id	sid	tid	token	lemma	pos
ejpam-5838	1	1	european	european	PROPN
ejpam-5838	1	2	journal	journal	PROPN
ejpam-5838	1	3	of	of	ADP
ejpam-5838	1	4	pure	pure	ADJ
ejpam-5838	1	5	and	and	CCONJ
ejpam-5838	1	6	applied	applied	ADJ
ejpam-5838	1	7	mathematics	mathematic	NOUN
ejpam-5838	1	8	2025	2025	NUM
ejpam-5838	1	9	,	,	PUNCT
ejpam-5838	1	10	vol	vol	NOUN
ejpam-5838	1	11	.	.	PROPN
ejpam-5838	1	12	18	18	NUM
ejpam-5838	1	13	,	,	PUNCT
ejpam-5838	1	14	issue	issue	NOUN
ejpam-5838	1	15	2	2	NUM
ejpam-5838	1	16	,	,	PUNCT
ejpam-5838	1	17	article	article	NOUN
ejpam-5838	1	18	number	number	NOUN
ejpam-5838	1	19	5838	5838	NUM
ejpam-5838	1	20	issn	issn	VERB
ejpam-5838	1	21	1307	1307	NUM
ejpam-5838	1	22	-	-	SYM
ejpam-5838	1	23	5543	5543	NUM
ejpam-5838	1	24	–	–	PUNCT
ejpam-5838	1	25	ejpam.com	ejpam.com	X
ejpam-5838	1	26	published	publish	VERB
ejpam-5838	1	27	by	by	ADP
ejpam-5838	1	28	new	new	PROPN
ejpam-5838	1	29	york	york	PROPN
ejpam-5838	1	30	business	business	PROPN
ejpam-5838	1	31	global	global	ADJ
ejpam-5838	1	32	characterization	characterization	NOUN
ejpam-5838	1	33	and	and	CCONJ
ejpam-5838	1	34	application	application	NOUN
ejpam-5838	1	35	of	of	ADP
ejpam-5838	1	36	fixed	fix	VERB
ejpam-5838	1	37	point	point	NOUN
ejpam-5838	1	38	theorems	theorem	NOUN
ejpam-5838	1	39	for	for	ADP
ejpam-5838	1	40	3	3	NUM
ejpam-5838	1	41	-	-	PUNCT
ejpam-5838	1	42	self	self	NOUN
ejpam-5838	1	43	mappings	mapping	NOUN
ejpam-5838	1	44	in	in	ADP
ejpam-5838	1	45	generalized	generalized	ADJ
ejpam-5838	1	46	metric	metric	ADJ
ejpam-5838	1	47	spaces	space	NOUN
ejpam-5838	1	48	maha	maha	PROPN
ejpam-5838	1	49	noorwali1	noorwali1	PROPN
ejpam-5838	1	50	,	,	PUNCT
ejpam-5838	1	51	raed	raed	PROPN
ejpam-5838	1	52	hatamleh2	hatamleh2	PROPN
ejpam-5838	1	53	,	,	PUNCT
ejpam-5838	1	54	ahmad	ahmad	PROPN
ejpam-5838	1	55	a.	a.	PROPN
ejpam-5838	1	56	abubaker3	abubaker3	PROPN
ejpam-5838	1	57	,	,	PUNCT
ejpam-5838	1	58	abdallah	abdallah	PROPN
ejpam-5838	1	59	al	al	PROPN
ejpam-5838	1	60	-	-	PUNCT
ejpam-5838	1	61	husban4	husban4	PROPN
ejpam-5838	1	62	,	,	PUNCT
ejpam-5838	1	63	jamil	jamil	PROPN
ejpam-5838	1	64	j.	j.	PROPN
ejpam-5838	1	65	hamja5	hamja5	PROPN
ejpam-5838	1	66	,	,	PUNCT
ejpam-5838	1	67	giorgio	giorgio	PROPN
ejpam-5838	1	68	nordo6	nordo6	PROPN
ejpam-5838	1	69	,	,	PUNCT
ejpam-5838	1	70	takaaki	takaaki	NOUN
ejpam-5838	1	71	fujita7	fujita7	PROPN
ejpam-5838	1	72	,	,	PUNCT
ejpam-5838	1	73	arif	arif	PROPN
ejpam-5838	1	74	mehmood8,∗	mehmood8,∗	PROPN
ejpam-5838	1	75	1	1	NUM
ejpam-5838	1	76	department	department	NOUN
ejpam-5838	1	77	of	of	ADP
ejpam-5838	1	78	mathematics	mathematic	NOUN
ejpam-5838	1	79	,	,	PUNCT
ejpam-5838	1	80	king	king	PROPN
ejpam-5838	1	81	abdulaziz	abdulaziz	PROPN
ejpam-5838	1	82	university	university	PROPN
ejpam-5838	1	83	,	,	PUNCT
ejpam-5838	1	84	jeddah	jeddah	PROPN
ejpam-5838	1	85	,	,	PUNCT
ejpam-5838	1	86	saudi	saudi	PROPN
ejpam-5838	1	87	arabia	arabia	PROPN
ejpam-5838	1	88	2	2	NUM
ejpam-5838	1	89	department	department	NOUN
ejpam-5838	1	90	of	of	ADP
ejpam-5838	1	91	mathematics	mathematic	NOUN
ejpam-5838	1	92	,	,	PUNCT
ejpam-5838	1	93	faculty	faculty	NOUN
ejpam-5838	1	94	of	of	ADP
ejpam-5838	1	95	science	science	NOUN
ejpam-5838	1	96	,	,	PUNCT
ejpam-5838	1	97	jadara	jadara	PROPN
ejpam-5838	1	98	university	university	PROPN
ejpam-5838	1	99	,	,	PUNCT
ejpam-5838	1	100	p.o	p.o	PROPN
ejpam-5838	1	101	.	.	PROPN
ejpam-5838	1	102	box	box	PROPN
ejpam-5838	1	103	733	733	NUM
ejpam-5838	1	104	,	,	PUNCT
ejpam-5838	1	105	irbid	irbid	ADJ
ejpam-5838	1	106	21110	21110	NUM
ejpam-5838	1	107	,	,	PUNCT
ejpam-5838	1	108	jordan	jordan	PROPN
ejpam-5838	1	109	3	3	NUM
ejpam-5838	1	110	faculty	faculty	NOUN
ejpam-5838	1	111	of	of	ADP
ejpam-5838	1	112	computer	computer	NOUN
ejpam-5838	1	113	studies	study	NOUN
ejpam-5838	1	114	,	,	PUNCT
ejpam-5838	1	115	arab	arab	ADJ
ejpam-5838	1	116	open	open	PROPN
ejpam-5838	1	117	university	university	PROPN
ejpam-5838	1	118	,	,	PUNCT
ejpam-5838	1	119	saudi	saudi	PROPN
ejpam-5838	1	120	arabia	arabia	PROPN
ejpam-5838	1	121	4	4	NUM
ejpam-5838	1	122	department	department	NOUN
ejpam-5838	1	123	of	of	ADP
ejpam-5838	1	124	mathematics	mathematic	NOUN
ejpam-5838	1	125	,	,	PUNCT
ejpam-5838	1	126	faculty	faculty	NOUN
ejpam-5838	1	127	of	of	ADP
ejpam-5838	1	128	science	science	NOUN
ejpam-5838	1	129	and	and	CCONJ
ejpam-5838	1	130	technology	technology	NOUN
ejpam-5838	1	131	,	,	PUNCT
ejpam-5838	1	132	irbid	irbid	VERB
ejpam-5838	1	133	national	national	ADJ
ejpam-5838	1	134	university	university	PROPN
ejpam-5838	1	135	,	,	PUNCT
ejpam-5838	1	136	p.o	p.o	PROPN
ejpam-5838	1	137	.	.	PROPN
ejpam-5838	1	138	box	box	PROPN
ejpam-5838	1	139	:	:	PUNCT
ejpam-5838	1	140	2600	2600	NUM
ejpam-5838	1	141	irbid	irbid	ADJ
ejpam-5838	1	142	,	,	PUNCT
ejpam-5838	1	143	jordan	jordan	PROPN
ejpam-5838	1	144	5	5	NUM
ejpam-5838	1	145	department	department	NOUN
ejpam-5838	1	146	of	of	ADP
ejpam-5838	1	147	mathematics	mathematic	NOUN
ejpam-5838	1	148	,	,	PUNCT
ejpam-5838	1	149	college	college	NOUN
ejpam-5838	1	150	of	of	ADP
ejpam-5838	1	151	arts	art	NOUN
ejpam-5838	1	152	and	and	CCONJ
ejpam-5838	1	153	sciences	science	NOUN
ejpam-5838	1	154	,	,	PUNCT
ejpam-5838	1	155	msu	msu	PROPN
ejpam-5838	1	156	-	-	PUNCT
ejpam-5838	1	157	tawi	tawi	NOUN
ejpam-5838	1	158	-	-	PUNCT
ejpam-5838	1	159	tawi	tawi	NOUN
ejpam-5838	1	160	college	college	PROPN
ejpam-5838	1	161	of	of	ADP
ejpam-5838	1	162	technology	technology	NOUN
ejpam-5838	1	163	and	and	CCONJ
ejpam-5838	1	164	oceanography	oceanography	NOUN
ejpam-5838	1	165	,	,	PUNCT
ejpam-5838	1	166	7500	7500	NUM
ejpam-5838	1	167	philippines	philippine	NOUN
ejpam-5838	1	168	6	6	NUM
ejpam-5838	1	169	mift	mift	NOUN
ejpam-5838	1	170	department	department	NOUN
ejpam-5838	1	171	(	(	PUNCT
ejpam-5838	1	172	mathematical	mathematical	ADJ
ejpam-5838	1	173	and	and	CCONJ
ejpam-5838	1	174	computer	computer	NOUN
ejpam-5838	1	175	science	science	NOUN
ejpam-5838	1	176	,	,	PUNCT
ejpam-5838	1	177	physical	physical	ADJ
ejpam-5838	1	178	sciences	science	NOUN
ejpam-5838	1	179	and	and	CCONJ
ejpam-5838	1	180	earth	earth	NOUN
ejpam-5838	1	181	sciences	sciences	PROPN
ejpam-5838	1	182	)	)	PUNCT
ejpam-5838	1	183	university	university	PROPN
ejpam-5838	1	184	of	of	ADP
ejpam-5838	1	185	messina	messina	PROPN
ejpam-5838	1	186	,	,	PUNCT
ejpam-5838	1	187	98166	98166	NUM
ejpam-5838	1	188	sant’agata	sant’agata	ADJ
ejpam-5838	1	189	,	,	PUNCT
ejpam-5838	1	190	messina	messina	PROPN
ejpam-5838	1	191	,	,	PUNCT
ejpam-5838	1	192	italy	italy	PROPN
ejpam-5838	1	193	7	7	NUM
ejpam-5838	1	194	independent	independent	ADJ
ejpam-5838	1	195	researcher	researcher	NOUN
ejpam-5838	1	196	,	,	PUNCT
ejpam-5838	1	197	shinjuku	shinjuku	PROPN
ejpam-5838	1	198	,	,	PUNCT
ejpam-5838	1	199	shinjuku	shinjuku	PROPN
ejpam-5838	1	200	-	-	PUNCT
ejpam-5838	1	201	ku	ku	PROPN
ejpam-5838	1	202	,	,	PUNCT
ejpam-5838	1	203	tokyo	tokyo	PROPN
ejpam-5838	1	204	,	,	PUNCT
ejpam-5838	1	205	japan	japan	PROPN
ejpam-5838	1	206	.	.	PROPN
ejpam-5838	2	1	8	8	NUM
ejpam-5838	2	2	department	department	NOUN
ejpam-5838	2	3	of	of	ADP
ejpam-5838	2	4	mathematics	mathematics	PROPN
ejpam-5838	2	5	,	,	PUNCT
ejpam-5838	2	6	institute	institute	PROPN
ejpam-5838	2	7	of	of	ADP
ejpam-5838	2	8	numerical	numerical	PROPN
ejpam-5838	2	9	sciences	sciences	PROPN
ejpam-5838	2	10	,	,	PUNCT
ejpam-5838	2	11	gomal	gomal	ADJ
ejpam-5838	2	12	university	university	NOUN
ejpam-5838	2	13	,	,	PUNCT
ejpam-5838	2	14	dera	dera	PROPN
ejpam-5838	2	15	ismail	ismail	PROPN
ejpam-5838	2	16	khan	khan	PROPN
ejpam-5838	2	17	29050	29050	NUM
ejpam-5838	2	18	,	,	PUNCT
ejpam-5838	2	19	kpk	kpk	PROPN
ejpam-5838	2	20	,	,	PUNCT
ejpam-5838	2	21	pakistan	pakistan	PROPN
ejpam-5838	2	22	abstract	abstract	NOUN
ejpam-5838	2	23	.	.	PUNCT
ejpam-5838	3	1	in	in	ADP
ejpam-5838	3	2	this	this	DET
ejpam-5838	3	3	paper	paper	NOUN
ejpam-5838	3	4	,	,	PUNCT
ejpam-5838	3	5	we	we	PRON
ejpam-5838	3	6	investigate	investigate	VERB
ejpam-5838	3	7	new	new	ADJ
ejpam-5838	3	8	contraction	contraction	NOUN
ejpam-5838	3	9	results	result	VERB
ejpam-5838	3	10	for	for	ADP
ejpam-5838	3	11	3	3	NUM
ejpam-5838	3	12	-	-	PUNCT
ejpam-5838	3	13	self	self	NOUN
ejpam-5838	3	14	-	-	PUNCT
ejpam-5838	3	15	mappings	mapping	NOUN
ejpam-5838	3	16	on	on	ADP
ejpam-5838	3	17	generalized	generalized	ADJ
ejpam-5838	3	18	metric	metric	ADJ
ejpam-5838	3	19	spaces	space	NOUN
ejpam-5838	3	20	(	(	PUNCT
ejpam-5838	3	21	gm	gm	NOUN
ejpam-5838	3	22	-	-	PUNCT
ejpam-5838	3	23	spaces	space	NOUN
ejpam-5838	3	24	)	)	PUNCT
ejpam-5838	3	25	and	and	CCONJ
ejpam-5838	3	26	develop	develop	VERB
ejpam-5838	3	27	and	and	CCONJ
ejpam-5838	3	28	highlight	highlight	VERB
ejpam-5838	3	29	the	the	DET
ejpam-5838	3	30	importance	importance	NOUN
ejpam-5838	3	31	of	of	ADP
ejpam-5838	3	32	several	several	ADJ
ejpam-5838	3	33	particular	particular	ADJ
ejpam-5838	3	34	common	common	ADJ
ejpam-5838	3	35	fixed	fix	VERB
ejpam-5838	3	36	point	point	NOUN
ejpam-5838	3	37	(	(	PUNCT
ejpam-5838	3	38	cfp	cfp	NOUN
ejpam-5838	3	39	)	)	PUNCT
ejpam-5838	3	40	theorems	theorem	NOUN
ejpam-5838	3	41	.	.	PUNCT
ejpam-5838	4	1	our	our	PRON
ejpam-5838	4	2	study	study	NOUN
ejpam-5838	4	3	contributes	contribute	VERB
ejpam-5838	4	4	to	to	ADP
ejpam-5838	4	5	the	the	DET
ejpam-5838	4	6	theoretical	theoretical	ADJ
ejpam-5838	4	7	framework	framework	NOUN
ejpam-5838	4	8	of	of	ADP
ejpam-5838	4	9	fixed	fix	VERB
ejpam-5838	4	10	point	point	NOUN
ejpam-5838	4	11	theory	theory	NOUN
ejpam-5838	4	12	by	by	ADP
ejpam-5838	4	13	highlighting	highlight	VERB
ejpam-5838	4	14	the	the	DET
ejpam-5838	4	15	existence	existence	NOUN
ejpam-5838	4	16	of	of	ADP
ejpam-5838	4	17	such	such	ADJ
ejpam-5838	4	18	points	point	NOUN
ejpam-5838	4	19	and	and	CCONJ
ejpam-5838	4	20	thoroughly	thoroughly	ADV
ejpam-5838	4	21	proving	prove	VERB
ejpam-5838	4	22	their	their	PRON
ejpam-5838	4	23	uniqueness	uniqueness	NOUN
ejpam-5838	4	24	.	.	PUNCT
ejpam-5838	5	1	as	as	ADP
ejpam-5838	5	2	a	a	DET
ejpam-5838	5	3	practical	practical	ADJ
ejpam-5838	5	4	application	application	NOUN
ejpam-5838	5	5	of	of	ADP
ejpam-5838	5	6	our	our	PRON
ejpam-5838	5	7	theoretical	theoretical	ADJ
ejpam-5838	5	8	findings	finding	NOUN
ejpam-5838	5	9	,	,	PUNCT
ejpam-5838	5	10	we	we	PRON
ejpam-5838	5	11	design	design	VERB
ejpam-5838	5	12	and	and	CCONJ
ejpam-5838	5	13	analyze	analyze	VERB
ejpam-5838	5	14	a	a	DET
ejpam-5838	5	15	convincing	convincing	ADJ
ejpam-5838	5	16	case	case	NOUN
ejpam-5838	5	17	including	include	VERB
ejpam-5838	5	18	3	3	NUM
ejpam-5838	5	19	-	-	PUNCT
ejpam-5838	5	20	self	self	NOUN
ejpam-5838	5	21	mappings	mapping	NOUN
ejpam-5838	5	22	to	to	PART
ejpam-5838	5	23	further	far	ADV
ejpam-5838	5	24	support	support	VERB
ejpam-5838	5	25	the	the	DET
ejpam-5838	5	26	uniqueness	uniqueness	NOUN
ejpam-5838	5	27	of	of	ADP
ejpam-5838	5	28	a	a	DET
ejpam-5838	5	29	cfp	cfp	NOUN
ejpam-5838	5	30	for	for	ADP
ejpam-5838	5	31	generalized	generalized	ADJ
ejpam-5838	5	32	contractions	contraction	NOUN
ejpam-5838	5	33	in	in	ADP
ejpam-5838	5	34	the	the	DET
ejpam-5838	5	35	given	give	VERB
ejpam-5838	5	36	space	space	NOUN
ejpam-5838	5	37	.	.	PUNCT
ejpam-5838	6	1	we	we	PRON
ejpam-5838	6	2	also	also	ADV
ejpam-5838	6	3	provide	provide	VERB
ejpam-5838	6	4	a	a	DET
ejpam-5838	6	5	solid	solid	ADJ
ejpam-5838	6	6	and	and	CCONJ
ejpam-5838	6	7	perceptive	perceptive	ADJ
ejpam-5838	6	8	application	application	NOUN
ejpam-5838	6	9	pertaining	pertain	VERB
ejpam-5838	6	10	to	to	ADP
ejpam-5838	6	11	nonlinear	nonlinear	ADJ
ejpam-5838	6	12	integral	integral	ADJ
ejpam-5838	6	13	equations	equation	NOUN
ejpam-5838	6	14	to	to	PART
ejpam-5838	6	15	further	far	ADV
ejpam-5838	6	16	support	support	VERB
ejpam-5838	6	17	the	the	DET
ejpam-5838	6	18	wider	wide	ADJ
ejpam-5838	6	19	applicability	applicability	NOUN
ejpam-5838	6	20	of	of	ADP
ejpam-5838	6	21	our	our	PRON
ejpam-5838	6	22	primary	primary	ADJ
ejpam-5838	6	23	contributions	contribution	NOUN
ejpam-5838	6	24	,	,	PUNCT
ejpam-5838	6	25	demonstrating	demonstrate	VERB
ejpam-5838	6	26	the	the	DET
ejpam-5838	6	27	usefulness	usefulness	NOUN
ejpam-5838	6	28	of	of	ADP
ejpam-5838	6	29	our	our	PRON
ejpam-5838	6	30	discoveries	discovery	NOUN
ejpam-5838	6	31	in	in	ADP
ejpam-5838	6	32	mathematical	mathematical	ADJ
ejpam-5838	6	33	analysis	analysis	NOUN
ejpam-5838	6	34	and	and	CCONJ
ejpam-5838	6	35	beyond	beyond	ADP
ejpam-5838	6	36	.	.	PUNCT
ejpam-5838	7	1	an	an	DET
ejpam-5838	7	2	excellent	excellent	ADJ
ejpam-5838	7	3	example	example	NOUN
ejpam-5838	7	4	is	be	AUX
ejpam-5838	7	5	developed	develop	VERB
ejpam-5838	7	6	for	for	ADP
ejpam-5838	7	7	better	well	ADJ
ejpam-5838	7	8	understanding	understand	VERB
ejpam-5838	7	9	the	the	DET
ejpam-5838	7	10	results	result	NOUN
ejpam-5838	7	11	.	.	PUNCT
ejpam-5838	8	1	2020	2020	NUM
ejpam-5838	8	2	mathematics	mathematic	NOUN
ejpam-5838	8	3	subject	subject	NOUN
ejpam-5838	8	4	classifications	classification	NOUN
ejpam-5838	8	5	:	:	PUNCT
ejpam-5838	8	6	54a05	54a05	NUM
ejpam-5838	8	7	key	key	ADJ
ejpam-5838	8	8	words	word	NOUN
ejpam-5838	8	9	and	and	CCONJ
ejpam-5838	8	10	phrases	phrase	NOUN
ejpam-5838	8	11	:	:	PUNCT
ejpam-5838	8	12	common	common	ADJ
ejpam-5838	8	13	fixed	fix	VERB
ejpam-5838	8	14	point	point	NOUN
ejpam-5838	8	15	gm	gm	NOUN
ejpam-5838	8	16	-	-	PUNCT
ejpam-5838	8	17	space	space	NOUN
ejpam-5838	8	18	,	,	PUNCT
ejpam-5838	8	19	contraction	contraction	NOUN
ejpam-5838	8	20	conditions	condition	NOUN
ejpam-5838	8	21	,	,	PUNCT
ejpam-5838	8	22	nonlinear	nonlinear	ADJ
ejpam-5838	8	23	integral	integral	ADJ
ejpam-5838	8	24	equations	equation	NOUN
ejpam-5838	8	25	1	1	NUM
ejpam-5838	8	26	.	.	PUNCT
ejpam-5838	9	1	introduction	introduction	NOUN
ejpam-5838	9	2	due	due	ADP
ejpam-5838	9	3	to	to	ADP
ejpam-5838	9	4	its	its	PRON
ejpam-5838	9	5	theoretical	theoretical	ADJ
ejpam-5838	9	6	significance	significance	NOUN
ejpam-5838	9	7	and	and	CCONJ
ejpam-5838	9	8	wide	wide	ADJ
ejpam-5838	9	9	range	range	NOUN
ejpam-5838	9	10	of	of	ADP
ejpam-5838	9	11	applications	application	NOUN
ejpam-5838	9	12	,	,	PUNCT
ejpam-5838	9	13	the	the	DET
ejpam-5838	9	14	study	study	NOUN
ejpam-5838	9	15	of	of	ADP
ejpam-5838	9	16	f	f	PROPN
ejpam-5838	9	17	-points	-point	NOUN
ejpam-5838	9	18	in	in	ADP
ejpam-5838	9	19	gm	gm	PROPN
ejpam-5838	9	20	-	-	PUNCT
ejpam-5838	9	21	spaces	space	NOUN
ejpam-5838	9	22	under	under	ADP
ejpam-5838	9	23	generalized	generalized	ADJ
ejpam-5838	9	24	contractions	contraction	NOUN
ejpam-5838	9	25	has	have	AUX
ejpam-5838	9	26	garnered	garner	VERB
ejpam-5838	9	27	a	a	DET
ejpam-5838	9	28	lot	lot	NOUN
ejpam-5838	9	29	of	of	ADP
ejpam-5838	9	30	interest	interest	NOUN
ejpam-5838	9	31	.	.	PUNCT
ejpam-5838	10	1	the	the	DET
ejpam-5838	10	2	presence	presence	NOUN
ejpam-5838	10	3	and	and	CCONJ
ejpam-5838	10	4	uniqueness	uniqueness	NOUN
ejpam-5838	10	5	of	of	ADP
ejpam-5838	10	6	f	f	PROPN
ejpam-5838	10	7	-points	-point	NOUN
ejpam-5838	10	8	,	,	PUNCT
ejpam-5838	10	9	the	the	DET
ejpam-5838	10	10	convergence	convergence	NOUN
ejpam-5838	10	11	behavior	behavior	NOUN
ejpam-5838	10	12	of	of	ADP
ejpam-5838	10	13	iterative	iterative	NOUN
ejpam-5838	10	14	sequences	sequence	NOUN
ejpam-5838	10	15	produced	produce	VERB
ejpam-5838	10	16	by	by	ADP
ejpam-5838	10	17	generalized	generalized	ADJ
ejpam-5838	10	18	contractions	contraction	NOUN
ejpam-5838	10	19	,	,	PUNCT
ejpam-5838	10	20	and	and	CCONJ
ejpam-5838	10	21	the	the	DET
ejpam-5838	10	22	creation	creation	NOUN
ejpam-5838	10	23	of	of	ADP
ejpam-5838	10	24	mathematical	mathematical	ADJ
ejpam-5838	10	25	models	model	NOUN
ejpam-5838	10	26	for	for	ADP
ejpam-5838	10	27	practical	practical	ADJ
ejpam-5838	10	28	issues	issue	NOUN
ejpam-5838	10	29	are	be	AUX
ejpam-5838	10	30	among	among	ADP
ejpam-5838	10	31	the	the	DET
ejpam-5838	10	32	main	main	ADJ
ejpam-5838	10	33	areas	area	NOUN
ejpam-5838	10	34	of	of	ADP
ejpam-5838	10	35	interest	interest	NOUN
ejpam-5838	10	36	for	for	ADP
ejpam-5838	10	37	this	this	DET
ejpam-5838	10	38	field	field	NOUN
ejpam-5838	10	39	of	of	ADP
ejpam-5838	10	40	study	study	NOUN
ejpam-5838	10	41	.	.	PUNCT
ejpam-5838	11	1	although	although	SCONJ
ejpam-5838	11	2	the	the	DET
ejpam-5838	11	3	idea	idea	NOUN
ejpam-5838	11	4	of	of	ADP
ejpam-5838	11	5	fixed	fix	VERB
ejpam-5838	11	6	point	point	NOUN
ejpam-5838	11	7	theory	theory	NOUN
ejpam-5838	11	8	(	(	PUNCT
ejpam-5838	11	9	fpt	fpt	PROPN
ejpam-5838	11	10	)	)	PUNCT
ejpam-5838	11	11	was	be	AUX
ejpam-5838	11	12	first	first	ADV
ejpam-5838	11	13	proposed	propose	VERB
ejpam-5838	11	14	by	by	ADP
ejpam-5838	11	15	liouville	liouville	NOUN
ejpam-5838	11	16	in	in	ADP
ejpam-5838	11	17	1837	1837	NUM
ejpam-5838	11	18	and	and	CCONJ
ejpam-5838	11	19	picard	picard	NOUN
ejpam-5838	11	20	in	in	ADP
ejpam-5838	11	21	1890	1890	NUM
ejpam-5838	11	22	,	,	PUNCT
ejpam-5838	11	23	banach	banach	NOUN
ejpam-5838	11	24	[	[	X
ejpam-5838	11	25	1	1	NUM
ejpam-5838	11	26	]	]	PUNCT
ejpam-5838	11	27	established	establish	VERB
ejpam-5838	11	28	the	the	DET
ejpam-5838	11	29	fundamentals	fundamental	NOUN
ejpam-5838	11	30	of	of	ADP
ejpam-5838	11	31	∗corresponding	∗corresponde	VERB
ejpam-5838	11	32	author	author	NOUN
ejpam-5838	11	33	.	.	PUNCT
ejpam-5838	12	1	doi	doi	NOUN
ejpam-5838	12	2	:	:	PUNCT
ejpam-5838	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5838	https://doi.org/10.29020/nybg.ejpam.v18i2.5838	NOUN
ejpam-5838	12	4	email	email	NOUN
ejpam-5838	12	5	addresses	address	NOUN
ejpam-5838	12	6	:	:	PUNCT
ejpam-5838	12	7	(	(	PUNCT
ejpam-5838	12	8	mnorwali@kau.edu.sa	mnorwali@kau.edu.sa	NOUN
ejpam-5838	12	9	)	)	PUNCT
ejpam-5838	12	10	(	(	PUNCT
ejpam-5838	12	11	m.	m.	NOUN
ejpam-5838	12	12	noorwali	noorwali	PROPN
ejpam-5838	12	13	)	)	PUNCT
ejpam-5838	12	14	,	,	PUNCT
ejpam-5838	12	15	(	(	PUNCT
ejpam-5838	12	16	raed@jadara.edu.jo	raed@jadara.edu.jo	NOUN
ejpam-5838	12	17	)	)	PUNCT
ejpam-5838	12	18	(	(	PUNCT
ejpam-5838	12	19	r.	r.	PROPN
ejpam-5838	12	20	hatamleh	hatamleh	PROPN
ejpam-5838	12	21	)	)	PUNCT
ejpam-5838	12	22	,	,	PUNCT
ejpam-5838	12	23	(	(	PUNCT
ejpam-5838	12	24	a.abubaker@arabou.edu.sa	a.abubaker@arabou.edu.sa	PROPN
ejpam-5838	12	25	)	)	PUNCT
ejpam-5838	12	26	(	(	PUNCT
ejpam-5838	12	27	a.	a.	NOUN
ejpam-5838	12	28	a.	a.	NOUN
ejpam-5838	12	29	abubaker	abubaker	PROPN
ejpam-5838	12	30	)	)	PUNCT
ejpam-5838	12	31	,	,	PUNCT
ejpam-5838	12	32	(	(	PUNCT
ejpam-5838	12	33	dralhosban@inu.edu.jo	dralhosban@inu.edu.jo	NOUN
ejpam-5838	12	34	)	)	PUNCT
ejpam-5838	12	35	(	(	PUNCT
ejpam-5838	12	36	a.	a.	PROPN
ejpam-5838	12	37	al	al	PROPN
ejpam-5838	12	38	-	-	PUNCT
ejpam-5838	12	39	husban	husban	PROPN
ejpam-5838	12	40	)	)	PUNCT
ejpam-5838	12	41	,	,	PUNCT
ejpam-5838	12	42	(	(	PUNCT
ejpam-5838	12	43	jamilhamja@msutawi-tawi.edu.ph	jamilhamja@msutawi-tawi.edu.ph	PROPN
ejpam-5838	12	44	)	)	PUNCT
ejpam-5838	12	45	(	(	PUNCT
ejpam-5838	12	46	j.	j.	PROPN
ejpam-5838	12	47	j.	j.	PROPN
ejpam-5838	12	48	hamja	hamja	PROPN
ejpam-5838	12	49	)	)	PUNCT
ejpam-5838	12	50	,	,	PUNCT
ejpam-5838	12	51	(	(	PUNCT
ejpam-5838	12	52	giorgio.nordo@unime.it	giorgio.nordo@unime.it	PROPN
ejpam-5838	12	53	)	)	PUNCT
ejpam-5838	12	54	(	(	PUNCT
ejpam-5838	12	55	g.	g.	PROPN
ejpam-5838	12	56	nordo	nordo	PROPN
ejpam-5838	12	57	)	)	PUNCT
ejpam-5838	12	58	,	,	PUNCT
ejpam-5838	12	59	(	(	PUNCT
ejpam-5838	12	60	t171d603@gunma-u.ac.jp	t171d603@gunma-u.ac.jp	NUM
ejpam-5838	12	61	)	)	PUNCT
ejpam-5838	12	62	(	(	PUNCT
ejpam-5838	12	63	t.	t.	PROPN
ejpam-5838	12	64	fujita	fujita	PROPN
ejpam-5838	12	65	)	)	PUNCT
ejpam-5838	12	66	,	,	PUNCT
ejpam-5838	12	67	(	(	PUNCT
ejpam-5838	12	68	mehdaniyal@gmail.com	mehdaniyal@gmail.com	X
ejpam-5838	12	69	)	)	PUNCT
ejpam-5838	12	70	(	(	PUNCT
ejpam-5838	12	71	a.	a.	PROPN
ejpam-5838	12	72	mehmood	mehmood	PROPN
ejpam-5838	12	73	)	)	PUNCT
ejpam-5838	12	74	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5838	12	75	1	1	NUM
ejpam-5838	12	76	copyright	copyright	NOUN
ejpam-5838	12	77	:	:	PUNCT
ejpam-5838	13	1	©	©	PROPN
ejpam-5838	13	2	2025	2025	NUM
ejpam-5838	13	3	the	the	DET
ejpam-5838	13	4	author(s	author(s	NOUN
ejpam-5838	13	5	)	)	PUNCT
ejpam-5838	13	6	.	.	PUNCT
ejpam-5838	14	1	(	(	PUNCT
ejpam-5838	14	2	cc	cc	NOUN
ejpam-5838	14	3	by	by	ADP
ejpam-5838	14	4	-	-	PUNCT
ejpam-5838	14	5	nc	nc	PROPN
ejpam-5838	14	6	4.0	4.0	NUM
ejpam-5838	14	7	)	)	PUNCT
ejpam-5838	14	8	m.	m.	NOUN
ejpam-5838	14	9	noorwali	noorwali	PROPN
ejpam-5838	14	10	et	et	PROPN
ejpam-5838	14	11	al/	al/	PROPN
ejpam-5838	14	12	/	/	SYM
ejpam-5838	14	13	eur	eur	PROPN
ejpam-5838	14	14	.	.	PUNCT
ejpam-5838	15	1	j.	j.	PROPN
ejpam-5838	15	2	pure	pure	PROPN
ejpam-5838	15	3	appl	appl	PROPN
ejpam-5838	15	4	.	.	PROPN
ejpam-5838	15	5	math	math	PROPN
ejpam-5838	15	6	,	,	PUNCT
ejpam-5838	15	7	18	18	NUM
ejpam-5838	15	8	(	(	PUNCT
ejpam-5838	15	9	2	2	NUM
ejpam-5838	15	10	)	)	PUNCT
ejpam-5838	15	11	(	(	PUNCT
ejpam-5838	15	12	2025	2025	NUM
ejpam-5838	15	13	)	)	PUNCT
ejpam-5838	15	14	,	,	PUNCT
ejpam-5838	15	15	5838	5838	NUM
ejpam-5838	15	16	2	2	NUM
ejpam-5838	15	17	of	of	ADP
ejpam-5838	15	18	16	16	NUM
ejpam-5838	15	19	fpt	fpt	NOUN
ejpam-5838	15	20	with	with	ADP
ejpam-5838	15	21	a	a	DET
ejpam-5838	15	22	famous	famous	ADJ
ejpam-5838	15	23	theorem	theorem	NOUN
ejpam-5838	15	24	.	.	PUNCT
ejpam-5838	16	1	a	a	DET
ejpam-5838	16	2	single	single	ADV
ejpam-5838	16	3	-	-	PUNCT
ejpam-5838	16	4	valued	value	VERB
ejpam-5838	16	5	contractive	contractive	ADJ
ejpam-5838	16	6	mapping	mapping	NOUN
ejpam-5838	16	7	with	with	ADP
ejpam-5838	16	8	a	a	DET
ejpam-5838	16	9	unique	unique	ADJ
ejpam-5838	16	10	fixed	fix	VERB
ejpam-5838	16	11	point	point	NOUN
ejpam-5838	16	12	(	(	PUNCT
ejpam-5838	16	13	fp	fp	X
ejpam-5838	16	14	)	)	PUNCT
ejpam-5838	16	15	in	in	ADP
ejpam-5838	16	16	a	a	DET
ejpam-5838	16	17	complete	complete	ADJ
ejpam-5838	16	18	metric	metric	ADJ
ejpam-5838	16	19	space	space	NOUN
ejpam-5838	16	20	(	(	PUNCT
ejpam-5838	16	21	cms	cms	NOUN
ejpam-5838	16	22	)	)	PUNCT
ejpam-5838	16	23	is	be	AUX
ejpam-5838	16	24	the	the	DET
ejpam-5838	16	25	subject	subject	NOUN
ejpam-5838	16	26	of	of	ADP
ejpam-5838	16	27	the	the	DET
ejpam-5838	16	28	banach	banach	NOUN
ejpam-5838	16	29	contraction	contraction	NOUN
ejpam-5838	16	30	principle	principle	NOUN
ejpam-5838	16	31	(	(	PUNCT
ejpam-5838	16	32	bcp	bcp	PROPN
ejpam-5838	16	33	)	)	PUNCT
ejpam-5838	16	34	.	.	PUNCT
ejpam-5838	17	1	an	an	DET
ejpam-5838	17	2	inventive	inventive	ADJ
ejpam-5838	17	3	extension	extension	NOUN
ejpam-5838	17	4	of	of	ADP
ejpam-5838	17	5	kannan	kannan	PROPN
ejpam-5838	17	6	contractions	contraction	NOUN
ejpam-5838	17	7	and	and	CCONJ
ejpam-5838	17	8	associated	associate	VERB
ejpam-5838	17	9	fixed	fix	VERB
ejpam-5838	17	10	point	point	NOUN
ejpam-5838	17	11	results	result	NOUN
ejpam-5838	17	12	was	be	AUX
ejpam-5838	17	13	presented	present	VERB
ejpam-5838	17	14	by	by	ADP
ejpam-5838	17	15	batra	batra	PROPN
ejpam-5838	17	16	et	et	PROPN
ejpam-5838	17	17	al	al	PROPN
ejpam-5838	17	18	.	.	PUNCT
ejpam-5838	18	1	[	[	X
ejpam-5838	18	2	2	2	NUM
ejpam-5838	18	3	]	]	PUNCT
ejpam-5838	18	4	.	.	PUNCT
ejpam-5838	19	1	debnath	debnath	PROPN
ejpam-5838	20	1	[	[	X
ejpam-5838	20	2	3	3	X
ejpam-5838	20	3	]	]	PUNCT
ejpam-5838	20	4	proved	prove	VERB
ejpam-5838	20	5	the	the	DET
ejpam-5838	20	6	common	common	ADJ
ejpam-5838	20	7	fixed	fix	VERB
ejpam-5838	20	8	point	point	NOUN
ejpam-5838	20	9	(	(	PUNCT
ejpam-5838	20	10	cfp	cfp	NOUN
ejpam-5838	20	11	)	)	PUNCT
ejpam-5838	20	12	results	result	NOUN
ejpam-5838	20	13	of	of	ADP
ejpam-5838	20	14	contractive	contractive	ADJ
ejpam-5838	20	15	inequalities	inequality	NOUN
ejpam-5838	20	16	for	for	ADP
ejpam-5838	20	17	multivalued	multivalued	ADJ
ejpam-5838	20	18	mappings	mapping	NOUN
ejpam-5838	20	19	without	without	ADP
ejpam-5838	20	20	assuming	assume	VERB
ejpam-5838	20	21	that	that	SCONJ
ejpam-5838	20	22	the	the	DET
ejpam-5838	20	23	pictures	picture	NOUN
ejpam-5838	20	24	under	under	ADP
ejpam-5838	20	25	these	these	DET
ejpam-5838	20	26	mappings	mapping	NOUN
ejpam-5838	20	27	are	be	AUX
ejpam-5838	20	28	compact	compact	ADJ
ejpam-5838	20	29	.	.	PUNCT
ejpam-5838	21	1	the	the	DET
ejpam-5838	21	2	idea	idea	NOUN
ejpam-5838	21	3	of	of	ADP
ejpam-5838	21	4	common	common	ADJ
ejpam-5838	21	5	fixed	fix	VERB
ejpam-5838	21	6	points	point	NOUN
ejpam-5838	21	7	in	in	ADP
ejpam-5838	21	8	cone	cone	NOUN
ejpam-5838	21	9	metric	metric	ADJ
ejpam-5838	21	10	spaces	space	NOUN
ejpam-5838	21	11	was	be	AUX
ejpam-5838	21	12	altered	alter	VERB
ejpam-5838	21	13	by	by	ADP
ejpam-5838	21	14	palermo	palermo	NOUN
ejpam-5838	21	15	[	[	X
ejpam-5838	21	16	4	4	NUM
ejpam-5838	21	17	]	]	PUNCT
ejpam-5838	21	18	.	.	PUNCT
ejpam-5838	22	1	fixed	fix	VERB
ejpam-5838	22	2	point	point	NOUN
ejpam-5838	22	3	theorems	theorem	NOUN
ejpam-5838	22	4	for	for	ADP
ejpam-5838	22	5	contractive	contractive	ADJ
ejpam-5838	22	6	mappings	mapping	NOUN
ejpam-5838	22	7	were	be	AUX
ejpam-5838	22	8	established	establish	VERB
ejpam-5838	22	9	by	by	ADP
ejpam-5838	22	10	huang	huang	PROPN
ejpam-5838	22	11	et	et	PROPN
ejpam-5838	22	12	al	al	PROPN
ejpam-5838	22	13	.	.	PUNCT
ejpam-5838	23	1	[	[	X
ejpam-5838	23	2	5	5	NUM
ejpam-5838	23	3	]	]	PUNCT
ejpam-5838	23	4	through	through	ADP
ejpam-5838	23	5	their	their	PRON
ejpam-5838	23	6	analysis	analysis	NOUN
ejpam-5838	23	7	of	of	ADP
ejpam-5838	23	8	cone	cone	NOUN
ejpam-5838	23	9	metric	metric	ADJ
ejpam-5838	23	10	spaces	space	NOUN
ejpam-5838	23	11	.	.	PUNCT
ejpam-5838	24	1	in	in	ADP
ejpam-5838	24	2	[	[	X
ejpam-5838	24	3	6	6	NUM
ejpam-5838	24	4	]	]	PUNCT
ejpam-5838	24	5	,	,	PUNCT
ejpam-5838	24	6	a	a	DET
ejpam-5838	24	7	graph	graph	NOUN
ejpam-5838	24	8	was	be	AUX
ejpam-5838	24	9	introduced	introduce	VERB
ejpam-5838	24	10	to	to	PART
ejpam-5838	24	11	study	study	VERB
ejpam-5838	24	12	fixed	fix	VERB
ejpam-5838	24	13	point	point	NOUN
ejpam-5838	24	14	theorems	theorem	NOUN
ejpam-5838	24	15	about	about	ADP
ejpam-5838	24	16	reich	reich	NOUN
ejpam-5838	24	17	-	-	PUNCT
ejpam-5838	24	18	type	type	NOUN
ejpam-5838	24	19	contractions	contraction	NOUN
ejpam-5838	24	20	in	in	ADP
ejpam-5838	24	21	metric	metric	ADJ
ejpam-5838	24	22	spaces	space	NOUN
ejpam-5838	24	23	.	.	PUNCT
ejpam-5838	25	1	common	common	ADJ
ejpam-5838	25	2	fixed	fix	VERB
ejpam-5838	25	3	point	point	NOUN
ejpam-5838	25	4	theorems	theorem	NOUN
ejpam-5838	25	5	and	and	CCONJ
ejpam-5838	25	6	fixed	fix	VERB
ejpam-5838	25	7	point	point	NOUN
ejpam-5838	25	8	results	result	NOUN
ejpam-5838	25	9	for	for	ADP
ejpam-5838	25	10	pointwise	pointwise	ADJ
ejpam-5838	25	11	contractions	contraction	NOUN
ejpam-5838	25	12	were	be	AUX
ejpam-5838	25	13	presented	present	VERB
ejpam-5838	25	14	in	in	ADP
ejpam-5838	25	15	[	[	X
ejpam-5838	25	16	7	7	NUM
ejpam-5838	25	17	,	,	PUNCT
ejpam-5838	25	18	8	8	NUM
ejpam-5838	25	19	]	]	PUNCT
ejpam-5838	25	20	with	with	ADP
ejpam-5838	25	21	respect	respect	NOUN
ejpam-5838	25	22	to	to	ADP
ejpam-5838	25	23	modular	modular	ADJ
ejpam-5838	25	24	metric	metric	ADJ
ejpam-5838	25	25	spaces	space	NOUN
ejpam-5838	25	26	.	.	PUNCT
ejpam-5838	26	1	fixed	fix	VERB
ejpam-5838	26	2	point	point	NOUN
ejpam-5838	26	3	theory	theory	NOUN
ejpam-5838	26	4	was	be	AUX
ejpam-5838	26	5	greatly	greatly	ADV
ejpam-5838	26	6	expanded	expand	VERB
ejpam-5838	26	7	when	when	SCONJ
ejpam-5838	26	8	mustafa	mustafa	PROPN
ejpam-5838	26	9	and	and	CCONJ
ejpam-5838	26	10	sims	sim	NOUN
ejpam-5838	26	11	[	[	X
ejpam-5838	26	12	9	9	NUM
ejpam-5838	26	13	]	]	PUNCT
ejpam-5838	26	14	later	later	ADV
ejpam-5838	26	15	established	establish	VERB
ejpam-5838	26	16	the	the	DET
ejpam-5838	26	17	idea	idea	NOUN
ejpam-5838	26	18	of	of	ADP
ejpam-5838	26	19	generalized	generalized	ADJ
ejpam-5838	26	20	metric	metric	ADJ
ejpam-5838	26	21	spaces	space	NOUN
ejpam-5838	26	22	(	(	PUNCT
ejpam-5838	26	23	gm	gm	NOUN
ejpam-5838	26	24	-	-	PUNCT
ejpam-5838	26	25	spaces	space	NOUN
ejpam-5838	26	26	)	)	PUNCT
ejpam-5838	26	27	.	.	PUNCT
ejpam-5838	27	1	das	das	PROPN
ejpam-5838	27	2	et	et	PROPN
ejpam-5838	27	3	al	al	PROPN
ejpam-5838	27	4	.	.	PUNCT
ejpam-5838	28	1	[	[	X
ejpam-5838	28	2	10	10	NUM
ejpam-5838	28	3	]	]	PUNCT
ejpam-5838	28	4	built	build	VERB
ejpam-5838	28	5	on	on	ADP
ejpam-5838	28	6	this	this	DET
ejpam-5838	28	7	foundation	foundation	NOUN
ejpam-5838	28	8	by	by	ADP
ejpam-5838	28	9	establishing	establish	VERB
ejpam-5838	28	10	specific	specific	ADJ
ejpam-5838	28	11	single	single	ADV
ejpam-5838	28	12	-	-	PUNCT
ejpam-5838	28	13	valued	value	VERB
ejpam-5838	28	14	contractive	contractive	ADJ
ejpam-5838	28	15	type	type	NOUN
ejpam-5838	28	16	mappings	mapping	NOUN
ejpam-5838	28	17	(	(	PUNCT
ejpam-5838	28	18	s	s	NOUN
ejpam-5838	28	19	-	-	ADJ
ejpam-5838	28	20	vctm	vctm	NOUN
ejpam-5838	28	21	)	)	PUNCT
ejpam-5838	28	22	and	and	CCONJ
ejpam-5838	28	23	altering	alter	VERB
ejpam-5838	28	24	fixed	fix	VERB
ejpam-5838	28	25	point	point	NOUN
ejpam-5838	28	26	outcomes	outcome	NOUN
ejpam-5838	28	27	that	that	PRON
ejpam-5838	28	28	were	be	AUX
ejpam-5838	28	29	already	already	ADV
ejpam-5838	28	30	in	in	ADP
ejpam-5838	28	31	place	place	NOUN
ejpam-5838	28	32	within	within	ADP
ejpam-5838	28	33	gm	gm	PROPN
ejpam-5838	28	34	-	-	PUNCT
ejpam-5838	28	35	spaces	space	NOUN
ejpam-5838	28	36	.	.	PUNCT
ejpam-5838	29	1	to	to	PART
ejpam-5838	29	2	illustrate	illustrate	VERB
ejpam-5838	29	3	the	the	DET
ejpam-5838	29	4	applicability	applicability	NOUN
ejpam-5838	29	5	of	of	ADP
ejpam-5838	29	6	their	their	PRON
ejpam-5838	29	7	methodology	methodology	NOUN
ejpam-5838	29	8	,	,	PUNCT
ejpam-5838	29	9	mustafa	mustafa	NOUN
ejpam-5838	29	10	and	and	CCONJ
ejpam-5838	29	11	sims	sim	NOUN
ejpam-5838	29	12	[	[	X
ejpam-5838	29	13	11	11	NUM
ejpam-5838	29	14	]	]	PUNCT
ejpam-5838	29	15	particularly	particularly	ADV
ejpam-5838	29	16	applied	apply	VERB
ejpam-5838	29	17	fixed	fix	VERB
ejpam-5838	29	18	point	point	NOUN
ejpam-5838	29	19	theorems	theorem	NOUN
ejpam-5838	29	20	to	to	ADP
ejpam-5838	29	21	contractive	contractive	ADJ
ejpam-5838	29	22	mappings	mapping	NOUN
ejpam-5838	29	23	in	in	ADP
ejpam-5838	29	24	entire	entire	ADJ
ejpam-5838	29	25	gm	gm	NOUN
ejpam-5838	29	26	-	-	PUNCT
ejpam-5838	29	27	spaces	space	NOUN
ejpam-5838	29	28	.	.	PUNCT
ejpam-5838	30	1	furthermore	furthermore	ADV
ejpam-5838	30	2	,	,	PUNCT
ejpam-5838	30	3	mustafa	mustafa	PROPN
ejpam-5838	30	4	et	et	PROPN
ejpam-5838	30	5	al	al	PROPN
ejpam-5838	30	6	.	.	PUNCT
ejpam-5838	31	1	[	[	X
ejpam-5838	31	2	12	12	NUM
ejpam-5838	31	3	]	]	PUNCT
ejpam-5838	31	4	investigated	investigate	VERB
ejpam-5838	31	5	further	far	ADV
ejpam-5838	31	6	fixed	fix	VERB
ejpam-5838	31	7	point	point	NOUN
ejpam-5838	31	8	theorems	theorem	NOUN
ejpam-5838	31	9	for	for	ADP
ejpam-5838	31	10	different	different	ADJ
ejpam-5838	31	11	mappings	mapping	NOUN
ejpam-5838	31	12	in	in	ADP
ejpam-5838	31	13	entire	entire	ADJ
ejpam-5838	31	14	gm	gm	NOUN
ejpam-5838	31	15	-	-	PUNCT
ejpam-5838	31	16	spaces	space	NOUN
ejpam-5838	31	17	.	.	PUNCT
ejpam-5838	32	1	notably	notably	ADV
ejpam-5838	32	2	,	,	PUNCT
ejpam-5838	32	3	the	the	DET
ejpam-5838	32	4	work	work	NOUN
ejpam-5838	32	5	in	in	ADP
ejpam-5838	32	6	[	[	X
ejpam-5838	32	7	13	13	NUM
ejpam-5838	32	8	]	]	PUNCT
ejpam-5838	32	9	looked	look	VERB
ejpam-5838	32	10	at	at	ADP
ejpam-5838	32	11	common	common	ADJ
ejpam-5838	32	12	fixed	fix	VERB
ejpam-5838	32	13	point	point	NOUN
ejpam-5838	32	14	outcomes	outcome	NOUN
ejpam-5838	32	15	,	,	PUNCT
ejpam-5838	32	16	including	include	VERB
ejpam-5838	32	17	non	non	ADJ
ejpam-5838	32	18	-	-	ADJ
ejpam-5838	32	19	commuting	commuting	ADJ
ejpam-5838	32	20	mappings	mapping	NOUN
ejpam-5838	32	21	in	in	ADP
ejpam-5838	32	22	gm	gm	PROPN
ejpam-5838	32	23	-	-	PUNCT
ejpam-5838	32	24	spaces	space	NOUN
ejpam-5838	32	25	that	that	PRON
ejpam-5838	32	26	do	do	AUX
ejpam-5838	32	27	not	not	PART
ejpam-5838	32	28	presuppose	presuppose	VERB
ejpam-5838	32	29	continuity	continuity	NOUN
ejpam-5838	32	30	.	.	PUNCT
ejpam-5838	33	1	by	by	ADP
ejpam-5838	33	2	examining	examine	VERB
ejpam-5838	33	3	periodic	periodic	ADJ
ejpam-5838	33	4	point	point	NOUN
ejpam-5838	33	5	results	result	NOUN
ejpam-5838	33	6	and	and	CCONJ
ejpam-5838	33	7	demonstrating	demonstrate	VERB
ejpam-5838	33	8	the	the	DET
ejpam-5838	33	9	diversity	diversity	NOUN
ejpam-5838	33	10	of	of	ADP
ejpam-5838	33	11	fixed	fix	VERB
ejpam-5838	33	12	point	point	NOUN
ejpam-5838	33	13	phenomena	phenomenon	NOUN
ejpam-5838	33	14	in	in	ADP
ejpam-5838	33	15	these	these	DET
ejpam-5838	33	16	spaces	space	NOUN
ejpam-5838	33	17	,	,	PUNCT
ejpam-5838	33	18	nazir	nazir	PROPN
ejpam-5838	33	19	et	et	PROPN
ejpam-5838	33	20	al	al	PROPN
ejpam-5838	33	21	.	.	PUNCT
ejpam-5838	34	1	[	[	X
ejpam-5838	34	2	14	14	NUM
ejpam-5838	34	3	]	]	PUNCT
ejpam-5838	34	4	made	make	VERB
ejpam-5838	34	5	a	a	DET
ejpam-5838	34	6	contribution	contribution	NOUN
ejpam-5838	34	7	to	to	ADP
ejpam-5838	34	8	this	this	DET
ejpam-5838	34	9	field	field	NOUN
ejpam-5838	34	10	.	.	PUNCT
ejpam-5838	35	1	the	the	DET
ejpam-5838	35	2	usefulness	usefulness	NOUN
ejpam-5838	35	3	of	of	ADP
ejpam-5838	35	4	gm	gm	PROPN
ejpam-5838	35	5	-	-	PUNCT
ejpam-5838	35	6	spaces	space	NOUN
ejpam-5838	35	7	in	in	ADP
ejpam-5838	35	8	fixed	fix	VERB
ejpam-5838	35	9	point	point	NOUN
ejpam-5838	35	10	theory	theory	NOUN
ejpam-5838	35	11	is	be	AUX
ejpam-5838	35	12	confirmed	confirm	VERB
ejpam-5838	35	13	by	by	ADP
ejpam-5838	35	14	shatanawi	shatanawi	PROPN
ejpam-5838	35	15	et	et	PROPN
ejpam-5838	35	16	al	al	PROPN
ejpam-5838	35	17	.	.	PUNCT
ejpam-5838	36	1	[	[	X
ejpam-5838	36	2	15	15	NUM
ejpam-5838	36	3	]	]	X
ejpam-5838	36	4	,	,	PUNCT
ejpam-5838	36	5	who	who	PRON
ejpam-5838	36	6	claim	claim	VERB
ejpam-5838	36	7	that	that	SCONJ
ejpam-5838	36	8	fixed	fix	VERB
ejpam-5838	36	9	point	point	NOUN
ejpam-5838	36	10	outcomes	outcome	NOUN
ejpam-5838	36	11	do	do	AUX
ejpam-5838	36	12	exist	exist	VERB
ejpam-5838	36	13	in	in	ADP
ejpam-5838	36	14	these	these	DET
ejpam-5838	36	15	spaces	space	NOUN
ejpam-5838	36	16	.	.	PUNCT
ejpam-5838	37	1	the	the	DET
ejpam-5838	37	2	study	study	NOUN
ejpam-5838	37	3	of	of	ADP
ejpam-5838	37	4	fixed	fix	VERB
ejpam-5838	37	5	point	point	NOUN
ejpam-5838	37	6	theorems	theorem	NOUN
ejpam-5838	37	7	in	in	ADP
ejpam-5838	37	8	g	g	NOUN
ejpam-5838	37	9	-	-	PUNCT
ejpam-5838	37	10	partially	partially	ADV
ejpam-5838	37	11	ordered	order	VERB
ejpam-5838	37	12	gm	gm	PROPN
ejpam-5838	37	13	-	-	PUNCT
ejpam-5838	37	14	spaces	space	NOUN
ejpam-5838	37	15	was	be	AUX
ejpam-5838	37	16	tried	try	VERB
ejpam-5838	37	17	by	by	ADP
ejpam-5838	37	18	vaezpour	vaezpour	NOUN
ejpam-5838	37	19	et	et	PROPN
ejpam-5838	37	20	al	al	PROPN
ejpam-5838	37	21	.	.	PUNCT
ejpam-5838	38	1	[	[	X
ejpam-5838	38	2	16	16	NUM
ejpam-5838	38	3	]	]	X
ejpam-5838	38	4	,	,	PUNCT
ejpam-5838	38	5	which	which	PRON
ejpam-5838	38	6	added	add	VERB
ejpam-5838	38	7	another	another	DET
ejpam-5838	38	8	level	level	NOUN
ejpam-5838	38	9	of	of	ADP
ejpam-5838	38	10	complexity	complexity	NOUN
ejpam-5838	38	11	and	and	CCONJ
ejpam-5838	38	12	relevance	relevance	NOUN
ejpam-5838	38	13	to	to	ADP
ejpam-5838	38	14	the	the	DET
ejpam-5838	38	15	area	area	NOUN
ejpam-5838	38	16	.	.	PUNCT
ejpam-5838	39	1	mohanta	mohanta	NOUN
ejpam-5838	39	2	et	et	PROPN
ejpam-5838	39	3	al	al	PROPN
ejpam-5838	39	4	.	.	PUNCT
ejpam-5838	40	1	[	[	X
ejpam-5838	40	2	17	17	NUM
ejpam-5838	40	3	]	]	PUNCT
ejpam-5838	40	4	looked	look	VERB
ejpam-5838	40	5	into	into	ADP
ejpam-5838	40	6	a	a	DET
ejpam-5838	40	7	common	common	ADJ
ejpam-5838	40	8	fixed	fix	VERB
ejpam-5838	40	9	point	point	NOUN
ejpam-5838	40	10	theorem	theorem	VERB
ejpam-5838	40	11	unique	unique	ADJ
ejpam-5838	40	12	to	to	ADP
ejpam-5838	40	13	gm	gm	NOUN
ejpam-5838	40	14	-	-	PUNCT
ejpam-5838	40	15	spaces	space	NOUN
ejpam-5838	40	16	,	,	PUNCT
ejpam-5838	40	17	whereas	whereas	SCONJ
ejpam-5838	40	18	choudhury	choudhury	PROPN
ejpam-5838	40	19	et	et	PROPN
ejpam-5838	40	20	al	al	PROPN
ejpam-5838	40	21	.	.	PUNCT
ejpam-5838	41	1	[	[	X
ejpam-5838	41	2	18	18	NUM
ejpam-5838	41	3	]	]	PUNCT
ejpam-5838	41	4	made	make	VERB
ejpam-5838	41	5	more	more	ADJ
ejpam-5838	41	6	progress	progress	NOUN
ejpam-5838	41	7	by	by	ADP
ejpam-5838	41	8	identifying	identify	VERB
ejpam-5838	41	9	linked	link	VERB
ejpam-5838	41	10	fixed	fix	VERB
ejpam-5838	41	11	point	point	NOUN
ejpam-5838	41	12	findings	finding	NOUN
ejpam-5838	41	13	in	in	ADP
ejpam-5838	41	14	gm	gm	PROPN
ejpam-5838	41	15	-	-	PUNCT
ejpam-5838	41	16	spaces	space	NOUN
ejpam-5838	41	17	.	.	PUNCT
ejpam-5838	42	1	khan	khan	PROPN
ejpam-5838	42	2	et	et	PROPN
ejpam-5838	42	3	al	al	PROPN
ejpam-5838	42	4	.	.	PUNCT
ejpam-5838	43	1	[	[	X
ejpam-5838	43	2	19	19	NUM
ejpam-5838	43	3	]	]	PUNCT
ejpam-5838	43	4	demonstrated	demonstrate	VERB
ejpam-5838	43	5	the	the	DET
ejpam-5838	43	6	interaction	interaction	NOUN
ejpam-5838	43	7	between	between	ADP
ejpam-5838	43	8	several	several	ADJ
ejpam-5838	43	9	spaces	space	NOUN
ejpam-5838	43	10	in	in	ADP
ejpam-5838	43	11	a	a	DET
ejpam-5838	43	12	similar	similar	ADJ
ejpam-5838	43	13	study	study	NOUN
ejpam-5838	43	14	by	by	ADP
ejpam-5838	43	15	presenting	present	VERB
ejpam-5838	43	16	linked	link	VERB
ejpam-5838	43	17	common	common	ADJ
ejpam-5838	43	18	fixed	fix	VERB
ejpam-5838	43	19	point	point	NOUN
ejpam-5838	43	20	data	datum	NOUN
ejpam-5838	43	21	in	in	ADP
ejpam-5838	43	22	two	two	NUM
ejpam-5838	43	23	separate	separate	ADJ
ejpam-5838	43	24	gm	gm	NOUN
ejpam-5838	43	25	-	-	PUNCT
ejpam-5838	43	26	spaces	space	NOUN
ejpam-5838	43	27	.	.	PUNCT
ejpam-5838	44	1	if	if	SCONJ
ejpam-5838	44	2	x	x	X
ejpam-5838	44	3	=	=	SYM
ejpam-5838	44	4	r	r	NOUN
ejpam-5838	44	5	(	(	PUNCT
ejpam-5838	44	6	the	the	DET
ejpam-5838	44	7	set	set	NOUN
ejpam-5838	44	8	of	of	ADP
ejpam-5838	44	9	real	real	ADJ
ejpam-5838	44	10	numbers	number	NOUN
ejpam-5838	44	11	)	)	PUNCT
ejpam-5838	44	12	and	and	CCONJ
ejpam-5838	44	13	define	define	VERB
ejpam-5838	44	14	a	a	DET
ejpam-5838	44	15	function	function	NOUN
ejpam-5838	44	16	d	d	NOUN
ejpam-5838	44	17	:	:	PUNCT
ejpam-5838	44	18	x	x	SYM
ejpam-5838	44	19	×	×	NOUN
ejpam-5838	44	20	x	x	INTJ
ejpam-5838	44	21	→	→	X
ejpam-5838	45	1	[	[	X
ejpam-5838	45	2	0,∞	0,∞	NOUN
ejpam-5838	45	3	)	)	PUNCT
ejpam-5838	45	4	by	by	ADP
ejpam-5838	45	5	:	:	PUNCT
ejpam-5838	45	6	d(x	d(x	PROPN
ejpam-5838	45	7	,	,	PUNCT
ejpam-5838	45	8	y	y	NOUN
ejpam-5838	45	9	)	)	PUNCT
ejpam-5838	45	10	=	=	PRON
ejpam-5838	45	11	{	{	PUNCT
ejpam-5838	45	12	|x−	|x−	NOUN
ejpam-5838	45	13	y|	y|	NOUN
ejpam-5838	45	14	if	if	SCONJ
ejpam-5838	45	15	x	x	PROPN
ejpam-5838	45	16	̸=	̸=	PROPN
ejpam-5838	45	17	y	y	NOUN
ejpam-5838	45	18	1	1	NUM
ejpam-5838	45	19	if	if	SCONJ
ejpam-5838	45	20	x	x	PROPN
ejpam-5838	45	21	̸=	̸=	PROPN
ejpam-5838	45	22	y	y	NOUN
ejpam-5838	45	23	we	we	PRON
ejpam-5838	45	24	see	see	VERB
ejpam-5838	45	25	that	that	SCONJ
ejpam-5838	45	26	this	this	PRON
ejpam-5838	45	27	is	be	AUX
ejpam-5838	45	28	a	a	DET
ejpam-5838	45	29	gms	gms	NOUN
ejpam-5838	45	30	but	but	CCONJ
ejpam-5838	45	31	not	not	PART
ejpam-5838	45	32	a	a	DET
ejpam-5838	45	33	metric	metric	NOUN
ejpam-5838	45	34	.	.	PUNCT
ejpam-5838	46	1	by	by	ADP
ejpam-5838	46	2	demonstrating	demonstrate	VERB
ejpam-5838	46	3	fixed	fix	VERB
ejpam-5838	46	4	point	point	NOUN
ejpam-5838	46	5	theorems	theorem	NOUN
ejpam-5838	46	6	for	for	ADP
ejpam-5838	46	7	generalized	generalized	ADJ
ejpam-5838	46	8	contractions	contraction	NOUN
ejpam-5838	46	9	in	in	ADP
ejpam-5838	46	10	partial	partial	ADJ
ejpam-5838	46	11	metric	metric	ADJ
ejpam-5838	46	12	spaces	space	NOUN
ejpam-5838	46	13	,	,	PUNCT
ejpam-5838	46	14	romaguera	romaguera	NOUN
ejpam-5838	46	15	[	[	X
ejpam-5838	46	16	20	20	NUM
ejpam-5838	46	17	]	]	PUNCT
ejpam-5838	46	18	added	add	VERB
ejpam-5838	46	19	to	to	ADP
ejpam-5838	46	20	the	the	DET
ejpam-5838	46	21	conversation	conversation	NOUN
ejpam-5838	46	22	.	.	PUNCT
ejpam-5838	47	1	by	by	ADP
ejpam-5838	47	2	developing	develop	VERB
ejpam-5838	47	3	common	common	ADJ
ejpam-5838	47	4	fixed	fix	VERB
ejpam-5838	47	5	point	point	NOUN
ejpam-5838	47	6	results	result	NOUN
ejpam-5838	47	7	in	in	ADP
ejpam-5838	47	8	gm	gm	PROPN
ejpam-5838	47	9	-	-	PUNCT
ejpam-5838	47	10	spaces	space	NOUN
ejpam-5838	47	11	and	and	CCONJ
ejpam-5838	47	12	outlining	outline	VERB
ejpam-5838	47	13	their	their	PRON
ejpam-5838	47	14	useful	useful	ADJ
ejpam-5838	47	15	applications	application	NOUN
ejpam-5838	47	16	,	,	PUNCT
ejpam-5838	47	17	gugnani	gugnani	PROPN
ejpam-5838	47	18	et	et	PROPN
ejpam-5838	47	19	al	al	PROPN
ejpam-5838	47	20	.	.	PUNCT
ejpam-5838	48	1	[	[	X
ejpam-5838	48	2	21	21	NUM
ejpam-5838	48	3	]	]	X
ejpam-5838	48	4	advanced	advance	VERB
ejpam-5838	48	5	the	the	DET
ejpam-5838	48	6	conversation	conversation	NOUN
ejpam-5838	48	7	.	.	PUNCT
ejpam-5838	49	1	a	a	DET
ejpam-5838	49	2	kannan	kannan	PROPN
ejpam-5838	49	3	theorem	theorem	NOUN
ejpam-5838	49	4	was	be	AUX
ejpam-5838	49	5	investigated	investigate	VERB
ejpam-5838	49	6	by	by	ADP
ejpam-5838	49	7	arshad	arshad	PROPN
ejpam-5838	49	8	et	et	PROPN
ejpam-5838	49	9	al	al	PROPN
ejpam-5838	49	10	.	.	PUNCT
ejpam-5838	50	1	[	[	X
ejpam-5838	50	2	22	22	NUM
ejpam-5838	50	3	]	]	PUNCT
ejpam-5838	50	4	in	in	ADP
ejpam-5838	50	5	the	the	DET
ejpam-5838	50	6	context	context	NOUN
ejpam-5838	50	7	of	of	ADP
ejpam-5838	50	8	gm	gm	PROPN
ejpam-5838	50	9	-	-	PUNCT
ejpam-5838	50	10	spaces	space	NOUN
ejpam-5838	50	11	,	,	PUNCT
ejpam-5838	50	12	highlighting	highlight	VERB
ejpam-5838	50	13	the	the	DET
ejpam-5838	50	14	continued	continue	VERB
ejpam-5838	50	15	applicability	applicability	NOUN
ejpam-5838	50	16	of	of	ADP
ejpam-5838	50	17	traditional	traditional	ADJ
ejpam-5838	50	18	conclusions	conclusion	NOUN
ejpam-5838	50	19	in	in	ADP
ejpam-5838	50	20	this	this	DET
ejpam-5838	50	21	novel	novel	NOUN
ejpam-5838	50	22	setting	setting	NOUN
ejpam-5838	50	23	.	.	PUNCT
ejpam-5838	51	1	several	several	ADJ
ejpam-5838	51	2	more	more	ADJ
ejpam-5838	51	3	fixed	fix	VERB
ejpam-5838	51	4	point	point	NOUN
ejpam-5838	51	5	theorems	theorem	NOUN
ejpam-5838	51	6	were	be	AUX
ejpam-5838	51	7	derived	derive	VERB
ejpam-5838	51	8	in	in	ADP
ejpam-5838	51	9	[	[	X
ejpam-5838	51	10	23	23	NUM
ejpam-5838	51	11	]	]	PUNCT
ejpam-5838	51	12	,	,	PUNCT
ejpam-5838	51	13	which	which	PRON
ejpam-5838	51	14	examined	examine	VERB
ejpam-5838	51	15	and	and	CCONJ
ejpam-5838	51	16	improved	improve	VERB
ejpam-5838	51	17	the	the	DET
ejpam-5838	51	18	framework	framework	NOUN
ejpam-5838	51	19	created	create	VERB
ejpam-5838	51	20	by	by	ADP
ejpam-5838	51	21	gugnani	gugnani	PROPN
ejpam-5838	51	22	et	et	PROPN
ejpam-5838	51	23	al	al	PROPN
ejpam-5838	52	1	[	[	X
ejpam-5838	52	2	21	21	NUM
ejpam-5838	52	3	]	]	PUNCT
ejpam-5838	52	4	.	.	PUNCT
ejpam-5838	53	1	the	the	DET
ejpam-5838	53	2	notions	notion	NOUN
ejpam-5838	53	3	’	'	PUNCT
ejpam-5838	53	4	adaptability	adaptability	NOUN
ejpam-5838	53	5	was	be	AUX
ejpam-5838	53	6	demonstrated	demonstrate	VERB
ejpam-5838	53	7	in	in	ADP
ejpam-5838	53	8	[	[	X
ejpam-5838	53	9	24	24	NUM
ejpam-5838	53	10	]	]	PUNCT
ejpam-5838	53	11	,	,	PUNCT
ejpam-5838	53	12	when	when	SCONJ
ejpam-5838	53	13	research	research	NOUN
ejpam-5838	53	14	on	on	ADP
ejpam-5838	53	15	fixed	fix	VERB
ejpam-5838	53	16	point	point	NOUN
ejpam-5838	53	17	theorems	theorem	NOUN
ejpam-5838	53	18	pertaining	pertain	VERB
ejpam-5838	53	19	to	to	ADP
ejpam-5838	53	20	multi	multi	VERB
ejpam-5838	53	21	-	-	ADJ
ejpam-5838	53	22	valued	value	VERB
ejpam-5838	53	23	contractive	contractive	ADJ
ejpam-5838	53	24	operators	operator	NOUN
ejpam-5838	53	25	in	in	ADP
ejpam-5838	53	26	gm	gm	PROPN
ejpam-5838	53	27	-	-	PUNCT
ejpam-5838	53	28	spaces	space	NOUN
ejpam-5838	53	29	was	be	AUX
ejpam-5838	53	30	presented	present	VERB
ejpam-5838	53	31	.	.	PUNCT
ejpam-5838	54	1	finally	finally	ADV
ejpam-5838	54	2	,	,	PUNCT
ejpam-5838	54	3	in	in	ADP
ejpam-5838	54	4	[	[	X
ejpam-5838	54	5	25	25	NUM
ejpam-5838	54	6	,	,	PUNCT
ejpam-5838	54	7	26	26	NUM
ejpam-5838	54	8	]	]	PUNCT
ejpam-5838	54	9	,	,	PUNCT
ejpam-5838	54	10	new	new	ADJ
ejpam-5838	54	11	definitions	definition	NOUN
ejpam-5838	54	12	of	of	ADP
ejpam-5838	54	13	fixed	fix	VERB
ejpam-5838	54	14	point	point	NOUN
ejpam-5838	54	15	theorems	theorem	NOUN
ejpam-5838	54	16	and	and	CCONJ
ejpam-5838	54	17	their	their	PRON
ejpam-5838	54	18	different	different	ADJ
ejpam-5838	54	19	applications	application	NOUN
ejpam-5838	54	20	in	in	ADP
ejpam-5838	54	21	gm	gm	PROPN
ejpam-5838	54	22	-	-	PUNCT
ejpam-5838	54	23	spaces	space	NOUN
ejpam-5838	54	24	were	be	AUX
ejpam-5838	54	25	presented	present	VERB
ejpam-5838	54	26	,	,	PUNCT
ejpam-5838	54	27	highlighting	highlight	VERB
ejpam-5838	54	28	how	how	SCONJ
ejpam-5838	54	29	dynamic	dynamic	ADJ
ejpam-5838	54	30	and	and	CCONJ
ejpam-5838	54	31	ever	ever	ADV
ejpam-5838	54	32	-	-	PUNCT
ejpam-5838	54	33	evolving	evolve	VERB
ejpam-5838	54	34	this	this	DET
ejpam-5838	54	35	field	field	NOUN
ejpam-5838	54	36	of	of	ADP
ejpam-5838	54	37	study	study	NOUN
ejpam-5838	54	38	.	.	PUNCT
ejpam-5838	55	1	because	because	SCONJ
ejpam-5838	55	2	of	of	ADP
ejpam-5838	55	3	its	its	PRON
ejpam-5838	55	4	theoretical	theoretical	ADJ
ejpam-5838	55	5	significance	significance	NOUN
ejpam-5838	55	6	and	and	CCONJ
ejpam-5838	55	7	real	real	ADJ
ejpam-5838	55	8	-	-	PUNCT
ejpam-5838	55	9	world	world	NOUN
ejpam-5838	55	10	implications	implication	NOUN
ejpam-5838	55	11	,	,	PUNCT
ejpam-5838	55	12	the	the	DET
ejpam-5838	55	13	study	study	NOUN
ejpam-5838	55	14	of	of	ADP
ejpam-5838	55	15	f	f	PROPN
ejpam-5838	55	16	-points	-point	NOUN
ejpam-5838	55	17	in	in	ADP
ejpam-5838	55	18	gm	gm	PROPN
ejpam-5838	55	19	-	-	PUNCT
ejpam-5838	55	20	spaces	space	NOUN
ejpam-5838	55	21	under	under	ADP
ejpam-5838	55	22	generalized	generalized	ADJ
ejpam-5838	55	23	contractions	contraction	NOUN
ejpam-5838	55	24	has	have	AUX
ejpam-5838	55	25	attracted	attract	VERB
ejpam-5838	55	26	a	a	DET
ejpam-5838	55	27	lot	lot	NOUN
ejpam-5838	55	28	of	of	ADP
ejpam-5838	55	29	attention	attention	NOUN
ejpam-5838	55	30	.	.	PUNCT
ejpam-5838	56	1	the	the	DET
ejpam-5838	56	2	convergence	convergence	NOUN
ejpam-5838	56	3	behaviour	behaviour	NOUN
ejpam-5838	56	4	of	of	ADP
ejpam-5838	56	5	iterative	iterative	ADJ
ejpam-5838	56	6	sequences	sequence	NOUN
ejpam-5838	56	7	in	in	ADP
ejpam-5838	56	8	generalized	generalized	ADJ
ejpam-5838	56	9	contractions	contraction	NOUN
ejpam-5838	56	10	,	,	PUNCT
ejpam-5838	56	11	the	the	DET
ejpam-5838	56	12	presence	presence	NOUN
ejpam-5838	56	13	and	and	CCONJ
ejpam-5838	56	14	uniqueness	uniqueness	NOUN
ejpam-5838	56	15	of	of	ADP
ejpam-5838	56	16	f	f	PROPN
ejpam-5838	56	17	-points	-point	NOUN
ejpam-5838	56	18	,	,	PUNCT
ejpam-5838	56	19	and	and	CCONJ
ejpam-5838	56	20	the	the	DET
ejpam-5838	56	21	creation	creation	NOUN
ejpam-5838	56	22	of	of	ADP
ejpam-5838	56	23	mathematical	mathematical	ADJ
ejpam-5838	56	24	models	model	NOUN
ejpam-5838	56	25	for	for	ADP
ejpam-5838	56	26	practical	practical	ADJ
ejpam-5838	56	27	issues	issue	NOUN
ejpam-5838	56	28	are	be	AUX
ejpam-5838	56	29	all	all	PRON
ejpam-5838	56	30	examined	examine	VERB
ejpam-5838	56	31	in	in	ADP
ejpam-5838	56	32	this	this	DET
ejpam-5838	56	33	study	study	NOUN
ejpam-5838	56	34	.	.	PUNCT
ejpam-5838	57	1	by	by	ADP
ejpam-5838	57	2	following	follow	VERB
ejpam-5838	57	3	the	the	DET
ejpam-5838	57	4	development	development	NOUN
ejpam-5838	57	5	of	of	ADP
ejpam-5838	57	6	fixed	fix	VERB
ejpam-5838	57	7	point	point	NOUN
ejpam-5838	57	8	theory	theory	NOUN
ejpam-5838	57	9	(	(	PUNCT
ejpam-5838	57	10	fpt	fpt	PROPN
ejpam-5838	57	11	)	)	PUNCT
ejpam-5838	57	12	from	from	ADP
ejpam-5838	57	13	banach	banach	NOUN
ejpam-5838	57	14	’s	’s	PART
ejpam-5838	57	15	contraction	contraction	NOUN
ejpam-5838	57	16	principle	principle	NOUN
ejpam-5838	57	17	to	to	ADP
ejpam-5838	57	18	contemporary	contemporary	ADJ
ejpam-5838	57	19	developments	development	NOUN
ejpam-5838	57	20	in	in	ADP
ejpam-5838	57	21	gm	gm	PROPN
ejpam-5838	57	22	-	-	PUNCT
ejpam-5838	57	23	spaces	space	NOUN
ejpam-5838	57	24	,	,	PUNCT
ejpam-5838	57	25	the	the	DET
ejpam-5838	57	26	study	study	NOUN
ejpam-5838	57	27	expands	expand	VERB
ejpam-5838	57	28	on	on	ADP
ejpam-5838	57	29	earlier	early	ADJ
ejpam-5838	57	30	research	research	NOUN
ejpam-5838	57	31	in	in	ADP
ejpam-5838	57	32	this	this	DET
ejpam-5838	57	33	field	field	NOUN
ejpam-5838	57	34	.	.	PUNCT
ejpam-5838	58	1	important	important	ADJ
ejpam-5838	58	2	contributions	contribution	NOUN
ejpam-5838	58	3	from	from	ADP
ejpam-5838	58	4	different	different	ADJ
ejpam-5838	58	5	scholars	scholar	NOUN
ejpam-5838	58	6	are	be	AUX
ejpam-5838	58	7	described	describe	VERB
ejpam-5838	58	8	,	,	PUNCT
ejpam-5838	58	9	such	such	ADJ
ejpam-5838	58	10	as	as	ADP
ejpam-5838	58	11	the	the	DET
ejpam-5838	58	12	development	development	NOUN
ejpam-5838	58	13	of	of	ADP
ejpam-5838	58	14	common	common	ADJ
ejpam-5838	58	15	fixed	fix	VERB
ejpam-5838	58	16	point	point	NOUN
ejpam-5838	58	17	results	result	NOUN
ejpam-5838	58	18	and	and	CCONJ
ejpam-5838	58	19	single	single	ADV
ejpam-5838	58	20	-	-	PUNCT
ejpam-5838	58	21	valued	value	VERB
ejpam-5838	58	22	contractive	contractive	ADJ
ejpam-5838	58	23	type	type	NOUN
ejpam-5838	58	24	mappings	mapping	NOUN
ejpam-5838	58	25	(	(	PUNCT
ejpam-5838	58	26	s	s	NOUN
ejpam-5838	58	27	-	-	ADJ
ejpam-5838	58	28	vctm	vctm	NOUN
ejpam-5838	58	29	)	)	PUNCT
ejpam-5838	58	30	.	.	PUNCT
ejpam-5838	59	1	m.	m.	PROPN
ejpam-5838	59	2	noorwali	noorwali	PROPN
ejpam-5838	59	3	et	et	PROPN
ejpam-5838	59	4	al/	al/	PROPN
ejpam-5838	59	5	/	/	SYM
ejpam-5838	59	6	eur	eur	PROPN
ejpam-5838	59	7	.	.	PUNCT
ejpam-5838	60	1	j.	j.	PROPN
ejpam-5838	60	2	pure	pure	PROPN
ejpam-5838	60	3	appl	appl	PROPN
ejpam-5838	60	4	.	.	PROPN
ejpam-5838	60	5	math	math	PROPN
ejpam-5838	60	6	,	,	PUNCT
ejpam-5838	60	7	18	18	NUM
ejpam-5838	60	8	(	(	PUNCT
ejpam-5838	60	9	2	2	NUM
ejpam-5838	60	10	)	)	PUNCT
ejpam-5838	60	11	(	(	PUNCT
ejpam-5838	60	12	2025	2025	NUM
ejpam-5838	60	13	)	)	PUNCT
ejpam-5838	60	14	,	,	PUNCT
ejpam-5838	60	15	5838	5838	NUM
ejpam-5838	60	16	3	3	NUM
ejpam-5838	60	17	of	of	ADP
ejpam-5838	60	18	16	16	NUM
ejpam-5838	60	19	1.1	1.1	NUM
ejpam-5838	60	20	.	.	PUNCT
ejpam-5838	61	1	problem	problem	NOUN
ejpam-5838	61	2	statement	statement	NOUN
ejpam-5838	61	3	while	while	SCONJ
ejpam-5838	61	4	fixed	fixed	ADJ
ejpam-5838	61	5	point	point	NOUN
ejpam-5838	61	6	theory	theory	NOUN
ejpam-5838	61	7	has	have	AUX
ejpam-5838	61	8	seen	see	VERB
ejpam-5838	61	9	extensive	extensive	ADJ
ejpam-5838	61	10	development	development	NOUN
ejpam-5838	61	11	,	,	PUNCT
ejpam-5838	61	12	particularly	particularly	ADV
ejpam-5838	61	13	in	in	ADP
ejpam-5838	61	14	the	the	DET
ejpam-5838	61	15	study	study	NOUN
ejpam-5838	61	16	of	of	ADP
ejpam-5838	61	17	selfmappings	selfmapping	NOUN
ejpam-5838	61	18	on	on	ADP
ejpam-5838	61	19	various	various	ADJ
ejpam-5838	61	20	types	type	NOUN
ejpam-5838	61	21	of	of	ADP
ejpam-5838	61	22	metric	metric	ADJ
ejpam-5838	61	23	spaces	space	NOUN
ejpam-5838	61	24	,	,	PUNCT
ejpam-5838	61	25	the	the	DET
ejpam-5838	61	26	literature	literature	NOUN
ejpam-5838	61	27	reveals	reveal	VERB
ejpam-5838	61	28	a	a	DET
ejpam-5838	61	29	noticeable	noticeable	ADJ
ejpam-5838	61	30	gap	gap	NOUN
ejpam-5838	61	31	in	in	ADP
ejpam-5838	61	32	the	the	DET
ejpam-5838	61	33	context	context	NOUN
ejpam-5838	61	34	of	of	ADP
ejpam-5838	61	35	common	common	ADJ
ejpam-5838	61	36	fixed	fix	VERB
ejpam-5838	61	37	points	point	NOUN
ejpam-5838	61	38	(	(	PUNCT
ejpam-5838	61	39	cfps	cfps	NOUN
ejpam-5838	61	40	)	)	PUNCT
ejpam-5838	61	41	for	for	ADP
ejpam-5838	61	42	multiple	multiple	ADJ
ejpam-5838	61	43	(	(	PUNCT
ejpam-5838	61	44	specifically	specifically	ADV
ejpam-5838	61	45	,	,	PUNCT
ejpam-5838	61	46	three	three	NUM
ejpam-5838	61	47	)	)	PUNCT
ejpam-5838	61	48	self	self	NOUN
ejpam-5838	61	49	-	-	PUNCT
ejpam-5838	61	50	mappings	mapping	NOUN
ejpam-5838	61	51	in	in	ADP
ejpam-5838	61	52	generalized	generalized	ADJ
ejpam-5838	61	53	metric	metric	ADJ
ejpam-5838	61	54	spaces	space	NOUN
ejpam-5838	61	55	(	(	PUNCT
ejpam-5838	61	56	gm	gm	NOUN
ejpam-5838	61	57	-	-	PUNCT
ejpam-5838	61	58	spaces	space	NOUN
ejpam-5838	61	59	)	)	PUNCT
ejpam-5838	61	60	.	.	PUNCT
ejpam-5838	62	1	existing	exist	VERB
ejpam-5838	62	2	contraction	contraction	NOUN
ejpam-5838	62	3	-	-	PUNCT
ejpam-5838	62	4	type	type	NOUN
ejpam-5838	62	5	results	result	NOUN
ejpam-5838	62	6	predominantly	predominantly	ADV
ejpam-5838	62	7	focus	focus	VERB
ejpam-5838	62	8	on	on	ADP
ejpam-5838	62	9	single	single	ADJ
ejpam-5838	62	10	or	or	CCONJ
ejpam-5838	62	11	pairwise	pairwise	NOUN
ejpam-5838	62	12	mappings	mapping	NOUN
ejpam-5838	62	13	and	and	CCONJ
ejpam-5838	62	14	are	be	AUX
ejpam-5838	62	15	often	often	ADV
ejpam-5838	62	16	restricted	restrict	VERB
ejpam-5838	62	17	to	to	ADP
ejpam-5838	62	18	classical	classical	ADJ
ejpam-5838	62	19	metric	metric	ADJ
ejpam-5838	62	20	frameworks	framework	NOUN
ejpam-5838	62	21	.	.	PUNCT
ejpam-5838	63	1	moreover	moreover	ADV
ejpam-5838	63	2	,	,	PUNCT
ejpam-5838	63	3	although	although	SCONJ
ejpam-5838	63	4	generalized	generalized	ADJ
ejpam-5838	63	5	contractions	contraction	NOUN
ejpam-5838	63	6	have	have	AUX
ejpam-5838	63	7	been	be	AUX
ejpam-5838	63	8	introduced	introduce	VERB
ejpam-5838	63	9	in	in	ADP
ejpam-5838	63	10	recent	recent	ADJ
ejpam-5838	63	11	years	year	NOUN
ejpam-5838	63	12	,	,	PUNCT
ejpam-5838	63	13	their	their	PRON
ejpam-5838	63	14	application	application	NOUN
ejpam-5838	63	15	to	to	ADP
ejpam-5838	63	16	multiple	multiple	ADJ
ejpam-5838	63	17	self	self	NOUN
ejpam-5838	63	18	-	-	PUNCT
ejpam-5838	63	19	mappings	mapping	NOUN
ejpam-5838	63	20	—	—	PUNCT
ejpam-5838	63	21	especially	especially	ADV
ejpam-5838	63	22	in	in	ADP
ejpam-5838	63	23	proving	prove	VERB
ejpam-5838	63	24	uniqueness	uniqueness	NOUN
ejpam-5838	63	25	and	and	CCONJ
ejpam-5838	63	26	existence	existence	NOUN
ejpam-5838	63	27	of	of	ADP
ejpam-5838	63	28	cfps	cfps	NOUN
ejpam-5838	63	29	-	-	PUNCT
ejpam-5838	63	30	remains	remain	VERB
ejpam-5838	63	31	underexplored	underexplored	ADJ
ejpam-5838	63	32	.	.	PUNCT
ejpam-5838	64	1	there	there	PRON
ejpam-5838	64	2	is	be	VERB
ejpam-5838	64	3	also	also	ADV
ejpam-5838	64	4	a	a	DET
ejpam-5838	64	5	lack	lack	NOUN
ejpam-5838	64	6	of	of	ADP
ejpam-5838	64	7	comprehensive	comprehensive	ADJ
ejpam-5838	64	8	examples	example	NOUN
ejpam-5838	64	9	and	and	CCONJ
ejpam-5838	64	10	practical	practical	ADJ
ejpam-5838	64	11	applications	application	NOUN
ejpam-5838	64	12	,	,	PUNCT
ejpam-5838	64	13	such	such	ADJ
ejpam-5838	64	14	as	as	ADP
ejpam-5838	64	15	in	in	ADP
ejpam-5838	64	16	the	the	DET
ejpam-5838	64	17	analysis	analysis	NOUN
ejpam-5838	64	18	of	of	ADP
ejpam-5838	64	19	nonlinear	nonlinear	ADJ
ejpam-5838	64	20	integral	integral	ADJ
ejpam-5838	64	21	equations	equation	NOUN
ejpam-5838	64	22	,	,	PUNCT
ejpam-5838	64	23	that	that	PRON
ejpam-5838	64	24	showcase	showcase	VERB
ejpam-5838	64	25	the	the	DET
ejpam-5838	64	26	effectiveness	effectiveness	NOUN
ejpam-5838	64	27	and	and	CCONJ
ejpam-5838	64	28	broader	broad	ADJ
ejpam-5838	64	29	applicability	applicability	NOUN
ejpam-5838	64	30	of	of	ADP
ejpam-5838	64	31	these	these	DET
ejpam-5838	64	32	theoretical	theoretical	ADJ
ejpam-5838	64	33	advancements	advancement	NOUN
ejpam-5838	64	34	.	.	PUNCT
ejpam-5838	65	1	this	this	DET
ejpam-5838	65	2	research	research	NOUN
ejpam-5838	65	3	seeks	seek	VERB
ejpam-5838	65	4	to	to	PART
ejpam-5838	65	5	fill	fill	VERB
ejpam-5838	65	6	this	this	DET
ejpam-5838	65	7	gap	gap	NOUN
ejpam-5838	65	8	by	by	ADP
ejpam-5838	65	9	developing	develop	VERB
ejpam-5838	65	10	new	new	ADJ
ejpam-5838	65	11	contraction	contraction	NOUN
ejpam-5838	65	12	results	result	NOUN
ejpam-5838	65	13	specifically	specifically	ADV
ejpam-5838	65	14	tailored	tailor	VERB
ejpam-5838	65	15	for	for	ADP
ejpam-5838	65	16	three	three	NUM
ejpam-5838	65	17	selfmappings	selfmapping	NOUN
ejpam-5838	65	18	on	on	ADP
ejpam-5838	65	19	gm	gm	NOUN
ejpam-5838	65	20	-	-	PUNCT
ejpam-5838	65	21	spaces	space	NOUN
ejpam-5838	65	22	,	,	PUNCT
ejpam-5838	65	23	and	and	CCONJ
ejpam-5838	65	24	by	by	ADP
ejpam-5838	65	25	establishing	establish	VERB
ejpam-5838	65	26	robust	robust	ADJ
ejpam-5838	65	27	cfp	cfp	NOUN
ejpam-5838	65	28	theorems	theorem	NOUN
ejpam-5838	65	29	that	that	PRON
ejpam-5838	65	30	ensure	ensure	VERB
ejpam-5838	65	31	both	both	DET
ejpam-5838	65	32	existence	existence	NOUN
ejpam-5838	65	33	and	and	CCONJ
ejpam-5838	65	34	uniqueness	uniqueness	NOUN
ejpam-5838	65	35	.	.	PUNCT
ejpam-5838	66	1	furthermore	furthermore	ADV
ejpam-5838	66	2	,	,	PUNCT
ejpam-5838	66	3	we	we	PRON
ejpam-5838	66	4	aim	aim	VERB
ejpam-5838	66	5	to	to	PART
ejpam-5838	66	6	enhance	enhance	VERB
ejpam-5838	66	7	the	the	DET
ejpam-5838	66	8	practical	practical	ADJ
ejpam-5838	66	9	value	value	NOUN
ejpam-5838	66	10	of	of	ADP
ejpam-5838	66	11	these	these	DET
ejpam-5838	66	12	results	result	NOUN
ejpam-5838	66	13	by	by	ADP
ejpam-5838	66	14	presenting	present	VERB
ejpam-5838	66	15	wellconstructed	wellconstructe	VERB
ejpam-5838	66	16	examples	example	NOUN
ejpam-5838	66	17	and	and	CCONJ
ejpam-5838	66	18	meaningful	meaningful	ADJ
ejpam-5838	66	19	applications	application	NOUN
ejpam-5838	66	20	.	.	PUNCT
ejpam-5838	67	1	1.2	1.2	NUM
ejpam-5838	67	2	.	.	PUNCT
ejpam-5838	67	3	organization	organization	NOUN
ejpam-5838	67	4	the	the	DET
ejpam-5838	67	5	paper	paper	NOUN
ejpam-5838	67	6	is	be	AUX
ejpam-5838	67	7	structured	structure	VERB
ejpam-5838	67	8	as	as	SCONJ
ejpam-5838	67	9	follows	follow	VERB
ejpam-5838	67	10	:	:	PUNCT
ejpam-5838	67	11	section	section	NOUN
ejpam-5838	67	12	2	2	NUM
ejpam-5838	67	13	:	:	PUNCT
ejpam-5838	67	14	provides	provide	VERB
ejpam-5838	67	15	pertinent	pertinent	ADJ
ejpam-5838	67	16	preliminaries	preliminary	NOUN
ejpam-5838	67	17	and	and	CCONJ
ejpam-5838	67	18	definitions	definition	NOUN
ejpam-5838	67	19	necessary	necessary	ADJ
ejpam-5838	67	20	for	for	ADP
ejpam-5838	67	21	understanding	understand	VERB
ejpam-5838	67	22	the	the	DET
ejpam-5838	67	23	subsequent	subsequent	ADJ
ejpam-5838	67	24	results	result	NOUN
ejpam-5838	67	25	.	.	PUNCT
ejpam-5838	68	1	section	section	NOUN
ejpam-5838	68	2	3	3	NUM
ejpam-5838	68	3	:	:	PUNCT
ejpam-5838	68	4	introduces	introduce	VERB
ejpam-5838	68	5	the	the	DET
ejpam-5838	68	6	key	key	ADJ
ejpam-5838	68	7	results	result	NOUN
ejpam-5838	68	8	on	on	ADP
ejpam-5838	68	9	fixed	fix	VERB
ejpam-5838	68	10	point	point	NOUN
ejpam-5838	68	11	theorems	theorem	NOUN
ejpam-5838	68	12	in	in	ADP
ejpam-5838	68	13	gm	gm	PROPN
ejpam-5838	68	14	-	-	PUNCT
ejpam-5838	68	15	spaces	space	NOUN
ejpam-5838	68	16	.	.	PUNCT
ejpam-5838	69	1	section	section	NOUN
ejpam-5838	69	2	4	4	NUM
ejpam-5838	69	3	:	:	PUNCT
ejpam-5838	69	4	discusses	discuss	VERB
ejpam-5838	69	5	the	the	DET
ejpam-5838	69	6	applications	application	NOUN
ejpam-5838	69	7	of	of	ADP
ejpam-5838	69	8	the	the	DET
ejpam-5838	69	9	fixed	fix	VERB
ejpam-5838	69	10	point	point	NOUN
ejpam-5838	69	11	theorems	theorem	NOUN
ejpam-5838	69	12	presented	present	VERB
ejpam-5838	69	13	in	in	ADP
ejpam-5838	69	14	the	the	DET
ejpam-5838	69	15	previous	previous	ADJ
ejpam-5838	69	16	section	section	NOUN
ejpam-5838	69	17	.	.	PUNCT
ejpam-5838	70	1	section	section	NOUN
ejpam-5838	70	2	5	5	NUM
ejpam-5838	70	3	:	:	PUNCT
ejpam-5838	70	4	presents	present	VERB
ejpam-5838	70	5	the	the	DET
ejpam-5838	70	6	conclusions	conclusion	NOUN
ejpam-5838	70	7	and	and	CCONJ
ejpam-5838	70	8	outlines	outline	VERB
ejpam-5838	70	9	possible	possible	ADJ
ejpam-5838	70	10	directions	direction	NOUN
ejpam-5838	70	11	for	for	ADP
ejpam-5838	70	12	future	future	ADJ
ejpam-5838	70	13	research	research	NOUN
ejpam-5838	70	14	,	,	PUNCT
ejpam-5838	70	15	emphasizing	emphasize	VERB
ejpam-5838	70	16	the	the	DET
ejpam-5838	70	17	growing	grow	VERB
ejpam-5838	70	18	importance	importance	NOUN
ejpam-5838	70	19	of	of	ADP
ejpam-5838	70	20	gm	gm	PROPN
ejpam-5838	70	21	-	-	PUNCT
ejpam-5838	70	22	spaces	space	NOUN
ejpam-5838	70	23	in	in	ADP
ejpam-5838	70	24	fixed	fix	VERB
ejpam-5838	70	25	point	point	NOUN
ejpam-5838	70	26	theory	theory	NOUN
ejpam-5838	70	27	.	.	PUNCT
ejpam-5838	71	1	2	2	X
ejpam-5838	71	2	.	.	X
ejpam-5838	71	3	preliminaries	preliminary	NOUN
ejpam-5838	71	4	this	this	DET
ejpam-5838	71	5	section	section	NOUN
ejpam-5838	71	6	is	be	AUX
ejpam-5838	71	7	devoted	devote	VERB
ejpam-5838	71	8	to	to	ADP
ejpam-5838	71	9	some	some	DET
ejpam-5838	71	10	fundamental	fundamental	ADJ
ejpam-5838	71	11	definitions	definition	NOUN
ejpam-5838	71	12	,	,	PUNCT
ejpam-5838	71	13	which	which	PRON
ejpam-5838	71	14	are	be	AUX
ejpam-5838	71	15	necessary	necessary	ADJ
ejpam-5838	71	16	for	for	ADP
ejpam-5838	71	17	the	the	DET
ejpam-5838	71	18	upcoming	upcoming	ADJ
ejpam-5838	71	19	sections	section	NOUN
ejpam-5838	71	20	.	.	PUNCT
ejpam-5838	72	1	2.1	2.1	NUM
ejpam-5838	72	2	.	.	PUNCT
ejpam-5838	73	1	generalized	generalize	VERB
ejpam-5838	73	2	metric	metric	ADJ
ejpam-5838	73	3	space	space	NOUN
ejpam-5838	73	4	definition	definition	NOUN
ejpam-5838	73	5	1	1	NUM
ejpam-5838	73	6	.	.	PUNCT
ejpam-5838	74	1	[	[	X
ejpam-5838	74	2	9	9	NUM
ejpam-5838	74	3	]	]	PUNCT
ejpam-5838	74	4	assume	assume	VERB
ejpam-5838	74	5	ê	ê	X
ejpam-5838	74	6	̸=	̸=	PROPN
ejpam-5838	74	7	∅	∅	NOUN
ejpam-5838	74	8	set	set	VERB
ejpam-5838	74	9	and	and	CCONJ
ejpam-5838	74	10	g	g	NOUN
ejpam-5838	74	11	:	:	PUNCT
ejpam-5838	74	12	ê×	ê×	PROPN
ejpam-5838	74	13	ê×	ê×	PROPN
ejpam-5838	74	14	ê	ê	PROPN
ejpam-5838	74	15	→	→	PUNCT
ejpam-5838	74	16	[	[	X
ejpam-5838	74	17	0,∞	0,∞	NUM
ejpam-5838	74	18	)	)	PUNCT
ejpam-5838	74	19	is	be	AUX
ejpam-5838	74	20	a	a	DET
ejpam-5838	74	21	generalized	generalized	ADJ
ejpam-5838	74	22	metric	metric	ADJ
ejpam-5838	74	23	space	space	NOUN
ejpam-5838	74	24	(	(	PUNCT
ejpam-5838	74	25	gm	gm	NOUN
ejpam-5838	74	26	-	-	PUNCT
ejpam-5838	74	27	space	space	NOUN
ejpam-5838	74	28	)	)	PUNCT
ejpam-5838	75	1	if	if	SCONJ
ejpam-5838	75	2	and	and	CCONJ
ejpam-5838	75	3	only	only	ADV
ejpam-5838	75	4	if	if	SCONJ
ejpam-5838	75	5	the	the	DET
ejpam-5838	75	6	axioms	axiom	NOUN
ejpam-5838	75	7	below	below	ADV
ejpam-5838	75	8	are	be	AUX
ejpam-5838	75	9	true	true	ADJ
ejpam-5838	75	10	.	.	PUNCT
ejpam-5838	76	1	i.	i.	PROPN
ejpam-5838	76	2	g(ê1	g(ê1	PROPN
ejpam-5838	76	3	,	,	PUNCT
ejpam-5838	76	4	ê2	ê2	PROPN
ejpam-5838	76	5	,	,	PUNCT
ejpam-5838	76	6	ê3	ê3	PUNCT
ejpam-5838	76	7	)	)	PUNCT
ejpam-5838	76	8	=	=	SYM
ejpam-5838	76	9	0	0	NUM
ejpam-5838	77	1	iff	iff	PROPN
ejpam-5838	77	2	ê1	ê1	PROPN
ejpam-5838	77	3	=	=	PROPN
ejpam-5838	77	4	ê2	ê2	PROPN
ejpam-5838	77	5	=	=	SYM
ejpam-5838	77	6	ê3	ê3	PROPN
ejpam-5838	77	7	,	,	PUNCT
ejpam-5838	77	8	ii	ii	PROPN
ejpam-5838	77	9	.	.	PROPN
ejpam-5838	77	10	0	0	PUNCT
ejpam-5838	78	1	<	<	X
ejpam-5838	78	2	g(ê1	g(ê1	PROPN
ejpam-5838	78	3	,	,	PUNCT
ejpam-5838	78	4	ê1	ê1	PROPN
ejpam-5838	78	5	,	,	PUNCT
ejpam-5838	78	6	ê2	ê2	PROPN
ejpam-5838	78	7	)	)	PUNCT
ejpam-5838	78	8	∀	∀	PUNCT
ejpam-5838	79	1	ê1	ê1	PROPN
ejpam-5838	79	2	,	,	PUNCT
ejpam-5838	79	3	ê2	ê2	PROPN
ejpam-5838	79	4	∈	∈	PROPN
ejpam-5838	79	5	ê	ê	PROPN
ejpam-5838	79	6	,	,	PUNCT
ejpam-5838	79	7	with	with	ADP
ejpam-5838	79	8	ê1	ê1	PROPN
ejpam-5838	79	9	̸=	̸=	PROPN
ejpam-5838	79	10	ê2	ê2	PROPN
ejpam-5838	79	11	,	,	PUNCT
ejpam-5838	79	12	iii	iii	PROPN
ejpam-5838	79	13	.	.	PUNCT
ejpam-5838	80	1	g(ê1	g(ê1	PROPN
ejpam-5838	80	2	,	,	PUNCT
ejpam-5838	80	3	ê1	ê1	PROPN
ejpam-5838	80	4	,	,	PUNCT
ejpam-5838	80	5	ê2	ê2	PROPN
ejpam-5838	80	6	)	)	PUNCT
ejpam-5838	80	7	≤	≤	PUNCT
ejpam-5838	81	1	g(ê1	g(ê1	PROPN
ejpam-5838	81	2	,	,	PUNCT
ejpam-5838	81	3	ê2	ê2	PROPN
ejpam-5838	81	4	,	,	PUNCT
ejpam-5838	81	5	ê3	ê3	PROPN
ejpam-5838	81	6	)	)	PUNCT
ejpam-5838	81	7	∀	∀	PUNCT
ejpam-5838	82	1	ê1	ê1	PROPN
ejpam-5838	82	2	,	,	PUNCT
ejpam-5838	82	3	ê2	ê2	PROPN
ejpam-5838	82	4	,	,	PUNCT
ejpam-5838	82	5	ê3	ê3	PROPN
ejpam-5838	82	6	∈	∈	PROPN
ejpam-5838	82	7	ê	ê	PROPN
ejpam-5838	82	8	,	,	PUNCT
ejpam-5838	82	9	with	with	ADP
ejpam-5838	82	10	ê1	ê1	PROPN
ejpam-5838	82	11	̸=	̸=	PROPN
ejpam-5838	82	12	ê2	ê2	PROPN
ejpam-5838	82	13	,	,	PUNCT
ejpam-5838	82	14	iv	iv	X
ejpam-5838	82	15	.	.	PUNCT
ejpam-5838	83	1	g(ê1	g(ê1	NOUN
ejpam-5838	83	2	,	,	PUNCT
ejpam-5838	83	3	ê2	ê2	PROPN
ejpam-5838	83	4	,	,	PUNCT
ejpam-5838	83	5	ê3	ê3	X
ejpam-5838	83	6	)	)	PUNCT
ejpam-5838	83	7	=	=	PUNCT
ejpam-5838	84	1	g{p(ê1	g{p(ê1	NOUN
ejpam-5838	84	2	,	,	PUNCT
ejpam-5838	84	3	ê2	ê2	PROPN
ejpam-5838	84	4	,	,	PUNCT
ejpam-5838	84	5	ê3	ê3	PROPN
ejpam-5838	84	6	)	)	PUNCT
ejpam-5838	84	7	}	}	PUNCT
ejpam-5838	84	8	where	where	SCONJ
ejpam-5838	84	9	p	p	NOUN
ejpam-5838	84	10	is	be	AUX
ejpam-5838	84	11	a	a	DET
ejpam-5838	84	12	permutation	permutation	NOUN
ejpam-5838	84	13	of	of	ADP
ejpam-5838	84	14	ê1	ê1	PROPN
ejpam-5838	84	15	,	,	PUNCT
ejpam-5838	84	16	ê2	ê2	PROPN
ejpam-5838	84	17	,	,	PUNCT
ejpam-5838	84	18	ê3	ê3	PROPN
ejpam-5838	84	19	(	(	PUNCT
ejpam-5838	84	20	symmetry	symmetry	PROPN
ejpam-5838	84	21	)	)	PUNCT
ejpam-5838	84	22	,	,	PUNCT
ejpam-5838	84	23	v.	v.	PROPN
ejpam-5838	84	24	g(ê1	g(ê1	PROPN
ejpam-5838	84	25	,	,	PUNCT
ejpam-5838	84	26	ê2	ê2	PROPN
ejpam-5838	84	27	,	,	PUNCT
ejpam-5838	84	28	ê3	ê3	NOUN
ejpam-5838	84	29	)	)	PUNCT
ejpam-5838	84	30	≤	≤	PUNCT
ejpam-5838	85	1	g(ê1	g(ê1	PROPN
ejpam-5838	85	2	,	,	PUNCT
ejpam-5838	85	3	â	â	ADV
ejpam-5838	85	4	,	,	PUNCT
ejpam-5838	85	5	â	â	ADJ
ejpam-5838	85	6	)	)	PUNCT
ejpam-5838	85	7	+	+	ADJ
ejpam-5838	85	8	g(â	g(â	NOUN
ejpam-5838	85	9	,	,	PUNCT
ejpam-5838	85	10	ê2	ê2	PROPN
ejpam-5838	85	11	,	,	PUNCT
ejpam-5838	85	12	ê3	ê3	PROPN
ejpam-5838	85	13	)	)	PUNCT
ejpam-5838	85	14	∀	∀	PUNCT
ejpam-5838	86	1	ê1	ê1	PROPN
ejpam-5838	86	2	,	,	PUNCT
ejpam-5838	86	3	ê2	ê2	PROPN
ejpam-5838	86	4	,	,	PUNCT
ejpam-5838	86	5	ê3	ê3	PROPN
ejpam-5838	86	6	∈	∈	PROPN
ejpam-5838	86	7	ê.	ê.	VERB
ejpam-5838	86	8	a	a	DET
ejpam-5838	86	9	gm	gm	PROPN
ejpam-5838	86	10	is	be	AUX
ejpam-5838	86	11	symmetric	symmetric	ADJ
ejpam-5838	86	12	if	if	SCONJ
ejpam-5838	86	13	g(ê1	g(ê1	PROPN
ejpam-5838	86	14	,	,	PUNCT
ejpam-5838	86	15	ê2	ê2	NOUN
ejpam-5838	86	16	,	,	PUNCT
ejpam-5838	86	17	ê2	ê2	ADJ
ejpam-5838	86	18	)	)	PUNCT
ejpam-5838	86	19	=	=	SYM
ejpam-5838	86	20	g(ê2	g(ê2	PROPN
ejpam-5838	86	21	,	,	PUNCT
ejpam-5838	86	22	ê1	ê1	PROPN
ejpam-5838	86	23	,	,	PUNCT
ejpam-5838	86	24	ê1	ê1	PROPN
ejpam-5838	86	25	)	)	PUNCT
ejpam-5838	86	26	∀	∀	PUNCT
ejpam-5838	87	1	ê1	ê1	PROPN
ejpam-5838	87	2	,	,	PUNCT
ejpam-5838	87	3	ê2	ê2	PROPN
ejpam-5838	87	4	∈	∈	PROPN
ejpam-5838	87	5	ê	ê	PROPN
ejpam-5838	87	6	,	,	PUNCT
ejpam-5838	87	7	then	then	ADV
ejpam-5838	87	8	(	(	PUNCT
ejpam-5838	87	9	ê	ê	PROPN
ejpam-5838	87	10	,	,	PUNCT
ejpam-5838	87	11	g	g	NOUN
ejpam-5838	87	12	)	)	PUNCT
ejpam-5838	87	13	is	be	AUX
ejpam-5838	87	14	known	know	VERB
ejpam-5838	87	15	as	as	ADP
ejpam-5838	87	16	a	a	DET
ejpam-5838	87	17	gm	gm	NOUN
ejpam-5838	87	18	-	-	PUNCT
ejpam-5838	87	19	space	space	NOUN
ejpam-5838	87	20	.	.	PUNCT
ejpam-5838	88	1	the	the	DET
ejpam-5838	88	2	significance	significance	NOUN
ejpam-5838	88	3	of	of	ADP
ejpam-5838	88	4	this	this	DET
ejpam-5838	88	5	study	study	NOUN
ejpam-5838	88	6	is	be	AUX
ejpam-5838	88	7	as	as	SCONJ
ejpam-5838	88	8	follows	follow	VERB
ejpam-5838	88	9	:	:	PUNCT
ejpam-5838	88	10	it	it	PRON
ejpam-5838	88	11	introduces	introduce	VERB
ejpam-5838	88	12	a	a	DET
ejpam-5838	88	13	novel	novel	NOUN
ejpam-5838	88	14	and	and	CCONJ
ejpam-5838	88	15	generalized	generalized	ADJ
ejpam-5838	88	16	family	family	NOUN
ejpam-5838	88	17	of	of	ADP
ejpam-5838	88	18	contraction	contraction	NOUN
ejpam-5838	88	19	mappings	mapping	NOUN
ejpam-5838	88	20	,	,	PUNCT
ejpam-5838	88	21	termed	term	VERB
ejpam-5838	88	22	f	f	PROPN
ejpam-5838	88	23	-kannan	-kannan	ADJ
ejpam-5838	88	24	contractions	contraction	NOUN
ejpam-5838	88	25	,	,	PUNCT
ejpam-5838	88	26	contributing	contribute	VERB
ejpam-5838	88	27	a	a	DET
ejpam-5838	88	28	new	new	ADJ
ejpam-5838	88	29	direction	direction	NOUN
ejpam-5838	88	30	in	in	ADP
ejpam-5838	88	31	fixed	fix	VERB
ejpam-5838	88	32	point	point	NOUN
ejpam-5838	88	33	theory	theory	NOUN
ejpam-5838	88	34	.	.	PUNCT
ejpam-5838	89	1	by	by	ADP
ejpam-5838	89	2	identifying	identify	VERB
ejpam-5838	89	3	and	and	CCONJ
ejpam-5838	89	4	correcting	correct	VERB
ejpam-5838	89	5	a	a	DET
ejpam-5838	89	6	previous	previous	ADJ
ejpam-5838	89	7	error	error	NOUN
ejpam-5838	89	8	in	in	ADP
ejpam-5838	89	9	the	the	DET
ejpam-5838	89	10	literature	literature	NOUN
ejpam-5838	89	11	,	,	PUNCT
ejpam-5838	89	12	the	the	DET
ejpam-5838	89	13	study	study	NOUN
ejpam-5838	89	14	not	not	PART
ejpam-5838	89	15	only	only	ADV
ejpam-5838	89	16	clarifies	clarify	VERB
ejpam-5838	89	17	conceptual	conceptual	ADJ
ejpam-5838	89	18	misunderstandings	misunderstanding	NOUN
ejpam-5838	89	19	but	but	CCONJ
ejpam-5838	89	20	also	also	ADV
ejpam-5838	89	21	strengthens	strengthen	VERB
ejpam-5838	89	22	the	the	DET
ejpam-5838	89	23	theoretical	theoretical	ADJ
ejpam-5838	89	24	foundation	foundation	NOUN
ejpam-5838	89	25	of	of	ADP
ejpam-5838	89	26	contraction	contraction	NOUN
ejpam-5838	89	27	mappings	mapping	NOUN
ejpam-5838	89	28	.	.	PUNCT
ejpam-5838	90	1	the	the	DET
ejpam-5838	90	2	proposed	propose	VERB
ejpam-5838	90	3	f	f	PROPN
ejpam-5838	90	4	-kannan	-kannan	ADJ
ejpam-5838	90	5	framework	framework	NOUN
ejpam-5838	90	6	extends	extend	VERB
ejpam-5838	90	7	the	the	DET
ejpam-5838	90	8	well	well	ADV
ejpam-5838	90	9	-	-	PUNCT
ejpam-5838	90	10	known	know	VERB
ejpam-5838	90	11	concept	concept	NOUN
ejpam-5838	90	12	of	of	ADP
ejpam-5838	90	13	f	f	PROPN
ejpam-5838	90	14	contractions	contraction	NOUN
ejpam-5838	90	15	and	and	CCONJ
ejpam-5838	90	16	provides	provide	VERB
ejpam-5838	90	17	new	new	ADJ
ejpam-5838	90	18	fixed	fix	VERB
ejpam-5838	90	19	point	point	NOUN
ejpam-5838	90	20	results	result	NOUN
ejpam-5838	90	21	that	that	PRON
ejpam-5838	90	22	hold	hold	VERB
ejpam-5838	90	23	even	even	ADV
ejpam-5838	90	24	in	in	ADP
ejpam-5838	90	25	non	non	ADJ
ejpam-5838	90	26	-	-	ADJ
ejpam-5838	90	27	complete	complete	ADJ
ejpam-5838	90	28	metric	metric	ADJ
ejpam-5838	90	29	spaces	space	NOUN
ejpam-5838	90	30	a	a	DET
ejpam-5838	90	31	significant	significant	ADJ
ejpam-5838	90	32	relaxation	relaxation	NOUN
ejpam-5838	90	33	of	of	ADP
ejpam-5838	90	34	classical	classical	ADJ
ejpam-5838	90	35	assumptions	assumption	NOUN
ejpam-5838	90	36	.	.	PUNCT
ejpam-5838	91	1	furthermore	furthermore	ADV
ejpam-5838	91	2	,	,	PUNCT
ejpam-5838	91	3	the	the	DET
ejpam-5838	91	4	validation	validation	NOUN
ejpam-5838	91	5	of	of	ADP
ejpam-5838	91	6	subrahmanyam	subrahmanyam	NOUN
ejpam-5838	91	7	’s	’s	PART
ejpam-5838	91	8	characterization	characterization	NOUN
ejpam-5838	91	9	of	of	ADP
ejpam-5838	91	10	completeness	completeness	NOUN
ejpam-5838	91	11	within	within	ADP
ejpam-5838	91	12	this	this	DET
ejpam-5838	91	13	broader	broad	ADJ
ejpam-5838	91	14	context	context	NOUN
ejpam-5838	91	15	underscores	underscore	VERB
ejpam-5838	91	16	the	the	DET
ejpam-5838	91	17	robustness	robustness	NOUN
ejpam-5838	91	18	and	and	CCONJ
ejpam-5838	91	19	m.	m.	NOUN
ejpam-5838	91	20	noorwali	noorwali	PROPN
ejpam-5838	91	21	et	et	PROPN
ejpam-5838	91	22	al/	al/	PROPN
ejpam-5838	91	23	/	/	SYM
ejpam-5838	91	24	eur	eur	PROPN
ejpam-5838	91	25	.	.	PUNCT
ejpam-5838	92	1	j.	j.	PROPN
ejpam-5838	92	2	pure	pure	PROPN
ejpam-5838	92	3	appl	appl	PROPN
ejpam-5838	92	4	.	.	PROPN
ejpam-5838	92	5	math	math	PROPN
ejpam-5838	92	6	,	,	PUNCT
ejpam-5838	92	7	18	18	NUM
ejpam-5838	92	8	(	(	PUNCT
ejpam-5838	92	9	2	2	NUM
ejpam-5838	92	10	)	)	PUNCT
ejpam-5838	92	11	(	(	PUNCT
ejpam-5838	92	12	2025	2025	NUM
ejpam-5838	92	13	)	)	PUNCT
ejpam-5838	92	14	,	,	PUNCT
ejpam-5838	92	15	5838	5838	NUM
ejpam-5838	92	16	4	4	NUM
ejpam-5838	92	17	of	of	ADP
ejpam-5838	92	18	16	16	NUM
ejpam-5838	92	19	applicability	applicability	NOUN
ejpam-5838	92	20	of	of	ADP
ejpam-5838	92	21	the	the	DET
ejpam-5838	92	22	new	new	ADJ
ejpam-5838	92	23	class	class	NOUN
ejpam-5838	92	24	.	.	PUNCT
ejpam-5838	93	1	this	this	DET
ejpam-5838	93	2	advancement	advancement	NOUN
ejpam-5838	93	3	opens	open	VERB
ejpam-5838	93	4	up	up	ADP
ejpam-5838	93	5	new	new	ADJ
ejpam-5838	93	6	possibilities	possibility	NOUN
ejpam-5838	93	7	for	for	ADP
ejpam-5838	93	8	research	research	NOUN
ejpam-5838	93	9	and	and	CCONJ
ejpam-5838	93	10	application	application	NOUN
ejpam-5838	93	11	in	in	ADP
ejpam-5838	93	12	areas	area	NOUN
ejpam-5838	93	13	that	that	PRON
ejpam-5838	93	14	rely	rely	VERB
ejpam-5838	93	15	on	on	ADP
ejpam-5838	93	16	fixed	fix	VERB
ejpam-5838	93	17	point	point	NOUN
ejpam-5838	93	18	theorems	theorem	NOUN
ejpam-5838	93	19	,	,	PUNCT
ejpam-5838	93	20	such	such	ADJ
ejpam-5838	93	21	as	as	ADP
ejpam-5838	93	22	nonlinear	nonlinear	ADJ
ejpam-5838	93	23	analysis	analysis	NOUN
ejpam-5838	93	24	,	,	PUNCT
ejpam-5838	93	25	optimization	optimization	NOUN
ejpam-5838	93	26	,	,	PUNCT
ejpam-5838	93	27	and	and	CCONJ
ejpam-5838	93	28	mathematical	mathematical	ADJ
ejpam-5838	93	29	modeling	modeling	NOUN
ejpam-5838	93	30	.	.	PUNCT
ejpam-5838	94	1	definition	definition	NOUN
ejpam-5838	94	2	2	2	NUM
ejpam-5838	94	3	.	.	PUNCT
ejpam-5838	95	1	[	[	X
ejpam-5838	95	2	9	9	NUM
ejpam-5838	95	3	]	]	X
ejpam-5838	95	4	let	let	ADJ
ejpam-5838	95	5	(	(	PUNCT
ejpam-5838	95	6	ê	ê	NOUN
ejpam-5838	95	7	,	,	PUNCT
ejpam-5838	95	8	g	g	NOUN
ejpam-5838	95	9	)	)	PUNCT
ejpam-5838	95	10	be	be	AUX
ejpam-5838	95	11	a	a	DET
ejpam-5838	95	12	gm	gm	PROPN
ejpam-5838	95	13	-space	-space	NOUN
ejpam-5838	95	14	while	while	SCONJ
ejpam-5838	95	15	{	{	PUNCT
ejpam-5838	95	16	êi	êi	AUX
ejpam-5838	95	17	}	}	PUNCT
ejpam-5838	95	18	be	be	AUX
ejpam-5838	95	19	a	a	DET
ejpam-5838	95	20	sequence	sequence	NOUN
ejpam-5838	95	21	in	in	ADP
ejpam-5838	95	22	ê.	ê.	NOUN
ejpam-5838	95	23	then	then	ADV
ejpam-5838	95	24	,	,	PUNCT
ejpam-5838	95	25	i.	i.	NOUN
ejpam-5838	95	26	{	{	PUNCT
ejpam-5838	95	27	êi	êi	X
ejpam-5838	95	28	}	}	PUNCT
ejpam-5838	95	29	in	in	ADP
ejpam-5838	95	30	a	a	DET
ejpam-5838	95	31	gm	gm	NOUN
ejpam-5838	95	32	-	-	PUNCT
ejpam-5838	95	33	space	space	NOUN
ejpam-5838	95	34	is	be	AUX
ejpam-5838	95	35	called	call	VERB
ejpam-5838	95	36	a	a	DET
ejpam-5838	95	37	g	g	NOUN
ejpam-5838	95	38	-	-	PUNCT
ejpam-5838	95	39	cauchy	cauchy	ADJ
ejpam-5838	95	40	sequence	sequence	NOUN
ejpam-5838	95	41	(	(	PUNCT
ejpam-5838	95	42	g	g	NOUN
ejpam-5838	95	43	-	-	PUNCT
ejpam-5838	95	44	cs	cs	ADJ
ejpam-5838	95	45	)	)	PUNCT
ejpam-5838	95	46	if	if	SCONJ
ejpam-5838	95	47	for	for	ADP
ejpam-5838	95	48	any	any	DET
ejpam-5838	95	49	ε	ε	PROPN
ejpam-5838	95	50	>	>	X
ejpam-5838	95	51	0	0	PROPN
ejpam-5838	95	52	,	,	PUNCT
ejpam-5838	95	53	∃	∃	PROPN
ejpam-5838	95	54	n0	n0	PROPN
ejpam-5838	95	55	∈	∈	PROPN
ejpam-5838	95	56	n	n	PROPN
ejpam-5838	95	57	s.t	s.t	PROPN
ejpam-5838	95	58	g(êi	g(êi	PROPN
ejpam-5838	95	59	,	,	PUNCT
ejpam-5838	95	60	êm	êm	NOUN
ejpam-5838	95	61	,	,	PUNCT
ejpam-5838	95	62	êl	êl	PROPN
ejpam-5838	95	63	)	)	PUNCT
ejpam-5838	96	1	<	<	X
ejpam-5838	96	2	ε	ε	X
ejpam-5838	96	3	∀	∀	X
ejpam-5838	96	4	i	i	PROPN
ejpam-5838	96	5	,	,	PUNCT
ejpam-5838	96	6	m	m	PROPN
ejpam-5838	96	7	,	,	PUNCT
ejpam-5838	96	8	l	l	PROPN
ejpam-5838	96	9	≥	≥	PROPN
ejpam-5838	96	10	n0	n0	NUM
ejpam-5838	96	11	.	.	PUNCT
ejpam-5838	96	12	ii	ii	PROPN
ejpam-5838	96	13	.	.	PUNCT
ejpam-5838	96	14	{	{	PUNCT
ejpam-5838	96	15	êi	êi	X
ejpam-5838	96	16	}	}	PUNCT
ejpam-5838	96	17	is	be	AUX
ejpam-5838	96	18	convergent	convergent	ADJ
ejpam-5838	96	19	to	to	ADP
ejpam-5838	96	20	an	an	DET
ejpam-5838	96	21	element	element	NOUN
ejpam-5838	96	22	ê	ê	PROPN
ejpam-5838	96	23	∈	∈	PROPN
ejpam-5838	96	24	ê	ê	PROPN
ejpam-5838	97	1	if	if	SCONJ
ejpam-5838	97	2	∀	∀	NOUN
ejpam-5838	97	3	any	any	DET
ejpam-5838	97	4	given	give	VERB
ejpam-5838	97	5	a	a	DET
ejpam-5838	97	6	real	real	ADJ
ejpam-5838	97	7	number	number	NOUN
ejpam-5838	97	8	ε	ε	PROPN
ejpam-5838	97	9	>	>	X
ejpam-5838	97	10	0	0	PROPN
ejpam-5838	97	11	,	,	PUNCT
ejpam-5838	97	12	∃	∃	PROPN
ejpam-5838	97	13	n0	n0	PROPN
ejpam-5838	97	14	∈	∈	PROPN
ejpam-5838	97	15	n	n	PRON
ejpam-5838	97	16	so	so	ADV
ejpam-5838	97	17	that	that	SCONJ
ejpam-5838	97	18	;	;	PUNCT
ejpam-5838	97	19	g(ê	g(ê	NOUN
ejpam-5838	97	20	,	,	PUNCT
ejpam-5838	97	21	êi	êi	PROPN
ejpam-5838	97	22	,	,	PUNCT
ejpam-5838	97	23	êm	êm	NOUN
ejpam-5838	97	24	)	)	PUNCT
ejpam-5838	97	25	<	<	X
ejpam-5838	97	26	ε	ε	PROPN
ejpam-5838	97	27	,	,	PUNCT
ejpam-5838	97	28	whenever	whenever	SCONJ
ejpam-5838	97	29	m	m	PROPN
ejpam-5838	97	30	≥	≥	PROPN
ejpam-5838	97	31	n0	n0	PROPN
ejpam-5838	97	32	.	.	PUNCT
ejpam-5838	97	33	iii	iii	PROPN
ejpam-5838	97	34	.	.	PUNCT
ejpam-5838	98	1	(	(	PUNCT
ejpam-5838	98	2	ê	ê	PROPN
ejpam-5838	98	3	,	,	PUNCT
ejpam-5838	98	4	g	g	NOUN
ejpam-5838	98	5	)	)	PUNCT
ejpam-5838	98	6	is	be	AUX
ejpam-5838	98	7	complete	complete	ADJ
ejpam-5838	98	8	if	if	SCONJ
ejpam-5838	98	9	every	every	DET
ejpam-5838	98	10	g	g	NOUN
ejpam-5838	98	11	-	-	PUNCT
ejpam-5838	98	12	cs	cs	PROPN
ejpam-5838	98	13	is	be	AUX
ejpam-5838	98	14	g	g	NOUN
ejpam-5838	98	15	-	-	PUNCT
ejpam-5838	98	16	convergent	convergent	NOUN
ejpam-5838	98	17	in	in	ADP
ejpam-5838	98	18	ê.	ê.	ADJ
ejpam-5838	98	19	proposition	proposition	NOUN
ejpam-5838	98	20	1	1	NUM
ejpam-5838	98	21	.	.	PUNCT
ejpam-5838	99	1	[	[	X
ejpam-5838	99	2	9	9	NUM
ejpam-5838	99	3	]	]	X
ejpam-5838	99	4	let	let	ADJ
ejpam-5838	99	5	(	(	PUNCT
ejpam-5838	99	6	ê	ê	NOUN
ejpam-5838	99	7	,	,	PUNCT
ejpam-5838	99	8	g	g	NOUN
ejpam-5838	99	9	)	)	PUNCT
ejpam-5838	99	10	be	be	AUX
ejpam-5838	99	11	a	a	DET
ejpam-5838	99	12	gm	gm	NOUN
ejpam-5838	99	13	-	-	PUNCT
ejpam-5838	99	14	space	space	NOUN
ejpam-5838	99	15	,	,	PUNCT
ejpam-5838	99	16	then	then	ADV
ejpam-5838	99	17	for	for	ADP
ejpam-5838	99	18	any	any	DET
ejpam-5838	99	19	ê1	ê1	PROPN
ejpam-5838	99	20	,	,	PUNCT
ejpam-5838	99	21	ê2	ê2	PROPN
ejpam-5838	99	22	,	,	PUNCT
ejpam-5838	99	23	ê3	ê3	PROPN
ejpam-5838	99	24	∈	∈	PROPN
ejpam-5838	99	25	ê	ê	PROPN
ejpam-5838	99	26	the	the	DET
ejpam-5838	99	27	following	follow	VERB
ejpam-5838	99	28	hold	hold	NOUN
ejpam-5838	99	29	:	:	PUNCT
ejpam-5838	99	30	i.	i.	NOUN
ejpam-5838	99	31	if	if	SCONJ
ejpam-5838	99	32	g(ê1	g(ê1	PROPN
ejpam-5838	99	33	,	,	PUNCT
ejpam-5838	99	34	ê2	ê2	PROPN
ejpam-5838	99	35	,	,	PUNCT
ejpam-5838	99	36	ê3	ê3	PUNCT
ejpam-5838	99	37	)	)	PUNCT
ejpam-5838	99	38	=	=	SYM
ejpam-5838	99	39	0	0	NUM
ejpam-5838	99	40	,	,	PUNCT
ejpam-5838	99	41	then	then	ADV
ejpam-5838	99	42	ê1	ê1	PROPN
ejpam-5838	99	43	=	=	SYM
ejpam-5838	100	1	ê2	ê2	PROPN
ejpam-5838	100	2	=	=	SYM
ejpam-5838	100	3	ê3	ê3	PROPN
ejpam-5838	100	4	,	,	PUNCT
ejpam-5838	100	5	ii	ii	PROPN
ejpam-5838	100	6	.	.	PUNCT
ejpam-5838	101	1	g(ê1	g(ê1	NOUN
ejpam-5838	101	2	,	,	PUNCT
ejpam-5838	101	3	ê2	ê2	PROPN
ejpam-5838	101	4	,	,	PUNCT
ejpam-5838	101	5	ê3	ê3	NOUN
ejpam-5838	101	6	)	)	PUNCT
ejpam-5838	101	7	≤	≤	PUNCT
ejpam-5838	102	1	g(ê1	g(ê1	PROPN
ejpam-5838	102	2	,	,	PUNCT
ejpam-5838	102	3	ê1	ê1	PROPN
ejpam-5838	102	4	,	,	PUNCT
ejpam-5838	102	5	ê3	ê3	PROPN
ejpam-5838	102	6	)	)	PUNCT
ejpam-5838	102	7	,	,	PUNCT
ejpam-5838	102	8	iii	iii	X
ejpam-5838	102	9	.	.	PUNCT
ejpam-5838	103	1	g(ê1	g(ê1	NOUN
ejpam-5838	103	2	,	,	PUNCT
ejpam-5838	103	3	ê2	ê2	NOUN
ejpam-5838	103	4	,	,	PUNCT
ejpam-5838	103	5	ê2	ê2	NOUN
ejpam-5838	103	6	)	)	PUNCT
ejpam-5838	103	7	≤	≤	NUM
ejpam-5838	103	8	2g(ê2	2g(ê2	NUM
ejpam-5838	103	9	,	,	PUNCT
ejpam-5838	103	10	ê1	ê1	PROPN
ejpam-5838	103	11	,	,	PUNCT
ejpam-5838	103	12	ê1	ê1	PROPN
ejpam-5838	103	13	)	)	PUNCT
ejpam-5838	103	14	,	,	PUNCT
ejpam-5838	103	15	iv	iv	X
ejpam-5838	103	16	.	.	PUNCT
ejpam-5838	104	1	g(ê1	g(ê1	NOUN
ejpam-5838	104	2	,	,	PUNCT
ejpam-5838	104	3	ê2	ê2	PROPN
ejpam-5838	104	4	,	,	PUNCT
ejpam-5838	104	5	ê3	ê3	NOUN
ejpam-5838	104	6	)	)	PUNCT
ejpam-5838	104	7	≤	≤	PUNCT
ejpam-5838	105	1	g(ê1	g(ê1	PROPN
ejpam-5838	105	2	,	,	PUNCT
ejpam-5838	105	3	ê	ê	PROPN
ejpam-5838	105	4	,	,	PUNCT
ejpam-5838	105	5	ê3	ê3	PUNCT
ejpam-5838	105	6	)	)	PUNCT
ejpam-5838	106	1	+	+	NOUN
ejpam-5838	106	2	g(ê	g(ê	PROPN
ejpam-5838	106	3	,	,	PUNCT
ejpam-5838	106	4	ê2	ê2	NOUN
ejpam-5838	106	5	,	,	PUNCT
ejpam-5838	106	6	ê3	ê3	PROPN
ejpam-5838	106	7	)	)	PUNCT
ejpam-5838	106	8	,	,	PUNCT
ejpam-5838	106	9	v.	v.	PROPN
ejpam-5838	106	10	g(ê1	g(ê1	PROPN
ejpam-5838	106	11	,	,	PUNCT
ejpam-5838	106	12	ê2	ê2	PROPN
ejpam-5838	106	13	,	,	PUNCT
ejpam-5838	106	14	ê3	ê3	NOUN
ejpam-5838	106	15	)	)	PUNCT
ejpam-5838	106	16	≤	≤	NUM
ejpam-5838	106	17	2	2	NUM
ejpam-5838	106	18	3	3	NUM
ejpam-5838	106	19	(	(	PUNCT
ejpam-5838	106	20	g(ê1	g(ê1	PROPN
ejpam-5838	106	21	,	,	PUNCT
ejpam-5838	106	22	ê2	ê2	PROPN
ejpam-5838	106	23	,	,	PUNCT
ejpam-5838	106	24	ê	ê	NOUN
ejpam-5838	106	25	)	)	PUNCT
ejpam-5838	107	1	+	+	NOUN
ejpam-5838	107	2	g(ê1	g(ê1	PROPN
ejpam-5838	107	3	,	,	PUNCT
ejpam-5838	107	4	ê	ê	PROPN
ejpam-5838	107	5	,	,	PUNCT
ejpam-5838	107	6	ê3	ê3	PUNCT
ejpam-5838	107	7	)	)	PUNCT
ejpam-5838	108	1	+	+	NOUN
ejpam-5838	108	2	g(ê	g(ê	PROPN
ejpam-5838	108	3	,	,	PUNCT
ejpam-5838	108	4	ê2	ê2	NOUN
ejpam-5838	108	5	,	,	PUNCT
ejpam-5838	108	6	ê3	ê3	PROPN
ejpam-5838	108	7	)	)	PUNCT
ejpam-5838	108	8	)	)	PUNCT
ejpam-5838	108	9	,	,	PUNCT
ejpam-5838	108	10	vi	vi	X
ejpam-5838	108	11	.	.	PUNCT
ejpam-5838	109	1	g(ê1	g(ê1	NOUN
ejpam-5838	109	2	,	,	PUNCT
ejpam-5838	109	3	ê2	ê2	PROPN
ejpam-5838	109	4	,	,	PUNCT
ejpam-5838	109	5	ê3	ê3	PROPN
ejpam-5838	109	6	)	)	PUNCT
ejpam-5838	109	7	≤	≤	NOUN
ejpam-5838	109	8	(	(	PUNCT
ejpam-5838	109	9	g(ê1	g(ê1	PROPN
ejpam-5838	109	10	,	,	PUNCT
ejpam-5838	109	11	ê	ê	PROPN
ejpam-5838	109	12	,	,	PUNCT
ejpam-5838	109	13	ê	ê	NOUN
ejpam-5838	109	14	)	)	PUNCT
ejpam-5838	110	1	+	+	ADJ
ejpam-5838	110	2	g(ê2	g(ê2	PROPN
ejpam-5838	110	3	,	,	PUNCT
ejpam-5838	110	4	ê	ê	PROPN
ejpam-5838	110	5	,	,	PUNCT
ejpam-5838	110	6	ê	ê	NOUN
ejpam-5838	110	7	)	)	PUNCT
ejpam-5838	111	1	+	+	PROPN
ejpam-5838	111	2	g(ê3	g(ê3	PROPN
ejpam-5838	111	3	,	,	PUNCT
ejpam-5838	111	4	ê	ê	PROPN
ejpam-5838	111	5	,	,	PUNCT
ejpam-5838	111	6	ê	ê	NOUN
ejpam-5838	111	7	)	)	PUNCT
ejpam-5838	111	8	)	)	PUNCT
ejpam-5838	112	1	,	,	PUNCT
ejpam-5838	112	2	vii	vii	PROPN
ejpam-5838	112	3	.	.	PUNCT
ejpam-5838	112	4	|g(ê1	|g(ê1	PROPN
ejpam-5838	112	5	,	,	PUNCT
ejpam-5838	112	6	ê2	ê2	PROPN
ejpam-5838	112	7	,	,	PUNCT
ejpam-5838	112	8	ê3)−g(ê1	ê3)−g(ê1	PROPN
ejpam-5838	112	9	,	,	PUNCT
ejpam-5838	112	10	ê2	ê2	PROPN
ejpam-5838	112	11	,	,	PUNCT
ejpam-5838	112	12	ê)|	ê)|	PROPN
ejpam-5838	112	13	≤	≤	ADJ
ejpam-5838	112	14	max{g(ê	max{g(ê	NUM
ejpam-5838	112	15	,	,	PUNCT
ejpam-5838	112	16	ê3	ê3	PROPN
ejpam-5838	112	17	,	,	PUNCT
ejpam-5838	112	18	ê3	ê3	PROPN
ejpam-5838	112	19	)	)	PUNCT
ejpam-5838	112	20	,	,	PUNCT
ejpam-5838	112	21	g(ê3	g(ê3	PROPN
ejpam-5838	112	22	,	,	PUNCT
ejpam-5838	112	23	ê	ê	PROPN
ejpam-5838	112	24	,	,	PUNCT
ejpam-5838	112	25	ê	ê	NOUN
ejpam-5838	112	26	)	)	PUNCT
ejpam-5838	112	27	}	}	PUNCT
ejpam-5838	112	28	,	,	PUNCT
ejpam-5838	112	29	viii	viii	PROPN
ejpam-5838	112	30	.	.	PUNCT
ejpam-5838	113	1	|g(ê1	|g(ê1	PROPN
ejpam-5838	113	2	,	,	PUNCT
ejpam-5838	113	3	ê2	ê2	PROPN
ejpam-5838	113	4	,	,	PUNCT
ejpam-5838	113	5	ê3)−g(ê1	ê3)−g(ê1	PROPN
ejpam-5838	113	6	,	,	PUNCT
ejpam-5838	113	7	ê2	ê2	PROPN
ejpam-5838	113	8	,	,	PUNCT
ejpam-5838	113	9	ê)|	ê)|	PROPN
ejpam-5838	113	10	≤	≤	X
ejpam-5838	114	1	g(ê1	g(ê1	PROPN
ejpam-5838	114	2	,	,	PUNCT
ejpam-5838	114	3	ê	ê	PROPN
ejpam-5838	114	4	,	,	PUNCT
ejpam-5838	114	5	ê3	ê3	PROPN
ejpam-5838	114	6	)	)	PUNCT
ejpam-5838	114	7	,	,	PUNCT
ejpam-5838	114	8	ix	ix	PROPN
ejpam-5838	114	9	.	.	PUNCT
ejpam-5838	115	1	|g(ê1	|g(ê1	PROPN
ejpam-5838	115	2	,	,	PUNCT
ejpam-5838	115	3	ê2	ê2	PROPN
ejpam-5838	115	4	,	,	PUNCT
ejpam-5838	115	5	ê3)−g(q	ê3)−g(q	PROPN
ejpam-5838	115	6	,	,	PUNCT
ejpam-5838	115	7	ê3	ê3	PROPN
ejpam-5838	115	8	,	,	PUNCT
ejpam-5838	115	9	ê3)|	ê3)|	PROPN
ejpam-5838	115	10	≤	≤	PUNCT
ejpam-5838	115	11	max{g(ê1	max{g(ê1	NOUN
ejpam-5838	115	12	,	,	PUNCT
ejpam-5838	115	13	ê3	ê3	PROPN
ejpam-5838	115	14	,	,	PUNCT
ejpam-5838	115	15	ê3	ê3	PROPN
ejpam-5838	115	16	)	)	PUNCT
ejpam-5838	115	17	,	,	PUNCT
ejpam-5838	115	18	g(ê3	g(ê3	PROPN
ejpam-5838	115	19	,	,	PUNCT
ejpam-5838	115	20	ê1	ê1	PROPN
ejpam-5838	115	21	,	,	PUNCT
ejpam-5838	115	22	ê1	ê1	PROPN
ejpam-5838	115	23	)	)	PUNCT
ejpam-5838	115	24	}	}	PUNCT
ejpam-5838	115	25	,	,	PUNCT
ejpam-5838	115	26	x.	x.	PROPN
ejpam-5838	115	27	|g(ê1	|g(ê1	PROPN
ejpam-5838	115	28	,	,	PUNCT
ejpam-5838	115	29	ê2	ê2	PROPN
ejpam-5838	115	30	,	,	PUNCT
ejpam-5838	115	31	ê2)−g(ê2	ê2)−g(ê2	NUM
ejpam-5838	115	32	,	,	PUNCT
ejpam-5838	115	33	ê1	ê1	PROPN
ejpam-5838	115	34	,	,	PUNCT
ejpam-5838	115	35	ê1)|	ê1)|	PROPN
ejpam-5838	115	36	≤	≤	NUM
ejpam-5838	115	37	max{g(ê2	max{g(ê2	NOUN
ejpam-5838	115	38	,	,	PUNCT
ejpam-5838	115	39	ê1	ê1	PROPN
ejpam-5838	115	40	,	,	PUNCT
ejpam-5838	115	41	ê1	ê1	PROPN
ejpam-5838	115	42	)	)	PUNCT
ejpam-5838	115	43	,	,	PUNCT
ejpam-5838	115	44	g(ê1	g(ê1	PROPN
ejpam-5838	115	45	,	,	PUNCT
ejpam-5838	115	46	ê2	ê2	NOUN
ejpam-5838	115	47	,	,	PUNCT
ejpam-5838	115	48	ê2	ê2	NOUN
ejpam-5838	115	49	)	)	PUNCT
ejpam-5838	115	50	}	}	PUNCT
ejpam-5838	115	51	.	.	PUNCT
ejpam-5838	116	1	example	example	NOUN
ejpam-5838	117	1	1	1	NUM
ejpam-5838	117	2	.	.	PUNCT
ejpam-5838	118	1	[	[	X
ejpam-5838	118	2	9	9	NUM
ejpam-5838	118	3	]	]	PUNCT
ejpam-5838	118	4	let	let	VERB
ejpam-5838	118	5	ê	ê	PROPN
ejpam-5838	119	1	=	=	PRON
ejpam-5838	119	2	{	{	PUNCT
ejpam-5838	119	3	a	a	DET
ejpam-5838	119	4	,	,	PUNCT
ejpam-5838	119	5	b	b	NOUN
ejpam-5838	119	6	}	}	PUNCT
ejpam-5838	119	7	,	,	PUNCT
ejpam-5838	119	8	let	let	VERB
ejpam-5838	119	9	i.	i.	PROPN
ejpam-5838	119	10	g(a	g(a	PROPN
ejpam-5838	119	11	,	,	PUNCT
ejpam-5838	119	12	a	a	PRON
ejpam-5838	119	13	,	,	PUNCT
ejpam-5838	119	14	a	a	NOUN
ejpam-5838	119	15	)	)	PUNCT
ejpam-5838	119	16	=	=	SYM
ejpam-5838	120	1	g(b	g(b	X
ejpam-5838	120	2	,	,	PUNCT
ejpam-5838	120	3	b	b	NOUN
ejpam-5838	120	4	,	,	PUNCT
ejpam-5838	120	5	b	b	NOUN
ejpam-5838	120	6	)	)	PUNCT
ejpam-5838	120	7	=	=	SYM
ejpam-5838	120	8	0	0	NUM
ejpam-5838	120	9	ii	ii	PROPN
ejpam-5838	120	10	.	.	PUNCT
ejpam-5838	121	1	g(a	g(a	PROPN
ejpam-5838	121	2	,	,	PUNCT
ejpam-5838	121	3	a	a	DET
ejpam-5838	121	4	,	,	PUNCT
ejpam-5838	121	5	b	b	NOUN
ejpam-5838	121	6	)	)	PUNCT
ejpam-5838	121	7	=	=	SYM
ejpam-5838	121	8	1	1	NUM
ejpam-5838	121	9	,	,	PUNCT
ejpam-5838	121	10	g(a	g(a	PROPN
ejpam-5838	121	11	,	,	PUNCT
ejpam-5838	121	12	b	b	PROPN
ejpam-5838	121	13	,	,	PUNCT
ejpam-5838	121	14	b	b	NOUN
ejpam-5838	121	15	)	)	PUNCT
ejpam-5838	121	16	=	=	SYM
ejpam-5838	121	17	2	2	NUM
ejpam-5838	121	18	and	and	CCONJ
ejpam-5838	121	19	extend	extend	VERB
ejpam-5838	121	20	g	g	NOUN
ejpam-5838	121	21	to	to	ADP
ejpam-5838	121	22	all	all	PRON
ejpam-5838	121	23	of	of	ADP
ejpam-5838	121	24	ê	ê	PROPN
ejpam-5838	121	25	×	×	PROPN
ejpam-5838	121	26	ê	ê	PROPN
ejpam-5838	121	27	×	×	PROPN
ejpam-5838	121	28	ê	ê	PROPN
ejpam-5838	121	29	by	by	ADP
ejpam-5838	121	30	symmetry	symmetry	NOUN
ejpam-5838	121	31	in	in	ADP
ejpam-5838	121	32	the	the	DET
ejpam-5838	121	33	variables	variable	NOUN
ejpam-5838	121	34	.	.	PUNCT
ejpam-5838	122	1	then	then	ADV
ejpam-5838	122	2	it	it	PRON
ejpam-5838	122	3	is	be	AUX
ejpam-5838	122	4	easily	easily	ADV
ejpam-5838	122	5	verified	verify	VERB
ejpam-5838	122	6	that	that	SCONJ
ejpam-5838	122	7	g	g	PROPN
ejpam-5838	122	8	is	be	AUX
ejpam-5838	122	9	a	a	DET
ejpam-5838	122	10	g	g	NOUN
ejpam-5838	122	11	-	-	PUNCT
ejpam-5838	122	12	metric	metric	ADJ
ejpam-5838	122	13	,	,	PUNCT
ejpam-5838	122	14	but	but	CCONJ
ejpam-5838	122	15	g(a	g(a	PROPN
ejpam-5838	122	16	,	,	PUNCT
ejpam-5838	122	17	b	b	PROPN
ejpam-5838	122	18	,	,	PUNCT
ejpam-5838	122	19	b	b	NOUN
ejpam-5838	122	20	)	)	PUNCT
ejpam-5838	122	21	̸=	̸=	PROPN
ejpam-5838	122	22	g(a	g(a	PROPN
ejpam-5838	122	23	,	,	PUNCT
ejpam-5838	122	24	a	a	DET
ejpam-5838	122	25	,	,	PUNCT
ejpam-5838	122	26	b	b	NOUN
ejpam-5838	122	27	)	)	PUNCT
ejpam-5838	122	28	.	.	PUNCT
ejpam-5838	123	1	proposition	proposition	NOUN
ejpam-5838	123	2	2	2	NUM
ejpam-5838	123	3	(	(	PUNCT
ejpam-5838	123	4	9	9	NUM
ejpam-5838	123	5	)	)	PUNCT
ejpam-5838	123	6	.	.	PUNCT
ejpam-5838	124	1	let	let	AUX
ejpam-5838	124	2	(	(	PUNCT
ejpam-5838	124	3	ê	ê	NOUN
ejpam-5838	124	4	,	,	PUNCT
ejpam-5838	124	5	g	g	NOUN
ejpam-5838	124	6	)	)	PUNCT
ejpam-5838	124	7	be	be	AUX
ejpam-5838	124	8	a	a	DET
ejpam-5838	124	9	gm	gm	NOUN
ejpam-5838	124	10	-	-	PUNCT
ejpam-5838	124	11	space	space	NOUN
ejpam-5838	124	12	,	,	PUNCT
ejpam-5838	124	13	and	and	CCONJ
ejpam-5838	124	14	let	let	VERB
ejpam-5838	124	15	k	k	PRON
ejpam-5838	124	16	>	>	X
ejpam-5838	124	17	0	0	PROPN
ejpam-5838	124	18	,	,	PUNCT
ejpam-5838	124	19	then	then	ADV
ejpam-5838	124	20	g1	g1	PROPN
ejpam-5838	124	21	and	and	CCONJ
ejpam-5838	124	22	g2	g2	PROPN
ejpam-5838	124	23	are	be	AUX
ejpam-5838	124	24	also	also	ADV
ejpam-5838	124	25	g	g	NOUN
ejpam-5838	124	26	-	-	PUNCT
ejpam-5838	124	27	metrics	metric	NOUN
ejpam-5838	124	28	on	on	ADP
ejpam-5838	124	29	ê	ê	PROPN
ejpam-5838	124	30	,	,	PUNCT
ejpam-5838	124	31	where	where	SCONJ
ejpam-5838	124	32	,	,	PUNCT
ejpam-5838	124	33	i.	i.	PROPN
ejpam-5838	124	34	g1(ê1	g1(ê1	PROPN
ejpam-5838	124	35	,	,	PUNCT
ejpam-5838	124	36	ê2	ê2	PROPN
ejpam-5838	124	37	,	,	PUNCT
ejpam-5838	124	38	ê3	ê3	PUNCT
ejpam-5838	124	39	)	)	PUNCT
ejpam-5838	125	1	=	=	NOUN
ejpam-5838	125	2	min{k	min{k	NOUN
ejpam-5838	125	3	,	,	PUNCT
ejpam-5838	125	4	g(ê1	g(ê1	PROPN
ejpam-5838	125	5	,	,	PUNCT
ejpam-5838	125	6	ê2	ê2	PROPN
ejpam-5838	125	7	,	,	PUNCT
ejpam-5838	125	8	ê3	ê3	PROPN
ejpam-5838	125	9	)	)	PUNCT
ejpam-5838	125	10	}	}	PUNCT
ejpam-5838	125	11	,	,	PUNCT
ejpam-5838	125	12	and	and	CCONJ
ejpam-5838	125	13	ii	ii	X
ejpam-5838	125	14	.	.	PUNCT
ejpam-5838	126	1	g2(ê1	g2(ê1	PROPN
ejpam-5838	126	2	,	,	PUNCT
ejpam-5838	126	3	ê2	ê2	PROPN
ejpam-5838	126	4	,	,	PUNCT
ejpam-5838	126	5	ê3	ê3	PUNCT
ejpam-5838	126	6	)	)	PUNCT
ejpam-5838	126	7	=	=	SYM
ejpam-5838	126	8	g(ê1	g(ê1	PROPN
ejpam-5838	126	9	,	,	PUNCT
ejpam-5838	126	10	ê2	ê2	PROPN
ejpam-5838	126	11	,	,	PUNCT
ejpam-5838	126	12	ê3	ê3	PROPN
ejpam-5838	126	13	)	)	PUNCT
ejpam-5838	126	14	k	k	PROPN
ejpam-5838	127	1	+	+	PROPN
ejpam-5838	127	2	g(ê1	g(ê1	PROPN
ejpam-5838	127	3	,	,	PUNCT
ejpam-5838	127	4	ê2	ê2	PROPN
ejpam-5838	127	5	,	,	PUNCT
ejpam-5838	127	6	ê3	ê3	PROPN
ejpam-5838	127	7	)	)	PUNCT
ejpam-5838	127	8	.	.	PUNCT
ejpam-5838	128	1	further	far	ADV
ejpam-5838	128	2	,	,	PUNCT
ejpam-5838	128	3	if	if	SCONJ
ejpam-5838	128	4	ê	ê	PROPN
ejpam-5838	128	5	=	=	SYM
ejpam-5838	128	6	⋃n	⋃n	NOUN
ejpam-5838	128	7	i=1ai	i=1ai	VERB
ejpam-5838	128	8	is	be	AUX
ejpam-5838	128	9	any	any	DET
ejpam-5838	128	10	partition	partition	NOUN
ejpam-5838	128	11	of	of	ADP
ejpam-5838	128	12	ê	ê	PROPN
ejpam-5838	128	13	then	then	ADV
ejpam-5838	128	14	,	,	PUNCT
ejpam-5838	128	15	iii	iii	X
ejpam-5838	128	16	.	.	PUNCT
ejpam-5838	129	1	g3(ê1	g3(ê1	NOUN
ejpam-5838	129	2	,	,	PUNCT
ejpam-5838	129	3	ê2	ê2	PROPN
ejpam-5838	129	4	,	,	PUNCT
ejpam-5838	129	5	ê3	ê3	PUNCT
ejpam-5838	129	6	)	)	PUNCT
ejpam-5838	129	7	=	=	PRON
ejpam-5838	129	8	{	{	PUNCT
ejpam-5838	129	9	g(ê1	g(ê1	NOUN
ejpam-5838	129	10	,	,	PUNCT
ejpam-5838	129	11	ê2	ê2	PROPN
ejpam-5838	129	12	,	,	PUNCT
ejpam-5838	129	13	ê3	ê3	PROPN
ejpam-5838	129	14	)	)	PUNCT
ejpam-5838	129	15	,	,	PUNCT
ejpam-5838	129	16	if	if	SCONJ
ejpam-5838	129	17	for	for	ADP
ejpam-5838	129	18	some	some	PRON
ejpam-5838	130	1	i	i	PRON
ejpam-5838	130	2	we	we	PRON
ejpam-5838	130	3	have	have	VERB
ejpam-5838	130	4	ê1	ê1	PROPN
ejpam-5838	130	5	,	,	PUNCT
ejpam-5838	130	6	ê2	ê2	PROPN
ejpam-5838	130	7	,	,	PUNCT
ejpam-5838	130	8	ê3	ê3	VERB
ejpam-5838	131	1	∈	∈	PROPN
ejpam-5838	131	2	ai	ai	VERB
ejpam-5838	131	3	k	k	PROPN
ejpam-5838	131	4	+	+	PROPN
ejpam-5838	131	5	g(ê1	g(ê1	PROPN
ejpam-5838	131	6	,	,	PUNCT
ejpam-5838	131	7	ê2	ê2	PROPN
ejpam-5838	131	8	,	,	PUNCT
ejpam-5838	131	9	ê3	ê3	PROPN
ejpam-5838	131	10	)	)	PUNCT
ejpam-5838	131	11	,	,	PUNCT
ejpam-5838	131	12	otherwise	otherwise	ADV
ejpam-5838	131	13	,	,	PUNCT
ejpam-5838	131	14	is	be	AUX
ejpam-5838	131	15	also	also	ADV
ejpam-5838	131	16	a	a	DET
ejpam-5838	131	17	g	g	NOUN
ejpam-5838	131	18	-	-	PUNCT
ejpam-5838	131	19	metric	metric	ADJ
ejpam-5838	131	20	.	.	PUNCT
ejpam-5838	132	1	proposition	proposition	NOUN
ejpam-5838	132	2	3	3	NUM
ejpam-5838	132	3	.	.	PUNCT
ejpam-5838	133	1	[	[	X
ejpam-5838	133	2	9	9	NUM
ejpam-5838	133	3	]	]	X
ejpam-5838	133	4	let	let	ADJ
ejpam-5838	133	5	(	(	PUNCT
ejpam-5838	133	6	ê	ê	NOUN
ejpam-5838	133	7	,	,	PUNCT
ejpam-5838	133	8	g	g	NOUN
ejpam-5838	133	9	)	)	PUNCT
ejpam-5838	133	10	be	be	AUX
ejpam-5838	133	11	a	a	DET
ejpam-5838	133	12	gm	gm	NOUN
ejpam-5838	133	13	-	-	PUNCT
ejpam-5838	133	14	space	space	NOUN
ejpam-5838	133	15	,	,	PUNCT
ejpam-5838	133	16	the	the	DET
ejpam-5838	133	17	following	follow	VERB
ejpam-5838	133	18	are	be	AUX
ejpam-5838	133	19	equivalent	equivalent	ADJ
ejpam-5838	133	20	.	.	PUNCT
ejpam-5838	134	1	m.	m.	NOUN
ejpam-5838	134	2	noorwali	noorwali	PROPN
ejpam-5838	134	3	et	et	PROPN
ejpam-5838	134	4	al/	al/	PROPN
ejpam-5838	134	5	/	/	SYM
ejpam-5838	134	6	eur	eur	PROPN
ejpam-5838	134	7	.	.	PUNCT
ejpam-5838	135	1	j.	j.	PROPN
ejpam-5838	135	2	pure	pure	PROPN
ejpam-5838	135	3	appl	appl	PROPN
ejpam-5838	135	4	.	.	PROPN
ejpam-5838	135	5	math	math	PROPN
ejpam-5838	135	6	,	,	PUNCT
ejpam-5838	135	7	18	18	NUM
ejpam-5838	135	8	(	(	PUNCT
ejpam-5838	135	9	2	2	NUM
ejpam-5838	135	10	)	)	PUNCT
ejpam-5838	135	11	(	(	PUNCT
ejpam-5838	135	12	2025	2025	NUM
ejpam-5838	135	13	)	)	PUNCT
ejpam-5838	135	14	,	,	PUNCT
ejpam-5838	135	15	5838	5838	NUM
ejpam-5838	135	16	5	5	NUM
ejpam-5838	135	17	of	of	ADP
ejpam-5838	135	18	16	16	NUM
ejpam-5838	135	19	i.	i.	NOUN
ejpam-5838	135	20	(	(	PUNCT
ejpam-5838	135	21	ê	ê	PROPN
ejpam-5838	135	22	,	,	PUNCT
ejpam-5838	135	23	g	g	NOUN
ejpam-5838	135	24	)	)	PUNCT
ejpam-5838	135	25	is	be	AUX
ejpam-5838	135	26	symmetric	symmetric	ADJ
ejpam-5838	135	27	.	.	PUNCT
ejpam-5838	135	28	ii	ii	PROPN
ejpam-5838	135	29	.	.	PUNCT
ejpam-5838	136	1	g(ê1	g(ê1	NOUN
ejpam-5838	136	2	,	,	PUNCT
ejpam-5838	136	3	ê2	ê2	NOUN
ejpam-5838	136	4	,	,	PUNCT
ejpam-5838	136	5	ê2	ê2	NOUN
ejpam-5838	136	6	)	)	PUNCT
ejpam-5838	136	7	≤	≤	PUNCT
ejpam-5838	137	1	g(ê1	g(ê1	PROPN
ejpam-5838	137	2	,	,	PUNCT
ejpam-5838	137	3	ê2	ê2	PROPN
ejpam-5838	137	4	,	,	PUNCT
ejpam-5838	137	5	a	a	PRON
ejpam-5838	137	6	)	)	PUNCT
ejpam-5838	137	7	,	,	PUNCT
ejpam-5838	137	8	for	for	ADP
ejpam-5838	137	9	all	all	DET
ejpam-5838	137	10	ê1	ê1	PROPN
ejpam-5838	137	11	,	,	PUNCT
ejpam-5838	137	12	ê2	ê2	PROPN
ejpam-5838	137	13	,	,	PUNCT
ejpam-5838	137	14	a	a	DET
ejpam-5838	137	15	∈	∈	PROPN
ejpam-5838	137	16	ê.	ê.	NOUN
ejpam-5838	137	17	iii	iii	PROPN
ejpam-5838	137	18	.	.	PUNCT
ejpam-5838	138	1	g(ê1	g(ê1	NOUN
ejpam-5838	138	2	,	,	PUNCT
ejpam-5838	138	3	ê2	ê2	PROPN
ejpam-5838	138	4	,	,	PUNCT
ejpam-5838	138	5	ê3	ê3	NOUN
ejpam-5838	138	6	)	)	PUNCT
ejpam-5838	138	7	≤	≤	PUNCT
ejpam-5838	139	1	g(ê1	g(ê1	PROPN
ejpam-5838	139	2	,	,	PUNCT
ejpam-5838	139	3	ê2	ê2	PROPN
ejpam-5838	139	4	,	,	PUNCT
ejpam-5838	139	5	a	a	PRON
ejpam-5838	139	6	)	)	PUNCT
ejpam-5838	139	7	+	+	PROPN
ejpam-5838	139	8	g(ê3	g(ê3	PROPN
ejpam-5838	139	9	,	,	PUNCT
ejpam-5838	139	10	ê2	ê2	PROPN
ejpam-5838	139	11	,	,	PUNCT
ejpam-5838	139	12	b	b	NOUN
ejpam-5838	139	13	)	)	PUNCT
ejpam-5838	139	14	,	,	PUNCT
ejpam-5838	139	15	for	for	ADP
ejpam-5838	139	16	all	all	DET
ejpam-5838	139	17	ê1	ê1	PROPN
ejpam-5838	139	18	,	,	PUNCT
ejpam-5838	139	19	ê2	ê2	PROPN
ejpam-5838	139	20	,	,	PUNCT
ejpam-5838	139	21	ê3	ê3	PROPN
ejpam-5838	139	22	,	,	PUNCT
ejpam-5838	139	23	a	a	PRON
ejpam-5838	139	24	,	,	PUNCT
ejpam-5838	139	25	b	b	PROPN
ejpam-5838	139	26	∈	∈	PROPN
ejpam-5838	139	27	ê.	ê.	NOUN
ejpam-5838	139	28	proof	proof	NOUN
ejpam-5838	139	29	.	.	PUNCT
ejpam-5838	140	1	(	(	PUNCT
ejpam-5838	140	2	1	1	X
ejpam-5838	140	3	)	)	PUNCT
ejpam-5838	140	4	implies	imply	VERB
ejpam-5838	140	5	(	(	PUNCT
ejpam-5838	140	6	2	2	X
ejpam-5838	140	7	)	)	PUNCT
ejpam-5838	140	8	follows	follow	VERB
ejpam-5838	140	9	from	from	ADP
ejpam-5838	140	10	(	(	PUNCT
ejpam-5838	140	11	g3	g3	NOUN
ejpam-5838	140	12	)	)	PUNCT
ejpam-5838	140	13	whenever	whenever	SCONJ
ejpam-5838	140	14	a	a	DET
ejpam-5838	140	15	̸=	̸=	PROPN
ejpam-5838	140	16	x	x	PUNCT
ejpam-5838	140	17	and	and	CCONJ
ejpam-5838	140	18	from	from	ADP
ejpam-5838	140	19	(	(	PUNCT
ejpam-5838	140	20	ê	ê	NOUN
ejpam-5838	140	21	,	,	PUNCT
ejpam-5838	140	22	g	g	NOUN
ejpam-5838	140	23	)	)	PUNCT
ejpam-5838	140	24	being	be	AUX
ejpam-5838	140	25	symmetric	symmetric	ADJ
ejpam-5838	140	26	when	when	SCONJ
ejpam-5838	140	27	a	a	DET
ejpam-5838	140	28	=	=	NOUN
ejpam-5838	140	29	x.	x.	NOUN
ejpam-5838	140	30	combining	combine	VERB
ejpam-5838	140	31	(	(	PUNCT
ejpam-5838	140	32	2	2	NUM
ejpam-5838	140	33	)	)	PUNCT
ejpam-5838	140	34	of	of	ADP
ejpam-5838	140	35	proposition	proposition	NOUN
ejpam-5838	140	36	1	1	NUM
ejpam-5838	140	37	and	and	CCONJ
ejpam-5838	140	38	(	(	PUNCT
ejpam-5838	140	39	2	2	NUM
ejpam-5838	140	40	)	)	PUNCT
ejpam-5838	140	41	above	above	ADP
ejpam-5838	140	42	we	we	PRON
ejpam-5838	140	43	have	have	VERB
ejpam-5838	140	44	g(ê1	g(ê1	PROPN
ejpam-5838	140	45	,	,	PUNCT
ejpam-5838	140	46	ê2	ê2	PROPN
ejpam-5838	140	47	,	,	PUNCT
ejpam-5838	140	48	ê3	ê3	NOUN
ejpam-5838	140	49	)	)	PUNCT
ejpam-5838	140	50	≤	≤	PUNCT
ejpam-5838	141	1	g(ê1	g(ê1	PROPN
ejpam-5838	141	2	,	,	PUNCT
ejpam-5838	141	3	ê2	ê2	NOUN
ejpam-5838	141	4	,	,	PUNCT
ejpam-5838	141	5	ê2	ê2	PROPN
ejpam-5838	141	6	)	)	PUNCT
ejpam-5838	141	7	+	+	PROPN
ejpam-5838	141	8	g(ê3	g(ê3	PROPN
ejpam-5838	141	9	,	,	PUNCT
ejpam-5838	141	10	ê2	ê2	NOUN
ejpam-5838	141	11	,	,	PUNCT
ejpam-5838	141	12	ê2	ê2	NOUN
ejpam-5838	141	13	)	)	PUNCT
ejpam-5838	141	14	≤	≤	PUNCT
ejpam-5838	142	1	g(ê1	g(ê1	PROPN
ejpam-5838	142	2	,	,	PUNCT
ejpam-5838	142	3	ê2	ê2	PROPN
ejpam-5838	142	4	,	,	PUNCT
ejpam-5838	142	5	a	a	PRON
ejpam-5838	142	6	)	)	PUNCT
ejpam-5838	142	7	+	+	PROPN
ejpam-5838	142	8	g(ê3	g(ê3	PROPN
ejpam-5838	142	9	,	,	PUNCT
ejpam-5838	142	10	ê2	ê2	PROPN
ejpam-5838	142	11	,	,	PUNCT
ejpam-5838	142	12	b	b	NOUN
ejpam-5838	142	13	)	)	PUNCT
ejpam-5838	142	14	,	,	PUNCT
ejpam-5838	142	15	so	so	CCONJ
ejpam-5838	142	16	(	(	PUNCT
ejpam-5838	142	17	2	2	X
ejpam-5838	142	18	)	)	PUNCT
ejpam-5838	142	19	implies	imply	VERB
ejpam-5838	142	20	(	(	PUNCT
ejpam-5838	142	21	3	3	NUM
ejpam-5838	142	22	)	)	PUNCT
ejpam-5838	142	23	.	.	PUNCT
ejpam-5838	143	1	finally	finally	ADV
ejpam-5838	143	2	,	,	PUNCT
ejpam-5838	143	3	(	(	PUNCT
ejpam-5838	143	4	3	3	X
ejpam-5838	143	5	)	)	PUNCT
ejpam-5838	143	6	implies	imply	VERB
ejpam-5838	143	7	(	(	PUNCT
ejpam-5838	143	8	1	1	X
ejpam-5838	143	9	)	)	PUNCT
ejpam-5838	143	10	follows	follow	VERB
ejpam-5838	143	11	by	by	ADP
ejpam-5838	143	12	taking	take	VERB
ejpam-5838	143	13	a	a	DET
ejpam-5838	143	14	=	=	NOUN
ejpam-5838	143	15	x	x	NOUN
ejpam-5838	143	16	,	,	PUNCT
ejpam-5838	143	17	and	and	CCONJ
ejpam-5838	143	18	b	b	X
ejpam-5838	143	19	=	=	SYM
ejpam-5838	143	20	y	y	PROPN
ejpam-5838	143	21	in	in	ADP
ejpam-5838	143	22	(	(	PUNCT
ejpam-5838	143	23	3	3	NUM
ejpam-5838	143	24	)	)	PUNCT
ejpam-5838	143	25	.	.	PUNCT
ejpam-5838	144	1	3	3	X
ejpam-5838	144	2	.	.	X
ejpam-5838	144	3	main	main	ADJ
ejpam-5838	144	4	results	result	NOUN
ejpam-5838	144	5	in	in	ADP
ejpam-5838	144	6	this	this	DET
ejpam-5838	144	7	particular	particular	ADJ
ejpam-5838	144	8	section	section	NOUN
ejpam-5838	144	9	,	,	PUNCT
ejpam-5838	144	10	two	two	NUM
ejpam-5838	144	11	important	important	ADJ
ejpam-5838	144	12	theorems	theorem	NOUN
ejpam-5838	144	13	are	be	AUX
ejpam-5838	144	14	addressed	address	VERB
ejpam-5838	144	15	.	.	PUNCT
ejpam-5838	145	1	for	for	ADP
ejpam-5838	145	2	the	the	DET
ejpam-5838	145	3	justification	justification	NOUN
ejpam-5838	145	4	of	of	ADP
ejpam-5838	145	5	these	these	DET
ejpam-5838	145	6	theorems	theorem	NOUN
ejpam-5838	145	7	suitable	suitable	ADJ
ejpam-5838	145	8	examples	example	NOUN
ejpam-5838	145	9	are	be	AUX
ejpam-5838	145	10	generated	generate	VERB
ejpam-5838	145	11	.	.	PUNCT
ejpam-5838	146	1	in	in	ADP
ejpam-5838	146	2	continuation	continuation	NOUN
ejpam-5838	146	3	,	,	PUNCT
ejpam-5838	146	4	applications	application	NOUN
ejpam-5838	146	5	of	of	ADP
ejpam-5838	146	6	these	these	DET
ejpam-5838	146	7	particular	particular	ADJ
ejpam-5838	146	8	theorems	theorem	NOUN
ejpam-5838	146	9	are	be	AUX
ejpam-5838	146	10	reflected	reflect	VERB
ejpam-5838	146	11	.	.	PUNCT
ejpam-5838	147	1	in	in	ADP
ejpam-5838	147	2	specifically	specifically	ADV
ejpam-5838	147	3	,	,	PUNCT
ejpam-5838	147	4	the	the	DET
ejpam-5838	147	5	parameters	parameter	NOUN
ejpam-5838	147	6	α	α	PROPN
ejpam-5838	147	7	and	and	CCONJ
ejpam-5838	147	8	β	β	X
ejpam-5838	147	9	must	must	AUX
ejpam-5838	147	10	be	be	AUX
ejpam-5838	147	11	non	non	ADJ
ejpam-5838	147	12	-	-	ADJ
ejpam-5838	147	13	negative	negative	ADJ
ejpam-5838	147	14	and	and	CCONJ
ejpam-5838	147	15	less	less	ADJ
ejpam-5838	147	16	than	than	ADP
ejpam-5838	147	17	one	one	NUM
ejpam-5838	147	18	,	,	PUNCT
ejpam-5838	147	19	with	with	ADP
ejpam-5838	147	20	their	their	PRON
ejpam-5838	147	21	sum	sum	NOUN
ejpam-5838	147	22	being	be	AUX
ejpam-5838	147	23	limited	limit	VERB
ejpam-5838	147	24	to	to	ADP
ejpam-5838	147	25	less	less	ADJ
ejpam-5838	147	26	than	than	ADP
ejpam-5838	147	27	one	one	NUM
ejpam-5838	147	28	for	for	ADP
ejpam-5838	147	29	uniqueness	uniqueness	NOUN
ejpam-5838	147	30	.	.	PUNCT
ejpam-5838	148	1	the	the	DET
ejpam-5838	148	2	conclusions	conclusion	NOUN
ejpam-5838	148	3	are	be	AUX
ejpam-5838	148	4	based	base	VERB
ejpam-5838	148	5	on	on	ADP
ejpam-5838	148	6	the	the	DET
ejpam-5838	148	7	contractive	contractive	ADJ
ejpam-5838	148	8	property	property	NOUN
ejpam-5838	148	9	that	that	PRON
ejpam-5838	148	10	the	the	DET
ejpam-5838	148	11	mappings	mapping	NOUN
ejpam-5838	148	12	exhibit	exhibit	VERB
ejpam-5838	148	13	.	.	PUNCT
ejpam-5838	149	1	ultimately	ultimately	ADV
ejpam-5838	149	2	,	,	PUNCT
ejpam-5838	149	3	the	the	DET
ejpam-5838	149	4	sequence	sequence	NOUN
ejpam-5838	149	5	converges	converge	VERB
ejpam-5838	149	6	to	to	ADP
ejpam-5838	149	7	a	a	DET
ejpam-5838	149	8	unique	unique	ADJ
ejpam-5838	149	9	cfp	cfp	NOUN
ejpam-5838	149	10	because	because	SCONJ
ejpam-5838	149	11	the	the	DET
ejpam-5838	149	12	iterative	iterative	NOUN
ejpam-5838	149	13	sequences	sequence	NOUN
ejpam-5838	149	14	provided	provide	VERB
ejpam-5838	149	15	in	in	ADP
ejpam-5838	149	16	the	the	DET
ejpam-5838	149	17	proof	proof	NOUN
ejpam-5838	149	18	show	show	VERB
ejpam-5838	149	19	that	that	SCONJ
ejpam-5838	149	20	the	the	DET
ejpam-5838	149	21	mappings	mapping	NOUN
ejpam-5838	149	22	compress	compress	VERB
ejpam-5838	149	23	distances	distance	NOUN
ejpam-5838	149	24	in	in	ADP
ejpam-5838	149	25	a	a	DET
ejpam-5838	149	26	way	way	NOUN
ejpam-5838	149	27	that	that	PRON
ejpam-5838	149	28	guarantees	guarantee	VERB
ejpam-5838	149	29	convergence	convergence	NOUN
ejpam-5838	149	30	to	to	ADP
ejpam-5838	149	31	a	a	DET
ejpam-5838	149	32	point	point	NOUN
ejpam-5838	149	33	in	in	ADP
ejpam-5838	149	34	the	the	DET
ejpam-5838	149	35	whole	whole	ADJ
ejpam-5838	149	36	gm	gm	NOUN
ejpam-5838	149	37	-	-	PUNCT
ejpam-5838	149	38	space	space	NOUN
ejpam-5838	149	39	.	.	PUNCT
ejpam-5838	150	1	furthermore	furthermore	ADV
ejpam-5838	150	2	,	,	PUNCT
ejpam-5838	150	3	the	the	DET
ejpam-5838	150	4	context	context	NOUN
ejpam-5838	150	5	within	within	ADP
ejpam-5838	150	6	which	which	PRON
ejpam-5838	150	7	these	these	DET
ejpam-5838	150	8	results	result	NOUN
ejpam-5838	150	9	can	can	AUX
ejpam-5838	150	10	be	be	AUX
ejpam-5838	150	11	applied	apply	VERB
ejpam-5838	150	12	is	be	AUX
ejpam-5838	150	13	expanded	expand	VERB
ejpam-5838	150	14	by	by	ADP
ejpam-5838	150	15	the	the	DET
ejpam-5838	150	16	corollaries	corollary	NOUN
ejpam-5838	150	17	obtained	obtain	VERB
ejpam-5838	150	18	from	from	ADP
ejpam-5838	150	19	theorem	theorem	VERB
ejpam-5838	150	20	,	,	PUNCT
ejpam-5838	150	21	which	which	PRON
ejpam-5838	150	22	support	support	VERB
ejpam-5838	150	23	the	the	DET
ejpam-5838	150	24	applicability	applicability	NOUN
ejpam-5838	150	25	of	of	ADP
ejpam-5838	150	26	these	these	DET
ejpam-5838	150	27	discoveries	discovery	NOUN
ejpam-5838	150	28	under	under	ADP
ejpam-5838	150	29	more	more	ADV
ejpam-5838	150	30	particular	particular	ADJ
ejpam-5838	150	31	constraints	constraint	NOUN
ejpam-5838	150	32	for	for	ADP
ejpam-5838	150	33	α	α	NOUN
ejpam-5838	150	34	and	and	CCONJ
ejpam-5838	150	35	β	β	X
ejpam-5838	150	36	.	.	PUNCT
ejpam-5838	151	1	by	by	ADP
ejpam-5838	151	2	showing	show	VERB
ejpam-5838	151	3	that	that	SCONJ
ejpam-5838	151	4	the	the	DET
ejpam-5838	151	5	existence	existence	NOUN
ejpam-5838	151	6	and	and	CCONJ
ejpam-5838	151	7	uniqueness	uniqueness	NOUN
ejpam-5838	151	8	of	of	ADP
ejpam-5838	151	9	fixed	fix	VERB
ejpam-5838	151	10	points	point	NOUN
ejpam-5838	151	11	are	be	AUX
ejpam-5838	151	12	directly	directly	ADV
ejpam-5838	151	13	influenced	influence	VERB
ejpam-5838	151	14	by	by	ADP
ejpam-5838	151	15	the	the	DET
ejpam-5838	151	16	interaction	interaction	NOUN
ejpam-5838	151	17	between	between	ADP
ejpam-5838	151	18	the	the	DET
ejpam-5838	151	19	contraction	contraction	NOUN
ejpam-5838	151	20	qualities	quality	NOUN
ejpam-5838	151	21	of	of	ADP
ejpam-5838	151	22	the	the	DET
ejpam-5838	151	23	mappings	mapping	NOUN
ejpam-5838	151	24	,	,	PUNCT
ejpam-5838	151	25	the	the	DET
ejpam-5838	151	26	theorem	theorem	NOUN
ejpam-5838	151	27	and	and	CCONJ
ejpam-5838	151	28	its	its	PRON
ejpam-5838	151	29	corollaries	corollary	NOUN
ejpam-5838	151	30	thus	thus	ADV
ejpam-5838	151	31	make	make	VERB
ejpam-5838	151	32	a	a	DET
ejpam-5838	151	33	substantial	substantial	ADJ
ejpam-5838	151	34	contribution	contribution	NOUN
ejpam-5838	151	35	to	to	ADP
ejpam-5838	151	36	the	the	DET
ejpam-5838	151	37	understanding	understanding	NOUN
ejpam-5838	151	38	of	of	ADP
ejpam-5838	151	39	fixed	fix	VERB
ejpam-5838	151	40	point	point	NOUN
ejpam-5838	151	41	theory	theory	NOUN
ejpam-5838	151	42	in	in	ADP
ejpam-5838	151	43	the	the	DET
ejpam-5838	151	44	setting	setting	NOUN
ejpam-5838	151	45	of	of	ADP
ejpam-5838	151	46	gm	gm	PROPN
ejpam-5838	151	47	-	-	PUNCT
ejpam-5838	151	48	spaces	space	NOUN
ejpam-5838	151	49	.	.	PUNCT
ejpam-5838	152	1	this	this	PRON
ejpam-5838	152	2	is	be	AUX
ejpam-5838	152	3	a	a	DET
ejpam-5838	152	4	useful	useful	ADJ
ejpam-5838	152	5	tool	tool	NOUN
ejpam-5838	152	6	for	for	ADP
ejpam-5838	152	7	additional	additional	ADJ
ejpam-5838	152	8	research	research	NOUN
ejpam-5838	152	9	in	in	ADP
ejpam-5838	152	10	a	a	DET
ejpam-5838	152	11	variety	variety	NOUN
ejpam-5838	152	12	of	of	ADP
ejpam-5838	152	13	applied	apply	VERB
ejpam-5838	152	14	and	and	CCONJ
ejpam-5838	152	15	mathematical	mathematical	ADJ
ejpam-5838	152	16	situations	situation	NOUN
ejpam-5838	152	17	where	where	SCONJ
ejpam-5838	152	18	these	these	DET
ejpam-5838	152	19	mappings	mapping	NOUN
ejpam-5838	152	20	are	be	AUX
ejpam-5838	152	21	pertinent	pertinent	ADJ
ejpam-5838	152	22	.	.	PUNCT
ejpam-5838	153	1	theorem	theorem	NOUN
ejpam-5838	153	2	1	1	NUM
ejpam-5838	153	3	.	.	PUNCT
ejpam-5838	154	1	let	let	AUX
ejpam-5838	154	2	(	(	PUNCT
ejpam-5838	154	3	ê	ê	NOUN
ejpam-5838	154	4	,	,	PUNCT
ejpam-5838	154	5	g	g	NOUN
ejpam-5838	154	6	)	)	PUNCT
ejpam-5838	154	7	be	be	AUX
ejpam-5838	154	8	a	a	DET
ejpam-5838	154	9	gm	gm	PROPN
ejpam-5838	154	10	-space	-space	NOUN
ejpam-5838	154	11	and	and	CCONJ
ejpam-5838	154	12	f1	f1	NOUN
ejpam-5838	154	13	,	,	PUNCT
ejpam-5838	154	14	f2	f2	PROPN
ejpam-5838	154	15	,	,	PUNCT
ejpam-5838	154	16	f3	f3	PROPN
ejpam-5838	154	17	:	:	PUNCT
ejpam-5838	154	18	ê	ê	PROPN
ejpam-5838	154	19	→	→	SYM
ejpam-5838	154	20	ê	ê	PROPN
ejpam-5838	154	21	be	be	AUX
ejpam-5838	154	22	3	3	NUM
ejpam-5838	154	23	-	-	PUNCT
ejpam-5838	154	24	self	self	NOUN
ejpam-5838	154	25	-	-	PUNCT
ejpam-5838	154	26	mappings	mapping	NOUN
ejpam-5838	154	27	satisfying	satisfying	ADJ
ejpam-5838	154	28	:	:	PUNCT
ejpam-5838	155	1	g(f1ê1	g(f1ê1	NOUN
ejpam-5838	155	2	,	,	PUNCT
ejpam-5838	155	3	f2ê2	f2ê2	NOUN
ejpam-5838	155	4	,	,	PUNCT
ejpam-5838	155	5	f3ê3	f3ê3	PROPN
ejpam-5838	155	6	)	)	PUNCT
ejpam-5838	155	7	≤	≤	NOUN
ejpam-5838	155	8	αg(ê1	αg(ê1	PROPN
ejpam-5838	155	9	,	,	PUNCT
ejpam-5838	155	10	ê2	ê2	PROPN
ejpam-5838	155	11	,	,	PUNCT
ejpam-5838	155	12	ê3	ê3	PUNCT
ejpam-5838	155	13	)	)	PUNCT
ejpam-5838	156	1	+	+	CCONJ
ejpam-5838	156	2	β	β	X
ejpam-5838	156	3	(	(	PUNCT
ejpam-5838	156	4	g(ê1	g(ê1	PROPN
ejpam-5838	156	5	,	,	PUNCT
ejpam-5838	156	6	f2ê2	f2ê2	ADJ
ejpam-5838	156	7	,	,	PUNCT
ejpam-5838	156	8	f2ê2	f2ê2	NOUN
ejpam-5838	156	9	)	)	PUNCT
ejpam-5838	156	10	·	·	PUNCT
ejpam-5838	156	11	g(ê1	g(ê1	PROPN
ejpam-5838	156	12	,	,	PUNCT
ejpam-5838	156	13	f3ê3	f3ê3	PROPN
ejpam-5838	156	14	,	,	PUNCT
ejpam-5838	156	15	f3ê3	f3ê3	PROPN
ejpam-5838	156	16	)	)	PUNCT
ejpam-5838	156	17	·	·	PUNCT
ejpam-5838	156	18	g(ê2	g(ê2	PROPN
ejpam-5838	156	19	,	,	PUNCT
ejpam-5838	156	20	f1ê1	f1ê1	PROPN
ejpam-5838	156	21	,	,	PUNCT
ejpam-5838	156	22	f1ê1	f1ê1	PROPN
ejpam-5838	156	23	)	)	PUNCT
ejpam-5838	156	24	1	1	NUM
ejpam-5838	157	1	+	+	CCONJ
ejpam-5838	158	1	[	[	X
ejpam-5838	158	2	g(ê2	g(ê2	ADJ
ejpam-5838	158	3	,	,	PUNCT
ejpam-5838	158	4	f1ê1	f1ê1	PROPN
ejpam-5838	158	5	,	,	PUNCT
ejpam-5838	158	6	f1ê1	f1ê1	PROPN
ejpam-5838	158	7	)	)	PUNCT
ejpam-5838	158	8	·	·	PUNCT
ejpam-5838	158	9	g(ê3	g(ê3	PROPN
ejpam-5838	158	10	,	,	PUNCT
ejpam-5838	158	11	f2ê2	f2ê2	NOUN
ejpam-5838	158	12	,	,	PUNCT
ejpam-5838	158	13	f2ê2	f2ê2	NOUN
ejpam-5838	158	14	)	)	PUNCT
ejpam-5838	158	15	·	·	PUNCT
ejpam-5838	158	16	g(ê1	g(ê1	PROPN
ejpam-5838	158	17	,	,	PUNCT
ejpam-5838	158	18	f3ê3	f3ê3	PROPN
ejpam-5838	158	19	,	,	PUNCT
ejpam-5838	158	20	f3ê3	f3ê3	PROPN
ejpam-5838	158	21	)	)	PUNCT
ejpam-5838	158	22	]	]	PUNCT
ejpam-5838	158	23	+	+	CCONJ
ejpam-5838	158	24	g(ê2	g(ê2	PROPN
ejpam-5838	158	25	,	,	PUNCT
ejpam-5838	158	26	f3ê3	f3ê3	PROPN
ejpam-5838	158	27	,	,	PUNCT
ejpam-5838	158	28	f3ê3	f3ê3	PROPN
ejpam-5838	158	29	)	)	PUNCT
ejpam-5838	158	30	·	·	PUNCT
ejpam-5838	158	31	g(ê3	g(ê3	PROPN
ejpam-5838	158	32	,	,	PUNCT
ejpam-5838	158	33	f1ê1	f1ê1	PROPN
ejpam-5838	158	34	,	,	PUNCT
ejpam-5838	158	35	f1ê1	f1ê1	PROPN
ejpam-5838	158	36	)	)	PUNCT
ejpam-5838	158	37	·	·	PUNCT
ejpam-5838	158	38	g(ê3	g(ê3	PROPN
ejpam-5838	158	39	,	,	PUNCT
ejpam-5838	158	40	f2ê2	f2ê2	NOUN
ejpam-5838	158	41	,	,	PUNCT
ejpam-5838	158	42	f2ê2	f2ê2	NOUN
ejpam-5838	158	43	)	)	PUNCT
ejpam-5838	158	44	1	1	NUM
ejpam-5838	158	45	+	+	CCONJ
ejpam-5838	159	1	[	[	X
ejpam-5838	159	2	g(ê2	g(ê2	ADJ
ejpam-5838	159	3	,	,	PUNCT
ejpam-5838	159	4	f1ê1	f1ê1	PROPN
ejpam-5838	159	5	,	,	PUNCT
ejpam-5838	159	6	f1ê1	f1ê1	PROPN
ejpam-5838	159	7	)	)	PUNCT
ejpam-5838	159	8	·	·	PUNCT
ejpam-5838	159	9	g(ê3	g(ê3	PROPN
ejpam-5838	159	10	,	,	PUNCT
ejpam-5838	159	11	f2ê2	f2ê2	NOUN
ejpam-5838	159	12	,	,	PUNCT
ejpam-5838	159	13	f2ê2	f2ê2	NOUN
ejpam-5838	159	14	)	)	PUNCT
ejpam-5838	159	15	·	·	PUNCT
ejpam-5838	159	16	g(ê1	g(ê1	PROPN
ejpam-5838	159	17	,	,	PUNCT
ejpam-5838	159	18	f3ê3	f3ê3	PROPN
ejpam-5838	159	19	,	,	PUNCT
ejpam-5838	159	20	f3ê3	f3ê3	PROPN
ejpam-5838	159	21	)	)	PUNCT
ejpam-5838	159	22	]	]	PUNCT
ejpam-5838	159	23	)	)	PUNCT
ejpam-5838	159	24	(	(	PUNCT
ejpam-5838	159	25	3.1	3.1	NUM
ejpam-5838	159	26	)	)	PUNCT
ejpam-5838	159	27	for	for	ADP
ejpam-5838	159	28	all	all	DET
ejpam-5838	159	29	ê1	ê1	PROPN
ejpam-5838	159	30	,	,	PUNCT
ejpam-5838	159	31	ê2	ê2	PROPN
ejpam-5838	159	32	,	,	PUNCT
ejpam-5838	159	33	ê3	ê3	PROPN
ejpam-5838	159	34	∈	∈	PROPN
ejpam-5838	159	35	ê	ê	PROPN
ejpam-5838	159	36	and	and	CCONJ
ejpam-5838	159	37	α	α	PROPN
ejpam-5838	159	38	,	,	PUNCT
ejpam-5838	159	39	β	β	X
ejpam-5838	159	40	≥	≥	NOUN
ejpam-5838	159	41	0	0	NUM
ejpam-5838	159	42	with	with	ADP
ejpam-5838	159	43	α	α	PROPN
ejpam-5838	159	44	,	,	PUNCT
ejpam-5838	159	45	β	β	X
ejpam-5838	159	46	<	<	X
ejpam-5838	159	47	1	1	NUM
ejpam-5838	159	48	.	.	PUNCT
ejpam-5838	160	1	the	the	DET
ejpam-5838	160	2	3	3	NUM
ejpam-5838	160	3	-	-	PUNCT
ejpam-5838	160	4	self	self	NOUN
ejpam-5838	160	5	-	-	PUNCT
ejpam-5838	160	6	mapping	mapping	NOUN
ejpam-5838	160	7	followed	follow	VERB
ejpam-5838	160	8	f1	f1	NOUN
ejpam-5838	160	9	,	,	PUNCT
ejpam-5838	160	10	f2	f2	PROPN
ejpam-5838	160	11	&	&	CCONJ
ejpam-5838	160	12	f3	f3	PROPN
ejpam-5838	160	13	has	have	VERB
ejpam-5838	160	14	a	a	DET
ejpam-5838	160	15	cfp	cfp	NOUN
ejpam-5838	160	16	in	in	ADP
ejpam-5838	160	17	ê.	ê.	NOUN
ejpam-5838	160	18	also	also	ADV
ejpam-5838	160	19	,	,	PUNCT
ejpam-5838	160	20	if	if	SCONJ
ejpam-5838	160	21	(	(	PUNCT
ejpam-5838	160	22	α+	α+	X
ejpam-5838	160	23	β	β	X
ejpam-5838	160	24	)	)	PUNCT
ejpam-5838	160	25	<	<	X
ejpam-5838	160	26	1	1	NUM
ejpam-5838	160	27	,	,	PUNCT
ejpam-5838	160	28	then	then	ADV
ejpam-5838	160	29	f1	f1	NOUN
ejpam-5838	160	30	,	,	PUNCT
ejpam-5838	160	31	f2	f2	PROPN
ejpam-5838	160	32	&	&	CCONJ
ejpam-5838	160	33	f3	f3	PROPN
ejpam-5838	160	34	have	have	VERB
ejpam-5838	160	35	a	a	DET
ejpam-5838	160	36	unique	unique	ADJ
ejpam-5838	160	37	cfp	cfp	NOUN
ejpam-5838	160	38	in	in	ADP
ejpam-5838	160	39	ê.	ê.	NOUN
ejpam-5838	160	40	proof	proof	NOUN
ejpam-5838	160	41	.	.	PUNCT
ejpam-5838	161	1	fix	fix	VERB
ejpam-5838	161	2	ê0	ê0	PROPN
ejpam-5838	161	3	∈	∈	PROPN
ejpam-5838	161	4	ê	ê	PROPN
ejpam-5838	161	5	,	,	PUNCT
ejpam-5838	161	6	we	we	PRON
ejpam-5838	161	7	now	now	ADV
ejpam-5838	161	8	define	define	VERB
ejpam-5838	161	9	iterative	iterative	ADJ
ejpam-5838	161	10	sequences	sequence	NOUN
ejpam-5838	161	11	in	in	ADP
ejpam-5838	161	12	ê	ê	PROPN
ejpam-5838	161	13	as	as	SCONJ
ejpam-5838	161	14	follows	follow	VERB
ejpam-5838	161	15	:	:	PUNCT
ejpam-5838	162	1	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	162	2	=	=	SYM
ejpam-5838	162	3	f1ê3⋎	f1ê3⋎	SYM
ejpam-5838	162	4	,	,	PUNCT
ejpam-5838	162	5	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	162	6	=	=	SYM
ejpam-5838	162	7	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	162	8	,	,	PUNCT
ejpam-5838	162	9	and	and	CCONJ
ejpam-5838	162	10	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	162	11	=	=	PUNCT
ejpam-5838	162	12	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	162	13	∀⋎	∀⋎	VERB
ejpam-5838	162	14	≥	≥	NOUN
ejpam-5838	162	15	0	0	NUM
ejpam-5838	162	16	.	.	PUNCT
ejpam-5838	163	1	by	by	ADP
ejpam-5838	163	2	using	use	VERB
ejpam-5838	163	3	(	(	PUNCT
ejpam-5838	163	4	3.1	3.1	NUM
ejpam-5838	163	5	)	)	PUNCT
ejpam-5838	163	6	,	,	PUNCT
ejpam-5838	163	7	we	we	PRON
ejpam-5838	163	8	have	have	VERB
ejpam-5838	163	9	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	163	10	,	,	PUNCT
ejpam-5838	163	11	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	163	12	,	,	PUNCT
ejpam-5838	163	13	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	163	14	)	)	PUNCT
ejpam-5838	164	1	=	=	SYM
ejpam-5838	164	2	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	164	3	,	,	PUNCT
ejpam-5838	164	4	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	164	5	,	,	PUNCT
ejpam-5838	164	6	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	164	7	)	)	PUNCT
ejpam-5838	164	8	≤	≤	NOUN
ejpam-5838	164	9	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	164	10	,	,	PUNCT
ejpam-5838	164	11	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	164	12	,	,	PUNCT
ejpam-5838	164	13	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	164	14	)	)	PUNCT
ejpam-5838	165	1	+	+	CCONJ
ejpam-5838	165	2	β	β	X
ejpam-5838	165	3	(	(	PUNCT
ejpam-5838	165	4	n	n	NOUN
ejpam-5838	165	5	d	d	NOUN
ejpam-5838	165	6	)	)	PUNCT
ejpam-5838	165	7	n	n	NOUN
ejpam-5838	165	8	=	=	SYM
ejpam-5838	165	9	g(ê3⋎	g(ê3⋎	NUM
ejpam-5838	165	10	,	,	PUNCT
ejpam-5838	165	11	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	165	12	,	,	PUNCT
ejpam-5838	165	13	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	165	14	)	)	PUNCT
ejpam-5838	165	15	·	·	PUNCT
ejpam-5838	165	16	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	165	17	,	,	PUNCT
ejpam-5838	165	18	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	165	19	,	,	PUNCT
ejpam-5838	165	20	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	165	21	)	)	PUNCT
ejpam-5838	165	22	·	·	PUNCT
ejpam-5838	165	23	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	165	24	,	,	PUNCT
ejpam-5838	165	25	f1ê3⋎	f1ê3⋎	X
ejpam-5838	165	26	,	,	PUNCT
ejpam-5838	165	27	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	165	28	)	)	PUNCT
ejpam-5838	165	29	·	·	PUNCT
ejpam-5838	165	30	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	165	31	,	,	PUNCT
ejpam-5838	165	32	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	165	33	,	,	PUNCT
ejpam-5838	165	34	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	165	35	)	)	PUNCT
ejpam-5838	165	36	·	·	PUNCT
ejpam-5838	165	37	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	165	38	,	,	PUNCT
ejpam-5838	165	39	f1ê3⋎	f1ê3⋎	X
ejpam-5838	165	40	,	,	PUNCT
ejpam-5838	165	41	f1ê3⋎	f1ê3⋎	X
ejpam-5838	165	42	)	)	PUNCT
ejpam-5838	165	43	·	·	PUNCT
ejpam-5838	165	44	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	165	45	,	,	PUNCT
ejpam-5838	165	46	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	165	47	,	,	PUNCT
ejpam-5838	165	48	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	165	49	)	)	PUNCT
ejpam-5838	165	50	d	d	NOUN
ejpam-5838	165	51	=	=	SYM
ejpam-5838	165	52	1	1	NUM
ejpam-5838	165	53	+	+	NOUN
ejpam-5838	165	54	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	165	55	,	,	PUNCT
ejpam-5838	165	56	f1ê3⋎	f1ê3⋎	X
ejpam-5838	165	57	,	,	PUNCT
ejpam-5838	165	58	f1ê3⋎	f1ê3⋎	X
ejpam-5838	165	59	)	)	PUNCT
ejpam-5838	165	60	·	·	PUNCT
ejpam-5838	165	61	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	165	62	,	,	PUNCT
ejpam-5838	165	63	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	165	64	,	,	PUNCT
ejpam-5838	165	65	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	165	66	)	)	PUNCT
ejpam-5838	165	67	·	·	PUNCT
ejpam-5838	165	68	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	165	69	,	,	PUNCT
ejpam-5838	165	70	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	165	71	,	,	PUNCT
ejpam-5838	165	72	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	165	73	)	)	PUNCT
ejpam-5838	165	74	m.	m.	NOUN
ejpam-5838	165	75	noorwali	noorwali	PROPN
ejpam-5838	165	76	et	et	PROPN
ejpam-5838	165	77	al/	al/	PROPN
ejpam-5838	165	78	/	/	SYM
ejpam-5838	165	79	eur	eur	PROPN
ejpam-5838	165	80	.	.	PUNCT
ejpam-5838	166	1	j.	j.	PROPN
ejpam-5838	166	2	pure	pure	PROPN
ejpam-5838	166	3	appl	appl	PROPN
ejpam-5838	166	4	.	.	PROPN
ejpam-5838	166	5	math	math	PROPN
ejpam-5838	166	6	,	,	PUNCT
ejpam-5838	166	7	18	18	NUM
ejpam-5838	166	8	(	(	PUNCT
ejpam-5838	166	9	2	2	NUM
ejpam-5838	166	10	)	)	PUNCT
ejpam-5838	166	11	(	(	PUNCT
ejpam-5838	166	12	2025	2025	NUM
ejpam-5838	166	13	)	)	PUNCT
ejpam-5838	166	14	,	,	PUNCT
ejpam-5838	166	15	5838	5838	NUM
ejpam-5838	166	16	6	6	NUM
ejpam-5838	166	17	of	of	ADP
ejpam-5838	166	18	16	16	NUM
ejpam-5838	166	19	≤	≤	NUM
ejpam-5838	166	20	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	166	21	,	,	PUNCT
ejpam-5838	166	22	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	166	23	,	,	PUNCT
ejpam-5838	166	24	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	166	25	)	)	PUNCT
ejpam-5838	167	1	+	+	CCONJ
ejpam-5838	167	2	β	β	X
ejpam-5838	167	3			PROPN
ejpam-5838	167	4	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	167	5	,	,	PUNCT
ejpam-5838	167	6	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	167	7	,	,	PUNCT
ejpam-5838	167	8	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	167	9	)	)	PUNCT
ejpam-5838	167	10	·	·	PUNCT
ejpam-5838	167	11	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	167	12	,	,	PUNCT
ejpam-5838	167	13	ê3⋎+3	ê3⋎+3	NUM
ejpam-5838	167	14	,	,	PUNCT
ejpam-5838	167	15	ê3⋎+3	ê3⋎+3	X
ejpam-5838	167	16	)	)	PUNCT
ejpam-5838	167	17	·	·	PUNCT
ejpam-5838	167	18	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	167	19	,	,	PUNCT
ejpam-5838	167	20	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	167	21	,	,	PUNCT
ejpam-5838	167	22	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	167	23	)	)	PUNCT
ejpam-5838	168	1	+	+	NOUN
ejpam-5838	168	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	168	3	,	,	PUNCT
ejpam-5838	168	4	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	168	5	,	,	PUNCT
ejpam-5838	168	6	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	168	7	)	)	PUNCT
ejpam-5838	168	8	·	·	PUNCT
ejpam-5838	168	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	168	10	,	,	PUNCT
ejpam-5838	168	11	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	168	12	,	,	PUNCT
ejpam-5838	168	13	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	168	14	)	)	PUNCT
ejpam-5838	168	15	·	·	PUNCT
ejpam-5838	168	16	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	168	17	,	,	PUNCT
ejpam-5838	168	18	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	168	19	,	,	PUNCT
ejpam-5838	168	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	168	21	)	)	PUNCT
ejpam-5838	168	22	1	1	NUM
ejpam-5838	169	1	+	+	CCONJ
ejpam-5838	169	2	[	[	X
ejpam-5838	169	3	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	169	4	,	,	PUNCT
ejpam-5838	169	5	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	169	6	,	,	PUNCT
ejpam-5838	169	7	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	169	8	)	)	PUNCT
ejpam-5838	169	9	·	·	PUNCT
ejpam-5838	170	1	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	170	2	,	,	PUNCT
ejpam-5838	170	3	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	170	4	,	,	PUNCT
ejpam-5838	170	5	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	170	6	)	)	PUNCT
ejpam-5838	170	7	·	·	PUNCT
ejpam-5838	170	8	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	170	9	,	,	PUNCT
ejpam-5838	170	10	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	170	11	,	,	PUNCT
ejpam-5838	170	12	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	170	13	)	)	PUNCT
ejpam-5838	170	14	]	]	PUNCT
ejpam-5838	171	1			ADP
ejpam-5838	171	2	after	after	ADP
ejpam-5838	171	3	simplification	simplification	NOUN
ejpam-5838	171	4	,	,	PUNCT
ejpam-5838	171	5	we	we	PRON
ejpam-5838	171	6	have	have	VERB
ejpam-5838	171	7	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	171	8	,	,	PUNCT
ejpam-5838	171	9	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	171	10	,	,	PUNCT
ejpam-5838	171	11	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	171	12	)	)	PUNCT
ejpam-5838	171	13	≤	≤	NUM
ejpam-5838	171	14	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	171	15	,	,	PUNCT
ejpam-5838	171	16	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	171	17	,	,	PUNCT
ejpam-5838	171	18	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	171	19	)	)	PUNCT
ejpam-5838	171	20	(	(	PUNCT
ejpam-5838	171	21	1	1	X
ejpam-5838	171	22	)	)	PUNCT
ejpam-5838	171	23	similarly	similarly	ADV
ejpam-5838	171	24	,	,	PUNCT
ejpam-5838	171	25	again	again	ADV
ejpam-5838	171	26	by	by	ADP
ejpam-5838	171	27	the	the	DET
ejpam-5838	171	28	view	view	NOUN
ejpam-5838	171	29	of	of	ADP
ejpam-5838	171	30	(	(	PUNCT
ejpam-5838	171	31	3.1	3.1	NUM
ejpam-5838	171	32	)	)	PUNCT
ejpam-5838	171	33	,	,	PUNCT
ejpam-5838	171	34	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	171	35	,	,	PUNCT
ejpam-5838	171	36	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	171	37	,	,	PUNCT
ejpam-5838	171	38	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	171	39	)	)	PUNCT
ejpam-5838	172	1	=	=	SYM
ejpam-5838	172	2	g(f1ê3⋎+1	g(f1ê3⋎+1	ADJ
ejpam-5838	172	3	,	,	PUNCT
ejpam-5838	172	4	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	172	5	,	,	PUNCT
ejpam-5838	172	6	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	172	7	)	)	PUNCT
ejpam-5838	172	8	≤	≤	NOUN
ejpam-5838	172	9	αg(ê3⋎+1	αg(ê3⋎+1	ADJ
ejpam-5838	172	10	,	,	PUNCT
ejpam-5838	172	11	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	172	12	,	,	PUNCT
ejpam-5838	172	13	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	172	14	)	)	PUNCT
ejpam-5838	172	15	+	+	CCONJ
ejpam-5838	172	16	β	β	X
ejpam-5838	172	17			NOUN
ejpam-5838	172	18	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	172	19	,	,	PUNCT
ejpam-5838	172	20	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	172	21	,	,	PUNCT
ejpam-5838	172	22	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	172	23	)	)	PUNCT
ejpam-5838	172	24	·	·	PUNCT
ejpam-5838	172	25	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	172	26	,	,	PUNCT
ejpam-5838	172	27	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	172	28	,	,	PUNCT
ejpam-5838	172	29	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	172	30	)	)	PUNCT
ejpam-5838	172	31	·	·	PUNCT
ejpam-5838	172	32	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	172	33	,	,	PUNCT
ejpam-5838	172	34	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	172	35	,	,	PUNCT
ejpam-5838	172	36	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	172	37	)	)	PUNCT
ejpam-5838	173	1	+	+	NOUN
ejpam-5838	173	2	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	173	3	,	,	PUNCT
ejpam-5838	173	4	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	173	5	,	,	PUNCT
ejpam-5838	173	6	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	173	7	)	)	PUNCT
ejpam-5838	173	8	·	·	PUNCT
ejpam-5838	173	9	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	173	10	,	,	PUNCT
ejpam-5838	173	11	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	173	12	,	,	PUNCT
ejpam-5838	173	13	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	173	14	)	)	PUNCT
ejpam-5838	173	15	·	·	PUNCT
ejpam-5838	173	16	g(ê3⋎+3	g(ê3⋎+3	NOUN
ejpam-5838	173	17	,	,	PUNCT
ejpam-5838	173	18	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	173	19	,	,	PUNCT
ejpam-5838	173	20	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	173	21	)	)	PUNCT
ejpam-5838	173	22	1	1	NUM
ejpam-5838	174	1	+	+	CCONJ
ejpam-5838	174	2	[	[	X
ejpam-5838	174	3	g(ê3⋎+2	g(ê3⋎+2	X
ejpam-5838	174	4	,	,	PUNCT
ejpam-5838	174	5	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	174	6	,	,	PUNCT
ejpam-5838	174	7	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	174	8	)	)	PUNCT
ejpam-5838	174	9	·	·	PUNCT
ejpam-5838	174	10	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	174	11	,	,	PUNCT
ejpam-5838	174	12	f2ê3⋎+3	f2ê3⋎+3	NOUN
ejpam-5838	174	13	,	,	PUNCT
ejpam-5838	174	14	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	174	15	)	)	PUNCT
ejpam-5838	174	16	·	·	PUNCT
ejpam-5838	174	17	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	174	18	,	,	PUNCT
ejpam-5838	174	19	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	174	20	,	,	PUNCT
ejpam-5838	174	21	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	174	22	)	)	PUNCT
ejpam-5838	174	23	]	]	PUNCT
ejpam-5838	174	24			PROPN
ejpam-5838	174	25	≤	≤	PROPN
ejpam-5838	174	26	αg(ê3⋎+1	αg(ê3⋎+1	PROPN
ejpam-5838	174	27	,	,	PUNCT
ejpam-5838	174	28	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	174	29	,	,	PUNCT
ejpam-5838	174	30	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	174	31	)	)	PUNCT
ejpam-5838	175	1	+	+	CCONJ
ejpam-5838	175	2	β	β	NUM
ejpam-5838	175	3			NOUN
ejpam-5838	175	4	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	175	5	,	,	PUNCT
ejpam-5838	175	6	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	175	7	,	,	PUNCT
ejpam-5838	175	8	ê3⋎+3	ê3⋎+3	X
ejpam-5838	175	9	)	)	PUNCT
ejpam-5838	175	10	·	·	PUNCT
ejpam-5838	175	11	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	175	12	,	,	PUNCT
ejpam-5838	175	13	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	175	14	,	,	PUNCT
ejpam-5838	175	15	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	175	16	)	)	PUNCT
ejpam-5838	175	17	·	·	PUNCT
ejpam-5838	175	18	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	175	19	,	,	PUNCT
ejpam-5838	175	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	175	21	,	,	PUNCT
ejpam-5838	175	22	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	175	23	)	)	PUNCT
ejpam-5838	176	1	+	+	ADP
ejpam-5838	176	2	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	176	3	,	,	PUNCT
ejpam-5838	176	4	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	176	5	,	,	PUNCT
ejpam-5838	176	6	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	176	7	)	)	PUNCT
ejpam-5838	176	8	·	·	PUNCT
ejpam-5838	176	9	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	176	10	,	,	PUNCT
ejpam-5838	176	11	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	176	12	,	,	PUNCT
ejpam-5838	176	13	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	176	14	)	)	PUNCT
ejpam-5838	176	15	·	·	PUNCT
ejpam-5838	176	16	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	176	17	,	,	PUNCT
ejpam-5838	176	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	176	19	,	,	PUNCT
ejpam-5838	176	20	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	176	21	)	)	PUNCT
ejpam-5838	176	22	1	1	NUM
ejpam-5838	177	1	+	+	ADV
ejpam-5838	177	2	g(ê3⋎+2	g(ê3⋎+2	VERB
ejpam-5838	177	3	,	,	PUNCT
ejpam-5838	177	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	177	5	,	,	PUNCT
ejpam-5838	177	6	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	177	7	)	)	PUNCT
ejpam-5838	177	8	·	·	PUNCT
ejpam-5838	177	9	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	177	10	,	,	PUNCT
ejpam-5838	177	11	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	177	12	,	,	PUNCT
ejpam-5838	177	13	ê3⋎+3	ê3⋎+3	X
ejpam-5838	177	14	)	)	PUNCT
ejpam-5838	177	15	·	·	PUNCT
ejpam-5838	177	16	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	177	17	,	,	PUNCT
ejpam-5838	177	18	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	177	19	,	,	PUNCT
ejpam-5838	177	20	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	177	21	)	)	PUNCT
ejpam-5838	177	22			NOUN
ejpam-5838	177	23	after	after	ADP
ejpam-5838	177	24	simplification	simplification	NOUN
ejpam-5838	177	25	,	,	PUNCT
ejpam-5838	177	26	we	we	PRON
ejpam-5838	177	27	have	have	VERB
ejpam-5838	177	28	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	177	29	,	,	PUNCT
ejpam-5838	177	30	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	177	31	,	,	PUNCT
ejpam-5838	177	32	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	177	33	)	)	PUNCT
ejpam-5838	177	34	≤	≤	NOUN
ejpam-5838	177	35	αg(ê3⋎+1	αg(ê3⋎+1	ADJ
ejpam-5838	177	36	,	,	PUNCT
ejpam-5838	177	37	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	177	38	,	,	PUNCT
ejpam-5838	177	39	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	177	40	)	)	PUNCT
ejpam-5838	177	41	(	(	PUNCT
ejpam-5838	177	42	2	2	X
ejpam-5838	177	43	)	)	PUNCT
ejpam-5838	177	44	by	by	ADP
ejpam-5838	177	45	a	a	DET
ejpam-5838	177	46	similar	similar	ADJ
ejpam-5838	177	47	argument	argument	NOUN
ejpam-5838	177	48	as	as	ADP
ejpam-5838	177	49	in	in	ADP
ejpam-5838	177	50	above	above	ADV
ejpam-5838	177	51	,	,	PUNCT
ejpam-5838	177	52	we	we	PRON
ejpam-5838	177	53	can	can	AUX
ejpam-5838	177	54	show	show	VERB
ejpam-5838	177	55	that	that	DET
ejpam-5838	177	56	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	177	57	,	,	PUNCT
ejpam-5838	177	58	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	177	59	,	,	PUNCT
ejpam-5838	177	60	ê3⋎+5	ê3⋎+5	X
ejpam-5838	177	61	)	)	PUNCT
ejpam-5838	177	62	≤	≤	NOUN
ejpam-5838	177	63	αg(ê3⋎+2	αg(ê3⋎+2	PROPN
ejpam-5838	177	64	,	,	PUNCT
ejpam-5838	177	65	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	177	66	,	,	PUNCT
ejpam-5838	177	67	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	177	68	)	)	PUNCT
ejpam-5838	177	69	.	.	PUNCT
ejpam-5838	178	1	(	(	PUNCT
ejpam-5838	178	2	3	3	X
ejpam-5838	178	3	)	)	PUNCT
ejpam-5838	178	4	now	now	ADV
ejpam-5838	178	5	,	,	PUNCT
ejpam-5838	178	6	from	from	ADP
ejpam-5838	178	7	(	(	PUNCT
ejpam-5838	178	8	1	1	NUM
ejpam-5838	178	9	)	)	PUNCT
ejpam-5838	178	10	,	,	PUNCT
ejpam-5838	178	11	(	(	PUNCT
ejpam-5838	178	12	2	2	X
ejpam-5838	178	13	)	)	PUNCT
ejpam-5838	178	14	and	and	CCONJ
ejpam-5838	178	15	(	(	PUNCT
ejpam-5838	178	16	3	3	NUM
ejpam-5838	178	17	)	)	PUNCT
ejpam-5838	178	18	,	,	PUNCT
ejpam-5838	178	19	we	we	PRON
ejpam-5838	178	20	conclude	conclude	VERB
ejpam-5838	178	21	that	that	DET
ejpam-5838	178	22	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	178	23	,	,	PUNCT
ejpam-5838	178	24	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	178	25	,	,	PUNCT
ejpam-5838	178	26	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	178	27	)	)	PUNCT
ejpam-5838	178	28	≤	≤	NUM
ejpam-5838	178	29	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	178	30	,	,	PUNCT
ejpam-5838	178	31	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	178	32	,	,	PUNCT
ejpam-5838	178	33	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	178	34	)	)	PUNCT
ejpam-5838	178	35	≤	≤	NUM
ejpam-5838	178	36	α2g(ê3⋎−1	α2g(ê3⋎−1	NOUN
ejpam-5838	178	37	,	,	PUNCT
ejpam-5838	178	38	ê3⋎	ê3⋎	NUM
ejpam-5838	178	39	,	,	PUNCT
ejpam-5838	178	40	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	178	41	)	)	PUNCT
ejpam-5838	178	42	≤	≤	NOUN
ejpam-5838	178	43	·	·	PUNCT
ejpam-5838	178	44	·	·	PUNCT
ejpam-5838	178	45	·	·	PUNCT
ejpam-5838	179	1	≤	≤	NUM
ejpam-5838	179	2	α3⋎g(ê1	α3⋎g(ê1	NOUN
ejpam-5838	179	3	,	,	PUNCT
ejpam-5838	179	4	ê2	ê2	NOUN
ejpam-5838	179	5	,	,	PUNCT
ejpam-5838	179	6	ê3	ê3	PROPN
ejpam-5838	179	7	)	)	PUNCT
ejpam-5838	179	8	≤	≤	PROPN
ejpam-5838	179	9	α3⋎+1g(ê0	α3⋎+1g(ê0	PROPN
ejpam-5838	179	10	,	,	PUNCT
ejpam-5838	179	11	ê1	ê1	PROPN
ejpam-5838	179	12	,	,	PUNCT
ejpam-5838	179	13	ê2	ê2	PROPN
ejpam-5838	179	14	)	)	PUNCT
ejpam-5838	179	15	.	.	PUNCT
ejpam-5838	180	1	(	(	PUNCT
ejpam-5838	180	2	4	4	X
ejpam-5838	180	3	)	)	PUNCT
ejpam-5838	180	4	hence	hence	ADV
ejpam-5838	180	5	proved	prove	VERB
ejpam-5838	180	6	that	that	SCONJ
ejpam-5838	180	7	the	the	DET
ejpam-5838	180	8	sequence	sequence	NOUN
ejpam-5838	180	9	{	{	PUNCT
ejpam-5838	180	10	ê⋎	ê⋎	NOUN
ejpam-5838	180	11	}	}	PUNCT
ejpam-5838	180	12	is	be	AUX
ejpam-5838	180	13	contractive	contractive	ADJ
ejpam-5838	180	14	under	under	ADP
ejpam-5838	180	15	the	the	DET
ejpam-5838	180	16	gm	gm	PROPN
ejpam-5838	180	17	-space	-space	NOUN
ejpam-5838	180	18	for	for	ADP
ejpam-5838	180	19	3	3	NUM
ejpam-5838	180	20	-	-	PUNCT
ejpam-5838	180	21	self	self	NOUN
ejpam-5838	180	22	-	-	PUNCT
ejpam-5838	180	23	mappings	mapping	NOUN
ejpam-5838	180	24	.	.	PUNCT
ejpam-5838	181	1	therefore	therefore	ADV
ejpam-5838	181	2	,	,	PUNCT
ejpam-5838	181	3	lim	lim	PROPN
ejpam-5838	181	4	⋎→∞	⋎→∞	PROPN
ejpam-5838	181	5	g(ê⋎	g(ê⋎	PROPN
ejpam-5838	181	6	,	,	PUNCT
ejpam-5838	181	7	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	181	8	,	,	PUNCT
ejpam-5838	181	9	ê⋎+2	ê⋎+2	VERB
ejpam-5838	181	10	)	)	PUNCT
ejpam-5838	181	11	=	=	SYM
ejpam-5838	181	12	0	0	X
ejpam-5838	181	13	.	.	PUNCT
ejpam-5838	182	1	(	(	PUNCT
ejpam-5838	182	2	5	5	X
ejpam-5838	182	3	)	)	PUNCT
ejpam-5838	182	4	m.	m.	NOUN
ejpam-5838	182	5	noorwali	noorwali	PROPN
ejpam-5838	182	6	et	et	PROPN
ejpam-5838	182	7	al/	al/	PROPN
ejpam-5838	182	8	/	/	SYM
ejpam-5838	182	9	eur	eur	PROPN
ejpam-5838	182	10	.	.	PUNCT
ejpam-5838	183	1	j.	j.	PROPN
ejpam-5838	183	2	pure	pure	PROPN
ejpam-5838	183	3	appl	appl	PROPN
ejpam-5838	183	4	.	.	PROPN
ejpam-5838	183	5	math	math	PROPN
ejpam-5838	183	6	,	,	PUNCT
ejpam-5838	183	7	18	18	NUM
ejpam-5838	183	8	(	(	PUNCT
ejpam-5838	183	9	2	2	NUM
ejpam-5838	183	10	)	)	PUNCT
ejpam-5838	183	11	(	(	PUNCT
ejpam-5838	183	12	2025	2025	NUM
ejpam-5838	183	13	)	)	PUNCT
ejpam-5838	183	14	,	,	PUNCT
ejpam-5838	183	15	5838	5838	NUM
ejpam-5838	183	16	7	7	NUM
ejpam-5838	183	17	of	of	ADP
ejpam-5838	183	18	16	16	NUM
ejpam-5838	183	19	next	next	ADV
ejpam-5838	183	20	,	,	PUNCT
ejpam-5838	183	21	we	we	PRON
ejpam-5838	183	22	will	will	AUX
ejpam-5838	183	23	show	show	VERB
ejpam-5838	183	24	that	that	SCONJ
ejpam-5838	183	25	{	{	PUNCT
ejpam-5838	183	26	ê⋎	ê⋎	NOUN
ejpam-5838	183	27	}	}	PUNCT
ejpam-5838	183	28	is	be	AUX
ejpam-5838	183	29	a	a	DET
ejpam-5838	183	30	g	g	NOUN
ejpam-5838	183	31	-	-	PUNCT
ejpam-5838	183	32	cs	cs	PROPN
ejpam-5838	183	33	in	in	ADP
ejpam-5838	183	34	ê	ê	PROPN
ejpam-5838	183	35	,	,	PUNCT
ejpam-5838	183	36	for	for	ADP
ejpam-5838	183	37	all	all	DET
ejpam-5838	183	38	⋎,m	⋎,m	NOUN
ejpam-5838	183	39	∈	∈	PROPN
ejpam-5838	183	40	n	n	NOUN
ejpam-5838	183	41	and	and	CCONJ
ejpam-5838	183	42	m	m	PROPN
ejpam-5838	183	43	>	>	X
ejpam-5838	183	44	⋎	⋎	PROPN
ejpam-5838	183	45	,	,	PUNCT
ejpam-5838	183	46	with	with	ADP
ejpam-5838	183	47	the	the	DET
ejpam-5838	183	48	aid	aid	NOUN
ejpam-5838	183	49	of	of	ADP
ejpam-5838	183	50	(	(	PUNCT
ejpam-5838	183	51	4	4	NUM
ejpam-5838	183	52	)	)	PUNCT
ejpam-5838	183	53	,	,	PUNCT
ejpam-5838	183	54	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	183	55	,	,	PUNCT
ejpam-5838	183	56	êm	êm	PROPN
ejpam-5838	183	57	,	,	PUNCT
ejpam-5838	183	58	êm	êm	NOUN
ejpam-5838	183	59	)	)	PUNCT
ejpam-5838	183	60	≤	≤	NOUN
ejpam-5838	183	61	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	183	62	,	,	PUNCT
ejpam-5838	183	63	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	183	64	,	,	PUNCT
ejpam-5838	183	65	ê⋎+1	ê⋎+1	NUM
ejpam-5838	183	66	)	)	PUNCT
ejpam-5838	184	1	+	+	PROPN
ejpam-5838	184	2	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	184	3	,	,	PUNCT
ejpam-5838	184	4	êm	êm	PROPN
ejpam-5838	184	5	,	,	PUNCT
ejpam-5838	184	6	êm	êm	NOUN
ejpam-5838	184	7	)	)	PUNCT
ejpam-5838	184	8	≤	≤	NOUN
ejpam-5838	184	9	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	184	10	,	,	PUNCT
ejpam-5838	184	11	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	184	12	,	,	PUNCT
ejpam-5838	184	13	ê⋎+1	ê⋎+1	NUM
ejpam-5838	184	14	)	)	PUNCT
ejpam-5838	185	1	+	+	PROPN
ejpam-5838	185	2	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	185	3	,	,	PUNCT
ejpam-5838	185	4	ê⋎+2	ê⋎+2	VERB
ejpam-5838	185	5	,	,	PUNCT
ejpam-5838	185	6	ê⋎+2	ê⋎+2	VERB
ejpam-5838	185	7	)	)	PUNCT
ejpam-5838	185	8	+	+	NUM
ejpam-5838	185	9	·	·	PUNCT
ejpam-5838	185	10	·	·	PUNCT
ejpam-5838	185	11	·	·	PUNCT
ejpam-5838	185	12	+	+	NOUN
ejpam-5838	185	13	g(êm−1	g(êm−1	PROPN
ejpam-5838	185	14	,	,	PUNCT
ejpam-5838	185	15	êm	êm	PROPN
ejpam-5838	185	16	,	,	PUNCT
ejpam-5838	185	17	êm	êm	NOUN
ejpam-5838	185	18	)	)	PUNCT
ejpam-5838	185	19	≤	≤	NOUN
ejpam-5838	185	20	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	185	21	,	,	PUNCT
ejpam-5838	185	22	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	185	23	,	,	PUNCT
ejpam-5838	185	24	ê⋎+2	ê⋎+2	VERB
ejpam-5838	185	25	)	)	PUNCT
ejpam-5838	185	26	+	+	SYM
ejpam-5838	185	27	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	185	28	,	,	PUNCT
ejpam-5838	185	29	ê⋎+2	ê⋎+2	VERB
ejpam-5838	185	30	,	,	PUNCT
ejpam-5838	185	31	ê⋎+3	ê⋎+3	ADJ
ejpam-5838	185	32	)	)	PUNCT
ejpam-5838	185	33	+	+	CCONJ
ejpam-5838	185	34	·	·	PUNCT
ejpam-5838	185	35	·	·	PUNCT
ejpam-5838	185	36	·	·	PUNCT
ejpam-5838	186	1	+	+	NOUN
ejpam-5838	186	2	g(êm−1	g(êm−1	PROPN
ejpam-5838	186	3	,	,	PUNCT
ejpam-5838	186	4	êm	êm	PROPN
ejpam-5838	186	5	,	,	PUNCT
ejpam-5838	186	6	êm+1	êm+1	PROPN
ejpam-5838	186	7	)	)	PUNCT
ejpam-5838	186	8	≤	≤	PROPN
ejpam-5838	186	9	η⋎g(ê0	η⋎g(ê0	PROPN
ejpam-5838	186	10	,	,	PUNCT
ejpam-5838	186	11	ê1	ê1	PROPN
ejpam-5838	186	12	,	,	PUNCT
ejpam-5838	186	13	ê1	ê1	PROPN
ejpam-5838	186	14	)	)	PUNCT
ejpam-5838	187	1	+	+	CCONJ
ejpam-5838	187	2	η⋎+1g(ê0	η⋎+1g(ê0	ADJ
ejpam-5838	187	3	,	,	PUNCT
ejpam-5838	187	4	ê1	ê1	PROPN
ejpam-5838	187	5	,	,	PUNCT
ejpam-5838	187	6	ê1	ê1	PROPN
ejpam-5838	187	7	)	)	PUNCT
ejpam-5838	187	8	+	+	CCONJ
ejpam-5838	187	9	·	·	PUNCT
ejpam-5838	187	10	·	·	PUNCT
ejpam-5838	187	11	·	·	PUNCT
ejpam-5838	188	1	+	+	NUM
ejpam-5838	188	2	ηm−1g(ê0	ηm−1g(ê0	NOUN
ejpam-5838	188	3	,	,	PUNCT
ejpam-5838	188	4	ê1	ê1	PROPN
ejpam-5838	188	5	,	,	PUNCT
ejpam-5838	188	6	ê1	ê1	PROPN
ejpam-5838	188	7	)	)	PUNCT
ejpam-5838	188	8	≤	≤	PUNCT
ejpam-5838	188	9	η⋎	η⋎	PROPN
ejpam-5838	188	10	[	[	PUNCT
ejpam-5838	188	11	g(ê0	g(ê0	PROPN
ejpam-5838	188	12	,	,	PUNCT
ejpam-5838	188	13	ê1	ê1	PROPN
ejpam-5838	188	14	,	,	PUNCT
ejpam-5838	188	15	ê1	ê1	PROPN
ejpam-5838	188	16	)	)	PUNCT
ejpam-5838	189	1	+	+	NUM
ejpam-5838	189	2	η1g(ê0	η1g(ê0	PROPN
ejpam-5838	189	3	,	,	PUNCT
ejpam-5838	189	4	ê1	ê1	PROPN
ejpam-5838	189	5	,	,	PUNCT
ejpam-5838	189	6	ê1	ê1	PROPN
ejpam-5838	189	7	)	)	PUNCT
ejpam-5838	190	1	+	+	CCONJ
ejpam-5838	190	2	η2g(ê0	η2g(ê0	PROPN
ejpam-5838	190	3	,	,	PUNCT
ejpam-5838	190	4	ê1	ê1	PROPN
ejpam-5838	190	5	,	,	PUNCT
ejpam-5838	190	6	ê1	ê1	PROPN
ejpam-5838	190	7	)	)	PUNCT
ejpam-5838	191	1	+	+	CCONJ
ejpam-5838	191	2	·	·	PUNCT
ejpam-5838	191	3	·	·	PUNCT
ejpam-5838	191	4	·	·	PUNCT
ejpam-5838	191	5	+	+	NUM
ejpam-5838	191	6	ηm−1g(ê0	ηm−1g(ê0	NOUN
ejpam-5838	191	7	,	,	PUNCT
ejpam-5838	191	8	ê1	ê1	PROPN
ejpam-5838	191	9	,	,	PUNCT
ejpam-5838	191	10	ê1	ê1	PROPN
ejpam-5838	191	11	)	)	PUNCT
ejpam-5838	191	12	]	]	PUNCT
ejpam-5838	192	1	this	this	PRON
ejpam-5838	192	2	implies	imply	VERB
ejpam-5838	192	3	that	that	SCONJ
ejpam-5838	192	4	,	,	PUNCT
ejpam-5838	192	5	g(ê⋎	g(ê⋎	PROPN
ejpam-5838	192	6	,	,	PUNCT
ejpam-5838	192	7	êm	êm	PROPN
ejpam-5838	192	8	,	,	PUNCT
ejpam-5838	192	9	êm	êm	NOUN
ejpam-5838	192	10	)	)	PUNCT
ejpam-5838	192	11	≤	≤	NOUN
ejpam-5838	192	12	η⋎	η⋎	PROPN
ejpam-5838	192	13	1−	1−	NUM
ejpam-5838	192	14	η	η	PROPN
ejpam-5838	192	15	g(ê0	g(ê0	PROPN
ejpam-5838	192	16	,	,	PUNCT
ejpam-5838	192	17	ê1	ê1	PROPN
ejpam-5838	192	18	,	,	PUNCT
ejpam-5838	192	19	ê1	ê1	PROPN
ejpam-5838	192	20	)	)	PUNCT
ejpam-5838	192	21	.	.	PUNCT
ejpam-5838	193	1	(	(	PUNCT
ejpam-5838	193	2	6	6	NUM
ejpam-5838	193	3	)	)	PUNCT
ejpam-5838	193	4	if	if	SCONJ
ejpam-5838	193	5	we	we	PRON
ejpam-5838	193	6	take	take	VERB
ejpam-5838	193	7	the	the	DET
ejpam-5838	193	8	limit	limit	NOUN
ejpam-5838	193	9	as	as	ADP
ejpam-5838	193	10	⋎,m	⋎,m	NOUN
ejpam-5838	193	11	,	,	PUNCT
ejpam-5838	193	12	l	l	NOUN
ejpam-5838	193	13	→	→	SYM
ejpam-5838	193	14	∞	∞	NUM
ejpam-5838	193	15	we	we	PRON
ejpam-5838	193	16	get	get	VERB
ejpam-5838	193	17	g(ê⋎	g(ê⋎	ADJ
ejpam-5838	193	18	,	,	PUNCT
ejpam-5838	193	19	êm	êm	PROPN
ejpam-5838	193	20	,	,	PUNCT
ejpam-5838	193	21	êl	êl	PROPN
ejpam-5838	193	22	)	)	PUNCT
ejpam-5838	193	23	→	→	SYM
ejpam-5838	194	1	0	0	X
ejpam-5838	194	2	.	.	PUNCT
ejpam-5838	195	1	hence	hence	ADV
ejpam-5838	195	2	{	{	PUNCT
ejpam-5838	195	3	ê⋎	ê⋎	ADJ
ejpam-5838	195	4	}	}	PUNCT
ejpam-5838	195	5	is	be	AUX
ejpam-5838	195	6	a	a	DET
ejpam-5838	195	7	g	g	NOUN
ejpam-5838	195	8	-	-	PUNCT
ejpam-5838	195	9	cs	cs	PROPN
ejpam-5838	195	10	.	.	PUNCT
ejpam-5838	196	1	since	since	SCONJ
ejpam-5838	196	2	,	,	PUNCT
ejpam-5838	196	3	(	(	PUNCT
ejpam-5838	196	4	ê	ê	NOUN
ejpam-5838	196	5	,	,	PUNCT
ejpam-5838	196	6	g	g	NOUN
ejpam-5838	196	7	)	)	PUNCT
ejpam-5838	196	8	is	be	AUX
ejpam-5838	196	9	complete	complete	ADJ
ejpam-5838	196	10	,	,	PUNCT
ejpam-5838	196	11	there	there	PRON
ejpam-5838	196	12	exists	exist	VERB
ejpam-5838	196	13	z	z	PROPN
ejpam-5838	196	14	∈	∈	PROPN
ejpam-5838	196	15	ê	ê	PROPN
ejpam-5838	196	16	,	,	PUNCT
ejpam-5838	196	17	such	such	ADJ
ejpam-5838	196	18	that	that	SCONJ
ejpam-5838	196	19	,	,	PUNCT
ejpam-5838	196	20	ê⋎	ê⋎	PROPN
ejpam-5838	196	21	→	→	X
ejpam-5838	196	22	z	z	NOUN
ejpam-5838	196	23	as	as	ADP
ejpam-5838	196	24	⋎	⋎	NOUN
ejpam-5838	196	25	→	→	SYM
ejpam-5838	196	26	∞	∞	NUM
ejpam-5838	196	27	or	or	CCONJ
ejpam-5838	196	28	lim⋎→∞	lim⋎→∞	NOUN
ejpam-5838	196	29	ê⋎	ê⋎	PROPN
ejpam-5838	196	30	=	=	PUNCT
ejpam-5838	197	1	z.	z.	PROPN
ejpam-5838	197	2	we	we	PRON
ejpam-5838	197	3	now	now	ADV
ejpam-5838	197	4	show	show	VERB
ejpam-5838	197	5	that	that	SCONJ
ejpam-5838	197	6	f1z	f1z	ADJ
ejpam-5838	197	7	=	=	SYM
ejpam-5838	197	8	z	z	NOUN
ejpam-5838	197	9	by	by	ADP
ejpam-5838	197	10	contrary	contrary	ADJ
ejpam-5838	197	11	case	case	NOUN
ejpam-5838	197	12	.	.	PUNCT
ejpam-5838	198	1	let	let	VERB
ejpam-5838	198	2	f1z	f1z	VERB
ejpam-5838	198	3	̸=	̸=	PROPN
ejpam-5838	198	4	z.	z.	X
ejpam-5838	198	5	by	by	ADP
ejpam-5838	198	6	using	use	VERB
ejpam-5838	198	7	(	(	PUNCT
ejpam-5838	198	8	3.1	3.1	NUM
ejpam-5838	198	9	)	)	PUNCT
ejpam-5838	198	10	,	,	PUNCT
ejpam-5838	198	11	we	we	PRON
ejpam-5838	198	12	have	have	VERB
ejpam-5838	198	13	that	that	PRON
ejpam-5838	198	14	g(f1z	g(f1z	VERB
ejpam-5838	198	15	,	,	PUNCT
ejpam-5838	198	16	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	198	17	,	,	PUNCT
ejpam-5838	198	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	198	19	)	)	PUNCT
ejpam-5838	198	20	=	=	SYM
ejpam-5838	199	1	g(f1z	g(f1z	ADJ
ejpam-5838	199	2	,	,	PUNCT
ejpam-5838	199	3	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	199	4	,	,	PUNCT
ejpam-5838	199	5	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	199	6	)	)	PUNCT
ejpam-5838	199	7	≤	≤	NOUN
ejpam-5838	199	8	αg(z	αg(z	ADJ
ejpam-5838	199	9	,	,	PUNCT
ejpam-5838	199	10	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	199	11	,	,	PUNCT
ejpam-5838	199	12	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	199	13	)	)	PUNCT
ejpam-5838	200	1	+	+	CCONJ
ejpam-5838	200	2	β	β	X
ejpam-5838	200	3			X
ejpam-5838	200	4	g(z	g(z	ADJ
ejpam-5838	200	5	,	,	PUNCT
ejpam-5838	200	6	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	200	7	,	,	PUNCT
ejpam-5838	200	8	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	200	9	)	)	PUNCT
ejpam-5838	200	10	·	·	PUNCT
ejpam-5838	200	11	g(z	g(z	ADJ
ejpam-5838	200	12	,	,	PUNCT
ejpam-5838	200	13	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	200	14	,	,	PUNCT
ejpam-5838	200	15	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	200	16	)	)	PUNCT
ejpam-5838	200	17	·	·	PUNCT
ejpam-5838	200	18	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	200	19	,	,	PUNCT
ejpam-5838	200	20	f1z	f1z	ADJ
ejpam-5838	200	21	,	,	PUNCT
ejpam-5838	200	22	f1z	f1z	ADJ
ejpam-5838	200	23	)	)	PUNCT
ejpam-5838	200	24	+	+	NOUN
ejpam-5838	200	25	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	200	26	,	,	PUNCT
ejpam-5838	200	27	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	200	28	,	,	PUNCT
ejpam-5838	200	29	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	200	30	)	)	PUNCT
ejpam-5838	200	31	·	·	PUNCT
ejpam-5838	200	32	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	200	33	,	,	PUNCT
ejpam-5838	200	34	f1z	f1z	ADJ
ejpam-5838	200	35	,	,	PUNCT
ejpam-5838	200	36	f1z	f1z	NOUN
ejpam-5838	200	37	)	)	PUNCT
ejpam-5838	200	38	·	·	PUNCT
ejpam-5838	200	39	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	200	40	,	,	PUNCT
ejpam-5838	200	41	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	200	42	,	,	PUNCT
ejpam-5838	200	43	f2ê3⋎+1	f2ê3⋎+1	NOUN
ejpam-5838	200	44	)	)	PUNCT
ejpam-5838	200	45	1	1	NUM
ejpam-5838	201	1	+	+	NOUN
ejpam-5838	201	2	g(ê3⋎+1	g(ê3⋎+1	ADJ
ejpam-5838	201	3	,	,	PUNCT
ejpam-5838	201	4	f1z	f1z	ADJ
ejpam-5838	201	5	,	,	PUNCT
ejpam-5838	201	6	f1z	f1z	NOUN
ejpam-5838	201	7	)	)	PUNCT
ejpam-5838	201	8	·	·	PUNCT
ejpam-5838	201	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	201	10	,	,	PUNCT
ejpam-5838	201	11	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	201	12	,	,	PUNCT
ejpam-5838	201	13	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	201	14	)	)	PUNCT
ejpam-5838	201	15	·	·	PUNCT
ejpam-5838	201	16	g(z	g(z	ADJ
ejpam-5838	201	17	,	,	PUNCT
ejpam-5838	201	18	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	201	19	,	,	PUNCT
ejpam-5838	201	20	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	201	21	)	)	PUNCT
ejpam-5838	202	1			PROPN
ejpam-5838	202	2	≤	≤	NOUN
ejpam-5838	202	3	αg(z	αg(z	ADJ
ejpam-5838	202	4	,	,	PUNCT
ejpam-5838	202	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	202	6	,	,	PUNCT
ejpam-5838	202	7	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	202	8	)	)	PUNCT
ejpam-5838	203	1	+	+	CCONJ
ejpam-5838	203	2	β	β	X
ejpam-5838	203	3			X
ejpam-5838	203	4	g(z	g(z	PROPN
ejpam-5838	203	5	,	,	PUNCT
ejpam-5838	203	6	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	203	7	,	,	PUNCT
ejpam-5838	203	8	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	203	9	)	)	PUNCT
ejpam-5838	203	10	·	·	PUNCT
ejpam-5838	204	1	g(z	g(z	ADJ
ejpam-5838	204	2	,	,	PUNCT
ejpam-5838	204	3	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	204	4	,	,	PUNCT
ejpam-5838	204	5	ê3⋎+3	ê3⋎+3	X
ejpam-5838	204	6	)	)	PUNCT
ejpam-5838	204	7	·	·	PUNCT
ejpam-5838	204	8	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	204	9	,	,	PUNCT
ejpam-5838	204	10	f1z	f1z	ADJ
ejpam-5838	204	11	,	,	PUNCT
ejpam-5838	204	12	f1z	f1z	ADJ
ejpam-5838	204	13	)	)	PUNCT
ejpam-5838	205	1	+	+	NOUN
ejpam-5838	205	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	205	3	,	,	PUNCT
ejpam-5838	205	4	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	205	5	,	,	PUNCT
ejpam-5838	205	6	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	205	7	)	)	PUNCT
ejpam-5838	205	8	·	·	PUNCT
ejpam-5838	205	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	205	10	,	,	PUNCT
ejpam-5838	205	11	f1z	f1z	ADJ
ejpam-5838	205	12	,	,	PUNCT
ejpam-5838	205	13	f1z	f1z	NOUN
ejpam-5838	205	14	)	)	PUNCT
ejpam-5838	205	15	·	·	PUNCT
ejpam-5838	205	16	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	205	17	,	,	PUNCT
ejpam-5838	205	18	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	205	19	,	,	PUNCT
ejpam-5838	205	20	ê3⋎+2	ê3⋎+2	VERB
ejpam-5838	205	21	)	)	PUNCT
ejpam-5838	205	22	1	1	NUM
ejpam-5838	206	1	+	+	NOUN
ejpam-5838	206	2	g(ê3⋎+1	g(ê3⋎+1	ADJ
ejpam-5838	206	3	,	,	PUNCT
ejpam-5838	206	4	f1z	f1z	ADJ
ejpam-5838	206	5	,	,	PUNCT
ejpam-5838	206	6	f1z	f1z	NOUN
ejpam-5838	206	7	)	)	PUNCT
ejpam-5838	206	8	·	·	PUNCT
ejpam-5838	206	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	206	10	,	,	PUNCT
ejpam-5838	206	11	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	206	12	,	,	PUNCT
ejpam-5838	206	13	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	206	14	)	)	PUNCT
ejpam-5838	206	15	·	·	PUNCT
ejpam-5838	206	16	g(z	g(z	ADJ
ejpam-5838	206	17	,	,	PUNCT
ejpam-5838	206	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	206	19	,	,	PUNCT
ejpam-5838	206	20	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	206	21	)	)	PUNCT
ejpam-5838	206	22			NOUN
ejpam-5838	206	23	applying	apply	VERB
ejpam-5838	206	24	limn→∞	limn→∞	PROPN
ejpam-5838	206	25	and	and	CCONJ
ejpam-5838	206	26	after	after	ADP
ejpam-5838	206	27	simplification	simplification	NOUN
ejpam-5838	206	28	,	,	PUNCT
ejpam-5838	206	29	we	we	PRON
ejpam-5838	206	30	obtained	obtain	VERB
ejpam-5838	206	31	g(f1z	g(f1z	PROPN
ejpam-5838	206	32	,	,	PUNCT
ejpam-5838	206	33	z	z	PROPN
ejpam-5838	206	34	,	,	PUNCT
ejpam-5838	206	35	z	z	NOUN
ejpam-5838	206	36	)	)	PUNCT
ejpam-5838	206	37	≤	≤	NOUN
ejpam-5838	206	38	αg(z	αg(z	NOUN
ejpam-5838	206	39	,	,	PUNCT
ejpam-5838	206	40	z	z	NOUN
ejpam-5838	206	41	,	,	PUNCT
ejpam-5838	206	42	z	z	NOUN
ejpam-5838	206	43	)	)	PUNCT
ejpam-5838	206	44	.	.	PUNCT
ejpam-5838	207	1	this	this	PRON
ejpam-5838	207	2	implies	imply	VERB
ejpam-5838	207	3	that	that	SCONJ
ejpam-5838	207	4	,	,	PUNCT
ejpam-5838	207	5	g(f1z	g(f1z	ADJ
ejpam-5838	207	6	,	,	PUNCT
ejpam-5838	207	7	z	z	NOUN
ejpam-5838	207	8	,	,	PUNCT
ejpam-5838	207	9	z	z	NOUN
ejpam-5838	207	10	)	)	PUNCT
ejpam-5838	207	11	=	=	SYM
ejpam-5838	207	12	0	0	X
ejpam-5838	207	13	.	.	PUNCT
ejpam-5838	208	1	thus	thus	ADV
ejpam-5838	208	2	,	,	PUNCT
ejpam-5838	208	3	f1z	f1z	PROPN
ejpam-5838	208	4	=	=	SYM
ejpam-5838	208	5	z.	z.	X
ejpam-5838	208	6	(	(	PUNCT
ejpam-5838	208	7	7	7	NUM
ejpam-5838	208	8	)	)	PUNCT
ejpam-5838	208	9	next	next	ADV
ejpam-5838	208	10	,	,	PUNCT
ejpam-5838	208	11	we	we	PRON
ejpam-5838	208	12	show	show	VERB
ejpam-5838	208	13	that	that	SCONJ
ejpam-5838	208	14	f2z	f2z	NOUN
ejpam-5838	208	15	=	=	SYM
ejpam-5838	208	16	z	z	NOUN
ejpam-5838	208	17	by	by	ADP
ejpam-5838	208	18	contrary	contrary	ADJ
ejpam-5838	208	19	case	case	NOUN
ejpam-5838	208	20	.	.	PUNCT
ejpam-5838	209	1	let	let	VERB
ejpam-5838	209	2	f2z	f2z	NOUN
ejpam-5838	209	3	̸=	̸=	PROPN
ejpam-5838	209	4	z.	z.	X
ejpam-5838	209	5	by	by	ADP
ejpam-5838	209	6	using	use	VERB
ejpam-5838	209	7	(	(	PUNCT
ejpam-5838	209	8	3.1	3.1	NUM
ejpam-5838	209	9	)	)	PUNCT
ejpam-5838	209	10	,	,	PUNCT
ejpam-5838	209	11	we	we	PRON
ejpam-5838	209	12	have	have	VERB
ejpam-5838	209	13	that	that	DET
ejpam-5838	209	14	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	209	15	,	,	PUNCT
ejpam-5838	209	16	f2z	f2z	NOUN
ejpam-5838	209	17	,	,	PUNCT
ejpam-5838	209	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	209	19	)	)	PUNCT
ejpam-5838	210	1	=	=	SYM
ejpam-5838	210	2	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	210	3	,	,	PUNCT
ejpam-5838	210	4	f2z	f2z	NOUN
ejpam-5838	210	5	,	,	PUNCT
ejpam-5838	210	6	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	210	7	)	)	PUNCT
ejpam-5838	210	8	≤	≤	NOUN
ejpam-5838	210	9	αg(ê3⋎	αg(ê3⋎	PROPN
ejpam-5838	210	10	,	,	PUNCT
ejpam-5838	210	11	z	z	NOUN
ejpam-5838	210	12	,	,	PUNCT
ejpam-5838	210	13	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	210	14	)	)	PUNCT
ejpam-5838	211	1	+	+	CCONJ
ejpam-5838	211	2	β	β	X
ejpam-5838	211	3			NOUN
ejpam-5838	211	4	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	211	5	,	,	PUNCT
ejpam-5838	211	6	f2z	f2z	NOUN
ejpam-5838	211	7	,	,	PUNCT
ejpam-5838	211	8	f2z	f2z	NOUN
ejpam-5838	211	9	)	)	PUNCT
ejpam-5838	211	10	·	·	PUNCT
ejpam-5838	211	11	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	211	12	,	,	PUNCT
ejpam-5838	211	13	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	211	14	,	,	PUNCT
ejpam-5838	211	15	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	211	16	)	)	PUNCT
ejpam-5838	211	17	·	·	PUNCT
ejpam-5838	211	18	g(z	g(z	PROPN
ejpam-5838	211	19	,	,	PUNCT
ejpam-5838	211	20	f1ê3⋎	f1ê3⋎	X
ejpam-5838	211	21	,	,	PUNCT
ejpam-5838	211	22	f1ê3⋎	f1ê3⋎	X
ejpam-5838	211	23	)	)	PUNCT
ejpam-5838	212	1	+	+	NOUN
ejpam-5838	212	2	g(z	g(z	ADJ
ejpam-5838	212	3	,	,	PUNCT
ejpam-5838	212	4	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	212	5	,	,	PUNCT
ejpam-5838	212	6	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	212	7	)	)	PUNCT
ejpam-5838	212	8	·	·	PUNCT
ejpam-5838	212	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	212	10	,	,	PUNCT
ejpam-5838	212	11	f1ê3⋎	f1ê3⋎	X
ejpam-5838	212	12	,	,	PUNCT
ejpam-5838	212	13	f1ê3⋎	f1ê3⋎	X
ejpam-5838	212	14	)	)	PUNCT
ejpam-5838	212	15	·	·	PUNCT
ejpam-5838	212	16	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	212	17	,	,	PUNCT
ejpam-5838	212	18	f2z	f2z	NOUN
ejpam-5838	212	19	,	,	PUNCT
ejpam-5838	212	20	f2z	f2z	NOUN
ejpam-5838	212	21	)	)	PUNCT
ejpam-5838	212	22	1	1	NUM
ejpam-5838	213	1	+	+	PUNCT
ejpam-5838	213	2	g(z	g(z	ADJ
ejpam-5838	213	3	,	,	PUNCT
ejpam-5838	213	4	f1ê3⋎	f1ê3⋎	X
ejpam-5838	213	5	,	,	PUNCT
ejpam-5838	213	6	f1ê3⋎	f1ê3⋎	X
ejpam-5838	213	7	)	)	PUNCT
ejpam-5838	213	8	·	·	PUNCT
ejpam-5838	213	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	213	10	,	,	PUNCT
ejpam-5838	213	11	f2z	f2z	NOUN
ejpam-5838	213	12	,	,	PUNCT
ejpam-5838	213	13	f2z	f2z	NOUN
ejpam-5838	213	14	)	)	PUNCT
ejpam-5838	213	15	·	·	PUNCT
ejpam-5838	213	16	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	213	17	,	,	PUNCT
ejpam-5838	213	18	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	213	19	,	,	PUNCT
ejpam-5838	213	20	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	213	21	)	)	PUNCT
ejpam-5838	213	22			PROPN
ejpam-5838	213	23	≤	≤	NUM
ejpam-5838	213	24	αg(ê3⋎	αg(ê3⋎	NOUN
ejpam-5838	213	25	,	,	PUNCT
ejpam-5838	213	26	z	z	NOUN
ejpam-5838	213	27	,	,	PUNCT
ejpam-5838	213	28	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	213	29	)	)	PUNCT
ejpam-5838	213	30	m.	m.	NOUN
ejpam-5838	213	31	noorwali	noorwali	PROPN
ejpam-5838	213	32	et	et	PROPN
ejpam-5838	213	33	al/	al/	PROPN
ejpam-5838	213	34	/	/	SYM
ejpam-5838	213	35	eur	eur	PROPN
ejpam-5838	213	36	.	.	PUNCT
ejpam-5838	214	1	j.	j.	PROPN
ejpam-5838	214	2	pure	pure	PROPN
ejpam-5838	214	3	appl	appl	PROPN
ejpam-5838	214	4	.	.	PROPN
ejpam-5838	214	5	math	math	PROPN
ejpam-5838	214	6	,	,	PUNCT
ejpam-5838	214	7	18	18	NUM
ejpam-5838	214	8	(	(	PUNCT
ejpam-5838	214	9	2	2	NUM
ejpam-5838	214	10	)	)	PUNCT
ejpam-5838	214	11	(	(	PUNCT
ejpam-5838	214	12	2025	2025	NUM
ejpam-5838	214	13	)	)	PUNCT
ejpam-5838	214	14	,	,	PUNCT
ejpam-5838	214	15	5838	5838	NUM
ejpam-5838	214	16	8	8	NUM
ejpam-5838	214	17	of	of	ADP
ejpam-5838	214	18	16	16	NUM
ejpam-5838	214	19	+	+	CCONJ
ejpam-5838	214	20	β	β	X
ejpam-5838	214	21			NOUN
ejpam-5838	214	22	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	214	23	,	,	PUNCT
ejpam-5838	214	24	f2z	f2z	NOUN
ejpam-5838	214	25	,	,	PUNCT
ejpam-5838	214	26	f2z	f2z	NOUN
ejpam-5838	214	27	)	)	PUNCT
ejpam-5838	214	28	·	·	PUNCT
ejpam-5838	214	29	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	214	30	,	,	PUNCT
ejpam-5838	214	31	ê3⋎+3	ê3⋎+3	NUM
ejpam-5838	214	32	,	,	PUNCT
ejpam-5838	214	33	ê3⋎+3	ê3⋎+3	X
ejpam-5838	214	34	)	)	PUNCT
ejpam-5838	214	35	·	·	PUNCT
ejpam-5838	215	1	g(z	g(z	ADJ
ejpam-5838	215	2	,	,	PUNCT
ejpam-5838	215	3	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	215	4	,	,	PUNCT
ejpam-5838	215	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	215	6	)	)	PUNCT
ejpam-5838	216	1	+	+	PUNCT
ejpam-5838	216	2	g(z	g(z	ADJ
ejpam-5838	216	3	,	,	PUNCT
ejpam-5838	216	4	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	216	5	,	,	PUNCT
ejpam-5838	216	6	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	216	7	)	)	PUNCT
ejpam-5838	216	8	·	·	PUNCT
ejpam-5838	216	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	216	10	,	,	PUNCT
ejpam-5838	216	11	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	216	12	,	,	PUNCT
ejpam-5838	216	13	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	216	14	)	)	PUNCT
ejpam-5838	216	15	·	·	PUNCT
ejpam-5838	216	16	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	216	17	,	,	PUNCT
ejpam-5838	216	18	f2z	f2z	NOUN
ejpam-5838	216	19	,	,	PUNCT
ejpam-5838	216	20	f2z	f2z	NOUN
ejpam-5838	216	21	)	)	PUNCT
ejpam-5838	216	22	1	1	NUM
ejpam-5838	217	1	+	+	PUNCT
ejpam-5838	217	2	g(z	g(z	ADJ
ejpam-5838	217	3	,	,	PUNCT
ejpam-5838	217	4	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	217	5	,	,	PUNCT
ejpam-5838	217	6	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	217	7	)	)	PUNCT
ejpam-5838	217	8	·	·	PUNCT
ejpam-5838	217	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	217	10	,	,	PUNCT
ejpam-5838	217	11	f2z	f2z	NOUN
ejpam-5838	217	12	,	,	PUNCT
ejpam-5838	217	13	f2z	f2z	NOUN
ejpam-5838	217	14	)	)	PUNCT
ejpam-5838	217	15	·	·	PUNCT
ejpam-5838	217	16	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	217	17	,	,	PUNCT
ejpam-5838	217	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	217	19	,	,	PUNCT
ejpam-5838	217	20	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	217	21	)	)	PUNCT
ejpam-5838	217	22			NOUN
ejpam-5838	217	23	applying	apply	VERB
ejpam-5838	217	24	limn→∞	limn→∞	PROPN
ejpam-5838	217	25	and	and	CCONJ
ejpam-5838	217	26	after	after	ADP
ejpam-5838	217	27	simplification	simplification	NOUN
ejpam-5838	217	28	,	,	PUNCT
ejpam-5838	217	29	we	we	PRON
ejpam-5838	217	30	obtained	obtain	VERB
ejpam-5838	217	31	g(z	g(z	PROPN
ejpam-5838	217	32	,	,	PUNCT
ejpam-5838	217	33	f2z	f2z	NOUN
ejpam-5838	217	34	,	,	PUNCT
ejpam-5838	217	35	z	z	NOUN
ejpam-5838	217	36	)	)	PUNCT
ejpam-5838	217	37	≤	≤	NOUN
ejpam-5838	217	38	αg(z	αg(z	NOUN
ejpam-5838	217	39	,	,	PUNCT
ejpam-5838	217	40	z	z	NOUN
ejpam-5838	217	41	,	,	PUNCT
ejpam-5838	217	42	z	z	NOUN
ejpam-5838	217	43	)	)	PUNCT
ejpam-5838	217	44	.	.	PUNCT
ejpam-5838	218	1	this	this	PRON
ejpam-5838	218	2	implies	imply	VERB
ejpam-5838	218	3	that	that	SCONJ
ejpam-5838	218	4	,	,	PUNCT
ejpam-5838	218	5	g(z	g(z	ADJ
ejpam-5838	218	6	,	,	PUNCT
ejpam-5838	218	7	f2z	f2z	NOUN
ejpam-5838	218	8	,	,	PUNCT
ejpam-5838	218	9	z	z	NOUN
ejpam-5838	218	10	)	)	PUNCT
ejpam-5838	218	11	=	=	SYM
ejpam-5838	218	12	0	0	X
ejpam-5838	218	13	.	.	PUNCT
ejpam-5838	219	1	thus	thus	ADV
ejpam-5838	219	2	,	,	PUNCT
ejpam-5838	219	3	f2z	f2z	PROPN
ejpam-5838	219	4	=	=	PUNCT
ejpam-5838	219	5	z.	z.	PROPN
ejpam-5838	219	6	(	(	PUNCT
ejpam-5838	219	7	8)	8)	NUM
ejpam-5838	219	8	next	next	ADV
ejpam-5838	219	9	,	,	PUNCT
ejpam-5838	219	10	we	we	PRON
ejpam-5838	219	11	show	show	VERB
ejpam-5838	219	12	that	that	SCONJ
ejpam-5838	219	13	f3z	f3z	NOUN
ejpam-5838	219	14	=	=	SYM
ejpam-5838	219	15	z	z	NOUN
ejpam-5838	219	16	by	by	ADP
ejpam-5838	219	17	contrary	contrary	ADJ
ejpam-5838	219	18	case	case	NOUN
ejpam-5838	219	19	.	.	PUNCT
ejpam-5838	220	1	let	let	VERB
ejpam-5838	220	2	f3z	f3z	NOUN
ejpam-5838	220	3	̸=	̸=	PROPN
ejpam-5838	220	4	z.	z.	PROPN
ejpam-5838	220	5	by	by	ADP
ejpam-5838	220	6	using	use	VERB
ejpam-5838	220	7	(	(	PUNCT
ejpam-5838	220	8	3.1	3.1	NUM
ejpam-5838	220	9	)	)	PUNCT
ejpam-5838	220	10	,	,	PUNCT
ejpam-5838	220	11	we	we	PRON
ejpam-5838	220	12	have	have	VERB
ejpam-5838	220	13	that	that	DET
ejpam-5838	220	14	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	220	15	,	,	PUNCT
ejpam-5838	220	16	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	220	17	,	,	PUNCT
ejpam-5838	220	18	f3z	f3z	NOUN
ejpam-5838	220	19	)	)	PUNCT
ejpam-5838	220	20	=	=	SYM
ejpam-5838	220	21	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	220	22	,	,	PUNCT
ejpam-5838	220	23	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	220	24	,	,	PUNCT
ejpam-5838	220	25	f3z	f3z	NOUN
ejpam-5838	220	26	)	)	PUNCT
ejpam-5838	220	27	≤	≤	NOUN
ejpam-5838	220	28	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	220	29	,	,	PUNCT
ejpam-5838	220	30	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	220	31	,	,	PUNCT
ejpam-5838	220	32	z	z	NOUN
ejpam-5838	220	33	)	)	PUNCT
ejpam-5838	221	1	+	+	CCONJ
ejpam-5838	221	2	β	β	X
ejpam-5838	221	3			NOUN
ejpam-5838	221	4	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	221	5	,	,	PUNCT
ejpam-5838	221	6	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	221	7	,	,	PUNCT
ejpam-5838	221	8	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	221	9	)	)	PUNCT
ejpam-5838	221	10	·	·	PUNCT
ejpam-5838	221	11	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	221	12	,	,	PUNCT
ejpam-5838	221	13	f3z	f3z	NOUN
ejpam-5838	221	14	,	,	PUNCT
ejpam-5838	221	15	f3z	f3z	NOUN
ejpam-5838	221	16	)	)	PUNCT
ejpam-5838	221	17	·	·	PUNCT
ejpam-5838	221	18	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	221	19	,	,	PUNCT
ejpam-5838	221	20	f1ê3⋎	f1ê3⋎	X
ejpam-5838	221	21	,	,	PUNCT
ejpam-5838	221	22	f1ê3⋎	f1ê3⋎	X
ejpam-5838	221	23	)	)	PUNCT
ejpam-5838	221	24	+	+	NOUN
ejpam-5838	221	25	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	221	26	,	,	PUNCT
ejpam-5838	221	27	f3z	f3z	NOUN
ejpam-5838	221	28	,	,	PUNCT
ejpam-5838	221	29	f3z	f3z	NOUN
ejpam-5838	221	30	)	)	PUNCT
ejpam-5838	221	31	·	·	PUNCT
ejpam-5838	221	32	g(z	g(z	PROPN
ejpam-5838	221	33	,	,	PUNCT
ejpam-5838	221	34	f1ê3⋎	f1ê3⋎	X
ejpam-5838	221	35	,	,	PUNCT
ejpam-5838	221	36	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	221	37	)	)	PUNCT
ejpam-5838	221	38	·	·	PUNCT
ejpam-5838	221	39	g(z	g(z	ADJ
ejpam-5838	221	40	,	,	PUNCT
ejpam-5838	221	41	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	221	42	,	,	PUNCT
ejpam-5838	221	43	f2ê3⋎+1	f2ê3⋎+1	NOUN
ejpam-5838	221	44	)	)	PUNCT
ejpam-5838	221	45			NOUN
ejpam-5838	221	46	1	1	NUM
ejpam-5838	221	47	+	+	NOUN
ejpam-5838	221	48	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	221	49	,	,	PUNCT
ejpam-5838	221	50	f1ê3⋎	f1ê3⋎	X
ejpam-5838	221	51	,	,	PUNCT
ejpam-5838	221	52	f1ê3⋎	f1ê3⋎	X
ejpam-5838	221	53	)	)	PUNCT
ejpam-5838	221	54	·	·	PUNCT
ejpam-5838	221	55	g(z	g(z	ADJ
ejpam-5838	221	56	,	,	PUNCT
ejpam-5838	221	57	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	221	58	,	,	PUNCT
ejpam-5838	221	59	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	221	60	)	)	PUNCT
ejpam-5838	221	61	·	·	PUNCT
ejpam-5838	221	62	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	221	63	,	,	PUNCT
ejpam-5838	221	64	f3z	f3z	NOUN
ejpam-5838	221	65	,	,	PUNCT
ejpam-5838	221	66	f3z	f3z	NOUN
ejpam-5838	221	67	)	)	PUNCT
ejpam-5838	221	68			PROPN
ejpam-5838	221	69	≤	≤	PROPN
ejpam-5838	221	70	αg(ê3⋎	αg(ê3⋎	PROPN
ejpam-5838	221	71	,	,	PUNCT
ejpam-5838	221	72	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	221	73	,	,	PUNCT
ejpam-5838	221	74	z	z	NOUN
ejpam-5838	221	75	)	)	PUNCT
ejpam-5838	221	76	+	+	CCONJ
ejpam-5838	221	77	β	β	X
ejpam-5838	221	78			NOUN
ejpam-5838	221	79	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	221	80	,	,	PUNCT
ejpam-5838	221	81	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	221	82	,	,	PUNCT
ejpam-5838	221	83	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	221	84	)	)	PUNCT
ejpam-5838	221	85	·	·	PUNCT
ejpam-5838	221	86	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	221	87	,	,	PUNCT
ejpam-5838	221	88	f3z	f3z	NOUN
ejpam-5838	221	89	,	,	PUNCT
ejpam-5838	221	90	f3z	f3z	NOUN
ejpam-5838	221	91	)	)	PUNCT
ejpam-5838	221	92	·	·	PUNCT
ejpam-5838	221	93	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	221	94	,	,	PUNCT
ejpam-5838	221	95	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	221	96	,	,	PUNCT
ejpam-5838	221	97	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	221	98	)	)	PUNCT
ejpam-5838	222	1	+	+	NOUN
ejpam-5838	222	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	222	3	,	,	PUNCT
ejpam-5838	222	4	f3z	f3z	NOUN
ejpam-5838	222	5	,	,	PUNCT
ejpam-5838	222	6	f3z	f3z	NOUN
ejpam-5838	222	7	)	)	PUNCT
ejpam-5838	222	8	·	·	PUNCT
ejpam-5838	222	9	g(z	g(z	ADJ
ejpam-5838	222	10	,	,	PUNCT
ejpam-5838	222	11	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	222	12	,	,	PUNCT
ejpam-5838	222	13	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	222	14	)	)	PUNCT
ejpam-5838	222	15	·	·	PUNCT
ejpam-5838	222	16	g(z	g(z	ADJ
ejpam-5838	222	17	,	,	PUNCT
ejpam-5838	222	18	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	222	19	,	,	PUNCT
ejpam-5838	222	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	222	21	)	)	PUNCT
ejpam-5838	222	22			NOUN
ejpam-5838	222	23	1	1	NUM
ejpam-5838	222	24	+	+	NOUN
ejpam-5838	222	25	g(ê3⋎+1	g(ê3⋎+1	ADJ
ejpam-5838	222	26	,	,	PUNCT
ejpam-5838	222	27	ê3⋎+1	ê3⋎+1	ADJ
ejpam-5838	222	28	,	,	PUNCT
ejpam-5838	222	29	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	222	30	)	)	PUNCT
ejpam-5838	222	31	·	·	PUNCT
ejpam-5838	223	1	g(z	g(z	ADJ
ejpam-5838	223	2	,	,	PUNCT
ejpam-5838	223	3	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	223	4	,	,	PUNCT
ejpam-5838	223	5	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	223	6	)	)	PUNCT
ejpam-5838	223	7	·	·	PUNCT
ejpam-5838	223	8	g(ê3⋎	g(ê3⋎	ADJ
ejpam-5838	223	9	,	,	PUNCT
ejpam-5838	223	10	f3z	f3z	NOUN
ejpam-5838	223	11	,	,	PUNCT
ejpam-5838	223	12	f3z	f3z	NOUN
ejpam-5838	223	13	)	)	PUNCT
ejpam-5838	223	14			PROPN
ejpam-5838	223	15	applying	apply	VERB
ejpam-5838	223	16	limn→∞	limn→∞	PROPN
ejpam-5838	223	17	and	and	CCONJ
ejpam-5838	223	18	after	after	ADP
ejpam-5838	223	19	simplification	simplification	NOUN
ejpam-5838	223	20	,	,	PUNCT
ejpam-5838	223	21	we	we	PRON
ejpam-5838	223	22	obtained	obtain	VERB
ejpam-5838	223	23	g(z	g(z	PROPN
ejpam-5838	223	24	,	,	PUNCT
ejpam-5838	223	25	z	z	NOUN
ejpam-5838	223	26	,	,	PUNCT
ejpam-5838	223	27	f3z	f3z	NOUN
ejpam-5838	223	28	)	)	PUNCT
ejpam-5838	223	29	≤	≤	NOUN
ejpam-5838	223	30	αg(z	αg(z	NOUN
ejpam-5838	223	31	,	,	PUNCT
ejpam-5838	223	32	z	z	NOUN
ejpam-5838	223	33	,	,	PUNCT
ejpam-5838	223	34	z	z	NOUN
ejpam-5838	223	35	)	)	PUNCT
ejpam-5838	223	36	.	.	PUNCT
ejpam-5838	224	1	this	this	PRON
ejpam-5838	224	2	implies	imply	VERB
ejpam-5838	224	3	that	that	SCONJ
ejpam-5838	224	4	,	,	PUNCT
ejpam-5838	224	5	g(z	g(z	PROPN
ejpam-5838	224	6	,	,	PUNCT
ejpam-5838	224	7	z	z	NOUN
ejpam-5838	224	8	,	,	PUNCT
ejpam-5838	224	9	f3z	f3z	NOUN
ejpam-5838	224	10	)	)	PUNCT
ejpam-5838	224	11	=	=	SYM
ejpam-5838	224	12	0	0	X
ejpam-5838	224	13	.	.	PUNCT
ejpam-5838	225	1	thus	thus	ADV
ejpam-5838	225	2	,	,	PUNCT
ejpam-5838	225	3	f3z	f3z	PROPN
ejpam-5838	225	4	=	=	SYM
ejpam-5838	225	5	z.	z.	PROPN
ejpam-5838	225	6	(	(	PUNCT
ejpam-5838	225	7	9	9	NUM
ejpam-5838	225	8	)	)	PUNCT
ejpam-5838	225	9	thus	thus	ADV
ejpam-5838	225	10	,	,	PUNCT
ejpam-5838	225	11	(	(	PUNCT
ejpam-5838	225	12	7	7	NUM
ejpam-5838	225	13	)	)	PUNCT
ejpam-5838	225	14	,	,	PUNCT
ejpam-5838	225	15	(	(	PUNCT
ejpam-5838	225	16	8)	8)	NUM
ejpam-5838	225	17	,	,	PUNCT
ejpam-5838	225	18	and	and	CCONJ
ejpam-5838	225	19	(	(	PUNCT
ejpam-5838	225	20	9	9	X
ejpam-5838	225	21	)	)	PUNCT
ejpam-5838	225	22	proved	prove	VERB
ejpam-5838	225	23	that	that	SCONJ
ejpam-5838	225	24	“	"	PUNCT
ejpam-5838	225	25	z	z	X
ejpam-5838	225	26	”	"	PUNCT
ejpam-5838	225	27	is	be	AUX
ejpam-5838	225	28	a	a	DET
ejpam-5838	225	29	cfp	cfp	NOUN
ejpam-5838	225	30	of	of	ADP
ejpam-5838	225	31	f1	f1	NOUN
ejpam-5838	225	32	,	,	PUNCT
ejpam-5838	225	33	f2	f2	PROPN
ejpam-5838	225	34	and	and	CCONJ
ejpam-5838	225	35	f3	f3	ADJ
ejpam-5838	225	36	,	,	PUNCT
ejpam-5838	225	37	that	that	PRON
ejpam-5838	225	38	is	be	AUX
ejpam-5838	225	39	f1z	f1z	ADJ
ejpam-5838	225	40	=	=	ADJ
ejpam-5838	225	41	f2z	f2z	NOUN
ejpam-5838	225	42	=	=	PUNCT
ejpam-5838	225	43	f3z	f3z	PROPN
ejpam-5838	225	44	=	=	PUNCT
ejpam-5838	225	45	z.	z.	PROPN
ejpam-5838	225	46	uniqueness	uniqueness	PROPN
ejpam-5838	225	47	:	:	PUNCT
ejpam-5838	225	48	assume	assume	VERB
ejpam-5838	225	49	that	that	SCONJ
ejpam-5838	225	50	z∗	z∗	PROPN
ejpam-5838	225	51	∈	∈	PROPN
ejpam-5838	225	52	ê	ê	PROPN
ejpam-5838	225	53	is	be	AUX
ejpam-5838	225	54	another	another	DET
ejpam-5838	225	55	cfp	cfp	NOUN
ejpam-5838	225	56	of	of	ADP
ejpam-5838	225	57	mappings	mapping	NOUN
ejpam-5838	225	58	f1	f1	NOUN
ejpam-5838	225	59	,	,	PUNCT
ejpam-5838	225	60	f2	f2	PROPN
ejpam-5838	225	61	,	,	PUNCT
ejpam-5838	225	62	and	and	CCONJ
ejpam-5838	225	63	f3	f3	NOUN
ejpam-5838	225	64	that	that	PRON
ejpam-5838	225	65	is	be	AUX
ejpam-5838	225	66	f1z	f1z	ADJ
ejpam-5838	225	67	∗	∗	NOUN
ejpam-5838	225	68	=	=	SYM
ejpam-5838	225	69	f2z	f2z	NOUN
ejpam-5838	225	70	∗	∗	NOUN
ejpam-5838	225	71	=	=	PUNCT
ejpam-5838	225	72	f3z	f3z	NOUN
ejpam-5838	225	73	∗	∗	NOUN
ejpam-5838	225	74	=	=	SYM
ejpam-5838	225	75	z∗.	z∗.	PROPN
ejpam-5838	225	76	m.	m.	NOUN
ejpam-5838	225	77	noorwali	noorwali	PROPN
ejpam-5838	225	78	et	et	PROPN
ejpam-5838	225	79	al/	al/	PROPN
ejpam-5838	225	80	/	/	SYM
ejpam-5838	225	81	eur	eur	PROPN
ejpam-5838	225	82	.	.	PUNCT
ejpam-5838	226	1	j.	j.	PROPN
ejpam-5838	226	2	pure	pure	PROPN
ejpam-5838	226	3	appl	appl	PROPN
ejpam-5838	226	4	.	.	PROPN
ejpam-5838	226	5	math	math	PROPN
ejpam-5838	226	6	,	,	PUNCT
ejpam-5838	226	7	18	18	NUM
ejpam-5838	226	8	(	(	PUNCT
ejpam-5838	226	9	2	2	NUM
ejpam-5838	226	10	)	)	PUNCT
ejpam-5838	226	11	(	(	PUNCT
ejpam-5838	226	12	2025	2025	NUM
ejpam-5838	226	13	)	)	PUNCT
ejpam-5838	226	14	,	,	PUNCT
ejpam-5838	226	15	5838	5838	NUM
ejpam-5838	226	16	9	9	NUM
ejpam-5838	226	17	of	of	ADP
ejpam-5838	226	18	16	16	NUM
ejpam-5838	226	19	then	then	ADV
ejpam-5838	226	20	from	from	ADP
ejpam-5838	226	21	(	(	PUNCT
ejpam-5838	226	22	3.1	3.1	NUM
ejpam-5838	226	23	)	)	PUNCT
ejpam-5838	226	24	,	,	PUNCT
ejpam-5838	226	25	we	we	PRON
ejpam-5838	226	26	have	have	VERB
ejpam-5838	226	27	that	that	DET
ejpam-5838	226	28	g(z	g(z	ADJ
ejpam-5838	226	29	,	,	PUNCT
ejpam-5838	226	30	z∗	z∗	PROPN
ejpam-5838	226	31	,	,	PUNCT
ejpam-5838	226	32	z∗	z∗	NOUN
ejpam-5838	226	33	)	)	PUNCT
ejpam-5838	226	34	=	=	PUNCT
ejpam-5838	226	35	g(f1z	g(f1z	ADJ
ejpam-5838	226	36	,	,	PUNCT
ejpam-5838	226	37	f2z	f2z	ADJ
ejpam-5838	226	38	∗	∗	NOUN
ejpam-5838	226	39	,	,	PUNCT
ejpam-5838	226	40	f3z	f3z	NOUN
ejpam-5838	226	41	∗	∗	NOUN
ejpam-5838	226	42	)	)	PUNCT
ejpam-5838	226	43	≤	≤	NOUN
ejpam-5838	226	44	αg(z	αg(z	ADJ
ejpam-5838	226	45	,	,	PUNCT
ejpam-5838	226	46	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	226	47	,	,	PUNCT
ejpam-5838	226	48	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	226	49	)	)	PUNCT
ejpam-5838	227	1	+	+	CCONJ
ejpam-5838	227	2	β	β	X
ejpam-5838	227	3			NOUN
ejpam-5838	227	4	g(z	g(z	PROPN
ejpam-5838	227	5	,	,	PUNCT
ejpam-5838	227	6	f2ê3⋎+1	f2ê3⋎+1	PRON
ejpam-5838	227	7	,	,	PUNCT
ejpam-5838	227	8	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	227	9	)	)	PUNCT
ejpam-5838	227	10	·	·	PUNCT
ejpam-5838	228	1	g(z	g(z	ADJ
ejpam-5838	228	2	,	,	PUNCT
ejpam-5838	228	3	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	228	4	,	,	PUNCT
ejpam-5838	228	5	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	228	6	)	)	PUNCT
ejpam-5838	228	7	·	·	PUNCT
ejpam-5838	228	8	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	228	9	,	,	PUNCT
ejpam-5838	228	10	f1z	f1z	ADJ
ejpam-5838	228	11	,	,	PUNCT
ejpam-5838	228	12	f1z	f1z	ADJ
ejpam-5838	228	13	)	)	PUNCT
ejpam-5838	228	14	+	+	NOUN
ejpam-5838	228	15	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	228	16	,	,	PUNCT
ejpam-5838	228	17	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	228	18	,	,	PUNCT
ejpam-5838	228	19	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	228	20	)	)	PUNCT
ejpam-5838	228	21	·	·	PUNCT
ejpam-5838	228	22	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	228	23	,	,	PUNCT
ejpam-5838	228	24	f1z	f1z	ADJ
ejpam-5838	228	25	,	,	PUNCT
ejpam-5838	228	26	f1z	f1z	NOUN
ejpam-5838	228	27	)	)	PUNCT
ejpam-5838	228	28	·	·	PUNCT
ejpam-5838	228	29	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	228	30	,	,	PUNCT
ejpam-5838	228	31	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	228	32	,	,	PUNCT
ejpam-5838	228	33	f2ê3⋎+1	f2ê3⋎+1	NOUN
ejpam-5838	228	34	)	)	PUNCT
ejpam-5838	228	35			NOUN
ejpam-5838	228	36	1	1	NUM
ejpam-5838	228	37	+	+	NOUN
ejpam-5838	228	38	g(ê3⋎+1	g(ê3⋎+1	ADJ
ejpam-5838	228	39	,	,	PUNCT
ejpam-5838	228	40	f1z	f1z	ADJ
ejpam-5838	228	41	,	,	PUNCT
ejpam-5838	228	42	f1z	f1z	NOUN
ejpam-5838	228	43	)	)	PUNCT
ejpam-5838	228	44	·	·	PUNCT
ejpam-5838	228	45	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	228	46	,	,	PUNCT
ejpam-5838	228	47	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	228	48	,	,	PUNCT
ejpam-5838	228	49	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	228	50	)	)	PUNCT
ejpam-5838	228	51	·	·	PUNCT
ejpam-5838	228	52	g(z	g(z	ADJ
ejpam-5838	228	53	,	,	PUNCT
ejpam-5838	228	54	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	228	55	,	,	PUNCT
ejpam-5838	228	56	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	228	57	)	)	PUNCT
ejpam-5838	228	58			PROPN
ejpam-5838	228	59	≤	≤	PROPN
ejpam-5838	228	60	αg(z	αg(z	PROPN
ejpam-5838	228	61	,	,	PUNCT
ejpam-5838	228	62	z∗	z∗	PROPN
ejpam-5838	228	63	,	,	PUNCT
ejpam-5838	228	64	z∗	z∗	PROPN
ejpam-5838	228	65	)	)	PUNCT
ejpam-5838	229	1	+	+	CCONJ
ejpam-5838	229	2	β	β	X
ejpam-5838	229	3			NOUN
ejpam-5838	229	4	g(z	g(z	PROPN
ejpam-5838	229	5	,	,	PUNCT
ejpam-5838	229	6	f2z	f2z	ADJ
ejpam-5838	229	7	∗	∗	NOUN
ejpam-5838	229	8	,	,	PUNCT
ejpam-5838	229	9	f2z	f2z	ADJ
ejpam-5838	229	10	∗	∗	NOUN
ejpam-5838	229	11	)	)	PUNCT
ejpam-5838	229	12	·	·	PUNCT
ejpam-5838	230	1	g(z	g(z	ADJ
ejpam-5838	230	2	,	,	PUNCT
ejpam-5838	230	3	f3z	f3z	NOUN
ejpam-5838	230	4	∗	∗	NOUN
ejpam-5838	230	5	,	,	PUNCT
ejpam-5838	230	6	f3z	f3z	NOUN
ejpam-5838	230	7	∗	∗	NOUN
ejpam-5838	230	8	)	)	PUNCT
ejpam-5838	230	9	·	·	PUNCT
ejpam-5838	230	10	g(z	g(z	ADJ
ejpam-5838	230	11	,	,	PUNCT
ejpam-5838	230	12	f1z	f1z	ADJ
ejpam-5838	230	13	,	,	PUNCT
ejpam-5838	230	14	f1z	f1z	NUM
ejpam-5838	230	15	)	)	PUNCT
ejpam-5838	231	1	+	+	NOUN
ejpam-5838	231	2	g(z∗	g(z∗	ADJ
ejpam-5838	231	3	,	,	PUNCT
ejpam-5838	231	4	f3z	f3z	NOUN
ejpam-5838	231	5	∗	∗	NOUN
ejpam-5838	231	6	,	,	PUNCT
ejpam-5838	231	7	f3z	f3z	NOUN
ejpam-5838	231	8	∗	∗	NOUN
ejpam-5838	231	9	)	)	PUNCT
ejpam-5838	231	10	·	·	PUNCT
ejpam-5838	231	11	g(z∗	g(z∗	X
ejpam-5838	231	12	,	,	PUNCT
ejpam-5838	231	13	f1z	f1z	ADJ
ejpam-5838	231	14	,	,	PUNCT
ejpam-5838	231	15	f1z	f1z	NOUN
ejpam-5838	231	16	)	)	PUNCT
ejpam-5838	231	17	·	·	PUNCT
ejpam-5838	231	18	g(z∗	g(z∗	X
ejpam-5838	231	19	,	,	PUNCT
ejpam-5838	231	20	f2z	f2z	ADJ
ejpam-5838	231	21	∗	∗	NOUN
ejpam-5838	231	22	,	,	PUNCT
ejpam-5838	231	23	f2z	f2z	ADJ
ejpam-5838	231	24	∗	∗	NOUN
ejpam-5838	231	25	)	)	PUNCT
ejpam-5838	231	26	}	}	PUNCT
ejpam-5838	231	27	1	1	NUM
ejpam-5838	231	28	+	+	NOUN
ejpam-5838	231	29	g(z∗	g(z∗	ADJ
ejpam-5838	231	30	,	,	PUNCT
ejpam-5838	231	31	f1z	f1z	ADJ
ejpam-5838	231	32	,	,	PUNCT
ejpam-5838	231	33	f1z	f1z	NOUN
ejpam-5838	231	34	)	)	PUNCT
ejpam-5838	231	35	·	·	PUNCT
ejpam-5838	231	36	g(z∗	g(z∗	X
ejpam-5838	231	37	,	,	PUNCT
ejpam-5838	231	38	f2z∗	f2z∗	NOUN
ejpam-5838	231	39	,	,	PUNCT
ejpam-5838	231	40	f2z∗	f2z∗	NOUN
ejpam-5838	231	41	)	)	PUNCT
ejpam-5838	231	42	·	·	PUNCT
ejpam-5838	231	43	g(z	g(z	PROPN
ejpam-5838	231	44	,	,	PUNCT
ejpam-5838	231	45	f3z∗	f3z∗	PROPN
ejpam-5838	231	46	,	,	PUNCT
ejpam-5838	231	47	f3z∗	f3z∗	NOUN
ejpam-5838	231	48	)	)	PUNCT
ejpam-5838	231	49			NOUN
ejpam-5838	231	50	after	after	ADP
ejpam-5838	231	51	simplification	simplification	NOUN
ejpam-5838	231	52	,	,	PUNCT
ejpam-5838	231	53	we	we	PRON
ejpam-5838	231	54	get	get	VERB
ejpam-5838	231	55	that	that	DET
ejpam-5838	231	56	g(z	g(z	NOUN
ejpam-5838	231	57	,	,	PUNCT
ejpam-5838	231	58	z∗	z∗	PROPN
ejpam-5838	231	59	,	,	PUNCT
ejpam-5838	231	60	z∗	z∗	NOUN
ejpam-5838	231	61	)	)	PUNCT
ejpam-5838	231	62	≤	≤	NOUN
ejpam-5838	231	63	αg(z	αg(z	NOUN
ejpam-5838	231	64	,	,	PUNCT
ejpam-5838	231	65	z∗	z∗	PROPN
ejpam-5838	231	66	,	,	PUNCT
ejpam-5838	231	67	z∗	z∗	PROPN
ejpam-5838	231	68	)	)	PUNCT
ejpam-5838	231	69	which	which	PRON
ejpam-5838	231	70	implies	imply	VERB
ejpam-5838	231	71	that	that	SCONJ
ejpam-5838	231	72	(	(	PUNCT
ejpam-5838	231	73	1−α)g(z	1−α)g(z	NOUN
ejpam-5838	231	74	,	,	PUNCT
ejpam-5838	231	75	z∗	z∗	NOUN
ejpam-5838	231	76	,	,	PUNCT
ejpam-5838	231	77	z∗	z∗	PROPN
ejpam-5838	231	78	)	)	PUNCT
ejpam-5838	231	79	is	be	AUX
ejpam-5838	231	80	a	a	DET
ejpam-5838	231	81	contradiction	contradiction	NOUN
ejpam-5838	231	82	,	,	PUNCT
ejpam-5838	231	83	since	since	SCONJ
ejpam-5838	231	84	(	(	PUNCT
ejpam-5838	231	85	1−	1−	NUM
ejpam-5838	231	86	α	α	NOUN
ejpam-5838	231	87	)	)	PUNCT
ejpam-5838	231	88	>	>	X
ejpam-5838	232	1	0	0	X
ejpam-5838	232	2	.	.	PUNCT
ejpam-5838	233	1	therefore	therefore	ADV
ejpam-5838	233	2	,	,	PUNCT
ejpam-5838	233	3	g(z	g(z	PROPN
ejpam-5838	233	4	,	,	PUNCT
ejpam-5838	233	5	z∗	z∗	PROPN
ejpam-5838	233	6	,	,	PUNCT
ejpam-5838	233	7	z∗	z∗	NOUN
ejpam-5838	233	8	)	)	PUNCT
ejpam-5838	233	9	=	=	SYM
ejpam-5838	233	10	0	0	NUM
ejpam-5838	233	11	,	,	PUNCT
ejpam-5838	233	12	and	and	CCONJ
ejpam-5838	233	13	so	so	ADV
ejpam-5838	233	14	z	z	NOUN
ejpam-5838	233	15	=	=	SYM
ejpam-5838	233	16	z∗.	z∗.	NOUN
ejpam-5838	233	17	if	if	SCONJ
ejpam-5838	233	18	α	α	PROPN
ejpam-5838	233	19	=	=	NOUN
ejpam-5838	233	20	0	0	NUM
ejpam-5838	233	21	in	in	ADP
ejpam-5838	233	22	theorem	theorem	NOUN
ejpam-5838	233	23	1	1	NUM
ejpam-5838	233	24	,	,	PUNCT
ejpam-5838	233	25	produces	produce	VERB
ejpam-5838	233	26	the	the	DET
ejpam-5838	233	27	following	following	NOUN
ejpam-5838	233	28	.	.	PUNCT
ejpam-5838	234	1	corollary	corollary	ADJ
ejpam-5838	234	2	1	1	NUM
ejpam-5838	234	3	.	.	PUNCT
ejpam-5838	235	1	let	let	AUX
ejpam-5838	235	2	(	(	PUNCT
ejpam-5838	235	3	ê	ê	NOUN
ejpam-5838	235	4	,	,	PUNCT
ejpam-5838	235	5	g	g	NOUN
ejpam-5838	235	6	)	)	PUNCT
ejpam-5838	235	7	be	be	AUX
ejpam-5838	235	8	a	a	DET
ejpam-5838	235	9	gm	gm	PROPN
ejpam-5838	235	10	-space	-space	PROPN
ejpam-5838	235	11	&	&	CCONJ
ejpam-5838	235	12	f1	f1	NOUN
ejpam-5838	235	13	,	,	PUNCT
ejpam-5838	235	14	f2	f2	PROPN
ejpam-5838	235	15	,	,	PUNCT
ejpam-5838	235	16	f3	f3	PROPN
ejpam-5838	235	17	:	:	PUNCT
ejpam-5838	235	18	ê	ê	PROPN
ejpam-5838	235	19	→	→	SYM
ejpam-5838	235	20	ê	ê	PROPN
ejpam-5838	235	21	be	be	AUX
ejpam-5838	235	22	three	three	NUM
ejpam-5838	235	23	self	self	NOUN
ejpam-5838	235	24	-	-	PUNCT
ejpam-5838	235	25	mappings	mapping	NOUN
ejpam-5838	235	26	satisfies	satisfie	NOUN
ejpam-5838	235	27	:	:	PUNCT
ejpam-5838	235	28	g(f1ê1	g(f1ê1	NOUN
ejpam-5838	235	29	,	,	PUNCT
ejpam-5838	235	30	f2ê2	f2ê2	NOUN
ejpam-5838	235	31	,	,	PUNCT
ejpam-5838	235	32	f3ê3	f3ê3	PROPN
ejpam-5838	235	33	)	)	PUNCT
ejpam-5838	235	34	≤	≤	NOUN
ejpam-5838	235	35	αg(ê1	αg(ê1	PROPN
ejpam-5838	235	36	,	,	PUNCT
ejpam-5838	235	37	ê2	ê2	PROPN
ejpam-5838	235	38	,	,	PUNCT
ejpam-5838	235	39	ê3	ê3	PROPN
ejpam-5838	235	40	)	)	PUNCT
ejpam-5838	235	41	for	for	ADP
ejpam-5838	235	42	all	all	DET
ejpam-5838	235	43	ê1	ê1	PROPN
ejpam-5838	235	44	,	,	PUNCT
ejpam-5838	235	45	ê2	ê2	PROPN
ejpam-5838	235	46	,	,	PUNCT
ejpam-5838	235	47	ê3	ê3	PROPN
ejpam-5838	235	48	∈	∈	PROPN
ejpam-5838	235	49	ê	ê	PROPN
ejpam-5838	235	50	and	and	CCONJ
ejpam-5838	235	51	α	α	PRON
ejpam-5838	235	52	,	,	PUNCT
ejpam-5838	235	53	β	β	X
ejpam-5838	235	54	=	=	SYM
ejpam-5838	235	55	0	0	NUM
ejpam-5838	235	56	with	with	ADP
ejpam-5838	235	57	α	α	PROPN
ejpam-5838	235	58	,	,	PUNCT
ejpam-5838	235	59	β	β	X
ejpam-5838	235	60	<	<	X
ejpam-5838	235	61	1	1	NUM
ejpam-5838	235	62	.	.	PUNCT
ejpam-5838	236	1	then	then	ADV
ejpam-5838	236	2	the	the	DET
ejpam-5838	236	3	3	3	NUM
ejpam-5838	236	4	-	-	PUNCT
ejpam-5838	236	5	self	self	NOUN
ejpam-5838	236	6	-	-	PUNCT
ejpam-5838	236	7	mapping	mapping	NOUN
ejpam-5838	236	8	have	have	VERB
ejpam-5838	236	9	a	a	DET
ejpam-5838	236	10	cfp	cfp	NOUN
ejpam-5838	236	11	in	in	ADP
ejpam-5838	236	12	ê	ê	PROPN
ejpam-5838	236	13	,	,	PUNCT
ejpam-5838	236	14	if	if	SCONJ
ejpam-5838	236	15	(	(	PUNCT
ejpam-5838	236	16	α+	α+	X
ejpam-5838	236	17	β	β	NOUN
ejpam-5838	236	18	)	)	PUNCT
ejpam-5838	236	19	≤	≤	NUM
ejpam-5838	236	20	1	1	NUM
ejpam-5838	236	21	,	,	PUNCT
ejpam-5838	236	22	then	then	ADV
ejpam-5838	236	23	f1	f1	NOUN
ejpam-5838	236	24	,	,	PUNCT
ejpam-5838	236	25	f2	f2	PROPN
ejpam-5838	236	26	&	&	CCONJ
ejpam-5838	236	27	f3	f3	PROPN
ejpam-5838	236	28	have	have	VERB
ejpam-5838	236	29	a	a	DET
ejpam-5838	236	30	unique	unique	ADJ
ejpam-5838	236	31	cfp	cfp	NOUN
ejpam-5838	236	32	in	in	ADP
ejpam-5838	236	33	ê.	ê.	NOUN
ejpam-5838	236	34	by	by	ADP
ejpam-5838	236	35	specializing	specialize	VERB
ejpam-5838	236	36	α	α	PROPN
ejpam-5838	236	37	=	=	SYM
ejpam-5838	236	38	0	0	NUM
ejpam-5838	236	39	,	,	PUNCT
ejpam-5838	236	40	in	in	ADP
ejpam-5838	236	41	theorem	theorem	NOUN
ejpam-5838	236	42	1	1	NUM
ejpam-5838	236	43	,	,	PUNCT
ejpam-5838	236	44	we	we	PRON
ejpam-5838	236	45	get	get	VERB
ejpam-5838	236	46	the	the	DET
ejpam-5838	236	47	following	follow	VERB
ejpam-5838	236	48	corollary	corollary	NOUN
ejpam-5838	236	49	.	.	PUNCT
ejpam-5838	237	1	corollary	corollary	ADJ
ejpam-5838	237	2	2	2	NUM
ejpam-5838	237	3	.	.	PUNCT
ejpam-5838	238	1	let	let	AUX
ejpam-5838	238	2	(	(	PUNCT
ejpam-5838	238	3	ê	ê	NOUN
ejpam-5838	238	4	,	,	PUNCT
ejpam-5838	238	5	g	g	NOUN
ejpam-5838	238	6	)	)	PUNCT
ejpam-5838	238	7	be	be	AUX
ejpam-5838	238	8	a	a	DET
ejpam-5838	238	9	gm	gm	PROPN
ejpam-5838	238	10	-space	-space	NOUN
ejpam-5838	238	11	and	and	CCONJ
ejpam-5838	238	12	f1	f1	NOUN
ejpam-5838	238	13	,	,	PUNCT
ejpam-5838	238	14	f2	f2	PROPN
ejpam-5838	238	15	,	,	PUNCT
ejpam-5838	238	16	f3	f3	PROPN
ejpam-5838	238	17	:	:	PUNCT
ejpam-5838	238	18	ê	ê	PROPN
ejpam-5838	238	19	→	→	SYM
ejpam-5838	238	20	ê	ê	PROPN
ejpam-5838	238	21	be	be	AUX
ejpam-5838	238	22	3	3	NUM
ejpam-5838	238	23	-	-	PUNCT
ejpam-5838	238	24	self	self	NOUN
ejpam-5838	238	25	-	-	PUNCT
ejpam-5838	238	26	mappings	mapping	NOUN
ejpam-5838	238	27	as	as	ADP
ejpam-5838	238	28	:	:	PUNCT
ejpam-5838	238	29	g(f1ê1	g(f1ê1	PROPN
ejpam-5838	238	30	,	,	PUNCT
ejpam-5838	238	31	f2ê2	f2ê2	NOUN
ejpam-5838	238	32	,	,	PUNCT
ejpam-5838	238	33	f3ê3	f3ê3	PROPN
ejpam-5838	238	34	)	)	PUNCT
ejpam-5838	238	35	≤	≤	NOUN
ejpam-5838	239	1	β	β	X
ejpam-5838	239	2			X
ejpam-5838	240	1	g(ê1	g(ê1	NOUN
ejpam-5838	240	2	,	,	PUNCT
ejpam-5838	240	3	f2ê2	f2ê2	NOUN
ejpam-5838	240	4	,	,	PUNCT
ejpam-5838	240	5	f2ê2	f2ê2	NOUN
ejpam-5838	240	6	)	)	PUNCT
ejpam-5838	240	7	·	·	PUNCT
ejpam-5838	240	8	g(ê1	g(ê1	PROPN
ejpam-5838	240	9	,	,	PUNCT
ejpam-5838	240	10	f3ê3	f3ê3	PROPN
ejpam-5838	240	11	,	,	PUNCT
ejpam-5838	240	12	f3ê3	f3ê3	PROPN
ejpam-5838	240	13	)	)	PUNCT
ejpam-5838	240	14	·	·	PUNCT
ejpam-5838	240	15	g(ê2	g(ê2	PROPN
ejpam-5838	240	16	,	,	PUNCT
ejpam-5838	240	17	f1ê1	f1ê1	PROPN
ejpam-5838	240	18	,	,	PUNCT
ejpam-5838	240	19	f1ê1	f1ê1	PROPN
ejpam-5838	240	20	)	)	PUNCT
ejpam-5838	240	21	+	+	ADJ
ejpam-5838	240	22	g(ê2	g(ê2	PROPN
ejpam-5838	240	23	,	,	PUNCT
ejpam-5838	240	24	f3ê3	f3ê3	PROPN
ejpam-5838	240	25	,	,	PUNCT
ejpam-5838	240	26	f3ê3	f3ê3	PROPN
ejpam-5838	240	27	)	)	PUNCT
ejpam-5838	240	28	·	·	PUNCT
ejpam-5838	240	29	g(ê3	g(ê3	PROPN
ejpam-5838	240	30	,	,	PUNCT
ejpam-5838	240	31	f1ê1	f1ê1	PROPN
ejpam-5838	240	32	,	,	PUNCT
ejpam-5838	240	33	f1ê1	f1ê1	PROPN
ejpam-5838	240	34	)	)	PUNCT
ejpam-5838	240	35	·	·	PUNCT
ejpam-5838	240	36	g(ê3	g(ê3	PROPN
ejpam-5838	240	37	,	,	PUNCT
ejpam-5838	240	38	f2ê2	f2ê2	NOUN
ejpam-5838	240	39	,	,	PUNCT
ejpam-5838	240	40	f2ê2	f2ê2	NOUN
ejpam-5838	240	41	)	)	PUNCT
ejpam-5838	240	42	1	1	NUM
ejpam-5838	241	1	+	+	CCONJ
ejpam-5838	242	1	[	[	X
ejpam-5838	242	2	g(ê2	g(ê2	ADJ
ejpam-5838	242	3	,	,	PUNCT
ejpam-5838	242	4	f1ê1	f1ê1	PROPN
ejpam-5838	242	5	,	,	PUNCT
ejpam-5838	242	6	f1ê1	f1ê1	PROPN
ejpam-5838	242	7	)	)	PUNCT
ejpam-5838	242	8	·	·	PUNCT
ejpam-5838	242	9	g(ê3	g(ê3	PROPN
ejpam-5838	242	10	,	,	PUNCT
ejpam-5838	242	11	f2ê2	f2ê2	NOUN
ejpam-5838	242	12	,	,	PUNCT
ejpam-5838	242	13	f2ê2	f2ê2	NOUN
ejpam-5838	242	14	)	)	PUNCT
ejpam-5838	242	15	·	·	PUNCT
ejpam-5838	242	16	g(ê1	g(ê1	PROPN
ejpam-5838	242	17	,	,	PUNCT
ejpam-5838	242	18	f3ê3	f3ê3	PROPN
ejpam-5838	242	19	,	,	PUNCT
ejpam-5838	242	20	f3ê3	f3ê3	PROPN
ejpam-5838	242	21	)	)	PUNCT
ejpam-5838	242	22	]	]	PUNCT
ejpam-5838	242	23			VERB
ejpam-5838	242	24	for	for	ADP
ejpam-5838	242	25	all	all	DET
ejpam-5838	242	26	ê1	ê1	PROPN
ejpam-5838	242	27	,	,	PUNCT
ejpam-5838	242	28	ê2	ê2	PROPN
ejpam-5838	242	29	,	,	PUNCT
ejpam-5838	242	30	ê3	ê3	PROPN
ejpam-5838	242	31	∈	∈	PROPN
ejpam-5838	242	32	ê	ê	PROPN
ejpam-5838	242	33	and	and	CCONJ
ejpam-5838	242	34	α	α	PROPN
ejpam-5838	242	35	,	,	PUNCT
ejpam-5838	242	36	β	β	X
ejpam-5838	242	37	≥	≥	NOUN
ejpam-5838	242	38	0	0	NUM
ejpam-5838	242	39	s.t	s.t	PROPN
ejpam-5838	242	40	β	β	X
ejpam-5838	242	41	<	<	X
ejpam-5838	242	42	1	1	NUM
ejpam-5838	242	43	.	.	PUNCT
ejpam-5838	243	1	then	then	ADV
ejpam-5838	243	2	the	the	DET
ejpam-5838	243	3	three	three	NUM
ejpam-5838	243	4	self	self	NOUN
ejpam-5838	243	5	-	-	PUNCT
ejpam-5838	243	6	mapping	mapping	NOUN
ejpam-5838	243	7	f1	f1	NOUN
ejpam-5838	243	8	,	,	PUNCT
ejpam-5838	243	9	f2	f2	PROPN
ejpam-5838	243	10	and	and	CCONJ
ejpam-5838	243	11	f3	f3	PROPN
ejpam-5838	243	12	have	have	VERB
ejpam-5838	243	13	a	a	DET
ejpam-5838	243	14	cfp	cfp	NOUN
ejpam-5838	243	15	in	in	ADP
ejpam-5838	243	16	ê.	ê.	NOUN
ejpam-5838	243	17	if	if	SCONJ
ejpam-5838	243	18	β	β	X
ejpam-5838	243	19	<	<	X
ejpam-5838	243	20	1	1	NUM
ejpam-5838	243	21	,	,	PUNCT
ejpam-5838	243	22	then	then	ADV
ejpam-5838	243	23	f1	f1	NOUN
ejpam-5838	243	24	,	,	PUNCT
ejpam-5838	243	25	f2	f2	PROPN
ejpam-5838	243	26	,	,	PUNCT
ejpam-5838	243	27	and	and	CCONJ
ejpam-5838	243	28	f3	f3	PROPN
ejpam-5838	243	29	have	have	VERB
ejpam-5838	243	30	a	a	DET
ejpam-5838	243	31	unique	unique	ADJ
ejpam-5838	243	32	cfp	cfp	NOUN
ejpam-5838	243	33	in	in	ADP
ejpam-5838	243	34	ê.	ê.	NOUN
ejpam-5838	243	35	theorem	theorem	PROPN
ejpam-5838	243	36	2	2	X
ejpam-5838	243	37	.	.	PUNCT
ejpam-5838	244	1	let	let	AUX
ejpam-5838	244	2	(	(	PUNCT
ejpam-5838	244	3	ê	ê	NOUN
ejpam-5838	244	4	,	,	PUNCT
ejpam-5838	244	5	g	g	NOUN
ejpam-5838	244	6	)	)	PUNCT
ejpam-5838	244	7	be	be	AUX
ejpam-5838	244	8	a	a	DET
ejpam-5838	244	9	gm	gm	PROPN
ejpam-5838	244	10	-space	-space	NOUN
ejpam-5838	244	11	and	and	CCONJ
ejpam-5838	244	12	f1	f1	NOUN
ejpam-5838	244	13	,	,	PUNCT
ejpam-5838	244	14	f2	f2	PROPN
ejpam-5838	244	15	,	,	PUNCT
ejpam-5838	244	16	f3	f3	PROPN
ejpam-5838	244	17	:	:	PUNCT
ejpam-5838	244	18	ê	ê	PROPN
ejpam-5838	244	19	→	→	SYM
ejpam-5838	244	20	ê	ê	PROPN
ejpam-5838	244	21	be	be	AUX
ejpam-5838	244	22	3	3	NUM
ejpam-5838	244	23	-	-	PUNCT
ejpam-5838	244	24	self	self	NOUN
ejpam-5838	244	25	-	-	PUNCT
ejpam-5838	244	26	mappings	mapping	NOUN
ejpam-5838	244	27	satisfies	satisfie	NOUN
ejpam-5838	244	28	:	:	PUNCT
ejpam-5838	244	29	g(f1ê1	g(f1ê1	NOUN
ejpam-5838	244	30	,	,	PUNCT
ejpam-5838	244	31	f2ê2	f2ê2	NOUN
ejpam-5838	244	32	,	,	PUNCT
ejpam-5838	244	33	f3ê3	f3ê3	PROPN
ejpam-5838	244	34	)	)	PUNCT
ejpam-5838	244	35	≤	≤	NOUN
ejpam-5838	244	36	αg(ê1	αg(ê1	PROPN
ejpam-5838	244	37	,	,	PUNCT
ejpam-5838	244	38	ê2	ê2	PROPN
ejpam-5838	244	39	,	,	PUNCT
ejpam-5838	244	40	ê3	ê3	PUNCT
ejpam-5838	244	41	)	)	PUNCT
ejpam-5838	245	1	+	+	CCONJ
ejpam-5838	245	2	β	β	X
ejpam-5838	245	3	g(ê1	g(ê1	PROPN
ejpam-5838	245	4	,	,	PUNCT
ejpam-5838	245	5	f1ê1	f1ê1	PROPN
ejpam-5838	245	6	,	,	PUNCT
ejpam-5838	245	7	f1ê1	f1ê1	PROPN
ejpam-5838	245	8	)	)	PUNCT
ejpam-5838	245	9	·	·	PUNCT
ejpam-5838	245	10	g(ê2	g(ê2	ADJ
ejpam-5838	245	11	,	,	PUNCT
ejpam-5838	245	12	f2ê2	f2ê2	NOUN
ejpam-5838	245	13	,	,	PUNCT
ejpam-5838	245	14	f2ê2	f2ê2	NOUN
ejpam-5838	245	15	)	)	PUNCT
ejpam-5838	245	16	·	·	PUNCT
ejpam-5838	245	17	g(ê3	g(ê3	PROPN
ejpam-5838	245	18	,	,	PUNCT
ejpam-5838	245	19	f3ê3	f3ê3	PROPN
ejpam-5838	245	20	,	,	PUNCT
ejpam-5838	245	21	f3ê3	f3ê3	PROPN
ejpam-5838	245	22	)	)	PUNCT
ejpam-5838	245	23	1	1	NUM
ejpam-5838	246	1	+	+	ADJ
ejpam-5838	246	2	g(ê2	g(ê2	ADJ
ejpam-5838	246	3	,	,	PUNCT
ejpam-5838	246	4	f2ê2	f2ê2	NOUN
ejpam-5838	246	5	,	,	PUNCT
ejpam-5838	246	6	f3ê3	f3ê3	NUM
ejpam-5838	246	7	)	)	PUNCT
ejpam-5838	246	8	·	·	PUNCT
ejpam-5838	246	9	g(f2y	g(f2y	NOUN
ejpam-5838	246	10	,	,	PUNCT
ejpam-5838	246	11	f3ê3	f3ê3	PROPN
ejpam-5838	246	12	,	,	PUNCT
ejpam-5838	246	13	f3ê3	f3ê3	PROPN
ejpam-5838	246	14	)	)	PUNCT
ejpam-5838	246	15	(	(	PUNCT
ejpam-5838	246	16	10	10	NUM
ejpam-5838	246	17	)	)	PUNCT
ejpam-5838	246	18	for	for	ADP
ejpam-5838	246	19	all	all	DET
ejpam-5838	246	20	ê1	ê1	PROPN
ejpam-5838	246	21	,	,	PUNCT
ejpam-5838	246	22	ê2	ê2	PROPN
ejpam-5838	246	23	,	,	PUNCT
ejpam-5838	246	24	ê3	ê3	PROPN
ejpam-5838	246	25	∈	∈	PROPN
ejpam-5838	246	26	ê	ê	PROPN
ejpam-5838	246	27	and	and	CCONJ
ejpam-5838	246	28	α	α	PROPN
ejpam-5838	246	29	,	,	PUNCT
ejpam-5838	246	30	β	β	X
ejpam-5838	246	31	≥	≥	NOUN
ejpam-5838	246	32	0	0	NUM
ejpam-5838	246	33	with	with	ADP
ejpam-5838	246	34	α+	α+	X
ejpam-5838	246	35	β	β	X
ejpam-5838	246	36	<	<	X
ejpam-5838	246	37	1	1	NUM
ejpam-5838	246	38	.	.	PUNCT
ejpam-5838	246	39	then	then	ADV
ejpam-5838	246	40	the	the	DET
ejpam-5838	246	41	3	3	NUM
ejpam-5838	246	42	-	-	PUNCT
ejpam-5838	246	43	self	self	NOUN
ejpam-5838	246	44	-	-	PUNCT
ejpam-5838	246	45	mapping	mapping	NOUN
ejpam-5838	246	46	f1	f1	NOUN
ejpam-5838	246	47	,	,	PUNCT
ejpam-5838	246	48	f2	f2	PROPN
ejpam-5838	246	49	and	and	CCONJ
ejpam-5838	246	50	f3	f3	PROPN
ejpam-5838	246	51	have	have	VERB
ejpam-5838	246	52	a	a	DET
ejpam-5838	246	53	unique	unique	ADJ
ejpam-5838	246	54	cfp	cfp	NOUN
ejpam-5838	246	55	in	in	ADP
ejpam-5838	246	56	ê.	ê.	NOUN
ejpam-5838	246	57	proof	proof	NOUN
ejpam-5838	246	58	.	.	PUNCT
ejpam-5838	247	1	fix	fix	VERB
ejpam-5838	247	2	ê0	ê0	PROPN
ejpam-5838	247	3	∈	∈	PROPN
ejpam-5838	247	4	ê	ê	PROPN
ejpam-5838	247	5	,	,	PUNCT
ejpam-5838	247	6	we	we	PRON
ejpam-5838	247	7	now	now	ADV
ejpam-5838	247	8	define	define	VERB
ejpam-5838	247	9	iterative	iterative	ADJ
ejpam-5838	247	10	sequences	sequence	NOUN
ejpam-5838	247	11	in	in	ADP
ejpam-5838	247	12	ê	ê	PROPN
ejpam-5838	247	13	as	as	SCONJ
ejpam-5838	247	14	follows	follow	VERB
ejpam-5838	247	15	:	:	PUNCT
ejpam-5838	248	1	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	248	2	=	=	SYM
ejpam-5838	248	3	f1ê3⋎	f1ê3⋎	SYM
ejpam-5838	248	4	,	,	PUNCT
ejpam-5838	248	5	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	248	6	=	=	SYM
ejpam-5838	248	7	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	248	8	,	,	PUNCT
ejpam-5838	248	9	and	and	CCONJ
ejpam-5838	248	10	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	248	11	=	=	PUNCT
ejpam-5838	248	12	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	248	13	∀⋎	∀⋎	VERB
ejpam-5838	248	14	≥	≥	NOUN
ejpam-5838	248	15	0	0	NUM
ejpam-5838	248	16	.	.	PUNCT
ejpam-5838	249	1	m.	m.	PROPN
ejpam-5838	249	2	noorwali	noorwali	PROPN
ejpam-5838	249	3	et	et	PROPN
ejpam-5838	249	4	al/	al/	PROPN
ejpam-5838	249	5	/	/	SYM
ejpam-5838	249	6	eur	eur	PROPN
ejpam-5838	249	7	.	.	PUNCT
ejpam-5838	250	1	j.	j.	PROPN
ejpam-5838	250	2	pure	pure	PROPN
ejpam-5838	250	3	appl	appl	PROPN
ejpam-5838	250	4	.	.	PROPN
ejpam-5838	250	5	math	math	PROPN
ejpam-5838	250	6	,	,	PUNCT
ejpam-5838	250	7	18	18	NUM
ejpam-5838	250	8	(	(	PUNCT
ejpam-5838	250	9	2	2	NUM
ejpam-5838	250	10	)	)	PUNCT
ejpam-5838	250	11	(	(	PUNCT
ejpam-5838	250	12	2025	2025	NUM
ejpam-5838	250	13	)	)	PUNCT
ejpam-5838	250	14	,	,	PUNCT
ejpam-5838	250	15	5838	5838	NUM
ejpam-5838	250	16	10	10	NUM
ejpam-5838	250	17	of	of	ADP
ejpam-5838	250	18	16	16	NUM
ejpam-5838	250	19	by	by	ADP
ejpam-5838	250	20	using	use	VERB
ejpam-5838	250	21	(	(	PUNCT
ejpam-5838	250	22	10	10	NUM
ejpam-5838	250	23	)	)	PUNCT
ejpam-5838	250	24	,	,	PUNCT
ejpam-5838	250	25	we	we	PRON
ejpam-5838	250	26	have	have	VERB
ejpam-5838	250	27	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	250	28	,	,	PUNCT
ejpam-5838	250	29	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	250	30	,	,	PUNCT
ejpam-5838	250	31	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	250	32	)	)	PUNCT
ejpam-5838	250	33	≤	≤	NOUN
ejpam-5838	250	34	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	250	35	,	,	PUNCT
ejpam-5838	250	36	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	250	37	,	,	PUNCT
ejpam-5838	250	38	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	250	39	)	)	PUNCT
ejpam-5838	251	1	+	+	NOUN
ejpam-5838	251	2	β	β	X
ejpam-5838	251	3	g(ê3⋎	g(ê3⋎	NUM
ejpam-5838	251	4	,	,	PUNCT
ejpam-5838	251	5	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	251	6	,	,	PUNCT
ejpam-5838	251	7	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	251	8	)	)	PUNCT
ejpam-5838	251	9	·	·	PUNCT
ejpam-5838	251	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	251	11	,	,	PUNCT
ejpam-5838	251	12	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	251	13	,	,	PUNCT
ejpam-5838	251	14	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	251	15	)	)	PUNCT
ejpam-5838	251	16	·	·	PUNCT
ejpam-5838	251	17	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	251	18	,	,	PUNCT
ejpam-5838	251	19	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	251	20	,	,	PUNCT
ejpam-5838	251	21	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	251	22	)	)	PUNCT
ejpam-5838	251	23	1	1	NUM
ejpam-5838	251	24	+	+	NOUN
ejpam-5838	251	25	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	251	26	,	,	PUNCT
ejpam-5838	251	27	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	251	28	,	,	PUNCT
ejpam-5838	251	29	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	251	30	)	)	PUNCT
ejpam-5838	251	31	·	·	PUNCT
ejpam-5838	251	32	g(f2ê3⋎+1	g(f2ê3⋎+1	ADJ
ejpam-5838	251	33	,	,	PUNCT
ejpam-5838	251	34	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	251	35	,	,	PUNCT
ejpam-5838	251	36	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	251	37	)	)	PUNCT
ejpam-5838	251	38	≤	≤	NOUN
ejpam-5838	251	39	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	251	40	,	,	PUNCT
ejpam-5838	251	41	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	251	42	,	,	PUNCT
ejpam-5838	251	43	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	251	44	)	)	PUNCT
ejpam-5838	252	1	+	+	CCONJ
ejpam-5838	252	2	β	β	X
ejpam-5838	252	3	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	252	4	,	,	PUNCT
ejpam-5838	252	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	252	6	,	,	PUNCT
ejpam-5838	252	7	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	252	8	)	)	PUNCT
ejpam-5838	252	9	·	·	PUNCT
ejpam-5838	252	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	252	11	,	,	PUNCT
ejpam-5838	252	12	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	252	13	,	,	PUNCT
ejpam-5838	252	14	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	252	15	)	)	PUNCT
ejpam-5838	252	16	·	·	PUNCT
ejpam-5838	253	1	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	253	2	,	,	PUNCT
ejpam-5838	253	3	ê3⋎+3	ê3⋎+3	CCONJ
ejpam-5838	253	4	,	,	PUNCT
ejpam-5838	253	5	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	253	6	)	)	PUNCT
ejpam-5838	253	7	1	1	NUM
ejpam-5838	254	1	+	+	NOUN
ejpam-5838	254	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	254	3	,	,	PUNCT
ejpam-5838	254	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	254	5	,	,	PUNCT
ejpam-5838	254	6	ê3⋎+3	ê3⋎+3	X
ejpam-5838	254	7	)	)	PUNCT
ejpam-5838	254	8	·	·	PUNCT
ejpam-5838	254	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	254	10	,	,	PUNCT
ejpam-5838	254	11	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	254	12	,	,	PUNCT
ejpam-5838	254	13	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	254	14	)	)	PUNCT
ejpam-5838	254	15	≤	≤	NUM
ejpam-5838	254	16	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	254	17	,	,	PUNCT
ejpam-5838	254	18	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	254	19	,	,	PUNCT
ejpam-5838	254	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	254	21	)	)	PUNCT
ejpam-5838	255	1	+	+	CCONJ
ejpam-5838	255	2	β	β	X
ejpam-5838	255	3	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	255	4	,	,	PUNCT
ejpam-5838	255	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	255	6	,	,	PUNCT
ejpam-5838	255	7	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	255	8	)	)	PUNCT
ejpam-5838	255	9	·	·	PUNCT
ejpam-5838	255	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	255	11	,	,	PUNCT
ejpam-5838	255	12	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	255	13	,	,	PUNCT
ejpam-5838	255	14	ê3⋎+3	ê3⋎+3	X
ejpam-5838	255	15	)	)	PUNCT
ejpam-5838	255	16	·	·	PUNCT
ejpam-5838	255	17	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	255	18	,	,	PUNCT
ejpam-5838	255	19	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	255	20	,	,	PUNCT
ejpam-5838	255	21	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	255	22	)	)	PUNCT
ejpam-5838	255	23	1	1	NUM
ejpam-5838	256	1	+	+	NOUN
ejpam-5838	256	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	256	3	,	,	PUNCT
ejpam-5838	256	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	256	5	,	,	PUNCT
ejpam-5838	256	6	ê3⋎+3	ê3⋎+3	X
ejpam-5838	256	7	)	)	PUNCT
ejpam-5838	256	8	·	·	PUNCT
ejpam-5838	256	9	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	256	10	,	,	PUNCT
ejpam-5838	256	11	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	256	12	,	,	PUNCT
ejpam-5838	256	13	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	256	14	)	)	PUNCT
ejpam-5838	256	15	≤	≤	NOUN
ejpam-5838	256	16	(	(	PUNCT
ejpam-5838	256	17	α+	α+	X
ejpam-5838	256	18	β)g(ê3⋎	β)g(ê3⋎	ADJ
ejpam-5838	256	19	,	,	PUNCT
ejpam-5838	256	20	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	256	21	,	,	PUNCT
ejpam-5838	256	22	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	256	23	)	)	PUNCT
ejpam-5838	256	24	after	after	ADP
ejpam-5838	256	25	simplification	simplification	NOUN
ejpam-5838	256	26	,	,	PUNCT
ejpam-5838	256	27	we	we	PRON
ejpam-5838	256	28	have	have	VERB
ejpam-5838	256	29	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	256	30	,	,	PUNCT
ejpam-5838	256	31	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	256	32	,	,	PUNCT
ejpam-5838	256	33	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	256	34	)	)	PUNCT
ejpam-5838	256	35	≤	≤	NOUN
ejpam-5838	256	36	ηg(ê3⋎	ηg(ê3⋎	PROPN
ejpam-5838	256	37	,	,	PUNCT
ejpam-5838	256	38	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	256	39	,	,	PUNCT
ejpam-5838	256	40	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	256	41	)	)	PUNCT
ejpam-5838	256	42	,	,	PUNCT
ejpam-5838	257	1	where	where	SCONJ
ejpam-5838	257	2	(	(	PUNCT
ejpam-5838	257	3	α+	α+	X
ejpam-5838	257	4	β	β	X
ejpam-5838	257	5	)	)	PUNCT
ejpam-5838	257	6	=	=	SYM
ejpam-5838	257	7	η	η	PROPN
ejpam-5838	257	8	.	.	PROPN
ejpam-5838	257	9	(	(	PUNCT
ejpam-5838	257	10	11	11	NUM
ejpam-5838	257	11	)	)	PUNCT
ejpam-5838	257	12	similarly	similarly	ADV
ejpam-5838	257	13	,	,	PUNCT
ejpam-5838	257	14	again	again	ADV
ejpam-5838	257	15	by	by	ADP
ejpam-5838	257	16	the	the	DET
ejpam-5838	257	17	view	view	NOUN
ejpam-5838	257	18	of	of	ADP
ejpam-5838	257	19	(	(	PUNCT
ejpam-5838	257	20	10	10	NUM
ejpam-5838	257	21	)	)	PUNCT
ejpam-5838	257	22	,	,	PUNCT
ejpam-5838	257	23	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	257	24	,	,	PUNCT
ejpam-5838	257	25	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	257	26	,	,	PUNCT
ejpam-5838	257	27	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	257	28	)	)	PUNCT
ejpam-5838	257	29	=	=	SYM
ejpam-5838	257	30	g(f1ê3⋎+1	g(f1ê3⋎+1	ADJ
ejpam-5838	257	31	,	,	PUNCT
ejpam-5838	257	32	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	257	33	,	,	PUNCT
ejpam-5838	257	34	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	257	35	)	)	PUNCT
ejpam-5838	257	36	≤	≤	NOUN
ejpam-5838	257	37	αg(ê3⋎+1	αg(ê3⋎+1	ADJ
ejpam-5838	257	38	,	,	PUNCT
ejpam-5838	257	39	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	257	40	,	,	PUNCT
ejpam-5838	257	41	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	257	42	)	)	PUNCT
ejpam-5838	258	1	+	+	X
ejpam-5838	258	2	β	β	NOUN
ejpam-5838	258	3	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	258	4	,	,	PUNCT
ejpam-5838	258	5	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	258	6	,	,	PUNCT
ejpam-5838	258	7	f1ê3⋎+1	f1ê3⋎+1	ADJ
ejpam-5838	258	8	)	)	PUNCT
ejpam-5838	258	9	·	·	PUNCT
ejpam-5838	258	10	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	258	11	,	,	PUNCT
ejpam-5838	258	12	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	258	13	,	,	PUNCT
ejpam-5838	258	14	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	258	15	)	)	PUNCT
ejpam-5838	258	16	·	·	PUNCT
ejpam-5838	258	17	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	258	18	,	,	PUNCT
ejpam-5838	258	19	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	258	20	,	,	PUNCT
ejpam-5838	258	21	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	258	22	)	)	PUNCT
ejpam-5838	258	23	1	1	NUM
ejpam-5838	258	24	+	+	ADV
ejpam-5838	258	25	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	258	26	,	,	PUNCT
ejpam-5838	258	27	f2ê3⋎+2	f2ê3⋎+2	NOUN
ejpam-5838	258	28	,	,	PUNCT
ejpam-5838	258	29	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	258	30	)	)	PUNCT
ejpam-5838	258	31	·	·	PUNCT
ejpam-5838	258	32	g(f2ê3⋎+2	g(f2ê3⋎+2	NOUN
ejpam-5838	258	33	,	,	PUNCT
ejpam-5838	258	34	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	258	35	,	,	PUNCT
ejpam-5838	258	36	f3ê3⋎+3	f3ê3⋎+3	NOUN
ejpam-5838	258	37	)	)	PUNCT
ejpam-5838	258	38	≤	≤	NOUN
ejpam-5838	258	39	αg(ê3⋎+1	αg(ê3⋎+1	ADJ
ejpam-5838	258	40	,	,	PUNCT
ejpam-5838	258	41	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	258	42	,	,	PUNCT
ejpam-5838	258	43	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	258	44	)	)	PUNCT
ejpam-5838	259	1	+	+	X
ejpam-5838	259	2	β	β	NOUN
ejpam-5838	259	3	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	259	4	,	,	PUNCT
ejpam-5838	259	5	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	259	6	,	,	PUNCT
ejpam-5838	259	7	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	259	8	)	)	PUNCT
ejpam-5838	259	9	·	·	PUNCT
ejpam-5838	259	10	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	259	11	,	,	PUNCT
ejpam-5838	259	12	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	259	13	,	,	PUNCT
ejpam-5838	259	14	ê3⋎+3	ê3⋎+3	X
ejpam-5838	259	15	)	)	PUNCT
ejpam-5838	259	16	·	·	PUNCT
ejpam-5838	259	17	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	259	18	,	,	PUNCT
ejpam-5838	259	19	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	259	20	,	,	PUNCT
ejpam-5838	259	21	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	259	22	)	)	PUNCT
ejpam-5838	259	23	1	1	NUM
ejpam-5838	260	1	+	+	ADV
ejpam-5838	260	2	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	260	3	,	,	PUNCT
ejpam-5838	260	4	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	260	5	,	,	PUNCT
ejpam-5838	260	6	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	260	7	)	)	PUNCT
ejpam-5838	260	8	·	·	PUNCT
ejpam-5838	260	9	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	260	10	,	,	PUNCT
ejpam-5838	260	11	ê3⋎+4	ê3⋎+4	ADJ
ejpam-5838	260	12	,	,	PUNCT
ejpam-5838	260	13	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	260	14	)	)	PUNCT
ejpam-5838	260	15	≤	≤	NOUN
ejpam-5838	260	16	αg(ê3⋎+1	αg(ê3⋎+1	ADJ
ejpam-5838	260	17	,	,	PUNCT
ejpam-5838	260	18	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	260	19	,	,	PUNCT
ejpam-5838	260	20	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	260	21	)	)	PUNCT
ejpam-5838	260	22	+	+	CCONJ
ejpam-5838	260	23	β	β	NOUN
ejpam-5838	260	24	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	260	25	,	,	PUNCT
ejpam-5838	260	26	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	260	27	,	,	PUNCT
ejpam-5838	260	28	ê3⋎+3	ê3⋎+3	X
ejpam-5838	260	29	)	)	PUNCT
ejpam-5838	260	30	·	·	PUNCT
ejpam-5838	260	31	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	260	32	,	,	PUNCT
ejpam-5838	260	33	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	260	34	,	,	PUNCT
ejpam-5838	260	35	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	260	36	)	)	PUNCT
ejpam-5838	260	37	·	·	PUNCT
ejpam-5838	260	38	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	260	39	,	,	PUNCT
ejpam-5838	260	40	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	260	41	,	,	PUNCT
ejpam-5838	260	42	ê3⋎+5	ê3⋎+5	X
ejpam-5838	260	43	)	)	PUNCT
ejpam-5838	260	44	1	1	NUM
ejpam-5838	261	1	+	+	ADV
ejpam-5838	261	2	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	261	3	,	,	PUNCT
ejpam-5838	261	4	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	261	5	,	,	PUNCT
ejpam-5838	261	6	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	261	7	)	)	PUNCT
ejpam-5838	261	8	·	·	PUNCT
ejpam-5838	261	9	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	261	10	,	,	PUNCT
ejpam-5838	261	11	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	261	12	,	,	PUNCT
ejpam-5838	261	13	ê3⋎+5	ê3⋎+5	X
ejpam-5838	261	14	)	)	PUNCT
ejpam-5838	261	15	≤	≤	NOUN
ejpam-5838	261	16	(	(	PUNCT
ejpam-5838	261	17	α+	α+	X
ejpam-5838	261	18	β)g(ê3⋎+1	β)g(ê3⋎+1	NOUN
ejpam-5838	261	19	,	,	PUNCT
ejpam-5838	261	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	261	21	,	,	PUNCT
ejpam-5838	261	22	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	261	23	)	)	PUNCT
ejpam-5838	261	24	after	after	ADP
ejpam-5838	261	25	simplification	simplification	NOUN
ejpam-5838	261	26	,	,	PUNCT
ejpam-5838	261	27	we	we	PRON
ejpam-5838	261	28	have	have	VERB
ejpam-5838	261	29	g(ê3⋎+2	g(ê3⋎+2	NOUN
ejpam-5838	261	30	,	,	PUNCT
ejpam-5838	261	31	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	261	32	,	,	PUNCT
ejpam-5838	261	33	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	261	34	)	)	PUNCT
ejpam-5838	262	1	≤	≤	NUM
ejpam-5838	262	2	ηg(ê3⋎+1	ηg(ê3⋎+1	PROPN
ejpam-5838	262	3	,	,	PUNCT
ejpam-5838	262	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	262	5	,	,	PUNCT
ejpam-5838	262	6	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	262	7	)	)	PUNCT
ejpam-5838	262	8	,	,	PUNCT
ejpam-5838	262	9	where	where	SCONJ
ejpam-5838	262	10	(	(	PUNCT
ejpam-5838	262	11	α+	α+	X
ejpam-5838	262	12	β	β	X
ejpam-5838	262	13	)	)	PUNCT
ejpam-5838	262	14	=	=	SYM
ejpam-5838	262	15	η	η	PROPN
ejpam-5838	262	16	.	.	PROPN
ejpam-5838	262	17	(	(	PUNCT
ejpam-5838	262	18	12	12	NUM
ejpam-5838	262	19	)	)	PUNCT
ejpam-5838	262	20	by	by	ADP
ejpam-5838	262	21	a	a	DET
ejpam-5838	262	22	similar	similar	ADJ
ejpam-5838	262	23	argument	argument	NOUN
ejpam-5838	262	24	as	as	ADP
ejpam-5838	262	25	in	in	ADP
ejpam-5838	262	26	above	above	ADV
ejpam-5838	262	27	,	,	PUNCT
ejpam-5838	262	28	we	we	PRON
ejpam-5838	262	29	can	can	AUX
ejpam-5838	262	30	show	show	VERB
ejpam-5838	262	31	that	that	DET
ejpam-5838	262	32	g(ê3⋎+3	g(ê3⋎+3	PROPN
ejpam-5838	262	33	,	,	PUNCT
ejpam-5838	262	34	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	262	35	,	,	PUNCT
ejpam-5838	262	36	ê3⋎+5	ê3⋎+5	X
ejpam-5838	262	37	)	)	PUNCT
ejpam-5838	262	38	≤	≤	NUM
ejpam-5838	262	39	ηg(ê3⋎+2	ηg(ê3⋎+2	PROPN
ejpam-5838	262	40	,	,	PUNCT
ejpam-5838	262	41	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	262	42	,	,	PUNCT
ejpam-5838	262	43	ê3⋎+4	ê3⋎+4	NUM
ejpam-5838	262	44	)	)	PUNCT
ejpam-5838	262	45	.	.	PUNCT
ejpam-5838	263	1	(	(	PUNCT
ejpam-5838	263	2	13	13	NUM
ejpam-5838	263	3	)	)	PUNCT
ejpam-5838	263	4	now	now	ADV
ejpam-5838	263	5	,	,	PUNCT
ejpam-5838	263	6	from	from	ADP
ejpam-5838	263	7	(	(	PUNCT
ejpam-5838	263	8	11	11	NUM
ejpam-5838	263	9	)	)	PUNCT
ejpam-5838	263	10	,	,	PUNCT
ejpam-5838	263	11	(	(	PUNCT
ejpam-5838	263	12	12	12	NUM
ejpam-5838	263	13	)	)	PUNCT
ejpam-5838	263	14	and	and	CCONJ
ejpam-5838	263	15	(	(	PUNCT
ejpam-5838	263	16	13	13	NUM
ejpam-5838	263	17	)	)	PUNCT
ejpam-5838	263	18	,	,	PUNCT
ejpam-5838	263	19	we	we	PRON
ejpam-5838	263	20	conclude	conclude	VERB
ejpam-5838	263	21	that	that	DET
ejpam-5838	263	22	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	263	23	,	,	PUNCT
ejpam-5838	263	24	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	263	25	,	,	PUNCT
ejpam-5838	263	26	ê3⋎+3	ê3⋎+3	PROPN
ejpam-5838	263	27	)	)	PUNCT
ejpam-5838	263	28	≤	≤	NOUN
ejpam-5838	263	29	ηg(ê3⋎	ηg(ê3⋎	PROPN
ejpam-5838	263	30	,	,	PUNCT
ejpam-5838	263	31	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	263	32	,	,	PUNCT
ejpam-5838	263	33	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	263	34	)	)	PUNCT
ejpam-5838	263	35	≤	≤	NUM
ejpam-5838	263	36	η2g(ê3⋎−1	η2g(ê3⋎−1	PROPN
ejpam-5838	263	37	,	,	PUNCT
ejpam-5838	263	38	ê3⋎	ê3⋎	NUM
ejpam-5838	263	39	,	,	PUNCT
ejpam-5838	263	40	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	263	41	)	)	PUNCT
ejpam-5838	263	42	≤	≤	NOUN
ejpam-5838	263	43	·	·	PUNCT
ejpam-5838	263	44	·	·	PUNCT
ejpam-5838	263	45	·	·	PUNCT
ejpam-5838	264	1	≤	≤	NUM
ejpam-5838	264	2	η3⋎g(ê1	η3⋎g(ê1	NOUN
ejpam-5838	264	3	,	,	PUNCT
ejpam-5838	264	4	ê2	ê2	PROPN
ejpam-5838	264	5	,	,	PUNCT
ejpam-5838	264	6	ê3	ê3	PROPN
ejpam-5838	264	7	)	)	PUNCT
ejpam-5838	264	8	≤	≤	PROPN
ejpam-5838	264	9	η3⋎+1g(ê0	η3⋎+1g(ê0	PROPN
ejpam-5838	264	10	,	,	PUNCT
ejpam-5838	264	11	ê1	ê1	PROPN
ejpam-5838	264	12	,	,	PUNCT
ejpam-5838	264	13	ê2	ê2	PROPN
ejpam-5838	264	14	)	)	PUNCT
ejpam-5838	264	15	.	.	PUNCT
ejpam-5838	265	1	(	(	PUNCT
ejpam-5838	265	2	14	14	NUM
ejpam-5838	265	3	)	)	PUNCT
ejpam-5838	265	4	hence	hence	ADV
ejpam-5838	265	5	proved	prove	VERB
ejpam-5838	265	6	that	that	SCONJ
ejpam-5838	265	7	the	the	DET
ejpam-5838	265	8	sequence	sequence	NOUN
ejpam-5838	265	9	{	{	PUNCT
ejpam-5838	265	10	ê⋎	ê⋎	NOUN
ejpam-5838	265	11	}	}	PUNCT
ejpam-5838	265	12	is	be	AUX
ejpam-5838	265	13	contractive	contractive	ADJ
ejpam-5838	265	14	under	under	ADP
ejpam-5838	265	15	the	the	DET
ejpam-5838	265	16	gm	gm	PROPN
ejpam-5838	265	17	-space	-space	NOUN
ejpam-5838	265	18	for	for	ADP
ejpam-5838	265	19	3	3	NUM
ejpam-5838	265	20	-	-	PUNCT
ejpam-5838	265	21	self	self	NOUN
ejpam-5838	265	22	-	-	PUNCT
ejpam-5838	265	23	mappings	mapping	NOUN
ejpam-5838	265	24	.	.	PUNCT
ejpam-5838	266	1	therefore	therefore	ADV
ejpam-5838	266	2	,	,	PUNCT
ejpam-5838	266	3	lim	lim	PROPN
ejpam-5838	266	4	⋎→∞	⋎→∞	PROPN
ejpam-5838	266	5	g(ê⋎	g(ê⋎	PROPN
ejpam-5838	266	6	,	,	PUNCT
ejpam-5838	266	7	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	266	8	,	,	PUNCT
ejpam-5838	266	9	ê⋎+2	ê⋎+2	VERB
ejpam-5838	266	10	)	)	PUNCT
ejpam-5838	266	11	=	=	SYM
ejpam-5838	266	12	0	0	X
ejpam-5838	266	13	.	.	PUNCT
ejpam-5838	267	1	(	(	PUNCT
ejpam-5838	267	2	15	15	NUM
ejpam-5838	267	3	)	)	PUNCT
ejpam-5838	267	4	m.	m.	NOUN
ejpam-5838	267	5	noorwali	noorwali	PROPN
ejpam-5838	267	6	et	et	PROPN
ejpam-5838	267	7	al/	al/	PROPN
ejpam-5838	267	8	/	/	SYM
ejpam-5838	267	9	eur	eur	PROPN
ejpam-5838	267	10	.	.	PUNCT
ejpam-5838	268	1	j.	j.	PROPN
ejpam-5838	268	2	pure	pure	PROPN
ejpam-5838	268	3	appl	appl	PROPN
ejpam-5838	268	4	.	.	PROPN
ejpam-5838	268	5	math	math	PROPN
ejpam-5838	268	6	,	,	PUNCT
ejpam-5838	268	7	18	18	NUM
ejpam-5838	268	8	(	(	PUNCT
ejpam-5838	268	9	2	2	NUM
ejpam-5838	268	10	)	)	PUNCT
ejpam-5838	268	11	(	(	PUNCT
ejpam-5838	268	12	2025	2025	NUM
ejpam-5838	268	13	)	)	PUNCT
ejpam-5838	268	14	,	,	PUNCT
ejpam-5838	268	15	5838	5838	NUM
ejpam-5838	268	16	11	11	NUM
ejpam-5838	268	17	of	of	ADP
ejpam-5838	268	18	16	16	NUM
ejpam-5838	268	19	to	to	PART
ejpam-5838	268	20	prove	prove	VERB
ejpam-5838	268	21	{	{	PUNCT
ejpam-5838	268	22	ê⋎	ê⋎	ADJ
ejpam-5838	268	23	}	}	PUNCT
ejpam-5838	268	24	is	be	AUX
ejpam-5838	268	25	a	a	DET
ejpam-5838	268	26	g	g	NOUN
ejpam-5838	268	27	-	-	PUNCT
ejpam-5838	268	28	cs	cs	PROPN
ejpam-5838	268	29	in	in	ADP
ejpam-5838	268	30	ê	ê	PROPN
ejpam-5838	268	31	,	,	PUNCT
ejpam-5838	268	32	for	for	ADP
ejpam-5838	268	33	all	all	DET
ejpam-5838	268	34	⋎,m	⋎,m	NOUN
ejpam-5838	268	35	∈	∈	PROPN
ejpam-5838	268	36	n	n	NOUN
ejpam-5838	268	37	&	&	CCONJ
ejpam-5838	268	38	m	m	PROPN
ejpam-5838	268	39	>	>	X
ejpam-5838	268	40	⋎	⋎	PROPN
ejpam-5838	268	41	,	,	PUNCT
ejpam-5838	268	42	with	with	ADP
ejpam-5838	268	43	the	the	DET
ejpam-5838	268	44	aid	aid	NOUN
ejpam-5838	268	45	of	of	ADP
ejpam-5838	268	46	(	(	PUNCT
ejpam-5838	268	47	14	14	NUM
ejpam-5838	268	48	)	)	PUNCT
ejpam-5838	268	49	,	,	PUNCT
ejpam-5838	268	50	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	268	51	,	,	PUNCT
ejpam-5838	268	52	êm	êm	PROPN
ejpam-5838	268	53	,	,	PUNCT
ejpam-5838	268	54	êm	êm	NOUN
ejpam-5838	268	55	)	)	PUNCT
ejpam-5838	268	56	≤	≤	NOUN
ejpam-5838	268	57	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	268	58	,	,	PUNCT
ejpam-5838	268	59	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	268	60	,	,	PUNCT
ejpam-5838	268	61	ê⋎+1	ê⋎+1	NUM
ejpam-5838	268	62	)	)	PUNCT
ejpam-5838	269	1	+	+	PROPN
ejpam-5838	269	2	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	269	3	,	,	PUNCT
ejpam-5838	269	4	êm	êm	PROPN
ejpam-5838	269	5	,	,	PUNCT
ejpam-5838	269	6	êm	êm	NOUN
ejpam-5838	269	7	)	)	PUNCT
ejpam-5838	269	8	≤	≤	NOUN
ejpam-5838	269	9	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	269	10	,	,	PUNCT
ejpam-5838	269	11	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	269	12	,	,	PUNCT
ejpam-5838	269	13	ê⋎+1	ê⋎+1	NUM
ejpam-5838	269	14	)	)	PUNCT
ejpam-5838	270	1	+	+	PROPN
ejpam-5838	270	2	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	270	3	,	,	PUNCT
ejpam-5838	270	4	ê⋎+2	ê⋎+2	VERB
ejpam-5838	270	5	,	,	PUNCT
ejpam-5838	270	6	ê⋎+2	ê⋎+2	VERB
ejpam-5838	270	7	)	)	PUNCT
ejpam-5838	270	8	+	+	NUM
ejpam-5838	270	9	·	·	PUNCT
ejpam-5838	270	10	·	·	PUNCT
ejpam-5838	270	11	·	·	PUNCT
ejpam-5838	270	12	+	+	NOUN
ejpam-5838	270	13	g(êm−1	g(êm−1	PROPN
ejpam-5838	270	14	,	,	PUNCT
ejpam-5838	270	15	êm	êm	PROPN
ejpam-5838	270	16	,	,	PUNCT
ejpam-5838	270	17	êm	êm	NOUN
ejpam-5838	270	18	)	)	PUNCT
ejpam-5838	270	19	≤	≤	NOUN
ejpam-5838	270	20	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	270	21	,	,	PUNCT
ejpam-5838	270	22	ê⋎+1	ê⋎+1	ADJ
ejpam-5838	270	23	,	,	PUNCT
ejpam-5838	270	24	ê⋎+2	ê⋎+2	VERB
ejpam-5838	270	25	)	)	PUNCT
ejpam-5838	270	26	+	+	SYM
ejpam-5838	270	27	g(ê⋎+1	g(ê⋎+1	PROPN
ejpam-5838	270	28	,	,	PUNCT
ejpam-5838	270	29	ê⋎+2	ê⋎+2	VERB
ejpam-5838	270	30	,	,	PUNCT
ejpam-5838	270	31	ê⋎+3	ê⋎+3	ADJ
ejpam-5838	270	32	)	)	PUNCT
ejpam-5838	270	33	+	+	CCONJ
ejpam-5838	270	34	·	·	PUNCT
ejpam-5838	270	35	·	·	PUNCT
ejpam-5838	270	36	·	·	PUNCT
ejpam-5838	271	1	+	+	NOUN
ejpam-5838	271	2	g(êm−1	g(êm−1	PROPN
ejpam-5838	271	3	,	,	PUNCT
ejpam-5838	271	4	êm	êm	PROPN
ejpam-5838	271	5	,	,	PUNCT
ejpam-5838	271	6	êm+1	êm+1	PROPN
ejpam-5838	271	7	)	)	PUNCT
ejpam-5838	271	8	≤	≤	PROPN
ejpam-5838	271	9	η⋎g(ê0	η⋎g(ê0	PROPN
ejpam-5838	271	10	,	,	PUNCT
ejpam-5838	271	11	ê1	ê1	PROPN
ejpam-5838	271	12	,	,	PUNCT
ejpam-5838	271	13	ê1	ê1	PROPN
ejpam-5838	271	14	)	)	PUNCT
ejpam-5838	272	1	+	+	CCONJ
ejpam-5838	272	2	η⋎+1g(ê0	η⋎+1g(ê0	ADJ
ejpam-5838	272	3	,	,	PUNCT
ejpam-5838	272	4	ê1	ê1	PROPN
ejpam-5838	272	5	,	,	PUNCT
ejpam-5838	272	6	ê1	ê1	PROPN
ejpam-5838	272	7	)	)	PUNCT
ejpam-5838	272	8	+	+	CCONJ
ejpam-5838	272	9	·	·	PUNCT
ejpam-5838	272	10	·	·	PUNCT
ejpam-5838	272	11	·	·	PUNCT
ejpam-5838	273	1	+	+	NUM
ejpam-5838	273	2	ηm−1g(ê0	ηm−1g(ê0	NOUN
ejpam-5838	273	3	,	,	PUNCT
ejpam-5838	273	4	ê1	ê1	PROPN
ejpam-5838	273	5	,	,	PUNCT
ejpam-5838	273	6	ê1	ê1	PROPN
ejpam-5838	273	7	)	)	PUNCT
ejpam-5838	273	8	≤	≤	PUNCT
ejpam-5838	273	9	η⋎	η⋎	PROPN
ejpam-5838	273	10	[	[	PUNCT
ejpam-5838	273	11	g(ê0	g(ê0	PROPN
ejpam-5838	273	12	,	,	PUNCT
ejpam-5838	273	13	ê1	ê1	PROPN
ejpam-5838	273	14	,	,	PUNCT
ejpam-5838	273	15	ê1	ê1	PROPN
ejpam-5838	273	16	)	)	PUNCT
ejpam-5838	274	1	+	+	NUM
ejpam-5838	274	2	η1g(ê0	η1g(ê0	PROPN
ejpam-5838	274	3	,	,	PUNCT
ejpam-5838	274	4	ê1	ê1	PROPN
ejpam-5838	274	5	,	,	PUNCT
ejpam-5838	274	6	ê1	ê1	PROPN
ejpam-5838	274	7	)	)	PUNCT
ejpam-5838	275	1	+	+	CCONJ
ejpam-5838	275	2	η2g(ê0	η2g(ê0	PROPN
ejpam-5838	275	3	,	,	PUNCT
ejpam-5838	275	4	ê1	ê1	PROPN
ejpam-5838	275	5	,	,	PUNCT
ejpam-5838	275	6	ê1	ê1	PROPN
ejpam-5838	275	7	)	)	PUNCT
ejpam-5838	276	1	+	+	CCONJ
ejpam-5838	276	2	·	·	PUNCT
ejpam-5838	276	3	·	·	PUNCT
ejpam-5838	276	4	·	·	PUNCT
ejpam-5838	276	5	+	+	NUM
ejpam-5838	276	6	ηm−1g(ê0	ηm−1g(ê0	NOUN
ejpam-5838	276	7	,	,	PUNCT
ejpam-5838	276	8	ê1	ê1	PROPN
ejpam-5838	276	9	,	,	PUNCT
ejpam-5838	276	10	ê1	ê1	PROPN
ejpam-5838	276	11	)	)	PUNCT
ejpam-5838	276	12	]	]	PUNCT
ejpam-5838	277	1	=	=	NOUN
ejpam-5838	277	2	⇒	⇒	NOUN
ejpam-5838	277	3	g(ê⋎	g(ê⋎	NOUN
ejpam-5838	277	4	,	,	PUNCT
ejpam-5838	277	5	êm	êm	PROPN
ejpam-5838	277	6	,	,	PUNCT
ejpam-5838	277	7	êm	êm	NOUN
ejpam-5838	277	8	)	)	PUNCT
ejpam-5838	277	9	≤	≤	NOUN
ejpam-5838	277	10	η⋎	η⋎	PROPN
ejpam-5838	277	11	1−	1−	NUM
ejpam-5838	277	12	η	η	PROPN
ejpam-5838	277	13	g(ê0	g(ê0	PROPN
ejpam-5838	277	14	,	,	PUNCT
ejpam-5838	277	15	ê1	ê1	PROPN
ejpam-5838	277	16	,	,	PUNCT
ejpam-5838	277	17	ê1	ê1	PROPN
ejpam-5838	277	18	)	)	PUNCT
ejpam-5838	277	19	.	.	PUNCT
ejpam-5838	278	1	(	(	PUNCT
ejpam-5838	278	2	16	16	X
ejpam-5838	278	3	)	)	PUNCT
ejpam-5838	278	4	taking	take	VERB
ejpam-5838	278	5	limit	limit	NOUN
ejpam-5838	278	6	as	as	ADP
ejpam-5838	278	7	⋎,m	⋎,m	NOUN
ejpam-5838	278	8	,	,	PUNCT
ejpam-5838	278	9	l	l	NOUN
ejpam-5838	278	10	→	→	SYM
ejpam-5838	278	11	∞	∞	NUM
ejpam-5838	278	12	we	we	PRON
ejpam-5838	278	13	get	get	VERB
ejpam-5838	278	14	g(ê⋎	g(ê⋎	ADJ
ejpam-5838	278	15	,	,	PUNCT
ejpam-5838	278	16	êm	êm	PROPN
ejpam-5838	278	17	,	,	PUNCT
ejpam-5838	278	18	êl	êl	PROPN
ejpam-5838	278	19	)	)	PUNCT
ejpam-5838	278	20	→	→	SYM
ejpam-5838	279	1	0	0	X
ejpam-5838	279	2	.	.	PUNCT
ejpam-5838	280	1	hence	hence	ADV
ejpam-5838	280	2	{	{	PUNCT
ejpam-5838	280	3	ê⋎	ê⋎	ADJ
ejpam-5838	280	4	}	}	PUNCT
ejpam-5838	280	5	is	be	AUX
ejpam-5838	280	6	a	a	DET
ejpam-5838	280	7	g	g	NOUN
ejpam-5838	280	8	-	-	PUNCT
ejpam-5838	280	9	ms	ms	NOUN
ejpam-5838	280	10	.	.	PROPN
ejpam-5838	280	11	since	since	SCONJ
ejpam-5838	280	12	,	,	PUNCT
ejpam-5838	280	13	(	(	PUNCT
ejpam-5838	280	14	ê	ê	NOUN
ejpam-5838	280	15	,	,	PUNCT
ejpam-5838	280	16	g	g	NOUN
ejpam-5838	280	17	)	)	PUNCT
ejpam-5838	280	18	is	be	AUX
ejpam-5838	280	19	complete	complete	ADJ
ejpam-5838	280	20	,	,	PUNCT
ejpam-5838	280	21	there	there	PRON
ejpam-5838	280	22	exists	exist	VERB
ejpam-5838	280	23	z	z	PROPN
ejpam-5838	280	24	∈	∈	PROPN
ejpam-5838	280	25	ê	ê	PROPN
ejpam-5838	280	26	,	,	PUNCT
ejpam-5838	280	27	such	such	ADJ
ejpam-5838	280	28	that	that	SCONJ
ejpam-5838	280	29	,	,	PUNCT
ejpam-5838	280	30	ê⋎	ê⋎	PROPN
ejpam-5838	280	31	→	→	X
ejpam-5838	280	32	z	z	NOUN
ejpam-5838	280	33	as	as	ADP
ejpam-5838	280	34	⋎	⋎	NOUN
ejpam-5838	280	35	→	→	SYM
ejpam-5838	280	36	∞	∞	NUM
ejpam-5838	280	37	or	or	CCONJ
ejpam-5838	280	38	lim⋎→∞	lim⋎→∞	NOUN
ejpam-5838	280	39	ê⋎	ê⋎	PROPN
ejpam-5838	280	40	=	=	PUNCT
ejpam-5838	281	1	z.	z.	PROPN
ejpam-5838	281	2	we	we	PRON
ejpam-5838	281	3	now	now	ADV
ejpam-5838	281	4	show	show	VERB
ejpam-5838	281	5	that	that	SCONJ
ejpam-5838	281	6	f1z	f1z	ADJ
ejpam-5838	281	7	=	=	SYM
ejpam-5838	281	8	z	z	NOUN
ejpam-5838	281	9	by	by	ADP
ejpam-5838	281	10	contrary	contrary	ADJ
ejpam-5838	281	11	case	case	NOUN
ejpam-5838	281	12	.	.	PUNCT
ejpam-5838	282	1	let	let	VERB
ejpam-5838	282	2	f1z	f1z	VERB
ejpam-5838	282	3	̸=	̸=	PROPN
ejpam-5838	282	4	z.	z.	X
ejpam-5838	282	5	by	by	ADP
ejpam-5838	282	6	using	use	VERB
ejpam-5838	282	7	(	(	PUNCT
ejpam-5838	282	8	10	10	NUM
ejpam-5838	282	9	)	)	PUNCT
ejpam-5838	282	10	,	,	PUNCT
ejpam-5838	282	11	we	we	PRON
ejpam-5838	282	12	have	have	VERB
ejpam-5838	282	13	that	that	PRON
ejpam-5838	282	14	g(f1z	g(f1z	VERB
ejpam-5838	282	15	,	,	PUNCT
ejpam-5838	282	16	f2ê3⋎+1	f2ê3⋎+1	ADJ
ejpam-5838	282	17	,	,	PUNCT
ejpam-5838	282	18	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	282	19	)	)	PUNCT
ejpam-5838	282	20	≤	≤	NOUN
ejpam-5838	282	21	αg(z	αg(z	ADJ
ejpam-5838	282	22	,	,	PUNCT
ejpam-5838	282	23	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	282	24	,	,	PUNCT
ejpam-5838	282	25	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	282	26	)	)	PUNCT
ejpam-5838	283	1	+	+	CCONJ
ejpam-5838	284	1	β	β	X
ejpam-5838	284	2	g(z	g(z	PROPN
ejpam-5838	284	3	,	,	PUNCT
ejpam-5838	284	4	f1z	f1z	ADJ
ejpam-5838	284	5	,	,	PUNCT
ejpam-5838	284	6	f1z	f1z	NOUN
ejpam-5838	284	7	)	)	PUNCT
ejpam-5838	284	8	·	·	PUNCT
ejpam-5838	284	9	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	284	10	,	,	PUNCT
ejpam-5838	284	11	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	284	12	,	,	PUNCT
ejpam-5838	284	13	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	284	14	)	)	PUNCT
ejpam-5838	284	15	·	·	PUNCT
ejpam-5838	284	16	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	284	17	,	,	PUNCT
ejpam-5838	284	18	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	284	19	,	,	PUNCT
ejpam-5838	284	20	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	284	21	)	)	PUNCT
ejpam-5838	284	22	1	1	NUM
ejpam-5838	284	23	+	+	NOUN
ejpam-5838	284	24	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	284	25	,	,	PUNCT
ejpam-5838	284	26	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	284	27	,	,	PUNCT
ejpam-5838	284	28	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	284	29	)	)	PUNCT
ejpam-5838	284	30	·	·	PUNCT
ejpam-5838	284	31	g(f2ê3⋎+1	g(f2ê3⋎+1	ADJ
ejpam-5838	284	32	,	,	PUNCT
ejpam-5838	284	33	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	284	34	,	,	PUNCT
ejpam-5838	284	35	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	284	36	)	)	PUNCT
ejpam-5838	284	37	≤	≤	NOUN
ejpam-5838	284	38	αg(z	αg(z	ADJ
ejpam-5838	284	39	,	,	PUNCT
ejpam-5838	284	40	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	284	41	,	,	PUNCT
ejpam-5838	284	42	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	284	43	)	)	PUNCT
ejpam-5838	285	1	+	+	ADP
ejpam-5838	285	2	β	β	X
ejpam-5838	285	3	g(z	g(z	ADJ
ejpam-5838	285	4	,	,	PUNCT
ejpam-5838	285	5	f1z	f1z	ADJ
ejpam-5838	285	6	,	,	PUNCT
ejpam-5838	285	7	f1z	f1z	NOUN
ejpam-5838	285	8	)	)	PUNCT
ejpam-5838	285	9	·	·	PUNCT
ejpam-5838	285	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	285	11	,	,	PUNCT
ejpam-5838	285	12	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	285	13	,	,	PUNCT
ejpam-5838	285	14	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	285	15	)	)	PUNCT
ejpam-5838	285	16	·	·	PUNCT
ejpam-5838	285	17	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	285	18	,	,	PUNCT
ejpam-5838	285	19	ê3⋎+3	ê3⋎+3	CCONJ
ejpam-5838	285	20	,	,	PUNCT
ejpam-5838	285	21	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	285	22	)	)	PUNCT
ejpam-5838	285	23	1	1	NUM
ejpam-5838	286	1	+	+	NOUN
ejpam-5838	286	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	286	3	,	,	PUNCT
ejpam-5838	286	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	286	5	,	,	PUNCT
ejpam-5838	286	6	ê3⋎+3	ê3⋎+3	X
ejpam-5838	286	7	)	)	PUNCT
ejpam-5838	286	8	·	·	PUNCT
ejpam-5838	286	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	286	10	,	,	PUNCT
ejpam-5838	286	11	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	286	12	,	,	PUNCT
ejpam-5838	286	13	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	286	14	)	)	PUNCT
ejpam-5838	286	15	.	.	PUNCT
ejpam-5838	287	1	applying	apply	VERB
ejpam-5838	287	2	limn→∞	limn→∞	PROPN
ejpam-5838	287	3	and	and	CCONJ
ejpam-5838	287	4	after	after	ADP
ejpam-5838	287	5	simplification	simplification	NOUN
ejpam-5838	287	6	,	,	PUNCT
ejpam-5838	287	7	we	we	PRON
ejpam-5838	287	8	obtained	obtain	VERB
ejpam-5838	287	9	g(f1z	g(f1z	PROPN
ejpam-5838	287	10	,	,	PUNCT
ejpam-5838	287	11	z	z	PROPN
ejpam-5838	287	12	,	,	PUNCT
ejpam-5838	287	13	z	z	NOUN
ejpam-5838	287	14	)	)	PUNCT
ejpam-5838	287	15	≤	≤	NOUN
ejpam-5838	287	16	αg(z	αg(z	NOUN
ejpam-5838	287	17	,	,	PUNCT
ejpam-5838	287	18	z	z	NOUN
ejpam-5838	287	19	,	,	PUNCT
ejpam-5838	287	20	z	z	NOUN
ejpam-5838	287	21	)	)	PUNCT
ejpam-5838	287	22	.	.	PUNCT
ejpam-5838	288	1	this	this	PRON
ejpam-5838	288	2	implies	imply	VERB
ejpam-5838	288	3	that	that	SCONJ
ejpam-5838	288	4	,	,	PUNCT
ejpam-5838	288	5	g(f1z	g(f1z	ADJ
ejpam-5838	288	6	,	,	PUNCT
ejpam-5838	288	7	z	z	NOUN
ejpam-5838	288	8	,	,	PUNCT
ejpam-5838	288	9	z	z	NOUN
ejpam-5838	288	10	)	)	PUNCT
ejpam-5838	288	11	=	=	SYM
ejpam-5838	288	12	0	0	X
ejpam-5838	288	13	.	.	PUNCT
ejpam-5838	289	1	thus	thus	ADV
ejpam-5838	289	2	,	,	PUNCT
ejpam-5838	289	3	f1z	f1z	PROPN
ejpam-5838	289	4	=	=	SYM
ejpam-5838	289	5	z.	z.	X
ejpam-5838	289	6	(	(	PUNCT
ejpam-5838	289	7	17	17	NUM
ejpam-5838	289	8	)	)	PUNCT
ejpam-5838	289	9	again	again	ADV
ejpam-5838	289	10	,	,	PUNCT
ejpam-5838	289	11	we	we	PRON
ejpam-5838	289	12	show	show	VERB
ejpam-5838	289	13	that	that	SCONJ
ejpam-5838	289	14	f2z	f2z	NOUN
ejpam-5838	289	15	=	=	SYM
ejpam-5838	289	16	z	z	NOUN
ejpam-5838	289	17	by	by	ADP
ejpam-5838	289	18	contrary	contrary	ADJ
ejpam-5838	289	19	case	case	NOUN
ejpam-5838	289	20	.	.	PUNCT
ejpam-5838	290	1	let	let	VERB
ejpam-5838	290	2	f2z	f2z	NOUN
ejpam-5838	290	3	̸=	̸=	PROPN
ejpam-5838	290	4	z.	z.	X
ejpam-5838	290	5	by	by	ADP
ejpam-5838	290	6	using	use	VERB
ejpam-5838	290	7	(	(	PUNCT
ejpam-5838	290	8	10	10	NUM
ejpam-5838	290	9	)	)	PUNCT
ejpam-5838	290	10	,	,	PUNCT
ejpam-5838	290	11	we	we	PRON
ejpam-5838	290	12	have	have	VERB
ejpam-5838	290	13	that	that	DET
ejpam-5838	290	14	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	290	15	,	,	PUNCT
ejpam-5838	290	16	f2z	f2z	NOUN
ejpam-5838	290	17	,	,	PUNCT
ejpam-5838	290	18	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	290	19	)	)	PUNCT
ejpam-5838	291	1	=	=	SYM
ejpam-5838	291	2	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	291	3	,	,	PUNCT
ejpam-5838	291	4	f2z	f2z	NOUN
ejpam-5838	291	5	,	,	PUNCT
ejpam-5838	291	6	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	291	7	)	)	PUNCT
ejpam-5838	291	8	≤	≤	NOUN
ejpam-5838	291	9	αg(ê3⋎	αg(ê3⋎	PROPN
ejpam-5838	291	10	,	,	PUNCT
ejpam-5838	291	11	z	z	NOUN
ejpam-5838	291	12	,	,	PUNCT
ejpam-5838	291	13	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	291	14	)	)	PUNCT
ejpam-5838	292	1	+	+	CCONJ
ejpam-5838	292	2	β	β	X
ejpam-5838	292	3	g(ê3⋎	g(ê3⋎	NUM
ejpam-5838	292	4	,	,	PUNCT
ejpam-5838	292	5	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	292	6	,	,	PUNCT
ejpam-5838	292	7	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	292	8	)	)	PUNCT
ejpam-5838	292	9	·	·	PUNCT
ejpam-5838	292	10	g(z	g(z	ADJ
ejpam-5838	292	11	,	,	PUNCT
ejpam-5838	292	12	f2z	f2z	NOUN
ejpam-5838	292	13	,	,	PUNCT
ejpam-5838	292	14	f2z	f2z	NOUN
ejpam-5838	292	15	)	)	PUNCT
ejpam-5838	292	16	·	·	PUNCT
ejpam-5838	292	17	g(ê3⋎+2	g(ê3⋎+2	VERB
ejpam-5838	292	18	,	,	PUNCT
ejpam-5838	292	19	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	292	20	,	,	PUNCT
ejpam-5838	292	21	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	292	22	)	)	PUNCT
ejpam-5838	292	23	1	1	NUM
ejpam-5838	293	1	+	+	PUNCT
ejpam-5838	293	2	g(z	g(z	ADJ
ejpam-5838	293	3	,	,	PUNCT
ejpam-5838	293	4	f2z	f2z	NOUN
ejpam-5838	293	5	,	,	PUNCT
ejpam-5838	293	6	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	293	7	)	)	PUNCT
ejpam-5838	293	8	·	·	PUNCT
ejpam-5838	293	9	g(f2z	g(f2z	ADP
ejpam-5838	293	10	,	,	PUNCT
ejpam-5838	293	11	f3ê3⋎+2	f3ê3⋎+2	PROPN
ejpam-5838	293	12	,	,	PUNCT
ejpam-5838	293	13	f3ê3⋎+2	f3ê3⋎+2	NOUN
ejpam-5838	293	14	)	)	PUNCT
ejpam-5838	293	15	≤	≤	NOUN
ejpam-5838	293	16	αg(ê3⋎	αg(ê3⋎	PROPN
ejpam-5838	293	17	,	,	PUNCT
ejpam-5838	293	18	z	z	NOUN
ejpam-5838	293	19	,	,	PUNCT
ejpam-5838	293	20	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	293	21	)	)	PUNCT
ejpam-5838	294	1	+	+	CCONJ
ejpam-5838	294	2	β	β	X
ejpam-5838	294	3	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	294	4	,	,	PUNCT
ejpam-5838	294	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	294	6	,	,	PUNCT
ejpam-5838	294	7	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	294	8	)	)	PUNCT
ejpam-5838	294	9	·	·	PUNCT
ejpam-5838	295	1	g(z	g(z	ADJ
ejpam-5838	295	2	,	,	PUNCT
ejpam-5838	295	3	f2z	f2z	NOUN
ejpam-5838	295	4	,	,	PUNCT
ejpam-5838	295	5	f2z	f2z	NOUN
ejpam-5838	295	6	)	)	PUNCT
ejpam-5838	295	7	·	·	PUNCT
ejpam-5838	295	8	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	295	9	,	,	PUNCT
ejpam-5838	295	10	ê3⋎+3	ê3⋎+3	CCONJ
ejpam-5838	295	11	,	,	PUNCT
ejpam-5838	295	12	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	295	13	)	)	PUNCT
ejpam-5838	295	14	1	1	NUM
ejpam-5838	296	1	+	+	PUNCT
ejpam-5838	296	2	g(z	g(z	ADJ
ejpam-5838	296	3	,	,	PUNCT
ejpam-5838	296	4	f2z	f2z	NOUN
ejpam-5838	296	5	,	,	PUNCT
ejpam-5838	296	6	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	296	7	)	)	PUNCT
ejpam-5838	296	8	·	·	PUNCT
ejpam-5838	296	9	g(f2z	g(f2z	ADP
ejpam-5838	296	10	,	,	PUNCT
ejpam-5838	296	11	ê3⋎+3	ê3⋎+3	ADJ
ejpam-5838	296	12	,	,	PUNCT
ejpam-5838	296	13	ê3⋎+3	ê3⋎+3	NOUN
ejpam-5838	296	14	)	)	PUNCT
ejpam-5838	296	15	.	.	PUNCT
ejpam-5838	297	1	applying	apply	VERB
ejpam-5838	297	2	limn→∞	limn→∞	PROPN
ejpam-5838	297	3	and	and	CCONJ
ejpam-5838	297	4	after	after	ADP
ejpam-5838	297	5	simplification	simplification	NOUN
ejpam-5838	297	6	,	,	PUNCT
ejpam-5838	297	7	we	we	PRON
ejpam-5838	297	8	obtain	obtain	VERB
ejpam-5838	297	9	g(z	g(z	ADJ
ejpam-5838	297	10	,	,	PUNCT
ejpam-5838	297	11	f2z	f2z	NOUN
ejpam-5838	297	12	,	,	PUNCT
ejpam-5838	297	13	z	z	NOUN
ejpam-5838	297	14	)	)	PUNCT
ejpam-5838	297	15	≤	≤	NOUN
ejpam-5838	297	16	αg(z	αg(z	NOUN
ejpam-5838	297	17	,	,	PUNCT
ejpam-5838	297	18	z	z	NOUN
ejpam-5838	297	19	,	,	PUNCT
ejpam-5838	297	20	z	z	NOUN
ejpam-5838	297	21	)	)	PUNCT
ejpam-5838	297	22	.	.	PUNCT
ejpam-5838	298	1	this	this	PRON
ejpam-5838	298	2	implies	imply	VERB
ejpam-5838	298	3	that	that	SCONJ
ejpam-5838	298	4	,	,	PUNCT
ejpam-5838	298	5	g(z	g(z	ADJ
ejpam-5838	298	6	,	,	PUNCT
ejpam-5838	298	7	f2z	f2z	NOUN
ejpam-5838	298	8	,	,	PUNCT
ejpam-5838	298	9	z	z	NOUN
ejpam-5838	298	10	)	)	PUNCT
ejpam-5838	298	11	=	=	SYM
ejpam-5838	298	12	0	0	X
ejpam-5838	298	13	.	.	PUNCT
ejpam-5838	299	1	thus	thus	ADV
ejpam-5838	299	2	,	,	PUNCT
ejpam-5838	299	3	f2z	f2z	PROPN
ejpam-5838	299	4	=	=	PUNCT
ejpam-5838	299	5	z.	z.	PROPN
ejpam-5838	299	6	(	(	PUNCT
ejpam-5838	299	7	18	18	NUM
ejpam-5838	299	8	)	)	PUNCT
ejpam-5838	299	9	to	to	PART
ejpam-5838	299	10	prove	prove	VERB
ejpam-5838	299	11	f3z	f3z	NOUN
ejpam-5838	299	12	=	=	PUNCT
ejpam-5838	299	13	z	z	AUX
ejpam-5838	299	14	we	we	PRON
ejpam-5838	299	15	again	again	ADV
ejpam-5838	299	16	use	use	VERB
ejpam-5838	299	17	the	the	DET
ejpam-5838	299	18	contrary	contrary	ADJ
ejpam-5838	299	19	case	case	NOUN
ejpam-5838	299	20	.	.	PUNCT
ejpam-5838	300	1	let	let	VERB
ejpam-5838	300	2	f3z	f3z	NOUN
ejpam-5838	300	3	̸=	̸=	PROPN
ejpam-5838	300	4	z.	z.	PROPN
ejpam-5838	300	5	by	by	ADP
ejpam-5838	300	6	using	use	VERB
ejpam-5838	300	7	(	(	PUNCT
ejpam-5838	300	8	10	10	NUM
ejpam-5838	300	9	)	)	PUNCT
ejpam-5838	300	10	,	,	PUNCT
ejpam-5838	300	11	we	we	PRON
ejpam-5838	300	12	have	have	VERB
ejpam-5838	300	13	that	that	DET
ejpam-5838	300	14	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	300	15	,	,	PUNCT
ejpam-5838	300	16	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	300	17	,	,	PUNCT
ejpam-5838	300	18	f3z	f3z	NOUN
ejpam-5838	300	19	)	)	PUNCT
ejpam-5838	300	20	=	=	SYM
ejpam-5838	300	21	g(f1ê3⋎	g(f1ê3⋎	PROPN
ejpam-5838	300	22	,	,	PUNCT
ejpam-5838	300	23	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	300	24	,	,	PUNCT
ejpam-5838	300	25	f3z	f3z	NOUN
ejpam-5838	300	26	)	)	PUNCT
ejpam-5838	300	27	≤	≤	NOUN
ejpam-5838	300	28	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	300	29	,	,	PUNCT
ejpam-5838	300	30	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	300	31	,	,	PUNCT
ejpam-5838	300	32	z	z	NOUN
ejpam-5838	300	33	)	)	PUNCT
ejpam-5838	301	1	+	+	CCONJ
ejpam-5838	301	2	β	β	X
ejpam-5838	301	3	g(ê3⋎	g(ê3⋎	NUM
ejpam-5838	301	4	,	,	PUNCT
ejpam-5838	301	5	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	301	6	,	,	PUNCT
ejpam-5838	301	7	f1ê3⋎	f1ê3⋎	NUM
ejpam-5838	301	8	)	)	PUNCT
ejpam-5838	301	9	·	·	PUNCT
ejpam-5838	301	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	301	11	,	,	PUNCT
ejpam-5838	301	12	f2ê3⋎+1	f2ê3⋎+1	ADV
ejpam-5838	301	13	,	,	PUNCT
ejpam-5838	301	14	f2ê3⋎+1	f2ê3⋎+1	NUM
ejpam-5838	301	15	)	)	PUNCT
ejpam-5838	301	16	·	·	PUNCT
ejpam-5838	301	17	g(z	g(z	ADJ
ejpam-5838	301	18	,	,	PUNCT
ejpam-5838	301	19	f3z	f3z	NOUN
ejpam-5838	301	20	,	,	PUNCT
ejpam-5838	301	21	f3z	f3z	NOUN
ejpam-5838	301	22	)	)	PUNCT
ejpam-5838	301	23	1	1	NUM
ejpam-5838	302	1	+	+	NOUN
ejpam-5838	302	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	302	3	,	,	PUNCT
ejpam-5838	302	4	f2ê3⋎+1	f2ê3⋎+1	PRON
ejpam-5838	302	5	,	,	PUNCT
ejpam-5838	302	6	f3z	f3z	NOUN
ejpam-5838	302	7	)	)	PUNCT
ejpam-5838	302	8	·	·	PUNCT
ejpam-5838	302	9	g(f2ê3⋎+1	g(f2ê3⋎+1	PROPN
ejpam-5838	302	10	,	,	PUNCT
ejpam-5838	302	11	f3z	f3z	NOUN
ejpam-5838	302	12	,	,	PUNCT
ejpam-5838	302	13	f3z	f3z	NOUN
ejpam-5838	302	14	)	)	PUNCT
ejpam-5838	302	15	m.	m.	NOUN
ejpam-5838	302	16	noorwali	noorwali	PROPN
ejpam-5838	302	17	et	et	PROPN
ejpam-5838	302	18	al/	al/	PROPN
ejpam-5838	302	19	/	/	SYM
ejpam-5838	302	20	eur	eur	PROPN
ejpam-5838	302	21	.	.	PUNCT
ejpam-5838	303	1	j.	j.	PROPN
ejpam-5838	303	2	pure	pure	PROPN
ejpam-5838	303	3	appl	appl	PROPN
ejpam-5838	303	4	.	.	PROPN
ejpam-5838	303	5	math	math	PROPN
ejpam-5838	303	6	,	,	PUNCT
ejpam-5838	303	7	18	18	NUM
ejpam-5838	303	8	(	(	PUNCT
ejpam-5838	303	9	2	2	NUM
ejpam-5838	303	10	)	)	PUNCT
ejpam-5838	303	11	(	(	PUNCT
ejpam-5838	303	12	2025	2025	NUM
ejpam-5838	303	13	)	)	PUNCT
ejpam-5838	303	14	,	,	PUNCT
ejpam-5838	303	15	5838	5838	NUM
ejpam-5838	303	16	12	12	NUM
ejpam-5838	303	17	of	of	ADP
ejpam-5838	303	18	16	16	NUM
ejpam-5838	303	19	≤	≤	NUM
ejpam-5838	303	20	αg(ê3⋎	αg(ê3⋎	VERB
ejpam-5838	303	21	,	,	PUNCT
ejpam-5838	303	22	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	303	23	,	,	PUNCT
ejpam-5838	303	24	z	z	NOUN
ejpam-5838	303	25	)	)	PUNCT
ejpam-5838	304	1	+	+	CCONJ
ejpam-5838	304	2	β	β	X
ejpam-5838	304	3	g(ê3⋎	g(ê3⋎	NOUN
ejpam-5838	304	4	,	,	PUNCT
ejpam-5838	304	5	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	304	6	,	,	PUNCT
ejpam-5838	304	7	ê3⋎+1	ê3⋎+1	NOUN
ejpam-5838	304	8	)	)	PUNCT
ejpam-5838	304	9	·	·	PUNCT
ejpam-5838	304	10	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	304	11	,	,	PUNCT
ejpam-5838	304	12	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	304	13	,	,	PUNCT
ejpam-5838	304	14	ê3⋎+2	ê3⋎+2	NUM
ejpam-5838	304	15	)	)	PUNCT
ejpam-5838	304	16	·	·	PUNCT
ejpam-5838	305	1	g(z	g(z	ADJ
ejpam-5838	305	2	,	,	PUNCT
ejpam-5838	305	3	f3z	f3z	NOUN
ejpam-5838	305	4	,	,	PUNCT
ejpam-5838	305	5	f3z	f3z	NOUN
ejpam-5838	305	6	)	)	PUNCT
ejpam-5838	305	7	1	1	NUM
ejpam-5838	306	1	+	+	NOUN
ejpam-5838	306	2	g(ê3⋎+1	g(ê3⋎+1	NOUN
ejpam-5838	306	3	,	,	PUNCT
ejpam-5838	306	4	ê3⋎+2	ê3⋎+2	NOUN
ejpam-5838	306	5	,	,	PUNCT
ejpam-5838	306	6	f3z	f3z	NOUN
ejpam-5838	306	7	)	)	PUNCT
ejpam-5838	306	8	·	·	PUNCT
ejpam-5838	306	9	g(ê3⋎+2	g(ê3⋎+2	PROPN
ejpam-5838	306	10	,	,	PUNCT
ejpam-5838	306	11	f3z	f3z	NOUN
ejpam-5838	306	12	,	,	PUNCT
ejpam-5838	306	13	f3z	f3z	NOUN
ejpam-5838	306	14	)	)	PUNCT
ejpam-5838	306	15	.	.	PUNCT
ejpam-5838	307	1	applying	apply	VERB
ejpam-5838	307	2	limn→∞	limn→∞	PROPN
ejpam-5838	307	3	and	and	CCONJ
ejpam-5838	307	4	after	after	ADP
ejpam-5838	307	5	simplification	simplification	NOUN
ejpam-5838	307	6	,	,	PUNCT
ejpam-5838	307	7	we	we	PRON
ejpam-5838	307	8	obtained	obtain	VERB
ejpam-5838	307	9	g(z	g(z	PROPN
ejpam-5838	307	10	,	,	PUNCT
ejpam-5838	307	11	z	z	NOUN
ejpam-5838	307	12	,	,	PUNCT
ejpam-5838	307	13	f3z	f3z	NOUN
ejpam-5838	307	14	)	)	PUNCT
ejpam-5838	307	15	≤	≤	NOUN
ejpam-5838	307	16	αg(z	αg(z	NOUN
ejpam-5838	307	17	,	,	PUNCT
ejpam-5838	307	18	z	z	NOUN
ejpam-5838	307	19	,	,	PUNCT
ejpam-5838	307	20	z	z	NOUN
ejpam-5838	307	21	)	)	PUNCT
ejpam-5838	307	22	.	.	PUNCT
ejpam-5838	308	1	this	this	PRON
ejpam-5838	308	2	implies	imply	VERB
ejpam-5838	308	3	that	that	SCONJ
ejpam-5838	308	4	,	,	PUNCT
ejpam-5838	308	5	g(z	g(z	PROPN
ejpam-5838	308	6	,	,	PUNCT
ejpam-5838	308	7	z	z	NOUN
ejpam-5838	308	8	,	,	PUNCT
ejpam-5838	308	9	f3z	f3z	NOUN
ejpam-5838	308	10	)	)	PUNCT
ejpam-5838	308	11	=	=	SYM
ejpam-5838	308	12	0	0	X
ejpam-5838	308	13	.	.	PUNCT
ejpam-5838	309	1	thus	thus	ADV
ejpam-5838	309	2	,	,	PUNCT
ejpam-5838	309	3	f3z	f3z	PROPN
ejpam-5838	309	4	=	=	SYM
ejpam-5838	309	5	z.	z.	PROPN
ejpam-5838	309	6	(	(	PUNCT
ejpam-5838	309	7	19	19	NUM
ejpam-5838	309	8	)	)	PUNCT
ejpam-5838	309	9	thus	thus	ADV
ejpam-5838	309	10	,	,	PUNCT
ejpam-5838	309	11	(	(	PUNCT
ejpam-5838	309	12	17	17	NUM
ejpam-5838	309	13	)	)	PUNCT
ejpam-5838	309	14	,	,	PUNCT
ejpam-5838	309	15	(	(	PUNCT
ejpam-5838	309	16	18	18	NUM
ejpam-5838	309	17	)	)	PUNCT
ejpam-5838	309	18	,	,	PUNCT
ejpam-5838	309	19	and	and	CCONJ
ejpam-5838	309	20	(	(	PUNCT
ejpam-5838	309	21	20	20	NUM
ejpam-5838	309	22	)	)	PUNCT
ejpam-5838	309	23	proved	prove	VERB
ejpam-5838	309	24	that	that	SCONJ
ejpam-5838	309	25	“	"	PUNCT
ejpam-5838	309	26	z	z	X
ejpam-5838	309	27	”	"	PUNCT
ejpam-5838	309	28	is	be	AUX
ejpam-5838	309	29	a	a	DET
ejpam-5838	309	30	cfp	cfp	NOUN
ejpam-5838	309	31	of	of	ADP
ejpam-5838	309	32	f1	f1	NOUN
ejpam-5838	309	33	,	,	PUNCT
ejpam-5838	309	34	f2	f2	PROPN
ejpam-5838	309	35	and	and	CCONJ
ejpam-5838	309	36	f3	f3	ADJ
ejpam-5838	309	37	,	,	PUNCT
ejpam-5838	309	38	that	that	PRON
ejpam-5838	309	39	is	be	AUX
ejpam-5838	309	40	f1z	f1z	ADJ
ejpam-5838	309	41	=	=	ADJ
ejpam-5838	309	42	f2z	f2z	NOUN
ejpam-5838	309	43	=	=	PUNCT
ejpam-5838	309	44	f3z	f3z	PROPN
ejpam-5838	309	45	=	=	PUNCT
ejpam-5838	309	46	z.	z.	PROPN
ejpam-5838	309	47	uniqueness	uniqueness	PROPN
ejpam-5838	309	48	:	:	PUNCT
ejpam-5838	309	49	assume	assume	VERB
ejpam-5838	309	50	that	that	SCONJ
ejpam-5838	309	51	z∗	z∗	PROPN
ejpam-5838	309	52	∈	∈	PROPN
ejpam-5838	309	53	ê	ê	PROPN
ejpam-5838	309	54	is	be	AUX
ejpam-5838	309	55	another	another	DET
ejpam-5838	309	56	cfp	cfp	NOUN
ejpam-5838	309	57	of	of	ADP
ejpam-5838	309	58	mappings	mapping	NOUN
ejpam-5838	309	59	f1	f1	NOUN
ejpam-5838	309	60	,	,	PUNCT
ejpam-5838	309	61	f2	f2	PROPN
ejpam-5838	309	62	,	,	PUNCT
ejpam-5838	309	63	and	and	CCONJ
ejpam-5838	309	64	f3	f3	NOUN
ejpam-5838	309	65	that	that	PRON
ejpam-5838	309	66	is	be	AUX
ejpam-5838	309	67	f1z	f1z	ADJ
ejpam-5838	309	68	∗	∗	NOUN
ejpam-5838	309	69	=	=	SYM
ejpam-5838	309	70	f2z	f2z	NOUN
ejpam-5838	309	71	∗	∗	NOUN
ejpam-5838	309	72	=	=	PUNCT
ejpam-5838	309	73	f3z	f3z	NOUN
ejpam-5838	309	74	∗	∗	NOUN
ejpam-5838	309	75	=	=	SYM
ejpam-5838	309	76	z∗.	z∗.	NOUN
ejpam-5838	309	77	then	then	ADV
ejpam-5838	309	78	from	from	ADP
ejpam-5838	309	79	(	(	PUNCT
ejpam-5838	309	80	[	[	X
ejpam-5838	309	81	27	27	NUM
ejpam-5838	309	82	]	]	NUM
ejpam-5838	309	83	)	)	PUNCT
ejpam-5838	309	84	,	,	PUNCT
ejpam-5838	309	85	we	we	PRON
ejpam-5838	309	86	have	have	VERB
ejpam-5838	309	87	that	that	PRON
ejpam-5838	309	88	g(f1z	g(f1z	VERB
ejpam-5838	309	89	,	,	PUNCT
ejpam-5838	309	90	f2z	f2z	ADJ
ejpam-5838	309	91	∗	∗	NOUN
ejpam-5838	309	92	,	,	PUNCT
ejpam-5838	309	93	f3z	f3z	NOUN
ejpam-5838	309	94	∗	∗	NOUN
ejpam-5838	309	95	)	)	PUNCT
ejpam-5838	309	96	≤	≤	NOUN
ejpam-5838	309	97	αg(z	αg(z	NOUN
ejpam-5838	309	98	,	,	PUNCT
ejpam-5838	309	99	z∗	z∗	PROPN
ejpam-5838	309	100	,	,	PUNCT
ejpam-5838	309	101	z∗	z∗	PROPN
ejpam-5838	309	102	)	)	PUNCT
ejpam-5838	310	1	+	+	CCONJ
ejpam-5838	310	2	β	β	X
ejpam-5838	310	3	g(z	g(z	PROPN
ejpam-5838	310	4	,	,	PUNCT
ejpam-5838	310	5	f1z	f1z	ADJ
ejpam-5838	310	6	,	,	PUNCT
ejpam-5838	310	7	f1z	f1z	NOUN
ejpam-5838	310	8	)	)	PUNCT
ejpam-5838	310	9	·	·	PUNCT
ejpam-5838	310	10	g(z∗	g(z∗	X
ejpam-5838	310	11	,	,	PUNCT
ejpam-5838	310	12	f2z	f2z	ADJ
ejpam-5838	310	13	∗	∗	NOUN
ejpam-5838	310	14	,	,	PUNCT
ejpam-5838	310	15	f2z	f2z	ADJ
ejpam-5838	310	16	∗	∗	NOUN
ejpam-5838	310	17	)	)	PUNCT
ejpam-5838	310	18	·	·	PUNCT
ejpam-5838	310	19	g(z∗	g(z∗	X
ejpam-5838	310	20	,	,	PUNCT
ejpam-5838	310	21	f3z	f3z	NOUN
ejpam-5838	310	22	∗	∗	NOUN
ejpam-5838	310	23	,	,	PUNCT
ejpam-5838	310	24	f3z	f3z	NOUN
ejpam-5838	310	25	∗	∗	NOUN
ejpam-5838	310	26	)	)	PUNCT
ejpam-5838	310	27	1	1	NUM
ejpam-5838	311	1	+	+	NOUN
ejpam-5838	311	2	g(z∗	g(z∗	ADJ
ejpam-5838	311	3	,	,	PUNCT
ejpam-5838	311	4	f2z∗	f2z∗	NOUN
ejpam-5838	311	5	,	,	PUNCT
ejpam-5838	311	6	f3z∗	f3z∗	PROPN
ejpam-5838	311	7	)	)	PUNCT
ejpam-5838	311	8	·	·	PUNCT
ejpam-5838	311	9	g(f2z∗	g(f2z∗	PROPN
ejpam-5838	311	10	,	,	PUNCT
ejpam-5838	311	11	f3z∗	f3z∗	PROPN
ejpam-5838	311	12	,	,	PUNCT
ejpam-5838	311	13	f3z∗	f3z∗	NOUN
ejpam-5838	311	14	)	)	PUNCT
ejpam-5838	311	15	g(z	g(z	PROPN
ejpam-5838	311	16	,	,	PUNCT
ejpam-5838	311	17	z∗	z∗	PROPN
ejpam-5838	311	18	,	,	PUNCT
ejpam-5838	311	19	z∗	z∗	NOUN
ejpam-5838	311	20	)	)	PUNCT
ejpam-5838	311	21	≤	≤	NOUN
ejpam-5838	311	22	αg(z	αg(z	NOUN
ejpam-5838	311	23	,	,	PUNCT
ejpam-5838	311	24	z∗	z∗	PROPN
ejpam-5838	311	25	,	,	PUNCT
ejpam-5838	311	26	z∗	z∗	PROPN
ejpam-5838	311	27	)	)	PUNCT
ejpam-5838	311	28	+	+	CCONJ
ejpam-5838	311	29	β	β	X
ejpam-5838	311	30	g(z	g(z	PROPN
ejpam-5838	311	31	,	,	PUNCT
ejpam-5838	311	32	z	z	PROPN
ejpam-5838	311	33	,	,	PUNCT
ejpam-5838	311	34	z	z	NOUN
ejpam-5838	311	35	)	)	PUNCT
ejpam-5838	311	36	·	·	PUNCT
ejpam-5838	311	37	g(z∗	g(z∗	X
ejpam-5838	311	38	,	,	PUNCT
ejpam-5838	311	39	z∗	z∗	NOUN
ejpam-5838	311	40	,	,	PUNCT
ejpam-5838	311	41	z∗	z∗	NOUN
ejpam-5838	311	42	)	)	PUNCT
ejpam-5838	311	43	·	·	PUNCT
ejpam-5838	311	44	g(z∗	g(z∗	X
ejpam-5838	311	45	,	,	PUNCT
ejpam-5838	311	46	z∗	z∗	NOUN
ejpam-5838	311	47	,	,	PUNCT
ejpam-5838	311	48	z∗	z∗	NOUN
ejpam-5838	311	49	)	)	PUNCT
ejpam-5838	311	50	1	1	NUM
ejpam-5838	312	1	+	+	NOUN
ejpam-5838	312	2	g(z∗	g(z∗	ADJ
ejpam-5838	312	3	,	,	PUNCT
ejpam-5838	312	4	z∗	z∗	NOUN
ejpam-5838	312	5	,	,	PUNCT
ejpam-5838	312	6	z∗	z∗	NOUN
ejpam-5838	312	7	)	)	PUNCT
ejpam-5838	312	8	·	·	PUNCT
ejpam-5838	312	9	g(z∗	g(z∗	X
ejpam-5838	312	10	,	,	PUNCT
ejpam-5838	312	11	z∗	z∗	NOUN
ejpam-5838	312	12	,	,	PUNCT
ejpam-5838	312	13	z∗	z∗	PROPN
ejpam-5838	312	14	)	)	PUNCT
ejpam-5838	312	15	.	.	PUNCT
ejpam-5838	313	1	so	so	ADV
ejpam-5838	313	2	,	,	PUNCT
ejpam-5838	313	3	g(z	g(z	PROPN
ejpam-5838	313	4	,	,	PUNCT
ejpam-5838	313	5	z∗	z∗	PROPN
ejpam-5838	313	6	,	,	PUNCT
ejpam-5838	313	7	z∗	z∗	NOUN
ejpam-5838	313	8	)	)	PUNCT
ejpam-5838	313	9	≤	≤	NOUN
ejpam-5838	313	10	αg(z	αg(z	NOUN
ejpam-5838	313	11	,	,	PUNCT
ejpam-5838	313	12	z∗	z∗	PROPN
ejpam-5838	313	13	,	,	PUNCT
ejpam-5838	313	14	z∗	z∗	PROPN
ejpam-5838	313	15	)	)	PUNCT
ejpam-5838	313	16	.	.	PUNCT
ejpam-5838	314	1	which	which	PRON
ejpam-5838	314	2	implies	imply	VERB
ejpam-5838	314	3	that	that	SCONJ
ejpam-5838	314	4	(	(	PUNCT
ejpam-5838	314	5	1	1	NUM
ejpam-5838	314	6	−	−	NOUN
ejpam-5838	314	7	α)g(z	α)g(z	NOUN
ejpam-5838	314	8	,	,	PUNCT
ejpam-5838	314	9	z∗	z∗	PROPN
ejpam-5838	314	10	,	,	PUNCT
ejpam-5838	314	11	z∗	z∗	NOUN
ejpam-5838	314	12	)	)	PUNCT
ejpam-5838	314	13	≤	≤	NOUN
ejpam-5838	314	14	0	0	NUM
ejpam-5838	314	15	is	be	AUX
ejpam-5838	314	16	a	a	DET
ejpam-5838	314	17	contradiction	contradiction	NOUN
ejpam-5838	314	18	,	,	PUNCT
ejpam-5838	314	19	since	since	SCONJ
ejpam-5838	314	20	(	(	PUNCT
ejpam-5838	314	21	1−	1−	NUM
ejpam-5838	314	22	α	α	NOUN
ejpam-5838	314	23	)	)	PUNCT
ejpam-5838	314	24	>	>	X
ejpam-5838	315	1	0	0	X
ejpam-5838	315	2	.	.	PUNCT
ejpam-5838	316	1	therefore	therefore	ADV
ejpam-5838	316	2	,	,	PUNCT
ejpam-5838	316	3	g(z	g(z	PROPN
ejpam-5838	316	4	,	,	PUNCT
ejpam-5838	316	5	z∗	z∗	PROPN
ejpam-5838	316	6	,	,	PUNCT
ejpam-5838	316	7	z∗	z∗	NOUN
ejpam-5838	316	8	)	)	PUNCT
ejpam-5838	316	9	=	=	SYM
ejpam-5838	316	10	0	0	NUM
ejpam-5838	316	11	,	,	PUNCT
ejpam-5838	316	12	and	and	CCONJ
ejpam-5838	316	13	so	so	ADV
ejpam-5838	316	14	z	z	NOUN
ejpam-5838	316	15	=	=	SYM
ejpam-5838	316	16	z∗.	z∗.	PROPN
ejpam-5838	316	17	example	example	NOUN
ejpam-5838	316	18	2	2	X
ejpam-5838	316	19	.	.	X
ejpam-5838	317	1	let	let	AUX
ejpam-5838	317	2	(	(	PUNCT
ejpam-5838	317	3	ê	ê	NOUN
ejpam-5838	317	4	,	,	PUNCT
ejpam-5838	317	5	g	g	NOUN
ejpam-5838	317	6	)	)	PUNCT
ejpam-5838	317	7	be	be	AUX
ejpam-5838	317	8	a	a	DET
ejpam-5838	317	9	gm	gm	PROPN
ejpam-5838	317	10	space	space	NOUN
ejpam-5838	317	11	,	,	PUNCT
ejpam-5838	317	12	where	where	SCONJ
ejpam-5838	317	13	ê	ê	PROPN
ejpam-5838	317	14	=	=	SYM
ejpam-5838	317	15	r	r	NOUN
ejpam-5838	317	16	and	and	CCONJ
ejpam-5838	317	17	define	define	VERB
ejpam-5838	317	18	the	the	DET
ejpam-5838	317	19	gm	gm	PROPN
ejpam-5838	317	20	space	space	NOUN
ejpam-5838	317	21	:	:	PUNCT
ejpam-5838	318	1	g(ê1	g(ê1	PROPN
ejpam-5838	318	2	,	,	PUNCT
ejpam-5838	318	3	ê2	ê2	PROPN
ejpam-5838	318	4	,	,	PUNCT
ejpam-5838	318	5	ê3	ê3	PUNCT
ejpam-5838	318	6	)	)	PUNCT
ejpam-5838	318	7	=	=	PUNCT
ejpam-5838	319	1	(	(	PUNCT
ejpam-5838	319	2	|ê1	|ê1	PROPN
ejpam-5838	319	3	−	−	PROPN
ejpam-5838	319	4	ê2|+	ê2|+	PROPN
ejpam-5838	319	5	|ê2	|ê2	ADJ
ejpam-5838	319	6	−	−	PROPN
ejpam-5838	319	7	ê3|+	ê3|+	NOUN
ejpam-5838	319	8	|ê3	|ê3	PROPN
ejpam-5838	319	9	−	−	PROPN
ejpam-5838	319	10	ê1|	ê1|	PROPN
ejpam-5838	319	11	)	)	PUNCT
ejpam-5838	319	12	for	for	ADP
ejpam-5838	319	13	all	all	DET
ejpam-5838	319	14	ê1	ê1	PROPN
ejpam-5838	319	15	,	,	PUNCT
ejpam-5838	319	16	ê2	ê2	PROPN
ejpam-5838	319	17	,	,	PUNCT
ejpam-5838	319	18	ê3	ê3	PROPN
ejpam-5838	319	19	∈	∈	PROPN
ejpam-5838	319	20	ê.	ê.	ADV
ejpam-5838	319	21	now	now	ADV
ejpam-5838	319	22	,	,	PUNCT
ejpam-5838	319	23	we	we	PRON
ejpam-5838	319	24	define	define	VERB
ejpam-5838	319	25	the	the	DET
ejpam-5838	319	26	3	3	NUM
ejpam-5838	319	27	-	-	PUNCT
ejpam-5838	319	28	self	self	NOUN
ejpam-5838	319	29	-	-	PUNCT
ejpam-5838	319	30	mappings	mapping	NOUN
ejpam-5838	319	31	on	on	ADP
ejpam-5838	319	32	r	r	NOUN
ejpam-5838	319	33	:	:	PUNCT
ejpam-5838	319	34	f1ê1	f1ê1	PROPN
ejpam-5838	319	35	=	=	PUNCT
ejpam-5838	319	36	ê1	ê1	PROPN
ejpam-5838	319	37	2	2	NUM
ejpam-5838	319	38	,	,	PUNCT
ejpam-5838	319	39	f2ê1	f2ê1	X
ejpam-5838	319	40	=	=	PUNCT
ejpam-5838	319	41	ê1	ê1	NOUN
ejpam-5838	320	1	+	+	CCONJ
ejpam-5838	320	2	1	1	NUM
ejpam-5838	320	3	3	3	NUM
ejpam-5838	320	4	,	,	PUNCT
ejpam-5838	320	5	f3ê1	f3ê1	X
ejpam-5838	320	6	=	=	PUNCT
ejpam-5838	320	7	ê1	ê1	PROPN
ejpam-5838	320	8	+	+	CCONJ
ejpam-5838	320	9	2	2	NUM
ejpam-5838	320	10	4	4	NUM
ejpam-5838	320	11	.	.	PUNCT
ejpam-5838	321	1	now	now	ADV
ejpam-5838	321	2	,	,	PUNCT
ejpam-5838	321	3	take	take	VERB
ejpam-5838	321	4	α	α	NOUN
ejpam-5838	321	5	=	=	NOUN
ejpam-5838	321	6	0.3	0.3	NUM
ejpam-5838	321	7	,	,	PUNCT
ejpam-5838	321	8	β	β	X
ejpam-5838	321	9	=	=	SYM
ejpam-5838	321	10	0.5	0.5	NUM
ejpam-5838	321	11	,	,	PUNCT
ejpam-5838	321	12	so	so	SCONJ
ejpam-5838	321	13	that	that	SCONJ
ejpam-5838	321	14	α+	α+	PRON
ejpam-5838	321	15	β	β	X
ejpam-5838	321	16	=	=	PUNCT
ejpam-5838	321	17	0.8	0.8	NUM
ejpam-5838	321	18	<	<	X
ejpam-5838	321	19	1	1	NUM
ejpam-5838	321	20	.	.	PUNCT
ejpam-5838	322	1	let	let	VERB
ejpam-5838	322	2	us	we	PRON
ejpam-5838	322	3	check	check	VERB
ejpam-5838	322	4	if	if	SCONJ
ejpam-5838	322	5	the	the	DET
ejpam-5838	322	6	condition	condition	NOUN
ejpam-5838	322	7	in	in	ADP
ejpam-5838	322	8	theorem	theorem	NOUN
ejpam-5838	322	9	3.4	3.4	NUM
ejpam-5838	322	10	is	be	AUX
ejpam-5838	322	11	satisfied	satisfied	ADJ
ejpam-5838	322	12	for	for	ADP
ejpam-5838	322	13	ê1	ê1	NOUN
ejpam-5838	322	14	=	=	SYM
ejpam-5838	322	15	2	2	NUM
ejpam-5838	322	16	,	,	PUNCT
ejpam-5838	322	17	ê2	ê2	NOUN
ejpam-5838	322	18	=	=	SYM
ejpam-5838	322	19	3	3	NUM
ejpam-5838	322	20	,	,	PUNCT
ejpam-5838	322	21	ê3	ê3	PROPN
ejpam-5838	323	1	=	=	SYM
ejpam-5838	323	2	4	4	NUM
ejpam-5838	323	3	,	,	PUNCT
ejpam-5838	323	4	g(f1ê1	g(f1ê1	PROPN
ejpam-5838	323	5	,	,	PUNCT
ejpam-5838	323	6	f2ê2	f2ê2	NOUN
ejpam-5838	323	7	,	,	PUNCT
ejpam-5838	323	8	f3ê3	f3ê3	PROPN
ejpam-5838	323	9	)	)	PUNCT
ejpam-5838	323	10	=	=	SYM
ejpam-5838	323	11	g	g	PROPN
ejpam-5838	323	12	(	(	PUNCT
ejpam-5838	323	13	1	1	NUM
ejpam-5838	323	14	,	,	PUNCT
ejpam-5838	323	15	4	4	NUM
ejpam-5838	323	16	3	3	NUM
ejpam-5838	323	17	,	,	PUNCT
ejpam-5838	323	18	6	6	NUM
ejpam-5838	323	19	4	4	NUM
ejpam-5838	323	20	)	)	PUNCT
ejpam-5838	323	21	=	=	SYM
ejpam-5838	324	1	g(1	g(1	NOUN
ejpam-5838	324	2	,	,	PUNCT
ejpam-5838	324	3	1.33	1.33	NUM
ejpam-5838	324	4	,	,	PUNCT
ejpam-5838	324	5	1.5	1.5	NUM
ejpam-5838	324	6	)	)	PUNCT
ejpam-5838	324	7	=	=	SYM
ejpam-5838	324	8	(	(	PUNCT
ejpam-5838	324	9	|1−	|1−	INTJ
ejpam-5838	324	10	1.33|+	1.33|+	NUM
ejpam-5838	324	11	|1.33−	|1.33−	PROPN
ejpam-5838	324	12	1.5|+	1.5|+	PROPN
ejpam-5838	324	13	|1.5−	|1.5−	NUM
ejpam-5838	324	14	1|	1|	NUM
ejpam-5838	324	15	)	)	PUNCT
ejpam-5838	324	16	=	=	PUNCT
ejpam-5838	325	1	0.33	0.33	NUM
ejpam-5838	325	2	+	+	NUM
ejpam-5838	325	3	0.17	0.17	NUM
ejpam-5838	325	4	+	+	NUM
ejpam-5838	325	5	0.5	0.5	NUM
ejpam-5838	325	6	=	=	SYM
ejpam-5838	325	7	1	1	NUM
ejpam-5838	325	8	.	.	PUNCT
ejpam-5838	326	1	now	now	ADV
ejpam-5838	326	2	,	,	PUNCT
ejpam-5838	326	3	compute	compute	VERB
ejpam-5838	326	4	the	the	DET
ejpam-5838	326	5	r.h.s	r.h.s	NOUN
ejpam-5838	326	6	:	:	PUNCT
ejpam-5838	326	7	g(ê1	g(ê1	PROPN
ejpam-5838	326	8	,	,	PUNCT
ejpam-5838	326	9	ê2	ê2	PROPN
ejpam-5838	326	10	,	,	PUNCT
ejpam-5838	326	11	ê3	ê3	X
ejpam-5838	326	12	)	)	PUNCT
ejpam-5838	327	1	=	=	SYM
ejpam-5838	327	2	g(2	g(2	PROPN
ejpam-5838	327	3	,	,	PUNCT
ejpam-5838	327	4	3	3	NUM
ejpam-5838	327	5	,	,	PUNCT
ejpam-5838	327	6	4	4	NUM
ejpam-5838	327	7	)	)	PUNCT
ejpam-5838	327	8	=	=	NOUN
ejpam-5838	328	1	|2−	|2−	PROPN
ejpam-5838	328	2	3|+	3|+	PROPN
ejpam-5838	329	1	|3−	|3−	PROPN
ejpam-5838	329	2	4|+	4|+	NUM
ejpam-5838	329	3	|4−	|4−	VERB
ejpam-5838	329	4	2|	2|	NUM
ejpam-5838	329	5	=	=	SYM
ejpam-5838	329	6	1	1	NUM
ejpam-5838	330	1	+	+	NUM
ejpam-5838	330	2	1	1	NUM
ejpam-5838	330	3	+	+	SYM
ejpam-5838	330	4	2	2	NUM
ejpam-5838	330	5	=	=	SYM
ejpam-5838	330	6	4	4	NUM
ejpam-5838	330	7	.	.	PUNCT
ejpam-5838	331	1	so	so	ADV
ejpam-5838	331	2	,	,	PUNCT
ejpam-5838	331	3	r.h.s=	r.h.s=	PROPN
ejpam-5838	331	4	αg(ê1	αg(ê1	PROPN
ejpam-5838	331	5	,	,	PUNCT
ejpam-5838	331	6	ê2	ê2	PROPN
ejpam-5838	331	7	,	,	PUNCT
ejpam-5838	331	8	ê3	ê3	PUNCT
ejpam-5838	331	9	)	)	PUNCT
ejpam-5838	332	1	+	+	CCONJ
ejpam-5838	332	2	β[product	β[product	ADP
ejpam-5838	332	3	term	term	NOUN
ejpam-5838	332	4	]	]	PUNCT
ejpam-5838	332	5	(	(	PUNCT
ejpam-5838	332	6	assume	assume	VERB
ejpam-5838	332	7	the	the	DET
ejpam-5838	332	8	long	long	ADJ
ejpam-5838	332	9	product	product	NOUN
ejpam-5838	332	10	term	term	NOUN
ejpam-5838	332	11	is	be	AUX
ejpam-5838	332	12	≤	≤	NUM
ejpam-5838	332	13	1	1	NUM
ejpam-5838	332	14	for	for	ADP
ejpam-5838	332	15	simplicity	simplicity	NOUN
ejpam-5838	332	16	)	)	PUNCT
ejpam-5838	333	1	so	so	ADV
ejpam-5838	333	2	,	,	PUNCT
ejpam-5838	333	3	r.h.s≤	r.h.s≤	NOUN
ejpam-5838	333	4	0.3	0.3	NUM
ejpam-5838	333	5	·	·	SYM
ejpam-5838	333	6	4	4	NUM
ejpam-5838	333	7	+	+	SYM
ejpam-5838	333	8	0.5	0.5	NUM
ejpam-5838	333	9	·	·	SYM
ejpam-5838	333	10	1	1	NUM
ejpam-5838	333	11	=	=	SYM
ejpam-5838	333	12	1.2	1.2	NUM
ejpam-5838	333	13	+	+	SYM
ejpam-5838	333	14	0.5	0.5	NUM
ejpam-5838	333	15	=	=	SYM
ejpam-5838	333	16	1.7	1.7	NUM
ejpam-5838	333	17	,	,	PUNCT
ejpam-5838	333	18	since	since	SCONJ
ejpam-5838	333	19	l.h.s	l.h.s	VERB
ejpam-5838	333	20	1.0	1.0	NUM
ejpam-5838	333	21	≤	≤	NUM
ejpam-5838	333	22	1.7	1.7	NUM
ejpam-5838	333	23	,	,	PUNCT
ejpam-5838	333	24	the	the	DET
ejpam-5838	333	25	condition	condition	NOUN
ejpam-5838	333	26	is	be	AUX
ejpam-5838	333	27	satisfied	satisfied	ADJ
ejpam-5838	333	28	.	.	PUNCT
ejpam-5838	334	1	thus	thus	ADV
ejpam-5838	334	2	,	,	PUNCT
ejpam-5838	334	3	by	by	ADP
ejpam-5838	334	4	theorem	theorem	NOUN
ejpam-5838	334	5	2	2	NUM
ejpam-5838	334	6	hence	hence	ADV
ejpam-5838	334	7	,	,	PUNCT
ejpam-5838	334	8	the	the	DET
ejpam-5838	334	9	3	3	NUM
ejpam-5838	334	10	-	-	PUNCT
ejpam-5838	334	11	mappings	mapping	NOUN
ejpam-5838	334	12	f1	f1	NOUN
ejpam-5838	334	13	,	,	PUNCT
ejpam-5838	334	14	f2	f2	PROPN
ejpam-5838	334	15	and	and	CCONJ
ejpam-5838	334	16	f3	f3	PROPN
ejpam-5838	334	17	have	have	VERB
ejpam-5838	334	18	a	a	DET
ejpam-5838	334	19	common	common	ADJ
ejpam-5838	334	20	fixed	fix	VERB
ejpam-5838	334	21	point	point	NOUN
ejpam-5838	334	22	(	(	PUNCT
ejpam-5838	334	23	cfp	cfp	NOUN
ejpam-5838	334	24	)	)	PUNCT
ejpam-5838	334	25	in	in	ADP
ejpam-5838	334	26	r	r	NOUN
ejpam-5838	335	1	and	and	CCONJ
ejpam-5838	335	2	it	it	PRON
ejpam-5838	335	3	is	be	AUX
ejpam-5838	335	4	unique	unique	ADJ
ejpam-5838	335	5	because	because	SCONJ
ejpam-5838	335	6	α+	α+	X
ejpam-5838	335	7	β	β	X
ejpam-5838	335	8	<	<	X
ejpam-5838	335	9	1	1	NUM
ejpam-5838	335	10	.	.	PUNCT
ejpam-5838	335	11	m.	m.	PROPN
ejpam-5838	335	12	noorwali	noorwali	PROPN
ejpam-5838	335	13	et	et	PROPN
ejpam-5838	335	14	al/	al/	PROPN
ejpam-5838	335	15	/	/	SYM
ejpam-5838	335	16	eur	eur	PROPN
ejpam-5838	335	17	.	.	PUNCT
ejpam-5838	336	1	j.	j.	PROPN
ejpam-5838	336	2	pure	pure	PROPN
ejpam-5838	336	3	appl	appl	PROPN
ejpam-5838	336	4	.	.	PROPN
ejpam-5838	336	5	math	math	PROPN
ejpam-5838	336	6	,	,	PUNCT
ejpam-5838	336	7	18	18	NUM
ejpam-5838	336	8	(	(	PUNCT
ejpam-5838	336	9	2	2	NUM
ejpam-5838	336	10	)	)	PUNCT
ejpam-5838	336	11	(	(	PUNCT
ejpam-5838	336	12	2025	2025	NUM
ejpam-5838	336	13	)	)	PUNCT
ejpam-5838	336	14	,	,	PUNCT
ejpam-5838	336	15	5838	5838	NUM
ejpam-5838	336	16	13	13	NUM
ejpam-5838	336	17	of	of	ADP
ejpam-5838	336	18	16	16	NUM
ejpam-5838	336	19	4	4	NUM
ejpam-5838	336	20	.	.	PUNCT
ejpam-5838	337	1	application	application	NOUN
ejpam-5838	337	2	we	we	PRON
ejpam-5838	337	3	apply	apply	VERB
ejpam-5838	337	4	nonlinear	nonlinear	ADJ
ejpam-5838	337	5	integral	integral	ADJ
ejpam-5838	337	6	equations	equation	NOUN
ejpam-5838	337	7	(	(	PUNCT
ejpam-5838	337	8	nlies	nlie	NOUN
ejpam-5838	337	9	)	)	PUNCT
ejpam-5838	337	10	in	in	ADP
ejpam-5838	337	11	this	this	DET
ejpam-5838	337	12	part	part	NOUN
ejpam-5838	337	13	to	to	PART
ejpam-5838	337	14	provide	provide	VERB
ejpam-5838	337	15	evidence	evidence	NOUN
ejpam-5838	337	16	for	for	ADP
ejpam-5838	337	17	our	our	PRON
ejpam-5838	337	18	findings	finding	NOUN
ejpam-5838	337	19	.	.	PUNCT
ejpam-5838	338	1	the	the	DET
ejpam-5838	338	2	shape	shape	NOUN
ejpam-5838	338	3	of	of	ADP
ejpam-5838	338	4	the	the	DET
ejpam-5838	338	5	nlies	nlie	NOUN
ejpam-5838	338	6	is	be	AUX
ejpam-5838	338	7	;	;	PUNCT
ejpam-5838	338	8	ê1(µ	ê1(µ	ADV
ejpam-5838	338	9	)	)	PUNCT
ejpam-5838	338	10	=	=	SYM
ejpam-5838	338	11	∫	∫	PROPN
ejpam-5838	338	12	a2	a2	PROPN
ejpam-5838	338	13	a1	a1	PROPN
ejpam-5838	338	14	δ1(µ	δ1(µ	PROPN
ejpam-5838	338	15	,	,	PUNCT
ejpam-5838	338	16	s	s	NOUN
ejpam-5838	338	17	,	,	PUNCT
ejpam-5838	338	18	ê1(s	ê1(s	NOUN
ejpam-5838	338	19	)	)	PUNCT
ejpam-5838	338	20	)	)	PUNCT
ejpam-5838	338	21	ds	ds	ADJ
ejpam-5838	338	22	,	,	PUNCT
ejpam-5838	338	23	ê2(µ	ê2(µ	NOUN
ejpam-5838	338	24	)	)	PUNCT
ejpam-5838	339	1	=	=	SYM
ejpam-5838	339	2	∫	∫	PROPN
ejpam-5838	339	3	a2	a2	PROPN
ejpam-5838	339	4	a1	a1	PROPN
ejpam-5838	339	5	δ2(µ	δ2(µ	PROPN
ejpam-5838	339	6	,	,	PUNCT
ejpam-5838	339	7	s	s	NOUN
ejpam-5838	339	8	,	,	PUNCT
ejpam-5838	339	9	ê2(s	ê2(s	NOUN
ejpam-5838	339	10	)	)	PUNCT
ejpam-5838	339	11	)	)	PUNCT
ejpam-5838	340	1	ds	ds	PROPN
ejpam-5838	340	2	,	,	PUNCT
ejpam-5838	340	3	(	(	PUNCT
ejpam-5838	340	4	20	20	NUM
ejpam-5838	340	5	)	)	PUNCT
ejpam-5838	340	6	ê3(µ	ê3(µ	PROPN
ejpam-5838	340	7	)	)	PUNCT
ejpam-5838	340	8	=	=	SYM
ejpam-5838	341	1	∫	∫	PROPN
ejpam-5838	341	2	a2	a2	PROPN
ejpam-5838	341	3	a1	a1	PROPN
ejpam-5838	341	4	δ3(µ	δ3(µ	PROPN
ejpam-5838	341	5	,	,	PUNCT
ejpam-5838	341	6	s	s	NOUN
ejpam-5838	341	7	,	,	PUNCT
ejpam-5838	341	8	ê3(s	ê3(s	NOUN
ejpam-5838	341	9	)	)	PUNCT
ejpam-5838	341	10	)	)	PUNCT
ejpam-5838	341	11	ds	ds	PROPN
ejpam-5838	341	12	.	.	INTJ
ejpam-5838	341	13	where	where	SCONJ
ejpam-5838	341	14	µ	µ	PRON
ejpam-5838	341	15	∈	∈	PROPN
ejpam-5838	341	16	[	[	X
ejpam-5838	341	17	a1	a1	NOUN
ejpam-5838	341	18	,	,	PUNCT
ejpam-5838	341	19	a2	a2	PROPN
ejpam-5838	341	20	]	]	PUNCT
ejpam-5838	341	21	for	for	ADP
ejpam-5838	341	22	all	all	DET
ejpam-5838	341	23	ê1	ê1	PROPN
ejpam-5838	341	24	,	,	PUNCT
ejpam-5838	341	25	ê2	ê2	PROPN
ejpam-5838	341	26	,	,	PUNCT
ejpam-5838	341	27	ê3	ê3	PROPN
ejpam-5838	341	28	∈	∈	PROPN
ejpam-5838	341	29	ê	ê	PROPN
ejpam-5838	341	30	where	where	SCONJ
ejpam-5838	341	31	ê	ê	PROPN
ejpam-5838	341	32	=	=	SYM
ejpam-5838	341	33	c([a1	c([a1	ADJ
ejpam-5838	341	34	,	,	PUNCT
ejpam-5838	341	35	a2],r	a2],r	PROPN
ejpam-5838	341	36	)	)	PUNCT
ejpam-5838	341	37	is	be	AUX
ejpam-5838	341	38	the	the	DET
ejpam-5838	341	39	set	set	NOUN
ejpam-5838	341	40	of	of	ADP
ejpam-5838	341	41	all	all	DET
ejpam-5838	341	42	real	real	ADV
ejpam-5838	341	43	-	-	PUNCT
ejpam-5838	341	44	valued	value	VERB
ejpam-5838	341	45	continuous	continuous	ADJ
ejpam-5838	341	46	functions	function	NOUN
ejpam-5838	341	47	on	on	ADP
ejpam-5838	341	48	[	[	X
ejpam-5838	341	49	a1	a1	NOUN
ejpam-5838	341	50	,	,	PUNCT
ejpam-5838	341	51	a2	a2	PROPN
ejpam-5838	341	52	]	]	PUNCT
ejpam-5838	341	53	and	and	CCONJ
ejpam-5838	341	54	δ1	δ1	NOUN
ejpam-5838	341	55	,	,	PUNCT
ejpam-5838	341	56	δ2	δ2	VERB
ejpam-5838	341	57	,	,	PUNCT
ejpam-5838	341	58	δ3	δ3	PROPN
ejpam-5838	341	59	:	:	PUNCT
ejpam-5838	341	60	[	[	X
ejpam-5838	341	61	a1	a1	NOUN
ejpam-5838	341	62	,	,	PUNCT
ejpam-5838	341	63	a2]×	a2]×	PROPN
ejpam-5838	341	64	[	[	X
ejpam-5838	341	65	a1	a1	NOUN
ejpam-5838	341	66	,	,	PUNCT
ejpam-5838	341	67	a2]×	a2]×	PROPN
ejpam-5838	341	68	r	r	NOUN
ejpam-5838	341	69	→	→	SYM
ejpam-5838	341	70	r.	r.	NOUN
ejpam-5838	341	71	theorem	theorem	NOUN
ejpam-5838	341	72	3	3	X
ejpam-5838	341	73	.	.	PUNCT
ejpam-5838	342	1	let	let	VERB
ejpam-5838	342	2	a1	a1	NOUN
ejpam-5838	342	3	and	and	CCONJ
ejpam-5838	342	4	a2	a2	PROPN
ejpam-5838	342	5	be	be	AUX
ejpam-5838	342	6	fixed	fix	VERB
ejpam-5838	342	7	real	real	ADJ
ejpam-5838	342	8	numbers	number	NOUN
ejpam-5838	342	9	with	with	ADP
ejpam-5838	342	10	a1	a1	NOUN
ejpam-5838	342	11	<	<	X
ejpam-5838	342	12	a2	a2	PROPN
ejpam-5838	342	13	.	.	PUNCT
ejpam-5838	343	1	consider	consider	VERB
ejpam-5838	343	2	the	the	DET
ejpam-5838	343	3	non	non	ADJ
ejpam-5838	343	4	-	-	ADJ
ejpam-5838	343	5	linear	linear	ADJ
ejpam-5838	343	6	integral	integral	ADJ
ejpam-5838	343	7	equations	equation	NOUN
ejpam-5838	343	8	(	(	PUNCT
ejpam-5838	343	9	nlies	nlie	NOUN
ejpam-5838	343	10	)	)	PUNCT
ejpam-5838	343	11	defined	define	VERB
ejpam-5838	343	12	as	as	SCONJ
ejpam-5838	343	13	follows	follow	VERB
ejpam-5838	343	14	:	:	PUNCT
ejpam-5838	343	15	ê1(µ	ê1(µ	ADJ
ejpam-5838	343	16	)	)	PUNCT
ejpam-5838	343	17	=	=	SYM
ejpam-5838	343	18	∫	∫	PROPN
ejpam-5838	343	19	a2	a2	PROPN
ejpam-5838	343	20	a1	a1	PROPN
ejpam-5838	343	21	δ1(µ	δ1(µ	PROPN
ejpam-5838	343	22	,	,	PUNCT
ejpam-5838	343	23	s	s	NOUN
ejpam-5838	343	24	,	,	PUNCT
ejpam-5838	343	25	ê1(s	ê1(s	NOUN
ejpam-5838	343	26	)	)	PUNCT
ejpam-5838	343	27	)	)	PUNCT
ejpam-5838	343	28	ds	ds	ADJ
ejpam-5838	343	29	,	,	PUNCT
ejpam-5838	343	30	ê2(µ	ê2(µ	NOUN
ejpam-5838	343	31	)	)	PUNCT
ejpam-5838	343	32	=	=	SYM
ejpam-5838	343	33	∫	∫	PROPN
ejpam-5838	343	34	a2	a2	PROPN
ejpam-5838	343	35	a1	a1	PROPN
ejpam-5838	343	36	δ2(µ	δ2(µ	PROPN
ejpam-5838	343	37	,	,	PUNCT
ejpam-5838	343	38	s	s	NOUN
ejpam-5838	343	39	,	,	PUNCT
ejpam-5838	343	40	ê2(s	ê2(s	NOUN
ejpam-5838	343	41	)	)	PUNCT
ejpam-5838	343	42	)	)	PUNCT
ejpam-5838	344	1	ds	ds	PROPN
ejpam-5838	344	2	,	,	PUNCT
ejpam-5838	344	3	(	(	PUNCT
ejpam-5838	344	4	21	21	NUM
ejpam-5838	344	5	)	)	PUNCT
ejpam-5838	344	6	ê3(µ	ê3(µ	PROPN
ejpam-5838	344	7	)	)	PUNCT
ejpam-5838	344	8	=	=	SYM
ejpam-5838	344	9	∫	∫	PROPN
ejpam-5838	344	10	a2	a2	PROPN
ejpam-5838	344	11	a1	a1	PROPN
ejpam-5838	344	12	δ3(µ	δ3(µ	PROPN
ejpam-5838	344	13	,	,	PUNCT
ejpam-5838	344	14	s	s	NOUN
ejpam-5838	344	15	,	,	PUNCT
ejpam-5838	344	16	ê3(s	ê3(s	NOUN
ejpam-5838	344	17	)	)	PUNCT
ejpam-5838	344	18	)	)	PUNCT
ejpam-5838	345	1	ds	ds	PROPN
ejpam-5838	345	2	.	.	NOUN
ejpam-5838	345	3	where	where	SCONJ
ejpam-5838	345	4	µ	µ	NOUN
ejpam-5838	345	5	is	be	AUX
ejpam-5838	345	6	a	a	DET
ejpam-5838	345	7	parameter	parameter	NOUN
ejpam-5838	345	8	that	that	PRON
ejpam-5838	345	9	lies	lie	VERB
ejpam-5838	345	10	in	in	ADP
ejpam-5838	345	11	the	the	DET
ejpam-5838	345	12	interval	interval	NOUN
ejpam-5838	345	13	[	[	X
ejpam-5838	345	14	a1	a1	NOUN
ejpam-5838	345	15	,	,	PUNCT
ejpam-5838	345	16	a2	a2	PROPN
ejpam-5838	345	17	]	]	PUNCT
ejpam-5838	345	18	and	and	CCONJ
ejpam-5838	345	19	the	the	DET
ejpam-5838	345	20	functions	function	NOUN
ejpam-5838	345	21	ê1	ê1	PROPN
ejpam-5838	345	22	,	,	PUNCT
ejpam-5838	345	23	ê2	ê2	PROPN
ejpam-5838	345	24	,	,	PUNCT
ejpam-5838	345	25	ê3	ê3	X
ejpam-5838	345	26	are	be	AUX
ejpam-5838	345	27	from	from	ADP
ejpam-5838	345	28	the	the	DET
ejpam-5838	345	29	set	set	NOUN
ejpam-5838	345	30	ê	ê	X
ejpam-5838	345	31	=	=	SYM
ejpam-5838	345	32	c([a1	c([a1	ADJ
ejpam-5838	345	33	,	,	PUNCT
ejpam-5838	345	34	a2],r	a2],r	PROPN
ejpam-5838	345	35	)	)	PUNCT
ejpam-5838	345	36	.	.	PUNCT
ejpam-5838	346	1	the	the	DET
ejpam-5838	346	2	functions	function	NOUN
ejpam-5838	346	3	δ1	δ1	NOUN
ejpam-5838	346	4	,	,	PUNCT
ejpam-5838	346	5	δ2	δ2	VERB
ejpam-5838	346	6	,	,	PUNCT
ejpam-5838	346	7	δ3	δ3	PROPN
ejpam-5838	346	8	are	be	AUX
ejpam-5838	346	9	defined	define	VERB
ejpam-5838	346	10	as	as	ADP
ejpam-5838	346	11	δ1	δ1	NOUN
ejpam-5838	346	12	,	,	PUNCT
ejpam-5838	346	13	δ2	δ2	VERB
ejpam-5838	346	14	,	,	PUNCT
ejpam-5838	346	15	δ3	δ3	PROPN
ejpam-5838	346	16	:	:	PUNCT
ejpam-5838	346	17	[	[	X
ejpam-5838	346	18	a1	a1	NOUN
ejpam-5838	346	19	,	,	PUNCT
ejpam-5838	346	20	a2]×[a1	a2]×[a1	NOUN
ejpam-5838	346	21	,	,	PUNCT
ejpam-5838	346	22	a2]×r	a2]×r	PUNCT
ejpam-5838	346	23	→	→	SYM
ejpam-5838	346	24	r.	r.	PROPN
ejpam-5838	346	25	if	if	SCONJ
ejpam-5838	346	26	the	the	DET
ejpam-5838	346	27	functions	function	NOUN
ejpam-5838	346	28	δ1	δ1	NOUN
ejpam-5838	346	29	,	,	PUNCT
ejpam-5838	346	30	δ2	δ2	VERB
ejpam-5838	346	31	and	and	CCONJ
ejpam-5838	346	32	δ3	δ3	PROPN
ejpam-5838	346	33	satisfy	satisfy	VERB
ejpam-5838	346	34	certain	certain	ADJ
ejpam-5838	346	35	conditions	condition	NOUN
ejpam-5838	346	36	,	,	PUNCT
ejpam-5838	346	37	then	then	ADV
ejpam-5838	346	38	there	there	PRON
ejpam-5838	346	39	exists	exist	VERB
ejpam-5838	346	40	a	a	DET
ejpam-5838	346	41	unique	unique	ADJ
ejpam-5838	346	42	solution	solution	NOUN
ejpam-5838	346	43	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	346	44	)	)	PUNCT
ejpam-5838	346	45	in	in	ADP
ejpam-5838	346	46	the	the	DET
ejpam-5838	346	47	set	set	NOUN
ejpam-5838	346	48	ê	ê	PROPN
ejpam-5838	346	49	that	that	PRON
ejpam-5838	346	50	simultaneously	simultaneously	ADV
ejpam-5838	346	51	satisfies	satisfy	VERB
ejpam-5838	346	52	the	the	DET
ejpam-5838	346	53	nlies	nlie	NOUN
ejpam-5838	346	54	(	(	PUNCT
ejpam-5838	346	55	4.1	4.1	NUM
ejpam-5838	346	56	)	)	PUNCT
ejpam-5838	346	57	for	for	ADP
ejpam-5838	346	58	all	all	DET
ejpam-5838	346	59	µ	µ	NOUN
ejpam-5838	346	60	in	in	ADP
ejpam-5838	346	61	the	the	DET
ejpam-5838	346	62	interval	interval	NOUN
ejpam-5838	346	63	[	[	X
ejpam-5838	346	64	a1	a1	NOUN
ejpam-5838	346	65	,	,	PUNCT
ejpam-5838	346	66	a2	a2	PROPN
ejpam-5838	346	67	]	]	PUNCT
ejpam-5838	346	68	.	.	PUNCT
ejpam-5838	347	1	proof	proof	NOUN
ejpam-5838	347	2	.	.	PUNCT
ejpam-5838	348	1	define	define	VERB
ejpam-5838	348	2	the	the	DET
ejpam-5838	348	3	integral	integral	ADJ
ejpam-5838	348	4	operators	operator	NOUN
ejpam-5838	348	5	k1,k2,k3	k1,k2,k3	VERB
ejpam-5838	348	6	:	:	PUNCT
ejpam-5838	348	7	ê	ê	PROPN
ejpam-5838	348	8	→	→	SYM
ejpam-5838	348	9	ê	ê	PROPN
ejpam-5838	348	10	as	as	SCONJ
ejpam-5838	348	11	follows	follow	VERB
ejpam-5838	348	12	:	:	PUNCT
ejpam-5838	348	13	k1(ê)(µ	k1(ê)(µ	X
ejpam-5838	348	14	)	)	PUNCT
ejpam-5838	348	15	=	=	SYM
ejpam-5838	348	16	∫	∫	PROPN
ejpam-5838	348	17	a2	a2	PROPN
ejpam-5838	348	18	a1	a1	PROPN
ejpam-5838	348	19	δ1(µ	δ1(µ	PROPN
ejpam-5838	348	20	,	,	PUNCT
ejpam-5838	348	21	s	s	NOUN
ejpam-5838	348	22	,	,	PUNCT
ejpam-5838	348	23	ê1(s	ê1(s	NOUN
ejpam-5838	348	24	)	)	PUNCT
ejpam-5838	348	25	)	)	PUNCT
ejpam-5838	348	26	ds	ds	PROPN
ejpam-5838	348	27	,	,	PUNCT
ejpam-5838	348	28	k2(ê)(µ	k2(ê)(µ	PROPN
ejpam-5838	348	29	)	)	PUNCT
ejpam-5838	348	30	=	=	SYM
ejpam-5838	348	31	∫	∫	PROPN
ejpam-5838	348	32	a2	a2	PROPN
ejpam-5838	348	33	a1	a1	PROPN
ejpam-5838	348	34	δ2(µ	δ2(µ	PROPN
ejpam-5838	348	35	,	,	PUNCT
ejpam-5838	348	36	s	s	NOUN
ejpam-5838	348	37	,	,	PUNCT
ejpam-5838	348	38	ê2(s	ê2(s	NOUN
ejpam-5838	348	39	)	)	PUNCT
ejpam-5838	348	40	)	)	PUNCT
ejpam-5838	348	41	ds	ds	PROPN
ejpam-5838	348	42	,	,	PUNCT
ejpam-5838	348	43	k3(ê)(µ	k3(ê)(µ	NOUN
ejpam-5838	348	44	)	)	PUNCT
ejpam-5838	348	45	=	=	SYM
ejpam-5838	348	46	∫	∫	PROPN
ejpam-5838	348	47	a2	a2	PROPN
ejpam-5838	348	48	a1	a1	PROPN
ejpam-5838	348	49	δ3(µ	δ3(µ	PROPN
ejpam-5838	348	50	,	,	PUNCT
ejpam-5838	348	51	s	s	NOUN
ejpam-5838	348	52	,	,	PUNCT
ejpam-5838	348	53	ê3(s	ê3(s	NOUN
ejpam-5838	348	54	)	)	PUNCT
ejpam-5838	348	55	)	)	PUNCT
ejpam-5838	349	1	ds	ds	PROPN
ejpam-5838	349	2	.	.	PUNCT
ejpam-5838	350	1	we	we	PRON
ejpam-5838	350	2	need	need	VERB
ejpam-5838	350	3	to	to	PART
ejpam-5838	350	4	show	show	VERB
ejpam-5838	350	5	that	that	SCONJ
ejpam-5838	350	6	k	k	PROPN
ejpam-5838	350	7	is	be	AUX
ejpam-5838	350	8	a	a	DET
ejpam-5838	350	9	contraction	contraction	NOUN
ejpam-5838	350	10	mapping	mapping	NOUN
ejpam-5838	350	11	on	on	ADP
ejpam-5838	350	12	ê.	ê.	NOUN
ejpam-5838	350	13	to	to	PART
ejpam-5838	350	14	do	do	VERB
ejpam-5838	350	15	this	this	PRON
ejpam-5838	350	16	we	we	PRON
ejpam-5838	350	17	prove	prove	VERB
ejpam-5838	350	18	that	that	SCONJ
ejpam-5838	350	19	there	there	PRON
ejpam-5838	350	20	exists	exist	VERB
ejpam-5838	350	21	a	a	DET
ejpam-5838	350	22	constant	constant	ADJ
ejpam-5838	350	23	0	0	NUM
ejpam-5838	350	24	<	<	X
ejpam-5838	350	25	k	k	X
ejpam-5838	350	26	<	<	X
ejpam-5838	350	27	1	1	NUM
ejpam-5838	350	28	such	such	ADJ
ejpam-5838	350	29	that	that	PRON
ejpam-5838	350	30	for	for	ADP
ejpam-5838	350	31	any	any	DET
ejpam-5838	350	32	ê	ê	NOUN
ejpam-5838	350	33	,	,	PUNCT
ejpam-5838	350	34	˜̂e	˜̂e	PROPN
ejpam-5838	350	35	∈	∈	PROPN
ejpam-5838	350	36	ê	ê	NOUN
ejpam-5838	350	37	:	:	PUNCT
ejpam-5838	350	38	d(k(ê),k(˜̂e	d(k(ê),k(˜̂e	PROPN
ejpam-5838	350	39	)	)	PUNCT
ejpam-5838	350	40	)	)	PUNCT
ejpam-5838	351	1	≤	≤	PUNCT
ejpam-5838	352	1	k	k	X
ejpam-5838	352	2	·	·	PUNCT
ejpam-5838	352	3	d(ê	d(ê	NOUN
ejpam-5838	352	4	,	,	PUNCT
ejpam-5838	352	5	˜̂e	˜̂e	NOUN
ejpam-5838	352	6	)	)	PUNCT
ejpam-5838	352	7	.	.	PUNCT
ejpam-5838	353	1	let	let	VERB
ejpam-5838	353	2	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	353	3	)	)	PUNCT
ejpam-5838	353	4	be	be	AUX
ejpam-5838	353	5	the	the	DET
ejpam-5838	353	6	fp	fp	NOUN
ejpam-5838	353	7	of	of	ADP
ejpam-5838	353	8	the	the	DET
ejpam-5838	353	9	operators	operator	NOUN
ejpam-5838	353	10	k	k	X
ejpam-5838	353	11	i.e.	i.e.	X
ejpam-5838	353	12	k(ê∗)(µ	k(ê∗)(µ	NOUN
ejpam-5838	353	13	)	)	PUNCT
ejpam-5838	354	1	=	=	SYM
ejpam-5838	354	2	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	354	3	)	)	PUNCT
ejpam-5838	354	4	for	for	ADP
ejpam-5838	354	5	all	all	DET
ejpam-5838	354	6	µ	µ	NOUN
ejpam-5838	354	7	in	in	ADP
ejpam-5838	354	8	[	[	X
ejpam-5838	354	9	a1	a1	NOUN
ejpam-5838	354	10	,	,	PUNCT
ejpam-5838	354	11	a2	a2	PROPN
ejpam-5838	354	12	]	]	PUNCT
ejpam-5838	354	13	.	.	PUNCT
ejpam-5838	355	1	hence	hence	ADV
ejpam-5838	355	2	now	now	ADV
ejpam-5838	355	3	we	we	PRON
ejpam-5838	355	4	will	will	AUX
ejpam-5838	355	5	show	show	VERB
ejpam-5838	355	6	that	that	SCONJ
ejpam-5838	355	7	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	355	8	)	)	PUNCT
ejpam-5838	355	9	satisfies	satisfy	VERB
ejpam-5838	355	10	all	all	DET
ejpam-5838	355	11	three	three	NUM
ejpam-5838	355	12	nlies	nlie	NOUN
ejpam-5838	355	13	(	(	PUNCT
ejpam-5838	355	14	4.1	4.1	NUM
ejpam-5838	355	15	)	)	PUNCT
ejpam-5838	355	16	simultaneously	simultaneously	ADV
ejpam-5838	355	17	,	,	PUNCT
ejpam-5838	355	18	for	for	SCONJ
ejpam-5838	355	19	each	each	DET
ejpam-5838	355	20	µ	µ	NOUN
ejpam-5838	355	21	in	in	ADP
ejpam-5838	355	22	[	[	X
ejpam-5838	355	23	a1	a1	NOUN
ejpam-5838	355	24	,	,	PUNCT
ejpam-5838	355	25	a2	a2	PROPN
ejpam-5838	355	26	]	]	PUNCT
ejpam-5838	355	27	we	we	PRON
ejpam-5838	355	28	have	have	VERB
ejpam-5838	355	29	,	,	PUNCT
ejpam-5838	355	30	ê∗1(µ	ê∗1(µ	ADJ
ejpam-5838	355	31	)	)	PUNCT
ejpam-5838	355	32	=	=	SYM
ejpam-5838	355	33	k(ê∗1)(µ	k(ê∗1)(µ	PROPN
ejpam-5838	355	34	)	)	PUNCT
ejpam-5838	356	1	=	=	SYM
ejpam-5838	356	2	∫	∫	PROPN
ejpam-5838	356	3	a2	a2	PROPN
ejpam-5838	356	4	a1	a1	PROPN
ejpam-5838	356	5	δ1(µ	δ1(µ	PROPN
ejpam-5838	356	6	,	,	PUNCT
ejpam-5838	356	7	s	s	PROPN
ejpam-5838	356	8	,	,	PUNCT
ejpam-5838	356	9	ê	ê	PROPN
ejpam-5838	356	10	∗	∗	NOUN
ejpam-5838	356	11	1(s	1(s	NUM
ejpam-5838	356	12	)	)	PUNCT
ejpam-5838	356	13	)	)	PUNCT
ejpam-5838	356	14	ds	ds	NOUN
ejpam-5838	356	15	(	(	PUNCT
ejpam-5838	356	16	by	by	ADP
ejpam-5838	356	17	definition	definition	NOUN
ejpam-5838	356	18	of	of	ADP
ejpam-5838	356	19	k	k	NOUN
ejpam-5838	356	20	)	)	PUNCT
ejpam-5838	356	21	,	,	PUNCT
ejpam-5838	356	22	ê∗2(µ	ê∗2(µ	PROPN
ejpam-5838	356	23	)	)	PUNCT
ejpam-5838	356	24	=	=	SYM
ejpam-5838	356	25	k(ê∗2)(µ	k(ê∗2)(µ	PROPN
ejpam-5838	356	26	)	)	PUNCT
ejpam-5838	356	27	=	=	SYM
ejpam-5838	357	1	∫	∫	PROPN
ejpam-5838	357	2	a2	a2	PROPN
ejpam-5838	357	3	a1	a1	PROPN
ejpam-5838	357	4	δ2(µ	δ2(µ	PROPN
ejpam-5838	357	5	,	,	PUNCT
ejpam-5838	357	6	s	s	PROPN
ejpam-5838	357	7	,	,	PUNCT
ejpam-5838	357	8	ê	ê	PROPN
ejpam-5838	357	9	∗	∗	NOUN
ejpam-5838	357	10	1(s	1(s	NUM
ejpam-5838	357	11	)	)	PUNCT
ejpam-5838	357	12	)	)	PUNCT
ejpam-5838	357	13	ds	ds	NOUN
ejpam-5838	357	14	(	(	PUNCT
ejpam-5838	357	15	by	by	ADP
ejpam-5838	357	16	definition	definition	NOUN
ejpam-5838	357	17	of	of	ADP
ejpam-5838	357	18	k	k	NOUN
ejpam-5838	357	19	)	)	PUNCT
ejpam-5838	357	20	,	,	PUNCT
ejpam-5838	357	21	ê∗3(µ	ê∗3(µ	PROPN
ejpam-5838	357	22	)	)	PUNCT
ejpam-5838	357	23	=	=	SYM
ejpam-5838	357	24	k(ê∗3)(µ	k(ê∗3)(µ	PROPN
ejpam-5838	357	25	)	)	PUNCT
ejpam-5838	357	26	=	=	SYM
ejpam-5838	358	1	∫	∫	PROPN
ejpam-5838	358	2	a2	a2	PROPN
ejpam-5838	358	3	a1	a1	PROPN
ejpam-5838	358	4	δ3(µ	δ3(µ	PROPN
ejpam-5838	358	5	,	,	PUNCT
ejpam-5838	358	6	s	s	PROPN
ejpam-5838	358	7	,	,	PUNCT
ejpam-5838	358	8	ê	ê	PROPN
ejpam-5838	358	9	∗	∗	NOUN
ejpam-5838	358	10	1(s	1(s	NUM
ejpam-5838	358	11	)	)	PUNCT
ejpam-5838	358	12	)	)	PUNCT
ejpam-5838	359	1	ds	ds	NOUN
ejpam-5838	359	2	(	(	PUNCT
ejpam-5838	359	3	by	by	ADP
ejpam-5838	359	4	definition	definition	NOUN
ejpam-5838	359	5	of	of	ADP
ejpam-5838	359	6	k	k	NOUN
ejpam-5838	359	7	)	)	PUNCT
ejpam-5838	359	8	.	.	PUNCT
ejpam-5838	360	1	m.	m.	PROPN
ejpam-5838	360	2	noorwali	noorwali	PROPN
ejpam-5838	360	3	et	et	PROPN
ejpam-5838	360	4	al/	al/	PROPN
ejpam-5838	360	5	/	/	SYM
ejpam-5838	360	6	eur	eur	PROPN
ejpam-5838	360	7	.	.	PUNCT
ejpam-5838	361	1	j.	j.	PROPN
ejpam-5838	361	2	pure	pure	PROPN
ejpam-5838	361	3	appl	appl	PROPN
ejpam-5838	361	4	.	.	PROPN
ejpam-5838	361	5	math	math	PROPN
ejpam-5838	361	6	,	,	PUNCT
ejpam-5838	361	7	18	18	NUM
ejpam-5838	361	8	(	(	PUNCT
ejpam-5838	361	9	2	2	NUM
ejpam-5838	361	10	)	)	PUNCT
ejpam-5838	361	11	(	(	PUNCT
ejpam-5838	361	12	2025	2025	NUM
ejpam-5838	361	13	)	)	PUNCT
ejpam-5838	361	14	,	,	PUNCT
ejpam-5838	361	15	5838	5838	NUM
ejpam-5838	361	16	14	14	NUM
ejpam-5838	361	17	of	of	ADP
ejpam-5838	361	18	16	16	NUM
ejpam-5838	361	19	thus	thus	ADV
ejpam-5838	361	20	,	,	PUNCT
ejpam-5838	361	21	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	361	22	)	)	PUNCT
ejpam-5838	361	23	is	be	AUX
ejpam-5838	361	24	a	a	DET
ejpam-5838	361	25	solution	solution	NOUN
ejpam-5838	361	26	to	to	ADP
ejpam-5838	361	27	all	all	DET
ejpam-5838	361	28	three	three	NUM
ejpam-5838	361	29	nlies	nlie	NOUN
ejpam-5838	361	30	.	.	PUNCT
ejpam-5838	362	1	now	now	ADV
ejpam-5838	362	2	we	we	PRON
ejpam-5838	362	3	prove	prove	VERB
ejpam-5838	362	4	the	the	DET
ejpam-5838	362	5	uniqueness	uniqueness	NOUN
ejpam-5838	362	6	of	of	ADP
ejpam-5838	362	7	the	the	DET
ejpam-5838	362	8	solution	solution	NOUN
ejpam-5838	362	9	’s	’s	ADV
ejpam-5838	362	10	for	for	ADP
ejpam-5838	362	11	this	this	PRON
ejpam-5838	362	12	suppose	suppose	VERB
ejpam-5838	362	13	that	that	SCONJ
ejpam-5838	362	14	there	there	PRON
ejpam-5838	362	15	exists	exist	VERB
ejpam-5838	362	16	two	two	NUM
ejpam-5838	362	17	solutions	solution	NOUN
ejpam-5838	362	18	ê∗1(µ	ê∗1(µ	NOUN
ejpam-5838	362	19	)	)	PUNCT
ejpam-5838	362	20	and	and	CCONJ
ejpam-5838	362	21	ê∗2(µ	ê∗2(µ	PROPN
ejpam-5838	362	22	)	)	PUNCT
ejpam-5838	362	23	that	that	PRON
ejpam-5838	362	24	satisfy	satisfy	VERB
ejpam-5838	362	25	all	all	DET
ejpam-5838	362	26	three	three	NUM
ejpam-5838	362	27	nlies	nlie	NOUN
ejpam-5838	362	28	for	for	ADP
ejpam-5838	362	29	all	all	DET
ejpam-5838	362	30	µ	µ	NOUN
ejpam-5838	362	31	in	in	ADP
ejpam-5838	362	32	[	[	X
ejpam-5838	362	33	a1	a1	NOUN
ejpam-5838	362	34	,	,	PUNCT
ejpam-5838	362	35	a2	a2	PROPN
ejpam-5838	362	36	]	]	PUNCT
ejpam-5838	362	37	.	.	PUNCT
ejpam-5838	363	1	consider	consider	VERB
ejpam-5838	363	2	the	the	DET
ejpam-5838	363	3	function	function	NOUN
ejpam-5838	363	4	g(s	g(s	NOUN
ejpam-5838	363	5	)	)	PUNCT
ejpam-5838	363	6	=	=	SYM
ejpam-5838	364	1	d(ê∗1(µ	d(ê∗1(µ	NOUN
ejpam-5838	364	2	)	)	PUNCT
ejpam-5838	364	3	,	,	PUNCT
ejpam-5838	364	4	ê	ê	PROPN
ejpam-5838	364	5	∗	∗	NOUN
ejpam-5838	364	6	2(µ	2(µ	NUM
ejpam-5838	364	7	)	)	PUNCT
ejpam-5838	364	8	)	)	PUNCT
ejpam-5838	364	9	.	.	PUNCT
ejpam-5838	365	1	clearly	clearly	ADV
ejpam-5838	365	2	,	,	PUNCT
ejpam-5838	365	3	g(s	g(s	NOUN
ejpam-5838	365	4	)	)	PUNCT
ejpam-5838	365	5	=	=	SYM
ejpam-5838	365	6	0	0	NUM
ejpam-5838	365	7	for	for	ADP
ejpam-5838	365	8	all	all	DET
ejpam-5838	365	9	µ	µ	NOUN
ejpam-5838	365	10	in	in	ADP
ejpam-5838	365	11	[	[	X
ejpam-5838	365	12	a1	a1	NOUN
ejpam-5838	365	13	,	,	PUNCT
ejpam-5838	365	14	a2	a2	PROPN
ejpam-5838	365	15	]	]	PUNCT
ejpam-5838	365	16	because	because	SCONJ
ejpam-5838	365	17	ê∗1(µ	ê∗1(µ	NOUN
ejpam-5838	365	18	)	)	PUNCT
ejpam-5838	365	19	and	and	CCONJ
ejpam-5838	365	20	ê∗2(µ	ê∗2(µ	PROPN
ejpam-5838	365	21	)	)	PUNCT
ejpam-5838	365	22	are	be	AUX
ejpam-5838	365	23	identical	identical	ADJ
ejpam-5838	365	24	solutions	solution	NOUN
ejpam-5838	365	25	.	.	PUNCT
ejpam-5838	366	1	since	since	SCONJ
ejpam-5838	366	2	we	we	PRON
ejpam-5838	366	3	have	have	AUX
ejpam-5838	366	4	established	establish	VERB
ejpam-5838	366	5	the	the	DET
ejpam-5838	366	6	existence	existence	NOUN
ejpam-5838	366	7	and	and	CCONJ
ejpam-5838	366	8	uniqueness	uniqueness	NOUN
ejpam-5838	366	9	of	of	ADP
ejpam-5838	366	10	the	the	DET
ejpam-5838	366	11	solution	solution	NOUN
ejpam-5838	366	12	ê∗(µ	ê∗(µ	PROPN
ejpam-5838	366	13	)	)	PUNCT
ejpam-5838	366	14	for	for	ADP
ejpam-5838	366	15	all	all	DET
ejpam-5838	366	16	µ	µ	NOUN
ejpam-5838	366	17	in	in	ADP
ejpam-5838	366	18	[	[	X
ejpam-5838	366	19	a1	a1	NOUN
ejpam-5838	366	20	,	,	PUNCT
ejpam-5838	366	21	a2	a2	PROPN
ejpam-5838	366	22	]	]	PUNCT
ejpam-5838	366	23	that	that	PRON
ejpam-5838	366	24	satisfies	satisfy	VERB
ejpam-5838	366	25	the	the	DET
ejpam-5838	366	26	nlies	nlie	NOUN
ejpam-5838	366	27	(	(	PUNCT
ejpam-5838	366	28	4.1	4.1	NUM
ejpam-5838	366	29	)	)	PUNCT
ejpam-5838	366	30	,	,	PUNCT
ejpam-5838	366	31	the	the	DET
ejpam-5838	366	32	theorem	theorem	NOUN
ejpam-5838	366	33	is	be	AUX
ejpam-5838	366	34	proved	prove	VERB
ejpam-5838	366	35	.	.	PUNCT
ejpam-5838	367	1	5	5	X
ejpam-5838	367	2	.	.	X
ejpam-5838	367	3	conclusion	conclusion	NOUN
ejpam-5838	367	4	one	one	NUM
ejpam-5838	367	5	of	of	ADP
ejpam-5838	367	6	the	the	DET
ejpam-5838	367	7	most	most	ADV
ejpam-5838	367	8	important	important	ADJ
ejpam-5838	367	9	branches	branch	NOUN
ejpam-5838	367	10	of	of	ADP
ejpam-5838	367	11	mathematics	mathematic	NOUN
ejpam-5838	367	12	,	,	PUNCT
ejpam-5838	367	13	spanning	span	VERB
ejpam-5838	367	14	both	both	CCONJ
ejpam-5838	367	15	pure	pure	ADJ
ejpam-5838	367	16	and	and	CCONJ
ejpam-5838	367	17	practical	practical	ADJ
ejpam-5838	367	18	fields	field	NOUN
ejpam-5838	367	19	,	,	PUNCT
ejpam-5838	367	20	is	be	AUX
ejpam-5838	367	21	fixed	fix	VERB
ejpam-5838	367	22	point	point	NOUN
ejpam-5838	367	23	theory	theory	NOUN
ejpam-5838	367	24	.	.	PUNCT
ejpam-5838	368	1	functional	functional	ADJ
ejpam-5838	368	2	analysis	analysis	NOUN
ejpam-5838	368	3	,	,	PUNCT
ejpam-5838	368	4	an	an	DET
ejpam-5838	368	5	intriguing	intriguing	ADJ
ejpam-5838	368	6	area	area	NOUN
ejpam-5838	368	7	of	of	ADP
ejpam-5838	368	8	mathematics	mathematic	NOUN
ejpam-5838	368	9	with	with	ADP
ejpam-5838	368	10	broad	broad	ADJ
ejpam-5838	368	11	applications	application	NOUN
ejpam-5838	368	12	,	,	PUNCT
ejpam-5838	368	13	is	be	AUX
ejpam-5838	368	14	built	build	VERB
ejpam-5838	368	15	upon	upon	SCONJ
ejpam-5838	368	16	it	it	PRON
ejpam-5838	368	17	.	.	PUNCT
ejpam-5838	369	1	finding	find	VERB
ejpam-5838	369	2	the	the	DET
ejpam-5838	369	3	fixed	fix	VERB
ejpam-5838	369	4	points	point	NOUN
ejpam-5838	369	5	of	of	ADP
ejpam-5838	369	6	functions	function	NOUN
ejpam-5838	369	7	is	be	AUX
ejpam-5838	369	8	an	an	DET
ejpam-5838	369	9	efficient	efficient	ADJ
ejpam-5838	369	10	way	way	NOUN
ejpam-5838	369	11	to	to	PART
ejpam-5838	369	12	solve	solve	VERB
ejpam-5838	369	13	a	a	DET
ejpam-5838	369	14	lot	lot	NOUN
ejpam-5838	369	15	of	of	ADP
ejpam-5838	369	16	mathematical	mathematical	ADJ
ejpam-5838	369	17	issues	issue	NOUN
ejpam-5838	369	18	.	.	PUNCT
ejpam-5838	370	1	several	several	ADJ
ejpam-5838	370	2	generalized	generalized	ADJ
ejpam-5838	370	3	common	common	ADJ
ejpam-5838	370	4	fixed	fix	VERB
ejpam-5838	370	5	point	point	NOUN
ejpam-5838	370	6	(	(	PUNCT
ejpam-5838	370	7	cfp	cfp	NOUN
ejpam-5838	370	8	)	)	PUNCT
ejpam-5838	370	9	theorems	theorem	NOUN
ejpam-5838	370	10	for	for	ADP
ejpam-5838	370	11	three	three	NUM
ejpam-5838	370	12	self	self	NOUN
ejpam-5838	370	13	-	-	PUNCT
ejpam-5838	370	14	mappings	mapping	NOUN
ejpam-5838	370	15	in	in	ADP
ejpam-5838	370	16	generalized	generalized	ADJ
ejpam-5838	370	17	metric	metric	ADJ
ejpam-5838	370	18	spaces	space	NOUN
ejpam-5838	370	19	(	(	PUNCT
ejpam-5838	370	20	gm	gm	NOUN
ejpam-5838	370	21	-	-	PUNCT
ejpam-5838	370	22	spaces	space	NOUN
ejpam-5838	370	23	)	)	PUNCT
ejpam-5838	370	24	are	be	AUX
ejpam-5838	370	25	investigated	investigate	VERB
ejpam-5838	370	26	in	in	ADP
ejpam-5838	370	27	this	this	DET
ejpam-5838	370	28	work	work	NOUN
ejpam-5838	370	29	.	.	PUNCT
ejpam-5838	371	1	for	for	ADP
ejpam-5838	371	2	these	these	DET
ejpam-5838	371	3	mappings	mapping	NOUN
ejpam-5838	371	4	,	,	PUNCT
ejpam-5838	371	5	we	we	PRON
ejpam-5838	371	6	proved	prove	VERB
ejpam-5838	371	7	various	various	ADJ
ejpam-5838	371	8	cfp	cfp	NOUN
ejpam-5838	371	9	and	and	CCONJ
ejpam-5838	371	10	contractive	contractive	ADJ
ejpam-5838	371	11	-	-	PUNCT
ejpam-5838	371	12	type	type	NOUN
ejpam-5838	371	13	fixed	fix	VERB
ejpam-5838	371	14	point	point	NOUN
ejpam-5838	371	15	results	result	NOUN
ejpam-5838	371	16	using	use	VERB
ejpam-5838	371	17	various	various	ADJ
ejpam-5838	371	18	kinds	kind	NOUN
ejpam-5838	371	19	of	of	ADP
ejpam-5838	371	20	integral	integral	ADJ
ejpam-5838	371	21	operators	operator	NOUN
ejpam-5838	371	22	.	.	PUNCT
ejpam-5838	372	1	furthermore	furthermore	ADV
ejpam-5838	372	2	,	,	PUNCT
ejpam-5838	372	3	we	we	PRON
ejpam-5838	372	4	gave	give	VERB
ejpam-5838	372	5	a	a	DET
ejpam-5838	372	6	convincing	convincing	ADJ
ejpam-5838	372	7	example	example	NOUN
ejpam-5838	372	8	showing	show	VERB
ejpam-5838	372	9	that	that	SCONJ
ejpam-5838	372	10	a	a	DET
ejpam-5838	372	11	cfp	cfp	NOUN
ejpam-5838	372	12	for	for	ADP
ejpam-5838	372	13	generalized	generalized	ADJ
ejpam-5838	372	14	contractions	contraction	NOUN
ejpam-5838	372	15	in	in	ADP
ejpam-5838	372	16	the	the	DET
ejpam-5838	372	17	given	give	VERB
ejpam-5838	372	18	space	space	NOUN
ejpam-5838	372	19	is	be	AUX
ejpam-5838	372	20	unique	unique	ADJ
ejpam-5838	372	21	.	.	PUNCT
ejpam-5838	373	1	we	we	PRON
ejpam-5838	373	2	also	also	ADV
ejpam-5838	373	3	explored	explore	VERB
ejpam-5838	373	4	a	a	DET
ejpam-5838	373	5	nonlinear	nonlinear	ADJ
ejpam-5838	373	6	integral	integral	ADJ
ejpam-5838	373	7	equation	equation	NOUN
ejpam-5838	373	8	application	application	NOUN
ejpam-5838	373	9	to	to	PART
ejpam-5838	373	10	support	support	VERB
ejpam-5838	373	11	our	our	PRON
ejpam-5838	373	12	results	result	NOUN
ejpam-5838	373	13	on	on	ADP
ejpam-5838	373	14	the	the	DET
ejpam-5838	373	15	presence	presence	NOUN
ejpam-5838	373	16	of	of	ADP
ejpam-5838	373	17	a	a	DET
ejpam-5838	373	18	unique	unique	ADJ
ejpam-5838	373	19	common	common	ADJ
ejpam-5838	373	20	solution	solution	NOUN
ejpam-5838	373	21	.	.	PUNCT
ejpam-5838	374	1	looking	look	VERB
ejpam-5838	374	2	ahead	ahead	ADV
ejpam-5838	374	3	,	,	PUNCT
ejpam-5838	374	4	we	we	PRON
ejpam-5838	374	5	aim	aim	VERB
ejpam-5838	374	6	to	to	PART
ejpam-5838	374	7	extend	extend	VERB
ejpam-5838	374	8	our	our	PRON
ejpam-5838	374	9	research	research	NOUN
ejpam-5838	374	10	by	by	ADP
ejpam-5838	374	11	developing	develop	VERB
ejpam-5838	374	12	fixed	fix	VERB
ejpam-5838	374	13	point	point	NOUN
ejpam-5838	374	14	theorems	theorem	NOUN
ejpam-5838	374	15	in	in	ADP
ejpam-5838	374	16	generalized	generalized	ADJ
ejpam-5838	374	17	soft	soft	ADJ
ejpam-5838	374	18	metric	metric	ADJ
ejpam-5838	374	19	spaces	space	NOUN
ejpam-5838	374	20	,	,	PUNCT
ejpam-5838	374	21	looking	look	VERB
ejpam-5838	374	22	at	at	ADP
ejpam-5838	374	23	fresh	fresh	ADJ
ejpam-5838	374	24	ways	way	NOUN
ejpam-5838	374	25	to	to	PART
ejpam-5838	374	26	apply	apply	VERB
ejpam-5838	374	27	these	these	DET
ejpam-5838	374	28	theorems	theorem	NOUN
ejpam-5838	374	29	in	in	ADP
ejpam-5838	374	30	different	different	ADJ
ejpam-5838	374	31	mathematical	mathematical	ADJ
ejpam-5838	374	32	contexts	contexts	NOUN
ejpam-5838	374	33	,	,	PUNCT
ejpam-5838	374	34	and	and	CCONJ
ejpam-5838	374	35	examining	examine	VERB
ejpam-5838	374	36	how	how	SCONJ
ejpam-5838	374	37	fixed	fix	VERB
ejpam-5838	374	38	point	point	NOUN
ejpam-5838	374	39	theory	theory	NOUN
ejpam-5838	374	40	interacts	interact	VERB
ejpam-5838	374	41	with	with	ADP
ejpam-5838	374	42	other	other	ADJ
ejpam-5838	374	43	fields	field	NOUN
ejpam-5838	374	44	like	like	ADP
ejpam-5838	374	45	dynamical	dynamical	ADJ
ejpam-5838	374	46	systems	system	NOUN
ejpam-5838	374	47	and	and	CCONJ
ejpam-5838	374	48	optimization	optimization	NOUN
ejpam-5838	374	49	.	.	PUNCT
ejpam-5838	375	1	in	in	ADP
ejpam-5838	375	2	addition	addition	NOUN
ejpam-5838	375	3	to	to	ADP
ejpam-5838	375	4	adding	add	VERB
ejpam-5838	375	5	to	to	ADP
ejpam-5838	375	6	the	the	DET
ejpam-5838	375	7	theoretical	theoretical	ADJ
ejpam-5838	375	8	framework	framework	NOUN
ejpam-5838	375	9	,	,	PUNCT
ejpam-5838	375	10	this	this	DET
ejpam-5838	375	11	upcoming	upcoming	ADJ
ejpam-5838	375	12	study	study	NOUN
ejpam-5838	375	13	will	will	AUX
ejpam-5838	375	14	improve	improve	VERB
ejpam-5838	375	15	real	real	ADJ
ejpam-5838	375	16	-	-	PUNCT
ejpam-5838	375	17	world	world	NOUN
ejpam-5838	375	18	practical	practical	ADJ
ejpam-5838	375	19	applications	application	NOUN
ejpam-5838	375	20	.	.	PUNCT
ejpam-5838	376	1	in	in	ADP
ejpam-5838	376	2	future	future	ADJ
ejpam-5838	376	3	research	research	NOUN
ejpam-5838	376	4	,	,	PUNCT
ejpam-5838	376	5	we	we	PRON
ejpam-5838	376	6	aim	aim	VERB
ejpam-5838	376	7	to	to	PART
ejpam-5838	376	8	generalize	generalize	VERB
ejpam-5838	376	9	our	our	PRON
ejpam-5838	376	10	results	result	NOUN
ejpam-5838	376	11	to	to	ADP
ejpam-5838	376	12	systems	system	NOUN
ejpam-5838	376	13	involving	involve	VERB
ejpam-5838	376	14	four	four	NUM
ejpam-5838	376	15	or	or	CCONJ
ejpam-5838	376	16	more	more	ADJ
ejpam-5838	376	17	self	self	NOUN
ejpam-5838	376	18	-	-	PUNCT
ejpam-5838	376	19	mappings	mapping	NOUN
ejpam-5838	376	20	under	under	ADP
ejpam-5838	376	21	similar	similar	ADJ
ejpam-5838	376	22	contractive	contractive	ADJ
ejpam-5838	376	23	-	-	PUNCT
ejpam-5838	376	24	type	type	NOUN
ejpam-5838	376	25	conditions	condition	NOUN
ejpam-5838	376	26	.	.	PUNCT
ejpam-5838	377	1	extending	extend	VERB
ejpam-5838	377	2	the	the	DET
ejpam-5838	377	3	framework	framework	NOUN
ejpam-5838	377	4	to	to	ADP
ejpam-5838	377	5	n	n	CCONJ
ejpam-5838	377	6	-	-	PUNCT
ejpam-5838	377	7	self	self	NOUN
ejpam-5838	377	8	-	-	PUNCT
ejpam-5838	377	9	mappings	mapping	NOUN
ejpam-5838	377	10	will	will	AUX
ejpam-5838	377	11	require	require	VERB
ejpam-5838	377	12	the	the	DET
ejpam-5838	377	13	definition	definition	NOUN
ejpam-5838	377	14	of	of	ADP
ejpam-5838	377	15	a	a	DET
ejpam-5838	377	16	suitable	suitable	ADJ
ejpam-5838	377	17	iterative	iterative	NOUN
ejpam-5838	377	18	sequence	sequence	NOUN
ejpam-5838	377	19	and	and	CCONJ
ejpam-5838	377	20	the	the	DET
ejpam-5838	377	21	establishment	establishment	NOUN
ejpam-5838	377	22	of	of	ADP
ejpam-5838	377	23	a	a	DET
ejpam-5838	377	24	generalized	generalize	VERB
ejpam-5838	377	25	contractive	contractive	ADJ
ejpam-5838	377	26	inequality	inequality	NOUN
ejpam-5838	377	27	that	that	PRON
ejpam-5838	377	28	effectively	effectively	ADV
ejpam-5838	377	29	captures	capture	VERB
ejpam-5838	377	30	the	the	DET
ejpam-5838	377	31	interactions	interaction	NOUN
ejpam-5838	377	32	among	among	ADP
ejpam-5838	377	33	multiple	multiple	ADJ
ejpam-5838	377	34	mappings	mapping	NOUN
ejpam-5838	377	35	.	.	PUNCT
ejpam-5838	378	1	while	while	SCONJ
ejpam-5838	378	2	this	this	DET
ejpam-5838	378	3	generalization	generalization	NOUN
ejpam-5838	378	4	is	be	AUX
ejpam-5838	378	5	conceptually	conceptually	ADV
ejpam-5838	378	6	similar	similar	ADJ
ejpam-5838	378	7	to	to	ADP
ejpam-5838	378	8	the	the	DET
ejpam-5838	378	9	approach	approach	NOUN
ejpam-5838	378	10	used	use	VERB
ejpam-5838	378	11	for	for	ADP
ejpam-5838	378	12	three	three	NUM
ejpam-5838	378	13	mappings	mapping	NOUN
ejpam-5838	378	14	,	,	PUNCT
ejpam-5838	378	15	it	it	PRON
ejpam-5838	378	16	introduces	introduce	VERB
ejpam-5838	378	17	additional	additional	ADJ
ejpam-5838	378	18	combinatorial	combinatorial	ADJ
ejpam-5838	378	19	and	and	CCONJ
ejpam-5838	378	20	analytical	analytical	ADJ
ejpam-5838	378	21	challenges	challenge	NOUN
ejpam-5838	378	22	.	.	PUNCT
ejpam-5838	379	1	several	several	ADJ
ejpam-5838	379	2	important	important	ADJ
ejpam-5838	379	3	considerations	consideration	NOUN
ejpam-5838	379	4	will	will	AUX
ejpam-5838	379	5	guide	guide	VERB
ejpam-5838	379	6	this	this	DET
ejpam-5838	379	7	extension	extension	NOUN
ejpam-5838	379	8	:	:	PUNCT
ejpam-5838	379	9	(	(	PUNCT
ejpam-5838	379	10	i	i	NOUN
ejpam-5838	379	11	)	)	PUNCT
ejpam-5838	379	12	structural	structural	ADJ
ejpam-5838	379	13	complexity	complexity	NOUN
ejpam-5838	379	14	:	:	PUNCT
ejpam-5838	379	15	the	the	DET
ejpam-5838	379	16	contractive	contractive	ADJ
ejpam-5838	379	17	condition	condition	NOUN
ejpam-5838	379	18	becomes	become	VERB
ejpam-5838	379	19	increasingly	increasingly	ADV
ejpam-5838	379	20	intricate	intricate	ADJ
ejpam-5838	379	21	,	,	PUNCT
ejpam-5838	379	22	as	as	SCONJ
ejpam-5838	379	23	additional	additional	ADJ
ejpam-5838	379	24	terms	term	NOUN
ejpam-5838	379	25	are	be	AUX
ejpam-5838	379	26	needed	need	VERB
ejpam-5838	379	27	to	to	PART
ejpam-5838	379	28	account	account	VERB
ejpam-5838	379	29	for	for	ADP
ejpam-5838	379	30	all	all	DET
ejpam-5838	379	31	pairwise	pairwise	NOUN
ejpam-5838	379	32	,	,	PUNCT
ejpam-5838	379	33	triplet	triplet	NOUN
ejpam-5838	379	34	,	,	PUNCT
ejpam-5838	379	35	and	and	CCONJ
ejpam-5838	379	36	potentially	potentially	ADV
ejpam-5838	379	37	higherorder	higherorder	VERB
ejpam-5838	379	38	interactions	interaction	NOUN
ejpam-5838	379	39	among	among	ADP
ejpam-5838	379	40	the	the	DET
ejpam-5838	379	41	mappings	mapping	NOUN
ejpam-5838	379	42	.	.	PUNCT
ejpam-5838	380	1	(	(	PUNCT
ejpam-5838	380	2	ii	ii	NOUN
ejpam-5838	380	3	)	)	PUNCT
ejpam-5838	380	4	convergence	convergence	NOUN
ejpam-5838	380	5	analysis	analysis	NOUN
ejpam-5838	380	6	:	:	PUNCT
ejpam-5838	380	7	the	the	DET
ejpam-5838	380	8	iterative	iterative	NOUN
ejpam-5838	380	9	scheme	scheme	NOUN
ejpam-5838	380	10	for	for	ADP
ejpam-5838	380	11	n	n	NOUN
ejpam-5838	380	12	-	-	PUNCT
ejpam-5838	380	13	mappings	mapping	NOUN
ejpam-5838	380	14	will	will	AUX
ejpam-5838	380	15	likely	likely	ADV
ejpam-5838	380	16	necessitate	necessitate	ADJ
ejpam-5838	380	17	more	more	ADV
ejpam-5838	380	18	generalized	generalized	ADJ
ejpam-5838	380	19	recurrence	recurrence	NOUN
ejpam-5838	380	20	relations	relation	NOUN
ejpam-5838	380	21	and	and	CCONJ
ejpam-5838	380	22	potentially	potentially	ADV
ejpam-5838	380	23	stronger	strong	ADJ
ejpam-5838	380	24	assumptions	assumption	NOUN
ejpam-5838	380	25	to	to	PART
ejpam-5838	380	26	ensure	ensure	VERB
ejpam-5838	380	27	convergence	convergence	NOUN
ejpam-5838	380	28	.	.	PUNCT
ejpam-5838	381	1	(	(	PUNCT
ejpam-5838	381	2	iii	iii	X
ejpam-5838	381	3	)	)	PUNCT
ejpam-5838	381	4	uniqueness	uniqueness	NOUN
ejpam-5838	381	5	conditions	condition	NOUN
ejpam-5838	381	6	:	:	PUNCT
ejpam-5838	381	7	for	for	ADP
ejpam-5838	381	8	n	n	PROPN
ejpam-5838	381	9	>	>	X
ejpam-5838	381	10	3	3	NUM
ejpam-5838	381	11	,	,	PUNCT
ejpam-5838	381	12	further	further	ADJ
ejpam-5838	381	13	conditions	condition	NOUN
ejpam-5838	381	14	may	may	AUX
ejpam-5838	381	15	be	be	AUX
ejpam-5838	381	16	required	require	VERB
ejpam-5838	381	17	to	to	PART
ejpam-5838	381	18	establish	establish	VERB
ejpam-5838	381	19	the	the	DET
ejpam-5838	381	20	uniqueness	uniqueness	NOUN
ejpam-5838	381	21	of	of	ADP
ejpam-5838	381	22	a	a	DET
ejpam-5838	381	23	common	common	ADJ
ejpam-5838	381	24	fixed	fix	VERB
ejpam-5838	381	25	point	point	NOUN
ejpam-5838	381	26	.	.	PUNCT
ejpam-5838	382	1	despite	despite	SCONJ
ejpam-5838	382	2	these	these	DET
ejpam-5838	382	3	challenges	challenge	NOUN
ejpam-5838	382	4	,	,	PUNCT
ejpam-5838	382	5	the	the	DET
ejpam-5838	382	6	foundational	foundational	ADJ
ejpam-5838	382	7	principles	principle	NOUN
ejpam-5838	382	8	of	of	ADP
ejpam-5838	382	9	our	our	PRON
ejpam-5838	382	10	current	current	ADJ
ejpam-5838	382	11	approach	approach	NOUN
ejpam-5838	382	12	remain	remain	VERB
ejpam-5838	382	13	applicable	applicable	ADJ
ejpam-5838	382	14	.	.	PUNCT
ejpam-5838	383	1	we	we	PRON
ejpam-5838	383	2	believe	believe	VERB
ejpam-5838	383	3	that	that	SCONJ
ejpam-5838	383	4	with	with	ADP
ejpam-5838	383	5	suitable	suitable	ADJ
ejpam-5838	383	6	modifications	modification	NOUN
ejpam-5838	383	7	,	,	PUNCT
ejpam-5838	383	8	the	the	DET
ejpam-5838	383	9	results	result	NOUN
ejpam-5838	383	10	can	can	AUX
ejpam-5838	383	11	be	be	AUX
ejpam-5838	383	12	effectively	effectively	ADV
ejpam-5838	383	13	extended	extend	VERB
ejpam-5838	383	14	to	to	ADP
ejpam-5838	383	15	n	n	CCONJ
ejpam-5838	383	16	-	-	PUNCT
ejpam-5838	383	17	mappings	mapping	NOUN
ejpam-5838	383	18	.	.	PUNCT
ejpam-5838	384	1	exploring	explore	VERB
ejpam-5838	384	2	these	these	DET
ejpam-5838	384	3	generalizations	generalization	NOUN
ejpam-5838	384	4	represents	represent	VERB
ejpam-5838	384	5	a	a	DET
ejpam-5838	384	6	promising	promising	ADJ
ejpam-5838	384	7	and	and	CCONJ
ejpam-5838	384	8	natural	natural	ADJ
ejpam-5838	384	9	continuation	continuation	NOUN
ejpam-5838	384	10	of	of	ADP
ejpam-5838	384	11	the	the	DET
ejpam-5838	384	12	present	present	ADJ
ejpam-5838	384	13	work	work	NOUN
ejpam-5838	384	14	,	,	PUNCT
ejpam-5838	384	15	and	and	CCONJ
ejpam-5838	384	16	we	we	PRON
ejpam-5838	384	17	intend	intend	VERB
ejpam-5838	384	18	to	to	PART
ejpam-5838	384	19	pursue	pursue	VERB
ejpam-5838	384	20	this	this	DET
ejpam-5838	384	21	direction	direction	NOUN
ejpam-5838	384	22	in	in	ADP
ejpam-5838	384	23	our	our	PRON
ejpam-5838	384	24	forthcoming	forthcoming	ADJ
ejpam-5838	384	25	studies	study	NOUN
ejpam-5838	384	26	.	.	PUNCT
ejpam-5838	385	1	acknowledgements	acknowledgement	NOUN
ejpam-5838	385	2	the	the	DET
ejpam-5838	385	3	authors	author	NOUN
ejpam-5838	385	4	extend	extend	VERB
ejpam-5838	385	5	their	their	PRON
ejpam-5838	385	6	appreciation	appreciation	NOUN
ejpam-5838	385	7	to	to	ADP
ejpam-5838	385	8	the	the	DET
ejpam-5838	385	9	arab	arab	PROPN
ejpam-5838	385	10	open	open	PROPN
ejpam-5838	385	11	university	university	PROPN
ejpam-5838	385	12	for	for	ADP
ejpam-5838	385	13	supporting	support	VERB
ejpam-5838	385	14	this	this	DET
ejpam-5838	385	15	work	work	NOUN
ejpam-5838	385	16	.	.	PUNCT
ejpam-5838	386	1	m.	m.	NOUN
ejpam-5838	386	2	noorwali	noorwali	PROPN
ejpam-5838	386	3	et	et	PROPN
ejpam-5838	386	4	al/	al/	PROPN
ejpam-5838	386	5	/	/	SYM
ejpam-5838	386	6	eur	eur	PROPN
ejpam-5838	386	7	.	.	PUNCT
ejpam-5838	387	1	j.	j.	PROPN
ejpam-5838	387	2	pure	pure	PROPN
ejpam-5838	387	3	appl	appl	PROPN
ejpam-5838	387	4	.	.	PROPN
ejpam-5838	387	5	math	math	PROPN
ejpam-5838	387	6	,	,	PUNCT
ejpam-5838	387	7	18	18	NUM
ejpam-5838	387	8	(	(	PUNCT
ejpam-5838	387	9	2	2	NUM
ejpam-5838	387	10	)	)	PUNCT
ejpam-5838	387	11	(	(	PUNCT
ejpam-5838	387	12	2025	2025	NUM
ejpam-5838	387	13	)	)	PUNCT
ejpam-5838	387	14	,	,	PUNCT
ejpam-5838	387	15	5838	5838	NUM
ejpam-5838	387	16	15	15	NUM
ejpam-5838	387	17	of	of	ADP
ejpam-5838	387	18	16	16	NUM
ejpam-5838	387	19	author	author	NOUN
ejpam-5838	387	20	contributions	contribution	NOUN
ejpam-5838	387	21	:	:	PUNCT
ejpam-5838	387	22	all	all	DET
ejpam-5838	387	23	authors	author	NOUN
ejpam-5838	387	24	equally	equally	ADV
ejpam-5838	387	25	contributed	contribute	VERB
ejpam-5838	387	26	.	.	PUNCT
ejpam-5838	388	1	conflicts	conflict	NOUN
ejpam-5838	388	2	of	of	ADP
ejpam-5838	388	3	interest	interest	NOUN
ejpam-5838	388	4	:	:	PUNCT
ejpam-5838	388	5	the	the	DET
ejpam-5838	388	6	authors	author	NOUN
ejpam-5838	388	7	declare	declare	VERB
ejpam-5838	388	8	no	no	DET
ejpam-5838	388	9	conflict	conflict	NOUN
ejpam-5838	388	10	of	of	ADP
ejpam-5838	388	11	interest	interest	NOUN
ejpam-5838	388	12	.	.	PUNCT
ejpam-5838	389	1	data	datum	NOUN
ejpam-5838	389	2	availability	availability	NOUN
ejpam-5838	389	3	:	:	PUNCT
ejpam-5838	389	4	all	all	DET
ejpam-5838	389	5	the	the	DET
ejpam-5838	389	6	data	datum	NOUN
ejpam-5838	389	7	is	be	AUX
ejpam-5838	389	8	provided	provide	VERB
ejpam-5838	389	9	in	in	ADP
ejpam-5838	389	10	the	the	DET
ejpam-5838	389	11	manuscript	manuscript	NOUN
ejpam-5838	389	12	.	.	PUNCT
ejpam-5838	390	1	references	reference	NOUN
ejpam-5838	390	2	[	[	X
ejpam-5838	390	3	1	1	X
ejpam-5838	390	4	]	]	PUNCT
ejpam-5838	390	5	s.	s.	PROPN
ejpam-5838	390	6	banach	banach	PROPN
ejpam-5838	390	7	.	.	PUNCT
ejpam-5838	391	1	sur	sur	PROPN
ejpam-5838	391	2	les	les	X
ejpam-5838	391	3	opérations	opération	NOUN
ejpam-5838	391	4	dans	dan	NOUN
ejpam-5838	391	5	les	les	X
ejpam-5838	391	6	ensembles	ensemble	NOUN
ejpam-5838	391	7	abstraits	abstrait	NOUN
ejpam-5838	391	8	et	et	PROPN
ejpam-5838	391	9	leur	leur	X
ejpam-5838	391	10	application	application	PROPN
ejpam-5838	391	11	aux	aux	PROPN
ejpam-5838	391	12	équations	équations	PROPN
ejpam-5838	391	13	intégrales	intégrale	NOUN
ejpam-5838	391	14	.	.	PUNCT
ejpam-5838	392	1	fundamenta	fundamenta	PROPN
ejpam-5838	392	2	mathematicae	mathematicae	PROPN
ejpam-5838	392	3	,	,	PUNCT
ejpam-5838	392	4	3(1):133–181	3(1):133–181	NUM
ejpam-5838	392	5	,	,	PUNCT
ejpam-5838	392	6	1922	1922	NUM
ejpam-5838	392	7	.	.	PUNCT
ejpam-5838	393	1	[	[	X
ejpam-5838	393	2	2	2	NUM
ejpam-5838	393	3	]	]	X
ejpam-5838	393	4	r.	r.	PROPN
ejpam-5838	393	5	batra	batra	PROPN
ejpam-5838	393	6	,	,	PUNCT
ejpam-5838	393	7	r.	r.	PROPN
ejpam-5838	393	8	gupta	gupta	PROPN
ejpam-5838	393	9	,	,	PUNCT
ejpam-5838	393	10	and	and	CCONJ
ejpam-5838	393	11	p.	p.	PROPN
ejpam-5838	393	12	sahni	sahni	PROPN
ejpam-5838	393	13	.	.	PUNCT
ejpam-5838	394	1	a	a	DET
ejpam-5838	394	2	new	new	ADJ
ejpam-5838	394	3	extension	extension	NOUN
ejpam-5838	394	4	of	of	ADP
ejpam-5838	394	5	kannan	kannan	PROPN
ejpam-5838	394	6	contractions	contraction	NOUN
ejpam-5838	394	7	and	and	CCONJ
ejpam-5838	394	8	related	relate	VERB
ejpam-5838	394	9	fixed	fix	VERB
ejpam-5838	394	10	point	point	NOUN
ejpam-5838	394	11	results	result	NOUN
ejpam-5838	394	12	.	.	PUNCT
ejpam-5838	395	1	the	the	DET
ejpam-5838	395	2	journal	journal	NOUN
ejpam-5838	395	3	of	of	ADP
ejpam-5838	395	4	analysis	analysis	NOUN
ejpam-5838	395	5	,	,	PUNCT
ejpam-5838	395	6	28(4):1143–1154	28(4):1143–1154	NUM
ejpam-5838	395	7	,	,	PUNCT
ejpam-5838	395	8	2020	2020	NUM
ejpam-5838	395	9	.	.	PUNCT
ejpam-5838	396	1	[	[	X
ejpam-5838	396	2	3	3	X
ejpam-5838	396	3	]	]	X
ejpam-5838	396	4	p.	p.	NOUN
ejpam-5838	396	5	debnath	debnath	PROPN
ejpam-5838	396	6	.	.	PUNCT
ejpam-5838	397	1	banach	banach	PROPN
ejpam-5838	397	2	,	,	PUNCT
ejpam-5838	397	3	kannan	kannan	PROPN
ejpam-5838	397	4	,	,	PUNCT
ejpam-5838	397	5	chatterjea	chatterjea	PROPN
ejpam-5838	397	6	,	,	PUNCT
ejpam-5838	397	7	and	and	CCONJ
ejpam-5838	397	8	reich	reich	NOUN
ejpam-5838	397	9	-	-	PUNCT
ejpam-5838	397	10	type	type	NOUN
ejpam-5838	397	11	contractive	contractive	ADJ
ejpam-5838	397	12	inequalities	inequality	NOUN
ejpam-5838	397	13	for	for	ADP
ejpam-5838	397	14	multivalued	multivalued	ADJ
ejpam-5838	397	15	mappings	mapping	NOUN
ejpam-5838	397	16	and	and	CCONJ
ejpam-5838	397	17	their	their	PRON
ejpam-5838	397	18	common	common	ADJ
ejpam-5838	397	19	fixed	fix	VERB
ejpam-5838	397	20	points	point	NOUN
ejpam-5838	397	21	.	.	PUNCT
ejpam-5838	398	1	mathematical	mathematical	ADJ
ejpam-5838	398	2	methods	method	NOUN
ejpam-5838	398	3	in	in	ADP
ejpam-5838	398	4	the	the	DET
ejpam-5838	398	5	applied	apply	VERB
ejpam-5838	398	6	sciences	science	NOUN
ejpam-5838	398	7	,	,	PUNCT
ejpam-5838	398	8	45(3):1587–1596	45(3):1587–1596	NUM
ejpam-5838	398	9	,	,	PUNCT
ejpam-5838	398	10	2022	2022	NUM
ejpam-5838	398	11	.	.	PUNCT
ejpam-5838	399	1	[	[	X
ejpam-5838	399	2	4	4	NUM
ejpam-5838	399	3	]	]	X
ejpam-5838	399	4	di	di	X
ejpam-5838	399	5	palermo	palermo	NOUN
ejpam-5838	399	6	.	.	PUNCT
ejpam-5838	400	1	supplemento	supplemento	NOUN
ejpam-5838	400	2	ai	ai	VERB
ejpam-5838	400	3	rendiconti	rendiconti	ADJ
ejpam-5838	400	4	del	del	X
ejpam-5838	400	5	circolo	circolo	PROPN
ejpam-5838	400	6	matematico	matematico	NOUN
ejpam-5838	400	7	di	di	NOUN
ejpam-5838	400	8	palermo	palermo	PROPN
ejpam-5838	400	9	.	.	PUNCT
ejpam-5838	401	1	rendiconti	rendiconti	PROPN
ejpam-5838	401	2	del	del	PROPN
ejpam-5838	401	3	circolo	circolo	PROPN
ejpam-5838	401	4	matematico	matematico	NOUN
ejpam-5838	401	5	di	di	NOUN
ejpam-5838	401	6	palermo	palermo	NOUN
ejpam-5838	401	7	,	,	PUNCT
ejpam-5838	401	8	38–40:3	38–40:3	NUM
ejpam-5838	401	9	,	,	PUNCT
ejpam-5838	401	10	1995	1995	NUM
ejpam-5838	401	11	.	.	PUNCT
ejpam-5838	402	1	[	[	X
ejpam-5838	402	2	5	5	X
ejpam-5838	402	3	]	]	PUNCT
ejpam-5838	402	4	l.	l.	PROPN
ejpam-5838	402	5	g.	g.	PROPN
ejpam-5838	402	6	huang	huang	PROPN
ejpam-5838	402	7	and	and	CCONJ
ejpam-5838	402	8	x.	x.	PROPN
ejpam-5838	402	9	zhang	zhang	PROPN
ejpam-5838	402	10	.	.	PUNCT
ejpam-5838	403	1	cone	cone	PROPN
ejpam-5838	403	2	metric	metric	ADJ
ejpam-5838	403	3	spaces	space	NOUN
ejpam-5838	403	4	and	and	CCONJ
ejpam-5838	403	5	fixed	fix	VERB
ejpam-5838	403	6	point	point	NOUN
ejpam-5838	403	7	theorems	theorem	NOUN
ejpam-5838	403	8	of	of	ADP
ejpam-5838	403	9	contractive	contractive	ADJ
ejpam-5838	403	10	mappings	mapping	NOUN
ejpam-5838	403	11	.	.	PUNCT
ejpam-5838	404	1	journal	journal	PROPN
ejpam-5838	404	2	of	of	ADP
ejpam-5838	404	3	mathematical	mathematical	ADJ
ejpam-5838	404	4	analysis	analysis	NOUN
ejpam-5838	404	5	and	and	CCONJ
ejpam-5838	404	6	applications	application	NOUN
ejpam-5838	404	7	,	,	PUNCT
ejpam-5838	404	8	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-5838	404	9	,	,	PUNCT
ejpam-5838	404	10	2007	2007	NUM
ejpam-5838	404	11	.	.	PUNCT
ejpam-5838	405	1	[	[	X
ejpam-5838	405	2	6	6	NUM
ejpam-5838	405	3	]	]	X
ejpam-5838	405	4	florin	florin	PROPN
ejpam-5838	405	5	bojor	bojor	PROPN
ejpam-5838	405	6	.	.	PUNCT
ejpam-5838	406	1	fixed	fix	VERB
ejpam-5838	406	2	point	point	NOUN
ejpam-5838	406	3	theorems	theorem	NOUN
ejpam-5838	406	4	for	for	ADP
ejpam-5838	406	5	reich	reich	NOUN
ejpam-5838	406	6	type	type	NOUN
ejpam-5838	406	7	contractions	contraction	NOUN
ejpam-5838	406	8	on	on	ADP
ejpam-5838	406	9	metric	metric	ADJ
ejpam-5838	406	10	spaces	space	NOUN
ejpam-5838	406	11	with	with	ADP
ejpam-5838	406	12	a	a	DET
ejpam-5838	406	13	graph	graph	NOUN
ejpam-5838	406	14	.	.	PUNCT
ejpam-5838	407	1	nonlinear	nonlinear	ADJ
ejpam-5838	407	2	analysis	analysis	NOUN
ejpam-5838	407	3	:	:	PUNCT
ejpam-5838	407	4	theory	theory	NOUN
ejpam-5838	407	5	,	,	PUNCT
ejpam-5838	407	6	methods	method	NOUN
ejpam-5838	407	7	&	&	CCONJ
ejpam-5838	407	8	applications	application	NOUN
ejpam-5838	407	9	,	,	PUNCT
ejpam-5838	407	10	75(9):3895–3901	75(9):3895–3901	NUM
ejpam-5838	407	11	,	,	PUNCT
ejpam-5838	407	12	2012	2012	NUM
ejpam-5838	407	13	.	.	PUNCT
ejpam-5838	408	1	[	[	X
ejpam-5838	408	2	7	7	X
ejpam-5838	408	3	]	]	PUNCT
ejpam-5838	408	4	a.	a.	NOUN
ejpam-5838	408	5	a.	a.	PROPN
ejpam-5838	408	6	n.	n.	PROPN
ejpam-5838	408	7	abdou	abdou	PROPN
ejpam-5838	408	8	and	and	CCONJ
ejpam-5838	408	9	m.	m.	NOUN
ejpam-5838	408	10	a.	a.	NOUN
ejpam-5838	408	11	khamsi	khamsi	PROPN
ejpam-5838	408	12	.	.	PUNCT
ejpam-5838	409	1	fixed	fix	VERB
ejpam-5838	409	2	point	point	NOUN
ejpam-5838	409	3	results	result	NOUN
ejpam-5838	409	4	of	of	ADP
ejpam-5838	409	5	pointwise	pointwise	ADJ
ejpam-5838	409	6	contractions	contraction	NOUN
ejpam-5838	409	7	in	in	ADP
ejpam-5838	409	8	modular	modular	ADJ
ejpam-5838	409	9	metric	metric	ADJ
ejpam-5838	409	10	spaces	space	NOUN
ejpam-5838	409	11	.	.	PUNCT
ejpam-5838	410	1	fixed	fix	VERB
ejpam-5838	410	2	point	point	NOUN
ejpam-5838	410	3	theory	theory	NOUN
ejpam-5838	410	4	and	and	CCONJ
ejpam-5838	410	5	applications	application	NOUN
ejpam-5838	410	6	,	,	PUNCT
ejpam-5838	410	7	2013:163	2013:163	NUM
ejpam-5838	410	8	,	,	PUNCT
ejpam-5838	410	9	2013	2013	NUM
ejpam-5838	410	10	.	.	PUNCT
ejpam-5838	411	1	[	[	X
ejpam-5838	411	2	8	8	NUM
ejpam-5838	411	3	]	]	PUNCT
ejpam-5838	411	4	a.	a.	NOUN
ejpam-5838	411	5	ebadian	ebadian	PROPN
ejpam-5838	411	6	,	,	PUNCT
ejpam-5838	411	7	m.	m.	PROPN
ejpam-5838	411	8	e.	e.	PROPN
ejpam-5838	411	9	gordji	gordji	PROPN
ejpam-5838	411	10	,	,	PUNCT
ejpam-5838	411	11	a.	a.	NOUN
ejpam-5838	411	12	zohri	zohri	PROPN
ejpam-5838	411	13	,	,	PUNCT
ejpam-5838	411	14	and	and	CCONJ
ejpam-5838	411	15	i.	i.	PROPN
ejpam-5838	411	16	r.	r.	PROPN
ejpam-5838	411	17	a.	a.	PROPN
ejpam-5838	411	18	n.	n.	PROPN
ejpam-5838	411	19	semnan	semnan	PROPN
ejpam-5838	411	20	.	.	PUNCT
ejpam-5838	412	1	common	common	ADJ
ejpam-5838	412	2	fixed	fix	VERB
ejpam-5838	412	3	point	point	NOUN
ejpam-5838	412	4	theorems	theorem	NOUN
ejpam-5838	412	5	in	in	ADP
ejpam-5838	412	6	modular	modular	ADJ
ejpam-5838	412	7	metric	metric	ADJ
ejpam-5838	412	8	spaces	space	NOUN
ejpam-5838	412	9	.	.	PUNCT
ejpam-5838	413	1	international	international	ADJ
ejpam-5838	413	2	journal	journal	NOUN
ejpam-5838	413	3	of	of	ADP
ejpam-5838	413	4	pure	pure	ADJ
ejpam-5838	413	5	and	and	CCONJ
ejpam-5838	413	6	applied	applied	ADJ
ejpam-5838	413	7	mathematics	mathematic	NOUN
ejpam-5838	413	8	,	,	PUNCT
ejpam-5838	413	9	99(3):373–383	99(3):373–383	PROPN
ejpam-5838	413	10	,	,	PUNCT
ejpam-5838	413	11	2015	2015	NUM
ejpam-5838	413	12	.	.	PUNCT
ejpam-5838	414	1	[	[	X
ejpam-5838	414	2	9	9	NUM
ejpam-5838	414	3	]	]	PUNCT
ejpam-5838	414	4	z.	z.	PROPN
ejpam-5838	414	5	mustafa	mustafa	PROPN
ejpam-5838	414	6	and	and	CCONJ
ejpam-5838	414	7	b.	b.	PROPN
ejpam-5838	414	8	sims	sim	NOUN
ejpam-5838	414	9	.	.	PUNCT
ejpam-5838	415	1	a	a	DET
ejpam-5838	415	2	new	new	ADJ
ejpam-5838	415	3	approach	approach	NOUN
ejpam-5838	415	4	to	to	ADP
ejpam-5838	415	5	generalized	generalize	VERB
ejpam-5838	415	6	metric	metric	ADJ
ejpam-5838	415	7	spaces	space	NOUN
ejpam-5838	415	8	.	.	PUNCT
ejpam-5838	416	1	journal	journal	PROPN
ejpam-5838	416	2	of	of	ADP
ejpam-5838	416	3	nonlinear	nonlinear	ADJ
ejpam-5838	416	4	and	and	CCONJ
ejpam-5838	416	5	convex	convex	ADJ
ejpam-5838	416	6	analysis	analysis	NOUN
ejpam-5838	416	7	,	,	PUNCT
ejpam-5838	416	8	7(2):289–297	7(2):289–297	NOUN
ejpam-5838	416	9	,	,	PUNCT
ejpam-5838	416	10	2006	2006	NUM
ejpam-5838	416	11	.	.	PUNCT
ejpam-5838	417	1	[	[	X
ejpam-5838	417	2	10	10	NUM
ejpam-5838	417	3	]	]	PUNCT
ejpam-5838	417	4	p.	p.	NOUN
ejpam-5838	417	5	das	das	PROPN
ejpam-5838	417	6	and	and	CCONJ
ejpam-5838	417	7	l.	l.	PROPN
ejpam-5838	417	8	k.	k.	PROPN
ejpam-5838	417	9	dey	dey	PROPN
ejpam-5838	417	10	.	.	PUNCT
ejpam-5838	418	1	a	a	DET
ejpam-5838	418	2	fixed	fix	VERB
ejpam-5838	418	3	point	point	NOUN
ejpam-5838	418	4	theorem	theorem	VERB
ejpam-5838	418	5	in	in	ADP
ejpam-5838	418	6	a	a	DET
ejpam-5838	418	7	generalized	generalized	ADJ
ejpam-5838	418	8	metric	metric	ADJ
ejpam-5838	418	9	space	space	NOUN
ejpam-5838	418	10	.	.	PUNCT
ejpam-5838	419	1	soochow	soochow	PROPN
ejpam-5838	419	2	journal	journal	PROPN
ejpam-5838	419	3	of	of	ADP
ejpam-5838	419	4	mathematics	mathematic	NOUN
ejpam-5838	419	5	,	,	PUNCT
ejpam-5838	419	6	33(1):33–41	33(1):33–41	NOUN
ejpam-5838	419	7	,	,	PUNCT
ejpam-5838	419	8	2007	2007	NUM
ejpam-5838	419	9	.	.	PUNCT
ejpam-5838	420	1	[	[	X
ejpam-5838	420	2	11	11	NUM
ejpam-5838	420	3	]	]	X
ejpam-5838	420	4	shu	shu	PROPN
ejpam-5838	420	5	mustafa	mustafa	PROPN
ejpam-5838	420	6	and	and	CCONJ
ejpam-5838	420	7	b.	b.	PROPN
ejpam-5838	420	8	sims	sim	NOUN
ejpam-5838	420	9	.	.	PUNCT
ejpam-5838	421	1	fixed	fix	VERB
ejpam-5838	421	2	point	point	NOUN
ejpam-5838	421	3	theorems	theorem	NOUN
ejpam-5838	421	4	for	for	ADP
ejpam-5838	421	5	contractive	contractive	ADJ
ejpam-5838	421	6	mappings	mapping	NOUN
ejpam-5838	421	7	in	in	ADP
ejpam-5838	421	8	complete	complete	ADJ
ejpam-5838	421	9	g	g	NOUN
ejpam-5838	421	10	-	-	PUNCT
ejpam-5838	421	11	metric	metric	ADJ
ejpam-5838	421	12	spaces	space	NOUN
ejpam-5838	421	13	.	.	PUNCT
ejpam-5838	422	1	fixed	fix	VERB
ejpam-5838	422	2	point	point	NOUN
ejpam-5838	422	3	theory	theory	NOUN
ejpam-5838	422	4	and	and	CCONJ
ejpam-5838	422	5	applications	application	NOUN
ejpam-5838	422	6	,	,	PUNCT
ejpam-5838	422	7	2009:917175	2009:917175	NUM
ejpam-5838	422	8	,	,	PUNCT
ejpam-5838	422	9	2009	2009	NUM
ejpam-5838	422	10	.	.	PUNCT
ejpam-5838	423	1	[	[	X
ejpam-5838	423	2	12	12	NUM
ejpam-5838	423	3	]	]	PUNCT
ejpam-5838	423	4	z.	z.	PROPN
ejpam-5838	423	5	mustafa	mustafa	PROPN
ejpam-5838	423	6	,	,	PUNCT
ejpam-5838	423	7	h.	h.	PROPN
ejpam-5838	423	8	obiedat	obiedat	PROPN
ejpam-5838	423	9	,	,	PUNCT
ejpam-5838	423	10	and	and	CCONJ
ejpam-5838	423	11	f.	f.	PROPN
ejpam-5838	423	12	awawdeh	awawdeh	PROPN
ejpam-5838	423	13	.	.	PUNCT
ejpam-5838	424	1	some	some	DET
ejpam-5838	424	2	fixed	fix	VERB
ejpam-5838	424	3	point	point	NOUN
ejpam-5838	424	4	theorems	theorem	NOUN
ejpam-5838	424	5	for	for	ADP
ejpam-5838	424	6	mapping	mapping	NOUN
ejpam-5838	424	7	on	on	ADP
ejpam-5838	424	8	complete	complete	ADJ
ejpam-5838	424	9	g	g	NOUN
ejpam-5838	424	10	-	-	PUNCT
ejpam-5838	424	11	metric	metric	ADJ
ejpam-5838	424	12	spaces	space	NOUN
ejpam-5838	424	13	.	.	PUNCT
ejpam-5838	425	1	fixed	fix	VERB
ejpam-5838	425	2	point	point	NOUN
ejpam-5838	425	3	theory	theory	NOUN
ejpam-5838	425	4	and	and	CCONJ
ejpam-5838	425	5	applications	application	NOUN
ejpam-5838	425	6	,	,	PUNCT
ejpam-5838	425	7	2008:189870	2008:189870	NUM
ejpam-5838	425	8	,	,	PUNCT
ejpam-5838	425	9	2008	2008	NUM
ejpam-5838	425	10	.	.	PUNCT
ejpam-5838	426	1	[	[	X
ejpam-5838	426	2	13	13	NUM
ejpam-5838	426	3	]	]	PUNCT
ejpam-5838	426	4	m.	m.	NOUN
ejpam-5838	426	5	abbas	abbas	PROPN
ejpam-5838	426	6	and	and	CCONJ
ejpam-5838	426	7	b.	b.	PROPN
ejpam-5838	426	8	e.	e.	PROPN
ejpam-5838	426	9	rhoades	rhoades	PROPN
ejpam-5838	426	10	.	.	PUNCT
ejpam-5838	427	1	common	common	ADJ
ejpam-5838	427	2	fixed	fix	VERB
ejpam-5838	427	3	point	point	NOUN
ejpam-5838	427	4	results	result	NOUN
ejpam-5838	427	5	for	for	ADP
ejpam-5838	427	6	non	non	ADJ
ejpam-5838	427	7	-	-	ADJ
ejpam-5838	427	8	commuting	commuting	ADJ
ejpam-5838	427	9	mappings	mapping	NOUN
ejpam-5838	427	10	without	without	ADP
ejpam-5838	427	11	continuity	continuity	NOUN
ejpam-5838	427	12	in	in	ADP
ejpam-5838	427	13	generalized	generalized	ADJ
ejpam-5838	427	14	metric	metric	ADJ
ejpam-5838	427	15	spaces	space	NOUN
ejpam-5838	427	16	.	.	PUNCT
ejpam-5838	428	1	applied	apply	VERB
ejpam-5838	428	2	mathematics	mathematic	NOUN
ejpam-5838	428	3	and	and	CCONJ
ejpam-5838	428	4	computation	computation	NOUN
ejpam-5838	428	5	,	,	PUNCT
ejpam-5838	428	6	215(1):262–269	215(1):262–269	NUM
ejpam-5838	428	7	,	,	PUNCT
ejpam-5838	428	8	2009	2009	NUM
ejpam-5838	428	9	.	.	PUNCT
ejpam-5838	429	1	[	[	X
ejpam-5838	429	2	14	14	NUM
ejpam-5838	429	3	]	]	X
ejpam-5838	429	4	t.	t.	PROPN
ejpam-5838	429	5	nazir	nazir	PROPN
ejpam-5838	429	6	and	and	CCONJ
ejpam-5838	429	7	s.	s.	PROPN
ejpam-5838	430	1	radenović.	radenović.	INTJ
ejpam-5838	430	2	some	some	DET
ejpam-5838	430	3	periodic	periodic	ADJ
ejpam-5838	430	4	point	point	NOUN
ejpam-5838	430	5	results	result	NOUN
ejpam-5838	430	6	in	in	ADP
ejpam-5838	430	7	generalized	generalized	ADJ
ejpam-5838	430	8	metric	metric	ADJ
ejpam-5838	430	9	spaces	space	NOUN
ejpam-5838	430	10	.	.	PUNCT
ejpam-5838	431	1	applied	apply	VERB
ejpam-5838	431	2	mathematics	mathematic	NOUN
ejpam-5838	431	3	and	and	CCONJ
ejpam-5838	431	4	computation	computation	NOUN
ejpam-5838	431	5	,	,	PUNCT
ejpam-5838	431	6	217(8):4094–4099	217(8):4094–4099	NUM
ejpam-5838	431	7	,	,	PUNCT
ejpam-5838	431	8	2010	2010	NUM
ejpam-5838	431	9	.	.	PUNCT
ejpam-5838	432	1	[	[	X
ejpam-5838	432	2	15	15	NUM
ejpam-5838	432	3	]	]	X
ejpam-5838	432	4	w.	w.	PROPN
ejpam-5838	432	5	shatanawi	shatanawi	PROPN
ejpam-5838	432	6	,	,	PUNCT
ejpam-5838	432	7	m.	m.	NOUN
ejpam-5838	432	8	bataineh	bataineh	PROPN
ejpam-5838	432	9	,	,	PUNCT
ejpam-5838	432	10	and	and	CCONJ
ejpam-5838	432	11	a.	a.	NOUN
ejpam-5838	432	12	volodin	volodin	PROPN
ejpam-5838	432	13	.	.	PUNCT
ejpam-5838	433	1	existence	existence	NOUN
ejpam-5838	433	2	of	of	ADP
ejpam-5838	433	3	fixed	fix	VERB
ejpam-5838	433	4	point	point	NOUN
ejpam-5838	433	5	results	result	NOUN
ejpam-5838	433	6	in	in	ADP
ejpam-5838	433	7	g	g	NOUN
ejpam-5838	433	8	-	-	PUNCT
ejpam-5838	433	9	metric	metric	ADJ
ejpam-5838	433	10	spaces	space	NOUN
ejpam-5838	433	11	.	.	PUNCT
ejpam-5838	434	1	international	international	ADJ
ejpam-5838	434	2	journal	journal	PROPN
ejpam-5838	434	3	of	of	ADP
ejpam-5838	434	4	mathematics	mathematics	PROPN
ejpam-5838	434	5	and	and	CCONJ
ejpam-5838	434	6	mathematical	mathematical	ADJ
ejpam-5838	434	7	sciences	science	NOUN
ejpam-5838	434	8	,	,	PUNCT
ejpam-5838	434	9	2009:283028	2009:283028	NUM
ejpam-5838	434	10	,	,	PUNCT
ejpam-5838	434	11	2009	2009	NUM
ejpam-5838	434	12	.	.	PUNCT
ejpam-5838	435	1	[	[	X
ejpam-5838	435	2	16	16	NUM
ejpam-5838	435	3	]	]	PUNCT
ejpam-5838	435	4	s.	s.	PROPN
ejpam-5838	435	5	m.	m.	PROPN
ejpam-5838	435	6	vaezpour	vaezpour	PROPN
ejpam-5838	435	7	,	,	PUNCT
ejpam-5838	435	8	p.	p.	NOUN
ejpam-5838	435	9	vetro	vetro	PROPN
ejpam-5838	435	10	,	,	PUNCT
ejpam-5838	435	11	and	and	CCONJ
ejpam-5838	435	12	b.	b.	PROPN
ejpam-5838	435	13	e.	e.	PROPN
ejpam-5838	435	14	rhoades	rhoades	PROPN
ejpam-5838	435	15	.	.	PUNCT
ejpam-5838	436	1	fixed	fix	VERB
ejpam-5838	436	2	point	point	NOUN
ejpam-5838	436	3	theorems	theorem	NOUN
ejpam-5838	436	4	in	in	ADP
ejpam-5838	436	5	generalized	generalize	VERB
ejpam-5838	436	6	partially	partially	ADV
ejpam-5838	436	7	ordered	order	VERB
ejpam-5838	436	8	g	g	NOUN
ejpam-5838	436	9	-	-	PUNCT
ejpam-5838	436	10	metric	metric	ADJ
ejpam-5838	436	11	spaces	space	NOUN
ejpam-5838	436	12	.	.	PUNCT
ejpam-5838	437	1	mathematical	mathematical	ADJ
ejpam-5838	437	2	and	and	CCONJ
ejpam-5838	437	3	computer	computer	NOUN
ejpam-5838	437	4	modelling	modelling	NOUN
ejpam-5838	437	5	,	,	PUNCT
ejpam-5838	437	6	52(5	52(5	NUM
ejpam-5838	437	7	-	-	PUNCT
ejpam-5838	437	8	6):797–801	6):797–801	NUM
ejpam-5838	437	9	,	,	PUNCT
ejpam-5838	437	10	2010	2010	NUM
ejpam-5838	437	11	.	.	PUNCT
ejpam-5838	438	1	[	[	X
ejpam-5838	438	2	17	17	NUM
ejpam-5838	438	3	]	]	PUNCT
ejpam-5838	438	4	s.	s.	PROPN
ejpam-5838	438	5	k.	k.	PROPN
ejpam-5838	438	6	mohanta	mohanta	PROPN
ejpam-5838	438	7	and	and	CCONJ
ejpam-5838	438	8	s.	s.	PROPN
ejpam-5838	438	9	mohanta	mohanta	PROPN
ejpam-5838	438	10	.	.	PUNCT
ejpam-5838	439	1	a	a	DET
ejpam-5838	439	2	common	common	ADJ
ejpam-5838	439	3	fixed	fix	VERB
ejpam-5838	439	4	point	point	NOUN
ejpam-5838	439	5	theorem	theorem	VERB
ejpam-5838	439	6	in	in	ADP
ejpam-5838	439	7	g	g	NOUN
ejpam-5838	439	8	-	-	PUNCT
ejpam-5838	439	9	metric	metric	ADJ
ejpam-5838	439	10	spaces	space	NOUN
ejpam-5838	439	11	.	.	PUNCT
ejpam-5838	440	1	cubo	cubo	NOUN
ejpam-5838	440	2	,	,	PUNCT
ejpam-5838	440	3	14(3):85–101	14(3):85–101	NUM
ejpam-5838	440	4	,	,	PUNCT
ejpam-5838	440	5	2012	2012	NUM
ejpam-5838	440	6	.	.	PUNCT
ejpam-5838	441	1	[	[	X
ejpam-5838	441	2	18	18	NUM
ejpam-5838	441	3	]	]	X
ejpam-5838	441	4	b.	b.	PROPN
ejpam-5838	441	5	s.	s.	PROPN
ejpam-5838	441	6	choudhury	choudhury	PROPN
ejpam-5838	441	7	and	and	CCONJ
ejpam-5838	441	8	p.	p.	PROPN
ejpam-5838	441	9	maity	maity	NOUN
ejpam-5838	441	10	.	.	PUNCT
ejpam-5838	442	1	coupled	couple	VERB
ejpam-5838	442	2	fixed	fix	VERB
ejpam-5838	442	3	point	point	NOUN
ejpam-5838	442	4	results	result	NOUN
ejpam-5838	442	5	in	in	ADP
ejpam-5838	442	6	generalized	generalized	ADJ
ejpam-5838	442	7	metric	metric	ADJ
ejpam-5838	442	8	spaces	space	NOUN
ejpam-5838	442	9	.	.	PUNCT
ejpam-5838	443	1	mathematical	mathematical	ADJ
ejpam-5838	443	2	and	and	CCONJ
ejpam-5838	443	3	computer	computer	NOUN
ejpam-5838	443	4	modelling	modelling	NOUN
ejpam-5838	443	5	,	,	PUNCT
ejpam-5838	443	6	54(1	54(1	NUM
ejpam-5838	443	7	-	-	SYM
ejpam-5838	443	8	2):73–79	2):73–79	NUM
ejpam-5838	443	9	,	,	PUNCT
ejpam-5838	443	10	2011	2011	NUM
ejpam-5838	443	11	.	.	PUNCT
ejpam-5838	444	1	[	[	X
ejpam-5838	444	2	19	19	NUM
ejpam-5838	444	3	]	]	PUNCT
ejpam-5838	444	4	a.	a.	PROPN
ejpam-5838	444	5	r.	r.	PROPN
ejpam-5838	444	6	khan	khan	PROPN
ejpam-5838	444	7	and	and	CCONJ
ejpam-5838	444	8	t.	t.	PROPN
ejpam-5838	444	9	nazir	nazir	PROPN
ejpam-5838	444	10	.	.	PUNCT
ejpam-5838	445	1	coupled	couple	VERB
ejpam-5838	445	2	common	common	ADJ
ejpam-5838	445	3	fixed	fix	VERB
ejpam-5838	445	4	point	point	NOUN
ejpam-5838	445	5	results	result	NOUN
ejpam-5838	445	6	in	in	ADP
ejpam-5838	445	7	two	two	NUM
ejpam-5838	445	8	generalized	generalized	ADJ
ejpam-5838	445	9	metric	metric	ADJ
ejpam-5838	445	10	spaces	space	NOUN
ejpam-5838	445	11	.	.	PUNCT
ejpam-5838	446	1	applied	apply	VERB
ejpam-5838	446	2	mathematics	mathematic	NOUN
ejpam-5838	446	3	and	and	CCONJ
ejpam-5838	446	4	computation	computation	NOUN
ejpam-5838	446	5	,	,	PUNCT
ejpam-5838	446	6	217(13):6328–6336	217(13):6328–6336	NUM
ejpam-5838	446	7	,	,	PUNCT
ejpam-5838	446	8	2011	2011	NUM
ejpam-5838	446	9	.	.	PUNCT
ejpam-5838	447	1	m.	m.	PROPN
ejpam-5838	447	2	noorwali	noorwali	PROPN
ejpam-5838	447	3	et	et	PROPN
ejpam-5838	447	4	al/	al/	PROPN
ejpam-5838	447	5	/	/	SYM
ejpam-5838	447	6	eur	eur	PROPN
ejpam-5838	447	7	.	.	PUNCT
ejpam-5838	448	1	j.	j.	PROPN
ejpam-5838	448	2	pure	pure	PROPN
ejpam-5838	448	3	appl	appl	PROPN
ejpam-5838	448	4	.	.	PROPN
ejpam-5838	448	5	math	math	PROPN
ejpam-5838	448	6	,	,	PUNCT
ejpam-5838	448	7	18	18	NUM
ejpam-5838	448	8	(	(	PUNCT
ejpam-5838	448	9	2	2	NUM
ejpam-5838	448	10	)	)	PUNCT
ejpam-5838	448	11	(	(	PUNCT
ejpam-5838	448	12	2025	2025	NUM
ejpam-5838	448	13	)	)	PUNCT
ejpam-5838	448	14	,	,	PUNCT
ejpam-5838	448	15	5838	5838	NUM
ejpam-5838	448	16	16	16	NUM
ejpam-5838	448	17	of	of	ADP
ejpam-5838	448	18	16	16	NUM
ejpam-5838	448	19	[	[	X
ejpam-5838	448	20	20	20	NUM
ejpam-5838	448	21	]	]	PUNCT
ejpam-5838	448	22	s.	s.	PROPN
ejpam-5838	448	23	romaguera	romaguera	PROPN
ejpam-5838	448	24	.	.	PUNCT
ejpam-5838	449	1	fixed	fix	VERB
ejpam-5838	449	2	point	point	NOUN
ejpam-5838	449	3	theorems	theorem	NOUN
ejpam-5838	449	4	for	for	ADP
ejpam-5838	449	5	generalized	generalized	ADJ
ejpam-5838	449	6	contractions	contraction	NOUN
ejpam-5838	449	7	on	on	ADP
ejpam-5838	449	8	partial	partial	ADJ
ejpam-5838	449	9	metric	metric	ADJ
ejpam-5838	449	10	spaces	space	NOUN
ejpam-5838	449	11	.	.	PUNCT
ejpam-5838	450	1	topology	topology	NOUN
ejpam-5838	450	2	and	and	CCONJ
ejpam-5838	450	3	its	its	PRON
ejpam-5838	450	4	applications	application	NOUN
ejpam-5838	450	5	,	,	PUNCT
ejpam-5838	450	6	159(1):194–199	159(1):194–199	NUM
ejpam-5838	450	7	,	,	PUNCT
ejpam-5838	450	8	2012	2012	NUM
ejpam-5838	450	9	.	.	PUNCT
ejpam-5838	451	1	[	[	X
ejpam-5838	451	2	21	21	NUM
ejpam-5838	451	3	]	]	PUNCT
ejpam-5838	451	4	m.	m.	NOUN
ejpam-5838	451	5	gugnani	gugnani	PROPN
ejpam-5838	451	6	,	,	PUNCT
ejpam-5838	451	7	m.	m.	NOUN
ejpam-5838	451	8	aggarwal	aggarwal	NOUN
ejpam-5838	451	9	,	,	PUNCT
ejpam-5838	451	10	and	and	CCONJ
ejpam-5838	451	11	r.	r.	PROPN
ejpam-5838	451	12	chugh	chugh	NOUN
ejpam-5838	451	13	.	.	PUNCT
ejpam-5838	452	1	common	common	ADJ
ejpam-5838	452	2	fixed	fix	VERB
ejpam-5838	452	3	point	point	NOUN
ejpam-5838	452	4	results	result	NOUN
ejpam-5838	452	5	in	in	ADP
ejpam-5838	452	6	g	g	NOUN
ejpam-5838	452	7	-	-	PUNCT
ejpam-5838	452	8	metric	metric	ADJ
ejpam-5838	452	9	spaces	space	NOUN
ejpam-5838	452	10	and	and	CCONJ
ejpam-5838	452	11	applications	application	NOUN
ejpam-5838	452	12	.	.	PUNCT
ejpam-5838	453	1	international	international	ADJ
ejpam-5838	453	2	journal	journal	PROPN
ejpam-5838	453	3	of	of	ADP
ejpam-5838	453	4	computer	computer	NOUN
ejpam-5838	453	5	applications	application	NOUN
ejpam-5838	453	6	,	,	PUNCT
ejpam-5838	453	7	43(11):38–42	43(11):38–42	NOUN
ejpam-5838	453	8	,	,	PUNCT
ejpam-5838	453	9	2012	2012	NUM
ejpam-5838	453	10	.	.	PUNCT
ejpam-5838	454	1	[	[	X
ejpam-5838	454	2	22	22	NUM
ejpam-5838	454	3	]	]	PUNCT
ejpam-5838	454	4	m.	m.	NOUN
ejpam-5838	454	5	arshad	arshad	PROPN
ejpam-5838	454	6	and	and	CCONJ
ejpam-5838	454	7	c.	c.	PROPN
ejpam-5838	454	8	vetro	vetro	PROPN
ejpam-5838	454	9	.	.	PUNCT
ejpam-5838	455	1	on	on	ADP
ejpam-5838	455	2	a	a	DET
ejpam-5838	455	3	theorem	theorem	NOUN
ejpam-5838	455	4	of	of	ADP
ejpam-5838	455	5	khan	khan	PROPN
ejpam-5838	455	6	in	in	ADP
ejpam-5838	455	7	a	a	DET
ejpam-5838	455	8	generalized	generalized	ADJ
ejpam-5838	455	9	metric	metric	ADJ
ejpam-5838	455	10	space	space	NOUN
ejpam-5838	455	11	.	.	PUNCT
ejpam-5838	456	1	international	international	ADJ
ejpam-5838	456	2	journal	journal	NOUN
ejpam-5838	456	3	of	of	ADP
ejpam-5838	456	4	analysis	analysis	NOUN
ejpam-5838	456	5	,	,	PUNCT
ejpam-5838	456	6	2013:852727	2013:852727	NUM
ejpam-5838	456	7	,	,	PUNCT
ejpam-5838	456	8	2013	2013	NUM
ejpam-5838	456	9	.	.	PUNCT
ejpam-5838	457	1	[	[	X
ejpam-5838	457	2	23	23	NUM
ejpam-5838	457	3	]	]	PUNCT
ejpam-5838	457	4	m.	m.	NOUN
ejpam-5838	457	5	jleli	jleli	PROPN
ejpam-5838	457	6	and	and	CCONJ
ejpam-5838	457	7	b.	b.	PROPN
ejpam-5838	457	8	samet	samet	PROPN
ejpam-5838	457	9	.	.	PUNCT
ejpam-5838	458	1	a	a	DET
ejpam-5838	458	2	generalized	generalize	VERB
ejpam-5838	458	3	metric	metric	ADJ
ejpam-5838	458	4	space	space	NOUN
ejpam-5838	458	5	and	and	CCONJ
ejpam-5838	458	6	related	relate	VERB
ejpam-5838	458	7	fixed	fix	VERB
ejpam-5838	458	8	point	point	NOUN
ejpam-5838	458	9	theorems	theorem	NOUN
ejpam-5838	458	10	.	.	PUNCT
ejpam-5838	459	1	fixed	fix	VERB
ejpam-5838	459	2	point	point	NOUN
ejpam-5838	459	3	theory	theory	NOUN
ejpam-5838	459	4	and	and	CCONJ
ejpam-5838	459	5	applications	application	NOUN
ejpam-5838	459	6	,	,	PUNCT
ejpam-5838	459	7	2015:61	2015:61	NUM
ejpam-5838	459	8	,	,	PUNCT
ejpam-5838	459	9	2015	2015	NUM
ejpam-5838	459	10	.	.	PUNCT
ejpam-5838	460	1	[	[	X
ejpam-5838	460	2	24	24	NUM
ejpam-5838	460	3	]	]	X
ejpam-5838	460	4	l.	l.	PROPN
ejpam-5838	460	5	guran	guran	PROPN
ejpam-5838	460	6	and	and	CCONJ
ejpam-5838	460	7	a.	a.	PROPN
ejpam-5838	460	8	latif	latif	PROPN
ejpam-5838	460	9	.	.	PUNCT
ejpam-5838	461	1	fixed	fix	VERB
ejpam-5838	461	2	point	point	NOUN
ejpam-5838	461	3	theorems	theorem	NOUN
ejpam-5838	461	4	for	for	ADP
ejpam-5838	461	5	multivalued	multivalued	ADJ
ejpam-5838	461	6	contractive	contractive	ADJ
ejpam-5838	461	7	operators	operator	NOUN
ejpam-5838	461	8	on	on	ADP
ejpam-5838	461	9	generalized	generalized	ADJ
ejpam-5838	461	10	metric	metric	ADJ
ejpam-5838	461	11	spaces	space	NOUN
ejpam-5838	461	12	.	.	PUNCT
ejpam-5838	462	1	fixed	fix	VERB
ejpam-5838	462	2	point	point	NOUN
ejpam-5838	462	3	theory	theory	NOUN
ejpam-5838	462	4	,	,	PUNCT
ejpam-5838	462	5	16(2):327–336	16(2):327–336	PROPN
ejpam-5838	462	6	,	,	PUNCT
ejpam-5838	462	7	2015	2015	NUM
ejpam-5838	462	8	.	.	PUNCT
ejpam-5838	463	1	[	[	X
ejpam-5838	463	2	25	25	NUM
ejpam-5838	463	3	]	]	PUNCT
ejpam-5838	463	4	r.	r.	PROPN
ejpam-5838	463	5	k.	k.	PROPN
ejpam-5838	463	6	vats	vats	PROPN
ejpam-5838	463	7	,	,	PUNCT
ejpam-5838	463	8	m.	m.	NOUN
ejpam-5838	463	9	grewal	grewal	PROPN
ejpam-5838	463	10	,	,	PUNCT
ejpam-5838	463	11	and	and	CCONJ
ejpam-5838	463	12	a.	a.	PROPN
ejpam-5838	463	13	kumar	kumar	PROPN
ejpam-5838	463	14	.	.	PUNCT
ejpam-5838	464	1	some	some	DET
ejpam-5838	464	2	fixed	fix	VERB
ejpam-5838	464	3	point	point	NOUN
ejpam-5838	464	4	theorem	theorem	VERB
ejpam-5838	464	5	in	in	ADP
ejpam-5838	464	6	generalized	generalized	ADJ
ejpam-5838	464	7	metric	metric	ADJ
ejpam-5838	464	8	spaces	space	NOUN
ejpam-5838	464	9	.	.	PUNCT
ejpam-5838	465	1	advances	advance	NOUN
ejpam-5838	465	2	in	in	ADP
ejpam-5838	465	3	fixed	fix	VERB
ejpam-5838	465	4	point	point	NOUN
ejpam-5838	465	5	theory	theory	NOUN
ejpam-5838	465	6	,	,	PUNCT
ejpam-5838	465	7	6(3):254–261	6(3):254–261	NOUN
ejpam-5838	465	8	,	,	PUNCT
ejpam-5838	465	9	2016	2016	NUM
ejpam-5838	465	10	.	.	PUNCT
ejpam-5838	466	1	[	[	X
ejpam-5838	466	2	26	26	NUM
ejpam-5838	466	3	]	]	X
ejpam-5838	466	4	y.	y.	PROPN
ejpam-5838	466	5	elkouck	elkouck	PROPN
ejpam-5838	466	6	and	and	CCONJ
ejpam-5838	466	7	e.	e.	PROPN
ejpam-5838	466	8	m.	m.	PROPN
ejpam-5838	466	9	marhrani	marhrani	PROPN
ejpam-5838	466	10	.	.	PUNCT
ejpam-5838	467	1	on	on	ADP
ejpam-5838	467	2	some	some	DET
ejpam-5838	467	3	fixed	fix	VERB
ejpam-5838	467	4	point	point	NOUN
ejpam-5838	467	5	theorems	theorem	NOUN
ejpam-5838	467	6	in	in	ADP
ejpam-5838	467	7	generalized	generalized	ADJ
ejpam-5838	467	8	metric	metric	ADJ
ejpam-5838	467	9	spaces	space	NOUN
ejpam-5838	467	10	.	.	PUNCT
ejpam-5838	468	1	fixed	fix	VERB
ejpam-5838	468	2	point	point	NOUN
ejpam-5838	468	3	theory	theory	NOUN
ejpam-5838	468	4	and	and	CCONJ
ejpam-5838	468	5	applications	application	NOUN
ejpam-5838	468	6	,	,	PUNCT
ejpam-5838	468	7	2017:13	2017:13	NUM
ejpam-5838	468	8	,	,	PUNCT
ejpam-5838	468	9	2017	2017	NUM
ejpam-5838	468	10	.	.	PUNCT
ejpam-5838	469	1	[	[	X
ejpam-5838	469	2	27	27	NUM
ejpam-5838	469	3	]	]	PUNCT
ejpam-5838	469	4	z.	z.	PROPN
ejpam-5838	469	5	mustafa	mustafa	PROPN
ejpam-5838	469	6	and	and	CCONJ
ejpam-5838	469	7	b.	b.	PROPN
ejpam-5838	469	8	sims	sim	NOUN
ejpam-5838	469	9	.	.	PUNCT
ejpam-5838	470	1	fixed	fix	VERB
ejpam-5838	470	2	point	point	NOUN
ejpam-5838	470	3	theorems	theorem	NOUN
ejpam-5838	470	4	for	for	ADP
ejpam-5838	470	5	contractive	contractive	ADJ
ejpam-5838	470	6	mappings	mapping	NOUN
ejpam-5838	470	7	in	in	ADP
ejpam-5838	470	8	complete	complete	ADJ
ejpam-5838	470	9	gmetric	gmetric	ADJ
ejpam-5838	470	10	spaces	space	NOUN
ejpam-5838	470	11	.	.	PUNCT
ejpam-5838	471	1	fixed	fix	VERB
ejpam-5838	471	2	point	point	NOUN
ejpam-5838	471	3	theory	theory	NOUN
ejpam-5838	471	4	and	and	CCONJ
ejpam-5838	471	5	applications	application	NOUN
ejpam-5838	471	6	,	,	PUNCT
ejpam-5838	471	7	page	page	NOUN
ejpam-5838	471	8	917175	917175	NUM
ejpam-5838	471	9	,	,	PUNCT
ejpam-5838	471	10	2009	2009	NUM
ejpam-5838	471	11	.	.	PUNCT