id	sid	tid	token	lemma	pos
ejpam-5428	1	1	european	european	PROPN
ejpam-5428	1	2	journal	journal	PROPN
ejpam-5428	1	3	of	of	ADP
ejpam-5428	1	4	pure	pure	ADJ
ejpam-5428	1	5	and	and	CCONJ
ejpam-5428	1	6	applied	apply	VERB
ejpam-5428	1	7	mathematics	mathematic	NOUN
ejpam-5428	1	8	vol	vol	NOUN
ejpam-5428	1	9	.	.	PROPN
ejpam-5428	2	1	17	17	NUM
ejpam-5428	2	2	,	,	PUNCT
ejpam-5428	2	3	no	no	INTJ
ejpam-5428	2	4	.	.	NOUN
ejpam-5428	2	5	4	4	NUM
ejpam-5428	2	6	,	,	PUNCT
ejpam-5428	2	7	2024	2024	NUM
ejpam-5428	2	8	,	,	PUNCT
ejpam-5428	2	9	2384	2384	NUM
ejpam-5428	2	10	-	-	SYM
ejpam-5428	2	11	2404	2404	NUM
ejpam-5428	2	12	issn	issn	PROPN
ejpam-5428	2	13	1307	1307	NUM
ejpam-5428	2	14	-	-	SYM
ejpam-5428	2	15	5543	5543	NUM
ejpam-5428	2	16	–	–	PUNCT
ejpam-5428	2	17	ejpam.com	ejpam.com	X
ejpam-5428	2	18	published	publish	VERB
ejpam-5428	2	19	by	by	ADP
ejpam-5428	3	1	new	new	PROPN
ejpam-5428	3	2	york	york	PROPN
ejpam-5428	3	3	business	business	PROPN
ejpam-5428	3	4	global	global	PROPN
ejpam-5428	3	5	some	some	DET
ejpam-5428	3	6	geraghty	geraghty	PROPN
ejpam-5428	3	7	type	type	NOUN
ejpam-5428	3	8	inequalities	inequality	NOUN
ejpam-5428	3	9	in	in	ADP
ejpam-5428	3	10	b	b	NOUN
ejpam-5428	3	11	-	-	PUNCT
ejpam-5428	3	12	fuzzy	fuzzy	ADJ
ejpam-5428	3	13	metric	metric	ADJ
ejpam-5428	3	14	spaces	space	NOUN
ejpam-5428	3	15	with	with	ADP
ejpam-5428	3	16	an	an	DET
ejpam-5428	3	17	application	application	NOUN
ejpam-5428	3	18	vineeta	vineeta	NOUN
ejpam-5428	3	19	chandra1	chandra1	NOUN
ejpam-5428	3	20	,	,	PUNCT
ejpam-5428	3	21	uma	uma	PROPN
ejpam-5428	3	22	devi	devi	PROPN
ejpam-5428	3	23	patel1,∗	patel1,∗	PROPN
ejpam-5428	3	24	,	,	PUNCT
ejpam-5428	3	25	stojan	stojan	ADJ
ejpam-5428	3	26	radenović2	radenović2	PROPN
ejpam-5428	3	27	1department	1department	NUM
ejpam-5428	3	28	of	of	ADP
ejpam-5428	3	29	mathematics	mathematic	NOUN
ejpam-5428	3	30	,	,	PUNCT
ejpam-5428	3	31	guru	guru	NOUN
ejpam-5428	3	32	ghasidas	ghasidas	PROPN
ejpam-5428	3	33	vishwavidyalaya	vishwavidyalaya	PROPN
ejpam-5428	3	34	(	(	PUNCT
ejpam-5428	3	35	a	a	DET
ejpam-5428	3	36	central	central	ADJ
ejpam-5428	3	37	university	university	NOUN
ejpam-5428	3	38	)	)	PUNCT
ejpam-5428	3	39	,	,	PUNCT
ejpam-5428	3	40	koni	koni	NOUN
ejpam-5428	3	41	,	,	PUNCT
ejpam-5428	3	42	bilaspur-495009	bilaspur-495009	NOUN
ejpam-5428	3	43	,	,	PUNCT
ejpam-5428	3	44	chhattisgarh	chhattisgarh	NOUN
ejpam-5428	3	45	,	,	PUNCT
ejpam-5428	3	46	india	india	PROPN
ejpam-5428	3	47	2faculty	2faculty	NUM
ejpam-5428	3	48	of	of	ADP
ejpam-5428	3	49	mechanical	mechanical	ADJ
ejpam-5428	3	50	engineering	engineering	NOUN
ejpam-5428	3	51	,	,	PUNCT
ejpam-5428	3	52	university	university	PROPN
ejpam-5428	3	53	of	of	ADP
ejpam-5428	3	54	belgrade	belgrade	PROPN
ejpam-5428	3	55	,	,	PUNCT
ejpam-5428	3	56	11120	11120	NUM
ejpam-5428	3	57	belgrade	belgrade	NOUN
ejpam-5428	3	58	,	,	PUNCT
ejpam-5428	3	59	serbia	serbia	PROPN
ejpam-5428	3	60	abstract	abstract	ADJ
ejpam-5428	3	61	.	.	PUNCT
ejpam-5428	4	1	in	in	ADP
ejpam-5428	4	2	this	this	DET
ejpam-5428	4	3	note	note	NOUN
ejpam-5428	4	4	,	,	PUNCT
ejpam-5428	4	5	we	we	PRON
ejpam-5428	4	6	introduce	introduce	VERB
ejpam-5428	4	7	novel	novel	ADJ
ejpam-5428	4	8	geraghty	geraghty	VERB
ejpam-5428	4	9	-	-	PUNCT
ejpam-5428	4	10	type	type	NOUN
ejpam-5428	4	11	inequalities	inequality	NOUN
ejpam-5428	4	12	within	within	ADP
ejpam-5428	4	13	the	the	DET
ejpam-5428	4	14	framework	framework	NOUN
ejpam-5428	4	15	of	of	ADP
ejpam-5428	4	16	a	a	DET
ejpam-5428	4	17	b	b	NOUN
ejpam-5428	4	18	-	-	PUNCT
ejpam-5428	4	19	fuzzy	fuzzy	ADJ
ejpam-5428	4	20	metric	metric	ADJ
ejpam-5428	4	21	space	space	NOUN
ejpam-5428	4	22	and	and	CCONJ
ejpam-5428	4	23	develop	develop	VERB
ejpam-5428	4	24	new	new	ADJ
ejpam-5428	4	25	fixed	fix	VERB
ejpam-5428	4	26	point	point	NOUN
ejpam-5428	4	27	theorems	theorem	NOUN
ejpam-5428	4	28	for	for	ADP
ejpam-5428	4	29	such	such	ADJ
ejpam-5428	4	30	mappings	mapping	NOUN
ejpam-5428	4	31	in	in	ADP
ejpam-5428	4	32	a	a	DET
ejpam-5428	4	33	g	g	NOUN
ejpam-5428	4	34	-	-	PUNCT
ejpam-5428	4	35	complete	complete	ADJ
ejpam-5428	4	36	b	b	NOUN
ejpam-5428	4	37	-	-	PUNCT
ejpam-5428	4	38	fuzzy	fuzzy	ADJ
ejpam-5428	4	39	metric	metric	ADJ
ejpam-5428	4	40	space	space	NOUN
ejpam-5428	4	41	.	.	PUNCT
ejpam-5428	5	1	to	to	PART
ejpam-5428	5	2	substantiate	substantiate	VERB
ejpam-5428	5	3	our	our	PRON
ejpam-5428	5	4	findings	finding	NOUN
ejpam-5428	5	5	,	,	PUNCT
ejpam-5428	5	6	we	we	PRON
ejpam-5428	5	7	present	present	VERB
ejpam-5428	5	8	several	several	ADJ
ejpam-5428	5	9	illustrative	illustrative	ADJ
ejpam-5428	5	10	examples	example	NOUN
ejpam-5428	5	11	using	use	VERB
ejpam-5428	5	12	graphical	graphical	ADJ
ejpam-5428	5	13	methods	method	NOUN
ejpam-5428	5	14	.	.	PUNCT
ejpam-5428	6	1	additionally	additionally	ADV
ejpam-5428	6	2	,	,	PUNCT
ejpam-5428	6	3	we	we	PRON
ejpam-5428	6	4	demonstrate	demonstrate	VERB
ejpam-5428	6	5	the	the	DET
ejpam-5428	6	6	application	application	NOUN
ejpam-5428	6	7	of	of	ADP
ejpam-5428	6	8	our	our	PRON
ejpam-5428	6	9	introduced	introduce	VERB
ejpam-5428	6	10	theorems	theorem	NOUN
ejpam-5428	6	11	by	by	ADP
ejpam-5428	6	12	solving	solve	VERB
ejpam-5428	6	13	a	a	DET
ejpam-5428	6	14	non	non	ADJ
ejpam-5428	6	15	-	-	ADJ
ejpam-5428	6	16	linear	linear	ADJ
ejpam-5428	6	17	integral	integral	ADJ
ejpam-5428	6	18	equation	equation	NOUN
ejpam-5428	6	19	,	,	PUNCT
ejpam-5428	6	20	showing	show	VERB
ejpam-5428	6	21	the	the	DET
ejpam-5428	6	22	practical	practical	ADJ
ejpam-5428	6	23	utility	utility	NOUN
ejpam-5428	6	24	of	of	ADP
ejpam-5428	6	25	our	our	PRON
ejpam-5428	6	26	results	result	NOUN
ejpam-5428	6	27	.	.	PUNCT
ejpam-5428	7	1	2020	2020	NUM
ejpam-5428	7	2	mathematics	mathematic	NOUN
ejpam-5428	7	3	subject	subject	NOUN
ejpam-5428	7	4	classifications	classification	NOUN
ejpam-5428	7	5	:	:	PUNCT
ejpam-5428	7	6	54h25	54h25	NUM
ejpam-5428	7	7	,	,	PUNCT
ejpam-5428	7	8	47h10	47h10	PRON
ejpam-5428	7	9	key	key	ADJ
ejpam-5428	7	10	words	word	NOUN
ejpam-5428	7	11	and	and	CCONJ
ejpam-5428	7	12	phrases	phrase	NOUN
ejpam-5428	7	13	:	:	PUNCT
ejpam-5428	7	14	b	b	X
ejpam-5428	7	15	-	-	PUNCT
ejpam-5428	7	16	fuzzy	fuzzy	ADJ
ejpam-5428	7	17	metric	metric	ADJ
ejpam-5428	7	18	space	space	NOUN
ejpam-5428	7	19	,	,	PUNCT
ejpam-5428	7	20	geraghty	geraghty	PROPN
ejpam-5428	7	21	type	type	NOUN
ejpam-5428	7	22	mapping	mapping	NOUN
ejpam-5428	7	23	,	,	PUNCT
ejpam-5428	7	24	α	α	PROPN
ejpam-5428	7	25	-	-	PUNCT
ejpam-5428	7	26	suzuki	suzuki	NOUN
ejpam-5428	7	27	geraghty	geraghty	PROPN
ejpam-5428	7	28	type	type	NOUN
ejpam-5428	7	29	contraction	contraction	NOUN
ejpam-5428	7	30	1	1	NUM
ejpam-5428	7	31	.	.	PUNCT
ejpam-5428	7	32	introduction	introduction	NOUN
ejpam-5428	7	33	and	and	CCONJ
ejpam-5428	7	34	preliminaries	preliminary	NOUN
ejpam-5428	7	35	for	for	ADP
ejpam-5428	7	36	the	the	DET
ejpam-5428	7	37	first	first	ADJ
ejpam-5428	7	38	time	time	NOUN
ejpam-5428	7	39	,	,	PUNCT
ejpam-5428	7	40	the	the	DET
ejpam-5428	7	41	traditional	traditional	ADJ
ejpam-5428	7	42	metric	metric	ADJ
ejpam-5428	7	43	space	space	NOUN
ejpam-5428	7	44	framework	framework	NOUN
ejpam-5428	7	45	was	be	AUX
ejpam-5428	7	46	extended	extend	VERB
ejpam-5428	7	47	by	by	ADP
ejpam-5428	7	48	incorporating	incorporate	VERB
ejpam-5428	7	49	fuzzy	fuzzy	ADJ
ejpam-5428	7	50	logic	logic	NOUN
ejpam-5428	7	51	to	to	PART
ejpam-5428	7	52	address	address	VERB
ejpam-5428	7	53	uncertainties	uncertainty	NOUN
ejpam-5428	7	54	in	in	ADP
ejpam-5428	7	55	distance	distance	NOUN
ejpam-5428	7	56	measurements	measurement	NOUN
ejpam-5428	7	57	by	by	ADP
ejpam-5428	7	58	kramosil	kramosil	NOUN
ejpam-5428	7	59	and	and	CCONJ
ejpam-5428	7	60	michálek	michálek	ADJ
ejpam-5428	7	61	[	[	X
ejpam-5428	7	62	7	7	NUM
ejpam-5428	7	63	]	]	PUNCT
ejpam-5428	7	64	.	.	PUNCT
ejpam-5428	8	1	in	in	ADP
ejpam-5428	8	2	a	a	DET
ejpam-5428	8	3	classical	classical	ADJ
ejpam-5428	8	4	metric	metric	ADJ
ejpam-5428	8	5	space	space	NOUN
ejpam-5428	8	6	,	,	PUNCT
ejpam-5428	8	7	the	the	DET
ejpam-5428	8	8	distance	distance	NOUN
ejpam-5428	8	9	between	between	ADP
ejpam-5428	8	10	two	two	NUM
ejpam-5428	8	11	points	point	NOUN
ejpam-5428	8	12	is	be	AUX
ejpam-5428	8	13	precisely	precisely	ADV
ejpam-5428	8	14	defined	define	VERB
ejpam-5428	8	15	by	by	ADP
ejpam-5428	8	16	a	a	DET
ejpam-5428	8	17	real	real	ADJ
ejpam-5428	8	18	number	number	NOUN
ejpam-5428	8	19	,	,	PUNCT
ejpam-5428	8	20	adhering	adhere	VERB
ejpam-5428	8	21	to	to	ADP
ejpam-5428	8	22	strict	strict	ADJ
ejpam-5428	8	23	metric	metric	ADJ
ejpam-5428	8	24	properties	property	NOUN
ejpam-5428	8	25	.	.	PUNCT
ejpam-5428	9	1	however	however	ADV
ejpam-5428	9	2	,	,	PUNCT
ejpam-5428	9	3	in	in	ADP
ejpam-5428	9	4	a	a	DET
ejpam-5428	9	5	fuzzy	fuzzy	ADJ
ejpam-5428	9	6	metric	metric	ADJ
ejpam-5428	9	7	space	space	NOUN
ejpam-5428	9	8	,	,	PUNCT
ejpam-5428	9	9	distances	distance	NOUN
ejpam-5428	9	10	are	be	AUX
ejpam-5428	9	11	represented	represent	VERB
ejpam-5428	9	12	by	by	ADP
ejpam-5428	9	13	fuzzy	fuzzy	ADJ
ejpam-5428	9	14	sets	set	NOUN
ejpam-5428	9	15	,	,	PUNCT
ejpam-5428	9	16	allowing	allow	VERB
ejpam-5428	9	17	for	for	ADP
ejpam-5428	9	18	a	a	DET
ejpam-5428	9	19	range	range	NOUN
ejpam-5428	9	20	of	of	ADP
ejpam-5428	9	21	values	value	NOUN
ejpam-5428	9	22	that	that	PRON
ejpam-5428	9	23	reflect	reflect	VERB
ejpam-5428	9	24	varying	vary	VERB
ejpam-5428	9	25	degrees	degree	NOUN
ejpam-5428	9	26	of	of	ADP
ejpam-5428	9	27	proximity	proximity	NOUN
ejpam-5428	9	28	.	.	PUNCT
ejpam-5428	10	1	later	later	ADV
ejpam-5428	10	2	,	,	PUNCT
ejpam-5428	10	3	george	george	PROPN
ejpam-5428	10	4	and	and	CCONJ
ejpam-5428	10	5	veermani	veermani	NOUN
ejpam-5428	11	1	[	[	X
ejpam-5428	11	2	4	4	X
ejpam-5428	11	3	]	]	PUNCT
ejpam-5428	11	4	modified	modify	VERB
ejpam-5428	11	5	the	the	DET
ejpam-5428	11	6	definition	definition	NOUN
ejpam-5428	11	7	of	of	ADP
ejpam-5428	11	8	fuzzy	fuzzy	ADJ
ejpam-5428	11	9	metric	metric	ADJ
ejpam-5428	11	10	space	space	NOUN
ejpam-5428	11	11	given	give	VERB
ejpam-5428	11	12	by	by	ADP
ejpam-5428	11	13	kramosil	kramosil	NOUN
ejpam-5428	11	14	and	and	CCONJ
ejpam-5428	11	15	michálek	michálek	ADJ
ejpam-5428	12	1	[	[	X
ejpam-5428	12	2	7	7	NUM
ejpam-5428	12	3	]	]	PUNCT
ejpam-5428	13	1	and	and	CCONJ
ejpam-5428	13	2	proved	prove	VERB
ejpam-5428	13	3	some	some	DET
ejpam-5428	13	4	fixed	fix	VERB
ejpam-5428	13	5	point	point	NOUN
ejpam-5428	13	6	results	result	NOUN
ejpam-5428	13	7	.	.	PUNCT
ejpam-5428	14	1	inspired	inspire	VERB
ejpam-5428	14	2	by	by	ADP
ejpam-5428	14	3	this	this	PRON
ejpam-5428	14	4	,	,	PUNCT
ejpam-5428	14	5	concept	concept	NOUN
ejpam-5428	14	6	of	of	ADP
ejpam-5428	14	7	fuzzy	fuzzy	ADJ
ejpam-5428	14	8	b	b	X
ejpam-5428	14	9	-	-	PUNCT
ejpam-5428	14	10	metric	metric	ADJ
ejpam-5428	14	11	space	space	NOUN
ejpam-5428	14	12	was	be	AUX
ejpam-5428	14	13	introduced	introduce	VERB
ejpam-5428	14	14	by	by	ADP
ejpam-5428	14	15	sedghi	sedghi	VERB
ejpam-5428	14	16	et	et	PROPN
ejpam-5428	14	17	al	al	PROPN
ejpam-5428	14	18	.	.	PUNCT
ejpam-5428	15	1	[	[	X
ejpam-5428	15	2	15	15	NUM
ejpam-5428	15	3	]	]	PUNCT
ejpam-5428	15	4	,	,	PUNCT
ejpam-5428	15	5	where	where	SCONJ
ejpam-5428	15	6	the	the	DET
ejpam-5428	15	7	triangle	triangle	NOUN
ejpam-5428	15	8	inequality	inequality	NOUN
ejpam-5428	15	9	is	be	AUX
ejpam-5428	15	10	replaced	replace	VERB
ejpam-5428	15	11	by	by	ADP
ejpam-5428	15	12	a	a	DET
ejpam-5428	15	13	weaker	weak	ADJ
ejpam-5428	15	14	one	one	NUM
ejpam-5428	15	15	by	by	ADP
ejpam-5428	15	16	involving	involve	VERB
ejpam-5428	15	17	b	b	PROPN
ejpam-5428	15	18	>	>	X
ejpam-5428	15	19	1	1	NUM
ejpam-5428	15	20	,	,	PUNCT
ejpam-5428	15	21	with	with	ADP
ejpam-5428	15	22	this	this	DET
ejpam-5428	15	23	weaker	weak	ADJ
ejpam-5428	15	24	inequality	inequality	NOUN
ejpam-5428	15	25	,	,	PUNCT
ejpam-5428	15	26	the	the	DET
ejpam-5428	15	27	researchers	researcher	NOUN
ejpam-5428	15	28	introduced	introduce	VERB
ejpam-5428	15	29	many	many	ADJ
ejpam-5428	15	30	contractive	contractive	ADJ
ejpam-5428	15	31	inequalities	inequality	NOUN
ejpam-5428	15	32	to	to	PART
ejpam-5428	15	33	obtain	obtain	VERB
ejpam-5428	15	34	fixed	fixed	ADJ
ejpam-5428	15	35	point	point	NOUN
ejpam-5428	15	36	,	,	PUNCT
ejpam-5428	15	37	see([1	see([1	X
ejpam-5428	15	38	]	]	X
ejpam-5428	15	39	,	,	PUNCT
ejpam-5428	15	40	[	[	X
ejpam-5428	15	41	3	3	NUM
ejpam-5428	15	42	]	]	PUNCT
ejpam-5428	15	43	,	,	PUNCT
ejpam-5428	15	44	[	[	X
ejpam-5428	15	45	6	6	NUM
ejpam-5428	15	46	]	]	PUNCT
ejpam-5428	15	47	,	,	PUNCT
ejpam-5428	15	48	[	[	X
ejpam-5428	15	49	8	8	NUM
ejpam-5428	15	50	]	]	NUM
ejpam-5428	15	51	)	)	PUNCT
ejpam-5428	15	52	.	.	PUNCT
ejpam-5428	16	1	in	in	ADP
ejpam-5428	16	2	the	the	DET
ejpam-5428	16	3	line	line	NOUN
ejpam-5428	16	4	of	of	ADP
ejpam-5428	16	5	this	this	PRON
ejpam-5428	16	6	,	,	PUNCT
ejpam-5428	16	7	we	we	PRON
ejpam-5428	16	8	introduce	introduce	VERB
ejpam-5428	16	9	the	the	DET
ejpam-5428	16	10	concepts	concept	NOUN
ejpam-5428	16	11	of	of	ADP
ejpam-5428	16	12	geraghty	geraghty	PROPN
ejpam-5428	16	13	type	type	NOUN
ejpam-5428	16	14	inequalities	inequality	NOUN
ejpam-5428	16	15	in	in	ADP
ejpam-5428	16	16	this	this	DET
ejpam-5428	16	17	b	b	NOUN
ejpam-5428	16	18	-	-	PUNCT
ejpam-5428	16	19	fuzzy	fuzzy	ADJ
ejpam-5428	16	20	metric	metric	ADJ
ejpam-5428	16	21	spaces	space	NOUN
ejpam-5428	16	22	and	and	CCONJ
ejpam-5428	16	23	we	we	PRON
ejpam-5428	16	24	introduce	introduce	VERB
ejpam-5428	16	25	the	the	DET
ejpam-5428	16	26	notion	notion	NOUN
ejpam-5428	16	27	of	of	ADP
ejpam-5428	16	28	fuzzy	fuzzy	ADJ
ejpam-5428	16	29	α	α	PROPN
ejpam-5428	16	30	-	-	PUNCT
ejpam-5428	16	31	geraghty	geraghty	VERB
ejpam-5428	16	32	type	type	NOUN
ejpam-5428	16	33	mapping	mapping	NOUN
ejpam-5428	16	34	within	within	ADP
ejpam-5428	16	35	the	the	DET
ejpam-5428	16	36	context	context	NOUN
ejpam-5428	16	37	of	of	ADP
ejpam-5428	16	38	b	b	NOUN
ejpam-5428	16	39	-	-	PUNCT
ejpam-5428	16	40	fuzzy	fuzzy	ADJ
ejpam-5428	16	41	metric	metric	ADJ
ejpam-5428	16	42	space	space	NOUN
ejpam-5428	16	43	.	.	PUNCT
ejpam-5428	17	1	additionally	additionally	ADV
ejpam-5428	17	2	,	,	PUNCT
ejpam-5428	17	3	we	we	PRON
ejpam-5428	17	4	∗corresponding	∗corresponde	VERB
ejpam-5428	17	5	author	author	NOUN
ejpam-5428	17	6	.	.	PUNCT
ejpam-5428	18	1	doi	doi	NOUN
ejpam-5428	18	2	:	:	PUNCT
ejpam-5428	18	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5428	https://doi.org/10.29020/nybg.ejpam.v17i4.5428	ADP
ejpam-5428	18	4	email	email	NOUN
ejpam-5428	18	5	addresses	address	NOUN
ejpam-5428	18	6	:	:	PUNCT
ejpam-5428	18	7	umadevipatel@yahoo.co.in	umadevipatel@yahoo.co.in	ADV
ejpam-5428	18	8	(	(	PUNCT
ejpam-5428	18	9	u.	u.	PROPN
ejpam-5428	18	10	d.	d.	PROPN
ejpam-5428	18	11	patel	patel	PROPN
ejpam-5428	18	12	)	)	PUNCT
ejpam-5428	18	13	,	,	PUNCT
ejpam-5428	18	14	vineetachandra4@gmail.com	vineetachandra4@gmail.com	X
ejpam-5428	18	15	(	(	PUNCT
ejpam-5428	18	16	v.	v.	ADP
ejpam-5428	18	17	chandra	chandra	PROPN
ejpam-5428	18	18	)	)	PUNCT
ejpam-5428	18	19	,	,	PUNCT
ejpam-5428	18	20	radens@beotel.net	radens@beotel.net	PROPN
ejpam-5428	18	21	(	(	PUNCT
ejpam-5428	18	22	s.	s.	PROPN
ejpam-5428	18	23	radenović	radenović	ADJ
ejpam-5428	18	24	)	)	PUNCT
ejpam-5428	18	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5428	18	26	2384	2384	NUM
ejpam-5428	18	27	copyright	copyright	NOUN
ejpam-5428	18	28	:	:	PUNCT
ejpam-5428	18	29	©	©	PROPN
ejpam-5428	18	30	2024	2024	NUM
ejpam-5428	18	31	the	the	DET
ejpam-5428	18	32	author(s	author(s	NOUN
ejpam-5428	18	33	)	)	PUNCT
ejpam-5428	18	34	.	.	PUNCT
ejpam-5428	19	1	(	(	PUNCT
ejpam-5428	19	2	cc	cc	NOUN
ejpam-5428	19	3	by	by	ADP
ejpam-5428	19	4	-	-	PUNCT
ejpam-5428	19	5	nc	nc	PROPN
ejpam-5428	19	6	4.0	4.0	NUM
ejpam-5428	19	7	)	)	PUNCT
ejpam-5428	19	8	v.	v.	ADP
ejpam-5428	19	9	chandra	chandra	PROPN
ejpam-5428	19	10	,	,	PUNCT
ejpam-5428	19	11	u.	u.	PROPN
ejpam-5428	19	12	d.	d.	PROPN
ejpam-5428	19	13	patel	patel	PROPN
ejpam-5428	19	14	,	,	PUNCT
ejpam-5428	19	15	s.	s.	PROPN
ejpam-5428	19	16	radenović	radenović	PROPN
ejpam-5428	19	17	/	/	SYM
ejpam-5428	19	18	eur	eur	PROPN
ejpam-5428	19	19	.	.	PUNCT
ejpam-5428	20	1	j.	j.	PROPN
ejpam-5428	20	2	pure	pure	PROPN
ejpam-5428	20	3	appl	appl	PROPN
ejpam-5428	20	4	.	.	PROPN
ejpam-5428	20	5	math	math	PROPN
ejpam-5428	20	6	,	,	PUNCT
ejpam-5428	20	7	17	17	NUM
ejpam-5428	20	8	(	(	PUNCT
ejpam-5428	20	9	4	4	NUM
ejpam-5428	20	10	)	)	PUNCT
ejpam-5428	20	11	(	(	PUNCT
ejpam-5428	20	12	2024	2024	NUM
ejpam-5428	20	13	)	)	PUNCT
ejpam-5428	20	14	,	,	PUNCT
ejpam-5428	20	15	2384	2384	NUM
ejpam-5428	20	16	-	-	SYM
ejpam-5428	20	17	2404	2404	NUM
ejpam-5428	20	18	2385	2385	NUM
ejpam-5428	20	19	introduce	introduce	VERB
ejpam-5428	20	20	the	the	DET
ejpam-5428	20	21	idea	idea	NOUN
ejpam-5428	20	22	of	of	ADP
ejpam-5428	20	23	α	α	NOUN
ejpam-5428	20	24	-	-	PUNCT
ejpam-5428	20	25	suzuki	suzuki	NOUN
ejpam-5428	20	26	geraghty	geraghty	PROPN
ejpam-5428	20	27	type	type	NOUN
ejpam-5428	20	28	mapping	mapping	NOUN
ejpam-5428	20	29	in	in	ADP
ejpam-5428	20	30	the	the	DET
ejpam-5428	20	31	framework	framework	NOUN
ejpam-5428	20	32	of	of	ADP
ejpam-5428	20	33	g	g	NOUN
ejpam-5428	20	34	-	-	PUNCT
ejpam-5428	20	35	complete	complete	ADJ
ejpam-5428	20	36	b	b	X
ejpam-5428	20	37	-	-	PUNCT
ejpam-5428	20	38	fuzzy	fuzzy	ADJ
ejpam-5428	20	39	metric	metric	ADJ
ejpam-5428	20	40	space	space	NOUN
ejpam-5428	20	41	,	,	PUNCT
ejpam-5428	20	42	and	and	CCONJ
ejpam-5428	20	43	we	we	PRON
ejpam-5428	20	44	investigate	investigate	VERB
ejpam-5428	20	45	specific	specific	ADJ
ejpam-5428	20	46	fixed	fix	VERB
ejpam-5428	20	47	point	point	NOUN
ejpam-5428	20	48	problems	problem	NOUN
ejpam-5428	20	49	associated	associate	VERB
ejpam-5428	20	50	with	with	ADP
ejpam-5428	20	51	this	this	DET
ejpam-5428	20	52	generalizations	generalization	NOUN
ejpam-5428	20	53	.	.	PUNCT
ejpam-5428	21	1	we	we	PRON
ejpam-5428	21	2	offer	offer	VERB
ejpam-5428	21	3	several	several	ADJ
ejpam-5428	21	4	illustrative	illustrative	ADJ
ejpam-5428	21	5	examples	example	NOUN
ejpam-5428	21	6	with	with	ADP
ejpam-5428	21	7	the	the	DET
ejpam-5428	21	8	graphical	graphical	ADJ
ejpam-5428	21	9	approach	approach	NOUN
ejpam-5428	21	10	in	in	ADP
ejpam-5428	21	11	the	the	DET
ejpam-5428	21	12	support	support	NOUN
ejpam-5428	21	13	of	of	ADP
ejpam-5428	21	14	our	our	PRON
ejpam-5428	21	15	findings	finding	NOUN
ejpam-5428	21	16	.	.	PUNCT
ejpam-5428	22	1	in	in	ADP
ejpam-5428	22	2	last	last	ADJ
ejpam-5428	22	3	,	,	PUNCT
ejpam-5428	22	4	as	as	ADP
ejpam-5428	22	5	an	an	DET
ejpam-5428	22	6	application	application	NOUN
ejpam-5428	22	7	,	,	PUNCT
ejpam-5428	22	8	we	we	PRON
ejpam-5428	22	9	discuss	discuss	VERB
ejpam-5428	22	10	a	a	DET
ejpam-5428	22	11	solution	solution	NOUN
ejpam-5428	22	12	to	to	ADP
ejpam-5428	22	13	a	a	DET
ejpam-5428	22	14	non	non	ADJ
ejpam-5428	22	15	-	-	ADJ
ejpam-5428	22	16	linear	linear	ADJ
ejpam-5428	22	17	integral	integral	ADJ
ejpam-5428	22	18	equation	equation	NOUN
ejpam-5428	22	19	via	via	ADP
ejpam-5428	22	20	fixed	fix	VERB
ejpam-5428	22	21	point	point	NOUN
ejpam-5428	22	22	tools	tool	NOUN
ejpam-5428	22	23	.	.	PUNCT
ejpam-5428	23	1	we	we	PRON
ejpam-5428	23	2	must	must	AUX
ejpam-5428	23	3	need	need	VERB
ejpam-5428	23	4	the	the	DET
ejpam-5428	23	5	following	following	NOUN
ejpam-5428	23	6	:	:	PUNCT
ejpam-5428	23	7	definition	definition	NOUN
ejpam-5428	23	8	1	1	NUM
ejpam-5428	23	9	.	.	PUNCT
ejpam-5428	24	1	(	(	PUNCT
ejpam-5428	24	2	[	[	X
ejpam-5428	24	3	14	14	NUM
ejpam-5428	24	4	]	]	NUM
ejpam-5428	24	5	)	)	PUNCT
ejpam-5428	24	6	.	.	PUNCT
ejpam-5428	25	1	a	a	DET
ejpam-5428	25	2	function	function	NOUN
ejpam-5428	25	3	⋄	⋄	NOUN
ejpam-5428	25	4	:	:	PUNCT
ejpam-5428	26	1	[	[	X
ejpam-5428	26	2	0	0	NUM
ejpam-5428	26	3	,	,	PUNCT
ejpam-5428	26	4	1]2	1]2	NUM
ejpam-5428	26	5	→	→	PUNCT
ejpam-5428	26	6	[	[	X
ejpam-5428	26	7	0	0	NUM
ejpam-5428	26	8	,	,	PUNCT
ejpam-5428	26	9	1	1	NUM
ejpam-5428	26	10	]	]	PUNCT
ejpam-5428	26	11	is	be	AUX
ejpam-5428	26	12	called	call	VERB
ejpam-5428	26	13	a	a	DET
ejpam-5428	26	14	continuous	continuous	ADJ
ejpam-5428	26	15	triangular	triangular	NOUN
ejpam-5428	26	16	-	-	PUNCT
ejpam-5428	26	17	norm	norm	NOUN
ejpam-5428	26	18	if	if	SCONJ
ejpam-5428	26	19	•	•	NUM
ejpam-5428	26	20	⋄	⋄	PROPN
ejpam-5428	26	21	is	be	AUX
ejpam-5428	26	22	commutative	commutative	ADJ
ejpam-5428	26	23	and	and	CCONJ
ejpam-5428	26	24	associative	associative	ADJ
ejpam-5428	26	25	;	;	PUNCT
ejpam-5428	26	26	•	•	NUM
ejpam-5428	26	27	⋄	⋄	NOUN
ejpam-5428	26	28	is	be	AUX
ejpam-5428	26	29	continuous	continuous	ADJ
ejpam-5428	26	30	;	;	PUNCT
ejpam-5428	26	31	•	•	NUM
ejpam-5428	26	32	1	1	NUM
ejpam-5428	26	33	⋄	⋄	NOUN
ejpam-5428	26	34	a	a	DET
ejpam-5428	26	35	=	=	SYM
ejpam-5428	26	36	a	a	NOUN
ejpam-5428	26	37	;	;	PUNCT
ejpam-5428	26	38	•	•	ADP
ejpam-5428	26	39	a	a	DET
ejpam-5428	26	40	⋄	⋄	PROPN
ejpam-5428	26	41	b	b	NUM
ejpam-5428	26	42	≥	≥	NOUN
ejpam-5428	26	43	c	c	NOUN
ejpam-5428	26	44	⋄	⋄	PROPN
ejpam-5428	26	45	d	d	NOUN
ejpam-5428	26	46	,	,	PUNCT
ejpam-5428	26	47	whenever	whenever	SCONJ
ejpam-5428	26	48	a	a	DET
ejpam-5428	26	49	≥	≥	NOUN
ejpam-5428	26	50	c	c	NOUN
ejpam-5428	26	51	and	and	CCONJ
ejpam-5428	26	52	b	b	PROPN
ejpam-5428	26	53	≥	≥	X
ejpam-5428	26	54	d.	d.	NOUN
ejpam-5428	26	55	for	for	ADP
ejpam-5428	26	56	all	all	DET
ejpam-5428	26	57	a	a	DET
ejpam-5428	26	58	,	,	PUNCT
ejpam-5428	26	59	b	b	NOUN
ejpam-5428	26	60	,	,	PUNCT
ejpam-5428	26	61	c	c	NOUN
ejpam-5428	26	62	,	,	PUNCT
ejpam-5428	26	63	d	d	PROPN
ejpam-5428	26	64	∈	∈	PROPN
ejpam-5428	27	1	[	[	X
ejpam-5428	27	2	0	0	NUM
ejpam-5428	27	3	,	,	PUNCT
ejpam-5428	27	4	1	1	NUM
ejpam-5428	27	5	]	]	PUNCT
ejpam-5428	27	6	.	.	PUNCT
ejpam-5428	28	1	some	some	PRON
ejpam-5428	28	2	of	of	ADP
ejpam-5428	28	3	the	the	DET
ejpam-5428	28	4	l	l	NOUN
ejpam-5428	28	5	-	-	PUNCT
ejpam-5428	28	6	norms	norm	NOUN
ejpam-5428	28	7	are	be	AUX
ejpam-5428	28	8	a	a	DET
ejpam-5428	28	9	⋄m	⋄m	ADJ
ejpam-5428	28	10	b	b	NOUN
ejpam-5428	28	11	=	=	SYM
ejpam-5428	28	12	min{a	min{a	NOUN
ejpam-5428	28	13	,	,	PUNCT
ejpam-5428	28	14	b	b	NOUN
ejpam-5428	28	15	}	}	PUNCT
ejpam-5428	28	16	(	(	PUNCT
ejpam-5428	28	17	minimum	minimum	NOUN
ejpam-5428	28	18	)	)	PUNCT
ejpam-5428	28	19	,	,	PUNCT
ejpam-5428	28	20	a	a	DET
ejpam-5428	28	21	⋄p	⋄p	NUM
ejpam-5428	28	22	b	b	PROPN
ejpam-5428	28	23	=	=	SYM
ejpam-5428	28	24	ab	ab	PROPN
ejpam-5428	28	25	(	(	PUNCT
ejpam-5428	28	26	product	product	NOUN
ejpam-5428	28	27	)	)	PUNCT
ejpam-5428	28	28	,	,	PUNCT
ejpam-5428	28	29	a	a	DET
ejpam-5428	28	30	⋄l	⋄l	PROPN
ejpam-5428	28	31	b	b	X
ejpam-5428	28	32	=	=	SYM
ejpam-5428	28	33	max{a+	max{a+	PROPN
ejpam-5428	28	34	b−	b−	PROPN
ejpam-5428	28	35	1	1	NUM
ejpam-5428	28	36	,	,	PUNCT
ejpam-5428	28	37	0	0	NUM
ejpam-5428	28	38	}	}	PUNCT
ejpam-5428	28	39	.	.	PUNCT
ejpam-5428	29	1	definition	definition	NOUN
ejpam-5428	29	2	2	2	NUM
ejpam-5428	29	3	.	.	PUNCT
ejpam-5428	30	1	[	[	X
ejpam-5428	30	2	6	6	NUM
ejpam-5428	30	3	]	]	PUNCT
ejpam-5428	30	4	.	.	PUNCT
ejpam-5428	31	1	a	a	DET
ejpam-5428	31	2	b	b	X
ejpam-5428	31	3	-	-	PUNCT
ejpam-5428	31	4	fuzzy	fuzzy	ADJ
ejpam-5428	31	5	metric	metric	ADJ
ejpam-5428	31	6	space	space	NOUN
ejpam-5428	31	7	is	be	AUX
ejpam-5428	31	8	an	an	DET
ejpam-5428	31	9	ordered	ordered	ADJ
ejpam-5428	31	10	triple	triple	ADJ
ejpam-5428	31	11	(	(	PUNCT
ejpam-5428	31	12	ȳ	ȳ	NOUN
ejpam-5428	31	13	=	=	NOUN
ejpam-5428	31	14	̸	̸	NUM
ejpam-5428	31	15	ϕ,mz	ϕ,mz	PUNCT
ejpam-5428	31	16	,	,	PUNCT
ejpam-5428	31	17	⋄	⋄	PROPN
ejpam-5428	31	18	)	)	PUNCT
ejpam-5428	31	19	,	,	PUNCT
ejpam-5428	31	20	where	where	SCONJ
ejpam-5428	31	21	mz	mz	PROPN
ejpam-5428	31	22	:	:	PUNCT
ejpam-5428	31	23	ȳ2	ȳ2	VERB
ejpam-5428	31	24	×	×	PROPN
ejpam-5428	31	25	(	(	PUNCT
ejpam-5428	31	26	0,+∞	0,+∞	NUM
ejpam-5428	31	27	)	)	PUNCT
ejpam-5428	31	28	→	→	PUNCT
ejpam-5428	32	1	[	[	X
ejpam-5428	32	2	0	0	NUM
ejpam-5428	32	3	,	,	PUNCT
ejpam-5428	32	4	1	1	NUM
ejpam-5428	32	5	]	]	X
ejpam-5428	32	6	satisfying	satisfying	NOUN
ejpam-5428	32	7	(	(	PUNCT
ejpam-5428	32	8	i	i	NOUN
ejpam-5428	32	9	)	)	PUNCT
ejpam-5428	32	10	mz(δ	mz(δ	PROPN
ejpam-5428	32	11	,	,	PUNCT
ejpam-5428	32	12	γ	γ	X
ejpam-5428	32	13	,	,	PUNCT
ejpam-5428	32	14	l	l	NOUN
ejpam-5428	32	15	)	)	PUNCT
ejpam-5428	32	16	>	>	X
ejpam-5428	32	17	0	0	NUM
ejpam-5428	32	18	;	;	PUNCT
ejpam-5428	32	19	(	(	PUNCT
ejpam-5428	32	20	ii	ii	NOUN
ejpam-5428	32	21	)	)	PUNCT
ejpam-5428	32	22	mz(δ	mz(δ	PROPN
ejpam-5428	32	23	,	,	PUNCT
ejpam-5428	32	24	γ	γ	X
ejpam-5428	32	25	,	,	PUNCT
ejpam-5428	32	26	l	l	NOUN
ejpam-5428	32	27	)	)	PUNCT
ejpam-5428	32	28	=	=	SYM
ejpam-5428	32	29	1	1	NUM
ejpam-5428	32	30	if	if	SCONJ
ejpam-5428	32	31	and	and	CCONJ
ejpam-5428	32	32	only	only	ADV
ejpam-5428	32	33	if	if	SCONJ
ejpam-5428	32	34	δ	δ	PROPN
ejpam-5428	32	35	=	=	SYM
ejpam-5428	32	36	γ	γ	X
ejpam-5428	32	37	;	;	PUNCT
ejpam-5428	32	38	(	(	PUNCT
ejpam-5428	32	39	iii	iii	NOUN
ejpam-5428	32	40	)	)	PUNCT
ejpam-5428	32	41	mz(δ	mz(δ	PROPN
ejpam-5428	32	42	,	,	PUNCT
ejpam-5428	32	43	γ	γ	X
ejpam-5428	32	44	,	,	PUNCT
ejpam-5428	32	45	l	l	NOUN
ejpam-5428	32	46	)	)	PUNCT
ejpam-5428	32	47	=	=	SYM
ejpam-5428	32	48	mz(γ	mz(γ	X
ejpam-5428	32	49	,	,	PUNCT
ejpam-5428	32	50	δ	δ	PROPN
ejpam-5428	32	51	,	,	PUNCT
ejpam-5428	32	52	l	l	PROPN
ejpam-5428	32	53	)	)	PUNCT
ejpam-5428	32	54	;	;	PUNCT
ejpam-5428	32	55	(	(	PUNCT
ejpam-5428	32	56	iv	iv	X
ejpam-5428	32	57	)	)	PUNCT
ejpam-5428	32	58	mz(δ	mz(δ	PROPN
ejpam-5428	32	59	,	,	PUNCT
ejpam-5428	32	60	γ	γ	X
ejpam-5428	32	61	,	,	PUNCT
ejpam-5428	32	62	b(l	b(l	PROPN
ejpam-5428	32	63	+	+	CCONJ
ejpam-5428	32	64	r	r	NOUN
ejpam-5428	32	65	)	)	PUNCT
ejpam-5428	32	66	)	)	PUNCT
ejpam-5428	32	67	≥	≥	NOUN
ejpam-5428	32	68	mz(δ	mz(δ	PROPN
ejpam-5428	32	69	,	,	PUNCT
ejpam-5428	32	70	η	η	NOUN
ejpam-5428	32	71	,	,	PUNCT
ejpam-5428	32	72	l	l	NOUN
ejpam-5428	32	73	)	)	PUNCT
ejpam-5428	32	74	⋄mz(η	⋄mz(η	NOUN
ejpam-5428	32	75	,	,	PUNCT
ejpam-5428	32	76	γ	γ	X
ejpam-5428	32	77	,	,	PUNCT
ejpam-5428	32	78	r	r	NOUN
ejpam-5428	32	79	)	)	PUNCT
ejpam-5428	32	80	,	,	PUNCT
ejpam-5428	32	81	where	where	SCONJ
ejpam-5428	32	82	b	b	X
ejpam-5428	32	83	≥	≥	NOUN
ejpam-5428	32	84	1	1	NUM
ejpam-5428	32	85	;	;	PUNCT
ejpam-5428	32	86	(	(	PUNCT
ejpam-5428	32	87	v	v	NOUN
ejpam-5428	32	88	)	)	PUNCT
ejpam-5428	32	89	mz(δ	mz(δ	PROPN
ejpam-5428	32	90	,	,	PUNCT
ejpam-5428	32	91	γ	γ	X
ejpam-5428	32	92	,	,	PUNCT
ejpam-5428	32	93	.	.	PUNCT
ejpam-5428	32	94	)	)	PUNCT
ejpam-5428	32	95	:	:	PUNCT
ejpam-5428	32	96	(	(	PUNCT
ejpam-5428	32	97	0,+∞	0,+∞	NUM
ejpam-5428	32	98	)	)	PUNCT
ejpam-5428	32	99	→	→	SYM
ejpam-5428	32	100	(	(	PUNCT
ejpam-5428	32	101	0	0	NUM
ejpam-5428	32	102	,	,	PUNCT
ejpam-5428	32	103	1	1	NUM
ejpam-5428	32	104	]	]	PUNCT
ejpam-5428	32	105	is	be	AUX
ejpam-5428	32	106	continuous	continuous	ADJ
ejpam-5428	32	107	from	from	ADP
ejpam-5428	32	108	left	left	ADJ
ejpam-5428	32	109	and	and	CCONJ
ejpam-5428	32	110	lim	lim	PROPN
ejpam-5428	32	111	l→+∞	l→+∞	PROPN
ejpam-5428	32	112	mz(δ	mz(δ	PROPN
ejpam-5428	32	113	,	,	PUNCT
ejpam-5428	32	114	γ	γ	X
ejpam-5428	32	115	,	,	PUNCT
ejpam-5428	32	116	l	l	NOUN
ejpam-5428	32	117	)	)	PUNCT
ejpam-5428	32	118	=	=	SYM
ejpam-5428	33	1	1	1	X
ejpam-5428	33	2	.	.	X
ejpam-5428	33	3	for	for	ADP
ejpam-5428	33	4	all	all	DET
ejpam-5428	33	5	δ	δ	PROPN
ejpam-5428	33	6	,	,	PUNCT
ejpam-5428	33	7	γ	γ	PROPN
ejpam-5428	33	8	,	,	PUNCT
ejpam-5428	33	9	η	η	PROPN
ejpam-5428	33	10	∈	∈	PROPN
ejpam-5428	33	11	ȳ	ȳ	PROPN
ejpam-5428	33	12	and	and	CCONJ
ejpam-5428	33	13	l	l	NOUN
ejpam-5428	33	14	,	,	PUNCT
ejpam-5428	33	15	r	r	NOUN
ejpam-5428	33	16	>	>	X
ejpam-5428	33	17	0	0	X
ejpam-5428	33	18	.	.	PUNCT
ejpam-5428	34	1	note	note	NOUN
ejpam-5428	34	2	:	:	PUNCT
ejpam-5428	34	3	if	if	SCONJ
ejpam-5428	34	4	b	b	X
ejpam-5428	34	5	=	=	SYM
ejpam-5428	34	6	1	1	NUM
ejpam-5428	34	7	then	then	ADV
ejpam-5428	34	8	definition	definition	NOUN
ejpam-5428	34	9	(	(	PUNCT
ejpam-5428	34	10	2	2	X
ejpam-5428	34	11	)	)	PUNCT
ejpam-5428	34	12	will	will	AUX
ejpam-5428	34	13	become	become	VERB
ejpam-5428	34	14	a	a	DET
ejpam-5428	34	15	fuzzy	fuzzy	ADJ
ejpam-5428	34	16	metric	metric	ADJ
ejpam-5428	34	17	space	space	NOUN
ejpam-5428	34	18	.	.	PUNCT
ejpam-5428	35	1	example	example	NOUN
ejpam-5428	36	1	1	1	NUM
ejpam-5428	36	2	.	.	PUNCT
ejpam-5428	37	1	let	let	VERB
ejpam-5428	37	2	mz(δ	mz(δ	PROPN
ejpam-5428	37	3	,	,	PUNCT
ejpam-5428	37	4	γ	γ	X
ejpam-5428	37	5	,	,	PUNCT
ejpam-5428	37	6	l	l	NOUN
ejpam-5428	37	7	)	)	PUNCT
ejpam-5428	37	8	=	=	SYM
ejpam-5428	37	9	e−	e−	PROPN
ejpam-5428	37	10	|δ	|δ	NOUN
ejpam-5428	37	11	–	–	PUNCT
ejpam-5428	37	12	γ|p	γ|p	PUNCT
ejpam-5428	37	13	l	l	NOUN
ejpam-5428	37	14	,	,	PUNCT
ejpam-5428	37	15	where	where	SCONJ
ejpam-5428	37	16	p	p	NOUN
ejpam-5428	37	17	>	>	X
ejpam-5428	37	18	1	1	NUM
ejpam-5428	37	19	is	be	AUX
ejpam-5428	37	20	a	a	DET
ejpam-5428	37	21	real	real	ADJ
ejpam-5428	37	22	number	number	NOUN
ejpam-5428	37	23	,	,	PUNCT
ejpam-5428	37	24	mz	mz	PROPN
ejpam-5428	37	25	is	be	AUX
ejpam-5428	37	26	a	a	DET
ejpam-5428	37	27	b	b	NOUN
ejpam-5428	37	28	-	-	PUNCT
ejpam-5428	37	29	fuzzy	fuzzy	ADJ
ejpam-5428	37	30	metric	metric	NOUN
ejpam-5428	37	31	with	with	ADP
ejpam-5428	37	32	b	b	PROPN
ejpam-5428	37	33	=	=	SYM
ejpam-5428	37	34	2p–1	2p–1	PROPN
ejpam-5428	37	35	but	but	CCONJ
ejpam-5428	37	36	not	not	PART
ejpam-5428	37	37	fuzzy	fuzzy	ADJ
ejpam-5428	37	38	metric	metric	ADJ
ejpam-5428	37	39	space	space	NOUN
ejpam-5428	37	40	.	.	PUNCT
ejpam-5428	38	1	definition	definition	NOUN
ejpam-5428	38	2	3	3	NUM
ejpam-5428	38	3	.	.	PUNCT
ejpam-5428	39	1	[	[	X
ejpam-5428	39	2	8	8	NUM
ejpam-5428	39	3	]	]	PUNCT
ejpam-5428	39	4	suppose	suppose	VERB
ejpam-5428	39	5	(	(	PUNCT
ejpam-5428	39	6	ȳ,mz	ȳ,mz	NUM
ejpam-5428	39	7	,	,	PUNCT
ejpam-5428	39	8	⋄	⋄	PROPN
ejpam-5428	39	9	)	)	PUNCT
ejpam-5428	39	10	is	be	AUX
ejpam-5428	39	11	a	a	DET
ejpam-5428	39	12	b	b	NOUN
ejpam-5428	39	13	-	-	PUNCT
ejpam-5428	39	14	fuzzy	fuzzy	ADJ
ejpam-5428	39	15	metric	metric	ADJ
ejpam-5428	39	16	space	space	NOUN
ejpam-5428	39	17	.	.	PUNCT
ejpam-5428	40	1	then	then	ADV
ejpam-5428	40	2	(	(	PUNCT
ejpam-5428	40	3	i	i	NOUN
ejpam-5428	40	4	)	)	PUNCT
ejpam-5428	40	5	{	{	PUNCT
ejpam-5428	40	6	δn	δn	X
ejpam-5428	40	7	}	}	PUNCT
ejpam-5428	40	8	is	be	AUX
ejpam-5428	40	9	called	call	VERB
ejpam-5428	40	10	g	g	NOUN
ejpam-5428	40	11	-	-	PUNCT
ejpam-5428	40	12	convergent	convergent	NOUN
ejpam-5428	40	13	sequence	sequence	NOUN
ejpam-5428	40	14	if	if	SCONJ
ejpam-5428	40	15	there	there	PRON
ejpam-5428	40	16	exists	exist	VERB
ejpam-5428	40	17	δ	δ	PROPN
ejpam-5428	40	18	∈	∈	PROPN
ejpam-5428	40	19	ȳ	ȳ	PROPN
ejpam-5428	41	1	such	such	ADJ
ejpam-5428	41	2	that	that	SCONJ
ejpam-5428	41	3	lim	lim	PROPN
ejpam-5428	41	4	n→+∞	n→+∞	PROPN
ejpam-5428	41	5	mz(δn	mz(δn	PROPN
ejpam-5428	41	6	,	,	PUNCT
ejpam-5428	41	7	δ	δ	PROPN
ejpam-5428	41	8	,	,	PUNCT
ejpam-5428	41	9	l	l	NOUN
ejpam-5428	41	10	)	)	PUNCT
ejpam-5428	41	11	=	=	SYM
ejpam-5428	41	12	1	1	X
ejpam-5428	41	13	.	.	X
ejpam-5428	41	14	v.	v.	PROPN
ejpam-5428	41	15	chandra	chandra	PROPN
ejpam-5428	41	16	,	,	PUNCT
ejpam-5428	41	17	u.	u.	PROPN
ejpam-5428	41	18	d.	d.	PROPN
ejpam-5428	41	19	patel	patel	PROPN
ejpam-5428	41	20	,	,	PUNCT
ejpam-5428	41	21	s.	s.	PROPN
ejpam-5428	41	22	radenović	radenović	PROPN
ejpam-5428	41	23	/	/	SYM
ejpam-5428	41	24	eur	eur	PROPN
ejpam-5428	41	25	.	.	PUNCT
ejpam-5428	42	1	j.	j.	PROPN
ejpam-5428	42	2	pure	pure	PROPN
ejpam-5428	42	3	appl	appl	PROPN
ejpam-5428	42	4	.	.	PROPN
ejpam-5428	42	5	math	math	PROPN
ejpam-5428	42	6	,	,	PUNCT
ejpam-5428	42	7	17	17	NUM
ejpam-5428	42	8	(	(	PUNCT
ejpam-5428	42	9	4	4	NUM
ejpam-5428	42	10	)	)	PUNCT
ejpam-5428	42	11	(	(	PUNCT
ejpam-5428	42	12	2024	2024	NUM
ejpam-5428	42	13	)	)	PUNCT
ejpam-5428	42	14	,	,	PUNCT
ejpam-5428	42	15	2384	2384	NUM
ejpam-5428	42	16	-	-	SYM
ejpam-5428	42	17	2404	2404	NUM
ejpam-5428	42	18	2386	2386	NUM
ejpam-5428	42	19	(	(	PUNCT
ejpam-5428	42	20	ii	ii	NOUN
ejpam-5428	42	21	)	)	PUNCT
ejpam-5428	42	22	{	{	PUNCT
ejpam-5428	42	23	δn	δn	NOUN
ejpam-5428	42	24	}	}	PUNCT
ejpam-5428	42	25	in	in	ADP
ejpam-5428	42	26	ȳ	ȳ	PROPN
ejpam-5428	42	27	is	be	AUX
ejpam-5428	42	28	called	call	VERB
ejpam-5428	42	29	a	a	DET
ejpam-5428	42	30	g	g	NOUN
ejpam-5428	42	31	-	-	PUNCT
ejpam-5428	42	32	cauchy	cauchy	ADJ
ejpam-5428	42	33	sequence	sequence	NOUN
ejpam-5428	42	34	if	if	SCONJ
ejpam-5428	42	35	lim	lim	PROPN
ejpam-5428	42	36	n	n	CCONJ
ejpam-5428	42	37	,	,	PUNCT
ejpam-5428	42	38	m→+∞	m→+∞	PROPN
ejpam-5428	42	39	mz(δn	mz(δn	PROPN
ejpam-5428	42	40	,	,	PUNCT
ejpam-5428	42	41	δm	δm	PROPN
ejpam-5428	42	42	,	,	PUNCT
ejpam-5428	42	43	l	l	NOUN
ejpam-5428	42	44	)	)	PUNCT
ejpam-5428	42	45	=	=	SYM
ejpam-5428	42	46	1	1	NUM
ejpam-5428	42	47	for	for	ADP
ejpam-5428	42	48	all	all	DET
ejpam-5428	42	49	m	m	PROPN
ejpam-5428	42	50	,	,	PUNCT
ejpam-5428	42	51	n	n	PROPN
ejpam-5428	42	52	∈	∈	PROPN
ejpam-5428	42	53	n	n	NOUN
ejpam-5428	42	54	and	and	CCONJ
ejpam-5428	42	55	l	l	NOUN
ejpam-5428	42	56	>	>	X
ejpam-5428	43	1	0	0	X
ejpam-5428	43	2	.	.	PUNCT
ejpam-5428	43	3	(	(	PUNCT
ejpam-5428	43	4	iii	iii	X
ejpam-5428	43	5	)	)	PUNCT
ejpam-5428	43	6	the	the	DET
ejpam-5428	43	7	space	space	NOUN
ejpam-5428	43	8	is	be	AUX
ejpam-5428	43	9	called	call	VERB
ejpam-5428	43	10	complete	complete	ADJ
ejpam-5428	43	11	if	if	SCONJ
ejpam-5428	43	12	every	every	DET
ejpam-5428	43	13	cauchy	cauchy	ADJ
ejpam-5428	43	14	sequence	sequence	NOUN
ejpam-5428	43	15	is	be	AUX
ejpam-5428	43	16	convergent	convergent	ADJ
ejpam-5428	43	17	in	in	ADP
ejpam-5428	43	18	ȳ.	ȳ.	NOUN
ejpam-5428	43	19	geraghty	geraghty	PROPN
ejpam-5428	43	20	(	(	PUNCT
ejpam-5428	43	21	[	[	X
ejpam-5428	43	22	5	5	NUM
ejpam-5428	43	23	]	]	PUNCT
ejpam-5428	43	24	)	)	PUNCT
ejpam-5428	43	25	introduced	introduce	VERB
ejpam-5428	43	26	a	a	DET
ejpam-5428	43	27	category	category	NOUN
ejpam-5428	43	28	denoted	denote	VERB
ejpam-5428	43	29	as	as	ADP
ejpam-5428	43	30	b	b	NUM
ejpam-5428	43	31	which	which	PRON
ejpam-5428	43	32	is	be	AUX
ejpam-5428	43	33	a	a	DET
ejpam-5428	43	34	collection	collection	NOUN
ejpam-5428	43	35	of	of	ADP
ejpam-5428	43	36	maps	map	NOUN
ejpam-5428	43	37	defined	define	VERB
ejpam-5428	43	38	as	as	ADP
ejpam-5428	43	39	β	β	X
ejpam-5428	43	40	:	:	PUNCT
ejpam-5428	44	1	[	[	X
ejpam-5428	44	2	0,+∞	0,+∞	NUM
ejpam-5428	44	3	)	)	PUNCT
ejpam-5428	44	4	→	→	PUNCT
ejpam-5428	45	1	[	[	X
ejpam-5428	45	2	0	0	NUM
ejpam-5428	45	3	,	,	PUNCT
ejpam-5428	45	4	1	1	NUM
ejpam-5428	45	5	)	)	PUNCT
ejpam-5428	45	6	satisfying	satisfy	VERB
ejpam-5428	45	7	β(tn	β(tn	NOUN
ejpam-5428	45	8	)	)	PUNCT
ejpam-5428	45	9	→	→	SYM
ejpam-5428	45	10	1	1	NUM
ejpam-5428	45	11	as	as	ADP
ejpam-5428	45	12	n	n	NOUN
ejpam-5428	45	13	→	→	SYM
ejpam-5428	45	14	+	+	ADJ
ejpam-5428	45	15	∞	∞	PROPN
ejpam-5428	45	16	⇒	⇒	NOUN
ejpam-5428	45	17	tn	tn	PROPN
ejpam-5428	45	18	→	→	SYM
ejpam-5428	45	19	0	0	NUM
ejpam-5428	45	20	as	as	ADP
ejpam-5428	45	21	n	n	PRON
ejpam-5428	45	22	→	→	SYM
ejpam-5428	45	23	+	+	ADJ
ejpam-5428	45	24	∞.	∞.	PROPN
ejpam-5428	45	25	researchers	researcher	NOUN
ejpam-5428	45	26	introduced	introduce	VERB
ejpam-5428	45	27	many	many	ADJ
ejpam-5428	45	28	contractive	contractive	ADJ
ejpam-5428	45	29	inequalities	inequality	NOUN
ejpam-5428	45	30	to	to	PART
ejpam-5428	45	31	obtain	obtain	VERB
ejpam-5428	45	32	fixed	fix	VERB
ejpam-5428	45	33	points	point	NOUN
ejpam-5428	45	34	in	in	ADP
ejpam-5428	45	35	this	this	DET
ejpam-5428	45	36	fuzzy	fuzzy	ADJ
ejpam-5428	45	37	space	space	NOUN
ejpam-5428	45	38	.	.	PUNCT
ejpam-5428	46	1	in	in	ADP
ejpam-5428	46	2	the	the	DET
ejpam-5428	46	3	line	line	NOUN
ejpam-5428	46	4	of	of	ADP
ejpam-5428	46	5	this	this	PRON
ejpam-5428	46	6	,	,	PUNCT
ejpam-5428	46	7	we	we	PRON
ejpam-5428	46	8	introduce	introduce	VERB
ejpam-5428	46	9	the	the	DET
ejpam-5428	46	10	concepts	concept	NOUN
ejpam-5428	46	11	of	of	ADP
ejpam-5428	46	12	geraghty	geraghty	PROPN
ejpam-5428	46	13	type	type	NOUN
ejpam-5428	46	14	inequalities	inequality	NOUN
ejpam-5428	46	15	in	in	ADP
ejpam-5428	46	16	this	this	DET
ejpam-5428	46	17	b	b	NOUN
ejpam-5428	46	18	-	-	PUNCT
ejpam-5428	46	19	fuzzy	fuzzy	ADJ
ejpam-5428	46	20	metric	metric	ADJ
ejpam-5428	46	21	space	space	NOUN
ejpam-5428	46	22	and	and	CCONJ
ejpam-5428	46	23	we	we	PRON
ejpam-5428	46	24	inject	inject	VERB
ejpam-5428	46	25	the	the	DET
ejpam-5428	46	26	notion	notion	NOUN
ejpam-5428	46	27	of	of	ADP
ejpam-5428	46	28	fuzzy	fuzzy	ADJ
ejpam-5428	46	29	α	α	PROPN
ejpam-5428	46	30	-	-	PUNCT
ejpam-5428	46	31	geraghty	geraghty	VERB
ejpam-5428	46	32	type	type	NOUN
ejpam-5428	46	33	mapping	mapping	NOUN
ejpam-5428	46	34	within	within	ADP
ejpam-5428	46	35	the	the	DET
ejpam-5428	46	36	context	context	NOUN
ejpam-5428	46	37	of	of	ADP
ejpam-5428	46	38	b	b	NOUN
ejpam-5428	46	39	-	-	PUNCT
ejpam-5428	46	40	fuzzy	fuzzy	ADJ
ejpam-5428	46	41	metric	metric	ADJ
ejpam-5428	46	42	space	space	NOUN
ejpam-5428	46	43	.	.	PUNCT
ejpam-5428	47	1	additionally	additionally	ADV
ejpam-5428	47	2	,	,	PUNCT
ejpam-5428	47	3	we	we	PRON
ejpam-5428	47	4	introduce	introduce	VERB
ejpam-5428	47	5	the	the	DET
ejpam-5428	47	6	idea	idea	NOUN
ejpam-5428	47	7	of	of	ADP
ejpam-5428	47	8	α	α	PROPN
ejpam-5428	47	9	-	-	PUNCT
ejpam-5428	47	10	suzuki	suzuki	NOUN
ejpam-5428	47	11	-	-	PUNCT
ejpam-5428	47	12	geraghty	geraghty	VERB
ejpam-5428	47	13	type	type	NOUN
ejpam-5428	47	14	mapping	mapping	NOUN
ejpam-5428	47	15	in	in	ADP
ejpam-5428	47	16	g	g	NOUN
ejpam-5428	47	17	-	-	PUNCT
ejpam-5428	47	18	complete	complete	ADJ
ejpam-5428	47	19	b	b	X
ejpam-5428	47	20	-	-	PUNCT
ejpam-5428	47	21	fuzzy	fuzzy	ADJ
ejpam-5428	47	22	metric	metric	ADJ
ejpam-5428	47	23	space	space	NOUN
ejpam-5428	47	24	,	,	PUNCT
ejpam-5428	47	25	and	and	CCONJ
ejpam-5428	47	26	we	we	PRON
ejpam-5428	47	27	investigate	investigate	VERB
ejpam-5428	47	28	specific	specific	ADJ
ejpam-5428	47	29	fixed	fix	VERB
ejpam-5428	47	30	point	point	NOUN
ejpam-5428	47	31	problems	problem	NOUN
ejpam-5428	47	32	associated	associate	VERB
ejpam-5428	47	33	with	with	ADP
ejpam-5428	47	34	these	these	DET
ejpam-5428	47	35	generalizations	generalization	NOUN
ejpam-5428	47	36	.	.	PUNCT
ejpam-5428	48	1	we	we	PRON
ejpam-5428	48	2	offer	offer	VERB
ejpam-5428	48	3	several	several	ADJ
ejpam-5428	48	4	illustrative	illustrative	ADJ
ejpam-5428	48	5	examples	example	NOUN
ejpam-5428	48	6	with	with	ADP
ejpam-5428	48	7	the	the	DET
ejpam-5428	48	8	graphical	graphical	ADJ
ejpam-5428	48	9	approach	approach	NOUN
ejpam-5428	48	10	in	in	ADP
ejpam-5428	48	11	support	support	NOUN
ejpam-5428	48	12	of	of	ADP
ejpam-5428	48	13	our	our	PRON
ejpam-5428	48	14	findings	finding	NOUN
ejpam-5428	48	15	.	.	PUNCT
ejpam-5428	49	1	in	in	ADP
ejpam-5428	49	2	last	last	ADJ
ejpam-5428	49	3	,	,	PUNCT
ejpam-5428	49	4	as	as	ADP
ejpam-5428	49	5	an	an	DET
ejpam-5428	49	6	application	application	NOUN
ejpam-5428	49	7	,	,	PUNCT
ejpam-5428	49	8	we	we	PRON
ejpam-5428	49	9	discuss	discuss	VERB
ejpam-5428	49	10	a	a	DET
ejpam-5428	49	11	solution	solution	NOUN
ejpam-5428	49	12	to	to	ADP
ejpam-5428	49	13	a	a	DET
ejpam-5428	49	14	non	non	ADJ
ejpam-5428	49	15	-	-	ADJ
ejpam-5428	49	16	linear	linear	ADJ
ejpam-5428	49	17	integral	integral	ADJ
ejpam-5428	49	18	equation	equation	NOUN
ejpam-5428	49	19	via	via	ADP
ejpam-5428	49	20	fixed	fix	VERB
ejpam-5428	49	21	point	point	NOUN
ejpam-5428	49	22	tools	tool	NOUN
ejpam-5428	49	23	.	.	PUNCT
ejpam-5428	50	1	2	2	X
ejpam-5428	50	2	.	.	X
ejpam-5428	50	3	main	main	ADJ
ejpam-5428	50	4	results	result	NOUN
ejpam-5428	50	5	we	we	PRON
ejpam-5428	50	6	must	must	AUX
ejpam-5428	50	7	require	require	VERB
ejpam-5428	50	8	to	to	PART
ejpam-5428	50	9	introduce	introduce	VERB
ejpam-5428	50	10	the	the	DET
ejpam-5428	50	11	following	follow	VERB
ejpam-5428	50	12	definitions	definition	NOUN
ejpam-5428	50	13	.	.	PUNCT
ejpam-5428	51	1	definition	definition	NOUN
ejpam-5428	51	2	4	4	NUM
ejpam-5428	51	3	.	.	PUNCT
ejpam-5428	52	1	a	a	DET
ejpam-5428	52	2	b	b	NOUN
ejpam-5428	52	3	-	-	PUNCT
ejpam-5428	52	4	fuzzy	fuzzy	ADJ
ejpam-5428	52	5	metric	metric	NOUN
ejpam-5428	52	6	mz	mz	PROPN
ejpam-5428	52	7	is	be	AUX
ejpam-5428	52	8	said	say	VERB
ejpam-5428	52	9	to	to	PART
ejpam-5428	52	10	be	be	AUX
ejpam-5428	52	11	c	c	NOUN
ejpam-5428	52	12	-	-	PUNCT
ejpam-5428	52	13	triangular	triangular	NOUN
ejpam-5428	52	14	,	,	PUNCT
ejpam-5428	52	15	if	if	SCONJ
ejpam-5428	52	16	for	for	ADP
ejpam-5428	52	17	all	all	DET
ejpam-5428	52	18	δ	δ	PROPN
ejpam-5428	52	19	,	,	PUNCT
ejpam-5428	52	20	γ	γ	PROPN
ejpam-5428	52	21	,	,	PUNCT
ejpam-5428	52	22	η	η	PROPN
ejpam-5428	52	23	∈	∈	PROPN
ejpam-5428	52	24	ȳ	ȳ	PROPN
ejpam-5428	52	25	and	and	CCONJ
ejpam-5428	52	26	l	l	NOUN
ejpam-5428	52	27	>	>	X
ejpam-5428	52	28	0	0	NUM
ejpam-5428	52	29	,	,	PUNCT
ejpam-5428	52	30	mz(δ	mz(δ	NUM
ejpam-5428	52	31	,	,	PUNCT
ejpam-5428	52	32	γ	γ	X
ejpam-5428	52	33	,	,	PUNCT
ejpam-5428	52	34	l	l	NOUN
ejpam-5428	52	35	)	)	PUNCT
ejpam-5428	52	36	≥	≥	NOUN
ejpam-5428	52	37	mz(δ	mz(δ	NUM
ejpam-5428	52	38	,	,	PUNCT
ejpam-5428	52	39	η	η	NOUN
ejpam-5428	52	40	,	,	PUNCT
ejpam-5428	52	41	l	l	NOUN
ejpam-5428	52	42	)	)	PUNCT
ejpam-5428	52	43	+	+	NOUN
ejpam-5428	52	44	mz(η	mz(η	NOUN
ejpam-5428	52	45	,	,	PUNCT
ejpam-5428	52	46	γ	γ	X
ejpam-5428	52	47	,	,	PUNCT
ejpam-5428	52	48	l)−	l)−	PROPN
ejpam-5428	52	49	1	1	NUM
ejpam-5428	52	50	(	(	PUNCT
ejpam-5428	52	51	1	1	NUM
ejpam-5428	52	52	)	)	PUNCT
ejpam-5428	52	53	holds	hold	VERB
ejpam-5428	52	54	.	.	PUNCT
ejpam-5428	53	1	definition	definition	NOUN
ejpam-5428	53	2	5	5	NUM
ejpam-5428	53	3	.	.	PUNCT
ejpam-5428	54	1	a	a	DET
ejpam-5428	54	2	self	self	NOUN
ejpam-5428	54	3	map	map	NOUN
ejpam-5428	54	4	l	l	NOUN
ejpam-5428	54	5	defined	define	VERB
ejpam-5428	54	6	on	on	ADP
ejpam-5428	54	7	a	a	DET
ejpam-5428	54	8	g	g	NOUN
ejpam-5428	54	9	-	-	PUNCT
ejpam-5428	54	10	complete	complete	ADJ
ejpam-5428	54	11	b	b	NOUN
ejpam-5428	54	12	-	-	PUNCT
ejpam-5428	54	13	fuzzy	fuzzy	ADJ
ejpam-5428	54	14	metric	metric	ADJ
ejpam-5428	54	15	space	space	NOUN
ejpam-5428	54	16	(	(	PUNCT
ejpam-5428	54	17	ȳ,mz	ȳ,mz	NUM
ejpam-5428	54	18	,	,	PUNCT
ejpam-5428	54	19	⋄	⋄	PROPN
ejpam-5428	54	20	)	)	PUNCT
ejpam-5428	54	21	is	be	AUX
ejpam-5428	54	22	called	call	VERB
ejpam-5428	54	23	a	a	DET
ejpam-5428	54	24	geragthy	geragthy	ADJ
ejpam-5428	54	25	type	type	NOUN
ejpam-5428	54	26	-	-	PUNCT
ejpam-5428	54	27	i	i	PRON
ejpam-5428	54	28	contractive	contractive	ADJ
ejpam-5428	54	29	if	if	SCONJ
ejpam-5428	54	30	1−mz(lδ	1−mz(lδ	NUM
ejpam-5428	54	31	,	,	PUNCT
ejpam-5428	54	32	lγ	lγ	ADP
ejpam-5428	54	33	,	,	PUNCT
ejpam-5428	54	34	l	l	NOUN
ejpam-5428	54	35	)	)	PUNCT
ejpam-5428	54	36	≤	≤	NOUN
ejpam-5428	54	37	(	(	PUNCT
ejpam-5428	54	38	1−mz(δ	1−mz(δ	NUM
ejpam-5428	54	39	,	,	PUNCT
ejpam-5428	54	40	γ	γ	X
ejpam-5428	54	41	,	,	PUNCT
ejpam-5428	54	42	l	l	NOUN
ejpam-5428	54	43	)	)	PUNCT
ejpam-5428	54	44	)	)	PUNCT
ejpam-5428	54	45	·	·	PUNCT
ejpam-5428	55	1	β(1−mz(δ	β(1−mz(δ	PROPN
ejpam-5428	55	2	,	,	PUNCT
ejpam-5428	55	3	γ	γ	X
ejpam-5428	55	4	,	,	PUNCT
ejpam-5428	55	5	l	l	NOUN
ejpam-5428	55	6	)	)	PUNCT
ejpam-5428	55	7	)	)	PUNCT
ejpam-5428	55	8	(	(	PUNCT
ejpam-5428	55	9	2	2	X
ejpam-5428	55	10	)	)	PUNCT
ejpam-5428	55	11	where	where	SCONJ
ejpam-5428	55	12	β	β	X
ejpam-5428	55	13	∈	∈	PROPN
ejpam-5428	55	14	b	b	PROPN
ejpam-5428	55	15	,	,	PUNCT
ejpam-5428	55	16	for	for	ADP
ejpam-5428	55	17	all	all	DET
ejpam-5428	55	18	δ	δ	PROPN
ejpam-5428	55	19	,	,	PUNCT
ejpam-5428	55	20	γ	γ	PROPN
ejpam-5428	55	21	∈	∈	PROPN
ejpam-5428	55	22	ȳ	ȳ	NOUN
ejpam-5428	55	23	and	and	CCONJ
ejpam-5428	55	24	l	l	NOUN
ejpam-5428	55	25	>	>	X
ejpam-5428	55	26	0	0	X
ejpam-5428	55	27	.	.	PUNCT
ejpam-5428	56	1	now	now	ADV
ejpam-5428	56	2	we	we	PRON
ejpam-5428	56	3	write	write	VERB
ejpam-5428	56	4	a	a	DET
ejpam-5428	56	5	theorem	theorem	NOUN
ejpam-5428	56	6	for	for	ADP
ejpam-5428	56	7	such	such	ADJ
ejpam-5428	56	8	introduced	introduce	VERB
ejpam-5428	56	9	geraghty	geraghty	VERB
ejpam-5428	56	10	type	type	NOUN
ejpam-5428	56	11	-	-	PUNCT
ejpam-5428	56	12	i	i	PRON
ejpam-5428	56	13	contractive	contractive	ADJ
ejpam-5428	56	14	mapping	mapping	NOUN
ejpam-5428	56	15	using	use	VERB
ejpam-5428	56	16	c	c	NOUN
ejpam-5428	56	17	-	-	PUNCT
ejpam-5428	56	18	triangular	triangular	NOUN
ejpam-5428	56	19	property	property	NOUN
ejpam-5428	56	20	.	.	PUNCT
ejpam-5428	57	1	theorem	theorem	NOUN
ejpam-5428	57	2	1	1	NUM
ejpam-5428	57	3	.	.	PUNCT
ejpam-5428	58	1	suppose	suppose	VERB
ejpam-5428	58	2	(	(	PUNCT
ejpam-5428	58	3	ȳ,mz	ȳ,mz	NUM
ejpam-5428	58	4	,	,	PUNCT
ejpam-5428	58	5	⋄	⋄	PROPN
ejpam-5428	58	6	)	)	PUNCT
ejpam-5428	58	7	is	be	AUX
ejpam-5428	58	8	a	a	DET
ejpam-5428	58	9	g	g	NOUN
ejpam-5428	58	10	-	-	PUNCT
ejpam-5428	58	11	complete	complete	ADJ
ejpam-5428	58	12	b	b	NOUN
ejpam-5428	58	13	-	-	PUNCT
ejpam-5428	58	14	fuzzy	fuzzy	ADJ
ejpam-5428	58	15	metric	metric	ADJ
ejpam-5428	58	16	space	space	NOUN
ejpam-5428	58	17	with	with	ADP
ejpam-5428	58	18	c	c	NOUN
ejpam-5428	58	19	-	-	PUNCT
ejpam-5428	58	20	triangular	triangular	ADJ
ejpam-5428	58	21	fuzzy	fuzzy	ADJ
ejpam-5428	58	22	metric	metric	NOUN
ejpam-5428	58	23	and	and	CCONJ
ejpam-5428	58	24	a	a	DET
ejpam-5428	58	25	self	self	NOUN
ejpam-5428	58	26	map	map	NOUN
ejpam-5428	59	1	l	l	NOUN
ejpam-5428	59	2	defined	define	VERB
ejpam-5428	59	3	on	on	ADP
ejpam-5428	59	4	ȳ	ȳ	PROPN
ejpam-5428	59	5	is	be	AUX
ejpam-5428	59	6	a	a	DET
ejpam-5428	59	7	geraghty	geraghty	ADJ
ejpam-5428	59	8	type	type	NOUN
ejpam-5428	59	9	-	-	PUNCT
ejpam-5428	59	10	i	i	PRON
ejpam-5428	59	11	contractive	contractive	ADJ
ejpam-5428	59	12	map	map	NOUN
ejpam-5428	59	13	.	.	PUNCT
ejpam-5428	60	1	then	then	ADV
ejpam-5428	60	2	l	l	PROPN
ejpam-5428	60	3	has	have	VERB
ejpam-5428	60	4	a	a	DET
ejpam-5428	60	5	unique	unique	ADJ
ejpam-5428	60	6	fixed	fix	VERB
ejpam-5428	60	7	point	point	NOUN
ejpam-5428	60	8	in	in	ADP
ejpam-5428	60	9	ȳ.	ȳ.	NOUN
ejpam-5428	60	10	v.	v.	PROPN
ejpam-5428	60	11	chandra	chandra	PROPN
ejpam-5428	60	12	,	,	PUNCT
ejpam-5428	60	13	u.	u.	PROPN
ejpam-5428	60	14	d.	d.	PROPN
ejpam-5428	60	15	patel	patel	PROPN
ejpam-5428	60	16	,	,	PUNCT
ejpam-5428	60	17	s.	s.	PROPN
ejpam-5428	60	18	radenović	radenović	PROPN
ejpam-5428	60	19	/	/	SYM
ejpam-5428	60	20	eur	eur	PROPN
ejpam-5428	60	21	.	.	PUNCT
ejpam-5428	61	1	j.	j.	PROPN
ejpam-5428	61	2	pure	pure	PROPN
ejpam-5428	61	3	appl	appl	PROPN
ejpam-5428	61	4	.	.	PROPN
ejpam-5428	61	5	math	math	PROPN
ejpam-5428	61	6	,	,	PUNCT
ejpam-5428	61	7	17	17	NUM
ejpam-5428	61	8	(	(	PUNCT
ejpam-5428	61	9	4	4	NUM
ejpam-5428	61	10	)	)	PUNCT
ejpam-5428	61	11	(	(	PUNCT
ejpam-5428	61	12	2024	2024	NUM
ejpam-5428	61	13	)	)	PUNCT
ejpam-5428	61	14	,	,	PUNCT
ejpam-5428	61	15	2384	2384	NUM
ejpam-5428	61	16	-	-	SYM
ejpam-5428	61	17	2404	2404	NUM
ejpam-5428	61	18	2387	2387	NUM
ejpam-5428	61	19	proof	proof	NOUN
ejpam-5428	61	20	.	.	PUNCT
ejpam-5428	62	1	consider	consider	VERB
ejpam-5428	62	2	a	a	DET
ejpam-5428	62	3	picard	picard	NOUN
ejpam-5428	62	4	sequence	sequence	NOUN
ejpam-5428	62	5	{	{	PUNCT
ejpam-5428	62	6	δn	δn	NOUN
ejpam-5428	62	7	}	}	PUNCT
ejpam-5428	62	8	such	such	ADJ
ejpam-5428	62	9	that	that	DET
ejpam-5428	62	10	δn+1	δn+1	PROPN
ejpam-5428	62	11	=	=	SYM
ejpam-5428	62	12	lδn	lδn	PROPN
ejpam-5428	62	13	.	.	PUNCT
ejpam-5428	63	1	we	we	PRON
ejpam-5428	63	2	assume	assume	VERB
ejpam-5428	63	3	that	that	SCONJ
ejpam-5428	63	4	δn	δn	PROPN
ejpam-5428	63	5	̸=	̸=	PROPN
ejpam-5428	63	6	δn+1	δn+1	VERB
ejpam-5428	63	7	for	for	ADP
ejpam-5428	63	8	all	all	PRON
ejpam-5428	63	9	n	n	PRON
ejpam-5428	63	10	∈	∈	NOUN
ejpam-5428	63	11	n	n	NOUN
ejpam-5428	63	12	∪	∪	X
ejpam-5428	63	13	{	{	PUNCT
ejpam-5428	63	14	0	0	NUM
ejpam-5428	63	15	}	}	PUNCT
ejpam-5428	63	16	,	,	PUNCT
ejpam-5428	63	17	otherwise	otherwise	ADV
ejpam-5428	63	18	we	we	PRON
ejpam-5428	63	19	will	will	AUX
ejpam-5428	63	20	get	get	VERB
ejpam-5428	63	21	fixed	fix	VERB
ejpam-5428	63	22	point	point	NOUN
ejpam-5428	63	23	.	.	PUNCT
ejpam-5428	64	1	now	now	ADV
ejpam-5428	64	2	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	64	3	,	,	PUNCT
ejpam-5428	64	4	δn+2	δn+2	X
ejpam-5428	64	5	,	,	PUNCT
ejpam-5428	64	6	l	l	NOUN
ejpam-5428	64	7	)	)	PUNCT
ejpam-5428	64	8	≤	≤	NOUN
ejpam-5428	64	9	β(1−mz(δn	β(1−mz(δn	NUM
ejpam-5428	64	10	,	,	PUNCT
ejpam-5428	64	11	δn+1	δn+1	PROPN
ejpam-5428	64	12	,	,	PUNCT
ejpam-5428	64	13	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	64	14	,	,	PUNCT
ejpam-5428	64	15	δn+1	δn+1	PROPN
ejpam-5428	64	16	,	,	PUNCT
ejpam-5428	64	17	l	l	NOUN
ejpam-5428	64	18	)	)	PUNCT
ejpam-5428	64	19	)	)	PUNCT
ejpam-5428	65	1	<	<	X
ejpam-5428	65	2	1−mz(δn	1−mz(δn	NUM
ejpam-5428	65	3	,	,	PUNCT
ejpam-5428	65	4	δn+1	δn+1	PROPN
ejpam-5428	65	5	,	,	PUNCT
ejpam-5428	65	6	l	l	NOUN
ejpam-5428	65	7	)	)	PUNCT
ejpam-5428	65	8	(	(	PUNCT
ejpam-5428	65	9	3	3	X
ejpam-5428	65	10	)	)	PUNCT
ejpam-5428	65	11	thus	thus	ADV
ejpam-5428	65	12	,	,	PUNCT
ejpam-5428	65	13	we	we	PRON
ejpam-5428	65	14	conclude	conclude	VERB
ejpam-5428	65	15	that	that	DET
ejpam-5428	65	16	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	65	17	,	,	PUNCT
ejpam-5428	65	18	δn+2	δn+2	X
ejpam-5428	65	19	,	,	PUNCT
ejpam-5428	65	20	l	l	NOUN
ejpam-5428	65	21	)	)	PUNCT
ejpam-5428	65	22	≥	≥	NOUN
ejpam-5428	65	23	mz(δn	mz(δn	PROPN
ejpam-5428	65	24	,	,	PUNCT
ejpam-5428	65	25	δn+1	δn+1	PROPN
ejpam-5428	65	26	,	,	PUNCT
ejpam-5428	65	27	l	l	NOUN
ejpam-5428	65	28	)	)	PUNCT
ejpam-5428	65	29	for	for	ADP
ejpam-5428	65	30	all	all	DET
ejpam-5428	65	31	n	n	PRON
ejpam-5428	65	32	∈	∈	PROPN
ejpam-5428	65	33	n.	n.	NOUN
ejpam-5428	65	34	hence	hence	ADV
ejpam-5428	65	35	{	{	PUNCT
ejpam-5428	65	36	mz(δn+1	mz(δn+1	PROPN
ejpam-5428	65	37	,	,	PUNCT
ejpam-5428	65	38	δn	δn	NOUN
ejpam-5428	65	39	,	,	PUNCT
ejpam-5428	65	40	l	l	NOUN
ejpam-5428	65	41	)	)	PUNCT
ejpam-5428	65	42	}	}	PUNCT
ejpam-5428	65	43	is	be	AUX
ejpam-5428	65	44	an	an	DET
ejpam-5428	65	45	increasing	increase	VERB
ejpam-5428	65	46	sequence	sequence	NOUN
ejpam-5428	65	47	of	of	ADP
ejpam-5428	65	48	positive	positive	ADJ
ejpam-5428	65	49	real	real	ADJ
ejpam-5428	65	50	numbers	number	NOUN
ejpam-5428	65	51	in	in	ADP
ejpam-5428	65	52	(	(	PUNCT
ejpam-5428	65	53	0	0	NUM
ejpam-5428	65	54	,	,	PUNCT
ejpam-5428	65	55	1	1	NUM
ejpam-5428	65	56	]	]	PUNCT
ejpam-5428	65	57	.	.	PUNCT
ejpam-5428	66	1	so	so	ADV
ejpam-5428	66	2	,	,	PUNCT
ejpam-5428	66	3	there	there	PRON
ejpam-5428	66	4	exists	exist	VERB
ejpam-5428	66	5	s(l	s(l	NOUN
ejpam-5428	66	6	)	)	PUNCT
ejpam-5428	66	7	∈	∈	PROPN
ejpam-5428	66	8	(	(	PUNCT
ejpam-5428	66	9	0	0	NUM
ejpam-5428	66	10	,	,	PUNCT
ejpam-5428	66	11	1	1	NUM
ejpam-5428	66	12	]	]	PUNCT
ejpam-5428	66	13	such	such	ADJ
ejpam-5428	66	14	that	that	SCONJ
ejpam-5428	66	15	lim	lim	PROPN
ejpam-5428	66	16	n→+∞	n→+∞	PROPN
ejpam-5428	66	17	mz(δn	mz(δn	PROPN
ejpam-5428	66	18	,	,	PUNCT
ejpam-5428	66	19	δn+1	δn+1	PROPN
ejpam-5428	66	20	,	,	PUNCT
ejpam-5428	66	21	l	l	NOUN
ejpam-5428	66	22	)	)	PUNCT
ejpam-5428	66	23	=	=	SYM
ejpam-5428	66	24	s(l	s(l	X
ejpam-5428	66	25	)	)	PUNCT
ejpam-5428	66	26	for	for	ADP
ejpam-5428	66	27	all	all	DET
ejpam-5428	66	28	l	l	NOUN
ejpam-5428	66	29	>	>	X
ejpam-5428	66	30	0	0	X
ejpam-5428	66	31	.	.	PUNCT
ejpam-5428	67	1	now	now	ADV
ejpam-5428	67	2	,	,	PUNCT
ejpam-5428	67	3	we	we	PRON
ejpam-5428	67	4	need	need	VERB
ejpam-5428	67	5	to	to	PART
ejpam-5428	67	6	prove	prove	VERB
ejpam-5428	67	7	s(l	s(l	NUM
ejpam-5428	67	8	)	)	PUNCT
ejpam-5428	67	9	=	=	SYM
ejpam-5428	67	10	1	1	X
ejpam-5428	67	11	.	.	PUNCT
ejpam-5428	67	12	suppose	suppose	VERB
ejpam-5428	67	13	s(l0	s(l0	NOUN
ejpam-5428	67	14	)	)	PUNCT
ejpam-5428	67	15	<	<	X
ejpam-5428	68	1	1	1	NUM
ejpam-5428	68	2	,	,	PUNCT
ejpam-5428	68	3	for	for	ADP
ejpam-5428	68	4	any	any	DET
ejpam-5428	68	5	l0	l0	PROPN
ejpam-5428	68	6	>	>	X
ejpam-5428	68	7	0	0	X
ejpam-5428	68	8	.	.	PUNCT
ejpam-5428	69	1	by	by	ADP
ejpam-5428	69	2	(	(	PUNCT
ejpam-5428	69	3	3	3	NUM
ejpam-5428	69	4	)	)	PUNCT
ejpam-5428	69	5	,	,	PUNCT
ejpam-5428	69	6	we	we	PRON
ejpam-5428	69	7	obtain	obtain	VERB
ejpam-5428	69	8	lim	lim	PROPN
ejpam-5428	69	9	n→+∞	n→+∞	PROPN
ejpam-5428	69	10	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	69	11	,	,	PUNCT
ejpam-5428	69	12	δn+1	δn+1	PROPN
ejpam-5428	69	13	,	,	PUNCT
ejpam-5428	69	14	l	l	NOUN
ejpam-5428	69	15	)	)	PUNCT
ejpam-5428	69	16	)	)	PUNCT
ejpam-5428	70	1	=	=	PUNCT
ejpam-5428	70	2	1	1	X
ejpam-5428	70	3	.	.	PUNCT
ejpam-5428	70	4	since	since	SCONJ
ejpam-5428	70	5	β	β	PROPN
ejpam-5428	70	6	∈	∈	PROPN
ejpam-5428	70	7	b.	b.	PROPN
ejpam-5428	70	8	this	this	PRON
ejpam-5428	70	9	implies	imply	VERB
ejpam-5428	70	10	that	that	SCONJ
ejpam-5428	70	11	lim	lim	PROPN
ejpam-5428	70	12	n→+∞	n→+∞	PROPN
ejpam-5428	70	13	mz(δn	mz(δn	PROPN
ejpam-5428	70	14	,	,	PUNCT
ejpam-5428	70	15	δn+1	δn+1	PROPN
ejpam-5428	70	16	,	,	PUNCT
ejpam-5428	70	17	l	l	NOUN
ejpam-5428	70	18	)	)	PUNCT
ejpam-5428	70	19	=	=	SYM
ejpam-5428	70	20	s(l	s(l	X
ejpam-5428	70	21	)	)	PUNCT
ejpam-5428	70	22	=	=	SYM
ejpam-5428	70	23	1	1	NUM
ejpam-5428	70	24	,	,	PUNCT
ejpam-5428	70	25	a	a	DET
ejpam-5428	70	26	contradiction	contradiction	NOUN
ejpam-5428	70	27	to	to	ADP
ejpam-5428	70	28	our	our	PRON
ejpam-5428	70	29	assumption	assumption	NOUN
ejpam-5428	70	30	.	.	PUNCT
ejpam-5428	71	1	hence	hence	ADV
ejpam-5428	71	2	,	,	PUNCT
ejpam-5428	71	3	we	we	PRON
ejpam-5428	71	4	conclude	conclude	VERB
ejpam-5428	71	5	that	that	SCONJ
ejpam-5428	71	6	lim	lim	PROPN
ejpam-5428	71	7	n→+∞	n→+∞	PROPN
ejpam-5428	71	8	mz(δn	mz(δn	PROPN
ejpam-5428	71	9	,	,	PUNCT
ejpam-5428	71	10	δn+1	δn+1	PROPN
ejpam-5428	71	11	,	,	PUNCT
ejpam-5428	71	12	l	l	NOUN
ejpam-5428	71	13	)	)	PUNCT
ejpam-5428	71	14	=	=	SYM
ejpam-5428	71	15	1	1	NUM
ejpam-5428	71	16	,	,	PUNCT
ejpam-5428	71	17	(	(	PUNCT
ejpam-5428	71	18	4	4	NUM
ejpam-5428	71	19	)	)	PUNCT
ejpam-5428	71	20	for	for	ADP
ejpam-5428	71	21	all	all	DET
ejpam-5428	71	22	l	l	NOUN
ejpam-5428	71	23	>	>	X
ejpam-5428	71	24	0	0	X
ejpam-5428	71	25	.	.	PUNCT
ejpam-5428	72	1	next	next	ADV
ejpam-5428	72	2	,	,	PUNCT
ejpam-5428	72	3	we	we	PRON
ejpam-5428	72	4	need	need	VERB
ejpam-5428	72	5	to	to	PART
ejpam-5428	72	6	show	show	VERB
ejpam-5428	72	7	{	{	PUNCT
ejpam-5428	72	8	δn	δn	NOUN
ejpam-5428	72	9	}	}	PUNCT
ejpam-5428	72	10	is	be	AUX
ejpam-5428	72	11	a	a	DET
ejpam-5428	72	12	cauchy	cauchy	ADJ
ejpam-5428	72	13	sequence	sequence	NOUN
ejpam-5428	72	14	.	.	PUNCT
ejpam-5428	73	1	consider	consider	VERB
ejpam-5428	73	2	a	a	DET
ejpam-5428	73	3	contrary	contrary	NOUN
ejpam-5428	73	4	,	,	PUNCT
ejpam-5428	73	5	λ	λ	PROPN
ejpam-5428	73	6	=	=	PROPN
ejpam-5428	73	7	lim	lim	PROPN
ejpam-5428	73	8	n	n	CCONJ
ejpam-5428	73	9	,	,	PUNCT
ejpam-5428	73	10	m→+∞	m→+∞	PROPN
ejpam-5428	73	11	mz(δn	mz(δn	PROPN
ejpam-5428	73	12	,	,	PUNCT
ejpam-5428	73	13	δm	δm	PROPN
ejpam-5428	73	14	,	,	PUNCT
ejpam-5428	73	15	l	l	NOUN
ejpam-5428	73	16	)	)	PUNCT
ejpam-5428	73	17	<	<	X
ejpam-5428	74	1	1	1	X
ejpam-5428	74	2	.	.	PUNCT
ejpam-5428	74	3	(	(	PUNCT
ejpam-5428	74	4	5	5	NUM
ejpam-5428	74	5	)	)	PUNCT
ejpam-5428	74	6	by	by	ADP
ejpam-5428	74	7	(	(	PUNCT
ejpam-5428	74	8	2	2	NUM
ejpam-5428	74	9	)	)	PUNCT
ejpam-5428	74	10	,	,	PUNCT
ejpam-5428	74	11	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	74	12	,	,	PUNCT
ejpam-5428	74	13	δm+1	δm+1	PROPN
ejpam-5428	74	14	,	,	PUNCT
ejpam-5428	74	15	l	l	NOUN
ejpam-5428	74	16	)	)	PUNCT
ejpam-5428	74	17	≤	≤	NOUN
ejpam-5428	74	18	β(1−mz(δn	β(1−mz(δn	NUM
ejpam-5428	74	19	,	,	PUNCT
ejpam-5428	74	20	δm	δm	ADV
ejpam-5428	74	21	,	,	PUNCT
ejpam-5428	74	22	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	74	23	,	,	PUNCT
ejpam-5428	74	24	δm	δm	PROPN
ejpam-5428	74	25	,	,	PUNCT
ejpam-5428	74	26	l	l	NOUN
ejpam-5428	74	27	)	)	PUNCT
ejpam-5428	74	28	)	)	PUNCT
ejpam-5428	74	29	.	.	PUNCT
ejpam-5428	75	1	taking	take	VERB
ejpam-5428	75	2	the	the	DET
ejpam-5428	75	3	limit	limit	NOUN
ejpam-5428	75	4	as	as	ADP
ejpam-5428	75	5	n	n	CCONJ
ejpam-5428	75	6	,	,	PUNCT
ejpam-5428	75	7	m	m	VERB
ejpam-5428	75	8	→	→	SYM
ejpam-5428	75	9	+	+	ADJ
ejpam-5428	75	10	∞	∞	PROPN
ejpam-5428	75	11	in	in	ADP
ejpam-5428	75	12	the	the	DET
ejpam-5428	75	13	above	above	ADJ
ejpam-5428	75	14	inequality	inequality	NOUN
ejpam-5428	75	15	where	where	SCONJ
ejpam-5428	75	16	n	n	CCONJ
ejpam-5428	75	17	>	>	X
ejpam-5428	75	18	m	m	PROPN
ejpam-5428	75	19	,	,	PUNCT
ejpam-5428	75	20	then	then	ADV
ejpam-5428	75	21	we	we	PRON
ejpam-5428	75	22	get	get	VERB
ejpam-5428	75	23	lim	lim	PROPN
ejpam-5428	75	24	n	n	CCONJ
ejpam-5428	75	25	,	,	PUNCT
ejpam-5428	75	26	m→+∞	m→+∞	PROPN
ejpam-5428	75	27	(	(	PUNCT
ejpam-5428	75	28	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	75	29	,	,	PUNCT
ejpam-5428	75	30	δm+1	δm+1	PROPN
ejpam-5428	75	31	,	,	PUNCT
ejpam-5428	75	32	l	l	NOUN
ejpam-5428	75	33	)	)	PUNCT
ejpam-5428	75	34	)	)	PUNCT
ejpam-5428	75	35	≤	≤	NOUN
ejpam-5428	75	36	lim	lim	PROPN
ejpam-5428	75	37	n	n	CCONJ
ejpam-5428	75	38	,	,	PUNCT
ejpam-5428	75	39	m→+∞	m→+∞	PROPN
ejpam-5428	75	40	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	75	41	,	,	PUNCT
ejpam-5428	75	42	δm	δm	ADV
ejpam-5428	75	43	,	,	PUNCT
ejpam-5428	75	44	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	75	45	,	,	PUNCT
ejpam-5428	75	46	δm	δm	PROPN
ejpam-5428	75	47	,	,	PUNCT
ejpam-5428	75	48	l	l	NOUN
ejpam-5428	75	49	)	)	PUNCT
ejpam-5428	75	50	)	)	PUNCT
ejpam-5428	75	51	.	.	PUNCT
ejpam-5428	76	1	by	by	ADP
ejpam-5428	76	2	using	use	VERB
ejpam-5428	76	3	(	(	PUNCT
ejpam-5428	76	4	5	5	NUM
ejpam-5428	76	5	)	)	PUNCT
ejpam-5428	76	6	,	,	PUNCT
ejpam-5428	76	7	we	we	PRON
ejpam-5428	76	8	get	get	VERB
ejpam-5428	76	9	lim	lim	PROPN
ejpam-5428	76	10	n	n	CCONJ
ejpam-5428	76	11	,	,	PUNCT
ejpam-5428	76	12	m→+∞	m→+∞	PROPN
ejpam-5428	76	13	(	(	PUNCT
ejpam-5428	76	14	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	76	15	,	,	PUNCT
ejpam-5428	76	16	δm+1	δm+1	PROPN
ejpam-5428	76	17	,	,	PUNCT
ejpam-5428	76	18	l	l	NOUN
ejpam-5428	76	19	)	)	PUNCT
ejpam-5428	76	20	)	)	PUNCT
ejpam-5428	76	21	≤	≤	NOUN
ejpam-5428	76	22	lim	lim	PROPN
ejpam-5428	76	23	n	n	CCONJ
ejpam-5428	76	24	,	,	PUNCT
ejpam-5428	76	25	m→+∞	m→+∞	PROPN
ejpam-5428	76	26	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	76	27	,	,	PUNCT
ejpam-5428	76	28	δm	δm	PRON
ejpam-5428	76	29	,	,	PUNCT
ejpam-5428	76	30	l))(1−	l))(1−	PROPN
ejpam-5428	76	31	λ	λ	PROPN
ejpam-5428	76	32	)	)	PUNCT
ejpam-5428	76	33	.	.	PUNCT
ejpam-5428	77	1	(	(	PUNCT
ejpam-5428	77	2	6	6	NUM
ejpam-5428	77	3	)	)	PUNCT
ejpam-5428	77	4	on	on	ADP
ejpam-5428	77	5	the	the	DET
ejpam-5428	77	6	flip	flip	ADJ
ejpam-5428	77	7	side	side	NOUN
ejpam-5428	77	8	,	,	PUNCT
ejpam-5428	77	9	using	use	VERB
ejpam-5428	77	10	c	c	NOUN
ejpam-5428	77	11	-	-	PUNCT
ejpam-5428	77	12	traingular	traingular	ADJ
ejpam-5428	77	13	property	property	NOUN
ejpam-5428	77	14	1−mz(δn	1−mz(δn	NUM
ejpam-5428	77	15	,	,	PUNCT
ejpam-5428	77	16	δm	δm	PROPN
ejpam-5428	77	17	,	,	PUNCT
ejpam-5428	77	18	l	l	NOUN
ejpam-5428	77	19	)	)	PUNCT
ejpam-5428	77	20	≤	≤	NOUN
ejpam-5428	77	21	1−mz(δn	1−mz(δn	NUM
ejpam-5428	77	22	,	,	PUNCT
ejpam-5428	77	23	δn+1	δn+1	PROPN
ejpam-5428	77	24	,	,	PUNCT
ejpam-5428	77	25	l	l	NOUN
ejpam-5428	77	26	)	)	PUNCT
ejpam-5428	77	27	+	+	NOUN
ejpam-5428	78	1	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	78	2	,	,	PUNCT
ejpam-5428	78	3	δm	δm	ADP
ejpam-5428	78	4	,	,	PUNCT
ejpam-5428	78	5	l	l	NOUN
ejpam-5428	78	6	)	)	PUNCT
ejpam-5428	78	7	≤	≤	NOUN
ejpam-5428	78	8	1−mz(δn	1−mz(δn	NUM
ejpam-5428	78	9	,	,	PUNCT
ejpam-5428	78	10	δn+1	δn+1	PROPN
ejpam-5428	78	11	,	,	PUNCT
ejpam-5428	78	12	l	l	NOUN
ejpam-5428	78	13	)	)	PUNCT
ejpam-5428	78	14	+	+	CCONJ
ejpam-5428	78	15	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	78	16	,	,	PUNCT
ejpam-5428	78	17	δm+1	δm+1	PROPN
ejpam-5428	78	18	,	,	PUNCT
ejpam-5428	78	19	l	l	NOUN
ejpam-5428	78	20	)	)	PUNCT
ejpam-5428	78	21	+	+	CCONJ
ejpam-5428	78	22	1−mz(δm+1	1−mz(δm+1	NUM
ejpam-5428	78	23	,	,	PUNCT
ejpam-5428	78	24	δm	δm	PROPN
ejpam-5428	78	25	,	,	PUNCT
ejpam-5428	78	26	l	l	NOUN
ejpam-5428	78	27	)	)	PUNCT
ejpam-5428	78	28	.	.	PUNCT
ejpam-5428	79	1	putting	put	VERB
ejpam-5428	79	2	limit	limit	NOUN
ejpam-5428	79	3	as	as	ADP
ejpam-5428	79	4	n	n	X
ejpam-5428	79	5	,	,	PUNCT
ejpam-5428	79	6	m	m	PROPN
ejpam-5428	79	7	→	→	SYM
ejpam-5428	79	8	+	+	ADJ
ejpam-5428	79	9	∞	∞	NUM
ejpam-5428	79	10	and	and	CCONJ
ejpam-5428	79	11	using	use	VERB
ejpam-5428	79	12	(	(	PUNCT
ejpam-5428	79	13	4	4	NUM
ejpam-5428	79	14	)	)	PUNCT
ejpam-5428	79	15	and	and	CCONJ
ejpam-5428	79	16	(	(	PUNCT
ejpam-5428	79	17	6	6	NUM
ejpam-5428	79	18	)	)	PUNCT
ejpam-5428	79	19	,	,	PUNCT
ejpam-5428	79	20	we	we	PRON
ejpam-5428	79	21	get	get	VERB
ejpam-5428	79	22	(	(	PUNCT
ejpam-5428	79	23	1−	1−	NUM
ejpam-5428	79	24	λ	λ	NOUN
ejpam-5428	79	25	)	)	PUNCT
ejpam-5428	79	26	≤	≤	NOUN
ejpam-5428	79	27	lim	lim	PROPN
ejpam-5428	79	28	n	n	CCONJ
ejpam-5428	79	29	,	,	PUNCT
ejpam-5428	79	30	m→+∞	m→+∞	PROPN
ejpam-5428	79	31	(	(	PUNCT
ejpam-5428	79	32	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	79	33	,	,	PUNCT
ejpam-5428	79	34	δm+1	δm+1	PROPN
ejpam-5428	79	35	,	,	PUNCT
ejpam-5428	79	36	l	l	NOUN
ejpam-5428	79	37	)	)	PUNCT
ejpam-5428	79	38	)	)	PUNCT
ejpam-5428	80	1	≤	≤	NOUN
ejpam-5428	80	2	lim	lim	PROPN
ejpam-5428	80	3	n	n	CCONJ
ejpam-5428	80	4	,	,	PUNCT
ejpam-5428	80	5	m→+∞	m→+∞	PROPN
ejpam-5428	80	6	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	80	7	,	,	PUNCT
ejpam-5428	80	8	δm	δm	PRON
ejpam-5428	80	9	,	,	PUNCT
ejpam-5428	80	10	l))(1−	l))(1−	PROPN
ejpam-5428	80	11	λ	λ	PROPN
ejpam-5428	80	12	)	)	PUNCT
ejpam-5428	80	13	v.	v.	ADP
ejpam-5428	80	14	chandra	chandra	PROPN
ejpam-5428	80	15	,	,	PUNCT
ejpam-5428	80	16	u.	u.	PROPN
ejpam-5428	80	17	d.	d.	PROPN
ejpam-5428	80	18	patel	patel	PROPN
ejpam-5428	80	19	,	,	PUNCT
ejpam-5428	80	20	s.	s.	PROPN
ejpam-5428	80	21	radenović	radenović	PROPN
ejpam-5428	80	22	/	/	SYM
ejpam-5428	80	23	eur	eur	PROPN
ejpam-5428	80	24	.	.	PUNCT
ejpam-5428	81	1	j.	j.	PROPN
ejpam-5428	81	2	pure	pure	PROPN
ejpam-5428	81	3	appl	appl	PROPN
ejpam-5428	81	4	.	.	PROPN
ejpam-5428	81	5	math	math	PROPN
ejpam-5428	81	6	,	,	PUNCT
ejpam-5428	81	7	17	17	NUM
ejpam-5428	81	8	(	(	PUNCT
ejpam-5428	81	9	4	4	NUM
ejpam-5428	81	10	)	)	PUNCT
ejpam-5428	81	11	(	(	PUNCT
ejpam-5428	81	12	2024	2024	NUM
ejpam-5428	81	13	)	)	PUNCT
ejpam-5428	81	14	,	,	PUNCT
ejpam-5428	81	15	2384	2384	NUM
ejpam-5428	81	16	-	-	SYM
ejpam-5428	81	17	2404	2404	NUM
ejpam-5428	81	18	2388	2388	NUM
ejpam-5428	81	19	this	this	PRON
ejpam-5428	81	20	implies	imply	VERB
ejpam-5428	81	21	lim	lim	PROPN
ejpam-5428	81	22	n	n	CCONJ
ejpam-5428	81	23	,	,	PUNCT
ejpam-5428	81	24	m→+∞	m→+∞	PROPN
ejpam-5428	81	25	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	81	26	,	,	PUNCT
ejpam-5428	81	27	δm	δm	PROPN
ejpam-5428	81	28	,	,	PUNCT
ejpam-5428	81	29	l	l	NOUN
ejpam-5428	81	30	)	)	PUNCT
ejpam-5428	81	31	)	)	PUNCT
ejpam-5428	82	1	=	=	SYM
ejpam-5428	82	2	1	1	NUM
ejpam-5428	82	3	which	which	PRON
ejpam-5428	82	4	implies	imply	VERB
ejpam-5428	82	5	lim	lim	PROPN
ejpam-5428	82	6	n	n	CCONJ
ejpam-5428	82	7	,	,	PUNCT
ejpam-5428	82	8	m→+∞	m→+∞	PROPN
ejpam-5428	82	9	(	(	PUNCT
ejpam-5428	82	10	1−mz(δn	1−mz(δn	NUM
ejpam-5428	82	11	,	,	PUNCT
ejpam-5428	82	12	δm	δm	PROPN
ejpam-5428	82	13	,	,	PUNCT
ejpam-5428	82	14	l	l	NOUN
ejpam-5428	82	15	)	)	PUNCT
ejpam-5428	82	16	)	)	PUNCT
ejpam-5428	83	1	=	=	PUNCT
ejpam-5428	83	2	0	0	X
ejpam-5428	83	3	.	.	PUNCT
ejpam-5428	84	1	this	this	DET
ejpam-5428	84	2	yields	yield	NOUN
ejpam-5428	84	3	that	that	PRON
ejpam-5428	84	4	lim	lim	PROPN
ejpam-5428	84	5	n	n	CCONJ
ejpam-5428	84	6	,	,	PUNCT
ejpam-5428	84	7	m→+∞	m→+∞	PROPN
ejpam-5428	84	8	mz(δn	mz(δn	PROPN
ejpam-5428	84	9	,	,	PUNCT
ejpam-5428	84	10	δm	δm	PROPN
ejpam-5428	84	11	,	,	PUNCT
ejpam-5428	84	12	l	l	NOUN
ejpam-5428	84	13	)	)	PUNCT
ejpam-5428	84	14	=	=	SYM
ejpam-5428	85	1	λ	λ	NOUN
ejpam-5428	85	2	=	=	SYM
ejpam-5428	85	3	1	1	NUM
ejpam-5428	85	4	,	,	PUNCT
ejpam-5428	85	5	a	a	DET
ejpam-5428	85	6	contradiction	contradiction	NOUN
ejpam-5428	85	7	with	with	ADP
ejpam-5428	85	8	the	the	DET
ejpam-5428	85	9	assumption	assumption	NOUN
ejpam-5428	85	10	(	(	PUNCT
ejpam-5428	85	11	5	5	NUM
ejpam-5428	85	12	)	)	PUNCT
ejpam-5428	85	13	.	.	PUNCT
ejpam-5428	86	1	therefore	therefore	ADV
ejpam-5428	86	2	,	,	PUNCT
ejpam-5428	86	3	sequence	sequence	NOUN
ejpam-5428	86	4	{	{	PUNCT
ejpam-5428	86	5	δn	δn	NOUN
ejpam-5428	86	6	}	}	PUNCT
ejpam-5428	86	7	is	be	AUX
ejpam-5428	86	8	a	a	DET
ejpam-5428	86	9	g	g	NOUN
ejpam-5428	86	10	-	-	PUNCT
ejpam-5428	86	11	cauchy	cauchy	NOUN
ejpam-5428	86	12	in	in	ADP
ejpam-5428	86	13	ȳ.	ȳ.	NOUN
ejpam-5428	86	14	since	since	SCONJ
ejpam-5428	86	15	the	the	DET
ejpam-5428	86	16	space	space	NOUN
ejpam-5428	86	17	ȳ	ȳ	PROPN
ejpam-5428	86	18	is	be	AUX
ejpam-5428	86	19	complete	complete	ADJ
ejpam-5428	86	20	then	then	ADV
ejpam-5428	86	21	there	there	PRON
ejpam-5428	86	22	exists	exist	VERB
ejpam-5428	86	23	u	u	PROPN
ejpam-5428	86	24	∈	∈	PROPN
ejpam-5428	86	25	ȳ	ȳ	NOUN
ejpam-5428	86	26	such	such	ADJ
ejpam-5428	86	27	that	that	DET
ejpam-5428	86	28	sequence	sequence	NOUN
ejpam-5428	86	29	{	{	PUNCT
ejpam-5428	86	30	δn	δn	NOUN
ejpam-5428	86	31	}	}	PUNCT
ejpam-5428	86	32	converges	converge	NOUN
ejpam-5428	86	33	to	to	ADP
ejpam-5428	86	34	u	u	PRON
ejpam-5428	86	35	,	,	PUNCT
ejpam-5428	86	36	lim	lim	PROPN
ejpam-5428	86	37	n→+∞	n→+∞	PROPN
ejpam-5428	86	38	mz(δn	mz(δn	PROPN
ejpam-5428	86	39	,	,	PUNCT
ejpam-5428	86	40	u	u	NOUN
ejpam-5428	86	41	,	,	PUNCT
ejpam-5428	86	42	l	l	NOUN
ejpam-5428	86	43	)	)	PUNCT
ejpam-5428	86	44	=	=	SYM
ejpam-5428	86	45	1	1	NUM
ejpam-5428	86	46	,	,	PUNCT
ejpam-5428	86	47	(	(	PUNCT
ejpam-5428	86	48	7	7	X
ejpam-5428	86	49	)	)	PUNCT
ejpam-5428	86	50	for	for	ADP
ejpam-5428	86	51	all	all	DET
ejpam-5428	86	52	l	l	NOUN
ejpam-5428	86	53	>	>	X
ejpam-5428	86	54	0	0	X
ejpam-5428	86	55	.	.	PUNCT
ejpam-5428	87	1	next	next	ADV
ejpam-5428	87	2	we	we	PRON
ejpam-5428	87	3	need	need	VERB
ejpam-5428	87	4	to	to	PART
ejpam-5428	87	5	show	show	VERB
ejpam-5428	87	6	u	u	NOUN
ejpam-5428	87	7	is	be	AUX
ejpam-5428	87	8	a	a	DET
ejpam-5428	87	9	fixed	fix	VERB
ejpam-5428	87	10	point	point	NOUN
ejpam-5428	87	11	of	of	ADP
ejpam-5428	87	12	l.	l.	PROPN
ejpam-5428	87	13	1−mz(δn+1,lu	1−mz(δn+1,lu	PROPN
ejpam-5428	87	14	,	,	PUNCT
ejpam-5428	87	15	l	l	NOUN
ejpam-5428	87	16	)	)	PUNCT
ejpam-5428	87	17	≤	≤	NOUN
ejpam-5428	87	18	(	(	PUNCT
ejpam-5428	87	19	1−mz(δn	1−mz(δn	NUM
ejpam-5428	87	20	,	,	PUNCT
ejpam-5428	87	21	u	u	NOUN
ejpam-5428	87	22	,	,	PUNCT
ejpam-5428	87	23	l))β(1−mz(δn	l))β(1−mz(δn	PROPN
ejpam-5428	87	24	,	,	PUNCT
ejpam-5428	87	25	u	u	NOUN
ejpam-5428	87	26	,	,	PUNCT
ejpam-5428	87	27	l	l	NOUN
ejpam-5428	87	28	)	)	PUNCT
ejpam-5428	87	29	)	)	PUNCT
ejpam-5428	87	30	,	,	PUNCT
ejpam-5428	87	31	consider	consider	VERB
ejpam-5428	87	32	limit	limit	NOUN
ejpam-5428	87	33	as	as	ADP
ejpam-5428	87	34	n	n	PROPN
ejpam-5428	87	35	→	→	SYM
ejpam-5428	87	36	+	+	PROPN
ejpam-5428	87	37	∞	∞	PROPN
ejpam-5428	87	38	,	,	PUNCT
ejpam-5428	87	39	this	this	PRON
ejpam-5428	87	40	implies	imply	VERB
ejpam-5428	87	41	lim	lim	PROPN
ejpam-5428	87	42	n→+∞	n→+∞	PROPN
ejpam-5428	87	43	mz(δn+1,lu	mz(δn+1,lu	PROPN
ejpam-5428	87	44	,	,	PUNCT
ejpam-5428	87	45	l	l	NOUN
ejpam-5428	87	46	)	)	PUNCT
ejpam-5428	87	47	=	=	SYM
ejpam-5428	87	48	1	1	NUM
ejpam-5428	87	49	,	,	PUNCT
ejpam-5428	87	50	(	(	PUNCT
ejpam-5428	87	51	8)	8)	NUM
ejpam-5428	87	52	for	for	ADP
ejpam-5428	87	53	all	all	DET
ejpam-5428	87	54	l	l	NOUN
ejpam-5428	87	55	>	>	X
ejpam-5428	87	56	0	0	X
ejpam-5428	87	57	.	.	X
ejpam-5428	88	1	using	use	VERB
ejpam-5428	88	2	triangle	triangle	NOUN
ejpam-5428	88	3	inequality	inequality	NOUN
ejpam-5428	88	4	,	,	PUNCT
ejpam-5428	88	5	we	we	PRON
ejpam-5428	88	6	write	write	VERB
ejpam-5428	88	7	mz(u	mz(u	PROPN
ejpam-5428	88	8	,	,	PUNCT
ejpam-5428	88	9	lu	lu	PROPN
ejpam-5428	88	10	,	,	PUNCT
ejpam-5428	88	11	l	l	NOUN
ejpam-5428	88	12	)	)	PUNCT
ejpam-5428	88	13	≥	≥	NOUN
ejpam-5428	88	14	mz(u	mz(u	PROPN
ejpam-5428	88	15	,	,	PUNCT
ejpam-5428	88	16	δn+1	δn+1	PROPN
ejpam-5428	88	17	,	,	PUNCT
ejpam-5428	88	18	l	l	NOUN
ejpam-5428	88	19	)	)	PUNCT
ejpam-5428	88	20	⋄mz(δn+1,lu	⋄mz(δn+1,lu	PROPN
ejpam-5428	88	21	,	,	PUNCT
ejpam-5428	88	22	l	l	NOUN
ejpam-5428	88	23	)	)	PUNCT
ejpam-5428	88	24	.	.	PUNCT
ejpam-5428	89	1	considering	consider	VERB
ejpam-5428	89	2	limit	limit	NOUN
ejpam-5428	89	3	as	as	ADP
ejpam-5428	89	4	n	n	PROPN
ejpam-5428	89	5	→	→	SYM
ejpam-5428	89	6	+	+	NOUN
ejpam-5428	89	7	∞	∞	PROPN
ejpam-5428	89	8	and	and	CCONJ
ejpam-5428	89	9	with	with	ADP
ejpam-5428	89	10	(	(	PUNCT
ejpam-5428	89	11	4	4	NUM
ejpam-5428	89	12	)	)	PUNCT
ejpam-5428	89	13	and	and	CCONJ
ejpam-5428	89	14	(	(	PUNCT
ejpam-5428	89	15	8)	8)	NUM
ejpam-5428	89	16	,	,	PUNCT
ejpam-5428	89	17	we	we	PRON
ejpam-5428	89	18	obtain	obtain	VERB
ejpam-5428	89	19	mz(u	mz(u	PUNCT
ejpam-5428	89	20	,	,	PUNCT
ejpam-5428	89	21	lu	lu	PROPN
ejpam-5428	89	22	,	,	PUNCT
ejpam-5428	89	23	l	l	NOUN
ejpam-5428	89	24	)	)	PUNCT
ejpam-5428	89	25	=	=	SYM
ejpam-5428	89	26	1	1	NUM
ejpam-5428	89	27	for	for	ADP
ejpam-5428	89	28	all	all	DET
ejpam-5428	89	29	l	l	NOUN
ejpam-5428	89	30	>	>	X
ejpam-5428	89	31	0	0	X
ejpam-5428	89	32	.	.	PUNCT
ejpam-5428	90	1	consider	consider	VERB
ejpam-5428	90	2	v	v	NOUN
ejpam-5428	90	3	is	be	AUX
ejpam-5428	90	4	another	another	DET
ejpam-5428	90	5	fixed	fix	VERB
ejpam-5428	90	6	point	point	NOUN
ejpam-5428	90	7	of	of	ADP
ejpam-5428	90	8	l	l	NOUN
ejpam-5428	91	1	such	such	ADJ
ejpam-5428	91	2	that	that	SCONJ
ejpam-5428	91	3	u	u	PROPN
ejpam-5428	91	4	̸=	̸=	PROPN
ejpam-5428	91	5	v	v	NOUN
ejpam-5428	91	6	,	,	PUNCT
ejpam-5428	91	7	mz(u	mz(u	ADJ
ejpam-5428	91	8	,	,	PUNCT
ejpam-5428	91	9	v	v	NOUN
ejpam-5428	91	10	,	,	PUNCT
ejpam-5428	91	11	l	l	NOUN
ejpam-5428	91	12	)	)	PUNCT
ejpam-5428	91	13	<	<	X
ejpam-5428	91	14	1	1	X
ejpam-5428	91	15	.	.	PUNCT
ejpam-5428	91	16	thus	thus	ADV
ejpam-5428	91	17	1−mz(u	1−mz(u	NUM
ejpam-5428	91	18	,	,	PUNCT
ejpam-5428	91	19	v	v	NOUN
ejpam-5428	91	20	,	,	PUNCT
ejpam-5428	91	21	l	l	NOUN
ejpam-5428	91	22	)	)	PUNCT
ejpam-5428	91	23	=	=	SYM
ejpam-5428	91	24	1−mz(lu	1−mz(lu	NUM
ejpam-5428	91	25	,	,	PUNCT
ejpam-5428	91	26	lv	lv	PROPN
ejpam-5428	91	27	,	,	PUNCT
ejpam-5428	91	28	l	l	NOUN
ejpam-5428	91	29	)	)	PUNCT
ejpam-5428	91	30	≤	≤	NOUN
ejpam-5428	91	31	(	(	PUNCT
ejpam-5428	91	32	1−mz(u	1−mz(u	NUM
ejpam-5428	91	33	,	,	PUNCT
ejpam-5428	91	34	v	v	NOUN
ejpam-5428	91	35	,	,	PUNCT
ejpam-5428	91	36	l))β(1−mz(u	l))β(1−mz(u	PROPN
ejpam-5428	91	37	,	,	PUNCT
ejpam-5428	91	38	v	v	NOUN
ejpam-5428	91	39	,	,	PUNCT
ejpam-5428	91	40	l	l	NOUN
ejpam-5428	91	41	)	)	PUNCT
ejpam-5428	91	42	)	)	PUNCT
ejpam-5428	91	43	<	<	X
ejpam-5428	91	44	1−mz(u	1−mz(u	NUM
ejpam-5428	91	45	,	,	PUNCT
ejpam-5428	91	46	v	v	NOUN
ejpam-5428	91	47	,	,	PUNCT
ejpam-5428	91	48	l	l	NOUN
ejpam-5428	91	49	)	)	PUNCT
ejpam-5428	91	50	.	.	PUNCT
ejpam-5428	92	1	we	we	PRON
ejpam-5428	92	2	get	get	VERB
ejpam-5428	92	3	a	a	DET
ejpam-5428	92	4	contrary	contrary	NOUN
ejpam-5428	92	5	,	,	PUNCT
ejpam-5428	92	6	thus	thus	ADV
ejpam-5428	92	7	fixed	fix	VERB
ejpam-5428	92	8	point	point	NOUN
ejpam-5428	92	9	is	be	AUX
ejpam-5428	92	10	unique	unique	ADJ
ejpam-5428	92	11	.	.	PUNCT
ejpam-5428	93	1	example	example	NOUN
ejpam-5428	93	2	2	2	NUM
ejpam-5428	93	3	.	.	X
ejpam-5428	93	4	consider	consider	VERB
ejpam-5428	93	5	ȳ	ȳ	NOUN
ejpam-5428	93	6	=	=	PUNCT
ejpam-5428	94	1	[	[	X
ejpam-5428	94	2	0	0	NUM
ejpam-5428	94	3	,	,	PUNCT
ejpam-5428	94	4	1	1	NUM
ejpam-5428	94	5	]	]	PUNCT
ejpam-5428	94	6	and	and	CCONJ
ejpam-5428	94	7	let	let	VERB
ejpam-5428	94	8	mz	mz	PROPN
ejpam-5428	94	9	:	:	PUNCT
ejpam-5428	94	10	ȳ	ȳ	PROPN
ejpam-5428	94	11	×	×	NOUN
ejpam-5428	94	12	ȳ	ȳ	NOUN
ejpam-5428	94	13	→	→	PUNCT
ejpam-5428	95	1	[	[	X
ejpam-5428	95	2	0	0	NUM
ejpam-5428	95	3	,	,	PUNCT
ejpam-5428	95	4	1	1	NUM
ejpam-5428	95	5	]	]	PUNCT
ejpam-5428	95	6	defined	define	VERB
ejpam-5428	95	7	by	by	ADP
ejpam-5428	95	8	mz(δ	mz(δ	PROPN
ejpam-5428	95	9	,	,	PUNCT
ejpam-5428	95	10	γ	γ	X
ejpam-5428	95	11	,	,	PUNCT
ejpam-5428	95	12	l	l	NOUN
ejpam-5428	95	13	)	)	PUNCT
ejpam-5428	95	14	=	=	SYM
ejpam-5428	95	15	e−	e−	NUM
ejpam-5428	95	16	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	95	17	l+0.5	l+0.5	NOUN
ejpam-5428	95	18	and	and	CCONJ
ejpam-5428	95	19	mz	mz	PROPN
ejpam-5428	95	20	be	be	AUX
ejpam-5428	95	21	a	a	DET
ejpam-5428	95	22	c	c	NOUN
ejpam-5428	95	23	-	-	PUNCT
ejpam-5428	95	24	triangular	triangular	NOUN
ejpam-5428	95	25	for	for	ADP
ejpam-5428	95	26	all	all	DET
ejpam-5428	95	27	δ	δ	PROPN
ejpam-5428	95	28	,	,	PUNCT
ejpam-5428	95	29	γ	γ	PROPN
ejpam-5428	95	30	∈	∈	PROPN
ejpam-5428	95	31	ȳ	ȳ	NOUN
ejpam-5428	95	32	and	and	CCONJ
ejpam-5428	95	33	l	l	NOUN
ejpam-5428	95	34	>	>	X
ejpam-5428	96	1	0	0	X
ejpam-5428	96	2	.	.	PUNCT
ejpam-5428	96	3	then	then	ADV
ejpam-5428	96	4	(	(	PUNCT
ejpam-5428	96	5	ȳ,mz	ȳ,mz	NUM
ejpam-5428	96	6	,	,	PUNCT
ejpam-5428	96	7	⋄	⋄	PROPN
ejpam-5428	96	8	)	)	PUNCT
ejpam-5428	96	9	is	be	AUX
ejpam-5428	96	10	a	a	DET
ejpam-5428	96	11	g	g	NOUN
ejpam-5428	96	12	-	-	PUNCT
ejpam-5428	96	13	complete	complete	ADJ
ejpam-5428	96	14	b	b	NOUN
ejpam-5428	96	15	-	-	PUNCT
ejpam-5428	96	16	fuzzy	fuzzy	ADJ
ejpam-5428	96	17	metric	metric	ADJ
ejpam-5428	96	18	space	space	NOUN
ejpam-5428	96	19	.	.	PUNCT
ejpam-5428	97	1	consider	consider	VERB
ejpam-5428	97	2	the	the	DET
ejpam-5428	97	3	mapping	mapping	NOUN
ejpam-5428	97	4	l	l	NOUN
ejpam-5428	98	1	:	:	PUNCT
ejpam-5428	98	2	ȳ	ȳ	PROPN
ejpam-5428	98	3	→	→	SYM
ejpam-5428	98	4	ȳ	ȳ	PROPN
ejpam-5428	98	5	defined	define	VERB
ejpam-5428	98	6	by	by	ADP
ejpam-5428	98	7	l(δ	l(δ	NOUN
ejpam-5428	98	8	)	)	PUNCT
ejpam-5428	99	1	=	=	PRON
ejpam-5428	99	2	{	{	PUNCT
ejpam-5428	99	3	1	1	NUM
ejpam-5428	99	4	3δ	3δ	NUM
ejpam-5428	99	5	2	2	NUM
ejpam-5428	99	6	,	,	PUNCT
ejpam-5428	99	7	if	if	SCONJ
ejpam-5428	99	8	δ	δ	PROPN
ejpam-5428	99	9	∈	∈	PROPN
ejpam-5428	100	1	[	[	X
ejpam-5428	100	2	0	0	NUM
ejpam-5428	100	3	,	,	PUNCT
ejpam-5428	100	4	1	1	NUM
ejpam-5428	100	5	)	)	PUNCT
ejpam-5428	100	6	1	1	NUM
ejpam-5428	100	7	4	4	NUM
ejpam-5428	100	8	,	,	PUNCT
ejpam-5428	100	9	if	if	SCONJ
ejpam-5428	100	10	δ	δ	PROPN
ejpam-5428	100	11	=	=	SYM
ejpam-5428	100	12	1	1	NUM
ejpam-5428	100	13	,	,	PUNCT
ejpam-5428	100	14	for	for	ADP
ejpam-5428	100	15	all	all	DET
ejpam-5428	100	16	δ	δ	PROPN
ejpam-5428	100	17	,	,	PUNCT
ejpam-5428	100	18	γ	γ	PROPN
ejpam-5428	100	19	∈	∈	PROPN
ejpam-5428	100	20	ȳ	ȳ	NOUN
ejpam-5428	100	21	and	and	CCONJ
ejpam-5428	100	22	l	l	NOUN
ejpam-5428	100	23	>	>	X
ejpam-5428	101	1	0	0	X
ejpam-5428	101	2	.	.	PUNCT
ejpam-5428	102	1	now	now	ADV
ejpam-5428	102	2	,	,	PUNCT
ejpam-5428	102	3	in	in	ADP
ejpam-5428	102	4	the	the	DET
ejpam-5428	102	5	following	follow	VERB
ejpam-5428	102	6	three	three	NUM
ejpam-5428	102	7	cases	case	NOUN
ejpam-5428	102	8	will	will	AUX
ejpam-5428	102	9	be	be	AUX
ejpam-5428	102	10	formed	form	VERB
ejpam-5428	102	11	for	for	ADP
ejpam-5428	102	12	which	which	PRON
ejpam-5428	102	13	geraghty	geraghty	PROPN
ejpam-5428	102	14	type	type	NOUN
ejpam-5428	102	15	-	-	PUNCT
ejpam-5428	102	16	i	i	PRON
ejpam-5428	102	17	contraction	contraction	NOUN
ejpam-5428	102	18	is	be	AUX
ejpam-5428	102	19	to	to	PART
ejpam-5428	102	20	be	be	AUX
ejpam-5428	102	21	verified	verify	VERB
ejpam-5428	102	22	for	for	ADP
ejpam-5428	102	23	β(t1	β(t1	NOUN
ejpam-5428	102	24	)	)	PUNCT
ejpam-5428	102	25	=	=	SYM
ejpam-5428	102	26	1−	1−	NUM
ejpam-5428	102	27	t1	t1	NOUN
ejpam-5428	102	28	.	.	PUNCT
ejpam-5428	103	1	case	case	NOUN
ejpam-5428	103	2	1	1	X
ejpam-5428	103	3	.	.	PUNCT
ejpam-5428	104	1	if	if	SCONJ
ejpam-5428	104	2	δ	δ	PROPN
ejpam-5428	104	3	,	,	PUNCT
ejpam-5428	104	4	γ	γ	PROPN
ejpam-5428	104	5	∈	∈	PROPN
ejpam-5428	105	1	[	[	X
ejpam-5428	105	2	0	0	NUM
ejpam-5428	105	3	,	,	PUNCT
ejpam-5428	105	4	1	1	NUM
ejpam-5428	105	5	)	)	PUNCT
ejpam-5428	105	6	then	then	ADV
ejpam-5428	105	7	mz(lδ	mz(lδ	VERB
ejpam-5428	105	8	,	,	PUNCT
ejpam-5428	105	9	lγ	lγ	PROPN
ejpam-5428	105	10	,	,	PUNCT
ejpam-5428	105	11	l	l	NOUN
ejpam-5428	105	12	)	)	PUNCT
ejpam-5428	105	13	=	=	SYM
ejpam-5428	105	14	e−	e−	NUM
ejpam-5428	105	15	|lδ−lγ|2	|lδ−lγ|2	NOUN
ejpam-5428	105	16	l+0.5	l+0.5	PROPN
ejpam-5428	105	17	v.	v.	PROPN
ejpam-5428	105	18	chandra	chandra	PROPN
ejpam-5428	105	19	,	,	PUNCT
ejpam-5428	105	20	u.	u.	PROPN
ejpam-5428	105	21	d.	d.	PROPN
ejpam-5428	105	22	patel	patel	PROPN
ejpam-5428	105	23	,	,	PUNCT
ejpam-5428	105	24	s.	s.	PROPN
ejpam-5428	105	25	radenović	radenović	PROPN
ejpam-5428	105	26	/	/	SYM
ejpam-5428	105	27	eur	eur	PROPN
ejpam-5428	105	28	.	.	PUNCT
ejpam-5428	106	1	j.	j.	PROPN
ejpam-5428	106	2	pure	pure	PROPN
ejpam-5428	106	3	appl	appl	PROPN
ejpam-5428	106	4	.	.	PROPN
ejpam-5428	106	5	math	math	PROPN
ejpam-5428	106	6	,	,	PUNCT
ejpam-5428	106	7	17	17	NUM
ejpam-5428	106	8	(	(	PUNCT
ejpam-5428	106	9	4	4	NUM
ejpam-5428	106	10	)	)	PUNCT
ejpam-5428	106	11	(	(	PUNCT
ejpam-5428	106	12	2024	2024	NUM
ejpam-5428	106	13	)	)	PUNCT
ejpam-5428	106	14	,	,	PUNCT
ejpam-5428	106	15	2384	2384	NUM
ejpam-5428	106	16	-	-	SYM
ejpam-5428	106	17	2404	2404	NUM
ejpam-5428	106	18	2389	2389	NUM
ejpam-5428	106	19	=	=	PUNCT
ejpam-5428	107	1	e−	e−	X
ejpam-5428	107	2	1	1	NUM
ejpam-5428	107	3	9	9	NUM
ejpam-5428	107	4	|δ2−γ2|2	|δ2−γ2|2	PROPN
ejpam-5428	107	5	l+0.5	l+0.5	PROPN
ejpam-5428	107	6	1−mz(lδ	1−mz(lδ	NUM
ejpam-5428	107	7	,	,	PUNCT
ejpam-5428	107	8	lγ	lγ	PROPN
ejpam-5428	107	9	,	,	PUNCT
ejpam-5428	107	10	l	l	NOUN
ejpam-5428	107	11	)	)	PUNCT
ejpam-5428	107	12	=	=	SYM
ejpam-5428	107	13	(	(	PUNCT
ejpam-5428	107	14	1−	1−	NUM
ejpam-5428	107	15	e−	e−	NUM
ejpam-5428	107	16	|lδ−lγ|2	|lδ−lγ|2	NOUN
ejpam-5428	107	17	l+0.5	l+0.5	PROPN
ejpam-5428	107	18	)	)	PUNCT
ejpam-5428	107	19	=	=	PUNCT
ejpam-5428	107	20	(	(	PUNCT
ejpam-5428	107	21	1−	1−	NUM
ejpam-5428	107	22	e−	e−	NUM
ejpam-5428	107	23	1	1	NUM
ejpam-5428	107	24	9	9	NUM
ejpam-5428	107	25	|δ2−γ2|2	|δ2−γ2|2	PROPN
ejpam-5428	107	26	l+0.5	l+0.5	PROPN
ejpam-5428	107	27	)	)	PUNCT
ejpam-5428	107	28	≤	≤	NOUN
ejpam-5428	107	29	e−	e−	NUM
ejpam-5428	107	30	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	107	31	l+0.5	l+0.5	NOUN
ejpam-5428	107	32	(	(	PUNCT
ejpam-5428	107	33	1−	1−	NUM
ejpam-5428	107	34	e−	e−	NUM
ejpam-5428	107	35	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	107	36	l+0.5	l+0.5	NOUN
ejpam-5428	107	37	)	)	PUNCT
ejpam-5428	107	38	(	(	PUNCT
ejpam-5428	107	39	9	9	NUM
ejpam-5428	107	40	)	)	PUNCT
ejpam-5428	107	41	=	=	SYM
ejpam-5428	107	42	β(1−mz(δ	β(1−mz(δ	PROPN
ejpam-5428	107	43	,	,	PUNCT
ejpam-5428	107	44	γ	γ	X
ejpam-5428	107	45	,	,	PUNCT
ejpam-5428	107	46	l))(1−mz(δ	l))(1−mz(δ	PROPN
ejpam-5428	107	47	,	,	PUNCT
ejpam-5428	107	48	γ	γ	X
ejpam-5428	107	49	,	,	PUNCT
ejpam-5428	107	50	l	l	NOUN
ejpam-5428	107	51	)	)	PUNCT
ejpam-5428	107	52	)	)	PUNCT
ejpam-5428	107	53	,	,	PUNCT
ejpam-5428	107	54	case	case	NOUN
ejpam-5428	107	55	2	2	X
ejpam-5428	107	56	.	.	PUNCT
ejpam-5428	108	1	if	if	SCONJ
ejpam-5428	108	2	δ	δ	PROPN
ejpam-5428	108	3	∈	∈	PROPN
ejpam-5428	109	1	[	[	X
ejpam-5428	109	2	0	0	NUM
ejpam-5428	109	3	,	,	PUNCT
ejpam-5428	109	4	1	1	NUM
ejpam-5428	109	5	)	)	PUNCT
ejpam-5428	109	6	,	,	PUNCT
ejpam-5428	109	7	γ	γ	X
ejpam-5428	109	8	=	=	SYM
ejpam-5428	109	9	1	1	NUM
ejpam-5428	109	10	then	then	ADV
ejpam-5428	109	11	mz(lδ	mz(lδ	VERB
ejpam-5428	109	12	,	,	PUNCT
ejpam-5428	109	13	lγ	lγ	PROPN
ejpam-5428	109	14	,	,	PUNCT
ejpam-5428	109	15	l	l	NOUN
ejpam-5428	109	16	)	)	PUNCT
ejpam-5428	109	17	=	=	SYM
ejpam-5428	110	1	e−	e−	NUM
ejpam-5428	110	2	|lδ−lγ|2	|lδ−lγ|2	NOUN
ejpam-5428	110	3	l+0.5	l+0.5	NOUN
ejpam-5428	110	4	=	=	SYM
ejpam-5428	110	5	e−	e−	PROPN
ejpam-5428	110	6	|	|	ADV
ejpam-5428	110	7	δ	δ	PROPN
ejpam-5428	110	8	2	2	NUM
ejpam-5428	110	9	3	3	NUM
ejpam-5428	110	10	−	−	NOUN
ejpam-5428	110	11	1	1	NUM
ejpam-5428	110	12	4	4	NUM
ejpam-5428	110	13	|2	|2	NUM
ejpam-5428	110	14	l+0.5	l+0.5	NOUN
ejpam-5428	110	15	1−mz(lδ	1−mz(lδ	NUM
ejpam-5428	110	16	,	,	PUNCT
ejpam-5428	110	17	lγ	lγ	PROPN
ejpam-5428	110	18	,	,	PUNCT
ejpam-5428	110	19	l	l	NOUN
ejpam-5428	110	20	)	)	PUNCT
ejpam-5428	110	21	=	=	SYM
ejpam-5428	110	22	1−	1−	NUM
ejpam-5428	110	23	e−	e−	NUM
ejpam-5428	110	24	|	|	ADV
ejpam-5428	110	25	δ	δ	PROPN
ejpam-5428	110	26	2	2	NUM
ejpam-5428	110	27	3	3	NUM
ejpam-5428	110	28	−	−	NOUN
ejpam-5428	110	29	1	1	NUM
ejpam-5428	110	30	4	4	NUM
ejpam-5428	110	31	|2	|2	NUM
ejpam-5428	110	32	l+0.5	l+0.5	NOUN
ejpam-5428	110	33	≤	≤	NOUN
ejpam-5428	110	34	e−	e−	PROPN
ejpam-5428	110	35	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	110	36	l+0.5	l+0.5	PROPN
ejpam-5428	110	37	(	(	PUNCT
ejpam-5428	110	38	1−	1−	NUM
ejpam-5428	110	39	e−	e−	NUM
ejpam-5428	110	40	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	110	41	l+0.5	l+0.5	PROPN
ejpam-5428	110	42	)	)	PUNCT
ejpam-5428	110	43	(	(	PUNCT
ejpam-5428	110	44	10	10	NUM
ejpam-5428	110	45	)	)	PUNCT
ejpam-5428	111	1	=	=	SYM
ejpam-5428	111	2	β(1−mz(δ	β(1−mz(δ	PROPN
ejpam-5428	111	3	,	,	PUNCT
ejpam-5428	111	4	γ	γ	X
ejpam-5428	111	5	,	,	PUNCT
ejpam-5428	111	6	l))(1−mz(δ	l))(1−mz(δ	PROPN
ejpam-5428	111	7	,	,	PUNCT
ejpam-5428	111	8	γ	γ	X
ejpam-5428	111	9	,	,	PUNCT
ejpam-5428	111	10	l	l	NOUN
ejpam-5428	111	11	)	)	PUNCT
ejpam-5428	111	12	)	)	PUNCT
ejpam-5428	111	13	,	,	PUNCT
ejpam-5428	111	14	case	case	NOUN
ejpam-5428	111	15	3	3	X
ejpam-5428	111	16	.	.	PUNCT
ejpam-5428	112	1	if	if	SCONJ
ejpam-5428	112	2	δ	δ	PROPN
ejpam-5428	112	3	=	=	SYM
ejpam-5428	112	4	γ	γ	X
ejpam-5428	112	5	=	=	SYM
ejpam-5428	112	6	0	0	PROPN
ejpam-5428	112	7	then	then	ADV
ejpam-5428	112	8	the	the	DET
ejpam-5428	112	9	geragthy	geragthy	ADJ
ejpam-5428	112	10	type	type	NOUN
ejpam-5428	112	11	-	-	PUNCT
ejpam-5428	112	12	i	i	PRON
ejpam-5428	112	13	contraction	contraction	NOUN
ejpam-5428	112	14	trivially	trivially	ADV
ejpam-5428	112	15	holds	hold	VERB
ejpam-5428	112	16	.	.	PUNCT
ejpam-5428	113	1	now	now	ADV
ejpam-5428	113	2	,	,	PUNCT
ejpam-5428	113	3	the	the	DET
ejpam-5428	113	4	graphical	graphical	ADJ
ejpam-5428	113	5	representation	representation	NOUN
ejpam-5428	113	6	of	of	ADP
ejpam-5428	113	7	cases	case	NOUN
ejpam-5428	113	8	1	1	NUM
ejpam-5428	113	9	and	and	CCONJ
ejpam-5428	113	10	2	2	NUM
ejpam-5428	113	11	;	;	PUNCT
ejpam-5428	113	12	graphs	graph	NOUN
ejpam-5428	113	13	of	of	ADP
ejpam-5428	113	14	two	two	NUM
ejpam-5428	113	15	functions	function	NOUN
ejpam-5428	113	16	:	:	PUNCT
ejpam-5428	113	17	yellow	yellow	ADJ
ejpam-5428	113	18	1	1	NUM
ejpam-5428	113	19	-	-	PUNCT
ejpam-5428	113	20	exp@	exp@	NOUN
ejpam-5428	113	21	-1	-1	PUNCT
ejpam-5428	113	22	9	9	NUM
ejpam-5428	113	23	abs@∆^2	abs@∆^2	NOUN
ejpam-5428	113	24	-	-	PUNCT
ejpam-5428	113	25	γ^2d^2	γ^2d^2	NOUN
ejpam-5428	113	26	�	�	PROPN
ejpam-5428	113	27	ld	ld	PROPN
ejpam-5428	113	28	,	,	PUNCT
ejpam-5428	113	29	red	red	ADJ
ejpam-5428	113	30	exp@	exp@	NOUN
ejpam-5428	113	31	-abs@∆	-abs@∆	PROPN
ejpam-5428	113	32	γd^2	γd^2	NOUN
ejpam-5428	113	33	l	l	NOUN
ejpam-5428	113	34	d	d	X
ejpam-5428	113	35	h1	h1	PROPN
ejpam-5428	113	36	-	-	PUNCT
ejpam-5428	113	37	exp@-abs@∆-γd^2	exp@-abs@∆-γd^2	NOUN
ejpam-5428	113	38	�	�	NOUN
ejpam-5428	113	39	ldll	ldll	PROPN
ejpam-5428	113	40	0.0	0.0	NUM
ejpam-5428	113	41	0.2	0.2	NUM
ejpam-5428	113	42	0.4	0.4	NUM
ejpam-5428	113	43	0.6	0.6	NUM
ejpam-5428	113	44	0.8	0.8	NUM
ejpam-5428	113	45	∆	∆	PROPN
ejpam-5428	113	46	0.0	0.0	NUM
ejpam-5428	113	47	0.2	0.2	NUM
ejpam-5428	113	48	0.4	0.4	NUM
ejpam-5428	113	49	0.6	0.6	NUM
ejpam-5428	113	50	0.8	0.8	NUM
ejpam-5428	113	51	γ	γ	PROPN
ejpam-5428	113	52	0.0	0.0	NUM
ejpam-5428	113	53	0.1	0.1	NUM
ejpam-5428	113	54	0.2	0.2	NUM
ejpam-5428	113	55	z	z	NOUN
ejpam-5428	113	56	figure	figure	NOUN
ejpam-5428	113	57	1	1	NUM
ejpam-5428	113	58	:	:	PUNCT
ejpam-5428	113	59	(	(	PUNCT
ejpam-5428	113	60	1−	1−	NUM
ejpam-5428	113	61	e−	e−	NUM
ejpam-5428	113	62	1	1	NUM
ejpam-5428	113	63	9	9	NUM
ejpam-5428	113	64	|δ2−γ2|2	|δ2−γ2|2	PROPN
ejpam-5428	113	65	l+0.5	l+0.5	PROPN
ejpam-5428	113	66	)	)	PUNCT
ejpam-5428	113	67	≤	≤	NOUN
ejpam-5428	114	1	e−	e−	NUM
ejpam-5428	114	2	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	114	3	l+0.5	l+0.5	NOUN
ejpam-5428	114	4	(	(	PUNCT
ejpam-5428	114	5	1−	1−	NUM
ejpam-5428	114	6	e−	e−	NUM
ejpam-5428	114	7	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	114	8	l+0.5	l+0.5	NOUN
ejpam-5428	114	9	)	)	PUNCT
ejpam-5428	114	10	graphs	graph	NOUN
ejpam-5428	114	11	of	of	ADP
ejpam-5428	114	12	two	two	NUM
ejpam-5428	114	13	functions	function	NOUN
ejpam-5428	114	14	:	:	PUNCT
ejpam-5428	114	15	yellow	yellow	ADJ
ejpam-5428	114	16	1	1	NUM
ejpam-5428	114	17	-	-	PUNCT
ejpam-5428	114	18	exp@-abs@	exp@-abs@	NOUN
ejpam-5428	114	19	∆^2	∆^2	NOUN
ejpam-5428	114	20	3	3	NUM
ejpam-5428	114	21	1	1	NUM
ejpam-5428	114	22	4	4	NUM
ejpam-5428	114	23	d^2	d^2	PROPN
ejpam-5428	114	24	�	�	PROPN
ejpam-5428	114	25	ld	ld	PROPN
ejpam-5428	114	26	,	,	PUNCT
ejpam-5428	114	27	red	red	ADJ
ejpam-5428	114	28	exp@	exp@	NOUN
ejpam-5428	114	29	-abs@∆	-abs@∆	PROPN
ejpam-5428	114	30	1d^2	1d^2	NUM
ejpam-5428	114	31	l	l	NOUN
ejpam-5428	115	1	d	d	X
ejpam-5428	115	2	h1	h1	PROPN
ejpam-5428	115	3	-	-	PUNCT
ejpam-5428	115	4	exp@-abs@∆-1d^2	exp@-abs@∆-1d^2	PROPN
ejpam-5428	115	5	�	�	PROPN
ejpam-5428	115	6	ldll	ldll	PROPN
ejpam-5428	115	7	0.0	0.0	NUM
ejpam-5428	115	8	0.2	0.2	NUM
ejpam-5428	115	9	0.4	0.4	NUM
ejpam-5428	115	10	0.6	0.6	NUM
ejpam-5428	115	11	0.8	0.8	NUM
ejpam-5428	115	12	∆	∆	PROPN
ejpam-5428	115	13	0.6	0.6	NUM
ejpam-5428	115	14	0.8	0.8	NUM
ejpam-5428	115	15	1.0	1.0	NUM
ejpam-5428	115	16	γ	γ	PROPN
ejpam-5428	115	17	0.0	0.0	NUM
ejpam-5428	115	18	0.1	0.1	NUM
ejpam-5428	115	19	0.2	0.2	NUM
ejpam-5428	115	20	z	z	NOUN
ejpam-5428	115	21	figure	figure	NOUN
ejpam-5428	115	22	2	2	NUM
ejpam-5428	115	23	:	:	PUNCT
ejpam-5428	115	24	1−	1−	NUM
ejpam-5428	115	25	e−	e−	NUM
ejpam-5428	115	26	|	|	ADV
ejpam-5428	115	27	δ	δ	PROPN
ejpam-5428	115	28	2	2	NUM
ejpam-5428	115	29	3	3	NUM
ejpam-5428	115	30	−	−	NOUN
ejpam-5428	115	31	1	1	NUM
ejpam-5428	115	32	4	4	NUM
ejpam-5428	115	33	|2	|2	NUM
ejpam-5428	115	34	l+0.5	l+0.5	NOUN
ejpam-5428	115	35	≤	≤	NOUN
ejpam-5428	115	36	e−	e−	PROPN
ejpam-5428	115	37	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	115	38	l+0.5	l+0.5	PROPN
ejpam-5428	115	39	(	(	PUNCT
ejpam-5428	115	40	1−	1−	NUM
ejpam-5428	115	41	e−	e−	NUM
ejpam-5428	115	42	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	115	43	l+0.5	l+0.5	PROPN
ejpam-5428	115	44	)	)	PUNCT
ejpam-5428	115	45	v.	v.	CCONJ
ejpam-5428	115	46	chandra	chandra	PROPN
ejpam-5428	115	47	,	,	PUNCT
ejpam-5428	115	48	u.	u.	PROPN
ejpam-5428	115	49	d.	d.	PROPN
ejpam-5428	115	50	patel	patel	PROPN
ejpam-5428	115	51	,	,	PUNCT
ejpam-5428	115	52	s.	s.	PROPN
ejpam-5428	115	53	radenović	radenović	PROPN
ejpam-5428	115	54	/	/	SYM
ejpam-5428	115	55	eur	eur	PROPN
ejpam-5428	115	56	.	.	PUNCT
ejpam-5428	116	1	j.	j.	PROPN
ejpam-5428	116	2	pure	pure	PROPN
ejpam-5428	116	3	appl	appl	PROPN
ejpam-5428	116	4	.	.	PROPN
ejpam-5428	116	5	math	math	PROPN
ejpam-5428	116	6	,	,	PUNCT
ejpam-5428	116	7	17	17	NUM
ejpam-5428	116	8	(	(	PUNCT
ejpam-5428	116	9	4	4	NUM
ejpam-5428	116	10	)	)	PUNCT
ejpam-5428	116	11	(	(	PUNCT
ejpam-5428	116	12	2024	2024	NUM
ejpam-5428	116	13	)	)	PUNCT
ejpam-5428	116	14	,	,	PUNCT
ejpam-5428	116	15	2384	2384	NUM
ejpam-5428	116	16	-	-	SYM
ejpam-5428	116	17	2404	2404	NUM
ejpam-5428	116	18	2390	2390	NUM
ejpam-5428	116	19	in	in	ADP
ejpam-5428	116	20	figure	figure	NOUN
ejpam-5428	116	21	1	1	NUM
ejpam-5428	116	22	,	,	PUNCT
ejpam-5428	116	23	the	the	DET
ejpam-5428	116	24	yellow	yellow	ADJ
ejpam-5428	116	25	colour	colour	NOUN
ejpam-5428	116	26	represents	represent	VERB
ejpam-5428	116	27	the	the	DET
ejpam-5428	116	28	l.h.s	l.h.s	NOUN
ejpam-5428	116	29	.	.	PUNCT
ejpam-5428	117	1	and	and	CCONJ
ejpam-5428	117	2	the	the	DET
ejpam-5428	117	3	red	red	ADJ
ejpam-5428	117	4	colour	colour	NOUN
ejpam-5428	117	5	represents	represent	VERB
ejpam-5428	117	6	the	the	DET
ejpam-5428	117	7	r.h.s	r.h.s	NOUN
ejpam-5428	117	8	.	.	PUNCT
ejpam-5428	117	9	of	of	ADP
ejpam-5428	117	10	equation	equation	NOUN
ejpam-5428	117	11	(	(	PUNCT
ejpam-5428	117	12	9	9	NUM
ejpam-5428	117	13	)	)	PUNCT
ejpam-5428	117	14	,	,	PUNCT
ejpam-5428	117	15	and	and	CCONJ
ejpam-5428	117	16	in	in	ADP
ejpam-5428	117	17	figure	figure	NOUN
ejpam-5428	117	18	2	2	NUM
ejpam-5428	117	19	,	,	PUNCT
ejpam-5428	117	20	the	the	DET
ejpam-5428	117	21	yellow	yellow	ADJ
ejpam-5428	117	22	colour	colour	NOUN
ejpam-5428	117	23	represents	represent	VERB
ejpam-5428	117	24	the	the	DET
ejpam-5428	117	25	l.h.s	l.h.s	NOUN
ejpam-5428	117	26	.	.	PUNCT
ejpam-5428	118	1	the	the	DET
ejpam-5428	118	2	red	red	ADJ
ejpam-5428	118	3	colour	colour	NOUN
ejpam-5428	118	4	represents	represent	VERB
ejpam-5428	118	5	the	the	DET
ejpam-5428	118	6	r.h.s	r.h.s	NOUN
ejpam-5428	118	7	.	.	PUNCT
ejpam-5428	118	8	of	of	ADP
ejpam-5428	118	9	equation	equation	NOUN
ejpam-5428	118	10	(	(	PUNCT
ejpam-5428	118	11	10	10	NUM
ejpam-5428	118	12	)	)	PUNCT
ejpam-5428	118	13	.	.	PUNCT
ejpam-5428	119	1	from	from	ADP
ejpam-5428	119	2	the	the	DET
ejpam-5428	119	3	graphical	graphical	ADJ
ejpam-5428	119	4	representations	representation	NOUN
ejpam-5428	119	5	it	it	PRON
ejpam-5428	119	6	is	be	AUX
ejpam-5428	119	7	clearly	clearly	ADV
ejpam-5428	119	8	visible	visible	ADJ
ejpam-5428	119	9	that	that	SCONJ
ejpam-5428	119	10	the	the	DET
ejpam-5428	119	11	contraction	contraction	NOUN
ejpam-5428	119	12	(	(	PUNCT
ejpam-5428	119	13	2	2	X
ejpam-5428	119	14	)	)	PUNCT
ejpam-5428	119	15	is	be	AUX
ejpam-5428	119	16	satisfied	satisfied	ADJ
ejpam-5428	119	17	.	.	PUNCT
ejpam-5428	120	1	hence	hence	ADV
ejpam-5428	120	2	,	,	PUNCT
ejpam-5428	120	3	the	the	DET
ejpam-5428	120	4	inequality	inequality	NOUN
ejpam-5428	120	5	holds	hold	VERB
ejpam-5428	120	6	in	in	ADP
ejpam-5428	120	7	these	these	DET
ejpam-5428	120	8	cases	case	NOUN
ejpam-5428	120	9	for	for	ADP
ejpam-5428	120	10	l	l	NOUN
ejpam-5428	120	11	>	>	X
ejpam-5428	120	12	0	0	PUNCT
ejpam-5428	120	13	and	and	CCONJ
ejpam-5428	120	14	β(t1	β(t1	NOUN
ejpam-5428	120	15	)	)	PUNCT
ejpam-5428	120	16	=	=	SYM
ejpam-5428	121	1	1	1	NUM
ejpam-5428	121	2	−	−	NOUN
ejpam-5428	121	3	t1	t1	NOUN
ejpam-5428	121	4	.	.	PUNCT
ejpam-5428	122	1	now	now	ADV
ejpam-5428	122	2	,	,	PUNCT
ejpam-5428	122	3	for	for	ADP
ejpam-5428	122	4	all	all	DET
ejpam-5428	122	5	δ	δ	PROPN
ejpam-5428	122	6	,	,	PUNCT
ejpam-5428	122	7	γ	γ	PROPN
ejpam-5428	122	8	,	,	PUNCT
ejpam-5428	122	9	η	η	PROPN
ejpam-5428	122	10	∈	∈	PROPN
ejpam-5428	122	11	[	[	X
ejpam-5428	122	12	0	0	NUM
ejpam-5428	122	13	,	,	PUNCT
ejpam-5428	122	14	1	1	NUM
ejpam-5428	122	15	]	]	PUNCT
ejpam-5428	122	16	,	,	PUNCT
ejpam-5428	122	17	then	then	ADV
ejpam-5428	122	18	it	it	PRON
ejpam-5428	122	19	is	be	AUX
ejpam-5428	122	20	easy	easy	ADJ
ejpam-5428	122	21	to	to	PART
ejpam-5428	122	22	check	check	VERB
ejpam-5428	122	23	that	that	SCONJ
ejpam-5428	122	24	mz	mz	PROPN
ejpam-5428	122	25	is	be	AUX
ejpam-5428	122	26	c	c	NOUN
ejpam-5428	122	27	-	-	PUNCT
ejpam-5428	122	28	triangular	triangular	NOUN
ejpam-5428	122	29	.	.	PUNCT
ejpam-5428	123	1	hence	hence	ADV
ejpam-5428	123	2	,	,	PUNCT
ejpam-5428	123	3	all	all	DET
ejpam-5428	123	4	assumptions	assumption	NOUN
ejpam-5428	123	5	of	of	ADP
ejpam-5428	123	6	theorem	theorem	NOUN
ejpam-5428	123	7	(	(	PUNCT
ejpam-5428	123	8	1	1	NUM
ejpam-5428	123	9	)	)	PUNCT
ejpam-5428	123	10	are	be	AUX
ejpam-5428	123	11	satisfied	satisfied	ADJ
ejpam-5428	123	12	for	for	ADP
ejpam-5428	123	13	l	l	NOUN
ejpam-5428	123	14	>	>	X
ejpam-5428	123	15	0	0	PUNCT
ejpam-5428	123	16	and	and	CCONJ
ejpam-5428	123	17	β(t1	β(t1	NOUN
ejpam-5428	123	18	)	)	PUNCT
ejpam-5428	123	19	=	=	SYM
ejpam-5428	123	20	1−	1−	NUM
ejpam-5428	123	21	t1	t1	NOUN
ejpam-5428	123	22	,	,	PUNCT
ejpam-5428	123	23	and	and	CCONJ
ejpam-5428	123	24	0	0	NUM
ejpam-5428	123	25	is	be	AUX
ejpam-5428	123	26	a	a	DET
ejpam-5428	123	27	unique	unique	ADJ
ejpam-5428	123	28	fixed	fix	VERB
ejpam-5428	123	29	point	point	NOUN
ejpam-5428	123	30	of	of	ADP
ejpam-5428	123	31	l.	l.	PROPN
ejpam-5428	123	32	now	now	ADV
ejpam-5428	123	33	we	we	PRON
ejpam-5428	123	34	recall	recall	VERB
ejpam-5428	123	35	the	the	DET
ejpam-5428	123	36	following	follow	VERB
ejpam-5428	123	37	definitions	definition	NOUN
ejpam-5428	123	38	from	from	ADP
ejpam-5428	123	39	[	[	X
ejpam-5428	123	40	2	2	NUM
ejpam-5428	123	41	]	]	PUNCT
ejpam-5428	123	42	.	.	PUNCT
ejpam-5428	124	1	definition	definition	NOUN
ejpam-5428	124	2	6	6	NUM
ejpam-5428	124	3	.	.	PUNCT
ejpam-5428	125	1	[	[	X
ejpam-5428	125	2	2	2	X
ejpam-5428	125	3	]	]	PUNCT
ejpam-5428	125	4	a	a	DET
ejpam-5428	125	5	self	self	NOUN
ejpam-5428	125	6	map	map	NOUN
ejpam-5428	125	7	l	l	NOUN
ejpam-5428	125	8	is	be	AUX
ejpam-5428	125	9	said	say	VERB
ejpam-5428	125	10	to	to	PART
ejpam-5428	125	11	be	be	AUX
ejpam-5428	125	12	a	a	DET
ejpam-5428	125	13	triangular	triangular	NOUN
ejpam-5428	125	14	α	α	NOUN
ejpam-5428	125	15	-	-	ADJ
ejpam-5428	125	16	admissible	admissible	ADJ
ejpam-5428	125	17	if	if	SCONJ
ejpam-5428	125	18	there	there	PRON
ejpam-5428	125	19	exists	exist	VERB
ejpam-5428	125	20	α	α	NOUN
ejpam-5428	125	21	:	:	PUNCT
ejpam-5428	125	22	ȳ2	ȳ2	VERB
ejpam-5428	125	23	×	×	NOUN
ejpam-5428	125	24	(	(	PUNCT
ejpam-5428	125	25	0,+∞	0,+∞	NUM
ejpam-5428	125	26	)	)	PUNCT
ejpam-5428	126	1	→	→	SYM
ejpam-5428	126	2	r	r	NOUN
ejpam-5428	126	3	such	such	ADJ
ejpam-5428	126	4	that	that	PRON
ejpam-5428	126	5	(	(	PUNCT
ejpam-5428	126	6	i	i	NOUN
ejpam-5428	126	7	)	)	PUNCT
ejpam-5428	126	8	α(δ	α(δ	PROPN
ejpam-5428	126	9	,	,	PUNCT
ejpam-5428	126	10	γ	γ	X
ejpam-5428	126	11	,	,	PUNCT
ejpam-5428	126	12	l	l	NOUN
ejpam-5428	126	13	)	)	PUNCT
ejpam-5428	126	14	≥	≥	NOUN
ejpam-5428	126	15	1	1	NUM
ejpam-5428	126	16	⇒	⇒	NOUN
ejpam-5428	126	17	α(lδ	α(lδ	NUM
ejpam-5428	126	18	,	,	PUNCT
ejpam-5428	126	19	lγ	lγ	ADP
ejpam-5428	126	20	,	,	PUNCT
ejpam-5428	126	21	l	l	NOUN
ejpam-5428	126	22	)	)	PUNCT
ejpam-5428	126	23	≥	≥	NOUN
ejpam-5428	126	24	1	1	NUM
ejpam-5428	126	25	(	(	PUNCT
ejpam-5428	126	26	ii	ii	NOUN
ejpam-5428	126	27	)	)	PUNCT
ejpam-5428	126	28	α(δ	α(δ	PROPN
ejpam-5428	126	29	,	,	PUNCT
ejpam-5428	126	30	η	η	NOUN
ejpam-5428	126	31	,	,	PUNCT
ejpam-5428	126	32	l	l	NOUN
ejpam-5428	126	33	)	)	PUNCT
ejpam-5428	126	34	≥	≥	NOUN
ejpam-5428	126	35	1	1	NUM
ejpam-5428	126	36	and	and	CCONJ
ejpam-5428	126	37	α(η	α(η	PROPN
ejpam-5428	126	38	,	,	PUNCT
ejpam-5428	126	39	γ	γ	X
ejpam-5428	126	40	,	,	PUNCT
ejpam-5428	126	41	l	l	NOUN
ejpam-5428	126	42	)	)	PUNCT
ejpam-5428	126	43	≥	≥	NOUN
ejpam-5428	126	44	1	1	NUM
ejpam-5428	126	45	⇒	⇒	NOUN
ejpam-5428	126	46	α(δ	α(δ	PROPN
ejpam-5428	126	47	,	,	PUNCT
ejpam-5428	126	48	γ	γ	X
ejpam-5428	126	49	,	,	PUNCT
ejpam-5428	126	50	l	l	NOUN
ejpam-5428	126	51	)	)	PUNCT
ejpam-5428	126	52	≥	≥	NOUN
ejpam-5428	126	53	1	1	NUM
ejpam-5428	126	54	for	for	ADP
ejpam-5428	126	55	all	all	DET
ejpam-5428	126	56	δ	δ	PROPN
ejpam-5428	126	57	,	,	PUNCT
ejpam-5428	126	58	γ	γ	PROPN
ejpam-5428	126	59	,	,	PUNCT
ejpam-5428	126	60	η	η	PROPN
ejpam-5428	126	61	∈	∈	PROPN
ejpam-5428	126	62	ȳ	ȳ	PROPN
ejpam-5428	126	63	and	and	CCONJ
ejpam-5428	126	64	any	any	DET
ejpam-5428	126	65	l	l	NOUN
ejpam-5428	126	66	>	>	X
ejpam-5428	126	67	0	0	X
ejpam-5428	126	68	.	.	PUNCT
ejpam-5428	127	1	lemma	lemma	PROPN
ejpam-5428	127	2	1	1	NUM
ejpam-5428	127	3	.	.	PUNCT
ejpam-5428	128	1	[	[	X
ejpam-5428	128	2	2	2	X
ejpam-5428	128	3	]	]	PUNCT
ejpam-5428	128	4	consider	consider	VERB
ejpam-5428	128	5	a	a	DET
ejpam-5428	128	6	fuzzy	fuzzy	ADJ
ejpam-5428	128	7	metric	metric	ADJ
ejpam-5428	128	8	space	space	NOUN
ejpam-5428	128	9	denoted	denote	VERB
ejpam-5428	128	10	by	by	ADP
ejpam-5428	128	11	(	(	PUNCT
ejpam-5428	128	12	ȳ,mz	ȳ,mz	NUM
ejpam-5428	128	13	,	,	PUNCT
ejpam-5428	128	14	⋄	⋄	PROPN
ejpam-5428	128	15	)	)	PUNCT
ejpam-5428	128	16	and	and	CCONJ
ejpam-5428	128	17	let	let	VERB
ejpam-5428	128	18	l	l	NOUN
ejpam-5428	128	19	:	:	PUNCT
ejpam-5428	128	20	ȳ	ȳ	PROPN
ejpam-5428	128	21	→	→	SYM
ejpam-5428	128	22	ȳ	ȳ	PROPN
ejpam-5428	128	23	be	be	AUX
ejpam-5428	128	24	a	a	DET
ejpam-5428	128	25	triangular	triangular	NOUN
ejpam-5428	128	26	α	α	NOUN
ejpam-5428	128	27	-	-	ADJ
ejpam-5428	128	28	admissible	admissible	ADJ
ejpam-5428	128	29	mapping	mapping	NOUN
ejpam-5428	128	30	.	.	PUNCT
ejpam-5428	129	1	suppose	suppose	VERB
ejpam-5428	129	2	there	there	PRON
ejpam-5428	129	3	exists	exist	VERB
ejpam-5428	129	4	an	an	DET
ejpam-5428	129	5	element	element	NOUN
ejpam-5428	129	6	δ0	δ0	NOUN
ejpam-5428	129	7	∈	∈	NOUN
ejpam-5428	129	8	ȳ	ȳ	NOUN
ejpam-5428	129	9	such	such	ADJ
ejpam-5428	129	10	that	that	PRON
ejpam-5428	129	11	α(δ0,lδ0	α(δ0,lδ0	PROPN
ejpam-5428	129	12	,	,	PUNCT
ejpam-5428	129	13	l	l	NOUN
ejpam-5428	129	14	)	)	PUNCT
ejpam-5428	129	15	≥	≥	NOUN
ejpam-5428	129	16	1	1	NUM
ejpam-5428	129	17	.	.	PUNCT
ejpam-5428	130	1	let	let	VERB
ejpam-5428	130	2	us	we	PRON
ejpam-5428	130	3	define	define	VERB
ejpam-5428	130	4	a	a	DET
ejpam-5428	130	5	{	{	PUNCT
ejpam-5428	130	6	δn	δn	NOUN
ejpam-5428	130	7	}	}	PUNCT
ejpam-5428	130	8	recursively	recursively	ADV
ejpam-5428	130	9	by	by	ADP
ejpam-5428	130	10	setting	set	VERB
ejpam-5428	130	11	δn+1	δn+1	PROPN
ejpam-5428	130	12	=	=	SYM
ejpam-5428	130	13	lδn	lδn	PROPN
ejpam-5428	130	14	.	.	PUNCT
ejpam-5428	131	1	then	then	ADV
ejpam-5428	131	2	α(δm	α(δm	PROPN
ejpam-5428	131	3	,	,	PUNCT
ejpam-5428	131	4	δn	δn	NOUN
ejpam-5428	131	5	,	,	PUNCT
ejpam-5428	131	6	l	l	NOUN
ejpam-5428	131	7	)	)	PUNCT
ejpam-5428	131	8	≥	≥	NOUN
ejpam-5428	131	9	1	1	NUM
ejpam-5428	131	10	,	,	PUNCT
ejpam-5428	131	11	for	for	ADP
ejpam-5428	131	12	all	all	DET
ejpam-5428	131	13	m	m	PROPN
ejpam-5428	131	14	,	,	PUNCT
ejpam-5428	131	15	n	n	PROPN
ejpam-5428	131	16	∈	∈	PROPN
ejpam-5428	131	17	n	n	X
ejpam-5428	131	18	with	with	ADP
ejpam-5428	131	19	m	m	PROPN
ejpam-5428	131	20	<	<	X
ejpam-5428	131	21	n	n	NOUN
ejpam-5428	131	22	and	and	CCONJ
ejpam-5428	131	23	l	l	NOUN
ejpam-5428	131	24	>	>	X
ejpam-5428	131	25	0	0	X
ejpam-5428	131	26	.	.	PUNCT
ejpam-5428	132	1	next	next	ADV
ejpam-5428	132	2	we	we	PRON
ejpam-5428	132	3	define	define	VERB
ejpam-5428	132	4	a	a	DET
ejpam-5428	132	5	new	new	ADJ
ejpam-5428	132	6	contractive	contractive	ADJ
ejpam-5428	132	7	inequality	inequality	NOUN
ejpam-5428	132	8	in	in	ADP
ejpam-5428	132	9	suzuki	suzuki	PROPN
ejpam-5428	132	10	view	view	NOUN
ejpam-5428	132	11	.	.	PUNCT
ejpam-5428	133	1	definition	definition	NOUN
ejpam-5428	133	2	7	7	NUM
ejpam-5428	133	3	.	.	PUNCT
ejpam-5428	133	4	a	a	DET
ejpam-5428	133	5	triangular	triangular	NOUN
ejpam-5428	133	6	α	α	NOUN
ejpam-5428	133	7	-	-	ADJ
ejpam-5428	133	8	admissible	admissible	ADJ
ejpam-5428	133	9	self	self	NOUN
ejpam-5428	133	10	mapping	mapping	NOUN
ejpam-5428	133	11	l	l	NOUN
ejpam-5428	133	12	defined	define	VERB
ejpam-5428	133	13	on	on	ADP
ejpam-5428	133	14	a	a	DET
ejpam-5428	133	15	b	b	NOUN
ejpam-5428	133	16	-	-	PUNCT
ejpam-5428	133	17	fuzzy	fuzzy	ADJ
ejpam-5428	133	18	metric	metric	ADJ
ejpam-5428	133	19	space	space	NOUN
ejpam-5428	133	20	(	(	PUNCT
ejpam-5428	133	21	ȳ,mz	ȳ,mz	NUM
ejpam-5428	133	22	,	,	PUNCT
ejpam-5428	133	23	⋄	⋄	PROPN
ejpam-5428	133	24	)	)	PUNCT
ejpam-5428	133	25	is	be	AUX
ejpam-5428	133	26	called	call	VERB
ejpam-5428	133	27	a	a	DET
ejpam-5428	133	28	α	α	PROPN
ejpam-5428	133	29	-	-	PUNCT
ejpam-5428	133	30	suzuki	suzuki	NOUN
ejpam-5428	133	31	-	-	PUNCT
ejpam-5428	133	32	geraghty	geraghty	VERB
ejpam-5428	133	33	type	type	NOUN
ejpam-5428	133	34	-	-	PUNCT
ejpam-5428	133	35	i	i	PRON
ejpam-5428	133	36	if	if	SCONJ
ejpam-5428	133	37	there	there	PRON
ejpam-5428	133	38	exists	exist	VERB
ejpam-5428	133	39	a	a	DET
ejpam-5428	133	40	β	β	X
ejpam-5428	133	41	∈	∈	PROPN
ejpam-5428	133	42	b	b	NOUN
ejpam-5428	133	43	such	such	ADJ
ejpam-5428	133	44	that	that	DET
ejpam-5428	133	45	mz(δ	mz(δ	PROPN
ejpam-5428	133	46	,	,	PUNCT
ejpam-5428	133	47	lδ	lδ	PROPN
ejpam-5428	133	48	,	,	PUNCT
ejpam-5428	133	49	l	l	NOUN
ejpam-5428	133	50	)	)	PUNCT
ejpam-5428	133	51	>	>	X
ejpam-5428	134	1	q	q	X
ejpam-5428	134	2	·	·	PUNCT
ejpam-5428	134	3	mz(δ	mz(δ	NUM
ejpam-5428	134	4	,	,	PUNCT
ejpam-5428	134	5	γ	γ	X
ejpam-5428	134	6	,	,	PUNCT
ejpam-5428	134	7	l	l	NOUN
ejpam-5428	134	8	)	)	PUNCT
ejpam-5428	134	9	⇒	⇒	NOUN
ejpam-5428	134	10	α(δ	α(δ	PROPN
ejpam-5428	134	11	,	,	PUNCT
ejpam-5428	134	12	γ	γ	X
ejpam-5428	134	13	,	,	PUNCT
ejpam-5428	134	14	l)(1−mz(lδ	l)(1−mz(lδ	NOUN
ejpam-5428	134	15	,	,	PUNCT
ejpam-5428	134	16	lγ	lγ	PROPN
ejpam-5428	134	17	,	,	PUNCT
ejpam-5428	134	18	l	l	NOUN
ejpam-5428	134	19	)	)	PUNCT
ejpam-5428	134	20	)	)	PUNCT
ejpam-5428	134	21	≤	≤	PUNCT
ejpam-5428	135	1	β(1−mz(δ	β(1−mz(δ	PROPN
ejpam-5428	135	2	,	,	PUNCT
ejpam-5428	135	3	γ	γ	X
ejpam-5428	135	4	,	,	PUNCT
ejpam-5428	135	5	l))(1−mz(δ	l))(1−mz(δ	PROPN
ejpam-5428	135	6	,	,	PUNCT
ejpam-5428	135	7	γ	γ	X
ejpam-5428	135	8	,	,	PUNCT
ejpam-5428	135	9	l	l	NOUN
ejpam-5428	135	10	)	)	PUNCT
ejpam-5428	135	11	)	)	PUNCT
ejpam-5428	135	12	(	(	PUNCT
ejpam-5428	135	13	11	11	NUM
ejpam-5428	135	14	)	)	PUNCT
ejpam-5428	135	15	where	where	SCONJ
ejpam-5428	135	16	q	q	PROPN
ejpam-5428	135	17	∈	∈	PROPN
ejpam-5428	135	18	(	(	PUNCT
ejpam-5428	135	19	0	0	NUM
ejpam-5428	135	20	,	,	PUNCT
ejpam-5428	135	21	1	1	NUM
ejpam-5428	135	22	)	)	PUNCT
ejpam-5428	135	23	and	and	CCONJ
ejpam-5428	135	24	δ	δ	PROPN
ejpam-5428	135	25	,	,	PUNCT
ejpam-5428	135	26	γ	γ	PROPN
ejpam-5428	135	27	∈	∈	PROPN
ejpam-5428	135	28	ȳ.	ȳ.	NOUN
ejpam-5428	135	29	now	now	ADV
ejpam-5428	135	30	we	we	PRON
ejpam-5428	135	31	write	write	VERB
ejpam-5428	135	32	a	a	DET
ejpam-5428	135	33	few	few	ADJ
ejpam-5428	135	34	definitions	definition	NOUN
ejpam-5428	135	35	which	which	PRON
ejpam-5428	135	36	are	be	AUX
ejpam-5428	135	37	essential	essential	ADJ
ejpam-5428	135	38	for	for	ADP
ejpam-5428	135	39	our	our	PRON
ejpam-5428	135	40	next	next	ADJ
ejpam-5428	135	41	result	result	NOUN
ejpam-5428	135	42	.	.	PUNCT
ejpam-5428	136	1	definition	definition	NOUN
ejpam-5428	136	2	8	8	NUM
ejpam-5428	136	3	.	.	PUNCT
ejpam-5428	137	1	a	a	DET
ejpam-5428	137	2	triangular	triangular	NOUN
ejpam-5428	137	3	α	α	NOUN
ejpam-5428	137	4	-	-	ADJ
ejpam-5428	137	5	admissible	admissible	ADJ
ejpam-5428	137	6	self	self	NOUN
ejpam-5428	137	7	mapping	mapping	NOUN
ejpam-5428	137	8	l	l	NOUN
ejpam-5428	137	9	is	be	AUX
ejpam-5428	137	10	defined	define	VERB
ejpam-5428	137	11	on	on	ADP
ejpam-5428	137	12	a	a	DET
ejpam-5428	137	13	b	b	NOUN
ejpam-5428	137	14	-	-	PUNCT
ejpam-5428	137	15	fuzzy	fuzzy	ADJ
ejpam-5428	137	16	metric	metric	ADJ
ejpam-5428	137	17	space	space	NOUN
ejpam-5428	137	18	(	(	PUNCT
ejpam-5428	137	19	ȳ,mz	ȳ,mz	NUM
ejpam-5428	137	20	,	,	PUNCT
ejpam-5428	137	21	⋄	⋄	PROPN
ejpam-5428	137	22	)	)	PUNCT
ejpam-5428	137	23	is	be	AUX
ejpam-5428	137	24	said	say	VERB
ejpam-5428	137	25	to	to	PART
ejpam-5428	137	26	have	have	VERB
ejpam-5428	137	27	property	property	NOUN
ejpam-5428	137	28	g1	g1	NOUN
ejpam-5428	137	29	if	if	SCONJ
ejpam-5428	137	30	for	for	ADP
ejpam-5428	137	31	any	any	DET
ejpam-5428	137	32	two	two	NUM
ejpam-5428	137	33	sequences	sequence	NOUN
ejpam-5428	137	34	{	{	PUNCT
ejpam-5428	137	35	δn	δn	NOUN
ejpam-5428	137	36	}	}	PUNCT
ejpam-5428	137	37	,	,	PUNCT
ejpam-5428	137	38	{	{	PUNCT
ejpam-5428	137	39	δm	δm	ADP
ejpam-5428	137	40	}	}	PUNCT
ejpam-5428	137	41	in	in	ADP
ejpam-5428	137	42	ȳ	ȳ	NUM
ejpam-5428	137	43	such	such	ADJ
ejpam-5428	137	44	that	that	SCONJ
ejpam-5428	137	45	lim	lim	PROPN
ejpam-5428	137	46	n	n	CCONJ
ejpam-5428	137	47	,	,	PUNCT
ejpam-5428	137	48	m→+∞	m→+∞	PROPN
ejpam-5428	137	49	mz(δn	mz(δn	PROPN
ejpam-5428	137	50	,	,	PUNCT
ejpam-5428	137	51	δm	δm	PROPN
ejpam-5428	137	52	,	,	PUNCT
ejpam-5428	137	53	l	l	NOUN
ejpam-5428	137	54	)	)	PUNCT
ejpam-5428	137	55	=	=	SYM
ejpam-5428	137	56	a(l	a(l	PROPN
ejpam-5428	137	57	)	)	PUNCT
ejpam-5428	137	58	∈	∈	PROPN
ejpam-5428	137	59	(	(	PUNCT
ejpam-5428	137	60	0	0	NUM
ejpam-5428	137	61	,	,	PUNCT
ejpam-5428	137	62	1	1	NUM
ejpam-5428	137	63	]	]	PUNCT
ejpam-5428	137	64	,	,	PUNCT
ejpam-5428	137	65	where	where	SCONJ
ejpam-5428	137	66	n	n	X
ejpam-5428	137	67	>	>	X
ejpam-5428	137	68	m	m	PROPN
ejpam-5428	137	69	and	and	CCONJ
ejpam-5428	137	70	n	n	CCONJ
ejpam-5428	137	71	,	,	PUNCT
ejpam-5428	137	72	m	m	VERB
ejpam-5428	137	73	∈	∈	PROPN
ejpam-5428	137	74	n	n	CCONJ
ejpam-5428	137	75	,	,	PUNCT
ejpam-5428	137	76	q	q	PROPN
ejpam-5428	137	77	∈	∈	PROPN
ejpam-5428	137	78	(	(	PUNCT
ejpam-5428	137	79	0	0	NUM
ejpam-5428	137	80	,	,	PUNCT
ejpam-5428	137	81	1	1	NUM
ejpam-5428	137	82	)	)	PUNCT
ejpam-5428	137	83	,	,	PUNCT
ejpam-5428	137	84	then	then	ADV
ejpam-5428	137	85	mz(δn	mz(δn	PROPN
ejpam-5428	137	86	,	,	PUNCT
ejpam-5428	137	87	δn+1	δn+1	PROPN
ejpam-5428	137	88	,	,	PUNCT
ejpam-5428	137	89	l	l	NOUN
ejpam-5428	137	90	)	)	PUNCT
ejpam-5428	137	91	>	>	X
ejpam-5428	137	92	q	q	PUNCT
ejpam-5428	137	93	·	·	PUNCT
ejpam-5428	137	94	mz(δn	mz(δn	PROPN
ejpam-5428	137	95	,	,	PUNCT
ejpam-5428	137	96	δm	δm	PROPN
ejpam-5428	137	97	,	,	PUNCT
ejpam-5428	137	98	l	l	NOUN
ejpam-5428	137	99	)	)	PUNCT
ejpam-5428	137	100	,	,	PUNCT
ejpam-5428	137	101	for	for	ADP
ejpam-5428	137	102	all	all	DET
ejpam-5428	137	103	l	l	NOUN
ejpam-5428	137	104	>	>	X
ejpam-5428	137	105	0	0	X
ejpam-5428	137	106	.	.	PUNCT
ejpam-5428	138	1	v.	v.	PROPN
ejpam-5428	138	2	chandra	chandra	PROPN
ejpam-5428	138	3	,	,	PUNCT
ejpam-5428	138	4	u.	u.	PROPN
ejpam-5428	138	5	d.	d.	PROPN
ejpam-5428	138	6	patel	patel	PROPN
ejpam-5428	138	7	,	,	PUNCT
ejpam-5428	138	8	s.	s.	PROPN
ejpam-5428	138	9	radenović	radenović	PROPN
ejpam-5428	138	10	/	/	SYM
ejpam-5428	138	11	eur	eur	PROPN
ejpam-5428	138	12	.	.	PUNCT
ejpam-5428	139	1	j.	j.	PROPN
ejpam-5428	139	2	pure	pure	PROPN
ejpam-5428	139	3	appl	appl	PROPN
ejpam-5428	139	4	.	.	PROPN
ejpam-5428	139	5	math	math	PROPN
ejpam-5428	139	6	,	,	PUNCT
ejpam-5428	139	7	17	17	NUM
ejpam-5428	139	8	(	(	PUNCT
ejpam-5428	139	9	4	4	NUM
ejpam-5428	139	10	)	)	PUNCT
ejpam-5428	139	11	(	(	PUNCT
ejpam-5428	139	12	2024	2024	NUM
ejpam-5428	139	13	)	)	PUNCT
ejpam-5428	139	14	,	,	PUNCT
ejpam-5428	139	15	2384	2384	NUM
ejpam-5428	139	16	-	-	SYM
ejpam-5428	139	17	2404	2404	NUM
ejpam-5428	139	18	2391	2391	NUM
ejpam-5428	139	19	definition	definition	NOUN
ejpam-5428	139	20	9	9	NUM
ejpam-5428	139	21	.	.	PUNCT
ejpam-5428	140	1	a	a	DET
ejpam-5428	140	2	triangular	triangular	NOUN
ejpam-5428	140	3	α	α	NOUN
ejpam-5428	140	4	-	-	ADJ
ejpam-5428	140	5	admissible	admissible	ADJ
ejpam-5428	140	6	self	self	NOUN
ejpam-5428	140	7	mapping	mapping	NOUN
ejpam-5428	140	8	l	l	NOUN
ejpam-5428	140	9	is	be	AUX
ejpam-5428	140	10	defined	define	VERB
ejpam-5428	140	11	on	on	ADP
ejpam-5428	140	12	a	a	DET
ejpam-5428	140	13	b	b	NOUN
ejpam-5428	140	14	-	-	PUNCT
ejpam-5428	140	15	fuzzy	fuzzy	ADJ
ejpam-5428	140	16	metric	metric	ADJ
ejpam-5428	140	17	space	space	NOUN
ejpam-5428	140	18	(	(	PUNCT
ejpam-5428	140	19	ȳ,mz	ȳ,mz	NUM
ejpam-5428	140	20	,	,	PUNCT
ejpam-5428	140	21	⋄	⋄	PROPN
ejpam-5428	140	22	)	)	PUNCT
ejpam-5428	140	23	is	be	AUX
ejpam-5428	140	24	said	say	VERB
ejpam-5428	140	25	to	to	PART
ejpam-5428	140	26	have	have	VERB
ejpam-5428	140	27	property	property	NOUN
ejpam-5428	140	28	g2	g2	PROPN
ejpam-5428	140	29	if	if	SCONJ
ejpam-5428	140	30	for	for	ADP
ejpam-5428	140	31	any	any	DET
ejpam-5428	140	32	convergent	convergent	NOUN
ejpam-5428	140	33	sequence	sequence	NOUN
ejpam-5428	140	34	{	{	PUNCT
ejpam-5428	140	35	δn	δn	NOUN
ejpam-5428	140	36	}	}	PUNCT
ejpam-5428	140	37	in	in	ADP
ejpam-5428	140	38	ȳ	ȳ	PROPN
ejpam-5428	140	39	converging	converge	VERB
ejpam-5428	140	40	to	to	ADP
ejpam-5428	140	41	u	u	PROPN
ejpam-5428	140	42	,	,	PUNCT
ejpam-5428	140	43	mz(δn	mz(δn	PROPN
ejpam-5428	140	44	,	,	PUNCT
ejpam-5428	140	45	lδn	lδn	PROPN
ejpam-5428	140	46	,	,	PUNCT
ejpam-5428	140	47	l	l	NOUN
ejpam-5428	140	48	)	)	PUNCT
ejpam-5428	140	49	>	>	X
ejpam-5428	141	1	q	q	PUNCT
ejpam-5428	141	2	·	·	PUNCT
ejpam-5428	141	3	mz(δn	mz(δn	X
ejpam-5428	141	4	,	,	PUNCT
ejpam-5428	141	5	u	u	NOUN
ejpam-5428	141	6	,	,	PUNCT
ejpam-5428	141	7	l	l	NOUN
ejpam-5428	141	8	)	)	PUNCT
ejpam-5428	141	9	,	,	PUNCT
ejpam-5428	141	10	where	where	SCONJ
ejpam-5428	141	11	n	n	X
ejpam-5428	141	12	∈	∈	PROPN
ejpam-5428	141	13	n	n	NOUN
ejpam-5428	141	14	and	and	CCONJ
ejpam-5428	141	15	q	q	PROPN
ejpam-5428	141	16	∈	∈	PROPN
ejpam-5428	141	17	(	(	PUNCT
ejpam-5428	141	18	0	0	NUM
ejpam-5428	141	19	,	,	PUNCT
ejpam-5428	141	20	1	1	NUM
ejpam-5428	141	21	)	)	PUNCT
ejpam-5428	141	22	.	.	PUNCT
ejpam-5428	142	1	example	example	NOUN
ejpam-5428	143	1	3	3	X
ejpam-5428	143	2	.	.	PUNCT
ejpam-5428	143	3	let	let	VERB
ejpam-5428	143	4	ȳ	ȳ	NOUN
ejpam-5428	143	5	=	=	PUNCT
ejpam-5428	144	1	[	[	X
ejpam-5428	144	2	0	0	NUM
ejpam-5428	144	3	,	,	PUNCT
ejpam-5428	144	4	1	1	NUM
ejpam-5428	144	5	]	]	PUNCT
ejpam-5428	144	6	and	and	CCONJ
ejpam-5428	144	7	define	define	VERB
ejpam-5428	144	8	mz(δ	mz(δ	PROPN
ejpam-5428	144	9	,	,	PUNCT
ejpam-5428	144	10	γ	γ	X
ejpam-5428	144	11	,	,	PUNCT
ejpam-5428	144	12	l	l	NOUN
ejpam-5428	144	13	)	)	PUNCT
ejpam-5428	145	1	=	=	SYM
ejpam-5428	145	2	l	l	NOUN
ejpam-5428	145	3	l+|δ−γ|2	l+|δ−γ|2	PROPN
ejpam-5428	145	4	.	.	PUNCT
ejpam-5428	146	1	let	let	VERB
ejpam-5428	146	2	(	(	PUNCT
ejpam-5428	146	3	ȳ,mz	ȳ,mz	NUM
ejpam-5428	146	4	,	,	PUNCT
ejpam-5428	146	5	⋄	⋄	PROPN
ejpam-5428	146	6	)	)	PUNCT
ejpam-5428	146	7	is	be	AUX
ejpam-5428	146	8	a	a	DET
ejpam-5428	146	9	gcomplete	gcomplete	ADJ
ejpam-5428	146	10	b	b	NOUN
ejpam-5428	146	11	-	-	PUNCT
ejpam-5428	146	12	fuzzy	fuzzy	ADJ
ejpam-5428	146	13	metric	metric	ADJ
ejpam-5428	146	14	space	space	NOUN
ejpam-5428	146	15	.	.	PUNCT
ejpam-5428	147	1	let	let	VERB
ejpam-5428	147	2	a	a	DET
ejpam-5428	147	3	self	self	NOUN
ejpam-5428	147	4	-	-	PUNCT
ejpam-5428	147	5	map	map	NOUN
ejpam-5428	147	6	l	l	NOUN
ejpam-5428	147	7	:	:	PUNCT
ejpam-5428	147	8	ȳ	ȳ	PROPN
ejpam-5428	147	9	→	→	SYM
ejpam-5428	147	10	ȳ	ȳ	PROPN
ejpam-5428	147	11	defined	define	VERB
ejpam-5428	147	12	by	by	ADP
ejpam-5428	147	13	l(δ	l(δ	NOUN
ejpam-5428	147	14	)	)	PUNCT
ejpam-5428	147	15	=	=	PRON
ejpam-5428	147	16	{	{	PUNCT
ejpam-5428	147	17	1	1	NUM
ejpam-5428	147	18	,	,	PUNCT
ejpam-5428	147	19	if	if	SCONJ
ejpam-5428	147	20	δ	δ	PROPN
ejpam-5428	147	21	∈	∈	PROPN
ejpam-5428	147	22	(	(	PUNCT
ejpam-5428	147	23	0	0	NUM
ejpam-5428	147	24	,	,	PUNCT
ejpam-5428	147	25	1	1	NUM
ejpam-5428	147	26	]	]	PUNCT
ejpam-5428	147	27	0	0	PUNCT
ejpam-5428	148	1	otherwise	otherwise	ADV
ejpam-5428	148	2	.	.	PUNCT
ejpam-5428	149	1	let	let	VERB
ejpam-5428	149	2	δn	δn	VERB
ejpam-5428	149	3	=	=	SYM
ejpam-5428	149	4	1−	1−	NUM
ejpam-5428	149	5	1	1	NUM
ejpam-5428	149	6	n	n	NOUN
ejpam-5428	149	7	and	and	CCONJ
ejpam-5428	149	8	δm	δm	ADV
ejpam-5428	149	9	=	=	SYM
ejpam-5428	149	10	1−	1−	NUM
ejpam-5428	149	11	1	1	NUM
ejpam-5428	149	12	m	m	NOUN
ejpam-5428	149	13	,	,	PUNCT
ejpam-5428	149	14	with	with	ADP
ejpam-5428	149	15	n	n	CCONJ
ejpam-5428	149	16	,	,	PUNCT
ejpam-5428	149	17	m	m	PROPN
ejpam-5428	149	18	∈	∈	NOUN
ejpam-5428	149	19	n.	n.	NOUN
ejpam-5428	149	20	since	since	SCONJ
ejpam-5428	149	21	lim	lim	PROPN
ejpam-5428	149	22	n→+∞	n→+∞	PROPN
ejpam-5428	149	23	mz(δn	mz(δn	PROPN
ejpam-5428	149	24	,	,	PUNCT
ejpam-5428	149	25	δn+1	δn+1	PROPN
ejpam-5428	149	26	,	,	PUNCT
ejpam-5428	149	27	l	l	NOUN
ejpam-5428	149	28	)	)	PUNCT
ejpam-5428	150	1	=	=	SYM
ejpam-5428	150	2	lim	lim	PROPN
ejpam-5428	150	3	n→+∞	n→+∞	VERB
ejpam-5428	150	4	mz	mz	PROPN
ejpam-5428	150	5	(	(	PUNCT
ejpam-5428	150	6	1−	1−	NUM
ejpam-5428	150	7	1	1	NUM
ejpam-5428	150	8	n	n	NOUN
ejpam-5428	150	9	,	,	PUNCT
ejpam-5428	150	10	1−	1−	NUM
ejpam-5428	150	11	1	1	NUM
ejpam-5428	150	12	n+	n+	SYM
ejpam-5428	150	13	1	1	NUM
ejpam-5428	150	14	,	,	PUNCT
ejpam-5428	150	15	l	l	NOUN
ejpam-5428	150	16	)	)	PUNCT
ejpam-5428	150	17	∈	∈	PROPN
ejpam-5428	150	18	(	(	PUNCT
ejpam-5428	150	19	0	0	NUM
ejpam-5428	150	20	,	,	PUNCT
ejpam-5428	150	21	1	1	NUM
ejpam-5428	150	22	]	]	PUNCT
ejpam-5428	150	23	,	,	PUNCT
ejpam-5428	150	24	then	then	ADV
ejpam-5428	150	25	,	,	PUNCT
ejpam-5428	150	26	mz(δn	mz(δn	PROPN
ejpam-5428	150	27	,	,	PUNCT
ejpam-5428	150	28	δn+1	δn+1	PROPN
ejpam-5428	150	29	,	,	PUNCT
ejpam-5428	150	30	l	l	NOUN
ejpam-5428	150	31	)	)	PUNCT
ejpam-5428	150	32	>	>	X
ejpam-5428	150	33	q	q	PUNCT
ejpam-5428	150	34	·	·	PUNCT
ejpam-5428	150	35	mz(δn	mz(δn	PROPN
ejpam-5428	150	36	,	,	PUNCT
ejpam-5428	150	37	δm	δm	PROPN
ejpam-5428	150	38	,	,	PUNCT
ejpam-5428	150	39	l	l	NOUN
ejpam-5428	150	40	)	)	PUNCT
ejpam-5428	151	1	where	where	SCONJ
ejpam-5428	151	2	q	q	NOUN
ejpam-5428	151	3	=	=	NOUN
ejpam-5428	151	4	1	1	NUM
ejpam-5428	151	5	2	2	NUM
ejpam-5428	151	6	,	,	PUNCT
ejpam-5428	151	7	definition	definition	NOUN
ejpam-5428	151	8	(	(	PUNCT
ejpam-5428	151	9	8)	8)	NUM
ejpam-5428	151	10	satisfied	satisfied	ADJ
ejpam-5428	151	11	.	.	PUNCT
ejpam-5428	152	1	we	we	PRON
ejpam-5428	152	2	have	have	VERB
ejpam-5428	152	3	mz(δn	mz(δn	PROPN
ejpam-5428	152	4	,	,	PUNCT
ejpam-5428	152	5	lδn	lδn	PROPN
ejpam-5428	152	6	,	,	PUNCT
ejpam-5428	152	7	l	l	NOUN
ejpam-5428	152	8	)	)	PUNCT
ejpam-5428	152	9	=	=	SYM
ejpam-5428	152	10	mz(1−	mz(1−	PROPN
ejpam-5428	152	11	1	1	NUM
ejpam-5428	152	12	n	n	NUM
ejpam-5428	152	13	,	,	PUNCT
ejpam-5428	152	14	1	1	NUM
ejpam-5428	152	15	,	,	PUNCT
ejpam-5428	152	16	l	l	NOUN
ejpam-5428	152	17	)	)	PUNCT
ejpam-5428	152	18	>	>	X
ejpam-5428	152	19	q	q	PUNCT
ejpam-5428	152	20	·	·	PUNCT
ejpam-5428	152	21	mz(1−	mz(1−	PROPN
ejpam-5428	152	22	1	1	NUM
ejpam-5428	152	23	n	n	NUM
ejpam-5428	152	24	,	,	PUNCT
ejpam-5428	152	25	1	1	NUM
ejpam-5428	152	26	,	,	PUNCT
ejpam-5428	152	27	l	l	NOUN
ejpam-5428	152	28	)	)	PUNCT
ejpam-5428	152	29	for	for	ADP
ejpam-5428	152	30	all	all	PRON
ejpam-5428	152	31	n	n	PRON
ejpam-5428	152	32	∈	∈	NOUN
ejpam-5428	152	33	n	n	NOUN
ejpam-5428	152	34	and	and	CCONJ
ejpam-5428	152	35	q	q	PROPN
ejpam-5428	152	36	∈	∈	PROPN
ejpam-5428	152	37	(	(	PUNCT
ejpam-5428	152	38	0	0	NUM
ejpam-5428	152	39	,	,	PUNCT
ejpam-5428	152	40	1	1	NUM
ejpam-5428	152	41	)	)	PUNCT
ejpam-5428	152	42	.	.	PUNCT
ejpam-5428	153	1	hence	hence	ADV
ejpam-5428	153	2	,	,	PUNCT
ejpam-5428	153	3	definition	definition	NOUN
ejpam-5428	153	4	9	9	NUM
ejpam-5428	153	5	holds	hold	NOUN
ejpam-5428	153	6	.	.	PUNCT
ejpam-5428	154	1	theorem	theorem	NOUN
ejpam-5428	154	2	2	2	NUM
ejpam-5428	154	3	.	.	X
ejpam-5428	154	4	consider	consider	VERB
ejpam-5428	154	5	a	a	DET
ejpam-5428	154	6	self	self	NOUN
ejpam-5428	154	7	map	map	NOUN
ejpam-5428	154	8	l	l	NOUN
ejpam-5428	154	9	defined	define	VERB
ejpam-5428	154	10	on	on	ADP
ejpam-5428	154	11	a	a	DET
ejpam-5428	154	12	g	g	NOUN
ejpam-5428	154	13	-	-	PUNCT
ejpam-5428	154	14	complete	complete	ADJ
ejpam-5428	154	15	b	b	NOUN
ejpam-5428	154	16	-	-	PUNCT
ejpam-5428	154	17	fuzzy	fuzzy	ADJ
ejpam-5428	154	18	metric	metric	ADJ
ejpam-5428	154	19	space	space	NOUN
ejpam-5428	154	20	(	(	PUNCT
ejpam-5428	154	21	ȳ,mz	ȳ,mz	NUM
ejpam-5428	154	22	,	,	PUNCT
ejpam-5428	154	23	⋄	⋄	PROPN
ejpam-5428	154	24	)	)	PUNCT
ejpam-5428	154	25	where	where	SCONJ
ejpam-5428	154	26	fuzzy	fuzzy	ADJ
ejpam-5428	154	27	metric	metric	NOUN
ejpam-5428	154	28	is	be	AUX
ejpam-5428	154	29	ctriangular	ctriangular	ADJ
ejpam-5428	154	30	satisfying	satisfying	NOUN
ejpam-5428	154	31	:	:	PUNCT
ejpam-5428	154	32	(	(	PUNCT
ejpam-5428	154	33	i	i	NOUN
ejpam-5428	154	34	)	)	PUNCT
ejpam-5428	154	35	map	map	NOUN
ejpam-5428	154	36	l	l	NOUN
ejpam-5428	154	37	is	be	AUX
ejpam-5428	154	38	b	b	NOUN
ejpam-5428	154	39	-	-	PUNCT
ejpam-5428	154	40	fuzzy	fuzzy	ADJ
ejpam-5428	154	41	α	α	NOUN
ejpam-5428	154	42	-	-	PUNCT
ejpam-5428	154	43	suzuki	suzuki	NOUN
ejpam-5428	154	44	-	-	PUNCT
ejpam-5428	154	45	geraghty	geraghty	VERB
ejpam-5428	154	46	type	type	PROPN
ejpam-5428	154	47	-	-	PUNCT
ejpam-5428	154	48	i	i	NOUN
ejpam-5428	154	49	;	;	PUNCT
ejpam-5428	154	50	(	(	PUNCT
ejpam-5428	154	51	ii	ii	NOUN
ejpam-5428	154	52	)	)	PUNCT
ejpam-5428	154	53	l	l	NOUN
ejpam-5428	154	54	has	have	VERB
ejpam-5428	154	55	property	property	NOUN
ejpam-5428	154	56	g1	g1	NOUN
ejpam-5428	154	57	and	and	CCONJ
ejpam-5428	154	58	g2	g2	PROPN
ejpam-5428	154	59	;	;	PUNCT
ejpam-5428	154	60	(	(	PUNCT
ejpam-5428	154	61	iii	iii	X
ejpam-5428	154	62	)	)	PUNCT
ejpam-5428	154	63	there	there	PRON
ejpam-5428	154	64	exists	exist	VERB
ejpam-5428	154	65	δ0	δ0	NOUN
ejpam-5428	154	66	∈	∈	PROPN
ejpam-5428	154	67	ȳ	ȳ	NOUN
ejpam-5428	154	68	such	such	ADJ
ejpam-5428	154	69	that	that	DET
ejpam-5428	154	70	α(δ0,lδ0	α(δ0,lδ0	PROPN
ejpam-5428	154	71	,	,	PUNCT
ejpam-5428	154	72	l	l	NOUN
ejpam-5428	154	73	)	)	PUNCT
ejpam-5428	154	74	≥	≥	NOUN
ejpam-5428	154	75	1	1	NUM
ejpam-5428	154	76	for	for	ADP
ejpam-5428	154	77	all	all	DET
ejpam-5428	154	78	l	l	NOUN
ejpam-5428	154	79	>	>	X
ejpam-5428	154	80	0	0	NUM
ejpam-5428	154	81	;	;	PUNCT
ejpam-5428	154	82	(	(	PUNCT
ejpam-5428	154	83	iv	iv	X
ejpam-5428	154	84	)	)	PUNCT
ejpam-5428	154	85	if	if	SCONJ
ejpam-5428	154	86	α(δn	α(δn	NUM
ejpam-5428	154	87	,	,	PUNCT
ejpam-5428	154	88	δn+1	δn+1	PROPN
ejpam-5428	154	89	,	,	PUNCT
ejpam-5428	154	90	l	l	NOUN
ejpam-5428	154	91	)	)	PUNCT
ejpam-5428	154	92	≥	≥	NOUN
ejpam-5428	154	93	1	1	NUM
ejpam-5428	154	94	and	and	CCONJ
ejpam-5428	154	95	δn	δn	NOUN
ejpam-5428	154	96	→	→	SYM
ejpam-5428	154	97	u	u	NOUN
ejpam-5428	154	98	as	as	ADP
ejpam-5428	154	99	n	n	PROPN
ejpam-5428	154	100	→	→	SYM
ejpam-5428	154	101	+	+	PROPN
ejpam-5428	154	102	∞	∞	PROPN
ejpam-5428	154	103	,	,	PUNCT
ejpam-5428	154	104	then	then	ADV
ejpam-5428	154	105	α(δn	α(δn	NUM
ejpam-5428	154	106	,	,	PUNCT
ejpam-5428	154	107	u	u	NOUN
ejpam-5428	154	108	,	,	PUNCT
ejpam-5428	154	109	l	l	NOUN
ejpam-5428	154	110	)	)	PUNCT
ejpam-5428	154	111	≥	≥	NOUN
ejpam-5428	154	112	1	1	NUM
ejpam-5428	154	113	for	for	ADP
ejpam-5428	154	114	all	all	DET
ejpam-5428	154	115	n	n	DET
ejpam-5428	154	116	∈	∈	PROPN
ejpam-5428	154	117	n.	n.	NOUN
ejpam-5428	154	118	then	then	ADV
ejpam-5428	154	119	l	l	PROPN
ejpam-5428	154	120	has	have	VERB
ejpam-5428	154	121	a	a	DET
ejpam-5428	154	122	fixed	fix	VERB
ejpam-5428	154	123	point	point	NOUN
ejpam-5428	154	124	.	.	PUNCT
ejpam-5428	155	1	proof	proof	NOUN
ejpam-5428	155	2	.	.	PUNCT
ejpam-5428	156	1	by	by	ADP
ejpam-5428	156	2	assumption	assumption	NOUN
ejpam-5428	156	3	(	(	PUNCT
ejpam-5428	156	4	3	3	NUM
ejpam-5428	156	5	)	)	PUNCT
ejpam-5428	156	6	,	,	PUNCT
ejpam-5428	156	7	there	there	PRON
ejpam-5428	156	8	exists	exist	VERB
ejpam-5428	156	9	δ0	δ0	NOUN
ejpam-5428	156	10	∈	∈	PROPN
ejpam-5428	156	11	ȳ	ȳ	NOUN
ejpam-5428	156	12	such	such	ADJ
ejpam-5428	156	13	that	that	DET
ejpam-5428	156	14	α(δ0	α(δ0	NOUN
ejpam-5428	156	15	,	,	PUNCT
ejpam-5428	156	16	δ1	δ1	NOUN
ejpam-5428	156	17	,	,	PUNCT
ejpam-5428	156	18	l	l	NOUN
ejpam-5428	156	19	)	)	PUNCT
ejpam-5428	156	20	≥	≥	NOUN
ejpam-5428	156	21	1	1	NUM
ejpam-5428	156	22	for	for	ADP
ejpam-5428	156	23	all	all	DET
ejpam-5428	156	24	l	l	NOUN
ejpam-5428	156	25	>	>	X
ejpam-5428	156	26	0	0	PUNCT
ejpam-5428	156	27	and	and	CCONJ
ejpam-5428	156	28	define	define	VERB
ejpam-5428	156	29	a	a	DET
ejpam-5428	156	30	sequence	sequence	NOUN
ejpam-5428	156	31	{	{	PUNCT
ejpam-5428	156	32	δn	δn	NOUN
ejpam-5428	156	33	}	}	PUNCT
ejpam-5428	156	34	in	in	ADP
ejpam-5428	156	35	ȳ	ȳ	NUM
ejpam-5428	156	36	by	by	ADP
ejpam-5428	156	37	δn+1	δn+1	PROPN
ejpam-5428	156	38	=	=	SYM
ejpam-5428	156	39	lδn	lδn	PROPN
ejpam-5428	156	40	for	for	ADP
ejpam-5428	156	41	all	all	PRON
ejpam-5428	156	42	n	n	DET
ejpam-5428	156	43	∈	∈	PROPN
ejpam-5428	156	44	n.	n.	NOUN
ejpam-5428	156	45	suppose	suppose	VERB
ejpam-5428	156	46	that	that	SCONJ
ejpam-5428	156	47	δn	δn	NOUN
ejpam-5428	156	48	=	=	SYM
ejpam-5428	156	49	δn+1	δn+1	NOUN
ejpam-5428	156	50	for	for	ADP
ejpam-5428	156	51	some	some	DET
ejpam-5428	156	52	n	n	PRON
ejpam-5428	156	53	∈	∈	PROPN
ejpam-5428	156	54	n∪{0	n∪{0	NOUN
ejpam-5428	156	55	}	}	PUNCT
ejpam-5428	156	56	no	no	DET
ejpam-5428	156	57	need	need	NOUN
ejpam-5428	156	58	to	to	PART
ejpam-5428	156	59	prove	prove	VERB
ejpam-5428	156	60	anything	anything	PRON
ejpam-5428	156	61	automatically	automatically	ADV
ejpam-5428	156	62	completed	complete	VERB
ejpam-5428	156	63	.	.	PUNCT
ejpam-5428	157	1	suppose	suppose	VERB
ejpam-5428	157	2	δn	δn	SCONJ
ejpam-5428	157	3	̸=	̸=	PROPN
ejpam-5428	157	4	δn+1	δn+1	VERB
ejpam-5428	157	5	for	for	ADP
ejpam-5428	157	6	all	all	DET
ejpam-5428	157	7	n	n	PRON
ejpam-5428	157	8	∈	∈	PROPN
ejpam-5428	157	9	n.	n.	NOUN
ejpam-5428	157	10	by	by	ADP
ejpam-5428	157	11	lemma	lemma	PROPN
ejpam-5428	157	12	1	1	NUM
ejpam-5428	157	13	,	,	PUNCT
ejpam-5428	157	14	we	we	PRON
ejpam-5428	157	15	have	have	VERB
ejpam-5428	157	16	α(δn	α(δn	NUM
ejpam-5428	157	17	,	,	PUNCT
ejpam-5428	157	18	δn+1	δn+1	PROPN
ejpam-5428	157	19	,	,	PUNCT
ejpam-5428	157	20	l	l	NOUN
ejpam-5428	157	21	)	)	PUNCT
ejpam-5428	157	22	≥	≥	NOUN
ejpam-5428	157	23	1	1	NUM
ejpam-5428	157	24	,	,	PUNCT
ejpam-5428	157	25	(	(	PUNCT
ejpam-5428	157	26	12	12	NUM
ejpam-5428	157	27	)	)	PUNCT
ejpam-5428	157	28	for	for	ADP
ejpam-5428	157	29	all	all	PRON
ejpam-5428	157	30	n	n	PRON
ejpam-5428	157	31	∈	∈	PROPN
ejpam-5428	157	32	n	n	NOUN
ejpam-5428	157	33	and	and	CCONJ
ejpam-5428	157	34	l	l	NOUN
ejpam-5428	157	35	>	>	X
ejpam-5428	157	36	0	0	X
ejpam-5428	157	37	.	.	PUNCT
ejpam-5428	158	1	by	by	ADP
ejpam-5428	158	2	(	(	PUNCT
ejpam-5428	158	3	11	11	NUM
ejpam-5428	158	4	)	)	PUNCT
ejpam-5428	158	5	,	,	PUNCT
ejpam-5428	158	6	mz(δn	mz(δn	PROPN
ejpam-5428	158	7	,	,	PUNCT
ejpam-5428	158	8	lδn	lδn	PROPN
ejpam-5428	158	9	,	,	PUNCT
ejpam-5428	158	10	l	l	NOUN
ejpam-5428	158	11	)	)	PUNCT
ejpam-5428	158	12	>	>	X
ejpam-5428	158	13	q	q	PUNCT
ejpam-5428	158	14	·	·	PUNCT
ejpam-5428	158	15	mz(δn	mz(δn	PROPN
ejpam-5428	158	16	,	,	PUNCT
ejpam-5428	158	17	δn+1	δn+1	PROPN
ejpam-5428	158	18	,	,	PUNCT
ejpam-5428	158	19	l	l	NOUN
ejpam-5428	158	20	)	)	PUNCT
ejpam-5428	158	21	implies	imply	VERB
ejpam-5428	158	22	v.	v.	ADP
ejpam-5428	158	23	chandra	chandra	PROPN
ejpam-5428	158	24	,	,	PUNCT
ejpam-5428	158	25	u.	u.	PROPN
ejpam-5428	158	26	d.	d.	PROPN
ejpam-5428	158	27	patel	patel	PROPN
ejpam-5428	158	28	,	,	PUNCT
ejpam-5428	158	29	s.	s.	PROPN
ejpam-5428	158	30	radenović	radenović	PROPN
ejpam-5428	158	31	/	/	SYM
ejpam-5428	158	32	eur	eur	PROPN
ejpam-5428	158	33	.	.	PUNCT
ejpam-5428	159	1	j.	j.	PROPN
ejpam-5428	159	2	pure	pure	PROPN
ejpam-5428	159	3	appl	appl	PROPN
ejpam-5428	159	4	.	.	PROPN
ejpam-5428	159	5	math	math	PROPN
ejpam-5428	159	6	,	,	PUNCT
ejpam-5428	159	7	17	17	NUM
ejpam-5428	159	8	(	(	PUNCT
ejpam-5428	159	9	4	4	NUM
ejpam-5428	159	10	)	)	PUNCT
ejpam-5428	159	11	(	(	PUNCT
ejpam-5428	159	12	2024	2024	NUM
ejpam-5428	159	13	)	)	PUNCT
ejpam-5428	159	14	,	,	PUNCT
ejpam-5428	159	15	2384	2384	NUM
ejpam-5428	159	16	-	-	SYM
ejpam-5428	159	17	2404	2404	NUM
ejpam-5428	159	18	2392	2392	NUM
ejpam-5428	159	19	α(δn	α(δn	NUM
ejpam-5428	159	20	,	,	PUNCT
ejpam-5428	159	21	δn+1	δn+1	PROPN
ejpam-5428	159	22	,	,	PUNCT
ejpam-5428	159	23	l)(1−mz(lδn	l)(1−mz(lδn	PROPN
ejpam-5428	159	24	,	,	PUNCT
ejpam-5428	159	25	lδn+1	lδn+1	PROPN
ejpam-5428	159	26	,	,	PUNCT
ejpam-5428	159	27	l	l	NOUN
ejpam-5428	159	28	)	)	PUNCT
ejpam-5428	159	29	)	)	PUNCT
ejpam-5428	159	30	≤	≤	NOUN
ejpam-5428	159	31	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	159	32	,	,	PUNCT
ejpam-5428	159	33	δn+1	δn+1	PROPN
ejpam-5428	159	34	,	,	PUNCT
ejpam-5428	159	35	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	159	36	,	,	PUNCT
ejpam-5428	159	37	δn+1	δn+1	PROPN
ejpam-5428	159	38	,	,	PUNCT
ejpam-5428	159	39	l	l	NOUN
ejpam-5428	159	40	)	)	PUNCT
ejpam-5428	159	41	)	)	PUNCT
ejpam-5428	159	42	.	.	PUNCT
ejpam-5428	160	1	now	now	ADV
ejpam-5428	160	2	(	(	PUNCT
ejpam-5428	160	3	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	160	4	,	,	PUNCT
ejpam-5428	160	5	δn+2	δn+2	X
ejpam-5428	160	6	,	,	PUNCT
ejpam-5428	160	7	l	l	NOUN
ejpam-5428	160	8	)	)	PUNCT
ejpam-5428	160	9	)	)	PUNCT
ejpam-5428	161	1	=	=	PRON
ejpam-5428	161	2	(	(	PUNCT
ejpam-5428	161	3	1−mz(lδn	1−mz(lδn	NUM
ejpam-5428	161	4	,	,	PUNCT
ejpam-5428	161	5	lδn+1	lδn+1	NOUN
ejpam-5428	161	6	,	,	PUNCT
ejpam-5428	161	7	l	l	NOUN
ejpam-5428	161	8	)	)	PUNCT
ejpam-5428	161	9	)	)	PUNCT
ejpam-5428	161	10	≤	≤	NOUN
ejpam-5428	161	11	α(δn	α(δn	NUM
ejpam-5428	161	12	,	,	PUNCT
ejpam-5428	161	13	δn+1	δn+1	PROPN
ejpam-5428	161	14	,	,	PUNCT
ejpam-5428	161	15	l)(1−mz(lδn	l)(1−mz(lδn	PROPN
ejpam-5428	161	16	,	,	PUNCT
ejpam-5428	161	17	lδn+1	lδn+1	PROPN
ejpam-5428	161	18	,	,	PUNCT
ejpam-5428	161	19	l	l	NOUN
ejpam-5428	161	20	)	)	PUNCT
ejpam-5428	161	21	)	)	PUNCT
ejpam-5428	161	22	≤	≤	NOUN
ejpam-5428	161	23	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	161	24	,	,	PUNCT
ejpam-5428	161	25	δn+1	δn+1	PROPN
ejpam-5428	161	26	,	,	PUNCT
ejpam-5428	161	27	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	161	28	,	,	PUNCT
ejpam-5428	161	29	δn+1	δn+1	PROPN
ejpam-5428	161	30	,	,	PUNCT
ejpam-5428	161	31	l	l	NOUN
ejpam-5428	161	32	)	)	PUNCT
ejpam-5428	161	33	)	)	PUNCT
ejpam-5428	162	1	<	<	X
ejpam-5428	162	2	(	(	PUNCT
ejpam-5428	162	3	1−mz(δn	1−mz(δn	NUM
ejpam-5428	162	4	,	,	PUNCT
ejpam-5428	162	5	δn+1	δn+1	PROPN
ejpam-5428	162	6	,	,	PUNCT
ejpam-5428	162	7	l	l	NOUN
ejpam-5428	162	8	)	)	PUNCT
ejpam-5428	162	9	)	)	PUNCT
ejpam-5428	162	10	.	.	PUNCT
ejpam-5428	163	1	(	(	PUNCT
ejpam-5428	163	2	13	13	NUM
ejpam-5428	163	3	)	)	PUNCT
ejpam-5428	163	4	this	this	PRON
ejpam-5428	163	5	concludes	conclude	VERB
ejpam-5428	163	6	that	that	SCONJ
ejpam-5428	163	7	{	{	PUNCT
ejpam-5428	163	8	mz(δn	mz(δn	PROPN
ejpam-5428	163	9	,	,	PUNCT
ejpam-5428	163	10	δn+1	δn+1	PROPN
ejpam-5428	163	11	,	,	PUNCT
ejpam-5428	163	12	l	l	NOUN
ejpam-5428	163	13	)	)	PUNCT
ejpam-5428	163	14	}	}	PUNCT
ejpam-5428	163	15	is	be	AUX
ejpam-5428	163	16	non	non	ADJ
ejpam-5428	163	17	-	-	ADJ
ejpam-5428	163	18	decreasing	decrease	VERB
ejpam-5428	163	19	sequence	sequence	NOUN
ejpam-5428	163	20	of	of	ADP
ejpam-5428	163	21	positive	positive	ADJ
ejpam-5428	163	22	real	real	ADJ
ejpam-5428	163	23	number	number	NOUN
ejpam-5428	163	24	in	in	ADP
ejpam-5428	163	25	(	(	PUNCT
ejpam-5428	163	26	0	0	NUM
ejpam-5428	163	27	,	,	PUNCT
ejpam-5428	163	28	1	1	NUM
ejpam-5428	163	29	]	]	PUNCT
ejpam-5428	163	30	.	.	PUNCT
ejpam-5428	164	1	so	so	ADV
ejpam-5428	164	2	there	there	PRON
ejpam-5428	164	3	exists	exist	VERB
ejpam-5428	164	4	s(l	s(l	NOUN
ejpam-5428	164	5	)	)	PUNCT
ejpam-5428	164	6	∈	∈	PROPN
ejpam-5428	164	7	(	(	PUNCT
ejpam-5428	164	8	0	0	NUM
ejpam-5428	164	9	,	,	PUNCT
ejpam-5428	164	10	1	1	NUM
ejpam-5428	164	11	]	]	PUNCT
ejpam-5428	164	12	such	such	ADJ
ejpam-5428	164	13	that	that	SCONJ
ejpam-5428	164	14	lim	lim	PROPN
ejpam-5428	164	15	n→+∞	n→+∞	PROPN
ejpam-5428	164	16	mz(δn	mz(δn	PROPN
ejpam-5428	164	17	,	,	PUNCT
ejpam-5428	164	18	δn+1	δn+1	PROPN
ejpam-5428	164	19	,	,	PUNCT
ejpam-5428	164	20	l	l	NOUN
ejpam-5428	164	21	)	)	PUNCT
ejpam-5428	164	22	=	=	SYM
ejpam-5428	164	23	s(l	s(l	NUM
ejpam-5428	164	24	)	)	PUNCT
ejpam-5428	164	25	.	.	PUNCT
ejpam-5428	165	1	suppose	suppose	VERB
ejpam-5428	165	2	to	to	ADP
ejpam-5428	165	3	the	the	DET
ejpam-5428	165	4	contrary	contrary	ADJ
ejpam-5428	165	5	,	,	PUNCT
ejpam-5428	165	6	s(l0	s(l0	NOUN
ejpam-5428	165	7	)	)	PUNCT
ejpam-5428	165	8	<	<	X
ejpam-5428	165	9	1	1	NUM
ejpam-5428	165	10	for	for	ADP
ejpam-5428	165	11	any	any	DET
ejpam-5428	165	12	l0	l0	PROPN
ejpam-5428	165	13	>	>	X
ejpam-5428	165	14	0	0	X
ejpam-5428	165	15	.	.	PUNCT
ejpam-5428	166	1	now	now	ADV
ejpam-5428	166	2	put	put	VERB
ejpam-5428	166	3	limit	limit	NOUN
ejpam-5428	166	4	as	as	ADP
ejpam-5428	166	5	n	n	PROPN
ejpam-5428	166	6	→	→	SYM
ejpam-5428	166	7	+	+	PROPN
ejpam-5428	166	8	∞	∞	PROPN
ejpam-5428	166	9	lim	lim	PROPN
ejpam-5428	166	10	n→+∞	n→+∞	PROPN
ejpam-5428	166	11	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	166	12	,	,	PUNCT
ejpam-5428	166	13	δn+1	δn+1	PROPN
ejpam-5428	166	14	,	,	PUNCT
ejpam-5428	166	15	l	l	NOUN
ejpam-5428	166	16	)	)	PUNCT
ejpam-5428	166	17	)	)	PUNCT
ejpam-5428	167	1	=	=	SYM
ejpam-5428	167	2	1	1	X
ejpam-5428	167	3	.	.	PUNCT
ejpam-5428	167	4	by	by	ADP
ejpam-5428	167	5	the	the	DET
ejpam-5428	167	6	characteristic	characteristic	NOUN
ejpam-5428	167	7	of	of	ADP
ejpam-5428	167	8	b	b	X
ejpam-5428	167	9	,	,	PUNCT
ejpam-5428	167	10	we	we	PRON
ejpam-5428	167	11	have	have	VERB
ejpam-5428	167	12	lim	lim	PROPN
ejpam-5428	167	13	n→+∞	n→+∞	PROPN
ejpam-5428	167	14	mz(δn	mz(δn	PROPN
ejpam-5428	167	15	,	,	PUNCT
ejpam-5428	167	16	δn+1	δn+1	PROPN
ejpam-5428	167	17	,	,	PUNCT
ejpam-5428	167	18	l	l	NOUN
ejpam-5428	167	19	)	)	PUNCT
ejpam-5428	167	20	=	=	SYM
ejpam-5428	167	21	1	1	NUM
ejpam-5428	167	22	,	,	PUNCT
ejpam-5428	167	23	(	(	PUNCT
ejpam-5428	167	24	14	14	NUM
ejpam-5428	167	25	)	)	PUNCT
ejpam-5428	167	26	a	a	DET
ejpam-5428	167	27	contradiction	contradiction	NOUN
ejpam-5428	167	28	.	.	PUNCT
ejpam-5428	168	1	hence	hence	ADV
ejpam-5428	168	2	,	,	PUNCT
ejpam-5428	168	3	we	we	PRON
ejpam-5428	168	4	need	need	VERB
ejpam-5428	168	5	to	to	PART
ejpam-5428	168	6	show	show	VERB
ejpam-5428	168	7	{	{	PUNCT
ejpam-5428	168	8	δn	δn	NOUN
ejpam-5428	168	9	}	}	PUNCT
ejpam-5428	168	10	is	be	AUX
ejpam-5428	168	11	a	a	DET
ejpam-5428	168	12	g	g	NOUN
ejpam-5428	168	13	-	-	PUNCT
ejpam-5428	168	14	cauchy	cauchy	ADJ
ejpam-5428	168	15	sequence	sequence	NOUN
ejpam-5428	168	16	.	.	PUNCT
ejpam-5428	169	1	suppose	suppose	VERB
ejpam-5428	169	2	λ	λ	X
ejpam-5428	169	3	=	=	SYM
ejpam-5428	169	4	mz(δn	mz(δn	PROPN
ejpam-5428	169	5	,	,	PUNCT
ejpam-5428	169	6	δm	δm	PROPN
ejpam-5428	169	7	,	,	PUNCT
ejpam-5428	169	8	l	l	NOUN
ejpam-5428	169	9	)	)	PUNCT
ejpam-5428	169	10	<	<	X
ejpam-5428	169	11	1	1	NUM
ejpam-5428	169	12	,	,	PUNCT
ejpam-5428	169	13	by	by	ADP
ejpam-5428	169	14	using	use	VERB
ejpam-5428	169	15	property	property	NOUN
ejpam-5428	169	16	(	(	PUNCT
ejpam-5428	169	17	g1	g1	PROPN
ejpam-5428	169	18	)	)	PUNCT
ejpam-5428	169	19	,	,	PUNCT
ejpam-5428	169	20	mz(δn	mz(δn	PROPN
ejpam-5428	169	21	,	,	PUNCT
ejpam-5428	169	22	δn+1	δn+1	PROPN
ejpam-5428	169	23	,	,	PUNCT
ejpam-5428	169	24	l	l	NOUN
ejpam-5428	169	25	)	)	PUNCT
ejpam-5428	169	26	>	>	X
ejpam-5428	170	1	q	q	PUNCT
ejpam-5428	170	2	·	·	PUNCT
ejpam-5428	170	3	mz(δn	mz(δn	PROPN
ejpam-5428	170	4	,	,	PUNCT
ejpam-5428	170	5	δm	δm	PROPN
ejpam-5428	170	6	,	,	PUNCT
ejpam-5428	170	7	l	l	NOUN
ejpam-5428	170	8	)	)	PUNCT
ejpam-5428	170	9	implies	imply	VERB
ejpam-5428	170	10	α(δn	α(δn	NUM
ejpam-5428	170	11	,	,	PUNCT
ejpam-5428	170	12	δm	δm	PROPN
ejpam-5428	170	13	,	,	PUNCT
ejpam-5428	170	14	l)(1−mz(lδn	l)(1−mz(lδn	PROPN
ejpam-5428	170	15	,	,	PUNCT
ejpam-5428	170	16	lδm	lδm	NOUN
ejpam-5428	170	17	,	,	PUNCT
ejpam-5428	170	18	l	l	NOUN
ejpam-5428	170	19	)	)	PUNCT
ejpam-5428	170	20	)	)	PUNCT
ejpam-5428	170	21	≤	≤	NUM
ejpam-5428	170	22	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	170	23	,	,	PUNCT
ejpam-5428	170	24	δm	δm	ADV
ejpam-5428	170	25	,	,	PUNCT
ejpam-5428	170	26	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	170	27	,	,	PUNCT
ejpam-5428	170	28	δm	δm	PROPN
ejpam-5428	170	29	,	,	PUNCT
ejpam-5428	170	30	l	l	NOUN
ejpam-5428	170	31	)	)	PUNCT
ejpam-5428	170	32	)	)	PUNCT
ejpam-5428	170	33	.	.	PUNCT
ejpam-5428	171	1	we	we	PRON
ejpam-5428	171	2	have	have	VERB
ejpam-5428	171	3	(	(	PUNCT
ejpam-5428	171	4	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	171	5	,	,	PUNCT
ejpam-5428	171	6	δm+1	δm+1	PROPN
ejpam-5428	171	7	,	,	PUNCT
ejpam-5428	171	8	l	l	NOUN
ejpam-5428	171	9	)	)	PUNCT
ejpam-5428	171	10	)	)	PUNCT
ejpam-5428	172	1	=	=	SYM
ejpam-5428	172	2	(	(	PUNCT
ejpam-5428	172	3	1−mz(lδn	1−mz(lδn	NUM
ejpam-5428	172	4	,	,	PUNCT
ejpam-5428	172	5	lδm	lδm	NOUN
ejpam-5428	172	6	,	,	PUNCT
ejpam-5428	172	7	l	l	NOUN
ejpam-5428	172	8	)	)	PUNCT
ejpam-5428	172	9	)	)	PUNCT
ejpam-5428	172	10	≤	≤	NOUN
ejpam-5428	173	1	α(δn	α(δn	NUM
ejpam-5428	173	2	,	,	PUNCT
ejpam-5428	173	3	δm	δm	PROPN
ejpam-5428	173	4	,	,	PUNCT
ejpam-5428	173	5	l)(1−mz(lδn	l)(1−mz(lδn	PROPN
ejpam-5428	173	6	,	,	PUNCT
ejpam-5428	173	7	lδm	lδm	NOUN
ejpam-5428	173	8	,	,	PUNCT
ejpam-5428	173	9	l	l	NOUN
ejpam-5428	173	10	)	)	PUNCT
ejpam-5428	173	11	)	)	PUNCT
ejpam-5428	173	12	≤	≤	NUM
ejpam-5428	173	13	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	173	14	,	,	PUNCT
ejpam-5428	173	15	δm	δm	ADV
ejpam-5428	173	16	,	,	PUNCT
ejpam-5428	173	17	l))(1−mz(δn	l))(1−mz(δn	PROPN
ejpam-5428	173	18	,	,	PUNCT
ejpam-5428	173	19	δm	δm	PROPN
ejpam-5428	173	20	,	,	PUNCT
ejpam-5428	173	21	l	l	NOUN
ejpam-5428	173	22	)	)	PUNCT
ejpam-5428	173	23	)	)	PUNCT
ejpam-5428	173	24	.	.	PUNCT
ejpam-5428	174	1	taking	take	VERB
ejpam-5428	174	2	the	the	DET
ejpam-5428	174	3	limit	limit	NOUN
ejpam-5428	174	4	as	as	ADP
ejpam-5428	174	5	n	n	CCONJ
ejpam-5428	174	6	,	,	PUNCT
ejpam-5428	174	7	m	m	PROPN
ejpam-5428	174	8	→	→	SYM
ejpam-5428	174	9	+	+	ADJ
ejpam-5428	174	10	∞	∞	PROPN
ejpam-5428	174	11	and	and	CCONJ
ejpam-5428	174	12	lemma	lemma	PROPN
ejpam-5428	174	13	1	1	NUM
ejpam-5428	174	14	,	,	PUNCT
ejpam-5428	174	15	lim	lim	PROPN
ejpam-5428	174	16	n	n	CCONJ
ejpam-5428	174	17	,	,	PUNCT
ejpam-5428	174	18	m→+∞	m→+∞	PROPN
ejpam-5428	174	19	(	(	PUNCT
ejpam-5428	174	20	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	174	21	,	,	PUNCT
ejpam-5428	174	22	δm+1	δm+1	PROPN
ejpam-5428	174	23	,	,	PUNCT
ejpam-5428	174	24	l	l	NOUN
ejpam-5428	174	25	)	)	PUNCT
ejpam-5428	174	26	)	)	PUNCT
ejpam-5428	174	27	≤	≤	NOUN
ejpam-5428	174	28	lim	lim	PROPN
ejpam-5428	174	29	n	n	CCONJ
ejpam-5428	174	30	,	,	PUNCT
ejpam-5428	174	31	m→+∞	m→+∞	PROPN
ejpam-5428	174	32	α(δn	α(δn	PROPN
ejpam-5428	174	33	,	,	PUNCT
ejpam-5428	174	34	δm	δm	ADV
ejpam-5428	174	35	,	,	PUNCT
ejpam-5428	174	36	l)(1−mz(δn+1	l)(1−mz(δn+1	NOUN
ejpam-5428	174	37	,	,	PUNCT
ejpam-5428	174	38	δm+1	δm+1	PROPN
ejpam-5428	174	39	,	,	PUNCT
ejpam-5428	174	40	l	l	NOUN
ejpam-5428	174	41	)	)	PUNCT
ejpam-5428	174	42	)	)	PUNCT
ejpam-5428	174	43	≤	≤	NOUN
ejpam-5428	174	44	lim	lim	PROPN
ejpam-5428	174	45	n	n	CCONJ
ejpam-5428	174	46	,	,	PUNCT
ejpam-5428	174	47	m→+∞	m→+∞	PROPN
ejpam-5428	174	48	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	174	49	,	,	PUNCT
ejpam-5428	174	50	δm	δm	PRON
ejpam-5428	174	51	,	,	PUNCT
ejpam-5428	174	52	l))(1−	l))(1−	PROPN
ejpam-5428	174	53	λ	λ	PROPN
ejpam-5428	174	54	)	)	PUNCT
ejpam-5428	174	55	.	.	PUNCT
ejpam-5428	175	1	(	(	PUNCT
ejpam-5428	175	2	15	15	NUM
ejpam-5428	175	3	)	)	PUNCT
ejpam-5428	175	4	on	on	ADP
ejpam-5428	175	5	the	the	DET
ejpam-5428	175	6	flip	flip	ADJ
ejpam-5428	175	7	side	side	NOUN
ejpam-5428	175	8	,	,	PUNCT
ejpam-5428	175	9	(	(	PUNCT
ejpam-5428	175	10	1−mz(δn	1−mz(δn	NUM
ejpam-5428	175	11	,	,	PUNCT
ejpam-5428	175	12	δm	δm	PROPN
ejpam-5428	175	13	,	,	PUNCT
ejpam-5428	175	14	l	l	NOUN
ejpam-5428	175	15	)	)	PUNCT
ejpam-5428	175	16	)	)	PUNCT
ejpam-5428	175	17	≤	≤	NOUN
ejpam-5428	175	18	(	(	PUNCT
ejpam-5428	175	19	1−mz(δn	1−mz(δn	NUM
ejpam-5428	175	20	,	,	PUNCT
ejpam-5428	175	21	δn+1	δn+1	PROPN
ejpam-5428	175	22	,	,	PUNCT
ejpam-5428	175	23	l	l	NOUN
ejpam-5428	175	24	)	)	PUNCT
ejpam-5428	175	25	)	)	PUNCT
ejpam-5428	176	1	+	+	CCONJ
ejpam-5428	176	2	(	(	PUNCT
ejpam-5428	176	3	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	176	4	,	,	PUNCT
ejpam-5428	176	5	δm	δm	PROPN
ejpam-5428	176	6	,	,	PUNCT
ejpam-5428	176	7	l	l	NOUN
ejpam-5428	176	8	)	)	PUNCT
ejpam-5428	176	9	)	)	PUNCT
ejpam-5428	176	10	≤	≤	NOUN
ejpam-5428	176	11	(	(	PUNCT
ejpam-5428	176	12	1−mz(δn	1−mz(δn	NUM
ejpam-5428	176	13	,	,	PUNCT
ejpam-5428	176	14	δn+1	δn+1	PROPN
ejpam-5428	176	15	,	,	PUNCT
ejpam-5428	176	16	l	l	NOUN
ejpam-5428	176	17	)	)	PUNCT
ejpam-5428	176	18	)	)	PUNCT
ejpam-5428	177	1	+	+	CCONJ
ejpam-5428	177	2	(	(	PUNCT
ejpam-5428	177	3	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	177	4	,	,	PUNCT
ejpam-5428	177	5	δm+1	δm+1	PROPN
ejpam-5428	177	6	,	,	PUNCT
ejpam-5428	177	7	l	l	NOUN
ejpam-5428	177	8	)	)	PUNCT
ejpam-5428	177	9	)	)	PUNCT
ejpam-5428	178	1	+	+	CCONJ
ejpam-5428	178	2	(	(	PUNCT
ejpam-5428	178	3	1−mz(δm+1	1−mz(δm+1	NUM
ejpam-5428	178	4	,	,	PUNCT
ejpam-5428	178	5	δm	δm	PROPN
ejpam-5428	178	6	,	,	PUNCT
ejpam-5428	178	7	l	l	NOUN
ejpam-5428	178	8	)	)	PUNCT
ejpam-5428	178	9	)	)	PUNCT
ejpam-5428	178	10	.	.	PUNCT
ejpam-5428	179	1	v.	v.	PROPN
ejpam-5428	179	2	chandra	chandra	PROPN
ejpam-5428	179	3	,	,	PUNCT
ejpam-5428	179	4	u.	u.	PROPN
ejpam-5428	179	5	d.	d.	PROPN
ejpam-5428	179	6	patel	patel	PROPN
ejpam-5428	179	7	,	,	PUNCT
ejpam-5428	179	8	s.	s.	PROPN
ejpam-5428	179	9	radenović	radenović	PROPN
ejpam-5428	179	10	/	/	SYM
ejpam-5428	179	11	eur	eur	PROPN
ejpam-5428	179	12	.	.	PUNCT
ejpam-5428	180	1	j.	j.	PROPN
ejpam-5428	180	2	pure	pure	PROPN
ejpam-5428	180	3	appl	appl	PROPN
ejpam-5428	180	4	.	.	PROPN
ejpam-5428	180	5	math	math	PROPN
ejpam-5428	180	6	,	,	PUNCT
ejpam-5428	180	7	17	17	NUM
ejpam-5428	180	8	(	(	PUNCT
ejpam-5428	180	9	4	4	NUM
ejpam-5428	180	10	)	)	PUNCT
ejpam-5428	180	11	(	(	PUNCT
ejpam-5428	180	12	2024	2024	NUM
ejpam-5428	180	13	)	)	PUNCT
ejpam-5428	180	14	,	,	PUNCT
ejpam-5428	180	15	2384	2384	NUM
ejpam-5428	180	16	-	-	SYM
ejpam-5428	180	17	2404	2404	NUM
ejpam-5428	180	18	2393	2393	NUM
ejpam-5428	180	19	putting	putting	NOUN
ejpam-5428	180	20	limit	limit	NOUN
ejpam-5428	180	21	as	as	ADP
ejpam-5428	180	22	n	n	X
ejpam-5428	180	23	,	,	PUNCT
ejpam-5428	180	24	m	m	PROPN
ejpam-5428	180	25	→	→	SYM
ejpam-5428	180	26	+	+	ADJ
ejpam-5428	180	27	∞	∞	NUM
ejpam-5428	180	28	and	and	CCONJ
ejpam-5428	180	29	using	use	VERB
ejpam-5428	180	30	(	(	PUNCT
ejpam-5428	180	31	14	14	NUM
ejpam-5428	180	32	)	)	PUNCT
ejpam-5428	180	33	and	and	CCONJ
ejpam-5428	180	34	(	(	PUNCT
ejpam-5428	180	35	15	15	NUM
ejpam-5428	180	36	)	)	PUNCT
ejpam-5428	180	37	,	,	PUNCT
ejpam-5428	180	38	(	(	PUNCT
ejpam-5428	180	39	1−	1−	NUM
ejpam-5428	180	40	λ	λ	NOUN
ejpam-5428	180	41	)	)	PUNCT
ejpam-5428	180	42	≤	≤	NOUN
ejpam-5428	180	43	lim	lim	PROPN
ejpam-5428	180	44	n	n	CCONJ
ejpam-5428	180	45	,	,	PUNCT
ejpam-5428	180	46	m→+∞	m→+∞	PROPN
ejpam-5428	180	47	(	(	PUNCT
ejpam-5428	180	48	1−mz(δn+1	1−mz(δn+1	NUM
ejpam-5428	180	49	,	,	PUNCT
ejpam-5428	180	50	δm+1	δm+1	PROPN
ejpam-5428	180	51	,	,	PUNCT
ejpam-5428	180	52	l	l	NOUN
ejpam-5428	180	53	)	)	PUNCT
ejpam-5428	180	54	)	)	PUNCT
ejpam-5428	180	55	≤	≤	NOUN
ejpam-5428	180	56	lim	lim	PROPN
ejpam-5428	180	57	n	n	CCONJ
ejpam-5428	180	58	,	,	PUNCT
ejpam-5428	180	59	m→+∞	m→+∞	PROPN
ejpam-5428	180	60	β(1−mz(δn	β(1−mz(δn	PROPN
ejpam-5428	180	61	,	,	PUNCT
ejpam-5428	180	62	δm	δm	PRON
ejpam-5428	180	63	,	,	PUNCT
ejpam-5428	180	64	l))(1−	l))(1−	PROPN
ejpam-5428	180	65	λ	λ	PROPN
ejpam-5428	180	66	)	)	PUNCT
ejpam-5428	180	67	.	.	PUNCT
ejpam-5428	181	1	which	which	PRON
ejpam-5428	181	2	gives	give	VERB
ejpam-5428	181	3	lim	lim	PROPN
ejpam-5428	181	4	n	n	PRON
ejpam-5428	181	5	,	,	PUNCT
ejpam-5428	181	6	m→+∞	m→+∞	PROPN
ejpam-5428	181	7	β(1−mz(δm	β(1−mz(δm	PROPN
ejpam-5428	181	8	,	,	PUNCT
ejpam-5428	181	9	δn	δn	NOUN
ejpam-5428	181	10	,	,	PUNCT
ejpam-5428	181	11	l	l	NOUN
ejpam-5428	181	12	)	)	PUNCT
ejpam-5428	181	13	)	)	PUNCT
ejpam-5428	182	1	=	=	SYM
ejpam-5428	182	2	1	1	X
ejpam-5428	182	3	,	,	PUNCT
ejpam-5428	182	4	lim	lim	PROPN
ejpam-5428	182	5	n	n	CCONJ
ejpam-5428	182	6	,	,	PUNCT
ejpam-5428	182	7	m→+∞	m→+∞	PROPN
ejpam-5428	182	8	mz(δm	mz(δm	PROPN
ejpam-5428	182	9	,	,	PUNCT
ejpam-5428	182	10	δn	δn	NOUN
ejpam-5428	182	11	,	,	PUNCT
ejpam-5428	182	12	l	l	NOUN
ejpam-5428	182	13	)	)	PUNCT
ejpam-5428	182	14	=	=	SYM
ejpam-5428	183	1	1	1	X
ejpam-5428	183	2	.	.	NOUN
ejpam-5428	183	3	which	which	PRON
ejpam-5428	183	4	is	be	AUX
ejpam-5428	183	5	a	a	DET
ejpam-5428	183	6	contradiction	contradiction	NOUN
ejpam-5428	183	7	with	with	ADP
ejpam-5428	183	8	λ	λ	NOUN
ejpam-5428	183	9	.	.	PUNCT
ejpam-5428	183	10	thus	thus	ADV
ejpam-5428	183	11	,	,	PUNCT
ejpam-5428	183	12	{	{	PUNCT
ejpam-5428	183	13	δn	δn	NOUN
ejpam-5428	183	14	}	}	PUNCT
ejpam-5428	183	15	is	be	AUX
ejpam-5428	183	16	a	a	DET
ejpam-5428	183	17	g	g	NOUN
ejpam-5428	183	18	-	-	PUNCT
ejpam-5428	183	19	cauchy	cauchy	ADJ
ejpam-5428	183	20	sequence	sequence	NOUN
ejpam-5428	183	21	.	.	PUNCT
ejpam-5428	184	1	since	since	SCONJ
ejpam-5428	184	2	ȳ	ȳ	PROPN
ejpam-5428	184	3	is	be	AUX
ejpam-5428	184	4	a	a	DET
ejpam-5428	184	5	g	g	NOUN
ejpam-5428	184	6	-	-	PUNCT
ejpam-5428	184	7	complete	complete	ADJ
ejpam-5428	184	8	,	,	PUNCT
ejpam-5428	184	9	there	there	PRON
ejpam-5428	184	10	exists	exist	VERB
ejpam-5428	184	11	u	u	PROPN
ejpam-5428	184	12	∈	∈	PROPN
ejpam-5428	184	13	ȳ	ȳ	NOUN
ejpam-5428	184	14	such	such	ADJ
ejpam-5428	184	15	that	that	SCONJ
ejpam-5428	184	16	lim	lim	PROPN
ejpam-5428	184	17	n→+∞	n→+∞	PROPN
ejpam-5428	184	18	mz(δn	mz(δn	PROPN
ejpam-5428	184	19	,	,	PUNCT
ejpam-5428	184	20	u	u	NOUN
ejpam-5428	184	21	,	,	PUNCT
ejpam-5428	184	22	l	l	NOUN
ejpam-5428	184	23	)	)	PUNCT
ejpam-5428	184	24	=	=	SYM
ejpam-5428	185	1	1	1	X
ejpam-5428	185	2	.	.	PUNCT
ejpam-5428	185	3	(	(	PUNCT
ejpam-5428	185	4	16	16	NUM
ejpam-5428	185	5	)	)	PUNCT
ejpam-5428	185	6	by	by	ADP
ejpam-5428	185	7	the	the	DET
ejpam-5428	185	8	property	property	NOUN
ejpam-5428	185	9	of	of	ADP
ejpam-5428	185	10	(	(	PUNCT
ejpam-5428	185	11	g2	g2	PROPN
ejpam-5428	185	12	)	)	PUNCT
ejpam-5428	185	13	,	,	PUNCT
ejpam-5428	185	14	mz(δn−1,lδn−1	mz(δn−1,lδn−1	PROPN
ejpam-5428	185	15	,	,	PUNCT
ejpam-5428	185	16	l	l	NOUN
ejpam-5428	185	17	)	)	PUNCT
ejpam-5428	185	18	>	>	X
ejpam-5428	185	19	q	q	X
ejpam-5428	185	20	·	·	PUNCT
ejpam-5428	185	21	mz(δn−1	mz(δn−1	PROPN
ejpam-5428	185	22	,	,	PUNCT
ejpam-5428	185	23	u	u	NOUN
ejpam-5428	185	24	,	,	PUNCT
ejpam-5428	185	25	l	l	NOUN
ejpam-5428	185	26	)	)	PUNCT
ejpam-5428	185	27	⇒	⇒	PROPN
ejpam-5428	185	28	α(δn−1	α(δn−1	PROPN
ejpam-5428	185	29	,	,	PUNCT
ejpam-5428	185	30	u	u	NOUN
ejpam-5428	185	31	,	,	PUNCT
ejpam-5428	185	32	l)(1−mz(lδn−1,lu	l)(1−mz(lδn−1,lu	PROPN
ejpam-5428	185	33	,	,	PUNCT
ejpam-5428	185	34	l	l	NOUN
ejpam-5428	185	35	)	)	PUNCT
ejpam-5428	185	36	)	)	PUNCT
ejpam-5428	185	37	≤	≤	PUNCT
ejpam-5428	186	1	β(1−mz(δn−1	β(1−mz(δn−1	PROPN
ejpam-5428	186	2	,	,	PUNCT
ejpam-5428	186	3	u	u	NOUN
ejpam-5428	186	4	,	,	PUNCT
ejpam-5428	186	5	l))(1−mz(δn−1	l))(1−mz(δn−1	PROPN
ejpam-5428	186	6	,	,	PUNCT
ejpam-5428	186	7	u	u	NOUN
ejpam-5428	186	8	,	,	PUNCT
ejpam-5428	186	9	l	l	NOUN
ejpam-5428	186	10	)	)	PUNCT
ejpam-5428	186	11	)	)	PUNCT
ejpam-5428	186	12	(	(	PUNCT
ejpam-5428	186	13	1−mz(lδn−1,lu	1−mz(lδn−1,lu	NUM
ejpam-5428	186	14	,	,	PUNCT
ejpam-5428	186	15	l	l	NOUN
ejpam-5428	186	16	)	)	PUNCT
ejpam-5428	186	17	)	)	PUNCT
ejpam-5428	186	18	≤	≤	NOUN
ejpam-5428	186	19	α(δn−1	α(δn−1	X
ejpam-5428	186	20	,	,	PUNCT
ejpam-5428	186	21	u	u	NOUN
ejpam-5428	186	22	,	,	PUNCT
ejpam-5428	186	23	l)(1−mz(lδn−1,lu	l)(1−mz(lδn−1,lu	PROPN
ejpam-5428	186	24	,	,	PUNCT
ejpam-5428	186	25	l	l	NOUN
ejpam-5428	186	26	)	)	PUNCT
ejpam-5428	186	27	)	)	PUNCT
ejpam-5428	186	28	≤	≤	PUNCT
ejpam-5428	187	1	β(1−mz(δn−1	β(1−mz(δn−1	PROPN
ejpam-5428	187	2	,	,	PUNCT
ejpam-5428	187	3	u	u	NOUN
ejpam-5428	187	4	,	,	PUNCT
ejpam-5428	187	5	l))(1−m(δn−1	l))(1−m(δn−1	PROPN
ejpam-5428	187	6	,	,	PUNCT
ejpam-5428	187	7	u	u	NOUN
ejpam-5428	187	8	,	,	PUNCT
ejpam-5428	187	9	l	l	NOUN
ejpam-5428	187	10	)	)	PUNCT
ejpam-5428	187	11	)	)	PUNCT
ejpam-5428	187	12	<	<	X
ejpam-5428	187	13	(	(	PUNCT
ejpam-5428	187	14	1−m(δn−1	1−m(δn−1	NUM
ejpam-5428	187	15	,	,	PUNCT
ejpam-5428	187	16	u	u	NOUN
ejpam-5428	187	17	,	,	PUNCT
ejpam-5428	187	18	l	l	NOUN
ejpam-5428	187	19	)	)	PUNCT
ejpam-5428	187	20	)	)	PUNCT
ejpam-5428	187	21	1−mz(δn	1−mz(δn	NUM
ejpam-5428	187	22	,	,	PUNCT
ejpam-5428	187	23	lu	lu	PROPN
ejpam-5428	187	24	,	,	PUNCT
ejpam-5428	187	25	l	l	NOUN
ejpam-5428	187	26	)	)	PUNCT
ejpam-5428	187	27	<	<	X
ejpam-5428	187	28	1−mz(δn−1	1−mz(δn−1	PROPN
ejpam-5428	187	29	,	,	PUNCT
ejpam-5428	187	30	u	u	NOUN
ejpam-5428	187	31	,	,	PUNCT
ejpam-5428	187	32	l	l	NOUN
ejpam-5428	187	33	)	)	PUNCT
ejpam-5428	187	34	,	,	PUNCT
ejpam-5428	187	35	put	put	VERB
ejpam-5428	187	36	limit	limit	NOUN
ejpam-5428	187	37	as	as	ADP
ejpam-5428	187	38	n	n	PROPN
ejpam-5428	187	39	→	→	SYM
ejpam-5428	187	40	+	+	NOUN
ejpam-5428	187	41	∞	∞	PROPN
ejpam-5428	187	42	,	,	PUNCT
ejpam-5428	187	43	we	we	PRON
ejpam-5428	187	44	get	get	VERB
ejpam-5428	187	45	mz(u	mz(u	PROPN
ejpam-5428	187	46	,	,	PUNCT
ejpam-5428	187	47	lu	lu	PROPN
ejpam-5428	187	48	,	,	PUNCT
ejpam-5428	187	49	l	l	NOUN
ejpam-5428	187	50	)	)	PUNCT
ejpam-5428	187	51	=	=	SYM
ejpam-5428	187	52	1	1	X
ejpam-5428	187	53	.	.	X
ejpam-5428	188	1	that	that	PRON
ejpam-5428	188	2	is	be	AUX
ejpam-5428	188	3	,	,	PUNCT
ejpam-5428	188	4	lu	lu	PROPN
ejpam-5428	188	5	=	=	PUNCT
ejpam-5428	189	1	u.	u.	PROPN
ejpam-5428	189	2	next	next	ADV
ejpam-5428	189	3	,	,	PUNCT
ejpam-5428	189	4	assume	assume	VERB
ejpam-5428	189	5	v	v	PRON
ejpam-5428	189	6	is	be	AUX
ejpam-5428	189	7	another	another	DET
ejpam-5428	189	8	fixed	fix	VERB
ejpam-5428	189	9	point	point	NOUN
ejpam-5428	189	10	of	of	ADP
ejpam-5428	189	11	l	l	NOUN
ejpam-5428	189	12	such	such	ADJ
ejpam-5428	189	13	that	that	SCONJ
ejpam-5428	189	14	u	u	PROPN
ejpam-5428	189	15	̸=	̸=	PROPN
ejpam-5428	189	16	v	v	NOUN
ejpam-5428	189	17	that	that	PRON
ejpam-5428	189	18	is	be	AUX
ejpam-5428	189	19	mz(u	mz(u	ADJ
ejpam-5428	189	20	,	,	PUNCT
ejpam-5428	189	21	v	v	NOUN
ejpam-5428	189	22	,	,	PUNCT
ejpam-5428	189	23	l	l	NOUN
ejpam-5428	189	24	)	)	PUNCT
ejpam-5428	189	25	<	<	X
ejpam-5428	190	1	1	1	X
ejpam-5428	190	2	.	.	PUNCT
ejpam-5428	190	3	by	by	ADP
ejpam-5428	190	4	the	the	DET
ejpam-5428	190	5	property	property	NOUN
ejpam-5428	190	6	of	of	ADP
ejpam-5428	190	7	g2	g2	PROPN
ejpam-5428	190	8	,	,	PUNCT
ejpam-5428	190	9	we	we	PRON
ejpam-5428	190	10	know	know	VERB
ejpam-5428	190	11	that	that	SCONJ
ejpam-5428	190	12	mz(u	mz(u	PROPN
ejpam-5428	190	13	,	,	PUNCT
ejpam-5428	190	14	u	u	NOUN
ejpam-5428	190	15	,	,	PUNCT
ejpam-5428	190	16	l	l	NOUN
ejpam-5428	190	17	)	)	PUNCT
ejpam-5428	190	18	=	=	PUNCT
ejpam-5428	190	19	mz(u	mz(u	PROPN
ejpam-5428	190	20	,	,	PUNCT
ejpam-5428	190	21	lu	lu	PROPN
ejpam-5428	190	22	,	,	PUNCT
ejpam-5428	190	23	l	l	NOUN
ejpam-5428	190	24	)	)	PUNCT
ejpam-5428	190	25	>	>	X
ejpam-5428	190	26	q	q	X
ejpam-5428	190	27	·	·	PUNCT
ejpam-5428	190	28	mz(u	mz(u	PROPN
ejpam-5428	190	29	,	,	PUNCT
ejpam-5428	190	30	v	v	NOUN
ejpam-5428	190	31	,	,	PUNCT
ejpam-5428	190	32	l	l	NOUN
ejpam-5428	190	33	)	)	PUNCT
ejpam-5428	190	34	⇒	⇒	NOUN
ejpam-5428	190	35	(	(	PUNCT
ejpam-5428	190	36	1−mz(u	1−mz(u	NUM
ejpam-5428	190	37	,	,	PUNCT
ejpam-5428	190	38	v	v	NOUN
ejpam-5428	190	39	,	,	PUNCT
ejpam-5428	190	40	l	l	NOUN
ejpam-5428	190	41	)	)	PUNCT
ejpam-5428	190	42	)	)	PUNCT
ejpam-5428	191	1	=	=	SYM
ejpam-5428	191	2	(	(	PUNCT
ejpam-5428	191	3	1−mz(lu	1−mz(lu	NUM
ejpam-5428	191	4	,	,	PUNCT
ejpam-5428	191	5	lv	lv	PROPN
ejpam-5428	191	6	,	,	PUNCT
ejpam-5428	191	7	l	l	NOUN
ejpam-5428	191	8	)	)	PUNCT
ejpam-5428	191	9	)	)	PUNCT
ejpam-5428	191	10	≤	≤	PUNCT
ejpam-5428	192	1	α(u	α(u	NOUN
ejpam-5428	192	2	,	,	PUNCT
ejpam-5428	192	3	v	v	NOUN
ejpam-5428	192	4	,	,	PUNCT
ejpam-5428	192	5	l)(1−mz(lu	l)(1−mz(lu	NOUN
ejpam-5428	192	6	,	,	PUNCT
ejpam-5428	192	7	lv	lv	PROPN
ejpam-5428	192	8	,	,	PUNCT
ejpam-5428	192	9	l	l	NOUN
ejpam-5428	192	10	)	)	PUNCT
ejpam-5428	192	11	)	)	PUNCT
ejpam-5428	192	12	≤	≤	PROPN
ejpam-5428	193	1	β(1−mz(u	β(1−mz(u	PROPN
ejpam-5428	193	2	,	,	PUNCT
ejpam-5428	193	3	v	v	NOUN
ejpam-5428	193	4	,	,	PUNCT
ejpam-5428	193	5	l))(1−mz(u	l))(1−mz(u	PROPN
ejpam-5428	193	6	,	,	PUNCT
ejpam-5428	193	7	v	v	NOUN
ejpam-5428	193	8	,	,	PUNCT
ejpam-5428	193	9	l	l	NOUN
ejpam-5428	193	10	)	)	PUNCT
ejpam-5428	193	11	)	)	PUNCT
ejpam-5428	194	1	<	<	X
ejpam-5428	194	2	(	(	PUNCT
ejpam-5428	194	3	1−mz(u	1−mz(u	NUM
ejpam-5428	194	4	,	,	PUNCT
ejpam-5428	194	5	v	v	NOUN
ejpam-5428	194	6	,	,	PUNCT
ejpam-5428	194	7	l	l	NOUN
ejpam-5428	194	8	)	)	PUNCT
ejpam-5428	194	9	)	)	PUNCT
ejpam-5428	194	10	,	,	PUNCT
ejpam-5428	194	11	a	a	DET
ejpam-5428	194	12	contradiction	contradiction	NOUN
ejpam-5428	194	13	with	with	ADP
ejpam-5428	194	14	the	the	DET
ejpam-5428	194	15	assumption	assumption	NOUN
ejpam-5428	194	16	,	,	PUNCT
ejpam-5428	194	17	so	so	ADV
ejpam-5428	194	18	fixed	fix	VERB
ejpam-5428	194	19	point	point	NOUN
ejpam-5428	194	20	u	u	NOUN
ejpam-5428	194	21	is	be	AUX
ejpam-5428	194	22	unique	unique	ADJ
ejpam-5428	194	23	.	.	PUNCT
ejpam-5428	195	1	now	now	ADV
ejpam-5428	195	2	we	we	PRON
ejpam-5428	195	3	write	write	VERB
ejpam-5428	195	4	an	an	DET
ejpam-5428	195	5	example	example	NOUN
ejpam-5428	195	6	which	which	PRON
ejpam-5428	195	7	is	be	AUX
ejpam-5428	195	8	α	α	X
ejpam-5428	195	9	-	-	PUNCT
ejpam-5428	195	10	suzuki	suzuki	NOUN
ejpam-5428	195	11	geraghty	geraghty	PROPN
ejpam-5428	195	12	type	type	PROPN
ejpam-5428	195	13	-	-	PUNCT
ejpam-5428	195	14	i	i	PRON
ejpam-5428	195	15	contractive	contractive	ADJ
ejpam-5428	195	16	mapping	mapping	NOUN
ejpam-5428	195	17	but	but	CCONJ
ejpam-5428	195	18	not	not	PART
ejpam-5428	195	19	a	a	DET
ejpam-5428	195	20	geraghty	geraghty	ADJ
ejpam-5428	195	21	type	type	NOUN
ejpam-5428	195	22	-	-	PUNCT
ejpam-5428	195	23	i	i	NOUN
ejpam-5428	195	24	mapping	mapping	NOUN
ejpam-5428	195	25	.	.	PUNCT
ejpam-5428	196	1	example	example	NOUN
ejpam-5428	197	1	4	4	NUM
ejpam-5428	197	2	.	.	PUNCT
ejpam-5428	197	3	define	define	VERB
ejpam-5428	197	4	a	a	DET
ejpam-5428	197	5	fuzzy	fuzzy	ADJ
ejpam-5428	197	6	metric	metric	ADJ
ejpam-5428	197	7	mz(δ	mz(δ	PROPN
ejpam-5428	197	8	,	,	PUNCT
ejpam-5428	197	9	γ	γ	X
ejpam-5428	197	10	,	,	PUNCT
ejpam-5428	197	11	l	l	NOUN
ejpam-5428	197	12	)	)	PUNCT
ejpam-5428	197	13	=	=	SYM
ejpam-5428	198	1	e−	e−	NUM
ejpam-5428	198	2	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	198	3	l	l	NOUN
ejpam-5428	198	4	for	for	ADP
ejpam-5428	198	5	all	all	DET
ejpam-5428	198	6	l	l	NOUN
ejpam-5428	198	7	>	>	X
ejpam-5428	198	8	0	0	PUNCT
ejpam-5428	198	9	on	on	ADP
ejpam-5428	198	10	[	[	X
ejpam-5428	198	11	0	0	NUM
ejpam-5428	198	12	,	,	PUNCT
ejpam-5428	198	13	1	1	NUM
ejpam-5428	198	14	]	]	PUNCT
ejpam-5428	198	15	with	with	ADP
ejpam-5428	198	16	standard	standard	ADJ
ejpam-5428	198	17	triangular	triangular	NOUN
ejpam-5428	198	18	norm	norm	NOUN
ejpam-5428	198	19	and	and	CCONJ
ejpam-5428	198	20	space	space	NOUN
ejpam-5428	198	21	is	be	AUX
ejpam-5428	198	22	g	g	NOUN
ejpam-5428	198	23	-	-	PUNCT
ejpam-5428	198	24	complete	complete	ADJ
ejpam-5428	198	25	and	and	CCONJ
ejpam-5428	198	26	define	define	VERB
ejpam-5428	198	27	a	a	DET
ejpam-5428	198	28	self	self	NOUN
ejpam-5428	198	29	map	map	NOUN
ejpam-5428	198	30	like	like	ADP
ejpam-5428	198	31	l(δ	l(δ	NOUN
ejpam-5428	198	32	)	)	PUNCT
ejpam-5428	199	1	=	=	PRON
ejpam-5428	199	2	{	{	PUNCT
ejpam-5428	199	3	δ	δ	NOUN
ejpam-5428	199	4	2	2	NUM
ejpam-5428	199	5	,	,	PUNCT
ejpam-5428	199	6	if	if	SCONJ
ejpam-5428	199	7	δ	δ	PROPN
ejpam-5428	199	8	∈	∈	PROPN
ejpam-5428	200	1	[	[	X
ejpam-5428	200	2	0	0	NUM
ejpam-5428	200	3	,	,	PUNCT
ejpam-5428	200	4	1	1	NUM
ejpam-5428	200	5	)	)	PUNCT
ejpam-5428	200	6	0	0	NUM
ejpam-5428	200	7	,	,	PUNCT
ejpam-5428	200	8	δ	δ	X
ejpam-5428	200	9	=	=	VERB
ejpam-5428	200	10	1	1	X
ejpam-5428	200	11	.	.	X
ejpam-5428	201	1	v.	v.	PROPN
ejpam-5428	201	2	chandra	chandra	PROPN
ejpam-5428	201	3	,	,	PUNCT
ejpam-5428	201	4	u.	u.	PROPN
ejpam-5428	201	5	d.	d.	PROPN
ejpam-5428	201	6	patel	patel	PROPN
ejpam-5428	201	7	,	,	PUNCT
ejpam-5428	201	8	s.	s.	PROPN
ejpam-5428	201	9	radenović	radenović	PROPN
ejpam-5428	201	10	/	/	SYM
ejpam-5428	201	11	eur	eur	PROPN
ejpam-5428	201	12	.	.	PUNCT
ejpam-5428	202	1	j.	j.	PROPN
ejpam-5428	202	2	pure	pure	PROPN
ejpam-5428	202	3	appl	appl	PROPN
ejpam-5428	202	4	.	.	PROPN
ejpam-5428	202	5	math	math	PROPN
ejpam-5428	202	6	,	,	PUNCT
ejpam-5428	202	7	17	17	NUM
ejpam-5428	202	8	(	(	PUNCT
ejpam-5428	202	9	4	4	NUM
ejpam-5428	202	10	)	)	PUNCT
ejpam-5428	202	11	(	(	PUNCT
ejpam-5428	202	12	2024	2024	NUM
ejpam-5428	202	13	)	)	PUNCT
ejpam-5428	202	14	,	,	PUNCT
ejpam-5428	202	15	2384	2384	NUM
ejpam-5428	202	16	-	-	SYM
ejpam-5428	202	17	2404	2404	NUM
ejpam-5428	202	18	2394	2394	NUM
ejpam-5428	202	19	also	also	ADV
ejpam-5428	202	20	define	define	VERB
ejpam-5428	202	21	function	function	NOUN
ejpam-5428	202	22	α	α	NOUN
ejpam-5428	202	23	by	by	ADP
ejpam-5428	202	24	α(δ	α(δ	PROPN
ejpam-5428	202	25	,	,	PUNCT
ejpam-5428	202	26	γ	γ	X
ejpam-5428	202	27	,	,	PUNCT
ejpam-5428	202	28	l	l	NOUN
ejpam-5428	202	29	)	)	PUNCT
ejpam-5428	202	30	=	=	NOUN
ejpam-5428	202	31	{	{	PUNCT
ejpam-5428	203	1	1	1	NUM
ejpam-5428	203	2	,	,	PUNCT
ejpam-5428	203	3	if	if	SCONJ
ejpam-5428	203	4	δ	δ	PROPN
ejpam-5428	203	5	,	,	PUNCT
ejpam-5428	203	6	γ	γ	PROPN
ejpam-5428	203	7	∈	∈	PROPN
ejpam-5428	204	1	[	[	X
ejpam-5428	204	2	0	0	NUM
ejpam-5428	204	3	,	,	PUNCT
ejpam-5428	204	4	1	1	NUM
ejpam-5428	204	5	)	)	PUNCT
ejpam-5428	204	6	0	0	NUM
ejpam-5428	204	7	,	,	PUNCT
ejpam-5428	204	8	otherwise	otherwise	ADV
ejpam-5428	204	9	.	.	PUNCT
ejpam-5428	205	1	for	for	ADP
ejpam-5428	205	2	all	all	DET
ejpam-5428	205	3	l	l	NOUN
ejpam-5428	205	4	>	>	X
ejpam-5428	205	5	0	0	PUNCT
ejpam-5428	205	6	and	and	CCONJ
ejpam-5428	205	7	β(t1	β(t1	NOUN
ejpam-5428	205	8	)	)	PUNCT
ejpam-5428	205	9	=	=	SYM
ejpam-5428	205	10	e−t1	e−t1	NOUN
ejpam-5428	205	11	.	.	NOUN
ejpam-5428	205	12	suppose	suppose	VERB
ejpam-5428	205	13	q	q	X
ejpam-5428	205	14	=	=	SYM
ejpam-5428	205	15	1	1	NUM
ejpam-5428	205	16	2	2	NUM
ejpam-5428	205	17	.	.	PUNCT
ejpam-5428	206	1	put	put	VERB
ejpam-5428	206	2	the	the	DET
ejpam-5428	206	3	following	follow	VERB
ejpam-5428	206	4	cases	case	NOUN
ejpam-5428	206	5	to	to	PART
ejpam-5428	206	6	verify	verify	VERB
ejpam-5428	206	7	the	the	DET
ejpam-5428	206	8	α	α	NOUN
ejpam-5428	206	9	-	-	PUNCT
ejpam-5428	206	10	suzuki	suzuki	NOUN
ejpam-5428	206	11	-	-	PUNCT
ejpam-5428	206	12	geraghty	geraghty	VERB
ejpam-5428	206	13	type	type	PROPN
ejpam-5428	206	14	-	-	PUNCT
ejpam-5428	206	15	i	i	PRON
ejpam-5428	206	16	contraction	contraction	NOUN
ejpam-5428	206	17	mapping	mapping	NOUN
ejpam-5428	206	18	:	:	PUNCT
ejpam-5428	206	19	case	case	NOUN
ejpam-5428	206	20	1	1	X
ejpam-5428	206	21	.	.	PUNCT
ejpam-5428	207	1	if	if	SCONJ
ejpam-5428	207	2	δ	δ	PROPN
ejpam-5428	207	3	,	,	PUNCT
ejpam-5428	207	4	γ	γ	PROPN
ejpam-5428	207	5	∈	∈	PROPN
ejpam-5428	208	1	[	[	X
ejpam-5428	208	2	0	0	NUM
ejpam-5428	208	3	,	,	PUNCT
ejpam-5428	208	4	1	1	NUM
ejpam-5428	208	5	)	)	PUNCT
ejpam-5428	208	6	then	then	ADV
ejpam-5428	208	7	α(δ	α(δ	NUM
ejpam-5428	208	8	,	,	PUNCT
ejpam-5428	208	9	γ	γ	X
ejpam-5428	208	10	,	,	PUNCT
ejpam-5428	208	11	l	l	NOUN
ejpam-5428	208	12	)	)	PUNCT
ejpam-5428	208	13	=	=	SYM
ejpam-5428	208	14	1	1	NUM
ejpam-5428	208	15	,	,	PUNCT
ejpam-5428	208	16	mz(δ	mz(δ	PROPN
ejpam-5428	208	17	,	,	PUNCT
ejpam-5428	208	18	δ	δ	PROPN
ejpam-5428	208	19	2	2	NUM
ejpam-5428	208	20	,	,	PUNCT
ejpam-5428	208	21	l	l	NOUN
ejpam-5428	208	22	)	)	PUNCT
ejpam-5428	208	23	>	>	X
ejpam-5428	208	24	q	q	X
ejpam-5428	208	25	·	·	PUNCT
ejpam-5428	208	26	mz(δ	mz(δ	NUM
ejpam-5428	208	27	,	,	PUNCT
ejpam-5428	208	28	γ	γ	X
ejpam-5428	208	29	,	,	PUNCT
ejpam-5428	208	30	l	l	NOUN
ejpam-5428	208	31	)	)	PUNCT
ejpam-5428	208	32	,	,	PUNCT
ejpam-5428	208	33	that	that	ADV
ejpam-5428	208	34	is	is	ADV
ejpam-5428	208	35	,	,	PUNCT
ejpam-5428	208	36	e	e	NOUN
ejpam-5428	208	37	−	−	PROPN
ejpam-5428	208	38	|δ−	|δ−	NOUN
ejpam-5428	208	39	δ	δ	PROPN
ejpam-5428	208	40	2	2	NUM
ejpam-5428	208	41	|2	|2	NUM
ejpam-5428	208	42	l	l	NOUN
ejpam-5428	208	43	>	>	X
ejpam-5428	208	44	q	q	X
ejpam-5428	208	45	·	·	PUNCT
ejpam-5428	208	46	e−	e−	NUM
ejpam-5428	208	47	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	208	48	l	l	NOUN
ejpam-5428	208	49	implies	imply	VERB
ejpam-5428	208	50	α(δ	α(δ	PROPN
ejpam-5428	208	51	,	,	PUNCT
ejpam-5428	208	52	γ	γ	X
ejpam-5428	208	53	,	,	PUNCT
ejpam-5428	208	54	l)[1−	l)[1−	NOUN
ejpam-5428	208	55	e−	e−	PROPN
ejpam-5428	208	56	|	|	ADV
ejpam-5428	208	57	δ2−	δ2−	PROPN
ejpam-5428	208	58	γ	γ	X
ejpam-5428	208	59	2	2	NUM
ejpam-5428	208	60	|2	|2	NUM
ejpam-5428	208	61	l	l	NOUN
ejpam-5428	208	62	]	]	PUNCT
ejpam-5428	208	63	≤	≤	NUM
ejpam-5428	208	64	e−(1−e−	e−(1−e−	VERB
ejpam-5428	208	65	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	208	66	l	l	NOUN
ejpam-5428	208	67	)	)	PUNCT
ejpam-5428	209	1	[	[	X
ejpam-5428	209	2	1−	1−	NUM
ejpam-5428	209	3	e−	e−	NUM
ejpam-5428	209	4	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	209	5	l	l	NOUN
ejpam-5428	209	6	]	]	PUNCT
ejpam-5428	209	7	.	.	PUNCT
ejpam-5428	210	1	graphs	graph	NOUN
ejpam-5428	210	2	of	of	ADP
ejpam-5428	210	3	two	two	NUM
ejpam-5428	210	4	functions	function	NOUN
ejpam-5428	210	5	:	:	PUNCT
ejpam-5428	210	6	yellow	yellow	ADJ
ejpam-5428	210	7	exp@	exp@	PROPN
ejpam-5428	210	8	-absa∆	-absa∆	PROPN
ejpam-5428	210	9	∆	∆	PROPN
ejpam-5428	210	10	2	2	NUM
ejpam-5428	210	11	e^2	e^2	NOUN
ejpam-5428	210	12	l	l	NOUN
ejpam-5428	210	13	d	d	PROPN
ejpam-5428	210	14	,	,	PUNCT
ejpam-5428	210	15	red	red	ADJ
ejpam-5428	210	16	1	1	NUM
ejpam-5428	210	17	2	2	NUM
ejpam-5428	210	18	hexp@	hexp@	NOUN
ejpam-5428	210	19	-abs@∆	-abs@∆	NOUN
ejpam-5428	210	20	γd^2	γd^2	NOUN
ejpam-5428	210	21	l	l	PROPN
ejpam-5428	210	22	dll	dll	NOUN
ejpam-5428	210	23	0.0	0.0	NUM
ejpam-5428	210	24	0.5	0.5	NUM
ejpam-5428	210	25	1.0	1.0	NUM
ejpam-5428	210	26	∆	∆	PROPN
ejpam-5428	210	27	0.0	0.0	NUM
ejpam-5428	210	28	0.5	0.5	NUM
ejpam-5428	210	29	1.0	1.0	NUM
ejpam-5428	210	30	γ	γ	PROPN
ejpam-5428	210	31	0.0	0.0	NUM
ejpam-5428	210	32	0.5	0.5	NUM
ejpam-5428	210	33	1.0	1.0	NUM
ejpam-5428	210	34	z	z	NOUN
ejpam-5428	210	35	figure	figure	NOUN
ejpam-5428	210	36	3	3	NUM
ejpam-5428	210	37	:	:	PUNCT
ejpam-5428	210	38	e−	e−	PROPN
ejpam-5428	210	39	|δ−	|δ−	NOUN
ejpam-5428	210	40	δ	δ	PROPN
ejpam-5428	210	41	2	2	NUM
ejpam-5428	210	42	|2	|2	NUM
ejpam-5428	210	43	l	l	NOUN
ejpam-5428	210	44	>	>	X
ejpam-5428	210	45	q	q	X
ejpam-5428	210	46	·	·	PUNCT
ejpam-5428	210	47	e−	e−	NUM
ejpam-5428	210	48	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	210	49	l	l	NOUN
ejpam-5428	210	50	graphs	graph	NOUN
ejpam-5428	210	51	of	of	ADP
ejpam-5428	210	52	two	two	NUM
ejpam-5428	210	53	functions	function	NOUN
ejpam-5428	210	54	:	:	PUNCT
ejpam-5428	210	55	yellow	yellow	ADJ
ejpam-5428	210	56	1	1	NUM
ejpam-5428	210	57	exp@-abs@∆	exp@-abs@∆	NOUN
ejpam-5428	210	58	�	�	NOUN
ejpam-5428	210	59	2	2	NUM
ejpam-5428	210	60	γ	γ	X
ejpam-5428	210	61	�	�	PROPN
ejpam-5428	210	62	2d^2	2d^2	NUM
ejpam-5428	210	63	�	�	PROPN
ejpam-5428	210	64	ld	ld	PROPN
ejpam-5428	210	65	,	,	PUNCT
ejpam-5428	210	66	red	red	ADJ
ejpam-5428	210	67	exp@-1d	exp@-1d	PROPN
ejpam-5428	210	68	h1	h1	PROPN
ejpam-5428	210	69	exp@-abs@∆	exp@-abs@∆	VERB
ejpam-5428	210	70	γd^2	γd^2	NOUN
ejpam-5428	210	71	�	�	NOUN
ejpam-5428	210	72	ldl	ldl	NOUN
ejpam-5428	210	73	0.0	0.0	NUM
ejpam-5428	210	74	0.5	0.5	NUM
ejpam-5428	210	75	1.0	1.0	NUM
ejpam-5428	210	76	∆	∆	PROPN
ejpam-5428	210	77	0.0	0.0	NUM
ejpam-5428	210	78	0.5	0.5	NUM
ejpam-5428	210	79	1.0	1.0	NUM
ejpam-5428	210	80	γ	γ	PROPN
ejpam-5428	210	81	0.0	0.0	NUM
ejpam-5428	210	82	0.2	0.2	NUM
ejpam-5428	210	83	0.4	0.4	NUM
ejpam-5428	210	84	0.6	0.6	NUM
ejpam-5428	210	85	0.8	0.8	NUM
ejpam-5428	210	86	z	z	NOUN
ejpam-5428	210	87	figure	figure	NOUN
ejpam-5428	210	88	4	4	NUM
ejpam-5428	210	89	:	:	PUNCT
ejpam-5428	210	90	α(δ	α(δ	PROPN
ejpam-5428	210	91	,	,	PUNCT
ejpam-5428	210	92	γ	γ	X
ejpam-5428	210	93	,	,	PUNCT
ejpam-5428	210	94	l)[1−	l)[1−	NOUN
ejpam-5428	210	95	e−	e−	PROPN
ejpam-5428	210	96	|	|	ADV
ejpam-5428	210	97	δ	δ	PROPN
ejpam-5428	210	98	2	2	NUM
ejpam-5428	210	99	−	−	NOUN
ejpam-5428	210	100	γ	γ	X
ejpam-5428	210	101	2	2	NUM
ejpam-5428	210	102	|2	|2	NUM
ejpam-5428	210	103	l	l	NOUN
ejpam-5428	210	104	]	]	PUNCT
ejpam-5428	210	105	≤	≤	NUM
ejpam-5428	210	106	e−(1−e	e−(1−e	PROPN
ejpam-5428	210	107	−	−	PROPN
ejpam-5428	210	108	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	210	109	l	l	NOUN
ejpam-5428	210	110	)	)	PUNCT
ejpam-5428	211	1	[	[	X
ejpam-5428	211	2	1−	1−	NUM
ejpam-5428	211	3	e−	e−	NUM
ejpam-5428	211	4	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	211	5	l	l	NOUN
ejpam-5428	211	6	]	]	PUNCT
ejpam-5428	211	7	figure	figure	NOUN
ejpam-5428	211	8	3	3	NUM
ejpam-5428	211	9	.	.	PUNCT
ejpam-5428	212	1	the	the	DET
ejpam-5428	212	2	yellow	yellow	ADJ
ejpam-5428	212	3	colour	colour	NOUN
ejpam-5428	212	4	represents	represent	VERB
ejpam-5428	212	5	the	the	DET
ejpam-5428	212	6	value	value	NOUN
ejpam-5428	212	7	of	of	ADP
ejpam-5428	212	8	e−	e−	PROPN
ejpam-5428	212	9	|δ−	|δ−	NOUN
ejpam-5428	212	10	δ	δ	PROPN
ejpam-5428	212	11	2	2	NUM
ejpam-5428	212	12	|2	|2	NUM
ejpam-5428	212	13	l	l	NOUN
ejpam-5428	212	14	,	,	PUNCT
ejpam-5428	212	15	and	and	CCONJ
ejpam-5428	212	16	the	the	DET
ejpam-5428	212	17	red	red	ADJ
ejpam-5428	212	18	colour	colour	NOUN
ejpam-5428	212	19	represents	represent	VERB
ejpam-5428	212	20	the	the	DET
ejpam-5428	212	21	value	value	NOUN
ejpam-5428	212	22	of	of	ADP
ejpam-5428	212	23	q	q	PROPN
ejpam-5428	212	24	·	·	PUNCT
ejpam-5428	212	25	e−	e−	NUM
ejpam-5428	212	26	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	212	27	l	l	NOUN
ejpam-5428	212	28	and	and	CCONJ
ejpam-5428	212	29	figure	figure	VERB
ejpam-5428	212	30	4	4	NUM
ejpam-5428	212	31	.	.	PUNCT
ejpam-5428	213	1	the	the	DET
ejpam-5428	213	2	yellow	yellow	ADJ
ejpam-5428	213	3	colour	colour	NOUN
ejpam-5428	213	4	represents	represent	VERB
ejpam-5428	213	5	the	the	DET
ejpam-5428	213	6	value	value	NOUN
ejpam-5428	213	7	of	of	ADP
ejpam-5428	213	8	α(δ	α(δ	PROPN
ejpam-5428	213	9	,	,	PUNCT
ejpam-5428	213	10	γ	γ	X
ejpam-5428	213	11	,	,	PUNCT
ejpam-5428	213	12	l)[1	l)[1	PROPN
ejpam-5428	213	13	−	−	PROPN
ejpam-5428	213	14	e−	e−	PROPN
ejpam-5428	213	15	|	|	ADV
ejpam-5428	213	16	δ2−	δ2−	PROPN
ejpam-5428	213	17	γ	γ	X
ejpam-5428	213	18	2	2	NUM
ejpam-5428	213	19	|2	|2	NUM
ejpam-5428	213	20	l	l	NOUN
ejpam-5428	213	21	]	]	PUNCT
ejpam-5428	213	22	,	,	PUNCT
ejpam-5428	213	23	and	and	CCONJ
ejpam-5428	213	24	the	the	DET
ejpam-5428	213	25	red	red	ADJ
ejpam-5428	213	26	colour	colour	NOUN
ejpam-5428	213	27	represents	represent	VERB
ejpam-5428	213	28	the	the	DET
ejpam-5428	213	29	value	value	NOUN
ejpam-5428	213	30	of	of	ADP
ejpam-5428	213	31	e−(1−e−	e−(1−e−	VERB
ejpam-5428	213	32	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	213	33	l	l	NOUN
ejpam-5428	213	34	)	)	PUNCT
ejpam-5428	213	35	(	(	PUNCT
ejpam-5428	213	36	1	1	NUM
ejpam-5428	213	37	−	−	PROPN
ejpam-5428	213	38	v.	v.	PROPN
ejpam-5428	213	39	chandra	chandra	PROPN
ejpam-5428	213	40	,	,	PUNCT
ejpam-5428	213	41	u.	u.	PROPN
ejpam-5428	213	42	d.	d.	PROPN
ejpam-5428	213	43	patel	patel	PROPN
ejpam-5428	213	44	,	,	PUNCT
ejpam-5428	214	1	s.	s.	PROPN
ejpam-5428	214	2	radenović	radenović	PROPN
ejpam-5428	214	3	/	/	SYM
ejpam-5428	214	4	eur	eur	PROPN
ejpam-5428	214	5	.	.	PUNCT
ejpam-5428	215	1	j.	j.	PROPN
ejpam-5428	215	2	pure	pure	PROPN
ejpam-5428	215	3	appl	appl	PROPN
ejpam-5428	215	4	.	.	PROPN
ejpam-5428	215	5	math	math	PROPN
ejpam-5428	215	6	,	,	PUNCT
ejpam-5428	215	7	17	17	NUM
ejpam-5428	215	8	(	(	PUNCT
ejpam-5428	215	9	4	4	NUM
ejpam-5428	215	10	)	)	PUNCT
ejpam-5428	215	11	(	(	PUNCT
ejpam-5428	215	12	2024	2024	NUM
ejpam-5428	215	13	)	)	PUNCT
ejpam-5428	215	14	,	,	PUNCT
ejpam-5428	215	15	2384	2384	NUM
ejpam-5428	215	16	-	-	SYM
ejpam-5428	215	17	2404	2404	NUM
ejpam-5428	215	18	2395	2395	NUM
ejpam-5428	216	1	e−	e−	PROPN
ejpam-5428	216	2	|δ−γ|2	|δ−γ|2	ADJ
ejpam-5428	216	3	l	l	NOUN
ejpam-5428	216	4	)	)	PUNCT
ejpam-5428	216	5	.	.	PUNCT
ejpam-5428	217	1	hence	hence	ADV
ejpam-5428	217	2	,	,	PUNCT
ejpam-5428	217	3	it	it	PRON
ejpam-5428	217	4	is	be	AUX
ejpam-5428	217	5	clear	clear	ADJ
ejpam-5428	217	6	that	that	SCONJ
ejpam-5428	217	7	the	the	DET
ejpam-5428	217	8	hypothesis	hypothesis	NOUN
ejpam-5428	217	9	of	of	ADP
ejpam-5428	217	10	inequality	inequality	NOUN
ejpam-5428	217	11	does	do	AUX
ejpam-5428	217	12	not	not	PART
ejpam-5428	217	13	hold	hold	VERB
ejpam-5428	217	14	,	,	PUNCT
ejpam-5428	217	15	and	and	CCONJ
ejpam-5428	217	16	also	also	ADV
ejpam-5428	217	17	the	the	DET
ejpam-5428	217	18	conclusion	conclusion	NOUN
ejpam-5428	217	19	part	part	NOUN
ejpam-5428	217	20	does	do	AUX
ejpam-5428	217	21	not	not	PART
ejpam-5428	217	22	hold	hold	VERB
ejpam-5428	217	23	.	.	PUNCT
ejpam-5428	218	1	so	so	ADV
ejpam-5428	218	2	,	,	PUNCT
ejpam-5428	218	3	the	the	DET
ejpam-5428	218	4	inequality	inequality	NOUN
ejpam-5428	218	5	holds	hold	VERB
ejpam-5428	218	6	for	for	ADP
ejpam-5428	218	7	this	this	DET
ejpam-5428	218	8	particular	particular	ADJ
ejpam-5428	218	9	case	case	NOUN
ejpam-5428	218	10	.	.	PUNCT
ejpam-5428	219	1	case	case	NOUN
ejpam-5428	219	2	2	2	X
ejpam-5428	219	3	.	.	PUNCT
ejpam-5428	220	1	if	if	SCONJ
ejpam-5428	220	2	δ	δ	PROPN
ejpam-5428	220	3	∈	∈	PROPN
ejpam-5428	221	1	[	[	X
ejpam-5428	221	2	0	0	NUM
ejpam-5428	221	3	,	,	PUNCT
ejpam-5428	221	4	1	1	NUM
ejpam-5428	221	5	)	)	PUNCT
ejpam-5428	221	6	and	and	CCONJ
ejpam-5428	221	7	γ	γ	X
ejpam-5428	221	8	=	=	SYM
ejpam-5428	221	9	1	1	NUM
ejpam-5428	221	10	,	,	PUNCT
ejpam-5428	221	11	then	then	ADV
ejpam-5428	221	12	α(δ	α(δ	PROPN
ejpam-5428	221	13	,	,	PUNCT
ejpam-5428	221	14	γ	γ	X
ejpam-5428	221	15	,	,	PUNCT
ejpam-5428	221	16	l	l	NOUN
ejpam-5428	221	17	)	)	PUNCT
ejpam-5428	221	18	=	=	SYM
ejpam-5428	221	19	0	0	NUM
ejpam-5428	221	20	,	,	PUNCT
ejpam-5428	221	21	mz(δ	mz(δ	PROPN
ejpam-5428	221	22	,	,	PUNCT
ejpam-5428	221	23	1	1	NUM
ejpam-5428	221	24	,	,	PUNCT
ejpam-5428	221	25	l	l	NOUN
ejpam-5428	221	26	)	)	PUNCT
ejpam-5428	221	27	>	>	X
ejpam-5428	222	1	q	q	X
ejpam-5428	222	2	·	·	PUNCT
ejpam-5428	222	3	mz(δ	mz(δ	NUM
ejpam-5428	222	4	,	,	PUNCT
ejpam-5428	222	5	1	1	NUM
ejpam-5428	222	6	,	,	PUNCT
ejpam-5428	222	7	l	l	NOUN
ejpam-5428	222	8	)	)	PUNCT
ejpam-5428	222	9	,	,	PUNCT
ejpam-5428	222	10	that	that	ADV
ejpam-5428	222	11	is	is	ADV
ejpam-5428	222	12	,	,	PUNCT
ejpam-5428	222	13	e−	e−	PROPN
ejpam-5428	222	14	|δ−	|δ−	NOUN
ejpam-5428	222	15	δ	δ	PROPN
ejpam-5428	222	16	2	2	NUM
ejpam-5428	222	17	|2	|2	NUM
ejpam-5428	222	18	l	l	NOUN
ejpam-5428	222	19	>	>	X
ejpam-5428	222	20	q	q	X
ejpam-5428	222	21	·	·	PUNCT
ejpam-5428	222	22	e−	e−	NUM
ejpam-5428	222	23	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	222	24	l	l	NOUN
ejpam-5428	222	25	.	.	PUNCT
ejpam-5428	223	1	since	since	SCONJ
ejpam-5428	223	2	the	the	DET
ejpam-5428	223	3	hypothesis	hypothesis	NOUN
ejpam-5428	223	4	inequality	inequality	NOUN
ejpam-5428	223	5	is	be	AUX
ejpam-5428	223	6	not	not	PART
ejpam-5428	223	7	supportive	supportive	ADJ
ejpam-5428	223	8	,	,	PUNCT
ejpam-5428	223	9	there	there	PRON
ejpam-5428	223	10	is	be	VERB
ejpam-5428	223	11	no	no	DET
ejpam-5428	223	12	need	need	NOUN
ejpam-5428	223	13	to	to	PART
ejpam-5428	223	14	continue	continue	VERB
ejpam-5428	223	15	for	for	ADP
ejpam-5428	223	16	further	further	ADJ
ejpam-5428	223	17	calculations	calculation	NOUN
ejpam-5428	223	18	,	,	PUNCT
ejpam-5428	223	19	but	but	CCONJ
ejpam-5428	223	20	even	even	ADV
ejpam-5428	223	21	then	then	ADV
ejpam-5428	223	22	,	,	PUNCT
ejpam-5428	223	23	0	0	NUM
ejpam-5428	223	24	≤	≤	NUM
ejpam-5428	223	25	e−(1−e−	e−(1−e−	VERB
ejpam-5428	223	26	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	223	27	l	l	NOUN
ejpam-5428	223	28	)	)	PUNCT
ejpam-5428	224	1	[	[	X
ejpam-5428	224	2	1−	1−	NUM
ejpam-5428	224	3	e−	e−	NUM
ejpam-5428	224	4	|δ−1|2	|δ−1|2	PROPN
ejpam-5428	224	5	l	l	NOUN
ejpam-5428	224	6	]	]	PUNCT
ejpam-5428	224	7	.	.	PUNCT
ejpam-5428	225	1	hence	hence	ADV
ejpam-5428	225	2	,	,	PUNCT
ejpam-5428	225	3	the	the	DET
ejpam-5428	225	4	inequality	inequality	NOUN
ejpam-5428	225	5	holds	hold	VERB
ejpam-5428	225	6	for	for	ADP
ejpam-5428	225	7	this	this	DET
ejpam-5428	225	8	case	case	NOUN
ejpam-5428	225	9	.	.	PUNCT
ejpam-5428	226	1	case	case	NOUN
ejpam-5428	226	2	3	3	X
ejpam-5428	226	3	.	.	PUNCT
ejpam-5428	227	1	if	if	SCONJ
ejpam-5428	227	2	δ	δ	PROPN
ejpam-5428	227	3	=	=	SYM
ejpam-5428	227	4	γ	γ	X
ejpam-5428	227	5	=	=	SYM
ejpam-5428	227	6	1	1	NUM
ejpam-5428	227	7	,	,	PUNCT
ejpam-5428	227	8	then	then	ADV
ejpam-5428	227	9	α(δ	α(δ	PROPN
ejpam-5428	227	10	,	,	PUNCT
ejpam-5428	227	11	γ	γ	X
ejpam-5428	227	12	,	,	PUNCT
ejpam-5428	227	13	l	l	NOUN
ejpam-5428	227	14	)	)	PUNCT
ejpam-5428	227	15	=	=	SYM
ejpam-5428	228	1	0	0	X
ejpam-5428	228	2	.	.	PUNCT
ejpam-5428	229	1	mz(1	mz(1	VERB
ejpam-5428	229	2	,	,	PUNCT
ejpam-5428	229	3	1	1	NUM
ejpam-5428	229	4	2	2	NUM
ejpam-5428	229	5	,	,	PUNCT
ejpam-5428	229	6	l	l	NOUN
ejpam-5428	229	7	)	)	PUNCT
ejpam-5428	229	8	>	>	X
ejpam-5428	229	9	q	q	PUNCT
ejpam-5428	229	10	·	·	PUNCT
ejpam-5428	229	11	mz(1	mz(1	ADJ
ejpam-5428	229	12	,	,	PUNCT
ejpam-5428	229	13	1	1	NUM
ejpam-5428	229	14	,	,	PUNCT
ejpam-5428	229	15	l	l	NOUN
ejpam-5428	229	16	)	)	PUNCT
ejpam-5428	229	17	,	,	PUNCT
ejpam-5428	229	18	that	that	ADV
ejpam-5428	229	19	is	is	ADV
ejpam-5428	229	20	,	,	PUNCT
ejpam-5428	229	21	e	e	NOUN
ejpam-5428	229	22	−	−	PROPN
ejpam-5428	229	23	1	1	NUM
ejpam-5428	229	24	4l	4l	NOUN
ejpam-5428	229	25	>	>	X
ejpam-5428	229	26	q	q	PUNCT
ejpam-5428	229	27	·	·	PUNCT
ejpam-5428	229	28	1	1	NUM
ejpam-5428	229	29	implies	imply	VERB
ejpam-5428	229	30	0	0	NUM
ejpam-5428	229	31	≤	≤	NUM
ejpam-5428	229	32	0	0	NUM
ejpam-5428	229	33	.	.	PUNCT
ejpam-5428	229	34	case	case	NOUN
ejpam-5428	229	35	4	4	NUM
ejpam-5428	229	36	.	.	PUNCT
ejpam-5428	230	1	if	if	SCONJ
ejpam-5428	230	2	δ	δ	PROPN
ejpam-5428	230	3	=	=	SYM
ejpam-5428	230	4	1	1	NUM
ejpam-5428	230	5	and	and	CCONJ
ejpam-5428	230	6	γ	γ	PRON
ejpam-5428	230	7	∈	∈	PROPN
ejpam-5428	231	1	[	[	X
ejpam-5428	231	2	0	0	NUM
ejpam-5428	231	3	,	,	PUNCT
ejpam-5428	231	4	1	1	NUM
ejpam-5428	231	5	)	)	PUNCT
ejpam-5428	231	6	,	,	PUNCT
ejpam-5428	231	7	then	then	ADV
ejpam-5428	231	8	α(δ	α(δ	PROPN
ejpam-5428	231	9	,	,	PUNCT
ejpam-5428	231	10	γ	γ	X
ejpam-5428	231	11	,	,	PUNCT
ejpam-5428	231	12	l	l	NOUN
ejpam-5428	231	13	)	)	PUNCT
ejpam-5428	231	14	=	=	SYM
ejpam-5428	231	15	0	0	NUM
ejpam-5428	231	16	,	,	PUNCT
ejpam-5428	231	17	mz(1	mz(1	NOUN
ejpam-5428	231	18	,	,	PUNCT
ejpam-5428	231	19	0	0	NUM
ejpam-5428	231	20	,	,	PUNCT
ejpam-5428	231	21	l	l	NOUN
ejpam-5428	231	22	)	)	PUNCT
ejpam-5428	231	23	>	>	X
ejpam-5428	231	24	q	q	X
ejpam-5428	231	25	·	·	PUNCT
ejpam-5428	231	26	mz(1	mz(1	ADJ
ejpam-5428	231	27	,	,	PUNCT
ejpam-5428	231	28	γ	γ	X
ejpam-5428	231	29	,	,	PUNCT
ejpam-5428	231	30	l	l	NOUN
ejpam-5428	231	31	)	)	PUNCT
ejpam-5428	231	32	,	,	PUNCT
ejpam-5428	231	33	that	that	ADV
ejpam-5428	231	34	is	is	ADV
ejpam-5428	231	35	,	,	PUNCT
ejpam-5428	231	36	e−	e−	PROPN
ejpam-5428	231	37	1	1	NUM
ejpam-5428	231	38	l	l	NOUN
ejpam-5428	231	39	>	>	X
ejpam-5428	231	40	q	q	X
ejpam-5428	231	41	·	·	PUNCT
ejpam-5428	232	1	e−	e−	X
ejpam-5428	232	2	|1−γ|2	|1−γ|2	PROPN
ejpam-5428	232	3	l	l	NOUN
ejpam-5428	232	4	.	.	PUNCT
ejpam-5428	233	1	the	the	DET
ejpam-5428	233	2	hypothesis	hypothesis	NOUN
ejpam-5428	233	3	is	be	AUX
ejpam-5428	233	4	not	not	PART
ejpam-5428	233	5	supportive	supportive	ADJ
ejpam-5428	233	6	,	,	PUNCT
ejpam-5428	233	7	there	there	PRON
ejpam-5428	233	8	is	be	VERB
ejpam-5428	233	9	no	no	DET
ejpam-5428	233	10	need	need	NOUN
ejpam-5428	233	11	to	to	PART
ejpam-5428	233	12	continue	continue	VERB
ejpam-5428	233	13	further	further	ADJ
ejpam-5428	233	14	calculations	calculation	NOUN
ejpam-5428	233	15	,	,	PUNCT
ejpam-5428	233	16	but	but	CCONJ
ejpam-5428	233	17	even	even	ADV
ejpam-5428	233	18	then	then	ADV
ejpam-5428	233	19	,	,	PUNCT
ejpam-5428	233	20	we	we	PRON
ejpam-5428	233	21	get	get	VERB
ejpam-5428	233	22	conclusion	conclusion	NOUN
ejpam-5428	233	23	part	part	NOUN
ejpam-5428	233	24	will	will	AUX
ejpam-5428	233	25	be	be	AUX
ejpam-5428	233	26	zero	zero	NUM
ejpam-5428	233	27	from	from	ADP
ejpam-5428	233	28	both	both	DET
ejpam-5428	233	29	sides	side	NOUN
ejpam-5428	233	30	.	.	PUNCT
ejpam-5428	234	1	hence	hence	ADV
ejpam-5428	234	2	,	,	PUNCT
ejpam-5428	234	3	the	the	DET
ejpam-5428	234	4	inequality	inequality	NOUN
ejpam-5428	234	5	holds	hold	VERB
ejpam-5428	234	6	in	in	ADP
ejpam-5428	234	7	this	this	DET
ejpam-5428	234	8	case	case	NOUN
ejpam-5428	234	9	.	.	PUNCT
ejpam-5428	235	1	this	this	DET
ejpam-5428	235	2	example	example	NOUN
ejpam-5428	235	3	demonstrate	demonstrate	VERB
ejpam-5428	235	4	that	that	SCONJ
ejpam-5428	235	5	the	the	DET
ejpam-5428	235	6	self	self	NOUN
ejpam-5428	235	7	-	-	PUNCT
ejpam-5428	235	8	mapping	mapping	NOUN
ejpam-5428	235	9	l	l	NOUN
ejpam-5428	235	10	is	be	AUX
ejpam-5428	235	11	α	α	X
ejpam-5428	235	12	-	-	PUNCT
ejpam-5428	235	13	suzuki	suzuki	NOUN
ejpam-5428	235	14	geraghty	geraghty	PROPN
ejpam-5428	235	15	type	type	PROPN
ejpam-5428	235	16	-	-	PUNCT
ejpam-5428	235	17	i	i	PRON
ejpam-5428	235	18	contractive	contractive	ADJ
ejpam-5428	235	19	mapping	mapping	NOUN
ejpam-5428	235	20	but	but	CCONJ
ejpam-5428	235	21	not	not	PART
ejpam-5428	235	22	a	a	DET
ejpam-5428	235	23	geraghty	geraghty	ADJ
ejpam-5428	235	24	type	type	NOUN
ejpam-5428	235	25	-	-	PUNCT
ejpam-5428	235	26	i	i	NOUN
ejpam-5428	235	27	mapping	mapping	NOUN
ejpam-5428	235	28	.	.	PUNCT
ejpam-5428	236	1	let	let	VERB
ejpam-5428	237	1	δ	δ	PROPN
ejpam-5428	237	2	,	,	PUNCT
ejpam-5428	237	3	γ	γ	PROPN
ejpam-5428	237	4	∈	∈	PROPN
ejpam-5428	237	5	ȳ	ȳ	NOUN
ejpam-5428	237	6	for	for	ADP
ejpam-5428	237	7	all	all	DET
ejpam-5428	237	8	l	l	NOUN
ejpam-5428	237	9	>	>	X
ejpam-5428	237	10	0	0	NUM
ejpam-5428	237	11	such	such	ADJ
ejpam-5428	237	12	that	that	SCONJ
ejpam-5428	237	13	α(δ	α(δ	PROPN
ejpam-5428	237	14	,	,	PUNCT
ejpam-5428	237	15	γ	γ	X
ejpam-5428	237	16	,	,	PUNCT
ejpam-5428	237	17	l	l	NOUN
ejpam-5428	237	18	)	)	PUNCT
ejpam-5428	237	19	≥	≥	NOUN
ejpam-5428	237	20	1	1	NUM
ejpam-5428	237	21	this	this	PRON
ejpam-5428	237	22	implies	imply	VERB
ejpam-5428	237	23	that	that	SCONJ
ejpam-5428	237	24	δ	δ	PROPN
ejpam-5428	237	25	,	,	PUNCT
ejpam-5428	237	26	γ	γ	PROPN
ejpam-5428	237	27	∈	∈	PROPN
ejpam-5428	238	1	[	[	X
ejpam-5428	238	2	0	0	NUM
ejpam-5428	238	3	,	,	PUNCT
ejpam-5428	238	4	1	1	NUM
ejpam-5428	238	5	)	)	PUNCT
ejpam-5428	238	6	,	,	PUNCT
ejpam-5428	238	7	then	then	ADV
ejpam-5428	238	8	lδ	lδ	VERB
ejpam-5428	238	9	,	,	PUNCT
ejpam-5428	238	10	lγ	lγ	ADP
ejpam-5428	238	11	∈	∈	PROPN
ejpam-5428	239	1	[	[	X
ejpam-5428	239	2	0	0	NUM
ejpam-5428	239	3	,	,	PUNCT
ejpam-5428	239	4	1	1	NUM
ejpam-5428	239	5	)	)	PUNCT
ejpam-5428	239	6	.	.	PUNCT
ejpam-5428	240	1	thus	thus	ADV
ejpam-5428	240	2	,	,	PUNCT
ejpam-5428	240	3	α(lδ	α(lδ	ADJ
ejpam-5428	240	4	,	,	PUNCT
ejpam-5428	240	5	lγ	lγ	ADP
ejpam-5428	240	6	,	,	PUNCT
ejpam-5428	240	7	l	l	NOUN
ejpam-5428	240	8	)	)	PUNCT
ejpam-5428	240	9	=	=	SYM
ejpam-5428	240	10	1	1	NUM
ejpam-5428	240	11	for	for	ADP
ejpam-5428	240	12	all	all	DET
ejpam-5428	240	13	l	l	NOUN
ejpam-5428	240	14	>	>	X
ejpam-5428	240	15	0	0	X
ejpam-5428	240	16	.	.	PUNCT
ejpam-5428	241	1	let	let	VERB
ejpam-5428	242	1	δ	δ	PROPN
ejpam-5428	242	2	,	,	PUNCT
ejpam-5428	242	3	γ	γ	PROPN
ejpam-5428	242	4	,	,	PUNCT
ejpam-5428	242	5	η	η	PROPN
ejpam-5428	242	6	∈	∈	PROPN
ejpam-5428	243	1	[	[	X
ejpam-5428	243	2	0	0	NUM
ejpam-5428	243	3	,	,	PUNCT
ejpam-5428	243	4	1	1	NUM
ejpam-5428	243	5	]	]	PUNCT
ejpam-5428	244	1	such	such	ADJ
ejpam-5428	244	2	that	that	SCONJ
ejpam-5428	244	3	α(δ	α(δ	PROPN
ejpam-5428	244	4	,	,	PUNCT
ejpam-5428	244	5	η	η	NOUN
ejpam-5428	244	6	,	,	PUNCT
ejpam-5428	244	7	l	l	NOUN
ejpam-5428	244	8	)	)	PUNCT
ejpam-5428	244	9	≥	≥	NOUN
ejpam-5428	244	10	1	1	NUM
ejpam-5428	244	11	and	and	CCONJ
ejpam-5428	244	12	α(η	α(η	PROPN
ejpam-5428	244	13	,	,	PUNCT
ejpam-5428	244	14	γ	γ	X
ejpam-5428	244	15	,	,	PUNCT
ejpam-5428	244	16	l	l	NOUN
ejpam-5428	244	17	)	)	PUNCT
ejpam-5428	244	18	≥	≥	NOUN
ejpam-5428	244	19	1	1	NUM
ejpam-5428	244	20	for	for	ADP
ejpam-5428	244	21	all	all	DET
ejpam-5428	244	22	l	l	NOUN
ejpam-5428	244	23	>	>	X
ejpam-5428	244	24	0	0	X
ejpam-5428	244	25	.	.	PUNCT
ejpam-5428	245	1	this	this	PRON
ejpam-5428	245	2	implies	imply	VERB
ejpam-5428	245	3	that	that	SCONJ
ejpam-5428	245	4	δ	δ	PROPN
ejpam-5428	245	5	,	,	PUNCT
ejpam-5428	245	6	γ	γ	PROPN
ejpam-5428	245	7	,	,	PUNCT
ejpam-5428	245	8	η	η	PROPN
ejpam-5428	245	9	∈	∈	PROPN
ejpam-5428	246	1	[	[	X
ejpam-5428	246	2	0	0	NUM
ejpam-5428	246	3	,	,	PUNCT
ejpam-5428	246	4	1	1	NUM
ejpam-5428	246	5	)	)	PUNCT
ejpam-5428	246	6	.	.	PUNCT
ejpam-5428	247	1	so	so	ADV
ejpam-5428	247	2	,	,	PUNCT
ejpam-5428	247	3	α(δ	α(δ	PROPN
ejpam-5428	247	4	,	,	PUNCT
ejpam-5428	247	5	γ	γ	X
ejpam-5428	247	6	,	,	PUNCT
ejpam-5428	247	7	l	l	NOUN
ejpam-5428	247	8	)	)	PUNCT
ejpam-5428	247	9	≥	≥	NOUN
ejpam-5428	247	10	1	1	NUM
ejpam-5428	247	11	for	for	ADP
ejpam-5428	247	12	all	all	DET
ejpam-5428	247	13	l	l	NOUN
ejpam-5428	247	14	>	>	X
ejpam-5428	247	15	0	0	X
ejpam-5428	247	16	.	.	PUNCT
ejpam-5428	248	1	therefore	therefore	ADV
ejpam-5428	248	2	,	,	PUNCT
ejpam-5428	248	3	l	l	NOUN
ejpam-5428	248	4	is	be	AUX
ejpam-5428	248	5	triangular	triangular	ADJ
ejpam-5428	248	6	α	α	NOUN
ejpam-5428	248	7	-	-	ADJ
ejpam-5428	248	8	admissible	admissible	ADJ
ejpam-5428	248	9	.	.	PUNCT
ejpam-5428	249	1	hence	hence	ADV
ejpam-5428	249	2	all	all	DET
ejpam-5428	249	3	the	the	DET
ejpam-5428	249	4	assumptions	assumption	NOUN
ejpam-5428	249	5	of	of	ADP
ejpam-5428	249	6	the	the	DET
ejpam-5428	249	7	above	above	ADJ
ejpam-5428	249	8	theorem	theorem	NOUN
ejpam-5428	249	9	are	be	AUX
ejpam-5428	249	10	gratified	gratify	VERB
ejpam-5428	249	11	and	and	CCONJ
ejpam-5428	249	12	also	also	ADV
ejpam-5428	249	13	hold	hold	VERB
ejpam-5428	249	14	property	property	NOUN
ejpam-5428	249	15	g1	g1	NOUN
ejpam-5428	249	16	,	,	PUNCT
ejpam-5428	249	17	g2	g2	PROPN
ejpam-5428	249	18	and	and	CCONJ
ejpam-5428	249	19	condition	condition	NOUN
ejpam-5428	249	20	(	(	PUNCT
ejpam-5428	249	21	3	3	NUM
ejpam-5428	249	22	)	)	PUNCT
ejpam-5428	249	23	for	for	ADP
ejpam-5428	249	24	q	q	NOUN
ejpam-5428	249	25	=	=	SYM
ejpam-5428	249	26	0.5	0.5	NUM
ejpam-5428	249	27	,	,	PUNCT
ejpam-5428	249	28	β(t1	β(t1	PUNCT
ejpam-5428	249	29	)	)	PUNCT
ejpam-5428	250	1	=	=	SYM
ejpam-5428	250	2	e−t1	e−t1	NOUN
ejpam-5428	250	3	.	.	PUNCT
ejpam-5428	251	1	so	so	ADV
ejpam-5428	251	2	,	,	PUNCT
ejpam-5428	251	3	δ	δ	PROPN
ejpam-5428	251	4	=	=	SYM
ejpam-5428	251	5	0	0	NUM
ejpam-5428	251	6	is	be	AUX
ejpam-5428	251	7	a	a	DET
ejpam-5428	251	8	fixed	fix	VERB
ejpam-5428	251	9	point	point	NOUN
ejpam-5428	251	10	of	of	ADP
ejpam-5428	251	11	l.	l.	PROPN
ejpam-5428	251	12	this	this	PRON
ejpam-5428	251	13	is	be	AUX
ejpam-5428	251	14	another	another	DET
ejpam-5428	251	15	supportive	supportive	ADJ
ejpam-5428	251	16	example	example	NOUN
ejpam-5428	251	17	of	of	ADP
ejpam-5428	251	18	our	our	PRON
ejpam-5428	251	19	results	result	NOUN
ejpam-5428	251	20	.	.	PUNCT
ejpam-5428	252	1	example	example	NOUN
ejpam-5428	252	2	5	5	NUM
ejpam-5428	252	3	.	.	PUNCT
ejpam-5428	253	1	let	let	VERB
ejpam-5428	253	2	ȳ	ȳ	PROPN
ejpam-5428	253	3	=	=	PUNCT
ejpam-5428	253	4	{	{	PUNCT
ejpam-5428	253	5	0	0	NUM
ejpam-5428	253	6	,	,	PUNCT
ejpam-5428	253	7	12	12	NUM
ejpam-5428	253	8	,	,	PUNCT
ejpam-5428	253	9	1	1	NUM
ejpam-5428	253	10	,	,	PUNCT
ejpam-5428	253	11	2	2	NUM
ejpam-5428	253	12	}	}	PUNCT
ejpam-5428	253	13	with	with	ADP
ejpam-5428	253	14	mz(δ	mz(δ	PROPN
ejpam-5428	253	15	,	,	PUNCT
ejpam-5428	253	16	γ	γ	X
ejpam-5428	253	17	,	,	PUNCT
ejpam-5428	253	18	l	l	NOUN
ejpam-5428	253	19	)	)	PUNCT
ejpam-5428	254	1	=	=	SYM
ejpam-5428	254	2	l	l	PROPN
ejpam-5428	254	3	l+|δ−γ|2	l+|δ−γ|2	PROPN
ejpam-5428	254	4	for	for	ADP
ejpam-5428	254	5	l	l	PROPN
ejpam-5428	254	6	>	>	X
ejpam-5428	254	7	0	0	PUNCT
ejpam-5428	254	8	is	be	AUX
ejpam-5428	254	9	a	a	DET
ejpam-5428	254	10	g	g	NOUN
ejpam-5428	254	11	-	-	PUNCT
ejpam-5428	254	12	complete	complete	ADJ
ejpam-5428	254	13	b	b	NOUN
ejpam-5428	254	14	-	-	PUNCT
ejpam-5428	254	15	fuzzy	fuzzy	ADJ
ejpam-5428	254	16	metric	metric	ADJ
ejpam-5428	254	17	space	space	NOUN
ejpam-5428	254	18	.	.	PUNCT
ejpam-5428	255	1	define	define	VERB
ejpam-5428	255	2	l(0	l(0	PROPN
ejpam-5428	255	3	)	)	PUNCT
ejpam-5428	255	4	=	=	SYM
ejpam-5428	255	5	l(12	l(12	ADJ
ejpam-5428	256	1	)	)	PUNCT
ejpam-5428	256	2	=	=	SYM
ejpam-5428	256	3	l(1	l(1	PROPN
ejpam-5428	256	4	)	)	PUNCT
ejpam-5428	256	5	=	=	SYM
ejpam-5428	256	6	1	1	NUM
ejpam-5428	256	7	2	2	NUM
ejpam-5428	256	8	and	and	CCONJ
ejpam-5428	256	9	l(2	l(2	PROPN
ejpam-5428	256	10	)	)	PUNCT
ejpam-5428	256	11	=	=	NOUN
ejpam-5428	257	1	1	1	X
ejpam-5428	257	2	.	.	X
ejpam-5428	257	3	we	we	PRON
ejpam-5428	257	4	can	can	AUX
ejpam-5428	257	5	calculate	calculate	VERB
ejpam-5428	257	6	l	l	NOUN
ejpam-5428	257	7	satisfies	satisfie	NOUN
ejpam-5428	257	8	each	each	DET
ejpam-5428	257	9	assumptions	assumption	NOUN
ejpam-5428	257	10	theorem	theorem	VERB
ejpam-5428	257	11	2	2	NUM
ejpam-5428	257	12	with	with	ADP
ejpam-5428	257	13	unique	unique	ADJ
ejpam-5428	257	14	fixed	fix	VERB
ejpam-5428	257	15	point	point	NOUN
ejpam-5428	257	16	δ	δ	X
ejpam-5428	257	17	=	=	SYM
ejpam-5428	257	18	1	1	NUM
ejpam-5428	257	19	2	2	NUM
ejpam-5428	257	20	for	for	ADP
ejpam-5428	257	21	function	function	NOUN
ejpam-5428	257	22	α	α	NOUN
ejpam-5428	257	23	like	like	ADP
ejpam-5428	257	24	α(δ	α(δ	PROPN
ejpam-5428	257	25	,	,	PUNCT
ejpam-5428	257	26	γ	γ	X
ejpam-5428	257	27	,	,	PUNCT
ejpam-5428	257	28	l	l	NOUN
ejpam-5428	257	29	)	)	PUNCT
ejpam-5428	257	30	=	=	NOUN
ejpam-5428	257	31	{	{	PUNCT
ejpam-5428	257	32	1	1	NUM
ejpam-5428	257	33	,	,	PUNCT
ejpam-5428	257	34	if	if	SCONJ
ejpam-5428	257	35	δ	δ	PROPN
ejpam-5428	257	36	,	,	PUNCT
ejpam-5428	257	37	γ	γ	PROPN
ejpam-5428	257	38	∈	∈	PROPN
ejpam-5428	257	39	{	{	PUNCT
ejpam-5428	257	40	0	0	NUM
ejpam-5428	257	41	,	,	PUNCT
ejpam-5428	257	42	12	12	NUM
ejpam-5428	257	43	,	,	PUNCT
ejpam-5428	257	44	1	1	NUM
ejpam-5428	257	45	}	}	PUNCT
ejpam-5428	257	46	0	0	NUM
ejpam-5428	257	47	otherwise	otherwise	ADV
ejpam-5428	257	48	.	.	PUNCT
ejpam-5428	258	1	for	for	ADP
ejpam-5428	258	2	all	all	DET
ejpam-5428	258	3	l	l	NOUN
ejpam-5428	258	4	>	>	X
ejpam-5428	258	5	0	0	NUM
ejpam-5428	258	6	,	,	PUNCT
ejpam-5428	258	7	β(t1	β(t1	PUNCT
ejpam-5428	258	8	)	)	PUNCT
ejpam-5428	258	9	=	=	SYM
ejpam-5428	258	10	1−	1−	NUM
ejpam-5428	258	11	t1	t1	NOUN
ejpam-5428	258	12	and	and	CCONJ
ejpam-5428	258	13	q	q	ADJ
ejpam-5428	258	14	∈	∈	PROPN
ejpam-5428	258	15	(	(	PUNCT
ejpam-5428	258	16	0	0	NUM
ejpam-5428	258	17	,	,	PUNCT
ejpam-5428	258	18	1	1	NUM
ejpam-5428	258	19	)	)	PUNCT
ejpam-5428	258	20	.	.	PUNCT
ejpam-5428	259	1	now	now	ADV
ejpam-5428	259	2	we	we	PRON
ejpam-5428	259	3	introduce	introduce	VERB
ejpam-5428	259	4	one	one	NUM
ejpam-5428	259	5	more	more	ADJ
ejpam-5428	259	6	inequality	inequality	NOUN
ejpam-5428	259	7	.	.	PUNCT
ejpam-5428	260	1	definition	definition	NOUN
ejpam-5428	260	2	10	10	NUM
ejpam-5428	260	3	.	.	PUNCT
ejpam-5428	261	1	a	a	DET
ejpam-5428	261	2	triangular	triangular	NOUN
ejpam-5428	261	3	α	α	NOUN
ejpam-5428	261	4	-	-	ADJ
ejpam-5428	261	5	admissible	admissible	ADJ
ejpam-5428	261	6	self	self	NOUN
ejpam-5428	261	7	mapping	mapping	NOUN
ejpam-5428	261	8	l	l	NOUN
ejpam-5428	261	9	defined	define	VERB
ejpam-5428	261	10	on	on	ADP
ejpam-5428	261	11	a	a	DET
ejpam-5428	261	12	b	b	NOUN
ejpam-5428	261	13	-	-	PUNCT
ejpam-5428	261	14	fuzzy	fuzzy	ADJ
ejpam-5428	261	15	metric	metric	ADJ
ejpam-5428	261	16	space	space	NOUN
ejpam-5428	261	17	(	(	PUNCT
ejpam-5428	261	18	ȳ,mz	ȳ,mz	NUM
ejpam-5428	261	19	,	,	PUNCT
ejpam-5428	261	20	⋄	⋄	PROPN
ejpam-5428	261	21	)	)	PUNCT
ejpam-5428	261	22	is	be	AUX
ejpam-5428	261	23	called	call	VERB
ejpam-5428	261	24	a	a	DET
ejpam-5428	261	25	α	α	PROPN
ejpam-5428	261	26	-	-	PUNCT
ejpam-5428	261	27	suzuki	suzuki	NOUN
ejpam-5428	261	28	-	-	PUNCT
ejpam-5428	261	29	geraghty	geraghty	VERB
ejpam-5428	261	30	type	type	PROPN
ejpam-5428	261	31	-	-	PUNCT
ejpam-5428	261	32	ii	ii	NOUN
ejpam-5428	261	33	if	if	SCONJ
ejpam-5428	261	34	there	there	PRON
ejpam-5428	261	35	exists	exist	VERB
ejpam-5428	261	36	a	a	DET
ejpam-5428	261	37	β	β	X
ejpam-5428	261	38	∈	∈	PROPN
ejpam-5428	261	39	b	b	NOUN
ejpam-5428	261	40	such	such	ADJ
ejpam-5428	261	41	that	that	DET
ejpam-5428	261	42	mz(δ	mz(δ	PROPN
ejpam-5428	261	43	,	,	PUNCT
ejpam-5428	261	44	lδ	lδ	PROPN
ejpam-5428	261	45	,	,	PUNCT
ejpam-5428	261	46	l	l	NOUN
ejpam-5428	261	47	)	)	PUNCT
ejpam-5428	261	48	>	>	X
ejpam-5428	261	49	q	q	X
ejpam-5428	261	50	·	·	PUNCT
ejpam-5428	261	51	mz(δ	mz(δ	NUM
ejpam-5428	261	52	,	,	PUNCT
ejpam-5428	261	53	γ	γ	X
ejpam-5428	261	54	,	,	PUNCT
ejpam-5428	261	55	l	l	NOUN
ejpam-5428	261	56	)	)	PUNCT
ejpam-5428	261	57	implies	imply	VERB
ejpam-5428	261	58	α(δ	α(δ	PROPN
ejpam-5428	261	59	,	,	PUNCT
ejpam-5428	261	60	γ	γ	X
ejpam-5428	261	61	,	,	PUNCT
ejpam-5428	261	62	l	l	NOUN
ejpam-5428	261	63	)	)	PUNCT
ejpam-5428	261	64	(	(	PUNCT
ejpam-5428	261	65	1	1	NUM
ejpam-5428	261	66	mz(lδ	mz(lδ	NOUN
ejpam-5428	261	67	,	,	PUNCT
ejpam-5428	261	68	lγ	lγ	PROPN
ejpam-5428	261	69	,	,	PUNCT
ejpam-5428	261	70	l	l	NOUN
ejpam-5428	261	71	)	)	PUNCT
ejpam-5428	261	72	−	−	PROPN
ejpam-5428	261	73	1	1	NUM
ejpam-5428	261	74	)	)	PUNCT
ejpam-5428	261	75	≤	≤	NOUN
ejpam-5428	261	76	β	β	X
ejpam-5428	261	77	(	(	PUNCT
ejpam-5428	261	78	1	1	NUM
ejpam-5428	261	79	mz(δ	mz(δ	NUM
ejpam-5428	261	80	,	,	PUNCT
ejpam-5428	261	81	γ	γ	X
ejpam-5428	261	82	,	,	PUNCT
ejpam-5428	261	83	l	l	NOUN
ejpam-5428	261	84	)	)	PUNCT
ejpam-5428	261	85	−	−	PROPN
ejpam-5428	261	86	1	1	NUM
ejpam-5428	261	87	)	)	PUNCT
ejpam-5428	261	88	(	(	PUNCT
ejpam-5428	261	89	1	1	NUM
ejpam-5428	261	90	mz(δ	mz(δ	NUM
ejpam-5428	261	91	,	,	PUNCT
ejpam-5428	261	92	γ	γ	X
ejpam-5428	261	93	,	,	PUNCT
ejpam-5428	261	94	l	l	NOUN
ejpam-5428	261	95	)	)	PUNCT
ejpam-5428	261	96	−	−	PROPN
ejpam-5428	261	97	1	1	NUM
ejpam-5428	261	98	)	)	PUNCT
ejpam-5428	261	99	,	,	PUNCT
ejpam-5428	261	100	(	(	PUNCT
ejpam-5428	261	101	17	17	NUM
ejpam-5428	261	102	)	)	PUNCT
ejpam-5428	261	103	for	for	ADP
ejpam-5428	261	104	all	all	DET
ejpam-5428	261	105	δ	δ	PROPN
ejpam-5428	261	106	,	,	PUNCT
ejpam-5428	261	107	γ	γ	PROPN
ejpam-5428	261	108	∈	∈	PROPN
ejpam-5428	261	109	ȳ	ȳ	NOUN
ejpam-5428	261	110	and	and	CCONJ
ejpam-5428	261	111	l	l	NOUN
ejpam-5428	261	112	>	>	X
ejpam-5428	261	113	0	0	NUM
ejpam-5428	261	114	,	,	PUNCT
ejpam-5428	261	115	q	q	PROPN
ejpam-5428	261	116	∈	∈	PROPN
ejpam-5428	261	117	(	(	PUNCT
ejpam-5428	261	118	0	0	NUM
ejpam-5428	261	119	,	,	PUNCT
ejpam-5428	261	120	1	1	NUM
ejpam-5428	261	121	)	)	PUNCT
ejpam-5428	261	122	.	.	PUNCT
ejpam-5428	262	1	v.	v.	PROPN
ejpam-5428	262	2	chandra	chandra	PROPN
ejpam-5428	262	3	,	,	PUNCT
ejpam-5428	262	4	u.	u.	PROPN
ejpam-5428	262	5	d.	d.	PROPN
ejpam-5428	262	6	patel	patel	PROPN
ejpam-5428	262	7	,	,	PUNCT
ejpam-5428	262	8	s.	s.	PROPN
ejpam-5428	262	9	radenović	radenović	PROPN
ejpam-5428	262	10	/	/	SYM
ejpam-5428	262	11	eur	eur	PROPN
ejpam-5428	262	12	.	.	PUNCT
ejpam-5428	263	1	j.	j.	PROPN
ejpam-5428	263	2	pure	pure	PROPN
ejpam-5428	263	3	appl	appl	PROPN
ejpam-5428	263	4	.	.	PROPN
ejpam-5428	263	5	math	math	PROPN
ejpam-5428	263	6	,	,	PUNCT
ejpam-5428	263	7	17	17	NUM
ejpam-5428	263	8	(	(	PUNCT
ejpam-5428	263	9	4	4	NUM
ejpam-5428	263	10	)	)	PUNCT
ejpam-5428	263	11	(	(	PUNCT
ejpam-5428	263	12	2024	2024	NUM
ejpam-5428	263	13	)	)	PUNCT
ejpam-5428	263	14	,	,	PUNCT
ejpam-5428	263	15	2384	2384	NUM
ejpam-5428	263	16	-	-	SYM
ejpam-5428	263	17	2404	2404	NUM
ejpam-5428	263	18	2396	2396	NUM
ejpam-5428	263	19	theorem	theorem	NOUN
ejpam-5428	263	20	3	3	NUM
ejpam-5428	263	21	.	.	X
ejpam-5428	263	22	consider	consider	VERB
ejpam-5428	263	23	a	a	DET
ejpam-5428	263	24	self	self	NOUN
ejpam-5428	263	25	map	map	NOUN
ejpam-5428	263	26	l	l	NOUN
ejpam-5428	263	27	defined	define	VERB
ejpam-5428	263	28	on	on	ADP
ejpam-5428	263	29	a	a	DET
ejpam-5428	263	30	g	g	NOUN
ejpam-5428	263	31	-	-	PUNCT
ejpam-5428	263	32	complete	complete	ADJ
ejpam-5428	263	33	b	b	NOUN
ejpam-5428	263	34	-	-	PUNCT
ejpam-5428	263	35	fuzzy	fuzzy	ADJ
ejpam-5428	263	36	metric	metric	ADJ
ejpam-5428	263	37	space	space	NOUN
ejpam-5428	263	38	(	(	PUNCT
ejpam-5428	263	39	ȳ,mz	ȳ,mz	NUM
ejpam-5428	263	40	,	,	PUNCT
ejpam-5428	263	41	⋄	⋄	PROPN
ejpam-5428	263	42	)	)	PUNCT
ejpam-5428	263	43	where	where	SCONJ
ejpam-5428	263	44	fuzzy	fuzzy	ADJ
ejpam-5428	263	45	metric	metric	NOUN
ejpam-5428	263	46	is	be	AUX
ejpam-5428	263	47	triangular	triangular	NOUN
ejpam-5428	263	48	satisfying	satisfying	ADJ
ejpam-5428	263	49	:	:	PUNCT
ejpam-5428	263	50	(	(	PUNCT
ejpam-5428	263	51	i	i	NOUN
ejpam-5428	263	52	)	)	PUNCT
ejpam-5428	263	53	map	map	NOUN
ejpam-5428	263	54	l	l	NOUN
ejpam-5428	263	55	is	be	AUX
ejpam-5428	263	56	b	b	NOUN
ejpam-5428	263	57	-	-	PUNCT
ejpam-5428	263	58	fuzzy	fuzzy	ADJ
ejpam-5428	263	59	α	α	NOUN
ejpam-5428	263	60	-	-	PUNCT
ejpam-5428	263	61	suzuki	suzuki	NOUN
ejpam-5428	263	62	-	-	PUNCT
ejpam-5428	263	63	geraghty	geraghty	VERB
ejpam-5428	263	64	type	type	PROPN
ejpam-5428	263	65	-	-	PUNCT
ejpam-5428	263	66	ii	ii	NOUN
ejpam-5428	263	67	;	;	PUNCT
ejpam-5428	263	68	(	(	PUNCT
ejpam-5428	263	69	ii	ii	NOUN
ejpam-5428	263	70	)	)	PUNCT
ejpam-5428	263	71	l	l	NOUN
ejpam-5428	263	72	has	have	VERB
ejpam-5428	263	73	property	property	NOUN
ejpam-5428	263	74	g1	g1	NOUN
ejpam-5428	263	75	and	and	CCONJ
ejpam-5428	263	76	g2	g2	PROPN
ejpam-5428	263	77	;	;	PUNCT
ejpam-5428	263	78	(	(	PUNCT
ejpam-5428	263	79	iii	iii	X
ejpam-5428	263	80	)	)	PUNCT
ejpam-5428	263	81	there	there	PRON
ejpam-5428	263	82	exists	exist	VERB
ejpam-5428	263	83	δ0	δ0	NOUN
ejpam-5428	263	84	∈	∈	PROPN
ejpam-5428	263	85	ȳ	ȳ	NOUN
ejpam-5428	263	86	such	such	ADJ
ejpam-5428	263	87	that	that	DET
ejpam-5428	263	88	α(δ0,lδ0	α(δ0,lδ0	PROPN
ejpam-5428	263	89	,	,	PUNCT
ejpam-5428	263	90	l	l	NOUN
ejpam-5428	263	91	)	)	PUNCT
ejpam-5428	263	92	≥	≥	NOUN
ejpam-5428	263	93	1	1	NUM
ejpam-5428	263	94	for	for	ADP
ejpam-5428	263	95	all	all	DET
ejpam-5428	263	96	l	l	NOUN
ejpam-5428	263	97	>	>	X
ejpam-5428	263	98	0	0	NUM
ejpam-5428	263	99	;	;	PUNCT
ejpam-5428	263	100	(	(	PUNCT
ejpam-5428	263	101	iv	iv	X
ejpam-5428	263	102	)	)	PUNCT
ejpam-5428	263	103	if	if	SCONJ
ejpam-5428	263	104	α(δn	α(δn	NUM
ejpam-5428	263	105	,	,	PUNCT
ejpam-5428	263	106	δn+1	δn+1	PROPN
ejpam-5428	263	107	,	,	PUNCT
ejpam-5428	263	108	l	l	NOUN
ejpam-5428	263	109	)	)	PUNCT
ejpam-5428	263	110	≥	≥	NOUN
ejpam-5428	263	111	1	1	NUM
ejpam-5428	263	112	and	and	CCONJ
ejpam-5428	263	113	δn	δn	NOUN
ejpam-5428	263	114	→	→	SYM
ejpam-5428	263	115	u	u	NOUN
ejpam-5428	263	116	as	as	ADP
ejpam-5428	263	117	n	n	PROPN
ejpam-5428	263	118	→	→	SYM
ejpam-5428	263	119	+	+	PROPN
ejpam-5428	263	120	∞	∞	PROPN
ejpam-5428	263	121	,	,	PUNCT
ejpam-5428	263	122	then	then	ADV
ejpam-5428	263	123	α(δn	α(δn	NUM
ejpam-5428	263	124	,	,	PUNCT
ejpam-5428	263	125	u	u	NOUN
ejpam-5428	263	126	,	,	PUNCT
ejpam-5428	263	127	l	l	NOUN
ejpam-5428	263	128	)	)	PUNCT
ejpam-5428	263	129	≥	≥	NOUN
ejpam-5428	263	130	1	1	NUM
ejpam-5428	263	131	for	for	ADP
ejpam-5428	263	132	all	all	DET
ejpam-5428	263	133	n	n	DET
ejpam-5428	263	134	∈	∈	PROPN
ejpam-5428	263	135	n.	n.	NOUN
ejpam-5428	263	136	then	then	ADV
ejpam-5428	263	137	l	l	PROPN
ejpam-5428	263	138	has	have	VERB
ejpam-5428	263	139	a	a	DET
ejpam-5428	263	140	fixed	fix	VERB
ejpam-5428	263	141	point	point	NOUN
ejpam-5428	263	142	.	.	PUNCT
ejpam-5428	264	1	proof	proof	NOUN
ejpam-5428	264	2	.	.	PUNCT
ejpam-5428	265	1	constructing	construct	VERB
ejpam-5428	265	2	of	of	ADP
ejpam-5428	265	3	picard	picard	NOUN
ejpam-5428	265	4	sequence	sequence	NOUN
ejpam-5428	265	5	such	such	ADJ
ejpam-5428	265	6	that	that	DET
ejpam-5428	265	7	δn	δn	NOUN
ejpam-5428	265	8	̸=	̸=	PROPN
ejpam-5428	265	9	δn+1	δn+1	NOUN
ejpam-5428	265	10	for	for	ADP
ejpam-5428	265	11	all	all	DET
ejpam-5428	265	12	n	n	PRON
ejpam-5428	265	13	∈	∈	PROPN
ejpam-5428	265	14	n.	n.	NOUN
ejpam-5428	265	15	by	by	ADP
ejpam-5428	265	16	lemma	lemma	PROPN
ejpam-5428	265	17	1	1	NUM
ejpam-5428	265	18	,	,	PUNCT
ejpam-5428	265	19	we	we	PRON
ejpam-5428	265	20	have	have	VERB
ejpam-5428	265	21	α(δn	α(δn	NUM
ejpam-5428	265	22	,	,	PUNCT
ejpam-5428	265	23	δn+1	δn+1	PROPN
ejpam-5428	265	24	,	,	PUNCT
ejpam-5428	265	25	l	l	NOUN
ejpam-5428	265	26	)	)	PUNCT
ejpam-5428	265	27	≥	≥	NOUN
ejpam-5428	265	28	1	1	NUM
ejpam-5428	265	29	for	for	ADP
ejpam-5428	265	30	all	all	PRON
ejpam-5428	265	31	n	n	PRON
ejpam-5428	265	32	∈	∈	NOUN
ejpam-5428	265	33	n	n	NOUN
ejpam-5428	265	34	and	and	CCONJ
ejpam-5428	265	35	l	l	NOUN
ejpam-5428	265	36	>	>	X
ejpam-5428	265	37	0	0	X
ejpam-5428	265	38	.	.	PUNCT
ejpam-5428	266	1	by	by	ADP
ejpam-5428	266	2	the	the	DET
ejpam-5428	266	3	α	α	PROPN
ejpam-5428	266	4	-	-	PUNCT
ejpam-5428	266	5	suzuki	suzuki	NOUN
ejpam-5428	266	6	-	-	PUNCT
ejpam-5428	266	7	geraghty	geraghty	VERB
ejpam-5428	266	8	type	type	NOUN
ejpam-5428	266	9	-ii	-ii	NOUN
ejpam-5428	266	10	contraction	contraction	NOUN
ejpam-5428	266	11	,	,	PUNCT
ejpam-5428	266	12	we	we	PRON
ejpam-5428	266	13	have	have	VERB
ejpam-5428	266	14	mz(δn	mz(δn	PROPN
ejpam-5428	266	15	,	,	PUNCT
ejpam-5428	266	16	δn+1	δn+1	PROPN
ejpam-5428	266	17	,	,	PUNCT
ejpam-5428	266	18	l	l	NOUN
ejpam-5428	266	19	)	)	PUNCT
ejpam-5428	266	20	>	>	X
ejpam-5428	267	1	q	q	PUNCT
ejpam-5428	267	2	·	·	PUNCT
ejpam-5428	267	3	mz(δn	mz(δn	PROPN
ejpam-5428	267	4	,	,	PUNCT
ejpam-5428	267	5	δn+1	δn+1	PROPN
ejpam-5428	267	6	,	,	PUNCT
ejpam-5428	267	7	l	l	NOUN
ejpam-5428	267	8	)	)	PUNCT
ejpam-5428	267	9	⇒α(δn	⇒α(δn	PROPN
ejpam-5428	267	10	,	,	PUNCT
ejpam-5428	267	11	δn+1	δn+1	PROPN
ejpam-5428	267	12	,	,	PUNCT
ejpam-5428	267	13	l	l	NOUN
ejpam-5428	267	14	)	)	PUNCT
ejpam-5428	267	15	(	(	PUNCT
ejpam-5428	267	16	1	1	NUM
ejpam-5428	267	17	mz(lδn	mz(lδn	PROPN
ejpam-5428	267	18	,	,	PUNCT
ejpam-5428	267	19	lδn+1	lδn+1	PROPN
ejpam-5428	267	20	,	,	PUNCT
ejpam-5428	267	21	l	l	NOUN
ejpam-5428	267	22	)	)	PUNCT
ejpam-5428	267	23	−	−	PROPN
ejpam-5428	267	24	1	1	NUM
ejpam-5428	267	25	)	)	PUNCT
ejpam-5428	267	26	≤	≤	NOUN
ejpam-5428	267	27	β	β	X
ejpam-5428	267	28	(	(	PUNCT
ejpam-5428	267	29	1	1	NUM
ejpam-5428	267	30	mz(δn	mz(δn	PROPN
ejpam-5428	267	31	,	,	PUNCT
ejpam-5428	267	32	δn+1	δn+1	PROPN
ejpam-5428	267	33	,	,	PUNCT
ejpam-5428	267	34	l	l	NOUN
ejpam-5428	267	35	)	)	PUNCT
ejpam-5428	267	36	−	−	PROPN
ejpam-5428	267	37	1	1	NUM
ejpam-5428	267	38	)	)	PUNCT
ejpam-5428	267	39	(	(	PUNCT
ejpam-5428	267	40	1	1	NUM
ejpam-5428	267	41	mz(δn	mz(δn	PROPN
ejpam-5428	267	42	,	,	PUNCT
ejpam-5428	267	43	δn+1	δn+1	PROPN
ejpam-5428	267	44	,	,	PUNCT
ejpam-5428	267	45	l	l	NOUN
ejpam-5428	267	46	)	)	PUNCT
ejpam-5428	267	47	−	−	PROPN
ejpam-5428	267	48	1	1	NUM
ejpam-5428	267	49	)	)	PUNCT
ejpam-5428	267	50	for	for	ADP
ejpam-5428	267	51	all	all	DET
ejpam-5428	267	52	l	l	NOUN
ejpam-5428	267	53	>	>	X
ejpam-5428	267	54	0	0	X
ejpam-5428	267	55	.	.	PUNCT
ejpam-5428	268	1	(	(	PUNCT
ejpam-5428	268	2	1	1	NUM
ejpam-5428	268	3	mz(lδn	mz(lδn	PROPN
ejpam-5428	268	4	,	,	PUNCT
ejpam-5428	268	5	lδn+1	lδn+1	PROPN
ejpam-5428	268	6	,	,	PUNCT
ejpam-5428	268	7	l	l	NOUN
ejpam-5428	268	8	)	)	PUNCT
ejpam-5428	268	9	−	−	PROPN
ejpam-5428	268	10	1	1	X
ejpam-5428	268	11	)	)	PUNCT
ejpam-5428	268	12	≤	≤	NOUN
ejpam-5428	268	13	α(δn	α(δn	NUM
ejpam-5428	268	14	,	,	PUNCT
ejpam-5428	268	15	δn+1	δn+1	PROPN
ejpam-5428	268	16	,	,	PUNCT
ejpam-5428	268	17	l	l	NOUN
ejpam-5428	268	18	)	)	PUNCT
ejpam-5428	268	19	(	(	PUNCT
ejpam-5428	268	20	1	1	NUM
ejpam-5428	268	21	mz(lδn	mz(lδn	PROPN
ejpam-5428	268	22	,	,	PUNCT
ejpam-5428	268	23	lδn+1	lδn+1	PROPN
ejpam-5428	268	24	,	,	PUNCT
ejpam-5428	268	25	l	l	NOUN
ejpam-5428	268	26	)	)	PUNCT
ejpam-5428	268	27	−	−	PROPN
ejpam-5428	268	28	1	1	NUM
ejpam-5428	268	29	)	)	PUNCT
ejpam-5428	268	30	≤	≤	NOUN
ejpam-5428	269	1	β	β	X
ejpam-5428	269	2	(	(	PUNCT
ejpam-5428	269	3	1	1	NUM
ejpam-5428	269	4	mz(δn	mz(δn	PROPN
ejpam-5428	269	5	,	,	PUNCT
ejpam-5428	269	6	δn+1	δn+1	PROPN
ejpam-5428	269	7	,	,	PUNCT
ejpam-5428	269	8	l	l	NOUN
ejpam-5428	269	9	)	)	PUNCT
ejpam-5428	269	10	−	−	PROPN
ejpam-5428	269	11	1	1	NUM
ejpam-5428	269	12	)	)	PUNCT
ejpam-5428	269	13	(	(	PUNCT
ejpam-5428	269	14	1	1	NUM
ejpam-5428	269	15	mz(δn	mz(δn	PROPN
ejpam-5428	269	16	,	,	PUNCT
ejpam-5428	269	17	δn+1	δn+1	PROPN
ejpam-5428	269	18	,	,	PUNCT
ejpam-5428	269	19	l	l	NOUN
ejpam-5428	269	20	)	)	PUNCT
ejpam-5428	269	21	−	−	PROPN
ejpam-5428	269	22	1	1	NUM
ejpam-5428	269	23	)	)	PUNCT
ejpam-5428	269	24	<	<	X
ejpam-5428	269	25	(	(	PUNCT
ejpam-5428	269	26	1	1	NUM
ejpam-5428	269	27	mz(δn	mz(δn	PROPN
ejpam-5428	269	28	,	,	PUNCT
ejpam-5428	269	29	δn+1	δn+1	PROPN
ejpam-5428	269	30	,	,	PUNCT
ejpam-5428	269	31	l	l	NOUN
ejpam-5428	269	32	)	)	PUNCT
ejpam-5428	269	33	−	−	PROPN
ejpam-5428	269	34	1	1	NUM
ejpam-5428	269	35	)	)	PUNCT
ejpam-5428	269	36	.	.	PUNCT
ejpam-5428	270	1	(	(	PUNCT
ejpam-5428	270	2	18	18	NUM
ejpam-5428	270	3	)	)	PUNCT
ejpam-5428	270	4	we	we	PRON
ejpam-5428	270	5	conclude	conclude	VERB
ejpam-5428	270	6	that	that	DET
ejpam-5428	270	7	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	270	8	,	,	PUNCT
ejpam-5428	270	9	δn+2	δn+2	X
ejpam-5428	270	10	,	,	PUNCT
ejpam-5428	270	11	l	l	NOUN
ejpam-5428	270	12	)	)	PUNCT
ejpam-5428	270	13	>	>	X
ejpam-5428	271	1	mz(δn	mz(δn	PROPN
ejpam-5428	271	2	,	,	PUNCT
ejpam-5428	271	3	δn+1	δn+1	PROPN
ejpam-5428	271	4	,	,	PUNCT
ejpam-5428	271	5	l	l	NOUN
ejpam-5428	271	6	)	)	PUNCT
ejpam-5428	271	7	for	for	ADP
ejpam-5428	271	8	all	all	DET
ejpam-5428	271	9	n	n	PRON
ejpam-5428	271	10	∈	∈	NOUN
ejpam-5428	271	11	n	n	PRON
ejpam-5428	271	12	it	it	PRON
ejpam-5428	271	13	means	mean	VERB
ejpam-5428	271	14	,	,	PUNCT
ejpam-5428	271	15	it	it	PRON
ejpam-5428	271	16	is	be	AUX
ejpam-5428	271	17	nondecreasing	nondecrease	VERB
ejpam-5428	271	18	sequence	sequence	NOUN
ejpam-5428	271	19	of	of	ADP
ejpam-5428	271	20	positive	positive	ADJ
ejpam-5428	271	21	real	real	ADJ
ejpam-5428	271	22	numbers	number	NOUN
ejpam-5428	271	23	.	.	PUNCT
ejpam-5428	272	1	so	so	ADV
ejpam-5428	272	2	there	there	PRON
ejpam-5428	272	3	exists	exist	VERB
ejpam-5428	272	4	s(l	s(l	NOUN
ejpam-5428	272	5	)	)	PUNCT
ejpam-5428	272	6	∈	∈	PROPN
ejpam-5428	272	7	(	(	PUNCT
ejpam-5428	272	8	0	0	NUM
ejpam-5428	272	9	,	,	PUNCT
ejpam-5428	272	10	1	1	NUM
ejpam-5428	272	11	]	]	PUNCT
ejpam-5428	272	12	such	such	ADJ
ejpam-5428	272	13	that	that	SCONJ
ejpam-5428	272	14	lim	lim	PROPN
ejpam-5428	272	15	n→+∞	n→+∞	PROPN
ejpam-5428	272	16	mz(δn	mz(δn	PROPN
ejpam-5428	272	17	,	,	PUNCT
ejpam-5428	272	18	δn+1	δn+1	PROPN
ejpam-5428	272	19	,	,	PUNCT
ejpam-5428	272	20	l	l	NOUN
ejpam-5428	272	21	)	)	PUNCT
ejpam-5428	272	22	=	=	SYM
ejpam-5428	272	23	s(l	s(l	NUM
ejpam-5428	272	24	)	)	PUNCT
ejpam-5428	272	25	,	,	PUNCT
ejpam-5428	272	26	for	for	ADP
ejpam-5428	272	27	all	all	DET
ejpam-5428	272	28	l	l	NOUN
ejpam-5428	272	29	>	>	X
ejpam-5428	272	30	0	0	X
ejpam-5428	272	31	.	.	PUNCT
ejpam-5428	273	1	next	next	ADV
ejpam-5428	273	2	,	,	PUNCT
ejpam-5428	273	3	we	we	PRON
ejpam-5428	273	4	require	require	VERB
ejpam-5428	273	5	to	to	PART
ejpam-5428	273	6	prove	prove	VERB
ejpam-5428	273	7	s(l	s(l	NUM
ejpam-5428	273	8	)	)	PUNCT
ejpam-5428	273	9	=	=	SYM
ejpam-5428	273	10	1	1	X
ejpam-5428	273	11	.	.	PUNCT
ejpam-5428	273	12	taken	take	VERB
ejpam-5428	273	13	a	a	DET
ejpam-5428	273	14	contrary	contrary	ADJ
ejpam-5428	273	15	,	,	PUNCT
ejpam-5428	273	16	s(l0	s(l0	NOUN
ejpam-5428	273	17	)	)	PUNCT
ejpam-5428	273	18	<	<	X
ejpam-5428	273	19	1	1	NUM
ejpam-5428	273	20	for	for	ADP
ejpam-5428	273	21	all	all	DET
ejpam-5428	273	22	l0	l0	PROPN
ejpam-5428	273	23	>	>	X
ejpam-5428	273	24	0	0	X
ejpam-5428	273	25	.	.	PUNCT
ejpam-5428	274	1	now	now	ADV
ejpam-5428	274	2	taking	take	VERB
ejpam-5428	274	3	limit	limit	NOUN
ejpam-5428	274	4	as	as	ADP
ejpam-5428	274	5	n	n	PROPN
ejpam-5428	274	6	→	→	SYM
ejpam-5428	274	7	+	+	PROPN
ejpam-5428	274	8	∞	∞	PROPN
ejpam-5428	274	9	lim	lim	PROPN
ejpam-5428	274	10	n→+∞	n→+∞	VERB
ejpam-5428	274	11	β	β	X
ejpam-5428	274	12	(	(	PUNCT
ejpam-5428	274	13	1	1	NUM
ejpam-5428	274	14	mz(δn	mz(δn	PROPN
ejpam-5428	274	15	,	,	PUNCT
ejpam-5428	274	16	δn+1	δn+1	PROPN
ejpam-5428	274	17	,	,	PUNCT
ejpam-5428	274	18	l	l	NOUN
ejpam-5428	274	19	)	)	PUNCT
ejpam-5428	275	1	−	−	PROPN
ejpam-5428	275	2	1	1	NUM
ejpam-5428	275	3	)	)	PUNCT
ejpam-5428	275	4	=	=	SYM
ejpam-5428	275	5	1	1	NUM
ejpam-5428	275	6	⇒	⇒	NOUN
ejpam-5428	275	7	lim	lim	PROPN
ejpam-5428	275	8	n→+∞	n→+∞	PROPN
ejpam-5428	275	9	mz(δn	mz(δn	PROPN
ejpam-5428	275	10	,	,	PUNCT
ejpam-5428	275	11	δn+1	δn+1	PROPN
ejpam-5428	275	12	,	,	PUNCT
ejpam-5428	275	13	l	l	NOUN
ejpam-5428	275	14	)	)	PUNCT
ejpam-5428	275	15	=	=	SYM
ejpam-5428	275	16	1	1	NUM
ejpam-5428	275	17	,	,	PUNCT
ejpam-5428	275	18	(	(	PUNCT
ejpam-5428	275	19	19	19	NUM
ejpam-5428	275	20	)	)	PUNCT
ejpam-5428	275	21	a	a	DET
ejpam-5428	275	22	contradiction	contradiction	NOUN
ejpam-5428	275	23	.	.	PUNCT
ejpam-5428	276	1	next	next	ADV
ejpam-5428	276	2	we	we	PRON
ejpam-5428	276	3	must	must	AUX
ejpam-5428	276	4	prove	prove	VERB
ejpam-5428	276	5	that	that	SCONJ
ejpam-5428	276	6	sequence	sequence	NOUN
ejpam-5428	276	7	is	be	AUX
ejpam-5428	276	8	a	a	DET
ejpam-5428	276	9	g	g	NOUN
ejpam-5428	276	10	-	-	PUNCT
ejpam-5428	276	11	cauchy	cauchy	ADJ
ejpam-5428	276	12	sequence	sequence	NOUN
ejpam-5428	276	13	.	.	PUNCT
ejpam-5428	277	1	suppose	suppose	VERB
ejpam-5428	277	2	λ	λ	X
ejpam-5428	277	3	=	=	SYM
ejpam-5428	277	4	mz(δn	mz(δn	PROPN
ejpam-5428	277	5	,	,	PUNCT
ejpam-5428	277	6	δm	δm	PROPN
ejpam-5428	277	7	,	,	PUNCT
ejpam-5428	277	8	l	l	NOUN
ejpam-5428	277	9	)	)	PUNCT
ejpam-5428	277	10	<	<	X
ejpam-5428	277	11	1	1	X
ejpam-5428	277	12	.	.	PUNCT
ejpam-5428	278	1	by	by	ADP
ejpam-5428	278	2	(	(	PUNCT
ejpam-5428	278	3	g1	g1	PROPN
ejpam-5428	278	4	)	)	PUNCT
ejpam-5428	278	5	property	property	NOUN
ejpam-5428	278	6	,	,	PUNCT
ejpam-5428	278	7	mz(δn	mz(δn	PROPN
ejpam-5428	278	8	,	,	PUNCT
ejpam-5428	278	9	δn+1	δn+1	PROPN
ejpam-5428	278	10	,	,	PUNCT
ejpam-5428	278	11	l	l	NOUN
ejpam-5428	278	12	)	)	PUNCT
ejpam-5428	278	13	>	>	X
ejpam-5428	278	14	q	q	PUNCT
ejpam-5428	278	15	·	·	PUNCT
ejpam-5428	278	16	mz(δn	mz(δn	PROPN
ejpam-5428	278	17	,	,	PUNCT
ejpam-5428	278	18	δm	δm	PROPN
ejpam-5428	278	19	,	,	PUNCT
ejpam-5428	278	20	l	l	NOUN
ejpam-5428	278	21	)	)	PUNCT
ejpam-5428	278	22	implies	imply	VERB
ejpam-5428	278	23	α(δn	α(δn	NUM
ejpam-5428	278	24	,	,	PUNCT
ejpam-5428	278	25	δm	δm	PROPN
ejpam-5428	278	26	,	,	PUNCT
ejpam-5428	278	27	l	l	NOUN
ejpam-5428	278	28	)	)	PUNCT
ejpam-5428	278	29	(	(	PUNCT
ejpam-5428	278	30	1	1	NUM
ejpam-5428	278	31	mz(lδn	mz(lδn	PROPN
ejpam-5428	278	32	,	,	PUNCT
ejpam-5428	278	33	lδm	lδm	NOUN
ejpam-5428	278	34	,	,	PUNCT
ejpam-5428	278	35	l	l	NOUN
ejpam-5428	278	36	)	)	PUNCT
ejpam-5428	278	37	−	−	PROPN
ejpam-5428	278	38	1	1	NUM
ejpam-5428	278	39	)	)	PUNCT
ejpam-5428	278	40	≤	≤	NOUN
ejpam-5428	278	41	β	β	X
ejpam-5428	278	42	(	(	PUNCT
ejpam-5428	278	43	1	1	NUM
ejpam-5428	278	44	mz(δn	mz(δn	PROPN
ejpam-5428	278	45	,	,	PUNCT
ejpam-5428	278	46	δm	δm	PROPN
ejpam-5428	278	47	,	,	PUNCT
ejpam-5428	278	48	l	l	NOUN
ejpam-5428	278	49	)	)	PUNCT
ejpam-5428	278	50	−	−	PROPN
ejpam-5428	278	51	1	1	NUM
ejpam-5428	278	52	)	)	PUNCT
ejpam-5428	278	53	(	(	PUNCT
ejpam-5428	278	54	1	1	NUM
ejpam-5428	278	55	mz(δn	mz(δn	PROPN
ejpam-5428	278	56	,	,	PUNCT
ejpam-5428	278	57	δm	δm	PROPN
ejpam-5428	278	58	,	,	PUNCT
ejpam-5428	278	59	l	l	NOUN
ejpam-5428	278	60	)	)	PUNCT
ejpam-5428	278	61	−	−	PROPN
ejpam-5428	278	62	1	1	NUM
ejpam-5428	278	63	)	)	PUNCT
ejpam-5428	278	64	.	.	PUNCT
ejpam-5428	279	1	v.	v.	CCONJ
ejpam-5428	279	2	chandra	chandra	PROPN
ejpam-5428	279	3	,	,	PUNCT
ejpam-5428	279	4	u.	u.	PROPN
ejpam-5428	279	5	d.	d.	PROPN
ejpam-5428	279	6	patel	patel	PROPN
ejpam-5428	279	7	,	,	PUNCT
ejpam-5428	279	8	s.	s.	PROPN
ejpam-5428	279	9	radenović	radenović	PROPN
ejpam-5428	279	10	/	/	SYM
ejpam-5428	279	11	eur	eur	PROPN
ejpam-5428	279	12	.	.	PUNCT
ejpam-5428	280	1	j.	j.	PROPN
ejpam-5428	280	2	pure	pure	PROPN
ejpam-5428	280	3	appl	appl	PROPN
ejpam-5428	280	4	.	.	PROPN
ejpam-5428	280	5	math	math	PROPN
ejpam-5428	280	6	,	,	PUNCT
ejpam-5428	280	7	17	17	NUM
ejpam-5428	280	8	(	(	PUNCT
ejpam-5428	280	9	4	4	NUM
ejpam-5428	280	10	)	)	PUNCT
ejpam-5428	280	11	(	(	PUNCT
ejpam-5428	280	12	2024	2024	NUM
ejpam-5428	280	13	)	)	PUNCT
ejpam-5428	280	14	,	,	PUNCT
ejpam-5428	280	15	2384	2384	NUM
ejpam-5428	280	16	-	-	SYM
ejpam-5428	280	17	2404	2404	NUM
ejpam-5428	280	18	2397	2397	NUM
ejpam-5428	280	19	by	by	ADP
ejpam-5428	280	20	(	(	PUNCT
ejpam-5428	280	21	17	17	NUM
ejpam-5428	280	22	)	)	PUNCT
ejpam-5428	280	23	and	and	CCONJ
ejpam-5428	280	24	lemma	lemma	PROPN
ejpam-5428	280	25	(	(	PUNCT
ejpam-5428	280	26	1	1	NUM
ejpam-5428	280	27	)	)	PUNCT
ejpam-5428	280	28	,	,	PUNCT
ejpam-5428	280	29	we	we	PRON
ejpam-5428	280	30	get	get	VERB
ejpam-5428	280	31	(	(	PUNCT
ejpam-5428	280	32	1	1	NUM
ejpam-5428	280	33	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	280	34	,	,	PUNCT
ejpam-5428	280	35	δm+1	δm+1	PROPN
ejpam-5428	280	36	,	,	PUNCT
ejpam-5428	280	37	l	l	NOUN
ejpam-5428	280	38	)	)	PUNCT
ejpam-5428	280	39	−	−	PROPN
ejpam-5428	280	40	1	1	NUM
ejpam-5428	280	41	)	)	PUNCT
ejpam-5428	280	42	=	=	SYM
ejpam-5428	280	43	(	(	PUNCT
ejpam-5428	280	44	1	1	NUM
ejpam-5428	280	45	mz(lδn	mz(lδn	PROPN
ejpam-5428	280	46	,	,	PUNCT
ejpam-5428	280	47	lδm	lδm	NOUN
ejpam-5428	280	48	,	,	PUNCT
ejpam-5428	280	49	l	l	NOUN
ejpam-5428	280	50	)	)	PUNCT
ejpam-5428	280	51	−	−	PROPN
ejpam-5428	280	52	1	1	X
ejpam-5428	280	53	)	)	PUNCT
ejpam-5428	280	54	≤	≤	NOUN
ejpam-5428	280	55	α(δn	α(δn	NUM
ejpam-5428	280	56	,	,	PUNCT
ejpam-5428	280	57	δm	δm	PROPN
ejpam-5428	280	58	,	,	PUNCT
ejpam-5428	280	59	l	l	NOUN
ejpam-5428	280	60	)	)	PUNCT
ejpam-5428	280	61	(	(	PUNCT
ejpam-5428	280	62	1	1	NUM
ejpam-5428	280	63	mz(lδn	mz(lδn	PROPN
ejpam-5428	280	64	,	,	PUNCT
ejpam-5428	280	65	lδm	lδm	NOUN
ejpam-5428	280	66	,	,	PUNCT
ejpam-5428	280	67	l	l	NOUN
ejpam-5428	280	68	)	)	PUNCT
ejpam-5428	280	69	−	−	PROPN
ejpam-5428	280	70	1	1	NUM
ejpam-5428	280	71	)	)	PUNCT
ejpam-5428	280	72	≤	≤	NOUN
ejpam-5428	281	1	β	β	X
ejpam-5428	281	2	(	(	PUNCT
ejpam-5428	281	3	1	1	NUM
ejpam-5428	281	4	mz(δn	mz(δn	PROPN
ejpam-5428	281	5	,	,	PUNCT
ejpam-5428	281	6	δm	δm	PROPN
ejpam-5428	281	7	,	,	PUNCT
ejpam-5428	281	8	l	l	NOUN
ejpam-5428	281	9	)	)	PUNCT
ejpam-5428	281	10	−	−	PROPN
ejpam-5428	281	11	1	1	NUM
ejpam-5428	281	12	)	)	PUNCT
ejpam-5428	281	13	(	(	PUNCT
ejpam-5428	281	14	1	1	NUM
ejpam-5428	281	15	mz(δn	mz(δn	PROPN
ejpam-5428	281	16	,	,	PUNCT
ejpam-5428	281	17	δm	δm	PROPN
ejpam-5428	281	18	,	,	PUNCT
ejpam-5428	281	19	l	l	NOUN
ejpam-5428	281	20	)	)	PUNCT
ejpam-5428	281	21	−	−	PROPN
ejpam-5428	281	22	1	1	NUM
ejpam-5428	281	23	)	)	PUNCT
ejpam-5428	281	24	<	<	X
ejpam-5428	281	25	(	(	PUNCT
ejpam-5428	281	26	1	1	NUM
ejpam-5428	281	27	mz(δn	mz(δn	PROPN
ejpam-5428	281	28	,	,	PUNCT
ejpam-5428	281	29	δm	δm	PROPN
ejpam-5428	281	30	,	,	PUNCT
ejpam-5428	281	31	l	l	NOUN
ejpam-5428	281	32	)	)	PUNCT
ejpam-5428	281	33	−	−	PROPN
ejpam-5428	281	34	1	1	X
ejpam-5428	281	35	)	)	PUNCT
ejpam-5428	281	36	taking	take	VERB
ejpam-5428	281	37	limit	limit	NOUN
ejpam-5428	281	38	on	on	ADP
ejpam-5428	281	39	both	both	DET
ejpam-5428	281	40	sides	side	NOUN
ejpam-5428	281	41	,	,	PUNCT
ejpam-5428	281	42	lim	lim	PROPN
ejpam-5428	281	43	n	n	CCONJ
ejpam-5428	281	44	,	,	PUNCT
ejpam-5428	281	45	m→+∞	m→+∞	PROPN
ejpam-5428	281	46	(	(	PUNCT
ejpam-5428	281	47	1	1	NUM
ejpam-5428	281	48	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	281	49	,	,	PUNCT
ejpam-5428	281	50	δm+1	δm+1	PROPN
ejpam-5428	281	51	,	,	PUNCT
ejpam-5428	281	52	l	l	NOUN
ejpam-5428	281	53	)	)	PUNCT
ejpam-5428	281	54	−	−	PROPN
ejpam-5428	281	55	1	1	X
ejpam-5428	281	56	)	)	PUNCT
ejpam-5428	281	57	≤	≤	NOUN
ejpam-5428	281	58	lim	lim	PROPN
ejpam-5428	281	59	n	n	CCONJ
ejpam-5428	281	60	,	,	PUNCT
ejpam-5428	281	61	m→+∞	m→+∞	PROPN
ejpam-5428	281	62	α(δn	α(δn	PROPN
ejpam-5428	281	63	,	,	PUNCT
ejpam-5428	281	64	δm	δm	PROPN
ejpam-5428	281	65	,	,	PUNCT
ejpam-5428	281	66	l	l	NOUN
ejpam-5428	281	67	)	)	PUNCT
ejpam-5428	281	68	(	(	PUNCT
ejpam-5428	281	69	1	1	NUM
ejpam-5428	281	70	mz(lδn	mz(lδn	PROPN
ejpam-5428	281	71	,	,	PUNCT
ejpam-5428	281	72	lδm	lδm	NOUN
ejpam-5428	281	73	,	,	PUNCT
ejpam-5428	281	74	l	l	NOUN
ejpam-5428	281	75	)	)	PUNCT
ejpam-5428	281	76	−	−	PROPN
ejpam-5428	281	77	1	1	X
ejpam-5428	281	78	)	)	PUNCT
ejpam-5428	281	79	≤	≤	NOUN
ejpam-5428	281	80	lim	lim	PROPN
ejpam-5428	281	81	n	n	CCONJ
ejpam-5428	281	82	,	,	PUNCT
ejpam-5428	281	83	m→+∞	m→+∞	PROPN
ejpam-5428	281	84	β	β	X
ejpam-5428	281	85	(	(	PUNCT
ejpam-5428	281	86	1	1	NUM
ejpam-5428	281	87	mz(δn	mz(δn	PROPN
ejpam-5428	281	88	,	,	PUNCT
ejpam-5428	281	89	δm	δm	PROPN
ejpam-5428	281	90	,	,	PUNCT
ejpam-5428	281	91	l	l	NOUN
ejpam-5428	281	92	)	)	PUNCT
ejpam-5428	281	93	−	−	PROPN
ejpam-5428	281	94	1	1	NUM
ejpam-5428	281	95	)	)	PUNCT
ejpam-5428	281	96	(	(	PUNCT
ejpam-5428	281	97	1	1	NUM
ejpam-5428	281	98	λ	λ	NOUN
ejpam-5428	281	99	−	−	PROPN
ejpam-5428	281	100	1	1	NUM
ejpam-5428	281	101	)	)	PUNCT
ejpam-5428	281	102	<	<	X
ejpam-5428	281	103	(	(	PUNCT
ejpam-5428	281	104	1	1	NUM
ejpam-5428	281	105	λ	λ	NOUN
ejpam-5428	281	106	−	−	PROPN
ejpam-5428	281	107	1	1	NUM
ejpam-5428	281	108	)	)	PUNCT
ejpam-5428	281	109	.	.	PUNCT
ejpam-5428	282	1	(	(	PUNCT
ejpam-5428	282	2	20	20	NUM
ejpam-5428	282	3	)	)	PUNCT
ejpam-5428	282	4	on	on	ADP
ejpam-5428	282	5	the	the	DET
ejpam-5428	282	6	flip	flip	ADJ
ejpam-5428	282	7	side	side	NOUN
ejpam-5428	282	8	,	,	PUNCT
ejpam-5428	282	9	(	(	PUNCT
ejpam-5428	282	10	1	1	NUM
ejpam-5428	282	11	mz(δn	mz(δn	PROPN
ejpam-5428	282	12	,	,	PUNCT
ejpam-5428	282	13	δm	δm	PROPN
ejpam-5428	282	14	,	,	PUNCT
ejpam-5428	282	15	l	l	NOUN
ejpam-5428	282	16	)	)	PUNCT
ejpam-5428	282	17	−	−	PROPN
ejpam-5428	282	18	1	1	X
ejpam-5428	282	19	)	)	PUNCT
ejpam-5428	282	20	≤	≤	NOUN
ejpam-5428	282	21	(	(	PUNCT
ejpam-5428	282	22	1	1	NUM
ejpam-5428	282	23	mz(δn	mz(δn	PROPN
ejpam-5428	282	24	,	,	PUNCT
ejpam-5428	282	25	δn+1	δn+1	PROPN
ejpam-5428	282	26	,	,	PUNCT
ejpam-5428	282	27	l	l	NOUN
ejpam-5428	282	28	)	)	PUNCT
ejpam-5428	282	29	−	−	PROPN
ejpam-5428	282	30	1	1	NUM
ejpam-5428	282	31	)	)	PUNCT
ejpam-5428	283	1	+	+	CCONJ
ejpam-5428	283	2	(	(	PUNCT
ejpam-5428	283	3	1	1	NUM
ejpam-5428	283	4	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	283	5	,	,	PUNCT
ejpam-5428	283	6	δm	δm	PROPN
ejpam-5428	283	7	,	,	PUNCT
ejpam-5428	283	8	l	l	NOUN
ejpam-5428	283	9	)	)	PUNCT
ejpam-5428	283	10	−	−	PROPN
ejpam-5428	283	11	1	1	X
ejpam-5428	283	12	)	)	PUNCT
ejpam-5428	283	13	≤	≤	NOUN
ejpam-5428	283	14	(	(	PUNCT
ejpam-5428	283	15	1	1	NUM
ejpam-5428	283	16	mz(δn	mz(δn	PROPN
ejpam-5428	283	17	,	,	PUNCT
ejpam-5428	283	18	δn+1	δn+1	PROPN
ejpam-5428	283	19	,	,	PUNCT
ejpam-5428	283	20	l	l	NOUN
ejpam-5428	283	21	)	)	PUNCT
ejpam-5428	283	22	−	−	PROPN
ejpam-5428	283	23	1	1	NUM
ejpam-5428	283	24	)	)	PUNCT
ejpam-5428	284	1	+	+	CCONJ
ejpam-5428	284	2	(	(	PUNCT
ejpam-5428	284	3	1	1	NUM
ejpam-5428	284	4	mz(δn+1	mz(δn+1	NOUN
ejpam-5428	284	5	,	,	PUNCT
ejpam-5428	284	6	δm+1	δm+1	PROPN
ejpam-5428	284	7	,	,	PUNCT
ejpam-5428	284	8	l	l	NOUN
ejpam-5428	284	9	)	)	PUNCT
ejpam-5428	284	10	−	−	PROPN
ejpam-5428	284	11	1	1	NUM
ejpam-5428	284	12	)	)	PUNCT
ejpam-5428	284	13	+	+	CCONJ
ejpam-5428	284	14	(	(	PUNCT
ejpam-5428	284	15	1	1	NUM
ejpam-5428	284	16	mz(δm+1	mz(δm+1	PROPN
ejpam-5428	284	17	,	,	PUNCT
ejpam-5428	284	18	δm	δm	PROPN
ejpam-5428	284	19	,	,	PUNCT
ejpam-5428	284	20	l	l	NOUN
ejpam-5428	284	21	)	)	PUNCT
ejpam-5428	284	22	−	−	PROPN
ejpam-5428	284	23	1	1	NUM
ejpam-5428	284	24	)	)	PUNCT
ejpam-5428	284	25	.	.	PUNCT
ejpam-5428	285	1	taking	take	VERB
ejpam-5428	285	2	limit	limit	NOUN
ejpam-5428	285	3	as	as	ADP
ejpam-5428	285	4	n	n	X
ejpam-5428	285	5	,	,	PUNCT
ejpam-5428	285	6	m	m	PROPN
ejpam-5428	285	7	→	→	SYM
ejpam-5428	285	8	+	+	ADJ
ejpam-5428	285	9	∞	∞	NUM
ejpam-5428	285	10	and	and	CCONJ
ejpam-5428	285	11	using	use	VERB
ejpam-5428	285	12	(	(	PUNCT
ejpam-5428	285	13	19	19	NUM
ejpam-5428	285	14	,	,	PUNCT
ejpam-5428	285	15	20	20	NUM
ejpam-5428	285	16	)	)	PUNCT
ejpam-5428	285	17	,	,	PUNCT
ejpam-5428	285	18	lim	lim	PROPN
ejpam-5428	285	19	n	n	CCONJ
ejpam-5428	285	20	,	,	PUNCT
ejpam-5428	285	21	m→+∞	m→+∞	PROPN
ejpam-5428	285	22	(	(	PUNCT
ejpam-5428	285	23	1	1	NUM
ejpam-5428	285	24	mz(δn	mz(δn	PROPN
ejpam-5428	285	25	,	,	PUNCT
ejpam-5428	285	26	δm	δm	PROPN
ejpam-5428	285	27	,	,	PUNCT
ejpam-5428	285	28	l	l	NOUN
ejpam-5428	285	29	)	)	PUNCT
ejpam-5428	285	30	−	−	PROPN
ejpam-5428	285	31	1	1	X
ejpam-5428	285	32	)	)	PUNCT
ejpam-5428	285	33	≤	≤	NOUN
ejpam-5428	285	34	lim	lim	PROPN
ejpam-5428	285	35	n	n	CCONJ
ejpam-5428	285	36	,	,	PUNCT
ejpam-5428	285	37	m→+∞	m→+∞	PROPN
ejpam-5428	285	38	α(δn	α(δn	PROPN
ejpam-5428	285	39	,	,	PUNCT
ejpam-5428	285	40	δm	δm	PROPN
ejpam-5428	285	41	,	,	PUNCT
ejpam-5428	285	42	l	l	NOUN
ejpam-5428	285	43	)	)	PUNCT
ejpam-5428	285	44	(	(	PUNCT
ejpam-5428	285	45	1	1	NUM
ejpam-5428	285	46	mz(lδn	mz(lδn	PROPN
ejpam-5428	285	47	,	,	PUNCT
ejpam-5428	285	48	lδm	lδm	NOUN
ejpam-5428	285	49	,	,	PUNCT
ejpam-5428	285	50	l	l	NOUN
ejpam-5428	285	51	)	)	PUNCT
ejpam-5428	285	52	−	−	PROPN
ejpam-5428	285	53	1	1	X
ejpam-5428	285	54	)	)	PUNCT
ejpam-5428	285	55	≤	≤	NOUN
ejpam-5428	285	56	lim	lim	PROPN
ejpam-5428	285	57	n	n	CCONJ
ejpam-5428	285	58	,	,	PUNCT
ejpam-5428	285	59	m→+∞	m→+∞	PROPN
ejpam-5428	285	60	β	β	X
ejpam-5428	285	61	(	(	PUNCT
ejpam-5428	285	62	1	1	NUM
ejpam-5428	285	63	mz(δn	mz(δn	PROPN
ejpam-5428	285	64	,	,	PUNCT
ejpam-5428	285	65	δm	δm	PROPN
ejpam-5428	285	66	,	,	PUNCT
ejpam-5428	285	67	l	l	NOUN
ejpam-5428	285	68	)	)	PUNCT
ejpam-5428	285	69	−	−	PROPN
ejpam-5428	285	70	1	1	X
ejpam-5428	285	71	)	)	PUNCT
ejpam-5428	285	72	lim	lim	PROPN
ejpam-5428	285	73	n	n	CCONJ
ejpam-5428	285	74	,	,	PUNCT
ejpam-5428	285	75	m→+∞	m→+∞	PROPN
ejpam-5428	285	76	(	(	PUNCT
ejpam-5428	285	77	1	1	NUM
ejpam-5428	285	78	mz(δn	mz(δn	PROPN
ejpam-5428	285	79	,	,	PUNCT
ejpam-5428	285	80	δm	δm	PROPN
ejpam-5428	285	81	,	,	PUNCT
ejpam-5428	285	82	l	l	NOUN
ejpam-5428	285	83	)	)	PUNCT
ejpam-5428	285	84	−	−	PROPN
ejpam-5428	285	85	1	1	NUM
ejpam-5428	285	86	)	)	PUNCT
ejpam-5428	285	87	<	<	X
ejpam-5428	285	88	lim	lim	PROPN
ejpam-5428	285	89	n	n	PROPN
ejpam-5428	285	90	,	,	PUNCT
ejpam-5428	285	91	m→+∞	m→+∞	PROPN
ejpam-5428	285	92	(	(	PUNCT
ejpam-5428	285	93	1	1	NUM
ejpam-5428	285	94	mz(δn	mz(δn	PROPN
ejpam-5428	285	95	,	,	PUNCT
ejpam-5428	285	96	δm	δm	PROPN
ejpam-5428	285	97	,	,	PUNCT
ejpam-5428	285	98	l	l	NOUN
ejpam-5428	285	99	)	)	PUNCT
ejpam-5428	285	100	−	−	PROPN
ejpam-5428	285	101	1	1	NUM
ejpam-5428	285	102	)	)	PUNCT
ejpam-5428	285	103	1	1	NUM
ejpam-5428	285	104	λ	λ	NOUN
ejpam-5428	285	105	−	−	PROPN
ejpam-5428	285	106	1	1	NUM
ejpam-5428	285	107	≤	≤	NOUN
ejpam-5428	285	108	lim	lim	PROPN
ejpam-5428	285	109	n	n	CCONJ
ejpam-5428	285	110	,	,	PUNCT
ejpam-5428	285	111	m→+∞	m→+∞	PROPN
ejpam-5428	285	112	(	(	PUNCT
ejpam-5428	285	113	1	1	NUM
ejpam-5428	285	114	mz(lδn	mz(lδn	PROPN
ejpam-5428	285	115	,	,	PUNCT
ejpam-5428	285	116	lδm	lδm	NOUN
ejpam-5428	285	117	,	,	PUNCT
ejpam-5428	285	118	l	l	NOUN
ejpam-5428	285	119	)	)	PUNCT
ejpam-5428	285	120	−	−	PROPN
ejpam-5428	285	121	1	1	X
ejpam-5428	285	122	)	)	PUNCT
ejpam-5428	285	123	≤	≤	NOUN
ejpam-5428	285	124	lim	lim	PROPN
ejpam-5428	285	125	n	n	CCONJ
ejpam-5428	285	126	,	,	PUNCT
ejpam-5428	285	127	m→+∞	m→+∞	PROPN
ejpam-5428	285	128	β	β	X
ejpam-5428	285	129	(	(	PUNCT
ejpam-5428	285	130	1	1	NUM
ejpam-5428	285	131	mz(δn	mz(δn	PROPN
ejpam-5428	285	132	,	,	PUNCT
ejpam-5428	285	133	δm	δm	PROPN
ejpam-5428	285	134	,	,	PUNCT
ejpam-5428	285	135	l	l	NOUN
ejpam-5428	285	136	)	)	PUNCT
ejpam-5428	285	137	−	−	PROPN
ejpam-5428	285	138	1	1	NUM
ejpam-5428	285	139	)	)	PUNCT
ejpam-5428	285	140	(	(	PUNCT
ejpam-5428	285	141	1	1	NUM
ejpam-5428	285	142	λ	λ	NOUN
ejpam-5428	285	143	−	−	NOUN
ejpam-5428	285	144	1	1	NUM
ejpam-5428	285	145	)	)	PUNCT
ejpam-5428	285	146	<	<	X
ejpam-5428	285	147	1	1	NUM
ejpam-5428	285	148	λ	λ	SYM
ejpam-5428	285	149	−	−	PROPN
ejpam-5428	285	150	1	1	NUM
ejpam-5428	285	151	.	.	NOUN
ejpam-5428	285	152	which	which	PRON
ejpam-5428	285	153	suggest	suggest	VERB
ejpam-5428	285	154	that	that	SCONJ
ejpam-5428	285	155	lim	lim	PROPN
ejpam-5428	285	156	n	n	CCONJ
ejpam-5428	285	157	,	,	PUNCT
ejpam-5428	285	158	m→+∞	m→+∞	PROPN
ejpam-5428	285	159	β	β	X
ejpam-5428	285	160	(	(	PUNCT
ejpam-5428	285	161	1	1	NUM
ejpam-5428	285	162	mz(δn	mz(δn	PROPN
ejpam-5428	285	163	,	,	PUNCT
ejpam-5428	285	164	δm	δm	PROPN
ejpam-5428	285	165	,	,	PUNCT
ejpam-5428	285	166	l	l	NOUN
ejpam-5428	285	167	)	)	PUNCT
ejpam-5428	285	168	−	−	PROPN
ejpam-5428	285	169	1	1	NUM
ejpam-5428	285	170	)	)	PUNCT
ejpam-5428	285	171	=	=	SYM
ejpam-5428	285	172	1	1	NUM
ejpam-5428	285	173	⇒	⇒	NOUN
ejpam-5428	285	174	lim	lim	PROPN
ejpam-5428	285	175	n	n	CCONJ
ejpam-5428	285	176	,	,	PUNCT
ejpam-5428	285	177	m→+∞	m→+∞	PROPN
ejpam-5428	285	178	1	1	NUM
ejpam-5428	285	179	mz(δn	mz(δn	PROPN
ejpam-5428	285	180	,	,	PUNCT
ejpam-5428	285	181	δm	δm	PROPN
ejpam-5428	285	182	,	,	PUNCT
ejpam-5428	285	183	l	l	NOUN
ejpam-5428	285	184	)	)	PUNCT
ejpam-5428	286	1	=	=	SYM
ejpam-5428	286	2	1	1	NUM
ejpam-5428	286	3	,	,	PUNCT
ejpam-5428	286	4	v.	v.	PROPN
ejpam-5428	286	5	chandra	chandra	PROPN
ejpam-5428	286	6	,	,	PUNCT
ejpam-5428	286	7	u.	u.	PROPN
ejpam-5428	286	8	d.	d.	PROPN
ejpam-5428	286	9	patel	patel	PROPN
ejpam-5428	286	10	,	,	PUNCT
ejpam-5428	286	11	s.	s.	PROPN
ejpam-5428	286	12	radenović	radenović	PROPN
ejpam-5428	286	13	/	/	SYM
ejpam-5428	286	14	eur	eur	PROPN
ejpam-5428	286	15	.	.	PUNCT
ejpam-5428	287	1	j.	j.	PROPN
ejpam-5428	287	2	pure	pure	PROPN
ejpam-5428	287	3	appl	appl	PROPN
ejpam-5428	287	4	.	.	PROPN
ejpam-5428	287	5	math	math	PROPN
ejpam-5428	287	6	,	,	PUNCT
ejpam-5428	287	7	17	17	NUM
ejpam-5428	287	8	(	(	PUNCT
ejpam-5428	287	9	4	4	NUM
ejpam-5428	287	10	)	)	PUNCT
ejpam-5428	287	11	(	(	PUNCT
ejpam-5428	287	12	2024	2024	NUM
ejpam-5428	287	13	)	)	PUNCT
ejpam-5428	287	14	,	,	PUNCT
ejpam-5428	287	15	2384	2384	NUM
ejpam-5428	287	16	-	-	SYM
ejpam-5428	287	17	2404	2404	NUM
ejpam-5428	287	18	2398	2398	NUM
ejpam-5428	287	19	a	a	DET
ejpam-5428	287	20	contradiction	contradiction	NOUN
ejpam-5428	287	21	.	.	PUNCT
ejpam-5428	288	1	thus	thus	ADV
ejpam-5428	288	2	,	,	PUNCT
ejpam-5428	288	3	{	{	PUNCT
ejpam-5428	288	4	δn	δn	NOUN
ejpam-5428	288	5	}	}	PUNCT
ejpam-5428	288	6	is	be	AUX
ejpam-5428	288	7	a	a	DET
ejpam-5428	288	8	g	g	NOUN
ejpam-5428	288	9	-	-	PUNCT
ejpam-5428	288	10	cauchy	cauchy	ADJ
ejpam-5428	288	11	sequence	sequence	NOUN
ejpam-5428	288	12	.	.	PUNCT
ejpam-5428	289	1	since	since	SCONJ
ejpam-5428	289	2	ȳ	ȳ	PROPN
ejpam-5428	289	3	is	be	AUX
ejpam-5428	289	4	a	a	DET
ejpam-5428	289	5	g	g	NOUN
ejpam-5428	289	6	-	-	PUNCT
ejpam-5428	289	7	complete	complete	ADJ
ejpam-5428	289	8	then	then	ADV
ejpam-5428	289	9	there	there	PRON
ejpam-5428	289	10	exists	exist	VERB
ejpam-5428	289	11	u	u	PROPN
ejpam-5428	289	12	∈	∈	PROPN
ejpam-5428	289	13	ȳ	ȳ	NOUN
ejpam-5428	289	14	such	such	ADJ
ejpam-5428	289	15	that	that	SCONJ
ejpam-5428	289	16	lim	lim	PROPN
ejpam-5428	289	17	n→+∞	n→+∞	PROPN
ejpam-5428	289	18	mz(δn	mz(δn	PROPN
ejpam-5428	289	19	,	,	PUNCT
ejpam-5428	289	20	u	u	NOUN
ejpam-5428	289	21	,	,	PUNCT
ejpam-5428	289	22	l	l	NOUN
ejpam-5428	289	23	)	)	PUNCT
ejpam-5428	289	24	=	=	SYM
ejpam-5428	289	25	1	1	X
ejpam-5428	289	26	.	.	PUNCT
ejpam-5428	289	27	(	(	PUNCT
ejpam-5428	289	28	21	21	NUM
ejpam-5428	289	29	)	)	PUNCT
ejpam-5428	289	30	next	next	ADV
ejpam-5428	289	31	to	to	PART
ejpam-5428	289	32	prove	prove	VERB
ejpam-5428	289	33	fixed	fixed	ADJ
ejpam-5428	289	34	point	point	NOUN
ejpam-5428	289	35	of	of	ADP
ejpam-5428	289	36	map	map	NOUN
ejpam-5428	289	37	l	l	NOUN
ejpam-5428	289	38	,	,	PUNCT
ejpam-5428	289	39	we	we	PRON
ejpam-5428	289	40	require	require	VERB
ejpam-5428	289	41	property	property	NOUN
ejpam-5428	289	42	(	(	PUNCT
ejpam-5428	289	43	g2	g2	PROPN
ejpam-5428	289	44	)	)	PUNCT
ejpam-5428	289	45	,	,	PUNCT
ejpam-5428	289	46	mz(δn	mz(δn	PROPN
ejpam-5428	289	47	,	,	PUNCT
ejpam-5428	289	48	lδn	lδn	PROPN
ejpam-5428	289	49	,	,	PUNCT
ejpam-5428	289	50	l	l	NOUN
ejpam-5428	289	51	)	)	PUNCT
ejpam-5428	289	52	>	>	X
ejpam-5428	289	53	q	q	X
ejpam-5428	289	54	·	·	PUNCT
ejpam-5428	289	55	mz(δn−1	mz(δn−1	PROPN
ejpam-5428	289	56	,	,	PUNCT
ejpam-5428	289	57	u	u	NOUN
ejpam-5428	289	58	,	,	PUNCT
ejpam-5428	289	59	l	l	NOUN
ejpam-5428	289	60	)	)	PUNCT
ejpam-5428	289	61	implies	imply	VERB
ejpam-5428	289	62	α(δn−1	α(δn−1	PROPN
ejpam-5428	289	63	,	,	PUNCT
ejpam-5428	289	64	u	u	NOUN
ejpam-5428	289	65	,	,	PUNCT
ejpam-5428	289	66	l	l	NOUN
ejpam-5428	289	67	)	)	PUNCT
ejpam-5428	289	68	(	(	PUNCT
ejpam-5428	289	69	1	1	NUM
ejpam-5428	289	70	mz(δn	mz(δn	X
ejpam-5428	289	71	,	,	PUNCT
ejpam-5428	289	72	lu	lu	PROPN
ejpam-5428	289	73	,	,	PUNCT
ejpam-5428	289	74	l	l	NOUN
ejpam-5428	289	75	)	)	PUNCT
ejpam-5428	290	1	−	−	PROPN
ejpam-5428	290	2	1	1	NUM
ejpam-5428	290	3	)	)	PUNCT
ejpam-5428	290	4	≤	≤	NOUN
ejpam-5428	291	1	β	β	X
ejpam-5428	291	2	(	(	PUNCT
ejpam-5428	291	3	1	1	NUM
ejpam-5428	291	4	mz(δn−1	mz(δn−1	PROPN
ejpam-5428	291	5	,	,	PUNCT
ejpam-5428	291	6	u	u	NOUN
ejpam-5428	291	7	,	,	PUNCT
ejpam-5428	291	8	l	l	NOUN
ejpam-5428	291	9	)	)	PUNCT
ejpam-5428	291	10	−	−	PROPN
ejpam-5428	291	11	1	1	NUM
ejpam-5428	291	12	)	)	PUNCT
ejpam-5428	291	13	(	(	PUNCT
ejpam-5428	291	14	1	1	NUM
ejpam-5428	291	15	mz(δn−1	mz(δn−1	ADJ
ejpam-5428	291	16	,	,	PUNCT
ejpam-5428	291	17	u	u	NOUN
ejpam-5428	291	18	,	,	PUNCT
ejpam-5428	291	19	l	l	NOUN
ejpam-5428	291	20	)	)	PUNCT
ejpam-5428	291	21	−	−	PROPN
ejpam-5428	291	22	1	1	NUM
ejpam-5428	291	23	)	)	PUNCT
ejpam-5428	291	24	(	(	PUNCT
ejpam-5428	291	25	1	1	NUM
ejpam-5428	291	26	mz(δn	mz(δn	X
ejpam-5428	291	27	,	,	PUNCT
ejpam-5428	291	28	lu	lu	PROPN
ejpam-5428	291	29	,	,	PUNCT
ejpam-5428	291	30	l	l	NOUN
ejpam-5428	291	31	)	)	PUNCT
ejpam-5428	291	32	−	−	PROPN
ejpam-5428	291	33	1	1	X
ejpam-5428	291	34	)	)	PUNCT
ejpam-5428	291	35	≤	≤	NOUN
ejpam-5428	291	36	α(δn−1	α(δn−1	NOUN
ejpam-5428	291	37	,	,	PUNCT
ejpam-5428	291	38	u	u	NOUN
ejpam-5428	291	39	,	,	PUNCT
ejpam-5428	291	40	l	l	NOUN
ejpam-5428	291	41	)	)	PUNCT
ejpam-5428	291	42	(	(	PUNCT
ejpam-5428	291	43	1	1	NUM
ejpam-5428	291	44	mz(δn	mz(δn	X
ejpam-5428	291	45	,	,	PUNCT
ejpam-5428	291	46	lu	lu	PROPN
ejpam-5428	291	47	,	,	PUNCT
ejpam-5428	291	48	l	l	NOUN
ejpam-5428	291	49	)	)	PUNCT
ejpam-5428	291	50	−	−	PROPN
ejpam-5428	291	51	1	1	NUM
ejpam-5428	291	52	)	)	PUNCT
ejpam-5428	291	53	≤	≤	NOUN
ejpam-5428	291	54	β	β	X
ejpam-5428	291	55	(	(	PUNCT
ejpam-5428	291	56	1	1	NUM
ejpam-5428	291	57	mz(δn−1	mz(δn−1	PROPN
ejpam-5428	291	58	,	,	PUNCT
ejpam-5428	291	59	u	u	NOUN
ejpam-5428	291	60	,	,	PUNCT
ejpam-5428	291	61	l	l	NOUN
ejpam-5428	291	62	)	)	PUNCT
ejpam-5428	291	63	−	−	PROPN
ejpam-5428	291	64	1	1	NUM
ejpam-5428	291	65	)	)	PUNCT
ejpam-5428	291	66	(	(	PUNCT
ejpam-5428	291	67	1	1	NUM
ejpam-5428	291	68	mz(δn−1	mz(δn−1	ADJ
ejpam-5428	291	69	,	,	PUNCT
ejpam-5428	291	70	u	u	NOUN
ejpam-5428	291	71	,	,	PUNCT
ejpam-5428	291	72	l	l	NOUN
ejpam-5428	291	73	)	)	PUNCT
ejpam-5428	291	74	−	−	PROPN
ejpam-5428	291	75	1	1	NUM
ejpam-5428	291	76	)	)	PUNCT
ejpam-5428	291	77	.	.	PUNCT
ejpam-5428	292	1	put	put	VERB
ejpam-5428	292	2	limit	limit	NOUN
ejpam-5428	292	3	as	as	ADP
ejpam-5428	292	4	n	n	PROPN
ejpam-5428	292	5	→	→	SYM
ejpam-5428	292	6	+	+	PROPN
ejpam-5428	292	7	∞	∞	PROPN
ejpam-5428	292	8	,	,	PUNCT
ejpam-5428	292	9	lim	lim	PROPN
ejpam-5428	292	10	n→+∞	n→+∞	PROPN
ejpam-5428	292	11	(	(	PUNCT
ejpam-5428	292	12	1	1	NUM
ejpam-5428	292	13	mz(δn−1,lu	mz(δn−1,lu	X
ejpam-5428	292	14	,	,	PUNCT
ejpam-5428	292	15	l	l	NOUN
ejpam-5428	292	16	)	)	PUNCT
ejpam-5428	293	1	−	−	PROPN
ejpam-5428	293	2	1	1	X
ejpam-5428	293	3	)	)	PUNCT
ejpam-5428	293	4	≤	≤	NOUN
ejpam-5428	293	5	0	0	NUM
ejpam-5428	293	6	.	.	PUNCT
ejpam-5428	294	1	so	so	ADV
ejpam-5428	294	2	,	,	PUNCT
ejpam-5428	294	3	mz(u	mz(u	ADV
ejpam-5428	294	4	,	,	PUNCT
ejpam-5428	294	5	lu	lu	PROPN
ejpam-5428	294	6	,	,	PUNCT
ejpam-5428	294	7	l	l	NOUN
ejpam-5428	294	8	)	)	PUNCT
ejpam-5428	294	9	=	=	SYM
ejpam-5428	294	10	1	1	NUM
ejpam-5428	294	11	that	that	PRON
ejpam-5428	294	12	is	be	AUX
ejpam-5428	294	13	lu	lu	PROPN
ejpam-5428	295	1	=	=	PUNCT
ejpam-5428	295	2	u.	u.	PROPN
ejpam-5428	295	3	finally	finally	ADV
ejpam-5428	295	4	,	,	PUNCT
ejpam-5428	295	5	we	we	PRON
ejpam-5428	295	6	require	require	VERB
ejpam-5428	295	7	to	to	PART
ejpam-5428	295	8	show	show	VERB
ejpam-5428	295	9	uniqueness	uniqueness	NOUN
ejpam-5428	295	10	of	of	ADP
ejpam-5428	295	11	the	the	DET
ejpam-5428	295	12	fixed	fix	VERB
ejpam-5428	295	13	point	point	NOUN
ejpam-5428	295	14	.	.	PUNCT
ejpam-5428	296	1	consider	consider	VERB
ejpam-5428	296	2	another	another	DET
ejpam-5428	296	3	fixed	fix	VERB
ejpam-5428	296	4	point	point	NOUN
ejpam-5428	296	5	v	v	ADP
ejpam-5428	296	6	such	such	ADJ
ejpam-5428	296	7	that	that	DET
ejpam-5428	296	8	u	u	NOUN
ejpam-5428	296	9	̸=	̸=	PROPN
ejpam-5428	296	10	v	v	NUM
ejpam-5428	296	11	,	,	PUNCT
ejpam-5428	296	12	it	it	PRON
ejpam-5428	296	13	means	mean	VERB
ejpam-5428	296	14	mz(u	mz(u	PROPN
ejpam-5428	296	15	,	,	PUNCT
ejpam-5428	296	16	v	v	NOUN
ejpam-5428	296	17	,	,	PUNCT
ejpam-5428	296	18	l	l	NOUN
ejpam-5428	296	19	)	)	PUNCT
ejpam-5428	296	20	<	<	X
ejpam-5428	297	1	1	1	X
ejpam-5428	297	2	.	.	X
ejpam-5428	297	3	using	use	VERB
ejpam-5428	297	4	(	(	PUNCT
ejpam-5428	297	5	g2	g2	PROPN
ejpam-5428	297	6	)	)	PUNCT
ejpam-5428	297	7	property	property	NOUN
ejpam-5428	297	8	,	,	PUNCT
ejpam-5428	297	9	mz(u	mz(u	PROPN
ejpam-5428	297	10	,	,	PUNCT
ejpam-5428	297	11	u	u	NOUN
ejpam-5428	297	12	,	,	PUNCT
ejpam-5428	297	13	l	l	NOUN
ejpam-5428	297	14	)	)	PUNCT
ejpam-5428	297	15	=	=	PUNCT
ejpam-5428	297	16	mz(u	mz(u	PROPN
ejpam-5428	297	17	,	,	PUNCT
ejpam-5428	297	18	lu	lu	PROPN
ejpam-5428	297	19	,	,	PUNCT
ejpam-5428	297	20	l	l	NOUN
ejpam-5428	297	21	)	)	PUNCT
ejpam-5428	297	22	>	>	X
ejpam-5428	297	23	q	q	X
ejpam-5428	297	24	·	·	PUNCT
ejpam-5428	297	25	mz(u	mz(u	PROPN
ejpam-5428	297	26	,	,	PUNCT
ejpam-5428	297	27	v	v	NOUN
ejpam-5428	297	28	,	,	PUNCT
ejpam-5428	297	29	l	l	NOUN
ejpam-5428	297	30	)	)	PUNCT
ejpam-5428	297	31	implies	imply	VERB
ejpam-5428	297	32	α(u	α(u	PROPN
ejpam-5428	297	33	,	,	PUNCT
ejpam-5428	297	34	v	v	NOUN
ejpam-5428	297	35	,	,	PUNCT
ejpam-5428	297	36	l	l	NOUN
ejpam-5428	297	37	)	)	PUNCT
ejpam-5428	297	38	(	(	PUNCT
ejpam-5428	297	39	1	1	NUM
ejpam-5428	297	40	mz(u	mz(u	ADJ
ejpam-5428	297	41	,	,	PUNCT
ejpam-5428	297	42	v	v	NOUN
ejpam-5428	297	43	,	,	PUNCT
ejpam-5428	297	44	l	l	NOUN
ejpam-5428	297	45	)	)	PUNCT
ejpam-5428	297	46	−	−	PROPN
ejpam-5428	297	47	1	1	NUM
ejpam-5428	297	48	)	)	PUNCT
ejpam-5428	297	49	≤	≤	NOUN
ejpam-5428	298	1	β	β	X
ejpam-5428	298	2	(	(	PUNCT
ejpam-5428	298	3	1	1	NUM
ejpam-5428	298	4	mz(u	mz(u	ADJ
ejpam-5428	298	5	,	,	PUNCT
ejpam-5428	298	6	v	v	NOUN
ejpam-5428	298	7	,	,	PUNCT
ejpam-5428	298	8	l	l	NOUN
ejpam-5428	298	9	)	)	PUNCT
ejpam-5428	298	10	−	−	PROPN
ejpam-5428	298	11	1	1	NUM
ejpam-5428	298	12	)	)	PUNCT
ejpam-5428	298	13	(	(	PUNCT
ejpam-5428	298	14	1	1	NUM
ejpam-5428	298	15	mz(u	mz(u	ADJ
ejpam-5428	298	16	,	,	PUNCT
ejpam-5428	298	17	v	v	NOUN
ejpam-5428	298	18	,	,	PUNCT
ejpam-5428	298	19	l	l	NOUN
ejpam-5428	298	20	)	)	PUNCT
ejpam-5428	298	21	−	−	PROPN
ejpam-5428	298	22	1	1	NUM
ejpam-5428	298	23	)	)	PUNCT
ejpam-5428	298	24	1	1	NUM
ejpam-5428	298	25	mz(u	mz(u	NOUN
ejpam-5428	298	26	,	,	PUNCT
ejpam-5428	298	27	v	v	NOUN
ejpam-5428	298	28	,	,	PUNCT
ejpam-5428	298	29	l	l	NOUN
ejpam-5428	298	30	)	)	PUNCT
ejpam-5428	298	31	−	−	PROPN
ejpam-5428	298	32	1	1	NUM
ejpam-5428	298	33	≤	≤	NOUN
ejpam-5428	298	34	α(u	α(u	NOUN
ejpam-5428	298	35	,	,	PUNCT
ejpam-5428	298	36	v	v	NOUN
ejpam-5428	298	37	,	,	PUNCT
ejpam-5428	298	38	l	l	NOUN
ejpam-5428	298	39	)	)	PUNCT
ejpam-5428	298	40	(	(	PUNCT
ejpam-5428	298	41	1	1	NUM
ejpam-5428	298	42	mz(u	mz(u	ADJ
ejpam-5428	298	43	,	,	PUNCT
ejpam-5428	298	44	v	v	NOUN
ejpam-5428	298	45	,	,	PUNCT
ejpam-5428	298	46	l	l	NOUN
ejpam-5428	298	47	)	)	PUNCT
ejpam-5428	298	48	−	−	PROPN
ejpam-5428	298	49	1	1	NUM
ejpam-5428	298	50	)	)	PUNCT
ejpam-5428	298	51	≤	≤	NOUN
ejpam-5428	298	52	β	β	X
ejpam-5428	298	53	(	(	PUNCT
ejpam-5428	298	54	1	1	NUM
ejpam-5428	298	55	mz(u	mz(u	ADJ
ejpam-5428	298	56	,	,	PUNCT
ejpam-5428	298	57	v	v	NOUN
ejpam-5428	298	58	,	,	PUNCT
ejpam-5428	298	59	l	l	NOUN
ejpam-5428	298	60	)	)	PUNCT
ejpam-5428	298	61	−	−	PROPN
ejpam-5428	298	62	1	1	NUM
ejpam-5428	298	63	)	)	PUNCT
ejpam-5428	298	64	(	(	PUNCT
ejpam-5428	298	65	1	1	NUM
ejpam-5428	298	66	mz(u	mz(u	ADJ
ejpam-5428	298	67	,	,	PUNCT
ejpam-5428	298	68	v	v	NOUN
ejpam-5428	298	69	,	,	PUNCT
ejpam-5428	298	70	l	l	NOUN
ejpam-5428	298	71	)	)	PUNCT
ejpam-5428	298	72	−	−	PROPN
ejpam-5428	298	73	1	1	NUM
ejpam-5428	298	74	)	)	PUNCT
ejpam-5428	298	75	<	<	X
ejpam-5428	298	76	1	1	NUM
ejpam-5428	298	77	mz(u	mz(u	PROPN
ejpam-5428	298	78	,	,	PUNCT
ejpam-5428	298	79	v	v	NOUN
ejpam-5428	298	80	,	,	PUNCT
ejpam-5428	298	81	l	l	NOUN
ejpam-5428	298	82	)	)	PUNCT
ejpam-5428	298	83	−	−	PROPN
ejpam-5428	298	84	1	1	NUM
ejpam-5428	298	85	,	,	PUNCT
ejpam-5428	298	86	a	a	DET
ejpam-5428	298	87	contradiction	contradiction	NOUN
ejpam-5428	298	88	.	.	PUNCT
ejpam-5428	299	1	hence	hence	ADV
ejpam-5428	299	2	,	,	PUNCT
ejpam-5428	299	3	u	u	PROPN
ejpam-5428	299	4	is	be	AUX
ejpam-5428	299	5	a	a	DET
ejpam-5428	299	6	unique	unique	ADJ
ejpam-5428	299	7	fixed	fix	VERB
ejpam-5428	299	8	point	point	NOUN
ejpam-5428	299	9	for	for	ADP
ejpam-5428	299	10	self	self	NOUN
ejpam-5428	299	11	map	map	NOUN
ejpam-5428	299	12	l.	l.	PROPN
ejpam-5428	299	13	remark	remark	PROPN
ejpam-5428	299	14	1	1	NUM
ejpam-5428	299	15	.	.	PUNCT
ejpam-5428	300	1	if	if	SCONJ
ejpam-5428	300	2	α(δ	α(δ	PROPN
ejpam-5428	300	3	,	,	PUNCT
ejpam-5428	300	4	γ	γ	X
ejpam-5428	300	5	,	,	PUNCT
ejpam-5428	300	6	l	l	NOUN
ejpam-5428	300	7	)	)	PUNCT
ejpam-5428	300	8	=	=	SYM
ejpam-5428	300	9	1	1	NUM
ejpam-5428	300	10	in	in	ADP
ejpam-5428	300	11	definition	definition	NOUN
ejpam-5428	300	12	(	(	PUNCT
ejpam-5428	300	13	10	10	NUM
ejpam-5428	300	14	)	)	PUNCT
ejpam-5428	300	15	,	,	PUNCT
ejpam-5428	300	16	then	then	ADV
ejpam-5428	300	17	mapping	mapping	NOUN
ejpam-5428	300	18	l	l	NOUN
ejpam-5428	300	19	becomes	become	VERB
ejpam-5428	300	20	a	a	DET
ejpam-5428	300	21	suzuki	suzuki	NOUN
ejpam-5428	300	22	geraghty	geraghty	PROPN
ejpam-5428	300	23	type	type	PROPN
ejpam-5428	300	24	-	-	PUNCT
ejpam-5428	300	25	ii	ii	NOUN
ejpam-5428	300	26	contractive	contractive	ADJ
ejpam-5428	300	27	map	map	NOUN
ejpam-5428	300	28	.	.	PUNCT
ejpam-5428	301	1	corollary	corollary	ADJ
ejpam-5428	301	2	1	1	PROPN
ejpam-5428	301	3	.	.	PUNCT
ejpam-5428	302	1	suppose	suppose	VERB
ejpam-5428	302	2	(	(	PUNCT
ejpam-5428	302	3	ȳ,mz	ȳ,mz	NUM
ejpam-5428	302	4	,	,	PUNCT
ejpam-5428	302	5	⋄	⋄	PROPN
ejpam-5428	302	6	)	)	PUNCT
ejpam-5428	302	7	is	be	AUX
ejpam-5428	302	8	a	a	DET
ejpam-5428	302	9	g	g	NOUN
ejpam-5428	302	10	-	-	PUNCT
ejpam-5428	302	11	complete	complete	ADJ
ejpam-5428	302	12	b	b	NOUN
ejpam-5428	302	13	-	-	PUNCT
ejpam-5428	302	14	fuzzy	fuzzy	ADJ
ejpam-5428	302	15	metric	metric	ADJ
ejpam-5428	302	16	space	space	NOUN
ejpam-5428	302	17	with	with	ADP
ejpam-5428	302	18	triangular	triangular	NOUN
ejpam-5428	302	19	fuzzy	fuzzy	ADJ
ejpam-5428	302	20	metric	metric	ADJ
ejpam-5428	302	21	and	and	CCONJ
ejpam-5428	302	22	a	a	DET
ejpam-5428	302	23	self	self	NOUN
ejpam-5428	302	24	map	map	NOUN
ejpam-5428	302	25	l	l	NOUN
ejpam-5428	302	26	defined	define	VERB
ejpam-5428	302	27	on	on	ADP
ejpam-5428	302	28	ȳ	ȳ	PROPN
ejpam-5428	302	29	is	be	AUX
ejpam-5428	302	30	a	a	DET
ejpam-5428	302	31	suzuki	suzuki	NOUN
ejpam-5428	302	32	geraghty	geraghty	PROPN
ejpam-5428	302	33	type	type	PROPN
ejpam-5428	302	34	-	-	PUNCT
ejpam-5428	302	35	ii	ii	NOUN
ejpam-5428	302	36	contractive	contractive	ADJ
ejpam-5428	302	37	map	map	NOUN
ejpam-5428	302	38	with	with	ADP
ejpam-5428	302	39	properties	property	NOUN
ejpam-5428	302	40	(	(	PUNCT
ejpam-5428	302	41	g1	g1	PROPN
ejpam-5428	302	42	)	)	PUNCT
ejpam-5428	302	43	and	and	CCONJ
ejpam-5428	302	44	(	(	PUNCT
ejpam-5428	302	45	g2	g2	PROPN
ejpam-5428	302	46	)	)	PUNCT
ejpam-5428	302	47	.	.	PUNCT
ejpam-5428	303	1	then	then	ADV
ejpam-5428	303	2	l	l	PROPN
ejpam-5428	303	3	has	have	VERB
ejpam-5428	303	4	a	a	DET
ejpam-5428	303	5	unique	unique	ADJ
ejpam-5428	303	6	fixed	fix	VERB
ejpam-5428	303	7	point	point	NOUN
ejpam-5428	303	8	.	.	PUNCT
ejpam-5428	304	1	now	now	ADV
ejpam-5428	304	2	we	we	PRON
ejpam-5428	304	3	present	present	VERB
ejpam-5428	304	4	another	another	DET
ejpam-5428	304	5	definition	definition	NOUN
ejpam-5428	304	6	which	which	PRON
ejpam-5428	304	7	is	be	AUX
ejpam-5428	304	8	not	not	PART
ejpam-5428	304	9	in	in	ADP
ejpam-5428	304	10	view	view	NOUN
ejpam-5428	304	11	of	of	ADP
ejpam-5428	304	12	suzuki	suzuki	NOUN
ejpam-5428	304	13	type	type	NOUN
ejpam-5428	304	14	.	.	PUNCT
ejpam-5428	305	1	definition	definition	NOUN
ejpam-5428	305	2	11	11	NUM
ejpam-5428	305	3	.	.	PUNCT
ejpam-5428	306	1	a	a	DET
ejpam-5428	306	2	triangular	triangular	NOUN
ejpam-5428	306	3	α	α	NOUN
ejpam-5428	306	4	-	-	ADJ
ejpam-5428	306	5	admissible	admissible	ADJ
ejpam-5428	306	6	self	self	NOUN
ejpam-5428	306	7	mapping	mapping	NOUN
ejpam-5428	306	8	l	l	NOUN
ejpam-5428	306	9	defined	define	VERB
ejpam-5428	306	10	on	on	ADP
ejpam-5428	306	11	a	a	DET
ejpam-5428	306	12	b	b	NOUN
ejpam-5428	306	13	-	-	PUNCT
ejpam-5428	306	14	fuzzy	fuzzy	ADJ
ejpam-5428	306	15	metric	metric	ADJ
ejpam-5428	306	16	space	space	NOUN
ejpam-5428	306	17	(	(	PUNCT
ejpam-5428	306	18	ȳ,mz	ȳ,mz	NUM
ejpam-5428	306	19	,	,	PUNCT
ejpam-5428	306	20	⋄	⋄	PROPN
ejpam-5428	306	21	)	)	PUNCT
ejpam-5428	306	22	is	be	AUX
ejpam-5428	306	23	called	call	VERB
ejpam-5428	306	24	a	a	DET
ejpam-5428	306	25	α	α	NOUN
ejpam-5428	306	26	-	-	PUNCT
ejpam-5428	306	27	geraghty	geraghty	VERB
ejpam-5428	306	28	type	type	NOUN
ejpam-5428	306	29	-	-	PUNCT
ejpam-5428	306	30	ii	ii	NOUN
ejpam-5428	306	31	if	if	SCONJ
ejpam-5428	306	32	there	there	PRON
ejpam-5428	306	33	exists	exist	VERB
ejpam-5428	306	34	a	a	DET
ejpam-5428	306	35	β	β	X
ejpam-5428	306	36	∈	∈	PROPN
ejpam-5428	306	37	b	b	NOUN
ejpam-5428	306	38	such	such	ADJ
ejpam-5428	307	1	that	that	SCONJ
ejpam-5428	307	2	α(δ	α(δ	PROPN
ejpam-5428	307	3	,	,	PUNCT
ejpam-5428	307	4	γ	γ	X
ejpam-5428	307	5	,	,	PUNCT
ejpam-5428	307	6	l	l	NOUN
ejpam-5428	307	7	)	)	PUNCT
ejpam-5428	307	8	(	(	PUNCT
ejpam-5428	307	9	1	1	NUM
ejpam-5428	307	10	mz(lδ	mz(lδ	NOUN
ejpam-5428	307	11	,	,	PUNCT
ejpam-5428	307	12	lγ	lγ	PROPN
ejpam-5428	307	13	,	,	PUNCT
ejpam-5428	307	14	l	l	NOUN
ejpam-5428	307	15	)	)	PUNCT
ejpam-5428	307	16	−	−	PROPN
ejpam-5428	307	17	1	1	NUM
ejpam-5428	307	18	)	)	PUNCT
ejpam-5428	307	19	≤	≤	NOUN
ejpam-5428	307	20	β	β	X
ejpam-5428	307	21	(	(	PUNCT
ejpam-5428	307	22	1	1	NUM
ejpam-5428	307	23	mz(δ	mz(δ	NUM
ejpam-5428	307	24	,	,	PUNCT
ejpam-5428	307	25	γ	γ	X
ejpam-5428	307	26	,	,	PUNCT
ejpam-5428	307	27	l	l	NOUN
ejpam-5428	307	28	)	)	PUNCT
ejpam-5428	307	29	−	−	PROPN
ejpam-5428	307	30	1	1	NUM
ejpam-5428	307	31	)	)	PUNCT
ejpam-5428	307	32	(	(	PUNCT
ejpam-5428	307	33	1	1	NUM
ejpam-5428	307	34	mz(δ	mz(δ	NUM
ejpam-5428	307	35	,	,	PUNCT
ejpam-5428	307	36	γ	γ	X
ejpam-5428	307	37	,	,	PUNCT
ejpam-5428	307	38	l	l	NOUN
ejpam-5428	307	39	)	)	PUNCT
ejpam-5428	307	40	−	−	PROPN
ejpam-5428	307	41	1	1	NUM
ejpam-5428	307	42	)	)	PUNCT
ejpam-5428	307	43	,	,	PUNCT
ejpam-5428	307	44	(	(	PUNCT
ejpam-5428	307	45	22	22	NUM
ejpam-5428	307	46	)	)	PUNCT
ejpam-5428	307	47	q	q	NOUN
ejpam-5428	307	48	∈	∈	PROPN
ejpam-5428	307	49	(	(	PUNCT
ejpam-5428	307	50	0	0	NUM
ejpam-5428	307	51	,	,	PUNCT
ejpam-5428	307	52	1	1	NUM
ejpam-5428	307	53	)	)	PUNCT
ejpam-5428	307	54	,	,	PUNCT
ejpam-5428	307	55	for	for	ADP
ejpam-5428	307	56	all	all	DET
ejpam-5428	307	57	δ	δ	PROPN
ejpam-5428	307	58	,	,	PUNCT
ejpam-5428	307	59	γ	γ	PROPN
ejpam-5428	307	60	∈	∈	PROPN
ejpam-5428	307	61	ȳ	ȳ	NOUN
ejpam-5428	307	62	and	and	CCONJ
ejpam-5428	307	63	l	l	NOUN
ejpam-5428	307	64	>	>	X
ejpam-5428	307	65	0	0	X
ejpam-5428	307	66	.	.	PUNCT
ejpam-5428	308	1	v.	v.	PROPN
ejpam-5428	308	2	chandra	chandra	PROPN
ejpam-5428	308	3	,	,	PUNCT
ejpam-5428	308	4	u.	u.	PROPN
ejpam-5428	308	5	d.	d.	PROPN
ejpam-5428	308	6	patel	patel	PROPN
ejpam-5428	308	7	,	,	PUNCT
ejpam-5428	308	8	s.	s.	PROPN
ejpam-5428	308	9	radenović	radenović	PROPN
ejpam-5428	308	10	/	/	SYM
ejpam-5428	308	11	eur	eur	PROPN
ejpam-5428	308	12	.	.	PUNCT
ejpam-5428	309	1	j.	j.	PROPN
ejpam-5428	309	2	pure	pure	PROPN
ejpam-5428	309	3	appl	appl	PROPN
ejpam-5428	309	4	.	.	PROPN
ejpam-5428	309	5	math	math	PROPN
ejpam-5428	309	6	,	,	PUNCT
ejpam-5428	309	7	17	17	NUM
ejpam-5428	309	8	(	(	PUNCT
ejpam-5428	309	9	4	4	NUM
ejpam-5428	309	10	)	)	PUNCT
ejpam-5428	309	11	(	(	PUNCT
ejpam-5428	309	12	2024	2024	NUM
ejpam-5428	309	13	)	)	PUNCT
ejpam-5428	309	14	,	,	PUNCT
ejpam-5428	309	15	2384	2384	NUM
ejpam-5428	309	16	-	-	SYM
ejpam-5428	309	17	2404	2404	NUM
ejpam-5428	309	18	2399	2399	NUM
ejpam-5428	309	19	theorem	theorem	VERB
ejpam-5428	309	20	4	4	NUM
ejpam-5428	309	21	.	.	PUNCT
ejpam-5428	309	22	consider	consider	VERB
ejpam-5428	309	23	a	a	DET
ejpam-5428	309	24	self	self	NOUN
ejpam-5428	309	25	map	map	NOUN
ejpam-5428	309	26	l	l	NOUN
ejpam-5428	309	27	defined	define	VERB
ejpam-5428	309	28	on	on	ADP
ejpam-5428	309	29	a	a	DET
ejpam-5428	309	30	g	g	NOUN
ejpam-5428	309	31	-	-	PUNCT
ejpam-5428	309	32	complete	complete	ADJ
ejpam-5428	309	33	b	b	NOUN
ejpam-5428	309	34	-	-	PUNCT
ejpam-5428	309	35	fuzzy	fuzzy	ADJ
ejpam-5428	309	36	metric	metric	ADJ
ejpam-5428	309	37	space	space	NOUN
ejpam-5428	309	38	(	(	PUNCT
ejpam-5428	309	39	ȳ,mz	ȳ,mz	NUM
ejpam-5428	309	40	,	,	PUNCT
ejpam-5428	309	41	⋄	⋄	PROPN
ejpam-5428	309	42	)	)	PUNCT
ejpam-5428	309	43	where	where	SCONJ
ejpam-5428	309	44	fuzzy	fuzzy	ADJ
ejpam-5428	309	45	metric	metric	NOUN
ejpam-5428	309	46	is	be	AUX
ejpam-5428	309	47	triangular	triangular	NOUN
ejpam-5428	309	48	satisfying	satisfying	ADJ
ejpam-5428	309	49	:	:	PUNCT
ejpam-5428	309	50	(	(	PUNCT
ejpam-5428	309	51	i	i	NOUN
ejpam-5428	309	52	)	)	PUNCT
ejpam-5428	309	53	map	map	NOUN
ejpam-5428	309	54	l	l	NOUN
ejpam-5428	309	55	is	be	AUX
ejpam-5428	309	56	b	b	NOUN
ejpam-5428	309	57	-	-	PUNCT
ejpam-5428	309	58	fuzzy	fuzzy	ADJ
ejpam-5428	309	59	α	α	NOUN
ejpam-5428	309	60	-	-	PUNCT
ejpam-5428	309	61	geraghty	geraghty	VERB
ejpam-5428	309	62	type	type	PROPN
ejpam-5428	309	63	-	-	PUNCT
ejpam-5428	309	64	ii	ii	NOUN
ejpam-5428	309	65	;	;	PUNCT
ejpam-5428	309	66	(	(	PUNCT
ejpam-5428	309	67	ii	ii	NOUN
ejpam-5428	309	68	)	)	PUNCT
ejpam-5428	309	69	there	there	PRON
ejpam-5428	309	70	exists	exist	VERB
ejpam-5428	309	71	δ0	δ0	NOUN
ejpam-5428	309	72	∈	∈	PROPN
ejpam-5428	309	73	ȳ	ȳ	NOUN
ejpam-5428	309	74	such	such	ADJ
ejpam-5428	309	75	that	that	DET
ejpam-5428	309	76	α(δ0,lδ0	α(δ0,lδ0	PROPN
ejpam-5428	309	77	,	,	PUNCT
ejpam-5428	309	78	l	l	NOUN
ejpam-5428	309	79	)	)	PUNCT
ejpam-5428	309	80	≥	≥	NOUN
ejpam-5428	309	81	1	1	NUM
ejpam-5428	309	82	for	for	ADP
ejpam-5428	309	83	all	all	DET
ejpam-5428	309	84	l	l	NOUN
ejpam-5428	309	85	>	>	X
ejpam-5428	309	86	0	0	NUM
ejpam-5428	309	87	;	;	PUNCT
ejpam-5428	309	88	(	(	PUNCT
ejpam-5428	309	89	iii	iii	X
ejpam-5428	309	90	)	)	PUNCT
ejpam-5428	309	91	if	if	SCONJ
ejpam-5428	309	92	α(δn	α(δn	NUM
ejpam-5428	309	93	,	,	PUNCT
ejpam-5428	309	94	δn+1	δn+1	PROPN
ejpam-5428	309	95	,	,	PUNCT
ejpam-5428	309	96	l	l	NOUN
ejpam-5428	309	97	)	)	PUNCT
ejpam-5428	309	98	≥	≥	NOUN
ejpam-5428	309	99	1	1	NUM
ejpam-5428	309	100	and	and	CCONJ
ejpam-5428	309	101	δn	δn	NOUN
ejpam-5428	309	102	→	→	SYM
ejpam-5428	309	103	u	u	NOUN
ejpam-5428	309	104	as	as	ADP
ejpam-5428	309	105	n	n	PROPN
ejpam-5428	309	106	→	→	SYM
ejpam-5428	309	107	+	+	PROPN
ejpam-5428	309	108	∞	∞	PROPN
ejpam-5428	309	109	,	,	PUNCT
ejpam-5428	309	110	then	then	ADV
ejpam-5428	309	111	α(δn	α(δn	NUM
ejpam-5428	309	112	,	,	PUNCT
ejpam-5428	309	113	u	u	NOUN
ejpam-5428	309	114	,	,	PUNCT
ejpam-5428	309	115	l	l	NOUN
ejpam-5428	309	116	)	)	PUNCT
ejpam-5428	309	117	≥	≥	NOUN
ejpam-5428	309	118	1	1	NUM
ejpam-5428	309	119	for	for	ADP
ejpam-5428	309	120	all	all	DET
ejpam-5428	309	121	n	n	DET
ejpam-5428	309	122	∈	∈	PROPN
ejpam-5428	309	123	n.	n.	NOUN
ejpam-5428	309	124	then	then	ADV
ejpam-5428	309	125	l	l	PROPN
ejpam-5428	309	126	has	have	VERB
ejpam-5428	309	127	a	a	DET
ejpam-5428	309	128	fixed	fix	VERB
ejpam-5428	309	129	point	point	NOUN
ejpam-5428	309	130	.	.	PUNCT
ejpam-5428	310	1	remark	remark	NOUN
ejpam-5428	310	2	2	2	NUM
ejpam-5428	310	3	.	.	PUNCT
ejpam-5428	311	1	α(δ	α(δ	PROPN
ejpam-5428	311	2	,	,	PUNCT
ejpam-5428	311	3	γ	γ	X
ejpam-5428	311	4	,	,	PUNCT
ejpam-5428	311	5	l	l	NOUN
ejpam-5428	311	6	)	)	PUNCT
ejpam-5428	311	7	=	=	SYM
ejpam-5428	311	8	1	1	NUM
ejpam-5428	311	9	in	in	ADP
ejpam-5428	311	10	definition	definition	NOUN
ejpam-5428	311	11	(	(	PUNCT
ejpam-5428	311	12	11	11	NUM
ejpam-5428	311	13	)	)	PUNCT
ejpam-5428	311	14	results	result	NOUN
ejpam-5428	311	15	in	in	ADP
ejpam-5428	311	16	the	the	DET
ejpam-5428	311	17	following	following	NOUN
ejpam-5428	311	18	:	:	PUNCT
ejpam-5428	311	19	corollary	corollary	ADJ
ejpam-5428	311	20	2	2	NUM
ejpam-5428	311	21	.	.	PUNCT
ejpam-5428	311	22	consider	consider	VERB
ejpam-5428	311	23	a	a	DET
ejpam-5428	311	24	self	self	NOUN
ejpam-5428	311	25	map	map	NOUN
ejpam-5428	311	26	l	l	NOUN
ejpam-5428	311	27	which	which	PRON
ejpam-5428	311	28	is	be	AUX
ejpam-5428	311	29	geraghty	geraghty	ADJ
ejpam-5428	311	30	type	type	PROPN
ejpam-5428	311	31	-	-	PUNCT
ejpam-5428	311	32	ii	ii	NOUN
ejpam-5428	311	33	contractive	contractive	NOUN
ejpam-5428	311	34	defined	define	VERB
ejpam-5428	311	35	on	on	ADP
ejpam-5428	311	36	a	a	DET
ejpam-5428	311	37	g	g	NOUN
ejpam-5428	311	38	-	-	PUNCT
ejpam-5428	311	39	complete	complete	ADJ
ejpam-5428	311	40	b	b	NOUN
ejpam-5428	311	41	-	-	PUNCT
ejpam-5428	311	42	fuzzy	fuzzy	ADJ
ejpam-5428	311	43	metric	metric	ADJ
ejpam-5428	311	44	space	space	NOUN
ejpam-5428	311	45	(	(	PUNCT
ejpam-5428	311	46	ȳ,mz	ȳ,mz	NUM
ejpam-5428	311	47	,	,	PUNCT
ejpam-5428	311	48	⋄	⋄	PROPN
ejpam-5428	311	49	)	)	PUNCT
ejpam-5428	311	50	where	where	SCONJ
ejpam-5428	311	51	fuzzy	fuzzy	ADJ
ejpam-5428	311	52	metric	metric	NOUN
ejpam-5428	311	53	is	be	AUX
ejpam-5428	311	54	triangular	triangular	NOUN
ejpam-5428	311	55	then	then	ADV
ejpam-5428	311	56	the	the	DET
ejpam-5428	311	57	self	self	NOUN
ejpam-5428	311	58	-	-	PUNCT
ejpam-5428	311	59	mapping	mapping	NOUN
ejpam-5428	311	60	l	l	NOUN
ejpam-5428	311	61	has	have	VERB
ejpam-5428	311	62	a	a	DET
ejpam-5428	311	63	unique	unique	ADJ
ejpam-5428	311	64	fixed	fix	VERB
ejpam-5428	311	65	point	point	NOUN
ejpam-5428	311	66	.	.	PUNCT
ejpam-5428	312	1	in	in	ADP
ejpam-5428	312	2	the	the	DET
ejpam-5428	312	3	support	support	NOUN
ejpam-5428	312	4	of	of	ADP
ejpam-5428	312	5	corollary	corollary	ADJ
ejpam-5428	312	6	2	2	NUM
ejpam-5428	312	7	,	,	PUNCT
ejpam-5428	312	8	we	we	PRON
ejpam-5428	312	9	have	have	VERB
ejpam-5428	312	10	an	an	DET
ejpam-5428	312	11	example	example	NOUN
ejpam-5428	312	12	.	.	PUNCT
ejpam-5428	313	1	example	example	NOUN
ejpam-5428	314	1	6	6	NUM
ejpam-5428	314	2	.	.	PUNCT
ejpam-5428	314	3	consider	consider	VERB
ejpam-5428	314	4	a	a	DET
ejpam-5428	314	5	fuzzy	fuzzy	ADJ
ejpam-5428	314	6	metric	metric	ADJ
ejpam-5428	314	7	mz(δ	mz(δ	PROPN
ejpam-5428	314	8	,	,	PUNCT
ejpam-5428	314	9	γ	γ	X
ejpam-5428	314	10	,	,	PUNCT
ejpam-5428	314	11	l	l	NOUN
ejpam-5428	314	12	)	)	PUNCT
ejpam-5428	314	13	=	=	PUNCT
ejpam-5428	314	14	l+0.3	l+0.3	PROPN
ejpam-5428	314	15	l+0.3+|δ−γ|2	l+0.3+|δ−γ|2	NOUN
ejpam-5428	314	16	for	for	ADP
ejpam-5428	314	17	all	all	DET
ejpam-5428	314	18	δ	δ	PROPN
ejpam-5428	314	19	,	,	PUNCT
ejpam-5428	314	20	γ	γ	PROPN
ejpam-5428	314	21	∈	∈	PROPN
ejpam-5428	314	22	ȳ	ȳ	NOUN
ejpam-5428	315	1	=	=	PUNCT
ejpam-5428	316	1	[	[	X
ejpam-5428	316	2	0	0	NUM
ejpam-5428	316	3	,	,	PUNCT
ejpam-5428	316	4	1	1	NUM
ejpam-5428	316	5	]	]	PUNCT
ejpam-5428	316	6	and	and	CCONJ
ejpam-5428	316	7	l	l	NOUN
ejpam-5428	316	8	>	>	X
ejpam-5428	317	1	0	0	X
ejpam-5428	317	2	.	.	PUNCT
ejpam-5428	318	1	we	we	PRON
ejpam-5428	318	2	can	can	AUX
ejpam-5428	318	3	check	check	VERB
ejpam-5428	318	4	it	it	PRON
ejpam-5428	318	5	is	be	AUX
ejpam-5428	318	6	a	a	DET
ejpam-5428	318	7	g	g	NOUN
ejpam-5428	318	8	-	-	PUNCT
ejpam-5428	318	9	complete	complete	ADJ
ejpam-5428	318	10	b	b	NOUN
ejpam-5428	318	11	-	-	PUNCT
ejpam-5428	318	12	fuzzy	fuzzy	ADJ
ejpam-5428	318	13	metric	metric	ADJ
ejpam-5428	318	14	space	space	NOUN
ejpam-5428	318	15	with	with	ADP
ejpam-5428	318	16	respect	respect	NOUN
ejpam-5428	318	17	to	to	ADP
ejpam-5428	318	18	standard	standard	ADJ
ejpam-5428	318	19	triangular	triangular	NOUN
ejpam-5428	318	20	norm	norm	NOUN
ejpam-5428	318	21	.	.	PUNCT
ejpam-5428	319	1	define	define	VERB
ejpam-5428	319	2	a	a	DET
ejpam-5428	319	3	self	self	NOUN
ejpam-5428	319	4	map	map	NOUN
ejpam-5428	319	5	l	l	NOUN
ejpam-5428	319	6	such	such	ADJ
ejpam-5428	319	7	as	as	ADP
ejpam-5428	319	8	l(δ	l(δ	NOUN
ejpam-5428	319	9	)	)	PUNCT
ejpam-5428	319	10	=	=	PRON
ejpam-5428	319	11	{	{	PUNCT
ejpam-5428	319	12	δ	δ	NOUN
ejpam-5428	319	13	2	2	NUM
ejpam-5428	319	14	,	,	PUNCT
ejpam-5428	319	15	if	if	SCONJ
ejpam-5428	319	16	δ	δ	PROPN
ejpam-5428	319	17	,	,	PUNCT
ejpam-5428	319	18	γ	γ	PROPN
ejpam-5428	319	19	∈	∈	PROPN
ejpam-5428	319	20	(	(	PUNCT
ejpam-5428	319	21	0	0	NUM
ejpam-5428	319	22	,	,	PUNCT
ejpam-5428	319	23	1	1	NUM
ejpam-5428	319	24	]	]	SYM
ejpam-5428	319	25	0	0	NUM
ejpam-5428	319	26	,	,	PUNCT
ejpam-5428	319	27	if	if	SCONJ
ejpam-5428	319	28	δ	δ	PROPN
ejpam-5428	319	29	=	=	NOUN
ejpam-5428	319	30	0	0	PROPN
ejpam-5428	319	31	.	.	PUNCT
ejpam-5428	319	32	to	to	PART
ejpam-5428	319	33	show	show	VERB
ejpam-5428	319	34	mapping	mapping	NOUN
ejpam-5428	319	35	l	l	NOUN
ejpam-5428	319	36	is	be	AUX
ejpam-5428	319	37	a	a	DET
ejpam-5428	319	38	geraghty	geraghty	ADJ
ejpam-5428	319	39	type	type	NOUN
ejpam-5428	319	40	-	-	PUNCT
ejpam-5428	319	41	ii	ii	NOUN
ejpam-5428	319	42	contractive	contractive	ADJ
ejpam-5428	319	43	with	with	ADP
ejpam-5428	319	44	β(t1	β(t1	NOUN
ejpam-5428	319	45	)	)	PUNCT
ejpam-5428	319	46	=	=	PUNCT
ejpam-5428	319	47	1	1	NUM
ejpam-5428	319	48	1+t1	1+t1	NUM
ejpam-5428	319	49	.	.	PUNCT
ejpam-5428	320	1	case	case	NOUN
ejpam-5428	320	2	1	1	X
ejpam-5428	320	3	.	.	PUNCT
ejpam-5428	321	1	if	if	SCONJ
ejpam-5428	321	2	δ	δ	PROPN
ejpam-5428	321	3	,	,	PUNCT
ejpam-5428	321	4	γ	γ	PROPN
ejpam-5428	321	5	∈	∈	PROPN
ejpam-5428	321	6	(	(	PUNCT
ejpam-5428	321	7	0	0	NUM
ejpam-5428	321	8	,	,	PUNCT
ejpam-5428	321	9	1	1	NUM
ejpam-5428	321	10	]	]	PUNCT
ejpam-5428	321	11	then	then	ADV
ejpam-5428	321	12	1	1	NUM
ejpam-5428	321	13	mz(lδ	mz(lδ	NOUN
ejpam-5428	321	14	,	,	PUNCT
ejpam-5428	321	15	lγ	lγ	PROPN
ejpam-5428	321	16	,	,	PUNCT
ejpam-5428	321	17	l	l	NOUN
ejpam-5428	321	18	)	)	PUNCT
ejpam-5428	321	19	−	−	NOUN
ejpam-5428	321	20	1	1	NUM
ejpam-5428	321	21	=	=	SYM
ejpam-5428	321	22	1	1	NUM
ejpam-5428	321	23	l+0.3	l+0.3	PROPN
ejpam-5428	321	24	l+0.3+|lδ−lγ|2	l+0.3+|lδ−lγ|2	ADP
ejpam-5428	321	25	−	−	PROPN
ejpam-5428	321	26	1	1	NUM
ejpam-5428	321	27	=	=	SYM
ejpam-5428	321	28	1	1	NUM
ejpam-5428	321	29	l+0.3	l+0.3	NUM
ejpam-5428	321	30	l+0.3	l+0.3	PROPN
ejpam-5428	321	31	+	+	NOUN
ejpam-5428	321	32	1	1	NUM
ejpam-5428	321	33	4	4	NUM
ejpam-5428	321	34	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	321	35	−	−	PROPN
ejpam-5428	321	36	1	1	NUM
ejpam-5428	321	37	=	=	SYM
ejpam-5428	321	38	1−	1−	NUM
ejpam-5428	321	39	l+0.3	l+0.3	NUM
ejpam-5428	321	40	l+0.3	l+0.3	PROPN
ejpam-5428	321	41	+	+	NOUN
ejpam-5428	321	42	1	1	NUM
ejpam-5428	321	43	4	4	NUM
ejpam-5428	321	44	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	321	45	l+0.3	l+0.3	NUM
ejpam-5428	321	46	l+0.3	l+0.3	PROPN
ejpam-5428	321	47	+	+	NOUN
ejpam-5428	321	48	1	1	NUM
ejpam-5428	321	49	4	4	NUM
ejpam-5428	321	50	|δ−γ|2	|δ−γ|2	VERB
ejpam-5428	321	51	=	=	SYM
ejpam-5428	321	52	1	1	NUM
ejpam-5428	321	53	4	4	NUM
ejpam-5428	321	54	|δ	|δ	NOUN
ejpam-5428	321	55	−	−	PROPN
ejpam-5428	322	1	γ|2	γ|2	ADJ
ejpam-5428	322	2	l	l	NOUN
ejpam-5428	322	3	+	+	NUM
ejpam-5428	322	4	0.3	0.3	NUM
ejpam-5428	322	5	+	+	SYM
ejpam-5428	322	6	1	1	NUM
ejpam-5428	322	7	4	4	NUM
ejpam-5428	322	8	|δ	|δ	NOUN
ejpam-5428	322	9	−	−	ADP
ejpam-5428	322	10	γ|2	γ|2	ADJ
ejpam-5428	322	11	·	·	PUNCT
ejpam-5428	322	12	l	l	NOUN
ejpam-5428	322	13	+	+	CCONJ
ejpam-5428	322	14	0.3	0.3	NUM
ejpam-5428	322	15	+	+	SYM
ejpam-5428	322	16	1	1	NUM
ejpam-5428	322	17	4	4	NUM
ejpam-5428	322	18	|δ	|δ	NOUN
ejpam-5428	322	19	−	−	PROPN
ejpam-5428	323	1	γ|2	γ|2	ADJ
ejpam-5428	323	2	l	l	NOUN
ejpam-5428	323	3	+	+	CCONJ
ejpam-5428	323	4	0.3	0.3	NUM
ejpam-5428	323	5	=	=	SYM
ejpam-5428	323	6	1	1	NUM
ejpam-5428	323	7	4	4	NUM
ejpam-5428	323	8	|δ	|δ	NOUN
ejpam-5428	323	9	−	−	PROPN
ejpam-5428	323	10	γ|2	γ|2	ADJ
ejpam-5428	323	11	l	l	NOUN
ejpam-5428	323	12	+	+	CCONJ
ejpam-5428	323	13	0.3	0.3	NUM
ejpam-5428	323	14	≤	≤	NOUN
ejpam-5428	323	15	|δ	|δ	NOUN
ejpam-5428	323	16	−	−	PROPN
ejpam-5428	323	17	γ|2	γ|2	ADJ
ejpam-5428	323	18	l	l	NOUN
ejpam-5428	323	19	+	+	CCONJ
ejpam-5428	323	20	0.3	0.3	NUM
ejpam-5428	323	21	+	+	NOUN
ejpam-5428	323	22	|δ	|δ	NOUN
ejpam-5428	323	23	−	−	PROPN
ejpam-5428	323	24	γ|2	γ|2	NOUN
ejpam-5428	323	25	=	=	NOUN
ejpam-5428	323	26	1−	1−	NUM
ejpam-5428	323	27	l	l	NOUN
ejpam-5428	324	1	+	+	CCONJ
ejpam-5428	324	2	0.3	0.3	NUM
ejpam-5428	324	3	l	l	NOUN
ejpam-5428	324	4	+	+	CCONJ
ejpam-5428	324	5	0.3	0.3	NUM
ejpam-5428	324	6	+	+	NOUN
ejpam-5428	324	7	|δ	|δ	NOUN
ejpam-5428	324	8	−	−	PROPN
ejpam-5428	324	9	γ|2	γ|2	PROPN
ejpam-5428	324	10	v.	v.	ADP
ejpam-5428	324	11	chandra	chandra	PROPN
ejpam-5428	324	12	,	,	PUNCT
ejpam-5428	324	13	u.	u.	PROPN
ejpam-5428	324	14	d.	d.	PROPN
ejpam-5428	324	15	patel	patel	PROPN
ejpam-5428	324	16	,	,	PUNCT
ejpam-5428	324	17	s.	s.	PROPN
ejpam-5428	324	18	radenović	radenović	PROPN
ejpam-5428	324	19	/	/	SYM
ejpam-5428	324	20	eur	eur	PROPN
ejpam-5428	324	21	.	.	PUNCT
ejpam-5428	325	1	j.	j.	PROPN
ejpam-5428	325	2	pure	pure	PROPN
ejpam-5428	325	3	appl	appl	PROPN
ejpam-5428	325	4	.	.	PROPN
ejpam-5428	325	5	math	math	PROPN
ejpam-5428	325	6	,	,	PUNCT
ejpam-5428	325	7	17	17	NUM
ejpam-5428	325	8	(	(	PUNCT
ejpam-5428	325	9	4	4	NUM
ejpam-5428	325	10	)	)	PUNCT
ejpam-5428	325	11	(	(	PUNCT
ejpam-5428	325	12	2024	2024	NUM
ejpam-5428	325	13	)	)	PUNCT
ejpam-5428	325	14	,	,	PUNCT
ejpam-5428	325	15	2384	2384	NUM
ejpam-5428	325	16	-	-	SYM
ejpam-5428	325	17	2404	2404	NUM
ejpam-5428	325	18	2400	2400	NUM
ejpam-5428	325	19	=	=	SYM
ejpam-5428	325	20	β	β	X
ejpam-5428	325	21	(	(	PUNCT
ejpam-5428	325	22	1	1	NUM
ejpam-5428	325	23	mz(δ	mz(δ	NUM
ejpam-5428	325	24	,	,	PUNCT
ejpam-5428	325	25	γ	γ	X
ejpam-5428	325	26	,	,	PUNCT
ejpam-5428	325	27	l	l	NOUN
ejpam-5428	325	28	)	)	PUNCT
ejpam-5428	325	29	−	−	PROPN
ejpam-5428	325	30	1	1	NUM
ejpam-5428	325	31	)	)	PUNCT
ejpam-5428	325	32	(	(	PUNCT
ejpam-5428	325	33	1	1	NUM
ejpam-5428	325	34	mz(δ	mz(δ	NUM
ejpam-5428	325	35	,	,	PUNCT
ejpam-5428	325	36	γ	γ	X
ejpam-5428	325	37	,	,	PUNCT
ejpam-5428	325	38	l	l	NOUN
ejpam-5428	325	39	)	)	PUNCT
ejpam-5428	325	40	−	−	PROPN
ejpam-5428	325	41	1	1	NUM
ejpam-5428	325	42	)	)	PUNCT
ejpam-5428	325	43	,	,	PUNCT
ejpam-5428	325	44	case2	case2	PROPN
ejpam-5428	325	45	.	.	PUNCT
ejpam-5428	326	1	if	if	SCONJ
ejpam-5428	326	2	δ	δ	PROPN
ejpam-5428	326	3	=	=	SYM
ejpam-5428	326	4	0	0	PROPN
ejpam-5428	326	5	,	,	PUNCT
ejpam-5428	326	6	γ	γ	X
ejpam-5428	326	7	∈	∈	X
ejpam-5428	326	8	(	(	PUNCT
ejpam-5428	326	9	0	0	NUM
ejpam-5428	326	10	,	,	PUNCT
ejpam-5428	326	11	1	1	NUM
ejpam-5428	326	12	]	]	PUNCT
ejpam-5428	326	13	then	then	ADV
ejpam-5428	326	14	1	1	NUM
ejpam-5428	326	15	mz(lδ	mz(lδ	NOUN
ejpam-5428	326	16	,	,	PUNCT
ejpam-5428	326	17	lγ	lγ	PROPN
ejpam-5428	326	18	,	,	PUNCT
ejpam-5428	326	19	l	l	NOUN
ejpam-5428	326	20	)	)	PUNCT
ejpam-5428	326	21	−	−	NOUN
ejpam-5428	326	22	1	1	NUM
ejpam-5428	326	23	=	=	SYM
ejpam-5428	326	24	1	1	NUM
ejpam-5428	326	25	l+0.3	l+0.3	PROPN
ejpam-5428	326	26	l+0.3+|lδ−lγ|2	l+0.3+|lδ−lγ|2	ADP
ejpam-5428	326	27	−	−	PROPN
ejpam-5428	326	28	1	1	NUM
ejpam-5428	326	29	=	=	SYM
ejpam-5428	326	30	1	1	NUM
ejpam-5428	326	31	l+0.3	l+0.3	NUM
ejpam-5428	326	32	l+0.3	l+0.3	PROPN
ejpam-5428	326	33	+	+	NUM
ejpam-5428	326	34	1	1	NUM
ejpam-5428	326	35	4	4	NUM
ejpam-5428	326	36	|γ|2	|γ|2	ADJ
ejpam-5428	326	37	−	−	NOUN
ejpam-5428	326	38	1	1	NUM
ejpam-5428	326	39	=	=	SYM
ejpam-5428	326	40	1	1	NUM
ejpam-5428	326	41	4	4	NUM
ejpam-5428	326	42	|γ|	|γ|	ADP
ejpam-5428	326	43	2	2	NUM
ejpam-5428	326	44	l	l	NOUN
ejpam-5428	326	45	+	+	NUM
ejpam-5428	326	46	0.3	0.3	NUM
ejpam-5428	326	47	≤	≤	NOUN
ejpam-5428	326	48	|γ|2	|γ|2	ADJ
ejpam-5428	326	49	l	l	NOUN
ejpam-5428	326	50	+	+	CCONJ
ejpam-5428	326	51	0.3	0.3	NUM
ejpam-5428	326	52	+	+	CCONJ
ejpam-5428	326	53	|γ|2	|γ|2	ADJ
ejpam-5428	326	54	=	=	SYM
ejpam-5428	326	55	1−	1−	NUM
ejpam-5428	326	56	l	l	NOUN
ejpam-5428	327	1	+	+	CCONJ
ejpam-5428	327	2	0.3	0.3	NUM
ejpam-5428	327	3	l	l	NOUN
ejpam-5428	327	4	+	+	CCONJ
ejpam-5428	327	5	0.3	0.3	NUM
ejpam-5428	327	6	+	+	CCONJ
ejpam-5428	327	7	|γ|2	|γ|2	ADJ
ejpam-5428	327	8	=	=	SYM
ejpam-5428	327	9	β	β	X
ejpam-5428	327	10	(	(	PUNCT
ejpam-5428	327	11	1	1	NUM
ejpam-5428	327	12	mz(δ	mz(δ	NUM
ejpam-5428	327	13	,	,	PUNCT
ejpam-5428	327	14	γ	γ	X
ejpam-5428	327	15	,	,	PUNCT
ejpam-5428	327	16	l	l	NOUN
ejpam-5428	327	17	)	)	PUNCT
ejpam-5428	327	18	−	−	PROPN
ejpam-5428	327	19	1	1	NUM
ejpam-5428	327	20	)	)	PUNCT
ejpam-5428	327	21	(	(	PUNCT
ejpam-5428	327	22	1	1	NUM
ejpam-5428	327	23	mz(δ	mz(δ	NUM
ejpam-5428	327	24	,	,	PUNCT
ejpam-5428	327	25	γ	γ	X
ejpam-5428	327	26	,	,	PUNCT
ejpam-5428	327	27	l	l	NOUN
ejpam-5428	327	28	)	)	PUNCT
ejpam-5428	327	29	−	−	PROPN
ejpam-5428	327	30	1	1	NUM
ejpam-5428	327	31	)	)	PUNCT
ejpam-5428	327	32	,	,	PUNCT
ejpam-5428	327	33	case	case	NOUN
ejpam-5428	327	34	3	3	X
ejpam-5428	327	35	.	.	PUNCT
ejpam-5428	328	1	if	if	SCONJ
ejpam-5428	328	2	δ	δ	PROPN
ejpam-5428	328	3	=	=	SYM
ejpam-5428	328	4	γ	γ	X
ejpam-5428	328	5	=	=	SYM
ejpam-5428	328	6	0	0	NUM
ejpam-5428	328	7	then	then	ADV
ejpam-5428	328	8	it	it	PRON
ejpam-5428	328	9	is	be	AUX
ejpam-5428	328	10	trivial	trivial	ADJ
ejpam-5428	328	11	.	.	PUNCT
ejpam-5428	329	1	it	it	PRON
ejpam-5428	329	2	is	be	AUX
ejpam-5428	329	3	easy	easy	ADJ
ejpam-5428	329	4	to	to	PART
ejpam-5428	329	5	check	check	VERB
ejpam-5428	329	6	that	that	SCONJ
ejpam-5428	329	7	mz	mz	PROPN
ejpam-5428	329	8	is	be	AUX
ejpam-5428	329	9	triangular	triangular	NOUN
ejpam-5428	329	10	.	.	PUNCT
ejpam-5428	330	1	hence	hence	ADV
ejpam-5428	330	2	,	,	PUNCT
ejpam-5428	330	3	δ	δ	PROPN
ejpam-5428	330	4	=	=	SYM
ejpam-5428	330	5	0	0	NUM
ejpam-5428	330	6	is	be	AUX
ejpam-5428	330	7	a	a	DET
ejpam-5428	330	8	unique	unique	ADJ
ejpam-5428	330	9	fixed	fix	VERB
ejpam-5428	330	10	point	point	NOUN
ejpam-5428	330	11	of	of	ADP
ejpam-5428	330	12	l.	l.	PROPN
ejpam-5428	330	13	3	3	NUM
ejpam-5428	330	14	.	.	PUNCT
ejpam-5428	330	15	application	application	NOUN
ejpam-5428	330	16	in	in	ADP
ejpam-5428	330	17	this	this	DET
ejpam-5428	330	18	section	section	NOUN
ejpam-5428	330	19	,	,	PUNCT
ejpam-5428	330	20	we	we	PRON
ejpam-5428	330	21	discuss	discuss	VERB
ejpam-5428	330	22	the	the	DET
ejpam-5428	330	23	existence	existence	NOUN
ejpam-5428	330	24	of	of	ADP
ejpam-5428	330	25	a	a	DET
ejpam-5428	330	26	unique	unique	ADJ
ejpam-5428	330	27	solution	solution	NOUN
ejpam-5428	330	28	of	of	ADP
ejpam-5428	330	29	a	a	DET
ejpam-5428	330	30	non	non	ADJ
ejpam-5428	330	31	-	-	ADJ
ejpam-5428	330	32	linear	linear	ADJ
ejpam-5428	330	33	integral	integral	ADJ
ejpam-5428	330	34	equation	equation	NOUN
ejpam-5428	330	35	and	and	CCONJ
ejpam-5428	330	36	need	need	VERB
ejpam-5428	330	37	some	some	DET
ejpam-5428	330	38	specific	specific	ADJ
ejpam-5428	330	39	conditions	condition	NOUN
ejpam-5428	330	40	for	for	ADP
ejpam-5428	330	41	the	the	DET
ejpam-5428	330	42	solution	solution	NOUN
ejpam-5428	330	43	.	.	PUNCT
ejpam-5428	331	1	a	a	DET
ejpam-5428	331	2	b	b	X
ejpam-5428	331	3	-	-	PUNCT
ejpam-5428	331	4	fuzzy	fuzzy	ADJ
ejpam-5428	331	5	metric	metric	ADJ
ejpam-5428	331	6	space	space	NOUN
ejpam-5428	331	7	that	that	PRON
ejpam-5428	331	8	resembles	resemble	VERB
ejpam-5428	331	9	c	c	NOUN
ejpam-5428	331	10	(	(	PUNCT
ejpam-5428	331	11	[	[	X
ejpam-5428	331	12	a	a	PRON
ejpam-5428	331	13	,	,	PUNCT
ejpam-5428	331	14	b],r	b],r	NOUN
ejpam-5428	331	15	)	)	PUNCT
ejpam-5428	331	16	is	be	AUX
ejpam-5428	331	17	the	the	DET
ejpam-5428	331	18	space	space	NOUN
ejpam-5428	331	19	ȳ	ȳ	NOUN
ejpam-5428	331	20	of	of	ADP
ejpam-5428	331	21	all	all	DET
ejpam-5428	331	22	continuous	continuous	ADJ
ejpam-5428	331	23	real	real	ADJ
ejpam-5428	331	24	valued	value	VERB
ejpam-5428	331	25	functions	function	NOUN
ejpam-5428	331	26	defined	define	VERB
ejpam-5428	331	27	on	on	ADP
ejpam-5428	331	28	the	the	DET
ejpam-5428	331	29	interval	interval	NOUN
ejpam-5428	331	30	[	[	X
ejpam-5428	331	31	a	a	X
ejpam-5428	331	32	,	,	PUNCT
ejpam-5428	331	33	b	b	NOUN
ejpam-5428	331	34	]	]	X
ejpam-5428	331	35	with	with	ADP
ejpam-5428	331	36	the	the	DET
ejpam-5428	331	37	b	b	NOUN
ejpam-5428	331	38	-	-	PUNCT
ejpam-5428	331	39	fuzzy	fuzzy	ADJ
ejpam-5428	331	40	metric	metric	ADJ
ejpam-5428	331	41	mz(δ	mz(δ	PROPN
ejpam-5428	331	42	,	,	PUNCT
ejpam-5428	331	43	γ	γ	X
ejpam-5428	331	44	,	,	PUNCT
ejpam-5428	331	45	l	l	NOUN
ejpam-5428	331	46	)	)	PUNCT
ejpam-5428	331	47	=	=	SYM
ejpam-5428	332	1	l	l	NOUN
ejpam-5428	332	2	l	l	NOUN
ejpam-5428	333	1	+	+	CCONJ
ejpam-5428	333	2	max	max	PROPN
ejpam-5428	333	3	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	333	4	|δ(s1)−	|δ(s1)−	PROPN
ejpam-5428	333	5	γ(s1)|2	γ(s1)|2	PROPN
ejpam-5428	333	6	.	.	PUNCT
ejpam-5428	333	7	consider	consider	VERB
ejpam-5428	333	8	an	an	DET
ejpam-5428	333	9	integral	integral	ADJ
ejpam-5428	333	10	equation	equation	NOUN
ejpam-5428	333	11	δ(l1	δ(l1	NOUN
ejpam-5428	333	12	)	)	PUNCT
ejpam-5428	333	13	=	=	SYM
ejpam-5428	333	14	f(l1	f(l1	PROPN
ejpam-5428	333	15	)	)	PUNCT
ejpam-5428	334	1	+	+	CCONJ
ejpam-5428	334	2	∫	∫	PROPN
ejpam-5428	334	3	b	b	PROPN
ejpam-5428	334	4	a	a	DET
ejpam-5428	334	5	h(l1	h(l1	PROPN
ejpam-5428	334	6	,	,	PUNCT
ejpam-5428	334	7	s1)f	s1)f	ADJ
ejpam-5428	334	8	(	(	PUNCT
ejpam-5428	334	9	l1	l1	PROPN
ejpam-5428	334	10	,	,	PUNCT
ejpam-5428	334	11	s1	s1	NOUN
ejpam-5428	334	12	,	,	PUNCT
ejpam-5428	334	13	δ(s1))ds1	δ(s1))ds1	PROPN
ejpam-5428	334	14	,	,	PUNCT
ejpam-5428	334	15	(	(	PUNCT
ejpam-5428	334	16	23	23	NUM
ejpam-5428	334	17	)	)	PUNCT
ejpam-5428	335	1	where	where	SCONJ
ejpam-5428	335	2	f	f	NOUN
ejpam-5428	335	3	:	:	PUNCT
ejpam-5428	336	1	[	[	X
ejpam-5428	336	2	a	a	X
ejpam-5428	336	3	,	,	PUNCT
ejpam-5428	336	4	b	b	NOUN
ejpam-5428	336	5	]	]	X
ejpam-5428	336	6	→	→	SYM
ejpam-5428	336	7	r	r	NOUN
ejpam-5428	336	8	,	,	PUNCT
ejpam-5428	336	9	h	h	NOUN
ejpam-5428	336	10	:	:	PUNCT
ejpam-5428	337	1	[	[	X
ejpam-5428	337	2	a	a	X
ejpam-5428	337	3	,	,	PUNCT
ejpam-5428	337	4	b	b	NOUN
ejpam-5428	337	5	]	]	X
ejpam-5428	337	6	×	×	NOUN
ejpam-5428	337	7	[	[	X
ejpam-5428	337	8	a	a	X
ejpam-5428	337	9	,	,	PUNCT
ejpam-5428	337	10	b	b	NOUN
ejpam-5428	337	11	]	]	X
ejpam-5428	337	12	→	→	SYM
ejpam-5428	337	13	r	r	NOUN
ejpam-5428	337	14	and	and	CCONJ
ejpam-5428	337	15	f	f	NOUN
ejpam-5428	337	16	:	:	PUNCT
ejpam-5428	338	1	[	[	X
ejpam-5428	338	2	a	a	X
ejpam-5428	338	3	,	,	PUNCT
ejpam-5428	338	4	b	b	NOUN
ejpam-5428	338	5	]	]	X
ejpam-5428	338	6	×	×	NOUN
ejpam-5428	338	7	[	[	X
ejpam-5428	338	8	a	a	X
ejpam-5428	338	9	,	,	PUNCT
ejpam-5428	338	10	b	b	NOUN
ejpam-5428	338	11	]	]	X
ejpam-5428	338	12	×	×	NOUN
ejpam-5428	338	13	r	r	NOUN
ejpam-5428	338	14	→	→	SYM
ejpam-5428	338	15	r	r	NOUN
ejpam-5428	338	16	are	be	AUX
ejpam-5428	338	17	continuous	continuous	ADJ
ejpam-5428	338	18	functions	function	NOUN
ejpam-5428	338	19	.	.	PUNCT
ejpam-5428	339	1	theorem	theorem	NOUN
ejpam-5428	339	2	5	5	NUM
ejpam-5428	339	3	.	.	PUNCT
ejpam-5428	340	1	suppose	suppose	VERB
ejpam-5428	340	2	(	(	PUNCT
ejpam-5428	340	3	i	i	NOUN
ejpam-5428	340	4	)	)	PUNCT
ejpam-5428	340	5	for	for	ADP
ejpam-5428	340	6	all	all	DET
ejpam-5428	340	7	l1	l1	PROPN
ejpam-5428	340	8	,	,	PUNCT
ejpam-5428	340	9	s1	s1	PROPN
ejpam-5428	340	10	∈	∈	PROPN
ejpam-5428	341	1	[	[	X
ejpam-5428	341	2	a	a	X
ejpam-5428	341	3	,	,	PUNCT
ejpam-5428	341	4	b	b	NOUN
ejpam-5428	341	5	]	]	X
ejpam-5428	341	6	,	,	PUNCT
ejpam-5428	341	7	δ	δ	PROPN
ejpam-5428	341	8	,	,	PUNCT
ejpam-5428	341	9	γ	γ	PROPN
ejpam-5428	341	10	∈	∈	PROPN
ejpam-5428	341	11	ȳ	ȳ	PROPN
ejpam-5428	341	12	mz(δ(s1),l(δ(s1	mz(δ(s1),l(δ(s1	PROPN
ejpam-5428	341	13	)	)	PUNCT
ejpam-5428	341	14	)	)	PUNCT
ejpam-5428	341	15	,	,	PUNCT
ejpam-5428	341	16	l	l	NOUN
ejpam-5428	341	17	)	)	PUNCT
ejpam-5428	341	18	>	>	X
ejpam-5428	341	19	q	q	X
ejpam-5428	341	20	·	·	PUNCT
ejpam-5428	341	21	mz(δ(s1	mz(δ(s1	ADJ
ejpam-5428	341	22	)	)	PUNCT
ejpam-5428	341	23	,	,	PUNCT
ejpam-5428	341	24	γ(s1	γ(s1	NOUN
ejpam-5428	341	25	)	)	PUNCT
ejpam-5428	341	26	,	,	PUNCT
ejpam-5428	341	27	l	l	NOUN
ejpam-5428	341	28	)	)	PUNCT
ejpam-5428	341	29	⇒	⇒	NOUN
ejpam-5428	341	30	|f	|f	PROPN
ejpam-5428	341	31	(	(	PUNCT
ejpam-5428	341	32	l1	l1	PROPN
ejpam-5428	341	33	,	,	PUNCT
ejpam-5428	341	34	s1	s1	NOUN
ejpam-5428	341	35	,	,	PUNCT
ejpam-5428	341	36	δ(s1))−	δ(s1))−	ADJ
ejpam-5428	341	37	f	f	X
ejpam-5428	341	38	(	(	PUNCT
ejpam-5428	341	39	l1	l1	PROPN
ejpam-5428	341	40	,	,	PUNCT
ejpam-5428	341	41	s1	s1	PROPN
ejpam-5428	341	42	,	,	PUNCT
ejpam-5428	341	43	γ(s1))|2	γ(s1))|2	PROPN
ejpam-5428	341	44	≤	≤	NOUN
ejpam-5428	342	1	e−	e−	PROPN
ejpam-5428	342	2	maxa≤s1≤b	maxa≤s1≤b	PROPN
ejpam-5428	342	3	|δ(s1)−γ(s1)|	|δ(s1)−γ(s1)|	NOUN
ejpam-5428	342	4	2	2	NUM
ejpam-5428	342	5	l	l	NOUN
ejpam-5428	342	6	|δ(s1)−	|δ(s1)−	PROPN
ejpam-5428	342	7	γ(s1)|2	γ(s1)|2	PROPN
ejpam-5428	342	8	,	,	PUNCT
ejpam-5428	342	9	v.	v.	PROPN
ejpam-5428	342	10	chandra	chandra	PROPN
ejpam-5428	342	11	,	,	PUNCT
ejpam-5428	342	12	u.	u.	PROPN
ejpam-5428	342	13	d.	d.	PROPN
ejpam-5428	342	14	patel	patel	PROPN
ejpam-5428	342	15	,	,	PUNCT
ejpam-5428	342	16	s.	s.	PROPN
ejpam-5428	342	17	radenović	radenović	PROPN
ejpam-5428	342	18	/	/	SYM
ejpam-5428	342	19	eur	eur	PROPN
ejpam-5428	342	20	.	.	PUNCT
ejpam-5428	343	1	j.	j.	PROPN
ejpam-5428	343	2	pure	pure	PROPN
ejpam-5428	343	3	appl	appl	PROPN
ejpam-5428	343	4	.	.	PROPN
ejpam-5428	343	5	math	math	PROPN
ejpam-5428	343	6	,	,	PUNCT
ejpam-5428	343	7	17	17	NUM
ejpam-5428	343	8	(	(	PUNCT
ejpam-5428	343	9	4	4	NUM
ejpam-5428	343	10	)	)	PUNCT
ejpam-5428	343	11	(	(	PUNCT
ejpam-5428	343	12	2024	2024	NUM
ejpam-5428	343	13	)	)	PUNCT
ejpam-5428	343	14	,	,	PUNCT
ejpam-5428	343	15	2384	2384	NUM
ejpam-5428	343	16	-	-	SYM
ejpam-5428	343	17	2404	2404	NUM
ejpam-5428	343	18	2401	2401	NUM
ejpam-5428	343	19	(	(	PUNCT
ejpam-5428	343	20	ii	ii	NOUN
ejpam-5428	343	21	)	)	PUNCT
ejpam-5428	343	22	for	for	ADP
ejpam-5428	343	23	all	all	DET
ejpam-5428	343	24	l1	l1	PROPN
ejpam-5428	343	25	,	,	PUNCT
ejpam-5428	343	26	s1	s1	PROPN
ejpam-5428	343	27	∈	∈	PROPN
ejpam-5428	344	1	[	[	X
ejpam-5428	344	2	a	a	X
ejpam-5428	344	3	,	,	PUNCT
ejpam-5428	344	4	b	b	NOUN
ejpam-5428	344	5	]	]	X
ejpam-5428	344	6	(	(	PUNCT
ejpam-5428	344	7	∫	∫	PROPN
ejpam-5428	344	8	b	b	PROPN
ejpam-5428	344	9	a	a	DET
ejpam-5428	344	10	h(l1	h(l1	PROPN
ejpam-5428	344	11	,	,	PUNCT
ejpam-5428	344	12	s1)ds1	s1)ds1	ADJ
ejpam-5428	344	13	)	)	PUNCT
ejpam-5428	344	14	2	2	NUM
ejpam-5428	344	15	≤	≤	NUM
ejpam-5428	344	16	1	1	NUM
ejpam-5428	344	17	b−	b−	NOUN
ejpam-5428	344	18	a	a	PRON
ejpam-5428	344	19	.	.	PUNCT
ejpam-5428	345	1	(	(	PUNCT
ejpam-5428	345	2	iii	iii	X
ejpam-5428	345	3	)	)	PUNCT
ejpam-5428	345	4	if	if	SCONJ
ejpam-5428	345	5	{	{	PUNCT
ejpam-5428	345	6	δn(l1	δn(l1	NOUN
ejpam-5428	345	7	)	)	PUNCT
ejpam-5428	345	8	}	}	PUNCT
ejpam-5428	345	9	and	and	CCONJ
ejpam-5428	345	10	{	{	PUNCT
ejpam-5428	345	11	δm(l1	δm(l1	NOUN
ejpam-5428	345	12	)	)	PUNCT
ejpam-5428	345	13	}	}	PUNCT
ejpam-5428	345	14	are	be	AUX
ejpam-5428	345	15	the	the	DET
ejpam-5428	345	16	two	two	NUM
ejpam-5428	345	17	sequences	sequence	NOUN
ejpam-5428	345	18	in	in	ADP
ejpam-5428	345	19	ȳ	ȳ	NUM
ejpam-5428	345	20	such	such	ADJ
ejpam-5428	345	21	that	that	SCONJ
ejpam-5428	345	22	lim	lim	PROPN
ejpam-5428	345	23	n	n	CCONJ
ejpam-5428	345	24	,	,	PUNCT
ejpam-5428	345	25	m→+∞	m→+∞	PROPN
ejpam-5428	345	26	max	max	PROPN
ejpam-5428	345	27	a≤l1≤b	a≤l1≤b	PROPN
ejpam-5428	345	28	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	345	29	δm(l1)|2	δm(l1)|2	X
ejpam-5428	345	30	→	→	SYM
ejpam-5428	345	31	r(k	r(k	ADJ
ejpam-5428	345	32	)	)	PUNCT
ejpam-5428	345	33	⇒	⇒	NOUN
ejpam-5428	345	34	q	q	PROPN
ejpam-5428	345	35	·	·	PUNCT
ejpam-5428	345	36	(	(	PUNCT
ejpam-5428	345	37	l	l	NOUN
ejpam-5428	345	38	+	+	CCONJ
ejpam-5428	345	39	max	max	PROPN
ejpam-5428	345	40	a≤l1≤b	a≤l1≤b	PROPN
ejpam-5428	345	41	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	345	42	δn+1(l1)|)2	δn+1(l1)|)2	NOUN
ejpam-5428	345	43	<	<	X
ejpam-5428	345	44	(	(	PUNCT
ejpam-5428	345	45	l	l	NOUN
ejpam-5428	345	46	+	+	CCONJ
ejpam-5428	345	47	max	max	PROPN
ejpam-5428	345	48	a≤l1≤b	a≤l1≤b	PROPN
ejpam-5428	345	49	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	345	50	δm(l1)|2	δm(l1)|2	NOUN
ejpam-5428	345	51	)	)	PUNCT
ejpam-5428	345	52	,	,	PUNCT
ejpam-5428	345	53	for	for	ADP
ejpam-5428	345	54	all	all	DET
ejpam-5428	345	55	n	n	CCONJ
ejpam-5428	345	56	,	,	PUNCT
ejpam-5428	345	57	m	m	VERB
ejpam-5428	345	58	∈	∈	NOUN
ejpam-5428	345	59	n	n	PRON
ejpam-5428	345	60	such	such	ADJ
ejpam-5428	345	61	that	that	SCONJ
ejpam-5428	345	62	n	n	PROPN
ejpam-5428	345	63	>	>	X
ejpam-5428	345	64	m	m	PROPN
ejpam-5428	345	65	,	,	PUNCT
ejpam-5428	345	66	q	q	PROPN
ejpam-5428	345	67	∈	∈	PROPN
ejpam-5428	345	68	(	(	PUNCT
ejpam-5428	345	69	0	0	NUM
ejpam-5428	345	70	,	,	PUNCT
ejpam-5428	345	71	1	1	NUM
ejpam-5428	345	72	)	)	PUNCT
ejpam-5428	345	73	.	.	PUNCT
ejpam-5428	346	1	(	(	PUNCT
ejpam-5428	346	2	iv	iv	X
ejpam-5428	346	3	)	)	PUNCT
ejpam-5428	346	4	if	if	SCONJ
ejpam-5428	346	5	{	{	PUNCT
ejpam-5428	346	6	δn(l1	δn(l1	PROPN
ejpam-5428	346	7	)	)	PUNCT
ejpam-5428	346	8	}	}	PUNCT
ejpam-5428	346	9	is	be	AUX
ejpam-5428	346	10	a	a	DET
ejpam-5428	346	11	sequence	sequence	NOUN
ejpam-5428	346	12	in	in	ADP
ejpam-5428	346	13	c	c	PROPN
ejpam-5428	346	14	(	(	PUNCT
ejpam-5428	346	15	[	[	X
ejpam-5428	346	16	a	a	PRON
ejpam-5428	346	17	,	,	PUNCT
ejpam-5428	346	18	b],r	b],r	NOUN
ejpam-5428	346	19	)	)	PUNCT
ejpam-5428	346	20	such	such	ADJ
ejpam-5428	346	21	that	that	PRON
ejpam-5428	346	22	δn(l1	δn(l1	PROPN
ejpam-5428	346	23	)	)	PUNCT
ejpam-5428	346	24	→	→	SYM
ejpam-5428	346	25	δ(l1	δ(l1	PROPN
ejpam-5428	346	26	)	)	PUNCT
ejpam-5428	346	27	⇒	⇒	NOUN
ejpam-5428	346	28	q	q	PROPN
ejpam-5428	346	29	·	·	PUNCT
ejpam-5428	346	30	(	(	PUNCT
ejpam-5428	346	31	l	l	NOUN
ejpam-5428	346	32	+	+	CCONJ
ejpam-5428	346	33	max	max	PROPN
ejpam-5428	346	34	a≤l1≤b	a≤l1≤b	PROPN
ejpam-5428	346	35	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	346	36	δn+1(l1)|2	δn+1(l1)|2	NOUN
ejpam-5428	346	37	)	)	PUNCT
ejpam-5428	346	38	<	<	X
ejpam-5428	346	39	(	(	PUNCT
ejpam-5428	346	40	l	l	NOUN
ejpam-5428	346	41	+	+	CCONJ
ejpam-5428	346	42	max	max	PROPN
ejpam-5428	346	43	a≤l1≤b	a≤l1≤b	PROPN
ejpam-5428	346	44	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	346	45	δ(l1)|2	δ(l1)|2	NUM
ejpam-5428	346	46	)	)	PUNCT
ejpam-5428	346	47	,	,	PUNCT
ejpam-5428	346	48	for	for	ADP
ejpam-5428	346	49	all	all	DET
ejpam-5428	346	50	n	n	PRON
ejpam-5428	346	51	∈	∈	PROPN
ejpam-5428	346	52	n	n	NOUN
ejpam-5428	346	53	and	and	CCONJ
ejpam-5428	346	54	l	l	NOUN
ejpam-5428	346	55	>	>	X
ejpam-5428	346	56	0	0	NUM
ejpam-5428	346	57	,	,	PUNCT
ejpam-5428	346	58	q	q	PROPN
ejpam-5428	346	59	∈	∈	PROPN
ejpam-5428	346	60	(	(	PUNCT
ejpam-5428	346	61	0	0	NUM
ejpam-5428	346	62	,	,	PUNCT
ejpam-5428	346	63	1	1	NUM
ejpam-5428	346	64	)	)	PUNCT
ejpam-5428	346	65	.	.	PUNCT
ejpam-5428	347	1	then	then	ADV
ejpam-5428	347	2	the	the	DET
ejpam-5428	347	3	integral	integral	ADJ
ejpam-5428	347	4	equation	equation	NOUN
ejpam-5428	347	5	(	(	PUNCT
ejpam-5428	347	6	23	23	NUM
ejpam-5428	347	7	)	)	PUNCT
ejpam-5428	347	8	has	have	VERB
ejpam-5428	347	9	a	a	DET
ejpam-5428	347	10	solution	solution	NOUN
ejpam-5428	347	11	in	in	ADP
ejpam-5428	347	12	ȳ.	ȳ.	NOUN
ejpam-5428	347	13	proof	proof	NOUN
ejpam-5428	347	14	.	.	PUNCT
ejpam-5428	348	1	suppose	suppose	VERB
ejpam-5428	348	2	l	l	NOUN
ejpam-5428	348	3	:	:	PUNCT
ejpam-5428	348	4	ȳ	ȳ	PROPN
ejpam-5428	348	5	→	→	SYM
ejpam-5428	348	6	ȳ	ȳ	PROPN
ejpam-5428	348	7	is	be	AUX
ejpam-5428	348	8	an	an	DET
ejpam-5428	348	9	integral	integral	ADJ
ejpam-5428	348	10	operator	operator	NOUN
ejpam-5428	348	11	lδ(l1	lδ(l1	PROPN
ejpam-5428	348	12	)	)	PUNCT
ejpam-5428	348	13	=	=	SYM
ejpam-5428	348	14	f(l1	f(l1	PROPN
ejpam-5428	348	15	)	)	PUNCT
ejpam-5428	349	1	+	+	CCONJ
ejpam-5428	350	1	∫	∫	PROPN
ejpam-5428	350	2	b	b	PROPN
ejpam-5428	350	3	a	a	DET
ejpam-5428	350	4	h(l1	h(l1	PROPN
ejpam-5428	350	5	,	,	PUNCT
ejpam-5428	350	6	s1)f	s1)f	ADJ
ejpam-5428	350	7	(	(	PUNCT
ejpam-5428	350	8	l1	l1	PROPN
ejpam-5428	350	9	,	,	PUNCT
ejpam-5428	350	10	s1	s1	NOUN
ejpam-5428	350	11	,	,	PUNCT
ejpam-5428	350	12	δ(s1))ds1	δ(s1))ds1	PROPN
ejpam-5428	350	13	,	,	PUNCT
ejpam-5428	350	14	for	for	ADP
ejpam-5428	350	15	δ	δ	PROPN
ejpam-5428	350	16	∈	∈	PROPN
ejpam-5428	350	17	ȳ.	ȳ.	NOUN
ejpam-5428	350	18	now	now	ADV
ejpam-5428	350	19	1	1	NUM
ejpam-5428	350	20	mz(lδ	mz(lδ	NOUN
ejpam-5428	350	21	,	,	PUNCT
ejpam-5428	350	22	lγ	lγ	PROPN
ejpam-5428	350	23	,	,	PUNCT
ejpam-5428	350	24	l	l	NOUN
ejpam-5428	350	25	)	)	PUNCT
ejpam-5428	350	26	−	−	NOUN
ejpam-5428	350	27	1	1	NUM
ejpam-5428	350	28	=	=	SYM
ejpam-5428	350	29	1	1	NUM
ejpam-5428	350	30	l	l	NOUN
ejpam-5428	350	31	l+	l+	PUNCT
ejpam-5428	350	32	max	max	PROPN
ejpam-5428	350	33	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	34	|lδ(s1)−lγ(s1)|2	|lδ(s1)−lγ(s1)|2	PROPN
ejpam-5428	350	35	−	−	NOUN
ejpam-5428	350	36	1	1	NUM
ejpam-5428	350	37	=	=	SYM
ejpam-5428	350	38	1−	1−	NUM
ejpam-5428	350	39	l	l	NOUN
ejpam-5428	350	40	l+	l+	PUNCT
ejpam-5428	350	41	max	max	PROPN
ejpam-5428	350	42	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	43	|lδ(s1)−lγ(s1)|2	|lδ(s1)−lγ(s1)|2	PROPN
ejpam-5428	350	44	l	l	NOUN
ejpam-5428	350	45	l+	l+	PUNCT
ejpam-5428	350	46	max	max	PROPN
ejpam-5428	350	47	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	48	|lδ(s1)−lγ(s1)|2	|lδ(s1)−lγ(s1)|2	PROPN
ejpam-5428	350	49	=	=	SYM
ejpam-5428	350	50	max	max	PROPN
ejpam-5428	350	51	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	52	|lδ(s1)−	|lδ(s1)−	PROPN
ejpam-5428	350	53	lγ(s1)|2	lγ(s1)|2	NOUN
ejpam-5428	350	54	l	l	NOUN
ejpam-5428	350	55	=	=	SYM
ejpam-5428	350	56	max	max	PROPN
ejpam-5428	350	57	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	58	|	|	ADV
ejpam-5428	350	59	∫	∫	PROPN
ejpam-5428	350	60	b	b	PROPN
ejpam-5428	350	61	a	a	DET
ejpam-5428	350	62	h(l1	h(l1	PROPN
ejpam-5428	350	63	,	,	PUNCT
ejpam-5428	350	64	s1)f	s1)f	ADJ
ejpam-5428	350	65	(	(	PUNCT
ejpam-5428	350	66	l1	l1	PROPN
ejpam-5428	350	67	,	,	PUNCT
ejpam-5428	350	68	s1	s1	NOUN
ejpam-5428	350	69	,	,	PUNCT
ejpam-5428	350	70	δ(s1))ds1	δ(s1))ds1	PROPN
ejpam-5428	350	71	−	−	PROPN
ejpam-5428	350	72	∫	∫	PROPN
ejpam-5428	350	73	b	b	PROPN
ejpam-5428	350	74	a	a	DET
ejpam-5428	350	75	h(l1	h(l1	PROPN
ejpam-5428	350	76	,	,	PUNCT
ejpam-5428	350	77	s1)f	s1)f	ADJ
ejpam-5428	350	78	(	(	PUNCT
ejpam-5428	350	79	l1	l1	PROPN
ejpam-5428	350	80	,	,	PUNCT
ejpam-5428	350	81	s1	s1	PROPN
ejpam-5428	350	82	,	,	PUNCT
ejpam-5428	350	83	y(s1))ds1|2	y(s1))ds1|2	NUM
ejpam-5428	350	84	l	l	NOUN
ejpam-5428	350	85	≤	≤	NUM
ejpam-5428	350	86	max	max	PROPN
ejpam-5428	350	87	a≤s1≤b	a≤s1≤b	PROPN
ejpam-5428	350	88	e−	e−	PROPN
ejpam-5428	350	89	|δ(s1)−γ(s1)|	|δ(s1)−γ(s1)|	VERB
ejpam-5428	350	90	2	2	NUM
ejpam-5428	350	91	l	l	NOUN
ejpam-5428	350	92	·	·	PUNCT
ejpam-5428	350	93	|δ(s1)−	|δ(s1)−	NOUN
ejpam-5428	350	94	γ(s1)|2	γ(s1)|2	X
ejpam-5428	350	95	l	l	NOUN
ejpam-5428	351	1	≤	≤	X
ejpam-5428	351	2	β	β	X
ejpam-5428	351	3	(	(	PUNCT
ejpam-5428	351	4	1	1	NUM
ejpam-5428	351	5	mz(δ	mz(δ	NUM
ejpam-5428	351	6	,	,	PUNCT
ejpam-5428	351	7	γ	γ	X
ejpam-5428	351	8	,	,	PUNCT
ejpam-5428	351	9	l	l	NOUN
ejpam-5428	351	10	)	)	PUNCT
ejpam-5428	351	11	−	−	PROPN
ejpam-5428	351	12	1	1	NUM
ejpam-5428	351	13	)	)	PUNCT
ejpam-5428	351	14	(	(	PUNCT
ejpam-5428	351	15	1	1	NUM
ejpam-5428	351	16	mz(δ	mz(δ	NUM
ejpam-5428	351	17	,	,	PUNCT
ejpam-5428	351	18	γ	γ	X
ejpam-5428	351	19	,	,	PUNCT
ejpam-5428	351	20	l	l	NOUN
ejpam-5428	351	21	)	)	PUNCT
ejpam-5428	351	22	−	−	PROPN
ejpam-5428	351	23	1	1	NUM
ejpam-5428	351	24	)	)	PUNCT
ejpam-5428	351	25	.	.	PUNCT
ejpam-5428	352	1	v.	v.	CCONJ
ejpam-5428	352	2	chandra	chandra	PROPN
ejpam-5428	352	3	,	,	PUNCT
ejpam-5428	352	4	u.	u.	PROPN
ejpam-5428	352	5	d.	d.	PROPN
ejpam-5428	352	6	patel	patel	PROPN
ejpam-5428	352	7	,	,	PUNCT
ejpam-5428	352	8	s.	s.	PROPN
ejpam-5428	352	9	radenović	radenović	PROPN
ejpam-5428	352	10	/	/	SYM
ejpam-5428	352	11	eur	eur	PROPN
ejpam-5428	352	12	.	.	PUNCT
ejpam-5428	353	1	j.	j.	PROPN
ejpam-5428	353	2	pure	pure	PROPN
ejpam-5428	353	3	appl	appl	PROPN
ejpam-5428	353	4	.	.	PROPN
ejpam-5428	353	5	math	math	PROPN
ejpam-5428	353	6	,	,	PUNCT
ejpam-5428	353	7	17	17	NUM
ejpam-5428	353	8	(	(	PUNCT
ejpam-5428	353	9	4	4	NUM
ejpam-5428	353	10	)	)	PUNCT
ejpam-5428	353	11	(	(	PUNCT
ejpam-5428	353	12	2024	2024	NUM
ejpam-5428	353	13	)	)	PUNCT
ejpam-5428	353	14	,	,	PUNCT
ejpam-5428	353	15	2384	2384	NUM
ejpam-5428	353	16	-	-	SYM
ejpam-5428	353	17	2404	2404	NUM
ejpam-5428	353	18	2402	2402	NUM
ejpam-5428	353	19	therefore	therefore	ADV
ejpam-5428	353	20	,	,	PUNCT
ejpam-5428	353	21	l	l	NOUN
ejpam-5428	353	22	is	be	AUX
ejpam-5428	353	23	a	a	DET
ejpam-5428	353	24	suzuki	suzuki	NOUN
ejpam-5428	353	25	geraghty	geraghty	PROPN
ejpam-5428	353	26	type	type	PROPN
ejpam-5428	353	27	-	-	PUNCT
ejpam-5428	353	28	ii	ii	NOUN
ejpam-5428	353	29	contractive	contractive	ADJ
ejpam-5428	353	30	mapping	mapping	NOUN
ejpam-5428	353	31	for	for	ADP
ejpam-5428	353	32	β(t1	β(t1	NOUN
ejpam-5428	353	33	)	)	PUNCT
ejpam-5428	353	34	=	=	PUNCT
ejpam-5428	353	35	e−t1	e−t1	NOUN
ejpam-5428	353	36	and	and	CCONJ
ejpam-5428	353	37	l1	l1	PROPN
ejpam-5428	353	38	>	>	X
ejpam-5428	353	39	0	0	X
ejpam-5428	353	40	.	.	PUNCT
ejpam-5428	354	1	for	for	ADP
ejpam-5428	354	2	two	two	NUM
ejpam-5428	354	3	sequences	sequence	NOUN
ejpam-5428	354	4	in	in	ADP
ejpam-5428	354	5	ȳ	ȳ	NUM
ejpam-5428	354	6	such	such	ADJ
ejpam-5428	354	7	that	that	SCONJ
ejpam-5428	354	8	n	n	PROPN
ejpam-5428	354	9	>	>	X
ejpam-5428	354	10	m	m	PROPN
ejpam-5428	354	11	and	and	CCONJ
ejpam-5428	354	12	n	n	CCONJ
ejpam-5428	354	13	,	,	PUNCT
ejpam-5428	354	14	m	m	VERB
ejpam-5428	354	15	∈	∈	PROPN
ejpam-5428	354	16	n	n	CCONJ
ejpam-5428	354	17	,	,	PUNCT
ejpam-5428	354	18	by	by	ADP
ejpam-5428	354	19	using	use	VERB
ejpam-5428	354	20	the	the	DET
ejpam-5428	354	21	assumption	assumption	NOUN
ejpam-5428	354	22	(	(	PUNCT
ejpam-5428	354	23	3	3	X
ejpam-5428	354	24	)	)	PUNCT
ejpam-5428	354	25	mz	mz	PROPN
ejpam-5428	354	26	(	(	PUNCT
ejpam-5428	354	27	δn(l1	δn(l1	PROPN
ejpam-5428	354	28	)	)	PUNCT
ejpam-5428	354	29	,	,	PUNCT
ejpam-5428	354	30	δm(l1	δm(l1	PROPN
ejpam-5428	354	31	)	)	PUNCT
ejpam-5428	354	32	,	,	PUNCT
ejpam-5428	354	33	l	l	NOUN
ejpam-5428	354	34	)	)	PUNCT
ejpam-5428	354	35	=	=	SYM
ejpam-5428	354	36	l	l	NOUN
ejpam-5428	354	37	l	l	NOUN
ejpam-5428	354	38	+	+	PUNCT
ejpam-5428	354	39	maxa≤l1≤b	maxa≤l1≤b	PROPN
ejpam-5428	354	40	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	354	41	δm(l1)|2	δm(l1)|2	X
ejpam-5428	354	42	>	>	X
ejpam-5428	354	43	q	q	X
ejpam-5428	354	44	·	·	PUNCT
ejpam-5428	354	45	l	l	X
ejpam-5428	354	46	l	l	NOUN
ejpam-5428	354	47	+	+	PUNCT
ejpam-5428	354	48	r(k	r(k	ADJ
ejpam-5428	354	49	)	)	PUNCT
ejpam-5428	354	50	=	=	SYM
ejpam-5428	354	51	r(l	r(l	NOUN
ejpam-5428	354	52	)	)	PUNCT
ejpam-5428	354	53	∈	∈	PROPN
ejpam-5428	354	54	(	(	PUNCT
ejpam-5428	354	55	0	0	NUM
ejpam-5428	354	56	,	,	PUNCT
ejpam-5428	354	57	1	1	NUM
ejpam-5428	354	58	]	]	PUNCT
ejpam-5428	354	59	implies	imply	VERB
ejpam-5428	354	60	mz	mz	PROPN
ejpam-5428	354	61	(	(	PUNCT
ejpam-5428	354	62	δn(l1	δn(l1	PROPN
ejpam-5428	354	63	)	)	PUNCT
ejpam-5428	354	64	,	,	PUNCT
ejpam-5428	354	65	δn+1(l1	δn+1(l1	NUM
ejpam-5428	354	66	)	)	PUNCT
ejpam-5428	354	67	,	,	PUNCT
ejpam-5428	354	68	l	l	NOUN
ejpam-5428	354	69	)	)	PUNCT
ejpam-5428	354	70	=	=	SYM
ejpam-5428	355	1	l	l	NOUN
ejpam-5428	355	2	l	l	NOUN
ejpam-5428	355	3	+	+	PUNCT
ejpam-5428	355	4	maxa≤l1≤b	maxa≤l1≤b	PROPN
ejpam-5428	355	5	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	355	6	δn+1(l1)|2	δn+1(l1)|2	NOUN
ejpam-5428	355	7	>	>	X
ejpam-5428	355	8	q	q	X
ejpam-5428	355	9	·	·	PUNCT
ejpam-5428	355	10	l	l	NOUN
ejpam-5428	355	11	l	l	PUNCT
ejpam-5428	356	1	+	+	PUNCT
ejpam-5428	356	2	maxa≤l1≤b	maxa≤l1≤b	PROPN
ejpam-5428	356	3	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	356	4	δm(l1)|2	δm(l1)|2	X
ejpam-5428	356	5	=	=	SYM
ejpam-5428	356	6	q	q	X
ejpam-5428	356	7	·	·	PUNCT
ejpam-5428	356	8	mz	mz	PROPN
ejpam-5428	356	9	(	(	PUNCT
ejpam-5428	356	10	δn(l1	δn(l1	PROPN
ejpam-5428	356	11	)	)	PUNCT
ejpam-5428	356	12	,	,	PUNCT
ejpam-5428	356	13	δm(l1	δm(l1	PROPN
ejpam-5428	356	14	)	)	PUNCT
ejpam-5428	356	15	,	,	PUNCT
ejpam-5428	356	16	l	l	NOUN
ejpam-5428	356	17	)	)	PUNCT
ejpam-5428	356	18	.	.	PUNCT
ejpam-5428	357	1	hence	hence	ADV
ejpam-5428	357	2	,	,	PUNCT
ejpam-5428	357	3	property-(g1	property-(g1	ADJ
ejpam-5428	357	4	)	)	PUNCT
ejpam-5428	357	5	holds	hold	VERB
ejpam-5428	357	6	.	.	PUNCT
ejpam-5428	358	1	if	if	SCONJ
ejpam-5428	358	2	a	a	DET
ejpam-5428	358	3	sequence	sequence	NOUN
ejpam-5428	358	4	{	{	PUNCT
ejpam-5428	358	5	δn(l1	δn(l1	PROPN
ejpam-5428	358	6	)	)	PUNCT
ejpam-5428	358	7	}	}	PUNCT
ejpam-5428	358	8	in	in	ADP
ejpam-5428	358	9	ȳ	ȳ	NUM
ejpam-5428	358	10	such	such	ADJ
ejpam-5428	358	11	that	that	PRON
ejpam-5428	358	12	δn(l1	δn(l1	PROPN
ejpam-5428	358	13	)	)	PUNCT
ejpam-5428	358	14	→	→	SYM
ejpam-5428	358	15	δ(l1	δ(l1	NOUN
ejpam-5428	358	16	)	)	PUNCT
ejpam-5428	358	17	in	in	ADP
ejpam-5428	358	18	ȳ	ȳ	NUM
ejpam-5428	358	19	by	by	ADP
ejpam-5428	358	20	using	use	VERB
ejpam-5428	358	21	assumption	assumption	NOUN
ejpam-5428	358	22	(	(	PUNCT
ejpam-5428	358	23	4	4	NUM
ejpam-5428	358	24	)	)	PUNCT
ejpam-5428	358	25	,	,	PUNCT
ejpam-5428	358	26	mz	mz	PROPN
ejpam-5428	358	27	(	(	PUNCT
ejpam-5428	358	28	δn(l1	δn(l1	PROPN
ejpam-5428	358	29	)	)	PUNCT
ejpam-5428	358	30	,	,	PUNCT
ejpam-5428	358	31	δn+1(l1	δn+1(l1	NUM
ejpam-5428	358	32	)	)	PUNCT
ejpam-5428	358	33	,	,	PUNCT
ejpam-5428	358	34	l	l	NOUN
ejpam-5428	358	35	)	)	PUNCT
ejpam-5428	358	36	=	=	SYM
ejpam-5428	359	1	l	l	NOUN
ejpam-5428	359	2	l	l	NOUN
ejpam-5428	359	3	+	+	PUNCT
ejpam-5428	359	4	maxa≤l1≤b	maxa≤l1≤b	PROPN
ejpam-5428	359	5	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	359	6	δn+1(l1)|2	δn+1(l1)|2	NOUN
ejpam-5428	359	7	>	>	X
ejpam-5428	359	8	q	q	X
ejpam-5428	359	9	·	·	PUNCT
ejpam-5428	359	10	l	l	NOUN
ejpam-5428	359	11	l	l	PUNCT
ejpam-5428	360	1	+	+	PUNCT
ejpam-5428	360	2	maxa≤l1≤b	maxa≤l1≤b	PROPN
ejpam-5428	360	3	|δn(l1)−	|δn(l1)−	PROPN
ejpam-5428	360	4	δ(l1)|2	δ(l1)|2	NUM
ejpam-5428	360	5	=	=	PUNCT
ejpam-5428	360	6	q	q	X
ejpam-5428	360	7	·	·	PUNCT
ejpam-5428	360	8	mz	mz	PROPN
ejpam-5428	360	9	(	(	PUNCT
ejpam-5428	360	10	δn(l1	δn(l1	PROPN
ejpam-5428	360	11	)	)	PUNCT
ejpam-5428	360	12	,	,	PUNCT
ejpam-5428	360	13	δ(l1	δ(l1	PROPN
ejpam-5428	360	14	)	)	PUNCT
ejpam-5428	360	15	,	,	PUNCT
ejpam-5428	360	16	l	l	NOUN
ejpam-5428	360	17	)	)	PUNCT
ejpam-5428	360	18	.	.	PUNCT
ejpam-5428	361	1	therefore	therefore	ADV
ejpam-5428	361	2	,	,	PUNCT
ejpam-5428	361	3	property	property	NOUN
ejpam-5428	361	4	(	(	PUNCT
ejpam-5428	361	5	g2	g2	PROPN
ejpam-5428	361	6	)	)	PUNCT
ejpam-5428	361	7	holds	hold	VERB
ejpam-5428	361	8	.	.	PUNCT
ejpam-5428	362	1	therefore	therefore	ADV
ejpam-5428	362	2	every	every	DET
ejpam-5428	362	3	requirements	requirement	NOUN
ejpam-5428	362	4	of	of	ADP
ejpam-5428	362	5	corollary	corollary	ADJ
ejpam-5428	362	6	(	(	PUNCT
ejpam-5428	362	7	2	2	NUM
ejpam-5428	362	8	)	)	PUNCT
ejpam-5428	362	9	are	be	AUX
ejpam-5428	362	10	gratified	gratify	VERB
ejpam-5428	362	11	with	with	ADP
ejpam-5428	362	12	the	the	DET
ejpam-5428	362	13	consideration	consideration	NOUN
ejpam-5428	362	14	of	of	ADP
ejpam-5428	362	15	the	the	DET
ejpam-5428	362	16	function	function	NOUN
ejpam-5428	362	17	β(t1	β(t1	PUNCT
ejpam-5428	362	18	)	)	PUNCT
ejpam-5428	363	1	=	=	PUNCT
ejpam-5428	363	2	e−t1	e−t1	NOUN
ejpam-5428	363	3	.	.	PUNCT
ejpam-5428	364	1	hence	hence	ADV
ejpam-5428	364	2	,	,	PUNCT
ejpam-5428	364	3	we	we	PRON
ejpam-5428	364	4	conclude	conclude	VERB
ejpam-5428	364	5	that	that	SCONJ
ejpam-5428	364	6	there	there	PRON
ejpam-5428	364	7	exists	exist	VERB
ejpam-5428	364	8	δ(l1	δ(l1	NOUN
ejpam-5428	364	9	)	)	PUNCT
ejpam-5428	364	10	∈	∈	PROPN
ejpam-5428	364	11	c	c	NOUN
ejpam-5428	364	12	(	(	PUNCT
ejpam-5428	364	13	[	[	X
ejpam-5428	364	14	a	a	PRON
ejpam-5428	364	15	,	,	PUNCT
ejpam-5428	364	16	b],r	b],r	NOUN
ejpam-5428	364	17	)	)	PUNCT
ejpam-5428	364	18	such	such	ADJ
ejpam-5428	364	19	that	that	PRON
ejpam-5428	364	20	lδ(l1	lδ(l1	PROPN
ejpam-5428	364	21	)	)	PUNCT
ejpam-5428	364	22	=	=	SYM
ejpam-5428	364	23	δ(l1	δ(l1	NOUN
ejpam-5428	364	24	)	)	PUNCT
ejpam-5428	364	25	and	and	CCONJ
ejpam-5428	364	26	the	the	DET
ejpam-5428	364	27	integral	integral	ADJ
ejpam-5428	364	28	equations	equation	NOUN
ejpam-5428	364	29	(	(	PUNCT
ejpam-5428	364	30	23	23	NUM
ejpam-5428	364	31	)	)	PUNCT
ejpam-5428	364	32	has	have	VERB
ejpam-5428	364	33	a	a	DET
ejpam-5428	364	34	solution	solution	NOUN
ejpam-5428	364	35	.	.	PUNCT
ejpam-5428	365	1	this	this	DET
ejpam-5428	365	2	way	way	NOUN
ejpam-5428	365	3	we	we	PRON
ejpam-5428	365	4	complete	complete	VERB
ejpam-5428	365	5	the	the	DET
ejpam-5428	365	6	proof	proof	NOUN
ejpam-5428	365	7	.	.	PUNCT
ejpam-5428	366	1	4	4	X
ejpam-5428	366	2	.	.	X
ejpam-5428	366	3	conclusion	conclusion	NOUN
ejpam-5428	366	4	and	and	CCONJ
ejpam-5428	366	5	future	future	ADJ
ejpam-5428	366	6	work	work	NOUN
ejpam-5428	366	7	in	in	ADP
ejpam-5428	366	8	this	this	DET
ejpam-5428	366	9	study	study	NOUN
ejpam-5428	366	10	,	,	PUNCT
ejpam-5428	366	11	we	we	PRON
ejpam-5428	366	12	explore	explore	VERB
ejpam-5428	366	13	the	the	DET
ejpam-5428	366	14	concept	concept	NOUN
ejpam-5428	366	15	of	of	ADP
ejpam-5428	366	16	fuzzy	fuzzy	ADJ
ejpam-5428	366	17	α	α	PROPN
ejpam-5428	366	18	-	-	PUNCT
ejpam-5428	366	19	geraghty	geraghty	VERB
ejpam-5428	366	20	type	type	NOUN
ejpam-5428	366	21	mappings	mapping	NOUN
ejpam-5428	366	22	and	and	CCONJ
ejpam-5428	366	23	α	α	NOUN
ejpam-5428	366	24	-	-	PUNCT
ejpam-5428	366	25	suzukigeraghty	suzukigeraghty	VERB
ejpam-5428	366	26	type	type	NOUN
ejpam-5428	366	27	mappings	mapping	NOUN
ejpam-5428	366	28	within	within	ADP
ejpam-5428	366	29	the	the	DET
ejpam-5428	366	30	framework	framework	NOUN
ejpam-5428	366	31	of	of	ADP
ejpam-5428	366	32	b	b	NOUN
ejpam-5428	366	33	-	-	PUNCT
ejpam-5428	366	34	fuzzy	fuzzy	ADJ
ejpam-5428	366	35	metric	metric	ADJ
ejpam-5428	366	36	space	space	NOUN
ejpam-5428	366	37	.	.	PUNCT
ejpam-5428	367	1	we	we	PRON
ejpam-5428	367	2	extended	extend	VERB
ejpam-5428	367	3	the	the	DET
ejpam-5428	367	4	theory	theory	NOUN
ejpam-5428	367	5	of	of	ADP
ejpam-5428	367	6	fixed	fix	VERB
ejpam-5428	367	7	-	-	PUNCT
ejpam-5428	367	8	point	point	NOUN
ejpam-5428	367	9	theorems	theorem	NOUN
ejpam-5428	367	10	by	by	ADP
ejpam-5428	367	11	employing	employ	VERB
ejpam-5428	367	12	these	these	DET
ejpam-5428	367	13	mappings	mapping	NOUN
ejpam-5428	367	14	and	and	CCONJ
ejpam-5428	367	15	demonstrated	demonstrate	VERB
ejpam-5428	367	16	their	their	PRON
ejpam-5428	367	17	utility	utility	NOUN
ejpam-5428	367	18	through	through	ADP
ejpam-5428	367	19	several	several	ADJ
ejpam-5428	367	20	illustrative	illustrative	ADJ
ejpam-5428	367	21	examples	example	NOUN
ejpam-5428	367	22	,	,	PUNCT
ejpam-5428	367	23	including	include	VERB
ejpam-5428	367	24	a	a	DET
ejpam-5428	367	25	graphical	graphical	ADJ
ejpam-5428	367	26	approach	approach	NOUN
ejpam-5428	367	27	for	for	ADP
ejpam-5428	367	28	better	well	ADJ
ejpam-5428	367	29	visualization	visualization	NOUN
ejpam-5428	367	30	.	.	PUNCT
ejpam-5428	368	1	our	our	PRON
ejpam-5428	368	2	findings	finding	NOUN
ejpam-5428	368	3	provide	provide	VERB
ejpam-5428	368	4	a	a	DET
ejpam-5428	368	5	foundation	foundation	NOUN
ejpam-5428	368	6	for	for	ADP
ejpam-5428	368	7	solving	solve	VERB
ejpam-5428	368	8	fixed	fix	VERB
ejpam-5428	368	9	-	-	PUNCT
ejpam-5428	368	10	point	point	NOUN
ejpam-5428	368	11	problems	problem	NOUN
ejpam-5428	368	12	in	in	ADP
ejpam-5428	368	13	more	more	ADJ
ejpam-5428	368	14	generalized	generalized	ADJ
ejpam-5428	368	15	settings	setting	NOUN
ejpam-5428	368	16	,	,	PUNCT
ejpam-5428	368	17	such	such	ADJ
ejpam-5428	368	18	as	as	ADP
ejpam-5428	368	19	g	g	NOUN
ejpam-5428	368	20	-	-	PUNCT
ejpam-5428	368	21	complete	complete	ADJ
ejpam-5428	368	22	b	b	X
ejpam-5428	368	23	-	-	PUNCT
ejpam-5428	368	24	fuzzy	fuzzy	ADJ
ejpam-5428	368	25	metric	metric	ADJ
ejpam-5428	368	26	space	space	NOUN
ejpam-5428	368	27	.	.	PUNCT
ejpam-5428	369	1	the	the	DET
ejpam-5428	369	2	application	application	NOUN
ejpam-5428	369	3	to	to	ADP
ejpam-5428	369	4	nonlinear	nonlinear	ADJ
ejpam-5428	369	5	integral	integral	ADJ
ejpam-5428	369	6	equations	equation	NOUN
ejpam-5428	369	7	highlights	highlight	VERB
ejpam-5428	369	8	the	the	DET
ejpam-5428	369	9	practical	practical	ADJ
ejpam-5428	369	10	significance	significance	NOUN
ejpam-5428	369	11	of	of	ADP
ejpam-5428	369	12	these	these	DET
ejpam-5428	369	13	results	result	NOUN
ejpam-5428	369	14	.	.	PUNCT
ejpam-5428	370	1	future	future	ADJ
ejpam-5428	370	2	research	research	NOUN
ejpam-5428	370	3	could	could	AUX
ejpam-5428	370	4	focus	focus	VERB
ejpam-5428	370	5	on	on	ADP
ejpam-5428	370	6	expanding	expand	VERB
ejpam-5428	370	7	these	these	DET
ejpam-5428	370	8	concepts	concept	NOUN
ejpam-5428	370	9	to	to	ADP
ejpam-5428	370	10	more	more	ADV
ejpam-5428	370	11	complex	complex	ADJ
ejpam-5428	370	12	metric	metric	ADJ
ejpam-5428	370	13	spaces	space	NOUN
ejpam-5428	370	14	or	or	CCONJ
ejpam-5428	370	15	hybrid	hybrid	NOUN
ejpam-5428	370	16	structures	structure	NOUN
ejpam-5428	370	17	,	,	PUNCT
ejpam-5428	370	18	exploring	explore	VERB
ejpam-5428	370	19	their	their	PRON
ejpam-5428	370	20	applications	application	NOUN
ejpam-5428	370	21	in	in	ADP
ejpam-5428	370	22	various	various	ADJ
ejpam-5428	370	23	fields	field	NOUN
ejpam-5428	370	24	such	such	ADJ
ejpam-5428	370	25	as	as	ADP
ejpam-5428	370	26	optimization	optimization	NOUN
ejpam-5428	370	27	,	,	PUNCT
ejpam-5428	370	28	dynamic	dynamic	ADJ
ejpam-5428	370	29	systems	system	NOUN
ejpam-5428	370	30	,	,	PUNCT
ejpam-5428	370	31	and	and	CCONJ
ejpam-5428	370	32	network	network	NOUN
ejpam-5428	370	33	theory	theory	NOUN
ejpam-5428	370	34	.	.	PUNCT
ejpam-5428	371	1	additionally	additionally	ADV
ejpam-5428	371	2	,	,	PUNCT
ejpam-5428	371	3	investigating	investigate	VERB
ejpam-5428	371	4	the	the	DET
ejpam-5428	371	5	interplay	interplay	NOUN
ejpam-5428	371	6	between	between	ADP
ejpam-5428	371	7	different	different	ADJ
ejpam-5428	371	8	types	type	NOUN
ejpam-5428	371	9	of	of	ADP
ejpam-5428	371	10	fuzzy	fuzzy	ADJ
ejpam-5428	371	11	metrics	metric	NOUN
ejpam-5428	371	12	and	and	CCONJ
ejpam-5428	371	13	mappings	mapping	NOUN
ejpam-5428	371	14	could	could	AUX
ejpam-5428	371	15	lead	lead	VERB
ejpam-5428	371	16	to	to	ADP
ejpam-5428	371	17	new	new	ADJ
ejpam-5428	371	18	insights	insight	NOUN
ejpam-5428	371	19	and	and	CCONJ
ejpam-5428	371	20	fixed	fix	VERB
ejpam-5428	371	21	-	-	PUNCT
ejpam-5428	371	22	point	point	NOUN
ejpam-5428	371	23	results	result	NOUN
ejpam-5428	371	24	with	with	ADP
ejpam-5428	371	25	broader	broad	ADJ
ejpam-5428	371	26	implications	implication	NOUN
ejpam-5428	371	27	.	.	PUNCT
ejpam-5428	372	1	these	these	DET
ejpam-5428	372	2	results	result	NOUN
ejpam-5428	372	3	can	can	AUX
ejpam-5428	372	4	be	be	AUX
ejpam-5428	372	5	expanded	expand	VERB
ejpam-5428	372	6	upon	upon	SCONJ
ejpam-5428	372	7	by	by	ADP
ejpam-5428	372	8	readers	reader	NOUN
ejpam-5428	372	9	with	with	ADP
ejpam-5428	372	10	applications	application	NOUN
ejpam-5428	372	11	in	in	ADP
ejpam-5428	372	12	fuzzy	fuzzy	ADJ
ejpam-5428	372	13	contexts	contexts	NOUN
ejpam-5428	372	14	,	,	PUNCT
ejpam-5428	372	15	refer	refer	VERB
ejpam-5428	372	16	[	[	X
ejpam-5428	372	17	9	9	NUM
ejpam-5428	372	18	]	]	PUNCT
ejpam-5428	372	19	,	,	PUNCT
ejpam-5428	373	1	[	[	X
ejpam-5428	373	2	10	10	NUM
ejpam-5428	373	3	]	]	PUNCT
ejpam-5428	373	4	,	,	PUNCT
ejpam-5428	373	5	[	[	X
ejpam-5428	373	6	12	12	NUM
ejpam-5428	373	7	]	]	PUNCT
ejpam-5428	373	8	,	,	PUNCT
ejpam-5428	374	1	[	[	X
ejpam-5428	374	2	11	11	NUM
ejpam-5428	374	3	]	]	PUNCT
ejpam-5428	374	4	,	,	PUNCT
ejpam-5428	374	5	[	[	X
ejpam-5428	374	6	13	13	NUM
ejpam-5428	374	7	]	]	PUNCT
ejpam-5428	374	8	.	.	PUNCT
ejpam-5428	375	1	references	reference	NOUN
ejpam-5428	375	2	2403	2403	NUM
ejpam-5428	375	3	acknowledgements	acknowledgement	NOUN
ejpam-5428	375	4	the	the	DET
ejpam-5428	375	5	first	first	ADJ
ejpam-5428	375	6	author	author	NOUN
ejpam-5428	375	7	is	be	AUX
ejpam-5428	375	8	thankful	thankful	ADJ
ejpam-5428	375	9	to	to	ADP
ejpam-5428	375	10	department	department	PROPN
ejpam-5428	375	11	of	of	ADP
ejpam-5428	375	12	science	science	NOUN
ejpam-5428	375	13	and	and	CCONJ
ejpam-5428	375	14	technology	technology	NOUN
ejpam-5428	375	15	,	,	PUNCT
ejpam-5428	375	16	new	new	ADJ
ejpam-5428	375	17	delhi	delhi	PROPN
ejpam-5428	375	18	,	,	PUNCT
ejpam-5428	375	19	india	india	PROPN
ejpam-5428	375	20	for	for	ADP
ejpam-5428	375	21	approving	approve	VERB
ejpam-5428	375	22	the	the	DET
ejpam-5428	375	23	proposal	proposal	NOUN
ejpam-5428	375	24	under	under	ADP
ejpam-5428	375	25	the	the	DET
ejpam-5428	375	26	scheme	scheme	NOUN
ejpam-5428	375	27	fist	fist	NOUN
ejpam-5428	375	28	program	program	NOUN
ejpam-5428	375	29	(	(	PUNCT
ejpam-5428	375	30	ref	ref	NOUN
ejpam-5428	375	31	.	.	PUNCT
ejpam-5428	376	1	no	no	INTJ
ejpam-5428	376	2	.	.	PUNCT
ejpam-5428	377	1	sr	sr	PROPN
ejpam-5428	377	2	/	/	SYM
ejpam-5428	377	3	fst	fst	PROPN
ejpam-5428	377	4	/	/	SYM
ejpam-5428	377	5	ms/2022/122	ms/2022/122	PROPN
ejpam-5428	377	6	dated	date	VERB
ejpam-5428	377	7	19/12/2022	19/12/2022	NUM
ejpam-5428	377	8	)	)	PUNCT
ejpam-5428	377	9	.	.	PUNCT
ejpam-5428	378	1	all	all	DET
ejpam-5428	378	2	the	the	DET
ejpam-5428	378	3	authors	author	NOUN
ejpam-5428	378	4	are	be	AUX
ejpam-5428	378	5	grateful	grateful	ADJ
ejpam-5428	378	6	to	to	ADP
ejpam-5428	378	7	the	the	DET
ejpam-5428	378	8	editor	editor	NOUN
ejpam-5428	378	9	and	and	CCONJ
ejpam-5428	378	10	referees	referee	NOUN
ejpam-5428	378	11	of	of	ADP
ejpam-5428	378	12	the	the	DET
ejpam-5428	378	13	journal	journal	NOUN
ejpam-5428	378	14	for	for	ADP
ejpam-5428	378	15	their	their	PRON
ejpam-5428	378	16	constructive	constructive	ADJ
ejpam-5428	378	17	suggestions	suggestion	NOUN
ejpam-5428	378	18	for	for	ADP
ejpam-5428	378	19	the	the	DET
ejpam-5428	378	20	improvement	improvement	NOUN
ejpam-5428	378	21	and	and	CCONJ
ejpam-5428	378	22	preparation	preparation	NOUN
ejpam-5428	378	23	of	of	ADP
ejpam-5428	378	24	the	the	DET
ejpam-5428	378	25	manuscript	manuscript	NOUN
ejpam-5428	378	26	.	.	PUNCT
ejpam-5428	379	1	references	reference	NOUN
ejpam-5428	379	2	[	[	X
ejpam-5428	379	3	1	1	NUM
ejpam-5428	379	4	]	]	X
ejpam-5428	379	5	s	s	PART
ejpam-5428	379	6	czerwik	czerwik	PROPN
ejpam-5428	379	7	.	.	PUNCT
ejpam-5428	380	1	contraction	contraction	NOUN
ejpam-5428	380	2	mappings	mapping	NOUN
ejpam-5428	380	3	in	in	ADP
ejpam-5428	380	4	b	b	NOUN
ejpam-5428	380	5	-	-	ADJ
ejpam-5428	380	6	metric	metric	ADJ
ejpam-5428	380	7	spaces	space	NOUN
ejpam-5428	380	8	.	.	PUNCT
ejpam-5428	381	1	acta	acta	PROPN
ejpam-5428	381	2	mathematica	mathematica	PROPN
ejpam-5428	381	3	et	et	PROPN
ejpam-5428	381	4	informatica	informatica	PROPN
ejpam-5428	381	5	universitatis	universitatis	PROPN
ejpam-5428	381	6	ostraviensis	ostraviensis	PROPN
ejpam-5428	381	7	,	,	PUNCT
ejpam-5428	381	8	1(1):5–11	1(1):5–11	NUM
ejpam-5428	381	9	,	,	PUNCT
ejpam-5428	381	10	1993	1993	NUM
ejpam-5428	381	11	.	.	PUNCT
ejpam-5428	382	1	[	[	X
ejpam-5428	382	2	2	2	NUM
ejpam-5428	382	3	]	]	PUNCT
ejpam-5428	382	4	m	m	VERB
ejpam-5428	382	5	dinarvand	dinarvand	ADJ
ejpam-5428	382	6	.	.	PUNCT
ejpam-5428	383	1	some	some	DET
ejpam-5428	383	2	fixed	fix	VERB
ejpam-5428	383	3	point	point	NOUN
ejpam-5428	383	4	results	result	NOUN
ejpam-5428	383	5	for	for	ADP
ejpam-5428	383	6	admissible	admissible	ADJ
ejpam-5428	383	7	geraghty	geraghty	PROPN
ejpam-5428	383	8	contraction	contraction	NOUN
ejpam-5428	383	9	type	type	NOUN
ejpam-5428	383	10	mapping	mapping	NOUN
ejpam-5428	383	11	in	in	ADP
ejpam-5428	383	12	fuzzy	fuzzy	ADJ
ejpam-5428	383	13	metric	metric	ADJ
ejpam-5428	383	14	spaces	space	NOUN
ejpam-5428	383	15	.	.	PUNCT
ejpam-5428	384	1	iranian	iranian	ADJ
ejpam-5428	384	2	journal	journal	PROPN
ejpam-5428	384	3	of	of	ADP
ejpam-5428	384	4	fuzzy	fuzzy	ADJ
ejpam-5428	384	5	systems	system	NOUN
ejpam-5428	384	6	,	,	PUNCT
ejpam-5428	384	7	14(3):161–177	14(3):161–177	NUM
ejpam-5428	384	8	,	,	PUNCT
ejpam-5428	384	9	2017	2017	NUM
ejpam-5428	384	10	.	.	PUNCT
ejpam-5428	385	1	[	[	X
ejpam-5428	385	2	3	3	X
ejpam-5428	385	3	]	]	PUNCT
ejpam-5428	385	4	h	h	NOUN
ejpam-5428	385	5	faraji	faraji	NOUN
ejpam-5428	385	6	,	,	PUNCT
ejpam-5428	385	7	d	d	X
ejpam-5428	385	8	savić	savić	ADV
ejpam-5428	385	9	,	,	PUNCT
ejpam-5428	385	10	and	and	CCONJ
ejpam-5428	385	11	s	s	VERB
ejpam-5428	385	12	radenović.	radenović.	NOUN
ejpam-5428	385	13	fixed	fix	VERB
ejpam-5428	385	14	point	point	NOUN
ejpam-5428	385	15	theorems	theorem	NOUN
ejpam-5428	385	16	for	for	ADP
ejpam-5428	385	17	geraghty	geraghty	PROPN
ejpam-5428	385	18	contraction	contraction	NOUN
ejpam-5428	385	19	type	type	NOUN
ejpam-5428	385	20	mappings	mapping	NOUN
ejpam-5428	385	21	in	in	ADP
ejpam-5428	385	22	b	b	NOUN
ejpam-5428	385	23	-	-	ADJ
ejpam-5428	385	24	metric	metric	ADJ
ejpam-5428	385	25	spaces	space	NOUN
ejpam-5428	385	26	and	and	CCONJ
ejpam-5428	385	27	applications	application	NOUN
ejpam-5428	385	28	.	.	PUNCT
ejpam-5428	386	1	axioms	axiom	NOUN
ejpam-5428	386	2	,	,	PUNCT
ejpam-5428	386	3	8(1):34	8(1):34	NUM
ejpam-5428	386	4	,	,	PUNCT
ejpam-5428	386	5	2019	2019	NUM
ejpam-5428	386	6	.	.	PUNCT
ejpam-5428	387	1	[	[	X
ejpam-5428	387	2	4	4	X
ejpam-5428	387	3	]	]	X
ejpam-5428	387	4	a	a	DET
ejpam-5428	387	5	george	george	NOUN
ejpam-5428	387	6	and	and	CCONJ
ejpam-5428	387	7	p	p	NOUN
ejpam-5428	387	8	veeramani	veeramani	NOUN
ejpam-5428	387	9	.	.	PUNCT
ejpam-5428	388	1	on	on	ADP
ejpam-5428	388	2	some	some	DET
ejpam-5428	388	3	results	result	NOUN
ejpam-5428	388	4	in	in	ADP
ejpam-5428	388	5	fuzzy	fuzzy	ADJ
ejpam-5428	388	6	metric	metric	ADJ
ejpam-5428	388	7	spaces	space	NOUN
ejpam-5428	388	8	.	.	PUNCT
ejpam-5428	389	1	fuzzy	fuzzy	ADJ
ejpam-5428	389	2	sets	set	NOUN
ejpam-5428	389	3	and	and	CCONJ
ejpam-5428	389	4	systems	system	NOUN
ejpam-5428	389	5	,	,	PUNCT
ejpam-5428	389	6	64(3):395–399	64(3):395–399	PROPN
ejpam-5428	389	7	,	,	PUNCT
ejpam-5428	389	8	1994	1994	NUM
ejpam-5428	389	9	.	.	PUNCT
ejpam-5428	390	1	[	[	X
ejpam-5428	390	2	5	5	NUM
ejpam-5428	390	3	]	]	X
ejpam-5428	390	4	m	m	VERB
ejpam-5428	390	5	a	a	DET
ejpam-5428	390	6	geraghty	geraghty	NOUN
ejpam-5428	390	7	.	.	PUNCT
ejpam-5428	391	1	on	on	ADP
ejpam-5428	391	2	contractive	contractive	ADJ
ejpam-5428	391	3	mappings	mapping	NOUN
ejpam-5428	391	4	.	.	PUNCT
ejpam-5428	392	1	proceedings	proceeding	NOUN
ejpam-5428	392	2	of	of	ADP
ejpam-5428	392	3	the	the	DET
ejpam-5428	392	4	american	american	PROPN
ejpam-5428	392	5	mathematical	mathematical	PROPN
ejpam-5428	392	6	society	society	NOUN
ejpam-5428	392	7	,	,	PUNCT
ejpam-5428	392	8	40(2):604–608	40(2):604–608	NOUN
ejpam-5428	392	9	,	,	PUNCT
ejpam-5428	392	10	1973	1973	NUM
ejpam-5428	392	11	.	.	PUNCT
ejpam-5428	393	1	[	[	X
ejpam-5428	393	2	6	6	NUM
ejpam-5428	393	3	]	]	PUNCT
ejpam-5428	393	4	n	n	X
ejpam-5428	393	5	hussain	hussain	NOUN
ejpam-5428	393	6	,	,	PUNCT
ejpam-5428	393	7	p	p	NOUN
ejpam-5428	393	8	salimi	salimi	NOUN
ejpam-5428	393	9	,	,	PUNCT
ejpam-5428	393	10	and	and	CCONJ
ejpam-5428	393	11	v	v	ADP
ejpam-5428	393	12	parvaneh	parvaneh	NOUN
ejpam-5428	393	13	.	.	PUNCT
ejpam-5428	394	1	fixed	fix	VERB
ejpam-5428	394	2	point	point	NOUN
ejpam-5428	394	3	results	result	NOUN
ejpam-5428	394	4	for	for	ADP
ejpam-5428	394	5	various	various	ADJ
ejpam-5428	394	6	contractions	contraction	NOUN
ejpam-5428	394	7	in	in	ADP
ejpam-5428	394	8	parametric	parametric	ADJ
ejpam-5428	394	9	and	and	CCONJ
ejpam-5428	394	10	fuzzy	fuzzy	ADJ
ejpam-5428	394	11	b	b	X
ejpam-5428	394	12	-	-	PUNCT
ejpam-5428	394	13	metric	metric	ADJ
ejpam-5428	394	14	spaces	space	NOUN
ejpam-5428	394	15	.	.	PUNCT
ejpam-5428	395	1	j.	j.	PROPN
ejpam-5428	395	2	nonlinear	nonlinear	PROPN
ejpam-5428	395	3	sci	sci	PROPN
ejpam-5428	395	4	.	.	PUNCT
ejpam-5428	395	5	appl	appl	PROPN
ejpam-5428	395	6	,	,	PUNCT
ejpam-5428	395	7	8(5):719–739	8(5):719–739	NUM
ejpam-5428	395	8	,	,	PUNCT
ejpam-5428	395	9	2015	2015	NUM
ejpam-5428	395	10	.	.	PUNCT
ejpam-5428	396	1	[	[	X
ejpam-5428	396	2	7	7	X
ejpam-5428	396	3	]	]	X
ejpam-5428	396	4	i	i	PRON
ejpam-5428	396	5	kramosil	kramosil	PROPN
ejpam-5428	396	6	and	and	CCONJ
ejpam-5428	396	7	j	j	PROPN
ejpam-5428	396	8	michálek	michálek	ADJ
ejpam-5428	396	9	.	.	NOUN
ejpam-5428	396	10	fuzzy	fuzzy	ADJ
ejpam-5428	396	11	metrics	metric	NOUN
ejpam-5428	396	12	and	and	CCONJ
ejpam-5428	396	13	statistical	statistical	ADJ
ejpam-5428	396	14	metric	metric	ADJ
ejpam-5428	396	15	spaces	space	NOUN
ejpam-5428	396	16	.	.	PUNCT
ejpam-5428	397	1	kybernetika	kybernetika	PROPN
ejpam-5428	397	2	,	,	PUNCT
ejpam-5428	397	3	11(5):336–344	11(5):336–344	PROPN
ejpam-5428	397	4	,	,	PUNCT
ejpam-5428	397	5	1975	1975	NUM
ejpam-5428	397	6	.	.	PUNCT
ejpam-5428	398	1	[	[	X
ejpam-5428	398	2	8	8	NUM
ejpam-5428	398	3	]	]	SYM
ejpam-5428	398	4	s	s	NOUN
ejpam-5428	398	5	nădăban	nădăban	PROPN
ejpam-5428	398	6	.	.	PUNCT
ejpam-5428	399	1	fuzzy	fuzzy	ADJ
ejpam-5428	399	2	b	b	X
ejpam-5428	399	3	-	-	PUNCT
ejpam-5428	399	4	metric	metric	ADJ
ejpam-5428	399	5	spaces	space	NOUN
ejpam-5428	399	6	.	.	PUNCT
ejpam-5428	400	1	international	international	ADJ
ejpam-5428	400	2	journal	journal	PROPN
ejpam-5428	400	3	of	of	ADP
ejpam-5428	400	4	computers	computer	NOUN
ejpam-5428	400	5	communications	communication	NOUN
ejpam-5428	400	6	and	and	CCONJ
ejpam-5428	400	7	control	control	NOUN
ejpam-5428	400	8	,	,	PUNCT
ejpam-5428	400	9	11(2):273–281	11(2):273–281	PROPN
ejpam-5428	400	10	,	,	PUNCT
ejpam-5428	400	11	2016	2016	NUM
ejpam-5428	400	12	.	.	PUNCT
ejpam-5428	401	1	[	[	X
ejpam-5428	401	2	9	9	NUM
ejpam-5428	401	3	]	]	SYM
ejpam-5428	401	4	u	u	NOUN
ejpam-5428	401	5	d	d	X
ejpam-5428	401	6	patel	patel	NOUN
ejpam-5428	401	7	and	and	CCONJ
ejpam-5428	401	8	s	s	NOUN
ejpam-5428	401	9	radenović.	radenović.	PROPN
ejpam-5428	401	10	suzuki	suzuki	NOUN
ejpam-5428	401	11	-	-	PUNCT
ejpam-5428	401	12	type	type	ADJ
ejpam-5428	401	13	fuzzy	fuzzy	ADJ
ejpam-5428	401	14	contractive	contractive	ADJ
ejpam-5428	401	15	inequalities	inequality	NOUN
ejpam-5428	401	16	in	in	ADP
ejpam-5428	401	17	1	1	NUM
ejpam-5428	401	18	-	-	PUNCT
ejpam-5428	401	19	z	z	NOUN
ejpam-5428	401	20	-	-	PUNCT
ejpam-5428	401	21	complete	complete	ADJ
ejpam-5428	401	22	fuzzy	fuzzy	ADJ
ejpam-5428	401	23	metric	metric	ADJ
ejpam-5428	401	24	-	-	PUNCT
ejpam-5428	401	25	like	like	ADJ
ejpam-5428	401	26	spaces	space	NOUN
ejpam-5428	401	27	with	with	ADP
ejpam-5428	401	28	an	an	DET
ejpam-5428	401	29	application	application	NOUN
ejpam-5428	401	30	.	.	PUNCT
ejpam-5428	402	1	nonlinear	nonlinear	ADJ
ejpam-5428	402	2	analysis	analysis	NOUN
ejpam-5428	402	3	:	:	PUNCT
ejpam-5428	402	4	modelling	modelling	NOUN
ejpam-5428	402	5	and	and	CCONJ
ejpam-5428	402	6	control	control	NOUN
ejpam-5428	402	7	,	,	PUNCT
ejpam-5428	402	8	28:1–17	28:1–17	NUM
ejpam-5428	402	9	,	,	PUNCT
ejpam-5428	402	10	2023	2023	NUM
ejpam-5428	402	11	.	.	PUNCT
ejpam-5428	403	1	[	[	X
ejpam-5428	403	2	10	10	NUM
ejpam-5428	403	3	]	]	X
ejpam-5428	403	4	m	m	PROPN
ejpam-5428	403	5	rashid	rashid	PROPN
ejpam-5428	403	6	,	,	PUNCT
ejpam-5428	403	7	n	n	X
ejpam-5428	403	8	saleem	saleem	NOUN
ejpam-5428	403	9	,	,	PUNCT
ejpam-5428	403	10	r	r	NOUN
ejpam-5428	403	11	bibi	bibi	NOUN
ejpam-5428	403	12	,	,	PUNCT
ejpam-5428	403	13	and	and	CCONJ
ejpam-5428	403	14	r	r	NOUN
ejpam-5428	403	15	george	george	PROPN
ejpam-5428	403	16	.	.	PUNCT
ejpam-5428	404	1	solution	solution	NOUN
ejpam-5428	404	2	of	of	ADP
ejpam-5428	404	3	integral	integral	ADJ
ejpam-5428	404	4	equations	equation	NOUN
ejpam-5428	404	5	using	use	VERB
ejpam-5428	404	6	some	some	DET
ejpam-5428	404	7	multiple	multiple	ADJ
ejpam-5428	404	8	fixed	fix	VERB
ejpam-5428	404	9	point	point	NOUN
ejpam-5428	404	10	results	result	NOUN
ejpam-5428	404	11	in	in	ADP
ejpam-5428	404	12	special	special	ADJ
ejpam-5428	404	13	kinds	kind	NOUN
ejpam-5428	404	14	of	of	ADP
ejpam-5428	404	15	distance	distance	NOUN
ejpam-5428	404	16	spaces	space	NOUN
ejpam-5428	404	17	.	.	PUNCT
ejpam-5428	405	1	mathematics	mathematic	NOUN
ejpam-5428	405	2	,	,	PUNCT
ejpam-5428	405	3	10(24):4707	10(24):4707	NUM
ejpam-5428	405	4	,	,	PUNCT
ejpam-5428	405	5	2022	2022	NUM
ejpam-5428	405	6	.	.	PUNCT
ejpam-5428	406	1	[	[	X
ejpam-5428	406	2	11	11	NUM
ejpam-5428	406	3	]	]	PUNCT
ejpam-5428	406	4	n	n	X
ejpam-5428	406	5	saleem	saleem	NOUN
ejpam-5428	406	6	,	,	PUNCT
ejpam-5428	406	7	u	u	NOUN
ejpam-5428	406	8	ishtiaq	ishtiaq	NOUN
ejpam-5428	406	9	,	,	PUNCT
ejpam-5428	406	10	k	k	PROPN
ejpam-5428	406	11	ahmad	ahmad	PROPN
ejpam-5428	406	12	,	,	PUNCT
ejpam-5428	406	13	and	and	CCONJ
ejpam-5428	406	14	m	m	PROPN
ejpam-5428	406	15	de	de	X
ejpam-5428	406	16	la	la	PROPN
ejpam-5428	406	17	sen	sen	PROPN
ejpam-5428	406	18	.	.	PROPN
ejpam-5428	406	19	multivalued	multivalue	VERB
ejpam-5428	406	20	neutrosophic	neutrosophic	ADJ
ejpam-5428	406	21	fractals	fractal	NOUN
ejpam-5428	406	22	and	and	CCONJ
ejpam-5428	406	23	hutchinson	hutchinson	PROPN
ejpam-5428	406	24	-	-	PUNCT
ejpam-5428	406	25	barnsley	barnsley	NOUN
ejpam-5428	406	26	operator	operator	NOUN
ejpam-5428	406	27	in	in	ADP
ejpam-5428	406	28	neutrosophic	neutrosophic	ADJ
ejpam-5428	406	29	metric	metric	ADJ
ejpam-5428	406	30	space	space	NOUN
ejpam-5428	406	31	.	.	PUNCT
ejpam-5428	407	1	chaos	chaos	NOUN
ejpam-5428	407	2	,	,	PUNCT
ejpam-5428	407	3	solitons	soliton	NOUN
ejpam-5428	407	4	&	&	CCONJ
ejpam-5428	407	5	fractals	fractal	NOUN
ejpam-5428	407	6	,	,	PUNCT
ejpam-5428	407	7	172:113607	172:113607	NUM
ejpam-5428	407	8	,	,	PUNCT
ejpam-5428	407	9	2023	2023	NUM
ejpam-5428	407	10	.	.	PUNCT
ejpam-5428	408	1	references	reference	NOUN
ejpam-5428	408	2	2404	2404	NUM
ejpam-5428	409	1	[	[	X
ejpam-5428	409	2	12	12	NUM
ejpam-5428	409	3	]	]	PUNCT
ejpam-5428	409	4	n	n	X
ejpam-5428	409	5	saleem	saleem	NOUN
ejpam-5428	409	6	,	,	PUNCT
ejpam-5428	409	7	u	u	NOUN
ejpam-5428	409	8	ishtiaq	ishtiaq	NOUN
ejpam-5428	409	9	,	,	PUNCT
ejpam-5428	409	10	f	f	PROPN
ejpam-5428	409	11	uddin	uddin	PROPN
ejpam-5428	409	12	,	,	PUNCT
ejpam-5428	409	13	s	s	VERB
ejpam-5428	409	14	sessa	sessa	NOUN
ejpam-5428	409	15	,	,	PUNCT
ejpam-5428	409	16	k	k	PROPN
ejpam-5428	409	17	ahmad	ahmad	PROPN
ejpam-5428	409	18	,	,	PUNCT
ejpam-5428	409	19	and	and	CCONJ
ejpam-5428	409	20	f	f	PROPN
ejpam-5428	409	21	di	di	PROPN
ejpam-5428	409	22	martino	martino	PROPN
ejpam-5428	409	23	.	.	PUNCT
ejpam-5428	410	1	graphical	graphical	ADJ
ejpam-5428	410	2	views	view	NOUN
ejpam-5428	410	3	of	of	ADP
ejpam-5428	410	4	intuitionistic	intuitionistic	ADJ
ejpam-5428	410	5	fuzzy	fuzzy	ADJ
ejpam-5428	410	6	double	double	ADJ
ejpam-5428	410	7	-	-	PUNCT
ejpam-5428	410	8	controlled	control	VERB
ejpam-5428	410	9	metric	metric	ADJ
ejpam-5428	410	10	-	-	PUNCT
ejpam-5428	410	11	like	like	ADJ
ejpam-5428	410	12	spaces	space	NOUN
ejpam-5428	410	13	and	and	CCONJ
ejpam-5428	410	14	certain	certain	ADJ
ejpam-5428	410	15	fixedpoint	fixedpoint	NOUN
ejpam-5428	410	16	results	result	NOUN
ejpam-5428	410	17	with	with	ADP
ejpam-5428	410	18	application	application	NOUN
ejpam-5428	410	19	.	.	PUNCT
ejpam-5428	411	1	symmetry	symmetry	NOUN
ejpam-5428	411	2	,	,	PUNCT
ejpam-5428	411	3	14(11):2364	14(11):2364	NUM
ejpam-5428	411	4	,	,	PUNCT
ejpam-5428	411	5	2022	2022	NUM
ejpam-5428	411	6	.	.	PUNCT
ejpam-5428	412	1	[	[	X
ejpam-5428	412	2	13	13	NUM
ejpam-5428	412	3	]	]	PUNCT
ejpam-5428	412	4	n	n	DET
ejpam-5428	412	5	saleem	saleem	NOUN
ejpam-5428	412	6	,	,	PUNCT
ejpam-5428	412	7	m	m	VERB
ejpam-5428	412	8	zhou	zhou	ADJ
ejpam-5428	412	9	,	,	PUNCT
ejpam-5428	412	10	and	and	CCONJ
ejpam-5428	412	11	s	s	VERB
ejpam-5428	412	12	bashir	bashir	NOUN
ejpam-5428	412	13	.	.	PUNCT
ejpam-5428	413	1	solution	solution	NOUN
ejpam-5428	413	2	of	of	ADP
ejpam-5428	413	3	fractional	fractional	ADJ
ejpam-5428	413	4	integral	integral	ADJ
ejpam-5428	413	5	equations	equation	NOUN
ejpam-5428	413	6	via	via	ADP
ejpam-5428	413	7	fixed	fix	VERB
ejpam-5428	413	8	point	point	NOUN
ejpam-5428	413	9	results	result	NOUN
ejpam-5428	413	10	.	.	PUNCT
ejpam-5428	414	1	journal	journal	NOUN
ejpam-5428	414	2	of	of	ADP
ejpam-5428	414	3	inequalities	inequality	NOUN
ejpam-5428	414	4	and	and	CCONJ
ejpam-5428	414	5	applications	application	NOUN
ejpam-5428	414	6	,	,	PUNCT
ejpam-5428	414	7	2022(1):148	2022(1):148	NUM
ejpam-5428	414	8	,	,	PUNCT
ejpam-5428	414	9	2022	2022	NUM
ejpam-5428	414	10	.	.	PUNCT
ejpam-5428	415	1	[	[	X
ejpam-5428	415	2	14	14	NUM
ejpam-5428	415	3	]	]	SYM
ejpam-5428	415	4	b	b	PROPN
ejpam-5428	415	5	schweizer	schweizer	PROPN
ejpam-5428	415	6	and	and	CCONJ
ejpam-5428	415	7	a	a	DET
ejpam-5428	415	8	sklar	sklar	NOUN
ejpam-5428	415	9	.	.	PUNCT
ejpam-5428	416	1	probabilistic	probabilistic	ADJ
ejpam-5428	416	2	metric	metric	ADJ
ejpam-5428	416	3	spaces	space	NOUN
ejpam-5428	416	4	.	.	PUNCT
ejpam-5428	417	1	north	north	NOUN
ejpam-5428	417	2	holland	holland	PROPN
ejpam-5428	417	3	series	series	PROPN
ejpam-5428	417	4	in	in	ADP
ejpam-5428	417	5	probability	probability	NOUN
ejpam-5428	417	6	and	and	CCONJ
ejpam-5428	417	7	applied	apply	VERB
ejpam-5428	417	8	mathematics	mathematic	NOUN
ejpam-5428	417	9	.	.	PUNCT
ejpam-5428	418	1	elsevier	elsevier	PROPN
ejpam-5428	418	2	,	,	PUNCT
ejpam-5428	418	3	new	new	PROPN
ejpam-5428	418	4	york	york	PROPN
ejpam-5428	418	5	,	,	PUNCT
ejpam-5428	418	6	1983	1983	NUM
ejpam-5428	418	7	.	.	PUNCT
ejpam-5428	419	1	[	[	X
ejpam-5428	419	2	15	15	NUM
ejpam-5428	419	3	]	]	X
ejpam-5428	419	4	s	s	VERB
ejpam-5428	419	5	sedghi	sedghi	X
ejpam-5428	419	6	and	and	CCONJ
ejpam-5428	419	7	n.	n.	PROPN
ejpam-5428	419	8	shobe	shobe	PROPN
ejpam-5428	419	9	.	.	PUNCT
ejpam-5428	420	1	common	common	ADJ
ejpam-5428	420	2	fixed	fix	VERB
ejpam-5428	420	3	point	point	NOUN
ejpam-5428	420	4	theorems	theorem	NOUN
ejpam-5428	420	5	in	in	ADP
ejpam-5428	420	6	b	b	NOUN
ejpam-5428	420	7	-	-	PUNCT
ejpam-5428	420	8	fuzzy	fuzzy	ADJ
ejpam-5428	420	9	metric	metric	ADJ
ejpam-5428	420	10	spaces	space	NOUN
ejpam-5428	420	11	.	.	PUNCT
ejpam-5428	421	1	nonlinear	nonlinear	ADJ
ejpam-5428	421	2	functional	functional	ADJ
ejpam-5428	421	3	analysis	analysis	NOUN
ejpam-5428	421	4	and	and	CCONJ
ejpam-5428	421	5	applications	application	NOUN
ejpam-5428	421	6	,	,	PUNCT
ejpam-5428	421	7	17(3):349–359	17(3):349–359	NUM
ejpam-5428	421	8	,	,	PUNCT
ejpam-5428	421	9	2013	2013	NUM
ejpam-5428	421	10	.	.	PUNCT