id	sid	tid	token	lemma	pos
ejpam-3371	1	1	european	european	PROPN
ejpam-3371	1	2	journal	journal	PROPN
ejpam-3371	1	3	of	of	ADP
ejpam-3371	1	4	pure	pure	ADJ
ejpam-3371	1	5	and	and	CCONJ
ejpam-3371	1	6	applied	apply	VERB
ejpam-3371	1	7	mathematics	mathematic	NOUN
ejpam-3371	1	8	vol	vol	NOUN
ejpam-3371	1	9	.	.	PROPN
ejpam-3371	2	1	12	12	NUM
ejpam-3371	2	2	,	,	PUNCT
ejpam-3371	2	3	no	no	INTJ
ejpam-3371	2	4	.	.	NOUN
ejpam-3371	2	5	2	2	NUM
ejpam-3371	2	6	,	,	PUNCT
ejpam-3371	2	7	2019	2019	NUM
ejpam-3371	2	8	,	,	PUNCT
ejpam-3371	2	9	348	348	NUM
ejpam-3371	2	10	-	-	SYM
ejpam-3371	2	11	357	357	NUM
ejpam-3371	2	12	issn	issn	PROPN
ejpam-3371	2	13	1307	1307	NUM
ejpam-3371	2	14	-	-	SYM
ejpam-3371	2	15	5543	5543	NUM
ejpam-3371	2	16	–	–	PUNCT
ejpam-3371	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3371	2	18	published	publish	VERB
ejpam-3371	2	19	by	by	ADP
ejpam-3371	2	20	new	new	PROPN
ejpam-3371	2	21	york	york	PROPN
ejpam-3371	2	22	business	business	PROPN
ejpam-3371	2	23	global	global	ADJ
ejpam-3371	2	24	common	common	ADJ
ejpam-3371	2	25	fixed	fix	VERB
ejpam-3371	2	26	points	point	NOUN
ejpam-3371	2	27	of	of	ADP
ejpam-3371	2	28	two	two	NUM
ejpam-3371	2	29	multivalued	multivalued	ADJ
ejpam-3371	2	30	asymptotically	asymptotically	ADV
ejpam-3371	2	31	nonexpansive	nonexpansive	ADJ
ejpam-3371	2	32	mappings	mapping	NOUN
ejpam-3371	2	33	safeer	safeer	VERB
ejpam-3371	2	34	hussain	hussain	PROPN
ejpam-3371	2	35	khan1,∗	khan1,∗	PROPN
ejpam-3371	2	36	,	,	PUNCT
ejpam-3371	2	37	hira	hira	PROPN
ejpam-3371	2	38	iqbal2	iqbal2	PROPN
ejpam-3371	2	39	,	,	PUNCT
ejpam-3371	2	40	mujahid	mujahid	NOUN
ejpam-3371	2	41	abbas3,4	abbas3,4	PROPN
ejpam-3371	2	42	1department	1department	NUM
ejpam-3371	2	43	of	of	ADP
ejpam-3371	2	44	mathematics	mathematic	NOUN
ejpam-3371	2	45	,	,	PUNCT
ejpam-3371	2	46	statistics	statistic	NOUN
ejpam-3371	2	47	and	and	CCONJ
ejpam-3371	2	48	physics	physics	PROPN
ejpam-3371	2	49	,	,	PUNCT
ejpam-3371	2	50	qatar	qatar	PROPN
ejpam-3371	2	51	university	university	PROPN
ejpam-3371	2	52	,	,	PUNCT
ejpam-3371	2	53	doha	doha	PROPN
ejpam-3371	2	54	,	,	PUNCT
ejpam-3371	2	55	2713,qatar	2713,qatar	NUM
ejpam-3371	2	56	2	2	NUM
ejpam-3371	2	57	department	department	NOUN
ejpam-3371	2	58	of	of	ADP
ejpam-3371	2	59	sciences	science	NOUN
ejpam-3371	2	60	and	and	CCONJ
ejpam-3371	2	61	humanities	humanity	NOUN
ejpam-3371	2	62	,	,	PUNCT
ejpam-3371	2	63	national	national	ADJ
ejpam-3371	2	64	university	university	PROPN
ejpam-3371	2	65	of	of	ADP
ejpam-3371	2	66	computer	computer	NOUN
ejpam-3371	2	67	and	and	CCONJ
ejpam-3371	2	68	emerging	emerge	VERB
ejpam-3371	2	69	sciences	science	NOUN
ejpam-3371	2	70	,	,	PUNCT
ejpam-3371	2	71	lahore	lahore	NOUN
ejpam-3371	2	72	campus	campus	NOUN
ejpam-3371	2	73	,	,	PUNCT
ejpam-3371	2	74	pakistan	pakistan	PROPN
ejpam-3371	2	75	3department	3department	NUM
ejpam-3371	2	76	of	of	ADP
ejpam-3371	2	77	mathematics	mathematic	NOUN
ejpam-3371	2	78	,	,	PUNCT
ejpam-3371	2	79	government	government	NOUN
ejpam-3371	2	80	college	college	NOUN
ejpam-3371	2	81	university	university	PROPN
ejpam-3371	2	82	lahore	lahore	NOUN
ejpam-3371	2	83	54000	54000	NUM
ejpam-3371	2	84	,	,	PUNCT
ejpam-3371	2	85	pakistan	pakistan	PROPN
ejpam-3371	2	86	4department	4department	NUM
ejpam-3371	2	87	of	of	ADP
ejpam-3371	2	88	mathematics	mathematic	NOUN
ejpam-3371	2	89	,	,	PUNCT
ejpam-3371	2	90	king	king	PROPN
ejpam-3371	2	91	abdulaziz	abdulaziz	PROPN
ejpam-3371	2	92	university	university	PROPN
ejpam-3371	2	93	,	,	PUNCT
ejpam-3371	2	94	p.	p.	PROPN
ejpam-3371	2	95	o.	o.	PROPN
ejpam-3371	2	96	box	box	PROPN
ejpam-3371	2	97	.	.	PUNCT
ejpam-3371	2	98	80203	80203	NUM
ejpam-3371	2	99	,	,	PUNCT
ejpam-3371	2	100	jeddah	jeddah	PROPN
ejpam-3371	2	101	21589	21589	NUM
ejpam-3371	2	102	,	,	PUNCT
ejpam-3371	2	103	saudi	saudi	PROPN
ejpam-3371	2	104	arabia	arabia	PROPN
ejpam-3371	2	105	abstract	abstract	NOUN
ejpam-3371	2	106	.	.	PUNCT
ejpam-3371	3	1	in	in	ADP
ejpam-3371	3	2	this	this	DET
ejpam-3371	3	3	paper	paper	NOUN
ejpam-3371	3	4	,	,	PUNCT
ejpam-3371	3	5	we	we	PRON
ejpam-3371	3	6	construct	construct	VERB
ejpam-3371	3	7	a	a	DET
ejpam-3371	3	8	modified	modify	VERB
ejpam-3371	3	9	ishikawa	ishikawa	PROPN
ejpam-3371	3	10	iterative	iterative	NOUN
ejpam-3371	3	11	process	process	NOUN
ejpam-3371	3	12	to	to	PART
ejpam-3371	3	13	approximate	approximate	VERB
ejpam-3371	3	14	common	common	ADJ
ejpam-3371	3	15	fixed	fix	VERB
ejpam-3371	3	16	points	point	NOUN
ejpam-3371	3	17	of	of	ADP
ejpam-3371	3	18	two	two	NUM
ejpam-3371	3	19	multivalued	multivalued	ADJ
ejpam-3371	3	20	asymptotically	asymptotically	ADV
ejpam-3371	3	21	nonexpansive	nonexpansive	ADJ
ejpam-3371	3	22	mappings	mapping	NOUN
ejpam-3371	3	23	and	and	CCONJ
ejpam-3371	3	24	prove	prove	VERB
ejpam-3371	3	25	some	some	DET
ejpam-3371	3	26	convergence	convergence	NOUN
ejpam-3371	3	27	theorems	theorem	NOUN
ejpam-3371	3	28	in	in	ADP
ejpam-3371	3	29	uniformly	uniformly	ADV
ejpam-3371	3	30	convex	convex	VERB
ejpam-3371	3	31	hyperbolic	hyperbolic	ADJ
ejpam-3371	3	32	spaces	space	NOUN
ejpam-3371	3	33	.	.	PUNCT
ejpam-3371	4	1	2010	2010	NUM
ejpam-3371	4	2	mathematics	mathematic	NOUN
ejpam-3371	4	3	subject	subject	NOUN
ejpam-3371	4	4	classifications	classification	NOUN
ejpam-3371	4	5	:	:	PUNCT
ejpam-3371	4	6	ams	am	NOUN
ejpam-3371	4	7	47h10	47h10	NUM
ejpam-3371	4	8	,	,	PUNCT
ejpam-3371	4	9	47h09	47h09	NUM
ejpam-3371	4	10	key	key	ADJ
ejpam-3371	4	11	words	word	NOUN
ejpam-3371	4	12	and	and	CCONJ
ejpam-3371	4	13	phrases	phrase	NOUN
ejpam-3371	4	14	:	:	PUNCT
ejpam-3371	4	15	asymptotically	asymptotically	ADV
ejpam-3371	4	16	nonexpansive	nonexpansive	ADJ
ejpam-3371	4	17	mapping	mapping	NOUN
ejpam-3371	4	18	,	,	PUNCT
ejpam-3371	4	19	multivalued	multivalued	ADJ
ejpam-3371	4	20	mapping	mapping	NOUN
ejpam-3371	4	21	,	,	PUNCT
ejpam-3371	4	22	common	common	ADJ
ejpam-3371	4	23	fixed	fix	VERB
ejpam-3371	4	24	point	point	NOUN
ejpam-3371	4	25	,	,	PUNCT
ejpam-3371	4	26	ishikawa	ishikawa	PROPN
ejpam-3371	4	27	iteration	iteration	NOUN
ejpam-3371	4	28	process	process	NOUN
ejpam-3371	4	29	1	1	NUM
ejpam-3371	4	30	.	.	PUNCT
ejpam-3371	5	1	introduction	introduction	NOUN
ejpam-3371	5	2	let	let	VERB
ejpam-3371	5	3	d	d	PRON
ejpam-3371	5	4	be	be	AUX
ejpam-3371	5	5	a	a	DET
ejpam-3371	5	6	nonempty	nonempty	ADJ
ejpam-3371	5	7	subset	subset	NOUN
ejpam-3371	5	8	of	of	ADP
ejpam-3371	5	9	a	a	DET
ejpam-3371	5	10	metric	metric	ADJ
ejpam-3371	5	11	space	space	NOUN
ejpam-3371	5	12	(	(	PUNCT
ejpam-3371	5	13	x	x	X
ejpam-3371	5	14	,	,	PUNCT
ejpam-3371	5	15	d	d	NOUN
ejpam-3371	5	16	)	)	PUNCT
ejpam-3371	5	17	.	.	PUNCT
ejpam-3371	6	1	a	a	DET
ejpam-3371	6	2	mapping	mapping	NOUN
ejpam-3371	6	3	t	t	NOUN
ejpam-3371	6	4	:	:	PUNCT
ejpam-3371	6	5	d	d	X
ejpam-3371	6	6	→	→	PUNCT
ejpam-3371	6	7	d	d	X
ejpam-3371	6	8	is	be	AUX
ejpam-3371	6	9	called	call	VERB
ejpam-3371	6	10	asymptotically	asymptotically	ADV
ejpam-3371	6	11	nonexpansive	nonexpansive	ADJ
ejpam-3371	6	12	if	if	SCONJ
ejpam-3371	6	13	for	for	ADP
ejpam-3371	6	14	any	any	DET
ejpam-3371	6	15	x	x	NOUN
ejpam-3371	6	16	,	,	PUNCT
ejpam-3371	6	17	y	y	PROPN
ejpam-3371	6	18	∈	∈	PROPN
ejpam-3371	6	19	d	d	NOUN
ejpam-3371	6	20	,	,	PUNCT
ejpam-3371	6	21	there	there	PRON
ejpam-3371	6	22	exists	exist	VERB
ejpam-3371	6	23	a	a	DET
ejpam-3371	6	24	sequence	sequence	NOUN
ejpam-3371	6	25	{	{	PUNCT
ejpam-3371	6	26	kn	kn	NOUN
ejpam-3371	6	27	}	}	PUNCT
ejpam-3371	6	28	with	with	ADP
ejpam-3371	6	29	kn	kn	PROPN
ejpam-3371	6	30	≥	≥	NUM
ejpam-3371	6	31	1	1	NUM
ejpam-3371	6	32	and	and	CCONJ
ejpam-3371	6	33	lim	lim	PROPN
ejpam-3371	6	34	n→∞	n→∞	PRON
ejpam-3371	7	1	kn	kn	PROPN
ejpam-3371	7	2	=	=	NOUN
ejpam-3371	7	3	1	1	NUM
ejpam-3371	8	1	such	such	ADJ
ejpam-3371	8	2	that	that	DET
ejpam-3371	8	3	d(tnx	d(tnx	NOUN
ejpam-3371	8	4	,	,	PUNCT
ejpam-3371	8	5	tny	tny	PROPN
ejpam-3371	8	6	)	)	PUNCT
ejpam-3371	8	7	≤	≤	NUM
ejpam-3371	8	8	knd(x	knd(x	PROPN
ejpam-3371	8	9	,	,	PUNCT
ejpam-3371	8	10	y	y	NOUN
ejpam-3371	8	11	)	)	PUNCT
ejpam-3371	8	12	.	.	PUNCT
ejpam-3371	9	1	let	let	VERB
ejpam-3371	9	2	p	p	NOUN
ejpam-3371	9	3	(	(	PUNCT
ejpam-3371	9	4	d	d	NOUN
ejpam-3371	9	5	)	)	PUNCT
ejpam-3371	9	6	represent	represent	VERB
ejpam-3371	9	7	the	the	DET
ejpam-3371	9	8	set	set	NOUN
ejpam-3371	9	9	of	of	ADP
ejpam-3371	9	10	all	all	DET
ejpam-3371	9	11	nonempty	nonempty	X
ejpam-3371	9	12	subsets	subset	NOUN
ejpam-3371	9	13	ofd	ofd	VERB
ejpam-3371	9	14	,	,	PUNCT
ejpam-3371	9	15	cl(d	cl(d	NUM
ejpam-3371	9	16	)	)	PUNCT
ejpam-3371	9	17	denote	denote	VERB
ejpam-3371	9	18	the	the	DET
ejpam-3371	9	19	set	set	NOUN
ejpam-3371	9	20	all	all	DET
ejpam-3371	9	21	nonempty	nonempty	ADV
ejpam-3371	9	22	closed	close	VERB
ejpam-3371	9	23	subsets	subset	NOUN
ejpam-3371	9	24	of	of	ADP
ejpam-3371	9	25	d	d	PROPN
ejpam-3371	9	26	and	and	CCONJ
ejpam-3371	9	27	cb(d	cb(d	NOUN
ejpam-3371	9	28	)	)	PUNCT
ejpam-3371	9	29	denote	denote	VERB
ejpam-3371	9	30	the	the	DET
ejpam-3371	9	31	set	set	NOUN
ejpam-3371	10	1	all	all	PRON
ejpam-3371	10	2	nonempty	nonempty	ADV
ejpam-3371	10	3	closed	close	VERB
ejpam-3371	10	4	and	and	CCONJ
ejpam-3371	10	5	bounded	bound	VERB
ejpam-3371	10	6	subsets	subset	NOUN
ejpam-3371	10	7	of	of	ADP
ejpam-3371	10	8	d	d	PROPN
ejpam-3371	10	9	.	.	PUNCT
ejpam-3371	11	1	for	for	ADP
ejpam-3371	11	2	a	a	DET
ejpam-3371	11	3	,	,	PUNCT
ejpam-3371	11	4	b	b	PROPN
ejpam-3371	11	5	∈	∈	PROPN
ejpam-3371	11	6	cb(d	cb(d	NOUN
ejpam-3371	11	7	)	)	PUNCT
ejpam-3371	11	8	and	and	CCONJ
ejpam-3371	11	9	x	x	X
ejpam-3371	11	10	,	,	PUNCT
ejpam-3371	11	11	y	y	PROPN
ejpam-3371	11	12	∈	∈	PROPN
ejpam-3371	11	13	d	d	NOUN
ejpam-3371	11	14	,	,	PUNCT
ejpam-3371	11	15	define	define	VERB
ejpam-3371	11	16	d(x	d(x	PROPN
ejpam-3371	11	17	,	,	PUNCT
ejpam-3371	11	18	a	a	PRON
ejpam-3371	11	19	)	)	PUNCT
ejpam-3371	11	20	=	=	SYM
ejpam-3371	11	21	inf	inf	PROPN
ejpam-3371	11	22	a∈a	a∈a	ADJ
ejpam-3371	11	23	d(x	d(x	PROPN
ejpam-3371	11	24	,	,	PUNCT
ejpam-3371	11	25	a	a	PRON
ejpam-3371	11	26	)	)	PUNCT
ejpam-3371	11	27	.	.	PUNCT
ejpam-3371	12	1	then	then	ADV
ejpam-3371	12	2	h	h	PROPN
ejpam-3371	12	3	is	be	AUX
ejpam-3371	12	4	known	know	VERB
ejpam-3371	12	5	as	as	ADP
ejpam-3371	12	6	the	the	DET
ejpam-3371	12	7	generalized	generalize	VERB
ejpam-3371	12	8	pompeiu	pompeiu	NOUN
ejpam-3371	12	9	-	-	PUNCT
ejpam-3371	12	10	hausdorff	hausdorff	NOUN
ejpam-3371	12	11	distance	distance	NOUN
ejpam-3371	12	12	induced	induce	VERB
ejpam-3371	12	13	by	by	ADP
ejpam-3371	12	14	d	d	PROPN
ejpam-3371	12	15	if	if	SCONJ
ejpam-3371	12	16	h(a	h(a	PROPN
ejpam-3371	12	17	,	,	PUNCT
ejpam-3371	12	18	b	b	NOUN
ejpam-3371	12	19	)	)	PUNCT
ejpam-3371	12	20	=	=	SYM
ejpam-3371	12	21	max{sup	max{sup	NOUN
ejpam-3371	12	22	a∈a	a∈a	VERB
ejpam-3371	12	23	d(a	d(a	PROPN
ejpam-3371	12	24	,	,	PUNCT
ejpam-3371	12	25	b	b	NOUN
ejpam-3371	12	26	)	)	PUNCT
ejpam-3371	12	27	,	,	PUNCT
ejpam-3371	12	28	sup	sup	NOUN
ejpam-3371	12	29	b∈b	b∈b	NOUN
ejpam-3371	12	30	d(a	d(a	PROPN
ejpam-3371	12	31	,	,	PUNCT
ejpam-3371	12	32	b	b	NOUN
ejpam-3371	12	33	)	)	PUNCT
ejpam-3371	12	34	}	}	PUNCT
ejpam-3371	12	35	.	.	PUNCT
ejpam-3371	13	1	∗corresponding	∗corresponde	VERB
ejpam-3371	13	2	author	author	NOUN
ejpam-3371	13	3	.	.	PUNCT
ejpam-3371	14	1	doi	doi	NOUN
ejpam-3371	14	2	:	:	PUNCT
ejpam-3371	14	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3371	https://doi.org/10.29020/nybg.ejpam.v12i2.3371	ADJ
ejpam-3371	14	4	email	email	NOUN
ejpam-3371	14	5	addresses	address	NOUN
ejpam-3371	14	6	:	:	PUNCT
ejpam-3371	14	7	safeer@qu.edu.qa	safeer@qu.edu.qa	PROPN
ejpam-3371	14	8	(	(	PUNCT
ejpam-3371	14	9	s.	s.	PROPN
ejpam-3371	14	10	h.	h.	PROPN
ejpam-3371	14	11	khan	khan	PROPN
ejpam-3371	14	12	)	)	PUNCT
ejpam-3371	14	13	,	,	PUNCT
ejpam-3371	14	14	hira.iqbal@nu.edu.pk	hira.iqbal@nu.edu.pk	PROPN
ejpam-3371	14	15	(	(	PUNCT
ejpam-3371	14	16	h.	h.	PROPN
ejpam-3371	14	17	iqbal	iqbal	PROPN
ejpam-3371	14	18	)	)	PUNCT
ejpam-3371	14	19	,	,	PUNCT
ejpam-3371	14	20	abbas.mujahid@gmail.com	abbas.mujahid@gmail.com	X
ejpam-3371	14	21	(	(	PUNCT
ejpam-3371	14	22	m.	m.	NOUN
ejpam-3371	14	23	abbas	abbas	PROPN
ejpam-3371	14	24	)	)	PUNCT
ejpam-3371	14	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3371	15	1	348	348	NUM
ejpam-3371	15	2	c	c	X
ejpam-3371	15	3	©	©	PROPN
ejpam-3371	15	4	2019	2019	NUM
ejpam-3371	15	5	ejpam	ejpam	NOUN
ejpam-3371	15	6	all	all	DET
ejpam-3371	15	7	rights	right	NOUN
ejpam-3371	15	8	reserved	reserve	VERB
ejpam-3371	15	9	.	.	PUNCT
ejpam-3371	16	1	s.	s.	PROPN
ejpam-3371	16	2	h.	h.	PROPN
ejpam-3371	16	3	khan	khan	PROPN
ejpam-3371	16	4	,	,	PUNCT
ejpam-3371	16	5	h.	h.	PROPN
ejpam-3371	16	6	iqbal	iqbal	PROPN
ejpam-3371	16	7	,	,	PUNCT
ejpam-3371	16	8	m.	m.	NOUN
ejpam-3371	16	9	abbas	abbas	PROPN
ejpam-3371	16	10	/	/	SYM
ejpam-3371	16	11	eur	eur	PROPN
ejpam-3371	16	12	.	.	PUNCT
ejpam-3371	17	1	j.	j.	PROPN
ejpam-3371	17	2	pure	pure	PROPN
ejpam-3371	17	3	appl	appl	PROPN
ejpam-3371	17	4	.	.	PROPN
ejpam-3371	17	5	math	math	PROPN
ejpam-3371	17	6	,	,	PUNCT
ejpam-3371	17	7	12	12	NUM
ejpam-3371	17	8	(	(	PUNCT
ejpam-3371	17	9	2	2	NUM
ejpam-3371	17	10	)	)	PUNCT
ejpam-3371	17	11	(	(	PUNCT
ejpam-3371	17	12	2019	2019	NUM
ejpam-3371	17	13	)	)	PUNCT
ejpam-3371	17	14	,	,	PUNCT
ejpam-3371	17	15	348	348	NUM
ejpam-3371	17	16	-	-	SYM
ejpam-3371	17	17	357	357	NUM
ejpam-3371	17	18	349	349	NUM
ejpam-3371	17	19	we	we	PRON
ejpam-3371	17	20	say	say	VERB
ejpam-3371	17	21	that	that	SCONJ
ejpam-3371	17	22	a	a	DET
ejpam-3371	17	23	multivalued	multivalue	VERB
ejpam-3371	17	24	mapping	mapping	NOUN
ejpam-3371	17	25	t	t	NOUN
ejpam-3371	17	26	:	:	PUNCT
ejpam-3371	17	27	d	d	X
ejpam-3371	17	28	→	→	SYM
ejpam-3371	17	29	p	p	X
ejpam-3371	17	30	(	(	PUNCT
ejpam-3371	17	31	d	d	NOUN
ejpam-3371	17	32	)	)	PUNCT
ejpam-3371	17	33	has	have	VERB
ejpam-3371	17	34	a	a	DET
ejpam-3371	17	35	fixed	fixed	ADJ
ejpam-3371	17	36	point	point	NOUN
ejpam-3371	17	37	x	x	PUNCT
ejpam-3371	17	38	if	if	SCONJ
ejpam-3371	17	39	x	x	PROPN
ejpam-3371	17	40	∈	∈	PROPN
ejpam-3371	17	41	tx	tx	PROPN
ejpam-3371	17	42	.	.	PUNCT
ejpam-3371	18	1	it	it	PRON
ejpam-3371	18	2	is	be	AUX
ejpam-3371	18	3	obvious	obvious	ADJ
ejpam-3371	18	4	that	that	SCONJ
ejpam-3371	18	5	the	the	DET
ejpam-3371	18	6	theory	theory	NOUN
ejpam-3371	18	7	of	of	ADP
ejpam-3371	18	8	mutlivalued	mutlivalue	VERB
ejpam-3371	18	9	mappings	mapping	NOUN
ejpam-3371	18	10	is	be	AUX
ejpam-3371	18	11	more	more	ADV
ejpam-3371	18	12	complicated	complicated	ADJ
ejpam-3371	18	13	than	than	ADP
ejpam-3371	18	14	that	that	PRON
ejpam-3371	18	15	of	of	ADP
ejpam-3371	18	16	the	the	DET
ejpam-3371	18	17	single	single	ADJ
ejpam-3371	18	18	valued	value	VERB
ejpam-3371	18	19	mappings	mapping	NOUN
ejpam-3371	18	20	.	.	PUNCT
ejpam-3371	19	1	many	many	ADJ
ejpam-3371	19	2	different	different	ADJ
ejpam-3371	19	3	techniques	technique	NOUN
ejpam-3371	19	4	have	have	AUX
ejpam-3371	19	5	been	be	AUX
ejpam-3371	19	6	employed	employ	VERB
ejpam-3371	19	7	to	to	PART
ejpam-3371	19	8	approximate	approximate	VERB
ejpam-3371	19	9	fixed	fix	VERB
ejpam-3371	19	10	points	point	NOUN
ejpam-3371	19	11	of	of	ADP
ejpam-3371	19	12	multivalued	multivalue	VERB
ejpam-3371	19	13	mappings	mapping	NOUN
ejpam-3371	19	14	.	.	PUNCT
ejpam-3371	20	1	rus	rus	NOUN
ejpam-3371	21	1	[	[	X
ejpam-3371	21	2	7	7	NUM
ejpam-3371	21	3	]	]	PUNCT
ejpam-3371	21	4	introduced	introduce	VERB
ejpam-3371	21	5	the	the	DET
ejpam-3371	21	6	concept	concept	NOUN
ejpam-3371	21	7	of	of	ADP
ejpam-3371	21	8	generalized	generalized	ADJ
ejpam-3371	21	9	orbits	orbit	NOUN
ejpam-3371	21	10	in	in	ADP
ejpam-3371	21	11	multivalued	multivalued	ADJ
ejpam-3371	21	12	mappings	mapping	NOUN
ejpam-3371	21	13	.	.	PUNCT
ejpam-3371	22	1	khamsi	khamsi	NOUN
ejpam-3371	22	2	and	and	CCONJ
ejpam-3371	22	3	kirk	kirk	PROPN
ejpam-3371	22	4	extended	extend	VERB
ejpam-3371	22	5	this	this	DET
ejpam-3371	22	6	concept	concept	NOUN
ejpam-3371	22	7	of	of	ADP
ejpam-3371	22	8	generalized	generalized	ADJ
ejpam-3371	22	9	orbits	orbit	NOUN
ejpam-3371	22	10	for	for	ADP
ejpam-3371	22	11	the	the	DET
ejpam-3371	22	12	iterates	iterate	NOUN
ejpam-3371	22	13	of	of	ADP
ejpam-3371	22	14	a	a	DET
ejpam-3371	22	15	multivalued	multivalue	VERB
ejpam-3371	22	16	mapping	mapping	NOUN
ejpam-3371	22	17	in	in	ADP
ejpam-3371	22	18	[	[	X
ejpam-3371	22	19	3	3	NUM
ejpam-3371	22	20	]	]	PUNCT
ejpam-3371	22	21	.	.	PUNCT
ejpam-3371	23	1	definition	definition	NOUN
ejpam-3371	23	2	1	1	NUM
ejpam-3371	23	3	.	.	PUNCT
ejpam-3371	24	1	let	let	VERB
ejpam-3371	24	2	d	d	PRON
ejpam-3371	24	3	be	be	AUX
ejpam-3371	24	4	a	a	DET
ejpam-3371	24	5	nonempty	nonempty	ADJ
ejpam-3371	24	6	subset	subset	NOUN
ejpam-3371	24	7	of	of	ADP
ejpam-3371	24	8	x	x	PUNCT
ejpam-3371	24	9	and	and	CCONJ
ejpam-3371	24	10	t	t	PROPN
ejpam-3371	24	11	:	:	PUNCT
ejpam-3371	24	12	d	d	X
ejpam-3371	24	13	→	→	SYM
ejpam-3371	24	14	p	p	X
ejpam-3371	24	15	(	(	PUNCT
ejpam-3371	24	16	d	d	NOUN
ejpam-3371	24	17	)	)	PUNCT
ejpam-3371	24	18	be	be	AUX
ejpam-3371	24	19	a	a	DET
ejpam-3371	24	20	multivalued	multivalue	VERB
ejpam-3371	24	21	mapping	mapping	NOUN
ejpam-3371	24	22	.	.	PUNCT
ejpam-3371	25	1	we	we	PRON
ejpam-3371	25	2	call	call	VERB
ejpam-3371	25	3	o(x	o(x	PROPN
ejpam-3371	25	4	,	,	PUNCT
ejpam-3371	25	5	t	t	NOUN
ejpam-3371	25	6	)	)	PUNCT
ejpam-3371	25	7	=	=	PUNCT
ejpam-3371	26	1	{	{	PUNCT
ejpam-3371	26	2	xn	xn	X
ejpam-3371	26	3	}	}	PUNCT
ejpam-3371	26	4	a	a	DET
ejpam-3371	26	5	generalized	generalize	VERB
ejpam-3371	26	6	orbit	orbit	NOUN
ejpam-3371	26	7	of	of	ADP
ejpam-3371	26	8	x	x	PRON
ejpam-3371	26	9	if	if	SCONJ
ejpam-3371	26	10	for	for	ADP
ejpam-3371	26	11	any	any	DET
ejpam-3371	26	12	x	x	SYM
ejpam-3371	26	13	∈	∈	PROPN
ejpam-3371	26	14	d	d	NOUN
ejpam-3371	26	15	and	and	CCONJ
ejpam-3371	26	16	n	n	PRON
ejpam-3371	26	17	≥	≥	NOUN
ejpam-3371	26	18	0	0	NUM
ejpam-3371	26	19	,	,	PUNCT
ejpam-3371	26	20	the	the	DET
ejpam-3371	26	21	sequence	sequence	NOUN
ejpam-3371	26	22	{	{	PUNCT
ejpam-3371	26	23	xn	xn	NOUN
ejpam-3371	26	24	}	}	PUNCT
ejpam-3371	26	25	is	be	AUX
ejpam-3371	26	26	defined	define	VERB
ejpam-3371	26	27	by	by	ADP
ejpam-3371	26	28	x0	x0	PROPN
ejpam-3371	26	29	=	=	PUNCT
ejpam-3371	27	1	x	x	PUNCT
ejpam-3371	27	2	and	and	CCONJ
ejpam-3371	27	3	xn+1	xn+1	PROPN
ejpam-3371	27	4	∈	∈	PROPN
ejpam-3371	27	5	t	t	PROPN
ejpam-3371	27	6	(	(	PUNCT
ejpam-3371	27	7	xn	xn	PROPN
ejpam-3371	27	8	)	)	PUNCT
ejpam-3371	27	9	where	where	SCONJ
ejpam-3371	27	10	n	n	X
ejpam-3371	27	11	∈	∈	PROPN
ejpam-3371	27	12	n	n	PART
ejpam-3371	27	13	∪	∪	X
ejpam-3371	27	14	{	{	PUNCT
ejpam-3371	27	15	0	0	NUM
ejpam-3371	27	16	}	}	PUNCT
ejpam-3371	27	17	.	.	PUNCT
ejpam-3371	28	1	recently	recently	ADV
ejpam-3371	28	2	,	,	PUNCT
ejpam-3371	28	3	in	in	ADP
ejpam-3371	28	4	2017	2017	NUM
ejpam-3371	28	5	,	,	PUNCT
ejpam-3371	28	6	khamsi	khamsi	NOUN
ejpam-3371	28	7	and	and	CCONJ
ejpam-3371	28	8	khan	khan	PROPN
ejpam-3371	28	9	[	[	X
ejpam-3371	28	10	2	2	NUM
ejpam-3371	28	11	]	]	PUNCT
ejpam-3371	28	12	,	,	PUNCT
ejpam-3371	28	13	introduced	introduce	VERB
ejpam-3371	28	14	the	the	DET
ejpam-3371	28	15	concept	concept	NOUN
ejpam-3371	28	16	of	of	ADP
ejpam-3371	28	17	a	a	DET
ejpam-3371	28	18	multivalued	multivalue	VERB
ejpam-3371	28	19	asymptotically	asymptotically	ADV
ejpam-3371	28	20	nonexpansive	nonexpansive	ADJ
ejpam-3371	28	21	mapping	mapping	NOUN
ejpam-3371	28	22	.	.	PUNCT
ejpam-3371	29	1	definition	definition	NOUN
ejpam-3371	29	2	2	2	NUM
ejpam-3371	29	3	.	.	PUNCT
ejpam-3371	30	1	a	a	DET
ejpam-3371	30	2	mapping	mapping	NOUN
ejpam-3371	30	3	t	t	NOUN
ejpam-3371	30	4	:	:	PUNCT
ejpam-3371	30	5	d	d	X
ejpam-3371	30	6	→	→	SYM
ejpam-3371	30	7	p	p	X
ejpam-3371	30	8	(	(	PUNCT
ejpam-3371	30	9	d	d	NOUN
ejpam-3371	30	10	)	)	PUNCT
ejpam-3371	30	11	is	be	AUX
ejpam-3371	30	12	called	call	VERB
ejpam-3371	30	13	a	a	DET
ejpam-3371	30	14	multivalued	multivalue	VERB
ejpam-3371	30	15	asymptotically	asymptotically	ADV
ejpam-3371	30	16	nonexpansive	nonexpansive	ADJ
ejpam-3371	30	17	mapping	mapping	NOUN
ejpam-3371	30	18	if	if	SCONJ
ejpam-3371	30	19	there	there	PRON
ejpam-3371	30	20	exists	exist	VERB
ejpam-3371	30	21	a	a	DET
ejpam-3371	30	22	sequence	sequence	NOUN
ejpam-3371	30	23	{	{	PUNCT
ejpam-3371	30	24	kn	kn	NOUN
ejpam-3371	30	25	}	}	PUNCT
ejpam-3371	30	26	with	with	ADP
ejpam-3371	30	27	kn	kn	PROPN
ejpam-3371	30	28	≥	≥	NUM
ejpam-3371	30	29	1	1	NUM
ejpam-3371	30	30	and	and	CCONJ
ejpam-3371	30	31	limn→∞	limn→∞	PROPN
ejpam-3371	31	1	kn	kn	NOUN
ejpam-3371	31	2	=	=	PROPN
ejpam-3371	31	3	1	1	NUM
ejpam-3371	31	4	such	such	ADJ
ejpam-3371	31	5	that	that	PRON
ejpam-3371	31	6	for	for	ADP
ejpam-3371	31	7	any	any	DET
ejpam-3371	31	8	x	x	NOUN
ejpam-3371	31	9	,	,	PUNCT
ejpam-3371	31	10	y	y	PROPN
ejpam-3371	31	11	∈	∈	PROPN
ejpam-3371	31	12	d	d	NOUN
ejpam-3371	31	13	,	,	PUNCT
ejpam-3371	31	14	and	and	CCONJ
ejpam-3371	31	15	any	any	DET
ejpam-3371	31	16	generalized	generalized	ADJ
ejpam-3371	31	17	orbit	orbit	NOUN
ejpam-3371	31	18	o(x	o(x	PROPN
ejpam-3371	31	19	,	,	PUNCT
ejpam-3371	31	20	t	t	PROPN
ejpam-3371	31	21	)	)	PUNCT
ejpam-3371	31	22	=	=	PUNCT
ejpam-3371	31	23	{	{	PUNCT
ejpam-3371	31	24	xn	xn	NOUN
ejpam-3371	31	25	}	}	PUNCT
ejpam-3371	31	26	of	of	ADP
ejpam-3371	31	27	x	x	NOUN
ejpam-3371	31	28	,	,	PUNCT
ejpam-3371	31	29	there	there	PRON
ejpam-3371	31	30	exists	exist	VERB
ejpam-3371	31	31	a	a	DET
ejpam-3371	31	32	generalized	generalized	ADJ
ejpam-3371	31	33	orbit	orbit	NOUN
ejpam-3371	31	34	o(y	o(y	PROPN
ejpam-3371	31	35	,	,	PUNCT
ejpam-3371	31	36	t	t	NOUN
ejpam-3371	31	37	)	)	PUNCT
ejpam-3371	32	1	=	=	PRON
ejpam-3371	32	2	{	{	PUNCT
ejpam-3371	32	3	yn	yn	NOUN
ejpam-3371	32	4	}	}	PUNCT
ejpam-3371	32	5	of	of	ADP
ejpam-3371	32	6	y	y	PRON
ejpam-3371	32	7	such	such	ADJ
ejpam-3371	32	8	that	that	SCONJ
ejpam-3371	32	9	d(xn+h	d(xn+h	PROPN
ejpam-3371	32	10	,	,	PUNCT
ejpam-3371	32	11	yh	yh	NOUN
ejpam-3371	32	12	)	)	PUNCT
ejpam-3371	32	13	≤	≤	NOUN
ejpam-3371	32	14	khd(xn	khd(xn	NOUN
ejpam-3371	32	15	,	,	PUNCT
ejpam-3371	32	16	y	y	NOUN
ejpam-3371	32	17	)	)	PUNCT
ejpam-3371	32	18	,	,	PUNCT
ejpam-3371	32	19	where	where	SCONJ
ejpam-3371	32	20	n	n	CCONJ
ejpam-3371	32	21	,	,	PUNCT
ejpam-3371	32	22	h	h	PROPN
ejpam-3371	32	23	∈	∈	PROPN
ejpam-3371	32	24	n.	n.	NOUN
ejpam-3371	32	25	they	they	PRON
ejpam-3371	32	26	established	establish	VERB
ejpam-3371	32	27	the	the	DET
ejpam-3371	32	28	existence	existence	NOUN
ejpam-3371	32	29	of	of	ADP
ejpam-3371	32	30	a	a	DET
ejpam-3371	32	31	fixed	fix	VERB
ejpam-3371	32	32	point	point	NOUN
ejpam-3371	32	33	for	for	ADP
ejpam-3371	32	34	a	a	DET
ejpam-3371	32	35	multivalued	multivalue	VERB
ejpam-3371	32	36	asymptotically	asymptotically	ADV
ejpam-3371	32	37	nonexpansive	nonexpansive	ADJ
ejpam-3371	32	38	mapping	mapping	NOUN
ejpam-3371	32	39	in	in	ADP
ejpam-3371	32	40	hyperbolic	hyperbolic	ADJ
ejpam-3371	32	41	metric	metric	ADJ
ejpam-3371	32	42	spaces	space	NOUN
ejpam-3371	32	43	.	.	PUNCT
ejpam-3371	33	1	they	they	PRON
ejpam-3371	33	2	also	also	ADV
ejpam-3371	33	3	proved	prove	VERB
ejpam-3371	33	4	the	the	DET
ejpam-3371	33	5	convergence	convergence	NOUN
ejpam-3371	33	6	of	of	ADP
ejpam-3371	33	7	a	a	DET
ejpam-3371	33	8	modified	modify	VERB
ejpam-3371	33	9	mann	mann	NOUN
ejpam-3371	33	10	iterative	iterative	NOUN
ejpam-3371	33	11	process	process	NOUN
ejpam-3371	33	12	.	.	PUNCT
ejpam-3371	34	1	motivated	motivate	VERB
ejpam-3371	34	2	by	by	ADP
ejpam-3371	34	3	this	this	PRON
ejpam-3371	34	4	,	,	PUNCT
ejpam-3371	34	5	we	we	PRON
ejpam-3371	34	6	construct	construct	VERB
ejpam-3371	34	7	a	a	DET
ejpam-3371	34	8	modified	modify	VERB
ejpam-3371	34	9	ishikawa	ishikawa	PROPN
ejpam-3371	34	10	iterative	iterative	NOUN
ejpam-3371	34	11	process	process	NOUN
ejpam-3371	34	12	for	for	ADP
ejpam-3371	34	13	two	two	NUM
ejpam-3371	34	14	multivalued	multivalue	VERB
ejpam-3371	34	15	asymptotically	asymptotically	ADV
ejpam-3371	34	16	nonexpansive	nonexpansive	ADJ
ejpam-3371	34	17	mappings	mapping	NOUN
ejpam-3371	34	18	and	and	CCONJ
ejpam-3371	34	19	then	then	ADV
ejpam-3371	34	20	prove	prove	VERB
ejpam-3371	34	21	some	some	DET
ejpam-3371	34	22	convergence	convergence	NOUN
ejpam-3371	34	23	theorems	theorem	NOUN
ejpam-3371	34	24	in	in	ADP
ejpam-3371	34	25	uniformly	uniformly	ADV
ejpam-3371	34	26	convex	convex	VERB
ejpam-3371	34	27	hyperbolic	hyperbolic	ADJ
ejpam-3371	34	28	metric	metric	ADJ
ejpam-3371	34	29	spaces	space	NOUN
ejpam-3371	34	30	.	.	PUNCT
ejpam-3371	35	1	next	next	ADV
ejpam-3371	35	2	we	we	PRON
ejpam-3371	35	3	recall	recall	VERB
ejpam-3371	35	4	the	the	DET
ejpam-3371	35	5	concept	concept	NOUN
ejpam-3371	35	6	of	of	ADP
ejpam-3371	35	7	hyperbolic	hyperbolic	ADJ
ejpam-3371	35	8	metric	metric	ADJ
ejpam-3371	35	9	spaces	space	NOUN
ejpam-3371	35	10	.	.	PUNCT
ejpam-3371	36	1	let	let	VERB
ejpam-3371	36	2	(	(	PUNCT
ejpam-3371	36	3	x	x	NOUN
ejpam-3371	36	4	,	,	PUNCT
ejpam-3371	36	5	d	d	NOUN
ejpam-3371	36	6	)	)	PUNCT
ejpam-3371	36	7	be	be	AUX
ejpam-3371	36	8	a	a	DET
ejpam-3371	36	9	metric	metric	ADJ
ejpam-3371	36	10	space	space	NOUN
ejpam-3371	36	11	and	and	CCONJ
ejpam-3371	36	12	x	x	NOUN
ejpam-3371	36	13	,	,	PUNCT
ejpam-3371	36	14	y	y	PROPN
ejpam-3371	36	15	be	be	VERB
ejpam-3371	36	16	any	any	DET
ejpam-3371	36	17	two	two	NUM
ejpam-3371	36	18	points	point	NOUN
ejpam-3371	36	19	in	in	ADP
ejpam-3371	36	20	x.	x.	NOUN
ejpam-3371	36	21	then	then	ADV
ejpam-3371	36	22	the	the	DET
ejpam-3371	36	23	unique	unique	ADJ
ejpam-3371	36	24	metric	metric	ADJ
ejpam-3371	36	25	segment	segment	NOUN
ejpam-3371	36	26	[	[	X
ejpam-3371	36	27	x	x	X
ejpam-3371	36	28	,	,	PUNCT
ejpam-3371	36	29	y	y	PROPN
ejpam-3371	36	30	]	]	X
ejpam-3371	36	31	is	be	AUX
ejpam-3371	36	32	an	an	DET
ejpam-3371	36	33	isometric	isometric	ADJ
ejpam-3371	36	34	image	image	NOUN
ejpam-3371	36	35	of	of	ADP
ejpam-3371	36	36	the	the	DET
ejpam-3371	36	37	real	real	ADJ
ejpam-3371	36	38	line	line	NOUN
ejpam-3371	36	39	interval	interval	NOUN
ejpam-3371	36	40	[	[	X
ejpam-3371	36	41	0	0	NUM
ejpam-3371	36	42	,	,	PUNCT
ejpam-3371	36	43	d(x	d(x	PROPN
ejpam-3371	36	44	,	,	PUNCT
ejpam-3371	36	45	y	y	PROPN
ejpam-3371	36	46	)	)	PUNCT
ejpam-3371	36	47	]	]	PUNCT
ejpam-3371	36	48	.	.	PUNCT
ejpam-3371	37	1	a	a	DET
ejpam-3371	37	2	point	point	NOUN
ejpam-3371	37	3	z	z	NOUN
ejpam-3371	37	4	in	in	ADP
ejpam-3371	37	5	[	[	X
ejpam-3371	37	6	x	x	NOUN
ejpam-3371	37	7	,	,	PUNCT
ejpam-3371	37	8	y	y	PROPN
ejpam-3371	37	9	]	]	PUNCT
ejpam-3371	37	10	is	be	AUX
ejpam-3371	37	11	denoted	denote	VERB
ejpam-3371	37	12	as	as	ADP
ejpam-3371	37	13	βx	βx	ADP
ejpam-3371	37	14	⊕	⊕	PROPN
ejpam-3371	37	15	(	(	PUNCT
ejpam-3371	37	16	1	1	NUM
ejpam-3371	37	17	−	−	NOUN
ejpam-3371	37	18	β)y	β)y	PUNCT
ejpam-3371	37	19	which	which	PRON
ejpam-3371	37	20	satisfies	satisfy	VERB
ejpam-3371	37	21	d(x	d(x	PROPN
ejpam-3371	37	22	,	,	PUNCT
ejpam-3371	37	23	z	z	NOUN
ejpam-3371	37	24	)	)	PUNCT
ejpam-3371	37	25	=	=	SYM
ejpam-3371	37	26	(	(	PUNCT
ejpam-3371	37	27	1−	1−	NUM
ejpam-3371	37	28	β)d(x	β)d(x	X
ejpam-3371	37	29	,	,	PUNCT
ejpam-3371	37	30	y	y	NOUN
ejpam-3371	37	31	)	)	PUNCT
ejpam-3371	37	32	and	and	CCONJ
ejpam-3371	37	33	d(z	d(z	PROPN
ejpam-3371	37	34	,	,	PUNCT
ejpam-3371	37	35	y	y	NOUN
ejpam-3371	37	36	)	)	PUNCT
ejpam-3371	38	1	=	=	PUNCT
ejpam-3371	38	2	βd(x	βd(x	X
ejpam-3371	38	3	,	,	PUNCT
ejpam-3371	38	4	y	y	NOUN
ejpam-3371	38	5	)	)	PUNCT
ejpam-3371	38	6	where	where	SCONJ
ejpam-3371	38	7	β	β	X
ejpam-3371	38	8	∈	∈	PROPN
ejpam-3371	39	1	[	[	X
ejpam-3371	39	2	0	0	NUM
ejpam-3371	39	3	,	,	PUNCT
ejpam-3371	39	4	1	1	NUM
ejpam-3371	39	5	]	]	PUNCT
ejpam-3371	39	6	.	.	PUNCT
ejpam-3371	40	1	metric	metric	ADJ
ejpam-3371	40	2	spaces	space	NOUN
ejpam-3371	40	3	with	with	ADP
ejpam-3371	40	4	the	the	DET
ejpam-3371	40	5	class	class	NOUN
ejpam-3371	40	6	of	of	ADP
ejpam-3371	40	7	metric	metric	ADJ
ejpam-3371	40	8	segments	segment	NOUN
ejpam-3371	40	9	are	be	AUX
ejpam-3371	40	10	usually	usually	ADV
ejpam-3371	40	11	called	call	VERB
ejpam-3371	40	12	convex	convex	ADJ
ejpam-3371	40	13	metric	metric	ADJ
ejpam-3371	40	14	spaces	space	NOUN
ejpam-3371	40	15	[	[	X
ejpam-3371	40	16	5	5	NUM
ejpam-3371	40	17	]	]	PUNCT
ejpam-3371	40	18	.	.	PUNCT
ejpam-3371	41	1	further	far	ADV
ejpam-3371	41	2	,	,	PUNCT
ejpam-3371	41	3	if	if	SCONJ
ejpam-3371	41	4	d(αu⊕	d(αu⊕	NOUN
ejpam-3371	41	5	(	(	PUNCT
ejpam-3371	41	6	1−	1−	NUM
ejpam-3371	41	7	α)x	α)x	NUM
ejpam-3371	41	8	,	,	PUNCT
ejpam-3371	41	9	αv	αv	ADP
ejpam-3371	41	10	⊕	⊕	PROPN
ejpam-3371	41	11	(	(	PUNCT
ejpam-3371	41	12	1−	1−	NUM
ejpam-3371	41	13	α)y	α)y	NOUN
ejpam-3371	41	14	)	)	PUNCT
ejpam-3371	41	15	≤	≤	NOUN
ejpam-3371	41	16	αd(u	αd(u	X
ejpam-3371	41	17	,	,	PUNCT
ejpam-3371	41	18	v	v	NOUN
ejpam-3371	41	19	)	)	PUNCT
ejpam-3371	41	20	+	+	CCONJ
ejpam-3371	41	21	(	(	PUNCT
ejpam-3371	41	22	1−	1−	NUM
ejpam-3371	41	23	α)d(x	α)d(x	NOUN
ejpam-3371	41	24	,	,	PUNCT
ejpam-3371	41	25	y	y	NOUN
ejpam-3371	41	26	)	)	PUNCT
ejpam-3371	41	27	is	be	AUX
ejpam-3371	41	28	satisfied	satisfied	ADJ
ejpam-3371	41	29	for	for	ADP
ejpam-3371	41	30	any	any	DET
ejpam-3371	41	31	x	x	NOUN
ejpam-3371	41	32	,	,	PUNCT
ejpam-3371	41	33	y	y	PROPN
ejpam-3371	41	34	,	,	PUNCT
ejpam-3371	41	35	u	u	NOUN
ejpam-3371	41	36	,	,	PUNCT
ejpam-3371	41	37	v	v	NOUN
ejpam-3371	41	38	∈	∈	NOUN
ejpam-3371	41	39	x	x	X
ejpam-3371	41	40	and	and	CCONJ
ejpam-3371	41	41	α	α	NOUN
ejpam-3371	41	42	∈	∈	PROPN
ejpam-3371	42	1	[	[	X
ejpam-3371	42	2	0	0	NUM
ejpam-3371	42	3	,	,	PUNCT
ejpam-3371	42	4	1	1	NUM
ejpam-3371	42	5	]	]	PUNCT
ejpam-3371	42	6	,	,	PUNCT
ejpam-3371	42	7	then	then	ADV
ejpam-3371	42	8	x	x	PUNCT
ejpam-3371	42	9	is	be	AUX
ejpam-3371	42	10	said	say	VERB
ejpam-3371	42	11	to	to	PART
ejpam-3371	42	12	be	be	AUX
ejpam-3371	42	13	a	a	DET
ejpam-3371	42	14	hyperbolic	hyperbolic	ADJ
ejpam-3371	42	15	metric	metric	ADJ
ejpam-3371	42	16	space	space	NOUN
ejpam-3371	43	1	[	[	X
ejpam-3371	43	2	6	6	NUM
ejpam-3371	43	3	]	]	PUNCT
ejpam-3371	43	4	.	.	PUNCT
ejpam-3371	44	1	the	the	DET
ejpam-3371	44	2	following	follow	VERB
ejpam-3371	44	3	definition	definition	NOUN
ejpam-3371	44	4	of	of	ADP
ejpam-3371	44	5	uniformly	uniformly	ADV
ejpam-3371	44	6	convex	convex	VERB
ejpam-3371	44	7	hyperbolic	hyperbolic	ADJ
ejpam-3371	44	8	metric	metric	ADJ
ejpam-3371	44	9	space	space	NOUN
ejpam-3371	44	10	can	can	AUX
ejpam-3371	44	11	be	be	AUX
ejpam-3371	44	12	found	find	VERB
ejpam-3371	44	13	in	in	ADP
ejpam-3371	44	14	[	[	X
ejpam-3371	44	15	1	1	NUM
ejpam-3371	44	16	]	]	PUNCT
ejpam-3371	44	17	.	.	PUNCT
ejpam-3371	45	1	definition	definition	NOUN
ejpam-3371	45	2	3	3	NUM
ejpam-3371	45	3	.	.	PUNCT
ejpam-3371	46	1	a	a	DET
ejpam-3371	46	2	hyperbolic	hyperbolic	ADJ
ejpam-3371	46	3	metric	metric	ADJ
ejpam-3371	46	4	space	space	NOUN
ejpam-3371	46	5	(	(	PUNCT
ejpam-3371	46	6	x	x	X
ejpam-3371	46	7	,	,	PUNCT
ejpam-3371	46	8	d	d	NOUN
ejpam-3371	46	9	)	)	PUNCT
ejpam-3371	46	10	is	be	AUX
ejpam-3371	46	11	called	call	VERB
ejpam-3371	46	12	uniformly	uniformly	ADV
ejpam-3371	46	13	convex	convex	NOUN
ejpam-3371	46	14	if	if	SCONJ
ejpam-3371	46	15	for	for	ADP
ejpam-3371	46	16	any	any	DET
ejpam-3371	46	17	x	x	NOUN
ejpam-3371	46	18	,	,	PUNCT
ejpam-3371	46	19	y	y	PROPN
ejpam-3371	46	20	,	,	PUNCT
ejpam-3371	46	21	w	w	PROPN
ejpam-3371	46	22	∈	∈	PROPN
ejpam-3371	46	23	x	x	X
ejpam-3371	46	24	,	,	PUNCT
ejpam-3371	46	25	for	for	ADP
ejpam-3371	46	26	every	every	DET
ejpam-3371	46	27	r	r	NOUN
ejpam-3371	46	28	>	>	X
ejpam-3371	46	29	0	0	NUM
ejpam-3371	46	30	,	,	PUNCT
ejpam-3371	46	31	and	and	CCONJ
ejpam-3371	46	32	for	for	ADP
ejpam-3371	46	33	each	each	DET
ejpam-3371	46	34	ε	ε	PROPN
ejpam-3371	46	35	>	>	X
ejpam-3371	46	36	0	0	PUNCT
ejpam-3371	46	37	δ(r	δ(r	NOUN
ejpam-3371	46	38	,	,	PUNCT
ejpam-3371	46	39	ε	ε	PROPN
ejpam-3371	46	40	)	)	PUNCT
ejpam-3371	46	41	=	=	SYM
ejpam-3371	46	42	inf	inf	NOUN
ejpam-3371	46	43	{	{	PUNCT
ejpam-3371	46	44	1−	1−	NUM
ejpam-3371	46	45	1	1	NUM
ejpam-3371	46	46	r	r	NOUN
ejpam-3371	46	47	d	d	PROPN
ejpam-3371	46	48	(	(	PUNCT
ejpam-3371	46	49	1	1	NUM
ejpam-3371	46	50	2	2	NUM
ejpam-3371	46	51	x⊕	x⊕	NUM
ejpam-3371	46	52	1	1	NUM
ejpam-3371	46	53	2	2	NUM
ejpam-3371	46	54	y	y	PROPN
ejpam-3371	46	55	,	,	PUNCT
ejpam-3371	46	56	w	w	PROPN
ejpam-3371	46	57	)	)	PUNCT
ejpam-3371	46	58	;	;	PUNCT
ejpam-3371	46	59	s.	s.	PROPN
ejpam-3371	46	60	h.	h.	PROPN
ejpam-3371	46	61	khan	khan	PROPN
ejpam-3371	46	62	,	,	PUNCT
ejpam-3371	46	63	h.	h.	PROPN
ejpam-3371	46	64	iqbal	iqbal	PROPN
ejpam-3371	46	65	,	,	PUNCT
ejpam-3371	46	66	m.	m.	NOUN
ejpam-3371	46	67	abbas	abbas	PROPN
ejpam-3371	46	68	/	/	SYM
ejpam-3371	46	69	eur	eur	PROPN
ejpam-3371	46	70	.	.	PUNCT
ejpam-3371	47	1	j.	j.	PROPN
ejpam-3371	47	2	pure	pure	PROPN
ejpam-3371	47	3	appl	appl	PROPN
ejpam-3371	47	4	.	.	PROPN
ejpam-3371	47	5	math	math	PROPN
ejpam-3371	47	6	,	,	PUNCT
ejpam-3371	47	7	12	12	NUM
ejpam-3371	47	8	(	(	PUNCT
ejpam-3371	47	9	2	2	NUM
ejpam-3371	47	10	)	)	PUNCT
ejpam-3371	47	11	(	(	PUNCT
ejpam-3371	47	12	2019	2019	NUM
ejpam-3371	47	13	)	)	PUNCT
ejpam-3371	47	14	,	,	PUNCT
ejpam-3371	47	15	348	348	NUM
ejpam-3371	47	16	-	-	SYM
ejpam-3371	47	17	357	357	NUM
ejpam-3371	47	18	350	350	NUM
ejpam-3371	47	19	d(x	d(x	NOUN
ejpam-3371	47	20	,	,	PUNCT
ejpam-3371	47	21	w	w	NOUN
ejpam-3371	47	22	)	)	PUNCT
ejpam-3371	47	23	≤	≤	NOUN
ejpam-3371	47	24	r	r	NOUN
ejpam-3371	47	25	,	,	PUNCT
ejpam-3371	47	26	d(y	d(y	PROPN
ejpam-3371	47	27	,	,	PUNCT
ejpam-3371	47	28	w	w	NOUN
ejpam-3371	47	29	)	)	PUNCT
ejpam-3371	47	30	≤	≤	NOUN
ejpam-3371	47	31	r	r	NOUN
ejpam-3371	47	32	,	,	PUNCT
ejpam-3371	47	33	d(x	d(x	PROPN
ejpam-3371	47	34	,	,	PUNCT
ejpam-3371	47	35	y	y	PROPN
ejpam-3371	47	36	)	)	PUNCT
ejpam-3371	47	37	≥	≥	NOUN
ejpam-3371	47	38	rε	rε	NOUN
ejpam-3371	47	39	}	}	PUNCT
ejpam-3371	47	40	>	>	X
ejpam-3371	47	41	0	0	X
ejpam-3371	47	42	.	.	PUNCT
ejpam-3371	48	1	following	follow	VERB
ejpam-3371	48	2	is	be	AUX
ejpam-3371	48	3	an	an	DET
ejpam-3371	48	4	important	important	ADJ
ejpam-3371	48	5	result	result	NOUN
ejpam-3371	48	6	in	in	ADP
ejpam-3371	48	7	a	a	DET
ejpam-3371	48	8	uniformly	uniformly	ADV
ejpam-3371	48	9	convex	convex	ADJ
ejpam-3371	48	10	hyperbolic	hyperbolic	ADJ
ejpam-3371	48	11	metric	metric	ADJ
ejpam-3371	48	12	space	space	NOUN
ejpam-3371	48	13	which	which	PRON
ejpam-3371	48	14	will	will	AUX
ejpam-3371	48	15	be	be	AUX
ejpam-3371	48	16	used	use	VERB
ejpam-3371	48	17	later	later	ADV
ejpam-3371	48	18	.	.	PUNCT
ejpam-3371	49	1	theorem	theorem	VERB
ejpam-3371	49	2	1	1	NUM
ejpam-3371	49	3	.	.	PUNCT
ejpam-3371	50	1	[	[	X
ejpam-3371	50	2	4	4	X
ejpam-3371	50	3	]	]	X
ejpam-3371	50	4	let	let	VERB
ejpam-3371	50	5	(	(	PUNCT
ejpam-3371	50	6	x	x	NOUN
ejpam-3371	50	7	,	,	PUNCT
ejpam-3371	50	8	d	d	NOUN
ejpam-3371	50	9	)	)	PUNCT
ejpam-3371	50	10	be	be	AUX
ejpam-3371	50	11	a	a	DET
ejpam-3371	50	12	uniformly	uniformly	ADV
ejpam-3371	50	13	convex	convex	ADJ
ejpam-3371	50	14	complete	complete	ADJ
ejpam-3371	50	15	hyperbolic	hyperbolic	ADJ
ejpam-3371	50	16	metric	metric	ADJ
ejpam-3371	50	17	space	space	NOUN
ejpam-3371	50	18	.	.	PUNCT
ejpam-3371	51	1	let	let	VERB
ejpam-3371	51	2	c	c	PRON
ejpam-3371	51	3	>	>	X
ejpam-3371	51	4	0	0	PUNCT
ejpam-3371	52	1	and	and	CCONJ
ejpam-3371	52	2	z	z	PROPN
ejpam-3371	52	3	∈	∈	PROPN
ejpam-3371	52	4	x.	x.	NOUN
ejpam-3371	52	5	assume	assume	VERB
ejpam-3371	52	6	that	that	SCONJ
ejpam-3371	52	7	{	{	PUNCT
ejpam-3371	52	8	xn	xn	X
ejpam-3371	52	9	}	}	PUNCT
ejpam-3371	52	10	and	and	CCONJ
ejpam-3371	52	11	{	{	PUNCT
ejpam-3371	52	12	yn	yn	NOUN
ejpam-3371	52	13	}	}	PUNCT
ejpam-3371	52	14	are	be	AUX
ejpam-3371	52	15	two	two	NUM
ejpam-3371	52	16	sequences	sequence	NOUN
ejpam-3371	52	17	in	in	ADP
ejpam-3371	52	18	x	x	PUNCT
ejpam-3371	52	19	such	such	ADJ
ejpam-3371	52	20	that	that	SCONJ
ejpam-3371	52	21	lim	lim	PROPN
ejpam-3371	52	22	sup	sup	VERB
ejpam-3371	52	23	n→∞	n→∞	X
ejpam-3371	53	1	d(xn	d(xn	ADJ
ejpam-3371	53	2	,	,	PUNCT
ejpam-3371	53	3	z	z	NOUN
ejpam-3371	53	4	)	)	PUNCT
ejpam-3371	53	5	≤	≤	NOUN
ejpam-3371	53	6	c	c	X
ejpam-3371	53	7	,	,	PUNCT
ejpam-3371	53	8	lim	lim	PROPN
ejpam-3371	53	9	sup	sup	VERB
ejpam-3371	53	10	n→∞	n→∞	NUM
ejpam-3371	53	11	d(yn	d(yn	NOUN
ejpam-3371	53	12	,	,	PUNCT
ejpam-3371	53	13	z	z	NOUN
ejpam-3371	53	14	)	)	PUNCT
ejpam-3371	53	15	≤	≤	NOUN
ejpam-3371	54	1	c	c	NOUN
ejpam-3371	54	2	,	,	PUNCT
ejpam-3371	54	3	and	and	CCONJ
ejpam-3371	54	4	,	,	PUNCT
ejpam-3371	54	5	lim	lim	PROPN
ejpam-3371	54	6	n→∞	n→∞	NUM
ejpam-3371	54	7	d(αxn	d(αxn	PROPN
ejpam-3371	54	8	⊕	⊕	PROPN
ejpam-3371	54	9	(	(	PUNCT
ejpam-3371	54	10	1−	1−	NUM
ejpam-3371	54	11	α)yn	α)yn	PROPN
ejpam-3371	54	12	,	,	PUNCT
ejpam-3371	54	13	z	z	NOUN
ejpam-3371	54	14	)	)	PUNCT
ejpam-3371	55	1	=	=	SYM
ejpam-3371	55	2	c	c	X
ejpam-3371	55	3	,	,	PUNCT
ejpam-3371	55	4	then	then	ADV
ejpam-3371	55	5	we	we	PRON
ejpam-3371	55	6	have	have	VERB
ejpam-3371	55	7	lim	lim	PROPN
ejpam-3371	55	8	n→∞	n→∞	X
ejpam-3371	55	9	d(xn	d(xn	PROPN
ejpam-3371	55	10	,	,	PUNCT
ejpam-3371	55	11	yn	yn	PROPN
ejpam-3371	55	12	)	)	PUNCT
ejpam-3371	55	13	=	=	SYM
ejpam-3371	56	1	0	0	X
ejpam-3371	56	2	.	.	PUNCT
ejpam-3371	57	1	the	the	DET
ejpam-3371	57	2	following	follow	VERB
ejpam-3371	57	3	definition	definition	NOUN
ejpam-3371	57	4	is	be	AUX
ejpam-3371	57	5	needed	need	VERB
ejpam-3371	57	6	in	in	ADP
ejpam-3371	57	7	the	the	DET
ejpam-3371	57	8	sequel	sequel	NOUN
ejpam-3371	57	9	.	.	PUNCT
ejpam-3371	58	1	definition	definition	NOUN
ejpam-3371	58	2	4	4	NUM
ejpam-3371	58	3	.	.	PUNCT
ejpam-3371	59	1	a	a	DET
ejpam-3371	59	2	multivalued	multivalue	VERB
ejpam-3371	59	3	mapping	mapping	NOUN
ejpam-3371	59	4	t	t	NOUN
ejpam-3371	59	5	:	:	PUNCT
ejpam-3371	60	1	d	d	X
ejpam-3371	60	2	→	→	SYM
ejpam-3371	60	3	p	p	X
ejpam-3371	60	4	(	(	PUNCT
ejpam-3371	60	5	d	d	NOUN
ejpam-3371	60	6	)	)	PUNCT
ejpam-3371	60	7	is	be	AUX
ejpam-3371	60	8	said	say	VERB
ejpam-3371	60	9	to	to	PART
ejpam-3371	60	10	be	be	AUX
ejpam-3371	60	11	h	h	NOUN
ejpam-3371	60	12	-	-	ADJ
ejpam-3371	60	13	continuous	continuous	ADJ
ejpam-3371	60	14	if	if	SCONJ
ejpam-3371	60	15	for	for	ADP
ejpam-3371	60	16	any	any	DET
ejpam-3371	60	17	sequence	sequence	NOUN
ejpam-3371	60	18	{	{	PUNCT
ejpam-3371	60	19	xn	xn	NOUN
ejpam-3371	60	20	}	}	PUNCT
ejpam-3371	60	21	which	which	PRON
ejpam-3371	60	22	converges	converge	VERB
ejpam-3371	60	23	to	to	ADP
ejpam-3371	60	24	x	x	PUNCT
ejpam-3371	60	25	in	in	ADP
ejpam-3371	60	26	d	d	PROPN
ejpam-3371	60	27	,	,	PUNCT
ejpam-3371	60	28	we	we	PRON
ejpam-3371	60	29	have	have	VERB
ejpam-3371	60	30	lim	lim	PROPN
ejpam-3371	60	31	n→∞	n→∞	NUM
ejpam-3371	60	32	d(yn	d(yn	NOUN
ejpam-3371	60	33	,	,	PUNCT
ejpam-3371	60	34	t	t	PROPN
ejpam-3371	60	35	(	(	PUNCT
ejpam-3371	60	36	x	x	NOUN
ejpam-3371	60	37	)	)	PUNCT
ejpam-3371	60	38	)	)	PUNCT
ejpam-3371	61	1	=	=	SYM
ejpam-3371	61	2	0	0	NUM
ejpam-3371	61	3	for	for	ADP
ejpam-3371	61	4	any	any	DET
ejpam-3371	61	5	sequence	sequence	NOUN
ejpam-3371	61	6	{	{	PUNCT
ejpam-3371	61	7	yn	yn	NOUN
ejpam-3371	61	8	}	}	PUNCT
ejpam-3371	61	9	such	such	ADJ
ejpam-3371	61	10	that	that	SCONJ
ejpam-3371	61	11	yn	yn	PROPN
ejpam-3371	61	12	∈	∈	PROPN
ejpam-3371	61	13	txn	txn	NOUN
ejpam-3371	61	14	for	for	ADP
ejpam-3371	61	15	any	any	DET
ejpam-3371	61	16	n	n	PRON
ejpam-3371	61	17	∈	∈	PROPN
ejpam-3371	61	18	n.	n.	NOUN
ejpam-3371	61	19	khamsi	khamsi	NOUN
ejpam-3371	61	20	and	and	CCONJ
ejpam-3371	61	21	khan	khan	PROPN
ejpam-3371	61	22	[	[	X
ejpam-3371	61	23	2	2	X
ejpam-3371	61	24	]	]	PUNCT
ejpam-3371	61	25	have	have	AUX
ejpam-3371	61	26	shown	show	VERB
ejpam-3371	61	27	that	that	SCONJ
ejpam-3371	61	28	every	every	DET
ejpam-3371	61	29	multivalued	multivalue	VERB
ejpam-3371	61	30	asymptotically	asymptotically	ADV
ejpam-3371	61	31	nonexpansive	nonexpansive	ADJ
ejpam-3371	61	32	mappings	mapping	NOUN
ejpam-3371	61	33	is	be	AUX
ejpam-3371	61	34	h	h	NOUN
ejpam-3371	61	35	-	-	PUNCT
ejpam-3371	61	36	continuous	continuous	ADJ
ejpam-3371	61	37	.	.	PUNCT
ejpam-3371	62	1	in	in	ADP
ejpam-3371	62	2	this	this	DET
ejpam-3371	62	3	paper	paper	NOUN
ejpam-3371	62	4	,	,	PUNCT
ejpam-3371	62	5	we	we	PRON
ejpam-3371	62	6	construct	construct	VERB
ejpam-3371	62	7	a	a	DET
ejpam-3371	62	8	modified	modify	VERB
ejpam-3371	62	9	ishikawa	ishikawa	PROPN
ejpam-3371	62	10	iterative	iterative	NOUN
ejpam-3371	62	11	process	process	NOUN
ejpam-3371	62	12	which	which	PRON
ejpam-3371	62	13	extends	extend	VERB
ejpam-3371	62	14	the	the	DET
ejpam-3371	62	15	mann	mann	PROPN
ejpam-3371	62	16	type	type	NOUN
ejpam-3371	62	17	iterative	iterative	NOUN
ejpam-3371	62	18	process	process	NOUN
ejpam-3371	62	19	considered	consider	VERB
ejpam-3371	62	20	by	by	ADP
ejpam-3371	62	21	khamsi	khamsi	NOUN
ejpam-3371	62	22	and	and	CCONJ
ejpam-3371	62	23	khan	khan	PROPN
ejpam-3371	63	1	[	[	X
ejpam-3371	63	2	2	2	NUM
ejpam-3371	63	3	]	]	PUNCT
ejpam-3371	63	4	.	.	PUNCT
ejpam-3371	64	1	we	we	PRON
ejpam-3371	64	2	use	use	VERB
ejpam-3371	64	3	this	this	DET
ejpam-3371	64	4	iterative	iterative	NOUN
ejpam-3371	64	5	process	process	NOUN
ejpam-3371	64	6	to	to	PART
ejpam-3371	64	7	approximate	approximate	VERB
ejpam-3371	64	8	common	common	ADJ
ejpam-3371	64	9	fixed	fix	VERB
ejpam-3371	64	10	points	point	NOUN
ejpam-3371	64	11	for	for	ADP
ejpam-3371	64	12	two	two	NUM
ejpam-3371	64	13	multivalued	multivalue	VERB
ejpam-3371	64	14	asymptotically	asymptotically	ADV
ejpam-3371	64	15	nonexpansive	nonexpansive	ADJ
ejpam-3371	64	16	mappings	mapping	NOUN
ejpam-3371	64	17	and	and	CCONJ
ejpam-3371	64	18	prove	prove	VERB
ejpam-3371	64	19	some	some	DET
ejpam-3371	64	20	convergence	convergence	NOUN
ejpam-3371	64	21	theorems	theorem	NOUN
ejpam-3371	64	22	in	in	ADP
ejpam-3371	64	23	uniformly	uniformly	ADV
ejpam-3371	64	24	convex	convex	VERB
ejpam-3371	64	25	hyperbolic	hyperbolic	ADJ
ejpam-3371	64	26	spaces	space	NOUN
ejpam-3371	64	27	.	.	PUNCT
ejpam-3371	65	1	2	2	X
ejpam-3371	65	2	.	.	X
ejpam-3371	65	3	main	main	ADJ
ejpam-3371	65	4	results	result	NOUN
ejpam-3371	65	5	let	let	VERB
ejpam-3371	65	6	t1	t1	NOUN
ejpam-3371	65	7	and	and	CCONJ
ejpam-3371	65	8	t2	t2	NOUN
ejpam-3371	65	9	be	be	VERB
ejpam-3371	65	10	two	two	NUM
ejpam-3371	65	11	multivalued	multivalued	ADJ
ejpam-3371	65	12	asymptotically	asymptotically	ADV
ejpam-3371	65	13	nonexpansive	nonexpansive	ADJ
ejpam-3371	65	14	mappings	mapping	NOUN
ejpam-3371	65	15	such	such	ADJ
ejpam-3371	65	16	that	that	SCONJ
ejpam-3371	65	17	there	there	PRON
ejpam-3371	65	18	exist	exist	VERB
ejpam-3371	65	19	sequences	sequence	NOUN
ejpam-3371	65	20	of	of	ADP
ejpam-3371	65	21	positive	positive	ADJ
ejpam-3371	65	22	numbers	number	NOUN
ejpam-3371	65	23	{	{	PUNCT
ejpam-3371	65	24	k(1)m	k(1)m	X
ejpam-3371	65	25	}	}	PUNCT
ejpam-3371	65	26	and	and	CCONJ
ejpam-3371	65	27	{	{	PUNCT
ejpam-3371	65	28	k(2)m	k(2)m	X
ejpam-3371	65	29	}	}	PUNCT
ejpam-3371	65	30	with	with	ADP
ejpam-3371	65	31	k	k	PROPN
ejpam-3371	65	32	(	(	PUNCT
ejpam-3371	65	33	i	i	NOUN
ejpam-3371	65	34	)	)	PUNCT
ejpam-3371	65	35	m	m	VERB
ejpam-3371	65	36	∈	∈	PROPN
ejpam-3371	66	1	[	[	X
ejpam-3371	66	2	1,∞	1,∞	NUM
ejpam-3371	66	3	)	)	PUNCT
ejpam-3371	66	4	and	and	CCONJ
ejpam-3371	66	5	∑	∑	PROPN
ejpam-3371	66	6	(	(	PUNCT
ejpam-3371	66	7	k	k	X
ejpam-3371	66	8	(	(	PUNCT
ejpam-3371	66	9	i	i	NOUN
ejpam-3371	66	10	)	)	PUNCT
ejpam-3371	66	11	m	m	VERB
ejpam-3371	66	12	−	−	NOUN
ejpam-3371	66	13	1	1	NUM
ejpam-3371	66	14	)	)	PUNCT
ejpam-3371	66	15	<	<	X
ejpam-3371	66	16	∞.	∞.	PROPN
ejpam-3371	66	17	let	let	VERB
ejpam-3371	66	18	km	km	NOUN
ejpam-3371	66	19	=	=	SYM
ejpam-3371	66	20	max{k(1)m	max{k(1)m	NOUN
ejpam-3371	66	21	,	,	PUNCT
ejpam-3371	66	22	k(2)m	k(2)m	X
ejpam-3371	66	23	}	}	PUNCT
ejpam-3371	66	24	,	,	PUNCT
ejpam-3371	66	25	then	then	ADV
ejpam-3371	66	26	∑	∑	INTJ
ejpam-3371	66	27	(	(	PUNCT
ejpam-3371	66	28	km	km	NOUN
ejpam-3371	66	29	−	−	NOUN
ejpam-3371	66	30	1	1	NUM
ejpam-3371	66	31	)	)	PUNCT
ejpam-3371	67	1	<	<	X
ejpam-3371	67	2	∞.	∞.	PROPN
ejpam-3371	67	3	so	so	ADV
ejpam-3371	67	4	,	,	PUNCT
ejpam-3371	67	5	we	we	PRON
ejpam-3371	67	6	take	take	VERB
ejpam-3371	67	7	{	{	PUNCT
ejpam-3371	67	8	km	km	NOUN
ejpam-3371	67	9	}	}	PUNCT
ejpam-3371	67	10	for	for	ADP
ejpam-3371	67	11	both	both	CCONJ
ejpam-3371	67	12	t1	t1	NOUN
ejpam-3371	67	13	and	and	CCONJ
ejpam-3371	67	14	t2	t2	NOUN
ejpam-3371	67	15	.	.	PUNCT
ejpam-3371	68	1	now	now	ADV
ejpam-3371	68	2	,	,	PUNCT
ejpam-3371	68	3	we	we	PRON
ejpam-3371	68	4	construct	construct	VERB
ejpam-3371	68	5	modified	modify	VERB
ejpam-3371	68	6	ishikawa	ishikawa	PROPN
ejpam-3371	68	7	iterative	iterative	NOUN
ejpam-3371	68	8	process	process	NOUN
ejpam-3371	68	9	as	as	SCONJ
ejpam-3371	68	10	follows	follow	VERB
ejpam-3371	68	11	:	:	PUNCT
ejpam-3371	68	12	let	let	VERB
ejpam-3371	68	13	o(x1	o(x1	PROPN
ejpam-3371	68	14	,	,	PUNCT
ejpam-3371	68	15	t1	t1	NOUN
ejpam-3371	68	16	)	)	PUNCT
ejpam-3371	68	17	=	=	SYM
ejpam-3371	68	18	{	{	PUNCT
ejpam-3371	68	19	x́1n	x́1n	PROPN
ejpam-3371	68	20	}	}	PUNCT
ejpam-3371	68	21	be	be	AUX
ejpam-3371	68	22	a	a	DET
ejpam-3371	68	23	generalized	generalized	ADJ
ejpam-3371	68	24	orbit	orbit	NOUN
ejpam-3371	68	25	of	of	ADP
ejpam-3371	68	26	x1	x1	PROPN
ejpam-3371	68	27	associated	associate	VERB
ejpam-3371	68	28	with	with	ADP
ejpam-3371	68	29	t1	t1	PROPN
ejpam-3371	68	30	and	and	CCONJ
ejpam-3371	68	31	o(x1	o(x1	PROPN
ejpam-3371	68	32	,	,	PUNCT
ejpam-3371	68	33	t2	t2	NOUN
ejpam-3371	68	34	)	)	PUNCT
ejpam-3371	68	35	=	=	PUNCT
ejpam-3371	68	36	{	{	PUNCT
ejpam-3371	68	37	x1n	x1n	NOUN
ejpam-3371	68	38	}	}	PUNCT
ejpam-3371	68	39	be	be	AUX
ejpam-3371	68	40	a	a	DET
ejpam-3371	68	41	generalized	generalized	ADJ
ejpam-3371	68	42	orbit	orbit	NOUN
ejpam-3371	68	43	of	of	ADP
ejpam-3371	68	44	x1	x1	PROPN
ejpam-3371	68	45	associated	associate	VERB
ejpam-3371	68	46	with	with	ADP
ejpam-3371	68	47	t2	t2	NOUN
ejpam-3371	68	48	.	.	PUNCT
ejpam-3371	69	1	fix	fix	NOUN
ejpam-3371	69	2	0	0	NUM
ejpam-3371	69	3	<	<	X
ejpam-3371	69	4	α	α	PROPN
ejpam-3371	69	5	,	,	PUNCT
ejpam-3371	69	6	β	β	X
ejpam-3371	69	7	<	<	X
ejpam-3371	69	8	1	1	NUM
ejpam-3371	69	9	and	and	CCONJ
ejpam-3371	69	10	set	set	VERB
ejpam-3371	69	11	x2	x2	PROPN
ejpam-3371	69	12	=	=	PUNCT
ejpam-3371	69	13	αx1	αx1	PROPN
ejpam-3371	69	14	⊕	⊕	PROPN
ejpam-3371	69	15	(	(	PUNCT
ejpam-3371	69	16	1−	1−	NUM
ejpam-3371	69	17	α)ý11	α)ý11	VERB
ejpam-3371	69	18	,	,	PUNCT
ejpam-3371	69	19	s.	s.	PROPN
ejpam-3371	69	20	h.	h.	PROPN
ejpam-3371	69	21	khan	khan	PROPN
ejpam-3371	69	22	,	,	PUNCT
ejpam-3371	69	23	h.	h.	PROPN
ejpam-3371	69	24	iqbal	iqbal	PROPN
ejpam-3371	69	25	,	,	PUNCT
ejpam-3371	69	26	m.	m.	NOUN
ejpam-3371	69	27	abbas	abbas	PROPN
ejpam-3371	69	28	/	/	SYM
ejpam-3371	69	29	eur	eur	PROPN
ejpam-3371	69	30	.	.	PUNCT
ejpam-3371	70	1	j.	j.	PROPN
ejpam-3371	70	2	pure	pure	PROPN
ejpam-3371	70	3	appl	appl	PROPN
ejpam-3371	70	4	.	.	PROPN
ejpam-3371	70	5	math	math	PROPN
ejpam-3371	70	6	,	,	PUNCT
ejpam-3371	70	7	12	12	NUM
ejpam-3371	70	8	(	(	PUNCT
ejpam-3371	70	9	2	2	NUM
ejpam-3371	70	10	)	)	PUNCT
ejpam-3371	70	11	(	(	PUNCT
ejpam-3371	70	12	2019	2019	NUM
ejpam-3371	70	13	)	)	PUNCT
ejpam-3371	70	14	,	,	PUNCT
ejpam-3371	70	15	348	348	NUM
ejpam-3371	70	16	-	-	SYM
ejpam-3371	70	17	357	357	NUM
ejpam-3371	70	18	351	351	NUM
ejpam-3371	70	19	y1	y1	NOUN
ejpam-3371	70	20	=	=	SYM
ejpam-3371	70	21	βx1	βx1	PROPN
ejpam-3371	70	22	⊕	⊕	PROPN
ejpam-3371	70	23	(	(	PUNCT
ejpam-3371	70	24	1−	1−	NUM
ejpam-3371	70	25	β)x11	β)x11	PUNCT
ejpam-3371	70	26	.	.	PUNCT
ejpam-3371	71	1	again	again	ADV
ejpam-3371	71	2	,	,	PUNCT
ejpam-3371	71	3	let	let	VERB
ejpam-3371	71	4	o(x2	o(x2	NOUN
ejpam-3371	71	5	,	,	PUNCT
ejpam-3371	71	6	t1	t1	NOUN
ejpam-3371	71	7	)	)	PUNCT
ejpam-3371	71	8	=	=	PRON
ejpam-3371	71	9	{	{	PUNCT
ejpam-3371	71	10	x́2n	x́2n	PROPN
ejpam-3371	71	11	}	}	PUNCT
ejpam-3371	71	12	be	be	AUX
ejpam-3371	71	13	a	a	DET
ejpam-3371	71	14	generalized	generalized	ADJ
ejpam-3371	71	15	orbit	orbit	NOUN
ejpam-3371	71	16	of	of	ADP
ejpam-3371	71	17	x2	x2	PROPN
ejpam-3371	71	18	associated	associate	VERB
ejpam-3371	71	19	with	with	ADP
ejpam-3371	71	20	t1	t1	NOUN
ejpam-3371	71	21	and	and	CCONJ
ejpam-3371	71	22	o(x2	o(x2	NOUN
ejpam-3371	71	23	,	,	PUNCT
ejpam-3371	71	24	t2	t2	NOUN
ejpam-3371	71	25	)	)	PUNCT
ejpam-3371	71	26	=	=	PRON
ejpam-3371	72	1	{	{	PUNCT
ejpam-3371	72	2	x2n	x2n	AUX
ejpam-3371	72	3	}	}	PUNCT
ejpam-3371	72	4	be	be	AUX
ejpam-3371	72	5	a	a	DET
ejpam-3371	72	6	generalized	generalized	ADJ
ejpam-3371	72	7	orbit	orbit	NOUN
ejpam-3371	72	8	of	of	ADP
ejpam-3371	72	9	x2	x2	PROPN
ejpam-3371	72	10	associated	associate	VERB
ejpam-3371	72	11	with	with	ADP
ejpam-3371	72	12	t2	t2	NOUN
ejpam-3371	72	13	where	where	SCONJ
ejpam-3371	72	14	d(x1n+h	d(x1n+h	NOUN
ejpam-3371	72	15	,	,	PUNCT
ejpam-3371	72	16	x	x	PROPN
ejpam-3371	72	17	2	2	NUM
ejpam-3371	72	18	h	h	NOUN
ejpam-3371	72	19	)	)	PUNCT
ejpam-3371	72	20	≤	≤	NUM
ejpam-3371	73	1	khd(x1n	khd(x1n	PROPN
ejpam-3371	73	2	,	,	PUNCT
ejpam-3371	73	3	x	x	NOUN
ejpam-3371	73	4	2	2	NUM
ejpam-3371	73	5	)	)	PUNCT
ejpam-3371	73	6	,	,	PUNCT
ejpam-3371	73	7	and	and	CCONJ
ejpam-3371	73	8	d	d	X
ejpam-3371	73	9	(	(	PUNCT
ejpam-3371	73	10	´	´	NOUN
ejpam-3371	73	11	x1n+h	x1n+h	PROPN
ejpam-3371	73	12	,	,	PUNCT
ejpam-3371	73	13	x́	x́	PROPN
ejpam-3371	73	14	2	2	NUM
ejpam-3371	73	15	h	h	NOUN
ejpam-3371	73	16	)	)	PUNCT
ejpam-3371	73	17	≤	≤	NOUN
ejpam-3371	73	18	khd(x́1n	khd(x́1n	PROPN
ejpam-3371	73	19	,	,	PUNCT
ejpam-3371	73	20	x	x	NOUN
ejpam-3371	73	21	2	2	NUM
ejpam-3371	73	22	)	)	PUNCT
ejpam-3371	73	23	.	.	PUNCT
ejpam-3371	74	1	hence	hence	ADV
ejpam-3371	74	2	,	,	PUNCT
ejpam-3371	74	3	using	use	VERB
ejpam-3371	74	4	induction	induction	NOUN
ejpam-3371	74	5	for	for	ADP
ejpam-3371	74	6	any	any	DET
ejpam-3371	74	7	m	m	PROPN
ejpam-3371	74	8	≥	≥	NOUN
ejpam-3371	74	9	1	1	NUM
ejpam-3371	74	10	we	we	PRON
ejpam-3371	74	11	have	have	VERB
ejpam-3371	74	12	a	a	DET
ejpam-3371	74	13	sequence	sequence	NOUN
ejpam-3371	74	14	{	{	PUNCT
ejpam-3371	74	15	xm	xm	NOUN
ejpam-3371	74	16	}	}	PUNCT
ejpam-3371	74	17	in	in	ADP
ejpam-3371	74	18	d	d	PROPN
ejpam-3371	74	19	and	and	CCONJ
ejpam-3371	74	20	the	the	DET
ejpam-3371	74	21	orbits	orbit	NOUN
ejpam-3371	74	22	o(xm	o(xm	PROPN
ejpam-3371	74	23	,	,	PUNCT
ejpam-3371	74	24	t1	t1	NOUN
ejpam-3371	74	25	)	)	PUNCT
ejpam-3371	74	26	=	=	SYM
ejpam-3371	74	27	{	{	PUNCT
ejpam-3371	74	28	x́mn	x́mn	PROPN
ejpam-3371	74	29	}	}	PUNCT
ejpam-3371	74	30	and	and	CCONJ
ejpam-3371	74	31	o(xm	o(xm	PROPN
ejpam-3371	74	32	,	,	PUNCT
ejpam-3371	74	33	t2	t2	NOUN
ejpam-3371	74	34	)	)	PUNCT
ejpam-3371	74	35	=	=	PRON
ejpam-3371	74	36	{	{	PUNCT
ejpam-3371	74	37	xmn	xmn	NOUN
ejpam-3371	74	38	}	}	PUNCT
ejpam-3371	74	39	such	such	ADJ
ejpam-3371	74	40	that	that	SCONJ
ejpam-3371	74	41	xm+1	xm+1	PROPN
ejpam-3371	74	42	=	=	PUNCT
ejpam-3371	74	43	αxm	αxm	NOUN
ejpam-3371	74	44	⊕	⊕	PROPN
ejpam-3371	74	45	(	(	PUNCT
ejpam-3371	74	46	1−	1−	NUM
ejpam-3371	74	47	α)ýmm	α)ýmm	PROPN
ejpam-3371	74	48	,	,	PUNCT
ejpam-3371	74	49	ym	ym	NOUN
ejpam-3371	74	50	=	=	SYM
ejpam-3371	74	51	βxm	βxm	PROPN
ejpam-3371	74	52	⊕	⊕	PROPN
ejpam-3371	74	53	(	(	PUNCT
ejpam-3371	74	54	1−	1−	NUM
ejpam-3371	74	55	β)xmm	β)xmm	ADV
ejpam-3371	74	56	(	(	PUNCT
ejpam-3371	74	57	1	1	NUM
ejpam-3371	74	58	)	)	PUNCT
ejpam-3371	74	59	and	and	CCONJ
ejpam-3371	74	60	d(xm−1n+h	d(xm−1n+h	PROPN
ejpam-3371	74	61	,	,	PUNCT
ejpam-3371	74	62	x	x	VERB
ejpam-3371	74	63	m	m	NOUN
ejpam-3371	74	64	h	h	NOUN
ejpam-3371	74	65	)	)	PUNCT
ejpam-3371	74	66	≤	≤	NUM
ejpam-3371	74	67	khd(xm−1n	khd(xm−1n	NOUN
ejpam-3371	74	68	,	,	PUNCT
ejpam-3371	74	69	xm	xm	PROPN
ejpam-3371	74	70	)	)	PUNCT
ejpam-3371	74	71	,	,	PUNCT
ejpam-3371	74	72	and	and	CCONJ
ejpam-3371	74	73	d	d	X
ejpam-3371	74	74	(	(	PUNCT
ejpam-3371	74	75	´	´	NOUN
ejpam-3371	74	76	xm−1n+h	xm−1n+h	NUM
ejpam-3371	74	77	,	,	PUNCT
ejpam-3371	74	78	x́	x́	PROPN
ejpam-3371	74	79	m	m	PROPN
ejpam-3371	74	80	h	h	NOUN
ejpam-3371	74	81	)	)	PUNCT
ejpam-3371	74	82	≤	≤	PUNCT
ejpam-3371	75	1	khd	khd	NOUN
ejpam-3371	75	2	(	(	PUNCT
ejpam-3371	75	3	´	´	PROPN
ejpam-3371	75	4	xm−1n	xm−1n	PROPN
ejpam-3371	75	5	,	,	PUNCT
ejpam-3371	75	6	xm	xm	PROPN
ejpam-3371	75	7	)	)	PUNCT
ejpam-3371	75	8	.	.	PUNCT
ejpam-3371	76	1	throughout	throughout	ADP
ejpam-3371	76	2	this	this	DET
ejpam-3371	76	3	section	section	NOUN
ejpam-3371	76	4	,	,	PUNCT
ejpam-3371	76	5	we	we	PRON
ejpam-3371	76	6	denote	denote	VERB
ejpam-3371	76	7	f	f	PROPN
ejpam-3371	76	8	=	=	SYM
ejpam-3371	76	9	f	f	PROPN
ejpam-3371	76	10	(	(	PUNCT
ejpam-3371	76	11	t1	t1	NOUN
ejpam-3371	76	12	)	)	PUNCT
ejpam-3371	76	13	∩	∩	PROPN
ejpam-3371	76	14	f	f	PROPN
ejpam-3371	76	15	(	(	PUNCT
ejpam-3371	76	16	t2	t2	PROPN
ejpam-3371	76	17	)	)	PUNCT
ejpam-3371	76	18	.	.	PUNCT
ejpam-3371	77	1	lemma	lemma	PROPN
ejpam-3371	77	2	1	1	X
ejpam-3371	77	3	.	.	PUNCT
ejpam-3371	78	1	let	let	AUX
ejpam-3371	78	2	(	(	PUNCT
ejpam-3371	78	3	x	x	NOUN
ejpam-3371	78	4	,	,	PUNCT
ejpam-3371	78	5	d	d	NOUN
ejpam-3371	78	6	)	)	PUNCT
ejpam-3371	78	7	be	be	AUX
ejpam-3371	78	8	a	a	DET
ejpam-3371	78	9	complete	complete	ADJ
ejpam-3371	78	10	uniformly	uniformly	ADV
ejpam-3371	78	11	convex	convex	ADJ
ejpam-3371	78	12	hyperbolic	hyperbolic	ADJ
ejpam-3371	78	13	metric	metric	ADJ
ejpam-3371	78	14	space	space	NOUN
ejpam-3371	78	15	.	.	PUNCT
ejpam-3371	79	1	let	let	VERB
ejpam-3371	79	2	d	d	PRON
ejpam-3371	79	3	be	be	AUX
ejpam-3371	79	4	a	a	DET
ejpam-3371	79	5	nonempty	nonempty	ADV
ejpam-3371	79	6	bounded	bound	VERB
ejpam-3371	79	7	,	,	PUNCT
ejpam-3371	79	8	closed	closed	ADJ
ejpam-3371	79	9	and	and	CCONJ
ejpam-3371	79	10	convex	convex	PROPN
ejpam-3371	79	11	subset	subset	NOUN
ejpam-3371	79	12	of	of	ADP
ejpam-3371	79	13	x.	x.	PROPN
ejpam-3371	79	14	let	let	VERB
ejpam-3371	79	15	t1	t1	NOUN
ejpam-3371	79	16	and	and	CCONJ
ejpam-3371	79	17	t2	t2	NOUN
ejpam-3371	79	18	be	be	AUX
ejpam-3371	79	19	multivalued	multivalue	VERB
ejpam-3371	79	20	asymptotically	asymptotically	ADV
ejpam-3371	79	21	nonexpansive	nonexpansive	ADJ
ejpam-3371	79	22	mappings	mapping	NOUN
ejpam-3371	79	23	with	with	ADP
ejpam-3371	79	24	km	km	PROPN
ejpam-3371	79	25	∈	∈	PROPN
ejpam-3371	80	1	[	[	X
ejpam-3371	80	2	1,∞	1,∞	NUM
ejpam-3371	80	3	)	)	PUNCT
ejpam-3371	80	4	and	and	CCONJ
ejpam-3371	80	5	∑∞	∑∞	X
ejpam-3371	81	1	m=1(km	m=1(km	X
ejpam-3371	81	2	−	−	PROPN
ejpam-3371	81	3	1	1	NUM
ejpam-3371	81	4	)	)	PUNCT
ejpam-3371	81	5	<	<	X
ejpam-3371	81	6	∞.	∞.	PROPN
ejpam-3371	81	7	define	define	VERB
ejpam-3371	81	8	the	the	DET
ejpam-3371	81	9	sequence	sequence	NOUN
ejpam-3371	81	10	as	as	ADP
ejpam-3371	81	11	in	in	ADP
ejpam-3371	81	12	(	(	PUNCT
ejpam-3371	81	13	1	1	NUM
ejpam-3371	81	14	)	)	PUNCT
ejpam-3371	81	15	.	.	PUNCT
ejpam-3371	82	1	if	if	SCONJ
ejpam-3371	82	2	lim	lim	PROPN
ejpam-3371	82	3	m→∞	m→∞	NOUN
ejpam-3371	82	4	d(xm	d(xm	PROPN
ejpam-3371	82	5	,	,	PUNCT
ejpam-3371	82	6	xmm	xmm	X
ejpam-3371	82	7	)	)	PUNCT
ejpam-3371	82	8	=	=	SYM
ejpam-3371	82	9	0	0	X
ejpam-3371	83	1	=	=	SYM
ejpam-3371	83	2	lim	lim	PROPN
ejpam-3371	83	3	m→∞	m→∞	NUM
ejpam-3371	83	4	d(xm	d(xm	PROPN
ejpam-3371	83	5	,	,	PUNCT
ejpam-3371	83	6	x́mm	x́mm	NUM
ejpam-3371	83	7	)	)	PUNCT
ejpam-3371	83	8	,	,	PUNCT
ejpam-3371	83	9	then	then	ADV
ejpam-3371	83	10	lim	lim	PROPN
ejpam-3371	83	11	m→∞	m→∞	PROPN
ejpam-3371	83	12	d(xm	d(xm	PROPN
ejpam-3371	83	13	,	,	PUNCT
ejpam-3371	83	14	xm1	xm1	PROPN
ejpam-3371	83	15	)	)	PUNCT
ejpam-3371	83	16	=	=	PUNCT
ejpam-3371	83	17	0	0	X
ejpam-3371	84	1	=	=	SYM
ejpam-3371	84	2	lim	lim	PROPN
ejpam-3371	84	3	m→∞	m→∞	NUM
ejpam-3371	84	4	d(xm	d(xm	PROPN
ejpam-3371	84	5	,	,	PUNCT
ejpam-3371	84	6	x́m1	x́m1	PROPN
ejpam-3371	84	7	)	)	PUNCT
ejpam-3371	84	8	.	.	PUNCT
ejpam-3371	85	1	proof	proof	NOUN
ejpam-3371	85	2	.	.	PUNCT
ejpam-3371	86	1	let	let	VERB
ejpam-3371	86	2	d(xm	d(xm	PROPN
ejpam-3371	86	3	,	,	PUNCT
ejpam-3371	86	4	x́mm	x́mm	NUM
ejpam-3371	86	5	)	)	PUNCT
ejpam-3371	86	6	=	=	PRON
ejpam-3371	86	7	am	be	AUX
ejpam-3371	86	8	,	,	PUNCT
ejpam-3371	86	9	and	and	CCONJ
ejpam-3371	86	10	d(xm	d(xm	PROPN
ejpam-3371	86	11	,	,	PUNCT
ejpam-3371	86	12	xmm	xmm	X
ejpam-3371	86	13	)	)	PUNCT
ejpam-3371	87	1	=	=	SYM
ejpam-3371	87	2	bm	bm	PROPN
ejpam-3371	87	3	.	.	PUNCT
ejpam-3371	88	1	since	since	SCONJ
ejpam-3371	88	2	xm+1	xm+1	PROPN
ejpam-3371	88	3	=	=	SYM
ejpam-3371	88	4	αxm	αxm	NOUN
ejpam-3371	88	5	⊕	⊕	PROPN
ejpam-3371	88	6	(	(	PUNCT
ejpam-3371	88	7	1−	1−	NUM
ejpam-3371	88	8	α)ýmm	α)ýmm	PROPN
ejpam-3371	88	9	,	,	PUNCT
ejpam-3371	88	10	we	we	PRON
ejpam-3371	88	11	have	have	VERB
ejpam-3371	88	12	d(xm+1	d(xm+1	PROPN
ejpam-3371	88	13	,	,	PUNCT
ejpam-3371	88	14	xm	xm	PROPN
ejpam-3371	88	15	)	)	PUNCT
ejpam-3371	88	16	≤	≤	NOUN
ejpam-3371	88	17	(	(	PUNCT
ejpam-3371	88	18	1−	1−	NUM
ejpam-3371	88	19	α)d(xm	α)d(xm	NUM
ejpam-3371	88	20	,	,	PUNCT
ejpam-3371	88	21	ýmm	ýmm	NUM
ejpam-3371	88	22	)	)	PUNCT
ejpam-3371	88	23	≤	≤	PROPN
ejpam-3371	89	1	d(xm	d(xm	PROPN
ejpam-3371	89	2	,	,	PUNCT
ejpam-3371	89	3	ýmm	ýmm	NUM
ejpam-3371	89	4	)	)	PUNCT
ejpam-3371	89	5	≤	≤	PROPN
ejpam-3371	90	1	d(xm	d(xm	PROPN
ejpam-3371	90	2	,	,	PUNCT
ejpam-3371	90	3	x́mm	x́mm	NUM
ejpam-3371	90	4	)	)	PUNCT
ejpam-3371	91	1	+	+	X
ejpam-3371	91	2	d(x́mm	d(x́mm	PROPN
ejpam-3371	91	3	,	,	PUNCT
ejpam-3371	91	4	ý	ý	PROPN
ejpam-3371	91	5	m	m	NOUN
ejpam-3371	91	6	m	m	NOUN
ejpam-3371	91	7	)	)	PUNCT
ejpam-3371	91	8	≤	≤	NUM
ejpam-3371	91	9	am	be	AUX
ejpam-3371	91	10	+	+	X
ejpam-3371	91	11	d(x́mm	d(x́mm	PROPN
ejpam-3371	91	12	,	,	PUNCT
ejpam-3371	91	13	x́	x́	PROPN
ejpam-3371	91	14	m	m	PROPN
ejpam-3371	91	15	m+m	m+m	NUM
ejpam-3371	91	16	)	)	PUNCT
ejpam-3371	92	1	+	+	CCONJ
ejpam-3371	92	2	d(x́mm+m	d(x́mm+m	PROPN
ejpam-3371	92	3	,	,	PUNCT
ejpam-3371	92	4	ý	ý	PROPN
ejpam-3371	92	5	m	m	NOUN
ejpam-3371	92	6	m	m	NOUN
ejpam-3371	92	7	)	)	PUNCT
ejpam-3371	92	8	≤	≤	NUM
ejpam-3371	92	9	am	be	AUX
ejpam-3371	92	10	+	+	X
ejpam-3371	92	11	kmd(x́mm	kmd(x́mm	ADJ
ejpam-3371	92	12	,	,	PUNCT
ejpam-3371	92	13	x	x	NOUN
ejpam-3371	92	14	m	m	VERB
ejpam-3371	92	15	)	)	PUNCT
ejpam-3371	93	1	+	+	CCONJ
ejpam-3371	93	2	kmd(x́mm	kmd(x́mm	PROPN
ejpam-3371	93	3	,	,	PUNCT
ejpam-3371	93	4	y	y	PROPN
ejpam-3371	93	5	m	m	PROPN
ejpam-3371	93	6	)	)	PUNCT
ejpam-3371	93	7	≤	≤	NUM
ejpam-3371	93	8	am	be	AUX
ejpam-3371	93	9	+	+	X
ejpam-3371	93	10	kmam	kmam	NOUN
ejpam-3371	93	11	+	+	X
ejpam-3371	93	12	km(βd(x́mm	km(βd(x́mm	PROPN
ejpam-3371	93	13	,	,	PUNCT
ejpam-3371	93	14	x	x	NOUN
ejpam-3371	93	15	m	m	NOUN
ejpam-3371	93	16	)	)	PUNCT
ejpam-3371	93	17	s.	s.	PROPN
ejpam-3371	93	18	h.	h.	PROPN
ejpam-3371	93	19	khan	khan	PROPN
ejpam-3371	93	20	,	,	PUNCT
ejpam-3371	93	21	h.	h.	PROPN
ejpam-3371	93	22	iqbal	iqbal	PROPN
ejpam-3371	93	23	,	,	PUNCT
ejpam-3371	93	24	m.	m.	NOUN
ejpam-3371	93	25	abbas	abbas	PROPN
ejpam-3371	93	26	/	/	SYM
ejpam-3371	93	27	eur	eur	PROPN
ejpam-3371	93	28	.	.	PUNCT
ejpam-3371	94	1	j.	j.	PROPN
ejpam-3371	94	2	pure	pure	PROPN
ejpam-3371	94	3	appl	appl	PROPN
ejpam-3371	94	4	.	.	PROPN
ejpam-3371	94	5	math	math	PROPN
ejpam-3371	94	6	,	,	PUNCT
ejpam-3371	94	7	12	12	NUM
ejpam-3371	94	8	(	(	PUNCT
ejpam-3371	94	9	2	2	NUM
ejpam-3371	94	10	)	)	PUNCT
ejpam-3371	94	11	(	(	PUNCT
ejpam-3371	94	12	2019	2019	NUM
ejpam-3371	94	13	)	)	PUNCT
ejpam-3371	94	14	,	,	PUNCT
ejpam-3371	94	15	348	348	NUM
ejpam-3371	94	16	-	-	SYM
ejpam-3371	94	17	357	357	NUM
ejpam-3371	94	18	352	352	NUM
ejpam-3371	94	19	+	+	ADJ
ejpam-3371	94	20	(	(	PUNCT
ejpam-3371	94	21	1−	1−	NUM
ejpam-3371	94	22	β)d(x́mm	β)d(x́mm	PROPN
ejpam-3371	94	23	,	,	PUNCT
ejpam-3371	94	24	x	x	X
ejpam-3371	94	25	m	m	VERB
ejpam-3371	94	26	m	m	ADJ
ejpam-3371	94	27	)	)	PUNCT
ejpam-3371	94	28	)	)	PUNCT
ejpam-3371	95	1	≤	≤	NUM
ejpam-3371	95	2	am	be	AUX
ejpam-3371	95	3	+	+	X
ejpam-3371	95	4	kmam	kmam	NOUN
ejpam-3371	95	5	+	+	CCONJ
ejpam-3371	95	6	kmβam	kmβam	NOUN
ejpam-3371	95	7	+	+	CCONJ
ejpam-3371	95	8	km(1−	km(1−	PROPN
ejpam-3371	95	9	β)d(x́mm	β)d(x́mm	PROPN
ejpam-3371	95	10	,	,	PUNCT
ejpam-3371	95	11	x	x	X
ejpam-3371	95	12	m	m	VERB
ejpam-3371	95	13	)	)	PUNCT
ejpam-3371	96	1	+	+	ADJ
ejpam-3371	96	2	km(1−	km(1−	PROPN
ejpam-3371	96	3	β)d(xmm	β)d(xmm	NUM
ejpam-3371	96	4	,	,	PUNCT
ejpam-3371	96	5	x	x	NOUN
ejpam-3371	96	6	m	m	NOUN
ejpam-3371	96	7	)	)	PUNCT
ejpam-3371	96	8	≤	≤	NUM
ejpam-3371	96	9	am	be	AUX
ejpam-3371	96	10	+	+	X
ejpam-3371	96	11	kmam	kmam	NOUN
ejpam-3371	96	12	+	+	CCONJ
ejpam-3371	96	13	kmβam	kmβam	NOUN
ejpam-3371	97	1	+	+	ADJ
ejpam-3371	97	2	km(1−	km(1−	PROPN
ejpam-3371	97	3	β)am	β)am	PROPN
ejpam-3371	97	4	+	+	CCONJ
ejpam-3371	97	5	km(1−	km(1−	PROPN
ejpam-3371	97	6	β)bm	β)bm	PROPN
ejpam-3371	97	7	≤	≤	PROPN
ejpam-3371	97	8	(	(	PUNCT
ejpam-3371	97	9	1	1	NUM
ejpam-3371	97	10	+	+	NUM
ejpam-3371	97	11	2km)am	2km)am	NUM
ejpam-3371	97	12	+	+	NUM
ejpam-3371	97	13	kmbm	kmbm	PROPN
ejpam-3371	97	14	.	.	PUNCT
ejpam-3371	98	1	taking	take	VERB
ejpam-3371	98	2	limm→∞	limm→∞	PROPN
ejpam-3371	98	3	in	in	ADP
ejpam-3371	98	4	the	the	DET
ejpam-3371	98	5	above	above	ADJ
ejpam-3371	98	6	inequality	inequality	NOUN
ejpam-3371	98	7	,	,	PUNCT
ejpam-3371	98	8	we	we	PRON
ejpam-3371	98	9	get	get	VERB
ejpam-3371	98	10	lim	lim	PROPN
ejpam-3371	98	11	m→∞	m→∞	NOUN
ejpam-3371	98	12	d(xm+1	d(xm+1	PROPN
ejpam-3371	98	13	,	,	PUNCT
ejpam-3371	98	14	xm	xm	PROPN
ejpam-3371	98	15	)	)	PUNCT
ejpam-3371	98	16	≤	≤	NOUN
ejpam-3371	99	1	lim	lim	PROPN
ejpam-3371	99	2	m→∞	m→∞	NUM
ejpam-3371	99	3	(	(	PUNCT
ejpam-3371	99	4	1	1	NUM
ejpam-3371	99	5	+	+	NUM
ejpam-3371	99	6	2km)am	2km)am	NUM
ejpam-3371	99	7	+	+	CCONJ
ejpam-3371	99	8	lim	lim	PROPN
ejpam-3371	99	9	m→∞	m→∞	NOUN
ejpam-3371	99	10	kmbm	kmbm	X
ejpam-3371	99	11	=	=	SYM
ejpam-3371	99	12	0	0	X
ejpam-3371	99	13	.	.	PUNCT
ejpam-3371	100	1	that	that	PRON
ejpam-3371	100	2	is	be	AUX
ejpam-3371	100	3	lim	lim	PROPN
ejpam-3371	100	4	m→∞	m→∞	NUM
ejpam-3371	100	5	d(xm+1	d(xm+1	PROPN
ejpam-3371	100	6	,	,	PUNCT
ejpam-3371	100	7	xm	xm	PROPN
ejpam-3371	100	8	)	)	PUNCT
ejpam-3371	101	1	=	=	SYM
ejpam-3371	101	2	0	0	PUNCT
ejpam-3371	101	3	(	(	PUNCT
ejpam-3371	101	4	2	2	NUM
ejpam-3371	101	5	)	)	PUNCT
ejpam-3371	101	6	moreover	moreover	ADV
ejpam-3371	101	7	,	,	PUNCT
ejpam-3371	101	8	from	from	ADP
ejpam-3371	101	9	(	(	PUNCT
ejpam-3371	101	10	2	2	NUM
ejpam-3371	101	11	)	)	PUNCT
ejpam-3371	101	12	d(xm+1	d(xm+1	PROPN
ejpam-3371	101	13	,	,	PUNCT
ejpam-3371	101	14	´	´	NOUN
ejpam-3371	101	15	xm+1	xm+1	X
ejpam-3371	101	16	1	1	X
ejpam-3371	101	17	)	)	PUNCT
ejpam-3371	101	18	≤	≤	NOUN
ejpam-3371	101	19	d(xm+1	d(xm+1	PROPN
ejpam-3371	101	20	,	,	PUNCT
ejpam-3371	101	21	´	´	NOUN
ejpam-3371	101	22	xm+1	xm+1	X
ejpam-3371	101	23	m+1	m+1	NUM
ejpam-3371	101	24	)	)	PUNCT
ejpam-3371	101	25	+	+	CCONJ
ejpam-3371	102	1	d	d	X
ejpam-3371	102	2	(	(	PUNCT
ejpam-3371	102	3	´	´	NOUN
ejpam-3371	102	4	xm+1	xm+1	PROPN
ejpam-3371	102	5	m+1	m+1	PROPN
ejpam-3371	102	6	,	,	PUNCT
ejpam-3371	102	7	´	´	NOUN
ejpam-3371	102	8	xm+1	xm+1	X
ejpam-3371	102	9	1	1	NUM
ejpam-3371	102	10	)	)	PUNCT
ejpam-3371	102	11	,	,	PUNCT
ejpam-3371	102	12	≤	≤	PROPN
ejpam-3371	102	13	am+1	am+1	PROPN
ejpam-3371	102	14	+	+	PROPN
ejpam-3371	102	15	k1d(xm+1	k1d(xm+1	PROPN
ejpam-3371	102	16	,	,	PUNCT
ejpam-3371	102	17	´	´	PROPN
ejpam-3371	102	18	xm+1	xm+1	PROPN
ejpam-3371	102	19	m	m	PROPN
ejpam-3371	102	20	)	)	PUNCT
ejpam-3371	102	21	,	,	PUNCT
ejpam-3371	102	22	≤	≤	NUM
ejpam-3371	102	23	am+1	am+1	PROPN
ejpam-3371	102	24	+	+	CCONJ
ejpam-3371	102	25	k1[d(xm	k1[d(xm	PROPN
ejpam-3371	102	26	,	,	PUNCT
ejpam-3371	102	27	xm+1	xm+1	NUM
ejpam-3371	102	28	)	)	PUNCT
ejpam-3371	102	29	+	+	CCONJ
ejpam-3371	102	30	d(xm	d(xm	PROPN
ejpam-3371	102	31	,	,	PUNCT
ejpam-3371	102	32	x́mm	x́mm	NUM
ejpam-3371	102	33	)	)	PUNCT
ejpam-3371	102	34	+	+	X
ejpam-3371	102	35	d(x́mm	d(x́mm	PROPN
ejpam-3371	102	36	,	,	PUNCT
ejpam-3371	102	37	´	´	NOUN
ejpam-3371	102	38	xm+1	xm+1	PROPN
ejpam-3371	102	39	m	m	PROPN
ejpam-3371	102	40	)	)	PUNCT
ejpam-3371	102	41	]	]	PUNCT
ejpam-3371	102	42	,	,	PUNCT
ejpam-3371	102	43	≤	≤	NUM
ejpam-3371	102	44	am+1	am+1	PROPN
ejpam-3371	102	45	+	+	CCONJ
ejpam-3371	102	46	k1[d(xm	k1[d(xm	PROPN
ejpam-3371	102	47	,	,	PUNCT
ejpam-3371	102	48	xm+1	xm+1	NUM
ejpam-3371	102	49	)	)	PUNCT
ejpam-3371	102	50	+	+	CCONJ
ejpam-3371	102	51	d(xm	d(xm	PROPN
ejpam-3371	102	52	,	,	PUNCT
ejpam-3371	102	53	x́mm	x́mm	NUM
ejpam-3371	102	54	)	)	PUNCT
ejpam-3371	103	1	+	+	CCONJ
ejpam-3371	103	2	kmd(xm	kmd(xm	ADJ
ejpam-3371	103	3	,	,	PUNCT
ejpam-3371	103	4	xm+1	xm+1	PROPN
ejpam-3371	103	5	)	)	PUNCT
ejpam-3371	103	6	]	]	PUNCT
ejpam-3371	103	7	,	,	PUNCT
ejpam-3371	103	8	=	=	SYM
ejpam-3371	103	9	am+1	am+1	PROPN
ejpam-3371	103	10	+	+	NUM
ejpam-3371	103	11	k1[am	k1[am	PROPN
ejpam-3371	103	12	+	+	CCONJ
ejpam-3371	103	13	(	(	PUNCT
ejpam-3371	103	14	1	1	NUM
ejpam-3371	103	15	+	+	CCONJ
ejpam-3371	103	16	km)d(xm	km)d(xm	PROPN
ejpam-3371	103	17	,	,	PUNCT
ejpam-3371	103	18	xm+1	xm+1	NUM
ejpam-3371	103	19	)	)	PUNCT
ejpam-3371	103	20	]	]	PUNCT
ejpam-3371	103	21	.	.	PUNCT
ejpam-3371	104	1	then	then	ADV
ejpam-3371	104	2	lim	lim	PROPN
ejpam-3371	104	3	m→∞	m→∞	NUM
ejpam-3371	104	4	d(xm+1	d(xm+1	PROPN
ejpam-3371	104	5	,	,	PUNCT
ejpam-3371	104	6	´	´	NOUN
ejpam-3371	104	7	xm+1	xm+1	X
ejpam-3371	104	8	1	1	X
ejpam-3371	104	9	)	)	PUNCT
ejpam-3371	104	10	≤	≤	NOUN
ejpam-3371	104	11	lim	lim	PROPN
ejpam-3371	104	12	m→∞	m→∞	NOUN
ejpam-3371	104	13	am+1	am+1	PROPN
ejpam-3371	104	14	+	+	CCONJ
ejpam-3371	104	15	k1	k1	PROPN
ejpam-3371	104	16	lim	lim	PROPN
ejpam-3371	104	17	m→∞	m→∞	NOUN
ejpam-3371	105	1	[	[	X
ejpam-3371	105	2	am	be	AUX
ejpam-3371	105	3	+	+	X
ejpam-3371	105	4	(	(	PUNCT
ejpam-3371	105	5	1	1	NUM
ejpam-3371	105	6	+	+	NUM
ejpam-3371	105	7	km)d(xm	km)d(xm	PROPN
ejpam-3371	105	8	,	,	PUNCT
ejpam-3371	105	9	xm+1	xm+1	NUM
ejpam-3371	105	10	)	)	PUNCT
ejpam-3371	105	11	]	]	PUNCT
ejpam-3371	105	12	=	=	PUNCT
ejpam-3371	105	13	0	0	X
ejpam-3371	105	14	.	.	PUNCT
ejpam-3371	106	1	hence	hence	ADV
ejpam-3371	106	2	lim	lim	PROPN
ejpam-3371	106	3	m→∞	m→∞	NUM
ejpam-3371	106	4	d(xm	d(xm	PROPN
ejpam-3371	106	5	,	,	PUNCT
ejpam-3371	106	6	x́m1	x́m1	PUNCT
ejpam-3371	106	7	)	)	PUNCT
ejpam-3371	107	1	=	=	PUNCT
ejpam-3371	107	2	0	0	X
ejpam-3371	107	3	.	.	PUNCT
ejpam-3371	107	4	similarly	similarly	ADV
ejpam-3371	107	5	d(xm+1	d(xm+1	PROPN
ejpam-3371	107	6	,	,	PUNCT
ejpam-3371	107	7	xm+1	xm+1	PROPN
ejpam-3371	107	8	1	1	NUM
ejpam-3371	107	9	)	)	PUNCT
ejpam-3371	107	10	≤	≤	NOUN
ejpam-3371	107	11	d(xm+1	d(xm+1	PROPN
ejpam-3371	107	12	,	,	PUNCT
ejpam-3371	107	13	xm+1	xm+1	PROPN
ejpam-3371	107	14	m+1	m+1	X
ejpam-3371	107	15	)	)	PUNCT
ejpam-3371	107	16	+	+	CCONJ
ejpam-3371	107	17	d(xm+1	d(xm+1	PROPN
ejpam-3371	107	18	m+1	m+1	NUM
ejpam-3371	107	19	,	,	PUNCT
ejpam-3371	107	20	x	x	PUNCT
ejpam-3371	107	21	m+1	m+1	NUM
ejpam-3371	107	22	1	1	NUM
ejpam-3371	107	23	)	)	PUNCT
ejpam-3371	107	24	≤	≤	NOUN
ejpam-3371	107	25	bm+1	bm+1	PROPN
ejpam-3371	108	1	+	+	CCONJ
ejpam-3371	108	2	k1d(xm+1	k1d(xm+1	PROPN
ejpam-3371	108	3	,	,	PUNCT
ejpam-3371	108	4	xm+1	xm+1	PROPN
ejpam-3371	108	5	m	m	NOUN
ejpam-3371	108	6	)	)	PUNCT
ejpam-3371	108	7	≤	≤	NUM
ejpam-3371	109	1	bm+1	bm+1	PROPN
ejpam-3371	109	2	+	+	CCONJ
ejpam-3371	109	3	k1[d(xm	k1[d(xm	PROPN
ejpam-3371	109	4	,	,	PUNCT
ejpam-3371	109	5	xm+1	xm+1	NUM
ejpam-3371	109	6	)	)	PUNCT
ejpam-3371	109	7	+	+	CCONJ
ejpam-3371	109	8	d(xm	d(xm	PROPN
ejpam-3371	109	9	,	,	PUNCT
ejpam-3371	109	10	xmm	xmm	PROPN
ejpam-3371	109	11	)	)	PUNCT
ejpam-3371	110	1	+	+	CCONJ
ejpam-3371	110	2	d(xmm	d(xmm	VERB
ejpam-3371	110	3	,	,	PUNCT
ejpam-3371	110	4	x	x	X
ejpam-3371	110	5	m+1	m+1	NUM
ejpam-3371	110	6	m	m	NOUN
ejpam-3371	110	7	)	)	PUNCT
ejpam-3371	110	8	]	]	PUNCT
ejpam-3371	111	1	≤	≤	NUM
ejpam-3371	111	2	bm+1	bm+1	PROPN
ejpam-3371	111	3	+	+	CCONJ
ejpam-3371	111	4	k1[d(xm	k1[d(xm	PROPN
ejpam-3371	111	5	,	,	PUNCT
ejpam-3371	111	6	xm+1	xm+1	NUM
ejpam-3371	111	7	)	)	PUNCT
ejpam-3371	111	8	+	+	CCONJ
ejpam-3371	111	9	d(xm	d(xm	PROPN
ejpam-3371	111	10	,	,	PUNCT
ejpam-3371	111	11	xmm	xmm	PROPN
ejpam-3371	111	12	)	)	PUNCT
ejpam-3371	111	13	+	+	CCONJ
ejpam-3371	111	14	kmd(xm	kmd(xm	ADJ
ejpam-3371	111	15	,	,	PUNCT
ejpam-3371	111	16	xm+1	xm+1	NUM
ejpam-3371	111	17	)	)	PUNCT
ejpam-3371	111	18	]	]	PUNCT
ejpam-3371	111	19	=	=	SYM
ejpam-3371	111	20	bm+1	bm+1	PROPN
ejpam-3371	111	21	+	+	CCONJ
ejpam-3371	111	22	k1[bm	k1[bm	NOUN
ejpam-3371	111	23	+	+	CCONJ
ejpam-3371	111	24	(	(	PUNCT
ejpam-3371	111	25	1	1	NUM
ejpam-3371	111	26	+	+	CCONJ
ejpam-3371	111	27	km)d(xm	km)d(xm	PROPN
ejpam-3371	111	28	,	,	PUNCT
ejpam-3371	111	29	xm+1	xm+1	NUM
ejpam-3371	111	30	)	)	PUNCT
ejpam-3371	111	31	]	]	PUNCT
ejpam-3371	111	32	.	.	PUNCT
ejpam-3371	112	1	consequently	consequently	ADV
ejpam-3371	112	2	lim	lim	PROPN
ejpam-3371	112	3	m→∞	m→∞	NUM
ejpam-3371	112	4	d(xm	d(xm	PROPN
ejpam-3371	112	5	,	,	PUNCT
ejpam-3371	112	6	xm1	xm1	PROPN
ejpam-3371	112	7	)	)	PUNCT
ejpam-3371	113	1	=	=	PUNCT
ejpam-3371	113	2	0	0	X
ejpam-3371	113	3	.	.	PUNCT
ejpam-3371	113	4	s.	s.	PROPN
ejpam-3371	113	5	h.	h.	PROPN
ejpam-3371	113	6	khan	khan	PROPN
ejpam-3371	113	7	,	,	PUNCT
ejpam-3371	113	8	h.	h.	PROPN
ejpam-3371	113	9	iqbal	iqbal	PROPN
ejpam-3371	113	10	,	,	PUNCT
ejpam-3371	113	11	m.	m.	NOUN
ejpam-3371	113	12	abbas	abbas	PROPN
ejpam-3371	113	13	/	/	SYM
ejpam-3371	113	14	eur	eur	PROPN
ejpam-3371	113	15	.	.	PUNCT
ejpam-3371	114	1	j.	j.	PROPN
ejpam-3371	114	2	pure	pure	PROPN
ejpam-3371	114	3	appl	appl	PROPN
ejpam-3371	114	4	.	.	PROPN
ejpam-3371	114	5	math	math	PROPN
ejpam-3371	114	6	,	,	PUNCT
ejpam-3371	114	7	12	12	NUM
ejpam-3371	114	8	(	(	PUNCT
ejpam-3371	114	9	2	2	NUM
ejpam-3371	114	10	)	)	PUNCT
ejpam-3371	114	11	(	(	PUNCT
ejpam-3371	114	12	2019	2019	NUM
ejpam-3371	114	13	)	)	PUNCT
ejpam-3371	114	14	,	,	PUNCT
ejpam-3371	114	15	348	348	NUM
ejpam-3371	114	16	-	-	SYM
ejpam-3371	114	17	357	357	NUM
ejpam-3371	114	18	353	353	NUM
ejpam-3371	114	19	theorem	theorem	NOUN
ejpam-3371	114	20	2	2	NUM
ejpam-3371	114	21	.	.	PUNCT
ejpam-3371	115	1	let	let	AUX
ejpam-3371	115	2	(	(	PUNCT
ejpam-3371	115	3	x	x	NOUN
ejpam-3371	115	4	,	,	PUNCT
ejpam-3371	115	5	d	d	NOUN
ejpam-3371	115	6	)	)	PUNCT
ejpam-3371	115	7	be	be	AUX
ejpam-3371	115	8	a	a	DET
ejpam-3371	115	9	complete	complete	ADJ
ejpam-3371	115	10	uniformly	uniformly	ADV
ejpam-3371	115	11	convex	convex	ADJ
ejpam-3371	115	12	hyperbolic	hyperbolic	ADJ
ejpam-3371	115	13	metric	metric	ADJ
ejpam-3371	115	14	space	space	NOUN
ejpam-3371	115	15	.	.	PUNCT
ejpam-3371	116	1	let	let	VERB
ejpam-3371	116	2	d	d	PRON
ejpam-3371	116	3	be	be	AUX
ejpam-3371	116	4	a	a	DET
ejpam-3371	116	5	nonempty	nonempty	ADV
ejpam-3371	116	6	bounded	bound	VERB
ejpam-3371	116	7	,	,	PUNCT
ejpam-3371	116	8	closed	closed	ADJ
ejpam-3371	116	9	and	and	CCONJ
ejpam-3371	116	10	convex	convex	PROPN
ejpam-3371	116	11	subset	subset	NOUN
ejpam-3371	116	12	of	of	ADP
ejpam-3371	116	13	x.	x.	PROPN
ejpam-3371	116	14	let	let	VERB
ejpam-3371	116	15	t1	t1	NOUN
ejpam-3371	116	16	and	and	CCONJ
ejpam-3371	116	17	t2	t2	NOUN
ejpam-3371	116	18	be	be	AUX
ejpam-3371	116	19	multivalued	multivalue	VERB
ejpam-3371	116	20	asymptotically	asymptotically	ADV
ejpam-3371	116	21	nonexpansive	nonexpansive	ADJ
ejpam-3371	116	22	mappings	mapping	NOUN
ejpam-3371	116	23	.	.	PUNCT
ejpam-3371	117	1	let	let	VERB
ejpam-3371	117	2	km	km	NOUN
ejpam-3371	117	3	be	be	AUX
ejpam-3371	117	4	the	the	DET
ejpam-3371	117	5	lipschitz	lipschitz	NOUN
ejpam-3371	117	6	sequence	sequence	NOUN
ejpam-3371	117	7	associated	associate	VERB
ejpam-3371	117	8	with	with	ADP
ejpam-3371	117	9	t1	t1	NOUN
ejpam-3371	117	10	and	and	CCONJ
ejpam-3371	117	11	t2	t2	NOUN
ejpam-3371	117	12	such	such	ADJ
ejpam-3371	117	13	that	that	SCONJ
ejpam-3371	117	14	km	km	PROPN
ejpam-3371	117	15	∈	∈	PROPN
ejpam-3371	118	1	[	[	X
ejpam-3371	118	2	1,∞	1,∞	NUM
ejpam-3371	118	3	]	]	PUNCT
ejpam-3371	118	4	and	and	CCONJ
ejpam-3371	118	5	∑∞	∑∞	NOUN
ejpam-3371	118	6	m=1(km−1	m=1(km−1	NUM
ejpam-3371	118	7	)	)	PUNCT
ejpam-3371	119	1	<	<	X
ejpam-3371	119	2	∞.	∞.	PROPN
ejpam-3371	119	3	let	let	VERB
ejpam-3371	119	4	f	f	PROPN
ejpam-3371	119	5	6=	6=	PROPN
ejpam-3371	119	6	∅	∅	NOUN
ejpam-3371	119	7	and	and	CCONJ
ejpam-3371	119	8	t1p	t1p	NOUN
ejpam-3371	119	9	=	=	SYM
ejpam-3371	119	10	t2p	t2p	X
ejpam-3371	119	11	=	=	PUNCT
ejpam-3371	119	12	{	{	PUNCT
ejpam-3371	119	13	p	p	X
ejpam-3371	119	14	}	}	PUNCT
ejpam-3371	119	15	for	for	ADP
ejpam-3371	119	16	p	p	PROPN
ejpam-3371	119	17	∈	∈	PROPN
ejpam-3371	119	18	f.	f.	NOUN
ejpam-3371	119	19	fix	fix	VERB
ejpam-3371	119	20	x1	x1	PROPN
ejpam-3371	119	21	∈	∈	PROPN
ejpam-3371	119	22	d	d	NOUN
ejpam-3371	119	23	and	and	CCONJ
ejpam-3371	119	24	α	α	PRON
ejpam-3371	119	25	∈	∈	PROPN
ejpam-3371	119	26	(	(	PUNCT
ejpam-3371	119	27	0,∞	0,∞	NOUN
ejpam-3371	119	28	)	)	PUNCT
ejpam-3371	119	29	.	.	PUNCT
ejpam-3371	120	1	suppose	suppose	VERB
ejpam-3371	120	2	xm	xm	PROPN
ejpam-3371	120	3	is	be	AUX
ejpam-3371	120	4	defined	define	VERB
ejpam-3371	120	5	as	as	ADP
ejpam-3371	120	6	in	in	ADP
ejpam-3371	120	7	(	(	PUNCT
ejpam-3371	120	8	1	1	NUM
ejpam-3371	120	9	)	)	PUNCT
ejpam-3371	120	10	.	.	PUNCT
ejpam-3371	121	1	then	then	ADV
ejpam-3371	121	2	,	,	PUNCT
ejpam-3371	121	3	lim	lim	PROPN
ejpam-3371	121	4	m→∞	m→∞	NOUN
ejpam-3371	121	5	d(xm	d(xm	PROPN
ejpam-3371	121	6	,	,	PUNCT
ejpam-3371	121	7	xm1	xm1	PROPN
ejpam-3371	121	8	)	)	PUNCT
ejpam-3371	122	1	=	=	PUNCT
ejpam-3371	122	2	0	0	NUM
ejpam-3371	122	3	,	,	PUNCT
ejpam-3371	122	4	and	and	CCONJ
ejpam-3371	122	5	lim	lim	PROPN
ejpam-3371	122	6	m→∞	m→∞	PROPN
ejpam-3371	122	7	d(xm	d(xm	PROPN
ejpam-3371	122	8	,	,	PUNCT
ejpam-3371	122	9	x́m1	x́m1	PUNCT
ejpam-3371	122	10	)	)	PUNCT
ejpam-3371	123	1	=	=	PUNCT
ejpam-3371	123	2	0	0	X
ejpam-3371	123	3	.	.	PUNCT
ejpam-3371	124	1	that	that	PRON
ejpam-3371	124	2	is	is	ADV
ejpam-3371	124	3	,	,	PUNCT
ejpam-3371	124	4	lim	lim	PROPN
ejpam-3371	124	5	m→∞	m→∞	NUM
ejpam-3371	124	6	d(xm	d(xm	PROPN
ejpam-3371	124	7	,	,	PUNCT
ejpam-3371	124	8	t1x	t1x	PROPN
ejpam-3371	124	9	m	m	NOUN
ejpam-3371	124	10	)	)	PUNCT
ejpam-3371	124	11	=	=	SYM
ejpam-3371	124	12	0	0	NUM
ejpam-3371	124	13	,	,	PUNCT
ejpam-3371	124	14	and	and	CCONJ
ejpam-3371	124	15	lim	lim	PROPN
ejpam-3371	124	16	m→∞	m→∞	NUM
ejpam-3371	124	17	d(xm	d(xm	PROPN
ejpam-3371	124	18	,	,	PUNCT
ejpam-3371	124	19	t2x	t2x	NOUN
ejpam-3371	124	20	m	m	VERB
ejpam-3371	124	21	)	)	PUNCT
ejpam-3371	125	1	=	=	SYM
ejpam-3371	125	2	0	0	X
ejpam-3371	125	3	.	.	PUNCT
ejpam-3371	126	1	proof	proof	NOUN
ejpam-3371	126	2	.	.	PUNCT
ejpam-3371	127	1	let	let	VERB
ejpam-3371	127	2	p	p	PRON
ejpam-3371	127	3	∈	∈	PROPN
ejpam-3371	127	4	d	d	AUX
ejpam-3371	127	5	be	be	AUX
ejpam-3371	127	6	such	such	ADJ
ejpam-3371	127	7	that	that	SCONJ
ejpam-3371	127	8	p	p	PROPN
ejpam-3371	127	9	∈	∈	PROPN
ejpam-3371	127	10	f	f	PROPN
ejpam-3371	127	11	and	and	CCONJ
ejpam-3371	127	12	t1p	t1p	NOUN
ejpam-3371	127	13	=	=	SYM
ejpam-3371	127	14	t2p	t2p	X
ejpam-3371	127	15	=	=	PUNCT
ejpam-3371	127	16	{	{	PUNCT
ejpam-3371	127	17	p	p	X
ejpam-3371	127	18	}	}	PUNCT
ejpam-3371	127	19	.	.	PUNCT
ejpam-3371	128	1	then	then	ADV
ejpam-3371	128	2	d	d	X
ejpam-3371	128	3	(	(	PUNCT
ejpam-3371	128	4	´	´	NOUN
ejpam-3371	128	5	xmn+h	xmn+h	PROPN
ejpam-3371	128	6	,	,	PUNCT
ejpam-3371	128	7	p	p	NOUN
ejpam-3371	128	8	)	)	PUNCT
ejpam-3371	128	9	≤	≤	NUM
ejpam-3371	128	10	khd(xmn	khd(xmn	NOUN
ejpam-3371	128	11	,	,	PUNCT
ejpam-3371	128	12	p	p	X
ejpam-3371	128	13	)	)	PUNCT
ejpam-3371	128	14	and	and	CCONJ
ejpam-3371	128	15	d(xmn+h	d(xmn+h	PROPN
ejpam-3371	128	16	,	,	PUNCT
ejpam-3371	128	17	p	p	NOUN
ejpam-3371	128	18	)	)	PUNCT
ejpam-3371	128	19	≤	≤	NUM
ejpam-3371	128	20	khd(xmn	khd(xmn	NOUN
ejpam-3371	128	21	,	,	PUNCT
ejpam-3371	128	22	p	p	NOUN
ejpam-3371	128	23	)	)	PUNCT
ejpam-3371	128	24	.	.	PUNCT
ejpam-3371	129	1	now	now	ADV
ejpam-3371	129	2	d(xm+1	d(xm+1	X
ejpam-3371	129	3	,	,	PUNCT
ejpam-3371	129	4	p	p	X
ejpam-3371	129	5	)	)	PUNCT
ejpam-3371	129	6	≤	≤	PROPN
ejpam-3371	129	7	αd(xm	αd(xm	PROPN
ejpam-3371	129	8	,	,	PUNCT
ejpam-3371	129	9	p	p	X
ejpam-3371	129	10	)	)	PUNCT
ejpam-3371	129	11	+	+	CCONJ
ejpam-3371	129	12	(	(	PUNCT
ejpam-3371	129	13	1−	1−	NUM
ejpam-3371	129	14	α)d(ýmm	α)d(ýmm	PROPN
ejpam-3371	129	15	,	,	PUNCT
ejpam-3371	129	16	p	p	NOUN
ejpam-3371	129	17	)	)	PUNCT
ejpam-3371	129	18	≤	≤	PROPN
ejpam-3371	129	19	αd(xm	αd(xm	PROPN
ejpam-3371	129	20	,	,	PUNCT
ejpam-3371	129	21	p	p	X
ejpam-3371	129	22	)	)	PUNCT
ejpam-3371	129	23	+	+	CCONJ
ejpam-3371	129	24	(	(	PUNCT
ejpam-3371	129	25	1−	1−	NUM
ejpam-3371	129	26	α)kmd(ym	α)kmd(ym	PROPN
ejpam-3371	129	27	,	,	PUNCT
ejpam-3371	129	28	p	p	NOUN
ejpam-3371	129	29	)	)	PUNCT
ejpam-3371	129	30	(	(	PUNCT
ejpam-3371	129	31	3	3	NUM
ejpam-3371	129	32	)	)	PUNCT
ejpam-3371	129	33	and	and	CCONJ
ejpam-3371	129	34	d(ym	d(ym	PROPN
ejpam-3371	129	35	,	,	PUNCT
ejpam-3371	129	36	p	p	NOUN
ejpam-3371	129	37	)	)	PUNCT
ejpam-3371	129	38	≤	≤	NOUN
ejpam-3371	129	39	βd(xm	βd(xm	PROPN
ejpam-3371	129	40	,	,	PUNCT
ejpam-3371	129	41	p	p	X
ejpam-3371	129	42	)	)	PUNCT
ejpam-3371	129	43	+	+	CCONJ
ejpam-3371	129	44	(	(	PUNCT
ejpam-3371	129	45	1−	1−	NUM
ejpam-3371	129	46	β)d(x́mm	β)d(x́mm	PROPN
ejpam-3371	129	47	,	,	PUNCT
ejpam-3371	129	48	p	p	NOUN
ejpam-3371	129	49	)	)	PUNCT
ejpam-3371	129	50	≤	≤	NOUN
ejpam-3371	129	51	β	β	X
ejpam-3371	129	52	d(xm	d(xm	PROPN
ejpam-3371	129	53	,	,	PUNCT
ejpam-3371	129	54	p	p	X
ejpam-3371	129	55	)	)	PUNCT
ejpam-3371	129	56	+	+	CCONJ
ejpam-3371	129	57	(	(	PUNCT
ejpam-3371	129	58	1−	1−	NUM
ejpam-3371	129	59	β)kmd(xm	β)kmd(xm	PROPN
ejpam-3371	129	60	,	,	PUNCT
ejpam-3371	129	61	p	p	NOUN
ejpam-3371	129	62	)	)	PUNCT
ejpam-3371	129	63	.	.	PUNCT
ejpam-3371	130	1	(	(	PUNCT
ejpam-3371	130	2	4	4	X
ejpam-3371	130	3	)	)	PUNCT
ejpam-3371	130	4	inequalities	inequality	NOUN
ejpam-3371	130	5	(	(	PUNCT
ejpam-3371	130	6	3	3	NUM
ejpam-3371	130	7	)	)	PUNCT
ejpam-3371	130	8	and	and	CCONJ
ejpam-3371	130	9	(	(	PUNCT
ejpam-3371	130	10	4	4	X
ejpam-3371	130	11	)	)	PUNCT
ejpam-3371	130	12	imply	imply	NOUN
ejpam-3371	130	13	,	,	PUNCT
ejpam-3371	130	14	d(xm+1	d(xm+1	PROPN
ejpam-3371	130	15	,	,	PUNCT
ejpam-3371	130	16	p	p	ADJ
ejpam-3371	130	17	)	)	PUNCT
ejpam-3371	130	18	≤	≤	PROPN
ejpam-3371	130	19	αd(xm	αd(xm	PROPN
ejpam-3371	130	20	,	,	PUNCT
ejpam-3371	130	21	p	p	X
ejpam-3371	130	22	)	)	PUNCT
ejpam-3371	130	23	+	+	CCONJ
ejpam-3371	130	24	(	(	PUNCT
ejpam-3371	130	25	1−	1−	NUM
ejpam-3371	130	26	α)km[β	α)km[β	NOUN
ejpam-3371	130	27	+	+	CCONJ
ejpam-3371	130	28	(	(	PUNCT
ejpam-3371	130	29	1−	1−	NUM
ejpam-3371	130	30	β)km]d(xm	β)km]d(xm	NOUN
ejpam-3371	130	31	,	,	PUNCT
ejpam-3371	130	32	p	p	NOUN
ejpam-3371	130	33	)	)	PUNCT
ejpam-3371	130	34	=	=	PUNCT
ejpam-3371	131	1	[	[	X
ejpam-3371	131	2	α+	α+	X
ejpam-3371	131	3	β(1−	β(1−	PUNCT
ejpam-3371	132	1	α)km	α)km	ADJ
ejpam-3371	132	2	+	+	CCONJ
ejpam-3371	132	3	(	(	PUNCT
ejpam-3371	132	4	1−	1−	NUM
ejpam-3371	132	5	β)(1−	β)(1−	NOUN
ejpam-3371	132	6	α)k2m]d(xm	α)k2m]d(xm	NOUN
ejpam-3371	132	7	,	,	PUNCT
ejpam-3371	132	8	p	p	NOUN
ejpam-3371	132	9	)	)	PUNCT
ejpam-3371	132	10	=	=	SYM
ejpam-3371	132	11	vmd(xm	vmd(xm	NOUN
ejpam-3371	132	12	,	,	PUNCT
ejpam-3371	132	13	p	p	NOUN
ejpam-3371	132	14	)	)	PUNCT
ejpam-3371	132	15	,	,	PUNCT
ejpam-3371	132	16	where	where	SCONJ
ejpam-3371	132	17	vm	vm	PROPN
ejpam-3371	132	18	=	=	PUNCT
ejpam-3371	132	19	α+	α+	PUNCT
ejpam-3371	132	20	β(1−	β(1−	PUNCT
ejpam-3371	133	1	α)km	α)km	ADJ
ejpam-3371	133	2	+	+	CCONJ
ejpam-3371	133	3	(	(	PUNCT
ejpam-3371	133	4	1−	1−	NUM
ejpam-3371	133	5	β)(1−	β)(1−	PROPN
ejpam-3371	133	6	α)k2	α)k2	PROPN
ejpam-3371	133	7	m.	m.	NOUN
ejpam-3371	133	8	this	this	PRON
ejpam-3371	133	9	implies	imply	VERB
ejpam-3371	133	10	,	,	PUNCT
ejpam-3371	133	11	d(xm+1	d(xm+1	PROPN
ejpam-3371	133	12	,	,	PUNCT
ejpam-3371	133	13	p)−	p)−	PROPN
ejpam-3371	133	14	d(xm	d(xm	PROPN
ejpam-3371	133	15	,	,	PUNCT
ejpam-3371	133	16	p	p	X
ejpam-3371	133	17	)	)	PUNCT
ejpam-3371	133	18	≤	≤	NOUN
ejpam-3371	133	19	(	(	PUNCT
ejpam-3371	133	20	vm	vm	NOUN
ejpam-3371	133	21	−	−	PROPN
ejpam-3371	133	22	1)d(xm	1)d(xm	NUM
ejpam-3371	133	23	,	,	PUNCT
ejpam-3371	133	24	p	p	NOUN
ejpam-3371	133	25	)	)	PUNCT
ejpam-3371	133	26	≤	≤	NOUN
ejpam-3371	133	27	(	(	PUNCT
ejpam-3371	133	28	vm	vm	NOUN
ejpam-3371	133	29	−	−	PROPN
ejpam-3371	133	30	1)δ(d	1)δ(d	NUM
ejpam-3371	133	31	)	)	PUNCT
ejpam-3371	133	32	for	for	ADP
ejpam-3371	133	33	any	any	DET
ejpam-3371	133	34	m	m	NOUN
ejpam-3371	133	35	∈	∈	NOUN
ejpam-3371	133	36	n	n	CCONJ
ejpam-3371	133	37	,	,	PUNCT
ejpam-3371	133	38	where	where	SCONJ
ejpam-3371	133	39	δ(d	δ(d	PROPN
ejpam-3371	133	40	)	)	PUNCT
ejpam-3371	133	41	=	=	SYM
ejpam-3371	133	42	supx	supx	PROPN
ejpam-3371	133	43	,	,	PUNCT
ejpam-3371	133	44	y∈d	y∈d	NOUN
ejpam-3371	133	45	{	{	PUNCT
ejpam-3371	133	46	d(x	d(x	PROPN
ejpam-3371	133	47	,	,	PUNCT
ejpam-3371	133	48	y	y	NOUN
ejpam-3371	133	49	)	)	PUNCT
ejpam-3371	133	50	}	}	PUNCT
ejpam-3371	133	51	is	be	AUX
ejpam-3371	133	52	the	the	DET
ejpam-3371	133	53	diameter	diameter	NOUN
ejpam-3371	133	54	of	of	ADP
ejpam-3371	133	55	d.	d.	PROPN
ejpam-3371	133	56	therefore	therefore	ADV
ejpam-3371	133	57	,	,	PUNCT
ejpam-3371	133	58	d(xm+h	d(xm+h	PROPN
ejpam-3371	133	59	,	,	PUNCT
ejpam-3371	133	60	p)−	p)−	PROPN
ejpam-3371	133	61	d(xm	d(xm	PROPN
ejpam-3371	133	62	,	,	PUNCT
ejpam-3371	133	63	p	p	X
ejpam-3371	133	64	)	)	PUNCT
ejpam-3371	133	65	≤	≤	NOUN
ejpam-3371	133	66	m+(h−1)∑	m+(h−1)∑	VERB
ejpam-3371	133	67	i	i	PRON
ejpam-3371	133	68	=	=	NOUN
ejpam-3371	133	69	m	m	PROPN
ejpam-3371	133	70	(	(	PUNCT
ejpam-3371	133	71	vi	vi	PROPN
ejpam-3371	133	72	−	−	PROPN
ejpam-3371	133	73	1)δ(d	1)δ(d	NUM
ejpam-3371	133	74	)	)	PUNCT
ejpam-3371	133	75	.	.	PUNCT
ejpam-3371	134	1	since	since	SCONJ
ejpam-3371	134	2	∑∞	∑∞	NOUN
ejpam-3371	134	3	m=1(km	m=1(km	PROPN
ejpam-3371	134	4	−	−	PROPN
ejpam-3371	134	5	1	1	NUM
ejpam-3371	134	6	)	)	PUNCT
ejpam-3371	134	7	<	<	X
ejpam-3371	134	8	∞	∞	NUM
ejpam-3371	134	9	so	so	ADJ
ejpam-3371	134	10	∑∞	∑∞	NOUN
ejpam-3371	134	11	m=1(vm	m=1(vm	X
ejpam-3371	134	12	−	−	PROPN
ejpam-3371	134	13	1	1	NUM
ejpam-3371	134	14	)	)	PUNCT
ejpam-3371	134	15	<	<	X
ejpam-3371	134	16	∞.	∞.	PROPN
ejpam-3371	134	17	let	let	VERB
ejpam-3371	134	18	h→∞	h→∞	NUM
ejpam-3371	134	19	,	,	PUNCT
ejpam-3371	134	20	lim	lim	PROPN
ejpam-3371	134	21	sup	sup	VERB
ejpam-3371	134	22	n→∞	n→∞	X
ejpam-3371	135	1	d(xn	d(xn	ADJ
ejpam-3371	135	2	,	,	PUNCT
ejpam-3371	135	3	p)−	p)−	PROPN
ejpam-3371	135	4	d(xm	d(xm	PROPN
ejpam-3371	135	5	,	,	PUNCT
ejpam-3371	135	6	p	p	X
ejpam-3371	135	7	)	)	PUNCT
ejpam-3371	135	8	≤	≤	NUM
ejpam-3371	135	9	δ(d	δ(d	PROPN
ejpam-3371	135	10	)	)	PUNCT
ejpam-3371	136	1	∞∑	∞∑	NUM
ejpam-3371	136	2	i	i	PRON
ejpam-3371	136	3	=	=	NOUN
ejpam-3371	136	4	m	m	PROPN
ejpam-3371	136	5	(	(	PUNCT
ejpam-3371	136	6	vi	vi	NOUN
ejpam-3371	136	7	−	−	NOUN
ejpam-3371	136	8	1	1	NUM
ejpam-3371	136	9	)	)	PUNCT
ejpam-3371	136	10	,	,	PUNCT
ejpam-3371	136	11	s.	s.	PROPN
ejpam-3371	136	12	h.	h.	PROPN
ejpam-3371	136	13	khan	khan	PROPN
ejpam-3371	136	14	,	,	PUNCT
ejpam-3371	136	15	h.	h.	PROPN
ejpam-3371	136	16	iqbal	iqbal	PROPN
ejpam-3371	136	17	,	,	PUNCT
ejpam-3371	136	18	m.	m.	NOUN
ejpam-3371	136	19	abbas	abbas	PROPN
ejpam-3371	136	20	/	/	SYM
ejpam-3371	136	21	eur	eur	PROPN
ejpam-3371	136	22	.	.	PUNCT
ejpam-3371	137	1	j.	j.	PROPN
ejpam-3371	137	2	pure	pure	PROPN
ejpam-3371	137	3	appl	appl	PROPN
ejpam-3371	137	4	.	.	PROPN
ejpam-3371	137	5	math	math	PROPN
ejpam-3371	137	6	,	,	PUNCT
ejpam-3371	137	7	12	12	NUM
ejpam-3371	137	8	(	(	PUNCT
ejpam-3371	137	9	2	2	NUM
ejpam-3371	137	10	)	)	PUNCT
ejpam-3371	137	11	(	(	PUNCT
ejpam-3371	137	12	2019	2019	NUM
ejpam-3371	137	13	)	)	PUNCT
ejpam-3371	137	14	,	,	PUNCT
ejpam-3371	137	15	348	348	NUM
ejpam-3371	137	16	-	-	SYM
ejpam-3371	137	17	357	357	NUM
ejpam-3371	137	18	354	354	NUM
ejpam-3371	137	19	for	for	ADP
ejpam-3371	137	20	any	any	DET
ejpam-3371	137	21	m	m	PROPN
ejpam-3371	137	22	∈	∈	PROPN
ejpam-3371	137	23	n.	n.	NOUN
ejpam-3371	137	24	now	now	ADV
ejpam-3371	137	25	letting	let	VERB
ejpam-3371	137	26	m→∞	m→∞	NOUN
ejpam-3371	138	1	,	,	PUNCT
ejpam-3371	138	2	lim	lim	PROPN
ejpam-3371	138	3	sup	sup	VERB
ejpam-3371	138	4	n→∞	n→∞	X
ejpam-3371	139	1	d(xn	d(xn	NOUN
ejpam-3371	139	2	,	,	PUNCT
ejpam-3371	139	3	p	p	NOUN
ejpam-3371	139	4	)	)	PUNCT
ejpam-3371	139	5	≤	≤	PROPN
ejpam-3371	139	6	lim	lim	PROPN
ejpam-3371	139	7	inf	inf	PROPN
ejpam-3371	139	8	m→∞	m→∞	NUM
ejpam-3371	139	9	d(xm	d(xm	PROPN
ejpam-3371	139	10	,	,	PUNCT
ejpam-3371	139	11	p	p	NOUN
ejpam-3371	139	12	)	)	PUNCT
ejpam-3371	139	13	.	.	PUNCT
ejpam-3371	140	1	this	this	PRON
ejpam-3371	140	2	implies	imply	VERB
ejpam-3371	140	3	{	{	PUNCT
ejpam-3371	140	4	d(xn	d(xn	PROPN
ejpam-3371	140	5	,	,	PUNCT
ejpam-3371	140	6	p	p	NOUN
ejpam-3371	140	7	)	)	PUNCT
ejpam-3371	140	8	}	}	PUNCT
ejpam-3371	140	9	is	be	AUX
ejpam-3371	140	10	convergent	convergent	ADJ
ejpam-3371	140	11	.	.	PUNCT
ejpam-3371	141	1	let	let	VERB
ejpam-3371	141	2	c	c	NOUN
ejpam-3371	141	3	=	=	SYM
ejpam-3371	141	4	lim	lim	PROPN
ejpam-3371	141	5	n→∞	n→∞	X
ejpam-3371	142	1	d(xn	d(xn	PROPN
ejpam-3371	142	2	,	,	PUNCT
ejpam-3371	142	3	p	p	NOUN
ejpam-3371	142	4	)	)	PUNCT
ejpam-3371	142	5	.	.	PUNCT
ejpam-3371	143	1	(	(	PUNCT
ejpam-3371	143	2	5	5	X
ejpam-3371	143	3	)	)	PUNCT
ejpam-3371	143	4	if	if	SCONJ
ejpam-3371	143	5	c	c	NOUN
ejpam-3371	143	6	=	=	SYM
ejpam-3371	143	7	0	0	NUM
ejpam-3371	143	8	,	,	PUNCT
ejpam-3371	143	9	then	then	ADV
ejpam-3371	143	10	we	we	PRON
ejpam-3371	143	11	have	have	VERB
ejpam-3371	143	12	nothing	nothing	PRON
ejpam-3371	143	13	to	to	PART
ejpam-3371	143	14	prove	prove	VERB
ejpam-3371	143	15	.	.	PUNCT
ejpam-3371	144	1	so	so	ADV
ejpam-3371	144	2	we	we	PRON
ejpam-3371	144	3	take	take	VERB
ejpam-3371	144	4	c	c	NOUN
ejpam-3371	144	5	>	>	X
ejpam-3371	145	1	0	0	X
ejpam-3371	146	1	.	.	PUNCT
ejpam-3371	147	1	since	since	SCONJ
ejpam-3371	147	2	d(xnn	d(xnn	PROPN
ejpam-3371	147	3	,	,	PUNCT
ejpam-3371	147	4	p	p	NOUN
ejpam-3371	147	5	)	)	PUNCT
ejpam-3371	147	6	≤	≤	NOUN
ejpam-3371	147	7	knd(xn	knd(xn	NOUN
ejpam-3371	147	8	,	,	PUNCT
ejpam-3371	147	9	p	p	NOUN
ejpam-3371	147	10	)	)	PUNCT
ejpam-3371	147	11	,	,	PUNCT
ejpam-3371	147	12	lim	lim	PROPN
ejpam-3371	147	13	sup	sup	VERB
ejpam-3371	147	14	n→∞	n→∞	X
ejpam-3371	147	15	d(xnn	d(xnn	PROPN
ejpam-3371	147	16	,	,	PUNCT
ejpam-3371	147	17	p	p	NOUN
ejpam-3371	147	18	)	)	PUNCT
ejpam-3371	147	19	≤	≤	NOUN
ejpam-3371	147	20	c.	c.	NOUN
ejpam-3371	147	21	(	(	PUNCT
ejpam-3371	147	22	6	6	NUM
ejpam-3371	147	23	)	)	PUNCT
ejpam-3371	147	24	also	also	ADV
ejpam-3371	147	25	,	,	PUNCT
ejpam-3371	147	26	lim	lim	PROPN
ejpam-3371	147	27	sup	sup	NOUN
ejpam-3371	147	28	n→∞	n→∞	NUM
ejpam-3371	147	29	d(yn	d(yn	NOUN
ejpam-3371	147	30	,	,	PUNCT
ejpam-3371	147	31	p	p	NOUN
ejpam-3371	147	32	)	)	PUNCT
ejpam-3371	147	33	≤	≤	NOUN
ejpam-3371	147	34	c.	c.	NOUN
ejpam-3371	147	35	(	(	PUNCT
ejpam-3371	147	36	7	7	X
ejpam-3371	147	37	)	)	PUNCT
ejpam-3371	147	38	we	we	PRON
ejpam-3371	147	39	know	know	VERB
ejpam-3371	147	40	that	that	SCONJ
ejpam-3371	147	41	if	if	SCONJ
ejpam-3371	147	42	limn→∞	limn→∞	PROPN
ejpam-3371	147	43	kn	kn	PROPN
ejpam-3371	147	44	=	=	NOUN
ejpam-3371	147	45	1	1	NUM
ejpam-3371	147	46	then	then	ADV
ejpam-3371	147	47	limn→∞	limn→∞	VERB
ejpam-3371	147	48	k	k	PROPN
ejpam-3371	147	49	2	2	NUM
ejpam-3371	147	50	n	n	NOUN
ejpam-3371	147	51	=	=	SYM
ejpam-3371	147	52	1	1	NUM
ejpam-3371	147	53	,	,	PUNCT
ejpam-3371	147	54	therefore	therefore	ADV
ejpam-3371	147	55	,	,	PUNCT
ejpam-3371	147	56	lim	lim	PROPN
ejpam-3371	147	57	sup	sup	PROPN
ejpam-3371	147	58	n→∞	n→∞	NUM
ejpam-3371	147	59	d(ýnn	d(ýnn	PROPN
ejpam-3371	147	60	,	,	PUNCT
ejpam-3371	147	61	p	p	NOUN
ejpam-3371	147	62	)	)	PUNCT
ejpam-3371	147	63	≤	≤	NOUN
ejpam-3371	147	64	lim	lim	PROPN
ejpam-3371	147	65	sup	sup	VERB
ejpam-3371	147	66	n→∞	n→∞	NUM
ejpam-3371	147	67	knd(yn	knd(yn	NOUN
ejpam-3371	147	68	,	,	PUNCT
ejpam-3371	147	69	p	p	NOUN
ejpam-3371	147	70	)	)	PUNCT
ejpam-3371	147	71	≤	≤	NOUN
ejpam-3371	147	72	lim	lim	PROPN
ejpam-3371	147	73	sup	sup	PROPN
ejpam-3371	147	74	n→∞	n→∞	NUM
ejpam-3371	147	75	kn[βd(xn	kn[βd(xn	NOUN
ejpam-3371	147	76	,	,	PUNCT
ejpam-3371	147	77	p	p	X
ejpam-3371	147	78	)	)	PUNCT
ejpam-3371	148	1	+	+	CCONJ
ejpam-3371	148	2	(	(	PUNCT
ejpam-3371	148	3	1−	1−	NUM
ejpam-3371	148	4	β)d(xnn	β)d(xnn	NUM
ejpam-3371	148	5	,	,	PUNCT
ejpam-3371	148	6	p	p	NOUN
ejpam-3371	148	7	)	)	PUNCT
ejpam-3371	148	8	]	]	PUNCT
ejpam-3371	148	9	≤	≤	NUM
ejpam-3371	148	10	lim	lim	PROPN
ejpam-3371	148	11	sup	sup	PROPN
ejpam-3371	148	12	n→∞	n→∞	NUM
ejpam-3371	148	13	kn[βd(xn	kn[βd(xn	NOUN
ejpam-3371	148	14	,	,	PUNCT
ejpam-3371	148	15	p	p	X
ejpam-3371	148	16	)	)	PUNCT
ejpam-3371	149	1	+	+	CCONJ
ejpam-3371	149	2	(	(	PUNCT
ejpam-3371	149	3	1−	1−	NUM
ejpam-3371	149	4	β)knd(xn	β)knd(xn	NOUN
ejpam-3371	149	5	,	,	PUNCT
ejpam-3371	149	6	p	p	NOUN
ejpam-3371	149	7	)	)	PUNCT
ejpam-3371	149	8	]	]	PUNCT
ejpam-3371	150	1	=	=	PUNCT
ejpam-3371	150	2	c	c	X
ejpam-3371	150	3	,	,	PUNCT
ejpam-3371	150	4	and	and	CCONJ
ejpam-3371	150	5	c	c	X
ejpam-3371	150	6	=	=	SYM
ejpam-3371	150	7	lim	lim	PROPN
ejpam-3371	150	8	n→∞	n→∞	X
ejpam-3371	151	1	d(xn+1	d(xn+1	PROPN
ejpam-3371	151	2	,	,	PUNCT
ejpam-3371	151	3	p	p	NOUN
ejpam-3371	151	4	)	)	PUNCT
ejpam-3371	151	5	=	=	SYM
ejpam-3371	151	6	lim	lim	PROPN
ejpam-3371	151	7	n→∞	n→∞	NUM
ejpam-3371	151	8	d(αxn	d(αxn	PROPN
ejpam-3371	151	9	⊕	⊕	PROPN
ejpam-3371	151	10	(	(	PUNCT
ejpam-3371	151	11	1−	1−	NUM
ejpam-3371	151	12	α)ýnn	α)ýnn	NOUN
ejpam-3371	151	13	,	,	PUNCT
ejpam-3371	151	14	p	p	NOUN
ejpam-3371	151	15	)	)	PUNCT
ejpam-3371	151	16	.	.	PUNCT
ejpam-3371	152	1	(	(	PUNCT
ejpam-3371	152	2	8)	8)	NUM
ejpam-3371	152	3	then	then	ADV
ejpam-3371	152	4	,	,	PUNCT
ejpam-3371	152	5	from	from	ADP
ejpam-3371	152	6	theorem	theorem	NOUN
ejpam-3371	152	7	1	1	NUM
ejpam-3371	152	8	,	,	PUNCT
ejpam-3371	152	9	(	(	PUNCT
ejpam-3371	152	10	5	5	NUM
ejpam-3371	152	11	)	)	PUNCT
ejpam-3371	152	12	,	,	PUNCT
ejpam-3371	152	13	(	(	PUNCT
ejpam-3371	152	14	7	7	X
ejpam-3371	152	15	)	)	PUNCT
ejpam-3371	152	16	and	and	CCONJ
ejpam-3371	152	17	(	(	PUNCT
ejpam-3371	152	18	8)	8)	NUM
ejpam-3371	152	19	,	,	PUNCT
ejpam-3371	152	20	we	we	PRON
ejpam-3371	152	21	get	get	VERB
ejpam-3371	152	22	lim	lim	PROPN
ejpam-3371	152	23	n→∞	n→∞	X
ejpam-3371	152	24	d(xn	d(xn	PROPN
ejpam-3371	152	25	,	,	PUNCT
ejpam-3371	152	26	ýnn	ýnn	X
ejpam-3371	152	27	)	)	PUNCT
ejpam-3371	153	1	=	=	NOUN
ejpam-3371	153	2	0	0	X
ejpam-3371	153	3	.	.	PUNCT
ejpam-3371	154	1	(	(	PUNCT
ejpam-3371	154	2	9	9	NUM
ejpam-3371	154	3	)	)	PUNCT
ejpam-3371	154	4	next	next	ADJ
ejpam-3371	154	5	d(xn	d(xn	PROPN
ejpam-3371	154	6	,	,	PUNCT
ejpam-3371	154	7	p	p	X
ejpam-3371	154	8	)	)	PUNCT
ejpam-3371	154	9	≤	≤	NOUN
ejpam-3371	155	1	d(xn	d(xn	PROPN
ejpam-3371	155	2	,	,	PUNCT
ejpam-3371	155	3	ýnn	ýnn	X
ejpam-3371	155	4	)	)	PUNCT
ejpam-3371	155	5	+	+	CCONJ
ejpam-3371	156	1	d(ýnn	d(ýnn	PROPN
ejpam-3371	156	2	,	,	PUNCT
ejpam-3371	156	3	p	p	NOUN
ejpam-3371	156	4	)	)	PUNCT
ejpam-3371	156	5	≤	≤	NOUN
ejpam-3371	156	6	d(xn	d(xn	PROPN
ejpam-3371	156	7	,	,	PUNCT
ejpam-3371	156	8	ýnn	ýnn	X
ejpam-3371	156	9	)	)	PUNCT
ejpam-3371	157	1	+	+	CCONJ
ejpam-3371	157	2	knd(p	knd(p	PROPN
ejpam-3371	157	3	,	,	PUNCT
ejpam-3371	157	4	yn	yn	PROPN
ejpam-3371	157	5	)	)	PUNCT
ejpam-3371	157	6	implies	imply	VERB
ejpam-3371	157	7	lim	lim	PROPN
ejpam-3371	157	8	inf	inf	PROPN
ejpam-3371	157	9	n→∞	n→∞	X
ejpam-3371	157	10	d(xn	d(xn	PROPN
ejpam-3371	157	11	,	,	PUNCT
ejpam-3371	157	12	p	p	NOUN
ejpam-3371	157	13	)	)	PUNCT
ejpam-3371	157	14	≤	≤	PROPN
ejpam-3371	157	15	lim	lim	PROPN
ejpam-3371	157	16	inf	inf	PROPN
ejpam-3371	157	17	n→∞	n→∞	X
ejpam-3371	157	18	(	(	PUNCT
ejpam-3371	157	19	d(xn	d(xn	PROPN
ejpam-3371	157	20	,	,	PUNCT
ejpam-3371	157	21	ýnn	ýnn	X
ejpam-3371	157	22	)	)	PUNCT
ejpam-3371	158	1	+	+	CCONJ
ejpam-3371	158	2	knd(p	knd(p	PROPN
ejpam-3371	158	3	,	,	PUNCT
ejpam-3371	158	4	yn	yn	PROPN
ejpam-3371	158	5	)	)	PUNCT
ejpam-3371	158	6	)	)	PUNCT
ejpam-3371	158	7	.	.	PUNCT
ejpam-3371	159	1	using	use	VERB
ejpam-3371	159	2	(	(	PUNCT
ejpam-3371	159	3	5	5	NUM
ejpam-3371	159	4	)	)	PUNCT
ejpam-3371	159	5	and	and	CCONJ
ejpam-3371	159	6	(	(	PUNCT
ejpam-3371	159	7	9	9	NUM
ejpam-3371	159	8	)	)	PUNCT
ejpam-3371	159	9	,	,	PUNCT
ejpam-3371	159	10	we	we	PRON
ejpam-3371	159	11	get	get	VERB
ejpam-3371	159	12	c	c	NOUN
ejpam-3371	159	13	≤	≤	PROPN
ejpam-3371	159	14	lim	lim	PROPN
ejpam-3371	159	15	inf	inf	PROPN
ejpam-3371	159	16	n→∞	n→∞	X
ejpam-3371	159	17	d(yn	d(yn	NOUN
ejpam-3371	159	18	,	,	PUNCT
ejpam-3371	159	19	p	p	NOUN
ejpam-3371	159	20	)	)	PUNCT
ejpam-3371	159	21	.	.	PUNCT
ejpam-3371	160	1	(	(	PUNCT
ejpam-3371	160	2	10	10	NUM
ejpam-3371	160	3	)	)	PUNCT
ejpam-3371	160	4	then	then	ADV
ejpam-3371	160	5	(	(	PUNCT
ejpam-3371	160	6	7	7	X
ejpam-3371	160	7	)	)	PUNCT
ejpam-3371	160	8	and	and	CCONJ
ejpam-3371	160	9	(	(	PUNCT
ejpam-3371	160	10	10	10	NUM
ejpam-3371	160	11	)	)	PUNCT
ejpam-3371	160	12	imply	imply	VERB
ejpam-3371	160	13	lim	lim	PROPN
ejpam-3371	160	14	n→∞	n→∞	X
ejpam-3371	160	15	d(yn	d(yn	ADJ
ejpam-3371	160	16	,	,	PUNCT
ejpam-3371	160	17	p	p	NOUN
ejpam-3371	160	18	)	)	PUNCT
ejpam-3371	161	1	=	=	SYM
ejpam-3371	161	2	c.	c.	NOUN
ejpam-3371	161	3	(	(	PUNCT
ejpam-3371	161	4	11	11	NUM
ejpam-3371	161	5	)	)	PUNCT
ejpam-3371	161	6	s.	s.	PROPN
ejpam-3371	161	7	h.	h.	PROPN
ejpam-3371	161	8	khan	khan	PROPN
ejpam-3371	161	9	,	,	PUNCT
ejpam-3371	161	10	h.	h.	PROPN
ejpam-3371	161	11	iqbal	iqbal	PROPN
ejpam-3371	161	12	,	,	PUNCT
ejpam-3371	161	13	m.	m.	NOUN
ejpam-3371	161	14	abbas	abbas	PROPN
ejpam-3371	161	15	/	/	SYM
ejpam-3371	161	16	eur	eur	PROPN
ejpam-3371	161	17	.	.	PUNCT
ejpam-3371	162	1	j.	j.	PROPN
ejpam-3371	162	2	pure	pure	PROPN
ejpam-3371	162	3	appl	appl	PROPN
ejpam-3371	162	4	.	.	PROPN
ejpam-3371	162	5	math	math	PROPN
ejpam-3371	162	6	,	,	PUNCT
ejpam-3371	162	7	12	12	NUM
ejpam-3371	162	8	(	(	PUNCT
ejpam-3371	162	9	2	2	NUM
ejpam-3371	162	10	)	)	PUNCT
ejpam-3371	162	11	(	(	PUNCT
ejpam-3371	162	12	2019	2019	NUM
ejpam-3371	162	13	)	)	PUNCT
ejpam-3371	162	14	,	,	PUNCT
ejpam-3371	162	15	348	348	NUM
ejpam-3371	162	16	-	-	SYM
ejpam-3371	162	17	357	357	NUM
ejpam-3371	162	18	355	355	NUM
ejpam-3371	162	19	that	that	PRON
ejpam-3371	162	20	is	be	AUX
ejpam-3371	162	21	,	,	PUNCT
ejpam-3371	162	22	c	c	PROPN
ejpam-3371	162	23	=	=	SYM
ejpam-3371	162	24	lim	lim	PROPN
ejpam-3371	162	25	n→∞	n→∞	X
ejpam-3371	162	26	d(yn	d(yn	ADJ
ejpam-3371	162	27	,	,	PUNCT
ejpam-3371	162	28	p	p	NOUN
ejpam-3371	162	29	)	)	PUNCT
ejpam-3371	162	30	=	=	SYM
ejpam-3371	162	31	lim	lim	PROPN
ejpam-3371	162	32	n→∞	n→∞	NUM
ejpam-3371	162	33	d(βxn	d(βxn	PROPN
ejpam-3371	162	34	⊕	⊕	PROPN
ejpam-3371	162	35	(	(	PUNCT
ejpam-3371	162	36	1−	1−	NUM
ejpam-3371	162	37	β)xnn	β)xnn	NUM
ejpam-3371	162	38	)	)	PUNCT
ejpam-3371	162	39	.	.	PUNCT
ejpam-3371	163	1	(	(	PUNCT
ejpam-3371	163	2	12	12	NUM
ejpam-3371	163	3	)	)	PUNCT
ejpam-3371	163	4	from	from	ADP
ejpam-3371	163	5	theorem	theorem	ADJ
ejpam-3371	163	6	1	1	NUM
ejpam-3371	163	7	,	,	PUNCT
ejpam-3371	163	8	(	(	PUNCT
ejpam-3371	163	9	5	5	NUM
ejpam-3371	163	10	)	)	PUNCT
ejpam-3371	163	11	,	,	PUNCT
ejpam-3371	163	12	(	(	PUNCT
ejpam-3371	163	13	6	6	NUM
ejpam-3371	163	14	)	)	PUNCT
ejpam-3371	163	15	and	and	CCONJ
ejpam-3371	163	16	(	(	PUNCT
ejpam-3371	163	17	12	12	NUM
ejpam-3371	163	18	)	)	PUNCT
ejpam-3371	163	19	,	,	PUNCT
ejpam-3371	163	20	we	we	PRON
ejpam-3371	163	21	get	get	VERB
ejpam-3371	163	22	,	,	PUNCT
ejpam-3371	163	23	d(xn	d(xn	PROPN
ejpam-3371	163	24	,	,	PUNCT
ejpam-3371	163	25	xnn	xnn	PRON
ejpam-3371	163	26	)	)	PUNCT
ejpam-3371	164	1	=	=	SYM
ejpam-3371	164	2	0	0	X
ejpam-3371	164	3	.	.	PUNCT
ejpam-3371	165	1	(	(	PUNCT
ejpam-3371	165	2	13	13	NUM
ejpam-3371	165	3	)	)	PUNCT
ejpam-3371	165	4	also	also	ADV
ejpam-3371	165	5	,	,	PUNCT
ejpam-3371	165	6	d(xn	d(xn	PROPN
ejpam-3371	165	7	,	,	PUNCT
ejpam-3371	165	8	x́nn	x́nn	PROPN
ejpam-3371	165	9	)	)	PUNCT
ejpam-3371	165	10	≤	≤	PUNCT
ejpam-3371	166	1	d(xn	d(xn	PROPN
ejpam-3371	166	2	,	,	PUNCT
ejpam-3371	166	3	ýnn	ýnn	X
ejpam-3371	166	4	)	)	PUNCT
ejpam-3371	166	5	+	+	CCONJ
ejpam-3371	167	1	d(ýnn	d(ýnn	PROPN
ejpam-3371	167	2	,	,	PUNCT
ejpam-3371	167	3	x́	x́	PROPN
ejpam-3371	167	4	n	n	CCONJ
ejpam-3371	167	5	n	n	CCONJ
ejpam-3371	167	6	)	)	PUNCT
ejpam-3371	167	7	≤	≤	NOUN
ejpam-3371	168	1	d(xn	d(xn	PROPN
ejpam-3371	168	2	,	,	PUNCT
ejpam-3371	168	3	ýnn	ýnn	X
ejpam-3371	168	4	)	)	PUNCT
ejpam-3371	168	5	+	+	CCONJ
ejpam-3371	168	6	knd(xn	knd(xn	PROPN
ejpam-3371	168	7	,	,	PUNCT
ejpam-3371	168	8	yn	yn	PROPN
ejpam-3371	168	9	)	)	PUNCT
ejpam-3371	168	10	≤	≤	PUNCT
ejpam-3371	169	1	d(xn	d(xn	PROPN
ejpam-3371	169	2	,	,	PUNCT
ejpam-3371	169	3	ýnn	ýnn	X
ejpam-3371	169	4	)	)	PUNCT
ejpam-3371	170	1	+	+	CCONJ
ejpam-3371	170	2	kn(1−	kn(1−	PROPN
ejpam-3371	170	3	α)d(xn	α)d(xn	NUM
ejpam-3371	170	4	,	,	PUNCT
ejpam-3371	170	5	xnn	xnn	NUM
ejpam-3371	170	6	)	)	PUNCT
ejpam-3371	170	7	.	.	PUNCT
ejpam-3371	171	1	hence	hence	ADV
ejpam-3371	171	2	,	,	PUNCT
ejpam-3371	171	3	(	(	PUNCT
ejpam-3371	171	4	9	9	NUM
ejpam-3371	171	5	)	)	PUNCT
ejpam-3371	171	6	and	and	CCONJ
ejpam-3371	171	7	(	(	PUNCT
ejpam-3371	171	8	13	13	NUM
ejpam-3371	171	9	)	)	PUNCT
ejpam-3371	171	10	give	give	VERB
ejpam-3371	171	11	lim	lim	PROPN
ejpam-3371	171	12	n→∞	n→∞	X
ejpam-3371	171	13	d(xn	d(xn	PROPN
ejpam-3371	171	14	,	,	PUNCT
ejpam-3371	171	15	x́nn	x́nn	PROPN
ejpam-3371	171	16	)	)	PUNCT
ejpam-3371	171	17	=	=	SYM
ejpam-3371	172	1	0	0	X
ejpam-3371	172	2	.	.	PUNCT
ejpam-3371	173	1	(	(	PUNCT
ejpam-3371	173	2	14	14	NUM
ejpam-3371	173	3	)	)	PUNCT
ejpam-3371	173	4	now	now	ADV
ejpam-3371	173	5	using	use	VERB
ejpam-3371	173	6	lemma	lemma	PROPN
ejpam-3371	173	7	1	1	NUM
ejpam-3371	173	8	,	,	PUNCT
ejpam-3371	173	9	(	(	PUNCT
ejpam-3371	173	10	13	13	NUM
ejpam-3371	173	11	)	)	PUNCT
ejpam-3371	173	12	and	and	CCONJ
ejpam-3371	173	13	(	(	PUNCT
ejpam-3371	173	14	14	14	NUM
ejpam-3371	173	15	)	)	PUNCT
ejpam-3371	173	16	,	,	PUNCT
ejpam-3371	173	17	we	we	PRON
ejpam-3371	173	18	get	get	VERB
ejpam-3371	173	19	our	our	PRON
ejpam-3371	173	20	desired	desire	VERB
ejpam-3371	173	21	results	result	NOUN
ejpam-3371	173	22	.	.	PUNCT
ejpam-3371	174	1	we	we	PRON
ejpam-3371	174	2	now	now	ADV
ejpam-3371	174	3	give	give	VERB
ejpam-3371	174	4	some	some	DET
ejpam-3371	174	5	convergence	convergence	NOUN
ejpam-3371	174	6	results	result	NOUN
ejpam-3371	174	7	.	.	PUNCT
ejpam-3371	175	1	theorem	theorem	NOUN
ejpam-3371	175	2	3	3	X
ejpam-3371	175	3	.	.	PUNCT
ejpam-3371	176	1	let	let	VERB
ejpam-3371	176	2	d	d	PRON
ejpam-3371	176	3	be	be	AUX
ejpam-3371	176	4	a	a	DET
ejpam-3371	176	5	compact	compact	ADJ
ejpam-3371	176	6	and	and	CCONJ
ejpam-3371	176	7	convex	convex	NOUN
ejpam-3371	176	8	subset	subset	NOUN
ejpam-3371	176	9	of	of	ADP
ejpam-3371	176	10	a	a	DET
ejpam-3371	176	11	uniformly	uniformly	ADV
ejpam-3371	176	12	convex	convex	ADJ
ejpam-3371	176	13	hyperbolic	hyperbolic	ADJ
ejpam-3371	176	14	space	space	NOUN
ejpam-3371	176	15	.	.	PUNCT
ejpam-3371	177	1	let	let	VERB
ejpam-3371	177	2	t1	t1	NOUN
ejpam-3371	177	3	,	,	PUNCT
ejpam-3371	177	4	t2	t2	PROPN
ejpam-3371	177	5	and	and	CCONJ
ejpam-3371	177	6	xn	xn	PROPN
ejpam-3371	177	7	be	be	AUX
ejpam-3371	177	8	as	as	ADP
ejpam-3371	177	9	in	in	ADP
ejpam-3371	177	10	theorem	theorem	NOUN
ejpam-3371	177	11	2	2	NUM
ejpam-3371	177	12	.	.	PUNCT
ejpam-3371	178	1	if	if	SCONJ
ejpam-3371	178	2	f	f	PROPN
ejpam-3371	178	3	6=	6=	PROPN
ejpam-3371	178	4	∅	∅	NOUN
ejpam-3371	178	5	with	with	ADP
ejpam-3371	178	6	t1p	t1p	PUNCT
ejpam-3371	178	7	=	=	PUNCT
ejpam-3371	178	8	t2p	t2p	X
ejpam-3371	178	9	=	=	PUNCT
ejpam-3371	178	10	{	{	PUNCT
ejpam-3371	178	11	p	p	X
ejpam-3371	178	12	}	}	PUNCT
ejpam-3371	178	13	for	for	ADP
ejpam-3371	178	14	p	p	PROPN
ejpam-3371	178	15	∈	∈	PROPN
ejpam-3371	179	1	f	f	X
ejpam-3371	180	1	then	then	ADV
ejpam-3371	180	2	there	there	PRON
ejpam-3371	180	3	is	be	VERB
ejpam-3371	180	4	a	a	DET
ejpam-3371	180	5	subsequence	subsequence	NOUN
ejpam-3371	180	6	of	of	ADP
ejpam-3371	180	7	{	{	PUNCT
ejpam-3371	180	8	xn	xn	NOUN
ejpam-3371	180	9	}	}	PUNCT
ejpam-3371	180	10	which	which	PRON
ejpam-3371	180	11	converges	converge	VERB
ejpam-3371	180	12	to	to	ADP
ejpam-3371	180	13	a	a	DET
ejpam-3371	180	14	common	common	ADJ
ejpam-3371	180	15	fixed	fix	VERB
ejpam-3371	180	16	point	point	NOUN
ejpam-3371	180	17	of	of	ADP
ejpam-3371	180	18	t1	t1	NOUN
ejpam-3371	180	19	and	and	CCONJ
ejpam-3371	180	20	t2	t2	NOUN
ejpam-3371	180	21	.	.	PUNCT
ejpam-3371	181	1	proof	proof	NOUN
ejpam-3371	181	2	.	.	PUNCT
ejpam-3371	182	1	since	since	SCONJ
ejpam-3371	182	2	d	d	PROPN
ejpam-3371	182	3	is	be	AUX
ejpam-3371	182	4	compact	compact	ADJ
ejpam-3371	182	5	so	so	ADV
ejpam-3371	182	6	there	there	PRON
ejpam-3371	182	7	exists	exist	VERB
ejpam-3371	182	8	a	a	DET
ejpam-3371	182	9	subsequence	subsequence	NOUN
ejpam-3371	182	10	{	{	PUNCT
ejpam-3371	182	11	xnk	xnk	PROPN
ejpam-3371	182	12	}	}	PUNCT
ejpam-3371	182	13	of	of	ADP
ejpam-3371	182	14	{	{	PUNCT
ejpam-3371	182	15	xn	xn	NOUN
ejpam-3371	182	16	}	}	PUNCT
ejpam-3371	182	17	such	such	ADJ
ejpam-3371	182	18	that	that	SCONJ
ejpam-3371	182	19	{	{	PUNCT
ejpam-3371	182	20	xnk	xnk	PROPN
ejpam-3371	182	21	}	}	PUNCT
ejpam-3371	182	22	converges	converge	VERB
ejpam-3371	182	23	to	to	ADP
ejpam-3371	182	24	some	some	DET
ejpam-3371	182	25	z	z	PROPN
ejpam-3371	182	26	∈	∈	PROPN
ejpam-3371	182	27	d.	d.	PROPN
ejpam-3371	182	28	from	from	ADP
ejpam-3371	182	29	theorem	theorem	NOUN
ejpam-3371	182	30	2	2	NUM
ejpam-3371	182	31	we	we	PRON
ejpam-3371	182	32	know	know	VERB
ejpam-3371	182	33	that	that	SCONJ
ejpam-3371	182	34	lim	lim	PROPN
ejpam-3371	182	35	m→∞	m→∞	NOUN
ejpam-3371	182	36	d(xn	d(xn	PROPN
ejpam-3371	182	37	,	,	PUNCT
ejpam-3371	182	38	xn1	xn1	NUM
ejpam-3371	182	39	)	)	PUNCT
ejpam-3371	182	40	=	=	SYM
ejpam-3371	182	41	0	0	NUM
ejpam-3371	182	42	,	,	PUNCT
ejpam-3371	182	43	and	and	CCONJ
ejpam-3371	182	44	lim	lim	PROPN
ejpam-3371	182	45	n→∞	n→∞	X
ejpam-3371	182	46	d(xn	d(xn	PROPN
ejpam-3371	182	47	,	,	PUNCT
ejpam-3371	182	48	x́n1	x́n1	PUNCT
ejpam-3371	182	49	)	)	PUNCT
ejpam-3371	183	1	=	=	PUNCT
ejpam-3371	183	2	0	0	X
ejpam-3371	183	3	.	.	X
ejpam-3371	183	4	applying	apply	VERB
ejpam-3371	183	5	h	h	NOUN
ejpam-3371	183	6	-	-	PUNCT
ejpam-3371	183	7	continuity	continuity	NOUN
ejpam-3371	183	8	of	of	ADP
ejpam-3371	183	9	t1	t1	NOUN
ejpam-3371	183	10	and	and	CCONJ
ejpam-3371	183	11	t2	t2	NOUN
ejpam-3371	183	12	,	,	PUNCT
ejpam-3371	183	13	we	we	PRON
ejpam-3371	183	14	have	have	VERB
ejpam-3371	183	15	lim	lim	PROPN
ejpam-3371	183	16	n→∞	n→∞	X
ejpam-3371	183	17	d(tz	d(tz	PROPN
ejpam-3371	183	18	,	,	PUNCT
ejpam-3371	183	19	xnk	xnk	PROPN
ejpam-3371	183	20	1	1	X
ejpam-3371	183	21	)	)	PUNCT
ejpam-3371	184	1	=	=	VERB
ejpam-3371	184	2	lim	lim	PROPN
ejpam-3371	184	3	n→∞	n→∞	X
ejpam-3371	184	4	d(t1z	d(t1z	PROPN
ejpam-3371	184	5	,	,	PUNCT
ejpam-3371	184	6	´	´	PROPN
ejpam-3371	184	7	xnk	xnk	X
ejpam-3371	184	8	1	1	NUM
ejpam-3371	184	9	)	)	PUNCT
ejpam-3371	184	10	=	=	SYM
ejpam-3371	184	11	0	0	NUM
ejpam-3371	185	1	where	where	SCONJ
ejpam-3371	185	2	xnk	xnk	PROPN
ejpam-3371	185	3	1	1	NUM
ejpam-3371	185	4	∈	∈	PROPN
ejpam-3371	185	5	t1xnk	t1xnk	NOUN
ejpam-3371	185	6	and	and	CCONJ
ejpam-3371	185	7	´	´	NOUN
ejpam-3371	185	8	xnk	xnk	VERB
ejpam-3371	185	9	1	1	NUM
ejpam-3371	185	10	∈	∈	PROPN
ejpam-3371	185	11	t2xnk	t2xnk	NOUN
ejpam-3371	185	12	.	.	PUNCT
ejpam-3371	186	1	thus	thus	ADV
ejpam-3371	186	2	d(z	d(z	PROPN
ejpam-3371	186	3	,	,	PUNCT
ejpam-3371	186	4	t1z	t1z	PROPN
ejpam-3371	186	5	)	)	PUNCT
ejpam-3371	186	6	≤	≤	X
ejpam-3371	186	7	d(t1z	d(t1z	PROPN
ejpam-3371	186	8	,	,	PUNCT
ejpam-3371	186	9	´	´	PROPN
ejpam-3371	186	10	xnk	xnk	X
ejpam-3371	186	11	1	1	NUM
ejpam-3371	186	12	)	)	PUNCT
ejpam-3371	186	13	+	+	CCONJ
ejpam-3371	186	14	d(z	d(z	PROPN
ejpam-3371	186	15	,	,	PUNCT
ejpam-3371	186	16	xnk	xnk	PROPN
ejpam-3371	186	17	)	)	PUNCT
ejpam-3371	187	1	+	+	CCONJ
ejpam-3371	188	1	d	d	X
ejpam-3371	188	2	(	(	PUNCT
ejpam-3371	188	3	´	´	NOUN
ejpam-3371	188	4	xnk	xnk	X
ejpam-3371	188	5	1	1	NUM
ejpam-3371	188	6	,	,	PUNCT
ejpam-3371	188	7	xnk	xnk	PROPN
ejpam-3371	188	8	)	)	PUNCT
ejpam-3371	188	9	.	.	PUNCT
ejpam-3371	189	1	therefore	therefore	ADV
ejpam-3371	189	2	,	,	PUNCT
ejpam-3371	189	3	as	as	ADP
ejpam-3371	189	4	n→∞	n→∞	NUM
ejpam-3371	189	5	d(z	d(z	PROPN
ejpam-3371	189	6	,	,	PUNCT
ejpam-3371	189	7	t1z	t1z	PROPN
ejpam-3371	189	8	)	)	PUNCT
ejpam-3371	189	9	=	=	SYM
ejpam-3371	189	10	0	0	X
ejpam-3371	189	11	.	.	PUNCT
ejpam-3371	189	12	similarly	similarly	ADV
ejpam-3371	189	13	,	,	PUNCT
ejpam-3371	189	14	d(z	d(z	PROPN
ejpam-3371	189	15	,	,	PUNCT
ejpam-3371	189	16	t2z	t2z	NOUN
ejpam-3371	189	17	)	)	PUNCT
ejpam-3371	189	18	≤	≤	PROPN
ejpam-3371	189	19	d(t2z	d(t2z	NOUN
ejpam-3371	189	20	,	,	PUNCT
ejpam-3371	189	21	´	´	PROPN
ejpam-3371	189	22	xnk	xnk	X
ejpam-3371	189	23	1	1	NUM
ejpam-3371	189	24	)	)	PUNCT
ejpam-3371	189	25	+	+	CCONJ
ejpam-3371	189	26	d(z	d(z	PROPN
ejpam-3371	189	27	,	,	PUNCT
ejpam-3371	189	28	xnk	xnk	PROPN
ejpam-3371	189	29	)	)	PUNCT
ejpam-3371	190	1	+	+	CCONJ
ejpam-3371	191	1	d	d	X
ejpam-3371	191	2	(	(	PUNCT
ejpam-3371	191	3	´	´	NOUN
ejpam-3371	191	4	xnk	xnk	X
ejpam-3371	191	5	1	1	NUM
ejpam-3371	191	6	,	,	PUNCT
ejpam-3371	191	7	xnk	xnk	PROPN
ejpam-3371	191	8	)	)	PUNCT
ejpam-3371	191	9	.	.	PUNCT
ejpam-3371	192	1	thus	thus	ADV
ejpam-3371	192	2	,	,	PUNCT
ejpam-3371	192	3	as	as	ADP
ejpam-3371	192	4	n→∞	n→∞	NUM
ejpam-3371	192	5	,	,	PUNCT
ejpam-3371	192	6	d(z	d(z	PROPN
ejpam-3371	192	7	,	,	PUNCT
ejpam-3371	192	8	t2z	t2z	NOUN
ejpam-3371	192	9	)	)	PUNCT
ejpam-3371	192	10	=	=	SYM
ejpam-3371	192	11	0	0	X
ejpam-3371	192	12	.	.	PUNCT
ejpam-3371	193	1	hence	hence	ADV
ejpam-3371	193	2	,	,	PUNCT
ejpam-3371	193	3	z	z	PROPN
ejpam-3371	193	4	is	be	AUX
ejpam-3371	193	5	a	a	DET
ejpam-3371	193	6	common	common	ADJ
ejpam-3371	193	7	fixed	fix	VERB
ejpam-3371	193	8	point	point	NOUN
ejpam-3371	193	9	of	of	ADP
ejpam-3371	193	10	t1	t1	NOUN
ejpam-3371	193	11	and	and	CCONJ
ejpam-3371	193	12	t2	t2	NOUN
ejpam-3371	193	13	.	.	PUNCT
ejpam-3371	194	1	s.	s.	PROPN
ejpam-3371	194	2	h.	h.	PROPN
ejpam-3371	194	3	khan	khan	PROPN
ejpam-3371	194	4	,	,	PUNCT
ejpam-3371	194	5	h.	h.	PROPN
ejpam-3371	194	6	iqbal	iqbal	PROPN
ejpam-3371	194	7	,	,	PUNCT
ejpam-3371	194	8	m.	m.	NOUN
ejpam-3371	194	9	abbas	abbas	PROPN
ejpam-3371	194	10	/	/	SYM
ejpam-3371	194	11	eur	eur	PROPN
ejpam-3371	194	12	.	.	PUNCT
ejpam-3371	195	1	j.	j.	PROPN
ejpam-3371	195	2	pure	pure	PROPN
ejpam-3371	195	3	appl	appl	PROPN
ejpam-3371	195	4	.	.	PROPN
ejpam-3371	195	5	math	math	PROPN
ejpam-3371	195	6	,	,	PUNCT
ejpam-3371	195	7	12	12	NUM
ejpam-3371	195	8	(	(	PUNCT
ejpam-3371	195	9	2	2	NUM
ejpam-3371	195	10	)	)	PUNCT
ejpam-3371	195	11	(	(	PUNCT
ejpam-3371	195	12	2019	2019	NUM
ejpam-3371	195	13	)	)	PUNCT
ejpam-3371	195	14	,	,	PUNCT
ejpam-3371	195	15	348	348	NUM
ejpam-3371	195	16	-	-	SYM
ejpam-3371	195	17	357	357	NUM
ejpam-3371	195	18	356	356	NUM
ejpam-3371	195	19	theorem	theorem	VERB
ejpam-3371	195	20	4	4	NUM
ejpam-3371	195	21	.	.	PUNCT
ejpam-3371	196	1	let	let	VERB
ejpam-3371	196	2	d	d	PRON
ejpam-3371	196	3	be	be	AUX
ejpam-3371	196	4	a	a	DET
ejpam-3371	196	5	nonempty	nonempty	ADJ
ejpam-3371	196	6	,	,	PUNCT
ejpam-3371	196	7	closed	closed	ADJ
ejpam-3371	196	8	,	,	PUNCT
ejpam-3371	196	9	convex	convex	NOUN
ejpam-3371	196	10	and	and	CCONJ
ejpam-3371	196	11	bounded	bound	VERB
ejpam-3371	196	12	subset	subset	NOUN
ejpam-3371	196	13	of	of	ADP
ejpam-3371	196	14	a	a	DET
ejpam-3371	196	15	complete	complete	ADJ
ejpam-3371	196	16	uniformly	uniformly	ADV
ejpam-3371	196	17	convex	convex	ADJ
ejpam-3371	196	18	hyperbolic	hyperbolic	ADJ
ejpam-3371	196	19	space	space	NOUN
ejpam-3371	196	20	(	(	PUNCT
ejpam-3371	196	21	x	x	X
ejpam-3371	196	22	,	,	PUNCT
ejpam-3371	196	23	d	d	NOUN
ejpam-3371	196	24	)	)	PUNCT
ejpam-3371	196	25	.	.	PUNCT
ejpam-3371	197	1	let	let	VERB
ejpam-3371	197	2	t1	t1	NOUN
ejpam-3371	197	3	,	,	PUNCT
ejpam-3371	197	4	t2	t2	PROPN
ejpam-3371	197	5	and	and	CCONJ
ejpam-3371	197	6	xn	xn	PROPN
ejpam-3371	197	7	be	be	AUX
ejpam-3371	197	8	as	as	ADP
ejpam-3371	197	9	in	in	ADP
ejpam-3371	197	10	theorem	theorem	NOUN
ejpam-3371	197	11	2	2	NUM
ejpam-3371	197	12	.	.	PUNCT
ejpam-3371	198	1	if	if	SCONJ
ejpam-3371	198	2	f	f	PROPN
ejpam-3371	198	3	6=	6=	PROPN
ejpam-3371	198	4	∅	∅	NOUN
ejpam-3371	198	5	with	with	ADP
ejpam-3371	198	6	t1p	t1p	PUNCT
ejpam-3371	198	7	=	=	PUNCT
ejpam-3371	198	8	t2p	t2p	X
ejpam-3371	198	9	=	=	PUNCT
ejpam-3371	198	10	{	{	PUNCT
ejpam-3371	198	11	p	p	X
ejpam-3371	198	12	}	}	PUNCT
ejpam-3371	198	13	for	for	ADP
ejpam-3371	198	14	p	p	PROPN
ejpam-3371	198	15	∈	∈	PROPN
ejpam-3371	199	1	f	f	X
ejpam-3371	199	2	,	,	PUNCT
ejpam-3371	199	3	then	then	ADV
ejpam-3371	199	4	{	{	PUNCT
ejpam-3371	199	5	xn	xn	X
ejpam-3371	199	6	}	}	PUNCT
ejpam-3371	199	7	converges	converge	NOUN
ejpam-3371	199	8	to	to	ADP
ejpam-3371	199	9	a	a	DET
ejpam-3371	199	10	common	common	ADJ
ejpam-3371	199	11	fixed	fix	VERB
ejpam-3371	199	12	point	point	NOUN
ejpam-3371	199	13	of	of	ADP
ejpam-3371	199	14	t1	t1	NOUN
ejpam-3371	199	15	and	and	CCONJ
ejpam-3371	199	16	t2	t2	NOUN
ejpam-3371	199	17	if	if	SCONJ
ejpam-3371	199	18	and	and	CCONJ
ejpam-3371	199	19	only	only	ADV
ejpam-3371	199	20	if	if	SCONJ
ejpam-3371	199	21	lim	lim	PROPN
ejpam-3371	199	22	infn→∞	infn→∞	PROPN
ejpam-3371	199	23	d(xn	d(xn	PROPN
ejpam-3371	199	24	,	,	PUNCT
ejpam-3371	199	25	f	f	X
ejpam-3371	199	26	)	)	PUNCT
ejpam-3371	199	27	=	=	PUNCT
ejpam-3371	199	28	0	0	NUM
ejpam-3371	199	29	where	where	SCONJ
ejpam-3371	199	30	d(xn	d(xn	X
ejpam-3371	199	31	,	,	PUNCT
ejpam-3371	199	32	f	f	NOUN
ejpam-3371	199	33	)	)	PUNCT
ejpam-3371	200	1	=	=	SYM
ejpam-3371	200	2	inf{d(xn	inf{d(xn	PROPN
ejpam-3371	200	3	,	,	PUNCT
ejpam-3371	200	4	p	p	NOUN
ejpam-3371	200	5	)	)	PUNCT
ejpam-3371	200	6	:	:	PUNCT
ejpam-3371	200	7	p	p	X
ejpam-3371	200	8	∈	∈	PROPN
ejpam-3371	200	9	f	f	X
ejpam-3371	200	10	}	}	PUNCT
ejpam-3371	200	11	.	.	PUNCT
ejpam-3371	201	1	proof	proof	NOUN
ejpam-3371	201	2	.	.	PUNCT
ejpam-3371	202	1	the	the	DET
ejpam-3371	202	2	necessity	necessity	NOUN
ejpam-3371	202	3	of	of	ADP
ejpam-3371	202	4	the	the	DET
ejpam-3371	202	5	conditions	condition	NOUN
ejpam-3371	202	6	is	be	AUX
ejpam-3371	202	7	obvious	obvious	ADJ
ejpam-3371	202	8	.	.	PUNCT
ejpam-3371	203	1	conversely	conversely	ADV
ejpam-3371	203	2	,	,	PUNCT
ejpam-3371	203	3	suppose	suppose	VERB
ejpam-3371	203	4	that	that	SCONJ
ejpam-3371	203	5	lim	lim	PROPN
ejpam-3371	203	6	infn→∞	infn→∞	PROPN
ejpam-3371	203	7	d(xn	d(xn	PROPN
ejpam-3371	203	8	,	,	PUNCT
ejpam-3371	203	9	f	f	X
ejpam-3371	203	10	)	)	PUNCT
ejpam-3371	203	11	=	=	PUNCT
ejpam-3371	204	1	0	0	X
ejpam-3371	204	2	.	.	PUNCT
ejpam-3371	204	3	since	since	ADV
ejpam-3371	204	4	,	,	PUNCT
ejpam-3371	204	5	d(xn+1	d(xn+1	PROPN
ejpam-3371	204	6	,	,	PUNCT
ejpam-3371	204	7	p	p	NOUN
ejpam-3371	204	8	)	)	PUNCT
ejpam-3371	204	9	≤	≤	NOUN
ejpam-3371	204	10	vnd(xn	vnd(xn	ADP
ejpam-3371	204	11	,	,	PUNCT
ejpam-3371	204	12	p	p	NOUN
ejpam-3371	204	13	)	)	PUNCT
ejpam-3371	204	14	⇒	⇒	NOUN
ejpam-3371	204	15	d(xn+1	d(xn+1	PROPN
ejpam-3371	204	16	,	,	PUNCT
ejpam-3371	204	17	f	f	PROPN
ejpam-3371	204	18	)	)	PUNCT
ejpam-3371	204	19	≤	≤	NOUN
ejpam-3371	204	20	vnd(xn	vnd(xn	ADP
ejpam-3371	204	21	,	,	PUNCT
ejpam-3371	204	22	f	f	PROPN
ejpam-3371	204	23	)	)	PUNCT
ejpam-3371	204	24	.	.	PUNCT
ejpam-3371	205	1	thus	thus	ADV
ejpam-3371	205	2	,	,	PUNCT
ejpam-3371	205	3	limn→∞(xn	limn→∞(xn	NUM
ejpam-3371	205	4	,	,	PUNCT
ejpam-3371	205	5	f	f	PROPN
ejpam-3371	205	6	)	)	PUNCT
ejpam-3371	205	7	exists	exist	VERB
ejpam-3371	205	8	.	.	PUNCT
ejpam-3371	206	1	since	since	SCONJ
ejpam-3371	206	2	lim	lim	PROPN
ejpam-3371	206	3	infn→∞	infn→∞	PROPN
ejpam-3371	206	4	d(xn	d(xn	PROPN
ejpam-3371	206	5	,	,	PUNCT
ejpam-3371	206	6	f	f	X
ejpam-3371	206	7	)	)	PUNCT
ejpam-3371	206	8	=	=	SYM
ejpam-3371	206	9	0	0	NUM
ejpam-3371	206	10	,	,	PUNCT
ejpam-3371	206	11	limn→∞(xn	limn→∞(xn	NUM
ejpam-3371	206	12	,	,	PUNCT
ejpam-3371	206	13	f	f	X
ejpam-3371	206	14	)	)	PUNCT
ejpam-3371	206	15	=	=	PUNCT
ejpam-3371	207	1	0	0	X
ejpam-3371	207	2	.	.	PUNCT
ejpam-3371	208	1	next	next	ADV
ejpam-3371	208	2	,	,	PUNCT
ejpam-3371	208	3	from	from	ADP
ejpam-3371	208	4	1	1	NUM
ejpam-3371	208	5	+	+	CCONJ
ejpam-3371	208	6	x	x	SYM
ejpam-3371	208	7	≤	≤	ADJ
ejpam-3371	208	8	ex	ex	X
ejpam-3371	208	9	for	for	ADP
ejpam-3371	208	10	all	all	PRON
ejpam-3371	208	11	x	x	PRON
ejpam-3371	208	12	≥	≥	NOUN
ejpam-3371	208	13	0	0	NUM
ejpam-3371	208	14	,	,	PUNCT
ejpam-3371	208	15	we	we	PRON
ejpam-3371	208	16	obtain	obtain	VERB
ejpam-3371	208	17	d(xn+k	d(xn+k	PROPN
ejpam-3371	208	18	,	,	PUNCT
ejpam-3371	208	19	p	p	NOUN
ejpam-3371	208	20	)	)	PUNCT
ejpam-3371	208	21	≤	≤	NOUN
ejpam-3371	208	22	vn+(k−1)d(xn+(k−1	vn+(k−1)d(xn+(k−1	NUM
ejpam-3371	208	23	)	)	PUNCT
ejpam-3371	208	24	,	,	PUNCT
ejpam-3371	208	25	p	p	NOUN
ejpam-3371	208	26	)	)	PUNCT
ejpam-3371	208	27	=	=	SYM
ejpam-3371	208	28	(	(	PUNCT
ejpam-3371	208	29	1	1	NUM
ejpam-3371	208	30	+	+	CCONJ
ejpam-3371	208	31	(	(	PUNCT
ejpam-3371	208	32	vn+(k−1	vn+(k−1	ADV
ejpam-3371	208	33	)	)	PUNCT
ejpam-3371	208	34	−	−	PROPN
ejpam-3371	208	35	1))d(xn+(k−1	1))d(xn+(k−1	NUM
ejpam-3371	208	36	)	)	PUNCT
ejpam-3371	208	37	,	,	PUNCT
ejpam-3371	208	38	p	p	X
ejpam-3371	208	39	)	)	PUNCT
ejpam-3371	208	40	≤	≤	NOUN
ejpam-3371	208	41	evn+(k−1)−1d(xn+(k−1	evn+(k−1)−1d(xn+(k−1	PROPN
ejpam-3371	208	42	)	)	PUNCT
ejpam-3371	208	43	,	,	PUNCT
ejpam-3371	208	44	p	p	X
ejpam-3371	208	45	)	)	PUNCT
ejpam-3371	208	46	≤	≤	NOUN
ejpam-3371	208	47	evn+(k−1)−1evn+(k−2)−1d(xn+(k−2	evn+(k−1)−1evn+(k−2)−1d(xn+(k−2	NOUN
ejpam-3371	208	48	)	)	PUNCT
ejpam-3371	208	49	,	,	PUNCT
ejpam-3371	208	50	p	p	X
ejpam-3371	208	51	)	)	PUNCT
ejpam-3371	208	52	≤	≤	NUM
ejpam-3371	208	53	:	:	PUNCT
ejpam-3371	208	54	:	:	PUNCT
ejpam-3371	208	55	:	:	PUNCT
ejpam-3371	209	1	≤	≤	NUM
ejpam-3371	209	2	:	:	PUNCT
ejpam-3371	209	3	:	:	PUNCT
ejpam-3371	209	4	:	:	PUNCT
ejpam-3371	209	5	≤	≤	X
ejpam-3371	209	6	e	e	X
ejpam-3371	209	7	∑n+(k−1	∑n+(k−1	PROPN
ejpam-3371	209	8	)	)	PUNCT
ejpam-3371	209	9	i	i	PROPN
ejpam-3371	209	10	=	=	NOUN
ejpam-3371	209	11	n	n	X
ejpam-3371	209	12	(	(	PUNCT
ejpam-3371	209	13	vi−1)d(xn	vi−1)d(xn	X
ejpam-3371	209	14	,	,	PUNCT
ejpam-3371	209	15	p	p	NOUN
ejpam-3371	209	16	)	)	PUNCT
ejpam-3371	209	17	.	.	PUNCT
ejpam-3371	210	1	we	we	PRON
ejpam-3371	210	2	know	know	VERB
ejpam-3371	210	3	that	that	SCONJ
ejpam-3371	210	4	∑	∑	ADP
ejpam-3371	210	5	n(vn	n(vn	X
ejpam-3371	210	6	−	−	PROPN
ejpam-3371	210	7	1	1	X
ejpam-3371	210	8	)	)	PUNCT
ejpam-3371	210	9	<	<	X
ejpam-3371	210	10	∞,so	∞,so	X
ejpam-3371	210	11	there	there	PRON
ejpam-3371	210	12	exists	exist	VERB
ejpam-3371	210	13	some	some	PRON
ejpam-3371	210	14	w	w	ADP
ejpam-3371	210	15	such	such	ADJ
ejpam-3371	210	16	that	that	SCONJ
ejpam-3371	210	17	,	,	PUNCT
ejpam-3371	210	18	d(xn+k	d(xn+k	PROPN
ejpam-3371	210	19	,	,	PUNCT
ejpam-3371	210	20	p	p	NOUN
ejpam-3371	210	21	)	)	PUNCT
ejpam-3371	210	22	≤wd(xn	≤wd(xn	NOUN
ejpam-3371	210	23	,	,	PUNCT
ejpam-3371	210	24	p	p	NOUN
ejpam-3371	210	25	)	)	PUNCT
ejpam-3371	210	26	for	for	ADP
ejpam-3371	210	27	all	all	DET
ejpam-3371	210	28	p	p	PROPN
ejpam-3371	210	29	∈	∈	PROPN
ejpam-3371	210	30	f	f	NOUN
ejpam-3371	210	31	and	and	CCONJ
ejpam-3371	210	32	n	n	CCONJ
ejpam-3371	210	33	∈	∈	PROPN
ejpam-3371	210	34	n.	n.	NOUN
ejpam-3371	210	35	since	since	SCONJ
ejpam-3371	210	36	limn→∞	limn→∞	PROPN
ejpam-3371	210	37	d(xn	d(xn	PROPN
ejpam-3371	210	38	,	,	PUNCT
ejpam-3371	210	39	f	f	X
ejpam-3371	210	40	)	)	PUNCT
ejpam-3371	211	1	=	=	SYM
ejpam-3371	211	2	0	0	NUM
ejpam-3371	211	3	,	,	PUNCT
ejpam-3371	211	4	∃	∃	PROPN
ejpam-3371	211	5	n0	n0	PROPN
ejpam-3371	211	6	such	such	ADJ
ejpam-3371	211	7	that	that	SCONJ
ejpam-3371	211	8	d(xn0	d(xn0	NOUN
ejpam-3371	211	9	,	,	PUNCT
ejpam-3371	211	10	f	f	PROPN
ejpam-3371	211	11	)	)	PUNCT
ejpam-3371	211	12	<	<	X
ejpam-3371	211	13	ε	ε	PROPN
ejpam-3371	211	14	w	w	PROPN
ejpam-3371	211	15	+	+	PROPN
ejpam-3371	211	16	1	1	NUM
ejpam-3371	211	17	.	.	PUNCT
ejpam-3371	212	1	thus	thus	ADV
ejpam-3371	212	2	there	there	PRON
ejpam-3371	212	3	must	must	AUX
ejpam-3371	212	4	exist	exist	VERB
ejpam-3371	212	5	p∗	p∗	ADJ
ejpam-3371	212	6	such	such	DET
ejpam-3371	212	7	that	that	DET
ejpam-3371	212	8	d(xn0	d(xn0	NOUN
ejpam-3371	212	9	,	,	PUNCT
ejpam-3371	212	10	p∗	p∗	PROPN
ejpam-3371	212	11	)	)	PUNCT
ejpam-3371	212	12	<	<	X
ejpam-3371	212	13	ε	ε	PROPN
ejpam-3371	212	14	w	w	PROPN
ejpam-3371	213	1	+	+	PROPN
ejpam-3371	213	2	1	1	NUM
ejpam-3371	213	3	.	.	PUNCT
ejpam-3371	214	1	hence	hence	ADV
ejpam-3371	214	2	d(xn0+k	d(xn0+k	PROPN
ejpam-3371	214	3	,	,	PUNCT
ejpam-3371	214	4	xn0	xn0	PROPN
ejpam-3371	214	5	)	)	PUNCT
ejpam-3371	215	1	≤	≤	PUNCT
ejpam-3371	216	1	d(xn0+k	d(xn0+k	PROPN
ejpam-3371	216	2	,	,	PUNCT
ejpam-3371	216	3	p∗	p∗	PROPN
ejpam-3371	216	4	)	)	PUNCT
ejpam-3371	217	1	+	+	CCONJ
ejpam-3371	217	2	d(p∗	d(p∗	ADV
ejpam-3371	217	3	,	,	PUNCT
ejpam-3371	217	4	xn0	xn0	PROPN
ejpam-3371	217	5	)	)	PUNCT
ejpam-3371	218	1	≤wd(p∗	≤wd(p∗	PROPN
ejpam-3371	218	2	,	,	PUNCT
ejpam-3371	218	3	xn0	xn0	PUNCT
ejpam-3371	218	4	)	)	PUNCT
ejpam-3371	219	1	+	+	CCONJ
ejpam-3371	219	2	d(p∗	d(p∗	ADV
ejpam-3371	219	3	,	,	PUNCT
ejpam-3371	219	4	xn0	xn0	PROPN
ejpam-3371	219	5	)	)	PUNCT
ejpam-3371	220	1	<	<	X
ejpam-3371	220	2	w	w	PROPN
ejpam-3371	220	3	(	(	PUNCT
ejpam-3371	220	4	ε	ε	PROPN
ejpam-3371	220	5	w	w	PROPN
ejpam-3371	220	6	+	+	PROPN
ejpam-3371	220	7	1	1	NUM
ejpam-3371	220	8	)	)	PUNCT
ejpam-3371	221	1	+	+	CCONJ
ejpam-3371	221	2	ε	ε	PROPN
ejpam-3371	221	3	w	w	PROPN
ejpam-3371	221	4	+	+	PROPN
ejpam-3371	221	5	1	1	NUM
ejpam-3371	221	6	=	=	SYM
ejpam-3371	221	7	ε	ε	PROPN
ejpam-3371	221	8	.	.	PUNCT
ejpam-3371	221	9	references	reference	NOUN
ejpam-3371	221	10	357	357	NUM
ejpam-3371	221	11	this	this	PRON
ejpam-3371	221	12	shows	show	VERB
ejpam-3371	221	13	that	that	SCONJ
ejpam-3371	221	14	{	{	PUNCT
ejpam-3371	221	15	xn	xn	X
ejpam-3371	221	16	}	}	PUNCT
ejpam-3371	221	17	is	be	AUX
ejpam-3371	221	18	cauchy	cauchy	PROPN
ejpam-3371	221	19	in	in	ADP
ejpam-3371	221	20	d.	d.	PROPN
ejpam-3371	221	21	since	since	SCONJ
ejpam-3371	221	22	d	d	PROPN
ejpam-3371	221	23	is	be	AUX
ejpam-3371	221	24	closed	closed	ADJ
ejpam-3371	221	25	,	,	PUNCT
ejpam-3371	221	26	xn	xn	PROPN
ejpam-3371	221	27	converges	converge	VERB
ejpam-3371	221	28	to	to	ADP
ejpam-3371	221	29	some	some	DET
ejpam-3371	221	30	z	z	NOUN
ejpam-3371	221	31	in	in	ADP
ejpam-3371	221	32	d.	d.	PROPN
ejpam-3371	221	33	next	next	ADV
ejpam-3371	221	34	,	,	PUNCT
ejpam-3371	221	35	we	we	PRON
ejpam-3371	221	36	show	show	VERB
ejpam-3371	221	37	that	that	SCONJ
ejpam-3371	221	38	z	z	PROPN
ejpam-3371	221	39	∈	∈	PROPN
ejpam-3371	221	40	f.	f.	PROPN
ejpam-3371	221	41	let	let	VERB
ejpam-3371	221	42	d(z	d(z	PROPN
ejpam-3371	221	43	,	,	PUNCT
ejpam-3371	221	44	xn	xn	PROPN
ejpam-3371	221	45	)	)	PUNCT
ejpam-3371	221	46	<	<	X
ejpam-3371	221	47	ε	ε	PROPN
ejpam-3371	221	48	4(k1	4(k1	PROPN
ejpam-3371	221	49	+	+	PROPN
ejpam-3371	221	50	1	1	NUM
ejpam-3371	221	51	)	)	PUNCT
ejpam-3371	221	52	and	and	CCONJ
ejpam-3371	221	53	let	let	VERB
ejpam-3371	221	54	z∗	z∗	PROPN
ejpam-3371	221	55	∈	∈	PROPN
ejpam-3371	221	56	f.	f.	NOUN
ejpam-3371	221	57	then	then	ADV
ejpam-3371	221	58	d(xn	d(xn	PROPN
ejpam-3371	221	59	,	,	PUNCT
ejpam-3371	221	60	z∗	z∗	NOUN
ejpam-3371	221	61	)	)	PUNCT
ejpam-3371	221	62	<	<	X
ejpam-3371	221	63	ε	ε	PROPN
ejpam-3371	221	64	4(k1	4(k1	PROPN
ejpam-3371	221	65	+	+	PROPN
ejpam-3371	221	66	1	1	NUM
ejpam-3371	221	67	)	)	PUNCT
ejpam-3371	221	68	and	and	CCONJ
ejpam-3371	221	69	d(z∗	d(z∗	NUM
ejpam-3371	221	70	,	,	PUNCT
ejpam-3371	221	71	t	t	PROPN
ejpam-3371	221	72	z	z	PROPN
ejpam-3371	221	73	)	)	PUNCT
ejpam-3371	221	74	<	<	X
ejpam-3371	221	75	ε	ε	PROPN
ejpam-3371	221	76	2(k1	2(k1	PROPN
ejpam-3371	221	77	+	+	PROPN
ejpam-3371	221	78	1	1	NUM
ejpam-3371	221	79	)	)	PUNCT
ejpam-3371	221	80	so	so	SCONJ
ejpam-3371	221	81	that	that	SCONJ
ejpam-3371	221	82	d(z	d(z	PROPN
ejpam-3371	221	83	,	,	PUNCT
ejpam-3371	221	84	z∗	z∗	PROPN
ejpam-3371	221	85	)	)	PUNCT
ejpam-3371	221	86	<	<	X
ejpam-3371	221	87	d(z	d(z	PROPN
ejpam-3371	221	88	,	,	PUNCT
ejpam-3371	221	89	xn	xn	PUNCT
ejpam-3371	221	90	)	)	PUNCT
ejpam-3371	222	1	+	+	CCONJ
ejpam-3371	222	2	d(xn	d(xn	ADJ
ejpam-3371	222	3	,	,	PUNCT
ejpam-3371	222	4	z∗	z∗	NOUN
ejpam-3371	222	5	)	)	PUNCT
ejpam-3371	222	6	<	<	X
ejpam-3371	222	7	ε	ε	PROPN
ejpam-3371	222	8	2(k1	2(k1	PROPN
ejpam-3371	222	9	+	+	CCONJ
ejpam-3371	222	10	1	1	NUM
ejpam-3371	222	11	)	)	PUNCT
ejpam-3371	222	12	.	.	PUNCT
ejpam-3371	223	1	finally	finally	ADV
ejpam-3371	223	2	,	,	PUNCT
ejpam-3371	223	3	d(z	d(z	PROPN
ejpam-3371	223	4	,	,	PUNCT
ejpam-3371	223	5	t1z	t1z	PROPN
ejpam-3371	223	6	)	)	PUNCT
ejpam-3371	223	7	≤	≤	NOUN
ejpam-3371	223	8	d(z	d(z	PROPN
ejpam-3371	223	9	,	,	PUNCT
ejpam-3371	223	10	xn	xn	PUNCT
ejpam-3371	223	11	)	)	PUNCT
ejpam-3371	224	1	+	+	CCONJ
ejpam-3371	224	2	d(xn	d(xn	ADJ
ejpam-3371	224	3	,	,	PUNCT
ejpam-3371	224	4	z∗	z∗	NOUN
ejpam-3371	224	5	)	)	PUNCT
ejpam-3371	224	6	+	+	NUM
ejpam-3371	224	7	d(z∗	d(z∗	NUM
ejpam-3371	224	8	,	,	PUNCT
ejpam-3371	224	9	t1z	t1z	PROPN
ejpam-3371	224	10	)	)	PUNCT
ejpam-3371	224	11	≤	≤	NOUN
ejpam-3371	224	12	d(z	d(z	PROPN
ejpam-3371	224	13	,	,	PUNCT
ejpam-3371	224	14	xn	xn	PUNCT
ejpam-3371	224	15	)	)	PUNCT
ejpam-3371	225	1	+	+	CCONJ
ejpam-3371	225	2	d(xn	d(xn	ADJ
ejpam-3371	225	3	,	,	PUNCT
ejpam-3371	225	4	z∗	z∗	NOUN
ejpam-3371	225	5	)	)	PUNCT
ejpam-3371	225	6	+	+	CCONJ
ejpam-3371	225	7	k1d(z∗	k1d(z∗	PROPN
ejpam-3371	225	8	,	,	PUNCT
ejpam-3371	225	9	z	z	NOUN
ejpam-3371	225	10	)	)	PUNCT
ejpam-3371	225	11	<	<	X
ejpam-3371	225	12	ε	ε	PROPN
ejpam-3371	225	13	4(k1	4(k1	PROPN
ejpam-3371	226	1	+	+	CCONJ
ejpam-3371	226	2	1	1	NUM
ejpam-3371	226	3	)	)	PUNCT
ejpam-3371	227	1	+	+	CCONJ
ejpam-3371	227	2	ε	ε	PROPN
ejpam-3371	227	3	4(k1	4(k1	PROPN
ejpam-3371	228	1	+	+	CCONJ
ejpam-3371	228	2	1	1	NUM
ejpam-3371	228	3	)	)	PUNCT
ejpam-3371	229	1	+	+	CCONJ
ejpam-3371	229	2	ε	ε	PROPN
ejpam-3371	229	3	2(k1	2(k1	PROPN
ejpam-3371	229	4	+	+	CCONJ
ejpam-3371	229	5	1	1	X
ejpam-3371	229	6	)	)	PUNCT
ejpam-3371	229	7	<	<	X
ejpam-3371	229	8	ε	ε	PROPN
ejpam-3371	229	9	.	.	PUNCT
ejpam-3371	230	1	therefore	therefore	ADV
ejpam-3371	230	2	z	z	PROPN
ejpam-3371	230	3	∈	∈	PROPN
ejpam-3371	230	4	t1z	t1z	PROPN
ejpam-3371	230	5	.	.	PUNCT
ejpam-3371	231	1	similarly	similarly	ADV
ejpam-3371	231	2	z	z	PROPN
ejpam-3371	231	3	∈	∈	PROPN
ejpam-3371	231	4	t2z	t2z	NOUN
ejpam-3371	231	5	.	.	PUNCT
ejpam-3371	232	1	hence	hence	ADV
ejpam-3371	232	2	t1	t1	PROPN
ejpam-3371	232	3	and	and	CCONJ
ejpam-3371	232	4	t2	t2	PROPN
ejpam-3371	232	5	have	have	VERB
ejpam-3371	232	6	a	a	DET
ejpam-3371	232	7	common	common	ADJ
ejpam-3371	232	8	fixed	fix	VERB
ejpam-3371	232	9	point	point	NOUN
ejpam-3371	232	10	.	.	PUNCT
ejpam-3371	233	1	references	reference	NOUN
ejpam-3371	233	2	[	[	X
ejpam-3371	233	3	1	1	NUM
ejpam-3371	233	4	]	]	X
ejpam-3371	233	5	k	k	PROPN
ejpam-3371	233	6	goebel	goebel	PROPN
ejpam-3371	233	7	and	and	CCONJ
ejpam-3371	233	8	w	w	ADP
ejpam-3371	233	9	a	a	DET
ejpam-3371	233	10	kirk	kirk	NOUN
ejpam-3371	233	11	.	.	PUNCT
ejpam-3371	234	1	topics	topic	NOUN
ejpam-3371	234	2	in	in	ADP
ejpam-3371	234	3	metric	metric	ADJ
ejpam-3371	234	4	fixed	fix	VERB
ejpam-3371	234	5	point	point	NOUN
ejpam-3371	234	6	theory	theory	NOUN
ejpam-3371	234	7	.	.	PUNCT
ejpam-3371	235	1	cambridge	cambridge	PROPN
ejpam-3371	235	2	university	university	PROPN
ejpam-3371	235	3	press	press	NOUN
ejpam-3371	235	4	,	,	PUNCT
ejpam-3371	235	5	1990	1990	NUM
ejpam-3371	235	6	.	.	PUNCT
ejpam-3371	236	1	[	[	X
ejpam-3371	236	2	2	2	NUM
ejpam-3371	236	3	]	]	X
ejpam-3371	236	4	m	m	VERB
ejpam-3371	236	5	a	a	DET
ejpam-3371	236	6	khamsi	khamsi	NOUN
ejpam-3371	236	7	and	and	CCONJ
ejpam-3371	236	8	a	a	DET
ejpam-3371	236	9	r	r	NOUN
ejpam-3371	236	10	khan	khan	PROPN
ejpam-3371	236	11	.	.	PUNCT
ejpam-3371	237	1	goebel	goebel	PROPN
ejpam-3371	237	2	and	and	CCONJ
ejpam-3371	237	3	kirk	kirk	PROPN
ejpam-3371	237	4	fixed	fix	VERB
ejpam-3371	237	5	point	point	NOUN
ejpam-3371	237	6	theorem	theorem	VERB
ejpam-3371	237	7	for	for	ADP
ejpam-3371	237	8	multivalued	multivalued	ADJ
ejpam-3371	237	9	symptotically	symptotically	ADV
ejpam-3371	237	10	nonexpansive	nonexpansive	ADJ
ejpam-3371	237	11	mappings	mapping	NOUN
ejpam-3371	237	12	.	.	PUNCT
ejpam-3371	238	1	carpathian	carpathian	ADJ
ejpam-3371	238	2	journal	journal	PROPN
ejpam-3371	238	3	of	of	ADP
ejpam-3371	238	4	mathematics	mathematic	NOUN
ejpam-3371	238	5	,	,	PUNCT
ejpam-3371	238	6	33(3):335	33(3):335	NUM
ejpam-3371	238	7	–	–	PUNCT
ejpam-3371	238	8	342	342	NUM
ejpam-3371	238	9	,	,	PUNCT
ejpam-3371	238	10	2017	2017	NUM
ejpam-3371	238	11	.	.	PUNCT
ejpam-3371	239	1	[	[	X
ejpam-3371	239	2	3	3	X
ejpam-3371	239	3	]	]	X
ejpam-3371	239	4	m	m	VERB
ejpam-3371	239	5	a	a	DET
ejpam-3371	239	6	khamsi	khamsi	NOUN
ejpam-3371	239	7	and	and	CCONJ
ejpam-3371	239	8	w	w	ADP
ejpam-3371	239	9	a	a	DET
ejpam-3371	239	10	kirk	kirk	NOUN
ejpam-3371	239	11	.	.	PUNCT
ejpam-3371	240	1	on	on	ADP
ejpam-3371	240	2	uniformly	uniformly	ADV
ejpam-3371	240	3	lipschitzian	lipschitzian	ADJ
ejpam-3371	240	4	multivalued	multivalued	ADJ
ejpam-3371	240	5	mappings	mapping	NOUN
ejpam-3371	240	6	in	in	ADP
ejpam-3371	240	7	banach	banach	NOUN
ejpam-3371	240	8	and	and	CCONJ
ejpam-3371	240	9	metric	metric	ADJ
ejpam-3371	240	10	spaces	space	NOUN
ejpam-3371	240	11	.	.	PUNCT
ejpam-3371	241	1	nonlinear	nonlinear	ADJ
ejpam-3371	241	2	analysis	analysis	NOUN
ejpam-3371	241	3	,	,	PUNCT
ejpam-3371	241	4	72:2080–2085	72:2080–2085	NOUN
ejpam-3371	241	5	,	,	PUNCT
ejpam-3371	241	6	2010	2010	NUM
ejpam-3371	241	7	.	.	PUNCT
ejpam-3371	242	1	[	[	X
ejpam-3371	242	2	4	4	X
ejpam-3371	242	3	]	]	PUNCT
ejpam-3371	242	4	a	a	DET
ejpam-3371	242	5	r	r	NOUN
ejpam-3371	242	6	khan	khan	PROPN
ejpam-3371	242	7	and	and	CCONJ
ejpam-3371	242	8	m	m	PROPN
ejpam-3371	242	9	a	a	DET
ejpam-3371	242	10	a	a	DET
ejpam-3371	242	11	khan	khan	PROPN
ejpam-3371	242	12	.	.	PUNCT
ejpam-3371	243	1	an	an	DET
ejpam-3371	243	2	implicit	implicit	ADJ
ejpam-3371	243	3	algorithm	algorithm	NOUN
ejpam-3371	243	4	for	for	ADP
ejpam-3371	243	5	two	two	NUM
ejpam-3371	243	6	finite	finite	ADJ
ejpam-3371	243	7	families	family	NOUN
ejpam-3371	243	8	of	of	ADP
ejpam-3371	243	9	nonexpansive	nonexpansive	ADJ
ejpam-3371	243	10	maps	map	NOUN
ejpam-3371	243	11	in	in	ADP
ejpam-3371	243	12	hyperbolic	hyperbolic	ADJ
ejpam-3371	243	13	spaces	space	NOUN
ejpam-3371	243	14	.	.	PUNCT
ejpam-3371	244	1	fixed	fix	VERB
ejpam-3371	244	2	point	point	NOUN
ejpam-3371	244	3	theory	theory	NOUN
ejpam-3371	244	4	and	and	CCONJ
ejpam-3371	244	5	applications	application	NOUN
ejpam-3371	244	6	,	,	PUNCT
ejpam-3371	244	7	2012:54	2012:54	NUM
ejpam-3371	244	8	,	,	PUNCT
ejpam-3371	244	9	2012	2012	NUM
ejpam-3371	244	10	.	.	PUNCT
ejpam-3371	245	1	[	[	X
ejpam-3371	245	2	5	5	NUM
ejpam-3371	245	3	]	]	X
ejpam-3371	245	4	k	k	PROPN
ejpam-3371	245	5	menger	menger	PROPN
ejpam-3371	245	6	.	.	PUNCT
ejpam-3371	246	1	untersuchungen	untersuchungen	PROPN
ejpam-3371	246	2	über	über	PROPN
ejpam-3371	246	3	allgemeine	allgemeine	PROPN
ejpam-3371	246	4	metrik	metrik	PROPN
ejpam-3371	246	5	.	.	PUNCT
ejpam-3371	247	1	mathematische	mathematische	PROPN
ejpam-3371	247	2	annalen	annalen	PROPN
ejpam-3371	247	3	,	,	PUNCT
ejpam-3371	247	4	100:75	100:75	NUM
ejpam-3371	247	5	–	–	PUNCT
ejpam-3371	247	6	163	163	NUM
ejpam-3371	247	7	,	,	PUNCT
ejpam-3371	247	8	1928	1928	NUM
ejpam-3371	247	9	.	.	PUNCT
ejpam-3371	248	1	[	[	X
ejpam-3371	248	2	6	6	NUM
ejpam-3371	248	3	]	]	SYM
ejpam-3371	248	4	s	s	PART
ejpam-3371	248	5	reich	reich	PROPN
ejpam-3371	248	6	and	and	CCONJ
ejpam-3371	248	7	i	i	PRON
ejpam-3371	248	8	shafrir	shafrir	PROPN
ejpam-3371	248	9	.	.	PUNCT
ejpam-3371	249	1	nonexpansive	nonexpansive	ADJ
ejpam-3371	249	2	iterations	iteration	NOUN
ejpam-3371	249	3	in	in	ADP
ejpam-3371	249	4	hyperbolic	hyperbolic	ADJ
ejpam-3371	249	5	spaces	space	NOUN
ejpam-3371	249	6	.	.	PUNCT
ejpam-3371	250	1	nonlinear	nonlinear	ADJ
ejpam-3371	250	2	analysis	analysis	NOUN
ejpam-3371	250	3	,	,	PUNCT
ejpam-3371	250	4	15:537–558	15:537–558	NUM
ejpam-3371	250	5	,	,	PUNCT
ejpam-3371	250	6	1990	1990	NUM
ejpam-3371	250	7	.	.	PUNCT
ejpam-3371	251	1	[	[	X
ejpam-3371	251	2	7	7	X
ejpam-3371	251	3	]	]	X
ejpam-3371	251	4	i	i	PRON
ejpam-3371	251	5	a	a	DET
ejpam-3371	251	6	rus	rus	NOUN
ejpam-3371	251	7	.	.	PUNCT
ejpam-3371	251	8	basic	basic	ADJ
ejpam-3371	251	9	problems	problem	NOUN
ejpam-3371	251	10	of	of	ADP
ejpam-3371	251	11	the	the	DET
ejpam-3371	251	12	metric	metric	ADJ
ejpam-3371	251	13	fixed	fix	VERB
ejpam-3371	251	14	point	point	NOUN
ejpam-3371	251	15	theory	theory	NOUN
ejpam-3371	251	16	revisited	revisit	VERB
ejpam-3371	251	17	,	,	PUNCT
ejpam-3371	251	18	ii	ii	PROPN
ejpam-3371	251	19	.	.	PUNCT
ejpam-3371	251	20	studia	studia	PROPN
ejpam-3371	251	21	universitatis	universitatis	PROPN
ejpam-3371	251	22	babe	babe	NOUN
ejpam-3371	251	23	-	-	PUNCT
ejpam-3371	251	24	bolyai	bolyai	NOUN
ejpam-3371	251	25	mathematica	mathematica	PROPN
ejpam-3371	251	26	,	,	PUNCT
ejpam-3371	251	27	36:81–99	36:81–99	NUM
ejpam-3371	251	28	,	,	PUNCT
ejpam-3371	251	29	1991	1991	NUM
ejpam-3371	251	30	.	.	PUNCT