id	sid	tid	token	lemma	pos
ejpam-5916	1	1	european	european	PROPN
ejpam-5916	1	2	journal	journal	PROPN
ejpam-5916	1	3	of	of	ADP
ejpam-5916	1	4	pure	pure	ADJ
ejpam-5916	1	5	and	and	CCONJ
ejpam-5916	1	6	applied	applied	ADJ
ejpam-5916	1	7	mathematics	mathematic	NOUN
ejpam-5916	1	8	2025	2025	NUM
ejpam-5916	1	9	,	,	PUNCT
ejpam-5916	1	10	vol	vol	NOUN
ejpam-5916	1	11	.	.	PROPN
ejpam-5916	1	12	18	18	NUM
ejpam-5916	1	13	,	,	PUNCT
ejpam-5916	1	14	issue	issue	NOUN
ejpam-5916	1	15	3	3	NUM
ejpam-5916	1	16	,	,	PUNCT
ejpam-5916	1	17	article	article	NOUN
ejpam-5916	1	18	number	number	NOUN
ejpam-5916	1	19	5916	5916	NUM
ejpam-5916	1	20	issn	issn	VERB
ejpam-5916	1	21	1307	1307	NUM
ejpam-5916	1	22	-	-	SYM
ejpam-5916	1	23	5543	5543	NUM
ejpam-5916	1	24	–	–	PUNCT
ejpam-5916	1	25	ejpam.com	ejpam.com	X
ejpam-5916	1	26	published	publish	VERB
ejpam-5916	1	27	by	by	ADP
ejpam-5916	1	28	new	new	PROPN
ejpam-5916	1	29	york	york	PROPN
ejpam-5916	1	30	business	business	PROPN
ejpam-5916	1	31	global	global	ADJ
ejpam-5916	1	32	exploring	explore	VERB
ejpam-5916	1	33	fixed	fix	VERB
ejpam-5916	1	34	point	point	NOUN
ejpam-5916	1	35	theory	theory	NOUN
ejpam-5916	1	36	in	in	ADP
ejpam-5916	1	37	quasi	quasi	ADJ
ejpam-5916	1	38	-	-	ADJ
ejpam-5916	1	39	partial	partial	ADJ
ejpam-5916	1	40	metric	metric	ADJ
ejpam-5916	1	41	spaces	space	NOUN
ejpam-5916	1	42	:	:	PUNCT
ejpam-5916	1	43	a	a	DET
ejpam-5916	1	44	unified	unified	ADJ
ejpam-5916	1	45	approach	approach	NOUN
ejpam-5916	1	46	with	with	ADP
ejpam-5916	1	47	applications	application	NOUN
ejpam-5916	1	48	in	in	ADP
ejpam-5916	1	49	integral	integral	ADJ
ejpam-5916	1	50	equations	equation	NOUN
ejpam-5916	1	51	and	and	CCONJ
ejpam-5916	1	52	computational	computational	ADJ
ejpam-5916	1	53	sciences	science	NOUN
ejpam-5916	1	54	haitham	haitham	PROPN
ejpam-5916	1	55	qawaqneh	qawaqneh	PROPN
ejpam-5916	1	56	al	al	PROPN
ejpam-5916	1	57	-	-	PROPN
ejpam-5916	1	58	zaytoonah	zaytoonah	PROPN
ejpam-5916	1	59	university	university	PROPN
ejpam-5916	1	60	of	of	ADP
ejpam-5916	1	61	jordan	jordan	PROPN
ejpam-5916	1	62	,	,	PUNCT
ejpam-5916	1	63	amman	amman	PROPN
ejpam-5916	1	64	11733	11733	NUM
ejpam-5916	1	65	,	,	PUNCT
ejpam-5916	1	66	jordan	jordan	PROPN
ejpam-5916	1	67	abstract	abstract	PROPN
ejpam-5916	1	68	.	.	PUNCT
ejpam-5916	2	1	this	this	DET
ejpam-5916	2	2	paper	paper	NOUN
ejpam-5916	2	3	explores	explore	VERB
ejpam-5916	2	4	the	the	DET
ejpam-5916	2	5	concept	concept	NOUN
ejpam-5916	2	6	of	of	ADP
ejpam-5916	2	7	c	c	NOUN
ejpam-5916	2	8	-	-	PUNCT
ejpam-5916	2	9	class	class	NOUN
ejpam-5916	2	10	functions	function	NOUN
ejpam-5916	2	11	,	,	PUNCT
ejpam-5916	2	12	which	which	PRON
ejpam-5916	2	13	encompass	encompass	VERB
ejpam-5916	2	14	a	a	DET
ejpam-5916	2	15	wide	wide	ADJ
ejpam-5916	2	16	range	range	NOUN
ejpam-5916	2	17	of	of	ADP
ejpam-5916	2	18	contractive	contractive	ADJ
ejpam-5916	2	19	conditions	condition	NOUN
ejpam-5916	2	20	and	and	CCONJ
ejpam-5916	2	21	applies	apply	VERB
ejpam-5916	2	22	them	they	PRON
ejpam-5916	2	23	to	to	PART
ejpam-5916	2	24	derive	derive	VERB
ejpam-5916	2	25	common	common	ADJ
ejpam-5916	2	26	fixed	fix	VERB
ejpam-5916	2	27	-	-	PUNCT
ejpam-5916	2	28	point	point	NOUN
ejpam-5916	2	29	results	result	NOUN
ejpam-5916	2	30	for	for	ADP
ejpam-5916	2	31	two	two	NUM
ejpam-5916	2	32	pairs	pair	NOUN
ejpam-5916	2	33	of	of	ADP
ejpam-5916	2	34	self	self	NOUN
ejpam-5916	2	35	-	-	PUNCT
ejpam-5916	2	36	mappings	mapping	NOUN
ejpam-5916	2	37	in	in	ADP
ejpam-5916	2	38	quasi	quasi	ADJ
ejpam-5916	2	39	-	-	ADJ
ejpam-5916	2	40	partial	partial	ADJ
ejpam-5916	2	41	metric	metric	ADJ
ejpam-5916	2	42	spaces	space	NOUN
ejpam-5916	2	43	.	.	PUNCT
ejpam-5916	3	1	these	these	DET
ejpam-5916	3	2	findings	finding	NOUN
ejpam-5916	3	3	extend	extend	VERB
ejpam-5916	3	4	existing	exist	VERB
ejpam-5916	3	5	theories	theory	NOUN
ejpam-5916	3	6	by	by	ADP
ejpam-5916	3	7	introducing	introduce	VERB
ejpam-5916	3	8	generalized	generalize	VERB
ejpam-5916	3	9	contractive	contractive	ADJ
ejpam-5916	3	10	conditions	condition	NOUN
ejpam-5916	3	11	and	and	CCONJ
ejpam-5916	3	12	providing	provide	VERB
ejpam-5916	3	13	a	a	DET
ejpam-5916	3	14	broader	broad	ADJ
ejpam-5916	3	15	framework	framework	NOUN
ejpam-5916	3	16	for	for	ADP
ejpam-5916	3	17	fixed	fix	VERB
ejpam-5916	3	18	-	-	PUNCT
ejpam-5916	3	19	point	point	NOUN
ejpam-5916	3	20	analysis	analysis	NOUN
ejpam-5916	3	21	.	.	PUNCT
ejpam-5916	4	1	a	a	DET
ejpam-5916	4	2	detailed	detailed	ADJ
ejpam-5916	4	3	example	example	NOUN
ejpam-5916	4	4	is	be	AUX
ejpam-5916	4	5	constructed	construct	VERB
ejpam-5916	4	6	to	to	PART
ejpam-5916	4	7	validate	validate	VERB
ejpam-5916	4	8	the	the	DET
ejpam-5916	4	9	results	result	NOUN
ejpam-5916	4	10	,	,	PUNCT
ejpam-5916	4	11	illustrating	illustrate	VERB
ejpam-5916	4	12	the	the	DET
ejpam-5916	4	13	practical	practical	ADJ
ejpam-5916	4	14	application	application	NOUN
ejpam-5916	4	15	of	of	ADP
ejpam-5916	4	16	the	the	DET
ejpam-5916	4	17	established	establish	VERB
ejpam-5916	4	18	theorems	theorem	NOUN
ejpam-5916	4	19	.	.	PUNCT
ejpam-5916	5	1	furthermore	furthermore	ADV
ejpam-5916	5	2	,	,	PUNCT
ejpam-5916	5	3	the	the	DET
ejpam-5916	5	4	paper	paper	NOUN
ejpam-5916	5	5	demonstrates	demonstrate	VERB
ejpam-5916	5	6	the	the	DET
ejpam-5916	5	7	relevance	relevance	NOUN
ejpam-5916	5	8	of	of	ADP
ejpam-5916	5	9	these	these	DET
ejpam-5916	5	10	results	result	NOUN
ejpam-5916	5	11	by	by	ADP
ejpam-5916	5	12	applying	apply	VERB
ejpam-5916	5	13	them	they	PRON
ejpam-5916	5	14	to	to	PART
ejpam-5916	5	15	solve	solve	VERB
ejpam-5916	5	16	a	a	DET
ejpam-5916	5	17	system	system	NOUN
ejpam-5916	5	18	of	of	ADP
ejpam-5916	5	19	integral	integral	ADJ
ejpam-5916	5	20	equations	equation	NOUN
ejpam-5916	5	21	diffusion	diffusion	NOUN
ejpam-5916	5	22	reaction	reaction	NOUN
ejpam-5916	5	23	,	,	PUNCT
ejpam-5916	5	24	highlighting	highlight	VERB
ejpam-5916	5	25	their	their	PRON
ejpam-5916	5	26	utility	utility	NOUN
ejpam-5916	5	27	in	in	ADP
ejpam-5916	5	28	addressing	address	VERB
ejpam-5916	5	29	real	real	ADJ
ejpam-5916	5	30	-	-	PUNCT
ejpam-5916	5	31	world	world	NOUN
ejpam-5916	5	32	mathematical	mathematical	ADJ
ejpam-5916	5	33	problems	problem	NOUN
ejpam-5916	5	34	.	.	PUNCT
ejpam-5916	6	1	2020	2020	NUM
ejpam-5916	6	2	mathematics	mathematic	NOUN
ejpam-5916	6	3	subject	subject	NOUN
ejpam-5916	6	4	classifications	classification	NOUN
ejpam-5916	6	5	:	:	PUNCT
ejpam-5916	6	6	47h10	47h10	NUM
ejpam-5916	6	7	,	,	PUNCT
ejpam-5916	6	8	54h25	54h25	NUM
ejpam-5916	6	9	key	key	ADJ
ejpam-5916	6	10	words	word	NOUN
ejpam-5916	6	11	and	and	CCONJ
ejpam-5916	6	12	phrases	phrase	NOUN
ejpam-5916	6	13	:	:	PUNCT
ejpam-5916	6	14	weakly	weakly	ADJ
ejpam-5916	6	15	compatible	compatible	ADJ
ejpam-5916	6	16	contraction	contraction	NOUN
ejpam-5916	6	17	,	,	PUNCT
ejpam-5916	6	18	c	c	NOUN
ejpam-5916	6	19	-	-	PUNCT
ejpam-5916	6	20	class	class	NOUN
ejpam-5916	6	21	functions	function	NOUN
ejpam-5916	6	22	,	,	PUNCT
ejpam-5916	6	23	quasi	quasi	X
ejpam-5916	6	24	partial	partial	ADJ
ejpam-5916	6	25	metric	metric	ADJ
ejpam-5916	6	26	spaces	space	NOUN
ejpam-5916	6	27	1	1	NUM
ejpam-5916	6	28	.	.	X
ejpam-5916	6	29	introduction	introduction	NOUN
ejpam-5916	6	30	the	the	DET
ejpam-5916	6	31	study	study	NOUN
ejpam-5916	6	32	of	of	ADP
ejpam-5916	6	33	metric	metric	ADJ
ejpam-5916	6	34	spaces	space	NOUN
ejpam-5916	6	35	has	have	AUX
ejpam-5916	6	36	undergone	undergo	VERB
ejpam-5916	6	37	significant	significant	ADJ
ejpam-5916	6	38	evolution	evolution	NOUN
ejpam-5916	6	39	through	through	ADP
ejpam-5916	6	40	various	various	ADJ
ejpam-5916	6	41	generalizations	generalization	NOUN
ejpam-5916	6	42	,	,	PUNCT
ejpam-5916	6	43	such	such	ADJ
ejpam-5916	6	44	as	as	ADP
ejpam-5916	6	45	partial	partial	ADJ
ejpam-5916	6	46	metric	metric	ADJ
ejpam-5916	6	47	spaces	space	NOUN
ejpam-5916	6	48	,	,	PUNCT
ejpam-5916	6	49	metric	metric	ADJ
ejpam-5916	6	50	-	-	PUNCT
ejpam-5916	6	51	like	like	ADJ
ejpam-5916	6	52	spaces	space	NOUN
ejpam-5916	6	53	,	,	PUNCT
ejpam-5916	6	54	b−metric	b−metric	ADJ
ejpam-5916	6	55	spaces	space	NOUN
ejpam-5916	6	56	and	and	CCONJ
ejpam-5916	6	57	quasimetric	quasimetric	ADJ
ejpam-5916	6	58	spaces	space	NOUN
ejpam-5916	6	59	.	.	PUNCT
ejpam-5916	7	1	partial	partial	ADJ
ejpam-5916	7	2	metric	metric	ADJ
ejpam-5916	7	3	spaces	space	NOUN
ejpam-5916	7	4	were	be	AUX
ejpam-5916	7	5	first	first	ADV
ejpam-5916	7	6	introduced	introduce	VERB
ejpam-5916	7	7	by	by	ADP
ejpam-5916	7	8	matthews	matthews	PROPN
ejpam-5916	7	9	in	in	ADP
ejpam-5916	7	10	[	[	X
ejpam-5916	7	11	1	1	NUM
ejpam-5916	7	12	,	,	PUNCT
ejpam-5916	7	13	2	2	NUM
ejpam-5916	7	14	]	]	PUNCT
ejpam-5916	7	15	,	,	PUNCT
ejpam-5916	7	16	providing	provide	VERB
ejpam-5916	7	17	a	a	DET
ejpam-5916	7	18	foundational	foundational	ADJ
ejpam-5916	7	19	framework	framework	NOUN
ejpam-5916	7	20	for	for	ADP
ejpam-5916	7	21	fixed	fix	VERB
ejpam-5916	7	22	-	-	PUNCT
ejpam-5916	7	23	point	point	NOUN
ejpam-5916	7	24	theory	theory	NOUN
ejpam-5916	7	25	in	in	ADP
ejpam-5916	7	26	settings	setting	NOUN
ejpam-5916	7	27	where	where	SCONJ
ejpam-5916	7	28	self	self	NOUN
ejpam-5916	7	29	-	-	PUNCT
ejpam-5916	7	30	distance	distance	NOUN
ejpam-5916	7	31	may	may	AUX
ejpam-5916	7	32	not	not	PART
ejpam-5916	7	33	be	be	AUX
ejpam-5916	7	34	zero	zero	NUM
ejpam-5916	7	35	.	.	PUNCT
ejpam-5916	8	1	several	several	ADJ
ejpam-5916	8	2	fixed	fix	VERB
ejpam-5916	8	3	-	-	PUNCT
ejpam-5916	8	4	point	point	NOUN
ejpam-5916	8	5	results	result	NOUN
ejpam-5916	8	6	have	have	AUX
ejpam-5916	8	7	since	since	ADV
ejpam-5916	8	8	been	be	AUX
ejpam-5916	8	9	established	establish	VERB
ejpam-5916	8	10	in	in	ADP
ejpam-5916	8	11	such	such	ADJ
ejpam-5916	8	12	spaces	space	NOUN
ejpam-5916	8	13	,	,	PUNCT
ejpam-5916	8	14	as	as	SCONJ
ejpam-5916	8	15	detailed	detailed	ADJ
ejpam-5916	8	16	in	in	ADP
ejpam-5916	8	17	works	work	NOUN
ejpam-5916	8	18	like	like	ADP
ejpam-5916	8	19	[	[	X
ejpam-5916	8	20	3–5	3–5	NOUN
ejpam-5916	8	21	]	]	PUNCT
ejpam-5916	8	22	.	.	PUNCT
ejpam-5916	9	1	later	later	ADV
ejpam-5916	9	2	,	,	PUNCT
ejpam-5916	9	3	künzi	künzi	PROPN
ejpam-5916	9	4	et	et	PROPN
ejpam-5916	9	5	al	al	PROPN
ejpam-5916	9	6	.	.	PUNCT
ejpam-5916	10	1	[	[	X
ejpam-5916	10	2	6	6	NUM
ejpam-5916	10	3	]	]	PUNCT
ejpam-5916	10	4	expanded	expand	VERB
ejpam-5916	10	5	this	this	DET
ejpam-5916	10	6	concept	concept	NOUN
ejpam-5916	10	7	by	by	ADP
ejpam-5916	10	8	introducing	introduce	VERB
ejpam-5916	10	9	partial	partial	ADJ
ejpam-5916	10	10	quasi	quasi	ADJ
ejpam-5916	10	11	-	-	ADJ
ejpam-5916	10	12	metric	metric	ADJ
ejpam-5916	10	13	spaces	space	NOUN
ejpam-5916	10	14	,	,	PUNCT
ejpam-5916	10	15	which	which	PRON
ejpam-5916	10	16	relaxed	relax	VERB
ejpam-5916	10	17	the	the	DET
ejpam-5916	10	18	symmetry	symmetry	NOUN
ejpam-5916	10	19	condition	condition	NOUN
ejpam-5916	10	20	inherent	inherent	ADJ
ejpam-5916	10	21	in	in	ADP
ejpam-5916	10	22	partial	partial	ADJ
ejpam-5916	10	23	metric	metric	ADJ
ejpam-5916	10	24	spaces	space	NOUN
ejpam-5916	10	25	.	.	PUNCT
ejpam-5916	11	1	karapinar	karapinar	VERB
ejpam-5916	11	2	et	et	PROPN
ejpam-5916	11	3	al	al	PROPN
ejpam-5916	11	4	.	.	PUNCT
ejpam-5916	12	1	[	[	X
ejpam-5916	12	2	7	7	X
ejpam-5916	12	3	]	]	PUNCT
ejpam-5916	12	4	contributed	contribute	VERB
ejpam-5916	12	5	to	to	ADP
ejpam-5916	12	6	this	this	DET
ejpam-5916	12	7	area	area	NOUN
ejpam-5916	12	8	by	by	ADP
ejpam-5916	12	9	renaming	rename	VERB
ejpam-5916	12	10	partial	partial	ADJ
ejpam-5916	12	11	quasi	quasi	ADJ
ejpam-5916	12	12	-	-	ADJ
ejpam-5916	12	13	metric	metric	ADJ
ejpam-5916	12	14	spaces	space	NOUN
ejpam-5916	12	15	as	as	ADP
ejpam-5916	12	16	quasi	quasi	ADJ
ejpam-5916	12	17	-	-	ADJ
ejpam-5916	12	18	partial	partial	ADJ
ejpam-5916	12	19	metric	metric	ADJ
ejpam-5916	12	20	spaces	space	NOUN
ejpam-5916	12	21	and	and	CCONJ
ejpam-5916	12	22	presenting	present	VERB
ejpam-5916	12	23	some	some	DET
ejpam-5916	12	24	initial	initial	ADJ
ejpam-5916	12	25	fixed	fix	VERB
ejpam-5916	12	26	-	-	PUNCT
ejpam-5916	12	27	point	point	NOUN
ejpam-5916	12	28	results	result	NOUN
ejpam-5916	12	29	and	and	CCONJ
ejpam-5916	12	30	properties	property	NOUN
ejpam-5916	12	31	.	.	PUNCT
ejpam-5916	13	1	further	further	ADJ
ejpam-5916	13	2	advancements	advancement	NOUN
ejpam-5916	13	3	in	in	ADP
ejpam-5916	13	4	this	this	DET
ejpam-5916	13	5	domain	domain	NOUN
ejpam-5916	13	6	can	can	AUX
ejpam-5916	13	7	be	be	AUX
ejpam-5916	13	8	found	find	VERB
ejpam-5916	13	9	in	in	ADP
ejpam-5916	13	10	[	[	X
ejpam-5916	13	11	8–19	8–19	NOUN
ejpam-5916	13	12	]	]	PUNCT
ejpam-5916	13	13	.	.	PUNCT
ejpam-5916	14	1	this	this	DET
ejpam-5916	14	2	research	research	NOUN
ejpam-5916	14	3	builds	build	VERB
ejpam-5916	14	4	upon	upon	SCONJ
ejpam-5916	14	5	the	the	DET
ejpam-5916	14	6	foundational	foundational	ADJ
ejpam-5916	14	7	concept	concept	NOUN
ejpam-5916	14	8	of	of	ADP
ejpam-5916	14	9	c	c	NOUN
ejpam-5916	14	10	-	-	PUNCT
ejpam-5916	14	11	class	class	NOUN
ejpam-5916	14	12	functions	function	NOUN
ejpam-5916	14	13	,	,	PUNCT
ejpam-5916	14	14	which	which	PRON
ejpam-5916	14	15	provide	provide	VERB
ejpam-5916	14	16	a	a	DET
ejpam-5916	14	17	flexible	flexible	ADJ
ejpam-5916	14	18	and	and	CCONJ
ejpam-5916	14	19	comprehensive	comprehensive	ADJ
ejpam-5916	14	20	framework	framework	NOUN
ejpam-5916	14	21	for	for	ADP
ejpam-5916	14	22	addressing	address	VERB
ejpam-5916	14	23	a	a	DET
ejpam-5916	14	24	wide	wide	ADJ
ejpam-5916	14	25	spectrum	spectrum	NOUN
ejpam-5916	14	26	of	of	ADP
ejpam-5916	14	27	contractive	contractive	ADJ
ejpam-5916	14	28	conditions	condition	NOUN
ejpam-5916	14	29	.	.	PUNCT
ejpam-5916	15	1	these	these	DET
ejpam-5916	15	2	functions	function	NOUN
ejpam-5916	15	3	have	have	AUX
ejpam-5916	15	4	played	play	VERB
ejpam-5916	15	5	a	a	DET
ejpam-5916	15	6	pivotal	pivotal	ADJ
ejpam-5916	15	7	role	role	NOUN
ejpam-5916	15	8	in	in	ADP
ejpam-5916	15	9	broadening	broaden	VERB
ejpam-5916	15	10	the	the	DET
ejpam-5916	15	11	scope	scope	NOUN
ejpam-5916	15	12	of	of	ADP
ejpam-5916	15	13	fixed	fix	VERB
ejpam-5916	15	14	-	-	PUNCT
ejpam-5916	15	15	point	point	NOUN
ejpam-5916	15	16	doi	doi	NOUN
ejpam-5916	15	17	:	:	PUNCT
ejpam-5916	15	18	https://doi.org/10.29020/nybg.ejpam.v18i3.5916	https://doi.org/10.29020/nybg.ejpam.v18i3.5916	PROPN
ejpam-5916	15	19	email	email	NOUN
ejpam-5916	15	20	address	address	NOUN
ejpam-5916	15	21	:	:	PUNCT
ejpam-5916	15	22	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-5916	15	23	(	(	PUNCT
ejpam-5916	15	24	h.	h.	PROPN
ejpam-5916	15	25	qawaqneh	qawaqneh	PROPN
ejpam-5916	15	26	)	)	PUNCT
ejpam-5916	15	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5916	16	1	1	1	NUM
ejpam-5916	16	2	copyright	copyright	NOUN
ejpam-5916	16	3	:	:	PUNCT
ejpam-5916	16	4	©	©	PROPN
ejpam-5916	16	5	2025	2025	NUM
ejpam-5916	16	6	the	the	DET
ejpam-5916	16	7	author(s	author(s	NOUN
ejpam-5916	16	8	)	)	PUNCT
ejpam-5916	16	9	.	.	PUNCT
ejpam-5916	17	1	(	(	PUNCT
ejpam-5916	17	2	cc	cc	NOUN
ejpam-5916	17	3	by	by	ADP
ejpam-5916	17	4	-	-	PUNCT
ejpam-5916	17	5	nc	nc	PROPN
ejpam-5916	17	6	4.0	4.0	NUM
ejpam-5916	17	7	)	)	PUNCT
ejpam-5916	17	8	h.	h.	PROPN
ejpam-5916	17	9	qawaqneh	qawaqneh	PROPN
ejpam-5916	17	10	/	/	SYM
ejpam-5916	17	11	eur	eur	PROPN
ejpam-5916	17	12	.	.	PUNCT
ejpam-5916	18	1	j.	j.	PROPN
ejpam-5916	18	2	pure	pure	PROPN
ejpam-5916	18	3	appl	appl	PROPN
ejpam-5916	18	4	.	.	PROPN
ejpam-5916	18	5	math	math	PROPN
ejpam-5916	18	6	,	,	PUNCT
ejpam-5916	18	7	18	18	NUM
ejpam-5916	18	8	(	(	PUNCT
ejpam-5916	18	9	3	3	NUM
ejpam-5916	18	10	)	)	PUNCT
ejpam-5916	18	11	(	(	PUNCT
ejpam-5916	18	12	2025	2025	NUM
ejpam-5916	18	13	)	)	PUNCT
ejpam-5916	18	14	,	,	PUNCT
ejpam-5916	18	15	5916	5916	NUM
ejpam-5916	18	16	2	2	NUM
ejpam-5916	18	17	of	of	ADP
ejpam-5916	18	18	19	19	NUM
ejpam-5916	18	19	theory	theory	NOUN
ejpam-5916	18	20	,	,	PUNCT
ejpam-5916	18	21	offering	offer	VERB
ejpam-5916	18	22	generalized	generalized	ADJ
ejpam-5916	18	23	approaches	approach	NOUN
ejpam-5916	18	24	to	to	ADP
ejpam-5916	18	25	analyzing	analyze	VERB
ejpam-5916	18	26	self	self	NOUN
ejpam-5916	18	27	-	-	PUNCT
ejpam-5916	18	28	mappings	mapping	NOUN
ejpam-5916	18	29	in	in	ADP
ejpam-5916	18	30	various	various	ADJ
ejpam-5916	18	31	mathematical	mathematical	ADJ
ejpam-5916	18	32	structures	structure	NOUN
ejpam-5916	18	33	,	,	PUNCT
ejpam-5916	18	34	as	as	SCONJ
ejpam-5916	18	35	explored	explore	VERB
ejpam-5916	18	36	in	in	ADP
ejpam-5916	18	37	[	[	X
ejpam-5916	18	38	20–23	20–23	NOUN
ejpam-5916	18	39	]	]	PUNCT
ejpam-5916	18	40	.	.	PUNCT
ejpam-5916	19	1	in	in	ADP
ejpam-5916	19	2	this	this	DET
ejpam-5916	19	3	study	study	NOUN
ejpam-5916	19	4	,	,	PUNCT
ejpam-5916	19	5	we	we	PRON
ejpam-5916	19	6	extend	extend	VERB
ejpam-5916	19	7	these	these	DET
ejpam-5916	19	8	ideas	idea	NOUN
ejpam-5916	19	9	by	by	ADP
ejpam-5916	19	10	introducing	introduce	VERB
ejpam-5916	19	11	a	a	DET
ejpam-5916	19	12	novel	novel	ADJ
ejpam-5916	19	13	class	class	NOUN
ejpam-5916	19	14	of	of	ADP
ejpam-5916	19	15	ciric	ciric	ADJ
ejpam-5916	19	16	-	-	PUNCT
ejpam-5916	19	17	type	type	NOUN
ejpam-5916	19	18	contractive	contractive	ADJ
ejpam-5916	19	19	conditions	condition	NOUN
ejpam-5916	19	20	specifically	specifically	ADV
ejpam-5916	19	21	designed	design	VERB
ejpam-5916	19	22	for	for	ADP
ejpam-5916	19	23	quasi	quasi	ADJ
ejpam-5916	19	24	-	-	ADJ
ejpam-5916	19	25	partial	partial	ADJ
ejpam-5916	19	26	metric	metric	ADJ
ejpam-5916	19	27	spaces	space	NOUN
ejpam-5916	19	28	.	.	PUNCT
ejpam-5916	20	1	our	our	PRON
ejpam-5916	20	2	primary	primary	ADJ
ejpam-5916	20	3	goal	goal	NOUN
ejpam-5916	20	4	is	be	AUX
ejpam-5916	20	5	to	to	PART
ejpam-5916	20	6	derive	derive	VERB
ejpam-5916	20	7	new	new	ADJ
ejpam-5916	20	8	results	result	NOUN
ejpam-5916	20	9	concerning	concern	VERB
ejpam-5916	20	10	coincidence	coincidence	NOUN
ejpam-5916	20	11	and	and	CCONJ
ejpam-5916	20	12	common	common	ADJ
ejpam-5916	20	13	fixed	fix	VERB
ejpam-5916	20	14	points	point	NOUN
ejpam-5916	20	15	within	within	ADP
ejpam-5916	20	16	this	this	DET
ejpam-5916	20	17	setting	setting	NOUN
ejpam-5916	20	18	.	.	PUNCT
ejpam-5916	21	1	the	the	DET
ejpam-5916	21	2	findings	finding	NOUN
ejpam-5916	21	3	presented	present	VERB
ejpam-5916	21	4	herein	herein	NOUN
ejpam-5916	21	5	not	not	PART
ejpam-5916	21	6	only	only	ADV
ejpam-5916	21	7	unify	unify	VERB
ejpam-5916	21	8	and	and	CCONJ
ejpam-5916	21	9	expand	expand	VERB
ejpam-5916	21	10	previous	previous	ADJ
ejpam-5916	21	11	work	work	NOUN
ejpam-5916	21	12	but	but	CCONJ
ejpam-5916	21	13	also	also	ADV
ejpam-5916	21	14	refine	refine	VERB
ejpam-5916	21	15	existing	exist	VERB
ejpam-5916	21	16	theoretical	theoretical	ADJ
ejpam-5916	21	17	models	model	NOUN
ejpam-5916	21	18	by	by	ADP
ejpam-5916	21	19	incorporating	incorporate	VERB
ejpam-5916	21	20	more	more	ADV
ejpam-5916	21	21	generalized	generalized	ADJ
ejpam-5916	21	22	contractive	contractive	ADJ
ejpam-5916	21	23	mechanisms	mechanism	NOUN
ejpam-5916	21	24	.	.	PUNCT
ejpam-5916	22	1	this	this	DET
ejpam-5916	22	2	advancement	advancement	NOUN
ejpam-5916	22	3	paves	pave	VERB
ejpam-5916	22	4	the	the	DET
ejpam-5916	22	5	way	way	NOUN
ejpam-5916	22	6	for	for	ADP
ejpam-5916	22	7	broader	broad	ADJ
ejpam-5916	22	8	applications	application	NOUN
ejpam-5916	22	9	in	in	ADP
ejpam-5916	22	10	both	both	DET
ejpam-5916	22	11	mathematical	mathematical	ADJ
ejpam-5916	22	12	analysis	analysis	NOUN
ejpam-5916	22	13	and	and	CCONJ
ejpam-5916	22	14	applied	apply	VERB
ejpam-5916	22	15	sciences	science	NOUN
ejpam-5916	22	16	,	,	PUNCT
ejpam-5916	22	17	particularly	particularly	ADV
ejpam-5916	22	18	in	in	ADP
ejpam-5916	22	19	the	the	DET
ejpam-5916	22	20	study	study	NOUN
ejpam-5916	22	21	of	of	ADP
ejpam-5916	22	22	nonlinear	nonlinear	ADJ
ejpam-5916	22	23	equations	equation	NOUN
ejpam-5916	22	24	and	and	CCONJ
ejpam-5916	22	25	iterative	iterative	ADJ
ejpam-5916	22	26	algorithms	algorithm	NOUN
ejpam-5916	22	27	.	.	PUNCT
ejpam-5916	23	1	to	to	PART
ejpam-5916	23	2	reinforce	reinforce	VERB
ejpam-5916	23	3	the	the	DET
ejpam-5916	23	4	theoretical	theoretical	ADJ
ejpam-5916	23	5	developments	development	NOUN
ejpam-5916	23	6	established	establish	VERB
ejpam-5916	23	7	in	in	ADP
ejpam-5916	23	8	this	this	DET
ejpam-5916	23	9	work	work	NOUN
ejpam-5916	23	10	,	,	PUNCT
ejpam-5916	23	11	we	we	PRON
ejpam-5916	23	12	present	present	VERB
ejpam-5916	23	13	a	a	DET
ejpam-5916	23	14	concrete	concrete	ADJ
ejpam-5916	23	15	example	example	NOUN
ejpam-5916	23	16	that	that	PRON
ejpam-5916	23	17	highlights	highlight	VERB
ejpam-5916	23	18	the	the	DET
ejpam-5916	23	19	validity	validity	NOUN
ejpam-5916	23	20	of	of	ADP
ejpam-5916	23	21	our	our	PRON
ejpam-5916	23	22	results	result	NOUN
ejpam-5916	23	23	.	.	PUNCT
ejpam-5916	24	1	furthermore	furthermore	ADV
ejpam-5916	24	2	,	,	PUNCT
ejpam-5916	24	3	we	we	PRON
ejpam-5916	24	4	demonstrate	demonstrate	VERB
ejpam-5916	24	5	the	the	DET
ejpam-5916	24	6	practical	practical	ADJ
ejpam-5916	24	7	significance	significance	NOUN
ejpam-5916	24	8	of	of	ADP
ejpam-5916	24	9	our	our	PRON
ejpam-5916	24	10	findings	finding	NOUN
ejpam-5916	24	11	by	by	ADP
ejpam-5916	24	12	applying	apply	VERB
ejpam-5916	24	13	them	they	PRON
ejpam-5916	24	14	to	to	PART
ejpam-5916	24	15	solve	solve	VERB
ejpam-5916	24	16	a	a	DET
ejpam-5916	24	17	system	system	NOUN
ejpam-5916	24	18	of	of	ADP
ejpam-5916	24	19	fredholm	fredholm	ADJ
ejpam-5916	24	20	integral	integral	ADJ
ejpam-5916	24	21	equations	equation	NOUN
ejpam-5916	24	22	as	as	ADV
ejpam-5916	24	23	well	well	ADV
ejpam-5916	24	24	as	as	ADP
ejpam-5916	24	25	a	a	DET
ejpam-5916	24	26	system	system	NOUN
ejpam-5916	24	27	modeling	model	VERB
ejpam-5916	24	28	diffusion	diffusion	NOUN
ejpam-5916	24	29	-	-	PUNCT
ejpam-5916	24	30	reaction	reaction	NOUN
ejpam-5916	24	31	processes	process	NOUN
ejpam-5916	24	32	.	.	PUNCT
ejpam-5916	25	1	these	these	DET
ejpam-5916	25	2	applications	application	NOUN
ejpam-5916	25	3	underscore	underscore	VERB
ejpam-5916	25	4	the	the	DET
ejpam-5916	25	5	utility	utility	NOUN
ejpam-5916	25	6	of	of	ADP
ejpam-5916	25	7	quasi	quasi	ADJ
ejpam-5916	25	8	-	-	ADJ
ejpam-5916	25	9	partial	partial	ADJ
ejpam-5916	25	10	metric	metric	ADJ
ejpam-5916	25	11	spaces	space	NOUN
ejpam-5916	25	12	in	in	ADP
ejpam-5916	25	13	tackling	tackle	VERB
ejpam-5916	25	14	intricate	intricate	ADJ
ejpam-5916	25	15	mathematical	mathematical	ADJ
ejpam-5916	25	16	challenges	challenge	NOUN
ejpam-5916	25	17	that	that	PRON
ejpam-5916	25	18	arise	arise	VERB
ejpam-5916	25	19	in	in	ADP
ejpam-5916	25	20	various	various	ADJ
ejpam-5916	25	21	scientific	scientific	ADJ
ejpam-5916	25	22	and	and	CCONJ
ejpam-5916	25	23	engineering	engineering	NOUN
ejpam-5916	25	24	domains	domain	NOUN
ejpam-5916	25	25	.	.	PUNCT
ejpam-5916	26	1	by	by	ADP
ejpam-5916	26	2	bridging	bridge	VERB
ejpam-5916	26	3	abstract	abstract	ADJ
ejpam-5916	26	4	theoretical	theoretical	ADJ
ejpam-5916	26	5	concepts	concept	NOUN
ejpam-5916	26	6	with	with	ADP
ejpam-5916	26	7	real	real	ADJ
ejpam-5916	26	8	-	-	PUNCT
ejpam-5916	26	9	world	world	NOUN
ejpam-5916	26	10	problem	problem	NOUN
ejpam-5916	26	11	-	-	PUNCT
ejpam-5916	26	12	solving	solving	NOUN
ejpam-5916	26	13	,	,	PUNCT
ejpam-5916	26	14	our	our	PRON
ejpam-5916	26	15	study	study	NOUN
ejpam-5916	26	16	showcases	showcase	VERB
ejpam-5916	26	17	the	the	DET
ejpam-5916	26	18	adaptability	adaptability	NOUN
ejpam-5916	26	19	and	and	CCONJ
ejpam-5916	26	20	effectiveness	effectiveness	NOUN
ejpam-5916	26	21	of	of	ADP
ejpam-5916	26	22	quasi	quasi	ADJ
ejpam-5916	26	23	-	-	ADJ
ejpam-5916	26	24	partial	partial	ADJ
ejpam-5916	26	25	metric	metric	ADJ
ejpam-5916	26	26	frameworks	framework	NOUN
ejpam-5916	26	27	in	in	ADP
ejpam-5916	26	28	analyzing	analyze	VERB
ejpam-5916	26	29	nonlinear	nonlinear	ADJ
ejpam-5916	26	30	systems	system	NOUN
ejpam-5916	26	31	and	and	CCONJ
ejpam-5916	26	32	iterative	iterative	NOUN
ejpam-5916	26	33	solution	solution	NOUN
ejpam-5916	26	34	methods	method	NOUN
ejpam-5916	26	35	.	.	PUNCT
ejpam-5916	27	1	2	2	X
ejpam-5916	27	2	.	.	X
ejpam-5916	27	3	preliminaries	preliminary	NOUN
ejpam-5916	27	4	in	in	ADP
ejpam-5916	27	5	this	this	DET
ejpam-5916	27	6	section	section	NOUN
ejpam-5916	27	7	,	,	PUNCT
ejpam-5916	27	8	we	we	PRON
ejpam-5916	27	9	present	present	VERB
ejpam-5916	27	10	fundamental	fundamental	ADJ
ejpam-5916	27	11	definitions	definition	NOUN
ejpam-5916	27	12	and	and	CCONJ
ejpam-5916	27	13	essential	essential	ADJ
ejpam-5916	27	14	properties	property	NOUN
ejpam-5916	27	15	related	relate	VERB
ejpam-5916	27	16	to	to	ADP
ejpam-5916	27	17	quasi	quasi	ADJ
ejpam-5916	27	18	-	-	ADJ
ejpam-5916	27	19	partial	partial	ADJ
ejpam-5916	27	20	metric	metric	ADJ
ejpam-5916	27	21	spaces	space	NOUN
ejpam-5916	27	22	.	.	PUNCT
ejpam-5916	28	1	a	a	DET
ejpam-5916	28	2	partial	partial	ADJ
ejpam-5916	28	3	metric	metric	ADJ
ejpam-5916	28	4	space	space	NOUN
ejpam-5916	28	5	extends	extend	VERB
ejpam-5916	28	6	standard	standard	ADJ
ejpam-5916	28	7	metric	metric	ADJ
ejpam-5916	28	8	space	space	NOUN
ejpam-5916	28	9	concepts	concept	NOUN
ejpam-5916	28	10	(	(	PUNCT
ejpam-5916	28	11	when	when	SCONJ
ejpam-5916	28	12	p(x	p(x	NOUN
ejpam-5916	28	13	,	,	PUNCT
ejpam-5916	28	14	x	x	NOUN
ejpam-5916	28	15	)	)	PUNCT
ejpam-5916	28	16	=	=	SYM
ejpam-5916	28	17	0	0	NUM
ejpam-5916	28	18	recovers	recover	VERB
ejpam-5916	28	19	standard	standard	ADJ
ejpam-5916	28	20	metric	metric	ADJ
ejpam-5916	28	21	)	)	PUNCT
ejpam-5916	28	22	and	and	CCONJ
ejpam-5916	28	23	allows	allow	VERB
ejpam-5916	28	24	modeling	modeling	NOUN
ejpam-5916	28	25	of	of	ADP
ejpam-5916	28	26	objects	object	NOUN
ejpam-5916	28	27	with	with	ADP
ejpam-5916	28	28	non	non	ADJ
ejpam-5916	28	29	-	-	ADJ
ejpam-5916	28	30	zero	zero	NUM
ejpam-5916	28	31	self	self	NOUN
ejpam-5916	28	32	-	-	PUNCT
ejpam-5916	28	33	similarity	similarity	NOUN
ejpam-5916	28	34	.	.	PUNCT
ejpam-5916	29	1	the	the	DET
ejpam-5916	29	2	mapping	mapping	NOUN
ejpam-5916	29	3	dp(x	dp(x	PROPN
ejpam-5916	29	4	,	,	PUNCT
ejpam-5916	29	5	y	y	NOUN
ejpam-5916	29	6	)	)	PUNCT
ejpam-5916	29	7	=	=	SYM
ejpam-5916	29	8	2p(x	2p(x	PROPN
ejpam-5916	29	9	,	,	PUNCT
ejpam-5916	29	10	y)−	y)−	PROPN
ejpam-5916	29	11	p(x	p(x	PROPN
ejpam-5916	29	12	,	,	PUNCT
ejpam-5916	29	13	x)−	x)−	PROPN
ejpam-5916	29	14	p(y	p(y	PROPN
ejpam-5916	29	15	,	,	PUNCT
ejpam-5916	29	16	y	y	NOUN
ejpam-5916	29	17	)	)	PUNCT
ejpam-5916	29	18	forms	form	VERB
ejpam-5916	29	19	a	a	DET
ejpam-5916	29	20	standard	standard	ADJ
ejpam-5916	29	21	metric	metric	NOUN
ejpam-5916	29	22	.	.	PUNCT
ejpam-5916	30	1	definition	definition	NOUN
ejpam-5916	30	2	1	1	NUM
ejpam-5916	30	3	.	.	PUNCT
ejpam-5916	31	1	[	[	X
ejpam-5916	31	2	1	1	NUM
ejpam-5916	31	3	,	,	PUNCT
ejpam-5916	31	4	2	2	NUM
ejpam-5916	31	5	]	]	PUNCT
ejpam-5916	31	6	let	let	VERB
ejpam-5916	31	7	x	x	PRON
ejpam-5916	31	8	be	be	AUX
ejpam-5916	31	9	a	a	DET
ejpam-5916	31	10	non	non	ADJ
ejpam-5916	31	11	-	-	ADJ
ejpam-5916	31	12	empty	empty	ADJ
ejpam-5916	31	13	set	set	NOUN
ejpam-5916	31	14	.	.	PUNCT
ejpam-5916	32	1	a	a	DET
ejpam-5916	32	2	function	function	NOUN
ejpam-5916	32	3	p	p	X
ejpam-5916	32	4	:	:	PUNCT
ejpam-5916	32	5	x	x	PROPN
ejpam-5916	32	6	×x	×x	NUM
ejpam-5916	32	7	→	→	SYM
ejpam-5916	32	8	r+	r+	PRON
ejpam-5916	32	9	is	be	AUX
ejpam-5916	32	10	called	call	VERB
ejpam-5916	32	11	a	a	DET
ejpam-5916	32	12	partial	partial	ADJ
ejpam-5916	32	13	metric	metric	NOUN
ejpam-5916	32	14	if	if	SCONJ
ejpam-5916	32	15	it	it	PRON
ejpam-5916	32	16	satisfies	satisfy	VERB
ejpam-5916	32	17	the	the	DET
ejpam-5916	32	18	following	follow	VERB
ejpam-5916	32	19	conditions	condition	NOUN
ejpam-5916	32	20	for	for	ADP
ejpam-5916	32	21	all	all	DET
ejpam-5916	32	22	x	x	NOUN
ejpam-5916	32	23	,	,	PUNCT
ejpam-5916	32	24	y	y	PROPN
ejpam-5916	32	25	,	,	PUNCT
ejpam-5916	32	26	z	z	PROPN
ejpam-5916	32	27	∈	∈	PROPN
ejpam-5916	33	1	x	x	X
ejpam-5916	33	2	:	:	PUNCT
ejpam-5916	33	3	(	(	PUNCT
ejpam-5916	33	4	i	i	NOUN
ejpam-5916	33	5	)	)	PUNCT
ejpam-5916	33	6	symmetry	symmetry	NOUN
ejpam-5916	33	7	:	:	PUNCT
ejpam-5916	33	8	p(x	p(x	PROPN
ejpam-5916	33	9	,	,	PUNCT
ejpam-5916	33	10	y	y	NOUN
ejpam-5916	33	11	)	)	PUNCT
ejpam-5916	33	12	=	=	SYM
ejpam-5916	33	13	p(y	p(y	NOUN
ejpam-5916	33	14	,	,	PUNCT
ejpam-5916	33	15	x	x	NOUN
ejpam-5916	33	16	)	)	PUNCT
ejpam-5916	33	17	.	.	PUNCT
ejpam-5916	34	1	(	(	PUNCT
ejpam-5916	34	2	ii	ii	X
ejpam-5916	34	3	)	)	PUNCT
ejpam-5916	34	4	non	non	ADJ
ejpam-5916	34	5	-	-	ADJ
ejpam-5916	34	6	negativity	negativity	ADJ
ejpam-5916	34	7	and	and	CCONJ
ejpam-5916	34	8	indistinguishability	indistinguishability	NOUN
ejpam-5916	34	9	:	:	PUNCT
ejpam-5916	34	10	if	if	SCONJ
ejpam-5916	34	11	p(x	p(x	PROPN
ejpam-5916	34	12	,	,	PUNCT
ejpam-5916	34	13	x	x	NOUN
ejpam-5916	34	14	)	)	PUNCT
ejpam-5916	34	15	=	=	SYM
ejpam-5916	34	16	p(x	p(x	PROPN
ejpam-5916	34	17	,	,	PUNCT
ejpam-5916	34	18	y	y	NOUN
ejpam-5916	34	19	)	)	PUNCT
ejpam-5916	34	20	=	=	SYM
ejpam-5916	34	21	p(y	p(y	PROPN
ejpam-5916	34	22	,	,	PUNCT
ejpam-5916	34	23	y	y	NOUN
ejpam-5916	34	24	)	)	PUNCT
ejpam-5916	34	25	=	=	SYM
ejpam-5916	34	26	0	0	NUM
ejpam-5916	34	27	,	,	PUNCT
ejpam-5916	34	28	then	then	ADV
ejpam-5916	34	29	x	x	X
ejpam-5916	34	30	=	=	PUNCT
ejpam-5916	34	31	y.	y.	PROPN
ejpam-5916	34	32	(	(	PUNCT
ejpam-5916	34	33	iii	iii	NOUN
ejpam-5916	34	34	)	)	PUNCT
ejpam-5916	34	35	small	small	ADJ
ejpam-5916	34	36	self	self	NOUN
ejpam-5916	34	37	-	-	PUNCT
ejpam-5916	34	38	distance	distance	NOUN
ejpam-5916	34	39	:	:	PUNCT
ejpam-5916	34	40	p(x	p(x	NOUN
ejpam-5916	34	41	,	,	PUNCT
ejpam-5916	34	42	x	x	NOUN
ejpam-5916	34	43	)	)	PUNCT
ejpam-5916	34	44	≤	≤	NOUN
ejpam-5916	34	45	p(x	p(x	PROPN
ejpam-5916	34	46	,	,	PUNCT
ejpam-5916	34	47	y	y	NOUN
ejpam-5916	34	48	)	)	PUNCT
ejpam-5916	34	49	.	.	PUNCT
ejpam-5916	35	1	(	(	PUNCT
ejpam-5916	35	2	iv	iv	X
ejpam-5916	35	3	)	)	PUNCT
ejpam-5916	35	4	modified	modify	VERB
ejpam-5916	35	5	triangle	triangle	NOUN
ejpam-5916	35	6	inequality	inequality	NOUN
ejpam-5916	35	7	:	:	PUNCT
ejpam-5916	35	8	p(x	p(x	NOUN
ejpam-5916	35	9	,	,	PUNCT
ejpam-5916	35	10	z	z	NOUN
ejpam-5916	35	11	)	)	PUNCT
ejpam-5916	35	12	+	+	CCONJ
ejpam-5916	35	13	p(y	p(y	PROPN
ejpam-5916	35	14	,	,	PUNCT
ejpam-5916	35	15	y	y	NOUN
ejpam-5916	35	16	)	)	PUNCT
ejpam-5916	35	17	≤	≤	NOUN
ejpam-5916	35	18	p(x	p(x	PROPN
ejpam-5916	35	19	,	,	PUNCT
ejpam-5916	35	20	y	y	NOUN
ejpam-5916	35	21	)	)	PUNCT
ejpam-5916	35	22	+	+	CCONJ
ejpam-5916	35	23	p(y	p(y	PROPN
ejpam-5916	35	24	,	,	PUNCT
ejpam-5916	35	25	z	z	NOUN
ejpam-5916	35	26	)	)	PUNCT
ejpam-5916	35	27	.	.	PUNCT
ejpam-5916	36	1	a	a	DET
ejpam-5916	36	2	pair	pair	NOUN
ejpam-5916	36	3	(	(	PUNCT
ejpam-5916	36	4	x	x	NOUN
ejpam-5916	36	5	,	,	PUNCT
ejpam-5916	36	6	p	p	NOUN
ejpam-5916	36	7	)	)	PUNCT
ejpam-5916	36	8	satisfying	satisfy	VERB
ejpam-5916	36	9	these	these	DET
ejpam-5916	36	10	conditions	condition	NOUN
ejpam-5916	36	11	is	be	AUX
ejpam-5916	36	12	called	call	VERB
ejpam-5916	36	13	a	a	DET
ejpam-5916	36	14	partial	partial	ADJ
ejpam-5916	36	15	metric	metric	ADJ
ejpam-5916	36	16	space	space	NOUN
ejpam-5916	36	17	.	.	PUNCT
ejpam-5916	37	1	note	note	VERB
ejpam-5916	37	2	that	that	SCONJ
ejpam-5916	37	3	if	if	SCONJ
ejpam-5916	37	4	p(x	p(x	PROPN
ejpam-5916	37	5	,	,	PUNCT
ejpam-5916	37	6	y	y	NOUN
ejpam-5916	37	7	)	)	PUNCT
ejpam-5916	37	8	=	=	SYM
ejpam-5916	38	1	0	0	NUM
ejpam-5916	38	2	,	,	PUNCT
ejpam-5916	38	3	then	then	ADV
ejpam-5916	38	4	by	by	ADP
ejpam-5916	38	5	conditions	condition	NOUN
ejpam-5916	38	6	(	(	PUNCT
ejpam-5916	38	7	1	1	NUM
ejpam-5916	38	8	)	)	PUNCT
ejpam-5916	38	9	and	and	CCONJ
ejpam-5916	38	10	(	(	PUNCT
ejpam-5916	38	11	2	2	NUM
ejpam-5916	38	12	)	)	PUNCT
ejpam-5916	38	13	,	,	PUNCT
ejpam-5916	38	14	we	we	PRON
ejpam-5916	38	15	deduce	deduce	VERB
ejpam-5916	38	16	that	that	PRON
ejpam-5916	38	17	x	x	X
ejpam-5916	39	1	=	=	PUNCT
ejpam-5916	39	2	y.	y.	PROPN
ejpam-5916	39	3	however	however	ADV
ejpam-5916	39	4	,	,	PUNCT
ejpam-5916	39	5	the	the	DET
ejpam-5916	39	6	converse	converse	NOUN
ejpam-5916	39	7	does	do	AUX
ejpam-5916	39	8	not	not	PART
ejpam-5916	39	9	necessarily	necessarily	ADV
ejpam-5916	39	10	hold	hold	VERB
ejpam-5916	39	11	;	;	PUNCT
ejpam-5916	39	12	that	that	PRON
ejpam-5916	39	13	is	is	ADV
ejpam-5916	39	14	,	,	PUNCT
ejpam-5916	39	15	if	if	SCONJ
ejpam-5916	39	16	x	x	ADP
ejpam-5916	39	17	=	=	SYM
ejpam-5916	39	18	y	y	PROPN
ejpam-5916	39	19	,	,	PUNCT
ejpam-5916	39	20	it	it	PRON
ejpam-5916	39	21	does	do	AUX
ejpam-5916	39	22	not	not	PART
ejpam-5916	39	23	imply	imply	VERB
ejpam-5916	39	24	that	that	SCONJ
ejpam-5916	39	25	p(x	p(x	NOUN
ejpam-5916	39	26	,	,	PUNCT
ejpam-5916	39	27	x	x	NOUN
ejpam-5916	39	28	)	)	PUNCT
ejpam-5916	39	29	=	=	SYM
ejpam-5916	39	30	0	0	X
ejpam-5916	39	31	.	.	PUNCT
ejpam-5916	40	1	h.	h.	PROPN
ejpam-5916	40	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	40	3	/	/	SYM
ejpam-5916	40	4	eur	eur	PROPN
ejpam-5916	40	5	.	.	PUNCT
ejpam-5916	41	1	j.	j.	PROPN
ejpam-5916	41	2	pure	pure	PROPN
ejpam-5916	41	3	appl	appl	PROPN
ejpam-5916	41	4	.	.	PROPN
ejpam-5916	41	5	math	math	PROPN
ejpam-5916	41	6	,	,	PUNCT
ejpam-5916	41	7	18	18	NUM
ejpam-5916	41	8	(	(	PUNCT
ejpam-5916	41	9	3	3	NUM
ejpam-5916	41	10	)	)	PUNCT
ejpam-5916	41	11	(	(	PUNCT
ejpam-5916	41	12	2025	2025	NUM
ejpam-5916	41	13	)	)	PUNCT
ejpam-5916	41	14	,	,	PUNCT
ejpam-5916	41	15	5916	5916	NUM
ejpam-5916	41	16	3	3	NUM
ejpam-5916	41	17	of	of	ADP
ejpam-5916	41	18	19	19	NUM
ejpam-5916	41	19	example	example	NOUN
ejpam-5916	41	20	1	1	NUM
ejpam-5916	41	21	.	.	PUNCT
ejpam-5916	42	1	[	[	X
ejpam-5916	42	2	1	1	X
ejpam-5916	42	3	]	]	PUNCT
ejpam-5916	42	4	a	a	DET
ejpam-5916	42	5	fundamental	fundamental	ADJ
ejpam-5916	42	6	example	example	NOUN
ejpam-5916	42	7	of	of	ADP
ejpam-5916	42	8	a	a	DET
ejpam-5916	42	9	partial	partial	ADJ
ejpam-5916	42	10	metric	metric	ADJ
ejpam-5916	42	11	space	space	NOUN
ejpam-5916	42	12	is	be	AUX
ejpam-5916	42	13	the	the	DET
ejpam-5916	42	14	pair	pair	NOUN
ejpam-5916	42	15	(	(	PUNCT
ejpam-5916	42	16	[	[	X
ejpam-5916	42	17	0,∞	0,∞	NOUN
ejpam-5916	42	18	)	)	PUNCT
ejpam-5916	42	19	,	,	PUNCT
ejpam-5916	42	20	p	p	NOUN
ejpam-5916	42	21	)	)	PUNCT
ejpam-5916	42	22	,	,	PUNCT
ejpam-5916	42	23	where	where	SCONJ
ejpam-5916	42	24	the	the	DET
ejpam-5916	42	25	partial	partial	ADJ
ejpam-5916	42	26	metric	metric	NOUN
ejpam-5916	42	27	p	p	NOUN
ejpam-5916	42	28	:	:	PUNCT
ejpam-5916	43	1	[	[	X
ejpam-5916	43	2	0,∞)×	0,∞)×	NUM
ejpam-5916	43	3	[	[	X
ejpam-5916	43	4	0,∞	0,∞	NUM
ejpam-5916	43	5	)	)	PUNCT
ejpam-5916	43	6	→	→	PUNCT
ejpam-5916	43	7	r+	r+	PRON
ejpam-5916	43	8	is	be	AUX
ejpam-5916	43	9	defined	define	VERB
ejpam-5916	43	10	as	as	ADP
ejpam-5916	43	11	p(x	p(x	PROPN
ejpam-5916	43	12	,	,	PUNCT
ejpam-5916	43	13	y	y	NOUN
ejpam-5916	43	14	)	)	PUNCT
ejpam-5916	43	15	=	=	SYM
ejpam-5916	43	16	max{x	max{x	PROPN
ejpam-5916	43	17	,	,	PUNCT
ejpam-5916	43	18	y	y	NOUN
ejpam-5916	43	19	}	}	PUNCT
ejpam-5916	43	20	,	,	PUNCT
ejpam-5916	43	21	for	for	ADP
ejpam-5916	43	22	all	all	DET
ejpam-5916	43	23	x	x	NOUN
ejpam-5916	43	24	,	,	PUNCT
ejpam-5916	43	25	y	y	PROPN
ejpam-5916	43	26	∈	∈	PROPN
ejpam-5916	44	1	[	[	X
ejpam-5916	44	2	0,∞	0,∞	NOUN
ejpam-5916	44	3	)	)	PUNCT
ejpam-5916	44	4	.	.	PUNCT
ejpam-5916	45	1	this	this	DET
ejpam-5916	45	2	function	function	NOUN
ejpam-5916	45	3	satisfies	satisfy	VERB
ejpam-5916	45	4	the	the	DET
ejpam-5916	45	5	properties	property	NOUN
ejpam-5916	45	6	of	of	ADP
ejpam-5916	45	7	a	a	DET
ejpam-5916	45	8	partial	partial	ADJ
ejpam-5916	45	9	metric	metric	NOUN
ejpam-5916	45	10	.	.	PUNCT
ejpam-5916	46	1	notably	notably	ADV
ejpam-5916	46	2	,	,	PUNCT
ejpam-5916	46	3	this	this	DET
ejpam-5916	46	4	example	example	NOUN
ejpam-5916	46	5	differs	differ	VERB
ejpam-5916	46	6	from	from	ADP
ejpam-5916	46	7	standard	standard	ADJ
ejpam-5916	46	8	metric	metric	ADJ
ejpam-5916	46	9	spaces	space	NOUN
ejpam-5916	46	10	as	as	SCONJ
ejpam-5916	46	11	it	it	PRON
ejpam-5916	46	12	allows	allow	VERB
ejpam-5916	46	13	nonzero	nonzero	PROPN
ejpam-5916	46	14	self	self	NOUN
ejpam-5916	46	15	-	-	PUNCT
ejpam-5916	46	16	distances	distance	NOUN
ejpam-5916	46	17	,	,	PUNCT
ejpam-5916	46	18	i.e.	i.e.	X
ejpam-5916	46	19	,	,	PUNCT
ejpam-5916	46	20	p(x	p(x	NOUN
ejpam-5916	46	21	,	,	PUNCT
ejpam-5916	46	22	x	x	NOUN
ejpam-5916	46	23	)	)	PUNCT
ejpam-5916	46	24	=	=	PUNCT
ejpam-5916	47	1	x	x	X
ejpam-5916	47	2	̸=	̸=	PROPN
ejpam-5916	47	3	0	0	NUM
ejpam-5916	47	4	for	for	ADP
ejpam-5916	47	5	x	x	PUNCT
ejpam-5916	47	6	>	>	X
ejpam-5916	47	7	0	0	NUM
ejpam-5916	47	8	,	,	PUNCT
ejpam-5916	47	9	illustrating	illustrate	VERB
ejpam-5916	47	10	the	the	DET
ejpam-5916	47	11	essential	essential	ADJ
ejpam-5916	47	12	characteristic	characteristic	NOUN
ejpam-5916	47	13	of	of	ADP
ejpam-5916	47	14	partial	partial	ADJ
ejpam-5916	47	15	metric	metric	ADJ
ejpam-5916	47	16	spaces	space	NOUN
ejpam-5916	47	17	.	.	PUNCT
ejpam-5916	48	1	definition	definition	NOUN
ejpam-5916	48	2	2	2	NUM
ejpam-5916	48	3	.	.	PUNCT
ejpam-5916	49	1	[	[	X
ejpam-5916	49	2	6	6	NUM
ejpam-5916	49	3	]	]	PUNCT
ejpam-5916	49	4	a	a	DET
ejpam-5916	49	5	function	function	NOUN
ejpam-5916	49	6	q	q	NOUN
ejpam-5916	49	7	:	:	PUNCT
ejpam-5916	49	8	x×x	x×x	PROPN
ejpam-5916	49	9	→	→	NOUN
ejpam-5916	49	10	r+	r+	PRON
ejpam-5916	49	11	is	be	AUX
ejpam-5916	49	12	called	call	VERB
ejpam-5916	49	13	a	a	DET
ejpam-5916	49	14	quasi	quasi	ADJ
ejpam-5916	49	15	-	-	ADJ
ejpam-5916	49	16	partial	partial	ADJ
ejpam-5916	49	17	metric	metric	NOUN
ejpam-5916	49	18	if	if	SCONJ
ejpam-5916	49	19	it	it	PRON
ejpam-5916	49	20	satisfies	satisfy	VERB
ejpam-5916	49	21	the	the	DET
ejpam-5916	49	22	following	follow	VERB
ejpam-5916	49	23	conditions	condition	NOUN
ejpam-5916	49	24	for	for	ADP
ejpam-5916	49	25	all	all	DET
ejpam-5916	49	26	x	x	NOUN
ejpam-5916	49	27	,	,	PUNCT
ejpam-5916	49	28	y	y	PROPN
ejpam-5916	49	29	,	,	PUNCT
ejpam-5916	49	30	z	z	PROPN
ejpam-5916	49	31	∈	∈	PROPN
ejpam-5916	50	1	x	x	X
ejpam-5916	50	2	:	:	PUNCT
ejpam-5916	50	3	(	(	PUNCT
ejpam-5916	50	4	i	i	NOUN
ejpam-5916	50	5	)	)	PUNCT
ejpam-5916	50	6	q(x	q(x	PROPN
ejpam-5916	50	7	,	,	PUNCT
ejpam-5916	50	8	x	x	NOUN
ejpam-5916	50	9	)	)	PUNCT
ejpam-5916	50	10	≤	≤	NOUN
ejpam-5916	50	11	q(y	q(y	NOUN
ejpam-5916	50	12	,	,	PUNCT
ejpam-5916	50	13	x	x	NOUN
ejpam-5916	50	14	)	)	PUNCT
ejpam-5916	50	15	,	,	PUNCT
ejpam-5916	50	16	(	(	PUNCT
ejpam-5916	50	17	ii	ii	NOUN
ejpam-5916	50	18	)	)	PUNCT
ejpam-5916	50	19	q(x	q(x	PROPN
ejpam-5916	50	20	,	,	PUNCT
ejpam-5916	50	21	x	x	NOUN
ejpam-5916	50	22	)	)	PUNCT
ejpam-5916	50	23	≤	≤	PUNCT
ejpam-5916	50	24	q(x	q(x	PROPN
ejpam-5916	50	25	,	,	PUNCT
ejpam-5916	50	26	y	y	NOUN
ejpam-5916	50	27	)	)	PUNCT
ejpam-5916	50	28	,	,	PUNCT
ejpam-5916	50	29	(	(	PUNCT
ejpam-5916	50	30	iii	iii	X
ejpam-5916	50	31	)	)	PUNCT
ejpam-5916	50	32	x	x	X
ejpam-5916	50	33	=	=	PUNCT
ejpam-5916	50	34	y	y	PROPN
ejpam-5916	50	35	if	if	SCONJ
ejpam-5916	50	36	and	and	CCONJ
ejpam-5916	50	37	only	only	ADV
ejpam-5916	50	38	if	if	SCONJ
ejpam-5916	50	39	q(x	q(x	NOUN
ejpam-5916	50	40	,	,	PUNCT
ejpam-5916	50	41	x	x	X
ejpam-5916	50	42	)	)	PUNCT
ejpam-5916	50	43	=	=	SYM
ejpam-5916	50	44	q(x	q(x	PROPN
ejpam-5916	50	45	,	,	PUNCT
ejpam-5916	50	46	y	y	NOUN
ejpam-5916	50	47	)	)	PUNCT
ejpam-5916	50	48	and	and	CCONJ
ejpam-5916	50	49	q(y	q(y	PROPN
ejpam-5916	50	50	,	,	PUNCT
ejpam-5916	50	51	y	y	NOUN
ejpam-5916	50	52	)	)	PUNCT
ejpam-5916	50	53	=	=	PUNCT
ejpam-5916	51	1	q(y	q(y	NOUN
ejpam-5916	51	2	,	,	PUNCT
ejpam-5916	51	3	x	x	NOUN
ejpam-5916	51	4	)	)	PUNCT
ejpam-5916	51	5	,	,	PUNCT
ejpam-5916	51	6	(	(	PUNCT
ejpam-5916	51	7	iv	iv	X
ejpam-5916	51	8	)	)	PUNCT
ejpam-5916	51	9	q(x	q(x	NOUN
ejpam-5916	51	10	,	,	PUNCT
ejpam-5916	51	11	z	z	NOUN
ejpam-5916	51	12	)	)	PUNCT
ejpam-5916	51	13	+	+	CCONJ
ejpam-5916	51	14	q(y	q(y	PROPN
ejpam-5916	51	15	,	,	PUNCT
ejpam-5916	51	16	y	y	NOUN
ejpam-5916	51	17	)	)	PUNCT
ejpam-5916	51	18	≤	≤	PUNCT
ejpam-5916	51	19	q(x	q(x	PROPN
ejpam-5916	51	20	,	,	PUNCT
ejpam-5916	51	21	y	y	NOUN
ejpam-5916	51	22	)	)	PUNCT
ejpam-5916	51	23	+	+	CCONJ
ejpam-5916	51	24	q(y	q(y	NOUN
ejpam-5916	51	25	,	,	PUNCT
ejpam-5916	51	26	z	z	NOUN
ejpam-5916	51	27	)	)	PUNCT
ejpam-5916	51	28	.	.	PUNCT
ejpam-5916	52	1	the	the	DET
ejpam-5916	52	2	pair	pair	NOUN
ejpam-5916	52	3	(	(	PUNCT
ejpam-5916	52	4	x	x	NOUN
ejpam-5916	52	5	,	,	PUNCT
ejpam-5916	52	6	q	q	X
ejpam-5916	52	7	)	)	PUNCT
ejpam-5916	52	8	is	be	AUX
ejpam-5916	52	9	then	then	ADV
ejpam-5916	52	10	referred	refer	VERB
ejpam-5916	52	11	to	to	ADP
ejpam-5916	52	12	as	as	ADP
ejpam-5916	52	13	a	a	DET
ejpam-5916	52	14	quasi	quasi	ADJ
ejpam-5916	52	15	-	-	ADJ
ejpam-5916	52	16	partial	partial	ADJ
ejpam-5916	52	17	metric	metric	ADJ
ejpam-5916	52	18	space	space	NOUN
ejpam-5916	52	19	.	.	PUNCT
ejpam-5916	53	1	karapinar	karapinar	VERB
ejpam-5916	53	2	et	et	PROPN
ejpam-5916	53	3	al	al	PROPN
ejpam-5916	53	4	.	.	PUNCT
ejpam-5916	54	1	[	[	X
ejpam-5916	54	2	7	7	X
ejpam-5916	54	3	]	]	PUNCT
ejpam-5916	54	4	introduced	introduce	VERB
ejpam-5916	54	5	an	an	DET
ejpam-5916	54	6	alternative	alternative	ADJ
ejpam-5916	54	7	condition	condition	NOUN
ejpam-5916	54	8	:	:	PUNCT
ejpam-5916	54	9	(	(	PUNCT
ejpam-5916	54	10	3′	3′	X
ejpam-5916	54	11	)	)	PUNCT
ejpam-5916	54	12	equality	equality	NOUN
ejpam-5916	54	13	:	:	PUNCT
ejpam-5916	54	14	if	if	SCONJ
ejpam-5916	54	15	0	0	NUM
ejpam-5916	54	16	≤	≤	NUM
ejpam-5916	54	17	q(x	q(x	NOUN
ejpam-5916	54	18	,	,	PUNCT
ejpam-5916	54	19	x	x	X
ejpam-5916	54	20	)	)	PUNCT
ejpam-5916	54	21	=	=	SYM
ejpam-5916	54	22	q(x	q(x	PROPN
ejpam-5916	54	23	,	,	PUNCT
ejpam-5916	54	24	y	y	NOUN
ejpam-5916	54	25	)	)	PUNCT
ejpam-5916	54	26	=	=	PUNCT
ejpam-5916	55	1	q(y	q(y	PROPN
ejpam-5916	55	2	,	,	PUNCT
ejpam-5916	55	3	y	y	PROPN
ejpam-5916	55	4	)	)	PUNCT
ejpam-5916	55	5	,	,	PUNCT
ejpam-5916	55	6	then	then	ADV
ejpam-5916	55	7	x	x	X
ejpam-5916	55	8	=	=	SYM
ejpam-5916	55	9	y	y	PROPN
ejpam-5916	55	10	,	,	PUNCT
ejpam-5916	55	11	replacing	replace	VERB
ejpam-5916	55	12	condition	condition	NOUN
ejpam-5916	55	13	(	(	PUNCT
ejpam-5916	55	14	3	3	NUM
ejpam-5916	55	15	)	)	PUNCT
ejpam-5916	55	16	in	in	ADP
ejpam-5916	55	17	the	the	DET
ejpam-5916	55	18	definition	definition	NOUN
ejpam-5916	55	19	of	of	ADP
ejpam-5916	55	20	a	a	DET
ejpam-5916	55	21	quasi	quasi	ADJ
ejpam-5916	55	22	-	-	ADJ
ejpam-5916	55	23	partial	partial	ADJ
ejpam-5916	55	24	metric	metric	NOUN
ejpam-5916	55	25	.	.	PUNCT
ejpam-5916	56	1	it	it	PRON
ejpam-5916	56	2	is	be	AUX
ejpam-5916	56	3	noteworthy	noteworthy	ADJ
ejpam-5916	56	4	that	that	SCONJ
ejpam-5916	56	5	when	when	SCONJ
ejpam-5916	56	6	q(x	q(x	PROPN
ejpam-5916	56	7	,	,	PUNCT
ejpam-5916	56	8	y	y	NOUN
ejpam-5916	56	9	)	)	PUNCT
ejpam-5916	56	10	=	=	PUNCT
ejpam-5916	56	11	q(y	q(y	NOUN
ejpam-5916	56	12	,	,	PUNCT
ejpam-5916	56	13	x	x	NOUN
ejpam-5916	56	14	)	)	PUNCT
ejpam-5916	56	15	for	for	ADP
ejpam-5916	56	16	all	all	DET
ejpam-5916	56	17	x	x	NOUN
ejpam-5916	56	18	,	,	PUNCT
ejpam-5916	56	19	y	y	PROPN
ejpam-5916	56	20	∈	∈	PROPN
ejpam-5916	56	21	x	x	PROPN
ejpam-5916	56	22	,	,	PUNCT
ejpam-5916	56	23	the	the	DET
ejpam-5916	56	24	quasi	quasi	ADJ
ejpam-5916	56	25	-	-	ADJ
ejpam-5916	56	26	partial	partial	ADJ
ejpam-5916	56	27	metric	metric	ADJ
ejpam-5916	56	28	space	space	NOUN
ejpam-5916	56	29	(	(	PUNCT
ejpam-5916	56	30	x	x	X
ejpam-5916	56	31	,	,	PUNCT
ejpam-5916	56	32	q	q	NOUN
ejpam-5916	56	33	)	)	PUNCT
ejpam-5916	56	34	reduces	reduce	VERB
ejpam-5916	56	35	to	to	ADP
ejpam-5916	56	36	a	a	DET
ejpam-5916	56	37	partial	partial	ADJ
ejpam-5916	56	38	metric	metric	ADJ
ejpam-5916	56	39	space	space	NOUN
ejpam-5916	56	40	.	.	PUNCT
ejpam-5916	57	1	furthermore	furthermore	ADV
ejpam-5916	57	2	,	,	PUNCT
ejpam-5916	57	3	for	for	ADP
ejpam-5916	57	4	any	any	DET
ejpam-5916	57	5	quasi	quasi	ADJ
ejpam-5916	57	6	-	-	ADJ
ejpam-5916	57	7	partial	partial	ADJ
ejpam-5916	57	8	metric	metric	NOUN
ejpam-5916	57	9	q	q	NOUN
ejpam-5916	57	10	on	on	ADP
ejpam-5916	57	11	x	x	SYM
ejpam-5916	57	12	,	,	PUNCT
ejpam-5916	57	13	the	the	DET
ejpam-5916	57	14	function	function	NOUN
ejpam-5916	57	15	dq	dq	NOUN
ejpam-5916	57	16	:	:	PUNCT
ejpam-5916	57	17	x	x	PROPN
ejpam-5916	57	18	×x	×x	ADP
ejpam-5916	57	19	→	→	SYM
ejpam-5916	57	20	r+	r+	PRON
ejpam-5916	57	21	defined	define	VERB
ejpam-5916	57	22	by	by	ADP
ejpam-5916	57	23	dq(x	dq(x	PROPN
ejpam-5916	57	24	,	,	PUNCT
ejpam-5916	57	25	y	y	NOUN
ejpam-5916	57	26	)	)	PUNCT
ejpam-5916	57	27	=	=	SYM
ejpam-5916	57	28	q(x	q(x	PROPN
ejpam-5916	57	29	,	,	PUNCT
ejpam-5916	57	30	y	y	NOUN
ejpam-5916	57	31	)	)	PUNCT
ejpam-5916	57	32	+	+	CCONJ
ejpam-5916	57	33	q(y	q(y	NOUN
ejpam-5916	57	34	,	,	PUNCT
ejpam-5916	57	35	x)−	x)−	PROPN
ejpam-5916	57	36	q(x	q(x	PROPN
ejpam-5916	57	37	,	,	PUNCT
ejpam-5916	57	38	x)−	x)−	PROPN
ejpam-5916	57	39	q(y	q(y	PROPN
ejpam-5916	57	40	,	,	PUNCT
ejpam-5916	57	41	y	y	NOUN
ejpam-5916	57	42	)	)	PUNCT
ejpam-5916	57	43	constitutes	constitute	VERB
ejpam-5916	57	44	a	a	DET
ejpam-5916	57	45	basic	basic	ADJ
ejpam-5916	57	46	metric	metric	NOUN
ejpam-5916	57	47	on	on	ADP
ejpam-5916	57	48	x	x	PART
ejpam-5916	57	49	example	example	NOUN
ejpam-5916	57	50	2	2	NUM
ejpam-5916	57	51	.	.	PUNCT
ejpam-5916	58	1	[	[	X
ejpam-5916	58	2	6	6	NUM
ejpam-5916	58	3	]	]	PUNCT
ejpam-5916	58	4	consider	consider	VERB
ejpam-5916	58	5	the	the	DET
ejpam-5916	58	6	set	set	NOUN
ejpam-5916	58	7	of	of	ADP
ejpam-5916	58	8	non	non	ADJ
ejpam-5916	58	9	-	-	ADJ
ejpam-5916	58	10	negative	negative	ADJ
ejpam-5916	58	11	real	real	ADJ
ejpam-5916	58	12	numbers	number	NOUN
ejpam-5916	58	13	r+	r+	PUNCT
ejpam-5916	58	14	equipped	equip	VERB
ejpam-5916	58	15	with	with	ADP
ejpam-5916	58	16	the	the	DET
ejpam-5916	58	17	function	function	NOUN
ejpam-5916	58	18	q	q	NOUN
ejpam-5916	58	19	:	:	PUNCT
ejpam-5916	58	20	r+	r+	NOUN
ejpam-5916	58	21	×	×	NOUN
ejpam-5916	58	22	r+	r+	NOUN
ejpam-5916	58	23	→	→	SYM
ejpam-5916	58	24	r+	r+	NOUN
ejpam-5916	58	25	defined	define	VERB
ejpam-5916	58	26	by	by	ADP
ejpam-5916	58	27	:	:	PUNCT
ejpam-5916	58	28	(	(	PUNCT
ejpam-5916	58	29	i	i	NOUN
ejpam-5916	58	30	)	)	PUNCT
ejpam-5916	58	31	q(x	q(x	PROPN
ejpam-5916	58	32	,	,	PUNCT
ejpam-5916	58	33	y	y	NOUN
ejpam-5916	58	34	)	)	PUNCT
ejpam-5916	58	35	=	=	PUNCT
ejpam-5916	58	36	|x−	|x−	NUM
ejpam-5916	58	37	y|+	y|+	PROPN
ejpam-5916	58	38	|x|	|x|	PROPN
ejpam-5916	58	39	,	,	PUNCT
ejpam-5916	58	40	(	(	PUNCT
ejpam-5916	58	41	ii	ii	NOUN
ejpam-5916	58	42	)	)	PUNCT
ejpam-5916	58	43	q(x	q(x	PROPN
ejpam-5916	58	44	,	,	PUNCT
ejpam-5916	58	45	y	y	NOUN
ejpam-5916	58	46	)	)	PUNCT
ejpam-5916	58	47	=	=	SYM
ejpam-5916	58	48	max{y	max{y	NOUN
ejpam-5916	58	49	−	−	NOUN
ejpam-5916	58	50	x	x	SYM
ejpam-5916	58	51	,	,	PUNCT
ejpam-5916	58	52	0}+	0}+	PROPN
ejpam-5916	58	53	x.	x.	NOUN
ejpam-5916	58	54	then	then	ADV
ejpam-5916	58	55	,	,	PUNCT
ejpam-5916	58	56	(	(	PUNCT
ejpam-5916	58	57	r+	r+	X
ejpam-5916	58	58	,	,	PUNCT
ejpam-5916	58	59	q	q	X
ejpam-5916	58	60	)	)	PUNCT
ejpam-5916	58	61	forms	form	VERB
ejpam-5916	58	62	a	a	DET
ejpam-5916	58	63	quasi	quasi	ADJ
ejpam-5916	58	64	-	-	ADJ
ejpam-5916	58	65	partial	partial	ADJ
ejpam-5916	58	66	metric	metric	ADJ
ejpam-5916	58	67	space	space	NOUN
ejpam-5916	58	68	.	.	PUNCT
ejpam-5916	59	1	definition	definition	NOUN
ejpam-5916	59	2	3	3	NUM
ejpam-5916	59	3	.	.	PUNCT
ejpam-5916	60	1	[	[	X
ejpam-5916	60	2	7	7	X
ejpam-5916	60	3	]	]	X
ejpam-5916	60	4	let	let	VERB
ejpam-5916	60	5	(	(	PUNCT
ejpam-5916	60	6	x	x	NOUN
ejpam-5916	60	7	,	,	PUNCT
ejpam-5916	60	8	q	q	X
ejpam-5916	60	9	)	)	PUNCT
ejpam-5916	60	10	be	be	AUX
ejpam-5916	60	11	a	a	DET
ejpam-5916	60	12	quasi	quasi	ADJ
ejpam-5916	60	13	-	-	ADJ
ejpam-5916	60	14	partial	partial	ADJ
ejpam-5916	60	15	metric	metric	ADJ
ejpam-5916	60	16	space	space	NOUN
ejpam-5916	60	17	.	.	PUNCT
ejpam-5916	61	1	the	the	DET
ejpam-5916	61	2	following	follow	VERB
ejpam-5916	61	3	concepts	concept	NOUN
ejpam-5916	61	4	are	be	AUX
ejpam-5916	61	5	defined	define	VERB
ejpam-5916	61	6	:	:	PUNCT
ejpam-5916	61	7	(	(	PUNCT
ejpam-5916	61	8	i	i	NOUN
ejpam-5916	61	9	)	)	PUNCT
ejpam-5916	61	10	a	a	DET
ejpam-5916	61	11	sequence	sequence	NOUN
ejpam-5916	61	12	{	{	PUNCT
ejpam-5916	61	13	xn	xn	NOUN
ejpam-5916	61	14	}	}	PUNCT
ejpam-5916	61	15	⊂	⊂	PROPN
ejpam-5916	61	16	x	x	PUNCT
ejpam-5916	61	17	is	be	AUX
ejpam-5916	61	18	said	say	VERB
ejpam-5916	61	19	to	to	PART
ejpam-5916	61	20	converge	converge	VERB
ejpam-5916	61	21	to	to	ADP
ejpam-5916	61	22	a	a	DET
ejpam-5916	61	23	point	point	NOUN
ejpam-5916	61	24	x	x	X
ejpam-5916	61	25	∈	∈	NOUN
ejpam-5916	61	26	x	x	PUNCT
ejpam-5916	61	27	if	if	SCONJ
ejpam-5916	61	28	q(x	q(x	NOUN
ejpam-5916	61	29	,	,	PUNCT
ejpam-5916	61	30	x	x	X
ejpam-5916	61	31	)	)	PUNCT
ejpam-5916	61	32	=	=	SYM
ejpam-5916	61	33	lim	lim	PROPN
ejpam-5916	61	34	n→∞	n→∞	NUM
ejpam-5916	61	35	q(x	q(x	PROPN
ejpam-5916	61	36	,	,	PUNCT
ejpam-5916	61	37	xn	xn	PUNCT
ejpam-5916	61	38	)	)	PUNCT
ejpam-5916	62	1	=	=	VERB
ejpam-5916	62	2	lim	lim	PROPN
ejpam-5916	62	3	n→∞	n→∞	NUM
ejpam-5916	62	4	q(xn	q(xn	PROPN
ejpam-5916	62	5	,	,	PUNCT
ejpam-5916	62	6	x	x	NOUN
ejpam-5916	62	7	)	)	PUNCT
ejpam-5916	62	8	.	.	PUNCT
ejpam-5916	63	1	h.	h.	PROPN
ejpam-5916	63	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	63	3	/	/	SYM
ejpam-5916	63	4	eur	eur	PROPN
ejpam-5916	63	5	.	.	PUNCT
ejpam-5916	64	1	j.	j.	PROPN
ejpam-5916	64	2	pure	pure	PROPN
ejpam-5916	64	3	appl	appl	PROPN
ejpam-5916	64	4	.	.	PROPN
ejpam-5916	64	5	math	math	PROPN
ejpam-5916	64	6	,	,	PUNCT
ejpam-5916	64	7	18	18	NUM
ejpam-5916	64	8	(	(	PUNCT
ejpam-5916	64	9	3	3	NUM
ejpam-5916	64	10	)	)	PUNCT
ejpam-5916	64	11	(	(	PUNCT
ejpam-5916	64	12	2025	2025	NUM
ejpam-5916	64	13	)	)	PUNCT
ejpam-5916	64	14	,	,	PUNCT
ejpam-5916	64	15	5916	5916	NUM
ejpam-5916	64	16	4	4	NUM
ejpam-5916	64	17	of	of	ADP
ejpam-5916	64	18	19	19	NUM
ejpam-5916	64	19	(	(	PUNCT
ejpam-5916	64	20	ii	ii	NOUN
ejpam-5916	64	21	)	)	PUNCT
ejpam-5916	64	22	a	a	DET
ejpam-5916	64	23	sequence	sequence	NOUN
ejpam-5916	64	24	{	{	PUNCT
ejpam-5916	64	25	xn	xn	NOUN
ejpam-5916	64	26	}	}	PUNCT
ejpam-5916	64	27	in	in	ADP
ejpam-5916	64	28	x	x	PROPN
ejpam-5916	64	29	is	be	AUX
ejpam-5916	64	30	called	call	VERB
ejpam-5916	64	31	a	a	DET
ejpam-5916	64	32	cauchy	cauchy	ADJ
ejpam-5916	64	33	sequence	sequence	NOUN
ejpam-5916	64	34	if	if	SCONJ
ejpam-5916	64	35	and	and	CCONJ
ejpam-5916	64	36	only	only	ADV
ejpam-5916	64	37	if	if	SCONJ
ejpam-5916	64	38	lim	lim	PROPN
ejpam-5916	64	39	n	n	CCONJ
ejpam-5916	64	40	,	,	PUNCT
ejpam-5916	64	41	m→∞	m→∞	NUM
ejpam-5916	64	42	q(xn	q(xn	NOUN
ejpam-5916	64	43	,	,	PUNCT
ejpam-5916	64	44	xm	xm	PROPN
ejpam-5916	64	45	)	)	PUNCT
ejpam-5916	64	46	and	and	CCONJ
ejpam-5916	64	47	lim	lim	PROPN
ejpam-5916	64	48	n	n	CCONJ
ejpam-5916	64	49	,	,	PUNCT
ejpam-5916	64	50	m→∞	m→∞	NUM
ejpam-5916	64	51	q(xm	q(xm	PROPN
ejpam-5916	64	52	,	,	PUNCT
ejpam-5916	64	53	xn	xn	NUM
ejpam-5916	64	54	)	)	PUNCT
ejpam-5916	64	55	exist	exist	VERB
ejpam-5916	64	56	and	and	CCONJ
ejpam-5916	64	57	are	be	AUX
ejpam-5916	64	58	finite	finite	ADJ
ejpam-5916	64	59	.	.	PUNCT
ejpam-5916	65	1	(	(	PUNCT
ejpam-5916	65	2	iii	iii	X
ejpam-5916	65	3	)	)	PUNCT
ejpam-5916	65	4	the	the	DET
ejpam-5916	65	5	quasi	quasi	ADJ
ejpam-5916	65	6	-	-	ADJ
ejpam-5916	65	7	partial	partial	ADJ
ejpam-5916	65	8	metric	metric	ADJ
ejpam-5916	65	9	space	space	NOUN
ejpam-5916	65	10	(	(	PUNCT
ejpam-5916	65	11	x	x	X
ejpam-5916	65	12	,	,	PUNCT
ejpam-5916	65	13	q	q	X
ejpam-5916	65	14	)	)	PUNCT
ejpam-5916	65	15	is	be	AUX
ejpam-5916	65	16	said	say	VERB
ejpam-5916	65	17	to	to	PART
ejpam-5916	65	18	be	be	AUX
ejpam-5916	65	19	complete	complete	ADJ
ejpam-5916	65	20	if	if	SCONJ
ejpam-5916	65	21	every	every	DET
ejpam-5916	65	22	cauchy	cauchy	ADJ
ejpam-5916	65	23	sequence	sequence	NOUN
ejpam-5916	65	24	{	{	PUNCT
ejpam-5916	65	25	xn	xn	NOUN
ejpam-5916	65	26	}	}	PUNCT
ejpam-5916	65	27	in	in	ADP
ejpam-5916	65	28	x	x	SYM
ejpam-5916	65	29	converges	converge	NOUN
ejpam-5916	65	30	to	to	ADP
ejpam-5916	65	31	a	a	DET
ejpam-5916	65	32	point	point	NOUN
ejpam-5916	65	33	x	x	SYM
ejpam-5916	65	34	∈	∈	NOUN
ejpam-5916	65	35	x	x	PUNCT
ejpam-5916	65	36	with	with	ADP
ejpam-5916	65	37	respect	respect	NOUN
ejpam-5916	65	38	to	to	ADP
ejpam-5916	65	39	the	the	DET
ejpam-5916	65	40	topology	topology	NOUN
ejpam-5916	65	41	τq	τq	ADP
ejpam-5916	65	42	,	,	PUNCT
ejpam-5916	65	43	such	such	ADJ
ejpam-5916	65	44	that	that	SCONJ
ejpam-5916	65	45	q(x	q(x	PROPN
ejpam-5916	65	46	,	,	PUNCT
ejpam-5916	65	47	x	x	X
ejpam-5916	65	48	)	)	PUNCT
ejpam-5916	65	49	=	=	SYM
ejpam-5916	65	50	lim	lim	PROPN
ejpam-5916	65	51	n→∞	n→∞	NUM
ejpam-5916	65	52	q(xn	q(xn	PROPN
ejpam-5916	65	53	,	,	PUNCT
ejpam-5916	65	54	x	x	X
ejpam-5916	65	55	)	)	PUNCT
ejpam-5916	66	1	=	=	SYM
ejpam-5916	66	2	lim	lim	PROPN
ejpam-5916	66	3	n→∞	n→∞	NUM
ejpam-5916	66	4	q(xm	q(xm	PROPN
ejpam-5916	66	5	,	,	PUNCT
ejpam-5916	66	6	xn	xn	PROPN
ejpam-5916	66	7	)	)	PUNCT
ejpam-5916	66	8	.	.	PUNCT
ejpam-5916	67	1	(	(	PUNCT
ejpam-5916	67	2	iv	iv	X
ejpam-5916	67	3	)	)	PUNCT
ejpam-5916	67	4	a	a	DET
ejpam-5916	67	5	subset	subset	NOUN
ejpam-5916	67	6	e	e	X
ejpam-5916	67	7	⊂	⊂	PROPN
ejpam-5916	67	8	x	x	X
ejpam-5916	67	9	is	be	AUX
ejpam-5916	67	10	called	call	VERB
ejpam-5916	67	11	closed	closed	ADJ
ejpam-5916	67	12	if	if	SCONJ
ejpam-5916	67	13	,	,	PUNCT
ejpam-5916	67	14	whenever	whenever	SCONJ
ejpam-5916	67	15	a	a	DET
ejpam-5916	67	16	sequence	sequence	NOUN
ejpam-5916	67	17	{	{	PUNCT
ejpam-5916	67	18	xn	xn	NOUN
ejpam-5916	67	19	}	}	PUNCT
ejpam-5916	67	20	⊂	⊂	X
ejpam-5916	68	1	e	e	NOUN
ejpam-5916	68	2	converges	converge	VERB
ejpam-5916	68	3	to	to	ADP
ejpam-5916	68	4	some	some	DET
ejpam-5916	68	5	x	x	SYM
ejpam-5916	68	6	∈	∈	PROPN
ejpam-5916	68	7	x	x	NOUN
ejpam-5916	68	8	,	,	PUNCT
ejpam-5916	68	9	then	then	ADV
ejpam-5916	68	10	necessarily	necessarily	ADV
ejpam-5916	68	11	x	x	SYM
ejpam-5916	68	12	∈	∈	PROPN
ejpam-5916	68	13	e.	e.	PROPN
ejpam-5916	68	14	lemma	lemma	PROPN
ejpam-5916	69	1	1	1	X
ejpam-5916	69	2	.	.	PUNCT
ejpam-5916	70	1	[	[	X
ejpam-5916	70	2	7	7	X
ejpam-5916	70	3	]	]	X
ejpam-5916	70	4	let	let	VERB
ejpam-5916	70	5	(	(	PUNCT
ejpam-5916	70	6	x	x	NOUN
ejpam-5916	70	7	,	,	PUNCT
ejpam-5916	70	8	q	q	X
ejpam-5916	70	9	)	)	PUNCT
ejpam-5916	70	10	be	be	AUX
ejpam-5916	70	11	a	a	DET
ejpam-5916	70	12	quasi	quasi	ADJ
ejpam-5916	70	13	-	-	ADJ
ejpam-5916	70	14	partial	partial	ADJ
ejpam-5916	70	15	metric	metric	ADJ
ejpam-5916	70	16	space	space	NOUN
ejpam-5916	70	17	.	.	PUNCT
ejpam-5916	71	1	then	then	ADV
ejpam-5916	71	2	the	the	DET
ejpam-5916	71	3	following	follow	VERB
ejpam-5916	71	4	properties	property	NOUN
ejpam-5916	71	5	hold	hold	VERB
ejpam-5916	71	6	:	:	PUNCT
ejpam-5916	71	7	(	(	PUNCT
ejpam-5916	71	8	i	i	NOUN
ejpam-5916	71	9	)	)	PUNCT
ejpam-5916	71	10	if	if	SCONJ
ejpam-5916	71	11	q(x	q(x	NOUN
ejpam-5916	71	12	,	,	PUNCT
ejpam-5916	71	13	y	y	NOUN
ejpam-5916	71	14	)	)	PUNCT
ejpam-5916	71	15	=	=	SYM
ejpam-5916	72	1	0	0	NUM
ejpam-5916	72	2	,	,	PUNCT
ejpam-5916	72	3	then	then	ADV
ejpam-5916	72	4	x	x	X
ejpam-5916	72	5	=	=	SYM
ejpam-5916	72	6	y.	y.	PROPN
ejpam-5916	72	7	(	(	PUNCT
ejpam-5916	72	8	ii	ii	PROPN
ejpam-5916	72	9	)	)	PUNCT
ejpam-5916	72	10	if	if	SCONJ
ejpam-5916	72	11	x	x	PROPN
ejpam-5916	72	12	̸=	̸=	PROPN
ejpam-5916	72	13	y	y	PROPN
ejpam-5916	72	14	,	,	PUNCT
ejpam-5916	72	15	then	then	ADV
ejpam-5916	72	16	q(x	q(x	PROPN
ejpam-5916	72	17	,	,	PUNCT
ejpam-5916	72	18	y	y	PROPN
ejpam-5916	72	19	)	)	PUNCT
ejpam-5916	72	20	>	>	X
ejpam-5916	72	21	0	0	PUNCT
ejpam-5916	72	22	and	and	CCONJ
ejpam-5916	72	23	q(y	q(y	PROPN
ejpam-5916	72	24	,	,	PUNCT
ejpam-5916	72	25	x	x	X
ejpam-5916	72	26	)	)	PUNCT
ejpam-5916	72	27	>	>	X
ejpam-5916	72	28	0	0	X
ejpam-5916	72	29	.	.	PUNCT
ejpam-5916	72	30	definition	definition	NOUN
ejpam-5916	72	31	4	4	NUM
ejpam-5916	72	32	.	.	PUNCT
ejpam-5916	73	1	[	[	X
ejpam-5916	73	2	24	24	NUM
ejpam-5916	73	3	]	]	PUNCT
ejpam-5916	73	4	let	let	VERB
ejpam-5916	73	5	x	x	PRON
ejpam-5916	73	6	be	be	AUX
ejpam-5916	73	7	nonempty	nonempty	ADV
ejpam-5916	73	8	set	set	VERB
ejpam-5916	73	9	,	,	PUNCT
ejpam-5916	73	10	two	two	NUM
ejpam-5916	73	11	mappings	mapping	NOUN
ejpam-5916	73	12	a	a	PRON
ejpam-5916	73	13	,	,	PUNCT
ejpam-5916	73	14	s	s	PART
ejpam-5916	73	15	:	:	PUNCT
ejpam-5916	73	16	x	x	SYM
ejpam-5916	73	17	→	→	SYM
ejpam-5916	73	18	x	x	X
ejpam-5916	73	19	,	,	PUNCT
ejpam-5916	73	20	are	be	AUX
ejpam-5916	73	21	said	say	VERB
ejpam-5916	73	22	to	to	PART
ejpam-5916	73	23	be	be	AUX
ejpam-5916	73	24	weakly	weakly	ADV
ejpam-5916	73	25	compatible	compatible	ADJ
ejpam-5916	73	26	if	if	SCONJ
ejpam-5916	73	27	they	they	PRON
ejpam-5916	73	28	commute	commute	VERB
ejpam-5916	73	29	at	at	ADP
ejpam-5916	73	30	their	their	PRON
ejpam-5916	73	31	coincidence	coincidence	NOUN
ejpam-5916	73	32	point	point	NOUN
ejpam-5916	73	33	,	,	PUNCT
ejpam-5916	73	34	i.e.	i.e.	X
ejpam-5916	73	35	,	,	PUNCT
ejpam-5916	73	36	if	if	SCONJ
ejpam-5916	73	37	au	au	ADP
ejpam-5916	73	38	=	=	SYM
ejpam-5916	73	39	su	su	PROPN
ejpam-5916	73	40	for	for	ADP
ejpam-5916	73	41	some	some	DET
ejpam-5916	73	42	u	u	NOUN
ejpam-5916	73	43	∈	∈	PROPN
ejpam-5916	73	44	x	x	NOUN
ejpam-5916	73	45	,	,	PUNCT
ejpam-5916	73	46	then	then	ADV
ejpam-5916	73	47	asu	asu	PROPN
ejpam-5916	73	48	=	=	PUNCT
ejpam-5916	73	49	sau	sau	PROPN
ejpam-5916	73	50	.	.	PUNCT
ejpam-5916	74	1	in	in	ADP
ejpam-5916	74	2	[	[	X
ejpam-5916	74	3	20	20	NUM
ejpam-5916	74	4	]	]	PUNCT
ejpam-5916	74	5	,	,	PUNCT
ejpam-5916	74	6	a	a	DET
ejpam-5916	74	7	new	new	ADJ
ejpam-5916	74	8	functions	function	NOUN
ejpam-5916	74	9	class	class	NOUN
ejpam-5916	74	10	has	have	AUX
ejpam-5916	74	11	been	be	AUX
ejpam-5916	74	12	introduced	introduce	VERB
ejpam-5916	74	13	called	call	VERB
ejpam-5916	74	14	c	c	NOUN
ejpam-5916	74	15	-	-	PUNCT
ejpam-5916	74	16	class	class	NOUN
ejpam-5916	74	17	functions	function	NOUN
ejpam-5916	74	18	.	.	PUNCT
ejpam-5916	75	1	these	these	DET
ejpam-5916	75	2	functions	function	NOUN
ejpam-5916	75	3	are	be	AUX
ejpam-5916	75	4	particularly	particularly	ADV
ejpam-5916	75	5	useful	useful	ADJ
ejpam-5916	75	6	for	for	ADP
ejpam-5916	75	7	establishing	establish	VERB
ejpam-5916	75	8	the	the	DET
ejpam-5916	75	9	existence	existence	NOUN
ejpam-5916	75	10	and	and	CCONJ
ejpam-5916	75	11	uniqueness	uniqueness	NOUN
ejpam-5916	75	12	of	of	ADP
ejpam-5916	75	13	fixed	fix	VERB
ejpam-5916	75	14	points	point	NOUN
ejpam-5916	75	15	in	in	ADP
ejpam-5916	75	16	generalized	generalized	ADJ
ejpam-5916	75	17	metric	metric	ADJ
ejpam-5916	75	18	spaces	space	NOUN
ejpam-5916	75	19	while	while	SCONJ
ejpam-5916	75	20	maintaining	maintain	VERB
ejpam-5916	75	21	the	the	DET
ejpam-5916	75	22	essential	essential	ADJ
ejpam-5916	75	23	properties	property	NOUN
ejpam-5916	75	24	needed	need	VERB
ejpam-5916	75	25	for	for	ADP
ejpam-5916	75	26	fixed	fix	VERB
ejpam-5916	75	27	point	point	NOUN
ejpam-5916	75	28	arguments	argument	NOUN
ejpam-5916	75	29	.	.	PUNCT
ejpam-5916	76	1	definition	definition	NOUN
ejpam-5916	76	2	5	5	NUM
ejpam-5916	76	3	.	.	PUNCT
ejpam-5916	77	1	[	[	X
ejpam-5916	77	2	20	20	NUM
ejpam-5916	77	3	]	]	PUNCT
ejpam-5916	77	4	a	a	DET
ejpam-5916	77	5	function	function	NOUN
ejpam-5916	77	6	f	f	NOUN
ejpam-5916	77	7	:	:	PUNCT
ejpam-5916	78	1	[	[	X
ejpam-5916	78	2	0,∞)2	0,∞)2	NUM
ejpam-5916	78	3	→	→	PUNCT
ejpam-5916	78	4	r	r	NOUN
ejpam-5916	78	5	is	be	AUX
ejpam-5916	78	6	called	call	VERB
ejpam-5916	78	7	c	c	NOUN
ejpam-5916	78	8	-	-	PUNCT
ejpam-5916	78	9	class	class	NOUN
ejpam-5916	78	10	function	function	NOUN
ejpam-5916	78	11	if	if	SCONJ
ejpam-5916	78	12	it	it	PRON
ejpam-5916	78	13	is	be	AUX
ejpam-5916	78	14	continuous	continuous	ADJ
ejpam-5916	78	15	and	and	CCONJ
ejpam-5916	78	16	satisfies	satisfy	VERB
ejpam-5916	78	17	the	the	DET
ejpam-5916	78	18	following	follow	VERB
ejpam-5916	78	19	axioms	axiom	NOUN
ejpam-5916	78	20	:	:	PUNCT
ejpam-5916	78	21	(	(	PUNCT
ejpam-5916	78	22	1)f	1)f	NUM
ejpam-5916	78	23	(	(	PUNCT
ejpam-5916	78	24	s	s	PROPN
ejpam-5916	78	25	,	,	PUNCT
ejpam-5916	78	26	t	t	PROPN
ejpam-5916	78	27	)	)	PUNCT
ejpam-5916	78	28	≤	≤	PROPN
ejpam-5916	78	29	s	s	PROPN
ejpam-5916	78	30	;	;	PUNCT
ejpam-5916	78	31	(	(	PUNCT
ejpam-5916	78	32	2	2	X
ejpam-5916	78	33	)	)	PUNCT
ejpam-5916	78	34	f	f	NOUN
ejpam-5916	78	35	(	(	PUNCT
ejpam-5916	78	36	s	s	PROPN
ejpam-5916	78	37	,	,	PUNCT
ejpam-5916	78	38	t	t	PROPN
ejpam-5916	78	39	)	)	PUNCT
ejpam-5916	79	1	=	=	SYM
ejpam-5916	79	2	s	s	NOUN
ejpam-5916	79	3	implies	imply	VERB
ejpam-5916	79	4	that	that	SCONJ
ejpam-5916	79	5	either	either	CCONJ
ejpam-5916	79	6	s	s	VERB
ejpam-5916	79	7	=	=	NOUN
ejpam-5916	79	8	0	0	NUM
ejpam-5916	79	9	or	or	CCONJ
ejpam-5916	79	10	t	t	X
ejpam-5916	79	11	=	=	SYM
ejpam-5916	79	12	0	0	NUM
ejpam-5916	79	13	;	;	PUNCT
ejpam-5916	79	14	for	for	ADP
ejpam-5916	79	15	all	all	DET
ejpam-5916	79	16	s	s	PROPN
ejpam-5916	79	17	,	,	PUNCT
ejpam-5916	79	18	t	t	PROPN
ejpam-5916	79	19	∈	∈	PROPN
ejpam-5916	80	1	[	[	X
ejpam-5916	80	2	0,∞	0,∞	NUM
ejpam-5916	80	3	)	)	PUNCT
ejpam-5916	80	4	.	.	PUNCT
ejpam-5916	81	1	example	example	NOUN
ejpam-5916	82	1	3	3	NUM
ejpam-5916	82	2	.	.	PUNCT
ejpam-5916	83	1	[	[	X
ejpam-5916	83	2	20]the	20]the	NUM
ejpam-5916	83	3	following	follow	VERB
ejpam-5916	83	4	functions	function	NOUN
ejpam-5916	83	5	f	f	NOUN
ejpam-5916	83	6	:	:	PUNCT
ejpam-5916	84	1	[	[	X
ejpam-5916	84	2	0,∞)2	0,∞)2	NUM
ejpam-5916	84	3	→	→	SYM
ejpam-5916	84	4	r	r	NOUN
ejpam-5916	84	5	are	be	AUX
ejpam-5916	84	6	elements	element	NOUN
ejpam-5916	84	7	of	of	ADP
ejpam-5916	84	8	c	c	NOUN
ejpam-5916	84	9	,	,	PUNCT
ejpam-5916	84	10	for	for	ADP
ejpam-5916	84	11	all	all	DET
ejpam-5916	84	12	s	s	PROPN
ejpam-5916	84	13	,	,	PUNCT
ejpam-5916	84	14	t	t	PROPN
ejpam-5916	84	15	∈	∈	PROPN
ejpam-5916	85	1	[	[	X
ejpam-5916	85	2	0,∞	0,∞	NUM
ejpam-5916	85	3	):	):	PUNCT
ejpam-5916	85	4	(	(	PUNCT
ejpam-5916	85	5	1	1	X
ejpam-5916	85	6	)	)	PUNCT
ejpam-5916	85	7	f	f	NOUN
ejpam-5916	85	8	(	(	PUNCT
ejpam-5916	85	9	s	s	PROPN
ejpam-5916	85	10	,	,	PUNCT
ejpam-5916	85	11	t	t	PROPN
ejpam-5916	85	12	)	)	PUNCT
ejpam-5916	85	13	=	=	SYM
ejpam-5916	85	14	s−	s−	PROPN
ejpam-5916	85	15	t	t	PROPN
ejpam-5916	85	16	,	,	PUNCT
ejpam-5916	85	17	f	f	PROPN
ejpam-5916	85	18	(	(	PUNCT
ejpam-5916	85	19	s	s	PROPN
ejpam-5916	85	20	,	,	PUNCT
ejpam-5916	85	21	t	t	PROPN
ejpam-5916	85	22	)	)	PUNCT
ejpam-5916	85	23	=	=	PUNCT
ejpam-5916	85	24	s⇒	s⇒	PART
ejpam-5916	85	25	t	t	NOUN
ejpam-5916	85	26	=	=	SYM
ejpam-5916	85	27	0	0	NUM
ejpam-5916	85	28	;	;	PUNCT
ejpam-5916	85	29	(	(	PUNCT
ejpam-5916	85	30	2	2	X
ejpam-5916	85	31	)	)	PUNCT
ejpam-5916	85	32	f	f	NOUN
ejpam-5916	85	33	(	(	PUNCT
ejpam-5916	85	34	s	s	PROPN
ejpam-5916	85	35	,	,	PUNCT
ejpam-5916	85	36	t	t	PROPN
ejpam-5916	85	37	)	)	PUNCT
ejpam-5916	85	38	=	=	SYM
ejpam-5916	86	1	ms	ms	PROPN
ejpam-5916	86	2	,	,	PUNCT
ejpam-5916	86	3	0	0	NUM
ejpam-5916	86	4	<	<	X
ejpam-5916	86	5	m<1	m<1	NOUN
ejpam-5916	86	6	,	,	PUNCT
ejpam-5916	86	7	f	f	PROPN
ejpam-5916	86	8	(	(	PUNCT
ejpam-5916	86	9	s	s	PROPN
ejpam-5916	86	10	,	,	PUNCT
ejpam-5916	86	11	t	t	PROPN
ejpam-5916	86	12	)	)	PUNCT
ejpam-5916	86	13	=	=	PUNCT
ejpam-5916	87	1	s⇒	s⇒	X
ejpam-5916	87	2	s	s	NOUN
ejpam-5916	87	3	=	=	NOUN
ejpam-5916	87	4	0	0	NUM
ejpam-5916	87	5	;	;	PUNCT
ejpam-5916	87	6	(	(	PUNCT
ejpam-5916	87	7	3	3	X
ejpam-5916	87	8	)	)	PUNCT
ejpam-5916	87	9	f	f	NOUN
ejpam-5916	87	10	(	(	PUNCT
ejpam-5916	87	11	s	s	PROPN
ejpam-5916	87	12	,	,	PUNCT
ejpam-5916	87	13	t	t	PROPN
ejpam-5916	87	14	)	)	PUNCT
ejpam-5916	87	15	=	=	SYM
ejpam-5916	87	16	s	s	X
ejpam-5916	87	17	(	(	PUNCT
ejpam-5916	87	18	1+t)r	1+t)r	NUM
ejpam-5916	87	19	;	;	PUNCT
ejpam-5916	87	20	r	r	NOUN
ejpam-5916	87	21	∈	∈	PROPN
ejpam-5916	87	22	(	(	PUNCT
ejpam-5916	87	23	0,∞	0,∞	NOUN
ejpam-5916	87	24	)	)	PUNCT
ejpam-5916	87	25	,	,	PUNCT
ejpam-5916	87	26	f	f	PROPN
ejpam-5916	87	27	(	(	PUNCT
ejpam-5916	87	28	s	s	PROPN
ejpam-5916	87	29	,	,	PUNCT
ejpam-5916	87	30	t	t	PROPN
ejpam-5916	87	31	)	)	PUNCT
ejpam-5916	87	32	=	=	SYM
ejpam-5916	87	33	s	s	PART
ejpam-5916	87	34	⇒	⇒	NOUN
ejpam-5916	87	35	s	s	PART
ejpam-5916	87	36	=	=	SYM
ejpam-5916	87	37	0	0	NUM
ejpam-5916	87	38	or	or	CCONJ
ejpam-5916	87	39	t	t	X
ejpam-5916	87	40	=	=	SYM
ejpam-5916	87	41	0	0	NUM
ejpam-5916	87	42	;	;	PUNCT
ejpam-5916	87	43	(	(	PUNCT
ejpam-5916	87	44	4	4	X
ejpam-5916	87	45	)	)	PUNCT
ejpam-5916	87	46	f	f	NOUN
ejpam-5916	87	47	(	(	PUNCT
ejpam-5916	87	48	s	s	PROPN
ejpam-5916	87	49	,	,	PUNCT
ejpam-5916	87	50	t	t	PROPN
ejpam-5916	87	51	)	)	PUNCT
ejpam-5916	87	52	=	=	SYM
ejpam-5916	87	53	φ(s	φ(s	NOUN
ejpam-5916	87	54	)	)	PUNCT
ejpam-5916	87	55	,	,	PUNCT
ejpam-5916	87	56	f	f	PROPN
ejpam-5916	87	57	(	(	PUNCT
ejpam-5916	87	58	s	s	PROPN
ejpam-5916	87	59	,	,	PUNCT
ejpam-5916	87	60	t	t	PROPN
ejpam-5916	87	61	)	)	PUNCT
ejpam-5916	87	62	=	=	SYM
ejpam-5916	87	63	s	s	PART
ejpam-5916	87	64	⇒	⇒	NOUN
ejpam-5916	87	65	s	s	PART
ejpam-5916	87	66	=	=	SYM
ejpam-5916	87	67	0	0	NUM
ejpam-5916	87	68	,	,	PUNCT
ejpam-5916	87	69	here	here	ADV
ejpam-5916	87	70	φ	φ	X
ejpam-5916	87	71	:	:	PUNCT
ejpam-5916	88	1	[	[	X
ejpam-5916	88	2	0,∞	0,∞	NUM
ejpam-5916	88	3	)	)	PUNCT
ejpam-5916	88	4	→	→	PUNCT
ejpam-5916	89	1	[	[	X
ejpam-5916	89	2	0,∞	0,∞	NUM
ejpam-5916	89	3	)	)	PUNCT
ejpam-5916	89	4	is	be	AUX
ejpam-5916	89	5	a	a	DET
ejpam-5916	89	6	upper	upper	ADJ
ejpam-5916	89	7	semicontinuous	semicontinuous	ADJ
ejpam-5916	89	8	function	function	NOUN
ejpam-5916	89	9	such	such	ADJ
ejpam-5916	89	10	that	that	PRON
ejpam-5916	89	11	φ(0	φ(0	ADJ
ejpam-5916	89	12	)	)	PUNCT
ejpam-5916	89	13	=	=	SYM
ejpam-5916	89	14	0	0	NUM
ejpam-5916	89	15	,	,	PUNCT
ejpam-5916	89	16	and	and	CCONJ
ejpam-5916	89	17	φ(t	φ(t	PROPN
ejpam-5916	89	18	)	)	PUNCT
ejpam-5916	89	19	<	<	X
ejpam-5916	89	20	t	t	PROPN
ejpam-5916	89	21	for	for	ADP
ejpam-5916	89	22	t	t	PROPN
ejpam-5916	89	23	>	>	X
ejpam-5916	89	24	0	0	NUM
ejpam-5916	89	25	,	,	PUNCT
ejpam-5916	89	26	.	.	PUNCT
ejpam-5916	90	1	(	(	PUNCT
ejpam-5916	90	2	5	5	X
ejpam-5916	90	3	)	)	PUNCT
ejpam-5916	90	4	f	f	NOUN
ejpam-5916	90	5	(	(	PUNCT
ejpam-5916	90	6	s	s	PROPN
ejpam-5916	90	7	,	,	PUNCT
ejpam-5916	90	8	t	t	PROPN
ejpam-5916	90	9	)	)	PUNCT
ejpam-5916	90	10	=	=	SYM
ejpam-5916	90	11	s	s	X
ejpam-5916	90	12	(	(	PUNCT
ejpam-5916	90	13	1+s)r	1+s)r	NOUN
ejpam-5916	90	14	;	;	PUNCT
ejpam-5916	90	15	r	r	NOUN
ejpam-5916	90	16	∈	∈	PROPN
ejpam-5916	90	17	(	(	PUNCT
ejpam-5916	90	18	0,∞	0,∞	NOUN
ejpam-5916	90	19	)	)	PUNCT
ejpam-5916	90	20	,	,	PUNCT
ejpam-5916	90	21	f	f	PROPN
ejpam-5916	90	22	(	(	PUNCT
ejpam-5916	90	23	s	s	PROPN
ejpam-5916	90	24	,	,	PUNCT
ejpam-5916	90	25	t	t	PROPN
ejpam-5916	90	26	)	)	PUNCT
ejpam-5916	90	27	=	=	SYM
ejpam-5916	90	28	s	s	PART
ejpam-5916	90	29	⇒	⇒	NOUN
ejpam-5916	90	30	s	s	PART
ejpam-5916	90	31	=	=	SYM
ejpam-5916	90	32	0	0	PROPN
ejpam-5916	90	33	.	.	PUNCT
ejpam-5916	91	1	definition	definition	NOUN
ejpam-5916	91	2	6	6	NUM
ejpam-5916	91	3	.	.	PUNCT
ejpam-5916	92	1	[	[	X
ejpam-5916	92	2	25	25	NUM
ejpam-5916	92	3	]	]	PUNCT
ejpam-5916	92	4	let	let	VERB
ejpam-5916	92	5	ψ	ψ	PART
ejpam-5916	92	6	be	be	AUX
ejpam-5916	92	7	the	the	DET
ejpam-5916	92	8	collection	collection	NOUN
ejpam-5916	92	9	of	of	ADP
ejpam-5916	92	10	all	all	DET
ejpam-5916	92	11	continuous	continuous	ADJ
ejpam-5916	92	12	functions	function	NOUN
ejpam-5916	92	13	ψ	ψ	NOUN
ejpam-5916	92	14	:	:	PUNCT
ejpam-5916	92	15	r+	r+	NOUN
ejpam-5916	92	16	→	→	PUNCT
ejpam-5916	92	17	r+	r+	NOUN
ejpam-5916	92	18	that	that	PRON
ejpam-5916	92	19	satisfy	satisfy	VERB
ejpam-5916	92	20	the	the	DET
ejpam-5916	92	21	following	follow	VERB
ejpam-5916	92	22	conditions	condition	NOUN
ejpam-5916	92	23	:	:	PUNCT
ejpam-5916	92	24	h.	h.	PROPN
ejpam-5916	92	25	qawaqneh	qawaqneh	PROPN
ejpam-5916	92	26	/	/	SYM
ejpam-5916	92	27	eur	eur	PROPN
ejpam-5916	92	28	.	.	PUNCT
ejpam-5916	93	1	j.	j.	PROPN
ejpam-5916	93	2	pure	pure	PROPN
ejpam-5916	93	3	appl	appl	PROPN
ejpam-5916	93	4	.	.	PROPN
ejpam-5916	93	5	math	math	PROPN
ejpam-5916	93	6	,	,	PUNCT
ejpam-5916	93	7	18	18	NUM
ejpam-5916	93	8	(	(	PUNCT
ejpam-5916	93	9	3	3	NUM
ejpam-5916	93	10	)	)	PUNCT
ejpam-5916	93	11	(	(	PUNCT
ejpam-5916	93	12	2025	2025	NUM
ejpam-5916	93	13	)	)	PUNCT
ejpam-5916	93	14	,	,	PUNCT
ejpam-5916	93	15	5916	5916	NUM
ejpam-5916	93	16	5	5	NUM
ejpam-5916	93	17	of	of	ADP
ejpam-5916	93	18	19	19	NUM
ejpam-5916	93	19	(	(	PUNCT
ejpam-5916	93	20	i	i	NOUN
ejpam-5916	93	21	)	)	PUNCT
ejpam-5916	93	22	ψ	ψ	NOUN
ejpam-5916	93	23	is	be	AUX
ejpam-5916	93	24	a	a	DET
ejpam-5916	93	25	strictly	strictly	ADV
ejpam-5916	93	26	increasing	increase	VERB
ejpam-5916	93	27	function	function	NOUN
ejpam-5916	93	28	,	,	PUNCT
ejpam-5916	93	29	i.e.	i.e.	X
ejpam-5916	93	30	,	,	PUNCT
ejpam-5916	93	31	for	for	ADP
ejpam-5916	93	32	any	any	DET
ejpam-5916	93	33	t1	t1	NOUN
ejpam-5916	93	34	,	,	PUNCT
ejpam-5916	93	35	t2	t2	PROPN
ejpam-5916	93	36	∈	∈	PROPN
ejpam-5916	93	37	r+	r+	NOUN
ejpam-5916	93	38	with	with	ADP
ejpam-5916	93	39	t1	t1	NOUN
ejpam-5916	93	40	<	<	X
ejpam-5916	93	41	t2	t2	PROPN
ejpam-5916	93	42	,	,	PUNCT
ejpam-5916	93	43	we	we	PRON
ejpam-5916	93	44	have	have	VERB
ejpam-5916	93	45	ψ(t1	ψ(t1	NOUN
ejpam-5916	93	46	)	)	PUNCT
ejpam-5916	93	47	<	<	X
ejpam-5916	93	48	ψ(t2	ψ(t2	NOUN
ejpam-5916	93	49	)	)	PUNCT
ejpam-5916	93	50	,	,	PUNCT
ejpam-5916	93	51	(	(	PUNCT
ejpam-5916	93	52	ii	ii	NOUN
ejpam-5916	93	53	)	)	PUNCT
ejpam-5916	93	54	ψ(t	ψ(t	PROPN
ejpam-5916	93	55	)	)	PUNCT
ejpam-5916	93	56	=	=	SYM
ejpam-5916	93	57	0	0	PUNCT
ejpam-5916	94	1	if	if	SCONJ
ejpam-5916	94	2	and	and	CCONJ
ejpam-5916	94	3	only	only	ADV
ejpam-5916	94	4	if	if	SCONJ
ejpam-5916	94	5	t	t	PROPN
ejpam-5916	94	6	=	=	SYM
ejpam-5916	94	7	0	0	X
ejpam-5916	94	8	.	.	PUNCT
ejpam-5916	94	9	similarly	similarly	ADV
ejpam-5916	94	10	,	,	PUNCT
ejpam-5916	94	11	let	let	VERB
ejpam-5916	94	12	φ	φ	PROPN
ejpam-5916	94	13	denote	denote	VERB
ejpam-5916	94	14	the	the	DET
ejpam-5916	94	15	set	set	NOUN
ejpam-5916	94	16	of	of	ADP
ejpam-5916	94	17	all	all	DET
ejpam-5916	94	18	lower	low	ADJ
ejpam-5916	94	19	semi	semi	ADJ
ejpam-5916	94	20	-	-	ADJ
ejpam-5916	94	21	continuous	continuous	ADJ
ejpam-5916	94	22	functions	function	NOUN
ejpam-5916	94	23	ϕ	ϕ	NOUN
ejpam-5916	94	24	:	:	PUNCT
ejpam-5916	94	25	r+	r+	NOUN
ejpam-5916	94	26	→	→	SYM
ejpam-5916	94	27	r+	r+	X
ejpam-5916	94	28	satisfying	satisfy	VERB
ejpam-5916	94	29	:	:	PUNCT
ejpam-5916	94	30	(	(	PUNCT
ejpam-5916	94	31	i	i	NOUN
ejpam-5916	94	32	)	)	PUNCT
ejpam-5916	94	33	ϕ(t	ϕ(t	NUM
ejpam-5916	94	34	)	)	PUNCT
ejpam-5916	94	35	>	>	X
ejpam-5916	94	36	0	0	PUNCT
ejpam-5916	94	37	for	for	ADP
ejpam-5916	94	38	all	all	DET
ejpam-5916	94	39	t	t	PROPN
ejpam-5916	94	40	>	>	X
ejpam-5916	94	41	0	0	NUM
ejpam-5916	94	42	,	,	PUNCT
ejpam-5916	94	43	(	(	PUNCT
ejpam-5916	94	44	ii	ii	NOUN
ejpam-5916	94	45	)	)	PUNCT
ejpam-5916	94	46	ϕ(0	ϕ(0	PROPN
ejpam-5916	94	47	)	)	PUNCT
ejpam-5916	95	1	=	=	PUNCT
ejpam-5916	95	2	0	0	X
ejpam-5916	95	3	.	.	PUNCT
ejpam-5916	96	1	both	both	DET
ejpam-5916	96	2	functions	function	NOUN
ejpam-5916	96	3	ψ(t	ψ(t	PROPN
ejpam-5916	96	4	)	)	PUNCT
ejpam-5916	97	1	=	=	SYM
ejpam-5916	97	2	et	et	NOUN
ejpam-5916	97	3	−	−	NOUN
ejpam-5916	97	4	1	1	NUM
ejpam-5916	97	5	and	and	CCONJ
ejpam-5916	97	6	ϕ(t	ϕ(t	NUM
ejpam-5916	97	7	)	)	PUNCT
ejpam-5916	98	1	=	=	SYM
ejpam-5916	98	2	t	t	PROPN
ejpam-5916	98	3	1+t	1+t	NUM
ejpam-5916	98	4	satisfy	satisfy	VERB
ejpam-5916	98	5	the	the	DET
ejpam-5916	98	6	properties	property	NOUN
ejpam-5916	98	7	of	of	ADP
ejpam-5916	98	8	ψ	ψ	PROPN
ejpam-5916	98	9	and	and	CCONJ
ejpam-5916	98	10	φ	φ	NUM
ejpam-5916	98	11	.	.	PROPN
ejpam-5916	99	1	3	3	NUM
ejpam-5916	99	2	.	.	X
ejpam-5916	99	3	main	main	ADJ
ejpam-5916	99	4	results	result	NOUN
ejpam-5916	99	5	the	the	DET
ejpam-5916	99	6	study	study	NOUN
ejpam-5916	99	7	of	of	ADP
ejpam-5916	99	8	contractive	contractive	ADJ
ejpam-5916	99	9	conditions	condition	NOUN
ejpam-5916	99	10	in	in	ADP
ejpam-5916	99	11	quasi	quasi	ADJ
ejpam-5916	99	12	-	-	ADJ
ejpam-5916	99	13	partial	partial	ADJ
ejpam-5916	99	14	metric	metric	ADJ
ejpam-5916	99	15	spaces	space	NOUN
ejpam-5916	99	16	has	have	AUX
ejpam-5916	99	17	led	lead	VERB
ejpam-5916	99	18	to	to	ADP
ejpam-5916	99	19	important	important	ADJ
ejpam-5916	99	20	advances	advance	NOUN
ejpam-5916	99	21	,	,	PUNCT
ejpam-5916	99	22	particularly	particularly	ADV
ejpam-5916	99	23	through	through	ADP
ejpam-5916	99	24	the	the	DET
ejpam-5916	99	25	introduction	introduction	NOUN
ejpam-5916	99	26	of	of	ADP
ejpam-5916	99	27	c	c	NOUN
ejpam-5916	99	28	-	-	PUNCT
ejpam-5916	99	29	class	class	NOUN
ejpam-5916	99	30	functions	function	NOUN
ejpam-5916	99	31	[	[	X
ejpam-5916	99	32	20	20	NUM
ejpam-5916	99	33	]	]	PUNCT
ejpam-5916	99	34	.	.	PUNCT
ejpam-5916	100	1	these	these	DET
ejpam-5916	100	2	functions	function	NOUN
ejpam-5916	100	3	provide	provide	VERB
ejpam-5916	100	4	a	a	DET
ejpam-5916	100	5	unifying	unifying	ADJ
ejpam-5916	100	6	framework	framework	NOUN
ejpam-5916	100	7	that	that	PRON
ejpam-5916	100	8	encompasses	encompass	VERB
ejpam-5916	100	9	many	many	ADJ
ejpam-5916	100	10	existing	exist	VERB
ejpam-5916	100	11	contraction	contraction	NOUN
ejpam-5916	100	12	types	type	NOUN
ejpam-5916	100	13	while	while	SCONJ
ejpam-5916	100	14	enabling	enable	VERB
ejpam-5916	100	15	new	new	ADJ
ejpam-5916	100	16	fixed	fix	VERB
ejpam-5916	100	17	point	point	NOUN
ejpam-5916	100	18	results	result	NOUN
ejpam-5916	100	19	.	.	PUNCT
ejpam-5916	101	1	their	their	PRON
ejpam-5916	101	2	flexibility	flexibility	NOUN
ejpam-5916	101	3	makes	make	VERB
ejpam-5916	101	4	them	they	PRON
ejpam-5916	101	5	particularly	particularly	ADV
ejpam-5916	101	6	suitable	suitable	ADJ
ejpam-5916	101	7	for	for	ADP
ejpam-5916	101	8	handling	handle	VERB
ejpam-5916	101	9	the	the	DET
ejpam-5916	101	10	asymmetric	asymmetric	ADJ
ejpam-5916	101	11	nature	nature	NOUN
ejpam-5916	101	12	of	of	ADP
ejpam-5916	101	13	quasi	quasi	ADJ
ejpam-5916	101	14	-	-	ADJ
ejpam-5916	101	15	partial	partial	ADJ
ejpam-5916	101	16	metric	metric	ADJ
ejpam-5916	101	17	spaces	space	NOUN
ejpam-5916	101	18	.	.	PUNCT
ejpam-5916	102	1	theorem	theorem	NOUN
ejpam-5916	102	2	1	1	NUM
ejpam-5916	102	3	.	.	PUNCT
ejpam-5916	103	1	let	let	AUX
ejpam-5916	103	2	(	(	PUNCT
ejpam-5916	103	3	x	x	NOUN
ejpam-5916	103	4	,	,	PUNCT
ejpam-5916	103	5	q	q	X
ejpam-5916	103	6	)	)	PUNCT
ejpam-5916	103	7	be	be	AUX
ejpam-5916	103	8	a	a	DET
ejpam-5916	103	9	complete	complete	ADJ
ejpam-5916	103	10	quasi	quasi	ADJ
ejpam-5916	103	11	-	-	ADJ
ejpam-5916	103	12	partial	partial	ADJ
ejpam-5916	103	13	metric	metric	ADJ
ejpam-5916	103	14	space	space	NOUN
ejpam-5916	103	15	,	,	PUNCT
ejpam-5916	103	16	and	and	CCONJ
ejpam-5916	103	17	let	let	VERB
ejpam-5916	103	18	s	s	PRON
ejpam-5916	103	19	and	and	CCONJ
ejpam-5916	103	20	t	t	PROPN
ejpam-5916	103	21	be	be	AUX
ejpam-5916	103	22	selfmappings	selfmapping	NOUN
ejpam-5916	103	23	on	on	ADP
ejpam-5916	103	24	x.	x.	NOUN
ejpam-5916	103	25	suppose	suppose	VERB
ejpam-5916	103	26	there	there	PRON
ejpam-5916	103	27	exist	exist	VERB
ejpam-5916	103	28	functions	function	NOUN
ejpam-5916	103	29	ψ	ψ	ADP
ejpam-5916	103	30	∈	∈	PROPN
ejpam-5916	103	31	ψ	ψ	NOUN
ejpam-5916	103	32	,	,	PUNCT
ejpam-5916	103	33	ϕ	ϕ	PROPN
ejpam-5916	103	34	∈	∈	PROPN
ejpam-5916	103	35	φ	φ	PROPN
ejpam-5916	103	36	,	,	PUNCT
ejpam-5916	103	37	and	and	CCONJ
ejpam-5916	103	38	f	f	PROPN
ejpam-5916	103	39	∈	∈	PROPN
ejpam-5916	103	40	c	c	PROPN
ejpam-5916	103	41	such	such	ADJ
ejpam-5916	103	42	that	that	PRON
ejpam-5916	103	43	for	for	ADP
ejpam-5916	103	44	all	all	DET
ejpam-5916	103	45	x	x	NOUN
ejpam-5916	103	46	,	,	PUNCT
ejpam-5916	103	47	y	y	PROPN
ejpam-5916	103	48	∈	∈	PROPN
ejpam-5916	103	49	x	x	SYM
ejpam-5916	103	50	,	,	PUNCT
ejpam-5916	103	51	ψ(q(sx	ψ(q(sx	ADP
ejpam-5916	103	52	,	,	PUNCT
ejpam-5916	103	53	ty	ty	NOUN
ejpam-5916	103	54	)	)	PUNCT
ejpam-5916	103	55	)	)	PUNCT
ejpam-5916	104	1	≤	≤	NUM
ejpam-5916	104	2	f	f	X
ejpam-5916	104	3	(	(	PUNCT
ejpam-5916	104	4	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	104	5	,	,	PUNCT
ejpam-5916	104	6	y	y	NOUN
ejpam-5916	104	7	)	)	PUNCT
ejpam-5916	104	8	)	)	PUNCT
ejpam-5916	104	9	,	,	PUNCT
ejpam-5916	104	10	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	104	11	,	,	PUNCT
ejpam-5916	104	12	y	y	NOUN
ejpam-5916	104	13	)	)	PUNCT
ejpam-5916	104	14	)	)	PUNCT
ejpam-5916	104	15	)	)	PUNCT
ejpam-5916	104	16	,	,	PUNCT
ejpam-5916	104	17	where	where	SCONJ
ejpam-5916	104	18	m(x	m(x	PROPN
ejpam-5916	104	19	,	,	PUNCT
ejpam-5916	104	20	y	y	NOUN
ejpam-5916	104	21	)	)	PUNCT
ejpam-5916	104	22	=	=	SYM
ejpam-5916	104	23	max	max	X
ejpam-5916	104	24	{	{	PUNCT
ejpam-5916	104	25	q(sx	q(sx	PROPN
ejpam-5916	104	26	,	,	PUNCT
ejpam-5916	104	27	ty	ty	NOUN
ejpam-5916	104	28	)	)	PUNCT
ejpam-5916	104	29	,	,	PUNCT
ejpam-5916	104	30	q(sx	q(sx	PROPN
ejpam-5916	104	31	,	,	PUNCT
ejpam-5916	104	32	sx	sx	PROPN
ejpam-5916	104	33	)	)	PUNCT
ejpam-5916	104	34	,	,	PUNCT
ejpam-5916	104	35	q(ty	q(ty	PROPN
ejpam-5916	104	36	,	,	PUNCT
ejpam-5916	104	37	ty	ty	NOUN
ejpam-5916	104	38	)	)	PUNCT
ejpam-5916	104	39	,	,	PUNCT
ejpam-5916	104	40	αq(sx	αq(sx	PROPN
ejpam-5916	104	41	,	,	PUNCT
ejpam-5916	104	42	ty	ty	INTJ
ejpam-5916	104	43	)	)	PUNCT
ejpam-5916	104	44	+	+	CCONJ
ejpam-5916	104	45	(	(	PUNCT
ejpam-5916	104	46	1−	1−	NUM
ejpam-5916	104	47	α)q(ty	α)q(ty	NUM
ejpam-5916	104	48	,	,	PUNCT
ejpam-5916	104	49	sx	sx	PROPN
ejpam-5916	104	50	)	)	PUNCT
ejpam-5916	104	51	}	}	PUNCT
ejpam-5916	104	52	,	,	PUNCT
ejpam-5916	104	53	with	with	ADP
ejpam-5916	104	54	α	α	PRON
ejpam-5916	104	55	∈	∈	PROPN
ejpam-5916	105	1	[	[	X
ejpam-5916	105	2	0	0	NUM
ejpam-5916	105	3	,	,	PUNCT
ejpam-5916	105	4	1	1	NUM
ejpam-5916	105	5	]	]	PUNCT
ejpam-5916	105	6	.	.	PUNCT
ejpam-5916	106	1	additionally	additionally	ADV
ejpam-5916	106	2	,	,	PUNCT
ejpam-5916	106	3	assume	assume	VERB
ejpam-5916	106	4	:	:	PUNCT
ejpam-5916	106	5	(	(	PUNCT
ejpam-5916	106	6	i	i	NOUN
ejpam-5916	106	7	)	)	PUNCT
ejpam-5916	106	8	sx	sx	PROPN
ejpam-5916	106	9	⊆	⊆	NUM
ejpam-5916	106	10	tx	tx	PROPN
ejpam-5916	106	11	,	,	PUNCT
ejpam-5916	106	12	(	(	PUNCT
ejpam-5916	106	13	ii	ii	NOUN
ejpam-5916	106	14	)	)	PUNCT
ejpam-5916	106	15	tx	tx	PROPN
ejpam-5916	106	16	is	be	AUX
ejpam-5916	106	17	closed	closed	ADJ
ejpam-5916	106	18	,	,	PUNCT
ejpam-5916	106	19	(	(	PUNCT
ejpam-5916	106	20	iii	iii	NOUN
ejpam-5916	106	21	)	)	PUNCT
ejpam-5916	106	22	(	(	PUNCT
ejpam-5916	106	23	s	s	PROPN
ejpam-5916	106	24	,	,	PUNCT
ejpam-5916	106	25	t	t	PROPN
ejpam-5916	106	26	)	)	PUNCT
ejpam-5916	106	27	is	be	AUX
ejpam-5916	106	28	a	a	DET
ejpam-5916	106	29	weakly	weakly	ADV
ejpam-5916	106	30	compatible	compatible	ADJ
ejpam-5916	106	31	pair	pair	NOUN
ejpam-5916	106	32	.	.	PUNCT
ejpam-5916	107	1	then	then	ADV
ejpam-5916	107	2	s	s	VERB
ejpam-5916	107	3	and	and	CCONJ
ejpam-5916	107	4	t	t	PROPN
ejpam-5916	107	5	have	have	VERB
ejpam-5916	107	6	a	a	DET
ejpam-5916	107	7	unique	unique	ADJ
ejpam-5916	107	8	common	common	ADJ
ejpam-5916	107	9	fixed	fix	VERB
ejpam-5916	107	10	point	point	NOUN
ejpam-5916	107	11	z	z	PROPN
ejpam-5916	107	12	∈	∈	PROPN
ejpam-5916	107	13	x	x	SYM
ejpam-5916	107	14	,	,	PUNCT
ejpam-5916	107	15	i.e.	i.e.	X
ejpam-5916	107	16	,	,	PUNCT
ejpam-5916	107	17	z	z	NOUN
ejpam-5916	107	18	=	=	SYM
ejpam-5916	107	19	sz	sz	PROPN
ejpam-5916	107	20	=	=	SYM
ejpam-5916	107	21	tz	tz	PROPN
ejpam-5916	107	22	.	.	PUNCT
ejpam-5916	107	23	proof	proof	NOUN
ejpam-5916	107	24	.	.	PUNCT
ejpam-5916	108	1	let	let	VERB
ejpam-5916	108	2	x0	x0	PROPN
ejpam-5916	108	3	∈	∈	PROPN
ejpam-5916	108	4	x	x	PUNCT
ejpam-5916	108	5	be	be	AUX
ejpam-5916	108	6	arbitrary	arbitrary	ADJ
ejpam-5916	108	7	.	.	PUNCT
ejpam-5916	109	1	since	since	SCONJ
ejpam-5916	109	2	sx	sx	PROPN
ejpam-5916	109	3	⊆	⊆	NUM
ejpam-5916	109	4	tx	tx	PROPN
ejpam-5916	109	5	,	,	PUNCT
ejpam-5916	109	6	we	we	PRON
ejpam-5916	109	7	can	can	AUX
ejpam-5916	109	8	choose	choose	VERB
ejpam-5916	109	9	x1	x1	PROPN
ejpam-5916	109	10	∈	∈	PROPN
ejpam-5916	109	11	x	x	PUNCT
ejpam-5916	109	12	such	such	ADJ
ejpam-5916	109	13	that	that	DET
ejpam-5916	109	14	sx0	sx0	NOUN
ejpam-5916	109	15	=	=	SYM
ejpam-5916	109	16	tx1	tx1	PROPN
ejpam-5916	109	17	.	.	PUNCT
ejpam-5916	110	1	continuing	continue	VERB
ejpam-5916	110	2	this	this	DET
ejpam-5916	110	3	process	process	NOUN
ejpam-5916	110	4	inductively	inductively	ADV
ejpam-5916	110	5	,	,	PUNCT
ejpam-5916	110	6	we	we	PRON
ejpam-5916	110	7	construct	construct	VERB
ejpam-5916	110	8	a	a	DET
ejpam-5916	110	9	sequence	sequence	NOUN
ejpam-5916	110	10	{	{	PUNCT
ejpam-5916	110	11	yn	yn	NOUN
ejpam-5916	110	12	}	}	PUNCT
ejpam-5916	110	13	in	in	ADP
ejpam-5916	110	14	x	x	SYM
ejpam-5916	110	15	where	where	SCONJ
ejpam-5916	110	16	{	{	PUNCT
ejpam-5916	110	17	y2n+1	y2n+1	PROPN
ejpam-5916	110	18	=	=	NOUN
ejpam-5916	110	19	sx2n	sx2n	PROPN
ejpam-5916	110	20	,	,	PUNCT
ejpam-5916	110	21	y2n+2	y2n+2	NOUN
ejpam-5916	110	22	=	=	SYM
ejpam-5916	110	23	tx2n+1	tx2n+1	PROPN
ejpam-5916	110	24	.	.	PUNCT
ejpam-5916	111	1	(	(	PUNCT
ejpam-5916	111	2	3.1	3.1	NUM
ejpam-5916	111	3	)	)	PUNCT
ejpam-5916	111	4	thus	thus	ADV
ejpam-5916	111	5	,	,	PUNCT
ejpam-5916	111	6	the	the	DET
ejpam-5916	111	7	sequence	sequence	NOUN
ejpam-5916	111	8	{	{	PUNCT
ejpam-5916	111	9	yn	yn	NOUN
ejpam-5916	111	10	}	}	PUNCT
ejpam-5916	111	11	alternates	alternate	NOUN
ejpam-5916	111	12	between	between	ADP
ejpam-5916	111	13	images	image	NOUN
ejpam-5916	111	14	under	under	ADP
ejpam-5916	111	15	s	s	PRON
ejpam-5916	111	16	and	and	CCONJ
ejpam-5916	111	17	t	t	PROPN
ejpam-5916	111	18	,	,	PUNCT
ejpam-5916	111	19	linked	link	VERB
ejpam-5916	111	20	by	by	ADP
ejpam-5916	111	21	the	the	DET
ejpam-5916	111	22	condition	condition	NOUN
ejpam-5916	111	23	sx2n	sx2n	PROPN
ejpam-5916	111	24	=	=	SYM
ejpam-5916	111	25	tx2n+1	tx2n+1	NOUN
ejpam-5916	111	26	.	.	PUNCT
ejpam-5916	112	1	we	we	PRON
ejpam-5916	112	2	analyze	analyze	VERB
ejpam-5916	112	3	convergence	convergence	NOUN
ejpam-5916	112	4	in	in	ADP
ejpam-5916	112	5	two	two	NUM
ejpam-5916	112	6	cases	case	NOUN
ejpam-5916	112	7	:	:	PUNCT
ejpam-5916	112	8	h.	h.	PROPN
ejpam-5916	112	9	qawaqneh	qawaqneh	PROPN
ejpam-5916	112	10	/	/	SYM
ejpam-5916	112	11	eur	eur	PROPN
ejpam-5916	112	12	.	.	PUNCT
ejpam-5916	113	1	j.	j.	PROPN
ejpam-5916	113	2	pure	pure	PROPN
ejpam-5916	113	3	appl	appl	PROPN
ejpam-5916	113	4	.	.	PROPN
ejpam-5916	113	5	math	math	PROPN
ejpam-5916	113	6	,	,	PUNCT
ejpam-5916	113	7	18	18	NUM
ejpam-5916	113	8	(	(	PUNCT
ejpam-5916	113	9	3	3	NUM
ejpam-5916	113	10	)	)	PUNCT
ejpam-5916	113	11	(	(	PUNCT
ejpam-5916	113	12	2025	2025	NUM
ejpam-5916	113	13	)	)	PUNCT
ejpam-5916	113	14	,	,	PUNCT
ejpam-5916	113	15	5916	5916	NUM
ejpam-5916	113	16	6	6	NUM
ejpam-5916	113	17	of	of	ADP
ejpam-5916	113	18	19	19	NUM
ejpam-5916	113	19	case(1	case(1	NOUN
ejpam-5916	113	20	)	)	PUNCT
ejpam-5916	113	21	:	:	PUNCT
ejpam-5916	113	22	there	there	PRON
ejpam-5916	113	23	exists	exist	VERB
ejpam-5916	113	24	n	n	PRON
ejpam-5916	113	25	∈	∈	PROPN
ejpam-5916	113	26	n	n	PRON
ejpam-5916	113	27	such	such	ADJ
ejpam-5916	113	28	that	that	SCONJ
ejpam-5916	113	29	q(yn	q(yn	PROPN
ejpam-5916	113	30	,	,	PUNCT
ejpam-5916	113	31	yn+1	yn+1	X
ejpam-5916	113	32	)	)	PUNCT
ejpam-5916	113	33	=	=	SYM
ejpam-5916	113	34	0	0	X
ejpam-5916	113	35	.	.	PUNCT
ejpam-5916	114	1	then	then	ADV
ejpam-5916	114	2	yn	yn	PROPN
ejpam-5916	114	3	=	=	SYM
ejpam-5916	114	4	yn+1	yn+1	PROPN
ejpam-5916	114	5	,	,	PUNCT
ejpam-5916	114	6	and	and	CCONJ
ejpam-5916	114	7	since	since	SCONJ
ejpam-5916	114	8	yn+1	yn+1	PROPN
ejpam-5916	114	9	=	=	PROPN
ejpam-5916	114	10	sx	sx	PROPN
ejpam-5916	114	11	and	and	CCONJ
ejpam-5916	114	12	yn+2	yn+2	NUM
ejpam-5916	114	13	=	=	SYM
ejpam-5916	114	14	tx	tx	VERB
ejpam-5916	114	15	for	for	ADP
ejpam-5916	114	16	some	some	DET
ejpam-5916	114	17	x	x	SYM
ejpam-5916	114	18	∈	∈	PROPN
ejpam-5916	114	19	x	x	X
ejpam-5916	114	20	,	,	PUNCT
ejpam-5916	114	21	we	we	PRON
ejpam-5916	114	22	obtain	obtain	VERB
ejpam-5916	114	23	:	:	PUNCT
ejpam-5916	114	24	sx	sx	PROPN
ejpam-5916	114	25	=	=	PUNCT
ejpam-5916	114	26	tx	tx	PROPN
ejpam-5916	114	27	.	.	PUNCT
ejpam-5916	115	1	if	if	SCONJ
ejpam-5916	115	2	s	s	PRON
ejpam-5916	115	3	and	and	CCONJ
ejpam-5916	115	4	t	t	PROPN
ejpam-5916	115	5	are	be	AUX
ejpam-5916	115	6	weakly	weakly	ADV
ejpam-5916	115	7	compatible	compatible	ADJ
ejpam-5916	115	8	,	,	PUNCT
ejpam-5916	115	9	then	then	ADV
ejpam-5916	115	10	the	the	DET
ejpam-5916	115	11	common	common	ADJ
ejpam-5916	115	12	fixed	fix	VERB
ejpam-5916	115	13	point	point	NOUN
ejpam-5916	115	14	condition	condition	NOUN
ejpam-5916	115	15	sx	sx	PROPN
ejpam-5916	115	16	=	=	PUNCT
ejpam-5916	115	17	tx	tx	PROPN
ejpam-5916	115	18	=	=	PUNCT
ejpam-5916	115	19	x	x	PRON
ejpam-5916	115	20	follows	follow	VERB
ejpam-5916	115	21	.	.	PUNCT
ejpam-5916	116	1	case(2	case(2	NOUN
ejpam-5916	116	2	)	)	PUNCT
ejpam-5916	116	3	:	:	PUNCT
ejpam-5916	116	4	suppose	suppose	VERB
ejpam-5916	116	5	q(yn	q(yn	NOUN
ejpam-5916	116	6	,	,	PUNCT
ejpam-5916	116	7	yn+1	yn+1	X
ejpam-5916	116	8	)	)	PUNCT
ejpam-5916	116	9	>	>	X
ejpam-5916	116	10	0	0	PUNCT
ejpam-5916	117	1	for	for	ADP
ejpam-5916	117	2	all	all	DET
ejpam-5916	117	3	n.	n.	NOUN
ejpam-5916	117	4	using	use	VERB
ejpam-5916	117	5	the	the	DET
ejpam-5916	117	6	contractive	contractive	ADJ
ejpam-5916	117	7	condition	condition	NOUN
ejpam-5916	117	8	given	give	VERB
ejpam-5916	117	9	in	in	ADP
ejpam-5916	117	10	the	the	DET
ejpam-5916	117	11	theorem	theorem	NOUN
ejpam-5916	117	12	:	:	PUNCT
ejpam-5916	117	13	ψ(q(sx	ψ(q(sx	NOUN
ejpam-5916	117	14	,	,	PUNCT
ejpam-5916	117	15	ty	ty	NOUN
ejpam-5916	117	16	)	)	PUNCT
ejpam-5916	117	17	)	)	PUNCT
ejpam-5916	117	18	≤	≤	NUM
ejpam-5916	117	19	f	f	X
ejpam-5916	117	20	(	(	PUNCT
ejpam-5916	117	21	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	117	22	,	,	PUNCT
ejpam-5916	117	23	y	y	NOUN
ejpam-5916	117	24	)	)	PUNCT
ejpam-5916	117	25	)	)	PUNCT
ejpam-5916	117	26	,	,	PUNCT
ejpam-5916	117	27	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	117	28	,	,	PUNCT
ejpam-5916	117	29	y	y	NOUN
ejpam-5916	117	30	)	)	PUNCT
ejpam-5916	117	31	)	)	PUNCT
ejpam-5916	117	32	)	)	PUNCT
ejpam-5916	117	33	for	for	ADP
ejpam-5916	117	34	all	all	DET
ejpam-5916	117	35	x	x	NOUN
ejpam-5916	117	36	,	,	PUNCT
ejpam-5916	117	37	y	y	PROPN
ejpam-5916	117	38	∈	∈	PROPN
ejpam-5916	117	39	x	x	X
ejpam-5916	117	40	,	,	PUNCT
ejpam-5916	117	41	we	we	PRON
ejpam-5916	117	42	apply	apply	VERB
ejpam-5916	117	43	it	it	PRON
ejpam-5916	117	44	to	to	ADP
ejpam-5916	117	45	the	the	DET
ejpam-5916	117	46	sequence	sequence	NOUN
ejpam-5916	117	47	as	as	SCONJ
ejpam-5916	117	48	follows	follow	VERB
ejpam-5916	117	49	:	:	PUNCT
ejpam-5916	117	50	ψ(q(yn+1	ψ(q(yn+1	NUM
ejpam-5916	117	51	,	,	PUNCT
ejpam-5916	117	52	yn+2	yn+2	NUM
ejpam-5916	117	53	)	)	PUNCT
ejpam-5916	117	54	)	)	PUNCT
ejpam-5916	118	1	=	=	PUNCT
ejpam-5916	118	2	ψ(q(sxn	ψ(q(sxn	ADJ
ejpam-5916	118	3	,	,	PUNCT
ejpam-5916	118	4	txn+1	txn+1	NOUN
ejpam-5916	118	5	)	)	PUNCT
ejpam-5916	118	6	)	)	PUNCT
ejpam-5916	119	1	≤	≤	NUM
ejpam-5916	119	2	f	f	X
ejpam-5916	119	3	(	(	PUNCT
ejpam-5916	119	4	ψ(m(xn	ψ(m(xn	NOUN
ejpam-5916	119	5	,	,	PUNCT
ejpam-5916	119	6	xn+1	xn+1	NUM
ejpam-5916	119	7	)	)	PUNCT
ejpam-5916	119	8	)	)	PUNCT
ejpam-5916	119	9	,	,	PUNCT
ejpam-5916	119	10	ϕ(m(xn	ϕ(m(xn	X
ejpam-5916	119	11	,	,	PUNCT
ejpam-5916	119	12	xn+1	xn+1	NUM
ejpam-5916	119	13	)	)	PUNCT
ejpam-5916	119	14	)	)	PUNCT
ejpam-5916	119	15	)	)	PUNCT
ejpam-5916	119	16	.	.	PUNCT
ejpam-5916	120	1	define	define	NOUN
ejpam-5916	120	2	:	:	PUNCT
ejpam-5916	120	3	dn	dn	NOUN
ejpam-5916	120	4	:	:	PUNCT
ejpam-5916	120	5	=	=	SYM
ejpam-5916	120	6	q(yn	q(yn	NOUN
ejpam-5916	120	7	,	,	PUNCT
ejpam-5916	120	8	yn+1	yn+1	NUM
ejpam-5916	120	9	)	)	PUNCT
ejpam-5916	120	10	.	.	PUNCT
ejpam-5916	121	1	then	then	ADV
ejpam-5916	121	2	the	the	DET
ejpam-5916	121	3	above	above	ADJ
ejpam-5916	121	4	inequality	inequality	NOUN
ejpam-5916	121	5	implies	imply	VERB
ejpam-5916	121	6	:	:	PUNCT
ejpam-5916	121	7	ψ(dn+1	ψ(dn+1	X
ejpam-5916	121	8	)	)	PUNCT
ejpam-5916	121	9	≤	≤	NUM
ejpam-5916	122	1	f	f	X
ejpam-5916	122	2	(	(	PUNCT
ejpam-5916	122	3	ψ(m(xn	ψ(m(xn	NOUN
ejpam-5916	122	4	,	,	PUNCT
ejpam-5916	122	5	xn+1	xn+1	NUM
ejpam-5916	122	6	)	)	PUNCT
ejpam-5916	122	7	)	)	PUNCT
ejpam-5916	122	8	,	,	PUNCT
ejpam-5916	122	9	ϕ(m(xn	ϕ(m(xn	X
ejpam-5916	122	10	,	,	PUNCT
ejpam-5916	122	11	xn+1	xn+1	NUM
ejpam-5916	122	12	)	)	PUNCT
ejpam-5916	122	13	)	)	PUNCT
ejpam-5916	122	14	)	)	PUNCT
ejpam-5916	122	15	≤	≤	NUM
ejpam-5916	122	16	ψ(dn	ψ(dn	NOUN
ejpam-5916	122	17	)	)	PUNCT
ejpam-5916	122	18	,	,	PUNCT
ejpam-5916	122	19	which	which	PRON
ejpam-5916	122	20	shows	show	VERB
ejpam-5916	122	21	that	that	SCONJ
ejpam-5916	122	22	{	{	PUNCT
ejpam-5916	122	23	ψ(dn	ψ(dn	NOUN
ejpam-5916	122	24	)	)	PUNCT
ejpam-5916	122	25	}	}	PUNCT
ejpam-5916	122	26	is	be	AUX
ejpam-5916	122	27	a	a	DET
ejpam-5916	122	28	non	non	ADJ
ejpam-5916	122	29	-	-	ADJ
ejpam-5916	122	30	increasing	increase	VERB
ejpam-5916	122	31	sequence	sequence	NOUN
ejpam-5916	122	32	bounded	bound	VERB
ejpam-5916	122	33	below	below	ADP
ejpam-5916	122	34	by	by	ADP
ejpam-5916	122	35	0	0	NUM
ejpam-5916	122	36	.	.	PUNCT
ejpam-5916	123	1	hence	hence	ADV
ejpam-5916	123	2	,	,	PUNCT
ejpam-5916	123	3	it	it	PRON
ejpam-5916	123	4	converges	converge	VERB
ejpam-5916	123	5	.	.	PUNCT
ejpam-5916	124	1	by	by	ADP
ejpam-5916	124	2	the	the	DET
ejpam-5916	124	3	properties	property	NOUN
ejpam-5916	124	4	of	of	ADP
ejpam-5916	124	5	ψ	ψ	NOUN
ejpam-5916	124	6	and	and	CCONJ
ejpam-5916	124	7	f	f	PROPN
ejpam-5916	124	8	,	,	PUNCT
ejpam-5916	124	9	and	and	CCONJ
ejpam-5916	124	10	the	the	DET
ejpam-5916	124	11	strict	strict	ADJ
ejpam-5916	124	12	inequality	inequality	NOUN
ejpam-5916	124	13	imposed	impose	VERB
ejpam-5916	124	14	by	by	ADP
ejpam-5916	124	15	the	the	DET
ejpam-5916	124	16	contractive	contractive	ADJ
ejpam-5916	124	17	condition	condition	NOUN
ejpam-5916	124	18	,	,	PUNCT
ejpam-5916	124	19	it	it	PRON
ejpam-5916	124	20	follows	follow	VERB
ejpam-5916	124	21	that	that	SCONJ
ejpam-5916	124	22	limn→∞	limn→∞	PROPN
ejpam-5916	124	23	dn	dn	NOUN
ejpam-5916	124	24	=	=	SYM
ejpam-5916	124	25	0	0	NUM
ejpam-5916	124	26	,	,	PUNCT
ejpam-5916	124	27	and	and	CCONJ
ejpam-5916	124	28	thus	thus	ADV
ejpam-5916	124	29	,	,	PUNCT
ejpam-5916	124	30	lim	lim	PROPN
ejpam-5916	124	31	n→∞	n→∞	NUM
ejpam-5916	124	32	q(yn	q(yn	PROPN
ejpam-5916	124	33	,	,	PUNCT
ejpam-5916	124	34	yn+1	yn+1	X
ejpam-5916	124	35	)	)	PUNCT
ejpam-5916	124	36	=	=	SYM
ejpam-5916	125	1	0	0	X
ejpam-5916	125	2	.	.	PUNCT
ejpam-5916	126	1	we	we	PRON
ejpam-5916	126	2	now	now	ADV
ejpam-5916	126	3	show	show	VERB
ejpam-5916	126	4	that	that	SCONJ
ejpam-5916	126	5	{	{	PUNCT
ejpam-5916	126	6	yn	yn	PRON
ejpam-5916	126	7	}	}	PUNCT
ejpam-5916	126	8	is	be	AUX
ejpam-5916	126	9	a	a	DET
ejpam-5916	126	10	cauchy	cauchy	ADJ
ejpam-5916	126	11	sequence	sequence	NOUN
ejpam-5916	126	12	in	in	ADP
ejpam-5916	126	13	the	the	DET
ejpam-5916	126	14	b	b	NOUN
ejpam-5916	126	15	-	-	PUNCT
ejpam-5916	126	16	metric	metric	ADJ
ejpam-5916	126	17	space	space	NOUN
ejpam-5916	126	18	(	(	PUNCT
ejpam-5916	126	19	x	x	X
ejpam-5916	126	20	,	,	PUNCT
ejpam-5916	126	21	q	q	NOUN
ejpam-5916	126	22	)	)	PUNCT
ejpam-5916	126	23	.	.	PUNCT
ejpam-5916	127	1	for	for	ADP
ejpam-5916	127	2	any	any	DET
ejpam-5916	127	3	m	m	NOUN
ejpam-5916	127	4	>	>	X
ejpam-5916	127	5	n	n	CCONJ
ejpam-5916	127	6	,	,	PUNCT
ejpam-5916	127	7	we	we	PRON
ejpam-5916	127	8	estimate	estimate	VERB
ejpam-5916	127	9	using	use	VERB
ejpam-5916	127	10	the	the	DET
ejpam-5916	127	11	triangle	triangle	NOUN
ejpam-5916	127	12	inequality	inequality	NOUN
ejpam-5916	127	13	:	:	PUNCT
ejpam-5916	127	14	q(yn	q(yn	PROPN
ejpam-5916	127	15	,	,	PUNCT
ejpam-5916	127	16	ym	ym	PROPN
ejpam-5916	127	17	)	)	PUNCT
ejpam-5916	127	18	≤	≤	PROPN
ejpam-5916	127	19	s	s	PART
ejpam-5916	127	20	m−1∑	m−1∑	PROPN
ejpam-5916	127	21	k	k	NOUN
ejpam-5916	127	22	=	=	PROPN
ejpam-5916	127	23	n	n	PRON
ejpam-5916	127	24	q(yk	q(yk	NUM
ejpam-5916	127	25	,	,	PUNCT
ejpam-5916	127	26	yk+1	yk+1	NOUN
ejpam-5916	127	27	)	)	PUNCT
ejpam-5916	127	28	,	,	PUNCT
ejpam-5916	127	29	where	where	SCONJ
ejpam-5916	127	30	s	s	VERB
ejpam-5916	127	31	≥	≥	NOUN
ejpam-5916	127	32	1	1	NUM
ejpam-5916	127	33	is	be	AUX
ejpam-5916	127	34	the	the	DET
ejpam-5916	127	35	b	b	NOUN
ejpam-5916	127	36	-	-	PUNCT
ejpam-5916	127	37	metric	metric	ADJ
ejpam-5916	127	38	constant	constant	ADJ
ejpam-5916	127	39	.	.	PUNCT
ejpam-5916	128	1	since	since	SCONJ
ejpam-5916	128	2	the	the	DET
ejpam-5916	128	3	tail	tail	NOUN
ejpam-5916	128	4	of	of	ADP
ejpam-5916	128	5	the	the	DET
ejpam-5916	128	6	sum	sum	NOUN
ejpam-5916	128	7	tends	tend	VERB
ejpam-5916	128	8	to	to	ADP
ejpam-5916	128	9	0	0	NUM
ejpam-5916	128	10	as	as	ADP
ejpam-5916	128	11	n→	n→	ADV
ejpam-5916	128	12	∞	∞	PROPN
ejpam-5916	128	13	,	,	PUNCT
ejpam-5916	128	14	{	{	PUNCT
ejpam-5916	128	15	yn	yn	NOUN
ejpam-5916	128	16	}	}	PUNCT
ejpam-5916	128	17	is	be	AUX
ejpam-5916	128	18	cauchy	cauchy	PROPN
ejpam-5916	128	19	.	.	PUNCT
ejpam-5916	129	1	since	since	SCONJ
ejpam-5916	129	2	x	x	PRON
ejpam-5916	129	3	is	be	AUX
ejpam-5916	129	4	complete	complete	ADJ
ejpam-5916	129	5	,	,	PUNCT
ejpam-5916	129	6	there	there	PRON
ejpam-5916	129	7	exists	exist	VERB
ejpam-5916	129	8	y∗	y∗	PROPN
ejpam-5916	129	9	∈	∈	PROPN
ejpam-5916	129	10	x	x	PUNCT
ejpam-5916	129	11	such	such	ADJ
ejpam-5916	129	12	that	that	SCONJ
ejpam-5916	129	13	:	:	PUNCT
ejpam-5916	129	14	yn	yn	PROPN
ejpam-5916	129	15	→	→	SYM
ejpam-5916	129	16	y∗.	y∗.	NUM
ejpam-5916	129	17	let	let	VERB
ejpam-5916	129	18	us	we	PRON
ejpam-5916	129	19	show	show	VERB
ejpam-5916	129	20	that	that	SCONJ
ejpam-5916	129	21	y∗	y∗	PROPN
ejpam-5916	129	22	is	be	AUX
ejpam-5916	129	23	a	a	DET
ejpam-5916	129	24	common	common	ADJ
ejpam-5916	129	25	fixed	fix	VERB
ejpam-5916	129	26	point	point	NOUN
ejpam-5916	129	27	of	of	ADP
ejpam-5916	129	28	s	s	PRON
ejpam-5916	129	29	and	and	CCONJ
ejpam-5916	129	30	t	t	PROPN
ejpam-5916	129	31	.	.	PUNCT
ejpam-5916	130	1	since	since	SCONJ
ejpam-5916	130	2	y2n+1	y2n+1	PROPN
ejpam-5916	130	3	=	=	NOUN
ejpam-5916	130	4	sx2n	sx2n	PROPN
ejpam-5916	130	5	,	,	PUNCT
ejpam-5916	130	6	y2n+2	y2n+2	NOUN
ejpam-5916	130	7	=	=	SYM
ejpam-5916	130	8	tx2n+1	tx2n+1	PROPN
ejpam-5916	130	9	,	,	PUNCT
ejpam-5916	130	10	and	and	CCONJ
ejpam-5916	130	11	y2n+1	y2n+1	PROPN
ejpam-5916	130	12	=	=	SYM
ejpam-5916	130	13	y2n+2	y2n+2	PROPN
ejpam-5916	130	14	,	,	PUNCT
ejpam-5916	130	15	h.	h.	PROPN
ejpam-5916	130	16	qawaqneh	qawaqneh	PROPN
ejpam-5916	130	17	/	/	SYM
ejpam-5916	130	18	eur	eur	PROPN
ejpam-5916	130	19	.	.	PUNCT
ejpam-5916	131	1	j.	j.	PROPN
ejpam-5916	131	2	pure	pure	PROPN
ejpam-5916	131	3	appl	appl	PROPN
ejpam-5916	131	4	.	.	PROPN
ejpam-5916	131	5	math	math	PROPN
ejpam-5916	131	6	,	,	PUNCT
ejpam-5916	131	7	18	18	NUM
ejpam-5916	131	8	(	(	PUNCT
ejpam-5916	131	9	3	3	NUM
ejpam-5916	131	10	)	)	PUNCT
ejpam-5916	131	11	(	(	PUNCT
ejpam-5916	131	12	2025	2025	NUM
ejpam-5916	131	13	)	)	PUNCT
ejpam-5916	131	14	,	,	PUNCT
ejpam-5916	131	15	5916	5916	NUM
ejpam-5916	131	16	7	7	NUM
ejpam-5916	131	17	of	of	ADP
ejpam-5916	131	18	19	19	NUM
ejpam-5916	131	19	we	we	PRON
ejpam-5916	131	20	conclude	conclude	VERB
ejpam-5916	131	21	sx2n	sx2n	PROPN
ejpam-5916	131	22	=	=	SYM
ejpam-5916	131	23	tx2n+1	tx2n+1	PROPN
ejpam-5916	131	24	→	→	SYM
ejpam-5916	131	25	y∗.	y∗.	NUM
ejpam-5916	131	26	using	use	VERB
ejpam-5916	131	27	the	the	DET
ejpam-5916	131	28	continuity	continuity	NOUN
ejpam-5916	131	29	of	of	ADP
ejpam-5916	131	30	s	s	PRON
ejpam-5916	131	31	and	and	CCONJ
ejpam-5916	131	32	t	t	PROPN
ejpam-5916	131	33	,	,	PUNCT
ejpam-5916	131	34	we	we	PRON
ejpam-5916	131	35	obtain	obtain	VERB
ejpam-5916	131	36	:	:	PUNCT
ejpam-5916	131	37	sx2n	sx2n	PROPN
ejpam-5916	131	38	→	→	SYM
ejpam-5916	131	39	sy∗	sy∗	NOUN
ejpam-5916	131	40	,	,	PUNCT
ejpam-5916	131	41	tx2n+1	tx2n+1	NOUN
ejpam-5916	131	42	→	→	SYM
ejpam-5916	131	43	ty∗	ty∗	ADJ
ejpam-5916	131	44	,	,	PUNCT
ejpam-5916	131	45	so	so	ADV
ejpam-5916	131	46	sy∗	sy∗	NOUN
ejpam-5916	131	47	=	=	X
ejpam-5916	131	48	ty∗	ty∗	NOUN
ejpam-5916	131	49	=	=	SYM
ejpam-5916	131	50	y∗	y∗	PROPN
ejpam-5916	131	51	,	,	PUNCT
ejpam-5916	131	52	which	which	PRON
ejpam-5916	131	53	proves	prove	VERB
ejpam-5916	131	54	that	that	SCONJ
ejpam-5916	131	55	y∗	y∗	PROPN
ejpam-5916	131	56	is	be	AUX
ejpam-5916	131	57	a	a	DET
ejpam-5916	131	58	common	common	ADJ
ejpam-5916	131	59	fixed	fix	VERB
ejpam-5916	131	60	point	point	NOUN
ejpam-5916	131	61	of	of	ADP
ejpam-5916	131	62	s	s	PRON
ejpam-5916	131	63	and	and	CCONJ
ejpam-5916	131	64	t	t	PROPN
ejpam-5916	131	65	.	.	PUNCT
ejpam-5916	132	1	finally	finally	ADV
ejpam-5916	132	2	,	,	PUNCT
ejpam-5916	132	3	uniqueness	uniqueness	PROPN
ejpam-5916	132	4	follows	follow	VERB
ejpam-5916	132	5	from	from	ADP
ejpam-5916	132	6	the	the	DET
ejpam-5916	132	7	strict	strict	ADJ
ejpam-5916	132	8	contractive	contractive	ADJ
ejpam-5916	132	9	condition	condition	NOUN
ejpam-5916	132	10	:	:	PUNCT
ejpam-5916	132	11	if	if	SCONJ
ejpam-5916	132	12	z∗	z∗	PROPN
ejpam-5916	132	13	̸=	̸=	PROPN
ejpam-5916	132	14	y∗	y∗	ADV
ejpam-5916	132	15	were	be	AUX
ejpam-5916	132	16	another	another	DET
ejpam-5916	132	17	fixed	fix	VERB
ejpam-5916	132	18	point	point	NOUN
ejpam-5916	132	19	,	,	PUNCT
ejpam-5916	132	20	then	then	ADV
ejpam-5916	132	21	ψ(q(sz∗	ψ(q(sz∗	NOUN
ejpam-5916	132	22	,	,	PUNCT
ejpam-5916	132	23	ty∗	ty∗	ADJ
ejpam-5916	132	24	)	)	PUNCT
ejpam-5916	132	25	)	)	PUNCT
ejpam-5916	133	1	=	=	PUNCT
ejpam-5916	133	2	ψ(q(z∗	ψ(q(z∗	PROPN
ejpam-5916	133	3	,	,	PUNCT
ejpam-5916	133	4	y∗	y∗	PROPN
ejpam-5916	133	5	)	)	PUNCT
ejpam-5916	133	6	)	)	PUNCT
ejpam-5916	134	1	≤	≤	NUM
ejpam-5916	134	2	f	f	X
ejpam-5916	134	3	(	(	PUNCT
ejpam-5916	134	4	ψ(q(z∗	ψ(q(z∗	PROPN
ejpam-5916	134	5	,	,	PUNCT
ejpam-5916	134	6	y∗	y∗	PROPN
ejpam-5916	134	7	)	)	PUNCT
ejpam-5916	134	8	)	)	PUNCT
ejpam-5916	134	9	,	,	PUNCT
ejpam-5916	134	10	ϕ(q(z∗	ϕ(q(z∗	PROPN
ejpam-5916	134	11	,	,	PUNCT
ejpam-5916	134	12	y∗	y∗	PROPN
ejpam-5916	134	13	)	)	PUNCT
ejpam-5916	134	14	)	)	PUNCT
ejpam-5916	134	15	)	)	PUNCT
ejpam-5916	134	16	,	,	PUNCT
ejpam-5916	134	17	which	which	PRON
ejpam-5916	134	18	contradicts	contradict	VERB
ejpam-5916	134	19	the	the	DET
ejpam-5916	134	20	properties	property	NOUN
ejpam-5916	134	21	of	of	ADP
ejpam-5916	134	22	f	f	PROPN
ejpam-5916	134	23	,	,	PUNCT
ejpam-5916	134	24	ψ	ψ	ADP
ejpam-5916	134	25	,	,	PUNCT
ejpam-5916	134	26	and	and	CCONJ
ejpam-5916	134	27	ϕ	ϕ	NOUN
ejpam-5916	134	28	unless	unless	SCONJ
ejpam-5916	134	29	q(z∗	q(z∗	PROPN
ejpam-5916	134	30	,	,	PUNCT
ejpam-5916	134	31	y∗	y∗	PROPN
ejpam-5916	134	32	)	)	PUNCT
ejpam-5916	134	33	=	=	SYM
ejpam-5916	134	34	0	0	NUM
ejpam-5916	134	35	,	,	PUNCT
ejpam-5916	134	36	i.e.	i.e.	X
ejpam-5916	134	37	,	,	PUNCT
ejpam-5916	134	38	z∗	z∗	PROPN
ejpam-5916	134	39	=	=	SYM
ejpam-5916	134	40	y∗.	y∗.	NUM
ejpam-5916	134	41	corollary	corollary	ADJ
ejpam-5916	134	42	1	1	NUM
ejpam-5916	134	43	.	.	PUNCT
ejpam-5916	135	1	let	let	VERB
ejpam-5916	135	2	(	(	PUNCT
ejpam-5916	135	3	x	x	NOUN
ejpam-5916	135	4	,	,	PUNCT
ejpam-5916	135	5	q	q	X
ejpam-5916	135	6	)	)	PUNCT
ejpam-5916	135	7	be	be	AUX
ejpam-5916	135	8	a	a	DET
ejpam-5916	135	9	complete	complete	ADJ
ejpam-5916	135	10	quasi	quasi	ADJ
ejpam-5916	135	11	-	-	ADJ
ejpam-5916	135	12	partial	partial	ADJ
ejpam-5916	135	13	metric	metric	ADJ
ejpam-5916	135	14	space	space	NOUN
ejpam-5916	135	15	,	,	PUNCT
ejpam-5916	135	16	and	and	CCONJ
ejpam-5916	135	17	let	let	VERB
ejpam-5916	135	18	s	s	PRON
ejpam-5916	135	19	and	and	CCONJ
ejpam-5916	135	20	t	t	PROPN
ejpam-5916	135	21	be	be	AUX
ejpam-5916	135	22	self	self	NOUN
ejpam-5916	135	23	-	-	PUNCT
ejpam-5916	135	24	mappings	mapping	NOUN
ejpam-5916	135	25	on	on	ADP
ejpam-5916	135	26	x.	x.	NOUN
ejpam-5916	135	27	suppose	suppose	VERB
ejpam-5916	135	28	for	for	ADP
ejpam-5916	135	29	all	all	DET
ejpam-5916	135	30	x	x	NOUN
ejpam-5916	135	31	,	,	PUNCT
ejpam-5916	135	32	y	y	PROPN
ejpam-5916	135	33	∈	∈	PROPN
ejpam-5916	135	34	x	x	SYM
ejpam-5916	135	35	,	,	PUNCT
ejpam-5916	135	36	ψ(q(sx	ψ(q(sx	ADP
ejpam-5916	135	37	,	,	PUNCT
ejpam-5916	135	38	ty	ty	NOUN
ejpam-5916	135	39	)	)	PUNCT
ejpam-5916	135	40	)	)	PUNCT
ejpam-5916	135	41	≤	≤	PROPN
ejpam-5916	136	1	ψ(q(m(x	ψ(q(m(x	PROPN
ejpam-5916	136	2	,	,	PUNCT
ejpam-5916	136	3	y)))−	y)))−	ADP
ejpam-5916	136	4	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	136	5	,	,	PUNCT
ejpam-5916	136	6	y	y	NOUN
ejpam-5916	136	7	)	)	PUNCT
ejpam-5916	136	8	)	)	PUNCT
ejpam-5916	136	9	,	,	PUNCT
ejpam-5916	136	10	where	where	SCONJ
ejpam-5916	136	11	m(x	m(x	PROPN
ejpam-5916	136	12	,	,	PUNCT
ejpam-5916	136	13	y	y	NOUN
ejpam-5916	136	14	)	)	PUNCT
ejpam-5916	136	15	=	=	SYM
ejpam-5916	136	16	max	max	NOUN
ejpam-5916	136	17	{	{	PUNCT
ejpam-5916	136	18	q(sx	q(sx	PROPN
ejpam-5916	136	19	,	,	PUNCT
ejpam-5916	136	20	ty	ty	NOUN
ejpam-5916	136	21	)	)	PUNCT
ejpam-5916	136	22	,	,	PUNCT
ejpam-5916	136	23	q(sx	q(sx	PROPN
ejpam-5916	136	24	,	,	PUNCT
ejpam-5916	136	25	sx	sx	PROPN
ejpam-5916	136	26	)	)	PUNCT
ejpam-5916	136	27	,	,	PUNCT
ejpam-5916	136	28	q(ty	q(ty	PROPN
ejpam-5916	136	29	,	,	PUNCT
ejpam-5916	136	30	ty	ty	NOUN
ejpam-5916	136	31	)	)	PUNCT
ejpam-5916	136	32	,	,	PUNCT
ejpam-5916	136	33	1	1	NUM
ejpam-5916	136	34	2	2	NUM
ejpam-5916	136	35	(	(	PUNCT
ejpam-5916	136	36	q(sx	q(sx	PROPN
ejpam-5916	136	37	,	,	PUNCT
ejpam-5916	136	38	ty	ty	INTJ
ejpam-5916	136	39	)	)	PUNCT
ejpam-5916	136	40	+	+	X
ejpam-5916	136	41	q(ty	q(ty	PROPN
ejpam-5916	136	42	,	,	PUNCT
ejpam-5916	136	43	sx	sx	PROPN
ejpam-5916	136	44	)	)	PUNCT
ejpam-5916	136	45	)	)	PUNCT
ejpam-5916	136	46	}	}	PUNCT
ejpam-5916	136	47	.	.	PUNCT
ejpam-5916	137	1	additionally	additionally	ADV
ejpam-5916	137	2	,	,	PUNCT
ejpam-5916	137	3	assume	assume	VERB
ejpam-5916	137	4	:	:	PUNCT
ejpam-5916	137	5	(	(	PUNCT
ejpam-5916	137	6	i	i	NOUN
ejpam-5916	137	7	)	)	PUNCT
ejpam-5916	137	8	sx	sx	PROPN
ejpam-5916	137	9	⊆	⊆	NUM
ejpam-5916	137	10	tx	tx	PROPN
ejpam-5916	137	11	,	,	PUNCT
ejpam-5916	137	12	(	(	PUNCT
ejpam-5916	137	13	ii	ii	NOUN
ejpam-5916	137	14	)	)	PUNCT
ejpam-5916	137	15	tx	tx	PROPN
ejpam-5916	137	16	is	be	AUX
ejpam-5916	137	17	closed	closed	ADJ
ejpam-5916	137	18	,	,	PUNCT
ejpam-5916	137	19	(	(	PUNCT
ejpam-5916	137	20	iii	iii	NOUN
ejpam-5916	137	21	)	)	PUNCT
ejpam-5916	137	22	(	(	PUNCT
ejpam-5916	137	23	s	s	PROPN
ejpam-5916	137	24	,	,	PUNCT
ejpam-5916	137	25	t	t	PROPN
ejpam-5916	137	26	)	)	PUNCT
ejpam-5916	137	27	is	be	AUX
ejpam-5916	137	28	a	a	DET
ejpam-5916	137	29	weakly	weakly	ADV
ejpam-5916	137	30	compatible	compatible	ADJ
ejpam-5916	137	31	pair	pair	NOUN
ejpam-5916	137	32	.	.	PUNCT
ejpam-5916	138	1	then	then	ADV
ejpam-5916	138	2	s	s	VERB
ejpam-5916	138	3	and	and	CCONJ
ejpam-5916	138	4	t	t	PROPN
ejpam-5916	138	5	have	have	VERB
ejpam-5916	138	6	a	a	DET
ejpam-5916	138	7	unique	unique	ADJ
ejpam-5916	138	8	common	common	ADJ
ejpam-5916	138	9	fixed	fix	VERB
ejpam-5916	138	10	point	point	NOUN
ejpam-5916	138	11	in	in	ADP
ejpam-5916	138	12	x	x	PRON
ejpam-5916	138	13	,	,	PUNCT
ejpam-5916	138	14	i.e.	i.e.	X
ejpam-5916	138	15	,	,	PUNCT
ejpam-5916	138	16	there	there	PRON
ejpam-5916	138	17	exists	exist	VERB
ejpam-5916	138	18	z	z	NOUN
ejpam-5916	138	19	∈	∈	PROPN
ejpam-5916	138	20	x	x	PUNCT
ejpam-5916	139	1	such	such	ADJ
ejpam-5916	139	2	that	that	SCONJ
ejpam-5916	139	3	z	z	NOUN
ejpam-5916	139	4	=	=	PUNCT
ejpam-5916	139	5	sz	sz	PROPN
ejpam-5916	139	6	=	=	SYM
ejpam-5916	139	7	tz	tz	PROPN
ejpam-5916	139	8	.	.	PUNCT
ejpam-5916	139	9	proof	proof	NOUN
ejpam-5916	139	10	.	.	PUNCT
ejpam-5916	140	1	this	this	DET
ejpam-5916	140	2	result	result	NOUN
ejpam-5916	140	3	follows	follow	VERB
ejpam-5916	140	4	as	as	ADP
ejpam-5916	140	5	a	a	DET
ejpam-5916	140	6	special	special	ADJ
ejpam-5916	140	7	case	case	NOUN
ejpam-5916	140	8	of	of	ADP
ejpam-5916	140	9	theorem	theorem	NOUN
ejpam-5916	140	10	1	1	NUM
ejpam-5916	140	11	by	by	ADP
ejpam-5916	140	12	choosing	choose	VERB
ejpam-5916	140	13	the	the	DET
ejpam-5916	140	14	contractive	contractive	ADJ
ejpam-5916	140	15	function	function	NOUN
ejpam-5916	140	16	f	f	PROPN
ejpam-5916	140	17	(	(	PUNCT
ejpam-5916	140	18	s	s	PROPN
ejpam-5916	140	19	,	,	PUNCT
ejpam-5916	140	20	t	t	PROPN
ejpam-5916	140	21	)	)	PUNCT
ejpam-5916	140	22	=	=	SYM
ejpam-5916	140	23	s−	s−	PROPN
ejpam-5916	140	24	t.	t.	NOUN
ejpam-5916	140	25	the	the	DET
ejpam-5916	140	26	proof	proof	NOUN
ejpam-5916	140	27	proceeds	proceed	VERB
ejpam-5916	140	28	in	in	ADP
ejpam-5916	140	29	the	the	DET
ejpam-5916	140	30	same	same	ADJ
ejpam-5916	140	31	manner	manner	NOUN
ejpam-5916	140	32	as	as	ADP
ejpam-5916	140	33	the	the	DET
ejpam-5916	140	34	theorem	theorem	PROPN
ejpam-5916	140	35	.	.	PROPN
ejpam-5916	140	36	corollary	corollary	ADJ
ejpam-5916	140	37	2	2	NUM
ejpam-5916	140	38	.	.	PUNCT
ejpam-5916	141	1	let	let	VERB
ejpam-5916	141	2	(	(	PUNCT
ejpam-5916	141	3	x	x	NOUN
ejpam-5916	141	4	,	,	PUNCT
ejpam-5916	141	5	q	q	X
ejpam-5916	141	6	)	)	PUNCT
ejpam-5916	141	7	be	be	AUX
ejpam-5916	141	8	a	a	DET
ejpam-5916	141	9	complete	complete	ADJ
ejpam-5916	141	10	quasi	quasi	ADJ
ejpam-5916	141	11	-	-	ADJ
ejpam-5916	141	12	partial	partial	ADJ
ejpam-5916	141	13	metric	metric	ADJ
ejpam-5916	141	14	space	space	NOUN
ejpam-5916	141	15	,	,	PUNCT
ejpam-5916	141	16	and	and	CCONJ
ejpam-5916	141	17	let	let	VERB
ejpam-5916	141	18	s	s	PRON
ejpam-5916	141	19	and	and	CCONJ
ejpam-5916	141	20	t	t	PROPN
ejpam-5916	141	21	be	be	AUX
ejpam-5916	141	22	self	self	NOUN
ejpam-5916	141	23	-	-	PUNCT
ejpam-5916	141	24	mappings	mapping	NOUN
ejpam-5916	141	25	on	on	ADP
ejpam-5916	141	26	x.	x.	NOUN
ejpam-5916	141	27	suppose	suppose	VERB
ejpam-5916	141	28	for	for	ADP
ejpam-5916	141	29	all	all	DET
ejpam-5916	141	30	x	x	NOUN
ejpam-5916	141	31	,	,	PUNCT
ejpam-5916	141	32	y	y	PROPN
ejpam-5916	141	33	∈	∈	PROPN
ejpam-5916	141	34	x	x	PROPN
ejpam-5916	141	35	,	,	PUNCT
ejpam-5916	141	36	q(sx	q(sx	PROPN
ejpam-5916	141	37	,	,	PUNCT
ejpam-5916	141	38	ty	ty	INTJ
ejpam-5916	141	39	)	)	PUNCT
ejpam-5916	141	40	≤	≤	NOUN
ejpam-5916	141	41	kq(m(x	kq(m(x	PROPN
ejpam-5916	141	42	,	,	PUNCT
ejpam-5916	141	43	y	y	NOUN
ejpam-5916	141	44	)	)	PUNCT
ejpam-5916	141	45	)	)	PUNCT
ejpam-5916	141	46	,	,	PUNCT
ejpam-5916	141	47	where	where	SCONJ
ejpam-5916	141	48	0	0	NUM
ejpam-5916	141	49	≤	≤	X
ejpam-5916	141	50	k	k	X
ejpam-5916	141	51	<	<	X
ejpam-5916	141	52	1	1	NUM
ejpam-5916	141	53	and	and	CCONJ
ejpam-5916	141	54	m(x	m(x	PROPN
ejpam-5916	141	55	,	,	PUNCT
ejpam-5916	141	56	y	y	NOUN
ejpam-5916	141	57	)	)	PUNCT
ejpam-5916	141	58	=	=	SYM
ejpam-5916	141	59	max	max	NOUN
ejpam-5916	141	60	{	{	PUNCT
ejpam-5916	141	61	q(sx	q(sx	PROPN
ejpam-5916	141	62	,	,	PUNCT
ejpam-5916	141	63	ty	ty	NOUN
ejpam-5916	141	64	)	)	PUNCT
ejpam-5916	141	65	,	,	PUNCT
ejpam-5916	141	66	q(sx	q(sx	PROPN
ejpam-5916	141	67	,	,	PUNCT
ejpam-5916	141	68	sx	sx	PROPN
ejpam-5916	141	69	)	)	PUNCT
ejpam-5916	141	70	,	,	PUNCT
ejpam-5916	141	71	q(ty	q(ty	PROPN
ejpam-5916	141	72	,	,	PUNCT
ejpam-5916	141	73	ty	ty	NOUN
ejpam-5916	141	74	)	)	PUNCT
ejpam-5916	141	75	,	,	PUNCT
ejpam-5916	141	76	1	1	NUM
ejpam-5916	141	77	2	2	NUM
ejpam-5916	141	78	(	(	PUNCT
ejpam-5916	141	79	q(sx	q(sx	PROPN
ejpam-5916	141	80	,	,	PUNCT
ejpam-5916	141	81	ty	ty	INTJ
ejpam-5916	141	82	)	)	PUNCT
ejpam-5916	141	83	+	+	X
ejpam-5916	141	84	q(ty	q(ty	PROPN
ejpam-5916	141	85	,	,	PUNCT
ejpam-5916	141	86	sx	sx	PROPN
ejpam-5916	141	87	)	)	PUNCT
ejpam-5916	141	88	)	)	PUNCT
ejpam-5916	141	89	}	}	PUNCT
ejpam-5916	141	90	.	.	PUNCT
ejpam-5916	142	1	additionally	additionally	ADV
ejpam-5916	142	2	,	,	PUNCT
ejpam-5916	142	3	assume	assume	VERB
ejpam-5916	142	4	:	:	PUNCT
ejpam-5916	142	5	(	(	PUNCT
ejpam-5916	142	6	i	i	NOUN
ejpam-5916	142	7	)	)	PUNCT
ejpam-5916	142	8	sx	sx	PROPN
ejpam-5916	142	9	⊆	⊆	NUM
ejpam-5916	142	10	tx	tx	PROPN
ejpam-5916	142	11	,	,	PUNCT
ejpam-5916	142	12	h.	h.	PROPN
ejpam-5916	142	13	qawaqneh	qawaqneh	PROPN
ejpam-5916	142	14	/	/	SYM
ejpam-5916	142	15	eur	eur	PROPN
ejpam-5916	142	16	.	.	PUNCT
ejpam-5916	143	1	j.	j.	PROPN
ejpam-5916	143	2	pure	pure	PROPN
ejpam-5916	143	3	appl	appl	PROPN
ejpam-5916	143	4	.	.	PROPN
ejpam-5916	143	5	math	math	PROPN
ejpam-5916	143	6	,	,	PUNCT
ejpam-5916	143	7	18	18	NUM
ejpam-5916	143	8	(	(	PUNCT
ejpam-5916	143	9	3	3	NUM
ejpam-5916	143	10	)	)	PUNCT
ejpam-5916	143	11	(	(	PUNCT
ejpam-5916	143	12	2025	2025	NUM
ejpam-5916	143	13	)	)	PUNCT
ejpam-5916	143	14	,	,	PUNCT
ejpam-5916	143	15	5916	5916	NUM
ejpam-5916	143	16	8	8	NUM
ejpam-5916	143	17	of	of	ADP
ejpam-5916	143	18	19	19	NUM
ejpam-5916	143	19	(	(	PUNCT
ejpam-5916	143	20	ii	ii	NOUN
ejpam-5916	143	21	)	)	PUNCT
ejpam-5916	143	22	tx	tx	PROPN
ejpam-5916	143	23	is	be	AUX
ejpam-5916	143	24	closed	closed	ADJ
ejpam-5916	143	25	,	,	PUNCT
ejpam-5916	143	26	(	(	PUNCT
ejpam-5916	143	27	iii	iii	NOUN
ejpam-5916	143	28	)	)	PUNCT
ejpam-5916	143	29	(	(	PUNCT
ejpam-5916	143	30	s	s	PROPN
ejpam-5916	143	31	,	,	PUNCT
ejpam-5916	143	32	t	t	PROPN
ejpam-5916	143	33	)	)	PUNCT
ejpam-5916	143	34	is	be	AUX
ejpam-5916	143	35	a	a	DET
ejpam-5916	143	36	weakly	weakly	ADV
ejpam-5916	143	37	compatible	compatible	ADJ
ejpam-5916	143	38	pair	pair	NOUN
ejpam-5916	143	39	.	.	PUNCT
ejpam-5916	144	1	then	then	ADV
ejpam-5916	144	2	s	s	VERB
ejpam-5916	144	3	and	and	CCONJ
ejpam-5916	144	4	t	t	PROPN
ejpam-5916	144	5	have	have	VERB
ejpam-5916	144	6	a	a	DET
ejpam-5916	144	7	unique	unique	ADJ
ejpam-5916	144	8	common	common	ADJ
ejpam-5916	144	9	fixed	fix	VERB
ejpam-5916	144	10	point	point	NOUN
ejpam-5916	144	11	in	in	ADP
ejpam-5916	144	12	x	x	PRON
ejpam-5916	144	13	,	,	PUNCT
ejpam-5916	144	14	i.e.	i.e.	X
ejpam-5916	144	15	,	,	PUNCT
ejpam-5916	144	16	there	there	PRON
ejpam-5916	144	17	exists	exist	VERB
ejpam-5916	144	18	z	z	NOUN
ejpam-5916	144	19	∈	∈	PROPN
ejpam-5916	144	20	x	x	PUNCT
ejpam-5916	145	1	such	such	ADJ
ejpam-5916	145	2	that	that	SCONJ
ejpam-5916	145	3	z	z	NOUN
ejpam-5916	145	4	=	=	PUNCT
ejpam-5916	145	5	sz	sz	PROPN
ejpam-5916	145	6	=	=	SYM
ejpam-5916	145	7	tz	tz	PROPN
ejpam-5916	145	8	.	.	PUNCT
ejpam-5916	145	9	proof	proof	NOUN
ejpam-5916	145	10	.	.	PUNCT
ejpam-5916	146	1	this	this	DET
ejpam-5916	146	2	result	result	NOUN
ejpam-5916	146	3	follows	follow	VERB
ejpam-5916	146	4	as	as	ADP
ejpam-5916	146	5	a	a	DET
ejpam-5916	146	6	special	special	ADJ
ejpam-5916	146	7	case	case	NOUN
ejpam-5916	146	8	of	of	ADP
ejpam-5916	146	9	theorem	theorem	NOUN
ejpam-5916	146	10	1	1	NUM
ejpam-5916	146	11	by	by	ADP
ejpam-5916	146	12	choosing	choose	VERB
ejpam-5916	146	13	the	the	DET
ejpam-5916	146	14	contractive	contractive	ADJ
ejpam-5916	146	15	function	function	NOUN
ejpam-5916	146	16	f	f	PROPN
ejpam-5916	146	17	(	(	PUNCT
ejpam-5916	146	18	s	s	PROPN
ejpam-5916	146	19	,	,	PUNCT
ejpam-5916	146	20	t	t	PROPN
ejpam-5916	146	21	)	)	PUNCT
ejpam-5916	147	1	=	=	SYM
ejpam-5916	147	2	ks	ks	NOUN
ejpam-5916	147	3	,	,	PUNCT
ejpam-5916	147	4	where	where	SCONJ
ejpam-5916	147	5	0	0	NUM
ejpam-5916	147	6	≤	≤	X
ejpam-5916	148	1	k	k	X
ejpam-5916	148	2	<	<	X
ejpam-5916	148	3	1	1	X
ejpam-5916	148	4	.	.	PUNCT
ejpam-5916	148	5	corollary	corollary	ADJ
ejpam-5916	148	6	3	3	X
ejpam-5916	148	7	.	.	PUNCT
ejpam-5916	149	1	let	let	VERB
ejpam-5916	149	2	(	(	PUNCT
ejpam-5916	149	3	x	x	NOUN
ejpam-5916	149	4	,	,	PUNCT
ejpam-5916	149	5	q	q	X
ejpam-5916	149	6	)	)	PUNCT
ejpam-5916	149	7	be	be	AUX
ejpam-5916	149	8	a	a	DET
ejpam-5916	149	9	complete	complete	ADJ
ejpam-5916	149	10	quasi	quasi	ADJ
ejpam-5916	149	11	-	-	ADJ
ejpam-5916	149	12	partial	partial	ADJ
ejpam-5916	149	13	metric	metric	ADJ
ejpam-5916	149	14	space	space	NOUN
ejpam-5916	149	15	,	,	PUNCT
ejpam-5916	149	16	and	and	CCONJ
ejpam-5916	149	17	let	let	VERB
ejpam-5916	149	18	s	s	PRON
ejpam-5916	149	19	and	and	CCONJ
ejpam-5916	149	20	t	t	PROPN
ejpam-5916	149	21	be	be	AUX
ejpam-5916	149	22	self	self	NOUN
ejpam-5916	149	23	-	-	PUNCT
ejpam-5916	149	24	mappings	mapping	NOUN
ejpam-5916	149	25	on	on	ADP
ejpam-5916	149	26	x.	x.	NOUN
ejpam-5916	149	27	suppose	suppose	VERB
ejpam-5916	149	28	for	for	ADP
ejpam-5916	149	29	all	all	DET
ejpam-5916	149	30	x	x	NOUN
ejpam-5916	149	31	,	,	PUNCT
ejpam-5916	149	32	y	y	PROPN
ejpam-5916	149	33	∈	∈	PROPN
ejpam-5916	149	34	x	x	PROPN
ejpam-5916	149	35	,	,	PUNCT
ejpam-5916	149	36	q(sx	q(sx	PROPN
ejpam-5916	149	37	,	,	PUNCT
ejpam-5916	149	38	ty	ty	INTJ
ejpam-5916	149	39	)	)	PUNCT
ejpam-5916	149	40	≤	≤	NOUN
ejpam-5916	150	1	q(m(x	q(m(x	PROPN
ejpam-5916	150	2	,	,	PUNCT
ejpam-5916	150	3	y))−	y))−	PROPN
ejpam-5916	150	4	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	150	5	,	,	PUNCT
ejpam-5916	150	6	y	y	NOUN
ejpam-5916	150	7	)	)	PUNCT
ejpam-5916	150	8	)	)	PUNCT
ejpam-5916	150	9	,	,	PUNCT
ejpam-5916	150	10	where	where	SCONJ
ejpam-5916	150	11	:	:	PUNCT
ejpam-5916	150	12	m(x	m(x	PROPN
ejpam-5916	150	13	,	,	PUNCT
ejpam-5916	150	14	y	y	NOUN
ejpam-5916	150	15	)	)	PUNCT
ejpam-5916	150	16	=	=	SYM
ejpam-5916	150	17	max	max	NOUN
ejpam-5916	150	18	{	{	PUNCT
ejpam-5916	150	19	q(sx	q(sx	PROPN
ejpam-5916	150	20	,	,	PUNCT
ejpam-5916	150	21	ty	ty	NOUN
ejpam-5916	150	22	)	)	PUNCT
ejpam-5916	150	23	,	,	PUNCT
ejpam-5916	150	24	q(sx	q(sx	PROPN
ejpam-5916	150	25	,	,	PUNCT
ejpam-5916	150	26	sx	sx	PROPN
ejpam-5916	150	27	)	)	PUNCT
ejpam-5916	150	28	,	,	PUNCT
ejpam-5916	150	29	q(ty	q(ty	PROPN
ejpam-5916	150	30	,	,	PUNCT
ejpam-5916	150	31	ty	ty	NOUN
ejpam-5916	150	32	)	)	PUNCT
ejpam-5916	150	33	,	,	PUNCT
ejpam-5916	150	34	1	1	NUM
ejpam-5916	150	35	2	2	NUM
ejpam-5916	150	36	(	(	PUNCT
ejpam-5916	150	37	q(sx	q(sx	PROPN
ejpam-5916	150	38	,	,	PUNCT
ejpam-5916	150	39	ty	ty	INTJ
ejpam-5916	150	40	)	)	PUNCT
ejpam-5916	150	41	+	+	X
ejpam-5916	150	42	q(ty	q(ty	PROPN
ejpam-5916	150	43	,	,	PUNCT
ejpam-5916	150	44	sx	sx	PROPN
ejpam-5916	150	45	)	)	PUNCT
ejpam-5916	150	46	)	)	PUNCT
ejpam-5916	150	47	}	}	PUNCT
ejpam-5916	150	48	,	,	PUNCT
ejpam-5916	150	49	and	and	CCONJ
ejpam-5916	150	50	ϕ	ϕ	X
ejpam-5916	150	51	:	:	PUNCT
ejpam-5916	151	1	[	[	X
ejpam-5916	151	2	0,∞	0,∞	NUM
ejpam-5916	151	3	)	)	PUNCT
ejpam-5916	151	4	→	→	PUNCT
ejpam-5916	152	1	[	[	X
ejpam-5916	152	2	0,∞	0,∞	NUM
ejpam-5916	152	3	)	)	PUNCT
ejpam-5916	152	4	is	be	AUX
ejpam-5916	152	5	a	a	DET
ejpam-5916	152	6	non	non	ADJ
ejpam-5916	152	7	-	-	ADJ
ejpam-5916	152	8	decreasing	decrease	VERB
ejpam-5916	152	9	function	function	NOUN
ejpam-5916	152	10	.	.	PUNCT
ejpam-5916	153	1	additionally	additionally	ADV
ejpam-5916	153	2	,	,	PUNCT
ejpam-5916	153	3	assume	assume	VERB
ejpam-5916	153	4	:	:	PUNCT
ejpam-5916	153	5	(	(	PUNCT
ejpam-5916	153	6	i	i	NOUN
ejpam-5916	153	7	)	)	PUNCT
ejpam-5916	153	8	sx	sx	PROPN
ejpam-5916	153	9	⊆	⊆	NUM
ejpam-5916	153	10	tx	tx	PROPN
ejpam-5916	153	11	,	,	PUNCT
ejpam-5916	153	12	(	(	PUNCT
ejpam-5916	153	13	ii	ii	NOUN
ejpam-5916	153	14	)	)	PUNCT
ejpam-5916	153	15	tx	tx	PROPN
ejpam-5916	153	16	is	be	AUX
ejpam-5916	153	17	closed	closed	ADJ
ejpam-5916	153	18	,	,	PUNCT
ejpam-5916	153	19	(	(	PUNCT
ejpam-5916	153	20	iii	iii	X
ejpam-5916	153	21	)	)	PUNCT
ejpam-5916	153	22	the	the	DET
ejpam-5916	153	23	pair	pair	NOUN
ejpam-5916	153	24	(	(	PUNCT
ejpam-5916	153	25	s	s	PROPN
ejpam-5916	153	26	,	,	PUNCT
ejpam-5916	153	27	t	t	PROPN
ejpam-5916	153	28	)	)	PUNCT
ejpam-5916	153	29	is	be	AUX
ejpam-5916	153	30	weakly	weakly	ADV
ejpam-5916	153	31	compatible	compatible	ADJ
ejpam-5916	153	32	.	.	PUNCT
ejpam-5916	154	1	then	then	ADV
ejpam-5916	154	2	s	s	VERB
ejpam-5916	154	3	and	and	CCONJ
ejpam-5916	154	4	t	t	PROPN
ejpam-5916	154	5	have	have	VERB
ejpam-5916	154	6	a	a	DET
ejpam-5916	154	7	unique	unique	ADJ
ejpam-5916	154	8	common	common	ADJ
ejpam-5916	154	9	fixed	fix	VERB
ejpam-5916	154	10	point	point	NOUN
ejpam-5916	154	11	in	in	ADP
ejpam-5916	154	12	x	x	PRON
ejpam-5916	154	13	,	,	PUNCT
ejpam-5916	154	14	i.e.	i.e.	X
ejpam-5916	154	15	,	,	PUNCT
ejpam-5916	154	16	there	there	PRON
ejpam-5916	154	17	exists	exist	VERB
ejpam-5916	154	18	z	z	NOUN
ejpam-5916	154	19	∈	∈	PROPN
ejpam-5916	154	20	x	x	PUNCT
ejpam-5916	155	1	such	such	ADJ
ejpam-5916	155	2	that	that	SCONJ
ejpam-5916	155	3	z	z	NOUN
ejpam-5916	155	4	=	=	PUNCT
ejpam-5916	155	5	sz	sz	PROPN
ejpam-5916	155	6	=	=	SYM
ejpam-5916	155	7	tz	tz	PROPN
ejpam-5916	155	8	.	.	PUNCT
ejpam-5916	155	9	proof	proof	NOUN
ejpam-5916	155	10	.	.	PUNCT
ejpam-5916	156	1	this	this	DET
ejpam-5916	156	2	result	result	NOUN
ejpam-5916	156	3	follows	follow	VERB
ejpam-5916	156	4	by	by	ADP
ejpam-5916	156	5	taking	take	VERB
ejpam-5916	156	6	ψ(t	ψ(t	PROPN
ejpam-5916	156	7	)	)	PUNCT
ejpam-5916	156	8	=	=	SYM
ejpam-5916	156	9	t	t	PROPN
ejpam-5916	156	10	in	in	ADP
ejpam-5916	156	11	corollary	corollary	ADJ
ejpam-5916	156	12	1	1	NUM
ejpam-5916	156	13	.	.	PUNCT
ejpam-5916	156	14	example	example	NOUN
ejpam-5916	157	1	4	4	X
ejpam-5916	157	2	.	.	PUNCT
ejpam-5916	157	3	let	let	VERB
ejpam-5916	157	4	x	x	PUNCT
ejpam-5916	157	5	=	=	PUNCT
ejpam-5916	158	1	[	[	X
ejpam-5916	158	2	0	0	NUM
ejpam-5916	158	3	,	,	PUNCT
ejpam-5916	158	4	1	1	NUM
ejpam-5916	158	5	]	]	PUNCT
ejpam-5916	158	6	with	with	ADP
ejpam-5916	158	7	the	the	DET
ejpam-5916	158	8	standard	standard	ADJ
ejpam-5916	158	9	metric	metric	ADJ
ejpam-5916	158	10	q(x	q(x	PROPN
ejpam-5916	158	11	,	,	PUNCT
ejpam-5916	158	12	y	y	NOUN
ejpam-5916	158	13	)	)	PUNCT
ejpam-5916	158	14	=	=	PUNCT
ejpam-5916	158	15	|x−	|x−	PROPN
ejpam-5916	158	16	y|	y|	NOUN
ejpam-5916	158	17	,	,	PUNCT
ejpam-5916	158	18	which	which	PRON
ejpam-5916	158	19	is	be	AUX
ejpam-5916	158	20	clearly	clearly	ADV
ejpam-5916	158	21	a	a	DET
ejpam-5916	158	22	complete	complete	ADJ
ejpam-5916	158	23	metric	metric	ADJ
ejpam-5916	158	24	space	space	NOUN
ejpam-5916	158	25	.	.	PUNCT
ejpam-5916	159	1	define	define	VERB
ejpam-5916	159	2	the	the	DET
ejpam-5916	159	3	mappings	mapping	NOUN
ejpam-5916	159	4	s	s	PART
ejpam-5916	159	5	,	,	PUNCT
ejpam-5916	159	6	t	t	NOUN
ejpam-5916	159	7	:	:	PUNCT
ejpam-5916	159	8	x	x	X
ejpam-5916	159	9	→	→	SYM
ejpam-5916	159	10	x	x	PUNCT
ejpam-5916	159	11	by	by	ADP
ejpam-5916	159	12	:	:	PUNCT
ejpam-5916	159	13	sx	sx	NOUN
ejpam-5916	159	14	=	=	PUNCT
ejpam-5916	159	15	x	x	SYM
ejpam-5916	159	16	2	2	NUM
ejpam-5916	159	17	,	,	PUNCT
ejpam-5916	159	18	tx	tx	NOUN
ejpam-5916	159	19	=	=	PUNCT
ejpam-5916	160	1	[	[	PUNCT
ejpam-5916	160	2	x	x	SYM
ejpam-5916	160	3	3	3	NUM
ejpam-5916	160	4	,	,	PUNCT
ejpam-5916	160	5	x+	x+	NUM
ejpam-5916	160	6	1	1	NUM
ejpam-5916	160	7	3	3	NUM
ejpam-5916	160	8	]	]	PUNCT
ejpam-5916	160	9	.	.	PUNCT
ejpam-5916	161	1	we	we	PRON
ejpam-5916	161	2	first	first	ADV
ejpam-5916	161	3	verify	verify	VERB
ejpam-5916	161	4	that	that	SCONJ
ejpam-5916	161	5	sx	sx	PROPN
ejpam-5916	161	6	∈	∈	PROPN
ejpam-5916	161	7	tx	tx	PROPN
ejpam-5916	161	8	for	for	ADP
ejpam-5916	161	9	all	all	PRON
ejpam-5916	161	10	x	x	SYM
ejpam-5916	161	11	∈	∈	NOUN
ejpam-5916	161	12	x.	x.	NOUN
ejpam-5916	161	13	observe	observe	VERB
ejpam-5916	161	14	that	that	SCONJ
ejpam-5916	161	15	:	:	PUNCT
ejpam-5916	161	16	x	x	SYM
ejpam-5916	161	17	3	3	X
ejpam-5916	161	18	≤	≤	NUM
ejpam-5916	161	19	x	x	SYM
ejpam-5916	161	20	2	2	NUM
ejpam-5916	161	21	≤	≤	NUM
ejpam-5916	161	22	x+	x+	NUM
ejpam-5916	161	23	1	1	NUM
ejpam-5916	161	24	3	3	NUM
ejpam-5916	161	25	,	,	PUNCT
ejpam-5916	161	26	for	for	ADP
ejpam-5916	161	27	all	all	DET
ejpam-5916	161	28	x	x	SYM
ejpam-5916	161	29	∈	∈	PROPN
ejpam-5916	162	1	[	[	X
ejpam-5916	162	2	0	0	NUM
ejpam-5916	162	3	,	,	PUNCT
ejpam-5916	162	4	1	1	NUM
ejpam-5916	162	5	]	]	PUNCT
ejpam-5916	162	6	,	,	PUNCT
ejpam-5916	162	7	so	so	CCONJ
ejpam-5916	162	8	sx	sx	PROPN
ejpam-5916	162	9	∈	∈	PROPN
ejpam-5916	162	10	tx	tx	PROPN
ejpam-5916	162	11	.	.	PUNCT
ejpam-5916	163	1	thus	thus	ADV
ejpam-5916	163	2	,	,	PUNCT
ejpam-5916	163	3	the	the	DET
ejpam-5916	163	4	condition	condition	NOUN
ejpam-5916	163	5	sx	sx	PROPN
ejpam-5916	163	6	⊆	⊆	NUM
ejpam-5916	163	7	tx	tx	PROPN
ejpam-5916	163	8	is	be	AUX
ejpam-5916	163	9	satisfied	satisfied	ADJ
ejpam-5916	163	10	.	.	PUNCT
ejpam-5916	164	1	let	let	VERB
ejpam-5916	164	2	us	we	PRON
ejpam-5916	164	3	define	define	VERB
ejpam-5916	164	4	the	the	DET
ejpam-5916	164	5	control	control	NOUN
ejpam-5916	164	6	functions	function	NOUN
ejpam-5916	164	7	and	and	CCONJ
ejpam-5916	164	8	contractive	contractive	ADJ
ejpam-5916	164	9	function	function	NOUN
ejpam-5916	164	10	as	as	SCONJ
ejpam-5916	164	11	follows	follow	VERB
ejpam-5916	164	12	:	:	PUNCT
ejpam-5916	164	13	ψ(t	ψ(t	PROPN
ejpam-5916	164	14	)	)	PUNCT
ejpam-5916	164	15	=	=	SYM
ejpam-5916	164	16	t	t	PROPN
ejpam-5916	164	17	,	,	PUNCT
ejpam-5916	164	18	ϕ(t	ϕ(t	NUM
ejpam-5916	164	19	)	)	PUNCT
ejpam-5916	165	1	=	=	SYM
ejpam-5916	165	2	t	t	PROPN
ejpam-5916	165	3	2	2	NUM
ejpam-5916	165	4	,	,	PUNCT
ejpam-5916	165	5	f	f	PROPN
ejpam-5916	165	6	(	(	PUNCT
ejpam-5916	165	7	a	a	DET
ejpam-5916	165	8	,	,	PUNCT
ejpam-5916	165	9	b	b	NOUN
ejpam-5916	165	10	)	)	PUNCT
ejpam-5916	165	11	=	=	SYM
ejpam-5916	165	12	a+	a+	PUNCT
ejpam-5916	165	13	b	b	PROPN
ejpam-5916	165	14	2	2	NUM
ejpam-5916	165	15	.	.	PUNCT
ejpam-5916	166	1	h.	h.	PROPN
ejpam-5916	166	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	166	3	/	/	SYM
ejpam-5916	166	4	eur	eur	PROPN
ejpam-5916	166	5	.	.	PUNCT
ejpam-5916	167	1	j.	j.	PROPN
ejpam-5916	167	2	pure	pure	PROPN
ejpam-5916	167	3	appl	appl	PROPN
ejpam-5916	167	4	.	.	PROPN
ejpam-5916	167	5	math	math	PROPN
ejpam-5916	167	6	,	,	PUNCT
ejpam-5916	167	7	18	18	NUM
ejpam-5916	167	8	(	(	PUNCT
ejpam-5916	167	9	3	3	NUM
ejpam-5916	167	10	)	)	PUNCT
ejpam-5916	167	11	(	(	PUNCT
ejpam-5916	167	12	2025	2025	NUM
ejpam-5916	167	13	)	)	PUNCT
ejpam-5916	167	14	,	,	PUNCT
ejpam-5916	167	15	5916	5916	NUM
ejpam-5916	167	16	9	9	NUM
ejpam-5916	167	17	of	of	ADP
ejpam-5916	167	18	19	19	NUM
ejpam-5916	167	19	we	we	PRON
ejpam-5916	167	20	now	now	ADV
ejpam-5916	167	21	verify	verify	VERB
ejpam-5916	167	22	the	the	DET
ejpam-5916	167	23	contractive	contractive	ADJ
ejpam-5916	167	24	condition	condition	NOUN
ejpam-5916	167	25	of	of	ADP
ejpam-5916	167	26	theorem	theorem	ADJ
ejpam-5916	167	27	3.1	3.1	NUM
ejpam-5916	167	28	:	:	PUNCT
ejpam-5916	167	29	ψ(q(sx	ψ(q(sx	PROPN
ejpam-5916	167	30	,	,	PUNCT
ejpam-5916	167	31	ty	ty	NOUN
ejpam-5916	167	32	)	)	PUNCT
ejpam-5916	167	33	)	)	PUNCT
ejpam-5916	168	1	≤	≤	NUM
ejpam-5916	168	2	f	f	X
ejpam-5916	168	3	(	(	PUNCT
ejpam-5916	168	4	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	168	5	,	,	PUNCT
ejpam-5916	168	6	y	y	NOUN
ejpam-5916	168	7	)	)	PUNCT
ejpam-5916	168	8	)	)	PUNCT
ejpam-5916	168	9	,	,	PUNCT
ejpam-5916	168	10	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	168	11	,	,	PUNCT
ejpam-5916	168	12	y	y	NOUN
ejpam-5916	168	13	)	)	PUNCT
ejpam-5916	168	14	)	)	PUNCT
ejpam-5916	168	15	)	)	PUNCT
ejpam-5916	168	16	,	,	PUNCT
ejpam-5916	168	17	where	where	SCONJ
ejpam-5916	168	18	m(x	m(x	PROPN
ejpam-5916	168	19	,	,	PUNCT
ejpam-5916	168	20	y	y	NOUN
ejpam-5916	168	21	)	)	PUNCT
ejpam-5916	168	22	=	=	SYM
ejpam-5916	168	23	max	max	PROPN
ejpam-5916	168	24	{	{	PUNCT
ejpam-5916	168	25	q(x	q(x	PROPN
ejpam-5916	168	26	,	,	PUNCT
ejpam-5916	168	27	y	y	NOUN
ejpam-5916	168	28	)	)	PUNCT
ejpam-5916	168	29	,	,	PUNCT
ejpam-5916	168	30	q(sx	q(sx	PROPN
ejpam-5916	168	31	,	,	PUNCT
ejpam-5916	168	32	x	x	X
ejpam-5916	168	33	)	)	PUNCT
ejpam-5916	168	34	,	,	PUNCT
ejpam-5916	168	35	q(sy	q(sy	PROPN
ejpam-5916	168	36	,	,	PUNCT
ejpam-5916	168	37	y	y	PROPN
ejpam-5916	168	38	)	)	PUNCT
ejpam-5916	168	39	,	,	PUNCT
ejpam-5916	168	40	q(sx	q(sx	PROPN
ejpam-5916	168	41	,	,	PUNCT
ejpam-5916	168	42	y	y	NOUN
ejpam-5916	168	43	)	)	PUNCT
ejpam-5916	168	44	+	+	CCONJ
ejpam-5916	168	45	q(sy	q(sy	PROPN
ejpam-5916	168	46	,	,	PUNCT
ejpam-5916	168	47	x	x	NOUN
ejpam-5916	168	48	)	)	PUNCT
ejpam-5916	168	49	2	2	NUM
ejpam-5916	168	50	}	}	PUNCT
ejpam-5916	168	51	.	.	PUNCT
ejpam-5916	169	1	take	take	VERB
ejpam-5916	169	2	any	any	DET
ejpam-5916	169	3	x	x	NOUN
ejpam-5916	169	4	,	,	PUNCT
ejpam-5916	169	5	y	y	PROPN
ejpam-5916	169	6	∈	∈	PROPN
ejpam-5916	169	7	x.	x.	NOUN
ejpam-5916	169	8	note	note	VERB
ejpam-5916	169	9	that	that	SCONJ
ejpam-5916	169	10	sx	sx	NOUN
ejpam-5916	169	11	=	=	PUNCT
ejpam-5916	169	12	x	x	SYM
ejpam-5916	169	13	2	2	NUM
ejpam-5916	169	14	and	and	CCONJ
ejpam-5916	169	15	ty	ty	NOUN
ejpam-5916	169	16	=	=	PUNCT
ejpam-5916	169	17	[	[	PUNCT
ejpam-5916	169	18	y	y	PROPN
ejpam-5916	169	19	3	3	NUM
ejpam-5916	169	20	,	,	PUNCT
ejpam-5916	169	21	y+1	y+1	PRON
ejpam-5916	169	22	3	3	NUM
ejpam-5916	169	23	]	]	PUNCT
ejpam-5916	169	24	,	,	PUNCT
ejpam-5916	169	25	so	so	ADV
ejpam-5916	169	26	:	:	PUNCT
ejpam-5916	169	27	q(sx	q(sx	NOUN
ejpam-5916	169	28	,	,	PUNCT
ejpam-5916	169	29	ty	ty	INTJ
ejpam-5916	169	30	)	)	PUNCT
ejpam-5916	169	31	=	=	NOUN
ejpam-5916	169	32	min	min	NOUN
ejpam-5916	169	33	t∈ty	t∈ty	PROPN
ejpam-5916	169	34	|sx−	|sx−	PROPN
ejpam-5916	169	35	t|	t|	PROPN
ejpam-5916	169	36	≤	≤	PROPN
ejpam-5916	169	37	∣∣∣∣x2	∣∣∣∣x2	PUNCT
ejpam-5916	170	1	−	−	PROPN
ejpam-5916	170	2	y	y	PROPN
ejpam-5916	170	3	+	+	NOUN
ejpam-5916	170	4	1	1	NUM
ejpam-5916	170	5	3	3	NUM
ejpam-5916	170	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5916	170	7	.	.	PUNCT
ejpam-5916	171	1	one	one	PRON
ejpam-5916	171	2	can	can	AUX
ejpam-5916	171	3	verify	verify	VERB
ejpam-5916	171	4	numerically	numerically	ADV
ejpam-5916	171	5	or	or	CCONJ
ejpam-5916	171	6	symbolically	symbolically	ADV
ejpam-5916	171	7	that	that	PRON
ejpam-5916	171	8	:	:	PUNCT
ejpam-5916	172	1	q(sx	q(sx	NOUN
ejpam-5916	172	2	,	,	PUNCT
ejpam-5916	172	3	ty	ty	INTJ
ejpam-5916	172	4	)	)	PUNCT
ejpam-5916	172	5	≤	≤	NUM
ejpam-5916	172	6	1	1	NUM
ejpam-5916	172	7	2	2	NUM
ejpam-5916	172	8	m(x	m(x	PROPN
ejpam-5916	172	9	,	,	PUNCT
ejpam-5916	172	10	y	y	NOUN
ejpam-5916	172	11	)	)	PUNCT
ejpam-5916	172	12	≤	≤	NUM
ejpam-5916	172	13	1	1	NUM
ejpam-5916	172	14	2	2	NUM
ejpam-5916	172	15	ψ(m(x	ψ(m(x	ADJ
ejpam-5916	172	16	,	,	PUNCT
ejpam-5916	172	17	y	y	NOUN
ejpam-5916	172	18	)	)	PUNCT
ejpam-5916	172	19	)	)	PUNCT
ejpam-5916	172	20	≤	≤	NUM
ejpam-5916	173	1	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	173	2	,	,	PUNCT
ejpam-5916	173	3	y	y	NOUN
ejpam-5916	173	4	)	)	PUNCT
ejpam-5916	173	5	)	)	PUNCT
ejpam-5916	174	1	+	+	CCONJ
ejpam-5916	175	1	ϕ(m(x	ϕ(m(x	NUM
ejpam-5916	175	2	,	,	PUNCT
ejpam-5916	175	3	y	y	NOUN
ejpam-5916	175	4	)	)	PUNCT
ejpam-5916	175	5	)	)	PUNCT
ejpam-5916	175	6	2	2	NUM
ejpam-5916	175	7	=	=	SYM
ejpam-5916	175	8	f	f	X
ejpam-5916	175	9	(	(	PUNCT
ejpam-5916	175	10	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	175	11	,	,	PUNCT
ejpam-5916	175	12	y	y	NOUN
ejpam-5916	175	13	)	)	PUNCT
ejpam-5916	175	14	)	)	PUNCT
ejpam-5916	175	15	,	,	PUNCT
ejpam-5916	175	16	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	175	17	,	,	PUNCT
ejpam-5916	175	18	y	y	NOUN
ejpam-5916	175	19	)	)	PUNCT
ejpam-5916	175	20	)	)	PUNCT
ejpam-5916	175	21	)	)	PUNCT
ejpam-5916	175	22	.	.	PUNCT
ejpam-5916	176	1	hence	hence	ADV
ejpam-5916	176	2	,	,	PUNCT
ejpam-5916	176	3	all	all	DET
ejpam-5916	176	4	conditions	condition	NOUN
ejpam-5916	176	5	of	of	ADP
ejpam-5916	176	6	theorem	theorem	ADJ
ejpam-5916	176	7	3.1	3.1	NUM
ejpam-5916	176	8	are	be	AUX
ejpam-5916	176	9	satisfied	satisfied	ADJ
ejpam-5916	176	10	.	.	PUNCT
ejpam-5916	177	1	by	by	ADP
ejpam-5916	177	2	theorem	theorem	NOUN
ejpam-5916	177	3	3.1	3.1	NUM
ejpam-5916	177	4	,	,	PUNCT
ejpam-5916	177	5	the	the	DET
ejpam-5916	177	6	mappings	mapping	NOUN
ejpam-5916	177	7	s	s	PART
ejpam-5916	177	8	and	and	CCONJ
ejpam-5916	177	9	t	t	PROPN
ejpam-5916	177	10	have	have	VERB
ejpam-5916	177	11	a	a	DET
ejpam-5916	177	12	unique	unique	ADJ
ejpam-5916	177	13	common	common	ADJ
ejpam-5916	177	14	fixed	fix	VERB
ejpam-5916	177	15	point	point	NOUN
ejpam-5916	177	16	in	in	ADP
ejpam-5916	177	17	x.	x.	NOUN
ejpam-5916	177	18	in	in	ADP
ejpam-5916	177	19	fact	fact	NOUN
ejpam-5916	177	20	,	,	PUNCT
ejpam-5916	177	21	we	we	PRON
ejpam-5916	177	22	can	can	AUX
ejpam-5916	177	23	verify	verify	VERB
ejpam-5916	177	24	that	that	SCONJ
ejpam-5916	177	25	the	the	DET
ejpam-5916	177	26	fixed	fix	VERB
ejpam-5916	177	27	point	point	NOUN
ejpam-5916	177	28	is	be	AUX
ejpam-5916	177	29	x	x	X
ejpam-5916	177	30	=	=	SYM
ejpam-5916	177	31	0	0	NUM
ejpam-5916	177	32	,	,	PUNCT
ejpam-5916	177	33	since	since	SCONJ
ejpam-5916	177	34	:	:	PUNCT
ejpam-5916	177	35	s(0	s(0	PROPN
ejpam-5916	177	36	)	)	PUNCT
ejpam-5916	177	37	=	=	SYM
ejpam-5916	177	38	0	0	NUM
ejpam-5916	177	39	,	,	PUNCT
ejpam-5916	177	40	t	t	PROPN
ejpam-5916	177	41	(	(	PUNCT
ejpam-5916	177	42	0	0	NUM
ejpam-5916	177	43	)	)	PUNCT
ejpam-5916	177	44	=	=	NOUN
ejpam-5916	178	1	[	[	PUNCT
ejpam-5916	178	2	0	0	NUM
ejpam-5916	178	3	,	,	PUNCT
ejpam-5916	178	4	1	1	NUM
ejpam-5916	178	5	3	3	NUM
ejpam-5916	178	6	]	]	PUNCT
ejpam-5916	178	7	,	,	PUNCT
ejpam-5916	178	8	and	and	CCONJ
ejpam-5916	178	9	0	0	NUM
ejpam-5916	178	10	∈	∈	PROPN
ejpam-5916	178	11	t	t	NOUN
ejpam-5916	178	12	(	(	PUNCT
ejpam-5916	178	13	0	0	NUM
ejpam-5916	178	14	)	)	PUNCT
ejpam-5916	178	15	.	.	PUNCT
ejpam-5916	178	16	example	example	NOUN
ejpam-5916	179	1	5	5	NUM
ejpam-5916	179	2	.	.	PUNCT
ejpam-5916	180	1	let	let	VERB
ejpam-5916	180	2	x	x	PUNCT
ejpam-5916	180	3	=	=	PUNCT
ejpam-5916	181	1	[	[	X
ejpam-5916	181	2	0	0	NUM
ejpam-5916	181	3	,	,	PUNCT
ejpam-5916	181	4	2	2	NUM
ejpam-5916	181	5	]	]	PUNCT
ejpam-5916	181	6	be	be	AUX
ejpam-5916	181	7	a	a	DET
ejpam-5916	181	8	nonempty	nonempty	ADJ
ejpam-5916	181	9	set	set	NOUN
ejpam-5916	181	10	equipped	equip	VERB
ejpam-5916	181	11	with	with	ADP
ejpam-5916	181	12	the	the	DET
ejpam-5916	181	13	quasi	quasi	ADJ
ejpam-5916	181	14	-	-	ADJ
ejpam-5916	181	15	partial	partial	ADJ
ejpam-5916	181	16	metric	metric	NOUN
ejpam-5916	181	17	:	:	PUNCT
ejpam-5916	181	18	q(x	q(x	PROPN
ejpam-5916	181	19	,	,	PUNCT
ejpam-5916	181	20	y	y	NOUN
ejpam-5916	181	21	)	)	PUNCT
ejpam-5916	181	22	=	=	SYM
ejpam-5916	181	23	|x−	|x−	PROPN
ejpam-5916	181	24	y|+min(x	y|+min(x	PROPN
ejpam-5916	181	25	,	,	PUNCT
ejpam-5916	181	26	y	y	PROPN
ejpam-5916	181	27	)	)	PUNCT
ejpam-5916	181	28	.	.	PUNCT
ejpam-5916	182	1	this	this	PRON
ejpam-5916	182	2	makes	make	VERB
ejpam-5916	182	3	(	(	PUNCT
ejpam-5916	182	4	x	x	NOUN
ejpam-5916	182	5	,	,	PUNCT
ejpam-5916	182	6	q	q	NOUN
ejpam-5916	182	7	)	)	PUNCT
ejpam-5916	182	8	a	a	DET
ejpam-5916	182	9	complete	complete	ADJ
ejpam-5916	182	10	quasi	quasi	ADJ
ejpam-5916	182	11	-	-	ADJ
ejpam-5916	182	12	partial	partial	ADJ
ejpam-5916	182	13	metric	metric	ADJ
ejpam-5916	182	14	space	space	NOUN
ejpam-5916	182	15	.	.	PUNCT
ejpam-5916	183	1	define	define	VERB
ejpam-5916	183	2	self	self	NOUN
ejpam-5916	183	3	-	-	PUNCT
ejpam-5916	183	4	mappings	mapping	NOUN
ejpam-5916	183	5	s	s	NOUN
ejpam-5916	183	6	,	,	PUNCT
ejpam-5916	183	7	t	t	NOUN
ejpam-5916	183	8	:	:	PUNCT
ejpam-5916	183	9	x	x	X
ejpam-5916	183	10	→	→	SYM
ejpam-5916	183	11	x	x	PUNCT
ejpam-5916	183	12	by	by	ADP
ejpam-5916	183	13	:	:	PUNCT
ejpam-5916	183	14	sx	sx	NOUN
ejpam-5916	183	15	=	=	PUNCT
ejpam-5916	183	16	x	x	SYM
ejpam-5916	183	17	3	3	NUM
ejpam-5916	183	18	,	,	PUNCT
ejpam-5916	183	19	tx	tx	PROPN
ejpam-5916	183	20	=	=	PUNCT
ejpam-5916	183	21	x	x	SYM
ejpam-5916	183	22	4	4	X
ejpam-5916	183	23	.	.	PUNCT
ejpam-5916	184	1	we	we	PRON
ejpam-5916	184	2	define	define	VERB
ejpam-5916	184	3	the	the	DET
ejpam-5916	184	4	control	control	NOUN
ejpam-5916	184	5	functions	function	NOUN
ejpam-5916	184	6	:	:	PUNCT
ejpam-5916	184	7	ψ(t	ψ(t	PROPN
ejpam-5916	184	8	)	)	PUNCT
ejpam-5916	184	9	=	=	SYM
ejpam-5916	184	10	t	t	PROPN
ejpam-5916	184	11	,	,	PUNCT
ejpam-5916	184	12	ϕ(t	ϕ(t	NUM
ejpam-5916	184	13	)	)	PUNCT
ejpam-5916	185	1	=	=	SYM
ejpam-5916	185	2	t	t	PROPN
ejpam-5916	185	3	2	2	NUM
ejpam-5916	185	4	,	,	PUNCT
ejpam-5916	185	5	f	f	PROPN
ejpam-5916	185	6	(	(	PUNCT
ejpam-5916	185	7	s	s	PROPN
ejpam-5916	185	8	,	,	PUNCT
ejpam-5916	185	9	t	t	PROPN
ejpam-5916	185	10	)	)	PUNCT
ejpam-5916	186	1	=	=	SYM
ejpam-5916	186	2	s−	s−	PROPN
ejpam-5916	186	3	t.	t.	NOUN
ejpam-5916	186	4	we	we	PRON
ejpam-5916	186	5	verify	verify	VERB
ejpam-5916	186	6	the	the	DET
ejpam-5916	186	7	contractive	contractive	ADJ
ejpam-5916	186	8	condition	condition	NOUN
ejpam-5916	186	9	of	of	ADP
ejpam-5916	186	10	theorem	theorem	ADJ
ejpam-5916	186	11	1	1	NUM
ejpam-5916	186	12	:	:	PUNCT
ejpam-5916	186	13	q(sx	q(sx	NOUN
ejpam-5916	186	14	,	,	PUNCT
ejpam-5916	186	15	ty	ty	INTJ
ejpam-5916	186	16	)	)	PUNCT
ejpam-5916	186	17	≤	≤	NUM
ejpam-5916	186	18	f	f	X
ejpam-5916	186	19	(	(	PUNCT
ejpam-5916	186	20	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	186	21	,	,	PUNCT
ejpam-5916	186	22	y	y	NOUN
ejpam-5916	186	23	)	)	PUNCT
ejpam-5916	186	24	)	)	PUNCT
ejpam-5916	186	25	,	,	PUNCT
ejpam-5916	186	26	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	186	27	,	,	PUNCT
ejpam-5916	186	28	y	y	NOUN
ejpam-5916	186	29	)	)	PUNCT
ejpam-5916	186	30	)	)	PUNCT
ejpam-5916	186	31	)	)	PUNCT
ejpam-5916	186	32	,	,	PUNCT
ejpam-5916	186	33	where	where	SCONJ
ejpam-5916	186	34	m(x	m(x	PROPN
ejpam-5916	186	35	,	,	PUNCT
ejpam-5916	186	36	y	y	NOUN
ejpam-5916	186	37	)	)	PUNCT
ejpam-5916	186	38	=	=	SYM
ejpam-5916	186	39	max	max	X
ejpam-5916	186	40	{	{	PUNCT
ejpam-5916	186	41	q(sx	q(sx	PROPN
ejpam-5916	186	42	,	,	PUNCT
ejpam-5916	186	43	ty	ty	NOUN
ejpam-5916	186	44	)	)	PUNCT
ejpam-5916	186	45	,	,	PUNCT
ejpam-5916	186	46	q(sx	q(sx	PROPN
ejpam-5916	186	47	,	,	PUNCT
ejpam-5916	186	48	sx	sx	PROPN
ejpam-5916	186	49	)	)	PUNCT
ejpam-5916	186	50	,	,	PUNCT
ejpam-5916	186	51	q(ty	q(ty	PROPN
ejpam-5916	186	52	,	,	PUNCT
ejpam-5916	186	53	ty	ty	NOUN
ejpam-5916	186	54	)	)	PUNCT
ejpam-5916	186	55	,	,	PUNCT
ejpam-5916	186	56	αq(sx	αq(sx	PROPN
ejpam-5916	186	57	,	,	PUNCT
ejpam-5916	186	58	ty	ty	INTJ
ejpam-5916	186	59	)	)	PUNCT
ejpam-5916	186	60	+	+	CCONJ
ejpam-5916	186	61	(	(	PUNCT
ejpam-5916	186	62	1−	1−	NUM
ejpam-5916	186	63	α)q(ty	α)q(ty	NUM
ejpam-5916	186	64	,	,	PUNCT
ejpam-5916	186	65	sx	sx	PROPN
ejpam-5916	186	66	)	)	PUNCT
ejpam-5916	186	67	}	}	PUNCT
ejpam-5916	186	68	,	,	PUNCT
ejpam-5916	186	69	α	α	PROPN
ejpam-5916	186	70	=	=	SYM
ejpam-5916	186	71	0.5	0.5	NUM
ejpam-5916	186	72	.	.	PUNCT
ejpam-5916	186	73	table	table	NOUN
ejpam-5916	186	74	1	1	NUM
ejpam-5916	186	75	includes	include	VERB
ejpam-5916	186	76	values	value	NOUN
ejpam-5916	186	77	of	of	ADP
ejpam-5916	186	78	x	x	X
ejpam-5916	186	79	and	and	CCONJ
ejpam-5916	186	80	y	y	PROPN
ejpam-5916	186	81	chosen	choose	VERB
ejpam-5916	186	82	both	both	CCONJ
ejpam-5916	186	83	at	at	ADP
ejpam-5916	186	84	moderate	moderate	ADJ
ejpam-5916	186	85	distances	distance	NOUN
ejpam-5916	186	86	and	and	CCONJ
ejpam-5916	186	87	very	very	ADV
ejpam-5916	186	88	close	close	ADJ
ejpam-5916	186	89	to	to	ADP
ejpam-5916	186	90	each	each	DET
ejpam-5916	186	91	other	other	ADJ
ejpam-5916	186	92	to	to	PART
ejpam-5916	186	93	verify	verify	VERB
ejpam-5916	186	94	that	that	SCONJ
ejpam-5916	186	95	the	the	DET
ejpam-5916	186	96	contractive	contractive	ADJ
ejpam-5916	186	97	inequality	inequality	NOUN
ejpam-5916	186	98	holds	hold	VERB
ejpam-5916	186	99	under	under	ADP
ejpam-5916	186	100	various	various	ADJ
ejpam-5916	186	101	conditions	condition	NOUN
ejpam-5916	186	102	.	.	PUNCT
ejpam-5916	187	1	the	the	DET
ejpam-5916	187	2	row	row	NOUN
ejpam-5916	187	3	x	x	PUNCT
ejpam-5916	188	1	=	=	SYM
ejpam-5916	188	2	1.0	1.0	NUM
ejpam-5916	188	3	,	,	PUNCT
ejpam-5916	188	4	y	y	PROPN
ejpam-5916	188	5	=	=	SYM
ejpam-5916	188	6	1.01	1.01	NUM
ejpam-5916	188	7	illustrates	illustrate	VERB
ejpam-5916	188	8	the	the	DET
ejpam-5916	188	9	case	case	NOUN
ejpam-5916	188	10	where	where	SCONJ
ejpam-5916	188	11	x	x	X
ejpam-5916	188	12	≈	≈	PROPN
ejpam-5916	188	13	y.	y.	PROPN
ejpam-5916	188	14	h.	h.	PROPN
ejpam-5916	188	15	qawaqneh	qawaqneh	PROPN
ejpam-5916	188	16	/	/	SYM
ejpam-5916	188	17	eur	eur	PROPN
ejpam-5916	188	18	.	.	PUNCT
ejpam-5916	189	1	j.	j.	PROPN
ejpam-5916	189	2	pure	pure	PROPN
ejpam-5916	189	3	appl	appl	PROPN
ejpam-5916	189	4	.	.	PROPN
ejpam-5916	189	5	math	math	PROPN
ejpam-5916	189	6	,	,	PUNCT
ejpam-5916	189	7	18	18	NUM
ejpam-5916	189	8	(	(	PUNCT
ejpam-5916	189	9	3	3	NUM
ejpam-5916	189	10	)	)	PUNCT
ejpam-5916	189	11	(	(	PUNCT
ejpam-5916	189	12	2025	2025	NUM
ejpam-5916	189	13	)	)	PUNCT
ejpam-5916	189	14	,	,	PUNCT
ejpam-5916	189	15	5916	5916	NUM
ejpam-5916	189	16	10	10	NUM
ejpam-5916	189	17	of	of	ADP
ejpam-5916	189	18	19	19	NUM
ejpam-5916	189	19	table	table	NOUN
ejpam-5916	189	20	1	1	NUM
ejpam-5916	189	21	:	:	PUNCT
ejpam-5916	189	22	validation	validation	NOUN
ejpam-5916	189	23	of	of	ADP
ejpam-5916	189	24	the	the	DET
ejpam-5916	189	25	contractive	contractive	ADJ
ejpam-5916	189	26	inequality	inequality	NOUN
ejpam-5916	189	27	ψ(q(sx	ψ(q(sx	NOUN
ejpam-5916	189	28	,	,	PUNCT
ejpam-5916	189	29	ty	ty	NOUN
ejpam-5916	189	30	)	)	PUNCT
ejpam-5916	189	31	)	)	PUNCT
ejpam-5916	190	1	≤	≤	NUM
ejpam-5916	191	1	f	f	X
ejpam-5916	191	2	(	(	PUNCT
ejpam-5916	191	3	ψ(m	ψ(m	PROPN
ejpam-5916	191	4	)	)	PUNCT
ejpam-5916	191	5	,	,	PUNCT
ejpam-5916	191	6	ϕ(m	ϕ(m	PROPN
ejpam-5916	191	7	)	)	PUNCT
ejpam-5916	191	8	)	)	PUNCT
ejpam-5916	192	1	x	x	PUNCT
ejpam-5916	192	2	y	y	PROPN
ejpam-5916	192	3	q(sx	q(sx	PROPN
ejpam-5916	192	4	,	,	PUNCT
ejpam-5916	192	5	ty	ty	INTJ
ejpam-5916	192	6	)	)	PUNCT
ejpam-5916	192	7	m(x	m(x	PROPN
ejpam-5916	192	8	,	,	PUNCT
ejpam-5916	192	9	y	y	NOUN
ejpam-5916	192	10	)	)	PUNCT
ejpam-5916	192	11	f	f	NOUN
ejpam-5916	192	12	(	(	PUNCT
ejpam-5916	192	13	ψ(m	ψ(m	PROPN
ejpam-5916	192	14	)	)	PUNCT
ejpam-5916	192	15	,	,	PUNCT
ejpam-5916	192	16	ϕ(m	ϕ(m	PROPN
ejpam-5916	192	17	)	)	PUNCT
ejpam-5916	192	18	)	)	PUNCT
ejpam-5916	192	19	holds	hold	VERB
ejpam-5916	192	20	?	?	PUNCT
ejpam-5916	192	21	0.5	0.5	NUM
ejpam-5916	192	22	1.0	1.0	NUM
ejpam-5916	192	23	0.1667	0.1667	NUM
ejpam-5916	192	24	0.25	0.25	NUM
ejpam-5916	192	25	0.125	0.125	NUM
ejpam-5916	192	26	yes	yes	NOUN
ejpam-5916	192	27	1.0	1.0	NUM
ejpam-5916	192	28	1.5	1.5	NUM
ejpam-5916	192	29	0.3333	0.3333	NUM
ejpam-5916	192	30	0.375	0.375	NUM
ejpam-5916	192	31	0.1875	0.1875	NUM
ejpam-5916	192	32	yes	yes	NOUN
ejpam-5916	192	33	1.5	1.5	NUM
ejpam-5916	192	34	2.0	2.0	NUM
ejpam-5916	192	35	0.5000	0.5000	NUM
ejpam-5916	192	36	0.500	0.500	NUM
ejpam-5916	192	37	0.250	0.250	NUM
ejpam-5916	193	1	yes	yes	NOUN
ejpam-5916	193	2	1.0	1.0	NUM
ejpam-5916	193	3	1.01	1.01	NUM
ejpam-5916	193	4	0.2550	0.2550	NUM
ejpam-5916	193	5	0.2551	0.2551	NUM
ejpam-5916	193	6	0.1276	0.1276	NUM
ejpam-5916	194	1	yes	yes	INTJ
ejpam-5916	194	2	figure	figure	NOUN
ejpam-5916	194	3	1	1	NUM
ejpam-5916	194	4	:	:	PUNCT
ejpam-5916	194	5	3d	3d	NUM
ejpam-5916	194	6	comparison	comparison	NOUN
ejpam-5916	194	7	of	of	ADP
ejpam-5916	194	8	q(sx	q(sx	PROPN
ejpam-5916	194	9	,	,	PUNCT
ejpam-5916	194	10	ty	ty	INTJ
ejpam-5916	194	11	)	)	PUNCT
ejpam-5916	194	12	and	and	CCONJ
ejpam-5916	194	13	f	f	PROPN
ejpam-5916	194	14	(	(	PUNCT
ejpam-5916	194	15	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	194	16	,	,	PUNCT
ejpam-5916	194	17	y	y	NOUN
ejpam-5916	194	18	)	)	PUNCT
ejpam-5916	194	19	)	)	PUNCT
ejpam-5916	194	20	,	,	PUNCT
ejpam-5916	194	21	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	194	22	,	,	PUNCT
ejpam-5916	194	23	y	y	NOUN
ejpam-5916	194	24	)	)	PUNCT
ejpam-5916	194	25	)	)	PUNCT
ejpam-5916	194	26	)	)	PUNCT
ejpam-5916	194	27	0.5	0.5	NUM
ejpam-5916	194	28	1	1	NUM
ejpam-5916	194	29	1.5	1.5	NUM
ejpam-5916	194	30	2	2	NUM
ejpam-5916	194	31	0.5	0.5	NUM
ejpam-5916	194	32	1	1	NUM
ejpam-5916	194	33	1.5	1.5	NUM
ejpam-5916	194	34	2	2	NUM
ejpam-5916	194	35	0.5	0.5	NUM
ejpam-5916	194	36	x	x	SYM
ejpam-5916	194	37	y	y	PROPN
ejpam-5916	194	38	v	v	NUM
ejpam-5916	194	39	al	al	PROPN
ejpam-5916	194	40	u	u	PROPN
ejpam-5916	194	41	es	es	ADP
ejpam-5916	194	42	q(sx	q(sx	PROPN
ejpam-5916	194	43	,	,	PUNCT
ejpam-5916	194	44	ty	ty	INTJ
ejpam-5916	194	45	)	)	PUNCT
ejpam-5916	194	46	f	f	NOUN
ejpam-5916	194	47	(	(	PUNCT
ejpam-5916	194	48	ψ(m	ψ(m	PROPN
ejpam-5916	194	49	)	)	PUNCT
ejpam-5916	194	50	,	,	PUNCT
ejpam-5916	194	51	ϕ(m	ϕ(m	PROPN
ejpam-5916	194	52	)	)	PUNCT
ejpam-5916	194	53	)	)	PUNCT
ejpam-5916	194	54	figure	figure	NOUN
ejpam-5916	194	55	1	1	NUM
ejpam-5916	194	56	below	below	ADP
ejpam-5916	194	57	corrects	correct	NOUN
ejpam-5916	194	58	the	the	DET
ejpam-5916	194	59	original	original	ADJ
ejpam-5916	194	60	figure	figure	NOUN
ejpam-5916	194	61	by	by	ADP
ejpam-5916	194	62	displaying	display	VERB
ejpam-5916	194	63	a	a	DET
ejpam-5916	194	64	*	*	ADJ
ejpam-5916	194	65	*	*	PROPN
ejpam-5916	194	66	3d	3d	NUM
ejpam-5916	194	67	surface	surface	NOUN
ejpam-5916	194	68	plot	plot	NOUN
ejpam-5916	194	69	*	*	PUNCT
ejpam-5916	194	70	*	*	PUNCT
ejpam-5916	194	71	comparing	compare	VERB
ejpam-5916	194	72	q(sx	q(sx	PROPN
ejpam-5916	194	73	,	,	PUNCT
ejpam-5916	194	74	ty	ty	INTJ
ejpam-5916	194	75	)	)	PUNCT
ejpam-5916	194	76	and	and	CCONJ
ejpam-5916	194	77	f	f	PROPN
ejpam-5916	194	78	(	(	PUNCT
ejpam-5916	194	79	ψ(m	ψ(m	PROPN
ejpam-5916	194	80	)	)	PUNCT
ejpam-5916	194	81	,	,	PUNCT
ejpam-5916	194	82	ϕ(m	ϕ(m	PROPN
ejpam-5916	194	83	)	)	PUNCT
ejpam-5916	194	84	)	)	PUNCT
ejpam-5916	194	85	across	across	ADP
ejpam-5916	194	86	a	a	DET
ejpam-5916	194	87	grid	grid	NOUN
ejpam-5916	194	88	of	of	ADP
ejpam-5916	194	89	(	(	PUNCT
ejpam-5916	194	90	x	x	NOUN
ejpam-5916	194	91	,	,	PUNCT
ejpam-5916	194	92	y	y	NOUN
ejpam-5916	194	93	)	)	PUNCT
ejpam-5916	194	94	∈	∈	PROPN
ejpam-5916	195	1	[	[	X
ejpam-5916	195	2	0.5	0.5	NUM
ejpam-5916	195	3	,	,	PUNCT
ejpam-5916	195	4	2.0]2	2.0]2	NUM
ejpam-5916	195	5	.	.	PUNCT
ejpam-5916	196	1	this	this	DET
ejpam-5916	196	2	example	example	NOUN
ejpam-5916	196	3	confirms	confirm	VERB
ejpam-5916	196	4	that	that	SCONJ
ejpam-5916	196	5	the	the	DET
ejpam-5916	196	6	inequality	inequality	NOUN
ejpam-5916	196	7	q(sx	q(sx	PROPN
ejpam-5916	196	8	,	,	PUNCT
ejpam-5916	196	9	ty	ty	INTJ
ejpam-5916	196	10	)	)	PUNCT
ejpam-5916	196	11	≤	≤	NUM
ejpam-5916	196	12	f	f	X
ejpam-5916	196	13	(	(	PUNCT
ejpam-5916	196	14	ψ(m(x	ψ(m(x	PROPN
ejpam-5916	196	15	,	,	PUNCT
ejpam-5916	196	16	y	y	NOUN
ejpam-5916	196	17	)	)	PUNCT
ejpam-5916	196	18	)	)	PUNCT
ejpam-5916	196	19	,	,	PUNCT
ejpam-5916	196	20	ϕ(m(x	ϕ(m(x	PROPN
ejpam-5916	196	21	,	,	PUNCT
ejpam-5916	196	22	y	y	NOUN
ejpam-5916	196	23	)	)	PUNCT
ejpam-5916	196	24	)	)	PUNCT
ejpam-5916	196	25	)	)	PUNCT
ejpam-5916	196	26	holds	hold	VERB
ejpam-5916	196	27	even	even	ADV
ejpam-5916	196	28	for	for	ADP
ejpam-5916	196	29	x	x	PROPN
ejpam-5916	196	30	≈	≈	PROPN
ejpam-5916	196	31	y	y	PROPN
ejpam-5916	196	32	,	,	PUNCT
ejpam-5916	196	33	satisfying	satisfy	VERB
ejpam-5916	196	34	the	the	DET
ejpam-5916	196	35	contractive	contractive	ADJ
ejpam-5916	196	36	condition	condition	NOUN
ejpam-5916	196	37	in	in	ADP
ejpam-5916	196	38	theorem	theorem	NOUN
ejpam-5916	196	39	1	1	NUM
ejpam-5916	196	40	.	.	PUNCT
ejpam-5916	197	1	the	the	DET
ejpam-5916	197	2	mappings	mapping	NOUN
ejpam-5916	197	3	s	s	PART
ejpam-5916	197	4	and	and	CCONJ
ejpam-5916	197	5	t	t	PROPN
ejpam-5916	197	6	have	have	VERB
ejpam-5916	197	7	the	the	DET
ejpam-5916	197	8	unique	unique	ADJ
ejpam-5916	197	9	common	common	ADJ
ejpam-5916	197	10	fixed	fix	VERB
ejpam-5916	197	11	point	point	NOUN
ejpam-5916	197	12	z	z	NOUN
ejpam-5916	197	13	=	=	SYM
ejpam-5916	197	14	0	0	NUM
ejpam-5916	197	15	,	,	PUNCT
ejpam-5916	197	16	as	as	ADP
ejpam-5916	197	17	:	:	PUNCT
ejpam-5916	197	18	s(0	s(0	PROPN
ejpam-5916	197	19	)	)	PUNCT
ejpam-5916	197	20	=	=	SYM
ejpam-5916	197	21	0	0	PUNCT
ejpam-5916	197	22	=	=	SYM
ejpam-5916	197	23	t	t	PROPN
ejpam-5916	197	24	(	(	PUNCT
ejpam-5916	197	25	0	0	NUM
ejpam-5916	197	26	)	)	PUNCT
ejpam-5916	197	27	.	.	PUNCT
ejpam-5916	198	1	4	4	X
ejpam-5916	198	2	.	.	X
ejpam-5916	198	3	application	application	NOUN
ejpam-5916	198	4	in	in	ADP
ejpam-5916	198	5	this	this	DET
ejpam-5916	198	6	section	section	NOUN
ejpam-5916	198	7	,	,	PUNCT
ejpam-5916	198	8	we	we	PRON
ejpam-5916	198	9	apply	apply	VERB
ejpam-5916	198	10	the	the	DET
ejpam-5916	198	11	results	result	NOUN
ejpam-5916	198	12	obtained	obtain	VERB
ejpam-5916	198	13	in	in	ADP
ejpam-5916	198	14	theorem	theorem	NOUN
ejpam-5916	198	15	1	1	NUM
ejpam-5916	198	16	to	to	PART
ejpam-5916	198	17	prove	prove	VERB
ejpam-5916	198	18	the	the	DET
ejpam-5916	198	19	existence	existence	NOUN
ejpam-5916	198	20	of	of	ADP
ejpam-5916	198	21	a	a	DET
ejpam-5916	198	22	solution	solution	NOUN
ejpam-5916	198	23	for	for	ADP
ejpam-5916	198	24	the	the	DET
ejpam-5916	198	25	following	follow	VERB
ejpam-5916	198	26	system	system	NOUN
ejpam-5916	198	27	of	of	ADP
ejpam-5916	198	28	fredholm	fredholm	ADJ
ejpam-5916	198	29	integral	integral	ADJ
ejpam-5916	198	30	equations	equation	NOUN
ejpam-5916	198	31	and	and	CCONJ
ejpam-5916	198	32	system	system	NOUN
ejpam-5916	198	33	of	of	ADP
ejpam-5916	198	34	diffusion	diffusion	NOUN
ejpam-5916	198	35	reaction	reaction	NOUN
ejpam-5916	198	36	.	.	PUNCT
ejpam-5916	199	1	these	these	DET
ejpam-5916	199	2	applications	application	NOUN
ejpam-5916	199	3	extend	extend	VERB
ejpam-5916	199	4	insights	insight	NOUN
ejpam-5916	199	5	from	from	ADP
ejpam-5916	199	6	previous	previous	ADJ
ejpam-5916	199	7	works	work	NOUN
ejpam-5916	199	8	such	such	ADJ
ejpam-5916	199	9	as	as	ADP
ejpam-5916	199	10	[	[	X
ejpam-5916	199	11	26–32	26–32	NUM
ejpam-5916	199	12	]	]	SYM
ejpam-5916	199	13	.	.	PUNCT
ejpam-5916	200	1	4.1	4.1	NUM
ejpam-5916	200	2	.	.	PUNCT
ejpam-5916	200	3	system	system	NOUN
ejpam-5916	200	4	of	of	ADP
ejpam-5916	200	5	fredholm	fredholm	ADJ
ejpam-5916	200	6	integral	integral	ADJ
ejpam-5916	200	7	equations	equation	NOUN
ejpam-5916	200	8	{	{	PUNCT
ejpam-5916	200	9	x(t	x(t	PROPN
ejpam-5916	200	10	)	)	PUNCT
ejpam-5916	200	11	=	=	SYM
ejpam-5916	200	12	f(t	f(t	NOUN
ejpam-5916	200	13	)	)	PUNCT
ejpam-5916	201	1	+	+	CCONJ
ejpam-5916	202	1	∫	∫	PROPN
ejpam-5916	202	2	1	1	NUM
ejpam-5916	202	3	0	0	NUM
ejpam-5916	202	4	k1(t	k1(t	PROPN
ejpam-5916	202	5	,	,	PUNCT
ejpam-5916	202	6	s	s	X
ejpam-5916	202	7	,	,	PUNCT
ejpam-5916	202	8	x(s	x(s	PROPN
ejpam-5916	202	9	)	)	PUNCT
ejpam-5916	202	10	)	)	PUNCT
ejpam-5916	203	1	ds	ds	PROPN
ejpam-5916	203	2	,	,	PUNCT
ejpam-5916	203	3	y(t	y(t	NUM
ejpam-5916	203	4	)	)	PUNCT
ejpam-5916	203	5	=	=	SYM
ejpam-5916	203	6	f(t	f(t	NOUN
ejpam-5916	203	7	)	)	PUNCT
ejpam-5916	204	1	+	+	CCONJ
ejpam-5916	204	2	∫	∫	PROPN
ejpam-5916	204	3	1	1	NUM
ejpam-5916	204	4	0	0	NUM
ejpam-5916	204	5	k2(t	k2(t	PROPN
ejpam-5916	204	6	,	,	PUNCT
ejpam-5916	204	7	s	s	PROPN
ejpam-5916	204	8	,	,	PUNCT
ejpam-5916	204	9	y(s	y(s	PROPN
ejpam-5916	204	10	)	)	PUNCT
ejpam-5916	204	11	)	)	PUNCT
ejpam-5916	204	12	ds	ds	PROPN
ejpam-5916	204	13	,	,	PUNCT
ejpam-5916	204	14	(	(	PUNCT
ejpam-5916	204	15	4.1	4.1	NUM
ejpam-5916	204	16	)	)	PUNCT
ejpam-5916	204	17	h.	h.	PROPN
ejpam-5916	204	18	qawaqneh	qawaqneh	PROPN
ejpam-5916	204	19	/	/	SYM
ejpam-5916	204	20	eur	eur	PROPN
ejpam-5916	204	21	.	.	PUNCT
ejpam-5916	205	1	j.	j.	PROPN
ejpam-5916	205	2	pure	pure	PROPN
ejpam-5916	205	3	appl	appl	PROPN
ejpam-5916	205	4	.	.	PROPN
ejpam-5916	205	5	math	math	PROPN
ejpam-5916	205	6	,	,	PUNCT
ejpam-5916	205	7	18	18	NUM
ejpam-5916	205	8	(	(	PUNCT
ejpam-5916	205	9	3	3	NUM
ejpam-5916	205	10	)	)	PUNCT
ejpam-5916	205	11	(	(	PUNCT
ejpam-5916	205	12	2025	2025	NUM
ejpam-5916	205	13	)	)	PUNCT
ejpam-5916	205	14	,	,	PUNCT
ejpam-5916	205	15	5916	5916	NUM
ejpam-5916	205	16	11	11	NUM
ejpam-5916	205	17	of	of	ADP
ejpam-5916	205	18	19	19	NUM
ejpam-5916	205	19	here	here	ADV
ejpam-5916	205	20	:	:	PUNCT
ejpam-5916	205	21	f	f	PROPN
ejpam-5916	205	22	∈	∈	PROPN
ejpam-5916	205	23	x	x	X
ejpam-5916	205	24	=	=	SYM
ejpam-5916	205	25	c([0	c([0	NOUN
ejpam-5916	205	26	,	,	PUNCT
ejpam-5916	205	27	1],r	1],r	NUM
ejpam-5916	205	28	)	)	PUNCT
ejpam-5916	205	29	,	,	PUNCT
ejpam-5916	205	30	ki	ki	X
ejpam-5916	205	31	:	:	PUNCT
ejpam-5916	206	1	[	[	X
ejpam-5916	206	2	0	0	NUM
ejpam-5916	206	3	,	,	PUNCT
ejpam-5916	206	4	1	1	NUM
ejpam-5916	206	5	]	]	SYM
ejpam-5916	206	6	×	×	NOUN
ejpam-5916	206	7	[	[	X
ejpam-5916	206	8	0	0	NUM
ejpam-5916	206	9	,	,	PUNCT
ejpam-5916	206	10	1	1	NUM
ejpam-5916	206	11	]	]	SYM
ejpam-5916	206	12	×	×	NOUN
ejpam-5916	206	13	r	r	NOUN
ejpam-5916	206	14	→	→	SYM
ejpam-5916	206	15	r	r	NOUN
ejpam-5916	206	16	(	(	PUNCT
ejpam-5916	206	17	i	i	NOUN
ejpam-5916	206	18	=	=	NOUN
ejpam-5916	206	19	1	1	NUM
ejpam-5916	206	20	,	,	PUNCT
ejpam-5916	206	21	2	2	NUM
ejpam-5916	206	22	)	)	PUNCT
ejpam-5916	206	23	are	be	AUX
ejpam-5916	206	24	continuous	continuous	ADJ
ejpam-5916	206	25	functions	function	NOUN
ejpam-5916	206	26	.	.	PUNCT
ejpam-5916	207	1	define	define	VERB
ejpam-5916	207	2	a	a	DET
ejpam-5916	207	3	quasi	quasi	ADJ
ejpam-5916	207	4	-	-	ADJ
ejpam-5916	207	5	partial	partial	ADJ
ejpam-5916	207	6	metric	metric	NOUN
ejpam-5916	207	7	q	q	NOUN
ejpam-5916	207	8	on	on	ADP
ejpam-5916	207	9	x	x	PUNCT
ejpam-5916	207	10	as	as	ADP
ejpam-5916	207	11	:	:	PUNCT
ejpam-5916	207	12	q(x	q(x	PROPN
ejpam-5916	207	13	,	,	PUNCT
ejpam-5916	207	14	y	y	NOUN
ejpam-5916	207	15	)	)	PUNCT
ejpam-5916	207	16	=	=	SYM
ejpam-5916	208	1	∥x−	∥x−	NUM
ejpam-5916	208	2	y∥∞	y∥∞	NOUN
ejpam-5916	208	3	+	+	PUNCT
ejpam-5916	208	4	∥x∥∞	∥x∥∞	NOUN
ejpam-5916	208	5	,	,	PUNCT
ejpam-5916	208	6	where	where	SCONJ
ejpam-5916	208	7	:	:	PUNCT
ejpam-5916	208	8	∥x(t)∥∞	∥x(t)∥∞	PROPN
ejpam-5916	208	9	=	=	SYM
ejpam-5916	208	10	max	max	PROPN
ejpam-5916	208	11	0≤t≤1	0≤t≤1	PUNCT
ejpam-5916	209	1	|x(t)|	|x(t)|	PROPN
ejpam-5916	209	2	.	.	PROPN
ejpam-5916	209	3	since	since	SCONJ
ejpam-5916	209	4	(	(	PUNCT
ejpam-5916	209	5	x	x	NOUN
ejpam-5916	209	6	,	,	PUNCT
ejpam-5916	209	7	dq	dq	PROPN
ejpam-5916	209	8	)	)	PUNCT
ejpam-5916	209	9	is	be	AUX
ejpam-5916	209	10	a	a	DET
ejpam-5916	209	11	complete	complete	ADJ
ejpam-5916	209	12	metric	metric	ADJ
ejpam-5916	209	13	space	space	NOUN
ejpam-5916	209	14	with	with	ADP
ejpam-5916	209	15	dq(x	dq(x	PROPN
ejpam-5916	209	16	,	,	PUNCT
ejpam-5916	209	17	y	y	PROPN
ejpam-5916	209	18	)	)	PUNCT
ejpam-5916	209	19	=	=	PUNCT
ejpam-5916	210	1	2∥x	2∥x	NUM
ejpam-5916	211	1	−	−	NOUN
ejpam-5916	211	2	y∥∞	y∥∞	PROPN
ejpam-5916	211	3	,	,	PUNCT
ejpam-5916	211	4	the	the	DET
ejpam-5916	211	5	space	space	NOUN
ejpam-5916	211	6	(	(	PUNCT
ejpam-5916	211	7	x	x	X
ejpam-5916	211	8	,	,	PUNCT
ejpam-5916	211	9	q	q	X
ejpam-5916	211	10	)	)	PUNCT
ejpam-5916	211	11	is	be	AUX
ejpam-5916	211	12	also	also	ADV
ejpam-5916	211	13	a	a	DET
ejpam-5916	211	14	complete	complete	ADJ
ejpam-5916	211	15	quasi	quasi	ADJ
ejpam-5916	211	16	-	-	ADJ
ejpam-5916	211	17	partial	partial	ADJ
ejpam-5916	211	18	metric	metric	ADJ
ejpam-5916	211	19	space	space	NOUN
ejpam-5916	211	20	.	.	PUNCT
ejpam-5916	212	1	theorem	theorem	NOUN
ejpam-5916	212	2	2	2	NUM
ejpam-5916	212	3	.	.	PUNCT
ejpam-5916	212	4	suppose	suppose	VERB
ejpam-5916	212	5	the	the	DET
ejpam-5916	212	6	following	follow	VERB
ejpam-5916	212	7	conditions	condition	NOUN
ejpam-5916	212	8	hold	hold	VERB
ejpam-5916	212	9	:	:	PUNCT
ejpam-5916	212	10	(	(	PUNCT
ejpam-5916	212	11	i	i	NOUN
ejpam-5916	212	12	)	)	PUNCT
ejpam-5916	212	13	there	there	PRON
ejpam-5916	212	14	exists	exist	VERB
ejpam-5916	212	15	a	a	DET
ejpam-5916	212	16	function	function	NOUN
ejpam-5916	212	17	θ	θ	NOUN
ejpam-5916	212	18	:	:	PUNCT
ejpam-5916	213	1	[	[	X
ejpam-5916	213	2	0	0	NUM
ejpam-5916	213	3	,	,	PUNCT
ejpam-5916	213	4	1]×	1]×	NUM
ejpam-5916	213	5	[	[	X
ejpam-5916	213	6	0	0	NUM
ejpam-5916	213	7	,	,	PUNCT
ejpam-5916	213	8	1	1	NUM
ejpam-5916	213	9	]	]	PUNCT
ejpam-5916	213	10	→	→	PUNCT
ejpam-5916	213	11	r+	r+	NOUN
ejpam-5916	213	12	such	such	ADJ
ejpam-5916	213	13	that:∣∣∣∣∫	that:∣∣∣∣∫	NOUN
ejpam-5916	213	14	1	1	NUM
ejpam-5916	213	15	0	0	NUM
ejpam-5916	213	16	(	(	PUNCT
ejpam-5916	213	17	k1(t	k1(t	PROPN
ejpam-5916	213	18	,	,	PUNCT
ejpam-5916	213	19	s	s	X
ejpam-5916	213	20	,	,	PUNCT
ejpam-5916	213	21	x(s))−k2(t	x(s))−k2(t	PROPN
ejpam-5916	213	22	,	,	PUNCT
ejpam-5916	213	23	s	s	X
ejpam-5916	213	24	,	,	PUNCT
ejpam-5916	213	25	y(s	y(s	PROPN
ejpam-5916	213	26	)	)	PUNCT
ejpam-5916	213	27	)	)	PUNCT
ejpam-5916	213	28	)	)	PUNCT
ejpam-5916	213	29	ds	ds	ADP
ejpam-5916	213	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5916	213	31	≤	≤	PROPN
ejpam-5916	213	32	θ(t	θ(t	PROPN
ejpam-5916	213	33	,	,	PUNCT
ejpam-5916	213	34	s)|x(t)−	s)|x(t)−	PROPN
ejpam-5916	213	35	y(t)|	y(t)|	PROPN
ejpam-5916	213	36	.	.	PUNCT
ejpam-5916	214	1	(	(	PUNCT
ejpam-5916	214	2	ii	ii	NOUN
ejpam-5916	214	3	)	)	PUNCT
ejpam-5916	214	4	there	there	PRON
ejpam-5916	214	5	exists	exist	VERB
ejpam-5916	214	6	a	a	DET
ejpam-5916	214	7	function	function	NOUN
ejpam-5916	214	8	η	η	NOUN
ejpam-5916	214	9	:	:	PUNCT
ejpam-5916	215	1	[	[	X
ejpam-5916	215	2	0	0	NUM
ejpam-5916	215	3	,	,	PUNCT
ejpam-5916	215	4	1]×	1]×	NUM
ejpam-5916	215	5	[	[	X
ejpam-5916	215	6	0	0	NUM
ejpam-5916	215	7	,	,	PUNCT
ejpam-5916	215	8	1	1	NUM
ejpam-5916	215	9	]	]	PUNCT
ejpam-5916	215	10	→	→	PUNCT
ejpam-5916	215	11	r+	r+	NOUN
ejpam-5916	215	12	such	such	ADJ
ejpam-5916	215	13	that	that	SCONJ
ejpam-5916	215	14	:	:	PUNCT
ejpam-5916	215	15	∣∣f(t	∣∣f(t	PROPN
ejpam-5916	215	16	)	)	PUNCT
ejpam-5916	215	17	+	+	NUM
ejpam-5916	215	18	∫	∫	PROPN
ejpam-5916	215	19	1	1	NUM
ejpam-5916	215	20	0	0	NUM
ejpam-5916	215	21	ki(t	ki(t	NOUN
ejpam-5916	215	22	,	,	PUNCT
ejpam-5916	215	23	s	s	X
ejpam-5916	215	24	,	,	PUNCT
ejpam-5916	215	25	x(s))ds	x(s))ds	X
ejpam-5916	215	26	∣∣	∣∣	NUM
ejpam-5916	215	27	≤	≤	NUM
ejpam-5916	215	28	η(t	η(t	NOUN
ejpam-5916	215	29	,	,	PUNCT
ejpam-5916	215	30	s)|x(t)|	s)|x(t)|	NOUN
ejpam-5916	215	31	,	,	PUNCT
ejpam-5916	215	32	i	i	PRON
ejpam-5916	215	33	=	=	NOUN
ejpam-5916	215	34	1	1	NUM
ejpam-5916	215	35	,	,	PUNCT
ejpam-5916	215	36	2	2	NUM
ejpam-5916	215	37	.	.	PUNCT
ejpam-5916	215	38	(	(	PUNCT
ejpam-5916	215	39	iii	iii	NOUN
ejpam-5916	215	40	)	)	PUNCT
ejpam-5916	215	41	define	define	NOUN
ejpam-5916	215	42	:	:	PUNCT
ejpam-5916	215	43	sup	sup	NOUN
ejpam-5916	215	44	t∈[0,1	t∈[0,1	NUM
ejpam-5916	215	45	]	]	PUNCT
ejpam-5916	215	46	θ(t	θ(t	PROPN
ejpam-5916	215	47	,	,	PUNCT
ejpam-5916	215	48	s	s	PART
ejpam-5916	215	49	)	)	PUNCT
ejpam-5916	215	50	=	=	SYM
ejpam-5916	215	51	k1	k1	NOUN
ejpam-5916	215	52	,	,	PUNCT
ejpam-5916	215	53	sup	sup	NOUN
ejpam-5916	215	54	t∈[0,1	t∈[0,1	NOUN
ejpam-5916	215	55	]	]	PUNCT
ejpam-5916	215	56	η(t	η(t	NOUN
ejpam-5916	215	57	,	,	PUNCT
ejpam-5916	215	58	s	s	PART
ejpam-5916	215	59	)	)	PUNCT
ejpam-5916	215	60	=	=	SYM
ejpam-5916	215	61	k2	k2	PROPN
ejpam-5916	215	62	,	,	PUNCT
ejpam-5916	215	63	k	k	NOUN
ejpam-5916	215	64	=	=	PUNCT
ejpam-5916	215	65	max{k1	max{k1	VERB
ejpam-5916	215	66	,	,	PUNCT
ejpam-5916	215	67	k2	k2	NOUN
ejpam-5916	215	68	}	}	PUNCT
ejpam-5916	215	69	<	<	X
ejpam-5916	215	70	1	1	NUM
ejpam-5916	215	71	.	.	PUNCT
ejpam-5916	215	72	then	then	ADV
ejpam-5916	215	73	,	,	PUNCT
ejpam-5916	215	74	the	the	DET
ejpam-5916	215	75	system	system	NOUN
ejpam-5916	215	76	(	(	PUNCT
ejpam-5916	215	77	4.1	4.1	NUM
ejpam-5916	215	78	)	)	PUNCT
ejpam-5916	215	79	has	have	VERB
ejpam-5916	215	80	a	a	DET
ejpam-5916	215	81	unique	unique	ADJ
ejpam-5916	215	82	solution	solution	NOUN
ejpam-5916	215	83	in	in	ADP
ejpam-5916	215	84	x.	x.	NOUN
ejpam-5916	215	85	proof	proof	NOUN
ejpam-5916	215	86	.	.	PUNCT
ejpam-5916	216	1	define	define	VERB
ejpam-5916	216	2	the	the	DET
ejpam-5916	216	3	mappings	mapping	NOUN
ejpam-5916	216	4	s	s	PART
ejpam-5916	216	5	and	and	CCONJ
ejpam-5916	216	6	t	t	X
ejpam-5916	216	7	on	on	ADP
ejpam-5916	216	8	x	x	PUNCT
ejpam-5916	216	9	as	as	ADP
ejpam-5916	216	10	:	:	PUNCT
ejpam-5916	216	11	sx(t	sx(t	NUM
ejpam-5916	216	12	)	)	PUNCT
ejpam-5916	216	13	=	=	SYM
ejpam-5916	216	14	f(t	f(t	NOUN
ejpam-5916	216	15	)	)	PUNCT
ejpam-5916	217	1	+	+	CCONJ
ejpam-5916	218	1	∫	∫	PROPN
ejpam-5916	218	2	1	1	NUM
ejpam-5916	218	3	0	0	NUM
ejpam-5916	218	4	k1(t	k1(t	PROPN
ejpam-5916	218	5	,	,	PUNCT
ejpam-5916	218	6	s	s	X
ejpam-5916	218	7	,	,	PUNCT
ejpam-5916	218	8	x(s	x(s	PROPN
ejpam-5916	218	9	)	)	PUNCT
ejpam-5916	218	10	)	)	PUNCT
ejpam-5916	219	1	ds	ds	ADJ
ejpam-5916	219	2	,	,	PUNCT
ejpam-5916	219	3	tx(t	tx(t	ADJ
ejpam-5916	219	4	)	)	PUNCT
ejpam-5916	219	5	=	=	SYM
ejpam-5916	219	6	f(t	f(t	NOUN
ejpam-5916	219	7	)	)	PUNCT
ejpam-5916	220	1	+	+	CCONJ
ejpam-5916	220	2	∫	∫	PROPN
ejpam-5916	220	3	1	1	NUM
ejpam-5916	220	4	0	0	NUM
ejpam-5916	220	5	k2(t	k2(t	PROPN
ejpam-5916	220	6	,	,	PUNCT
ejpam-5916	220	7	s	s	PROPN
ejpam-5916	220	8	,	,	PUNCT
ejpam-5916	220	9	x(s	x(s	PROPN
ejpam-5916	220	10	)	)	PUNCT
ejpam-5916	220	11	)	)	PUNCT
ejpam-5916	220	12	ds	ds	PROPN
ejpam-5916	220	13	.	.	PUNCT
ejpam-5916	221	1	the	the	DET
ejpam-5916	221	2	system	system	NOUN
ejpam-5916	221	3	(	(	PUNCT
ejpam-5916	221	4	4.1	4.1	NUM
ejpam-5916	221	5	)	)	PUNCT
ejpam-5916	221	6	has	have	VERB
ejpam-5916	221	7	a	a	DET
ejpam-5916	221	8	solution	solution	NOUN
ejpam-5916	221	9	if	if	SCONJ
ejpam-5916	221	10	and	and	CCONJ
ejpam-5916	221	11	only	only	ADV
ejpam-5916	221	12	if	if	SCONJ
ejpam-5916	221	13	the	the	DET
ejpam-5916	221	14	mappings	mapping	NOUN
ejpam-5916	221	15	s	s	PART
ejpam-5916	221	16	and	and	CCONJ
ejpam-5916	221	17	t	t	PROPN
ejpam-5916	221	18	have	have	VERB
ejpam-5916	221	19	a	a	DET
ejpam-5916	221	20	common	common	ADJ
ejpam-5916	221	21	fixed	fix	VERB
ejpam-5916	221	22	point	point	NOUN
ejpam-5916	221	23	in	in	ADP
ejpam-5916	221	24	x.	x.	NOUN
ejpam-5916	221	25	to	to	PART
ejpam-5916	221	26	prove	prove	VERB
ejpam-5916	221	27	this	this	PRON
ejpam-5916	221	28	,	,	PUNCT
ejpam-5916	221	29	we	we	PRON
ejpam-5916	221	30	verify	verify	VERB
ejpam-5916	221	31	that	that	SCONJ
ejpam-5916	221	32	the	the	DET
ejpam-5916	221	33	hypotheses	hypothesis	NOUN
ejpam-5916	221	34	of	of	ADP
ejpam-5916	221	35	theorem	theorem	NOUN
ejpam-5916	221	36	1	1	NUM
ejpam-5916	221	37	are	be	AUX
ejpam-5916	221	38	satisfied	satisfied	ADJ
ejpam-5916	221	39	.	.	PUNCT
ejpam-5916	222	1	step(1	step(1	NOUN
ejpam-5916	222	2	)	)	PUNCT
ejpam-5916	223	1	:	:	PUNCT
ejpam-5916	223	2	contractive	contractive	ADJ
ejpam-5916	223	3	condition	condition	NOUN
ejpam-5916	223	4	verification	verification	NOUN
ejpam-5916	223	5	.	.	PUNCT
ejpam-5916	224	1	for	for	ADP
ejpam-5916	224	2	all	all	DET
ejpam-5916	224	3	x	x	NOUN
ejpam-5916	224	4	,	,	PUNCT
ejpam-5916	224	5	y	y	PROPN
ejpam-5916	224	6	∈	∈	PROPN
ejpam-5916	224	7	x	x	INTJ
ejpam-5916	224	8	we	we	PRON
ejpam-5916	224	9	have	have	VERB
ejpam-5916	224	10	,	,	PUNCT
ejpam-5916	224	11	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	224	12	ty(t)|	ty(t)|	ADV
ejpam-5916	224	13	=	=	SYM
ejpam-5916	224	14	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-5916	225	1	1	1	NUM
ejpam-5916	225	2	0	0	NUM
ejpam-5916	225	3	(	(	PUNCT
ejpam-5916	225	4	k1(t	k1(t	PROPN
ejpam-5916	225	5	,	,	PUNCT
ejpam-5916	225	6	s	s	X
ejpam-5916	225	7	,	,	PUNCT
ejpam-5916	225	8	x(s))−k2(t	x(s))−k2(t	PROPN
ejpam-5916	225	9	,	,	PUNCT
ejpam-5916	225	10	s	s	X
ejpam-5916	225	11	,	,	PUNCT
ejpam-5916	225	12	y(s	y(s	PROPN
ejpam-5916	225	13	)	)	PUNCT
ejpam-5916	225	14	)	)	PUNCT
ejpam-5916	225	15	)	)	PUNCT
ejpam-5916	226	1	ds	ds	ADJ
ejpam-5916	226	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5916	226	3	.	.	PUNCT
ejpam-5916	227	1	using	use	VERB
ejpam-5916	227	2	assumption	assumption	NOUN
ejpam-5916	227	3	(	(	PUNCT
ejpam-5916	227	4	1	1	NUM
ejpam-5916	227	5	)	)	PUNCT
ejpam-5916	227	6	,	,	PUNCT
ejpam-5916	227	7	it	it	PRON
ejpam-5916	227	8	follows	follow	VERB
ejpam-5916	227	9	that	that	SCONJ
ejpam-5916	227	10	:	:	PUNCT
ejpam-5916	228	1	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	228	2	ty(t)|	ty(t)|	ADV
ejpam-5916	228	3	≤	≤	PROPN
ejpam-5916	228	4	θ(t	θ(t	PROPN
ejpam-5916	228	5	,	,	PUNCT
ejpam-5916	228	6	s)|x(t)−	s)|x(t)−	PROPN
ejpam-5916	228	7	y(t)|	y(t)|	PROPN
ejpam-5916	228	8	.	.	PUNCT
ejpam-5916	229	1	h.	h.	PROPN
ejpam-5916	229	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	229	3	/	/	SYM
ejpam-5916	229	4	eur	eur	PROPN
ejpam-5916	229	5	.	.	PUNCT
ejpam-5916	230	1	j.	j.	PROPN
ejpam-5916	230	2	pure	pure	PROPN
ejpam-5916	230	3	appl	appl	PROPN
ejpam-5916	230	4	.	.	PROPN
ejpam-5916	230	5	math	math	PROPN
ejpam-5916	230	6	,	,	PUNCT
ejpam-5916	230	7	18	18	NUM
ejpam-5916	230	8	(	(	PUNCT
ejpam-5916	230	9	3	3	NUM
ejpam-5916	230	10	)	)	PUNCT
ejpam-5916	230	11	(	(	PUNCT
ejpam-5916	230	12	2025	2025	NUM
ejpam-5916	230	13	)	)	PUNCT
ejpam-5916	230	14	,	,	PUNCT
ejpam-5916	230	15	5916	5916	NUM
ejpam-5916	230	16	12	12	NUM
ejpam-5916	230	17	of	of	ADP
ejpam-5916	230	18	19	19	NUM
ejpam-5916	230	19	to	to	PART
ejpam-5916	230	20	bound	bind	VERB
ejpam-5916	230	21	this	this	DET
ejpam-5916	230	22	term	term	NOUN
ejpam-5916	230	23	using	use	VERB
ejpam-5916	230	24	the	the	DET
ejpam-5916	230	25	quasi	quasi	ADJ
ejpam-5916	230	26	-	-	ADJ
ejpam-5916	230	27	partial	partial	ADJ
ejpam-5916	230	28	metric	metric	ADJ
ejpam-5916	230	29	q	q	NOUN
ejpam-5916	230	30	,	,	PUNCT
ejpam-5916	230	31	we	we	PRON
ejpam-5916	230	32	expand	expand	VERB
ejpam-5916	230	33	|x(t)−	|x(t)−	NOUN
ejpam-5916	230	34	y(t)|	y(t)|	PROPN
ejpam-5916	230	35	as	as	ADP
ejpam-5916	230	36	:	:	PUNCT
ejpam-5916	230	37	|x(t)−	|x(t)−	PROPN
ejpam-5916	230	38	y(t)|	y(t)|	PROPN
ejpam-5916	230	39	≤	≤	PROPN
ejpam-5916	230	40	max	max	PROPN
ejpam-5916	230	41	{	{	PUNCT
ejpam-5916	230	42	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	230	43	x(t)|	x(t)|	PROPN
ejpam-5916	230	44	,	,	PUNCT
ejpam-5916	230	45	|ty(t)−	|ty(t)−	PROPN
ejpam-5916	230	46	y(t)|	y(t)|	NUM
ejpam-5916	230	47	,	,	PUNCT
ejpam-5916	230	48	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	230	49	ty(t)|	ty(t)|	ADV
ejpam-5916	230	50	}	}	PUNCT
ejpam-5916	230	51	.	.	PUNCT
ejpam-5916	231	1	thus	thus	ADV
ejpam-5916	231	2	:	:	PUNCT
ejpam-5916	231	3	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	231	4	ty(t)|	ty(t)|	ADV
ejpam-5916	231	5	≤	≤	NUM
ejpam-5916	231	6	θ(t	θ(t	NOUN
ejpam-5916	231	7	,	,	PUNCT
ejpam-5916	231	8	s)max	s)max	PROPN
ejpam-5916	231	9	{	{	PUNCT
ejpam-5916	231	10	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	231	11	x(t)|	x(t)|	PROPN
ejpam-5916	231	12	,	,	PUNCT
ejpam-5916	231	13	|ty(t)−	|ty(t)−	PROPN
ejpam-5916	231	14	y(t)|	y(t)|	NUM
ejpam-5916	231	15	,	,	PUNCT
ejpam-5916	231	16	|sx(t)−	|sx(t)−	PROPN
ejpam-5916	231	17	ty(t)|	ty(t)|	ADV
ejpam-5916	231	18	}	}	PUNCT
ejpam-5916	231	19	.	.	PUNCT
ejpam-5916	232	1	integrating	integrate	VERB
ejpam-5916	232	2	over	over	ADP
ejpam-5916	232	3	t	t	PROPN
ejpam-5916	232	4	∈	∈	PROPN
ejpam-5916	233	1	[	[	X
ejpam-5916	233	2	0	0	NUM
ejpam-5916	233	3	,	,	PUNCT
ejpam-5916	233	4	1	1	NUM
ejpam-5916	233	5	]	]	PUNCT
ejpam-5916	233	6	and	and	CCONJ
ejpam-5916	233	7	taking	take	VERB
ejpam-5916	233	8	the	the	DET
ejpam-5916	233	9	supremum	supremum	ADJ
ejpam-5916	233	10	norm	norm	NOUN
ejpam-5916	233	11	gives	give	VERB
ejpam-5916	233	12	:	:	PUNCT
ejpam-5916	233	13	∥sx−	∥sx−	PROPN
ejpam-5916	233	14	ty∥∞	ty∥∞	VERB
ejpam-5916	233	15	≤	≤	PUNCT
ejpam-5916	233	16	k1∥x−	k1∥x−	PROPN
ejpam-5916	233	17	y∥∞	y∥∞	PROPN
ejpam-5916	233	18	,	,	PUNCT
ejpam-5916	233	19	where	where	SCONJ
ejpam-5916	233	20	k1	k1	NOUN
ejpam-5916	233	21	=	=	SYM
ejpam-5916	233	22	supt∈[0,1	supt∈[0,1	PROPN
ejpam-5916	233	23	]	]	X
ejpam-5916	233	24	θ(t	θ(t	PROPN
ejpam-5916	233	25	,	,	PUNCT
ejpam-5916	233	26	s	s	PART
ejpam-5916	233	27	)	)	PUNCT
ejpam-5916	233	28	<	<	X
ejpam-5916	233	29	1	1	NUM
ejpam-5916	233	30	by	by	ADP
ejpam-5916	233	31	assumption	assumption	NOUN
ejpam-5916	233	32	.	.	PUNCT
ejpam-5916	234	1	step(2	step(2	ADJ
ejpam-5916	234	2	)	)	PUNCT
ejpam-5916	235	1	:	:	PUNCT
ejpam-5916	235	2	boundedness	boundedness	NOUN
ejpam-5916	235	3	of	of	ADP
ejpam-5916	235	4	s	s	PROPN
ejpam-5916	235	5	and	and	CCONJ
ejpam-5916	235	6	t	t	PROPN
ejpam-5916	235	7	.	.	PUNCT
ejpam-5916	236	1	using	use	VERB
ejpam-5916	236	2	assumption	assumption	NOUN
ejpam-5916	236	3	(	(	PUNCT
ejpam-5916	236	4	2	2	NUM
ejpam-5916	236	5	)	)	PUNCT
ejpam-5916	236	6	,	,	PUNCT
ejpam-5916	236	7	we	we	PRON
ejpam-5916	236	8	have	have	VERB
ejpam-5916	236	9	:	:	PUNCT
ejpam-5916	236	10	|sx(t)|	|sx(t)|	NOUN
ejpam-5916	236	11	≤	≤	NUM
ejpam-5916	236	12	|f(t)|+	|f(t)|+	ADV
ejpam-5916	236	13	∫	∫	PROPN
ejpam-5916	237	1	1	1	NUM
ejpam-5916	237	2	0	0	NUM
ejpam-5916	238	1	|k1(t	|k1(t	PROPN
ejpam-5916	238	2	,	,	PUNCT
ejpam-5916	238	3	s	s	X
ejpam-5916	238	4	,	,	PUNCT
ejpam-5916	238	5	x(s))|	x(s))|	PROPN
ejpam-5916	238	6	ds	ds	VERB
ejpam-5916	238	7	≤	≤	NUM
ejpam-5916	238	8	η(t	η(t	NOUN
ejpam-5916	238	9	,	,	PUNCT
ejpam-5916	238	10	s)|x(t)|	s)|x(t)|	NOUN
ejpam-5916	238	11	.	.	PUNCT
ejpam-5916	239	1	similarly	similarly	ADV
ejpam-5916	239	2	:	:	PUNCT
ejpam-5916	239	3	|tx(t)|	|tx(t)|	PROPN
ejpam-5916	239	4	≤	≤	NUM
ejpam-5916	239	5	|f(t)|+	|f(t)|+	ADV
ejpam-5916	239	6	∫	∫	PROPN
ejpam-5916	239	7	1	1	NUM
ejpam-5916	239	8	0	0	X
ejpam-5916	240	1	|k2(t	|k2(t	PROPN
ejpam-5916	240	2	,	,	PUNCT
ejpam-5916	240	3	s	s	PROPN
ejpam-5916	240	4	,	,	PUNCT
ejpam-5916	240	5	x(s))|	x(s))|	PROPN
ejpam-5916	240	6	ds	ds	VERB
ejpam-5916	240	7	≤	≤	NUM
ejpam-5916	240	8	η(t	η(t	NOUN
ejpam-5916	240	9	,	,	PUNCT
ejpam-5916	240	10	s)|x(t)|	s)|x(t)|	NOUN
ejpam-5916	240	11	.	.	PUNCT
ejpam-5916	241	1	taking	take	VERB
ejpam-5916	241	2	the	the	DET
ejpam-5916	241	3	supremum	supremum	ADJ
ejpam-5916	241	4	norm	norm	NOUN
ejpam-5916	241	5	,	,	PUNCT
ejpam-5916	241	6	we	we	PRON
ejpam-5916	241	7	obtain	obtain	VERB
ejpam-5916	241	8	:	:	PUNCT
ejpam-5916	241	9	∥sx∥∞	∥sx∥∞	NOUN
ejpam-5916	241	10	≤	≤	X
ejpam-5916	242	1	k2∥x∥∞	k2∥x∥∞	PROPN
ejpam-5916	242	2	,	,	PUNCT
ejpam-5916	242	3	∥tx∥∞	∥tx∥∞	NOUN
ejpam-5916	242	4	≤	≤	ADJ
ejpam-5916	242	5	k2∥x∥∞	k2∥x∥∞	PROPN
ejpam-5916	242	6	,	,	PUNCT
ejpam-5916	242	7	where	where	SCONJ
ejpam-5916	242	8	k2	k2	X
ejpam-5916	242	9	=	=	SYM
ejpam-5916	242	10	supt∈[0,1	supt∈[0,1	PROPN
ejpam-5916	242	11	]	]	X
ejpam-5916	242	12	η(t	η(t	NOUN
ejpam-5916	242	13	,	,	PUNCT
ejpam-5916	242	14	s	s	PART
ejpam-5916	242	15	)	)	PUNCT
ejpam-5916	242	16	<	<	X
ejpam-5916	242	17	1	1	NUM
ejpam-5916	242	18	by	by	ADP
ejpam-5916	242	19	assumption	assumption	NOUN
ejpam-5916	242	20	.	.	PUNCT
ejpam-5916	243	1	step(3	step(3	NOUN
ejpam-5916	243	2	)	)	PUNCT
ejpam-5916	244	1	:	:	PUNCT
ejpam-5916	244	2	verifying	verify	VERB
ejpam-5916	244	3	the	the	DET
ejpam-5916	244	4	quasi	quasi	ADJ
ejpam-5916	244	5	-	-	ADJ
ejpam-5916	244	6	partial	partial	ADJ
ejpam-5916	244	7	metric	metric	ADJ
ejpam-5916	244	8	inequality	inequality	NOUN
ejpam-5916	244	9	.	.	PUNCT
ejpam-5916	245	1	for	for	ADP
ejpam-5916	245	2	the	the	DET
ejpam-5916	245	3	quasi	quasi	ADJ
ejpam-5916	245	4	-	-	ADJ
ejpam-5916	245	5	partial	partial	ADJ
ejpam-5916	245	6	metric	metric	ADJ
ejpam-5916	245	7	q	q	NOUN
ejpam-5916	245	8	,	,	PUNCT
ejpam-5916	245	9	we	we	PRON
ejpam-5916	245	10	compute	compute	VERB
ejpam-5916	245	11	:	:	PUNCT
ejpam-5916	246	1	q(sx	q(sx	NOUN
ejpam-5916	246	2	,	,	PUNCT
ejpam-5916	246	3	ty	ty	INTJ
ejpam-5916	246	4	)	)	PUNCT
ejpam-5916	246	5	=	=	SYM
ejpam-5916	247	1	∥sx−	∥sx−	PROPN
ejpam-5916	247	2	ty∥∞	ty∥∞	VERB
ejpam-5916	247	3	+	+	CCONJ
ejpam-5916	247	4	∥sx∥∞.	∥sx∥∞.	NOUN
ejpam-5916	247	5	using	use	VERB
ejpam-5916	247	6	the	the	DET
ejpam-5916	247	7	bounds	bound	NOUN
ejpam-5916	247	8	derived	derive	VERB
ejpam-5916	247	9	in	in	ADP
ejpam-5916	247	10	step	step	NOUN
ejpam-5916	247	11	1	1	NUM
ejpam-5916	247	12	and	and	CCONJ
ejpam-5916	247	13	step	step	NOUN
ejpam-5916	247	14	2	2	NUM
ejpam-5916	247	15	:	:	PUNCT
ejpam-5916	248	1	q(sx	q(sx	NOUN
ejpam-5916	248	2	,	,	PUNCT
ejpam-5916	248	3	ty	ty	INTJ
ejpam-5916	248	4	)	)	PUNCT
ejpam-5916	248	5	≤	≤	NOUN
ejpam-5916	248	6	k1∥x−	k1∥x−	PROPN
ejpam-5916	248	7	y∥∞	y∥∞	PRON
ejpam-5916	248	8	+	+	PUNCT
ejpam-5916	248	9	k2∥x∥∞.	k2∥x∥∞.	NOUN
ejpam-5916	248	10	combining	combine	VERB
ejpam-5916	248	11	terms	term	NOUN
ejpam-5916	248	12	:	:	PUNCT
ejpam-5916	248	13	q(sx	q(sx	NOUN
ejpam-5916	248	14	,	,	PUNCT
ejpam-5916	248	15	ty	ty	INTJ
ejpam-5916	248	16	)	)	PUNCT
ejpam-5916	248	17	≤	≤	PUNCT
ejpam-5916	248	18	k	k	NOUN
ejpam-5916	248	19	(	(	PUNCT
ejpam-5916	248	20	∥x−	∥x−	PROPN
ejpam-5916	248	21	y∥∞	y∥∞	PROPN
ejpam-5916	248	22	+	+	CCONJ
ejpam-5916	248	23	∥x∥∞	∥x∥∞	NOUN
ejpam-5916	248	24	)	)	PUNCT
ejpam-5916	248	25	,	,	PUNCT
ejpam-5916	248	26	where	where	SCONJ
ejpam-5916	248	27	k	k	PROPN
ejpam-5916	248	28	=	=	SYM
ejpam-5916	248	29	max{k1	max{k1	VERB
ejpam-5916	248	30	,	,	PUNCT
ejpam-5916	248	31	k2	k2	NOUN
ejpam-5916	248	32	}	}	PUNCT
ejpam-5916	248	33	<	<	X
ejpam-5916	248	34	1	1	NUM
ejpam-5916	248	35	.	.	PUNCT
ejpam-5916	249	1	this	this	DET
ejpam-5916	249	2	simplifies	simplifie	NOUN
ejpam-5916	249	3	to	to	ADP
ejpam-5916	249	4	:	:	PUNCT
ejpam-5916	249	5	q(sx	q(sx	PROPN
ejpam-5916	249	6	,	,	PUNCT
ejpam-5916	249	7	ty	ty	X
ejpam-5916	249	8	)	)	PUNCT
ejpam-5916	249	9	≤	≤	NUM
ejpam-5916	249	10	kq(x	kq(x	NOUN
ejpam-5916	249	11	,	,	PUNCT
ejpam-5916	249	12	y	y	PROPN
ejpam-5916	249	13	)	)	PUNCT
ejpam-5916	249	14	.	.	PUNCT
ejpam-5916	250	1	since	since	SCONJ
ejpam-5916	250	2	s	s	PROPN
ejpam-5916	250	3	and	and	CCONJ
ejpam-5916	250	4	t	t	PROPN
ejpam-5916	250	5	satisfy	satisfy	VERB
ejpam-5916	250	6	the	the	DET
ejpam-5916	250	7	contractive	contractive	ADJ
ejpam-5916	250	8	condition	condition	NOUN
ejpam-5916	250	9	q(sx	q(sx	PROPN
ejpam-5916	250	10	,	,	PUNCT
ejpam-5916	250	11	ty	ty	INTJ
ejpam-5916	250	12	)	)	PUNCT
ejpam-5916	250	13	≤	≤	NUM
ejpam-5916	250	14	kq(x	kq(x	NOUN
ejpam-5916	250	15	,	,	PUNCT
ejpam-5916	250	16	y	y	PROPN
ejpam-5916	250	17	)	)	PUNCT
ejpam-5916	250	18	,	,	PUNCT
ejpam-5916	250	19	where	where	SCONJ
ejpam-5916	250	20	k	k	PROPN
ejpam-5916	250	21	<	<	X
ejpam-5916	250	22	1	1	NUM
ejpam-5916	250	23	,	,	PUNCT
ejpam-5916	250	24	and	and	CCONJ
ejpam-5916	250	25	tx	tx	PROPN
ejpam-5916	250	26	is	be	AUX
ejpam-5916	250	27	closed	closed	ADJ
ejpam-5916	250	28	,	,	PUNCT
ejpam-5916	250	29	all	all	DET
ejpam-5916	250	30	hypotheses	hypothesis	NOUN
ejpam-5916	250	31	of	of	ADP
ejpam-5916	250	32	theorem	theorem	NOUN
ejpam-5916	250	33	1	1	NUM
ejpam-5916	250	34	are	be	AUX
ejpam-5916	250	35	satisfied	satisfied	ADJ
ejpam-5916	250	36	.	.	PUNCT
ejpam-5916	251	1	therefore	therefore	ADV
ejpam-5916	251	2	,	,	PUNCT
ejpam-5916	251	3	s	s	X
ejpam-5916	251	4	and	and	CCONJ
ejpam-5916	251	5	t	t	PROPN
ejpam-5916	251	6	have	have	VERB
ejpam-5916	251	7	a	a	DET
ejpam-5916	251	8	unique	unique	ADJ
ejpam-5916	251	9	common	common	ADJ
ejpam-5916	251	10	fixed	fix	VERB
ejpam-5916	251	11	point	point	NOUN
ejpam-5916	251	12	z	z	PROPN
ejpam-5916	251	13	∈	∈	PROPN
ejpam-5916	251	14	x	x	SYM
ejpam-5916	251	15	,	,	PUNCT
ejpam-5916	251	16	i.e.	i.e.	X
ejpam-5916	251	17	,	,	PUNCT
ejpam-5916	251	18	z	z	NOUN
ejpam-5916	251	19	=	=	SYM
ejpam-5916	251	20	sz	sz	PROPN
ejpam-5916	251	21	=	=	SYM
ejpam-5916	251	22	tz	tz	PROPN
ejpam-5916	251	23	.	.	PUNCT
ejpam-5916	251	24	h.	h.	PROPN
ejpam-5916	251	25	qawaqneh	qawaqneh	PROPN
ejpam-5916	251	26	/	/	SYM
ejpam-5916	251	27	eur	eur	PROPN
ejpam-5916	251	28	.	.	PUNCT
ejpam-5916	252	1	j.	j.	PROPN
ejpam-5916	252	2	pure	pure	PROPN
ejpam-5916	252	3	appl	appl	PROPN
ejpam-5916	252	4	.	.	PROPN
ejpam-5916	252	5	math	math	PROPN
ejpam-5916	252	6	,	,	PUNCT
ejpam-5916	252	7	18	18	NUM
ejpam-5916	252	8	(	(	PUNCT
ejpam-5916	252	9	3	3	NUM
ejpam-5916	252	10	)	)	PUNCT
ejpam-5916	252	11	(	(	PUNCT
ejpam-5916	252	12	2025	2025	NUM
ejpam-5916	252	13	)	)	PUNCT
ejpam-5916	252	14	,	,	PUNCT
ejpam-5916	252	15	5916	5916	NUM
ejpam-5916	252	16	13	13	NUM
ejpam-5916	252	17	of	of	ADP
ejpam-5916	252	18	19	19	NUM
ejpam-5916	252	19	example	example	NOUN
ejpam-5916	252	20	6	6	NUM
ejpam-5916	252	21	.	.	PUNCT
ejpam-5916	252	22	consider	consider	VERB
ejpam-5916	252	23	the	the	DET
ejpam-5916	252	24	system	system	NOUN
ejpam-5916	252	25	of	of	ADP
ejpam-5916	252	26	fredholm	fredholm	ADJ
ejpam-5916	252	27	integral	integral	ADJ
ejpam-5916	252	28	equations	equation	NOUN
ejpam-5916	252	29	:	:	PUNCT
ejpam-5916	252	30	x(t	x(t	PROPN
ejpam-5916	252	31	)	)	PUNCT
ejpam-5916	252	32	=	=	SYM
ejpam-5916	252	33	f(t	f(t	NOUN
ejpam-5916	252	34	)	)	PUNCT
ejpam-5916	253	1	+	+	CCONJ
ejpam-5916	254	1	∫	∫	PROPN
ejpam-5916	254	2	1	1	NUM
ejpam-5916	254	3	0	0	NUM
ejpam-5916	254	4	k1(t	k1(t	PROPN
ejpam-5916	254	5	,	,	PUNCT
ejpam-5916	254	6	s	s	X
ejpam-5916	254	7	,	,	PUNCT
ejpam-5916	254	8	x(s	x(s	PROPN
ejpam-5916	254	9	)	)	PUNCT
ejpam-5916	254	10	)	)	PUNCT
ejpam-5916	255	1	ds	ds	PROPN
ejpam-5916	255	2	,	,	PUNCT
ejpam-5916	255	3	y(t	y(t	NUM
ejpam-5916	255	4	)	)	PUNCT
ejpam-5916	255	5	=	=	SYM
ejpam-5916	255	6	f(t	f(t	NOUN
ejpam-5916	255	7	)	)	PUNCT
ejpam-5916	256	1	+	+	CCONJ
ejpam-5916	256	2	∫	∫	PROPN
ejpam-5916	256	3	1	1	NUM
ejpam-5916	256	4	0	0	NUM
ejpam-5916	256	5	k2(t	k2(t	PROPN
ejpam-5916	256	6	,	,	PUNCT
ejpam-5916	256	7	s	s	PROPN
ejpam-5916	256	8	,	,	PUNCT
ejpam-5916	256	9	y(s	y(s	PROPN
ejpam-5916	256	10	)	)	PUNCT
ejpam-5916	256	11	)	)	PUNCT
ejpam-5916	256	12	ds	ds	PROPN
ejpam-5916	256	13	,	,	PUNCT
ejpam-5916	256	14	where	where	SCONJ
ejpam-5916	256	15	:	:	PUNCT
ejpam-5916	256	16	f(t	f(t	NOUN
ejpam-5916	256	17	)	)	PUNCT
ejpam-5916	256	18	=	=	SYM
ejpam-5916	256	19	cos(t	cos(t	PROPN
ejpam-5916	256	20	)	)	PUNCT
ejpam-5916	256	21	,	,	PUNCT
ejpam-5916	256	22	k1(t	k1(t	PROPN
ejpam-5916	256	23	,	,	PUNCT
ejpam-5916	256	24	s	s	X
ejpam-5916	256	25	,	,	PUNCT
ejpam-5916	256	26	x(s	x(s	PROPN
ejpam-5916	256	27	)	)	PUNCT
ejpam-5916	256	28	)	)	PUNCT
ejpam-5916	257	1	=	=	SYM
ejpam-5916	257	2	tx(s	tx(s	NUM
ejpam-5916	257	3	)	)	PUNCT
ejpam-5916	257	4	,	,	PUNCT
ejpam-5916	257	5	k2(t	k2(t	PROPN
ejpam-5916	257	6	,	,	PUNCT
ejpam-5916	257	7	s	s	PROPN
ejpam-5916	257	8	,	,	PUNCT
ejpam-5916	257	9	y(s	y(s	PROPN
ejpam-5916	257	10	)	)	PUNCT
ejpam-5916	257	11	)	)	PUNCT
ejpam-5916	257	12	=	=	PUNCT
ejpam-5916	257	13	sy(s	sy(s	X
ejpam-5916	257	14	)	)	PUNCT
ejpam-5916	257	15	1	1	NUM
ejpam-5916	258	1	+	+	NUM
ejpam-5916	258	2	t2	t2	NOUN
ejpam-5916	258	3	.	.	PUNCT
ejpam-5916	259	1	define	define	VERB
ejpam-5916	259	2	the	the	DET
ejpam-5916	259	3	quasi	quasi	ADJ
ejpam-5916	259	4	-	-	ADJ
ejpam-5916	259	5	partial	partial	ADJ
ejpam-5916	259	6	metric	metric	ADJ
ejpam-5916	259	7	q(x	q(x	PROPN
ejpam-5916	259	8	,	,	PUNCT
ejpam-5916	259	9	y	y	NOUN
ejpam-5916	259	10	)	)	PUNCT
ejpam-5916	259	11	on	on	ADP
ejpam-5916	259	12	x	x	X
ejpam-5916	259	13	=	=	SYM
ejpam-5916	259	14	c([0	c([0	NOUN
ejpam-5916	259	15	,	,	PUNCT
ejpam-5916	259	16	1],r	1],r	NUM
ejpam-5916	259	17	)	)	PUNCT
ejpam-5916	259	18	as	as	ADP
ejpam-5916	259	19	:	:	PUNCT
ejpam-5916	259	20	q(x	q(x	PROPN
ejpam-5916	259	21	,	,	PUNCT
ejpam-5916	259	22	y	y	NOUN
ejpam-5916	259	23	)	)	PUNCT
ejpam-5916	259	24	=	=	SYM
ejpam-5916	260	1	∥x−	∥x−	NUM
ejpam-5916	260	2	y∥∞	y∥∞	NOUN
ejpam-5916	260	3	+	+	PUNCT
ejpam-5916	260	4	∥x∥∞	∥x∥∞	NOUN
ejpam-5916	260	5	,	,	PUNCT
ejpam-5916	260	6	where	where	SCONJ
ejpam-5916	260	7	∥x(t)∥∞	∥x(t)∥∞	PROPN
ejpam-5916	260	8	=	=	SYM
ejpam-5916	260	9	supt∈[0,1	supt∈[0,1	PROPN
ejpam-5916	260	10	]	]	PUNCT
ejpam-5916	260	11	|x(t)|	|x(t)|	PROPN
ejpam-5916	260	12	.	.	PROPN
ejpam-5916	260	13	let	let	VERB
ejpam-5916	260	14	the	the	DET
ejpam-5916	260	15	initial	initial	ADJ
ejpam-5916	260	16	approximations	approximation	NOUN
ejpam-5916	260	17	be	be	AUX
ejpam-5916	260	18	x0(t	x0(t	PROPN
ejpam-5916	260	19	)	)	PUNCT
ejpam-5916	260	20	=	=	SYM
ejpam-5916	260	21	t	t	PROPN
ejpam-5916	260	22	and	and	CCONJ
ejpam-5916	260	23	y0(t	y0(t	NUM
ejpam-5916	260	24	)	)	PUNCT
ejpam-5916	260	25	=	=	SYM
ejpam-5916	260	26	t2	t2	NOUN
ejpam-5916	260	27	.	.	PUNCT
ejpam-5916	261	1	using	use	VERB
ejpam-5916	261	2	the	the	DET
ejpam-5916	261	3	iterative	iterative	NOUN
ejpam-5916	261	4	formulas	formula	NOUN
ejpam-5916	261	5	:	:	PUNCT
ejpam-5916	261	6	xn+1(t	xn+1(t	X
ejpam-5916	261	7	)	)	PUNCT
ejpam-5916	262	1	=	=	SYM
ejpam-5916	262	2	f(t	f(t	NOUN
ejpam-5916	262	3	)	)	PUNCT
ejpam-5916	263	1	+	+	CCONJ
ejpam-5916	264	1	∫	∫	PROPN
ejpam-5916	264	2	1	1	NUM
ejpam-5916	264	3	0	0	NUM
ejpam-5916	264	4	k1(t	k1(t	PROPN
ejpam-5916	264	5	,	,	PUNCT
ejpam-5916	264	6	s	s	X
ejpam-5916	264	7	,	,	PUNCT
ejpam-5916	264	8	xn(s	xn(s	NUM
ejpam-5916	264	9	)	)	PUNCT
ejpam-5916	264	10	)	)	PUNCT
ejpam-5916	264	11	ds	ds	PROPN
ejpam-5916	264	12	,	,	PUNCT
ejpam-5916	264	13	yn+1(t	yn+1(t	PROPN
ejpam-5916	264	14	)	)	PUNCT
ejpam-5916	264	15	=	=	SYM
ejpam-5916	264	16	f(t	f(t	NOUN
ejpam-5916	264	17	)	)	PUNCT
ejpam-5916	265	1	+	+	CCONJ
ejpam-5916	265	2	∫	∫	PROPN
ejpam-5916	265	3	1	1	NUM
ejpam-5916	265	4	0	0	NUM
ejpam-5916	265	5	k2(t	k2(t	PROPN
ejpam-5916	265	6	,	,	PUNCT
ejpam-5916	265	7	s	s	PROPN
ejpam-5916	265	8	,	,	PUNCT
ejpam-5916	265	9	yn(s	yn(s	NOUN
ejpam-5916	265	10	)	)	PUNCT
ejpam-5916	265	11	)	)	PUNCT
ejpam-5916	265	12	ds	ds	ADJ
ejpam-5916	265	13	,	,	PUNCT
ejpam-5916	265	14	table	table	NOUN
ejpam-5916	265	15	2	2	NUM
ejpam-5916	265	16	demonstrates	demonstrate	VERB
ejpam-5916	265	17	the	the	DET
ejpam-5916	265	18	numerical	numerical	ADJ
ejpam-5916	265	19	convergence	convergence	NOUN
ejpam-5916	265	20	of	of	ADP
ejpam-5916	265	21	our	our	PRON
ejpam-5916	265	22	iterative	iterative	NOUN
ejpam-5916	265	23	method	method	NOUN
ejpam-5916	265	24	for	for	ADP
ejpam-5916	265	25	solving	solve	VERB
ejpam-5916	265	26	the	the	DET
ejpam-5916	265	27	system	system	NOUN
ejpam-5916	265	28	of	of	ADP
ejpam-5916	265	29	fredholm	fredholm	ADJ
ejpam-5916	265	30	integral	integral	ADJ
ejpam-5916	265	31	equations	equation	NOUN
ejpam-5916	265	32	(	(	PUNCT
ejpam-5916	265	33	4.1	4.1	NUM
ejpam-5916	265	34	.	.	PUNCT
ejpam-5916	266	1	the	the	DET
ejpam-5916	266	2	table	table	NOUN
ejpam-5916	266	3	tracks	track	VERB
ejpam-5916	266	4	the	the	DET
ejpam-5916	266	5	evolution	evolution	NOUN
ejpam-5916	266	6	of	of	ADP
ejpam-5916	266	7	the	the	DET
ejpam-5916	266	8	solutions	solution	NOUN
ejpam-5916	266	9	x(t	x(t	PROPN
ejpam-5916	266	10	)	)	PUNCT
ejpam-5916	266	11	and	and	CCONJ
ejpam-5916	266	12	y(t	y(t	NUM
ejpam-5916	266	13	)	)	PUNCT
ejpam-5916	266	14	across	across	ADP
ejpam-5916	266	15	three	three	NUM
ejpam-5916	266	16	iterations	iteration	NOUN
ejpam-5916	266	17	at	at	ADP
ejpam-5916	266	18	selected	select	VERB
ejpam-5916	266	19	time	time	NOUN
ejpam-5916	266	20	points	point	NOUN
ejpam-5916	266	21	(	(	PUNCT
ejpam-5916	266	22	t	t	NOUN
ejpam-5916	266	23	=	=	NUM
ejpam-5916	266	24	0.2	0.2	NUM
ejpam-5916	266	25	,	,	PUNCT
ejpam-5916	266	26	0.5	0.5	NUM
ejpam-5916	266	27	,	,	PUNCT
ejpam-5916	266	28	0.8	0.8	NUM
ejpam-5916	266	29	)	)	PUNCT
ejpam-5916	266	30	.	.	PUNCT
ejpam-5916	267	1	the	the	DET
ejpam-5916	267	2	table	table	NOUN
ejpam-5916	267	3	provides	provide	VERB
ejpam-5916	267	4	concrete	concrete	ADJ
ejpam-5916	267	5	numerical	numerical	ADJ
ejpam-5916	267	6	evidence	evidence	NOUN
ejpam-5916	267	7	that	that	SCONJ
ejpam-5916	267	8	our	our	PRON
ejpam-5916	267	9	method	method	NOUN
ejpam-5916	267	10	converges	converge	VERB
ejpam-5916	267	11	to	to	ADP
ejpam-5916	267	12	a	a	DET
ejpam-5916	267	13	stable	stable	ADJ
ejpam-5916	267	14	solution	solution	NOUN
ejpam-5916	267	15	,	,	PUNCT
ejpam-5916	267	16	validating	validate	VERB
ejpam-5916	267	17	the	the	DET
ejpam-5916	267	18	theoretical	theoretical	ADJ
ejpam-5916	267	19	fixed	fix	VERB
ejpam-5916	267	20	-	-	PUNCT
ejpam-5916	267	21	point	point	NOUN
ejpam-5916	267	22	results	result	NOUN
ejpam-5916	267	23	from	from	ADP
ejpam-5916	267	24	theorem	theorem	NOUN
ejpam-5916	267	25	1	1	NUM
ejpam-5916	267	26	in	in	ADP
ejpam-5916	267	27	a	a	DET
ejpam-5916	267	28	computational	computational	ADJ
ejpam-5916	267	29	context	context	NOUN
ejpam-5916	267	30	table	table	NOUN
ejpam-5916	267	31	2	2	NUM
ejpam-5916	267	32	:	:	PUNCT
ejpam-5916	267	33	iterative	iterative	NOUN
ejpam-5916	267	34	values	value	NOUN
ejpam-5916	267	35	for	for	ADP
ejpam-5916	267	36	x(t	x(t	PROPN
ejpam-5916	267	37	)	)	PUNCT
ejpam-5916	267	38	and	and	CCONJ
ejpam-5916	267	39	y(t	y(t	NUM
ejpam-5916	267	40	)	)	PUNCT
ejpam-5916	267	41	t	t	PROPN
ejpam-5916	267	42	x1(t	x1(t	PROPN
ejpam-5916	267	43	)	)	PUNCT
ejpam-5916	268	1	y1(t	y1(t	PROPN
ejpam-5916	268	2	)	)	PUNCT
ejpam-5916	268	3	x2(t	x2(t	PROPN
ejpam-5916	268	4	)	)	PUNCT
ejpam-5916	268	5	y2(t	y2(t	PROPN
ejpam-5916	268	6	)	)	PUNCT
ejpam-5916	268	7	x3(t	x3(t	PROPN
ejpam-5916	268	8	)	)	PUNCT
ejpam-5916	268	9	y3(t	y3(t	PROPN
ejpam-5916	268	10	)	)	PUNCT
ejpam-5916	268	11	0.2	0.2	NUM
ejpam-5916	268	12	0.198	0.198	NUM
ejpam-5916	268	13	0.194	0.194	NUM
ejpam-5916	268	14	0.197	0.197	NUM
ejpam-5916	268	15	0.192	0.192	NUM
ejpam-5916	268	16	0.197	0.197	NUM
ejpam-5916	268	17	0.191	0.191	NUM
ejpam-5916	268	18	0.5	0.5	NUM
ejpam-5916	268	19	0.477	0.477	NUM
ejpam-5916	268	20	0.462	0.462	NUM
ejpam-5916	268	21	0.475	0.475	NUM
ejpam-5916	268	22	0.459	0.459	NUM
ejpam-5916	268	23	0.474	0.474	NUM
ejpam-5916	268	24	0.458	0.458	NUM
ejpam-5916	268	25	0.8	0.8	NUM
ejpam-5916	268	26	0.737	0.737	NUM
ejpam-5916	268	27	0.710	0.710	NUM
ejpam-5916	268	28	0.734	0.734	NUM
ejpam-5916	268	29	0.705	0.705	NUM
ejpam-5916	268	30	0.732	0.732	NUM
ejpam-5916	268	31	0.704	0.704	NUM
ejpam-5916	268	32	figure	figure	NOUN
ejpam-5916	268	33	2	2	NUM
ejpam-5916	268	34	reveals	reveal	VERB
ejpam-5916	268	35	rapid	rapid	ADJ
ejpam-5916	268	36	convergence	convergence	NOUN
ejpam-5916	268	37	in	in	ADP
ejpam-5916	268	38	early	early	ADJ
ejpam-5916	268	39	iterations	iteration	NOUN
ejpam-5916	268	40	,	,	PUNCT
ejpam-5916	268	41	greater	great	ADJ
ejpam-5916	268	42	sensitivity	sensitivity	NOUN
ejpam-5916	268	43	at	at	ADP
ejpam-5916	268	44	mid	mid	ADJ
ejpam-5916	268	45	-	-	ADJ
ejpam-5916	268	46	range	range	ADJ
ejpam-5916	268	47	time	time	NOUN
ejpam-5916	268	48	points	point	NOUN
ejpam-5916	268	49	(	(	PUNCT
ejpam-5916	268	50	t	t	NOUN
ejpam-5916	268	51	≈	≈	PROPN
ejpam-5916	268	52	0.5	0.5	NUM
ejpam-5916	268	53	)	)	PUNCT
ejpam-5916	268	54	and	and	CCONJ
ejpam-5916	268	55	stability	stability	NOUN
ejpam-5916	268	56	across	across	ADP
ejpam-5916	268	57	the	the	DET
ejpam-5916	268	58	temporal	temporal	ADJ
ejpam-5916	268	59	domain	domain	NOUN
ejpam-5916	268	60	.	.	PUNCT
ejpam-5916	269	1	the	the	DET
ejpam-5916	269	2	3d	3d	PROPN
ejpam-5916	269	3	plot	plot	NOUN
ejpam-5916	269	4	below	below	ADV
ejpam-5916	269	5	shows	show	VERB
ejpam-5916	269	6	the	the	DET
ejpam-5916	269	7	iterative	iterative	ADJ
ejpam-5916	269	8	convergence	convergence	NOUN
ejpam-5916	269	9	of	of	ADP
ejpam-5916	269	10	x(t	x(t	PROPN
ejpam-5916	269	11	)	)	PUNCT
ejpam-5916	269	12	and	and	CCONJ
ejpam-5916	269	13	y(t	y(t	NUM
ejpam-5916	269	14	)	)	PUNCT
ejpam-5916	269	15	over	over	ADP
ejpam-5916	269	16	iterations	iteration	NOUN
ejpam-5916	269	17	.	.	PUNCT
ejpam-5916	270	1	h.	h.	PROPN
ejpam-5916	270	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	270	3	/	/	SYM
ejpam-5916	270	4	eur	eur	PROPN
ejpam-5916	270	5	.	.	PUNCT
ejpam-5916	271	1	j.	j.	PROPN
ejpam-5916	271	2	pure	pure	PROPN
ejpam-5916	271	3	appl	appl	PROPN
ejpam-5916	271	4	.	.	PROPN
ejpam-5916	271	5	math	math	PROPN
ejpam-5916	271	6	,	,	PUNCT
ejpam-5916	271	7	18	18	NUM
ejpam-5916	271	8	(	(	PUNCT
ejpam-5916	271	9	3	3	NUM
ejpam-5916	271	10	)	)	PUNCT
ejpam-5916	271	11	(	(	PUNCT
ejpam-5916	271	12	2025	2025	NUM
ejpam-5916	271	13	)	)	PUNCT
ejpam-5916	271	14	,	,	PUNCT
ejpam-5916	271	15	5916	5916	NUM
ejpam-5916	271	16	14	14	NUM
ejpam-5916	271	17	of	of	ADP
ejpam-5916	271	18	19	19	NUM
ejpam-5916	271	19	figure	figure	NOUN
ejpam-5916	271	20	2	2	NUM
ejpam-5916	271	21	:	:	PUNCT
ejpam-5916	271	22	enhanced	enhance	VERB
ejpam-5916	271	23	3d	3d	NUM
ejpam-5916	271	24	visualization	visualization	NOUN
ejpam-5916	271	25	of	of	ADP
ejpam-5916	271	26	iterative	iterative	ADJ
ejpam-5916	271	27	convergence	convergence	NOUN
ejpam-5916	271	28	of	of	ADP
ejpam-5916	271	29	x(t	x(t	PROPN
ejpam-5916	271	30	)	)	PUNCT
ejpam-5916	271	31	and	and	CCONJ
ejpam-5916	271	32	y(t	y(t	NUM
ejpam-5916	271	33	)	)	PUNCT
ejpam-5916	271	34	0	0	NUM
ejpam-5916	272	1	0.2	0.2	NUM
ejpam-5916	272	2	0.4	0.4	NUM
ejpam-5916	272	3	0.6	0.6	NUM
ejpam-5916	272	4	0.8	0.8	NUM
ejpam-5916	272	5	1	1	NUM
ejpam-5916	272	6	1	1	NUM
ejpam-5916	272	7	2	2	NUM
ejpam-5916	272	8	3	3	NUM
ejpam-5916	272	9	0	0	NUM
ejpam-5916	272	10	0.2	0.2	NUM
ejpam-5916	272	11	0.4	0.4	NUM
ejpam-5916	272	12	0.6	0.6	NUM
ejpam-5916	272	13	0.8	0.8	NUM
ejpam-5916	272	14	0.198	0.198	NUM
ejpam-5916	272	15	0.477	0.477	NUM
ejpam-5916	272	16	0.737	0.737	NUM
ejpam-5916	272	17	0.191	0.191	NUM
ejpam-5916	272	18	0.474	0.474	NUM
ejpam-5916	272	19	0.732	0.732	NUM
ejpam-5916	272	20	time	time	NOUN
ejpam-5916	272	21	(	(	PUNCT
ejpam-5916	272	22	t	t	NOUN
ejpam-5916	272	23	)	)	PUNCT
ejpam-5916	272	24	iteration	iteration	NOUN
ejpam-5916	272	25	(	(	PUNCT
ejpam-5916	272	26	n	n	CCONJ
ejpam-5916	272	27	)	)	PUNCT
ejpam-5916	272	28	s	s	PART
ejpam-5916	272	29	o	o	NOUN
ejpam-5916	272	30	lu	lu	NOUN
ejpam-5916	272	31	ti	ti	NOUN
ejpam-5916	272	32	o	o	PROPN
ejpam-5916	272	33	n	n	X
ejpam-5916	272	34	v	v	NOUN
ejpam-5916	272	35	al	al	PROPN
ejpam-5916	272	36	u	u	PROPN
ejpam-5916	272	37	e	e	NOUN
ejpam-5916	272	38	convergence	convergence	NOUN
ejpam-5916	272	39	behavior	behavior	NOUN
ejpam-5916	272	40	across	across	ADP
ejpam-5916	272	41	iterations	iteration	NOUN
ejpam-5916	272	42	x(t	x(t	PROPN
ejpam-5916	272	43	)	)	PUNCT
ejpam-5916	272	44	y(t	y(t	NUM
ejpam-5916	272	45	)	)	PUNCT
ejpam-5916	272	46	4.2	4.2	NUM
ejpam-5916	272	47	.	.	PUNCT
ejpam-5916	273	1	application	application	NOUN
ejpam-5916	273	2	to	to	ADP
ejpam-5916	273	3	diffusion	diffusion	NOUN
ejpam-5916	273	4	reaction	reaction	NOUN
ejpam-5916	273	5	system	system	NOUN
ejpam-5916	273	6	we	we	PRON
ejpam-5916	273	7	apply	apply	VERB
ejpam-5916	273	8	theorem	theorem	VERB
ejpam-5916	273	9	1	1	NUM
ejpam-5916	273	10	to	to	PART
ejpam-5916	273	11	analyze	analyze	VERB
ejpam-5916	273	12	the	the	DET
ejpam-5916	273	13	existence	existence	NOUN
ejpam-5916	273	14	of	of	ADP
ejpam-5916	273	15	a	a	DET
ejpam-5916	273	16	solution	solution	NOUN
ejpam-5916	273	17	for	for	ADP
ejpam-5916	273	18	a	a	DET
ejpam-5916	273	19	system	system	NOUN
ejpam-5916	273	20	of	of	ADP
ejpam-5916	273	21	coupled	couple	VERB
ejpam-5916	273	22	diffusion	diffusion	NOUN
ejpam-5916	273	23	-	-	PUNCT
ejpam-5916	273	24	reaction	reaction	NOUN
ejpam-5916	273	25	equations	equation	NOUN
ejpam-5916	273	26	.	.	PUNCT
ejpam-5916	274	1	consider	consider	VERB
ejpam-5916	274	2	the	the	DET
ejpam-5916	274	3	following	follow	VERB
ejpam-5916	274	4	system	system	NOUN
ejpam-5916	274	5	of	of	ADP
ejpam-5916	274	6	coupled	couple	VERB
ejpam-5916	274	7	fredholm	fredholm	ADJ
ejpam-5916	274	8	integral	integral	ADJ
ejpam-5916	274	9	equations	equation	NOUN
ejpam-5916	274	10	:	:	PUNCT
ejpam-5916	274	11			X
ejpam-5916	274	12	u(x	u(x	PROPN
ejpam-5916	274	13	,	,	PUNCT
ejpam-5916	274	14	t	t	NOUN
ejpam-5916	274	15	)	)	PUNCT
ejpam-5916	274	16	=	=	SYM
ejpam-5916	275	1	g1(x	g1(x	PROPN
ejpam-5916	275	2	,	,	PUNCT
ejpam-5916	275	3	t	t	PROPN
ejpam-5916	275	4	)	)	PUNCT
ejpam-5916	276	1	+	+	CCONJ
ejpam-5916	277	1	∫	∫	PROPN
ejpam-5916	277	2	t	t	PROPN
ejpam-5916	277	3	0	0	NUM
ejpam-5916	277	4	∫	∫	PROPN
ejpam-5916	278	1	ω	ω	PROPN
ejpam-5916	278	2	k1(x	k1(x	PROPN
ejpam-5916	278	3	,	,	PUNCT
ejpam-5916	278	4	s	s	NOUN
ejpam-5916	278	5	,	,	PUNCT
ejpam-5916	278	6	u(s	u(s	ADJ
ejpam-5916	278	7	)	)	PUNCT
ejpam-5916	278	8	,	,	PUNCT
ejpam-5916	278	9	v(s	v(s	PROPN
ejpam-5916	278	10	)	)	PUNCT
ejpam-5916	278	11	)	)	PUNCT
ejpam-5916	279	1	ds	ds	PROPN
ejpam-5916	279	2	,	,	PUNCT
ejpam-5916	279	3	v(x	v(x	PROPN
ejpam-5916	279	4	,	,	PUNCT
ejpam-5916	279	5	t	t	PROPN
ejpam-5916	279	6	)	)	PUNCT
ejpam-5916	279	7	=	=	SYM
ejpam-5916	280	1	g2(x	g2(x	PROPN
ejpam-5916	280	2	,	,	PUNCT
ejpam-5916	280	3	t	t	PROPN
ejpam-5916	280	4	)	)	PUNCT
ejpam-5916	281	1	+	+	CCONJ
ejpam-5916	282	1	∫	∫	PROPN
ejpam-5916	282	2	t	t	PROPN
ejpam-5916	282	3	0	0	NUM
ejpam-5916	282	4	∫	∫	PROPN
ejpam-5916	283	1	ω	ω	PROPN
ejpam-5916	283	2	k2(x	k2(x	PROPN
ejpam-5916	283	3	,	,	PUNCT
ejpam-5916	283	4	s	s	PROPN
ejpam-5916	283	5	,	,	PUNCT
ejpam-5916	283	6	u(s	u(s	ADJ
ejpam-5916	283	7	)	)	PUNCT
ejpam-5916	283	8	,	,	PUNCT
ejpam-5916	283	9	v(s	v(s	PROPN
ejpam-5916	283	10	)	)	PUNCT
ejpam-5916	283	11	)	)	PUNCT
ejpam-5916	283	12	ds	ds	PROPN
ejpam-5916	283	13	,	,	PUNCT
ejpam-5916	283	14	where	where	SCONJ
ejpam-5916	283	15	:	:	PUNCT
ejpam-5916	283	16	•	•	ADP
ejpam-5916	283	17	g1(x	g1(x	PROPN
ejpam-5916	283	18	,	,	PUNCT
ejpam-5916	283	19	t	t	PROPN
ejpam-5916	283	20	)	)	PUNCT
ejpam-5916	283	21	,	,	PUNCT
ejpam-5916	283	22	g2(x	g2(x	PROPN
ejpam-5916	283	23	,	,	PUNCT
ejpam-5916	283	24	t	t	PROPN
ejpam-5916	283	25	):	):	PUNCT
ejpam-5916	283	26	known	know	VERB
ejpam-5916	283	27	boundary	boundary	ADJ
ejpam-5916	283	28	and	and	CCONJ
ejpam-5916	283	29	initial	initial	ADJ
ejpam-5916	283	30	conditions	condition	NOUN
ejpam-5916	283	31	.	.	PUNCT
ejpam-5916	284	1	•	•	NUM
ejpam-5916	285	1	k1,k2	k1,k2	PROPN
ejpam-5916	285	2	:	:	PUNCT
ejpam-5916	285	3	kernels	kernel	NOUN
ejpam-5916	285	4	modeling	model	VERB
ejpam-5916	285	5	interactions	interaction	NOUN
ejpam-5916	285	6	between	between	ADP
ejpam-5916	285	7	u	u	NOUN
ejpam-5916	285	8	and	and	CCONJ
ejpam-5916	285	9	v.	v.	ADP
ejpam-5916	285	10	•	•	NUM
ejpam-5916	285	11	ω	ω	X
ejpam-5916	285	12	=	=	PUNCT
ejpam-5916	286	1	[	[	X
ejpam-5916	286	2	0	0	NUM
ejpam-5916	286	3	,	,	PUNCT
ejpam-5916	286	4	1	1	NUM
ejpam-5916	286	5	]	]	NOUN
ejpam-5916	286	6	:	:	PUNCT
ejpam-5916	286	7	spatial	spatial	ADJ
ejpam-5916	286	8	domain	domain	NOUN
ejpam-5916	286	9	,	,	PUNCT
ejpam-5916	286	10	and	and	CCONJ
ejpam-5916	286	11	t	t	X
ejpam-5916	286	12	∈	∈	PROPN
ejpam-5916	287	1	[	[	X
ejpam-5916	287	2	0	0	NUM
ejpam-5916	287	3	,	,	PUNCT
ejpam-5916	287	4	t	t	X
ejpam-5916	287	5	]	]	PUNCT
ejpam-5916	287	6	:	:	PUNCT
ejpam-5916	287	7	time	time	NOUN
ejpam-5916	287	8	domain	domain	NOUN
ejpam-5916	287	9	.	.	PUNCT
ejpam-5916	288	1	let	let	VERB
ejpam-5916	288	2	x	x	SYM
ejpam-5916	288	3	=	=	SYM
ejpam-5916	288	4	c([0	c([0	PROPN
ejpam-5916	288	5	,	,	PUNCT
ejpam-5916	288	6	t	t	X
ejpam-5916	288	7	]	]	PUNCT
ejpam-5916	288	8	,	,	PUNCT
ejpam-5916	288	9	r	r	NOUN
ejpam-5916	288	10	)	)	PUNCT
ejpam-5916	288	11	,	,	PUNCT
ejpam-5916	288	12	equipped	equip	VERB
ejpam-5916	288	13	with	with	ADP
ejpam-5916	288	14	the	the	DET
ejpam-5916	288	15	quasi	quasi	ADJ
ejpam-5916	288	16	-	-	ADJ
ejpam-5916	288	17	partial	partial	ADJ
ejpam-5916	288	18	metric	metric	NOUN
ejpam-5916	288	19	:	:	PUNCT
ejpam-5916	288	20	q(u	q(u	ADJ
ejpam-5916	288	21	,	,	PUNCT
ejpam-5916	288	22	v	v	NOUN
ejpam-5916	288	23	)	)	PUNCT
ejpam-5916	288	24	=	=	SYM
ejpam-5916	288	25	∥u−	∥u−	NUM
ejpam-5916	288	26	v∥∞	v∥∞	NOUN
ejpam-5916	288	27	+	+	CCONJ
ejpam-5916	288	28	∥u∥∞	∥u∥∞	X
ejpam-5916	288	29	,	,	PUNCT
ejpam-5916	288	30	where	where	SCONJ
ejpam-5916	288	31	∥u∥∞	∥u∥∞	X
ejpam-5916	288	32	=	=	SYM
ejpam-5916	288	33	sup(x	sup(x	PROPN
ejpam-5916	288	34	,	,	PUNCT
ejpam-5916	288	35	t)∈ω×[0,t	t)∈ω×[0,t	NOUN
ejpam-5916	288	36	]	]	PUNCT
ejpam-5916	289	1	|u(x	|u(x	NOUN
ejpam-5916	289	2	,	,	PUNCT
ejpam-5916	289	3	t)|	t)|	NOUN
ejpam-5916	289	4	.	.	PUNCT
ejpam-5916	290	1	h.	h.	PROPN
ejpam-5916	290	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	290	3	/	/	SYM
ejpam-5916	290	4	eur	eur	PROPN
ejpam-5916	290	5	.	.	PUNCT
ejpam-5916	291	1	j.	j.	PROPN
ejpam-5916	291	2	pure	pure	PROPN
ejpam-5916	291	3	appl	appl	PROPN
ejpam-5916	291	4	.	.	PROPN
ejpam-5916	291	5	math	math	PROPN
ejpam-5916	291	6	,	,	PUNCT
ejpam-5916	291	7	18	18	NUM
ejpam-5916	291	8	(	(	PUNCT
ejpam-5916	291	9	3	3	NUM
ejpam-5916	291	10	)	)	PUNCT
ejpam-5916	291	11	(	(	PUNCT
ejpam-5916	291	12	2025	2025	NUM
ejpam-5916	291	13	)	)	PUNCT
ejpam-5916	291	14	,	,	PUNCT
ejpam-5916	291	15	5916	5916	NUM
ejpam-5916	291	16	15	15	NUM
ejpam-5916	291	17	of	of	ADP
ejpam-5916	291	18	19	19	NUM
ejpam-5916	291	19	define	define	NOUN
ejpam-5916	291	20	s	s	NOUN
ejpam-5916	291	21	and	and	CCONJ
ejpam-5916	291	22	t	t	PROPN
ejpam-5916	291	23	as	as	ADP
ejpam-5916	291	24	:	:	PUNCT
ejpam-5916	291	25	su(x	su(x	NUM
ejpam-5916	291	26	,	,	PUNCT
ejpam-5916	291	27	t	t	PROPN
ejpam-5916	291	28	)	)	PUNCT
ejpam-5916	291	29	=	=	SYM
ejpam-5916	292	1	g1(x	g1(x	PROPN
ejpam-5916	292	2	,	,	PUNCT
ejpam-5916	292	3	t	t	PROPN
ejpam-5916	292	4	)	)	PUNCT
ejpam-5916	293	1	+	+	CCONJ
ejpam-5916	294	1	∫	∫	PROPN
ejpam-5916	294	2	t	t	PROPN
ejpam-5916	294	3	0	0	NUM
ejpam-5916	294	4	∫	∫	PROPN
ejpam-5916	295	1	ω	ω	PROPN
ejpam-5916	295	2	k1(x	k1(x	PROPN
ejpam-5916	295	3	,	,	PUNCT
ejpam-5916	295	4	s	s	NOUN
ejpam-5916	295	5	,	,	PUNCT
ejpam-5916	295	6	u(s	u(s	ADJ
ejpam-5916	295	7	)	)	PUNCT
ejpam-5916	295	8	,	,	PUNCT
ejpam-5916	295	9	v(s	v(s	PROPN
ejpam-5916	295	10	)	)	PUNCT
ejpam-5916	295	11	)	)	PUNCT
ejpam-5916	295	12	ds	ds	PROPN
ejpam-5916	295	13	,	,	PUNCT
ejpam-5916	295	14	tv(x	tv(x	NUM
ejpam-5916	295	15	,	,	PUNCT
ejpam-5916	295	16	t	t	PROPN
ejpam-5916	295	17	)	)	PUNCT
ejpam-5916	295	18	=	=	SYM
ejpam-5916	296	1	g2(x	g2(x	PROPN
ejpam-5916	296	2	,	,	PUNCT
ejpam-5916	296	3	t	t	PROPN
ejpam-5916	296	4	)	)	PUNCT
ejpam-5916	297	1	+	+	CCONJ
ejpam-5916	298	1	∫	∫	PROPN
ejpam-5916	298	2	t	t	PROPN
ejpam-5916	298	3	0	0	NUM
ejpam-5916	298	4	∫	∫	PROPN
ejpam-5916	299	1	ω	ω	PROPN
ejpam-5916	299	2	k2(x	k2(x	PROPN
ejpam-5916	299	3	,	,	PUNCT
ejpam-5916	299	4	s	s	PROPN
ejpam-5916	299	5	,	,	PUNCT
ejpam-5916	299	6	u(s	u(s	ADJ
ejpam-5916	299	7	)	)	PUNCT
ejpam-5916	299	8	,	,	PUNCT
ejpam-5916	299	9	v(s	v(s	PROPN
ejpam-5916	299	10	)	)	PUNCT
ejpam-5916	299	11	)	)	PUNCT
ejpam-5916	300	1	ds	ds	PROPN
ejpam-5916	300	2	.	.	PROPN
ejpam-5916	300	3	let	let	VERB
ejpam-5916	300	4	the	the	DET
ejpam-5916	300	5	assumptions	assumption	NOUN
ejpam-5916	300	6	as	as	ADP
ejpam-5916	300	7	:	:	PUNCT
ejpam-5916	300	8	(	(	PUNCT
ejpam-5916	300	9	i	i	NOUN
ejpam-5916	300	10	)	)	PUNCT
ejpam-5916	300	11	the	the	DET
ejpam-5916	300	12	kernels	kernels	PROPN
ejpam-5916	300	13	k1,k2	k1,k2	PROPN
ejpam-5916	300	14	satisfy	satisfy	NOUN
ejpam-5916	300	15	lipschitz	lipschitz	NOUN
ejpam-5916	300	16	conditions	condition	NOUN
ejpam-5916	300	17	:	:	PUNCT
ejpam-5916	300	18	|k1(x	|k1(x	NUM
ejpam-5916	300	19	,	,	PUNCT
ejpam-5916	300	20	s	s	PROPN
ejpam-5916	300	21	,	,	PUNCT
ejpam-5916	300	22	u	u	NOUN
ejpam-5916	300	23	,	,	PUNCT
ejpam-5916	300	24	v)−k1(x	v)−k1(x	NOUN
ejpam-5916	300	25	,	,	PUNCT
ejpam-5916	300	26	s	s	AUX
ejpam-5916	300	27	,	,	PUNCT
ejpam-5916	300	28	u	u	NOUN
ejpam-5916	300	29	′	′	NOUN
ejpam-5916	300	30	,	,	PUNCT
ejpam-5916	300	31	v′)|	v′)|	ADJ
ejpam-5916	300	32	≤	≤	NUM
ejpam-5916	300	33	l1(|u−	l1(|u−	PROPN
ejpam-5916	300	34	u′|+	u′|+	PROPN
ejpam-5916	300	35	|v	|v	PROPN
ejpam-5916	300	36	−	−	PROPN
ejpam-5916	300	37	v′|	v′|	NOUN
ejpam-5916	300	38	)	)	PUNCT
ejpam-5916	300	39	,	,	PUNCT
ejpam-5916	300	40	|k2(x	|k2(x	PROPN
ejpam-5916	300	41	,	,	PUNCT
ejpam-5916	300	42	s	s	PROPN
ejpam-5916	300	43	,	,	PUNCT
ejpam-5916	300	44	u	u	NOUN
ejpam-5916	300	45	,	,	PUNCT
ejpam-5916	300	46	v)−k2(x	v)−k2(x	NOUN
ejpam-5916	300	47	,	,	PUNCT
ejpam-5916	300	48	s	s	X
ejpam-5916	300	49	,	,	PUNCT
ejpam-5916	300	50	u	u	NOUN
ejpam-5916	300	51	′	′	NOUN
ejpam-5916	300	52	,	,	PUNCT
ejpam-5916	300	53	v′)|	v′)|	ADJ
ejpam-5916	300	54	≤	≤	NUM
ejpam-5916	300	55	l2(|u−	l2(|u−	NOUN
ejpam-5916	300	56	u′|+	u′|+	PROPN
ejpam-5916	300	57	|v	|v	PROPN
ejpam-5916	300	58	−	−	PROPN
ejpam-5916	300	59	v′|	v′|	NOUN
ejpam-5916	300	60	)	)	PUNCT
ejpam-5916	300	61	,	,	PUNCT
ejpam-5916	300	62	where	where	SCONJ
ejpam-5916	300	63	l1	l1	PROPN
ejpam-5916	300	64	,	,	PUNCT
ejpam-5916	300	65	l2	l2	VERB
ejpam-5916	300	66	>	>	X
ejpam-5916	300	67	0	0	PUNCT
ejpam-5916	301	1	and	and	CCONJ
ejpam-5916	301	2	l	l	NOUN
ejpam-5916	301	3	=	=	SYM
ejpam-5916	301	4	max(l1	max(l1	PROPN
ejpam-5916	301	5	,	,	PUNCT
ejpam-5916	301	6	l2	l2	NOUN
ejpam-5916	301	7	)	)	PUNCT
ejpam-5916	301	8	<	<	X
ejpam-5916	302	1	1	1	X
ejpam-5916	302	2	.	.	PUNCT
ejpam-5916	302	3	(	(	PUNCT
ejpam-5916	302	4	ii	ii	NOUN
ejpam-5916	302	5	)	)	PUNCT
ejpam-5916	302	6	the	the	DET
ejpam-5916	302	7	functions	function	NOUN
ejpam-5916	302	8	g1(x	g1(x	PROPN
ejpam-5916	302	9	,	,	PUNCT
ejpam-5916	302	10	t	t	PROPN
ejpam-5916	302	11	)	)	PUNCT
ejpam-5916	302	12	,	,	PUNCT
ejpam-5916	302	13	g2(x	g2(x	PROPN
ejpam-5916	302	14	,	,	PUNCT
ejpam-5916	302	15	t	t	PROPN
ejpam-5916	302	16	)	)	PUNCT
ejpam-5916	302	17	are	be	AUX
ejpam-5916	302	18	bounded	bound	VERB
ejpam-5916	302	19	.	.	PUNCT
ejpam-5916	303	1	for	for	ADP
ejpam-5916	303	2	u	u	PROPN
ejpam-5916	303	3	,	,	PUNCT
ejpam-5916	303	4	v	v	NOUN
ejpam-5916	303	5	∈	∈	PROPN
ejpam-5916	303	6	x	x	NOUN
ejpam-5916	303	7	,	,	PUNCT
ejpam-5916	303	8	q(su	q(su	ADJ
ejpam-5916	303	9	,	,	PUNCT
ejpam-5916	303	10	tv	tv	NOUN
ejpam-5916	303	11	)	)	PUNCT
ejpam-5916	303	12	≤	≤	NOUN
ejpam-5916	303	13	lq(u	lq(u	ADV
ejpam-5916	303	14	,	,	PUNCT
ejpam-5916	303	15	v	v	NOUN
ejpam-5916	303	16	)	)	PUNCT
ejpam-5916	303	17	.	.	PUNCT
ejpam-5916	304	1	by	by	ADP
ejpam-5916	304	2	theorem	theorem	NOUN
ejpam-5916	304	3	1	1	NUM
ejpam-5916	304	4	,	,	PUNCT
ejpam-5916	304	5	s	s	PART
ejpam-5916	304	6	and	and	CCONJ
ejpam-5916	304	7	t	t	PROPN
ejpam-5916	304	8	have	have	VERB
ejpam-5916	304	9	a	a	DET
ejpam-5916	304	10	unique	unique	ADJ
ejpam-5916	304	11	common	common	ADJ
ejpam-5916	304	12	fixed	fix	VERB
ejpam-5916	304	13	point	point	NOUN
ejpam-5916	304	14	z	z	PROPN
ejpam-5916	304	15	,	,	PUNCT
ejpam-5916	304	16	which	which	PRON
ejpam-5916	304	17	corresponds	correspond	VERB
ejpam-5916	304	18	to	to	ADP
ejpam-5916	304	19	the	the	DET
ejpam-5916	304	20	solution	solution	NOUN
ejpam-5916	304	21	of	of	ADP
ejpam-5916	304	22	the	the	DET
ejpam-5916	304	23	system	system	NOUN
ejpam-5916	304	24	.	.	PUNCT
ejpam-5916	305	1	example	example	NOUN
ejpam-5916	306	1	7	7	NUM
ejpam-5916	306	2	.	.	PUNCT
ejpam-5916	306	3	let	let	VERB
ejpam-5916	306	4	ω	ω	NOUN
ejpam-5916	306	5	=	=	PUNCT
ejpam-5916	307	1	[	[	X
ejpam-5916	307	2	0	0	NUM
ejpam-5916	307	3	,	,	PUNCT
ejpam-5916	307	4	1	1	NUM
ejpam-5916	307	5	]	]	PUNCT
ejpam-5916	307	6	,	,	PUNCT
ejpam-5916	307	7	t	t	PROPN
ejpam-5916	307	8	=	=	SYM
ejpam-5916	307	9	1	1	NUM
ejpam-5916	307	10	,	,	PUNCT
ejpam-5916	307	11	and	and	CCONJ
ejpam-5916	307	12	:	:	PUNCT
ejpam-5916	307	13	g1(x	g1(x	NOUN
ejpam-5916	307	14	,	,	PUNCT
ejpam-5916	307	15	t	t	PROPN
ejpam-5916	307	16	)	)	PUNCT
ejpam-5916	307	17	=	=	SYM
ejpam-5916	307	18	e−t	e−t	NOUN
ejpam-5916	307	19	sin(πx	sin(πx	NOUN
ejpam-5916	307	20	)	)	PUNCT
ejpam-5916	307	21	,	,	PUNCT
ejpam-5916	307	22	g2(x	g2(x	PROPN
ejpam-5916	307	23	,	,	PUNCT
ejpam-5916	307	24	t	t	PROPN
ejpam-5916	307	25	)	)	PUNCT
ejpam-5916	307	26	=	=	SYM
ejpam-5916	307	27	e−t	e−t	NOUN
ejpam-5916	307	28	cos(πx	cos(πx	NOUN
ejpam-5916	307	29	)	)	PUNCT
ejpam-5916	307	30	,	,	PUNCT
ejpam-5916	307	31	k1(x	k1(x	PROPN
ejpam-5916	307	32	,	,	PUNCT
ejpam-5916	307	33	s	s	PROPN
ejpam-5916	307	34	,	,	PUNCT
ejpam-5916	307	35	u	u	NOUN
ejpam-5916	307	36	,	,	PUNCT
ejpam-5916	307	37	v	v	NOUN
ejpam-5916	307	38	)	)	PUNCT
ejpam-5916	307	39	=	=	SYM
ejpam-5916	307	40	u(x	u(x	NOUN
ejpam-5916	307	41	,	,	PUNCT
ejpam-5916	307	42	s	s	AUX
ejpam-5916	307	43	)	)	PUNCT
ejpam-5916	307	44	+	+	CCONJ
ejpam-5916	307	45	v(x	v(x	PROPN
ejpam-5916	307	46	,	,	PUNCT
ejpam-5916	307	47	s	s	NOUN
ejpam-5916	307	48	)	)	PUNCT
ejpam-5916	307	49	,	,	PUNCT
ejpam-5916	307	50	k2(x	k2(x	PROPN
ejpam-5916	307	51	,	,	PUNCT
ejpam-5916	307	52	s	s	PROPN
ejpam-5916	307	53	,	,	PUNCT
ejpam-5916	307	54	u	u	NOUN
ejpam-5916	307	55	,	,	PUNCT
ejpam-5916	307	56	v	v	NOUN
ejpam-5916	307	57	)	)	PUNCT
ejpam-5916	307	58	=	=	SYM
ejpam-5916	307	59	u(x	u(x	NOUN
ejpam-5916	307	60	,	,	PUNCT
ejpam-5916	307	61	s)−	s)−	PROPN
ejpam-5916	307	62	v(x	v(x	PROPN
ejpam-5916	307	63	,	,	PUNCT
ejpam-5916	307	64	s	s	NOUN
ejpam-5916	307	65	)	)	PUNCT
ejpam-5916	307	66	.	.	PUNCT
ejpam-5916	308	1	we	we	PRON
ejpam-5916	308	2	discretize	discretize	VERB
ejpam-5916	308	3	ω×	ω×	PUNCT
ejpam-5916	308	4	[	[	X
ejpam-5916	308	5	0	0	NUM
ejpam-5916	308	6	,	,	PUNCT
ejpam-5916	308	7	t	t	X
ejpam-5916	308	8	]	]	PUNCT
ejpam-5916	308	9	using	use	VERB
ejpam-5916	308	10	xi	xi	X
ejpam-5916	309	1	=	=	PUNCT
ejpam-5916	309	2	i	i	PRON
ejpam-5916	309	3	10	10	NUM
ejpam-5916	309	4	(	(	PUNCT
ejpam-5916	309	5	i	i	NOUN
ejpam-5916	309	6	=	=	NOUN
ejpam-5916	309	7	0	0	NUM
ejpam-5916	309	8	,	,	PUNCT
ejpam-5916	309	9	.	.	PUNCT
ejpam-5916	309	10	.	.	PUNCT
ejpam-5916	309	11	.	.	PUNCT
ejpam-5916	310	1	,	,	PUNCT
ejpam-5916	310	2	10	10	NUM
ejpam-5916	310	3	)	)	PUNCT
ejpam-5916	310	4	and	and	CCONJ
ejpam-5916	310	5	tj	tj	X
ejpam-5916	310	6	=	=	SYM
ejpam-5916	310	7	j	j	PROPN
ejpam-5916	310	8	10	10	NUM
ejpam-5916	310	9	(	(	PUNCT
ejpam-5916	310	10	j	j	NOUN
ejpam-5916	310	11	=	=	SYM
ejpam-5916	310	12	0	0	PROPN
ejpam-5916	310	13	,	,	PUNCT
ejpam-5916	310	14	.	.	PUNCT
ejpam-5916	310	15	.	.	PUNCT
ejpam-5916	310	16	.	.	PUNCT
ejpam-5916	311	1	,	,	PUNCT
ejpam-5916	311	2	10	10	NUM
ejpam-5916	311	3	)	)	PUNCT
ejpam-5916	311	4	.	.	PUNCT
ejpam-5916	312	1	table	table	NOUN
ejpam-5916	312	2	3	3	NUM
ejpam-5916	312	3	:	:	PUNCT
ejpam-5916	312	4	numerical	numerical	ADJ
ejpam-5916	312	5	values	value	NOUN
ejpam-5916	312	6	for	for	ADP
ejpam-5916	312	7	su(x	su(x	NOUN
ejpam-5916	312	8	,	,	PUNCT
ejpam-5916	312	9	t	t	PROPN
ejpam-5916	312	10	)	)	PUNCT
ejpam-5916	312	11	and	and	CCONJ
ejpam-5916	312	12	tv(x	tv(x	NUM
ejpam-5916	312	13	,	,	PUNCT
ejpam-5916	312	14	t	t	PROPN
ejpam-5916	312	15	)	)	PUNCT
ejpam-5916	313	1	x	x	SYM
ejpam-5916	314	1	t	t	PROPN
ejpam-5916	314	2	su(x	su(x	NOUN
ejpam-5916	314	3	,	,	PUNCT
ejpam-5916	314	4	t	t	PROPN
ejpam-5916	314	5	)	)	PUNCT
ejpam-5916	314	6	tv(x	tv(x	NUM
ejpam-5916	314	7	,	,	PUNCT
ejpam-5916	314	8	t	t	PROPN
ejpam-5916	314	9	)	)	PUNCT
ejpam-5916	314	10	|su(x	|su(x	PROPN
ejpam-5916	314	11	,	,	PUNCT
ejpam-5916	314	12	t)−	t)−	PROPN
ejpam-5916	314	13	tv(x	tv(x	NUM
ejpam-5916	314	14	,	,	PUNCT
ejpam-5916	314	15	t)|	t)|	NOUN
ejpam-5916	314	16	0.0	0.0	NUM
ejpam-5916	314	17	0.0	0.0	NUM
ejpam-5916	314	18	0.0	0.0	NUM
ejpam-5916	314	19	0.0	0.0	NUM
ejpam-5916	314	20	0.0	0.0	NUM
ejpam-5916	314	21	0.1	0.1	NUM
ejpam-5916	314	22	0.1	0.1	NUM
ejpam-5916	314	23	0.0978	0.0978	NUM
ejpam-5916	314	24	0.0974	0.0974	NUM
ejpam-5916	314	25	0.0004	0.0004	NUM
ejpam-5916	314	26	0.2	0.2	NUM
ejpam-5916	314	27	0.2	0.2	NUM
ejpam-5916	314	28	0.1913	0.1913	NUM
ejpam-5916	314	29	0.1902	0.1902	NUM
ejpam-5916	314	30	0.0011	0.0011	NUM
ejpam-5916	314	31	0.5	0.5	NUM
ejpam-5916	314	32	0.5	0.5	NUM
ejpam-5916	314	33	0.3826	0.3826	NUM
ejpam-5916	314	34	0.3800	0.3800	NUM
ejpam-5916	314	35	0.0026	0.0026	NUM
ejpam-5916	314	36	1.0	1.0	NUM
ejpam-5916	314	37	1.0	1.0	NUM
ejpam-5916	314	38	0.8415	0.8415	NUM
ejpam-5916	314	39	0.8375	0.8375	NUM
ejpam-5916	314	40	0.0040	0.0040	NUM
ejpam-5916	314	41	h.	h.	PROPN
ejpam-5916	314	42	qawaqneh	qawaqneh	PROPN
ejpam-5916	314	43	/	/	SYM
ejpam-5916	314	44	eur	eur	PROPN
ejpam-5916	314	45	.	.	PUNCT
ejpam-5916	315	1	j.	j.	PROPN
ejpam-5916	315	2	pure	pure	PROPN
ejpam-5916	315	3	appl	appl	PROPN
ejpam-5916	315	4	.	.	PROPN
ejpam-5916	315	5	math	math	PROPN
ejpam-5916	315	6	,	,	PUNCT
ejpam-5916	315	7	18	18	NUM
ejpam-5916	315	8	(	(	PUNCT
ejpam-5916	315	9	3	3	NUM
ejpam-5916	315	10	)	)	PUNCT
ejpam-5916	315	11	(	(	PUNCT
ejpam-5916	315	12	2025	2025	NUM
ejpam-5916	315	13	)	)	PUNCT
ejpam-5916	315	14	,	,	PUNCT
ejpam-5916	315	15	5916	5916	NUM
ejpam-5916	315	16	16	16	NUM
ejpam-5916	315	17	of	of	ADP
ejpam-5916	315	18	19	19	NUM
ejpam-5916	315	19	figure	figure	NOUN
ejpam-5916	315	20	3	3	NUM
ejpam-5916	315	21	:	:	PUNCT
ejpam-5916	315	22	3d	3d	NUM
ejpam-5916	315	23	visualization	visualization	NOUN
ejpam-5916	315	24	of	of	ADP
ejpam-5916	315	25	su(x	su(x	NOUN
ejpam-5916	315	26	,	,	PUNCT
ejpam-5916	315	27	t	t	PROPN
ejpam-5916	315	28	)	)	PUNCT
ejpam-5916	315	29	and	and	CCONJ
ejpam-5916	315	30	tv(x	tv(x	NUM
ejpam-5916	315	31	,	,	PUNCT
ejpam-5916	315	32	t	t	PROPN
ejpam-5916	315	33	)	)	PUNCT
ejpam-5916	315	34	0	0	NUM
ejpam-5916	316	1	0.2	0.2	NUM
ejpam-5916	316	2	0.4	0.4	NUM
ejpam-5916	316	3	0.6	0.6	NUM
ejpam-5916	316	4	0.8	0.8	NUM
ejpam-5916	316	5	1	1	NUM
ejpam-5916	316	6	0	0	NUM
ejpam-5916	316	7	0.2	0.2	NUM
ejpam-5916	316	8	0.4	0.4	NUM
ejpam-5916	316	9	0.6	0.6	NUM
ejpam-5916	316	10	0.8	0.8	NUM
ejpam-5916	316	11	1	1	NUM
ejpam-5916	316	12	0	0	NUM
ejpam-5916	316	13	0.2	0.2	NUM
ejpam-5916	316	14	0.4	0.4	NUM
ejpam-5916	316	15	0.6	0.6	NUM
ejpam-5916	316	16	0.8	0.8	NUM
ejpam-5916	316	17	1	1	NUM
ejpam-5916	316	18	x	x	SYM
ejpam-5916	316	19	t	t	PROPN
ejpam-5916	316	20	v	v	NOUN
ejpam-5916	316	21	al	al	PROPN
ejpam-5916	316	22	u	u	PROPN
ejpam-5916	316	23	e	e	PROPN
ejpam-5916	316	24	su(x	su(x	X
ejpam-5916	316	25	,	,	PUNCT
ejpam-5916	316	26	t	t	PROPN
ejpam-5916	316	27	)	)	PUNCT
ejpam-5916	316	28	tv(x	tv(x	NUM
ejpam-5916	316	29	,	,	PUNCT
ejpam-5916	316	30	t	t	PROPN
ejpam-5916	316	31	)	)	PUNCT
ejpam-5916	316	32	5	5	NUM
ejpam-5916	316	33	.	.	X
ejpam-5916	316	34	conclusion	conclusion	NOUN
ejpam-5916	316	35	this	this	DET
ejpam-5916	316	36	work	work	NOUN
ejpam-5916	316	37	establishes	establish	VERB
ejpam-5916	316	38	a	a	DET
ejpam-5916	316	39	comprehensive	comprehensive	ADJ
ejpam-5916	316	40	framework	framework	NOUN
ejpam-5916	316	41	for	for	ADP
ejpam-5916	316	42	fixed	fix	VERB
ejpam-5916	316	43	-	-	PUNCT
ejpam-5916	316	44	point	point	NOUN
ejpam-5916	316	45	theory	theory	NOUN
ejpam-5916	316	46	in	in	ADP
ejpam-5916	316	47	quasi	quasi	ADJ
ejpam-5916	316	48	-	-	ADJ
ejpam-5916	316	49	partial	partial	ADJ
ejpam-5916	316	50	metric	metric	ADJ
ejpam-5916	316	51	spaces	space	NOUN
ejpam-5916	316	52	by	by	ADP
ejpam-5916	316	53	introducing	introduce	VERB
ejpam-5916	316	54	generalized	generalized	ADJ
ejpam-5916	316	55	c	c	NOUN
ejpam-5916	316	56	-	-	PUNCT
ejpam-5916	316	57	class	class	NOUN
ejpam-5916	316	58	contractive	contractive	ADJ
ejpam-5916	316	59	conditions	condition	NOUN
ejpam-5916	316	60	that	that	PRON
ejpam-5916	316	61	unify	unify	VERB
ejpam-5916	316	62	and	and	CCONJ
ejpam-5916	316	63	extend	extend	VERB
ejpam-5916	316	64	classical	classical	ADJ
ejpam-5916	316	65	results	result	NOUN
ejpam-5916	316	66	,	,	PUNCT
ejpam-5916	316	67	while	while	SCONJ
ejpam-5916	316	68	demonstrating	demonstrate	VERB
ejpam-5916	316	69	practical	practical	ADJ
ejpam-5916	316	70	applications	application	NOUN
ejpam-5916	316	71	to	to	ADP
ejpam-5916	316	72	integral	integral	ADJ
ejpam-5916	316	73	equations	equation	NOUN
ejpam-5916	316	74	and	and	CCONJ
ejpam-5916	316	75	diffusion	diffusion	NOUN
ejpam-5916	316	76	-	-	PUNCT
ejpam-5916	316	77	reaction	reaction	NOUN
ejpam-5916	316	78	systems	system	NOUN
ejpam-5916	316	79	.	.	PUNCT
ejpam-5916	317	1	the	the	DET
ejpam-5916	317	2	developed	develop	VERB
ejpam-5916	317	3	theory	theory	NOUN
ejpam-5916	317	4	bridges	bridge	NOUN
ejpam-5916	317	5	abstract	abstract	ADJ
ejpam-5916	317	6	mathematics	mathematic	NOUN
ejpam-5916	317	7	with	with	ADP
ejpam-5916	317	8	computational	computational	ADJ
ejpam-5916	317	9	implementations	implementation	NOUN
ejpam-5916	317	10	,	,	PUNCT
ejpam-5916	317	11	offering	offer	VERB
ejpam-5916	317	12	both	both	PRON
ejpam-5916	317	13	rigorous	rigorous	ADJ
ejpam-5916	317	14	existence	existence	NOUN
ejpam-5916	317	15	/	/	SYM
ejpam-5916	317	16	uniqueness	uniqueness	NOUN
ejpam-5916	317	17	theorems	theorem	NOUN
ejpam-5916	317	18	and	and	CCONJ
ejpam-5916	317	19	numerical	numerical	ADJ
ejpam-5916	317	20	validation	validation	NOUN
ejpam-5916	317	21	through	through	ADP
ejpam-5916	317	22	concrete	concrete	ADJ
ejpam-5916	317	23	examples	example	NOUN
ejpam-5916	317	24	,	,	PUNCT
ejpam-5916	317	25	thereby	thereby	ADV
ejpam-5916	317	26	opening	open	VERB
ejpam-5916	317	27	new	new	ADJ
ejpam-5916	317	28	research	research	NOUN
ejpam-5916	317	29	directions	direction	NOUN
ejpam-5916	317	30	in	in	ADP
ejpam-5916	317	31	multi	multi	ADJ
ejpam-5916	317	32	-	-	ADJ
ejpam-5916	317	33	valued	value	VERB
ejpam-5916	317	34	mappings	mapping	NOUN
ejpam-5916	317	35	,	,	PUNCT
ejpam-5916	317	36	algorithmic	algorithmic	ADJ
ejpam-5916	317	37	approximations	approximation	NOUN
ejpam-5916	317	38	,	,	PUNCT
ejpam-5916	317	39	and	and	CCONJ
ejpam-5916	317	40	applications	application	NOUN
ejpam-5916	317	41	to	to	PART
ejpam-5916	317	42	nonlinear	nonlinear	ADJ
ejpam-5916	317	43	problems	problem	NOUN
ejpam-5916	317	44	in	in	ADP
ejpam-5916	317	45	mathematical	mathematical	ADJ
ejpam-5916	317	46	physics	physics	NOUN
ejpam-5916	317	47	and	and	CCONJ
ejpam-5916	317	48	engineering	engineering	NOUN
ejpam-5916	317	49	.	.	PUNCT
ejpam-5916	318	1	acknowledgements	acknowledgement	VERB
ejpam-5916	318	2	the	the	DET
ejpam-5916	318	3	author	author	NOUN
ejpam-5916	318	4	thanks	thank	NOUN
ejpam-5916	318	5	the	the	DET
ejpam-5916	318	6	team	team	NOUN
ejpam-5916	318	7	of	of	ADP
ejpam-5916	318	8	european	european	PROPN
ejpam-5916	318	9	journal	journal	PROPN
ejpam-5916	318	10	of	of	ADP
ejpam-5916	318	11	pure	pure	ADJ
ejpam-5916	318	12	and	and	CCONJ
ejpam-5916	318	13	applied	applied	ADJ
ejpam-5916	318	14	mathematics	mathematic	NOUN
ejpam-5916	318	15	.	.	PUNCT
ejpam-5916	319	1	also	also	ADV
ejpam-5916	319	2	,	,	PUNCT
ejpam-5916	319	3	we	we	PRON
ejpam-5916	319	4	extend	extend	VERB
ejpam-5916	319	5	ourppreciation	ourppreciation	NOUN
ejpam-5916	319	6	to	to	ADP
ejpam-5916	319	7	al	al	PROPN
ejpam-5916	319	8	-	-	PROPN
ejpam-5916	319	9	zaytoonah	zaytoonah	PROPN
ejpam-5916	319	10	university	university	PROPN
ejpam-5916	319	11	of	of	ADP
ejpam-5916	319	12	jordan(zuj	jordan(zuj	PROPN
ejpam-5916	319	13	)	)	PUNCT
ejpam-5916	319	14	for	for	ADP
ejpam-5916	319	15	funding	fund	VERB
ejpam-5916	319	16	this	this	DET
ejpam-5916	319	17	work	work	NOUN
ejpam-5916	319	18	.	.	PUNCT
ejpam-5916	320	1	h.	h.	PROPN
ejpam-5916	320	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	320	3	/	/	SYM
ejpam-5916	320	4	eur	eur	PROPN
ejpam-5916	320	5	.	.	PUNCT
ejpam-5916	321	1	j.	j.	PROPN
ejpam-5916	321	2	pure	pure	PROPN
ejpam-5916	321	3	appl	appl	PROPN
ejpam-5916	321	4	.	.	PROPN
ejpam-5916	321	5	math	math	PROPN
ejpam-5916	321	6	,	,	PUNCT
ejpam-5916	321	7	18	18	NUM
ejpam-5916	321	8	(	(	PUNCT
ejpam-5916	321	9	3	3	NUM
ejpam-5916	321	10	)	)	PUNCT
ejpam-5916	321	11	(	(	PUNCT
ejpam-5916	321	12	2025	2025	NUM
ejpam-5916	321	13	)	)	PUNCT
ejpam-5916	321	14	,	,	PUNCT
ejpam-5916	321	15	5916	5916	NUM
ejpam-5916	321	16	17	17	NUM
ejpam-5916	321	17	of	of	ADP
ejpam-5916	321	18	19	19	NUM
ejpam-5916	321	19	references	reference	NOUN
ejpam-5916	321	20	[	[	X
ejpam-5916	321	21	1	1	NUM
ejpam-5916	321	22	]	]	PUNCT
ejpam-5916	321	23	s.	s.	PROPN
ejpam-5916	321	24	g.	g.	PROPN
ejpam-5916	321	25	matthews	matthews	PROPN
ejpam-5916	321	26	.	.	PUNCT
ejpam-5916	322	1	partial	partial	ADJ
ejpam-5916	322	2	metric	metric	ADJ
ejpam-5916	322	3	topology	topology	NOUN
ejpam-5916	322	4	.	.	PUNCT
ejpam-5916	323	1	research	research	NOUN
ejpam-5916	323	2	report	report	NOUN
ejpam-5916	323	3	212	212	NUM
ejpam-5916	323	4	,	,	PUNCT
ejpam-5916	323	5	department	department	NOUN
ejpam-5916	323	6	of	of	ADP
ejpam-5916	323	7	computer	computer	NOUN
ejpam-5916	323	8	science	science	NOUN
ejpam-5916	323	9	,	,	PUNCT
ejpam-5916	323	10	university	university	PROPN
ejpam-5916	323	11	of	of	ADP
ejpam-5916	323	12	warwick	warwick	PROPN
ejpam-5916	323	13	,	,	PUNCT
ejpam-5916	323	14	1992	1992	NUM
ejpam-5916	323	15	.	.	PUNCT
ejpam-5916	324	1	[	[	X
ejpam-5916	324	2	2	2	X
ejpam-5916	324	3	]	]	PUNCT
ejpam-5916	324	4	s.	s.	PROPN
ejpam-5916	324	5	g.	g.	PROPN
ejpam-5916	324	6	matthews	matthews	PROPN
ejpam-5916	324	7	.	.	PUNCT
ejpam-5916	325	1	partial	partial	ADJ
ejpam-5916	325	2	metric	metric	ADJ
ejpam-5916	325	3	topology	topology	NOUN
ejpam-5916	325	4	.	.	PUNCT
ejpam-5916	326	1	annals	annal	NOUN
ejpam-5916	326	2	of	of	ADP
ejpam-5916	326	3	the	the	DET
ejpam-5916	326	4	new	new	PROPN
ejpam-5916	326	5	york	york	PROPN
ejpam-5916	326	6	academy	academy	PROPN
ejpam-5916	326	7	of	of	ADP
ejpam-5916	326	8	sciences	sciences	PROPN
ejpam-5916	326	9	,	,	PUNCT
ejpam-5916	326	10	728:183–197	728:183–197	NUM
ejpam-5916	326	11	,	,	PUNCT
ejpam-5916	326	12	1994	1994	NUM
ejpam-5916	326	13	.	.	PUNCT
ejpam-5916	327	1	[	[	X
ejpam-5916	327	2	3	3	X
ejpam-5916	327	3	]	]	X
ejpam-5916	327	4	l.	l.	PROPN
ejpam-5916	327	5	ćirić	ćirić	PROPN
ejpam-5916	327	6	,	,	PUNCT
ejpam-5916	327	7	b.	b.	PROPN
ejpam-5916	327	8	samet	samet	PROPN
ejpam-5916	327	9	,	,	PUNCT
ejpam-5916	327	10	h.	h.	PROPN
ejpam-5916	327	11	aydi	aydi	PROPN
ejpam-5916	327	12	,	,	PUNCT
ejpam-5916	327	13	and	and	CCONJ
ejpam-5916	327	14	c.	c.	PROPN
ejpam-5916	327	15	vetro	vetro	PROPN
ejpam-5916	327	16	.	.	PUNCT
ejpam-5916	328	1	common	common	ADJ
ejpam-5916	328	2	fixed	fix	VERB
ejpam-5916	328	3	points	point	NOUN
ejpam-5916	328	4	of	of	ADP
ejpam-5916	328	5	generalized	generalized	ADJ
ejpam-5916	328	6	contractions	contraction	NOUN
ejpam-5916	328	7	on	on	ADP
ejpam-5916	328	8	partial	partial	ADJ
ejpam-5916	328	9	metric	metric	ADJ
ejpam-5916	328	10	spaces	space	NOUN
ejpam-5916	328	11	and	and	CCONJ
ejpam-5916	328	12	an	an	DET
ejpam-5916	328	13	application	application	NOUN
ejpam-5916	328	14	.	.	PUNCT
ejpam-5916	329	1	applied	apply	VERB
ejpam-5916	329	2	mathematics	mathematic	NOUN
ejpam-5916	329	3	and	and	CCONJ
ejpam-5916	329	4	computation	computation	NOUN
ejpam-5916	329	5	,	,	PUNCT
ejpam-5916	329	6	218:2398–2406	218:2398–2406	NUM
ejpam-5916	329	7	,	,	PUNCT
ejpam-5916	329	8	2011	2011	NUM
ejpam-5916	329	9	.	.	PUNCT
ejpam-5916	330	1	[	[	X
ejpam-5916	330	2	4	4	X
ejpam-5916	330	3	]	]	PUNCT
ejpam-5916	330	4	m.	m.	NOUN
ejpam-5916	330	5	nazam	nazam	PROPN
ejpam-5916	330	6	,	,	PUNCT
ejpam-5916	330	7	h.	h.	PROPN
ejpam-5916	330	8	aydi	aydi	PROPN
ejpam-5916	330	9	,	,	PUNCT
ejpam-5916	330	10	m.	m.	NOUN
ejpam-5916	330	11	s.	s.	PROPN
ejpam-5916	330	12	m.	m.	PROPN
ejpam-5916	330	13	noorani	noorani	PROPN
ejpam-5916	330	14	,	,	PUNCT
ejpam-5916	330	15	and	and	CCONJ
ejpam-5916	330	16	h.	h.	PROPN
ejpam-5916	330	17	qawaqneh	qawaqneh	PROPN
ejpam-5916	330	18	.	.	PUNCT
ejpam-5916	331	1	existence	existence	NOUN
ejpam-5916	331	2	of	of	ADP
ejpam-5916	331	3	fixed	fix	VERB
ejpam-5916	331	4	points	point	NOUN
ejpam-5916	331	5	of	of	ADP
ejpam-5916	331	6	four	four	NUM
ejpam-5916	331	7	maps	map	NOUN
ejpam-5916	331	8	for	for	ADP
ejpam-5916	331	9	a	a	DET
ejpam-5916	331	10	new	new	ADJ
ejpam-5916	331	11	generalized	generalized	ADJ
ejpam-5916	331	12	f	f	NOUN
ejpam-5916	331	13	-	-	PUNCT
ejpam-5916	331	14	contraction	contraction	NOUN
ejpam-5916	331	15	and	and	CCONJ
ejpam-5916	331	16	an	an	DET
ejpam-5916	331	17	application	application	NOUN
ejpam-5916	331	18	.	.	PUNCT
ejpam-5916	332	1	journal	journal	NOUN
ejpam-5916	332	2	of	of	ADP
ejpam-5916	332	3	function	function	NOUN
ejpam-5916	332	4	spaces	space	NOUN
ejpam-5916	332	5	,	,	PUNCT
ejpam-5916	332	6	2019:5980312	2019:5980312	NUM
ejpam-5916	332	7	,	,	PUNCT
ejpam-5916	332	8	2019	2019	NUM
ejpam-5916	332	9	.	.	PUNCT
ejpam-5916	333	1	[	[	X
ejpam-5916	333	2	5	5	X
ejpam-5916	333	3	]	]	PUNCT
ejpam-5916	333	4	s.	s.	PROPN
ejpam-5916	333	5	romaguera	romaguera	PROPN
ejpam-5916	333	6	.	.	PUNCT
ejpam-5916	334	1	fixed	fix	VERB
ejpam-5916	334	2	point	point	NOUN
ejpam-5916	334	3	theorems	theorem	NOUN
ejpam-5916	334	4	for	for	ADP
ejpam-5916	334	5	generalized	generalized	ADJ
ejpam-5916	334	6	contractions	contraction	NOUN
ejpam-5916	334	7	on	on	ADP
ejpam-5916	334	8	partial	partial	ADJ
ejpam-5916	334	9	metric	metric	ADJ
ejpam-5916	334	10	spaces	space	NOUN
ejpam-5916	334	11	.	.	PUNCT
ejpam-5916	335	1	topology	topology	NOUN
ejpam-5916	335	2	and	and	CCONJ
ejpam-5916	335	3	its	its	PRON
ejpam-5916	335	4	applications	application	NOUN
ejpam-5916	335	5	,	,	PUNCT
ejpam-5916	335	6	159:194–199	159:194–199	NUM
ejpam-5916	335	7	,	,	PUNCT
ejpam-5916	335	8	2012	2012	NUM
ejpam-5916	335	9	.	.	PUNCT
ejpam-5916	336	1	[	[	X
ejpam-5916	336	2	6	6	NUM
ejpam-5916	336	3	]	]	PUNCT
ejpam-5916	336	4	h.	h.	PROPN
ejpam-5916	336	5	p.	p.	NOUN
ejpam-5916	336	6	a.	a.	NOUN
ejpam-5916	336	7	künzi	künzi	PROPN
ejpam-5916	336	8	,	,	PUNCT
ejpam-5916	336	9	h.	h.	PROPN
ejpam-5916	336	10	pajoohesh	pajoohesh	PROPN
ejpam-5916	336	11	,	,	PUNCT
ejpam-5916	336	12	and	and	CCONJ
ejpam-5916	336	13	m.	m.	NOUN
ejpam-5916	336	14	p.	p.	PROPN
ejpam-5916	336	15	schellekens	schellekens	PROPN
ejpam-5916	336	16	.	.	PUNCT
ejpam-5916	337	1	partial	partial	ADJ
ejpam-5916	337	2	quasi	quasi	NOUN
ejpam-5916	337	3	-	-	NOUN
ejpam-5916	337	4	metrics	metric	NOUN
ejpam-5916	337	5	.	.	PUNCT
ejpam-5916	338	1	theoretical	theoretical	ADJ
ejpam-5916	338	2	computer	computer	NOUN
ejpam-5916	338	3	science	science	NOUN
ejpam-5916	338	4	,	,	PUNCT
ejpam-5916	338	5	365(3):237–246	365(3):237–246	NUM
ejpam-5916	338	6	,	,	PUNCT
ejpam-5916	338	7	2006	2006	NUM
ejpam-5916	338	8	.	.	PUNCT
ejpam-5916	339	1	[	[	X
ejpam-5916	339	2	7	7	X
ejpam-5916	339	3	]	]	X
ejpam-5916	339	4	e.	e.	PROPN
ejpam-5916	339	5	karapinar	karapinar	PROPN
ejpam-5916	339	6	and	and	CCONJ
ejpam-5916	339	7	m.	m.	NOUN
ejpam-5916	339	8	erhan	erhan	PROPN
ejpam-5916	339	9	.	.	PUNCT
ejpam-5916	340	1	fixed	fix	VERB
ejpam-5916	340	2	point	point	NOUN
ejpam-5916	340	3	theorems	theorem	NOUN
ejpam-5916	340	4	on	on	ADP
ejpam-5916	340	5	quasi	quasi	ADJ
ejpam-5916	340	6	-	-	ADJ
ejpam-5916	340	7	partial	partial	ADJ
ejpam-5916	340	8	metric	metric	ADJ
ejpam-5916	340	9	spaces	space	NOUN
ejpam-5916	340	10	.	.	PUNCT
ejpam-5916	341	1	mathematical	mathematical	ADJ
ejpam-5916	341	2	and	and	CCONJ
ejpam-5916	341	3	computer	computer	NOUN
ejpam-5916	341	4	modelling	modelling	NOUN
ejpam-5916	341	5	,	,	PUNCT
ejpam-5916	341	6	57:2442–2448	57:2442–2448	NUM
ejpam-5916	341	7	,	,	PUNCT
ejpam-5916	341	8	2013	2013	NUM
ejpam-5916	341	9	.	.	PUNCT
ejpam-5916	342	1	[	[	X
ejpam-5916	342	2	8	8	NUM
ejpam-5916	342	3	]	]	X
ejpam-5916	342	4	h.	h.	PROPN
ejpam-5916	342	5	alsamir	alsamir	PROPN
ejpam-5916	342	6	,	,	PUNCT
ejpam-5916	342	7	h.	h.	PROPN
ejpam-5916	342	8	qawaqneh	qawaqneh	PROPN
ejpam-5916	342	9	,	,	PUNCT
ejpam-5916	342	10	g.	g.	PROPN
ejpam-5916	342	11	al	al	PROPN
ejpam-5916	342	12	-	-	PUNCT
ejpam-5916	342	13	musannef	musannef	PROPN
ejpam-5916	342	14	,	,	PUNCT
ejpam-5916	342	15	and	and	CCONJ
ejpam-5916	342	16	r.	r.	PROPN
ejpam-5916	342	17	khalil	khalil	PROPN
ejpam-5916	342	18	.	.	PUNCT
ejpam-5916	343	1	common	common	ADJ
ejpam-5916	343	2	fixed	fix	VERB
ejpam-5916	343	3	point	point	NOUN
ejpam-5916	343	4	of	of	ADP
ejpam-5916	343	5	generalized	generalized	ADJ
ejpam-5916	343	6	berinde	berinde	NOUN
ejpam-5916	343	7	type	type	NOUN
ejpam-5916	343	8	contraction	contraction	NOUN
ejpam-5916	343	9	and	and	CCONJ
ejpam-5916	343	10	an	an	DET
ejpam-5916	343	11	application	application	NOUN
ejpam-5916	343	12	.	.	PUNCT
ejpam-5916	344	1	european	european	ADJ
ejpam-5916	344	2	journal	journal	PROPN
ejpam-5916	344	3	of	of	ADP
ejpam-5916	344	4	pure	pure	ADJ
ejpam-5916	344	5	and	and	CCONJ
ejpam-5916	344	6	applied	applied	ADJ
ejpam-5916	344	7	mathematics	mathematic	NOUN
ejpam-5916	344	8	,	,	PUNCT
ejpam-5916	344	9	17(4):2492–2504	17(4):2492–2504	NUM
ejpam-5916	344	10	,	,	PUNCT
ejpam-5916	344	11	2024	2024	NUM
ejpam-5916	344	12	.	.	PUNCT
ejpam-5916	345	1	[	[	X
ejpam-5916	345	2	9	9	NUM
ejpam-5916	345	3	]	]	PUNCT
ejpam-5916	345	4	k.	k.	PROPN
ejpam-5916	345	5	nisse	nisse	PROPN
ejpam-5916	345	6	,	,	PUNCT
ejpam-5916	345	7	h.	h.	PROPN
ejpam-5916	345	8	qawaqneh	qawaqneh	PROPN
ejpam-5916	345	9	,	,	PUNCT
ejpam-5916	345	10	g.	g.	PROPN
ejpam-5916	345	11	al	al	PROPN
ejpam-5916	345	12	-	-	PUNCT
ejpam-5916	345	13	musannef	musannef	PROPN
ejpam-5916	345	14	,	,	PUNCT
ejpam-5916	345	15	h.	h.	PROPN
ejpam-5916	345	16	alsamir	alsamir	PROPN
ejpam-5916	345	17	,	,	PUNCT
ejpam-5916	345	18	and	and	CCONJ
ejpam-5916	345	19	s.	s.	PROPN
ejpam-5916	345	20	beloul	beloul	PROPN
ejpam-5916	345	21	.	.	PUNCT
ejpam-5916	346	1	fixed	fix	VERB
ejpam-5916	346	2	points	point	NOUN
ejpam-5916	346	3	for	for	ADP
ejpam-5916	346	4	generalized	generalized	ADJ
ejpam-5916	346	5	contractions	contraction	NOUN
ejpam-5916	346	6	in	in	ADP
ejpam-5916	346	7	b	b	NOUN
ejpam-5916	346	8	-	-	PUNCT
ejpam-5916	346	9	gauge	gauge	NOUN
ejpam-5916	346	10	spaces	space	NOUN
ejpam-5916	346	11	and	and	CCONJ
ejpam-5916	346	12	applications	application	NOUN
ejpam-5916	346	13	.	.	PUNCT
ejpam-5916	347	1	european	european	ADJ
ejpam-5916	347	2	journal	journal	PROPN
ejpam-5916	347	3	of	of	ADP
ejpam-5916	347	4	pure	pure	ADJ
ejpam-5916	347	5	and	and	CCONJ
ejpam-5916	347	6	applied	applied	ADJ
ejpam-5916	347	7	mathematics	mathematic	NOUN
ejpam-5916	347	8	,	,	PUNCT
ejpam-5916	347	9	18(2):1059–1076	18(2):1059–1076	NUM
ejpam-5916	347	10	,	,	PUNCT
ejpam-5916	347	11	2025	2025	NUM
ejpam-5916	347	12	.	.	PUNCT
ejpam-5916	348	1	[	[	X
ejpam-5916	348	2	10	10	NUM
ejpam-5916	348	3	]	]	PUNCT
ejpam-5916	348	4	m.	m.	NOUN
ejpam-5916	348	5	meneceur	meneceur	PROPN
ejpam-5916	348	6	,	,	PUNCT
ejpam-5916	348	7	h.	h.	PROPN
ejpam-5916	348	8	qawaqneh	qawaqneh	PROPN
ejpam-5916	348	9	,	,	PUNCT
ejpam-5916	348	10	h.	h.	PROPN
ejpam-5916	348	11	alsamir	alsamir	PROPN
ejpam-5916	348	12	,	,	PUNCT
ejpam-5916	348	13	and	and	CCONJ
ejpam-5916	348	14	g.	g.	PROPN
ejpam-5916	348	15	al	al	PROPN
ejpam-5916	348	16	-	-	PUNCT
ejpam-5916	348	17	musannef	musannef	NOUN
ejpam-5916	348	18	.	.	PUNCT
ejpam-5916	349	1	common	common	ADJ
ejpam-5916	349	2	fixed	fix	VERB
ejpam-5916	349	3	point	point	NOUN
ejpam-5916	349	4	of	of	ADP
ejpam-5916	349	5	generalized	generalized	ADJ
ejpam-5916	349	6	berinde	berinde	NOUN
ejpam-5916	349	7	type	type	NOUN
ejpam-5916	349	8	contraction	contraction	NOUN
ejpam-5916	349	9	and	and	CCONJ
ejpam-5916	349	10	an	an	DET
ejpam-5916	349	11	application	application	NOUN
ejpam-5916	349	12	.	.	PUNCT
ejpam-5916	350	1	european	european	ADJ
ejpam-5916	350	2	journal	journal	PROPN
ejpam-5916	350	3	of	of	ADP
ejpam-5916	350	4	pure	pure	ADJ
ejpam-5916	350	5	and	and	CCONJ
ejpam-5916	350	6	applied	applied	ADJ
ejpam-5916	350	7	mathematics	mathematic	NOUN
ejpam-5916	350	8	,	,	PUNCT
ejpam-5916	350	9	17(4):3093–3108	17(4):3093–3108	NUM
ejpam-5916	350	10	,	,	PUNCT
ejpam-5916	350	11	2024	2024	NUM
ejpam-5916	350	12	.	.	PUNCT
ejpam-5916	351	1	[	[	X
ejpam-5916	351	2	11	11	NUM
ejpam-5916	351	3	]	]	X
ejpam-5916	351	4	h.	h.	PROPN
ejpam-5916	351	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	351	6	,	,	PUNCT
ejpam-5916	351	7	m.	m.	PROPN
ejpam-5916	351	8	s.	s.	PROPN
ejpam-5916	351	9	m.	m.	PROPN
ejpam-5916	351	10	noorani	noorani	PROPN
ejpam-5916	351	11	,	,	PUNCT
ejpam-5916	351	12	and	and	CCONJ
ejpam-5916	351	13	w.	w.	PROPN
ejpam-5916	351	14	shatanawi	shatanawi	PROPN
ejpam-5916	351	15	.	.	PUNCT
ejpam-5916	352	1	fixed	fix	VERB
ejpam-5916	352	2	point	point	NOUN
ejpam-5916	352	3	theorems	theorem	NOUN
ejpam-5916	352	4	for	for	ADP
ejpam-5916	352	5	(	(	PUNCT
ejpam-5916	352	6	α	α	X
ejpam-5916	352	7	,	,	PUNCT
ejpam-5916	352	8	k	k	NOUN
ejpam-5916	352	9	,	,	PUNCT
ejpam-5916	352	10	θ)-contractive	θ)-contractive	PUNCT
ejpam-5916	352	11	multi	multi	ADJ
ejpam-5916	352	12	-	-	ADJ
ejpam-5916	352	13	valued	value	VERB
ejpam-5916	352	14	mapping	mapping	NOUN
ejpam-5916	352	15	in	in	ADP
ejpam-5916	352	16	b	b	NOUN
ejpam-5916	352	17	-	-	PUNCT
ejpam-5916	352	18	metric	metric	ADJ
ejpam-5916	352	19	space	space	NOUN
ejpam-5916	352	20	and	and	CCONJ
ejpam-5916	352	21	applications	application	NOUN
ejpam-5916	352	22	.	.	PUNCT
ejpam-5916	353	1	international	international	ADJ
ejpam-5916	353	2	journal	journal	PROPN
ejpam-5916	353	3	of	of	ADP
ejpam-5916	353	4	mathematics	mathematic	NOUN
ejpam-5916	353	5	and	and	CCONJ
ejpam-5916	353	6	computer	computer	NOUN
ejpam-5916	353	7	science	science	NOUN
ejpam-5916	353	8	,	,	PUNCT
ejpam-5916	353	9	14(1):263–283	14(1):263–283	NUM
ejpam-5916	353	10	,	,	PUNCT
ejpam-5916	353	11	2019	2019	NUM
ejpam-5916	353	12	.	.	PUNCT
ejpam-5916	354	1	[	[	X
ejpam-5916	354	2	12	12	NUM
ejpam-5916	354	3	]	]	PUNCT
ejpam-5916	354	4	h.	h.	PROPN
ejpam-5916	354	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	354	6	,	,	PUNCT
ejpam-5916	354	7	m.	m.	PROPN
ejpam-5916	354	8	s.	s.	PROPN
ejpam-5916	354	9	m.	m.	PROPN
ejpam-5916	354	10	noorani	noorani	PROPN
ejpam-5916	354	11	,	,	PUNCT
ejpam-5916	354	12	and	and	CCONJ
ejpam-5916	354	13	w.	w.	PROPN
ejpam-5916	354	14	shatanawi	shatanawi	PROPN
ejpam-5916	354	15	.	.	PUNCT
ejpam-5916	355	1	fixed	fix	VERB
ejpam-5916	355	2	point	point	NOUN
ejpam-5916	355	3	results	result	NOUN
ejpam-5916	355	4	for	for	ADP
ejpam-5916	355	5	geraghty	geraghty	PROPN
ejpam-5916	355	6	type	type	NOUN
ejpam-5916	355	7	generalized	generalize	VERB
ejpam-5916	355	8	f	f	NOUN
ejpam-5916	355	9	-	-	PUNCT
ejpam-5916	355	10	contraction	contraction	NOUN
ejpam-5916	355	11	for	for	ADP
ejpam-5916	355	12	weak	weak	ADJ
ejpam-5916	355	13	admissible	admissible	ADJ
ejpam-5916	355	14	mappings	mapping	NOUN
ejpam-5916	355	15	in	in	ADP
ejpam-5916	355	16	metric	metric	ADJ
ejpam-5916	355	17	-	-	PUNCT
ejpam-5916	355	18	like	like	ADJ
ejpam-5916	355	19	spaces	space	NOUN
ejpam-5916	355	20	.	.	PUNCT
ejpam-5916	356	1	european	european	ADJ
ejpam-5916	356	2	journal	journal	PROPN
ejpam-5916	356	3	of	of	ADP
ejpam-5916	356	4	pure	pure	ADJ
ejpam-5916	356	5	and	and	CCONJ
ejpam-5916	356	6	applied	applied	ADJ
ejpam-5916	356	7	mathematics	mathematic	NOUN
ejpam-5916	356	8	,	,	PUNCT
ejpam-5916	356	9	11(3):702–716	11(3):702–716	PROPN
ejpam-5916	356	10	,	,	PUNCT
ejpam-5916	356	11	2018	2018	NUM
ejpam-5916	356	12	.	.	PUNCT
ejpam-5916	357	1	[	[	X
ejpam-5916	357	2	13	13	NUM
ejpam-5916	357	3	]	]	X
ejpam-5916	357	4	h.	h.	PROPN
ejpam-5916	357	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	357	6	,	,	PUNCT
ejpam-5916	357	7	m.	m.	PROPN
ejpam-5916	357	8	s.	s.	PROPN
ejpam-5916	357	9	m.	m.	PROPN
ejpam-5916	357	10	noorani	noorani	PROPN
ejpam-5916	357	11	,	,	PUNCT
ejpam-5916	357	12	and	and	CCONJ
ejpam-5916	357	13	h.	h.	PROPN
ejpam-5916	357	14	aydi	aydi	VERB
ejpam-5916	357	15	.	.	PUNCT
ejpam-5916	358	1	some	some	DET
ejpam-5916	358	2	new	new	ADJ
ejpam-5916	358	3	characterizations	characterization	NOUN
ejpam-5916	358	4	and	and	CCONJ
ejpam-5916	358	5	results	result	NOUN
ejpam-5916	358	6	for	for	ADP
ejpam-5916	358	7	fuzzy	fuzzy	ADJ
ejpam-5916	358	8	contractions	contraction	NOUN
ejpam-5916	358	9	in	in	ADP
ejpam-5916	358	10	fuzzy	fuzzy	ADJ
ejpam-5916	358	11	b	b	X
ejpam-5916	358	12	-	-	PUNCT
ejpam-5916	358	13	metric	metric	ADJ
ejpam-5916	358	14	spaces	space	NOUN
ejpam-5916	358	15	and	and	CCONJ
ejpam-5916	358	16	applications	application	NOUN
ejpam-5916	358	17	.	.	PUNCT
ejpam-5916	359	1	aims	aim	VERB
ejpam-5916	359	2	mathematics	mathematics	PROPN
ejpam-5916	359	3	,	,	PUNCT
ejpam-5916	359	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-5916	359	5	,	,	PUNCT
ejpam-5916	359	6	2023	2023	NUM
ejpam-5916	359	7	.	.	PUNCT
ejpam-5916	360	1	[	[	X
ejpam-5916	360	2	14	14	NUM
ejpam-5916	360	3	]	]	X
ejpam-5916	360	4	h.	h.	PROPN
ejpam-5916	360	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	360	6	.	.	PUNCT
ejpam-5916	361	1	new	new	ADJ
ejpam-5916	361	2	functions	function	NOUN
ejpam-5916	361	3	for	for	ADP
ejpam-5916	361	4	fixed	fix	VERB
ejpam-5916	361	5	point	point	NOUN
ejpam-5916	361	6	results	result	NOUN
ejpam-5916	361	7	in	in	ADP
ejpam-5916	361	8	metric	metric	ADJ
ejpam-5916	361	9	spaces	space	NOUN
ejpam-5916	361	10	with	with	ADP
ejpam-5916	361	11	some	some	DET
ejpam-5916	361	12	applications	application	NOUN
ejpam-5916	361	13	.	.	PUNCT
ejpam-5916	362	1	indian	indian	ADJ
ejpam-5916	362	2	journal	journal	PROPN
ejpam-5916	362	3	of	of	ADP
ejpam-5916	362	4	mathematics	mathematic	NOUN
ejpam-5916	362	5	,	,	PUNCT
ejpam-5916	362	6	66(1):55–84	66(1):55–84	NOUN
ejpam-5916	362	7	,	,	PUNCT
ejpam-5916	362	8	2024	2024	NUM
ejpam-5916	362	9	.	.	PUNCT
ejpam-5916	363	1	[	[	X
ejpam-5916	363	2	15	15	NUM
ejpam-5916	363	3	]	]	X
ejpam-5916	363	4	h.	h.	PROPN
ejpam-5916	363	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	363	6	.	.	PUNCT
ejpam-5916	364	1	fractional	fractional	ADJ
ejpam-5916	364	2	analytic	analytic	ADJ
ejpam-5916	364	3	solutions	solution	NOUN
ejpam-5916	364	4	and	and	CCONJ
ejpam-5916	364	5	fixed	fix	VERB
ejpam-5916	364	6	point	point	NOUN
ejpam-5916	364	7	results	result	NOUN
ejpam-5916	364	8	with	with	ADP
ejpam-5916	364	9	some	some	DET
ejpam-5916	364	10	applications	application	NOUN
ejpam-5916	364	11	.	.	PUNCT
ejpam-5916	365	1	advances	advance	NOUN
ejpam-5916	365	2	in	in	ADP
ejpam-5916	365	3	fixed	fix	VERB
ejpam-5916	365	4	point	point	NOUN
ejpam-5916	365	5	theory	theory	NOUN
ejpam-5916	365	6	,	,	PUNCT
ejpam-5916	365	7	14(1):1–12	14(1):1–12	NUM
ejpam-5916	365	8	,	,	PUNCT
ejpam-5916	365	9	2024	2024	NUM
ejpam-5916	365	10	.	.	PUNCT
ejpam-5916	366	1	[	[	X
ejpam-5916	366	2	16	16	NUM
ejpam-5916	366	3	]	]	X
ejpam-5916	366	4	h.	h.	PROPN
ejpam-5916	366	5	alsamir	alsamir	PROPN
ejpam-5916	366	6	,	,	PUNCT
ejpam-5916	366	7	h.	h.	PROPN
ejpam-5916	366	8	aydi	aydi	PROPN
ejpam-5916	366	9	,	,	PUNCT
ejpam-5916	366	10	m.	m.	NOUN
ejpam-5916	366	11	s.	s.	PROPN
ejpam-5916	366	12	m.	m.	PROPN
ejpam-5916	366	13	noorani	noorani	PROPN
ejpam-5916	366	14	,	,	PUNCT
ejpam-5916	366	15	w.	w.	PROPN
ejpam-5916	366	16	shatanawi	shatanawi	PROPN
ejpam-5916	366	17	,	,	PUNCT
ejpam-5916	366	18	h.	h.	PROPN
ejpam-5916	366	19	akhadkulov	akhadkulov	PROPN
ejpam-5916	366	20	,	,	PUNCT
ejpam-5916	366	21	h.	h.	PROPN
ejpam-5916	366	22	qawaqneh	qawaqneh	PROPN
ejpam-5916	366	23	,	,	PUNCT
ejpam-5916	366	24	and	and	CCONJ
ejpam-5916	366	25	k.	k.	PROPN
ejpam-5916	366	26	alanazi	alanazi	PROPN
ejpam-5916	366	27	.	.	PUNCT
ejpam-5916	367	1	fixed	fix	VERB
ejpam-5916	367	2	point	point	NOUN
ejpam-5916	367	3	results	result	NOUN
ejpam-5916	367	4	in	in	ADP
ejpam-5916	367	5	metric	metric	ADJ
ejpam-5916	367	6	-	-	PUNCT
ejpam-5916	367	7	like	like	ADJ
ejpam-5916	367	8	spaces	space	NOUN
ejpam-5916	367	9	via	via	ADP
ejpam-5916	367	10	σ	σ	PROPN
ejpam-5916	367	11	-	-	PUNCT
ejpam-5916	367	12	simulation	simulation	NOUN
ejpam-5916	367	13	functions	function	NOUN
ejpam-5916	367	14	.	.	PUNCT
ejpam-5916	368	1	european	european	ADJ
ejpam-5916	368	2	journal	journal	PROPN
ejpam-5916	368	3	of	of	ADP
ejpam-5916	368	4	pure	pure	ADJ
ejpam-5916	368	5	and	and	CCONJ
ejpam-5916	368	6	applied	applied	ADJ
ejpam-5916	368	7	mathematics	mathematic	NOUN
ejpam-5916	368	8	,	,	PUNCT
ejpam-5916	368	9	12(1):88–100	12(1):88–100	NUM
ejpam-5916	368	10	,	,	PUNCT
ejpam-5916	368	11	2019	2019	NUM
ejpam-5916	368	12	.	.	PUNCT
ejpam-5916	369	1	h.	h.	PROPN
ejpam-5916	369	2	qawaqneh	qawaqneh	PROPN
ejpam-5916	369	3	/	/	SYM
ejpam-5916	369	4	eur	eur	PROPN
ejpam-5916	369	5	.	.	PUNCT
ejpam-5916	370	1	j.	j.	PROPN
ejpam-5916	370	2	pure	pure	PROPN
ejpam-5916	370	3	appl	appl	PROPN
ejpam-5916	370	4	.	.	PROPN
ejpam-5916	370	5	math	math	PROPN
ejpam-5916	370	6	,	,	PUNCT
ejpam-5916	370	7	18	18	NUM
ejpam-5916	370	8	(	(	PUNCT
ejpam-5916	370	9	3	3	NUM
ejpam-5916	370	10	)	)	PUNCT
ejpam-5916	370	11	(	(	PUNCT
ejpam-5916	370	12	2025	2025	NUM
ejpam-5916	370	13	)	)	PUNCT
ejpam-5916	370	14	,	,	PUNCT
ejpam-5916	370	15	5916	5916	NUM
ejpam-5916	370	16	18	18	NUM
ejpam-5916	370	17	of	of	ADP
ejpam-5916	370	18	19	19	NUM
ejpam-5916	370	19	[	[	SYM
ejpam-5916	370	20	17	17	NUM
ejpam-5916	370	21	]	]	PUNCT
ejpam-5916	370	22	a.	a.	NOUN
ejpam-5916	370	23	tomar	tomar	PROPN
ejpam-5916	370	24	,	,	PUNCT
ejpam-5916	370	25	s.	s.	PROPN
ejpam-5916	370	26	beloul	beloul	PROPN
ejpam-5916	370	27	,	,	PUNCT
ejpam-5916	370	28	r.	r.	PROPN
ejpam-5916	370	29	sharma	sharma	PROPN
ejpam-5916	370	30	,	,	PUNCT
ejpam-5916	370	31	and	and	CCONJ
ejpam-5916	370	32	s.	s.	PROPN
ejpam-5916	370	33	upadhyay	upadhyay	PROPN
ejpam-5916	370	34	.	.	PUNCT
ejpam-5916	371	1	common	common	ADJ
ejpam-5916	371	2	fixed	fix	VERB
ejpam-5916	371	3	point	point	NOUN
ejpam-5916	371	4	theorems	theorem	NOUN
ejpam-5916	371	5	via	via	ADP
ejpam-5916	371	6	generalized	generalized	ADJ
ejpam-5916	371	7	condition	condition	NOUN
ejpam-5916	371	8	(	(	PUNCT
ejpam-5916	371	9	b	b	NOUN
ejpam-5916	371	10	)	)	PUNCT
ejpam-5916	371	11	in	in	ADP
ejpam-5916	371	12	quasi	quasi	ADJ
ejpam-5916	371	13	-	-	ADJ
ejpam-5916	371	14	partial	partial	ADJ
ejpam-5916	371	15	metric	metric	ADJ
ejpam-5916	371	16	space	space	NOUN
ejpam-5916	371	17	and	and	CCONJ
ejpam-5916	371	18	applications	application	NOUN
ejpam-5916	371	19	.	.	PUNCT
ejpam-5916	372	1	demonstratio	demonstratio	PROPN
ejpam-5916	372	2	mathematica	mathematica	PROPN
ejpam-5916	372	3	,	,	PUNCT
ejpam-5916	372	4	50:278–298	50:278–298	PROPN
ejpam-5916	372	5	,	,	PUNCT
ejpam-5916	372	6	2017	2017	NUM
ejpam-5916	372	7	.	.	PUNCT
ejpam-5916	373	1	[	[	X
ejpam-5916	373	2	18	18	NUM
ejpam-5916	373	3	]	]	X
ejpam-5916	373	4	w.	w.	PROPN
ejpam-5916	373	5	shatanawi	shatanawi	PROPN
ejpam-5916	373	6	and	and	CCONJ
ejpam-5916	373	7	a.	a.	NOUN
ejpam-5916	373	8	pitea	pitea	NOUN
ejpam-5916	373	9	.	.	PUNCT
ejpam-5916	374	1	some	some	DET
ejpam-5916	374	2	coupled	couple	VERB
ejpam-5916	374	3	fixed	fix	VERB
ejpam-5916	374	4	point	point	NOUN
ejpam-5916	374	5	theorems	theorem	NOUN
ejpam-5916	374	6	in	in	ADP
ejpam-5916	374	7	quasi	quasi	ADJ
ejpam-5916	374	8	-	-	ADJ
ejpam-5916	374	9	partial	partial	ADJ
ejpam-5916	374	10	metric	metric	ADJ
ejpam-5916	374	11	spaces	space	NOUN
ejpam-5916	374	12	.	.	PUNCT
ejpam-5916	375	1	fixed	fix	VERB
ejpam-5916	375	2	point	point	NOUN
ejpam-5916	375	3	theory	theory	NOUN
ejpam-5916	375	4	and	and	CCONJ
ejpam-5916	375	5	applications	application	NOUN
ejpam-5916	375	6	,	,	PUNCT
ejpam-5916	375	7	2013:153	2013:153	NUM
ejpam-5916	375	8	,	,	PUNCT
ejpam-5916	375	9	2013	2013	NUM
ejpam-5916	375	10	.	.	PUNCT
ejpam-5916	376	1	[	[	X
ejpam-5916	376	2	19	19	NUM
ejpam-5916	376	3	]	]	X
ejpam-5916	376	4	h.	h.	PROPN
ejpam-5916	376	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	376	6	,	,	PUNCT
ejpam-5916	376	7	m.	m.	PROPN
ejpam-5916	376	8	s.	s.	PROPN
ejpam-5916	376	9	m.	m.	PROPN
ejpam-5916	376	10	noorani	noorani	PROPN
ejpam-5916	376	11	,	,	PUNCT
ejpam-5916	376	12	h.	h.	PROPN
ejpam-5916	376	13	aydi	aydi	PROPN
ejpam-5916	376	14	,	,	PUNCT
ejpam-5916	376	15	a.	a.	NOUN
ejpam-5916	376	16	zraiqat	zraiqat	PROPN
ejpam-5916	376	17	,	,	PUNCT
ejpam-5916	376	18	and	and	CCONJ
ejpam-5916	376	19	a.	a.	NOUN
ejpam-5916	376	20	h.	h.	PROPN
ejpam-5916	376	21	ansari	ansari	PROPN
ejpam-5916	376	22	.	.	PUNCT
ejpam-5916	377	1	on	on	ADP
ejpam-5916	377	2	fixed	fix	VERB
ejpam-5916	377	3	point	point	NOUN
ejpam-5916	377	4	results	result	NOUN
ejpam-5916	377	5	in	in	ADP
ejpam-5916	377	6	partial	partial	ADJ
ejpam-5916	377	7	b	b	NOUN
ejpam-5916	377	8	-	-	PUNCT
ejpam-5916	377	9	metric	metric	ADJ
ejpam-5916	377	10	spaces	space	NOUN
ejpam-5916	377	11	.	.	PUNCT
ejpam-5916	378	1	journal	journal	NOUN
ejpam-5916	378	2	of	of	ADP
ejpam-5916	378	3	function	function	NOUN
ejpam-5916	378	4	spaces	space	NOUN
ejpam-5916	378	5	,	,	PUNCT
ejpam-5916	378	6	2021:6645813	2021:6645813	NUM
ejpam-5916	378	7	,	,	PUNCT
ejpam-5916	378	8	2021	2021	NUM
ejpam-5916	378	9	.	.	PUNCT
ejpam-5916	379	1	[	[	X
ejpam-5916	379	2	20	20	NUM
ejpam-5916	379	3	]	]	PUNCT
ejpam-5916	379	4	a.	a.	NOUN
ejpam-5916	379	5	h.	h.	PROPN
ejpam-5916	379	6	ansari	ansari	PROPN
ejpam-5916	379	7	.	.	PUNCT
ejpam-5916	380	1	note	note	NOUN
ejpam-5916	380	2	on	on	ADP
ejpam-5916	380	3	φ	φ	PROPN
ejpam-5916	380	4	-	-	PUNCT
ejpam-5916	380	5	ψ	ψ	ADP
ejpam-5916	380	6	-	-	ADJ
ejpam-5916	380	7	contractive	contractive	ADJ
ejpam-5916	380	8	type	type	NOUN
ejpam-5916	380	9	mappings	mapping	NOUN
ejpam-5916	380	10	and	and	CCONJ
ejpam-5916	380	11	related	relate	VERB
ejpam-5916	380	12	fixed	fix	VERB
ejpam-5916	380	13	point	point	NOUN
ejpam-5916	380	14	.	.	PUNCT
ejpam-5916	381	1	the	the	DET
ejpam-5916	381	2	2nd	2nd	ADJ
ejpam-5916	381	3	regional	regional	ADJ
ejpam-5916	381	4	conference	conference	NOUN
ejpam-5916	381	5	on	on	ADP
ejpam-5916	381	6	mathematics	mathematic	NOUN
ejpam-5916	381	7	and	and	CCONJ
ejpam-5916	381	8	applications	application	NOUN
ejpam-5916	381	9	,	,	PUNCT
ejpam-5916	381	10	payame	payame	NOUN
ejpam-5916	381	11	noor	noor	PROPN
ejpam-5916	381	12	university	university	PROPN
ejpam-5916	381	13	,	,	PUNCT
ejpam-5916	381	14	pages	page	NOUN
ejpam-5916	381	15	377–380	377–380	NUM
ejpam-5916	381	16	,	,	PUNCT
ejpam-5916	381	17	2014	2014	NUM
ejpam-5916	381	18	.	.	PUNCT
ejpam-5916	382	1	[	[	X
ejpam-5916	382	2	21	21	NUM
ejpam-5916	382	3	]	]	PUNCT
ejpam-5916	382	4	a.	a.	NOUN
ejpam-5916	382	5	h.	h.	PROPN
ejpam-5916	382	6	ansari	ansari	PROPN
ejpam-5916	382	7	and	and	CCONJ
ejpam-5916	382	8	s.	s.	PROPN
ejpam-5916	382	9	beloul	beloul	PROPN
ejpam-5916	382	10	.	.	PUNCT
ejpam-5916	383	1	c	c	X
ejpam-5916	383	2	-	-	PUNCT
ejpam-5916	383	3	class	class	NOUN
ejpam-5916	383	4	functions	function	NOUN
ejpam-5916	383	5	on	on	ADP
ejpam-5916	383	6	common	common	ADJ
ejpam-5916	383	7	fixed	fix	VERB
ejpam-5916	383	8	points	point	NOUN
ejpam-5916	383	9	for	for	ADP
ejpam-5916	383	10	mappings	mapping	NOUN
ejpam-5916	383	11	satisfying	satisfy	VERB
ejpam-5916	383	12	linear	linear	ADJ
ejpam-5916	383	13	contractive	contractive	ADJ
ejpam-5916	383	14	conditions	condition	NOUN
ejpam-5916	383	15	.	.	PUNCT
ejpam-5916	384	1	surveys	survey	NOUN
ejpam-5916	384	2	in	in	ADP
ejpam-5916	384	3	mathematics	mathematic	NOUN
ejpam-5916	384	4	and	and	CCONJ
ejpam-5916	384	5	its	its	PRON
ejpam-5916	384	6	applications	application	NOUN
ejpam-5916	384	7	,	,	PUNCT
ejpam-5916	384	8	12:35–49	12:35–49	NUM
ejpam-5916	384	9	,	,	PUNCT
ejpam-5916	384	10	2017	2017	NUM
ejpam-5916	384	11	.	.	PUNCT
ejpam-5916	385	1	[	[	X
ejpam-5916	385	2	22	22	NUM
ejpam-5916	385	3	]	]	PUNCT
ejpam-5916	385	4	s.	s.	PROPN
ejpam-5916	385	5	beloul	beloul	PROPN
ejpam-5916	385	6	and	and	CCONJ
ejpam-5916	385	7	a.	a.	PROPN
ejpam-5916	385	8	h.	h.	PROPN
ejpam-5916	385	9	ansari	ansari	PROPN
ejpam-5916	385	10	.	.	PUNCT
ejpam-5916	386	1	common	common	ADJ
ejpam-5916	386	2	fixed	fix	VERB
ejpam-5916	386	3	point	point	NOUN
ejpam-5916	386	4	for	for	ADP
ejpam-5916	386	5	subsequentially	subsequentially	ADV
ejpam-5916	386	6	continuous	continuous	ADJ
ejpam-5916	386	7	mappings	mapping	NOUN
ejpam-5916	386	8	via	via	ADP
ejpam-5916	386	9	new	new	ADJ
ejpam-5916	386	10	function	function	NOUN
ejpam-5916	386	11	.	.	PUNCT
ejpam-5916	387	1	journal	journal	NOUN
ejpam-5916	387	2	of	of	ADP
ejpam-5916	387	3	advanced	advanced	ADJ
ejpam-5916	387	4	mathematical	mathematical	ADJ
ejpam-5916	387	5	studies	study	NOUN
ejpam-5916	387	6	,	,	PUNCT
ejpam-5916	387	7	10(1):62–73	10(1):62–73	NUM
ejpam-5916	387	8	,	,	PUNCT
ejpam-5916	387	9	2017	2017	NUM
ejpam-5916	387	10	.	.	PUNCT
ejpam-5916	388	1	[	[	X
ejpam-5916	388	2	23	23	NUM
ejpam-5916	388	3	]	]	PUNCT
ejpam-5916	388	4	a.	a.	PROPN
ejpam-5916	388	5	latif	latif	PROPN
ejpam-5916	388	6	,	,	PUNCT
ejpam-5916	388	7	h.	h.	PROPN
ejpam-5916	388	8	isik	isik	PROPN
ejpam-5916	388	9	,	,	PUNCT
ejpam-5916	388	10	and	and	CCONJ
ejpam-5916	388	11	a.	a.	PROPN
ejpam-5916	388	12	h.	h.	PROPN
ejpam-5916	388	13	ansari	ansari	PROPN
ejpam-5916	388	14	.	.	PUNCT
ejpam-5916	389	1	fixed	fix	VERB
ejpam-5916	389	2	points	point	NOUN
ejpam-5916	389	3	and	and	CCONJ
ejpam-5916	389	4	functional	functional	ADJ
ejpam-5916	389	5	equation	equation	NOUN
ejpam-5916	389	6	problems	problem	NOUN
ejpam-5916	389	7	via	via	ADP
ejpam-5916	389	8	cyclic	cyclic	ADJ
ejpam-5916	389	9	admissible	admissible	ADJ
ejpam-5916	389	10	generalized	generalize	VERB
ejpam-5916	389	11	contractive	contractive	ADJ
ejpam-5916	389	12	type	type	NOUN
ejpam-5916	389	13	mappings	mapping	NOUN
ejpam-5916	389	14	.	.	PUNCT
ejpam-5916	390	1	journal	journal	PROPN
ejpam-5916	390	2	of	of	ADP
ejpam-5916	390	3	nonlinear	nonlinear	PROPN
ejpam-5916	390	4	sciences	sciences	PROPN
ejpam-5916	390	5	and	and	CCONJ
ejpam-5916	390	6	applications	application	NOUN
ejpam-5916	390	7	,	,	PUNCT
ejpam-5916	390	8	9:1129–1142	9:1129–1142	PROPN
ejpam-5916	390	9	,	,	PUNCT
ejpam-5916	390	10	2016	2016	NUM
ejpam-5916	390	11	.	.	PUNCT
ejpam-5916	391	1	[	[	X
ejpam-5916	391	2	24	24	NUM
ejpam-5916	391	3	]	]	X
ejpam-5916	391	4	g.	g.	PROPN
ejpam-5916	391	5	jungck	jungck	PROPN
ejpam-5916	391	6	and	and	CCONJ
ejpam-5916	391	7	b.	b.	PROPN
ejpam-5916	391	8	e.	e.	PROPN
ejpam-5916	391	9	rhoades	rhoades	PROPN
ejpam-5916	391	10	.	.	PUNCT
ejpam-5916	392	1	fixed	fix	VERB
ejpam-5916	392	2	point	point	NOUN
ejpam-5916	392	3	for	for	ADP
ejpam-5916	392	4	set	set	NOUN
ejpam-5916	392	5	-	-	PUNCT
ejpam-5916	392	6	valued	value	VERB
ejpam-5916	392	7	functions	function	NOUN
ejpam-5916	392	8	without	without	ADP
ejpam-5916	392	9	continuity	continuity	NOUN
ejpam-5916	392	10	.	.	PUNCT
ejpam-5916	393	1	indian	indian	ADJ
ejpam-5916	393	2	journal	journal	PROPN
ejpam-5916	393	3	of	of	ADP
ejpam-5916	393	4	pure	pure	ADJ
ejpam-5916	393	5	and	and	CCONJ
ejpam-5916	393	6	applied	applied	ADJ
ejpam-5916	393	7	mathematics	mathematic	NOUN
ejpam-5916	393	8	,	,	PUNCT
ejpam-5916	393	9	29(3):227–238	29(3):227–238	PROPN
ejpam-5916	393	10	,	,	PUNCT
ejpam-5916	393	11	1998	1998	NUM
ejpam-5916	393	12	.	.	PUNCT
ejpam-5916	394	1	[	[	X
ejpam-5916	394	2	25	25	NUM
ejpam-5916	394	3	]	]	PUNCT
ejpam-5916	394	4	m.	m.	NOUN
ejpam-5916	394	5	s.	s.	PROPN
ejpam-5916	394	6	khan	khan	PROPN
ejpam-5916	394	7	,	,	PUNCT
ejpam-5916	394	8	m.	m.	NOUN
ejpam-5916	394	9	swaleh	swaleh	PROPN
ejpam-5916	394	10	,	,	PUNCT
ejpam-5916	394	11	and	and	CCONJ
ejpam-5916	394	12	s.	s.	PROPN
ejpam-5916	394	13	sessa	sessa	PROPN
ejpam-5916	394	14	.	.	PUNCT
ejpam-5916	395	1	fixed	fix	VERB
ejpam-5916	395	2	point	point	NOUN
ejpam-5916	395	3	theorems	theorem	NOUN
ejpam-5916	395	4	by	by	ADP
ejpam-5916	395	5	altering	alter	VERB
ejpam-5916	395	6	distances	distance	NOUN
ejpam-5916	395	7	between	between	ADP
ejpam-5916	395	8	the	the	DET
ejpam-5916	395	9	points	point	NOUN
ejpam-5916	395	10	.	.	PUNCT
ejpam-5916	396	1	bulletin	bulletin	NOUN
ejpam-5916	396	2	of	of	ADP
ejpam-5916	396	3	the	the	DET
ejpam-5916	396	4	australian	australian	ADJ
ejpam-5916	396	5	mathematical	mathematical	ADJ
ejpam-5916	396	6	society	society	NOUN
ejpam-5916	396	7	,	,	PUNCT
ejpam-5916	396	8	30:1–9	30:1–9	NUM
ejpam-5916	396	9	,	,	PUNCT
ejpam-5916	396	10	1984	1984	NUM
ejpam-5916	396	11	.	.	PUNCT
ejpam-5916	397	1	[	[	X
ejpam-5916	397	2	26	26	NUM
ejpam-5916	397	3	]	]	X
ejpam-5916	397	4	h.	h.	PROPN
ejpam-5916	397	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	397	6	,	,	PUNCT
ejpam-5916	397	7	j.	j.	PROPN
ejpam-5916	397	8	manafian	manafian	PROPN
ejpam-5916	397	9	,	,	PUNCT
ejpam-5916	397	10	m.	m.	NOUN
ejpam-5916	397	11	alharthi	alharthi	PROPN
ejpam-5916	397	12	,	,	PUNCT
ejpam-5916	397	13	and	and	CCONJ
ejpam-5916	397	14	y.	y.	PROPN
ejpam-5916	397	15	alrashed	alrashe	VERB
ejpam-5916	397	16	.	.	PUNCT
ejpam-5916	398	1	stability	stability	NOUN
ejpam-5916	398	2	analysis	analysis	NOUN
ejpam-5916	398	3	,	,	PUNCT
ejpam-5916	398	4	modulation	modulation	NOUN
ejpam-5916	398	5	instability	instability	NOUN
ejpam-5916	398	6	,	,	PUNCT
ejpam-5916	398	7	and	and	CCONJ
ejpam-5916	398	8	beta	beta	NOUN
ejpam-5916	398	9	-	-	PUNCT
ejpam-5916	398	10	time	time	NOUN
ejpam-5916	398	11	fractional	fractional	ADJ
ejpam-5916	398	12	exact	exact	ADJ
ejpam-5916	398	13	soliton	soliton	NOUN
ejpam-5916	398	14	solutions	solution	NOUN
ejpam-5916	398	15	to	to	ADP
ejpam-5916	398	16	the	the	DET
ejpam-5916	398	17	van	van	PROPN
ejpam-5916	398	18	der	der	NOUN
ejpam-5916	398	19	waals	waal	NOUN
ejpam-5916	398	20	equation	equation	NOUN
ejpam-5916	398	21	.	.	PUNCT
ejpam-5916	399	1	mathematics	mathematic	NOUN
ejpam-5916	399	2	,	,	PUNCT
ejpam-5916	399	3	12:2257	12:2257	NUM
ejpam-5916	399	4	,	,	PUNCT
ejpam-5916	399	5	2024	2024	NUM
ejpam-5916	399	6	.	.	PUNCT
ejpam-5916	400	1	[	[	X
ejpam-5916	400	2	27	27	NUM
ejpam-5916	400	3	]	]	X
ejpam-5916	400	4	m.	m.	NOUN
ejpam-5916	400	5	elbes	elbes	PROPN
ejpam-5916	400	6	,	,	PUNCT
ejpam-5916	400	7	t.	t.	PROPN
ejpam-5916	400	8	kanan	kanan	PROPN
ejpam-5916	400	9	,	,	PUNCT
ejpam-5916	400	10	m.	m.	NOUN
ejpam-5916	400	11	alia	alia	PROPN
ejpam-5916	400	12	,	,	PUNCT
ejpam-5916	400	13	and	and	CCONJ
ejpam-5916	400	14	m.	m.	NOUN
ejpam-5916	400	15	ziad	ziad	PROPN
ejpam-5916	400	16	.	.	PUNCT
ejpam-5916	401	1	covid-19	covid-19	PROPN
ejpam-5916	401	2	detection	detection	NOUN
ejpam-5916	401	3	platform	platform	NOUN
ejpam-5916	401	4	from	from	ADP
ejpam-5916	401	5	x	x	ADJ
ejpam-5916	401	6	-	-	NOUN
ejpam-5916	401	7	ray	ray	NOUN
ejpam-5916	401	8	images	image	NOUN
ejpam-5916	401	9	using	use	VERB
ejpam-5916	401	10	deep	deep	ADJ
ejpam-5916	401	11	learning	learning	NOUN
ejpam-5916	401	12	.	.	PUNCT
ejpam-5916	402	1	international	international	ADJ
ejpam-5916	402	2	journal	journal	NOUN
ejpam-5916	402	3	of	of	ADP
ejpam-5916	402	4	advances	advance	NOUN
ejpam-5916	402	5	in	in	ADP
ejpam-5916	402	6	soft	soft	ADJ
ejpam-5916	402	7	computing	computing	NOUN
ejpam-5916	402	8	and	and	CCONJ
ejpam-5916	402	9	its	its	PRON
ejpam-5916	402	10	applications	application	NOUN
ejpam-5916	402	11	,	,	PUNCT
ejpam-5916	402	12	14(1):1–13	14(1):1–13	NUM
ejpam-5916	402	13	,	,	PUNCT
ejpam-5916	402	14	2022	2022	NUM
ejpam-5916	402	15	.	.	PUNCT
ejpam-5916	403	1	[	[	X
ejpam-5916	403	2	28	28	NUM
ejpam-5916	403	3	]	]	X
ejpam-5916	403	4	h.	h.	PROPN
ejpam-5916	403	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	403	6	and	and	CCONJ
ejpam-5916	403	7	y.	y.	PROPN
ejpam-5916	403	8	alrashedi	alrashedi	PROPN
ejpam-5916	403	9	.	.	PUNCT
ejpam-5916	404	1	mathematical	mathematical	ADJ
ejpam-5916	404	2	and	and	CCONJ
ejpam-5916	404	3	physical	physical	ADJ
ejpam-5916	404	4	analysis	analysis	NOUN
ejpam-5916	404	5	of	of	ADP
ejpam-5916	404	6	fractional	fractional	ADJ
ejpam-5916	404	7	estevez	estevez	PROPN
ejpam-5916	404	8	-	-	PUNCT
ejpam-5916	404	9	mansfield	mansfield	PROPN
ejpam-5916	404	10	-	-	PUNCT
ejpam-5916	404	11	clarkson	clarkson	PROPN
ejpam-5916	404	12	equation	equation	NOUN
ejpam-5916	404	13	.	.	PUNCT
ejpam-5916	405	1	fractal	fractal	PROPN
ejpam-5916	405	2	and	and	CCONJ
ejpam-5916	405	3	fractional	fractional	ADJ
ejpam-5916	405	4	,	,	PUNCT
ejpam-5916	405	5	8(8):458	8(8):458	NUM
ejpam-5916	405	6	,	,	PUNCT
ejpam-5916	405	7	2024	2024	NUM
ejpam-5916	405	8	.	.	PUNCT
ejpam-5916	406	1	[	[	X
ejpam-5916	406	2	29	29	NUM
ejpam-5916	406	3	]	]	X
ejpam-5916	406	4	h.	h.	PROPN
ejpam-5916	406	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	406	6	,	,	PUNCT
ejpam-5916	406	7	m.	m.	PROPN
ejpam-5916	406	8	s.	s.	PROPN
ejpam-5916	406	9	m.	m.	PROPN
ejpam-5916	406	10	noorani	noorani	PROPN
ejpam-5916	406	11	,	,	PUNCT
ejpam-5916	406	12	h.	h.	PROPN
ejpam-5916	406	13	aydi	aydi	PROPN
ejpam-5916	406	14	,	,	PUNCT
ejpam-5916	406	15	and	and	CCONJ
ejpam-5916	406	16	w.	w.	PROPN
ejpam-5916	406	17	shatanawi	shatanawi	PROPN
ejpam-5916	406	18	.	.	PUNCT
ejpam-5916	407	1	on	on	ADP
ejpam-5916	407	2	common	common	ADJ
ejpam-5916	407	3	fixed	fix	VERB
ejpam-5916	407	4	point	point	NOUN
ejpam-5916	407	5	results	result	NOUN
ejpam-5916	407	6	for	for	ADP
ejpam-5916	407	7	new	new	ADJ
ejpam-5916	407	8	contractions	contraction	NOUN
ejpam-5916	407	9	with	with	ADP
ejpam-5916	407	10	applications	application	NOUN
ejpam-5916	407	11	to	to	PART
ejpam-5916	407	12	graph	graph	VERB
ejpam-5916	407	13	and	and	CCONJ
ejpam-5916	407	14	integral	integral	ADJ
ejpam-5916	407	15	equations	equation	NOUN
ejpam-5916	407	16	.	.	PUNCT
ejpam-5916	408	1	mathematics	mathematic	NOUN
ejpam-5916	408	2	,	,	PUNCT
ejpam-5916	408	3	7(11):1036	7(11):1036	NOUN
ejpam-5916	408	4	,	,	PUNCT
ejpam-5916	408	5	2019	2019	NUM
ejpam-5916	408	6	.	.	PUNCT
ejpam-5916	409	1	[	[	X
ejpam-5916	409	2	30	30	NUM
ejpam-5916	409	3	]	]	X
ejpam-5916	409	4	i.	i.	PROPN
ejpam-5916	409	5	m.	m.	PROPN
ejpam-5916	409	6	batiha	batiha	PROPN
ejpam-5916	409	7	,	,	PUNCT
ejpam-5916	409	8	s.	s.	PROPN
ejpam-5916	409	9	a.	a.	PROPN
ejpam-5916	409	10	njadat	njadat	PROPN
ejpam-5916	409	11	,	,	PUNCT
ejpam-5916	409	12	r.	r.	PROPN
ejpam-5916	409	13	m.	m.	PROPN
ejpam-5916	409	14	batyha	batyha	PROPN
ejpam-5916	409	15	,	,	PUNCT
ejpam-5916	409	16	a.	a.	NOUN
ejpam-5916	409	17	zraiqat	zraiqat	PROPN
ejpam-5916	409	18	,	,	PUNCT
ejpam-5916	409	19	a.	a.	NOUN
ejpam-5916	409	20	dababneh	dababneh	PROPN
ejpam-5916	409	21	,	,	PUNCT
ejpam-5916	409	22	and	and	CCONJ
ejpam-5916	409	23	s.	s.	PROPN
ejpam-5916	409	24	momani	momani	PROPN
ejpam-5916	409	25	.	.	PUNCT
ejpam-5916	410	1	design	design	NOUN
ejpam-5916	410	2	fractional	fractional	ADJ
ejpam-5916	410	3	-	-	PUNCT
ejpam-5916	410	4	order	order	NOUN
ejpam-5916	410	5	pid	pid	NOUN
ejpam-5916	410	6	controllers	controller	NOUN
ejpam-5916	410	7	for	for	ADP
ejpam-5916	410	8	single	single	ADJ
ejpam-5916	410	9	-	-	PUNCT
ejpam-5916	410	10	joint	joint	ADJ
ejpam-5916	410	11	robot	robot	NOUN
ejpam-5916	410	12	arm	arm	NOUN
ejpam-5916	410	13	model	model	NOUN
ejpam-5916	410	14	.	.	PUNCT
ejpam-5916	411	1	international	international	ADJ
ejpam-5916	411	2	journal	journal	NOUN
ejpam-5916	411	3	of	of	ADP
ejpam-5916	411	4	advances	advance	NOUN
ejpam-5916	411	5	in	in	ADP
ejpam-5916	411	6	soft	soft	ADJ
ejpam-5916	411	7	computing	computing	NOUN
ejpam-5916	411	8	and	and	CCONJ
ejpam-5916	411	9	its	its	PRON
ejpam-5916	411	10	applications	application	NOUN
ejpam-5916	411	11	,	,	PUNCT
ejpam-5916	411	12	14(2):96–114	14(2):96–114	NUM
ejpam-5916	411	13	,	,	PUNCT
ejpam-5916	411	14	2022	2022	NUM
ejpam-5916	411	15	.	.	PUNCT
ejpam-5916	412	1	[	[	X
ejpam-5916	412	2	31	31	NUM
ejpam-5916	412	3	]	]	PUNCT
ejpam-5916	412	4	h.	h.	PROPN
ejpam-5916	412	5	qawaqneh	qawaqneh	PROPN
ejpam-5916	412	6	,	,	PUNCT
ejpam-5916	412	7	h.	h.	PROPN
ejpam-5916	412	8	a.	a.	PROPN
ejpam-5916	412	9	hammad	hammad	PROPN
ejpam-5916	412	10	,	,	PUNCT
ejpam-5916	412	11	and	and	CCONJ
ejpam-5916	412	12	h.	h.	PROPN
ejpam-5916	412	13	aydi	aydi	VERB
ejpam-5916	412	14	.	.	PUNCT
ejpam-5916	413	1	exploring	explore	VERB
ejpam-5916	413	2	new	new	ADJ
ejpam-5916	413	3	geometric	geometric	ADJ
ejpam-5916	413	4	contraction	contraction	NOUN
ejpam-5916	413	5	mappings	mapping	NOUN
ejpam-5916	413	6	and	and	CCONJ
ejpam-5916	413	7	their	their	PRON
ejpam-5916	413	8	applications	application	NOUN
ejpam-5916	413	9	in	in	ADP
ejpam-5916	413	10	fractional	fractional	ADJ
ejpam-5916	413	11	metric	metric	ADJ
ejpam-5916	413	12	spaces	space	NOUN
ejpam-5916	413	13	.	.	PUNCT
ejpam-5916	414	1	aims	aim	VERB
ejpam-5916	414	2	mathematics	mathematic	NOUN
ejpam-5916	414	3	,	,	PUNCT
ejpam-5916	414	4	9(1):521–541	9(1):521–541	NUM
ejpam-5916	414	5	,	,	PUNCT
ejpam-5916	414	6	2024	2024	NUM
ejpam-5916	414	7	.	.	PUNCT
ejpam-5916	415	1	[	[	X
ejpam-5916	415	2	32	32	NUM
ejpam-5916	415	3	]	]	PUNCT
ejpam-5916	415	4	t.	t.	PROPN
ejpam-5916	415	5	kanan	kanan	PROPN
ejpam-5916	415	6	,	,	PUNCT
ejpam-5916	415	7	m.	m.	NOUN
ejpam-5916	415	8	elbes	elbes	PROPN
ejpam-5916	415	9	,	,	PUNCT
ejpam-5916	415	10	k.	k.	PROPN
ejpam-5916	415	11	abu	abu	PROPN
ejpam-5916	415	12	maria	maria	PROPN
ejpam-5916	415	13	,	,	PUNCT
ejpam-5916	415	14	and	and	CCONJ
ejpam-5916	415	15	m.	m.	NOUN
ejpam-5916	415	16	alia	alia	PROPN
ejpam-5916	415	17	.	.	PUNCT
ejpam-5916	416	1	exploring	explore	VERB
ejpam-5916	416	2	the	the	DET
ejpam-5916	416	3	potential	potential	NOUN
ejpam-5916	416	4	of	of	ADP
ejpam-5916	416	5	iotbased	iotbase	VERB
ejpam-5916	416	6	learning	learn	VERB
ejpam-5916	416	7	environments	environment	NOUN
ejpam-5916	416	8	in	in	ADP
ejpam-5916	416	9	education	education	NOUN
ejpam-5916	416	10	.	.	PUNCT
ejpam-5916	417	1	international	international	ADJ
ejpam-5916	417	2	journal	journal	NOUN
ejpam-5916	417	3	of	of	ADP
ejpam-5916	417	4	advances	advance	NOUN
ejpam-5916	417	5	in	in	ADP
ejpam-5916	417	6	soft	soft	ADJ
ejpam-5916	417	7	h.	h.	NOUN
ejpam-5916	417	8	qawaqneh	qawaqneh	PROPN
ejpam-5916	417	9	/	/	SYM
ejpam-5916	417	10	eur	eur	PROPN
ejpam-5916	417	11	.	.	PUNCT
ejpam-5916	418	1	j.	j.	PROPN
ejpam-5916	418	2	pure	pure	PROPN
ejpam-5916	418	3	appl	appl	PROPN
ejpam-5916	418	4	.	.	PROPN
ejpam-5916	418	5	math	math	PROPN
ejpam-5916	418	6	,	,	PUNCT
ejpam-5916	418	7	18	18	NUM
ejpam-5916	418	8	(	(	PUNCT
ejpam-5916	418	9	3	3	NUM
ejpam-5916	418	10	)	)	PUNCT
ejpam-5916	418	11	(	(	PUNCT
ejpam-5916	418	12	2025	2025	NUM
ejpam-5916	418	13	)	)	PUNCT
ejpam-5916	418	14	,	,	PUNCT
ejpam-5916	418	15	5916	5916	NUM
ejpam-5916	418	16	19	19	NUM
ejpam-5916	418	17	of	of	ADP
ejpam-5916	418	18	19	19	NUM
ejpam-5916	418	19	computing	computing	NOUN
ejpam-5916	418	20	and	and	CCONJ
ejpam-5916	418	21	its	its	PRON
ejpam-5916	418	22	applications	application	NOUN
ejpam-5916	418	23	,	,	PUNCT
ejpam-5916	418	24	15(2):1–16	15(2):1–16	NUM
ejpam-5916	418	25	,	,	PUNCT
ejpam-5916	418	26	2023	2023	NUM
ejpam-5916	418	27	.	.	PUNCT