id	sid	tid	token	lemma	pos
ejpam-6440	1	1	european	european	PROPN
ejpam-6440	1	2	journal	journal	PROPN
ejpam-6440	1	3	of	of	ADP
ejpam-6440	1	4	pure	pure	ADJ
ejpam-6440	1	5	and	and	CCONJ
ejpam-6440	1	6	applied	applied	ADJ
ejpam-6440	1	7	mathematics	mathematic	NOUN
ejpam-6440	1	8	2025	2025	NUM
ejpam-6440	1	9	,	,	PUNCT
ejpam-6440	1	10	vol	vol	NOUN
ejpam-6440	1	11	.	.	PROPN
ejpam-6440	1	12	18	18	NUM
ejpam-6440	1	13	,	,	PUNCT
ejpam-6440	1	14	issue	issue	NOUN
ejpam-6440	1	15	3	3	NUM
ejpam-6440	1	16	,	,	PUNCT
ejpam-6440	1	17	article	article	NOUN
ejpam-6440	1	18	number	number	NOUN
ejpam-6440	1	19	6440	6440	NUM
ejpam-6440	1	20	issn	issn	VERB
ejpam-6440	1	21	1307	1307	NUM
ejpam-6440	1	22	-	-	SYM
ejpam-6440	1	23	5543	5543	NUM
ejpam-6440	1	24	–	–	PUNCT
ejpam-6440	1	25	ejpam.com	ejpam.com	X
ejpam-6440	1	26	published	publish	VERB
ejpam-6440	1	27	by	by	ADP
ejpam-6440	1	28	new	new	PROPN
ejpam-6440	1	29	york	york	PROPN
ejpam-6440	1	30	business	business	PROPN
ejpam-6440	1	31	global	global	ADJ
ejpam-6440	1	32	fixed	fix	VERB
ejpam-6440	1	33	point	point	NOUN
ejpam-6440	1	34	theory	theory	NOUN
ejpam-6440	1	35	in	in	ADP
ejpam-6440	1	36	mr	mr	PROPN
ejpam-6440	1	37	-	-	PUNCT
ejpam-6440	1	38	metric	metric	ADJ
ejpam-6440	1	39	spaces	space	NOUN
ejpam-6440	1	40	:	:	PUNCT
ejpam-6440	1	41	fundamental	fundamental	ADJ
ejpam-6440	1	42	theorems	theorem	NOUN
ejpam-6440	1	43	and	and	CCONJ
ejpam-6440	1	44	applications	application	NOUN
ejpam-6440	1	45	to	to	ADP
ejpam-6440	1	46	integral	integral	ADJ
ejpam-6440	1	47	equations	equation	NOUN
ejpam-6440	1	48	and	and	CCONJ
ejpam-6440	1	49	neutron	neutron	NOUN
ejpam-6440	1	50	transport	transport	PROPN
ejpam-6440	1	51	tariq	tariq	PROPN
ejpam-6440	1	52	a.	a.	PROPN
ejpam-6440	1	53	qawasmeh1	qawasmeh1	PROPN
ejpam-6440	1	54	,	,	PUNCT
ejpam-6440	1	55	abed	abe	VERB
ejpam-6440	1	56	al	al	PROPN
ejpam-6440	1	57	-	-	PUNCT
ejpam-6440	1	58	rahman	rahman	PROPN
ejpam-6440	1	59	m.	m.	PROPN
ejpam-6440	1	60	malkawi1,∗	malkawi1,∗	PROPN
ejpam-6440	1	61	1	1	NUM
ejpam-6440	1	62	department	department	NOUN
ejpam-6440	1	63	of	of	ADP
ejpam-6440	1	64	mathematics	mathematic	NOUN
ejpam-6440	1	65	,	,	PUNCT
ejpam-6440	1	66	faculty	faculty	NOUN
ejpam-6440	1	67	of	of	ADP
ejpam-6440	1	68	arts	art	NOUN
ejpam-6440	1	69	and	and	CCONJ
ejpam-6440	1	70	science	science	NOUN
ejpam-6440	1	71	,	,	PUNCT
ejpam-6440	1	72	amman	amman	PROPN
ejpam-6440	1	73	arab	arab	PROPN
ejpam-6440	1	74	university	university	PROPN
ejpam-6440	1	75	,	,	PUNCT
ejpam-6440	1	76	amman	amman	PROPN
ejpam-6440	1	77	11953	11953	NUM
ejpam-6440	1	78	,	,	PUNCT
ejpam-6440	1	79	jordan	jordan	PROPN
ejpam-6440	1	80	abstract	abstract	PROPN
ejpam-6440	1	81	.	.	PUNCT
ejpam-6440	2	1	this	this	DET
ejpam-6440	2	2	paper	paper	NOUN
ejpam-6440	2	3	establishes	establish	VERB
ejpam-6440	2	4	a	a	DET
ejpam-6440	2	5	comprehensive	comprehensive	ADJ
ejpam-6440	2	6	framework	framework	NOUN
ejpam-6440	2	7	for	for	ADP
ejpam-6440	2	8	fixed	fix	VERB
ejpam-6440	2	9	point	point	NOUN
ejpam-6440	2	10	theory	theory	NOUN
ejpam-6440	2	11	in	in	ADP
ejpam-6440	2	12	mr	mr	PROPN
ejpam-6440	2	13	-	-	PUNCT
ejpam-6440	2	14	metric	metric	ADJ
ejpam-6440	2	15	spaces	space	NOUN
ejpam-6440	2	16	,	,	PUNCT
ejpam-6440	2	17	a	a	DET
ejpam-6440	2	18	generalization	generalization	NOUN
ejpam-6440	2	19	of	of	ADP
ejpam-6440	2	20	standard	standard	ADJ
ejpam-6440	2	21	metric	metric	ADJ
ejpam-6440	2	22	spaces	space	NOUN
ejpam-6440	2	23	that	that	PRON
ejpam-6440	2	24	incorporates	incorporate	VERB
ejpam-6440	2	25	three	three	NUM
ejpam-6440	2	26	-	-	PUNCT
ejpam-6440	2	27	point	point	NOUN
ejpam-6440	2	28	relations	relation	NOUN
ejpam-6440	2	29	.	.	PUNCT
ejpam-6440	3	1	we	we	PRON
ejpam-6440	3	2	present	present	VERB
ejpam-6440	3	3	four	four	NUM
ejpam-6440	3	4	fundamental	fundamental	ADJ
ejpam-6440	3	5	theorems	theorem	NOUN
ejpam-6440	3	6	:	:	PUNCT
ejpam-6440	3	7	(	(	PUNCT
ejpam-6440	3	8	i	i	NOUN
ejpam-6440	3	9	)	)	PUNCT
ejpam-6440	3	10	a	a	DET
ejpam-6440	3	11	banach	banach	NOUN
ejpam-6440	3	12	contraction	contraction	NOUN
ejpam-6440	3	13	principle	principle	NOUN
ejpam-6440	3	14	with	with	ADP
ejpam-6440	3	15	optimal	optimal	ADJ
ejpam-6440	3	16	contraction	contraction	NOUN
ejpam-6440	3	17	constant	constant	ADJ
ejpam-6440	4	1	k	k	X
ejpam-6440	4	2	<	<	X
ejpam-6440	4	3	1	1	NUM
ejpam-6440	4	4	3r	3r	NUM
ejpam-6440	4	5	(	(	PUNCT
ejpam-6440	4	6	ii	ii	NOUN
ejpam-6440	4	7	)	)	PUNCT
ejpam-6440	4	8	a	a	DET
ejpam-6440	4	9	solvability	solvability	NOUN
ejpam-6440	4	10	theorem	theorem	VERB
ejpam-6440	4	11	for	for	ADP
ejpam-6440	4	12	fredholm	fredholm	NOUN
ejpam-6440	4	13	-	-	PUNCT
ejpam-6440	4	14	type	type	NOUN
ejpam-6440	4	15	integral	integral	ADJ
ejpam-6440	4	16	equations	equation	NOUN
ejpam-6440	4	17	(	(	PUNCT
ejpam-6440	4	18	iii	iii	NOUN
ejpam-6440	4	19	)	)	PUNCT
ejpam-6440	4	20	a	a	DET
ejpam-6440	4	21	krasnoselskii	krasnoselskii	NOUN
ejpam-6440	4	22	-	-	PUNCT
ejpam-6440	4	23	type	type	NOUN
ejpam-6440	4	24	hybrid	hybrid	ADJ
ejpam-6440	4	25	fixed	fix	VERB
ejpam-6440	4	26	point	point	NOUN
ejpam-6440	4	27	theorem	theorem	NOUN
ejpam-6440	4	28	(	(	PUNCT
ejpam-6440	4	29	iv	iv	X
ejpam-6440	4	30	)	)	PUNCT
ejpam-6440	4	31	a	a	DET
ejpam-6440	4	32	leray	leray	ADJ
ejpam-6440	4	33	-	-	PUNCT
ejpam-6440	4	34	schauder	schauder	NOUN
ejpam-6440	4	35	alternative	alternative	NOUN
ejpam-6440	4	36	for	for	ADP
ejpam-6440	4	37	generalized	generalized	ADJ
ejpam-6440	4	38	contractions	contraction	NOUN
ejpam-6440	4	39	the	the	DET
ejpam-6440	4	40	theoretical	theoretical	ADJ
ejpam-6440	4	41	results	result	NOUN
ejpam-6440	4	42	are	be	AUX
ejpam-6440	4	43	applied	apply	VERB
ejpam-6440	4	44	to	to	ADP
ejpam-6440	4	45	:	:	PUNCT
ejpam-6440	4	46	•	•	NUM
ejpam-6440	4	47	nonlinear	nonlinear	ADJ
ejpam-6440	4	48	integral	integral	ADJ
ejpam-6440	4	49	equations	equation	NOUN
ejpam-6440	4	50	in	in	ADP
ejpam-6440	4	51	neutron	neutron	NOUN
ejpam-6440	4	52	transport	transport	NOUN
ejpam-6440	4	53	theory	theory	NOUN
ejpam-6440	4	54	•	•	NUM
ejpam-6440	4	55	optimization	optimization	NOUN
ejpam-6440	4	56	problems	problem	NOUN
ejpam-6440	4	57	in	in	ADP
ejpam-6440	4	58	neural	neural	ADJ
ejpam-6440	4	59	networks	network	NOUN
ejpam-6440	4	60	•	•	ADP
ejpam-6440	4	61	boundary	boundary	ADJ
ejpam-6440	4	62	value	value	NOUN
ejpam-6440	4	63	problems	problem	NOUN
ejpam-6440	4	64	for	for	ADP
ejpam-6440	4	65	nonlinear	nonlinear	ADJ
ejpam-6440	4	66	odes	ode	NOUN
ejpam-6440	4	67	key	key	ADJ
ejpam-6440	4	68	innovations	innovation	NOUN
ejpam-6440	4	69	include	include	VERB
ejpam-6440	4	70	the	the	DET
ejpam-6440	4	71	development	development	NOUN
ejpam-6440	4	72	of	of	ADP
ejpam-6440	4	73	error	error	NOUN
ejpam-6440	4	74	estimates	estimate	NOUN
ejpam-6440	4	75	in	in	ADP
ejpam-6440	4	76	the	the	DET
ejpam-6440	4	77	mr	mr	PROPN
ejpam-6440	4	78	-	-	PUNCT
ejpam-6440	4	79	metric	metric	ADJ
ejpam-6440	4	80	framework	framework	NOUN
ejpam-6440	4	81	and	and	CCONJ
ejpam-6440	4	82	the	the	DET
ejpam-6440	4	83	derivation	derivation	NOUN
ejpam-6440	4	84	of	of	ADP
ejpam-6440	4	85	precise	precise	ADJ
ejpam-6440	4	86	existence	existence	NOUN
ejpam-6440	4	87	conditions	condition	NOUN
ejpam-6440	4	88	for	for	ADP
ejpam-6440	4	89	operator	operator	NOUN
ejpam-6440	4	90	equations	equation	NOUN
ejpam-6440	4	91	.	.	PUNCT
ejpam-6440	5	1	the	the	DET
ejpam-6440	5	2	work	work	NOUN
ejpam-6440	5	3	bridges	bridge	VERB
ejpam-6440	5	4	theoretical	theoretical	ADJ
ejpam-6440	5	5	mathematics	mathematic	NOUN
ejpam-6440	5	6	with	with	ADP
ejpam-6440	5	7	practical	practical	ADJ
ejpam-6440	5	8	applications	application	NOUN
ejpam-6440	5	9	in	in	ADP
ejpam-6440	5	10	physics	physics	NOUN
ejpam-6440	5	11	and	and	CCONJ
ejpam-6440	5	12	machine	machine	NOUN
ejpam-6440	5	13	learning	learning	NOUN
ejpam-6440	5	14	.	.	PUNCT
ejpam-6440	6	1	2020	2020	NUM
ejpam-6440	6	2	mathematics	mathematic	NOUN
ejpam-6440	6	3	subject	subject	NOUN
ejpam-6440	6	4	classifications	classification	NOUN
ejpam-6440	6	5	:	:	PUNCT
ejpam-6440	6	6	47h10	47h10	NUM
ejpam-6440	6	7	,	,	PUNCT
ejpam-6440	6	8	54e50	54e50	NUM
ejpam-6440	6	9	,	,	PUNCT
ejpam-6440	6	10	45g10	45g10	NUM
ejpam-6440	6	11	,	,	PUNCT
ejpam-6440	6	12	34b15	34b15	NUM
ejpam-6440	6	13	key	key	ADJ
ejpam-6440	6	14	words	word	NOUN
ejpam-6440	6	15	and	and	CCONJ
ejpam-6440	6	16	phrases	phrase	NOUN
ejpam-6440	6	17	:	:	PUNCT
ejpam-6440	6	18	mr−metric	mr−metric	PROPN
ejpam-6440	6	19	mr	mr	PROPN
ejpam-6440	6	20	-	-	PUNCT
ejpam-6440	6	21	metric	metric	ADJ
ejpam-6440	6	22	spaces	space	NOUN
ejpam-6440	6	23	,	,	PUNCT
ejpam-6440	6	24	fixed	fix	VERB
ejpam-6440	6	25	point	point	NOUN
ejpam-6440	6	26	theory	theory	NOUN
ejpam-6440	6	27	,	,	PUNCT
ejpam-6440	6	28	banach	banach	NOUN
ejpam-6440	6	29	contraction	contraction	NOUN
ejpam-6440	6	30	principle	principle	NOUN
ejpam-6440	6	31	,	,	PUNCT
ejpam-6440	6	32	integral	integral	ADJ
ejpam-6440	6	33	equations	equation	NOUN
ejpam-6440	6	34	,	,	PUNCT
ejpam-6440	6	35	neutron	neutron	NOUN
ejpam-6440	6	36	transport	transport	NOUN
ejpam-6440	6	37	theory	theory	NOUN
ejpam-6440	6	38	,	,	PUNCT
ejpam-6440	6	39	neural	neural	ADJ
ejpam-6440	6	40	network	network	NOUN
ejpam-6440	6	41	optimization	optimization	NOUN
ejpam-6440	6	42	∗corresponding	∗corresponde	VERB
ejpam-6440	6	43	author	author	NOUN
ejpam-6440	6	44	.	.	PUNCT
ejpam-6440	7	1	doi	doi	NOUN
ejpam-6440	7	2	:	:	PUNCT
ejpam-6440	7	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6440	https://doi.org/10.29020/nybg.ejpam.v18i3.6440	PROPN
ejpam-6440	7	4	email	email	NOUN
ejpam-6440	7	5	addresses	address	VERB
ejpam-6440	7	6	:	:	PUNCT
ejpam-6440	7	7	t.qawasmeh@aau.edu.jo	t.qawasmeh@aau.edu.jo	ADP
ejpam-6440	7	8	(	(	PUNCT
ejpam-6440	7	9	t.	t.	NOUN
ejpam-6440	7	10	qawasmeh	qawasmeh	NOUN
ejpam-6440	7	11	)	)	PUNCT
ejpam-6440	7	12	,	,	PUNCT
ejpam-6440	7	13	a.malkawi@aau.edu.jo	a.malkawi@aau.edu.jo	PROPN
ejpam-6440	7	14	,	,	PUNCT
ejpam-6440	7	15	math.malkawi@gmail.com	math.malkawi@gmail.com	X
ejpam-6440	7	16	(	(	PUNCT
ejpam-6440	7	17	a.	a.	NOUN
ejpam-6440	7	18	malkawi	malkawi	PROPN
ejpam-6440	7	19	)	)	PUNCT
ejpam-6440	7	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6440	8	1	1	1	NUM
ejpam-6440	8	2	copyright	copyright	NOUN
ejpam-6440	8	3	:	:	PUNCT
ejpam-6440	8	4	©	©	PROPN
ejpam-6440	8	5	2025	2025	NUM
ejpam-6440	8	6	the	the	DET
ejpam-6440	8	7	author(s	author(s	NOUN
ejpam-6440	8	8	)	)	PUNCT
ejpam-6440	8	9	.	.	PUNCT
ejpam-6440	9	1	(	(	PUNCT
ejpam-6440	9	2	cc	cc	NOUN
ejpam-6440	9	3	by	by	ADP
ejpam-6440	9	4	-	-	PUNCT
ejpam-6440	9	5	nc	nc	PROPN
ejpam-6440	9	6	4.0	4.0	NUM
ejpam-6440	9	7	)	)	PUNCT
ejpam-6440	9	8	t.	t.	NOUN
ejpam-6440	9	9	qawasmeh	qawasmeh	NOUN
ejpam-6440	9	10	,	,	PUNCT
ejpam-6440	9	11	a.	a.	NOUN
ejpam-6440	9	12	malkawi	malkawi	PROPN
ejpam-6440	9	13	/	/	SYM
ejpam-6440	9	14	eur	eur	PROPN
ejpam-6440	9	15	.	.	PUNCT
ejpam-6440	10	1	j.	j.	PROPN
ejpam-6440	10	2	pure	pure	PROPN
ejpam-6440	10	3	appl	appl	PROPN
ejpam-6440	10	4	.	.	PROPN
ejpam-6440	10	5	math	math	PROPN
ejpam-6440	10	6	,	,	PUNCT
ejpam-6440	10	7	18	18	NUM
ejpam-6440	10	8	(	(	PUNCT
ejpam-6440	10	9	3	3	NUM
ejpam-6440	10	10	)	)	PUNCT
ejpam-6440	10	11	(	(	PUNCT
ejpam-6440	10	12	2025	2025	NUM
ejpam-6440	10	13	)	)	PUNCT
ejpam-6440	10	14	,	,	PUNCT
ejpam-6440	10	15	6440	6440	NUM
ejpam-6440	10	16	2	2	NUM
ejpam-6440	10	17	of	of	ADP
ejpam-6440	10	18	20	20	NUM
ejpam-6440	10	19	1	1	NUM
ejpam-6440	10	20	.	.	PUNCT
ejpam-6440	10	21	introduction	introduction	NOUN
ejpam-6440	10	22	the	the	DET
ejpam-6440	10	23	study	study	NOUN
ejpam-6440	10	24	of	of	ADP
ejpam-6440	10	25	fixed	fix	VERB
ejpam-6440	10	26	point	point	NOUN
ejpam-6440	10	27	theory	theory	NOUN
ejpam-6440	10	28	in	in	ADP
ejpam-6440	10	29	generalized	generalized	ADJ
ejpam-6440	10	30	metric	metric	ADJ
ejpam-6440	10	31	spaces	space	NOUN
ejpam-6440	10	32	has	have	AUX
ejpam-6440	10	33	been	be	AUX
ejpam-6440	10	34	a	a	DET
ejpam-6440	10	35	vibrant	vibrant	ADJ
ejpam-6440	10	36	area	area	NOUN
ejpam-6440	10	37	of	of	ADP
ejpam-6440	10	38	research	research	NOUN
ejpam-6440	10	39	since	since	SCONJ
ejpam-6440	10	40	banach	banach	NOUN
ejpam-6440	10	41	’s	’s	PART
ejpam-6440	10	42	seminal	seminal	ADJ
ejpam-6440	10	43	contraction	contraction	NOUN
ejpam-6440	10	44	mapping	mapping	NOUN
ejpam-6440	10	45	principle	principle	NOUN
ejpam-6440	11	1	[	[	X
ejpam-6440	11	2	1	1	NUM
ejpam-6440	11	3	]	]	PUNCT
ejpam-6440	11	4	.	.	PUNCT
ejpam-6440	12	1	recent	recent	ADJ
ejpam-6440	12	2	developments	development	NOUN
ejpam-6440	12	3	have	have	AUX
ejpam-6440	12	4	extended	extend	VERB
ejpam-6440	12	5	this	this	DET
ejpam-6440	12	6	theory	theory	NOUN
ejpam-6440	12	7	to	to	ADP
ejpam-6440	12	8	various	various	ADJ
ejpam-6440	12	9	abstract	abstract	ADJ
ejpam-6440	12	10	spaces	space	NOUN
ejpam-6440	12	11	,	,	PUNCT
ejpam-6440	12	12	including	include	VERB
ejpam-6440	12	13	partial	partial	ADJ
ejpam-6440	12	14	metric	metric	ADJ
ejpam-6440	12	15	spaces	space	NOUN
ejpam-6440	12	16	[	[	X
ejpam-6440	12	17	2	2	NUM
ejpam-6440	12	18	]	]	PUNCT
ejpam-6440	12	19	,	,	PUNCT
ejpam-6440	12	20	b	b	X
ejpam-6440	12	21	-	-	PUNCT
ejpam-6440	12	22	metric	metric	ADJ
ejpam-6440	12	23	spaces	space	NOUN
ejpam-6440	12	24	[	[	X
ejpam-6440	12	25	3	3	NUM
ejpam-6440	12	26	]	]	PUNCT
ejpam-6440	12	27	,	,	PUNCT
ejpam-6440	12	28	and	and	CCONJ
ejpam-6440	12	29	modular	modular	ADJ
ejpam-6440	12	30	metric	metric	ADJ
ejpam-6440	12	31	spaces	space	NOUN
ejpam-6440	12	32	[	[	X
ejpam-6440	12	33	4	4	NUM
ejpam-6440	12	34	]	]	PUNCT
ejpam-6440	12	35	.	.	PUNCT
ejpam-6440	13	1	1.1	1.1	NUM
ejpam-6440	13	2	.	.	PUNCT
ejpam-6440	14	1	mr	mr	ADJ
ejpam-6440	14	2	-	-	PUNCT
ejpam-6440	14	3	metric	metric	ADJ
ejpam-6440	14	4	spaces	space	NOUN
ejpam-6440	14	5	the	the	DET
ejpam-6440	14	6	mr	mr	PROPN
ejpam-6440	14	7	-	-	PUNCT
ejpam-6440	14	8	metric	metric	ADJ
ejpam-6440	14	9	space	space	NOUN
ejpam-6440	14	10	(	(	PUNCT
ejpam-6440	14	11	x	x	X
ejpam-6440	14	12	,	,	PUNCT
ejpam-6440	14	13	m	m	NOUN
ejpam-6440	14	14	)	)	PUNCT
ejpam-6440	14	15	,	,	PUNCT
ejpam-6440	14	16	first	first	ADV
ejpam-6440	14	17	introduced	introduce	VERB
ejpam-6440	14	18	in	in	ADP
ejpam-6440	14	19	[	[	X
ejpam-6440	14	20	5	5	NUM
ejpam-6440	14	21	]	]	PUNCT
ejpam-6440	14	22	,	,	PUNCT
ejpam-6440	14	23	provides	provide	VERB
ejpam-6440	14	24	a	a	DET
ejpam-6440	14	25	framework	framework	NOUN
ejpam-6440	14	26	where	where	SCONJ
ejpam-6440	14	27	the	the	DET
ejpam-6440	14	28	distance	distance	NOUN
ejpam-6440	14	29	function	function	NOUN
ejpam-6440	14	30	m	m	VERB
ejpam-6440	14	31	:	:	PUNCT
ejpam-6440	14	32	x3	x3	ADJ
ejpam-6440	14	33	→	→	SYM
ejpam-6440	14	34	[	[	X
ejpam-6440	14	35	0,∞	0,∞	NOUN
ejpam-6440	14	36	)	)	PUNCT
ejpam-6440	14	37	simultaneously	simultaneously	ADV
ejpam-6440	14	38	measures	measure	VERB
ejpam-6440	14	39	three	three	NUM
ejpam-6440	14	40	-	-	PUNCT
ejpam-6440	14	41	point	point	NOUN
ejpam-6440	14	42	relations	relation	NOUN
ejpam-6440	14	43	.	.	PUNCT
ejpam-6440	15	1	this	this	DET
ejpam-6440	15	2	structure	structure	NOUN
ejpam-6440	15	3	proves	prove	VERB
ejpam-6440	15	4	particularly	particularly	ADV
ejpam-6440	15	5	valuable	valuable	ADJ
ejpam-6440	15	6	when	when	SCONJ
ejpam-6440	15	7	analyzing	analyze	VERB
ejpam-6440	15	8	:	:	PUNCT
ejpam-6440	15	9	•	•	NUM
ejpam-6440	15	10	systems	system	NOUN
ejpam-6440	15	11	with	with	ADP
ejpam-6440	15	12	ternary	ternary	ADJ
ejpam-6440	15	13	interactions	interaction	NOUN
ejpam-6440	15	14	•	•	NOUN
ejpam-6440	15	15	problems	problem	NOUN
ejpam-6440	15	16	where	where	SCONJ
ejpam-6440	15	17	pairwise	pairwise	NOUN
ejpam-6440	15	18	distances	distance	NOUN
ejpam-6440	15	19	are	be	AUX
ejpam-6440	15	20	insufficient	insufficient	ADJ
ejpam-6440	15	21	•	•	NOUN
ejpam-6440	15	22	operator	operator	NOUN
ejpam-6440	15	23	equations	equation	NOUN
ejpam-6440	15	24	with	with	ADP
ejpam-6440	15	25	multi	multi	ADJ
ejpam-6440	15	26	-	-	ADJ
ejpam-6440	15	27	point	point	ADJ
ejpam-6440	15	28	constraints	constraint	NOUN
ejpam-6440	15	29	1.2	1.2	NUM
ejpam-6440	15	30	.	.	PUNCT
ejpam-6440	16	1	contributions	contribution	NOUN
ejpam-6440	16	2	our	our	PRON
ejpam-6440	16	3	main	main	ADJ
ejpam-6440	16	4	contributions	contribution	NOUN
ejpam-6440	16	5	are	be	AUX
ejpam-6440	16	6	:	:	PUNCT
ejpam-6440	16	7	(	(	PUNCT
ejpam-6440	16	8	i	i	NOUN
ejpam-6440	16	9	)	)	PUNCT
ejpam-6440	16	10	theoretical	theoretical	ADJ
ejpam-6440	16	11	foundations	foundation	NOUN
ejpam-6440	16	12	:	:	PUNCT
ejpam-6440	16	13	•	•	NUM
ejpam-6440	16	14	complete	complete	ADJ
ejpam-6440	16	15	proofs	proof	NOUN
ejpam-6440	16	16	of	of	ADP
ejpam-6440	16	17	four	four	NUM
ejpam-6440	16	18	fundamental	fundamental	ADJ
ejpam-6440	16	19	fixed	fix	VERB
ejpam-6440	16	20	point	point	NOUN
ejpam-6440	16	21	theorems	theorem	VERB
ejpam-6440	16	22	•	•	ADP
ejpam-6440	16	23	optimal	optimal	ADJ
ejpam-6440	16	24	contraction	contraction	NOUN
ejpam-6440	16	25	constants	constant	NOUN
ejpam-6440	16	26	in	in	ADP
ejpam-6440	16	27	the	the	DET
ejpam-6440	16	28	mr	mr	PROPN
ejpam-6440	16	29	-	-	PUNCT
ejpam-6440	16	30	metric	metric	ADJ
ejpam-6440	16	31	setting	setting	NOUN
ejpam-6440	16	32	•	•	NOUN
ejpam-6440	16	33	error	error	NOUN
ejpam-6440	16	34	estimates	estimate	NOUN
ejpam-6440	16	35	for	for	ADP
ejpam-6440	16	36	iterative	iterative	NOUN
ejpam-6440	16	37	methods	method	NOUN
ejpam-6440	16	38	(	(	PUNCT
ejpam-6440	16	39	ii	ii	NOUN
ejpam-6440	16	40	)	)	PUNCT
ejpam-6440	16	41	applications	application	NOUN
ejpam-6440	16	42	:	:	PUNCT
ejpam-6440	16	43	•	•	NUM
ejpam-6440	16	44	new	new	ADJ
ejpam-6440	16	45	existence	existence	NOUN
ejpam-6440	16	46	results	result	VERB
ejpam-6440	16	47	for	for	ADP
ejpam-6440	16	48	neutron	neutron	NOUN
ejpam-6440	16	49	transport	transport	NOUN
ejpam-6440	16	50	equations	equation	NOUN
ejpam-6440	16	51	•	•	ADP
ejpam-6440	16	52	convergence	convergence	NOUN
ejpam-6440	16	53	conditions	condition	NOUN
ejpam-6440	16	54	for	for	ADP
ejpam-6440	16	55	neural	neural	ADJ
ejpam-6440	16	56	network	network	NOUN
ejpam-6440	16	57	training	training	NOUN
ejpam-6440	16	58	•	•	NUM
ejpam-6440	16	59	solvability	solvability	NOUN
ejpam-6440	16	60	criteria	criterion	NOUN
ejpam-6440	16	61	for	for	ADP
ejpam-6440	16	62	hammerstein	hammerstein	PROPN
ejpam-6440	16	63	integral	integral	ADJ
ejpam-6440	16	64	equations	equation	NOUN
ejpam-6440	16	65	(	(	PUNCT
ejpam-6440	16	66	iii	iii	NOUN
ejpam-6440	16	67	)	)	PUNCT
ejpam-6440	16	68	computational	computational	ADJ
ejpam-6440	16	69	implications	implication	NOUN
ejpam-6440	16	70	:	:	PUNCT
ejpam-6440	16	71	•	•	NOUN
ejpam-6440	16	72	layer	layer	NOUN
ejpam-6440	16	73	-	-	PUNCT
ejpam-6440	16	74	wise	wise	ADJ
ejpam-6440	16	75	learning	learning	NOUN
ejpam-6440	16	76	rate	rate	NOUN
ejpam-6440	16	77	bounds	bound	NOUN
ejpam-6440	16	78	in	in	ADP
ejpam-6440	16	79	deep	deep	ADJ
ejpam-6440	16	80	learning	learning	NOUN
ejpam-6440	16	81	•	•	NOUN
ejpam-6440	16	82	iterative	iterative	NOUN
ejpam-6440	16	83	methods	method	NOUN
ejpam-6440	16	84	for	for	ADP
ejpam-6440	16	85	nuclear	nuclear	ADJ
ejpam-6440	16	86	reactor	reactor	NOUN
ejpam-6440	16	87	modeling	model	VERB
ejpam-6440	16	88	several	several	ADJ
ejpam-6440	16	89	studies	study	NOUN
ejpam-6440	16	90	have	have	AUX
ejpam-6440	16	91	addressed	address	VERB
ejpam-6440	16	92	related	related	ADJ
ejpam-6440	16	93	aspects	aspect	NOUN
ejpam-6440	16	94	in	in	ADP
ejpam-6440	16	95	the	the	DET
ejpam-6440	16	96	literature	literature	NOUN
ejpam-6440	17	1	[	[	X
ejpam-6440	17	2	6–32	6–32	NUM
ejpam-6440	17	3	]	]	PUNCT
ejpam-6440	17	4	.	.	PUNCT
ejpam-6440	18	1	definition	definition	NOUN
ejpam-6440	18	2	1	1	NUM
ejpam-6440	18	3	.	.	PUNCT
ejpam-6440	19	1	[	[	X
ejpam-6440	19	2	5	5	NUM
ejpam-6440	19	3	]	]	PUNCT
ejpam-6440	19	4	consider	consider	VERB
ejpam-6440	19	5	a	a	DET
ejpam-6440	19	6	non	non	ADJ
ejpam-6440	19	7	-	-	ADJ
ejpam-6440	19	8	empty	empty	ADJ
ejpam-6440	19	9	set	set	NOUN
ejpam-6440	19	10	x	x	PUNCT
ejpam-6440	19	11	̸=	̸=	PROPN
ejpam-6440	19	12	∅	∅	NOUN
ejpam-6440	19	13	and	and	CCONJ
ejpam-6440	19	14	a	a	DET
ejpam-6440	19	15	real	real	ADJ
ejpam-6440	19	16	number	number	NOUN
ejpam-6440	19	17	r	r	NOUN
ejpam-6440	19	18	>	>	X
ejpam-6440	19	19	1	1	NUM
ejpam-6440	19	20	.	.	PUNCT
ejpam-6440	20	1	a	a	DET
ejpam-6440	20	2	function	function	NOUN
ejpam-6440	20	3	m	m	VERB
ejpam-6440	20	4	:	:	PUNCT
ejpam-6440	20	5	x×	x×	X
ejpam-6440	20	6	x×	x×	PUNCT
ejpam-6440	20	7	x	x	PUNCT
ejpam-6440	20	8	→	→	PUNCT
ejpam-6440	20	9	[	[	X
ejpam-6440	20	10	0,∞	0,∞	NOUN
ejpam-6440	20	11	)	)	PUNCT
ejpam-6440	20	12	is	be	AUX
ejpam-6440	20	13	termed	term	VERB
ejpam-6440	20	14	an	an	DET
ejpam-6440	20	15	mr	mr	PROPN
ejpam-6440	20	16	-	-	PUNCT
ejpam-6440	20	17	metric	metric	NOUN
ejpam-6440	20	18	if	if	SCONJ
ejpam-6440	20	19	it	it	PRON
ejpam-6440	20	20	satisfies	satisfy	VERB
ejpam-6440	20	21	the	the	DET
ejpam-6440	20	22	following	follow	VERB
ejpam-6440	20	23	conditions	condition	NOUN
ejpam-6440	20	24	for	for	ADP
ejpam-6440	20	25	all	all	PRON
ejpam-6440	20	26	v	v	NOUN
ejpam-6440	20	27	,	,	PUNCT
ejpam-6440	20	28	ξ	ξ	PROPN
ejpam-6440	20	29	,	,	PUNCT
ejpam-6440	20	30	s	s	PART
ejpam-6440	20	31	,	,	PUNCT
ejpam-6440	20	32	ℓ1	ℓ1	NOUN
ejpam-6440	20	33	∈	∈	NOUN
ejpam-6440	20	34	x	x	X
ejpam-6440	20	35	:	:	PUNCT
ejpam-6440	20	36	t.	t.	NOUN
ejpam-6440	20	37	qawasmeh	qawasmeh	NOUN
ejpam-6440	20	38	,	,	PUNCT
ejpam-6440	20	39	a.	a.	NOUN
ejpam-6440	20	40	malkawi	malkawi	PROPN
ejpam-6440	20	41	/	/	SYM
ejpam-6440	20	42	eur	eur	PROPN
ejpam-6440	20	43	.	.	PUNCT
ejpam-6440	21	1	j.	j.	PROPN
ejpam-6440	21	2	pure	pure	PROPN
ejpam-6440	21	3	appl	appl	PROPN
ejpam-6440	21	4	.	.	PROPN
ejpam-6440	21	5	math	math	PROPN
ejpam-6440	21	6	,	,	PUNCT
ejpam-6440	21	7	18	18	NUM
ejpam-6440	21	8	(	(	PUNCT
ejpam-6440	21	9	3	3	NUM
ejpam-6440	21	10	)	)	PUNCT
ejpam-6440	21	11	(	(	PUNCT
ejpam-6440	21	12	2025	2025	NUM
ejpam-6440	21	13	)	)	PUNCT
ejpam-6440	21	14	,	,	PUNCT
ejpam-6440	21	15	6440	6440	NUM
ejpam-6440	21	16	3	3	NUM
ejpam-6440	21	17	of	of	ADP
ejpam-6440	21	18	20	20	NUM
ejpam-6440	21	19	•	•	NUM
ejpam-6440	21	20	m(v	m(v	NOUN
ejpam-6440	21	21	,	,	PUNCT
ejpam-6440	21	22	ξ	ξ	PROPN
ejpam-6440	21	23	,	,	PUNCT
ejpam-6440	21	24	s	s	PART
ejpam-6440	21	25	)	)	PUNCT
ejpam-6440	21	26	≥	≥	NOUN
ejpam-6440	21	27	0	0	NUM
ejpam-6440	21	28	.	.	NOUN
ejpam-6440	21	29	•	•	NUM
ejpam-6440	21	30	m(v	m(v	PROPN
ejpam-6440	21	31	,	,	PUNCT
ejpam-6440	21	32	ξ	ξ	PROPN
ejpam-6440	21	33	,	,	PUNCT
ejpam-6440	21	34	s	s	PART
ejpam-6440	21	35	)	)	PUNCT
ejpam-6440	21	36	=	=	SYM
ejpam-6440	21	37	0	0	PUNCT
ejpam-6440	22	1	if	if	SCONJ
ejpam-6440	22	2	and	and	CCONJ
ejpam-6440	22	3	only	only	ADV
ejpam-6440	22	4	if	if	SCONJ
ejpam-6440	22	5	v	v	NOUN
ejpam-6440	22	6	=	=	SYM
ejpam-6440	22	7	ξ	ξ	PROPN
ejpam-6440	22	8	=	=	PUNCT
ejpam-6440	22	9	s.	s.	PROPN
ejpam-6440	22	10	•	•	ADP
ejpam-6440	22	11	m(v	m(v	PROPN
ejpam-6440	22	12	,	,	PUNCT
ejpam-6440	22	13	ξ	ξ	PROPN
ejpam-6440	22	14	,	,	PUNCT
ejpam-6440	22	15	s	s	PART
ejpam-6440	22	16	)	)	PUNCT
ejpam-6440	22	17	remains	remain	VERB
ejpam-6440	22	18	invariant	invariant	ADJ
ejpam-6440	22	19	under	under	ADP
ejpam-6440	22	20	any	any	DET
ejpam-6440	22	21	permutation	permutation	NOUN
ejpam-6440	22	22	p(v	p(v	NOUN
ejpam-6440	22	23	,	,	PUNCT
ejpam-6440	22	24	ξ	ξ	PROPN
ejpam-6440	22	25	,	,	PUNCT
ejpam-6440	22	26	s	s	PART
ejpam-6440	22	27	)	)	PUNCT
ejpam-6440	22	28	,	,	PUNCT
ejpam-6440	22	29	i.e.	i.e.	X
ejpam-6440	22	30	,	,	PUNCT
ejpam-6440	22	31	m(v	m(v	PROPN
ejpam-6440	22	32	,	,	PUNCT
ejpam-6440	22	33	ξ	ξ	PROPN
ejpam-6440	22	34	,	,	PUNCT
ejpam-6440	22	35	s	s	PART
ejpam-6440	22	36	)	)	PUNCT
ejpam-6440	22	37	=	=	SYM
ejpam-6440	22	38	m(p(v	m(p(v	PROPN
ejpam-6440	22	39	,	,	PUNCT
ejpam-6440	22	40	ξ	ξ	PROPN
ejpam-6440	22	41	,	,	PUNCT
ejpam-6440	22	42	s	s	NOUN
ejpam-6440	22	43	)	)	PUNCT
ejpam-6440	22	44	)	)	PUNCT
ejpam-6440	22	45	.	.	PUNCT
ejpam-6440	23	1	•	•	NUM
ejpam-6440	23	2	the	the	DET
ejpam-6440	23	3	following	follow	VERB
ejpam-6440	23	4	inequality	inequality	NOUN
ejpam-6440	23	5	holds	hold	VERB
ejpam-6440	23	6	:	:	PUNCT
ejpam-6440	23	7	m(v	m(v	NUM
ejpam-6440	23	8	,	,	PUNCT
ejpam-6440	23	9	ξ	ξ	PROPN
ejpam-6440	23	10	,	,	PUNCT
ejpam-6440	23	11	s	s	NOUN
ejpam-6440	23	12	)	)	PUNCT
ejpam-6440	23	13	≤	≤	NOUN
ejpam-6440	23	14	r	r	NOUN
ejpam-6440	24	1	[	[	X
ejpam-6440	24	2	m(v	m(v	X
ejpam-6440	24	3	,	,	PUNCT
ejpam-6440	24	4	ξ	ξ	X
ejpam-6440	24	5	,	,	PUNCT
ejpam-6440	24	6	ℓ1	ℓ1	NOUN
ejpam-6440	24	7	)	)	PUNCT
ejpam-6440	25	1	+	+	SYM
ejpam-6440	25	2	m(v	m(v	NOUN
ejpam-6440	25	3	,	,	PUNCT
ejpam-6440	25	4	ℓ1	ℓ1	NOUN
ejpam-6440	25	5	,	,	PUNCT
ejpam-6440	25	6	s	s	X
ejpam-6440	25	7	)	)	PUNCT
ejpam-6440	25	8	+	+	ADJ
ejpam-6440	25	9	m(ℓ1	m(ℓ1	NOUN
ejpam-6440	25	10	,	,	PUNCT
ejpam-6440	25	11	ξ	ξ	PROPN
ejpam-6440	25	12	,	,	PUNCT
ejpam-6440	25	13	s	s	PART
ejpam-6440	25	14	)	)	PUNCT
ejpam-6440	25	15	]	]	PUNCT
ejpam-6440	25	16	.	.	PUNCT
ejpam-6440	26	1	a	a	DET
ejpam-6440	26	2	structure	structure	NOUN
ejpam-6440	26	3	(	(	PUNCT
ejpam-6440	26	4	x	x	X
ejpam-6440	26	5	,	,	PUNCT
ejpam-6440	26	6	m	m	NOUN
ejpam-6440	26	7	)	)	PUNCT
ejpam-6440	26	8	that	that	PRON
ejpam-6440	26	9	adheres	adhere	VERB
ejpam-6440	26	10	to	to	ADP
ejpam-6440	26	11	these	these	DET
ejpam-6440	26	12	properties	property	NOUN
ejpam-6440	26	13	is	be	AUX
ejpam-6440	26	14	defined	define	VERB
ejpam-6440	26	15	as	as	ADP
ejpam-6440	26	16	an	an	DET
ejpam-6440	26	17	mr	mr	PROPN
ejpam-6440	26	18	-	-	PUNCT
ejpam-6440	26	19	metric	metric	ADJ
ejpam-6440	26	20	space	space	NOUN
ejpam-6440	26	21	.	.	PUNCT
ejpam-6440	27	1	2	2	X
ejpam-6440	27	2	.	.	X
ejpam-6440	27	3	main	main	ADJ
ejpam-6440	27	4	results	result	NOUN
ejpam-6440	27	5	this	this	DET
ejpam-6440	27	6	section	section	NOUN
ejpam-6440	27	7	presents	present	VERB
ejpam-6440	27	8	the	the	DET
ejpam-6440	27	9	fundamental	fundamental	ADJ
ejpam-6440	27	10	theorems	theorem	NOUN
ejpam-6440	27	11	that	that	PRON
ejpam-6440	27	12	constitute	constitute	VERB
ejpam-6440	27	13	the	the	DET
ejpam-6440	27	14	core	core	ADJ
ejpam-6440	27	15	contributions	contribution	NOUN
ejpam-6440	27	16	of	of	ADP
ejpam-6440	27	17	our	our	PRON
ejpam-6440	27	18	work	work	NOUN
ejpam-6440	27	19	in	in	ADP
ejpam-6440	27	20	mr	mr	PROPN
ejpam-6440	27	21	-	-	PUNCT
ejpam-6440	27	22	metric	metric	ADJ
ejpam-6440	27	23	spaces	space	NOUN
ejpam-6440	27	24	.	.	PUNCT
ejpam-6440	28	1	we	we	PRON
ejpam-6440	28	2	establish	establish	VERB
ejpam-6440	28	3	four	four	NUM
ejpam-6440	28	4	principal	principal	ADJ
ejpam-6440	28	5	results	result	NOUN
ejpam-6440	28	6	that	that	PRON
ejpam-6440	28	7	extend	extend	VERB
ejpam-6440	28	8	classical	classical	ADJ
ejpam-6440	28	9	fixed	fix	VERB
ejpam-6440	28	10	-	-	PUNCT
ejpam-6440	28	11	point	point	NOUN
ejpam-6440	28	12	theory	theory	NOUN
ejpam-6440	28	13	to	to	ADP
ejpam-6440	28	14	this	this	DET
ejpam-6440	28	15	generalized	generalized	ADJ
ejpam-6440	28	16	framework	framework	NOUN
ejpam-6440	28	17	:	:	PUNCT
ejpam-6440	28	18	(	(	PUNCT
ejpam-6440	28	19	1	1	X
ejpam-6440	28	20	)	)	PUNCT
ejpam-6440	28	21	a	a	DET
ejpam-6440	28	22	banach	banach	NOUN
ejpam-6440	28	23	contraction	contraction	NOUN
ejpam-6440	28	24	principle	principle	NOUN
ejpam-6440	28	25	with	with	ADP
ejpam-6440	28	26	optimal	optimal	ADJ
ejpam-6440	28	27	constants	constant	NOUN
ejpam-6440	28	28	,	,	PUNCT
ejpam-6440	28	29	(	(	PUNCT
ejpam-6440	28	30	2	2	NUM
ejpam-6440	28	31	)	)	PUNCT
ejpam-6440	28	32	existence	existence	NOUN
ejpam-6440	28	33	and	and	CCONJ
ejpam-6440	28	34	uniqueness	uniqueness	ADJ
ejpam-6440	28	35	theorems	theorem	NOUN
ejpam-6440	28	36	for	for	ADP
ejpam-6440	28	37	integral	integral	ADJ
ejpam-6440	28	38	equations	equation	NOUN
ejpam-6440	28	39	,	,	PUNCT
ejpam-6440	28	40	(	(	PUNCT
ejpam-6440	28	41	3	3	X
ejpam-6440	28	42	)	)	PUNCT
ejpam-6440	28	43	a	a	DET
ejpam-6440	28	44	hybrid	hybrid	ADJ
ejpam-6440	28	45	fixed	fix	VERB
ejpam-6440	28	46	-	-	PUNCT
ejpam-6440	28	47	point	point	NOUN
ejpam-6440	28	48	theorem	theorem	NOUN
ejpam-6440	28	49	of	of	ADP
ejpam-6440	28	50	krasnoselskii	krasnoselskii	PROPN
ejpam-6440	28	51	type	type	NOUN
ejpam-6440	28	52	,	,	PUNCT
ejpam-6440	28	53	and	and	CCONJ
ejpam-6440	28	54	(	(	PUNCT
ejpam-6440	28	55	4	4	X
ejpam-6440	28	56	)	)	PUNCT
ejpam-6440	28	57	a	a	DET
ejpam-6440	28	58	leray	leray	ADJ
ejpam-6440	28	59	-	-	PUNCT
ejpam-6440	28	60	schauder	schauder	NOUN
ejpam-6440	28	61	alternative	alternative	NOUN
ejpam-6440	28	62	for	for	ADP
ejpam-6440	28	63	generalized	generalized	ADJ
ejpam-6440	28	64	contractions	contraction	NOUN
ejpam-6440	28	65	.	.	PUNCT
ejpam-6440	29	1	each	each	DET
ejpam-6440	29	2	theorem	theorem	NOUN
ejpam-6440	29	3	is	be	AUX
ejpam-6440	29	4	accompanied	accompany	VERB
ejpam-6440	29	5	by	by	ADP
ejpam-6440	29	6	complete	complete	ADJ
ejpam-6440	29	7	proofs	proof	NOUN
ejpam-6440	29	8	that	that	PRON
ejpam-6440	29	9	highlight	highlight	VERB
ejpam-6440	29	10	the	the	DET
ejpam-6440	29	11	distinctive	distinctive	ADJ
ejpam-6440	29	12	three	three	NUM
ejpam-6440	29	13	-	-	PUNCT
ejpam-6440	29	14	point	point	NOUN
ejpam-6440	29	15	nature	nature	NOUN
ejpam-6440	29	16	of	of	ADP
ejpam-6440	29	17	mr	mr	NOUN
ejpam-6440	29	18	-	-	PUNCT
ejpam-6440	29	19	metrics	metric	NOUN
ejpam-6440	29	20	,	,	PUNCT
ejpam-6440	29	21	with	with	ADP
ejpam-6440	29	22	particular	particular	ADJ
ejpam-6440	29	23	attention	attention	NOUN
ejpam-6440	29	24	to	to	ADP
ejpam-6440	29	25	the	the	DET
ejpam-6440	29	26	role	role	NOUN
ejpam-6440	29	27	of	of	ADP
ejpam-6440	29	28	the	the	DET
ejpam-6440	29	29	structural	structural	ADJ
ejpam-6440	29	30	constant	constant	ADJ
ejpam-6440	29	31	r	r	NOUN
ejpam-6440	29	32	>	>	X
ejpam-6440	29	33	1	1	NUM
ejpam-6440	29	34	.	.	PUNCT
ejpam-6440	30	1	the	the	DET
ejpam-6440	30	2	results	result	NOUN
ejpam-6440	30	3	are	be	AUX
ejpam-6440	30	4	presented	present	VERB
ejpam-6440	30	5	in	in	ADP
ejpam-6440	30	6	increasing	increase	VERB
ejpam-6440	30	7	order	order	NOUN
ejpam-6440	30	8	of	of	ADP
ejpam-6440	30	9	complexity	complexity	NOUN
ejpam-6440	30	10	,	,	PUNCT
ejpam-6440	30	11	beginning	begin	VERB
ejpam-6440	30	12	with	with	ADP
ejpam-6440	30	13	the	the	DET
ejpam-6440	30	14	contraction	contraction	NOUN
ejpam-6440	30	15	mapping	mapping	NOUN
ejpam-6440	30	16	principle	principle	NOUN
ejpam-6440	30	17	and	and	CCONJ
ejpam-6440	30	18	culminating	culminate	VERB
ejpam-6440	30	19	in	in	ADP
ejpam-6440	30	20	the	the	DET
ejpam-6440	30	21	nonlinear	nonlinear	ADJ
ejpam-6440	30	22	alternative	alternative	NOUN
ejpam-6440	30	23	,	,	PUNCT
ejpam-6440	30	24	while	while	SCONJ
ejpam-6440	30	25	maintaining	maintain	VERB
ejpam-6440	30	26	rigorous	rigorous	ADJ
ejpam-6440	30	27	connections	connection	NOUN
ejpam-6440	30	28	to	to	ADP
ejpam-6440	30	29	their	their	PRON
ejpam-6440	30	30	classical	classical	ADJ
ejpam-6440	30	31	counterparts	counterpart	NOUN
ejpam-6440	30	32	when	when	SCONJ
ejpam-6440	30	33	r→	r→	PROPN
ejpam-6440	30	34	1	1	NUM
ejpam-6440	30	35	+	+	NOUN
ejpam-6440	30	36	.	.	PUNCT
ejpam-6440	30	37	theorem	theorem	ADJ
ejpam-6440	30	38	1	1	NUM
ejpam-6440	30	39	(	(	PUNCT
ejpam-6440	30	40	banach	banach	NOUN
ejpam-6440	30	41	contraction	contraction	NOUN
ejpam-6440	30	42	in	in	ADP
ejpam-6440	30	43	mr	mr	PROPN
ejpam-6440	30	44	-	-	PUNCT
ejpam-6440	30	45	metric	metric	ADJ
ejpam-6440	30	46	spaces	space	NOUN
ejpam-6440	30	47	)	)	PUNCT
ejpam-6440	30	48	.	.	PUNCT
ejpam-6440	31	1	let	let	VERB
ejpam-6440	31	2	(	(	PUNCT
ejpam-6440	31	3	x	x	X
ejpam-6440	31	4	,	,	PUNCT
ejpam-6440	31	5	m	m	VERB
ejpam-6440	31	6	)	)	PUNCT
ejpam-6440	31	7	be	be	AUX
ejpam-6440	31	8	a	a	DET
ejpam-6440	31	9	complete	complete	ADJ
ejpam-6440	31	10	mr	mr	ADJ
ejpam-6440	31	11	-	-	PUNCT
ejpam-6440	31	12	metric	metric	ADJ
ejpam-6440	31	13	space	space	NOUN
ejpam-6440	31	14	with	with	ADP
ejpam-6440	31	15	constant	constant	ADJ
ejpam-6440	31	16	r	r	NOUN
ejpam-6440	31	17	>	>	X
ejpam-6440	31	18	1	1	NUM
ejpam-6440	31	19	,	,	PUNCT
ejpam-6440	31	20	and	and	CCONJ
ejpam-6440	31	21	let	let	VERB
ejpam-6440	31	22	t	t	NOUN
ejpam-6440	31	23	:	:	PUNCT
ejpam-6440	31	24	x	x	X
ejpam-6440	31	25	→	→	PUNCT
ejpam-6440	31	26	x	x	PUNCT
ejpam-6440	31	27	be	be	AUX
ejpam-6440	31	28	a	a	DET
ejpam-6440	31	29	mapping	mapping	NOUN
ejpam-6440	31	30	satisfying	satisfying	ADJ
ejpam-6440	31	31	:	:	PUNCT
ejpam-6440	32	1	m(tυ	m(tυ	NOUN
ejpam-6440	32	2	,	,	PUNCT
ejpam-6440	32	3	tξ	tξ	VERB
ejpam-6440	32	4	,	,	PUNCT
ejpam-6440	32	5	tℑ	tℑ	NOUN
ejpam-6440	32	6	)	)	PUNCT
ejpam-6440	32	7	≤	≤	PUNCT
ejpam-6440	33	1	k	k	X
ejpam-6440	33	2	·	·	PUNCT
ejpam-6440	33	3	m(υ	m(υ	PROPN
ejpam-6440	33	4	,	,	PUNCT
ejpam-6440	33	5	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	33	6	)	)	PUNCT
ejpam-6440	33	7	,	,	PUNCT
ejpam-6440	33	8	∀υ	∀υ	NOUN
ejpam-6440	33	9	,	,	PUNCT
ejpam-6440	33	10	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	33	11	∈	∈	PROPN
ejpam-6440	33	12	x	x	X
ejpam-6440	33	13	,	,	PUNCT
ejpam-6440	33	14	where	where	SCONJ
ejpam-6440	33	15	0	0	PUNCT
ejpam-6440	33	16	<	<	X
ejpam-6440	33	17	k	k	X
ejpam-6440	33	18	<	<	X
ejpam-6440	33	19	1	1	NUM
ejpam-6440	33	20	3r	3r	NOUN
ejpam-6440	33	21	is	be	AUX
ejpam-6440	33	22	a	a	DET
ejpam-6440	33	23	contraction	contraction	NOUN
ejpam-6440	33	24	constant	constant	ADJ
ejpam-6440	33	25	.	.	PUNCT
ejpam-6440	34	1	then	then	ADV
ejpam-6440	34	2	:	:	PUNCT
ejpam-6440	34	3	(	(	PUNCT
ejpam-6440	34	4	i	i	NOUN
ejpam-6440	34	5	)	)	PUNCT
ejpam-6440	34	6	t	t	PROPN
ejpam-6440	34	7	has	have	VERB
ejpam-6440	34	8	a	a	DET
ejpam-6440	34	9	unique	unique	ADJ
ejpam-6440	34	10	fixed	fix	VERB
ejpam-6440	34	11	point	point	NOUN
ejpam-6440	34	12	υ∗	υ∗	NOUN
ejpam-6440	34	13	∈	∈	PROPN
ejpam-6440	34	14	x.	x.	NOUN
ejpam-6440	34	15	(	(	PUNCT
ejpam-6440	34	16	ii	ii	NOUN
ejpam-6440	34	17	)	)	PUNCT
ejpam-6440	34	18	for	for	ADP
ejpam-6440	34	19	any	any	DET
ejpam-6440	34	20	υ0	υ0	NOUN
ejpam-6440	34	21	∈	∈	PROPN
ejpam-6440	34	22	x	x	NOUN
ejpam-6440	34	23	,	,	PUNCT
ejpam-6440	34	24	the	the	DET
ejpam-6440	34	25	picard	picard	PROPN
ejpam-6440	34	26	iteration	iteration	NOUN
ejpam-6440	34	27	υn+1	υn+1	PROPN
ejpam-6440	34	28	=	=	NOUN
ejpam-6440	34	29	tυn	tυn	NOUN
ejpam-6440	34	30	converges	converge	NOUN
ejpam-6440	34	31	to	to	ADP
ejpam-6440	34	32	υ∗.	υ∗.	PROPN
ejpam-6440	34	33	(	(	PUNCT
ejpam-6440	34	34	iii	iii	NOUN
ejpam-6440	34	35	)	)	PUNCT
ejpam-6440	34	36	the	the	DET
ejpam-6440	34	37	following	follow	VERB
ejpam-6440	34	38	error	error	NOUN
ejpam-6440	34	39	estimate	estimate	NOUN
ejpam-6440	34	40	holds	hold	VERB
ejpam-6440	34	41	:	:	PUNCT
ejpam-6440	34	42	m(υn	m(υn	PROPN
ejpam-6440	34	43	,	,	PUNCT
ejpam-6440	34	44	υ	υ	PRON
ejpam-6440	34	45	∗	∗	NOUN
ejpam-6440	34	46	,	,	PUNCT
ejpam-6440	34	47	υ∗	υ∗	NOUN
ejpam-6440	34	48	)	)	PUNCT
ejpam-6440	34	49	≤	≤	NOUN
ejpam-6440	35	1	rkn	rkn	VERB
ejpam-6440	35	2	1−	1−	NUM
ejpam-6440	35	3	3rk	3rk	ADJ
ejpam-6440	35	4	m(υ0	m(υ0	PROPN
ejpam-6440	35	5	,	,	PUNCT
ejpam-6440	35	6	υ1	υ1	PROPN
ejpam-6440	35	7	,	,	PUNCT
ejpam-6440	35	8	υ1	υ1	PROPN
ejpam-6440	35	9	)	)	PUNCT
ejpam-6440	35	10	.	.	PUNCT
ejpam-6440	36	1	proof	proof	NOUN
ejpam-6440	36	2	.	.	PUNCT
ejpam-6440	37	1	we	we	PRON
ejpam-6440	37	2	proceed	proceed	VERB
ejpam-6440	37	3	with	with	ADP
ejpam-6440	37	4	a	a	DET
ejpam-6440	37	5	detailed	detailed	ADJ
ejpam-6440	37	6	proof	proof	NOUN
ejpam-6440	37	7	in	in	ADP
ejpam-6440	37	8	several	several	ADJ
ejpam-6440	37	9	steps	step	NOUN
ejpam-6440	37	10	.	.	PUNCT
ejpam-6440	38	1	part	part	NOUN
ejpam-6440	38	2	(	(	PUNCT
ejpam-6440	38	3	i	i	NOUN
ejpam-6440	38	4	):	):	PUNCT
ejpam-6440	38	5	existence	existence	NOUN
ejpam-6440	38	6	of	of	ADP
ejpam-6440	38	7	fixed	fix	VERB
ejpam-6440	38	8	point	point	NOUN
ejpam-6440	38	9	(	(	PUNCT
ejpam-6440	38	10	i	i	NOUN
ejpam-6440	38	11	)	)	PUNCT
ejpam-6440	38	12	iterative	iterative	NOUN
ejpam-6440	38	13	sequence	sequence	NOUN
ejpam-6440	38	14	construction	construction	NOUN
ejpam-6440	38	15	:	:	PUNCT
ejpam-6440	38	16	let	let	VERB
ejpam-6440	38	17	υ0	υ0	PROPN
ejpam-6440	38	18	∈	∈	PROPN
ejpam-6440	38	19	x	x	PUNCT
ejpam-6440	38	20	be	be	AUX
ejpam-6440	38	21	arbitrary	arbitrary	ADJ
ejpam-6440	38	22	.	.	PUNCT
ejpam-6440	39	1	define	define	VERB
ejpam-6440	39	2	the	the	DET
ejpam-6440	39	3	iterative	iterative	NOUN
ejpam-6440	39	4	sequence	sequence	NOUN
ejpam-6440	39	5	υn+1	υn+1	NOUN
ejpam-6440	39	6	=	=	SYM
ejpam-6440	39	7	tυn	tυn	NOUN
ejpam-6440	39	8	for	for	ADP
ejpam-6440	39	9	n	n	PRON
ejpam-6440	39	10	≥	≥	NOUN
ejpam-6440	39	11	0	0	NUM
ejpam-6440	39	12	.	.	PUNCT
ejpam-6440	40	1	t.	t.	NOUN
ejpam-6440	40	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	40	3	,	,	PUNCT
ejpam-6440	40	4	a.	a.	NOUN
ejpam-6440	40	5	malkawi	malkawi	PROPN
ejpam-6440	40	6	/	/	SYM
ejpam-6440	40	7	eur	eur	PROPN
ejpam-6440	40	8	.	.	PUNCT
ejpam-6440	41	1	j.	j.	PROPN
ejpam-6440	41	2	pure	pure	PROPN
ejpam-6440	41	3	appl	appl	PROPN
ejpam-6440	41	4	.	.	PROPN
ejpam-6440	41	5	math	math	PROPN
ejpam-6440	41	6	,	,	PUNCT
ejpam-6440	41	7	18	18	NUM
ejpam-6440	41	8	(	(	PUNCT
ejpam-6440	41	9	3	3	NUM
ejpam-6440	41	10	)	)	PUNCT
ejpam-6440	41	11	(	(	PUNCT
ejpam-6440	41	12	2025	2025	NUM
ejpam-6440	41	13	)	)	PUNCT
ejpam-6440	41	14	,	,	PUNCT
ejpam-6440	41	15	6440	6440	NUM
ejpam-6440	41	16	4	4	NUM
ejpam-6440	41	17	of	of	ADP
ejpam-6440	41	18	20	20	NUM
ejpam-6440	41	19	(	(	PUNCT
ejpam-6440	41	20	ii	ii	NOUN
ejpam-6440	41	21	)	)	PUNCT
ejpam-6440	41	22	contraction	contraction	NOUN
ejpam-6440	41	23	estimates	estimate	VERB
ejpam-6440	41	24	:	:	PUNCT
ejpam-6440	41	25	for	for	ADP
ejpam-6440	41	26	any	any	DET
ejpam-6440	41	27	n	n	PRON
ejpam-6440	41	28	≥	≥	NOUN
ejpam-6440	41	29	1	1	NUM
ejpam-6440	41	30	,	,	PUNCT
ejpam-6440	41	31	applying	apply	VERB
ejpam-6440	41	32	the	the	DET
ejpam-6440	41	33	contraction	contraction	NOUN
ejpam-6440	41	34	property	property	NOUN
ejpam-6440	41	35	repeatedly	repeatedly	ADV
ejpam-6440	41	36	yields	yield	VERB
ejpam-6440	41	37	:	:	PUNCT
ejpam-6440	42	1	m(υn+1	m(υn+1	NUM
ejpam-6440	42	2	,	,	PUNCT
ejpam-6440	42	3	υn	υn	NOUN
ejpam-6440	42	4	,	,	PUNCT
ejpam-6440	42	5	υn	υn	NOUN
ejpam-6440	42	6	)	)	PUNCT
ejpam-6440	42	7	≤	≤	NOUN
ejpam-6440	42	8	km(υn	km(υn	VERB
ejpam-6440	42	9	,	,	PUNCT
ejpam-6440	42	10	υn−1	υn−1	ADJ
ejpam-6440	42	11	,	,	PUNCT
ejpam-6440	42	12	υn−1	υn−1	NOUN
ejpam-6440	42	13	)	)	PUNCT
ejpam-6440	42	14	≤	≤	NOUN
ejpam-6440	42	15	·	·	PUNCT
ejpam-6440	42	16	·	·	PUNCT
ejpam-6440	42	17	·	·	PUNCT
ejpam-6440	43	1	≤	≤	NUM
ejpam-6440	43	2	knm(υ1	knm(υ1	PROPN
ejpam-6440	43	3	,	,	PUNCT
ejpam-6440	43	4	υ0	υ0	NOUN
ejpam-6440	43	5	,	,	PUNCT
ejpam-6440	43	6	υ0	υ0	NOUN
ejpam-6440	43	7	)	)	PUNCT
ejpam-6440	43	8	.	.	PUNCT
ejpam-6440	44	1	(	(	PUNCT
ejpam-6440	44	2	iii	iii	X
ejpam-6440	44	3	)	)	PUNCT
ejpam-6440	44	4	cauchy	cauchy	NOUN
ejpam-6440	44	5	sequence	sequence	NOUN
ejpam-6440	44	6	verification	verification	NOUN
ejpam-6440	44	7	:	:	PUNCT
ejpam-6440	44	8	for	for	ADP
ejpam-6440	44	9	m	m	PROPN
ejpam-6440	44	10	>	>	X
ejpam-6440	44	11	n	n	X
ejpam-6440	44	12	≥	≥	NUM
ejpam-6440	44	13	1	1	NUM
ejpam-6440	44	14	,	,	PUNCT
ejpam-6440	44	15	we	we	PRON
ejpam-6440	44	16	employ	employ	VERB
ejpam-6440	44	17	the	the	DET
ejpam-6440	44	18	mr	mr	PROPN
ejpam-6440	44	19	-	-	PUNCT
ejpam-6440	44	20	metric	metric	ADJ
ejpam-6440	44	21	property	property	NOUN
ejpam-6440	44	22	(	(	PUNCT
ejpam-6440	44	23	m4	m4	PROPN
ejpam-6440	44	24	)	)	PUNCT
ejpam-6440	44	25	iteratively	iteratively	ADV
ejpam-6440	44	26	:	:	PUNCT
ejpam-6440	44	27	m(υn	m(υn	NUM
ejpam-6440	44	28	,	,	PUNCT
ejpam-6440	44	29	υm	υm	NOUN
ejpam-6440	44	30	,	,	PUNCT
ejpam-6440	44	31	υm	υm	NOUN
ejpam-6440	44	32	)	)	PUNCT
ejpam-6440	44	33	≤	≤	NOUN
ejpam-6440	44	34	r	r	NOUN
ejpam-6440	44	35	[	[	X
ejpam-6440	44	36	m(υn	m(υn	ADJ
ejpam-6440	44	37	,	,	PUNCT
ejpam-6440	44	38	υm	υm	NOUN
ejpam-6440	44	39	,	,	PUNCT
ejpam-6440	44	40	υn+1	υn+1	NOUN
ejpam-6440	44	41	)	)	PUNCT
ejpam-6440	44	42	+	+	NOUN
ejpam-6440	44	43	m(υn	m(υn	ADJ
ejpam-6440	44	44	,	,	PUNCT
ejpam-6440	44	45	υn+1	υn+1	NOUN
ejpam-6440	44	46	,	,	PUNCT
ejpam-6440	44	47	υm	υm	NOUN
ejpam-6440	44	48	)	)	PUNCT
ejpam-6440	44	49	+	+	NOUN
ejpam-6440	44	50	m(υn+1	m(υn+1	NUM
ejpam-6440	44	51	,	,	PUNCT
ejpam-6440	44	52	υm	υm	NOUN
ejpam-6440	44	53	,	,	PUNCT
ejpam-6440	44	54	υm	υm	PROPN
ejpam-6440	44	55	)	)	PUNCT
ejpam-6440	44	56	]	]	PUNCT
ejpam-6440	44	57	≤	≤	NUM
ejpam-6440	44	58	r	r	NOUN
ejpam-6440	44	59	[	[	X
ejpam-6440	44	60	m(υn	m(υn	ADJ
ejpam-6440	44	61	,	,	PUNCT
ejpam-6440	44	62	υn+1	υn+1	NOUN
ejpam-6440	44	63	,	,	PUNCT
ejpam-6440	44	64	υn+1	υn+1	NOUN
ejpam-6440	44	65	)	)	PUNCT
ejpam-6440	44	66	+	+	SYM
ejpam-6440	44	67	m(υn+1	m(υn+1	NUM
ejpam-6440	44	68	,	,	PUNCT
ejpam-6440	44	69	υm	υm	NOUN
ejpam-6440	44	70	,	,	PUNCT
ejpam-6440	44	71	υm	υm	PROPN
ejpam-6440	44	72	)	)	PUNCT
ejpam-6440	44	73	]	]	PUNCT
ejpam-6440	45	1	+	+	CCONJ
ejpam-6440	45	2	symmetric	symmetric	ADJ
ejpam-6440	45	3	terms	term	NOUN
ejpam-6440	45	4	.	.	PUNCT
ejpam-6440	46	1	by	by	ADP
ejpam-6440	46	2	induction	induction	NOUN
ejpam-6440	46	3	,	,	PUNCT
ejpam-6440	46	4	this	this	PRON
ejpam-6440	46	5	leads	lead	VERB
ejpam-6440	46	6	to	to	ADP
ejpam-6440	46	7	:	:	PUNCT
ejpam-6440	46	8	m(υn	m(υn	ADJ
ejpam-6440	46	9	,	,	PUNCT
ejpam-6440	46	10	υm	υm	NOUN
ejpam-6440	46	11	,	,	PUNCT
ejpam-6440	46	12	υm	υm	NOUN
ejpam-6440	46	13	)	)	PUNCT
ejpam-6440	46	14	≤	≤	NOUN
ejpam-6440	46	15	r	r	NOUN
ejpam-6440	46	16	m−1∑	m−1∑	NUM
ejpam-6440	46	17	i	i	NOUN
ejpam-6440	46	18	=	=	PROPN
ejpam-6440	46	19	n	n	PRON
ejpam-6440	46	20	m(υi	m(υi	PROPN
ejpam-6440	46	21	,	,	PUNCT
ejpam-6440	46	22	υi+1	υi+1	ADV
ejpam-6440	46	23	,	,	PUNCT
ejpam-6440	46	24	υi+1	υi+1	X
ejpam-6440	46	25	)	)	PUNCT
ejpam-6440	46	26	≤	≤	NUM
ejpam-6440	47	1	r	r	NOUN
ejpam-6440	47	2	m−1∑	m−1∑	NUM
ejpam-6440	47	3	i	i	NOUN
ejpam-6440	47	4	=	=	NOUN
ejpam-6440	47	5	n	n	PRON
ejpam-6440	47	6	kim(υ1	kim(υ1	NOUN
ejpam-6440	47	7	,	,	PUNCT
ejpam-6440	47	8	υ0	υ0	NOUN
ejpam-6440	47	9	,	,	PUNCT
ejpam-6440	47	10	υ0	υ0	NOUN
ejpam-6440	47	11	)	)	PUNCT
ejpam-6440	47	12	.	.	PUNCT
ejpam-6440	48	1	the	the	DET
ejpam-6440	48	2	geometric	geometric	ADJ
ejpam-6440	48	3	series	series	NOUN
ejpam-6440	48	4	converges	converge	VERB
ejpam-6440	48	5	since	since	SCONJ
ejpam-6440	48	6	k	k	PROPN
ejpam-6440	48	7	<	<	X
ejpam-6440	48	8	1	1	NUM
ejpam-6440	48	9	,	,	PUNCT
ejpam-6440	48	10	proving	prove	VERB
ejpam-6440	48	11	{	{	PUNCT
ejpam-6440	48	12	υn	υn	NOUN
ejpam-6440	48	13	}	}	PUNCT
ejpam-6440	48	14	is	be	AUX
ejpam-6440	48	15	cauchy	cauchy	PROPN
ejpam-6440	48	16	.	.	PUNCT
ejpam-6440	49	1	(	(	PUNCT
ejpam-6440	49	2	iv	iv	X
ejpam-6440	49	3	)	)	PUNCT
ejpam-6440	49	4	convergence	convergence	NOUN
ejpam-6440	49	5	:	:	PUNCT
ejpam-6440	49	6	by	by	ADP
ejpam-6440	49	7	completeness	completeness	NOUN
ejpam-6440	49	8	of	of	ADP
ejpam-6440	49	9	x	x	PRON
ejpam-6440	49	10	,	,	PUNCT
ejpam-6440	49	11	there	there	PRON
ejpam-6440	49	12	exists	exist	VERB
ejpam-6440	49	13	υ∗	υ∗	NOUN
ejpam-6440	49	14	∈	∈	PROPN
ejpam-6440	49	15	x	x	PUNCT
ejpam-6440	49	16	such	such	ADJ
ejpam-6440	49	17	that	that	SCONJ
ejpam-6440	49	18	limn→∞	limn→∞	PROPN
ejpam-6440	49	19	υn	υn	NOUN
ejpam-6440	49	20	=	=	SYM
ejpam-6440	49	21	υ∗.	υ∗.	PROPN
ejpam-6440	49	22	(	(	PUNCT
ejpam-6440	49	23	v	v	NOUN
ejpam-6440	49	24	)	)	PUNCT
ejpam-6440	49	25	fixed	fix	VERB
ejpam-6440	49	26	point	point	NOUN
ejpam-6440	49	27	property	property	NOUN
ejpam-6440	49	28	:	:	PUNCT
ejpam-6440	49	29	using	use	VERB
ejpam-6440	49	30	the	the	DET
ejpam-6440	49	31	continuity	continuity	NOUN
ejpam-6440	49	32	of	of	ADP
ejpam-6440	49	33	m	m	PROPN
ejpam-6440	49	34	and	and	CCONJ
ejpam-6440	49	35	the	the	DET
ejpam-6440	49	36	contraction	contraction	NOUN
ejpam-6440	49	37	property	property	NOUN
ejpam-6440	49	38	:	:	PUNCT
ejpam-6440	49	39	m(tυ∗	m(tυ∗	PROPN
ejpam-6440	49	40	,	,	PUNCT
ejpam-6440	49	41	υ∗	υ∗	NOUN
ejpam-6440	49	42	,	,	PUNCT
ejpam-6440	49	43	υ∗	υ∗	NOUN
ejpam-6440	49	44	)	)	PUNCT
ejpam-6440	50	1	=	=	PROPN
ejpam-6440	50	2	lim	lim	PROPN
ejpam-6440	50	3	n→∞	n→∞	X
ejpam-6440	50	4	m(υn+1	m(υn+1	PROPN
ejpam-6440	50	5	,	,	PUNCT
ejpam-6440	50	6	υn	υn	NOUN
ejpam-6440	50	7	,	,	PUNCT
ejpam-6440	50	8	υn	υn	NOUN
ejpam-6440	50	9	)	)	PUNCT
ejpam-6440	50	10	≤	≤	NOUN
ejpam-6440	50	11	lim	lim	PROPN
ejpam-6440	50	12	n→∞	n→∞	NUM
ejpam-6440	51	1	knm(υ1	knm(υ1	PROPN
ejpam-6440	51	2	,	,	PUNCT
ejpam-6440	51	3	υ0	υ0	NOUN
ejpam-6440	51	4	,	,	PUNCT
ejpam-6440	51	5	υ0	υ0	NOUN
ejpam-6440	51	6	)	)	PUNCT
ejpam-6440	51	7	=	=	SYM
ejpam-6440	52	1	0	0	X
ejpam-6440	52	2	.	.	PUNCT
ejpam-6440	52	3	thus	thus	ADV
ejpam-6440	52	4	tυ∗	tυ∗	PUNCT
ejpam-6440	53	1	=	=	SYM
ejpam-6440	53	2	υ∗.	υ∗.	ADJ
ejpam-6440	53	3	part	part	NOUN
ejpam-6440	53	4	(	(	PUNCT
ejpam-6440	53	5	ii	ii	NOUN
ejpam-6440	53	6	):	):	PUNCT
ejpam-6440	53	7	uniqueness	uniqueness	NOUN
ejpam-6440	53	8	of	of	ADP
ejpam-6440	53	9	fixed	fix	VERB
ejpam-6440	53	10	point	point	NOUN
ejpam-6440	53	11	suppose	suppose	VERB
ejpam-6440	53	12	υ∗	υ∗	NOUN
ejpam-6440	53	13	and	and	CCONJ
ejpam-6440	53	14	ξ∗	ξ∗	PROPN
ejpam-6440	53	15	are	be	AUX
ejpam-6440	53	16	both	both	PRON
ejpam-6440	53	17	fixed	fix	VERB
ejpam-6440	53	18	points	point	NOUN
ejpam-6440	53	19	.	.	PUNCT
ejpam-6440	54	1	then	then	ADV
ejpam-6440	54	2	:	:	PUNCT
ejpam-6440	54	3	m(υ∗	m(υ∗	ADV
ejpam-6440	54	4	,	,	PUNCT
ejpam-6440	54	5	ξ∗	ξ∗	NOUN
ejpam-6440	54	6	,	,	PUNCT
ejpam-6440	54	7	ξ∗	ξ∗	ADJ
ejpam-6440	54	8	)	)	PUNCT
ejpam-6440	55	1	=	=	NOUN
ejpam-6440	55	2	m(tυ∗	m(tυ∗	PROPN
ejpam-6440	55	3	,	,	PUNCT
ejpam-6440	55	4	t	t	PROPN
ejpam-6440	55	5	ξ∗	ξ∗	NOUN
ejpam-6440	55	6	,	,	PUNCT
ejpam-6440	55	7	t	t	PROPN
ejpam-6440	55	8	ξ∗	ξ∗	NOUN
ejpam-6440	55	9	)	)	PUNCT
ejpam-6440	55	10	≤	≤	NUM
ejpam-6440	55	11	km(υ∗	km(υ∗	NOUN
ejpam-6440	55	12	,	,	PUNCT
ejpam-6440	55	13	ξ∗	ξ∗	NOUN
ejpam-6440	55	14	,	,	PUNCT
ejpam-6440	55	15	ξ∗	ξ∗	NOUN
ejpam-6440	55	16	)	)	PUNCT
ejpam-6440	55	17	.	.	PUNCT
ejpam-6440	56	1	since	since	SCONJ
ejpam-6440	56	2	k	k	PROPN
ejpam-6440	56	3	<	<	X
ejpam-6440	56	4	1	1	NUM
ejpam-6440	56	5	,	,	PUNCT
ejpam-6440	56	6	this	this	PRON
ejpam-6440	56	7	implies	imply	VERB
ejpam-6440	56	8	m(υ∗	m(υ∗	ADV
ejpam-6440	56	9	,	,	PUNCT
ejpam-6440	56	10	ξ∗	ξ∗	NOUN
ejpam-6440	56	11	,	,	PUNCT
ejpam-6440	56	12	ξ∗	ξ∗	ADJ
ejpam-6440	56	13	)	)	PUNCT
ejpam-6440	56	14	=	=	SYM
ejpam-6440	56	15	0	0	NUM
ejpam-6440	56	16	,	,	PUNCT
ejpam-6440	56	17	and	and	CCONJ
ejpam-6440	56	18	by	by	ADP
ejpam-6440	56	19	property	property	NOUN
ejpam-6440	56	20	(	(	PUNCT
ejpam-6440	56	21	m2	m2	PROPN
ejpam-6440	56	22	)	)	PUNCT
ejpam-6440	56	23	of	of	ADP
ejpam-6440	56	24	mr	mr	PROPN
ejpam-6440	56	25	-	-	PUNCT
ejpam-6440	56	26	metrics	metric	NOUN
ejpam-6440	56	27	,	,	PUNCT
ejpam-6440	57	1	υ∗	υ∗	NOUN
ejpam-6440	57	2	=	=	PRON
ejpam-6440	57	3	ξ∗.	ξ∗.	PROPN
ejpam-6440	57	4	part	part	NOUN
ejpam-6440	57	5	(	(	PUNCT
ejpam-6440	57	6	iii	iii	NOUN
ejpam-6440	57	7	):	):	PUNCT
ejpam-6440	57	8	error	error	NOUN
ejpam-6440	57	9	estimation	estimation	NOUN
ejpam-6440	57	10	for	for	ADP
ejpam-6440	57	11	any	any	DET
ejpam-6440	57	12	n	n	PRON
ejpam-6440	57	13	≥	≥	NOUN
ejpam-6440	57	14	0	0	NUM
ejpam-6440	57	15	and	and	CCONJ
ejpam-6440	57	16	p	p	X
ejpam-6440	57	17	≥	≥	NUM
ejpam-6440	57	18	1	1	NUM
ejpam-6440	57	19	,	,	PUNCT
ejpam-6440	57	20	we	we	PRON
ejpam-6440	57	21	have	have	AUX
ejpam-6440	57	22	:	:	PUNCT
ejpam-6440	57	23	m(υn	m(υn	ADJ
ejpam-6440	57	24	,	,	PUNCT
ejpam-6440	57	25	υn+p	υn+p	PROPN
ejpam-6440	57	26	,	,	PUNCT
ejpam-6440	57	27	υn+p	υn+p	PROPN
ejpam-6440	57	28	)	)	PUNCT
ejpam-6440	57	29	≤	≤	NOUN
ejpam-6440	58	1	r	r	NOUN
ejpam-6440	58	2	n+p−1∑	n+p−1∑	PROPN
ejpam-6440	58	3	i	i	PROPN
ejpam-6440	58	4	=	=	PROPN
ejpam-6440	58	5	n	n	PRON
ejpam-6440	58	6	m(υi	m(υi	PROPN
ejpam-6440	58	7	,	,	PUNCT
ejpam-6440	58	8	υi+1	υi+1	ADV
ejpam-6440	58	9	,	,	PUNCT
ejpam-6440	58	10	υi+1	υi+1	X
ejpam-6440	58	11	)	)	PUNCT
ejpam-6440	58	12	≤	≤	NOUN
ejpam-6440	58	13	rkn	rkn	NOUN
ejpam-6440	58	14	1−	1−	NUM
ejpam-6440	58	15	kp	kp	PROPN
ejpam-6440	58	16	1−	1−	NUM
ejpam-6440	58	17	k	k	PROPN
ejpam-6440	58	18	m(υ0	m(υ0	PROPN
ejpam-6440	58	19	,	,	PUNCT
ejpam-6440	58	20	υ1	υ1	PROPN
ejpam-6440	58	21	,	,	PUNCT
ejpam-6440	58	22	υ1	υ1	PROPN
ejpam-6440	58	23	)	)	PUNCT
ejpam-6440	58	24	.	.	PUNCT
ejpam-6440	59	1	taking	take	VERB
ejpam-6440	59	2	p→	p→	VERB
ejpam-6440	59	3	∞	∞	PROPN
ejpam-6440	59	4	and	and	CCONJ
ejpam-6440	59	5	using	use	VERB
ejpam-6440	59	6	the	the	DET
ejpam-6440	59	7	continuity	continuity	NOUN
ejpam-6440	59	8	of	of	ADP
ejpam-6440	59	9	m	m	NOUN
ejpam-6440	59	10	:	:	PUNCT
ejpam-6440	59	11	m(υn	m(υn	ADJ
ejpam-6440	59	12	,	,	PUNCT
ejpam-6440	59	13	υ	υ	PRON
ejpam-6440	59	14	∗	∗	NOUN
ejpam-6440	59	15	,	,	PUNCT
ejpam-6440	59	16	υ∗	υ∗	NOUN
ejpam-6440	59	17	)	)	PUNCT
ejpam-6440	59	18	≤	≤	NUM
ejpam-6440	60	1	rkn	rkn	NOUN
ejpam-6440	60	2	1−	1−	NUM
ejpam-6440	60	3	k	k	X
ejpam-6440	60	4	m(υ0	m(υ0	PROPN
ejpam-6440	60	5	,	,	PUNCT
ejpam-6440	60	6	υ1	υ1	PROPN
ejpam-6440	60	7	,	,	PUNCT
ejpam-6440	60	8	υ1	υ1	PROPN
ejpam-6440	60	9	)	)	PUNCT
ejpam-6440	60	10	.	.	PUNCT
ejpam-6440	61	1	the	the	DET
ejpam-6440	61	2	stricter	strict	ADJ
ejpam-6440	61	3	bound	bind	VERB
ejpam-6440	61	4	1	1	NUM
ejpam-6440	61	5	1−3rk	1−3rk	NUM
ejpam-6440	61	6	comes	come	VERB
ejpam-6440	61	7	from	from	ADP
ejpam-6440	61	8	more	more	ADV
ejpam-6440	61	9	careful	careful	ADJ
ejpam-6440	61	10	estimation	estimation	NOUN
ejpam-6440	61	11	using	use	VERB
ejpam-6440	61	12	the	the	DET
ejpam-6440	61	13	mr	mr	PROPN
ejpam-6440	61	14	-	-	PUNCT
ejpam-6440	61	15	metric	metric	ADJ
ejpam-6440	61	16	property	property	NOUN
ejpam-6440	61	17	(	(	PUNCT
ejpam-6440	61	18	m4	m4	PROPN
ejpam-6440	61	19	)	)	PUNCT
ejpam-6440	61	20	with	with	ADP
ejpam-6440	61	21	all	all	DET
ejpam-6440	61	22	three	three	NUM
ejpam-6440	61	23	terms	term	NOUN
ejpam-6440	61	24	.	.	PUNCT
ejpam-6440	62	1	t.	t.	NOUN
ejpam-6440	62	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	62	3	,	,	PUNCT
ejpam-6440	62	4	a.	a.	NOUN
ejpam-6440	62	5	malkawi	malkawi	PROPN
ejpam-6440	62	6	/	/	SYM
ejpam-6440	62	7	eur	eur	PROPN
ejpam-6440	62	8	.	.	PUNCT
ejpam-6440	63	1	j.	j.	PROPN
ejpam-6440	63	2	pure	pure	PROPN
ejpam-6440	63	3	appl	appl	PROPN
ejpam-6440	63	4	.	.	PROPN
ejpam-6440	63	5	math	math	PROPN
ejpam-6440	63	6	,	,	PUNCT
ejpam-6440	63	7	18	18	NUM
ejpam-6440	63	8	(	(	PUNCT
ejpam-6440	63	9	3	3	NUM
ejpam-6440	63	10	)	)	PUNCT
ejpam-6440	63	11	(	(	PUNCT
ejpam-6440	63	12	2025	2025	NUM
ejpam-6440	63	13	)	)	PUNCT
ejpam-6440	63	14	,	,	PUNCT
ejpam-6440	63	15	6440	6440	NUM
ejpam-6440	63	16	5	5	NUM
ejpam-6440	63	17	of	of	ADP
ejpam-6440	63	18	20	20	NUM
ejpam-6440	63	19	remark	remark	NOUN
ejpam-6440	63	20	1	1	NUM
ejpam-6440	63	21	.	.	PUNCT
ejpam-6440	64	1	the	the	DET
ejpam-6440	64	2	condition	condition	NOUN
ejpam-6440	64	3	k	k	X
ejpam-6440	64	4	<	<	X
ejpam-6440	64	5	1	1	NUM
ejpam-6440	64	6	3r	3r	NUM
ejpam-6440	64	7	is	be	AUX
ejpam-6440	64	8	optimal	optimal	ADJ
ejpam-6440	64	9	in	in	ADP
ejpam-6440	64	10	the	the	DET
ejpam-6440	64	11	sense	sense	NOUN
ejpam-6440	64	12	that	that	PRON
ejpam-6440	64	13	:	:	PUNCT
ejpam-6440	64	14	•	•	NOUN
ejpam-6440	64	15	for	for	ADP
ejpam-6440	64	16	k	k	PROPN
ejpam-6440	64	17	≥	≥	NUM
ejpam-6440	64	18	1	1	NUM
ejpam-6440	64	19	3r	3r	NUM
ejpam-6440	64	20	,	,	PUNCT
ejpam-6440	64	21	the	the	DET
ejpam-6440	64	22	iterative	iterative	NOUN
ejpam-6440	64	23	sequence	sequence	NOUN
ejpam-6440	64	24	may	may	AUX
ejpam-6440	64	25	not	not	PART
ejpam-6440	64	26	converge	converge	VERB
ejpam-6440	64	27	•	•	ADP
ejpam-6440	64	28	the	the	DET
ejpam-6440	64	29	constant	constant	ADJ
ejpam-6440	64	30	3	3	NUM
ejpam-6440	64	31	appears	appear	VERB
ejpam-6440	64	32	from	from	ADP
ejpam-6440	64	33	the	the	DET
ejpam-6440	64	34	mr	mr	PROPN
ejpam-6440	64	35	-	-	PUNCT
ejpam-6440	64	36	metric	metric	ADJ
ejpam-6440	64	37	axiom	axiom	NOUN
ejpam-6440	64	38	(	(	PUNCT
ejpam-6440	64	39	m4	m4	PROPN
ejpam-6440	64	40	)	)	PUNCT
ejpam-6440	64	41	involving	involve	VERB
ejpam-6440	64	42	three	three	NUM
ejpam-6440	64	43	terms	term	NOUN
ejpam-6440	64	44	•	•	VERB
ejpam-6440	64	45	when	when	SCONJ
ejpam-6440	64	46	r→	r→	PROPN
ejpam-6440	64	47	1	1	NUM
ejpam-6440	64	48	+	+	PROPN
ejpam-6440	64	49	,	,	PUNCT
ejpam-6440	64	50	we	we	PRON
ejpam-6440	64	51	recover	recover	VERB
ejpam-6440	64	52	the	the	DET
ejpam-6440	64	53	classical	classical	ADJ
ejpam-6440	64	54	banach	banach	NOUN
ejpam-6440	64	55	contraction	contraction	NOUN
ejpam-6440	64	56	principle	principle	NOUN
ejpam-6440	64	57	lemma	lemma	PROPN
ejpam-6440	64	58	1	1	NUM
ejpam-6440	64	59	(	(	PUNCT
ejpam-6440	64	60	stability	stability	NOUN
ejpam-6440	64	61	of	of	ADP
ejpam-6440	64	62	iterations	iteration	NOUN
ejpam-6440	64	63	)	)	PUNCT
ejpam-6440	64	64	.	.	PUNCT
ejpam-6440	65	1	under	under	ADP
ejpam-6440	65	2	the	the	DET
ejpam-6440	65	3	conditions	condition	NOUN
ejpam-6440	65	4	of	of	ADP
ejpam-6440	65	5	theorem	theorem	NOUN
ejpam-6440	65	6	1	1	NUM
ejpam-6440	65	7	,	,	PUNCT
ejpam-6440	65	8	for	for	ADP
ejpam-6440	65	9	any	any	DET
ejpam-6440	65	10	two	two	NUM
ejpam-6440	65	11	initial	initial	ADJ
ejpam-6440	65	12	points	point	NOUN
ejpam-6440	65	13	υ0	υ0	NOUN
ejpam-6440	65	14	,	,	PUNCT
ejpam-6440	65	15	ξ0	ξ0	PROPN
ejpam-6440	65	16	∈	∈	PROPN
ejpam-6440	65	17	x	x	PRON
ejpam-6440	65	18	,	,	PUNCT
ejpam-6440	65	19	their	their	PRON
ejpam-6440	65	20	corresponding	correspond	VERB
ejpam-6440	65	21	picard	picard	NOUN
ejpam-6440	65	22	iterations	iteration	NOUN
ejpam-6440	65	23	satisfy	satisfy	VERB
ejpam-6440	65	24	:	:	PUNCT
ejpam-6440	65	25	m(υn	m(υn	NUM
ejpam-6440	65	26	,	,	PUNCT
ejpam-6440	65	27	ξn	ξn	PROPN
ejpam-6440	65	28	,	,	PUNCT
ejpam-6440	65	29	ξn	ξn	NOUN
ejpam-6440	65	30	)	)	PUNCT
ejpam-6440	65	31	≤	≤	NOUN
ejpam-6440	65	32	rkn	rkn	NOUN
ejpam-6440	65	33	1−	1−	NUM
ejpam-6440	65	34	3rk	3rk	NOUN
ejpam-6440	66	1	[	[	X
ejpam-6440	66	2	m(υ0	m(υ0	NOUN
ejpam-6440	66	3	,	,	PUNCT
ejpam-6440	66	4	tυ0	tυ0	ADJ
ejpam-6440	66	5	,	,	PUNCT
ejpam-6440	66	6	tυ0	tυ0	NOUN
ejpam-6440	66	7	)	)	PUNCT
ejpam-6440	67	1	+	+	NOUN
ejpam-6440	67	2	m(ξ0	m(ξ0	PROPN
ejpam-6440	67	3	,	,	PUNCT
ejpam-6440	67	4	t	t	PROPN
ejpam-6440	67	5	ξ0	ξ0	PROPN
ejpam-6440	67	6	,	,	PUNCT
ejpam-6440	67	7	t	t	PROPN
ejpam-6440	67	8	ξ0	ξ0	PROPN
ejpam-6440	67	9	)	)	PUNCT
ejpam-6440	67	10	]	]	PUNCT
ejpam-6440	67	11	.	.	PUNCT
ejpam-6440	68	1	proof	proof	NOUN
ejpam-6440	68	2	.	.	PUNCT
ejpam-6440	69	1	this	this	PRON
ejpam-6440	69	2	follows	follow	VERB
ejpam-6440	69	3	from	from	ADP
ejpam-6440	69	4	similar	similar	ADJ
ejpam-6440	69	5	estimates	estimate	NOUN
ejpam-6440	69	6	using	use	VERB
ejpam-6440	69	7	the	the	DET
ejpam-6440	69	8	mr	mr	PROPN
ejpam-6440	69	9	-	-	PUNCT
ejpam-6440	69	10	metric	metric	ADJ
ejpam-6440	69	11	properties	property	NOUN
ejpam-6440	69	12	and	and	CCONJ
ejpam-6440	69	13	the	the	DET
ejpam-6440	69	14	contraction	contraction	NOUN
ejpam-6440	69	15	condition	condition	NOUN
ejpam-6440	69	16	,	,	PUNCT
ejpam-6440	69	17	with	with	ADP
ejpam-6440	69	18	careful	careful	ADJ
ejpam-6440	69	19	handling	handling	NOUN
ejpam-6440	69	20	of	of	ADP
ejpam-6440	69	21	the	the	DET
ejpam-6440	69	22	triangle	triangle	NOUN
ejpam-6440	69	23	inequality	inequality	NOUN
ejpam-6440	69	24	for	for	ADP
ejpam-6440	69	25	three	three	NUM
ejpam-6440	69	26	points	point	NOUN
ejpam-6440	69	27	.	.	PUNCT
ejpam-6440	70	1	theorem	theorem	ADJ
ejpam-6440	70	2	2	2	NUM
ejpam-6440	70	3	(	(	PUNCT
ejpam-6440	70	4	solution	solution	NOUN
ejpam-6440	70	5	of	of	ADP
ejpam-6440	70	6	fredholm	fredholm	NOUN
ejpam-6440	70	7	-	-	PUNCT
ejpam-6440	70	8	type	type	NOUN
ejpam-6440	70	9	equation	equation	NOUN
ejpam-6440	70	10	in	in	ADP
ejpam-6440	70	11	mr	mr	PROPN
ejpam-6440	70	12	-	-	PUNCT
ejpam-6440	70	13	metric	metric	ADJ
ejpam-6440	70	14	spaces	space	NOUN
ejpam-6440	70	15	)	)	PUNCT
ejpam-6440	70	16	.	.	PUNCT
ejpam-6440	71	1	let	let	VERB
ejpam-6440	71	2	c([a	c([a	PROPN
ejpam-6440	71	3	,	,	PUNCT
ejpam-6440	71	4	b	b	NOUN
ejpam-6440	71	5	]	]	PUNCT
ejpam-6440	71	6	)	)	PUNCT
ejpam-6440	71	7	be	be	AUX
ejpam-6440	71	8	the	the	DET
ejpam-6440	71	9	space	space	NOUN
ejpam-6440	71	10	of	of	ADP
ejpam-6440	71	11	continuous	continuous	ADJ
ejpam-6440	71	12	real	real	ADV
ejpam-6440	71	13	-	-	PUNCT
ejpam-6440	71	14	valued	value	VERB
ejpam-6440	71	15	functions	function	NOUN
ejpam-6440	71	16	on	on	ADP
ejpam-6440	71	17	[	[	X
ejpam-6440	71	18	a	a	X
ejpam-6440	71	19	,	,	PUNCT
ejpam-6440	71	20	b	b	NOUN
ejpam-6440	71	21	]	]	X
ejpam-6440	71	22	,	,	PUNCT
ejpam-6440	71	23	and	and	CCONJ
ejpam-6440	71	24	define	define	VERB
ejpam-6440	71	25	the	the	DET
ejpam-6440	71	26	mr	mr	PROPN
ejpam-6440	71	27	-	-	PUNCT
ejpam-6440	71	28	metric	metric	NOUN
ejpam-6440	71	29	:	:	PUNCT
ejpam-6440	71	30	m(f	m(f	PROPN
ejpam-6440	71	31	,	,	PUNCT
ejpam-6440	71	32	g	g	PROPN
ejpam-6440	71	33	,	,	PUNCT
ejpam-6440	71	34	h	h	NOUN
ejpam-6440	71	35	)	)	PUNCT
ejpam-6440	71	36	=	=	NOUN
ejpam-6440	71	37	sup	sup	NOUN
ejpam-6440	71	38	x∈[a	x∈[a	PROPN
ejpam-6440	71	39	,	,	PUNCT
ejpam-6440	71	40	b	b	X
ejpam-6440	71	41	]	]	X
ejpam-6440	71	42	(	(	PUNCT
ejpam-6440	71	43	|f(x)−	|f(x)−	NOUN
ejpam-6440	71	44	g(x)|+	g(x)|+	PROPN
ejpam-6440	71	45	|f(x)−	|f(x)−	PROPN
ejpam-6440	71	46	h(x)|+	h(x)|+	PROPN
ejpam-6440	71	47	|g(x)−	|g(x)−	PROPN
ejpam-6440	71	48	h(x)|	h(x)|	NOUN
ejpam-6440	71	49	)	)	PUNCT
ejpam-6440	71	50	.	.	PUNCT
ejpam-6440	72	1	consider	consider	VERB
ejpam-6440	72	2	the	the	DET
ejpam-6440	72	3	fredholm	fredholm	ADJ
ejpam-6440	72	4	integral	integral	ADJ
ejpam-6440	72	5	equation	equation	NOUN
ejpam-6440	72	6	:	:	PUNCT
ejpam-6440	72	7	f(x	f(x	PROPN
ejpam-6440	72	8	)	)	PUNCT
ejpam-6440	73	1	=	=	PUNCT
ejpam-6440	73	2	λ	λ	X
ejpam-6440	73	3	∫	∫	PROPN
ejpam-6440	73	4	b	b	PROPN
ejpam-6440	73	5	a	a	DET
ejpam-6440	73	6	k(x	k(x	PROPN
ejpam-6440	73	7	,	,	PUNCT
ejpam-6440	73	8	y	y	PROPN
ejpam-6440	73	9	,	,	PUNCT
ejpam-6440	73	10	f(y	f(y	NOUN
ejpam-6440	73	11	)	)	PUNCT
ejpam-6440	73	12	)	)	PUNCT
ejpam-6440	74	1	dy	dy	NOUN
ejpam-6440	74	2	+	+	CCONJ
ejpam-6440	74	3	ϕ(x	ϕ(x	NOUN
ejpam-6440	74	4	)	)	PUNCT
ejpam-6440	74	5	,	,	PUNCT
ejpam-6440	74	6	x	x	PUNCT
ejpam-6440	74	7	∈	∈	PROPN
ejpam-6440	75	1	[	[	X
ejpam-6440	75	2	a	a	X
ejpam-6440	75	3	,	,	PUNCT
ejpam-6440	75	4	b	b	NOUN
ejpam-6440	75	5	]	]	X
ejpam-6440	75	6	,	,	PUNCT
ejpam-6440	76	1	where	where	SCONJ
ejpam-6440	76	2	k	k	NOUN
ejpam-6440	76	3	:	:	PUNCT
ejpam-6440	77	1	[	[	X
ejpam-6440	77	2	a	a	X
ejpam-6440	77	3	,	,	PUNCT
ejpam-6440	77	4	b]×	b]×	NOUN
ejpam-6440	77	5	[	[	X
ejpam-6440	77	6	a	a	X
ejpam-6440	77	7	,	,	PUNCT
ejpam-6440	77	8	b]×	b]×	NOUN
ejpam-6440	77	9	r	r	NOUN
ejpam-6440	77	10	→	→	SYM
ejpam-6440	77	11	r	r	NOUN
ejpam-6440	77	12	and	and	CCONJ
ejpam-6440	77	13	ϕ	ϕ	PROPN
ejpam-6440	77	14	∈	∈	PROPN
ejpam-6440	77	15	c([a	c([a	PROPN
ejpam-6440	77	16	,	,	PUNCT
ejpam-6440	77	17	b	b	NOUN
ejpam-6440	77	18	]	]	X
ejpam-6440	77	19	)	)	PUNCT
ejpam-6440	77	20	.	.	PUNCT
ejpam-6440	78	1	if	if	SCONJ
ejpam-6440	78	2	:	:	PUNCT
ejpam-6440	78	3	(	(	PUNCT
ejpam-6440	78	4	i	i	NOUN
ejpam-6440	78	5	)	)	PUNCT
ejpam-6440	78	6	k	k	X
ejpam-6440	78	7	is	be	AUX
ejpam-6440	78	8	lipschitz	lipschitz	NOUN
ejpam-6440	78	9	in	in	ADP
ejpam-6440	78	10	the	the	DET
ejpam-6440	78	11	third	third	ADJ
ejpam-6440	78	12	variable	variable	NOUN
ejpam-6440	78	13	:	:	PUNCT
ejpam-6440	78	14	|k(x	|k(x	PROPN
ejpam-6440	78	15	,	,	PUNCT
ejpam-6440	78	16	y	y	PROPN
ejpam-6440	78	17	,	,	PUNCT
ejpam-6440	78	18	u)−k(x	u)−k(x	PROPN
ejpam-6440	78	19	,	,	PUNCT
ejpam-6440	78	20	y	y	PROPN
ejpam-6440	78	21	,	,	PUNCT
ejpam-6440	78	22	v)|	v)|	VERB
ejpam-6440	78	23	≤	≤	NOUN
ejpam-6440	78	24	l|u−	l|u−	X
ejpam-6440	78	25	v|	v|	NOUN
ejpam-6440	78	26	,	,	PUNCT
ejpam-6440	78	27	(	(	PUNCT
ejpam-6440	78	28	ii	ii	NOUN
ejpam-6440	78	29	)	)	PUNCT
ejpam-6440	78	30	|λ|l(b−	|λ|l(b−	VERB
ejpam-6440	78	31	a	a	PRON
ejpam-6440	78	32	)	)	PUNCT
ejpam-6440	78	33	<	<	X
ejpam-6440	78	34	1	1	NUM
ejpam-6440	78	35	3r	3r	NUM
ejpam-6440	78	36	,	,	PUNCT
ejpam-6440	78	37	then	then	ADV
ejpam-6440	78	38	the	the	DET
ejpam-6440	78	39	integral	integral	ADJ
ejpam-6440	78	40	equation	equation	NOUN
ejpam-6440	78	41	has	have	VERB
ejpam-6440	78	42	a	a	DET
ejpam-6440	78	43	unique	unique	ADJ
ejpam-6440	78	44	solution	solution	NOUN
ejpam-6440	78	45	f∗	f∗	NOUN
ejpam-6440	78	46	∈	∈	PROPN
ejpam-6440	78	47	c([a	c([a	PROPN
ejpam-6440	78	48	,	,	PUNCT
ejpam-6440	78	49	b	b	NOUN
ejpam-6440	78	50	]	]	X
ejpam-6440	78	51	)	)	PUNCT
ejpam-6440	78	52	,	,	PUNCT
ejpam-6440	78	53	obtainable	obtainable	ADJ
ejpam-6440	78	54	via	via	ADP
ejpam-6440	78	55	iteration	iteration	NOUN
ejpam-6440	78	56	.	.	PUNCT
ejpam-6440	79	1	proof	proof	NOUN
ejpam-6440	79	2	.	.	PUNCT
ejpam-6440	80	1	we	we	PRON
ejpam-6440	80	2	provide	provide	VERB
ejpam-6440	80	3	a	a	DET
ejpam-6440	80	4	comprehensive	comprehensive	ADJ
ejpam-6440	80	5	proof	proof	NOUN
ejpam-6440	80	6	with	with	ADP
ejpam-6440	80	7	detailed	detailed	ADJ
ejpam-6440	80	8	estimates	estimate	NOUN
ejpam-6440	80	9	:	:	PUNCT
ejpam-6440	80	10	step	step	NOUN
ejpam-6440	80	11	1	1	NUM
ejpam-6440	80	12	:	:	PUNCT
ejpam-6440	80	13	operator	operator	NOUN
ejpam-6440	80	14	formulation	formulation	NOUN
ejpam-6440	80	15	define	define	VERB
ejpam-6440	80	16	the	the	DET
ejpam-6440	80	17	nonlinear	nonlinear	ADJ
ejpam-6440	80	18	operator	operator	NOUN
ejpam-6440	80	19	t	t	NOUN
ejpam-6440	80	20	:	:	PUNCT
ejpam-6440	80	21	c([a	c([a	PROPN
ejpam-6440	80	22	,	,	PUNCT
ejpam-6440	80	23	b	b	NOUN
ejpam-6440	80	24	]	]	X
ejpam-6440	80	25	)	)	PUNCT
ejpam-6440	80	26	→	→	SYM
ejpam-6440	80	27	c([a	c([a	PROPN
ejpam-6440	80	28	,	,	PUNCT
ejpam-6440	80	29	b	b	NOUN
ejpam-6440	80	30	]	]	X
ejpam-6440	80	31	)	)	PUNCT
ejpam-6440	80	32	by	by	ADP
ejpam-6440	80	33	:	:	PUNCT
ejpam-6440	80	34	tf(x	tf(x	NUM
ejpam-6440	80	35	)	)	PUNCT
ejpam-6440	80	36	:	:	PUNCT
ejpam-6440	81	1	=	=	PUNCT
ejpam-6440	81	2	λ	λ	X
ejpam-6440	81	3	∫	∫	PROPN
ejpam-6440	81	4	b	b	PROPN
ejpam-6440	81	5	a	a	DET
ejpam-6440	81	6	k(x	k(x	PROPN
ejpam-6440	81	7	,	,	PUNCT
ejpam-6440	81	8	y	y	PROPN
ejpam-6440	81	9	,	,	PUNCT
ejpam-6440	81	10	f(y	f(y	NOUN
ejpam-6440	81	11	)	)	PUNCT
ejpam-6440	81	12	)	)	PUNCT
ejpam-6440	82	1	dy	dy	NOUN
ejpam-6440	82	2	+	+	CCONJ
ejpam-6440	82	3	ϕ(x	ϕ(x	PROPN
ejpam-6440	82	4	)	)	PUNCT
ejpam-6440	82	5	.	.	PUNCT
ejpam-6440	83	1	the	the	DET
ejpam-6440	83	2	fixed	fix	VERB
ejpam-6440	83	3	points	point	NOUN
ejpam-6440	83	4	of	of	ADP
ejpam-6440	83	5	t	t	PROPN
ejpam-6440	83	6	correspond	correspond	VERB
ejpam-6440	83	7	exactly	exactly	ADV
ejpam-6440	83	8	to	to	ADP
ejpam-6440	83	9	solutions	solution	NOUN
ejpam-6440	83	10	of	of	ADP
ejpam-6440	83	11	the	the	DET
ejpam-6440	83	12	integral	integral	ADJ
ejpam-6440	83	13	equation	equation	NOUN
ejpam-6440	83	14	.	.	PUNCT
ejpam-6440	84	1	step	step	NOUN
ejpam-6440	84	2	2	2	NUM
ejpam-6440	84	3	:	:	PUNCT
ejpam-6440	84	4	verification	verification	NOUN
ejpam-6440	84	5	of	of	ADP
ejpam-6440	84	6	continuity	continuity	NOUN
ejpam-6440	84	7	for	for	ADP
ejpam-6440	84	8	any	any	DET
ejpam-6440	84	9	f	f	PROPN
ejpam-6440	84	10	∈	∈	PROPN
ejpam-6440	84	11	c([a	c([a	PROPN
ejpam-6440	84	12	,	,	PUNCT
ejpam-6440	84	13	b	b	NOUN
ejpam-6440	84	14	]	]	X
ejpam-6440	84	15	)	)	PUNCT
ejpam-6440	84	16	,	,	PUNCT
ejpam-6440	84	17	the	the	DET
ejpam-6440	84	18	continuity	continuity	NOUN
ejpam-6440	84	19	of	of	ADP
ejpam-6440	84	20	tf	tf	PROPN
ejpam-6440	84	21	follows	follow	VERB
ejpam-6440	84	22	from	from	ADP
ejpam-6440	84	23	:	:	PUNCT
ejpam-6440	84	24	t.	t.	NOUN
ejpam-6440	84	25	qawasmeh	qawasmeh	NOUN
ejpam-6440	84	26	,	,	PUNCT
ejpam-6440	84	27	a.	a.	NOUN
ejpam-6440	84	28	malkawi	malkawi	PROPN
ejpam-6440	84	29	/	/	SYM
ejpam-6440	84	30	eur	eur	PROPN
ejpam-6440	84	31	.	.	PUNCT
ejpam-6440	85	1	j.	j.	PROPN
ejpam-6440	85	2	pure	pure	PROPN
ejpam-6440	85	3	appl	appl	PROPN
ejpam-6440	85	4	.	.	PROPN
ejpam-6440	85	5	math	math	PROPN
ejpam-6440	85	6	,	,	PUNCT
ejpam-6440	85	7	18	18	NUM
ejpam-6440	85	8	(	(	PUNCT
ejpam-6440	85	9	3	3	NUM
ejpam-6440	85	10	)	)	PUNCT
ejpam-6440	85	11	(	(	PUNCT
ejpam-6440	85	12	2025	2025	NUM
ejpam-6440	85	13	)	)	PUNCT
ejpam-6440	85	14	,	,	PUNCT
ejpam-6440	85	15	6440	6440	NUM
ejpam-6440	85	16	6	6	NUM
ejpam-6440	85	17	of	of	ADP
ejpam-6440	85	18	20	20	NUM
ejpam-6440	85	19	•	•	NUM
ejpam-6440	85	20	the	the	DET
ejpam-6440	85	21	continuity	continuity	NOUN
ejpam-6440	85	22	of	of	ADP
ejpam-6440	85	23	k	k	PROPN
ejpam-6440	85	24	in	in	ADP
ejpam-6440	85	25	its	its	PRON
ejpam-6440	85	26	first	first	ADJ
ejpam-6440	85	27	variable	variable	NOUN
ejpam-6440	85	28	•	•	ADP
ejpam-6440	85	29	the	the	DET
ejpam-6440	85	30	uniform	uniform	ADJ
ejpam-6440	85	31	continuity	continuity	NOUN
ejpam-6440	85	32	of	of	ADP
ejpam-6440	85	33	k	k	PROPN
ejpam-6440	85	34	on	on	ADP
ejpam-6440	85	35	the	the	DET
ejpam-6440	85	36	compact	compact	ADJ
ejpam-6440	85	37	set	set	NOUN
ejpam-6440	86	1	[	[	X
ejpam-6440	86	2	a	a	X
ejpam-6440	86	3	,	,	PUNCT
ejpam-6440	86	4	b]2×	b]2×	PROPN
ejpam-6440	87	1	[	[	X
ejpam-6440	87	2	−m	−m	NOUN
ejpam-6440	87	3	,	,	PUNCT
ejpam-6440	87	4	m	m	VERB
ejpam-6440	87	5	]	]	PUNCT
ejpam-6440	87	6	where	where	SCONJ
ejpam-6440	87	7	m	m	VERB
ejpam-6440	87	8	=	=	SYM
ejpam-6440	87	9	∥f∥∞	∥f∥∞	NUM
ejpam-6440	87	10	•	•	NUM
ejpam-6440	87	11	standard	standard	ADJ
ejpam-6440	87	12	results	result	NOUN
ejpam-6440	87	13	on	on	ADP
ejpam-6440	87	14	continuity	continuity	NOUN
ejpam-6440	87	15	of	of	ADP
ejpam-6440	87	16	parameter	parameter	NOUN
ejpam-6440	87	17	-	-	PUNCT
ejpam-6440	87	18	dependent	dependent	ADJ
ejpam-6440	87	19	integrals	integral	NOUN
ejpam-6440	87	20	step	step	VERB
ejpam-6440	87	21	3	3	NUM
ejpam-6440	87	22	:	:	PUNCT
ejpam-6440	87	23	contraction	contraction	NOUN
ejpam-6440	87	24	property	property	NOUN
ejpam-6440	87	25	in	in	ADP
ejpam-6440	87	26	mr	mr	PROPN
ejpam-6440	87	27	-	-	PUNCT
ejpam-6440	87	28	metric	metric	NOUN
ejpam-6440	87	29	for	for	ADP
ejpam-6440	87	30	any	any	DET
ejpam-6440	87	31	f	f	PROPN
ejpam-6440	87	32	,	,	PUNCT
ejpam-6440	87	33	g	g	PROPN
ejpam-6440	87	34	,	,	PUNCT
ejpam-6440	87	35	h	h	NOUN
ejpam-6440	87	36	∈	∈	PROPN
ejpam-6440	87	37	c([a	c([a	PROPN
ejpam-6440	87	38	,	,	PUNCT
ejpam-6440	87	39	b	b	NOUN
ejpam-6440	87	40	]	]	X
ejpam-6440	87	41	)	)	PUNCT
ejpam-6440	87	42	,	,	PUNCT
ejpam-6440	87	43	we	we	PRON
ejpam-6440	87	44	estimate	estimate	VERB
ejpam-6440	87	45	:	:	PUNCT
ejpam-6440	87	46	m(tf	m(tf	PROPN
ejpam-6440	87	47	,	,	PUNCT
ejpam-6440	87	48	tg	tg	PROPN
ejpam-6440	87	49	,	,	PUNCT
ejpam-6440	87	50	th	th	X
ejpam-6440	87	51	)	)	PUNCT
ejpam-6440	87	52	=	=	SYM
ejpam-6440	87	53	sup	sup	NOUN
ejpam-6440	87	54	x∈[a	x∈[a	PROPN
ejpam-6440	87	55	,	,	PUNCT
ejpam-6440	87	56	b	b	X
ejpam-6440	87	57	]	]	X
ejpam-6440	87	58	(	(	PUNCT
ejpam-6440	87	59	|tf(x)−	|tf(x)−	PROPN
ejpam-6440	87	60	tg(x)|+	tg(x)|+	PROPN
ejpam-6440	87	61	|tf(x)−	|tf(x)−	PROPN
ejpam-6440	88	1	th(x)|+	th(x)|+	PROPN
ejpam-6440	88	2	|tg(x)−	|tg(x)−	PROPN
ejpam-6440	88	3	th(x)|	th(x)|	PROPN
ejpam-6440	88	4	)	)	PUNCT
ejpam-6440	88	5	≤	≤	NUM
ejpam-6440	88	6	|λ|	|λ|	PROPN
ejpam-6440	88	7	sup	sup	NOUN
ejpam-6440	88	8	x∈[a	x∈[a	PROPN
ejpam-6440	88	9	,	,	PUNCT
ejpam-6440	88	10	b	b	X
ejpam-6440	88	11	]	]	X
ejpam-6440	88	12	∫	∫	PROPN
ejpam-6440	89	1	b	b	PROPN
ejpam-6440	89	2	a	a	PRON
ejpam-6440	89	3	(	(	PUNCT
ejpam-6440	89	4	|k(x	|k(x	PROPN
ejpam-6440	89	5	,	,	PUNCT
ejpam-6440	89	6	y	y	PROPN
ejpam-6440	89	7	,	,	PUNCT
ejpam-6440	89	8	f(y))−k(x	f(y))−k(x	PROPN
ejpam-6440	89	9	,	,	PUNCT
ejpam-6440	89	10	y	y	PROPN
ejpam-6440	89	11	,	,	PUNCT
ejpam-6440	89	12	g(y))|	g(y))|	VERB
ejpam-6440	90	1	+	+	SYM
ejpam-6440	90	2	|k(x	|k(x	PROPN
ejpam-6440	90	3	,	,	PUNCT
ejpam-6440	90	4	y	y	PROPN
ejpam-6440	90	5	,	,	PUNCT
ejpam-6440	90	6	f(y))−k(x	f(y))−k(x	PROPN
ejpam-6440	90	7	,	,	PUNCT
ejpam-6440	90	8	y	y	PROPN
ejpam-6440	90	9	,	,	PUNCT
ejpam-6440	90	10	h(y))|+	h(y))|+	PROPN
ejpam-6440	90	11	|k(x	|k(x	PROPN
ejpam-6440	90	12	,	,	PUNCT
ejpam-6440	90	13	y	y	PROPN
ejpam-6440	90	14	,	,	PUNCT
ejpam-6440	90	15	g(y))−k(x	g(y))−k(x	PROPN
ejpam-6440	90	16	,	,	PUNCT
ejpam-6440	90	17	y	y	PROPN
ejpam-6440	90	18	,	,	PUNCT
ejpam-6440	90	19	h(y))|	h(y))|	PROPN
ejpam-6440	90	20	)	)	PUNCT
ejpam-6440	90	21	dy	dy	NOUN
ejpam-6440	90	22	≤	≤	NUM
ejpam-6440	90	23	|λ|l	|λ|l	ADP
ejpam-6440	90	24	sup	sup	PROPN
ejpam-6440	90	25	x∈[a	x∈[a	PROPN
ejpam-6440	90	26	,	,	PUNCT
ejpam-6440	90	27	b	b	X
ejpam-6440	90	28	]	]	X
ejpam-6440	90	29	∫	∫	PROPN
ejpam-6440	91	1	b	b	PROPN
ejpam-6440	91	2	a	a	PRON
ejpam-6440	91	3	(	(	PUNCT
ejpam-6440	91	4	|f(y)−	|f(y)−	NOUN
ejpam-6440	91	5	g(y)|+	g(y)|+	PROPN
ejpam-6440	91	6	|f(y)−	|f(y)−	PROPN
ejpam-6440	91	7	h(y)|+	h(y)|+	NUM
ejpam-6440	91	8	|g(y)−	|g(y)−	PROPN
ejpam-6440	91	9	h(y)|	h(y)|	NOUN
ejpam-6440	91	10	)	)	PUNCT
ejpam-6440	91	11	dy	dy	NOUN
ejpam-6440	91	12	≤	≤	NUM
ejpam-6440	91	13	3|λ|l(b−	3|λ|l(b−	NUM
ejpam-6440	91	14	a)m(f	a)m(f	NOUN
ejpam-6440	91	15	,	,	PUNCT
ejpam-6440	91	16	g	g	NOUN
ejpam-6440	91	17	,	,	PUNCT
ejpam-6440	91	18	h	h	NOUN
ejpam-6440	91	19	)	)	PUNCT
ejpam-6440	91	20	step	step	NOUN
ejpam-6440	91	21	4	4	NUM
ejpam-6440	91	22	:	:	PUNCT
ejpam-6440	91	23	application	application	NOUN
ejpam-6440	91	24	of	of	ADP
ejpam-6440	91	25	banach	banach	ADV
ejpam-6440	91	26	fixed	fix	VERB
ejpam-6440	91	27	-	-	PUNCT
ejpam-6440	91	28	point	point	NOUN
ejpam-6440	91	29	theorem	theorem	NOUN
ejpam-6440	91	30	from	from	ADP
ejpam-6440	91	31	condition	condition	NOUN
ejpam-6440	91	32	(	(	PUNCT
ejpam-6440	91	33	ii	ii	NOUN
ejpam-6440	91	34	)	)	PUNCT
ejpam-6440	91	35	,	,	PUNCT
ejpam-6440	91	36	we	we	PRON
ejpam-6440	91	37	have	have	VERB
ejpam-6440	91	38	:	:	PUNCT
ejpam-6440	91	39	3|λ|l(b−	3|λ|l(b−	NUM
ejpam-6440	91	40	a	a	X
ejpam-6440	91	41	)	)	PUNCT
ejpam-6440	91	42	<	<	X
ejpam-6440	91	43	1	1	NUM
ejpam-6440	91	44	r	r	NOUN
ejpam-6440	91	45	thus	thus	ADV
ejpam-6440	91	46	,	,	PUNCT
ejpam-6440	91	47	defining	define	VERB
ejpam-6440	91	48	k	k	X
ejpam-6440	91	49	:	:	PUNCT
ejpam-6440	91	50	=	=	SYM
ejpam-6440	91	51	3|λ|l(b−	3|λ|l(b−	NUM
ejpam-6440	91	52	a	a	X
ejpam-6440	91	53	)	)	PUNCT
ejpam-6440	91	54	,	,	PUNCT
ejpam-6440	91	55	we	we	PRON
ejpam-6440	91	56	satisfy	satisfy	VERB
ejpam-6440	91	57	0	0	PUNCT
ejpam-6440	92	1	<	<	X
ejpam-6440	93	1	k	k	X
ejpam-6440	94	1	<	<	X
ejpam-6440	94	2	1	1	NUM
ejpam-6440	94	3	r	r	NOUN
ejpam-6440	94	4	<	<	X
ejpam-6440	94	5	1	1	NUM
ejpam-6440	94	6	3r	3r	NUM
ejpam-6440	94	7	(	(	PUNCT
ejpam-6440	94	8	since	since	SCONJ
ejpam-6440	94	9	r	r	NOUN
ejpam-6440	94	10	>	>	X
ejpam-6440	94	11	1	1	NUM
ejpam-6440	94	12	)	)	PUNCT
ejpam-6440	94	13	.	.	PUNCT
ejpam-6440	95	1	the	the	DET
ejpam-6440	95	2	operator	operator	NOUN
ejpam-6440	95	3	t	t	PROPN
ejpam-6440	95	4	is	be	AUX
ejpam-6440	95	5	therefore	therefore	ADV
ejpam-6440	95	6	a	a	DET
ejpam-6440	95	7	contraction	contraction	NOUN
ejpam-6440	95	8	on	on	ADP
ejpam-6440	95	9	the	the	DET
ejpam-6440	95	10	complete	complete	ADJ
ejpam-6440	95	11	mr	mr	PROPN
ejpam-6440	95	12	-	-	PUNCT
ejpam-6440	95	13	metric	metric	ADJ
ejpam-6440	95	14	space	space	NOUN
ejpam-6440	95	15	(	(	PUNCT
ejpam-6440	95	16	c([a	c([a	NOUN
ejpam-6440	95	17	,	,	PUNCT
ejpam-6440	95	18	b]),m	b]),m	PROPN
ejpam-6440	95	19	)	)	PUNCT
ejpam-6440	95	20	.	.	PUNCT
ejpam-6440	96	1	by	by	ADP
ejpam-6440	96	2	the	the	DET
ejpam-6440	96	3	banach	banach	ADV
ejpam-6440	96	4	fixed	fix	VERB
ejpam-6440	96	5	-	-	PUNCT
ejpam-6440	96	6	point	point	NOUN
ejpam-6440	96	7	theorem	theorem	NOUN
ejpam-6440	96	8	in	in	ADP
ejpam-6440	96	9	mr	mr	PROPN
ejpam-6440	96	10	-	-	PUNCT
ejpam-6440	96	11	metric	metric	ADJ
ejpam-6440	96	12	spaces	space	NOUN
ejpam-6440	96	13	(	(	PUNCT
ejpam-6440	96	14	theorem	theorem	NOUN
ejpam-6440	96	15	1	1	NUM
ejpam-6440	96	16	)	)	PUNCT
ejpam-6440	96	17	,	,	PUNCT
ejpam-6440	96	18	t	t	PROPN
ejpam-6440	96	19	has	have	VERB
ejpam-6440	96	20	a	a	DET
ejpam-6440	96	21	unique	unique	ADJ
ejpam-6440	96	22	fixed	fix	VERB
ejpam-6440	96	23	point	point	NOUN
ejpam-6440	96	24	f∗	f∗	NOUN
ejpam-6440	96	25	∈	∈	PROPN
ejpam-6440	96	26	c([a	c([a	PROPN
ejpam-6440	96	27	,	,	PUNCT
ejpam-6440	96	28	b	b	NOUN
ejpam-6440	96	29	]	]	X
ejpam-6440	96	30	)	)	PUNCT
ejpam-6440	96	31	.	.	PUNCT
ejpam-6440	97	1	step	step	NOUN
ejpam-6440	97	2	5	5	NUM
ejpam-6440	97	3	:	:	PUNCT
ejpam-6440	97	4	convergence	convergence	NOUN
ejpam-6440	97	5	of	of	ADP
ejpam-6440	97	6	iterations	iteration	NOUN
ejpam-6440	97	7	for	for	ADP
ejpam-6440	97	8	any	any	DET
ejpam-6440	97	9	initial	initial	ADJ
ejpam-6440	97	10	guess	guess	NOUN
ejpam-6440	97	11	f0	f0	PROPN
ejpam-6440	97	12	∈	∈	PROPN
ejpam-6440	97	13	c([a	c([a	PROPN
ejpam-6440	97	14	,	,	PUNCT
ejpam-6440	97	15	b	b	NOUN
ejpam-6440	97	16	]	]	X
ejpam-6440	97	17	)	)	PUNCT
ejpam-6440	97	18	,	,	PUNCT
ejpam-6440	97	19	the	the	DET
ejpam-6440	97	20	sequence	sequence	NOUN
ejpam-6440	97	21	defined	define	VERB
ejpam-6440	97	22	by	by	ADP
ejpam-6440	97	23	:	:	PUNCT
ejpam-6440	97	24	fn+1	fn+1	ADJ
ejpam-6440	97	25	=	=	SYM
ejpam-6440	97	26	tfn	tfn	NOUN
ejpam-6440	97	27	=	=	SYM
ejpam-6440	97	28	λ	λ	PROPN
ejpam-6440	97	29	∫	∫	PROPN
ejpam-6440	97	30	b	b	PROPN
ejpam-6440	97	31	a	a	DET
ejpam-6440	97	32	k(x	k(x	PROPN
ejpam-6440	97	33	,	,	PUNCT
ejpam-6440	97	34	y	y	PROPN
ejpam-6440	97	35	,	,	PUNCT
ejpam-6440	97	36	fn(y))dy	fn(y))dy	PROPN
ejpam-6440	97	37	+	+	CCONJ
ejpam-6440	97	38	ϕ(x	ϕ(x	NOUN
ejpam-6440	97	39	)	)	PUNCT
ejpam-6440	97	40	converges	converge	VERB
ejpam-6440	97	41	uniformly	uniformly	ADV
ejpam-6440	97	42	to	to	ADP
ejpam-6440	97	43	f∗	f∗	NOUN
ejpam-6440	97	44	with	with	ADP
ejpam-6440	97	45	the	the	DET
ejpam-6440	97	46	error	error	NOUN
ejpam-6440	97	47	estimate	estimate	NOUN
ejpam-6440	97	48	:	:	PUNCT
ejpam-6440	97	49	m(fn	m(fn	NUM
ejpam-6440	97	50	,	,	PUNCT
ejpam-6440	97	51	f	f	PROPN
ejpam-6440	97	52	∗	∗	NOUN
ejpam-6440	97	53	,	,	PUNCT
ejpam-6440	97	54	f∗	f∗	NOUN
ejpam-6440	97	55	)	)	PUNCT
ejpam-6440	97	56	≤	≤	NOUN
ejpam-6440	97	57	rkn	rkn	ADJ
ejpam-6440	97	58	1−	1−	NUM
ejpam-6440	97	59	3rk	3rk	PROPN
ejpam-6440	97	60	m(f0	m(f0	NOUN
ejpam-6440	97	61	,	,	PUNCT
ejpam-6440	97	62	f1	f1	NOUN
ejpam-6440	97	63	,	,	PUNCT
ejpam-6440	97	64	f1	f1	NOUN
ejpam-6440	97	65	)	)	PUNCT
ejpam-6440	97	66	step	step	NOUN
ejpam-6440	97	67	6	6	NUM
ejpam-6440	97	68	:	:	PUNCT
ejpam-6440	97	69	uniqueness	uniqueness	PROPN
ejpam-6440	97	70	suppose	suppose	VERB
ejpam-6440	97	71	f∗	f∗	NOUN
ejpam-6440	97	72	,	,	PUNCT
ejpam-6440	97	73	g∗	g∗	PROPN
ejpam-6440	97	74	are	be	AUX
ejpam-6440	97	75	both	both	DET
ejpam-6440	97	76	solutions	solution	NOUN
ejpam-6440	97	77	.	.	PUNCT
ejpam-6440	98	1	then	then	ADV
ejpam-6440	98	2	:	:	PUNCT
ejpam-6440	98	3	m(f∗	m(f∗	NOUN
ejpam-6440	98	4	,	,	PUNCT
ejpam-6440	98	5	g∗	g∗	PROPN
ejpam-6440	98	6	,	,	PUNCT
ejpam-6440	98	7	g∗	g∗	PROPN
ejpam-6440	98	8	)	)	PUNCT
ejpam-6440	98	9	=	=	NOUN
ejpam-6440	98	10	m(tf∗	m(tf∗	NOUN
ejpam-6440	98	11	,	,	PUNCT
ejpam-6440	98	12	t	t	PROPN
ejpam-6440	98	13	g∗	g∗	PROPN
ejpam-6440	98	14	,	,	PUNCT
ejpam-6440	98	15	t	t	PROPN
ejpam-6440	98	16	g∗	g∗	PROPN
ejpam-6440	98	17	)	)	PUNCT
ejpam-6440	98	18	≤	≤	PROPN
ejpam-6440	98	19	km(f∗	km(f∗	PROPN
ejpam-6440	98	20	,	,	PUNCT
ejpam-6440	98	21	g∗	g∗	PROPN
ejpam-6440	98	22	,	,	PUNCT
ejpam-6440	98	23	g∗	g∗	PROPN
ejpam-6440	98	24	)	)	PUNCT
ejpam-6440	98	25	since	since	SCONJ
ejpam-6440	98	26	k	k	PROPN
ejpam-6440	98	27	<	<	X
ejpam-6440	98	28	1	1	NUM
ejpam-6440	98	29	,	,	PUNCT
ejpam-6440	98	30	this	this	PRON
ejpam-6440	98	31	implies	imply	VERB
ejpam-6440	98	32	m(f∗	m(f∗	NOUN
ejpam-6440	98	33	,	,	PUNCT
ejpam-6440	98	34	g∗	g∗	PROPN
ejpam-6440	98	35	,	,	PUNCT
ejpam-6440	98	36	g∗	g∗	PROPN
ejpam-6440	98	37	)	)	PUNCT
ejpam-6440	98	38	=	=	SYM
ejpam-6440	98	39	0	0	NUM
ejpam-6440	98	40	,	,	PUNCT
ejpam-6440	98	41	hence	hence	ADV
ejpam-6440	98	42	f∗	f∗	NOUN
ejpam-6440	98	43	=	=	SYM
ejpam-6440	98	44	g∗	g∗	VERB
ejpam-6440	98	45	by	by	ADP
ejpam-6440	98	46	the	the	DET
ejpam-6440	98	47	properties	property	NOUN
ejpam-6440	98	48	of	of	ADP
ejpam-6440	98	49	the	the	DET
ejpam-6440	98	50	mr	mr	PROPN
ejpam-6440	98	51	-	-	PUNCT
ejpam-6440	98	52	metric	metric	NOUN
ejpam-6440	98	53	.	.	PUNCT
ejpam-6440	99	1	t.	t.	NOUN
ejpam-6440	99	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	99	3	,	,	PUNCT
ejpam-6440	99	4	a.	a.	NOUN
ejpam-6440	99	5	malkawi	malkawi	PROPN
ejpam-6440	99	6	/	/	SYM
ejpam-6440	99	7	eur	eur	PROPN
ejpam-6440	99	8	.	.	PUNCT
ejpam-6440	100	1	j.	j.	PROPN
ejpam-6440	100	2	pure	pure	PROPN
ejpam-6440	100	3	appl	appl	PROPN
ejpam-6440	100	4	.	.	PROPN
ejpam-6440	100	5	math	math	PROPN
ejpam-6440	100	6	,	,	PUNCT
ejpam-6440	100	7	18	18	NUM
ejpam-6440	100	8	(	(	PUNCT
ejpam-6440	100	9	3	3	NUM
ejpam-6440	100	10	)	)	PUNCT
ejpam-6440	100	11	(	(	PUNCT
ejpam-6440	100	12	2025	2025	NUM
ejpam-6440	100	13	)	)	PUNCT
ejpam-6440	100	14	,	,	PUNCT
ejpam-6440	100	15	6440	6440	NUM
ejpam-6440	100	16	7	7	NUM
ejpam-6440	100	17	of	of	ADP
ejpam-6440	100	18	20	20	NUM
ejpam-6440	100	19	remark	remark	NOUN
ejpam-6440	100	20	2	2	NUM
ejpam-6440	100	21	.	.	PUNCT
ejpam-6440	101	1	the	the	DET
ejpam-6440	101	2	factor	factor	NOUN
ejpam-6440	101	3	3	3	NUM
ejpam-6440	101	4	in	in	ADP
ejpam-6440	101	5	the	the	DET
ejpam-6440	101	6	contraction	contraction	NOUN
ejpam-6440	101	7	estimate	estimate	NOUN
ejpam-6440	101	8	arises	arise	VERB
ejpam-6440	101	9	from	from	ADP
ejpam-6440	101	10	:	:	PUNCT
ejpam-6440	101	11	m(f	m(f	PROPN
ejpam-6440	101	12	,	,	PUNCT
ejpam-6440	101	13	g	g	PROPN
ejpam-6440	101	14	,	,	PUNCT
ejpam-6440	101	15	h	h	NOUN
ejpam-6440	101	16	)	)	PUNCT
ejpam-6440	101	17	=	=	SYM
ejpam-6440	101	18	sup	sup	NOUN
ejpam-6440	101	19	x	x	SYM
ejpam-6440	101	20	(	(	PUNCT
ejpam-6440	101	21	|f	|f	X
ejpam-6440	101	22	−	−	PROPN
ejpam-6440	102	1	g|+	g|+	PROPN
ejpam-6440	102	2	|f	|f	PRON
ejpam-6440	102	3	−	−	PROPN
ejpam-6440	103	1	h|+	h|+	PROPN
ejpam-6440	103	2	|g	|g	VERB
ejpam-6440	103	3	−	−	PROPN
ejpam-6440	103	4	h|	h|	PROPN
ejpam-6440	103	5	)	)	PUNCT
ejpam-6440	103	6	which	which	PRON
ejpam-6440	103	7	naturally	naturally	ADV
ejpam-6440	103	8	leads	lead	VERB
ejpam-6440	103	9	to	to	ADP
ejpam-6440	103	10	three	three	NUM
ejpam-6440	103	11	terms	term	NOUN
ejpam-6440	103	12	when	when	SCONJ
ejpam-6440	103	13	estimatingm(tf	estimatingm(tf	PROPN
ejpam-6440	103	14	,	,	PUNCT
ejpam-6440	103	15	tg	tg	PROPN
ejpam-6440	103	16	,	,	PUNCT
ejpam-6440	103	17	th	th	X
ejpam-6440	103	18	)	)	PUNCT
ejpam-6440	103	19	.	.	PUNCT
ejpam-6440	104	1	this	this	PRON
ejpam-6440	104	2	is	be	AUX
ejpam-6440	104	3	characteristic	characteristic	ADJ
ejpam-6440	104	4	of	of	ADP
ejpam-6440	104	5	mr	mr	PROPN
ejpam-6440	104	6	-	-	PUNCT
ejpam-6440	104	7	metric	metric	ADJ
ejpam-6440	104	8	spaces	space	NOUN
ejpam-6440	104	9	and	and	CCONJ
ejpam-6440	104	10	differs	differ	VERB
ejpam-6440	104	11	from	from	ADP
ejpam-6440	104	12	standard	standard	ADJ
ejpam-6440	104	13	metric	metric	ADJ
ejpam-6440	104	14	fixed	fix	VERB
ejpam-6440	104	15	-	-	PUNCT
ejpam-6440	104	16	point	point	NOUN
ejpam-6440	104	17	theory	theory	NOUN
ejpam-6440	104	18	.	.	PUNCT
ejpam-6440	105	1	lemma	lemma	PROPN
ejpam-6440	105	2	2	2	NUM
ejpam-6440	105	3	(	(	PUNCT
ejpam-6440	105	4	regularity	regularity	NOUN
ejpam-6440	105	5	of	of	ADP
ejpam-6440	105	6	solutions	solution	NOUN
ejpam-6440	105	7	)	)	PUNCT
ejpam-6440	105	8	.	.	PUNCT
ejpam-6440	106	1	if	if	SCONJ
ejpam-6440	106	2	additionally	additionally	ADV
ejpam-6440	106	3	:	:	PUNCT
ejpam-6440	106	4	•	•	NUM
ejpam-6440	106	5	k(x	k(x	PROPN
ejpam-6440	106	6	,	,	PUNCT
ejpam-6440	106	7	y	y	PROPN
ejpam-6440	106	8	,	,	PUNCT
ejpam-6440	106	9	·	·	PUNCT
ejpam-6440	106	10	)	)	PUNCT
ejpam-6440	106	11	is	be	AUX
ejpam-6440	106	12	c1	c1	PROPN
ejpam-6440	106	13	for	for	ADP
ejpam-6440	106	14	each	each	DET
ejpam-6440	106	15	(	(	PUNCT
ejpam-6440	106	16	x	x	NOUN
ejpam-6440	106	17	,	,	PUNCT
ejpam-6440	106	18	y	y	NOUN
ejpam-6440	106	19	)	)	PUNCT
ejpam-6440	106	20	∈	∈	PROPN
ejpam-6440	107	1	[	[	X
ejpam-6440	107	2	a	a	X
ejpam-6440	107	3	,	,	PUNCT
ejpam-6440	107	4	b]2	b]2	PROPN
ejpam-6440	107	5	•	•	ADV
ejpam-6440	107	6	∂uk	∂uk	PROPN
ejpam-6440	107	7	is	be	AUX
ejpam-6440	107	8	continuous	continuous	ADJ
ejpam-6440	107	9	on	on	ADP
ejpam-6440	107	10	[	[	X
ejpam-6440	107	11	a	a	PRON
ejpam-6440	107	12	,	,	PUNCT
ejpam-6440	107	13	b]2	b]2	PROPN
ejpam-6440	107	14	×	×	PROPN
ejpam-6440	107	15	r	r	NOUN
ejpam-6440	107	16	then	then	ADV
ejpam-6440	107	17	the	the	DET
ejpam-6440	107	18	unique	unique	ADJ
ejpam-6440	107	19	solution	solution	NOUN
ejpam-6440	107	20	f∗	f∗	NOUN
ejpam-6440	107	21	is	be	AUX
ejpam-6440	107	22	lipschitz	lipschitz	ADV
ejpam-6440	107	23	continuous	continuous	ADJ
ejpam-6440	107	24	.	.	PUNCT
ejpam-6440	108	1	proof	proof	NOUN
ejpam-6440	108	2	.	.	PUNCT
ejpam-6440	109	1	differentiate	differentiate	VERB
ejpam-6440	109	2	the	the	DET
ejpam-6440	109	3	fixed	fix	VERB
ejpam-6440	109	4	point	point	NOUN
ejpam-6440	109	5	equation	equation	NOUN
ejpam-6440	109	6	and	and	CCONJ
ejpam-6440	109	7	use	use	VERB
ejpam-6440	109	8	the	the	DET
ejpam-6440	109	9	contraction	contraction	NOUN
ejpam-6440	109	10	properties	property	NOUN
ejpam-6440	109	11	to	to	PART
ejpam-6440	109	12	show	show	VERB
ejpam-6440	109	13	the	the	DET
ejpam-6440	109	14	derivative	derivative	ADJ
ejpam-6440	109	15	remains	remain	NOUN
ejpam-6440	109	16	bounded	bound	VERB
ejpam-6440	109	17	.	.	PUNCT
ejpam-6440	110	1	theorem	theorem	ADJ
ejpam-6440	110	2	3	3	NUM
ejpam-6440	110	3	(	(	PUNCT
ejpam-6440	110	4	krasnoselskii	krasnoselskii	NOUN
ejpam-6440	110	5	-	-	PUNCT
ejpam-6440	110	6	type	type	NOUN
ejpam-6440	110	7	hybrid	hybrid	ADJ
ejpam-6440	110	8	contraction	contraction	NOUN
ejpam-6440	110	9	)	)	PUNCT
ejpam-6440	110	10	.	.	PUNCT
ejpam-6440	111	1	let	let	VERB
ejpam-6440	111	2	(	(	PUNCT
ejpam-6440	111	3	x	x	X
ejpam-6440	111	4	,	,	PUNCT
ejpam-6440	111	5	m	m	VERB
ejpam-6440	111	6	)	)	PUNCT
ejpam-6440	111	7	be	be	AUX
ejpam-6440	111	8	a	a	DET
ejpam-6440	111	9	complete	complete	ADJ
ejpam-6440	111	10	mrmetric	mrmetric	ADJ
ejpam-6440	111	11	space	space	NOUN
ejpam-6440	111	12	with	with	ADP
ejpam-6440	111	13	r	r	NOUN
ejpam-6440	111	14	>	>	X
ejpam-6440	111	15	1	1	NUM
ejpam-6440	111	16	,	,	PUNCT
ejpam-6440	111	17	and	and	CCONJ
ejpam-6440	111	18	let	let	VERB
ejpam-6440	111	19	b	b	PRON
ejpam-6440	111	20	⊂	⊂	PROPN
ejpam-6440	111	21	x	x	X
ejpam-6440	111	22	be	be	AUX
ejpam-6440	111	23	a	a	DET
ejpam-6440	111	24	closed	closed	ADJ
ejpam-6440	111	25	convex	convex	NOUN
ejpam-6440	111	26	subset	subset	NOUN
ejpam-6440	111	27	.	.	PUNCT
ejpam-6440	112	1	suppose	suppose	VERB
ejpam-6440	112	2	:	:	PUNCT
ejpam-6440	112	3	(	(	PUNCT
ejpam-6440	112	4	i	i	NOUN
ejpam-6440	112	5	)	)	PUNCT
ejpam-6440	113	1	t1	t1	NOUN
ejpam-6440	113	2	:	:	PUNCT
ejpam-6440	113	3	b	b	X
ejpam-6440	113	4	→	→	PUNCT
ejpam-6440	113	5	x	x	X
ejpam-6440	113	6	is	be	AUX
ejpam-6440	113	7	a	a	DET
ejpam-6440	113	8	contraction	contraction	NOUN
ejpam-6440	113	9	with	with	ADP
ejpam-6440	113	10	constant	constant	ADJ
ejpam-6440	113	11	k	k	PROPN
ejpam-6440	113	12	∈	∈	PROPN
ejpam-6440	113	13	(	(	PUNCT
ejpam-6440	113	14	0	0	NUM
ejpam-6440	113	15	,	,	PUNCT
ejpam-6440	113	16	1	1	NUM
ejpam-6440	113	17	3r	3r	NUM
ejpam-6440	113	18	):	):	PUNCT
ejpam-6440	113	19	m(t1υ	m(t1υ	PROPN
ejpam-6440	113	20	,	,	PUNCT
ejpam-6440	113	21	t1ξ	t1ξ	X
ejpam-6440	113	22	,	,	PUNCT
ejpam-6440	113	23	t1ℑ	t1ℑ	NOUN
ejpam-6440	113	24	)	)	PUNCT
ejpam-6440	113	25	≤	≤	PUNCT
ejpam-6440	114	1	k	k	X
ejpam-6440	114	2	·	·	PUNCT
ejpam-6440	114	3	m(υ	m(υ	PROPN
ejpam-6440	114	4	,	,	PUNCT
ejpam-6440	114	5	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	114	6	)	)	PUNCT
ejpam-6440	114	7	,	,	PUNCT
ejpam-6440	114	8	∀υ	∀υ	NOUN
ejpam-6440	114	9	,	,	PUNCT
ejpam-6440	114	10	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	114	11	∈	∈	PROPN
ejpam-6440	114	12	b.	b.	PROPN
ejpam-6440	114	13	(	(	PUNCT
ejpam-6440	114	14	ii	ii	NOUN
ejpam-6440	114	15	)	)	PUNCT
ejpam-6440	114	16	t2	t2	NOUN
ejpam-6440	114	17	:	:	PUNCT
ejpam-6440	114	18	b	b	X
ejpam-6440	114	19	→	→	PUNCT
ejpam-6440	114	20	x	x	X
ejpam-6440	114	21	is	be	AUX
ejpam-6440	114	22	compact	compact	ADJ
ejpam-6440	114	23	and	and	CCONJ
ejpam-6440	114	24	continuous	continuous	ADJ
ejpam-6440	114	25	(	(	PUNCT
ejpam-6440	114	26	i.e.	i.e.	X
ejpam-6440	114	27	,	,	PUNCT
ejpam-6440	114	28	t2(b	t2(b	ADJ
ejpam-6440	114	29	)	)	PUNCT
ejpam-6440	114	30	is	be	AUX
ejpam-6440	114	31	relatively	relatively	ADV
ejpam-6440	114	32	compact	compact	ADJ
ejpam-6440	114	33	)	)	PUNCT
ejpam-6440	114	34	.	.	PUNCT
ejpam-6440	115	1	(	(	PUNCT
ejpam-6440	115	2	iii	iii	X
ejpam-6440	115	3	)	)	PUNCT
ejpam-6440	115	4	t1υ	t1υ	PROPN
ejpam-6440	115	5	+	+	PUNCT
ejpam-6440	115	6	t2ξ	t2ξ	PROPN
ejpam-6440	115	7	∈	∈	PROPN
ejpam-6440	115	8	b	b	PROPN
ejpam-6440	115	9	for	for	ADP
ejpam-6440	115	10	all	all	PRON
ejpam-6440	115	11	υ	υ	PROPN
ejpam-6440	115	12	,	,	PUNCT
ejpam-6440	115	13	ξ	ξ	PROPN
ejpam-6440	115	14	∈	∈	PROPN
ejpam-6440	115	15	b.	b.	PROPN
ejpam-6440	115	16	then	then	ADV
ejpam-6440	115	17	,	,	PUNCT
ejpam-6440	115	18	the	the	DET
ejpam-6440	115	19	operator	operator	NOUN
ejpam-6440	115	20	t	t	PROPN
ejpam-6440	115	21	=	=	PROPN
ejpam-6440	115	22	t1	t1	PROPN
ejpam-6440	115	23	+	+	NUM
ejpam-6440	115	24	t2	t2	PROPN
ejpam-6440	115	25	has	have	VERB
ejpam-6440	115	26	at	at	ADV
ejpam-6440	115	27	least	least	ADV
ejpam-6440	115	28	one	one	NUM
ejpam-6440	115	29	fixed	fix	VERB
ejpam-6440	115	30	point	point	NOUN
ejpam-6440	115	31	in	in	ADP
ejpam-6440	115	32	b.	b.	PROPN
ejpam-6440	115	33	proof	proof	NOUN
ejpam-6440	115	34	.	.	PUNCT
ejpam-6440	116	1	we	we	PRON
ejpam-6440	116	2	proceed	proceed	VERB
ejpam-6440	116	3	through	through	ADP
ejpam-6440	116	4	several	several	ADJ
ejpam-6440	116	5	carefully	carefully	ADV
ejpam-6440	116	6	constructed	construct	VERB
ejpam-6440	116	7	steps	step	NOUN
ejpam-6440	116	8	:	:	PUNCT
ejpam-6440	116	9	part	part	NOUN
ejpam-6440	116	10	1	1	NUM
ejpam-6440	116	11	:	:	PUNCT
ejpam-6440	116	12	construction	construction	NOUN
ejpam-6440	116	13	of	of	ADP
ejpam-6440	116	14	auxiliary	auxiliary	ADJ
ejpam-6440	116	15	mappings	mapping	NOUN
ejpam-6440	116	16	for	for	ADP
ejpam-6440	116	17	each	each	DET
ejpam-6440	116	18	fixed	fix	VERB
ejpam-6440	116	19	ξ	ξ	PROPN
ejpam-6440	116	20	∈	∈	PROPN
ejpam-6440	116	21	b	b	NOUN
ejpam-6440	116	22	,	,	PUNCT
ejpam-6440	116	23	define	define	VERB
ejpam-6440	116	24	the	the	DET
ejpam-6440	116	25	operator	operator	NOUN
ejpam-6440	116	26	fξ	fξ	PROPN
ejpam-6440	116	27	:	:	PUNCT
ejpam-6440	116	28	b	b	X
ejpam-6440	116	29	→	→	SYM
ejpam-6440	116	30	b	b	NOUN
ejpam-6440	116	31	by	by	ADP
ejpam-6440	116	32	:	:	PUNCT
ejpam-6440	116	33	fξ(υ	fξ(υ	NUM
ejpam-6440	116	34	)	)	PUNCT
ejpam-6440	116	35	=	=	SYM
ejpam-6440	117	1	t1υ	t1υ	PROPN
ejpam-6440	117	2	+	+	CCONJ
ejpam-6440	117	3	t2ξ	t2ξ	X
ejpam-6440	117	4	.	.	PUNCT
ejpam-6440	118	1	we	we	PRON
ejpam-6440	118	2	verify	verify	VERB
ejpam-6440	118	3	that	that	SCONJ
ejpam-6440	118	4	fξ	fξ	NOUN
ejpam-6440	118	5	is	be	AUX
ejpam-6440	118	6	well	well	ADV
ejpam-6440	118	7	-	-	PUNCT
ejpam-6440	118	8	defined	define	VERB
ejpam-6440	118	9	:	:	PUNCT
ejpam-6440	118	10	•	•	NUM
ejpam-6440	118	11	by	by	ADP
ejpam-6440	118	12	condition	condition	NOUN
ejpam-6440	118	13	(	(	PUNCT
ejpam-6440	118	14	iii	iii	NOUN
ejpam-6440	118	15	)	)	PUNCT
ejpam-6440	118	16	,	,	PUNCT
ejpam-6440	118	17	fξ	fξ	PROPN
ejpam-6440	118	18	maps	map	NOUN
ejpam-6440	118	19	b	b	PROPN
ejpam-6440	118	20	into	into	ADP
ejpam-6440	118	21	b	b	NOUN
ejpam-6440	118	22	•	•	NOUN
ejpam-6440	118	23	for	for	ADP
ejpam-6440	118	24	any	any	DET
ejpam-6440	118	25	υ	υ	NOUN
ejpam-6440	118	26	,	,	PUNCT
ejpam-6440	118	27	υ′	υ′	NUM
ejpam-6440	118	28	,	,	PUNCT
ejpam-6440	118	29	υ′′	υ′′	PROPN
ejpam-6440	118	30	∈	∈	PROPN
ejpam-6440	118	31	b	b	NOUN
ejpam-6440	118	32	,	,	PUNCT
ejpam-6440	118	33	we	we	PRON
ejpam-6440	118	34	have	have	VERB
ejpam-6440	118	35	the	the	DET
ejpam-6440	118	36	contraction	contraction	NOUN
ejpam-6440	118	37	estimate	estimate	NOUN
ejpam-6440	118	38	:	:	PUNCT
ejpam-6440	118	39	m(fξ(υ	m(fξ(υ	PROPN
ejpam-6440	118	40	)	)	PUNCT
ejpam-6440	118	41	,	,	PUNCT
ejpam-6440	118	42	fξ(υ	fξ(υ	X
ejpam-6440	118	43	′	′	NOUN
ejpam-6440	118	44	)	)	PUNCT
ejpam-6440	118	45	,	,	PUNCT
ejpam-6440	118	46	fξ(υ	fξ(υ	X
ejpam-6440	118	47	′′	′′	NOUN
ejpam-6440	118	48	)	)	PUNCT
ejpam-6440	118	49	)	)	PUNCT
ejpam-6440	119	1	=	=	NOUN
ejpam-6440	119	2	m(t1υ	m(t1υ	X
ejpam-6440	119	3	+	+	CCONJ
ejpam-6440	119	4	t2ξ	t2ξ	PROPN
ejpam-6440	119	5	,	,	PUNCT
ejpam-6440	119	6	t1υ	t1υ	NOUN
ejpam-6440	119	7	′	′	VERB
ejpam-6440	120	1	+	+	CCONJ
ejpam-6440	120	2	t2ξ	t2ξ	PROPN
ejpam-6440	120	3	,	,	PUNCT
ejpam-6440	120	4	t1υ	t1υ	PUNCT
ejpam-6440	120	5	′′	′′	PROPN
ejpam-6440	120	6	+	+	CCONJ
ejpam-6440	120	7	t2ξ	t2ξ	PROPN
ejpam-6440	120	8	)	)	PUNCT
ejpam-6440	120	9	≤	≤	PUNCT
ejpam-6440	121	1	k	k	X
ejpam-6440	121	2	·	·	PUNCT
ejpam-6440	121	3	m(υ	m(υ	PROPN
ejpam-6440	121	4	,	,	PUNCT
ejpam-6440	121	5	υ′	υ′	NUM
ejpam-6440	121	6	,	,	PUNCT
ejpam-6440	121	7	υ′′	υ′′	PROPN
ejpam-6440	121	8	)	)	PUNCT
ejpam-6440	121	9	using	use	VERB
ejpam-6440	121	10	the	the	DET
ejpam-6440	121	11	mr	mr	PROPN
ejpam-6440	121	12	-	-	PUNCT
ejpam-6440	121	13	metric	metric	ADJ
ejpam-6440	121	14	properties	property	NOUN
ejpam-6440	121	15	and	and	CCONJ
ejpam-6440	121	16	condition	condition	NOUN
ejpam-6440	121	17	(	(	PUNCT
ejpam-6440	121	18	i	i	NOUN
ejpam-6440	121	19	)	)	PUNCT
ejpam-6440	121	20	t.	t.	NOUN
ejpam-6440	121	21	qawasmeh	qawasmeh	NOUN
ejpam-6440	121	22	,	,	PUNCT
ejpam-6440	121	23	a.	a.	NOUN
ejpam-6440	121	24	malkawi	malkawi	PROPN
ejpam-6440	121	25	/	/	SYM
ejpam-6440	121	26	eur	eur	PROPN
ejpam-6440	121	27	.	.	PUNCT
ejpam-6440	122	1	j.	j.	PROPN
ejpam-6440	122	2	pure	pure	PROPN
ejpam-6440	122	3	appl	appl	PROPN
ejpam-6440	122	4	.	.	PROPN
ejpam-6440	122	5	math	math	PROPN
ejpam-6440	122	6	,	,	PUNCT
ejpam-6440	122	7	18	18	NUM
ejpam-6440	122	8	(	(	PUNCT
ejpam-6440	122	9	3	3	NUM
ejpam-6440	122	10	)	)	PUNCT
ejpam-6440	122	11	(	(	PUNCT
ejpam-6440	122	12	2025	2025	NUM
ejpam-6440	122	13	)	)	PUNCT
ejpam-6440	122	14	,	,	PUNCT
ejpam-6440	122	15	6440	6440	NUM
ejpam-6440	122	16	8	8	NUM
ejpam-6440	122	17	of	of	ADP
ejpam-6440	122	18	20	20	NUM
ejpam-6440	122	19	part	part	NOUN
ejpam-6440	122	20	2	2	NUM
ejpam-6440	122	21	:	:	PUNCT
ejpam-6440	122	22	fixed	fix	VERB
ejpam-6440	122	23	point	point	NOUN
ejpam-6440	122	24	argument	argument	NOUN
ejpam-6440	122	25	for	for	ADP
ejpam-6440	122	26	fξ	fξ	NOUN
ejpam-6440	122	27	since	since	SCONJ
ejpam-6440	122	28	fξ	fξ	PROPN
ejpam-6440	122	29	is	be	AUX
ejpam-6440	122	30	a	a	DET
ejpam-6440	122	31	contraction	contraction	NOUN
ejpam-6440	122	32	with	with	ADP
ejpam-6440	122	33	k	k	PROPN
ejpam-6440	122	34	<	<	X
ejpam-6440	122	35	1	1	NUM
ejpam-6440	122	36	3r	3r	NUM
ejpam-6440	122	37	<	<	X
ejpam-6440	122	38	1	1	NUM
ejpam-6440	122	39	r	r	NOUN
ejpam-6440	122	40	,	,	PUNCT
ejpam-6440	122	41	by	by	ADP
ejpam-6440	122	42	the	the	DET
ejpam-6440	122	43	banach	banach	ADV
ejpam-6440	122	44	fixed	fix	VERB
ejpam-6440	122	45	-	-	PUNCT
ejpam-6440	122	46	point	point	NOUN
ejpam-6440	122	47	theorem	theorem	NOUN
ejpam-6440	122	48	in	in	ADP
ejpam-6440	122	49	mr	mr	PROPN
ejpam-6440	122	50	-	-	PUNCT
ejpam-6440	122	51	metric	metric	ADJ
ejpam-6440	122	52	spaces	space	NOUN
ejpam-6440	122	53	(	(	PUNCT
ejpam-6440	122	54	theorem	theorem	NOUN
ejpam-6440	122	55	1	1	NUM
ejpam-6440	122	56	)	)	PUNCT
ejpam-6440	123	1	,	,	PUNCT
ejpam-6440	123	2	there	there	PRON
ejpam-6440	123	3	exists	exist	VERB
ejpam-6440	123	4	a	a	DET
ejpam-6440	123	5	unique	unique	ADJ
ejpam-6440	123	6	fixed	fix	VERB
ejpam-6440	123	7	point	point	NOUN
ejpam-6440	123	8	υξ	υξ	VERB
ejpam-6440	123	9	∈	∈	PROPN
ejpam-6440	123	10	b	b	PROPN
ejpam-6440	123	11	such	such	ADJ
ejpam-6440	123	12	that	that	PRON
ejpam-6440	123	13	:	:	PUNCT
ejpam-6440	123	14	υξ	υξ	NOUN
ejpam-6440	123	15	=	=	SYM
ejpam-6440	123	16	fξ(υξ	fξ(υξ	X
ejpam-6440	123	17	)	)	PUNCT
ejpam-6440	123	18	=	=	SYM
ejpam-6440	123	19	t1υξ	t1υξ	X
ejpam-6440	124	1	+	+	CCONJ
ejpam-6440	124	2	t2ξ	t2ξ	X
ejpam-6440	124	3	part	part	NOUN
ejpam-6440	124	4	3	3	NUM
ejpam-6440	124	5	:	:	PUNCT
ejpam-6440	124	6	definition	definition	NOUN
ejpam-6440	124	7	and	and	CCONJ
ejpam-6440	124	8	analysis	analysis	NOUN
ejpam-6440	124	9	of	of	ADP
ejpam-6440	124	10	operator	operator	NOUN
ejpam-6440	124	11	g	g	PROPN
ejpam-6440	124	12	define	define	VERB
ejpam-6440	124	13	the	the	DET
ejpam-6440	124	14	mapping	mapping	NOUN
ejpam-6440	124	15	g	g	NOUN
ejpam-6440	124	16	:	:	PUNCT
ejpam-6440	124	17	b	b	X
ejpam-6440	124	18	→	→	SYM
ejpam-6440	124	19	b	b	NOUN
ejpam-6440	124	20	by	by	ADP
ejpam-6440	124	21	g(ξ	g(ξ	PROPN
ejpam-6440	124	22	)	)	PUNCT
ejpam-6440	125	1	=	=	SYM
ejpam-6440	125	2	υξ	υξ	NOUN
ejpam-6440	125	3	,	,	PUNCT
ejpam-6440	125	4	where	where	SCONJ
ejpam-6440	125	5	υξ	υξ	NOUN
ejpam-6440	125	6	is	be	AUX
ejpam-6440	125	7	the	the	DET
ejpam-6440	125	8	unique	unique	ADJ
ejpam-6440	125	9	fixed	fix	VERB
ejpam-6440	125	10	point	point	NOUN
ejpam-6440	125	11	from	from	ADP
ejpam-6440	125	12	part	part	NOUN
ejpam-6440	125	13	2	2	NUM
ejpam-6440	125	14	.	.	PUNCT
ejpam-6440	126	1	we	we	PRON
ejpam-6440	126	2	analyze	analyze	VERB
ejpam-6440	126	3	g	g	NOUN
ejpam-6440	126	4	:	:	PUNCT
ejpam-6440	126	5	(	(	PUNCT
ejpam-6440	126	6	i	i	NOUN
ejpam-6440	126	7	)	)	PUNCT
ejpam-6440	126	8	continuity	continuity	NOUN
ejpam-6440	126	9	of	of	ADP
ejpam-6440	126	10	g	g	NOUN
ejpam-6440	126	11	:	:	PUNCT
ejpam-6440	126	12	let	let	VERB
ejpam-6440	126	13	ξn	ξn	PROPN
ejpam-6440	126	14	→	→	SYM
ejpam-6440	126	15	ξ	ξ	PROPN
ejpam-6440	126	16	in	in	ADP
ejpam-6440	126	17	b.	b.	PROPN
ejpam-6440	126	18	then	then	ADV
ejpam-6440	126	19	:	:	PUNCT
ejpam-6440	126	20	m(g(ξn	m(g(ξn	X
ejpam-6440	126	21	)	)	PUNCT
ejpam-6440	126	22	,	,	PUNCT
ejpam-6440	126	23	g(ξ	g(ξ	PROPN
ejpam-6440	126	24	)	)	PUNCT
ejpam-6440	126	25	,	,	PUNCT
ejpam-6440	126	26	g(ξ	g(ξ	PROPN
ejpam-6440	126	27	)	)	PUNCT
ejpam-6440	126	28	)	)	PUNCT
ejpam-6440	127	1	=	=	SYM
ejpam-6440	127	2	m(υξn	m(υξn	NOUN
ejpam-6440	127	3	,	,	PUNCT
ejpam-6440	127	4	υξ	υξ	NOUN
ejpam-6440	127	5	,	,	PUNCT
ejpam-6440	127	6	υξ	υξ	NOUN
ejpam-6440	127	7	)	)	PUNCT
ejpam-6440	127	8	≤m(t1υξn	≤m(t1υξn	PROPN
ejpam-6440	128	1	+	+	CCONJ
ejpam-6440	128	2	t2ξn	t2ξn	NUM
ejpam-6440	128	3	,	,	PUNCT
ejpam-6440	128	4	t1υξ	t1υξ	X
ejpam-6440	129	1	+	+	CCONJ
ejpam-6440	129	2	t2ξ	t2ξ	PROPN
ejpam-6440	129	3	,	,	PUNCT
ejpam-6440	129	4	t1υξ	t1υξ	X
ejpam-6440	130	1	+	+	CCONJ
ejpam-6440	130	2	t2ξ	t2ξ	X
ejpam-6440	130	3	)	)	PUNCT
ejpam-6440	130	4	≤	≤	PUNCT
ejpam-6440	131	1	km(υξn	km(υξn	PROPN
ejpam-6440	131	2	,	,	PUNCT
ejpam-6440	131	3	υξ	υξ	NOUN
ejpam-6440	131	4	,	,	PUNCT
ejpam-6440	131	5	υξ	υξ	NOUN
ejpam-6440	131	6	)	)	PUNCT
ejpam-6440	131	7	+	+	ADV
ejpam-6440	131	8	m(t2ξn	m(t2ξn	NUM
ejpam-6440	131	9	,	,	PUNCT
ejpam-6440	131	10	t2ξ	t2ξ	PROPN
ejpam-6440	131	11	,	,	PUNCT
ejpam-6440	131	12	t2ξ	t2ξ	NUM
ejpam-6440	131	13	)	)	PUNCT
ejpam-6440	131	14	by	by	ADP
ejpam-6440	131	15	the	the	DET
ejpam-6440	131	16	continuity	continuity	NOUN
ejpam-6440	131	17	of	of	ADP
ejpam-6440	131	18	t2	t2	NOUN
ejpam-6440	131	19	and	and	CCONJ
ejpam-6440	131	20	the	the	DET
ejpam-6440	131	21	contraction	contraction	NOUN
ejpam-6440	131	22	property	property	NOUN
ejpam-6440	131	23	,	,	PUNCT
ejpam-6440	131	24	g(ξn	g(ξn	NOUN
ejpam-6440	131	25	)	)	PUNCT
ejpam-6440	131	26	→	→	SYM
ejpam-6440	131	27	g(ξ	g(ξ	PROPN
ejpam-6440	131	28	)	)	PUNCT
ejpam-6440	131	29	.	.	PUNCT
ejpam-6440	132	1	(	(	PUNCT
ejpam-6440	132	2	ii	ii	NOUN
ejpam-6440	132	3	)	)	PUNCT
ejpam-6440	132	4	compactness	compactness	NOUN
ejpam-6440	132	5	of	of	ADP
ejpam-6440	132	6	g	g	NOUN
ejpam-6440	132	7	:	:	PUNCT
ejpam-6440	132	8	let	let	VERB
ejpam-6440	132	9	{	{	PUNCT
ejpam-6440	132	10	ξn	ξn	AUX
ejpam-6440	132	11	}	}	PUNCT
ejpam-6440	132	12	be	be	AUX
ejpam-6440	132	13	a	a	DET
ejpam-6440	132	14	bounded	bounded	ADJ
ejpam-6440	132	15	sequence	sequence	NOUN
ejpam-6440	132	16	in	in	ADP
ejpam-6440	132	17	b.	b.	PROPN
ejpam-6440	132	18	since	since	SCONJ
ejpam-6440	132	19	t2	t2	PROPN
ejpam-6440	132	20	is	be	AUX
ejpam-6440	132	21	compact	compact	ADJ
ejpam-6440	132	22	,	,	PUNCT
ejpam-6440	132	23	there	there	PRON
ejpam-6440	132	24	exists	exist	VERB
ejpam-6440	132	25	a	a	DET
ejpam-6440	132	26	convergent	convergent	NOUN
ejpam-6440	132	27	subsequence	subsequence	NOUN
ejpam-6440	132	28	t2ξnk	t2ξnk	NUM
ejpam-6440	132	29	→	→	SYM
ejpam-6440	132	30	y	y	PROPN
ejpam-6440	132	31	∈	∈	PROPN
ejpam-6440	132	32	x.	x.	NOUN
ejpam-6440	132	33	consider	consider	VERB
ejpam-6440	132	34	:	:	PUNCT
ejpam-6440	132	35	υnk	υnk	PROPN
ejpam-6440	132	36	=	=	SYM
ejpam-6440	132	37	g(ξnk	g(ξnk	PROPN
ejpam-6440	132	38	)	)	PUNCT
ejpam-6440	133	1	=	=	SYM
ejpam-6440	133	2	t1υnk	t1υnk	PROPN
ejpam-6440	133	3	+	+	CCONJ
ejpam-6440	133	4	t2ξnk	t2ξnk	NUM
ejpam-6440	133	5	the	the	DET
ejpam-6440	133	6	sequence	sequence	NOUN
ejpam-6440	133	7	{	{	PUNCT
ejpam-6440	133	8	υnk	υnk	PROPN
ejpam-6440	133	9	}	}	PUNCT
ejpam-6440	133	10	is	be	AUX
ejpam-6440	133	11	bounded	bound	VERB
ejpam-6440	133	12	,	,	PUNCT
ejpam-6440	133	13	and	and	CCONJ
ejpam-6440	133	14	by	by	ADP
ejpam-6440	133	15	the	the	DET
ejpam-6440	133	16	compactness	compactness	NOUN
ejpam-6440	133	17	of	of	ADP
ejpam-6440	133	18	t1	t1	NOUN
ejpam-6440	133	19	on	on	ADP
ejpam-6440	133	20	bounded	bounded	ADJ
ejpam-6440	133	21	sets	set	NOUN
ejpam-6440	133	22	(	(	PUNCT
ejpam-6440	133	23	as	as	SCONJ
ejpam-6440	133	24	it	it	PRON
ejpam-6440	133	25	’s	’	VERB
ejpam-6440	133	26	a	a	DET
ejpam-6440	133	27	contraction	contraction	NOUN
ejpam-6440	133	28	)	)	PUNCT
ejpam-6440	133	29	,	,	PUNCT
ejpam-6440	133	30	there	there	PRON
ejpam-6440	133	31	exists	exist	VERB
ejpam-6440	133	32	a	a	DET
ejpam-6440	133	33	further	further	ADJ
ejpam-6440	133	34	subsequence	subsequence	NOUN
ejpam-6440	133	35	converging	converge	VERB
ejpam-6440	133	36	to	to	ADP
ejpam-6440	133	37	some	some	DET
ejpam-6440	133	38	υ∗	υ∗	NOUN
ejpam-6440	133	39	∈	∈	PROPN
ejpam-6440	133	40	b.	b.	PROPN
ejpam-6440	133	41	part	part	NOUN
ejpam-6440	133	42	4	4	NUM
ejpam-6440	133	43	:	:	PUNCT
ejpam-6440	133	44	application	application	NOUN
ejpam-6440	133	45	of	of	ADP
ejpam-6440	133	46	schauder	schauder	PROPN
ejpam-6440	133	47	’s	’s	PART
ejpam-6440	133	48	fixed	fix	VERB
ejpam-6440	133	49	-	-	PUNCT
ejpam-6440	133	50	point	point	NOUN
ejpam-6440	133	51	theorem	theorem	VERB
ejpam-6440	133	52	the	the	DET
ejpam-6440	133	53	operator	operator	NOUN
ejpam-6440	133	54	g	g	PROPN
ejpam-6440	133	55	:	:	PUNCT
ejpam-6440	133	56	b	b	X
ejpam-6440	133	57	→	→	SYM
ejpam-6440	133	58	b	b	NOUN
ejpam-6440	133	59	satisfies	satisfie	NOUN
ejpam-6440	133	60	:	:	PUNCT
ejpam-6440	133	61	•	•	NUM
ejpam-6440	133	62	g	g	NOUN
ejpam-6440	133	63	is	be	AUX
ejpam-6440	133	64	continuous	continuous	ADJ
ejpam-6440	133	65	(	(	PUNCT
ejpam-6440	133	66	established	establish	VERB
ejpam-6440	133	67	above	above	ADV
ejpam-6440	133	68	)	)	PUNCT
ejpam-6440	133	69	•	•	NOUN
ejpam-6440	134	1	g(b	g(b	PROPN
ejpam-6440	134	2	)	)	PUNCT
ejpam-6440	134	3	is	be	AUX
ejpam-6440	134	4	relatively	relatively	ADV
ejpam-6440	134	5	compact	compact	ADJ
ejpam-6440	134	6	(	(	PUNCT
ejpam-6440	134	7	as	as	SCONJ
ejpam-6440	134	8	shown	show	VERB
ejpam-6440	134	9	in	in	ADP
ejpam-6440	134	10	the	the	DET
ejpam-6440	134	11	compactness	compactness	NOUN
ejpam-6440	134	12	analysis	analysis	NOUN
ejpam-6440	134	13	)	)	PUNCT
ejpam-6440	134	14	by	by	ADP
ejpam-6440	134	15	schauder	schauder	NOUN
ejpam-6440	134	16	’s	’s	PART
ejpam-6440	134	17	fixed	fix	VERB
ejpam-6440	134	18	-	-	PUNCT
ejpam-6440	134	19	point	point	NOUN
ejpam-6440	134	20	theorem	theorem	NOUN
ejpam-6440	134	21	,	,	PUNCT
ejpam-6440	134	22	there	there	PRON
ejpam-6440	134	23	exists	exist	VERB
ejpam-6440	134	24	υ∗	υ∗	PROPN
ejpam-6440	134	25	∈	∈	PROPN
ejpam-6440	135	1	b	b	PROPN
ejpam-6440	135	2	such	such	ADJ
ejpam-6440	135	3	that	that	PRON
ejpam-6440	135	4	:	:	PUNCT
ejpam-6440	135	5	υ∗	υ∗	NOUN
ejpam-6440	135	6	=	=	SYM
ejpam-6440	135	7	g(υ∗	g(υ∗	NOUN
ejpam-6440	135	8	)	)	PUNCT
ejpam-6440	135	9	=	=	SYM
ejpam-6440	136	1	t1υ	t1υ	NOUN
ejpam-6440	136	2	∗	∗	VERB
ejpam-6440	136	3	+	+	NUM
ejpam-6440	136	4	t2υ	t2υ	NOUN
ejpam-6440	136	5	∗	∗	NOUN
ejpam-6440	136	6	=	=	PUNCT
ejpam-6440	136	7	tυ∗	tυ∗	NOUN
ejpam-6440	136	8	this	this	PRON
ejpam-6440	136	9	completes	complete	VERB
ejpam-6440	136	10	the	the	DET
ejpam-6440	136	11	proof	proof	NOUN
ejpam-6440	136	12	of	of	ADP
ejpam-6440	136	13	existence	existence	NOUN
ejpam-6440	136	14	of	of	ADP
ejpam-6440	136	15	a	a	DET
ejpam-6440	136	16	fixed	fix	VERB
ejpam-6440	136	17	point	point	NOUN
ejpam-6440	136	18	for	for	ADP
ejpam-6440	136	19	t	t	PROPN
ejpam-6440	136	20	.	.	PUNCT
ejpam-6440	137	1	part	part	NOUN
ejpam-6440	137	2	5	5	NUM
ejpam-6440	137	3	:	:	PUNCT
ejpam-6440	137	4	verification	verification	NOUN
ejpam-6440	137	5	of	of	ADP
ejpam-6440	137	6	solution	solution	NOUN
ejpam-6440	137	7	properties	property	NOUN
ejpam-6440	137	8	the	the	DET
ejpam-6440	137	9	fixed	fixed	ADJ
ejpam-6440	137	10	point	point	NOUN
ejpam-6440	137	11	υ∗	υ∗	NOUN
ejpam-6440	137	12	satisfies	satisfie	NOUN
ejpam-6440	137	13	:	:	PUNCT
ejpam-6440	137	14	•	•	NUM
ejpam-6440	137	15	υ∗	υ∗	NOUN
ejpam-6440	137	16	∈	∈	PROPN
ejpam-6440	137	17	b	b	NOUN
ejpam-6440	137	18	by	by	ADP
ejpam-6440	137	19	construction	construction	NOUN
ejpam-6440	137	20	•	•	ADP
ejpam-6440	137	21	it	it	PRON
ejpam-6440	137	22	solves	solve	VERB
ejpam-6440	137	23	the	the	DET
ejpam-6440	137	24	operator	operator	NOUN
ejpam-6440	137	25	equation	equation	NOUN
ejpam-6440	137	26	tυ∗	tυ∗	NOUN
ejpam-6440	138	1	=	=	X
ejpam-6440	138	2	υ∗	υ∗	NOUN
ejpam-6440	138	3	•	•	ADP
ejpam-6440	138	4	the	the	DET
ejpam-6440	138	5	solution	solution	NOUN
ejpam-6440	138	6	is	be	AUX
ejpam-6440	138	7	constructed	construct	VERB
ejpam-6440	138	8	as	as	ADP
ejpam-6440	138	9	a	a	DET
ejpam-6440	138	10	limit	limit	NOUN
ejpam-6440	138	11	of	of	ADP
ejpam-6440	138	12	iterates	iterate	NOUN
ejpam-6440	138	13	t.	t.	NOUN
ejpam-6440	138	14	qawasmeh	qawasmeh	NOUN
ejpam-6440	138	15	,	,	PUNCT
ejpam-6440	138	16	a.	a.	NOUN
ejpam-6440	138	17	malkawi	malkawi	PROPN
ejpam-6440	138	18	/	/	SYM
ejpam-6440	138	19	eur	eur	PROPN
ejpam-6440	138	20	.	.	PUNCT
ejpam-6440	139	1	j.	j.	PROPN
ejpam-6440	139	2	pure	pure	PROPN
ejpam-6440	139	3	appl	appl	PROPN
ejpam-6440	139	4	.	.	PROPN
ejpam-6440	139	5	math	math	PROPN
ejpam-6440	139	6	,	,	PUNCT
ejpam-6440	139	7	18	18	NUM
ejpam-6440	139	8	(	(	PUNCT
ejpam-6440	139	9	3	3	NUM
ejpam-6440	139	10	)	)	PUNCT
ejpam-6440	139	11	(	(	PUNCT
ejpam-6440	139	12	2025	2025	NUM
ejpam-6440	139	13	)	)	PUNCT
ejpam-6440	139	14	,	,	PUNCT
ejpam-6440	139	15	6440	6440	NUM
ejpam-6440	139	16	9	9	NUM
ejpam-6440	139	17	of	of	ADP
ejpam-6440	139	18	20	20	NUM
ejpam-6440	139	19	remark	remark	NOUN
ejpam-6440	139	20	3	3	NUM
ejpam-6440	139	21	.	.	PUNCT
ejpam-6440	140	1	the	the	DET
ejpam-6440	140	2	condition	condition	NOUN
ejpam-6440	140	3	k	k	X
ejpam-6440	140	4	<	<	X
ejpam-6440	140	5	1	1	NUM
ejpam-6440	140	6	3r	3r	NOUN
ejpam-6440	140	7	is	be	AUX
ejpam-6440	140	8	crucial	crucial	ADJ
ejpam-6440	140	9	because	because	SCONJ
ejpam-6440	140	10	:	:	PUNCT
ejpam-6440	140	11	•	•	X
ejpam-6440	140	12	it	it	PRON
ejpam-6440	140	13	ensures	ensure	VERB
ejpam-6440	140	14	the	the	DET
ejpam-6440	140	15	contraction	contraction	NOUN
ejpam-6440	140	16	property	property	NOUN
ejpam-6440	140	17	in	in	ADP
ejpam-6440	140	18	the	the	DET
ejpam-6440	140	19	mr	mr	PROPN
ejpam-6440	140	20	-	-	PUNCT
ejpam-6440	140	21	metric	metric	ADJ
ejpam-6440	140	22	space	space	NOUN
ejpam-6440	140	23	•	•	ADP
ejpam-6440	140	24	the	the	DET
ejpam-6440	140	25	factor	factor	NOUN
ejpam-6440	140	26	3	3	NUM
ejpam-6440	140	27	accounts	account	NOUN
ejpam-6440	140	28	for	for	ADP
ejpam-6440	140	29	the	the	DET
ejpam-6440	140	30	three	three	NUM
ejpam-6440	140	31	-	-	PUNCT
ejpam-6440	140	32	term	term	NOUN
ejpam-6440	140	33	nature	nature	NOUN
ejpam-6440	140	34	of	of	ADP
ejpam-6440	140	35	the	the	DET
ejpam-6440	140	36	mr	mr	PROPN
ejpam-6440	140	37	-	-	PUNCT
ejpam-6440	140	38	metric	metric	ADJ
ejpam-6440	140	39	•	•	NOUN
ejpam-6440	140	40	when	when	SCONJ
ejpam-6440	140	41	r→	r→	PROPN
ejpam-6440	140	42	1	1	NUM
ejpam-6440	140	43	+	+	PROPN
ejpam-6440	140	44	,	,	PUNCT
ejpam-6440	140	45	we	we	PRON
ejpam-6440	140	46	recover	recover	VERB
ejpam-6440	140	47	the	the	DET
ejpam-6440	140	48	classical	classical	ADJ
ejpam-6440	140	49	krasnoselskii	krasnoselskii	ADJ
ejpam-6440	140	50	condition	condition	NOUN
ejpam-6440	140	51	proposition	proposition	NOUN
ejpam-6440	140	52	1	1	NUM
ejpam-6440	140	53	(	(	PUNCT
ejpam-6440	140	54	generalization	generalization	NOUN
ejpam-6440	140	55	to	to	ADP
ejpam-6440	140	56	weaker	weak	ADJ
ejpam-6440	140	57	conditions	condition	NOUN
ejpam-6440	140	58	)	)	PUNCT
ejpam-6440	140	59	.	.	PUNCT
ejpam-6440	141	1	the	the	DET
ejpam-6440	141	2	theorem	theorem	NOUN
ejpam-6440	141	3	remains	remain	VERB
ejpam-6440	141	4	valid	valid	ADJ
ejpam-6440	141	5	if	if	SCONJ
ejpam-6440	141	6	condition	condition	NOUN
ejpam-6440	141	7	(	(	PUNCT
ejpam-6440	141	8	iii	iii	NOUN
ejpam-6440	141	9	)	)	PUNCT
ejpam-6440	141	10	is	be	AUX
ejpam-6440	141	11	replaced	replace	VERB
ejpam-6440	141	12	by	by	ADP
ejpam-6440	141	13	:	:	PUNCT
ejpam-6440	141	14	(	(	PUNCT
ejpam-6440	141	15	iii	iii	NOUN
ejpam-6440	141	16	’	'	PUNCT
ejpam-6440	141	17	)	)	PUNCT
ejpam-6440	142	1	there	there	PRON
ejpam-6440	142	2	exists	exist	VERB
ejpam-6440	142	3	r	r	NOUN
ejpam-6440	142	4	>	>	X
ejpam-6440	142	5	0	0	NUM
ejpam-6440	142	6	such	such	ADJ
ejpam-6440	142	7	that	that	PRON
ejpam-6440	142	8	for	for	ADP
ejpam-6440	142	9	all	all	DET
ejpam-6440	142	10	υ	υ	PROPN
ejpam-6440	142	11	∈	∈	PROPN
ejpam-6440	142	12	∂br	∂br	PROPN
ejpam-6440	142	13	,	,	PUNCT
ejpam-6440	142	14	λ	λ	PROPN
ejpam-6440	142	15	∈	∈	PROPN
ejpam-6440	142	16	(	(	PUNCT
ejpam-6440	142	17	0	0	NUM
ejpam-6440	142	18	,	,	PUNCT
ejpam-6440	142	19	1	1	NUM
ejpam-6440	142	20	)	)	PUNCT
ejpam-6440	142	21	,	,	PUNCT
ejpam-6440	142	22	we	we	PRON
ejpam-6440	142	23	have	have	VERB
ejpam-6440	142	24	t1υ	t1υ	PRON
ejpam-6440	142	25	+	+	CCONJ
ejpam-6440	142	26	t2ξ	t2ξ	PROPN
ejpam-6440	142	27	̸=	̸=	PROPN
ejpam-6440	142	28	λυ	λυ	ADP
ejpam-6440	142	29	proof	proof	NOUN
ejpam-6440	142	30	.	.	PUNCT
ejpam-6440	143	1	this	this	PRON
ejpam-6440	143	2	follows	follow	VERB
ejpam-6440	143	3	from	from	ADP
ejpam-6440	143	4	the	the	DET
ejpam-6440	143	5	leray	leray	ADJ
ejpam-6440	143	6	-	-	PUNCT
ejpam-6440	143	7	schauder	schauder	NOUN
ejpam-6440	143	8	alternative	alternative	NOUN
ejpam-6440	143	9	applied	apply	VERB
ejpam-6440	143	10	to	to	ADP
ejpam-6440	143	11	the	the	DET
ejpam-6440	143	12	operator	operator	NOUN
ejpam-6440	143	13	g.	g.	PROPN
ejpam-6440	143	14	theorem	theorem	VERB
ejpam-6440	143	15	4	4	NUM
ejpam-6440	143	16	(	(	PUNCT
ejpam-6440	143	17	leray	leray	NOUN
ejpam-6440	143	18	-	-	PUNCT
ejpam-6440	143	19	schauder	schauder	NOUN
ejpam-6440	143	20	-	-	PUNCT
ejpam-6440	143	21	type	type	NOUN
ejpam-6440	143	22	alternative	alternative	NOUN
ejpam-6440	143	23	)	)	PUNCT
ejpam-6440	143	24	.	.	PUNCT
ejpam-6440	144	1	let	let	VERB
ejpam-6440	144	2	(	(	PUNCT
ejpam-6440	144	3	x	x	X
ejpam-6440	144	4	,	,	PUNCT
ejpam-6440	144	5	m	m	VERB
ejpam-6440	144	6	)	)	PUNCT
ejpam-6440	144	7	be	be	AUX
ejpam-6440	144	8	a	a	DET
ejpam-6440	144	9	complete	complete	ADJ
ejpam-6440	144	10	mr	mr	ADJ
ejpam-6440	144	11	-	-	PUNCT
ejpam-6440	144	12	metric	metric	ADJ
ejpam-6440	144	13	space	space	NOUN
ejpam-6440	144	14	with	with	ADP
ejpam-6440	144	15	r	r	NOUN
ejpam-6440	144	16	>	>	X
ejpam-6440	144	17	1	1	NUM
ejpam-6440	144	18	,	,	PUNCT
ejpam-6440	144	19	and	and	CCONJ
ejpam-6440	144	20	t	t	X
ejpam-6440	144	21	:	:	PUNCT
ejpam-6440	144	22	x	x	X
ejpam-6440	144	23	→	→	PUNCT
ejpam-6440	144	24	x	x	X
ejpam-6440	144	25	a	a	DET
ejpam-6440	144	26	continuous	continuous	ADJ
ejpam-6440	144	27	operator	operator	NOUN
ejpam-6440	144	28	satisfying	satisfy	VERB
ejpam-6440	144	29	:	:	PUNCT
ejpam-6440	144	30	(	(	PUNCT
ejpam-6440	144	31	i	i	NOUN
ejpam-6440	144	32	)	)	PUNCT
ejpam-6440	144	33	(	(	PUNCT
ejpam-6440	144	34	generalized	generalize	VERB
ejpam-6440	144	35	contraction	contraction	NOUN
ejpam-6440	144	36	)	)	PUNCT
ejpam-6440	144	37	there	there	PRON
ejpam-6440	144	38	exists	exist	VERB
ejpam-6440	144	39	ψ	ψ	X
ejpam-6440	144	40	:	:	PUNCT
ejpam-6440	145	1	[	[	X
ejpam-6440	145	2	0,∞	0,∞	NOUN
ejpam-6440	145	3	)	)	PUNCT
ejpam-6440	145	4	→	→	PUNCT
ejpam-6440	146	1	[	[	X
ejpam-6440	146	2	0,∞	0,∞	NUM
ejpam-6440	146	3	)	)	PUNCT
ejpam-6440	146	4	non	non	ADJ
ejpam-6440	146	5	-	-	ADJ
ejpam-6440	146	6	decreasing	decrease	VERB
ejpam-6440	146	7	with	with	ADP
ejpam-6440	146	8	ψn(t	ψn(t	NOUN
ejpam-6440	146	9	)	)	PUNCT
ejpam-6440	146	10	→	→	SYM
ejpam-6440	146	11	0	0	NUM
ejpam-6440	146	12	for	for	ADP
ejpam-6440	146	13	all	all	DET
ejpam-6440	146	14	t	t	PROPN
ejpam-6440	146	15	>	>	X
ejpam-6440	146	16	0	0	NUM
ejpam-6440	146	17	such	such	ADJ
ejpam-6440	146	18	that	that	SCONJ
ejpam-6440	146	19	:	:	PUNCT
ejpam-6440	146	20	m(tυ	m(tυ	NOUN
ejpam-6440	146	21	,	,	PUNCT
ejpam-6440	146	22	tξ	tξ	VERB
ejpam-6440	146	23	,	,	PUNCT
ejpam-6440	146	24	tℑ	tℑ	NOUN
ejpam-6440	146	25	)	)	PUNCT
ejpam-6440	146	26	≤	≤	NOUN
ejpam-6440	146	27	ψ	ψ	X
ejpam-6440	146	28	(	(	PUNCT
ejpam-6440	146	29	m(υ	m(υ	PROPN
ejpam-6440	146	30	,	,	PUNCT
ejpam-6440	146	31	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	146	32	)	)	PUNCT
ejpam-6440	146	33	)	)	PUNCT
ejpam-6440	146	34	,	,	PUNCT
ejpam-6440	146	35	∀υ	∀υ	PROPN
ejpam-6440	146	36	,	,	PUNCT
ejpam-6440	146	37	ξ,ℑ	ξ,ℑ	PROPN
ejpam-6440	146	38	∈	∈	PROPN
ejpam-6440	146	39	x.	x.	NOUN
ejpam-6440	146	40	(	(	PUNCT
ejpam-6440	146	41	ii	ii	PROPN
ejpam-6440	146	42	)	)	PUNCT
ejpam-6440	146	43	(	(	PUNCT
ejpam-6440	146	44	a	a	DET
ejpam-6440	146	45	priori	priori	ADV
ejpam-6440	146	46	bound	bind	VERB
ejpam-6440	146	47	)	)	PUNCT
ejpam-6440	146	48	for	for	ADP
ejpam-6440	146	49	any	any	DET
ejpam-6440	146	50	λ	λ	PROPN
ejpam-6440	146	51	∈	∈	PROPN
ejpam-6440	146	52	(	(	PUNCT
ejpam-6440	146	53	0	0	NUM
ejpam-6440	146	54	,	,	PUNCT
ejpam-6440	146	55	1	1	NUM
ejpam-6440	146	56	)	)	PUNCT
ejpam-6440	146	57	and	and	CCONJ
ejpam-6440	146	58	υ	υ	PRON
ejpam-6440	146	59	∈	∈	PROPN
ejpam-6440	146	60	x	x	X
ejpam-6440	146	61	,	,	PUNCT
ejpam-6440	146	62	if	if	SCONJ
ejpam-6440	146	63	υ	υ	PRON
ejpam-6440	146	64	=	=	SYM
ejpam-6440	146	65	λtυ	λtυ	NOUN
ejpam-6440	146	66	,	,	PUNCT
ejpam-6440	146	67	then	then	ADV
ejpam-6440	146	68	m(υ	m(υ	PROPN
ejpam-6440	146	69	,	,	PUNCT
ejpam-6440	146	70	υ0	υ0	NOUN
ejpam-6440	146	71	,	,	PUNCT
ejpam-6440	146	72	υ0	υ0	NOUN
ejpam-6440	146	73	)	)	PUNCT
ejpam-6440	146	74	≤	≤	NOUN
ejpam-6440	146	75	c	c	NOUN
ejpam-6440	146	76	for	for	ADP
ejpam-6440	146	77	some	some	DET
ejpam-6440	146	78	υ0	υ0	NOUN
ejpam-6440	146	79	∈	∈	PROPN
ejpam-6440	146	80	x	x	X
ejpam-6440	146	81	and	and	CCONJ
ejpam-6440	146	82	c	c	X
ejpam-6440	146	83	>	>	X
ejpam-6440	146	84	0	0	X
ejpam-6440	146	85	.	.	PUNCT
ejpam-6440	147	1	then	then	ADV
ejpam-6440	147	2	,	,	PUNCT
ejpam-6440	147	3	either	either	ADV
ejpam-6440	147	4	:	:	PUNCT
ejpam-6440	147	5	(	(	PUNCT
ejpam-6440	147	6	a	a	X
ejpam-6440	147	7	)	)	PUNCT
ejpam-6440	147	8	t	t	PROPN
ejpam-6440	147	9	has	have	VERB
ejpam-6440	147	10	a	a	DET
ejpam-6440	147	11	fixed	fix	VERB
ejpam-6440	147	12	point	point	NOUN
ejpam-6440	147	13	in	in	ADP
ejpam-6440	147	14	x	x	NOUN
ejpam-6440	147	15	,	,	PUNCT
ejpam-6440	147	16	or	or	CCONJ
ejpam-6440	147	17	(	(	PUNCT
ejpam-6440	147	18	b	b	X
ejpam-6440	147	19	)	)	PUNCT
ejpam-6440	147	20	the	the	DET
ejpam-6440	147	21	set	set	NOUN
ejpam-6440	147	22	{	{	PUNCT
ejpam-6440	147	23	υ	υ	NOUN
ejpam-6440	147	24	∈	∈	PROPN
ejpam-6440	147	25	x	x	X
ejpam-6440	147	26	:	:	PUNCT
ejpam-6440	147	27	υ	υ	NOUN
ejpam-6440	147	28	=	=	SYM
ejpam-6440	147	29	λtυ	λtυ	NOUN
ejpam-6440	147	30	,	,	PUNCT
ejpam-6440	147	31	λ	λ	PROPN
ejpam-6440	147	32	∈	∈	PROPN
ejpam-6440	147	33	(	(	PUNCT
ejpam-6440	147	34	0	0	NUM
ejpam-6440	147	35	,	,	PUNCT
ejpam-6440	147	36	1	1	NUM
ejpam-6440	147	37	)	)	PUNCT
ejpam-6440	147	38	}	}	PUNCT
ejpam-6440	147	39	is	be	AUX
ejpam-6440	147	40	unbounded	unbounded	ADJ
ejpam-6440	147	41	.	.	PUNCT
ejpam-6440	148	1	proof	proof	NOUN
ejpam-6440	148	2	.	.	PUNCT
ejpam-6440	149	1	we	we	PRON
ejpam-6440	149	2	present	present	VERB
ejpam-6440	149	3	a	a	DET
ejpam-6440	149	4	detailed	detailed	ADJ
ejpam-6440	149	5	and	and	CCONJ
ejpam-6440	149	6	rigorous	rigorous	ADJ
ejpam-6440	149	7	proof	proof	NOUN
ejpam-6440	149	8	in	in	ADP
ejpam-6440	149	9	several	several	ADJ
ejpam-6440	149	10	steps	step	NOUN
ejpam-6440	149	11	:	:	PUNCT
ejpam-6440	149	12	part	part	NOUN
ejpam-6440	149	13	1	1	NUM
ejpam-6440	149	14	:	:	PUNCT
ejpam-6440	149	15	preliminary	preliminary	ADJ
ejpam-6440	149	16	setup	setup	NOUN
ejpam-6440	149	17	and	and	CCONJ
ejpam-6440	149	18	assumptions	assumption	NOUN
ejpam-6440	149	19	assume	assume	VERB
ejpam-6440	149	20	alternative	alternative	ADJ
ejpam-6440	149	21	(	(	PUNCT
ejpam-6440	149	22	b	b	NOUN
ejpam-6440	149	23	)	)	PUNCT
ejpam-6440	149	24	does	do	AUX
ejpam-6440	149	25	not	not	PART
ejpam-6440	149	26	hold	hold	VERB
ejpam-6440	149	27	,	,	PUNCT
ejpam-6440	149	28	i.e.	i.e.	X
ejpam-6440	149	29	,	,	PUNCT
ejpam-6440	149	30	the	the	DET
ejpam-6440	149	31	set	set	NOUN
ejpam-6440	149	32	s	s	NOUN
ejpam-6440	149	33	is	be	AUX
ejpam-6440	149	34	bounded	bound	VERB
ejpam-6440	149	35	.	.	PUNCT
ejpam-6440	150	1	then	then	ADV
ejpam-6440	150	2	by	by	ADP
ejpam-6440	150	3	condition	condition	NOUN
ejpam-6440	150	4	(	(	PUNCT
ejpam-6440	150	5	ii	ii	NOUN
ejpam-6440	150	6	)	)	PUNCT
ejpam-6440	150	7	,	,	PUNCT
ejpam-6440	150	8	there	there	PRON
ejpam-6440	150	9	exists	exist	VERB
ejpam-6440	150	10	r	r	NOUN
ejpam-6440	150	11	>	>	X
ejpam-6440	150	12	0	0	NUM
ejpam-6440	150	13	such	such	ADJ
ejpam-6440	150	14	that	that	PRON
ejpam-6440	150	15	:	:	PUNCT
ejpam-6440	150	16	sup	sup	NOUN
ejpam-6440	150	17	υ∈s	υ∈	VERB
ejpam-6440	150	18	m(υ	m(υ	PROPN
ejpam-6440	150	19	,	,	PUNCT
ejpam-6440	150	20	υ0	υ0	NOUN
ejpam-6440	150	21	,	,	PUNCT
ejpam-6440	150	22	υ0	υ0	NOUN
ejpam-6440	150	23	)	)	PUNCT
ejpam-6440	150	24	≤	≤	NOUN
ejpam-6440	150	25	r	r	NOUN
ejpam-6440	150	26	where	where	SCONJ
ejpam-6440	150	27	υ0	υ0	NOUN
ejpam-6440	150	28	and	and	CCONJ
ejpam-6440	150	29	c	c	NOUN
ejpam-6440	150	30	are	be	AUX
ejpam-6440	150	31	as	as	ADP
ejpam-6440	150	32	in	in	ADP
ejpam-6440	150	33	condition	condition	NOUN
ejpam-6440	150	34	(	(	PUNCT
ejpam-6440	150	35	ii	ii	NOUN
ejpam-6440	150	36	)	)	PUNCT
ejpam-6440	150	37	,	,	PUNCT
ejpam-6440	150	38	and	and	CCONJ
ejpam-6440	150	39	we	we	PRON
ejpam-6440	150	40	take	take	VERB
ejpam-6440	150	41	r	r	NOUN
ejpam-6440	150	42	=	=	SYM
ejpam-6440	150	43	c.	c.	NOUN
ejpam-6440	150	44	part	part	NOUN
ejpam-6440	150	45	2	2	NUM
ejpam-6440	150	46	:	:	PUNCT
ejpam-6440	150	47	construction	construction	NOUN
ejpam-6440	150	48	of	of	ADP
ejpam-6440	150	49	the	the	DET
ejpam-6440	150	50	invariant	invariant	ADJ
ejpam-6440	150	51	ball	ball	NOUN
ejpam-6440	150	52	define	define	VERB
ejpam-6440	150	53	the	the	DET
ejpam-6440	150	54	closed	closed	ADJ
ejpam-6440	150	55	ball	ball	NOUN
ejpam-6440	150	56	:	:	PUNCT
ejpam-6440	150	57	br+rψ(r	br+rψ(r	NUM
ejpam-6440	150	58	)	)	PUNCT
ejpam-6440	151	1	=	=	PRON
ejpam-6440	151	2	{	{	PUNCT
ejpam-6440	151	3	υ	υ	NOUN
ejpam-6440	151	4	∈	∈	PROPN
ejpam-6440	151	5	x	x	X
ejpam-6440	151	6	:	:	PUNCT
ejpam-6440	151	7	m(υ	m(υ	ADJ
ejpam-6440	151	8	,	,	PUNCT
ejpam-6440	151	9	υ0	υ0	NOUN
ejpam-6440	151	10	,	,	PUNCT
ejpam-6440	151	11	υ0	υ0	NOUN
ejpam-6440	151	12	)	)	PUNCT
ejpam-6440	151	13	≤	≤	NOUN
ejpam-6440	152	1	r	r	NOUN
ejpam-6440	152	2	+	+	NOUN
ejpam-6440	152	3	rψ(r	rψ(r	NOUN
ejpam-6440	152	4	)	)	PUNCT
ejpam-6440	152	5	}	}	PUNCT
ejpam-6440	152	6	we	we	PRON
ejpam-6440	152	7	verify	verify	VERB
ejpam-6440	152	8	that	that	SCONJ
ejpam-6440	152	9	t	t	PROPN
ejpam-6440	152	10	maps	maps	PROPN
ejpam-6440	152	11	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	152	12	)	)	PUNCT
ejpam-6440	152	13	into	into	ADP
ejpam-6440	152	14	itself	itself	PRON
ejpam-6440	152	15	:	:	PUNCT
ejpam-6440	152	16	t.	t.	NOUN
ejpam-6440	152	17	qawasmeh	qawasmeh	NOUN
ejpam-6440	152	18	,	,	PUNCT
ejpam-6440	152	19	a.	a.	NOUN
ejpam-6440	152	20	malkawi	malkawi	PROPN
ejpam-6440	152	21	/	/	SYM
ejpam-6440	152	22	eur	eur	PROPN
ejpam-6440	152	23	.	.	PUNCT
ejpam-6440	153	1	j.	j.	PROPN
ejpam-6440	153	2	pure	pure	PROPN
ejpam-6440	153	3	appl	appl	PROPN
ejpam-6440	153	4	.	.	PROPN
ejpam-6440	153	5	math	math	PROPN
ejpam-6440	153	6	,	,	PUNCT
ejpam-6440	153	7	18	18	NUM
ejpam-6440	153	8	(	(	PUNCT
ejpam-6440	153	9	3	3	NUM
ejpam-6440	153	10	)	)	PUNCT
ejpam-6440	153	11	(	(	PUNCT
ejpam-6440	153	12	2025	2025	NUM
ejpam-6440	153	13	)	)	PUNCT
ejpam-6440	153	14	,	,	PUNCT
ejpam-6440	153	15	6440	6440	NUM
ejpam-6440	153	16	10	10	NUM
ejpam-6440	153	17	of	of	ADP
ejpam-6440	153	18	20	20	NUM
ejpam-6440	153	19	for	for	ADP
ejpam-6440	153	20	any	any	DET
ejpam-6440	153	21	υ	υ	PROPN
ejpam-6440	153	22	∈	∈	PROPN
ejpam-6440	153	23	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	153	24	):	):	PUNCT
ejpam-6440	153	25	m(tυ	m(tυ	NOUN
ejpam-6440	153	26	,	,	PUNCT
ejpam-6440	153	27	υ0	υ0	NOUN
ejpam-6440	153	28	,	,	PUNCT
ejpam-6440	153	29	υ0	υ0	NOUN
ejpam-6440	153	30	)	)	PUNCT
ejpam-6440	153	31	≤	≤	NOUN
ejpam-6440	154	1	ψ(m(υ	ψ(m(υ	PROPN
ejpam-6440	154	2	,	,	PUNCT
ejpam-6440	154	3	υ0	υ0	NOUN
ejpam-6440	154	4	,	,	PUNCT
ejpam-6440	154	5	υ0	υ0	NOUN
ejpam-6440	154	6	)	)	PUNCT
ejpam-6440	154	7	)	)	PUNCT
ejpam-6440	154	8	≤	≤	NUM
ejpam-6440	155	1	ψ(r	ψ(r	PROPN
ejpam-6440	155	2	+	+	NOUN
ejpam-6440	155	3	rψ(r	rψ(r	NOUN
ejpam-6440	155	4	)	)	PUNCT
ejpam-6440	155	5	)	)	PUNCT
ejpam-6440	156	1	≤	≤	NUM
ejpam-6440	156	2	r	r	NOUN
ejpam-6440	156	3	+	+	NOUN
ejpam-6440	156	4	rψ(r	rψ(r	NOUN
ejpam-6440	156	5	)	)	PUNCT
ejpam-6440	156	6	where	where	SCONJ
ejpam-6440	156	7	the	the	DET
ejpam-6440	156	8	last	last	ADJ
ejpam-6440	156	9	inequality	inequality	NOUN
ejpam-6440	156	10	follows	follow	VERB
ejpam-6440	156	11	from	from	ADP
ejpam-6440	156	12	the	the	DET
ejpam-6440	156	13	properties	property	NOUN
ejpam-6440	156	14	of	of	ADP
ejpam-6440	156	15	ψ	ψ	NOUN
ejpam-6440	156	16	and	and	CCONJ
ejpam-6440	156	17	the	the	DET
ejpam-6440	156	18	choice	choice	NOUN
ejpam-6440	156	19	of	of	ADP
ejpam-6440	156	20	r.	r.	PROPN
ejpam-6440	156	21	part	part	NOUN
ejpam-6440	156	22	3	3	NUM
ejpam-6440	156	23	:	:	PUNCT
ejpam-6440	156	24	verification	verification	NOUN
ejpam-6440	156	25	of	of	ADP
ejpam-6440	156	26	compactness	compactness	NOUN
ejpam-6440	156	27	conditions	condition	NOUN
ejpam-6440	156	28	(	(	PUNCT
ejpam-6440	156	29	i	i	NOUN
ejpam-6440	156	30	)	)	PUNCT
ejpam-6440	156	31	boundedness	boundedness	NOUN
ejpam-6440	156	32	of	of	ADP
ejpam-6440	156	33	t	t	PROPN
ejpam-6440	156	34	(	(	PUNCT
ejpam-6440	156	35	b	b	NOUN
ejpam-6440	156	36	):	):	PUNCT
ejpam-6440	156	37	for	for	ADP
ejpam-6440	156	38	any	any	DET
ejpam-6440	156	39	bounded	bounded	ADJ
ejpam-6440	156	40	set	set	NOUN
ejpam-6440	156	41	b	b	PROPN
ejpam-6440	156	42	⊂	⊂	PROPN
ejpam-6440	156	43	x	x	PROPN
ejpam-6440	156	44	,	,	PUNCT
ejpam-6440	156	45	t	t	PROPN
ejpam-6440	156	46	(	(	PUNCT
ejpam-6440	156	47	b	b	X
ejpam-6440	156	48	)	)	PUNCT
ejpam-6440	156	49	is	be	AUX
ejpam-6440	156	50	bounded	bound	VERB
ejpam-6440	156	51	since	since	SCONJ
ejpam-6440	156	52	:	:	PUNCT
ejpam-6440	156	53	sup	sup	VERB
ejpam-6440	156	54	υ∈b	υ∈b	NOUN
ejpam-6440	156	55	m(tυ	m(tυ	NOUN
ejpam-6440	156	56	,	,	PUNCT
ejpam-6440	156	57	υ0	υ0	NOUN
ejpam-6440	156	58	,	,	PUNCT
ejpam-6440	156	59	υ0	υ0	NOUN
ejpam-6440	156	60	)	)	PUNCT
ejpam-6440	156	61	≤	≤	NUM
ejpam-6440	156	62	ψ(diam(b	ψ(diam(b	NOUN
ejpam-6440	156	63	)	)	PUNCT
ejpam-6440	156	64	)	)	PUNCT
ejpam-6440	156	65	(	(	PUNCT
ejpam-6440	156	66	ii	ii	NOUN
ejpam-6440	156	67	)	)	PUNCT
ejpam-6440	156	68	total	total	ADJ
ejpam-6440	156	69	boundedness	boundedness	NOUN
ejpam-6440	156	70	:	:	PUNCT
ejpam-6440	156	71	given	give	VERB
ejpam-6440	156	72	ϵ	ϵ	PRON
ejpam-6440	156	73	>	>	X
ejpam-6440	156	74	0	0	NUM
ejpam-6440	156	75	,	,	PUNCT
ejpam-6440	156	76	choose	choose	VERB
ejpam-6440	156	77	n	n	ADV
ejpam-6440	156	78	large	large	ADJ
ejpam-6440	156	79	enough	enough	ADV
ejpam-6440	156	80	so	so	SCONJ
ejpam-6440	156	81	that	that	SCONJ
ejpam-6440	156	82	ψn(diam(b	ψn(diam(b	PROPN
ejpam-6440	156	83	)	)	PUNCT
ejpam-6440	156	84	)	)	PUNCT
ejpam-6440	157	1	<	<	X
ejpam-6440	157	2	ϵ.	ϵ.	NOUN
ejpam-6440	157	3	then	then	ADV
ejpam-6440	157	4	the	the	DET
ejpam-6440	157	5	iterates	iterate	NOUN
ejpam-6440	157	6	tn(b	tn(b	PUNCT
ejpam-6440	157	7	)	)	PUNCT
ejpam-6440	157	8	form	form	VERB
ejpam-6440	157	9	an	an	DET
ejpam-6440	157	10	ϵ-net	ϵ-net	NOUN
ejpam-6440	157	11	for	for	ADP
ejpam-6440	157	12	t	t	PROPN
ejpam-6440	157	13	(	(	PUNCT
ejpam-6440	157	14	b	b	NOUN
ejpam-6440	157	15	)	)	PUNCT
ejpam-6440	157	16	.	.	PUNCT
ejpam-6440	158	1	part	part	NOUN
ejpam-6440	158	2	4	4	NUM
ejpam-6440	158	3	:	:	PUNCT
ejpam-6440	158	4	application	application	NOUN
ejpam-6440	158	5	of	of	ADP
ejpam-6440	158	6	the	the	DET
ejpam-6440	158	7	nonlinear	nonlinear	ADJ
ejpam-6440	158	8	alternative	alternative	NOUN
ejpam-6440	158	9	consider	consider	VERB
ejpam-6440	158	10	the	the	DET
ejpam-6440	158	11	homotopy	homotopy	NOUN
ejpam-6440	158	12	h	h	NOUN
ejpam-6440	158	13	:	:	PUNCT
ejpam-6440	159	1	[	[	X
ejpam-6440	159	2	0	0	NUM
ejpam-6440	159	3	,	,	PUNCT
ejpam-6440	159	4	1]×br+rψ(r	1]×br+rψ(r	PROPN
ejpam-6440	159	5	)	)	PUNCT
ejpam-6440	159	6	→	→	PUNCT
ejpam-6440	159	7	x	x	X
ejpam-6440	159	8	defined	define	VERB
ejpam-6440	159	9	by	by	ADP
ejpam-6440	159	10	:	:	PUNCT
ejpam-6440	159	11	h(λ	h(λ	PROPN
ejpam-6440	159	12	,	,	PUNCT
ejpam-6440	159	13	υ	υ	NOUN
ejpam-6440	159	14	)	)	PUNCT
ejpam-6440	159	15	=	=	SYM
ejpam-6440	159	16	λtυ	λtυ	NOUN
ejpam-6440	159	17	by	by	ADP
ejpam-6440	159	18	the	the	DET
ejpam-6440	159	19	a	a	DET
ejpam-6440	159	20	priori	priori	ADV
ejpam-6440	159	21	bound	bind	VERB
ejpam-6440	159	22	condition	condition	NOUN
ejpam-6440	159	23	,	,	PUNCT
ejpam-6440	159	24	h(λ	h(λ	PROPN
ejpam-6440	159	25	,	,	PUNCT
ejpam-6440	159	26	υ	υ	NOUN
ejpam-6440	159	27	)	)	PUNCT
ejpam-6440	159	28	̸=	̸=	PROPN
ejpam-6440	159	29	υ	υ	NOUN
ejpam-6440	159	30	for	for	ADP
ejpam-6440	159	31	all	all	PRON
ejpam-6440	159	32	υ	υ	PRON
ejpam-6440	159	33	∈	∈	PROPN
ejpam-6440	159	34	∂br+rψ(r	∂br+rψ(r	NUM
ejpam-6440	159	35	)	)	PUNCT
ejpam-6440	159	36	and	and	CCONJ
ejpam-6440	159	37	λ	λ	X
ejpam-6440	159	38	∈	∈	PROPN
ejpam-6440	160	1	[	[	X
ejpam-6440	160	2	0	0	NUM
ejpam-6440	160	3	,	,	PUNCT
ejpam-6440	160	4	1	1	NUM
ejpam-6440	160	5	]	]	PUNCT
ejpam-6440	160	6	.	.	PUNCT
ejpam-6440	161	1	therefore	therefore	ADV
ejpam-6440	161	2	,	,	PUNCT
ejpam-6440	161	3	by	by	ADP
ejpam-6440	161	4	the	the	DET
ejpam-6440	161	5	topological	topological	ADJ
ejpam-6440	161	6	degree	degree	NOUN
ejpam-6440	161	7	argument	argument	NOUN
ejpam-6440	161	8	adapted	adapt	VERB
ejpam-6440	161	9	to	to	ADP
ejpam-6440	161	10	mr	mr	PROPN
ejpam-6440	161	11	-	-	PUNCT
ejpam-6440	161	12	metric	metric	ADJ
ejpam-6440	161	13	spaces	space	NOUN
ejpam-6440	161	14	:	:	PUNCT
ejpam-6440	161	15	•	•	ADP
ejpam-6440	161	16	the	the	DET
ejpam-6440	161	17	leray	leray	ADJ
ejpam-6440	161	18	-	-	PUNCT
ejpam-6440	161	19	schauder	schauder	NOUN
ejpam-6440	161	20	degree	degree	NOUN
ejpam-6440	161	21	deg(i	deg(i	NOUN
ejpam-6440	161	22	−	−	NOUN
ejpam-6440	161	23	λt	λt	ADP
ejpam-6440	161	24	,	,	PUNCT
ejpam-6440	161	25	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	161	26	)	)	PUNCT
ejpam-6440	161	27	,	,	PUNCT
ejpam-6440	161	28	0	0	NUM
ejpam-6440	161	29	)	)	PUNCT
ejpam-6440	161	30	is	be	AUX
ejpam-6440	161	31	well	well	ADV
ejpam-6440	161	32	-	-	PUNCT
ejpam-6440	161	33	defined	define	VERB
ejpam-6440	161	34	for	for	ADP
ejpam-6440	161	35	all	all	DET
ejpam-6440	161	36	λ	λ	X
ejpam-6440	161	37	∈	∈	PROPN
ejpam-6440	162	1	[	[	X
ejpam-6440	162	2	0	0	NUM
ejpam-6440	162	3	,	,	PUNCT
ejpam-6440	162	4	1	1	NUM
ejpam-6440	162	5	]	]	PUNCT
ejpam-6440	162	6	•	•	NUM
ejpam-6440	162	7	the	the	DET
ejpam-6440	162	8	homotopy	homotopy	NOUN
ejpam-6440	162	9	invariance	invariance	NOUN
ejpam-6440	162	10	of	of	ADP
ejpam-6440	162	11	degree	degree	NOUN
ejpam-6440	162	12	implies	imply	VERB
ejpam-6440	162	13	:	:	PUNCT
ejpam-6440	162	14	deg(i	deg(i	ADP
ejpam-6440	162	15	−	−	PROPN
ejpam-6440	162	16	t	t	PROPN
ejpam-6440	162	17	,	,	PUNCT
ejpam-6440	162	18	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	162	19	)	)	PUNCT
ejpam-6440	162	20	,	,	PUNCT
ejpam-6440	162	21	0	0	X
ejpam-6440	162	22	)	)	PUNCT
ejpam-6440	163	1	=	=	SYM
ejpam-6440	163	2	deg(i	deg(i	PROPN
ejpam-6440	163	3	,	,	PUNCT
ejpam-6440	163	4	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	163	5	)	)	PUNCT
ejpam-6440	163	6	,	,	PUNCT
ejpam-6440	163	7	0	0	X
ejpam-6440	163	8	)	)	PUNCT
ejpam-6440	163	9	=	=	SYM
ejpam-6440	164	1	1	1	NUM
ejpam-6440	164	2	•	•	NOUN
ejpam-6440	164	3	hence	hence	ADV
ejpam-6440	165	1	,	,	PUNCT
ejpam-6440	165	2	there	there	PRON
ejpam-6440	165	3	exists	exist	VERB
ejpam-6440	165	4	υ∗	υ∗	PROPN
ejpam-6440	165	5	∈	∈	PROPN
ejpam-6440	165	6	br+rψ(r	br+rψ(r	PROPN
ejpam-6440	165	7	)	)	PUNCT
ejpam-6440	165	8	such	such	ADJ
ejpam-6440	165	9	that	that	DET
ejpam-6440	165	10	υ∗	υ∗	NOUN
ejpam-6440	165	11	=	=	PUNCT
ejpam-6440	165	12	tυ∗	tυ∗	NOUN
ejpam-6440	165	13	part	part	NOUN
ejpam-6440	165	14	5	5	NUM
ejpam-6440	165	15	:	:	PUNCT
ejpam-6440	165	16	unboundedness	unboundedness	NOUN
ejpam-6440	165	17	of	of	ADP
ejpam-6440	165	18	solution	solution	NOUN
ejpam-6440	165	19	set	set	VERB
ejpam-6440	165	20	if	if	SCONJ
ejpam-6440	165	21	alternative	alternative	ADJ
ejpam-6440	165	22	(	(	PUNCT
ejpam-6440	165	23	a	a	PRON
ejpam-6440	165	24	)	)	PUNCT
ejpam-6440	165	25	fails	fail	VERB
ejpam-6440	165	26	,	,	PUNCT
ejpam-6440	165	27	then	then	ADV
ejpam-6440	165	28	for	for	ADP
ejpam-6440	165	29	every	every	DET
ejpam-6440	165	30	n	n	PRON
ejpam-6440	165	31	∈	∈	PROPN
ejpam-6440	165	32	n	n	CCONJ
ejpam-6440	165	33	,	,	PUNCT
ejpam-6440	165	34	there	there	PRON
ejpam-6440	165	35	exists	exist	VERB
ejpam-6440	165	36	λn	λn	PROPN
ejpam-6440	165	37	∈	∈	PROPN
ejpam-6440	165	38	(	(	PUNCT
ejpam-6440	165	39	0	0	NUM
ejpam-6440	165	40	,	,	PUNCT
ejpam-6440	165	41	1	1	NUM
ejpam-6440	165	42	)	)	PUNCT
ejpam-6440	165	43	and	and	CCONJ
ejpam-6440	165	44	υn	υn	NOUN
ejpam-6440	165	45	∈	∈	PROPN
ejpam-6440	165	46	x	x	PUNCT
ejpam-6440	165	47	with	with	ADP
ejpam-6440	165	48	∥υn∥	∥υn∥	NOUN
ejpam-6440	165	49	→	→	SYM
ejpam-6440	165	50	∞	∞	NUM
ejpam-6440	165	51	such	such	ADJ
ejpam-6440	165	52	that	that	PRON
ejpam-6440	165	53	:	:	PUNCT
ejpam-6440	165	54	υn	υn	X
ejpam-6440	165	55	=	=	SYM
ejpam-6440	165	56	λntυn	λntυn	NOUN
ejpam-6440	165	57	this	this	PRON
ejpam-6440	165	58	establishes	establish	VERB
ejpam-6440	165	59	the	the	DET
ejpam-6440	165	60	unboundedness	unboundedness	NOUN
ejpam-6440	165	61	of	of	ADP
ejpam-6440	165	62	s	s	PROPN
ejpam-6440	165	63	.	.	PUNCT
ejpam-6440	166	1	part	part	NOUN
ejpam-6440	166	2	6	6	NUM
ejpam-6440	166	3	:	:	PUNCT
ejpam-6440	166	4	continuous	continuous	ADJ
ejpam-6440	166	5	dependence	dependence	NOUN
ejpam-6440	166	6	and	and	CCONJ
ejpam-6440	166	7	regularity	regularity	NOUN
ejpam-6440	166	8	under	under	ADP
ejpam-6440	166	9	additional	additional	ADJ
ejpam-6440	166	10	smoothness	smoothness	ADJ
ejpam-6440	166	11	assumptions	assumption	NOUN
ejpam-6440	166	12	on	on	ADP
ejpam-6440	166	13	ψ	ψ	SYM
ejpam-6440	166	14	,	,	PUNCT
ejpam-6440	166	15	the	the	DET
ejpam-6440	166	16	fixed	fix	VERB
ejpam-6440	166	17	points	point	NOUN
ejpam-6440	166	18	depend	depend	VERB
ejpam-6440	166	19	continuously	continuously	ADV
ejpam-6440	166	20	on	on	ADP
ejpam-6440	166	21	parameters	parameter	NOUN
ejpam-6440	166	22	.	.	PUNCT
ejpam-6440	167	1	if	if	SCONJ
ejpam-6440	167	2	ψ	ψ	NOUN
ejpam-6440	167	3	is	be	AUX
ejpam-6440	167	4	of	of	ADP
ejpam-6440	167	5	class	class	NOUN
ejpam-6440	167	6	c1	c1	NOUN
ejpam-6440	167	7	,	,	PUNCT
ejpam-6440	167	8	then	then	ADV
ejpam-6440	167	9	the	the	DET
ejpam-6440	167	10	fixed	fixed	ADJ
ejpam-6440	167	11	point	point	NOUN
ejpam-6440	167	12	set	set	NOUN
ejpam-6440	167	13	is	be	AUX
ejpam-6440	167	14	a	a	DET
ejpam-6440	167	15	c1	c1	PROPN
ejpam-6440	167	16	manifold	manifold	NOUN
ejpam-6440	167	17	.	.	PUNCT
ejpam-6440	168	1	remark	remark	PROPN
ejpam-6440	168	2	4	4	NUM
ejpam-6440	168	3	.	.	PUNCT
ejpam-6440	169	1	the	the	DET
ejpam-6440	169	2	comparison	comparison	NOUN
ejpam-6440	169	3	function	function	NOUN
ejpam-6440	169	4	ψ	ψ	NOUN
ejpam-6440	169	5	can	can	AUX
ejpam-6440	169	6	be	be	AUX
ejpam-6440	169	7	chosen	choose	VERB
ejpam-6440	169	8	from	from	ADP
ejpam-6440	169	9	several	several	ADJ
ejpam-6440	169	10	important	important	ADJ
ejpam-6440	169	11	classes	class	NOUN
ejpam-6440	169	12	:	:	PUNCT
ejpam-6440	169	13	•	•	NUM
ejpam-6440	169	14	ψ(t	ψ(t	PROPN
ejpam-6440	169	15	)	)	PUNCT
ejpam-6440	169	16	=	=	SYM
ejpam-6440	170	1	kt	kt	PROPN
ejpam-6440	170	2	for	for	ADP
ejpam-6440	170	3	k	k	PROPN
ejpam-6440	170	4	∈	∈	PROPN
ejpam-6440	170	5	(	(	PUNCT
ejpam-6440	170	6	0	0	NUM
ejpam-6440	170	7	,	,	PUNCT
ejpam-6440	170	8	1	1	NUM
ejpam-6440	170	9	3r	3r	NUM
ejpam-6440	170	10	)	)	PUNCT
ejpam-6440	170	11	(	(	PUNCT
ejpam-6440	170	12	banach	banach	NOUN
ejpam-6440	170	13	contraction	contraction	NOUN
ejpam-6440	170	14	)	)	PUNCT
ejpam-6440	170	15	t.	t.	NOUN
ejpam-6440	170	16	qawasmeh	qawasmeh	NOUN
ejpam-6440	170	17	,	,	PUNCT
ejpam-6440	170	18	a.	a.	NOUN
ejpam-6440	170	19	malkawi	malkawi	PROPN
ejpam-6440	170	20	/	/	SYM
ejpam-6440	170	21	eur	eur	PROPN
ejpam-6440	170	22	.	.	PUNCT
ejpam-6440	171	1	j.	j.	PROPN
ejpam-6440	171	2	pure	pure	PROPN
ejpam-6440	171	3	appl	appl	PROPN
ejpam-6440	171	4	.	.	PROPN
ejpam-6440	171	5	math	math	PROPN
ejpam-6440	171	6	,	,	PUNCT
ejpam-6440	171	7	18	18	NUM
ejpam-6440	171	8	(	(	PUNCT
ejpam-6440	171	9	3	3	NUM
ejpam-6440	171	10	)	)	PUNCT
ejpam-6440	171	11	(	(	PUNCT
ejpam-6440	171	12	2025	2025	NUM
ejpam-6440	171	13	)	)	PUNCT
ejpam-6440	171	14	,	,	PUNCT
ejpam-6440	171	15	6440	6440	NUM
ejpam-6440	171	16	11	11	NUM
ejpam-6440	171	17	of	of	ADP
ejpam-6440	171	18	20	20	NUM
ejpam-6440	171	19	•	•	NUM
ejpam-6440	171	20	ψ(t	ψ(t	PROPN
ejpam-6440	171	21	)	)	PUNCT
ejpam-6440	172	1	=	=	SYM
ejpam-6440	172	2	t	t	PROPN
ejpam-6440	172	3	1+t	1+t	NUM
ejpam-6440	172	4	(	(	PUNCT
ejpam-6440	172	5	nonlinear	nonlinear	ADJ
ejpam-6440	172	6	contraction	contraction	NOUN
ejpam-6440	172	7	)	)	PUNCT
ejpam-6440	173	1	•	•	NUM
ejpam-6440	174	1	ψ	ψ	PART
ejpam-6440	174	2	concave	concave	NOUN
ejpam-6440	174	3	with	with	ADP
ejpam-6440	174	4	ψ(t	ψ(t	PROPN
ejpam-6440	174	5	)	)	PUNCT
ejpam-6440	174	6	<	<	X
ejpam-6440	174	7	t	t	PROPN
ejpam-6440	174	8	for	for	ADP
ejpam-6440	174	9	t	t	PROPN
ejpam-6440	174	10	>	>	X
ejpam-6440	174	11	0	0	PUNCT
ejpam-6440	175	1	(	(	PUNCT
ejpam-6440	175	2	boyd	boyd	PROPN
ejpam-6440	175	3	-	-	PUNCT
ejpam-6440	175	4	wong	wong	PROPN
ejpam-6440	175	5	type	type	PROPN
ejpam-6440	175	6	)	)	PUNCT
ejpam-6440	175	7	lemma	lemma	PROPN
ejpam-6440	175	8	3	3	NUM
ejpam-6440	175	9	(	(	PUNCT
ejpam-6440	175	10	a	a	DET
ejpam-6440	175	11	priori	priori	ADJ
ejpam-6440	175	12	estimate	estimate	NOUN
ejpam-6440	175	13	)	)	PUNCT
ejpam-6440	175	14	.	.	PUNCT
ejpam-6440	176	1	under	under	ADP
ejpam-6440	176	2	the	the	DET
ejpam-6440	176	3	conditions	condition	NOUN
ejpam-6440	176	4	of	of	ADP
ejpam-6440	176	5	theorem	theorem	NOUN
ejpam-6440	176	6	3	3	NUM
ejpam-6440	176	7	,	,	PUNCT
ejpam-6440	176	8	any	any	DET
ejpam-6440	176	9	possible	possible	ADJ
ejpam-6440	176	10	solution	solution	NOUN
ejpam-6440	176	11	υ	υ	NOUN
ejpam-6440	176	12	=	=	PUNCT
ejpam-6440	176	13	λtυ	λtυ	NOUN
ejpam-6440	176	14	satisfies	satisfie	NOUN
ejpam-6440	176	15	:	:	PUNCT
ejpam-6440	176	16	m(υ	m(υ	ADJ
ejpam-6440	176	17	,	,	PUNCT
ejpam-6440	176	18	υ0	υ0	NOUN
ejpam-6440	176	19	,	,	PUNCT
ejpam-6440	176	20	υ0	υ0	NOUN
ejpam-6440	176	21	)	)	PUNCT
ejpam-6440	176	22	≤	≤	NUM
ejpam-6440	176	23	ψ(n)(m(tυ0	ψ(n)(m(tυ0	PROPN
ejpam-6440	176	24	,	,	PUNCT
ejpam-6440	176	25	υ0	υ0	NOUN
ejpam-6440	176	26	,	,	PUNCT
ejpam-6440	176	27	υ0	υ0	NOUN
ejpam-6440	176	28	)	)	PUNCT
ejpam-6440	176	29	)	)	PUNCT
ejpam-6440	176	30	where	where	SCONJ
ejpam-6440	176	31	ψ(n	ψ(n	NOUN
ejpam-6440	176	32	)	)	PUNCT
ejpam-6440	176	33	denotes	denote	VERB
ejpam-6440	176	34	the	the	DET
ejpam-6440	176	35	n	n	ADV
ejpam-6440	176	36	-	-	PUNCT
ejpam-6440	176	37	th	th	VERB
ejpam-6440	176	38	iterate	iterate	NOUN
ejpam-6440	176	39	of	of	ADP
ejpam-6440	176	40	ψ	ψ	NOUN
ejpam-6440	176	41	.	.	PUNCT
ejpam-6440	177	1	proof	proof	NOUN
ejpam-6440	177	2	.	.	PUNCT
ejpam-6440	178	1	for	for	ADP
ejpam-6440	178	2	any	any	DET
ejpam-6440	178	3	possible	possible	ADJ
ejpam-6440	178	4	solution	solution	NOUN
ejpam-6440	178	5	v	v	ADP
ejpam-6440	178	6	=	=	SYM
ejpam-6440	178	7	λtv	λtv	X
ejpam-6440	178	8	,	,	PUNCT
ejpam-6440	178	9	we	we	PRON
ejpam-6440	178	10	iteratively	iteratively	ADV
ejpam-6440	178	11	apply	apply	VERB
ejpam-6440	178	12	the	the	DET
ejpam-6440	178	13	generalized	generalized	ADJ
ejpam-6440	178	14	contraction	contraction	NOUN
ejpam-6440	178	15	condition	condition	NOUN
ejpam-6440	178	16	:	:	PUNCT
ejpam-6440	178	17	m(v	m(v	PROPN
ejpam-6440	178	18	,	,	PUNCT
ejpam-6440	178	19	v0	v0	PROPN
ejpam-6440	178	20	,	,	PUNCT
ejpam-6440	178	21	v0	v0	NOUN
ejpam-6440	178	22	)	)	PUNCT
ejpam-6440	179	1	=	=	SYM
ejpam-6440	179	2	m(λtv	m(λtv	X
ejpam-6440	179	3	,	,	PUNCT
ejpam-6440	179	4	λtv0	λtv0	PROPN
ejpam-6440	179	5	,	,	PUNCT
ejpam-6440	179	6	λtv0	λtv0	PROPN
ejpam-6440	179	7	)	)	PUNCT
ejpam-6440	179	8	≤	≤	PROPN
ejpam-6440	179	9	ψ(m(tv	ψ(m(tv	PROPN
ejpam-6440	179	10	,	,	PUNCT
ejpam-6440	179	11	tv0	tv0	NOUN
ejpam-6440	179	12	,	,	PUNCT
ejpam-6440	179	13	t	t	PROPN
ejpam-6440	179	14	v0	v0	PROPN
ejpam-6440	179	15	)	)	PUNCT
ejpam-6440	179	16	)	)	PUNCT
ejpam-6440	180	1	≤	≤	PUNCT
ejpam-6440	180	2	ψ(n)(m(tv0	ψ(n)(m(tv0	PROPN
ejpam-6440	180	3	,	,	PUNCT
ejpam-6440	180	4	v0	v0	PROPN
ejpam-6440	180	5	,	,	PUNCT
ejpam-6440	180	6	v0	v0	NOUN
ejpam-6440	180	7	)	)	PUNCT
ejpam-6440	180	8	)	)	PUNCT
ejpam-6440	180	9	where	where	SCONJ
ejpam-6440	180	10	ψ(n	ψ(n	NOUN
ejpam-6440	180	11	)	)	PUNCT
ejpam-6440	180	12	denotes	denote	VERB
ejpam-6440	180	13	the	the	DET
ejpam-6440	180	14	n	n	ADV
ejpam-6440	180	15	-	-	PUNCT
ejpam-6440	180	16	th	th	VERB
ejpam-6440	180	17	iterate	iterate	NOUN
ejpam-6440	180	18	of	of	ADP
ejpam-6440	180	19	ψ	ψ	NOUN
ejpam-6440	180	20	.	.	PUNCT
ejpam-6440	181	1	the	the	DET
ejpam-6440	181	2	result	result	NOUN
ejpam-6440	181	3	follows	follow	VERB
ejpam-6440	181	4	from	from	ADP
ejpam-6440	181	5	the	the	DET
ejpam-6440	181	6	properties	property	NOUN
ejpam-6440	181	7	of	of	ADP
ejpam-6440	181	8	ψ	ψ	NOUN
ejpam-6440	181	9	.	.	PUNCT
ejpam-6440	182	1	proposition	proposition	NOUN
ejpam-6440	182	2	2	2	NUM
ejpam-6440	182	3	(	(	PUNCT
ejpam-6440	182	4	global	global	ADJ
ejpam-6440	182	5	existence	existence	NOUN
ejpam-6440	182	6	)	)	PUNCT
ejpam-6440	182	7	.	.	PUNCT
ejpam-6440	183	1	if	if	SCONJ
ejpam-6440	183	2	the	the	DET
ejpam-6440	183	3	a	a	DET
ejpam-6440	183	4	priori	priori	ADV
ejpam-6440	183	5	bound	bind	VERB
ejpam-6440	183	6	condition	condition	NOUN
ejpam-6440	183	7	holds	hold	VERB
ejpam-6440	183	8	for	for	ADP
ejpam-6440	183	9	all	all	DET
ejpam-6440	183	10	c	c	PROPN
ejpam-6440	183	11	>	>	X
ejpam-6440	183	12	0	0	PROPN
ejpam-6440	183	13	,	,	PUNCT
ejpam-6440	183	14	then	then	ADV
ejpam-6440	183	15	t	t	PROPN
ejpam-6440	183	16	has	have	VERB
ejpam-6440	183	17	at	at	ADV
ejpam-6440	183	18	least	least	ADV
ejpam-6440	183	19	one	one	NUM
ejpam-6440	183	20	fixed	fix	VERB
ejpam-6440	183	21	point	point	NOUN
ejpam-6440	183	22	in	in	ADP
ejpam-6440	183	23	x.	x.	NOUN
ejpam-6440	183	24	proof	proof	NOUN
ejpam-6440	183	25	.	.	PUNCT
ejpam-6440	184	1	if	if	SCONJ
ejpam-6440	184	2	the	the	DET
ejpam-6440	184	3	a	a	DET
ejpam-6440	184	4	priori	priori	ADV
ejpam-6440	184	5	bound	bind	VERB
ejpam-6440	184	6	holds	hold	VERB
ejpam-6440	184	7	for	for	ADP
ejpam-6440	184	8	all	all	DET
ejpam-6440	184	9	c	c	PROPN
ejpam-6440	184	10	>	>	X
ejpam-6440	184	11	0	0	PROPN
ejpam-6440	184	12	,	,	PUNCT
ejpam-6440	184	13	then	then	ADV
ejpam-6440	184	14	the	the	DET
ejpam-6440	184	15	set	set	NOUN
ejpam-6440	184	16	{	{	PUNCT
ejpam-6440	184	17	v	v	NOUN
ejpam-6440	184	18	∈	∈	NOUN
ejpam-6440	184	19	x	x	PUNCT
ejpam-6440	184	20	:	:	PUNCT
ejpam-6440	184	21	v	v	X
ejpam-6440	184	22	=	=	SYM
ejpam-6440	184	23	λtv	λtv	X
ejpam-6440	184	24	,	,	PUNCT
ejpam-6440	184	25	λ	λ	PROPN
ejpam-6440	184	26	∈	∈	PROPN
ejpam-6440	184	27	(	(	PUNCT
ejpam-6440	184	28	0	0	NUM
ejpam-6440	184	29	,	,	PUNCT
ejpam-6440	184	30	1	1	NUM
ejpam-6440	184	31	)	)	PUNCT
ejpam-6440	184	32	}	}	PUNCT
ejpam-6440	184	33	is	be	AUX
ejpam-6440	184	34	bounded	bound	VERB
ejpam-6440	184	35	.	.	PUNCT
ejpam-6440	185	1	by	by	ADP
ejpam-6440	185	2	theorem	theorem	ADJ
ejpam-6440	185	3	4	4	NUM
ejpam-6440	185	4	(	(	PUNCT
ejpam-6440	185	5	leray	leray	ADJ
ejpam-6440	185	6	-	-	PUNCT
ejpam-6440	185	7	schauder	schauder	NOUN
ejpam-6440	185	8	alternative	alternative	NOUN
ejpam-6440	185	9	)	)	PUNCT
ejpam-6440	185	10	,	,	PUNCT
ejpam-6440	185	11	case	case	NOUN
ejpam-6440	185	12	(	(	PUNCT
ejpam-6440	185	13	a	a	X
ejpam-6440	185	14	)	)	PUNCT
ejpam-6440	185	15	must	must	AUX
ejpam-6440	185	16	occur	occur	VERB
ejpam-6440	185	17	,	,	PUNCT
ejpam-6440	185	18	guaranteeing	guarantee	VERB
ejpam-6440	185	19	a	a	DET
ejpam-6440	185	20	fixed	fix	VERB
ejpam-6440	185	21	point	point	NOUN
ejpam-6440	185	22	.	.	PUNCT
ejpam-6440	186	1	corollary	corollary	ADJ
ejpam-6440	186	2	1	1	NUM
ejpam-6440	186	3	(	(	PUNCT
ejpam-6440	186	4	existence	existence	NOUN
ejpam-6440	186	5	for	for	ADP
ejpam-6440	186	6	nonlinear	nonlinear	ADJ
ejpam-6440	186	7	integral	integral	ADJ
ejpam-6440	186	8	equations	equation	NOUN
ejpam-6440	186	9	)	)	PUNCT
ejpam-6440	186	10	.	.	PUNCT
ejpam-6440	187	1	let	let	VERB
ejpam-6440	187	2	(	(	PUNCT
ejpam-6440	187	3	x	x	X
ejpam-6440	187	4	,	,	PUNCT
ejpam-6440	187	5	m	m	VERB
ejpam-6440	187	6	)	)	PUNCT
ejpam-6440	187	7	be	be	AUX
ejpam-6440	187	8	as	as	ADV
ejpam-6440	187	9	above	above	ADV
ejpam-6440	187	10	,	,	PUNCT
ejpam-6440	187	11	and	and	CCONJ
ejpam-6440	187	12	t	t	X
ejpam-6440	187	13	:	:	PUNCT
ejpam-6440	187	14	x	x	X
ejpam-6440	187	15	→	→	SYM
ejpam-6440	187	16	x	x	PUNCT
ejpam-6440	187	17	defined	define	VERB
ejpam-6440	187	18	by	by	ADP
ejpam-6440	187	19	:	:	PUNCT
ejpam-6440	187	20	tυ(x	tυ(x	PUNCT
ejpam-6440	187	21	)	)	PUNCT
ejpam-6440	187	22	=	=	SYM
ejpam-6440	188	1	∫	∫	PROPN
ejpam-6440	188	2	b	b	PROPN
ejpam-6440	188	3	a	a	DET
ejpam-6440	188	4	k(x	k(x	PROPN
ejpam-6440	188	5	,	,	PUNCT
ejpam-6440	188	6	y	y	PROPN
ejpam-6440	188	7	,	,	PUNCT
ejpam-6440	188	8	υ(y	υ(y	PROPN
ejpam-6440	188	9	)	)	PUNCT
ejpam-6440	188	10	)	)	PUNCT
ejpam-6440	189	1	dy	dy	NOUN
ejpam-6440	189	2	,	,	PUNCT
ejpam-6440	189	3	where	where	SCONJ
ejpam-6440	189	4	k	k	PROPN
ejpam-6440	189	5	is	be	AUX
ejpam-6440	189	6	continuous	continuous	ADJ
ejpam-6440	189	7	and	and	CCONJ
ejpam-6440	189	8	|k(x	|k(x	PROPN
ejpam-6440	189	9	,	,	PUNCT
ejpam-6440	189	10	y	y	PROPN
ejpam-6440	189	11	,	,	PUNCT
ejpam-6440	189	12	u)|	u)|	PROPN
ejpam-6440	189	13	≤	≤	PROPN
ejpam-6440	189	14	ψ(|u|	ψ(|u|	PROPN
ejpam-6440	189	15	)	)	PUNCT
ejpam-6440	189	16	.	.	PUNCT
ejpam-6440	190	1	if	if	SCONJ
ejpam-6440	190	2	ψ	ψ	ADP
ejpam-6440	190	3	satisfies	satisfie	NOUN
ejpam-6440	190	4	(	(	PUNCT
ejpam-6440	190	5	i	i	NOUN
ejpam-6440	190	6	)	)	PUNCT
ejpam-6440	190	7	and	and	CCONJ
ejpam-6440	190	8	∃c	∃c	PROPN
ejpam-6440	190	9	>	>	X
ejpam-6440	190	10	0	0	NUM
ejpam-6440	190	11	such	such	ADJ
ejpam-6440	190	12	that	that	SCONJ
ejpam-6440	190	13	∥υ∥	∥υ∥	ADJ
ejpam-6440	190	14	≤	≤	NUM
ejpam-6440	190	15	c	c	NOUN
ejpam-6440	190	16	for	for	ADP
ejpam-6440	190	17	all	all	PRON
ejpam-6440	190	18	υ	υ	NOUN
ejpam-6440	190	19	=	=	NOUN
ejpam-6440	190	20	λtυ	λtυ	NOUN
ejpam-6440	190	21	,	,	PUNCT
ejpam-6440	190	22	then	then	ADV
ejpam-6440	190	23	t	t	PROPN
ejpam-6440	190	24	has	have	VERB
ejpam-6440	190	25	a	a	DET
ejpam-6440	190	26	fixed	fix	VERB
ejpam-6440	190	27	point	point	NOUN
ejpam-6440	190	28	.	.	PUNCT
ejpam-6440	191	1	3	3	X
ejpam-6440	191	2	.	.	X
ejpam-6440	191	3	applications	application	NOUN
ejpam-6440	191	4	and	and	CCONJ
ejpam-6440	191	5	examples	example	NOUN
ejpam-6440	191	6	of	of	ADP
ejpam-6440	191	7	mr	mr	PROPN
ejpam-6440	191	8	-	-	PUNCT
ejpam-6440	191	9	metric	metric	ADJ
ejpam-6440	191	10	space	space	NOUN
ejpam-6440	191	11	theorems	theorem	VERB
ejpam-6440	191	12	the	the	DET
ejpam-6440	191	13	theoretical	theoretical	ADJ
ejpam-6440	191	14	framework	framework	NOUN
ejpam-6440	191	15	developed	develop	VERB
ejpam-6440	191	16	in	in	ADP
ejpam-6440	191	17	section	section	NOUN
ejpam-6440	191	18	2	2	NUM
ejpam-6440	191	19	finds	find	VERB
ejpam-6440	191	20	substantive	substantive	ADJ
ejpam-6440	191	21	applications	application	NOUN
ejpam-6440	191	22	across	across	ADP
ejpam-6440	191	23	multiple	multiple	ADJ
ejpam-6440	191	24	disciplines	discipline	NOUN
ejpam-6440	191	25	.	.	PUNCT
ejpam-6440	192	1	we	we	PRON
ejpam-6440	192	2	demonstrate	demonstrate	VERB
ejpam-6440	192	3	how	how	SCONJ
ejpam-6440	192	4	mr	mr	PROPN
ejpam-6440	192	5	-	-	PUNCT
ejpam-6440	192	6	metric	metric	ADJ
ejpam-6440	192	7	fixed	fix	VERB
ejpam-6440	192	8	-	-	PUNCT
ejpam-6440	192	9	point	point	NOUN
ejpam-6440	192	10	theory	theory	NOUN
ejpam-6440	192	11	resolves	resolve	VERB
ejpam-6440	192	12	problems	problem	NOUN
ejpam-6440	192	13	in	in	ADP
ejpam-6440	192	14	nonlinear	nonlinear	ADJ
ejpam-6440	192	15	analysis	analysis	NOUN
ejpam-6440	192	16	,	,	PUNCT
ejpam-6440	192	17	nuclear	nuclear	ADJ
ejpam-6440	192	18	engineering	engineering	NOUN
ejpam-6440	192	19	,	,	PUNCT
ejpam-6440	192	20	and	and	CCONJ
ejpam-6440	192	21	machine	machine	NOUN
ejpam-6440	192	22	learning	learning	NOUN
ejpam-6440	192	23	that	that	PRON
ejpam-6440	192	24	resist	resist	VERB
ejpam-6440	192	25	treatment	treatment	NOUN
ejpam-6440	192	26	by	by	ADP
ejpam-6440	192	27	conventional	conventional	ADJ
ejpam-6440	192	28	methods	method	NOUN
ejpam-6440	192	29	.	.	PUNCT
ejpam-6440	193	1	each	each	DET
ejpam-6440	193	2	application	application	NOUN
ejpam-6440	193	3	is	be	AUX
ejpam-6440	193	4	paired	pair	VERB
ejpam-6440	193	5	with	with	ADP
ejpam-6440	193	6	a	a	DET
ejpam-6440	193	7	computational	computational	ADJ
ejpam-6440	193	8	example	example	NOUN
ejpam-6440	193	9	that	that	PRON
ejpam-6440	193	10	illustrates	illustrate	VERB
ejpam-6440	193	11	:	:	PUNCT
ejpam-6440	193	12	(	(	PUNCT
ejpam-6440	193	13	i	i	NOUN
ejpam-6440	193	14	)	)	PUNCT
ejpam-6440	193	15	the	the	DET
ejpam-6440	193	16	natural	natural	ADJ
ejpam-6440	193	17	emergence	emergence	NOUN
ejpam-6440	193	18	of	of	ADP
ejpam-6440	193	19	three	three	NUM
ejpam-6440	193	20	-	-	PUNCT
ejpam-6440	193	21	point	point	NOUN
ejpam-6440	193	22	relations	relation	NOUN
ejpam-6440	193	23	in	in	ADP
ejpam-6440	193	24	the	the	DET
ejpam-6440	193	25	problem	problem	NOUN
ejpam-6440	193	26	structure	structure	NOUN
ejpam-6440	193	27	,	,	PUNCT
ejpam-6440	193	28	(	(	PUNCT
ejpam-6440	193	29	ii	ii	NOUN
ejpam-6440	193	30	)	)	PUNCT
ejpam-6440	193	31	the	the	DET
ejpam-6440	193	32	explicit	explicit	ADJ
ejpam-6440	193	33	verification	verification	NOUN
ejpam-6440	193	34	of	of	ADP
ejpam-6440	193	35	mr	mr	PROPN
ejpam-6440	193	36	-	-	PUNCT
ejpam-6440	193	37	metric	metric	ADJ
ejpam-6440	193	38	conditions	condition	NOUN
ejpam-6440	193	39	,	,	PUNCT
ejpam-6440	193	40	and	and	CCONJ
ejpam-6440	193	41	(	(	PUNCT
ejpam-6440	193	42	iii	iii	X
ejpam-6440	193	43	)	)	PUNCT
ejpam-6440	193	44	quantitative	quantitative	ADJ
ejpam-6440	193	45	improvements	improvement	NOUN
ejpam-6440	193	46	over	over	ADP
ejpam-6440	193	47	standard	standard	ADJ
ejpam-6440	193	48	approaches	approach	NOUN
ejpam-6440	193	49	.	.	PUNCT
ejpam-6440	194	1	particular	particular	ADJ
ejpam-6440	194	2	emphasis	emphasis	NOUN
ejpam-6440	194	3	is	be	AUX
ejpam-6440	194	4	given	give	VERB
ejpam-6440	194	5	to	to	ADP
ejpam-6440	194	6	neutron	neutron	NOUN
ejpam-6440	194	7	transport	transport	NOUN
ejpam-6440	194	8	theory	theory	NOUN
ejpam-6440	194	9	where	where	SCONJ
ejpam-6440	194	10	ternary	ternary	ADJ
ejpam-6440	194	11	particle	particle	NOUN
ejpam-6440	194	12	interactions	interaction	NOUN
ejpam-6440	194	13	necessitate	necessitate	ADJ
ejpam-6440	194	14	mr	mr	NOUN
ejpam-6440	194	15	-	-	PUNCT
ejpam-6440	194	16	metrics	metric	NOUN
ejpam-6440	194	17	and	and	CCONJ
ejpam-6440	194	18	neural	neural	ADJ
ejpam-6440	194	19	network	network	NOUN
ejpam-6440	194	20	optimization	optimization	NOUN
ejpam-6440	194	21	,	,	PUNCT
ejpam-6440	194	22	where	where	SCONJ
ejpam-6440	194	23	the	the	DET
ejpam-6440	194	24	framework	framework	NOUN
ejpam-6440	194	25	provides	provide	VERB
ejpam-6440	194	26	layer	layer	NOUN
ejpam-6440	194	27	-	-	PUNCT
ejpam-6440	194	28	wise	wise	ADJ
ejpam-6440	194	29	convergence	convergence	NOUN
ejpam-6440	194	30	criteria	criterion	NOUN
ejpam-6440	194	31	.	.	PUNCT
ejpam-6440	195	1	the	the	DET
ejpam-6440	195	2	examples	example	NOUN
ejpam-6440	195	3	progress	progress	VERB
ejpam-6440	195	4	from	from	ADP
ejpam-6440	195	5	finite	finite	ADJ
ejpam-6440	195	6	-	-	ADJ
ejpam-6440	195	7	dimensional	dimensional	ADJ
ejpam-6440	195	8	systems	system	NOUN
ejpam-6440	195	9	to	to	ADP
ejpam-6440	195	10	integral	integral	ADJ
ejpam-6440	195	11	equations	equation	NOUN
ejpam-6440	195	12	and	and	CCONJ
ejpam-6440	195	13	boundary	boundary	ADJ
ejpam-6440	195	14	value	value	NOUN
ejpam-6440	195	15	problems	problem	NOUN
ejpam-6440	195	16	,	,	PUNCT
ejpam-6440	195	17	showcasing	showcase	VERB
ejpam-6440	195	18	the	the	DET
ejpam-6440	195	19	versatility	versatility	NOUN
ejpam-6440	195	20	of	of	ADP
ejpam-6440	195	21	our	our	PRON
ejpam-6440	195	22	results	result	NOUN
ejpam-6440	195	23	.	.	PUNCT
ejpam-6440	196	1	t.	t.	NOUN
ejpam-6440	196	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	196	3	,	,	PUNCT
ejpam-6440	196	4	a.	a.	NOUN
ejpam-6440	196	5	malkawi	malkawi	PROPN
ejpam-6440	196	6	/	/	SYM
ejpam-6440	196	7	eur	eur	PROPN
ejpam-6440	196	8	.	.	PUNCT
ejpam-6440	197	1	j.	j.	PROPN
ejpam-6440	197	2	pure	pure	PROPN
ejpam-6440	197	3	appl	appl	PROPN
ejpam-6440	197	4	.	.	PROPN
ejpam-6440	197	5	math	math	PROPN
ejpam-6440	197	6	,	,	PUNCT
ejpam-6440	197	7	18	18	NUM
ejpam-6440	197	8	(	(	PUNCT
ejpam-6440	197	9	3	3	NUM
ejpam-6440	197	10	)	)	PUNCT
ejpam-6440	197	11	(	(	PUNCT
ejpam-6440	197	12	2025	2025	NUM
ejpam-6440	197	13	)	)	PUNCT
ejpam-6440	197	14	,	,	PUNCT
ejpam-6440	197	15	6440	6440	NUM
ejpam-6440	197	16	12	12	NUM
ejpam-6440	197	17	of	of	ADP
ejpam-6440	197	18	20	20	NUM
ejpam-6440	197	19	3.1	3.1	NUM
ejpam-6440	197	20	.	.	PUNCT
ejpam-6440	198	1	banach	banach	NOUN
ejpam-6440	198	2	contraction	contraction	NOUN
ejpam-6440	198	3	principle	principle	NOUN
ejpam-6440	198	4	in	in	ADP
ejpam-6440	198	5	mr	mr	PROPN
ejpam-6440	198	6	-	-	PUNCT
ejpam-6440	198	7	metric	metric	ADJ
ejpam-6440	198	8	spaces	space	NOUN
ejpam-6440	198	9	example	example	NOUN
ejpam-6440	198	10	1	1	NUM
ejpam-6440	198	11	(	(	PUNCT
ejpam-6440	198	12	nonlinear	nonlinear	ADJ
ejpam-6440	198	13	system	system	NOUN
ejpam-6440	198	14	of	of	ADP
ejpam-6440	198	15	equations	equation	NOUN
ejpam-6440	198	16	)	)	PUNCT
ejpam-6440	198	17	.	.	PUNCT
ejpam-6440	199	1	consider	consider	VERB
ejpam-6440	199	2	x	x	SYM
ejpam-6440	199	3	=	=	SYM
ejpam-6440	199	4	rn	rn	PROPN
ejpam-6440	199	5	with	with	ADP
ejpam-6440	199	6	the	the	DET
ejpam-6440	199	7	mr	mr	PROPN
ejpam-6440	199	8	-	-	PUNCT
ejpam-6440	199	9	metric	metric	NOUN
ejpam-6440	199	10	:	:	PUNCT
ejpam-6440	199	11	m(u	m(u	PROPN
ejpam-6440	199	12	,	,	PUNCT
ejpam-6440	199	13	v	v	NOUN
ejpam-6440	199	14	,	,	PUNCT
ejpam-6440	199	15	w	w	NOUN
ejpam-6440	199	16	)	)	PUNCT
ejpam-6440	199	17	=	=	SYM
ejpam-6440	199	18	max	max	PROPN
ejpam-6440	199	19	1≤i≤n	1≤i≤n	NUM
ejpam-6440	199	20	(	(	PUNCT
ejpam-6440	199	21	|ui	|ui	NUM
ejpam-6440	199	22	−	−	NOUN
ejpam-6440	199	23	vi|+	vi|+	NOUN
ejpam-6440	199	24	|ui	|ui	ADJ
ejpam-6440	199	25	−	−	PROPN
ejpam-6440	199	26	wi|+	wi|+	NOUN
ejpam-6440	199	27	|vi	|vi	X
ejpam-6440	199	28	−	−	PROPN
ejpam-6440	199	29	wi|	wi|	PROPN
ejpam-6440	199	30	)	)	PUNCT
ejpam-6440	199	31	.	.	PUNCT
ejpam-6440	200	1	define	define	VERB
ejpam-6440	200	2	t	t	PROPN
ejpam-6440	200	3	:	:	PUNCT
ejpam-6440	200	4	rn	rn	PROPN
ejpam-6440	200	5	→	→	SYM
ejpam-6440	200	6	rn	rn	PROPN
ejpam-6440	200	7	by	by	ADP
ejpam-6440	200	8	:	:	PUNCT
ejpam-6440	200	9	tu	tu	PROPN
ejpam-6440	200	10	=	=	SYM
ejpam-6440	200	11	(	(	PUNCT
ejpam-6440	200	12	sin(u1	sin(u1	NOUN
ejpam-6440	200	13	)	)	PUNCT
ejpam-6440	200	14	3r	3r	NOUN
ejpam-6440	200	15	,	,	PUNCT
ejpam-6440	200	16	cos(u2	cos(u2	PROPN
ejpam-6440	200	17	)	)	PUNCT
ejpam-6440	200	18	3r	3r	NOUN
ejpam-6440	200	19	,	,	PUNCT
ejpam-6440	200	20	.	.	PUNCT
ejpam-6440	200	21	.	.	PUNCT
ejpam-6440	200	22	.	.	PUNCT
ejpam-6440	201	1	,	,	PUNCT
ejpam-6440	201	2	un	un	PROPN
ejpam-6440	201	3	3r(1	3r(1	PROPN
ejpam-6440	201	4	+	+	CCONJ
ejpam-6440	201	5	|un|	|un|	NOUN
ejpam-6440	201	6	)	)	PUNCT
ejpam-6440	201	7	)	)	PUNCT
ejpam-6440	201	8	.	.	PUNCT
ejpam-6440	202	1	then	then	ADV
ejpam-6440	202	2	:	:	PUNCT
ejpam-6440	202	3	•	•	ADP
ejpam-6440	202	4	t	t	NOUN
ejpam-6440	202	5	is	be	AUX
ejpam-6440	202	6	a	a	DET
ejpam-6440	202	7	contraction	contraction	NOUN
ejpam-6440	202	8	with	with	ADP
ejpam-6440	202	9	k	k	PROPN
ejpam-6440	202	10	=	=	SYM
ejpam-6440	202	11	1	1	NUM
ejpam-6440	202	12	3r	3r	NUM
ejpam-6440	202	13	•	•	NOUN
ejpam-6440	202	14	for	for	ADP
ejpam-6440	202	15	r	r	NOUN
ejpam-6440	202	16	=	=	SYM
ejpam-6440	202	17	1.2	1.2	NUM
ejpam-6440	202	18	,	,	PUNCT
ejpam-6440	202	19	k	k	NOUN
ejpam-6440	202	20	=	=	SYM
ejpam-6440	202	21	1	1	NUM
ejpam-6440	202	22	3.6	3.6	NUM
ejpam-6440	202	23	<	<	SYM
ejpam-6440	202	24	1	1	NUM
ejpam-6440	202	25	3r	3r	NUM
ejpam-6440	202	26	≈	≈	PROPN
ejpam-6440	202	27	0.278	0.278	NUM
ejpam-6440	202	28	by	by	ADP
ejpam-6440	202	29	theorem	theorem	NOUN
ejpam-6440	202	30	1	1	NUM
ejpam-6440	202	31	,	,	PUNCT
ejpam-6440	202	32	t	t	PROPN
ejpam-6440	202	33	has	have	VERB
ejpam-6440	202	34	a	a	DET
ejpam-6440	202	35	unique	unique	ADJ
ejpam-6440	202	36	fixed	fix	VERB
ejpam-6440	202	37	point	point	NOUN
ejpam-6440	202	38	computable	computable	ADJ
ejpam-6440	202	39	via	via	ADP
ejpam-6440	202	40	iteration	iteration	NOUN
ejpam-6440	202	41	.	.	PUNCT
ejpam-6440	203	1	application	application	NOUN
ejpam-6440	203	2	1	1	NUM
ejpam-6440	203	3	(	(	PUNCT
ejpam-6440	203	4	optimization	optimization	NOUN
ejpam-6440	203	5	in	in	ADP
ejpam-6440	203	6	neural	neural	ADJ
ejpam-6440	203	7	networks	network	NOUN
ejpam-6440	203	8	via	via	ADP
ejpam-6440	203	9	mr	mr	PROPN
ejpam-6440	203	10	-	-	PUNCT
ejpam-6440	203	11	metric	metric	ADJ
ejpam-6440	203	12	contractions	contraction	NOUN
ejpam-6440	203	13	)	)	PUNCT
ejpam-6440	203	14	.	.	PUNCT
ejpam-6440	204	1	consider	consider	VERB
ejpam-6440	204	2	a	a	DET
ejpam-6440	204	3	feedforward	feedforward	ADJ
ejpam-6440	204	4	neural	neural	ADJ
ejpam-6440	204	5	network	network	NOUN
ejpam-6440	204	6	with	with	ADP
ejpam-6440	204	7	parameters	parameter	NOUN
ejpam-6440	204	8	w	w	PROPN
ejpam-6440	204	9	∈	∈	PROPN
ejpam-6440	204	10	rd	rd	PROPN
ejpam-6440	204	11	and	and	CCONJ
ejpam-6440	204	12	loss	loss	NOUN
ejpam-6440	204	13	function	function	NOUN
ejpam-6440	204	14	l	l	NOUN
ejpam-6440	204	15	:	:	PUNCT
ejpam-6440	204	16	rd	rd	PROPN
ejpam-6440	204	17	→	→	SYM
ejpam-6440	204	18	r.	r.	VERB
ejpam-6440	204	19	the	the	DET
ejpam-6440	204	20	weight	weight	NOUN
ejpam-6440	204	21	update	update	NOUN
ejpam-6440	204	22	rule	rule	NOUN
ejpam-6440	204	23	can	can	AUX
ejpam-6440	204	24	be	be	AUX
ejpam-6440	204	25	formulated	formulate	VERB
ejpam-6440	204	26	as	as	ADP
ejpam-6440	204	27	a	a	DET
ejpam-6440	204	28	fixed	fix	VERB
ejpam-6440	204	29	-	-	PUNCT
ejpam-6440	204	30	point	point	NOUN
ejpam-6440	204	31	problem	problem	NOUN
ejpam-6440	204	32	in	in	ADP
ejpam-6440	204	33	an	an	DET
ejpam-6440	204	34	mr	mr	PROPN
ejpam-6440	204	35	-	-	PUNCT
ejpam-6440	204	36	metric	metric	ADJ
ejpam-6440	204	37	space	space	NOUN
ejpam-6440	204	38	:	:	PUNCT
ejpam-6440	204	39	mr	mr	ADJ
ejpam-6440	204	40	-	-	PUNCT
ejpam-6440	204	41	metric	metric	ADJ
ejpam-6440	204	42	formulation	formulation	NOUN
ejpam-6440	204	43	define	define	VERB
ejpam-6440	204	44	the	the	DET
ejpam-6440	204	45	mr	mr	NOUN
ejpam-6440	204	46	-	-	PUNCT
ejpam-6440	204	47	metric	metric	NOUN
ejpam-6440	204	48	on	on	ADP
ejpam-6440	204	49	the	the	DET
ejpam-6440	204	50	weight	weight	NOUN
ejpam-6440	204	51	space	space	NOUN
ejpam-6440	204	52	rd	rd	PROPN
ejpam-6440	204	53	as	as	ADP
ejpam-6440	204	54	:	:	PUNCT
ejpam-6440	204	55	m(w1,w2,w3	m(w1,w2,w3	NOUN
ejpam-6440	204	56	)	)	PUNCT
ejpam-6440	204	57	=	=	SYM
ejpam-6440	204	58	max	max	PROPN
ejpam-6440	204	59	1≤i≤d	1≤i≤d	NUM
ejpam-6440	204	60	(	(	PUNCT
ejpam-6440	204	61	|wi1	|wi1	PROPN
ejpam-6440	204	62	−	−	PROPN
ejpam-6440	204	63	wi2|+	wi2|+	PROPN
ejpam-6440	204	64	|wi1	|wi1	PROPN
ejpam-6440	204	65	−	−	PROPN
ejpam-6440	204	66	wi3|+	wi3|+	PROPN
ejpam-6440	204	67	|wi2	|wi2	PROPN
ejpam-6440	204	68	−	−	PROPN
ejpam-6440	204	69	wi3|	wi3|	PROPN
ejpam-6440	204	70	)	)	PUNCT
ejpam-6440	204	71	where	where	SCONJ
ejpam-6440	204	72	wj	wj	PROPN
ejpam-6440	204	73	=	=	SYM
ejpam-6440	204	74	(	(	PUNCT
ejpam-6440	204	75	w1	w1	PROPN
ejpam-6440	204	76	j	j	PROPN
ejpam-6440	204	77	,	,	PUNCT
ejpam-6440	204	78	.	.	PUNCT
ejpam-6440	204	79	.	.	PUNCT
ejpam-6440	205	1	.	.	PUNCT
ejpam-6440	206	1	,	,	PUNCT
ejpam-6440	206	2	w	w	PROPN
ejpam-6440	206	3	d	d	X
ejpam-6440	206	4	j	j	PROPN
ejpam-6440	206	5	)	)	PUNCT
ejpam-6440	206	6	.	.	PUNCT
ejpam-6440	207	1	contraction	contraction	NOUN
ejpam-6440	207	2	mapping	mapping	NOUN
ejpam-6440	207	3	for	for	ADP
ejpam-6440	207	4	gradient	gradient	ADJ
ejpam-6440	207	5	descent	descent	NOUN
ejpam-6440	207	6	the	the	DET
ejpam-6440	207	7	standard	standard	ADJ
ejpam-6440	207	8	gradient	gradient	ADJ
ejpam-6440	207	9	descent	descent	NOUN
ejpam-6440	207	10	update	update	NOUN
ejpam-6440	207	11	:	:	PUNCT
ejpam-6440	207	12	tw	tw	NOUN
ejpam-6440	207	13	=	=	SYM
ejpam-6440	208	1	w	w	PROPN
ejpam-6440	208	2	−	−	PROPN
ejpam-6440	208	3	η∇l(w	η∇l(w	NOUN
ejpam-6440	208	4	)	)	PUNCT
ejpam-6440	208	5	becomes	become	VERB
ejpam-6440	208	6	a	a	DET
ejpam-6440	208	7	contraction	contraction	NOUN
ejpam-6440	208	8	in	in	ADP
ejpam-6440	208	9	(	(	PUNCT
ejpam-6440	208	10	rd	rd	NOUN
ejpam-6440	208	11	,	,	PUNCT
ejpam-6440	208	12	m	m	PROPN
ejpam-6440	208	13	)	)	PUNCT
ejpam-6440	208	14	under	under	ADP
ejpam-6440	208	15	the	the	DET
ejpam-6440	208	16	following	following	ADJ
ejpam-6440	208	17	conditions	condition	NOUN
ejpam-6440	208	18	:	:	PUNCT
ejpam-6440	208	19	(	(	PUNCT
ejpam-6440	208	20	i	i	NOUN
ejpam-6440	208	21	)	)	PUNCT
ejpam-6440	208	22	the	the	DET
ejpam-6440	208	23	loss	loss	NOUN
ejpam-6440	208	24	function	function	NOUN
ejpam-6440	208	25	l	l	NOUN
ejpam-6440	208	26	is	be	AUX
ejpam-6440	208	27	l	l	NOUN
ejpam-6440	208	28	-	-	ADJ
ejpam-6440	208	29	smooth	smooth	ADJ
ejpam-6440	208	30	:	:	PUNCT
ejpam-6440	208	31	∥∇l(w)−∇l(v)∥∞	∥∇l(w)−∇l(v)∥∞	ADP
ejpam-6440	208	32	≤	≤	NUM
ejpam-6440	208	33	l∥w	l∥w	PROPN
ejpam-6440	208	34	−	−	PROPN
ejpam-6440	208	35	v∥∞	v∥∞	PROPN
ejpam-6440	208	36	(	(	PUNCT
ejpam-6440	208	37	ii	ii	PROPN
ejpam-6440	208	38	)	)	PUNCT
ejpam-6440	208	39	the	the	DET
ejpam-6440	208	40	learning	learning	PROPN
ejpam-6440	208	41	rate	rate	PROPN
ejpam-6440	208	42	η	η	PROPN
ejpam-6440	208	43	satisfies	satisfie	NOUN
ejpam-6440	208	44	:	:	PUNCT
ejpam-6440	208	45	0	0	NUM
ejpam-6440	208	46	<	<	X
ejpam-6440	208	47	η	η	X
ejpam-6440	208	48	<	<	X
ejpam-6440	208	49	1	1	NUM
ejpam-6440	208	50	3rl	3rl	NOUN
ejpam-6440	208	51	where	where	SCONJ
ejpam-6440	208	52	r	r	NOUN
ejpam-6440	208	53	>	>	X
ejpam-6440	208	54	1	1	NUM
ejpam-6440	208	55	is	be	AUX
ejpam-6440	208	56	the	the	DET
ejpam-6440	208	57	mr	mr	PROPN
ejpam-6440	208	58	-	-	PUNCT
ejpam-6440	208	59	metric	metric	ADJ
ejpam-6440	208	60	constant	constant	ADJ
ejpam-6440	208	61	.	.	PUNCT
ejpam-6440	209	1	t.	t.	NOUN
ejpam-6440	209	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	209	3	,	,	PUNCT
ejpam-6440	209	4	a.	a.	NOUN
ejpam-6440	209	5	malkawi	malkawi	PROPN
ejpam-6440	209	6	/	/	SYM
ejpam-6440	209	7	eur	eur	PROPN
ejpam-6440	209	8	.	.	PUNCT
ejpam-6440	210	1	j.	j.	PROPN
ejpam-6440	210	2	pure	pure	PROPN
ejpam-6440	210	3	appl	appl	PROPN
ejpam-6440	210	4	.	.	PROPN
ejpam-6440	210	5	math	math	PROPN
ejpam-6440	210	6	,	,	PUNCT
ejpam-6440	210	7	18	18	NUM
ejpam-6440	210	8	(	(	PUNCT
ejpam-6440	210	9	3	3	NUM
ejpam-6440	210	10	)	)	PUNCT
ejpam-6440	210	11	(	(	PUNCT
ejpam-6440	210	12	2025	2025	NUM
ejpam-6440	210	13	)	)	PUNCT
ejpam-6440	210	14	,	,	PUNCT
ejpam-6440	210	15	6440	6440	NUM
ejpam-6440	210	16	13	13	NUM
ejpam-6440	210	17	of	of	ADP
ejpam-6440	210	18	20	20	NUM
ejpam-6440	210	19	convergence	convergence	NOUN
ejpam-6440	210	20	proof	proof	NOUN
ejpam-6440	210	21	proof	proof	NOUN
ejpam-6440	210	22	.	.	PUNCT
ejpam-6440	211	1	for	for	ADP
ejpam-6440	211	2	any	any	DET
ejpam-6440	211	3	weight	weight	NOUN
ejpam-6440	211	4	vectors	vector	NOUN
ejpam-6440	211	5	w	w	PROPN
ejpam-6440	211	6	,	,	PUNCT
ejpam-6440	211	7	v	v	NOUN
ejpam-6440	211	8	,	,	PUNCT
ejpam-6440	211	9	u	u	PROPN
ejpam-6440	211	10	∈	∈	PROPN
ejpam-6440	211	11	rd	rd	PROPN
ejpam-6440	211	12	:	:	PUNCT
ejpam-6440	211	13	m(tw	m(tw	PROPN
ejpam-6440	211	14	,	,	PUNCT
ejpam-6440	211	15	tv	tv	NOUN
ejpam-6440	211	16	,	,	PUNCT
ejpam-6440	211	17	tu	tu	PROPN
ejpam-6440	211	18	)	)	PUNCT
ejpam-6440	211	19	=	=	SYM
ejpam-6440	212	1	max	max	PROPN
ejpam-6440	212	2	i	i	PRON
ejpam-6440	212	3	(	(	PUNCT
ejpam-6440	212	4	|twi	|twi	CCONJ
ejpam-6440	212	5	−	−	NUM
ejpam-6440	212	6	tvi|+	tvi|+	NOUN
ejpam-6440	212	7	|twi	|twi	PUNCT
ejpam-6440	212	8	−	−	NOUN
ejpam-6440	212	9	tui|+	tui|+	VERB
ejpam-6440	212	10	|tvi	|tvi	NOUN
ejpam-6440	212	11	−	−	NOUN
ejpam-6440	212	12	tui|	tui|	PROPN
ejpam-6440	212	13	)	)	PUNCT
ejpam-6440	213	1	=	=	SYM
ejpam-6440	214	1	max	max	PROPN
ejpam-6440	215	1	i	i	PRON
ejpam-6440	215	2	(	(	PUNCT
ejpam-6440	215	3	|(wi	|(wi	PROPN
ejpam-6440	215	4	−	−	PROPN
ejpam-6440	215	5	η∂il(w))−	η∂il(w))−	ADJ
ejpam-6440	215	6	(	(	PUNCT
ejpam-6440	215	7	vi	vi	PROPN
ejpam-6440	215	8	−	−	PROPN
ejpam-6440	215	9	η∂il(v))|+	η∂il(v))|+	X
ejpam-6440	215	10	·	·	PUNCT
ejpam-6440	215	11	·	·	PUNCT
ejpam-6440	215	12	·	·	PUNCT
ejpam-6440	215	13	)	)	PUNCT
ejpam-6440	215	14	≤	≤	NUM
ejpam-6440	216	1	max	max	PROPN
ejpam-6440	216	2	i	i	PRON
ejpam-6440	216	3	(	(	PUNCT
ejpam-6440	216	4	|wi	|wi	NOUN
ejpam-6440	216	5	−	−	PROPN
ejpam-6440	216	6	vi|+	vi|+	PROPN
ejpam-6440	216	7	η|∂il(w)−	η|∂il(w)−	VERB
ejpam-6440	216	8	∂il(v)|+	∂il(v)|+	PROPN
ejpam-6440	216	9	·	·	PUNCT
ejpam-6440	216	10	·	·	PUNCT
ejpam-6440	216	11	·	·	PUNCT
ejpam-6440	216	12	)	)	PUNCT
ejpam-6440	217	1	≤	≤	NUM
ejpam-6440	218	1	max	max	PROPN
ejpam-6440	218	2	i	i	PRON
ejpam-6440	218	3	(	(	PUNCT
ejpam-6440	218	4	|wi	|wi	NOUN
ejpam-6440	218	5	−	−	PROPN
ejpam-6440	218	6	vi|+	vi|+	PROPN
ejpam-6440	218	7	ηl∥w	ηl∥w	PROPN
ejpam-6440	219	1	−	−	PROPN
ejpam-6440	219	2	v∥∞	v∥∞	PROPN
ejpam-6440	219	3	+	+	X
ejpam-6440	219	4	·	·	PUNCT
ejpam-6440	219	5	·	·	PUNCT
ejpam-6440	219	6	·	·	PUNCT
ejpam-6440	219	7	)	)	PUNCT
ejpam-6440	219	8	≤	≤	NOUN
ejpam-6440	219	9	(	(	PUNCT
ejpam-6440	219	10	1	1	NUM
ejpam-6440	219	11	+	+	NUM
ejpam-6440	219	12	3ηl)m(w	3ηl)m(w	NUM
ejpam-6440	219	13	,	,	PUNCT
ejpam-6440	219	14	v	v	NOUN
ejpam-6440	219	15	,	,	PUNCT
ejpam-6440	219	16	u	u	NOUN
ejpam-6440	219	17	)	)	PUNCT
ejpam-6440	219	18	however	however	ADV
ejpam-6440	219	19	,	,	PUNCT
ejpam-6440	219	20	through	through	ADP
ejpam-6440	219	21	more	more	ADV
ejpam-6440	219	22	careful	careful	ADJ
ejpam-6440	219	23	estimation	estimation	NOUN
ejpam-6440	219	24	using	use	VERB
ejpam-6440	219	25	the	the	DET
ejpam-6440	219	26	mr	mr	PROPN
ejpam-6440	219	27	-	-	PUNCT
ejpam-6440	219	28	metric	metric	ADJ
ejpam-6440	219	29	properties	property	NOUN
ejpam-6440	219	30	,	,	PUNCT
ejpam-6440	219	31	we	we	PRON
ejpam-6440	219	32	obtain	obtain	VERB
ejpam-6440	219	33	the	the	DET
ejpam-6440	219	34	contraction	contraction	NOUN
ejpam-6440	219	35	factor	factor	NOUN
ejpam-6440	219	36	k	k	NOUN
ejpam-6440	220	1	=	=	PUNCT
ejpam-6440	220	2	3ηl	3ηl	ADJ
ejpam-6440	220	3	<	<	X
ejpam-6440	220	4	1	1	NUM
ejpam-6440	220	5	r	r	NOUN
ejpam-6440	220	6	.	.	PUNCT
ejpam-6440	221	1	by	by	ADP
ejpam-6440	221	2	the	the	DET
ejpam-6440	221	3	banach	banach	ADV
ejpam-6440	221	4	fixed	fix	VERB
ejpam-6440	221	5	-	-	PUNCT
ejpam-6440	221	6	point	point	NOUN
ejpam-6440	221	7	theorem	theorem	NOUN
ejpam-6440	221	8	in	in	ADP
ejpam-6440	221	9	mr	mr	PROPN
ejpam-6440	221	10	-	-	PUNCT
ejpam-6440	221	11	metric	metric	ADJ
ejpam-6440	221	12	spaces	space	NOUN
ejpam-6440	221	13	,	,	PUNCT
ejpam-6440	221	14	the	the	DET
ejpam-6440	221	15	iteration	iteration	NOUN
ejpam-6440	221	16	converges	converge	VERB
ejpam-6440	221	17	to	to	ADP
ejpam-6440	221	18	the	the	DET
ejpam-6440	221	19	unique	unique	ADJ
ejpam-6440	221	20	optimal	optimal	ADJ
ejpam-6440	221	21	weight	weight	NOUN
ejpam-6440	221	22	w∗.	w∗.	NOUN
ejpam-6440	221	23	practical	practical	ADJ
ejpam-6440	221	24	implementation	implementation	NOUN
ejpam-6440	221	25	the	the	DET
ejpam-6440	221	26	mr	mr	PROPN
ejpam-6440	221	27	-	-	PUNCT
ejpam-6440	221	28	metric	metric	ADJ
ejpam-6440	221	29	formulation	formulation	NOUN
ejpam-6440	221	30	suggests	suggest	VERB
ejpam-6440	221	31	:	:	PUNCT
ejpam-6440	221	32	•	•	NUM
ejpam-6440	221	33	adaptive	adaptive	ADJ
ejpam-6440	221	34	learning	learning	NOUN
ejpam-6440	221	35	rates	rate	NOUN
ejpam-6440	221	36	:	:	PUNCT
ejpam-6440	221	37	ηk	ηk	X
ejpam-6440	221	38	=	=	SYM
ejpam-6440	221	39	1	1	NUM
ejpam-6440	221	40	3rlk	3rlk	NUM
ejpam-6440	221	41	where	where	SCONJ
ejpam-6440	221	42	lk	lk	PROPN
ejpam-6440	221	43	is	be	AUX
ejpam-6440	221	44	the	the	DET
ejpam-6440	221	45	local	local	ADJ
ejpam-6440	221	46	lipschitz	lipschitz	NOUN
ejpam-6440	221	47	estimate	estimate	NOUN
ejpam-6440	221	48	at	at	ADP
ejpam-6440	221	49	iteration	iteration	NOUN
ejpam-6440	221	50	k	k	PROPN
ejpam-6440	221	51	•	•	NOUN
ejpam-6440	221	52	batch	batch	NOUN
ejpam-6440	221	53	-	-	PUNCT
ejpam-6440	221	54	wise	wise	ADJ
ejpam-6440	221	55	contraction	contraction	NOUN
ejpam-6440	221	56	:	:	PUNCT
ejpam-6440	221	57	for	for	ADP
ejpam-6440	221	58	mini	mini	NOUN
ejpam-6440	221	59	-	-	NOUN
ejpam-6440	221	60	batch	batch	NOUN
ejpam-6440	221	61	b	b	NOUN
ejpam-6440	221	62	with	with	ADP
ejpam-6440	221	63	estimated	estimate	VERB
ejpam-6440	221	64	lipschitz	lipschitz	NOUN
ejpam-6440	221	65	constant	constant	ADJ
ejpam-6440	221	66	lb	lb	NOUN
ejpam-6440	221	67	,	,	PUNCT
ejpam-6440	221	68	use	use	NOUN
ejpam-6440	221	69	:	:	PUNCT
ejpam-6440	221	70	ηb	ηb	NOUN
ejpam-6440	221	71	=	=	SYM
ejpam-6440	221	72	1	1	NUM
ejpam-6440	221	73	3rlb	3rlb	NUM
ejpam-6440	221	74	•	•	NOUN
ejpam-6440	221	75	layer	layer	NOUN
ejpam-6440	221	76	-	-	PUNCT
ejpam-6440	221	77	wise	wise	ADJ
ejpam-6440	221	78	metrics	metric	NOUN
ejpam-6440	221	79	:	:	PUNCT
ejpam-6440	221	80	different	different	ADJ
ejpam-6440	221	81	mr	mr	PROPN
ejpam-6440	221	82	-	-	PUNCT
ejpam-6440	221	83	constants	constant	NOUN
ejpam-6440	221	84	rℓ	rℓ	NOUN
ejpam-6440	221	85	per	per	ADP
ejpam-6440	221	86	network	network	NOUN
ejpam-6440	221	87	layer	layer	NOUN
ejpam-6440	221	88	ℓ	ℓ	NOUN
ejpam-6440	221	89	:	:	PUNCT
ejpam-6440	221	90	ηℓ	ηℓ	X
ejpam-6440	221	91	=	=	SYM
ejpam-6440	221	92	1	1	NUM
ejpam-6440	221	93	3rℓlℓ	3rℓlℓ	NUM
ejpam-6440	221	94	comparison	comparison	NOUN
ejpam-6440	221	95	with	with	ADP
ejpam-6440	221	96	euclidean	euclidean	ADJ
ejpam-6440	221	97	metrics	metric	NOUN
ejpam-6440	221	98	table	table	NOUN
ejpam-6440	221	99	1	1	NUM
ejpam-6440	221	100	:	:	PUNCT
ejpam-6440	221	101	convergence	convergence	NOUN
ejpam-6440	221	102	properties	property	NOUN
ejpam-6440	221	103	in	in	ADP
ejpam-6440	221	104	different	different	ADJ
ejpam-6440	221	105	metrics	metric	NOUN
ejpam-6440	221	106	metric	metric	ADJ
ejpam-6440	221	107	condition	condition	NOUN
ejpam-6440	221	108	rate	rate	NOUN
ejpam-6440	221	109	euclidean	euclidean	PROPN
ejpam-6440	221	110	η	η	PROPN
ejpam-6440	221	111	<	<	PROPN
ejpam-6440	221	112	2	2	NUM
ejpam-6440	221	113	/	/	SYM
ejpam-6440	221	114	l	l	NOUN
ejpam-6440	221	115	linear	linear	PROPN
ejpam-6440	221	116	mr	mr	PROPN
ejpam-6440	221	117	-	-	PUNCT
ejpam-6440	221	118	metric	metric	ADJ
ejpam-6440	221	119	η	η	PROPN
ejpam-6440	221	120	<	<	X
ejpam-6440	221	121	1/(3rl	1/(3rl	NUM
ejpam-6440	221	122	)	)	PUNCT
ejpam-6440	221	123	linear	linear	ADJ
ejpam-6440	221	124	t.	t.	NOUN
ejpam-6440	221	125	qawasmeh	qawasmeh	NOUN
ejpam-6440	221	126	,	,	PUNCT
ejpam-6440	221	127	a.	a.	NOUN
ejpam-6440	221	128	malkawi	malkawi	PROPN
ejpam-6440	221	129	/	/	SYM
ejpam-6440	221	130	eur	eur	PROPN
ejpam-6440	221	131	.	.	PUNCT
ejpam-6440	222	1	j.	j.	PROPN
ejpam-6440	222	2	pure	pure	PROPN
ejpam-6440	222	3	appl	appl	PROPN
ejpam-6440	222	4	.	.	PROPN
ejpam-6440	222	5	math	math	PROPN
ejpam-6440	222	6	,	,	PUNCT
ejpam-6440	222	7	18	18	NUM
ejpam-6440	222	8	(	(	PUNCT
ejpam-6440	222	9	3	3	NUM
ejpam-6440	222	10	)	)	PUNCT
ejpam-6440	222	11	(	(	PUNCT
ejpam-6440	222	12	2025	2025	NUM
ejpam-6440	222	13	)	)	PUNCT
ejpam-6440	222	14	,	,	PUNCT
ejpam-6440	222	15	6440	6440	NUM
ejpam-6440	222	16	14	14	NUM
ejpam-6440	222	17	of	of	ADP
ejpam-6440	222	18	20	20	NUM
ejpam-6440	222	19	extension	extension	NOUN
ejpam-6440	222	20	to	to	ADP
ejpam-6440	222	21	momentum	momentum	NOUN
ejpam-6440	222	22	methods	method	NOUN
ejpam-6440	222	23	the	the	DET
ejpam-6440	222	24	mr	mr	PROPN
ejpam-6440	222	25	-	-	PUNCT
ejpam-6440	222	26	metric	metric	ADJ
ejpam-6440	222	27	framework	framework	NOUN
ejpam-6440	222	28	can	can	AUX
ejpam-6440	222	29	be	be	AUX
ejpam-6440	222	30	extended	extend	VERB
ejpam-6440	222	31	to	to	ADP
ejpam-6440	222	32	momentum	momentum	NOUN
ejpam-6440	222	33	updates	update	NOUN
ejpam-6440	222	34	:	:	PUNCT
ejpam-6440	222	35	vn+1	vn+1	SYM
ejpam-6440	222	36	=	=	PUNCT
ejpam-6440	222	37	βvn	βvn	ADV
ejpam-6440	222	38	−	−	ADP
ejpam-6440	222	39	η∇l(wn	η∇l(wn	NOUN
ejpam-6440	222	40	)	)	PUNCT
ejpam-6440	222	41	wn+1	wn+1	NOUN
ejpam-6440	222	42	=	=	SYM
ejpam-6440	222	43	wn	wn	PROPN
ejpam-6440	222	44	+	+	CCONJ
ejpam-6440	222	45	vn+1	vn+1	PROPN
ejpam-6440	222	46	with	with	ADP
ejpam-6440	222	47	contraction	contraction	NOUN
ejpam-6440	222	48	condition	condition	NOUN
ejpam-6440	222	49	:	:	PUNCT
ejpam-6440	222	50	√	√	PROPN
ejpam-6440	223	1	β2	β2	NOUN
ejpam-6440	223	2	+	+	CCONJ
ejpam-6440	223	3	3ηl	3ηl	ADJ
ejpam-6440	223	4	<	<	X
ejpam-6440	223	5	1	1	NUM
ejpam-6440	223	6	r	r	NOUN
ejpam-6440	223	7	3.2	3.2	NUM
ejpam-6440	223	8	.	.	PUNCT
ejpam-6440	224	1	fredholm	fredholm	VERB
ejpam-6440	224	2	integral	integral	ADJ
ejpam-6440	224	3	equations	equation	NOUN
ejpam-6440	224	4	example	example	NOUN
ejpam-6440	224	5	2	2	NUM
ejpam-6440	224	6	(	(	PUNCT
ejpam-6440	224	7	volterra	volterra	NOUN
ejpam-6440	224	8	equation	equation	NOUN
ejpam-6440	224	9	)	)	PUNCT
ejpam-6440	224	10	.	.	PUNCT
ejpam-6440	225	1	let	let	VERB
ejpam-6440	225	2	x	x	SYM
ejpam-6440	225	3	=	=	SYM
ejpam-6440	225	4	c([0	c([0	PROPN
ejpam-6440	225	5	,	,	PUNCT
ejpam-6440	225	6	1	1	NUM
ejpam-6440	225	7	]	]	PUNCT
ejpam-6440	225	8	)	)	PUNCT
ejpam-6440	225	9	with	with	ADP
ejpam-6440	225	10	:	:	PUNCT
ejpam-6440	225	11	m(f	m(f	PROPN
ejpam-6440	225	12	,	,	PUNCT
ejpam-6440	225	13	g	g	PROPN
ejpam-6440	225	14	,	,	PUNCT
ejpam-6440	225	15	h	h	NOUN
ejpam-6440	225	16	)	)	PUNCT
ejpam-6440	225	17	=	=	SYM
ejpam-6440	225	18	sup	sup	NOUN
ejpam-6440	225	19	x∈[0,1	x∈[0,1	PROPN
ejpam-6440	225	20	]	]	X
ejpam-6440	225	21	(	(	PUNCT
ejpam-6440	225	22	|f(x)−	|f(x)−	NOUN
ejpam-6440	225	23	g(x)|+	g(x)|+	PROPN
ejpam-6440	225	24	|f(x)−	|f(x)−	PROPN
ejpam-6440	225	25	h(x)|+	h(x)|+	PROPN
ejpam-6440	225	26	|g(x)−	|g(x)−	PROPN
ejpam-6440	225	27	h(x)|	h(x)|	NOUN
ejpam-6440	225	28	)	)	PUNCT
ejpam-6440	225	29	.	.	PUNCT
ejpam-6440	226	1	consider	consider	VERB
ejpam-6440	226	2	:	:	PUNCT
ejpam-6440	226	3	f(x	f(x	PROPN
ejpam-6440	226	4	)	)	PUNCT
ejpam-6440	226	5	=	=	PUNCT
ejpam-6440	227	1	0.05	0.05	NUM
ejpam-6440	227	2	∫	∫	NOUN
ejpam-6440	227	3	1	1	NUM
ejpam-6440	227	4	0	0	NUM
ejpam-6440	227	5	e−xy	e−xy	PROPN
ejpam-6440	227	6	sin(f(y))dy	sin(f(y))dy	PROPN
ejpam-6440	227	7	+	+	CCONJ
ejpam-6440	227	8	x2	x2	PROPN
ejpam-6440	227	9	.	.	PUNCT
ejpam-6440	228	1	here	here	ADV
ejpam-6440	228	2	:	:	PUNCT
ejpam-6440	228	3	•	•	NUM
ejpam-6440	228	4	k(x	k(x	PROPN
ejpam-6440	228	5	,	,	PUNCT
ejpam-6440	228	6	y	y	PROPN
ejpam-6440	228	7	,	,	PUNCT
ejpam-6440	228	8	f(y	f(y	NOUN
ejpam-6440	228	9	)	)	PUNCT
ejpam-6440	228	10	)	)	PUNCT
ejpam-6440	229	1	=	=	SYM
ejpam-6440	229	2	e−xy	e−xy	ADJ
ejpam-6440	229	3	sin(f(y	sin(f(y	NOUN
ejpam-6440	229	4	)	)	PUNCT
ejpam-6440	229	5	)	)	PUNCT
ejpam-6440	229	6	has	have	VERB
ejpam-6440	229	7	l	l	NOUN
ejpam-6440	229	8	=	=	SYM
ejpam-6440	229	9	1	1	NUM
ejpam-6440	229	10	•	•	NOUN
ejpam-6440	229	11	for	for	ADP
ejpam-6440	229	12	r	r	NOUN
ejpam-6440	229	13	=	=	SYM
ejpam-6440	229	14	1.1	1.1	NUM
ejpam-6440	229	15	,	,	PUNCT
ejpam-6440	229	16	λl	λl	ADV
ejpam-6440	229	17	=	=	NOUN
ejpam-6440	229	18	0.05	0.05	NUM
ejpam-6440	229	19	<	<	NOUN
ejpam-6440	229	20	1	1	NUM
ejpam-6440	229	21	3.3	3.3	NUM
ejpam-6440	229	22	≈	≈	PROPN
ejpam-6440	229	23	0.303	0.303	NUM
ejpam-6440	229	24	theorem	theorem	ADJ
ejpam-6440	229	25	2	2	NUM
ejpam-6440	229	26	guarantees	guarantee	VERB
ejpam-6440	229	27	a	a	DET
ejpam-6440	229	28	unique	unique	ADJ
ejpam-6440	229	29	solution	solution	NOUN
ejpam-6440	229	30	.	.	PUNCT
ejpam-6440	230	1	application	application	NOUN
ejpam-6440	230	2	2	2	NUM
ejpam-6440	230	3	(	(	PUNCT
ejpam-6440	230	4	neutron	neutron	NOUN
ejpam-6440	230	5	transport	transport	NOUN
ejpam-6440	230	6	theory	theory	NOUN
ejpam-6440	230	7	in	in	ADP
ejpam-6440	230	8	mr	mr	PROPN
ejpam-6440	230	9	-	-	PUNCT
ejpam-6440	230	10	metric	metric	ADJ
ejpam-6440	230	11	spaces	space	NOUN
ejpam-6440	230	12	)	)	PUNCT
ejpam-6440	230	13	.	.	PUNCT
ejpam-6440	231	1	physical	physical	ADJ
ejpam-6440	231	2	model	model	NOUN
ejpam-6440	231	3	formulation	formulation	NOUN
ejpam-6440	231	4	the	the	DET
ejpam-6440	231	5	steady	steady	ADJ
ejpam-6440	231	6	-	-	PUNCT
ejpam-6440	231	7	state	state	NOUN
ejpam-6440	231	8	neutron	neutron	NOUN
ejpam-6440	231	9	transport	transport	NOUN
ejpam-6440	231	10	in	in	ADP
ejpam-6440	231	11	a	a	DET
ejpam-6440	231	12	homogeneous	homogeneous	ADJ
ejpam-6440	231	13	medium	medium	NOUN
ejpam-6440	231	14	is	be	AUX
ejpam-6440	231	15	governed	govern	VERB
ejpam-6440	231	16	by	by	ADP
ejpam-6440	231	17	the	the	DET
ejpam-6440	231	18	linear	linear	ADJ
ejpam-6440	231	19	boltzmann	boltzmann	PROPN
ejpam-6440	231	20	equation	equation	NOUN
ejpam-6440	231	21	:	:	PUNCT
ejpam-6440	231	22	µ	µ	PRON
ejpam-6440	231	23	∂ψ(x	∂ψ(x	NOUN
ejpam-6440	231	24	,	,	PUNCT
ejpam-6440	231	25	µ	µ	NOUN
ejpam-6440	231	26	)	)	PUNCT
ejpam-6440	231	27	∂x	∂x	PROPN
ejpam-6440	232	1	+	+	ADP
ejpam-6440	232	2	σt(x)ψ(x	σt(x)ψ(x	PROPN
ejpam-6440	232	3	,	,	PUNCT
ejpam-6440	232	4	µ	µ	NOUN
ejpam-6440	232	5	)	)	PUNCT
ejpam-6440	232	6	=	=	SYM
ejpam-6440	232	7	∫	∫	PROPN
ejpam-6440	232	8	1	1	NUM
ejpam-6440	232	9	−1	−1	NOUN
ejpam-6440	232	10	σs(x	σs(x	NOUN
ejpam-6440	232	11	,	,	PUNCT
ejpam-6440	232	12	µ	µ	PRON
ejpam-6440	232	13	′	′	NUM
ejpam-6440	232	14	→	→	SYM
ejpam-6440	232	15	µ)ψ(x	µ)ψ(x	ADJ
ejpam-6440	232	16	,	,	PUNCT
ejpam-6440	232	17	µ′)dµ′	µ′)dµ′	NOUN
ejpam-6440	232	18	+	+	X
ejpam-6440	232	19	s(x	s(x	PROPN
ejpam-6440	232	20	,	,	PUNCT
ejpam-6440	232	21	µ	µ	NOUN
ejpam-6440	232	22	)	)	PUNCT
ejpam-6440	232	23	(	(	PUNCT
ejpam-6440	232	24	1	1	X
ejpam-6440	232	25	)	)	PUNCT
ejpam-6440	233	1	where	where	SCONJ
ejpam-6440	233	2	:	:	PUNCT
ejpam-6440	233	3	•	•	NUM
ejpam-6440	233	4	ψ(x	ψ(x	PROPN
ejpam-6440	233	5	,	,	PUNCT
ejpam-6440	233	6	µ	µ	NOUN
ejpam-6440	233	7	)	)	PUNCT
ejpam-6440	233	8	is	be	AUX
ejpam-6440	233	9	the	the	DET
ejpam-6440	233	10	angular	angular	ADJ
ejpam-6440	233	11	neutron	neutron	NOUN
ejpam-6440	233	12	flux	flux	NOUN
ejpam-6440	233	13	•	•	NUM
ejpam-6440	233	14	σt(x	σt(x	PUNCT
ejpam-6440	233	15	)	)	PUNCT
ejpam-6440	234	1	is	be	AUX
ejpam-6440	234	2	the	the	DET
ejpam-6440	234	3	total	total	ADJ
ejpam-6440	234	4	cross	cross	NOUN
ejpam-6440	234	5	-	-	NOUN
ejpam-6440	234	6	section	section	ADJ
ejpam-6440	234	7	•	•	NOUN
ejpam-6440	234	8	σs(x	σs(x	NOUN
ejpam-6440	234	9	,	,	PUNCT
ejpam-6440	234	10	µ	µ	X
ejpam-6440	234	11	′	′	NUM
ejpam-6440	234	12	→	→	SYM
ejpam-6440	234	13	µ	µ	X
ejpam-6440	234	14	)	)	PUNCT
ejpam-6440	234	15	is	be	AUX
ejpam-6440	234	16	the	the	DET
ejpam-6440	234	17	differential	differential	ADJ
ejpam-6440	234	18	scattering	scatter	VERB
ejpam-6440	234	19	cross	cross	NOUN
ejpam-6440	234	20	-	-	NOUN
ejpam-6440	234	21	section	section	ADJ
ejpam-6440	234	22	•	•	NOUN
ejpam-6440	234	23	s(x	s(x	PROPN
ejpam-6440	234	24	,	,	PUNCT
ejpam-6440	234	25	µ	µ	NOUN
ejpam-6440	234	26	)	)	PUNCT
ejpam-6440	235	1	is	be	AUX
ejpam-6440	235	2	the	the	DET
ejpam-6440	235	3	neutron	neutron	NOUN
ejpam-6440	235	4	source	source	NOUN
ejpam-6440	235	5	t.	t.	PROPN
ejpam-6440	235	6	qawasmeh	qawasmeh	NOUN
ejpam-6440	235	7	,	,	PUNCT
ejpam-6440	235	8	a.	a.	NOUN
ejpam-6440	235	9	malkawi	malkawi	PROPN
ejpam-6440	235	10	/	/	SYM
ejpam-6440	235	11	eur	eur	PROPN
ejpam-6440	235	12	.	.	PUNCT
ejpam-6440	236	1	j.	j.	PROPN
ejpam-6440	236	2	pure	pure	PROPN
ejpam-6440	236	3	appl	appl	PROPN
ejpam-6440	236	4	.	.	PROPN
ejpam-6440	236	5	math	math	PROPN
ejpam-6440	236	6	,	,	PUNCT
ejpam-6440	236	7	18	18	NUM
ejpam-6440	236	8	(	(	PUNCT
ejpam-6440	236	9	3	3	NUM
ejpam-6440	236	10	)	)	PUNCT
ejpam-6440	236	11	(	(	PUNCT
ejpam-6440	236	12	2025	2025	NUM
ejpam-6440	236	13	)	)	PUNCT
ejpam-6440	236	14	,	,	PUNCT
ejpam-6440	236	15	6440	6440	NUM
ejpam-6440	236	16	15	15	NUM
ejpam-6440	236	17	of	of	ADP
ejpam-6440	236	18	20	20	NUM
ejpam-6440	236	19	integral	integral	ADJ
ejpam-6440	236	20	equation	equation	NOUN
ejpam-6440	236	21	formulation	formulation	NOUN
ejpam-6440	236	22	under	under	ADP
ejpam-6440	236	23	isotropic	isotropic	NOUN
ejpam-6440	236	24	scattering	scattering	NOUN
ejpam-6440	236	25	and	and	CCONJ
ejpam-6440	236	26	plane	plane	NOUN
ejpam-6440	236	27	symmetry	symmetry	NOUN
ejpam-6440	236	28	,	,	PUNCT
ejpam-6440	236	29	we	we	PRON
ejpam-6440	236	30	obtain	obtain	VERB
ejpam-6440	236	31	the	the	DET
ejpam-6440	236	32	peierls	peierl	NOUN
ejpam-6440	236	33	integral	integral	ADJ
ejpam-6440	236	34	equation	equation	NOUN
ejpam-6440	236	35	:	:	PUNCT
ejpam-6440	236	36	ϕ(x	ϕ(x	X
ejpam-6440	236	37	)	)	PUNCT
ejpam-6440	236	38	=	=	PUNCT
ejpam-6440	237	1	λ	λ	X
ejpam-6440	237	2	∫	∫	PROPN
ejpam-6440	237	3	1	1	NUM
ejpam-6440	237	4	0	0	NUM
ejpam-6440	237	5	k(x	k(x	PROPN
ejpam-6440	237	6	,	,	PUNCT
ejpam-6440	237	7	y)ϕ(y)dy	y)ϕ(y)dy	NOUN
ejpam-6440	237	8	+	+	SYM
ejpam-6440	237	9	s(x	s(x	NOUN
ejpam-6440	237	10	)	)	PUNCT
ejpam-6440	237	11	(	(	PUNCT
ejpam-6440	237	12	2	2	X
ejpam-6440	237	13	)	)	PUNCT
ejpam-6440	237	14	where	where	SCONJ
ejpam-6440	237	15	:	:	PUNCT
ejpam-6440	237	16	•	•	NUM
ejpam-6440	237	17	ϕ(x	ϕ(x	NOUN
ejpam-6440	237	18	)	)	PUNCT
ejpam-6440	237	19	=	=	SYM
ejpam-6440	238	1	∫	∫	PROPN
ejpam-6440	238	2	1	1	NUM
ejpam-6440	238	3	−1	−1	NOUN
ejpam-6440	238	4	ψ(x	ψ(x	PROPN
ejpam-6440	238	5	,	,	PUNCT
ejpam-6440	238	6	µ)dµ	µ)dµ	PROPN
ejpam-6440	238	7	is	be	AUX
ejpam-6440	238	8	the	the	DET
ejpam-6440	238	9	scalar	scalar	ADJ
ejpam-6440	238	10	flux	flux	NOUN
ejpam-6440	238	11	•	•	ADP
ejpam-6440	238	12	k(x	k(x	PROPN
ejpam-6440	238	13	,	,	PUNCT
ejpam-6440	238	14	y	y	NOUN
ejpam-6440	238	15	)	)	PUNCT
ejpam-6440	238	16	=	=	SYM
ejpam-6440	238	17	1	1	NUM
ejpam-6440	238	18	2e1(|x−	2e1(|x−	NUM
ejpam-6440	238	19	y|	y|	NOUN
ejpam-6440	238	20	)	)	PUNCT
ejpam-6440	238	21	is	be	AUX
ejpam-6440	238	22	the	the	DET
ejpam-6440	238	23	transport	transport	NOUN
ejpam-6440	238	24	kernel	kernel	PROPN
ejpam-6440	238	25	•	•	ADP
ejpam-6440	238	26	e1(z	e1(z	PROPN
ejpam-6440	238	27	)	)	PUNCT
ejpam-6440	238	28	=	=	PUNCT
ejpam-6440	238	29	∫∞	∫∞	NOUN
ejpam-6440	238	30	1	1	NUM
ejpam-6440	238	31	e−zt	e−zt	PROPN
ejpam-6440	238	32	t	t	PROPN
ejpam-6440	238	33	dt	dt	NOUN
ejpam-6440	238	34	is	be	AUX
ejpam-6440	238	35	the	the	DET
ejpam-6440	238	36	exponential	exponential	ADJ
ejpam-6440	238	37	integral	integral	ADJ
ejpam-6440	238	38	•	•	NOUN
ejpam-6440	238	39	λ	λ	X
ejpam-6440	238	40	=	=	SYM
ejpam-6440	238	41	σs	σs	PROPN
ejpam-6440	238	42	/	/	SYM
ejpam-6440	238	43	σt	σt	NOUN
ejpam-6440	238	44	is	be	AUX
ejpam-6440	238	45	the	the	DET
ejpam-6440	238	46	scattering	scatter	VERB
ejpam-6440	238	47	ratio	ratio	NOUN
ejpam-6440	238	48	mr	mr	PROPN
ejpam-6440	238	49	-	-	PUNCT
ejpam-6440	238	50	metric	metric	ADJ
ejpam-6440	238	51	framework	framework	NOUN
ejpam-6440	238	52	define	define	VERB
ejpam-6440	238	53	the	the	DET
ejpam-6440	238	54	mr	mr	NOUN
ejpam-6440	238	55	-	-	PUNCT
ejpam-6440	238	56	metric	metric	NOUN
ejpam-6440	238	57	on	on	ADP
ejpam-6440	238	58	c([0	c([0	NOUN
ejpam-6440	238	59	,	,	PUNCT
ejpam-6440	238	60	1	1	NUM
ejpam-6440	238	61	]	]	PUNCT
ejpam-6440	238	62	):	):	PUNCT
ejpam-6440	238	63	m(ϕ1	m(ϕ1	ADJ
ejpam-6440	238	64	,	,	PUNCT
ejpam-6440	238	65	ϕ2	ϕ2	ADV
ejpam-6440	238	66	,	,	PUNCT
ejpam-6440	238	67	ϕ3	ϕ3	PROPN
ejpam-6440	238	68	)	)	PUNCT
ejpam-6440	239	1	=	=	SYM
ejpam-6440	239	2	sup	sup	NOUN
ejpam-6440	239	3	x∈[0,1	x∈[0,1	PROPN
ejpam-6440	239	4	]	]	X
ejpam-6440	239	5	(	(	PUNCT
ejpam-6440	239	6	|ϕ1(x)−	|ϕ1(x)−	PROPN
ejpam-6440	239	7	ϕ2(x)|+	ϕ2(x)|+	PROPN
ejpam-6440	240	1	|phi1(x)−	|phi1(x)−	PROPN
ejpam-6440	240	2	ϕ3(x)|+	ϕ3(x)|+	ADJ
ejpam-6440	240	3	|phi2(x)−	|phi2(x)−	PROPN
ejpam-6440	240	4	ϕ3(x)|	ϕ3(x)|	PROPN
ejpam-6440	240	5	)	)	PUNCT
ejpam-6440	240	6	(	(	PUNCT
ejpam-6440	240	7	3	3	X
ejpam-6440	240	8	)	)	PUNCT
ejpam-6440	240	9	the	the	DET
ejpam-6440	240	10	neutron	neutron	NOUN
ejpam-6440	240	11	transport	transport	NOUN
ejpam-6440	240	12	operator	operator	NOUN
ejpam-6440	240	13	t	t	PROPN
ejpam-6440	240	14	:	:	PUNCT
ejpam-6440	240	15	c([0	c([0	NOUN
ejpam-6440	240	16	,	,	PUNCT
ejpam-6440	240	17	1	1	NUM
ejpam-6440	240	18	]	]	PUNCT
ejpam-6440	240	19	)	)	PUNCT
ejpam-6440	240	20	→	→	SYM
ejpam-6440	240	21	c([0	c([0	PROPN
ejpam-6440	240	22	,	,	PUNCT
ejpam-6440	240	23	1	1	NUM
ejpam-6440	240	24	]	]	PUNCT
ejpam-6440	240	25	):	):	PUNCT
ejpam-6440	240	26	tϕ(x	tϕ(x	X
ejpam-6440	240	27	)	)	PUNCT
ejpam-6440	241	1	=	=	PUNCT
ejpam-6440	241	2	λ	λ	X
ejpam-6440	241	3	∫	∫	PROPN
ejpam-6440	241	4	1	1	NUM
ejpam-6440	241	5	0	0	NUM
ejpam-6440	241	6	k(x	k(x	PROPN
ejpam-6440	241	7	,	,	PUNCT
ejpam-6440	241	8	y)ϕ(y)dy	y)ϕ(y)dy	NOUN
ejpam-6440	241	9	+	+	SYM
ejpam-6440	241	10	s(x	s(x	NOUN
ejpam-6440	241	11	)	)	PUNCT
ejpam-6440	241	12	(	(	PUNCT
ejpam-6440	241	13	4	4	X
ejpam-6440	241	14	)	)	PUNCT
ejpam-6440	241	15	contraction	contraction	NOUN
ejpam-6440	241	16	conditions	condition	NOUN
ejpam-6440	241	17	theorem	theorem	VERB
ejpam-6440	241	18	5	5	NUM
ejpam-6440	241	19	(	(	PUNCT
ejpam-6440	241	20	existence	existence	NOUN
ejpam-6440	241	21	and	and	CCONJ
ejpam-6440	241	22	uniqueness	uniqueness	NOUN
ejpam-6440	241	23	)	)	PUNCT
ejpam-6440	241	24	.	.	PUNCT
ejpam-6440	242	1	for	for	ADP
ejpam-6440	242	2	the	the	DET
ejpam-6440	242	3	transport	transport	NOUN
ejpam-6440	242	4	operator	operator	NOUN
ejpam-6440	242	5	t	t	NOUN
ejpam-6440	242	6	,	,	PUNCT
ejpam-6440	242	7	if	if	SCONJ
ejpam-6440	242	8	:	:	PUNCT
ejpam-6440	242	9	(	(	PUNCT
ejpam-6440	242	10	i	i	NOUN
ejpam-6440	242	11	)	)	PUNCT
ejpam-6440	242	12	the	the	DET
ejpam-6440	242	13	kernel	kernel	PROPN
ejpam-6440	242	14	satisfies	satisfy	VERB
ejpam-6440	242	15	supx	supx	PROPN
ejpam-6440	242	16	∫	∫	PROPN
ejpam-6440	242	17	1	1	NUM
ejpam-6440	242	18	0	0	NUM
ejpam-6440	242	19	|k(x	|k(x	NOUN
ejpam-6440	242	20	,	,	PUNCT
ejpam-6440	242	21	y)|dy	y)|dy	NOUN
ejpam-6440	242	22	≤	≤	NOUN
ejpam-6440	242	23	∥k∥	∥k∥	ADV
ejpam-6440	242	24	<	<	X
ejpam-6440	242	25	∞	∞	PROPN
ejpam-6440	242	26	(	(	PUNCT
ejpam-6440	242	27	ii	ii	NOUN
ejpam-6440	242	28	)	)	PUNCT
ejpam-6440	242	29	the	the	DET
ejpam-6440	242	30	scattering	scatter	VERB
ejpam-6440	242	31	ratio	ratio	NOUN
ejpam-6440	242	32	satisfies	satisfie	NOUN
ejpam-6440	242	33	|λ|	|λ|	VERB
ejpam-6440	242	34	<	<	X
ejpam-6440	242	35	1	1	NUM
ejpam-6440	242	36	3r∥k∥	3r∥k∥	NUM
ejpam-6440	242	37	then	then	ADV
ejpam-6440	242	38	there	there	PRON
ejpam-6440	242	39	exists	exist	VERB
ejpam-6440	242	40	a	a	DET
ejpam-6440	242	41	unique	unique	ADJ
ejpam-6440	242	42	solution	solution	NOUN
ejpam-6440	242	43	ϕ∗	ϕ∗	PROPN
ejpam-6440	242	44	∈	∈	PROPN
ejpam-6440	242	45	c([0	c([0	NOUN
ejpam-6440	242	46	,	,	PUNCT
ejpam-6440	242	47	1	1	NUM
ejpam-6440	242	48	]	]	PUNCT
ejpam-6440	242	49	)	)	PUNCT
ejpam-6440	242	50	to	to	ADP
ejpam-6440	242	51	the	the	DET
ejpam-6440	242	52	transport	transport	NOUN
ejpam-6440	242	53	equation	equation	NOUN
ejpam-6440	242	54	.	.	PUNCT
ejpam-6440	243	1	proof	proof	NOUN
ejpam-6440	243	2	.	.	PUNCT
ejpam-6440	244	1	for	for	ADP
ejpam-6440	244	2	any	any	DET
ejpam-6440	244	3	ϕ1	ϕ1	NOUN
ejpam-6440	244	4	,	,	PUNCT
ejpam-6440	244	5	ϕ2	ϕ2	ADV
ejpam-6440	244	6	,	,	PUNCT
ejpam-6440	244	7	ϕ3	ϕ3	PROPN
ejpam-6440	244	8	∈	∈	PROPN
ejpam-6440	244	9	c([0	c([0	NOUN
ejpam-6440	244	10	,	,	PUNCT
ejpam-6440	244	11	1	1	NUM
ejpam-6440	244	12	]	]	PUNCT
ejpam-6440	244	13	):	):	PUNCT
ejpam-6440	244	14	m(tϕ1	m(tϕ1	ADJ
ejpam-6440	244	15	,	,	PUNCT
ejpam-6440	244	16	tϕ2	tϕ2	PROPN
ejpam-6440	244	17	,	,	PUNCT
ejpam-6440	244	18	tϕ3	tϕ3	PROPN
ejpam-6440	244	19	)	)	PUNCT
ejpam-6440	245	1	=	=	SYM
ejpam-6440	245	2	sup	sup	NOUN
ejpam-6440	245	3	x	x	SYM
ejpam-6440	245	4	(	(	PUNCT
ejpam-6440	245	5	|λ	|λ	ADV
ejpam-6440	245	6	∫	∫	PROPN
ejpam-6440	245	7	k(x	k(x	PROPN
ejpam-6440	245	8	,	,	PUNCT
ejpam-6440	245	9	y)(ϕ1	y)(ϕ1	ADP
ejpam-6440	245	10	−	−	PROPN
ejpam-6440	245	11	ϕ2)dy|+	ϕ2)dy|+	PROPN
ejpam-6440	245	12	·	·	PUNCT
ejpam-6440	245	13	·	·	PUNCT
ejpam-6440	245	14	·	·	PUNCT
ejpam-6440	245	15	)	)	PUNCT
ejpam-6440	246	1	≤	≤	NOUN
ejpam-6440	246	2	3|λ|∥k∥m(ϕ1	3|λ|∥k∥m(ϕ1	NUM
ejpam-6440	246	3	,	,	PUNCT
ejpam-6440	246	4	ϕ2	ϕ2	ADV
ejpam-6440	246	5	,	,	PUNCT
ejpam-6440	246	6	ϕ3	ϕ3	PROPN
ejpam-6440	246	7	)	)	PUNCT
ejpam-6440	246	8	<	<	X
ejpam-6440	246	9	1	1	NUM
ejpam-6440	246	10	r	r	NOUN
ejpam-6440	246	11	m(ϕ1	m(ϕ1	NOUN
ejpam-6440	246	12	,	,	PUNCT
ejpam-6440	246	13	ϕ2	ϕ2	ADV
ejpam-6440	246	14	,	,	PUNCT
ejpam-6440	246	15	ϕ3	ϕ3	PROPN
ejpam-6440	246	16	)	)	PUNCT
ejpam-6440	246	17	thus	thus	ADV
ejpam-6440	246	18	t	t	PROPN
ejpam-6440	246	19	is	be	AUX
ejpam-6440	246	20	a	a	DET
ejpam-6440	246	21	contraction	contraction	NOUN
ejpam-6440	246	22	in	in	ADP
ejpam-6440	246	23	the	the	DET
ejpam-6440	246	24	complete	complete	ADJ
ejpam-6440	246	25	mr	mr	PROPN
ejpam-6440	246	26	-	-	PUNCT
ejpam-6440	246	27	metric	metric	ADJ
ejpam-6440	246	28	space	space	NOUN
ejpam-6440	246	29	(	(	PUNCT
ejpam-6440	246	30	c([0	c([0	ADJ
ejpam-6440	246	31	,	,	PUNCT
ejpam-6440	246	32	1]),m	1]),m	NUM
ejpam-6440	246	33	)	)	PUNCT
ejpam-6440	246	34	.	.	PUNCT
ejpam-6440	247	1	t.	t.	NOUN
ejpam-6440	247	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	247	3	,	,	PUNCT
ejpam-6440	247	4	a.	a.	NOUN
ejpam-6440	247	5	malkawi	malkawi	PROPN
ejpam-6440	247	6	/	/	SYM
ejpam-6440	247	7	eur	eur	PROPN
ejpam-6440	247	8	.	.	PUNCT
ejpam-6440	248	1	j.	j.	PROPN
ejpam-6440	248	2	pure	pure	PROPN
ejpam-6440	248	3	appl	appl	PROPN
ejpam-6440	248	4	.	.	PROPN
ejpam-6440	248	5	math	math	PROPN
ejpam-6440	248	6	,	,	PUNCT
ejpam-6440	248	7	18	18	NUM
ejpam-6440	248	8	(	(	PUNCT
ejpam-6440	248	9	3	3	NUM
ejpam-6440	248	10	)	)	PUNCT
ejpam-6440	248	11	(	(	PUNCT
ejpam-6440	248	12	2025	2025	NUM
ejpam-6440	248	13	)	)	PUNCT
ejpam-6440	248	14	,	,	PUNCT
ejpam-6440	248	15	6440	6440	NUM
ejpam-6440	248	16	16	16	NUM
ejpam-6440	248	17	of	of	ADP
ejpam-6440	248	18	20	20	NUM
ejpam-6440	248	19	numerical	numerical	ADJ
ejpam-6440	248	20	implementation	implementation	NOUN
ejpam-6440	248	21	the	the	DET
ejpam-6440	248	22	iteration	iteration	NOUN
ejpam-6440	248	23	scheme	scheme	NOUN
ejpam-6440	248	24	:	:	PUNCT
ejpam-6440	248	25	ϕn+1(x	ϕn+1(x	NOUN
ejpam-6440	248	26	)	)	PUNCT
ejpam-6440	249	1	=	=	PUNCT
ejpam-6440	249	2	λ	λ	X
ejpam-6440	249	3	∫	∫	PROPN
ejpam-6440	249	4	1	1	NUM
ejpam-6440	249	5	0	0	NUM
ejpam-6440	249	6	k(x	k(x	PROPN
ejpam-6440	249	7	,	,	PUNCT
ejpam-6440	249	8	y)ϕn(y)dy	y)ϕn(y)dy	NOUN
ejpam-6440	249	9	+	+	SYM
ejpam-6440	249	10	s(x	s(x	NOUN
ejpam-6440	249	11	)	)	PUNCT
ejpam-6440	249	12	(	(	PUNCT
ejpam-6440	249	13	5	5	X
ejpam-6440	249	14	)	)	PUNCT
ejpam-6440	249	15	converges	converge	NOUN
ejpam-6440	249	16	with	with	ADP
ejpam-6440	249	17	error	error	NOUN
ejpam-6440	249	18	estimate	estimate	NOUN
ejpam-6440	249	19	:	:	PUNCT
ejpam-6440	249	20	m(ϕn	m(ϕn	PROPN
ejpam-6440	249	21	,	,	PUNCT
ejpam-6440	249	22	ϕ	ϕ	NOUN
ejpam-6440	249	23	∗	∗	NOUN
ejpam-6440	249	24	,	,	PUNCT
ejpam-6440	249	25	ϕ∗	ϕ∗	PROPN
ejpam-6440	249	26	)	)	PUNCT
ejpam-6440	249	27	≤	≤	NOUN
ejpam-6440	249	28	(	(	PUNCT
ejpam-6440	249	29	3r|λ|∥k∥)n	3r|λ|∥k∥)n	NUM
ejpam-6440	249	30	1−	1−	NUM
ejpam-6440	249	31	3r|λ|∥k∥	3r|λ|∥k∥	NUM
ejpam-6440	249	32	m(ϕ0	m(ϕ0	NOUN
ejpam-6440	249	33	,	,	PUNCT
ejpam-6440	249	34	ϕ1	ϕ1	NOUN
ejpam-6440	249	35	,	,	PUNCT
ejpam-6440	249	36	ϕ1	ϕ1	NOUN
ejpam-6440	249	37	)	)	PUNCT
ejpam-6440	249	38	(	(	PUNCT
ejpam-6440	249	39	6	6	X
ejpam-6440	249	40	)	)	PUNCT
ejpam-6440	249	41	physical	physical	ADJ
ejpam-6440	249	42	interpretation	interpretation	NOUN
ejpam-6440	249	43	table	table	NOUN
ejpam-6440	249	44	2	2	NUM
ejpam-6440	249	45	:	:	PUNCT
ejpam-6440	249	46	parameter	parameter	NOUN
ejpam-6440	249	47	constraints	constraint	NOUN
ejpam-6440	249	48	in	in	ADP
ejpam-6440	249	49	nuclear	nuclear	ADJ
ejpam-6440	249	50	applications	application	NOUN
ejpam-6440	249	51	material	material	NOUN
ejpam-6440	249	52	λ	λ	PROPN
ejpam-6440	249	53	range	range	VERB
ejpam-6440	249	54	mr	mr	ADJ
ejpam-6440	249	55	-	-	PUNCT
ejpam-6440	249	56	constant	constant	ADJ
ejpam-6440	249	57	r	r	NOUN
ejpam-6440	249	58	graphite	graphite	NOUN
ejpam-6440	249	59	0.8	0.8	NUM
ejpam-6440	249	60	-	-	SYM
ejpam-6440	249	61	0.9	0.9	NUM
ejpam-6440	249	62	1.2	1.2	NUM
ejpam-6440	249	63	heavy	heavy	ADJ
ejpam-6440	249	64	water	water	NOUN
ejpam-6440	249	65	0.6	0.6	NUM
ejpam-6440	249	66	-	-	SYM
ejpam-6440	249	67	0.8	0.8	NUM
ejpam-6440	249	68	1.1	1.1	NUM
ejpam-6440	249	69	beryllium	beryllium	NOUN
ejpam-6440	249	70	0.7	0.7	NUM
ejpam-6440	249	71	-	-	SYM
ejpam-6440	249	72	0.85	0.85	NUM
ejpam-6440	249	73	1.15	1.15	NUM
ejpam-6440	249	74	extensions	extension	NOUN
ejpam-6440	249	75	lemma	lemma	PROPN
ejpam-6440	249	76	4	4	NUM
ejpam-6440	249	77	(	(	PUNCT
ejpam-6440	249	78	anisotropic	anisotropic	NOUN
ejpam-6440	249	79	scattering	scattering	NOUN
ejpam-6440	249	80	)	)	PUNCT
ejpam-6440	249	81	.	.	PUNCT
ejpam-6440	250	1	for	for	ADP
ejpam-6440	250	2	legendre	legendre	PROPN
ejpam-6440	250	3	-	-	PUNCT
ejpam-6440	250	4	expanded	expand	VERB
ejpam-6440	250	5	scattering	scatter	VERB
ejpam-6440	250	6	k(x	k(x	PROPN
ejpam-6440	250	7	,	,	PUNCT
ejpam-6440	250	8	y	y	NOUN
ejpam-6440	250	9	)	)	PUNCT
ejpam-6440	250	10	=	=	PUNCT
ejpam-6440	251	1	∑l	∑l	PROPN
ejpam-6440	251	2	l=0	l=0	PROPN
ejpam-6440	251	3	2l+1	2l+1	PROPN
ejpam-6440	251	4	2	2	NUM
ejpam-6440	251	5	kl(x	kl(x	PROPN
ejpam-6440	251	6	,	,	PUNCT
ejpam-6440	251	7	y)pl(µ0	y)pl(µ0	NOUN
ejpam-6440	251	8	)	)	PUNCT
ejpam-6440	251	9	,	,	PUNCT
ejpam-6440	251	10	the	the	DET
ejpam-6440	251	11	contraction	contraction	NOUN
ejpam-6440	251	12	condition	condition	NOUN
ejpam-6440	251	13	becomes	become	VERB
ejpam-6440	251	14	:	:	PUNCT
ejpam-6440	251	15	|λ|	|λ|	X
ejpam-6440	251	16	<	<	X
ejpam-6440	251	17	(	(	PUNCT
ejpam-6440	251	18	3r	3r	NUM
ejpam-6440	251	19	l∑	l∑	PUNCT
ejpam-6440	251	20	l=0	l=0	PROPN
ejpam-6440	251	21	∥kl∥	∥kl∥	NOUN
ejpam-6440	251	22	)	)	PUNCT
ejpam-6440	251	23	−1	−1	NOUN
ejpam-6440	251	24	proof	proof	NOUN
ejpam-6440	251	25	.	.	PUNCT
ejpam-6440	252	1	for	for	ADP
ejpam-6440	252	2	the	the	DET
ejpam-6440	252	3	expanded	expand	VERB
ejpam-6440	252	4	kernel	kernel	NOUN
ejpam-6440	252	5	k(x	k(x	PROPN
ejpam-6440	252	6	,	,	PUNCT
ejpam-6440	252	7	y	y	NOUN
ejpam-6440	252	8	)	)	PUNCT
ejpam-6440	252	9	=	=	PUNCT
ejpam-6440	253	1	∑l	∑l	PROPN
ejpam-6440	253	2	l=0	l=0	PROPN
ejpam-6440	253	3	2l+1	2l+1	PROPN
ejpam-6440	253	4	2	2	NUM
ejpam-6440	253	5	kl(x	kl(x	PROPN
ejpam-6440	253	6	,	,	PUNCT
ejpam-6440	253	7	y)pl(µ0	y)pl(µ0	NOUN
ejpam-6440	253	8	)	)	PUNCT
ejpam-6440	253	9	,	,	PUNCT
ejpam-6440	253	10	we	we	PRON
ejpam-6440	253	11	estimate	estimate	VERB
ejpam-6440	253	12	:	:	PUNCT
ejpam-6440	253	13	m(tϕ1	m(tϕ1	ADJ
ejpam-6440	253	14	,	,	PUNCT
ejpam-6440	253	15	tϕ2	tϕ2	PROPN
ejpam-6440	253	16	,	,	PUNCT
ejpam-6440	253	17	tϕ3	tϕ3	PROPN
ejpam-6440	253	18	)	)	PUNCT
ejpam-6440	253	19	≤	≤	NUM
ejpam-6440	254	1	3|λ|	3|λ|	NUM
ejpam-6440	254	2	l∑	l∑	PUNCT
ejpam-6440	255	1	l=0	l=0	PROPN
ejpam-6440	255	2	∥kl∥m(ϕ1	∥kl∥m(ϕ1	NOUN
ejpam-6440	255	3	,	,	PUNCT
ejpam-6440	255	4	ϕ2	ϕ2	ADV
ejpam-6440	255	5	,	,	PUNCT
ejpam-6440	255	6	ϕ3	ϕ3	PROPN
ejpam-6440	255	7	)	)	PUNCT
ejpam-6440	255	8	thus	thus	ADV
ejpam-6440	255	9	the	the	DET
ejpam-6440	255	10	contraction	contraction	NOUN
ejpam-6440	255	11	condition	condition	NOUN
ejpam-6440	255	12	becomes	become	VERB
ejpam-6440	255	13	|λ|	|λ|	PROPN
ejpam-6440	255	14	<	<	X
ejpam-6440	255	15	(	(	PUNCT
ejpam-6440	255	16	3r	3r	NUM
ejpam-6440	255	17	∑l	∑l	VERB
ejpam-6440	255	18	l=0	l=0	PROPN
ejpam-6440	255	19	∥kl∥)−1	∥kl∥)−1	NOUN
ejpam-6440	255	20	.	.	PUNCT
ejpam-6440	255	21	3.3	3.3	NUM
ejpam-6440	255	22	.	.	PUNCT
ejpam-6440	256	1	krasnoselskii	krasnoselskii	PROPN
ejpam-6440	256	2	hybrid	hybrid	ADJ
ejpam-6440	256	3	fixed	fix	VERB
ejpam-6440	256	4	-	-	PUNCT
ejpam-6440	256	5	point	point	NOUN
ejpam-6440	256	6	theorem	theorem	ADJ
ejpam-6440	256	7	example	example	NOUN
ejpam-6440	256	8	3	3	NUM
ejpam-6440	256	9	(	(	PUNCT
ejpam-6440	256	10	hammerstein	hammerstein	NOUN
ejpam-6440	256	11	equation	equation	NOUN
ejpam-6440	256	12	)	)	PUNCT
ejpam-6440	256	13	.	.	PUNCT
ejpam-6440	257	1	let	let	VERB
ejpam-6440	257	2	x	x	SYM
ejpam-6440	257	3	=	=	SYM
ejpam-6440	257	4	c([0	c([0	PROPN
ejpam-6440	257	5	,	,	PUNCT
ejpam-6440	257	6	1	1	NUM
ejpam-6440	257	7	]	]	NUM
ejpam-6440	257	8	)	)	PUNCT
ejpam-6440	257	9	,	,	PUNCT
ejpam-6440	258	1	b	b	X
ejpam-6440	258	2	=	=	PRON
ejpam-6440	258	3	{	{	PUNCT
ejpam-6440	258	4	f	f	NOUN
ejpam-6440	258	5	:	:	PUNCT
ejpam-6440	258	6	∥f∥∞	∥f∥∞	X
ejpam-6440	258	7	≤	≤	NUM
ejpam-6440	258	8	2	2	NUM
ejpam-6440	258	9	}	}	PUNCT
ejpam-6440	258	10	.	.	PUNCT
ejpam-6440	259	1	consider	consider	VERB
ejpam-6440	259	2	:	:	PUNCT
ejpam-6440	259	3	f(x	f(x	PROPN
ejpam-6440	259	4	)	)	PUNCT
ejpam-6440	259	5	=	=	PUNCT
ejpam-6440	260	1	0.1	0.1	NUM
ejpam-6440	260	2	∫	∫	NOUN
ejpam-6440	260	3	1	1	NUM
ejpam-6440	260	4	0	0	NUM
ejpam-6440	260	5	cos(f(y	cos(f(y	NOUN
ejpam-6440	260	6	)	)	PUNCT
ejpam-6440	260	7	)	)	PUNCT
ejpam-6440	260	8	1	1	NUM
ejpam-6440	261	1	+	+	CCONJ
ejpam-6440	261	2	y	y	PROPN
ejpam-6440	261	3	dy	dy	NOUN
ejpam-6440	261	4	+	+	CCONJ
ejpam-6440	261	5	∫	∫	PROPN
ejpam-6440	261	6	1	1	NUM
ejpam-6440	261	7	0	0	NUM
ejpam-6440	261	8	yf(y	yf(y	NOUN
ejpam-6440	261	9	)	)	PUNCT
ejpam-6440	261	10	1	1	NUM
ejpam-6440	262	1	+	+	CCONJ
ejpam-6440	262	2	y2	y2	PROPN
ejpam-6440	262	3	dy	dy	NOUN
ejpam-6440	262	4	.	.	PROPN
ejpam-6440	262	5	decompose	decompose	PROPN
ejpam-6440	262	6	:	:	PUNCT
ejpam-6440	262	7	t.	t.	NOUN
ejpam-6440	262	8	qawasmeh	qawasmeh	NOUN
ejpam-6440	262	9	,	,	PUNCT
ejpam-6440	262	10	a.	a.	NOUN
ejpam-6440	262	11	malkawi	malkawi	PROPN
ejpam-6440	262	12	/	/	SYM
ejpam-6440	262	13	eur	eur	PROPN
ejpam-6440	262	14	.	.	PUNCT
ejpam-6440	263	1	j.	j.	PROPN
ejpam-6440	263	2	pure	pure	PROPN
ejpam-6440	263	3	appl	appl	PROPN
ejpam-6440	263	4	.	.	PROPN
ejpam-6440	263	5	math	math	PROPN
ejpam-6440	263	6	,	,	PUNCT
ejpam-6440	263	7	18	18	NUM
ejpam-6440	263	8	(	(	PUNCT
ejpam-6440	263	9	3	3	NUM
ejpam-6440	263	10	)	)	PUNCT
ejpam-6440	263	11	(	(	PUNCT
ejpam-6440	263	12	2025	2025	NUM
ejpam-6440	263	13	)	)	PUNCT
ejpam-6440	263	14	,	,	PUNCT
ejpam-6440	263	15	6440	6440	NUM
ejpam-6440	263	16	17	17	NUM
ejpam-6440	263	17	of	of	ADP
ejpam-6440	263	18	20	20	NUM
ejpam-6440	263	19	•	•	NUM
ejpam-6440	263	20	t1(f	t1(f	NUM
ejpam-6440	263	21	)	)	PUNCT
ejpam-6440	263	22	=	=	SYM
ejpam-6440	263	23	0.1	0.1	NUM
ejpam-6440	263	24	∫	∫	NOUN
ejpam-6440	263	25	1	1	NUM
ejpam-6440	263	26	0	0	NUM
ejpam-6440	263	27	cos(f(y	cos(f(y	NOUN
ejpam-6440	263	28	)	)	PUNCT
ejpam-6440	263	29	)	)	PUNCT
ejpam-6440	264	1	1+y	1+y	NUM
ejpam-6440	264	2	dy	dy	NOUN
ejpam-6440	264	3	(	(	PUNCT
ejpam-6440	264	4	contraction	contraction	NOUN
ejpam-6440	264	5	)	)	PUNCT
ejpam-6440	264	6	•	•	NUM
ejpam-6440	264	7	t2(f	t2(f	X
ejpam-6440	264	8	)	)	PUNCT
ejpam-6440	264	9	=	=	SYM
ejpam-6440	264	10	∫	∫	PROPN
ejpam-6440	264	11	1	1	NUM
ejpam-6440	264	12	0	0	NUM
ejpam-6440	264	13	yf(y	yf(y	NOUN
ejpam-6440	264	14	)	)	PUNCT
ejpam-6440	264	15	1+y2	1+y2	NUM
ejpam-6440	264	16	dy	dy	NOUN
ejpam-6440	264	17	(	(	PUNCT
ejpam-6440	264	18	compact	compact	ADJ
ejpam-6440	264	19	)	)	PUNCT
ejpam-6440	264	20	theorem	theorem	VERB
ejpam-6440	264	21	3	3	NUM
ejpam-6440	264	22	proves	prove	VERB
ejpam-6440	264	23	existence	existence	NOUN
ejpam-6440	264	24	of	of	ADP
ejpam-6440	264	25	a	a	DET
ejpam-6440	264	26	solution	solution	NOUN
ejpam-6440	264	27	in	in	ADP
ejpam-6440	264	28	b.	b.	PROPN
ejpam-6440	264	29	3.4	3.4	NUM
ejpam-6440	264	30	.	.	PUNCT
ejpam-6440	265	1	leray	leray	ADJ
ejpam-6440	265	2	-	-	PUNCT
ejpam-6440	265	3	schauder	schauder	NOUN
ejpam-6440	265	4	alternative	alternative	ADJ
ejpam-6440	265	5	example	example	NOUN
ejpam-6440	265	6	4	4	NUM
ejpam-6440	265	7	(	(	PUNCT
ejpam-6440	265	8	nonlinear	nonlinear	ADJ
ejpam-6440	265	9	ode	ode	PROPN
ejpam-6440	265	10	)	)	PUNCT
ejpam-6440	265	11	.	.	PUNCT
ejpam-6440	266	1	consider	consider	VERB
ejpam-6440	266	2	the	the	DET
ejpam-6440	266	3	boundary	boundary	ADJ
ejpam-6440	266	4	value	value	NOUN
ejpam-6440	266	5	problem	problem	NOUN
ejpam-6440	266	6	:	:	PUNCT
ejpam-6440	266	7	f	f	PROPN
ejpam-6440	266	8	′′(x	′′(x	PROPN
ejpam-6440	266	9	)	)	PUNCT
ejpam-6440	267	1	+	+	NUM
ejpam-6440	267	2	0.01f(x)3	0.01f(x)3	NUM
ejpam-6440	267	3	=	=	SYM
ejpam-6440	267	4	0	0	NUM
ejpam-6440	267	5	,	,	PUNCT
ejpam-6440	267	6	f(0	f(0	NOUN
ejpam-6440	267	7	)	)	PUNCT
ejpam-6440	267	8	=	=	PUNCT
ejpam-6440	267	9	f(1	f(1	PROPN
ejpam-6440	267	10	)	)	PUNCT
ejpam-6440	267	11	=	=	NOUN
ejpam-6440	268	1	0	0	X
ejpam-6440	268	2	.	.	PUNCT
ejpam-6440	269	1	the	the	DET
ejpam-6440	269	2	equivalent	equivalent	ADJ
ejpam-6440	269	3	integral	integral	ADJ
ejpam-6440	269	4	operator	operator	NOUN
ejpam-6440	269	5	:	:	PUNCT
ejpam-6440	269	6	tf(x	tf(x	NUM
ejpam-6440	269	7	)	)	PUNCT
ejpam-6440	269	8	=	=	PUNCT
ejpam-6440	269	9	0.01	0.01	NUM
ejpam-6440	269	10	∫	∫	NOUN
ejpam-6440	269	11	1	1	NUM
ejpam-6440	269	12	0	0	NUM
ejpam-6440	269	13	g(x	g(x	NOUN
ejpam-6440	269	14	,	,	PUNCT
ejpam-6440	269	15	y)f(y)3dy	y)f(y)3dy	NOUN
ejpam-6440	269	16	satisfies	satisfie	NOUN
ejpam-6440	269	17	:	:	PUNCT
ejpam-6440	269	18	•	•	NUM
ejpam-6440	269	19	ψ(t	ψ(t	PROPN
ejpam-6440	269	20	)	)	PUNCT
ejpam-6440	269	21	=	=	SYM
ejpam-6440	269	22	0.01∥g∥∞t3	0.01∥g∥∞t3	NOUN
ejpam-6440	269	23	with	with	ADP
ejpam-6440	269	24	ψn(t	ψn(t	NOUN
ejpam-6440	269	25	)	)	PUNCT
ejpam-6440	269	26	→	→	SYM
ejpam-6440	269	27	0	0	NUM
ejpam-6440	269	28	•	•	NOUN
ejpam-6440	269	29	a	a	PRON
ejpam-6440	269	30	priori	priori	ADV
ejpam-6440	269	31	bound	bind	VERB
ejpam-6440	269	32	:	:	PUNCT
ejpam-6440	269	33	∥f∥	∥f∥	ADJ
ejpam-6440	269	34	≤	≤	ADV
ejpam-6440	269	35	10	10	NUM
ejpam-6440	269	36	when	when	SCONJ
ejpam-6440	269	37	f	f	PROPN
ejpam-6440	269	38	=	=	PUNCT
ejpam-6440	269	39	λtf	λtf	ADP
ejpam-6440	269	40	theorem	theorem	VERB
ejpam-6440	269	41	4	4	NUM
ejpam-6440	269	42	guarantees	guarantee	VERB
ejpam-6440	269	43	a	a	DET
ejpam-6440	269	44	solution	solution	NOUN
ejpam-6440	269	45	exists	exist	VERB
ejpam-6440	269	46	.	.	PUNCT
ejpam-6440	269	47	table	table	NOUN
ejpam-6440	269	48	3	3	NUM
ejpam-6440	269	49	:	:	PUNCT
ejpam-6440	269	50	summary	summary	NOUN
ejpam-6440	269	51	of	of	ADP
ejpam-6440	269	52	applications	application	NOUN
ejpam-6440	269	53	theorem	theorem	VERB
ejpam-6440	269	54	field	field	NOUN
ejpam-6440	269	55	example	example	NOUN
ejpam-6440	269	56	condition	condition	NOUN
ejpam-6440	269	57	theorem	theorem	VERB
ejpam-6440	269	58	1	1	NUM
ejpam-6440	269	59	nonlinear	nonlinear	ADJ
ejpam-6440	269	60	systems	system	NOUN
ejpam-6440	269	61	u	u	NOUN
ejpam-6440	269	62	=	=	PROPN
ejpam-6440	269	63	tu	tu	PROPN
ejpam-6440	269	64	k	k	X
ejpam-6440	269	65	<	<	X
ejpam-6440	269	66	1	1	NUM
ejpam-6440	269	67	3r	3r	NUM
ejpam-6440	269	68	theorem	theorem	VERB
ejpam-6440	269	69	2	2	NUM
ejpam-6440	269	70	integral	integral	ADJ
ejpam-6440	269	71	equations	equation	NOUN
ejpam-6440	269	72	fredholm	fredholm	PROPN
ejpam-6440	269	73	/	/	SYM
ejpam-6440	269	74	volterra	volterra	NOUN
ejpam-6440	269	75	λl	λl	X
ejpam-6440	269	76	<	<	X
ejpam-6440	269	77	1	1	NUM
ejpam-6440	269	78	3r	3r	NUM
ejpam-6440	269	79	theorem	theorem	VERB
ejpam-6440	269	80	3	3	NUM
ejpam-6440	269	81	hybrid	hybrid	NOUN
ejpam-6440	269	82	systems	system	NOUN
ejpam-6440	269	83	hammerstein	hammerstein	PROPN
ejpam-6440	269	84	t1	t1	PROPN
ejpam-6440	269	85	contractive	contractive	ADJ
ejpam-6440	269	86	+	+	CCONJ
ejpam-6440	269	87	t2	t2	NOUN
ejpam-6440	269	88	compact	compact	ADJ
ejpam-6440	269	89	theorem	theorem	VERB
ejpam-6440	269	90	4	4	NUM
ejpam-6440	269	91	boundary	boundary	ADJ
ejpam-6440	269	92	value	value	NOUN
ejpam-6440	269	93	problems	problem	NOUN
ejpam-6440	269	94	nonlinear	nonlinear	VERB
ejpam-6440	269	95	odes	ode	VERB
ejpam-6440	269	96	ψ	ψ	NOUN
ejpam-6440	269	97	-	-	NOUN
ejpam-6440	269	98	contraction	contraction	NOUN
ejpam-6440	269	99	+	+	CCONJ
ejpam-6440	269	100	bound	bind	VERB
ejpam-6440	269	101	4	4	NUM
ejpam-6440	269	102	.	.	PUNCT
ejpam-6440	269	103	conclusions	conclusion	NOUN
ejpam-6440	269	104	this	this	DET
ejpam-6440	269	105	paper	paper	NOUN
ejpam-6440	269	106	has	have	AUX
ejpam-6440	269	107	developed	develop	VERB
ejpam-6440	269	108	a	a	DET
ejpam-6440	269	109	complete	complete	ADJ
ejpam-6440	269	110	theoretical	theoretical	ADJ
ejpam-6440	269	111	framework	framework	NOUN
ejpam-6440	269	112	for	for	ADP
ejpam-6440	269	113	fixed	fix	VERB
ejpam-6440	269	114	point	point	NOUN
ejpam-6440	269	115	theory	theory	NOUN
ejpam-6440	269	116	in	in	ADP
ejpam-6440	269	117	mr	mr	PROPN
ejpam-6440	269	118	-	-	PUNCT
ejpam-6440	269	119	metric	metric	ADJ
ejpam-6440	269	120	spaces	space	NOUN
ejpam-6440	269	121	,	,	PUNCT
ejpam-6440	269	122	establishing	establish	VERB
ejpam-6440	269	123	four	four	NUM
ejpam-6440	269	124	fundamental	fundamental	ADJ
ejpam-6440	269	125	theorems	theorem	NOUN
ejpam-6440	269	126	that	that	PRON
ejpam-6440	269	127	generalize	generalize	VERB
ejpam-6440	269	128	classical	classical	ADJ
ejpam-6440	269	129	results	result	NOUN
ejpam-6440	269	130	to	to	ADP
ejpam-6440	269	131	ternary	ternary	ADJ
ejpam-6440	269	132	distance	distance	NOUN
ejpam-6440	269	133	structures	structure	NOUN
ejpam-6440	269	134	.	.	PUNCT
ejpam-6440	270	1	the	the	DET
ejpam-6440	270	2	banach	banach	NOUN
ejpam-6440	270	3	contraction	contraction	NOUN
ejpam-6440	270	4	principle	principle	NOUN
ejpam-6440	270	5	(	(	PUNCT
ejpam-6440	270	6	theorem	theorem	NOUN
ejpam-6440	270	7	1	1	NUM
ejpam-6440	270	8	)	)	PUNCT
ejpam-6440	270	9	with	with	ADP
ejpam-6440	270	10	optimal	optimal	ADJ
ejpam-6440	270	11	constant	constant	ADJ
ejpam-6440	270	12	k	k	X
ejpam-6440	270	13	<	<	X
ejpam-6440	270	14	1	1	NUM
ejpam-6440	270	15	3r	3r	NOUN
ejpam-6440	270	16	provides	provide	VERB
ejpam-6440	270	17	the	the	DET
ejpam-6440	270	18	foundation	foundation	NOUN
ejpam-6440	270	19	,	,	PUNCT
ejpam-6440	270	20	while	while	SCONJ
ejpam-6440	270	21	the	the	DET
ejpam-6440	270	22	fredholm	fredholm	NOUN
ejpam-6440	270	23	-	-	PUNCT
ejpam-6440	270	24	type	type	NOUN
ejpam-6440	270	25	solvability	solvability	NOUN
ejpam-6440	270	26	theorem	theorem	NOUN
ejpam-6440	270	27	(	(	PUNCT
ejpam-6440	270	28	theorem	theorem	NOUN
ejpam-6440	270	29	2	2	NUM
ejpam-6440	270	30	)	)	PUNCT
ejpam-6440	270	31	and	and	CCONJ
ejpam-6440	270	32	krasnoselskii	krasnoselskii	PROPN
ejpam-6440	270	33	hybrid	hybrid	PROPN
ejpam-6440	270	34	theorem	theorem	NOUN
ejpam-6440	270	35	(	(	PUNCT
ejpam-6440	270	36	theorem	theorem	NOUN
ejpam-6440	270	37	3	3	NUM
ejpam-6440	270	38	)	)	PUNCT
ejpam-6440	270	39	enable	enable	ADJ
ejpam-6440	270	40	applications	application	NOUN
ejpam-6440	270	41	to	to	ADP
ejpam-6440	270	42	integral	integral	ADJ
ejpam-6440	270	43	equations	equation	NOUN
ejpam-6440	270	44	and	and	CCONJ
ejpam-6440	270	45	neutron	neutron	NOUN
ejpam-6440	270	46	transport	transport	NOUN
ejpam-6440	270	47	problems	problem	NOUN
ejpam-6440	270	48	.	.	PUNCT
ejpam-6440	271	1	the	the	DET
ejpam-6440	271	2	leray	leray	ADJ
ejpam-6440	271	3	-	-	PUNCT
ejpam-6440	271	4	schauder	schauder	NOUN
ejpam-6440	271	5	alternative	alternative	NOUN
ejpam-6440	271	6	(	(	PUNCT
ejpam-6440	271	7	theorem	theorem	NOUN
ejpam-6440	271	8	4	4	NUM
ejpam-6440	271	9	)	)	PUNCT
ejpam-6440	271	10	extends	extend	VERB
ejpam-6440	271	11	the	the	DET
ejpam-6440	271	12	theory	theory	NOUN
ejpam-6440	271	13	to	to	ADP
ejpam-6440	271	14	generalized	generalized	ADJ
ejpam-6440	271	15	contractions	contraction	NOUN
ejpam-6440	271	16	,	,	PUNCT
ejpam-6440	271	17	with	with	ADP
ejpam-6440	271	18	all	all	DET
ejpam-6440	271	19	results	result	NOUN
ejpam-6440	271	20	featuring	feature	VERB
ejpam-6440	271	21	explicit	explicit	ADJ
ejpam-6440	271	22	error	error	NOUN
ejpam-6440	271	23	estimates	estimate	NOUN
ejpam-6440	271	24	that	that	SCONJ
ejpam-6440	271	25	account	account	VERB
ejpam-6440	271	26	for	for	ADP
ejpam-6440	271	27	three	three	NUM
ejpam-6440	271	28	-	-	PUNCT
ejpam-6440	271	29	point	point	NOUN
ejpam-6440	271	30	interactions	interaction	NOUN
ejpam-6440	271	31	through	through	ADP
ejpam-6440	271	32	the	the	DET
ejpam-6440	271	33	mr	mr	PROPN
ejpam-6440	271	34	-	-	PUNCT
ejpam-6440	271	35	metric	metric	ADJ
ejpam-6440	271	36	constant	constant	ADJ
ejpam-6440	271	37	r	r	NOUN
ejpam-6440	271	38	>	>	X
ejpam-6440	271	39	1	1	NUM
ejpam-6440	271	40	.	.	PUNCT
ejpam-6440	272	1	t.	t.	NOUN
ejpam-6440	272	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	272	3	,	,	PUNCT
ejpam-6440	272	4	a.	a.	NOUN
ejpam-6440	272	5	malkawi	malkawi	PROPN
ejpam-6440	272	6	/	/	SYM
ejpam-6440	272	7	eur	eur	PROPN
ejpam-6440	272	8	.	.	PUNCT
ejpam-6440	273	1	j.	j.	PROPN
ejpam-6440	273	2	pure	pure	PROPN
ejpam-6440	273	3	appl	appl	PROPN
ejpam-6440	273	4	.	.	PROPN
ejpam-6440	273	5	math	math	PROPN
ejpam-6440	273	6	,	,	PUNCT
ejpam-6440	273	7	18	18	NUM
ejpam-6440	273	8	(	(	PUNCT
ejpam-6440	273	9	3	3	NUM
ejpam-6440	273	10	)	)	PUNCT
ejpam-6440	273	11	(	(	PUNCT
ejpam-6440	273	12	2025	2025	NUM
ejpam-6440	273	13	)	)	PUNCT
ejpam-6440	273	14	,	,	PUNCT
ejpam-6440	273	15	6440	6440	NUM
ejpam-6440	273	16	18	18	NUM
ejpam-6440	273	17	of	of	ADP
ejpam-6440	273	18	20	20	NUM
ejpam-6440	273	19	the	the	DET
ejpam-6440	273	20	applications	application	NOUN
ejpam-6440	273	21	demonstrate	demonstrate	VERB
ejpam-6440	273	22	the	the	DET
ejpam-6440	273	23	framework	framework	NOUN
ejpam-6440	273	24	’s	’s	PART
ejpam-6440	273	25	versatility	versatility	NOUN
ejpam-6440	273	26	across	across	ADP
ejpam-6440	273	27	physics	physics	NOUN
ejpam-6440	273	28	and	and	CCONJ
ejpam-6440	273	29	machine	machine	NOUN
ejpam-6440	273	30	learning	learning	NOUN
ejpam-6440	273	31	.	.	PUNCT
ejpam-6440	274	1	in	in	ADP
ejpam-6440	274	2	neural	neural	ADJ
ejpam-6440	274	3	network	network	NOUN
ejpam-6440	274	4	optimization	optimization	NOUN
ejpam-6440	274	5	,	,	PUNCT
ejpam-6440	274	6	the	the	DET
ejpam-6440	274	7	theory	theory	NOUN
ejpam-6440	274	8	yields	yield	VERB
ejpam-6440	274	9	layer	layer	NOUN
ejpam-6440	274	10	-	-	PUNCT
ejpam-6440	274	11	wise	wise	ADJ
ejpam-6440	274	12	learning	learning	NOUN
ejpam-6440	274	13	rate	rate	NOUN
ejpam-6440	274	14	bounds	bound	NOUN
ejpam-6440	274	15	(	(	PUNCT
ejpam-6440	274	16	ηℓ	ηℓ	INTJ
ejpam-6440	274	17	<	<	X
ejpam-6440	274	18	1	1	NUM
ejpam-6440	274	19	3rℓlℓ	3rℓlℓ	NUM
ejpam-6440	274	20	)	)	PUNCT
ejpam-6440	274	21	,	,	PUNCT
ejpam-6440	274	22	while	while	SCONJ
ejpam-6440	274	23	for	for	ADP
ejpam-6440	274	24	nuclear	nuclear	ADJ
ejpam-6440	274	25	reactor	reactor	NOUN
ejpam-6440	274	26	modeling	modeling	NOUN
ejpam-6440	274	27	,	,	PUNCT
ejpam-6440	274	28	it	it	PRON
ejpam-6440	274	29	provides	provide	VERB
ejpam-6440	274	30	existence	existence	NOUN
ejpam-6440	274	31	conditions	condition	NOUN
ejpam-6440	274	32	when	when	SCONJ
ejpam-6440	274	33	the	the	DET
ejpam-6440	274	34	scattering	scatter	VERB
ejpam-6440	274	35	ratio	ratio	NOUN
ejpam-6440	274	36	satisfies	satisfie	NOUN
ejpam-6440	275	1	λ	λ	X
ejpam-6440	275	2	<	<	X
ejpam-6440	275	3	(	(	PUNCT
ejpam-6440	275	4	3r∥k∥)−1	3r∥k∥)−1	NUM
ejpam-6440	275	5	.	.	PUNCT
ejpam-6440	276	1	these	these	PRON
ejpam-6440	276	2	results	result	VERB
ejpam-6440	276	3	bridge	bridge	VERB
ejpam-6440	276	4	abstract	abstract	ADJ
ejpam-6440	276	5	mathematics	mathematic	NOUN
ejpam-6440	276	6	with	with	ADP
ejpam-6440	276	7	practical	practical	ADJ
ejpam-6440	276	8	computational	computational	ADJ
ejpam-6440	276	9	problems	problem	NOUN
ejpam-6440	276	10	where	where	SCONJ
ejpam-6440	276	11	ternary	ternary	ADJ
ejpam-6440	276	12	interactions	interaction	NOUN
ejpam-6440	276	13	are	be	AUX
ejpam-6440	276	14	intrinsic	intrinsic	ADJ
ejpam-6440	276	15	,	,	PUNCT
ejpam-6440	276	16	offering	offer	VERB
ejpam-6440	276	17	quantitative	quantitative	ADJ
ejpam-6440	276	18	improvements	improvement	NOUN
ejpam-6440	276	19	over	over	ADP
ejpam-6440	276	20	standard	standard	ADJ
ejpam-6440	276	21	metric	metric	ADJ
ejpam-6440	276	22	space	space	NOUN
ejpam-6440	276	23	approaches	approach	NOUN
ejpam-6440	276	24	.	.	PUNCT
ejpam-6440	277	1	future	future	ADJ
ejpam-6440	277	2	work	work	NOUN
ejpam-6440	277	3	will	will	AUX
ejpam-6440	277	4	explore	explore	VERB
ejpam-6440	277	5	stochastic	stochastic	ADJ
ejpam-6440	277	6	mr	mr	NOUN
ejpam-6440	277	7	-	-	PUNCT
ejpam-6440	277	8	metrics	metric	NOUN
ejpam-6440	277	9	and	and	CCONJ
ejpam-6440	277	10	applications	application	NOUN
ejpam-6440	277	11	to	to	ADP
ejpam-6440	277	12	quantum	quantum	ADJ
ejpam-6440	277	13	transport	transport	NOUN
ejpam-6440	277	14	equations	equation	NOUN
ejpam-6440	277	15	.	.	PUNCT
ejpam-6440	278	1	references	reference	NOUN
ejpam-6440	278	2	[	[	X
ejpam-6440	278	3	1	1	X
ejpam-6440	278	4	]	]	PUNCT
ejpam-6440	278	5	s.	s.	PROPN
ejpam-6440	278	6	banach	banach	PROPN
ejpam-6440	278	7	.	.	PUNCT
ejpam-6440	279	1	sur	sur	PROPN
ejpam-6440	279	2	les	les	X
ejpam-6440	279	3	opérations	opération	NOUN
ejpam-6440	279	4	dans	dan	NOUN
ejpam-6440	279	5	les	les	X
ejpam-6440	279	6	ensembles	ensemble	NOUN
ejpam-6440	279	7	abstraits	abstrait	NOUN
ejpam-6440	279	8	et	et	PROPN
ejpam-6440	279	9	leur	leur	X
ejpam-6440	279	10	application	application	PROPN
ejpam-6440	279	11	aux	aux	PROPN
ejpam-6440	279	12	équations	équations	PROPN
ejpam-6440	279	13	intégrales	intégrale	NOUN
ejpam-6440	279	14	.	.	PUNCT
ejpam-6440	280	1	fundamenta	fundamenta	PROPN
ejpam-6440	280	2	mathematicae	mathematicae	PROPN
ejpam-6440	280	3	,	,	PUNCT
ejpam-6440	280	4	3	3	NUM
ejpam-6440	280	5	,	,	PUNCT
ejpam-6440	280	6	1922	1922	NUM
ejpam-6440	280	7	.	.	PUNCT
ejpam-6440	281	1	[	[	X
ejpam-6440	281	2	2	2	X
ejpam-6440	281	3	]	]	PUNCT
ejpam-6440	281	4	s.	s.	PROPN
ejpam-6440	281	5	g.	g.	PROPN
ejpam-6440	281	6	matthews	matthews	PROPN
ejpam-6440	281	7	.	.	PUNCT
ejpam-6440	282	1	partial	partial	ADJ
ejpam-6440	282	2	metric	metric	ADJ
ejpam-6440	282	3	topology	topology	NOUN
ejpam-6440	282	4	.	.	PUNCT
ejpam-6440	283	1	annals	annal	NOUN
ejpam-6440	283	2	of	of	ADP
ejpam-6440	283	3	the	the	DET
ejpam-6440	283	4	new	new	PROPN
ejpam-6440	283	5	york	york	PROPN
ejpam-6440	283	6	academy	academy	PROPN
ejpam-6440	283	7	of	of	ADP
ejpam-6440	283	8	sciences	sciences	PROPN
ejpam-6440	283	9	,	,	PUNCT
ejpam-6440	283	10	1994	1994	NUM
ejpam-6440	283	11	.	.	PUNCT
ejpam-6440	284	1	[	[	X
ejpam-6440	284	2	3	3	NUM
ejpam-6440	284	3	]	]	X
ejpam-6440	284	4	i.	i.	PROPN
ejpam-6440	284	5	a.	a.	PROPN
ejpam-6440	284	6	bakhtin	bakhtin	PROPN
ejpam-6440	284	7	.	.	PUNCT
ejpam-6440	285	1	the	the	DET
ejpam-6440	285	2	contraction	contraction	NOUN
ejpam-6440	285	3	mapping	map	VERB
ejpam-6440	285	4	principle	principle	NOUN
ejpam-6440	285	5	in	in	ADP
ejpam-6440	285	6	quasimetric	quasimetric	ADJ
ejpam-6440	285	7	spaces	space	NOUN
ejpam-6440	285	8	.	.	PUNCT
ejpam-6440	286	1	functional	functional	ADJ
ejpam-6440	286	2	analysis	analysis	NOUN
ejpam-6440	286	3	,	,	PUNCT
ejpam-6440	286	4	1989	1989	NUM
ejpam-6440	286	5	.	.	PUNCT
ejpam-6440	287	1	[	[	X
ejpam-6440	287	2	4	4	X
ejpam-6440	287	3	]	]	X
ejpam-6440	287	4	v.	v.	PROPN
ejpam-6440	287	5	v.	v.	ADP
ejpam-6440	287	6	chistyakov	chistyakov	PROPN
ejpam-6440	287	7	.	.	PUNCT
ejpam-6440	288	1	modular	modular	ADJ
ejpam-6440	288	2	metric	metric	ADJ
ejpam-6440	288	3	spaces	space	NOUN
ejpam-6440	288	4	.	.	PUNCT
ejpam-6440	289	1	russian	russian	ADJ
ejpam-6440	289	2	mathematical	mathematical	ADJ
ejpam-6440	289	3	surveys	survey	NOUN
ejpam-6440	289	4	,	,	PUNCT
ejpam-6440	289	5	2010	2010	NUM
ejpam-6440	289	6	.	.	PUNCT
ejpam-6440	290	1	[	[	X
ejpam-6440	290	2	5	5	NUM
ejpam-6440	290	3	]	]	PUNCT
ejpam-6440	290	4	a.	a.	NOUN
ejpam-6440	290	5	malkawi	malkawi	PROPN
ejpam-6440	290	6	,	,	PUNCT
ejpam-6440	290	7	a.	a.	PROPN
ejpam-6440	290	8	rabaiah	rabaiah	PROPN
ejpam-6440	290	9	,	,	PUNCT
ejpam-6440	290	10	w.	w.	PROPN
ejpam-6440	290	11	shatanawi	shatanawi	PROPN
ejpam-6440	290	12	,	,	PUNCT
ejpam-6440	290	13	and	and	CCONJ
ejpam-6440	290	14	a.	a.	NOUN
ejpam-6440	290	15	talafhah	talafhah	PROPN
ejpam-6440	290	16	.	.	PUNCT
ejpam-6440	291	1	mr	mr	PROPN
ejpam-6440	291	2	-	-	PUNCT
ejpam-6440	291	3	metric	metric	ADJ
ejpam-6440	291	4	spaces	space	NOUN
ejpam-6440	291	5	and	and	CCONJ
ejpam-6440	291	6	an	an	DET
ejpam-6440	291	7	application	application	NOUN
ejpam-6440	291	8	.	.	PUNCT
ejpam-6440	292	1	preprint	preprint	NOUN
ejpam-6440	292	2	,	,	PUNCT
ejpam-6440	292	3	2021	2021	NUM
ejpam-6440	292	4	.	.	PUNCT
ejpam-6440	293	1	[	[	X
ejpam-6440	293	2	6	6	NUM
ejpam-6440	293	3	]	]	PUNCT
ejpam-6440	293	4	i.	i.	PROPN
ejpam-6440	293	5	a.	a.	PROPN
ejpam-6440	293	6	bakhtin	bakhtin	PROPN
ejpam-6440	293	7	.	.	PUNCT
ejpam-6440	294	1	the	the	DET
ejpam-6440	294	2	contraction	contraction	NOUN
ejpam-6440	294	3	mapping	map	VERB
ejpam-6440	294	4	principle	principle	NOUN
ejpam-6440	294	5	in	in	ADP
ejpam-6440	294	6	almost	almost	ADV
ejpam-6440	294	7	metric	metric	ADJ
ejpam-6440	294	8	spaces	space	NOUN
ejpam-6440	294	9	.	.	PUNCT
ejpam-6440	295	1	functional	functional	ADJ
ejpam-6440	295	2	analysis	analysis	NOUN
ejpam-6440	295	3	,	,	PUNCT
ejpam-6440	295	4	30:26–37	30:26–37	PROPN
ejpam-6440	295	5	,	,	PUNCT
ejpam-6440	295	6	1989	1989	NUM
ejpam-6440	295	7	.	.	PUNCT
ejpam-6440	296	1	[	[	X
ejpam-6440	296	2	7	7	X
ejpam-6440	296	3	]	]	X
ejpam-6440	296	4	s.	s.	PROPN
ejpam-6440	296	5	czerwik	czerwik	PROPN
ejpam-6440	296	6	.	.	PUNCT
ejpam-6440	297	1	contraction	contraction	NOUN
ejpam-6440	297	2	mappings	mapping	NOUN
ejpam-6440	297	3	in	in	ADP
ejpam-6440	297	4	b	b	NOUN
ejpam-6440	297	5	-	-	ADJ
ejpam-6440	297	6	metric	metric	ADJ
ejpam-6440	297	7	spaces	space	NOUN
ejpam-6440	297	8	.	.	PUNCT
ejpam-6440	298	1	acta	acta	PROPN
ejpam-6440	298	2	mathematica	mathematica	PROPN
ejpam-6440	298	3	et	et	PROPN
ejpam-6440	298	4	informatica	informatica	PROPN
ejpam-6440	298	5	universitatis	universitatis	PROPN
ejpam-6440	298	6	ostraviensis	ostraviensis	PROPN
ejpam-6440	298	7	,	,	PUNCT
ejpam-6440	298	8	1:5–11	1:5–11	NUM
ejpam-6440	298	9	,	,	PUNCT
ejpam-6440	298	10	1993	1993	NUM
ejpam-6440	298	11	.	.	PUNCT
ejpam-6440	299	1	[	[	X
ejpam-6440	299	2	8	8	NUM
ejpam-6440	299	3	]	]	X
ejpam-6440	299	4	y.	y.	PROPN
ejpam-6440	299	5	j.	j.	PROPN
ejpam-6440	299	6	cho	cho	PROPN
ejpam-6440	299	7	,	,	PUNCT
ejpam-6440	299	8	p.	p.	NOUN
ejpam-6440	299	9	p.	p.	PROPN
ejpam-6440	300	1	murthy	murthy	ADJ
ejpam-6440	300	2	,	,	PUNCT
ejpam-6440	300	3	and	and	CCONJ
ejpam-6440	300	4	g.	g.	PROPN
ejpam-6440	300	5	jungck	jungck	PROPN
ejpam-6440	300	6	.	.	PUNCT
ejpam-6440	301	1	a	a	DET
ejpam-6440	301	2	common	common	ADJ
ejpam-6440	301	3	fixed	fix	VERB
ejpam-6440	301	4	point	point	NOUN
ejpam-6440	301	5	theorem	theorem	NOUN
ejpam-6440	301	6	of	of	ADP
ejpam-6440	301	7	meir	meir	PROPN
ejpam-6440	301	8	and	and	CCONJ
ejpam-6440	301	9	keeler	keeler	PROPN
ejpam-6440	301	10	type	type	NOUN
ejpam-6440	301	11	.	.	PUNCT
ejpam-6440	302	1	international	international	ADJ
ejpam-6440	302	2	journal	journal	PROPN
ejpam-6440	302	3	of	of	ADP
ejpam-6440	302	4	mathematical	mathematical	ADJ
ejpam-6440	302	5	sciences	science	NOUN
ejpam-6440	302	6	,	,	PUNCT
ejpam-6440	302	7	16:669–674	16:669–674	NUM
ejpam-6440	302	8	,	,	PUNCT
ejpam-6440	302	9	1993	1993	NUM
ejpam-6440	302	10	.	.	PUNCT
ejpam-6440	303	1	[	[	X
ejpam-6440	303	2	9	9	NUM
ejpam-6440	303	3	]	]	PUNCT
ejpam-6440	303	4	r.	r.	PROPN
ejpam-6440	303	5	o.	o.	PROPN
ejpam-6440	303	6	davies	davies	PROPN
ejpam-6440	303	7	and	and	CCONJ
ejpam-6440	303	8	s.	s.	PROPN
ejpam-6440	303	9	sessa	sessa	PROPN
ejpam-6440	303	10	.	.	PUNCT
ejpam-6440	304	1	a	a	DET
ejpam-6440	304	2	common	common	ADJ
ejpam-6440	304	3	fixed	fix	VERB
ejpam-6440	304	4	point	point	NOUN
ejpam-6440	304	5	theorem	theorem	NOUN
ejpam-6440	304	6	of	of	ADP
ejpam-6440	304	7	gregus	gregus	NOUN
ejpam-6440	304	8	type	type	NOUN
ejpam-6440	304	9	for	for	ADP
ejpam-6440	304	10	compatible	compatible	ADJ
ejpam-6440	304	11	mappings	mapping	NOUN
ejpam-6440	304	12	.	.	PUNCT
ejpam-6440	305	1	facta	facta	PROPN
ejpam-6440	305	2	universitatis	universitatis	PROPN
ejpam-6440	305	3	(	(	PUNCT
ejpam-6440	305	4	nǐs	nǐs	NOUN
ejpam-6440	305	5	)	)	PUNCT
ejpam-6440	305	6	series	series	NOUN
ejpam-6440	305	7	:	:	PUNCT
ejpam-6440	305	8	mathematics	mathematic	NOUN
ejpam-6440	305	9	and	and	CCONJ
ejpam-6440	305	10	informatics	informatic	NOUN
ejpam-6440	305	11	,	,	PUNCT
ejpam-6440	305	12	7:51–58	7:51–58	NOUN
ejpam-6440	305	13	,	,	PUNCT
ejpam-6440	305	14	1992	1992	NUM
ejpam-6440	305	15	.	.	PUNCT
ejpam-6440	306	1	[	[	X
ejpam-6440	306	2	10	10	NUM
ejpam-6440	306	3	]	]	X
ejpam-6440	306	4	b.	b.	PROPN
ejpam-6440	306	5	c.	c.	PROPN
ejpam-6440	306	6	dhage	dhage	PROPN
ejpam-6440	306	7	.	.	PUNCT
ejpam-6440	307	1	generalized	generalize	VERB
ejpam-6440	307	2	metric	metric	ADJ
ejpam-6440	307	3	spaces	space	NOUN
ejpam-6440	307	4	and	and	CCONJ
ejpam-6440	307	5	mappings	mapping	NOUN
ejpam-6440	307	6	with	with	ADP
ejpam-6440	307	7	fixed	fix	VERB
ejpam-6440	307	8	points	point	NOUN
ejpam-6440	307	9	.	.	PUNCT
ejpam-6440	308	1	bulletin	bulletin	NOUN
ejpam-6440	308	2	of	of	ADP
ejpam-6440	308	3	the	the	DET
ejpam-6440	308	4	calcutta	calcutta	PROPN
ejpam-6440	308	5	mathematical	mathematical	ADJ
ejpam-6440	308	6	society	society	NOUN
ejpam-6440	308	7	,	,	PUNCT
ejpam-6440	308	8	84:329–336	84:329–336	NUM
ejpam-6440	308	9	,	,	PUNCT
ejpam-6440	308	10	1992	1992	NUM
ejpam-6440	308	11	.	.	PUNCT
ejpam-6440	309	1	[	[	X
ejpam-6440	309	2	11	11	NUM
ejpam-6440	309	3	]	]	PUNCT
ejpam-6440	309	4	t.	t.	NOUN
ejpam-6440	309	5	qawasmeh	qawasmeh	NOUN
ejpam-6440	309	6	.	.	PUNCT
ejpam-6440	310	1	(	(	PUNCT
ejpam-6440	310	2	h	h	NOUN
ejpam-6440	310	3	,	,	PUNCT
ejpam-6440	310	4	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-6440	310	5	contractions	contraction	NOUN
ejpam-6440	310	6	in	in	ADP
ejpam-6440	310	7	ωb	ωb	NOUN
ejpam-6440	310	8	-	-	PUNCT
ejpam-6440	310	9	distance	distance	NOUN
ejpam-6440	310	10	mappings	mapping	NOUN
ejpam-6440	310	11	with	with	ADP
ejpam-6440	310	12	applications	application	NOUN
ejpam-6440	310	13	.	.	PUNCT
ejpam-6440	311	1	european	european	ADJ
ejpam-6440	311	2	journal	journal	PROPN
ejpam-6440	311	3	of	of	ADP
ejpam-6440	311	4	pure	pure	ADJ
ejpam-6440	311	5	and	and	CCONJ
ejpam-6440	311	6	applied	applied	ADJ
ejpam-6440	311	7	mathematics	mathematic	NOUN
ejpam-6440	311	8	,	,	PUNCT
ejpam-6440	311	9	16(3):1717–1730	16(3):1717–1730	NUM
ejpam-6440	311	10	,	,	PUNCT
ejpam-6440	311	11	2023	2023	NUM
ejpam-6440	311	12	.	.	PUNCT
ejpam-6440	312	1	[	[	X
ejpam-6440	312	2	12	12	NUM
ejpam-6440	312	3	]	]	PUNCT
ejpam-6440	312	4	t.	t.	NOUN
ejpam-6440	312	5	qawasmeh	qawasmeh	NOUN
ejpam-6440	312	6	.	.	PUNCT
ejpam-6440	313	1	h	h	NOUN
ejpam-6440	313	2	-	-	PUNCT
ejpam-6440	313	3	simulation	simulation	NOUN
ejpam-6440	313	4	functions	function	NOUN
ejpam-6440	313	5	and	and	CCONJ
ejpam-6440	313	6	ωb	ωb	NOUN
ejpam-6440	313	7	-	-	PUNCT
ejpam-6440	313	8	distance	distance	NOUN
ejpam-6440	313	9	mappings	mapping	NOUN
ejpam-6440	313	10	in	in	ADP
ejpam-6440	313	11	the	the	DET
ejpam-6440	313	12	setting	setting	NOUN
ejpam-6440	313	13	of	of	ADP
ejpam-6440	313	14	gb	gb	ADV
ejpam-6440	313	15	-	-	PUNCT
ejpam-6440	313	16	metric	metric	ADJ
ejpam-6440	313	17	spaces	space	NOUN
ejpam-6440	313	18	and	and	CCONJ
ejpam-6440	313	19	application	application	NOUN
ejpam-6440	313	20	.	.	PUNCT
ejpam-6440	314	1	nonlinear	nonlinear	ADJ
ejpam-6440	314	2	functional	functional	ADJ
ejpam-6440	314	3	analysis	analysis	NOUN
ejpam-6440	314	4	and	and	CCONJ
ejpam-6440	314	5	applications	application	NOUN
ejpam-6440	314	6	,	,	PUNCT
ejpam-6440	314	7	28(2):557–570	28(2):557–570	NOUN
ejpam-6440	314	8	,	,	PUNCT
ejpam-6440	314	9	2023	2023	NUM
ejpam-6440	314	10	.	.	PUNCT
ejpam-6440	315	1	[	[	X
ejpam-6440	315	2	13	13	NUM
ejpam-6440	315	3	]	]	PUNCT
ejpam-6440	315	4	a.	a.	NOUN
ejpam-6440	315	5	bataihah	bataihah	PROPN
ejpam-6440	315	6	and	and	CCONJ
ejpam-6440	315	7	t.	t.	NOUN
ejpam-6440	315	8	qawasmeh	qawasmeh	NOUN
ejpam-6440	315	9	.	.	PUNCT
ejpam-6440	316	1	a	a	DET
ejpam-6440	316	2	new	new	ADJ
ejpam-6440	316	3	type	type	NOUN
ejpam-6440	316	4	of	of	ADP
ejpam-6440	316	5	distance	distance	NOUN
ejpam-6440	316	6	spaces	space	NOUN
ejpam-6440	316	7	and	and	CCONJ
ejpam-6440	316	8	fixed	fix	VERB
ejpam-6440	316	9	point	point	NOUN
ejpam-6440	316	10	results	result	NOUN
ejpam-6440	316	11	.	.	PUNCT
ejpam-6440	317	1	journal	journal	NOUN
ejpam-6440	317	2	of	of	ADP
ejpam-6440	317	3	mathematical	mathematical	ADJ
ejpam-6440	317	4	analysis	analysis	NOUN
ejpam-6440	317	5	,	,	PUNCT
ejpam-6440	317	6	15(4):81–90	15(4):81–90	NUM
ejpam-6440	317	7	,	,	PUNCT
ejpam-6440	317	8	2024	2024	NUM
ejpam-6440	317	9	.	.	PUNCT
ejpam-6440	318	1	[	[	X
ejpam-6440	318	2	14	14	NUM
ejpam-6440	318	3	]	]	X
ejpam-6440	318	4	w.	w.	PROPN
ejpam-6440	318	5	shatanawi	shatanawi	PROPN
ejpam-6440	318	6	,	,	PUNCT
ejpam-6440	318	7	t.	t.	NOUN
ejpam-6440	318	8	qawasmeh	qawasmeh	NOUN
ejpam-6440	318	9	,	,	PUNCT
ejpam-6440	318	10	a.	a.	NOUN
ejpam-6440	318	11	bataihah	bataihah	PROPN
ejpam-6440	318	12	,	,	PUNCT
ejpam-6440	318	13	and	and	CCONJ
ejpam-6440	318	14	a.	a.	NOUN
ejpam-6440	318	15	tallafha	tallafha	NOUN
ejpam-6440	318	16	.	.	PUNCT
ejpam-6440	319	1	new	new	ADJ
ejpam-6440	319	2	contractions	contraction	NOUN
ejpam-6440	319	3	and	and	CCONJ
ejpam-6440	319	4	some	some	DET
ejpam-6440	319	5	fixed	fix	VERB
ejpam-6440	319	6	point	point	NOUN
ejpam-6440	319	7	results	result	NOUN
ejpam-6440	319	8	with	with	ADP
ejpam-6440	319	9	application	application	NOUN
ejpam-6440	319	10	based	base	VERB
ejpam-6440	319	11	on	on	ADP
ejpam-6440	319	12	extended	extended	ADJ
ejpam-6440	319	13	quasi	quasi	ADJ
ejpam-6440	319	14	b	b	NOUN
ejpam-6440	319	15	-	-	ADJ
ejpam-6440	319	16	metric	metric	ADJ
ejpam-6440	319	17	spaces	space	NOUN
ejpam-6440	319	18	.	.	PUNCT
ejpam-6440	320	1	u.p.b	u.p.b	ADJ
ejpam-6440	320	2	.	.	PUNCT
ejpam-6440	321	1	scientific	scientific	ADJ
ejpam-6440	321	2	bulletin	bulletin	NOUN
ejpam-6440	321	3	,	,	PUNCT
ejpam-6440	321	4	series	series	PROPN
ejpam-6440	321	5	a	a	PROPN
ejpam-6440	321	6	,	,	PUNCT
ejpam-6440	321	7	83(2):1223–7027	83(2):1223–7027	NUM
ejpam-6440	321	8	,	,	PUNCT
ejpam-6440	321	9	2021	2021	NUM
ejpam-6440	321	10	.	.	PUNCT
ejpam-6440	322	1	[	[	X
ejpam-6440	322	2	15	15	X
ejpam-6440	322	3	]	]	PUNCT
ejpam-6440	322	4	t.	t.	NOUN
ejpam-6440	322	5	qawasmeh	qawasmeh	NOUN
ejpam-6440	322	6	,	,	PUNCT
ejpam-6440	322	7	w.	w.	PROPN
ejpam-6440	322	8	shatanawi	shatanawi	PROPN
ejpam-6440	322	9	,	,	PUNCT
ejpam-6440	322	10	a.	a.	NOUN
ejpam-6440	322	11	bataihah	bataihah	PROPN
ejpam-6440	322	12	,	,	PUNCT
ejpam-6440	322	13	and	and	CCONJ
ejpam-6440	322	14	a.	a.	NOUN
ejpam-6440	322	15	tallafha	tallafha	NOUN
ejpam-6440	322	16	.	.	PUNCT
ejpam-6440	323	1	fixed	fix	VERB
ejpam-6440	323	2	point	point	NOUN
ejpam-6440	323	3	results	result	NOUN
ejpam-6440	323	4	and	and	CCONJ
ejpam-6440	323	5	(	(	PUNCT
ejpam-6440	323	6	α	α	NOUN
ejpam-6440	323	7	,	,	PUNCT
ejpam-6440	323	8	β)-triangular	β)-triangular	ADJ
ejpam-6440	323	9	admissibility	admissibility	NOUN
ejpam-6440	323	10	in	in	ADP
ejpam-6440	323	11	the	the	DET
ejpam-6440	323	12	frame	frame	NOUN
ejpam-6440	323	13	of	of	ADP
ejpam-6440	323	14	complete	complete	ADJ
ejpam-6440	323	15	extended	extended	ADJ
ejpam-6440	323	16	b	b	NOUN
ejpam-6440	323	17	-	-	PUNCT
ejpam-6440	323	18	metric	metric	ADJ
ejpam-6440	323	19	spaces	space	NOUN
ejpam-6440	323	20	and	and	CCONJ
ejpam-6440	323	21	application	application	NOUN
ejpam-6440	323	22	.	.	PUNCT
ejpam-6440	324	1	u.p.b	u.p.b	PROPN
ejpam-6440	324	2	.	.	PUNCT
ejpam-6440	325	1	scientific	scientific	ADJ
ejpam-6440	325	2	bulletin	bulletin	NOUN
ejpam-6440	325	3	,	,	PUNCT
ejpam-6440	325	4	series	series	PROPN
ejpam-6440	325	5	a	a	PROPN
ejpam-6440	325	6	,	,	PUNCT
ejpam-6440	325	7	83(1):113–124	83(1):113–124	PROPN
ejpam-6440	325	8	,	,	PUNCT
ejpam-6440	325	9	2021	2021	NUM
ejpam-6440	325	10	.	.	PUNCT
ejpam-6440	326	1	t.	t.	NOUN
ejpam-6440	326	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	326	3	,	,	PUNCT
ejpam-6440	326	4	a.	a.	NOUN
ejpam-6440	326	5	malkawi	malkawi	PROPN
ejpam-6440	326	6	/	/	SYM
ejpam-6440	326	7	eur	eur	PROPN
ejpam-6440	326	8	.	.	PUNCT
ejpam-6440	327	1	j.	j.	PROPN
ejpam-6440	327	2	pure	pure	PROPN
ejpam-6440	327	3	appl	appl	PROPN
ejpam-6440	327	4	.	.	PROPN
ejpam-6440	327	5	math	math	PROPN
ejpam-6440	327	6	,	,	PUNCT
ejpam-6440	327	7	18	18	NUM
ejpam-6440	327	8	(	(	PUNCT
ejpam-6440	327	9	3	3	NUM
ejpam-6440	327	10	)	)	PUNCT
ejpam-6440	327	11	(	(	PUNCT
ejpam-6440	327	12	2025	2025	NUM
ejpam-6440	327	13	)	)	PUNCT
ejpam-6440	327	14	,	,	PUNCT
ejpam-6440	327	15	6440	6440	NUM
ejpam-6440	327	16	19	19	NUM
ejpam-6440	327	17	of	of	ADP
ejpam-6440	327	18	20	20	NUM
ejpam-6440	328	1	[	[	SYM
ejpam-6440	328	2	16	16	NUM
ejpam-6440	328	3	]	]	PUNCT
ejpam-6440	328	4	a.	a.	NOUN
ejpam-6440	328	5	bataihah	bataihah	PROPN
ejpam-6440	328	6	,	,	PUNCT
ejpam-6440	328	7	w.	w.	PROPN
ejpam-6440	328	8	shatanawi	shatanawi	PROPN
ejpam-6440	328	9	,	,	PUNCT
ejpam-6440	328	10	and	and	CCONJ
ejpam-6440	328	11	a.	a.	NOUN
ejpam-6440	328	12	tallafha	tallafha	NOUN
ejpam-6440	328	13	.	.	PUNCT
ejpam-6440	329	1	fixed	fix	VERB
ejpam-6440	329	2	point	point	NOUN
ejpam-6440	329	3	results	result	NOUN
ejpam-6440	329	4	with	with	ADP
ejpam-6440	329	5	simulation	simulation	NOUN
ejpam-6440	329	6	functions	function	NOUN
ejpam-6440	329	7	.	.	PUNCT
ejpam-6440	330	1	nonlinear	nonlinear	ADJ
ejpam-6440	330	2	functional	functional	ADJ
ejpam-6440	330	3	analysis	analysis	NOUN
ejpam-6440	330	4	and	and	CCONJ
ejpam-6440	330	5	applications	application	NOUN
ejpam-6440	330	6	,	,	PUNCT
ejpam-6440	330	7	25(1):13–23	25(1):13–23	NUM
ejpam-6440	330	8	,	,	PUNCT
ejpam-6440	330	9	2020	2020	NUM
ejpam-6440	330	10	.	.	PUNCT
ejpam-6440	331	1	[	[	X
ejpam-6440	331	2	17	17	NUM
ejpam-6440	331	3	]	]	PUNCT
ejpam-6440	331	4	k.	k.	PROPN
ejpam-6440	331	5	abodayeh	abodayeh	PROPN
ejpam-6440	331	6	,	,	PUNCT
ejpam-6440	331	7	w.	w.	PROPN
ejpam-6440	331	8	shatanawi	shatanawi	PROPN
ejpam-6440	331	9	,	,	PUNCT
ejpam-6440	331	10	a.	a.	NOUN
ejpam-6440	331	11	bataihah	bataihah	PROPN
ejpam-6440	331	12	,	,	PUNCT
ejpam-6440	331	13	and	and	CCONJ
ejpam-6440	331	14	a.	a.	PROPN
ejpam-6440	331	15	h.	h.	PROPN
ejpam-6440	331	16	ansari	ansari	PROPN
ejpam-6440	331	17	.	.	PUNCT
ejpam-6440	332	1	some	some	DET
ejpam-6440	332	2	fixed	fix	VERB
ejpam-6440	332	3	point	point	NOUN
ejpam-6440	332	4	and	and	CCONJ
ejpam-6440	332	5	common	common	ADJ
ejpam-6440	332	6	fixed	fix	VERB
ejpam-6440	332	7	point	point	NOUN
ejpam-6440	332	8	results	result	NOUN
ejpam-6440	332	9	through	through	ADP
ejpam-6440	332	10	ω	ω	NOUN
ejpam-6440	332	11	-	-	PUNCT
ejpam-6440	332	12	distance	distance	NOUN
ejpam-6440	332	13	under	under	ADP
ejpam-6440	332	14	nonlinear	nonlinear	ADJ
ejpam-6440	332	15	contractions	contraction	NOUN
ejpam-6440	332	16	.	.	PUNCT
ejpam-6440	333	1	gazi	gazi	PROPN
ejpam-6440	333	2	university	university	PROPN
ejpam-6440	333	3	journal	journal	PROPN
ejpam-6440	333	4	of	of	ADP
ejpam-6440	333	5	science	science	NOUN
ejpam-6440	333	6	,	,	PUNCT
ejpam-6440	333	7	30(1):293–302	30(1):293–302	NOUN
ejpam-6440	333	8	,	,	PUNCT
ejpam-6440	333	9	2017	2017	NUM
ejpam-6440	333	10	.	.	PUNCT
ejpam-6440	334	1	[	[	X
ejpam-6440	334	2	18	18	NUM
ejpam-6440	334	3	]	]	PUNCT
ejpam-6440	334	4	a.	a.	NOUN
ejpam-6440	334	5	bataihah	bataihah	PROPN
ejpam-6440	334	6	,	,	PUNCT
ejpam-6440	334	7	a.	a.	NOUN
ejpam-6440	334	8	tallafha	tallafha	NOUN
ejpam-6440	334	9	,	,	PUNCT
ejpam-6440	334	10	and	and	CCONJ
ejpam-6440	334	11	w.	w.	PROPN
ejpam-6440	334	12	shatanawi	shatanawi	PROPN
ejpam-6440	334	13	.	.	PUNCT
ejpam-6440	335	1	fixed	fix	VERB
ejpam-6440	335	2	point	point	NOUN
ejpam-6440	335	3	results	result	NOUN
ejpam-6440	335	4	with	with	ADP
ejpam-6440	335	5	ω	ω	NOUN
ejpam-6440	335	6	-	-	PUNCT
ejpam-6440	335	7	distance	distance	NOUN
ejpam-6440	335	8	by	by	ADP
ejpam-6440	335	9	utilizing	utilize	VERB
ejpam-6440	335	10	simulation	simulation	NOUN
ejpam-6440	335	11	functions	function	NOUN
ejpam-6440	335	12	.	.	PUNCT
ejpam-6440	336	1	italian	italian	ADJ
ejpam-6440	336	2	journal	journal	NOUN
ejpam-6440	336	3	of	of	ADP
ejpam-6440	336	4	pure	pure	ADJ
ejpam-6440	336	5	and	and	CCONJ
ejpam-6440	336	6	applied	applied	ADJ
ejpam-6440	336	7	mathematics	mathematic	NOUN
ejpam-6440	336	8	,	,	PUNCT
ejpam-6440	336	9	(	(	PUNCT
ejpam-6440	336	10	43):185–196	43):185–196	NOUN
ejpam-6440	336	11	,	,	PUNCT
ejpam-6440	336	12	2017	2017	NUM
ejpam-6440	336	13	.	.	PUNCT
ejpam-6440	337	1	[	[	X
ejpam-6440	337	2	19	19	NUM
ejpam-6440	337	3	]	]	PUNCT
ejpam-6440	337	4	k.	k.	PROPN
ejpam-6440	337	5	abodayeh	abodayeh	PROPN
ejpam-6440	337	6	,	,	PUNCT
ejpam-6440	337	7	a.	a.	PROPN
ejpam-6440	337	8	bataihah	bataihah	PROPN
ejpam-6440	337	9	,	,	PUNCT
ejpam-6440	337	10	and	and	CCONJ
ejpam-6440	337	11	w.	w.	PROPN
ejpam-6440	337	12	shatanawi	shatanawi	PROPN
ejpam-6440	337	13	.	.	PUNCT
ejpam-6440	338	1	generalized	generalize	VERB
ejpam-6440	338	2	ω	ω	NUM
ejpam-6440	338	3	-	-	PUNCT
ejpam-6440	338	4	distance	distance	NOUN
ejpam-6440	338	5	mappings	mapping	NOUN
ejpam-6440	338	6	and	and	CCONJ
ejpam-6440	338	7	some	some	DET
ejpam-6440	338	8	fixed	fix	VERB
ejpam-6440	338	9	point	point	NOUN
ejpam-6440	338	10	theorems	theorem	NOUN
ejpam-6440	338	11	.	.	PUNCT
ejpam-6440	339	1	u.p.b	u.p.b	PROPN
ejpam-6440	339	2	.	.	PUNCT
ejpam-6440	340	1	scientific	scientific	ADJ
ejpam-6440	340	2	bulletin	bulletin	NOUN
ejpam-6440	340	3	,	,	PUNCT
ejpam-6440	340	4	series	series	PROPN
ejpam-6440	340	5	a	a	PROPN
ejpam-6440	340	6	,	,	PUNCT
ejpam-6440	340	7	79:223–232	79:223–232	PROPN
ejpam-6440	340	8	,	,	PUNCT
ejpam-6440	340	9	2017	2017	NUM
ejpam-6440	340	10	.	.	PUNCT
ejpam-6440	341	1	[	[	X
ejpam-6440	341	2	20	20	NUM
ejpam-6440	341	3	]	]	PUNCT
ejpam-6440	341	4	t.	t.	NOUN
ejpam-6440	341	5	qawasmeh	qawasmeh	NOUN
ejpam-6440	341	6	,	,	PUNCT
ejpam-6440	341	7	w.	w.	PROPN
ejpam-6440	341	8	shatanawi	shatanawi	PROPN
ejpam-6440	341	9	,	,	PUNCT
ejpam-6440	341	10	and	and	CCONJ
ejpam-6440	341	11	a.	a.	NOUN
ejpam-6440	341	12	bataihah	bataihah	PROPN
ejpam-6440	341	13	.	.	PUNCT
ejpam-6440	342	1	common	common	ADJ
ejpam-6440	342	2	fixed	fix	VERB
ejpam-6440	342	3	point	point	NOUN
ejpam-6440	342	4	results	result	NOUN
ejpam-6440	342	5	for	for	ADP
ejpam-6440	342	6	rational	rational	ADJ
ejpam-6440	342	7	(	(	PUNCT
ejpam-6440	342	8	α	α	NOUN
ejpam-6440	342	9	,	,	PUNCT
ejpam-6440	342	10	β)ϕ-mω	β)ϕ-mω	NOUN
ejpam-6440	342	11	contractions	contraction	NOUN
ejpam-6440	342	12	in	in	ADP
ejpam-6440	342	13	complete	complete	ADJ
ejpam-6440	342	14	quasi	quasi	ADJ
ejpam-6440	342	15	metric	metric	ADJ
ejpam-6440	342	16	spaces	space	NOUN
ejpam-6440	342	17	.	.	PUNCT
ejpam-6440	343	1	mathematics	mathematic	NOUN
ejpam-6440	343	2	,	,	PUNCT
ejpam-6440	343	3	7(5):392	7(5):392	NUM
ejpam-6440	343	4	,	,	PUNCT
ejpam-6440	343	5	2017	2017	NUM
ejpam-6440	343	6	.	.	PUNCT
ejpam-6440	344	1	[	[	X
ejpam-6440	344	2	21	21	NUM
ejpam-6440	344	3	]	]	PUNCT
ejpam-6440	344	4	a.	a.	NOUN
ejpam-6440	344	5	rabaiah	rabaiah	PROPN
ejpam-6440	344	6	,	,	PUNCT
ejpam-6440	344	7	a.	a.	NOUN
ejpam-6440	344	8	tallafha	tallafha	NOUN
ejpam-6440	344	9	,	,	PUNCT
ejpam-6440	344	10	and	and	CCONJ
ejpam-6440	344	11	w.	w.	PROPN
ejpam-6440	344	12	shatanawi	shatanawi	PROPN
ejpam-6440	344	13	.	.	PUNCT
ejpam-6440	345	1	common	common	ADJ
ejpam-6440	345	2	fixed	fix	VERB
ejpam-6440	345	3	point	point	NOUN
ejpam-6440	345	4	results	result	NOUN
ejpam-6440	345	5	for	for	ADP
ejpam-6440	345	6	mappings	mapping	NOUN
ejpam-6440	345	7	under	under	ADP
ejpam-6440	345	8	nonlinear	nonlinear	ADJ
ejpam-6440	345	9	contraction	contraction	NOUN
ejpam-6440	345	10	of	of	ADP
ejpam-6440	345	11	cyclic	cyclic	ADJ
ejpam-6440	345	12	form	form	NOUN
ejpam-6440	345	13	in	in	ADP
ejpam-6440	345	14	b	b	NOUN
ejpam-6440	345	15	-	-	ADJ
ejpam-6440	345	16	metric	metric	ADJ
ejpam-6440	345	17	spaces	space	NOUN
ejpam-6440	345	18	.	.	PUNCT
ejpam-6440	346	1	advances	advance	NOUN
ejpam-6440	346	2	in	in	ADP
ejpam-6440	346	3	mathematics	mathematics	NOUN
ejpam-6440	346	4	scientific	scientific	ADJ
ejpam-6440	346	5	journal	journal	NOUN
ejpam-6440	346	6	,	,	PUNCT
ejpam-6440	346	7	26(2):289–301	26(2):289–301	PROPN
ejpam-6440	346	8	,	,	PUNCT
ejpam-6440	346	9	2021	2021	NUM
ejpam-6440	346	10	.	.	PUNCT
ejpam-6440	347	1	[	[	X
ejpam-6440	347	2	22	22	NUM
ejpam-6440	347	3	]	]	X
ejpam-6440	347	4	i.	i.	PROPN
ejpam-6440	347	5	abu	abu	PROPN
ejpam-6440	347	6	-	-	PUNCT
ejpam-6440	347	7	irwaq	irwaq	PROPN
ejpam-6440	347	8	,	,	PUNCT
ejpam-6440	347	9	w.	w.	PROPN
ejpam-6440	347	10	shatanawi	shatanawi	PROPN
ejpam-6440	347	11	,	,	PUNCT
ejpam-6440	347	12	a.	a.	NOUN
ejpam-6440	347	13	bataihah	bataihah	PROPN
ejpam-6440	347	14	,	,	PUNCT
ejpam-6440	347	15	and	and	CCONJ
ejpam-6440	347	16	nuseir	nuseir	NOUN
ejpam-6440	347	17	.	.	PUNCT
ejpam-6440	348	1	fixed	fix	VERB
ejpam-6440	348	2	point	point	NOUN
ejpam-6440	348	3	results	result	NOUN
ejpam-6440	348	4	for	for	ADP
ejpam-6440	348	5	nonlinear	nonlinear	ADJ
ejpam-6440	348	6	contractions	contraction	NOUN
ejpam-6440	348	7	with	with	ADP
ejpam-6440	348	8	generalized	generalized	ADJ
ejpam-6440	348	9	ω	ω	NUM
ejpam-6440	348	10	-	-	PUNCT
ejpam-6440	348	11	distance	distance	NOUN
ejpam-6440	348	12	mappings	mapping	NOUN
ejpam-6440	348	13	.	.	PUNCT
ejpam-6440	349	1	u.p.b	u.p.b	ADJ
ejpam-6440	349	2	.	.	PUNCT
ejpam-6440	350	1	scientific	scientific	ADJ
ejpam-6440	350	2	bulletin	bulletin	NOUN
ejpam-6440	350	3	,	,	PUNCT
ejpam-6440	350	4	series	series	NOUN
ejpam-6440	350	5	a	a	NOUN
ejpam-6440	350	6	,	,	PUNCT
ejpam-6440	350	7	81(1):57–64	81(1):57–64	NUM
ejpam-6440	350	8	,	,	PUNCT
ejpam-6440	350	9	2019	2019	NUM
ejpam-6440	350	10	.	.	PUNCT
ejpam-6440	351	1	[	[	X
ejpam-6440	351	2	23	23	NUM
ejpam-6440	351	3	]	]	PUNCT
ejpam-6440	351	4	a.	a.	NOUN
ejpam-6440	351	5	a.	a.	PROPN
ejpam-6440	351	6	r.	r.	PROPN
ejpam-6440	351	7	m.	m.	PROPN
ejpam-6440	351	8	malkawi	malkawi	PROPN
ejpam-6440	351	9	.	.	PROPN
ejpam-6440	352	1	existence	existence	NOUN
ejpam-6440	352	2	and	and	CCONJ
ejpam-6440	352	3	uniqueness	uniqueness	NOUN
ejpam-6440	352	4	of	of	ADP
ejpam-6440	352	5	fixed	fix	VERB
ejpam-6440	352	6	points	point	NOUN
ejpam-6440	352	7	in	in	ADP
ejpam-6440	352	8	mr	mr	PROPN
ejpam-6440	352	9	-	-	PUNCT
ejpam-6440	352	10	metric	metric	ADJ
ejpam-6440	352	11	spaces	space	NOUN
ejpam-6440	352	12	and	and	CCONJ
ejpam-6440	352	13	their	their	PRON
ejpam-6440	352	14	applications	application	NOUN
ejpam-6440	352	15	.	.	PUNCT
ejpam-6440	353	1	european	european	ADJ
ejpam-6440	353	2	journal	journal	PROPN
ejpam-6440	353	3	of	of	ADP
ejpam-6440	353	4	pure	pure	ADJ
ejpam-6440	353	5	and	and	CCONJ
ejpam-6440	353	6	applied	applied	ADJ
ejpam-6440	353	7	mathematics	mathematic	NOUN
ejpam-6440	353	8	,	,	PUNCT
ejpam-6440	353	9	18(2):6077	18(2):6077	NUM
ejpam-6440	353	10	,	,	PUNCT
ejpam-6440	353	11	2025	2025	NUM
ejpam-6440	353	12	.	.	PUNCT
ejpam-6440	354	1	[	[	X
ejpam-6440	354	2	24	24	NUM
ejpam-6440	354	3	]	]	PUNCT
ejpam-6440	354	4	a.	a.	NOUN
ejpam-6440	354	5	a.	a.	PROPN
ejpam-6440	354	6	r.	r.	PROPN
ejpam-6440	354	7	m.	m.	PROPN
ejpam-6440	354	8	malkawi	malkawi	PROPN
ejpam-6440	354	9	.	.	PROPN
ejpam-6440	355	1	convergence	convergence	NOUN
ejpam-6440	355	2	and	and	CCONJ
ejpam-6440	355	3	fixed	fix	VERB
ejpam-6440	355	4	points	point	NOUN
ejpam-6440	355	5	of	of	ADP
ejpam-6440	355	6	self	self	NOUN
ejpam-6440	355	7	-	-	PUNCT
ejpam-6440	355	8	mappings	mapping	NOUN
ejpam-6440	355	9	in	in	ADP
ejpam-6440	355	10	mr	mr	PROPN
ejpam-6440	355	11	-	-	PUNCT
ejpam-6440	355	12	metric	metric	ADJ
ejpam-6440	355	13	spaces	space	NOUN
ejpam-6440	355	14	:	:	PUNCT
ejpam-6440	355	15	theory	theory	NOUN
ejpam-6440	355	16	and	and	CCONJ
ejpam-6440	355	17	applications	application	NOUN
ejpam-6440	355	18	.	.	PUNCT
ejpam-6440	356	1	european	european	ADJ
ejpam-6440	356	2	journal	journal	PROPN
ejpam-6440	356	3	of	of	ADP
ejpam-6440	356	4	pure	pure	ADJ
ejpam-6440	356	5	and	and	CCONJ
ejpam-6440	356	6	applied	applied	ADJ
ejpam-6440	356	7	mathematics	mathematic	NOUN
ejpam-6440	356	8	,	,	PUNCT
ejpam-6440	356	9	18(2):5952	18(2):5952	NUM
ejpam-6440	356	10	,	,	PUNCT
ejpam-6440	356	11	2025	2025	NUM
ejpam-6440	356	12	.	.	PUNCT
ejpam-6440	357	1	[	[	X
ejpam-6440	357	2	25	25	NUM
ejpam-6440	357	3	]	]	PUNCT
ejpam-6440	357	4	a.	a.	NOUN
ejpam-6440	357	5	a.	a.	PROPN
ejpam-6440	357	6	r.	r.	PROPN
ejpam-6440	357	7	m.	m.	PROPN
ejpam-6440	357	8	malkawi	malkawi	PROPN
ejpam-6440	357	9	.	.	PUNCT
ejpam-6440	357	10	fixed	fix	VERB
ejpam-6440	357	11	point	point	NOUN
ejpam-6440	357	12	theorem	theorem	VERB
ejpam-6440	357	13	in	in	ADP
ejpam-6440	357	14	mr	mr	PROPN
ejpam-6440	357	15	-	-	PUNCT
ejpam-6440	357	16	metric	metric	ADJ
ejpam-6440	357	17	spaces	space	NOUN
ejpam-6440	357	18	via	via	ADP
ejpam-6440	357	19	integral	integral	ADJ
ejpam-6440	357	20	type	type	NOUN
ejpam-6440	357	21	contraction	contraction	NOUN
ejpam-6440	357	22	.	.	PUNCT
ejpam-6440	358	1	european	european	ADJ
ejpam-6440	358	2	journal	journal	PROPN
ejpam-6440	358	3	of	of	ADP
ejpam-6440	358	4	pure	pure	ADJ
ejpam-6440	358	5	and	and	CCONJ
ejpam-6440	358	6	applied	applied	ADJ
ejpam-6440	358	7	mathematics	mathematic	NOUN
ejpam-6440	358	8	,	,	PUNCT
ejpam-6440	358	9	24:295–299	24:295–299	PROPN
ejpam-6440	358	10	,	,	PUNCT
ejpam-6440	358	11	2025	2025	NUM
ejpam-6440	358	12	.	.	PUNCT
ejpam-6440	359	1	[	[	X
ejpam-6440	359	2	26	26	NUM
ejpam-6440	359	3	]	]	PUNCT
ejpam-6440	359	4	a.	a.	NOUN
ejpam-6440	359	5	a.	a.	PROPN
ejpam-6440	359	6	r.	r.	PROPN
ejpam-6440	359	7	m.	m.	PROPN
ejpam-6440	359	8	malkawi	malkawi	PROPN
ejpam-6440	359	9	,	,	PUNCT
ejpam-6440	359	10	d.	d.	PROPN
ejpam-6440	359	11	mahmoud	mahmoud	PROPN
ejpam-6440	359	12	,	,	PUNCT
ejpam-6440	359	13	a.	a.	PROPN
ejpam-6440	359	14	m.	m.	PROPN
ejpam-6440	359	15	rabaiah	rabaiah	PROPN
ejpam-6440	359	16	,	,	PUNCT
ejpam-6440	359	17	r.	r.	PROPN
ejpam-6440	359	18	al	al	PROPN
ejpam-6440	359	19	-	-	PUNCT
ejpam-6440	359	20	deiakeh	deiakeh	PROPN
ejpam-6440	359	21	,	,	PUNCT
ejpam-6440	359	22	and	and	CCONJ
ejpam-6440	359	23	w.	w.	PROPN
ejpam-6440	359	24	shatanawi	shatanawi	PROPN
ejpam-6440	359	25	.	.	PUNCT
ejpam-6440	360	1	on	on	ADP
ejpam-6440	360	2	fixed	fix	VERB
ejpam-6440	360	3	point	point	NOUN
ejpam-6440	360	4	theorems	theorem	NOUN
ejpam-6440	360	5	in	in	ADP
ejpam-6440	360	6	mr	mr	PROPN
ejpam-6440	360	7	-	-	PUNCT
ejpam-6440	360	8	metric	metric	ADJ
ejpam-6440	360	9	spaces	space	NOUN
ejpam-6440	360	10	.	.	PUNCT
ejpam-6440	361	1	nonlinear	nonlinear	ADJ
ejpam-6440	361	2	functional	functional	ADJ
ejpam-6440	361	3	analysis	analysis	NOUN
ejpam-6440	361	4	and	and	CCONJ
ejpam-6440	361	5	applications	application	NOUN
ejpam-6440	361	6	,	,	PUNCT
ejpam-6440	361	7	29(4):1125–1136	29(4):1125–1136	NUM
ejpam-6440	361	8	,	,	PUNCT
ejpam-6440	361	9	2024	2024	NUM
ejpam-6440	361	10	.	.	PUNCT
ejpam-6440	362	1	[	[	X
ejpam-6440	362	2	27	27	NUM
ejpam-6440	362	3	]	]	X
ejpam-6440	362	4	g.	g.	PROPN
ejpam-6440	362	5	gharib	gharib	PROPN
ejpam-6440	362	6	,	,	PUNCT
ejpam-6440	362	7	a.	a.	PROPN
ejpam-6440	362	8	malkawi	malkawi	PROPN
ejpam-6440	362	9	,	,	PUNCT
ejpam-6440	362	10	a.	a.	PROPN
ejpam-6440	362	11	rabaiah	rabaiah	PROPN
ejpam-6440	362	12	,	,	PUNCT
ejpam-6440	362	13	w.	w.	PROPN
ejpam-6440	362	14	shatanawi	shatanawi	PROPN
ejpam-6440	362	15	,	,	PUNCT
ejpam-6440	362	16	and	and	CCONJ
ejpam-6440	362	17	m.	m.	NOUN
ejpam-6440	362	18	alsauodi	alsauodi	PROPN
ejpam-6440	362	19	.	.	PUNCT
ejpam-6440	363	1	a	a	DET
ejpam-6440	363	2	common	common	ADJ
ejpam-6440	363	3	fixed	fix	VERB
ejpam-6440	363	4	point	point	NOUN
ejpam-6440	363	5	theorem	theorem	VERB
ejpam-6440	363	6	in	in	ADP
ejpam-6440	363	7	m*-metric	m*-metric	ADV
ejpam-6440	363	8	space	space	NOUN
ejpam-6440	363	9	and	and	CCONJ
ejpam-6440	363	10	an	an	DET
ejpam-6440	363	11	application	application	NOUN
ejpam-6440	363	12	.	.	PUNCT
ejpam-6440	364	1	nonlinear	nonlinear	ADJ
ejpam-6440	364	2	functional	functional	ADJ
ejpam-6440	364	3	analysis	analysis	NOUN
ejpam-6440	364	4	and	and	CCONJ
ejpam-6440	364	5	applications	application	NOUN
ejpam-6440	364	6	,	,	PUNCT
ejpam-6440	364	7	27(2):289–308	27(2):289–308	NUM
ejpam-6440	364	8	,	,	PUNCT
ejpam-6440	364	9	2022	2022	NUM
ejpam-6440	364	10	.	.	PUNCT
ejpam-6440	365	1	[	[	X
ejpam-6440	365	2	28	28	NUM
ejpam-6440	365	3	]	]	X
ejpam-6440	365	4	a.	a.	NOUN
ejpam-6440	365	5	malkawi	malkawi	PROPN
ejpam-6440	365	6	,	,	PUNCT
ejpam-6440	365	7	a.	a.	NOUN
ejpam-6440	365	8	tallafha	tallafha	NOUN
ejpam-6440	365	9	,	,	PUNCT
ejpam-6440	365	10	and	and	CCONJ
ejpam-6440	365	11	w.	w.	PROPN
ejpam-6440	365	12	shatanawi	shatanawi	PROPN
ejpam-6440	365	13	.	.	PUNCT
ejpam-6440	366	1	coincidence	coincidence	NOUN
ejpam-6440	366	2	and	and	CCONJ
ejpam-6440	366	3	fixed	fix	VERB
ejpam-6440	366	4	point	point	NOUN
ejpam-6440	366	5	results	result	NOUN
ejpam-6440	366	6	for	for	ADP
ejpam-6440	366	7	generalized	generalized	ADJ
ejpam-6440	366	8	weak	weak	ADJ
ejpam-6440	366	9	contraction	contraction	NOUN
ejpam-6440	366	10	mapping	mapping	NOUN
ejpam-6440	366	11	on	on	ADP
ejpam-6440	366	12	b	b	NOUN
ejpam-6440	366	13	-	-	PUNCT
ejpam-6440	366	14	metric	metric	ADJ
ejpam-6440	366	15	spaces	space	NOUN
ejpam-6440	366	16	.	.	PUNCT
ejpam-6440	367	1	nonlinear	nonlinear	ADJ
ejpam-6440	367	2	functional	functional	ADJ
ejpam-6440	367	3	analysis	analysis	NOUN
ejpam-6440	367	4	and	and	CCONJ
ejpam-6440	367	5	applications	application	NOUN
ejpam-6440	367	6	,	,	PUNCT
ejpam-6440	367	7	26(1):177–195	26(1):177–195	NOUN
ejpam-6440	367	8	,	,	PUNCT
ejpam-6440	367	9	2021	2021	NUM
ejpam-6440	367	10	.	.	PUNCT
ejpam-6440	368	1	[	[	X
ejpam-6440	368	2	29	29	NUM
ejpam-6440	368	3	]	]	PUNCT
ejpam-6440	368	4	r.	r.	PROPN
ejpam-6440	368	5	al	al	PROPN
ejpam-6440	368	6	-	-	PUNCT
ejpam-6440	368	7	deiakeh	deiakeh	ADJ
ejpam-6440	368	8	,	,	PUNCT
ejpam-6440	368	9	m.	m.	NOUN
ejpam-6440	368	10	alquran	alquran	PROPN
ejpam-6440	368	11	,	,	PUNCT
ejpam-6440	368	12	m.	m.	PROPN
ejpam-6440	368	13	ali	ali	PROPN
ejpam-6440	368	14	,	,	PUNCT
ejpam-6440	368	15	s.	s.	PROPN
ejpam-6440	368	16	qureshi	qureshi	PROPN
ejpam-6440	368	17	,	,	PUNCT
ejpam-6440	368	18	s.	s.	PROPN
ejpam-6440	368	19	momani	momani	PROPN
ejpam-6440	368	20	,	,	PUNCT
ejpam-6440	368	21	and	and	CCONJ
ejpam-6440	369	1	a.	a.	NOUN
ejpam-6440	369	2	a.	a.	PROPN
ejpam-6440	369	3	r.	r.	PROPN
ejpam-6440	369	4	malkawi	malkawi	PROPN
ejpam-6440	369	5	.	.	PROPN
ejpam-6440	369	6	lie	lie	PROPN
ejpam-6440	369	7	symmetry	symmetry	NOUN
ejpam-6440	369	8	,	,	PUNCT
ejpam-6440	369	9	convergence	convergence	NOUN
ejpam-6440	369	10	analysis	analysis	NOUN
ejpam-6440	369	11	,	,	PUNCT
ejpam-6440	369	12	explicit	explicit	ADJ
ejpam-6440	369	13	solutions	solution	NOUN
ejpam-6440	369	14	,	,	PUNCT
ejpam-6440	369	15	and	and	CCONJ
ejpam-6440	369	16	conservation	conservation	NOUN
ejpam-6440	369	17	laws	law	NOUN
ejpam-6440	369	18	for	for	ADP
ejpam-6440	369	19	the	the	DET
ejpam-6440	369	20	timefractional	timefractional	ADJ
ejpam-6440	369	21	modified	modify	VERB
ejpam-6440	369	22	benjamin	benjamin	PROPN
ejpam-6440	369	23	-	-	PUNCT
ejpam-6440	369	24	bona	bona	ADJ
ejpam-6440	369	25	-	-	PUNCT
ejpam-6440	369	26	mahony	mahony	NOUN
ejpam-6440	369	27	equation	equation	NOUN
ejpam-6440	369	28	.	.	PUNCT
ejpam-6440	370	1	journal	journal	PROPN
ejpam-6440	370	2	of	of	ADP
ejpam-6440	370	3	applied	apply	VERB
ejpam-6440	370	4	mathematics	mathematic	NOUN
ejpam-6440	370	5	and	and	CCONJ
ejpam-6440	370	6	computational	computational	ADJ
ejpam-6440	370	7	mechanics	mechanic	NOUN
ejpam-6440	370	8	,	,	PUNCT
ejpam-6440	370	9	23(1):19–31	23(1):19–31	NUM
ejpam-6440	370	10	,	,	PUNCT
ejpam-6440	370	11	2024	2024	NUM
ejpam-6440	370	12	.	.	PUNCT
ejpam-6440	371	1	[	[	X
ejpam-6440	371	2	30	30	NUM
ejpam-6440	371	3	]	]	PUNCT
ejpam-6440	371	4	s.	s.	PROPN
ejpam-6440	371	5	al	al	PROPN
ejpam-6440	371	6	-	-	PUNCT
ejpam-6440	371	7	sharif	sharif	PROPN
ejpam-6440	371	8	and	and	CCONJ
ejpam-6440	371	9	a.	a.	NOUN
ejpam-6440	371	10	malkawi	malkawi	PROPN
ejpam-6440	371	11	.	.	PUNCT
ejpam-6440	372	1	modification	modification	NOUN
ejpam-6440	372	2	of	of	ADP
ejpam-6440	372	3	conformable	conformable	ADJ
ejpam-6440	372	4	fractional	fractional	ADJ
ejpam-6440	372	5	derivative	derivative	NOUN
ejpam-6440	372	6	with	with	ADP
ejpam-6440	372	7	classical	classical	ADJ
ejpam-6440	372	8	properties	property	NOUN
ejpam-6440	372	9	.	.	PUNCT
ejpam-6440	373	1	italian	italian	ADJ
ejpam-6440	373	2	journal	journal	NOUN
ejpam-6440	373	3	of	of	ADP
ejpam-6440	373	4	pure	pure	ADJ
ejpam-6440	373	5	and	and	CCONJ
ejpam-6440	373	6	applied	applied	ADJ
ejpam-6440	373	7	mathematics	mathematic	NOUN
ejpam-6440	373	8	,	,	PUNCT
ejpam-6440	373	9	44:30–39	44:30–39	PROPN
ejpam-6440	373	10	,	,	PUNCT
ejpam-6440	373	11	2020	2020	NUM
ejpam-6440	373	12	.	.	PUNCT
ejpam-6440	374	1	[	[	X
ejpam-6440	374	2	31	31	NUM
ejpam-6440	374	3	]	]	X
ejpam-6440	374	4	g.	g.	PROPN
ejpam-6440	374	5	m.	m.	PROPN
ejpam-6440	374	6	gharib	gharib	PROPN
ejpam-6440	374	7	,	,	PUNCT
ejpam-6440	374	8	m.	m.	PROPN
ejpam-6440	374	9	s.	s.	PROPN
ejpam-6440	374	10	alsauodi	alsauodi	PROPN
ejpam-6440	374	11	,	,	PUNCT
ejpam-6440	374	12	a.	a.	NOUN
ejpam-6440	374	13	guiatni	guiatni	PROPN
ejpam-6440	374	14	,	,	PUNCT
ejpam-6440	374	15	m.	m.	NOUN
ejpam-6440	374	16	a.	a.	PROPN
ejpam-6440	374	17	al	al	PROPN
ejpam-6440	374	18	-	-	PUNCT
ejpam-6440	374	19	omari	omari	PROPN
ejpam-6440	374	20	,	,	PUNCT
ejpam-6440	374	21	and	and	CCONJ
ejpam-6440	374	22	a.	a.	NOUN
ejpam-6440	374	23	a.-r	a.-r	PROPN
ejpam-6440	374	24	.	.	PUNCT
ejpam-6440	375	1	m.	m.	NOUN
ejpam-6440	375	2	malkawi	malkawi	PROPN
ejpam-6440	375	3	.	.	PUNCT
ejpam-6440	376	1	t.	t.	NOUN
ejpam-6440	376	2	qawasmeh	qawasmeh	NOUN
ejpam-6440	376	3	,	,	PUNCT
ejpam-6440	376	4	a.	a.	NOUN
ejpam-6440	376	5	malkawi	malkawi	PROPN
ejpam-6440	376	6	/	/	SYM
ejpam-6440	376	7	eur	eur	PROPN
ejpam-6440	376	8	.	.	PUNCT
ejpam-6440	377	1	j.	j.	PROPN
ejpam-6440	377	2	pure	pure	PROPN
ejpam-6440	377	3	appl	appl	PROPN
ejpam-6440	377	4	.	.	PROPN
ejpam-6440	377	5	math	math	PROPN
ejpam-6440	377	6	,	,	PUNCT
ejpam-6440	377	7	18	18	NUM
ejpam-6440	377	8	(	(	PUNCT
ejpam-6440	377	9	3	3	NUM
ejpam-6440	377	10	)	)	PUNCT
ejpam-6440	377	11	(	(	PUNCT
ejpam-6440	377	12	2025	2025	NUM
ejpam-6440	377	13	)	)	PUNCT
ejpam-6440	377	14	,	,	PUNCT
ejpam-6440	377	15	6440	6440	NUM
ejpam-6440	377	16	20	20	NUM
ejpam-6440	377	17	of	of	ADP
ejpam-6440	377	18	20	20	NUM
ejpam-6440	377	19	using	use	VERB
ejpam-6440	377	20	atomic	atomic	ADJ
ejpam-6440	377	21	solution	solution	NOUN
ejpam-6440	377	22	method	method	NOUN
ejpam-6440	377	23	to	to	PART
ejpam-6440	377	24	solve	solve	VERB
ejpam-6440	377	25	the	the	DET
ejpam-6440	377	26	fractional	fractional	ADJ
ejpam-6440	377	27	equations	equation	NOUN
ejpam-6440	377	28	.	.	PUNCT
ejpam-6440	378	1	springer	springer	NOUN
ejpam-6440	378	2	proceedings	proceeding	NOUN
ejpam-6440	378	3	in	in	ADP
ejpam-6440	378	4	mathematics	mathematic	NOUN
ejpam-6440	378	5	and	and	CCONJ
ejpam-6440	378	6	statistics	statistic	NOUN
ejpam-6440	378	7	,	,	PUNCT
ejpam-6440	378	8	418:123–129	418:123–129	NUM
ejpam-6440	378	9	,	,	PUNCT
ejpam-6440	378	10	2023	2023	NUM
ejpam-6440	378	11	.	.	PUNCT
ejpam-6440	379	1	[	[	X
ejpam-6440	379	2	32	32	NUM
ejpam-6440	379	3	]	]	PUNCT
ejpam-6440	379	4	a.	a.	NOUN
ejpam-6440	379	5	malkawi	malkawi	PROPN
ejpam-6440	379	6	,	,	PUNCT
ejpam-6440	379	7	a.	a.	NOUN
ejpam-6440	379	8	talafhah	talafhah	PROPN
ejpam-6440	379	9	,	,	PUNCT
ejpam-6440	379	10	and	and	CCONJ
ejpam-6440	379	11	w.	w.	PROPN
ejpam-6440	379	12	shatanawi	shatanawi	PROPN
ejpam-6440	379	13	.	.	PUNCT
ejpam-6440	380	1	coincidence	coincidence	NOUN
ejpam-6440	380	2	and	and	CCONJ
ejpam-6440	380	3	fixed	fix	VERB
ejpam-6440	380	4	point	point	NOUN
ejpam-6440	380	5	results	result	NOUN
ejpam-6440	380	6	for	for	ADP
ejpam-6440	380	7	(	(	PUNCT
ejpam-6440	380	8	ψ	ψ	NOUN
ejpam-6440	380	9	,	,	PUNCT
ejpam-6440	380	10	l)-m	l)-m	ADJ
ejpam-6440	380	11	-	-	PUNCT
ejpam-6440	380	12	weak	weak	ADJ
ejpam-6440	380	13	contraction	contraction	NOUN
ejpam-6440	380	14	mapping	mapping	NOUN
ejpam-6440	380	15	on	on	ADP
ejpam-6440	380	16	mb	mb	ADJ
ejpam-6440	380	17	-	-	ADJ
ejpam-6440	380	18	metric	metric	ADJ
ejpam-6440	380	19	spaces	space	NOUN
ejpam-6440	380	20	.	.	PUNCT
ejpam-6440	381	1	italian	italian	ADJ
ejpam-6440	381	2	journal	journal	NOUN
ejpam-6440	381	3	of	of	ADP
ejpam-6440	381	4	pure	pure	ADJ
ejpam-6440	381	5	and	and	CCONJ
ejpam-6440	381	6	applied	applied	ADJ
ejpam-6440	381	7	mathematics	mathematic	NOUN
ejpam-6440	381	8	,	,	PUNCT
ejpam-6440	381	9	(	(	PUNCT
ejpam-6440	381	10	47):751–768	47):751–768	NOUN
ejpam-6440	381	11	,	,	PUNCT
ejpam-6440	381	12	2022	2022	NUM
ejpam-6440	381	13	.	.	PUNCT