl	α(xnl	PROPN
ejpam-3331	169	20	,	,	PUNCT
ejpam-3331	169	21	u)β(xnl	u)β(xnl	NUM
ejpam-3331	169	22	,	,	PUNCT
ejpam-3331	169	23	u)σ(xnl+1	u)σ(xnl+1	X
ejpam-3331	169	24	,	,	PUNCT
ejpam-3331	169	25	fu	fu	NOUN
ejpam-3331	169	26	)	)	PUNCT
ejpam-3331	169	27	(	(	PUNCT
ejpam-3331	169	28	17	17	NUM
ejpam-3331	169	29	)	)	PUNCT
ejpam-3331	169	30	which	which	PRON
ejpam-3331	169	31	is	be	AUX
ejpam-3331	169	32	equivalent	equivalent	ADJ
ejpam-3331	169	33	to	to	ADP
ejpam-3331	169	34	σ(xnl	σ(xnl	NOUN
ejpam-3331	169	35	+	+	CCONJ
ejpam-3331	169	36	1	1	NUM
ejpam-3331	169	37	,	,	PUNCT
ejpam-3331	169	38	fu	fu	NOUN
ejpam-3331	169	39	)	)	PUNCT
ejpam-3331	169	40	=	=	SYM
ejpam-3331	169	41	σ(fxnl	σ(fxnl	NOUN
ejpam-3331	169	42	,	,	PUNCT
ejpam-3331	169	43	fu	fu	NOUN
ejpam-3331	169	44	)	)	PUNCT
ejpam-3331	169	45	≤	≤	NUM
ejpam-3331	169	46	α(xnl	α(xnl	PUNCT
ejpam-3331	169	47	,	,	PUNCT
ejpam-3331	169	48	u)β(xnl	u)β(xnl	NUM
ejpam-3331	169	49	,	,	PUNCT
ejpam-3331	169	50	u)σ(fxn	u)σ(fxn	PROPN
ejpam-3331	169	51	,	,	PUNCT
ejpam-3331	169	52	fu	fu	NOUN
ejpam-3331	169	53	)	)	PUNCT
ejpam-3331	169	54	≤	≤	NUM
ejpam-3331	169	55	σ(xnl	σ(xnl	NOUN
ejpam-3331	169	56	,	,	PUNCT
ejpam-3331	169	57	u	u	NOUN
ejpam-3331	169	58	)	)	PUNCT
ejpam-3331	169	59	.	.	PUNCT
ejpam-3331	170	1	(	(	PUNCT
ejpam-3331	170	2	18	18	NUM
ejpam-3331	170	3	)	)	PUNCT
ejpam-3331	170	4	letting	let	VERB
ejpam-3331	170	5	l	l	NOUN
ejpam-3331	170	6	→	→	SYM
ejpam-3331	170	7	∞	∞	NUM
ejpam-3331	170	8	in	in	ADP
ejpam-3331	170	9	the	the	DET
ejpam-3331	170	10	above	above	ADJ
ejpam-3331	170	11	equality	equality	NOUN
ejpam-3331	170	12	,	,	PUNCT
ejpam-3331	170	13	we	we	PRON
ejpam-3331	170	14	have	have	VERB
ejpam-3331	170	15	σ(u	σ(u	NOUN
ejpam-3331	170	16	,	,	PUNCT
ejpam-3331	170	17	fu	fu	NOUN
ejpam-3331	170	18	)	)	PUNCT
ejpam-3331	170	19	=	=	SYM
ejpam-3331	171	1	0	0	X
ejpam-3331	171	2	.	.	PUNCT
ejpam-3331	171	3	using	use	VERB
ejpam-3331	171	4	similar	similar	ADJ
ejpam-3331	171	5	arguments	argument	NOUN
ejpam-3331	171	6	as	as	ADP
ejpam-3331	171	7	above	above	ADV
ejpam-3331	171	8	,	,	PUNCT
ejpam-3331	171	9	we	we	PRON
ejpam-3331	171	10	can	can	AUX
ejpam-3331	171	11	show	show	VERB
ejpam-3331	171	12	that	that	SCONJ
ejpam-3331	171	13	u	u	NOUN
ejpam-3331	171	14	is	be	AUX
ejpam-3331	171	15	a	a	DET
ejpam-3331	171	16	fixed	fix	VERB
ejpam-3331	171	17	point	point	NOUN
ejpam-3331	171	18	of	of	ADP
ejpam-3331	171	19	f.	f.	PROPN
ejpam-3331	171	20	the	the	DET
ejpam-3331	171	21	uniqueness	uniqueness	NOUN
ejpam-3331	171	22	of	of	ADP
ejpam-3331	171	23	the	the	DET
ejpam-3331	171	24	fixed	fix	VERB
ejpam-3331	171	25	point	point	NOUN
ejpam-3331	171	26	of	of	ADP
ejpam-3331	171	27	f	f	PROPN
ejpam-3331	171	28	is	be	AUX
ejpam-3331	171	29	obtained	obtain	VERB
ejpam-3331	171	30	by	by	ADP
ejpam-3331	171	31	similar	similar	ADJ
ejpam-3331	171	32	arguments	argument	NOUN
ejpam-3331	171	33	as	as	ADP
ejpam-3331	171	34	those	those	PRON
ejpam-3331	171	35	given	give	VERB
ejpam-3331	171	36	in	in	ADP
ejpam-3331	171	37	the	the	DET
ejpam-3331	171	38	proof	proof	NOUN
ejpam-3331	171	39	of	of	ADP
ejpam-3331	171	40	theorem	theorem	ADJ
ejpam-3331	171	41	2	2	NUM
ejpam-3331	171	42	.	.	PUNCT
ejpam-3331	171	43	h.	h.	PROPN
ejpam-3331	171	44	alsamir	alsamir	VERB
ejpam-3331	172	1	et	et	PROPN
ejpam-3331	172	2	al	al	PROPN
ejpam-3331	172	3	.	.	PUNCT
ejpam-3331	172	4	/	/	SYM
ejpam-3331	172	5	eur	eur	PROPN
ejpam-3331	172	6	.	.	PUNCT
ejpam-3331	173	1	j.	j.	PROPN
ejpam-3331	173	2	pure	pure	PROPN
ejpam-3331	173	3	appl	appl	PROPN
ejpam-3331	173	4	.	.	PROPN
ejpam-3331	173	5	math	math	PROPN
ejpam-3331	173	6	,	,	PUNCT
ejpam-3331	173	7	12	12	NUM
ejpam-3331	173	8	(	(	PUNCT
ejpam-3331	173	9	1	1	NUM
ejpam-3331	173	10	)	)	PUNCT
ejpam-3331	173	11	(	(	PUNCT
ejpam-3331	173	12	2019	2019	NUM
ejpam-3331	173	13	)	)	PUNCT
ejpam-3331	173	14	,	,	PUNCT
ejpam-3331	173	15	88	88	NUM
ejpam-3331	173	16	-	-	SYM
ejpam-3331	173	17	100	100	NUM
ejpam-3331	173	18	95	95	NUM
ejpam-3331	173	19	3	3	NUM
ejpam-3331	173	20	.	.	PUNCT
ejpam-3331	173	21	consequences	consequence	NOUN
ejpam-3331	173	22	in	in	ADP
ejpam-3331	173	23	this	this	DET
ejpam-3331	173	24	section	section	NOUN
ejpam-3331	174	1	,	,	PUNCT
ejpam-3331	174	2	we	we	PRON
ejpam-3331	174	3	apply	apply	VERB
ejpam-3331	174	4	theorem	theorem	VERB
ejpam-3331	174	5	2	2	NUM
ejpam-3331	174	6	to	to	PART
ejpam-3331	174	7	obtain	obtain	VERB
ejpam-3331	174	8	different	different	ADJ
ejpam-3331	174	9	results	result	NOUN
ejpam-3331	174	10	known	know	VERB
ejpam-3331	174	11	in	in	ADP
ejpam-3331	174	12	literature	literature	NOUN
ejpam-3331	174	13	.	.	PUNCT
ejpam-3331	175	1	the	the	DET
ejpam-3331	175	2	first	first	ADJ
ejpam-3331	175	3	one	one	NUM
ejpam-3331	175	4	is	be	AUX
ejpam-3331	175	5	of	of	ADP
ejpam-3331	175	6	banach	banach	ADJ
ejpam-3331	175	7	type	type	NOUN
ejpam-3331	175	8	.	.	PUNCT
ejpam-3331	176	1	corollary	corollary	ADJ
ejpam-3331	176	2	1	1	NUM
ejpam-3331	176	3	.	.	PUNCT
ejpam-3331	177	1	let	let	AUX
ejpam-3331	177	2	(	(	PUNCT
ejpam-3331	177	3	x	x	NOUN
ejpam-3331	177	4	,	,	PUNCT
ejpam-3331	177	5	σ	σ	PROPN
ejpam-3331	177	6	)	)	PUNCT
ejpam-3331	177	7	be	be	AUX
ejpam-3331	177	8	a	a	DET
ejpam-3331	177	9	complete	complete	ADJ
ejpam-3331	177	10	metric	metric	ADJ
ejpam-3331	177	11	-	-	PUNCT
ejpam-3331	177	12	like	like	ADJ
ejpam-3331	177	13	space	space	NOUN
ejpam-3331	177	14	and	and	CCONJ
ejpam-3331	177	15	let	let	VERB
ejpam-3331	177	16	f	f	PRON
ejpam-3331	177	17	be	be	AUX
ejpam-3331	177	18	a	a	DET
ejpam-3331	177	19	self	self	NOUN
ejpam-3331	177	20	-	-	PUNCT
ejpam-3331	177	21	mapping	mapping	NOUN
ejpam-3331	177	22	on	on	ADP
ejpam-3331	177	23	x	x	PUNCT
ejpam-3331	177	24	satisfying	satisfy	VERB
ejpam-3331	177	25	the	the	DET
ejpam-3331	177	26	following	follow	VERB
ejpam-3331	177	27	conditions	condition	NOUN
ejpam-3331	177	28	:	:	PUNCT
ejpam-3331	177	29	(	(	PUNCT
ejpam-3331	177	30	i	i	NOUN
ejpam-3331	177	31	)	)	PUNCT
ejpam-3331	177	32	f	f	PROPN
ejpam-3331	177	33	is	be	AUX
ejpam-3331	177	34	(	(	PUNCT
ejpam-3331	177	35	α	α	NOUN
ejpam-3331	177	36	,	,	PUNCT
ejpam-3331	177	37	β)-admissible	β)-admissible	PUNCT
ejpam-3331	177	38	;	;	PUNCT
ejpam-3331	177	39	(	(	PUNCT
ejpam-3331	177	40	ii	ii	NOUN
ejpam-3331	177	41	)	)	PUNCT
ejpam-3331	177	42	there	there	PRON
ejpam-3331	177	43	exists	exist	VERB
ejpam-3331	177	44	x0	x0	PROPN
ejpam-3331	177	45	∈	∈	PROPN
ejpam-3331	177	46	x	x	PUNCT
ejpam-3331	177	47	such	such	ADJ
ejpam-3331	177	48	that	that	DET
ejpam-3331	177	49	α(x0	α(x0	ADJ
ejpam-3331	177	50	,	,	PUNCT
ejpam-3331	177	51	fx0	fx0	PROPN
ejpam-3331	177	52	)	)	PUNCT
ejpam-3331	177	53	≥	≥	NOUN
ejpam-3331	177	54	1	1	NUM
ejpam-3331	177	55	and	and	CCONJ
ejpam-3331	177	56	β(x0	β(x0	ADJ
ejpam-3331	177	57	,	,	PUNCT
ejpam-3331	177	58	fx0	fx0	PROPN
ejpam-3331	177	59	)	)	PUNCT
ejpam-3331	177	60	≥	≥	NOUN
ejpam-3331	177	61	1	1	NUM
ejpam-3331	177	62	;	;	PUNCT
ejpam-3331	177	63	(	(	PUNCT
ejpam-3331	177	64	iii	iii	X
ejpam-3331	177	65	)	)	PUNCT
ejpam-3331	177	66	α(x	α(x	PROPN
ejpam-3331	177	67	,	,	PUNCT
ejpam-3331	177	68	y)β(x	y)β(x	NOUN
ejpam-3331	177	69	,	,	PUNCT
ejpam-3331	177	70	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	177	71	,	,	PUNCT
ejpam-3331	177	72	fy	fy	PROPN
ejpam-3331	177	73	)	)	PUNCT
ejpam-3331	177	74	≤	≤	NOUN
ejpam-3331	177	75	λσ(x	λσ(x	ADP
ejpam-3331	177	76	,	,	PUNCT
ejpam-3331	177	77	y	y	NOUN
ejpam-3331	177	78	)	)	PUNCT
ejpam-3331	177	79	,	,	PUNCT
ejpam-3331	177	80	for	for	ADP
ejpam-3331	177	81	all	all	DET
ejpam-3331	177	82	x	x	NOUN
ejpam-3331	177	83	,	,	PUNCT
ejpam-3331	177	84	y	y	PROPN
ejpam-3331	177	85	∈	∈	PROPN
ejpam-3331	177	86	x	x	X
ejpam-3331	177	87	and	and	CCONJ
ejpam-3331	177	88	λ	λ	X
ejpam-3331	177	89	∈	∈	PROPN
ejpam-3331	178	1	[	[	X
ejpam-3331	178	2	0	0	NUM
ejpam-3331	178	3	,	,	PUNCT
ejpam-3331	178	4	1	1	NUM
ejpam-3331	178	5	)	)	PUNCT
ejpam-3331	178	6	;	;	PUNCT
ejpam-3331	178	7	(	(	PUNCT
ejpam-3331	178	8	iv	iv	X
ejpam-3331	178	9	)	)	PUNCT
ejpam-3331	178	10	f	f	PROPN
ejpam-3331	178	11	is	be	AUX
ejpam-3331	178	12	σ	σ	NOUN
ejpam-3331	178	13	-	-	ADJ
ejpam-3331	178	14	continuous	continuous	ADJ
ejpam-3331	178	15	.	.	PUNCT
ejpam-3331	179	1	then	then	ADV
ejpam-3331	179	2	f	f	PROPN
ejpam-3331	179	3	has	have	VERB
ejpam-3331	179	4	a	a	DET
ejpam-3331	179	5	unique	unique	ADJ
ejpam-3331	179	6	fixed	fix	VERB
ejpam-3331	179	7	point	point	NOUN
ejpam-3331	179	8	u	u	NOUN
ejpam-3331	179	9	∈	∈	PROPN
ejpam-3331	179	10	x	x	PUNCT
ejpam-3331	179	11	with	with	ADP
ejpam-3331	179	12	σ(u	σ(u	NOUN
ejpam-3331	179	13	,	,	PUNCT
ejpam-3331	179	14	u	u	NOUN
ejpam-3331	179	15	)	)	PUNCT
ejpam-3331	179	16	=	=	SYM
ejpam-3331	179	17	0	0	X
ejpam-3331	179	18	.	.	PUNCT
ejpam-3331	180	1	proof	proof	NOUN
ejpam-3331	180	2	.	.	PUNCT
ejpam-3331	181	1	following	follow	VERB
ejpam-3331	181	2	the	the	DET
ejpam-3331	181	3	lines	line	NOUN
ejpam-3331	181	4	of	of	ADP
ejpam-3331	181	5	theorem	theorem	NOUN
ejpam-3331	181	6	2	2	NUM
ejpam-3331	181	7	,	,	PUNCT
ejpam-3331	181	8	by	by	ADP
ejpam-3331	181	9	taking	take	VERB
ejpam-3331	181	10	as	as	ADP
ejpam-3331	181	11	a	a	DET
ejpam-3331	181	12	σ	σ	PROPN
ejpam-3331	181	13	-	-	PUNCT
ejpam-3331	181	14	simulation	simulation	NOUN
ejpam-3331	181	15	function	function	NOUN
ejpam-3331	181	16	,	,	PUNCT
ejpam-3331	181	17	ζ(t	ζ(t	PROPN
ejpam-3331	181	18	,	,	PUNCT
ejpam-3331	181	19	s	s	NOUN
ejpam-3331	181	20	)	)	PUNCT
ejpam-3331	181	21	=	=	SYM
ejpam-3331	181	22	λs−	λs−	PUNCT
ejpam-3331	181	23	t.	t.	NOUN
ejpam-3331	181	24	corollary	corollary	NOUN
ejpam-3331	181	25	2	2	NUM
ejpam-3331	181	26	.	.	PUNCT
ejpam-3331	182	1	let	let	AUX
ejpam-3331	182	2	(	(	PUNCT
ejpam-3331	182	3	x	x	NOUN
ejpam-3331	182	4	,	,	PUNCT
ejpam-3331	182	5	σ	σ	PROPN
ejpam-3331	182	6	)	)	PUNCT
ejpam-3331	182	7	be	be	AUX
ejpam-3331	182	8	a	a	DET
ejpam-3331	182	9	complete	complete	ADJ
ejpam-3331	182	10	metric	metric	ADJ
ejpam-3331	182	11	-	-	PUNCT
ejpam-3331	182	12	like	like	ADJ
ejpam-3331	182	13	space	space	NOUN
ejpam-3331	182	14	and	and	CCONJ
ejpam-3331	182	15	let	let	VERB
ejpam-3331	182	16	f	f	PRON
ejpam-3331	182	17	be	be	AUX
ejpam-3331	182	18	a	a	DET
ejpam-3331	182	19	self	self	NOUN
ejpam-3331	182	20	-	-	PUNCT
ejpam-3331	182	21	mapping	mapping	NOUN
ejpam-3331	182	22	on	on	ADP
ejpam-3331	182	23	x	x	PUNCT
ejpam-3331	182	24	satisfying	satisfy	VERB
ejpam-3331	182	25	the	the	DET
ejpam-3331	182	26	following	follow	VERB
ejpam-3331	182	27	conditions	condition	NOUN
ejpam-3331	182	28	:	:	PUNCT
ejpam-3331	182	29	(	(	PUNCT
ejpam-3331	182	30	i	i	NOUN
ejpam-3331	182	31	)	)	PUNCT
ejpam-3331	182	32	f	f	PROPN
ejpam-3331	182	33	is	be	AUX
ejpam-3331	182	34	(	(	PUNCT
ejpam-3331	182	35	α	α	NOUN
ejpam-3331	182	36	,	,	PUNCT
ejpam-3331	182	37	β)-admissible	β)-admissible	PUNCT
ejpam-3331	182	38	;	;	PUNCT
ejpam-3331	182	39	(	(	PUNCT
ejpam-3331	182	40	ii	ii	NOUN
ejpam-3331	182	41	)	)	PUNCT
ejpam-3331	182	42	there	there	PRON
ejpam-3331	182	43	exists	exist	VERB
ejpam-3331	182	44	x0	x0	PROPN
ejpam-3331	182	45	∈	∈	PROPN
ejpam-3331	182	46	x	x	PUNCT
ejpam-3331	182	47	such	such	ADJ
ejpam-3331	182	48	that	that	DET
ejpam-3331	182	49	α(x0	α(x0	ADJ
ejpam-3331	182	50	,	,	PUNCT
ejpam-3331	182	51	fx0	fx0	PROPN
ejpam-3331	182	52	)	)	PUNCT
ejpam-3331	182	53	≥	≥	NOUN
ejpam-3331	182	54	1	1	NUM
ejpam-3331	182	55	and	and	CCONJ
ejpam-3331	182	56	β(x0	β(x0	ADJ
ejpam-3331	182	57	,	,	PUNCT
ejpam-3331	182	58	fx0	fx0	PROPN
ejpam-3331	182	59	)	)	PUNCT
ejpam-3331	182	60	≥	≥	NOUN
ejpam-3331	182	61	1	1	NUM
ejpam-3331	182	62	;	;	PUNCT
ejpam-3331	182	63	(	(	PUNCT
ejpam-3331	182	64	iii	iii	X
ejpam-3331	182	65	)	)	PUNCT
ejpam-3331	182	66	there	there	PRON
ejpam-3331	182	67	exists	exist	VERB
ejpam-3331	182	68	a	a	DET
ejpam-3331	182	69	lower	low	ADJ
ejpam-3331	182	70	semi	semi	ADJ
ejpam-3331	182	71	-	-	ADJ
ejpam-3331	182	72	continuous	continuous	ADJ
ejpam-3331	182	73	function	function	NOUN
ejpam-3331	182	74	ϕ	ϕ	NOUN
ejpam-3331	182	75	:	:	PUNCT
ejpam-3331	182	76	r+	r+	NOUN
ejpam-3331	182	77	→	→	SYM
ejpam-3331	182	78	r+	r+	NOUN
ejpam-3331	182	79	with	with	ADP
ejpam-3331	182	80	ϕ−1	ϕ−1	PROPN
ejpam-3331	182	81	=	=	SYM
ejpam-3331	182	82	{	{	PUNCT
ejpam-3331	182	83	0	0	NUM
ejpam-3331	182	84	}	}	PUNCT
ejpam-3331	182	85	such	such	ADJ
ejpam-3331	182	86	that	that	SCONJ
ejpam-3331	182	87	α(x	α(x	NOUN
ejpam-3331	182	88	,	,	PUNCT
ejpam-3331	182	89	y)β(x	y)β(x	NOUN
ejpam-3331	182	90	,	,	PUNCT
ejpam-3331	182	91	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	182	92	,	,	PUNCT
ejpam-3331	182	93	fy	fy	PROPN
ejpam-3331	182	94	)	)	PUNCT
ejpam-3331	182	95	≤	≤	NOUN
ejpam-3331	182	96	σ(x	σ(x	PROPN
ejpam-3331	182	97	,	,	PUNCT
ejpam-3331	182	98	y)−	y)−	PROPN
ejpam-3331	182	99	ϕ(σ(x	ϕ(σ(x	PROPN
ejpam-3331	182	100	,	,	PUNCT
ejpam-3331	182	101	y	y	NOUN
ejpam-3331	182	102	)	)	PUNCT
ejpam-3331	182	103	)	)	PUNCT
ejpam-3331	182	104	for	for	ADP
ejpam-3331	182	105	all	all	DET
ejpam-3331	182	106	x	x	NOUN
ejpam-3331	182	107	,	,	PUNCT
ejpam-3331	182	108	y	y	PROPN
ejpam-3331	182	109	∈	∈	PROPN
ejpam-3331	182	110	x	x	X
ejpam-3331	182	111	;	;	PUNCT
ejpam-3331	182	112	(	(	PUNCT
ejpam-3331	182	113	iv	iv	X
ejpam-3331	182	114	)	)	PUNCT
ejpam-3331	182	115	f	f	PROPN
ejpam-3331	182	116	is	be	AUX
ejpam-3331	182	117	σ	σ	NOUN
ejpam-3331	182	118	-	-	ADJ
ejpam-3331	182	119	continuous	continuous	ADJ
ejpam-3331	182	120	.	.	PUNCT
ejpam-3331	183	1	then	then	ADV
ejpam-3331	183	2	f	f	PROPN
ejpam-3331	183	3	has	have	VERB
ejpam-3331	183	4	a	a	DET
ejpam-3331	183	5	unique	unique	ADJ
ejpam-3331	183	6	fixed	fix	VERB
ejpam-3331	183	7	point	point	NOUN
ejpam-3331	183	8	u	u	NOUN
ejpam-3331	183	9	∈	∈	PROPN
ejpam-3331	183	10	x	x	PUNCT
ejpam-3331	183	11	with	with	ADP
ejpam-3331	183	12	σ(u	σ(u	NOUN
ejpam-3331	183	13	,	,	PUNCT
ejpam-3331	183	14	u	u	NOUN
ejpam-3331	183	15	)	)	PUNCT
ejpam-3331	183	16	=	=	SYM
ejpam-3331	183	17	0	0	X
ejpam-3331	183	18	.	.	PUNCT
ejpam-3331	184	1	proof	proof	NOUN
ejpam-3331	184	2	.	.	PUNCT
ejpam-3331	185	1	it	it	PRON
ejpam-3331	185	2	suffices	suffice	VERB
ejpam-3331	185	3	to	to	PART
ejpam-3331	185	4	take	take	VERB
ejpam-3331	185	5	ζ(t	ζ(t	NOUN
ejpam-3331	185	6	,	,	PUNCT
ejpam-3331	185	7	s	s	PART
ejpam-3331	185	8	)	)	PUNCT
ejpam-3331	185	9	=	=	VERB
ejpam-3331	185	10	s−	s−	PROPN
ejpam-3331	185	11	ϕ(s)−	ϕ(s)−	ADP
ejpam-3331	185	12	t.	t.	PROPN
ejpam-3331	185	13	if	if	SCONJ
ejpam-3331	185	14	we	we	PRON
ejpam-3331	185	15	consider	consider	VERB
ejpam-3331	185	16	in	in	ADP
ejpam-3331	185	17	theorem	theorem	ADJ
ejpam-3331	185	18	2	2	NUM
ejpam-3331	185	19	,	,	PUNCT
ejpam-3331	185	20	α(x	α(x	NOUN
ejpam-3331	185	21	,	,	PUNCT
ejpam-3331	185	22	y	y	NOUN
ejpam-3331	185	23	)	)	PUNCT
ejpam-3331	185	24	=	=	SYM
ejpam-3331	186	1	β(x	β(x	NOUN
ejpam-3331	186	2	,	,	PUNCT
ejpam-3331	186	3	y	y	NOUN
ejpam-3331	186	4	)	)	PUNCT
ejpam-3331	186	5	=	=	SYM
ejpam-3331	186	6	1	1	NUM
ejpam-3331	186	7	for	for	ADP
ejpam-3331	186	8	all	all	DET
ejpam-3331	186	9	x	x	NOUN
ejpam-3331	186	10	,	,	PUNCT
ejpam-3331	186	11	y	y	PROPN
ejpam-3331	186	12	∈	∈	PROPN
ejpam-3331	186	13	x	x	X
ejpam-3331	186	14	,	,	PUNCT
ejpam-3331	186	15	we	we	PRON
ejpam-3331	186	16	have	have	AUX
ejpam-3331	186	17	h.	h.	NOUN
ejpam-3331	186	18	alsamir	alsamir	VERB
ejpam-3331	186	19	et	et	PROPN
ejpam-3331	186	20	al	al	PROPN
ejpam-3331	186	21	.	.	PUNCT
ejpam-3331	186	22	/	/	SYM
ejpam-3331	186	23	eur	eur	PROPN
ejpam-3331	186	24	.	.	PUNCT
ejpam-3331	187	1	j.	j.	PROPN
ejpam-3331	187	2	pure	pure	PROPN
ejpam-3331	187	3	appl	appl	PROPN
ejpam-3331	187	4	.	.	PROPN
ejpam-3331	187	5	math	math	PROPN
ejpam-3331	187	6	,	,	PUNCT
ejpam-3331	187	7	12	12	NUM
ejpam-3331	187	8	(	(	PUNCT
ejpam-3331	187	9	1	1	NUM
ejpam-3331	187	10	)	)	PUNCT
ejpam-3331	187	11	(	(	PUNCT
ejpam-3331	187	12	2019	2019	NUM
ejpam-3331	187	13	)	)	PUNCT
ejpam-3331	187	14	,	,	PUNCT
ejpam-3331	187	15	88	88	NUM
ejpam-3331	187	16	-	-	SYM
ejpam-3331	187	17	100	100	NUM
ejpam-3331	187	18	96	96	NUM
ejpam-3331	187	19	corollary	corollary	ADJ
ejpam-3331	187	20	3	3	NUM
ejpam-3331	187	21	.	.	PUNCT
ejpam-3331	188	1	let	let	AUX
ejpam-3331	188	2	(	(	PUNCT
ejpam-3331	188	3	x	x	NOUN
ejpam-3331	188	4	,	,	PUNCT
ejpam-3331	188	5	σ	σ	PROPN
ejpam-3331	188	6	)	)	PUNCT
ejpam-3331	188	7	be	be	AUX
ejpam-3331	188	8	a	a	DET
ejpam-3331	188	9	complete	complete	ADJ
ejpam-3331	188	10	metric	metric	ADJ
ejpam-3331	188	11	-	-	PUNCT
ejpam-3331	188	12	like	like	ADJ
ejpam-3331	188	13	space	space	NOUN
ejpam-3331	188	14	and	and	CCONJ
ejpam-3331	188	15	let	let	VERB
ejpam-3331	188	16	f	f	PRON
ejpam-3331	188	17	be	be	AUX
ejpam-3331	188	18	a	a	DET
ejpam-3331	188	19	self	self	NOUN
ejpam-3331	188	20	-	-	PUNCT
ejpam-3331	188	21	mapping	mapping	NOUN
ejpam-3331	188	22	on	on	ADP
ejpam-3331	188	23	x.	x.	PROPN
ejpam-3331	188	24	suppose	suppose	VERB
ejpam-3331	188	25	that	that	SCONJ
ejpam-3331	188	26	there	there	PRON
ejpam-3331	188	27	exists	exist	VERB
ejpam-3331	188	28	a	a	DET
ejpam-3331	188	29	σ	σ	PROPN
ejpam-3331	188	30	-	-	PUNCT
ejpam-3331	188	31	simulation	simulation	NOUN
ejpam-3331	188	32	function	function	NOUN
ejpam-3331	188	33	ζ	ζ	NOUN
ejpam-3331	188	34	such	such	DET
ejpam-3331	188	35	that	that	DET
ejpam-3331	188	36	ζ(σ(fx	ζ(σ(fx	NOUN
ejpam-3331	188	37	,	,	PUNCT
ejpam-3331	188	38	fy	fy	PROPN
ejpam-3331	188	39	)	)	PUNCT
ejpam-3331	188	40	,	,	PUNCT
ejpam-3331	188	41	σ(x	σ(x	PROPN
ejpam-3331	188	42	,	,	PUNCT
ejpam-3331	188	43	y	y	NOUN
ejpam-3331	188	44	)	)	PUNCT
ejpam-3331	188	45	)	)	PUNCT
ejpam-3331	188	46	≥	≥	NOUN
ejpam-3331	188	47	0	0	NUM
ejpam-3331	188	48	(	(	PUNCT
ejpam-3331	188	49	19	19	NUM
ejpam-3331	188	50	)	)	PUNCT
ejpam-3331	188	51	for	for	ADP
ejpam-3331	188	52	all	all	DET
ejpam-3331	188	53	x	x	NOUN
ejpam-3331	188	54	,	,	PUNCT
ejpam-3331	188	55	y	y	PROPN
ejpam-3331	188	56	∈	∈	PROPN
ejpam-3331	189	1	x.	x.	NOUN
ejpam-3331	190	1	then	then	ADV
ejpam-3331	190	2	f	f	PROPN
ejpam-3331	190	3	has	have	VERB
ejpam-3331	190	4	a	a	DET
ejpam-3331	190	5	unique	unique	ADJ
ejpam-3331	190	6	fixed	fix	VERB
ejpam-3331	190	7	point	point	NOUN
ejpam-3331	190	8	u	u	NOUN
ejpam-3331	190	9	∈	∈	PROPN
ejpam-3331	190	10	x	x	PUNCT
ejpam-3331	190	11	with	with	ADP
ejpam-3331	190	12	σ(u	σ(u	NOUN
ejpam-3331	190	13	,	,	PUNCT
ejpam-3331	190	14	u	u	NOUN
ejpam-3331	190	15	)	)	PUNCT
ejpam-3331	190	16	=	=	SYM
ejpam-3331	191	1	0	0	X
ejpam-3331	191	2	.	.	PUNCT
ejpam-3331	192	1	we	we	PRON
ejpam-3331	192	2	present	present	VERB
ejpam-3331	192	3	the	the	DET
ejpam-3331	192	4	following	follow	VERB
ejpam-3331	192	5	illustrated	illustrated	ADJ
ejpam-3331	192	6	examples	example	NOUN
ejpam-3331	192	7	.	.	PUNCT
ejpam-3331	193	1	example	example	NOUN
ejpam-3331	194	1	3	3	X
ejpam-3331	194	2	.	.	PUNCT
ejpam-3331	194	3	let	let	VERB
ejpam-3331	194	4	x	x	PUNCT
ejpam-3331	194	5	=	=	PUNCT
ejpam-3331	195	1	[	[	X
ejpam-3331	195	2	0,∞	0,∞	NUM
ejpam-3331	195	3	)	)	PUNCT
ejpam-3331	195	4	,	,	PUNCT
ejpam-3331	195	5	σ(x	σ(x	PROPN
ejpam-3331	195	6	,	,	PUNCT
ejpam-3331	195	7	y	y	NOUN
ejpam-3331	195	8	)	)	PUNCT
ejpam-3331	195	9	=	=	SYM
ejpam-3331	196	1	(	(	PUNCT
ejpam-3331	196	2	x+	x+	PROPN
ejpam-3331	196	3	y	y	NOUN
ejpam-3331	196	4	)	)	PUNCT
ejpam-3331	196	5	for	for	ADP
ejpam-3331	196	6	all	all	DET
ejpam-3331	196	7	x	x	NOUN
ejpam-3331	196	8	,	,	PUNCT
ejpam-3331	196	9	y	y	PROPN
ejpam-3331	196	10	∈	∈	PROPN
ejpam-3331	196	11	x	x	X
ejpam-3331	196	12	and	and	CCONJ
ejpam-3331	196	13	f	f	X
ejpam-3331	196	14	:	:	PUNCT
ejpam-3331	196	15	x	x	X
ejpam-3331	196	16	→	→	PUNCT
ejpam-3331	196	17	x	x	AUX
ejpam-3331	196	18	be	be	AUX
ejpam-3331	196	19	defined	define	VERB
ejpam-3331	196	20	by	by	ADP
ejpam-3331	196	21	fx	fx	NOUN
ejpam-3331	196	22	=	=	PUNCT
ejpam-3331	196	23	{	{	PUNCT
ejpam-3331	196	24	1	1	NUM
ejpam-3331	196	25	4x	4x	NUM
ejpam-3331	196	26	if	if	SCONJ
ejpam-3331	196	27	0	0	NUM
ejpam-3331	196	28	≤	≤	NUM
ejpam-3331	196	29	x	x	SYM
ejpam-3331	196	30	≤	≤	NUM
ejpam-3331	196	31	1	1	NUM
ejpam-3331	196	32	4x	4x	NOUN
ejpam-3331	196	33	otherwise	otherwise	ADV
ejpam-3331	196	34	.	.	PUNCT
ejpam-3331	197	1	consider	consider	VERB
ejpam-3331	197	2	ζ(s	ζ(s	PROPN
ejpam-3331	197	3	,	,	PUNCT
ejpam-3331	197	4	t	t	PROPN
ejpam-3331	197	5	)	)	PUNCT
ejpam-3331	197	6	=	=	SYM
ejpam-3331	198	1	cs−	cs−	NUM
ejpam-3331	198	2	t	t	NOUN
ejpam-3331	198	3	,	,	PUNCT
ejpam-3331	198	4	where	where	SCONJ
ejpam-3331	198	5	0	0	NUM
ejpam-3331	198	6	≤	≤	NUM
ejpam-3331	198	7	1	1	NUM
ejpam-3331	198	8	4	4	NUM
ejpam-3331	198	9	<	<	X
ejpam-3331	198	10	c	c	X
ejpam-3331	198	11	<	<	X
ejpam-3331	198	12	1	1	NUM
ejpam-3331	198	13	.	.	PUNCT
ejpam-3331	198	14	define	define	VERB
ejpam-3331	198	15	α	α	NOUN
ejpam-3331	198	16	,	,	PUNCT
ejpam-3331	198	17	β	β	X
ejpam-3331	198	18	:	:	PUNCT
ejpam-3331	198	19	x	x	SYM
ejpam-3331	198	20	×x	×x	ADP
ejpam-3331	198	21	→	→	SYM
ejpam-3331	198	22	r+	r+	NOUN
ejpam-3331	198	23	as	as	ADP
ejpam-3331	198	24	α(x	α(x	NOUN
ejpam-3331	198	25	,	,	PUNCT
ejpam-3331	198	26	y	y	PROPN
ejpam-3331	198	27	)	)	PUNCT
ejpam-3331	198	28	=	=	PRON
ejpam-3331	198	29	{	{	PUNCT
ejpam-3331	198	30	4	4	NUM
ejpam-3331	198	31	3	3	NUM
ejpam-3331	198	32	if	if	SCONJ
ejpam-3331	198	33	0	0	NUM
ejpam-3331	198	34	≤	≤	NUM
ejpam-3331	198	35	x	x	X
ejpam-3331	198	36	,	,	PUNCT
ejpam-3331	198	37	y	y	PROPN
ejpam-3331	198	38	≤	≤	ADV
ejpam-3331	198	39	1	1	NUM
ejpam-3331	198	40	0	0	NUM
ejpam-3331	198	41	otherwise	otherwise	ADV
ejpam-3331	198	42	,	,	PUNCT
ejpam-3331	198	43	β(x	β(x	PROPN
ejpam-3331	198	44	,	,	PUNCT
ejpam-3331	198	45	y	y	NOUN
ejpam-3331	198	46	)	)	PUNCT
ejpam-3331	199	1	=	=	PRON
ejpam-3331	199	2	{	{	PUNCT
ejpam-3331	199	3	3	3	NUM
ejpam-3331	199	4	2	2	NUM
ejpam-3331	199	5	if	if	SCONJ
ejpam-3331	199	6	0	0	NUM
ejpam-3331	199	7	≤	≤	NUM
ejpam-3331	199	8	x	x	X
ejpam-3331	199	9	,	,	PUNCT
ejpam-3331	199	10	y	y	PROPN
ejpam-3331	199	11	≤	≤	ADV
ejpam-3331	199	12	1	1	NUM
ejpam-3331	199	13	0	0	NUM
ejpam-3331	199	14	otherwise	otherwise	ADV
ejpam-3331	199	15	.	.	PUNCT
ejpam-3331	200	1	we	we	PRON
ejpam-3331	200	2	shall	shall	AUX
ejpam-3331	200	3	prove	prove	VERB
ejpam-3331	200	4	that	that	PRON
ejpam-3331	200	5	corollary	corollary	NOUN
ejpam-3331	200	6	1	1	NUM
ejpam-3331	200	7	can	can	AUX
ejpam-3331	200	8	be	be	AUX
ejpam-3331	200	9	applied	apply	VERB
ejpam-3331	200	10	.	.	PUNCT
ejpam-3331	201	1	clearly	clearly	ADV
ejpam-3331	201	2	,	,	PUNCT
ejpam-3331	201	3	(	(	PUNCT
ejpam-3331	201	4	x	x	X
ejpam-3331	201	5	,	,	PUNCT
ejpam-3331	201	6	σ	σ	PROPN
ejpam-3331	201	7	)	)	PUNCT
ejpam-3331	201	8	is	be	AUX
ejpam-3331	201	9	a	a	DET
ejpam-3331	201	10	complete	complete	ADJ
ejpam-3331	201	11	metric	metric	ADJ
ejpam-3331	201	12	-	-	PUNCT
ejpam-3331	201	13	like	like	ADJ
ejpam-3331	201	14	space	space	NOUN
ejpam-3331	201	15	.	.	PUNCT
ejpam-3331	202	1	let	let	VERB
ejpam-3331	202	2	x	x	PRON
ejpam-3331	202	3	,	,	PUNCT
ejpam-3331	202	4	y	y	PROPN
ejpam-3331	202	5	∈	∈	PROPN
ejpam-3331	202	6	x	x	PUNCT
ejpam-3331	202	7	such	such	ADJ
ejpam-3331	202	8	that	that	DET
ejpam-3331	202	9	α(x	α(x	PROPN
ejpam-3331	202	10	,	,	PUNCT
ejpam-3331	202	11	y	y	PROPN
ejpam-3331	202	12	)	)	PUNCT
ejpam-3331	202	13	≥	≥	NOUN
ejpam-3331	202	14	1	1	NUM
ejpam-3331	202	15	and	and	CCONJ
ejpam-3331	202	16	β(x	β(x	PROPN
ejpam-3331	202	17	,	,	PUNCT
ejpam-3331	202	18	y	y	NOUN
ejpam-3331	202	19	)	)	PUNCT
ejpam-3331	202	20	≥	≥	NOUN
ejpam-3331	202	21	1	1	NUM
ejpam-3331	202	22	.	.	PUNCT
ejpam-3331	203	1	since	since	SCONJ
ejpam-3331	203	2	x	x	X
ejpam-3331	203	3	,	,	PUNCT
ejpam-3331	203	4	y	y	PROPN
ejpam-3331	203	5	∈	∈	PROPN
ejpam-3331	204	1	[	[	X
ejpam-3331	204	2	0	0	NUM
ejpam-3331	204	3	,	,	PUNCT
ejpam-3331	204	4	1	1	NUM
ejpam-3331	204	5	]	]	PUNCT
ejpam-3331	204	6	and	and	CCONJ
ejpam-3331	204	7	so	so	ADV
ejpam-3331	204	8	fx	fx	ADP
ejpam-3331	204	9	∈	∈	PROPN
ejpam-3331	205	1	[	[	X
ejpam-3331	205	2	0	0	NUM
ejpam-3331	205	3	,	,	PUNCT
ejpam-3331	205	4	1	1	NUM
ejpam-3331	205	5	]	]	PUNCT
ejpam-3331	205	6	,	,	PUNCT
ejpam-3331	205	7	fy	fy	PROPN
ejpam-3331	205	8	∈	∈	PROPN
ejpam-3331	206	1	[	[	X
ejpam-3331	206	2	0	0	NUM
ejpam-3331	206	3	,	,	PUNCT
ejpam-3331	206	4	1	1	NUM
ejpam-3331	206	5	]	]	PUNCT
ejpam-3331	206	6	and	and	CCONJ
ejpam-3331	206	7	α(fx	α(fx	PROPN
ejpam-3331	206	8	,	,	PUNCT
ejpam-3331	206	9	fy	fy	PROPN
ejpam-3331	206	10	)	)	PUNCT
ejpam-3331	206	11	=	=	SYM
ejpam-3331	206	12	1	1	NUM
ejpam-3331	206	13	and	and	CCONJ
ejpam-3331	206	14	β(fx	β(fx	NOUN
ejpam-3331	206	15	,	,	PUNCT
ejpam-3331	206	16	fy	fy	PROPN
ejpam-3331	206	17	)	)	PUNCT
ejpam-3331	207	1	=	=	SYM
ejpam-3331	207	2	1	1	X
ejpam-3331	207	3	.	.	X
ejpam-3331	208	1	hence	hence	ADV
ejpam-3331	208	2	f	f	PROPN
ejpam-3331	208	3	is	be	AUX
ejpam-3331	208	4	(	(	PUNCT
ejpam-3331	208	5	α	α	NOUN
ejpam-3331	208	6	,	,	PUNCT
ejpam-3331	208	7	β)-admissible	β)-admissible	PUNCT
ejpam-3331	208	8	.	.	PUNCT
ejpam-3331	209	1	condition	condition	NOUN
ejpam-3331	209	2	(	(	PUNCT
ejpam-3331	209	3	2	2	X
ejpam-3331	209	4	)	)	PUNCT
ejpam-3331	209	5	is	be	AUX
ejpam-3331	209	6	satisfied	satisfied	ADJ
ejpam-3331	209	7	with	with	ADP
ejpam-3331	209	8	x0	x0	PROPN
ejpam-3331	209	9	=	=	SYM
ejpam-3331	209	10	1	1	X
ejpam-3331	209	11	.	.	PUNCT
ejpam-3331	209	12	condition	condition	NOUN
ejpam-3331	209	13	(	(	PUNCT
ejpam-3331	209	14	4	4	X
ejpam-3331	209	15	)	)	PUNCT
ejpam-3331	209	16	is	be	AUX
ejpam-3331	209	17	satisfied	satisfied	ADJ
ejpam-3331	209	18	with	with	ADP
ejpam-3331	209	19	xn	xn	PROPN
ejpam-3331	210	1	=	=	SYM
ejpam-3331	210	2	fnx1	fnx1	PROPN
ejpam-3331	210	3	=	=	SYM
ejpam-3331	210	4	1	1	NUM
ejpam-3331	210	5	n	n	NOUN
ejpam-3331	210	6	.	.	PUNCT
ejpam-3331	211	1	if	if	SCONJ
ejpam-3331	211	2	0	0	NUM
ejpam-3331	211	3	≤	≤	NUM
ejpam-3331	211	4	x	x	SYM
ejpam-3331	211	5	≤	≤	NUM
ejpam-3331	211	6	1	1	NUM
ejpam-3331	211	7	,	,	PUNCT
ejpam-3331	211	8	then	then	ADV
ejpam-3331	211	9	α(x	α(x	PROPN
ejpam-3331	211	10	,	,	PUNCT
ejpam-3331	211	11	y	y	PROPN
ejpam-3331	211	12	)	)	PUNCT
ejpam-3331	211	13	=	=	SYM
ejpam-3331	211	14	4	4	NUM
ejpam-3331	211	15	3	3	NUM
ejpam-3331	211	16	and	and	CCONJ
ejpam-3331	211	17	β(x	β(x	PROPN
ejpam-3331	211	18	,	,	PUNCT
ejpam-3331	211	19	y	y	NOUN
ejpam-3331	211	20	)	)	PUNCT
ejpam-3331	211	21	=	=	SYM
ejpam-3331	211	22	3	3	NUM
ejpam-3331	211	23	2	2	NUM
ejpam-3331	211	24	.	.	PUNCT
ejpam-3331	212	1	we	we	PRON
ejpam-3331	212	2	have	have	VERB
ejpam-3331	212	3	ζ(α(x	ζ(α(x	NOUN
ejpam-3331	212	4	,	,	PUNCT
ejpam-3331	212	5	y)β(x	y)β(x	NOUN
ejpam-3331	212	6	,	,	PUNCT
ejpam-3331	212	7	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	212	8	,	,	PUNCT
ejpam-3331	212	9	fy	fy	PROPN
ejpam-3331	212	10	)	)	PUNCT
ejpam-3331	212	11	,	,	PUNCT
ejpam-3331	212	12	σ(x	σ(x	PROPN
ejpam-3331	212	13	,	,	PUNCT
ejpam-3331	212	14	y	y	NOUN
ejpam-3331	212	15	)	)	PUNCT
ejpam-3331	212	16	)	)	PUNCT
ejpam-3331	213	1	=	=	SYM
ejpam-3331	213	2	cσ(x	cσ(x	PROPN
ejpam-3331	213	3	,	,	PUNCT
ejpam-3331	213	4	y)−	y)−	PROPN
ejpam-3331	213	5	α(x	α(x	NOUN
ejpam-3331	213	6	,	,	PUNCT
ejpam-3331	213	7	y)β(x	y)β(x	NOUN
ejpam-3331	213	8	,	,	PUNCT
ejpam-3331	213	9	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	213	10	,	,	PUNCT
ejpam-3331	213	11	fy	fy	PROPN
ejpam-3331	213	12	)	)	PUNCT
ejpam-3331	213	13	=	=	SYM
ejpam-3331	213	14	3	3	NUM
ejpam-3331	213	15	4	4	NUM
ejpam-3331	213	16	(	(	PUNCT
ejpam-3331	213	17	x+	x+	X
ejpam-3331	213	18	y)−	y)−	PROPN
ejpam-3331	213	19	2	2	NUM
ejpam-3331	213	20	1	1	NUM
ejpam-3331	213	21	4	4	NUM
ejpam-3331	213	22	(	(	PUNCT
ejpam-3331	213	23	x+	x+	PROPN
ejpam-3331	213	24	y	y	NOUN
ejpam-3331	213	25	)	)	PUNCT
ejpam-3331	213	26	=	=	PUNCT
ejpam-3331	213	27	(	(	PUNCT
ejpam-3331	213	28	3	3	NUM
ejpam-3331	213	29	4	4	NUM
ejpam-3331	213	30	−	−	NUM
ejpam-3331	213	31	1	1	NUM
ejpam-3331	213	32	2	2	NUM
ejpam-3331	213	33	)	)	PUNCT
ejpam-3331	213	34	(	(	PUNCT
ejpam-3331	213	35	x+	x+	X
ejpam-3331	213	36	y	y	NOUN
ejpam-3331	213	37	)	)	PUNCT
ejpam-3331	213	38	=	=	SYM
ejpam-3331	213	39	1	1	NUM
ejpam-3331	213	40	4	4	NUM
ejpam-3331	213	41	(	(	PUNCT
ejpam-3331	213	42	x+	x+	PROPN
ejpam-3331	213	43	y	y	NOUN
ejpam-3331	213	44	)	)	PUNCT
ejpam-3331	213	45	≥	≥	NOUN
ejpam-3331	213	46	0	0	NUM
ejpam-3331	213	47	.	.	PUNCT
ejpam-3331	214	1	if	if	SCONJ
ejpam-3331	214	2	0	0	NUM
ejpam-3331	214	3	≤	≤	NUM
ejpam-3331	214	4	x	x	SYM
ejpam-3331	214	5	≤	≤	NUM
ejpam-3331	214	6	1	1	NUM
ejpam-3331	214	7	and	and	CCONJ
ejpam-3331	214	8	y	y	PROPN
ejpam-3331	214	9	>	>	X
ejpam-3331	214	10	1	1	NUM
ejpam-3331	214	11	,	,	PUNCT
ejpam-3331	214	12	then	then	ADV
ejpam-3331	214	13	ζ(α(x	ζ(α(x	NOUN
ejpam-3331	214	14	,	,	PUNCT
ejpam-3331	214	15	y)β(x	y)β(x	NOUN
ejpam-3331	214	16	,	,	PUNCT
ejpam-3331	214	17	y)σ(fx	y)σ(fx	NOUN
ejpam-3331	214	18	,	,	PUNCT
ejpam-3331	214	19	fy	fy	PROPN
ejpam-3331	214	20	)	)	PUNCT
ejpam-3331	214	21	,	,	PUNCT
ejpam-3331	214	22	σ(x	σ(x	PROPN
ejpam-3331	214	23	,	,	PUNCT
ejpam-3331	214	24	y	y	NOUN
ejpam-3331	214	25	)	)	PUNCT
ejpam-3331	214	26	)	)	PUNCT
ejpam-3331	214	27	≥	≥	NOUN
ejpam-3331	214	28	0	0	NUM
ejpam-3331	214	29	since	since	SCONJ
ejpam-3331	214	30	α(x	α(x	PROPN
ejpam-3331	214	31	,	,	PUNCT
ejpam-3331	214	32	y	y	NOUN
ejpam-3331	214	33	)	)	PUNCT
ejpam-3331	214	34	=	=	SYM
ejpam-3331	215	1	β(x	β(x	NOUN
ejpam-3331	215	2	,	,	PUNCT
ejpam-3331	215	3	y	y	NOUN
ejpam-3331	215	4	)	)	PUNCT
ejpam-3331	215	5	=	=	SYM
ejpam-3331	215	6	0	0	X
ejpam-3331	215	7	.	.	PUNCT
ejpam-3331	216	1	consequently	consequently	ADV
ejpam-3331	216	2	,	,	PUNCT
ejpam-3331	216	3	all	all	DET
ejpam-3331	216	4	assumptions	assumption	NOUN
ejpam-3331	216	5	of	of	ADP
ejpam-3331	216	6	corollary	corollary	ADJ
ejpam-3331	216	7	1	1	NUM
ejpam-3331	216	8	are	be	AUX
ejpam-3331	216	9	satisfied	satisfied	ADJ
ejpam-3331	216	10	and	and	CCONJ
ejpam-3331	216	11	hence	hence	ADV
ejpam-3331	216	12	f	f	PROPN
ejpam-3331	216	13	has	have	VERB
ejpam-3331	216	14	a	a	DET
ejpam-3331	216	15	unique	unique	ADJ
ejpam-3331	216	16	fixed	fix	VERB
ejpam-3331	216	17	point	point	NOUN
ejpam-3331	216	18	,	,	PUNCT
ejpam-3331	216	19	which	which	PRON
ejpam-3331	216	20	is	be	AUX
ejpam-3331	216	21	u	u	NOUN
ejpam-3331	216	22	=	=	PROPN
ejpam-3331	216	23	0	0	NUM
ejpam-3331	216	24	.	.	PUNCT
ejpam-3331	217	1	we	we	PRON
ejpam-3331	217	2	also	also	ADV
ejpam-3331	217	3	notice	notice	VERB
ejpam-3331	217	4	that	that	SCONJ
ejpam-3331	217	5	(	(	PUNCT
ejpam-3331	217	6	19	19	NUM
ejpam-3331	217	7	)	)	PUNCT
ejpam-3331	217	8	is	be	AUX
ejpam-3331	217	9	not	not	PART
ejpam-3331	217	10	satisfied	satisfied	ADJ
ejpam-3331	217	11	.	.	PUNCT
ejpam-3331	218	1	in	in	ADP
ejpam-3331	218	2	fact	fact	NOUN
ejpam-3331	218	3	,	,	PUNCT
ejpam-3331	218	4	for	for	ADP
ejpam-3331	218	5	x	x	SYM
ejpam-3331	218	6	=	=	SYM
ejpam-3331	218	7	1	1	NUM
ejpam-3331	218	8	,	,	PUNCT
ejpam-3331	218	9	y	y	PROPN
ejpam-3331	218	10	=	=	SYM
ejpam-3331	218	11	2	2	NUM
ejpam-3331	218	12	,	,	PUNCT
ejpam-3331	218	13	we	we	PRON
ejpam-3331	218	14	get	get	VERB
ejpam-3331	218	15	σ(f1	σ(f1	NOUN
ejpam-3331	218	16	,	,	PUNCT
ejpam-3331	218	17	f2	f2	PROPN
ejpam-3331	218	18	)	)	PUNCT
ejpam-3331	218	19	=	=	PUNCT
ejpam-3331	218	20	(	(	PUNCT
ejpam-3331	218	21	33	33	NUM
ejpam-3331	218	22	4	4	NUM
ejpam-3331	218	23	)	)	PUNCT
ejpam-3331	218	24	2	2	NUM
ejpam-3331	218	25	>	>	SYM
ejpam-3331	218	26	3	3	NUM
ejpam-3331	218	27	=	=	SYM
ejpam-3331	218	28	σ(x	σ(x	PROPN
ejpam-3331	218	29	,	,	PUNCT
ejpam-3331	218	30	y	y	PROPN
ejpam-3331	218	31	)	)	PUNCT
ejpam-3331	218	32	.	.	PUNCT
ejpam-3331	219	1	h.	h.	PROPN
ejpam-3331	219	2	alsamir	alsamir	VERB
ejpam-3331	219	3	et	et	PROPN
ejpam-3331	219	4	al	al	PROPN
ejpam-3331	219	5	.	.	PUNCT
ejpam-3331	219	6	/	/	SYM
ejpam-3331	219	7	eur	eur	PROPN
ejpam-3331	219	8	.	.	PUNCT
ejpam-3331	220	1	j.	j.	PROPN
ejpam-3331	220	2	pure	pure	PROPN
ejpam-3331	220	3	appl	appl	PROPN
ejpam-3331	220	4	.	.	PROPN
ejpam-3331	220	5	math	math	PROPN
ejpam-3331	220	6	,	,	PUNCT
ejpam-3331	220	7	12	12	NUM
ejpam-3331	220	8	(	(	PUNCT
ejpam-3331	220	9	1	1	NUM
ejpam-3331	220	10	)	)	PUNCT
ejpam-3331	220	11	(	(	PUNCT
ejpam-3331	220	12	2019	2019	NUM
ejpam-3331	220	13	)	)	PUNCT
ejpam-3331	220	14	,	,	PUNCT
ejpam-3331	220	15	88	88	NUM
ejpam-3331	220	16	-	-	SYM
ejpam-3331	220	17	100	100	NUM
ejpam-3331	220	18	97	97	NUM
ejpam-3331	220	19	example	example	NOUN
ejpam-3331	220	20	4	4	NUM
ejpam-3331	220	21	.	.	X
ejpam-3331	220	22	consider	consider	VERB
ejpam-3331	220	23	x	x	PUNCT
ejpam-3331	220	24	=	=	PRON
ejpam-3331	220	25	{	{	PUNCT
ejpam-3331	220	26	0	0	NUM
ejpam-3331	220	27	,	,	PUNCT
ejpam-3331	220	28	1	1	NUM
ejpam-3331	220	29	,	,	PUNCT
ejpam-3331	220	30	3	3	NUM
ejpam-3331	220	31	}	}	PUNCT
ejpam-3331	220	32	and	and	CCONJ
ejpam-3331	220	33	define	define	VERB
ejpam-3331	220	34	σ	σ	NOUN
ejpam-3331	220	35	:	:	PUNCT
ejpam-3331	220	36	x	x	X
ejpam-3331	220	37	×x	×x	ADP
ejpam-3331	220	38	→	→	SYM
ejpam-3331	220	39	r+	r+	NOUN
ejpam-3331	220	40	as	as	SCONJ
ejpam-3331	220	41	follows	follow	VERB
ejpam-3331	220	42	:	:	PUNCT
ejpam-3331	221	1	σ(0	σ(0	PROPN
ejpam-3331	221	2	,	,	PUNCT
ejpam-3331	221	3	0	0	NUM
ejpam-3331	221	4	)	)	PUNCT
ejpam-3331	221	5	=	=	SYM
ejpam-3331	221	6	0	0	NUM
ejpam-3331	221	7	,	,	PUNCT
ejpam-3331	221	8	σ(1	σ(1	PROPN
ejpam-3331	221	9	,	,	PUNCT
ejpam-3331	221	10	0	0	NUM
ejpam-3331	221	11	)	)	PUNCT
ejpam-3331	221	12	=	=	SYM
ejpam-3331	222	1	σ(0	σ(0	PROPN
ejpam-3331	222	2	,	,	PUNCT
ejpam-3331	222	3	1	1	NUM
ejpam-3331	222	4	)	)	PUNCT
ejpam-3331	222	5	=	=	SYM
ejpam-3331	222	6	1	1	NUM
ejpam-3331	222	7	10	10	NUM
ejpam-3331	222	8	,	,	PUNCT
ejpam-3331	222	9	σ(0	σ(0	PROPN
ejpam-3331	222	10	,	,	PUNCT
ejpam-3331	222	11	3	3	NUM
ejpam-3331	222	12	)	)	PUNCT
ejpam-3331	222	13	=	=	SYM
ejpam-3331	222	14	σ(3	σ(3	PROPN
ejpam-3331	222	15	,	,	PUNCT
ejpam-3331	222	16	0	0	NUM
ejpam-3331	222	17	)	)	PUNCT
ejpam-3331	222	18	=	=	SYM
ejpam-3331	222	19	1	1	NUM
ejpam-3331	222	20	2	2	NUM
ejpam-3331	222	21	,	,	PUNCT
ejpam-3331	222	22	σ(1	σ(1	PROPN
ejpam-3331	222	23	,	,	PUNCT
ejpam-3331	222	24	3	3	NUM
ejpam-3331	222	25	)	)	PUNCT
ejpam-3331	222	26	=	=	SYM
ejpam-3331	223	1	σ(3	σ(3	NOUN
ejpam-3331	223	2	,	,	PUNCT
ejpam-3331	223	3	1	1	X
ejpam-3331	223	4	)	)	PUNCT
ejpam-3331	223	5	=	=	SYM
ejpam-3331	223	6	2	2	NUM
ejpam-3331	223	7	3	3	NUM
ejpam-3331	223	8	,	,	PUNCT
ejpam-3331	223	9	σ(1	σ(1	PROPN
ejpam-3331	223	10	,	,	PUNCT
ejpam-3331	223	11	1	1	NUM
ejpam-3331	223	12	)	)	PUNCT
ejpam-3331	223	13	=	=	SYM
ejpam-3331	223	14	1	1	NUM
ejpam-3331	223	15	2	2	NUM
ejpam-3331	223	16	,	,	PUNCT
ejpam-3331	223	17	σ(3	σ(3	PROPN
ejpam-3331	223	18	,	,	PUNCT
ejpam-3331	223	19	3	3	X
ejpam-3331	223	20	)	)	PUNCT
ejpam-3331	223	21	=	=	SYM
ejpam-3331	223	22	7	7	NUM
ejpam-3331	223	23	2	2	NUM
ejpam-3331	223	24	.	.	PUNCT
ejpam-3331	223	25	note	note	VERB
ejpam-3331	223	26	that	that	SCONJ
ejpam-3331	223	27	σ(3	σ(3	NOUN
ejpam-3331	223	28	,	,	PUNCT
ejpam-3331	223	29	3	3	NUM
ejpam-3331	223	30	)	)	PUNCT
ejpam-3331	223	31	6=	6=	ADP
ejpam-3331	223	32	0	0	NUM
ejpam-3331	223	33	,	,	PUNCT
ejpam-3331	223	34	so	so	CCONJ
ejpam-3331	223	35	(	(	PUNCT
ejpam-3331	223	36	x	x	NOUN
ejpam-3331	223	37	,	,	PUNCT
ejpam-3331	223	38	σ	σ	PROPN
ejpam-3331	223	39	)	)	PUNCT
ejpam-3331	223	40	is	be	AUX
ejpam-3331	223	41	not	not	PART
ejpam-3331	223	42	a	a	DET
ejpam-3331	223	43	metric	metric	ADJ
ejpam-3331	223	44	and	and	CCONJ
ejpam-3331	223	45	σ(3	σ(3	PROPN
ejpam-3331	223	46	,	,	PUNCT
ejpam-3331	223	47	3	3	NUM
ejpam-3331	223	48	)	)	PUNCT
ejpam-3331	223	49	>	>	X
ejpam-3331	224	1	σ(0	σ(0	PROPN
ejpam-3331	224	2	,	,	PUNCT
ejpam-3331	224	3	3	3	NUM
ejpam-3331	224	4	)	)	PUNCT
ejpam-3331	224	5	,	,	PUNCT
ejpam-3331	224	6	so	so	CCONJ
ejpam-3331	224	7	(	(	PUNCT
ejpam-3331	224	8	x	x	NOUN
ejpam-3331	224	9	,	,	PUNCT
ejpam-3331	224	10	σ	σ	PROPN
ejpam-3331	224	11	)	)	PUNCT
ejpam-3331	224	12	is	be	AUX
ejpam-3331	224	13	not	not	PART
ejpam-3331	224	14	a	a	DET
ejpam-3331	224	15	partial	partial	ADJ
ejpam-3331	224	16	metric	metric	NOUN
ejpam-3331	224	17	.	.	PUNCT
ejpam-3331	225	1	clearly	clearly	ADV
ejpam-3331	225	2	,	,	PUNCT
ejpam-3331	225	3	(	(	PUNCT
ejpam-3331	225	4	x	x	X
ejpam-3331	225	5	,	,	PUNCT
ejpam-3331	225	6	σ	σ	PROPN
ejpam-3331	225	7	)	)	PUNCT
ejpam-3331	225	8	is	be	AUX
ejpam-3331	225	9	metric	metric	ADJ
ejpam-3331	225	10	-	-	PUNCT
ejpam-3331	225	11	like	like	ADJ
ejpam-3331	225	12	space	space	NOUN
ejpam-3331	225	13	.	.	PUNCT
ejpam-3331	226	1	let	let	VERB
ejpam-3331	226	2	f	f	NOUN
ejpam-3331	226	3	:	:	PUNCT
ejpam-3331	226	4	x	x	X
ejpam-3331	226	5	→	→	PUNCT
ejpam-3331	226	6	x	x	AUX
ejpam-3331	226	7	be	be	AUX
ejpam-3331	226	8	defined	define	VERB
ejpam-3331	226	9	by	by	ADP
ejpam-3331	226	10	f0	f0	PROPN
ejpam-3331	226	11	=	=	SYM
ejpam-3331	226	12	f1	f1	NOUN
ejpam-3331	226	13	=	=	SYM
ejpam-3331	226	14	0	0	NUM
ejpam-3331	226	15	and	and	CCONJ
ejpam-3331	226	16	f3	f3	PROPN
ejpam-3331	226	17	=	=	SYM
ejpam-3331	226	18	1	1	X
ejpam-3331	226	19	.	.	X
ejpam-3331	227	1	take	take	VERB
ejpam-3331	227	2	α	α	PRON
ejpam-3331	227	3	,	,	PUNCT
ejpam-3331	227	4	β	β	X
ejpam-3331	227	5	:	:	PUNCT
ejpam-3331	227	6	x	x	SYM
ejpam-3331	227	7	×x	×x	ADP
ejpam-3331	227	8	→	→	SYM
ejpam-3331	227	9	r+	r+	PRON
ejpam-3331	227	10	given	give	VERB
ejpam-3331	227	11	as	as	ADP
ejpam-3331	227	12	α(x	α(x	NOUN
ejpam-3331	227	13	,	,	PUNCT
ejpam-3331	227	14	y	y	PROPN
ejpam-3331	227	15	)	)	PUNCT
ejpam-3331	227	16	=	=	PRON
ejpam-3331	227	17	{	{	PUNCT
ejpam-3331	227	18	5	5	NUM
ejpam-3331	227	19	2	2	NUM
ejpam-3331	227	20	,	,	PUNCT
ejpam-3331	227	21	if	if	SCONJ
ejpam-3331	227	22	x	x	PROPN
ejpam-3331	227	23	∈{0,1,3	∈{0,1,3	NUM
ejpam-3331	227	24	}	}	PUNCT
ejpam-3331	227	25	,	,	PUNCT
ejpam-3331	227	26	0	0	NUM
ejpam-3331	227	27	,	,	PUNCT
ejpam-3331	227	28	otherwise	otherwise	ADV
ejpam-3331	227	29	,	,	PUNCT
ejpam-3331	227	30	β(x	β(x	PROPN
ejpam-3331	227	31	,	,	PUNCT
ejpam-3331	227	32	y	y	NOUN
ejpam-3331	227	33	)	)	PUNCT
ejpam-3331	227	34	=	=	PRON
ejpam-3331	227	35	{	{	PUNCT
ejpam-3331	228	1	1	1	NUM
ejpam-3331	228	2	,	,	PUNCT
ejpam-3331	228	3	if	if	SCONJ
ejpam-3331	228	4	x	x	PROPN
ejpam-3331	228	5	∈{0,1,3	∈{0,1,3	NUM
ejpam-3331	228	6	}	}	PUNCT
ejpam-3331	228	7	,	,	PUNCT
ejpam-3331	228	8	0	0	NUM
ejpam-3331	228	9	,	,	PUNCT
ejpam-3331	228	10	otherwise	otherwise	ADV
ejpam-3331	228	11	.	.	PUNCT
ejpam-3331	229	1	take	take	VERB
ejpam-3331	229	2	ζ	ζ	NOUN
ejpam-3331	229	3	:	:	PUNCT
ejpam-3331	229	4	x	x	SYM
ejpam-3331	229	5	×	×	NOUN
ejpam-3331	229	6	x	x	PUNCT
ejpam-3331	229	7	→	→	X
ejpam-3331	229	8	r+	r+	NOUN
ejpam-3331	229	9	by	by	ADP
ejpam-3331	229	10	ζ(t	ζ(t	PROPN
ejpam-3331	229	11	,	,	PUNCT
ejpam-3331	229	12	s	s	PART
ejpam-3331	229	13	)	)	PUNCT
ejpam-3331	229	14	=	=	SYM
ejpam-3331	229	15	1	1	NUM
ejpam-3331	229	16	2s	2s	NUM
ejpam-3331	229	17	−	−	NOUN
ejpam-3331	229	18	t.	t.	PROPN
ejpam-3331	229	19	let	let	VERB
ejpam-3331	229	20	x	x	PRON
ejpam-3331	229	21	,	,	PUNCT
ejpam-3331	229	22	y	y	PROPN
ejpam-3331	229	23	∈	∈	PROPN
ejpam-3331	229	24	x	x	AUX
ejpam-3331	229	25	be	be	AUX
ejpam-3331	229	26	such	such	ADJ
ejpam-3331	229	27	that	that	SCONJ
ejpam-3331	229	28	α(x	α(x	NOUN
ejpam-3331	229	29	,	,	PUNCT
ejpam-3331	229	30	y	y	PROPN
ejpam-3331	229	31	)	)	PUNCT
ejpam-3331	229	32	≥	≥	NOUN
ejpam-3331	229	33	1	1	NUM
ejpam-3331	229	34	and	and	CCONJ
ejpam-3331	229	35	β(x	β(x	PROPN
ejpam-3331	229	36	,	,	PUNCT
ejpam-3331	229	37	y	y	NOUN
ejpam-3331	229	38	)	)	PUNCT
ejpam-3331	229	39	≥	≥	NOUN
ejpam-3331	229	40	1	1	NUM
ejpam-3331	229	41	,	,	PUNCT
ejpam-3331	229	42	then	then	ADV
ejpam-3331	229	43	α(fx	α(fx	PROPN
ejpam-3331	229	44	,	,	PUNCT
ejpam-3331	229	45	fy	fy	PROPN
ejpam-3331	229	46	)	)	PUNCT
ejpam-3331	229	47	≥	≥	NOUN
ejpam-3331	229	48	1	1	NUM
ejpam-3331	229	49	and	and	CCONJ
ejpam-3331	229	50	β(fx	β(fx	PROPN
ejpam-3331	229	51	,	,	PUNCT
ejpam-3331	229	52	fy	fy	PROPN
ejpam-3331	229	53	)	)	PUNCT
ejpam-3331	229	54	≥	≥	NOUN
ejpam-3331	229	55	1	1	NUM
ejpam-3331	229	56	,	,	PUNCT
ejpam-3331	229	57	that	that	ADV
ejpam-3331	229	58	is	is	ADV
ejpam-3331	229	59	,	,	PUNCT
ejpam-3331	229	60	f	f	PROPN
ejpam-3331	229	61	is	be	AUX
ejpam-3331	229	62	(	(	PUNCT
ejpam-3331	229	63	α	α	NOUN
ejpam-3331	229	64	,	,	PUNCT
ejpam-3331	229	65	β)-admissible	β)-admissible	PUNCT
ejpam-3331	229	66	.	.	PUNCT
ejpam-3331	230	1	now	now	ADV
ejpam-3331	230	2	,	,	PUNCT
ejpam-3331	230	3	we	we	PRON
ejpam-3331	230	4	consider	consider	VERB
ejpam-3331	230	5	the	the	DET
ejpam-3331	230	6	following	follow	VERB
ejpam-3331	230	7	cases	case	NOUN
ejpam-3331	230	8	:	:	PUNCT
ejpam-3331	230	9	(	(	PUNCT
ejpam-3331	230	10	i	i	NOUN
ejpam-3331	230	11	)	)	PUNCT
ejpam-3331	230	12	case	case	NOUN
ejpam-3331	230	13	1	1	NUM
ejpam-3331	230	14	:	:	PUNCT
ejpam-3331	230	15	x	x	SYM
ejpam-3331	230	16	=	=	SYM
ejpam-3331	230	17	0	0	NUM
ejpam-3331	230	18	and	and	CCONJ
ejpam-3331	230	19	y	y	PROPN
ejpam-3331	230	20	=	=	SYM
ejpam-3331	230	21	0	0	X
ejpam-3331	230	22	.	.	PUNCT
ejpam-3331	231	1	we	we	PRON
ejpam-3331	231	2	have	have	VERB
ejpam-3331	231	3	ζ(α(0	ζ(α(0	PROPN
ejpam-3331	231	4	,	,	PUNCT
ejpam-3331	231	5	0)β(0	0)β(0	NOUN
ejpam-3331	231	6	,	,	PUNCT
ejpam-3331	231	7	0)σ(f0	0)σ(f0	PROPN
ejpam-3331	231	8	,	,	PUNCT
ejpam-3331	231	9	f0	f0	PROPN
ejpam-3331	231	10	)	)	PUNCT
ejpam-3331	231	11	,	,	PUNCT
ejpam-3331	231	12	σ(0	σ(0	PROPN
ejpam-3331	231	13	,	,	PUNCT
ejpam-3331	231	14	0	0	NUM
ejpam-3331	231	15	)	)	PUNCT
ejpam-3331	231	16	)	)	PUNCT
ejpam-3331	232	1	=	=	SYM
ejpam-3331	232	2	ζ	ζ	X
ejpam-3331	232	3	(	(	PUNCT
ejpam-3331	232	4	5	5	NUM
ejpam-3331	232	5	2	2	NUM
ejpam-3331	232	6	.1.0	.1.0	PROPN
ejpam-3331	232	7	,	,	PUNCT
ejpam-3331	232	8	0	0	NUM
ejpam-3331	232	9	)	)	PUNCT
ejpam-3331	232	10	=	=	SYM
ejpam-3331	232	11	ζ(0	ζ(0	NOUN
ejpam-3331	232	12	,	,	PUNCT
ejpam-3331	232	13	0	0	NUM
ejpam-3331	232	14	)	)	PUNCT
ejpam-3331	232	15	=	=	SYM
ejpam-3331	232	16	0	0	X
ejpam-3331	232	17	.	.	PUNCT
ejpam-3331	232	18	(	(	PUNCT
ejpam-3331	232	19	ii	ii	NOUN
ejpam-3331	232	20	)	)	PUNCT
ejpam-3331	232	21	case	case	NOUN
ejpam-3331	232	22	2	2	NUM
ejpam-3331	232	23	:	:	PUNCT
ejpam-3331	232	24	x	x	SYM
ejpam-3331	232	25	=	=	SYM
ejpam-3331	232	26	0	0	NUM
ejpam-3331	232	27	and	and	CCONJ
ejpam-3331	232	28	y	y	PROPN
ejpam-3331	232	29	=	=	SYM
ejpam-3331	232	30	1	1	X
ejpam-3331	232	31	.	.	PUNCT
ejpam-3331	233	1	here	here	ADV
ejpam-3331	233	2	,	,	PUNCT
ejpam-3331	233	3	ζ(α(0	ζ(α(0	PROPN
ejpam-3331	233	4	,	,	PUNCT
ejpam-3331	233	5	1)β(0	1)β(0	NUM
ejpam-3331	233	6	,	,	PUNCT
ejpam-3331	233	7	1)σ(f0	1)σ(f0	NUM
ejpam-3331	233	8	,	,	PUNCT
ejpam-3331	233	9	f1	f1	NOUN
ejpam-3331	233	10	)	)	PUNCT
ejpam-3331	233	11	,	,	PUNCT
ejpam-3331	233	12	σ(0	σ(0	PROPN
ejpam-3331	233	13	,	,	PUNCT
ejpam-3331	233	14	1	1	NUM
ejpam-3331	233	15	)	)	PUNCT
ejpam-3331	233	16	)	)	PUNCT
ejpam-3331	234	1	=	=	SYM
ejpam-3331	234	2	ζ	ζ	X
ejpam-3331	234	3	(	(	PUNCT
ejpam-3331	234	4	5	5	NUM
ejpam-3331	234	5	2	2	NUM
ejpam-3331	234	6	.1.0	.1.0	NOUN
ejpam-3331	234	7	,	,	PUNCT
ejpam-3331	234	8	1	1	X
ejpam-3331	234	9	)	)	PUNCT
ejpam-3331	234	10	=	=	SYM
ejpam-3331	234	11	ζ(0	ζ(0	NOUN
ejpam-3331	234	12	,	,	PUNCT
ejpam-3331	234	13	1	1	NUM
ejpam-3331	234	14	10	10	NUM
ejpam-3331	234	15	)	)	PUNCT
ejpam-3331	234	16	=	=	SYM
ejpam-3331	235	1	1	1	NUM
ejpam-3331	235	2	20	20	NUM
ejpam-3331	235	3	>	>	SYM
ejpam-3331	235	4	0	0	NUM
ejpam-3331	235	5	.	.	PUNCT
ejpam-3331	235	6	(	(	PUNCT
ejpam-3331	235	7	iii	iii	NOUN
ejpam-3331	235	8	)	)	PUNCT
ejpam-3331	235	9	case	case	NOUN
ejpam-3331	235	10	3	3	NUM
ejpam-3331	235	11	:	:	PUNCT
ejpam-3331	235	12	x	x	SYM
ejpam-3331	235	13	=	=	SYM
ejpam-3331	235	14	0	0	NUM
ejpam-3331	235	15	and	and	CCONJ
ejpam-3331	235	16	y	y	PROPN
ejpam-3331	236	1	=	=	SYM
ejpam-3331	236	2	3	3	X
ejpam-3331	236	3	.	.	X
ejpam-3331	237	1	we	we	PRON
ejpam-3331	237	2	have	have	VERB
ejpam-3331	237	3	ζ(α(0	ζ(α(0	PROPN
ejpam-3331	237	4	,	,	PUNCT
ejpam-3331	237	5	3)β(0	3)β(0	NUM
ejpam-3331	237	6	,	,	PUNCT
ejpam-3331	237	7	3)σ(f0	3)σ(f0	NOUN
ejpam-3331	237	8	,	,	PUNCT
ejpam-3331	237	9	f3	f3	NOUN
ejpam-3331	237	10	)	)	PUNCT
ejpam-3331	237	11	,	,	PUNCT
ejpam-3331	237	12	σ(0	σ(0	PROPN
ejpam-3331	237	13	,	,	PUNCT
ejpam-3331	237	14	3	3	NUM
ejpam-3331	237	15	)	)	PUNCT
ejpam-3331	237	16	)	)	PUNCT
ejpam-3331	238	1	=	=	SYM
ejpam-3331	238	2	ζ	ζ	X
ejpam-3331	238	3	(	(	PUNCT
ejpam-3331	238	4	5	5	NUM
ejpam-3331	238	5	2	2	NUM
ejpam-3331	238	6	.	.	PUNCT
ejpam-3331	238	7	1	1	NUM
ejpam-3331	238	8	10	10	NUM
ejpam-3331	238	9	,	,	PUNCT
ejpam-3331	238	10	1	1	NUM
ejpam-3331	238	11	2	2	NUM
ejpam-3331	238	12	)	)	PUNCT
ejpam-3331	238	13	=	=	SYM
ejpam-3331	238	14	ζ	ζ	NOUN
ejpam-3331	238	15	(	(	PUNCT
ejpam-3331	238	16	1	1	NUM
ejpam-3331	238	17	4	4	NUM
ejpam-3331	238	18	,	,	PUNCT
ejpam-3331	238	19	1	1	NUM
ejpam-3331	238	20	2	2	NUM
ejpam-3331	238	21	)	)	PUNCT
ejpam-3331	238	22	=	=	SYM
ejpam-3331	238	23	0	0	X
ejpam-3331	238	24	.	.	PUNCT
ejpam-3331	238	25	(	(	PUNCT
ejpam-3331	238	26	iv	iv	X
ejpam-3331	238	27	)	)	PUNCT
ejpam-3331	238	28	case	case	NOUN
ejpam-3331	238	29	4	4	NUM
ejpam-3331	238	30	:	:	PUNCT
ejpam-3331	238	31	x	x	SYM
ejpam-3331	238	32	=	=	SYM
ejpam-3331	238	33	1	1	NUM
ejpam-3331	238	34	and	and	CCONJ
ejpam-3331	238	35	y	y	NOUN
ejpam-3331	238	36	=	=	SYM
ejpam-3331	238	37	1	1	X
ejpam-3331	238	38	.	.	PUNCT
ejpam-3331	239	1	here	here	ADV
ejpam-3331	239	2	,	,	PUNCT
ejpam-3331	239	3	ζ(α(1	ζ(α(1	PROPN
ejpam-3331	239	4	,	,	PUNCT
ejpam-3331	239	5	1)β(1	1)β(1	NOUN
ejpam-3331	239	6	,	,	PUNCT
ejpam-3331	239	7	1)σ(f1	1)σ(f1	PROPN
ejpam-3331	239	8	,	,	PUNCT
ejpam-3331	239	9	f1	f1	NOUN
ejpam-3331	239	10	)	)	PUNCT
ejpam-3331	239	11	,	,	PUNCT
ejpam-3331	239	12	σ(1	σ(1	PROPN
ejpam-3331	239	13	,	,	PUNCT
ejpam-3331	239	14	1	1	NUM
ejpam-3331	239	15	)	)	PUNCT
ejpam-3331	239	16	)	)	PUNCT
ejpam-3331	240	1	=	=	SYM
ejpam-3331	240	2	ζ	ζ	X
ejpam-3331	240	3	(	(	PUNCT
ejpam-3331	240	4	5	5	NUM
ejpam-3331	240	5	2	2	NUM
ejpam-3331	240	6	.1.0	.1.0	NOUN
ejpam-3331	240	7	,	,	PUNCT
ejpam-3331	240	8	1	1	NUM
ejpam-3331	240	9	2	2	NUM
ejpam-3331	240	10	)	)	PUNCT
ejpam-3331	240	11	=	=	SYM
ejpam-3331	240	12	ζ(0	ζ(0	NOUN
ejpam-3331	240	13	,	,	PUNCT
ejpam-3331	240	14	1	1	NUM
ejpam-3331	240	15	2	2	NUM
ejpam-3331	240	16	)	)	PUNCT
ejpam-3331	240	17	=	=	SYM
ejpam-3331	240	18	1	1	NUM
ejpam-3331	240	19	4	4	NUM
ejpam-3331	240	20	>	>	SYM
ejpam-3331	240	21	0	0	NUM
ejpam-3331	240	22	.	.	PUNCT
ejpam-3331	240	23	(	(	PUNCT
ejpam-3331	240	24	v	v	NOUN
ejpam-3331	240	25	)	)	PUNCT
ejpam-3331	240	26	case	case	NOUN
ejpam-3331	240	27	5	5	NUM
ejpam-3331	240	28	:	:	PUNCT
ejpam-3331	240	29	x	x	SYM
ejpam-3331	240	30	=	=	SYM
ejpam-3331	240	31	1	1	NUM
ejpam-3331	240	32	and	and	CCONJ
ejpam-3331	240	33	y	y	NOUN
ejpam-3331	240	34	=	=	SYM
ejpam-3331	240	35	3	3	X
ejpam-3331	240	36	.	.	X
ejpam-3331	241	1	we	we	PRON
ejpam-3331	241	2	have	have	VERB
ejpam-3331	241	3	ζ(α(1	ζ(α(1	NOUN
ejpam-3331	241	4	,	,	PUNCT
ejpam-3331	241	5	3)β(1	3)β(1	NUM
ejpam-3331	241	6	,	,	PUNCT
ejpam-3331	241	7	3)σ(f1	3)σ(f1	ADJ
ejpam-3331	241	8	,	,	PUNCT
ejpam-3331	241	9	f3	f3	ADJ
ejpam-3331	241	10	)	)	PUNCT
ejpam-3331	241	11	,	,	PUNCT
ejpam-3331	241	12	σ(1	σ(1	PROPN
ejpam-3331	241	13	,	,	PUNCT
ejpam-3331	241	14	3	3	NUM
ejpam-3331	241	15	)	)	PUNCT
ejpam-3331	241	16	)	)	PUNCT
ejpam-3331	242	1	=	=	SYM
ejpam-3331	242	2	ζ	ζ	X
ejpam-3331	242	3	(	(	PUNCT
ejpam-3331	242	4	5	5	NUM
ejpam-3331	242	5	2	2	NUM
ejpam-3331	242	6	.1	.1	NOUN
ejpam-3331	242	7	.	.	PUNCT
ejpam-3331	243	1	1	1	NUM
ejpam-3331	243	2	10	10	NUM
ejpam-3331	243	3	,	,	PUNCT
ejpam-3331	243	4	2	2	NUM
ejpam-3331	243	5	3	3	NUM
ejpam-3331	243	6	)	)	PUNCT
ejpam-3331	244	1	=	=	SYM
ejpam-3331	244	2	ζ	ζ	X
ejpam-3331	244	3	(	(	PUNCT
ejpam-3331	244	4	1	1	NUM
ejpam-3331	244	5	4	4	NUM
ejpam-3331	244	6	,	,	PUNCT
ejpam-3331	244	7	2	2	NUM
ejpam-3331	244	8	3	3	NUM
ejpam-3331	244	9	)	)	PUNCT
ejpam-3331	244	10	=	=	SYM
ejpam-3331	245	1	1	1	NUM
ejpam-3331	245	2	12	12	NUM
ejpam-3331	245	3	>	>	SYM
ejpam-3331	245	4	0	0	NUM
ejpam-3331	245	5	.	.	PUNCT
ejpam-3331	245	6	(	(	PUNCT
ejpam-3331	245	7	vi	vi	NOUN
ejpam-3331	245	8	)	)	PUNCT
ejpam-3331	245	9	case	case	NOUN
ejpam-3331	245	10	6	6	NUM
ejpam-3331	245	11	:	:	SYM
ejpam-3331	245	12	x	x	SYM
ejpam-3331	245	13	=	=	SYM
ejpam-3331	245	14	3	3	NUM
ejpam-3331	245	15	and	and	CCONJ
ejpam-3331	245	16	y	y	NOUN
ejpam-3331	245	17	=	=	SYM
ejpam-3331	245	18	3	3	X
ejpam-3331	245	19	.	.	PUNCT
ejpam-3331	246	1	here	here	ADV
ejpam-3331	246	2	,	,	PUNCT
ejpam-3331	246	3	ζ(α(3	ζ(α(3	NOUN
ejpam-3331	246	4	,	,	PUNCT
ejpam-3331	246	5	3)β(3	3)β(3	NUM
ejpam-3331	246	6	,	,	PUNCT
ejpam-3331	246	7	3)σ(f3	3)σ(f3	NUM
ejpam-3331	246	8	,	,	PUNCT
ejpam-3331	246	9	f3	f3	NOUN
ejpam-3331	246	10	)	)	PUNCT
ejpam-3331	246	11	,	,	PUNCT
ejpam-3331	246	12	σ(3	σ(3	PROPN
ejpam-3331	246	13	,	,	PUNCT
ejpam-3331	246	14	3	3	NUM
ejpam-3331	246	15	)	)	PUNCT
ejpam-3331	246	16	)	)	PUNCT
ejpam-3331	247	1	=	=	SYM
ejpam-3331	247	2	ζ	ζ	X
ejpam-3331	247	3	(	(	PUNCT
ejpam-3331	247	4	5	5	NUM
ejpam-3331	247	5	2	2	NUM
ejpam-3331	247	6	.1	.1	NOUN
ejpam-3331	247	7	.	.	PUNCT
ejpam-3331	248	1	1	1	NUM
ejpam-3331	248	2	2	2	NUM
ejpam-3331	248	3	,	,	PUNCT
ejpam-3331	248	4	7	7	NUM
ejpam-3331	248	5	2	2	NUM
ejpam-3331	248	6	)	)	PUNCT
ejpam-3331	248	7	=	=	SYM
ejpam-3331	249	1	ζ	ζ	NOUN
ejpam-3331	249	2	(	(	PUNCT
ejpam-3331	249	3	5	5	NUM
ejpam-3331	249	4	4	4	NUM
ejpam-3331	249	5	,	,	PUNCT
ejpam-3331	249	6	7	7	NUM
ejpam-3331	249	7	2	2	NUM
ejpam-3331	249	8	)	)	PUNCT
ejpam-3331	249	9	=	=	SYM
ejpam-3331	250	1	1	1	NUM
ejpam-3331	250	2	2	2	NUM
ejpam-3331	250	3	>	>	SYM
ejpam-3331	250	4	0	0	NUM
ejpam-3331	250	5	.	.	PUNCT
ejpam-3331	251	1	thus	thus	ADV
ejpam-3331	251	2	,	,	PUNCT
ejpam-3331	251	3	f	f	PROPN
ejpam-3331	251	4	is	be	AUX
ejpam-3331	251	5	an	an	DET
ejpam-3331	251	6	(	(	PUNCT
ejpam-3331	251	7	α	α	NOUN
ejpam-3331	251	8	,	,	PUNCT
ejpam-3331	251	9	β)-admissible	β)-admissible	PUNCT
ejpam-3331	251	10	z	z	NOUN
ejpam-3331	251	11	-	-	PUNCT
ejpam-3331	251	12	contraction	contraction	NOUN
ejpam-3331	251	13	with	with	ADP
ejpam-3331	251	14	respect	respect	NOUN
ejpam-3331	251	15	to	to	ADP
ejpam-3331	251	16	ζ	ζ	NOUN
ejpam-3331	251	17	.	.	PUNCT
ejpam-3331	252	1	hence	hence	ADV
ejpam-3331	252	2	all	all	DET
ejpam-3331	252	3	conditions	condition	NOUN
ejpam-3331	252	4	of	of	ADP
ejpam-3331	252	5	theorem	theorem	ADJ
ejpam-3331	252	6	2	2	NUM
ejpam-3331	252	7	are	be	AUX
ejpam-3331	252	8	satisfied	satisfied	ADJ
ejpam-3331	252	9	and	and	CCONJ
ejpam-3331	252	10	f	f	PROPN
ejpam-3331	252	11	has	have	VERB
ejpam-3331	252	12	a	a	DET
ejpam-3331	252	13	unique	unique	ADJ
ejpam-3331	252	14	fixed	fix	VERB
ejpam-3331	252	15	point	point	NOUN
ejpam-3331	252	16	,	,	PUNCT
ejpam-3331	252	17	which	which	PRON
ejpam-3331	252	18	is	be	AUX
ejpam-3331	252	19	,	,	PUNCT
ejpam-3331	252	20	u	u	NOUN
ejpam-3331	252	21	=	=	PROPN
ejpam-3331	252	22	0	0	PROPN
ejpam-3331	252	23	.	.	PUNCT
ejpam-3331	253	1	references	reference	NOUN
ejpam-3331	253	2	98	98	NUM
ejpam-3331	253	3	acknowledgements	acknowledgement	NOUN
ejpam-3331	253	4	the	the	DET
ejpam-3331	253	5	authors	author	NOUN
ejpam-3331	253	6	would	would	AUX
ejpam-3331	253	7	like	like	VERB
ejpam-3331	253	8	to	to	PART
ejpam-3331	253	9	acknowledge	acknowledge	VERB
ejpam-3331	253	10	the	the	DET
ejpam-3331	253	11	grant	grant	NOUN
ejpam-3331	253	12	:	:	PUNCT
ejpam-3331	253	13	ukm	ukm	PROPN
ejpam-3331	253	14	grant	grant	PROPN
ejpam-3331	253	15	dip-2017	dip-2017	PROPN
ejpam-3331	253	16	-	-	PUNCT
ejpam-3331	253	17	011	011	NUM
ejpam-3331	253	18	and	and	CCONJ
ejpam-3331	253	19	ministry	ministry	PROPN
ejpam-3331	253	20	of	of	ADP
ejpam-3331	253	21	education	education	PROPN
ejpam-3331	253	22	,	,	PUNCT
ejpam-3331	253	23	malaysia	malaysia	PROPN
ejpam-3331	253	24	grant	grant	NOUN
ejpam-3331	253	25	frgs/1/2017	frgs/1/2017	NOUN
ejpam-3331	253	26	/	/	SYM
ejpam-3331	253	27	stg06	stg06	NOUN
ejpam-3331	253	28	/	/	SYM
ejpam-3331	253	29	ukm/01/1	ukm/01/1	NOUN
ejpam-3331	253	30	for	for	ADP
ejpam-3331	253	31	financial	financial	ADJ
ejpam-3331	253	32	support	support	NOUN
ejpam-3331	253	33	.	.	PUNCT
ejpam-3331	254	1	competing	compete	VERB
ejpam-3331	254	2	interests	interest	NOUN
ejpam-3331	254	3	the	the	DET
ejpam-3331	254	4	authors	author	NOUN
ejpam-3331	254	5	declare	declare	VERB
ejpam-3331	254	6	that	that	SCONJ
ejpam-3331	254	7	they	they	PRON
ejpam-3331	254	8	have	have	VERB
ejpam-3331	254	9	no	no	DET
ejpam-3331	254	10	competing	compete	VERB
ejpam-3331	254	11	interests	interest	NOUN
ejpam-3331	254	12	.	.	PUNCT
ejpam-3331	255	1	authors	author	NOUN
ejpam-3331	255	2	’	'	PUNCT
ejpam-3331	255	3	contributions	contribution	NOUN
ejpam-3331	255	4	all	all	DET
ejpam-3331	255	5	authors	author	NOUN
ejpam-3331	255	6	read	read	VERB
ejpam-3331	255	7	and	and	CCONJ
ejpam-3331	255	8	approved	approve	VERB
ejpam-3331	255	9	the	the	DET
ejpam-3331	255	10	manuscript	manuscript	NOUN
ejpam-3331	255	11	.	.	PUNCT
ejpam-3331	256	1	references	reference	NOUN
ejpam-3331	256	2	[	[	X
ejpam-3331	256	3	1	1	NUM
ejpam-3331	256	4	]	]	PUNCT
ejpam-3331	256	5	h.	h.	PROPN
ejpam-3331	256	6	alsamir	alsamir	PROPN
ejpam-3331	256	7	,	,	PUNCT
ejpam-3331	256	8	m.s.m	m.s.m	PROPN
ejpam-3331	256	9	.	.	PROPN
ejpam-3331	256	10	noorani	noorani	PROPN
ejpam-3331	256	11	,	,	PUNCT
ejpam-3331	256	12	w.	w.	PROPN
ejpam-3331	256	13	shatanawi	shatanawi	PROPN
ejpam-3331	256	14	,	,	PUNCT
ejpam-3331	256	15	on	on	ADP
ejpam-3331	256	16	new	new	ADJ
ejpam-3331	256	17	fixed	fix	VERB
ejpam-3331	256	18	point	point	NOUN
ejpam-3331	256	19	theorems	theorem	NOUN
ejpam-3331	256	20	for	for	ADP
ejpam-3331	256	21	three	three	NUM
ejpam-3331	256	22	types	type	NOUN
ejpam-3331	256	23	of	of	ADP
ejpam-3331	256	24	(	(	PUNCT
ejpam-3331	256	25	α	α	NOUN
ejpam-3331	256	26	,	,	PUNCT
ejpam-3331	256	27	β	β	NOUN
ejpam-3331	256	28	)	)	PUNCT
ejpam-3331	256	29	−	−	PROPN
ejpam-3331	256	30	(	(	PUNCT
ejpam-3331	256	31	ψ	ψ	X
ejpam-3331	256	32	,	,	PUNCT
ejpam-3331	256	33	θ	θ	PROPN
ejpam-3331	256	34	,	,	PUNCT
ejpam-3331	256	35	φ)-multivalued	φ)-multivalue	VERB
ejpam-3331	256	36	contractive	contractive	ADJ
ejpam-3331	256	37	mappings	mapping	NOUN
ejpam-3331	256	38	in	in	ADP
ejpam-3331	256	39	metric	metric	ADJ
ejpam-3331	256	40	spaces	space	NOUN
ejpam-3331	256	41	,	,	PUNCT
ejpam-3331	256	42	cogent	cogent	NOUN
ejpam-3331	256	43	mathematics	mathematic	NOUN
ejpam-3331	256	44	,	,	PUNCT
ejpam-3331	256	45	3(1	3(1	NUM
ejpam-3331	256	46	)	)	PUNCT
ejpam-3331	256	47	,	,	PUNCT
ejpam-3331	256	48	1257473	1257473	NUM
ejpam-3331	256	49	.	.	PUNCT
ejpam-3331	257	1	[	[	X
ejpam-3331	257	2	2	2	NUM
ejpam-3331	257	3	]	]	PUNCT
ejpam-3331	257	4	h.	h.	PROPN
ejpam-3331	257	5	alsamir	alsamir	PROPN
ejpam-3331	257	6	,	,	PUNCT
ejpam-3331	257	7	m.s.m	m.s.m	PROPN
ejpam-3331	257	8	.	.	PROPN
ejpam-3331	257	9	noorani	noorani	PROPN
ejpam-3331	257	10	,	,	PUNCT
ejpam-3331	257	11	w.	w.	PROPN
ejpam-3331	257	12	shatanawi	shatanawi	PROPN
ejpam-3331	257	13	,	,	PUNCT
ejpam-3331	257	14	on	on	ADP
ejpam-3331	257	15	fixed	fix	VERB
ejpam-3331	257	16	points	point	NOUN
ejpam-3331	257	17	of	of	ADP
ejpam-3331	257	18	(	(	PUNCT
ejpam-3331	257	19	η	η	PROPN
ejpam-3331	257	20	,	,	PUNCT
ejpam-3331	257	21	θ)-quasicontraction	θ)-quasicontraction	NUM
ejpam-3331	257	22	mappings	mapping	NOUN
ejpam-3331	257	23	in	in	ADP
ejpam-3331	257	24	generalized	generalized	ADJ
ejpam-3331	257	25	metric	metric	ADJ
ejpam-3331	257	26	spaces	space	NOUN
ejpam-3331	257	27	,	,	PUNCT
ejpam-3331	257	28	j.	j.	PROPN
ejpam-3331	257	29	nonlinear	nonlinear	PROPN
ejpam-3331	257	30	sci	sci	PROPN
ejpam-3331	257	31	.	.	PUNCT
ejpam-3331	257	32	appl	appl	PROPN
ejpam-3331	257	33	.	.	PROPN
ejpam-3331	258	1	9	9	NUM
ejpam-3331	258	2	(	(	PUNCT
ejpam-3331	258	3	2016	2016	NUM
ejpam-3331	258	4	)	)	PUNCT
ejpam-3331	258	5	,	,	PUNCT
ejpam-3331	258	6	4651	4651	NUM
ejpam-3331	258	7	-	-	SYM
ejpam-3331	258	8	4658	4658	NUM
ejpam-3331	258	9	.	.	PUNCT
ejpam-3331	259	1	[	[	X
ejpam-3331	259	2	3	3	X
ejpam-3331	259	3	]	]	X
ejpam-3331	259	4	h.h	h.h	PROPN
ejpam-3331	259	5	.	.	PROPN
ejpam-3331	259	6	alsulami	alsulami	PROPN
ejpam-3331	259	7	,	,	PUNCT
ejpam-3331	259	8	e.	e.	PROPN
ejpam-3331	259	9	karapinar	karapinar	PROPN
ejpam-3331	259	10	,	,	PUNCT
ejpam-3331	259	11	f.	f.	PROPN
ejpam-3331	259	12	khojasteh	khojasteh	PROPN
ejpam-3331	259	13	,	,	PUNCT
ejpam-3331	259	14	a.f	a.f	PROPN
ejpam-3331	259	15	.	.	PUNCT
ejpam-3331	259	16	roldan	roldan	PROPN
ejpam-3331	259	17	-	-	PUNCT
ejpam-3331	259	18	lopez	lopez	PROPN
ejpam-3331	259	19	-	-	PUNCT
ejpam-3331	259	20	de	de	NOUN
ejpam-3331	259	21	-	-	NOUN
ejpam-3331	259	22	hierro	hierro	ADJ
ejpam-3331	259	23	,	,	PUNCT
ejpam-3331	259	24	a	a	DET
ejpam-3331	259	25	proposal	proposal	NOUN
ejpam-3331	259	26	to	to	ADP
ejpam-3331	259	27	the	the	DET
ejpam-3331	259	28	study	study	NOUN
ejpam-3331	259	29	of	of	ADP
ejpam-3331	259	30	contractions	contraction	NOUN
ejpam-3331	259	31	in	in	ADP
ejpam-3331	259	32	quasi	quasi	ADJ
ejpam-3331	259	33	-	-	ADJ
ejpam-3331	259	34	metric	metric	ADJ
ejpam-3331	259	35	spaces	space	NOUN
ejpam-3331	259	36	,	,	PUNCT
ejpam-3331	259	37	discrete	discrete	ADJ
ejpam-3331	259	38	dynamics	dynamic	NOUN
ejpam-3331	259	39	in	in	ADP
ejpam-3331	259	40	nature	nature	NOUN
ejpam-3331	259	41	and	and	CCONJ
ejpam-3331	259	42	society	society	NOUN
ejpam-3331	259	43	,	,	PUNCT
ejpam-3331	259	44	article	article	NOUN
ejpam-3331	259	45	i	i	PROPN
ejpam-3331	259	46	d	d	PROPN
ejpam-3331	259	47	269286	269286	NUM
ejpam-3331	259	48	,	,	PUNCT
ejpam-3331	259	49	10	10	NUM
ejpam-3331	259	50	pages	page	NOUN
ejpam-3331	259	51	(	(	PUNCT
ejpam-3331	259	52	2014	2014	NUM
ejpam-3331	259	53	)	)	PUNCT
ejpam-3331	259	54	.	.	PUNCT
ejpam-3331	260	1	[	[	X
ejpam-3331	260	2	4	4	X
ejpam-3331	260	3	]	]	X
ejpam-3331	260	4	h.	h.	PROPN
ejpam-3331	260	5	argoubi	argoubi	PROPN
ejpam-3331	260	6	,	,	PUNCT
ejpam-3331	260	7	b.	b.	PROPN
ejpam-3331	260	8	samet	samet	PROPN
ejpam-3331	260	9	,	,	PUNCT
ejpam-3331	260	10	c.	c.	PROPN
ejpam-3331	260	11	vetro	vetro	PROPN
ejpam-3331	260	12	,	,	PUNCT
ejpam-3331	260	13	nonlinear	nonlinear	ADJ
ejpam-3331	260	14	contractions	contraction	NOUN
ejpam-3331	260	15	involving	involve	VERB
ejpam-3331	260	16	simulation	simulation	NOUN
ejpam-3331	260	17	functions	function	NOUN
ejpam-3331	260	18	in	in	ADP
ejpam-3331	260	19	a	a	DET
ejpam-3331	260	20	metric	metric	ADJ
ejpam-3331	260	21	space	space	NOUN
ejpam-3331	260	22	with	with	ADP
ejpam-3331	260	23	a	a	DET
ejpam-3331	260	24	partial	partial	ADJ
ejpam-3331	260	25	order	order	NOUN
ejpam-3331	260	26	,	,	PUNCT
ejpam-3331	260	27	j.	j.	PROPN
ejpam-3331	260	28	nonlinear	nonlinear	PROPN
ejpam-3331	260	29	sci	sci	PROPN
ejpam-3331	260	30	.	.	PUNCT
ejpam-3331	260	31	appl	appl	PROPN
ejpam-3331	260	32	.	.	PROPN
ejpam-3331	260	33	8	8	NUM
ejpam-3331	260	34	(	(	PUNCT
ejpam-3331	260	35	2015	2015	NUM
ejpam-3331	260	36	)	)	PUNCT
ejpam-3331	260	37	,	,	PUNCT
ejpam-3331	260	38	1082	1082	NUM
ejpam-3331	260	39	-	-	SYM
ejpam-3331	260	40	1094	1094	NUM
ejpam-3331	260	41	.	.	PUNCT
ejpam-3331	261	1	[	[	X
ejpam-3331	261	2	5	5	X
ejpam-3331	261	3	]	]	X
ejpam-3331	261	4	h.	h.	PROPN
ejpam-3331	261	5	aydi	aydi	PROPN
ejpam-3331	261	6	,	,	PUNCT
ejpam-3331	261	7	a.	a.	PROPN
ejpam-3331	261	8	felhi	felhi	PROPN
ejpam-3331	261	9	,	,	PUNCT
ejpam-3331	261	10	e.	e.	PROPN
ejpam-3331	261	11	karapinar	karapinar	PROPN
ejpam-3331	261	12	,	,	PUNCT
ejpam-3331	261	13	s.	s.	PROPN
ejpam-3331	261	14	sahmim	sahmim	PROPN
ejpam-3331	261	15	,	,	PUNCT
ejpam-3331	261	16	a	a	DET
ejpam-3331	261	17	nadler	nadler	NOUN
ejpam-3331	261	18	-	-	PUNCT
ejpam-3331	261	19	type	type	NOUN
ejpam-3331	261	20	fixed	fix	VERB
ejpam-3331	261	21	point	point	NOUN
ejpam-3331	261	22	theorem	theorem	VERB
ejpam-3331	261	23	in	in	ADP
ejpam-3331	261	24	dislocated	dislocate	VERB
ejpam-3331	261	25	spaces	space	NOUN
ejpam-3331	261	26	and	and	CCONJ
ejpam-3331	261	27	applications	application	NOUN
ejpam-3331	261	28	,	,	PUNCT
ejpam-3331	261	29	miscolc	miscolc	NOUN
ejpam-3331	261	30	math	math	NOUN
ejpam-3331	261	31	.	.	PUNCT
ejpam-3331	262	1	notes	note	NOUN
ejpam-3331	262	2	,	,	PUNCT
ejpam-3331	262	3	19	19	NUM
ejpam-3331	262	4	(	(	PUNCT
ejpam-3331	262	5	1	1	NUM
ejpam-3331	262	6	)	)	PUNCT
ejpam-3331	262	7	,	,	PUNCT
ejpam-3331	262	8	(	(	PUNCT
ejpam-3331	262	9	2018	2018	NUM
ejpam-3331	262	10	)	)	PUNCT
ejpam-3331	262	11	,	,	PUNCT
ejpam-3331	262	12	111	111	NUM
ejpam-3331	262	13	-	-	SYM
ejpam-3331	262	14	124	124	NUM
ejpam-3331	262	15	.	.	PUNCT
ejpam-3331	263	1	[	[	X
ejpam-3331	263	2	6	6	NUM
ejpam-3331	263	3	]	]	X
ejpam-3331	263	4	h.	h.	PROPN
ejpam-3331	263	5	aydi	aydi	PROPN
ejpam-3331	263	6	,	,	PUNCT
ejpam-3331	263	7	a.	a.	PROPN
ejpam-3331	263	8	felhi	felhi	PROPN
ejpam-3331	263	9	,	,	PUNCT
ejpam-3331	263	10	best	good	ADJ
ejpam-3331	263	11	proximity	proximity	NOUN
ejpam-3331	263	12	points	point	NOUN
ejpam-3331	263	13	for	for	ADP
ejpam-3331	263	14	cyclic	cyclic	PROPN
ejpam-3331	263	15	kannan	kannan	PROPN
ejpam-3331	263	16	-	-	PUNCT
ejpam-3331	263	17	chatterjeaciric	chatterjeaciric	PROPN
ejpam-3331	263	18	type	type	NOUN
ejpam-3331	263	19	contractions	contraction	NOUN
ejpam-3331	263	20	on	on	ADP
ejpam-3331	263	21	metric	metric	ADJ
ejpam-3331	263	22	-	-	PUNCT
ejpam-3331	263	23	like	like	ADJ
ejpam-3331	263	24	spaces	space	NOUN
ejpam-3331	263	25	,	,	PUNCT
ejpam-3331	263	26	j.	j.	PROPN
ejpam-3331	263	27	nonlinear	nonlinear	PROPN
ejpam-3331	263	28	sci	sci	PROPN
ejpam-3331	263	29	.	.	PUNCT
ejpam-3331	263	30	appl	appl	PROPN
ejpam-3331	263	31	.	.	PROPN
ejpam-3331	264	1	9	9	NUM
ejpam-3331	264	2	(	(	PUNCT
ejpam-3331	264	3	2016	2016	NUM
ejpam-3331	264	4	)	)	PUNCT
ejpam-3331	264	5	,	,	PUNCT
ejpam-3331	264	6	2458	2458	NUM
ejpam-3331	264	7	-	-	SYM
ejpam-3331	264	8	2466	2466	NUM
ejpam-3331	264	9	.	.	PUNCT
ejpam-3331	265	1	[	[	X
ejpam-3331	265	2	7	7	X
ejpam-3331	265	3	]	]	X
ejpam-3331	265	4	h.	h.	PROPN
ejpam-3331	265	5	aydi	aydi	PROPN
ejpam-3331	265	6	,	,	PUNCT
ejpam-3331	265	7	a.	a.	NOUN
ejpam-3331	265	8	felhi	felhi	PROPN
ejpam-3331	265	9	,	,	PUNCT
ejpam-3331	265	10	on	on	ADP
ejpam-3331	265	11	best	good	ADJ
ejpam-3331	265	12	proximity	proximity	NOUN
ejpam-3331	265	13	points	point	NOUN
ejpam-3331	265	14	for	for	ADP
ejpam-3331	265	15	various	various	ADJ
ejpam-3331	265	16	α	α	ADJ
ejpam-3331	265	17	-	-	ADJ
ejpam-3331	265	18	proximal	proximal	ADJ
ejpam-3331	265	19	contractions	contraction	NOUN
ejpam-3331	265	20	on	on	ADP
ejpam-3331	265	21	metric	metric	ADJ
ejpam-3331	265	22	-	-	PUNCT
ejpam-3331	265	23	like	like	ADJ
ejpam-3331	265	24	spaces	space	NOUN
ejpam-3331	265	25	,	,	PUNCT
ejpam-3331	265	26	journal	journal	NOUN
ejpam-3331	265	27	of	of	ADP
ejpam-3331	265	28	nonlinear	nonlinear	PROPN
ejpam-3331	265	29	sciences	sciences	PROPN
ejpam-3331	265	30	appl	appl	NOUN
ejpam-3331	265	31	.	.	PUNCT
ejpam-3331	265	32	9	9	NUM
ejpam-3331	265	33	(	(	PUNCT
ejpam-3331	265	34	2016	2016	NUM
ejpam-3331	265	35	)	)	PUNCT
ejpam-3331	265	36	,	,	PUNCT
ejpam-3331	265	37	5202	5202	NUM
ejpam-3331	265	38	-	-	SYM
ejpam-3331	265	39	5218	5218	NUM
ejpam-3331	265	40	.	.	PUNCT
ejpam-3331	266	1	[	[	X
ejpam-3331	266	2	8	8	NUM
ejpam-3331	266	3	]	]	X
ejpam-3331	266	4	h.	h.	PROPN
ejpam-3331	266	5	aydi	aydi	PROPN
ejpam-3331	266	6	,	,	PUNCT
ejpam-3331	266	7	a.	a.	PROPN
ejpam-3331	266	8	felhi	felhi	PROPN
ejpam-3331	266	9	,	,	PUNCT
ejpam-3331	266	10	h.	h.	PROPN
ejpam-3331	266	11	afshari	afshari	PROPN
ejpam-3331	266	12	,	,	PUNCT
ejpam-3331	266	13	new	new	ADJ
ejpam-3331	266	14	geraghty	geraghty	VERB
ejpam-3331	266	15	type	type	NOUN
ejpam-3331	266	16	contractions	contraction	NOUN
ejpam-3331	266	17	on	on	ADP
ejpam-3331	266	18	metric	metric	ADJ
ejpam-3331	266	19	-	-	PUNCT
ejpam-3331	266	20	like	like	ADJ
ejpam-3331	266	21	spaces	space	NOUN
ejpam-3331	266	22	,	,	PUNCT
ejpam-3331	266	23	j.	j.	PROPN
ejpam-3331	266	24	nonlinear	nonlinear	PROPN
ejpam-3331	266	25	sci	sci	PROPN
ejpam-3331	266	26	.	.	PUNCT
ejpam-3331	266	27	appl	appl	PROPN
ejpam-3331	266	28	.	.	PROPN
ejpam-3331	267	1	10	10	NUM
ejpam-3331	267	2	(	(	PUNCT
ejpam-3331	267	3	2017	2017	NUM
ejpam-3331	267	4	)	)	PUNCT
ejpam-3331	267	5	,	,	PUNCT
ejpam-3331	267	6	780	780	NUM
ejpam-3331	267	7	-	-	SYM
ejpam-3331	267	8	788	788	NUM
ejpam-3331	267	9	.	.	PUNCT
ejpam-3331	268	1	[	[	X
ejpam-3331	268	2	9	9	NUM
ejpam-3331	268	3	]	]	X
ejpam-3331	268	4	h.	h.	PROPN
ejpam-3331	268	5	aydi	aydi	PROPN
ejpam-3331	268	6	,	,	PUNCT
ejpam-3331	268	7	a.	a.	PROPN
ejpam-3331	268	8	felhi	felhi	PROPN
ejpam-3331	268	9	,	,	PUNCT
ejpam-3331	268	10	s.	s.	PROPN
ejpam-3331	268	11	sahmim	sahmim	PROPN
ejpam-3331	268	12	,	,	PUNCT
ejpam-3331	268	13	on	on	ADP
ejpam-3331	268	14	common	common	ADJ
ejpam-3331	268	15	fixed	fix	VERB
ejpam-3331	268	16	points	point	NOUN
ejpam-3331	268	17	for	for	ADP
ejpam-3331	268	18	(	(	PUNCT
ejpam-3331	268	19	α	α	NOUN
ejpam-3331	268	20	,	,	PUNCT
ejpam-3331	268	21	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3331	268	22	and	and	CCONJ
ejpam-3331	268	23	generalized	generalize	VERB
ejpam-3331	268	24	cyclic	cyclic	ADJ
ejpam-3331	268	25	contractions	contraction	NOUN
ejpam-3331	268	26	in	in	ADP
ejpam-3331	268	27	b	b	NOUN
ejpam-3331	268	28	-	-	PUNCT
ejpam-3331	268	29	metric	metric	ADJ
ejpam-3331	268	30	-	-	PUNCT
ejpam-3331	268	31	like	like	ADJ
ejpam-3331	268	32	spaces	space	NOUN
ejpam-3331	268	33	and	and	CCONJ
ejpam-3331	268	34	consequences	consequence	NOUN
ejpam-3331	268	35	,	,	PUNCT
ejpam-3331	268	36	j.	j.	PROPN
ejpam-3331	268	37	nonlinear	nonlinear	PROPN
ejpam-3331	268	38	sci	sci	PROPN
ejpam-3331	268	39	.	.	PUNCT
ejpam-3331	268	40	appl	appl	PROPN
ejpam-3331	268	41	.	.	PROPN
ejpam-3331	269	1	9	9	NUM
ejpam-3331	269	2	(	(	PUNCT
ejpam-3331	269	3	2016	2016	NUM
ejpam-3331	269	4	)	)	PUNCT
ejpam-3331	269	5	,	,	PUNCT
ejpam-3331	269	6	2492	2492	NUM
ejpam-3331	269	7	-	-	SYM
ejpam-3331	269	8	2510	2510	NUM
ejpam-3331	269	9	.	.	PUNCT
ejpam-3331	270	1	references	reference	NOUN
ejpam-3331	270	2	99	99	NUM
ejpam-3331	271	1	[	[	X
ejpam-3331	271	2	10	10	NUM
ejpam-3331	271	3	]	]	X
ejpam-3331	271	4	h.	h.	PROPN
ejpam-3331	271	5	aydi	aydi	PROPN
ejpam-3331	271	6	,	,	PUNCT
ejpam-3331	271	7	a.	a.	PROPN
ejpam-3331	271	8	felhi	felhi	PROPN
ejpam-3331	271	9	,	,	PUNCT
ejpam-3331	271	10	s.	s.	PROPN
ejpam-3331	271	11	sahmim	sahmim	PROPN
ejpam-3331	271	12	,	,	PUNCT
ejpam-3331	271	13	common	common	ADJ
ejpam-3331	271	14	fixed	fix	VERB
ejpam-3331	271	15	points	point	NOUN
ejpam-3331	271	16	via	via	ADP
ejpam-3331	271	17	implicit	implicit	ADJ
ejpam-3331	271	18	contractions	contraction	NOUN
ejpam-3331	271	19	on	on	ADP
ejpam-3331	271	20	b	b	X
ejpam-3331	271	21	-	-	PUNCT
ejpam-3331	271	22	metric	metric	ADJ
ejpam-3331	271	23	-	-	PUNCT
ejpam-3331	271	24	like	like	ADJ
ejpam-3331	271	25	spaces	space	NOUN
ejpam-3331	271	26	,	,	PUNCT
ejpam-3331	271	27	j.	j.	PROPN
ejpam-3331	271	28	nonlinear	nonlinear	PROPN
ejpam-3331	271	29	sci	sci	PROPN
ejpam-3331	271	30	.	.	PUNCT
ejpam-3331	271	31	appl	appl	PROPN
ejpam-3331	271	32	.	.	PROPN
ejpam-3331	272	1	10	10	NUM
ejpam-3331	272	2	(	(	PUNCT
ejpam-3331	272	3	2017	2017	NUM
ejpam-3331	272	4	)	)	PUNCT
ejpam-3331	272	5	,	,	PUNCT
ejpam-3331	272	6	1524	1524	NUM
ejpam-3331	272	7	-	-	SYM
ejpam-3331	272	8	1537	1537	NUM
ejpam-3331	272	9	.	.	PUNCT
ejpam-3331	273	1	[	[	X
ejpam-3331	273	2	11	11	NUM
ejpam-3331	273	3	]	]	X
ejpam-3331	273	4	h.	h.	PROPN
ejpam-3331	273	5	aydi	aydi	PROPN
ejpam-3331	273	6	,	,	PUNCT
ejpam-3331	273	7	e.	e.	PROPN
ejpam-3331	273	8	karapinar	karapinar	PROPN
ejpam-3331	273	9	,	,	PUNCT
ejpam-3331	273	10	and	and	CCONJ
ejpam-3331	273	11	b.	b.	PROPN
ejpam-3331	273	12	samet	samet	PROPN
ejpam-3331	273	13	,	,	PUNCT
ejpam-3331	273	14	fixed	fix	VERB
ejpam-3331	273	15	points	point	NOUN
ejpam-3331	273	16	for	for	ADP
ejpam-3331	273	17	generalized	generalized	ADJ
ejpam-3331	273	18	(	(	PUNCT
ejpam-3331	273	19	α	α	NOUN
ejpam-3331	273	20	,	,	PUNCT
ejpam-3331	273	21	ψ)-contractions	ψ)-contraction	NOUN
ejpam-3331	273	22	on	on	ADP
ejpam-3331	273	23	generalized	generalized	ADJ
ejpam-3331	273	24	metric	metric	ADJ
ejpam-3331	273	25	spaces	space	NOUN
ejpam-3331	273	26	,	,	PUNCT
ejpam-3331	273	27	journal	journal	NOUN
ejpam-3331	273	28	of	of	ADP
ejpam-3331	273	29	inequalities	inequality	NOUN
ejpam-3331	273	30	and	and	CCONJ
ejpam-3331	273	31	applications	application	NOUN
ejpam-3331	273	32	,	,	PUNCT
ejpam-3331	273	33	vol	vol	NOUN
ejpam-3331	273	34	.	.	PROPN
ejpam-3331	273	35	2014	2014	NUM
ejpam-3331	273	36	,	,	PUNCT
ejpam-3331	273	37	article	article	NOUN
ejpam-3331	273	38	229	229	NUM
ejpam-3331	273	39	,	,	PUNCT
ejpam-3331	273	40	2014	2014	NUM
ejpam-3331	273	41	.	.	PUNCT
ejpam-3331	274	1	[	[	X
ejpam-3331	274	2	12	12	NUM
ejpam-3331	274	3	]	]	X
ejpam-3331	274	4	s.	s.	PROPN
ejpam-3331	274	5	banach	banach	PROPN
ejpam-3331	274	6	,	,	PUNCT
ejpam-3331	274	7	sur	sur	PROPN
ejpam-3331	274	8	les	les	X
ejpam-3331	274	9	opérations	opération	NOUN
ejpam-3331	274	10	dans	dan	NOUN
ejpam-3331	274	11	les	les	X
ejpam-3331	274	12	ensembles	ensemble	NOUN
ejpam-3331	274	13	abstraits	abstrait	NOUN
ejpam-3331	274	14	et	et	PROPN
ejpam-3331	274	15	leur	leur	X
ejpam-3331	274	16	application	application	PROPN
ejpam-3331	274	17	aux	aux	PROPN
ejpam-3331	274	18	équations	équations	PROPN
ejpam-3331	274	19	intégrales	intégrale	NOUN
ejpam-3331	274	20	,	,	PUNCT
ejpam-3331	274	21	fundamenta	fundamenta	PROPN
ejpam-3331	274	22	mathematicae	mathematicae	PROPN
ejpam-3331	274	23	,	,	PUNCT
ejpam-3331	274	24	3	3	NUM
ejpam-3331	274	25	(	(	PUNCT
ejpam-3331	274	26	1922	1922	NUM
ejpam-3331	274	27	)	)	PUNCT
ejpam-3331	274	28	,	,	PUNCT
ejpam-3331	274	29	133–181	133–181	NUM
ejpam-3331	274	30	.	.	PUNCT
ejpam-3331	275	1	[	[	X
ejpam-3331	275	2	13	13	NUM
ejpam-3331	275	3	]	]	SYM
ejpam-3331	275	4	i.a	i.a	PROPN
ejpam-3331	275	5	.	.	PROPN
ejpam-3331	275	6	bakhtin	bakhtin	PROPN
ejpam-3331	275	7	,	,	PUNCT
ejpam-3331	275	8	the	the	DET
ejpam-3331	275	9	contraction	contraction	NOUN
ejpam-3331	275	10	principle	principle	NOUN
ejpam-3331	275	11	in	in	ADP
ejpam-3331	275	12	quasimetric	quasimetric	ADJ
ejpam-3331	275	13	spaces	space	NOUN
ejpam-3331	275	14	,	,	PUNCT
ejpam-3331	275	15	funct	funct	ADJ
ejpam-3331	275	16	.	.	PUNCT
ejpam-3331	276	1	anal	anal	PROPN
ejpam-3331	276	2	.	.	PUNCT
ejpam-3331	277	1	30	30	NUM
ejpam-3331	277	2	(	(	PUNCT
ejpam-3331	277	3	1989	1989	NUM
ejpam-3331	277	4	)	)	PUNCT
ejpam-3331	278	1	26–37	26–37	NOUN
ejpam-3331	278	2	.	.	PUNCT
ejpam-3331	279	1	[	[	X
ejpam-3331	279	2	14	14	NUM
ejpam-3331	279	3	]	]	X
ejpam-3331	279	4	s.	s.	PROPN
ejpam-3331	279	5	chandok	chandok	PROPN
ejpam-3331	279	6	,	,	PUNCT
ejpam-3331	279	7	some	some	DET
ejpam-3331	279	8	fixed	fix	VERB
ejpam-3331	279	9	point	point	NOUN
ejpam-3331	279	10	theorems	theorem	NOUN
ejpam-3331	279	11	for	for	ADP
ejpam-3331	279	12	(	(	PUNCT
ejpam-3331	279	13	α	α	X
ejpam-3331	279	14	,	,	PUNCT
ejpam-3331	279	15	β)-admissible	β)-admissible	PUNCT
ejpam-3331	279	16	geraghty	geraghty	PROPN
ejpam-3331	279	17	type	type	VERB
ejpam-3331	279	18	contractive	contractive	ADJ
ejpam-3331	279	19	mappings	mapping	NOUN
ejpam-3331	279	20	and	and	CCONJ
ejpam-3331	279	21	related	related	ADJ
ejpam-3331	279	22	results	result	NOUN
ejpam-3331	279	23	,	,	PUNCT
ejpam-3331	279	24	mathematical	mathematical	ADJ
ejpam-3331	279	25	sciences	science	NOUN
ejpam-3331	279	26	,	,	PUNCT
ejpam-3331	279	27	9.3	9.3	NUM
ejpam-3331	279	28	(	(	PUNCT
ejpam-3331	279	29	2015	2015	NUM
ejpam-3331	279	30	)	)	PUNCT
ejpam-3331	279	31	,	,	PUNCT
ejpam-3331	279	32	127	127	NUM
ejpam-3331	279	33	-	-	SYM
ejpam-3331	279	34	135	135	NUM
ejpam-3331	279	35	.	.	PUNCT
ejpam-3331	280	1	[	[	X
ejpam-3331	280	2	15	15	NUM
ejpam-3331	280	3	]	]	PUNCT
ejpam-3331	280	4	a.	a.	NOUN
ejpam-3331	280	5	felhi	felhi	PROPN
ejpam-3331	280	6	,	,	PUNCT
ejpam-3331	280	7	h.	h.	PROPN
ejpam-3331	280	8	aydi	aydi	PROPN
ejpam-3331	280	9	,	,	PUNCT
ejpam-3331	280	10	d.	d.	PROPN
ejpam-3331	280	11	zhang	zhang	PROPN
ejpam-3331	280	12	,	,	PUNCT
ejpam-3331	280	13	fixed	fix	VERB
ejpam-3331	280	14	points	point	NOUN
ejpam-3331	280	15	for	for	ADP
ejpam-3331	280	16	α	α	NOUN
ejpam-3331	280	17	-	-	ADJ
ejpam-3331	280	18	admissible	admissible	ADJ
ejpam-3331	280	19	contractive	contractive	ADJ
ejpam-3331	280	20	mappings	mapping	NOUN
ejpam-3331	280	21	via	via	ADP
ejpam-3331	280	22	simulation	simulation	NOUN
ejpam-3331	280	23	functions	function	NOUN
ejpam-3331	280	24	,	,	PUNCT
ejpam-3331	280	25	j.	j.	PROPN
ejpam-3331	280	26	nonlinear	nonlinear	PROPN
ejpam-3331	280	27	sci	sci	PROPN
ejpam-3331	280	28	.	.	PUNCT
ejpam-3331	280	29	appl	appl	PROPN
ejpam-3331	280	30	.	.	PROPN
ejpam-3331	280	31	9	9	NUM
ejpam-3331	280	32	(	(	PUNCT
ejpam-3331	280	33	10	10	NUM
ejpam-3331	280	34	)	)	PUNCT
ejpam-3331	280	35	(	(	PUNCT
ejpam-3331	280	36	2016	2016	NUM
ejpam-3331	280	37	)	)	PUNCT
ejpam-3331	280	38	,	,	PUNCT
ejpam-3331	280	39	5544–5560	5544–5560	NUM
ejpam-3331	280	40	.	.	PUNCT
ejpam-3331	281	1	[	[	X
ejpam-3331	281	2	16	16	NUM
ejpam-3331	281	3	]	]	X
ejpam-3331	281	4	a.a	a.a	PROPN
ejpam-3331	281	5	.	.	PROPN
ejpam-3331	281	6	harandi	harandi	PROPN
ejpam-3331	281	7	,	,	PUNCT
ejpam-3331	281	8	metric	metric	ADJ
ejpam-3331	281	9	-	-	PUNCT
ejpam-3331	281	10	like	like	ADJ
ejpam-3331	281	11	spaces	space	NOUN
ejpam-3331	281	12	,	,	PUNCT
ejpam-3331	281	13	partial	partial	ADJ
ejpam-3331	281	14	metric	metric	ADJ
ejpam-3331	281	15	spaces	space	NOUN
ejpam-3331	281	16	and	and	CCONJ
ejpam-3331	281	17	fixed	fix	VERB
ejpam-3331	281	18	points	point	NOUN
ejpam-3331	281	19	,	,	PUNCT
ejpam-3331	281	20	fixed	fix	VERB
ejpam-3331	281	21	point	point	NOUN
ejpam-3331	281	22	theory	theory	NOUN
ejpam-3331	281	23	appl	appl	NOUN
ejpam-3331	281	24	.	.	PUNCT
ejpam-3331	281	25	2012	2012	NUM
ejpam-3331	281	26	(	(	PUNCT
ejpam-3331	281	27	2012	2012	NUM
ejpam-3331	281	28	)	)	PUNCT
ejpam-3331	281	29	,	,	PUNCT
ejpam-3331	281	30	10	10	NUM
ejpam-3331	281	31	pages	page	NOUN
ejpam-3331	281	32	.	.	PUNCT
ejpam-3331	282	1	[	[	X
ejpam-3331	282	2	17	17	NUM
ejpam-3331	282	3	]	]	X
ejpam-3331	282	4	g.e	g.e	PROPN
ejpam-3331	282	5	.	.	PROPN
ejpam-3331	282	6	hardy	hardy	PROPN
ejpam-3331	282	7	,	,	PUNCT
ejpam-3331	282	8	t.d	t.d	PROPN
ejpam-3331	282	9	.	.	PROPN
ejpam-3331	282	10	rogers	rogers	PROPN
ejpam-3331	282	11	,	,	PUNCT
ejpam-3331	282	12	a	a	DET
ejpam-3331	282	13	generalization	generalization	NOUN
ejpam-3331	282	14	of	of	ADP
ejpam-3331	282	15	a	a	DET
ejpam-3331	282	16	fixed	fix	VERB
ejpam-3331	282	17	point	point	NOUN
ejpam-3331	282	18	theorem	theorem	NOUN
ejpam-3331	282	19	of	of	ADP
ejpam-3331	282	20	reich	reich	PROPN
ejpam-3331	282	21	,	,	PUNCT
ejpam-3331	282	22	can	can	AUX
ejpam-3331	282	23	.	.	PUNCT
ejpam-3331	283	1	math	math	NOUN
ejpam-3331	283	2	.	.	PUNCT
ejpam-3331	284	1	bull	bull	NOUN
ejpam-3331	284	2	.	.	PUNCT
ejpam-3331	285	1	16	16	NUM
ejpam-3331	285	2	(	(	PUNCT
ejpam-3331	285	3	1973	1973	NUM
ejpam-3331	285	4	)	)	PUNCT
ejpam-3331	285	5	,	,	PUNCT
ejpam-3331	285	6	201–206	201–206	NUM
ejpam-3331	285	7	.	.	PUNCT
ejpam-3331	286	1	[	[	X
ejpam-3331	286	2	18	18	NUM
ejpam-3331	286	3	]	]	X
ejpam-3331	286	4	r.	r.	PROPN
ejpam-3331	286	5	kannan	kannan	PROPN
ejpam-3331	286	6	,	,	PUNCT
ejpam-3331	286	7	some	some	DET
ejpam-3331	286	8	results	result	NOUN
ejpam-3331	286	9	on	on	ADP
ejpam-3331	286	10	fixed	fix	VERB
ejpam-3331	286	11	points	point	NOUN
ejpam-3331	286	12	,	,	PUNCT
ejpam-3331	286	13	bull	bull	NOUN
ejpam-3331	286	14	.	.	PUNCT
ejpam-3331	287	1	calcutta	calcutta	PROPN
ejpam-3331	287	2	math	math	PROPN
ejpam-3331	287	3	.	.	PUNCT
ejpam-3331	288	1	soc	soc	PROPN
ejpam-3331	288	2	.	.	PUNCT
ejpam-3331	289	1	60	60	NUM
ejpam-3331	289	2	(	(	PUNCT
ejpam-3331	289	3	1968	1968	NUM
ejpam-3331	289	4	)	)	PUNCT
ejpam-3331	289	5	,	,	PUNCT
ejpam-3331	289	6	71–76	71–76	NUM
ejpam-3331	289	7	.	.	PUNCT
ejpam-3331	290	1	[	[	X
ejpam-3331	290	2	19	19	NUM
ejpam-3331	290	3	]	]	PUNCT
ejpam-3331	290	4	f.	f.	PROPN
ejpam-3331	290	5	khojasteh	khojasteh	PROPN
ejpam-3331	290	6	,	,	PUNCT
ejpam-3331	290	7	s.	s.	PROPN
ejpam-3331	290	8	shukla	shukla	PROPN
ejpam-3331	290	9	,	,	PUNCT
ejpam-3331	290	10	s.	s.	PROPN
ejpam-3331	290	11	radenović	radenović	PROPN
ejpam-3331	290	12	,	,	PUNCT
ejpam-3331	290	13	a	a	DET
ejpam-3331	290	14	new	new	ADJ
ejpam-3331	290	15	approach	approach	NOUN
ejpam-3331	290	16	to	to	ADP
ejpam-3331	290	17	the	the	DET
ejpam-3331	290	18	study	study	NOUN
ejpam-3331	290	19	of	of	ADP
ejpam-3331	290	20	fixed	fix	VERB
ejpam-3331	290	21	point	point	NOUN
ejpam-3331	290	22	theorems	theorem	NOUN
ejpam-3331	290	23	via	via	ADP
ejpam-3331	290	24	simulation	simulation	NOUN
ejpam-3331	290	25	functions	function	NOUN
ejpam-3331	290	26	,	,	PUNCT
ejpam-3331	290	27	filomat	filomat	NOUN
ejpam-3331	290	28	,	,	PUNCT
ejpam-3331	290	29	29	29	NUM
ejpam-3331	290	30	(	(	PUNCT
ejpam-3331	290	31	2015	2015	NUM
ejpam-3331	290	32	)	)	PUNCT
ejpam-3331	290	33	,	,	PUNCT
ejpam-3331	290	34	1189–1194	1189–1194	NUM
ejpam-3331	290	35	.	.	PUNCT
ejpam-3331	291	1	[	[	X
ejpam-3331	291	2	20	20	NUM
ejpam-3331	291	3	]	]	PUNCT
ejpam-3331	291	4	h.	h.	PROPN
ejpam-3331	291	5	lakzian	lakzian	PROPN
ejpam-3331	291	6	,	,	PUNCT
ejpam-3331	291	7	h.	h.	PROPN
ejpam-3331	291	8	aydi	aydi	PROPN
ejpam-3331	291	9	,	,	PUNCT
ejpam-3331	291	10	b.e	b.e	PROPN
ejpam-3331	291	11	.	.	PROPN
ejpam-3331	291	12	rhoades	rhoade	NOUN
ejpam-3331	291	13	,	,	PUNCT
ejpam-3331	291	14	fixed	fix	VERB
ejpam-3331	291	15	points	point	NOUN
ejpam-3331	291	16	for	for	ADP
ejpam-3331	291	17	(	(	PUNCT
ejpam-3331	291	18	φ	φ	PROPN
ejpam-3331	291	19	,	,	PUNCT
ejpam-3331	291	20	ψ	ψ	SYM
ejpam-3331	291	21	,	,	PUNCT
ejpam-3331	291	22	p)-weakly	p)-weakly	ADV
ejpam-3331	291	23	contractive	contractive	ADJ
ejpam-3331	291	24	mappings	mapping	NOUN
ejpam-3331	291	25	in	in	ADP
ejpam-3331	291	26	metric	metric	ADJ
ejpam-3331	291	27	spaces	space	NOUN
ejpam-3331	291	28	with	with	ADP
ejpam-3331	291	29	w	w	NOUN
ejpam-3331	291	30	-	-	PUNCT
ejpam-3331	291	31	distance	distance	NOUN
ejpam-3331	291	32	,	,	PUNCT
ejpam-3331	291	33	applied	apply	VERB
ejpam-3331	291	34	math	math	NOUN
ejpam-3331	291	35	.	.	PUNCT
ejpam-3331	292	1	comput	comput	NOUN
ejpam-3331	292	2	.	.	PUNCT
ejpam-3331	293	1	219	219	NUM
ejpam-3331	293	2	(	(	PUNCT
ejpam-3331	293	3	2013	2013	NUM
ejpam-3331	293	4	)	)	PUNCT
ejpam-3331	293	5	,	,	PUNCT
ejpam-3331	293	6	6777	6777	NUM
ejpam-3331	293	7	-	-	SYM
ejpam-3331	293	8	6782	6782	NUM
ejpam-3331	293	9	.	.	PUNCT
ejpam-3331	294	1	[	[	X
ejpam-3331	294	2	21	21	NUM
ejpam-3331	294	3	]	]	X
ejpam-3331	294	4	s.g	s.g	PROPN
ejpam-3331	294	5	.	.	PROPN
ejpam-3331	294	6	matthews	matthews	PROPN
ejpam-3331	294	7	,	,	PUNCT
ejpam-3331	294	8	partial	partial	ADJ
ejpam-3331	294	9	metric	metric	ADJ
ejpam-3331	294	10	topology	topology	NOUN
ejpam-3331	294	11	,	,	PUNCT
ejpam-3331	294	12	proc	proc	NOUN
ejpam-3331	294	13	.	.	PUNCT
ejpam-3331	295	1	8th	8th	ADJ
ejpam-3331	295	2	summer	summer	NOUN
ejpam-3331	295	3	conference	conference	NOUN
ejpam-3331	295	4	on	on	ADP
ejpam-3331	295	5	general	general	ADJ
ejpam-3331	295	6	topology	topology	NOUN
ejpam-3331	295	7	and	and	CCONJ
ejpam-3331	295	8	applications	application	NOUN
ejpam-3331	295	9	,	,	PUNCT
ejpam-3331	295	10	ann	ann	PROPN
ejpam-3331	295	11	.	.	PROPN
ejpam-3331	296	1	new	new	PROPN
ejpam-3331	296	2	york	york	PROPN
ejpam-3331	296	3	acad	acad	PROPN
ejpam-3331	296	4	.	.	PUNCT
ejpam-3331	297	1	sci	sci	PROPN
ejpam-3331	297	2	.	.	PROPN
ejpam-3331	297	3	728	728	NUM
ejpam-3331	297	4	(	(	PUNCT
ejpam-3331	297	5	1994	1994	NUM
ejpam-3331	297	6	)	)	PUNCT
ejpam-3331	297	7	,	,	PUNCT
ejpam-3331	297	8	183	183	NUM
ejpam-3331	297	9	-	-	SYM
ejpam-3331	297	10	197	197	NUM
ejpam-3331	297	11	.	.	PUNCT
ejpam-3331	298	1	[	[	X
ejpam-3331	298	2	22	22	NUM
ejpam-3331	298	3	]	]	X
ejpam-3331	298	4	n.	n.	PROPN
ejpam-3331	298	5	mlaiki	mlaiki	PROPN
ejpam-3331	298	6	,	,	PUNCT
ejpam-3331	298	7	h.	h.	PROPN
ejpam-3331	298	8	aydi	aydi	PROPN
ejpam-3331	298	9	,	,	PUNCT
ejpam-3331	298	10	n.	n.	NOUN
ejpam-3331	298	11	souayah	souayah	NOUN
ejpam-3331	298	12	,	,	PUNCT
ejpam-3331	298	13	t.	t.	NOUN
ejpam-3331	298	14	abdeljawad	abdeljawad	PROPN
ejpam-3331	298	15	,	,	PUNCT
ejpam-3331	298	16	controlled	control	VERB
ejpam-3331	298	17	metric	metric	ADJ
ejpam-3331	298	18	type	type	NOUN
ejpam-3331	298	19	spaces	space	NOUN
ejpam-3331	298	20	and	and	CCONJ
ejpam-3331	298	21	the	the	DET
ejpam-3331	298	22	related	related	ADJ
ejpam-3331	298	23	contraction	contraction	NOUN
ejpam-3331	298	24	principle	principle	NOUN
ejpam-3331	298	25	,	,	PUNCT
ejpam-3331	298	26	mathematics	mathematic	NOUN
ejpam-3331	298	27	,	,	PUNCT
ejpam-3331	298	28	2018	2018	NUM
ejpam-3331	298	29	,	,	PUNCT
ejpam-3331	298	30	6(10	6(10	NUM
ejpam-3331	298	31	)	)	PUNCT
ejpam-3331	298	32	,	,	PUNCT
ejpam-3331	298	33	194	194	NUM
ejpam-3331	298	34	.	.	PUNCT
ejpam-3331	299	1	[	[	X
ejpam-3331	299	2	23	23	NUM
ejpam-3331	299	3	]	]	X
ejpam-3331	299	4	n.	n.	PROPN
ejpam-3331	299	5	mlaiki	mlaiki	PROPN
ejpam-3331	299	6	,	,	PUNCT
ejpam-3331	299	7	k.	k.	PROPN
ejpam-3331	299	8	abodayeh	abodayeh	PROPN
ejpam-3331	299	9	,	,	PUNCT
ejpam-3331	299	10	h.	h.	PROPN
ejpam-3331	299	11	aydi	aydi	PROPN
ejpam-3331	299	12	,	,	PUNCT
ejpam-3331	299	13	t.	t.	NOUN
ejpam-3331	299	14	abdeljawad	abdeljawad	NOUN
ejpam-3331	299	15	,	,	PUNCT
ejpam-3331	299	16	m.	m.	NOUN
ejpam-3331	299	17	abuloha	abuloha	PROPN
ejpam-3331	299	18	,	,	PUNCT
ejpam-3331	299	19	rectangular	rectangular	ADJ
ejpam-3331	299	20	metriclike	metriclike	NOUN
ejpam-3331	299	21	type	type	NOUN
ejpam-3331	299	22	spaces	space	NOUN
ejpam-3331	299	23	and	and	CCONJ
ejpam-3331	299	24	related	relate	VERB
ejpam-3331	299	25	fixed	fix	VERB
ejpam-3331	299	26	points	point	NOUN
ejpam-3331	299	27	,	,	PUNCT
ejpam-3331	299	28	volume	volume	NOUN
ejpam-3331	299	29	2018	2018	NUM
ejpam-3331	299	30	,	,	PUNCT
ejpam-3331	299	31	article	article	NOUN
ejpam-3331	299	32	i	i	PROPN
ejpam-3331	299	33	d	d	PROPN
ejpam-3331	299	34	3581768	3581768	NUM
ejpam-3331	299	35	,	,	PUNCT
ejpam-3331	299	36	7	7	NUM
ejpam-3331	299	37	pages	page	NOUN
ejpam-3331	299	38	.	.	PUNCT
ejpam-3331	300	1	[	[	X
ejpam-3331	300	2	24	24	NUM
ejpam-3331	300	3	]	]	PUNCT
ejpam-3331	300	4	z.	z.	PROPN
ejpam-3331	300	5	mustafa	mustafa	PROPN
ejpam-3331	300	6	,	,	PUNCT
ejpam-3331	300	7	h.	h.	PROPN
ejpam-3331	300	8	aydi	aydi	PROPN
ejpam-3331	300	9	,	,	PUNCT
ejpam-3331	300	10	e.	e.	PROPN
ejpam-3331	300	11	karapinar	karapinar	PROPN
ejpam-3331	300	12	,	,	PUNCT
ejpam-3331	300	13	generalized	generalized	ADJ
ejpam-3331	300	14	meir	meir	PROPN
ejpam-3331	300	15	-	-	PUNCT
ejpam-3331	300	16	keeler	keeler	PROPN
ejpam-3331	300	17	type	type	NOUN
ejpam-3331	300	18	contractions	contraction	NOUN
ejpam-3331	300	19	on	on	ADP
ejpam-3331	300	20	g	g	NOUN
ejpam-3331	300	21	-	-	PUNCT
ejpam-3331	300	22	metric	metric	ADJ
ejpam-3331	300	23	spaces	space	NOUN
ejpam-3331	300	24	,	,	PUNCT
ejpam-3331	300	25	applied	apply	VERB
ejpam-3331	300	26	math	math	NOUN
ejpam-3331	300	27	.	.	PUNCT
ejpam-3331	301	1	comput	comput	NOUN
ejpam-3331	301	2	.	.	PUNCT
ejpam-3331	302	1	219	219	NUM
ejpam-3331	302	2	(	(	PUNCT
ejpam-3331	302	3	2013	2013	NUM
ejpam-3331	302	4	)	)	PUNCT
ejpam-3331	302	5	,	,	PUNCT
ejpam-3331	302	6	10441	10441	NUM
ejpam-3331	302	7	-	-	SYM
ejpam-3331	302	8	10447	10447	NUM
ejpam-3331	302	9	.	.	PUNCT
ejpam-3331	303	1	[	[	X
ejpam-3331	303	2	25	25	NUM
ejpam-3331	303	3	]	]	PUNCT
ejpam-3331	303	4	s.	s.	PROPN
ejpam-3331	303	5	reich	reich	PROPN
ejpam-3331	303	6	,	,	PUNCT
ejpam-3331	303	7	some	some	DET
ejpam-3331	303	8	remarks	remark	NOUN
ejpam-3331	303	9	concerning	concern	VERB
ejpam-3331	303	10	contraction	contraction	NOUN
ejpam-3331	303	11	mappings	mapping	NOUN
ejpam-3331	303	12	,	,	PUNCT
ejpam-3331	303	13	can	can	AUX
ejpam-3331	303	14	.	.	PUNCT
ejpam-3331	304	1	math	math	NOUN
ejpam-3331	304	2	.	.	PUNCT
ejpam-3331	305	1	bull	bull	NOUN
ejpam-3331	305	2	.	.	PUNCT
ejpam-3331	306	1	14	14	NUM
ejpam-3331	306	2	(	(	PUNCT
ejpam-3331	306	3	1971	1971	NUM
ejpam-3331	306	4	)	)	PUNCT
ejpam-3331	306	5	,	,	PUNCT
ejpam-3331	306	6	121–124	121–124	NUM
ejpam-3331	306	7	.	.	PUNCT
ejpam-3331	307	1	references	reference	NOUN
ejpam-3331	307	2	100	100	NUM
ejpam-3331	307	3	[	[	X
ejpam-3331	307	4	26	26	NUM
ejpam-3331	307	5	]	]	PUNCT
ejpam-3331	307	6	b.	b.	PROPN
ejpam-3331	307	7	samet	samet	PROPN
ejpam-3331	307	8	,	,	PUNCT
ejpam-3331	307	9	c.	c.	PROPN
ejpam-3331	307	10	vetro	vetro	PROPN
ejpam-3331	307	11	,	,	PUNCT
ejpam-3331	307	12	p.	p.	NOUN
ejpam-3331	307	13	vetro	vetro	NOUN
ejpam-3331	307	14	,	,	PUNCT
ejpam-3331	307	15	fixed	fix	VERB
ejpam-3331	307	16	point	point	NOUN
ejpam-3331	307	17	theorem	theorem	NOUN
ejpam-3331	307	18	for	for	ADP
ejpam-3331	307	19	α−ψ	α−ψ	NOUN
ejpam-3331	307	20	-	-	PUNCT
ejpam-3331	307	21	contractive	contractive	ADJ
ejpam-3331	307	22	type	type	NOUN
ejpam-3331	307	23	mappings	mapping	NOUN
ejpam-3331	307	24	,	,	PUNCT
ejpam-3331	307	25	j.	j.	PROPN
ejpam-3331	307	26	nonlinear	nonlinear	PROPN
ejpam-3331	307	27	.	.	PUNCT
ejpam-3331	308	1	anal	anal	PROPN
ejpam-3331	308	2	.	.	PROPN
ejpam-3331	308	3	,	,	PUNCT
ejpam-3331	308	4	75	75	NUM
ejpam-3331	308	5	(	(	PUNCT
ejpam-3331	308	6	2012	2012	NUM
ejpam-3331	308	7	)	)	PUNCT
ejpam-3331	308	8	,	,	PUNCT
ejpam-3331	308	9	215	215	NUM
ejpam-3331	308	10	-	-	SYM
ejpam-3331	308	11	2165	2165	NUM
ejpam-3331	308	12	.	.	PUNCT
ejpam-3331	309	1	[	[	X
ejpam-3331	309	2	27	27	NUM
ejpam-3331	309	3	]	]	X
ejpam-3331	309	4	h.	h.	PROPN
ejpam-3331	309	5	qawaqneh	qawaqneh	PROPN
ejpam-3331	309	6	,	,	PUNCT
ejpam-3331	309	7	m.	m.	PROPN
ejpam-3331	309	8	s.	s.	PROPN
ejpam-3331	309	9	m.	m.	PROPN
ejpam-3331	309	10	noorani	noorani	PROPN
ejpam-3331	309	11	,	,	PUNCT
ejpam-3331	309	12	w.	w.	PROPN
ejpam-3331	309	13	shatanawi	shatanawi	PROPN
ejpam-3331	309	14	,	,	PUNCT
ejpam-3331	309	15	h.	h.	PROPN
ejpam-3331	309	16	alsamir	alsamir	PROPN
ejpam-3331	309	17	,	,	PUNCT
ejpam-3331	309	18	common	common	ADJ
ejpam-3331	309	19	fixed	fix	VERB
ejpam-3331	309	20	points	point	NOUN
ejpam-3331	309	21	for	for	ADP
ejpam-3331	309	22	pairs	pair	NOUN
ejpam-3331	309	23	of	of	ADP
ejpam-3331	309	24	triangular	triangular	NOUN
ejpam-3331	309	25	(	(	PUNCT
ejpam-3331	309	26	α)−admissible	α)−admissible	ADJ
ejpam-3331	309	27	mappings	mapping	NOUN
ejpam-3331	309	28	,	,	PUNCT
ejpam-3331	309	29	journal	journal	NOUN
ejpam-3331	309	30	of	of	ADP
ejpam-3331	309	31	nonlinear	nonlinear	PROPN
ejpam-3331	309	32	sciences	sciences	PROPN
ejpam-3331	309	33	and	and	CCONJ
ejpam-3331	309	34	application	application	NOUN
ejpam-3331	309	35	,	,	PUNCT
ejpam-3331	309	36	10	10	NUM
ejpam-3331	309	37	,	,	PUNCT
ejpam-3331	309	38	6192	6192	NUM
ejpam-3331	309	39	-	-	SYM
ejpam-3331	309	40	6204	6204	NUM
ejpam-3331	309	41	(	(	PUNCT
ejpam-3331	309	42	2017	2017	NUM
ejpam-3331	309	43	)	)	PUNCT
ejpam-3331	310	1	[	[	X
ejpam-3331	310	2	28	28	NUM
ejpam-3331	310	3	]	]	X
ejpam-3331	310	4	h.	h.	PROPN
ejpam-3331	310	5	qawaqneh	qawaqneh	PROPN
ejpam-3331	310	6	,	,	PUNCT
ejpam-3331	310	7	m.	m.	PROPN
ejpam-3331	310	8	s.	s.	PROPN
ejpam-3331	310	9	m.	m.	PROPN
ejpam-3331	310	10	noorani	noorani	PROPN
ejpam-3331	310	11	,	,	PUNCT
ejpam-3331	310	12	w.	w.	PROPN
ejpam-3331	310	13	shatanawi	shatanawi	PROPN
ejpam-3331	310	14	,	,	PUNCT
ejpam-3331	310	15	k.	k.	PROPN
ejpam-3331	310	16	abodayeh	abodayeh	PROPN
ejpam-3331	310	17	,	,	PUNCT
ejpam-3331	310	18	h.	h.	PROPN
ejpam-3331	310	19	alsamir	alsamir	PROPN
ejpam-3331	310	20	,	,	PUNCT
ejpam-3331	310	21	common	common	ADJ
ejpam-3331	310	22	fixed	fix	VERB
ejpam-3331	310	23	points	point	NOUN
ejpam-3331	310	24	for	for	ADP
ejpam-3331	310	25	pairs	pair	NOUN
ejpam-3331	310	26	of	of	ADP
ejpam-3331	310	27	triangular	triangular	NOUN
ejpam-3331	310	28	(	(	PUNCT
ejpam-3331	310	29	α)−admissible	α)−admissible	ADJ
ejpam-3331	310	30	mappings	mapping	NOUN
ejpam-3331	310	31	,	,	PUNCT
ejpam-3331	310	32	journal	journal	NOUN
ejpam-3331	310	33	of	of	ADP
ejpam-3331	310	34	mathematical	mathematical	ADJ
ejpam-3331	310	35	analysis	analysis	NOUN
ejpam-3331	310	36	,	,	PUNCT
ejpam-3331	310	37	9(1	9(1	NUM
ejpam-3331	310	38	)	)	PUNCT
ejpam-3331	310	39	,	,	PUNCT
ejpam-3331	310	40	38	38	NUM
ejpam-3331	310	41	-	-	SYM
ejpam-3331	310	42	51	51	NUM
ejpam-3331	310	43	,	,	PUNCT
ejpam-3331	310	44	(	(	PUNCT
ejpam-3331	310	45	2018	2018	NUM
ejpam-3331	310	46	)	)	PUNCT
ejpam-3331	311	1	[	[	X
ejpam-3331	311	2	29	29	NUM
ejpam-3331	311	3	]	]	X
ejpam-3331	311	4	h.	h.	PROPN
ejpam-3331	311	5	qawaqneh	qawaqneh	PROPN
ejpam-3331	311	6	,	,	PUNCT
ejpam-3331	311	7	m.	m.	PROPN
ejpam-3331	311	8	s.	s.	PROPN
ejpam-3331	311	9	m.	m.	PROPN
ejpam-3331	311	10	noorani	noorani	PROPN
ejpam-3331	311	11	,	,	PUNCT
ejpam-3331	311	12	w.	w.	PROPN
ejpam-3331	311	13	shatanawi	shatanawi	PROPN
ejpam-3331	311	14	,	,	PUNCT
ejpam-3331	311	15	fixed	fix	VERB
ejpam-3331	311	16	point	point	NOUN
ejpam-3331	311	17	results	result	NOUN
ejpam-3331	311	18	for	for	ADP
ejpam-3331	311	19	geraghty	geraghty	PROPN
ejpam-3331	311	20	type	type	NOUN
ejpam-3331	311	21	generalized	generalize	VERB
ejpam-3331	311	22	f−contraction	f−contraction	NOUN
ejpam-3331	311	23	for	for	ADP
ejpam-3331	311	24	weak	weak	ADJ
ejpam-3331	311	25	alpha	alpha	NOUN
ejpam-3331	311	26	-	-	PUNCT
ejpam-3331	311	27	admissible	admissible	ADJ
ejpam-3331	311	28	mapping	mapping	NOUN
ejpam-3331	311	29	in	in	ADP
ejpam-3331	311	30	metric	metric	ADJ
ejpam-3331	311	31	-	-	PUNCT
ejpam-3331	311	32	like	like	ADJ
ejpam-3331	311	33	spaces	space	NOUN
ejpam-3331	311	34	,	,	PUNCT
ejpam-3331	311	35	european	european	ADJ
ejpam-3331	311	36	journal	journal	PROPN
ejpam-3331	311	37	of	of	ADP
ejpam-3331	311	38	pure	pure	ADJ
ejpam-3331	311	39	and	and	CCONJ
ejpam-3331	311	40	applied	applied	ADJ
ejpam-3331	311	41	mathematics	mathematic	NOUN
ejpam-3331	311	42	,	,	PUNCT
ejpam-3331	311	43	11	11	NUM
ejpam-3331	311	44	(	(	PUNCT
ejpam-3331	311	45	2018	2018	NUM
ejpam-3331	311	46	)	)	PUNCT
ejpam-3331	311	47	,	,	PUNCT
ejpam-3331	311	48	702	702	NUM
ejpam-3331	311	49	-	-	SYM
ejpam-3331	311	50	716	716	NUM
ejpam-3331	311	51	.	.	PUNCT
ejpam-3331	312	1	[	[	X
ejpam-3331	312	2	30	30	NUM
ejpam-3331	312	3	]	]	X
ejpam-3331	312	4	w.	w.	PROPN
ejpam-3331	312	5	shatanawi	shatanawi	PROPN
ejpam-3331	312	6	,	,	PUNCT
ejpam-3331	312	7	m.s.m	m.s.m	PROPN
ejpam-3331	312	8	.	.	PROPN
ejpam-3331	312	9	norani	norani	PROPN
ejpam-3331	312	10	,	,	PUNCT
ejpam-3331	312	11	j.	j.	PROPN
ejpam-3331	312	12	ahmad	ahmad	PROPN
ejpam-3331	312	13	,	,	PUNCT
ejpam-3331	312	14	h.	h.	PROPN
ejpam-3331	312	15	alsamir	alsamir	PROPN
ejpam-3331	312	16	,	,	PUNCT
ejpam-3331	312	17	m.a	m.a	PROPN
ejpam-3331	312	18	.	.	PROPN
ejpam-3331	312	19	kutbi	kutbi	PROPN
ejpam-3331	312	20	,	,	PUNCT
ejpam-3331	312	21	some	some	DET
ejpam-3331	312	22	common	common	ADJ
ejpam-3331	312	23	fixed	fix	VERB
ejpam-3331	312	24	points	point	NOUN
ejpam-3331	312	25	of	of	ADP
ejpam-3331	312	26	multivalued	multivalued	ADJ
ejpam-3331	312	27	mappings	mapping	NOUN
ejpam-3331	312	28	on	on	ADP
ejpam-3331	312	29	complex	complex	ADV
ejpam-3331	312	30	-	-	PUNCT
ejpam-3331	312	31	valued	value	VERB
ejpam-3331	312	32	metric	metric	ADJ
ejpam-3331	312	33	spaces	space	NOUN
ejpam-3331	312	34	with	with	ADP
ejpam-3331	312	35	homotopy	homotopy	NOUN
ejpam-3331	312	36	result	result	NOUN
ejpam-3331	312	37	,	,	PUNCT
ejpam-3331	312	38	j.	j.	PROPN
ejpam-3331	312	39	nonlinear	nonlinear	PROPN
ejpam-3331	312	40	sci	sci	PROPN
ejpam-3331	312	41	.	.	PUNCT
ejpam-3331	312	42	appl	appl	PROPN
ejpam-3331	312	43	.	.	PROPN
ejpam-3331	313	1	10	10	NUM
ejpam-3331	313	2	(	(	PUNCT
ejpam-3331	313	3	2017	2017	NUM
ejpam-3331	313	4	)	)	PUNCT
ejpam-3331	313	5	,	,	PUNCT
ejpam-3331	313	6	3381	3381	NUM
ejpam-3331	313	7	-	-	SYM
ejpam-3331	313	8	3396	3396	NUM
ejpam-3331	313	9	.	.	PUNCT
ejpam-3331	314	1	[	[	X
ejpam-3331	314	2	31	31	NUM
ejpam-3331	314	3	]	]	X
ejpam-3331	314	4	a.f	a.f	PROPN
ejpam-3331	314	5	.	.	PUNCT
ejpam-3331	314	6	roldan	roldan	PROPN
ejpam-3331	314	7	-	-	PUNCT
ejpam-3331	314	8	lópez	lópez	ADV
ejpam-3331	314	9	-	-	PUNCT
ejpam-3331	314	10	de	de	NOUN
ejpam-3331	314	11	-	-	NOUN
ejpam-3331	314	12	hierro	hierro	ADJ
ejpam-3331	314	13	,	,	PUNCT
ejpam-3331	314	14	e.	e.	PROPN
ejpam-3331	314	15	karapinar	karapinar	PROPN
ejpam-3331	314	16	,	,	PUNCT
ejpam-3331	314	17	c.	c.	PROPN
ejpam-3331	314	18	roldán	roldán	PROPN
ejpam-3331	314	19	-	-	PUNCT
ejpam-3331	314	20	lópez	lópez	ADV
ejpam-3331	314	21	-	-	PUNCT
ejpam-3331	314	22	de	de	NOUN
ejpam-3331	314	23	-	-	NOUN
ejpam-3331	314	24	hierro	hierro	ADJ
ejpam-3331	314	25	,	,	PUNCT
ejpam-3331	314	26	j.	j.	PROPN
ejpam-3331	314	27	mart́ıinez	mart́ıinez	PROPN
ejpam-3331	314	28	-	-	PUNCT
ejpam-3331	314	29	moreno	moreno	PROPN
ejpam-3331	314	30	,	,	PUNCT
ejpam-3331	314	31	coincidence	coincidence	NOUN
ejpam-3331	314	32	point	point	NOUN
ejpam-3331	314	33	theorems	theorem	NOUN
ejpam-3331	314	34	on	on	ADP
ejpam-3331	314	35	metric	metric	ADJ
ejpam-3331	314	36	spaces	space	NOUN
ejpam-3331	314	37	via	via	ADP
ejpam-3331	314	38	simulation	simulation	NOUN
ejpam-3331	314	39	functions	function	NOUN
ejpam-3331	314	40	,	,	PUNCT
ejpam-3331	314	41	j.	j.	PROPN
ejpam-3331	314	42	comput	comput	PROPN
ejpam-3331	314	43	.	.	PUNCT
ejpam-3331	315	1	appl	appl	PROPN
ejpam-3331	315	2	.	.	PROPN
ejpam-3331	315	3	math	math	NOUN
ejpam-3331	315	4	.	.	PUNCT
ejpam-3331	316	1	275	275	NUM
ejpam-3331	316	2	(	(	PUNCT
ejpam-3331	316	3	2015	2015	NUM
ejpam-3331	316	4	)	)	PUNCT
ejpam-3331	316	5	,	,	PUNCT
ejpam-3331	316	6	345	345	NUM
ejpam-3331	316	7	-	-	SYM
ejpam-3331	316	8	355	355	NUM
ejpam-3331	316	9	.	.	PUNCT