id	sid	tid	token	lemma	pos
ejpam-4819	1	1	european	european	PROPN
ejpam-4819	1	2	journal	journal	PROPN
ejpam-4819	1	3	of	of	ADP
ejpam-4819	1	4	pure	pure	ADJ
ejpam-4819	1	5	and	and	CCONJ
ejpam-4819	1	6	applied	apply	VERB
ejpam-4819	1	7	mathematics	mathematic	NOUN
ejpam-4819	1	8	vol	vol	NOUN
ejpam-4819	1	9	.	.	PUNCT
ejpam-4819	2	1	16	16	NUM
ejpam-4819	2	2	,	,	PUNCT
ejpam-4819	2	3	no	no	INTJ
ejpam-4819	2	4	.	.	NOUN
ejpam-4819	2	5	3	3	NUM
ejpam-4819	2	6	,	,	PUNCT
ejpam-4819	2	7	2023	2023	NUM
ejpam-4819	2	8	,	,	PUNCT
ejpam-4819	2	9	1717	1717	NUM
ejpam-4819	2	10	-	-	SYM
ejpam-4819	2	11	1730	1730	NUM
ejpam-4819	3	1	issn	issn	PROPN
ejpam-4819	3	2	1307	1307	NUM
ejpam-4819	3	3	-	-	SYM
ejpam-4819	3	4	5543	5543	NUM
ejpam-4819	3	5	–	–	PUNCT
ejpam-4819	3	6	ejpam.com	ejpam.com	X
ejpam-4819	3	7	published	publish	VERB
ejpam-4819	3	8	by	by	ADP
ejpam-4819	3	9	new	new	PROPN
ejpam-4819	3	10	york	york	PROPN
ejpam-4819	3	11	business	business	PROPN
ejpam-4819	3	12	global	global	ADJ
ejpam-4819	3	13	(	(	PUNCT
ejpam-4819	3	14	h	h	NOUN
ejpam-4819	3	15	,	,	PUNCT
ejpam-4819	3	16	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	3	17	contractions	contraction	NOUN
ejpam-4819	3	18	in	in	ADP
ejpam-4819	3	19	ωb	ωb	NOUN
ejpam-4819	3	20	-	-	PUNCT
ejpam-4819	3	21	distance	distance	NOUN
ejpam-4819	3	22	mappings	mapping	NOUN
ejpam-4819	3	23	with	with	ADP
ejpam-4819	3	24	applications	application	NOUN
ejpam-4819	3	25	tariq	tariq	PROPN
ejpam-4819	3	26	qawasmeh	qawasmeh	PROPN
ejpam-4819	3	27	department	department	PROPN
ejpam-4819	3	28	of	of	ADP
ejpam-4819	3	29	mathematics	mathematic	NOUN
ejpam-4819	3	30	,	,	PUNCT
ejpam-4819	3	31	faculty	faculty	NOUN
ejpam-4819	3	32	of	of	ADP
ejpam-4819	3	33	science	science	NOUN
ejpam-4819	3	34	and	and	CCONJ
ejpam-4819	3	35	information	information	NOUN
ejpam-4819	3	36	technology	technology	NOUN
ejpam-4819	3	37	,	,	PUNCT
ejpam-4819	3	38	jadara	jadara	PROPN
ejpam-4819	3	39	university	university	PROPN
ejpam-4819	3	40	,	,	PUNCT
ejpam-4819	3	41	jordan	jordan	PROPN
ejpam-4819	3	42	abstract	abstract	PROPN
ejpam-4819	3	43	.	.	PUNCT
ejpam-4819	4	1	interpolative	interpolative	PROPN
ejpam-4819	4	2	kannan	kannan	PROPN
ejpam-4819	4	3	contractions	contraction	NOUN
ejpam-4819	4	4	are	be	AUX
ejpam-4819	4	5	a	a	DET
ejpam-4819	4	6	refinement	refinement	NOUN
ejpam-4819	4	7	of	of	ADP
ejpam-4819	4	8	kannan	kannan	PROPN
ejpam-4819	4	9	contraction	contraction	PROPN
ejpam-4819	4	10	,	,	PUNCT
ejpam-4819	4	11	which	which	PRON
ejpam-4819	4	12	is	be	AUX
ejpam-4819	4	13	considered	consider	VERB
ejpam-4819	4	14	as	as	ADP
ejpam-4819	4	15	one	one	NUM
ejpam-4819	4	16	of	of	ADP
ejpam-4819	4	17	the	the	DET
ejpam-4819	4	18	significant	significant	ADJ
ejpam-4819	4	19	notions	notion	NOUN
ejpam-4819	4	20	in	in	ADP
ejpam-4819	4	21	fixed	fix	VERB
ejpam-4819	4	22	point	point	NOUN
ejpam-4819	4	23	theory	theory	NOUN
ejpam-4819	4	24	.	.	PUNCT
ejpam-4819	5	1	gb	gb	NOUN
ejpam-4819	5	2	-	-	PUNCT
ejpam-4819	5	3	metric	metric	ADJ
ejpam-4819	5	4	spaces	space	NOUN
ejpam-4819	5	5	is	be	AUX
ejpam-4819	5	6	considered	consider	VERB
ejpam-4819	5	7	as	as	ADP
ejpam-4819	5	8	a	a	DET
ejpam-4819	5	9	generalized	generalized	ADJ
ejpam-4819	5	10	concept	concept	NOUN
ejpam-4819	5	11	of	of	ADP
ejpam-4819	5	12	both	both	DET
ejpam-4819	5	13	concepts	concept	NOUN
ejpam-4819	5	14	b	b	NOUN
ejpam-4819	5	15	-	-	PUNCT
ejpam-4819	5	16	metric	metric	ADJ
ejpam-4819	5	17	and	and	CCONJ
ejpam-4819	5	18	g	g	NOUN
ejpam-4819	5	19	-	-	PUNCT
ejpam-4819	5	20	metric	metric	ADJ
ejpam-4819	5	21	spaces	space	NOUN
ejpam-4819	5	22	therefore	therefore	ADV
ejpam-4819	5	23	,	,	PUNCT
ejpam-4819	5	24	the	the	DET
ejpam-4819	5	25	significant	significant	ADJ
ejpam-4819	5	26	fixed	fix	VERB
ejpam-4819	5	27	and	and	CCONJ
ejpam-4819	5	28	common	common	ADJ
ejpam-4819	5	29	fixed	fix	VERB
ejpam-4819	5	30	point	point	NOUN
ejpam-4819	5	31	results	result	NOUN
ejpam-4819	5	32	of	of	ADP
ejpam-4819	5	33	the	the	DET
ejpam-4819	5	34	contraction	contraction	NOUN
ejpam-4819	5	35	based	base	VERB
ejpam-4819	5	36	on	on	ADP
ejpam-4819	5	37	this	this	DET
ejpam-4819	5	38	concept	concept	NOUN
ejpam-4819	5	39	is	be	AUX
ejpam-4819	5	40	generalized	generalized	ADJ
ejpam-4819	5	41	results	result	NOUN
ejpam-4819	5	42	for	for	ADP
ejpam-4819	5	43	both	both	DET
ejpam-4819	5	44	concepts	concept	NOUN
ejpam-4819	5	45	.	.	PUNCT
ejpam-4819	6	1	the	the	DET
ejpam-4819	6	2	purpose	purpose	NOUN
ejpam-4819	6	3	of	of	ADP
ejpam-4819	6	4	this	this	DET
ejpam-4819	6	5	manuscript	manuscript	NOUN
ejpam-4819	6	6	,	,	PUNCT
ejpam-4819	6	7	is	be	AUX
ejpam-4819	6	8	to	to	PART
ejpam-4819	6	9	take	take	VERB
ejpam-4819	6	10	advantage	advantage	NOUN
ejpam-4819	6	11	to	to	ADP
ejpam-4819	6	12	interpolative	interpolative	ADJ
ejpam-4819	6	13	kannan	kannan	PROPN
ejpam-4819	6	14	contraction	contraction	NOUN
ejpam-4819	6	15	together	together	ADV
ejpam-4819	6	16	with	with	ADP
ejpam-4819	6	17	the	the	DET
ejpam-4819	6	18	notion	notion	NOUN
ejpam-4819	6	19	of	of	ADP
ejpam-4819	6	20	ωb	ωb	PRON
ejpam-4819	6	21	which	which	PRON
ejpam-4819	6	22	equipped	equip	VERB
ejpam-4819	6	23	with	with	ADP
ejpam-4819	6	24	gb	gb	ADV
ejpam-4819	6	25	-	-	PUNCT
ejpam-4819	6	26	metric	metric	ADJ
ejpam-4819	6	27	spaces	space	NOUN
ejpam-4819	6	28	and	and	CCONJ
ejpam-4819	6	29	h	h	PROPN
ejpam-4819	6	30	simulation	simulation	NOUN
ejpam-4819	6	31	functions	function	NOUN
ejpam-4819	6	32	to	to	PART
ejpam-4819	6	33	formulate	formulate	VERB
ejpam-4819	6	34	two	two	NUM
ejpam-4819	6	35	new	new	ADJ
ejpam-4819	6	36	interpolative	interpolative	ADJ
ejpam-4819	6	37	contractions	contraction	NOUN
ejpam-4819	6	38	namely	namely	ADV
ejpam-4819	6	39	,	,	PUNCT
ejpam-4819	6	40	(	(	PUNCT
ejpam-4819	6	41	h	h	NOUN
ejpam-4819	6	42	,	,	PUNCT
ejpam-4819	6	43	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	6	44	contraction	contraction	NOUN
ejpam-4819	6	45	for	for	ADP
ejpam-4819	6	46	self	self	NOUN
ejpam-4819	6	47	mapping	mapping	NOUN
ejpam-4819	6	48	f	f	NOUN
ejpam-4819	6	49	and	and	CCONJ
ejpam-4819	6	50	generalized	generalized	ADJ
ejpam-4819	6	51	(	(	PUNCT
ejpam-4819	6	52	h	h	NOUN
ejpam-4819	6	53	,	,	PUNCT
ejpam-4819	6	54	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	6	55	contraction	contraction	NOUN
ejpam-4819	6	56	for	for	ADP
ejpam-4819	6	57	pair	pair	NOUN
ejpam-4819	6	58	of	of	ADP
ejpam-4819	6	59	self	self	NOUN
ejpam-4819	6	60	mappings	mapping	NOUN
ejpam-4819	6	61	(	(	PUNCT
ejpam-4819	6	62	f1	f1	NOUN
ejpam-4819	6	63	,	,	PUNCT
ejpam-4819	6	64	f2	f2	PROPN
ejpam-4819	6	65	)	)	PUNCT
ejpam-4819	6	66	.	.	PUNCT
ejpam-4819	7	1	we	we	PRON
ejpam-4819	7	2	discuss	discuss	VERB
ejpam-4819	7	3	new	new	ADJ
ejpam-4819	7	4	fixed	fix	VERB
ejpam-4819	7	5	and	and	CCONJ
ejpam-4819	7	6	common	common	ADJ
ejpam-4819	7	7	fixed	fix	VERB
ejpam-4819	7	8	point	point	NOUN
ejpam-4819	7	9	theorems	theorem	NOUN
ejpam-4819	7	10	.	.	PUNCT
ejpam-4819	8	1	moreover	moreover	ADV
ejpam-4819	8	2	,	,	PUNCT
ejpam-4819	8	3	to	to	PART
ejpam-4819	8	4	demonstrate	demonstrate	VERB
ejpam-4819	8	5	the	the	DET
ejpam-4819	8	6	applicability	applicability	NOUN
ejpam-4819	8	7	and	and	CCONJ
ejpam-4819	8	8	novelty	novelty	NOUN
ejpam-4819	8	9	of	of	ADP
ejpam-4819	8	10	our	our	PRON
ejpam-4819	8	11	theorems	theorem	NOUN
ejpam-4819	8	12	,	,	PUNCT
ejpam-4819	8	13	we	we	PRON
ejpam-4819	8	14	formulate	formulate	VERB
ejpam-4819	8	15	numerical	numerical	ADJ
ejpam-4819	8	16	examples	example	NOUN
ejpam-4819	8	17	and	and	CCONJ
ejpam-4819	8	18	applications	application	NOUN
ejpam-4819	8	19	to	to	PART
ejpam-4819	8	20	illustrate	illustrate	VERB
ejpam-4819	8	21	the	the	DET
ejpam-4819	8	22	importance	importance	NOUN
ejpam-4819	8	23	of	of	ADP
ejpam-4819	8	24	fixed	fix	VERB
ejpam-4819	8	25	point	point	NOUN
ejpam-4819	8	26	theory	theory	NOUN
ejpam-4819	8	27	in	in	ADP
ejpam-4819	8	28	applied	apply	VERB
ejpam-4819	8	29	mathematics	mathematic	NOUN
ejpam-4819	8	30	and	and	CCONJ
ejpam-4819	8	31	other	other	ADJ
ejpam-4819	8	32	sciences	science	NOUN
ejpam-4819	8	33	.	.	PUNCT
ejpam-4819	9	1	2020	2020	NUM
ejpam-4819	9	2	mathematics	mathematic	NOUN
ejpam-4819	9	3	subject	subject	NOUN
ejpam-4819	9	4	classifications	classification	NOUN
ejpam-4819	9	5	:	:	PUNCT
ejpam-4819	9	6	54h25	54h25	NUM
ejpam-4819	9	7	,	,	PUNCT
ejpam-4819	9	8	47h10	47h10	NUM
ejpam-4819	9	9	,	,	PUNCT
ejpam-4819	9	10	34b15	34b15	NUM
ejpam-4819	9	11	key	key	ADJ
ejpam-4819	9	12	words	word	NOUN
ejpam-4819	9	13	and	and	CCONJ
ejpam-4819	9	14	phrases	phrase	NOUN
ejpam-4819	9	15	:	:	PUNCT
ejpam-4819	9	16	ωb	ωb	NUM
ejpam-4819	9	17	distance	distance	NOUN
ejpam-4819	9	18	mappings	mapping	NOUN
ejpam-4819	9	19	,	,	PUNCT
ejpam-4819	9	20	interpolative	interpolative	ADJ
ejpam-4819	9	21	kannan	kannan	PROPN
ejpam-4819	9	22	contractions	contractions	PROPN
ejpam-4819	9	23	,	,	PUNCT
ejpam-4819	9	24	h	h	NOUN
ejpam-4819	9	25	-	-	PUNCT
ejpam-4819	9	26	simulation	simulation	NOUN
ejpam-4819	9	27	functions	function	NOUN
ejpam-4819	9	28	,	,	PUNCT
ejpam-4819	9	29	gb	gb	ADV
ejpam-4819	9	30	-	-	PUNCT
ejpam-4819	9	31	metric	metric	ADJ
ejpam-4819	9	32	spaces	space	NOUN
ejpam-4819	9	33	1	1	NUM
ejpam-4819	9	34	.	.	PUNCT
ejpam-4819	10	1	introduction	introduction	NOUN
ejpam-4819	10	2	and	and	CCONJ
ejpam-4819	10	3	mathematical	mathematical	ADJ
ejpam-4819	10	4	preliminaries	preliminary	NOUN
ejpam-4819	10	5	the	the	DET
ejpam-4819	10	6	study	study	NOUN
ejpam-4819	10	7	of	of	ADP
ejpam-4819	10	8	fixed	fix	VERB
ejpam-4819	10	9	point	point	NOUN
ejpam-4819	10	10	theory	theory	NOUN
ejpam-4819	10	11	has	have	AUX
ejpam-4819	10	12	gained	gain	VERB
ejpam-4819	10	13	increasing	increase	VERB
ejpam-4819	10	14	importance	importance	NOUN
ejpam-4819	10	15	and	and	CCONJ
ejpam-4819	10	16	interest	interest	NOUN
ejpam-4819	10	17	in	in	ADP
ejpam-4819	10	18	pure	pure	ADJ
ejpam-4819	10	19	and	and	CCONJ
ejpam-4819	10	20	applied	applied	ADJ
ejpam-4819	10	21	mathematics	mathematic	NOUN
ejpam-4819	10	22	[	[	X
ejpam-4819	10	23	8]–[17	8]–[17	X
ejpam-4819	10	24	]	]	X
ejpam-4819	10	25	ever	ever	ADV
ejpam-4819	10	26	since	since	SCONJ
ejpam-4819	10	27	banach	banach	ADV
ejpam-4819	10	28	came	come	VERB
ejpam-4819	10	29	up	up	ADP
ejpam-4819	10	30	with	with	ADP
ejpam-4819	10	31	his	his	PRON
ejpam-4819	10	32	result	result	NOUN
ejpam-4819	10	33	(	(	PUNCT
ejpam-4819	10	34	banach	banach	NOUN
ejpam-4819	10	35	contraction	contraction	NOUN
ejpam-4819	10	36	principle	principle	NOUN
ejpam-4819	10	37	)	)	PUNCT
ejpam-4819	11	1	[	[	X
ejpam-4819	11	2	4	4	X
ejpam-4819	11	3	]	]	PUNCT
ejpam-4819	11	4	which	which	PRON
ejpam-4819	11	5	is	be	AUX
ejpam-4819	11	6	considered	consider	VERB
ejpam-4819	11	7	to	to	PART
ejpam-4819	11	8	be	be	AUX
ejpam-4819	11	9	one	one	NUM
ejpam-4819	11	10	of	of	ADP
ejpam-4819	11	11	the	the	DET
ejpam-4819	11	12	most	most	ADV
ejpam-4819	11	13	important	important	ADJ
ejpam-4819	11	14	results	result	NOUN
ejpam-4819	11	15	in	in	ADP
ejpam-4819	11	16	mathematics	mathematic	NOUN
ejpam-4819	11	17	as	as	ADV
ejpam-4819	11	18	well	well	ADV
ejpam-4819	11	19	as	as	ADP
ejpam-4819	11	20	other	other	ADJ
ejpam-4819	11	21	sciences	science	NOUN
ejpam-4819	11	22	.	.	PUNCT
ejpam-4819	12	1	since	since	SCONJ
ejpam-4819	12	2	then	then	ADV
ejpam-4819	12	3	,	,	PUNCT
ejpam-4819	12	4	many	many	ADJ
ejpam-4819	12	5	mathematicians	mathematician	NOUN
ejpam-4819	12	6	refined	refine	VERB
ejpam-4819	12	7	the	the	DET
ejpam-4819	12	8	result	result	NOUN
ejpam-4819	12	9	of	of	ADP
ejpam-4819	12	10	banach	banach	NOUN
ejpam-4819	12	11	in	in	ADP
ejpam-4819	12	12	two	two	NUM
ejpam-4819	12	13	directions	direction	NOUN
ejpam-4819	12	14	;	;	PUNCT
ejpam-4819	12	15	some	some	PRON
ejpam-4819	12	16	by	by	ADP
ejpam-4819	12	17	replacing	replace	VERB
ejpam-4819	12	18	the	the	DET
ejpam-4819	12	19	frame	frame	NOUN
ejpam-4819	12	20	of	of	ADP
ejpam-4819	12	21	distance	distance	NOUN
ejpam-4819	12	22	space	space	NOUN
ejpam-4819	12	23	such	such	ADJ
ejpam-4819	12	24	as	as	ADP
ejpam-4819	12	25	b	b	PROPN
ejpam-4819	12	26	,	,	PUNCT
ejpam-4819	12	27	gmetric	gmetric	ADJ
ejpam-4819	12	28	spaces	space	NOUN
ejpam-4819	12	29	,	,	PUNCT
ejpam-4819	12	30	modified	modify	VERB
ejpam-4819	12	31	ω	ω	PROPN
ejpam-4819	12	32	,	,	PUNCT
ejpam-4819	12	33	ω	ω	NUM
ejpam-4819	12	34	-	-	PUNCT
ejpam-4819	12	35	distance	distance	NOUN
ejpam-4819	12	36	mappings	mapping	NOUN
ejpam-4819	12	37	(	(	PUNCT
ejpam-4819	12	38	see	see	VERB
ejpam-4819	12	39	[	[	X
ejpam-4819	12	40	5]–[16	5]–[16	NUM
ejpam-4819	12	41	]	]	PUNCT
ejpam-4819	12	42	)	)	PUNCT
ejpam-4819	12	43	,	,	PUNCT
ejpam-4819	12	44	and	and	CCONJ
ejpam-4819	12	45	the	the	DET
ejpam-4819	12	46	others	other	NOUN
ejpam-4819	12	47	refined	refine	VERB
ejpam-4819	12	48	the	the	DET
ejpam-4819	12	49	contraction	contraction	NOUN
ejpam-4819	12	50	condition	condition	NOUN
ejpam-4819	12	51	(	(	PUNCT
ejpam-4819	12	52	for	for	ADP
ejpam-4819	12	53	example	example	NOUN
ejpam-4819	12	54	see	see	VERB
ejpam-4819	12	55	[	[	X
ejpam-4819	12	56	18]–[15	18]–[15	NOUN
ejpam-4819	12	57	]	]	NUM
ejpam-4819	12	58	)	)	PUNCT
ejpam-4819	12	59	.	.	PUNCT
ejpam-4819	13	1	kannan	kannan	PROPN
ejpam-4819	13	2	contraction	contraction	PROPN
ejpam-4819	13	3	principle	principle	NOUN
ejpam-4819	13	4	[	[	X
ejpam-4819	13	5	12	12	NUM
ejpam-4819	13	6	]	]	PUNCT
ejpam-4819	13	7	is	be	AUX
ejpam-4819	13	8	the	the	DET
ejpam-4819	13	9	first	first	ADJ
ejpam-4819	13	10	outstanding	outstanding	ADJ
ejpam-4819	13	11	result	result	NOUN
ejpam-4819	13	12	after	after	ADP
ejpam-4819	13	13	banach	banach	NOUN
ejpam-4819	13	14	contraction	contraction	NOUN
ejpam-4819	13	15	principle	principle	NOUN
ejpam-4819	13	16	,	,	PUNCT
ejpam-4819	13	17	and	and	CCONJ
ejpam-4819	13	18	it	it	PRON
ejpam-4819	13	19	is	be	AUX
ejpam-4819	13	20	important	important	ADJ
ejpam-4819	13	21	to	to	PART
ejpam-4819	13	22	mention	mention	VERB
ejpam-4819	13	23	that	that	SCONJ
ejpam-4819	13	24	this	this	DET
ejpam-4819	13	25	contraction	contraction	NOUN
ejpam-4819	13	26	characterizes	characterize	VERB
ejpam-4819	13	27	the	the	DET
ejpam-4819	13	28	metric	metric	ADJ
ejpam-4819	13	29	completeness	completeness	NOUN
ejpam-4819	13	30	.	.	PUNCT
ejpam-4819	14	1	many	many	ADJ
ejpam-4819	14	2	mathematicians	mathematician	NOUN
ejpam-4819	14	3	improved	improve	VERB
ejpam-4819	14	4	this	this	DET
ejpam-4819	14	5	contraction	contraction	NOUN
ejpam-4819	14	6	;	;	PUNCT
ejpam-4819	14	7	an	an	DET
ejpam-4819	14	8	interesting	interesting	ADJ
ejpam-4819	14	9	example	example	NOUN
ejpam-4819	14	10	of	of	ADP
ejpam-4819	14	11	this	this	DET
ejpam-4819	14	12	improving	improve	VERB
ejpam-4819	14	13	is	be	AUX
ejpam-4819	14	14	interpolative	interpolative	ADJ
ejpam-4819	14	15	kannan	kannan	PROPN
ejpam-4819	14	16	contractions	contraction	NOUN
ejpam-4819	15	1	[	[	X
ejpam-4819	15	2	10	10	NUM
ejpam-4819	15	3	,	,	PUNCT
ejpam-4819	15	4	13	13	NUM
ejpam-4819	15	5	]	]	PUNCT
ejpam-4819	15	6	.	.	PUNCT
ejpam-4819	16	1	since	since	SCONJ
ejpam-4819	16	2	then	then	ADV
ejpam-4819	16	3	,	,	PUNCT
ejpam-4819	16	4	many	many	ADJ
ejpam-4819	16	5	significant	significant	ADJ
ejpam-4819	16	6	doi	doi	NOUN
ejpam-4819	16	7	:	:	PUNCT
ejpam-4819	16	8	https://doi.org/10.29020/nybg.ejpam.v16i3.4819	https://doi.org/10.29020/nybg.ejpam.v16i3.4819	ADJ
ejpam-4819	16	9	email	email	NOUN
ejpam-4819	16	10	addresses	address	NOUN
ejpam-4819	16	11	:	:	PUNCT
ejpam-4819	16	12	ta.qawasmeh@jadara.edu.jo	ta.qawasmeh@jadara.edu.jo	NUM
ejpam-4819	16	13	,	,	PUNCT
ejpam-4819	16	14	jorqaw@yahoo.com	jorqaw@yahoo.com	X
ejpam-4819	16	15	(	(	PUNCT
ejpam-4819	16	16	t.	t.	NOUN
ejpam-4819	16	17	qawasmeh	qawasmeh	NOUN
ejpam-4819	16	18	)	)	PUNCT
ejpam-4819	16	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4819	16	20	1717	1717	NUM
ejpam-4819	16	21	©	©	PROPN
ejpam-4819	16	22	2023	2023	NUM
ejpam-4819	16	23	ejpam	ejpam	NOUN
ejpam-4819	16	24	all	all	DET
ejpam-4819	16	25	rights	right	NOUN
ejpam-4819	16	26	reserved	reserve	VERB
ejpam-4819	16	27	.	.	PUNCT
ejpam-4819	17	1	t.	t.	PROPN
ejpam-4819	17	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	17	3	/	/	SYM
ejpam-4819	17	4	eur	eur	PROPN
ejpam-4819	17	5	.	.	PUNCT
ejpam-4819	18	1	j.	j.	PROPN
ejpam-4819	18	2	pure	pure	PROPN
ejpam-4819	18	3	appl	appl	PROPN
ejpam-4819	18	4	.	.	PROPN
ejpam-4819	18	5	math	math	PROPN
ejpam-4819	18	6	,	,	PUNCT
ejpam-4819	18	7	16	16	NUM
ejpam-4819	18	8	(	(	PUNCT
ejpam-4819	18	9	3	3	NUM
ejpam-4819	18	10	)	)	PUNCT
ejpam-4819	18	11	(	(	PUNCT
ejpam-4819	18	12	2023	2023	NUM
ejpam-4819	18	13	)	)	PUNCT
ejpam-4819	18	14	,	,	PUNCT
ejpam-4819	18	15	1717	1717	NUM
ejpam-4819	18	16	-	-	SYM
ejpam-4819	18	17	1730	1730	NUM
ejpam-4819	18	18	1718	1718	NUM
ejpam-4819	18	19	contractions	contraction	NOUN
ejpam-4819	18	20	formulated	formulate	VERB
ejpam-4819	18	21	based	base	VERB
ejpam-4819	18	22	on	on	ADP
ejpam-4819	18	23	interpolative	interpolative	ADJ
ejpam-4819	18	24	contractions	contraction	NOUN
ejpam-4819	18	25	which	which	PRON
ejpam-4819	18	26	utilized	utilize	VERB
ejpam-4819	18	27	in	in	ADP
ejpam-4819	18	28	the	the	DET
ejpam-4819	18	29	literature	literature	NOUN
ejpam-4819	18	30	to	to	PART
ejpam-4819	18	31	investigate	investigate	VERB
ejpam-4819	18	32	significant	significant	ADJ
ejpam-4819	18	33	fixed	fix	VERB
ejpam-4819	18	34	and	and	CCONJ
ejpam-4819	18	35	common	common	ADJ
ejpam-4819	18	36	fixed	fix	VERB
ejpam-4819	18	37	point	point	NOUN
ejpam-4819	18	38	results	result	NOUN
ejpam-4819	18	39	such	such	ADJ
ejpam-4819	18	40	as	as	ADP
ejpam-4819	18	41	debnath	debnath	NOUN
ejpam-4819	18	42	et.al	et.al	PROPN
ejpam-4819	18	43	.	.	PUNCT
ejpam-4819	19	1	[	[	X
ejpam-4819	19	2	7	7	NUM
ejpam-4819	19	3	,	,	PUNCT
ejpam-4819	19	4	9	9	NUM
ejpam-4819	19	5	]	]	PUNCT
ejpam-4819	19	6	.	.	PUNCT
ejpam-4819	20	1	in	in	ADP
ejpam-4819	20	2	this	this	DET
ejpam-4819	20	3	study	study	NOUN
ejpam-4819	20	4	,	,	PUNCT
ejpam-4819	20	5	our	our	PRON
ejpam-4819	20	6	purpose	purpose	NOUN
ejpam-4819	20	7	is	be	AUX
ejpam-4819	20	8	to	to	PART
ejpam-4819	20	9	formulate	formulate	VERB
ejpam-4819	20	10	two	two	NUM
ejpam-4819	20	11	significant	significant	ADJ
ejpam-4819	20	12	interpolative	interpolative	ADJ
ejpam-4819	20	13	contractions	contraction	NOUN
ejpam-4819	20	14	in	in	ADP
ejpam-4819	20	15	the	the	DET
ejpam-4819	20	16	framework	framework	NOUN
ejpam-4819	20	17	of	of	ADP
ejpam-4819	20	18	ωb	ωb	NOUN
ejpam-4819	20	19	distance	distance	NOUN
ejpam-4819	20	20	mappings	mapping	NOUN
ejpam-4819	20	21	which	which	PRON
ejpam-4819	20	22	equipped	equip	VERB
ejpam-4819	20	23	withgb	withgb	ADJ
ejpam-4819	20	24	-	-	PUNCT
ejpam-4819	20	25	metric	metric	ADJ
ejpam-4819	20	26	spaces	space	NOUN
ejpam-4819	20	27	where	where	SCONJ
ejpam-4819	20	28	nontrivial	nontrivial	ADJ
ejpam-4819	20	29	generalisations	generalisation	NOUN
ejpam-4819	20	30	are	be	AUX
ejpam-4819	20	31	possible	possible	ADJ
ejpam-4819	20	32	and	and	CCONJ
ejpam-4819	20	33	as	as	SCONJ
ejpam-4819	20	34	such	such	ADJ
ejpam-4819	20	35	,	,	PUNCT
ejpam-4819	20	36	application	application	NOUN
ejpam-4819	20	37	of	of	ADP
ejpam-4819	20	38	the	the	DET
ejpam-4819	20	39	results	result	NOUN
ejpam-4819	20	40	in	in	ADP
ejpam-4819	20	41	relevant	relevant	ADJ
ejpam-4819	20	42	fields	field	NOUN
ejpam-4819	20	43	becomes	become	VERB
ejpam-4819	20	44	feasible	feasible	ADJ
ejpam-4819	20	45	and	and	CCONJ
ejpam-4819	20	46	easier	easy	ADJ
ejpam-4819	20	47	.	.	PUNCT
ejpam-4819	21	1	definition	definition	NOUN
ejpam-4819	21	2	1	1	NUM
ejpam-4819	21	3	.	.	PUNCT
ejpam-4819	22	1	[	[	X
ejpam-4819	22	2	10	10	NUM
ejpam-4819	22	3	,	,	PUNCT
ejpam-4819	22	4	13	13	NUM
ejpam-4819	22	5	]	]	PUNCT
ejpam-4819	22	6	suppose	suppose	VERB
ejpam-4819	22	7	(	(	PUNCT
ejpam-4819	22	8	c	c	X
ejpam-4819	22	9	,	,	PUNCT
ejpam-4819	22	10	d	d	NOUN
ejpam-4819	22	11	)	)	PUNCT
ejpam-4819	22	12	is	be	AUX
ejpam-4819	22	13	a	a	DET
ejpam-4819	22	14	metric	metric	ADJ
ejpam-4819	22	15	space	space	NOUN
ejpam-4819	22	16	and	and	CCONJ
ejpam-4819	22	17	f	f	X
ejpam-4819	22	18	,	,	PUNCT
ejpam-4819	22	19	g	g	PROPN
ejpam-4819	22	20	are	be	AUX
ejpam-4819	22	21	two	two	NUM
ejpam-4819	22	22	self	self	NOUN
ejpam-4819	22	23	mappings	mapping	NOUN
ejpam-4819	22	24	on	on	ADP
ejpam-4819	22	25	c	c	PROPN
ejpam-4819	22	26	and	and	CCONJ
ejpam-4819	22	27	λ	λ	X
ejpam-4819	22	28	∈	∈	PROPN
ejpam-4819	23	1	[	[	X
ejpam-4819	23	2	0	0	NUM
ejpam-4819	23	3	,	,	PUNCT
ejpam-4819	23	4	1	1	NUM
ejpam-4819	23	5	)	)	PUNCT
ejpam-4819	23	6	,	,	PUNCT
ejpam-4819	23	7	α	α	X
ejpam-4819	23	8	,	,	PUNCT
ejpam-4819	23	9	β	β	X
ejpam-4819	23	10	∈	∈	PROPN
ejpam-4819	23	11	(	(	PUNCT
ejpam-4819	23	12	0	0	NUM
ejpam-4819	23	13	,	,	PUNCT
ejpam-4819	23	14	1	1	NUM
ejpam-4819	23	15	)	)	PUNCT
ejpam-4819	23	16	where	where	SCONJ
ejpam-4819	23	17	β	β	X
ejpam-4819	23	18	+	+	NOUN
ejpam-4819	23	19	α	α	X
ejpam-4819	23	20	<	<	X
ejpam-4819	23	21	1	1	NUM
ejpam-4819	23	22	.	.	PUNCT
ejpam-4819	24	1	then	then	ADV
ejpam-4819	24	2	1	1	X
ejpam-4819	24	3	.	.	PUNCT
ejpam-4819	25	1	we	we	PRON
ejpam-4819	25	2	call	call	VERB
ejpam-4819	25	3	f	f	PROPN
ejpam-4819	25	4	a	a	DET
ejpam-4819	25	5	(	(	PUNCT
ejpam-4819	25	6	λ	λ	PROPN
ejpam-4819	25	7	,	,	PUNCT
ejpam-4819	25	8	α	α	X
ejpam-4819	25	9	,	,	PUNCT
ejpam-4819	25	10	β)-interpolative	β)-interpolative	PUNCT
ejpam-4819	25	11	kannan	kannan	PROPN
ejpam-4819	25	12	contraction	contraction	NOUN
ejpam-4819	25	13	if	if	SCONJ
ejpam-4819	25	14	d(fc1	d(fc1	PROPN
ejpam-4819	25	15	,	,	PUNCT
ejpam-4819	25	16	fc2	fc2	PROPN
ejpam-4819	25	17	)	)	PUNCT
ejpam-4819	25	18	≤	≤	PROPN
ejpam-4819	25	19	λd(c1	λd(c1	PROPN
ejpam-4819	25	20	,	,	PUNCT
ejpam-4819	25	21	fc1	fc1	PROPN
ejpam-4819	25	22	)	)	PUNCT
ejpam-4819	25	23	αd(c2	αd(c2	PROPN
ejpam-4819	25	24	,	,	PUNCT
ejpam-4819	25	25	fc2	fc2	PROPN
ejpam-4819	25	26	)	)	PUNCT
ejpam-4819	25	27	β	β	NOUN
ejpam-4819	25	28	,	,	PUNCT
ejpam-4819	25	29	(	(	PUNCT
ejpam-4819	25	30	1	1	X
ejpam-4819	25	31	)	)	PUNCT
ejpam-4819	25	32	∀	∀	NOUN
ejpam-4819	25	33	c1	c1	NOUN
ejpam-4819	25	34	,	,	PUNCT
ejpam-4819	25	35	c2	c2	PROPN
ejpam-4819	25	36	∈	∈	PROPN
ejpam-4819	25	37	c	c	PROPN
ejpam-4819	25	38	with	with	ADP
ejpam-4819	25	39	fc1	fc1	PROPN
ejpam-4819	25	40	̸=	̸=	PROPN
ejpam-4819	25	41	c1	c1	PROPN
ejpam-4819	25	42	and	and	CCONJ
ejpam-4819	25	43	fc2	fc2	PROPN
ejpam-4819	25	44	̸=	̸=	PROPN
ejpam-4819	25	45	c2	c2	PROPN
ejpam-4819	25	46	.	.	PUNCT
ejpam-4819	26	1	2	2	X
ejpam-4819	26	2	.	.	X
ejpam-4819	26	3	we	we	PRON
ejpam-4819	26	4	call	call	VERB
ejpam-4819	26	5	the	the	DET
ejpam-4819	26	6	pair	pair	NOUN
ejpam-4819	26	7	(	(	PUNCT
ejpam-4819	26	8	f	f	X
ejpam-4819	26	9	,	,	PUNCT
ejpam-4819	26	10	g	g	PROPN
ejpam-4819	26	11	)	)	PUNCT
ejpam-4819	26	12	a	a	DET
ejpam-4819	26	13	(	(	PUNCT
ejpam-4819	26	14	λ	λ	PROPN
ejpam-4819	26	15	,	,	PUNCT
ejpam-4819	26	16	α	α	X
ejpam-4819	26	17	,	,	PUNCT
ejpam-4819	26	18	β)-interpolative	β)-interpolative	PUNCT
ejpam-4819	26	19	kannan	kannan	PROPN
ejpam-4819	26	20	contraction	contraction	NOUN
ejpam-4819	26	21	pair	pair	NOUN
ejpam-4819	26	22	if	if	SCONJ
ejpam-4819	26	23	d(fc1	d(fc1	PROPN
ejpam-4819	26	24	,	,	PUNCT
ejpam-4819	26	25	gc2	gc2	NOUN
ejpam-4819	26	26	)	)	PUNCT
ejpam-4819	26	27	≤	≤	PROPN
ejpam-4819	26	28	λd(c1	λd(c1	PROPN
ejpam-4819	26	29	,	,	PUNCT
ejpam-4819	26	30	fc2	fc2	PROPN
ejpam-4819	26	31	)	)	PUNCT
ejpam-4819	26	32	αd(c2	αd(c2	PROPN
ejpam-4819	26	33	,	,	PUNCT
ejpam-4819	26	34	gc2	gc2	NOUN
ejpam-4819	26	35	)	)	PUNCT
ejpam-4819	26	36	β	β	NOUN
ejpam-4819	26	37	,	,	PUNCT
ejpam-4819	26	38	(	(	PUNCT
ejpam-4819	26	39	2	2	NUM
ejpam-4819	26	40	)	)	PUNCT
ejpam-4819	26	41	∀	∀	NOUN
ejpam-4819	26	42	c1	c1	NOUN
ejpam-4819	26	43	,	,	PUNCT
ejpam-4819	26	44	c2	c2	PROPN
ejpam-4819	26	45	∈	∈	PROPN
ejpam-4819	26	46	c	c	PROPN
ejpam-4819	26	47	with	with	ADP
ejpam-4819	26	48	fc1	fc1	PROPN
ejpam-4819	26	49	̸=	̸=	PROPN
ejpam-4819	26	50	c1	c1	PROPN
ejpam-4819	26	51	and	and	CCONJ
ejpam-4819	26	52	gc2	gc2	NOUN
ejpam-4819	26	53	̸=	̸=	PROPN
ejpam-4819	26	54	c2	c2	PROPN
ejpam-4819	26	55	.	.	PUNCT
ejpam-4819	27	1	the	the	DET
ejpam-4819	27	2	concept	concept	NOUN
ejpam-4819	27	3	of	of	ADP
ejpam-4819	27	4	gb	gb	NOUN
ejpam-4819	27	5	space	space	NOUN
ejpam-4819	27	6	has	have	AUX
ejpam-4819	27	7	been	be	AUX
ejpam-4819	27	8	formulated	formulate	VERB
ejpam-4819	27	9	by	by	ADP
ejpam-4819	27	10	a	a	DET
ejpam-4819	27	11	pioneer	pioneer	NOUN
ejpam-4819	27	12	mathematician	mathematician	NOUN
ejpam-4819	27	13	,	,	PUNCT
ejpam-4819	27	14	aghajani	aghajani	PROPN
ejpam-4819	27	15	et	et	PROPN
ejpam-4819	27	16	al	al	PROPN
ejpam-4819	27	17	.	.	PUNCT
ejpam-4819	28	1	[	[	X
ejpam-4819	28	2	2	2	NUM
ejpam-4819	28	3	]	]	PUNCT
ejpam-4819	28	4	,	,	PUNCT
ejpam-4819	28	5	providing	provide	VERB
ejpam-4819	28	6	a	a	DET
ejpam-4819	28	7	generalization	generalization	NOUN
ejpam-4819	28	8	of	of	ADP
ejpam-4819	28	9	the	the	DET
ejpam-4819	28	10	standard	standard	ADJ
ejpam-4819	28	11	concepts	concept	NOUN
ejpam-4819	28	12	of	of	ADP
ejpam-4819	28	13	g	g	NOUN
ejpam-4819	28	14	-	-	PUNCT
ejpam-4819	28	15	metric	metric	ADJ
ejpam-4819	28	16	space	space	NOUN
ejpam-4819	28	17	which	which	PRON
ejpam-4819	28	18	are	be	AUX
ejpam-4819	28	19	formulated	formulate	VERB
ejpam-4819	28	20	by	by	ADP
ejpam-4819	28	21	mustafa	mustafa	PROPN
ejpam-4819	28	22	and	and	CCONJ
ejpam-4819	28	23	sims	sim	NOUN
ejpam-4819	28	24	[	[	X
ejpam-4819	28	25	14	14	NUM
ejpam-4819	28	26	]	]	PUNCT
ejpam-4819	28	27	and	and	CCONJ
ejpam-4819	28	28	b	b	X
ejpam-4819	28	29	-	-	PUNCT
ejpam-4819	28	30	metric	metric	ADJ
ejpam-4819	28	31	space	space	NOUN
ejpam-4819	28	32	,	,	PUNCT
ejpam-4819	28	33	which	which	PRON
ejpam-4819	28	34	is	be	AUX
ejpam-4819	28	35	formulated	formulate	VERB
ejpam-4819	28	36	by	by	ADP
ejpam-4819	28	37	bakhtin	bakhtin	NOUN
ejpam-4819	28	38	[	[	X
ejpam-4819	28	39	3	3	NUM
ejpam-4819	28	40	]	]	PUNCT
ejpam-4819	28	41	as	as	SCONJ
ejpam-4819	28	42	follows	follow	VERB
ejpam-4819	28	43	:	:	PUNCT
ejpam-4819	28	44	definition	definition	NOUN
ejpam-4819	28	45	2	2	NUM
ejpam-4819	28	46	.	.	PUNCT
ejpam-4819	29	1	[	[	X
ejpam-4819	29	2	2	2	X
ejpam-4819	29	3	]	]	PUNCT
ejpam-4819	29	4	let	let	VERB
ejpam-4819	29	5	c	c	PRON
ejpam-4819	29	6	be	be	AUX
ejpam-4819	29	7	a	a	DET
ejpam-4819	29	8	non	non	ADJ
ejpam-4819	29	9	-	-	ADJ
ejpam-4819	29	10	empty	empty	ADJ
ejpam-4819	29	11	set	set	NOUN
ejpam-4819	29	12	and	and	CCONJ
ejpam-4819	29	13	b	b	NOUN
ejpam-4819	29	14	∈	∈	PROPN
ejpam-4819	30	1	[	[	X
ejpam-4819	30	2	1,+∞	1,+∞	NUM
ejpam-4819	30	3	)	)	PUNCT
ejpam-4819	30	4	.	.	PUNCT
ejpam-4819	31	1	assume	assume	VERB
ejpam-4819	31	2	that	that	SCONJ
ejpam-4819	31	3	the	the	DET
ejpam-4819	31	4	function	function	NOUN
ejpam-4819	31	5	gb	gb	ADP
ejpam-4819	31	6	:	:	PUNCT
ejpam-4819	32	1	c	c	X
ejpam-4819	32	2	×	×	NOUN
ejpam-4819	32	3	c	c	NOUN
ejpam-4819	32	4	×	×	NOUN
ejpam-4819	32	5	c	c	NOUN
ejpam-4819	32	6	→	→	PUNCT
ejpam-4819	32	7	[	[	X
ejpam-4819	32	8	0,+∞	0,+∞	NUM
ejpam-4819	32	9	)	)	PUNCT
ejpam-4819	32	10	fulfills	fulfill	VERB
ejpam-4819	32	11	the	the	DET
ejpam-4819	32	12	following	follow	VERB
ejpam-4819	32	13	conditions	condition	NOUN
ejpam-4819	32	14	:	:	PUNCT
ejpam-4819	32	15	1	1	X
ejpam-4819	32	16	.	.	X
ejpam-4819	32	17	gb(c	gb(c	NOUN
ejpam-4819	32	18	,	,	PUNCT
ejpam-4819	32	19	c	c	NOUN
ejpam-4819	32	20	′	′	NUM
ejpam-4819	32	21	,	,	PUNCT
ejpam-4819	32	22	c	c	X
ejpam-4819	32	23	′′	′′	PROPN
ejpam-4819	32	24	)	)	PUNCT
ejpam-4819	33	1	=	=	PUNCT
ejpam-4819	33	2	0	0	PUNCT
ejpam-4819	34	1	if	if	SCONJ
ejpam-4819	34	2	and	and	CCONJ
ejpam-4819	34	3	only	only	ADV
ejpam-4819	34	4	if	if	SCONJ
ejpam-4819	34	5	c	c	NOUN
ejpam-4819	34	6	=	=	PUNCT
ejpam-4819	35	1	c	c	NOUN
ejpam-4819	35	2	′	′	NOUN
ejpam-4819	36	1	=	=	PUNCT
ejpam-4819	36	2	c	c	NOUN
ejpam-4819	36	3	′′	′′	NOUN
ejpam-4819	36	4	;	;	PUNCT
ejpam-4819	36	5	2	2	X
ejpam-4819	36	6	.	.	X
ejpam-4819	36	7	gb(c	gb(c	NOUN
ejpam-4819	36	8	,	,	PUNCT
ejpam-4819	36	9	c	c	X
ejpam-4819	36	10	,	,	PUNCT
ejpam-4819	36	11	c	c	NOUN
ejpam-4819	36	12	′	′	NUM
ejpam-4819	36	13	)	)	PUNCT
ejpam-4819	36	14	≥	≥	NOUN
ejpam-4819	36	15	0	0	NUM
ejpam-4819	36	16	for	for	ADP
ejpam-4819	36	17	all	all	DET
ejpam-4819	36	18	c	c	NOUN
ejpam-4819	36	19	,	,	PUNCT
ejpam-4819	36	20	c	c	NOUN
ejpam-4819	36	21	′	′	NOUN
ejpam-4819	37	1	∈	∈	PROPN
ejpam-4819	37	2	c	c	NOUN
ejpam-4819	37	3	with	with	ADP
ejpam-4819	37	4	c	c	PROPN
ejpam-4819	37	5	̸=	̸=	PROPN
ejpam-4819	37	6	c	c	NOUN
ejpam-4819	37	7	′	′	NUM
ejpam-4819	37	8	;	;	PUNCT
ejpam-4819	37	9	3	3	X
ejpam-4819	37	10	.	.	X
ejpam-4819	37	11	gb(c	gb(c	NOUN
ejpam-4819	37	12	,	,	PUNCT
ejpam-4819	37	13	c	c	NOUN
ejpam-4819	37	14	′	′	NUM
ejpam-4819	37	15	,	,	PUNCT
ejpam-4819	37	16	c	c	NOUN
ejpam-4819	37	17	′	′	NUM
ejpam-4819	37	18	)	)	PUNCT
ejpam-4819	37	19	≤	≤	NOUN
ejpam-4819	37	20	gb(c	gb(c	NOUN
ejpam-4819	37	21	,	,	PUNCT
ejpam-4819	37	22	c	c	NOUN
ejpam-4819	37	23	′	′	NUM
ejpam-4819	37	24	,	,	PUNCT
ejpam-4819	37	25	c	c	X
ejpam-4819	37	26	′′	′′	PROPN
ejpam-4819	37	27	)	)	PUNCT
ejpam-4819	37	28	for	for	ADP
ejpam-4819	37	29	all	all	DET
ejpam-4819	37	30	c	c	NOUN
ejpam-4819	37	31	,	,	PUNCT
ejpam-4819	37	32	c	c	NOUN
ejpam-4819	37	33	′	′	NUM
ejpam-4819	37	34	,	,	PUNCT
ejpam-4819	37	35	c	c	X
ejpam-4819	38	1	′′	′′	PROPN
ejpam-4819	38	2	∈	∈	PROPN
ejpam-4819	38	3	c	c	NOUN
ejpam-4819	38	4	with	with	ADP
ejpam-4819	38	5	c	c	NOUN
ejpam-4819	38	6	′	′	NOUN
ejpam-4819	39	1	̸=	̸=	PROPN
ejpam-4819	39	2	c	c	NOUN
ejpam-4819	39	3	′′	′′	PROPN
ejpam-4819	39	4	;	;	PUNCT
ejpam-4819	39	5	4	4	X
ejpam-4819	39	6	.	.	X
ejpam-4819	39	7	gb(c	gb(c	NOUN
ejpam-4819	39	8	,	,	PUNCT
ejpam-4819	39	9	c	c	NOUN
ejpam-4819	39	10	′	′	NUM
ejpam-4819	39	11	,	,	PUNCT
ejpam-4819	39	12	c	c	X
ejpam-4819	39	13	′′	′′	PROPN
ejpam-4819	39	14	)	)	PUNCT
ejpam-4819	40	1	=	=	PUNCT
ejpam-4819	40	2	gb(p{c	gb(p{c	NOUN
ejpam-4819	40	3	,	,	PUNCT
ejpam-4819	40	4	c	c	NOUN
ejpam-4819	40	5	′	′	NUM
ejpam-4819	40	6	,	,	PUNCT
ejpam-4819	40	7	c	c	PROPN
ejpam-4819	40	8	′′	′′	PROPN
ejpam-4819	40	9	}	}	PUNCT
ejpam-4819	40	10	)	)	PUNCT
ejpam-4819	40	11	where	where	SCONJ
ejpam-4819	40	12	p	p	NOUN
ejpam-4819	40	13	is	be	AUX
ejpam-4819	40	14	a	a	DET
ejpam-4819	40	15	permutation	permutation	NOUN
ejpam-4819	40	16	of	of	ADP
ejpam-4819	40	17	c	c	NOUN
ejpam-4819	40	18	,	,	PUNCT
ejpam-4819	40	19	c	c	NOUN
ejpam-4819	40	20	′	′	NUM
ejpam-4819	40	21	,	,	PUNCT
ejpam-4819	40	22	c	c	X
ejpam-4819	41	1	′′	′′	NOUN
ejpam-4819	41	2	;	;	PUNCT
ejpam-4819	41	3	5	5	X
ejpam-4819	41	4	.	.	X
ejpam-4819	41	5	gb(c	gb(c	NOUN
ejpam-4819	41	6	,	,	PUNCT
ejpam-4819	41	7	c	c	NOUN
ejpam-4819	41	8	′	′	NUM
ejpam-4819	41	9	,	,	PUNCT
ejpam-4819	41	10	c	c	X
ejpam-4819	41	11	′′	′′	PROPN
ejpam-4819	41	12	)	)	PUNCT
ejpam-4819	41	13	≤	≤	PROPN
ejpam-4819	41	14	b[gb(c	b[gb(c	PROPN
ejpam-4819	41	15	,	,	PUNCT
ejpam-4819	41	16	a	a	PRON
ejpam-4819	41	17	,	,	PUNCT
ejpam-4819	41	18	a	a	NOUN
ejpam-4819	41	19	)	)	PUNCT
ejpam-4819	41	20	+	+	NOUN
ejpam-4819	41	21	gb(a	gb(a	NOUN
ejpam-4819	41	22	,	,	PUNCT
ejpam-4819	41	23	c	c	NOUN
ejpam-4819	41	24	′	′	NOUN
ejpam-4819	41	25	,	,	PUNCT
ejpam-4819	41	26	c	c	X
ejpam-4819	41	27	′′	′′	PROPN
ejpam-4819	41	28	)	)	PUNCT
ejpam-4819	41	29	]	]	PUNCT
ejpam-4819	41	30	for	for	ADP
ejpam-4819	41	31	all	all	DET
ejpam-4819	41	32	c	c	NOUN
ejpam-4819	41	33	,	,	PUNCT
ejpam-4819	41	34	c	c	NOUN
ejpam-4819	41	35	′	′	NUM
ejpam-4819	41	36	,	,	PUNCT
ejpam-4819	41	37	c	c	X
ejpam-4819	41	38	′′	′′	PROPN
ejpam-4819	41	39	,	,	PUNCT
ejpam-4819	41	40	a	a	DET
ejpam-4819	41	41	∈	∈	PROPN
ejpam-4819	41	42	c.	c.	NOUN
ejpam-4819	41	43	then	then	ADV
ejpam-4819	41	44	gb	gb	PRON
ejpam-4819	41	45	is	be	AUX
ejpam-4819	41	46	called	call	VERB
ejpam-4819	41	47	gb	gb	ADV
ejpam-4819	41	48	-	-	PUNCT
ejpam-4819	41	49	metric	metric	ADJ
ejpam-4819	41	50	on	on	ADP
ejpam-4819	41	51	c	c	PROPN
ejpam-4819	41	52	and	and	CCONJ
ejpam-4819	41	53	the	the	DET
ejpam-4819	41	54	pair	pair	NOUN
ejpam-4819	41	55	(	(	PUNCT
ejpam-4819	41	56	c	c	NOUN
ejpam-4819	41	57	,	,	PUNCT
ejpam-4819	41	58	gb	gb	NOUN
ejpam-4819	41	59	)	)	PUNCT
ejpam-4819	41	60	is	be	AUX
ejpam-4819	41	61	called	call	VERB
ejpam-4819	41	62	gb	gb	ADV
ejpam-4819	41	63	-	-	PUNCT
ejpam-4819	41	64	metric	metric	ADJ
ejpam-4819	41	65	spaces	space	NOUN
ejpam-4819	41	66	.	.	PUNCT
ejpam-4819	41	67	example	example	NOUN
ejpam-4819	42	1	1	1	NUM
ejpam-4819	42	2	.	.	PUNCT
ejpam-4819	43	1	[	[	X
ejpam-4819	43	2	2	2	X
ejpam-4819	43	3	]	]	X
ejpam-4819	43	4	if	if	SCONJ
ejpam-4819	43	5	(	(	PUNCT
ejpam-4819	43	6	c	c	X
ejpam-4819	43	7	,	,	PUNCT
ejpam-4819	43	8	g	g	NOUN
ejpam-4819	43	9	)	)	PUNCT
ejpam-4819	43	10	is	be	AUX
ejpam-4819	43	11	g	g	NOUN
ejpam-4819	43	12	-	-	PUNCT
ejpam-4819	43	13	metric	metric	ADJ
ejpam-4819	43	14	space	space	NOUN
ejpam-4819	43	15	and	and	CCONJ
ejpam-4819	43	16	p	p	NOUN
ejpam-4819	43	17	∈	∈	PROPN
ejpam-4819	43	18	(	(	PUNCT
ejpam-4819	43	19	1,+∞	1,+∞	NUM
ejpam-4819	43	20	)	)	PUNCT
ejpam-4819	43	21	.	.	PUNCT
ejpam-4819	44	1	define	define	VERB
ejpam-4819	44	2	gb	gb	PRON
ejpam-4819	44	3	:	:	PUNCT
ejpam-4819	44	4	c	c	NOUN
ejpam-4819	44	5	×	×	NOUN
ejpam-4819	44	6	c	c	NOUN
ejpam-4819	44	7	×	×	NOUN
ejpam-4819	44	8	c	c	NOUN
ejpam-4819	44	9	→	→	PUNCT
ejpam-4819	45	1	[	[	X
ejpam-4819	45	2	0,+∞	0,+∞	NUM
ejpam-4819	45	3	)	)	PUNCT
ejpam-4819	45	4	via	via	ADP
ejpam-4819	45	5	gb(c1	gb(c1	PROPN
ejpam-4819	45	6	,	,	PUNCT
ejpam-4819	45	7	c2	c2	PROPN
ejpam-4819	45	8	,	,	PUNCT
ejpam-4819	45	9	c3	c3	PROPN
ejpam-4819	45	10	)	)	PUNCT
ejpam-4819	46	1	=	=	SYM
ejpam-4819	46	2	(	(	PUNCT
ejpam-4819	46	3	g(c1	g(c1	PROPN
ejpam-4819	46	4	,	,	PUNCT
ejpam-4819	46	5	c2	c2	PROPN
ejpam-4819	46	6	,	,	PUNCT
ejpam-4819	46	7	c3	c3	PROPN
ejpam-4819	46	8	)	)	PUNCT
ejpam-4819	46	9	)	)	PUNCT
ejpam-4819	47	1	p.	p.	NOUN
ejpam-4819	47	2	then	then	ADV
ejpam-4819	47	3	gb	gb	PROPN
ejpam-4819	47	4	is	be	AUX
ejpam-4819	47	5	gb	gb	ADV
ejpam-4819	47	6	-	-	PUNCT
ejpam-4819	47	7	metric	metric	ADJ
ejpam-4819	47	8	space	space	NOUN
ejpam-4819	47	9	with	with	ADP
ejpam-4819	47	10	the	the	DET
ejpam-4819	47	11	base	base	NOUN
ejpam-4819	47	12	b	b	PROPN
ejpam-4819	47	13	=	=	SYM
ejpam-4819	47	14	2p−1	2p−1	NUM
ejpam-4819	47	15	.	.	PUNCT
ejpam-4819	48	1	henceforth	henceforth	ADV
ejpam-4819	48	2	,	,	PUNCT
ejpam-4819	48	3	(	(	PUNCT
ejpam-4819	48	4	c	c	X
ejpam-4819	48	5	,	,	PUNCT
ejpam-4819	48	6	gb	gb	NOUN
ejpam-4819	48	7	)	)	PUNCT
ejpam-4819	48	8	refers	refer	VERB
ejpam-4819	48	9	to	to	ADP
ejpam-4819	48	10	gb	gb	ADV
ejpam-4819	48	11	-	-	PUNCT
ejpam-4819	48	12	metric	metric	ADJ
ejpam-4819	48	13	spaces	space	NOUN
ejpam-4819	48	14	on	on	ADP
ejpam-4819	48	15	the	the	DET
ejpam-4819	48	16	set	set	NOUN
ejpam-4819	48	17	c.	c.	NOUN
ejpam-4819	48	18	in	in	ADP
ejpam-4819	48	19	the	the	DET
ejpam-4819	48	20	sub	sub	NOUN
ejpam-4819	48	21	-	-	NOUN
ejpam-4819	48	22	sequence	sequence	NOUN
ejpam-4819	48	23	,	,	PUNCT
ejpam-4819	48	24	c	c	PROPN
ejpam-4819	48	25	refers	refer	VERB
ejpam-4819	48	26	to	to	ADP
ejpam-4819	48	27	non	non	PRON
ejpam-4819	48	28	empty	empty	ADJ
ejpam-4819	48	29	set	set	NOUN
ejpam-4819	48	30	and	and	CCONJ
ejpam-4819	48	31	λf	λf	ADV
ejpam-4819	48	32	refers	refer	NOUN
ejpam-4819	48	33	to	to	ADP
ejpam-4819	48	34	the	the	DET
ejpam-4819	48	35	set	set	NOUN
ejpam-4819	48	36	of	of	ADP
ejpam-4819	48	37	all	all	DET
ejpam-4819	48	38	fixed	fix	VERB
ejpam-4819	48	39	points	point	NOUN
ejpam-4819	48	40	of	of	ADP
ejpam-4819	48	41	f	f	PROPN
ejpam-4819	48	42	in	in	ADP
ejpam-4819	48	43	c.	c.	PROPN
ejpam-4819	48	44	the	the	DET
ejpam-4819	48	45	concepts	concept	NOUN
ejpam-4819	48	46	of	of	ADP
ejpam-4819	48	47	gb	gb	NOUN
ejpam-4819	48	48	-	-	PUNCT
ejpam-4819	48	49	completeness	completeness	NOUN
ejpam-4819	48	50	and	and	CCONJ
ejpam-4819	48	51	gb	gb	NOUN
ejpam-4819	48	52	-	-	PUNCT
ejpam-4819	48	53	convergence	convergence	NOUN
ejpam-4819	48	54	are	be	AUX
ejpam-4819	48	55	as	as	ADV
ejpam-4819	48	56	below	below	ADV
ejpam-4819	48	57	:	:	PUNCT
ejpam-4819	49	1	t.	t.	PROPN
ejpam-4819	49	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	49	3	/	/	SYM
ejpam-4819	49	4	eur	eur	PROPN
ejpam-4819	49	5	.	.	PUNCT
ejpam-4819	50	1	j.	j.	PROPN
ejpam-4819	50	2	pure	pure	PROPN
ejpam-4819	50	3	appl	appl	PROPN
ejpam-4819	50	4	.	.	PROPN
ejpam-4819	50	5	math	math	PROPN
ejpam-4819	50	6	,	,	PUNCT
ejpam-4819	50	7	16	16	NUM
ejpam-4819	50	8	(	(	PUNCT
ejpam-4819	50	9	3	3	NUM
ejpam-4819	50	10	)	)	PUNCT
ejpam-4819	50	11	(	(	PUNCT
ejpam-4819	50	12	2023	2023	NUM
ejpam-4819	50	13	)	)	PUNCT
ejpam-4819	50	14	,	,	PUNCT
ejpam-4819	50	15	1717	1717	NUM
ejpam-4819	50	16	-	-	SYM
ejpam-4819	50	17	1730	1730	NUM
ejpam-4819	50	18	1719	1719	NUM
ejpam-4819	50	19	definition	definition	NOUN
ejpam-4819	50	20	3	3	NUM
ejpam-4819	50	21	.	.	PUNCT
ejpam-4819	51	1	[	[	X
ejpam-4819	51	2	2	2	X
ejpam-4819	51	3	]	]	X
ejpam-4819	51	4	assume	assume	VERB
ejpam-4819	51	5	(	(	PUNCT
ejpam-4819	51	6	cn	cn	INTJ
ejpam-4819	51	7	)	)	PUNCT
ejpam-4819	51	8	be	be	AUX
ejpam-4819	51	9	a	a	DET
ejpam-4819	51	10	sequence	sequence	NOUN
ejpam-4819	51	11	in	in	ADP
ejpam-4819	51	12	(	(	PUNCT
ejpam-4819	51	13	c	c	NOUN
ejpam-4819	51	14	,	,	PUNCT
ejpam-4819	51	15	gb	gb	NOUN
ejpam-4819	51	16	)	)	PUNCT
ejpam-4819	51	17	.	.	PUNCT
ejpam-4819	52	1	then	then	ADV
ejpam-4819	52	2	the	the	DET
ejpam-4819	52	3	sequence	sequence	NOUN
ejpam-4819	52	4	(	(	PUNCT
ejpam-4819	52	5	cn	cn	PROPN
ejpam-4819	52	6	)	)	PUNCT
ejpam-4819	52	7	is	be	AUX
ejpam-4819	52	8	a	a	DET
ejpam-4819	52	9	:	:	SYM
ejpam-4819	52	10	1	1	NUM
ejpam-4819	52	11	.	.	X
ejpam-4819	52	12	gb	gb	NOUN
ejpam-4819	52	13	-	-	PUNCT
ejpam-4819	52	14	cauchy	cauchy	NOUN
ejpam-4819	52	15	sequence	sequence	NOUN
ejpam-4819	52	16	if	if	SCONJ
ejpam-4819	52	17	∀ϵ	∀ϵ	NOUN
ejpam-4819	52	18	>	>	X
ejpam-4819	52	19	0	0	PUNCT
ejpam-4819	53	1	there	there	PRON
ejpam-4819	53	2	is	be	VERB
ejpam-4819	53	3	n	n	DET
ejpam-4819	53	4	∈	∈	PROPN
ejpam-4819	53	5	n	n	PRON
ejpam-4819	53	6	such	such	ADJ
ejpam-4819	53	7	that	that	SCONJ
ejpam-4819	53	8	∀n	∀n	PROPN
ejpam-4819	53	9	,	,	PUNCT
ejpam-4819	53	10	m	m	PROPN
ejpam-4819	53	11	,	,	PUNCT
ejpam-4819	53	12	l	l	PROPN
ejpam-4819	53	13	≥	≥	X
ejpam-4819	53	14	n	n	CCONJ
ejpam-4819	53	15	,	,	PUNCT
ejpam-4819	53	16	g(cn	g(cn	PROPN
ejpam-4819	53	17	,	,	PUNCT
ejpam-4819	53	18	cm	cm	NOUN
ejpam-4819	53	19	,	,	PUNCT
ejpam-4819	53	20	cl	cl	NOUN
ejpam-4819	53	21	)	)	PUNCT
ejpam-4819	53	22	<	<	X
ejpam-4819	53	23	ϵ	ϵ	X
ejpam-4819	53	24	;	;	PUNCT
ejpam-4819	53	25	2	2	NUM
ejpam-4819	53	26	.	.	X
ejpam-4819	53	27	gb	gb	NOUN
ejpam-4819	53	28	-	-	PUNCT
ejpam-4819	53	29	convergent	convergent	NOUN
ejpam-4819	53	30	sequence	sequence	NOUN
ejpam-4819	53	31	to	to	ADP
ejpam-4819	53	32	c	c	NOUN
ejpam-4819	53	33	if	if	SCONJ
ejpam-4819	53	34	∀ϵ	∀ϵ	NOUN
ejpam-4819	53	35	>	>	X
ejpam-4819	53	36	0	0	PUNCT
ejpam-4819	54	1	there	there	PRON
ejpam-4819	54	2	is	be	VERB
ejpam-4819	54	3	n	n	DET
ejpam-4819	54	4	∈	∈	PROPN
ejpam-4819	54	5	n	n	PRON
ejpam-4819	54	6	such	such	ADJ
ejpam-4819	54	7	that	that	SCONJ
ejpam-4819	54	8	∀n	∀n	PROPN
ejpam-4819	54	9	,	,	PUNCT
ejpam-4819	54	10	m	m	VERB
ejpam-4819	54	11	≥	≥	NOUN
ejpam-4819	54	12	n	n	CCONJ
ejpam-4819	54	13	,	,	PUNCT
ejpam-4819	54	14	g(c	g(c	PROPN
ejpam-4819	54	15	,	,	PUNCT
ejpam-4819	54	16	cn	cn	PROPN
ejpam-4819	54	17	,	,	PUNCT
ejpam-4819	54	18	cm	cm	NOUN
ejpam-4819	54	19	)	)	PUNCT
ejpam-4819	54	20	<	<	X
ejpam-4819	54	21	ϵ	ϵ	X
ejpam-4819	54	22	;	;	PUNCT
ejpam-4819	54	23	3	3	X
ejpam-4819	54	24	.	.	X
ejpam-4819	54	25	gb	gb	NOUN
ejpam-4819	54	26	-	-	PUNCT
ejpam-4819	54	27	complete	complete	ADJ
ejpam-4819	54	28	if	if	SCONJ
ejpam-4819	54	29	∀	∀	NOUN
ejpam-4819	54	30	gb	gb	NOUN
ejpam-4819	54	31	-	-	PUNCT
ejpam-4819	54	32	cauchy	cauchy	ADJ
ejpam-4819	54	33	sequence	sequence	NOUN
ejpam-4819	54	34	,	,	PUNCT
ejpam-4819	54	35	then	then	ADV
ejpam-4819	54	36	gb	gb	NOUN
ejpam-4819	54	37	is	be	AUX
ejpam-4819	54	38	convergent	convergent	ADJ
ejpam-4819	54	39	.	.	PUNCT
ejpam-4819	55	1	remark	remark	PROPN
ejpam-4819	55	2	1	1	NUM
ejpam-4819	55	3	.	.	PUNCT
ejpam-4819	56	1	a	a	DET
ejpam-4819	56	2	sequence	sequence	NOUN
ejpam-4819	56	3	(	(	PUNCT
ejpam-4819	56	4	cn	cn	PROPN
ejpam-4819	56	5	)	)	PUNCT
ejpam-4819	56	6	in	in	ADP
ejpam-4819	56	7	(	(	PUNCT
ejpam-4819	56	8	c	c	NOUN
ejpam-4819	56	9	,	,	PUNCT
ejpam-4819	56	10	gb	gb	NOUN
ejpam-4819	56	11	)	)	PUNCT
ejpam-4819	56	12	is	be	AUX
ejpam-4819	56	13	gb	gb	NOUN
ejpam-4819	56	14	-	-	PUNCT
ejpam-4819	56	15	convergent	convergent	NOUN
ejpam-4819	56	16	sequence	sequence	NOUN
ejpam-4819	56	17	if	if	SCONJ
ejpam-4819	56	18	one	one	NUM
ejpam-4819	56	19	of	of	ADP
ejpam-4819	56	20	the	the	DET
ejpam-4819	56	21	following	follow	VERB
ejpam-4819	56	22	conditions	condition	NOUN
ejpam-4819	56	23	is	be	AUX
ejpam-4819	56	24	true	true	ADJ
ejpam-4819	56	25	:	:	PUNCT
ejpam-4819	56	26	(	(	PUNCT
ejpam-4819	56	27	1	1	X
ejpam-4819	56	28	)	)	PUNCT
ejpam-4819	56	29	gb(cnc	gb(cnc	PROPN
ejpam-4819	56	30	,	,	PUNCT
ejpam-4819	56	31	c	c	NOUN
ejpam-4819	56	32	)	)	PUNCT
ejpam-4819	56	33	→	→	SYM
ejpam-4819	56	34	0	0	NUM
ejpam-4819	56	35	as	as	ADP
ejpam-4819	56	36	n	n	PRON
ejpam-4819	56	37	→	→	SYM
ejpam-4819	56	38	+	+	NOUN
ejpam-4819	56	39	∞	∞	NUM
ejpam-4819	56	40	;	;	PUNCT
ejpam-4819	56	41	(	(	PUNCT
ejpam-4819	56	42	2	2	X
ejpam-4819	56	43	)	)	PUNCT
ejpam-4819	56	44	gb(cn	gb(cn	PROPN
ejpam-4819	56	45	,	,	PUNCT
ejpam-4819	56	46	cn	cn	PROPN
ejpam-4819	56	47	,	,	PUNCT
ejpam-4819	56	48	c	c	NOUN
ejpam-4819	56	49	)	)	PUNCT
ejpam-4819	56	50	→	→	SYM
ejpam-4819	56	51	0	0	NUM
ejpam-4819	56	52	as	as	ADP
ejpam-4819	56	53	n	n	PRON
ejpam-4819	56	54	→	→	PUNCT
ejpam-4819	56	55	+	+	PROPN
ejpam-4819	56	56	∞.	∞.	PROPN
ejpam-4819	56	57	the	the	DET
ejpam-4819	56	58	concept	concept	NOUN
ejpam-4819	56	59	ωb	ωb	ADP
ejpam-4819	56	60	distance	distance	NOUN
ejpam-4819	56	61	mappings	mapping	NOUN
ejpam-4819	56	62	(	(	PUNCT
ejpam-4819	56	63	generalized	generalized	ADJ
ejpam-4819	56	64	ω	ω	NUM
ejpam-4819	56	65	distance	distance	NOUN
ejpam-4819	56	66	mappings	mapping	NOUN
ejpam-4819	56	67	)	)	PUNCT
ejpam-4819	56	68	was	be	AUX
ejpam-4819	56	69	introduced	introduce	VERB
ejpam-4819	56	70	by	by	ADP
ejpam-4819	56	71	abodayeh	abodayeh	PROPN
ejpam-4819	56	72	et.al	et.al	PROPN
ejpam-4819	56	73	.	.	PUNCT
ejpam-4819	57	1	[	[	X
ejpam-4819	57	2	1	1	X
ejpam-4819	57	3	]	]	PUNCT
ejpam-4819	57	4	and	and	CCONJ
ejpam-4819	57	5	they	they	PRON
ejpam-4819	57	6	utilized	utilize	VERB
ejpam-4819	57	7	this	this	DET
ejpam-4819	57	8	concept	concept	NOUN
ejpam-4819	57	9	to	to	PART
ejpam-4819	57	10	unify	unify	VERB
ejpam-4819	57	11	some	some	DET
ejpam-4819	57	12	fixed	fix	VERB
ejpam-4819	57	13	point	point	NOUN
ejpam-4819	57	14	results	result	NOUN
ejpam-4819	57	15	in	in	ADP
ejpam-4819	57	16	the	the	DET
ejpam-4819	57	17	literature	literature	NOUN
ejpam-4819	57	18	.	.	PUNCT
ejpam-4819	58	1	definition	definition	NOUN
ejpam-4819	58	2	4	4	NUM
ejpam-4819	58	3	.	.	PUNCT
ejpam-4819	59	1	[	[	X
ejpam-4819	59	2	1	1	X
ejpam-4819	59	3	]	]	X
ejpam-4819	59	4	an	an	DET
ejpam-4819	59	5	ωb	ωb	NOUN
ejpam-4819	59	6	-	-	PUNCT
ejpam-4819	59	7	distance	distance	NOUN
ejpam-4819	59	8	mappings	mapping	NOUN
ejpam-4819	59	9	on	on	ADP
ejpam-4819	59	10	(	(	PUNCT
ejpam-4819	59	11	c	c	NOUN
ejpam-4819	59	12	,	,	PUNCT
ejpam-4819	59	13	gb	gb	NOUN
ejpam-4819	59	14	)	)	PUNCT
ejpam-4819	59	15	is	be	AUX
ejpam-4819	59	16	a	a	DET
ejpam-4819	59	17	function	function	NOUN
ejpam-4819	59	18	ωb	ωb	NOUN
ejpam-4819	59	19	:	:	PUNCT
ejpam-4819	59	20	c	c	NOUN
ejpam-4819	59	21	×	×	NOUN
ejpam-4819	59	22	c	c	NOUN
ejpam-4819	59	23	×	×	NOUN
ejpam-4819	59	24	c	c	NOUN
ejpam-4819	59	25	→	→	PUNCT
ejpam-4819	59	26	[	[	X
ejpam-4819	59	27	0,+∞	0,+∞	NUM
ejpam-4819	59	28	)	)	PUNCT
ejpam-4819	59	29	fulfill	fulfill	NOUN
ejpam-4819	59	30	:	:	PUNCT
ejpam-4819	59	31	1	1	NUM
ejpam-4819	59	32	.	.	NUM
ejpam-4819	59	33	ωb(c	ωb(c	NUM
ejpam-4819	59	34	,	,	PUNCT
ejpam-4819	59	35	c	c	NOUN
ejpam-4819	59	36	′	′	NUM
ejpam-4819	59	37	,	,	PUNCT
ejpam-4819	60	1	c	c	X
ejpam-4819	60	2	′′	′′	PROPN
ejpam-4819	60	3	)	)	PUNCT
ejpam-4819	60	4	≤	≤	PROPN
ejpam-4819	60	5	b[ωb(c	b[ωb(c	PROPN
ejpam-4819	60	6	,	,	PUNCT
ejpam-4819	60	7	a	a	DET
ejpam-4819	60	8	,	,	PUNCT
ejpam-4819	60	9	a	a	NOUN
ejpam-4819	60	10	)	)	PUNCT
ejpam-4819	60	11	+	+	NOUN
ejpam-4819	60	12	ωb(a	ωb(a	NOUN
ejpam-4819	60	13	,	,	PUNCT
ejpam-4819	60	14	c	c	NOUN
ejpam-4819	60	15	′	′	NOUN
ejpam-4819	60	16	,	,	PUNCT
ejpam-4819	60	17	c	c	X
ejpam-4819	60	18	′′	′′	PROPN
ejpam-4819	60	19	)	)	PUNCT
ejpam-4819	60	20	]	]	PUNCT
ejpam-4819	60	21	for	for	ADP
ejpam-4819	60	22	all	all	DET
ejpam-4819	60	23	c	c	NOUN
ejpam-4819	60	24	,	,	PUNCT
ejpam-4819	60	25	c	c	NOUN
ejpam-4819	60	26	′	′	NUM
ejpam-4819	60	27	,	,	PUNCT
ejpam-4819	60	28	c	c	X
ejpam-4819	61	1	′′	′′	PROPN
ejpam-4819	61	2	,	,	PUNCT
ejpam-4819	61	3	a	a	DET
ejpam-4819	61	4	∈	∈	PROPN
ejpam-4819	61	5	c	c	X
ejpam-4819	61	6	,	,	PUNCT
ejpam-4819	61	7	b	b	X
ejpam-4819	61	8	∈	∈	PROPN
ejpam-4819	61	9	[	[	X
ejpam-4819	61	10	0,+∞	0,+∞	NUM
ejpam-4819	61	11	)	)	PUNCT
ejpam-4819	61	12	;	;	PUNCT
ejpam-4819	61	13	2	2	X
ejpam-4819	61	14	.	.	NUM
ejpam-4819	61	15	∀c	∀c	NOUN
ejpam-4819	61	16	,	,	PUNCT
ejpam-4819	61	17	c′	c′	NOUN
ejpam-4819	61	18	∈	∈	PROPN
ejpam-4819	61	19	c	c	NOUN
ejpam-4819	61	20	,	,	PUNCT
ejpam-4819	61	21	ωb(c	ωb(c	NUM
ejpam-4819	61	22	,	,	PUNCT
ejpam-4819	61	23	c	c	NOUN
ejpam-4819	61	24	′	′	NUM
ejpam-4819	61	25	,	,	PUNCT
ejpam-4819	61	26	.),ωb(c	.),ωb(c	PROPN
ejpam-4819	61	27	,	,	PUNCT
ejpam-4819	61	28	.	.	PUNCT
ejpam-4819	61	29	,	,	PUNCT
ejpam-4819	61	30	c	c	NOUN
ejpam-4819	61	31	′	′	NUM
ejpam-4819	61	32	)	)	PUNCT
ejpam-4819	61	33	:	:	PUNCT
ejpam-4819	61	34	c	c	X
ejpam-4819	61	35	→	→	SYM
ejpam-4819	61	36	c	c	X
ejpam-4819	61	37	are	be	AUX
ejpam-4819	61	38	lower	low	ADJ
ejpam-4819	61	39	semi	semi	ADJ
ejpam-4819	61	40	-	-	ADJ
ejpam-4819	61	41	continuous	continuous	ADJ
ejpam-4819	61	42	;	;	PUNCT
ejpam-4819	61	43	3	3	X
ejpam-4819	61	44	.	.	PUNCT
ejpam-4819	61	45	∀ϵ	∀ϵ	NOUN
ejpam-4819	61	46	>	>	PUNCT
ejpam-4819	61	47	0	0	PUNCT
ejpam-4819	62	1	there	there	PRON
ejpam-4819	62	2	is	be	VERB
ejpam-4819	62	3	an	an	DET
ejpam-4819	62	4	α	α	NOUN
ejpam-4819	62	5	>	>	X
ejpam-4819	62	6	0	0	NUM
ejpam-4819	62	7	,	,	PUNCT
ejpam-4819	62	8	if	if	SCONJ
ejpam-4819	62	9	ωb(c	ωb(c	NUM
ejpam-4819	62	10	,	,	PUNCT
ejpam-4819	62	11	a	a	PRON
ejpam-4819	62	12	,	,	PUNCT
ejpam-4819	62	13	a	a	PRON
ejpam-4819	62	14	)	)	PUNCT
ejpam-4819	62	15	≤	≤	NOUN
ejpam-4819	62	16	α	α	NOUN
ejpam-4819	62	17	and	and	CCONJ
ejpam-4819	62	18	ωb(a	ωb(a	NOUN
ejpam-4819	62	19	,	,	PUNCT
ejpam-4819	62	20	c	c	NOUN
ejpam-4819	62	21	′	′	NUM
ejpam-4819	62	22	,	,	PUNCT
ejpam-4819	62	23	c	c	X
ejpam-4819	62	24	′′	′′	PROPN
ejpam-4819	62	25	)	)	PUNCT
ejpam-4819	62	26	≤	≤	NOUN
ejpam-4819	63	1	α	α	X
ejpam-4819	63	2	,	,	PUNCT
ejpam-4819	63	3	then	then	ADV
ejpam-4819	63	4	gb(c	gb(c	VERB
ejpam-4819	63	5	,	,	PUNCT
ejpam-4819	63	6	c	c	NOUN
ejpam-4819	63	7	′	′	NUM
ejpam-4819	63	8	,	,	PUNCT
ejpam-4819	63	9	c	c	X
ejpam-4819	63	10	′′	′′	PROPN
ejpam-4819	63	11	)	)	PUNCT
ejpam-4819	63	12	≤	≤	PROPN
ejpam-4819	64	1	ϵ	ϵ	X
ejpam-4819	64	2	,	,	PUNCT
ejpam-4819	64	3	∀	∀	X
ejpam-4819	64	4	c	c	NOUN
ejpam-4819	64	5	,	,	PUNCT
ejpam-4819	64	6	c	c	NOUN
ejpam-4819	64	7	′	′	NUM
ejpam-4819	64	8	,	,	PUNCT
ejpam-4819	64	9	c	c	X
ejpam-4819	64	10	′′	′′	PROPN
ejpam-4819	64	11	∈	∈	PROPN
ejpam-4819	64	12	c.	c.	PROPN
ejpam-4819	64	13	definition	definition	NOUN
ejpam-4819	64	14	5	5	NUM
ejpam-4819	64	15	.	.	PUNCT
ejpam-4819	65	1	if	if	SCONJ
ejpam-4819	65	2	ωb	ωb	NOUN
ejpam-4819	65	3	distance	distance	NOUN
ejpam-4819	65	4	mappings	mapping	NOUN
ejpam-4819	65	5	is	be	AUX
ejpam-4819	65	6	equipped	equip	VERB
ejpam-4819	65	7	with	with	ADP
ejpam-4819	65	8	(	(	PUNCT
ejpam-4819	65	9	c	c	NOUN
ejpam-4819	65	10	,	,	PUNCT
ejpam-4819	65	11	gb	gb	NOUN
ejpam-4819	65	12	)	)	PUNCT
ejpam-4819	65	13	,	,	PUNCT
ejpam-4819	65	14	then	then	ADV
ejpam-4819	65	15	we	we	PRON
ejpam-4819	65	16	call	call	VERB
ejpam-4819	65	17	c	c	PROPN
ejpam-4819	65	18	bounded	bound	VERB
ejpam-4819	65	19	w.r.t	w.r.t	PROPN
ejpam-4819	65	20	.	.	PUNCT
ejpam-4819	66	1	ωb	ωb	INTJ
ejpam-4819	67	1	if	if	SCONJ
ejpam-4819	67	2	there	there	PRON
ejpam-4819	67	3	exists	exist	VERB
ejpam-4819	67	4	l	l	PROPN
ejpam-4819	67	5	≥	≥	NUM
ejpam-4819	67	6	1	1	NUM
ejpam-4819	67	7	with	with	ADP
ejpam-4819	67	8	ωb(c1	ωb(c1	NOUN
ejpam-4819	67	9	,	,	PUNCT
ejpam-4819	67	10	c2	c2	PROPN
ejpam-4819	67	11	,	,	PUNCT
ejpam-4819	67	12	c3	c3	PROPN
ejpam-4819	67	13	)	)	PUNCT
ejpam-4819	67	14	≤	≤	NUM
ejpam-4819	67	15	l	l	NOUN
ejpam-4819	67	16	for	for	ADP
ejpam-4819	67	17	all	all	DET
ejpam-4819	67	18	c1	c1	NOUN
ejpam-4819	67	19	,	,	PUNCT
ejpam-4819	67	20	c2	c2	PROPN
ejpam-4819	67	21	,	,	PUNCT
ejpam-4819	67	22	c3	c3	PROPN
ejpam-4819	67	23	∈	∈	PROPN
ejpam-4819	67	24	c.	c.	NOUN
ejpam-4819	67	25	the	the	DET
ejpam-4819	67	26	concept	concept	NOUN
ejpam-4819	67	27	of	of	ADP
ejpam-4819	67	28	h	h	NOUN
ejpam-4819	67	29	-	-	PUNCT
ejpam-4819	67	30	simulation	simulation	NOUN
ejpam-4819	67	31	functions	function	NOUN
ejpam-4819	67	32	which	which	PRON
ejpam-4819	67	33	formulated	formulate	VERB
ejpam-4819	67	34	by	by	ADP
ejpam-4819	67	35	bataihah	bataihah	PROPN
ejpam-4819	67	36	et.al	et.al	PROPN
ejpam-4819	67	37	in	in	ADP
ejpam-4819	67	38	2020	2020	NUM
ejpam-4819	67	39	is	be	AUX
ejpam-4819	67	40	as	as	ADP
ejpam-4819	67	41	belows	below	NOUN
ejpam-4819	67	42	:	:	PUNCT
ejpam-4819	67	43	definition	definition	NOUN
ejpam-4819	67	44	6	6	NUM
ejpam-4819	67	45	.	.	PUNCT
ejpam-4819	68	1	[	[	X
ejpam-4819	68	2	6	6	NUM
ejpam-4819	68	3	]	]	PUNCT
ejpam-4819	68	4	a	a	DET
ejpam-4819	68	5	set	set	NOUN
ejpam-4819	68	6	of	of	ADP
ejpam-4819	68	7	functions	function	NOUN
ejpam-4819	68	8	{	{	PUNCT
ejpam-4819	68	9	h	h	NOUN
ejpam-4819	68	10	:	:	PUNCT
ejpam-4819	69	1	[	[	X
ejpam-4819	69	2	1,+∞)×	1,+∞)×	NUM
ejpam-4819	69	3	[	[	X
ejpam-4819	69	4	1,+∞	1,+∞	NUM
ejpam-4819	69	5	)	)	PUNCT
ejpam-4819	69	6	→	→	SYM
ejpam-4819	69	7	r	r	X
ejpam-4819	69	8	}	}	PUNCT
ejpam-4819	69	9	is	be	AUX
ejpam-4819	69	10	called	call	VERB
ejpam-4819	69	11	h	h	NOUN
ejpam-4819	69	12	-	-	PUNCT
ejpam-4819	69	13	simulation	simulation	NOUN
ejpam-4819	69	14	functions	function	NOUN
ejpam-4819	69	15	if	if	SCONJ
ejpam-4819	69	16	h(c	h(c	PROPN
ejpam-4819	69	17	,	,	PUNCT
ejpam-4819	69	18	c	c	NOUN
ejpam-4819	69	19	′	′	NUM
ejpam-4819	69	20	)	)	PUNCT
ejpam-4819	70	1	≤	≤	NUM
ejpam-4819	71	1	c	c	NOUN
ejpam-4819	71	2	′	′	NUM
ejpam-4819	71	3	c	c	NOUN
ejpam-4819	71	4	∀c	∀c	NOUN
ejpam-4819	71	5	,	,	PUNCT
ejpam-4819	71	6	c′	c′	NOUN
ejpam-4819	71	7	∈	∈	PROPN
ejpam-4819	72	1	[	[	X
ejpam-4819	72	2	1,+∞	1,+∞	NUM
ejpam-4819	72	3	)	)	PUNCT
ejpam-4819	72	4	.	.	PUNCT
ejpam-4819	73	1	(	(	PUNCT
ejpam-4819	73	2	3	3	X
ejpam-4819	73	3	)	)	PUNCT
ejpam-4819	73	4	remark	remark	NOUN
ejpam-4819	73	5	2	2	NUM
ejpam-4819	73	6	.	.	PUNCT
ejpam-4819	74	1	[	[	X
ejpam-4819	74	2	6	6	NUM
ejpam-4819	74	3	]	]	PUNCT
ejpam-4819	74	4	if	if	SCONJ
ejpam-4819	74	5	h	h	PROPN
ejpam-4819	74	6	∈	∈	PROPN
ejpam-4819	74	7	h	h	NOUN
ejpam-4819	74	8	and	and	CCONJ
ejpam-4819	74	9	(	(	PUNCT
ejpam-4819	74	10	cn	cn	PROPN
ejpam-4819	74	11	)	)	PUNCT
ejpam-4819	74	12	,	,	PUNCT
ejpam-4819	74	13	(	(	PUNCT
ejpam-4819	74	14	c	c	NOUN
ejpam-4819	74	15	′	′	NUM
ejpam-4819	74	16	n	n	CCONJ
ejpam-4819	74	17	)	)	PUNCT
ejpam-4819	74	18	are	be	AUX
ejpam-4819	74	19	sequences	sequence	NOUN
ejpam-4819	74	20	in	in	ADP
ejpam-4819	74	21	[	[	X
ejpam-4819	74	22	1,+∞	1,+∞	NUM
ejpam-4819	74	23	)	)	PUNCT
ejpam-4819	74	24	with	with	ADP
ejpam-4819	74	25	1	1	NUM
ejpam-4819	74	26	≤	≤	NOUN
ejpam-4819	74	27	lim	lim	NOUN
ejpam-4819	74	28	n→+∞	n→+∞	VERB
ejpam-4819	74	29	c	c	PROPN
ejpam-4819	74	30	′	′	NOUN
ejpam-4819	74	31	n	n	CCONJ
ejpam-4819	74	32	<	<	X
ejpam-4819	74	33	lim	lim	PROPN
ejpam-4819	74	34	n→+∞	n→+∞	PROPN
ejpam-4819	74	35	cn	cn	PROPN
ejpam-4819	74	36	,	,	PUNCT
ejpam-4819	74	37	then	then	ADV
ejpam-4819	74	38	lim	lim	PROPN
ejpam-4819	74	39	sup	sup	PROPN
ejpam-4819	74	40	n→+∞	n→+∞	PROPN
ejpam-4819	74	41	h(cn	h(cn	PROPN
ejpam-4819	74	42	,	,	PUNCT
ejpam-4819	74	43	c	c	NOUN
ejpam-4819	74	44	′	′	NUM
ejpam-4819	74	45	n	n	CCONJ
ejpam-4819	74	46	)	)	PUNCT
ejpam-4819	74	47	<	<	X
ejpam-4819	75	1	1	1	X
ejpam-4819	75	2	.	.	PUNCT
ejpam-4819	75	3	(	(	PUNCT
ejpam-4819	75	4	4	4	X
ejpam-4819	75	5	)	)	PUNCT
ejpam-4819	75	6	definition	definition	NOUN
ejpam-4819	75	7	7	7	NUM
ejpam-4819	75	8	.	.	PUNCT
ejpam-4819	76	1	[	[	X
ejpam-4819	76	2	6	6	NUM
ejpam-4819	76	3	,	,	PUNCT
ejpam-4819	76	4	11	11	NUM
ejpam-4819	76	5	]	]	PUNCT
ejpam-4819	76	6	the	the	DET
ejpam-4819	76	7	class	class	NOUN
ejpam-4819	76	8	of	of	ADP
ejpam-4819	76	9	functions	function	NOUN
ejpam-4819	76	10	:	:	PUNCT
ejpam-4819	76	11	{	{	PUNCT
ejpam-4819	76	12	θ	θ	NOUN
ejpam-4819	76	13	:	:	PUNCT
ejpam-4819	77	1	[	[	X
ejpam-4819	77	2	0,+∞	0,+∞	NUM
ejpam-4819	77	3	)	)	PUNCT
ejpam-4819	77	4	→	→	PUNCT
ejpam-4819	78	1	[	[	X
ejpam-4819	78	2	1,+∞	1,+∞	NUM
ejpam-4819	78	3	)	)	PUNCT
ejpam-4819	78	4	}	}	PUNCT
ejpam-4819	78	5	,	,	PUNCT
ejpam-4819	78	6	θ	θ	PROPN
ejpam-4819	78	7	is	be	AUX
ejpam-4819	78	8	continuous	continuous	ADJ
ejpam-4819	78	9	and	and	CCONJ
ejpam-4819	78	10	none	none	NOUN
ejpam-4819	78	11	decreasing	decrease	VERB
ejpam-4819	78	12	functions	function	NOUN
ejpam-4819	78	13	fulfill	fulfill	VERB
ejpam-4819	78	14	the	the	DET
ejpam-4819	78	15	condition	condition	NOUN
ejpam-4819	78	16	:	:	PUNCT
ejpam-4819	78	17	∀(cn	∀(cn	NUM
ejpam-4819	78	18	)	)	PUNCT
ejpam-4819	78	19	a	a	DET
ejpam-4819	78	20	sequence	sequence	NOUN
ejpam-4819	78	21	in	in	ADP
ejpam-4819	78	22	[	[	X
ejpam-4819	78	23	0,+∞	0,+∞	NUM
ejpam-4819	78	24	)	)	PUNCT
ejpam-4819	78	25	,	,	PUNCT
ejpam-4819	78	26	lim	lim	PROPN
ejpam-4819	78	27	n→+∞	n→+∞	PROPN
ejpam-4819	78	28	θ(cn	θ(cn	PROPN
ejpam-4819	78	29	)	)	PUNCT
ejpam-4819	78	30	=	=	SYM
ejpam-4819	79	1	1	1	NUM
ejpam-4819	79	2	if	if	SCONJ
ejpam-4819	79	3	and	and	CCONJ
ejpam-4819	79	4	only	only	ADV
ejpam-4819	79	5	if	if	SCONJ
ejpam-4819	79	6	lim	lim	PROPN
ejpam-4819	79	7	n→+∞	n→+∞	VERB
ejpam-4819	79	8	cn	cn	PROPN
ejpam-4819	79	9	=	=	NOUN
ejpam-4819	80	1	0	0	PROPN
ejpam-4819	80	2	.	.	PUNCT
ejpam-4819	80	3	is	be	AUX
ejpam-4819	80	4	said	say	VERB
ejpam-4819	80	5	to	to	PART
ejpam-4819	80	6	be	be	AUX
ejpam-4819	80	7	θ	θ	PROPN
ejpam-4819	80	8	class	class	NOUN
ejpam-4819	80	9	remark	remark	NOUN
ejpam-4819	80	10	3	3	NUM
ejpam-4819	80	11	.	.	PUNCT
ejpam-4819	81	1	[	[	X
ejpam-4819	81	2	11	11	NUM
ejpam-4819	81	3	]	]	PUNCT
ejpam-4819	81	4	if	if	SCONJ
ejpam-4819	81	5	θ	θ	PROPN
ejpam-4819	81	6	∈	∈	PROPN
ejpam-4819	81	7	θ	θ	PROPN
ejpam-4819	81	8	,	,	PUNCT
ejpam-4819	81	9	then	then	ADV
ejpam-4819	81	10	θ−1	θ−1	PROPN
ejpam-4819	81	11	(	(	PUNCT
ejpam-4819	81	12	{	{	PUNCT
ejpam-4819	81	13	1})=0	1})=0	NOUN
ejpam-4819	81	14	.	.	PUNCT
ejpam-4819	82	1	t.	t.	NOUN
ejpam-4819	82	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	82	3	/	/	SYM
ejpam-4819	82	4	eur	eur	PROPN
ejpam-4819	82	5	.	.	PUNCT
ejpam-4819	83	1	j.	j.	PROPN
ejpam-4819	83	2	pure	pure	PROPN
ejpam-4819	83	3	appl	appl	PROPN
ejpam-4819	83	4	.	.	PROPN
ejpam-4819	83	5	math	math	PROPN
ejpam-4819	83	6	,	,	PUNCT
ejpam-4819	83	7	16	16	NUM
ejpam-4819	83	8	(	(	PUNCT
ejpam-4819	83	9	3	3	NUM
ejpam-4819	83	10	)	)	PUNCT
ejpam-4819	83	11	(	(	PUNCT
ejpam-4819	83	12	2023	2023	NUM
ejpam-4819	83	13	)	)	PUNCT
ejpam-4819	83	14	,	,	PUNCT
ejpam-4819	83	15	1717	1717	NUM
ejpam-4819	83	16	-	-	SYM
ejpam-4819	83	17	1730	1730	NUM
ejpam-4819	83	18	1720	1720	NUM
ejpam-4819	83	19	2	2	NUM
ejpam-4819	83	20	.	.	PUNCT
ejpam-4819	83	21	main	main	ADJ
ejpam-4819	83	22	results	result	NOUN
ejpam-4819	83	23	we	we	PRON
ejpam-4819	83	24	start	start	VERB
ejpam-4819	83	25	our	our	PRON
ejpam-4819	83	26	main	main	ADJ
ejpam-4819	83	27	results	result	NOUN
ejpam-4819	83	28	with	with	ADP
ejpam-4819	83	29	the	the	DET
ejpam-4819	83	30	following	follow	VERB
ejpam-4819	83	31	concepts	concept	NOUN
ejpam-4819	83	32	and	and	CCONJ
ejpam-4819	83	33	definitions	definition	NOUN
ejpam-4819	83	34	definition	definition	NOUN
ejpam-4819	83	35	8	8	NUM
ejpam-4819	83	36	.	.	PUNCT
ejpam-4819	84	1	suppose	suppose	VERB
ejpam-4819	84	2	(	(	PUNCT
ejpam-4819	84	3	c	c	X
ejpam-4819	84	4	,	,	PUNCT
ejpam-4819	84	5	gb	gb	NOUN
ejpam-4819	84	6	)	)	PUNCT
ejpam-4819	84	7	is	be	AUX
ejpam-4819	84	8	equipped	equip	VERB
ejpam-4819	84	9	with	with	ADP
ejpam-4819	84	10	ωb	ωb	NOUN
ejpam-4819	84	11	-	-	PUNCT
ejpam-4819	84	12	distance	distance	NOUN
ejpam-4819	84	13	mappings	mapping	NOUN
ejpam-4819	84	14	.	.	PUNCT
ejpam-4819	85	1	a	a	DET
ejpam-4819	85	2	mapping	mapping	NOUN
ejpam-4819	85	3	f	f	NOUN
ejpam-4819	85	4	:	:	PUNCT
ejpam-4819	85	5	c	c	X
ejpam-4819	85	6	→	→	PUNCT
ejpam-4819	85	7	c	c	PROPN
ejpam-4819	85	8	is	be	AUX
ejpam-4819	85	9	said	say	VERB
ejpam-4819	85	10	to	to	PART
ejpam-4819	85	11	be	be	AUX
ejpam-4819	85	12	(	(	PUNCT
ejpam-4819	85	13	h	h	NOUN
ejpam-4819	85	14	,	,	PUNCT
ejpam-4819	85	15	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	85	16	contraction	contraction	NOUN
ejpam-4819	85	17	if	if	SCONJ
ejpam-4819	85	18	there	there	PRON
ejpam-4819	85	19	are	be	VERB
ejpam-4819	85	20	b	b	PRON
ejpam-4819	85	21	∈	∈	PROPN
ejpam-4819	86	1	[	[	X
ejpam-4819	86	2	1,+∞	1,+∞	NUM
ejpam-4819	86	3	)	)	PUNCT
ejpam-4819	86	4	,	,	PUNCT
ejpam-4819	86	5	λi	λi	ADP
ejpam-4819	86	6	∈	∈	PROPN
ejpam-4819	86	7	(	(	PUNCT
ejpam-4819	86	8	0	0	NUM
ejpam-4819	86	9	,	,	PUNCT
ejpam-4819	86	10	1	1	NUM
ejpam-4819	86	11	)	)	PUNCT
ejpam-4819	86	12	with	with	ADP
ejpam-4819	86	13	i	i	PRON
ejpam-4819	86	14	∈	∈	PROPN
ejpam-4819	86	15	{	{	PUNCT
ejpam-4819	86	16	1	1	NUM
ejpam-4819	86	17	,	,	PUNCT
ejpam-4819	86	18	2	2	NUM
ejpam-4819	86	19	,	,	PUNCT
ejpam-4819	86	20	3	3	NUM
ejpam-4819	86	21	}	}	PUNCT
ejpam-4819	86	22	and	and	CCONJ
ejpam-4819	86	23	λ2	λ2	PROPN
ejpam-4819	87	1	+	+	CCONJ
ejpam-4819	88	1	λ3	λ3	PROPN
ejpam-4819	88	2	<	<	X
ejpam-4819	88	3	1	1	NUM
ejpam-4819	88	4	,	,	PUNCT
ejpam-4819	88	5	θ	θ	PROPN
ejpam-4819	88	6	∈	∈	PROPN
ejpam-4819	88	7	θ	θ	PROPN
ejpam-4819	88	8	and	and	CCONJ
ejpam-4819	88	9	h	h	NOUN
ejpam-4819	88	10	∈	∈	PROPN
ejpam-4819	88	11	h	h	NOUN
ejpam-4819	88	12	such	such	ADJ
ejpam-4819	88	13	that	that	SCONJ
ejpam-4819	88	14	∀	∀	NUM
ejpam-4819	88	15	c1	c1	PROPN
ejpam-4819	88	16	,	,	PUNCT
ejpam-4819	88	17	c2	c2	PROPN
ejpam-4819	88	18	,	,	PUNCT
ejpam-4819	88	19	c3	c3	PROPN
ejpam-4819	88	20	∈	∈	PROPN
ejpam-4819	89	1	c	c	X
ejpam-4819	89	2	we	we	PRON
ejpam-4819	89	3	have	have	VERB
ejpam-4819	89	4	:	:	PUNCT
ejpam-4819	89	5	1	1	NUM
ejpam-4819	89	6	≤	≤	NUM
ejpam-4819	89	7	h	h	NOUN
ejpam-4819	89	8	(	(	PUNCT
ejpam-4819	89	9	θbωb(fc1	θbωb(fc1	PROPN
ejpam-4819	89	10	,	,	PUNCT
ejpam-4819	89	11	f	f	PROPN
ejpam-4819	89	12	2c1	2c1	PROPN
ejpam-4819	89	13	,	,	PUNCT
ejpam-4819	89	14	fc2	fc2	PROPN
ejpam-4819	89	15	)	)	PUNCT
ejpam-4819	89	16	,	,	PUNCT
ejpam-4819	89	17	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	89	18	,	,	PUNCT
ejpam-4819	89	19	c2	c2	PROPN
ejpam-4819	89	20	,	,	PUNCT
ejpam-4819	89	21	c3	c3	PROPN
ejpam-4819	89	22	)	)	PUNCT
ejpam-4819	89	23	)	)	PUNCT
ejpam-4819	89	24	.	.	PUNCT
ejpam-4819	90	1	(	(	PUNCT
ejpam-4819	90	2	5	5	X
ejpam-4819	90	3	)	)	PUNCT
ejpam-4819	90	4	where	where	SCONJ
ejpam-4819	90	5	γ(c1	γ(c1	NOUN
ejpam-4819	90	6	,	,	PUNCT
ejpam-4819	90	7	c2	c2	PROPN
ejpam-4819	90	8	,	,	PUNCT
ejpam-4819	90	9	c3	c3	PROPN
ejpam-4819	90	10	)	)	PUNCT
ejpam-4819	90	11	=	=	SYM
ejpam-4819	90	12	max	max	PROPN
ejpam-4819	90	13	{	{	PUNCT
ejpam-4819	90	14	ωb(c1	ωb(c1	PROPN
ejpam-4819	90	15	,	,	PUNCT
ejpam-4819	90	16	fc1	fc1	PROPN
ejpam-4819	90	17	,	,	PUNCT
ejpam-4819	90	18	c2	c2	PROPN
ejpam-4819	90	19	)	)	PUNCT
ejpam-4819	90	20	,	,	PUNCT
ejpam-4819	90	21	[	[	X
ejpam-4819	90	22	ωb(c1	ωb(c1	NOUN
ejpam-4819	90	23	,	,	PUNCT
ejpam-4819	90	24	fc1	fc1	PROPN
ejpam-4819	90	25	,	,	PUNCT
ejpam-4819	90	26	fc1	fc1	PROPN
ejpam-4819	90	27	)	)	PUNCT
ejpam-4819	90	28	]	]	PUNCT
ejpam-4819	91	1	λ2	λ2	NOUN
ejpam-4819	91	2	[	[	X
ejpam-4819	91	3	ωb(c2	ωb(c2	PROPN
ejpam-4819	91	4	,	,	PUNCT
ejpam-4819	91	5	fc2	fc2	PROPN
ejpam-4819	91	6	,	,	PUNCT
ejpam-4819	91	7	fc2	fc2	NOUN
ejpam-4819	91	8	)	)	PUNCT
ejpam-4819	91	9	]	]	PUNCT
ejpam-4819	92	1	λ3	λ3	PROPN
ejpam-4819	92	2	}	}	PUNCT
ejpam-4819	92	3	.	.	PUNCT
ejpam-4819	93	1	lemma	lemma	PROPN
ejpam-4819	93	2	1	1	X
ejpam-4819	93	3	.	.	PUNCT
ejpam-4819	93	4	suppose	suppose	VERB
ejpam-4819	93	5	the	the	DET
ejpam-4819	93	6	self	self	NOUN
ejpam-4819	93	7	function	function	NOUN
ejpam-4819	93	8	f	f	NOUN
ejpam-4819	93	9	:	:	PUNCT
ejpam-4819	93	10	c	c	X
ejpam-4819	93	11	→	→	PUNCT
ejpam-4819	93	12	c	c	PROPN
ejpam-4819	93	13	fulfills	fulfill	VERB
ejpam-4819	93	14	the	the	DET
ejpam-4819	93	15	conditions	condition	NOUN
ejpam-4819	93	16	of	of	ADP
ejpam-4819	93	17	(	(	PUNCT
ejpam-4819	93	18	h	h	NOUN
ejpam-4819	93	19	,	,	PUNCT
ejpam-4819	93	20	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	93	21	contraction.then	contraction.then	PRON
ejpam-4819	93	22	1	1	NUM
ejpam-4819	93	23	.	.	NUM
ejpam-4819	93	24	γ(c1	γ(c1	PROPN
ejpam-4819	93	25	,	,	PUNCT
ejpam-4819	93	26	c2	c2	PROPN
ejpam-4819	93	27	,	,	PUNCT
ejpam-4819	93	28	c3	c3	PROPN
ejpam-4819	93	29	)	)	PUNCT
ejpam-4819	93	30	>	>	X
ejpam-4819	93	31	0	0	PUNCT
ejpam-4819	94	1	=	=	AUX
ejpam-4819	94	2	⇒	⇒	PROPN
ejpam-4819	94	3	ωb(fc1	ωb(fc1	NUM
ejpam-4819	94	4	,	,	PUNCT
ejpam-4819	94	5	f	f	PROPN
ejpam-4819	94	6	2c1	2c1	NUM
ejpam-4819	94	7	,	,	PUNCT
ejpam-4819	94	8	fc2	fc2	PROPN
ejpam-4819	94	9	)	)	PUNCT
ejpam-4819	94	10	≤	≤	NOUN
ejpam-4819	94	11	λ1	λ1	PROPN
ejpam-4819	94	12	b	b	PROPN
ejpam-4819	94	13	γ(c1	γ(c1	PROPN
ejpam-4819	94	14	,	,	PUNCT
ejpam-4819	94	15	c2	c2	PROPN
ejpam-4819	94	16	,	,	PUNCT
ejpam-4819	94	17	c3	c3	PROPN
ejpam-4819	94	18	)	)	PUNCT
ejpam-4819	94	19	;	;	PUNCT
ejpam-4819	94	20	2	2	X
ejpam-4819	94	21	.	.	NUM
ejpam-4819	94	22	γ(c1	γ(c1	PROPN
ejpam-4819	94	23	,	,	PUNCT
ejpam-4819	94	24	c2	c2	PROPN
ejpam-4819	94	25	,	,	PUNCT
ejpam-4819	94	26	c3	c3	PROPN
ejpam-4819	94	27	)	)	PUNCT
ejpam-4819	94	28	=	=	SYM
ejpam-4819	94	29	0	0	PUNCT
ejpam-4819	95	1	=	=	NOUN
ejpam-4819	95	2	⇒	⇒	PROPN
ejpam-4819	95	3	ωb(fc1	ωb(fc1	NUM
ejpam-4819	95	4	,	,	PUNCT
ejpam-4819	95	5	f	f	PROPN
ejpam-4819	95	6	2c1	2c1	NUM
ejpam-4819	95	7	,	,	PUNCT
ejpam-4819	95	8	fc2	fc2	PROPN
ejpam-4819	95	9	)	)	PUNCT
ejpam-4819	95	10	=	=	SYM
ejpam-4819	95	11	0	0	X
ejpam-4819	95	12	.	.	PUNCT
ejpam-4819	96	1	proof	proof	NOUN
ejpam-4819	96	2	.	.	PUNCT
ejpam-4819	97	1	(	(	PUNCT
ejpam-4819	97	2	1	1	X
ejpam-4819	97	3	)	)	PUNCT
ejpam-4819	97	4	if	if	SCONJ
ejpam-4819	97	5	γ(c1	γ(c1	PROPN
ejpam-4819	97	6	,	,	PUNCT
ejpam-4819	97	7	c2	c2	PROPN
ejpam-4819	97	8	,	,	PUNCT
ejpam-4819	97	9	c3	c3	PROPN
ejpam-4819	97	10	)	)	PUNCT
ejpam-4819	97	11	>	>	X
ejpam-4819	97	12	0	0	NUM
ejpam-4819	97	13	,	,	PUNCT
ejpam-4819	97	14	then	then	ADV
ejpam-4819	97	15	1	1	NUM
ejpam-4819	97	16	≤	≤	NOUN
ejpam-4819	97	17	h(θbωb(fc1	h(θbωb(fc1	PROPN
ejpam-4819	97	18	,	,	PUNCT
ejpam-4819	97	19	f	f	PROPN
ejpam-4819	97	20	2c1	2c1	NUM
ejpam-4819	97	21	,	,	PUNCT
ejpam-4819	97	22	fc2	fc2	PROPN
ejpam-4819	97	23	)	)	PUNCT
ejpam-4819	97	24	,	,	PUNCT
ejpam-4819	97	25	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	97	26	,	,	PUNCT
ejpam-4819	97	27	c2	c2	PROPN
ejpam-4819	97	28	,	,	PUNCT
ejpam-4819	97	29	c3	c3	PROPN
ejpam-4819	97	30	)	)	PUNCT
ejpam-4819	97	31	)	)	PUNCT
ejpam-4819	98	1	≤	≤	NUM
ejpam-4819	98	2	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	98	3	,	,	PUNCT
ejpam-4819	98	4	c2	c2	PROPN
ejpam-4819	98	5	,	,	PUNCT
ejpam-4819	98	6	c3	c3	PROPN
ejpam-4819	98	7	)	)	PUNCT
ejpam-4819	98	8	θbωb(fc1	θbωb(fc1	NOUN
ejpam-4819	98	9	,	,	PUNCT
ejpam-4819	98	10	f2c1	f2c1	PROPN
ejpam-4819	98	11	,	,	PUNCT
ejpam-4819	98	12	fc2	fc2	PROPN
ejpam-4819	98	13	)	)	PUNCT
ejpam-4819	98	14	.	.	PUNCT
ejpam-4819	99	1	this	this	PRON
ejpam-4819	99	2	implies	imply	VERB
ejpam-4819	99	3	that	that	SCONJ
ejpam-4819	99	4	,	,	PUNCT
ejpam-4819	99	5	θbωb(fc1	θbωb(fc1	PROPN
ejpam-4819	99	6	,	,	PUNCT
ejpam-4819	99	7	f	f	PROPN
ejpam-4819	99	8	2c1	2c1	PROPN
ejpam-4819	99	9	,	,	PUNCT
ejpam-4819	99	10	fc2	fc2	PROPN
ejpam-4819	99	11	)	)	PUNCT
ejpam-4819	99	12	≤	≤	NUM
ejpam-4819	99	13	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	99	14	,	,	PUNCT
ejpam-4819	99	15	c2	c2	PROPN
ejpam-4819	99	16	,	,	PUNCT
ejpam-4819	99	17	c3	c3	PROPN
ejpam-4819	99	18	)	)	PUNCT
ejpam-4819	99	19	.	.	PUNCT
ejpam-4819	100	1	due	due	ADP
ejpam-4819	100	2	to	to	ADP
ejpam-4819	100	3	the	the	DET
ejpam-4819	100	4	fact	fact	NOUN
ejpam-4819	100	5	that	that	SCONJ
ejpam-4819	100	6	the	the	DET
ejpam-4819	100	7	set	set	NOUN
ejpam-4819	100	8	θ	θ	PROPN
ejpam-4819	100	9	is	be	AUX
ejpam-4819	100	10	a	a	DET
ejpam-4819	100	11	non	non	ADJ
ejpam-4819	100	12	-	-	ADJ
ejpam-4819	100	13	decreasing	decrease	VERB
ejpam-4819	100	14	function	function	NOUN
ejpam-4819	100	15	,	,	PUNCT
ejpam-4819	100	16	we	we	PRON
ejpam-4819	100	17	conclude	conclude	VERB
ejpam-4819	100	18	:	:	PUNCT
ejpam-4819	100	19	ωb(fc1	ωb(fc1	NUM
ejpam-4819	100	20	,	,	PUNCT
ejpam-4819	100	21	f	f	PROPN
ejpam-4819	100	22	2c1	2c1	NUM
ejpam-4819	100	23	,	,	PUNCT
ejpam-4819	100	24	fc2	fc2	PROPN
ejpam-4819	100	25	)	)	PUNCT
ejpam-4819	100	26	≤	≤	NOUN
ejpam-4819	101	1	λ1	λ1	PROPN
ejpam-4819	101	2	b	b	PROPN
ejpam-4819	101	3	γ(c1	γ(c1	PROPN
ejpam-4819	101	4	,	,	PUNCT
ejpam-4819	101	5	c2	c2	PROPN
ejpam-4819	101	6	,	,	PUNCT
ejpam-4819	101	7	c3	c3	PROPN
ejpam-4819	101	8	)	)	PUNCT
ejpam-4819	101	9	.	.	PUNCT
ejpam-4819	102	1	hence	hence	ADV
ejpam-4819	102	2	the	the	DET
ejpam-4819	102	3	result	result	NOUN
ejpam-4819	102	4	.	.	PUNCT
ejpam-4819	103	1	(	(	PUNCT
ejpam-4819	103	2	2	2	X
ejpam-4819	103	3	)	)	PUNCT
ejpam-4819	103	4	if	if	SCONJ
ejpam-4819	103	5	γ(c1	γ(c1	PROPN
ejpam-4819	103	6	,	,	PUNCT
ejpam-4819	103	7	c2	c2	PROPN
ejpam-4819	103	8	,	,	PUNCT
ejpam-4819	103	9	c3	c3	PROPN
ejpam-4819	103	10	)	)	PUNCT
ejpam-4819	103	11	=	=	SYM
ejpam-4819	103	12	0	0	NUM
ejpam-4819	103	13	,	,	PUNCT
ejpam-4819	103	14	then	then	ADV
ejpam-4819	103	15	by	by	ADP
ejpam-4819	103	16	utilizing	utilize	VERB
ejpam-4819	103	17	condition	condition	NOUN
ejpam-4819	103	18	(	(	PUNCT
ejpam-4819	103	19	1	1	NUM
ejpam-4819	103	20	)	)	PUNCT
ejpam-4819	103	21	,	,	PUNCT
ejpam-4819	103	22	we	we	PRON
ejpam-4819	103	23	have	have	VERB
ejpam-4819	103	24	:	:	PUNCT
ejpam-4819	103	25	1	1	NUM
ejpam-4819	103	26	≤	≤	NOUN
ejpam-4819	104	1	θbωb(fc1	θbωb(fc1	NOUN
ejpam-4819	104	2	,	,	PUNCT
ejpam-4819	104	3	f	f	PROPN
ejpam-4819	104	4	2c1	2c1	NUM
ejpam-4819	104	5	,	,	PUNCT
ejpam-4819	104	6	fc2	fc2	PROPN
ejpam-4819	104	7	)	)	PUNCT
ejpam-4819	104	8	≤	≤	NOUN
ejpam-4819	104	9	θλγ(c1	θλγ(c1	PROPN
ejpam-4819	104	10	,	,	PUNCT
ejpam-4819	104	11	c2	c2	PROPN
ejpam-4819	104	12	,	,	PUNCT
ejpam-4819	104	13	c3	c3	PROPN
ejpam-4819	104	14	)	)	PUNCT
ejpam-4819	104	15	=	=	SYM
ejpam-4819	104	16	1	1	X
ejpam-4819	104	17	.	.	PUNCT
ejpam-4819	104	18	thus	thus	ADV
ejpam-4819	104	19	,	,	PUNCT
ejpam-4819	104	20	ωb(fc1	ωb(fc1	NUM
ejpam-4819	104	21	,	,	PUNCT
ejpam-4819	104	22	f	f	PROPN
ejpam-4819	104	23	2c1	2c1	NUM
ejpam-4819	104	24	,	,	PUNCT
ejpam-4819	104	25	fc2	fc2	PROPN
ejpam-4819	104	26	)	)	PUNCT
ejpam-4819	104	27	=	=	SYM
ejpam-4819	104	28	0	0	X
ejpam-4819	104	29	.	.	PUNCT
ejpam-4819	105	1	lemma	lemma	PROPN
ejpam-4819	105	2	2	2	X
ejpam-4819	105	3	.	.	PUNCT
ejpam-4819	105	4	suppose	suppose	VERB
ejpam-4819	105	5	the	the	DET
ejpam-4819	105	6	self	self	NOUN
ejpam-4819	105	7	function	function	NOUN
ejpam-4819	105	8	f	f	NOUN
ejpam-4819	105	9	:	:	PUNCT
ejpam-4819	105	10	c	c	X
ejpam-4819	105	11	→	→	PUNCT
ejpam-4819	105	12	c	c	PROPN
ejpam-4819	105	13	fulfills	fulfill	VERB
ejpam-4819	105	14	the	the	DET
ejpam-4819	105	15	conditions	condition	NOUN
ejpam-4819	105	16	of	of	ADP
ejpam-4819	105	17	(	(	PUNCT
ejpam-4819	105	18	h	h	NOUN
ejpam-4819	105	19	,	,	PUNCT
ejpam-4819	105	20	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	105	21	contraction	contraction	NOUN
ejpam-4819	105	22	.	.	PUNCT
ejpam-4819	106	1	then	then	ADV
ejpam-4819	106	2	λf	λf	PROPN
ejpam-4819	106	3	has	have	VERB
ejpam-4819	106	4	at	at	ADP
ejpam-4819	106	5	most	most	ADV
ejpam-4819	106	6	one	one	NUM
ejpam-4819	106	7	element	element	NOUN
ejpam-4819	106	8	.	.	PUNCT
ejpam-4819	107	1	proof	proof	NOUN
ejpam-4819	107	2	.	.	PUNCT
ejpam-4819	108	1	to	to	PART
ejpam-4819	108	2	prove	prove	VERB
ejpam-4819	108	3	that	that	SCONJ
ejpam-4819	108	4	λf	λf	PROPN
ejpam-4819	108	5	has	have	VERB
ejpam-4819	108	6	at	at	ADP
ejpam-4819	108	7	most	most	ADV
ejpam-4819	108	8	one	one	NUM
ejpam-4819	108	9	element	element	NOUN
ejpam-4819	108	10	,	,	PUNCT
ejpam-4819	108	11	first	first	ADV
ejpam-4819	108	12	we	we	PRON
ejpam-4819	108	13	claim	claim	VERB
ejpam-4819	108	14	that	that	SCONJ
ejpam-4819	108	15	,	,	PUNCT
ejpam-4819	108	16	ωb(α	ωb(α	NUM
ejpam-4819	108	17	,	,	PUNCT
ejpam-4819	108	18	α	α	X
ejpam-4819	108	19	,	,	PUNCT
ejpam-4819	108	20	α	α	NOUN
ejpam-4819	108	21	)	)	PUNCT
ejpam-4819	108	22	=	=	SYM
ejpam-4819	108	23	0	0	NUM
ejpam-4819	108	24	∀α	∀α	NOUN
ejpam-4819	108	25	∈	∈	PROPN
ejpam-4819	108	26	λf	λf	X
ejpam-4819	108	27	.	.	PUNCT
ejpam-4819	109	1	assume	assume	VERB
ejpam-4819	109	2	ωb(α	ωb(α	NOUN
ejpam-4819	109	3	,	,	PUNCT
ejpam-4819	109	4	α	α	X
ejpam-4819	109	5	,	,	PUNCT
ejpam-4819	109	6	α	α	NOUN
ejpam-4819	109	7	)	)	PUNCT
ejpam-4819	109	8	>	>	X
ejpam-4819	109	9	0	0	PUNCT
ejpam-4819	110	1	for	for	SCONJ
ejpam-4819	110	2	some	some	DET
ejpam-4819	110	3	α	α	NOUN
ejpam-4819	110	4	∈	∈	NOUN
ejpam-4819	110	5	λf	λf	X
ejpam-4819	110	6	,	,	PUNCT
ejpam-4819	110	7	then	then	ADV
ejpam-4819	110	8	by	by	ADP
ejpam-4819	110	9	employing	employ	VERB
ejpam-4819	110	10	lemma	lemma	PROPN
ejpam-4819	110	11	1	1	NUM
ejpam-4819	110	12	we	we	PRON
ejpam-4819	110	13	get	get	VERB
ejpam-4819	110	14	:	:	PUNCT
ejpam-4819	110	15	ωb(fα	ωb(fα	PROPN
ejpam-4819	110	16	,	,	PUNCT
ejpam-4819	110	17	f	f	PROPN
ejpam-4819	110	18	2α	2α	NOUN
ejpam-4819	110	19	,	,	PUNCT
ejpam-4819	110	20	fα	fα	NOUN
ejpam-4819	110	21	)	)	PUNCT
ejpam-4819	110	22	≤	≤	NOUN
ejpam-4819	111	1	λ1	λ1	PROPN
ejpam-4819	111	2	b	b	PROPN
ejpam-4819	111	3	γ(α	γ(α	PROPN
ejpam-4819	111	4	,	,	PUNCT
ejpam-4819	111	5	α	α	X
ejpam-4819	111	6	,	,	PUNCT
ejpam-4819	111	7	α	α	NOUN
ejpam-4819	111	8	)	)	PUNCT
ejpam-4819	111	9	=	=	SYM
ejpam-4819	111	10	λ1	λ1	PROPN
ejpam-4819	111	11	b	b	PROPN
ejpam-4819	111	12	max{ωb(α	max{ωb(α	PROPN
ejpam-4819	111	13	,	,	PUNCT
ejpam-4819	111	14	fα	fα	ADP
ejpam-4819	111	15	,	,	PUNCT
ejpam-4819	111	16	α	α	NOUN
ejpam-4819	111	17	)	)	PUNCT
ejpam-4819	111	18	,	,	PUNCT
ejpam-4819	111	19	[	[	X
ejpam-4819	111	20	ωb(α	ωb(α	NUM
ejpam-4819	111	21	,	,	PUNCT
ejpam-4819	111	22	fα	fα	ADP
ejpam-4819	111	23	,	,	PUNCT
ejpam-4819	111	24	fα	fα	NOUN
ejpam-4819	111	25	)	)	PUNCT
ejpam-4819	111	26	]	]	PUNCT
ejpam-4819	112	1	λ2	λ2	NOUN
ejpam-4819	112	2	[	[	X
ejpam-4819	112	3	ωb(α	ωb(α	NUM
ejpam-4819	112	4	,	,	PUNCT
ejpam-4819	112	5	fα	fα	ADP
ejpam-4819	112	6	,	,	PUNCT
ejpam-4819	112	7	fα	fα	NOUN
ejpam-4819	112	8	)	)	PUNCT
ejpam-4819	112	9	]	]	PUNCT
ejpam-4819	113	1	λ3	λ3	PROPN
ejpam-4819	113	2	}	}	PUNCT
ejpam-4819	113	3	<	<	X
ejpam-4819	113	4	ωb(α	ωb(α	NUM
ejpam-4819	113	5	,	,	PUNCT
ejpam-4819	113	6	α	α	X
ejpam-4819	113	7	,	,	PUNCT
ejpam-4819	113	8	α	α	NOUN
ejpam-4819	113	9	)	)	PUNCT
ejpam-4819	113	10	.	.	PUNCT
ejpam-4819	114	1	t.	t.	PROPN
ejpam-4819	114	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	114	3	/	/	SYM
ejpam-4819	114	4	eur	eur	PROPN
ejpam-4819	114	5	.	.	PUNCT
ejpam-4819	115	1	j.	j.	PROPN
ejpam-4819	115	2	pure	pure	PROPN
ejpam-4819	115	3	appl	appl	PROPN
ejpam-4819	115	4	.	.	PROPN
ejpam-4819	115	5	math	math	PROPN
ejpam-4819	115	6	,	,	PUNCT
ejpam-4819	115	7	16	16	NUM
ejpam-4819	115	8	(	(	PUNCT
ejpam-4819	115	9	3	3	NUM
ejpam-4819	115	10	)	)	PUNCT
ejpam-4819	115	11	(	(	PUNCT
ejpam-4819	115	12	2023	2023	NUM
ejpam-4819	115	13	)	)	PUNCT
ejpam-4819	115	14	,	,	PUNCT
ejpam-4819	115	15	1717	1717	NUM
ejpam-4819	115	16	-	-	SYM
ejpam-4819	115	17	1730	1730	NUM
ejpam-4819	115	18	1721	1721	NUM
ejpam-4819	115	19	a	a	DET
ejpam-4819	115	20	contradiction	contradiction	NOUN
ejpam-4819	115	21	.	.	PUNCT
ejpam-4819	116	1	hence	hence	ADV
ejpam-4819	116	2	the	the	DET
ejpam-4819	116	3	result	result	NOUN
ejpam-4819	116	4	.	.	PUNCT
ejpam-4819	117	1	now	now	ADV
ejpam-4819	117	2	assume	assume	VERB
ejpam-4819	117	3	that	that	SCONJ
ejpam-4819	117	4	there	there	PRON
ejpam-4819	117	5	is	be	VERB
ejpam-4819	117	6	c∗	c∗	ADJ
ejpam-4819	117	7	,	,	PUNCT
ejpam-4819	117	8	α	α	NOUN
ejpam-4819	117	9	∈	∈	NOUN
ejpam-4819	117	10	λf	λf	X
ejpam-4819	117	11	with	with	ADP
ejpam-4819	117	12	c∗	c∗	PROPN
ejpam-4819	117	13	̸=	̸=	PROPN
ejpam-4819	117	14	α	α	NOUN
ejpam-4819	117	15	,	,	PUNCT
ejpam-4819	117	16	assume	assume	VERB
ejpam-4819	117	17	that	that	SCONJ
ejpam-4819	117	18	ωb(c	ωb(c	PUNCT
ejpam-4819	117	19	∗	∗	NOUN
ejpam-4819	117	20	,	,	PUNCT
ejpam-4819	117	21	c∗	c∗	NOUN
ejpam-4819	117	22	,	,	PUNCT
ejpam-4819	117	23	α	α	NOUN
ejpam-4819	117	24	)	)	PUNCT
ejpam-4819	117	25	>	>	X
ejpam-4819	117	26	0	0	NUM
ejpam-4819	117	27	,	,	PUNCT
ejpam-4819	117	28	so	so	ADV
ejpam-4819	117	29	by	by	ADP
ejpam-4819	117	30	lemma	lemma	PROPN
ejpam-4819	117	31	1	1	NUM
ejpam-4819	117	32	we	we	PRON
ejpam-4819	117	33	have	have	VERB
ejpam-4819	117	34	:	:	PUNCT
ejpam-4819	117	35	ωb(c	ωb(c	NUM
ejpam-4819	117	36	∗	∗	NOUN
ejpam-4819	117	37	,	,	PUNCT
ejpam-4819	117	38	c∗	c∗	NOUN
ejpam-4819	117	39	,	,	PUNCT
ejpam-4819	117	40	α	α	NOUN
ejpam-4819	117	41	)	)	PUNCT
ejpam-4819	117	42	=	=	SYM
ejpam-4819	117	43	ωb(fc	ωb(fc	PROPN
ejpam-4819	117	44	∗	∗	NOUN
ejpam-4819	117	45	,	,	PUNCT
ejpam-4819	117	46	f2c∗	f2c∗	PROPN
ejpam-4819	117	47	,	,	PUNCT
ejpam-4819	117	48	fα	fα	NOUN
ejpam-4819	117	49	)	)	PUNCT
ejpam-4819	117	50	≤	≤	NOUN
ejpam-4819	118	1	λ1	λ1	PROPN
ejpam-4819	118	2	b	b	PROPN
ejpam-4819	118	3	γ(c∗	γ(c∗	PROPN
ejpam-4819	118	4	,	,	PUNCT
ejpam-4819	118	5	c∗	c∗	PROPN
ejpam-4819	118	6	,	,	PUNCT
ejpam-4819	118	7	α	α	NOUN
ejpam-4819	118	8	)	)	PUNCT
ejpam-4819	118	9	=	=	SYM
ejpam-4819	118	10	λ1	λ1	PROPN
ejpam-4819	118	11	b	b	PROPN
ejpam-4819	118	12	max{ωb(c	max{ωb(c	PROPN
ejpam-4819	118	13	∗	∗	NOUN
ejpam-4819	118	14	,	,	PUNCT
ejpam-4819	118	15	fc∗	fc∗	NOUN
ejpam-4819	118	16	,	,	PUNCT
ejpam-4819	118	17	α	α	NOUN
ejpam-4819	118	18	)	)	PUNCT
ejpam-4819	118	19	,	,	PUNCT
ejpam-4819	118	20	[	[	X
ejpam-4819	118	21	ωb(c	ωb(c	X
ejpam-4819	118	22	∗	∗	NOUN
ejpam-4819	118	23	,	,	PUNCT
ejpam-4819	118	24	c∗	c∗	NOUN
ejpam-4819	118	25	,	,	PUNCT
ejpam-4819	118	26	c∗)]λ2	c∗)]λ2	PROPN
ejpam-4819	118	27	[	[	NOUN
ejpam-4819	118	28	ωb(α	ωb(α	NUM
ejpam-4819	118	29	,	,	PUNCT
ejpam-4819	118	30	α	α	X
ejpam-4819	118	31	,	,	PUNCT
ejpam-4819	118	32	α	α	NOUN
ejpam-4819	118	33	)	)	PUNCT
ejpam-4819	118	34	]	]	PUNCT
ejpam-4819	119	1	λ3	λ3	PROPN
ejpam-4819	119	2	}	}	PUNCT
ejpam-4819	119	3	<	<	X
ejpam-4819	119	4	ωb(c	ωb(c	X
ejpam-4819	119	5	∗	∗	NOUN
ejpam-4819	119	6	,	,	PUNCT
ejpam-4819	119	7	c∗	c∗	NOUN
ejpam-4819	119	8	,	,	PUNCT
ejpam-4819	119	9	α	α	NOUN
ejpam-4819	119	10	)	)	PUNCT
ejpam-4819	119	11	.	.	PUNCT
ejpam-4819	120	1	a	a	DET
ejpam-4819	120	2	contradiction	contradiction	NOUN
ejpam-4819	120	3	.	.	PUNCT
ejpam-4819	121	1	therefore	therefore	ADV
ejpam-4819	121	2	,	,	PUNCT
ejpam-4819	121	3	ωb(c	ωb(c	PUNCT
ejpam-4819	121	4	∗	∗	NOUN
ejpam-4819	121	5	,	,	PUNCT
ejpam-4819	121	6	c∗	c∗	NOUN
ejpam-4819	121	7	,	,	PUNCT
ejpam-4819	121	8	α	α	NOUN
ejpam-4819	121	9	)	)	PUNCT
ejpam-4819	121	10	=	=	SYM
ejpam-4819	121	11	0	0	NUM
ejpam-4819	121	12	and	and	CCONJ
ejpam-4819	121	13	by	by	ADP
ejpam-4819	121	14	utilizing	utilize	VERB
ejpam-4819	121	15	the	the	DET
ejpam-4819	121	16	definition	definition	NOUN
ejpam-4819	121	17	of	of	ADP
ejpam-4819	121	18	of	of	ADP
ejpam-4819	121	19	ωb	ωb	NOUN
ejpam-4819	121	20	(	(	PUNCT
ejpam-4819	121	21	condition	condition	NOUN
ejpam-4819	121	22	(	(	PUNCT
ejpam-4819	121	23	3	3	NUM
ejpam-4819	121	24	)	)	PUNCT
ejpam-4819	121	25	)	)	PUNCT
ejpam-4819	121	26	and	and	CCONJ
ejpam-4819	121	27	since	since	SCONJ
ejpam-4819	121	28	ωb(c	ωb(c	ADP
ejpam-4819	121	29	∗	∗	NOUN
ejpam-4819	121	30	,	,	PUNCT
ejpam-4819	121	31	c∗	c∗	NOUN
ejpam-4819	121	32	,	,	PUNCT
ejpam-4819	121	33	c∗	c∗	NOUN
ejpam-4819	121	34	)	)	PUNCT
ejpam-4819	121	35	=	=	SYM
ejpam-4819	121	36	0	0	NUM
ejpam-4819	121	37	,	,	PUNCT
ejpam-4819	121	38	we	we	PRON
ejpam-4819	121	39	conclude	conclude	VERB
ejpam-4819	121	40	that	that	SCONJ
ejpam-4819	121	41	gb(c	gb(c	VERB
ejpam-4819	121	42	∗	∗	NOUN
ejpam-4819	121	43	,	,	PUNCT
ejpam-4819	121	44	c∗	c∗	NOUN
ejpam-4819	121	45	,	,	PUNCT
ejpam-4819	121	46	α	α	NOUN
ejpam-4819	121	47	)	)	PUNCT
ejpam-4819	121	48	=	=	SYM
ejpam-4819	121	49	0	0	PUNCT
ejpam-4819	121	50	therefore	therefore	ADV
ejpam-4819	121	51	,	,	PUNCT
ejpam-4819	121	52	c∗	c∗	PROPN
ejpam-4819	121	53	=	=	SYM
ejpam-4819	121	54	α	α	PROPN
ejpam-4819	121	55	.	.	PUNCT
ejpam-4819	122	1	for	for	ADP
ejpam-4819	122	2	an	an	DET
ejpam-4819	122	3	arbitrary	arbitrary	ADJ
ejpam-4819	122	4	point	point	NOUN
ejpam-4819	122	5	c0	c0	PROPN
ejpam-4819	122	6	∈	∈	PROPN
ejpam-4819	122	7	c	c	PROPN
ejpam-4819	122	8	the	the	DET
ejpam-4819	122	9	picard	picard	NOUN
ejpam-4819	122	10	sequence	sequence	NOUN
ejpam-4819	122	11	is	be	AUX
ejpam-4819	122	12	defined	define	VERB
ejpam-4819	122	13	by	by	ADP
ejpam-4819	122	14	iterating	iterate	VERB
ejpam-4819	122	15	f	f	PROPN
ejpam-4819	122	16	:	:	PUNCT
ejpam-4819	122	17	c	c	X
ejpam-4819	122	18	→	→	SYM
ejpam-4819	122	19	c	c	X
ejpam-4819	122	20	where	where	SCONJ
ejpam-4819	122	21	cn+1	cn+1	VERB
ejpam-4819	122	22	=	=	SYM
ejpam-4819	122	23	f(cn	f(cn	PROPN
ejpam-4819	122	24	)	)	PUNCT
ejpam-4819	122	25	=	=	SYM
ejpam-4819	122	26	fn(c0	fn(c0	PROPN
ejpam-4819	122	27	)	)	PUNCT
ejpam-4819	122	28	.	.	PUNCT
ejpam-4819	123	1	henceforth	henceforth	ADV
ejpam-4819	123	2	,	,	PUNCT
ejpam-4819	123	3	we	we	PRON
ejpam-4819	123	4	mean	mean	VERB
ejpam-4819	123	5	by	by	ADP
ejpam-4819	123	6	the	the	DET
ejpam-4819	123	7	sequence	sequence	NOUN
ejpam-4819	123	8	cn	cn	PROPN
ejpam-4819	123	9	the	the	DET
ejpam-4819	123	10	picard	picard	NOUN
ejpam-4819	123	11	sequence	sequence	NOUN
ejpam-4819	123	12	unless	unless	SCONJ
ejpam-4819	123	13	otherwise	otherwise	ADV
ejpam-4819	123	14	stated	state	VERB
ejpam-4819	123	15	.	.	PUNCT
ejpam-4819	124	1	lemma	lemma	PROPN
ejpam-4819	124	2	3	3	X
ejpam-4819	124	3	.	.	PUNCT
ejpam-4819	124	4	suppose	suppose	VERB
ejpam-4819	124	5	the	the	DET
ejpam-4819	124	6	self	self	NOUN
ejpam-4819	124	7	function	function	NOUN
ejpam-4819	124	8	f	f	NOUN
ejpam-4819	124	9	:	:	PUNCT
ejpam-4819	124	10	c	c	X
ejpam-4819	124	11	→	→	PUNCT
ejpam-4819	124	12	c	c	PROPN
ejpam-4819	124	13	fulfills	fulfill	VERB
ejpam-4819	124	14	the	the	DET
ejpam-4819	124	15	conditions	condition	NOUN
ejpam-4819	124	16	of	of	ADP
ejpam-4819	124	17	(	(	PUNCT
ejpam-4819	124	18	h	h	NOUN
ejpam-4819	124	19	,	,	PUNCT
ejpam-4819	124	20	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	124	21	contraction	contraction	NOUN
ejpam-4819	124	22	and	and	CCONJ
ejpam-4819	124	23	suppose	suppose	VERB
ejpam-4819	124	24	that	that	SCONJ
ejpam-4819	124	25	for	for	ADP
ejpam-4819	124	26	some	some	DET
ejpam-4819	124	27	k	k	PROPN
ejpam-4819	124	28	∈	∈	PROPN
ejpam-4819	124	29	n	n	CCONJ
ejpam-4819	124	30	we	we	PRON
ejpam-4819	124	31	have	have	VERB
ejpam-4819	124	32	ωb(ck−1	ωb(ck−1	NUM
ejpam-4819	124	33	,	,	PUNCT
ejpam-4819	124	34	ck	ck	ADJ
ejpam-4819	124	35	,	,	PUNCT
ejpam-4819	124	36	ck	ck	ADJ
ejpam-4819	124	37	)	)	PUNCT
ejpam-4819	124	38	=	=	SYM
ejpam-4819	125	1	0	0	X
ejpam-4819	125	2	.	.	PUNCT
ejpam-4819	126	1	then	then	ADV
ejpam-4819	126	2	,	,	PUNCT
ejpam-4819	126	3	λf	λf	ADV
ejpam-4819	126	4	=	=	X
ejpam-4819	126	5	{	{	PUNCT
ejpam-4819	126	6	ck	ck	ADJ
ejpam-4819	126	7	}	}	PUNCT
ejpam-4819	126	8	proof	proof	NOUN
ejpam-4819	126	9	.	.	PUNCT
ejpam-4819	127	1	note	note	VERB
ejpam-4819	127	2	that	that	SCONJ
ejpam-4819	127	3	γ(ck−1	γ(ck−1	PROPN
ejpam-4819	127	4	,	,	PUNCT
ejpam-4819	127	5	ck	ck	INTJ
ejpam-4819	127	6	,	,	PUNCT
ejpam-4819	127	7	ck	ck	ADJ
ejpam-4819	127	8	)	)	PUNCT
ejpam-4819	127	9	=	=	SYM
ejpam-4819	128	1	λ1	λ1	PROPN
ejpam-4819	128	2	b	b	PROPN
ejpam-4819	128	3	max	max	PROPN
ejpam-4819	128	4	{	{	PUNCT
ejpam-4819	128	5	ωb(ck−1	ωb(ck−1	PROPN
ejpam-4819	128	6	,	,	PUNCT
ejpam-4819	128	7	ck	ck	INTJ
ejpam-4819	128	8	,	,	PUNCT
ejpam-4819	128	9	ck	ck	ADJ
ejpam-4819	128	10	)	)	PUNCT
ejpam-4819	128	11	,	,	PUNCT
ejpam-4819	129	1	[	[	X
ejpam-4819	129	2	ωb(ck−1	ωb(ck−1	NUM
ejpam-4819	129	3	,	,	PUNCT
ejpam-4819	129	4	ck	ck	ADJ
ejpam-4819	129	5	,	,	PUNCT
ejpam-4819	129	6	ck	ck	ADJ
ejpam-4819	129	7	)	)	PUNCT
ejpam-4819	129	8	]	]	PUNCT
ejpam-4819	129	9	λ2	λ2	NOUN
ejpam-4819	130	1	[	[	X
ejpam-4819	130	2	ωb(ck	ωb(ck	ADJ
ejpam-4819	130	3	,	,	PUNCT
ejpam-4819	130	4	ck+1	ck+1	NOUN
ejpam-4819	130	5	,	,	PUNCT
ejpam-4819	130	6	ck+1	ck+1	NUM
ejpam-4819	130	7	)	)	PUNCT
ejpam-4819	130	8	]	]	PUNCT
ejpam-4819	131	1	λ3	λ3	PROPN
ejpam-4819	131	2	}	}	PUNCT
ejpam-4819	131	3	=	=	SYM
ejpam-4819	131	4	0	0	X
ejpam-4819	131	5	.	.	PUNCT
ejpam-4819	132	1	so	so	ADV
ejpam-4819	132	2	,	,	PUNCT
ejpam-4819	132	3	by	by	ADP
ejpam-4819	132	4	lemma	lemma	PROPN
ejpam-4819	132	5	1	1	NUM
ejpam-4819	132	6	,	,	PUNCT
ejpam-4819	132	7	we	we	PRON
ejpam-4819	132	8	get	get	VERB
ejpam-4819	132	9	that	that	DET
ejpam-4819	132	10	ωb(ck	ωb(ck	ADJ
ejpam-4819	132	11	,	,	PUNCT
ejpam-4819	132	12	ck+1	ck+1	NOUN
ejpam-4819	132	13	,	,	PUNCT
ejpam-4819	132	14	ck+1	ck+1	X
ejpam-4819	132	15	)	)	PUNCT
ejpam-4819	132	16	=	=	SYM
ejpam-4819	132	17	ωb(ck−1	ωb(ck−1	NUM
ejpam-4819	132	18	,	,	PUNCT
ejpam-4819	132	19	ck	ck	PROPN
ejpam-4819	132	20	,	,	PUNCT
ejpam-4819	132	21	ck	ck	ADJ
ejpam-4819	132	22	)	)	PUNCT
ejpam-4819	132	23	=	=	SYM
ejpam-4819	133	1	0	0	X
ejpam-4819	133	2	.	.	PUNCT
ejpam-4819	134	1	in	in	ADP
ejpam-4819	134	2	a	a	DET
ejpam-4819	134	3	similar	similar	ADJ
ejpam-4819	134	4	manner	manner	NOUN
ejpam-4819	134	5	,	,	PUNCT
ejpam-4819	134	6	we	we	PRON
ejpam-4819	134	7	can	can	AUX
ejpam-4819	134	8	verify	verify	VERB
ejpam-4819	134	9	that	that	SCONJ
ejpam-4819	134	10	ωb(ck+1	ωb(ck+1	NOUN
ejpam-4819	134	11	,	,	PUNCT
ejpam-4819	134	12	ck+2	ck+2	NOUN
ejpam-4819	134	13	,	,	PUNCT
ejpam-4819	134	14	ck+2	ck+2	NOUN
ejpam-4819	134	15	)	)	PUNCT
ejpam-4819	134	16	=	=	SYM
ejpam-4819	134	17	0	0	X
ejpam-4819	134	18	.	.	PUNCT
ejpam-4819	134	19	by	by	ADP
ejpam-4819	134	20	utilizing	utilize	VERB
ejpam-4819	134	21	the	the	DET
ejpam-4819	134	22	definition	definition	NOUN
ejpam-4819	134	23	of	of	ADP
ejpam-4819	134	24	ωb	ωb	NOUN
ejpam-4819	134	25	,	,	PUNCT
ejpam-4819	134	26	we	we	PRON
ejpam-4819	134	27	conclude	conclude	VERB
ejpam-4819	134	28	that	that	PRON
ejpam-4819	134	29	gb(ck−1	gb(ck−1	NOUN
ejpam-4819	134	30	,	,	PUNCT
ejpam-4819	134	31	ck+1	ck+1	X
ejpam-4819	134	32	,	,	PUNCT
ejpam-4819	134	33	ck+1	ck+1	X
ejpam-4819	134	34	)	)	PUNCT
ejpam-4819	134	35	=	=	SYM
ejpam-4819	134	36	0	0	PUNCT
ejpam-4819	135	1	and	and	CCONJ
ejpam-4819	135	2	so	so	ADV
ejpam-4819	135	3	ck−1	ck−1	NOUN
ejpam-4819	135	4	=	=	PUNCT
ejpam-4819	135	5	ck+1	ck+1	X
ejpam-4819	135	6	.	.	PUNCT
ejpam-4819	136	1	in	in	ADP
ejpam-4819	136	2	a	a	DET
ejpam-4819	136	3	typical	typical	ADJ
ejpam-4819	136	4	way	way	NOUN
ejpam-4819	136	5	,	,	PUNCT
ejpam-4819	136	6	we	we	PRON
ejpam-4819	136	7	can	can	AUX
ejpam-4819	136	8	prove	prove	VERB
ejpam-4819	136	9	that	that	SCONJ
ejpam-4819	136	10	ck	ck	ADV
ejpam-4819	136	11	=	=	SYM
ejpam-4819	136	12	ck+2	ck+2	NOUN
ejpam-4819	136	13	.	.	PUNCT
ejpam-4819	137	1	now	now	ADV
ejpam-4819	137	2	,	,	PUNCT
ejpam-4819	137	3	by	by	ADP
ejpam-4819	137	4	employing	employ	VERB
ejpam-4819	137	5	the	the	DET
ejpam-4819	137	6	triangle	triangle	NOUN
ejpam-4819	137	7	inequality	inequality	NOUN
ejpam-4819	137	8	of	of	ADP
ejpam-4819	137	9	ωb	ωb	NOUN
ejpam-4819	137	10	,	,	PUNCT
ejpam-4819	137	11	we	we	PRON
ejpam-4819	137	12	get	get	VERB
ejpam-4819	137	13	ωb(ck	ωb(ck	ADJ
ejpam-4819	137	14	,	,	PUNCT
ejpam-4819	137	15	ck	ck	ADJ
ejpam-4819	137	16	,	,	PUNCT
ejpam-4819	137	17	ck	ck	NOUN
ejpam-4819	137	18	)	)	PUNCT
ejpam-4819	137	19	≤	≤	NOUN
ejpam-4819	137	20	b[ωb(ck	b[ωb(ck	ADJ
ejpam-4819	137	21	,	,	PUNCT
ejpam-4819	137	22	ck+1	ck+1	NOUN
ejpam-4819	137	23	,	,	PUNCT
ejpam-4819	137	24	ck+1	ck+1	X
ejpam-4819	137	25	)	)	PUNCT
ejpam-4819	138	1	+	+	CCONJ
ejpam-4819	138	2	ωb(ck+1	ωb(ck+1	ADJ
ejpam-4819	138	3	,	,	PUNCT
ejpam-4819	138	4	ck	ck	INTJ
ejpam-4819	138	5	,	,	PUNCT
ejpam-4819	138	6	ck	ck	NOUN
ejpam-4819	138	7	)	)	PUNCT
ejpam-4819	138	8	]	]	PUNCT
ejpam-4819	139	1	=	=	PUNCT
ejpam-4819	139	2	b[ωb(ck	b[ωb(ck	ADJ
ejpam-4819	139	3	,	,	PUNCT
ejpam-4819	139	4	ck+1	ck+1	NOUN
ejpam-4819	139	5	,	,	PUNCT
ejpam-4819	139	6	ck+1	ck+1	X
ejpam-4819	139	7	)	)	PUNCT
ejpam-4819	139	8	+	+	CCONJ
ejpam-4819	139	9	ωb(ck+1	ωb(ck+1	ADJ
ejpam-4819	139	10	,	,	PUNCT
ejpam-4819	139	11	ck+2	ck+2	NOUN
ejpam-4819	139	12	,	,	PUNCT
ejpam-4819	139	13	ck+2	ck+2	NOUN
ejpam-4819	139	14	)	)	PUNCT
ejpam-4819	139	15	]	]	PUNCT
ejpam-4819	140	1	=	=	PUNCT
ejpam-4819	140	2	0	0	X
ejpam-4819	140	3	.	.	PUNCT
ejpam-4819	141	1	(	(	PUNCT
ejpam-4819	141	2	6	6	NUM
ejpam-4819	141	3	)	)	PUNCT
ejpam-4819	141	4	from	from	ADP
ejpam-4819	141	5	inequality	inequality	NOUN
ejpam-4819	141	6	(	(	PUNCT
ejpam-4819	141	7	6	6	NUM
ejpam-4819	141	8	)	)	PUNCT
ejpam-4819	141	9	and	and	CCONJ
ejpam-4819	141	10	ωb(ck	ωb(ck	ADJ
ejpam-4819	141	11	,	,	PUNCT
ejpam-4819	141	12	ck+1	ck+1	NOUN
ejpam-4819	141	13	,	,	PUNCT
ejpam-4819	141	14	ck+1	ck+1	X
ejpam-4819	141	15	)	)	PUNCT
ejpam-4819	141	16	=	=	SYM
ejpam-4819	141	17	0	0	NUM
ejpam-4819	141	18	,	,	PUNCT
ejpam-4819	141	19	we	we	PRON
ejpam-4819	141	20	conclude	conclude	VERB
ejpam-4819	141	21	that	that	SCONJ
ejpam-4819	142	1	ck	ck	PROPN
ejpam-4819	142	2	∈	∈	PROPN
ejpam-4819	142	3	λf	λf	X
ejpam-4819	142	4	and	and	CCONJ
ejpam-4819	142	5	lemma	lemma	PROPN
ejpam-4819	142	6	2	2	NUM
ejpam-4819	142	7	ensures	ensure	VERB
ejpam-4819	142	8	that	that	SCONJ
ejpam-4819	142	9	ck	ck	PROPN
ejpam-4819	142	10	is	be	AUX
ejpam-4819	142	11	the	the	DET
ejpam-4819	142	12	unique	unique	ADJ
ejpam-4819	142	13	element	element	NOUN
ejpam-4819	142	14	in	in	ADP
ejpam-4819	142	15	λf	λf	PROPN
ejpam-4819	142	16	.	.	PUNCT
ejpam-4819	143	1	theorem	theorem	NOUN
ejpam-4819	143	2	1	1	X
ejpam-4819	143	3	.	.	PUNCT
ejpam-4819	144	1	suppose	suppose	VERB
ejpam-4819	144	2	(	(	PUNCT
ejpam-4819	144	3	c	c	X
ejpam-4819	144	4	,	,	PUNCT
ejpam-4819	144	5	gb	gb	NOUN
ejpam-4819	144	6	)	)	PUNCT
ejpam-4819	144	7	is	be	AUX
ejpam-4819	144	8	gb	gb	ADV
ejpam-4819	144	9	-	-	PUNCT
ejpam-4819	144	10	complete	complete	NOUN
ejpam-4819	144	11	equipped	equip	VERB
ejpam-4819	144	12	with	with	ADP
ejpam-4819	144	13	ωb	ωb	NOUN
ejpam-4819	144	14	distance	distance	NOUN
ejpam-4819	144	15	mappings	mapping	NOUN
ejpam-4819	144	16	with	with	ADP
ejpam-4819	144	17	the	the	DET
ejpam-4819	144	18	base	base	NOUN
ejpam-4819	144	19	b	b	PROPN
ejpam-4819	144	20	∈	∈	PROPN
ejpam-4819	145	1	[	[	X
ejpam-4819	145	2	1,+∞	1,+∞	NUM
ejpam-4819	145	3	)	)	PUNCT
ejpam-4819	145	4	and	and	CCONJ
ejpam-4819	145	5	c	c	PROPN
ejpam-4819	145	6	is	be	AUX
ejpam-4819	145	7	bounded	bound	VERB
ejpam-4819	145	8	w.r.t	w.r.t	NOUN
ejpam-4819	145	9	.	.	PUNCT
ejpam-4819	146	1	ωb	ωb	X
ejpam-4819	146	2	.	.	PUNCT
ejpam-4819	146	3	suppose	suppose	VERB
ejpam-4819	146	4	there	there	PRON
ejpam-4819	146	5	are	be	VERB
ejpam-4819	146	6	λi	λi	ADP
ejpam-4819	146	7	∈	∈	PROPN
ejpam-4819	146	8	(	(	PUNCT
ejpam-4819	146	9	0	0	NUM
ejpam-4819	146	10	,	,	PUNCT
ejpam-4819	146	11	1	1	NUM
ejpam-4819	146	12	)	)	PUNCT
ejpam-4819	146	13	,	,	PUNCT
ejpam-4819	146	14	i	i	PRON
ejpam-4819	146	15	∈	∈	PROPN
ejpam-4819	146	16	{	{	PUNCT
ejpam-4819	146	17	1	1	NUM
ejpam-4819	146	18	,	,	PUNCT
ejpam-4819	146	19	2	2	NUM
ejpam-4819	146	20	,	,	PUNCT
ejpam-4819	146	21	3	3	NUM
ejpam-4819	146	22	}	}	PUNCT
ejpam-4819	146	23	with	with	ADP
ejpam-4819	146	24	λ2+λ3	λ2+λ3	ADP
ejpam-4819	146	25	<	<	X
ejpam-4819	146	26	1	1	NUM
ejpam-4819	146	27	,	,	PUNCT
ejpam-4819	146	28	θ	θ	PROPN
ejpam-4819	146	29	∈	∈	PROPN
ejpam-4819	146	30	θ	θ	PROPN
ejpam-4819	146	31	,	,	PUNCT
ejpam-4819	146	32	h	h	NOUN
ejpam-4819	146	33	∈	∈	PROPN
ejpam-4819	146	34	h	h	NOUN
ejpam-4819	146	35	such	such	ADJ
ejpam-4819	146	36	that	that	SCONJ
ejpam-4819	146	37	the	the	DET
ejpam-4819	146	38	mapping	mapping	NOUN
ejpam-4819	146	39	f	f	X
ejpam-4819	146	40	:	:	PUNCT
ejpam-4819	146	41	c	c	X
ejpam-4819	146	42	→	→	PUNCT
ejpam-4819	146	43	c	c	PROPN
ejpam-4819	146	44	is	be	AUX
ejpam-4819	146	45	a	a	DET
ejpam-4819	146	46	(	(	PUNCT
ejpam-4819	146	47	h	h	NOUN
ejpam-4819	146	48	,	,	PUNCT
ejpam-4819	146	49	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	146	50	contraction	contraction	NOUN
ejpam-4819	146	51	if	if	SCONJ
ejpam-4819	146	52	one	one	NUM
ejpam-4819	146	53	of	of	ADP
ejpam-4819	146	54	the	the	DET
ejpam-4819	146	55	following	follow	VERB
ejpam-4819	146	56	conditions	condition	NOUN
ejpam-4819	146	57	is	be	AUX
ejpam-4819	146	58	fulfilled	fulfil	VERB
ejpam-4819	146	59	:	:	PUNCT
ejpam-4819	146	60	1	1	X
ejpam-4819	146	61	.	.	X
ejpam-4819	146	62	the	the	DET
ejpam-4819	146	63	self	self	NOUN
ejpam-4819	146	64	mapping	mapping	NOUN
ejpam-4819	146	65	f	f	X
ejpam-4819	146	66	is	be	AUX
ejpam-4819	146	67	a	a	DET
ejpam-4819	146	68	continuous	continuous	ADJ
ejpam-4819	146	69	;	;	PUNCT
ejpam-4819	146	70	2	2	X
ejpam-4819	146	71	.	.	X
ejpam-4819	147	1	for	for	ADP
ejpam-4819	147	2	all	all	DET
ejpam-4819	147	3	c∗	c∗	PROPN
ejpam-4819	147	4	∈	∈	PROPN
ejpam-4819	147	5	c	c	NOUN
ejpam-4819	148	1	if	if	SCONJ
ejpam-4819	148	2	fc∗	fc∗	ADJ
ejpam-4819	148	3	̸=	̸=	PROPN
ejpam-4819	148	4	c∗	c∗	NOUN
ejpam-4819	148	5	,	,	PUNCT
ejpam-4819	148	6	then	then	ADV
ejpam-4819	148	7	0	0	NUM
ejpam-4819	148	8	<	<	X
ejpam-4819	148	9	inf{ωb(c	inf{ωb(c	PROPN
ejpam-4819	148	10	,	,	PUNCT
ejpam-4819	148	11	fc	fc	X
ejpam-4819	148	12	,	,	PUNCT
ejpam-4819	148	13	c	c	NOUN
ejpam-4819	148	14	∗	∗	NOUN
ejpam-4819	148	15	)	)	PUNCT
ejpam-4819	148	16	:	:	PUNCT
ejpam-4819	149	1	c	c	X
ejpam-4819	149	2	∈	∈	PROPN
ejpam-4819	149	3	c	c	X
ejpam-4819	149	4	}	}	PUNCT
ejpam-4819	149	5	,	,	PUNCT
ejpam-4819	149	6	then	then	ADV
ejpam-4819	149	7	λf	λf	PROPN
ejpam-4819	149	8	has	have	VERB
ejpam-4819	149	9	only	only	ADV
ejpam-4819	149	10	one	one	NUM
ejpam-4819	149	11	element	element	NOUN
ejpam-4819	149	12	.	.	PUNCT
ejpam-4819	150	1	t.	t.	PROPN
ejpam-4819	150	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	150	3	/	/	SYM
ejpam-4819	150	4	eur	eur	PROPN
ejpam-4819	150	5	.	.	PUNCT
ejpam-4819	151	1	j.	j.	PROPN
ejpam-4819	151	2	pure	pure	PROPN
ejpam-4819	151	3	appl	appl	PROPN
ejpam-4819	151	4	.	.	PROPN
ejpam-4819	151	5	math	math	PROPN
ejpam-4819	151	6	,	,	PUNCT
ejpam-4819	151	7	16	16	NUM
ejpam-4819	151	8	(	(	PUNCT
ejpam-4819	151	9	3	3	NUM
ejpam-4819	151	10	)	)	PUNCT
ejpam-4819	151	11	(	(	PUNCT
ejpam-4819	151	12	2023	2023	NUM
ejpam-4819	151	13	)	)	PUNCT
ejpam-4819	151	14	,	,	PUNCT
ejpam-4819	151	15	1717	1717	NUM
ejpam-4819	151	16	-	-	SYM
ejpam-4819	151	17	1730	1730	NUM
ejpam-4819	151	18	1722	1722	NUM
ejpam-4819	151	19	proof	proof	NOUN
ejpam-4819	151	20	.	.	PUNCT
ejpam-4819	152	1	let	let	VERB
ejpam-4819	152	2	c0	c0	PROPN
ejpam-4819	152	3	∈	∈	PROPN
ejpam-4819	152	4	c	c	PROPN
ejpam-4819	152	5	and	and	CCONJ
ejpam-4819	152	6	start	start	VERB
ejpam-4819	152	7	by	by	ADP
ejpam-4819	152	8	the	the	DET
ejpam-4819	152	9	picard	picard	NOUN
ejpam-4819	152	10	sequence	sequence	NOUN
ejpam-4819	152	11	(	(	PUNCT
ejpam-4819	152	12	cn	cn	PROPN
ejpam-4819	152	13	)	)	PUNCT
ejpam-4819	152	14	.	.	PUNCT
ejpam-4819	153	1	without	without	ADP
ejpam-4819	153	2	lose	lose	NOUN
ejpam-4819	153	3	of	of	ADP
ejpam-4819	153	4	generality	generality	NOUN
ejpam-4819	153	5	,	,	PUNCT
ejpam-4819	153	6	we	we	PRON
ejpam-4819	153	7	may	may	AUX
ejpam-4819	153	8	assume	assume	VERB
ejpam-4819	153	9	that	that	SCONJ
ejpam-4819	153	10	∀n	∀n	NUM
ejpam-4819	153	11	∈	∈	PROPN
ejpam-4819	153	12	n	n	CCONJ
ejpam-4819	153	13	,	,	PUNCT
ejpam-4819	153	14	we	we	PRON
ejpam-4819	153	15	have	have	VERB
ejpam-4819	153	16	ωb(cn	ωb(cn	PROPN
ejpam-4819	153	17	,	,	PUNCT
ejpam-4819	153	18	cn+1	cn+1	NUM
ejpam-4819	153	19	,	,	PUNCT
ejpam-4819	153	20	cn+1	cn+1	NUM
ejpam-4819	153	21	)	)	PUNCT
ejpam-4819	153	22	>	>	X
ejpam-4819	153	23	0	0	X
ejpam-4819	153	24	.	.	PUNCT
ejpam-4819	154	1	so	so	ADV
ejpam-4819	154	2	,	,	PUNCT
ejpam-4819	154	3	by	by	ADP
ejpam-4819	154	4	lemma	lemma	PROPN
ejpam-4819	154	5	1	1	NUM
ejpam-4819	154	6	,	,	PUNCT
ejpam-4819	154	7	we	we	PRON
ejpam-4819	154	8	have	have	VERB
ejpam-4819	154	9	ωb(cn	ωb(cn	PROPN
ejpam-4819	154	10	,	,	PUNCT
ejpam-4819	154	11	cn+1	cn+1	NUM
ejpam-4819	154	12	,	,	PUNCT
ejpam-4819	154	13	cn+1	cn+1	NOUN
ejpam-4819	154	14	)	)	PUNCT
ejpam-4819	154	15	≤	≤	PUNCT
ejpam-4819	155	1	λ1	λ1	PROPN
ejpam-4819	155	2	b	b	X
ejpam-4819	155	3	max	max	X
ejpam-4819	155	4	{	{	PUNCT
ejpam-4819	155	5	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	155	6	,	,	PUNCT
ejpam-4819	155	7	cn	cn	PROPN
ejpam-4819	155	8	,	,	PUNCT
ejpam-4819	155	9	cn	cn	PROPN
ejpam-4819	155	10	)	)	PUNCT
ejpam-4819	155	11	,	,	PUNCT
ejpam-4819	155	12	[	[	X
ejpam-4819	155	13	ωb(cn−1	ωb(cn−1	X
ejpam-4819	155	14	,	,	PUNCT
ejpam-4819	155	15	cn	cn	PROPN
ejpam-4819	155	16	,	,	PUNCT
ejpam-4819	155	17	cn	cn	PROPN
ejpam-4819	155	18	)	)	PUNCT
ejpam-4819	155	19	]	]	PUNCT
ejpam-4819	156	1	λ2	λ2	NOUN
ejpam-4819	156	2	[	[	X
ejpam-4819	156	3	ωb(cn	ωb(cn	PROPN
ejpam-4819	156	4	,	,	PUNCT
ejpam-4819	156	5	cn+1	cn+1	NUM
ejpam-4819	156	6	,	,	PUNCT
ejpam-4819	156	7	cn+1	cn+1	NUM
ejpam-4819	156	8	)	)	PUNCT
ejpam-4819	156	9	]	]	PUNCT
ejpam-4819	157	1	λ3	λ3	PROPN
ejpam-4819	157	2	}	}	PUNCT
ejpam-4819	157	3	.	.	PUNCT
ejpam-4819	158	1	(	(	PUNCT
ejpam-4819	158	2	7	7	X
ejpam-4819	158	3	)	)	PUNCT
ejpam-4819	158	4	if	if	SCONJ
ejpam-4819	158	5	max	max	PROPN
ejpam-4819	158	6	{	{	PUNCT
ejpam-4819	158	7	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	158	8	,	,	PUNCT
ejpam-4819	158	9	cn	cn	PROPN
ejpam-4819	158	10	,	,	PUNCT
ejpam-4819	158	11	cn	cn	PROPN
ejpam-4819	158	12	)	)	PUNCT
ejpam-4819	158	13	,	,	PUNCT
ejpam-4819	158	14	[	[	X
ejpam-4819	158	15	ωb(cn−1	ωb(cn−1	X
ejpam-4819	158	16	,	,	PUNCT
ejpam-4819	158	17	cn	cn	PROPN
ejpam-4819	158	18	,	,	PUNCT
ejpam-4819	158	19	cn	cn	PROPN
ejpam-4819	158	20	)	)	PUNCT
ejpam-4819	158	21	]	]	PUNCT
ejpam-4819	159	1	λ2	λ2	NOUN
ejpam-4819	159	2	[	[	X
ejpam-4819	159	3	ωb(cn	ωb(cn	PROPN
ejpam-4819	159	4	,	,	PUNCT
ejpam-4819	159	5	cn+1	cn+1	NUM
ejpam-4819	159	6	,	,	PUNCT
ejpam-4819	159	7	cn+1	cn+1	NUM
ejpam-4819	159	8	)	)	PUNCT
ejpam-4819	159	9	]	]	PUNCT
ejpam-4819	160	1	λ3	λ3	PROPN
ejpam-4819	160	2	}	}	PUNCT
ejpam-4819	160	3	=	=	SYM
ejpam-4819	160	4	ωb(cn−1	ωb(cn−1	ADJ
ejpam-4819	160	5	,	,	PUNCT
ejpam-4819	160	6	cn	cn	PROPN
ejpam-4819	160	7	,	,	PUNCT
ejpam-4819	160	8	cn	cn	PROPN
ejpam-4819	160	9	)	)	PUNCT
ejpam-4819	160	10	.	.	PUNCT
ejpam-4819	161	1	therefore	therefore	ADV
ejpam-4819	161	2	,	,	PUNCT
ejpam-4819	161	3	we	we	PRON
ejpam-4819	161	4	get	get	VERB
ejpam-4819	161	5	ωb(cn	ωb(cn	PROPN
ejpam-4819	161	6	,	,	PUNCT
ejpam-4819	161	7	cn+1	cn+1	NUM
ejpam-4819	161	8	,	,	PUNCT
ejpam-4819	161	9	cn+1	cn+1	NOUN
ejpam-4819	161	10	)	)	PUNCT
ejpam-4819	161	11	≤	≤	PUNCT
ejpam-4819	162	1	λ1	λ1	PROPN
ejpam-4819	162	2	b	b	X
ejpam-4819	162	3	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	162	4	,	,	PUNCT
ejpam-4819	162	5	cn	cn	PROPN
ejpam-4819	162	6	,	,	PUNCT
ejpam-4819	162	7	cn	cn	PROPN
ejpam-4819	162	8	)	)	PUNCT
ejpam-4819	162	9	;	;	PUNCT
ejpam-4819	162	10	(	(	PUNCT
ejpam-4819	162	11	8)	8)	NUM
ejpam-4819	162	12	else	else	ADV
ejpam-4819	162	13	,	,	PUNCT
ejpam-4819	162	14	we	we	PRON
ejpam-4819	162	15	have	have	VERB
ejpam-4819	162	16	[	[	X
ejpam-4819	162	17	ωb(cn	ωb(cn	PROPN
ejpam-4819	162	18	,	,	PUNCT
ejpam-4819	162	19	cn+1	cn+1	NUM
ejpam-4819	162	20	,	,	PUNCT
ejpam-4819	162	21	cn+1	cn+1	NUM
ejpam-4819	162	22	)	)	PUNCT
ejpam-4819	162	23	]	]	PUNCT
ejpam-4819	162	24	1−λ3	1−λ3	NUM
ejpam-4819	162	25	≤	≤	NUM
ejpam-4819	162	26	λ1	λ1	PROPN
ejpam-4819	162	27	b	b	PROPN
ejpam-4819	163	1	[	[	X
ejpam-4819	163	2	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	163	3	,	,	PUNCT
ejpam-4819	163	4	cn	cn	PROPN
ejpam-4819	163	5	,	,	PUNCT
ejpam-4819	163	6	cn	cn	PROPN
ejpam-4819	163	7	)	)	PUNCT
ejpam-4819	163	8	]	]	PUNCT
ejpam-4819	164	1	λ2	λ2	NOUN
ejpam-4819	164	2	<	<	X
ejpam-4819	164	3	λ1	λ1	PROPN
ejpam-4819	164	4	b	b	PROPN
ejpam-4819	165	1	[	[	X
ejpam-4819	165	2	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	165	3	,	,	PUNCT
ejpam-4819	165	4	cn	cn	PROPN
ejpam-4819	165	5	,	,	PUNCT
ejpam-4819	165	6	cn	cn	PROPN
ejpam-4819	165	7	)	)	PUNCT
ejpam-4819	165	8	]	]	PUNCT
ejpam-4819	165	9	1−λ3	1−λ3	NUM
ejpam-4819	165	10	.	.	PUNCT
ejpam-4819	166	1	(	(	PUNCT
ejpam-4819	166	2	9	9	NUM
ejpam-4819	166	3	)	)	PUNCT
ejpam-4819	166	4	from	from	ADP
ejpam-4819	166	5	the	the	DET
ejpam-4819	166	6	inequalities	inequality	NOUN
ejpam-4819	166	7	(	(	PUNCT
ejpam-4819	166	8	8)	8)	NUM
ejpam-4819	166	9	and	and	CCONJ
ejpam-4819	166	10	(	(	PUNCT
ejpam-4819	166	11	9	9	NUM
ejpam-4819	166	12	)	)	PUNCT
ejpam-4819	166	13	,	,	PUNCT
ejpam-4819	166	14	we	we	PRON
ejpam-4819	166	15	conclude	conclude	VERB
ejpam-4819	166	16	ωb(cn	ωb(cn	PROPN
ejpam-4819	166	17	,	,	PUNCT
ejpam-4819	166	18	cn+1	cn+1	NUM
ejpam-4819	166	19	,	,	PUNCT
ejpam-4819	166	20	cn+1	cn+1	NOUN
ejpam-4819	166	21	)	)	PUNCT
ejpam-4819	166	22	≤	≤	PUNCT
ejpam-4819	167	1	λ1	λ1	PROPN
ejpam-4819	167	2	b	b	X
ejpam-4819	167	3	ωb(cn−1	ωb(cn−1	PROPN
ejpam-4819	167	4	,	,	PUNCT
ejpam-4819	167	5	cn	cn	PROPN
ejpam-4819	167	6	,	,	PUNCT
ejpam-4819	167	7	cn	cn	PROPN
ejpam-4819	167	8	)	)	PUNCT
ejpam-4819	167	9	...	...	PUNCT
ejpam-4819	168	1	≤	≤	NUM
ejpam-4819	168	2	(	(	PUNCT
ejpam-4819	168	3	λ1	λ1	PROPN
ejpam-4819	168	4	b	b	PROPN
ejpam-4819	168	5	)	)	PUNCT
ejpam-4819	168	6	nωb(c0	nωb(c0	PROPN
ejpam-4819	168	7	,	,	PUNCT
ejpam-4819	168	8	c1	c1	PROPN
ejpam-4819	168	9	,	,	PUNCT
ejpam-4819	168	10	c1	c1	PROPN
ejpam-4819	168	11	)	)	PUNCT
ejpam-4819	168	12	.	.	PUNCT
ejpam-4819	169	1	(	(	PUNCT
ejpam-4819	169	2	10	10	NUM
ejpam-4819	169	3	)	)	PUNCT
ejpam-4819	169	4	then	then	ADV
ejpam-4819	169	5	there	there	PRON
ejpam-4819	169	6	is	be	VERB
ejpam-4819	169	7	l	l	PROPN
ejpam-4819	169	8	≥	≥	NUM
ejpam-4819	169	9	1	1	NUM
ejpam-4819	169	10	such	such	ADJ
ejpam-4819	169	11	that	that	PRON
ejpam-4819	169	12	ωb(cn	ωb(cn	PROPN
ejpam-4819	169	13	,	,	PUNCT
ejpam-4819	169	14	cn+1	cn+1	NUM
ejpam-4819	169	15	,	,	PUNCT
ejpam-4819	169	16	cn+1	cn+1	NOUN
ejpam-4819	169	17	)	)	PUNCT
ejpam-4819	169	18	≤	≤	NOUN
ejpam-4819	169	19	(	(	PUNCT
ejpam-4819	169	20	λ1	λ1	PROPN
ejpam-4819	169	21	b	b	PROPN
ejpam-4819	169	22	)	)	PUNCT
ejpam-4819	169	23	nl	nl	PROPN
ejpam-4819	169	24	.	.	PUNCT
ejpam-4819	170	1	(	(	PUNCT
ejpam-4819	170	2	11	11	NUM
ejpam-4819	170	3	)	)	PUNCT
ejpam-4819	170	4	to	to	PART
ejpam-4819	170	5	show	show	VERB
ejpam-4819	170	6	that	that	SCONJ
ejpam-4819	170	7	the	the	DET
ejpam-4819	170	8	iterative	iterative	NOUN
ejpam-4819	170	9	sequence	sequence	NOUN
ejpam-4819	170	10	(	(	PUNCT
ejpam-4819	170	11	cn	cn	PROPN
ejpam-4819	170	12	)	)	PUNCT
ejpam-4819	170	13	is	be	AUX
ejpam-4819	170	14	gb	gb	NOUN
ejpam-4819	170	15	-	-	PUNCT
ejpam-4819	170	16	cauchy	cauchy	NOUN
ejpam-4819	170	17	,	,	PUNCT
ejpam-4819	170	18	first	first	ADV
ejpam-4819	170	19	we	we	PRON
ejpam-4819	170	20	prove	prove	VERB
ejpam-4819	170	21	that	that	SCONJ
ejpam-4819	170	22	∀	∀	NOUN
ejpam-4819	170	23	m	m	VERB
ejpam-4819	170	24	,	,	PUNCT
ejpam-4819	170	25	l	l	PROPN
ejpam-4819	170	26	∈	∈	PROPN
ejpam-4819	170	27	n	n	X
ejpam-4819	170	28	with	with	ADP
ejpam-4819	170	29	m	m	PROPN
ejpam-4819	170	30	≤	≤	NUM
ejpam-4819	170	31	l	l	NOUN
ejpam-4819	170	32	we	we	PRON
ejpam-4819	170	33	have	have	VERB
ejpam-4819	170	34	:	:	PUNCT
ejpam-4819	170	35	ωb(cm−1	ωb(cm−1	NUM
ejpam-4819	170	36	,	,	PUNCT
ejpam-4819	170	37	cm	cm	NOUN
ejpam-4819	170	38	,	,	PUNCT
ejpam-4819	170	39	cl	cl	NOUN
ejpam-4819	170	40	)	)	PUNCT
ejpam-4819	170	41	≤	≤	NOUN
ejpam-4819	170	42	(	(	PUNCT
ejpam-4819	170	43	λ1	λ1	PROPN
ejpam-4819	170	44	b	b	PROPN
ejpam-4819	170	45	)	)	PUNCT
ejpam-4819	170	46	m−1l	m−1l	NOUN
ejpam-4819	170	47	.	.	PUNCT
ejpam-4819	171	1	(	(	PUNCT
ejpam-4819	171	2	12	12	NUM
ejpam-4819	171	3	)	)	PUNCT
ejpam-4819	171	4	now	now	ADV
ejpam-4819	171	5	,	,	PUNCT
ejpam-4819	171	6	ωb(cm−1	ωb(cm−1	PROPN
ejpam-4819	171	7	,	,	PUNCT
ejpam-4819	171	8	cm	cm	NOUN
ejpam-4819	171	9	,	,	PUNCT
ejpam-4819	171	10	cl	cl	NOUN
ejpam-4819	171	11	)	)	PUNCT
ejpam-4819	171	12	≤	≤	PUNCT
ejpam-4819	172	1	λ1	λ1	PROPN
ejpam-4819	172	2	b	b	X
ejpam-4819	172	3	max	max	PROPN
ejpam-4819	172	4	{	{	PUNCT
ejpam-4819	172	5	ωb(cm−2	ωb(cm−2	PROPN
ejpam-4819	172	6	,	,	PUNCT
ejpam-4819	172	7	cm−1	cm−1	NOUN
ejpam-4819	172	8	,	,	PUNCT
ejpam-4819	172	9	cl−1	cl−1	PROPN
ejpam-4819	172	10	)	)	PUNCT
ejpam-4819	172	11	,	,	PUNCT
ejpam-4819	173	1	[	[	X
ejpam-4819	173	2	ωb(cm−2	ωb(cm−2	X
ejpam-4819	173	3	,	,	PUNCT
ejpam-4819	173	4	cm−1	cm−1	NOUN
ejpam-4819	173	5	,	,	PUNCT
ejpam-4819	173	6	cm−1	cm−1	NOUN
ejpam-4819	173	7	)	)	PUNCT
ejpam-4819	173	8	]	]	PUNCT
ejpam-4819	174	1	λ2	λ2	NOUN
ejpam-4819	175	1	[	[	X
ejpam-4819	175	2	ωb(cl−1	ωb(cl−1	NOUN
ejpam-4819	175	3	,	,	PUNCT
ejpam-4819	175	4	cl	cl	NOUN
ejpam-4819	175	5	,	,	PUNCT
ejpam-4819	175	6	cl	cl	NOUN
ejpam-4819	175	7	)	)	PUNCT
ejpam-4819	175	8	]	]	PUNCT
ejpam-4819	176	1	λ3	λ3	PROPN
ejpam-4819	176	2	}	}	PUNCT
ejpam-4819	176	3	.	.	PUNCT
ejpam-4819	177	1	(	(	PUNCT
ejpam-4819	177	2	13	13	NUM
ejpam-4819	177	3	)	)	PUNCT
ejpam-4819	177	4	assume	assume	VERB
ejpam-4819	177	5	that	that	SCONJ
ejpam-4819	177	6	l	l	NOUN
ejpam-4819	177	7	=	=	PUNCT
ejpam-4819	177	8	m+	m+	NUM
ejpam-4819	177	9	t	t	PROPN
ejpam-4819	177	10	for	for	ADP
ejpam-4819	177	11	some	some	DET
ejpam-4819	177	12	t	t	NOUN
ejpam-4819	177	13	∈	∈	PROPN
ejpam-4819	177	14	n.	n.	NOUN
ejpam-4819	177	15	then	then	ADV
ejpam-4819	177	16	ωb(cl−1	ωb(cl−1	NUM
ejpam-4819	177	17	,	,	PUNCT
ejpam-4819	177	18	cl	cl	NOUN
ejpam-4819	177	19	,	,	PUNCT
ejpam-4819	177	20	cl	cl	NOUN
ejpam-4819	177	21	)	)	PUNCT
ejpam-4819	177	22	≤	≤	PUNCT
ejpam-4819	177	23	λ1	λ1	PROPN
ejpam-4819	177	24	b	b	X
ejpam-4819	177	25	max	max	PROPN
ejpam-4819	177	26	{	{	PUNCT
ejpam-4819	177	27	ωb(cl−2	ωb(cl−2	PROPN
ejpam-4819	177	28	,	,	PUNCT
ejpam-4819	177	29	cl−1	cl−1	NOUN
ejpam-4819	177	30	,	,	PUNCT
ejpam-4819	177	31	cl−1	cl−1	NOUN
ejpam-4819	177	32	)	)	PUNCT
ejpam-4819	177	33	,	,	PUNCT
ejpam-4819	177	34	[	[	X
ejpam-4819	177	35	ωb(cl−2	ωb(cl−2	NOUN
ejpam-4819	177	36	,	,	PUNCT
ejpam-4819	177	37	cl−1	cl−1	NOUN
ejpam-4819	177	38	,	,	PUNCT
ejpam-4819	177	39	cl−1	cl−1	NOUN
ejpam-4819	177	40	)	)	PUNCT
ejpam-4819	177	41	]	]	PUNCT
ejpam-4819	178	1	λ2	λ2	NOUN
ejpam-4819	179	1	[	[	X
ejpam-4819	179	2	ωb(cl−1	ωb(cl−1	NOUN
ejpam-4819	179	3	,	,	PUNCT
ejpam-4819	179	4	cl	cl	NOUN
ejpam-4819	179	5	,	,	PUNCT
ejpam-4819	179	6	cl	cl	NOUN
ejpam-4819	179	7	)	)	PUNCT
ejpam-4819	179	8	]	]	PUNCT
ejpam-4819	180	1	λ3	λ3	PROPN
ejpam-4819	180	2	}	}	PUNCT
ejpam-4819	180	3	=	=	SYM
ejpam-4819	180	4	λ1	λ1	PROPN
ejpam-4819	180	5	b	b	PROPN
ejpam-4819	180	6	ωb(cl−2	ωb(cl−2	PROPN
ejpam-4819	180	7	,	,	PUNCT
ejpam-4819	180	8	cl−1	cl−1	NOUN
ejpam-4819	180	9	,	,	PUNCT
ejpam-4819	180	10	cl−1	cl−1	NOUN
ejpam-4819	180	11	)	)	PUNCT
ejpam-4819	180	12	≤	≤	NOUN
ejpam-4819	180	13	(	(	PUNCT
ejpam-4819	180	14	λ1	λ1	PROPN
ejpam-4819	180	15	b	b	PROPN
ejpam-4819	180	16	)	)	PUNCT
ejpam-4819	180	17	tωb(cm−1	tωb(cm−1	PROPN
ejpam-4819	180	18	,	,	PUNCT
ejpam-4819	180	19	cm	cm	NOUN
ejpam-4819	180	20	,	,	PUNCT
ejpam-4819	180	21	cm	cm	NOUN
ejpam-4819	180	22	)	)	PUNCT
ejpam-4819	180	23	.	.	PUNCT
ejpam-4819	181	1	(	(	PUNCT
ejpam-4819	181	2	14	14	NUM
ejpam-4819	181	3	)	)	PUNCT
ejpam-4819	181	4	t.	t.	NOUN
ejpam-4819	181	5	qawasmeh	qawasmeh	NOUN
ejpam-4819	181	6	/	/	SYM
ejpam-4819	181	7	eur	eur	PROPN
ejpam-4819	181	8	.	.	PUNCT
ejpam-4819	182	1	j.	j.	PROPN
ejpam-4819	182	2	pure	pure	PROPN
ejpam-4819	182	3	appl	appl	PROPN
ejpam-4819	182	4	.	.	PROPN
ejpam-4819	182	5	math	math	PROPN
ejpam-4819	182	6	,	,	PUNCT
ejpam-4819	182	7	16	16	NUM
ejpam-4819	182	8	(	(	PUNCT
ejpam-4819	182	9	3	3	NUM
ejpam-4819	182	10	)	)	PUNCT
ejpam-4819	182	11	(	(	PUNCT
ejpam-4819	182	12	2023	2023	NUM
ejpam-4819	182	13	)	)	PUNCT
ejpam-4819	182	14	,	,	PUNCT
ejpam-4819	182	15	1717	1717	NUM
ejpam-4819	182	16	-	-	SYM
ejpam-4819	182	17	1730	1730	NUM
ejpam-4819	182	18	1723	1723	NUM
ejpam-4819	182	19	now	now	ADV
ejpam-4819	182	20	,	,	PUNCT
ejpam-4819	182	21	ωb(cm−1	ωb(cm−1	PROPN
ejpam-4819	182	22	,	,	PUNCT
ejpam-4819	182	23	cm	cm	NOUN
ejpam-4819	182	24	,	,	PUNCT
ejpam-4819	182	25	cl	cl	NOUN
ejpam-4819	182	26	)	)	PUNCT
ejpam-4819	182	27	≤	≤	PUNCT
ejpam-4819	183	1	λ1	λ1	PROPN
ejpam-4819	183	2	b	b	X
ejpam-4819	183	3	max	max	PROPN
ejpam-4819	183	4	{	{	PUNCT
ejpam-4819	183	5	ωb(cm−2	ωb(cm−2	PROPN
ejpam-4819	183	6	,	,	PUNCT
ejpam-4819	183	7	cm−1	cm−1	NOUN
ejpam-4819	183	8	,	,	PUNCT
ejpam-4819	183	9	cl−1	cl−1	PROPN
ejpam-4819	183	10	)	)	PUNCT
ejpam-4819	183	11	,	,	PUNCT
ejpam-4819	183	12	[	[	X
ejpam-4819	183	13	ωb(cm−2	ωb(cm−2	X
ejpam-4819	183	14	,	,	PUNCT
ejpam-4819	183	15	cm−1	cm−1	NOUN
ejpam-4819	183	16	,	,	PUNCT
ejpam-4819	183	17	cm−1	cm−1	NOUN
ejpam-4819	183	18	)	)	PUNCT
ejpam-4819	183	19	]	]	PUNCT
ejpam-4819	184	1	λ2+λ3	λ2+λ3	ADP
ejpam-4819	184	2	}	}	PUNCT
ejpam-4819	184	3	≤	≤	PROPN
ejpam-4819	184	4	λ1	λ1	PROPN
ejpam-4819	184	5	b	b	X
ejpam-4819	184	6	max	max	PROPN
ejpam-4819	184	7	{	{	PUNCT
ejpam-4819	184	8	λ1	λ1	PROPN
ejpam-4819	184	9	b	b	PROPN
ejpam-4819	184	10	max{ωb(cm−3	max{ωb(cm−3	PROPN
ejpam-4819	184	11	,	,	PUNCT
ejpam-4819	184	12	cm−2	cm−2	PROPN
ejpam-4819	184	13	,	,	PUNCT
ejpam-4819	184	14	cl−2	cl−2	PROPN
ejpam-4819	184	15	)	)	PUNCT
ejpam-4819	184	16	,	,	PUNCT
ejpam-4819	185	1	[	[	X
ejpam-4819	185	2	ωb(cm−3	ωb(cm−3	NUM
ejpam-4819	185	3	,	,	PUNCT
ejpam-4819	185	4	cm−2	cm−2	PROPN
ejpam-4819	185	5	,	,	PUNCT
ejpam-4819	185	6	cm−2	cm−2	PROPN
ejpam-4819	185	7	)	)	PUNCT
ejpam-4819	185	8	]	]	PUNCT
ejpam-4819	186	1	λ2+λ3	λ2+λ3	PROPN
ejpam-4819	186	2	}	}	PUNCT
ejpam-4819	186	3	,	,	PUNCT
ejpam-4819	186	4	[	[	X
ejpam-4819	186	5	ωb(cm−2	ωb(cm−2	X
ejpam-4819	186	6	,	,	PUNCT
ejpam-4819	186	7	cm−1	cm−1	NOUN
ejpam-4819	186	8	,	,	PUNCT
ejpam-4819	186	9	cm−1	cm−1	NOUN
ejpam-4819	186	10	)	)	PUNCT
ejpam-4819	186	11	]	]	PUNCT
ejpam-4819	187	1	λ2+λ3	λ2+λ3	ADP
ejpam-4819	187	2	}	}	PUNCT
ejpam-4819	187	3	≤	≤	NOUN
ejpam-4819	187	4	(	(	PUNCT
ejpam-4819	187	5	λ1	λ1	PROPN
ejpam-4819	187	6	b	b	PROPN
ejpam-4819	187	7	)	)	PUNCT
ejpam-4819	187	8	2	2	NUM
ejpam-4819	187	9	{	{	PUNCT
ejpam-4819	187	10	ωb(cm−3	ωb(cm−3	NOUN
ejpam-4819	187	11	,	,	PUNCT
ejpam-4819	187	12	cm−2	cm−2	NOUN
ejpam-4819	187	13	,	,	PUNCT
ejpam-4819	187	14	cl−2	cl−2	PROPN
ejpam-4819	187	15	)	)	PUNCT
ejpam-4819	187	16	,	,	PUNCT
ejpam-4819	187	17	[	[	X
ejpam-4819	187	18	ωb(cm−3	ωb(cm−3	NUM
ejpam-4819	187	19	,	,	PUNCT
ejpam-4819	187	20	cm−2	cm−2	PROPN
ejpam-4819	187	21	,	,	PUNCT
ejpam-4819	187	22	cm−2	cm−2	PROPN
ejpam-4819	187	23	)	)	PUNCT
ejpam-4819	187	24	]	]	PUNCT
ejpam-4819	188	1	λ2+λ3	λ2+λ3	ADP
ejpam-4819	188	2	}	}	PUNCT
ejpam-4819	188	3	...	...	PUNCT
ejpam-4819	188	4	≤	≤	NUM
ejpam-4819	188	5	(	(	PUNCT
ejpam-4819	188	6	λ1	λ1	PROPN
ejpam-4819	188	7	b	b	X
ejpam-4819	188	8	)	)	PUNCT
ejpam-4819	188	9	m−1	m−1	PROPN
ejpam-4819	188	10	{	{	PUNCT
ejpam-4819	188	11	ωb(c0	ωb(c0	NOUN
ejpam-4819	188	12	,	,	PUNCT
ejpam-4819	188	13	c1	c1	PROPN
ejpam-4819	188	14	,	,	PUNCT
ejpam-4819	188	15	ct	ct	PROPN
ejpam-4819	188	16	)	)	PUNCT
ejpam-4819	188	17	,	,	PUNCT
ejpam-4819	188	18	[	[	X
ejpam-4819	188	19	ωb(c0	ωb(c0	NUM
ejpam-4819	188	20	,	,	PUNCT
ejpam-4819	188	21	c1	c1	PROPN
ejpam-4819	188	22	,	,	PUNCT
ejpam-4819	188	23	c1	c1	PROPN
ejpam-4819	188	24	)	)	PUNCT
ejpam-4819	188	25	]	]	PUNCT
ejpam-4819	189	1	λ2+λ3	λ2+λ3	ADP
ejpam-4819	189	2	}	}	PUNCT
ejpam-4819	189	3	≤	≤	NOUN
ejpam-4819	189	4	(	(	PUNCT
ejpam-4819	189	5	λ1	λ1	PROPN
ejpam-4819	189	6	b	b	PROPN
ejpam-4819	189	7	)	)	PUNCT
ejpam-4819	189	8	m−1l	m−1l	NOUN
ejpam-4819	189	9	.	.	PUNCT
ejpam-4819	190	1	(	(	PUNCT
ejpam-4819	190	2	15	15	NUM
ejpam-4819	190	3	)	)	PUNCT
ejpam-4819	190	4	now	now	ADV
ejpam-4819	190	5	,	,	PUNCT
ejpam-4819	190	6	by	by	ADP
ejpam-4819	190	7	employing	employ	VERB
ejpam-4819	190	8	inequalities	inequality	NOUN
ejpam-4819	190	9	(	(	PUNCT
ejpam-4819	190	10	11	11	NUM
ejpam-4819	190	11	)	)	PUNCT
ejpam-4819	190	12	,	,	PUNCT
ejpam-4819	190	13	(	(	PUNCT
ejpam-4819	190	14	12	12	NUM
ejpam-4819	190	15	)	)	PUNCT
ejpam-4819	190	16	and	and	CCONJ
ejpam-4819	190	17	condition	condition	NOUN
ejpam-4819	190	18	(	(	PUNCT
ejpam-4819	190	19	1	1	NUM
ejpam-4819	190	20	)	)	PUNCT
ejpam-4819	190	21	of	of	ADP
ejpam-4819	190	22	the	the	DET
ejpam-4819	190	23	the	the	DET
ejpam-4819	190	24	definition	definition	NOUN
ejpam-4819	190	25	of	of	ADP
ejpam-4819	190	26	ωb	ωb	NOUN
ejpam-4819	191	1	∀n	∀n	PUNCT
ejpam-4819	191	2	<	<	X
ejpam-4819	192	1	m	m	VERB
ejpam-4819	192	2	≤	≤	NOUN
ejpam-4819	192	3	l	l	NOUN
ejpam-4819	192	4	,	,	PUNCT
ejpam-4819	192	5	we	we	PRON
ejpam-4819	192	6	get	get	VERB
ejpam-4819	192	7	:	:	PUNCT
ejpam-4819	192	8	ωb(cn	ωb(cn	PROPN
ejpam-4819	192	9	,	,	PUNCT
ejpam-4819	192	10	cm	cm	NOUN
ejpam-4819	192	11	,	,	PUNCT
ejpam-4819	192	12	cl	cl	NOUN
ejpam-4819	192	13	)	)	PUNCT
ejpam-4819	192	14	≤	≤	NOUN
ejpam-4819	192	15	bωb(cn	bωb(cn	NOUN
ejpam-4819	192	16	,	,	PUNCT
ejpam-4819	192	17	cn+1	cn+1	NUM
ejpam-4819	192	18	,	,	PUNCT
ejpam-4819	192	19	cn+1	cn+1	NUM
ejpam-4819	192	20	)	)	PUNCT
ejpam-4819	192	21	+	+	CCONJ
ejpam-4819	192	22	bωb(cn+1	bωb(cn+1	ADJ
ejpam-4819	192	23	,	,	PUNCT
ejpam-4819	192	24	cm	cm	NOUN
ejpam-4819	192	25	,	,	PUNCT
ejpam-4819	192	26	cl	cl	NOUN
ejpam-4819	192	27	)	)	PUNCT
ejpam-4819	192	28	≤	≤	NOUN
ejpam-4819	192	29	bωb(cn	bωb(cn	NOUN
ejpam-4819	192	30	,	,	PUNCT
ejpam-4819	192	31	cn+1	cn+1	NUM
ejpam-4819	192	32	,	,	PUNCT
ejpam-4819	192	33	cn+1	cn+1	NUM
ejpam-4819	192	34	)	)	PUNCT
ejpam-4819	193	1	+	+	CCONJ
ejpam-4819	193	2	b2ωb(cn+1	b2ωb(cn+1	NOUN
ejpam-4819	193	3	,	,	PUNCT
ejpam-4819	193	4	cn+2	cn+2	X
ejpam-4819	193	5	,	,	PUNCT
ejpam-4819	193	6	cn+2	cn+2	X
ejpam-4819	193	7	)	)	PUNCT
ejpam-4819	193	8	+	+	CCONJ
ejpam-4819	193	9	b2ωb(cn+2	b2ωb(cn+2	PROPN
ejpam-4819	193	10	,	,	PUNCT
ejpam-4819	193	11	cm	cm	NOUN
ejpam-4819	193	12	,	,	PUNCT
ejpam-4819	193	13	cl	cl	NOUN
ejpam-4819	193	14	)	)	PUNCT
ejpam-4819	193	15	...	...	PUNCT
ejpam-4819	194	1	≤	≤	NUM
ejpam-4819	194	2	bωb(cn	bωb(cn	NOUN
ejpam-4819	194	3	,	,	PUNCT
ejpam-4819	194	4	cn+1	cn+1	NUM
ejpam-4819	194	5	,	,	PUNCT
ejpam-4819	194	6	cn+1	cn+1	NUM
ejpam-4819	194	7	)	)	PUNCT
ejpam-4819	194	8	+	+	CCONJ
ejpam-4819	194	9	b2ωb(cn+1	b2ωb(cn+1	NOUN
ejpam-4819	194	10	,	,	PUNCT
ejpam-4819	194	11	cn+2	cn+2	X
ejpam-4819	194	12	,	,	PUNCT
ejpam-4819	194	13	cn+2	cn+2	X
ejpam-4819	194	14	)	)	PUNCT
ejpam-4819	194	15	+	+	CCONJ
ejpam-4819	194	16	·	·	PUNCT
ejpam-4819	194	17	·	·	PUNCT
ejpam-4819	194	18	·	·	PUNCT
ejpam-4819	195	1	+	+	PUNCT
ejpam-4819	195	2	bm−n−1ωb(cm−2	bm−n−1ωb(cm−2	X
ejpam-4819	195	3	,	,	PUNCT
ejpam-4819	195	4	cm−1	cm−1	NOUN
ejpam-4819	195	5	,	,	PUNCT
ejpam-4819	195	6	cm−1	cm−1	NOUN
ejpam-4819	195	7	)	)	PUNCT
ejpam-4819	196	1	+	+	NUM
ejpam-4819	196	2	bm−n−1ωb(cm−1	bm−n−1ωb(cm−1	PROPN
ejpam-4819	196	3	,	,	PUNCT
ejpam-4819	196	4	cm	cm	NOUN
ejpam-4819	196	5	,	,	PUNCT
ejpam-4819	196	6	cl	cl	NOUN
ejpam-4819	196	7	)	)	PUNCT
ejpam-4819	197	1	≤	≤	NOUN
ejpam-4819	197	2	b	b	X
ejpam-4819	197	3	(	(	PUNCT
ejpam-4819	197	4	λ1	λ1	PROPN
ejpam-4819	197	5	b	b	PROPN
ejpam-4819	197	6	)	)	PUNCT
ejpam-4819	197	7	nl+	nl+	NOUN
ejpam-4819	197	8	b2	b2	NOUN
ejpam-4819	197	9	(	(	PUNCT
ejpam-4819	197	10	λ1	λ1	PROPN
ejpam-4819	197	11	b	b	PROPN
ejpam-4819	197	12	)	)	PUNCT
ejpam-4819	197	13	n+1l+	n+1l+	PROPN
ejpam-4819	197	14	·	·	PUNCT
ejpam-4819	197	15	·	·	PUNCT
ejpam-4819	197	16	·	·	PUNCT
ejpam-4819	197	17	+	+	NUM
ejpam-4819	197	18	bm−n−1	bm−n−1	NOUN
ejpam-4819	197	19	(	(	PUNCT
ejpam-4819	197	20	λ1	λ1	PROPN
ejpam-4819	197	21	b	b	PROPN
ejpam-4819	197	22	)	)	PUNCT
ejpam-4819	197	23	m−1l	m−1l	PROPN
ejpam-4819	197	24	=	=	SYM
ejpam-4819	197	25	bl	bl	PROPN
ejpam-4819	197	26	(	(	PUNCT
ejpam-4819	197	27	λ1	λ1	PROPN
ejpam-4819	197	28	b	b	PROPN
ejpam-4819	197	29	)	)	PUNCT
ejpam-4819	197	30	n	n	CCONJ
ejpam-4819	197	31	[	[	PUNCT
ejpam-4819	197	32	1	1	NUM
ejpam-4819	197	33	+	+	NUM
ejpam-4819	197	34	λ1	λ1	ADJ
ejpam-4819	197	35	+	+	CCONJ
ejpam-4819	197	36	λ2	λ2	NOUN
ejpam-4819	197	37	1	1	NUM
ejpam-4819	197	38	+	+	NUM
ejpam-4819	197	39	·	·	PUNCT
ejpam-4819	197	40	·	·	PUNCT
ejpam-4819	197	41	·	·	PUNCT
ejpam-4819	197	42	+	+	NUM
ejpam-4819	197	43	λm−n−1	λm−n−1	NUM
ejpam-4819	197	44	1	1	NUM
ejpam-4819	197	45	]	]	PUNCT
ejpam-4819	197	46	=	=	PUNCT
ejpam-4819	197	47	bl	bl	PROPN
ejpam-4819	197	48	(	(	PUNCT
ejpam-4819	197	49	1−	1−	NUM
ejpam-4819	197	50	λm−n	λm−n	NOUN
ejpam-4819	197	51	1	1	NUM
ejpam-4819	197	52	1−	1−	NUM
ejpam-4819	197	53	λ1	λ1	ADJ
ejpam-4819	197	54	)	)	PUNCT
ejpam-4819	197	55	(	(	PUNCT
ejpam-4819	197	56	λ1	λ1	PROPN
ejpam-4819	197	57	b	b	PROPN
ejpam-4819	197	58	)	)	PUNCT
ejpam-4819	197	59	n.	n.	NOUN
ejpam-4819	197	60	(	(	PUNCT
ejpam-4819	197	61	16	16	NUM
ejpam-4819	197	62	)	)	PUNCT
ejpam-4819	197	63	by	by	ADP
ejpam-4819	197	64	taking	take	VERB
ejpam-4819	197	65	the	the	DET
ejpam-4819	197	66	limit	limit	NOUN
ejpam-4819	197	67	as	as	ADP
ejpam-4819	197	68	n	n	PROPN
ejpam-4819	197	69	→	→	SYM
ejpam-4819	197	70	+	+	NUM
ejpam-4819	197	71	∞	∞	NUM
ejpam-4819	197	72	in	in	ADP
ejpam-4819	197	73	above	above	ADP
ejpam-4819	197	74	inequality	inequality	NOUN
ejpam-4819	197	75	,	,	PUNCT
ejpam-4819	197	76	we	we	PRON
ejpam-4819	197	77	find	find	VERB
ejpam-4819	197	78	out	out	ADP
ejpam-4819	197	79	that	that	SCONJ
ejpam-4819	197	80	(	(	PUNCT
ejpam-4819	197	81	cn	cn	INTJ
ejpam-4819	197	82	)	)	PUNCT
ejpam-4819	197	83	is	be	AUX
ejpam-4819	197	84	a	a	DET
ejpam-4819	197	85	gb	gb	NOUN
ejpam-4819	197	86	-	-	PUNCT
ejpam-4819	197	87	cauchy	cauchy	ADJ
ejpam-4819	197	88	sequence	sequence	NOUN
ejpam-4819	197	89	,	,	PUNCT
ejpam-4819	197	90	and	and	CCONJ
ejpam-4819	197	91	since	since	SCONJ
ejpam-4819	197	92	(	(	PUNCT
ejpam-4819	197	93	c	c	NOUN
ejpam-4819	197	94	,	,	PUNCT
ejpam-4819	197	95	gb	gb	NOUN
ejpam-4819	197	96	)	)	PUNCT
ejpam-4819	197	97	is	be	AUX
ejpam-4819	197	98	gbcomplete	gbcomplete	ADJ
ejpam-4819	197	99	,	,	PUNCT
ejpam-4819	197	100	then	then	ADV
ejpam-4819	197	101	there	there	PRON
ejpam-4819	197	102	is	be	VERB
ejpam-4819	197	103	c∗	c∗	PROPN
ejpam-4819	197	104	∈	∈	PROPN
ejpam-4819	197	105	c	c	PROPN
ejpam-4819	197	106	s.t	s.t	PROPN
ejpam-4819	197	107	.	.	PUNCT
ejpam-4819	198	1	the	the	DET
ejpam-4819	198	2	sequence	sequence	NOUN
ejpam-4819	198	3	(	(	PUNCT
ejpam-4819	198	4	cn	cn	PROPN
ejpam-4819	198	5	)	)	PUNCT
ejpam-4819	198	6	is	be	AUX
ejpam-4819	198	7	gb	gb	NOUN
ejpam-4819	198	8	-	-	PUNCT
ejpam-4819	198	9	convergent	convergent	NOUN
ejpam-4819	198	10	to	to	PART
ejpam-4819	198	11	c∗.	c∗.	VERB
ejpam-4819	198	12	if	if	SCONJ
ejpam-4819	198	13	f	f	PROPN
ejpam-4819	198	14	is	be	AUX
ejpam-4819	198	15	any	any	DET
ejpam-4819	198	16	continuous	continuous	ADJ
ejpam-4819	198	17	mapping	mapping	NOUN
ejpam-4819	198	18	,	,	PUNCT
ejpam-4819	198	19	then	then	ADV
ejpam-4819	198	20	fc∗	fc∗	ADJ
ejpam-4819	198	21	=	=	PUNCT
ejpam-4819	198	22	c∗.	c∗.	NOUN
ejpam-4819	198	23	else	else	ADV
ejpam-4819	198	24	,	,	PUNCT
ejpam-4819	198	25	by	by	ADP
ejpam-4819	198	26	utilizing	utilize	VERB
ejpam-4819	198	27	the	the	DET
ejpam-4819	198	28	lower	low	ADJ
ejpam-4819	198	29	semi	semi	ADJ
ejpam-4819	198	30	continuity	continuity	NOUN
ejpam-4819	198	31	of	of	ADP
ejpam-4819	198	32	ωb	ωb	NOUN
ejpam-4819	198	33	,	,	PUNCT
ejpam-4819	198	34	we	we	PRON
ejpam-4819	198	35	obtain	obtain	VERB
ejpam-4819	198	36	:	:	PUNCT
ejpam-4819	198	37	ωb(cn	ωb(cn	PROPN
ejpam-4819	198	38	,	,	PUNCT
ejpam-4819	198	39	cm	cm	NOUN
ejpam-4819	198	40	,	,	PUNCT
ejpam-4819	198	41	c∗	c∗	NOUN
ejpam-4819	198	42	)	)	PUNCT
ejpam-4819	198	43	≤	≤	NOUN
ejpam-4819	199	1	lim	lim	PROPN
ejpam-4819	199	2	t→+∞	t→+∞	PROPN
ejpam-4819	199	3	ωb(cn	ωb(cn	PROPN
ejpam-4819	199	4	,	,	PUNCT
ejpam-4819	199	5	cm	cm	PROPN
ejpam-4819	199	6	,	,	PUNCT
ejpam-4819	199	7	ct	ct	PROPN
ejpam-4819	199	8	)	)	PUNCT
ejpam-4819	199	9	<	<	X
ejpam-4819	199	10	ϵ	ϵ	X
ejpam-4819	199	11	for	for	ADP
ejpam-4819	199	12	all	all	DET
ejpam-4819	199	13	n	n	CCONJ
ejpam-4819	199	14	,	,	PUNCT
ejpam-4819	199	15	m	m	VERB
ejpam-4819	199	16	≥	≥	NOUN
ejpam-4819	199	17	n	n	PRON
ejpam-4819	199	18	∀	∀	X
ejpam-4819	199	19	ϵ	ϵ	X
ejpam-4819	199	20	>	>	X
ejpam-4819	199	21	0	0	NUM
ejpam-4819	199	22	.	.	PUNCT
ejpam-4819	200	1	(	(	PUNCT
ejpam-4819	200	2	17	17	NUM
ejpam-4819	200	3	)	)	PUNCT
ejpam-4819	200	4	suppose	suppose	VERB
ejpam-4819	200	5	that	that	SCONJ
ejpam-4819	200	6	m	m	VERB
ejpam-4819	200	7	=	=	SYM
ejpam-4819	200	8	n+	n+	PUNCT
ejpam-4819	200	9	1	1	X
ejpam-4819	200	10	.	.	X
ejpam-4819	200	11	then	then	ADV
ejpam-4819	200	12	ωb(cn	ωb(cn	PROPN
ejpam-4819	200	13	,	,	PUNCT
ejpam-4819	200	14	cn+1	cn+1	NUM
ejpam-4819	200	15	,	,	PUNCT
ejpam-4819	200	16	c	c	NOUN
ejpam-4819	200	17	∗	∗	NOUN
ejpam-4819	200	18	)	)	PUNCT
ejpam-4819	200	19	≤	≤	NOUN
ejpam-4819	200	20	lim	lim	PROPN
ejpam-4819	200	21	t→+∞	t→+∞	PROPN
ejpam-4819	200	22	ωb(cn	ωb(cn	PROPN
ejpam-4819	200	23	,	,	PUNCT
ejpam-4819	200	24	cn+1	cn+1	NUM
ejpam-4819	200	25	,	,	PUNCT
ejpam-4819	200	26	ct	ct	PROPN
ejpam-4819	200	27	)	)	PUNCT
ejpam-4819	200	28	<	<	X
ejpam-4819	200	29	ϵ	ϵ	X
ejpam-4819	200	30	∀n	∀n	PUNCT
ejpam-4819	200	31	≥	≥	NOUN
ejpam-4819	200	32	n.	n.	NOUN
ejpam-4819	200	33	if	if	SCONJ
ejpam-4819	200	34	fc∗	fc∗	ADJ
ejpam-4819	200	35	̸=	̸=	PROPN
ejpam-4819	200	36	c∗	c∗	NOUN
ejpam-4819	200	37	,	,	PUNCT
ejpam-4819	200	38	we	we	PRON
ejpam-4819	200	39	obtain	obtain	VERB
ejpam-4819	200	40	:	:	PUNCT
ejpam-4819	200	41	0	0	NUM
ejpam-4819	200	42	<	<	X
ejpam-4819	200	43	inf{ωb(c	inf{ωb(c	PROPN
ejpam-4819	200	44	,	,	PUNCT
ejpam-4819	200	45	fc	fc	X
ejpam-4819	200	46	,	,	PUNCT
ejpam-4819	200	47	c	c	NOUN
ejpam-4819	200	48	∗	∗	NOUN
ejpam-4819	200	49	)	)	PUNCT
ejpam-4819	200	50	:	:	PUNCT
ejpam-4819	200	51	c	c	X
ejpam-4819	200	52	∈	∈	PROPN
ejpam-4819	200	53	c	c	X
ejpam-4819	200	54	}	}	PUNCT
ejpam-4819	200	55	≤	≤	NUM
ejpam-4819	200	56	inf{ωb(cn	inf{ωb(cn	NOUN
ejpam-4819	200	57	,	,	PUNCT
ejpam-4819	200	58	cn+1	cn+1	NUM
ejpam-4819	200	59	,	,	PUNCT
ejpam-4819	200	60	c	c	NOUN
ejpam-4819	200	61	∗	∗	NOUN
ejpam-4819	200	62	)	)	PUNCT
ejpam-4819	200	63	:	:	PUNCT
ejpam-4819	200	64	n	n	X
ejpam-4819	200	65	∈	∈	PROPN
ejpam-4819	200	66	n	n	CCONJ
ejpam-4819	200	67	}	}	PUNCT
ejpam-4819	200	68	<	<	X
ejpam-4819	200	69	ϵ	ϵ	X
ejpam-4819	200	70	∀	∀	X
ejpam-4819	200	71	ϵ	ϵ	X
ejpam-4819	200	72	>	>	X
ejpam-4819	200	73	0	0	NUM
ejpam-4819	200	74	,	,	PUNCT
ejpam-4819	200	75	(	(	PUNCT
ejpam-4819	200	76	18	18	NUM
ejpam-4819	200	77	)	)	PUNCT
ejpam-4819	200	78	t.	t.	NOUN
ejpam-4819	200	79	qawasmeh	qawasmeh	NOUN
ejpam-4819	200	80	/	/	SYM
ejpam-4819	200	81	eur	eur	PROPN
ejpam-4819	200	82	.	.	PUNCT
ejpam-4819	201	1	j.	j.	PROPN
ejpam-4819	201	2	pure	pure	PROPN
ejpam-4819	201	3	appl	appl	PROPN
ejpam-4819	201	4	.	.	PROPN
ejpam-4819	201	5	math	math	PROPN
ejpam-4819	201	6	,	,	PUNCT
ejpam-4819	201	7	16	16	NUM
ejpam-4819	201	8	(	(	PUNCT
ejpam-4819	201	9	3	3	NUM
ejpam-4819	201	10	)	)	PUNCT
ejpam-4819	201	11	(	(	PUNCT
ejpam-4819	201	12	2023	2023	NUM
ejpam-4819	201	13	)	)	PUNCT
ejpam-4819	201	14	,	,	PUNCT
ejpam-4819	201	15	1717	1717	NUM
ejpam-4819	201	16	-	-	SYM
ejpam-4819	201	17	1730	1730	NUM
ejpam-4819	201	18	1724	1724	NUM
ejpam-4819	201	19	a	a	DET
ejpam-4819	201	20	contradiction	contradiction	NOUN
ejpam-4819	201	21	.	.	PUNCT
ejpam-4819	202	1	hence	hence	ADV
ejpam-4819	202	2	,	,	PUNCT
ejpam-4819	202	3	c∗	c∗	PROPN
ejpam-4819	202	4	∈	∈	PROPN
ejpam-4819	202	5	λf	λf	ADV
ejpam-4819	202	6	,	,	PUNCT
ejpam-4819	202	7	the	the	DET
ejpam-4819	202	8	uniqueness	uniqueness	NOUN
ejpam-4819	202	9	follows	follow	VERB
ejpam-4819	202	10	from	from	ADP
ejpam-4819	202	11	lemma	lemma	PROPN
ejpam-4819	202	12	2	2	NUM
ejpam-4819	202	13	.	.	PUNCT
ejpam-4819	203	1	this	this	PRON
ejpam-4819	203	2	is	be	AUX
ejpam-4819	203	3	complete	complete	ADJ
ejpam-4819	203	4	the	the	DET
ejpam-4819	203	5	proof	proof	NOUN
ejpam-4819	203	6	.	.	PUNCT
ejpam-4819	204	1	in	in	ADP
ejpam-4819	204	2	the	the	DET
ejpam-4819	204	3	next	next	ADJ
ejpam-4819	204	4	two	two	NUM
ejpam-4819	204	5	examples	example	NOUN
ejpam-4819	204	6	we	we	PRON
ejpam-4819	204	7	consider	consider	VERB
ejpam-4819	204	8	the	the	DET
ejpam-4819	204	9	following	following	NOUN
ejpam-4819	204	10	:	:	PUNCT
ejpam-4819	204	11	define	define	VERB
ejpam-4819	204	12	h	h	NOUN
ejpam-4819	204	13	:	:	PUNCT
ejpam-4819	205	1	[	[	X
ejpam-4819	205	2	1,+∞	1,+∞	NUM
ejpam-4819	205	3	)	)	PUNCT
ejpam-4819	205	4	×	×	NOUN
ejpam-4819	206	1	[	[	X
ejpam-4819	206	2	1,+∞	1,+∞	NUM
ejpam-4819	206	3	)	)	PUNCT
ejpam-4819	206	4	→	→	PUNCT
ejpam-4819	207	1	[	[	X
ejpam-4819	207	2	0,+∞	0,+∞	NUM
ejpam-4819	207	3	)	)	PUNCT
ejpam-4819	207	4	,	,	PUNCT
ejpam-4819	207	5	θ	θ	NOUN
ejpam-4819	207	6	:	:	PUNCT
ejpam-4819	208	1	[	[	X
ejpam-4819	208	2	0,+∞	0,+∞	NUM
ejpam-4819	208	3	)	)	PUNCT
ejpam-4819	208	4	→	→	PUNCT
ejpam-4819	209	1	[	[	X
ejpam-4819	209	2	1,+∞	1,+∞	NUM
ejpam-4819	209	3	)	)	PUNCT
ejpam-4819	209	4	via	via	ADP
ejpam-4819	209	5	h(c1	h(c1	PROPN
ejpam-4819	209	6	,	,	PUNCT
ejpam-4819	209	7	c2	c2	PROPN
ejpam-4819	209	8	)	)	PUNCT
ejpam-4819	209	9	=	=	PROPN
ejpam-4819	209	10	c2	c2	PROPN
ejpam-4819	209	11	c1	c1	PROPN
ejpam-4819	209	12	,	,	PUNCT
ejpam-4819	209	13	θ(ω	θ(ω	PROPN
ejpam-4819	209	14	)	)	PUNCT
ejpam-4819	209	15	=	=	SYM
ejpam-4819	209	16	eω	eω	PROPN
ejpam-4819	209	17	,	,	PUNCT
ejpam-4819	209	18	∀ω	∀ω	PUNCT
ejpam-4819	209	19	∈	∈	PROPN
ejpam-4819	209	20	c	c	NOUN
ejpam-4819	209	21	respectively	respectively	ADV
ejpam-4819	209	22	,	,	PUNCT
ejpam-4819	209	23	then	then	ADV
ejpam-4819	209	24	h	h	PROPN
ejpam-4819	209	25	∈	∈	PROPN
ejpam-4819	209	26	h	h	NOUN
ejpam-4819	209	27	and	and	CCONJ
ejpam-4819	209	28	θ	θ	PROPN
ejpam-4819	209	29	∈	∈	PROPN
ejpam-4819	209	30	θ	θ	PROPN
ejpam-4819	209	31	.	.	PUNCT
ejpam-4819	209	32	also	also	ADV
ejpam-4819	209	33	,	,	PUNCT
ejpam-4819	209	34	define	define	VERB
ejpam-4819	209	35	:	:	PUNCT
ejpam-4819	209	36	gb	gb	ADP
ejpam-4819	209	37	:	:	PUNCT
ejpam-4819	209	38	c	c	VERB
ejpam-4819	209	39	×c	×c	X
ejpam-4819	209	40	×c	×c	X
ejpam-4819	209	41	→	→	PUNCT
ejpam-4819	209	42	[	[	X
ejpam-4819	209	43	0,+∞	0,+∞	NUM
ejpam-4819	209	44	)	)	PUNCT
ejpam-4819	209	45	by	by	ADP
ejpam-4819	209	46	gb(c1	gb(c1	PROPN
ejpam-4819	209	47	,	,	PUNCT
ejpam-4819	209	48	c2	c2	PROPN
ejpam-4819	209	49	,	,	PUNCT
ejpam-4819	209	50	c3	c3	PROPN
ejpam-4819	209	51	)	)	PUNCT
ejpam-4819	209	52	=	=	SYM
ejpam-4819	209	53	(	(	PUNCT
ejpam-4819	209	54	|c1−	|c1−	PROPN
ejpam-4819	209	55	c2|+	c2|+	PROPN
ejpam-4819	209	56	|c2−	|c2−	PROPN
ejpam-4819	210	1	c3|+	c3|+	PROPN
ejpam-4819	210	2	|c1−	|c1−	PROPN
ejpam-4819	210	3	c3|)2	c3|)2	NOUN
ejpam-4819	210	4	,	,	PUNCT
ejpam-4819	210	5	then	then	ADV
ejpam-4819	210	6	,	,	PUNCT
ejpam-4819	210	7	gb	gb	PRON
ejpam-4819	210	8	is	be	AUX
ejpam-4819	210	9	a	a	DET
ejpam-4819	210	10	complete	complete	ADJ
ejpam-4819	210	11	with	with	ADP
ejpam-4819	210	12	the	the	DET
ejpam-4819	210	13	base	base	NOUN
ejpam-4819	210	14	b	b	PROPN
ejpam-4819	210	15	=	=	SYM
ejpam-4819	210	16	2	2	NUM
ejpam-4819	210	17	.	.	PUNCT
ejpam-4819	211	1	moreover	moreover	ADV
ejpam-4819	211	2	,	,	PUNCT
ejpam-4819	211	3	define	define	VERB
ejpam-4819	211	4	ωb	ωb	NOUN
ejpam-4819	211	5	:	:	PUNCT
ejpam-4819	211	6	c	c	X
ejpam-4819	211	7	×	×	NOUN
ejpam-4819	211	8	c	c	NOUN
ejpam-4819	211	9	×	×	NOUN
ejpam-4819	211	10	c	c	NOUN
ejpam-4819	211	11	→	→	PUNCT
ejpam-4819	212	1	[	[	X
ejpam-4819	212	2	0,+∞	0,+∞	NUM
ejpam-4819	212	3	)	)	PUNCT
ejpam-4819	212	4	by	by	ADP
ejpam-4819	212	5	ωb(c1	ωb(c1	NOUN
ejpam-4819	212	6	,	,	PUNCT
ejpam-4819	212	7	c2	c2	PROPN
ejpam-4819	212	8	,	,	PUNCT
ejpam-4819	212	9	c3	c3	PROPN
ejpam-4819	212	10	)	)	PUNCT
ejpam-4819	213	1	=	=	SYM
ejpam-4819	213	2	(	(	PUNCT
ejpam-4819	213	3	|c1	|c1	NOUN
ejpam-4819	213	4	−	−	PROPN
ejpam-4819	213	5	c2|+	c2|+	PROPN
ejpam-4819	213	6	|c1	|c1	VERB
ejpam-4819	213	7	−	−	PROPN
ejpam-4819	213	8	c3|)2	c3|)2	NOUN
ejpam-4819	213	9	,	,	PUNCT
ejpam-4819	213	10	ωb	ωb	PROPN
ejpam-4819	213	11	is	be	AUX
ejpam-4819	213	12	a	a	DET
ejpam-4819	213	13	generalized	generalized	ADJ
ejpam-4819	213	14	ω	ω	NUM
ejpam-4819	213	15	-	-	PUNCT
ejpam-4819	213	16	distance	distance	NOUN
ejpam-4819	213	17	mapping	mapping	NOUN
ejpam-4819	213	18	equipped	equip	VERB
ejpam-4819	213	19	with	with	ADP
ejpam-4819	213	20	gb	gb	PROPN
ejpam-4819	213	21	.	.	PUNCT
ejpam-4819	213	22	example	example	NOUN
ejpam-4819	213	23	2	2	NUM
ejpam-4819	213	24	.	.	PUNCT
ejpam-4819	213	25	suppose	suppose	VERB
ejpam-4819	213	26	c	c	NOUN
ejpam-4819	213	27	=	=	SYM
ejpam-4819	213	28	{	{	PUNCT
ejpam-4819	213	29	0	0	NUM
ejpam-4819	213	30	,	,	PUNCT
ejpam-4819	213	31	1	1	NUM
ejpam-4819	213	32	,	,	PUNCT
ejpam-4819	213	33	...	...	PUNCT
ejpam-4819	213	34	,	,	PUNCT
ejpam-4819	213	35	10	10	NUM
ejpam-4819	213	36	}	}	PUNCT
ejpam-4819	213	37	,	,	PUNCT
ejpam-4819	213	38	define	define	VERB
ejpam-4819	213	39	mapping	mapping	NOUN
ejpam-4819	213	40	f	f	NOUN
ejpam-4819	213	41	:	:	PUNCT
ejpam-4819	213	42	c	c	X
ejpam-4819	213	43	→	→	SYM
ejpam-4819	213	44	c	c	NOUN
ejpam-4819	213	45	via	via	ADP
ejpam-4819	213	46	:	:	PUNCT
ejpam-4819	213	47	fc	fc	X
ejpam-4819	214	1	=	=	PUNCT
ejpam-4819	214	2			PROPN
ejpam-4819	214	3	0	0	NUM
ejpam-4819	214	4	,	,	PUNCT
ejpam-4819	214	5	c	c	PROPN
ejpam-4819	214	6	∈	∈	PROPN
ejpam-4819	214	7	{	{	PUNCT
ejpam-4819	214	8	0	0	NUM
ejpam-4819	214	9	,	,	PUNCT
ejpam-4819	214	10	1	1	NUM
ejpam-4819	214	11	,	,	PUNCT
ejpam-4819	214	12	2	2	NUM
ejpam-4819	214	13	}	}	PUNCT
ejpam-4819	214	14	;	;	PUNCT
ejpam-4819	214	15	1	1	NUM
ejpam-4819	214	16	,	,	PUNCT
ejpam-4819	214	17	c	c	PROPN
ejpam-4819	214	18	∈	∈	PROPN
ejpam-4819	214	19	{	{	PUNCT
ejpam-4819	214	20	3	3	NUM
ejpam-4819	214	21	,	,	PUNCT
ejpam-4819	214	22	4	4	NUM
ejpam-4819	214	23	,	,	PUNCT
ejpam-4819	214	24	5	5	NUM
ejpam-4819	214	25	}	}	PUNCT
ejpam-4819	214	26	;	;	PUNCT
ejpam-4819	214	27	2	2	NUM
ejpam-4819	214	28	,	,	PUNCT
ejpam-4819	214	29	c	c	PROPN
ejpam-4819	214	30	∈	∈	PROPN
ejpam-4819	214	31	{	{	PUNCT
ejpam-4819	214	32	6	6	NUM
ejpam-4819	214	33	,	,	PUNCT
ejpam-4819	214	34	7	7	NUM
ejpam-4819	214	35	,	,	PUNCT
ejpam-4819	214	36	...	...	PUNCT
ejpam-4819	214	37	,	,	PUNCT
ejpam-4819	214	38	10	10	NUM
ejpam-4819	214	39	}	}	PUNCT
ejpam-4819	214	40	.	.	PUNCT
ejpam-4819	215	1	then	then	ADV
ejpam-4819	215	2	λf	λf	PROPN
ejpam-4819	215	3	has	have	VERB
ejpam-4819	215	4	only	only	ADV
ejpam-4819	215	5	one	one	NUM
ejpam-4819	215	6	element	element	NOUN
ejpam-4819	215	7	.	.	PUNCT
ejpam-4819	216	1	to	to	PART
ejpam-4819	216	2	prove	prove	VERB
ejpam-4819	216	3	this	this	PRON
ejpam-4819	216	4	,	,	PUNCT
ejpam-4819	216	5	we	we	PRON
ejpam-4819	216	6	need	need	VERB
ejpam-4819	216	7	to	to	PART
ejpam-4819	216	8	show	show	VERB
ejpam-4819	216	9	that	that	SCONJ
ejpam-4819	216	10	∀	∀	NOUN
ejpam-4819	216	11	c1	c1	NOUN
ejpam-4819	216	12	,	,	PUNCT
ejpam-4819	216	13	c2	c2	PROPN
ejpam-4819	216	14	∈	∈	PROPN
ejpam-4819	216	15	c	c	X
ejpam-4819	216	16	,	,	PUNCT
ejpam-4819	216	17	we	we	PRON
ejpam-4819	216	18	have	have	VERB
ejpam-4819	216	19	1	1	NUM
ejpam-4819	216	20	≤	≤	NOUN
ejpam-4819	217	1	h(θbωb(fc1	h(θbωb(fc1	PROPN
ejpam-4819	217	2	,	,	PUNCT
ejpam-4819	217	3	f	f	PROPN
ejpam-4819	217	4	2c1	2c1	NUM
ejpam-4819	217	5	,	,	PUNCT
ejpam-4819	217	6	fc2	fc2	PROPN
ejpam-4819	217	7	)	)	PUNCT
ejpam-4819	217	8	,	,	PUNCT
ejpam-4819	217	9	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	217	10	,	,	PUNCT
ejpam-4819	217	11	c2	c2	PROPN
ejpam-4819	217	12	,	,	PUNCT
ejpam-4819	217	13	c3	c3	PROPN
ejpam-4819	217	14	)	)	PUNCT
ejpam-4819	217	15	)	)	PUNCT
ejpam-4819	217	16	.	.	PUNCT
ejpam-4819	218	1	first	first	ADV
ejpam-4819	218	2	it	it	PRON
ejpam-4819	218	3	is	be	AUX
ejpam-4819	218	4	not	not	PART
ejpam-4819	218	5	hard	hard	ADJ
ejpam-4819	218	6	to	to	PART
ejpam-4819	218	7	prove	prove	VERB
ejpam-4819	218	8	ωb(fc1	ωb(fc1	PROPN
ejpam-4819	218	9	,	,	PUNCT
ejpam-4819	218	10	f	f	PROPN
ejpam-4819	218	11	2c1	2c1	NUM
ejpam-4819	218	12	,	,	PUNCT
ejpam-4819	218	13	fc2	fc2	NOUN
ejpam-4819	218	14	)	)	PUNCT
ejpam-4819	218	15	≤	≤	NOUN
ejpam-4819	218	16	0.45max	0.45max	NUM
ejpam-4819	218	17	{	{	PUNCT
ejpam-4819	218	18	ωb(c1	ωb(c1	PROPN
ejpam-4819	218	19	,	,	PUNCT
ejpam-4819	218	20	fc1	fc1	PROPN
ejpam-4819	218	21	,	,	PUNCT
ejpam-4819	218	22	c2	c2	PROPN
ejpam-4819	218	23	)	)	PUNCT
ejpam-4819	218	24	,	,	PUNCT
ejpam-4819	219	1	[	[	X
ejpam-4819	219	2	ωb(c1	ωb(c1	NOUN
ejpam-4819	219	3	,	,	PUNCT
ejpam-4819	219	4	fc1	fc1	PROPN
ejpam-4819	219	5	,	,	PUNCT
ejpam-4819	219	6	fc1	fc1	PROPN
ejpam-4819	219	7	)	)	PUNCT
ejpam-4819	219	8	]	]	PUNCT
ejpam-4819	219	9	0.45[ωb(c2	0.45[ωb(c2	NUM
ejpam-4819	219	10	,	,	PUNCT
ejpam-4819	219	11	fc2	fc2	PROPN
ejpam-4819	219	12	,	,	PUNCT
ejpam-4819	219	13	fc2	fc2	NOUN
ejpam-4819	219	14	)	)	PUNCT
ejpam-4819	219	15	]	]	PUNCT
ejpam-4819	219	16	0.45	0.45	NUM
ejpam-4819	219	17	}	}	PUNCT
ejpam-4819	219	18	.	.	PUNCT
ejpam-4819	220	1	now	now	ADV
ejpam-4819	220	2	,	,	PUNCT
ejpam-4819	220	3	ωb(fc1	ωb(fc1	PROPN
ejpam-4819	220	4	,	,	PUNCT
ejpam-4819	220	5	f	f	PROPN
ejpam-4819	220	6	2c1	2c1	NUM
ejpam-4819	220	7	,	,	PUNCT
ejpam-4819	220	8	fc2	fc2	PROPN
ejpam-4819	220	9	)	)	PUNCT
ejpam-4819	220	10	≤	≤	PUNCT
ejpam-4819	220	11	λ1	λ1	PROPN
ejpam-4819	220	12	b	b	X
ejpam-4819	220	13	max	max	PROPN
ejpam-4819	220	14	{	{	PUNCT
ejpam-4819	220	15	ωb(c1	ωb(c1	PROPN
ejpam-4819	220	16	,	,	PUNCT
ejpam-4819	220	17	fc1	fc1	PROPN
ejpam-4819	220	18	,	,	PUNCT
ejpam-4819	220	19	c2	c2	PROPN
ejpam-4819	220	20	)	)	PUNCT
ejpam-4819	220	21	,	,	PUNCT
ejpam-4819	221	1	[	[	X
ejpam-4819	221	2	ωb(c1	ωb(c1	NOUN
ejpam-4819	221	3	,	,	PUNCT
ejpam-4819	221	4	fc1	fc1	PROPN
ejpam-4819	221	5	,	,	PUNCT
ejpam-4819	221	6	fc1	fc1	PROPN
ejpam-4819	221	7	)	)	PUNCT
ejpam-4819	221	8	]	]	PUNCT
ejpam-4819	221	9	λ2	λ2	NOUN
ejpam-4819	221	10	[	[	X
ejpam-4819	221	11	ωb(c2	ωb(c2	PROPN
ejpam-4819	221	12	,	,	PUNCT
ejpam-4819	221	13	fc2	fc2	PROPN
ejpam-4819	221	14	,	,	PUNCT
ejpam-4819	221	15	fc2	fc2	NOUN
ejpam-4819	221	16	)	)	PUNCT
ejpam-4819	221	17	]	]	PUNCT
ejpam-4819	222	1	λ3	λ3	PROPN
ejpam-4819	222	2	}	}	PUNCT
ejpam-4819	222	3	⇐	⇐	ADJ
ejpam-4819	222	4	⇒	⇒	NOUN
ejpam-4819	222	5	θbωb(fc1	θbωb(fc1	PROPN
ejpam-4819	222	6	,	,	PUNCT
ejpam-4819	222	7	f	f	PROPN
ejpam-4819	222	8	2c1	2c1	NUM
ejpam-4819	222	9	,	,	PUNCT
ejpam-4819	222	10	fc2	fc2	PROPN
ejpam-4819	222	11	)	)	PUNCT
ejpam-4819	222	12	≤	≤	NUM
ejpam-4819	222	13	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	222	14	,	,	PUNCT
ejpam-4819	222	15	c2	c2	PROPN
ejpam-4819	222	16	,	,	PUNCT
ejpam-4819	222	17	c3	c3	PROPN
ejpam-4819	222	18	)	)	PUNCT
ejpam-4819	222	19	)	)	PUNCT
ejpam-4819	223	1	⇐	⇐	ADJ
ejpam-4819	223	2	⇒	⇒	NOUN
ejpam-4819	223	3	1	1	NUM
ejpam-4819	223	4	≤	≤	ADV
ejpam-4819	224	1	h(θbωb(fc1	h(θbωb(fc1	PROPN
ejpam-4819	224	2	,	,	PUNCT
ejpam-4819	224	3	f	f	PROPN
ejpam-4819	224	4	2c1	2c1	NUM
ejpam-4819	224	5	,	,	PUNCT
ejpam-4819	224	6	fc2	fc2	PROPN
ejpam-4819	224	7	)	)	PUNCT
ejpam-4819	224	8	,	,	PUNCT
ejpam-4819	224	9	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	224	10	,	,	PUNCT
ejpam-4819	224	11	c2	c2	PROPN
ejpam-4819	224	12	,	,	PUNCT
ejpam-4819	224	13	c3	c3	PROPN
ejpam-4819	224	14	)	)	PUNCT
ejpam-4819	224	15	)	)	PUNCT
ejpam-4819	224	16	.	.	PUNCT
ejpam-4819	225	1	consequently	consequently	ADV
ejpam-4819	225	2	,	,	PUNCT
ejpam-4819	225	3	f	f	PROPN
ejpam-4819	225	4	satisfy	satisfy	VERB
ejpam-4819	225	5	all	all	DET
ejpam-4819	225	6	conditions	condition	NOUN
ejpam-4819	225	7	of	of	ADP
ejpam-4819	225	8	(	(	PUNCT
ejpam-4819	225	9	h	h	NOUN
ejpam-4819	225	10	,	,	PUNCT
ejpam-4819	225	11	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	225	12	contraction	contraction	NOUN
ejpam-4819	225	13	.	.	PUNCT
ejpam-4819	226	1	theorem	theorem	NOUN
ejpam-4819	226	2	1	1	NUM
ejpam-4819	226	3	confirms	confirm	VERB
ejpam-4819	226	4	that	that	SCONJ
ejpam-4819	226	5	λf	λf	PROPN
ejpam-4819	226	6	has	have	VERB
ejpam-4819	226	7	only	only	ADV
ejpam-4819	226	8	one	one	NUM
ejpam-4819	226	9	element	element	NOUN
ejpam-4819	226	10	.	.	PUNCT
ejpam-4819	227	1	example	example	NOUN
ejpam-4819	228	1	3	3	X
ejpam-4819	228	2	.	.	X
ejpam-4819	228	3	consider	consider	VERB
ejpam-4819	228	4	the	the	PRON
ejpam-4819	228	5	following	follow	VERB
ejpam-4819	228	6	mapping	mapping	NOUN
ejpam-4819	228	7	f(c	f(c	PROPN
ejpam-4819	228	8	)	)	PUNCT
ejpam-4819	229	1	=	=	SYM
ejpam-4819	230	1	1−	1−	NUM
ejpam-4819	230	2	cm	cm	NUM
ejpam-4819	230	3	b	b	PROPN
ejpam-4819	231	1	+	+	CCONJ
ejpam-4819	231	2	cm	cm	NOUN
ejpam-4819	231	3	where	where	SCONJ
ejpam-4819	231	4	m	m	VERB
ejpam-4819	231	5	∈	∈	PROPN
ejpam-4819	231	6	n−	n−	NOUN
ejpam-4819	231	7	{	{	PUNCT
ejpam-4819	231	8	1	1	NUM
ejpam-4819	231	9	}	}	PUNCT
ejpam-4819	231	10	and	and	CCONJ
ejpam-4819	231	11	b	b	NOUN
ejpam-4819	231	12	≥	≥	NOUN
ejpam-4819	231	13	√	√	NUM
ejpam-4819	231	14	2	2	NUM
ejpam-4819	231	15	m.	m.	NOUN
ejpam-4819	231	16	t.	t.	NOUN
ejpam-4819	231	17	qawasmeh	qawasmeh	NOUN
ejpam-4819	231	18	/	/	SYM
ejpam-4819	231	19	eur	eur	PROPN
ejpam-4819	231	20	.	.	PUNCT
ejpam-4819	232	1	j.	j.	PROPN
ejpam-4819	232	2	pure	pure	PROPN
ejpam-4819	232	3	appl	appl	PROPN
ejpam-4819	232	4	.	.	PROPN
ejpam-4819	232	5	math	math	PROPN
ejpam-4819	232	6	,	,	PUNCT
ejpam-4819	232	7	16	16	NUM
ejpam-4819	232	8	(	(	PUNCT
ejpam-4819	232	9	3	3	NUM
ejpam-4819	232	10	)	)	PUNCT
ejpam-4819	232	11	(	(	PUNCT
ejpam-4819	232	12	2023	2023	NUM
ejpam-4819	232	13	)	)	PUNCT
ejpam-4819	232	14	,	,	PUNCT
ejpam-4819	232	15	1717	1717	NUM
ejpam-4819	232	16	-	-	SYM
ejpam-4819	232	17	1730	1730	NUM
ejpam-4819	232	18	1725	1725	NUM
ejpam-4819	232	19	then	then	ADV
ejpam-4819	232	20	λf	λf	PROPN
ejpam-4819	232	21	has	have	VERB
ejpam-4819	232	22	only	only	ADV
ejpam-4819	232	23	one	one	NUM
ejpam-4819	232	24	element	element	NOUN
ejpam-4819	232	25	on	on	ADP
ejpam-4819	232	26	[	[	X
ejpam-4819	232	27	0	0	NUM
ejpam-4819	232	28	,	,	PUNCT
ejpam-4819	232	29	1	1	NUM
ejpam-4819	232	30	]	]	PUNCT
ejpam-4819	232	31	.	.	PUNCT
ejpam-4819	233	1	to	to	PART
ejpam-4819	233	2	prove	prove	VERB
ejpam-4819	233	3	this	this	PRON
ejpam-4819	233	4	,	,	PUNCT
ejpam-4819	233	5	let	let	VERB
ejpam-4819	233	6	c	c	NOUN
ejpam-4819	233	7	=	=	PUNCT
ejpam-4819	234	1	[	[	X
ejpam-4819	234	2	0	0	NUM
ejpam-4819	234	3	,	,	PUNCT
ejpam-4819	234	4	1	1	NUM
ejpam-4819	234	5	]	]	PUNCT
ejpam-4819	234	6	for	for	ADP
ejpam-4819	234	7	all	all	DET
ejpam-4819	234	8	c1	c1	PROPN
ejpam-4819	234	9	,	,	PUNCT
ejpam-4819	234	10	c2	c2	PROPN
ejpam-4819	234	11	,	,	PUNCT
ejpam-4819	234	12	c3	c3	PROPN
ejpam-4819	234	13	∈	∈	PROPN
ejpam-4819	234	14	c	c	AUX
ejpam-4819	234	15	,	,	PUNCT
ejpam-4819	234	16	assume	assume	VERB
ejpam-4819	234	17	fc	fc	PROPN
ejpam-4819	234	18	=	=	PROPN
ejpam-4819	234	19	s.	s.	PROPN
ejpam-4819	234	20	then	then	ADV
ejpam-4819	234	21	ωb(fc1	ωb(fc1	PROPN
ejpam-4819	234	22	,	,	PUNCT
ejpam-4819	234	23	f	f	PROPN
ejpam-4819	234	24	2c1	2c1	NUM
ejpam-4819	234	25	,	,	PUNCT
ejpam-4819	234	26	fc2	fc2	PROPN
ejpam-4819	234	27	)	)	PUNCT
ejpam-4819	234	28	=	=	PUNCT
ejpam-4819	235	1	[	[	X
ejpam-4819	235	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4819	235	3	1−	1−	NUM
ejpam-4819	235	4	cm1	cm1	PROPN
ejpam-4819	235	5	b	b	PROPN
ejpam-4819	235	6	+	+	PROPN
ejpam-4819	235	7	cm1	cm1	PROPN
ejpam-4819	235	8	−	−	PROPN
ejpam-4819	235	9	1−	1−	NUM
ejpam-4819	236	1	sm	sm	PROPN
ejpam-4819	236	2	b	b	PROPN
ejpam-4819	236	3	+	+	CCONJ
ejpam-4819	236	4	sm	sm	PROPN
ejpam-4819	236	5	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-4819	236	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4819	236	7	1−	1−	NUM
ejpam-4819	236	8	cm1	cm1	PROPN
ejpam-4819	236	9	b	b	PROPN
ejpam-4819	236	10	+	+	PROPN
ejpam-4819	236	11	cm1	cm1	PROPN
ejpam-4819	236	12	−	−	PROPN
ejpam-4819	236	13	1−	1−	NUM
ejpam-4819	236	14	cm2	cm2	PROPN
ejpam-4819	236	15	b	b	PROPN
ejpam-4819	236	16	+	+	CCONJ
ejpam-4819	236	17	cm2	cm2	PROPN
ejpam-4819	236	18	∣∣∣∣]2	∣∣∣∣]2	NOUN
ejpam-4819	236	19	=	=	PUNCT
ejpam-4819	237	1	[	[	PUNCT
ejpam-4819	237	2	1	1	NUM
ejpam-4819	237	3	(	(	PUNCT
ejpam-4819	237	4	b	b	PROPN
ejpam-4819	237	5	+	+	X
ejpam-4819	237	6	cm1	cm1	NOUN
ejpam-4819	237	7	)	)	PUNCT
ejpam-4819	237	8	(	(	PUNCT
ejpam-4819	237	9	b	b	X
ejpam-4819	237	10	+	+	CCONJ
ejpam-4819	237	11	sm	sm	PROPN
ejpam-4819	237	12	)	)	PUNCT
ejpam-4819	237	13	∣∣∣∣(1−	∣∣∣∣(1−	PROPN
ejpam-4819	237	14	cm1	cm1	PROPN
ejpam-4819	237	15	)	)	PUNCT
ejpam-4819	238	1	(	(	PUNCT
ejpam-4819	238	2	b	b	X
ejpam-4819	238	3	+	+	CCONJ
ejpam-4819	238	4	sm)−	sm)−	NOUN
ejpam-4819	238	5	(	(	PUNCT
ejpam-4819	238	6	1−	1−	NUM
ejpam-4819	238	7	sm)(b	sm)(b	PROPN
ejpam-4819	238	8	+	+	NUM
ejpam-4819	238	9	cm1	cm1	PROPN
ejpam-4819	238	10	)	)	PUNCT
ejpam-4819	238	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4819	239	1	+	+	NUM
ejpam-4819	239	2	1	1	NUM
ejpam-4819	239	3	(	(	PUNCT
ejpam-4819	239	4	b	b	PROPN
ejpam-4819	239	5	+	+	X
ejpam-4819	239	6	cm1	cm1	NOUN
ejpam-4819	239	7	)	)	PUNCT
ejpam-4819	239	8	(	(	PUNCT
ejpam-4819	239	9	b	b	X
ejpam-4819	239	10	+	+	CCONJ
ejpam-4819	239	11	cm2	cm2	NOUN
ejpam-4819	239	12	)	)	PUNCT
ejpam-4819	239	13	∣∣∣∣(1−	∣∣∣∣(1−	PROPN
ejpam-4819	239	14	cm1	cm1	PROPN
ejpam-4819	239	15	)	)	PUNCT
ejpam-4819	239	16	(	(	PUNCT
ejpam-4819	239	17	b	b	X
ejpam-4819	239	18	+	+	CCONJ
ejpam-4819	239	19	cm2	cm2	NOUN
ejpam-4819	239	20	)	)	PUNCT
ejpam-4819	239	21	−	−	PROPN
ejpam-4819	240	1	(	(	PUNCT
ejpam-4819	240	2	1−	1−	NUM
ejpam-4819	240	3	cm2	cm2	NOUN
ejpam-4819	240	4	)	)	PUNCT
ejpam-4819	240	5	(	(	PUNCT
ejpam-4819	240	6	b	b	X
ejpam-4819	240	7	+	+	SYM
ejpam-4819	240	8	cm1	cm1	NOUN
ejpam-4819	240	9	)	)	PUNCT
ejpam-4819	241	1	∣∣∣∣]2	∣∣∣∣]2	PROPN
ejpam-4819	241	2	≤	≤	PROPN
ejpam-4819	241	3	(	(	PUNCT
ejpam-4819	241	4	b	b	NOUN
ejpam-4819	241	5	−	−	PROPN
ejpam-4819	241	6	1)2	1)2	NUM
ejpam-4819	241	7	b4	b4	NOUN
ejpam-4819	241	8	[	[	PUNCT
ejpam-4819	241	9	|cm1	|cm1	PROPN
ejpam-4819	241	10	−	−	PROPN
ejpam-4819	241	11	sm|+	sm|+	PROPN
ejpam-4819	241	12	|cm1	|cm1	PROPN
ejpam-4819	242	1	−	−	PROPN
ejpam-4819	242	2	cm2	cm2	NOUN
ejpam-4819	243	1	|	|	NOUN
ejpam-4819	243	2	]	]	SYM
ejpam-4819	243	3	2	2	X
ejpam-4819	243	4	=	=	SYM
ejpam-4819	243	5	(	(	PUNCT
ejpam-4819	243	6	b	b	NOUN
ejpam-4819	243	7	−	−	PROPN
ejpam-4819	243	8	1)2m2	1)2m2	PROPN
ejpam-4819	243	9	b4	b4	NOUN
ejpam-4819	243	10	[	[	PUNCT
ejpam-4819	243	11	|c1	|c1	NOUN
ejpam-4819	243	12	−	−	NOUN
ejpam-4819	243	13	s|+	s|+	NOUN
ejpam-4819	243	14	|c1	|c1	NOUN
ejpam-4819	243	15	−	−	PROPN
ejpam-4819	243	16	c2|	c2|	NOUN
ejpam-4819	243	17	]	]	NUM
ejpam-4819	243	18	2	2	NUM
ejpam-4819	243	19	≤	≤	NOUN
ejpam-4819	243	20	(	(	PUNCT
ejpam-4819	243	21	b	b	NOUN
ejpam-4819	243	22	−	−	PROPN
ejpam-4819	243	23	1	1	NUM
ejpam-4819	243	24	)	)	PUNCT
ejpam-4819	243	25	2b2	2b2	NUM
ejpam-4819	243	26	[	[	PUNCT
ejpam-4819	243	27	|c1	|c1	NOUN
ejpam-4819	243	28	−	−	NOUN
ejpam-4819	243	29	fc1|+	fc1|+	NOUN
ejpam-4819	243	30	|c1	|c1	VERB
ejpam-4819	243	31	−	−	PROPN
ejpam-4819	243	32	c2|	c2|	NOUN
ejpam-4819	243	33	]	]	PUNCT
ejpam-4819	243	34	2	2	NUM
ejpam-4819	243	35	=	=	SYM
ejpam-4819	243	36	λ1	λ1	PROPN
ejpam-4819	243	37	b	b	PROPN
ejpam-4819	243	38	ωb(c1	ωb(c1	PROPN
ejpam-4819	243	39	,	,	PUNCT
ejpam-4819	243	40	fc1	fc1	PROPN
ejpam-4819	243	41	,	,	PUNCT
ejpam-4819	243	42	c2	c2	PROPN
ejpam-4819	243	43	)	)	PUNCT
ejpam-4819	243	44	.	.	PUNCT
ejpam-4819	244	1	notice	notice	VERB
ejpam-4819	244	2	that	that	SCONJ
ejpam-4819	244	3	λ1	λ1	PROPN
ejpam-4819	244	4	=	=	SYM
ejpam-4819	244	5	(	(	PUNCT
ejpam-4819	244	6	b	b	X
ejpam-4819	244	7	−	−	PROPN
ejpam-4819	244	8	1	1	NUM
ejpam-4819	244	9	b	b	NOUN
ejpam-4819	244	10	)	)	PUNCT
ejpam-4819	244	11	2	2	NUM
ejpam-4819	244	12	and	and	CCONJ
ejpam-4819	244	13	the	the	DET
ejpam-4819	244	14	base	base	NOUN
ejpam-4819	244	15	b	b	NOUN
ejpam-4819	244	16	=	=	SYM
ejpam-4819	244	17	2	2	X
ejpam-4819	244	18	.	.	PUNCT
ejpam-4819	245	1	now	now	ADV
ejpam-4819	245	2	,	,	PUNCT
ejpam-4819	245	3	bωb(fc1	bωb(fc1	PROPN
ejpam-4819	245	4	,	,	PUNCT
ejpam-4819	245	5	f	f	PROPN
ejpam-4819	245	6	2c1	2c1	NUM
ejpam-4819	245	7	,	,	PUNCT
ejpam-4819	245	8	fc2	fc2	NOUN
ejpam-4819	245	9	)	)	PUNCT
ejpam-4819	245	10	≤	≤	NOUN
ejpam-4819	245	11	λ1ωb(c1	λ1ωb(c1	PROPN
ejpam-4819	245	12	,	,	PUNCT
ejpam-4819	245	13	fc1	fc1	PROPN
ejpam-4819	245	14	,	,	PUNCT
ejpam-4819	245	15	c2	c2	PROPN
ejpam-4819	245	16	)	)	PUNCT
ejpam-4819	245	17	≤	≤	PUNCT
ejpam-4819	245	18	λ1γ(c1	λ1γ(c1	PROPN
ejpam-4819	245	19	,	,	PUNCT
ejpam-4819	245	20	c2	c2	PROPN
ejpam-4819	245	21	,	,	PUNCT
ejpam-4819	245	22	c3	c3	PROPN
ejpam-4819	245	23	)	)	PUNCT
ejpam-4819	245	24	⇐	⇐	ADJ
ejpam-4819	245	25	⇒	⇒	NOUN
ejpam-4819	245	26	ebωb(fc1,f	ebωb(fc1,f	ADJ
ejpam-4819	245	27	2c1,fc2	2c1,fc2	NUM
ejpam-4819	245	28	)	)	PUNCT
ejpam-4819	245	29	≤	≤	NUM
ejpam-4819	245	30	eλ1γ(c1,c2,c3	eλ1γ(c1,c2,c3	PROPN
ejpam-4819	245	31	)	)	PUNCT
ejpam-4819	245	32	⇐	⇐	ADJ
ejpam-4819	245	33	⇒	⇒	NOUN
ejpam-4819	245	34	1	1	NUM
ejpam-4819	245	35	≤	≤	NUM
ejpam-4819	245	36	eλ1γ(c1,c2,c3	eλ1γ(c1,c2,c3	PROPN
ejpam-4819	245	37	)	)	PUNCT
ejpam-4819	245	38	ebωb(fc1,f2c1,fc2	ebωb(fc1,f2c1,fc2	PROPN
ejpam-4819	245	39	)	)	PUNCT
ejpam-4819	245	40	⇐	⇐	ADJ
ejpam-4819	245	41	⇒	⇒	NOUN
ejpam-4819	245	42	1	1	NUM
ejpam-4819	245	43	≤	≤	ADV
ejpam-4819	245	44	h(θbωb(fc1	h(θbωb(fc1	PROPN
ejpam-4819	245	45	,	,	PUNCT
ejpam-4819	245	46	f	f	PROPN
ejpam-4819	245	47	2c1	2c1	NUM
ejpam-4819	245	48	,	,	PUNCT
ejpam-4819	245	49	fc2	fc2	PROPN
ejpam-4819	245	50	)	)	PUNCT
ejpam-4819	245	51	,	,	PUNCT
ejpam-4819	245	52	θλ1γ(c1	θλ1γ(c1	PROPN
ejpam-4819	245	53	,	,	PUNCT
ejpam-4819	245	54	c2	c2	PROPN
ejpam-4819	245	55	,	,	PUNCT
ejpam-4819	245	56	c3	c3	PROPN
ejpam-4819	245	57	)	)	PUNCT
ejpam-4819	245	58	.	.	PUNCT
ejpam-4819	246	1	consequently	consequently	ADV
ejpam-4819	246	2	,	,	PUNCT
ejpam-4819	246	3	f	f	PROPN
ejpam-4819	246	4	satisfy	satisfy	VERB
ejpam-4819	246	5	all	all	DET
ejpam-4819	246	6	conditions	condition	NOUN
ejpam-4819	246	7	of	of	ADP
ejpam-4819	246	8	(	(	PUNCT
ejpam-4819	246	9	h	h	NOUN
ejpam-4819	246	10	,	,	PUNCT
ejpam-4819	246	11	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	246	12	contraction	contraction	NOUN
ejpam-4819	246	13	.	.	PUNCT
ejpam-4819	247	1	theorem	theorem	NOUN
ejpam-4819	247	2	1	1	NUM
ejpam-4819	247	3	confirms	confirm	VERB
ejpam-4819	247	4	that	that	SCONJ
ejpam-4819	247	5	λf	λf	PROPN
ejpam-4819	247	6	has	have	VERB
ejpam-4819	247	7	only	only	ADV
ejpam-4819	247	8	one	one	NUM
ejpam-4819	247	9	element	element	NOUN
ejpam-4819	247	10	.	.	PUNCT
ejpam-4819	248	1	definition	definition	NOUN
ejpam-4819	248	2	9	9	NUM
ejpam-4819	248	3	.	.	PUNCT
ejpam-4819	248	4	suppose	suppose	VERB
ejpam-4819	248	5	that	that	SCONJ
ejpam-4819	248	6	(	(	PUNCT
ejpam-4819	248	7	c	c	X
ejpam-4819	248	8	,	,	PUNCT
ejpam-4819	248	9	gb	gb	NOUN
ejpam-4819	248	10	)	)	PUNCT
ejpam-4819	248	11	is	be	AUX
ejpam-4819	248	12	equipped	equip	VERB
ejpam-4819	248	13	with	with	ADP
ejpam-4819	248	14	ωb	ωb	NOUN
ejpam-4819	248	15	-	-	PUNCT
ejpam-4819	248	16	distance	distance	NOUN
ejpam-4819	248	17	mappings	mapping	NOUN
ejpam-4819	248	18	and	and	CCONJ
ejpam-4819	248	19	f1	f1	NOUN
ejpam-4819	248	20	,	,	PUNCT
ejpam-4819	248	21	f2	f2	PROPN
ejpam-4819	248	22	are	be	AUX
ejpam-4819	248	23	two	two	NUM
ejpam-4819	248	24	self	self	NOUN
ejpam-4819	248	25	mapping	mapping	NOUN
ejpam-4819	248	26	on	on	ADP
ejpam-4819	248	27	c.	c.	PROPN
ejpam-4819	248	28	we	we	PRON
ejpam-4819	248	29	called	call	VERB
ejpam-4819	248	30	the	the	DET
ejpam-4819	248	31	pair	pair	NOUN
ejpam-4819	248	32	(	(	PUNCT
ejpam-4819	248	33	f1	f1	NOUN
ejpam-4819	248	34	,	,	PUNCT
ejpam-4819	248	35	f2	f2	PROPN
ejpam-4819	248	36	)	)	PUNCT
ejpam-4819	248	37	is	be	AUX
ejpam-4819	248	38	a	a	DET
ejpam-4819	248	39	generalized	generalized	ADJ
ejpam-4819	248	40	(	(	PUNCT
ejpam-4819	248	41	h	h	NOUN
ejpam-4819	248	42	,	,	PUNCT
ejpam-4819	248	43	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	248	44	contraction	contraction	NOUN
ejpam-4819	248	45	if	if	SCONJ
ejpam-4819	248	46	there	there	PRON
ejpam-4819	248	47	exist	exist	VERB
ejpam-4819	248	48	b	b	PRON
ejpam-4819	248	49	∈	∈	PROPN
ejpam-4819	249	1	[	[	X
ejpam-4819	249	2	1,+∞	1,+∞	NUM
ejpam-4819	249	3	)	)	PUNCT
ejpam-4819	249	4	,	,	PUNCT
ejpam-4819	249	5	λi	λi	ADP
ejpam-4819	249	6	∈	∈	PROPN
ejpam-4819	249	7	(	(	PUNCT
ejpam-4819	249	8	0	0	NUM
ejpam-4819	249	9	,	,	PUNCT
ejpam-4819	249	10	1	1	NUM
ejpam-4819	249	11	)	)	PUNCT
ejpam-4819	249	12	with	with	ADP
ejpam-4819	249	13	i	i	PRON
ejpam-4819	249	14	∈	∈	PROPN
ejpam-4819	249	15	{	{	PUNCT
ejpam-4819	249	16	1	1	NUM
ejpam-4819	249	17	,	,	PUNCT
ejpam-4819	249	18	2	2	NUM
ejpam-4819	249	19	,	,	PUNCT
ejpam-4819	249	20	3	3	NUM
ejpam-4819	249	21	}	}	PUNCT
ejpam-4819	249	22	and	and	CCONJ
ejpam-4819	249	23	λ2	λ2	PROPN
ejpam-4819	250	1	+	+	CCONJ
ejpam-4819	251	1	λ3	λ3	PROPN
ejpam-4819	251	2	<	<	X
ejpam-4819	251	3	1	1	NUM
ejpam-4819	251	4	,	,	PUNCT
ejpam-4819	251	5	θ	θ	PROPN
ejpam-4819	251	6	∈	∈	PROPN
ejpam-4819	251	7	θ	θ	PROPN
ejpam-4819	251	8	and	and	CCONJ
ejpam-4819	251	9	h	h	NOUN
ejpam-4819	251	10	∈	∈	PROPN
ejpam-4819	251	11	h	h	PROPN
ejpam-4819	251	12	s.t	s.t	PROPN
ejpam-4819	251	13	.	.	PROPN
ejpam-4819	251	14	∀	∀	PROPN
ejpam-4819	251	15	c1	c1	PROPN
ejpam-4819	251	16	,	,	PUNCT
ejpam-4819	251	17	c2	c2	PROPN
ejpam-4819	251	18	,	,	PUNCT
ejpam-4819	251	19	c3	c3	PROPN
ejpam-4819	251	20	∈	∈	PROPN
ejpam-4819	252	1	c	c	X
ejpam-4819	252	2	we	we	PRON
ejpam-4819	252	3	have	have	VERB
ejpam-4819	252	4	:	:	PUNCT
ejpam-4819	252	5	1	1	NUM
ejpam-4819	252	6	≤	≤	NUM
ejpam-4819	252	7	h	h	NOUN
ejpam-4819	252	8	(	(	PUNCT
ejpam-4819	252	9	θbωb(f1c1	θbωb(f1c1	PROPN
ejpam-4819	252	10	,	,	PUNCT
ejpam-4819	252	11	f2(f1c1	f2(f1c1	NOUN
ejpam-4819	252	12	)	)	PUNCT
ejpam-4819	252	13	,	,	PUNCT
ejpam-4819	252	14	f2c2	f2c2	NOUN
ejpam-4819	252	15	)	)	PUNCT
ejpam-4819	252	16	,	,	PUNCT
ejpam-4819	252	17	θλ1γ1(c1	θλ1γ1(c1	PROPN
ejpam-4819	252	18	,	,	PUNCT
ejpam-4819	252	19	c2	c2	PROPN
ejpam-4819	252	20	,	,	PUNCT
ejpam-4819	252	21	c3	c3	PROPN
ejpam-4819	252	22	)	)	PUNCT
ejpam-4819	252	23	)	)	PUNCT
ejpam-4819	252	24	;	;	PUNCT
ejpam-4819	252	25	(	(	PUNCT
ejpam-4819	252	26	19	19	NUM
ejpam-4819	252	27	)	)	PUNCT
ejpam-4819	252	28	t.	t.	NOUN
ejpam-4819	252	29	qawasmeh	qawasmeh	NOUN
ejpam-4819	252	30	/	/	SYM
ejpam-4819	252	31	eur	eur	PROPN
ejpam-4819	252	32	.	.	PUNCT
ejpam-4819	253	1	j.	j.	PROPN
ejpam-4819	253	2	pure	pure	PROPN
ejpam-4819	253	3	appl	appl	PROPN
ejpam-4819	253	4	.	.	PROPN
ejpam-4819	253	5	math	math	PROPN
ejpam-4819	253	6	,	,	PUNCT
ejpam-4819	253	7	16	16	NUM
ejpam-4819	253	8	(	(	PUNCT
ejpam-4819	253	9	3	3	NUM
ejpam-4819	253	10	)	)	PUNCT
ejpam-4819	253	11	(	(	PUNCT
ejpam-4819	253	12	2023	2023	NUM
ejpam-4819	253	13	)	)	PUNCT
ejpam-4819	253	14	,	,	PUNCT
ejpam-4819	253	15	1717	1717	NUM
ejpam-4819	253	16	-	-	SYM
ejpam-4819	253	17	1730	1730	NUM
ejpam-4819	253	18	1726	1726	NUM
ejpam-4819	253	19	and	and	CCONJ
ejpam-4819	253	20	1	1	NUM
ejpam-4819	253	21	≤	≤	NUM
ejpam-4819	253	22	h	h	NOUN
ejpam-4819	253	23	(	(	PUNCT
ejpam-4819	253	24	θbωb(f2c1	θbωb(f2c1	PROPN
ejpam-4819	253	25	,	,	PUNCT
ejpam-4819	253	26	f1(f2c1	f1(f2c1	PROPN
ejpam-4819	253	27	)	)	PUNCT
ejpam-4819	253	28	,	,	PUNCT
ejpam-4819	253	29	f1c2	f1c2	X
ejpam-4819	253	30	)	)	PUNCT
ejpam-4819	253	31	,	,	PUNCT
ejpam-4819	253	32	θλ1γ2(c1	θλ1γ2(c1	PROPN
ejpam-4819	253	33	,	,	PUNCT
ejpam-4819	253	34	c2	c2	PROPN
ejpam-4819	253	35	,	,	PUNCT
ejpam-4819	253	36	c3	c3	PROPN
ejpam-4819	253	37	)	)	PUNCT
ejpam-4819	253	38	)	)	PUNCT
ejpam-4819	253	39	.	.	PUNCT
ejpam-4819	254	1	(	(	PUNCT
ejpam-4819	254	2	20	20	NUM
ejpam-4819	254	3	)	)	PUNCT
ejpam-4819	254	4	where	where	SCONJ
ejpam-4819	254	5	γ1(c1	γ1(c1	PROPN
ejpam-4819	254	6	,	,	PUNCT
ejpam-4819	254	7	c2	c2	PROPN
ejpam-4819	254	8	,	,	PUNCT
ejpam-4819	254	9	c3	c3	PROPN
ejpam-4819	254	10	)	)	PUNCT
ejpam-4819	254	11	=	=	SYM
ejpam-4819	254	12	max	max	PROPN
ejpam-4819	254	13	{	{	PUNCT
ejpam-4819	254	14	ωb(c1	ωb(c1	PROPN
ejpam-4819	254	15	,	,	PUNCT
ejpam-4819	254	16	f2c1	f2c1	PROPN
ejpam-4819	254	17	,	,	PUNCT
ejpam-4819	254	18	c2	c2	PROPN
ejpam-4819	254	19	)	)	PUNCT
ejpam-4819	254	20	,	,	PUNCT
ejpam-4819	255	1	[	[	X
ejpam-4819	255	2	ωb(c1	ωb(c1	NOUN
ejpam-4819	255	3	,	,	PUNCT
ejpam-4819	255	4	f1c1	f1c1	NOUN
ejpam-4819	255	5	,	,	PUNCT
ejpam-4819	255	6	f1c1	f1c1	NOUN
ejpam-4819	255	7	)	)	PUNCT
ejpam-4819	255	8	]	]	PUNCT
ejpam-4819	256	1	λ2	λ2	NOUN
ejpam-4819	257	1	[	[	X
ejpam-4819	257	2	ωb(c2	ωb(c2	NOUN
ejpam-4819	257	3	,	,	PUNCT
ejpam-4819	257	4	f2c2	f2c2	NOUN
ejpam-4819	257	5	,	,	PUNCT
ejpam-4819	257	6	f2c2	f2c2	NOUN
ejpam-4819	257	7	)	)	PUNCT
ejpam-4819	257	8	]	]	PUNCT
ejpam-4819	258	1	λ3	λ3	PROPN
ejpam-4819	258	2	}	}	PUNCT
ejpam-4819	258	3	;	;	PUNCT
ejpam-4819	258	4	and	and	CCONJ
ejpam-4819	258	5	γ2(c1	γ2(c1	NOUN
ejpam-4819	258	6	,	,	PUNCT
ejpam-4819	258	7	c2	c2	PROPN
ejpam-4819	258	8	,	,	PUNCT
ejpam-4819	258	9	c3	c3	PROPN
ejpam-4819	258	10	)	)	PUNCT
ejpam-4819	258	11	=	=	SYM
ejpam-4819	258	12	max	max	PROPN
ejpam-4819	258	13	{	{	PUNCT
ejpam-4819	258	14	ωb(c1	ωb(c1	PROPN
ejpam-4819	258	15	,	,	PUNCT
ejpam-4819	258	16	f1c1	f1c1	PROPN
ejpam-4819	258	17	,	,	PUNCT
ejpam-4819	258	18	c2	c2	PROPN
ejpam-4819	258	19	)	)	PUNCT
ejpam-4819	258	20	,	,	PUNCT
ejpam-4819	259	1	[	[	X
ejpam-4819	259	2	ωb(c1	ωb(c1	X
ejpam-4819	259	3	,	,	PUNCT
ejpam-4819	259	4	f2c1	f2c1	ADJ
ejpam-4819	259	5	,	,	PUNCT
ejpam-4819	259	6	f2c1	f2c1	NOUN
ejpam-4819	259	7	)	)	PUNCT
ejpam-4819	259	8	]	]	PUNCT
ejpam-4819	260	1	λ2	λ2	NOUN
ejpam-4819	261	1	[	[	X
ejpam-4819	261	2	ωb(c2	ωb(c2	PROPN
ejpam-4819	261	3	,	,	PUNCT
ejpam-4819	261	4	f1c2	f1c2	X
ejpam-4819	261	5	,	,	PUNCT
ejpam-4819	261	6	f1c2	f1c2	X
ejpam-4819	261	7	)	)	PUNCT
ejpam-4819	261	8	]	]	PUNCT
ejpam-4819	262	1	λ3	λ3	PROPN
ejpam-4819	262	2	}	}	PUNCT
ejpam-4819	262	3	.	.	PUNCT
ejpam-4819	263	1	theorem	theorem	NOUN
ejpam-4819	263	2	2	2	NUM
ejpam-4819	263	3	.	.	PUNCT
ejpam-4819	263	4	suppose	suppose	VERB
ejpam-4819	263	5	(	(	PUNCT
ejpam-4819	263	6	c	c	X
ejpam-4819	263	7	,	,	PUNCT
ejpam-4819	263	8	gb	gb	NOUN
ejpam-4819	263	9	)	)	PUNCT
ejpam-4819	263	10	is	be	AUX
ejpam-4819	263	11	gb	gb	ADV
ejpam-4819	263	12	-	-	PUNCT
ejpam-4819	263	13	complete	complete	NOUN
ejpam-4819	263	14	equipped	equip	VERB
ejpam-4819	263	15	with	with	ADP
ejpam-4819	263	16	ωb	ωb	NOUN
ejpam-4819	263	17	distance	distance	NOUN
ejpam-4819	263	18	mappings	mapping	NOUN
ejpam-4819	263	19	with	with	ADP
ejpam-4819	263	20	the	the	DET
ejpam-4819	263	21	base	base	NOUN
ejpam-4819	263	22	b	b	PROPN
ejpam-4819	263	23	∈	∈	PROPN
ejpam-4819	264	1	[	[	X
ejpam-4819	264	2	1,+∞	1,+∞	NUM
ejpam-4819	264	3	)	)	PUNCT
ejpam-4819	264	4	and	and	CCONJ
ejpam-4819	264	5	c	c	PROPN
ejpam-4819	264	6	is	be	AUX
ejpam-4819	264	7	bounded	bound	VERB
ejpam-4819	264	8	w.r.t	w.r.t	NOUN
ejpam-4819	264	9	.	.	PUNCT
ejpam-4819	265	1	ωb	ωb	X
ejpam-4819	265	2	.	.	PUNCT
ejpam-4819	265	3	suppose	suppose	VERB
ejpam-4819	265	4	there	there	PRON
ejpam-4819	265	5	are	be	VERB
ejpam-4819	265	6	λi	λi	ADP
ejpam-4819	265	7	∈	∈	PROPN
ejpam-4819	265	8	(	(	PUNCT
ejpam-4819	265	9	0	0	NUM
ejpam-4819	265	10	,	,	PUNCT
ejpam-4819	265	11	1	1	NUM
ejpam-4819	265	12	)	)	PUNCT
ejpam-4819	265	13	,	,	PUNCT
ejpam-4819	265	14	i	i	PRON
ejpam-4819	265	15	∈	∈	PROPN
ejpam-4819	265	16	{	{	PUNCT
ejpam-4819	265	17	1	1	NUM
ejpam-4819	265	18	,	,	PUNCT
ejpam-4819	265	19	2	2	NUM
ejpam-4819	265	20	,	,	PUNCT
ejpam-4819	265	21	3	3	NUM
ejpam-4819	265	22	}	}	PUNCT
ejpam-4819	265	23	with	with	ADP
ejpam-4819	265	24	λ2+λ3	λ2+λ3	ADP
ejpam-4819	265	25	<	<	X
ejpam-4819	265	26	1	1	NUM
ejpam-4819	265	27	,	,	PUNCT
ejpam-4819	265	28	θ	θ	PROPN
ejpam-4819	265	29	∈	∈	PROPN
ejpam-4819	265	30	θ	θ	PROPN
ejpam-4819	265	31	,	,	PUNCT
ejpam-4819	266	1	h	h	NOUN
ejpam-4819	266	2	∈	∈	PROPN
ejpam-4819	266	3	h	h	NOUN
ejpam-4819	266	4	s.t	s.t	PROPN
ejpam-4819	266	5	.	.	PUNCT
ejpam-4819	267	1	the	the	DET
ejpam-4819	267	2	pair	pair	NOUN
ejpam-4819	267	3	of	of	ADP
ejpam-4819	267	4	self	self	NOUN
ejpam-4819	267	5	mappings	mapping	NOUN
ejpam-4819	267	6	f1	f1	NOUN
ejpam-4819	267	7	,	,	PUNCT
ejpam-4819	267	8	f2	f2	PROPN
ejpam-4819	267	9	:	:	PUNCT
ejpam-4819	267	10	c	c	X
ejpam-4819	267	11	→	→	SYM
ejpam-4819	267	12	c	c	PROPN
ejpam-4819	267	13	is	be	AUX
ejpam-4819	267	14	a	a	DET
ejpam-4819	267	15	generalized	generalized	ADJ
ejpam-4819	267	16	(	(	PUNCT
ejpam-4819	267	17	h	h	NOUN
ejpam-4819	267	18	,	,	PUNCT
ejpam-4819	267	19	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	267	20	contraction	contraction	NOUN
ejpam-4819	267	21	if	if	SCONJ
ejpam-4819	267	22	one	one	NUM
ejpam-4819	267	23	of	of	ADP
ejpam-4819	267	24	the	the	DET
ejpam-4819	267	25	following	following	NOUN
ejpam-4819	267	26	fulfilled	fulfil	VERB
ejpam-4819	267	27	:	:	PUNCT
ejpam-4819	267	28	1	1	X
ejpam-4819	267	29	.	.	X
ejpam-4819	268	1	if	if	SCONJ
ejpam-4819	268	2	the	the	DET
ejpam-4819	268	3	mappings	mapping	NOUN
ejpam-4819	268	4	f1	f1	NOUN
ejpam-4819	268	5	,	,	PUNCT
ejpam-4819	268	6	f2	f2	PROPN
ejpam-4819	268	7	are	be	AUX
ejpam-4819	268	8	continuous	continuous	ADJ
ejpam-4819	268	9	;	;	PUNCT
ejpam-4819	268	10	2	2	X
ejpam-4819	268	11	.	.	X
ejpam-4819	269	1	if	if	SCONJ
ejpam-4819	269	2	one	one	NUM
ejpam-4819	269	3	of	of	ADP
ejpam-4819	269	4	the	the	DET
ejpam-4819	269	5	self	self	NOUN
ejpam-4819	269	6	mappings	mapping	NOUN
ejpam-4819	269	7	is	be	AUX
ejpam-4819	269	8	continuous	continuous	ADJ
ejpam-4819	269	9	and	and	CCONJ
ejpam-4819	269	10	for	for	ADP
ejpam-4819	269	11	all	all	DET
ejpam-4819	269	12	c∗	c∗	PROPN
ejpam-4819	269	13	∈	∈	PROPN
ejpam-4819	269	14	c	c	NOUN
ejpam-4819	270	1	if	if	SCONJ
ejpam-4819	270	2	f∗c∗	f∗c∗	VERB
ejpam-4819	270	3	̸=	̸=	PROPN
ejpam-4819	270	4	c∗	c∗	NOUN
ejpam-4819	270	5	,	,	PUNCT
ejpam-4819	270	6	then	then	ADV
ejpam-4819	270	7	0	0	NUM
ejpam-4819	270	8	<	<	X
ejpam-4819	270	9	inf{ωb(c	inf{ωb(c	PROPN
ejpam-4819	270	10	,	,	PUNCT
ejpam-4819	270	11	f	f	PROPN
ejpam-4819	270	12	∗c	∗c	PROPN
ejpam-4819	270	13	,	,	PUNCT
ejpam-4819	270	14	c∗	c∗	NOUN
ejpam-4819	270	15	)	)	PUNCT
ejpam-4819	270	16	:	:	PUNCT
ejpam-4819	271	1	c	c	X
ejpam-4819	271	2	∈	∈	PROPN
ejpam-4819	271	3	c	c	X
ejpam-4819	271	4	}	}	PUNCT
ejpam-4819	271	5	,	,	PUNCT
ejpam-4819	271	6	where	where	SCONJ
ejpam-4819	271	7	f∗	f∗	NOUN
ejpam-4819	271	8	refers	refer	VERB
ejpam-4819	271	9	to	to	ADP
ejpam-4819	271	10	non	non	ADJ
ejpam-4819	271	11	-	-	ADJ
ejpam-4819	271	12	continuous	continuous	ADJ
ejpam-4819	271	13	function	function	NOUN
ejpam-4819	271	14	f1	f1	NOUN
ejpam-4819	271	15	or	or	CCONJ
ejpam-4819	271	16	f2	f2	PROPN
ejpam-4819	271	17	.	.	PUNCT
ejpam-4819	272	1	then	then	ADV
ejpam-4819	272	2	λf	λf	PROPN
ejpam-4819	272	3	has	have	VERB
ejpam-4819	272	4	only	only	ADV
ejpam-4819	272	5	one	one	NUM
ejpam-4819	272	6	element	element	NOUN
ejpam-4819	272	7	.	.	PUNCT
ejpam-4819	273	1	proof	proof	NOUN
ejpam-4819	273	2	.	.	PUNCT
ejpam-4819	274	1	we	we	PRON
ejpam-4819	274	2	start	start	VERB
ejpam-4819	274	3	our	our	PRON
ejpam-4819	274	4	proof	proof	NOUN
ejpam-4819	274	5	our	our	PRON
ejpam-4819	274	6	by	by	ADP
ejpam-4819	274	7	setting	set	VERB
ejpam-4819	274	8	a	a	DET
ejpam-4819	274	9	constructive	constructive	ADJ
ejpam-4819	274	10	sequence	sequence	NOUN
ejpam-4819	274	11	(	(	PUNCT
ejpam-4819	274	12	cn	cn	NOUN
ejpam-4819	274	13	)	)	PUNCT
ejpam-4819	274	14	∈	∈	PROPN
ejpam-4819	274	15	c	c	NOUN
ejpam-4819	274	16	by	by	ADP
ejpam-4819	274	17	iterating	iterate	VERB
ejpam-4819	274	18	c2n+1	c2n+1	PROPN
ejpam-4819	274	19	=	=	SYM
ejpam-4819	274	20	f1c2n	f1c2n	PUNCT
ejpam-4819	274	21	and	and	CCONJ
ejpam-4819	274	22	c2n+2	c2n+2	ADV
ejpam-4819	274	23	=	=	SYM
ejpam-4819	274	24	f2c2n+1	f2c2n+1	NUM
ejpam-4819	274	25	for	for	ADP
ejpam-4819	274	26	n	n	PRON
ejpam-4819	274	27	∈	∈	PROPN
ejpam-4819	274	28	n	n	X
ejpam-4819	274	29	for	for	ADP
ejpam-4819	274	30	some	some	DET
ejpam-4819	274	31	arbitrary	arbitrary	ADJ
ejpam-4819	274	32	element	element	NOUN
ejpam-4819	274	33	c0	c0	PROPN
ejpam-4819	274	34	∈	∈	PROPN
ejpam-4819	274	35	c.	c.	PROPN
ejpam-4819	275	1	so	so	SCONJ
ejpam-4819	275	2	we	we	PRON
ejpam-4819	275	3	have	have	VERB
ejpam-4819	275	4	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	275	5	,	,	PUNCT
ejpam-4819	275	6	c2n+2	c2n+2	ADV
ejpam-4819	275	7	,	,	PUNCT
ejpam-4819	275	8	c2n+2	c2n+2	ADJ
ejpam-4819	275	9	)	)	PUNCT
ejpam-4819	275	10	=	=	SYM
ejpam-4819	275	11	ωb(f1c2n	ωb(f1c2n	NOUN
ejpam-4819	275	12	,	,	PUNCT
ejpam-4819	275	13	f2(f1c2n	f2(f1c2n	NOUN
ejpam-4819	275	14	)	)	PUNCT
ejpam-4819	275	15	,	,	PUNCT
ejpam-4819	275	16	f2c2n+1	f2c2n+1	NUM
ejpam-4819	275	17	)	)	PUNCT
ejpam-4819	275	18	,	,	PUNCT
ejpam-4819	275	19	and	and	CCONJ
ejpam-4819	275	20	so	so	ADV
ejpam-4819	275	21	1	1	NUM
ejpam-4819	275	22	≤	≤	NUM
ejpam-4819	275	23	h	h	NOUN
ejpam-4819	275	24	(	(	PUNCT
ejpam-4819	275	25	θbωb(c2n+1	θbωb(c2n+1	PROPN
ejpam-4819	275	26	,	,	PUNCT
ejpam-4819	275	27	c2n+2	c2n+2	ADV
ejpam-4819	275	28	,	,	PUNCT
ejpam-4819	275	29	c2n+2	c2n+2	ADV
ejpam-4819	275	30	)	)	PUNCT
ejpam-4819	275	31	,	,	PUNCT
ejpam-4819	275	32	θλ1γ(c2n	θλ1γ(c2n	PROPN
ejpam-4819	275	33	,	,	PUNCT
ejpam-4819	275	34	c2n	c2n	NOUN
ejpam-4819	275	35	,	,	PUNCT
ejpam-4819	275	36	c2n+1	c2n+1	NOUN
ejpam-4819	275	37	)	)	PUNCT
ejpam-4819	275	38	)	)	PUNCT
ejpam-4819	276	1	≤	≤	NUM
ejpam-4819	276	2	θλ1max	θλ1max	PROPN
ejpam-4819	276	3	{	{	PUNCT
ejpam-4819	276	4	ωb(c2n	ωb(c2n	NOUN
ejpam-4819	276	5	,	,	PUNCT
ejpam-4819	276	6	c2n+1	c2n+1	PROPN
ejpam-4819	276	7	,	,	PUNCT
ejpam-4819	276	8	c2n+1	c2n+1	PROPN
ejpam-4819	276	9	)	)	PUNCT
ejpam-4819	276	10	,	,	PUNCT
ejpam-4819	277	1	[	[	X
ejpam-4819	277	2	ωb(c2n	ωb(c2n	NOUN
ejpam-4819	277	3	,	,	PUNCT
ejpam-4819	277	4	c2n+1	c2n+1	PROPN
ejpam-4819	277	5	,	,	PUNCT
ejpam-4819	277	6	c2n+1	c2n+1	PROPN
ejpam-4819	277	7	)	)	PUNCT
ejpam-4819	277	8	]	]	PUNCT
ejpam-4819	278	1	λ2	λ2	NOUN
ejpam-4819	279	1	[	[	X
ejpam-4819	279	2	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	279	3	,	,	PUNCT
ejpam-4819	279	4	c2n+2	c2n+2	ADV
ejpam-4819	279	5	,	,	PUNCT
ejpam-4819	279	6	c2n+2	c2n+2	ADV
ejpam-4819	279	7	)	)	PUNCT
ejpam-4819	279	8	]	]	PUNCT
ejpam-4819	279	9	λ3	λ3	PROPN
ejpam-4819	279	10	}	}	PUNCT
ejpam-4819	279	11	θbωb(c2n+1	θbωb(c2n+1	PROPN
ejpam-4819	279	12	,	,	PUNCT
ejpam-4819	279	13	c2n+2	c2n+2	ADV
ejpam-4819	279	14	,	,	PUNCT
ejpam-4819	279	15	c2n+2	c2n+2	INTJ
ejpam-4819	279	16	)	)	PUNCT
ejpam-4819	279	17	.	.	PUNCT
ejpam-4819	280	1	(	(	PUNCT
ejpam-4819	280	2	21	21	NUM
ejpam-4819	280	3	)	)	PUNCT
ejpam-4819	280	4	therefore	therefore	ADV
ejpam-4819	280	5	,	,	PUNCT
ejpam-4819	280	6	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	280	7	,	,	PUNCT
ejpam-4819	280	8	c2n+2	c2n+2	ADV
ejpam-4819	280	9	,	,	PUNCT
ejpam-4819	280	10	c2n+2	c2n+2	ADV
ejpam-4819	280	11	)	)	PUNCT
ejpam-4819	280	12	≤	≤	PUNCT
ejpam-4819	281	1	λ1	λ1	PROPN
ejpam-4819	281	2	b	b	X
ejpam-4819	281	3	max	max	PROPN
ejpam-4819	281	4	{	{	PUNCT
ejpam-4819	281	5	ωb(c2n	ωb(c2n	NOUN
ejpam-4819	281	6	,	,	PUNCT
ejpam-4819	281	7	c2n+1	c2n+1	PROPN
ejpam-4819	281	8	,	,	PUNCT
ejpam-4819	281	9	c2n+1	c2n+1	PROPN
ejpam-4819	281	10	)	)	PUNCT
ejpam-4819	281	11	,	,	PUNCT
ejpam-4819	282	1	[	[	X
ejpam-4819	282	2	ωb(c2n	ωb(c2n	NOUN
ejpam-4819	282	3	,	,	PUNCT
ejpam-4819	282	4	c2n+1	c2n+1	PROPN
ejpam-4819	282	5	,	,	PUNCT
ejpam-4819	282	6	c2n+1	c2n+1	PROPN
ejpam-4819	282	7	)	)	PUNCT
ejpam-4819	282	8	]	]	PUNCT
ejpam-4819	283	1	λ2	λ2	NOUN
ejpam-4819	284	1	[	[	X
ejpam-4819	284	2	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	284	3	,	,	PUNCT
ejpam-4819	284	4	c2n+2	c2n+2	ADV
ejpam-4819	284	5	,	,	PUNCT
ejpam-4819	284	6	c2n+2	c2n+2	ADV
ejpam-4819	284	7	)	)	PUNCT
ejpam-4819	284	8	]	]	PUNCT
ejpam-4819	285	1	λ3	λ3	PROPN
ejpam-4819	285	2	}	}	PUNCT
ejpam-4819	285	3	.	.	PUNCT
ejpam-4819	286	1	by	by	ADP
ejpam-4819	286	2	employing	employ	VERB
ejpam-4819	286	3	the	the	DET
ejpam-4819	286	4	inequalities	inequality	NOUN
ejpam-4819	286	5	(	(	PUNCT
ejpam-4819	286	6	8)	8)	NUM
ejpam-4819	286	7	and	and	CCONJ
ejpam-4819	286	8	(	(	PUNCT
ejpam-4819	286	9	9	9	NUM
ejpam-4819	286	10	)	)	PUNCT
ejpam-4819	286	11	,	,	PUNCT
ejpam-4819	286	12	we	we	PRON
ejpam-4819	286	13	conclude	conclude	VERB
ejpam-4819	286	14	that	that	DET
ejpam-4819	286	15	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	286	16	,	,	PUNCT
ejpam-4819	286	17	c2n+2	c2n+2	ADV
ejpam-4819	286	18	,	,	PUNCT
ejpam-4819	286	19	c2n+2	c2n+2	ADV
ejpam-4819	286	20	)	)	PUNCT
ejpam-4819	286	21	≤	≤	PUNCT
ejpam-4819	287	1	λ1	λ1	ADJ
ejpam-4819	287	2	b	b	NOUN
ejpam-4819	287	3	ωb(c2n	ωb(c2n	NOUN
ejpam-4819	287	4	,	,	PUNCT
ejpam-4819	287	5	c2n+1	c2n+1	PROPN
ejpam-4819	287	6	,	,	PUNCT
ejpam-4819	287	7	c2n+1	c2n+1	PROPN
ejpam-4819	287	8	)	)	PUNCT
ejpam-4819	287	9	.	.	PUNCT
ejpam-4819	288	1	(	(	PUNCT
ejpam-4819	288	2	22	22	NUM
ejpam-4819	288	3	)	)	PUNCT
ejpam-4819	288	4	t.	t.	NOUN
ejpam-4819	288	5	qawasmeh	qawasmeh	NOUN
ejpam-4819	288	6	/	/	SYM
ejpam-4819	288	7	eur	eur	PROPN
ejpam-4819	288	8	.	.	PUNCT
ejpam-4819	289	1	j.	j.	PROPN
ejpam-4819	289	2	pure	pure	PROPN
ejpam-4819	289	3	appl	appl	PROPN
ejpam-4819	289	4	.	.	PROPN
ejpam-4819	289	5	math	math	PROPN
ejpam-4819	289	6	,	,	PUNCT
ejpam-4819	289	7	16	16	NUM
ejpam-4819	289	8	(	(	PUNCT
ejpam-4819	289	9	3	3	NUM
ejpam-4819	289	10	)	)	PUNCT
ejpam-4819	289	11	(	(	PUNCT
ejpam-4819	289	12	2023	2023	NUM
ejpam-4819	289	13	)	)	PUNCT
ejpam-4819	289	14	,	,	PUNCT
ejpam-4819	289	15	1717	1717	NUM
ejpam-4819	289	16	-	-	SYM
ejpam-4819	289	17	1730	1730	NUM
ejpam-4819	289	18	1727	1727	NUM
ejpam-4819	289	19	by	by	ADP
ejpam-4819	289	20	utilizing	utilize	VERB
ejpam-4819	289	21	typical	typical	ADJ
ejpam-4819	289	22	way	way	NOUN
ejpam-4819	290	1	,	,	PUNCT
ejpam-4819	290	2	we	we	PRON
ejpam-4819	290	3	can	can	AUX
ejpam-4819	290	4	easily	easily	ADV
ejpam-4819	290	5	show	show	VERB
ejpam-4819	290	6	that	that	SCONJ
ejpam-4819	290	7	ωb(c2n+2	ωb(c2n+2	PRON
ejpam-4819	290	8	,	,	PUNCT
ejpam-4819	290	9	c2n+3	c2n+3	PROPN
ejpam-4819	290	10	,	,	PUNCT
ejpam-4819	290	11	c2n+3	c2n+3	PROPN
ejpam-4819	290	12	)	)	PUNCT
ejpam-4819	290	13	≤	≤	PUNCT
ejpam-4819	290	14	λ1	λ1	PROPN
ejpam-4819	290	15	b	b	NOUN
ejpam-4819	290	16	ωb(c2n+1	ωb(c2n+1	NOUN
ejpam-4819	290	17	,	,	PUNCT
ejpam-4819	290	18	c2n+2	c2n+2	ADV
ejpam-4819	290	19	,	,	PUNCT
ejpam-4819	290	20	c2n+2	c2n+2	INTJ
ejpam-4819	290	21	)	)	PUNCT
ejpam-4819	290	22	.	.	PUNCT
ejpam-4819	291	1	(	(	PUNCT
ejpam-4819	291	2	23	23	NUM
ejpam-4819	291	3	)	)	PUNCT
ejpam-4819	291	4	hence	hence	ADV
ejpam-4819	291	5	,	,	PUNCT
ejpam-4819	291	6	we	we	PRON
ejpam-4819	291	7	get	get	VERB
ejpam-4819	291	8	ωb(cn+1	ωb(cn+1	ADJ
ejpam-4819	291	9	,	,	PUNCT
ejpam-4819	291	10	cn+2	cn+2	X
ejpam-4819	291	11	,	,	PUNCT
ejpam-4819	291	12	cn+2	cn+2	X
ejpam-4819	291	13	)	)	PUNCT
ejpam-4819	291	14	≤	≤	PUNCT
ejpam-4819	292	1	λ1	λ1	PROPN
ejpam-4819	292	2	b	b	PROPN
ejpam-4819	292	3	ωb(cn	ωb(cn	PROPN
ejpam-4819	292	4	,	,	PUNCT
ejpam-4819	292	5	cn+1	cn+1	NUM
ejpam-4819	292	6	,	,	PUNCT
ejpam-4819	292	7	cn+1	cn+1	NOUN
ejpam-4819	292	8	)	)	PUNCT
ejpam-4819	292	9	.	.	PUNCT
ejpam-4819	293	1	(	(	PUNCT
ejpam-4819	293	2	24	24	NUM
ejpam-4819	293	3	)	)	PUNCT
ejpam-4819	293	4	the	the	DET
ejpam-4819	293	5	completion	completion	NOUN
ejpam-4819	293	6	of	of	ADP
ejpam-4819	293	7	the	the	DET
ejpam-4819	293	8	proof	proof	NOUN
ejpam-4819	293	9	of	of	ADP
ejpam-4819	293	10	this	this	DET
ejpam-4819	293	11	theorem	theorem	NOUN
ejpam-4819	293	12	is	be	AUX
ejpam-4819	293	13	identical	identical	ADJ
ejpam-4819	293	14	to	to	ADP
ejpam-4819	293	15	the	the	DET
ejpam-4819	293	16	theorem	theorem	NOUN
ejpam-4819	293	17	1	1	NUM
ejpam-4819	293	18	,	,	PUNCT
ejpam-4819	293	19	and	and	CCONJ
ejpam-4819	293	20	this	this	PRON
ejpam-4819	293	21	is	be	AUX
ejpam-4819	293	22	complete	complete	ADJ
ejpam-4819	293	23	the	the	DET
ejpam-4819	293	24	proof	proof	NOUN
ejpam-4819	293	25	.	.	PUNCT
ejpam-4819	294	1	3	3	X
ejpam-4819	294	2	.	.	X
ejpam-4819	294	3	application	application	NOUN
ejpam-4819	294	4	throughout	throughout	ADP
ejpam-4819	294	5	this	this	DET
ejpam-4819	294	6	application	application	NOUN
ejpam-4819	294	7	,	,	PUNCT
ejpam-4819	294	8	we	we	PRON
ejpam-4819	294	9	will	will	AUX
ejpam-4819	294	10	emphasize	emphasize	VERB
ejpam-4819	294	11	the	the	DET
ejpam-4819	294	12	significant	significant	ADJ
ejpam-4819	294	13	idea	idea	NOUN
ejpam-4819	294	14	that	that	SCONJ
ejpam-4819	294	15	the	the	DET
ejpam-4819	294	16	solution	solution	NOUN
ejpam-4819	294	17	of	of	ADP
ejpam-4819	294	18	a	a	DET
ejpam-4819	294	19	fixed	fix	VERB
ejpam-4819	294	20	point	point	NOUN
ejpam-4819	294	21	equation	equation	NOUN
ejpam-4819	294	22	(	(	PUNCT
ejpam-4819	294	23	uniqueness	uniqueness	NOUN
ejpam-4819	294	24	and	and	CCONJ
ejpam-4819	294	25	existence	existence	NOUN
ejpam-4819	294	26	)	)	PUNCT
ejpam-4819	294	27	under	under	ADP
ejpam-4819	294	28	certain	certain	ADJ
ejpam-4819	294	29	conditions	condition	NOUN
ejpam-4819	294	30	is	be	AUX
ejpam-4819	294	31	often	often	ADV
ejpam-4819	294	32	comparable	comparable	ADJ
ejpam-4819	294	33	to	to	ADP
ejpam-4819	294	34	that	that	PRON
ejpam-4819	294	35	of	of	ADP
ejpam-4819	294	36	other	other	ADJ
ejpam-4819	294	37	equations	equation	NOUN
ejpam-4819	294	38	.	.	PUNCT
ejpam-4819	295	1	consider	consider	VERB
ejpam-4819	295	2	the	the	DET
ejpam-4819	295	3	following	follow	VERB
ejpam-4819	295	4	equation	equation	NOUN
ejpam-4819	295	5	:	:	PUNCT
ejpam-4819	296	1	cm+1	cm+1	PROPN
ejpam-4819	296	2	+	+	NOUN
ejpam-4819	296	3	cm	cm	NUM
ejpam-4819	296	4	+	+	PROPN
ejpam-4819	296	5	bc−	bc−	PROPN
ejpam-4819	296	6	1	1	NUM
ejpam-4819	296	7	,	,	PUNCT
ejpam-4819	296	8	where	where	SCONJ
ejpam-4819	296	9	b	b	X
ejpam-4819	296	10	≥	≥	NOUN
ejpam-4819	296	11	√	√	PROPN
ejpam-4819	296	12	2	2	NUM
ejpam-4819	296	13	m	m	NOUN
ejpam-4819	296	14	,	,	PUNCT
ejpam-4819	296	15	m	m	VERB
ejpam-4819	296	16	∈	∈	ADJ
ejpam-4819	296	17	n−	n−	NOUN
ejpam-4819	296	18	{	{	PUNCT
ejpam-4819	296	19	1	1	NUM
ejpam-4819	296	20	}	}	PUNCT
ejpam-4819	296	21	,	,	PUNCT
ejpam-4819	296	22	(	(	PUNCT
ejpam-4819	296	23	25	25	NUM
ejpam-4819	296	24	)	)	PUNCT
ejpam-4819	296	25	has	have	VERB
ejpam-4819	296	26	a	a	DET
ejpam-4819	296	27	unique	unique	ADJ
ejpam-4819	296	28	solution	solution	NOUN
ejpam-4819	296	29	in	in	ADP
ejpam-4819	296	30	the	the	DET
ejpam-4819	296	31	unit	unit	NOUN
ejpam-4819	296	32	interval	interval	NOUN
ejpam-4819	296	33	[	[	X
ejpam-4819	296	34	0	0	NUM
ejpam-4819	296	35	,	,	PUNCT
ejpam-4819	296	36	1	1	NUM
ejpam-4819	296	37	]	]	PUNCT
ejpam-4819	296	38	.	.	PUNCT
ejpam-4819	297	1	to	to	PART
ejpam-4819	297	2	prove	prove	VERB
ejpam-4819	297	3	this	this	PRON
ejpam-4819	297	4	,	,	PUNCT
ejpam-4819	297	5	it	it	PRON
ejpam-4819	297	6	is	be	AUX
ejpam-4819	297	7	typical	typical	ADJ
ejpam-4819	297	8	to	to	PART
ejpam-4819	297	9	prove	prove	VERB
ejpam-4819	297	10	that	that	SCONJ
ejpam-4819	297	11	the	the	DET
ejpam-4819	297	12	following	follow	VERB
ejpam-4819	297	13	self	self	NOUN
ejpam-4819	297	14	mapping	mapping	NOUN
ejpam-4819	297	15	f	f	NOUN
ejpam-4819	297	16	has	have	VERB
ejpam-4819	297	17	a	a	DET
ejpam-4819	297	18	unique	unique	ADJ
ejpam-4819	297	19	fixed	fix	VERB
ejpam-4819	297	20	point	point	NOUN
ejpam-4819	297	21	in	in	ADP
ejpam-4819	297	22	[	[	X
ejpam-4819	297	23	0	0	NUM
ejpam-4819	297	24	,	,	PUNCT
ejpam-4819	297	25	1	1	NUM
ejpam-4819	297	26	]	]	PUNCT
ejpam-4819	297	27	.	.	PUNCT
ejpam-4819	298	1	f(c	f(c	NOUN
ejpam-4819	298	2	)	)	PUNCT
ejpam-4819	299	1	=	=	SYM
ejpam-4819	300	1	1−	1−	NUM
ejpam-4819	300	2	cm	cm	NUM
ejpam-4819	300	3	b	b	PROPN
ejpam-4819	300	4	+	+	CCONJ
ejpam-4819	300	5	cm	cm	NOUN
ejpam-4819	300	6	,	,	PUNCT
ejpam-4819	300	7	b	b	PROPN
ejpam-4819	300	8	≥	≥	NOUN
ejpam-4819	300	9	√	√	PROPN
ejpam-4819	300	10	2	2	NUM
ejpam-4819	300	11	m	m	NOUN
ejpam-4819	300	12	,	,	PUNCT
ejpam-4819	300	13	m	m	VERB
ejpam-4819	300	14	∈	∈	ADJ
ejpam-4819	300	15	n−	n−	NOUN
ejpam-4819	300	16	{	{	PUNCT
ejpam-4819	300	17	1	1	NUM
ejpam-4819	300	18	}	}	PUNCT
ejpam-4819	300	19	.	.	PUNCT
ejpam-4819	301	1	example	example	NOUN
ejpam-4819	301	2	3	3	NUM
ejpam-4819	301	3	confirms	confirm	VERB
ejpam-4819	301	4	that	that	SCONJ
ejpam-4819	301	5	the	the	DET
ejpam-4819	301	6	self	self	NOUN
ejpam-4819	301	7	mapping	mapping	NOUN
ejpam-4819	301	8	f	f	X
ejpam-4819	301	9	has	have	VERB
ejpam-4819	301	10	a	a	DET
ejpam-4819	301	11	unique	unique	ADJ
ejpam-4819	301	12	fixed	fix	VERB
ejpam-4819	301	13	point	point	NOUN
ejpam-4819	301	14	and	and	CCONJ
ejpam-4819	301	15	hence	hence	ADV
ejpam-4819	301	16	,	,	PUNCT
ejpam-4819	301	17	the	the	DET
ejpam-4819	301	18	equation	equation	NOUN
ejpam-4819	301	19	(	(	PUNCT
ejpam-4819	301	20	25	25	NUM
ejpam-4819	301	21	)	)	PUNCT
ejpam-4819	301	22	has	have	VERB
ejpam-4819	301	23	a	a	DET
ejpam-4819	301	24	unique	unique	ADJ
ejpam-4819	301	25	solution	solution	NOUN
ejpam-4819	301	26	.	.	PUNCT
ejpam-4819	302	1	next	next	ADV
ejpam-4819	302	2	,	,	PUNCT
ejpam-4819	302	3	we	we	PRON
ejpam-4819	302	4	discuss	discuss	VERB
ejpam-4819	302	5	an	an	DET
ejpam-4819	302	6	application	application	NOUN
ejpam-4819	302	7	on	on	ADP
ejpam-4819	302	8	theorem	theorem	NOUN
ejpam-4819	302	9	1	1	X
ejpam-4819	302	10	.	.	PUNCT
ejpam-4819	303	1	we	we	PRON
ejpam-4819	303	2	employ	employ	VERB
ejpam-4819	303	3	theorem	theorem	ADJ
ejpam-4819	303	4	1	1	NUM
ejpam-4819	303	5	to	to	PART
ejpam-4819	303	6	prove	prove	VERB
ejpam-4819	303	7	the	the	DET
ejpam-4819	303	8	uniqueness	uniqueness	NOUN
ejpam-4819	303	9	and	and	CCONJ
ejpam-4819	303	10	existence	existence	NOUN
ejpam-4819	303	11	of	of	ADP
ejpam-4819	303	12	a	a	DET
ejpam-4819	303	13	solution	solution	NOUN
ejpam-4819	303	14	for	for	ADP
ejpam-4819	303	15	volterra	volterra	NOUN
ejpam-4819	303	16	type	type	NOUN
ejpam-4819	303	17	integral	integral	ADJ
ejpam-4819	303	18	equation	equation	NOUN
ejpam-4819	303	19	:	:	PUNCT
ejpam-4819	303	20	η(t	η(t	NOUN
ejpam-4819	303	21	)	)	PUNCT
ejpam-4819	304	1	=	=	NOUN
ejpam-4819	304	2	η0	η0	NOUN
ejpam-4819	304	3	+	+	CCONJ
ejpam-4819	304	4	∫	∫	PROPN
ejpam-4819	304	5	t	t	PROPN
ejpam-4819	304	6	t0	t0	PROPN
ejpam-4819	304	7	h(r	h(r	PROPN
ejpam-4819	304	8	,	,	PUNCT
ejpam-4819	304	9	η(r))dr	η(r))dr	PROPN
ejpam-4819	304	10	.	.	PUNCT
ejpam-4819	305	1	(	(	PUNCT
ejpam-4819	305	2	26	26	NUM
ejpam-4819	305	3	)	)	PUNCT
ejpam-4819	305	4	suppose	suppose	VERB
ejpam-4819	305	5	that	that	PRON
ejpam-4819	305	6	∥.∥∞	∥.∥∞	ADV
ejpam-4819	305	7	is	be	AUX
ejpam-4819	305	8	the	the	DET
ejpam-4819	305	9	superior	superior	ADJ
ejpam-4819	305	10	norm	norm	NOUN
ejpam-4819	305	11	on	on	ADP
ejpam-4819	305	12	c[0	c[0	PROPN
ejpam-4819	305	13	,	,	PUNCT
ejpam-4819	305	14	1	1	NUM
ejpam-4819	305	15	]	]	PUNCT
ejpam-4819	305	16	which	which	PRON
ejpam-4819	305	17	is	be	AUX
ejpam-4819	305	18	defined	define	VERB
ejpam-4819	305	19	by	by	ADP
ejpam-4819	305	20	∥v∥∞	∥v∥∞	NOUN
ejpam-4819	305	21	=	=	SYM
ejpam-4819	305	22	sup	sup	NOUN
ejpam-4819	305	23	t∈[0,1	t∈[0,1	NOUN
ejpam-4819	305	24	]	]	PUNCT
ejpam-4819	305	25	v(t	v(t	NOUN
ejpam-4819	305	26	)	)	PUNCT
ejpam-4819	305	27	.	.	PUNCT
ejpam-4819	306	1	in	in	ADP
ejpam-4819	306	2	this	this	DET
ejpam-4819	306	3	application	application	NOUN
ejpam-4819	306	4	,	,	PUNCT
ejpam-4819	306	5	we	we	PRON
ejpam-4819	306	6	consider	consider	VERB
ejpam-4819	306	7	that	that	DET
ejpam-4819	306	8	c	c	NOUN
ejpam-4819	306	9	=	=	SYM
ejpam-4819	306	10	c[0	c[0	PROPN
ejpam-4819	306	11	,	,	PUNCT
ejpam-4819	306	12	1	1	NUM
ejpam-4819	306	13	]	]	PUNCT
ejpam-4819	306	14	and	and	CCONJ
ejpam-4819	306	15	gb	gb	NOUN
ejpam-4819	306	16	,	,	PUNCT
ejpam-4819	306	17	ωb	ωb	INTJ
ejpam-4819	306	18	as	as	SCONJ
ejpam-4819	306	19	follows	follow	VERB
ejpam-4819	306	20	:	:	PUNCT
ejpam-4819	306	21	gb(u	gb(u	NUM
ejpam-4819	306	22	,	,	PUNCT
ejpam-4819	306	23	v	v	NOUN
ejpam-4819	306	24	,	,	PUNCT
ejpam-4819	306	25	w	w	NOUN
ejpam-4819	306	26	)	)	PUNCT
ejpam-4819	306	27	=	=	SYM
ejpam-4819	306	28	(	(	PUNCT
ejpam-4819	306	29	∥u−v∥∞+∥v−w∥∞+∥u−w∥∞)2	∥u−v∥∞+∥v−w∥∞+∥u−w∥∞)2	ADJ
ejpam-4819	306	30	,	,	PUNCT
ejpam-4819	306	31	ωb(u	ωb(u	NOUN
ejpam-4819	306	32	,	,	PUNCT
ejpam-4819	306	33	v	v	NOUN
ejpam-4819	306	34	,	,	PUNCT
ejpam-4819	306	35	w	w	NOUN
ejpam-4819	306	36	)	)	PUNCT
ejpam-4819	306	37	=	=	SYM
ejpam-4819	306	38	(	(	PUNCT
ejpam-4819	306	39	∥u−v∥∞+∥u−w∥∞)2	∥u−v∥∞+∥u−w∥∞)2	ADJ
ejpam-4819	306	40	.	.	PUNCT
ejpam-4819	307	1	(	(	PUNCT
ejpam-4819	307	2	27	27	NUM
ejpam-4819	307	3	)	)	PUNCT
ejpam-4819	307	4	next	next	ADV
ejpam-4819	307	5	,	,	PUNCT
ejpam-4819	307	6	we	we	PRON
ejpam-4819	307	7	have	have	VERB
ejpam-4819	307	8	the	the	DET
ejpam-4819	307	9	following	follow	VERB
ejpam-4819	307	10	theorem	theorem	NOUN
ejpam-4819	307	11	:	:	PUNCT
ejpam-4819	307	12	theorem	theorem	NOUN
ejpam-4819	307	13	3	3	X
ejpam-4819	307	14	.	.	PUNCT
ejpam-4819	307	15	suppose	suppose	VERB
ejpam-4819	308	1	that	that	SCONJ
ejpam-4819	308	2	h	h	NOUN
ejpam-4819	308	3	:	:	PUNCT
ejpam-4819	309	1	[	[	X
ejpam-4819	309	2	0	0	NUM
ejpam-4819	309	3	,	,	PUNCT
ejpam-4819	309	4	1	1	NUM
ejpam-4819	309	5	]	]	SYM
ejpam-4819	309	6	×	×	NOUN
ejpam-4819	309	7	r	r	NOUN
ejpam-4819	309	8	→	→	SYM
ejpam-4819	309	9	r	r	NOUN
ejpam-4819	309	10	is	be	AUX
ejpam-4819	309	11	a	a	DET
ejpam-4819	309	12	continuous	continuous	ADJ
ejpam-4819	309	13	function	function	NOUN
ejpam-4819	309	14	on	on	ADP
ejpam-4819	309	15	[	[	X
ejpam-4819	309	16	0	0	NUM
ejpam-4819	309	17	,	,	PUNCT
ejpam-4819	309	18	1	1	NUM
ejpam-4819	309	19	]	]	SYM
ejpam-4819	309	20	×	×	NOUN
ejpam-4819	309	21	r	r	NOUN
ejpam-4819	309	22	and	and	CCONJ
ejpam-4819	309	23	t0	t0	PROPN
ejpam-4819	309	24	is	be	AUX
ejpam-4819	309	25	the	the	DET
ejpam-4819	309	26	interior	interior	ADJ
ejpam-4819	309	27	point	point	NOUN
ejpam-4819	309	28	in	in	ADP
ejpam-4819	309	29	[	[	X
ejpam-4819	309	30	0	0	NUM
ejpam-4819	309	31	,	,	PUNCT
ejpam-4819	309	32	1	1	NUM
ejpam-4819	309	33	]	]	PUNCT
ejpam-4819	309	34	and	and	CCONJ
ejpam-4819	309	35	suppose	suppose	VERB
ejpam-4819	309	36	that	that	SCONJ
ejpam-4819	309	37	α0	α0	ADJ
ejpam-4819	309	38	>	>	X
ejpam-4819	309	39	0	0	NUM
ejpam-4819	309	40	such	such	ADJ
ejpam-4819	309	41	that	that	SCONJ
ejpam-4819	309	42	the	the	DET
ejpam-4819	309	43	function	function	NOUN
ejpam-4819	309	44	h	h	NOUN
ejpam-4819	309	45	fulfills	fulfill	VERB
ejpam-4819	309	46	the	the	DET
ejpam-4819	309	47	following	follow	VERB
ejpam-4819	309	48	:	:	PUNCT
ejpam-4819	309	49	|h(t	|h(t	ADJ
ejpam-4819	309	50	,	,	PUNCT
ejpam-4819	309	51	u)−h(t	u)−h(t	PRON
ejpam-4819	309	52	,	,	PUNCT
ejpam-4819	309	53	v)|	v)|	VERB
ejpam-4819	309	54	≤	≤	ADV
ejpam-4819	309	55	α0|u−	α0|u−	NOUN
ejpam-4819	309	56	v|	v|	ADV
ejpam-4819	309	57	for	for	ADP
ejpam-4819	309	58	all	all	DET
ejpam-4819	309	59	u	u	NOUN
ejpam-4819	309	60	,	,	PUNCT
ejpam-4819	309	61	v	v	NOUN
ejpam-4819	309	62	∈	∈	NOUN
ejpam-4819	309	63	r	r	NOUN
ejpam-4819	309	64	and	and	CCONJ
ejpam-4819	309	65	for	for	ADP
ejpam-4819	309	66	all	all	DET
ejpam-4819	309	67	t	t	NOUN
ejpam-4819	309	68	∈	∈	PROPN
ejpam-4819	310	1	[	[	X
ejpam-4819	310	2	0	0	NUM
ejpam-4819	310	3	,	,	PUNCT
ejpam-4819	310	4	1	1	NUM
ejpam-4819	310	5	]	]	PUNCT
ejpam-4819	310	6	.	.	PUNCT
ejpam-4819	311	1	(	(	PUNCT
ejpam-4819	311	2	28	28	NUM
ejpam-4819	311	3	)	)	PUNCT
ejpam-4819	311	4	then	then	ADV
ejpam-4819	311	5	the	the	DET
ejpam-4819	311	6	integral	integral	ADJ
ejpam-4819	311	7	equation	equation	NOUN
ejpam-4819	311	8	fη(t	fη(t	NOUN
ejpam-4819	311	9	)	)	PUNCT
ejpam-4819	312	1	=	=	PUNCT
ejpam-4819	312	2	η0	η0	NOUN
ejpam-4819	312	3	+	+	CCONJ
ejpam-4819	312	4	∫	∫	PROPN
ejpam-4819	312	5	t	t	PROPN
ejpam-4819	312	6	t0	t0	PROPN
ejpam-4819	312	7	h(r	h(r	PROPN
ejpam-4819	312	8	,	,	PUNCT
ejpam-4819	312	9	η(r))dr	η(r))dr	NOUN
ejpam-4819	312	10	has	have	VERB
ejpam-4819	312	11	a	a	DET
ejpam-4819	312	12	unique	unique	ADJ
ejpam-4819	312	13	solution	solution	NOUN
ejpam-4819	312	14	.	.	PUNCT
ejpam-4819	313	1	t.	t.	PROPN
ejpam-4819	313	2	qawasmeh	qawasmeh	NOUN
ejpam-4819	313	3	/	/	SYM
ejpam-4819	313	4	eur	eur	PROPN
ejpam-4819	313	5	.	.	PUNCT
ejpam-4819	314	1	j.	j.	PROPN
ejpam-4819	314	2	pure	pure	PROPN
ejpam-4819	314	3	appl	appl	PROPN
ejpam-4819	314	4	.	.	PROPN
ejpam-4819	314	5	math	math	PROPN
ejpam-4819	314	6	,	,	PUNCT
ejpam-4819	314	7	16	16	NUM
ejpam-4819	314	8	(	(	PUNCT
ejpam-4819	314	9	3	3	NUM
ejpam-4819	314	10	)	)	PUNCT
ejpam-4819	314	11	(	(	PUNCT
ejpam-4819	314	12	2023	2023	NUM
ejpam-4819	314	13	)	)	PUNCT
ejpam-4819	314	14	,	,	PUNCT
ejpam-4819	314	15	1717	1717	NUM
ejpam-4819	314	16	-	-	SYM
ejpam-4819	314	17	1730	1730	NUM
ejpam-4819	314	18	1728	1728	NUM
ejpam-4819	314	19	proof	proof	NOUN
ejpam-4819	314	20	.	.	PUNCT
ejpam-4819	315	1	let	let	VERB
ejpam-4819	315	2	ϵ	ϵ	PRON
ejpam-4819	315	3	>	>	X
ejpam-4819	315	4	0	0	PUNCT
ejpam-4819	316	1	with	with	ADP
ejpam-4819	316	2	ϵ	ϵ	PROPN
ejpam-4819	316	3	<	<	X
ejpam-4819	316	4	√	√	X
ejpam-4819	316	5	λ1	λ1	PROPN
ejpam-4819	316	6	bα2	bα2	NOUN
ejpam-4819	316	7	0	0	NUM
ejpam-4819	316	8	.	.	PUNCT
ejpam-4819	317	1	define	define	VERB
ejpam-4819	317	2	the	the	DET
ejpam-4819	317	3	self	self	NOUN
ejpam-4819	317	4	mapping	mapping	NOUN
ejpam-4819	318	1	f	f	NOUN
ejpam-4819	318	2	:	:	PUNCT
ejpam-4819	318	3	c[0	c[0	PROPN
ejpam-4819	318	4	,	,	PUNCT
ejpam-4819	318	5	1	1	NUM
ejpam-4819	318	6	]	]	PUNCT
ejpam-4819	318	7	→	→	X
ejpam-4819	318	8	c[0	c[0	PROPN
ejpam-4819	318	9	,	,	PUNCT
ejpam-4819	318	10	1	1	NUM
ejpam-4819	318	11	]	]	PUNCT
ejpam-4819	318	12	via	via	ADP
ejpam-4819	318	13	fη(t	fη(t	NOUN
ejpam-4819	318	14	)	)	PUNCT
ejpam-4819	318	15	=	=	PUNCT
ejpam-4819	319	1	η0	η0	NOUN
ejpam-4819	319	2	+	+	CCONJ
ejpam-4819	319	3	∫	∫	PROPN
ejpam-4819	319	4	t	t	PROPN
ejpam-4819	319	5	t0	t0	PROPN
ejpam-4819	319	6	h(r	h(r	PROPN
ejpam-4819	319	7	,	,	PUNCT
ejpam-4819	319	8	η(r))dr	η(r))dr	PROPN
ejpam-4819	319	9	.	.	PUNCT
ejpam-4819	320	1	(	(	PUNCT
ejpam-4819	320	2	29	29	NUM
ejpam-4819	320	3	)	)	PUNCT
ejpam-4819	320	4	then	then	ADV
ejpam-4819	320	5	we	we	PRON
ejpam-4819	320	6	show	show	VERB
ejpam-4819	320	7	that	that	SCONJ
ejpam-4819	320	8	f	f	PROPN
ejpam-4819	320	9	satisfies	satisfy	VERB
ejpam-4819	320	10	the	the	DET
ejpam-4819	320	11	condition	condition	NOUN
ejpam-4819	320	12	(	(	PUNCT
ejpam-4819	320	13	8)	8)	NUM
ejpam-4819	320	14	on	on	ADP
ejpam-4819	320	15	the	the	DET
ejpam-4819	320	16	interval	interval	NOUN
ejpam-4819	320	17	c0	c0	NOUN
ejpam-4819	320	18	=	=	PUNCT
ejpam-4819	321	1	[	[	X
ejpam-4819	321	2	t0	t0	PROPN
ejpam-4819	321	3	,	,	PUNCT
ejpam-4819	321	4	t0	t0	PROPN
ejpam-4819	321	5	+	+	CCONJ
ejpam-4819	321	6	ϵ	ϵ	X
ejpam-4819	321	7	]	]	X
ejpam-4819	321	8	.	.	PUNCT
ejpam-4819	322	1	it	it	PRON
ejpam-4819	322	2	suffices	suffice	VERB
ejpam-4819	322	3	to	to	PART
ejpam-4819	322	4	show	show	VERB
ejpam-4819	322	5	that	that	SCONJ
ejpam-4819	322	6	:	:	PUNCT
ejpam-4819	322	7	ωb(fu	ωb(fu	VERB
ejpam-4819	322	8	,	,	PUNCT
ejpam-4819	322	9	f	f	PROPN
ejpam-4819	322	10	2u	2u	PROPN
ejpam-4819	322	11	,	,	PUNCT
ejpam-4819	322	12	fv	fv	NOUN
ejpam-4819	322	13	)	)	PUNCT
ejpam-4819	322	14	≤	≤	NOUN
ejpam-4819	322	15	λ1	λ1	PROPN
ejpam-4819	322	16	b	b	PROPN
ejpam-4819	322	17	ωb(u	ωb(u	X
ejpam-4819	322	18	,	,	PUNCT
ejpam-4819	322	19	fu	fu	NOUN
ejpam-4819	322	20	,	,	PUNCT
ejpam-4819	322	21	v	v	NOUN
ejpam-4819	322	22	)	)	PUNCT
ejpam-4819	322	23	.	.	PUNCT
ejpam-4819	323	1	(	(	PUNCT
ejpam-4819	323	2	30	30	NUM
ejpam-4819	323	3	)	)	PUNCT
ejpam-4819	323	4	now	now	ADV
ejpam-4819	323	5	,	,	PUNCT
ejpam-4819	323	6	for	for	ADP
ejpam-4819	323	7	all	all	DET
ejpam-4819	323	8	u	u	NOUN
ejpam-4819	323	9	,	,	PUNCT
ejpam-4819	323	10	v	v	PROPN
ejpam-4819	323	11	∈	∈	PROPN
ejpam-4819	323	12	c[0	c[0	NOUN
ejpam-4819	323	13	,	,	PUNCT
ejpam-4819	323	14	1	1	NUM
ejpam-4819	323	15	]	]	PUNCT
ejpam-4819	323	16	,	,	PUNCT
ejpam-4819	323	17	we	we	PRON
ejpam-4819	323	18	obtain	obtain	VERB
ejpam-4819	323	19	:	:	PUNCT
ejpam-4819	323	20	∥fu−	∥fu−	ADJ
ejpam-4819	323	21	fv∥∞	fv∥∞	NOUN
ejpam-4819	323	22	=	=	NOUN
ejpam-4819	323	23	sup	sup	NOUN
ejpam-4819	323	24	t∈c0	t∈c0	VERB
ejpam-4819	323	25	|fu(t)−	|fu(t)−	PROPN
ejpam-4819	323	26	fv(t)|	fv(t)|	NUM
ejpam-4819	323	27	=	=	SYM
ejpam-4819	323	28	sup	sup	NOUN
ejpam-4819	323	29	t∈c0	t∈c0	NOUN
ejpam-4819	324	1	|	|	ADV
ejpam-4819	324	2	∫	∫	PROPN
ejpam-4819	324	3	t	t	PROPN
ejpam-4819	324	4	t0	t0	PROPN
ejpam-4819	324	5	(	(	PUNCT
ejpam-4819	324	6	h(r	h(r	NOUN
ejpam-4819	324	7	,	,	PUNCT
ejpam-4819	324	8	u(r))−h(r	u(r))−h(r	ADJ
ejpam-4819	324	9	,	,	PUNCT
ejpam-4819	324	10	v(r)))dr|	v(r)))dr|	NOUN
ejpam-4819	324	11	≤	≤	NUM
ejpam-4819	324	12	sup	sup	NOUN
ejpam-4819	324	13	t∈c0	t∈c0	NOUN
ejpam-4819	324	14	∫	∫	PROPN
ejpam-4819	324	15	t	t	PROPN
ejpam-4819	324	16	t0	t0	PROPN
ejpam-4819	324	17	|(h(r	|(h(r	NUM
ejpam-4819	324	18	,	,	PUNCT
ejpam-4819	324	19	u(r))−h(r	u(r))−h(r	ADJ
ejpam-4819	324	20	,	,	PUNCT
ejpam-4819	324	21	v(r)))dr|	v(r)))dr|	NOUN
ejpam-4819	324	22	≤	≤	NUM
ejpam-4819	324	23	sup	sup	NOUN
ejpam-4819	324	24	t∈c0	t∈c0	VERB
ejpam-4819	324	25	α0|u(t)−	α0|u(t)−	PROPN
ejpam-4819	324	26	v(t)|	v(t)|	PROPN
ejpam-4819	325	1	∫	∫	PROPN
ejpam-4819	325	2	t	t	PROPN
ejpam-4819	325	3	t0	t0	PROPN
ejpam-4819	325	4	dr	dr	PROPN
ejpam-4819	325	5	=	=	PROPN
ejpam-4819	325	6	α0∥u−	α0∥u−	PROPN
ejpam-4819	325	7	v∥∞(t−	v∥∞(t−	CCONJ
ejpam-4819	325	8	t0	t0	NOUN
ejpam-4819	325	9	)	)	PUNCT
ejpam-4819	326	1	=	=	SYM
ejpam-4819	327	1	ϵα0∥u−	ϵα0∥u−	NUM
ejpam-4819	327	2	v∥∞.	v∥∞.	NOUN
ejpam-4819	327	3	therefore	therefore	ADV
ejpam-4819	327	4	,	,	PUNCT
ejpam-4819	327	5	(	(	PUNCT
ejpam-4819	327	6	∥fu−	∥fu−	X
ejpam-4819	327	7	f2u∥∞	f2u∥∞	PROPN
ejpam-4819	327	8	+	+	PROPN
ejpam-4819	327	9	∥fu−	∥fu−	ADJ
ejpam-4819	327	10	fv∥∞)2	fv∥∞)2	ADJ
ejpam-4819	327	11	=	=	PUNCT
ejpam-4819	327	12	(	(	PUNCT
ejpam-4819	327	13	sup	sup	NOUN
ejpam-4819	327	14	t∈c0	t∈c0	VERB
ejpam-4819	327	15	|fu(t)−	|fu(t)−	PROPN
ejpam-4819	327	16	f2u(t)|+	f2u(t)|+	PROPN
ejpam-4819	327	17	sup	sup	PROPN
ejpam-4819	327	18	t∈c0	t∈c0	VERB
ejpam-4819	327	19	|fu(t)−	|fu(t)−	PROPN
ejpam-4819	327	20	fv(t)|)2	fv(t)|)2	NOUN
ejpam-4819	327	21	=	=	PUNCT
ejpam-4819	327	22	(	(	PUNCT
ejpam-4819	327	23	sup	sup	X
ejpam-4819	327	24	t∈c0	t∈c0	VERB
ejpam-4819	328	1	|	|	ADV
ejpam-4819	328	2	∫	∫	PROPN
ejpam-4819	328	3	t	t	PROPN
ejpam-4819	328	4	t0	t0	PROPN
ejpam-4819	328	5	(	(	PUNCT
ejpam-4819	328	6	h(r	h(r	NOUN
ejpam-4819	328	7	,	,	PUNCT
ejpam-4819	328	8	u(r))−h(r	u(r))−h(r	ADJ
ejpam-4819	328	9	,	,	PUNCT
ejpam-4819	328	10	fu(r))dr|	fu(r))dr|	NOUN
ejpam-4819	328	11	+	+	NOUN
ejpam-4819	328	12	sup	sup	NOUN
ejpam-4819	328	13	t∈c0	t∈c0	NOUN
ejpam-4819	328	14	|	|	ADV
ejpam-4819	328	15	∫	∫	PROPN
ejpam-4819	328	16	t	t	PROPN
ejpam-4819	328	17	t0	t0	PROPN
ejpam-4819	328	18	(	(	PUNCT
ejpam-4819	328	19	h(r	h(r	NOUN
ejpam-4819	328	20	,	,	PUNCT
ejpam-4819	328	21	u(r))−h(r	u(r))−h(r	ADJ
ejpam-4819	328	22	,	,	PUNCT
ejpam-4819	328	23	v(r))dr|	v(r))dr|	ADJ
ejpam-4819	328	24	)	)	PUNCT
ejpam-4819	328	25	2	2	NUM
ejpam-4819	328	26	≤	≤	NOUN
ejpam-4819	328	27	(	(	PUNCT
ejpam-4819	328	28	ϵα0	ϵα0	NOUN
ejpam-4819	328	29	)	)	PUNCT
ejpam-4819	328	30	2(∥u−	2(∥u−	NUM
ejpam-4819	328	31	fu∥∞	fu∥∞	NOUN
ejpam-4819	328	32	+	+	CCONJ
ejpam-4819	328	33	∥u−	∥u−	PROPN
ejpam-4819	328	34	v∥∞)2	v∥∞)2	NOUN
ejpam-4819	328	35	.	.	PUNCT
ejpam-4819	329	1	now	now	ADV
ejpam-4819	329	2	,	,	PUNCT
ejpam-4819	329	3	set	set	VERB
ejpam-4819	329	4	λ1	λ1	PROPN
ejpam-4819	329	5	b	b	PROPN
ejpam-4819	329	6	=	=	PUNCT
ejpam-4819	329	7	(	(	PUNCT
ejpam-4819	329	8	ϵα0	ϵα0	PROPN
ejpam-4819	329	9	)	)	PUNCT
ejpam-4819	329	10	2	2	NUM
ejpam-4819	329	11	,	,	PUNCT
ejpam-4819	329	12	we	we	PRON
ejpam-4819	329	13	get	get	VERB
ejpam-4819	329	14	the	the	DET
ejpam-4819	329	15	desire	desire	NOUN
ejpam-4819	329	16	result	result	NOUN
ejpam-4819	329	17	.	.	PUNCT
ejpam-4819	330	1	4	4	X
ejpam-4819	330	2	.	.	X
ejpam-4819	330	3	conclusion	conclusion	NOUN
ejpam-4819	330	4	in	in	ADP
ejpam-4819	330	5	this	this	DET
ejpam-4819	330	6	manuscript	manuscript	NOUN
ejpam-4819	330	7	,	,	PUNCT
ejpam-4819	330	8	we	we	PRON
ejpam-4819	330	9	formulated	formulate	VERB
ejpam-4819	330	10	two	two	NUM
ejpam-4819	330	11	significant	significant	ADJ
ejpam-4819	330	12	interpolative	interpolative	ADJ
ejpam-4819	330	13	contractions	contraction	NOUN
ejpam-4819	330	14	namely	namely	ADV
ejpam-4819	330	15	,	,	PUNCT
ejpam-4819	330	16	(	(	PUNCT
ejpam-4819	330	17	h	h	NOUN
ejpam-4819	330	18	,	,	PUNCT
ejpam-4819	330	19	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	330	20	contraction	contraction	NOUN
ejpam-4819	330	21	for	for	ADP
ejpam-4819	330	22	self	self	NOUN
ejpam-4819	330	23	mapping	mapping	NOUN
ejpam-4819	330	24	f	f	NOUN
ejpam-4819	330	25	and	and	CCONJ
ejpam-4819	330	26	generalized	generalized	ADJ
ejpam-4819	330	27	(	(	PUNCT
ejpam-4819	330	28	h	h	NOUN
ejpam-4819	330	29	,	,	PUNCT
ejpam-4819	330	30	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-4819	330	31	contraction	contraction	NOUN
ejpam-4819	330	32	for	for	ADP
ejpam-4819	330	33	pair	pair	NOUN
ejpam-4819	330	34	of	of	ADP
ejpam-4819	330	35	self	self	NOUN
ejpam-4819	330	36	mappings	mapping	NOUN
ejpam-4819	330	37	(	(	PUNCT
ejpam-4819	330	38	f1	f1	NOUN
ejpam-4819	330	39	,	,	PUNCT
ejpam-4819	330	40	f2	f2	PROPN
ejpam-4819	330	41	)	)	PUNCT
ejpam-4819	330	42	.	.	PUNCT
ejpam-4819	331	1	by	by	ADP
ejpam-4819	331	2	employing	employ	VERB
ejpam-4819	331	3	these	these	DET
ejpam-4819	331	4	contractions	contraction	NOUN
ejpam-4819	331	5	we	we	PRON
ejpam-4819	331	6	unify	unify	VERB
ejpam-4819	331	7	new	new	ADJ
ejpam-4819	331	8	fixed	fix	VERB
ejpam-4819	331	9	and	and	CCONJ
ejpam-4819	331	10	common	common	ADJ
ejpam-4819	331	11	fixed	fix	VERB
ejpam-4819	331	12	results	result	NOUN
ejpam-4819	331	13	.	.	PUNCT
ejpam-4819	332	1	we	we	PRON
ejpam-4819	332	2	formulated	formulate	VERB
ejpam-4819	332	3	some	some	DET
ejpam-4819	332	4	numerical	numerical	ADJ
ejpam-4819	332	5	examples	example	NOUN
ejpam-4819	332	6	and	and	CCONJ
ejpam-4819	332	7	applications	application	NOUN
ejpam-4819	332	8	to	to	PART
ejpam-4819	332	9	show	show	VERB
ejpam-4819	332	10	the	the	DET
ejpam-4819	332	11	novelty	novelty	NOUN
ejpam-4819	332	12	of	of	ADP
ejpam-4819	332	13	our	our	PRON
ejpam-4819	332	14	results	result	NOUN
ejpam-4819	332	15	;	;	PUNCT
ejpam-4819	332	16	one	one	NUM
ejpam-4819	332	17	of	of	ADP
ejpam-4819	332	18	these	these	DET
ejpam-4819	332	19	applications	application	NOUN
ejpam-4819	332	20	based	base	VERB
ejpam-4819	332	21	on	on	ADP
ejpam-4819	332	22	the	the	DET
ejpam-4819	332	23	significant	significant	ADJ
ejpam-4819	332	24	idea	idea	NOUN
ejpam-4819	332	25	references	reference	NOUN
ejpam-4819	332	26	1729	1729	NUM
ejpam-4819	332	27	that	that	SCONJ
ejpam-4819	332	28	the	the	DET
ejpam-4819	332	29	solution	solution	NOUN
ejpam-4819	332	30	of	of	ADP
ejpam-4819	332	31	a	a	DET
ejpam-4819	332	32	equation	equation	NOUN
ejpam-4819	332	33	in	in	ADP
ejpam-4819	332	34	a	a	DET
ejpam-4819	332	35	certain	certain	ADJ
ejpam-4819	332	36	conditions	condition	NOUN
ejpam-4819	332	37	is	be	AUX
ejpam-4819	332	38	typical	typical	ADJ
ejpam-4819	332	39	to	to	ADP
ejpam-4819	332	40	solution	solution	NOUN
ejpam-4819	332	41	of	of	ADP
ejpam-4819	332	42	fixed	fix	VERB
ejpam-4819	332	43	point	point	NOUN
ejpam-4819	332	44	equation	equation	NOUN
ejpam-4819	332	45	.	.	PUNCT
ejpam-4819	333	1	we	we	PRON
ejpam-4819	333	2	utilized	utilize	VERB
ejpam-4819	333	3	this	this	DET
ejpam-4819	333	4	idea	idea	NOUN
ejpam-4819	333	5	to	to	PART
ejpam-4819	333	6	prove	prove	VERB
ejpam-4819	333	7	that	that	SCONJ
ejpam-4819	333	8	this	this	DET
ejpam-4819	333	9	equation	equation	NOUN
ejpam-4819	333	10	not	not	PART
ejpam-4819	333	11	only	only	ADV
ejpam-4819	333	12	has	have	VERB
ejpam-4819	333	13	solution	solution	NOUN
ejpam-4819	333	14	as	as	SCONJ
ejpam-4819	333	15	the	the	DET
ejpam-4819	333	16	intermediate	intermediate	ADJ
ejpam-4819	333	17	value	value	NOUN
ejpam-4819	333	18	theorem	theorem	NOUN
ejpam-4819	333	19	says	say	VERB
ejpam-4819	333	20	but	but	CCONJ
ejpam-4819	333	21	also	also	ADV
ejpam-4819	333	22	,	,	PUNCT
ejpam-4819	333	23	this	this	DET
ejpam-4819	333	24	solution	solution	NOUN
ejpam-4819	333	25	is	be	AUX
ejpam-4819	333	26	unique	unique	ADJ
ejpam-4819	333	27	.	.	PUNCT
ejpam-4819	334	1	this	this	DET
ejpam-4819	334	2	research	research	NOUN
ejpam-4819	334	3	can	can	AUX
ejpam-4819	334	4	be	be	AUX
ejpam-4819	334	5	improved	improve	VERB
ejpam-4819	334	6	by	by	ADP
ejpam-4819	334	7	utilizing	utilize	VERB
ejpam-4819	334	8	the	the	DET
ejpam-4819	334	9	concept	concept	NOUN
ejpam-4819	334	10	of	of	ADP
ejpam-4819	334	11	extended	extended	ADJ
ejpam-4819	334	12	gb	gb	ADV
ejpam-4819	334	13	-	-	PUNCT
ejpam-4819	334	14	metric	metric	ADJ
ejpam-4819	334	15	spaces	space	NOUN
ejpam-4819	334	16	.	.	PUNCT
ejpam-4819	335	1	references	reference	NOUN
ejpam-4819	335	2	[	[	X
ejpam-4819	335	3	1	1	NUM
ejpam-4819	335	4	]	]	X
ejpam-4819	335	5	k	k	PROPN
ejpam-4819	335	6	abodayeh	abodayeh	PROPN
ejpam-4819	335	7	,	,	PUNCT
ejpam-4819	335	8	a	a	DET
ejpam-4819	335	9	bataihah	bataihah	ADJ
ejpam-4819	335	10	,	,	PUNCT
ejpam-4819	335	11	and	and	CCONJ
ejpam-4819	335	12	w	w	NOUN
ejpam-4819	335	13	shatanawi	shatanawi	ADJ
ejpam-4819	335	14	.	.	PUNCT
ejpam-4819	336	1	generalized	generalize	VERB
ejpam-4819	336	2	ω	ω	NUM
ejpam-4819	336	3	-	-	PUNCT
ejpam-4819	336	4	distance	distance	NOUN
ejpam-4819	336	5	mappings	mapping	NOUN
ejpam-4819	336	6	and	and	CCONJ
ejpam-4819	336	7	some	some	DET
ejpam-4819	336	8	fixed	fix	VERB
ejpam-4819	336	9	point	point	NOUN
ejpam-4819	336	10	theorems	theorem	NOUN
ejpam-4819	336	11	.	.	PUNCT
ejpam-4819	337	1	upb	upb	PROPN
ejpam-4819	337	2	sci	sci	PROPN
ejpam-4819	337	3	.	.	PUNCT
ejpam-4819	337	4	bull	bull	PROPN
ejpam-4819	337	5	.	.	PUNCT
ejpam-4819	338	1	ser	ser	PROPN
ejpam-4819	338	2	.	.	PROPN
ejpam-4819	338	3	,	,	PUNCT
ejpam-4819	338	4	79:223–232	79:223–232	PROPN
ejpam-4819	338	5	,	,	PUNCT
ejpam-4819	338	6	2017	2017	NUM
ejpam-4819	338	7	.	.	PUNCT
ejpam-4819	339	1	[	[	X
ejpam-4819	339	2	2	2	NUM
ejpam-4819	339	3	]	]	PUNCT
ejpam-4819	339	4	s	s	X
ejpam-4819	339	5	aghajani	aghajani	PROPN
ejpam-4819	339	6	,	,	PUNCT
ejpam-4819	339	7	m	m	NOUN
ejpam-4819	339	8	abbas	abbas	NOUN
ejpam-4819	339	9	,	,	PUNCT
ejpam-4819	339	10	and	and	CCONJ
ejpam-4819	339	11	j	j	PROPN
ejpam-4819	339	12	r	r	NOUN
ejpam-4819	339	13	roshan	roshan	PROPN
ejpam-4819	339	14	.	.	PUNCT
ejpam-4819	340	1	common	common	ADJ
ejpam-4819	340	2	fixed	fix	VERB
ejpam-4819	340	3	point	point	NOUN
ejpam-4819	340	4	of	of	ADP
ejpam-4819	340	5	generalized	generalized	ADJ
ejpam-4819	340	6	weak	weak	ADJ
ejpam-4819	340	7	contractive	contractive	ADJ
ejpam-4819	340	8	mappings	mapping	NOUN
ejpam-4819	340	9	in	in	ADP
ejpam-4819	340	10	partially	partially	ADV
ejpam-4819	340	11	ordered	order	VERB
ejpam-4819	340	12	gb	gb	ADV
ejpam-4819	340	13	-	-	PUNCT
ejpam-4819	340	14	metric	metric	ADJ
ejpam-4819	340	15	spaces	space	NOUN
ejpam-4819	340	16	.	.	PUNCT
ejpam-4819	341	1	filomat	filomat	NOUN
ejpam-4819	341	2	,	,	PUNCT
ejpam-4819	341	3	28:1087–1101	28:1087–1101	PROPN
ejpam-4819	341	4	,	,	PUNCT
ejpam-4819	341	5	01	01	NUM
ejpam-4819	341	6	2014	2014	NUM
ejpam-4819	341	7	.	.	PUNCT
ejpam-4819	342	1	[	[	X
ejpam-4819	342	2	3	3	X
ejpam-4819	342	3	]	]	X
ejpam-4819	342	4	i	i	PRON
ejpam-4819	342	5	a	a	DET
ejpam-4819	342	6	bakhtin	bakhtin	NOUN
ejpam-4819	342	7	.	.	PUNCT
ejpam-4819	343	1	the	the	DET
ejpam-4819	343	2	contraction	contraction	NOUN
ejpam-4819	343	3	mapping	map	VERB
ejpam-4819	343	4	principle	principle	NOUN
ejpam-4819	343	5	in	in	ADP
ejpam-4819	343	6	quasi	quasi	ADJ
ejpam-4819	343	7	-	-	ADJ
ejpam-4819	343	8	metric	metric	ADJ
ejpam-4819	343	9	spaces	space	NOUN
ejpam-4819	343	10	.	.	PUNCT
ejpam-4819	344	1	functional	functional	ADJ
ejpam-4819	344	2	analysis	analysis	NOUN
ejpam-4819	344	3	,	,	PUNCT
ejpam-4819	344	4	30:26–37	30:26–37	PROPN
ejpam-4819	344	5	,	,	PUNCT
ejpam-4819	344	6	1989	1989	NUM
ejpam-4819	344	7	.	.	PUNCT
ejpam-4819	345	1	[	[	X
ejpam-4819	345	2	4	4	NUM
ejpam-4819	345	3	]	]	PUNCT
ejpam-4819	345	4	s	s	VERB
ejpam-4819	345	5	banach	banach	NOUN
ejpam-4819	345	6	.	.	PUNCT
ejpam-4819	346	1	sur	sur	PROPN
ejpam-4819	346	2	les	les	X
ejpam-4819	346	3	opérations	opération	NOUN
ejpam-4819	346	4	dans	dan	NOUN
ejpam-4819	346	5	les	les	X
ejpam-4819	346	6	ensembles	ensemble	NOUN
ejpam-4819	346	7	abstraits	abstrait	NOUN
ejpam-4819	346	8	et	et	PROPN
ejpam-4819	346	9	leur	leur	X
ejpam-4819	346	10	application	application	PROPN
ejpam-4819	346	11	aux	aux	PROPN
ejpam-4819	346	12	équations	équations	PROPN
ejpam-4819	346	13	intégrales	intégrale	NOUN
ejpam-4819	346	14	.	.	PUNCT
ejpam-4819	347	1	fundamenta	fundamenta	PROPN
ejpam-4819	347	2	mathematicae	mathematicae	PROPN
ejpam-4819	347	3	,	,	PUNCT
ejpam-4819	347	4	3:133–181	3:133–181	NUM
ejpam-4819	347	5	,	,	PUNCT
ejpam-4819	347	6	1922	1922	NUM
ejpam-4819	347	7	.	.	PUNCT
ejpam-4819	348	1	[	[	X
ejpam-4819	348	2	5	5	NUM
ejpam-4819	348	3	]	]	PUNCT
ejpam-4819	348	4	a	a	DET
ejpam-4819	348	5	bataihah	bataihah	NOUN
ejpam-4819	348	6	,	,	PUNCT
ejpam-4819	348	7	t	t	NOUN
ejpam-4819	348	8	qawasmeh	qawasmeh	NOUN
ejpam-4819	348	9	,	,	PUNCT
ejpam-4819	348	10	and	and	CCONJ
ejpam-4819	348	11	m	m	VERB
ejpam-4819	348	12	shatnawi	shatnawi	ADJ
ejpam-4819	348	13	.	.	PUNCT
ejpam-4819	349	1	discussion	discussion	NOUN
ejpam-4819	349	2	on	on	ADP
ejpam-4819	349	3	b	b	X
ejpam-4819	349	4	-	-	ADJ
ejpam-4819	349	5	metric	metric	ADJ
ejpam-4819	349	6	spaces	space	NOUN
ejpam-4819	349	7	and	and	CCONJ
ejpam-4819	349	8	related	relate	VERB
ejpam-4819	349	9	results	result	NOUN
ejpam-4819	349	10	in	in	ADP
ejpam-4819	349	11	metric	metric	ADJ
ejpam-4819	349	12	and	and	CCONJ
ejpam-4819	349	13	gmetric	gmetric	ADJ
ejpam-4819	349	14	.	.	PUNCT
ejpam-4819	350	1	nonlinear	nonlinear	ADJ
ejpam-4819	350	2	functional	functional	ADJ
ejpam-4819	350	3	analysis	analysis	NOUN
ejpam-4819	350	4	and	and	CCONJ
ejpam-4819	350	5	applications	application	NOUN
ejpam-4819	350	6	,	,	PUNCT
ejpam-4819	350	7	27:233–247	27:233–247	NUM
ejpam-4819	350	8	,	,	PUNCT
ejpam-4819	350	9	06	06	NUM
ejpam-4819	350	10	2022	2022	NUM
ejpam-4819	350	11	.	.	PUNCT
ejpam-4819	351	1	[	[	X
ejpam-4819	351	2	6	6	NUM
ejpam-4819	351	3	]	]	X
ejpam-4819	351	4	a	a	DET
ejpam-4819	351	5	bataihah	bataihah	ADJ
ejpam-4819	351	6	,	,	PUNCT
ejpam-4819	351	7	w	w	PROPN
ejpam-4819	351	8	shatanawi	shatanawi	PROPN
ejpam-4819	351	9	,	,	PUNCT
ejpam-4819	351	10	t	t	NOUN
ejpam-4819	351	11	qawasmeh	qawasmeh	NOUN
ejpam-4819	351	12	,	,	PUNCT
ejpam-4819	351	13	and	and	CCONJ
ejpam-4819	351	14	r	r	NOUN
ejpam-4819	351	15	hatamleh	hatamleh	NOUN
ejpam-4819	351	16	.	.	PUNCT
ejpam-4819	352	1	onh	onh	PROPN
ejpam-4819	352	2	simulation	simulation	NOUN
ejpam-4819	352	3	functions	function	NOUN
ejpam-4819	352	4	and	and	CCONJ
ejpam-4819	352	5	fixed	fix	VERB
ejpam-4819	352	6	point	point	NOUN
ejpam-4819	352	7	results	result	NOUN
ejpam-4819	352	8	in	in	ADP
ejpam-4819	352	9	the	the	DET
ejpam-4819	352	10	setting	setting	NOUN
ejpam-4819	352	11	of	of	ADP
ejpam-4819	352	12	ωt	ωt	NOUN
ejpam-4819	352	13	-	-	PUNCT
ejpam-4819	352	14	distance	distance	NOUN
ejpam-4819	352	15	mappings	mapping	NOUN
ejpam-4819	352	16	with	with	ADP
ejpam-4819	352	17	application	application	NOUN
ejpam-4819	352	18	on	on	ADP
ejpam-4819	352	19	matrix	matrix	NOUN
ejpam-4819	352	20	equations	equation	NOUN
ejpam-4819	352	21	.	.	PUNCT
ejpam-4819	353	1	mathematics	mathematic	NOUN
ejpam-4819	353	2	,	,	PUNCT
ejpam-4819	353	3	8:837	8:837	NUM
ejpam-4819	353	4	,	,	PUNCT
ejpam-4819	353	5	05	05	NUM
ejpam-4819	353	6	2020	2020	NUM
ejpam-4819	353	7	.	.	PUNCT
ejpam-4819	354	1	[	[	X
ejpam-4819	354	2	7	7	X
ejpam-4819	354	3	]	]	X
ejpam-4819	354	4	p	p	X
ejpam-4819	354	5	debnath	debnath	NOUN
ejpam-4819	354	6	and	and	CCONJ
ejpam-4819	354	7	m	m	PROPN
ejpam-4819	354	8	de	de	X
ejpam-4819	354	9	la	la	PROPN
ejpam-4819	354	10	sen	sen	PROPN
ejpam-4819	354	11	.	.	PROPN
ejpam-4819	354	12	set	set	PROPN
ejpam-4819	354	13	-	-	PUNCT
ejpam-4819	354	14	valued	value	VERB
ejpam-4819	354	15	interpolative	interpolative	ADJ
ejpam-4819	354	16	hardy	hardy	ADJ
ejpam-4819	354	17	–	–	PUNCT
ejpam-4819	354	18	rogers	roger	NOUN
ejpam-4819	354	19	and	and	CCONJ
ejpam-4819	354	20	set	set	NOUN
ejpam-4819	354	21	-	-	PUNCT
ejpam-4819	354	22	valued	value	VERB
ejpam-4819	354	23	reich	reich	NOUN
ejpam-4819	354	24	–	–	PUNCT
ejpam-4819	354	25	rus	rus	NOUN
ejpam-4819	354	26	–	–	PUNCT
ejpam-4819	354	27	ćirić-type	ćirić-type	ADJ
ejpam-4819	354	28	contractions	contraction	NOUN
ejpam-4819	354	29	in	in	ADP
ejpam-4819	354	30	b	b	NOUN
ejpam-4819	354	31	-	-	ADJ
ejpam-4819	354	32	metric	metric	ADJ
ejpam-4819	354	33	spaces	space	NOUN
ejpam-4819	354	34	.	.	PUNCT
ejpam-4819	355	1	mathematics	mathematic	NOUN
ejpam-4819	355	2	,	,	PUNCT
ejpam-4819	355	3	7:849–849	7:849–849	NUM
ejpam-4819	355	4	,	,	PUNCT
ejpam-4819	355	5	09	09	NUM
ejpam-4819	355	6	2019	2019	NUM
ejpam-4819	355	7	.	.	PUNCT
ejpam-4819	356	1	[	[	X
ejpam-4819	356	2	8	8	X
ejpam-4819	356	3	]	]	X
ejpam-4819	356	4	p	p	NOUN
ejpam-4819	356	5	debnath	debnath	NOUN
ejpam-4819	356	6	,	,	PUNCT
ejpam-4819	356	7	n.	n.	PROPN
ejpam-4819	356	8	konwar	konwar	PROPN
ejpam-4819	356	9	,	,	PUNCT
ejpam-4819	356	10	and	and	CCONJ
ejpam-4819	356	11	s.	s.	PROPN
ejpam-4819	356	12	(	(	PUNCT
ejpam-4819	356	13	eds	eds	PROPN
ejpam-4819	356	14	.	.	PUNCT
ejpam-4819	356	15	)	)	PUNCT
ejpam-4819	357	1	radenović.	radenović.	PRON
ejpam-4819	357	2	metric	metric	ADJ
ejpam-4819	357	3	fixed	fix	VERB
ejpam-4819	357	4	point	point	NOUN
ejpam-4819	357	5	theory	theory	NOUN
ejpam-4819	357	6	:	:	PUNCT
ejpam-4819	357	7	applications	application	NOUN
ejpam-4819	357	8	in	in	ADP
ejpam-4819	357	9	science	science	NOUN
ejpam-4819	357	10	,	,	PUNCT
ejpam-4819	357	11	engineering	engineering	NOUN
ejpam-4819	357	12	and	and	CCONJ
ejpam-4819	357	13	behavioural	behavioural	ADJ
ejpam-4819	357	14	sciences	sciences	PROPN
ejpam-4819	357	15	.	.	PUNCT
ejpam-4819	358	1	singapore	singapore	PROPN
ejpam-4819	358	2	:	:	PUNCT
ejpam-4819	358	3	springer	springer	NOUN
ejpam-4819	358	4	,	,	PUNCT
ejpam-4819	358	5	2021	2021	NUM
ejpam-4819	358	6	.	.	PUNCT
ejpam-4819	359	1	[	[	X
ejpam-4819	359	2	9	9	NUM
ejpam-4819	359	3	]	]	X
ejpam-4819	359	4	p	p	NOUN
ejpam-4819	359	5	debnath	debnath	NOUN
ejpam-4819	359	6	,	,	PUNCT
ejpam-4819	359	7	d	d	X
ejpam-4819	359	8	mitrović	mitrović	ADJ
ejpam-4819	359	9	,	,	PUNCT
ejpam-4819	359	10	and	and	CCONJ
ejpam-4819	359	11	s	s	VERB
ejpam-4819	359	12	radenovic	radenovic	ADJ
ejpam-4819	359	13	.	.	PUNCT
ejpam-4819	360	1	interpolative	interpolative	ADJ
ejpam-4819	360	2	hardy	hardy	ADJ
ejpam-4819	360	3	-	-	PUNCT
ejpam-4819	360	4	rogers	roger	NOUN
ejpam-4819	360	5	and	and	CCONJ
ejpam-4819	360	6	reich	reich	NOUN
ejpam-4819	360	7	-	-	PUNCT
ejpam-4819	360	8	rusciric	rusciric	ADJ
ejpam-4819	360	9	type	type	NOUN
ejpam-4819	360	10	contractions	contraction	NOUN
ejpam-4819	360	11	in	in	ADP
ejpam-4819	360	12	b	b	NOUN
ejpam-4819	360	13	-	-	ADJ
ejpam-4819	360	14	metric	metric	ADJ
ejpam-4819	360	15	spaces	space	NOUN
ejpam-4819	360	16	and	and	CCONJ
ejpam-4819	360	17	rectangular	rectangular	ADJ
ejpam-4819	360	18	b	b	X
ejpam-4819	360	19	-	-	ADJ
ejpam-4819	360	20	metric	metric	ADJ
ejpam-4819	360	21	spaces	space	NOUN
ejpam-4819	360	22	.	.	PUNCT
ejpam-4819	361	1	math	math	NOUN
ejpam-4819	361	2	.	.	PUNCT
ejpam-4819	362	1	vesnik	vesnik	PROPN
ejpam-4819	362	2	,	,	PUNCT
ejpam-4819	362	3	72:368–374	72:368–374	PROPN
ejpam-4819	362	4	,	,	PUNCT
ejpam-4819	362	5	2020	2020	NUM
ejpam-4819	362	6	.	.	PUNCT
ejpam-4819	363	1	[	[	X
ejpam-4819	363	2	10	10	NUM
ejpam-4819	363	3	]	]	X
ejpam-4819	363	4	y	y	PROPN
ejpam-4819	363	5	gaba	gaba	PROPN
ejpam-4819	363	6	and	and	CCONJ
ejpam-4819	363	7	e	e	PROPN
ejpam-4819	363	8	karapınar	karapınar	NOUN
ejpam-4819	363	9	.	.	PUNCT
ejpam-4819	364	1	a	a	DET
ejpam-4819	364	2	new	new	ADJ
ejpam-4819	364	3	approach	approach	NOUN
ejpam-4819	364	4	to	to	ADP
ejpam-4819	364	5	the	the	DET
ejpam-4819	364	6	interpolative	interpolative	ADJ
ejpam-4819	364	7	contractions	contraction	NOUN
ejpam-4819	364	8	.	.	PUNCT
ejpam-4819	365	1	axioms	axiom	NOUN
ejpam-4819	365	2	,	,	PUNCT
ejpam-4819	365	3	8:110	8:110	NUM
ejpam-4819	365	4	,	,	PUNCT
ejpam-4819	365	5	10	10	NUM
ejpam-4819	365	6	2019	2019	NUM
ejpam-4819	365	7	.	.	PUNCT
ejpam-4819	366	1	[	[	X
ejpam-4819	366	2	11	11	NUM
ejpam-4819	366	3	]	]	X
ejpam-4819	366	4	m	m	VERB
ejpam-4819	366	5	jleli	jleli	ADJ
ejpam-4819	366	6	and	and	CCONJ
ejpam-4819	366	7	b	b	X
ejpam-4819	366	8	samet	samet	NOUN
ejpam-4819	366	9	.	.	PUNCT
ejpam-4819	367	1	a	a	DET
ejpam-4819	367	2	new	new	ADJ
ejpam-4819	367	3	generalization	generalization	NOUN
ejpam-4819	367	4	of	of	ADP
ejpam-4819	367	5	the	the	DET
ejpam-4819	367	6	banach	banach	NOUN
ejpam-4819	367	7	contraction	contraction	NOUN
ejpam-4819	367	8	principle	principle	NOUN
ejpam-4819	367	9	.	.	PUNCT
ejpam-4819	368	1	journal	journal	PROPN
ejpam-4819	368	2	of	of	ADP
ejpam-4819	368	3	inequalities	inequality	NOUN
ejpam-4819	368	4	and	and	CCONJ
ejpam-4819	368	5	applications	application	NOUN
ejpam-4819	368	6	,	,	PUNCT
ejpam-4819	368	7	2014	2014	NUM
ejpam-4819	368	8	,	,	PUNCT
ejpam-4819	368	9	01	01	NUM
ejpam-4819	368	10	2014	2014	NUM
ejpam-4819	368	11	.	.	PUNCT
ejpam-4819	369	1	[	[	X
ejpam-4819	369	2	12	12	NUM
ejpam-4819	369	3	]	]	X
ejpam-4819	369	4	r	r	NOUN
ejpam-4819	369	5	kannan	kannan	PROPN
ejpam-4819	369	6	.	.	PUNCT
ejpam-4819	370	1	some	some	DET
ejpam-4819	370	2	results	result	NOUN
ejpam-4819	370	3	on	on	ADP
ejpam-4819	370	4	fixed	fix	VERB
ejpam-4819	370	5	points	point	NOUN
ejpam-4819	370	6	.	.	PUNCT
ejpam-4819	371	1	bull	bull	NOUN
ejpam-4819	371	2	.	.	PUNCT
ejpam-4819	372	1	cal	cal	PROPN
ejpam-4819	372	2	.	.	PUNCT
ejpam-4819	373	1	math	math	NOUN
ejpam-4819	373	2	.	.	PUNCT
ejpam-4819	374	1	soc	soc	PROPN
ejpam-4819	374	2	.	.	PUNCT
ejpam-4819	375	1	,	,	PUNCT
ejpam-4819	375	2	60:71–76	60:71–76	PROPN
ejpam-4819	375	3	,	,	PUNCT
ejpam-4819	375	4	01	01	NUM
ejpam-4819	375	5	1968	1968	NUM
ejpam-4819	375	6	.	.	PUNCT
ejpam-4819	375	7	references	reference	NOUN
ejpam-4819	375	8	1730	1730	NUM
ejpam-4819	375	9	[	[	X
ejpam-4819	375	10	13	13	NUM
ejpam-4819	375	11	]	]	PUNCT
ejpam-4819	375	12	e	e	X
ejpam-4819	375	13	karapınar	karapınar	NOUN
ejpam-4819	375	14	.	.	PUNCT
ejpam-4819	376	1	revisiting	revisit	VERB
ejpam-4819	376	2	the	the	DET
ejpam-4819	376	3	kannan	kannan	PROPN
ejpam-4819	376	4	type	type	NOUN
ejpam-4819	376	5	contractions	contraction	NOUN
ejpam-4819	376	6	via	via	ADP
ejpam-4819	376	7	interpolation	interpolation	NOUN
ejpam-4819	376	8	.	.	PUNCT
ejpam-4819	377	1	advances	advance	NOUN
ejpam-4819	377	2	in	in	ADP
ejpam-4819	377	3	the	the	DET
ejpam-4819	377	4	theory	theory	NOUN
ejpam-4819	377	5	of	of	ADP
ejpam-4819	377	6	nonlinear	nonlinear	ADJ
ejpam-4819	377	7	analysis	analysis	NOUN
ejpam-4819	377	8	and	and	CCONJ
ejpam-4819	377	9	its	its	PRON
ejpam-4819	377	10	application	application	NOUN
ejpam-4819	377	11	,	,	PUNCT
ejpam-4819	377	12	2:85–87	2:85–87	NUM
ejpam-4819	377	13	,	,	PUNCT
ejpam-4819	377	14	06	06	NUM
ejpam-4819	377	15	2018	2018	NUM
ejpam-4819	377	16	.	.	PUNCT
ejpam-4819	378	1	[	[	X
ejpam-4819	378	2	14	14	NUM
ejpam-4819	378	3	]	]	X
ejpam-4819	378	4	z	z	NOUN
ejpam-4819	378	5	mustafa	mustafa	PROPN
ejpam-4819	378	6	and	and	CCONJ
ejpam-4819	378	7	b	b	NOUN
ejpam-4819	378	8	sims	sim	NOUN
ejpam-4819	378	9	.	.	PUNCT
ejpam-4819	379	1	a	a	DET
ejpam-4819	379	2	new	new	ADJ
ejpam-4819	379	3	approach	approach	NOUN
ejpam-4819	379	4	to	to	ADP
ejpam-4819	379	5	generalized	generalize	VERB
ejpam-4819	379	6	metric	metric	ADJ
ejpam-4819	379	7	spaces	space	NOUN
ejpam-4819	379	8	.	.	PUNCT
ejpam-4819	380	1	journal	journal	PROPN
ejpam-4819	380	2	of	of	ADP
ejpam-4819	380	3	nonlinear	nonlinear	ADJ
ejpam-4819	380	4	and	and	CCONJ
ejpam-4819	380	5	convex	convex	ADJ
ejpam-4819	380	6	analysis	analysis	NOUN
ejpam-4819	380	7	,	,	PUNCT
ejpam-4819	380	8	7:289–297	7:289–297	NUM
ejpam-4819	380	9	,	,	PUNCT
ejpam-4819	380	10	08	08	NUM
ejpam-4819	380	11	2006	2006	NUM
ejpam-4819	380	12	.	.	PUNCT
ejpam-4819	381	1	[	[	X
ejpam-4819	381	2	15	15	NUM
ejpam-4819	381	3	]	]	PUNCT
ejpam-4819	381	4	t	t	NOUN
ejpam-4819	381	5	qawasmeh	qawasmeh	NOUN
ejpam-4819	381	6	.	.	PUNCT
ejpam-4819	382	1	h	h	NOUN
ejpam-4819	382	2	-	-	PUNCT
ejpam-4819	382	3	simulation	simulation	NOUN
ejpam-4819	382	4	functions	function	NOUN
ejpam-4819	382	5	and	and	CCONJ
ejpam-4819	382	6	ωb	ωb	NOUN
ejpam-4819	382	7	-	-	PUNCT
ejpam-4819	382	8	distance	distance	NOUN
ejpam-4819	382	9	mappings	mapping	NOUN
ejpam-4819	382	10	in	in	ADP
ejpam-4819	382	11	the	the	DET
ejpam-4819	382	12	setting	setting	NOUN
ejpam-4819	382	13	of	of	ADP
ejpam-4819	382	14	gbmetric	gbmetric	ADJ
ejpam-4819	382	15	spaces	space	NOUN
ejpam-4819	382	16	and	and	CCONJ
ejpam-4819	382	17	applcation	applcation	NOUN
ejpam-4819	382	18	.	.	PUNCT
ejpam-4819	383	1	nonlinear	nonlinear	ADJ
ejpam-4819	383	2	functional	functional	ADJ
ejpam-4819	383	3	analysis	analysis	NOUN
ejpam-4819	383	4	and	and	CCONJ
ejpam-4819	383	5	applications	application	NOUN
ejpam-4819	383	6	,	,	PUNCT
ejpam-4819	383	7	28	28	NUM
ejpam-4819	383	8	(	(	PUNCT
ejpam-4819	383	9	2):557–570	2):557–570	NUM
ejpam-4819	383	10	,	,	PUNCT
ejpam-4819	383	11	2023	2023	NUM
ejpam-4819	383	12	.	.	PUNCT
ejpam-4819	384	1	[	[	X
ejpam-4819	384	2	16	16	NUM
ejpam-4819	384	3	]	]	PUNCT
ejpam-4819	384	4	t	t	PROPN
ejpam-4819	384	5	qawasmeh	qawasmeh	NOUN
ejpam-4819	384	6	,	,	PUNCT
ejpam-4819	384	7	w	w	PROPN
ejpam-4819	384	8	shatanawi	shatanawi	PROPN
ejpam-4819	384	9	,	,	PUNCT
ejpam-4819	384	10	a	a	DET
ejpam-4819	384	11	bataihah	bataihah	ADJ
ejpam-4819	384	12	,	,	PUNCT
ejpam-4819	384	13	and	and	CCONJ
ejpam-4819	384	14	a	a	DET
ejpam-4819	384	15	tallafha	tallafha	NOUN
ejpam-4819	384	16	.	.	PUNCT
ejpam-4819	385	1	fixed	fix	VERB
ejpam-4819	385	2	point	point	NOUN
ejpam-4819	385	3	results	result	NOUN
ejpam-4819	385	4	and	and	CCONJ
ejpam-4819	385	5	(	(	PUNCT
ejpam-4819	385	6	α	α	NOUN
ejpam-4819	385	7	,	,	PUNCT
ejpam-4819	385	8	β)-triangular	β)-triangular	ADJ
ejpam-4819	385	9	admissibility	admissibility	NOUN
ejpam-4819	385	10	in	in	ADP
ejpam-4819	385	11	the	the	DET
ejpam-4819	385	12	frame	frame	NOUN
ejpam-4819	385	13	of	of	ADP
ejpam-4819	385	14	complete	complete	ADJ
ejpam-4819	385	15	extended	extended	ADJ
ejpam-4819	385	16	b	b	NOUN
ejpam-4819	385	17	-	-	PUNCT
ejpam-4819	385	18	metric	metric	ADJ
ejpam-4819	385	19	spaces	space	NOUN
ejpam-4819	385	20	and	and	CCONJ
ejpam-4819	385	21	application	application	NOUN
ejpam-4819	385	22	.	.	PUNCT
ejpam-4819	386	1	upb	upb	PROPN
ejpam-4819	386	2	sci	sci	PROPN
ejpam-4819	386	3	.	.	PROPN
ejpam-4819	386	4	,	,	PUNCT
ejpam-4819	386	5	series	series	PROPN
ejpam-4819	386	6	a	a	X
ejpam-4819	386	7	,	,	PUNCT
ejpam-4819	386	8	83	83	NUM
ejpam-4819	386	9	(	(	PUNCT
ejpam-4819	386	10	1):113–124	1):113–124	NUM
ejpam-4819	386	11	,	,	PUNCT
ejpam-4819	386	12	2021	2021	NUM
ejpam-4819	386	13	.	.	PUNCT
ejpam-4819	387	1	[	[	X
ejpam-4819	387	2	17	17	NUM
ejpam-4819	387	3	]	]	X
ejpam-4819	387	4	w	w	NOUN
ejpam-4819	387	5	shatanawi	shatanawi	PROPN
ejpam-4819	387	6	,	,	PUNCT
ejpam-4819	387	7	a	a	DET
ejpam-4819	387	8	bataihah	bataihah	ADJ
ejpam-4819	387	9	,	,	PUNCT
ejpam-4819	387	10	and	and	CCONJ
ejpam-4819	387	11	a	a	DET
ejpam-4819	387	12	tallafha	tallafha	NOUN
ejpam-4819	387	13	.	.	PUNCT
ejpam-4819	388	1	four	four	NUM
ejpam-4819	388	2	-	-	PUNCT
ejpam-4819	388	3	step	step	NOUN
ejpam-4819	388	4	iteration	iteration	NOUN
ejpam-4819	388	5	scheme	scheme	NOUN
ejpam-4819	388	6	to	to	PART
ejpam-4819	388	7	approximate	approximate	VERB
ejpam-4819	388	8	fixed	fix	VERB
ejpam-4819	388	9	point	point	NOUN
ejpam-4819	388	10	for	for	ADP
ejpam-4819	388	11	weak	weak	ADJ
ejpam-4819	388	12	contractions	contraction	NOUN
ejpam-4819	388	13	.	.	PUNCT
ejpam-4819	389	1	comput	comput	NOUN
ejpam-4819	389	2	.	.	PUNCT
ejpam-4819	390	1	mater	mater	NOUN
ejpam-4819	390	2	.	.	PUNCT
ejpam-4819	391	1	contin	contin	NOUN
ejpam-4819	391	2	,	,	PUNCT
ejpam-4819	391	3	64:1491–1504	64:1491–1504	NUM
ejpam-4819	391	4	,	,	PUNCT
ejpam-4819	391	5	2020	2020	NUM
ejpam-4819	391	6	.	.	PUNCT
ejpam-4819	392	1	[	[	X
ejpam-4819	392	2	18	18	NUM
ejpam-4819	392	3	]	]	X
ejpam-4819	392	4	w	w	NOUN
ejpam-4819	392	5	shatanawi	shatanawi	NOUN
ejpam-4819	392	6	,	,	PUNCT
ejpam-4819	392	7	t	t	NOUN
ejpam-4819	392	8	qawasmeh	qawasmeh	NOUN
ejpam-4819	392	9	,	,	PUNCT
ejpam-4819	392	10	a	a	DET
ejpam-4819	392	11	bataihah	bataihah	ADJ
ejpam-4819	392	12	,	,	PUNCT
ejpam-4819	392	13	and	and	CCONJ
ejpam-4819	392	14	a	a	DET
ejpam-4819	392	15	tallafha	tallafha	NOUN
ejpam-4819	392	16	.	.	PUNCT
ejpam-4819	393	1	new	new	ADJ
ejpam-4819	393	2	contraction	contraction	NOUN
ejpam-4819	393	3	and	and	CCONJ
ejpam-4819	393	4	some	some	DET
ejpam-4819	393	5	fixed	fix	VERB
ejpam-4819	393	6	point	point	NOUN
ejpam-4819	393	7	results	result	NOUN
ejpam-4819	393	8	with	with	ADP
ejpam-4819	393	9	application	application	NOUN
ejpam-4819	393	10	based	base	VERB
ejpam-4819	393	11	on	on	ADP
ejpam-4819	393	12	extended	extended	ADJ
ejpam-4819	393	13	quasi	quasi	ADJ
ejpam-4819	393	14	b	b	NOUN
ejpam-4819	393	15	-	-	ADJ
ejpam-4819	393	16	metric	metric	ADJ
ejpam-4819	393	17	spaces	space	NOUN
ejpam-4819	393	18	.	.	PUNCT
ejpam-4819	394	1	upb	upb	PROPN
ejpam-4819	394	2	sci	sci	PROPN
ejpam-4819	394	3	.	.	PROPN
ejpam-4819	394	4	,	,	PUNCT
ejpam-4819	394	5	series	series	PROPN
ejpam-4819	394	6	a	a	X
ejpam-4819	394	7	,	,	PUNCT
ejpam-4819	394	8	83	83	NUM
ejpam-4819	394	9	(	(	PUNCT
ejpam-4819	394	10	2):39–48	2):39–48	NUM
ejpam-4819	394	11	,	,	PUNCT
ejpam-4819	394	12	2021	2021	NUM
ejpam-4819	394	13	.	.	PUNCT