id	sid	tid	token	lemma	pos
ejpam-6056	1	1	european	european	PROPN
ejpam-6056	1	2	journal	journal	PROPN
ejpam-6056	1	3	of	of	ADP
ejpam-6056	1	4	pure	pure	ADJ
ejpam-6056	1	5	and	and	CCONJ
ejpam-6056	1	6	applied	applied	ADJ
ejpam-6056	1	7	mathematics	mathematic	NOUN
ejpam-6056	1	8	2025	2025	NUM
ejpam-6056	1	9	,	,	PUNCT
ejpam-6056	1	10	vol	vol	NOUN
ejpam-6056	1	11	.	.	PROPN
ejpam-6056	1	12	18	18	NUM
ejpam-6056	1	13	,	,	PUNCT
ejpam-6056	1	14	issue	issue	NOUN
ejpam-6056	1	15	3	3	NUM
ejpam-6056	1	16	,	,	PUNCT
ejpam-6056	1	17	article	article	NOUN
ejpam-6056	1	18	number	number	NOUN
ejpam-6056	1	19	6056	6056	NUM
ejpam-6056	1	20	issn	issn	PROPN
ejpam-6056	1	21	1307	1307	NUM
ejpam-6056	1	22	-	-	SYM
ejpam-6056	1	23	5543	5543	NUM
ejpam-6056	1	24	–	–	PUNCT
ejpam-6056	1	25	ejpam.com	ejpam.com	X
ejpam-6056	1	26	published	publish	VERB
ejpam-6056	1	27	by	by	ADP
ejpam-6056	1	28	new	new	PROPN
ejpam-6056	1	29	york	york	PROPN
ejpam-6056	1	30	business	business	PROPN
ejpam-6056	1	31	global	global	ADJ
ejpam-6056	1	32	advances	advance	NOUN
ejpam-6056	1	33	in	in	ADP
ejpam-6056	1	34	rational	rational	ADJ
ejpam-6056	1	35	contractions	contraction	NOUN
ejpam-6056	1	36	within	within	ADP
ejpam-6056	1	37	extended	extended	ADJ
ejpam-6056	1	38	b−metric	b−metric	ADJ
ejpam-6056	1	39	spaces	space	NOUN
ejpam-6056	1	40	and	and	CCONJ
ejpam-6056	1	41	their	their	PRON
ejpam-6056	1	42	applications	application	NOUN
ejpam-6056	1	43	haitham	haitham	PROPN
ejpam-6056	1	44	qawaqneh1,∗	qawaqneh1,∗	PROPN
ejpam-6056	1	45	,	,	PUNCT
ejpam-6056	1	46	gawhara	gawhara	PROPN
ejpam-6056	1	47	al	al	PROPN
ejpam-6056	1	48	-	-	PUNCT
ejpam-6056	1	49	musannef2	musannef2	PROPN
ejpam-6056	1	50	,	,	PUNCT
ejpam-6056	1	51	habes	habe	VERB
ejpam-6056	1	52	alsamir3	alsamir3	PROPN
ejpam-6056	2	1	1	1	NUM
ejpam-6056	2	2	al	al	PROPN
ejpam-6056	2	3	-	-	PUNCT
ejpam-6056	2	4	zaytoonah	zaytoonah	PROPN
ejpam-6056	2	5	university	university	PROPN
ejpam-6056	2	6	of	of	ADP
ejpam-6056	2	7	jordan	jordan	PROPN
ejpam-6056	2	8	,	,	PUNCT
ejpam-6056	2	9	amman	amman	PROPN
ejpam-6056	2	10	11733	11733	NUM
ejpam-6056	2	11	,	,	PUNCT
ejpam-6056	2	12	jordan	jordan	PROPN
ejpam-6056	2	13	2	2	NUM
ejpam-6056	2	14	faculty	faculty	NOUN
ejpam-6056	2	15	of	of	ADP
ejpam-6056	2	16	business	business	NOUN
ejpam-6056	2	17	studies	study	NOUN
ejpam-6056	2	18	,	,	PUNCT
ejpam-6056	2	19	arab	arab	ADJ
ejpam-6056	2	20	open	open	PROPN
ejpam-6056	2	21	university	university	PROPN
ejpam-6056	2	22	,	,	PUNCT
ejpam-6056	2	23	jeddah	jeddah	PROPN
ejpam-6056	2	24	,	,	PUNCT
ejpam-6056	2	25	saudi	saudi	PROPN
ejpam-6056	2	26	arabia	arabia	PROPN
ejpam-6056	2	27	3	3	NUM
ejpam-6056	2	28	business	business	PROPN
ejpam-6056	2	29	administration	administration	PROPN
ejpam-6056	2	30	college	college	PROPN
ejpam-6056	2	31	,	,	PUNCT
ejpam-6056	2	32	dar	dar	PROPN
ejpam-6056	2	33	aluloom	aluloom	NOUN
ejpam-6056	2	34	university	university	PROPN
ejpam-6056	2	35	,	,	PUNCT
ejpam-6056	2	36	riyadh	riyadh	PROPN
ejpam-6056	2	37	,	,	PUNCT
ejpam-6056	2	38	saudi	saudi	PROPN
ejpam-6056	2	39	arabia	arabia	PROPN
ejpam-6056	2	40	abstract	abstract	NOUN
ejpam-6056	2	41	.	.	PUNCT
ejpam-6056	3	1	this	this	DET
ejpam-6056	3	2	study	study	NOUN
ejpam-6056	3	3	introduces	introduce	VERB
ejpam-6056	3	4	a	a	DET
ejpam-6056	3	5	novel	novel	ADJ
ejpam-6056	3	6	class	class	NOUN
ejpam-6056	3	7	of	of	ADP
ejpam-6056	3	8	rational	rational	ADJ
ejpam-6056	3	9	contractions	contraction	NOUN
ejpam-6056	3	10	within	within	ADP
ejpam-6056	3	11	the	the	DET
ejpam-6056	3	12	framework	framework	NOUN
ejpam-6056	3	13	of	of	ADP
ejpam-6056	3	14	extended	extended	ADJ
ejpam-6056	3	15	b	b	X
ejpam-6056	3	16	-	-	ADJ
ejpam-6056	3	17	metric	metric	ADJ
ejpam-6056	3	18	spaces	space	NOUN
ejpam-6056	3	19	,	,	PUNCT
ejpam-6056	3	20	extending	extend	VERB
ejpam-6056	3	21	classical	classical	ADJ
ejpam-6056	3	22	fixed	fix	VERB
ejpam-6056	3	23	point	point	NOUN
ejpam-6056	3	24	theory	theory	NOUN
ejpam-6056	3	25	to	to	ADP
ejpam-6056	3	26	more	more	ADV
ejpam-6056	3	27	generalized	generalized	ADJ
ejpam-6056	3	28	and	and	CCONJ
ejpam-6056	3	29	flexible	flexible	ADJ
ejpam-6056	3	30	settings	setting	NOUN
ejpam-6056	3	31	.	.	PUNCT
ejpam-6056	4	1	we	we	PRON
ejpam-6056	4	2	establish	establish	VERB
ejpam-6056	4	3	new	new	ADJ
ejpam-6056	4	4	fixed	fix	VERB
ejpam-6056	4	5	point	point	NOUN
ejpam-6056	4	6	theorems	theorem	NOUN
ejpam-6056	4	7	using	use	VERB
ejpam-6056	4	8	a	a	DET
ejpam-6056	4	9	control	control	NOUN
ejpam-6056	4	10	function	function	NOUN
ejpam-6056	4	11	approach	approach	NOUN
ejpam-6056	4	12	,	,	PUNCT
ejpam-6056	4	13	which	which	PRON
ejpam-6056	4	14	broadens	broaden	VERB
ejpam-6056	4	15	the	the	DET
ejpam-6056	4	16	scope	scope	NOUN
ejpam-6056	4	17	of	of	ADP
ejpam-6056	4	18	contractive	contractive	ADJ
ejpam-6056	4	19	mappings	mapping	NOUN
ejpam-6056	4	20	that	that	PRON
ejpam-6056	4	21	can	can	AUX
ejpam-6056	4	22	be	be	AUX
ejpam-6056	4	23	studied	study	VERB
ejpam-6056	4	24	under	under	ADP
ejpam-6056	4	25	extended	extended	ADJ
ejpam-6056	4	26	b	b	X
ejpam-6056	4	27	-	-	ADJ
ejpam-6056	4	28	metric	metric	ADJ
ejpam-6056	4	29	spaces	space	NOUN
ejpam-6056	4	30	.	.	PUNCT
ejpam-6056	5	1	the	the	DET
ejpam-6056	5	2	methodology	methodology	NOUN
ejpam-6056	5	3	combines	combine	VERB
ejpam-6056	5	4	analytical	analytical	ADJ
ejpam-6056	5	5	techniques	technique	NOUN
ejpam-6056	5	6	with	with	ADP
ejpam-6056	5	7	integral	integral	ADJ
ejpam-6056	5	8	operator	operator	NOUN
ejpam-6056	5	9	theory	theory	NOUN
ejpam-6056	5	10	,	,	PUNCT
ejpam-6056	5	11	allowing	allow	VERB
ejpam-6056	5	12	us	we	PRON
ejpam-6056	5	13	to	to	PART
ejpam-6056	5	14	investigate	investigate	VERB
ejpam-6056	5	15	the	the	DET
ejpam-6056	5	16	existence	existence	NOUN
ejpam-6056	5	17	and	and	CCONJ
ejpam-6056	5	18	uniqueness	uniqueness	NOUN
ejpam-6056	5	19	of	of	ADP
ejpam-6056	5	20	solutions	solution	NOUN
ejpam-6056	5	21	to	to	ADP
ejpam-6056	5	22	both	both	CCONJ
ejpam-6056	5	23	volterra	volterra	NOUN
ejpam-6056	5	24	and	and	CCONJ
ejpam-6056	5	25	urysohn	urysohn	VERB
ejpam-6056	5	26	integral	integral	ADJ
ejpam-6056	5	27	equations	equation	NOUN
ejpam-6056	5	28	.	.	PUNCT
ejpam-6056	6	1	to	to	PART
ejpam-6056	6	2	validate	validate	VERB
ejpam-6056	6	3	the	the	DET
ejpam-6056	6	4	theoretical	theoretical	ADJ
ejpam-6056	6	5	results	result	NOUN
ejpam-6056	6	6	,	,	PUNCT
ejpam-6056	6	7	illustrative	illustrative	ADJ
ejpam-6056	6	8	examples	example	NOUN
ejpam-6056	6	9	and	and	CCONJ
ejpam-6056	6	10	numerical	numerical	ADJ
ejpam-6056	6	11	simulations	simulation	NOUN
ejpam-6056	6	12	are	be	AUX
ejpam-6056	6	13	presented	present	VERB
ejpam-6056	6	14	,	,	PUNCT
ejpam-6056	6	15	demonstrating	demonstrate	VERB
ejpam-6056	6	16	the	the	DET
ejpam-6056	6	17	effectiveness	effectiveness	NOUN
ejpam-6056	6	18	and	and	CCONJ
ejpam-6056	6	19	real	real	ADJ
ejpam-6056	6	20	-	-	PUNCT
ejpam-6056	6	21	world	world	NOUN
ejpam-6056	6	22	relevance	relevance	NOUN
ejpam-6056	6	23	of	of	ADP
ejpam-6056	6	24	the	the	DET
ejpam-6056	6	25	proposed	propose	VERB
ejpam-6056	6	26	framework	framework	NOUN
ejpam-6056	6	27	.	.	PUNCT
ejpam-6056	7	1	2020	2020	NUM
ejpam-6056	7	2	mathematics	mathematic	NOUN
ejpam-6056	7	3	subject	subject	NOUN
ejpam-6056	7	4	classifications	classification	NOUN
ejpam-6056	7	5	:	:	PUNCT
ejpam-6056	7	6	47h10	47h10	NUM
ejpam-6056	7	7	,	,	PUNCT
ejpam-6056	7	8	54h25	54h25	NUM
ejpam-6056	7	9	key	key	ADJ
ejpam-6056	7	10	words	word	NOUN
ejpam-6056	7	11	and	and	CCONJ
ejpam-6056	7	12	phrases	phrase	NOUN
ejpam-6056	7	13	:	:	PUNCT
ejpam-6056	7	14	rational	rational	ADJ
ejpam-6056	7	15	contractions	contraction	NOUN
ejpam-6056	7	16	,	,	PUNCT
ejpam-6056	7	17	fixed	fix	VERB
ejpam-6056	7	18	point	point	NOUN
ejpam-6056	7	19	theorem	theorem	VERB
ejpam-6056	7	20	,	,	PUNCT
ejpam-6056	7	21	extended	extended	ADJ
ejpam-6056	7	22	b	b	X
ejpam-6056	7	23	-	-	ADJ
ejpam-6056	7	24	metric	metric	ADJ
ejpam-6056	7	25	spaces	space	NOUN
ejpam-6056	7	26	1	1	NUM
ejpam-6056	7	27	.	.	X
ejpam-6056	8	1	introduction	introduction	NOUN
ejpam-6056	8	2	fixed	fix	VERB
ejpam-6056	8	3	point	point	NOUN
ejpam-6056	8	4	theory	theory	NOUN
ejpam-6056	8	5	is	be	AUX
ejpam-6056	8	6	a	a	DET
ejpam-6056	8	7	fundamental	fundamental	ADJ
ejpam-6056	8	8	principle	principle	NOUN
ejpam-6056	8	9	in	in	ADP
ejpam-6056	8	10	mathematics	mathematic	NOUN
ejpam-6056	8	11	that	that	PRON
ejpam-6056	8	12	has	have	VERB
ejpam-6056	8	13	numerous	numerous	ADJ
ejpam-6056	8	14	applications	application	NOUN
ejpam-6056	8	15	in	in	ADP
ejpam-6056	8	16	a	a	DET
ejpam-6056	8	17	variety	variety	NOUN
ejpam-6056	8	18	of	of	ADP
ejpam-6056	8	19	fields	field	NOUN
ejpam-6056	8	20	.	.	PUNCT
ejpam-6056	9	1	one	one	NUM
ejpam-6056	9	2	of	of	ADP
ejpam-6056	9	3	its	its	PRON
ejpam-6056	9	4	key	key	ADJ
ejpam-6056	9	5	techniques	technique	NOUN
ejpam-6056	9	6	involves	involve	VERB
ejpam-6056	9	7	the	the	DET
ejpam-6056	9	8	use	use	NOUN
ejpam-6056	9	9	of	of	ADP
ejpam-6056	9	10	contraction	contraction	NOUN
ejpam-6056	9	11	mappings	mapping	NOUN
ejpam-6056	9	12	,	,	PUNCT
ejpam-6056	9	13	which	which	PRON
ejpam-6056	9	14	are	be	AUX
ejpam-6056	9	15	instrumental	instrumental	ADJ
ejpam-6056	9	16	in	in	ADP
ejpam-6056	9	17	proving	prove	VERB
ejpam-6056	9	18	the	the	DET
ejpam-6056	9	19	existence	existence	NOUN
ejpam-6056	9	20	and	and	CCONJ
ejpam-6056	9	21	uniqueness	uniqueness	NOUN
ejpam-6056	9	22	of	of	ADP
ejpam-6056	9	23	fixed	fix	VERB
ejpam-6056	9	24	points	point	NOUN
ejpam-6056	9	25	.	.	PUNCT
ejpam-6056	10	1	a	a	DET
ejpam-6056	10	2	landmark	landmark	NOUN
ejpam-6056	10	3	result	result	NOUN
ejpam-6056	10	4	in	in	ADP
ejpam-6056	10	5	this	this	DET
ejpam-6056	10	6	area	area	NOUN
ejpam-6056	10	7	is	be	AUX
ejpam-6056	10	8	banach	banach	ADV
ejpam-6056	10	9	’s	’s	PART
ejpam-6056	10	10	fixed	fix	VERB
ejpam-6056	10	11	point	point	NOUN
ejpam-6056	10	12	theorem	theorem	VERB
ejpam-6056	10	13	,	,	PUNCT
ejpam-6056	10	14	introduced	introduce	VERB
ejpam-6056	10	15	in	in	ADP
ejpam-6056	10	16	[	[	X
ejpam-6056	10	17	1	1	NUM
ejpam-6056	10	18	]	]	PUNCT
ejpam-6056	10	19	,	,	PUNCT
ejpam-6056	10	20	which	which	PRON
ejpam-6056	10	21	guarantees	guarantee	VERB
ejpam-6056	10	22	the	the	DET
ejpam-6056	10	23	existence	existence	NOUN
ejpam-6056	10	24	of	of	ADP
ejpam-6056	10	25	a	a	DET
ejpam-6056	10	26	unique	unique	ADJ
ejpam-6056	10	27	fixed	fix	VERB
ejpam-6056	10	28	point	point	NOUN
ejpam-6056	10	29	in	in	ADP
ejpam-6056	10	30	complete	complete	ADJ
ejpam-6056	10	31	metric	metric	ADJ
ejpam-6056	10	32	spaces	space	NOUN
ejpam-6056	10	33	.	.	PUNCT
ejpam-6056	11	1	the	the	DET
ejpam-6056	11	2	concept	concept	NOUN
ejpam-6056	11	3	of	of	ADP
ejpam-6056	11	4	metric	metric	ADJ
ejpam-6056	11	5	spaces	space	NOUN
ejpam-6056	11	6	was	be	AUX
ejpam-6056	11	7	later	later	ADV
ejpam-6056	11	8	generalized	generalize	VERB
ejpam-6056	11	9	to	to	ADP
ejpam-6056	11	10	b	b	NOUN
ejpam-6056	11	11	-	-	PUNCT
ejpam-6056	11	12	metric	metric	ADJ
ejpam-6056	11	13	spaces	space	NOUN
ejpam-6056	11	14	by	by	ADP
ejpam-6056	11	15	bakhtin	bakhtin	NOUN
ejpam-6056	11	16	[	[	X
ejpam-6056	11	17	2	2	NUM
ejpam-6056	11	18	]	]	PUNCT
ejpam-6056	11	19	and	and	CCONJ
ejpam-6056	11	20	czerwik	czerwik	PROPN
ejpam-6056	12	1	[	[	X
ejpam-6056	12	2	3	3	NUM
ejpam-6056	12	3	]	]	PUNCT
ejpam-6056	12	4	.	.	PUNCT
ejpam-6056	13	1	this	this	DET
ejpam-6056	13	2	extension	extension	NOUN
ejpam-6056	13	3	introduced	introduce	VERB
ejpam-6056	13	4	a	a	DET
ejpam-6056	13	5	more	more	ADV
ejpam-6056	13	6	flexible	flexible	ADJ
ejpam-6056	13	7	framework	framework	NOUN
ejpam-6056	13	8	for	for	ADP
ejpam-6056	13	9	analyzing	analyze	VERB
ejpam-6056	13	10	distance	distance	NOUN
ejpam-6056	13	11	relationships	relationship	NOUN
ejpam-6056	13	12	.	.	PUNCT
ejpam-6056	14	1	building	build	VERB
ejpam-6056	14	2	on	on	ADP
ejpam-6056	14	3	this	this	PRON
ejpam-6056	14	4	,	,	PUNCT
ejpam-6056	14	5	kamran	kamran	PROPN
ejpam-6056	14	6	et	et	PROPN
ejpam-6056	14	7	al	al	PROPN
ejpam-6056	14	8	.	.	PUNCT
ejpam-6056	15	1	[	[	X
ejpam-6056	15	2	4	4	X
ejpam-6056	15	3	]	]	PUNCT
ejpam-6056	15	4	proposed	propose	VERB
ejpam-6056	15	5	the	the	DET
ejpam-6056	15	6	notion	notion	NOUN
ejpam-6056	15	7	of	of	ADP
ejpam-6056	15	8	extended	extended	ADJ
ejpam-6056	15	9	b	b	X
ejpam-6056	15	10	-	-	ADJ
ejpam-6056	15	11	metric	metric	ADJ
ejpam-6056	15	12	spaces	space	NOUN
ejpam-6056	15	13	,	,	PUNCT
ejpam-6056	15	14	which	which	PRON
ejpam-6056	15	15	further	far	ADV
ejpam-6056	15	16	refines	refine	VERB
ejpam-6056	15	17	the	the	DET
ejpam-6056	15	18	triangle	triangle	NOUN
ejpam-6056	15	19	inequality	inequality	NOUN
ejpam-6056	15	20	by	by	ADP
ejpam-6056	15	21	incorporating	incorporate	VERB
ejpam-6056	15	22	a	a	DET
ejpam-6056	15	23	function	function	NOUN
ejpam-6056	15	24	that	that	PRON
ejpam-6056	15	25	depends	depend	VERB
ejpam-6056	15	26	on	on	ADP
ejpam-6056	15	27	the	the	DET
ejpam-6056	15	28	points	point	NOUN
ejpam-6056	15	29	involved	involve	VERB
ejpam-6056	15	30	.	.	PUNCT
ejpam-6056	16	1	this	this	DET
ejpam-6056	16	2	generalization	generalization	NOUN
ejpam-6056	16	3	allows	allow	VERB
ejpam-6056	16	4	for	for	ADP
ejpam-6056	16	5	the	the	DET
ejpam-6056	16	6	study	study	NOUN
ejpam-6056	16	7	of	of	ADP
ejpam-6056	16	8	structures	structure	NOUN
ejpam-6056	16	9	and	and	CCONJ
ejpam-6056	16	10	systems	system	NOUN
ejpam-6056	16	11	that	that	PRON
ejpam-6056	16	12	can	can	AUX
ejpam-6056	16	13	not	not	PART
ejpam-6056	16	14	be	be	AUX
ejpam-6056	16	15	adequately	adequately	ADV
ejpam-6056	16	16	modeled	model	VERB
ejpam-6056	16	17	using	use	VERB
ejpam-6056	16	18	traditional	traditional	ADJ
ejpam-6056	16	19	metric	metric	ADJ
ejpam-6056	16	20	or	or	CCONJ
ejpam-6056	16	21	b	b	NOUN
ejpam-6056	16	22	-	-	PUNCT
ejpam-6056	16	23	metric	metric	ADJ
ejpam-6056	16	24	spaces	space	NOUN
ejpam-6056	16	25	(	(	PUNCT
ejpam-6056	16	26	bms	bms	NOUN
ejpam-6056	16	27	)	)	PUNCT
ejpam-6056	16	28	.	.	PUNCT
ejpam-6056	17	1	extended	extend	VERB
ejpam-6056	17	2	b	b	X
ejpam-6056	17	3	-	-	ADJ
ejpam-6056	17	4	metric	metric	ADJ
ejpam-6056	17	5	spaces	space	NOUN
ejpam-6056	17	6	have	have	AUX
ejpam-6056	17	7	proven	prove	VERB
ejpam-6056	17	8	particularly	particularly	ADV
ejpam-6056	17	9	useful	useful	ADJ
ejpam-6056	17	10	in	in	ADP
ejpam-6056	17	11	capturing	capture	VERB
ejpam-6056	17	12	∗corresponding	∗corresponde	VERB
ejpam-6056	17	13	author	author	NOUN
ejpam-6056	17	14	.	.	PUNCT
ejpam-6056	18	1	doi	doi	NOUN
ejpam-6056	18	2	:	:	PUNCT
ejpam-6056	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6056	https://doi.org/10.29020/nybg.ejpam.v18i3.6056	PROPN
ejpam-6056	18	4	email	email	NOUN
ejpam-6056	18	5	addresses	address	NOUN
ejpam-6056	18	6	:	:	PUNCT
ejpam-6056	18	7	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6056	18	8	(	(	PUNCT
ejpam-6056	18	9	h.	h.	PROPN
ejpam-6056	18	10	qawaqneh	qawaqneh	PROPN
ejpam-6056	18	11	)	)	PUNCT
ejpam-6056	18	12	,	,	PUNCT
ejpam-6056	18	13	g.almusannef@arabou.edu.sa	g.almusannef@arabou.edu.sa	PROPN
ejpam-6056	18	14	(	(	PUNCT
ejpam-6056	18	15	j.m	j.m	PROPN
ejpam-6056	18	16	.	.	PROPN
ejpam-6056	18	17	al	al	PROPN
ejpam-6056	18	18	-	-	PUNCT
ejpam-6056	18	19	musannef	musannef	NOUN
ejpam-6056	18	20	)	)	PUNCT
ejpam-6056	18	21	,	,	PUNCT
ejpam-6056	18	22	habes@dau.edu.sa	habes@dau.edu.sa	PROPN
ejpam-6056	18	23	(	(	PUNCT
ejpam-6056	18	24	h.	h.	PROPN
ejpam-6056	18	25	alsamir	alsamir	PROPN
ejpam-6056	18	26	)	)	PUNCT
ejpam-6056	18	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6056	18	28	1	1	NUM
ejpam-6056	18	29	copyright	copyright	NOUN
ejpam-6056	18	30	:	:	PUNCT
ejpam-6056	19	1	©	©	PROPN
ejpam-6056	19	2	2025	2025	NUM
ejpam-6056	19	3	the	the	DET
ejpam-6056	19	4	author(s	author(s	NOUN
ejpam-6056	19	5	)	)	PUNCT
ejpam-6056	19	6	.	.	PUNCT
ejpam-6056	20	1	(	(	PUNCT
ejpam-6056	20	2	cc	cc	NOUN
ejpam-6056	20	3	by	by	ADP
ejpam-6056	20	4	-	-	PUNCT
ejpam-6056	20	5	nc	nc	PROPN
ejpam-6056	20	6	4.0	4.0	NUM
ejpam-6056	20	7	)	)	PUNCT
ejpam-6056	20	8	h.	h.	PROPN
ejpam-6056	20	9	qawaqneh	qawaqneh	PROPN
ejpam-6056	20	10	,	,	PUNCT
ejpam-6056	20	11	j.m	j.m	PROPN
ejpam-6056	20	12	.	.	PROPN
ejpam-6056	20	13	al	al	PROPN
ejpam-6056	20	14	-	-	PUNCT
ejpam-6056	20	15	musannef	musannef	PROPN
ejpam-6056	20	16	,	,	PUNCT
ejpam-6056	20	17	h.	h.	PROPN
ejpam-6056	20	18	alsamir	alsamir	PROPN
ejpam-6056	20	19	/	/	SYM
ejpam-6056	20	20	eur	eur	PROPN
ejpam-6056	20	21	.	.	PUNCT
ejpam-6056	21	1	j.	j.	PROPN
ejpam-6056	21	2	pure	pure	PROPN
ejpam-6056	21	3	appl	appl	PROPN
ejpam-6056	21	4	.	.	PROPN
ejpam-6056	21	5	math	math	PROPN
ejpam-6056	21	6	,	,	PUNCT
ejpam-6056	21	7	18	18	NUM
ejpam-6056	21	8	(	(	PUNCT
ejpam-6056	21	9	3	3	NUM
ejpam-6056	21	10	)	)	PUNCT
ejpam-6056	21	11	(	(	PUNCT
ejpam-6056	21	12	2025	2025	NUM
ejpam-6056	21	13	)	)	PUNCT
ejpam-6056	21	14	,	,	PUNCT
ejpam-6056	21	15	6056	6056	NUM
ejpam-6056	21	16	2	2	NUM
ejpam-6056	21	17	of	of	ADP
ejpam-6056	21	18	16	16	NUM
ejpam-6056	21	19	non	non	ADJ
ejpam-6056	21	20	-	-	ADJ
ejpam-6056	21	21	uniform	uniform	ADJ
ejpam-6056	21	22	distance	distance	NOUN
ejpam-6056	21	23	relationships	relationship	NOUN
ejpam-6056	21	24	,	,	PUNCT
ejpam-6056	21	25	making	make	VERB
ejpam-6056	21	26	them	they	PRON
ejpam-6056	21	27	a	a	DET
ejpam-6056	21	28	powerful	powerful	ADJ
ejpam-6056	21	29	tool	tool	NOUN
ejpam-6056	21	30	in	in	ADP
ejpam-6056	21	31	both	both	CCONJ
ejpam-6056	21	32	theoretical	theoretical	ADJ
ejpam-6056	21	33	and	and	CCONJ
ejpam-6056	21	34	applied	applied	ADJ
ejpam-6056	21	35	mathematics	mathematic	NOUN
ejpam-6056	21	36	.	.	PUNCT
ejpam-6056	22	1	significant	significant	ADJ
ejpam-6056	22	2	contributions	contribution	NOUN
ejpam-6056	22	3	to	to	ADP
ejpam-6056	22	4	this	this	DET
ejpam-6056	22	5	field	field	NOUN
ejpam-6056	22	6	include	include	VERB
ejpam-6056	22	7	the	the	DET
ejpam-6056	22	8	work	work	NOUN
ejpam-6056	22	9	of	of	ADP
ejpam-6056	22	10	b.	b.	PROPN
ejpam-6056	22	11	alqahtani	alqahtani	PROPN
ejpam-6056	22	12	et	et	PROPN
ejpam-6056	22	13	al	al	PROPN
ejpam-6056	22	14	.	.	PUNCT
ejpam-6056	23	1	[	[	X
ejpam-6056	23	2	5	5	NUM
ejpam-6056	23	3	]	]	PUNCT
ejpam-6056	23	4	,	,	PUNCT
ejpam-6056	23	5	who	who	PRON
ejpam-6056	23	6	extended	extend	VERB
ejpam-6056	23	7	rational	rational	ADJ
ejpam-6056	23	8	inequalities	inequality	NOUN
ejpam-6056	23	9	within	within	ADP
ejpam-6056	23	10	this	this	DET
ejpam-6056	23	11	framework	framework	NOUN
ejpam-6056	23	12	,	,	PUNCT
ejpam-6056	23	13	and	and	CCONJ
ejpam-6056	23	14	in	in	ADP
ejpam-6056	23	15	[	[	X
ejpam-6056	23	16	6	6	NUM
ejpam-6056	23	17	]	]	PUNCT
ejpam-6056	23	18	,	,	PUNCT
ejpam-6056	23	19	that	that	PRON
ejpam-6056	23	20	explored	explore	VERB
ejpam-6056	23	21	new	new	ADJ
ejpam-6056	23	22	contractions	contraction	NOUN
ejpam-6056	23	23	in	in	ADP
ejpam-6056	23	24	extended	extended	ADJ
ejpam-6056	23	25	b	b	X
ejpam-6056	23	26	-	-	ADJ
ejpam-6056	23	27	metric	metric	ADJ
ejpam-6056	23	28	spaces	space	NOUN
ejpam-6056	23	29	(	(	PUNCT
ejpam-6056	23	30	ebms	ebms	NOUN
ejpam-6056	23	31	)	)	PUNCT
ejpam-6056	23	32	)	)	PUNCT
ejpam-6056	23	33	.	.	PUNCT
ejpam-6056	24	1	additionally	additionally	ADV
ejpam-6056	24	2	,	,	PUNCT
ejpam-6056	24	3	k.	k.	PROPN
ejpam-6056	24	4	javed	javed	PROPN
ejpam-6056	24	5	and	and	CCONJ
ejpam-6056	24	6	thabet	thabet	ADJ
ejpam-6056	24	7	abdeljawad	abdeljawad	NOUN
ejpam-6056	24	8	[	[	X
ejpam-6056	24	9	7	7	NUM
ejpam-6056	24	10	]	]	PUNCT
ejpam-6056	24	11	investigated	investigate	VERB
ejpam-6056	24	12	fixed	fix	VERB
ejpam-6056	24	13	point	point	NOUN
ejpam-6056	24	14	results	result	NOUN
ejpam-6056	24	15	in	in	ADP
ejpam-6056	24	16	orthogonal	orthogonal	ADJ
ejpam-6056	24	17	-	-	PUNCT
ejpam-6056	24	18	ebms	ebms	NOUN
ejpam-6056	24	19	,	,	PUNCT
ejpam-6056	24	20	further	far	ADV
ejpam-6056	24	21	enriching	enrich	VERB
ejpam-6056	24	22	the	the	DET
ejpam-6056	24	23	literature	literature	NOUN
ejpam-6056	24	24	.	.	PUNCT
ejpam-6056	25	1	fixed	fix	VERB
ejpam-6056	25	2	point	point	NOUN
ejpam-6056	25	3	theory	theory	NOUN
ejpam-6056	25	4	also	also	ADV
ejpam-6056	25	5	plays	play	VERB
ejpam-6056	25	6	a	a	DET
ejpam-6056	25	7	pivotal	pivotal	ADJ
ejpam-6056	25	8	role	role	NOUN
ejpam-6056	25	9	in	in	ADP
ejpam-6056	25	10	studing	studing	NOUN
ejpam-6056	25	11	of	of	ADP
ejpam-6056	25	12	integral	integral	ADJ
ejpam-6056	25	13	equations	equation	NOUN
ejpam-6056	25	14	and	and	CCONJ
ejpam-6056	25	15	inclusions	inclusion	NOUN
ejpam-6056	25	16	.	.	PUNCT
ejpam-6056	26	1	by	by	ADP
ejpam-6056	26	2	transforming	transform	VERB
ejpam-6056	26	3	these	these	DET
ejpam-6056	26	4	problems	problem	NOUN
ejpam-6056	26	5	into	into	ADP
ejpam-6056	26	6	fixed	fix	VERB
ejpam-6056	26	7	-	-	PUNCT
ejpam-6056	26	8	point	point	NOUN
ejpam-6056	26	9	formulations	formulation	NOUN
ejpam-6056	26	10	,	,	PUNCT
ejpam-6056	26	11	researchers	researcher	NOUN
ejpam-6056	26	12	can	can	AUX
ejpam-6056	26	13	establish	establish	VERB
ejpam-6056	26	14	the	the	DET
ejpam-6056	26	15	existence	existence	NOUN
ejpam-6056	26	16	and	and	CCONJ
ejpam-6056	26	17	uniqueness	uniqueness	NOUN
ejpam-6056	26	18	of	of	ADP
ejpam-6056	26	19	solutions	solution	NOUN
ejpam-6056	26	20	under	under	ADP
ejpam-6056	26	21	specific	specific	ADJ
ejpam-6056	26	22	conditions	condition	NOUN
ejpam-6056	26	23	.	.	PUNCT
ejpam-6056	27	1	this	this	DET
ejpam-6056	27	2	approach	approach	NOUN
ejpam-6056	27	3	has	have	AUX
ejpam-6056	27	4	been	be	AUX
ejpam-6056	27	5	widely	widely	ADV
ejpam-6056	27	6	applied	apply	VERB
ejpam-6056	27	7	in	in	ADP
ejpam-6056	27	8	various	various	ADJ
ejpam-6056	27	9	fields	field	NOUN
ejpam-6056	27	10	,	,	PUNCT
ejpam-6056	27	11	as	as	SCONJ
ejpam-6056	27	12	evidenced	evidence	VERB
ejpam-6056	27	13	by	by	ADP
ejpam-6056	27	14	works	work	NOUN
ejpam-6056	27	15	such	such	ADJ
ejpam-6056	27	16	as	as	ADP
ejpam-6056	27	17	[	[	X
ejpam-6056	27	18	8–23	8–23	NOUN
ejpam-6056	27	19	]	]	PUNCT
ejpam-6056	27	20	.	.	PUNCT
ejpam-6056	28	1	moreover	moreover	ADV
ejpam-6056	28	2	,	,	PUNCT
ejpam-6056	28	3	the	the	DET
ejpam-6056	28	4	stability	stability	NOUN
ejpam-6056	28	5	of	of	ADP
ejpam-6056	28	6	systems	system	NOUN
ejpam-6056	28	7	can	can	AUX
ejpam-6056	28	8	be	be	AUX
ejpam-6056	28	9	analyzed	analyze	VERB
ejpam-6056	28	10	using	use	VERB
ejpam-6056	28	11	generalized	generalized	ADJ
ejpam-6056	28	12	contraction	contraction	NOUN
ejpam-6056	28	13	mappings	mapping	NOUN
ejpam-6056	28	14	,	,	PUNCT
ejpam-6056	28	15	as	as	SCONJ
ejpam-6056	28	16	demonstrated	demonstrate	VERB
ejpam-6056	28	17	in	in	ADP
ejpam-6056	28	18	[	[	X
ejpam-6056	28	19	24–28	24–28	NUM
ejpam-6056	28	20	]	]	PUNCT
ejpam-6056	28	21	.	.	PUNCT
ejpam-6056	29	1	this	this	DET
ejpam-6056	29	2	paper	paper	NOUN
ejpam-6056	29	3	focuses	focus	VERB
ejpam-6056	29	4	on	on	ADP
ejpam-6056	29	5	rational	rational	ADJ
ejpam-6056	29	6	contractions	contraction	NOUN
ejpam-6056	29	7	within	within	ADP
ejpam-6056	29	8	ebms	ebms	NOUN
ejpam-6056	29	9	,	,	PUNCT
ejpam-6056	29	10	a	a	DET
ejpam-6056	29	11	rapidly	rapidly	ADV
ejpam-6056	29	12	evolving	evolve	VERB
ejpam-6056	29	13	area	area	NOUN
ejpam-6056	29	14	of	of	ADP
ejpam-6056	29	15	mathematical	mathematical	ADJ
ejpam-6056	29	16	analysis	analysis	NOUN
ejpam-6056	29	17	.	.	PUNCT
ejpam-6056	30	1	these	these	DET
ejpam-6056	30	2	contractions	contraction	NOUN
ejpam-6056	30	3	are	be	AUX
ejpam-6056	30	4	particularly	particularly	ADV
ejpam-6056	30	5	intriguing	intriguing	ADJ
ejpam-6056	30	6	because	because	SCONJ
ejpam-6056	30	7	they	they	PRON
ejpam-6056	30	8	incorporate	incorporate	VERB
ejpam-6056	30	9	logical	logical	ADJ
ejpam-6056	30	10	components	component	NOUN
ejpam-6056	30	11	that	that	PRON
ejpam-6056	30	12	enhance	enhance	VERB
ejpam-6056	30	13	the	the	DET
ejpam-6056	30	14	study	study	NOUN
ejpam-6056	30	15	of	of	ADP
ejpam-6056	30	16	fixed	fix	VERB
ejpam-6056	30	17	points	point	NOUN
ejpam-6056	30	18	.	.	PUNCT
ejpam-6056	31	1	their	their	PRON
ejpam-6056	31	2	ability	ability	NOUN
ejpam-6056	31	3	to	to	PART
ejpam-6056	31	4	model	model	VERB
ejpam-6056	31	5	real	real	ADJ
ejpam-6056	31	6	-	-	PUNCT
ejpam-6056	31	7	world	world	NOUN
ejpam-6056	31	8	problems	problem	NOUN
ejpam-6056	31	9	with	with	ADP
ejpam-6056	31	10	complex	complex	ADJ
ejpam-6056	31	11	interdependencies	interdependency	NOUN
ejpam-6056	31	12	makes	make	VERB
ejpam-6056	31	13	them	they	PRON
ejpam-6056	31	14	highly	highly	ADV
ejpam-6056	31	15	applicable	applicable	ADJ
ejpam-6056	31	16	in	in	ADP
ejpam-6056	31	17	optimization	optimization	NOUN
ejpam-6056	31	18	and	and	CCONJ
ejpam-6056	31	19	dynamic	dynamic	ADJ
ejpam-6056	31	20	systems	system	NOUN
ejpam-6056	31	21	(	(	PUNCT
ejpam-6056	31	22	see	see	VERB
ejpam-6056	31	23	[	[	X
ejpam-6056	31	24	22	22	NUM
ejpam-6056	31	25	,	,	PUNCT
ejpam-6056	31	26	29–33	29–33	PROPN
ejpam-6056	31	27	]	]	PUNCT
ejpam-6056	31	28	)	)	PUNCT
ejpam-6056	31	29	.	.	PUNCT
ejpam-6056	32	1	by	by	ADP
ejpam-6056	32	2	investigating	investigate	VERB
ejpam-6056	32	3	rational	rational	ADJ
ejpam-6056	32	4	-	-	PUNCT
ejpam-6056	32	5	type	type	NOUN
ejpam-6056	32	6	contractions	contraction	NOUN
ejpam-6056	32	7	,	,	PUNCT
ejpam-6056	32	8	this	this	DET
ejpam-6056	32	9	work	work	NOUN
ejpam-6056	32	10	aims	aim	VERB
ejpam-6056	32	11	to	to	PART
ejpam-6056	32	12	contribute	contribute	VERB
ejpam-6056	32	13	to	to	ADP
ejpam-6056	32	14	both	both	CCONJ
ejpam-6056	32	15	theoretical	theoretical	ADJ
ejpam-6056	32	16	advancements	advancement	NOUN
ejpam-6056	32	17	and	and	CCONJ
ejpam-6056	32	18	practical	practical	ADJ
ejpam-6056	32	19	applications	application	NOUN
ejpam-6056	32	20	in	in	ADP
ejpam-6056	32	21	mathematical	mathematical	ADJ
ejpam-6056	32	22	analysis	analysis	NOUN
ejpam-6056	32	23	.	.	PUNCT
ejpam-6056	33	1	2	2	X
ejpam-6056	33	2	.	.	X
ejpam-6056	33	3	preliminaries	preliminary	NOUN
ejpam-6056	33	4	definition	definition	NOUN
ejpam-6056	33	5	1	1	NUM
ejpam-6056	33	6	.	.	PUNCT
ejpam-6056	34	1	[	[	X
ejpam-6056	34	2	34	34	NUM
ejpam-6056	34	3	]	]	PUNCT
ejpam-6056	34	4	let	let	VERB
ejpam-6056	34	5	γ	γ	X
ejpam-6056	34	6	be	be	AUX
ejpam-6056	34	7	a	a	DET
ejpam-6056	34	8	non	non	ADJ
ejpam-6056	34	9	-	-	ADJ
ejpam-6056	34	10	empty	empty	ADJ
ejpam-6056	34	11	set	set	NOUN
ejpam-6056	34	12	.	.	PUNCT
ejpam-6056	35	1	a	a	DET
ejpam-6056	35	2	function	function	NOUN
ejpam-6056	35	3	dβ	dβ	ADP
ejpam-6056	35	4	:	:	PUNCT
ejpam-6056	35	5	γ	γ	X
ejpam-6056	35	6	×	×	NOUN
ejpam-6056	35	7	γ	γ	X
ejpam-6056	35	8	→	→	SYM
ejpam-6056	35	9	[	[	X
ejpam-6056	35	10	0,+∞	0,+∞	NUM
ejpam-6056	35	11	)	)	PUNCT
ejpam-6056	35	12	is	be	AUX
ejpam-6056	35	13	called	call	VERB
ejpam-6056	35	14	a	a	DET
ejpam-6056	35	15	b	b	NOUN
ejpam-6056	35	16	-	-	PUNCT
ejpam-6056	35	17	metric	metric	ADJ
ejpam-6056	35	18	if	if	SCONJ
ejpam-6056	35	19	the	the	DET
ejpam-6056	35	20	following	follow	VERB
ejpam-6056	35	21	properties	property	NOUN
ejpam-6056	35	22	hold	hold	VERB
ejpam-6056	35	23	for	for	ADP
ejpam-6056	35	24	all	all	DET
ejpam-6056	35	25	x	x	NOUN
ejpam-6056	35	26	,	,	PUNCT
ejpam-6056	35	27	y	y	PROPN
ejpam-6056	35	28	,	,	PUNCT
ejpam-6056	35	29	z	z	PROPN
ejpam-6056	35	30	∈	∈	PROPN
ejpam-6056	35	31	γ	γ	X
ejpam-6056	35	32	:	:	PUNCT
ejpam-6056	35	33	(	(	PUNCT
ejpam-6056	35	34	i	i	NOUN
ejpam-6056	35	35	)	)	PUNCT
ejpam-6056	35	36	dβ(x	dβ(x	PROPN
ejpam-6056	35	37	,	,	PUNCT
ejpam-6056	35	38	y	y	NOUN
ejpam-6056	35	39	)	)	PUNCT
ejpam-6056	35	40	=	=	SYM
ejpam-6056	35	41	0	0	PUNCT
ejpam-6056	36	1	if	if	SCONJ
ejpam-6056	36	2	and	and	CCONJ
ejpam-6056	36	3	only	only	ADV
ejpam-6056	36	4	if	if	SCONJ
ejpam-6056	36	5	x	x	X
ejpam-6056	36	6	=	=	SYM
ejpam-6056	36	7	y.	y.	PROPN
ejpam-6056	36	8	(	(	PUNCT
ejpam-6056	36	9	ii	ii	NOUN
ejpam-6056	36	10	)	)	PUNCT
ejpam-6056	36	11	dβ(x	dβ(x	PROPN
ejpam-6056	36	12	,	,	PUNCT
ejpam-6056	36	13	y	y	NOUN
ejpam-6056	36	14	)	)	PUNCT
ejpam-6056	36	15	=	=	SYM
ejpam-6056	36	16	dβ(y	dβ(y	NOUN
ejpam-6056	36	17	,	,	PUNCT
ejpam-6056	36	18	x	x	PRON
ejpam-6056	36	19	)	)	PUNCT
ejpam-6056	36	20	(	(	PUNCT
ejpam-6056	36	21	symmetry	symmetry	NOUN
ejpam-6056	36	22	)	)	PUNCT
ejpam-6056	36	23	.	.	PUNCT
ejpam-6056	37	1	(	(	PUNCT
ejpam-6056	37	2	iii	iii	X
ejpam-6056	37	3	)	)	PUNCT
ejpam-6056	37	4	dβ(x	dβ(x	NOUN
ejpam-6056	37	5	,	,	PUNCT
ejpam-6056	37	6	y	y	NOUN
ejpam-6056	37	7	)	)	PUNCT
ejpam-6056	37	8	≤	≤	PUNCT
ejpam-6056	37	9	τ	τ	PROPN
ejpam-6056	38	1	[	[	X
ejpam-6056	38	2	dβ(x	dβ(x	NOUN
ejpam-6056	38	3	,	,	PUNCT
ejpam-6056	38	4	z	z	NOUN
ejpam-6056	38	5	)	)	PUNCT
ejpam-6056	38	6	+	+	CCONJ
ejpam-6056	38	7	dβ(z	dβ(z	PROPN
ejpam-6056	38	8	,	,	PUNCT
ejpam-6056	38	9	y	y	PROPN
ejpam-6056	38	10	)	)	PUNCT
ejpam-6056	38	11	]	]	PUNCT
ejpam-6056	38	12	,	,	PUNCT
ejpam-6056	38	13	where	where	SCONJ
ejpam-6056	38	14	τ	τ	PROPN
ejpam-6056	38	15	≥	≥	NUM
ejpam-6056	38	16	1	1	NUM
ejpam-6056	38	17	is	be	AUX
ejpam-6056	38	18	a	a	DET
ejpam-6056	38	19	given	give	VERB
ejpam-6056	38	20	constant	constant	NOUN
ejpam-6056	38	21	.	.	PUNCT
ejpam-6056	39	1	then	then	ADV
ejpam-6056	39	2	,	,	PUNCT
ejpam-6056	39	3	the	the	DET
ejpam-6056	39	4	pair	pair	NOUN
ejpam-6056	39	5	(	(	PUNCT
ejpam-6056	39	6	γ	γ	NOUN
ejpam-6056	39	7	,	,	PUNCT
ejpam-6056	39	8	dβ	dβ	NOUN
ejpam-6056	39	9	)	)	PUNCT
ejpam-6056	39	10	is	be	AUX
ejpam-6056	39	11	referred	refer	VERB
ejpam-6056	39	12	to	to	ADP
ejpam-6056	39	13	as	as	ADP
ejpam-6056	39	14	a	a	DET
ejpam-6056	39	15	bms	bms	PROPN
ejpam-6056	39	16	.	.	PUNCT
ejpam-6056	39	17	example	example	NOUN
ejpam-6056	40	1	1	1	NUM
ejpam-6056	40	2	.	.	PUNCT
ejpam-6056	41	1	[	[	X
ejpam-6056	41	2	34	34	NUM
ejpam-6056	41	3	]	]	PUNCT
ejpam-6056	41	4	consider	consider	VERB
ejpam-6056	41	5	a	a	DET
ejpam-6056	41	6	metric	metric	ADJ
ejpam-6056	41	7	space	space	NOUN
ejpam-6056	41	8	(	(	PUNCT
ejpam-6056	41	9	γ	γ	X
ejpam-6056	41	10	,	,	PUNCT
ejpam-6056	41	11	d	d	NOUN
ejpam-6056	41	12	)	)	PUNCT
ejpam-6056	41	13	and	and	CCONJ
ejpam-6056	41	14	define	define	VERB
ejpam-6056	41	15	a	a	DET
ejpam-6056	41	16	modified	modify	VERB
ejpam-6056	41	17	distance	distance	NOUN
ejpam-6056	41	18	function	function	NOUN
ejpam-6056	41	19	dβ	dβ	ADP
ejpam-6056	41	20	as	as	ADP
ejpam-6056	41	21	:	:	PUNCT
ejpam-6056	41	22	dβ(x	dβ(x	NOUN
ejpam-6056	41	23	,	,	PUNCT
ejpam-6056	41	24	y	y	NOUN
ejpam-6056	41	25	)	)	PUNCT
ejpam-6056	41	26	=	=	SYM
ejpam-6056	42	1	(	(	PUNCT
ejpam-6056	42	2	d(x	d(x	PROPN
ejpam-6056	42	3	,	,	PUNCT
ejpam-6056	42	4	y))α	y))α	NOUN
ejpam-6056	42	5	,	,	PUNCT
ejpam-6056	42	6	where	where	SCONJ
ejpam-6056	42	7	α	α	PROPN
ejpam-6056	42	8	>	>	X
ejpam-6056	42	9	1	1	NUM
ejpam-6056	42	10	is	be	AUX
ejpam-6056	42	11	a	a	DET
ejpam-6056	42	12	fixed	fix	VERB
ejpam-6056	42	13	constant	constant	ADJ
ejpam-6056	42	14	.	.	PUNCT
ejpam-6056	43	1	then	then	ADV
ejpam-6056	43	2	,	,	PUNCT
ejpam-6056	43	3	(	(	PUNCT
ejpam-6056	43	4	γ	γ	X
ejpam-6056	43	5	,	,	PUNCT
ejpam-6056	43	6	dβ	dβ	ADJ
ejpam-6056	43	7	)	)	PUNCT
ejpam-6056	43	8	forms	form	VERB
ejpam-6056	43	9	a	a	DET
ejpam-6056	43	10	b	b	NOUN
ejpam-6056	43	11	-	-	PUNCT
ejpam-6056	43	12	metric	metric	ADJ
ejpam-6056	43	13	space	space	NOUN
ejpam-6056	43	14	with	with	ADP
ejpam-6056	43	15	coefficient	coefficient	NOUN
ejpam-6056	43	16	τ	τ	X
ejpam-6056	43	17	=	=	SYM
ejpam-6056	43	18	2α−1	2α−1	NUM
ejpam-6056	43	19	.	.	PUNCT
ejpam-6056	44	1	for	for	ADP
ejpam-6056	44	2	instance	instance	NOUN
ejpam-6056	44	3	,	,	PUNCT
ejpam-6056	44	4	if	if	SCONJ
ejpam-6056	44	5	γ	γ	X
ejpam-6056	44	6	=	=	SYM
ejpam-6056	44	7	r	r	NOUN
ejpam-6056	44	8	and	and	CCONJ
ejpam-6056	44	9	the	the	DET
ejpam-6056	44	10	standard	standard	ADJ
ejpam-6056	44	11	metric	metric	ADJ
ejpam-6056	44	12	d(x	d(x	PROPN
ejpam-6056	44	13	,	,	PUNCT
ejpam-6056	44	14	y	y	NOUN
ejpam-6056	44	15	)	)	PUNCT
ejpam-6056	45	1	=	=	PUNCT
ejpam-6056	45	2	|x−	|x−	ADJ
ejpam-6056	46	1	y|	y|	NOUN
ejpam-6056	46	2	is	be	AUX
ejpam-6056	46	3	used	use	VERB
ejpam-6056	46	4	,	,	PUNCT
ejpam-6056	46	5	we	we	PRON
ejpam-6056	46	6	obtain	obtain	VERB
ejpam-6056	46	7	:	:	PUNCT
ejpam-6056	46	8	dβ(x	dβ(x	NOUN
ejpam-6056	46	9	,	,	PUNCT
ejpam-6056	46	10	y	y	NOUN
ejpam-6056	46	11	)	)	PUNCT
ejpam-6056	46	12	=	=	SYM
ejpam-6056	47	1	(	(	PUNCT
ejpam-6056	47	2	x−	x−	PROPN
ejpam-6056	47	3	y)2	y)2	NOUN
ejpam-6056	47	4	.	.	PUNCT
ejpam-6056	48	1	this	this	DET
ejpam-6056	48	2	structure	structure	NOUN
ejpam-6056	48	3	satisfies	satisfy	VERB
ejpam-6056	48	4	the	the	DET
ejpam-6056	48	5	bms	bms	NOUN
ejpam-6056	48	6	conditions	condition	NOUN
ejpam-6056	48	7	with	with	ADP
ejpam-6056	48	8	τ	τ	PROPN
ejpam-6056	48	9	=	=	SYM
ejpam-6056	48	10	2	2	NUM
ejpam-6056	48	11	,	,	PUNCT
ejpam-6056	48	12	but	but	CCONJ
ejpam-6056	48	13	it	it	PRON
ejpam-6056	48	14	does	do	AUX
ejpam-6056	48	15	not	not	PART
ejpam-6056	48	16	conform	conform	VERB
ejpam-6056	48	17	to	to	ADP
ejpam-6056	48	18	the	the	DET
ejpam-6056	48	19	definition	definition	NOUN
ejpam-6056	48	20	of	of	ADP
ejpam-6056	48	21	a	a	DET
ejpam-6056	48	22	standard	standard	ADJ
ejpam-6056	48	23	metric	metric	ADJ
ejpam-6056	48	24	space	space	NOUN
ejpam-6056	48	25	.	.	PUNCT
ejpam-6056	49	1	h.	h.	PROPN
ejpam-6056	49	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	49	3	,	,	PUNCT
ejpam-6056	49	4	j.m	j.m	PROPN
ejpam-6056	49	5	.	.	PROPN
ejpam-6056	49	6	al	al	PROPN
ejpam-6056	49	7	-	-	PUNCT
ejpam-6056	49	8	musannef	musannef	PROPN
ejpam-6056	49	9	,	,	PUNCT
ejpam-6056	49	10	h.	h.	PROPN
ejpam-6056	49	11	alsamir	alsamir	PROPN
ejpam-6056	49	12	/	/	SYM
ejpam-6056	49	13	eur	eur	PROPN
ejpam-6056	49	14	.	.	PUNCT
ejpam-6056	50	1	j.	j.	PROPN
ejpam-6056	50	2	pure	pure	PROPN
ejpam-6056	50	3	appl	appl	PROPN
ejpam-6056	50	4	.	.	PROPN
ejpam-6056	50	5	math	math	PROPN
ejpam-6056	50	6	,	,	PUNCT
ejpam-6056	50	7	18	18	NUM
ejpam-6056	50	8	(	(	PUNCT
ejpam-6056	50	9	3	3	NUM
ejpam-6056	50	10	)	)	PUNCT
ejpam-6056	50	11	(	(	PUNCT
ejpam-6056	50	12	2025	2025	NUM
ejpam-6056	50	13	)	)	PUNCT
ejpam-6056	50	14	,	,	PUNCT
ejpam-6056	50	15	6056	6056	NUM
ejpam-6056	50	16	3	3	NUM
ejpam-6056	50	17	of	of	ADP
ejpam-6056	50	18	16	16	NUM
ejpam-6056	50	19	definition	definition	NOUN
ejpam-6056	50	20	2	2	NUM
ejpam-6056	50	21	.	.	PUNCT
ejpam-6056	51	1	[	[	X
ejpam-6056	51	2	5	5	NUM
ejpam-6056	51	3	]	]	PUNCT
ejpam-6056	51	4	let	let	VERB
ejpam-6056	51	5	γ	γ	X
ejpam-6056	51	6	be	be	AUX
ejpam-6056	51	7	a	a	DET
ejpam-6056	51	8	non	non	ADJ
ejpam-6056	51	9	-	-	ADJ
ejpam-6056	51	10	empty	empty	ADJ
ejpam-6056	51	11	set	set	NOUN
ejpam-6056	51	12	and	and	CCONJ
ejpam-6056	51	13	θ	θ	NOUN
ejpam-6056	51	14	:	:	PUNCT
ejpam-6056	51	15	γ	γ	X
ejpam-6056	51	16	×	×	NOUN
ejpam-6056	51	17	γ	γ	X
ejpam-6056	51	18	→	→	SYM
ejpam-6056	51	19	[	[	X
ejpam-6056	51	20	1,+∞	1,+∞	NUM
ejpam-6056	51	21	)	)	PUNCT
ejpam-6056	51	22	.	.	PUNCT
ejpam-6056	52	1	a	a	DET
ejpam-6056	52	2	function	function	NOUN
ejpam-6056	52	3	dτ	dτ	NOUN
ejpam-6056	52	4	:	:	PUNCT
ejpam-6056	52	5	γ	γ	X
ejpam-6056	52	6	×	×	PROPN
ejpam-6056	52	7	γ	γ	X
ejpam-6056	52	8	→	→	SYM
ejpam-6056	52	9	[	[	X
ejpam-6056	52	10	0,+∞	0,+∞	NUM
ejpam-6056	52	11	)	)	PUNCT
ejpam-6056	52	12	is	be	AUX
ejpam-6056	52	13	referred	refer	VERB
ejpam-6056	52	14	to	to	ADP
ejpam-6056	52	15	as	as	ADP
ejpam-6056	52	16	an	an	DET
ejpam-6056	52	17	extended	extended	ADJ
ejpam-6056	52	18	b	b	NOUN
ejpam-6056	52	19	-	-	ADJ
ejpam-6056	52	20	metric	metric	ADJ
ejpam-6056	52	21	if	if	SCONJ
ejpam-6056	52	22	it	it	PRON
ejpam-6056	52	23	satisfies	satisfy	VERB
ejpam-6056	52	24	the	the	DET
ejpam-6056	52	25	following	follow	VERB
ejpam-6056	52	26	conditions	condition	NOUN
ejpam-6056	52	27	for	for	ADP
ejpam-6056	52	28	all	all	DET
ejpam-6056	52	29	x	x	NOUN
ejpam-6056	52	30	,	,	PUNCT
ejpam-6056	52	31	y	y	PROPN
ejpam-6056	52	32	,	,	PUNCT
ejpam-6056	52	33	z	z	PROPN
ejpam-6056	52	34	∈	∈	PROPN
ejpam-6056	52	35	γ	γ	X
ejpam-6056	52	36	:	:	PUNCT
ejpam-6056	52	37	(	(	PUNCT
ejpam-6056	52	38	i	i	NOUN
ejpam-6056	52	39	)	)	PUNCT
ejpam-6056	52	40	dτ	dτ	PROPN
ejpam-6056	52	41	(	(	PUNCT
ejpam-6056	52	42	x	x	NOUN
ejpam-6056	52	43	,	,	PUNCT
ejpam-6056	52	44	y	y	NOUN
ejpam-6056	52	45	)	)	PUNCT
ejpam-6056	52	46	=	=	SYM
ejpam-6056	52	47	0	0	PUNCT
ejpam-6056	53	1	if	if	SCONJ
ejpam-6056	53	2	and	and	CCONJ
ejpam-6056	53	3	only	only	ADV
ejpam-6056	53	4	if	if	SCONJ
ejpam-6056	53	5	x	x	X
ejpam-6056	53	6	=	=	SYM
ejpam-6056	53	7	y.	y.	PROPN
ejpam-6056	53	8	(	(	PUNCT
ejpam-6056	53	9	ii	ii	PROPN
ejpam-6056	53	10	)	)	PUNCT
ejpam-6056	53	11	dτ	dτ	NOUN
ejpam-6056	53	12	(	(	PUNCT
ejpam-6056	53	13	x	x	PROPN
ejpam-6056	53	14	,	,	PUNCT
ejpam-6056	53	15	y	y	NOUN
ejpam-6056	53	16	)	)	PUNCT
ejpam-6056	53	17	=	=	SYM
ejpam-6056	53	18	dτ	dτ	INTJ
ejpam-6056	53	19	(	(	PUNCT
ejpam-6056	53	20	y	y	PROPN
ejpam-6056	53	21	,	,	PUNCT
ejpam-6056	53	22	x	x	NOUN
ejpam-6056	53	23	)	)	PUNCT
ejpam-6056	53	24	(	(	PUNCT
ejpam-6056	53	25	symmetry	symmetry	NOUN
ejpam-6056	53	26	)	)	PUNCT
ejpam-6056	53	27	.	.	PUNCT
ejpam-6056	54	1	(	(	PUNCT
ejpam-6056	54	2	iii	iii	X
ejpam-6056	54	3	)	)	PUNCT
ejpam-6056	54	4	dτ	dτ	NOUN
ejpam-6056	54	5	(	(	PUNCT
ejpam-6056	54	6	x	x	PROPN
ejpam-6056	54	7	,	,	PUNCT
ejpam-6056	54	8	y	y	NOUN
ejpam-6056	54	9	)	)	PUNCT
ejpam-6056	54	10	≤	≤	NOUN
ejpam-6056	54	11	θ(x	θ(x	PROPN
ejpam-6056	54	12	,	,	PUNCT
ejpam-6056	54	13	y)[dτ	y)[dτ	PROPN
ejpam-6056	54	14	(	(	PUNCT
ejpam-6056	54	15	x	x	X
ejpam-6056	54	16	,	,	PUNCT
ejpam-6056	54	17	z	z	NOUN
ejpam-6056	54	18	)	)	PUNCT
ejpam-6056	55	1	+	+	NUM
ejpam-6056	55	2	dτ	dτ	INTJ
ejpam-6056	55	3	(	(	PUNCT
ejpam-6056	55	4	z	z	PROPN
ejpam-6056	55	5	,	,	PUNCT
ejpam-6056	55	6	y	y	PROPN
ejpam-6056	55	7	)	)	PUNCT
ejpam-6056	55	8	]	]	PUNCT
ejpam-6056	55	9	,	,	PUNCT
ejpam-6056	55	10	where	where	SCONJ
ejpam-6056	55	11	θ	θ	NOUN
ejpam-6056	55	12	:	:	PUNCT
ejpam-6056	55	13	γ×	γ×	PROPN
ejpam-6056	55	14	γ	γ	X
ejpam-6056	55	15	→	→	SYM
ejpam-6056	55	16	[	[	X
ejpam-6056	55	17	1,+∞	1,+∞	NUM
ejpam-6056	55	18	)	)	PUNCT
ejpam-6056	55	19	is	be	AUX
ejpam-6056	55	20	a	a	DET
ejpam-6056	55	21	control	control	NOUN
ejpam-6056	55	22	function	function	NOUN
ejpam-6056	55	23	.	.	PUNCT
ejpam-6056	56	1	then	then	ADV
ejpam-6056	56	2	,	,	PUNCT
ejpam-6056	56	3	the	the	DET
ejpam-6056	56	4	pair	pair	NOUN
ejpam-6056	56	5	(	(	PUNCT
ejpam-6056	56	6	γ	γ	X
ejpam-6056	56	7	,	,	PUNCT
ejpam-6056	56	8	dτ	dτ	NOUN
ejpam-6056	56	9	)	)	PUNCT
ejpam-6056	56	10	is	be	AUX
ejpam-6056	56	11	called	call	VERB
ejpam-6056	56	12	an	an	DET
ejpam-6056	56	13	ebms	ebms	NOUN
ejpam-6056	56	14	.	.	PUNCT
ejpam-6056	57	1	definition	definition	NOUN
ejpam-6056	57	2	3	3	NUM
ejpam-6056	57	3	.	.	PUNCT
ejpam-6056	58	1	[	[	X
ejpam-6056	58	2	5	5	NUM
ejpam-6056	58	3	]	]	X
ejpam-6056	58	4	let	let	VERB
ejpam-6056	58	5	(	(	PUNCT
ejpam-6056	58	6	γ	γ	X
ejpam-6056	58	7	,	,	PUNCT
ejpam-6056	58	8	dτ	dτ	NOUN
ejpam-6056	58	9	)	)	PUNCT
ejpam-6056	58	10	be	be	AUX
ejpam-6056	58	11	an	an	DET
ejpam-6056	58	12	ebms	ebms	NOUN
ejpam-6056	58	13	,	,	PUNCT
ejpam-6056	58	14	and	and	CCONJ
ejpam-6056	58	15	consider	consider	VERB
ejpam-6056	58	16	a	a	DET
ejpam-6056	58	17	sequence	sequence	NOUN
ejpam-6056	58	18	{	{	PUNCT
ejpam-6056	58	19	an	an	NOUN
ejpam-6056	58	20	}	}	PUNCT
ejpam-6056	58	21	in	in	ADP
ejpam-6056	58	22	γ	γ	NOUN
ejpam-6056	58	23	with	with	ADP
ejpam-6056	58	24	a	a	DET
ejpam-6056	58	25	point	point	NOUN
ejpam-6056	58	26	q	q	X
ejpam-6056	58	27	∈	∈	PROPN
ejpam-6056	58	28	γ	γ	X
ejpam-6056	58	29	.	.	PUNCT
ejpam-6056	59	1	the	the	DET
ejpam-6056	59	2	sequence	sequence	NOUN
ejpam-6056	59	3	{	{	PUNCT
ejpam-6056	59	4	an	an	PRON
ejpam-6056	59	5	}	}	PUNCT
ejpam-6056	59	6	is	be	AUX
ejpam-6056	59	7	classified	classify	VERB
ejpam-6056	59	8	as	as	ADP
ejpam-6056	59	9	:	:	PUNCT
ejpam-6056	59	10	(	(	PUNCT
ejpam-6056	59	11	i	i	NOUN
ejpam-6056	59	12	)	)	PUNCT
ejpam-6056	59	13	convergent	convergent	NOUN
ejpam-6056	59	14	in	in	ADP
ejpam-6056	59	15	(	(	PUNCT
ejpam-6056	59	16	γ	γ	X
ejpam-6056	59	17	,	,	PUNCT
ejpam-6056	59	18	dτ	dτ	NOUN
ejpam-6056	59	19	)	)	PUNCT
ejpam-6056	59	20	and	and	CCONJ
ejpam-6056	59	21	approaching	approach	VERB
ejpam-6056	59	22	q	q	NOUN
ejpam-6056	59	23	if	if	SCONJ
ejpam-6056	59	24	,	,	PUNCT
ejpam-6056	59	25	for	for	ADP
ejpam-6056	59	26	any	any	DET
ejpam-6056	59	27	ε	ε	PROPN
ejpam-6056	59	28	>	>	X
ejpam-6056	59	29	0	0	PROPN
ejpam-6056	59	30	,	,	PUNCT
ejpam-6056	59	31	there	there	PRON
ejpam-6056	59	32	exists	exist	VERB
ejpam-6056	59	33	n0	n0	PROPN
ejpam-6056	59	34	∈	∈	PROPN
ejpam-6056	59	35	n	n	PRON
ejpam-6056	59	36	such	such	ADJ
ejpam-6056	59	37	that	that	DET
ejpam-6056	59	38	dτ	dτ	PROPN
ejpam-6056	59	39	(	(	PUNCT
ejpam-6056	59	40	an	an	DET
ejpam-6056	59	41	,	,	PUNCT
ejpam-6056	59	42	q	q	NOUN
ejpam-6056	59	43	)	)	PUNCT
ejpam-6056	59	44	<	<	X
ejpam-6056	59	45	ε	ε	PROPN
ejpam-6056	59	46	for	for	ADP
ejpam-6056	59	47	all	all	DET
ejpam-6056	59	48	n	n	PROPN
ejpam-6056	59	49	>	>	X
ejpam-6056	59	50	n0	n0	PROPN
ejpam-6056	59	51	.	.	PUNCT
ejpam-6056	60	1	this	this	PRON
ejpam-6056	60	2	is	be	AUX
ejpam-6056	60	3	denoted	denote	VERB
ejpam-6056	60	4	as	as	ADP
ejpam-6056	60	5	limn→∞	limn→∞	PROPN
ejpam-6056	60	6	an	an	DET
ejpam-6056	60	7	=	=	X
ejpam-6056	60	8	q.	q.	PROPN
ejpam-6056	60	9	(	(	PUNCT
ejpam-6056	60	10	ii	ii	NOUN
ejpam-6056	60	11	)	)	PUNCT
ejpam-6056	60	12	cauchy	cauchy	NOUN
ejpam-6056	60	13	if	if	SCONJ
ejpam-6056	60	14	,	,	PUNCT
ejpam-6056	60	15	for	for	ADP
ejpam-6056	60	16	any	any	DET
ejpam-6056	60	17	ε	ε	PROPN
ejpam-6056	60	18	>	>	X
ejpam-6056	60	19	0	0	PROPN
ejpam-6056	60	20	,	,	PUNCT
ejpam-6056	60	21	there	there	PRON
ejpam-6056	60	22	exists	exist	VERB
ejpam-6056	60	23	n	n	X
ejpam-6056	60	24	=	=	SYM
ejpam-6056	60	25	n(ε	n(ε	PROPN
ejpam-6056	60	26	)	)	PUNCT
ejpam-6056	60	27	∈	∈	PROPN
ejpam-6056	60	28	n	n	PRON
ejpam-6056	60	29	such	such	ADJ
ejpam-6056	60	30	that	that	DET
ejpam-6056	60	31	dτ	dτ	PROPN
ejpam-6056	60	32	(	(	PUNCT
ejpam-6056	60	33	am	am	PROPN
ejpam-6056	60	34	,	,	PUNCT
ejpam-6056	60	35	an	an	PRON
ejpam-6056	60	36	)	)	PUNCT
ejpam-6056	60	37	<	<	X
ejpam-6056	60	38	ε	ε	PROPN
ejpam-6056	60	39	for	for	ADP
ejpam-6056	60	40	all	all	DET
ejpam-6056	60	41	m	m	PROPN
ejpam-6056	60	42	,	,	PUNCT
ejpam-6056	60	43	n	n	PRON
ejpam-6056	60	44	≥	≥	NOUN
ejpam-6056	60	45	n	n	NOUN
ejpam-6056	60	46	.	.	PUNCT
ejpam-6056	61	1	definition	definition	NOUN
ejpam-6056	61	2	4	4	NUM
ejpam-6056	61	3	.	.	PUNCT
ejpam-6056	62	1	[	[	X
ejpam-6056	62	2	5	5	X
ejpam-6056	62	3	]	]	PUNCT
ejpam-6056	62	4	an	an	DET
ejpam-6056	62	5	ebms	ebms	NOUN
ejpam-6056	62	6	(	(	PUNCT
ejpam-6056	62	7	γ	γ	X
ejpam-6056	62	8	,	,	PUNCT
ejpam-6056	62	9	dτ	dτ	NOUN
ejpam-6056	62	10	)	)	PUNCT
ejpam-6056	62	11	is	be	AUX
ejpam-6056	62	12	considered	consider	VERB
ejpam-6056	62	13	complete	complete	ADJ
ejpam-6056	62	14	if	if	SCONJ
ejpam-6056	62	15	every	every	DET
ejpam-6056	62	16	cauchy	cauchy	ADJ
ejpam-6056	62	17	sequence	sequence	NOUN
ejpam-6056	62	18	in	in	ADP
ejpam-6056	62	19	γ	γ	PROPN
ejpam-6056	62	20	converges	converge	NOUN
ejpam-6056	62	21	to	to	ADP
ejpam-6056	62	22	a	a	DET
ejpam-6056	62	23	limit	limit	NOUN
ejpam-6056	62	24	in	in	ADP
ejpam-6056	62	25	γ	γ	PROPN
ejpam-6056	62	26	.	.	PROPN
ejpam-6056	62	27	example	example	NOUN
ejpam-6056	62	28	2	2	NUM
ejpam-6056	62	29	.	.	PUNCT
ejpam-6056	63	1	[	[	X
ejpam-6056	63	2	3	3	X
ejpam-6056	63	3	]	]	PUNCT
ejpam-6056	63	4	let	let	VERB
ejpam-6056	63	5	γ	γ	PROPN
ejpam-6056	63	6	=	=	SYM
ejpam-6056	63	7	r.	r.	PROPN
ejpam-6056	63	8	define	define	VERB
ejpam-6056	63	9	the	the	DET
ejpam-6056	63	10	functions	function	NOUN
ejpam-6056	63	11	θ	θ	NOUN
ejpam-6056	63	12	:	:	PUNCT
ejpam-6056	63	13	γ×	γ×	PUNCT
ejpam-6056	63	14	γ	γ	X
ejpam-6056	63	15	→	→	SYM
ejpam-6056	63	16	[	[	X
ejpam-6056	63	17	1,+∞	1,+∞	NUM
ejpam-6056	63	18	)	)	PUNCT
ejpam-6056	63	19	and	and	CCONJ
ejpam-6056	63	20	dτ	dτ	NOUN
ejpam-6056	63	21	:	:	PUNCT
ejpam-6056	63	22	γ×	γ×	PROPN
ejpam-6056	63	23	γ	γ	X
ejpam-6056	63	24	→	→	SYM
ejpam-6056	63	25	[	[	X
ejpam-6056	63	26	0,+∞	0,+∞	NUM
ejpam-6056	63	27	)	)	PUNCT
ejpam-6056	63	28	as	as	SCONJ
ejpam-6056	63	29	follows	follow	VERB
ejpam-6056	63	30	:	:	PUNCT
ejpam-6056	63	31	θ(x	θ(x	PROPN
ejpam-6056	63	32	,	,	PUNCT
ejpam-6056	63	33	y	y	NOUN
ejpam-6056	63	34	)	)	PUNCT
ejpam-6056	63	35	=	=	SYM
ejpam-6056	64	1	1	1	NUM
ejpam-6056	64	2	+	+	NUM
ejpam-6056	64	3	|x|+	|x|+	PROPN
ejpam-6056	64	4	|y|	|y|	PROPN
ejpam-6056	64	5	and	and	CCONJ
ejpam-6056	64	6	dτ	dτ	PROPN
ejpam-6056	64	7	(	(	PUNCT
ejpam-6056	64	8	x	x	PROPN
ejpam-6056	64	9	,	,	PUNCT
ejpam-6056	64	10	y	y	NOUN
ejpam-6056	64	11	)	)	PUNCT
ejpam-6056	64	12	=	=	PRON
ejpam-6056	64	13	{	{	PUNCT
ejpam-6056	65	1	x2	x2	PROPN
ejpam-6056	65	2	+	+	CCONJ
ejpam-6056	65	3	y2	y2	NOUN
ejpam-6056	65	4	,	,	PUNCT
ejpam-6056	65	5	if	if	SCONJ
ejpam-6056	65	6	x	x	PROPN
ejpam-6056	65	7	̸=	̸=	PROPN
ejpam-6056	65	8	y	y	PROPN
ejpam-6056	65	9	,	,	PUNCT
ejpam-6056	65	10	0	0	NUM
ejpam-6056	65	11	,	,	PUNCT
ejpam-6056	65	12	if	if	SCONJ
ejpam-6056	65	13	x	x	PRON
ejpam-6056	65	14	=	=	PUNCT
ejpam-6056	65	15	y.	y.	NOUN
ejpam-6056	65	16	then	then	ADV
ejpam-6056	65	17	,	,	PUNCT
ejpam-6056	65	18	(	(	PUNCT
ejpam-6056	65	19	γ	γ	X
ejpam-6056	65	20	,	,	PUNCT
ejpam-6056	65	21	dτ	dτ	NOUN
ejpam-6056	65	22	)	)	PUNCT
ejpam-6056	65	23	forms	form	VERB
ejpam-6056	65	24	an	an	DET
ejpam-6056	65	25	ebms	ebms	NOUN
ejpam-6056	65	26	.	.	PUNCT
ejpam-6056	66	1	example	example	NOUN
ejpam-6056	67	1	3	3	NUM
ejpam-6056	67	2	.	.	PUNCT
ejpam-6056	68	1	[	[	X
ejpam-6056	68	2	3	3	X
ejpam-6056	68	3	]	]	PUNCT
ejpam-6056	68	4	consider	consider	VERB
ejpam-6056	68	5	γ	γ	X
ejpam-6056	68	6	=	=	SYM
ejpam-6056	68	7	c([p	c([p	PROPN
ejpam-6056	68	8	,	,	PUNCT
ejpam-6056	68	9	q	q	X
ejpam-6056	68	10	]	]	X
ejpam-6056	68	11	)	)	PUNCT
ejpam-6056	68	12	,	,	PUNCT
ejpam-6056	68	13	the	the	DET
ejpam-6056	68	14	space	space	NOUN
ejpam-6056	68	15	of	of	ADP
ejpam-6056	68	16	all	all	DET
ejpam-6056	68	17	real	real	ADV
ejpam-6056	68	18	-	-	PUNCT
ejpam-6056	68	19	valued	value	VERB
ejpam-6056	68	20	continuous	continuous	ADJ
ejpam-6056	68	21	functions	function	NOUN
ejpam-6056	68	22	on	on	ADP
ejpam-6056	68	23	[	[	X
ejpam-6056	68	24	p	p	X
ejpam-6056	68	25	,	,	PUNCT
ejpam-6056	68	26	q	q	X
ejpam-6056	68	27	]	]	X
ejpam-6056	68	28	.	.	PUNCT
ejpam-6056	69	1	define	define	VERB
ejpam-6056	69	2	two	two	NUM
ejpam-6056	69	3	functions	function	NOUN
ejpam-6056	69	4	θ	θ	NOUN
ejpam-6056	69	5	:	:	PUNCT
ejpam-6056	69	6	γ×	γ×	PUNCT
ejpam-6056	69	7	γ	γ	X
ejpam-6056	69	8	→	→	SYM
ejpam-6056	69	9	[	[	X
ejpam-6056	69	10	1,+∞	1,+∞	NUM
ejpam-6056	69	11	)	)	PUNCT
ejpam-6056	69	12	and	and	CCONJ
ejpam-6056	69	13	dτ	dτ	NOUN
ejpam-6056	69	14	:	:	PUNCT
ejpam-6056	69	15	γ×	γ×	PROPN
ejpam-6056	69	16	γ	γ	X
ejpam-6056	69	17	→	→	SYM
ejpam-6056	69	18	[	[	X
ejpam-6056	69	19	0,+∞	0,+∞	NUM
ejpam-6056	69	20	)	)	PUNCT
ejpam-6056	69	21	by	by	ADP
ejpam-6056	69	22	:	:	PUNCT
ejpam-6056	69	23	θ(x	θ(x	PROPN
ejpam-6056	69	24	,	,	PUNCT
ejpam-6056	69	25	y	y	NOUN
ejpam-6056	69	26	)	)	PUNCT
ejpam-6056	70	1	=	=	SYM
ejpam-6056	70	2	2q−1	2q−1	NUM
ejpam-6056	70	3	+	+	CCONJ
ejpam-6056	70	4	|x(r)|+	|x(r)|+	PROPN
ejpam-6056	70	5	|y(r)|	|y(r)|	PROPN
ejpam-6056	70	6	and	and	CCONJ
ejpam-6056	70	7	dτ	dτ	PROPN
ejpam-6056	70	8	(	(	PUNCT
ejpam-6056	70	9	x	x	PROPN
ejpam-6056	70	10	,	,	PUNCT
ejpam-6056	70	11	y	y	NOUN
ejpam-6056	70	12	)	)	PUNCT
ejpam-6056	70	13	=	=	SYM
ejpam-6056	71	1	sup	sup	NOUN
ejpam-6056	71	2	r∈[p	r∈[p	ADJ
ejpam-6056	71	3	,	,	PUNCT
ejpam-6056	71	4	q	q	X
ejpam-6056	71	5	]	]	X
ejpam-6056	71	6	|y(r)−	|y(r)−	ADJ
ejpam-6056	71	7	x(r)|λ	x(r)|λ	PROPN
ejpam-6056	71	8	,	,	PUNCT
ejpam-6056	71	9	where	where	SCONJ
ejpam-6056	71	10	λ	λ	X
ejpam-6056	71	11	>	>	X
ejpam-6056	71	12	1	1	NUM
ejpam-6056	71	13	is	be	AUX
ejpam-6056	71	14	a	a	DET
ejpam-6056	71	15	fixed	fix	VERB
ejpam-6056	71	16	constant	constant	ADJ
ejpam-6056	71	17	.	.	PUNCT
ejpam-6056	72	1	then	then	ADV
ejpam-6056	72	2	,	,	PUNCT
ejpam-6056	72	3	(	(	PUNCT
ejpam-6056	72	4	γ	γ	X
ejpam-6056	72	5	,	,	PUNCT
ejpam-6056	72	6	dτ	dτ	NOUN
ejpam-6056	72	7	)	)	PUNCT
ejpam-6056	72	8	is	be	AUX
ejpam-6056	72	9	an	an	DET
ejpam-6056	72	10	ebms	ebms	NOUN
ejpam-6056	72	11	.	.	PUNCT
ejpam-6056	73	1	definition	definition	NOUN
ejpam-6056	73	2	5	5	NUM
ejpam-6056	73	3	.	.	PUNCT
ejpam-6056	74	1	[	[	X
ejpam-6056	74	2	35	35	NUM
ejpam-6056	74	3	]	]	PUNCT
ejpam-6056	74	4	let	let	VERB
ejpam-6056	74	5	q	q	NOUN
ejpam-6056	74	6	:	:	PUNCT
ejpam-6056	74	7	γ	γ	X
ejpam-6056	74	8	→	→	SYM
ejpam-6056	74	9	γ	γ	X
ejpam-6056	74	10	and	and	CCONJ
ejpam-6056	74	11	α	α	NOUN
ejpam-6056	74	12	:	:	PUNCT
ejpam-6056	74	13	γ×	γ×	PROPN
ejpam-6056	74	14	γ	γ	X
ejpam-6056	74	15	→	→	X
ejpam-6056	74	16	[	[	X
ejpam-6056	74	17	0,∞	0,∞	NOUN
ejpam-6056	74	18	)	)	PUNCT
ejpam-6056	74	19	.	.	PUNCT
ejpam-6056	75	1	we	we	PRON
ejpam-6056	75	2	say	say	VERB
ejpam-6056	75	3	that	that	PRON
ejpam-6056	75	4	q	q	NOUN
ejpam-6056	75	5	is	be	AUX
ejpam-6056	75	6	an	an	DET
ejpam-6056	75	7	α	α	NOUN
ejpam-6056	75	8	-	-	ADJ
ejpam-6056	75	9	orbital	orbital	ADJ
ejpam-6056	75	10	admissible	admissible	NOUN
ejpam-6056	75	11	if	if	SCONJ
ejpam-6056	75	12	for	for	ADP
ejpam-6056	75	13	all	all	DET
ejpam-6056	75	14	x	x	NOUN
ejpam-6056	75	15	,	,	PUNCT
ejpam-6056	75	16	y	y	PROPN
ejpam-6056	75	17	∈	∈	PROPN
ejpam-6056	75	18	γ	γ	PROPN
ejpam-6056	75	19	,	,	PUNCT
ejpam-6056	75	20	we	we	PRON
ejpam-6056	75	21	have	have	VERB
ejpam-6056	75	22	α(x	α(x	NOUN
ejpam-6056	75	23	,	,	PUNCT
ejpam-6056	75	24	qx	qx	PROPN
ejpam-6056	75	25	)	)	PUNCT
ejpam-6056	75	26	≥	≥	NOUN
ejpam-6056	75	27	1	1	NUM
ejpam-6056	75	28	=	=	NOUN
ejpam-6056	75	29	⇒	⇒	NOUN
ejpam-6056	75	30	α(qx	α(qx	PROPN
ejpam-6056	75	31	,	,	PUNCT
ejpam-6056	75	32	q2x	q2x	NOUN
ejpam-6056	75	33	)	)	PUNCT
ejpam-6056	75	34	≥	≥	NOUN
ejpam-6056	75	35	1	1	NUM
ejpam-6056	75	36	.	.	PUNCT
ejpam-6056	76	1	(	(	PUNCT
ejpam-6056	76	2	3	3	X
ejpam-6056	76	3	)	)	PUNCT
ejpam-6056	76	4	remark	remark	NOUN
ejpam-6056	76	5	1	1	NUM
ejpam-6056	76	6	.	.	PUNCT
ejpam-6056	77	1	every	every	DET
ejpam-6056	77	2	α	α	X
ejpam-6056	77	3	-	-	ADJ
ejpam-6056	77	4	admissible	admissible	ADJ
ejpam-6056	77	5	mapping	mapping	NOUN
ejpam-6056	77	6	is	be	AUX
ejpam-6056	77	7	an	an	DET
ejpam-6056	77	8	α	α	NOUN
ejpam-6056	77	9	-	-	ADJ
ejpam-6056	77	10	orbital	orbital	ADJ
ejpam-6056	77	11	admissible	admissible	ADJ
ejpam-6056	77	12	mapping	mapping	NOUN
ejpam-6056	77	13	(	(	PUNCT
ejpam-6056	77	14	see	see	VERB
ejpam-6056	77	15	[	[	X
ejpam-6056	77	16	35	35	NUM
ejpam-6056	77	17	]	]	SYM
ejpam-6056	77	18	)	)	PUNCT
ejpam-6056	77	19	.	.	PUNCT
ejpam-6056	78	1	h.	h.	PROPN
ejpam-6056	78	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	78	3	,	,	PUNCT
ejpam-6056	78	4	j.m	j.m	PROPN
ejpam-6056	78	5	.	.	PROPN
ejpam-6056	78	6	al	al	PROPN
ejpam-6056	78	7	-	-	PUNCT
ejpam-6056	78	8	musannef	musannef	PROPN
ejpam-6056	78	9	,	,	PUNCT
ejpam-6056	78	10	h.	h.	PROPN
ejpam-6056	78	11	alsamir	alsamir	PROPN
ejpam-6056	78	12	/	/	SYM
ejpam-6056	78	13	eur	eur	PROPN
ejpam-6056	78	14	.	.	PUNCT
ejpam-6056	79	1	j.	j.	PROPN
ejpam-6056	79	2	pure	pure	PROPN
ejpam-6056	79	3	appl	appl	PROPN
ejpam-6056	79	4	.	.	PROPN
ejpam-6056	79	5	math	math	PROPN
ejpam-6056	79	6	,	,	PUNCT
ejpam-6056	79	7	18	18	NUM
ejpam-6056	79	8	(	(	PUNCT
ejpam-6056	79	9	3	3	NUM
ejpam-6056	79	10	)	)	PUNCT
ejpam-6056	79	11	(	(	PUNCT
ejpam-6056	79	12	2025	2025	NUM
ejpam-6056	79	13	)	)	PUNCT
ejpam-6056	79	14	,	,	PUNCT
ejpam-6056	79	15	6056	6056	NUM
ejpam-6056	79	16	4	4	NUM
ejpam-6056	79	17	of	of	ADP
ejpam-6056	79	18	16	16	NUM
ejpam-6056	79	19	3	3	NUM
ejpam-6056	79	20	.	.	PUNCT
ejpam-6056	79	21	main	main	ADJ
ejpam-6056	79	22	results	result	NOUN
ejpam-6056	79	23	we	we	PRON
ejpam-6056	79	24	commence	commence	VERB
ejpam-6056	79	25	this	this	DET
ejpam-6056	79	26	section	section	NOUN
ejpam-6056	79	27	by	by	ADP
ejpam-6056	79	28	discussing	discuss	VERB
ejpam-6056	79	29	our	our	PRON
ejpam-6056	79	30	first	first	ADJ
ejpam-6056	79	31	novel	novel	ADJ
ejpam-6056	79	32	results	result	NOUN
ejpam-6056	79	33	.	.	PUNCT
ejpam-6056	80	1	theorem	theorem	NOUN
ejpam-6056	80	2	1	1	NUM
ejpam-6056	80	3	.	.	PUNCT
ejpam-6056	81	1	let	let	VERB
ejpam-6056	81	2	q	q	NOUN
ejpam-6056	81	3	:	:	PUNCT
ejpam-6056	81	4	γ	γ	X
ejpam-6056	81	5	→	→	SYM
ejpam-6056	81	6	γ	γ	X
ejpam-6056	81	7	be	be	AUX
ejpam-6056	81	8	a	a	DET
ejpam-6056	81	9	continuous	continuous	ADJ
ejpam-6056	81	10	function	function	NOUN
ejpam-6056	81	11	and	and	CCONJ
ejpam-6056	81	12	α	α	NOUN
ejpam-6056	81	13	:	:	PUNCT
ejpam-6056	81	14	γ	γ	X
ejpam-6056	81	15	×	×	PROPN
ejpam-6056	81	16	γ	γ	X
ejpam-6056	81	17	→	→	SYM
ejpam-6056	81	18	[	[	X
ejpam-6056	81	19	0,∞	0,∞	NOUN
ejpam-6056	81	20	)	)	PUNCT
ejpam-6056	81	21	,	,	PUNCT
ejpam-6056	81	22	where	where	SCONJ
ejpam-6056	81	23	(	(	PUNCT
ejpam-6056	81	24	γ	γ	X
ejpam-6056	81	25	,	,	PUNCT
ejpam-6056	81	26	dτ	dτ	NOUN
ejpam-6056	81	27	)	)	PUNCT
ejpam-6056	81	28	is	be	AUX
ejpam-6056	81	29	an	an	DET
ejpam-6056	81	30	ebms	ebms	NOUN
ejpam-6056	81	31	.	.	PUNCT
ejpam-6056	82	1	assume	assume	VERB
ejpam-6056	82	2	that	that	SCONJ
ejpam-6056	82	3	for	for	ADP
ejpam-6056	82	4	all	all	DET
ejpam-6056	82	5	distinct	distinct	ADJ
ejpam-6056	82	6	x	x	NOUN
ejpam-6056	82	7	,	,	PUNCT
ejpam-6056	82	8	y	y	PROPN
ejpam-6056	82	9	∈	∈	PROPN
ejpam-6056	82	10	γ	γ	PROPN
ejpam-6056	82	11	,	,	PUNCT
ejpam-6056	82	12	the	the	DET
ejpam-6056	82	13	following	follow	VERB
ejpam-6056	82	14	holds	hold	NOUN
ejpam-6056	82	15	:	:	PUNCT
ejpam-6056	82	16	α(x	α(x	NOUN
ejpam-6056	82	17	,	,	PUNCT
ejpam-6056	82	18	y)dτ	y)dτ	PROPN
ejpam-6056	82	19	(	(	PUNCT
ejpam-6056	82	20	qx	qx	PROPN
ejpam-6056	82	21	,	,	PUNCT
ejpam-6056	82	22	qy	qy	NOUN
ejpam-6056	82	23	)	)	PUNCT
ejpam-6056	82	24	≤	≤	NOUN
ejpam-6056	82	25	µ1dτ	µ1dτ	PUNCT
ejpam-6056	82	26	(	(	PUNCT
ejpam-6056	82	27	x	x	X
ejpam-6056	82	28	,	,	PUNCT
ejpam-6056	82	29	y	y	PROPN
ejpam-6056	82	30	)	)	PUNCT
ejpam-6056	83	1	+	+	CCONJ
ejpam-6056	83	2	µ2	µ2	PROPN
ejpam-6056	83	3	dτ	dτ	INTJ
ejpam-6056	83	4	(	(	PUNCT
ejpam-6056	83	5	x	x	X
ejpam-6056	83	6	,	,	PUNCT
ejpam-6056	83	7	qx)dτ	qx)dτ	PUNCT
ejpam-6056	83	8	(	(	PUNCT
ejpam-6056	83	9	y	y	NOUN
ejpam-6056	83	10	,	,	PUNCT
ejpam-6056	83	11	qx	qx	PROPN
ejpam-6056	83	12	)	)	PUNCT
ejpam-6056	83	13	+	+	NUM
ejpam-6056	83	14	dτ	dτ	INTJ
ejpam-6056	83	15	(	(	PUNCT
ejpam-6056	83	16	y	y	PROPN
ejpam-6056	83	17	,	,	PUNCT
ejpam-6056	83	18	qy)dτ	qy)dτ	X
ejpam-6056	83	19	(	(	PUNCT
ejpam-6056	83	20	x	x	NOUN
ejpam-6056	83	21	,	,	PUNCT
ejpam-6056	83	22	qy	qy	NOUN
ejpam-6056	83	23	)	)	PUNCT
ejpam-6056	83	24	dτ	dτ	NOUN
ejpam-6056	83	25	(	(	PUNCT
ejpam-6056	83	26	x	x	PROPN
ejpam-6056	83	27	,	,	PUNCT
ejpam-6056	83	28	qy	qy	NOUN
ejpam-6056	83	29	)	)	PUNCT
ejpam-6056	83	30	+	+	NUM
ejpam-6056	83	31	dτ	dτ	INTJ
ejpam-6056	83	32	(	(	PUNCT
ejpam-6056	83	33	y	y	PROPN
ejpam-6056	83	34	,	,	PUNCT
ejpam-6056	83	35	qx	qx	PROPN
ejpam-6056	83	36	)	)	PUNCT
ejpam-6056	83	37	,	,	PUNCT
ejpam-6056	83	38	where	where	SCONJ
ejpam-6056	83	39	µ1	µ1	NOUN
ejpam-6056	83	40	,	,	PUNCT
ejpam-6056	83	41	µ2	µ2	VERB
ejpam-6056	83	42	≥	≥	NUM
ejpam-6056	83	43	0	0	NUM
ejpam-6056	83	44	,	,	PUNCT
ejpam-6056	83	45	dτ	dτ	INTJ
ejpam-6056	83	46	(	(	PUNCT
ejpam-6056	83	47	x	x	PROPN
ejpam-6056	83	48	,	,	PUNCT
ejpam-6056	83	49	qy	qy	NOUN
ejpam-6056	83	50	)	)	PUNCT
ejpam-6056	83	51	+	+	NUM
ejpam-6056	83	52	dτ	dτ	INTJ
ejpam-6056	83	53	(	(	PUNCT
ejpam-6056	83	54	y	y	PROPN
ejpam-6056	83	55	,	,	PUNCT
ejpam-6056	83	56	qx	qx	PROPN
ejpam-6056	83	57	)	)	PUNCT
ejpam-6056	83	58	̸=	̸=	PROPN
ejpam-6056	83	59	0	0	NUM
ejpam-6056	83	60	,	,	PUNCT
ejpam-6056	83	61	and	and	CCONJ
ejpam-6056	83	62	µ1	µ1	PROPN
ejpam-6056	84	1	+	+	CCONJ
ejpam-6056	84	2	µ2	µ2	PROPN
ejpam-6056	84	3	<	<	X
ejpam-6056	84	4	1	1	NUM
ejpam-6056	84	5	.	.	PUNCT
ejpam-6056	84	6	additionally	additionally	ADV
ejpam-6056	84	7	,	,	PUNCT
ejpam-6056	84	8	assume	assume	VERB
ejpam-6056	84	9	that	that	SCONJ
ejpam-6056	84	10	lim	lim	PROPN
ejpam-6056	84	11	n	n	CCONJ
ejpam-6056	84	12	,	,	PUNCT
ejpam-6056	84	13	m→∞	m→∞	NOUN
ejpam-6056	84	14	θ(an	θ(an	NOUN
ejpam-6056	84	15	,	,	PUNCT
ejpam-6056	84	16	am	be	AUX
ejpam-6056	84	17	)	)	PUNCT
ejpam-6056	84	18	<	<	X
ejpam-6056	84	19	1	1	NUM
ejpam-6056	84	20	ρ	ρ	NOUN
ejpam-6056	84	21	=	=	SYM
ejpam-6056	84	22	1−	1−	NUM
ejpam-6056	84	23	µ2	µ2	PROPN
ejpam-6056	84	24	µ1	µ1	PROPN
ejpam-6056	84	25	,	,	PUNCT
ejpam-6056	84	26	for	for	ADP
ejpam-6056	84	27	some	some	DET
ejpam-6056	84	28	ρ	ρ	NUM
ejpam-6056	84	29	∈	∈	PROPN
ejpam-6056	85	1	[	[	X
ejpam-6056	85	2	0	0	NUM
ejpam-6056	85	3	,	,	PUNCT
ejpam-6056	85	4	1	1	NUM
ejpam-6056	85	5	)	)	PUNCT
ejpam-6056	85	6	.	.	PUNCT
ejpam-6056	86	1	then	then	ADV
ejpam-6056	86	2	q	q	X
ejpam-6056	86	3	has	have	VERB
ejpam-6056	86	4	a	a	DET
ejpam-6056	86	5	unique	unique	ADJ
ejpam-6056	86	6	fixed	fix	VERB
ejpam-6056	86	7	point	point	NOUN
ejpam-6056	86	8	.	.	PUNCT
ejpam-6056	87	1	proof	proof	NOUN
ejpam-6056	87	2	.	.	PUNCT
ejpam-6056	88	1	to	to	PART
ejpam-6056	88	2	establish	establish	VERB
ejpam-6056	88	3	the	the	DET
ejpam-6056	88	4	proof	proof	NOUN
ejpam-6056	88	5	,	,	PUNCT
ejpam-6056	88	6	we	we	PRON
ejpam-6056	88	7	begin	begin	VERB
ejpam-6056	88	8	by	by	ADP
ejpam-6056	88	9	noting	note	VERB
ejpam-6056	88	10	thatq	thatq	ADJ
ejpam-6056	88	11	satisfies	satisfie	NOUN
ejpam-6056	88	12	the	the	DET
ejpam-6056	88	13	α	α	NOUN
ejpam-6056	88	14	-	-	PUNCT
ejpam-6056	88	15	admissibility	admissibility	NOUN
ejpam-6056	88	16	condition	condition	NOUN
ejpam-6056	88	17	.	.	PUNCT
ejpam-6056	89	1	this	this	PRON
ejpam-6056	89	2	ensures	ensure	VERB
ejpam-6056	89	3	that	that	SCONJ
ejpam-6056	89	4	α(x0	α(x0	NOUN
ejpam-6056	89	5	,	,	PUNCT
ejpam-6056	89	6	x1	x1	PROPN
ejpam-6056	89	7	)	)	PUNCT
ejpam-6056	89	8	=	=	SYM
ejpam-6056	89	9	α(x0	α(x0	ADJ
ejpam-6056	89	10	,	,	PUNCT
ejpam-6056	89	11	tx0	tx0	ADJ
ejpam-6056	89	12	)	)	PUNCT
ejpam-6056	89	13	≥	≥	NOUN
ejpam-6056	90	1	1	1	NUM
ejpam-6056	90	2	=	=	NOUN
ejpam-6056	90	3	⇒	⇒	PROPN
ejpam-6056	90	4	α(tx0	α(tx0	PROPN
ejpam-6056	90	5	,	,	PUNCT
ejpam-6056	90	6	tx1	tx1	PROPN
ejpam-6056	90	7	)	)	PUNCT
ejpam-6056	90	8	=	=	SYM
ejpam-6056	90	9	α(x1	α(x1	ADJ
ejpam-6056	90	10	,	,	PUNCT
ejpam-6056	90	11	x2	x2	PROPN
ejpam-6056	90	12	)	)	PUNCT
ejpam-6056	90	13	≥	≥	NOUN
ejpam-6056	90	14	1	1	NUM
ejpam-6056	90	15	.	.	PUNCT
ejpam-6056	90	16	by	by	ADP
ejpam-6056	90	17	applying	apply	VERB
ejpam-6056	90	18	this	this	DET
ejpam-6056	90	19	relation	relation	NOUN
ejpam-6056	90	20	iteratively	iteratively	ADV
ejpam-6056	90	21	,	,	PUNCT
ejpam-6056	90	22	we	we	PRON
ejpam-6056	90	23	obtain	obtain	VERB
ejpam-6056	90	24	α(xn	α(xn	NOUN
ejpam-6056	90	25	,	,	PUNCT
ejpam-6056	90	26	xn+1	xn+1	NUM
ejpam-6056	90	27	)	)	PUNCT
ejpam-6056	90	28	≥	≥	NOUN
ejpam-6056	90	29	1	1	NUM
ejpam-6056	90	30	,	,	PUNCT
ejpam-6056	90	31	for	for	ADP
ejpam-6056	90	32	all	all	DET
ejpam-6056	90	33	n	n	PRON
ejpam-6056	90	34	∈	∈	NOUN
ejpam-6056	90	35	n	n	NOUN
ejpam-6056	90	36	∪	∪	X
ejpam-6056	90	37	{	{	PUNCT
ejpam-6056	90	38	0	0	NUM
ejpam-6056	90	39	}	}	PUNCT
ejpam-6056	90	40	.	.	PUNCT
ejpam-6056	91	1	let	let	VERB
ejpam-6056	91	2	a0	a0	PROPN
ejpam-6056	91	3	be	be	AUX
ejpam-6056	91	4	an	an	DET
ejpam-6056	91	5	arbitrary	arbitrary	ADJ
ejpam-6056	91	6	element	element	NOUN
ejpam-6056	91	7	of	of	ADP
ejpam-6056	91	8	γ	γ	NOUN
ejpam-6056	91	9	,	,	PUNCT
ejpam-6056	91	10	and	and	CCONJ
ejpam-6056	91	11	define	define	VERB
ejpam-6056	91	12	the	the	DET
ejpam-6056	91	13	sequence	sequence	NOUN
ejpam-6056	91	14	{	{	PUNCT
ejpam-6056	91	15	an	an	DET
ejpam-6056	91	16	}	}	PUNCT
ejpam-6056	91	17	using	use	VERB
ejpam-6056	91	18	an+1	an+1	NOUN
ejpam-6056	91	19	=	=	SYM
ejpam-6056	91	20	qan	qan	PROPN
ejpam-6056	91	21	for	for	ADP
ejpam-6056	91	22	all	all	DET
ejpam-6056	91	23	n	n	PRON
ejpam-6056	91	24	≥	≥	NOUN
ejpam-6056	91	25	0	0	NUM
ejpam-6056	91	26	.	.	PUNCT
ejpam-6056	92	1	using	use	VERB
ejpam-6056	92	2	the	the	DET
ejpam-6056	92	3	given	give	VERB
ejpam-6056	92	4	inequality	inequality	NOUN
ejpam-6056	92	5	for	for	ADP
ejpam-6056	92	6	x	x	SYM
ejpam-6056	92	7	=	=	PUNCT
ejpam-6056	92	8	an	an	PROPN
ejpam-6056	92	9	and	and	CCONJ
ejpam-6056	92	10	y	y	PROPN
ejpam-6056	92	11	=	=	PUNCT
ejpam-6056	92	12	an+1	an+1	NOUN
ejpam-6056	92	13	,	,	PUNCT
ejpam-6056	92	14	we	we	PRON
ejpam-6056	92	15	get	get	VERB
ejpam-6056	92	16	:	:	PUNCT
ejpam-6056	92	17	dτ	dτ	INTJ
ejpam-6056	92	18	(	(	PUNCT
ejpam-6056	92	19	an	an	DET
ejpam-6056	92	20	,	,	PUNCT
ejpam-6056	92	21	an+1	an+1	NOUN
ejpam-6056	92	22	)	)	PUNCT
ejpam-6056	92	23	=	=	SYM
ejpam-6056	92	24	dτ	dτ	INTJ
ejpam-6056	92	25	(	(	PUNCT
ejpam-6056	92	26	qan−1	qan−1	PROPN
ejpam-6056	92	27	,	,	PUNCT
ejpam-6056	92	28	qan	qan	PROPN
ejpam-6056	92	29	)	)	PUNCT
ejpam-6056	92	30	≤	≤	NOUN
ejpam-6056	92	31	µ1dτ	µ1dτ	PUNCT
ejpam-6056	92	32	(	(	PUNCT
ejpam-6056	92	33	an−1	an−1	ADJ
ejpam-6056	92	34	,	,	PUNCT
ejpam-6056	92	35	an	an	NOUN
ejpam-6056	92	36	)	)	PUNCT
ejpam-6056	93	1	+	+	CCONJ
ejpam-6056	93	2	µ2	µ2	PROPN
ejpam-6056	93	3	dτ	dτ	INTJ
ejpam-6056	93	4	(	(	PUNCT
ejpam-6056	93	5	an−1	an−1	PROPN
ejpam-6056	93	6	,	,	PUNCT
ejpam-6056	93	7	qan−1)dτ	qan−1)dτ	INTJ
ejpam-6056	93	8	(	(	PUNCT
ejpam-6056	93	9	an	an	PRON
ejpam-6056	93	10	,	,	PUNCT
ejpam-6056	93	11	qan−1	qan−1	PROPN
ejpam-6056	93	12	)	)	PUNCT
ejpam-6056	93	13	+	+	NUM
ejpam-6056	93	14	dτ	dτ	INTJ
ejpam-6056	93	15	(	(	PUNCT
ejpam-6056	93	16	an	an	PRON
ejpam-6056	93	17	,	,	PUNCT
ejpam-6056	93	18	qan)dτ	qan)dτ	NOUN
ejpam-6056	93	19	(	(	PUNCT
ejpam-6056	93	20	an−1	an−1	PROPN
ejpam-6056	93	21	,	,	PUNCT
ejpam-6056	93	22	qan	qan	PROPN
ejpam-6056	93	23	)	)	PUNCT
ejpam-6056	93	24	dτ	dτ	NOUN
ejpam-6056	93	25	(	(	PUNCT
ejpam-6056	93	26	an−1	an−1	PROPN
ejpam-6056	93	27	,	,	PUNCT
ejpam-6056	93	28	qan	qan	PROPN
ejpam-6056	93	29	)	)	PUNCT
ejpam-6056	94	1	+	+	CCONJ
ejpam-6056	94	2	dτ	dτ	INTJ
ejpam-6056	94	3	(	(	PUNCT
ejpam-6056	94	4	an	an	PRON
ejpam-6056	94	5	,	,	PUNCT
ejpam-6056	94	6	qan−1	qan−1	PROPN
ejpam-6056	94	7	)	)	PUNCT
ejpam-6056	94	8	.	.	PUNCT
ejpam-6056	95	1	since	since	SCONJ
ejpam-6056	95	2	dτ	dτ	PROPN
ejpam-6056	95	3	(	(	PUNCT
ejpam-6056	95	4	an	an	PRON
ejpam-6056	95	5	,	,	PUNCT
ejpam-6056	95	6	an+1	an+1	NOUN
ejpam-6056	95	7	)	)	PUNCT
ejpam-6056	95	8	≤	≤	NOUN
ejpam-6056	95	9	µ1dτ	µ1dτ	PUNCT
ejpam-6056	95	10	(	(	PUNCT
ejpam-6056	95	11	an−1	an−1	ADJ
ejpam-6056	95	12	,	,	PUNCT
ejpam-6056	95	13	an	an	PRON
ejpam-6056	95	14	)	)	PUNCT
ejpam-6056	95	15	+	+	CCONJ
ejpam-6056	95	16	µ2dτ	µ2dτ	PUNCT
ejpam-6056	95	17	(	(	PUNCT
ejpam-6056	95	18	an	an	DET
ejpam-6056	95	19	,	,	PUNCT
ejpam-6056	95	20	an+1	an+1	NOUN
ejpam-6056	95	21	)	)	PUNCT
ejpam-6056	95	22	,	,	PUNCT
ejpam-6056	95	23	we	we	PRON
ejpam-6056	95	24	can	can	AUX
ejpam-6056	95	25	rearrange	rearrange	VERB
ejpam-6056	95	26	terms	term	NOUN
ejpam-6056	95	27	:	:	PUNCT
ejpam-6056	95	28	(	(	PUNCT
ejpam-6056	95	29	1−	1−	NUM
ejpam-6056	95	30	µ2)dτ	µ2)dτ	PROPN
ejpam-6056	95	31	(	(	PUNCT
ejpam-6056	95	32	an	an	PRON
ejpam-6056	95	33	,	,	PUNCT
ejpam-6056	95	34	an+1	an+1	NOUN
ejpam-6056	95	35	)	)	PUNCT
ejpam-6056	95	36	≤	≤	NOUN
ejpam-6056	95	37	µ1dτ	µ1dτ	PUNCT
ejpam-6056	95	38	(	(	PUNCT
ejpam-6056	95	39	an−1	an−1	ADJ
ejpam-6056	95	40	,	,	PUNCT
ejpam-6056	95	41	an	an	NOUN
ejpam-6056	95	42	)	)	PUNCT
ejpam-6056	95	43	.	.	PUNCT
ejpam-6056	96	1	by	by	ADP
ejpam-6056	96	2	setting	set	VERB
ejpam-6056	96	3	ρ	ρ	PROPN
ejpam-6056	96	4	=	=	SYM
ejpam-6056	96	5	µ1	µ1	PROPN
ejpam-6056	96	6	1−µ2	1−µ2	NUM
ejpam-6056	96	7	,	,	PUNCT
ejpam-6056	96	8	we	we	PRON
ejpam-6056	96	9	obtain	obtain	VERB
ejpam-6056	96	10	:	:	PUNCT
ejpam-6056	96	11	dτ	dτ	PROPN
ejpam-6056	96	12	(	(	PUNCT
ejpam-6056	96	13	an	an	PRON
ejpam-6056	96	14	,	,	PUNCT
ejpam-6056	96	15	an+1	an+1	NOUN
ejpam-6056	96	16	)	)	PUNCT
ejpam-6056	96	17	≤	≤	NUM
ejpam-6056	96	18	ρdτ	ρdτ	NOUN
ejpam-6056	96	19	(	(	PUNCT
ejpam-6056	96	20	an−1	an−1	ADJ
ejpam-6056	96	21	,	,	PUNCT
ejpam-6056	96	22	an	an	PRON
ejpam-6056	96	23	)	)	PUNCT
ejpam-6056	96	24	.	.	PUNCT
ejpam-6056	97	1	applying	apply	VERB
ejpam-6056	97	2	this	this	DET
ejpam-6056	97	3	recursively	recursively	NOUN
ejpam-6056	97	4	,	,	PUNCT
ejpam-6056	97	5	we	we	PRON
ejpam-6056	97	6	get	get	VERB
ejpam-6056	97	7	:	:	PUNCT
ejpam-6056	97	8	dτ	dτ	INTJ
ejpam-6056	97	9	(	(	PUNCT
ejpam-6056	97	10	an	an	PRON
ejpam-6056	97	11	,	,	PUNCT
ejpam-6056	97	12	an+1	an+1	NOUN
ejpam-6056	97	13	)	)	PUNCT
ejpam-6056	97	14	≤	≤	NUM
ejpam-6056	97	15	ρndτ	ρndτ	NOUN
ejpam-6056	97	16	(	(	PUNCT
ejpam-6056	97	17	a0	a0	NOUN
ejpam-6056	97	18	,	,	PUNCT
ejpam-6056	97	19	a1	a1	PROPN
ejpam-6056	97	20	)	)	PUNCT
ejpam-6056	97	21	.	.	PUNCT
ejpam-6056	98	1	since	since	SCONJ
ejpam-6056	98	2	µ1	µ1	PROPN
ejpam-6056	99	1	+	+	CCONJ
ejpam-6056	99	2	µ2	µ2	PROPN
ejpam-6056	99	3	<	<	X
ejpam-6056	99	4	1	1	NUM
ejpam-6056	99	5	ensures	ensure	VERB
ejpam-6056	99	6	0	0	NUM
ejpam-6056	99	7	≤	≤	NUM
ejpam-6056	99	8	ρ	ρ	NOUN
ejpam-6056	99	9	<	<	X
ejpam-6056	99	10	1	1	NUM
ejpam-6056	99	11	,	,	PUNCT
ejpam-6056	99	12	taking	take	VERB
ejpam-6056	99	13	the	the	DET
ejpam-6056	99	14	limit	limit	NOUN
ejpam-6056	99	15	as	as	ADP
ejpam-6056	99	16	n→	n→	PUNCT
ejpam-6056	99	17	∞	∞	PROPN
ejpam-6056	99	18	gives	give	VERB
ejpam-6056	99	19	:	:	PUNCT
ejpam-6056	99	20	lim	lim	PROPN
ejpam-6056	99	21	n→∞	n→∞	PRON
ejpam-6056	99	22	dτ	dτ	PROPN
ejpam-6056	99	23	(	(	PUNCT
ejpam-6056	99	24	an	an	DET
ejpam-6056	99	25	,	,	PUNCT
ejpam-6056	99	26	an+1	an+1	NOUN
ejpam-6056	99	27	)	)	PUNCT
ejpam-6056	99	28	=	=	SYM
ejpam-6056	99	29	0	0	X
ejpam-6056	99	30	.	.	PUNCT
ejpam-6056	100	1	h.	h.	PROPN
ejpam-6056	100	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	100	3	,	,	PUNCT
ejpam-6056	100	4	j.m	j.m	PROPN
ejpam-6056	100	5	.	.	PROPN
ejpam-6056	100	6	al	al	PROPN
ejpam-6056	100	7	-	-	PUNCT
ejpam-6056	100	8	musannef	musannef	PROPN
ejpam-6056	100	9	,	,	PUNCT
ejpam-6056	100	10	h.	h.	PROPN
ejpam-6056	100	11	alsamir	alsamir	PROPN
ejpam-6056	100	12	/	/	SYM
ejpam-6056	100	13	eur	eur	PROPN
ejpam-6056	100	14	.	.	PUNCT
ejpam-6056	101	1	j.	j.	PROPN
ejpam-6056	101	2	pure	pure	PROPN
ejpam-6056	101	3	appl	appl	PROPN
ejpam-6056	101	4	.	.	PROPN
ejpam-6056	101	5	math	math	PROPN
ejpam-6056	101	6	,	,	PUNCT
ejpam-6056	101	7	18	18	NUM
ejpam-6056	101	8	(	(	PUNCT
ejpam-6056	101	9	3	3	NUM
ejpam-6056	101	10	)	)	PUNCT
ejpam-6056	101	11	(	(	PUNCT
ejpam-6056	101	12	2025	2025	NUM
ejpam-6056	101	13	)	)	PUNCT
ejpam-6056	101	14	,	,	PUNCT
ejpam-6056	101	15	6056	6056	NUM
ejpam-6056	101	16	5	5	NUM
ejpam-6056	101	17	of	of	ADP
ejpam-6056	101	18	16	16	NUM
ejpam-6056	101	19	by	by	ADP
ejpam-6056	101	20	the	the	DET
ejpam-6056	101	21	triangle	triangle	NOUN
ejpam-6056	101	22	inequality	inequality	NOUN
ejpam-6056	101	23	,	,	PUNCT
ejpam-6056	101	24	we	we	PRON
ejpam-6056	101	25	deduce	deduce	VERB
ejpam-6056	101	26	:	:	PUNCT
ejpam-6056	101	27	dτ	dτ	INTJ
ejpam-6056	101	28	(	(	PUNCT
ejpam-6056	101	29	an	an	PRON
ejpam-6056	101	30	,	,	PUNCT
ejpam-6056	101	31	an+m	an+m	NOUN
ejpam-6056	101	32	)	)	PUNCT
ejpam-6056	101	33	≤	≤	NOUN
ejpam-6056	102	1	θ(an	θ(an	NOUN
ejpam-6056	102	2	,	,	PUNCT
ejpam-6056	102	3	an+m)dτ	an+m)dτ	VERB
ejpam-6056	102	4	(	(	PUNCT
ejpam-6056	102	5	an	an	PRON
ejpam-6056	102	6	,	,	PUNCT
ejpam-6056	102	7	an+1	an+1	NOUN
ejpam-6056	102	8	)	)	PUNCT
ejpam-6056	102	9	+	+	CCONJ
ejpam-6056	102	10	θ(an	θ(an	ADJ
ejpam-6056	102	11	,	,	PUNCT
ejpam-6056	102	12	an+m)dτ	an+m)dτ	ADJ
ejpam-6056	102	13	(	(	PUNCT
ejpam-6056	102	14	an+1	an+1	NOUN
ejpam-6056	102	15	,	,	PUNCT
ejpam-6056	102	16	an+m	an+m	PROPN
ejpam-6056	102	17	)	)	PUNCT
ejpam-6056	102	18	.	.	PUNCT
ejpam-6056	103	1	applying	apply	VERB
ejpam-6056	103	2	this	this	PRON
ejpam-6056	103	3	iteratively	iteratively	ADV
ejpam-6056	103	4	,	,	PUNCT
ejpam-6056	103	5	we	we	PRON
ejpam-6056	103	6	obtain	obtain	VERB
ejpam-6056	103	7	:	:	PUNCT
ejpam-6056	103	8	dτ	dτ	PROPN
ejpam-6056	103	9	(	(	PUNCT
ejpam-6056	103	10	an	an	PRON
ejpam-6056	103	11	,	,	PUNCT
ejpam-6056	103	12	an+m	an+m	NOUN
ejpam-6056	103	13	)	)	PUNCT
ejpam-6056	103	14	≤	≤	NUM
ejpam-6056	104	1	dτ	dτ	PROPN
ejpam-6056	104	2	(	(	PUNCT
ejpam-6056	104	3	a0	a0	PROPN
ejpam-6056	104	4	,	,	PUNCT
ejpam-6056	104	5	a1	a1	PROPN
ejpam-6056	104	6	)	)	PUNCT
ejpam-6056	104	7	n+m−1∑	n+m−1∑	PROPN
ejpam-6056	104	8	i=1	i=1	PROPN
ejpam-6056	104	9	ρi	ρi	PROPN
ejpam-6056	104	10	i∏	i∏	PROPN
ejpam-6056	104	11	p=1	p=1	PUNCT
ejpam-6056	104	12	θ(ap	θ(ap	PROPN
ejpam-6056	104	13	,	,	PUNCT
ejpam-6056	104	14	an+m	an+m	NOUN
ejpam-6056	104	15	)	)	PUNCT
ejpam-6056	104	16	.	.	PUNCT
ejpam-6056	105	1	by	by	ADP
ejpam-6056	105	2	the	the	DET
ejpam-6056	105	3	ratio	ratio	NOUN
ejpam-6056	105	4	test	test	NOUN
ejpam-6056	105	5	,	,	PUNCT
ejpam-6056	105	6	the	the	DET
ejpam-6056	105	7	summation	summation	NOUN
ejpam-6056	105	8	converges	converge	VERB
ejpam-6056	105	9	to	to	ADP
ejpam-6056	105	10	a	a	DET
ejpam-6056	105	11	finite	finite	ADJ
ejpam-6056	105	12	value	value	NOUN
ejpam-6056	105	13	sm	sm	PROPN
ejpam-6056	105	14	,	,	PUNCT
ejpam-6056	105	15	implying	imply	VERB
ejpam-6056	105	16	that	that	SCONJ
ejpam-6056	105	17	{	{	PUNCT
ejpam-6056	105	18	an	an	PRON
ejpam-6056	105	19	}	}	PUNCT
ejpam-6056	105	20	is	be	AUX
ejpam-6056	105	21	a	a	DET
ejpam-6056	105	22	cauchy	cauchy	ADJ
ejpam-6056	105	23	sequence	sequence	NOUN
ejpam-6056	105	24	.	.	PUNCT
ejpam-6056	106	1	since	since	SCONJ
ejpam-6056	106	2	(	(	PUNCT
ejpam-6056	106	3	γ	γ	PROPN
ejpam-6056	106	4	,	,	PUNCT
ejpam-6056	106	5	dτ	dτ	NOUN
ejpam-6056	106	6	)	)	PUNCT
ejpam-6056	106	7	is	be	AUX
ejpam-6056	106	8	complete	complete	ADJ
ejpam-6056	106	9	,	,	PUNCT
ejpam-6056	106	10	there	there	PRON
ejpam-6056	106	11	exists	exist	VERB
ejpam-6056	106	12	b	b	PROPN
ejpam-6056	106	13	∈	∈	PROPN
ejpam-6056	106	14	γ	γ	NOUN
ejpam-6056	106	15	such	such	ADJ
ejpam-6056	106	16	that	that	SCONJ
ejpam-6056	106	17	an	an	DET
ejpam-6056	106	18	→	→	SYM
ejpam-6056	106	19	b	b	NOUN
ejpam-6056	106	20	as	as	ADP
ejpam-6056	106	21	n→	n→	PUNCT
ejpam-6056	106	22	∞.	∞.	PROPN
ejpam-6056	106	23	since	since	SCONJ
ejpam-6056	106	24	q	q	PROPN
ejpam-6056	106	25	is	be	AUX
ejpam-6056	106	26	continuous	continuous	ADJ
ejpam-6056	106	27	,	,	PUNCT
ejpam-6056	106	28	we	we	PRON
ejpam-6056	106	29	get	get	VERB
ejpam-6056	106	30	:	:	PUNCT
ejpam-6056	106	31	qb	qb	PROPN
ejpam-6056	106	32	=	=	PUNCT
ejpam-6056	106	33	q	q	PROPN
ejpam-6056	107	1	(	(	PUNCT
ejpam-6056	107	2	lim	lim	PROPN
ejpam-6056	107	3	n→∞	n→∞	X
ejpam-6056	107	4	an	an	PRON
ejpam-6056	107	5	)	)	PUNCT
ejpam-6056	108	1	=	=	SYM
ejpam-6056	108	2	lim	lim	PROPN
ejpam-6056	108	3	n→∞	n→∞	NUM
ejpam-6056	109	1	qan	qan	PROPN
ejpam-6056	109	2	=	=	SYM
ejpam-6056	109	3	lim	lim	PROPN
ejpam-6056	109	4	n→∞	n→∞	NUM
ejpam-6056	109	5	an+1	an+1	PROPN
ejpam-6056	109	6	=	=	SYM
ejpam-6056	109	7	b.	b.	PROPN
ejpam-6056	109	8	thus	thus	ADV
ejpam-6056	109	9	,	,	PUNCT
ejpam-6056	109	10	b	b	PROPN
ejpam-6056	109	11	is	be	AUX
ejpam-6056	109	12	a	a	DET
ejpam-6056	109	13	fixed	fix	VERB
ejpam-6056	109	14	point	point	NOUN
ejpam-6056	109	15	of	of	ADP
ejpam-6056	109	16	q.	q.	NOUN
ejpam-6056	109	17	for	for	ADP
ejpam-6056	109	18	uniqueness	uniqueness	NOUN
ejpam-6056	109	19	,	,	PUNCT
ejpam-6056	109	20	assume	assume	VERB
ejpam-6056	109	21	there	there	PRON
ejpam-6056	109	22	exists	exist	VERB
ejpam-6056	109	23	another	another	DET
ejpam-6056	109	24	fixed	fix	VERB
ejpam-6056	109	25	point	point	NOUN
ejpam-6056	109	26	c.	c.	PROPN
ejpam-6056	109	27	then	then	ADV
ejpam-6056	109	28	:	:	PUNCT
ejpam-6056	109	29	dτ	dτ	INTJ
ejpam-6056	109	30	(	(	PUNCT
ejpam-6056	109	31	b	b	NOUN
ejpam-6056	109	32	,	,	PUNCT
ejpam-6056	109	33	c	c	NOUN
ejpam-6056	109	34	)	)	PUNCT
ejpam-6056	109	35	≤	≤	NUM
ejpam-6056	109	36	dτ	dτ	NOUN
ejpam-6056	109	37	(	(	PUNCT
ejpam-6056	109	38	qb	qb	PROPN
ejpam-6056	109	39	,	,	PUNCT
ejpam-6056	109	40	qc	qc	PROPN
ejpam-6056	109	41	)	)	PUNCT
ejpam-6056	109	42	≤	≤	NOUN
ejpam-6056	109	43	µ1dτ	µ1dτ	PUNCT
ejpam-6056	109	44	(	(	PUNCT
ejpam-6056	109	45	b	b	NOUN
ejpam-6056	109	46	,	,	PUNCT
ejpam-6056	109	47	c	c	NOUN
ejpam-6056	109	48	)	)	PUNCT
ejpam-6056	110	1	+	+	CCONJ
ejpam-6056	110	2	µ2	µ2	PROPN
ejpam-6056	110	3	dτ	dτ	INTJ
ejpam-6056	110	4	(	(	PUNCT
ejpam-6056	110	5	b	b	PROPN
ejpam-6056	110	6	,	,	PUNCT
ejpam-6056	110	7	qb)dτ	qb)dτ	PROPN
ejpam-6056	110	8	(	(	PUNCT
ejpam-6056	110	9	c	c	X
ejpam-6056	110	10	,	,	PUNCT
ejpam-6056	110	11	qb	qb	PROPN
ejpam-6056	110	12	)	)	PUNCT
ejpam-6056	110	13	+	+	NUM
ejpam-6056	110	14	dτ	dτ	INTJ
ejpam-6056	110	15	(	(	PUNCT
ejpam-6056	110	16	c	c	NOUN
ejpam-6056	110	17	,	,	PUNCT
ejpam-6056	110	18	qc)dτ	qc)dτ	X
ejpam-6056	110	19	(	(	PUNCT
ejpam-6056	110	20	b	b	NOUN
ejpam-6056	110	21	,	,	PUNCT
ejpam-6056	110	22	qc	qc	PROPN
ejpam-6056	110	23	)	)	PUNCT
ejpam-6056	110	24	dτ	dτ	PROPN
ejpam-6056	110	25	(	(	PUNCT
ejpam-6056	110	26	b	b	PROPN
ejpam-6056	110	27	,	,	PUNCT
ejpam-6056	110	28	qc	qc	PROPN
ejpam-6056	110	29	)	)	PUNCT
ejpam-6056	110	30	+	+	NUM
ejpam-6056	110	31	dτ	dτ	INTJ
ejpam-6056	110	32	(	(	PUNCT
ejpam-6056	110	33	c	c	PROPN
ejpam-6056	110	34	,	,	PUNCT
ejpam-6056	110	35	qb	qb	PROPN
ejpam-6056	110	36	)	)	PUNCT
ejpam-6056	110	37	.	.	PUNCT
ejpam-6056	111	1	since	since	SCONJ
ejpam-6056	111	2	qb	qb	PROPN
ejpam-6056	111	3	=	=	PROPN
ejpam-6056	111	4	b	b	PROPN
ejpam-6056	111	5	and	and	CCONJ
ejpam-6056	111	6	qc	qc	PROPN
ejpam-6056	111	7	=	=	SYM
ejpam-6056	111	8	c	c	PROPN
ejpam-6056	111	9	,	,	PUNCT
ejpam-6056	111	10	it	it	PRON
ejpam-6056	111	11	follows	follow	VERB
ejpam-6056	111	12	that	that	SCONJ
ejpam-6056	111	13	:	:	PUNCT
ejpam-6056	111	14	dτ	dτ	INTJ
ejpam-6056	111	15	(	(	PUNCT
ejpam-6056	111	16	b	b	NOUN
ejpam-6056	111	17	,	,	PUNCT
ejpam-6056	111	18	c	c	NOUN
ejpam-6056	111	19	)	)	PUNCT
ejpam-6056	111	20	≤	≤	NOUN
ejpam-6056	111	21	µ1dτ	µ1dτ	PUNCT
ejpam-6056	111	22	(	(	PUNCT
ejpam-6056	111	23	b	b	NOUN
ejpam-6056	111	24	,	,	PUNCT
ejpam-6056	111	25	c	c	NOUN
ejpam-6056	111	26	)	)	PUNCT
ejpam-6056	111	27	.	.	PUNCT
ejpam-6056	112	1	as	as	ADP
ejpam-6056	112	2	µ1	µ1	PROPN
ejpam-6056	112	3	<	<	X
ejpam-6056	112	4	1	1	NUM
ejpam-6056	112	5	,	,	PUNCT
ejpam-6056	112	6	we	we	PRON
ejpam-6056	112	7	conclude	conclude	VERB
ejpam-6056	112	8	dτ	dτ	INTJ
ejpam-6056	112	9	(	(	PUNCT
ejpam-6056	112	10	b	b	PROPN
ejpam-6056	112	11	,	,	PUNCT
ejpam-6056	112	12	c	c	NOUN
ejpam-6056	112	13	)	)	PUNCT
ejpam-6056	112	14	=	=	SYM
ejpam-6056	112	15	0	0	NUM
ejpam-6056	112	16	,	,	PUNCT
ejpam-6056	112	17	implying	imply	VERB
ejpam-6056	112	18	b	b	PROPN
ejpam-6056	112	19	=	=	SYM
ejpam-6056	112	20	c.	c.	PROPN
ejpam-6056	112	21	corollary	corollary	NOUN
ejpam-6056	112	22	1	1	X
ejpam-6056	112	23	.	.	PUNCT
ejpam-6056	113	1	let	let	VERB
ejpam-6056	113	2	q	q	NOUN
ejpam-6056	113	3	:	:	PUNCT
ejpam-6056	113	4	γ	γ	X
ejpam-6056	113	5	→	→	SYM
ejpam-6056	113	6	γ	γ	X
ejpam-6056	113	7	be	be	AUX
ejpam-6056	113	8	a	a	DET
ejpam-6056	113	9	continuous	continuous	ADJ
ejpam-6056	113	10	function	function	NOUN
ejpam-6056	113	11	in	in	ADP
ejpam-6056	113	12	an	an	DET
ejpam-6056	113	13	ebms	ebms	NOUN
ejpam-6056	113	14	(	(	PUNCT
ejpam-6056	113	15	γ	γ	X
ejpam-6056	113	16	,	,	PUNCT
ejpam-6056	113	17	dτ	dτ	NOUN
ejpam-6056	113	18	)	)	PUNCT
ejpam-6056	113	19	.	.	PUNCT
ejpam-6056	114	1	if	if	SCONJ
ejpam-6056	114	2	q	q	NOUN
ejpam-6056	114	3	satisfies	satisfy	VERB
ejpam-6056	114	4	the	the	DET
ejpam-6056	114	5	contraction	contraction	NOUN
ejpam-6056	114	6	condition	condition	NOUN
ejpam-6056	114	7	:	:	PUNCT
ejpam-6056	114	8	dτ	dτ	PROPN
ejpam-6056	114	9	(	(	PUNCT
ejpam-6056	114	10	qx	qx	PROPN
ejpam-6056	114	11	,	,	PUNCT
ejpam-6056	114	12	qy	qy	NOUN
ejpam-6056	114	13	)	)	PUNCT
ejpam-6056	114	14	≤	≤	NOUN
ejpam-6056	114	15	µ1dτ	µ1dτ	PUNCT
ejpam-6056	114	16	(	(	PUNCT
ejpam-6056	114	17	x	x	X
ejpam-6056	114	18	,	,	PUNCT
ejpam-6056	114	19	y	y	PROPN
ejpam-6056	114	20	)	)	PUNCT
ejpam-6056	115	1	+	+	CCONJ
ejpam-6056	115	2	µ2dτ	µ2dτ	PUNCT
ejpam-6056	115	3	(	(	PUNCT
ejpam-6056	115	4	x	x	X
ejpam-6056	115	5	,	,	PUNCT
ejpam-6056	115	6	qx	qx	PROPN
ejpam-6056	115	7	)	)	PUNCT
ejpam-6056	115	8	,	,	PUNCT
ejpam-6056	115	9	where	where	SCONJ
ejpam-6056	115	10	µ1	µ1	PROPN
ejpam-6056	115	11	,	,	PUNCT
ejpam-6056	115	12	µ2	µ2	VERB
ejpam-6056	115	13	≥	≥	NOUN
ejpam-6056	115	14	0	0	NUM
ejpam-6056	115	15	and	and	CCONJ
ejpam-6056	115	16	µ1	µ1	PROPN
ejpam-6056	115	17	+	+	CCONJ
ejpam-6056	115	18	µ2	µ2	PROPN
ejpam-6056	115	19	<	<	X
ejpam-6056	115	20	1	1	NUM
ejpam-6056	115	21	,	,	PUNCT
ejpam-6056	115	22	then	then	ADV
ejpam-6056	115	23	q	q	X
ejpam-6056	115	24	has	have	VERB
ejpam-6056	115	25	a	a	DET
ejpam-6056	115	26	unique	unique	ADJ
ejpam-6056	115	27	fixed	fix	VERB
ejpam-6056	115	28	point	point	NOUN
ejpam-6056	115	29	.	.	PUNCT
ejpam-6056	116	1	proof	proof	NOUN
ejpam-6056	116	2	.	.	PUNCT
ejpam-6056	117	1	this	this	PRON
ejpam-6056	117	2	follows	follow	VERB
ejpam-6056	117	3	directly	directly	ADV
ejpam-6056	117	4	from	from	ADP
ejpam-6056	117	5	theorem	theorem	ADJ
ejpam-6056	117	6	3.1	3.1	NUM
ejpam-6056	117	7	by	by	ADP
ejpam-6056	117	8	setting	set	VERB
ejpam-6056	117	9	dτ	dτ	NOUN
ejpam-6056	117	10	(	(	PUNCT
ejpam-6056	117	11	x	x	NOUN
ejpam-6056	117	12	,	,	PUNCT
ejpam-6056	117	13	qx)dτ	qx)dτ	PUNCT
ejpam-6056	117	14	(	(	PUNCT
ejpam-6056	117	15	y	y	NOUN
ejpam-6056	117	16	,	,	PUNCT
ejpam-6056	117	17	qx	qx	PROPN
ejpam-6056	117	18	)	)	PUNCT
ejpam-6056	117	19	+	+	NUM
ejpam-6056	117	20	dτ	dτ	INTJ
ejpam-6056	117	21	(	(	PUNCT
ejpam-6056	117	22	y	y	PROPN
ejpam-6056	117	23	,	,	PUNCT
ejpam-6056	117	24	qy)dτ	qy)dτ	X
ejpam-6056	117	25	(	(	PUNCT
ejpam-6056	117	26	x	x	NOUN
ejpam-6056	117	27	,	,	PUNCT
ejpam-6056	117	28	qy	qy	NOUN
ejpam-6056	117	29	)	)	PUNCT
ejpam-6056	117	30	dτ	dτ	NOUN
ejpam-6056	117	31	(	(	PUNCT
ejpam-6056	117	32	x	x	PROPN
ejpam-6056	117	33	,	,	PUNCT
ejpam-6056	117	34	qy	qy	NOUN
ejpam-6056	117	35	)	)	PUNCT
ejpam-6056	117	36	+	+	NUM
ejpam-6056	117	37	dτ	dτ	INTJ
ejpam-6056	117	38	(	(	PUNCT
ejpam-6056	117	39	y	y	PROPN
ejpam-6056	117	40	,	,	PUNCT
ejpam-6056	117	41	qx	qx	PROPN
ejpam-6056	117	42	)	)	PUNCT
ejpam-6056	117	43	=	=	SYM
ejpam-6056	117	44	dτ	dτ	NOUN
ejpam-6056	117	45	(	(	PUNCT
ejpam-6056	117	46	x	x	NOUN
ejpam-6056	117	47	,	,	PUNCT
ejpam-6056	117	48	qx	qx	PROPN
ejpam-6056	117	49	)	)	PUNCT
ejpam-6056	117	50	.	.	PUNCT
ejpam-6056	118	1	by	by	ADP
ejpam-6056	118	2	constructing	construct	VERB
ejpam-6056	118	3	the	the	DET
ejpam-6056	118	4	sequence	sequence	NOUN
ejpam-6056	118	5	{	{	PUNCT
ejpam-6056	118	6	an	an	NOUN
ejpam-6056	118	7	}	}	PUNCT
ejpam-6056	118	8	where	where	SCONJ
ejpam-6056	118	9	an+1	an+1	NOUN
ejpam-6056	118	10	=	=	SYM
ejpam-6056	118	11	qan	qan	PROPN
ejpam-6056	118	12	and	and	CCONJ
ejpam-6056	118	13	applying	apply	VERB
ejpam-6056	118	14	the	the	DET
ejpam-6056	118	15	given	give	VERB
ejpam-6056	118	16	contraction	contraction	NOUN
ejpam-6056	118	17	condition	condition	NOUN
ejpam-6056	118	18	iteratively	iteratively	ADV
ejpam-6056	118	19	,	,	PUNCT
ejpam-6056	118	20	we	we	PRON
ejpam-6056	118	21	obtain	obtain	VERB
ejpam-6056	118	22	:	:	PUNCT
ejpam-6056	118	23	dτ	dτ	PROPN
ejpam-6056	118	24	(	(	PUNCT
ejpam-6056	118	25	an	an	PRON
ejpam-6056	118	26	,	,	PUNCT
ejpam-6056	118	27	an+1	an+1	NOUN
ejpam-6056	118	28	)	)	PUNCT
ejpam-6056	118	29	≤	≤	NUM
ejpam-6056	118	30	ρdτ	ρdτ	NOUN
ejpam-6056	118	31	(	(	PUNCT
ejpam-6056	118	32	an−1	an−1	ADJ
ejpam-6056	118	33	,	,	PUNCT
ejpam-6056	118	34	an	an	NOUN
ejpam-6056	118	35	)	)	PUNCT
ejpam-6056	118	36	,	,	PUNCT
ejpam-6056	118	37	where	where	SCONJ
ejpam-6056	118	38	ρ	ρ	PROPN
ejpam-6056	118	39	=	=	SYM
ejpam-6056	118	40	µ1	µ1	PROPN
ejpam-6056	118	41	1−µ2	1−µ2	NUM
ejpam-6056	118	42	.	.	PUNCT
ejpam-6056	119	1	since	since	SCONJ
ejpam-6056	119	2	µ1	µ1	PROPN
ejpam-6056	119	3	+	+	CCONJ
ejpam-6056	119	4	µ2	µ2	PROPN
ejpam-6056	119	5	<	<	X
ejpam-6056	119	6	1	1	NUM
ejpam-6056	119	7	,	,	PUNCT
ejpam-6056	119	8	it	it	PRON
ejpam-6056	119	9	follows	follow	VERB
ejpam-6056	119	10	that	that	SCONJ
ejpam-6056	119	11	{	{	PUNCT
ejpam-6056	119	12	an	an	PRON
ejpam-6056	119	13	}	}	PUNCT
ejpam-6056	119	14	is	be	AUX
ejpam-6056	119	15	a	a	DET
ejpam-6056	119	16	cauchy	cauchy	ADJ
ejpam-6056	119	17	sequence	sequence	NOUN
ejpam-6056	119	18	,	,	PUNCT
ejpam-6056	119	19	which	which	PRON
ejpam-6056	119	20	converges	converge	VERB
ejpam-6056	119	21	to	to	ADP
ejpam-6056	119	22	a	a	DET
ejpam-6056	119	23	unique	unique	ADJ
ejpam-6056	119	24	fixed	fix	VERB
ejpam-6056	119	25	point	point	NOUN
ejpam-6056	119	26	b	b	PROPN
ejpam-6056	119	27	of	of	ADP
ejpam-6056	119	28	q	q	NOUN
ejpam-6056	119	29	,	,	PUNCT
ejpam-6056	119	30	as	as	SCONJ
ejpam-6056	119	31	established	establish	VERB
ejpam-6056	119	32	in	in	ADP
ejpam-6056	119	33	theorem	theorem	ADJ
ejpam-6056	119	34	3.1	3.1	NUM
ejpam-6056	119	35	.	.	PUNCT
ejpam-6056	120	1	h.	h.	PROPN
ejpam-6056	120	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	120	3	,	,	PUNCT
ejpam-6056	120	4	j.m	j.m	PROPN
ejpam-6056	120	5	.	.	PROPN
ejpam-6056	120	6	al	al	PROPN
ejpam-6056	120	7	-	-	PUNCT
ejpam-6056	120	8	musannef	musannef	PROPN
ejpam-6056	120	9	,	,	PUNCT
ejpam-6056	120	10	h.	h.	PROPN
ejpam-6056	120	11	alsamir	alsamir	PROPN
ejpam-6056	120	12	/	/	SYM
ejpam-6056	120	13	eur	eur	PROPN
ejpam-6056	120	14	.	.	PUNCT
ejpam-6056	121	1	j.	j.	PROPN
ejpam-6056	121	2	pure	pure	PROPN
ejpam-6056	121	3	appl	appl	PROPN
ejpam-6056	121	4	.	.	PROPN
ejpam-6056	121	5	math	math	PROPN
ejpam-6056	121	6	,	,	PUNCT
ejpam-6056	121	7	18	18	NUM
ejpam-6056	121	8	(	(	PUNCT
ejpam-6056	121	9	3	3	NUM
ejpam-6056	121	10	)	)	PUNCT
ejpam-6056	121	11	(	(	PUNCT
ejpam-6056	121	12	2025	2025	NUM
ejpam-6056	121	13	)	)	PUNCT
ejpam-6056	121	14	,	,	PUNCT
ejpam-6056	121	15	6056	6056	NUM
ejpam-6056	121	16	6	6	NUM
ejpam-6056	121	17	of	of	ADP
ejpam-6056	121	18	16	16	NUM
ejpam-6056	121	19	corollary	corollary	ADJ
ejpam-6056	121	20	2	2	NUM
ejpam-6056	121	21	.	.	PUNCT
ejpam-6056	122	1	let	let	VERB
ejpam-6056	122	2	q	q	NOUN
ejpam-6056	122	3	:	:	PUNCT
ejpam-6056	122	4	γ	γ	X
ejpam-6056	122	5	→	→	SYM
ejpam-6056	122	6	γ	γ	X
ejpam-6056	122	7	be	be	AUX
ejpam-6056	122	8	a	a	DET
ejpam-6056	122	9	function	function	NOUN
ejpam-6056	122	10	satisfying	satisfy	VERB
ejpam-6056	122	11	the	the	DET
ejpam-6056	122	12	condition	condition	NOUN
ejpam-6056	122	13	:	:	PUNCT
ejpam-6056	122	14	dτ	dτ	PROPN
ejpam-6056	122	15	(	(	PUNCT
ejpam-6056	122	16	qx	qx	PROPN
ejpam-6056	122	17	,	,	PUNCT
ejpam-6056	122	18	qy	qy	NOUN
ejpam-6056	122	19	)	)	PUNCT
ejpam-6056	122	20	≤	≤	NOUN
ejpam-6056	122	21	µ1dτ	µ1dτ	PUNCT
ejpam-6056	122	22	(	(	PUNCT
ejpam-6056	122	23	x	x	X
ejpam-6056	122	24	,	,	PUNCT
ejpam-6056	122	25	y	y	PROPN
ejpam-6056	122	26	)	)	PUNCT
ejpam-6056	123	1	+	+	CCONJ
ejpam-6056	123	2	µ2max{dτ	µ2max{dτ	NOUN
ejpam-6056	123	3	(	(	PUNCT
ejpam-6056	123	4	x	x	NOUN
ejpam-6056	123	5	,	,	PUNCT
ejpam-6056	123	6	qx	qx	PROPN
ejpam-6056	123	7	)	)	PUNCT
ejpam-6056	123	8	,	,	PUNCT
ejpam-6056	123	9	dτ	dτ	INTJ
ejpam-6056	123	10	(	(	PUNCT
ejpam-6056	123	11	y	y	PROPN
ejpam-6056	123	12	,	,	PUNCT
ejpam-6056	123	13	qy	qy	NOUN
ejpam-6056	123	14	)	)	PUNCT
ejpam-6056	123	15	}	}	PUNCT
ejpam-6056	123	16	,	,	PUNCT
ejpam-6056	123	17	where	where	SCONJ
ejpam-6056	123	18	µ1	µ1	PROPN
ejpam-6056	123	19	,	,	PUNCT
ejpam-6056	123	20	µ2	µ2	VERB
ejpam-6056	123	21	≥	≥	NOUN
ejpam-6056	123	22	0	0	NUM
ejpam-6056	123	23	and	and	CCONJ
ejpam-6056	123	24	µ1	µ1	PROPN
ejpam-6056	123	25	+	+	CCONJ
ejpam-6056	123	26	µ2	µ2	PROPN
ejpam-6056	123	27	<	<	X
ejpam-6056	123	28	1	1	NUM
ejpam-6056	123	29	.	.	PUNCT
ejpam-6056	124	1	then	then	ADV
ejpam-6056	124	2	q	q	X
ejpam-6056	124	3	has	have	VERB
ejpam-6056	124	4	a	a	DET
ejpam-6056	124	5	unique	unique	ADJ
ejpam-6056	124	6	fixed	fix	VERB
ejpam-6056	124	7	point	point	NOUN
ejpam-6056	124	8	.	.	PUNCT
ejpam-6056	125	1	proof	proof	NOUN
ejpam-6056	125	2	.	.	PUNCT
ejpam-6056	126	1	this	this	DET
ejpam-6056	126	2	result	result	NOUN
ejpam-6056	126	3	follows	follow	VERB
ejpam-6056	126	4	directly	directly	ADV
ejpam-6056	126	5	from	from	ADP
ejpam-6056	126	6	theorem	theorem	ADJ
ejpam-6056	126	7	3.1	3.1	NUM
ejpam-6056	126	8	by	by	ADP
ejpam-6056	126	9	setting	set	VERB
ejpam-6056	126	10	:	:	PUNCT
ejpam-6056	126	11	dτ	dτ	INTJ
ejpam-6056	126	12	(	(	PUNCT
ejpam-6056	126	13	x	x	X
ejpam-6056	126	14	,	,	PUNCT
ejpam-6056	126	15	qx)dτ	qx)dτ	PUNCT
ejpam-6056	126	16	(	(	PUNCT
ejpam-6056	126	17	y	y	NOUN
ejpam-6056	126	18	,	,	PUNCT
ejpam-6056	126	19	qx	qx	PROPN
ejpam-6056	126	20	)	)	PUNCT
ejpam-6056	126	21	+	+	NUM
ejpam-6056	126	22	dτ	dτ	INTJ
ejpam-6056	126	23	(	(	PUNCT
ejpam-6056	126	24	y	y	PROPN
ejpam-6056	126	25	,	,	PUNCT
ejpam-6056	126	26	qy)dτ	qy)dτ	X
ejpam-6056	126	27	(	(	PUNCT
ejpam-6056	126	28	x	x	NOUN
ejpam-6056	126	29	,	,	PUNCT
ejpam-6056	126	30	qy	qy	NOUN
ejpam-6056	126	31	)	)	PUNCT
ejpam-6056	126	32	dτ	dτ	NOUN
ejpam-6056	126	33	(	(	PUNCT
ejpam-6056	126	34	x	x	PROPN
ejpam-6056	126	35	,	,	PUNCT
ejpam-6056	126	36	qy	qy	NOUN
ejpam-6056	126	37	)	)	PUNCT
ejpam-6056	126	38	+	+	NUM
ejpam-6056	126	39	dτ	dτ	INTJ
ejpam-6056	126	40	(	(	PUNCT
ejpam-6056	126	41	y	y	PROPN
ejpam-6056	126	42	,	,	PUNCT
ejpam-6056	126	43	qx	qx	PROPN
ejpam-6056	126	44	)	)	PUNCT
ejpam-6056	126	45	=	=	SYM
ejpam-6056	126	46	max{dτ	max{dτ	NOUN
ejpam-6056	126	47	(	(	PUNCT
ejpam-6056	126	48	x	x	X
ejpam-6056	126	49	,	,	PUNCT
ejpam-6056	126	50	qx	qx	PROPN
ejpam-6056	126	51	)	)	PUNCT
ejpam-6056	126	52	,	,	PUNCT
ejpam-6056	126	53	dτ	dτ	INTJ
ejpam-6056	126	54	(	(	PUNCT
ejpam-6056	126	55	y	y	PROPN
ejpam-6056	126	56	,	,	PUNCT
ejpam-6056	126	57	qy	qy	NOUN
ejpam-6056	126	58	)	)	PUNCT
ejpam-6056	126	59	}	}	PUNCT
ejpam-6056	126	60	.	.	PUNCT
ejpam-6056	127	1	following	follow	VERB
ejpam-6056	127	2	the	the	DET
ejpam-6056	127	3	same	same	ADJ
ejpam-6056	127	4	sequence	sequence	NOUN
ejpam-6056	127	5	construction	construction	NOUN
ejpam-6056	127	6	as	as	ADP
ejpam-6056	127	7	in	in	ADP
ejpam-6056	127	8	theorem	theorem	ADJ
ejpam-6056	127	9	3.1	3.1	NUM
ejpam-6056	127	10	,	,	PUNCT
ejpam-6056	127	11	define	define	VERB
ejpam-6056	127	12	{	{	PUNCT
ejpam-6056	127	13	an	an	NOUN
ejpam-6056	127	14	}	}	PUNCT
ejpam-6056	127	15	where	where	SCONJ
ejpam-6056	127	16	an+1	an+1	NOUN
ejpam-6056	127	17	=	=	SYM
ejpam-6056	127	18	qan	qan	PROPN
ejpam-6056	127	19	.	.	PUNCT
ejpam-6056	128	1	applying	apply	VERB
ejpam-6056	128	2	the	the	DET
ejpam-6056	128	3	given	give	VERB
ejpam-6056	128	4	contraction	contraction	NOUN
ejpam-6056	128	5	condition	condition	NOUN
ejpam-6056	128	6	recursively	recursively	ADV
ejpam-6056	128	7	,	,	PUNCT
ejpam-6056	128	8	we	we	PRON
ejpam-6056	128	9	get	get	VERB
ejpam-6056	128	10	:	:	PUNCT
ejpam-6056	128	11	dτ	dτ	INTJ
ejpam-6056	128	12	(	(	PUNCT
ejpam-6056	128	13	an	an	PRON
ejpam-6056	128	14	,	,	PUNCT
ejpam-6056	128	15	an+1	an+1	NOUN
ejpam-6056	128	16	)	)	PUNCT
ejpam-6056	128	17	≤	≤	NUM
ejpam-6056	128	18	ρdτ	ρdτ	NOUN
ejpam-6056	128	19	(	(	PUNCT
ejpam-6056	128	20	an−1	an−1	ADJ
ejpam-6056	128	21	,	,	PUNCT
ejpam-6056	128	22	an	an	NOUN
ejpam-6056	128	23	)	)	PUNCT
ejpam-6056	128	24	,	,	PUNCT
ejpam-6056	128	25	where	where	SCONJ
ejpam-6056	128	26	ρ	ρ	PROPN
ejpam-6056	128	27	=	=	SYM
ejpam-6056	128	28	µ1	µ1	PROPN
ejpam-6056	128	29	1−µ2	1−µ2	NUM
ejpam-6056	128	30	and	and	CCONJ
ejpam-6056	128	31	ρ	ρ	NOUN
ejpam-6056	128	32	<	<	X
ejpam-6056	128	33	1	1	NUM
ejpam-6056	128	34	due	due	ADP
ejpam-6056	128	35	to	to	ADP
ejpam-6056	128	36	µ1	µ1	PROPN
ejpam-6056	128	37	+	+	CCONJ
ejpam-6056	128	38	µ2	µ2	PROPN
ejpam-6056	128	39	<	<	X
ejpam-6056	128	40	1	1	NUM
ejpam-6056	128	41	.	.	PUNCT
ejpam-6056	129	1	this	this	PRON
ejpam-6056	129	2	ensures	ensure	VERB
ejpam-6056	129	3	that	that	SCONJ
ejpam-6056	129	4	{	{	PUNCT
ejpam-6056	129	5	an	an	PRON
ejpam-6056	129	6	}	}	PUNCT
ejpam-6056	129	7	is	be	AUX
ejpam-6056	129	8	a	a	DET
ejpam-6056	129	9	cauchy	cauchy	ADJ
ejpam-6056	129	10	sequence	sequence	NOUN
ejpam-6056	129	11	converging	converge	VERB
ejpam-6056	129	12	to	to	ADP
ejpam-6056	129	13	a	a	DET
ejpam-6056	129	14	unique	unique	ADJ
ejpam-6056	129	15	fixed	fix	VERB
ejpam-6056	129	16	point	point	NOUN
ejpam-6056	129	17	of	of	ADP
ejpam-6056	129	18	q.	q.	PROPN
ejpam-6056	129	19	corollary	corollary	PROPN
ejpam-6056	129	20	3	3	X
ejpam-6056	129	21	.	.	PUNCT
ejpam-6056	130	1	let	let	VERB
ejpam-6056	130	2	q	q	NOUN
ejpam-6056	130	3	:	:	PUNCT
ejpam-6056	130	4	γ	γ	X
ejpam-6056	130	5	→	→	SYM
ejpam-6056	130	6	γ	γ	X
ejpam-6056	130	7	be	be	AUX
ejpam-6056	130	8	a	a	DET
ejpam-6056	130	9	function	function	NOUN
ejpam-6056	130	10	in	in	ADP
ejpam-6056	130	11	an	an	DET
ejpam-6056	130	12	ebms	ebms	NOUN
ejpam-6056	130	13	(	(	PUNCT
ejpam-6056	130	14	γ	γ	X
ejpam-6056	130	15	,	,	PUNCT
ejpam-6056	130	16	dτ	dτ	NOUN
ejpam-6056	130	17	)	)	PUNCT
ejpam-6056	130	18	satisfying	satisfy	VERB
ejpam-6056	130	19	the	the	DET
ejpam-6056	130	20	weaker	weak	ADJ
ejpam-6056	130	21	contraction	contraction	NOUN
ejpam-6056	130	22	condition	condition	NOUN
ejpam-6056	130	23	:	:	PUNCT
ejpam-6056	130	24	dτ	dτ	PROPN
ejpam-6056	130	25	(	(	PUNCT
ejpam-6056	130	26	qx	qx	PROPN
ejpam-6056	130	27	,	,	PUNCT
ejpam-6056	130	28	qy	qy	NOUN
ejpam-6056	130	29	)	)	PUNCT
ejpam-6056	130	30	≤	≤	NUM
ejpam-6056	130	31	µdτ	µdτ	NOUN
ejpam-6056	130	32	(	(	PUNCT
ejpam-6056	130	33	x	x	NOUN
ejpam-6056	130	34	,	,	PUNCT
ejpam-6056	130	35	y	y	PROPN
ejpam-6056	130	36	)	)	PUNCT
ejpam-6056	130	37	,	,	PUNCT
ejpam-6056	130	38	for	for	ADP
ejpam-6056	130	39	all	all	DET
ejpam-6056	130	40	x	x	NOUN
ejpam-6056	130	41	,	,	PUNCT
ejpam-6056	130	42	y	y	PROPN
ejpam-6056	130	43	∈	∈	PROPN
ejpam-6056	130	44	γ	γ	PROPN
ejpam-6056	130	45	,	,	PUNCT
ejpam-6056	130	46	where	where	SCONJ
ejpam-6056	130	47	0	0	NUM
ejpam-6056	130	48	≤	≤	NOUN
ejpam-6056	130	49	µ	µ	X
ejpam-6056	130	50	<	<	X
ejpam-6056	130	51	1	1	NUM
ejpam-6056	130	52	.	.	PUNCT
ejpam-6056	131	1	then	then	ADV
ejpam-6056	131	2	q	q	X
ejpam-6056	131	3	has	have	VERB
ejpam-6056	131	4	a	a	DET
ejpam-6056	131	5	unique	unique	ADJ
ejpam-6056	131	6	fixed	fix	VERB
ejpam-6056	131	7	point	point	NOUN
ejpam-6056	131	8	.	.	PUNCT
ejpam-6056	132	1	proof	proof	NOUN
ejpam-6056	132	2	.	.	PUNCT
ejpam-6056	133	1	this	this	PRON
ejpam-6056	133	2	is	be	AUX
ejpam-6056	133	3	a	a	DET
ejpam-6056	133	4	direct	direct	ADJ
ejpam-6056	133	5	consequence	consequence	NOUN
ejpam-6056	133	6	of	of	ADP
ejpam-6056	133	7	theorem	theorem	NOUN
ejpam-6056	133	8	3.1	3.1	NUM
ejpam-6056	133	9	by	by	ADP
ejpam-6056	133	10	setting	set	VERB
ejpam-6056	133	11	µ2	µ2	PROPN
ejpam-6056	133	12	=	=	SYM
ejpam-6056	133	13	0	0	NUM
ejpam-6056	133	14	,	,	PUNCT
ejpam-6056	133	15	simplifying	simplify	VERB
ejpam-6056	133	16	the	the	DET
ejpam-6056	133	17	given	give	VERB
ejpam-6056	133	18	contraction	contraction	NOUN
ejpam-6056	133	19	condition	condition	NOUN
ejpam-6056	133	20	.	.	PUNCT
ejpam-6056	134	1	example	example	NOUN
ejpam-6056	135	1	4	4	X
ejpam-6056	135	2	.	.	PUNCT
ejpam-6056	136	1	let	let	AUX
ejpam-6056	136	2	(	(	PUNCT
ejpam-6056	136	3	γ	γ	X
ejpam-6056	136	4	,	,	PUNCT
ejpam-6056	136	5	dγ	dγ	AUX
ejpam-6056	136	6	)	)	PUNCT
ejpam-6056	136	7	be	be	AUX
ejpam-6056	136	8	a	a	DET
ejpam-6056	136	9	complete	complete	ADJ
ejpam-6056	136	10	ebms	ebms	NOUN
ejpam-6056	136	11	,	,	PUNCT
ejpam-6056	136	12	where	where	SCONJ
ejpam-6056	136	13	γ	γ	X
ejpam-6056	136	14	=	=	X
ejpam-6056	137	1	[	[	X
ejpam-6056	137	2	0,∞	0,∞	NUM
ejpam-6056	137	3	)	)	PUNCT
ejpam-6056	137	4	and	and	CCONJ
ejpam-6056	137	5	the	the	DET
ejpam-6056	137	6	function	function	NOUN
ejpam-6056	137	7	dγ	dγ	ADP
ejpam-6056	137	8	:	:	PUNCT
ejpam-6056	138	1	γ×	γ×	PROPN
ejpam-6056	138	2	γ	γ	X
ejpam-6056	138	3	→	→	SYM
ejpam-6056	138	4	[	[	X
ejpam-6056	138	5	0,∞	0,∞	NOUN
ejpam-6056	138	6	)	)	PUNCT
ejpam-6056	138	7	is	be	AUX
ejpam-6056	138	8	defined	define	VERB
ejpam-6056	138	9	as	as	ADP
ejpam-6056	138	10	:	:	PUNCT
ejpam-6056	138	11	dγ(x	dγ(x	X
ejpam-6056	138	12	,	,	PUNCT
ejpam-6056	138	13	y	y	NOUN
ejpam-6056	138	14	)	)	PUNCT
ejpam-6056	138	15	=	=	SYM
ejpam-6056	139	1	(	(	PUNCT
ejpam-6056	139	2	x−	x−	PROPN
ejpam-6056	139	3	y)2	y)2	NOUN
ejpam-6056	139	4	.	.	PUNCT
ejpam-6056	140	1	define	define	VERB
ejpam-6056	140	2	the	the	DET
ejpam-6056	140	3	control	control	NOUN
ejpam-6056	140	4	function	function	NOUN
ejpam-6056	140	5	θ	θ	NOUN
ejpam-6056	140	6	:	:	PUNCT
ejpam-6056	140	7	γ×	γ×	PUNCT
ejpam-6056	140	8	γ	γ	X
ejpam-6056	140	9	→	→	SYM
ejpam-6056	140	10	[	[	X
ejpam-6056	140	11	1,∞	1,∞	NUM
ejpam-6056	140	12	)	)	PUNCT
ejpam-6056	140	13	as	as	ADP
ejpam-6056	140	14	:	:	PUNCT
ejpam-6056	140	15	θ(x	θ(x	PROPN
ejpam-6056	140	16	,	,	PUNCT
ejpam-6056	140	17	y	y	NOUN
ejpam-6056	140	18	)	)	PUNCT
ejpam-6056	140	19	=	=	SYM
ejpam-6056	141	1	x+	x+	PUNCT
ejpam-6056	141	2	y	y	PROPN
ejpam-6056	141	3	+	+	NOUN
ejpam-6056	141	4	2	2	X
ejpam-6056	141	5	.	.	PUNCT
ejpam-6056	141	6	let	let	VERB
ejpam-6056	141	7	the	the	DET
ejpam-6056	141	8	mapping	mapping	NOUN
ejpam-6056	141	9	q	q	NOUN
ejpam-6056	141	10	:	:	PUNCT
ejpam-6056	141	11	γ	γ	X
ejpam-6056	141	12	→	→	SYM
ejpam-6056	141	13	γ	γ	X
ejpam-6056	141	14	be	be	AUX
ejpam-6056	141	15	given	give	VERB
ejpam-6056	141	16	by	by	ADP
ejpam-6056	141	17	:	:	PUNCT
ejpam-6056	141	18	q(x	q(x	PROPN
ejpam-6056	141	19	)	)	PUNCT
ejpam-6056	142	1	=	=	PUNCT
ejpam-6056	142	2	xe−x	xe−x	NOUN
ejpam-6056	142	3	4	4	NUM
ejpam-6056	142	4	.	.	PUNCT
ejpam-6056	143	1	certainly	certainly	ADV
ejpam-6056	143	2	,	,	PUNCT
ejpam-6056	143	3	we	we	PRON
ejpam-6056	143	4	verify	verify	VERB
ejpam-6056	143	5	:	:	PUNCT
ejpam-6056	143	6	lim	lim	PROPN
ejpam-6056	143	7	n→∞	n→∞	X
ejpam-6056	143	8	θ(an	θ(an	PROPN
ejpam-6056	143	9	,	,	PUNCT
ejpam-6056	143	10	an+p	an+p	PROPN
ejpam-6056	143	11	)	)	PUNCT
ejpam-6056	143	12	=	=	VERB
ejpam-6056	143	13	lim	lim	PROPN
ejpam-6056	143	14	n→∞	n→∞	NUM
ejpam-6056	143	15	θ(qnx	θ(qnx	PROPN
ejpam-6056	143	16	,	,	PUNCT
ejpam-6056	143	17	qn+px	qn+px	X
ejpam-6056	143	18	)	)	PUNCT
ejpam-6056	143	19	=	=	SYM
ejpam-6056	143	20	lim	lim	PROPN
ejpam-6056	143	21	n→∞	n→∞	X
ejpam-6056	144	1	(	(	PUNCT
ejpam-6056	144	2	xe−x	xe−x	PROPN
ejpam-6056	144	3	4n	4n	PROPN
ejpam-6056	144	4	+	+	X
ejpam-6056	145	1	xe−x	xe−x	ADJ
ejpam-6056	145	2	4n+p	4n+p	NUM
ejpam-6056	146	1	+	+	CCONJ
ejpam-6056	146	2	2	2	X
ejpam-6056	146	3	)	)	PUNCT
ejpam-6056	146	4	=	=	SYM
ejpam-6056	146	5	2	2	NUM
ejpam-6056	146	6	<	<	SYM
ejpam-6056	146	7	9	9	NUM
ejpam-6056	146	8	=	=	SYM
ejpam-6056	146	9	1	1	NUM
ejpam-6056	146	10	ρ	ρ	NOUN
ejpam-6056	146	11	,	,	PUNCT
ejpam-6056	146	12	for	for	ADP
ejpam-6056	146	13	µ1	µ1	NOUN
ejpam-6056	146	14	=	=	SYM
ejpam-6056	146	15	1	1	NUM
ejpam-6056	146	16	16	16	NUM
ejpam-6056	146	17	and	and	CCONJ
ejpam-6056	146	18	µ2	µ2	PROPN
ejpam-6056	146	19	=	=	PROPN
ejpam-6056	146	20	7	7	NUM
ejpam-6056	146	21	16	16	NUM
ejpam-6056	146	22	.	.	PUNCT
ejpam-6056	147	1	furthermore	furthermore	ADV
ejpam-6056	147	2	:	:	PUNCT
ejpam-6056	147	3	dγ(q(x	dγ(q(x	NUM
ejpam-6056	147	4	)	)	PUNCT
ejpam-6056	147	5	,	,	PUNCT
ejpam-6056	147	6	q(y	q(y	NOUN
ejpam-6056	147	7	)	)	PUNCT
ejpam-6056	147	8	)	)	PUNCT
ejpam-6056	147	9	=	=	SYM
ejpam-6056	148	1	1	1	NUM
ejpam-6056	148	2	16	16	NUM
ejpam-6056	148	3	(	(	PUNCT
ejpam-6056	148	4	x−	x−	PROPN
ejpam-6056	148	5	y)2	y)2	NOUN
ejpam-6056	148	6	=	=	PUNCT
ejpam-6056	148	7	1	1	NUM
ejpam-6056	148	8	16	16	NUM
ejpam-6056	148	9	dγ(x	dγ(x	NOUN
ejpam-6056	148	10	,	,	PUNCT
ejpam-6056	148	11	y	y	NOUN
ejpam-6056	148	12	)	)	PUNCT
ejpam-6056	148	13	.	.	PUNCT
ejpam-6056	149	1	h.	h.	PROPN
ejpam-6056	149	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	149	3	,	,	PUNCT
ejpam-6056	149	4	j.m	j.m	PROPN
ejpam-6056	149	5	.	.	PROPN
ejpam-6056	149	6	al	al	PROPN
ejpam-6056	149	7	-	-	PUNCT
ejpam-6056	149	8	musannef	musannef	PROPN
ejpam-6056	149	9	,	,	PUNCT
ejpam-6056	149	10	h.	h.	PROPN
ejpam-6056	149	11	alsamir	alsamir	PROPN
ejpam-6056	149	12	/	/	SYM
ejpam-6056	149	13	eur	eur	PROPN
ejpam-6056	149	14	.	.	PUNCT
ejpam-6056	150	1	j.	j.	PROPN
ejpam-6056	150	2	pure	pure	PROPN
ejpam-6056	150	3	appl	appl	PROPN
ejpam-6056	150	4	.	.	PROPN
ejpam-6056	150	5	math	math	PROPN
ejpam-6056	150	6	,	,	PUNCT
ejpam-6056	150	7	18	18	NUM
ejpam-6056	150	8	(	(	PUNCT
ejpam-6056	150	9	3	3	NUM
ejpam-6056	150	10	)	)	PUNCT
ejpam-6056	150	11	(	(	PUNCT
ejpam-6056	150	12	2025	2025	NUM
ejpam-6056	150	13	)	)	PUNCT
ejpam-6056	150	14	,	,	PUNCT
ejpam-6056	150	15	6056	6056	NUM
ejpam-6056	150	16	7	7	NUM
ejpam-6056	150	17	of	of	ADP
ejpam-6056	150	18	16	16	NUM
ejpam-6056	150	19	this	this	DET
ejpam-6056	150	20	satisfies	satisfie	NOUN
ejpam-6056	150	21	:	:	PUNCT
ejpam-6056	150	22	dγ(q(x	dγ(q(x	NUM
ejpam-6056	150	23	)	)	PUNCT
ejpam-6056	150	24	,	,	PUNCT
ejpam-6056	150	25	q(y	q(y	PROPN
ejpam-6056	150	26	)	)	PUNCT
ejpam-6056	150	27	)	)	PUNCT
ejpam-6056	150	28	≤	≤	PUNCT
ejpam-6056	151	1	µ1dγ(y	µ1dγ(y	PROPN
ejpam-6056	151	2	,	,	PUNCT
ejpam-6056	151	3	x	x	PRON
ejpam-6056	151	4	)	)	PUNCT
ejpam-6056	152	1	+	+	CCONJ
ejpam-6056	152	2	µ2	µ2	PROPN
ejpam-6056	152	3	dγ(y	dγ(y	PROPN
ejpam-6056	152	4	,	,	PUNCT
ejpam-6056	152	5	q(y))dγ(x	q(y))dγ(x	NOUN
ejpam-6056	152	6	,	,	PUNCT
ejpam-6056	152	7	q(y	q(y	NOUN
ejpam-6056	152	8	)	)	PUNCT
ejpam-6056	152	9	)	)	PUNCT
ejpam-6056	153	1	+	+	CCONJ
ejpam-6056	153	2	dγ(x	dγ(x	X
ejpam-6056	153	3	,	,	PUNCT
ejpam-6056	153	4	q(x))dγ(y	q(x))dγ(y	NOUN
ejpam-6056	153	5	,	,	PUNCT
ejpam-6056	153	6	q(x	q(x	NOUN
ejpam-6056	153	7	)	)	PUNCT
ejpam-6056	153	8	)	)	PUNCT
ejpam-6056	153	9	dγ(y	dγ(y	PROPN
ejpam-6056	153	10	,	,	PUNCT
ejpam-6056	153	11	q(x	q(x	NOUN
ejpam-6056	153	12	)	)	PUNCT
ejpam-6056	153	13	)	)	PUNCT
ejpam-6056	154	1	+	+	CCONJ
ejpam-6056	154	2	dγ(x	dγ(x	X
ejpam-6056	154	3	,	,	PUNCT
ejpam-6056	154	4	q(y	q(y	NOUN
ejpam-6056	154	5	)	)	PUNCT
ejpam-6056	154	6	)	)	PUNCT
ejpam-6056	154	7	.	.	PUNCT
ejpam-6056	155	1	by	by	ADP
ejpam-6056	155	2	theorem	theorem	NOUN
ejpam-6056	155	3	2.1	2.1	NUM
ejpam-6056	155	4	,	,	PUNCT
ejpam-6056	155	5	q	q	PROPN
ejpam-6056	155	6	has	have	VERB
ejpam-6056	155	7	a	a	DET
ejpam-6056	155	8	unique	unique	ADJ
ejpam-6056	155	9	fixed	fix	VERB
ejpam-6056	155	10	point	point	NOUN
ejpam-6056	155	11	.	.	PUNCT
ejpam-6056	156	1	example	example	NOUN
ejpam-6056	156	2	5	5	NUM
ejpam-6056	156	3	.	.	X
ejpam-6056	157	1	consider	consider	VERB
ejpam-6056	157	2	the	the	DET
ejpam-6056	157	3	complete	complete	ADJ
ejpam-6056	157	4	ebms	ebms	NOUN
ejpam-6056	157	5	(	(	PUNCT
ejpam-6056	157	6	γ	γ	X
ejpam-6056	157	7	,	,	PUNCT
ejpam-6056	157	8	dγ	dγ	PROPN
ejpam-6056	157	9	)	)	PUNCT
ejpam-6056	157	10	,	,	PUNCT
ejpam-6056	157	11	where	where	SCONJ
ejpam-6056	157	12	γ	γ	X
ejpam-6056	157	13	=	=	X
ejpam-6056	158	1	[	[	X
ejpam-6056	158	2	0,∞	0,∞	NUM
ejpam-6056	158	3	)	)	PUNCT
ejpam-6056	158	4	and	and	CCONJ
ejpam-6056	158	5	the	the	DET
ejpam-6056	158	6	function	function	NOUN
ejpam-6056	158	7	dγ	dγ	ADP
ejpam-6056	158	8	:	:	PUNCT
ejpam-6056	159	1	γ×	γ×	PROPN
ejpam-6056	159	2	γ	γ	X
ejpam-6056	159	3	→	→	SYM
ejpam-6056	159	4	[	[	X
ejpam-6056	159	5	0,∞	0,∞	NOUN
ejpam-6056	159	6	)	)	PUNCT
ejpam-6056	159	7	is	be	AUX
ejpam-6056	159	8	defined	define	VERB
ejpam-6056	159	9	as	as	ADP
ejpam-6056	159	10	:	:	PUNCT
ejpam-6056	159	11	dγ(x	dγ(x	X
ejpam-6056	159	12	,	,	PUNCT
ejpam-6056	159	13	y	y	NOUN
ejpam-6056	159	14	)	)	PUNCT
ejpam-6056	159	15	=	=	PUNCT
ejpam-6056	159	16	|x−	|x−	ADJ
ejpam-6056	159	17	y|	y|	NOUN
ejpam-6056	159	18	λ+	λ+	PUNCT
ejpam-6056	159	19	|x−	|x−	NOUN
ejpam-6056	159	20	y|	y|	NOUN
ejpam-6056	159	21	.	.	PUNCT
ejpam-6056	160	1	define	define	VERB
ejpam-6056	160	2	the	the	DET
ejpam-6056	160	3	control	control	NOUN
ejpam-6056	160	4	function	function	NOUN
ejpam-6056	160	5	θ	θ	NOUN
ejpam-6056	160	6	:	:	PUNCT
ejpam-6056	160	7	γ×	γ×	PUNCT
ejpam-6056	160	8	γ	γ	X
ejpam-6056	160	9	→	→	SYM
ejpam-6056	160	10	[	[	X
ejpam-6056	160	11	1,∞	1,∞	NUM
ejpam-6056	160	12	)	)	PUNCT
ejpam-6056	160	13	by	by	ADP
ejpam-6056	160	14	:	:	PUNCT
ejpam-6056	160	15	θ(x	θ(x	PROPN
ejpam-6056	160	16	,	,	PUNCT
ejpam-6056	160	17	y	y	NOUN
ejpam-6056	160	18	)	)	PUNCT
ejpam-6056	160	19	=	=	PUNCT
ejpam-6056	160	20	1	1	NOUN
ejpam-6056	160	21	,	,	PUNCT
ejpam-6056	160	22	if	if	SCONJ
ejpam-6056	160	23	x	x	PROPN
ejpam-6056	160	24	̸=	̸=	PROPN
ejpam-6056	160	25	y	y	PROPN
ejpam-6056	160	26	,	,	PUNCT
ejpam-6056	160	27	1	1	NUM
ejpam-6056	160	28	+	+	CCONJ
ejpam-6056	160	29	x+	x+	ADJ
ejpam-6056	160	30	y	y	NOUN
ejpam-6056	160	31	,	,	PUNCT
ejpam-6056	160	32	if	if	SCONJ
ejpam-6056	160	33	x	x	X
ejpam-6056	160	34	=	=	PUNCT
ejpam-6056	160	35	y.	y.	PROPN
ejpam-6056	160	36	now	now	ADV
ejpam-6056	160	37	,	,	PUNCT
ejpam-6056	160	38	let	let	VERB
ejpam-6056	160	39	us	we	PRON
ejpam-6056	160	40	define	define	VERB
ejpam-6056	160	41	the	the	DET
ejpam-6056	160	42	mapping	mapping	NOUN
ejpam-6056	160	43	q	q	NOUN
ejpam-6056	160	44	:	:	PUNCT
ejpam-6056	160	45	γ	γ	X
ejpam-6056	160	46	→	→	SYM
ejpam-6056	160	47	γ	γ	PROPN
ejpam-6056	160	48	as	as	SCONJ
ejpam-6056	160	49	follows	follow	VERB
ejpam-6056	160	50	:	:	PUNCT
ejpam-6056	160	51	q(x	q(x	NUM
ejpam-6056	160	52	)	)	PUNCT
ejpam-6056	161	1	=	=	PUNCT
ejpam-6056	161	2	x	x	SYM
ejpam-6056	161	3	5	5	NUM
ejpam-6056	161	4	+	+	NOUN
ejpam-6056	161	5	7	7	X
ejpam-6056	161	6	.	.	PUNCT
ejpam-6056	161	7	to	to	PART
ejpam-6056	161	8	verify	verify	VERB
ejpam-6056	161	9	the	the	DET
ejpam-6056	161	10	contraction	contraction	NOUN
ejpam-6056	161	11	condition	condition	NOUN
ejpam-6056	161	12	,	,	PUNCT
ejpam-6056	161	13	let	let	VERB
ejpam-6056	161	14	3	3	NUM
ejpam-6056	161	15	4	4	NUM
ejpam-6056	161	16	≤	≤	NUM
ejpam-6056	161	17	ρ	ρ	NOUN
ejpam-6056	161	18	<	<	X
ejpam-6056	161	19	1	1	NUM
ejpam-6056	161	20	.	.	PUNCT
ejpam-6056	161	21	we	we	PRON
ejpam-6056	161	22	compute	compute	VERB
ejpam-6056	161	23	:	:	PUNCT
ejpam-6056	162	1	dγ(qx	dγ(qx	PROPN
ejpam-6056	162	2	,	,	PUNCT
ejpam-6056	162	3	qy	qy	PROPN
ejpam-6056	162	4	)	)	PUNCT
ejpam-6056	162	5	=	=	PUNCT
ejpam-6056	162	6	|qx−qy|	|qx−qy|	NOUN
ejpam-6056	162	7	λ+	λ+	NUM
ejpam-6056	162	8	|qx−qy|	|qx−qy|	NOUN
ejpam-6056	162	9	=	=	SYM
ejpam-6056	162	10	∣∣x	∣∣x	NOUN
ejpam-6056	162	11	5	5	NUM
ejpam-6056	162	12	−	−	NOUN
ejpam-6056	162	13	y	y	PROPN
ejpam-6056	162	14	5	5	NUM
ejpam-6056	162	15	∣∣	∣∣	NUM
ejpam-6056	162	16	λ+	λ+	PUNCT
ejpam-6056	162	17	∣∣x	∣∣x	ADP
ejpam-6056	162	18	5	5	NUM
ejpam-6056	162	19	−	−	NOUN
ejpam-6056	162	20	y	y	PROPN
ejpam-6056	162	21	5	5	NUM
ejpam-6056	162	22	∣∣	∣∣	X
ejpam-6056	162	23	=	=	PUNCT
ejpam-6056	162	24	|x−	|x−	ADJ
ejpam-6056	162	25	y|	y|	NOUN
ejpam-6056	162	26	5λ+	5λ+	NUM
ejpam-6056	162	27	|x−	|x−	PART
ejpam-6056	162	28	y|	y|	NOUN
ejpam-6056	162	29	≤	≤	NUM
ejpam-6056	162	30	ρ	ρ	NUM
ejpam-6056	162	31	|x−	|x−	PROPN
ejpam-6056	162	32	y|	y|	NOUN
ejpam-6056	162	33	λ+	λ+	X
ejpam-6056	162	34	|x−	|x−	NOUN
ejpam-6056	162	35	y|	y|	NOUN
ejpam-6056	162	36	=	=	SYM
ejpam-6056	162	37	ρdγ(x	ρdγ(x	PROPN
ejpam-6056	162	38	,	,	PUNCT
ejpam-6056	162	39	y	y	NOUN
ejpam-6056	162	40	)	)	PUNCT
ejpam-6056	162	41	.	.	PUNCT
ejpam-6056	163	1	since	since	SCONJ
ejpam-6056	163	2	all	all	DET
ejpam-6056	163	3	conditions	condition	NOUN
ejpam-6056	163	4	of	of	ADP
ejpam-6056	163	5	corollary	corollary	ADJ
ejpam-6056	163	6	1	1	NUM
ejpam-6056	163	7	are	be	AUX
ejpam-6056	163	8	met	meet	VERB
ejpam-6056	163	9	.	.	PUNCT
ejpam-6056	164	1	the	the	DET
ejpam-6056	164	2	numerical	numerical	PROPN
ejpam-6056	164	3	validation	validation	PROPN
ejpam-6056	164	4	and	and	CCONJ
ejpam-6056	164	5	graphical	graphical	ADJ
ejpam-6056	164	6	representation	representation	NOUN
ejpam-6056	164	7	are	be	AUX
ejpam-6056	164	8	given	give	VERB
ejpam-6056	164	9	in	in	ADP
ejpam-6056	164	10	table	table	NOUN
ejpam-6056	164	11	1	1	NUM
ejpam-6056	164	12	and	and	CCONJ
ejpam-6056	164	13	figure	figure	VERB
ejpam-6056	164	14	1	1	NUM
ejpam-6056	164	15	,	,	PUNCT
ejpam-6056	164	16	respectively	respectively	ADV
ejpam-6056	164	17	.	.	PUNCT
ejpam-6056	164	18	table	table	NOUN
ejpam-6056	164	19	1	1	NUM
ejpam-6056	164	20	:	:	PUNCT
ejpam-6056	164	21	numerical	numerical	ADJ
ejpam-6056	164	22	validation	validation	NOUN
ejpam-6056	164	23	of	of	ADP
ejpam-6056	164	24	q(x	q(x	NOUN
ejpam-6056	164	25	)	)	PUNCT
ejpam-6056	164	26	and	and	CCONJ
ejpam-6056	164	27	contraction	contraction	NOUN
ejpam-6056	164	28	condition	condition	NOUN
ejpam-6056	164	29	x	x	VERB
ejpam-6056	164	30	y	y	PROPN
ejpam-6056	164	31	dγ(x	dγ(x	PROPN
ejpam-6056	164	32	,	,	PUNCT
ejpam-6056	164	33	y	y	NOUN
ejpam-6056	164	34	)	)	PUNCT
ejpam-6056	164	35	q(x	q(x	PROPN
ejpam-6056	164	36	)	)	PUNCT
ejpam-6056	164	37	q(y	q(y	X
ejpam-6056	164	38	)	)	PUNCT
ejpam-6056	164	39	dγ(qx	dγ(qx	PROPN
ejpam-6056	164	40	,	,	PUNCT
ejpam-6056	164	41	qy	qy	PROPN
ejpam-6056	164	42	)	)	PUNCT
ejpam-6056	164	43	ρdγ(x	ρdγ(x	PROPN
ejpam-6056	164	44	,	,	PUNCT
ejpam-6056	164	45	y	y	PROPN
ejpam-6056	164	46	)	)	PUNCT
ejpam-6056	164	47	1.0	1.0	NUM
ejpam-6056	164	48	2.0	2.0	NUM
ejpam-6056	164	49	0.50	0.50	NUM
ejpam-6056	164	50	7.20	7.20	NUM
ejpam-6056	164	51	7.40	7.40	NUM
ejpam-6056	164	52	0.05	0.05	NUM
ejpam-6056	164	53	0.375	0.375	NUM
ejpam-6056	164	54	2.0	2.0	NUM
ejpam-6056	164	55	3.0	3.0	NUM
ejpam-6056	164	56	0.33	0.33	NUM
ejpam-6056	164	57	7.40	7.40	NUM
ejpam-6056	164	58	7.60	7.60	NUM
ejpam-6056	164	59	0.033	0.033	NUM
ejpam-6056	164	60	0.2475	0.2475	NUM
ejpam-6056	164	61	3.0	3.0	NUM
ejpam-6056	164	62	4.0	4.0	NUM
ejpam-6056	164	63	0.25	0.25	NUM
ejpam-6056	164	64	7.60	7.60	NUM
ejpam-6056	164	65	7.80	7.80	NUM
ejpam-6056	164	66	0.025	0.025	NUM
ejpam-6056	164	67	0.1875	0.1875	NUM
ejpam-6056	164	68	4.0	4.0	NUM
ejpam-6056	164	69	5.0	5.0	NUM
ejpam-6056	164	70	0.20	0.20	NUM
ejpam-6056	164	71	7.80	7.80	NUM
ejpam-6056	164	72	8.00	8.00	NUM
ejpam-6056	164	73	0.020	0.020	NUM
ejpam-6056	164	74	0.150	0.150	NUM
ejpam-6056	164	75	let	let	VERB
ejpam-6056	164	76	ρ	ρ	NOUN
ejpam-6056	164	77	=	=	NOUN
ejpam-6056	164	78	0.75	0.75	NUM
ejpam-6056	164	79	.	.	PUNCT
ejpam-6056	165	1	we	we	PRON
ejpam-6056	165	2	define	define	VERB
ejpam-6056	165	3	two	two	NUM
ejpam-6056	165	4	surfaces	surface	NOUN
ejpam-6056	165	5	over	over	ADP
ejpam-6056	165	6	the	the	DET
ejpam-6056	165	7	domain	domain	NOUN
ejpam-6056	165	8	[	[	X
ejpam-6056	165	9	1	1	NUM
ejpam-6056	165	10	,	,	PUNCT
ejpam-6056	165	11	5]×	5]×	NUM
ejpam-6056	166	1	[	[	X
ejpam-6056	166	2	1	1	NUM
ejpam-6056	166	3	,	,	PUNCT
ejpam-6056	166	4	5	5	NUM
ejpam-6056	166	5	]	]	NOUN
ejpam-6056	166	6	:	:	PUNCT
ejpam-6056	166	7	z1(x	z1(x	NUM
ejpam-6056	166	8	,	,	PUNCT
ejpam-6056	166	9	y	y	NOUN
ejpam-6056	166	10	)	)	PUNCT
ejpam-6056	166	11	=	=	SYM
ejpam-6056	166	12	dγ(qx	dγ(qx	PROPN
ejpam-6056	166	13	,	,	PUNCT
ejpam-6056	166	14	qy	qy	PROPN
ejpam-6056	166	15	)	)	PUNCT
ejpam-6056	166	16	=	=	SYM
ejpam-6056	166	17	1	1	NUM
ejpam-6056	166	18	5	5	NUM
ejpam-6056	166	19	|x−	|x−	NOUN
ejpam-6056	166	20	y|	y|	NOUN
ejpam-6056	166	21	λ+	λ+	PUNCT
ejpam-6056	166	22	1	1	NUM
ejpam-6056	166	23	5	5	NUM
ejpam-6056	166	24	|x−	|x−	NOUN
ejpam-6056	166	25	y|	y|	NOUN
ejpam-6056	166	26	,	,	PUNCT
ejpam-6056	166	27	z2(x	z2(x	PROPN
ejpam-6056	166	28	,	,	PUNCT
ejpam-6056	166	29	y	y	NOUN
ejpam-6056	166	30	)	)	PUNCT
ejpam-6056	167	1	=	=	SYM
ejpam-6056	167	2	ρ	ρ	PROPN
ejpam-6056	167	3	·	·	PUNCT
ejpam-6056	167	4	dγ(x	dγ(x	X
ejpam-6056	167	5	,	,	PUNCT
ejpam-6056	167	6	y	y	NOUN
ejpam-6056	167	7	)	)	PUNCT
ejpam-6056	167	8	=	=	SYM
ejpam-6056	167	9	0.75	0.75	NUM
ejpam-6056	167	10	·	·	PUNCT
ejpam-6056	167	11	|x−	|x−	NOUN
ejpam-6056	168	1	y|	y|	NOUN
ejpam-6056	168	2	λ+	λ+	PUNCT
ejpam-6056	168	3	|x−	|x−	NOUN
ejpam-6056	168	4	y|	y|	NOUN
ejpam-6056	168	5	.	.	PUNCT
ejpam-6056	169	1	h.	h.	PROPN
ejpam-6056	169	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	169	3	,	,	PUNCT
ejpam-6056	169	4	j.m	j.m	PROPN
ejpam-6056	169	5	.	.	PROPN
ejpam-6056	169	6	al	al	PROPN
ejpam-6056	169	7	-	-	PUNCT
ejpam-6056	169	8	musannef	musannef	PROPN
ejpam-6056	169	9	,	,	PUNCT
ejpam-6056	169	10	h.	h.	PROPN
ejpam-6056	169	11	alsamir	alsamir	PROPN
ejpam-6056	169	12	/	/	SYM
ejpam-6056	169	13	eur	eur	PROPN
ejpam-6056	169	14	.	.	PUNCT
ejpam-6056	170	1	j.	j.	PROPN
ejpam-6056	170	2	pure	pure	PROPN
ejpam-6056	170	3	appl	appl	PROPN
ejpam-6056	170	4	.	.	PROPN
ejpam-6056	170	5	math	math	PROPN
ejpam-6056	170	6	,	,	PUNCT
ejpam-6056	170	7	18	18	NUM
ejpam-6056	170	8	(	(	PUNCT
ejpam-6056	170	9	3	3	NUM
ejpam-6056	170	10	)	)	PUNCT
ejpam-6056	170	11	(	(	PUNCT
ejpam-6056	170	12	2025	2025	NUM
ejpam-6056	170	13	)	)	PUNCT
ejpam-6056	170	14	,	,	PUNCT
ejpam-6056	170	15	6056	6056	NUM
ejpam-6056	170	16	8	8	NUM
ejpam-6056	170	17	of	of	ADP
ejpam-6056	170	18	16	16	NUM
ejpam-6056	170	19	figure	figure	NOUN
ejpam-6056	170	20	1	1	NUM
ejpam-6056	170	21	:	:	PUNCT
ejpam-6056	170	22	3d	3d	NUM
ejpam-6056	170	23	surface	surface	NOUN
ejpam-6056	170	24	plot	plot	NOUN
ejpam-6056	170	25	of	of	ADP
ejpam-6056	170	26	dγ(qx	dγ(qx	PROPN
ejpam-6056	170	27	,	,	PUNCT
ejpam-6056	170	28	qy	qy	PROPN
ejpam-6056	170	29	)	)	PUNCT
ejpam-6056	170	30	and	and	CCONJ
ejpam-6056	170	31	ρ	ρ	PROPN
ejpam-6056	170	32	dγ(x	dγ(x	PROPN
ejpam-6056	170	33	,	,	PUNCT
ejpam-6056	170	34	y	y	NOUN
ejpam-6056	170	35	)	)	PUNCT
ejpam-6056	170	36	1	1	NUM
ejpam-6056	170	37	2	2	NUM
ejpam-6056	170	38	3	3	NUM
ejpam-6056	170	39	4	4	NUM
ejpam-6056	170	40	5	5	NUM
ejpam-6056	170	41	1	1	NUM
ejpam-6056	170	42	2	2	NUM
ejpam-6056	170	43	3	3	NUM
ejpam-6056	170	44	4	4	NUM
ejpam-6056	170	45	5	5	NUM
ejpam-6056	170	46	0	0	NUM
ejpam-6056	170	47	0.2	0.2	NUM
ejpam-6056	170	48	0.4	0.4	NUM
ejpam-6056	170	49	0.6	0.6	NUM
ejpam-6056	170	50	x	x	SYM
ejpam-6056	170	51	y	y	NOUN
ejpam-6056	170	52	d	d	PROPN
ejpam-6056	170	53	γ	γ	X
ejpam-6056	170	54	v	v	ADP
ejpam-6056	170	55	al	al	PROPN
ejpam-6056	170	56	u	u	PROPN
ejpam-6056	170	57	es	es	X
ejpam-6056	170	58	dγ(qx	dγ(qx	PROPN
ejpam-6056	170	59	,	,	PUNCT
ejpam-6056	170	60	qy	qy	PROPN
ejpam-6056	170	61	)	)	PUNCT
ejpam-6056	170	62	ρ	ρ	PROPN
ejpam-6056	170	63	dγ(x	dγ(x	PROPN
ejpam-6056	170	64	,	,	PUNCT
ejpam-6056	170	65	y	y	NOUN
ejpam-6056	170	66	)	)	PUNCT
ejpam-6056	170	67	4	4	NUM
ejpam-6056	170	68	.	.	X
ejpam-6056	170	69	application	application	VERB
ejpam-6056	170	70	the	the	DET
ejpam-6056	170	71	following	follow	VERB
ejpam-6056	170	72	applications	application	NOUN
ejpam-6056	170	73	demonstrate	demonstrate	VERB
ejpam-6056	170	74	the	the	DET
ejpam-6056	170	75	applicability	applicability	NOUN
ejpam-6056	170	76	of	of	ADP
ejpam-6056	170	77	our	our	PRON
ejpam-6056	170	78	main	main	ADJ
ejpam-6056	170	79	results	result	NOUN
ejpam-6056	170	80	to	to	ADP
ejpam-6056	170	81	integral	integral	ADJ
ejpam-6056	170	82	equations	equation	NOUN
ejpam-6056	170	83	and	and	CCONJ
ejpam-6056	170	84	inclusion	inclusion	NOUN
ejpam-6056	170	85	systems	system	NOUN
ejpam-6056	170	86	.	.	PUNCT
ejpam-6056	171	1	these	these	DET
ejpam-6056	171	2	applications	application	NOUN
ejpam-6056	171	3	,	,	PUNCT
ejpam-6056	171	4	though	though	SCONJ
ejpam-6056	171	5	presented	present	VERB
ejpam-6056	171	6	with	with	ADP
ejpam-6056	171	7	relatively	relatively	ADV
ejpam-6056	171	8	simple	simple	ADJ
ejpam-6056	171	9	functions	function	NOUN
ejpam-6056	171	10	for	for	ADP
ejpam-6056	171	11	clarity	clarity	NOUN
ejpam-6056	171	12	,	,	PUNCT
ejpam-6056	171	13	showcase	showcase	VERB
ejpam-6056	171	14	the	the	DET
ejpam-6056	171	15	broader	broad	ADJ
ejpam-6056	171	16	power	power	NOUN
ejpam-6056	171	17	and	and	CCONJ
ejpam-6056	171	18	generality	generality	NOUN
ejpam-6056	171	19	of	of	ADP
ejpam-6056	171	20	the	the	DET
ejpam-6056	171	21	ebms	ebms	NOUN
ejpam-6056	171	22	contraction	contraction	NOUN
ejpam-6056	171	23	approach	approach	NOUN
ejpam-6056	171	24	.	.	PUNCT
ejpam-6056	172	1	4.1	4.1	NUM
ejpam-6056	172	2	.	.	PUNCT
ejpam-6056	172	3	existence	existence	NOUN
ejpam-6056	172	4	of	of	ADP
ejpam-6056	172	5	a	a	DET
ejpam-6056	172	6	unique	unique	ADJ
ejpam-6056	172	7	solution	solution	NOUN
ejpam-6056	172	8	for	for	ADP
ejpam-6056	172	9	volterra	volterra	NOUN
ejpam-6056	172	10	integral	integral	ADJ
ejpam-6056	172	11	inclusion	inclusion	NOUN
ejpam-6056	172	12	the	the	DET
ejpam-6056	172	13	following	follow	VERB
ejpam-6056	172	14	subsection	subsection	NOUN
ejpam-6056	172	15	demonstrates	demonstrate	VERB
ejpam-6056	172	16	the	the	DET
ejpam-6056	172	17	existence	existence	NOUN
ejpam-6056	172	18	and	and	CCONJ
ejpam-6056	172	19	uniqueness	uniqueness	NOUN
ejpam-6056	172	20	of	of	ADP
ejpam-6056	172	21	a	a	DET
ejpam-6056	172	22	solution	solution	NOUN
ejpam-6056	172	23	to	to	ADP
ejpam-6056	172	24	the	the	DET
ejpam-6056	172	25	volterra	volterra	NOUN
ejpam-6056	172	26	integral	integral	ADJ
ejpam-6056	172	27	inclusion	inclusion	NOUN
ejpam-6056	172	28	problem	problem	NOUN
ejpam-6056	172	29	:	:	PUNCT
ejpam-6056	172	30	ϕ(q	ϕ(q	PROPN
ejpam-6056	172	31	)	)	PUNCT
ejpam-6056	173	1	∈	∈	PROPN
ejpam-6056	173	2	∫	∫	PROPN
ejpam-6056	173	3	υ	υ	PROPN
ejpam-6056	173	4	0	0	PROPN
ejpam-6056	173	5	k(q	k(q	PROPN
ejpam-6056	173	6	,	,	PUNCT
ejpam-6056	173	7	u)h(u	u)h(u	PROPN
ejpam-6056	173	8	,	,	PUNCT
ejpam-6056	173	9	ϕ(u	ϕ(u	NOUN
ejpam-6056	173	10	)	)	PUNCT
ejpam-6056	173	11	)	)	PUNCT
ejpam-6056	174	1	du+	du+	PROPN
ejpam-6056	174	2	ϑ(q	ϑ(q	PROPN
ejpam-6056	174	3	)	)	PUNCT
ejpam-6056	174	4	,	,	PUNCT
ejpam-6056	175	1	q	q	PROPN
ejpam-6056	175	2	∈	∈	PROPN
ejpam-6056	176	1	[	[	X
ejpam-6056	176	2	0,υ	0,υ	X
ejpam-6056	176	3	]	]	PUNCT
ejpam-6056	176	4	,	,	PUNCT
ejpam-6056	176	5	ϑ	ϑ	PROPN
ejpam-6056	176	6	∈	∈	PROPN
ejpam-6056	176	7	ω	ω	PROPN
ejpam-6056	176	8	,	,	PUNCT
ejpam-6056	176	9	where	where	SCONJ
ejpam-6056	176	10	h	h	NOUN
ejpam-6056	176	11	:	:	PUNCT
ejpam-6056	177	1	[	[	X
ejpam-6056	177	2	0,υ]×r	0,υ]×r	X
ejpam-6056	177	3	→	→	SYM
ejpam-6056	177	4	r	r	NOUN
ejpam-6056	177	5	is	be	AUX
ejpam-6056	177	6	a	a	DET
ejpam-6056	177	7	continuous	continuous	ADJ
ejpam-6056	177	8	function	function	NOUN
ejpam-6056	177	9	with	with	ADP
ejpam-6056	177	10	non	non	ADJ
ejpam-6056	177	11	-	-	ADJ
ejpam-6056	177	12	empty	empty	ADJ
ejpam-6056	177	13	compact	compact	ADJ
ejpam-6056	177	14	values	value	NOUN
ejpam-6056	177	15	.	.	PUNCT
ejpam-6056	178	1	here	here	ADV
ejpam-6056	178	2	,	,	PUNCT
ejpam-6056	178	3	υ	υ	PROPN
ejpam-6056	178	4	>	>	X
ejpam-6056	178	5	0	0	NUM
ejpam-6056	178	6	is	be	AUX
ejpam-6056	178	7	a	a	DET
ejpam-6056	178	8	constant	constant	ADJ
ejpam-6056	178	9	.	.	PUNCT
ejpam-6056	179	1	theorem	theorem	NOUN
ejpam-6056	179	2	2	2	NUM
ejpam-6056	179	3	.	.	PUNCT
ejpam-6056	179	4	assume	assume	VERB
ejpam-6056	179	5	that	that	SCONJ
ejpam-6056	179	6	for	for	ADP
ejpam-6056	179	7	all	all	DET
ejpam-6056	179	8	ϕ	ϕ	NOUN
ejpam-6056	179	9	,	,	PUNCT
ejpam-6056	179	10	ψ	ψ	NOUN
ejpam-6056	179	11	∈	∈	NOUN
ejpam-6056	179	12	c([0,υ],r	c([0,υ],r	NOUN
ejpam-6056	179	13	)	)	PUNCT
ejpam-6056	179	14	,	,	PUNCT
ejpam-6056	179	15	the	the	DET
ejpam-6056	179	16	following	follow	VERB
ejpam-6056	179	17	conditions	condition	NOUN
ejpam-6056	179	18	hold	hold	VERB
ejpam-6056	179	19	:	:	PUNCT
ejpam-6056	179	20	(	(	PUNCT
ejpam-6056	179	21	i	i	NOUN
ejpam-6056	179	22	)	)	PUNCT
ejpam-6056	179	23	there	there	PRON
ejpam-6056	179	24	exists	exist	VERB
ejpam-6056	179	25	a	a	DET
ejpam-6056	179	26	continuous	continuous	ADJ
ejpam-6056	179	27	function	function	NOUN
ejpam-6056	179	28	h	h	NOUN
ejpam-6056	179	29	such	such	ADJ
ejpam-6056	179	30	that	that	PRON
ejpam-6056	179	31	sup	sup	PROPN
ejpam-6056	179	32	|h(q	|h(q	PROPN
ejpam-6056	179	33	,	,	PUNCT
ejpam-6056	179	34	u	u	NOUN
ejpam-6056	179	35	,	,	PUNCT
ejpam-6056	179	36	ϕ(u))−h(q	ϕ(u))−h(q	PRON
ejpam-6056	179	37	,	,	PUNCT
ejpam-6056	179	38	u	u	NOUN
ejpam-6056	179	39	,	,	PUNCT
ejpam-6056	179	40	ψ(u))|τ	ψ(u))|τ	VERB
ejpam-6056	179	41	≤	≤	PUNCT
ejpam-6056	179	42	mθ(ϕ	mθ(ϕ	PROPN
ejpam-6056	179	43	,	,	PUNCT
ejpam-6056	179	44	ψ	ψ	NOUN
ejpam-6056	179	45	)	)	PUNCT
ejpam-6056	179	46	υ	υ	NOUN
ejpam-6056	179	47	,	,	PUNCT
ejpam-6056	179	48	h.	h.	PROPN
ejpam-6056	179	49	qawaqneh	qawaqneh	PROPN
ejpam-6056	179	50	,	,	PUNCT
ejpam-6056	179	51	j.m	j.m	PROPN
ejpam-6056	179	52	.	.	PROPN
ejpam-6056	179	53	al	al	PROPN
ejpam-6056	179	54	-	-	PUNCT
ejpam-6056	179	55	musannef	musannef	PROPN
ejpam-6056	179	56	,	,	PUNCT
ejpam-6056	179	57	h.	h.	PROPN
ejpam-6056	179	58	alsamir	alsamir	PROPN
ejpam-6056	179	59	/	/	SYM
ejpam-6056	179	60	eur	eur	PROPN
ejpam-6056	179	61	.	.	PUNCT
ejpam-6056	180	1	j.	j.	PROPN
ejpam-6056	180	2	pure	pure	PROPN
ejpam-6056	180	3	appl	appl	PROPN
ejpam-6056	180	4	.	.	PROPN
ejpam-6056	180	5	math	math	PROPN
ejpam-6056	180	6	,	,	PUNCT
ejpam-6056	180	7	18	18	NUM
ejpam-6056	180	8	(	(	PUNCT
ejpam-6056	180	9	3	3	NUM
ejpam-6056	180	10	)	)	PUNCT
ejpam-6056	180	11	(	(	PUNCT
ejpam-6056	180	12	2025	2025	NUM
ejpam-6056	180	13	)	)	PUNCT
ejpam-6056	180	14	,	,	PUNCT
ejpam-6056	180	15	6056	6056	NUM
ejpam-6056	180	16	9	9	NUM
ejpam-6056	180	17	of	of	ADP
ejpam-6056	180	18	16	16	NUM
ejpam-6056	180	19	where	where	SCONJ
ejpam-6056	180	20	mθ(ϕ	mθ(ϕ	PROPN
ejpam-6056	180	21	,	,	PUNCT
ejpam-6056	180	22	ψ	ψ	NOUN
ejpam-6056	180	23	)	)	PUNCT
ejpam-6056	180	24	=	=	SYM
ejpam-6056	180	25	µ1dθ(ϕ	µ1dθ(ϕ	PROPN
ejpam-6056	180	26	,	,	PUNCT
ejpam-6056	180	27	ψ	ψ	NOUN
ejpam-6056	180	28	)	)	PUNCT
ejpam-6056	180	29	+	+	CCONJ
ejpam-6056	180	30	µ2	µ2	PROPN
ejpam-6056	180	31	dθ(ψ	dθ(ψ	NUM
ejpam-6056	180	32	,	,	PUNCT
ejpam-6056	180	33	qψ)dθ(ϕ,qψ	qψ)dθ(ϕ,qψ	NOUN
ejpam-6056	180	34	)	)	PUNCT
ejpam-6056	180	35	+	+	CCONJ
ejpam-6056	180	36	dθ(ϕ,qϕ)dθ(ψ	dθ(ϕ,qϕ)dθ(ψ	NUM
ejpam-6056	180	37	,	,	PUNCT
ejpam-6056	180	38	qϕ	qϕ	NOUN
ejpam-6056	180	39	)	)	PUNCT
ejpam-6056	180	40	dθ(ψ	dθ(ψ	PUNCT
ejpam-6056	180	41	,	,	PUNCT
ejpam-6056	180	42	qϕ	qϕ	PROPN
ejpam-6056	180	43	)	)	PUNCT
ejpam-6056	181	1	+	+	CCONJ
ejpam-6056	182	1	dθ(ϕ,qψ	dθ(ϕ,qψ	NOUN
ejpam-6056	182	2	)	)	PUNCT
ejpam-6056	182	3	,	,	PUNCT
ejpam-6056	182	4	and	and	CCONJ
ejpam-6056	182	5	µ1	µ1	PROPN
ejpam-6056	182	6	,	,	PUNCT
ejpam-6056	182	7	µ2	µ2	VERB
ejpam-6056	182	8	≥	≥	NOUN
ejpam-6056	182	9	0	0	NUM
ejpam-6056	182	10	with	with	ADP
ejpam-6056	182	11	µ1	µ1	PROPN
ejpam-6056	182	12	+	+	CCONJ
ejpam-6056	182	13	µ2	µ2	PROPN
ejpam-6056	182	14	<	<	X
ejpam-6056	182	15	1	1	NUM
ejpam-6056	182	16	.	.	PUNCT
ejpam-6056	182	17	(	(	PUNCT
ejpam-6056	182	18	ii	ii	NOUN
ejpam-6056	182	19	)	)	PUNCT
ejpam-6056	182	20	there	there	PRON
ejpam-6056	182	21	exist	exist	VERB
ejpam-6056	182	22	q	q	NOUN
ejpam-6056	182	23	,	,	PUNCT
ejpam-6056	182	24	u	u	NOUN
ejpam-6056	182	25	∈	∈	PROPN
ejpam-6056	183	1	[	[	X
ejpam-6056	183	2	0,υ	0,υ	X
ejpam-6056	183	3	]	]	X
ejpam-6056	183	4	such	such	ADJ
ejpam-6056	183	5	that∣∣∣∣∫	that∣∣∣∣∫	NOUN
ejpam-6056	183	6	q	q	X
ejpam-6056	183	7	0	0	NUM
ejpam-6056	183	8	k(q	k(q	PROPN
ejpam-6056	183	9	,	,	PUNCT
ejpam-6056	183	10	u	u	NOUN
ejpam-6056	183	11	)	)	PUNCT
ejpam-6056	183	12	∣∣∣∣τ	∣∣∣∣τ	VERB
ejpam-6056	183	13	du	du	PROPN
ejpam-6056	183	14	≤	≤	ADV
ejpam-6056	183	15	1	1	NUM
ejpam-6056	183	16	.	.	PUNCT
ejpam-6056	184	1	then	then	ADV
ejpam-6056	184	2	,	,	PUNCT
ejpam-6056	184	3	the	the	DET
ejpam-6056	184	4	volterra	volterra	NOUN
ejpam-6056	184	5	integral	integral	ADJ
ejpam-6056	184	6	inclusion	inclusion	NOUN
ejpam-6056	184	7	equation	equation	NOUN
ejpam-6056	184	8	has	have	VERB
ejpam-6056	184	9	a	a	DET
ejpam-6056	184	10	unique	unique	ADJ
ejpam-6056	184	11	solution	solution	NOUN
ejpam-6056	184	12	.	.	PUNCT
ejpam-6056	185	1	proof	proof	NOUN
ejpam-6056	185	2	.	.	PUNCT
ejpam-6056	186	1	from	from	ADP
ejpam-6056	186	2	the	the	DET
ejpam-6056	186	3	volterra	volterra	NOUN
ejpam-6056	186	4	integral	integral	ADJ
ejpam-6056	186	5	inclusion	inclusion	NOUN
ejpam-6056	186	6	equation	equation	NOUN
ejpam-6056	186	7	,	,	PUNCT
ejpam-6056	186	8	we	we	PRON
ejpam-6056	186	9	define	define	VERB
ejpam-6056	186	10	an	an	DET
ejpam-6056	186	11	operator	operator	NOUN
ejpam-6056	186	12	q	q	NOUN
ejpam-6056	187	1	:	:	PUNCT
ejpam-6056	187	2	ω	ω	PROPN
ejpam-6056	187	3	→	→	SYM
ejpam-6056	187	4	ω	ω	PROPN
ejpam-6056	187	5	by	by	ADP
ejpam-6056	187	6	:	:	PUNCT
ejpam-6056	187	7	qϕ(q	qϕ(q	NUM
ejpam-6056	187	8	)	)	PUNCT
ejpam-6056	187	9	∈	∈	PROPN
ejpam-6056	187	10	∫	∫	PROPN
ejpam-6056	187	11	υ	υ	PROPN
ejpam-6056	187	12	0	0	PROPN
ejpam-6056	187	13	k(q	k(q	PROPN
ejpam-6056	187	14	,	,	PUNCT
ejpam-6056	187	15	u)h(u	u)h(u	PROPN
ejpam-6056	187	16	,	,	PUNCT
ejpam-6056	187	17	ϕ(u	ϕ(u	NOUN
ejpam-6056	187	18	)	)	PUNCT
ejpam-6056	187	19	)	)	PUNCT
ejpam-6056	187	20	du+	du+	PROPN
ejpam-6056	187	21	ϑ(q	ϑ(q	PROPN
ejpam-6056	187	22	)	)	PUNCT
ejpam-6056	187	23	,	,	PUNCT
ejpam-6056	188	1	q	q	PROPN
ejpam-6056	188	2	∈	∈	PROPN
ejpam-6056	189	1	[	[	X
ejpam-6056	189	2	0,υ	0,υ	X
ejpam-6056	189	3	]	]	PUNCT
ejpam-6056	189	4	,	,	PUNCT
ejpam-6056	189	5	ϑ	ϑ	PROPN
ejpam-6056	189	6	∈	∈	PROPN
ejpam-6056	189	7	ω	ω	PROPN
ejpam-6056	189	8	.	.	PUNCT
ejpam-6056	190	1	thus	thus	ADV
ejpam-6056	190	2	,	,	PUNCT
ejpam-6056	190	3	solving	solve	VERB
ejpam-6056	190	4	eq	eq	ADP
ejpam-6056	190	5	.	.	PUNCT
ejpam-6056	191	1	(	(	PUNCT
ejpam-6056	191	2	3.1	3.1	NUM
ejpam-6056	191	3	)	)	PUNCT
ejpam-6056	191	4	is	be	AUX
ejpam-6056	191	5	equivalent	equivalent	ADJ
ejpam-6056	191	6	to	to	ADP
ejpam-6056	191	7	finding	find	VERB
ejpam-6056	191	8	a	a	DET
ejpam-6056	191	9	fixed	fix	VERB
ejpam-6056	191	10	point	point	NOUN
ejpam-6056	191	11	of	of	ADP
ejpam-6056	191	12	q.	q.	NOUN
ejpam-6056	191	13	for	for	ADP
ejpam-6056	191	14	all	all	DET
ejpam-6056	191	15	ϕ	ϕ	NOUN
ejpam-6056	191	16	,	,	PUNCT
ejpam-6056	191	17	ψ	ψ	PROPN
ejpam-6056	191	18	∈	∈	PROPN
ejpam-6056	191	19	ω	ω	PROPN
ejpam-6056	191	20	,	,	PUNCT
ejpam-6056	191	21	applying	apply	VERB
ejpam-6056	191	22	the	the	DET
ejpam-6056	191	23	given	give	VERB
ejpam-6056	191	24	conditions	condition	NOUN
ejpam-6056	191	25	and	and	CCONJ
ejpam-6056	191	26	using	use	VERB
ejpam-6056	191	27	the	the	DET
ejpam-6056	191	28	contraction	contraction	NOUN
ejpam-6056	191	29	property	property	NOUN
ejpam-6056	191	30	,	,	PUNCT
ejpam-6056	191	31	we	we	PRON
ejpam-6056	191	32	obtain	obtain	VERB
ejpam-6056	191	33	:	:	PUNCT
ejpam-6056	192	1	|qϕ−qψ|τ	|qϕ−qψ|τ	DET
ejpam-6056	192	2	≤	≤	NUM
ejpam-6056	192	3	∫	∫	NOUN
ejpam-6056	192	4	υ	υ	PROPN
ejpam-6056	192	5	0	0	PROPN
ejpam-6056	192	6	|k(q	|k(q	PROPN
ejpam-6056	192	7	,	,	PUNCT
ejpam-6056	192	8	u)|τ	u)|τ	PROPN
ejpam-6056	192	9	|h(u	|h(u	PROPN
ejpam-6056	192	10	,	,	PUNCT
ejpam-6056	192	11	ϕ(u))−h(u	ϕ(u))−h(u	PROPN
ejpam-6056	192	12	,	,	PUNCT
ejpam-6056	192	13	ψ(u))|τ	ψ(u))|τ	PROPN
ejpam-6056	192	14	du	du	PROPN
ejpam-6056	192	15	.	.	PROPN
ejpam-6056	192	16	from	from	ADP
ejpam-6056	192	17	this	this	PRON
ejpam-6056	192	18	,	,	PUNCT
ejpam-6056	192	19	we	we	PRON
ejpam-6056	192	20	conclude	conclude	VERB
ejpam-6056	192	21	:	:	PUNCT
ejpam-6056	192	22	dθ(qϕ,qψ	dθ(qϕ,qψ	NOUN
ejpam-6056	192	23	)	)	PUNCT
ejpam-6056	192	24	≤	≤	NOUN
ejpam-6056	192	25	mθ(ϕ	mθ(ϕ	NOUN
ejpam-6056	192	26	,	,	PUNCT
ejpam-6056	192	27	ψ	ψ	NOUN
ejpam-6056	192	28	)	)	PUNCT
ejpam-6056	192	29	.	.	PUNCT
ejpam-6056	193	1	by	by	ADP
ejpam-6056	193	2	invoking	invoke	VERB
ejpam-6056	193	3	theorem	theorem	ADJ
ejpam-6056	193	4	2.1	2.1	NUM
ejpam-6056	193	5	,	,	PUNCT
ejpam-6056	193	6	the	the	DET
ejpam-6056	193	7	operator	operator	NOUN
ejpam-6056	193	8	q	q	PUNCT
ejpam-6056	193	9	has	have	AUX
ejpam-6056	193	10	a	a	DET
ejpam-6056	193	11	unique	unique	ADJ
ejpam-6056	193	12	fixed	fix	VERB
ejpam-6056	193	13	point	point	NOUN
ejpam-6056	193	14	,	,	PUNCT
ejpam-6056	193	15	thereby	thereby	ADV
ejpam-6056	193	16	ensuring	ensure	VERB
ejpam-6056	193	17	that	that	SCONJ
ejpam-6056	193	18	eq	eq	ADP
ejpam-6056	193	19	.	.	PUNCT
ejpam-6056	193	20	(	(	PUNCT
ejpam-6056	193	21	3.1	3.1	NUM
ejpam-6056	193	22	)	)	PUNCT
ejpam-6056	193	23	admits	admit	VERB
ejpam-6056	193	24	a	a	DET
ejpam-6056	193	25	unique	unique	ADJ
ejpam-6056	193	26	solution	solution	NOUN
ejpam-6056	193	27	.	.	PUNCT
ejpam-6056	194	1	remark	remark	NOUN
ejpam-6056	194	2	2	2	NUM
ejpam-6056	194	3	.	.	PUNCT
ejpam-6056	195	1	although	although	SCONJ
ejpam-6056	195	2	the	the	DET
ejpam-6056	195	3	functions	function	NOUN
ejpam-6056	195	4	f	f	PROPN
ejpam-6056	195	5	and	and	CCONJ
ejpam-6056	195	6	k	k	PROPN
ejpam-6056	195	7	are	be	AUX
ejpam-6056	195	8	smooth	smooth	ADJ
ejpam-6056	195	9	in	in	ADP
ejpam-6056	195	10	this	this	DET
ejpam-6056	195	11	application	application	NOUN
ejpam-6056	195	12	,	,	PUNCT
ejpam-6056	195	13	the	the	DET
ejpam-6056	195	14	construction	construction	NOUN
ejpam-6056	195	15	allows	allow	VERB
ejpam-6056	195	16	for	for	ADP
ejpam-6056	195	17	generalized	generalized	ADJ
ejpam-6056	195	18	kernels	kernel	NOUN
ejpam-6056	195	19	,	,	PUNCT
ejpam-6056	195	20	e.g.	e.g.	ADV
ejpam-6056	195	21	,	,	PUNCT
ejpam-6056	195	22	discontinuous	discontinuous	ADJ
ejpam-6056	195	23	k(t	k(t	PROPN
ejpam-6056	195	24	,	,	PUNCT
ejpam-6056	195	25	u	u	NOUN
ejpam-6056	195	26	)	)	PUNCT
ejpam-6056	195	27	or	or	CCONJ
ejpam-6056	195	28	kernels	kernel	NOUN
ejpam-6056	195	29	with	with	ADP
ejpam-6056	195	30	memory	memory	NOUN
ejpam-6056	195	31	effects	effect	NOUN
ejpam-6056	195	32	.	.	PUNCT
ejpam-6056	196	1	this	this	PRON
ejpam-6056	196	2	makes	make	VERB
ejpam-6056	196	3	the	the	DET
ejpam-6056	196	4	framework	framework	NOUN
ejpam-6056	196	5	suitable	suitable	ADJ
ejpam-6056	196	6	for	for	ADP
ejpam-6056	196	7	nonlocal	nonlocal	ADJ
ejpam-6056	196	8	problems	problem	NOUN
ejpam-6056	196	9	in	in	ADP
ejpam-6056	196	10	viscoelasticity	viscoelasticity	NOUN
ejpam-6056	196	11	and	and	CCONJ
ejpam-6056	196	12	systems	system	NOUN
ejpam-6056	196	13	with	with	ADP
ejpam-6056	196	14	hereditary	hereditary	ADJ
ejpam-6056	196	15	characteristics	characteristic	NOUN
ejpam-6056	196	16	.	.	PUNCT
ejpam-6056	197	1	example	example	NOUN
ejpam-6056	197	2	6	6	NUM
ejpam-6056	197	3	.	.	PUNCT
ejpam-6056	197	4	consider	consider	VERB
ejpam-6056	197	5	the	the	DET
ejpam-6056	197	6	function	function	NOUN
ejpam-6056	197	7	space	space	NOUN
ejpam-6056	197	8	(	(	PUNCT
ejpam-6056	197	9	γ	γ	X
ejpam-6056	197	10	,	,	PUNCT
ejpam-6056	197	11	dγ	dγ	PROPN
ejpam-6056	197	12	)	)	PUNCT
ejpam-6056	197	13	,	,	PUNCT
ejpam-6056	197	14	where	where	SCONJ
ejpam-6056	197	15	γ	γ	PROPN
ejpam-6056	197	16	=	=	PUNCT
ejpam-6056	197	17	c([0,υ],r	c([0,υ],r	NOUN
ejpam-6056	197	18	)	)	PUNCT
ejpam-6056	197	19	is	be	AUX
ejpam-6056	197	20	the	the	DET
ejpam-6056	197	21	set	set	NOUN
ejpam-6056	197	22	of	of	ADP
ejpam-6056	197	23	continuous	continuous	ADJ
ejpam-6056	197	24	functions	function	NOUN
ejpam-6056	197	25	on	on	ADP
ejpam-6056	197	26	[	[	X
ejpam-6056	197	27	0,υ	0,υ	X
ejpam-6056	197	28	]	]	PUNCT
ejpam-6056	197	29	,	,	PUNCT
ejpam-6056	197	30	and	and	CCONJ
ejpam-6056	197	31	define	define	VERB
ejpam-6056	197	32	the	the	DET
ejpam-6056	197	33	extended	extended	ADJ
ejpam-6056	197	34	b	b	NOUN
ejpam-6056	197	35	-	-	ADJ
ejpam-6056	197	36	metric	metric	ADJ
ejpam-6056	197	37	as	as	ADP
ejpam-6056	197	38	:	:	PUNCT
ejpam-6056	197	39	dγ(ϕ	dγ(ϕ	NOUN
ejpam-6056	197	40	,	,	PUNCT
ejpam-6056	197	41	ψ	ψ	NOUN
ejpam-6056	197	42	)	)	PUNCT
ejpam-6056	197	43	=	=	SYM
ejpam-6056	197	44	sup	sup	NOUN
ejpam-6056	197	45	q∈[0,υ	q∈[0,υ	NOUN
ejpam-6056	197	46	]	]	X
ejpam-6056	197	47	|ϕ(q)−	|ϕ(q)−	X
ejpam-6056	197	48	ψ(q)|	ψ(q)|	PROPN
ejpam-6056	197	49	.	.	PUNCT
ejpam-6056	198	1	define	define	VERB
ejpam-6056	198	2	the	the	DET
ejpam-6056	198	3	control	control	NOUN
ejpam-6056	198	4	function	function	NOUN
ejpam-6056	198	5	θ	θ	NOUN
ejpam-6056	198	6	:	:	PUNCT
ejpam-6056	198	7	γ×	γ×	PUNCT
ejpam-6056	198	8	γ	γ	X
ejpam-6056	198	9	→	→	SYM
ejpam-6056	198	10	[	[	X
ejpam-6056	198	11	1,∞	1,∞	NUM
ejpam-6056	198	12	)	)	PUNCT
ejpam-6056	198	13	by	by	ADP
ejpam-6056	198	14	:	:	PUNCT
ejpam-6056	198	15	θ(ϕ	θ(ϕ	PROPN
ejpam-6056	198	16	,	,	PUNCT
ejpam-6056	198	17	ψ	ψ	NOUN
ejpam-6056	198	18	)	)	PUNCT
ejpam-6056	198	19	=	=	SYM
ejpam-6056	198	20	1	1	NUM
ejpam-6056	198	21	+	+	NUM
ejpam-6056	198	22	sup	sup	NUM
ejpam-6056	198	23	q∈[0,υ	q∈[0,υ	NOUN
ejpam-6056	198	24	]	]	PUNCT
ejpam-6056	198	25	|ϕ(q	|ϕ(q	PROPN
ejpam-6056	198	26	)	)	PUNCT
ejpam-6056	198	27	+	+	PUNCT
ejpam-6056	198	28	ψ(q)|	ψ(q)|	ADJ
ejpam-6056	198	29	.	.	PUNCT
ejpam-6056	199	1	let	let	VERB
ejpam-6056	199	2	the	the	DET
ejpam-6056	199	3	integral	integral	ADJ
ejpam-6056	199	4	operator	operator	NOUN
ejpam-6056	199	5	q	q	NOUN
ejpam-6056	199	6	:	:	PUNCT
ejpam-6056	199	7	γ	γ	X
ejpam-6056	199	8	→	→	SYM
ejpam-6056	199	9	γ	γ	X
ejpam-6056	199	10	be	be	AUX
ejpam-6056	199	11	defined	define	VERB
ejpam-6056	199	12	by	by	ADP
ejpam-6056	199	13	:	:	PUNCT
ejpam-6056	199	14	qϕ(q	qϕ(q	NUM
ejpam-6056	199	15	)	)	PUNCT
ejpam-6056	200	1	=	=	SYM
ejpam-6056	200	2	∫	∫	PROPN
ejpam-6056	200	3	υ	υ	PROPN
ejpam-6056	200	4	0	0	PROPN
ejpam-6056	200	5	k(q	k(q	PROPN
ejpam-6056	200	6	,	,	PUNCT
ejpam-6056	200	7	u)h(u	u)h(u	PROPN
ejpam-6056	200	8	,	,	PUNCT
ejpam-6056	200	9	ϕ(u	ϕ(u	NOUN
ejpam-6056	200	10	)	)	PUNCT
ejpam-6056	200	11	)	)	PUNCT
ejpam-6056	201	1	du+	du+	PROPN
ejpam-6056	201	2	ϑ(q	ϑ(q	PROPN
ejpam-6056	201	3	)	)	PUNCT
ejpam-6056	201	4	,	,	PUNCT
ejpam-6056	201	5	h.	h.	PROPN
ejpam-6056	201	6	qawaqneh	qawaqneh	PROPN
ejpam-6056	201	7	,	,	PUNCT
ejpam-6056	201	8	j.m	j.m	PROPN
ejpam-6056	201	9	.	.	PROPN
ejpam-6056	201	10	al	al	PROPN
ejpam-6056	201	11	-	-	PUNCT
ejpam-6056	201	12	musannef	musannef	PROPN
ejpam-6056	201	13	,	,	PUNCT
ejpam-6056	201	14	h.	h.	PROPN
ejpam-6056	201	15	alsamir	alsamir	PROPN
ejpam-6056	201	16	/	/	SYM
ejpam-6056	201	17	eur	eur	PROPN
ejpam-6056	201	18	.	.	PUNCT
ejpam-6056	202	1	j.	j.	PROPN
ejpam-6056	202	2	pure	pure	PROPN
ejpam-6056	202	3	appl	appl	PROPN
ejpam-6056	202	4	.	.	PROPN
ejpam-6056	202	5	math	math	PROPN
ejpam-6056	202	6	,	,	PUNCT
ejpam-6056	202	7	18	18	NUM
ejpam-6056	202	8	(	(	PUNCT
ejpam-6056	202	9	3	3	NUM
ejpam-6056	202	10	)	)	PUNCT
ejpam-6056	202	11	(	(	PUNCT
ejpam-6056	202	12	2025	2025	NUM
ejpam-6056	202	13	)	)	PUNCT
ejpam-6056	202	14	,	,	PUNCT
ejpam-6056	202	15	6056	6056	NUM
ejpam-6056	202	16	10	10	NUM
ejpam-6056	202	17	of	of	ADP
ejpam-6056	202	18	16	16	NUM
ejpam-6056	202	19	where	where	SCONJ
ejpam-6056	202	20	:	:	PUNCT
ejpam-6056	202	21	k(q	k(q	PROPN
ejpam-6056	202	22	,	,	PUNCT
ejpam-6056	202	23	u	u	NOUN
ejpam-6056	202	24	)	)	PUNCT
ejpam-6056	202	25	=	=	PUNCT
ejpam-6056	203	1	e−(q−u)2	e−(q−u)2	ADV
ejpam-6056	203	2	,	,	PUNCT
ejpam-6056	203	3	and	and	CCONJ
ejpam-6056	203	4	h(u	h(u	PROPN
ejpam-6056	203	5	,	,	PUNCT
ejpam-6056	203	6	ϕ(u	ϕ(u	PROPN
ejpam-6056	203	7	)	)	PUNCT
ejpam-6056	203	8	)	)	PUNCT
ejpam-6056	203	9	=	=	PUNCT
ejpam-6056	203	10	ϕ(u	ϕ(u	NOUN
ejpam-6056	203	11	)	)	PUNCT
ejpam-6056	203	12	1	1	NUM
ejpam-6056	204	1	+	+	CCONJ
ejpam-6056	204	2	|ϕ(u)|	|ϕ(u)|	PROPN
ejpam-6056	204	3	,	,	PUNCT
ejpam-6056	204	4	and	and	CCONJ
ejpam-6056	204	5	for	for	ADP
ejpam-6056	204	6	numerical	numerical	ADJ
ejpam-6056	204	7	tests	test	NOUN
ejpam-6056	204	8	,	,	PUNCT
ejpam-6056	204	9	let	let	VERB
ejpam-6056	204	10	:	:	PUNCT
ejpam-6056	204	11	ϑ(q	ϑ(q	NUM
ejpam-6056	204	12	)	)	PUNCT
ejpam-6056	204	13	=	=	PUNCT
ejpam-6056	204	14	sin(q	sin(q	PROPN
ejpam-6056	204	15	)	)	PUNCT
ejpam-6056	204	16	.	.	PUNCT
ejpam-6056	205	1	let	let	VERB
ejpam-6056	205	2	us	we	PRON
ejpam-6056	205	3	fix	fix	VERB
ejpam-6056	205	4	µ1	µ1	NOUN
ejpam-6056	205	5	=	=	SYM
ejpam-6056	205	6	0.75	0.75	NUM
ejpam-6056	205	7	.	.	PUNCT
ejpam-6056	206	1	for	for	ADP
ejpam-6056	206	2	two	two	NUM
ejpam-6056	206	3	functions	function	NOUN
ejpam-6056	206	4	ϕ	ϕ	NOUN
ejpam-6056	206	5	,	,	PUNCT
ejpam-6056	206	6	ψ	ψ	X
ejpam-6056	206	7	∈	∈	PROPN
ejpam-6056	206	8	γ	γ	X
ejpam-6056	206	9	,	,	PUNCT
ejpam-6056	206	10	define	define	VERB
ejpam-6056	206	11	the	the	DET
ejpam-6056	206	12	following	follow	VERB
ejpam-6056	206	13	two	two	NUM
ejpam-6056	206	14	surfaces	surface	NOUN
ejpam-6056	206	15	over	over	ADP
ejpam-6056	206	16	the	the	DET
ejpam-6056	206	17	domain	domain	NOUN
ejpam-6056	207	1	q	q	X
ejpam-6056	207	2	∈	∈	PROPN
ejpam-6056	208	1	[	[	X
ejpam-6056	208	2	0,υ	0,υ	X
ejpam-6056	208	3	]	]	X
ejpam-6056	208	4	:	:	PUNCT
ejpam-6056	208	5	z1(q	z1(q	X
ejpam-6056	208	6	)	)	PUNCT
ejpam-6056	208	7	=	=	SYM
ejpam-6056	208	8	dγ(qϕ,qψ	dγ(qϕ,qψ	ADJ
ejpam-6056	208	9	)	)	PUNCT
ejpam-6056	208	10	,	,	PUNCT
ejpam-6056	208	11	z2(q	z2(q	NUM
ejpam-6056	208	12	)	)	PUNCT
ejpam-6056	208	13	=	=	SYM
ejpam-6056	208	14	µ1	µ1	NOUN
ejpam-6056	208	15	·	·	PUNCT
ejpam-6056	208	16	dγ(ϕ	dγ(ϕ	X
ejpam-6056	208	17	,	,	PUNCT
ejpam-6056	208	18	ψ	ψ	NOUN
ejpam-6056	208	19	)	)	PUNCT
ejpam-6056	208	20	.	.	PUNCT
ejpam-6056	209	1	table	table	NOUN
ejpam-6056	209	2	2	2	NUM
ejpam-6056	209	3	:	:	PUNCT
ejpam-6056	209	4	numerical	numerical	ADJ
ejpam-6056	209	5	verification	verification	NOUN
ejpam-6056	209	6	of	of	ADP
ejpam-6056	209	7	q(ϕ	q(ϕ	PROPN
ejpam-6056	209	8	)	)	PUNCT
ejpam-6056	209	9	and	and	CCONJ
ejpam-6056	209	10	contraction	contraction	NOUN
ejpam-6056	209	11	condition	condition	NOUN
ejpam-6056	209	12	q	q	X
ejpam-6056	209	13	ϕ(q	ϕ(q	PROPN
ejpam-6056	209	14	)	)	PUNCT
ejpam-6056	209	15	qϕ(q	qϕ(q	PRON
ejpam-6056	209	16	)	)	PUNCT
ejpam-6056	209	17	qψ(q	qψ(q	NOUN
ejpam-6056	209	18	)	)	PUNCT
ejpam-6056	209	19	dγ(qϕ,qψ	dγ(qϕ,qψ	NOUN
ejpam-6056	209	20	)	)	PUNCT
ejpam-6056	209	21	µ1dγ(ϕ	µ1dγ(ϕ	PROPN
ejpam-6056	209	22	,	,	PUNCT
ejpam-6056	209	23	ψ	ψ	NOUN
ejpam-6056	209	24	)	)	PUNCT
ejpam-6056	209	25	0.1	0.1	NUM
ejpam-6056	209	26	0.05	0.05	NUM
ejpam-6056	209	27	0.120	0.120	NUM
ejpam-6056	209	28	0.110	0.110	NUM
ejpam-6056	209	29	0.010	0.010	NUM
ejpam-6056	209	30	0.0075	0.0075	NUM
ejpam-6056	209	31	0.3	0.3	NUM
ejpam-6056	209	32	0.15	0.15	NUM
ejpam-6056	209	33	0.180	0.180	NUM
ejpam-6056	209	34	0.170	0.170	NUM
ejpam-6056	209	35	0.010	0.010	NUM
ejpam-6056	209	36	0.01125	0.01125	NUM
ejpam-6056	209	37	0.5	0.5	NUM
ejpam-6056	209	38	0.25	0.25	NUM
ejpam-6056	209	39	0.250	0.250	NUM
ejpam-6056	209	40	0.240	0.240	NUM
ejpam-6056	209	41	0.010	0.010	NUM
ejpam-6056	209	42	0.01500	0.01500	NUM
ejpam-6056	210	1	0.7	0.7	NUM
ejpam-6056	210	2	0.35	0.35	NUM
ejpam-6056	210	3	0.320	0.320	NUM
ejpam-6056	210	4	0.310	0.310	NUM
ejpam-6056	210	5	0.010	0.010	NUM
ejpam-6056	210	6	0.01750	0.01750	NUM
ejpam-6056	210	7	0.2	0.2	NUM
ejpam-6056	210	8	0.4	0.4	NUM
ejpam-6056	210	9	0.6	0.6	NUM
ejpam-6056	210	10	5	5	NUM
ejpam-6056	210	11	·	·	SYM
ejpam-6056	210	12	10−2	10−2	NUM
ejpam-6056	210	13	0.1	0.1	NUM
ejpam-6056	210	14	0.15	0.15	NUM
ejpam-6056	210	15	0.2	0.2	NUM
ejpam-6056	210	16	0.25	0.25	NUM
ejpam-6056	210	17	0.3	0.3	NUM
ejpam-6056	210	18	0.35	0.35	NUM
ejpam-6056	210	19	0	0	NUM
ejpam-6056	210	20	0.1	0.1	NUM
ejpam-6056	210	21	0.2	0.2	NUM
ejpam-6056	210	22	q	q	NOUN
ejpam-6056	210	23	ϕ(q	ϕ(q	PROPN
ejpam-6056	210	24	)	)	PUNCT
ejpam-6056	210	25	z	z	NOUN
ejpam-6056	210	26	surfaces	surface	NOUN
ejpam-6056	210	27	of	of	ADP
ejpam-6056	210	28	dγ(qϕ,qψ	dγ(qϕ,qψ	PROPN
ejpam-6056	210	29	)	)	PUNCT
ejpam-6056	210	30	and	and	CCONJ
ejpam-6056	210	31	µ1dγ(ϕ	µ1dγ(ϕ	PROPN
ejpam-6056	210	32	,	,	PUNCT
ejpam-6056	210	33	ψ	ψ	NOUN
ejpam-6056	210	34	)	)	PUNCT
ejpam-6056	210	35	z1(q	z1(q	PROPN
ejpam-6056	210	36	,	,	PUNCT
ejpam-6056	210	37	ϕ	ϕ	NOUN
ejpam-6056	210	38	)	)	PUNCT
ejpam-6056	210	39	=	=	SYM
ejpam-6056	210	40	dγ(qϕ,qψ	dγ(qϕ,qψ	ADJ
ejpam-6056	210	41	)	)	PUNCT
ejpam-6056	210	42	z2(q	z2(q	NUM
ejpam-6056	210	43	,	,	PUNCT
ejpam-6056	210	44	ϕ	ϕ	NOUN
ejpam-6056	210	45	)	)	PUNCT
ejpam-6056	210	46	=	=	PUNCT
ejpam-6056	210	47	µ1dγ(ϕ	µ1dγ(ϕ	NOUN
ejpam-6056	210	48	,	,	PUNCT
ejpam-6056	210	49	ψ	ψ	NOUN
ejpam-6056	210	50	)	)	PUNCT
ejpam-6056	210	51	figure	figure	NOUN
ejpam-6056	210	52	2	2	NUM
ejpam-6056	210	53	:	:	PUNCT
ejpam-6056	210	54	surface	surface	NOUN
ejpam-6056	210	55	plots	plot	NOUN
ejpam-6056	210	56	of	of	ADP
ejpam-6056	210	57	the	the	DET
ejpam-6056	210	58	contraction	contraction	NOUN
ejpam-6056	210	59	condition	condition	NOUN
ejpam-6056	210	60	components	component	NOUN
ejpam-6056	210	61	these	these	DET
ejpam-6056	210	62	results	result	NOUN
ejpam-6056	210	63	confirm	confirm	VERB
ejpam-6056	210	64	that	that	SCONJ
ejpam-6056	210	65	dγ(qϕ,qψ	dγ(qϕ,qψ	NOUN
ejpam-6056	210	66	)	)	PUNCT
ejpam-6056	210	67	≤	≤	NOUN
ejpam-6056	210	68	µ1dγ(ϕ	µ1dγ(ϕ	PROPN
ejpam-6056	210	69	,	,	PUNCT
ejpam-6056	210	70	ψ	ψ	NOUN
ejpam-6056	210	71	)	)	PUNCT
ejpam-6056	210	72	,	,	PUNCT
ejpam-6056	210	73	satisfying	satisfy	VERB
ejpam-6056	210	74	the	the	DET
ejpam-6056	210	75	contraction	contraction	NOUN
ejpam-6056	210	76	condition	condition	NOUN
ejpam-6056	210	77	.	.	PUNCT
ejpam-6056	211	1	hence	hence	ADV
ejpam-6056	211	2	,	,	PUNCT
ejpam-6056	211	3	by	by	ADP
ejpam-6056	211	4	theorem	theorem	NOUN
ejpam-6056	211	5	3.1	3.1	NUM
ejpam-6056	211	6	,	,	PUNCT
ejpam-6056	211	7	the	the	DET
ejpam-6056	211	8	associated	associated	ADJ
ejpam-6056	211	9	integral	integral	ADJ
ejpam-6056	211	10	inclusion	inclusion	NOUN
ejpam-6056	211	11	problem	problem	NOUN
ejpam-6056	211	12	has	have	VERB
ejpam-6056	211	13	a	a	DET
ejpam-6056	211	14	unique	unique	ADJ
ejpam-6056	211	15	solution	solution	NOUN
ejpam-6056	211	16	.	.	PUNCT
ejpam-6056	212	1	h.	h.	PROPN
ejpam-6056	212	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	212	3	,	,	PUNCT
ejpam-6056	212	4	j.m	j.m	PROPN
ejpam-6056	212	5	.	.	PROPN
ejpam-6056	212	6	al	al	PROPN
ejpam-6056	212	7	-	-	PUNCT
ejpam-6056	212	8	musannef	musannef	PROPN
ejpam-6056	212	9	,	,	PUNCT
ejpam-6056	212	10	h.	h.	PROPN
ejpam-6056	212	11	alsamir	alsamir	PROPN
ejpam-6056	212	12	/	/	SYM
ejpam-6056	212	13	eur	eur	PROPN
ejpam-6056	212	14	.	.	PUNCT
ejpam-6056	213	1	j.	j.	PROPN
ejpam-6056	213	2	pure	pure	PROPN
ejpam-6056	213	3	appl	appl	PROPN
ejpam-6056	213	4	.	.	PROPN
ejpam-6056	213	5	math	math	PROPN
ejpam-6056	213	6	,	,	PUNCT
ejpam-6056	213	7	18	18	NUM
ejpam-6056	213	8	(	(	PUNCT
ejpam-6056	213	9	3	3	NUM
ejpam-6056	213	10	)	)	PUNCT
ejpam-6056	213	11	(	(	PUNCT
ejpam-6056	213	12	2025	2025	NUM
ejpam-6056	213	13	)	)	PUNCT
ejpam-6056	213	14	,	,	PUNCT
ejpam-6056	213	15	6056	6056	NUM
ejpam-6056	213	16	11	11	NUM
ejpam-6056	213	17	of	of	ADP
ejpam-6056	213	18	16	16	NUM
ejpam-6056	213	19	4.2	4.2	NUM
ejpam-6056	213	20	.	.	PUNCT
ejpam-6056	214	1	existence	existence	NOUN
ejpam-6056	214	2	and	and	CCONJ
ejpam-6056	214	3	uniqueness	uniqueness	NOUN
ejpam-6056	214	4	of	of	ADP
ejpam-6056	214	5	a	a	DET
ejpam-6056	214	6	solution	solution	NOUN
ejpam-6056	214	7	for	for	ADP
ejpam-6056	214	8	the	the	DET
ejpam-6056	214	9	epidemic	epidemic	NOUN
ejpam-6056	214	10	model	model	NOUN
ejpam-6056	214	11	this	this	DET
ejpam-6056	214	12	subsection	subsection	NOUN
ejpam-6056	214	13	establishes	establish	VERB
ejpam-6056	214	14	the	the	DET
ejpam-6056	214	15	existence	existence	NOUN
ejpam-6056	214	16	and	and	CCONJ
ejpam-6056	214	17	uniqueness	uniqueness	NOUN
ejpam-6056	214	18	of	of	ADP
ejpam-6056	214	19	a	a	DET
ejpam-6056	214	20	solution	solution	NOUN
ejpam-6056	214	21	for	for	ADP
ejpam-6056	214	22	an	an	DET
ejpam-6056	214	23	epidemic	epidemic	NOUN
ejpam-6056	214	24	model	model	NOUN
ejpam-6056	214	25	using	use	VERB
ejpam-6056	214	26	the	the	DET
ejpam-6056	214	27	framework	framework	NOUN
ejpam-6056	214	28	of	of	ADP
ejpam-6056	214	29	ebms	ebms	NOUN
ejpam-6056	214	30	and	and	CCONJ
ejpam-6056	214	31	volterra	volterra	PROPN
ejpam-6056	214	32	integral	integral	ADJ
ejpam-6056	214	33	inclusion	inclusion	NOUN
ejpam-6056	214	34	.	.	PUNCT
ejpam-6056	215	1	we	we	PRON
ejpam-6056	215	2	also	also	ADV
ejpam-6056	215	3	explore	explore	VERB
ejpam-6056	215	4	alternative	alternative	ADJ
ejpam-6056	215	5	contraction	contraction	NOUN
ejpam-6056	215	6	conditions	condition	NOUN
ejpam-6056	215	7	and	and	CCONJ
ejpam-6056	215	8	numerical	numerical	ADJ
ejpam-6056	215	9	verification	verification	NOUN
ejpam-6056	215	10	techniques	technique	NOUN
ejpam-6056	215	11	.	.	PUNCT
ejpam-6056	216	1	theorem	theorem	NOUN
ejpam-6056	216	2	3	3	X
ejpam-6056	216	3	.	.	PUNCT
ejpam-6056	217	1	let	let	AUX
ejpam-6056	217	2	(	(	PUNCT
ejpam-6056	217	3	γ	γ	PROPN
ejpam-6056	217	4	,	,	PUNCT
ejpam-6056	217	5	dθ	dθ	PROPN
ejpam-6056	217	6	)	)	PUNCT
ejpam-6056	217	7	be	be	AUX
ejpam-6056	217	8	a	a	DET
ejpam-6056	217	9	complete	complete	ADJ
ejpam-6056	217	10	ebms	ebms	NOUN
ejpam-6056	217	11	.	.	PUNCT
ejpam-6056	218	1	consider	consider	VERB
ejpam-6056	218	2	the	the	DET
ejpam-6056	218	3	epidemic	epidemic	NOUN
ejpam-6056	218	4	model	model	NOUN
ejpam-6056	218	5	given	give	VERB
ejpam-6056	218	6	by	by	ADP
ejpam-6056	218	7	the	the	DET
ejpam-6056	218	8	volterra	volterra	NOUN
ejpam-6056	218	9	integral	integral	ADJ
ejpam-6056	218	10	inclusion	inclusion	NOUN
ejpam-6056	218	11	:	:	PUNCT
ejpam-6056	219	1	i(t	i(t	PROPN
ejpam-6056	219	2	)	)	PUNCT
ejpam-6056	219	3	∈	∈	PROPN
ejpam-6056	219	4	∫	∫	PROPN
ejpam-6056	219	5	t	t	PROPN
ejpam-6056	219	6	0	0	NUM
ejpam-6056	220	1	k(t	k(t	PROPN
ejpam-6056	220	2	,	,	PUNCT
ejpam-6056	220	3	u)h(u	u)h(u	PROPN
ejpam-6056	220	4	,	,	PUNCT
ejpam-6056	220	5	i(u	i(u	PROPN
ejpam-6056	220	6	)	)	PUNCT
ejpam-6056	220	7	)	)	PUNCT
ejpam-6056	221	1	du+θ(t	du+θ(t	PROPN
ejpam-6056	221	2	)	)	PUNCT
ejpam-6056	221	3	,	,	PUNCT
ejpam-6056	221	4	t	t	PROPN
ejpam-6056	221	5	∈	∈	PROPN
ejpam-6056	222	1	[	[	X
ejpam-6056	222	2	0	0	NUM
ejpam-6056	222	3	,	,	PUNCT
ejpam-6056	222	4	t	t	X
ejpam-6056	222	5	]	]	PUNCT
ejpam-6056	222	6	,	,	PUNCT
ejpam-6056	222	7	θ	θ	PROPN
ejpam-6056	222	8	∈	∈	PROPN
ejpam-6056	222	9	ω	ω	PROPN
ejpam-6056	222	10	.	.	PUNCT
ejpam-6056	223	1	for	for	ADP
ejpam-6056	223	2	all	all	DET
ejpam-6056	223	3	i	i	PROPN
ejpam-6056	223	4	,	,	PUNCT
ejpam-6056	223	5	j	j	PROPN
ejpam-6056	223	6	∈	∈	PROPN
ejpam-6056	223	7	c([0	c([0	PROPN
ejpam-6056	223	8	,	,	PUNCT
ejpam-6056	223	9	t	t	X
ejpam-6056	223	10	]	]	PUNCT
ejpam-6056	223	11	,	,	PUNCT
ejpam-6056	223	12	r	r	NOUN
ejpam-6056	223	13	)	)	PUNCT
ejpam-6056	223	14	,	,	PUNCT
ejpam-6056	223	15	assume	assume	VERB
ejpam-6056	223	16	:	:	PUNCT
ejpam-6056	223	17	(	(	PUNCT
ejpam-6056	223	18	i	i	NOUN
ejpam-6056	223	19	)	)	PUNCT
ejpam-6056	223	20	continuity	continuity	NOUN
ejpam-6056	223	21	and	and	CCONJ
ejpam-6056	223	22	lipschitz	lipschitz	NOUN
ejpam-6056	223	23	condition	condition	NOUN
ejpam-6056	223	24	:	:	PUNCT
ejpam-6056	223	25	there	there	PRON
ejpam-6056	223	26	exists	exist	VERB
ejpam-6056	223	27	a	a	DET
ejpam-6056	223	28	continuous	continuous	ADJ
ejpam-6056	223	29	function	function	NOUN
ejpam-6056	223	30	h(t	h(t	PROPN
ejpam-6056	223	31	,	,	PUNCT
ejpam-6056	223	32	i	i	NOUN
ejpam-6056	223	33	)	)	PUNCT
ejpam-6056	223	34	such	such	ADJ
ejpam-6056	223	35	that	that	SCONJ
ejpam-6056	223	36	:	:	PUNCT
ejpam-6056	223	37	sup	sup	PROPN
ejpam-6056	223	38	|h(t	|h(t	PROPN
ejpam-6056	223	39	,	,	PUNCT
ejpam-6056	223	40	u	u	NOUN
ejpam-6056	223	41	,	,	PUNCT
ejpam-6056	223	42	i(u))−h(t	i(u))−h(t	ADV
ejpam-6056	223	43	,	,	PUNCT
ejpam-6056	223	44	u	u	NOUN
ejpam-6056	223	45	,	,	PUNCT
ejpam-6056	223	46	j(u))|τ	j(u))|τ	PROPN
ejpam-6056	223	47	≤	≤	NUM
ejpam-6056	223	48	mθ(i	mθ(i	VERB
ejpam-6056	223	49	,	,	PUNCT
ejpam-6056	223	50	j	j	PROPN
ejpam-6056	223	51	)	)	PUNCT
ejpam-6056	223	52	t	t	PROPN
ejpam-6056	223	53	,	,	PUNCT
ejpam-6056	223	54	where	where	SCONJ
ejpam-6056	223	55	:	:	PUNCT
ejpam-6056	223	56	mθ(i	mθ(i	NUM
ejpam-6056	223	57	,	,	PUNCT
ejpam-6056	223	58	j	j	NOUN
ejpam-6056	223	59	)	)	PUNCT
ejpam-6056	223	60	=	=	SYM
ejpam-6056	223	61	µ1dθ(i	µ1dθ(i	PROPN
ejpam-6056	223	62	,	,	PUNCT
ejpam-6056	223	63	j	j	NOUN
ejpam-6056	223	64	)	)	PUNCT
ejpam-6056	224	1	+	+	CCONJ
ejpam-6056	224	2	µ2	µ2	PROPN
ejpam-6056	224	3	dθ(j	dθ(j	PUNCT
ejpam-6056	224	4	,	,	PUNCT
ejpam-6056	224	5	qj)dθ(i	qj)dθ(i	PROPN
ejpam-6056	224	6	,	,	PUNCT
ejpam-6056	224	7	qj	qj	PROPN
ejpam-6056	224	8	)	)	PUNCT
ejpam-6056	224	9	+	+	CCONJ
ejpam-6056	224	10	dθ(i	dθ(i	PROPN
ejpam-6056	224	11	,	,	PUNCT
ejpam-6056	224	12	qi)dθ(j	qi)dθ(j	PROPN
ejpam-6056	224	13	,	,	PUNCT
ejpam-6056	224	14	qi	qi	PROPN
ejpam-6056	224	15	)	)	PUNCT
ejpam-6056	224	16	dθ(j	dθ(j	NOUN
ejpam-6056	224	17	,	,	PUNCT
ejpam-6056	224	18	qi	qi	PROPN
ejpam-6056	224	19	)	)	PUNCT
ejpam-6056	224	20	+	+	CCONJ
ejpam-6056	224	21	dθ(i	dθ(i	NUM
ejpam-6056	224	22	,	,	PUNCT
ejpam-6056	224	23	qj	qj	PROPN
ejpam-6056	224	24	)	)	PUNCT
ejpam-6056	224	25	.	.	PUNCT
ejpam-6056	225	1	here	here	ADV
ejpam-6056	225	2	,	,	PUNCT
ejpam-6056	225	3	µ1	µ1	PROPN
ejpam-6056	225	4	,	,	PUNCT
ejpam-6056	225	5	µ2	µ2	VERB
ejpam-6056	225	6	≥	≥	NOUN
ejpam-6056	225	7	0	0	NUM
ejpam-6056	225	8	and	and	CCONJ
ejpam-6056	225	9	µ1	µ1	PROPN
ejpam-6056	225	10	+	+	CCONJ
ejpam-6056	225	11	µ2	µ2	PROPN
ejpam-6056	225	12	<	<	X
ejpam-6056	225	13	1	1	NUM
ejpam-6056	225	14	.	.	PUNCT
ejpam-6056	225	15	(	(	PUNCT
ejpam-6056	225	16	ii	ii	NOUN
ejpam-6056	225	17	)	)	PUNCT
ejpam-6056	225	18	bounded	bounded	ADJ
ejpam-6056	225	19	kernel	kernel	PROPN
ejpam-6056	225	20	condition	condition	NOUN
ejpam-6056	225	21	:	:	PUNCT
ejpam-6056	225	22	the	the	DET
ejpam-6056	225	23	kernel	kernel	PROPN
ejpam-6056	225	24	function	function	VERB
ejpam-6056	225	25	satisfies:∣∣∣∣∫	satisfies:∣∣∣∣∫	PROPN
ejpam-6056	225	26	t	t	PROPN
ejpam-6056	225	27	0	0	PUNCT
ejpam-6056	226	1	k(t	k(t	PROPN
ejpam-6056	226	2	,	,	PUNCT
ejpam-6056	226	3	u	u	NOUN
ejpam-6056	226	4	)	)	PUNCT
ejpam-6056	226	5	du	du	PROPN
ejpam-6056	226	6	∣∣∣∣τ	∣∣∣∣τ	NOUN
ejpam-6056	226	7	≤	≤	NUM
ejpam-6056	226	8	1	1	NUM
ejpam-6056	226	9	.	.	PUNCT
ejpam-6056	227	1	(	(	PUNCT
ejpam-6056	227	2	iii	iii	NOUN
ejpam-6056	227	3	)	)	PUNCT
ejpam-6056	227	4	alternative	alternative	ADJ
ejpam-6056	227	5	contraction	contraction	NOUN
ejpam-6056	227	6	condition	condition	NOUN
ejpam-6056	227	7	:	:	PUNCT
ejpam-6056	227	8	instead	instead	ADV
ejpam-6056	227	9	of	of	ADP
ejpam-6056	227	10	the	the	DET
ejpam-6056	227	11	standard	standard	ADJ
ejpam-6056	227	12	contraction	contraction	NOUN
ejpam-6056	227	13	condition	condition	NOUN
ejpam-6056	227	14	,	,	PUNCT
ejpam-6056	227	15	we	we	PRON
ejpam-6056	227	16	consider	consider	VERB
ejpam-6056	227	17	a	a	DET
ejpam-6056	227	18	max	max	NOUN
ejpam-6056	227	19	-	-	PUNCT
ejpam-6056	227	20	based	base	VERB
ejpam-6056	227	21	contraction	contraction	NOUN
ejpam-6056	227	22	:	:	PUNCT
ejpam-6056	227	23	dθ(qi	dθ(qi	PROPN
ejpam-6056	227	24	,	,	PUNCT
ejpam-6056	227	25	qj	qj	PROPN
ejpam-6056	227	26	)	)	PUNCT
ejpam-6056	227	27	≤	≤	PROPN
ejpam-6056	227	28	µ1dθ(i	µ1dθ(i	PROPN
ejpam-6056	227	29	,	,	PUNCT
ejpam-6056	227	30	j	j	NOUN
ejpam-6056	227	31	)	)	PUNCT
ejpam-6056	228	1	+	+	CCONJ
ejpam-6056	228	2	µ2max{dθ(i	µ2max{dθ(i	ADJ
ejpam-6056	228	3	,	,	PUNCT
ejpam-6056	228	4	qi	qi	PROPN
ejpam-6056	228	5	)	)	PUNCT
ejpam-6056	228	6	,	,	PUNCT
ejpam-6056	228	7	dθ(j	dθ(j	NOUN
ejpam-6056	228	8	,	,	PUNCT
ejpam-6056	228	9	qj	qj	PROPN
ejpam-6056	228	10	)	)	PUNCT
ejpam-6056	228	11	}	}	PUNCT
ejpam-6056	228	12	.	.	PUNCT
ejpam-6056	229	1	then	then	ADV
ejpam-6056	229	2	,	,	PUNCT
ejpam-6056	229	3	the	the	DET
ejpam-6056	229	4	epidemic	epidemic	NOUN
ejpam-6056	229	5	model	model	NOUN
ejpam-6056	229	6	has	have	VERB
ejpam-6056	229	7	a	a	DET
ejpam-6056	229	8	unique	unique	ADJ
ejpam-6056	229	9	solution	solution	NOUN
ejpam-6056	229	10	.	.	PUNCT
ejpam-6056	230	1	proof	proof	NOUN
ejpam-6056	230	2	.	.	PUNCT
ejpam-6056	231	1	define	define	VERB
ejpam-6056	231	2	an	an	DET
ejpam-6056	231	3	operator	operator	NOUN
ejpam-6056	231	4	q	q	NOUN
ejpam-6056	231	5	:	:	PUNCT
ejpam-6056	231	6	ω	ω	PROPN
ejpam-6056	231	7	→	→	SYM
ejpam-6056	231	8	ω	ω	PROPN
ejpam-6056	231	9	by	by	ADP
ejpam-6056	231	10	:	:	PUNCT
ejpam-6056	231	11	qi(t	qi(t	NOUN
ejpam-6056	231	12	)	)	PUNCT
ejpam-6056	232	1	∈	∈	PROPN
ejpam-6056	232	2	∫	∫	PROPN
ejpam-6056	232	3	t	t	PROPN
ejpam-6056	232	4	0	0	NUM
ejpam-6056	233	1	k(t	k(t	PROPN
ejpam-6056	233	2	,	,	PUNCT
ejpam-6056	233	3	u)h(u	u)h(u	PROPN
ejpam-6056	233	4	,	,	PUNCT
ejpam-6056	233	5	i(u	i(u	PROPN
ejpam-6056	233	6	)	)	PUNCT
ejpam-6056	233	7	)	)	PUNCT
ejpam-6056	234	1	du+θ(t	du+θ(t	PROPN
ejpam-6056	234	2	)	)	PUNCT
ejpam-6056	234	3	,	,	PUNCT
ejpam-6056	234	4	t	t	PROPN
ejpam-6056	234	5	∈	∈	PROPN
ejpam-6056	235	1	[	[	X
ejpam-6056	235	2	0	0	NUM
ejpam-6056	235	3	,	,	PUNCT
ejpam-6056	235	4	t	t	X
ejpam-6056	235	5	]	]	PUNCT
ejpam-6056	235	6	.	.	PUNCT
ejpam-6056	236	1	thus	thus	ADV
ejpam-6056	236	2	,	,	PUNCT
ejpam-6056	236	3	solving	solve	VERB
ejpam-6056	236	4	the	the	DET
ejpam-6056	236	5	epidemic	epidemic	NOUN
ejpam-6056	236	6	model	model	NOUN
ejpam-6056	236	7	is	be	AUX
ejpam-6056	236	8	equivalent	equivalent	ADJ
ejpam-6056	236	9	to	to	ADP
ejpam-6056	236	10	finding	find	VERB
ejpam-6056	236	11	a	a	DET
ejpam-6056	236	12	fixed	fix	VERB
ejpam-6056	236	13	point	point	NOUN
ejpam-6056	236	14	of	of	ADP
ejpam-6056	236	15	q.	q.	NOUN
ejpam-6056	236	16	using	use	VERB
ejpam-6056	236	17	the	the	DET
ejpam-6056	236	18	given	give	VERB
ejpam-6056	236	19	assumptions	assumption	NOUN
ejpam-6056	236	20	and	and	CCONJ
ejpam-6056	236	21	contraction	contraction	NOUN
ejpam-6056	236	22	properties	property	NOUN
ejpam-6056	236	23	,	,	PUNCT
ejpam-6056	236	24	we	we	PRON
ejpam-6056	236	25	obtain	obtain	VERB
ejpam-6056	236	26	:	:	PUNCT
ejpam-6056	236	27	|qi	|qi	NUM
ejpam-6056	236	28	−qj	−qj	PROPN
ejpam-6056	236	29	|τ	|τ	PROPN
ejpam-6056	236	30	≤	≤	NUM
ejpam-6056	236	31	∫	∫	PROPN
ejpam-6056	236	32	t	t	PROPN
ejpam-6056	236	33	0	0	NUM
ejpam-6056	236	34	|k(t	|k(t	PROPN
ejpam-6056	236	35	,	,	PUNCT
ejpam-6056	236	36	u)|τ	u)|τ	PROPN
ejpam-6056	236	37	|h(u	|h(u	PROPN
ejpam-6056	236	38	,	,	PUNCT
ejpam-6056	236	39	i(u))−h(u	i(u))−h(u	PROPN
ejpam-6056	236	40	,	,	PUNCT
ejpam-6056	236	41	j(u))|τ	j(u))|τ	PROPN
ejpam-6056	236	42	du	du	PROPN
ejpam-6056	236	43	.	.	PUNCT
ejpam-6056	237	1	this	this	PRON
ejpam-6056	237	2	implies	imply	VERB
ejpam-6056	237	3	:	:	PUNCT
ejpam-6056	237	4	dθ(qi	dθ(qi	PROPN
ejpam-6056	237	5	,	,	PUNCT
ejpam-6056	237	6	qj	qj	PROPN
ejpam-6056	237	7	)	)	PUNCT
ejpam-6056	237	8	≤mθ(i	≤mθ(i	PROPN
ejpam-6056	237	9	,	,	PUNCT
ejpam-6056	237	10	j	j	PROPN
ejpam-6056	237	11	)	)	PUNCT
ejpam-6056	237	12	.	.	PUNCT
ejpam-6056	238	1	by	by	ADP
ejpam-6056	238	2	invoking	invoke	VERB
ejpam-6056	238	3	theorem	theorem	ADJ
ejpam-6056	238	4	3.1	3.1	NUM
ejpam-6056	238	5	,	,	PUNCT
ejpam-6056	238	6	the	the	DET
ejpam-6056	238	7	operator	operator	NOUN
ejpam-6056	238	8	q	q	PUNCT
ejpam-6056	238	9	has	have	AUX
ejpam-6056	238	10	a	a	DET
ejpam-6056	238	11	unique	unique	ADJ
ejpam-6056	238	12	fixed	fix	VERB
ejpam-6056	238	13	point	point	NOUN
ejpam-6056	238	14	,	,	PUNCT
ejpam-6056	238	15	ensuring	ensure	VERB
ejpam-6056	238	16	that	that	SCONJ
ejpam-6056	238	17	the	the	DET
ejpam-6056	238	18	epidemic	epidemic	NOUN
ejpam-6056	238	19	model	model	NOUN
ejpam-6056	238	20	has	have	VERB
ejpam-6056	238	21	a	a	DET
ejpam-6056	238	22	unique	unique	ADJ
ejpam-6056	238	23	solution	solution	NOUN
ejpam-6056	238	24	.	.	PUNCT
ejpam-6056	239	1	h.	h.	PROPN
ejpam-6056	239	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	239	3	,	,	PUNCT
ejpam-6056	239	4	j.m	j.m	PROPN
ejpam-6056	239	5	.	.	PROPN
ejpam-6056	239	6	al	al	PROPN
ejpam-6056	239	7	-	-	PUNCT
ejpam-6056	239	8	musannef	musannef	PROPN
ejpam-6056	239	9	,	,	PUNCT
ejpam-6056	239	10	h.	h.	PROPN
ejpam-6056	239	11	alsamir	alsamir	PROPN
ejpam-6056	239	12	/	/	SYM
ejpam-6056	239	13	eur	eur	PROPN
ejpam-6056	239	14	.	.	PUNCT
ejpam-6056	240	1	j.	j.	PROPN
ejpam-6056	240	2	pure	pure	PROPN
ejpam-6056	240	3	appl	appl	PROPN
ejpam-6056	240	4	.	.	PROPN
ejpam-6056	240	5	math	math	PROPN
ejpam-6056	240	6	,	,	PUNCT
ejpam-6056	240	7	18	18	NUM
ejpam-6056	240	8	(	(	PUNCT
ejpam-6056	240	9	3	3	NUM
ejpam-6056	240	10	)	)	PUNCT
ejpam-6056	240	11	(	(	PUNCT
ejpam-6056	240	12	2025	2025	NUM
ejpam-6056	240	13	)	)	PUNCT
ejpam-6056	240	14	,	,	PUNCT
ejpam-6056	240	15	6056	6056	NUM
ejpam-6056	240	16	12	12	NUM
ejpam-6056	240	17	of	of	ADP
ejpam-6056	240	18	16	16	NUM
ejpam-6056	240	19	remark	remark	NOUN
ejpam-6056	240	20	3	3	NUM
ejpam-6056	240	21	.	.	PUNCT
ejpam-6056	241	1	this	this	DET
ejpam-6056	241	2	model	model	NOUN
ejpam-6056	241	3	generalizes	generalize	VERB
ejpam-6056	241	4	classical	classical	ADJ
ejpam-6056	241	5	sir	sir	ADJ
ejpam-6056	241	6	-	-	PUNCT
ejpam-6056	241	7	type	type	NOUN
ejpam-6056	241	8	dynamics	dynamic	NOUN
ejpam-6056	241	9	by	by	ADP
ejpam-6056	241	10	incorporating	incorporate	VERB
ejpam-6056	241	11	a	a	DET
ejpam-6056	241	12	nonlocal	nonlocal	ADJ
ejpam-6056	241	13	memory	memory	NOUN
ejpam-6056	241	14	kernel	kernel	NOUN
ejpam-6056	241	15	and	and	CCONJ
ejpam-6056	241	16	nonlinear	nonlinear	ADJ
ejpam-6056	241	17	feedback	feedback	NOUN
ejpam-6056	241	18	.	.	PUNCT
ejpam-6056	242	1	similar	similar	ADJ
ejpam-6056	242	2	forms	form	NOUN
ejpam-6056	242	3	are	be	AUX
ejpam-6056	242	4	used	use	VERB
ejpam-6056	242	5	in	in	ADP
ejpam-6056	242	6	modeling	model	VERB
ejpam-6056	242	7	dengue	dengue	NOUN
ejpam-6056	242	8	,	,	PUNCT
ejpam-6056	242	9	covid-19	covid-19	PROPN
ejpam-6056	242	10	with	with	ADP
ejpam-6056	242	11	control	control	NOUN
ejpam-6056	242	12	delays	delay	NOUN
ejpam-6056	242	13	,	,	PUNCT
ejpam-6056	242	14	and	and	CCONJ
ejpam-6056	242	15	rumor	rumor	NOUN
ejpam-6056	242	16	dynamics	dynamic	NOUN
ejpam-6056	242	17	in	in	ADP
ejpam-6056	242	18	networks	network	NOUN
ejpam-6056	242	19	.	.	PUNCT
ejpam-6056	243	1	example	example	NOUN
ejpam-6056	244	1	7	7	NUM
ejpam-6056	244	2	.	.	X
ejpam-6056	244	3	modeling	model	VERB
ejpam-6056	244	4	an	an	DET
ejpam-6056	244	5	epidemic	epidemic	NOUN
ejpam-6056	244	6	spread	spread	NOUN
ejpam-6056	244	7	we	we	PRON
ejpam-6056	244	8	now	now	ADV
ejpam-6056	244	9	illustrate	illustrate	VERB
ejpam-6056	244	10	our	our	PRON
ejpam-6056	244	11	results	result	NOUN
ejpam-6056	244	12	with	with	ADP
ejpam-6056	244	13	a	a	DET
ejpam-6056	244	14	numerical	numerical	ADJ
ejpam-6056	244	15	example	example	NOUN
ejpam-6056	244	16	using	use	VERB
ejpam-6056	244	17	realistic	realistic	ADJ
ejpam-6056	244	18	disease	disease	NOUN
ejpam-6056	244	19	parameters	parameter	NOUN
ejpam-6056	244	20	.	.	PUNCT
ejpam-6056	245	1	we	we	PRON
ejpam-6056	245	2	model	model	VERB
ejpam-6056	245	3	an	an	DET
ejpam-6056	245	4	infection	infection	NOUN
ejpam-6056	245	5	spreading	spread	VERB
ejpam-6056	245	6	in	in	ADP
ejpam-6056	245	7	a	a	DET
ejpam-6056	245	8	population	population	NOUN
ejpam-6056	245	9	,	,	PUNCT
ejpam-6056	245	10	where	where	SCONJ
ejpam-6056	245	11	:	:	PUNCT
ejpam-6056	245	12	•	•	NUM
ejpam-6056	245	13	infection	infection	NOUN
ejpam-6056	245	14	rate	rate	NOUN
ejpam-6056	245	15	function	function	NOUN
ejpam-6056	245	16	(	(	PUNCT
ejpam-6056	245	17	nonlinear	nonlinear	ADJ
ejpam-6056	245	18	growth	growth	NOUN
ejpam-6056	245	19	):	):	PUNCT
ejpam-6056	245	20	h(t	h(t	PROPN
ejpam-6056	245	21	,	,	PUNCT
ejpam-6056	245	22	i	i	NOUN
ejpam-6056	245	23	)	)	PUNCT
ejpam-6056	246	1	=	=	VERB
ejpam-6056	246	2	i	i	PRON
ejpam-6056	246	3	1	1	NUM
ejpam-6056	247	1	+	+	CCONJ
ejpam-6056	247	2	i	i	PRON
ejpam-6056	247	3	to	to	PART
ejpam-6056	247	4	incorporate	incorporate	VERB
ejpam-6056	247	5	saturation	saturation	NOUN
ejpam-6056	247	6	effects	effect	NOUN
ejpam-6056	247	7	in	in	ADP
ejpam-6056	247	8	disease	disease	NOUN
ejpam-6056	247	9	transmission	transmission	NOUN
ejpam-6056	247	10	.	.	PUNCT
ejpam-6056	248	1	•	•	NUM
ejpam-6056	248	2	time	time	NOUN
ejpam-6056	248	3	-	-	PUNCT
ejpam-6056	248	4	dependent	dependent	ADJ
ejpam-6056	248	5	transmission	transmission	NOUN
ejpam-6056	248	6	kernel	kernel	NOUN
ejpam-6056	248	7	:	:	PUNCT
ejpam-6056	248	8	k(t	k(t	NOUN
ejpam-6056	248	9	,	,	PUNCT
ejpam-6056	248	10	u	u	NOUN
ejpam-6056	248	11	)	)	PUNCT
ejpam-6056	248	12	=	=	PUNCT
ejpam-6056	248	13	e−(t−u)2	e−(t−u)2	ADV
ejpam-6056	248	14	to	to	PART
ejpam-6056	248	15	model	model	VERB
ejpam-6056	248	16	decreasing	decrease	VERB
ejpam-6056	248	17	infectivity	infectivity	NOUN
ejpam-6056	248	18	over	over	ADP
ejpam-6056	248	19	time	time	NOUN
ejpam-6056	248	20	.	.	PUNCT
ejpam-6056	249	1	•	•	NOUN
ejpam-6056	249	2	external	external	ADJ
ejpam-6056	249	3	intervention	intervention	NOUN
ejpam-6056	249	4	(	(	PUNCT
ejpam-6056	249	5	vaccination	vaccination	NOUN
ejpam-6056	249	6	or	or	CCONJ
ejpam-6056	249	7	quarantine	quarantine	NOUN
ejpam-6056	249	8	impact	impact	NOUN
ejpam-6056	249	9	):	):	PUNCT
ejpam-6056	249	10	θ(t	θ(t	NOUN
ejpam-6056	249	11	)	)	PUNCT
ejpam-6056	249	12	=	=	NOUN
ejpam-6056	249	13	0.1	0.1	NUM
ejpam-6056	249	14	sin(2πt	sin(2πt	NOUN
ejpam-6056	249	15	)	)	PUNCT
ejpam-6056	249	16	.	.	PUNCT
ejpam-6056	250	1	instead	instead	ADV
ejpam-6056	250	2	of	of	ADP
ejpam-6056	250	3	standard	standard	ADJ
ejpam-6056	250	4	numerical	numerical	ADJ
ejpam-6056	250	5	integration	integration	NOUN
ejpam-6056	250	6	,	,	PUNCT
ejpam-6056	250	7	we	we	PRON
ejpam-6056	250	8	utilize	utilize	VERB
ejpam-6056	250	9	:	:	PUNCT
ejpam-6056	250	10	•	•	NUM
ejpam-6056	250	11	euler	euler	PROPN
ejpam-6056	250	12	’s	’s	PART
ejpam-6056	250	13	method	method	NOUN
ejpam-6056	250	14	for	for	ADP
ejpam-6056	250	15	approximating	approximate	VERB
ejpam-6056	250	16	the	the	DET
ejpam-6056	250	17	integral	integral	ADJ
ejpam-6056	250	18	term	term	NOUN
ejpam-6056	250	19	.	.	PUNCT
ejpam-6056	251	1	•	•	ADP
ejpam-6056	251	2	runge	runge	NOUN
ejpam-6056	251	3	-	-	PUNCT
ejpam-6056	251	4	kutta	kutta	NOUN
ejpam-6056	251	5	(	(	PUNCT
ejpam-6056	251	6	rk4	rk4	NOUN
ejpam-6056	251	7	)	)	PUNCT
ejpam-6056	251	8	for	for	ADP
ejpam-6056	251	9	improved	improved	ADJ
ejpam-6056	251	10	accuracy	accuracy	NOUN
ejpam-6056	251	11	.	.	PUNCT
ejpam-6056	252	1	table	table	NOUN
ejpam-6056	252	2	3	3	NUM
ejpam-6056	252	3	:	:	PUNCT
ejpam-6056	252	4	numerical	numerical	ADJ
ejpam-6056	252	5	verification	verification	NOUN
ejpam-6056	252	6	of	of	ADP
ejpam-6056	252	7	i(t	i(t	PROPN
ejpam-6056	252	8	)	)	PUNCT
ejpam-6056	252	9	and	and	CCONJ
ejpam-6056	252	10	contraction	contraction	NOUN
ejpam-6056	252	11	condition	condition	NOUN
ejpam-6056	252	12	t	t	PROPN
ejpam-6056	252	13	i(t	i(t	PROPN
ejpam-6056	252	14	)	)	PUNCT
ejpam-6056	252	15	(	(	PUNCT
ejpam-6056	252	16	euler	euler	NOUN
ejpam-6056	252	17	)	)	PUNCT
ejpam-6056	252	18	i(t	i(t	PROPN
ejpam-6056	252	19	)	)	PUNCT
ejpam-6056	252	20	(	(	PUNCT
ejpam-6056	252	21	rk4	rk4	NOUN
ejpam-6056	252	22	)	)	PUNCT
ejpam-6056	252	23	dγ(qi	dγ(qi	NOUN
ejpam-6056	252	24	,	,	PUNCT
ejpam-6056	252	25	i	i	NOUN
ejpam-6056	252	26	)	)	PUNCT
ejpam-6056	252	27	µ1dγ(i	µ1dγ(i	PROPN
ejpam-6056	252	28	,	,	PUNCT
ejpam-6056	252	29	j	j	NOUN
ejpam-6056	252	30	)	)	PUNCT
ejpam-6056	252	31	0.2	0.2	NUM
ejpam-6056	252	32	0.050	0.050	NUM
ejpam-6056	252	33	0.055	0.055	NUM
ejpam-6056	252	34	0.030	0.030	NUM
ejpam-6056	252	35	0.022	0.022	NUM
ejpam-6056	252	36	0.5	0.5	NUM
ejpam-6056	252	37	0.120	0.120	NUM
ejpam-6056	252	38	0.125	0.125	NUM
ejpam-6056	252	39	0.032	0.032	NUM
ejpam-6056	252	40	0.027	0.027	NUM
ejpam-6056	252	41	1.0	1.0	NUM
ejpam-6056	252	42	0.220	0.220	NUM
ejpam-6056	252	43	0.226	0.226	NUM
ejpam-6056	252	44	0.040	0.040	NUM
ejpam-6056	252	45	0.035	0.035	NUM
ejpam-6056	252	46	1.5	1.5	NUM
ejpam-6056	252	47	0.300	0.300	NUM
ejpam-6056	252	48	0.310	0.310	NUM
ejpam-6056	252	49	0.035	0.035	NUM
ejpam-6056	252	50	0.038	0.038	NUM
ejpam-6056	252	51	2.0	2.0	NUM
ejpam-6056	252	52	0.350	0.350	NUM
ejpam-6056	252	53	0.365	0.365	NUM
ejpam-6056	252	54	0.033	0.033	NUM
ejpam-6056	252	55	0.041	0.041	NUM
ejpam-6056	252	56	the	the	DET
ejpam-6056	252	57	applications	application	NOUN
ejpam-6056	252	58	presented	present	VERB
ejpam-6056	252	59	above	above	ADV
ejpam-6056	252	60	are	be	AUX
ejpam-6056	252	61	simple	simple	ADJ
ejpam-6056	252	62	in	in	ADP
ejpam-6056	252	63	form	form	NOUN
ejpam-6056	252	64	but	but	CCONJ
ejpam-6056	252	65	structurally	structurally	ADV
ejpam-6056	252	66	rich	rich	ADJ
ejpam-6056	252	67	.	.	PUNCT
ejpam-6056	253	1	the	the	DET
ejpam-6056	253	2	operators	operator	NOUN
ejpam-6056	253	3	used	use	VERB
ejpam-6056	253	4	fall	fall	NOUN
ejpam-6056	253	5	into	into	ADP
ejpam-6056	253	6	the	the	DET
ejpam-6056	253	7	class	class	NOUN
ejpam-6056	253	8	of	of	ADP
ejpam-6056	253	9	generalized	generalized	ADJ
ejpam-6056	253	10	contractions	contraction	NOUN
ejpam-6056	253	11	under	under	ADP
ejpam-6056	253	12	the	the	DET
ejpam-6056	253	13	ebms	ebms	NOUN
ejpam-6056	253	14	framework	framework	NOUN
ejpam-6056	253	15	.	.	PUNCT
ejpam-6056	254	1	importantly	importantly	ADV
ejpam-6056	254	2	,	,	PUNCT
ejpam-6056	254	3	these	these	DET
ejpam-6056	254	4	applications	application	NOUN
ejpam-6056	254	5	represent	represent	VERB
ejpam-6056	254	6	a	a	DET
ejpam-6056	254	7	template	template	NOUN
ejpam-6056	254	8	for	for	ADP
ejpam-6056	254	9	a	a	DET
ejpam-6056	254	10	wider	wide	ADJ
ejpam-6056	254	11	class	class	NOUN
ejpam-6056	254	12	of	of	ADP
ejpam-6056	254	13	nonlinear	nonlinear	ADJ
ejpam-6056	254	14	systems	system	NOUN
ejpam-6056	254	15	,	,	PUNCT
ejpam-6056	254	16	such	such	ADJ
ejpam-6056	254	17	as	as	ADP
ejpam-6056	254	18	:	:	PUNCT
ejpam-6056	254	19	•	•	NOUN
ejpam-6056	254	20	fractional	fractional	ADJ
ejpam-6056	254	21	-	-	PUNCT
ejpam-6056	254	22	order	order	NOUN
ejpam-6056	254	23	systems	system	NOUN
ejpam-6056	254	24	,	,	PUNCT
ejpam-6056	254	25	•	•	NUM
ejpam-6056	254	26	neural	neural	ADJ
ejpam-6056	254	27	networks	network	NOUN
ejpam-6056	254	28	with	with	ADP
ejpam-6056	254	29	delay	delay	NOUN
ejpam-6056	254	30	,	,	PUNCT
ejpam-6056	254	31	•	•	NUM
ejpam-6056	254	32	viscoelastic	viscoelastic	NOUN
ejpam-6056	254	33	models	model	NOUN
ejpam-6056	254	34	with	with	ADP
ejpam-6056	254	35	integral	integral	ADJ
ejpam-6056	254	36	memory	memory	NOUN
ejpam-6056	254	37	.	.	PUNCT
ejpam-6056	255	1	thus	thus	ADV
ejpam-6056	255	2	,	,	PUNCT
ejpam-6056	255	3	the	the	DET
ejpam-6056	255	4	theoretical	theoretical	ADJ
ejpam-6056	255	5	results	result	NOUN
ejpam-6056	255	6	obtained	obtain	VERB
ejpam-6056	255	7	are	be	AUX
ejpam-6056	255	8	broadly	broadly	ADV
ejpam-6056	255	9	applicable	applicable	ADJ
ejpam-6056	255	10	beyond	beyond	ADP
ejpam-6056	255	11	the	the	DET
ejpam-6056	255	12	toy	toy	NOUN
ejpam-6056	255	13	models	model	NOUN
ejpam-6056	255	14	illustrated	illustrate	VERB
ejpam-6056	255	15	here	here	ADV
ejpam-6056	255	16	.	.	PUNCT
ejpam-6056	256	1	h.	h.	PROPN
ejpam-6056	256	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	256	3	,	,	PUNCT
ejpam-6056	256	4	j.m	j.m	PROPN
ejpam-6056	256	5	.	.	PROPN
ejpam-6056	256	6	al	al	PROPN
ejpam-6056	256	7	-	-	PUNCT
ejpam-6056	256	8	musannef	musannef	PROPN
ejpam-6056	256	9	,	,	PUNCT
ejpam-6056	256	10	h.	h.	PROPN
ejpam-6056	256	11	alsamir	alsamir	PROPN
ejpam-6056	256	12	/	/	SYM
ejpam-6056	256	13	eur	eur	PROPN
ejpam-6056	256	14	.	.	PUNCT
ejpam-6056	257	1	j.	j.	PROPN
ejpam-6056	257	2	pure	pure	PROPN
ejpam-6056	257	3	appl	appl	PROPN
ejpam-6056	257	4	.	.	PROPN
ejpam-6056	257	5	math	math	PROPN
ejpam-6056	257	6	,	,	PUNCT
ejpam-6056	257	7	18	18	NUM
ejpam-6056	257	8	(	(	PUNCT
ejpam-6056	257	9	3	3	NUM
ejpam-6056	257	10	)	)	PUNCT
ejpam-6056	257	11	(	(	PUNCT
ejpam-6056	257	12	2025	2025	NUM
ejpam-6056	257	13	)	)	PUNCT
ejpam-6056	257	14	,	,	PUNCT
ejpam-6056	257	15	6056	6056	NUM
ejpam-6056	257	16	13	13	NUM
ejpam-6056	257	17	of	of	ADP
ejpam-6056	257	18	16	16	NUM
ejpam-6056	257	19	0.2	0.2	NUM
ejpam-6056	257	20	0.5	0.5	NUM
ejpam-6056	257	21	1	1	NUM
ejpam-6056	257	22	1.5	1.5	NUM
ejpam-6056	257	23	2	2	NUM
ejpam-6056	257	24	0.1	0.1	NUM
ejpam-6056	257	25	0.2	0.2	NUM
ejpam-6056	257	26	0.3	0.3	NUM
ejpam-6056	257	27	0.4	0.4	NUM
ejpam-6056	257	28	2	2	NUM
ejpam-6056	257	29	4	4	NUM
ejpam-6056	257	30	·	·	SYM
ejpam-6056	257	31	10−2	10−2	NUM
ejpam-6056	257	32	t	t	PROPN
ejpam-6056	257	33	i(t	i(t	PROPN
ejpam-6056	257	34	)	)	PUNCT
ejpam-6056	257	35	dγ	dγ	ADP
ejpam-6056	257	36	values	value	NOUN
ejpam-6056	257	37	i(t	i(t	PROPN
ejpam-6056	257	38	)	)	PUNCT
ejpam-6056	257	39	(	(	PUNCT
ejpam-6056	257	40	rk4	rk4	NOUN
ejpam-6056	257	41	)	)	PUNCT
ejpam-6056	257	42	µ1dγ(i	µ1dγ(i	PROPN
ejpam-6056	257	43	,	,	PUNCT
ejpam-6056	257	44	j	j	NOUN
ejpam-6056	257	45	)	)	PUNCT
ejpam-6056	257	46	figure	figure	NOUN
ejpam-6056	257	47	3	3	NUM
ejpam-6056	257	48	:	:	PUNCT
ejpam-6056	258	1	3d	3d	NUM
ejpam-6056	258	2	representation	representation	NOUN
ejpam-6056	258	3	of	of	ADP
ejpam-6056	258	4	epidemic	epidemic	NOUN
ejpam-6056	258	5	dynamics	dynamic	NOUN
ejpam-6056	258	6	5	5	NUM
ejpam-6056	258	7	.	.	PUNCT
ejpam-6056	259	1	comparative	comparative	ADJ
ejpam-6056	259	2	advantages	advantage	NOUN
ejpam-6056	259	3	and	and	CCONJ
ejpam-6056	259	4	applicability	applicability	NOUN
ejpam-6056	259	5	the	the	DET
ejpam-6056	259	6	rational	rational	ADJ
ejpam-6056	259	7	-	-	PUNCT
ejpam-6056	259	8	type	type	NOUN
ejpam-6056	259	9	contractions	contraction	NOUN
ejpam-6056	259	10	in	in	ADP
ejpam-6056	259	11	extended	extended	ADJ
ejpam-6056	259	12	b	b	X
ejpam-6056	259	13	-	-	ADJ
ejpam-6056	259	14	metric	metric	ADJ
ejpam-6056	259	15	spaces	space	NOUN
ejpam-6056	259	16	(	(	PUNCT
ejpam-6056	259	17	ebms	ebms	NOUN
ejpam-6056	259	18	)	)	PUNCT
ejpam-6056	259	19	developed	develop	VERB
ejpam-6056	259	20	in	in	ADP
ejpam-6056	259	21	this	this	DET
ejpam-6056	259	22	work	work	NOUN
ejpam-6056	259	23	offer	offer	VERB
ejpam-6056	259	24	a	a	DET
ejpam-6056	259	25	flexible	flexible	ADJ
ejpam-6056	259	26	and	and	CCONJ
ejpam-6056	259	27	robust	robust	ADJ
ejpam-6056	259	28	framework	framework	NOUN
ejpam-6056	259	29	for	for	ADP
ejpam-6056	259	30	fixed	fix	VERB
ejpam-6056	259	31	-	-	PUNCT
ejpam-6056	259	32	point	point	NOUN
ejpam-6056	259	33	problems	problem	NOUN
ejpam-6056	259	34	where	where	SCONJ
ejpam-6056	259	35	classical	classical	ADJ
ejpam-6056	259	36	methods	method	NOUN
ejpam-6056	259	37	fail	fail	VERB
ejpam-6056	259	38	.	.	PUNCT
ejpam-6056	260	1	below	below	ADV
ejpam-6056	260	2	,	,	PUNCT
ejpam-6056	260	3	we	we	PRON
ejpam-6056	260	4	summarize	summarize	VERB
ejpam-6056	260	5	their	their	PRON
ejpam-6056	260	6	scope	scope	NOUN
ejpam-6056	260	7	,	,	PUNCT
ejpam-6056	260	8	strengths	strength	NOUN
ejpam-6056	260	9	,	,	PUNCT
ejpam-6056	260	10	and	and	CCONJ
ejpam-6056	260	11	limitations	limitation	NOUN
ejpam-6056	260	12	.	.	PUNCT
ejpam-6056	261	1	our	our	PRON
ejpam-6056	261	2	results	result	NOUN
ejpam-6056	261	3	are	be	AUX
ejpam-6056	261	4	particularly	particularly	ADV
ejpam-6056	261	5	effective	effective	ADJ
ejpam-6056	261	6	for	for	ADP
ejpam-6056	261	7	:	:	PUNCT
ejpam-6056	261	8	•	•	NUM
ejpam-6056	261	9	non	non	ADJ
ejpam-6056	261	10	-	-	ADJ
ejpam-6056	261	11	standard	standard	ADJ
ejpam-6056	261	12	metrics	metric	NOUN
ejpam-6056	261	13	:	:	PUNCT
ejpam-6056	261	14	problems	problem	NOUN
ejpam-6056	261	15	where	where	SCONJ
ejpam-6056	261	16	distances	distance	NOUN
ejpam-6056	261	17	violate	violate	VERB
ejpam-6056	261	18	the	the	DET
ejpam-6056	261	19	triangle	triangle	NOUN
ejpam-6056	261	20	inequality	inequality	NOUN
ejpam-6056	261	21	depend	depend	VERB
ejpam-6056	261	22	on	on	ADP
ejpam-6056	261	23	control	control	NOUN
ejpam-6056	261	24	functions	function	NOUN
ejpam-6056	261	25	θ(x	θ(x	PROPN
ejpam-6056	261	26	,	,	PUNCT
ejpam-6056	261	27	y	y	PROPN
ejpam-6056	261	28	)	)	PUNCT
ejpam-6056	261	29	.	.	PUNCT
ejpam-6056	262	1	•	•	NUM
ejpam-6056	262	2	nonlocal	nonlocal	ADJ
ejpam-6056	262	3	interactions	interaction	NOUN
ejpam-6056	262	4	:	:	PUNCT
ejpam-6056	262	5	systems	system	NOUN
ejpam-6056	262	6	with	with	ADP
ejpam-6056	262	7	memory	memory	NOUN
ejpam-6056	262	8	or	or	CCONJ
ejpam-6056	262	9	hereditary	hereditary	ADJ
ejpam-6056	262	10	effects	effect	NOUN
ejpam-6056	262	11	(	(	PUNCT
ejpam-6056	262	12	e.g.	e.g.	ADV
ejpam-6056	262	13	,	,	PUNCT
ejpam-6056	262	14	volterra	volterra	NOUN
ejpam-6056	262	15	integral	integral	ADJ
ejpam-6056	262	16	inclusions	inclusion	NOUN
ejpam-6056	262	17	in	in	ADP
ejpam-6056	262	18	theorem	theorem	NOUN
ejpam-6056	262	19	2	2	NUM
ejpam-6056	262	20	.	.	NOUN
ejpam-6056	262	21	•	•	NOUN
ejpam-6056	262	22	nonlinear	nonlinear	ADJ
ejpam-6056	262	23	dynamics	dynamic	NOUN
ejpam-6056	262	24	:	:	PUNCT
ejpam-6056	262	25	models	model	NOUN
ejpam-6056	262	26	with	with	ADP
ejpam-6056	262	27	saturation	saturation	NOUN
ejpam-6056	262	28	or	or	CCONJ
ejpam-6056	262	29	threshold	threshold	NOUN
ejpam-6056	262	30	effects	effect	NOUN
ejpam-6056	262	31	(	(	PUNCT
ejpam-6056	262	32	e.g.	e.g.	ADV
ejpam-6056	262	33	,	,	PUNCT
ejpam-6056	262	34	epidemic	epidemic	NOUN
ejpam-6056	262	35	models	model	NOUN
ejpam-6056	262	36	with	with	ADP
ejpam-6056	262	37	h(t	h(t	PROPN
ejpam-6056	262	38	,	,	PUNCT
ejpam-6056	262	39	i	i	NOUN
ejpam-6056	262	40	)	)	PUNCT
ejpam-6056	263	1	=	=	VERB
ejpam-6056	263	2	i	i	PRON
ejpam-6056	263	3	1+i	1+i	NUM
ejpam-6056	263	4	in	in	ADP
ejpam-6056	263	5	section	section	NOUN
ejpam-6056	263	6	4.2	4.2	NUM
ejpam-6056	263	7	)	)	PUNCT
ejpam-6056	263	8	.	.	PUNCT
ejpam-6056	264	1	key	key	ADJ
ejpam-6056	264	2	advantages	advantage	NOUN
ejpam-6056	264	3	•	•	ADP
ejpam-6056	264	4	generalized	generalized	ADJ
ejpam-6056	264	5	contractions	contraction	NOUN
ejpam-6056	264	6	:	:	PUNCT
ejpam-6056	264	7	the	the	DET
ejpam-6056	264	8	rational	rational	ADJ
ejpam-6056	264	9	term	term	NOUN
ejpam-6056	264	10	dτ	dτ	NOUN
ejpam-6056	264	11	(	(	PUNCT
ejpam-6056	264	12	x	x	X
ejpam-6056	264	13	,	,	PUNCT
ejpam-6056	264	14	qx)dτ	qx)dτ	PUNCT
ejpam-6056	264	15	(	(	PUNCT
ejpam-6056	264	16	y	y	NOUN
ejpam-6056	264	17	,	,	PUNCT
ejpam-6056	264	18	qx	qx	PROPN
ejpam-6056	264	19	)	)	PUNCT
ejpam-6056	264	20	+	+	NUM
ejpam-6056	264	21	dτ	dτ	INTJ
ejpam-6056	264	22	(	(	PUNCT
ejpam-6056	264	23	y	y	PROPN
ejpam-6056	264	24	,	,	PUNCT
ejpam-6056	264	25	qy)dτ	qy)dτ	X
ejpam-6056	264	26	(	(	PUNCT
ejpam-6056	264	27	x	x	NOUN
ejpam-6056	264	28	,	,	PUNCT
ejpam-6056	264	29	qy	qy	NOUN
ejpam-6056	264	30	)	)	PUNCT
ejpam-6056	264	31	dτ	dτ	NOUN
ejpam-6056	264	32	(	(	PUNCT
ejpam-6056	264	33	x	x	PROPN
ejpam-6056	264	34	,	,	PUNCT
ejpam-6056	264	35	qy	qy	NOUN
ejpam-6056	264	36	)	)	PUNCT
ejpam-6056	264	37	+	+	NUM
ejpam-6056	264	38	dτ	dτ	INTJ
ejpam-6056	264	39	(	(	PUNCT
ejpam-6056	264	40	y	y	PROPN
ejpam-6056	264	41	,	,	PUNCT
ejpam-6056	264	42	qx	qx	PROPN
ejpam-6056	264	43	)	)	PUNCT
ejpam-6056	264	44	allows	allow	VERB
ejpam-6056	264	45	tighter	tight	ADJ
ejpam-6056	264	46	control	control	NOUN
ejpam-6056	264	47	over	over	ADP
ejpam-6056	264	48	convergence	convergence	NOUN
ejpam-6056	264	49	compared	compare	VERB
ejpam-6056	264	50	to	to	ADP
ejpam-6056	264	51	linear	linear	ADJ
ejpam-6056	264	52	contractions	contraction	NOUN
ejpam-6056	264	53	.	.	PUNCT
ejpam-6056	265	1	•	•	NUM
ejpam-6056	265	2	broader	broad	ADJ
ejpam-6056	265	3	applicability	applicability	NOUN
ejpam-6056	265	4	:	:	PUNCT
ejpam-6056	265	5	works	work	VERB
ejpam-6056	265	6	in	in	ADP
ejpam-6056	265	7	spaces	space	NOUN
ejpam-6056	265	8	where	where	SCONJ
ejpam-6056	265	9	θ(x	θ(x	PROPN
ejpam-6056	265	10	,	,	PUNCT
ejpam-6056	265	11	y	y	NOUN
ejpam-6056	265	12	)	)	PUNCT
ejpam-6056	265	13	grows	grow	VERB
ejpam-6056	265	14	polynomially	polynomially	ADV
ejpam-6056	265	15	or	or	CCONJ
ejpam-6056	265	16	exponentially	exponentially	ADV
ejpam-6056	265	17	.	.	PUNCT
ejpam-6056	266	1	•	•	NUM
ejpam-6056	266	2	practical	practical	ADJ
ejpam-6056	266	3	validation	validation	NOUN
ejpam-6056	266	4	:	:	PUNCT
ejpam-6056	266	5	numerically	numerically	ADV
ejpam-6056	266	6	stable	stable	ADJ
ejpam-6056	266	7	even	even	ADV
ejpam-6056	266	8	for	for	ADP
ejpam-6056	266	9	discontinuous	discontinuous	ADJ
ejpam-6056	266	10	kernels	kernel	NOUN
ejpam-6056	266	11	(	(	PUNCT
ejpam-6056	266	12	table	table	NOUN
ejpam-6056	266	13	3	3	NUM
ejpam-6056	266	14	)	)	PUNCT
ejpam-6056	266	15	.	.	PUNCT
ejpam-6056	267	1	comparison	comparison	NOUN
ejpam-6056	267	2	to	to	ADP
ejpam-6056	267	3	existing	exist	VERB
ejpam-6056	267	4	techniques	technique	NOUN
ejpam-6056	267	5	this	this	DET
ejpam-6056	267	6	framework	framework	NOUN
ejpam-6056	267	7	bridges	bridge	NOUN
ejpam-6056	267	8	theoretical	theoretical	ADJ
ejpam-6056	267	9	generality	generality	NOUN
ejpam-6056	267	10	and	and	CCONJ
ejpam-6056	267	11	applied	apply	VERB
ejpam-6056	267	12	utility	utility	NOUN
ejpam-6056	267	13	:	:	PUNCT
ejpam-6056	267	14	h.	h.	PROPN
ejpam-6056	267	15	qawaqneh	qawaqneh	PROPN
ejpam-6056	267	16	,	,	PUNCT
ejpam-6056	267	17	j.m	j.m	PROPN
ejpam-6056	267	18	.	.	PROPN
ejpam-6056	267	19	al	al	PROPN
ejpam-6056	267	20	-	-	PUNCT
ejpam-6056	267	21	musannef	musannef	PROPN
ejpam-6056	267	22	,	,	PUNCT
ejpam-6056	267	23	h.	h.	PROPN
ejpam-6056	267	24	alsamir	alsamir	PROPN
ejpam-6056	267	25	/	/	SYM
ejpam-6056	267	26	eur	eur	PROPN
ejpam-6056	267	27	.	.	PUNCT
ejpam-6056	268	1	j.	j.	PROPN
ejpam-6056	268	2	pure	pure	PROPN
ejpam-6056	268	3	appl	appl	PROPN
ejpam-6056	268	4	.	.	PROPN
ejpam-6056	268	5	math	math	PROPN
ejpam-6056	268	6	,	,	PUNCT
ejpam-6056	268	7	18	18	NUM
ejpam-6056	268	8	(	(	PUNCT
ejpam-6056	268	9	3	3	NUM
ejpam-6056	268	10	)	)	PUNCT
ejpam-6056	268	11	(	(	PUNCT
ejpam-6056	268	12	2025	2025	NUM
ejpam-6056	268	13	)	)	PUNCT
ejpam-6056	268	14	,	,	PUNCT
ejpam-6056	268	15	6056	6056	NUM
ejpam-6056	268	16	14	14	NUM
ejpam-6056	268	17	of	of	ADP
ejpam-6056	268	18	16	16	NUM
ejpam-6056	268	19	table	table	NOUN
ejpam-6056	268	20	4	4	NUM
ejpam-6056	268	21	:	:	PUNCT
ejpam-6056	268	22	comparison	comparison	NOUN
ejpam-6056	268	23	of	of	ADP
ejpam-6056	268	24	contraction	contraction	NOUN
ejpam-6056	268	25	approaches	approach	VERB
ejpam-6056	268	26	scenario	scenario	ADJ
ejpam-6056	268	27	classical	classical	ADJ
ejpam-6056	268	28	banach	banach	NOUN
ejpam-6056	268	29	kannan	kannan	PROPN
ejpam-6056	268	30	/	/	SYM
ejpam-6056	268	31	ćirić	ćirić	PROPN
ejpam-6056	268	32	our	our	PRON
ejpam-6056	268	33	approach	approach	NOUN
ejpam-6056	268	34	space	space	NOUN
ejpam-6056	268	35	type	type	NOUN
ejpam-6056	268	36	strict	strict	ADJ
ejpam-6056	268	37	metric	metric	ADJ
ejpam-6056	268	38	spaces	space	NOUN
ejpam-6056	268	39	metric	metric	ADJ
ejpam-6056	268	40	/	/	SYM
ejpam-6056	268	41	b	b	NOUN
ejpam-6056	268	42	-	-	PUNCT
ejpam-6056	268	43	metric	metric	ADJ
ejpam-6056	268	44	spaces	space	NOUN
ejpam-6056	268	45	ebms	ebms	NOUN
ejpam-6056	268	46	(	(	PUNCT
ejpam-6056	268	47	variable	variable	NOUN
ejpam-6056	268	48	θ	θ	PROPN
ejpam-6056	268	49	)	)	PUNCT
ejpam-6056	268	50	contraction	contraction	NOUN
ejpam-6056	268	51	form	form	NOUN
ejpam-6056	268	52	linear	linear	PROPN
ejpam-6056	268	53	max	max	PROPN
ejpam-6056	268	54	-	-	PUNCT
ejpam-6056	268	55	type	type	NOUN
ejpam-6056	268	56	rational	rational	ADJ
ejpam-6056	268	57	nonlinear	nonlinear	ADJ
ejpam-6056	268	58	memory	memory	NOUN
ejpam-6056	268	59	effects	effect	NOUN
ejpam-6056	268	60	no	no	DET
ejpam-6056	268	61	limited	limited	ADJ
ejpam-6056	268	62	yes	yes	INTJ
ejpam-6056	268	63	parameter	parameter	NOUN
ejpam-6056	268	64	flexibility	flexibility	NOUN
ejpam-6056	268	65	λ	λ	X
ejpam-6056	268	66	∈	∈	PROPN
ejpam-6056	269	1	[	[	X
ejpam-6056	269	2	0	0	NUM
ejpam-6056	269	3	,	,	PUNCT
ejpam-6056	269	4	1	1	NUM
ejpam-6056	269	5	)	)	PUNCT
ejpam-6056	269	6	fixed	fix	VERB
ejpam-6056	269	7	λ	λ	X
ejpam-6056	269	8	∈	∈	PROPN
ejpam-6056	269	9	(	(	PUNCT
ejpam-6056	269	10	0	0	NUM
ejpam-6056	269	11	,	,	PUNCT
ejpam-6056	269	12	1/2	1/2	NUM
ejpam-6056	269	13	)	)	PUNCT
ejpam-6056	269	14	µ1	µ1	PROPN
ejpam-6056	270	1	+	+	CCONJ
ejpam-6056	270	2	µ2	µ2	PROPN
ejpam-6056	270	3	<	<	X
ejpam-6056	270	4	1	1	NUM
ejpam-6056	270	5	•	•	NOUN
ejpam-6056	270	6	theoretically	theoretically	ADV
ejpam-6056	270	7	,	,	PUNCT
ejpam-6056	270	8	it	it	PRON
ejpam-6056	270	9	extends	extend	VERB
ejpam-6056	270	10	fixed	fix	VERB
ejpam-6056	270	11	-	-	PUNCT
ejpam-6056	270	12	point	point	NOUN
ejpam-6056	270	13	theory	theory	NOUN
ejpam-6056	270	14	to	to	ADP
ejpam-6056	270	15	spaces	space	NOUN
ejpam-6056	270	16	with	with	ADP
ejpam-6056	270	17	non	non	ADJ
ejpam-6056	270	18	-	-	ADJ
ejpam-6056	270	19	uniform	uniform	ADJ
ejpam-6056	270	20	scaling	scaling	NOUN
ejpam-6056	270	21	.	.	PUNCT
ejpam-6056	271	1	•	•	X
ejpam-6056	271	2	practically	practically	ADV
ejpam-6056	271	3	,	,	PUNCT
ejpam-6056	271	4	it	it	PRON
ejpam-6056	271	5	solves	solve	VERB
ejpam-6056	271	6	integral	integral	ADJ
ejpam-6056	271	7	inclusions	inclusion	NOUN
ejpam-6056	271	8	and	and	CCONJ
ejpam-6056	271	9	epidemic	epidemic	NOUN
ejpam-6056	271	10	models	model	NOUN
ejpam-6056	271	11	that	that	PRON
ejpam-6056	271	12	resist	resist	VERB
ejpam-6056	271	13	classical	classical	ADJ
ejpam-6056	271	14	methods	method	NOUN
ejpam-6056	271	15	(	(	PUNCT
ejpam-6056	271	16	see	see	VERB
ejpam-6056	271	17	section	section	NOUN
ejpam-6056	271	18	4.2	4.2	NUM
ejpam-6056	271	19	)	)	PUNCT
ejpam-6056	271	20	.	.	PUNCT
ejpam-6056	272	1	6	6	X
ejpam-6056	272	2	.	.	X
ejpam-6056	272	3	conclusion	conclusion	NOUN
ejpam-6056	272	4	this	this	DET
ejpam-6056	272	5	work	work	NOUN
ejpam-6056	272	6	explores	explore	VERB
ejpam-6056	272	7	rational	rational	ADJ
ejpam-6056	272	8	-	-	PUNCT
ejpam-6056	272	9	type	type	NOUN
ejpam-6056	272	10	contractions	contraction	NOUN
ejpam-6056	272	11	within	within	ADP
ejpam-6056	272	12	the	the	DET
ejpam-6056	272	13	framework	framework	NOUN
ejpam-6056	272	14	of	of	ADP
ejpam-6056	272	15	ebms	ebms	NOUN
ejpam-6056	272	16	,	,	PUNCT
ejpam-6056	272	17	leading	lead	VERB
ejpam-6056	272	18	to	to	ADP
ejpam-6056	272	19	new	new	ADJ
ejpam-6056	272	20	fixed	fix	VERB
ejpam-6056	272	21	-	-	PUNCT
ejpam-6056	272	22	point	point	NOUN
ejpam-6056	272	23	results	result	NOUN
ejpam-6056	272	24	.	.	PUNCT
ejpam-6056	273	1	these	these	DET
ejpam-6056	273	2	findings	finding	NOUN
ejpam-6056	273	3	are	be	AUX
ejpam-6056	273	4	applied	apply	VERB
ejpam-6056	273	5	to	to	PART
ejpam-6056	273	6	analyze	analyze	VERB
ejpam-6056	273	7	the	the	DET
ejpam-6056	273	8	stability	stability	NOUN
ejpam-6056	273	9	of	of	ADP
ejpam-6056	273	10	integral	integral	ADJ
ejpam-6056	273	11	inclusions	inclusion	NOUN
ejpam-6056	273	12	and	and	CCONJ
ejpam-6056	273	13	integral	integral	ADJ
ejpam-6056	273	14	equations	equation	NOUN
ejpam-6056	273	15	,	,	PUNCT
ejpam-6056	273	16	demonstrating	demonstrate	VERB
ejpam-6056	273	17	their	their	PRON
ejpam-6056	273	18	effectiveness	effectiveness	NOUN
ejpam-6056	273	19	in	in	ADP
ejpam-6056	273	20	solving	solve	VERB
ejpam-6056	273	21	nonlinear	nonlinear	ADJ
ejpam-6056	273	22	problems	problem	NOUN
ejpam-6056	273	23	.	.	PUNCT
ejpam-6056	274	1	a	a	DET
ejpam-6056	274	2	key	key	ADJ
ejpam-6056	274	3	contribution	contribution	NOUN
ejpam-6056	274	4	of	of	ADP
ejpam-6056	274	5	this	this	DET
ejpam-6056	274	6	study	study	NOUN
ejpam-6056	274	7	is	be	AUX
ejpam-6056	274	8	the	the	DET
ejpam-6056	274	9	application	application	NOUN
ejpam-6056	274	10	of	of	ADP
ejpam-6056	274	11	these	these	DET
ejpam-6056	274	12	theoretical	theoretical	ADJ
ejpam-6056	274	13	results	result	NOUN
ejpam-6056	274	14	to	to	ADP
ejpam-6056	274	15	an	an	DET
ejpam-6056	274	16	epidemic	epidemic	NOUN
ejpam-6056	274	17	model	model	NOUN
ejpam-6056	274	18	using	use	VERB
ejpam-6056	274	19	volterra	volterra	NOUN
ejpam-6056	274	20	integral	integral	ADJ
ejpam-6056	274	21	inclusions	inclusion	NOUN
ejpam-6056	274	22	.	.	PUNCT
ejpam-6056	275	1	by	by	ADP
ejpam-6056	275	2	leveraging	leverage	VERB
ejpam-6056	275	3	the	the	DET
ejpam-6056	275	4	flexibility	flexibility	NOUN
ejpam-6056	275	5	of	of	ADP
ejpam-6056	275	6	rational	rational	ADJ
ejpam-6056	275	7	-	-	PUNCT
ejpam-6056	275	8	type	type	NOUN
ejpam-6056	275	9	contractions	contraction	NOUN
ejpam-6056	275	10	,	,	PUNCT
ejpam-6056	275	11	we	we	PRON
ejpam-6056	275	12	establish	establish	VERB
ejpam-6056	275	13	conditions	condition	NOUN
ejpam-6056	275	14	that	that	PRON
ejpam-6056	275	15	guarantee	guarantee	VERB
ejpam-6056	275	16	the	the	DET
ejpam-6056	275	17	existence	existence	NOUN
ejpam-6056	275	18	and	and	CCONJ
ejpam-6056	275	19	uniqueness	uniqueness	NOUN
ejpam-6056	275	20	of	of	ADP
ejpam-6056	275	21	solutions	solution	NOUN
ejpam-6056	275	22	.	.	PUNCT
ejpam-6056	276	1	the	the	DET
ejpam-6056	276	2	validity	validity	NOUN
ejpam-6056	276	3	of	of	ADP
ejpam-6056	276	4	our	our	PRON
ejpam-6056	276	5	approach	approach	NOUN
ejpam-6056	276	6	is	be	AUX
ejpam-6056	276	7	further	far	ADV
ejpam-6056	276	8	reinforced	reinforce	VERB
ejpam-6056	276	9	through	through	ADP
ejpam-6056	276	10	concrete	concrete	ADJ
ejpam-6056	276	11	examples	example	NOUN
ejpam-6056	276	12	and	and	CCONJ
ejpam-6056	276	13	numerical	numerical	ADJ
ejpam-6056	276	14	validation	validation	NOUN
ejpam-6056	276	15	.	.	PUNCT
ejpam-6056	277	1	beyond	beyond	ADP
ejpam-6056	277	2	theoretical	theoretical	ADJ
ejpam-6056	277	3	advancements	advancement	NOUN
ejpam-6056	277	4	,	,	PUNCT
ejpam-6056	277	5	this	this	DET
ejpam-6056	277	6	research	research	NOUN
ejpam-6056	277	7	highlights	highlight	VERB
ejpam-6056	277	8	the	the	DET
ejpam-6056	277	9	relevance	relevance	NOUN
ejpam-6056	277	10	of	of	ADP
ejpam-6056	277	11	ebms	ebms	NOUN
ejpam-6056	277	12	in	in	ADP
ejpam-6056	277	13	applied	applied	ADJ
ejpam-6056	277	14	mathematics	mathematic	NOUN
ejpam-6056	277	15	.	.	PUNCT
ejpam-6056	278	1	the	the	DET
ejpam-6056	278	2	results	result	NOUN
ejpam-6056	278	3	provide	provide	VERB
ejpam-6056	278	4	a	a	DET
ejpam-6056	278	5	bridge	bridge	NOUN
ejpam-6056	278	6	between	between	ADP
ejpam-6056	278	7	abstract	abstract	ADJ
ejpam-6056	278	8	mathematical	mathematical	ADJ
ejpam-6056	278	9	principles	principle	NOUN
ejpam-6056	278	10	and	and	CCONJ
ejpam-6056	278	11	their	their	PRON
ejpam-6056	278	12	implementation	implementation	NOUN
ejpam-6056	278	13	in	in	ADP
ejpam-6056	278	14	fields	field	NOUN
ejpam-6056	278	15	such	such	ADJ
ejpam-6056	278	16	as	as	ADP
ejpam-6056	278	17	epidemiology	epidemiology	NOUN
ejpam-6056	278	18	,	,	PUNCT
ejpam-6056	278	19	engineering	engineering	NOUN
ejpam-6056	278	20	,	,	PUNCT
ejpam-6056	278	21	and	and	CCONJ
ejpam-6056	278	22	dynamic	dynamic	ADJ
ejpam-6056	278	23	systems	system	NOUN
ejpam-6056	278	24	analysis	analysis	NOUN
ejpam-6056	278	25	.	.	PUNCT
ejpam-6056	279	1	future	future	ADJ
ejpam-6056	279	2	work	work	NOUN
ejpam-6056	279	3	may	may	AUX
ejpam-6056	279	4	extend	extend	VERB
ejpam-6056	279	5	these	these	DET
ejpam-6056	279	6	findings	finding	NOUN
ejpam-6056	279	7	to	to	ADP
ejpam-6056	279	8	broader	broad	ADJ
ejpam-6056	279	9	classes	class	NOUN
ejpam-6056	279	10	of	of	ADP
ejpam-6056	279	11	contractions	contraction	NOUN
ejpam-6056	279	12	and	and	CCONJ
ejpam-6056	279	13	explore	explore	VERB
ejpam-6056	279	14	further	further	ADJ
ejpam-6056	279	15	applications	application	NOUN
ejpam-6056	279	16	in	in	ADP
ejpam-6056	279	17	real	real	ADJ
ejpam-6056	279	18	-	-	PUNCT
ejpam-6056	279	19	world	world	NOUN
ejpam-6056	279	20	modeling	model	VERB
ejpam-6056	279	21	scenarios	scenario	NOUN
ejpam-6056	279	22	.	.	PUNCT
ejpam-6056	280	1	acknowledgements	acknowledgement	NOUN
ejpam-6056	280	2	the	the	DET
ejpam-6056	280	3	authors	author	NOUN
ejpam-6056	280	4	extend	extend	VERB
ejpam-6056	280	5	their	their	PRON
ejpam-6056	280	6	appreciation	appreciation	NOUN
ejpam-6056	280	7	to	to	ADP
ejpam-6056	280	8	al	al	PROPN
ejpam-6056	280	9	-	-	PROPN
ejpam-6056	280	10	zaytoonah	zaytoonah	PROPN
ejpam-6056	280	11	university	university	PROPN
ejpam-6056	280	12	of	of	ADP
ejpam-6056	280	13	jordan(zuj	jordan(zuj	PROPN
ejpam-6056	280	14	)	)	PUNCT
ejpam-6056	280	15	and	and	CCONJ
ejpam-6056	280	16	to	to	ADP
ejpam-6056	280	17	the	the	DET
ejpam-6056	280	18	arab	arab	PROPN
ejpam-6056	280	19	open	open	PROPN
ejpam-6056	280	20	university	university	PROPN
ejpam-6056	280	21	,	,	PUNCT
ejpam-6056	280	22	jeddah	jeddah	PROPN
ejpam-6056	280	23	,	,	PUNCT
ejpam-6056	280	24	saudi	saudi	PROPN
ejpam-6056	280	25	arabia	arabia	PROPN
ejpam-6056	280	26	for	for	ADP
ejpam-6056	280	27	funding	fund	VERB
ejpam-6056	280	28	this	this	DET
ejpam-6056	280	29	work	work	NOUN
ejpam-6056	280	30	.	.	PUNCT
ejpam-6056	281	1	references	reference	NOUN
ejpam-6056	281	2	[	[	X
ejpam-6056	281	3	1	1	NUM
ejpam-6056	281	4	]	]	PUNCT
ejpam-6056	281	5	s	s	VERB
ejpam-6056	281	6	banach	banach	NOUN
ejpam-6056	281	7	.	.	PUNCT
ejpam-6056	282	1	sur	sur	PROPN
ejpam-6056	282	2	les	les	X
ejpam-6056	282	3	opérations	opération	NOUN
ejpam-6056	282	4	dans	dan	NOUN
ejpam-6056	282	5	les	les	X
ejpam-6056	282	6	ensembles	ensemble	NOUN
ejpam-6056	282	7	abstraits	abstrait	NOUN
ejpam-6056	282	8	et	et	PROPN
ejpam-6056	282	9	leurs	leurs	PROPN
ejpam-6056	282	10	applications	applications	PROPN
ejpam-6056	282	11	aux	aux	PROPN
ejpam-6056	282	12	équations	équations	PROPN
ejpam-6056	282	13	intégrales	intégrale	NOUN
ejpam-6056	282	14	.	.	PUNCT
ejpam-6056	283	1	fund	fund	PROPN
ejpam-6056	283	2	.	.	PUNCT
ejpam-6056	284	1	math	math	NOUN
ejpam-6056	284	2	.	.	PUNCT
ejpam-6056	284	3	,	,	PUNCT
ejpam-6056	285	1	3:133–181	3:133–181	NUM
ejpam-6056	285	2	,	,	PUNCT
ejpam-6056	285	3	1922	1922	NUM
ejpam-6056	285	4	.	.	PUNCT
ejpam-6056	286	1	[	[	X
ejpam-6056	286	2	2	2	X
ejpam-6056	286	3	]	]	PUNCT
ejpam-6056	286	4	i	i	PRON
ejpam-6056	286	5	a	a	DET
ejpam-6056	286	6	bakhtin	bakhtin	NOUN
ejpam-6056	286	7	.	.	PUNCT
ejpam-6056	287	1	the	the	DET
ejpam-6056	287	2	contraction	contraction	NOUN
ejpam-6056	287	3	mapping	map	VERB
ejpam-6056	287	4	principle	principle	NOUN
ejpam-6056	287	5	in	in	ADP
ejpam-6056	287	6	quasimetric	quasimetric	ADJ
ejpam-6056	287	7	spaces	space	NOUN
ejpam-6056	287	8	.	.	PUNCT
ejpam-6056	288	1	funct	funct	ADJ
ejpam-6056	288	2	.	.	PUNCT
ejpam-6056	289	1	anal	anal	PROPN
ejpam-6056	289	2	.	.	PROPN
ejpam-6056	289	3	,	,	PUNCT
ejpam-6056	289	4	30:6–27	30:6–27	NUM
ejpam-6056	289	5	,	,	PUNCT
ejpam-6056	289	6	1989	1989	NUM
ejpam-6056	289	7	.	.	PUNCT
ejpam-6056	290	1	[	[	X
ejpam-6056	290	2	3	3	NUM
ejpam-6056	290	3	]	]	X
ejpam-6056	290	4	s	s	PART
ejpam-6056	290	5	czerwik	czerwik	PROPN
ejpam-6056	290	6	.	.	PUNCT
ejpam-6056	291	1	contraction	contraction	NOUN
ejpam-6056	291	2	mappings	mapping	NOUN
ejpam-6056	291	3	in	in	ADP
ejpam-6056	291	4	b	b	NOUN
ejpam-6056	291	5	-	-	ADJ
ejpam-6056	291	6	metric	metric	ADJ
ejpam-6056	291	7	spaces	space	NOUN
ejpam-6056	291	8	.	.	PUNCT
ejpam-6056	292	1	acta	acta	PROPN
ejpam-6056	292	2	math	math	PROPN
ejpam-6056	292	3	.	.	PUNCT
ejpam-6056	293	1	inform	inform	NOUN
ejpam-6056	293	2	.	.	PUNCT
ejpam-6056	294	1	univ	univ	PROPN
ejpam-6056	294	2	.	.	PUNCT
ejpam-6056	294	3	ostraviensis	ostraviensis	NOUN
ejpam-6056	294	4	,	,	PUNCT
ejpam-6056	294	5	1(1):5–11	1(1):5–11	NUM
ejpam-6056	294	6	,	,	PUNCT
ejpam-6056	294	7	1993	1993	NUM
ejpam-6056	294	8	.	.	PUNCT
ejpam-6056	295	1	h.	h.	PROPN
ejpam-6056	295	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	295	3	,	,	PUNCT
ejpam-6056	295	4	j.m	j.m	PROPN
ejpam-6056	295	5	.	.	PROPN
ejpam-6056	295	6	al	al	PROPN
ejpam-6056	295	7	-	-	PUNCT
ejpam-6056	295	8	musannef	musannef	PROPN
ejpam-6056	295	9	,	,	PUNCT
ejpam-6056	295	10	h.	h.	PROPN
ejpam-6056	295	11	alsamir	alsamir	PROPN
ejpam-6056	295	12	/	/	SYM
ejpam-6056	295	13	eur	eur	PROPN
ejpam-6056	295	14	.	.	PUNCT
ejpam-6056	296	1	j.	j.	PROPN
ejpam-6056	296	2	pure	pure	PROPN
ejpam-6056	296	3	appl	appl	PROPN
ejpam-6056	296	4	.	.	PROPN
ejpam-6056	296	5	math	math	PROPN
ejpam-6056	296	6	,	,	PUNCT
ejpam-6056	296	7	18	18	NUM
ejpam-6056	296	8	(	(	PUNCT
ejpam-6056	296	9	3	3	NUM
ejpam-6056	296	10	)	)	PUNCT
ejpam-6056	296	11	(	(	PUNCT
ejpam-6056	296	12	2025	2025	NUM
ejpam-6056	296	13	)	)	PUNCT
ejpam-6056	296	14	,	,	PUNCT
ejpam-6056	296	15	6056	6056	NUM
ejpam-6056	296	16	15	15	NUM
ejpam-6056	296	17	of	of	ADP
ejpam-6056	296	18	16	16	NUM
ejpam-6056	297	1	[	[	X
ejpam-6056	297	2	4	4	NUM
ejpam-6056	297	3	]	]	PUNCT
ejpam-6056	297	4	t	t	PROPN
ejpam-6056	297	5	kamran	kamran	PROPN
ejpam-6056	297	6	;	;	PUNCT
ejpam-6056	298	1	m	m	VERB
ejpam-6056	298	2	samreen	samreen	ADJ
ejpam-6056	298	3	and	and	CCONJ
ejpam-6056	298	4	q	q	NOUN
ejpam-6056	298	5	ul	ul	INTJ
ejpam-6056	298	6	ain	ain	PROPN
ejpam-6056	298	7	.	.	PUNCT
ejpam-6056	299	1	a	a	DET
ejpam-6056	299	2	generalization	generalization	NOUN
ejpam-6056	299	3	of	of	ADP
ejpam-6056	299	4	b	b	NOUN
ejpam-6056	299	5	-	-	PUNCT
ejpam-6056	299	6	metric	metric	ADJ
ejpam-6056	299	7	space	space	NOUN
ejpam-6056	299	8	and	and	CCONJ
ejpam-6056	299	9	some	some	DET
ejpam-6056	299	10	fixed	fix	VERB
ejpam-6056	299	11	point	point	NOUN
ejpam-6056	299	12	theorems	theorem	NOUN
ejpam-6056	299	13	.	.	PUNCT
ejpam-6056	300	1	mathematics	mathematic	NOUN
ejpam-6056	300	2	,	,	PUNCT
ejpam-6056	300	3	5(2	5(2	NUM
ejpam-6056	300	4	)	)	PUNCT
ejpam-6056	300	5	,	,	PUNCT
ejpam-6056	300	6	2017	2017	NUM
ejpam-6056	300	7	.	.	PUNCT
ejpam-6056	301	1	[	[	X
ejpam-6056	301	2	5	5	NUM
ejpam-6056	301	3	]	]	SYM
ejpam-6056	301	4	b	b	X
ejpam-6056	301	5	alqahtani	alqahtani	ADJ
ejpam-6056	301	6	;	;	PUNCT
ejpam-6056	301	7	a	a	DET
ejpam-6056	301	8	fulga	fulga	NOUN
ejpam-6056	301	9	;	;	PUNCT
ejpam-6056	301	10	e	e	X
ejpam-6056	301	11	karapınar	karapınar	NOUN
ejpam-6056	301	12	and	and	CCONJ
ejpam-6056	301	13	v	v	NOUN
ejpam-6056	301	14	rakocevic	rakocevic	ADJ
ejpam-6056	301	15	.	.	PUNCT
ejpam-6056	302	1	contractions	contraction	NOUN
ejpam-6056	302	2	with	with	ADP
ejpam-6056	302	3	rational	rational	ADJ
ejpam-6056	302	4	inequalities	inequality	NOUN
ejpam-6056	302	5	in	in	ADP
ejpam-6056	302	6	the	the	DET
ejpam-6056	302	7	extended	extended	ADJ
ejpam-6056	302	8	b	b	X
ejpam-6056	302	9	-	-	PUNCT
ejpam-6056	302	10	metric	metric	ADJ
ejpam-6056	302	11	space	space	NOUN
ejpam-6056	302	12	.	.	PUNCT
ejpam-6056	303	1	j.	j.	PROPN
ejpam-6056	303	2	inequal	inequal	PROPN
ejpam-6056	303	3	.	.	PUNCT
ejpam-6056	304	1	appl	appl	PROPN
ejpam-6056	304	2	.	.	PROPN
ejpam-6056	304	3	,	,	PUNCT
ejpam-6056	304	4	220	220	NUM
ejpam-6056	304	5	,	,	PUNCT
ejpam-6056	304	6	2019	2019	NUM
ejpam-6056	304	7	.	.	PUNCT
ejpam-6056	305	1	[	[	X
ejpam-6056	305	2	6	6	NUM
ejpam-6056	305	3	]	]	SYM
ejpam-6056	305	4	w	w	NOUN
ejpam-6056	305	5	shatanawi	shatanawi	ADJ
ejpam-6056	305	6	;	;	PUNCT
ejpam-6056	305	7	t	t	PROPN
ejpam-6056	305	8	a	a	DET
ejpam-6056	305	9	shatnawi	shatnawi	PROPN
ejpam-6056	305	10	.	.	PUNCT
ejpam-6056	306	1	some	some	DET
ejpam-6056	306	2	fixed	fix	VERB
ejpam-6056	306	3	point	point	NOUN
ejpam-6056	306	4	results	result	NOUN
ejpam-6056	306	5	based	base	VERB
ejpam-6056	306	6	on	on	ADP
ejpam-6056	306	7	contractions	contraction	NOUN
ejpam-6056	306	8	of	of	ADP
ejpam-6056	306	9	new	new	ADJ
ejpam-6056	306	10	types	type	NOUN
ejpam-6056	306	11	for	for	ADP
ejpam-6056	306	12	extended	extended	ADJ
ejpam-6056	306	13	b	b	X
ejpam-6056	306	14	-	-	ADJ
ejpam-6056	306	15	metric	metric	ADJ
ejpam-6056	306	16	spaces	space	NOUN
ejpam-6056	306	17	.	.	PUNCT
ejpam-6056	307	1	aims	aim	VERB
ejpam-6056	307	2	mathematics	mathematic	NOUN
ejpam-6056	307	3	,	,	PUNCT
ejpam-6056	307	4	8(5):10929–10946	8(5):10929–10946	PROPN
ejpam-6056	307	5	,	,	PUNCT
ejpam-6056	307	6	2023	2023	NUM
ejpam-6056	307	7	.	.	PUNCT
ejpam-6056	308	1	[	[	X
ejpam-6056	308	2	7	7	NUM
ejpam-6056	308	3	]	]	X
ejpam-6056	308	4	m	m	VERB
ejpam-6056	308	5	nadeem	nadeem	PROPN
ejpam-6056	308	6	k	k	PROPN
ejpam-6056	308	7	javed	javed	PROPN
ejpam-6056	308	8	and	and	CCONJ
ejpam-6056	308	9	t	t	PROPN
ejpam-6056	308	10	abdeljawad	abdeljawad	NOUN
ejpam-6056	308	11	.	.	PUNCT
ejpam-6056	309	1	existence	existence	NOUN
ejpam-6056	309	2	of	of	ADP
ejpam-6056	309	3	fixed	fix	VERB
ejpam-6056	309	4	point	point	NOUN
ejpam-6056	309	5	results	result	NOUN
ejpam-6056	309	6	in	in	ADP
ejpam-6056	309	7	orthogonal	orthogonal	ADJ
ejpam-6056	309	8	extended	extended	ADJ
ejpam-6056	309	9	b	b	NOUN
ejpam-6056	309	10	-	-	ADJ
ejpam-6056	309	11	metric	metric	ADJ
ejpam-6056	309	12	spaces	space	NOUN
ejpam-6056	309	13	with	with	ADP
ejpam-6056	309	14	application	application	NOUN
ejpam-6056	309	15	.	.	PUNCT
ejpam-6056	310	1	aims	aim	VERB
ejpam-6056	310	2	mathematics	mathematic	NOUN
ejpam-6056	310	3	,	,	PUNCT
ejpam-6056	310	4	7(4):6282–6293	7(4):6282–6293	NOUN
ejpam-6056	310	5	,	,	PUNCT
ejpam-6056	310	6	2022	2022	NUM
ejpam-6056	310	7	.	.	PUNCT
ejpam-6056	311	1	[	[	X
ejpam-6056	311	2	8	8	NUM
ejpam-6056	311	3	]	]	X
ejpam-6056	311	4	r	r	NOUN
ejpam-6056	311	5	mezghiche	mezghiche	NOUN
ejpam-6056	311	6	o	o	PROPN
ejpam-6056	311	7	abu	abu	PROPN
ejpam-6056	311	8	arqub	arqub	NOUN
ejpam-6056	311	9	and	and	CCONJ
ejpam-6056	311	10	b	b	NOUN
ejpam-6056	311	11	maayah	maayah	NOUN
ejpam-6056	311	12	.	.	PUNCT
ejpam-6056	312	1	fuzzy	fuzzy	ADJ
ejpam-6056	312	2	m	m	ADJ
ejpam-6056	312	3	-	-	PUNCT
ejpam-6056	312	4	fractional	fractional	ADJ
ejpam-6056	312	5	integrodifferential	integrodifferential	ADJ
ejpam-6056	312	6	models	model	NOUN
ejpam-6056	312	7	:	:	PUNCT
ejpam-6056	312	8	theoretical	theoretical	ADJ
ejpam-6056	312	9	existence	existence	NOUN
ejpam-6056	312	10	and	and	CCONJ
ejpam-6056	312	11	uniqueness	uniqueness	NOUN
ejpam-6056	312	12	results	result	NOUN
ejpam-6056	312	13	,	,	PUNCT
ejpam-6056	312	14	and	and	CCONJ
ejpam-6056	312	15	approximate	approximate	ADJ
ejpam-6056	312	16	solutions	solution	NOUN
ejpam-6056	312	17	.	.	PUNCT
ejpam-6056	313	1	front	front	ADJ
ejpam-6056	313	2	.	.	PUNCT
ejpam-6056	314	1	phys	phy	NOUN
ejpam-6056	314	2	.	.	PUNCT
ejpam-6056	314	3	,	,	PUNCT
ejpam-6056	314	4	11(1252919	11(1252919	NUM
ejpam-6056	314	5	)	)	PUNCT
ejpam-6056	314	6	,	,	PUNCT
ejpam-6056	314	7	2023	2023	NUM
ejpam-6056	314	8	.	.	PUNCT
ejpam-6056	315	1	[	[	X
ejpam-6056	315	2	9	9	NUM
ejpam-6056	315	3	]	]	X
ejpam-6056	315	4	h	h	NOUN
ejpam-6056	315	5	alsamir	alsamir	NOUN
ejpam-6056	315	6	;	;	PUNCT
ejpam-6056	315	7	h	h	NOUN
ejpam-6056	315	8	aydi	aydi	VERB
ejpam-6056	315	9	;	;	PUNCT
ejpam-6056	315	10	m	m	PROPN
ejpam-6056	315	11	s	s	PART
ejpam-6056	315	12	m	m	VERB
ejpam-6056	315	13	noorani	noorani	ADJ
ejpam-6056	315	14	;	;	PUNCT
ejpam-6056	315	15	w	w	NOUN
ejpam-6056	315	16	shatanawi	shatanawi	ADJ
ejpam-6056	315	17	;	;	PUNCT
ejpam-6056	315	18	h	h	NOUN
ejpam-6056	315	19	akhadkulov	akhadkulov	NOUN
ejpam-6056	315	20	;	;	PUNCT
ejpam-6056	315	21	h	h	NOUN
ejpam-6056	315	22	qawaqneh	qawaqneh	PROPN
ejpam-6056	315	23	and	and	CCONJ
ejpam-6056	315	24	k	k	PROPN
ejpam-6056	315	25	alanazi	alanazi	PROPN
ejpam-6056	315	26	.	.	PUNCT
ejpam-6056	316	1	fixed	fix	VERB
ejpam-6056	316	2	point	point	NOUN
ejpam-6056	316	3	results	result	NOUN
ejpam-6056	316	4	in	in	ADP
ejpam-6056	316	5	metric	metric	ADJ
ejpam-6056	316	6	-	-	PUNCT
ejpam-6056	316	7	like	like	ADJ
ejpam-6056	316	8	spaces	space	NOUN
ejpam-6056	316	9	via	via	ADP
ejpam-6056	316	10	σ	σ	PROPN
ejpam-6056	316	11	-	-	PUNCT
ejpam-6056	316	12	simulation	simulation	NOUN
ejpam-6056	316	13	functions	function	NOUN
ejpam-6056	316	14	.	.	PUNCT
ejpam-6056	317	1	eur	eur	PROPN
ejpam-6056	317	2	.	.	PUNCT
ejpam-6056	318	1	j.	j.	PROPN
ejpam-6056	318	2	pure	pure	PROPN
ejpam-6056	318	3	appl	appl	PROPN
ejpam-6056	318	4	.	.	PUNCT
ejpam-6056	318	5	math	math	PROPN
ejpam-6056	318	6	.	.	PUNCT
ejpam-6056	318	7	,	,	PUNCT
ejpam-6056	318	8	12(1):88–100	12(1):88–100	NUM
ejpam-6056	318	9	,	,	PUNCT
ejpam-6056	318	10	2019	2019	NUM
ejpam-6056	318	11	.	.	PUNCT
ejpam-6056	319	1	[	[	X
ejpam-6056	319	2	10	10	NUM
ejpam-6056	319	3	]	]	X
ejpam-6056	319	4	h	h	NOUN
ejpam-6056	319	5	alsamir	alsamir	NOUN
ejpam-6056	319	6	;	;	PUNCT
ejpam-6056	319	7	h	h	NOUN
ejpam-6056	319	8	qawaqneh	qawaqneh	NOUN
ejpam-6056	319	9	;	;	PUNCT
ejpam-6056	319	10	g	g	PROPN
ejpam-6056	319	11	al	al	PROPN
ejpam-6056	319	12	-	-	PUNCT
ejpam-6056	319	13	musannef	musannef	PROPN
ejpam-6056	319	14	and	and	CCONJ
ejpam-6056	319	15	r	r	NOUN
ejpam-6056	319	16	khalil	khalil	PROPN
ejpam-6056	319	17	.	.	PUNCT
ejpam-6056	320	1	common	common	ADJ
ejpam-6056	320	2	fixed	fix	VERB
ejpam-6056	320	3	point	point	NOUN
ejpam-6056	320	4	of	of	ADP
ejpam-6056	320	5	generalized	generalized	ADJ
ejpam-6056	320	6	berinde	berinde	NOUN
ejpam-6056	320	7	type	type	NOUN
ejpam-6056	320	8	contraction	contraction	NOUN
ejpam-6056	320	9	and	and	CCONJ
ejpam-6056	320	10	an	an	DET
ejpam-6056	320	11	application	application	NOUN
ejpam-6056	320	12	.	.	PUNCT
ejpam-6056	321	1	eur	eur	PROPN
ejpam-6056	321	2	.	.	PUNCT
ejpam-6056	322	1	j.	j.	PROPN
ejpam-6056	322	2	pure	pure	PROPN
ejpam-6056	322	3	appl	appl	PROPN
ejpam-6056	322	4	.	.	PUNCT
ejpam-6056	322	5	math	math	PROPN
ejpam-6056	322	6	.	.	PUNCT
ejpam-6056	322	7	,	,	PUNCT
ejpam-6056	322	8	17(4):2492–2504	17(4):2492–2504	NUM
ejpam-6056	322	9	,	,	PUNCT
ejpam-6056	322	10	2024	2024	NUM
ejpam-6056	322	11	.	.	PUNCT
ejpam-6056	323	1	[	[	X
ejpam-6056	323	2	11	11	NUM
ejpam-6056	323	3	]	]	X
ejpam-6056	323	4	h	h	NOUN
ejpam-6056	323	5	qawaqneh	qawaqneh	PROPN
ejpam-6056	323	6	.	.	PUNCT
ejpam-6056	324	1	fractional	fractional	ADJ
ejpam-6056	324	2	analytic	analytic	ADJ
ejpam-6056	324	3	solutions	solution	NOUN
ejpam-6056	324	4	and	and	CCONJ
ejpam-6056	324	5	fixed	fix	VERB
ejpam-6056	324	6	point	point	NOUN
ejpam-6056	324	7	results	result	NOUN
ejpam-6056	324	8	with	with	ADP
ejpam-6056	324	9	some	some	DET
ejpam-6056	324	10	applications	application	NOUN
ejpam-6056	324	11	.	.	PUNCT
ejpam-6056	325	1	adv	adv	PROPN
ejpam-6056	325	2	.	.	PUNCT
ejpam-6056	325	3	fixed	fix	VERB
ejpam-6056	325	4	point	point	NOUN
ejpam-6056	325	5	theory	theory	NOUN
ejpam-6056	325	6	,	,	PUNCT
ejpam-6056	325	7	14(1	14(1	NUM
ejpam-6056	325	8	)	)	PUNCT
ejpam-6056	325	9	,	,	PUNCT
ejpam-6056	325	10	2024	2024	NUM
ejpam-6056	325	11	.	.	PUNCT
ejpam-6056	326	1	[	[	X
ejpam-6056	326	2	12	12	NUM
ejpam-6056	326	3	]	]	X
ejpam-6056	326	4	h	h	NOUN
ejpam-6056	326	5	qawaqneh	qawaqneh	NOUN
ejpam-6056	326	6	;	;	PUNCT
ejpam-6056	326	7	m	m	PROPN
ejpam-6056	326	8	s	s	PART
ejpam-6056	326	9	m	m	VERB
ejpam-6056	326	10	noorani	noorani	ADJ
ejpam-6056	326	11	;	;	PUNCT
ejpam-6056	326	12	h	h	NOUN
ejpam-6056	326	13	aydi	aydi	VERB
ejpam-6056	326	14	;	;	PUNCT
ejpam-6056	326	15	a	a	DET
ejpam-6056	326	16	zraiqat	zraiqat	NOUN
ejpam-6056	326	17	and	and	CCONJ
ejpam-6056	326	18	a	a	DET
ejpam-6056	326	19	h	h	NOUN
ejpam-6056	326	20	ansari	ansari	ADJ
ejpam-6056	326	21	.	.	PUNCT
ejpam-6056	327	1	on	on	ADP
ejpam-6056	327	2	fixed	fix	VERB
ejpam-6056	327	3	point	point	NOUN
ejpam-6056	327	4	results	result	NOUN
ejpam-6056	327	5	in	in	ADP
ejpam-6056	327	6	partial	partial	ADJ
ejpam-6056	327	7	b	b	NOUN
ejpam-6056	327	8	-	-	PUNCT
ejpam-6056	327	9	metric	metric	ADJ
ejpam-6056	327	10	spaces	space	NOUN
ejpam-6056	327	11	.	.	PUNCT
ejpam-6056	328	1	journal	journal	NOUN
ejpam-6056	328	2	of	of	ADP
ejpam-6056	328	3	function	function	NOUN
ejpam-6056	328	4	spaces	space	NOUN
ejpam-6056	328	5	,	,	PUNCT
ejpam-6056	328	6	2021	2021	NUM
ejpam-6056	328	7	,	,	PUNCT
ejpam-6056	328	8	2021	2021	NUM
ejpam-6056	328	9	.	.	PUNCT
ejpam-6056	329	1	[	[	X
ejpam-6056	329	2	13	13	NUM
ejpam-6056	329	3	]	]	X
ejpam-6056	329	4	h	h	NOUN
ejpam-6056	329	5	qawaqneh	qawaqneh	NOUN
ejpam-6056	329	6	;	;	PUNCT
ejpam-6056	329	7	m	m	PROPN
ejpam-6056	329	8	s	s	VERB
ejpam-6056	329	9	m	m	NOUN
ejpam-6056	329	10	noorani	noorani	ADJ
ejpam-6056	329	11	and	and	CCONJ
ejpam-6056	329	12	h	h	PROPN
ejpam-6056	329	13	aydi	aydi	ADJ
ejpam-6056	329	14	.	.	PUNCT
ejpam-6056	330	1	some	some	DET
ejpam-6056	330	2	new	new	ADJ
ejpam-6056	330	3	characterizations	characterization	NOUN
ejpam-6056	330	4	and	and	CCONJ
ejpam-6056	330	5	results	result	NOUN
ejpam-6056	330	6	for	for	ADP
ejpam-6056	330	7	fuzzy	fuzzy	ADJ
ejpam-6056	330	8	contractions	contraction	NOUN
ejpam-6056	330	9	in	in	ADP
ejpam-6056	330	10	fuzzy	fuzzy	ADJ
ejpam-6056	330	11	b	b	X
ejpam-6056	330	12	-	-	PUNCT
ejpam-6056	330	13	metric	metric	ADJ
ejpam-6056	330	14	spaces	space	NOUN
ejpam-6056	330	15	and	and	CCONJ
ejpam-6056	330	16	applications	application	NOUN
ejpam-6056	330	17	.	.	PUNCT
ejpam-6056	331	1	aims	aim	VERB
ejpam-6056	331	2	mathematics	mathematics	PROPN
ejpam-6056	331	3	,	,	PUNCT
ejpam-6056	331	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6056	331	5	,	,	PUNCT
ejpam-6056	331	6	2023	2023	NUM
ejpam-6056	331	7	.	.	PUNCT
ejpam-6056	332	1	[	[	X
ejpam-6056	332	2	14	14	NUM
ejpam-6056	332	3	]	]	X
ejpam-6056	332	4	h	h	NOUN
ejpam-6056	332	5	qawagneh	qawagneh	PROPN
ejpam-6056	332	6	.	.	PUNCT
ejpam-6056	333	1	new	new	ADJ
ejpam-6056	333	2	functions	function	NOUN
ejpam-6056	333	3	for	for	ADP
ejpam-6056	333	4	fixed	fix	VERB
ejpam-6056	333	5	point	point	NOUN
ejpam-6056	333	6	results	result	NOUN
ejpam-6056	333	7	in	in	ADP
ejpam-6056	333	8	metric	metric	ADJ
ejpam-6056	333	9	spaces	space	NOUN
ejpam-6056	333	10	with	with	ADP
ejpam-6056	333	11	some	some	DET
ejpam-6056	333	12	applications	application	NOUN
ejpam-6056	333	13	.	.	PUNCT
ejpam-6056	334	1	indian	indian	ADJ
ejpam-6056	334	2	journal	journal	PROPN
ejpam-6056	334	3	of	of	ADP
ejpam-6056	334	4	mathematics	mathematic	NOUN
ejpam-6056	334	5	,	,	PUNCT
ejpam-6056	334	6	66(1):55–84	66(1):55–84	NOUN
ejpam-6056	334	7	,	,	PUNCT
ejpam-6056	334	8	2024	2024	NUM
ejpam-6056	334	9	.	.	PUNCT
ejpam-6056	335	1	[	[	X
ejpam-6056	335	2	15	15	NUM
ejpam-6056	335	3	]	]	X
ejpam-6056	335	4	h	h	NOUN
ejpam-6056	335	5	qawagneh	qawagneh	PROPN
ejpam-6056	335	6	;	;	PUNCT
ejpam-6056	335	7	m	m	PROPN
ejpam-6056	335	8	s	s	VERB
ejpam-6056	335	9	m	m	NOUN
ejpam-6056	335	10	noorani	noorani	ADJ
ejpam-6056	335	11	and	and	CCONJ
ejpam-6056	335	12	w	w	PROPN
ejpam-6056	335	13	shatanawi	shatanawi	PROPN
ejpam-6056	335	14	.	.	PUNCT
ejpam-6056	336	1	fixed	fix	VERB
ejpam-6056	336	2	point	point	NOUN
ejpam-6056	336	3	theorems	theorem	NOUN
ejpam-6056	336	4	for	for	ADP
ejpam-6056	336	5	(	(	PUNCT
ejpam-6056	336	6	α	α	X
ejpam-6056	336	7	,	,	PUNCT
ejpam-6056	336	8	k	k	PROPN
ejpam-6056	336	9	,	,	PUNCT
ejpam-6056	336	10	θ)contractive	θ)contractive	ADJ
ejpam-6056	336	11	multi	multi	ADJ
ejpam-6056	336	12	-	-	ADJ
ejpam-6056	336	13	valued	value	VERB
ejpam-6056	336	14	mapping	mapping	NOUN
ejpam-6056	336	15	in	in	ADP
ejpam-6056	336	16	b	b	NOUN
ejpam-6056	336	17	-	-	PUNCT
ejpam-6056	336	18	metric	metric	ADJ
ejpam-6056	336	19	space	space	NOUN
ejpam-6056	336	20	and	and	CCONJ
ejpam-6056	336	21	applications	application	NOUN
ejpam-6056	336	22	.	.	PUNCT
ejpam-6056	337	1	international	international	ADJ
ejpam-6056	337	2	journal	journal	PROPN
ejpam-6056	337	3	of	of	ADP
ejpam-6056	337	4	mathematics	mathematic	NOUN
ejpam-6056	337	5	and	and	CCONJ
ejpam-6056	337	6	computer	computer	NOUN
ejpam-6056	337	7	science	science	NOUN
ejpam-6056	337	8	,	,	PUNCT
ejpam-6056	337	9	14(1):263–283	14(1):263–283	NUM
ejpam-6056	337	10	,	,	PUNCT
ejpam-6056	337	11	2019	2019	NUM
ejpam-6056	337	12	.	.	PUNCT
ejpam-6056	338	1	[	[	X
ejpam-6056	338	2	16	16	NUM
ejpam-6056	338	3	]	]	X
ejpam-6056	338	4	h	h	NOUN
ejpam-6056	338	5	qawagneh	qawagneh	PROPN
ejpam-6056	338	6	;	;	PUNCT
ejpam-6056	338	7	h	h	PROPN
ejpam-6056	338	8	a	a	DET
ejpam-6056	338	9	hammad	hammad	PROPN
ejpam-6056	338	10	and	and	CCONJ
ejpam-6056	338	11	h	h	PROPN
ejpam-6056	338	12	aydi	aydi	ADJ
ejpam-6056	338	13	.	.	PUNCT
ejpam-6056	339	1	exploring	explore	VERB
ejpam-6056	339	2	new	new	ADJ
ejpam-6056	339	3	geometric	geometric	ADJ
ejpam-6056	339	4	contraction	contraction	NOUN
ejpam-6056	339	5	mappings	mapping	NOUN
ejpam-6056	339	6	and	and	CCONJ
ejpam-6056	339	7	their	their	PRON
ejpam-6056	339	8	applications	application	NOUN
ejpam-6056	339	9	in	in	ADP
ejpam-6056	339	10	fractional	fractional	ADJ
ejpam-6056	339	11	metric	metric	ADJ
ejpam-6056	339	12	spaces	space	NOUN
ejpam-6056	339	13	.	.	PUNCT
ejpam-6056	340	1	aims	aim	VERB
ejpam-6056	340	2	mathematics	mathematic	NOUN
ejpam-6056	340	3	,	,	PUNCT
ejpam-6056	340	4	9(1):521	9(1):521	NUM
ejpam-6056	340	5	–	–	PUNCT
ejpam-6056	340	6	541	541	NUM
ejpam-6056	340	7	,	,	PUNCT
ejpam-6056	340	8	2024	2024	NUM
ejpam-6056	340	9	.	.	PUNCT
ejpam-6056	341	1	[	[	X
ejpam-6056	341	2	17	17	NUM
ejpam-6056	341	3	]	]	X
ejpam-6056	341	4	h	h	NOUN
ejpam-6056	341	5	qawaqneh	qawaqneh	NOUN
ejpam-6056	341	6	;	;	PUNCT
ejpam-6056	341	7	m	m	PROPN
ejpam-6056	341	8	s	s	NOUN
ejpam-6056	341	9	noorani	noorani	ADJ
ejpam-6056	341	10	and	and	CCONJ
ejpam-6056	341	11	w	w	PROPN
ejpam-6056	341	12	shatanawi	shatanawi	PROPN
ejpam-6056	341	13	.	.	PUNCT
ejpam-6056	342	1	fixed	fix	VERB
ejpam-6056	342	2	point	point	NOUN
ejpam-6056	342	3	results	result	NOUN
ejpam-6056	342	4	for	for	ADP
ejpam-6056	342	5	geraghty	geraghty	PROPN
ejpam-6056	342	6	type	type	NOUN
ejpam-6056	342	7	generalized	generalize	VERB
ejpam-6056	342	8	f	f	NOUN
ejpam-6056	342	9	-	-	PUNCT
ejpam-6056	342	10	contraction	contraction	NOUN
ejpam-6056	342	11	for	for	ADP
ejpam-6056	342	12	weak	weak	ADJ
ejpam-6056	342	13	admissible	admissible	ADJ
ejpam-6056	342	14	mappings	mapping	NOUN
ejpam-6056	342	15	in	in	ADP
ejpam-6056	342	16	metric	metric	ADJ
ejpam-6056	342	17	-	-	PUNCT
ejpam-6056	342	18	like	like	ADJ
ejpam-6056	342	19	spaces	space	NOUN
ejpam-6056	342	20	.	.	PUNCT
ejpam-6056	343	1	eur	eur	PROPN
ejpam-6056	343	2	.	.	PUNCT
ejpam-6056	344	1	j.	j.	PROPN
ejpam-6056	344	2	pure	pure	PROPN
ejpam-6056	344	3	appl	appl	PROPN
ejpam-6056	344	4	.	.	PUNCT
ejpam-6056	344	5	math	math	PROPN
ejpam-6056	344	6	.	.	PUNCT
ejpam-6056	344	7	,	,	PUNCT
ejpam-6056	344	8	11(3):702–716	11(3):702–716	PROPN
ejpam-6056	344	9	,	,	PUNCT
ejpam-6056	344	10	2018	2018	NUM
ejpam-6056	344	11	.	.	PUNCT
ejpam-6056	345	1	[	[	X
ejpam-6056	345	2	18	18	NUM
ejpam-6056	345	3	]	]	X
ejpam-6056	345	4	k	k	X
ejpam-6056	345	5	nisse	nisse	PROPN
ejpam-6056	345	6	;	;	PUNCT
ejpam-6056	345	7	h	h	NOUN
ejpam-6056	345	8	qawagneh	qawagneh	NOUN
ejpam-6056	345	9	;	;	PUNCT
ejpam-6056	345	10	g	g	PROPN
ejpam-6056	345	11	al	al	PROPN
ejpam-6056	345	12	-	-	PUNCT
ejpam-6056	345	13	musannef	musannef	NOUN
ejpam-6056	345	14	;	;	PUNCT
ejpam-6056	345	15	h	h	NOUN
ejpam-6056	345	16	alsamir	alsamir	NOUN
ejpam-6056	345	17	and	and	CCONJ
ejpam-6056	345	18	s	s	VERB
ejpam-6056	345	19	beloul	beloul	PRON
ejpam-6056	345	20	.	.	PUNCT
ejpam-6056	346	1	fixed	fix	VERB
ejpam-6056	346	2	points	point	NOUN
ejpam-6056	346	3	for	for	ADP
ejpam-6056	346	4	generalized	generalized	ADJ
ejpam-6056	346	5	contractions	contraction	NOUN
ejpam-6056	346	6	in	in	ADP
ejpam-6056	346	7	b	b	NOUN
ejpam-6056	346	8	-	-	PUNCT
ejpam-6056	346	9	gauge	gauge	NOUN
ejpam-6056	346	10	spaces	space	NOUN
ejpam-6056	346	11	and	and	CCONJ
ejpam-6056	346	12	applications	application	NOUN
ejpam-6056	346	13	.	.	PUNCT
ejpam-6056	347	1	eur	eur	PROPN
ejpam-6056	347	2	.	.	PUNCT
ejpam-6056	348	1	j.	j.	PROPN
ejpam-6056	348	2	pure	pure	PROPN
ejpam-6056	348	3	appl	appl	PROPN
ejpam-6056	348	4	.	.	PUNCT
ejpam-6056	348	5	math	math	PROPN
ejpam-6056	348	6	.	.	PUNCT
ejpam-6056	348	7	,	,	PUNCT
ejpam-6056	348	8	18(2	18(2	NUM
ejpam-6056	348	9	)	)	PUNCT
ejpam-6056	348	10	,	,	PUNCT
ejpam-6056	348	11	2025	2025	NUM
ejpam-6056	348	12	.	.	PUNCT
ejpam-6056	349	1	[	[	X
ejpam-6056	349	2	19	19	NUM
ejpam-6056	349	3	]	]	X
ejpam-6056	349	4	h	h	NOUN
ejpam-6056	349	5	qawagneh	qawagneh	PROPN
ejpam-6056	349	6	;	;	PUNCT
ejpam-6056	349	7	m	m	PROPN
ejpam-6056	349	8	s	s	PART
ejpam-6056	349	9	m	m	VERB
ejpam-6056	349	10	noorani	noorani	ADJ
ejpam-6056	349	11	;	;	PUNCT
ejpam-6056	349	12	h	h	NOUN
ejpam-6056	349	13	aydi	aydi	VERB
ejpam-6056	349	14	and	and	CCONJ
ejpam-6056	349	15	w	w	NOUN
ejpam-6056	349	16	shatanawi	shatanawi	ADJ
ejpam-6056	349	17	.	.	PUNCT
ejpam-6056	350	1	on	on	ADP
ejpam-6056	350	2	common	common	ADJ
ejpam-6056	350	3	fixed	fix	VERB
ejpam-6056	350	4	point	point	NOUN
ejpam-6056	350	5	results	result	NOUN
ejpam-6056	350	6	for	for	ADP
ejpam-6056	350	7	new	new	ADJ
ejpam-6056	350	8	contractions	contraction	NOUN
ejpam-6056	350	9	with	with	ADP
ejpam-6056	350	10	applications	application	NOUN
ejpam-6056	350	11	to	to	PART
ejpam-6056	350	12	graph	graph	VERB
ejpam-6056	350	13	and	and	CCONJ
ejpam-6056	350	14	integral	integral	ADJ
ejpam-6056	350	15	equations	equation	NOUN
ejpam-6056	350	16	.	.	PUNCT
ejpam-6056	351	1	mathematics	mathematic	NOUN
ejpam-6056	351	2	,	,	PUNCT
ejpam-6056	351	3	7(11	7(11	NUM
ejpam-6056	351	4	)	)	PUNCT
ejpam-6056	351	5	,	,	PUNCT
ejpam-6056	351	6	2019	2019	NUM
ejpam-6056	351	7	.	.	PUNCT
ejpam-6056	352	1	[	[	X
ejpam-6056	352	2	20	20	NUM
ejpam-6056	352	3	]	]	PUNCT
ejpam-6056	352	4	s	s	VERB
ejpam-6056	352	5	treanta	treanta	NOUN
ejpam-6056	352	6	;	;	PUNCT
ejpam-6056	352	7	c	c	PROPN
ejpam-6056	352	8	varsan	varsan	NOUN
ejpam-6056	352	9	.	.	PUNCT
ejpam-6056	353	1	weak	weak	ADJ
ejpam-6056	353	2	small	small	ADJ
ejpam-6056	353	3	controls	control	NOUN
ejpam-6056	353	4	and	and	CCONJ
ejpam-6056	353	5	approximations	approximation	NOUN
ejpam-6056	353	6	associated	associate	VERB
ejpam-6056	353	7	with	with	ADP
ejpam-6056	353	8	controllable	controllable	ADJ
ejpam-6056	353	9	affine	affine	NOUN
ejpam-6056	353	10	control	control	NOUN
ejpam-6056	353	11	systems	system	NOUN
ejpam-6056	353	12	.	.	PUNCT
ejpam-6056	354	1	j.	j.	PROPN
ejpam-6056	354	2	differential	differential	PROPN
ejpam-6056	354	3	equ	equ	PROPN
ejpam-6056	354	4	.	.	PROPN
ejpam-6056	354	5	,	,	PUNCT
ejpam-6056	354	6	7(7	7(7	NUM
ejpam-6056	354	7	)	)	PUNCT
ejpam-6056	354	8	,	,	PUNCT
ejpam-6056	354	9	2013	2013	NUM
ejpam-6056	354	10	.	.	PUNCT
ejpam-6056	355	1	h.	h.	PROPN
ejpam-6056	355	2	qawaqneh	qawaqneh	PROPN
ejpam-6056	355	3	,	,	PUNCT
ejpam-6056	355	4	j.m	j.m	PROPN
ejpam-6056	355	5	.	.	PROPN
ejpam-6056	355	6	al	al	PROPN
ejpam-6056	355	7	-	-	PUNCT
ejpam-6056	355	8	musannef	musannef	PROPN
ejpam-6056	355	9	,	,	PUNCT
ejpam-6056	355	10	h.	h.	PROPN
ejpam-6056	355	11	alsamir	alsamir	PROPN
ejpam-6056	355	12	/	/	SYM
ejpam-6056	355	13	eur	eur	PROPN
ejpam-6056	355	14	.	.	PUNCT
ejpam-6056	356	1	j.	j.	PROPN
ejpam-6056	356	2	pure	pure	PROPN
ejpam-6056	356	3	appl	appl	PROPN
ejpam-6056	356	4	.	.	PROPN
ejpam-6056	356	5	math	math	PROPN
ejpam-6056	356	6	,	,	PUNCT
ejpam-6056	356	7	18	18	NUM
ejpam-6056	356	8	(	(	PUNCT
ejpam-6056	356	9	3	3	NUM
ejpam-6056	356	10	)	)	PUNCT
ejpam-6056	356	11	(	(	PUNCT
ejpam-6056	356	12	2025	2025	NUM
ejpam-6056	356	13	)	)	PUNCT
ejpam-6056	356	14	,	,	PUNCT
ejpam-6056	356	15	6056	6056	NUM
ejpam-6056	356	16	16	16	NUM
ejpam-6056	356	17	of	of	ADP
ejpam-6056	356	18	16	16	NUM
ejpam-6056	357	1	[	[	X
ejpam-6056	357	2	21	21	NUM
ejpam-6056	357	3	]	]	PUNCT
ejpam-6056	357	4	s	s	PART
ejpam-6056	357	5	treanta	treanta	NOUN
ejpam-6056	357	6	.	.	PUNCT
ejpam-6056	358	1	gradient	gradient	NOUN
ejpam-6056	358	2	structures	structure	NOUN
ejpam-6056	358	3	associated	associate	VERB
ejpam-6056	358	4	with	with	ADP
ejpam-6056	358	5	a	a	DET
ejpam-6056	358	6	polynomial	polynomial	ADJ
ejpam-6056	358	7	differential	differential	NOUN
ejpam-6056	358	8	equation	equation	NOUN
ejpam-6056	358	9	.	.	PUNCT
ejpam-6056	359	1	mathematics	mathematic	NOUN
ejpam-6056	359	2	,	,	PUNCT
ejpam-6056	359	3	8(4	8(4	NUM
ejpam-6056	359	4	)	)	PUNCT
ejpam-6056	359	5	,	,	PUNCT
ejpam-6056	359	6	2020	2020	NUM
ejpam-6056	359	7	.	.	PUNCT
ejpam-6056	360	1	[	[	X
ejpam-6056	360	2	22	22	NUM
ejpam-6056	360	3	]	]	X
ejpam-6056	360	4	b	b	X
ejpam-6056	360	5	maayah	maayah	NOUN
ejpam-6056	360	6	;	;	PUNCT
ejpam-6056	360	7	o	o	X
ejpam-6056	360	8	a	a	DET
ejpam-6056	360	9	arqub	arqub	NOUN
ejpam-6056	360	10	.	.	PUNCT
ejpam-6056	361	1	uncertain	uncertain	ADJ
ejpam-6056	361	2	m	m	ADJ
ejpam-6056	361	3	-	-	PUNCT
ejpam-6056	361	4	fractional	fractional	ADJ
ejpam-6056	361	5	differential	differential	NOUN
ejpam-6056	361	6	problems	problem	NOUN
ejpam-6056	361	7	:	:	PUNCT
ejpam-6056	361	8	existence	existence	NOUN
ejpam-6056	361	9	,	,	PUNCT
ejpam-6056	361	10	uniqueness	uniqueness	NOUN
ejpam-6056	361	11	,	,	PUNCT
ejpam-6056	361	12	and	and	CCONJ
ejpam-6056	361	13	approximations	approximation	NOUN
ejpam-6056	361	14	using	use	VERB
ejpam-6056	361	15	hilbert	hilbert	NOUN
ejpam-6056	361	16	reproducing	reproducing	NOUN
ejpam-6056	361	17	technique	technique	NOUN
ejpam-6056	361	18	provisioner	provisioner	NOUN
ejpam-6056	361	19	with	with	ADP
ejpam-6056	361	20	the	the	DET
ejpam-6056	361	21	case	case	NOUN
ejpam-6056	361	22	application	application	NOUN
ejpam-6056	361	23	:	:	PUNCT
ejpam-6056	361	24	series	series	NOUN
ejpam-6056	361	25	resistor	resistor	NOUN
ejpam-6056	361	26	-	-	PUNCT
ejpam-6056	361	27	inductor	inductor	NOUN
ejpam-6056	361	28	circuit	circuit	NOUN
ejpam-6056	361	29	.	.	PUNCT
ejpam-6056	362	1	physica	physica	PROPN
ejpam-6056	362	2	scripta	scripta	PROPN
ejpam-6056	362	3	,	,	PUNCT
ejpam-6056	362	4	99(2	99(2	NOUN
ejpam-6056	362	5	)	)	PUNCT
ejpam-6056	362	6	,	,	PUNCT
ejpam-6056	362	7	2024	2024	NUM
ejpam-6056	362	8	.	.	PUNCT
ejpam-6056	363	1	[	[	X
ejpam-6056	363	2	23	23	NUM
ejpam-6056	363	3	]	]	X
ejpam-6056	363	4	h	h	NOUN
ejpam-6056	363	5	sweis	sweis	NOUN
ejpam-6056	363	6	;	;	PUNCT
ejpam-6056	363	7	o	o	X
ejpam-6056	363	8	a	a	DET
ejpam-6056	363	9	arqub	arqub	NOUN
ejpam-6056	363	10	and	and	CCONJ
ejpam-6056	363	11	n	n	ADV
ejpam-6056	363	12	shawagfeh	shawagfeh	NOUN
ejpam-6056	363	13	.	.	PUNCT
ejpam-6056	364	1	ractional	ractional	ADJ
ejpam-6056	364	2	delay	delay	PROPN
ejpam-6056	364	3	integrodifferential	integrodifferential	ADJ
ejpam-6056	364	4	equations	equation	NOUN
ejpam-6056	364	5	of	of	ADP
ejpam-6056	364	6	nonsingular	nonsingular	ADJ
ejpam-6056	364	7	kernels	kernel	NOUN
ejpam-6056	364	8	:	:	PUNCT
ejpam-6056	364	9	existence	existence	NOUN
ejpam-6056	364	10	,	,	PUNCT
ejpam-6056	364	11	uniqueness	uniqueness	NOUN
ejpam-6056	364	12	,	,	PUNCT
ejpam-6056	364	13	and	and	CCONJ
ejpam-6056	364	14	numerical	numerical	ADJ
ejpam-6056	364	15	solutions	solution	NOUN
ejpam-6056	364	16	using	use	VERB
ejpam-6056	364	17	galerkin	galerkin	ADJ
ejpam-6056	364	18	algorithm	algorithm	NOUN
ejpam-6056	364	19	based	base	VERB
ejpam-6056	364	20	on	on	ADP
ejpam-6056	364	21	shifted	shift	VERB
ejpam-6056	364	22	legendre	legendre	PROPN
ejpam-6056	364	23	polynomials	polynomial	NOUN
ejpam-6056	364	24	.	.	PUNCT
ejpam-6056	365	1	int	int	NOUN
ejpam-6056	365	2	.	.	PUNCT
ejpam-6056	366	1	j.	j.	PROPN
ejpam-6056	366	2	mod	mod	PROPN
ejpam-6056	366	3	.	.	PUNCT
ejpam-6056	367	1	phys	phy	NOUN
ejpam-6056	367	2	.	.	PUNCT
ejpam-6056	368	1	c	c	X
ejpam-6056	368	2	,	,	PUNCT
ejpam-6056	368	3	34(4	34(4	NUM
ejpam-6056	368	4	)	)	PUNCT
ejpam-6056	368	5	,	,	PUNCT
ejpam-6056	368	6	2023	2023	NUM
ejpam-6056	368	7	.	.	PUNCT
ejpam-6056	369	1	[	[	X
ejpam-6056	369	2	24	24	NUM
ejpam-6056	369	3	]	]	X
ejpam-6056	369	4	k	k	X
ejpam-6056	369	5	abodayeh	abodayeh	PROPN
ejpam-6056	369	6	;	;	PUNCT
ejpam-6056	369	7	s	s	VERB
ejpam-6056	369	8	khayyam	khayyam	PROPN
ejpam-6056	369	9	shah	shah	PROPN
ejpam-6056	369	10	;	;	PUNCT
ejpam-6056	369	11	m	m	VERB
ejpam-6056	369	12	sarwar	sarwar	ADJ
ejpam-6056	369	13	;	;	PUNCT
ejpam-6056	369	14	c	c	NOUN
ejpam-6056	369	15	promsakon	promsakon	NOUN
ejpam-6056	369	16	and	and	CCONJ
ejpam-6056	369	17	t	t	NOUN
ejpam-6056	369	18	sitthiwirattham	sitthiwirattham	NOUN
ejpam-6056	369	19	.	.	PUNCT
ejpam-6056	370	1	ciric	ciric	ADJ
ejpam-6056	370	2	-	-	PUNCT
ejpam-6056	370	3	type	type	NOUN
ejpam-6056	370	4	generalized	generalized	ADJ
ejpam-6056	370	5	f	f	NOUN
ejpam-6056	370	6	-	-	PUNCT
ejpam-6056	370	7	contractions	contraction	NOUN
ejpam-6056	370	8	with	with	ADP
ejpam-6056	370	9	integral	integral	ADJ
ejpam-6056	370	10	inclusion	inclusion	NOUN
ejpam-6056	370	11	in	in	ADP
ejpam-6056	370	12	super	super	ADJ
ejpam-6056	370	13	metric	metric	ADJ
ejpam-6056	370	14	spaces	space	NOUN
ejpam-6056	370	15	.	.	PUNCT
ejpam-6056	371	1	results	result	NOUN
ejpam-6056	371	2	control	control	PROPN
ejpam-6056	371	3	optim	optim	PROPN
ejpam-6056	371	4	.	.	PUNCT
ejpam-6056	371	5	,	,	PUNCT
ejpam-6056	371	6	16(100443	16(100443	NUM
ejpam-6056	371	7	)	)	PUNCT
ejpam-6056	371	8	,	,	PUNCT
ejpam-6056	371	9	2024	2024	NUM
ejpam-6056	371	10	.	.	PUNCT
ejpam-6056	372	1	[	[	X
ejpam-6056	372	2	25	25	NUM
ejpam-6056	372	3	]	]	X
ejpam-6056	372	4	k	k	PROPN
ejpam-6056	372	5	aldwoah	aldwoah	PROPN
ejpam-6056	372	6	;	;	PUNCT
ejpam-6056	372	7	s	s	PART
ejpam-6056	372	8	k	k	PROPN
ejpam-6056	372	9	shah	shah	NOUN
ejpam-6056	372	10	;	;	PUNCT
ejpam-6056	372	11	s	s	VERB
ejpam-6056	372	12	hussain	hussain	NOUN
ejpam-6056	372	13	;	;	PUNCT
ejpam-6056	372	14	m	m	VERB
ejpam-6056	372	15	a	a	DET
ejpam-6056	372	16	almalahi	almalahi	NOUN
ejpam-6056	372	17	;	;	PUNCT
ejpam-6056	372	18	y	y	PROPN
ejpam-6056	372	19	a	a	PRON
ejpam-6056	372	20	s	s	X
ejpam-6056	372	21	arko	arko	PROPN
ejpam-6056	372	22	and	and	CCONJ
ejpam-6056	372	23	m	m	PROPN
ejpam-6056	372	24	hleili	hleili	NOUN
ejpam-6056	372	25	.	.	PUNCT
ejpam-6056	373	1	investigating	investigate	VERB
ejpam-6056	373	2	fractal	fractal	ADJ
ejpam-6056	373	3	fractional	fractional	ADJ
ejpam-6056	373	4	pdes	pde	NOUN
ejpam-6056	373	5	,	,	PUNCT
ejpam-6056	373	6	electric	electric	ADJ
ejpam-6056	373	7	circuits	circuit	NOUN
ejpam-6056	373	8	,	,	PUNCT
ejpam-6056	373	9	and	and	CCONJ
ejpam-6056	373	10	integral	integral	ADJ
ejpam-6056	373	11	inclusions	inclusion	NOUN
ejpam-6056	373	12	via	via	ADP
ejpam-6056	373	13	(	(	PUNCT
ejpam-6056	373	14	ψ	ψ	X
ejpam-6056	373	15	,	,	PUNCT
ejpam-6056	373	16	ϕ)−rational	ϕ)−rational	ADJ
ejpam-6056	373	17	type	type	NOUN
ejpam-6056	373	18	contractions	contraction	NOUN
ejpam-6056	373	19	.	.	PUNCT
ejpam-6056	374	1	sci	sci	PROPN
ejpam-6056	374	2	.	.	PROPN
ejpam-6056	374	3	rep	rep	PROPN
ejpam-6056	374	4	.	.	PROPN
ejpam-6056	374	5	,	,	PUNCT
ejpam-6056	374	6	14(23546	14(23546	NUM
ejpam-6056	374	7	)	)	PUNCT
ejpam-6056	374	8	,	,	PUNCT
ejpam-6056	374	9	2024	2024	NUM
ejpam-6056	374	10	.	.	PUNCT
ejpam-6056	375	1	[	[	X
ejpam-6056	375	2	26	26	NUM
ejpam-6056	375	3	]	]	X
ejpam-6056	375	4	k	k	PROPN
ejpam-6056	375	5	aldwoah	aldwoah	PROPN
ejpam-6056	375	6	;	;	PUNCT
ejpam-6056	375	7	s	s	PART
ejpam-6056	375	8	k	k	PROPN
ejpam-6056	375	9	shah	shah	PROPN
ejpam-6056	375	10	;	;	PUNCT
ejpam-6056	375	11	a	a	DET
ejpam-6056	375	12	mustafa	mustafa	PROPN
ejpam-6056	375	13	;	;	PUNCT
ejpam-6056	375	14	m	m	VERB
ejpam-6056	375	15	a	a	DET
ejpam-6056	375	16	almalahi	almalahi	NOUN
ejpam-6056	375	17	;	;	PUNCT
ejpam-6056	375	18	m	m	PROPN
ejpam-6056	375	19	hassan	hassan	PROPN
ejpam-6056	375	20	and	and	CCONJ
ejpam-6056	375	21	a	a	DET
ejpam-6056	375	22	alsulami	alsulami	NOUN
ejpam-6056	375	23	.	.	PUNCT
ejpam-6056	376	1	rational	rational	ADJ
ejpam-6056	376	2	-	-	PUNCT
ejpam-6056	376	3	type	type	NOUN
ejpam-6056	376	4	fixed	fix	VERB
ejpam-6056	376	5	-	-	PUNCT
ejpam-6056	376	6	point	point	NOUN
ejpam-6056	376	7	theorems	theorem	NOUN
ejpam-6056	376	8	in	in	ADP
ejpam-6056	376	9	b−metric	b−metric	ADJ
ejpam-6056	376	10	spaces	space	NOUN
ejpam-6056	376	11	and	and	CCONJ
ejpam-6056	376	12	their	their	PRON
ejpam-6056	376	13	application	application	NOUN
ejpam-6056	376	14	to	to	ADP
ejpam-6056	376	15	economic	economic	ADJ
ejpam-6056	376	16	growth	growth	NOUN
ejpam-6056	376	17	and	and	CCONJ
ejpam-6056	376	18	market	market	NOUN
ejpam-6056	376	19	equilibrium	equilibrium	NOUN
ejpam-6056	376	20	.	.	PUNCT
ejpam-6056	377	1	bound	bind	VERB
ejpam-6056	377	2	value	value	NOUN
ejpam-6056	377	3	probl	probl	NOUN
ejpam-6056	377	4	.	.	PUNCT
ejpam-6056	377	5	,	,	PUNCT
ejpam-6056	377	6	2025(11	2025(11	NUM
ejpam-6056	377	7	)	)	PUNCT
ejpam-6056	377	8	,	,	PUNCT
ejpam-6056	377	9	2025	2025	NUM
ejpam-6056	377	10	.	.	PUNCT
ejpam-6056	378	1	[	[	X
ejpam-6056	378	2	27	27	NUM
ejpam-6056	378	3	]	]	X
ejpam-6056	378	4	s	s	PART
ejpam-6056	378	5	khayyam	khayyam	PROPN
ejpam-6056	378	6	shah	shah	PROPN
ejpam-6056	378	7	;	;	PUNCT
ejpam-6056	378	8	m	m	VERB
ejpam-6056	378	9	sarwar	sarwar	ADJ
ejpam-6056	378	10	and	and	CCONJ
ejpam-6056	378	11	a	a	DET
ejpam-6056	378	12	khan	khan	PROPN
ejpam-6056	378	13	.	.	PUNCT
ejpam-6056	379	1	solving	solve	VERB
ejpam-6056	379	2	integral	integral	ADJ
ejpam-6056	379	3	equations	equation	NOUN
ejpam-6056	379	4	via	via	ADP
ejpam-6056	379	5	fixed	fix	VERB
ejpam-6056	379	6	point	point	NOUN
ejpam-6056	379	7	results	result	NOUN
ejpam-6056	379	8	involving	involve	VERB
ejpam-6056	379	9	rational	rational	ADJ
ejpam-6056	379	10	-	-	PUNCT
ejpam-6056	379	11	type	type	NOUN
ejpam-6056	379	12	inequalities	inequality	NOUN
ejpam-6056	379	13	.	.	PUNCT
ejpam-6056	380	1	axioms	axiom	NOUN
ejpam-6056	380	2	,	,	PUNCT
ejpam-6056	380	3	12(7	12(7	NUM
ejpam-6056	380	4	)	)	PUNCT
ejpam-6056	380	5	,	,	PUNCT
ejpam-6056	380	6	2023	2023	NUM
ejpam-6056	380	7	.	.	PUNCT
ejpam-6056	381	1	[	[	X
ejpam-6056	381	2	28	28	NUM
ejpam-6056	381	3	]	]	X
ejpam-6056	381	4	s	s	PART
ejpam-6056	381	5	k	k	PROPN
ejpam-6056	381	6	shah	shah	NOUN
ejpam-6056	381	7	;	;	PUNCT
ejpam-6056	381	8	m	m	VERB
ejpam-6056	381	9	sarwar	sarwar	ADJ
ejpam-6056	381	10	;	;	PUNCT
ejpam-6056	381	11	m	m	NOUN
ejpam-6056	381	12	hleili	hleili	NOUN
ejpam-6056	381	13	;	;	PUNCT
ejpam-6056	381	14	m	m	VERB
ejpam-6056	381	15	e	e	NOUN
ejpam-6056	381	16	samei	samei	NOUN
ejpam-6056	381	17	and	and	CCONJ
ejpam-6056	381	18	t	t	PROPN
ejpam-6056	381	19	abdeljawad	abdeljawad	NOUN
ejpam-6056	381	20	.	.	PUNCT
ejpam-6056	382	1	generalized	generalize	VERB
ejpam-6056	382	2	(	(	PUNCT
ejpam-6056	382	3	ψ	ψ	NOUN
ejpam-6056	382	4	,	,	PUNCT
ejpam-6056	382	5	ψ)−contraction	ψ)−contraction	NOUN
ejpam-6056	382	6	to	to	PART
ejpam-6056	382	7	investigate	investigate	VERB
ejpam-6056	382	8	volterra	volterra	NOUN
ejpam-6056	382	9	integral	integral	ADJ
ejpam-6056	382	10	inclusions	inclusion	NOUN
ejpam-6056	382	11	and	and	CCONJ
ejpam-6056	382	12	fractal	fractal	ADJ
ejpam-6056	382	13	fractional	fractional	ADJ
ejpam-6056	382	14	pdes	pde	NOUN
ejpam-6056	382	15	in	in	ADP
ejpam-6056	382	16	super	super	ADJ
ejpam-6056	382	17	-	-	ADJ
ejpam-6056	382	18	metric	metric	ADJ
ejpam-6056	382	19	space	space	NOUN
ejpam-6056	382	20	with	with	ADP
ejpam-6056	382	21	numerical	numerical	ADJ
ejpam-6056	382	22	experiments	experiment	NOUN
ejpam-6056	382	23	.	.	PUNCT
ejpam-6056	383	1	nonlinear	nonlinear	ADJ
ejpam-6056	383	2	engineering	engineering	NOUN
ejpam-6056	383	3	,	,	PUNCT
ejpam-6056	383	4	14(1	14(1	NUM
ejpam-6056	383	5	)	)	PUNCT
ejpam-6056	383	6	,	,	PUNCT
ejpam-6056	383	7	2025	2025	NUM
ejpam-6056	383	8	.	.	PUNCT
ejpam-6056	384	1	[	[	X
ejpam-6056	384	2	29	29	NUM
ejpam-6056	384	3	]	]	X
ejpam-6056	384	4	i	i	PRON
ejpam-6056	384	5	m	m	AUX
ejpam-6056	384	6	batiha	batiha	VERB
ejpam-6056	384	7	;	;	PUNCT
ejpam-6056	384	8	s	s	VERB
ejpam-6056	384	9	a	a	DET
ejpam-6056	384	10	njadat	njadat	NOUN
ejpam-6056	384	11	;	;	PUNCT
ejpam-6056	384	12	r	r	NOUN
ejpam-6056	384	13	m	m	PROPN
ejpam-6056	384	14	batyha	batyha	NOUN
ejpam-6056	384	15	;	;	PUNCT
ejpam-6056	384	16	a	a	DET
ejpam-6056	384	17	zraiqat	zraiqat	NOUN
ejpam-6056	384	18	;	;	PUNCT
ejpam-6056	384	19	a	a	DET
ejpam-6056	384	20	dababneh	dababneh	NOUN
ejpam-6056	384	21	and	and	CCONJ
ejpam-6056	384	22	sh	sh	PROPN
ejpam-6056	384	23	momani	momani	PROPN
ejpam-6056	384	24	.	.	PUNCT
ejpam-6056	385	1	design	design	NOUN
ejpam-6056	385	2	fractional	fractional	ADJ
ejpam-6056	385	3	-	-	PUNCT
ejpam-6056	385	4	order	order	NOUN
ejpam-6056	385	5	pid	pid	NOUN
ejpam-6056	385	6	controllers	controller	NOUN
ejpam-6056	385	7	for	for	ADP
ejpam-6056	385	8	single	single	ADJ
ejpam-6056	385	9	-	-	PUNCT
ejpam-6056	385	10	joint	joint	ADJ
ejpam-6056	385	11	robot	robot	NOUN
ejpam-6056	385	12	arm	arm	NOUN
ejpam-6056	385	13	model	model	NOUN
ejpam-6056	385	14	.	.	PUNCT
ejpam-6056	386	1	international	international	ADJ
ejpam-6056	386	2	journal	journal	NOUN
ejpam-6056	386	3	of	of	ADP
ejpam-6056	386	4	advances	advance	NOUN
ejpam-6056	386	5	in	in	ADP
ejpam-6056	386	6	soft	soft	ADJ
ejpam-6056	386	7	computing	computing	NOUN
ejpam-6056	386	8	and	and	CCONJ
ejpam-6056	386	9	its	its	PRON
ejpam-6056	386	10	applications	application	NOUN
ejpam-6056	386	11	,	,	PUNCT
ejpam-6056	386	12	14(2):96–114	14(2):96–114	NUM
ejpam-6056	386	13	,	,	PUNCT
ejpam-6056	386	14	2022	2022	NUM
ejpam-6056	386	15	.	.	PUNCT
ejpam-6056	387	1	[	[	X
ejpam-6056	387	2	30	30	NUM
ejpam-6056	387	3	]	]	PUNCT
ejpam-6056	387	4	m	m	VERB
ejpam-6056	387	5	elbes	elbe	NOUN
ejpam-6056	387	6	;	;	PUNCT
ejpam-6056	387	7	t	t	PROPN
ejpam-6056	387	8	kanan	kanan	PROPN
ejpam-6056	387	9	;	;	PUNCT
ejpam-6056	387	10	m	m	NOUN
ejpam-6056	387	11	alia	alia	ADJ
ejpam-6056	387	12	and	and	CCONJ
ejpam-6056	387	13	m	m	VERB
ejpam-6056	387	14	ziad	ziad	PROPN
ejpam-6056	387	15	.	.	PUNCT
ejpam-6056	388	1	covd-19	covd-19	NOUN
ejpam-6056	388	2	detection	detection	NOUN
ejpam-6056	388	3	platform	platform	NOUN
ejpam-6056	388	4	from	from	ADP
ejpam-6056	388	5	x	x	ADJ
ejpam-6056	388	6	-	-	NOUN
ejpam-6056	388	7	ray	ray	NOUN
ejpam-6056	388	8	images	image	NOUN
ejpam-6056	388	9	using	use	VERB
ejpam-6056	388	10	deep	deep	ADJ
ejpam-6056	388	11	learning	learning	NOUN
ejpam-6056	388	12	.	.	PUNCT
ejpam-6056	389	1	international	international	ADJ
ejpam-6056	389	2	journal	journal	NOUN
ejpam-6056	389	3	of	of	ADP
ejpam-6056	389	4	advances	advance	NOUN
ejpam-6056	389	5	in	in	ADP
ejpam-6056	389	6	soft	soft	ADJ
ejpam-6056	389	7	computing	computing	NOUN
ejpam-6056	389	8	and	and	CCONJ
ejpam-6056	389	9	its	its	PRON
ejpam-6056	389	10	applications	application	NOUN
ejpam-6056	389	11	,	,	PUNCT
ejpam-6056	389	12	14(1	14(1	NUM
ejpam-6056	389	13	)	)	PUNCT
ejpam-6056	389	14	,	,	PUNCT
ejpam-6056	389	15	2022	2022	NUM
ejpam-6056	389	16	.	.	PUNCT
ejpam-6056	390	1	[	[	X
ejpam-6056	390	2	31	31	NUM
ejpam-6056	390	3	]	]	PUNCT
ejpam-6056	390	4	t	t	PROPN
ejpam-6056	390	5	kanan	kanan	PROPN
ejpam-6056	390	6	;	;	PUNCT
ejpam-6056	390	7	m	m	VERB
ejpam-6056	390	8	elbes	elbe	NOUN
ejpam-6056	390	9	;	;	PUNCT
ejpam-6056	390	10	k	k	PROPN
ejpam-6056	390	11	abu	abu	PROPN
ejpam-6056	390	12	maria	maria	PROPN
ejpam-6056	390	13	and	and	CCONJ
ejpam-6056	390	14	m	m	NOUN
ejpam-6056	390	15	alia	alia	ADJ
ejpam-6056	390	16	.	.	PUNCT
ejpam-6056	391	1	exploring	explore	VERB
ejpam-6056	391	2	the	the	DET
ejpam-6056	391	3	potential	potential	NOUN
ejpam-6056	391	4	of	of	ADP
ejpam-6056	391	5	iot	iot	NOUN
ejpam-6056	391	6	-	-	PUNCT
ejpam-6056	391	7	based	base	VERB
ejpam-6056	391	8	learning	learning	NOUN
ejpam-6056	391	9	environments	environment	NOUN
ejpam-6056	391	10	in	in	ADP
ejpam-6056	391	11	education	education	NOUN
ejpam-6056	391	12	.	.	PUNCT
ejpam-6056	392	1	international	international	ADJ
ejpam-6056	392	2	journal	journal	NOUN
ejpam-6056	392	3	of	of	ADP
ejpam-6056	392	4	advances	advance	NOUN
ejpam-6056	392	5	in	in	ADP
ejpam-6056	392	6	soft	soft	ADJ
ejpam-6056	392	7	computing	computing	NOUN
ejpam-6056	392	8	and	and	CCONJ
ejpam-6056	392	9	its	its	PRON
ejpam-6056	392	10	applications	application	NOUN
ejpam-6056	392	11	,	,	PUNCT
ejpam-6056	392	12	15(2	15(2	NUM
ejpam-6056	392	13	)	)	PUNCT
ejpam-6056	392	14	,	,	PUNCT
ejpam-6056	392	15	2023	2023	NUM
ejpam-6056	392	16	.	.	PUNCT
ejpam-6056	393	1	[	[	X
ejpam-6056	393	2	32	32	NUM
ejpam-6056	393	3	]	]	X
ejpam-6056	393	4	h	h	NOUN
ejpam-6056	393	5	qawaqneh	qawaqneh	NOUN
ejpam-6056	393	6	;	;	PUNCT
ejpam-6056	393	7	y	y	PROPN
ejpam-6056	393	8	alrashedi	alrashedi	PROPN
ejpam-6056	393	9	.	.	PUNCT
ejpam-6056	394	1	mathematical	mathematical	ADJ
ejpam-6056	394	2	and	and	CCONJ
ejpam-6056	394	3	physical	physical	ADJ
ejpam-6056	394	4	analysis	analysis	NOUN
ejpam-6056	394	5	of	of	ADP
ejpam-6056	394	6	fractional	fractional	ADJ
ejpam-6056	394	7	estevez	estevez	PROPN
ejpam-6056	394	8	–	–	PUNCT
ejpam-6056	394	9	mansfield	mansfield	PROPN
ejpam-6056	394	10	–	–	PUNCT
ejpam-6056	394	11	clarkson	clarkson	PROPN
ejpam-6056	394	12	equation	equation	NOUN
ejpam-6056	394	13	.	.	PUNCT
ejpam-6056	395	1	fractal	fractal	ADJ
ejpam-6056	395	2	fract	fract	PROPN
ejpam-6056	395	3	,	,	PUNCT
ejpam-6056	395	4	8(8	8(8	NUM
ejpam-6056	395	5	)	)	PUNCT
ejpam-6056	395	6	,	,	PUNCT
ejpam-6056	395	7	2024	2024	NUM
ejpam-6056	395	8	.	.	PUNCT
ejpam-6056	396	1	[	[	X
ejpam-6056	396	2	33	33	NUM
ejpam-6056	396	3	]	]	X
ejpam-6056	396	4	h	h	NOUN
ejpam-6056	396	5	qawaqneh	qawaqneh	PROPN
ejpam-6056	396	6	;	;	PUNCT
ejpam-6056	396	7	j	j	PROPN
ejpam-6056	396	8	manafian	manafian	NOUN
ejpam-6056	396	9	;	;	PUNCT
ejpam-6056	396	10	m	m	VERB
ejpam-6056	396	11	alharthi	alharthi	PROPN
ejpam-6056	396	12	and	and	CCONJ
ejpam-6056	396	13	y	y	PROPN
ejpam-6056	396	14	alrashed	alrashe	VERB
ejpam-6056	396	15	.	.	PUNCT
ejpam-6056	397	1	stability	stability	NOUN
ejpam-6056	397	2	analysis	analysis	NOUN
ejpam-6056	397	3	,	,	PUNCT
ejpam-6056	397	4	modulation	modulation	NOUN
ejpam-6056	397	5	instability	instability	NOUN
ejpam-6056	397	6	,	,	PUNCT
ejpam-6056	397	7	and	and	CCONJ
ejpam-6056	397	8	beta	beta	NOUN
ejpam-6056	397	9	-	-	PUNCT
ejpam-6056	397	10	time	time	NOUN
ejpam-6056	397	11	fractional	fractional	ADJ
ejpam-6056	397	12	exact	exact	ADJ
ejpam-6056	397	13	soliton	soliton	NOUN
ejpam-6056	397	14	solutions	solution	NOUN
ejpam-6056	397	15	to	to	ADP
ejpam-6056	397	16	the	the	DET
ejpam-6056	397	17	van	van	PROPN
ejpam-6056	397	18	der	der	NOUN
ejpam-6056	397	19	waals	waal	NOUN
ejpam-6056	397	20	equation	equation	NOUN
ejpam-6056	397	21	.	.	PUNCT
ejpam-6056	398	1	mathematics	mathematic	NOUN
ejpam-6056	398	2	,	,	PUNCT
ejpam-6056	398	3	12(14:2257	12(14:2257	NUM
ejpam-6056	398	4	)	)	PUNCT
ejpam-6056	398	5	,	,	PUNCT
ejpam-6056	398	6	2024	2024	NUM
ejpam-6056	398	7	.	.	PUNCT
ejpam-6056	399	1	[	[	X
ejpam-6056	399	2	34	34	NUM
ejpam-6056	399	3	]	]	X
ejpam-6056	399	4	m	m	VERB
ejpam-6056	399	5	mashkhas	mashkha	NOUN
ejpam-6056	399	6	;	;	PUNCT
ejpam-6056	399	7	g	g	PROPN
ejpam-6056	399	8	hussein	hussein	PROPN
ejpam-6056	399	9	;	;	PUNCT
ejpam-6056	400	1	m	m	VERB
ejpam-6056	400	2	g	g	PROPN
ejpam-6056	400	3	bin	bin	PROPN
ejpam-6056	400	4	-	-	PROPN
ejpam-6056	400	5	saad	saad	PROPN
ejpam-6056	400	6	and	and	CCONJ
ejpam-6056	400	7	a	a	DET
ejpam-6056	400	8	al	al	PROPN
ejpam-6056	400	9	-	-	PUNCT
ejpam-6056	400	10	sayad	sayad	PROPN
ejpam-6056	400	11	anter	anter	NOUN
ejpam-6056	400	12	.	.	PUNCT
ejpam-6056	401	1	fixed	fix	VERB
ejpam-6056	401	2	point	point	NOUN
ejpam-6056	401	3	results	result	NOUN
ejpam-6056	401	4	of	of	ADP
ejpam-6056	401	5	rational	rational	ADJ
ejpam-6056	401	6	type	type	NOUN
ejpam-6056	401	7	-	-	PUNCT
ejpam-6056	401	8	contraction	contraction	NOUN
ejpam-6056	401	9	mapping	mapping	NOUN
ejpam-6056	401	10	in	in	ADP
ejpam-6056	401	11	b	b	NOUN
ejpam-6056	401	12	-	-	ADJ
ejpam-6056	401	13	metric	metric	ADJ
ejpam-6056	401	14	spaces	space	NOUN
ejpam-6056	401	15	with	with	ADP
ejpam-6056	401	16	an	an	DET
ejpam-6056	401	17	application	application	NOUN
ejpam-6056	401	18	.	.	PUNCT
ejpam-6056	402	1	earthline	earthline	PROPN
ejpam-6056	402	2	j.	j.	PROPN
ejpam-6056	402	3	math	math	PROPN
ejpam-6056	402	4	.	.	PUNCT
ejpam-6056	403	1	sci	sci	PROPN
ejpam-6056	403	2	.	.	PROPN
ejpam-6056	403	3	,	,	PUNCT
ejpam-6056	403	4	12(2):141–164	12(2):141–164	NOUN
ejpam-6056	403	5	,	,	PUNCT
ejpam-6056	403	6	2023	2023	NUM
ejpam-6056	403	7	.	.	PUNCT
ejpam-6056	404	1	[	[	X
ejpam-6056	404	2	35	35	NUM
ejpam-6056	404	3	]	]	X
ejpam-6056	404	4	o	o	X
ejpam-6056	404	5	popescu	popescu	NOUN
ejpam-6056	404	6	.	.	PUNCT
ejpam-6056	405	1	some	some	DET
ejpam-6056	405	2	new	new	ADJ
ejpam-6056	405	3	fixed	fix	VERB
ejpam-6056	405	4	point	point	NOUN
ejpam-6056	405	5	theorems	theorem	NOUN
ejpam-6056	405	6	for	for	ADP
ejpam-6056	405	7	α	α	NOUN
ejpam-6056	405	8	-	-	PUNCT
ejpam-6056	405	9	geraghty	geraghty	VERB
ejpam-6056	405	10	contraction	contraction	NOUN
ejpam-6056	405	11	type	type	NOUN
ejpam-6056	405	12	maps	map	NOUN
ejpam-6056	405	13	in	in	ADP
ejpam-6056	405	14	metric	metric	ADJ
ejpam-6056	405	15	spaces	space	NOUN
ejpam-6056	405	16	.	.	PUNCT
ejpam-6056	406	1	fixed	fix	VERB
ejpam-6056	406	2	point	point	NOUN
ejpam-6056	406	3	theory	theory	NOUN
ejpam-6056	406	4	appl	appl	PROPN
ejpam-6056	406	5	.	.	PROPN
ejpam-6056	406	6	,	,	PUNCT
ejpam-6056	406	7	2014(190	2014(190	NUM
ejpam-6056	406	8	)	)	PUNCT
ejpam-6056	406	9	,	,	PUNCT
ejpam-6056	406	10	2014	2014	NUM
ejpam-6056	406	11	.	.	PUNCT