id	sid	tid	token	lemma	pos
ejpam-6154	1	1	european	european	PROPN
ejpam-6154	1	2	journal	journal	PROPN
ejpam-6154	1	3	of	of	ADP
ejpam-6154	1	4	pure	pure	ADJ
ejpam-6154	1	5	and	and	CCONJ
ejpam-6154	1	6	applied	applied	ADJ
ejpam-6154	1	7	mathematics	mathematic	NOUN
ejpam-6154	1	8	2025	2025	NUM
ejpam-6154	1	9	,	,	PUNCT
ejpam-6154	1	10	vol	vol	NOUN
ejpam-6154	1	11	.	.	PROPN
ejpam-6154	1	12	18	18	NUM
ejpam-6154	1	13	,	,	PUNCT
ejpam-6154	1	14	issue	issue	NOUN
ejpam-6154	1	15	4	4	NUM
ejpam-6154	1	16	,	,	PUNCT
ejpam-6154	1	17	article	article	NOUN
ejpam-6154	1	18	number	number	NOUN
ejpam-6154	1	19	6154	6154	NUM
ejpam-6154	1	20	issn	issn	PROPN
ejpam-6154	1	21	1307	1307	NUM
ejpam-6154	1	22	-	-	SYM
ejpam-6154	1	23	5543	5543	NUM
ejpam-6154	1	24	–	–	PUNCT
ejpam-6154	1	25	ejpam.com	ejpam.com	X
ejpam-6154	1	26	published	publish	VERB
ejpam-6154	1	27	by	by	ADP
ejpam-6154	1	28	new	new	PROPN
ejpam-6154	1	29	york	york	PROPN
ejpam-6154	1	30	business	business	PROPN
ejpam-6154	1	31	global	global	ADJ
ejpam-6154	1	32	efficient	efficient	ADJ
ejpam-6154	1	33	viscosity	viscosity	NOUN
ejpam-6154	1	34	algorithms	algorithm	NOUN
ejpam-6154	1	35	for	for	ADP
ejpam-6154	1	36	solving	solve	VERB
ejpam-6154	1	37	the	the	DET
ejpam-6154	1	38	split	split	ADJ
ejpam-6154	1	39	equality	equality	NOUN
ejpam-6154	1	40	fixed	fix	VERB
ejpam-6154	1	41	-	-	PUNCT
ejpam-6154	1	42	point	point	NOUN
ejpam-6154	1	43	problem	problem	NOUN
ejpam-6154	1	44	l.	l.	PROPN
ejpam-6154	1	45	b.	b.	PROPN
ejpam-6154	1	46	mohammed1	mohammed1	PROPN
ejpam-6154	1	47	,	,	PUNCT
ejpam-6154	1	48	a.	a.	PROPN
ejpam-6154	1	49	kılıçman2,∗	kılıçman2,∗	PROPN
ejpam-6154	1	50	,	,	PUNCT
ejpam-6154	1	51	d.	d.	PROPN
ejpam-6154	1	52	bamanga1	bamanga1	PROPN
ejpam-6154	1	53	1	1	NUM
ejpam-6154	1	54	department	department	NOUN
ejpam-6154	1	55	of	of	ADP
ejpam-6154	1	56	mathematics	mathematic	NOUN
ejpam-6154	1	57	,	,	PUNCT
ejpam-6154	1	58	faculty	faculty	NOUN
ejpam-6154	1	59	of	of	ADP
ejpam-6154	1	60	physical	physical	ADJ
ejpam-6154	1	61	sciences	science	NOUN
ejpam-6154	1	62	,	,	PUNCT
ejpam-6154	1	63	federal	federal	ADJ
ejpam-6154	1	64	university	university	NOUN
ejpam-6154	1	65	dutse	dutse	PROPN
ejpam-6154	1	66	,	,	PUNCT
ejpam-6154	1	67	pmb	pmb	PROPN
ejpam-6154	1	68	7156	7156	NUM
ejpam-6154	1	69	,	,	PUNCT
ejpam-6154	1	70	dutse	dutse	PROPN
ejpam-6154	1	71	,	,	PUNCT
ejpam-6154	1	72	jigawa	jigawa	PROPN
ejpam-6154	1	73	state	state	PROPN
ejpam-6154	1	74	,	,	PUNCT
ejpam-6154	1	75	nigeria	nigeria	PROPN
ejpam-6154	1	76	2	2	NUM
ejpam-6154	1	77	faculty	faculty	NOUN
ejpam-6154	1	78	of	of	ADP
ejpam-6154	1	79	computer	computer	NOUN
ejpam-6154	1	80	and	and	CCONJ
ejpam-6154	1	81	mathematical	mathematical	ADJ
ejpam-6154	1	82	sciences	sciences	PROPN
ejpam-6154	1	83	,	,	PUNCT
ejpam-6154	1	84	universiti	universiti	PROPN
ejpam-6154	1	85	teknologi	teknologi	PROPN
ejpam-6154	1	86	mara	mara	PROPN
ejpam-6154	1	87	,	,	PUNCT
ejpam-6154	1	88	40450	40450	NUM
ejpam-6154	1	89	shah	shah	PROPN
ejpam-6154	1	90	alam	alam	PROPN
ejpam-6154	1	91	,	,	PUNCT
ejpam-6154	1	92	selangor	selangor	PROPN
ejpam-6154	1	93	,	,	PUNCT
ejpam-6154	1	94	malaysia	malaysia	PROPN
ejpam-6154	1	95	abstract	abstract	NOUN
ejpam-6154	1	96	.	.	PUNCT
ejpam-6154	2	1	solving	solve	VERB
ejpam-6154	2	2	the	the	DET
ejpam-6154	2	3	split	split	ADJ
ejpam-6154	2	4	equality	equality	NOUN
ejpam-6154	2	5	fixed	fix	VERB
ejpam-6154	2	6	-	-	PUNCT
ejpam-6154	2	7	point	point	NOUN
ejpam-6154	2	8	problem	problem	NOUN
ejpam-6154	2	9	(	(	PUNCT
ejpam-6154	2	10	sefpp	sefpp	NOUN
ejpam-6154	2	11	)	)	PUNCT
ejpam-6154	2	12	often	often	ADV
ejpam-6154	2	13	requires	require	VERB
ejpam-6154	2	14	computing	compute	VERB
ejpam-6154	2	15	the	the	DET
ejpam-6154	2	16	norms	norm	NOUN
ejpam-6154	2	17	of	of	ADP
ejpam-6154	2	18	bounded	bounded	ADJ
ejpam-6154	2	19	and	and	CCONJ
ejpam-6154	2	20	linear	linear	PROPN
ejpam-6154	2	21	operators	operator	NOUN
ejpam-6154	2	22	,	,	PUNCT
ejpam-6154	2	23	a	a	DET
ejpam-6154	2	24	task	task	NOUN
ejpam-6154	2	25	that	that	PRON
ejpam-6154	2	26	can	can	AUX
ejpam-6154	2	27	be	be	AUX
ejpam-6154	2	28	computationally	computationally	ADV
ejpam-6154	2	29	demanding	demanding	ADJ
ejpam-6154	2	30	.	.	PUNCT
ejpam-6154	3	1	to	to	PART
ejpam-6154	3	2	tackle	tackle	VERB
ejpam-6154	3	3	this	this	DET
ejpam-6154	3	4	challenge	challenge	NOUN
ejpam-6154	3	5	,	,	PUNCT
ejpam-6154	3	6	we	we	PRON
ejpam-6154	3	7	investigated	investigate	VERB
ejpam-6154	3	8	the	the	DET
ejpam-6154	3	9	sefpp	sefpp	NOUN
ejpam-6154	3	10	for	for	ADP
ejpam-6154	3	11	quasi	quasi	ADJ
ejpam-6154	3	12	-	-	ADJ
ejpam-6154	3	13	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	3	14	mappings	mapping	NOUN
ejpam-6154	3	15	in	in	ADP
ejpam-6154	3	16	hilbert	hilbert	NOUN
ejpam-6154	3	17	spaces	space	NOUN
ejpam-6154	3	18	and	and	CCONJ
ejpam-6154	3	19	proposed	propose	VERB
ejpam-6154	3	20	innovative	innovative	ADJ
ejpam-6154	3	21	viscosity	viscosity	NOUN
ejpam-6154	3	22	algorithms	algorithm	NOUN
ejpam-6154	3	23	to	to	PART
ejpam-6154	3	24	solve	solve	VERB
ejpam-6154	3	25	the	the	DET
ejpam-6154	3	26	problem	problem	NOUN
ejpam-6154	3	27	.	.	PUNCT
ejpam-6154	4	1	we	we	PRON
ejpam-6154	4	2	established	establish	VERB
ejpam-6154	4	3	the	the	DET
ejpam-6154	4	4	strong	strong	ADJ
ejpam-6154	4	5	convergence	convergence	NOUN
ejpam-6154	4	6	of	of	ADP
ejpam-6154	4	7	these	these	DET
ejpam-6154	4	8	algorithms	algorithm	NOUN
ejpam-6154	4	9	under	under	ADP
ejpam-6154	4	10	appropriate	appropriate	ADJ
ejpam-6154	4	11	conditions	condition	NOUN
ejpam-6154	4	12	.	.	PUNCT
ejpam-6154	5	1	to	to	PART
ejpam-6154	5	2	validate	validate	VERB
ejpam-6154	5	3	our	our	PRON
ejpam-6154	5	4	theoretical	theoretical	ADJ
ejpam-6154	5	5	results	result	NOUN
ejpam-6154	5	6	,	,	PUNCT
ejpam-6154	5	7	we	we	PRON
ejpam-6154	5	8	conducted	conduct	VERB
ejpam-6154	5	9	numerical	numerical	ADJ
ejpam-6154	5	10	experiments	experiment	NOUN
ejpam-6154	5	11	,	,	PUNCT
ejpam-6154	5	12	which	which	PRON
ejpam-6154	5	13	not	not	PART
ejpam-6154	5	14	only	only	ADV
ejpam-6154	5	15	confirmed	confirm	VERB
ejpam-6154	5	16	the	the	DET
ejpam-6154	5	17	efficacy	efficacy	NOUN
ejpam-6154	5	18	of	of	ADP
ejpam-6154	5	19	our	our	PRON
ejpam-6154	5	20	results	result	NOUN
ejpam-6154	5	21	but	but	CCONJ
ejpam-6154	5	22	also	also	ADV
ejpam-6154	5	23	demonstrated	demonstrate	VERB
ejpam-6154	5	24	their	their	PRON
ejpam-6154	5	25	advantages	advantage	NOUN
ejpam-6154	5	26	over	over	ADP
ejpam-6154	5	27	existing	exist	VERB
ejpam-6154	5	28	methods	method	NOUN
ejpam-6154	5	29	in	in	ADP
ejpam-6154	5	30	the	the	DET
ejpam-6154	5	31	literature	literature	NOUN
ejpam-6154	5	32	.	.	PUNCT
ejpam-6154	6	1	our	our	PRON
ejpam-6154	6	2	work	work	NOUN
ejpam-6154	6	3	generalizes	generalize	VERB
ejpam-6154	6	4	and	and	CCONJ
ejpam-6154	6	5	extends	extend	VERB
ejpam-6154	6	6	several	several	ADJ
ejpam-6154	6	7	significant	significant	ADJ
ejpam-6154	6	8	results	result	NOUN
ejpam-6154	6	9	from	from	ADP
ejpam-6154	6	10	prior	prior	ADJ
ejpam-6154	6	11	research	research	NOUN
ejpam-6154	6	12	,	,	PUNCT
ejpam-6154	6	13	contributing	contribute	VERB
ejpam-6154	6	14	to	to	ADP
ejpam-6154	6	15	the	the	DET
ejpam-6154	6	16	broader	broad	ADJ
ejpam-6154	6	17	understanding	understanding	NOUN
ejpam-6154	6	18	of	of	ADP
ejpam-6154	6	19	fixed	fix	VERB
ejpam-6154	6	20	-	-	PUNCT
ejpam-6154	6	21	point	point	NOUN
ejpam-6154	6	22	problems	problem	NOUN
ejpam-6154	6	23	and	and	CCONJ
ejpam-6154	6	24	related	related	ADJ
ejpam-6154	6	25	problems	problem	NOUN
ejpam-6154	6	26	.	.	PUNCT
ejpam-6154	7	1	2020	2020	NUM
ejpam-6154	7	2	mathematics	mathematic	NOUN
ejpam-6154	7	3	subject	subject	NOUN
ejpam-6154	7	4	classifications	classification	NOUN
ejpam-6154	7	5	:	:	PUNCT
ejpam-6154	7	6	47h09	47h09	NUM
ejpam-6154	7	7	,	,	PUNCT
ejpam-6154	7	8	47h10	47h10	NUM
ejpam-6154	7	9	,	,	PUNCT
ejpam-6154	7	10	47j25	47j25	NUM
ejpam-6154	7	11	key	key	ADJ
ejpam-6154	7	12	words	word	NOUN
ejpam-6154	7	13	and	and	CCONJ
ejpam-6154	7	14	phrases	phrase	NOUN
ejpam-6154	7	15	:	:	PUNCT
ejpam-6154	7	16	fixed	fix	VERB
ejpam-6154	7	17	point	point	NOUN
ejpam-6154	7	18	problem	problem	NOUN
ejpam-6154	7	19	,	,	PUNCT
ejpam-6154	7	20	iterative	iterative	NOUN
ejpam-6154	7	21	algorithm	algorithm	NOUN
ejpam-6154	7	22	,	,	PUNCT
ejpam-6154	7	23	nonlinear	nonlinear	ADJ
ejpam-6154	7	24	mappings	mapping	NOUN
ejpam-6154	7	25	,	,	PUNCT
ejpam-6154	7	26	weak	weak	ADJ
ejpam-6154	7	27	and	and	CCONJ
ejpam-6154	7	28	strong	strong	ADJ
ejpam-6154	7	29	convergence	convergence	NOUN
ejpam-6154	7	30	1	1	NUM
ejpam-6154	7	31	.	.	PUNCT
ejpam-6154	7	32	introduction	introduction	NOUN
ejpam-6154	7	33	for	for	ADP
ejpam-6154	7	34	j	j	PROPN
ejpam-6154	7	35	=	=	SYM
ejpam-6154	7	36	1	1	NUM
ejpam-6154	7	37	,	,	PUNCT
ejpam-6154	7	38	2	2	NUM
ejpam-6154	7	39	,	,	PUNCT
ejpam-6154	7	40	let	let	VERB
ejpam-6154	7	41	hj	hj	PART
ejpam-6154	7	42	be	be	AUX
ejpam-6154	7	43	hilbert	hilbert	NOUN
ejpam-6154	7	44	spaces	space	NOUN
ejpam-6154	7	45	,	,	PUNCT
ejpam-6154	7	46	cj	cj	PROPN
ejpam-6154	7	47	be	be	VERB
ejpam-6154	7	48	nonempty	nonempty	X
ejpam-6154	7	49	,	,	PUNCT
ejpam-6154	7	50	closed	closed	ADJ
ejpam-6154	7	51	,	,	PUNCT
ejpam-6154	7	52	and	and	CCONJ
ejpam-6154	7	53	convex	convex	ADJ
ejpam-6154	7	54	subsets	subset	NOUN
ejpam-6154	7	55	of	of	ADP
ejpam-6154	7	56	hj	hj	PROPN
ejpam-6154	7	57	,	,	PUNCT
ejpam-6154	7	58	and	and	CCONJ
ejpam-6154	7	59	aj	aj	PROPN
ejpam-6154	7	60	:	:	PUNCT
ejpam-6154	7	61	h1	h1	PROPN
ejpam-6154	7	62	→	→	SYM
ejpam-6154	7	63	h2	h2	NOUN
ejpam-6154	7	64	be	be	AUX
ejpam-6154	7	65	linear	linear	ADJ
ejpam-6154	7	66	and	and	CCONJ
ejpam-6154	7	67	bounded	bounded	ADJ
ejpam-6154	7	68	mappings	mapping	NOUN
ejpam-6154	7	69	,	,	PUNCT
ejpam-6154	7	70	with	with	ADP
ejpam-6154	7	71	a∗	a∗	PROPN
ejpam-6154	7	72	j	j	PROPN
ejpam-6154	7	73	denoting	denote	VERB
ejpam-6154	7	74	the	the	DET
ejpam-6154	7	75	adjoint	adjoint	NOUN
ejpam-6154	7	76	of	of	ADP
ejpam-6154	7	77	aj	aj	PROPN
ejpam-6154	7	78	.	.	PUNCT
ejpam-6154	8	1	the	the	DET
ejpam-6154	8	2	problem	problem	NOUN
ejpam-6154	8	3	of	of	ADP
ejpam-6154	8	4	finding	find	VERB
ejpam-6154	8	5	z	z	PROPN
ejpam-6154	8	6	∈	∈	PROPN
ejpam-6154	8	7	c1	c1	NOUN
ejpam-6154	8	8	such	such	ADJ
ejpam-6154	8	9	that	that	SCONJ
ejpam-6154	8	10	a1z	a1z	PROPN
ejpam-6154	8	11	∈	∈	PROPN
ejpam-6154	8	12	c2	c2	PROPN
ejpam-6154	8	13	,	,	PUNCT
ejpam-6154	8	14	(	(	PUNCT
ejpam-6154	8	15	1	1	X
ejpam-6154	8	16	)	)	PUNCT
ejpam-6154	8	17	is	be	AUX
ejpam-6154	8	18	known	know	VERB
ejpam-6154	8	19	as	as	ADP
ejpam-6154	8	20	the	the	DET
ejpam-6154	8	21	split	split	NOUN
ejpam-6154	8	22	feasibility	feasibility	NOUN
ejpam-6154	8	23	problem	problem	NOUN
ejpam-6154	8	24	(	(	PUNCT
ejpam-6154	8	25	sfp	sfp	NOUN
ejpam-6154	8	26	)	)	PUNCT
ejpam-6154	8	27	.	.	PUNCT
ejpam-6154	9	1	this	this	DET
ejpam-6154	9	2	problem	problem	NOUN
ejpam-6154	9	3	was	be	AUX
ejpam-6154	9	4	introduced	introduce	VERB
ejpam-6154	9	5	by	by	ADP
ejpam-6154	9	6	censor	censor	NOUN
ejpam-6154	9	7	et	et	PROPN
ejpam-6154	9	8	al	al	PROPN
ejpam-6154	9	9	.	.	PUNCT
ejpam-6154	10	1	[	[	X
ejpam-6154	10	2	1	1	NUM
ejpam-6154	10	3	]	]	PUNCT
ejpam-6154	10	4	.	.	PUNCT
ejpam-6154	11	1	to	to	PART
ejpam-6154	11	2	solve	solve	VERB
ejpam-6154	11	3	problem	problem	NOUN
ejpam-6154	11	4	(	(	PUNCT
ejpam-6154	11	5	1	1	NUM
ejpam-6154	11	6	)	)	PUNCT
ejpam-6154	11	7	,	,	PUNCT
ejpam-6154	11	8	byrne	byrne	PROPN
ejpam-6154	12	1	[	[	X
ejpam-6154	12	2	2	2	NUM
ejpam-6154	12	3	]	]	PUNCT
ejpam-6154	12	4	proposed	propose	VERB
ejpam-6154	12	5	the	the	DET
ejpam-6154	12	6	following	follow	VERB
ejpam-6154	12	7	algorithm	algorithm	NOUN
ejpam-6154	12	8	,	,	PUNCT
ejpam-6154	12	9	known	know	VERB
ejpam-6154	12	10	as	as	ADP
ejpam-6154	12	11	the	the	DET
ejpam-6154	12	12	”	"	PUNCT
ejpam-6154	12	13	cq	cq	NOUN
ejpam-6154	12	14	algorithm	algorithm	NOUN
ejpam-6154	12	15	”	"	PUNCT
ejpam-6154	12	16	:	:	PUNCT
ejpam-6154	12	17	∗corresponding	∗corresponde	VERB
ejpam-6154	12	18	author	author	NOUN
ejpam-6154	12	19	.	.	PUNCT
ejpam-6154	13	1	doi	doi	NOUN
ejpam-6154	13	2	:	:	PUNCT
ejpam-6154	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6154	https://doi.org/10.29020/nybg.ejpam.v18i4.6154	ADJ
ejpam-6154	13	4	email	email	NOUN
ejpam-6154	13	5	addresses	address	NOUN
ejpam-6154	13	6	:	:	PUNCT
ejpam-6154	14	1	lawanbulama@gmail.com	lawanbulama@gmail.com	X
ejpam-6154	14	2	(	(	PUNCT
ejpam-6154	14	3	l.	l.	PROPN
ejpam-6154	14	4	b.	b.	PROPN
ejpam-6154	14	5	mohammed	mohammed	PROPN
ejpam-6154	14	6	)	)	PUNCT
ejpam-6154	14	7	,	,	PUNCT
ejpam-6154	14	8	kilicman@uitm.edu.my	kilicman@uitm.edu.my	X
ejpam-6154	14	9	(	(	PUNCT
ejpam-6154	14	10	a.	a.	NOUN
ejpam-6154	14	11	kılıçman	kılıçman	PROPN
ejpam-6154	14	12	)	)	PUNCT
ejpam-6154	14	13	,	,	PUNCT
ejpam-6154	14	14	abudawud02@gmail.com	abudawud02@gmail.com	PROPN
ejpam-6154	14	15	(	(	PUNCT
ejpam-6154	14	16	d.	d.	PROPN
ejpam-6154	14	17	bamanga	bamanga	PROPN
ejpam-6154	14	18	)	)	PUNCT
ejpam-6154	14	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6154	15	1	1	1	NUM
ejpam-6154	15	2	copyright	copyright	NOUN
ejpam-6154	15	3	:	:	PUNCT
ejpam-6154	15	4	©	©	PROPN
ejpam-6154	15	5	2025	2025	NUM
ejpam-6154	15	6	the	the	DET
ejpam-6154	15	7	author(s	author(s	NOUN
ejpam-6154	15	8	)	)	PUNCT
ejpam-6154	15	9	.	.	PUNCT
ejpam-6154	16	1	(	(	PUNCT
ejpam-6154	16	2	cc	cc	NOUN
ejpam-6154	16	3	by	by	ADP
ejpam-6154	16	4	-	-	PUNCT
ejpam-6154	16	5	nc	nc	PROPN
ejpam-6154	16	6	4.0	4.0	NUM
ejpam-6154	16	7	)	)	PUNCT
ejpam-6154	16	8	l.	l.	PROPN
ejpam-6154	16	9	b.	b.	PROPN
ejpam-6154	16	10	mohammed	mohammed	PROPN
ejpam-6154	16	11	,	,	PUNCT
ejpam-6154	16	12	a.	a.	PROPN
ejpam-6154	16	13	kılıçman	kılıçman	PROPN
ejpam-6154	16	14	,	,	PUNCT
ejpam-6154	16	15	d.	d.	PROPN
ejpam-6154	16	16	bamanga	bamanga	PROPN
ejpam-6154	16	17	/	/	SYM
ejpam-6154	16	18	eur	eur	PROPN
ejpam-6154	16	19	.	.	PUNCT
ejpam-6154	17	1	j.	j.	PROPN
ejpam-6154	17	2	pure	pure	PROPN
ejpam-6154	17	3	appl	appl	PROPN
ejpam-6154	17	4	.	.	PROPN
ejpam-6154	17	5	math	math	PROPN
ejpam-6154	17	6	,	,	PUNCT
ejpam-6154	17	7	18	18	NUM
ejpam-6154	17	8	(	(	PUNCT
ejpam-6154	17	9	4	4	NUM
ejpam-6154	17	10	)	)	PUNCT
ejpam-6154	17	11	(	(	PUNCT
ejpam-6154	17	12	2025	2025	NUM
ejpam-6154	17	13	)	)	PUNCT
ejpam-6154	17	14	,	,	PUNCT
ejpam-6154	17	15	6154	6154	NUM
ejpam-6154	17	16	2	2	NUM
ejpam-6154	17	17	of	of	ADP
ejpam-6154	17	18	18	18	NUM
ejpam-6154	17	19	zn+1	zn+1	PROPN
ejpam-6154	17	20	=	=	SYM
ejpam-6154	17	21	pc1	pc1	PROPN
ejpam-6154	17	22	(	(	PUNCT
ejpam-6154	17	23	i	i	PRON
ejpam-6154	17	24	−	−	PROPN
ejpam-6154	17	25	λa∗	λa∗	X
ejpam-6154	18	1	1(i	1(i	NUM
ejpam-6154	18	2	−	−	PROPN
ejpam-6154	18	3	pc2)a1	pc2)a1	NOUN
ejpam-6154	18	4	)	)	PUNCT
ejpam-6154	18	5	zn	zn	PROPN
ejpam-6154	18	6	,	,	PUNCT
ejpam-6154	18	7	(	(	PUNCT
ejpam-6154	18	8	2	2	X
ejpam-6154	18	9	)	)	PUNCT
ejpam-6154	18	10	where	where	SCONJ
ejpam-6154	18	11	λ	λ	PROPN
ejpam-6154	18	12	∈	∈	PROPN
ejpam-6154	18	13	(	(	PUNCT
ejpam-6154	18	14	0	0	NUM
ejpam-6154	18	15	,	,	PUNCT
ejpam-6154	18	16	2	2	NUM
ejpam-6154	18	17	a1a∗	a1a∗	NOUN
ejpam-6154	18	18	1	1	NUM
ejpam-6154	18	19	)	)	PUNCT
ejpam-6154	18	20	.	.	PUNCT
ejpam-6154	19	1	this	this	DET
ejpam-6154	19	2	algorithm	algorithm	NOUN
ejpam-6154	19	3	requires	require	VERB
ejpam-6154	19	4	the	the	DET
ejpam-6154	19	5	computation	computation	NOUN
ejpam-6154	19	6	of	of	ADP
ejpam-6154	19	7	pcj	pcj	PROPN
ejpam-6154	19	8	onto	onto	ADP
ejpam-6154	19	9	cj	cj	PROPN
ejpam-6154	19	10	,	,	PUNCT
ejpam-6154	19	11	which	which	PRON
ejpam-6154	19	12	is	be	AUX
ejpam-6154	19	13	feasible	feasible	ADJ
ejpam-6154	19	14	when	when	SCONJ
ejpam-6154	19	15	these	these	DET
ejpam-6154	19	16	projections	projection	NOUN
ejpam-6154	19	17	have	have	VERB
ejpam-6154	19	18	closed	close	VERB
ejpam-6154	19	19	-	-	PUNCT
ejpam-6154	19	20	form	form	NOUN
ejpam-6154	19	21	expressions	expression	NOUN
ejpam-6154	19	22	.	.	PUNCT
ejpam-6154	20	1	more	more	ADJ
ejpam-6154	20	2	results	result	NOUN
ejpam-6154	20	3	on	on	ADP
ejpam-6154	20	4	the	the	DET
ejpam-6154	20	5	sfp	sfp	NOUN
ejpam-6154	20	6	and	and	CCONJ
ejpam-6154	20	7	its	its	PRON
ejpam-6154	20	8	applications	application	NOUN
ejpam-6154	20	9	can	can	AUX
ejpam-6154	20	10	be	be	AUX
ejpam-6154	20	11	found	find	VERB
ejpam-6154	20	12	in	in	ADP
ejpam-6154	20	13	[	[	X
ejpam-6154	20	14	3–7	3–7	NOUN
ejpam-6154	20	15	]	]	PUNCT
ejpam-6154	20	16	.	.	PUNCT
ejpam-6154	21	1	the	the	DET
ejpam-6154	21	2	split	split	ADJ
ejpam-6154	21	3	equality	equality	NOUN
ejpam-6154	21	4	problem	problem	NOUN
ejpam-6154	21	5	(	(	PUNCT
ejpam-6154	21	6	sep	sep	PROPN
ejpam-6154	21	7	)	)	PUNCT
ejpam-6154	21	8	,	,	PUNCT
ejpam-6154	21	9	which	which	PRON
ejpam-6154	21	10	is	be	AUX
ejpam-6154	21	11	related	relate	VERB
ejpam-6154	21	12	to	to	ADP
ejpam-6154	21	13	the	the	DET
ejpam-6154	21	14	sfp	sfp	NOUN
ejpam-6154	21	15	,	,	PUNCT
ejpam-6154	21	16	was	be	AUX
ejpam-6154	21	17	introduced	introduce	VERB
ejpam-6154	21	18	by	by	ADP
ejpam-6154	21	19	moudafi	moudafi	PROPN
ejpam-6154	21	20	and	and	CCONJ
ejpam-6154	21	21	al	al	PROPN
ejpam-6154	21	22	-	-	PUNCT
ejpam-6154	21	23	shemas	shemas	PROPN
ejpam-6154	22	1	[	[	X
ejpam-6154	22	2	8	8	NUM
ejpam-6154	22	3	]	]	PUNCT
ejpam-6154	22	4	.	.	PUNCT
ejpam-6154	23	1	the	the	DET
ejpam-6154	23	2	sep	sep	NOUN
ejpam-6154	23	3	involves	involve	VERB
ejpam-6154	23	4	finding	find	VERB
ejpam-6154	23	5	y	y	PROPN
ejpam-6154	23	6	∈	∈	PROPN
ejpam-6154	23	7	c1	c1	PROPN
ejpam-6154	23	8	and	and	CCONJ
ejpam-6154	23	9	z	z	PROPN
ejpam-6154	23	10	∈	∈	PROPN
ejpam-6154	23	11	c2	c2	PROPN
ejpam-6154	23	12	such	such	ADJ
ejpam-6154	23	13	that	that	SCONJ
ejpam-6154	23	14	a1y	a1y	PROPN
ejpam-6154	23	15	=	=	PUNCT
ejpam-6154	23	16	a2z	a2z	PROPN
ejpam-6154	23	17	.	.	PUNCT
ejpam-6154	24	1	(	(	PUNCT
ejpam-6154	24	2	3	3	X
ejpam-6154	24	3	)	)	PUNCT
ejpam-6154	24	4	by	by	ADP
ejpam-6154	24	5	setting	set	VERB
ejpam-6154	24	6	a2	a2	PROPN
ejpam-6154	24	7	=	=	PUNCT
ejpam-6154	25	1	i	i	NOUN
ejpam-6154	25	2	(	(	PUNCT
ejpam-6154	25	3	identity	identity	NOUN
ejpam-6154	25	4	mapping	mapping	NOUN
ejpam-6154	25	5	)	)	PUNCT
ejpam-6154	25	6	,	,	PUNCT
ejpam-6154	25	7	the	the	DET
ejpam-6154	25	8	sep	sep	NOUN
ejpam-6154	25	9	reduces	reduce	VERB
ejpam-6154	25	10	to	to	ADP
ejpam-6154	25	11	the	the	DET
ejpam-6154	25	12	sfp	sfp	NOUN
ejpam-6154	25	13	.	.	PUNCT
ejpam-6154	26	1	to	to	PART
ejpam-6154	26	2	solve	solve	VERB
ejpam-6154	26	3	problem	problem	NOUN
ejpam-6154	26	4	(	(	PUNCT
ejpam-6154	26	5	3	3	NUM
ejpam-6154	26	6	)	)	PUNCT
ejpam-6154	26	7	,	,	PUNCT
ejpam-6154	26	8	moudafi	moudafi	PROPN
ejpam-6154	26	9	and	and	CCONJ
ejpam-6154	26	10	al	al	PROPN
ejpam-6154	26	11	-	-	PUNCT
ejpam-6154	26	12	shemas	shemas	PROPN
ejpam-6154	27	1	[	[	X
ejpam-6154	27	2	8	8	NUM
ejpam-6154	27	3	]	]	PUNCT
ejpam-6154	27	4	proposed	propose	VERB
ejpam-6154	27	5	the	the	DET
ejpam-6154	27	6	following	follow	VERB
ejpam-6154	27	7	algorithm	algorithm	NOUN
ejpam-6154	27	8	:	:	PUNCT
ejpam-6154	27	9	{	{	PUNCT
ejpam-6154	27	10	yn+1	yn+1	PROPN
ejpam-6154	27	11	=	=	SYM
ejpam-6154	27	12	pc2	pc2	PROPN
ejpam-6154	27	13	(	(	PUNCT
ejpam-6154	27	14	yn	yn	PROPN
ejpam-6154	27	15	+	+	NUM
ejpam-6154	27	16	λna∗	λna∗	PROPN
ejpam-6154	27	17	2(a1yn	2(a1yn	PROPN
ejpam-6154	27	18	−a2zn	−a2zn	NUM
ejpam-6154	27	19	)	)	PUNCT
ejpam-6154	27	20	)	)	PUNCT
ejpam-6154	27	21	;	;	PUNCT
ejpam-6154	27	22	zn+1	zn+1	X
ejpam-6154	27	23	=	=	SYM
ejpam-6154	27	24	pc1	pc1	PROPN
ejpam-6154	27	25	(	(	PUNCT
ejpam-6154	27	26	zn	zn	PROPN
ejpam-6154	27	27	−	−	PROPN
ejpam-6154	28	1	λna∗	λna∗	PROPN
ejpam-6154	29	1	1(a1yn	1(a1yn	PROPN
ejpam-6154	30	1	−a2zn	−a2zn	NUM
ejpam-6154	30	2	)	)	PUNCT
ejpam-6154	30	3	)	)	PUNCT
ejpam-6154	30	4	,	,	PUNCT
ejpam-6154	31	1	n	n	X
ejpam-6154	31	2	≥	≥	NOUN
ejpam-6154	31	3	0	0	NUM
ejpam-6154	31	4	;	;	PUNCT
ejpam-6154	31	5	(	(	PUNCT
ejpam-6154	31	6	4	4	X
ejpam-6154	31	7	)	)	PUNCT
ejpam-6154	31	8	where	where	SCONJ
ejpam-6154	31	9	(	(	PUNCT
ejpam-6154	31	10	y0	y0	NOUN
ejpam-6154	31	11	,	,	PUNCT
ejpam-6154	31	12	z0	z0	PROPN
ejpam-6154	31	13	)	)	PUNCT
ejpam-6154	31	14	∈	∈	PROPN
ejpam-6154	31	15	h1	h1	PROPN
ejpam-6154	31	16	×h2	×h2	NOUN
ejpam-6154	31	17	are	be	AUX
ejpam-6154	31	18	chosen	choose	VERB
ejpam-6154	31	19	arbitrarily	arbitrarily	ADV
ejpam-6154	31	20	,	,	PUNCT
ejpam-6154	31	21	and	and	CCONJ
ejpam-6154	31	22	pcj	pcj	PROPN
ejpam-6154	31	23	,	,	PUNCT
ejpam-6154	31	24	are	be	AUX
ejpam-6154	31	25	metric	metric	ADJ
ejpam-6154	31	26	projections	projection	NOUN
ejpam-6154	31	27	onto	onto	ADP
ejpam-6154	31	28	cj	cj	NOUN
ejpam-6154	31	29	.	.	PUNCT
ejpam-6154	32	1	under	under	ADP
ejpam-6154	32	2	certain	certain	ADJ
ejpam-6154	32	3	conditions	condition	NOUN
ejpam-6154	32	4	imposed	impose	VERB
ejpam-6154	32	5	on	on	ADP
ejpam-6154	32	6	{	{	PUNCT
ejpam-6154	32	7	λn	λn	NOUN
ejpam-6154	32	8	}	}	PUNCT
ejpam-6154	32	9	,	,	PUNCT
ejpam-6154	32	10	a	a	DET
ejpam-6154	32	11	weak	weak	ADJ
ejpam-6154	32	12	convergence	convergence	NOUN
ejpam-6154	32	13	result	result	NOUN
ejpam-6154	32	14	was	be	AUX
ejpam-6154	32	15	obtained	obtain	VERB
ejpam-6154	32	16	.	.	PUNCT
ejpam-6154	33	1	since	since	SCONJ
ejpam-6154	33	2	any	any	DET
ejpam-6154	33	3	nonempty	nonempty	ADJ
ejpam-6154	33	4	,	,	PUNCT
ejpam-6154	33	5	closed	closed	ADJ
ejpam-6154	33	6	,	,	PUNCT
ejpam-6154	33	7	and	and	CCONJ
ejpam-6154	33	8	convex	convex	PROPN
ejpam-6154	33	9	subset	subset	NOUN
ejpam-6154	33	10	of	of	ADP
ejpam-6154	33	11	a	a	DET
ejpam-6154	33	12	hilbert	hilbert	NOUN
ejpam-6154	33	13	space	space	NOUN
ejpam-6154	33	14	can	can	AUX
ejpam-6154	33	15	be	be	AUX
ejpam-6154	33	16	represented	represent	VERB
ejpam-6154	33	17	as	as	ADP
ejpam-6154	33	18	the	the	DET
ejpam-6154	33	19	fixed	fix	VERB
ejpam-6154	33	20	point	point	NOUN
ejpam-6154	33	21	set	set	NOUN
ejpam-6154	33	22	of	of	ADP
ejpam-6154	33	23	its	its	PRON
ejpam-6154	33	24	corresponding	corresponding	ADJ
ejpam-6154	33	25	projector	projector	NOUN
ejpam-6154	33	26	,	,	PUNCT
ejpam-6154	33	27	see	see	VERB
ejpam-6154	33	28	[	[	X
ejpam-6154	33	29	7	7	NUM
ejpam-6154	33	30	]	]	PUNCT
ejpam-6154	33	31	,	,	PUNCT
ejpam-6154	33	32	therefore	therefore	ADV
ejpam-6154	33	33	,	,	PUNCT
ejpam-6154	33	34	equation	equation	NOUN
ejpam-6154	33	35	(	(	PUNCT
ejpam-6154	33	36	3	3	X
ejpam-6154	33	37	)	)	PUNCT
ejpam-6154	33	38	can	can	AUX
ejpam-6154	33	39	be	be	AUX
ejpam-6154	33	40	simplified	simplify	VERB
ejpam-6154	33	41	to	to	ADP
ejpam-6154	33	42	finding	find	VERB
ejpam-6154	33	43	y	y	PROPN
ejpam-6154	33	44	∈	∈	PROPN
ejpam-6154	33	45	fix(t1	fix(t1	X
ejpam-6154	33	46	)	)	PUNCT
ejpam-6154	33	47	and	and	CCONJ
ejpam-6154	33	48	z	z	NOUN
ejpam-6154	33	49	∈	∈	PROPN
ejpam-6154	33	50	fix(t2	fix(t2	NOUN
ejpam-6154	33	51	)	)	PUNCT
ejpam-6154	34	1	such	such	ADJ
ejpam-6154	34	2	that	that	SCONJ
ejpam-6154	34	3	a1y	a1y	PROPN
ejpam-6154	34	4	=	=	PUNCT
ejpam-6154	34	5	a2z	a2z	PROPN
ejpam-6154	34	6	,	,	PUNCT
ejpam-6154	34	7	(	(	PUNCT
ejpam-6154	34	8	5	5	NUM
ejpam-6154	34	9	)	)	PUNCT
ejpam-6154	34	10	where	where	SCONJ
ejpam-6154	34	11	tj	tj	NOUN
ejpam-6154	34	12	:	:	PUNCT
ejpam-6154	34	13	hj	hj	PROPN
ejpam-6154	34	14	→	→	SYM
ejpam-6154	34	15	hj	hj	PROPN
ejpam-6154	34	16	,	,	PUNCT
ejpam-6154	34	17	j	j	PROPN
ejpam-6154	34	18	=	=	SYM
ejpam-6154	34	19	1	1	NUM
ejpam-6154	34	20	,	,	PUNCT
ejpam-6154	34	21	2	2	NUM
ejpam-6154	34	22	,	,	PUNCT
ejpam-6154	34	23	are	be	AUX
ejpam-6154	34	24	nonlinear	nonlinear	ADJ
ejpam-6154	34	25	operators	operator	NOUN
ejpam-6154	34	26	with	with	ADP
ejpam-6154	34	27	fix(tj	fix(tj	NOUN
ejpam-6154	34	28	)	)	PUNCT
ejpam-6154	34	29	̸=	̸=	PROPN
ejpam-6154	34	30	∅.	∅.	PRON
ejpam-6154	34	31	problem	problem	NOUN
ejpam-6154	34	32	(	(	PUNCT
ejpam-6154	34	33	5	5	NUM
ejpam-6154	34	34	)	)	PUNCT
ejpam-6154	34	35	is	be	AUX
ejpam-6154	34	36	known	know	VERB
ejpam-6154	34	37	as	as	ADP
ejpam-6154	34	38	the	the	DET
ejpam-6154	34	39	split	split	ADJ
ejpam-6154	34	40	equality	equality	NOUN
ejpam-6154	34	41	fixed	fix	VERB
ejpam-6154	34	42	point	point	NOUN
ejpam-6154	34	43	problem	problem	NOUN
ejpam-6154	34	44	(	(	PUNCT
ejpam-6154	34	45	sefpp	sefpp	NOUN
ejpam-6154	34	46	)	)	PUNCT
ejpam-6154	34	47	.	.	PUNCT
ejpam-6154	35	1	motivated	motivate	VERB
ejpam-6154	35	2	by	by	ADP
ejpam-6154	35	3	the	the	DET
ejpam-6154	35	4	results	result	NOUN
ejpam-6154	35	5	in	in	ADP
ejpam-6154	35	6	[	[	X
ejpam-6154	35	7	8	8	NUM
ejpam-6154	35	8	]	]	PUNCT
ejpam-6154	35	9	,	,	PUNCT
ejpam-6154	35	10	moudafi	moudafi	PROPN
ejpam-6154	36	1	[	[	X
ejpam-6154	36	2	5	5	NUM
ejpam-6154	36	3	]	]	PUNCT
ejpam-6154	36	4	proposed	propose	VERB
ejpam-6154	36	5	the	the	DET
ejpam-6154	36	6	following	follow	VERB
ejpam-6154	36	7	algorithm	algorithm	NOUN
ejpam-6154	36	8	:	:	PUNCT
ejpam-6154	36	9	{	{	PUNCT
ejpam-6154	36	10	yn+1	yn+1	PROPN
ejpam-6154	36	11	=	=	PROPN
ejpam-6154	36	12	t2	t2	PROPN
ejpam-6154	36	13	(	(	PUNCT
ejpam-6154	36	14	yn	yn	PROPN
ejpam-6154	36	15	+	+	CCONJ
ejpam-6154	36	16	λna∗	λna∗	PROPN
ejpam-6154	36	17	2(a1yn	2(a1yn	PROPN
ejpam-6154	36	18	−a2zn	−a2zn	NUM
ejpam-6154	36	19	)	)	PUNCT
ejpam-6154	36	20	)	)	PUNCT
ejpam-6154	36	21	;	;	PUNCT
ejpam-6154	37	1	zn+1	zn+1	X
ejpam-6154	37	2	=	=	SYM
ejpam-6154	37	3	t1	t1	PROPN
ejpam-6154	37	4	(	(	PUNCT
ejpam-6154	37	5	zn	zn	PROPN
ejpam-6154	37	6	−	−	PROPN
ejpam-6154	38	1	λna∗	λna∗	PROPN
ejpam-6154	38	2	1(a1yn	1(a1yn	PROPN
ejpam-6154	38	3	−a2zn	−a2zn	NUM
ejpam-6154	38	4	)	)	PUNCT
ejpam-6154	38	5	)	)	PUNCT
ejpam-6154	38	6	,	,	PUNCT
ejpam-6154	38	7	n	n	X
ejpam-6154	38	8	≥	≥	NOUN
ejpam-6154	38	9	0	0	NUM
ejpam-6154	38	10	.	.	PUNCT
ejpam-6154	39	1	(	(	PUNCT
ejpam-6154	39	2	6	6	NUM
ejpam-6154	39	3	)	)	PUNCT
ejpam-6154	39	4	by	by	ADP
ejpam-6154	39	5	imposing	impose	VERB
ejpam-6154	39	6	certain	certain	ADJ
ejpam-6154	39	7	conditions	condition	NOUN
ejpam-6154	39	8	on	on	ADP
ejpam-6154	39	9	the	the	DET
ejpam-6154	39	10	parameters	parameter	NOUN
ejpam-6154	39	11	and	and	CCONJ
ejpam-6154	39	12	operators	operator	NOUN
ejpam-6154	39	13	involved	involve	VERB
ejpam-6154	39	14	,	,	PUNCT
ejpam-6154	39	15	a	a	DET
ejpam-6154	39	16	weak	weak	ADJ
ejpam-6154	39	17	convergence	convergence	NOUN
ejpam-6154	39	18	result	result	NOUN
ejpam-6154	39	19	for	for	ADP
ejpam-6154	39	20	algorithm	algorithm	NOUN
ejpam-6154	39	21	(	(	PUNCT
ejpam-6154	39	22	6	6	NUM
ejpam-6154	39	23	)	)	PUNCT
ejpam-6154	39	24	was	be	AUX
ejpam-6154	39	25	obtained	obtain	VERB
ejpam-6154	39	26	.	.	PUNCT
ejpam-6154	40	1	however	however	ADV
ejpam-6154	40	2	,	,	PUNCT
ejpam-6154	40	3	implementing	implement	VERB
ejpam-6154	40	4	this	this	DET
ejpam-6154	40	5	algorithm	algorithm	NOUN
ejpam-6154	40	6	requires	require	VERB
ejpam-6154	40	7	computing	compute	VERB
ejpam-6154	40	8	the	the	DET
ejpam-6154	40	9	inverse	inverse	NOUN
ejpam-6154	40	10	of	of	ADP
ejpam-6154	40	11	a	a	DET
ejpam-6154	40	12	bounded	bounded	ADJ
ejpam-6154	40	13	linear	linear	ADJ
ejpam-6154	40	14	operator	operator	NOUN
ejpam-6154	40	15	,	,	PUNCT
ejpam-6154	40	16	which	which	PRON
ejpam-6154	40	17	is	be	AUX
ejpam-6154	40	18	generally	generally	ADV
ejpam-6154	40	19	a	a	DET
ejpam-6154	40	20	difficult	difficult	ADJ
ejpam-6154	40	21	task	task	NOUN
ejpam-6154	40	22	.	.	PUNCT
ejpam-6154	41	1	to	to	PART
ejpam-6154	41	2	address	address	VERB
ejpam-6154	41	3	this	this	DET
ejpam-6154	41	4	challenge	challenge	NOUN
ejpam-6154	41	5	,	,	PUNCT
ejpam-6154	41	6	byrne	byrne	ADJ
ejpam-6154	42	1	[	[	X
ejpam-6154	42	2	2	2	NUM
ejpam-6154	42	3	]	]	PUNCT
ejpam-6154	42	4	introduced	introduce	VERB
ejpam-6154	42	5	an	an	DET
ejpam-6154	42	6	alternative	alternative	ADJ
ejpam-6154	42	7	algorithm	algorithm	NOUN
ejpam-6154	42	8	for	for	ADP
ejpam-6154	42	9	solving	solve	VERB
ejpam-6154	42	10	the	the	DET
ejpam-6154	42	11	sfp	sfp	NOUN
ejpam-6154	42	12	that	that	PRON
ejpam-6154	42	13	eliminates	eliminate	VERB
ejpam-6154	42	14	the	the	DET
ejpam-6154	42	15	need	need	NOUN
ejpam-6154	42	16	for	for	ADP
ejpam-6154	42	17	such	such	DET
ejpam-6154	42	18	an	an	DET
ejpam-6154	42	19	inverse	inverse	NOUN
ejpam-6154	42	20	.	.	PUNCT
ejpam-6154	43	1	moudafi	moudafi	PROPN
ejpam-6154	43	2	’s	’s	PART
ejpam-6154	43	3	algorithm	algorithm	NOUN
ejpam-6154	43	4	in	in	ADP
ejpam-6154	43	5	[	[	X
ejpam-6154	43	6	5	5	NUM
ejpam-6154	43	7	]	]	PUNCT
ejpam-6154	43	8	involved	involve	VERB
ejpam-6154	43	9	firmly	firmly	ADV
ejpam-6154	43	10	quasi	quasi	ADJ
ejpam-6154	43	11	-	-	ADJ
ejpam-6154	43	12	nonexpansive	nonexpansive	ADJ
ejpam-6154	43	13	mapping	mapping	NOUN
ejpam-6154	43	14	,	,	PUNCT
ejpam-6154	43	15	a	a	DET
ejpam-6154	43	16	class	class	NOUN
ejpam-6154	43	17	that	that	PRON
ejpam-6154	43	18	includes	include	VERB
ejpam-6154	43	19	quasi	quasi	ADJ
ejpam-6154	43	20	-	-	ADJ
ejpam-6154	43	21	nonexpansive	nonexpansive	ADJ
ejpam-6154	43	22	mapping	mapping	NOUN
ejpam-6154	43	23	.	.	PUNCT
ejpam-6154	44	1	since	since	SCONJ
ejpam-6154	44	2	quasi	quasi	ADJ
ejpam-6154	44	3	-	-	ADJ
ejpam-6154	44	4	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	44	5	mapping	mapping	NOUN
ejpam-6154	44	6	includes	include	VERB
ejpam-6154	44	7	firmly	firmly	ADV
ejpam-6154	44	8	quasi	quasi	ADJ
ejpam-6154	44	9	-	-	ADJ
ejpam-6154	44	10	nonexpansive	nonexpansive	ADJ
ejpam-6154	44	11	,	,	PUNCT
ejpam-6154	44	12	directed	direct	VERB
ejpam-6154	44	13	,	,	PUNCT
ejpam-6154	44	14	and	and	CCONJ
ejpam-6154	44	15	demicontractive	demicontractive	ADJ
ejpam-6154	44	16	mappings	mapping	NOUN
ejpam-6154	44	17	,	,	PUNCT
ejpam-6154	44	18	this	this	DET
ejpam-6154	44	19	motivated	motivated	ADJ
ejpam-6154	44	20	chang	chang	PROPN
ejpam-6154	44	21	et	et	PROPN
ejpam-6154	44	22	al	al	PROPN
ejpam-6154	44	23	.	.	PROPN
ejpam-6154	44	24	,	,	PUNCT
ejpam-6154	45	1	[	[	X
ejpam-6154	45	2	9	9	NUM
ejpam-6154	45	3	]	]	PUNCT
ejpam-6154	45	4	to	to	PART
ejpam-6154	45	5	introduce	introduce	VERB
ejpam-6154	45	6	the	the	DET
ejpam-6154	45	7	following	follow	VERB
ejpam-6154	45	8	algorithm	algorithm	NOUN
ejpam-6154	45	9	for	for	ADP
ejpam-6154	45	10	solving	solve	VERB
ejpam-6154	45	11	the	the	DET
ejpam-6154	45	12	sefpp	sefpp	NOUN
ejpam-6154	45	13	involving	involve	VERB
ejpam-6154	45	14	quasipseudocontractive	quasipseudocontractive	ADJ
ejpam-6154	45	15	mappings	mapping	NOUN
ejpam-6154	45	16	and	and	CCONJ
ejpam-6154	45	17	proved	prove	VERB
ejpam-6154	45	18	the	the	DET
ejpam-6154	45	19	weak	weak	ADJ
ejpam-6154	45	20	convergence	convergence	NOUN
ejpam-6154	45	21	result	result	NOUN
ejpam-6154	45	22	of	of	ADP
ejpam-6154	45	23	the	the	DET
ejpam-6154	45	24	algorithm:	algorithm:	PROPN
ejpam-6154	45	25	yn+1	yn+1	PROPN
ejpam-6154	45	26	=	=	NOUN
ejpam-6154	45	27	βnyn	βnyn	PROPN
ejpam-6154	45	28	+	+	CCONJ
ejpam-6154	45	29	(	(	PUNCT
ejpam-6154	45	30	1−	1−	NUM
ejpam-6154	45	31	βn	βn	NOUN
ejpam-6154	45	32	)	)	PUNCT
ejpam-6154	45	33	(	(	PUNCT
ejpam-6154	45	34	(	(	PUNCT
ejpam-6154	45	35	1−	1−	NUM
ejpam-6154	45	36	η)i	η)i	NOUN
ejpam-6154	45	37	+	+	CCONJ
ejpam-6154	45	38	ηt1((1−	ηt1((1−	ADJ
ejpam-6154	45	39	ζ)i	ζ)i	NOUN
ejpam-6154	45	40	+	+	CCONJ
ejpam-6154	45	41	ζt2	ζt2	NOUN
ejpam-6154	45	42	)	)	PUNCT
ejpam-6154	45	43	)	)	PUNCT
ejpam-6154	46	1	vn	vn	PROPN
ejpam-6154	46	2	;	;	PUNCT
ejpam-6154	46	3	vn	vn	PROPN
ejpam-6154	46	4	=	=	SYM
ejpam-6154	46	5	yn	yn	PROPN
ejpam-6154	47	1	+	+	CCONJ
ejpam-6154	47	2	λna∗	λna∗	PROPN
ejpam-6154	47	3	2(a1yn	2(a1yn	PROPN
ejpam-6154	47	4	−a2zn	−a2zn	NUM
ejpam-6154	47	5	)	)	PUNCT
ejpam-6154	47	6	;	;	PUNCT
ejpam-6154	47	7	zn+1	zn+1	X
ejpam-6154	47	8	=	=	SYM
ejpam-6154	47	9	βnzn	βnzn	NOUN
ejpam-6154	47	10	+	+	CCONJ
ejpam-6154	47	11	(	(	PUNCT
ejpam-6154	47	12	1−	1−	NUM
ejpam-6154	47	13	βn	βn	NOUN
ejpam-6154	47	14	)	)	PUNCT
ejpam-6154	47	15	(	(	PUNCT
ejpam-6154	47	16	(	(	PUNCT
ejpam-6154	47	17	1−	1−	NUM
ejpam-6154	47	18	η)i	η)i	NOUN
ejpam-6154	47	19	+	+	CCONJ
ejpam-6154	47	20	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	47	21	ζ)i	ζ)i	NOUN
ejpam-6154	47	22	+	+	CCONJ
ejpam-6154	47	23	ζt1	ζt1	PROPN
ejpam-6154	47	24	)	)	PUNCT
ejpam-6154	47	25	)	)	PUNCT
ejpam-6154	48	1	un	un	PROPN
ejpam-6154	48	2	;	;	PUNCT
ejpam-6154	48	3	un	un	PROPN
ejpam-6154	48	4	=	=	PROPN
ejpam-6154	48	5	zn	zn	PROPN
ejpam-6154	48	6	−	−	NUM
ejpam-6154	49	1	λna∗	λna∗	PROPN
ejpam-6154	49	2	1(a1yn	1(a1yn	PROPN
ejpam-6154	49	3	−a2zn	−a2zn	NUM
ejpam-6154	49	4	)	)	PUNCT
ejpam-6154	49	5	,	,	PUNCT
ejpam-6154	49	6	n	n	X
ejpam-6154	49	7	≥	≥	NOUN
ejpam-6154	49	8	0	0	NUM
ejpam-6154	49	9	.	.	PUNCT
ejpam-6154	50	1	(	(	PUNCT
ejpam-6154	50	2	7	7	X
ejpam-6154	50	3	)	)	PUNCT
ejpam-6154	50	4	l.	l.	PROPN
ejpam-6154	50	5	b.	b.	PROPN
ejpam-6154	50	6	mohammed	mohammed	PROPN
ejpam-6154	50	7	,	,	PUNCT
ejpam-6154	50	8	a.	a.	PROPN
ejpam-6154	50	9	kılıçman	kılıçman	PROPN
ejpam-6154	50	10	,	,	PUNCT
ejpam-6154	50	11	d.	d.	PROPN
ejpam-6154	50	12	bamanga	bamanga	PROPN
ejpam-6154	50	13	/	/	SYM
ejpam-6154	50	14	eur	eur	PROPN
ejpam-6154	50	15	.	.	PUNCT
ejpam-6154	51	1	j.	j.	PROPN
ejpam-6154	51	2	pure	pure	PROPN
ejpam-6154	51	3	appl	appl	PROPN
ejpam-6154	51	4	.	.	PROPN
ejpam-6154	51	5	math	math	PROPN
ejpam-6154	51	6	,	,	PUNCT
ejpam-6154	51	7	18	18	NUM
ejpam-6154	51	8	(	(	PUNCT
ejpam-6154	51	9	4	4	NUM
ejpam-6154	51	10	)	)	PUNCT
ejpam-6154	51	11	(	(	PUNCT
ejpam-6154	51	12	2025	2025	NUM
ejpam-6154	51	13	)	)	PUNCT
ejpam-6154	51	14	,	,	PUNCT
ejpam-6154	51	15	6154	6154	NUM
ejpam-6154	51	16	3	3	NUM
ejpam-6154	51	17	of	of	ADP
ejpam-6154	51	18	18	18	NUM
ejpam-6154	51	19	this	this	DET
ejpam-6154	51	20	algorithm	algorithm	NOUN
ejpam-6154	51	21	relies	rely	VERB
ejpam-6154	51	22	on	on	ADP
ejpam-6154	51	23	prior	prior	ADJ
ejpam-6154	51	24	knowledge	knowledge	NOUN
ejpam-6154	51	25	of	of	ADP
ejpam-6154	51	26	operator	operator	NOUN
ejpam-6154	51	27	norms	norm	NOUN
ejpam-6154	51	28	.	.	PUNCT
ejpam-6154	52	1	recently	recently	ADV
ejpam-6154	52	2	,	,	PUNCT
ejpam-6154	52	3	mohammed	mohammed	PROPN
ejpam-6154	52	4	and	and	CCONJ
ejpam-6154	52	5	kilicman	kilicman	NOUN
ejpam-6154	52	6	[	[	X
ejpam-6154	52	7	10	10	NUM
ejpam-6154	52	8	]	]	PUNCT
ejpam-6154	52	9	investigated	investigate	VERB
ejpam-6154	52	10	the	the	DET
ejpam-6154	52	11	sefpp	sefpp	NOUN
ejpam-6154	52	12	involving	involve	VERB
ejpam-6154	52	13	quasi	quasi	ADJ
ejpam-6154	52	14	-	-	ADJ
ejpam-6154	52	15	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	52	16	mappings	mapping	NOUN
ejpam-6154	52	17	in	in	ADP
ejpam-6154	52	18	hilbert	hilbert	PROPN
ejpam-6154	52	19	spaces	space	NOUN
ejpam-6154	52	20	.	.	PUNCT
ejpam-6154	53	1	they	they	PRON
ejpam-6154	53	2	developed	develop	VERB
ejpam-6154	53	3	innovative	innovative	ADJ
ejpam-6154	53	4	algorithms	algorithm	NOUN
ejpam-6154	53	5	and	and	CCONJ
ejpam-6154	53	6	demonstrated	demonstrate	VERB
ejpam-6154	53	7	their	their	PRON
ejpam-6154	53	8	convergences	convergence	NOUN
ejpam-6154	53	9	,	,	PUNCT
ejpam-6154	53	10	both	both	CCONJ
ejpam-6154	53	11	with	with	ADP
ejpam-6154	53	12	and	and	CCONJ
ejpam-6154	53	13	without	without	ADP
ejpam-6154	53	14	prior	prior	ADJ
ejpam-6154	53	15	knowledge	knowledge	NOUN
ejpam-6154	53	16	of	of	ADP
ejpam-6154	53	17	the	the	DET
ejpam-6154	53	18	operator	operator	NOUN
ejpam-6154	53	19	norm	norm	NOUN
ejpam-6154	53	20	for	for	ADP
ejpam-6154	53	21	bounded	bounded	ADJ
ejpam-6154	53	22	and	and	CCONJ
ejpam-6154	53	23	linear	linear	ADJ
ejpam-6154	53	24	mappings	mapping	NOUN
ejpam-6154	53	25	.	.	PUNCT
ejpam-6154	54	1	recently	recently	ADV
ejpam-6154	54	2	,	,	PUNCT
ejpam-6154	54	3	wang	wang	PROPN
ejpam-6154	54	4	et	et	PROPN
ejpam-6154	54	5	al	al	PROPN
ejpam-6154	54	6	.	.	PROPN
ejpam-6154	54	7	,	,	PUNCT
ejpam-6154	55	1	[	[	X
ejpam-6154	55	2	11	11	NUM
ejpam-6154	55	3	]	]	PUNCT
ejpam-6154	55	4	,	,	PUNCT
ejpam-6154	55	5	studied	study	VERB
ejpam-6154	55	6	the	the	DET
ejpam-6154	55	7	sefpp	sefpp	NOUN
ejpam-6154	55	8	for	for	ADP
ejpam-6154	55	9	the	the	DET
ejpam-6154	55	10	class	class	NOUN
ejpam-6154	55	11	of	of	ADP
ejpam-6154	55	12	demicontractive	demicontractive	ADJ
ejpam-6154	55	13	operators	operator	NOUN
ejpam-6154	55	14	in	in	ADP
ejpam-6154	55	15	hilbert	hilbert	PROPN
ejpam-6154	55	16	spaces	space	NOUN
ejpam-6154	55	17	and	and	CCONJ
ejpam-6154	55	18	proved	prove	VERB
ejpam-6154	55	19	the	the	DET
ejpam-6154	55	20	strong	strong	ADJ
ejpam-6154	55	21	convergence	convergence	NOUN
ejpam-6154	55	22	results	result	NOUN
ejpam-6154	55	23	by	by	ADP
ejpam-6154	55	24	proposing	propose	VERB
ejpam-6154	55	25	the	the	DET
ejpam-6154	55	26	following	follow	VERB
ejpam-6154	55	27	algorithm	algorithm	NOUN
ejpam-6154	55	28	:	:	PUNCT
ejpam-6154	55	29			NOUN
ejpam-6154	55	30	yn+1	yn+1	X
ejpam-6154	56	1	=	=	PUNCT
ejpam-6154	56	2	βng1(yn	βng1(yn	PROPN
ejpam-6154	56	3	)	)	PUNCT
ejpam-6154	57	1	+	+	CCONJ
ejpam-6154	57	2	(	(	PUNCT
ejpam-6154	57	3	1−	1−	NUM
ejpam-6154	57	4	βn)vn	βn)vn	NUM
ejpam-6154	57	5	,	,	PUNCT
ejpam-6154	57	6	vn	vn	PROPN
ejpam-6154	57	7	=	=	PROPN
ejpam-6154	57	8	yn	yn	PROPN
ejpam-6154	58	1	−	−	PROPN
ejpam-6154	58	2	λn	λn	PROPN
ejpam-6154	58	3	(	(	PUNCT
ejpam-6154	58	4	yn	yn	PROPN
ejpam-6154	58	5	−	−	PROPN
ejpam-6154	58	6	t1yn	t1yn	PUNCT
ejpam-6154	59	1	+	+	ADJ
ejpam-6154	59	2	a∗	a∗	ADJ
ejpam-6154	59	3	1	1	NUM
ejpam-6154	59	4	(	(	PUNCT
ejpam-6154	59	5	a1yn	a1yn	X
ejpam-6154	59	6	−a2zn	−a2zn	NUM
ejpam-6154	59	7	)	)	PUNCT
ejpam-6154	59	8	)	)	PUNCT
ejpam-6154	59	9	,	,	PUNCT
ejpam-6154	59	10	zn+1	zn+1	PROPN
ejpam-6154	59	11	=	=	SYM
ejpam-6154	59	12	βng2(yn	βng2(yn	PROPN
ejpam-6154	59	13	)	)	PUNCT
ejpam-6154	60	1	+	+	CCONJ
ejpam-6154	60	2	(	(	PUNCT
ejpam-6154	60	3	1−	1−	NUM
ejpam-6154	60	4	βn)wn	βn)wn	PROPN
ejpam-6154	60	5	,	,	PUNCT
ejpam-6154	60	6	wn	wn	PROPN
ejpam-6154	60	7	=	=	SYM
ejpam-6154	60	8	zn	zn	PROPN
ejpam-6154	60	9	−	−	PROPN
ejpam-6154	61	1	λn	λn	PROPN
ejpam-6154	61	2	(	(	PUNCT
ejpam-6154	61	3	zn	zn	PROPN
ejpam-6154	61	4	−	−	PROPN
ejpam-6154	61	5	t2zn	t2zn	PROPN
ejpam-6154	62	1	+	+	NUM
ejpam-6154	62	2	λna∗	λna∗	NOUN
ejpam-6154	62	3	2	2	NUM
ejpam-6154	62	4	(	(	PUNCT
ejpam-6154	62	5	a2zn	a2zn	ADP
ejpam-6154	62	6	−a1yn	−a1yn	NUM
ejpam-6154	62	7	)	)	PUNCT
ejpam-6154	62	8	)	)	PUNCT
ejpam-6154	62	9	,	,	PUNCT
ejpam-6154	62	10	n	n	X
ejpam-6154	62	11	≥	≥	NOUN
ejpam-6154	62	12	0	0	NUM
ejpam-6154	62	13	.	.	PUNCT
ejpam-6154	63	1	(	(	PUNCT
ejpam-6154	63	2	8)	8)	NUM
ejpam-6154	63	3	the	the	DET
ejpam-6154	63	4	results	result	NOUN
ejpam-6154	63	5	from	from	ADP
ejpam-6154	63	6	chang	chang	PROPN
ejpam-6154	63	7	et	et	PROPN
ejpam-6154	63	8	al	al	PROPN
ejpam-6154	63	9	.	.	PUNCT
ejpam-6154	64	1	[	[	X
ejpam-6154	64	2	9	9	NUM
ejpam-6154	64	3	]	]	PUNCT
ejpam-6154	64	4	and	and	CCONJ
ejpam-6154	64	5	mohammed	mohammed	PROPN
ejpam-6154	64	6	and	and	CCONJ
ejpam-6154	64	7	kilicman	kilicman	NOUN
ejpam-6154	64	8	[	[	X
ejpam-6154	64	9	10	10	NUM
ejpam-6154	64	10	]	]	PUNCT
ejpam-6154	64	11	,	,	PUNCT
ejpam-6154	64	12	on	on	ADP
ejpam-6154	64	13	the	the	DET
ejpam-6154	64	14	other	other	ADJ
ejpam-6154	64	15	hand	hand	NOUN
ejpam-6154	64	16	,	,	PUNCT
ejpam-6154	64	17	only	only	ADV
ejpam-6154	64	18	show	show	VERB
ejpam-6154	64	19	strong	strong	ADJ
ejpam-6154	64	20	convergence	convergence	NOUN
ejpam-6154	64	21	if	if	SCONJ
ejpam-6154	64	22	the	the	DET
ejpam-6154	64	23	operators	operator	NOUN
ejpam-6154	64	24	are	be	AUX
ejpam-6154	64	25	thought	think	VERB
ejpam-6154	64	26	to	to	PART
ejpam-6154	64	27	be	be	AUX
ejpam-6154	64	28	semi	semi	ADJ
ejpam-6154	64	29	-	-	ADJ
ejpam-6154	64	30	compact	compact	ADJ
ejpam-6154	64	31	.	.	PUNCT
ejpam-6154	65	1	this	this	DET
ejpam-6154	65	2	compactness	compactness	NOUN
ejpam-6154	65	3	condition	condition	NOUN
ejpam-6154	65	4	can	can	AUX
ejpam-6154	65	5	be	be	AUX
ejpam-6154	65	6	limiting	limit	VERB
ejpam-6154	65	7	,	,	PUNCT
ejpam-6154	65	8	as	as	SCONJ
ejpam-6154	65	9	many	many	ADJ
ejpam-6154	65	10	nonlinear	nonlinear	ADJ
ejpam-6154	65	11	mappings	mapping	NOUN
ejpam-6154	65	12	do	do	AUX
ejpam-6154	65	13	not	not	PART
ejpam-6154	65	14	satisfy	satisfy	VERB
ejpam-6154	65	15	the	the	DET
ejpam-6154	65	16	compactness	compactness	NOUN
ejpam-6154	65	17	condition	condition	NOUN
ejpam-6154	65	18	(	(	PUNCT
ejpam-6154	65	19	see	see	VERB
ejpam-6154	65	20	example	example	NOUN
ejpam-6154	65	21	1	1	NUM
ejpam-6154	65	22	for	for	ADP
ejpam-6154	65	23	more	more	ADJ
ejpam-6154	65	24	details	detail	NOUN
ejpam-6154	65	25	)	)	PUNCT
ejpam-6154	65	26	.	.	PUNCT
ejpam-6154	66	1	consequently	consequently	ADV
ejpam-6154	66	2	,	,	PUNCT
ejpam-6154	66	3	it	it	PRON
ejpam-6154	66	4	was	be	AUX
ejpam-6154	66	5	proposed	propose	VERB
ejpam-6154	66	6	that	that	SCONJ
ejpam-6154	66	7	future	future	ADJ
ejpam-6154	66	8	studies	study	NOUN
ejpam-6154	66	9	could	could	AUX
ejpam-6154	66	10	be	be	AUX
ejpam-6154	66	11	focused	focus	VERB
ejpam-6154	66	12	on	on	ADP
ejpam-6154	66	13	establishing	establish	VERB
ejpam-6154	66	14	strong	strong	ADJ
ejpam-6154	66	15	convergent	convergent	NOUN
ejpam-6154	66	16	results	result	NOUN
ejpam-6154	66	17	without	without	ADP
ejpam-6154	66	18	relying	rely	VERB
ejpam-6154	66	19	on	on	ADP
ejpam-6154	66	20	the	the	DET
ejpam-6154	66	21	compactness	compactness	NOUN
ejpam-6154	66	22	assumption	assumption	NOUN
ejpam-6154	66	23	.	.	PUNCT
ejpam-6154	67	1	in	in	ADP
ejpam-6154	67	2	this	this	DET
ejpam-6154	67	3	paper	paper	NOUN
ejpam-6154	67	4	,	,	PUNCT
ejpam-6154	67	5	we	we	PRON
ejpam-6154	67	6	aimed	aim	VERB
ejpam-6154	67	7	to	to	PART
ejpam-6154	67	8	obtain	obtain	VERB
ejpam-6154	67	9	the	the	DET
ejpam-6154	67	10	strong	strong	ADJ
ejpam-6154	67	11	convergence	convergence	NOUN
ejpam-6154	67	12	result	result	NOUN
ejpam-6154	67	13	of	of	ADP
ejpam-6154	67	14	the	the	DET
ejpam-6154	67	15	proposed	propose	VERB
ejpam-6154	67	16	algorithm	algorithm	NOUN
ejpam-6154	67	17	without	without	ADP
ejpam-6154	67	18	imposing	impose	VERB
ejpam-6154	67	19	the	the	DET
ejpam-6154	67	20	semi	semi	ADJ
ejpam-6154	67	21	-	-	ADJ
ejpam-6154	67	22	compactness	compactness	ADJ
ejpam-6154	67	23	condition	condition	NOUN
ejpam-6154	67	24	on	on	ADP
ejpam-6154	67	25	the	the	DET
ejpam-6154	67	26	operators	operator	NOUN
ejpam-6154	67	27	involved	involve	VERB
ejpam-6154	67	28	,	,	PUNCT
ejpam-6154	67	29	which	which	PRON
ejpam-6154	67	30	is	be	AUX
ejpam-6154	67	31	a	a	DET
ejpam-6154	67	32	critical	critical	ADJ
ejpam-6154	67	33	consideration	consideration	NOUN
ejpam-6154	67	34	in	in	ADP
ejpam-6154	67	35	infinite	infinite	ADJ
ejpam-6154	67	36	-	-	PUNCT
ejpam-6154	67	37	dimensional	dimensional	ADJ
ejpam-6154	67	38	spaces	space	NOUN
ejpam-6154	67	39	.	.	PUNCT
ejpam-6154	68	1	the	the	DET
ejpam-6154	68	2	paper	paper	NOUN
ejpam-6154	68	3	is	be	AUX
ejpam-6154	68	4	organized	organize	VERB
ejpam-6154	68	5	as	as	SCONJ
ejpam-6154	68	6	follows	follow	VERB
ejpam-6154	68	7	:	:	PUNCT
ejpam-6154	68	8	the	the	DET
ejpam-6154	68	9	introduction	introduction	NOUN
ejpam-6154	68	10	offers	offer	VERB
ejpam-6154	68	11	an	an	DET
ejpam-6154	68	12	overview	overview	NOUN
ejpam-6154	68	13	of	of	ADP
ejpam-6154	68	14	the	the	DET
ejpam-6154	68	15	study	study	NOUN
ejpam-6154	68	16	’s	’s	PART
ejpam-6154	68	17	background	background	NOUN
ejpam-6154	68	18	and	and	CCONJ
ejpam-6154	68	19	context	context	NOUN
ejpam-6154	68	20	.	.	PUNCT
ejpam-6154	69	1	this	this	PRON
ejpam-6154	69	2	is	be	AUX
ejpam-6154	69	3	followed	follow	VERB
ejpam-6154	69	4	by	by	ADP
ejpam-6154	69	5	the	the	DET
ejpam-6154	69	6	preliminary	preliminary	ADJ
ejpam-6154	69	7	section	section	NOUN
ejpam-6154	69	8	,	,	PUNCT
ejpam-6154	69	9	where	where	SCONJ
ejpam-6154	69	10	key	key	ADJ
ejpam-6154	69	11	definitions	definition	NOUN
ejpam-6154	69	12	and	and	CCONJ
ejpam-6154	69	13	lemmas	lemma	NOUN
ejpam-6154	69	14	are	be	AUX
ejpam-6154	69	15	introduced	introduce	VERB
ejpam-6154	69	16	.	.	PUNCT
ejpam-6154	70	1	section	section	NOUN
ejpam-6154	70	2	3	3	NUM
ejpam-6154	70	3	presents	present	VERB
ejpam-6154	70	4	the	the	DET
ejpam-6154	70	5	main	main	ADJ
ejpam-6154	70	6	results	result	NOUN
ejpam-6154	70	7	of	of	ADP
ejpam-6154	70	8	the	the	DET
ejpam-6154	70	9	research	research	NOUN
ejpam-6154	70	10	,	,	PUNCT
ejpam-6154	70	11	and	and	CCONJ
ejpam-6154	70	12	section	section	NOUN
ejpam-6154	70	13	4	4	NUM
ejpam-6154	70	14	discusses	discuss	VERB
ejpam-6154	70	15	the	the	DET
ejpam-6154	70	16	numerical	numerical	ADJ
ejpam-6154	70	17	results	result	NOUN
ejpam-6154	70	18	.	.	PUNCT
ejpam-6154	71	1	2	2	X
ejpam-6154	71	2	.	.	X
ejpam-6154	71	3	preliminaries	preliminary	NOUN
ejpam-6154	71	4	this	this	DET
ejpam-6154	71	5	section	section	NOUN
ejpam-6154	71	6	offers	offer	VERB
ejpam-6154	71	7	a	a	DET
ejpam-6154	71	8	few	few	ADJ
ejpam-6154	71	9	fundamental	fundamental	ADJ
ejpam-6154	71	10	findings	finding	NOUN
ejpam-6154	71	11	that	that	PRON
ejpam-6154	71	12	support	support	VERB
ejpam-6154	71	13	the	the	DET
ejpam-6154	71	14	paper	paper	NOUN
ejpam-6154	71	15	’s	’s	PART
ejpam-6154	71	16	primary	primary	ADJ
ejpam-6154	71	17	findings	finding	NOUN
ejpam-6154	71	18	.	.	PUNCT
ejpam-6154	72	1	definition	definition	NOUN
ejpam-6154	72	2	1	1	NUM
ejpam-6154	72	3	.	.	PUNCT
ejpam-6154	73	1	a	a	DET
ejpam-6154	73	2	mapping	mapping	NOUN
ejpam-6154	73	3	t1	t1	NOUN
ejpam-6154	73	4	:	:	PUNCT
ejpam-6154	73	5	h1	h1	PROPN
ejpam-6154	73	6	→	→	PUNCT
ejpam-6154	73	7	h1	h1	PROPN
ejpam-6154	73	8	is	be	AUX
ejpam-6154	73	9	said	say	VERB
ejpam-6154	73	10	to	to	PART
ejpam-6154	73	11	be	be	AUX
ejpam-6154	73	12	;	;	PUNCT
ejpam-6154	73	13	(	(	PUNCT
ejpam-6154	73	14	i	i	NOUN
ejpam-6154	73	15	)	)	PUNCT
ejpam-6154	73	16	fixed	fix	VERB
ejpam-6154	73	17	point	point	NOUN
ejpam-6154	73	18	of	of	ADP
ejpam-6154	73	19	t1	t1	PROPN
ejpam-6154	73	20	(	(	PUNCT
ejpam-6154	73	21	fix(t1	fix(t1	PROPN
ejpam-6154	73	22	)	)	PUNCT
ejpam-6154	73	23	)	)	PUNCT
ejpam-6154	74	1	if	if	SCONJ
ejpam-6154	74	2	t1z	t1z	PROPN
ejpam-6154	74	3	=	=	SYM
ejpam-6154	74	4	z	z	NOUN
ejpam-6154	74	5	,	,	PUNCT
ejpam-6154	74	6	for	for	ADP
ejpam-6154	74	7	all	all	DET
ejpam-6154	74	8	z	z	NOUN
ejpam-6154	74	9	∈	∈	PROPN
ejpam-6154	74	10	h1	h1	NOUN
ejpam-6154	74	11	,	,	PUNCT
ejpam-6154	74	12	and	and	CCONJ
ejpam-6154	74	13	we	we	PRON
ejpam-6154	74	14	denote	denote	VERB
ejpam-6154	74	15	the	the	DET
ejpam-6154	74	16	set	set	NOUN
ejpam-6154	74	17	of	of	ADP
ejpam-6154	74	18	fix(t1	fix(t1	NOUN
ejpam-6154	74	19	)	)	PUNCT
ejpam-6154	74	20	by	by	ADP
ejpam-6154	74	21	{	{	PUNCT
ejpam-6154	74	22	z	z	PROPN
ejpam-6154	74	23	∈	∈	PROPN
ejpam-6154	74	24	fix(t1	fix(t1	NOUN
ejpam-6154	74	25	)	)	PUNCT
ejpam-6154	74	26	:	:	PUNCT
ejpam-6154	75	1	t1z	t1z	PROPN
ejpam-6154	75	2	=	=	PUNCT
ejpam-6154	76	1	z	z	X
ejpam-6154	76	2	}	}	PUNCT
ejpam-6154	76	3	.	.	PUNCT
ejpam-6154	77	1	(	(	PUNCT
ejpam-6154	77	2	ii	ii	NOUN
ejpam-6154	77	3	)	)	PUNCT
ejpam-6154	77	4	nonexpansive	nonexpansive	ADJ
ejpam-6154	77	5	if	if	SCONJ
ejpam-6154	77	6	∥t1y	∥t1y	PROPN
ejpam-6154	77	7	−	−	PROPN
ejpam-6154	77	8	t1z∥	t1z∥	CCONJ
ejpam-6154	78	1	≤	≤	NUM
ejpam-6154	78	2	∥y	∥y	PROPN
ejpam-6154	78	3	−	−	PROPN
ejpam-6154	78	4	z∥,∀y	z∥,∀y	NUM
ejpam-6154	78	5	,	,	PUNCT
ejpam-6154	78	6	z	z	PROPN
ejpam-6154	78	7	∈	∈	PROPN
ejpam-6154	78	8	h1	h1	PROPN
ejpam-6154	78	9	.	.	PUNCT
ejpam-6154	79	1	(	(	PUNCT
ejpam-6154	79	2	iii	iii	X
ejpam-6154	79	3	)	)	PUNCT
ejpam-6154	79	4	quasi	quasi	ADJ
ejpam-6154	79	5	-	-	ADJ
ejpam-6154	79	6	nonexpansive	nonexpansive	ADJ
ejpam-6154	79	7	if	if	SCONJ
ejpam-6154	79	8	∥t1y	∥t1y	PROPN
ejpam-6154	79	9	−	−	PROPN
ejpam-6154	79	10	z∥	z∥	CCONJ
ejpam-6154	79	11	≤	≤	NOUN
ejpam-6154	79	12	∥y	∥y	PROPN
ejpam-6154	79	13	−	−	PROPN
ejpam-6154	79	14	z∥,∀y	z∥,∀y	PROPN
ejpam-6154	79	15	∈	∈	PROPN
ejpam-6154	79	16	h1	h1	PROPN
ejpam-6154	79	17	and	and	CCONJ
ejpam-6154	79	18	z	z	NOUN
ejpam-6154	79	19	∈	∈	PROPN
ejpam-6154	79	20	fix(t1	fix(t1	NOUN
ejpam-6154	79	21	)	)	PUNCT
ejpam-6154	79	22	.	.	PUNCT
ejpam-6154	80	1	(	(	PUNCT
ejpam-6154	80	2	iv	iv	X
ejpam-6154	80	3	)	)	PUNCT
ejpam-6154	80	4	directed	direct	VERB
ejpam-6154	80	5	if	if	SCONJ
ejpam-6154	80	6	∥t1y	∥t1y	PROPN
ejpam-6154	80	7	−	−	PROPN
ejpam-6154	80	8	z∥2	z∥2	VERB
ejpam-6154	80	9	≤	≤	NUM
ejpam-6154	80	10	∥y	∥y	PROPN
ejpam-6154	80	11	−	−	NOUN
ejpam-6154	80	12	z∥2	z∥2	NOUN
ejpam-6154	80	13	−	−	PROPN
ejpam-6154	80	14	∥t1y	∥t1y	PROPN
ejpam-6154	80	15	−	−	PROPN
ejpam-6154	80	16	y∥2,∀y	y∥2,∀y	NOUN
ejpam-6154	80	17	∈	∈	PROPN
ejpam-6154	80	18	h1	h1	PROPN
ejpam-6154	80	19	and	and	CCONJ
ejpam-6154	80	20	z	z	NOUN
ejpam-6154	80	21	∈	∈	PROPN
ejpam-6154	80	22	fix(t1	fix(t1	NOUN
ejpam-6154	80	23	)	)	PUNCT
ejpam-6154	80	24	.	.	PUNCT
ejpam-6154	81	1	(	(	PUNCT
ejpam-6154	81	2	v	v	X
ejpam-6154	81	3	)	)	PUNCT
ejpam-6154	81	4	demicontractive	demicontractive	ADJ
ejpam-6154	81	5	if	if	SCONJ
ejpam-6154	81	6	∥z	∥z	PROPN
ejpam-6154	81	7	−	−	PROPN
ejpam-6154	81	8	t1y∥2	t1y∥2	NOUN
ejpam-6154	81	9	≤	≤	NUM
ejpam-6154	81	10	∥z	∥z	PROPN
ejpam-6154	81	11	−	−	PROPN
ejpam-6154	81	12	y∥2	y∥2	NOUN
ejpam-6154	82	1	+	+	CCONJ
ejpam-6154	82	2	k∥y	k∥y	ADP
ejpam-6154	82	3	−	−	PROPN
ejpam-6154	82	4	t1y∥2	t1y∥2	NOUN
ejpam-6154	82	5	,	,	PUNCT
ejpam-6154	82	6	∀y	∀y	PROPN
ejpam-6154	82	7	∈	∈	PROPN
ejpam-6154	82	8	h1	h1	PROPN
ejpam-6154	82	9	,	,	PUNCT
ejpam-6154	82	10	z	z	PROPN
ejpam-6154	82	11	∈	∈	PROPN
ejpam-6154	82	12	fix(t1	fix(t1	NOUN
ejpam-6154	82	13	)	)	PUNCT
ejpam-6154	82	14	and	and	CCONJ
ejpam-6154	82	15	k	k	PROPN
ejpam-6154	82	16	∈	∈	PROPN
ejpam-6154	83	1	[	[	X
ejpam-6154	83	2	0	0	NUM
ejpam-6154	83	3	,	,	PUNCT
ejpam-6154	83	4	1	1	NUM
ejpam-6154	83	5	)	)	PUNCT
ejpam-6154	83	6	,	,	PUNCT
ejpam-6154	83	7	and	and	CCONJ
ejpam-6154	83	8	it	it	PRON
ejpam-6154	83	9	is	be	AUX
ejpam-6154	83	10	called	call	VERB
ejpam-6154	83	11	a	a	DET
ejpam-6154	83	12	quasi	quasi	NOUN
ejpam-6154	83	13	-	-	ADJ
ejpam-6154	83	14	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	83	15	if	if	SCONJ
ejpam-6154	83	16	k	k	PROPN
ejpam-6154	83	17	=	=	SYM
ejpam-6154	83	18	1	1	X
ejpam-6154	83	19	.	.	PUNCT
ejpam-6154	83	20	l.	l.	PROPN
ejpam-6154	83	21	b.	b.	PROPN
ejpam-6154	83	22	mohammed	mohammed	PROPN
ejpam-6154	83	23	,	,	PUNCT
ejpam-6154	83	24	a.	a.	PROPN
ejpam-6154	83	25	kılıçman	kılıçman	PROPN
ejpam-6154	83	26	,	,	PUNCT
ejpam-6154	83	27	d.	d.	PROPN
ejpam-6154	83	28	bamanga	bamanga	PROPN
ejpam-6154	83	29	/	/	SYM
ejpam-6154	83	30	eur	eur	PROPN
ejpam-6154	83	31	.	.	PUNCT
ejpam-6154	84	1	j.	j.	PROPN
ejpam-6154	84	2	pure	pure	PROPN
ejpam-6154	84	3	appl	appl	PROPN
ejpam-6154	84	4	.	.	PROPN
ejpam-6154	84	5	math	math	PROPN
ejpam-6154	84	6	,	,	PUNCT
ejpam-6154	84	7	18	18	NUM
ejpam-6154	84	8	(	(	PUNCT
ejpam-6154	84	9	4	4	NUM
ejpam-6154	84	10	)	)	PUNCT
ejpam-6154	84	11	(	(	PUNCT
ejpam-6154	84	12	2025	2025	NUM
ejpam-6154	84	13	)	)	PUNCT
ejpam-6154	84	14	,	,	PUNCT
ejpam-6154	84	15	6154	6154	NUM
ejpam-6154	84	16	4	4	NUM
ejpam-6154	84	17	of	of	ADP
ejpam-6154	84	18	18	18	NUM
ejpam-6154	84	19	(	(	PUNCT
ejpam-6154	84	20	vi	vi	NOUN
ejpam-6154	84	21	)	)	PUNCT
ejpam-6154	84	22	semi	semi	ADJ
ejpam-6154	84	23	-	-	ADJ
ejpam-6154	84	24	compact	compact	ADJ
ejpam-6154	84	25	if	if	SCONJ
ejpam-6154	84	26	for	for	ADP
ejpam-6154	84	27	any	any	DET
ejpam-6154	84	28	bounded	bounded	ADJ
ejpam-6154	84	29	sequence	sequence	NOUN
ejpam-6154	84	30	{	{	PUNCT
ejpam-6154	84	31	zn	zn	NOUN
ejpam-6154	84	32	}	}	PUNCT
ejpam-6154	84	33	⊆	⊆	NUM
ejpam-6154	84	34	h1	h1	NOUN
ejpam-6154	84	35	with	with	ADP
ejpam-6154	84	36	∥zn	∥zn	NUM
ejpam-6154	84	37	−	−	PROPN
ejpam-6154	84	38	t1zn∥	t1zn∥	NOUN
ejpam-6154	84	39	→	→	SYM
ejpam-6154	84	40	0	0	NUM
ejpam-6154	84	41	,	,	PUNCT
ejpam-6154	84	42	then	then	ADV
ejpam-6154	84	43	there	there	PRON
ejpam-6154	84	44	exist	exist	VERB
ejpam-6154	84	45	{	{	PUNCT
ejpam-6154	84	46	zni	zni	NOUN
ejpam-6154	84	47	}	}	PUNCT
ejpam-6154	84	48	⊆	⊆	NUM
ejpam-6154	84	49	{	{	PUNCT
ejpam-6154	84	50	zn	zn	NOUN
ejpam-6154	84	51	}	}	PUNCT
ejpam-6154	84	52	such	such	ADJ
ejpam-6154	84	53	that	that	SCONJ
ejpam-6154	84	54	zni	zni	NOUN
ejpam-6154	84	55	→	→	SYM
ejpam-6154	84	56	z	z	NOUN
ejpam-6154	84	57	∈	∈	PROPN
ejpam-6154	84	58	h1	h1	PROPN
ejpam-6154	84	59	.	.	PUNCT
ejpam-6154	84	60	remark	remark	PROPN
ejpam-6154	84	61	1	1	NUM
ejpam-6154	84	62	.	.	PUNCT
ejpam-6154	85	1	from	from	ADP
ejpam-6154	85	2	the	the	DET
ejpam-6154	85	3	definitions	definition	NOUN
ejpam-6154	85	4	provided	provide	VERB
ejpam-6154	85	5	above	above	ADV
ejpam-6154	85	6	,	,	PUNCT
ejpam-6154	85	7	we	we	PRON
ejpam-6154	85	8	observe	observe	VERB
ejpam-6154	85	9	that	that	SCONJ
ejpam-6154	85	10	the	the	DET
ejpam-6154	85	11	class	class	NOUN
ejpam-6154	85	12	of	of	ADP
ejpam-6154	85	13	quasi	quasi	ADJ
ejpam-6154	85	14	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	85	15	mapping	mapping	NOUN
ejpam-6154	85	16	is	be	AUX
ejpam-6154	85	17	fundamental	fundamental	ADJ
ejpam-6154	85	18	.	.	PUNCT
ejpam-6154	86	1	this	this	DET
ejpam-6154	86	2	class	class	NOUN
ejpam-6154	86	3	encompasses	encompass	VERB
ejpam-6154	86	4	various	various	ADJ
ejpam-6154	86	5	types	type	NOUN
ejpam-6154	86	6	of	of	ADP
ejpam-6154	86	7	nonlinear	nonlinear	ADJ
ejpam-6154	86	8	mappings	mapping	NOUN
ejpam-6154	86	9	,	,	PUNCT
ejpam-6154	86	10	including	include	VERB
ejpam-6154	86	11	demicontractive	demicontractive	ADJ
ejpam-6154	86	12	mapping	mapping	NOUN
ejpam-6154	86	13	,	,	PUNCT
ejpam-6154	86	14	directed	direct	VERB
ejpam-6154	86	15	mapping	mapping	NOUN
ejpam-6154	86	16	,	,	PUNCT
ejpam-6154	86	17	quasi	quasi	ADJ
ejpam-6154	86	18	-	-	ADJ
ejpam-6154	86	19	nonexpansive	nonexpansive	ADJ
ejpam-6154	86	20	mapping	mapping	NOUN
ejpam-6154	86	21	,	,	PUNCT
ejpam-6154	86	22	and	and	CCONJ
ejpam-6154	86	23	strictly	strictly	ADV
ejpam-6154	86	24	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	86	25	mapping	mapping	NOUN
ejpam-6154	86	26	,	,	PUNCT
ejpam-6154	86	27	all	all	PRON
ejpam-6154	86	28	of	of	ADP
ejpam-6154	86	29	which	which	PRON
ejpam-6154	86	30	serve	serve	VERB
ejpam-6154	86	31	as	as	ADP
ejpam-6154	86	32	special	special	ADJ
ejpam-6154	86	33	cases	case	NOUN
ejpam-6154	86	34	.	.	PUNCT
ejpam-6154	87	1	for	for	ADP
ejpam-6154	87	2	further	further	ADJ
ejpam-6154	87	3	details	detail	NOUN
ejpam-6154	87	4	and	and	CCONJ
ejpam-6154	87	5	examples	example	NOUN
ejpam-6154	87	6	,	,	PUNCT
ejpam-6154	87	7	see	see	VERB
ejpam-6154	87	8	[	[	X
ejpam-6154	87	9	9	9	NUM
ejpam-6154	87	10	,	,	PUNCT
ejpam-6154	87	11	10	10	NUM
ejpam-6154	87	12	]	]	PUNCT
ejpam-6154	87	13	.	.	PUNCT
ejpam-6154	88	1	remark	remark	PROPN
ejpam-6154	88	2	2	2	NUM
ejpam-6154	88	3	.	.	PUNCT
ejpam-6154	89	1	it	it	PRON
ejpam-6154	89	2	is	be	AUX
ejpam-6154	89	3	obvious	obvious	ADJ
ejpam-6154	89	4	that	that	SCONJ
ejpam-6154	89	5	if	if	SCONJ
ejpam-6154	89	6	t1	t1	NOUN
ejpam-6154	89	7	is	be	AUX
ejpam-6154	89	8	quasi	quasi	ADJ
ejpam-6154	89	9	-	-	ADJ
ejpam-6154	89	10	nonexpansive	nonexpansive	ADJ
ejpam-6154	89	11	then	then	ADV
ejpam-6154	89	12	∥t1y	∥t1y	PROPN
ejpam-6154	89	13	−	−	PROPN
ejpam-6154	89	14	y∥	y∥	VERB
ejpam-6154	89	15	≤	≤	NUM
ejpam-6154	89	16	2	2	NUM
ejpam-6154	89	17	⟨y	⟨y	NOUN
ejpam-6154	89	18	−	−	NOUN
ejpam-6154	89	19	t1y	t1y	PROPN
ejpam-6154	89	20	,	,	PUNCT
ejpam-6154	89	21	y	y	PROPN
ejpam-6154	89	22	−	−	PROPN
ejpam-6154	89	23	z⟩	z⟩	PROPN
ejpam-6154	89	24	.	.	PUNCT
ejpam-6154	90	1	lemma	lemma	PROPN
ejpam-6154	90	2	1	1	NUM
ejpam-6154	90	3	.	.	PUNCT
ejpam-6154	91	1	(	(	PUNCT
ejpam-6154	91	2	chang	chang	PROPN
ejpam-6154	91	3	et	et	PROPN
ejpam-6154	91	4	al	al	PROPN
ejpam-6154	91	5	.	.	PROPN
ejpam-6154	91	6	,	,	PUNCT
ejpam-6154	92	1	[	[	X
ejpam-6154	92	2	9	9	NUM
ejpam-6154	92	3	]	]	PUNCT
ejpam-6154	92	4	)	)	PUNCT
ejpam-6154	92	5	suppose	suppose	VERB
ejpam-6154	92	6	t1	t1	NOUN
ejpam-6154	92	7	:	:	PUNCT
ejpam-6154	92	8	h1	h1	PROPN
ejpam-6154	92	9	→	→	PUNCT
ejpam-6154	92	10	h1	h1	PROPN
ejpam-6154	92	11	is	be	AUX
ejpam-6154	92	12	lipschitz	lipschitz	NOUN
ejpam-6154	92	13	with	with	ADP
ejpam-6154	92	14	l	l	PROPN
ejpam-6154	92	15	>	>	X
ejpam-6154	92	16	0	0	NUM
ejpam-6154	92	17	,	,	PUNCT
ejpam-6154	92	18	and	and	CCONJ
ejpam-6154	92	19	u1	u1	VERB
ejpam-6154	92	20	:	:	PUNCT
ejpam-6154	92	21	=	=	SYM
ejpam-6154	92	22	(	(	PUNCT
ejpam-6154	92	23	1−	1−	NUM
ejpam-6154	92	24	η)i	η)i	NOUN
ejpam-6154	93	1	+	+	CCONJ
ejpam-6154	94	1	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	94	2	ζ)i	ζ)i	NOUN
ejpam-6154	94	3	+	+	CCONJ
ejpam-6154	94	4	ζt1	ζt1	PROPN
ejpam-6154	94	5	)	)	PUNCT
ejpam-6154	94	6	,	,	PUNCT
ejpam-6154	94	7	then	then	ADV
ejpam-6154	94	8	(	(	PUNCT
ejpam-6154	94	9	i	i	NOUN
ejpam-6154	94	10	)	)	PUNCT
ejpam-6154	94	11	fix(t1	fix(t1	PROPN
ejpam-6154	94	12	)	)	PUNCT
ejpam-6154	94	13	=	=	PUNCT
ejpam-6154	94	14	fix((1−	fix((1−	NOUN
ejpam-6154	94	15	η)i	η)i	ADJ
ejpam-6154	94	16	+	+	CCONJ
ejpam-6154	94	17	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	94	18	ζ)i	ζ)i	NOUN
ejpam-6154	94	19	+	+	CCONJ
ejpam-6154	94	20	ζt1	ζt1	NOUN
ejpam-6154	94	21	)	)	PUNCT
ejpam-6154	94	22	)	)	PUNCT
ejpam-6154	95	1	=	=	SYM
ejpam-6154	95	2	fix(u1	fix(u1	NOUN
ejpam-6154	95	3	)	)	PUNCT
ejpam-6154	95	4	;	;	PUNCT
ejpam-6154	95	5	(	(	PUNCT
ejpam-6154	95	6	ii	ii	NOUN
ejpam-6154	95	7	)	)	PUNCT
ejpam-6154	95	8	u1	u1	NOUN
ejpam-6154	95	9	is	be	AUX
ejpam-6154	95	10	demiclosed	demiclose	VERB
ejpam-6154	95	11	at	at	ADP
ejpam-6154	95	12	zero	zero	NUM
ejpam-6154	95	13	only	only	ADV
ejpam-6154	95	14	if	if	SCONJ
ejpam-6154	95	15	t	t	PROPN
ejpam-6154	95	16	is	be	AUX
ejpam-6154	95	17	demiclosed	demiclose	VERB
ejpam-6154	95	18	at	at	ADP
ejpam-6154	95	19	zero	zero	NUM
ejpam-6154	95	20	;	;	PUNCT
ejpam-6154	95	21	(	(	PUNCT
ejpam-6154	95	22	iii	iii	X
ejpam-6154	95	23	)	)	PUNCT
ejpam-6154	95	24	u1	u1	NOUN
ejpam-6154	95	25	is	be	AUX
ejpam-6154	95	26	l2−	l2−	NOUN
ejpam-6154	95	27	lipschitzian	lipschitzian	ADJ
ejpam-6154	95	28	;	;	PUNCT
ejpam-6154	95	29	(	(	PUNCT
ejpam-6154	95	30	iv	iv	X
ejpam-6154	95	31	)	)	PUNCT
ejpam-6154	95	32	u1	u1	NOUN
ejpam-6154	95	33	is	be	AUX
ejpam-6154	95	34	quasi	quasi	ADJ
ejpam-6154	95	35	-	-	ADJ
ejpam-6154	95	36	nonexpansive	nonexpansive	ADJ
ejpam-6154	95	37	only	only	ADV
ejpam-6154	95	38	if	if	SCONJ
ejpam-6154	95	39	t1	t1	NOUN
ejpam-6154	95	40	is	be	AUX
ejpam-6154	95	41	quasi	quasi	ADJ
ejpam-6154	95	42	-	-	ADJ
ejpam-6154	95	43	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	95	44	.	.	PUNCT
ejpam-6154	96	1	lemma	lemma	PROPN
ejpam-6154	96	2	2	2	NUM
ejpam-6154	96	3	.	.	PUNCT
ejpam-6154	97	1	(	(	PUNCT
ejpam-6154	97	2	xu	xu	INTJ
ejpam-6154	97	3	,	,	PUNCT
ejpam-6154	97	4	[	[	X
ejpam-6154	97	5	12	12	NUM
ejpam-6154	97	6	]	]	PUNCT
ejpam-6154	97	7	)	)	PUNCT
ejpam-6154	97	8	let	let	VERB
ejpam-6154	97	9	{	{	PUNCT
ejpam-6154	97	10	an	an	X
ejpam-6154	97	11	}	}	PUNCT
ejpam-6154	97	12	,	,	PUNCT
ejpam-6154	97	13	{	{	PUNCT
ejpam-6154	97	14	bn	bn	NOUN
ejpam-6154	97	15	}	}	PUNCT
ejpam-6154	97	16	⊆	⊆	NUM
ejpam-6154	97	17	r+	r+	NOUN
ejpam-6154	97	18	such	such	ADJ
ejpam-6154	97	19	that	that	DET
ejpam-6154	97	20	∑∞	∑∞	NOUN
ejpam-6154	97	21	n=0	n=0	ADV
ejpam-6154	98	1	bn	bn	ADP
ejpam-6154	98	2	<	<	X
ejpam-6154	98	3	∞.	∞.	PROPN
ejpam-6154	98	4	if	if	SCONJ
ejpam-6154	98	5	an+1	an+1	ADV
ejpam-6154	98	6	≤	≤	X
ejpam-6154	98	7	(	(	PUNCT
ejpam-6154	98	8	1	1	NUM
ejpam-6154	98	9	+	+	NUM
ejpam-6154	98	10	bn)an	bn)an	NOUN
ejpam-6154	99	1	or	or	CCONJ
ejpam-6154	99	2	an+1	an+1	VERB
ejpam-6154	99	3	≤	≤	NOUN
ejpam-6154	99	4	an	an	DET
ejpam-6154	99	5	+	+	NOUN
ejpam-6154	99	6	bn	bn	ADJ
ejpam-6154	99	7	,	,	PUNCT
ejpam-6154	99	8	∀n	∀n	NUM
ejpam-6154	99	9	≥	≥	NOUN
ejpam-6154	99	10	0	0	NUM
ejpam-6154	99	11	,	,	PUNCT
ejpam-6154	99	12	then	then	ADV
ejpam-6154	99	13	lim	lim	PROPN
ejpam-6154	99	14	n→∞	n→∞	PRON
ejpam-6154	99	15	an	an	DET
ejpam-6154	99	16	exists	exist	NOUN
ejpam-6154	99	17	.	.	PUNCT
ejpam-6154	100	1	lemma	lemma	PROPN
ejpam-6154	100	2	3	3	NUM
ejpam-6154	100	3	.	.	PUNCT
ejpam-6154	101	1	(	(	PUNCT
ejpam-6154	101	2	xu	xu	INTJ
ejpam-6154	101	3	,	,	PUNCT
ejpam-6154	101	4	[	[	X
ejpam-6154	101	5	12	12	NUM
ejpam-6154	101	6	]	]	PUNCT
ejpam-6154	101	7	)	)	PUNCT
ejpam-6154	101	8	let	let	VERB
ejpam-6154	101	9	bn	bn	INTJ
ejpam-6154	101	10	>	>	X
ejpam-6154	101	11	0	0	PUNCT
ejpam-6154	102	1	for	for	ADP
ejpam-6154	102	2	n	n	PRON
ejpam-6154	102	3	∈	∈	PROPN
ejpam-6154	102	4	n	n	CCONJ
ejpam-6154	102	5	,	,	PUNCT
ejpam-6154	102	6	and	and	CCONJ
ejpam-6154	102	7	suppose	suppose	VERB
ejpam-6154	102	8	the	the	DET
ejpam-6154	102	9	following	follow	VERB
ejpam-6154	102	10	recurrence	recurrence	NOUN
ejpam-6154	102	11	holds	hold	VERB
ejpam-6154	102	12	:	:	PUNCT
ejpam-6154	102	13	bn+1	bn+1	NUM
ejpam-6154	102	14	≤	≤	NOUN
ejpam-6154	102	15	(	(	PUNCT
ejpam-6154	102	16	1−	1−	NUM
ejpam-6154	102	17	αn)bn	αn)bn	NUM
ejpam-6154	102	18	+	+	NUM
ejpam-6154	102	19	αnθn	αnθn	NOUN
ejpam-6154	102	20	+	+	CCONJ
ejpam-6154	102	21	εn	εn	ADJ
ejpam-6154	102	22	,	,	PUNCT
ejpam-6154	102	23	n	n	PRON
ejpam-6154	102	24	≥	≥	NOUN
ejpam-6154	102	25	0	0	NUM
ejpam-6154	102	26	,	,	PUNCT
ejpam-6154	102	27	where	where	SCONJ
ejpam-6154	102	28	{	{	PUNCT
ejpam-6154	102	29	αn	αn	NOUN
ejpam-6154	102	30	}	}	PUNCT
ejpam-6154	102	31	⊂	⊂	PROPN
ejpam-6154	102	32	(	(	PUNCT
ejpam-6154	102	33	0	0	NUM
ejpam-6154	102	34	,	,	PUNCT
ejpam-6154	102	35	1	1	NUM
ejpam-6154	102	36	)	)	PUNCT
ejpam-6154	102	37	and	and	CCONJ
ejpam-6154	102	38	{	{	PUNCT
ejpam-6154	102	39	θn	θn	NOUN
ejpam-6154	102	40	}	}	PUNCT
ejpam-6154	102	41	⊂	⊂	PROPN
ejpam-6154	102	42	r	r	NOUN
ejpam-6154	102	43	satisfy	satisfy	VERB
ejpam-6154	102	44	the	the	DET
ejpam-6154	102	45	conditions	condition	NOUN
ejpam-6154	102	46	:	:	PUNCT
ejpam-6154	102	47	(	(	PUNCT
ejpam-6154	102	48	i	i	NOUN
ejpam-6154	102	49	)	)	PUNCT
ejpam-6154	102	50	∑∞	∑∞	NOUN
ejpam-6154	102	51	n=0	n=0	NUM
ejpam-6154	102	52	αn	αn	NOUN
ejpam-6154	102	53	=	=	SYM
ejpam-6154	102	54	∞	∞	PROPN
ejpam-6154	102	55	;	;	PUNCT
ejpam-6154	102	56	(	(	PUNCT
ejpam-6154	102	57	ii	ii	NOUN
ejpam-6154	102	58	)	)	PUNCT
ejpam-6154	102	59	εn	εn	ADP
ejpam-6154	102	60	≥	≥	NOUN
ejpam-6154	102	61	0	0	NUM
ejpam-6154	102	62	for	for	ADP
ejpam-6154	102	63	all	all	DET
ejpam-6154	102	64	n	n	PRON
ejpam-6154	102	65	≥	≥	NOUN
ejpam-6154	102	66	0	0	NUM
ejpam-6154	102	67	,	,	PUNCT
ejpam-6154	102	68	and	and	CCONJ
ejpam-6154	102	69	∑∞	∑∞	NOUN
ejpam-6154	102	70	n=0	n=0	PUNCT
ejpam-6154	102	71	εn	εn	ADP
ejpam-6154	102	72	<	<	X
ejpam-6154	102	73	∞	∞	PROPN
ejpam-6154	102	74	;	;	PUNCT
ejpam-6154	102	75	(	(	PUNCT
ejpam-6154	102	76	iii	iii	X
ejpam-6154	102	77	)	)	PUNCT
ejpam-6154	102	78	lim	lim	PROPN
ejpam-6154	102	79	sup	sup	VERB
ejpam-6154	102	80	n→∞	n→∞	NUM
ejpam-6154	103	1	θn	θn	ADP
ejpam-6154	103	2	≤	≤	PROPN
ejpam-6154	103	3	0	0	NUM
ejpam-6154	103	4	or	or	CCONJ
ejpam-6154	103	5	∑∞	∑∞	NOUN
ejpam-6154	103	6	n=1	n=1	PROPN
ejpam-6154	104	1	αn|θn|	αn|θn|	NOUN
ejpam-6154	104	2	<	<	X
ejpam-6154	104	3	∞.	∞.	PROPN
ejpam-6154	104	4	then	then	ADV
ejpam-6154	104	5	,	,	PUNCT
ejpam-6154	104	6	lim	lim	PROPN
ejpam-6154	104	7	n→∞	n→∞	X
ejpam-6154	105	1	bn	bn	NOUN
ejpam-6154	105	2	=	=	NOUN
ejpam-6154	105	3	0	0	PROPN
ejpam-6154	105	4	.	.	PUNCT
ejpam-6154	105	5	l.	l.	PROPN
ejpam-6154	105	6	b.	b.	PROPN
ejpam-6154	105	7	mohammed	mohammed	PROPN
ejpam-6154	105	8	,	,	PUNCT
ejpam-6154	105	9	a.	a.	PROPN
ejpam-6154	105	10	kılıçman	kılıçman	PROPN
ejpam-6154	105	11	,	,	PUNCT
ejpam-6154	105	12	d.	d.	PROPN
ejpam-6154	105	13	bamanga	bamanga	PROPN
ejpam-6154	105	14	/	/	SYM
ejpam-6154	105	15	eur	eur	PROPN
ejpam-6154	105	16	.	.	PUNCT
ejpam-6154	106	1	j.	j.	PROPN
ejpam-6154	106	2	pure	pure	PROPN
ejpam-6154	106	3	appl	appl	PROPN
ejpam-6154	106	4	.	.	PROPN
ejpam-6154	106	5	math	math	PROPN
ejpam-6154	106	6	,	,	PUNCT
ejpam-6154	106	7	18	18	NUM
ejpam-6154	106	8	(	(	PUNCT
ejpam-6154	106	9	4	4	NUM
ejpam-6154	106	10	)	)	PUNCT
ejpam-6154	106	11	(	(	PUNCT
ejpam-6154	106	12	2025	2025	NUM
ejpam-6154	106	13	)	)	PUNCT
ejpam-6154	106	14	,	,	PUNCT
ejpam-6154	106	15	6154	6154	NUM
ejpam-6154	106	16	5	5	NUM
ejpam-6154	106	17	of	of	ADP
ejpam-6154	106	18	18	18	NUM
ejpam-6154	106	19	3	3	NUM
ejpam-6154	106	20	.	.	PUNCT
ejpam-6154	106	21	main	main	ADJ
ejpam-6154	106	22	results	result	NOUN
ejpam-6154	106	23	in	in	ADP
ejpam-6154	106	24	what	what	PRON
ejpam-6154	106	25	follows	follow	VERB
ejpam-6154	106	26	,	,	PUNCT
ejpam-6154	106	27	s	s	VERB
ejpam-6154	106	28	will	will	AUX
ejpam-6154	106	29	denote	denote	VERB
ejpam-6154	106	30	the	the	DET
ejpam-6154	106	31	solution	solution	NOUN
ejpam-6154	106	32	set	set	VERB
ejpam-6154	106	33	of	of	ADP
ejpam-6154	106	34	equation	equation	NOUN
ejpam-6154	106	35	(	(	PUNCT
ejpam-6154	106	36	1	1	NUM
ejpam-6154	106	37	)	)	PUNCT
ejpam-6154	106	38	,	,	PUNCT
ejpam-6154	106	39	that	that	ADV
ejpam-6154	106	40	is	be	AUX
ejpam-6154	106	41	,	,	PUNCT
ejpam-6154	106	42	s	s	PART
ejpam-6154	106	43	:	:	PUNCT
ejpam-6154	106	44	=	=	SYM
ejpam-6154	106	45	{	{	PUNCT
ejpam-6154	106	46	y	y	PROPN
ejpam-6154	106	47	∈	∈	PROPN
ejpam-6154	106	48	fix(t1	fix(t1	X
ejpam-6154	106	49	)	)	PUNCT
ejpam-6154	106	50	and	and	CCONJ
ejpam-6154	106	51	z	z	NOUN
ejpam-6154	106	52	∈	∈	PROPN
ejpam-6154	106	53	fix(t2	fix(t2	NOUN
ejpam-6154	106	54	)	)	PUNCT
ejpam-6154	106	55	such	such	ADJ
ejpam-6154	106	56	that	that	SCONJ
ejpam-6154	106	57	a1y	a1y	NOUN
ejpam-6154	106	58	=	=	PUNCT
ejpam-6154	106	59	a2z	a2z	PROPN
ejpam-6154	106	60	}	}	PUNCT
ejpam-6154	106	61	.	.	PUNCT
ejpam-6154	107	1	(	(	PUNCT
ejpam-6154	107	2	9	9	X
ejpam-6154	107	3	)	)	PUNCT
ejpam-6154	107	4	suppose	suppose	VERB
ejpam-6154	107	5	that	that	SCONJ
ejpam-6154	107	6	for	for	ADP
ejpam-6154	107	7	j	j	PROPN
ejpam-6154	107	8	=	=	SYM
ejpam-6154	107	9	1	1	NUM
ejpam-6154	107	10	,	,	PUNCT
ejpam-6154	107	11	2	2	NUM
ejpam-6154	107	12	,	,	PUNCT
ejpam-6154	107	13	the	the	DET
ejpam-6154	107	14	following	follow	VERB
ejpam-6154	107	15	assumptions	assumption	NOUN
ejpam-6154	107	16	hold	hold	VERB
ejpam-6154	107	17	:	:	PUNCT
ejpam-6154	107	18	(	(	PUNCT
ejpam-6154	107	19	k1	k1	NOUN
ejpam-6154	107	20	)	)	PUNCT
ejpam-6154	107	21	tj	tj	NOUN
ejpam-6154	107	22	:	:	PUNCT
ejpam-6154	107	23	hj	hj	PROPN
ejpam-6154	107	24	→	→	SYM
ejpam-6154	107	25	hj	hj	PROPN
ejpam-6154	107	26	,	,	PUNCT
ejpam-6154	107	27	are	be	AUX
ejpam-6154	107	28	two	two	NUM
ejpam-6154	107	29	quasi	quasi	ADJ
ejpam-6154	107	30	-	-	ADJ
ejpam-6154	107	31	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	107	32	operators	operator	NOUN
ejpam-6154	107	33	with	with	ADP
ejpam-6154	107	34	fix(tj	fix(tj	NOUN
ejpam-6154	107	35	)	)	PUNCT
ejpam-6154	107	36	̸=	̸=	NOUN
ejpam-6154	107	37	∅	∅	NOUN
ejpam-6154	107	38	,	,	PUNCT
ejpam-6154	107	39	in	in	ADP
ejpam-6154	107	40	addition	addition	NOUN
ejpam-6154	107	41	,	,	PUNCT
ejpam-6154	107	42	t1	t1	PROPN
ejpam-6154	107	43	is	be	AUX
ejpam-6154	107	44	also	also	ADV
ejpam-6154	107	45	llipschitz	llipschitz	NOUN
ejpam-6154	107	46	.	.	PUNCT
ejpam-6154	108	1	(	(	PUNCT
ejpam-6154	108	2	k2	k2	PROPN
ejpam-6154	108	3	)	)	PUNCT
ejpam-6154	108	4	aj	aj	PROPN
ejpam-6154	108	5	:	:	PUNCT
ejpam-6154	108	6	hj	hj	PROPN
ejpam-6154	108	7	→	→	SYM
ejpam-6154	108	8	hj	hj	PROPN
ejpam-6154	108	9	are	be	AUX
ejpam-6154	108	10	linear	linear	ADJ
ejpam-6154	108	11	and	and	CCONJ
ejpam-6154	108	12	bounded	bound	VERB
ejpam-6154	108	13	operators	operator	NOUN
ejpam-6154	108	14	with	with	ADP
ejpam-6154	108	15	their	their	PRON
ejpam-6154	108	16	adjoints	adjoint	NOUN
ejpam-6154	108	17	a∗	a∗	PROPN
ejpam-6154	108	18	j	j	PROPN
ejpam-6154	108	19	.	.	PUNCT
ejpam-6154	109	1	(	(	PUNCT
ejpam-6154	109	2	k3	k3	PROPN
ejpam-6154	109	3	)	)	PUNCT
ejpam-6154	109	4	(	(	PUNCT
ejpam-6154	109	5	tj	tj	NOUN
ejpam-6154	109	6	−	−	PROPN
ejpam-6154	109	7	i	i	PROPN
ejpam-6154	109	8	)	)	PUNCT
ejpam-6154	109	9	are	be	AUX
ejpam-6154	109	10	demiclosed	demiclose	VERB
ejpam-6154	109	11	at	at	ADP
ejpam-6154	109	12	origin	origin	NOUN
ejpam-6154	109	13	.	.	PUNCT
ejpam-6154	110	1	(	(	PUNCT
ejpam-6154	110	2	k4	k4	PROPN
ejpam-6154	110	3	)	)	PUNCT
ejpam-6154	110	4	fj	fj	PROPN
ejpam-6154	110	5	:	:	PUNCT
ejpam-6154	110	6	hj	hj	PROPN
ejpam-6154	110	7	→	→	SYM
ejpam-6154	110	8	hj	hj	PROPN
ejpam-6154	110	9	are	be	AUX
ejpam-6154	110	10	contraction	contraction	NOUN
ejpam-6154	110	11	mappings	mapping	NOUN
ejpam-6154	110	12	with	with	ADP
ejpam-6154	110	13	contraction	contraction	NOUN
ejpam-6154	110	14	constant	constant	ADJ
ejpam-6154	110	15	ρ	ρ	PROPN
ejpam-6154	110	16	∈	∈	PROPN
ejpam-6154	110	17	(	(	PUNCT
ejpam-6154	110	18	0	0	NUM
ejpam-6154	110	19	,	,	PUNCT
ejpam-6154	110	20	1	1	NUM
ejpam-6154	110	21	]	]	PUNCT
ejpam-6154	110	22	;	;	PUNCT
ejpam-6154	110	23	(	(	PUNCT
ejpam-6154	110	24	k5	k5	PROPN
ejpam-6154	110	25	)	)	PUNCT
ejpam-6154	110	26	let	let	VERB
ejpam-6154	110	27	uj	uj	PROPN
ejpam-6154	110	28	=	=	SYM
ejpam-6154	110	29	(	(	PUNCT
ejpam-6154	110	30	1−	1−	NUM
ejpam-6154	110	31	η)i	η)i	NOUN
ejpam-6154	110	32	+	+	CCONJ
ejpam-6154	110	33	ηtj((1−	ηtj((1−	ADJ
ejpam-6154	110	34	ζ)i	ζ)i	NOUN
ejpam-6154	110	35	+	+	CCONJ
ejpam-6154	110	36	ζtj	ζtj	NOUN
ejpam-6154	110	37	)	)	PUNCT
ejpam-6154	110	38	,	,	PUNCT
ejpam-6154	110	39	and	and	CCONJ
ejpam-6154	110	40	define	define	VERB
ejpam-6154	110	41	(	(	PUNCT
ejpam-6154	110	42	yn	yn	PROPN
ejpam-6154	110	43	,	,	PUNCT
ejpam-6154	110	44	zn	zn	PROPN
ejpam-6154	110	45	)	)	PUNCT
ejpam-6154	110	46	⊆	⊆	NUM
ejpam-6154	110	47	h1	h1	PROPN
ejpam-6154	110	48	×h2	×h2	PROPN
ejpam-6154	110	49	by	by	PROPN
ejpam-6154	110	50	yn+1	yn+1	PROPN
ejpam-6154	110	51	=	=	PROPN
ejpam-6154	110	52	αnf1(vn	αnf1(vn	PROPN
ejpam-6154	110	53	)	)	PUNCT
ejpam-6154	111	1	+	+	CCONJ
ejpam-6154	111	2	(	(	PUNCT
ejpam-6154	111	3	1−	1−	NUM
ejpam-6154	111	4	αn)u1vn	αn)u1vn	NOUN
ejpam-6154	111	5	;	;	PUNCT
ejpam-6154	111	6	vn	vn	PROPN
ejpam-6154	111	7	=	=	SYM
ejpam-6154	111	8	(	(	PUNCT
ejpam-6154	111	9	1−	1−	NUM
ejpam-6154	111	10	τn)yn	τn)yn	PUNCT
ejpam-6154	112	1	+	+	CCONJ
ejpam-6154	112	2	τnu1yn	τnu1yn	PUNCT
ejpam-6154	112	3	+	+	NUM
ejpam-6154	112	4	τna∗	τna∗	NOUN
ejpam-6154	112	5	1(a1yn	1(a1yn	PROPN
ejpam-6154	112	6	−a2zn	−a2zn	NUM
ejpam-6154	112	7	)	)	PUNCT
ejpam-6154	112	8	;	;	PUNCT
ejpam-6154	112	9	zn+1	zn+1	X
ejpam-6154	112	10	=	=	SYM
ejpam-6154	112	11	αnf2(wn	αnf2(wn	NOUN
ejpam-6154	112	12	)	)	PUNCT
ejpam-6154	112	13	+	+	CCONJ
ejpam-6154	112	14	(	(	PUNCT
ejpam-6154	112	15	1−	1−	NUM
ejpam-6154	112	16	αn)u2wn	αn)u2wn	NUM
ejpam-6154	112	17	;	;	PUNCT
ejpam-6154	112	18	wn	wn	PROPN
ejpam-6154	112	19	=	=	PUNCT
ejpam-6154	112	20	(	(	PUNCT
ejpam-6154	112	21	1−	1−	NUM
ejpam-6154	112	22	τn)zn	τn)zn	NUM
ejpam-6154	112	23	+	+	CCONJ
ejpam-6154	112	24	τnu2zn	τnu2zn	PUNCT
ejpam-6154	113	1	+	+	CCONJ
ejpam-6154	113	2	τna∗	τna∗	NOUN
ejpam-6154	113	3	2(a2zn	2(a2zn	PROPN
ejpam-6154	113	4	−a1yn	−a1yn	NUM
ejpam-6154	113	5	)	)	PUNCT
ejpam-6154	113	6	,	,	PUNCT
ejpam-6154	113	7	∀n	∀n	NUM
ejpam-6154	113	8	≥	≥	NOUN
ejpam-6154	113	9	0	0	NUM
ejpam-6154	113	10	;	;	PUNCT
ejpam-6154	113	11	(	(	PUNCT
ejpam-6154	113	12	10	10	NUM
ejpam-6154	113	13	)	)	PUNCT
ejpam-6154	113	14	where	where	SCONJ
ejpam-6154	113	15	(	(	PUNCT
ejpam-6154	113	16	y0	y0	NOUN
ejpam-6154	113	17	,	,	PUNCT
ejpam-6154	113	18	z0	z0	PROPN
ejpam-6154	113	19	)	)	PUNCT
ejpam-6154	113	20	∈	∈	PROPN
ejpam-6154	113	21	h1	h1	PROPN
ejpam-6154	113	22	×	×	PROPN
ejpam-6154	113	23	h2	h2	NOUN
ejpam-6154	113	24	are	be	AUX
ejpam-6154	113	25	chosen	choose	VERB
ejpam-6154	113	26	arbitrary	arbitrary	ADJ
ejpam-6154	113	27	,	,	PUNCT
ejpam-6154	113	28	0	0	NUM
ejpam-6154	113	29	<	<	X
ejpam-6154	113	30	αn	αn	NOUN
ejpam-6154	113	31	<	<	X
ejpam-6154	113	32	1	1	NUM
ejpam-6154	113	33	such	such	ADJ
ejpam-6154	113	34	that	that	SCONJ
ejpam-6154	113	35	∑	∑	PUNCT
ejpam-6154	113	36	n≥1	n≥1	VERB
ejpam-6154	113	37	αn	αn	NOUN
ejpam-6154	113	38	=	=	SYM
ejpam-6154	113	39	∞,∑	∞,∑	X
ejpam-6154	113	40	n≥1	n≥1	NOUN
ejpam-6154	113	41	(	(	PUNCT
ejpam-6154	113	42	1−	1−	NUM
ejpam-6154	113	43	αn)αn	αn)αn	NUM
ejpam-6154	113	44	<	<	X
ejpam-6154	113	45	∞	∞	PROPN
ejpam-6154	113	46	,	,	PUNCT
ejpam-6154	113	47	and	and	CCONJ
ejpam-6154	113	48	lim	lim	PROPN
ejpam-6154	113	49	n→∞	n→∞	PRON
ejpam-6154	113	50	αn	αn	NOUN
ejpam-6154	113	51	=	=	SYM
ejpam-6154	113	52	0	0	NUM
ejpam-6154	113	53	,	,	PUNCT
ejpam-6154	113	54	and	and	CCONJ
ejpam-6154	113	55	0	0	X
ejpam-6154	113	56	<	<	X
ejpam-6154	113	57	τn	τn	X
ejpam-6154	113	58	<	<	X
ejpam-6154	113	59	1	1	NUM
ejpam-6154	113	60	such	such	ADJ
ejpam-6154	113	61	that	that	DET
ejpam-6154	113	62	inf	inf	ADJ
ejpam-6154	113	63	n≥1	n≥1	NOUN
ejpam-6154	113	64	τn	τn	ADP
ejpam-6154	113	65	(	(	PUNCT
ejpam-6154	113	66	(	(	PUNCT
ejpam-6154	113	67	1−	1−	NUM
ejpam-6154	113	68	αn(1−	αn(1−	NUM
ejpam-6154	113	69	2ρ2))λ−	2ρ2))λ−	NUM
ejpam-6154	113	70	τn	τn	NOUN
ejpam-6154	113	71	)	)	PUNCT
ejpam-6154	113	72	≥	≥	PROPN
ejpam-6154	113	73	β	β	X
ejpam-6154	113	74	>	>	X
ejpam-6154	113	75	0	0	PROPN
ejpam-6154	113	76	,	,	PUNCT
ejpam-6154	113	77	where	where	SCONJ
ejpam-6154	113	78	λ	λ	X
ejpam-6154	113	79	=	=	VERB
ejpam-6154	113	80	1	1	NUM
ejpam-6154	113	81	2max{1,∥a1∥2,∥a2∥2	2max{1,∥a1∥2,∥a2∥2	NUM
ejpam-6154	113	82	}	}	PUNCT
ejpam-6154	113	83	,	,	PUNCT
ejpam-6154	113	84	and	and	CCONJ
ejpam-6154	113	85	0	0	NUM
ejpam-6154	113	86	<	<	X
ejpam-6154	113	87	η	η	X
ejpam-6154	113	88	<	<	X
ejpam-6154	113	89	ζ	ζ	X
ejpam-6154	113	90	<	<	X
ejpam-6154	113	91	1	1	NUM
ejpam-6154	113	92	1	1	NUM
ejpam-6154	113	93	+	+	NUM
ejpam-6154	113	94	√	√	PROPN
ejpam-6154	113	95	1+l2	1+l2	NUM
ejpam-6154	113	96	.	.	PUNCT
ejpam-6154	114	1	lemma	lemma	PROPN
ejpam-6154	114	2	4	4	X
ejpam-6154	114	3	.	.	PUNCT
ejpam-6154	115	1	let	let	AUX
ejpam-6154	115	2	{	{	PUNCT
ejpam-6154	115	3	(	(	PUNCT
ejpam-6154	115	4	yn	yn	PROPN
ejpam-6154	115	5	,	,	PUNCT
ejpam-6154	115	6	zn	zn	PROPN
ejpam-6154	115	7	)	)	PUNCT
ejpam-6154	115	8	}	}	PUNCT
ejpam-6154	115	9	be	be	AUX
ejpam-6154	115	10	the	the	DET
ejpam-6154	115	11	sequence	sequence	NOUN
ejpam-6154	115	12	generated	generate	VERB
ejpam-6154	115	13	by	by	ADP
ejpam-6154	115	14	algorithm	algorithm	NOUN
ejpam-6154	115	15	(	(	PUNCT
ejpam-6154	115	16	10	10	NUM
ejpam-6154	115	17	)	)	PUNCT
ejpam-6154	115	18	,	,	PUNCT
ejpam-6154	115	19	then	then	ADV
ejpam-6154	115	20	(	(	PUNCT
ejpam-6154	115	21	i	i	NOUN
ejpam-6154	115	22	)	)	PUNCT
ejpam-6154	115	23	{	{	PUNCT
ejpam-6154	115	24	(	(	PUNCT
ejpam-6154	115	25	yn	yn	PROPN
ejpam-6154	115	26	,	,	PUNCT
ejpam-6154	115	27	zn	zn	PROPN
ejpam-6154	115	28	)	)	PUNCT
ejpam-6154	115	29	}	}	PUNCT
ejpam-6154	115	30	is	be	AUX
ejpam-6154	115	31	bounded	bound	VERB
ejpam-6154	115	32	;	;	PUNCT
ejpam-6154	115	33	(	(	PUNCT
ejpam-6154	115	34	ii	ii	X
ejpam-6154	115	35	)	)	PUNCT
ejpam-6154	115	36	lim	lim	PROPN
ejpam-6154	115	37	sup	sup	PROPN
ejpam-6154	115	38	n→∞	n→∞	X
ejpam-6154	116	1	∥u1yn	∥u1yn	PUNCT
ejpam-6154	116	2	−	−	PROPN
ejpam-6154	116	3	yn	yn	PROPN
ejpam-6154	117	1	+	+	NOUN
ejpam-6154	117	2	a∗	a∗	ADJ
ejpam-6154	117	3	1(a2zn	1(a2zn	NOUN
ejpam-6154	117	4	−a1yn)∥2	−a1yn)∥2	NOUN
ejpam-6154	117	5	=	=	SYM
ejpam-6154	117	6	0	0	NUM
ejpam-6154	117	7	,	,	PUNCT
ejpam-6154	117	8	and	and	CCONJ
ejpam-6154	117	9	lim	lim	PROPN
ejpam-6154	117	10	sup	sup	PROPN
ejpam-6154	117	11	n→∞	n→∞	X
ejpam-6154	117	12	∥u2zn	∥u2zn	PUNCT
ejpam-6154	117	13	−	−	PROPN
ejpam-6154	118	1	zn	zn	X
ejpam-6154	118	2	+	+	ADP
ejpam-6154	118	3	a∗	a∗	ADJ
ejpam-6154	118	4	2(a1yn	2(a1yn	ADJ
ejpam-6154	118	5	−a2zn)∥2	−a2zn)∥2	NOUN
ejpam-6154	118	6	=	=	SYM
ejpam-6154	118	7	0	0	NUM
ejpam-6154	118	8	;	;	PUNCT
ejpam-6154	118	9	(	(	PUNCT
ejpam-6154	118	10	iii	iii	X
ejpam-6154	118	11	)	)	PUNCT
ejpam-6154	118	12	lim	lim	PROPN
ejpam-6154	118	13	sup	sup	PROPN
ejpam-6154	118	14	n→∞	n→∞	X
ejpam-6154	118	15	∥u1yn	∥u1yn	PUNCT
ejpam-6154	118	16	−	−	VERB
ejpam-6154	118	17	yn∥	yn∥	PROPN
ejpam-6154	118	18	=	=	SYM
ejpam-6154	118	19	0	0	PROPN
ejpam-6154	118	20	,	,	PUNCT
ejpam-6154	118	21	lim	lim	PROPN
ejpam-6154	118	22	sup	sup	VERB
ejpam-6154	118	23	n→∞	n→∞	X
ejpam-6154	118	24	∥u2zn	∥u2zn	PRON
ejpam-6154	118	25	−	−	PROPN
ejpam-6154	118	26	zn∥	zn∥	NOUN
ejpam-6154	118	27	=	=	SYM
ejpam-6154	118	28	0	0	NUM
ejpam-6154	118	29	,	,	PUNCT
ejpam-6154	118	30	and	and	CCONJ
ejpam-6154	118	31	lim	lim	PROPN
ejpam-6154	118	32	sup	sup	PROPN
ejpam-6154	118	33	n→∞	n→∞	NUM
ejpam-6154	118	34	∥a1yn	∥a1yn	PUNCT
ejpam-6154	118	35	−a2zn∥	−a2zn∥	NOUN
ejpam-6154	118	36	=	=	SYM
ejpam-6154	118	37	0	0	X
ejpam-6154	118	38	.	.	PUNCT
ejpam-6154	119	1	proof	proof	NOUN
ejpam-6154	119	2	.	.	PUNCT
ejpam-6154	120	1	let	let	VERB
ejpam-6154	120	2	(	(	PUNCT
ejpam-6154	120	3	y	y	NOUN
ejpam-6154	120	4	,	,	PUNCT
ejpam-6154	120	5	z	z	NOUN
ejpam-6154	120	6	)	)	PUNCT
ejpam-6154	120	7	∈	∈	PROPN
ejpam-6154	120	8	s.	s.	PROPN
ejpam-6154	120	9	by	by	ADP
ejpam-6154	120	10	lemma	lemma	PROPN
ejpam-6154	120	11	1	1	NUM
ejpam-6154	120	12	,	,	PUNCT
ejpam-6154	120	13	it	it	PRON
ejpam-6154	120	14	follows	follow	VERB
ejpam-6154	120	15	that	that	SCONJ
ejpam-6154	120	16	u1	u1	NOUN
ejpam-6154	120	17	is	be	AUX
ejpam-6154	120	18	quasi	quasi	ADJ
ejpam-6154	120	19	-	-	ADJ
ejpam-6154	120	20	nonexpansive	nonexpansive	ADJ
ejpam-6154	120	21	.	.	PUNCT
ejpam-6154	121	1	by	by	ADP
ejpam-6154	121	2	algorithm	algorithm	NOUN
ejpam-6154	121	3	(	(	PUNCT
ejpam-6154	121	4	10	10	NUM
ejpam-6154	121	5	)	)	PUNCT
ejpam-6154	121	6	we	we	PRON
ejpam-6154	121	7	have	have	AUX
ejpam-6154	121	8	∥zn+1	∥zn+1	VERB
ejpam-6154	121	9	−	−	PRON
ejpam-6154	121	10	z∥2	z∥2	NOUN
ejpam-6154	121	11	=	=	SYM
ejpam-6154	121	12	∥αnf2(wn	∥αnf2(wn	NOUN
ejpam-6154	121	13	)	)	PUNCT
ejpam-6154	122	1	+	+	CCONJ
ejpam-6154	122	2	(	(	PUNCT
ejpam-6154	122	3	1−	1−	NUM
ejpam-6154	122	4	αn)u2wn	αn)u2wn	NOUN
ejpam-6154	123	1	−	−	NOUN
ejpam-6154	123	2	z∥2	z∥2	PROPN
ejpam-6154	123	3	l.	l.	PROPN
ejpam-6154	123	4	b.	b.	PROPN
ejpam-6154	123	5	mohammed	mohammed	PROPN
ejpam-6154	123	6	,	,	PUNCT
ejpam-6154	123	7	a.	a.	PROPN
ejpam-6154	123	8	kılıçman	kılıçman	PROPN
ejpam-6154	123	9	,	,	PUNCT
ejpam-6154	123	10	d.	d.	PROPN
ejpam-6154	123	11	bamanga	bamanga	PROPN
ejpam-6154	123	12	/	/	SYM
ejpam-6154	123	13	eur	eur	PROPN
ejpam-6154	123	14	.	.	PUNCT
ejpam-6154	124	1	j.	j.	PROPN
ejpam-6154	124	2	pure	pure	PROPN
ejpam-6154	124	3	appl	appl	PROPN
ejpam-6154	124	4	.	.	PROPN
ejpam-6154	124	5	math	math	PROPN
ejpam-6154	124	6	,	,	PUNCT
ejpam-6154	124	7	18	18	NUM
ejpam-6154	124	8	(	(	PUNCT
ejpam-6154	124	9	4	4	NUM
ejpam-6154	124	10	)	)	PUNCT
ejpam-6154	124	11	(	(	PUNCT
ejpam-6154	124	12	2025	2025	NUM
ejpam-6154	124	13	)	)	PUNCT
ejpam-6154	124	14	,	,	PUNCT
ejpam-6154	124	15	6154	6154	NUM
ejpam-6154	124	16	6	6	NUM
ejpam-6154	124	17	of	of	ADP
ejpam-6154	124	18	18	18	NUM
ejpam-6154	124	19	=	=	SYM
ejpam-6154	124	20	∥αn(f2(wn)−	∥αn(f2(wn)−	PROPN
ejpam-6154	124	21	z	z	PROPN
ejpam-6154	124	22	)	)	PUNCT
ejpam-6154	125	1	+	+	CCONJ
ejpam-6154	125	2	(	(	PUNCT
ejpam-6154	125	3	1−	1−	NUM
ejpam-6154	125	4	αn)(u2wn	αn)(u2wn	NUM
ejpam-6154	125	5	−	−	NOUN
ejpam-6154	125	6	z)∥2	z)∥2	NOUN
ejpam-6154	125	7	=	=	NOUN
ejpam-6154	125	8	αn	αn	NOUN
ejpam-6154	125	9	∥f2(wn)−f2(z	∥f2(wn)−f2(z	NOUN
ejpam-6154	125	10	)	)	PUNCT
ejpam-6154	126	1	+	+	CCONJ
ejpam-6154	126	2	f2(z)−	f2(z)−	X
ejpam-6154	126	3	z∥2	z∥2	NOUN
ejpam-6154	126	4	+	+	CCONJ
ejpam-6154	126	5	(	(	PUNCT
ejpam-6154	126	6	1−	1−	NUM
ejpam-6154	126	7	αn	αn	NOUN
ejpam-6154	126	8	)	)	PUNCT
ejpam-6154	126	9	∥u2wn	∥u2wn	PUNCT
ejpam-6154	126	10	−	−	PROPN
ejpam-6154	126	11	z∥2	z∥2	NOUN
ejpam-6154	126	12	−	−	PROPN
ejpam-6154	126	13	(	(	PUNCT
ejpam-6154	126	14	1−	1−	NUM
ejpam-6154	126	15	αn)αn	αn)αn	NUM
ejpam-6154	126	16	∥u2wn	∥u2wn	PUNCT
ejpam-6154	126	17	−f2(wn)∥2	−f2(wn)∥2	PROPN
ejpam-6154	126	18	≤(1−	≤(1−	PROPN
ejpam-6154	126	19	αn(1−	αn(1−	NUM
ejpam-6154	126	20	2ρ2	2ρ2	NUM
ejpam-6154	126	21	)	)	PUNCT
ejpam-6154	126	22	)	)	PUNCT
ejpam-6154	126	23	∥∥wn	∥∥wn	PART
ejpam-6154	127	1	−	−	NOUN
ejpam-6154	127	2	z∥2	z∥2	NOUN
ejpam-6154	127	3	+	+	NUM
ejpam-6154	127	4	2αn∥f2(z)−	2αn∥f2(z)−	NUM
ejpam-6154	127	5	z	z	SYM
ejpam-6154	127	6	∥∥2	∥∥2	PROPN
ejpam-6154	127	7	,	,	PUNCT
ejpam-6154	127	8	and	and	CCONJ
ejpam-6154	127	9	(	(	PUNCT
ejpam-6154	127	10	11	11	NUM
ejpam-6154	127	11	)	)	PUNCT
ejpam-6154	127	12	∥wn	∥wn	VERB
ejpam-6154	127	13	−	−	NOUN
ejpam-6154	127	14	z∥2	z∥2	NOUN
ejpam-6154	127	15	=	=	PUNCT
ejpam-6154	127	16	∥∥∥(1−	∥∥∥(1−	NOUN
ejpam-6154	127	17	τn)(zn	τn)(zn	PUNCT
ejpam-6154	127	18	−	−	PROPN
ejpam-6154	127	19	z	z	NOUN
ejpam-6154	127	20	)	)	PUNCT
ejpam-6154	128	1	+	+	CCONJ
ejpam-6154	128	2	τn	τn	ADP
ejpam-6154	128	3	(	(	PUNCT
ejpam-6154	128	4	u2zn	u2zn	X
ejpam-6154	128	5	+	+	ADJ
ejpam-6154	128	6	a∗	a∗	ADJ
ejpam-6154	128	7	2(a2zn	2(a2zn	NOUN
ejpam-6154	128	8	−a1yn)−	−a1yn)−	PROPN
ejpam-6154	128	9	z	z	NOUN
ejpam-6154	128	10	)	)	PUNCT
ejpam-6154	128	11	∥∥∥2	∥∥∥2	NOUN
ejpam-6154	128	12	=(	=(	PROPN
ejpam-6154	128	13	1−	1−	NUM
ejpam-6154	128	14	τn	τn	NOUN
ejpam-6154	128	15	)	)	PUNCT
ejpam-6154	128	16	∥zn	∥zn	PART
ejpam-6154	128	17	−	−	PROPN
ejpam-6154	128	18	z∥2	z∥2	NOUN
ejpam-6154	128	19	+	+	CCONJ
ejpam-6154	128	20	τn∥u2zn	τn∥u2zn	PROPN
ejpam-6154	128	21	−	−	PROPN
ejpam-6154	128	22	zn	zn	PROPN
ejpam-6154	129	1	+	+	NOUN
ejpam-6154	129	2	a∗	a∗	PROPN
ejpam-6154	129	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	129	4	−a1yn	−a1yn	NUM
ejpam-6154	129	5	)	)	PUNCT
ejpam-6154	130	1	+	+	CCONJ
ejpam-6154	130	2	zn	zn	NUM
ejpam-6154	130	3	−	−	NOUN
ejpam-6154	130	4	z∥2	z∥2	NOUN
ejpam-6154	130	5	−	−	PROPN
ejpam-6154	130	6	(	(	PUNCT
ejpam-6154	130	7	1−	1−	NUM
ejpam-6154	130	8	τn)τn∥u2zn	τn)τn∥u2zn	PUNCT
ejpam-6154	130	9	−	−	PROPN
ejpam-6154	131	1	zn	zn	PROPN
ejpam-6154	132	1	+	+	NOUN
ejpam-6154	132	2	a∗	a∗	ADJ
ejpam-6154	132	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	132	4	−a1yn)∥2	−a1yn)∥2	ADJ
ejpam-6154	132	5	≤∥zn	≤∥zn	NOUN
ejpam-6154	132	6	−	−	NOUN
ejpam-6154	132	7	z∥2	z∥2	NOUN
ejpam-6154	132	8	+	+	PUNCT
ejpam-6154	132	9	τ2n∥u2zn	τ2n∥u2zn	NUM
ejpam-6154	133	1	−	−	X
ejpam-6154	133	2	zn	zn	PROPN
ejpam-6154	134	1	+	+	ADJ
ejpam-6154	134	2	a∗	a∗	PROPN
ejpam-6154	134	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	134	4	−a1yn)∥2	−a1yn)∥2	ADJ
ejpam-6154	134	5	−	−	PROPN
ejpam-6154	134	6	2τn	2τn	ADJ
ejpam-6154	134	7	⟨zn	⟨zn	PROPN
ejpam-6154	135	1	−	−	PROPN
ejpam-6154	135	2	z	z	PROPN
ejpam-6154	135	3	,	,	PUNCT
ejpam-6154	135	4	zn	zn	PROPN
ejpam-6154	135	5	−	−	NOUN
ejpam-6154	135	6	u2zn	u2zn	PUNCT
ejpam-6154	136	1	−a∗	−a∗	PROPN
ejpam-6154	136	2	2(a2zn	2(a2zn	INTJ
ejpam-6154	136	3	−a1yn)⟩	−a1yn)⟩	PROPN
ejpam-6154	136	4	.	.	PUNCT
ejpam-6154	137	1	(	(	PUNCT
ejpam-6154	137	2	12	12	NUM
ejpam-6154	137	3	)	)	PUNCT
ejpam-6154	137	4	thus	thus	ADV
ejpam-6154	137	5	,	,	PUNCT
ejpam-6154	137	6	by	by	ADP
ejpam-6154	137	7	equations	equation	NOUN
ejpam-6154	137	8	(	(	PUNCT
ejpam-6154	137	9	11	11	NUM
ejpam-6154	137	10	)	)	PUNCT
ejpam-6154	137	11	and	and	CCONJ
ejpam-6154	137	12	(	(	PUNCT
ejpam-6154	137	13	12	12	NUM
ejpam-6154	137	14	)	)	PUNCT
ejpam-6154	137	15	,	,	PUNCT
ejpam-6154	137	16	we	we	PRON
ejpam-6154	137	17	have	have	AUX
ejpam-6154	137	18	∥zn+1	∥zn+1	VERB
ejpam-6154	137	19	−	−	NOUN
ejpam-6154	137	20	z∥2	z∥2	NOUN
ejpam-6154	137	21	≤(1−	≤(1−	PROPN
ejpam-6154	137	22	αn(1−	αn(1−	NUM
ejpam-6154	137	23	2ρ2	2ρ2	NUM
ejpam-6154	137	24	)	)	PUNCT
ejpam-6154	137	25	)	)	PUNCT
ejpam-6154	138	1	∥∥zn	∥∥zn	ADJ
ejpam-6154	138	2	−	−	NOUN
ejpam-6154	138	3	z∥2	z∥2	NOUN
ejpam-6154	138	4	+	+	NUM
ejpam-6154	138	5	2αn∥f2(z)−	2αn∥f2(z)−	NUM
ejpam-6154	138	6	z	z	SYM
ejpam-6154	138	7	∥∥2	∥∥2	PROPN
ejpam-6154	139	1	+	+	CCONJ
ejpam-6154	139	2	τ2n∥u2zn	τ2n∥u2zn	PUNCT
ejpam-6154	140	1	−	−	X
ejpam-6154	140	2	zn	zn	X
ejpam-6154	141	1	+	+	ADJ
ejpam-6154	141	2	a∗	a∗	PROPN
ejpam-6154	141	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	141	4	−a1yn)∥2	−a1yn)∥2	NOUN
ejpam-6154	141	5	−	−	PROPN
ejpam-6154	141	6	2(1−	2(1−	NUM
ejpam-6154	141	7	αn(1−	αn(1−	PROPN
ejpam-6154	141	8	2ρ2))τn	2ρ2))τn	NUM
ejpam-6154	141	9	⟨zn	⟨zn	NOUN
ejpam-6154	141	10	−	−	PROPN
ejpam-6154	142	1	z	z	PROPN
ejpam-6154	142	2	,	,	PUNCT
ejpam-6154	142	3	zn	zn	PROPN
ejpam-6154	142	4	−	−	NOUN
ejpam-6154	142	5	u2zn	u2zn	PUNCT
ejpam-6154	143	1	−a∗	−a∗	PROPN
ejpam-6154	143	2	2(a2zn	2(a2zn	INTJ
ejpam-6154	143	3	−a1yn)⟩	−a1yn)⟩	PROPN
ejpam-6154	143	4	.	.	PUNCT
ejpam-6154	144	1	(	(	PUNCT
ejpam-6154	144	2	13	13	NUM
ejpam-6154	144	3	)	)	PUNCT
ejpam-6154	144	4	similarly	similarly	ADV
ejpam-6154	144	5	,	,	PUNCT
ejpam-6154	144	6	∥yn+1	∥yn+1	ADP
ejpam-6154	144	7	−	−	PROPN
ejpam-6154	144	8	y∥2	y∥2	ADJ
ejpam-6154	144	9	≤(1−	≤(1−	PROPN
ejpam-6154	144	10	αn(1−	αn(1−	NUM
ejpam-6154	144	11	2ρ2	2ρ2	NUM
ejpam-6154	144	12	)	)	PUNCT
ejpam-6154	144	13	)	)	PUNCT
ejpam-6154	145	1	∥∥yn	∥∥yn	PRON
ejpam-6154	145	2	−	−	PROPN
ejpam-6154	145	3	y∥2	y∥2	NOUN
ejpam-6154	146	1	+	+	CCONJ
ejpam-6154	146	2	2αn∥f1(y)−	2αn∥f1(y)−	NUM
ejpam-6154	146	3	y	y	PROPN
ejpam-6154	146	4	∥∥2	∥∥2	PROPN
ejpam-6154	146	5	+	+	CCONJ
ejpam-6154	146	6	τ2n	τ2n	X
ejpam-6154	147	1	∥u1yn	∥u1yn	PUNCT
ejpam-6154	147	2	−	−	PROPN
ejpam-6154	147	3	yn	yn	PROPN
ejpam-6154	148	1	+	+	NOUN
ejpam-6154	148	2	a∗	a∗	PROPN
ejpam-6154	148	3	1(a1yn	1(a1yn	PROPN
ejpam-6154	148	4	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	148	5	−	−	NOUN
ejpam-6154	148	6	2(1−	2(1−	NUM
ejpam-6154	149	1	αn(1−	αn(1−	PROPN
ejpam-6154	149	2	2ρ2))τn	2ρ2))τn	NUM
ejpam-6154	149	3	⟨yn	⟨yn	SYM
ejpam-6154	149	4	−	−	PROPN
ejpam-6154	150	1	y	y	PROPN
ejpam-6154	150	2	,	,	PUNCT
ejpam-6154	150	3	yn	yn	PROPN
ejpam-6154	150	4	−	−	PROPN
ejpam-6154	150	5	u1yn	u1yn	PRON
ejpam-6154	151	1	−a∗	−a∗	PROPN
ejpam-6154	151	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	151	3	−a2zn)⟩	−a2zn)⟩	NOUN
ejpam-6154	151	4	.	.	PUNCT
ejpam-6154	152	1	(	(	PUNCT
ejpam-6154	152	2	14	14	NUM
ejpam-6154	152	3	)	)	PUNCT
ejpam-6154	152	4	by	by	ADP
ejpam-6154	152	5	equations	equation	NOUN
ejpam-6154	152	6	(	(	PUNCT
ejpam-6154	152	7	13	13	NUM
ejpam-6154	152	8	)	)	PUNCT
ejpam-6154	152	9	and	and	CCONJ
ejpam-6154	152	10	(	(	PUNCT
ejpam-6154	152	11	14	14	NUM
ejpam-6154	152	12	)	)	PUNCT
ejpam-6154	152	13	,	,	PUNCT
ejpam-6154	152	14	we	we	PRON
ejpam-6154	152	15	deduce	deduce	VERB
ejpam-6154	152	16	that	that	PRON
ejpam-6154	152	17	γn+1	γn+1	NOUN
ejpam-6154	152	18	≤(1−	≤(1−	PROPN
ejpam-6154	152	19	αn(1−	αn(1−	PROPN
ejpam-6154	152	20	2ρ2))γn	2ρ2))γn	NUM
ejpam-6154	152	21	+	+	CCONJ
ejpam-6154	152	22	2αn	2αn	ADJ
ejpam-6154	152	23	(	(	PUNCT
ejpam-6154	152	24	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	152	25	z∥2	z∥2	NOUN
ejpam-6154	152	26	+	+	CCONJ
ejpam-6154	152	27	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	152	28	y∥2	y∥2	NOUN
ejpam-6154	152	29	)	)	PUNCT
ejpam-6154	153	1	+	+	CCONJ
ejpam-6154	153	2	τ2nkn	τ2nkn	NUM
ejpam-6154	154	1	−	−	X
ejpam-6154	154	2	2τn(1−	2τn(1−	NUM
ejpam-6154	154	3	αn(1−	αn(1−	NUM
ejpam-6154	154	4	2ρ2	2ρ2	NUM
ejpam-6154	154	5	)	)	PUNCT
ejpam-6154	154	6	)	)	PUNCT
ejpam-6154	155	1	(	(	PUNCT
ejpam-6154	155	2	⟨zn	⟨zn	NUM
ejpam-6154	155	3	−	−	PROPN
ejpam-6154	155	4	z	z	PROPN
ejpam-6154	155	5	,	,	PUNCT
ejpam-6154	155	6	zn	zn	PROPN
ejpam-6154	155	7	−	−	NOUN
ejpam-6154	155	8	u2zn	u2zn	PUNCT
ejpam-6154	156	1	−a∗	−a∗	PROPN
ejpam-6154	156	2	2(a2zn	2(a2zn	NOUN
ejpam-6154	156	3	−a1yn)⟩	−a1yn)⟩	PROPN
ejpam-6154	156	4	+	+	PROPN
ejpam-6154	157	1	⟨yn	⟨yn	PROPN
ejpam-6154	157	2	−	−	PROPN
ejpam-6154	158	1	y	y	PROPN
ejpam-6154	158	2	,	,	PUNCT
ejpam-6154	158	3	yn	yn	PROPN
ejpam-6154	158	4	−	−	PROPN
ejpam-6154	158	5	u1yn	u1yn	PRON
ejpam-6154	159	1	−a∗	−a∗	PROPN
ejpam-6154	159	2	1(a1yn	1(a1yn	VERB
ejpam-6154	159	3	−a2zn)⟩	−a2zn)⟩	NOUN
ejpam-6154	159	4	)	)	PUNCT
ejpam-6154	159	5	,	,	PUNCT
ejpam-6154	159	6	(	(	PUNCT
ejpam-6154	159	7	15	15	NUM
ejpam-6154	159	8	)	)	PUNCT
ejpam-6154	159	9	where	where	SCONJ
ejpam-6154	159	10	γn	γn	X
ejpam-6154	159	11	:	:	PUNCT
ejpam-6154	159	12	=	=	SYM
ejpam-6154	159	13	∥yn	∥yn	NUM
ejpam-6154	159	14	−	−	PROPN
ejpam-6154	159	15	y∥2	y∥2	NOUN
ejpam-6154	159	16	+	+	CCONJ
ejpam-6154	159	17	∥zn	∥zn	NUM
ejpam-6154	159	18	−	−	PROPN
ejpam-6154	159	19	z∥2	z∥2	NOUN
ejpam-6154	159	20	,	,	PUNCT
ejpam-6154	159	21	and	and	CCONJ
ejpam-6154	159	22	kn	kn	NOUN
ejpam-6154	159	23	:	:	PUNCT
ejpam-6154	160	1	=	=	X
ejpam-6154	160	2	∥u2zn	∥u2zn	PUNCT
ejpam-6154	160	3	−	−	PROPN
ejpam-6154	160	4	zn	zn	X
ejpam-6154	161	1	+	+	ADJ
ejpam-6154	161	2	a∗	a∗	ADJ
ejpam-6154	161	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	161	4	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	162	1	+	+	CCONJ
ejpam-6154	162	2	∥u1yn	∥u1yn	PUNCT
ejpam-6154	162	3	−	−	PUNCT
ejpam-6154	162	4	yn	yn	PROPN
ejpam-6154	162	5	+	+	NOUN
ejpam-6154	162	6	a∗	a∗	PROPN
ejpam-6154	162	7	1(a1yn	1(a1yn	NUM
ejpam-6154	162	8	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	162	9	.	.	PUNCT
ejpam-6154	163	1	on	on	ADP
ejpam-6154	163	2	the	the	DET
ejpam-6154	163	3	other	other	ADJ
ejpam-6154	163	4	hand	hand	NOUN
ejpam-6154	163	5	,	,	PUNCT
ejpam-6154	163	6	⟨zn	⟨zn	PROPN
ejpam-6154	163	7	−	−	PROPN
ejpam-6154	163	8	z	z	PROPN
ejpam-6154	163	9	,	,	PUNCT
ejpam-6154	163	10	zn	zn	PROPN
ejpam-6154	163	11	−	−	NOUN
ejpam-6154	163	12	u2zn	u2zn	PUNCT
ejpam-6154	164	1	−a∗	−a∗	PROPN
ejpam-6154	164	2	2(a2zn	2(a2zn	INTJ
ejpam-6154	164	3	−a1yn)⟩	−a1yn)⟩	PROPN
ejpam-6154	164	4	=	=	NOUN
ejpam-6154	164	5	⟨zn	⟨zn	PROPN
ejpam-6154	165	1	−	−	PROPN
ejpam-6154	165	2	z	z	PROPN
ejpam-6154	165	3	,	,	PUNCT
ejpam-6154	165	4	zn	zn	PROPN
ejpam-6154	165	5	−	−	PROPN
ejpam-6154	166	1	u2zn⟩	u2zn⟩	PROPN
ejpam-6154	166	2	−	−	PROPN
ejpam-6154	166	3	⟨a2zn	⟨a2zn	PROPN
ejpam-6154	167	1	−a2z	−a2z	PROPN
ejpam-6154	167	2	,	,	PUNCT
ejpam-6154	167	3	a2zn	a2zn	ADP
ejpam-6154	167	4	−a1yn⟩	−a1yn⟩	PROPN
ejpam-6154	168	1	≥1	≥1	NUM
ejpam-6154	168	2	2	2	NUM
ejpam-6154	168	3	∥zn	∥zn	NOUN
ejpam-6154	168	4	−	−	PROPN
ejpam-6154	168	5	u2zn∥2	u2zn∥2	PROPN
ejpam-6154	168	6	l.	l.	PROPN
ejpam-6154	168	7	b.	b.	PROPN
ejpam-6154	168	8	mohammed	mohammed	PROPN
ejpam-6154	168	9	,	,	PUNCT
ejpam-6154	168	10	a.	a.	PROPN
ejpam-6154	168	11	kılıçman	kılıçman	PROPN
ejpam-6154	168	12	,	,	PUNCT
ejpam-6154	168	13	d.	d.	PROPN
ejpam-6154	168	14	bamanga	bamanga	PROPN
ejpam-6154	168	15	/	/	SYM
ejpam-6154	168	16	eur	eur	PROPN
ejpam-6154	168	17	.	.	PUNCT
ejpam-6154	169	1	j.	j.	PROPN
ejpam-6154	169	2	pure	pure	PROPN
ejpam-6154	169	3	appl	appl	PROPN
ejpam-6154	169	4	.	.	PROPN
ejpam-6154	169	5	math	math	PROPN
ejpam-6154	169	6	,	,	PUNCT
ejpam-6154	169	7	18	18	NUM
ejpam-6154	169	8	(	(	PUNCT
ejpam-6154	169	9	4	4	NUM
ejpam-6154	169	10	)	)	PUNCT
ejpam-6154	169	11	(	(	PUNCT
ejpam-6154	169	12	2025	2025	NUM
ejpam-6154	169	13	)	)	PUNCT
ejpam-6154	169	14	,	,	PUNCT
ejpam-6154	169	15	6154	6154	NUM
ejpam-6154	169	16	7	7	NUM
ejpam-6154	169	17	of	of	ADP
ejpam-6154	169	18	18	18	NUM
ejpam-6154	169	19	−	−	PROPN
ejpam-6154	169	20	⟨a2zn	⟨a2zn	PROPN
ejpam-6154	169	21	−a2z	−a2z	PROPN
ejpam-6154	169	22	,	,	PUNCT
ejpam-6154	169	23	a2zn	a2zn	ADP
ejpam-6154	169	24	−a1yn⟩	−a1yn⟩	NOUN
ejpam-6154	169	25	.	.	PUNCT
ejpam-6154	170	1	(	(	PUNCT
ejpam-6154	170	2	16	16	NUM
ejpam-6154	170	3	)	)	PUNCT
ejpam-6154	170	4	similarly	similarly	ADV
ejpam-6154	170	5	,	,	PUNCT
ejpam-6154	170	6	⟨yn	⟨yn	PROPN
ejpam-6154	170	7	−	−	PROPN
ejpam-6154	171	1	y	y	PROPN
ejpam-6154	171	2	,	,	PUNCT
ejpam-6154	171	3	yn	yn	PROPN
ejpam-6154	171	4	−	−	PROPN
ejpam-6154	171	5	u1yn	u1yn	PRON
ejpam-6154	172	1	−a∗	−a∗	PROPN
ejpam-6154	172	2	1(a1yn	1(a1yn	VERB
ejpam-6154	173	1	−a2zn)⟩	−a2zn)⟩	NOUN
ejpam-6154	173	2	≥	≥	NUM
ejpam-6154	173	3	1	1	NUM
ejpam-6154	173	4	2	2	NUM
ejpam-6154	173	5	∥yn	∥yn	NOUN
ejpam-6154	173	6	−	−	NOUN
ejpam-6154	173	7	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	173	8	−	−	PROPN
ejpam-6154	173	9	⟨a1yn	⟨a1yn	PRON
ejpam-6154	173	10	−a1y	−a1y	NUM
ejpam-6154	173	11	,	,	PUNCT
ejpam-6154	173	12	a1yn	a1yn	PROPN
ejpam-6154	173	13	−a2zn⟩	−a2zn⟩	NUM
ejpam-6154	173	14	.	.	PUNCT
ejpam-6154	174	1	(	(	PUNCT
ejpam-6154	174	2	17	17	NUM
ejpam-6154	174	3	)	)	PUNCT
ejpam-6154	174	4	by	by	ADP
ejpam-6154	174	5	(	(	PUNCT
ejpam-6154	174	6	16	16	NUM
ejpam-6154	174	7	)	)	PUNCT
ejpam-6154	174	8	and	and	CCONJ
ejpam-6154	174	9	(	(	PUNCT
ejpam-6154	174	10	17	17	NUM
ejpam-6154	174	11	)	)	PUNCT
ejpam-6154	174	12	,	,	PUNCT
ejpam-6154	174	13	and	and	CCONJ
ejpam-6154	174	14	the	the	DET
ejpam-6154	174	15	fact	fact	NOUN
ejpam-6154	174	16	that	that	SCONJ
ejpam-6154	174	17	a1y	a1y	PROPN
ejpam-6154	174	18	=	=	PUNCT
ejpam-6154	174	19	a2z	a2z	PROPN
ejpam-6154	174	20	,	,	PUNCT
ejpam-6154	174	21	we	we	PRON
ejpam-6154	174	22	have	have	AUX
ejpam-6154	174	23	⟨zn	⟨zn	NUM
ejpam-6154	174	24	−	−	PROPN
ejpam-6154	174	25	z	z	PROPN
ejpam-6154	174	26	,	,	PUNCT
ejpam-6154	174	27	zn	zn	PROPN
ejpam-6154	174	28	−	−	NOUN
ejpam-6154	174	29	u2zn	u2zn	PUNCT
ejpam-6154	175	1	−a∗	−a∗	PROPN
ejpam-6154	175	2	2(a2zn	2(a2zn	NOUN
ejpam-6154	175	3	−a1yn)⟩+	−a1yn)⟩+	NUM
ejpam-6154	175	4	⟨yn	⟨yn	SYM
ejpam-6154	175	5	−	−	PROPN
ejpam-6154	176	1	y	y	PROPN
ejpam-6154	176	2	,	,	PUNCT
ejpam-6154	176	3	yn	yn	PROPN
ejpam-6154	176	4	−	−	PROPN
ejpam-6154	176	5	u1yn	u1yn	PRON
ejpam-6154	177	1	−a∗	−a∗	PROPN
ejpam-6154	177	2	1(a1yn	1(a1yn	VERB
ejpam-6154	177	3	−a2zn)⟩	−a2zn)⟩	NOUN
ejpam-6154	177	4	≥1	≥1	PROPN
ejpam-6154	177	5	2	2	NUM
ejpam-6154	177	6	∥zn	∥zn	NOUN
ejpam-6154	177	7	−	−	PROPN
ejpam-6154	177	8	u2zn∥2	u2zn∥2	NOUN
ejpam-6154	177	9	−	−	PROPN
ejpam-6154	177	10	⟨a2zn	⟨a2zn	PROPN
ejpam-6154	177	11	−a2z	−a2z	PROPN
ejpam-6154	177	12	,	,	PUNCT
ejpam-6154	177	13	a2zn	a2zn	ADP
ejpam-6154	177	14	−a1yn⟩	−a1yn⟩	NOUN
ejpam-6154	177	15	+	+	NOUN
ejpam-6154	177	16	1	1	NUM
ejpam-6154	177	17	2	2	NUM
ejpam-6154	177	18	∥yn	∥yn	NOUN
ejpam-6154	177	19	−	−	NOUN
ejpam-6154	177	20	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	177	21	−	−	PROPN
ejpam-6154	178	1	⟨a1yn	⟨a1yn	DET
ejpam-6154	178	2	−a1y	−a1y	NUM
ejpam-6154	178	3	,	,	PUNCT
ejpam-6154	178	4	a1yn	a1yn	PROPN
ejpam-6154	178	5	−a2zn⟩	−a2zn⟩	X
ejpam-6154	178	6	=	=	SYM
ejpam-6154	178	7	1	1	NUM
ejpam-6154	178	8	2	2	NUM
ejpam-6154	178	9	(	(	PUNCT
ejpam-6154	178	10	∥zn	∥zn	NUM
ejpam-6154	178	11	−	−	PROPN
ejpam-6154	178	12	u2zn∥2	u2zn∥2	NOUN
ejpam-6154	178	13	+	+	CCONJ
ejpam-6154	178	14	∥a1yn	∥a1yn	AUX
ejpam-6154	178	15	−a2zn∥2	−a2zn∥2	NOUN
ejpam-6154	178	16	)	)	PUNCT
ejpam-6154	179	1	+	+	CCONJ
ejpam-6154	179	2	1	1	NUM
ejpam-6154	179	3	2	2	NUM
ejpam-6154	179	4	(	(	PUNCT
ejpam-6154	179	5	∥yn	∥yn	NOUN
ejpam-6154	179	6	−	−	NOUN
ejpam-6154	179	7	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	179	8	+	+	CCONJ
ejpam-6154	179	9	∥a1yn	∥a1yn	PUNCT
ejpam-6154	179	10	−a2zn∥2	−a2zn∥2	NOUN
ejpam-6154	179	11	)	)	PUNCT
ejpam-6154	179	12	≥1	≥1	SYM
ejpam-6154	179	13	2	2	NUM
ejpam-6154	179	14	(	(	PUNCT
ejpam-6154	179	15	∥zn	∥zn	NUM
ejpam-6154	179	16	−	−	PROPN
ejpam-6154	179	17	u2zn∥2	u2zn∥2	NOUN
ejpam-6154	179	18	+	+	CCONJ
ejpam-6154	179	19	1	1	NUM
ejpam-6154	179	20	∥a2∥2	∥a2∥2	NUM
ejpam-6154	179	21	∥a∗	∥a∗	NUM
ejpam-6154	179	22	2(a1yn	2(a1yn	PROPN
ejpam-6154	179	23	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	179	24	)	)	PUNCT
ejpam-6154	180	1	+	+	CCONJ
ejpam-6154	180	2	1	1	NUM
ejpam-6154	180	3	2	2	NUM
ejpam-6154	180	4	(	(	PUNCT
ejpam-6154	180	5	∥yn	∥yn	NOUN
ejpam-6154	180	6	−	−	NOUN
ejpam-6154	181	1	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	182	1	+	+	NOUN
ejpam-6154	182	2	1	1	NUM
ejpam-6154	182	3	∥a1∥2	∥a1∥2	ADV
ejpam-6154	182	4	∥a∗	∥a∗	NUM
ejpam-6154	182	5	1(a1yn	1(a1yn	NUM
ejpam-6154	182	6	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	182	7	)	)	PUNCT
ejpam-6154	182	8	≥	≥	NOUN
ejpam-6154	182	9	1	1	NUM
ejpam-6154	182	10	2max{1	2max{1	NUM
ejpam-6154	182	11	,	,	PUNCT
ejpam-6154	182	12	∥a2∥2	∥a2∥2	NUM
ejpam-6154	182	13	}	}	PUNCT
ejpam-6154	182	14	(	(	PUNCT
ejpam-6154	182	15	∥zn	∥zn	NUM
ejpam-6154	182	16	−	−	NOUN
ejpam-6154	182	17	u2zn∥2	u2zn∥2	NOUN
ejpam-6154	183	1	+	+	CCONJ
ejpam-6154	183	2	∥a∗	∥a∗	NUM
ejpam-6154	183	3	2(a1yn	2(a1yn	PROPN
ejpam-6154	183	4	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	183	5	)	)	PUNCT
ejpam-6154	184	1	+	+	CCONJ
ejpam-6154	184	2	1	1	NUM
ejpam-6154	184	3	2max{1	2max{1	NUM
ejpam-6154	184	4	,	,	PUNCT
ejpam-6154	184	5	∥a1∥2	∥a1∥2	ADV
ejpam-6154	184	6	}	}	PUNCT
ejpam-6154	184	7	(	(	PUNCT
ejpam-6154	184	8	∥yn	∥yn	PROPN
ejpam-6154	184	9	−	−	NOUN
ejpam-6154	184	10	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	184	11	+	+	CCONJ
ejpam-6154	184	12	∥a∗	∥a∗	NUM
ejpam-6154	184	13	1(a1yn	1(a1yn	NUM
ejpam-6154	184	14	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	184	15	)	)	PUNCT
ejpam-6154	184	16	≥	≥	NOUN
ejpam-6154	184	17	1	1	NUM
ejpam-6154	184	18	4max{1	4max{1	NUM
ejpam-6154	184	19	,	,	PUNCT
ejpam-6154	184	20	∥a1∥2	∥a1∥2	ADV
ejpam-6154	184	21	,	,	PUNCT
ejpam-6154	184	22	∥a2∥2	∥a2∥2	NUM
ejpam-6154	184	23	}	}	PUNCT
ejpam-6154	184	24	(	(	PUNCT
ejpam-6154	184	25	(	(	PUNCT
ejpam-6154	184	26	∥yn	∥yn	X
ejpam-6154	184	27	−	−	PROPN
ejpam-6154	184	28	u1yn∥	u1yn∥	VERB
ejpam-6154	184	29	+	+	ADJ
ejpam-6154	184	30	∥a∗	∥a∗	NUM
ejpam-6154	184	31	1(a1yn	1(a1yn	NUM
ejpam-6154	184	32	−a2zn)∥	−a2zn)∥	PROPN
ejpam-6154	184	33	)	)	PUNCT
ejpam-6154	184	34	2	2	NUM
ejpam-6154	184	35	+	+	CCONJ
ejpam-6154	184	36	(	(	PUNCT
ejpam-6154	184	37	∥zn	∥zn	NUM
ejpam-6154	184	38	−	−	NOUN
ejpam-6154	184	39	u2zn∥2	u2zn∥2	NOUN
ejpam-6154	184	40	+	+	CCONJ
ejpam-6154	184	41	∥a∗	∥a∗	NUM
ejpam-6154	184	42	2(a1yn	2(a1yn	PROPN
ejpam-6154	184	43	−a2zn)∥	−a2zn)∥	PROPN
ejpam-6154	184	44	)	)	PUNCT
ejpam-6154	184	45	2	2	NUM
ejpam-6154	184	46	)	)	PUNCT
ejpam-6154	184	47	≥λ	≥λ	X
ejpam-6154	184	48	2	2	NUM
ejpam-6154	184	49	(	(	PUNCT
ejpam-6154	184	50	∥zn	∥zn	NUM
ejpam-6154	184	51	−	−	NOUN
ejpam-6154	184	52	u2zn	u2zn	PUNCT
ejpam-6154	185	1	−a∗	−a∗	X
ejpam-6154	186	1	2(a2zn	2(a2zn	INTJ
ejpam-6154	186	2	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	187	1	+	+	NOUN
ejpam-6154	187	2	∥yn	∥yn	ADJ
ejpam-6154	187	3	−	−	PROPN
ejpam-6154	187	4	u1yn	u1yn	PRON
ejpam-6154	188	1	−a∗	−a∗	PROPN
ejpam-6154	188	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	188	3	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	188	4	)	)	PUNCT
ejpam-6154	188	5	.	.	PUNCT
ejpam-6154	189	1	(	(	PUNCT
ejpam-6154	189	2	18	18	NUM
ejpam-6154	189	3	)	)	PUNCT
ejpam-6154	189	4	by	by	ADP
ejpam-6154	189	5	equations	equation	NOUN
ejpam-6154	189	6	(	(	PUNCT
ejpam-6154	189	7	15	15	NUM
ejpam-6154	189	8	)	)	PUNCT
ejpam-6154	189	9	and	and	CCONJ
ejpam-6154	189	10	(	(	PUNCT
ejpam-6154	189	11	18	18	NUM
ejpam-6154	189	12	)	)	PUNCT
ejpam-6154	189	13	,	,	PUNCT
ejpam-6154	189	14	and	and	CCONJ
ejpam-6154	189	15	noticing	notice	VERB
ejpam-6154	189	16	that	that	PRON
ejpam-6154	189	17	(	(	PUNCT
ejpam-6154	189	18	1−	1−	NUM
ejpam-6154	189	19	αn(1−	αn(1−	NUM
ejpam-6154	189	20	2ρ2	2ρ2	NUM
ejpam-6154	189	21	)	)	PUNCT
ejpam-6154	189	22	)	)	PUNCT
ejpam-6154	189	23	>	>	X
ejpam-6154	190	1	0	0	NUM
ejpam-6154	190	2	,	,	PUNCT
ejpam-6154	190	3	we	we	PRON
ejpam-6154	190	4	have	have	VERB
ejpam-6154	190	5	l.	l.	PROPN
ejpam-6154	190	6	b.	b.	PROPN
ejpam-6154	190	7	mohammed	mohammed	PROPN
ejpam-6154	190	8	,	,	PUNCT
ejpam-6154	190	9	a.	a.	PROPN
ejpam-6154	190	10	kılıçman	kılıçman	PROPN
ejpam-6154	190	11	,	,	PUNCT
ejpam-6154	190	12	d.	d.	PROPN
ejpam-6154	190	13	bamanga	bamanga	PROPN
ejpam-6154	190	14	/	/	SYM
ejpam-6154	190	15	eur	eur	PROPN
ejpam-6154	190	16	.	.	PUNCT
ejpam-6154	191	1	j.	j.	PROPN
ejpam-6154	191	2	pure	pure	PROPN
ejpam-6154	191	3	appl	appl	PROPN
ejpam-6154	191	4	.	.	PROPN
ejpam-6154	191	5	math	math	PROPN
ejpam-6154	191	6	,	,	PUNCT
ejpam-6154	191	7	18	18	NUM
ejpam-6154	191	8	(	(	PUNCT
ejpam-6154	191	9	4	4	NUM
ejpam-6154	191	10	)	)	PUNCT
ejpam-6154	191	11	(	(	PUNCT
ejpam-6154	191	12	2025	2025	NUM
ejpam-6154	191	13	)	)	PUNCT
ejpam-6154	191	14	,	,	PUNCT
ejpam-6154	191	15	6154	6154	NUM
ejpam-6154	191	16	8	8	NUM
ejpam-6154	191	17	of	of	ADP
ejpam-6154	191	18	18	18	NUM
ejpam-6154	191	19	γn+1	γn+1	NUM
ejpam-6154	191	20	≤	≤	NOUN
ejpam-6154	191	21	(	(	PUNCT
ejpam-6154	191	22	1−	1−	NUM
ejpam-6154	191	23	αn(1−	αn(1−	PROPN
ejpam-6154	191	24	2ρ2))γn	2ρ2))γn	NUM
ejpam-6154	192	1	+	+	CCONJ
ejpam-6154	192	2	2αn	2αn	ADJ
ejpam-6154	192	3	(	(	PUNCT
ejpam-6154	192	4	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	192	5	z∥2	z∥2	NOUN
ejpam-6154	192	6	+	+	CCONJ
ejpam-6154	192	7	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	192	8	y∥2	y∥2	NOUN
ejpam-6154	192	9	)	)	PUNCT
ejpam-6154	193	1	−	−	ADP
ejpam-6154	193	2	τn	τn	ADP
ejpam-6154	193	3	(	(	PUNCT
ejpam-6154	193	4	(	(	PUNCT
ejpam-6154	193	5	1−	1−	NUM
ejpam-6154	193	6	αn(1−	αn(1−	NUM
ejpam-6154	193	7	2ρ2))λ−	2ρ2))λ−	NUM
ejpam-6154	193	8	τn	τn	NOUN
ejpam-6154	193	9	)	)	PUNCT
ejpam-6154	194	1	kn	kn	NOUN
ejpam-6154	194	2	(	(	PUNCT
ejpam-6154	194	3	19	19	NUM
ejpam-6154	194	4	)	)	PUNCT
ejpam-6154	194	5	≤	≤	NOUN
ejpam-6154	194	6	(	(	PUNCT
ejpam-6154	194	7	1−	1−	NUM
ejpam-6154	194	8	αn(1−	αn(1−	PROPN
ejpam-6154	194	9	2ρ2))γn	2ρ2))γn	NUM
ejpam-6154	195	1	+	+	CCONJ
ejpam-6154	195	2	2αn	2αn	ADJ
ejpam-6154	195	3	(	(	PUNCT
ejpam-6154	195	4	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	195	5	z∥2	z∥2	NOUN
ejpam-6154	195	6	+	+	CCONJ
ejpam-6154	195	7	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	195	8	y∥2	y∥2	NOUN
ejpam-6154	195	9	)	)	PUNCT
ejpam-6154	195	10	.	.	PUNCT
ejpam-6154	196	1	thus	thus	ADV
ejpam-6154	196	2	,	,	PUNCT
ejpam-6154	196	3	γn+1	γn+1	ADP
ejpam-6154	196	4	≤(1−	≤(1−	PROPN
ejpam-6154	196	5	αn(1−	αn(1−	PROPN
ejpam-6154	196	6	2ρ2))γn	2ρ2))γn	NUM
ejpam-6154	196	7	+	+	PUNCT
ejpam-6154	196	8	αn(1−	αn(1−	NUM
ejpam-6154	196	9	2ρ2	2ρ2	NUM
ejpam-6154	196	10	)	)	PUNCT
ejpam-6154	196	11	(	(	PUNCT
ejpam-6154	196	12	1−	1−	NUM
ejpam-6154	196	13	2ρ2	2ρ2	NUM
ejpam-6154	196	14	)	)	PUNCT
ejpam-6154	196	15	(	(	PUNCT
ejpam-6154	196	16	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	196	17	z∥2	z∥2	NOUN
ejpam-6154	196	18	+	+	CCONJ
ejpam-6154	196	19	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	196	20	y∥2	y∥2	NOUN
ejpam-6154	196	21	)	)	PUNCT
ejpam-6154	196	22	.	.	PUNCT
ejpam-6154	197	1	≤max	≤max	PUNCT
ejpam-6154	197	2	{	{	PUNCT
ejpam-6154	197	3	γn	γn	NOUN
ejpam-6154	197	4	,	,	PUNCT
ejpam-6154	197	5	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	197	6	z∥2	z∥2	NOUN
ejpam-6154	197	7	+	+	CCONJ
ejpam-6154	197	8	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	197	9	y∥2	y∥2	NOUN
ejpam-6154	197	10	}	}	PUNCT
ejpam-6154	197	11	.	.	PUNCT
ejpam-6154	198	1	by	by	ADP
ejpam-6154	198	2	induction	induction	NOUN
ejpam-6154	198	3	,	,	PUNCT
ejpam-6154	198	4	we	we	PRON
ejpam-6154	198	5	deduce	deduce	VERB
ejpam-6154	198	6	that	that	PRON
ejpam-6154	198	7	γn+1	γn+1	NUM
ejpam-6154	198	8	≤max	≤max	NUM
ejpam-6154	198	9	{	{	PUNCT
ejpam-6154	198	10	γ0	γ0	PROPN
ejpam-6154	198	11	,	,	PUNCT
ejpam-6154	198	12	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	198	13	z∥2	z∥2	NOUN
ejpam-6154	198	14	+	+	CCONJ
ejpam-6154	198	15	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	198	16	y∥2	y∥2	NOUN
ejpam-6154	198	17	}	}	PUNCT
ejpam-6154	198	18	.	.	PUNCT
ejpam-6154	199	1	thus	thus	ADV
ejpam-6154	199	2	γn	γn	ADP
ejpam-6154	199	3	:	:	PUNCT
ejpam-6154	199	4	=	=	X
ejpam-6154	199	5	∥zn	∥zn	ADP
ejpam-6154	199	6	−	−	PROPN
ejpam-6154	199	7	z∥2	z∥2	NOUN
ejpam-6154	199	8	+	+	NUM
ejpam-6154	199	9	∥yn	∥yn	NUM
ejpam-6154	199	10	−	−	NOUN
ejpam-6154	199	11	y∥2	y∥2	NOUN
ejpam-6154	199	12	is	be	AUX
ejpam-6154	199	13	bounded	bound	VERB
ejpam-6154	199	14	,	,	PUNCT
ejpam-6154	199	15	which	which	PRON
ejpam-6154	199	16	further	far	ADV
ejpam-6154	199	17	implies	imply	VERB
ejpam-6154	199	18	that	that	SCONJ
ejpam-6154	199	19	{	{	PUNCT
ejpam-6154	199	20	(	(	PUNCT
ejpam-6154	199	21	yn	yn	PROPN
ejpam-6154	199	22	,	,	PUNCT
ejpam-6154	199	23	zn	zn	PROPN
ejpam-6154	199	24	)	)	PUNCT
ejpam-6154	199	25	}	}	PUNCT
ejpam-6154	199	26	is	be	AUX
ejpam-6154	199	27	also	also	ADV
ejpam-6154	199	28	bounded	bound	VERB
ejpam-6154	199	29	.	.	PUNCT
ejpam-6154	200	1	by	by	ADP
ejpam-6154	200	2	equation	equation	NOUN
ejpam-6154	200	3	(	(	PUNCT
ejpam-6154	200	4	19	19	NUM
ejpam-6154	200	5	)	)	PUNCT
ejpam-6154	200	6	,	,	PUNCT
ejpam-6154	200	7	we	we	PRON
ejpam-6154	200	8	have	have	VERB
ejpam-6154	200	9	τn	τn	PART
ejpam-6154	200	10	(	(	PUNCT
ejpam-6154	200	11	(	(	PUNCT
ejpam-6154	200	12	1−	1−	NUM
ejpam-6154	200	13	αn(1−	αn(1−	NUM
ejpam-6154	200	14	2ρ2))λ−	2ρ2))λ−	NUM
ejpam-6154	200	15	τn	τn	NOUN
ejpam-6154	200	16	)	)	PUNCT
ejpam-6154	200	17	(	(	PUNCT
ejpam-6154	200	18	∥zn	∥zn	NUM
ejpam-6154	200	19	−	−	NOUN
ejpam-6154	200	20	u2zn	u2zn	PUNCT
ejpam-6154	201	1	−a∗	−a∗	PROPN
ejpam-6154	202	1	2(a2zn	2(a2zn	INTJ
ejpam-6154	202	2	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	203	1	+	+	CCONJ
ejpam-6154	203	2	∥yn	∥yn	PROPN
ejpam-6154	203	3	−	−	PROPN
ejpam-6154	203	4	u1yn	u1yn	PRON
ejpam-6154	204	1	−a∗	−a∗	PROPN
ejpam-6154	204	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	204	3	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	204	4	)	)	PUNCT
ejpam-6154	205	1	≤	≤	NOUN
ejpam-6154	205	2	∥zn	∥zn	PART
ejpam-6154	206	1	−	−	PROPN
ejpam-6154	206	2	z∥2	z∥2	NOUN
ejpam-6154	206	3	−	−	PROPN
ejpam-6154	206	4	∥zn+1	∥zn+1	NOUN
ejpam-6154	206	5	−	−	NOUN
ejpam-6154	206	6	z∥2	z∥2	NOUN
ejpam-6154	206	7	+	+	NUM
ejpam-6154	206	8	∥yn	∥yn	ADJ
ejpam-6154	206	9	−	−	PROPN
ejpam-6154	206	10	y∥2	y∥2	NOUN
ejpam-6154	206	11	−	−	PROPN
ejpam-6154	206	12	∥yn+1	∥yn+1	SYM
ejpam-6154	206	13	−	−	NOUN
ejpam-6154	206	14	y∥2	y∥2	NOUN
ejpam-6154	206	15	+	+	CCONJ
ejpam-6154	206	16	2αn	2αn	ADJ
ejpam-6154	206	17	(	(	PUNCT
ejpam-6154	206	18	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	206	19	z∥2	z∥2	NOUN
ejpam-6154	206	20	+	+	CCONJ
ejpam-6154	206	21	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	206	22	y∥2	y∥2	NOUN
ejpam-6154	206	23	)	)	PUNCT
ejpam-6154	206	24	.	.	PUNCT
ejpam-6154	207	1	since	since	SCONJ
ejpam-6154	207	2	inf	inf	PROPN
ejpam-6154	207	3	n≥1	n≥1	PROPN
ejpam-6154	207	4	τn	τn	ADP
ejpam-6154	207	5	(	(	PUNCT
ejpam-6154	207	6	(	(	PUNCT
ejpam-6154	207	7	1−	1−	NUM
ejpam-6154	207	8	αn(1−	αn(1−	NUM
ejpam-6154	207	9	2ρ2))λ−	2ρ2))λ−	NUM
ejpam-6154	207	10	τn	τn	NOUN
ejpam-6154	207	11	)	)	PUNCT
ejpam-6154	207	12	≥	≥	PROPN
ejpam-6154	207	13	β	β	NOUN
ejpam-6154	207	14	,	,	PUNCT
ejpam-6154	207	15	we	we	PRON
ejpam-6154	207	16	therefore	therefore	ADV
ejpam-6154	207	17	deduce	deduce	VERB
ejpam-6154	207	18	that	that	SCONJ
ejpam-6154	207	19	lim	lim	PROPN
ejpam-6154	207	20	sup	sup	PROPN
ejpam-6154	207	21	n→∞	n→∞	X
ejpam-6154	207	22	(	(	PUNCT
ejpam-6154	207	23	∥zn	∥zn	NUM
ejpam-6154	207	24	−	−	NOUN
ejpam-6154	207	25	u2zn	u2zn	PUNCT
ejpam-6154	208	1	−a∗	−a∗	PROPN
ejpam-6154	209	1	2(a2zn	2(a2zn	INTJ
ejpam-6154	209	2	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	210	1	+	+	CCONJ
ejpam-6154	210	2	∥yn	∥yn	PROPN
ejpam-6154	210	3	−	−	PROPN
ejpam-6154	210	4	u1yn	u1yn	PRON
ejpam-6154	211	1	−a∗	−a∗	PROPN
ejpam-6154	211	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	211	3	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	211	4	)	)	PUNCT
ejpam-6154	212	1	=	=	PUNCT
ejpam-6154	212	2	0	0	X
ejpam-6154	212	3	.	.	PUNCT
ejpam-6154	213	1	this	this	PRON
ejpam-6154	213	2	turns	turn	VERB
ejpam-6154	213	3	to	to	ADP
ejpam-6154	213	4	implies	implie	NOUN
ejpam-6154	213	5	that	that	SCONJ
ejpam-6154	213	6	lim	lim	PROPN
ejpam-6154	213	7	sup	sup	VERB
ejpam-6154	213	8	n→∞	n→∞	NUM
ejpam-6154	213	9	∥yn	∥yn	PROPN
ejpam-6154	213	10	−	−	PROPN
ejpam-6154	213	11	u1yn	u1yn	PROPN
ejpam-6154	214	1	−a∗	−a∗	PROPN
ejpam-6154	214	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	214	3	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	214	4	=	=	SYM
ejpam-6154	214	5	0	0	NUM
ejpam-6154	214	6	,	,	PUNCT
ejpam-6154	214	7	and	and	CCONJ
ejpam-6154	214	8	lim	lim	PROPN
ejpam-6154	214	9	sup	sup	PROPN
ejpam-6154	214	10	n→∞	n→∞	NUM
ejpam-6154	214	11	∥zn	∥zn	PRON
ejpam-6154	215	1	−	−	NOUN
ejpam-6154	216	1	u2zn	u2zn	PUNCT
ejpam-6154	217	1	−a∗	−a∗	PROPN
ejpam-6154	217	2	2(a2zn	2(a2zn	INTJ
ejpam-6154	218	1	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	219	1	=	=	NOUN
ejpam-6154	220	1	0	0	PROPN
ejpam-6154	220	2	.	.	PUNCT
ejpam-6154	221	1	(	(	PUNCT
ejpam-6154	221	2	20	20	NUM
ejpam-6154	221	3	)	)	PUNCT
ejpam-6154	221	4	since	since	SCONJ
ejpam-6154	221	5	u1	u1	NOUN
ejpam-6154	221	6	is	be	AUX
ejpam-6154	221	7	quasi	quasi	ADJ
ejpam-6154	221	8	-	-	ADJ
ejpam-6154	221	9	nonexpansive	nonexpansive	ADJ
ejpam-6154	221	10	mapping	mapping	NOUN
ejpam-6154	221	11	,	,	PUNCT
ejpam-6154	221	12	by	by	ADP
ejpam-6154	221	13	remark	remark	NOUN
ejpam-6154	221	14	2	2	NUM
ejpam-6154	221	15	,	,	PUNCT
ejpam-6154	221	16	we	we	PRON
ejpam-6154	221	17	have	have	VERB
ejpam-6154	221	18	1	1	NUM
ejpam-6154	221	19	2	2	NUM
ejpam-6154	221	20	∥yn	∥yn	NOUN
ejpam-6154	221	21	−	−	NOUN
ejpam-6154	221	22	u1yn∥2	u1yn∥2	NOUN
ejpam-6154	222	1	+	+	CCONJ
ejpam-6154	222	2	⟨a1yn	⟨a1yn	DET
ejpam-6154	222	3	−a2zn	−a2zn	NUM
ejpam-6154	222	4	,	,	PUNCT
ejpam-6154	222	5	a1yn	a1yn	PROPN
ejpam-6154	222	6	−a1y⟩	−a1y⟩	NOUN
ejpam-6154	222	7	≤	≤	PUNCT
ejpam-6154	223	1	⟨yn	⟨yn	ADV
ejpam-6154	224	1	−	−	ADP
ejpam-6154	224	2	u1yn	u1yn	PROPN
ejpam-6154	224	3	,	,	PUNCT
ejpam-6154	224	4	yn	yn	PROPN
ejpam-6154	224	5	−	−	PROPN
ejpam-6154	224	6	y⟩	y⟩	PROPN
ejpam-6154	224	7	l.	l.	PROPN
ejpam-6154	224	8	b.	b.	PROPN
ejpam-6154	224	9	mohammed	mohammed	PROPN
ejpam-6154	224	10	,	,	PUNCT
ejpam-6154	224	11	a.	a.	PROPN
ejpam-6154	224	12	kılıçman	kılıçman	PROPN
ejpam-6154	224	13	,	,	PUNCT
ejpam-6154	224	14	d.	d.	PROPN
ejpam-6154	224	15	bamanga	bamanga	PROPN
ejpam-6154	224	16	/	/	SYM
ejpam-6154	224	17	eur	eur	PROPN
ejpam-6154	224	18	.	.	PUNCT
ejpam-6154	225	1	j.	j.	PROPN
ejpam-6154	225	2	pure	pure	PROPN
ejpam-6154	225	3	appl	appl	PROPN
ejpam-6154	225	4	.	.	PROPN
ejpam-6154	225	5	math	math	PROPN
ejpam-6154	225	6	,	,	PUNCT
ejpam-6154	225	7	18	18	NUM
ejpam-6154	225	8	(	(	PUNCT
ejpam-6154	225	9	4	4	NUM
ejpam-6154	225	10	)	)	PUNCT
ejpam-6154	225	11	(	(	PUNCT
ejpam-6154	225	12	2025	2025	NUM
ejpam-6154	225	13	)	)	PUNCT
ejpam-6154	225	14	,	,	PUNCT
ejpam-6154	225	15	6154	6154	NUM
ejpam-6154	225	16	9	9	NUM
ejpam-6154	225	17	of	of	ADP
ejpam-6154	225	18	18	18	NUM
ejpam-6154	225	19	+	+	CCONJ
ejpam-6154	225	20	⟨a1yn	⟨a1yn	DET
ejpam-6154	225	21	−a2zn	−a2zn	NUM
ejpam-6154	225	22	,	,	PUNCT
ejpam-6154	225	23	a1yn	a1yn	X
ejpam-6154	225	24	−a1y⟩	−a1y⟩	X
ejpam-6154	226	1	=	=	PUNCT
ejpam-6154	227	1	⟨yn	⟨yn	PROPN
ejpam-6154	227	2	−	−	X
ejpam-6154	228	1	u1yn	u1yn	PRON
ejpam-6154	228	2	−a∗	−a∗	PROPN
ejpam-6154	228	3	1(a1yn	1(a1yn	VERB
ejpam-6154	228	4	−a2zn	−a2zn	NUM
ejpam-6154	228	5	)	)	PUNCT
ejpam-6154	228	6	,	,	PUNCT
ejpam-6154	229	1	yn	yn	PROPN
ejpam-6154	229	2	−	−	PROPN
ejpam-6154	229	3	y⟩	y⟩	NOUN
ejpam-6154	229	4	≤	≤	NUM
ejpam-6154	229	5	∥yn	∥yn	PROPN
ejpam-6154	229	6	−	−	PROPN
ejpam-6154	229	7	u1yn	u1yn	PROPN
ejpam-6154	230	1	−a∗	−a∗	PROPN
ejpam-6154	230	2	1(a1yn	1(a1yn	INTJ
ejpam-6154	230	3	−a2zn)∥∥yn	−a2zn)∥∥yn	PROPN
ejpam-6154	230	4	−	−	PROPN
ejpam-6154	231	1	y∥.	y∥.	NOUN
ejpam-6154	231	2	(	(	PUNCT
ejpam-6154	231	3	21	21	NUM
ejpam-6154	231	4	)	)	PUNCT
ejpam-6154	231	5	since	since	SCONJ
ejpam-6154	231	6	{	{	PUNCT
ejpam-6154	231	7	∥yn	∥yn	NUM
ejpam-6154	231	8	−	−	NOUN
ejpam-6154	231	9	y∥	y∥	NOUN
ejpam-6154	231	10	}	}	PUNCT
ejpam-6154	231	11	is	be	AUX
ejpam-6154	231	12	bounded	bound	VERB
ejpam-6154	231	13	,	,	PUNCT
ejpam-6154	231	14	thus	thus	ADV
ejpam-6154	231	15	,	,	PUNCT
ejpam-6154	231	16	by	by	ADP
ejpam-6154	231	17	equation	equation	NOUN
ejpam-6154	231	18	(	(	PUNCT
ejpam-6154	231	19	20	20	NUM
ejpam-6154	231	20	)	)	PUNCT
ejpam-6154	231	21	we	we	PRON
ejpam-6154	231	22	deduce	deduce	VERB
ejpam-6154	231	23	that	that	SCONJ
ejpam-6154	231	24	lim	lim	PROPN
ejpam-6154	231	25	sup	sup	VERB
ejpam-6154	231	26	n→∞	n→∞	NUM
ejpam-6154	231	27	∥yn	∥yn	PROPN
ejpam-6154	231	28	−	−	PROPN
ejpam-6154	231	29	u1yn∥	u1yn∥	VERB
ejpam-6154	231	30	=	=	X
ejpam-6154	231	31	0	0	NUM
ejpam-6154	231	32	.	.	PUNCT
ejpam-6154	232	1	(	(	PUNCT
ejpam-6154	232	2	22	22	NUM
ejpam-6154	232	3	)	)	PUNCT
ejpam-6154	232	4	similarly	similarly	ADV
ejpam-6154	232	5	,	,	PUNCT
ejpam-6154	232	6	lim	lim	PROPN
ejpam-6154	232	7	sup	sup	PROPN
ejpam-6154	232	8	n→∞	n→∞	NUM
ejpam-6154	232	9	∥zn	∥zn	PART
ejpam-6154	232	10	−	−	PROPN
ejpam-6154	232	11	u2zn∥	u2zn∥	NOUN
ejpam-6154	232	12	=	=	NOUN
ejpam-6154	232	13	0	0	PROPN
ejpam-6154	232	14	.	.	PUNCT
ejpam-6154	233	1	(	(	PUNCT
ejpam-6154	233	2	23	23	NUM
ejpam-6154	233	3	)	)	PUNCT
ejpam-6154	233	4	on	on	ADP
ejpam-6154	233	5	the	the	DET
ejpam-6154	233	6	other	other	ADJ
ejpam-6154	233	7	hand	hand	NOUN
ejpam-6154	233	8	,	,	PUNCT
ejpam-6154	233	9	∥a1yn	∥a1yn	X
ejpam-6154	233	10	−a2zn∥2	−a2zn∥2	NOUN
ejpam-6154	233	11	=	=	PUNCT
ejpam-6154	233	12	⟨a1yn	⟨a1yn	PRON
ejpam-6154	233	13	−a2zn	−a2zn	NUM
ejpam-6154	233	14	,	,	PUNCT
ejpam-6154	233	15	a1yn	a1yn	PROPN
ejpam-6154	233	16	−a2zn⟩	−a2zn⟩	PROPN
ejpam-6154	233	17	=	=	PUNCT
ejpam-6154	234	1	⟨a1yn	⟨a1yn	PRON
ejpam-6154	234	2	−a2zn	−a2zn	NUM
ejpam-6154	234	3	,	,	PUNCT
ejpam-6154	234	4	a1yn	a1yn	PROPN
ejpam-6154	234	5	−a1y⟩+	−a1y⟩+	NOUN
ejpam-6154	234	6	⟨a2zn	⟨a2zn	PROPN
ejpam-6154	234	7	−a1yn	−a1yn	NUM
ejpam-6154	234	8	,	,	PUNCT
ejpam-6154	234	9	a2zn	a2zn	PUNCT
ejpam-6154	234	10	−a2z⟩	−a2z⟩	VERB
ejpam-6154	234	11	,	,	PUNCT
ejpam-6154	234	12	=	=	SYM
ejpam-6154	234	13	⟨a∗	⟨a∗	NOUN
ejpam-6154	234	14	1(a1yn	1(a1yn	NUM
ejpam-6154	234	15	−a2zn	−a2zn	NUM
ejpam-6154	234	16	)	)	PUNCT
ejpam-6154	234	17	,	,	PUNCT
ejpam-6154	235	1	yn	yn	PRON
ejpam-6154	235	2	−	−	PROPN
ejpam-6154	235	3	y⟩+	y⟩+	PROPN
ejpam-6154	235	4	⟨a∗	⟨a∗	VERB
ejpam-6154	235	5	2(a2zn	2(a2zn	NOUN
ejpam-6154	235	6	−a1yn	−a1yn	NUM
ejpam-6154	235	7	)	)	PUNCT
ejpam-6154	235	8	,	,	PUNCT
ejpam-6154	235	9	zn	zn	PROPN
ejpam-6154	235	10	−	−	PROPN
ejpam-6154	235	11	z⟩	z⟩	X
ejpam-6154	235	12	≤∥a∗	≤∥a∗	PROPN
ejpam-6154	235	13	1(a1yn	1(a1yn	NUM
ejpam-6154	235	14	−a2zn	−a2zn	NUM
ejpam-6154	235	15	)	)	PUNCT
ejpam-6154	236	1	+	+	CCONJ
ejpam-6154	236	2	(	(	PUNCT
ejpam-6154	236	3	yn	yn	PROPN
ejpam-6154	236	4	−	−	PROPN
ejpam-6154	236	5	u1yn)−	u1yn)−	NOUN
ejpam-6154	236	6	(	(	PUNCT
ejpam-6154	236	7	yn	yn	INTJ
ejpam-6154	236	8	−	−	PROPN
ejpam-6154	236	9	u1yn)∥∥yn	u1yn)∥∥yn	PUNCT
ejpam-6154	236	10	−	−	PROPN
ejpam-6154	236	11	y∥∥	y∥∥	PROPN
ejpam-6154	236	12	+	+	CCONJ
ejpam-6154	236	13	∥a∗	∥a∗	PROPN
ejpam-6154	236	14	2(a2zn	2(a2zn	NOUN
ejpam-6154	236	15	−a1yn	−a1yn	NUM
ejpam-6154	236	16	)	)	PUNCT
ejpam-6154	237	1	+	+	CCONJ
ejpam-6154	237	2	(	(	PUNCT
ejpam-6154	237	3	zn	zn	NUM
ejpam-6154	237	4	−	−	PROPN
ejpam-6154	237	5	u2zn)−	u2zn)−	NOUN
ejpam-6154	237	6	(	(	PUNCT
ejpam-6154	237	7	zn	zn	NOUN
ejpam-6154	237	8	−	−	PROPN
ejpam-6154	237	9	u2zn)∥∥zn	u2zn)∥∥zn	PRON
ejpam-6154	237	10	−	−	PROPN
ejpam-6154	237	11	z∥	z∥	ADJ
ejpam-6154	237	12	≤∥a∗	≤∥a∗	NOUN
ejpam-6154	237	13	1(a1yn	1(a1yn	NUM
ejpam-6154	237	14	−a2zn)−	−a2zn)−	PROPN
ejpam-6154	237	15	(	(	PUNCT
ejpam-6154	237	16	yn	yn	INTJ
ejpam-6154	237	17	−	−	PROPN
ejpam-6154	237	18	u1yn)∥∥yn	u1yn)∥∥yn	PART
ejpam-6154	237	19	−	−	PROPN
ejpam-6154	237	20	y∥	y∥	NOUN
ejpam-6154	237	21	+	+	CCONJ
ejpam-6154	237	22	∥yn	∥yn	PROPN
ejpam-6154	237	23	−	−	PROPN
ejpam-6154	237	24	u1yn∥∥yn	u1yn∥∥yn	ADJ
ejpam-6154	237	25	−	−	NOUN
ejpam-6154	237	26	y∥	y∥	NOUN
ejpam-6154	237	27	+	+	PUNCT
ejpam-6154	237	28	∥a∗	∥a∗	PROPN
ejpam-6154	237	29	2(a2zn	2(a2zn	NUM
ejpam-6154	237	30	−a1yn)−	−a1yn)−	PROPN
ejpam-6154	237	31	(	(	PUNCT
ejpam-6154	237	32	zn	zn	PROPN
ejpam-6154	237	33	−	−	PROPN
ejpam-6154	237	34	u2zn)∥∥zn	u2zn)∥∥zn	PRON
ejpam-6154	238	1	−	−	PROPN
ejpam-6154	238	2	z∥	z∥	PROPN
ejpam-6154	238	3	+	+	NUM
ejpam-6154	238	4	∥zn	∥zn	PROPN
ejpam-6154	238	5	−	−	PROPN
ejpam-6154	238	6	u2zn∥∥zn	u2zn∥∥zn	ADJ
ejpam-6154	238	7	−	−	PROPN
ejpam-6154	238	8	z∥.	z∥.	PROPN
ejpam-6154	238	9	thus	thus	ADV
ejpam-6154	238	10	,	,	PUNCT
ejpam-6154	238	11	by	by	ADP
ejpam-6154	238	12	(	(	PUNCT
ejpam-6154	238	13	20	20	NUM
ejpam-6154	238	14	)	)	PUNCT
ejpam-6154	238	15	and	and	CCONJ
ejpam-6154	238	16	the	the	DET
ejpam-6154	238	17	fact	fact	NOUN
ejpam-6154	238	18	that	that	SCONJ
ejpam-6154	238	19	{	{	PUNCT
ejpam-6154	238	20	∥zn	∥zn	NUM
ejpam-6154	238	21	−	−	NOUN
ejpam-6154	238	22	z∥	z∥	NUM
ejpam-6154	238	23	}	}	PUNCT
ejpam-6154	238	24	and	and	CCONJ
ejpam-6154	238	25	{	{	PUNCT
ejpam-6154	238	26	∥yn	∥yn	NOUN
ejpam-6154	238	27	−	−	NOUN
ejpam-6154	238	28	y∥	y∥	NOUN
ejpam-6154	238	29	}	}	PUNCT
ejpam-6154	238	30	are	be	AUX
ejpam-6154	238	31	bounded	bound	VERB
ejpam-6154	238	32	,	,	PUNCT
ejpam-6154	238	33	we	we	PRON
ejpam-6154	238	34	see	see	VERB
ejpam-6154	238	35	that	that	SCONJ
ejpam-6154	238	36	lim	lim	PROPN
ejpam-6154	238	37	sup	sup	VERB
ejpam-6154	238	38	n→∞	n→∞	NUM
ejpam-6154	238	39	∥a1yn	∥a1yn	PUNCT
ejpam-6154	238	40	−a2zn∥	−a2zn∥	NOUN
ejpam-6154	238	41	=	=	NOUN
ejpam-6154	238	42	0	0	X
ejpam-6154	238	43	.	.	PUNCT
ejpam-6154	239	1	this	this	PRON
ejpam-6154	239	2	completes	complete	VERB
ejpam-6154	239	3	the	the	DET
ejpam-6154	239	4	proof	proof	NOUN
ejpam-6154	239	5	of	of	ADP
ejpam-6154	239	6	this	this	DET
ejpam-6154	239	7	lemma	lemma	PROPN
ejpam-6154	239	8	.	.	PUNCT
ejpam-6154	240	1	we	we	PRON
ejpam-6154	240	2	are	be	AUX
ejpam-6154	240	3	now	now	ADV
ejpam-6154	240	4	in	in	ADP
ejpam-6154	240	5	a	a	DET
ejpam-6154	240	6	position	position	NOUN
ejpam-6154	240	7	to	to	PART
ejpam-6154	240	8	prove	prove	VERB
ejpam-6154	240	9	that	that	SCONJ
ejpam-6154	240	10	(	(	PUNCT
ejpam-6154	240	11	yn	yn	PROPN
ejpam-6154	240	12	,	,	PUNCT
ejpam-6154	240	13	zn	zn	PROPN
ejpam-6154	240	14	)	)	PUNCT
ejpam-6154	240	15	→	→	SYM
ejpam-6154	240	16	(	(	PUNCT
ejpam-6154	240	17	y	y	PROPN
ejpam-6154	240	18	,	,	PUNCT
ejpam-6154	240	19	z	z	NOUN
ejpam-6154	240	20	)	)	PUNCT
ejpam-6154	240	21	.	.	PUNCT
ejpam-6154	241	1	theorem	theorem	NOUN
ejpam-6154	241	2	1	1	X
ejpam-6154	241	3	.	.	PUNCT
ejpam-6154	241	4	suppose	suppose	VERB
ejpam-6154	241	5	conditions	condition	NOUN
ejpam-6154	241	6	(	(	PUNCT
ejpam-6154	241	7	k1)–(k5	k1)–(k5	PROPN
ejpam-6154	241	8	)	)	PUNCT
ejpam-6154	241	9	are	be	AUX
ejpam-6154	241	10	satisfied	satisfied	ADJ
ejpam-6154	241	11	,	,	PUNCT
ejpam-6154	241	12	and	and	CCONJ
ejpam-6154	241	13	that	that	PRON
ejpam-6154	241	14	s	s	AUX
ejpam-6154	241	15	̸=	̸=	PROPN
ejpam-6154	241	16	∅.	∅.	ADP
ejpam-6154	241	17	then	then	ADV
ejpam-6154	241	18	the	the	DET
ejpam-6154	241	19	sequence	sequence	NOUN
ejpam-6154	241	20	{	{	PUNCT
ejpam-6154	241	21	(	(	PUNCT
ejpam-6154	241	22	yn	yn	PROPN
ejpam-6154	241	23	,	,	PUNCT
ejpam-6154	241	24	zn	zn	PROPN
ejpam-6154	241	25	)	)	PUNCT
ejpam-6154	241	26	}	}	PUNCT
ejpam-6154	241	27	generated	generate	VERB
ejpam-6154	241	28	by	by	ADP
ejpam-6154	241	29	algorithm	algorithm	NOUN
ejpam-6154	241	30	(	(	PUNCT
ejpam-6154	241	31	10	10	NUM
ejpam-6154	241	32	)	)	PUNCT
ejpam-6154	241	33	converges	converge	VERB
ejpam-6154	241	34	strongly	strongly	ADV
ejpam-6154	241	35	to	to	ADP
ejpam-6154	241	36	(	(	PUNCT
ejpam-6154	241	37	y	y	PROPN
ejpam-6154	241	38	,	,	PUNCT
ejpam-6154	241	39	z	z	NOUN
ejpam-6154	241	40	)	)	PUNCT
ejpam-6154	241	41	∈	∈	PROPN
ejpam-6154	241	42	s.	s.	PROPN
ejpam-6154	241	43	proof	proof	PROPN
ejpam-6154	241	44	.	.	PUNCT
ejpam-6154	242	1	let	let	VERB
ejpam-6154	242	2	(	(	PUNCT
ejpam-6154	242	3	y	y	NOUN
ejpam-6154	242	4	,	,	PUNCT
ejpam-6154	242	5	z	z	NOUN
ejpam-6154	242	6	)	)	PUNCT
ejpam-6154	242	7	∈	∈	PROPN
ejpam-6154	242	8	s	s	NOUN
ejpam-6154	242	9	,	,	PUNCT
ejpam-6154	242	10	then	then	ADV
ejpam-6154	242	11	by	by	ADP
ejpam-6154	242	12	lemma	lemma	PROPN
ejpam-6154	242	13	1	1	NUM
ejpam-6154	242	14	,	,	PUNCT
ejpam-6154	242	15	we	we	PRON
ejpam-6154	242	16	see	see	VERB
ejpam-6154	242	17	that	that	DET
ejpam-6154	242	18	u1	u1	NOUN
ejpam-6154	242	19	is	be	AUX
ejpam-6154	242	20	quasi	quasi	ADJ
ejpam-6154	242	21	-	-	ADJ
ejpam-6154	242	22	nonexpansive	nonexpansive	ADJ
ejpam-6154	242	23	,	,	PUNCT
ejpam-6154	242	24	and	and	CCONJ
ejpam-6154	242	25	by	by	ADP
ejpam-6154	242	26	algorithm	algorithm	NOUN
ejpam-6154	242	27	(	(	PUNCT
ejpam-6154	242	28	10	10	NUM
ejpam-6154	242	29	)	)	PUNCT
ejpam-6154	242	30	,	,	PUNCT
ejpam-6154	242	31	we	we	PRON
ejpam-6154	242	32	have	have	VERB
ejpam-6154	242	33	∥yn+1	∥yn+1	VERB
ejpam-6154	242	34	−	−	NOUN
ejpam-6154	242	35	y∥2	y∥2	ADJ
ejpam-6154	242	36	=	=	SYM
ejpam-6154	242	37	∥αn(f1(vn)−	∥αn(f1(vn)−	NOUN
ejpam-6154	242	38	y	y	NOUN
ejpam-6154	242	39	)	)	PUNCT
ejpam-6154	243	1	+	+	CCONJ
ejpam-6154	243	2	(	(	PUNCT
ejpam-6154	243	3	1−	1−	NUM
ejpam-6154	243	4	αn)(u1vn	αn)(u1vn	NUM
ejpam-6154	243	5	−	−	PROPN
ejpam-6154	243	6	y)∥2	y)∥2	NOUN
ejpam-6154	243	7	=	=	NOUN
ejpam-6154	243	8	α2	α2	ADJ
ejpam-6154	243	9	n	n	CCONJ
ejpam-6154	243	10	∥f1(vn)−	∥f1(vn)−	PROPN
ejpam-6154	243	11	y∥2	y∥2	NOUN
ejpam-6154	243	12	+	+	CCONJ
ejpam-6154	243	13	(	(	PUNCT
ejpam-6154	243	14	1−	1−	NUM
ejpam-6154	243	15	αn	αn	NOUN
ejpam-6154	243	16	)	)	PUNCT
ejpam-6154	244	1	2∥u1vn	2∥u1vn	NUM
ejpam-6154	244	2	−	−	NOUN
ejpam-6154	244	3	y∥2	y∥2	NOUN
ejpam-6154	244	4	+	+	CCONJ
ejpam-6154	244	5	2(1−	2(1−	NUM
ejpam-6154	244	6	αn)αn	αn)αn	NUM
ejpam-6154	244	7	⟨f1(vn)−	⟨f1(vn)−	X
ejpam-6154	244	8	y	y	PROPN
ejpam-6154	244	9	,	,	PUNCT
ejpam-6154	244	10	u1vn	u1vn	PROPN
ejpam-6154	244	11	−	−	PROPN
ejpam-6154	244	12	y⟩	y⟩	NOUN
ejpam-6154	244	13	=(	=(	PROPN
ejpam-6154	244	14	α2	α2	PROPN
ejpam-6154	244	15	nρ	nρ	PROPN
ejpam-6154	244	16	2	2	NUM
ejpam-6154	244	17	+	+	CCONJ
ejpam-6154	244	18	(	(	PUNCT
ejpam-6154	244	19	1−	1−	NUM
ejpam-6154	244	20	αn	αn	NOUN
ejpam-6154	244	21	)	)	PUNCT
ejpam-6154	244	22	2)∥vn	2)∥vn	X
ejpam-6154	245	1	−	−	PROPN
ejpam-6154	245	2	y∥2	y∥2	NOUN
ejpam-6154	245	3	+	+	CCONJ
ejpam-6154	245	4	α2	α2	ADJ
ejpam-6154	245	5	n	n	CCONJ
ejpam-6154	245	6	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	245	7	y∥2	y∥2	PROPN
ejpam-6154	245	8	l.	l.	PROPN
ejpam-6154	245	9	b.	b.	PROPN
ejpam-6154	245	10	mohammed	mohammed	PROPN
ejpam-6154	245	11	,	,	PUNCT
ejpam-6154	245	12	a.	a.	PROPN
ejpam-6154	245	13	kılıçman	kılıçman	PROPN
ejpam-6154	245	14	,	,	PUNCT
ejpam-6154	245	15	d.	d.	PROPN
ejpam-6154	245	16	bamanga	bamanga	PROPN
ejpam-6154	245	17	/	/	SYM
ejpam-6154	245	18	eur	eur	PROPN
ejpam-6154	245	19	.	.	PUNCT
ejpam-6154	246	1	j.	j.	PROPN
ejpam-6154	246	2	pure	pure	PROPN
ejpam-6154	246	3	appl	appl	PROPN
ejpam-6154	246	4	.	.	PROPN
ejpam-6154	246	5	math	math	PROPN
ejpam-6154	246	6	,	,	PUNCT
ejpam-6154	246	7	18	18	NUM
ejpam-6154	246	8	(	(	PUNCT
ejpam-6154	246	9	4	4	NUM
ejpam-6154	246	10	)	)	PUNCT
ejpam-6154	246	11	(	(	PUNCT
ejpam-6154	246	12	2025	2025	NUM
ejpam-6154	246	13	)	)	PUNCT
ejpam-6154	246	14	,	,	PUNCT
ejpam-6154	246	15	6154	6154	NUM
ejpam-6154	246	16	10	10	NUM
ejpam-6154	246	17	of	of	ADP
ejpam-6154	246	18	18	18	NUM
ejpam-6154	246	19	+	+	CCONJ
ejpam-6154	246	20	2(1−	2(1−	NUM
ejpam-6154	246	21	αn)αn	αn)αn	NUM
ejpam-6154	246	22	⟨f1(vn)−	⟨f1(vn)−	NOUN
ejpam-6154	246	23	y	y	PROPN
ejpam-6154	246	24	,	,	PUNCT
ejpam-6154	246	25	u1vn	u1vn	ADV
ejpam-6154	246	26	−	−	NOUN
ejpam-6154	246	27	y⟩	y⟩	NOUN
ejpam-6154	246	28	,	,	PUNCT
ejpam-6154	246	29	and	and	CCONJ
ejpam-6154	246	30	(	(	PUNCT
ejpam-6154	246	31	24	24	NUM
ejpam-6154	246	32	)	)	PUNCT
ejpam-6154	246	33	2	2	NUM
ejpam-6154	246	34	⟨f1(vn)−	⟨f1(vn)−	NOUN
ejpam-6154	246	35	y	y	PROPN
ejpam-6154	246	36	,	,	PUNCT
ejpam-6154	246	37	u1vn	u1vn	ADV
ejpam-6154	246	38	−	−	NOUN
ejpam-6154	246	39	y⟩	y⟩	NOUN
ejpam-6154	247	1	=	=	NOUN
ejpam-6154	247	2	2	2	NUM
ejpam-6154	247	3	⟨f1(vn)−f1(y),u1vn	⟨f1(vn)−f1(y),u1vn	NUM
ejpam-6154	248	1	−	−	NUM
ejpam-6154	248	2	y⟩+	y⟩+	NOUN
ejpam-6154	248	3	2	2	NUM
ejpam-6154	248	4	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	248	5	y	y	PROPN
ejpam-6154	248	6	,	,	PUNCT
ejpam-6154	248	7	u1vn	u1vn	ADP
ejpam-6154	248	8	−	−	PROPN
ejpam-6154	248	9	y⟩	y⟩	NOUN
ejpam-6154	249	1	≤(1	≤(1	PROPN
ejpam-6154	250	1	+	+	CCONJ
ejpam-6154	250	2	ρ2)∥vn	ρ2)∥vn	PUNCT
ejpam-6154	250	3	−	−	NOUN
ejpam-6154	250	4	y∥2	y∥2	NOUN
ejpam-6154	250	5	+	+	CCONJ
ejpam-6154	250	6	2	2	NUM
ejpam-6154	250	7	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	250	8	y	y	NOUN
ejpam-6154	250	9	,	,	PUNCT
ejpam-6154	250	10	u1vn	u1vn	ADP
ejpam-6154	250	11	−	−	PROPN
ejpam-6154	251	1	y⟩	y⟩	NOUN
ejpam-6154	251	2	≤(1	≤(1	PROPN
ejpam-6154	252	1	+	+	CCONJ
ejpam-6154	252	2	ρ2)∥vn	ρ2)∥vn	PUNCT
ejpam-6154	252	3	−	−	NOUN
ejpam-6154	252	4	y∥2	y∥2	ADJ
ejpam-6154	252	5	+	+	CCONJ
ejpam-6154	252	6	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	252	7	y∥2	y∥2	NOUN
ejpam-6154	252	8	+	+	NUM
ejpam-6154	252	9	∥u1vn	∥u1vn	PUNCT
ejpam-6154	252	10	−	−	NOUN
ejpam-6154	252	11	vn∥2	vn∥2	NOUN
ejpam-6154	252	12	+	+	CCONJ
ejpam-6154	252	13	2	2	NUM
ejpam-6154	252	14	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	252	15	y	y	PROPN
ejpam-6154	252	16	,	,	PUNCT
ejpam-6154	252	17	vn	vn	ADP
ejpam-6154	252	18	−	−	PROPN
ejpam-6154	252	19	y⟩	y⟩	NOUN
ejpam-6154	252	20	.	.	PUNCT
ejpam-6154	253	1	(	(	PUNCT
ejpam-6154	253	2	25	25	NUM
ejpam-6154	253	3	)	)	PUNCT
ejpam-6154	253	4	by	by	ADP
ejpam-6154	253	5	equations	equation	NOUN
ejpam-6154	253	6	(	(	PUNCT
ejpam-6154	253	7	24	24	NUM
ejpam-6154	253	8	)	)	PUNCT
ejpam-6154	253	9	and	and	CCONJ
ejpam-6154	253	10	(	(	PUNCT
ejpam-6154	253	11	25	25	NUM
ejpam-6154	253	12	)	)	PUNCT
ejpam-6154	253	13	,	,	PUNCT
ejpam-6154	253	14	we	we	PRON
ejpam-6154	253	15	have	have	VERB
ejpam-6154	253	16	∥yn+1	∥yn+1	VERB
ejpam-6154	253	17	−	−	NOUN
ejpam-6154	253	18	y∥2	y∥2	ADJ
ejpam-6154	254	1	≤(α2	≤(α2	PROPN
ejpam-6154	254	2	nρ	nρ	PROPN
ejpam-6154	254	3	2	2	NUM
ejpam-6154	255	1	+	+	CCONJ
ejpam-6154	255	2	(	(	PUNCT
ejpam-6154	255	3	1−	1−	NUM
ejpam-6154	255	4	αn	αn	NOUN
ejpam-6154	255	5	)	)	PUNCT
ejpam-6154	256	1	2)∥vn	2)∥vn	X
ejpam-6154	257	1	−	−	PROPN
ejpam-6154	257	2	y∥2	y∥2	NOUN
ejpam-6154	257	3	+	+	CCONJ
ejpam-6154	257	4	α2	α2	ADJ
ejpam-6154	257	5	n	n	NOUN
ejpam-6154	257	6	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	257	7	y∥2	y∥2	NOUN
ejpam-6154	257	8	+	+	CCONJ
ejpam-6154	257	9	(	(	PUNCT
ejpam-6154	257	10	1−	1−	NUM
ejpam-6154	257	11	αn)αn	αn)αn	NUM
ejpam-6154	257	12	(	(	PUNCT
ejpam-6154	257	13	(	(	PUNCT
ejpam-6154	257	14	1	1	NUM
ejpam-6154	257	15	+	+	NOUN
ejpam-6154	257	16	ρ2)∥vn	ρ2)∥vn	PUNCT
ejpam-6154	257	17	−	−	NOUN
ejpam-6154	257	18	y∥2	y∥2	ADJ
ejpam-6154	257	19	+	+	CCONJ
ejpam-6154	257	20	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	257	21	y∥2	y∥2	NOUN
ejpam-6154	257	22	+	+	NUM
ejpam-6154	257	23	∥u1vn	∥u1vn	PUNCT
ejpam-6154	257	24	−	−	NOUN
ejpam-6154	257	25	vn∥2	vn∥2	NOUN
ejpam-6154	257	26	+	+	CCONJ
ejpam-6154	257	27	2	2	NUM
ejpam-6154	257	28	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	257	29	y	y	PROPN
ejpam-6154	257	30	,	,	PUNCT
ejpam-6154	257	31	vn	vn	ADP
ejpam-6154	257	32	−	−	PROPN
ejpam-6154	257	33	y⟩	y⟩	NOUN
ejpam-6154	257	34	)	)	PUNCT
ejpam-6154	257	35	≤(1−	≤(1−	PROPN
ejpam-6154	257	36	(	(	PUNCT
ejpam-6154	257	37	1−	1−	NUM
ejpam-6154	257	38	ρ2)αn)∥vn	ρ2)αn)∥vn	VERB
ejpam-6154	257	39	−	−	PROPN
ejpam-6154	257	40	y∥2	y∥2	NOUN
ejpam-6154	257	41	+	+	CCONJ
ejpam-6154	257	42	αn∥f1(y)−	αn∥f1(y)−	NOUN
ejpam-6154	257	43	y∥2	y∥2	NOUN
ejpam-6154	257	44	+	+	CCONJ
ejpam-6154	257	45	(	(	PUNCT
ejpam-6154	257	46	1−	1−	NUM
ejpam-6154	257	47	αn)αn	αn)αn	NUM
ejpam-6154	257	48	(	(	PUNCT
ejpam-6154	257	49	∥u1vn	∥u1vn	PUNCT
ejpam-6154	257	50	−	−	PROPN
ejpam-6154	257	51	vn∥2	vn∥2	NOUN
ejpam-6154	257	52	+	+	CCONJ
ejpam-6154	257	53	2	2	NUM
ejpam-6154	257	54	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	257	55	y	y	PROPN
ejpam-6154	257	56	,	,	PUNCT
ejpam-6154	257	57	vn	vn	ADP
ejpam-6154	257	58	−	−	PROPN
ejpam-6154	257	59	y⟩	y⟩	NOUN
ejpam-6154	257	60	)	)	PUNCT
ejpam-6154	257	61	.	.	PUNCT
ejpam-6154	258	1	(	(	PUNCT
ejpam-6154	258	2	26	26	NUM
ejpam-6154	258	3	)	)	PUNCT
ejpam-6154	258	4	by	by	ADP
ejpam-6154	258	5	equations	equation	NOUN
ejpam-6154	258	6	(	(	PUNCT
ejpam-6154	258	7	12	12	NUM
ejpam-6154	258	8	)	)	PUNCT
ejpam-6154	258	9	and	and	CCONJ
ejpam-6154	258	10	(	(	PUNCT
ejpam-6154	258	11	26	26	NUM
ejpam-6154	258	12	)	)	PUNCT
ejpam-6154	258	13	,	,	PUNCT
ejpam-6154	258	14	we	we	PRON
ejpam-6154	258	15	see	see	VERB
ejpam-6154	258	16	that	that	PRON
ejpam-6154	258	17	∥yn+1	∥yn+1	ADP
ejpam-6154	258	18	−	−	PROPN
ejpam-6154	258	19	y∥2	y∥2	ADJ
ejpam-6154	258	20	≤(1−	≤(1−	PROPN
ejpam-6154	258	21	(	(	PUNCT
ejpam-6154	258	22	1−	1−	NUM
ejpam-6154	258	23	ρ2)αn	ρ2)αn	NOUN
ejpam-6154	258	24	)	)	PUNCT
ejpam-6154	258	25	∥yn	∥yn	ADP
ejpam-6154	258	26	−	−	PROPN
ejpam-6154	258	27	y∥2	y∥2	NOUN
ejpam-6154	258	28	+	+	CCONJ
ejpam-6154	258	29	αn∥f1(y)−	αn∥f1(y)−	NOUN
ejpam-6154	258	30	y∥2	y∥2	NOUN
ejpam-6154	258	31	+	+	CCONJ
ejpam-6154	258	32	(	(	PUNCT
ejpam-6154	258	33	1−	1−	NUM
ejpam-6154	258	34	(	(	PUNCT
ejpam-6154	258	35	1−	1−	NUM
ejpam-6154	258	36	ρ2)αn)τ	ρ2)αn)τ	NUM
ejpam-6154	258	37	2	2	NUM
ejpam-6154	258	38	n∥u1yn	n∥u1yn	NUM
ejpam-6154	258	39	−	−	PROPN
ejpam-6154	258	40	yn	yn	PROPN
ejpam-6154	259	1	+	+	NOUN
ejpam-6154	259	2	a∗	a∗	PROPN
ejpam-6154	259	3	1(a1yn	1(a1yn	PROPN
ejpam-6154	259	4	−a2zn)∥2	−a2zn)∥2	ADJ
ejpam-6154	259	5	−	−	PROPN
ejpam-6154	259	6	2(1−	2(1−	NUM
ejpam-6154	259	7	(	(	PUNCT
ejpam-6154	259	8	1−	1−	NUM
ejpam-6154	259	9	ρ2)αn)τn	ρ2)αn)τn	NUM
ejpam-6154	260	1	⟨yn	⟨yn	NUM
ejpam-6154	260	2	−	−	PROPN
ejpam-6154	261	1	y	y	PROPN
ejpam-6154	261	2	,	,	PUNCT
ejpam-6154	261	3	yn	yn	PROPN
ejpam-6154	261	4	−	−	PROPN
ejpam-6154	261	5	u1yn	u1yn	PRON
ejpam-6154	262	1	−a∗	−a∗	PROPN
ejpam-6154	262	2	1(a1yn	1(a1yn	VERB
ejpam-6154	263	1	−a2zn)⟩	−a2zn)⟩	NOUN
ejpam-6154	263	2	+	+	CCONJ
ejpam-6154	263	3	(	(	PUNCT
ejpam-6154	263	4	1−	1−	NUM
ejpam-6154	263	5	αn)αn	αn)αn	NUM
ejpam-6154	263	6	(	(	PUNCT
ejpam-6154	263	7	∥u1vn	∥u1vn	PUNCT
ejpam-6154	263	8	−	−	PROPN
ejpam-6154	263	9	vn∥2	vn∥2	NOUN
ejpam-6154	263	10	+	+	CCONJ
ejpam-6154	263	11	2	2	NUM
ejpam-6154	263	12	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	263	13	y	y	PROPN
ejpam-6154	263	14	,	,	PUNCT
ejpam-6154	263	15	vn	vn	ADP
ejpam-6154	263	16	−	−	PROPN
ejpam-6154	263	17	y⟩	y⟩	NOUN
ejpam-6154	263	18	)	)	PUNCT
ejpam-6154	263	19	.	.	PUNCT
ejpam-6154	264	1	(	(	PUNCT
ejpam-6154	264	2	27	27	NUM
ejpam-6154	264	3	)	)	PUNCT
ejpam-6154	264	4	similarly	similarly	ADV
ejpam-6154	264	5	,	,	PUNCT
ejpam-6154	264	6	∥zn+1	∥zn+1	VERB
ejpam-6154	264	7	−	−	NOUN
ejpam-6154	264	8	z∥2	z∥2	NUM
ejpam-6154	264	9	≤(1−	≤(1−	PROPN
ejpam-6154	264	10	(	(	PUNCT
ejpam-6154	264	11	1−	1−	NUM
ejpam-6154	264	12	ρ2)αn)∥zn	ρ2)αn)∥zn	NUM
ejpam-6154	264	13	−	−	PROPN
ejpam-6154	264	14	z∥2	z∥2	NOUN
ejpam-6154	264	15	+	+	NUM
ejpam-6154	264	16	αn∥f2(z)−	αn∥f2(z)−	NOUN
ejpam-6154	264	17	z∥2	z∥2	NOUN
ejpam-6154	264	18	+	+	CCONJ
ejpam-6154	264	19	(	(	PUNCT
ejpam-6154	264	20	1−	1−	NUM
ejpam-6154	264	21	(	(	PUNCT
ejpam-6154	264	22	1−	1−	NUM
ejpam-6154	264	23	ρ2)αn)τ	ρ2)αn)τ	NUM
ejpam-6154	264	24	2	2	NUM
ejpam-6154	264	25	n∥u2zn	n∥u2zn	NOUN
ejpam-6154	264	26	−	−	PROPN
ejpam-6154	264	27	zn	zn	PROPN
ejpam-6154	265	1	+	+	ADP
ejpam-6154	265	2	a∗	a∗	PROPN
ejpam-6154	265	3	2(a2zn	2(a2zn	NOUN
ejpam-6154	265	4	−a1yn)∥2	−a1yn)∥2	PROPN
ejpam-6154	265	5	−	−	PROPN
ejpam-6154	265	6	2(1−	2(1−	NUM
ejpam-6154	265	7	(	(	PUNCT
ejpam-6154	265	8	1−	1−	NUM
ejpam-6154	265	9	ρ2)αn)τn	ρ2)αn)τn	NUM
ejpam-6154	266	1	⟨zn	⟨zn	NOUN
ejpam-6154	267	1	−	−	PROPN
ejpam-6154	267	2	z	z	PROPN
ejpam-6154	267	3	,	,	PUNCT
ejpam-6154	267	4	zn	zn	PROPN
ejpam-6154	267	5	−	−	NOUN
ejpam-6154	267	6	u2zn	u2zn	PUNCT
ejpam-6154	268	1	−a∗	−a∗	PROPN
ejpam-6154	268	2	2(a2zn	2(a2zn	PROPN
ejpam-6154	268	3	−a1yn)⟩	−a1yn)⟩	PROPN
ejpam-6154	268	4	+	+	PROPN
ejpam-6154	269	1	(	(	PUNCT
ejpam-6154	269	2	1−	1−	NUM
ejpam-6154	269	3	αn)αn	αn)αn	NUM
ejpam-6154	269	4	(	(	PUNCT
ejpam-6154	269	5	∥u2wn	∥u2wn	PUNCT
ejpam-6154	269	6	−	−	NOUN
ejpam-6154	269	7	wn∥2	wn∥2	NOUN
ejpam-6154	269	8	+	+	NOUN
ejpam-6154	269	9	2	2	NUM
ejpam-6154	269	10	⟨f2(z)−	⟨f2(z)−	NUM
ejpam-6154	269	11	z	z	NOUN
ejpam-6154	269	12	,	,	PUNCT
ejpam-6154	269	13	wn	wn	PROPN
ejpam-6154	269	14	−	−	PROPN
ejpam-6154	269	15	z⟩	z⟩	PROPN
ejpam-6154	269	16	)	)	PUNCT
ejpam-6154	269	17	.	.	PUNCT
ejpam-6154	270	1	(	(	PUNCT
ejpam-6154	270	2	28	28	NUM
ejpam-6154	270	3	)	)	PUNCT
ejpam-6154	270	4	equations	equation	NOUN
ejpam-6154	270	5	(	(	PUNCT
ejpam-6154	270	6	18	18	NUM
ejpam-6154	270	7	)	)	PUNCT
ejpam-6154	270	8	,	,	PUNCT
ejpam-6154	270	9	(	(	PUNCT
ejpam-6154	270	10	27	27	NUM
ejpam-6154	270	11	)	)	PUNCT
ejpam-6154	270	12	,	,	PUNCT
ejpam-6154	270	13	and	and	CCONJ
ejpam-6154	270	14	(	(	PUNCT
ejpam-6154	270	15	28	28	NUM
ejpam-6154	270	16	)	)	PUNCT
ejpam-6154	270	17	give	give	VERB
ejpam-6154	270	18	γn+1	γn+1	PUNCT
ejpam-6154	270	19	≤(1−	≤(1−	PROPN
ejpam-6154	270	20	(	(	PUNCT
ejpam-6154	270	21	1−	1−	NUM
ejpam-6154	270	22	ρ2)αn)γn	ρ2)αn)γn	NOUN
ejpam-6154	271	1	+	+	CCONJ
ejpam-6154	271	2	αn	αn	NOUN
ejpam-6154	271	3	(	(	PUNCT
ejpam-6154	271	4	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	271	5	y∥2	y∥2	NOUN
ejpam-6154	271	6	+	+	CCONJ
ejpam-6154	271	7	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	271	8	z∥2	z∥2	NOUN
ejpam-6154	271	9	)	)	PUNCT
ejpam-6154	271	10	−	−	PROPN
ejpam-6154	271	11	τn((1−	τn((1−	PROPN
ejpam-6154	271	12	(	(	PUNCT
ejpam-6154	271	13	1−	1−	NUM
ejpam-6154	271	14	ρ2)αn)λ−	ρ2)αn)λ−	NOUN
ejpam-6154	271	15	τn)kn	τn)kn	PUNCT
ejpam-6154	272	1	+	+	CCONJ
ejpam-6154	272	2	(	(	PUNCT
ejpam-6154	272	3	1−	1−	NUM
ejpam-6154	272	4	αn)αn	αn)αn	NUM
ejpam-6154	272	5	(	(	PUNCT
ejpam-6154	272	6	∥u1vn	∥u1vn	PUNCT
ejpam-6154	272	7	−	−	PROPN
ejpam-6154	272	8	vn∥2	vn∥2	NOUN
ejpam-6154	272	9	+	+	CCONJ
ejpam-6154	272	10	∥u2wn	∥u2wn	PUNCT
ejpam-6154	272	11	−	−	PROPN
ejpam-6154	272	12	wn∥2	wn∥2	NOUN
ejpam-6154	272	13	+	+	NOUN
ejpam-6154	272	14	2	2	NUM
ejpam-6154	272	15	⟨f1(y)−	⟨f1(y)−	NUM
ejpam-6154	272	16	y	y	PROPN
ejpam-6154	272	17	,	,	PUNCT
ejpam-6154	272	18	vn	vn	VERB
ejpam-6154	272	19	−	−	PROPN
ejpam-6154	272	20	z⟩+	z⟩+	NOUN
ejpam-6154	272	21	2	2	NUM
ejpam-6154	272	22	⟨f2(z)−	⟨f2(z)−	NUM
ejpam-6154	273	1	z	z	NOUN
ejpam-6154	273	2	,	,	PUNCT
ejpam-6154	273	3	wn	wn	PROPN
ejpam-6154	273	4	−	−	PROPN
ejpam-6154	273	5	y⟩	y⟩	NOUN
ejpam-6154	273	6	)	)	PUNCT
ejpam-6154	273	7	≤(1−	≤(1−	PROPN
ejpam-6154	273	8	(	(	PUNCT
ejpam-6154	273	9	1−	1−	NUM
ejpam-6154	273	10	ρ2)αn)γn	ρ2)αn)γn	NOUN
ejpam-6154	274	1	+	+	CCONJ
ejpam-6154	274	2	αn	αn	NOUN
ejpam-6154	274	3	(	(	PUNCT
ejpam-6154	274	4	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	274	5	y∥2	y∥2	NOUN
ejpam-6154	274	6	+	+	CCONJ
ejpam-6154	274	7	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	274	8	z∥2	z∥2	NOUN
ejpam-6154	274	9	)	)	PUNCT
ejpam-6154	274	10	l.	l.	PROPN
ejpam-6154	274	11	b.	b.	PROPN
ejpam-6154	274	12	mohammed	mohammed	PROPN
ejpam-6154	274	13	,	,	PUNCT
ejpam-6154	274	14	a.	a.	PROPN
ejpam-6154	274	15	kılıçman	kılıçman	PROPN
ejpam-6154	274	16	,	,	PUNCT
ejpam-6154	274	17	d.	d.	PROPN
ejpam-6154	274	18	bamanga	bamanga	PROPN
ejpam-6154	274	19	/	/	SYM
ejpam-6154	274	20	eur	eur	PROPN
ejpam-6154	274	21	.	.	PUNCT
ejpam-6154	275	1	j.	j.	PROPN
ejpam-6154	275	2	pure	pure	PROPN
ejpam-6154	275	3	appl	appl	PROPN
ejpam-6154	275	4	.	.	PROPN
ejpam-6154	275	5	math	math	PROPN
ejpam-6154	275	6	,	,	PUNCT
ejpam-6154	275	7	18	18	NUM
ejpam-6154	275	8	(	(	PUNCT
ejpam-6154	275	9	4	4	NUM
ejpam-6154	275	10	)	)	PUNCT
ejpam-6154	275	11	(	(	PUNCT
ejpam-6154	275	12	2025	2025	NUM
ejpam-6154	275	13	)	)	PUNCT
ejpam-6154	275	14	,	,	PUNCT
ejpam-6154	275	15	6154	6154	NUM
ejpam-6154	275	16	11	11	NUM
ejpam-6154	275	17	of	of	ADP
ejpam-6154	275	18	18	18	NUM
ejpam-6154	275	19	+	+	CCONJ
ejpam-6154	275	20	(	(	PUNCT
ejpam-6154	275	21	1−	1−	NUM
ejpam-6154	275	22	αn)αn	αn)αn	NUM
ejpam-6154	275	23	(	(	PUNCT
ejpam-6154	275	24	∥u1vn	∥u1vn	PUNCT
ejpam-6154	275	25	−	−	PROPN
ejpam-6154	275	26	vn∥2	vn∥2	NOUN
ejpam-6154	275	27	+	+	CCONJ
ejpam-6154	275	28	∥u2wn	∥u2wn	PUNCT
ejpam-6154	275	29	−	−	PROPN
ejpam-6154	275	30	wn∥2	wn∥2	NOUN
ejpam-6154	275	31	+	+	NOUN
ejpam-6154	276	1	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	276	2	y∥∥vn	y∥∥vn	NUM
ejpam-6154	276	3	−	−	NOUN
ejpam-6154	277	1	y∥+	y∥+	PROPN
ejpam-6154	277	2	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	278	1	z∥∥wn	z∥∥wn	PROPN
ejpam-6154	278	2	−	−	PROPN
ejpam-6154	278	3	z∥	z∥	NUM
ejpam-6154	278	4	)	)	PUNCT
ejpam-6154	278	5	.	.	PUNCT
ejpam-6154	279	1	(	(	PUNCT
ejpam-6154	279	2	29	29	NUM
ejpam-6154	279	3	)	)	PUNCT
ejpam-6154	279	4	since	since	SCONJ
ejpam-6154	279	5	(	(	PUNCT
ejpam-6154	279	6	yn	yn	PROPN
ejpam-6154	279	7	,	,	PUNCT
ejpam-6154	279	8	zn	zn	PROPN
ejpam-6154	279	9	)	)	PUNCT
ejpam-6154	279	10	is	be	AUX
ejpam-6154	279	11	bounded	bound	VERB
ejpam-6154	279	12	,	,	PUNCT
ejpam-6154	279	13	we	we	PRON
ejpam-6154	279	14	see	see	VERB
ejpam-6154	279	15	that	that	SCONJ
ejpam-6154	279	16	∥wn	∥wn	ADP
ejpam-6154	279	17	−	−	PROPN
ejpam-6154	279	18	z∥	z∥	PROPN
ejpam-6154	279	19	is	be	AUX
ejpam-6154	279	20	bounded	bound	VERB
ejpam-6154	279	21	,	,	PUNCT
ejpam-6154	279	22	and	and	CCONJ
ejpam-6154	279	23	similarly	similarly	ADV
ejpam-6154	279	24	,	,	PUNCT
ejpam-6154	279	25	∥vn	∥vn	VERB
ejpam-6154	279	26	−	−	NOUN
ejpam-6154	279	27	y∥	y∥	NOUN
ejpam-6154	279	28	is	be	AUX
ejpam-6154	279	29	also	also	ADV
ejpam-6154	279	30	bounded	bound	VERB
ejpam-6154	279	31	.	.	PUNCT
ejpam-6154	280	1	on	on	ADP
ejpam-6154	280	2	the	the	DET
ejpam-6154	280	3	other	other	ADJ
ejpam-6154	280	4	hand	hand	NOUN
ejpam-6154	280	5	,	,	PUNCT
ejpam-6154	280	6	∥u1vn	∥u1vn	PUNCT
ejpam-6154	280	7	−	−	PROPN
ejpam-6154	280	8	vn∥	vn∥	PROPN
ejpam-6154	280	9	≤	≤	VERB
ejpam-6154	280	10	∥u1vn	∥u1vn	PUNCT
ejpam-6154	281	1	−	−	PROPN
ejpam-6154	281	2	y∥+	y∥+	PROPN
ejpam-6154	281	3	∥vn	∥vn	PROPN
ejpam-6154	281	4	−	−	PROPN
ejpam-6154	281	5	y∥	y∥	VERB
ejpam-6154	281	6	≤	≤	NOUN
ejpam-6154	282	1	2∥vn	2∥vn	NUM
ejpam-6154	282	2	−	−	NOUN
ejpam-6154	282	3	y∥.	y∥.	NOUN
ejpam-6154	282	4	(	(	PUNCT
ejpam-6154	282	5	30	30	NUM
ejpam-6154	282	6	)	)	PUNCT
ejpam-6154	282	7	similarly	similarly	ADV
ejpam-6154	282	8	,	,	PUNCT
ejpam-6154	282	9	∥u2wn	∥u2wn	PUNCT
ejpam-6154	282	10	−	−	PROPN
ejpam-6154	282	11	wn∥	wn∥	PROPN
ejpam-6154	282	12	≤	≤	NOUN
ejpam-6154	282	13	2∥wn	2∥wn	NUM
ejpam-6154	282	14	−	−	PROPN
ejpam-6154	282	15	z∥.	z∥.	PROPN
ejpam-6154	282	16	(	(	PUNCT
ejpam-6154	282	17	31	31	NUM
ejpam-6154	282	18	)	)	PUNCT
ejpam-6154	282	19	therefore	therefore	ADV
ejpam-6154	282	20	,	,	PUNCT
ejpam-6154	282	21	∥u1vn−vn∥	∥u1vn−vn∥	PROPN
ejpam-6154	282	22	and	and	CCONJ
ejpam-6154	282	23	∥u2wn−wn∥	∥u2wn−wn∥	NOUN
ejpam-6154	282	24	are	be	AUX
ejpam-6154	282	25	also	also	ADV
ejpam-6154	282	26	bounded	bound	VERB
ejpam-6154	282	27	.	.	PUNCT
ejpam-6154	283	1	since	since	SCONJ
ejpam-6154	283	2	(	(	PUNCT
ejpam-6154	283	3	yn	yn	PROPN
ejpam-6154	283	4	,	,	PUNCT
ejpam-6154	283	5	zn	zn	PROPN
ejpam-6154	283	6	)	)	PUNCT
ejpam-6154	283	7	is	be	AUX
ejpam-6154	283	8	bounded	bound	VERB
ejpam-6154	283	9	,	,	PUNCT
ejpam-6154	283	10	it	it	PRON
ejpam-6154	283	11	follows	follow	VERB
ejpam-6154	283	12	that	that	SCONJ
ejpam-6154	283	13	there	there	PRON
ejpam-6154	283	14	exist	exist	VERB
ejpam-6154	283	15	(	(	PUNCT
ejpam-6154	283	16	y	y	PROPN
ejpam-6154	283	17	,	,	PUNCT
ejpam-6154	283	18	z	z	NOUN
ejpam-6154	283	19	)	)	PUNCT
ejpam-6154	283	20	∈	∈	PROPN
ejpam-6154	283	21	s	s	NOUN
ejpam-6154	283	22	for	for	ADP
ejpam-6154	283	23	which	which	PRON
ejpam-6154	283	24	zn	zn	NOUN
ejpam-6154	283	25	⇀	⇀	PUNCT
ejpam-6154	284	1	z	z	PROPN
ejpam-6154	285	1	and	and	CCONJ
ejpam-6154	285	2	yn	yn	PRON
ejpam-6154	286	1	⇀	⇀	PROPN
ejpam-6154	286	2	y.	y.	PROPN
ejpam-6154	286	3	thus	thus	ADV
ejpam-6154	286	4	wn	wn	PROPN
ejpam-6154	286	5	=	=	PROPN
ejpam-6154	286	6	zn−τn(u2zn−	zn−τn(u2zn−	PROPN
ejpam-6154	286	7	zn	zn	PROPN
ejpam-6154	286	8	)	)	PUNCT
ejpam-6154	287	1	+	+	CCONJ
ejpam-6154	287	2	τna∗	τna∗	NOUN
ejpam-6154	287	3	1(a2zn	1(a2zn	PROPN
ejpam-6154	287	4	−a1yn	−a1yn	NUM
ejpam-6154	287	5	)	)	PUNCT
ejpam-6154	288	1	⇀	⇀	X
ejpam-6154	288	2	z	z	NOUN
ejpam-6154	289	1	and	and	CCONJ
ejpam-6154	289	2	vn	vn	PROPN
ejpam-6154	289	3	=	=	PROPN
ejpam-6154	289	4	yn	yn	PROPN
ejpam-6154	290	1	−	−	NOUN
ejpam-6154	290	2	τn(u1yn	τn(u1yn	INTJ
ejpam-6154	290	3	−	−	PROPN
ejpam-6154	290	4	yn	yn	PROPN
ejpam-6154	290	5	)	)	PUNCT
ejpam-6154	291	1	+	+	CCONJ
ejpam-6154	291	2	τna∗	τna∗	NOUN
ejpam-6154	291	3	2(a1yn	2(a1yn	PRON
ejpam-6154	291	4	−a2zn	−a2zn	NUM
ejpam-6154	291	5	)	)	PUNCT
ejpam-6154	292	1	⇀	⇀	PROPN
ejpam-6154	293	1	y.	y.	NOUN
ejpam-6154	293	2	on	on	ADP
ejpam-6154	293	3	the	the	DET
ejpam-6154	293	4	other	other	ADJ
ejpam-6154	293	5	hand	hand	NOUN
ejpam-6154	293	6	,	,	PUNCT
ejpam-6154	293	7	we	we	PRON
ejpam-6154	293	8	see	see	VERB
ejpam-6154	293	9	that	that	SCONJ
ejpam-6154	293	10	lim	lim	PROPN
ejpam-6154	293	11	sup	sup	VERB
ejpam-6154	293	12	n→∞	n→∞	NUM
ejpam-6154	293	13	(	(	PUNCT
ejpam-6154	293	14	∥u1vn	∥u1vn	PUNCT
ejpam-6154	293	15	−	−	PROPN
ejpam-6154	293	16	vn∥2	vn∥2	NOUN
ejpam-6154	293	17	+	+	CCONJ
ejpam-6154	293	18	∥u2wn	∥u2wn	PUNCT
ejpam-6154	293	19	−	−	PROPN
ejpam-6154	293	20	wn∥2	wn∥2	NOUN
ejpam-6154	293	21	+	+	PROPN
ejpam-6154	293	22	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	293	23	z∥∥wn	z∥∥wn	SYM
ejpam-6154	293	24	−	−	NOUN
ejpam-6154	293	25	z∥+	z∥+	NOUN
ejpam-6154	294	1	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	294	2	y∥∥vn	y∥∥vn	NUM
ejpam-6154	294	3	−	−	NOUN
ejpam-6154	294	4	y∥	y∥	NOUN
ejpam-6154	294	5	)	)	PUNCT
ejpam-6154	295	1	=	=	SYM
ejpam-6154	295	2	0	0	X
ejpam-6154	295	3	.	.	PUNCT
ejpam-6154	296	1	(	(	PUNCT
ejpam-6154	296	2	32	32	NUM
ejpam-6154	296	3	)	)	PUNCT
ejpam-6154	296	4	by	by	ADP
ejpam-6154	296	5	equation	equation	NOUN
ejpam-6154	296	6	(	(	PUNCT
ejpam-6154	296	7	29	29	NUM
ejpam-6154	296	8	)	)	PUNCT
ejpam-6154	296	9	,	,	PUNCT
ejpam-6154	296	10	we	we	PRON
ejpam-6154	296	11	deduce	deduce	VERB
ejpam-6154	296	12	that	that	PRON
ejpam-6154	296	13	γn+1	γn+1	VERB
ejpam-6154	296	14	≤(1−	≤(1−	PROPN
ejpam-6154	296	15	(	(	PUNCT
ejpam-6154	296	16	1−	1−	NUM
ejpam-6154	296	17	ρ2)αn)γn	ρ2)αn)γn	NOUN
ejpam-6154	296	18	+	+	CCONJ
ejpam-6154	297	1	(	(	PUNCT
ejpam-6154	297	2	1−	1−	NUM
ejpam-6154	297	3	ρ2)αn	ρ2)αn	NOUN
ejpam-6154	297	4	αn(∥f1(y)−	αn(∥f1(y)−	NUM
ejpam-6154	297	5	y∥2	y∥2	NOUN
ejpam-6154	297	6	+	+	CCONJ
ejpam-6154	297	7	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	297	8	z∥2	z∥2	NUM
ejpam-6154	297	9	)	)	PUNCT
ejpam-6154	297	10	(	(	PUNCT
ejpam-6154	297	11	1−	1−	NUM
ejpam-6154	297	12	ρ2	ρ2	NOUN
ejpam-6154	297	13	)	)	PUNCT
ejpam-6154	297	14	+	+	CCONJ
ejpam-6154	297	15	(	(	PUNCT
ejpam-6154	297	16	1−	1−	NUM
ejpam-6154	297	17	αn)αn	αn)αn	NUM
ejpam-6154	297	18	(	(	PUNCT
ejpam-6154	297	19	∥u1vn	∥u1vn	PUNCT
ejpam-6154	297	20	−	−	PROPN
ejpam-6154	297	21	vn∥2	vn∥2	NOUN
ejpam-6154	297	22	+	+	CCONJ
ejpam-6154	297	23	∥u2wn	∥u2wn	PUNCT
ejpam-6154	297	24	−	−	PROPN
ejpam-6154	297	25	wn∥2	wn∥2	NOUN
ejpam-6154	297	26	+	+	SYM
ejpam-6154	297	27	∥f1(y)−	∥f1(y)−	NUM
ejpam-6154	297	28	y∥2	y∥2	ADJ
ejpam-6154	297	29	+	+	CCONJ
ejpam-6154	297	30	∥f2(z)−	∥f2(z)−	NUM
ejpam-6154	297	31	z∥2	z∥2	NOUN
ejpam-6154	297	32	+	+	CCONJ
ejpam-6154	297	33	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	297	34	y∥∥vn	y∥∥vn	NUM
ejpam-6154	297	35	−	−	NOUN
ejpam-6154	298	1	y∥+	y∥+	PROPN
ejpam-6154	298	2	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	299	1	z∥∥wn	z∥∥wn	PROPN
ejpam-6154	299	2	−	−	PROPN
ejpam-6154	299	3	z∥	z∥	NUM
ejpam-6154	299	4	)	)	PUNCT
ejpam-6154	299	5	.	.	PUNCT
ejpam-6154	300	1	thus	thus	ADV
ejpam-6154	300	2	,	,	PUNCT
ejpam-6154	300	3	we	we	PRON
ejpam-6154	300	4	see	see	VERB
ejpam-6154	300	5	that	that	SCONJ
ejpam-6154	300	6	(	(	PUNCT
ejpam-6154	300	7	i	i	NOUN
ejpam-6154	300	8	)	)	PUNCT
ejpam-6154	300	9	∑	∑	PROPN
ejpam-6154	300	10	n≥0	n≥0	PROPN
ejpam-6154	300	11	(	(	PUNCT
ejpam-6154	300	12	1−	1−	NUM
ejpam-6154	300	13	ρ2)αn	ρ2)αn	NOUN
ejpam-6154	300	14	=	=	SYM
ejpam-6154	300	15	∞	∞	PROPN
ejpam-6154	300	16	;	;	PUNCT
ejpam-6154	300	17	(	(	PUNCT
ejpam-6154	300	18	ii	ii	X
ejpam-6154	300	19	)	)	PUNCT
ejpam-6154	300	20	lim	lim	PROPN
ejpam-6154	300	21	n→∞	n→∞	NUM
ejpam-6154	300	22	αn(∥f1(y)−y∥2+∥f2(z)−z∥2	αn(∥f1(y)−y∥2+∥f2(z)−z∥2	NOUN
ejpam-6154	300	23	)	)	PUNCT
ejpam-6154	300	24	(	(	PUNCT
ejpam-6154	300	25	1−ρ2	1−ρ2	NUM
ejpam-6154	300	26	)	)	PUNCT
ejpam-6154	300	27	=	=	SYM
ejpam-6154	300	28	0	0	NUM
ejpam-6154	300	29	;	;	PUNCT
ejpam-6154	300	30	and	and	CCONJ
ejpam-6154	300	31	∑	∑	ADV
ejpam-6154	300	32	n≥0	n≥0	PROPN
ejpam-6154	300	33	(	(	PUNCT
ejpam-6154	300	34	1−	1−	NUM
ejpam-6154	300	35	ρ2)α	ρ2)α	PROPN
ejpam-6154	300	36	2	2	NUM
ejpam-6154	300	37	n(∥f1(y)−y∥2+∥f2(z)−z∥2	n(∥f1(y)−y∥2+∥f2(z)−z∥2	NUM
ejpam-6154	300	38	)	)	PUNCT
ejpam-6154	300	39	(	(	PUNCT
ejpam-6154	300	40	1−ρ2	1−ρ2	NUM
ejpam-6154	300	41	)	)	PUNCT
ejpam-6154	300	42	<	<	X
ejpam-6154	300	43	∞	∞	PROPN
ejpam-6154	300	44	;	;	PUNCT
ejpam-6154	300	45	(	(	PUNCT
ejpam-6154	300	46	iii	iii	X
ejpam-6154	300	47	)	)	PUNCT
ejpam-6154	300	48	ηn	ηn	ADP
ejpam-6154	300	49	≥	≥	NOUN
ejpam-6154	300	50	0	0	NUM
ejpam-6154	300	51	and	and	CCONJ
ejpam-6154	300	52	∑	∑	ADV
ejpam-6154	300	53	n≥0	n≥0	ADJ
ejpam-6154	300	54	ηn	ηn	PROPN
ejpam-6154	300	55	<	<	X
ejpam-6154	300	56	∞	∞	PROPN
ejpam-6154	300	57	;	;	PUNCT
ejpam-6154	300	58	where	where	SCONJ
ejpam-6154	300	59	ηn	ηn	ADV
ejpam-6154	300	60	=	=	SYM
ejpam-6154	300	61	(	(	PUNCT
ejpam-6154	300	62	1	1	NUM
ejpam-6154	300	63	−	−	NOUN
ejpam-6154	300	64	αn)αn	αn)αn	NUM
ejpam-6154	300	65	(	(	PUNCT
ejpam-6154	300	66	∥u1vn	∥u1vn	PUNCT
ejpam-6154	300	67	−	−	PROPN
ejpam-6154	300	68	vn∥2	vn∥2	NOUN
ejpam-6154	300	69	+	+	CCONJ
ejpam-6154	300	70	∥u2wn	∥u2wn	PUNCT
ejpam-6154	300	71	−	−	PROPN
ejpam-6154	300	72	wn∥2	wn∥2	NOUN
ejpam-6154	300	73	+	+	NUM
ejpam-6154	300	74	∥f1(y	∥f1(y	PROPN
ejpam-6154	300	75	)	)	PUNCT
ejpam-6154	301	1	−	−	PROPN
ejpam-6154	301	2	y∥2	y∥2	NOUN
ejpam-6154	301	3	+	+	CCONJ
ejpam-6154	301	4	∥f2(z	∥f2(z	NOUN
ejpam-6154	301	5	)	)	PUNCT
ejpam-6154	301	6	−	−	NOUN
ejpam-6154	301	7	z∥2	z∥2	NOUN
ejpam-6154	301	8	+	+	CCONJ
ejpam-6154	301	9	2∥f1(y)−	2∥f1(y)−	NUM
ejpam-6154	301	10	y∥∥vn	y∥∥vn	NUM
ejpam-6154	301	11	−	−	NOUN
ejpam-6154	302	1	y∥+	y∥+	PROPN
ejpam-6154	302	2	2∥f2(z)−	2∥f2(z)−	NUM
ejpam-6154	303	1	z∥∥wn	z∥∥wn	PROPN
ejpam-6154	303	2	−	−	PROPN
ejpam-6154	303	3	z∥	z∥	NUM
ejpam-6154	303	4	)	)	PUNCT
ejpam-6154	303	5	.	.	PUNCT
ejpam-6154	304	1	l.	l.	PROPN
ejpam-6154	304	2	b.	b.	PROPN
ejpam-6154	304	3	mohammed	mohammed	PROPN
ejpam-6154	304	4	,	,	PUNCT
ejpam-6154	304	5	a.	a.	PROPN
ejpam-6154	304	6	kılıçman	kılıçman	PROPN
ejpam-6154	304	7	,	,	PUNCT
ejpam-6154	304	8	d.	d.	PROPN
ejpam-6154	304	9	bamanga	bamanga	PROPN
ejpam-6154	304	10	/	/	SYM
ejpam-6154	304	11	eur	eur	PROPN
ejpam-6154	304	12	.	.	PUNCT
ejpam-6154	305	1	j.	j.	PROPN
ejpam-6154	305	2	pure	pure	PROPN
ejpam-6154	305	3	appl	appl	PROPN
ejpam-6154	305	4	.	.	PROPN
ejpam-6154	305	5	math	math	PROPN
ejpam-6154	305	6	,	,	PUNCT
ejpam-6154	305	7	18	18	NUM
ejpam-6154	305	8	(	(	PUNCT
ejpam-6154	305	9	4	4	NUM
ejpam-6154	305	10	)	)	PUNCT
ejpam-6154	305	11	(	(	PUNCT
ejpam-6154	305	12	2025	2025	NUM
ejpam-6154	305	13	)	)	PUNCT
ejpam-6154	305	14	,	,	PUNCT
ejpam-6154	305	15	6154	6154	NUM
ejpam-6154	305	16	12	12	NUM
ejpam-6154	305	17	of	of	ADP
ejpam-6154	305	18	18	18	NUM
ejpam-6154	305	19	therefore	therefore	ADV
ejpam-6154	305	20	,	,	PUNCT
ejpam-6154	305	21	by	by	ADP
ejpam-6154	305	22	lemma	lemma	PROPN
ejpam-6154	305	23	3	3	NUM
ejpam-6154	305	24	,	,	PUNCT
ejpam-6154	305	25	we	we	PRON
ejpam-6154	305	26	deduce	deduce	VERB
ejpam-6154	305	27	that	that	SCONJ
ejpam-6154	305	28	lim	lim	PROPN
ejpam-6154	305	29	n→∞	n→∞	X
ejpam-6154	305	30	γn	γn	ADP
ejpam-6154	305	31	=	=	NOUN
ejpam-6154	305	32	0	0	PROPN
ejpam-6154	305	33	.	.	PUNCT
ejpam-6154	306	1	that	that	PRON
ejpam-6154	306	2	is	be	AUX
ejpam-6154	306	3	lim	lim	PROPN
ejpam-6154	306	4	n→∞	n→∞	NUM
ejpam-6154	306	5	(	(	PUNCT
ejpam-6154	306	6	∥yn	∥yn	NUM
ejpam-6154	306	7	−	−	PROPN
ejpam-6154	306	8	y∥2	y∥2	NOUN
ejpam-6154	306	9	+	+	CCONJ
ejpam-6154	306	10	∥zn	∥zn	NUM
ejpam-6154	306	11	−	−	PROPN
ejpam-6154	306	12	z∥2	z∥2	NOUN
ejpam-6154	306	13	)	)	PUNCT
ejpam-6154	307	1	=	=	SYM
ejpam-6154	307	2	0	0	X
ejpam-6154	307	3	.	.	PUNCT
ejpam-6154	308	1	finally	finally	ADV
ejpam-6154	308	2	,	,	PUNCT
ejpam-6154	308	3	we	we	PRON
ejpam-6154	308	4	show	show	VERB
ejpam-6154	308	5	that	that	SCONJ
ejpam-6154	308	6	(	(	PUNCT
ejpam-6154	308	7	y	y	NOUN
ejpam-6154	308	8	,	,	PUNCT
ejpam-6154	308	9	z	z	NOUN
ejpam-6154	308	10	)	)	PUNCT
ejpam-6154	308	11	∈	∈	PROPN
ejpam-6154	308	12	s.	s.	PROPN
ejpam-6154	308	13	since	since	SCONJ
ejpam-6154	308	14	,	,	PUNCT
ejpam-6154	308	15	u1	u1	PROPN
ejpam-6154	308	16	=	=	SYM
ejpam-6154	308	17	(	(	PUNCT
ejpam-6154	308	18	1	1	NUM
ejpam-6154	308	19	−	−	NOUN
ejpam-6154	308	20	η)i	η)i	ADJ
ejpam-6154	308	21	−	−	NOUN
ejpam-6154	308	22	ηt1((1	ηt1((1	PUNCT
ejpam-6154	308	23	−	−	PROPN
ejpam-6154	308	24	ζ)i	ζ)i	VERB
ejpam-6154	308	25	+	+	CCONJ
ejpam-6154	308	26	ζt1)i	ζt1)i	NOUN
ejpam-6154	308	27	,	,	PUNCT
ejpam-6154	308	28	where	where	SCONJ
ejpam-6154	308	29	0	0	X
ejpam-6154	308	30	<	<	X
ejpam-6154	308	31	η	η	X
ejpam-6154	308	32	<	<	X
ejpam-6154	308	33	ζ	ζ	X
ejpam-6154	308	34	<	<	X
ejpam-6154	308	35	1	1	NUM
ejpam-6154	308	36	1	1	NUM
ejpam-6154	308	37	+	+	NUM
ejpam-6154	308	38	√	√	PROPN
ejpam-6154	308	39	1+l2	1+l2	NUM
ejpam-6154	308	40	and	and	CCONJ
ejpam-6154	308	41	t1	t1	NOUN
ejpam-6154	308	42	is	be	AUX
ejpam-6154	308	43	lipschitz	lipschitz	ADJ
ejpam-6154	308	44	,	,	PUNCT
ejpam-6154	308	45	we	we	PRON
ejpam-6154	308	46	have	have	VERB
ejpam-6154	308	47	η∥yn	η∥yn	ADV
ejpam-6154	308	48	−	−	PROPN
ejpam-6154	308	49	t1yn∥	t1yn∥	NOUN
ejpam-6154	308	50	=	=	SYM
ejpam-6154	308	51	∥yn	∥yn	PROPN
ejpam-6154	308	52	−	−	PROPN
ejpam-6154	308	53	(	(	PUNCT
ejpam-6154	308	54	1−	1−	NUM
ejpam-6154	308	55	η)yn	η)yn	PROPN
ejpam-6154	308	56	−	−	PROPN
ejpam-6154	309	1	ηt1yn∥	ηt1yn∥	PROPN
ejpam-6154	309	2	=	=	SYM
ejpam-6154	309	3	∥yn	∥yn	PROPN
ejpam-6154	309	4	−	−	PROPN
ejpam-6154	309	5	(	(	PUNCT
ejpam-6154	309	6	1−	1−	NUM
ejpam-6154	309	7	η)yn	η)yn	PROPN
ejpam-6154	309	8	−	−	NOUN
ejpam-6154	309	9	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	309	10	ζ)i	ζ)i	NOUN
ejpam-6154	309	11	+	+	CCONJ
ejpam-6154	309	12	ζt1)yn	ζt1)yn	ADV
ejpam-6154	309	13	+	+	CCONJ
ejpam-6154	309	14	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	309	15	ζ)i	ζ)i	NOUN
ejpam-6154	309	16	+	+	CCONJ
ejpam-6154	309	17	ζt1)yn	ζt1)yn	NOUN
ejpam-6154	309	18	−	−	ADP
ejpam-6154	310	1	ηt1yn∥	ηt1yn∥	PROPN
ejpam-6154	310	2	≤	≤	NOUN
ejpam-6154	310	3	∥yn	∥yn	NOUN
ejpam-6154	310	4	−	−	PROPN
ejpam-6154	310	5	(	(	PUNCT
ejpam-6154	310	6	1−	1−	NUM
ejpam-6154	310	7	η)yn	η)yn	PROPN
ejpam-6154	310	8	−	−	PROPN
ejpam-6154	310	9	ηt1((1−	ηt1((1−	NOUN
ejpam-6154	310	10	ζ)i	ζ)i	NOUN
ejpam-6154	310	11	+	+	NUM
ejpam-6154	310	12	ζt1)yn∥	ζt1)yn∥	NOUN
ejpam-6154	310	13	+	+	X
ejpam-6154	310	14	∥ηt1((1−	∥ηt1((1−	PROPN
ejpam-6154	310	15	ζ)i	ζ)i	NOUN
ejpam-6154	310	16	+	+	CCONJ
ejpam-6154	310	17	ζt1)yn	ζt1)yn	ADV
ejpam-6154	310	18	−	−	ADP
ejpam-6154	310	19	ηt1yn∥	ηt1yn∥	PROPN
ejpam-6154	310	20	≤	≤	NOUN
ejpam-6154	310	21	∥yn	∥yn	PART
ejpam-6154	310	22	−	−	NOUN
ejpam-6154	310	23	u1yn∥+	u1yn∥+	NOUN
ejpam-6154	310	24	ηl∥((1−	ηl∥((1−	NOUN
ejpam-6154	310	25	ζ)i	ζ)i	NOUN
ejpam-6154	310	26	+	+	CCONJ
ejpam-6154	310	27	ζt1)yn	ζt1)yn	NOUN
ejpam-6154	310	28	−	−	NOUN
ejpam-6154	311	1	yn∥	yn∥	NOUN
ejpam-6154	311	2	=	=	SYM
ejpam-6154	311	3	∥yn	∥yn	ADP
ejpam-6154	311	4	−	−	PROPN
ejpam-6154	311	5	u1yn∥+	u1yn∥+	NOUN
ejpam-6154	311	6	ηζl∥yn	ηζl∥yn	NOUN
ejpam-6154	311	7	−	−	PROPN
ejpam-6154	311	8	t1yn∥.	t1yn∥.	PROPN
ejpam-6154	311	9	therefore	therefore	ADV
ejpam-6154	311	10	,	,	PUNCT
ejpam-6154	311	11	∥yn	∥yn	PROPN
ejpam-6154	311	12	−	−	PROPN
ejpam-6154	311	13	t1yn∥	t1yn∥	NOUN
ejpam-6154	311	14	≤	≤	NUM
ejpam-6154	311	15	1	1	NUM
ejpam-6154	311	16	(	(	PUNCT
ejpam-6154	311	17	1−	1−	NUM
ejpam-6154	311	18	ζl)η	ζl)η	PROPN
ejpam-6154	311	19	∥yn	∥yn	PROPN
ejpam-6154	311	20	−	−	PROPN
ejpam-6154	311	21	u1yn∥.	u1yn∥.	PROPN
ejpam-6154	311	22	(	(	PUNCT
ejpam-6154	311	23	33	33	NUM
ejpam-6154	311	24	)	)	PUNCT
ejpam-6154	311	25	similarly	similarly	ADV
ejpam-6154	311	26	,	,	PUNCT
ejpam-6154	311	27	∥zn	∥zn	NUM
ejpam-6154	311	28	−	−	NOUN
ejpam-6154	311	29	t2zn∥	t2zn∥	NOUN
ejpam-6154	311	30	≤	≤	NUM
ejpam-6154	311	31	1	1	NUM
ejpam-6154	311	32	(	(	PUNCT
ejpam-6154	311	33	1−	1−	NUM
ejpam-6154	311	34	ζl)η	ζl)η	PROPN
ejpam-6154	311	35	∥zn	∥zn	ADP
ejpam-6154	312	1	−	−	PROPN
ejpam-6154	313	1	u2zn∥.	u2zn∥.	PROPN
ejpam-6154	314	1	(	(	PUNCT
ejpam-6154	314	2	34	34	NUM
ejpam-6154	314	3	)	)	PUNCT
ejpam-6154	314	4	by	by	ADP
ejpam-6154	314	5	(	(	PUNCT
ejpam-6154	314	6	22	22	NUM
ejpam-6154	314	7	)	)	PUNCT
ejpam-6154	314	8	and	and	CCONJ
ejpam-6154	314	9	(	(	PUNCT
ejpam-6154	314	10	23	23	NUM
ejpam-6154	314	11	)	)	PUNCT
ejpam-6154	314	12	,	,	PUNCT
ejpam-6154	314	13	we	we	PRON
ejpam-6154	314	14	see	see	VERB
ejpam-6154	314	15	that	that	SCONJ
ejpam-6154	314	16	lim	lim	PROPN
ejpam-6154	314	17	n→∞	n→∞	PRON
ejpam-6154	314	18	∥yn	∥yn	PROPN
ejpam-6154	314	19	−	−	PROPN
ejpam-6154	314	20	t1yn∥	t1yn∥	NOUN
ejpam-6154	314	21	=	=	SYM
ejpam-6154	314	22	0	0	NUM
ejpam-6154	314	23	,	,	PUNCT
ejpam-6154	314	24	and	and	CCONJ
ejpam-6154	314	25	lim	lim	PROPN
ejpam-6154	314	26	n→∞	n→∞	PROPN
ejpam-6154	314	27	∥zn	∥zn	PROPN
ejpam-6154	314	28	−	−	PROPN
ejpam-6154	314	29	t2zn∥	t2zn∥	NOUN
ejpam-6154	314	30	=	=	PUNCT
ejpam-6154	314	31	0	0	NUM
ejpam-6154	314	32	.	.	PUNCT
ejpam-6154	315	1	(	(	PUNCT
ejpam-6154	315	2	35	35	NUM
ejpam-6154	315	3	)	)	PUNCT
ejpam-6154	315	4	now	now	ADV
ejpam-6154	315	5	that	that	SCONJ
ejpam-6154	315	6	yn	yn	PRON
ejpam-6154	315	7	→	→	SYM
ejpam-6154	315	8	y	y	PROPN
ejpam-6154	315	9	and	and	CCONJ
ejpam-6154	315	10	lim	lim	PROPN
ejpam-6154	315	11	n→∞	n→∞	X
ejpam-6154	315	12	∥t1yn	∥t1yn	PUNCT
ejpam-6154	315	13	−	−	PROPN
ejpam-6154	315	14	yn∥	yn∥	NOUN
ejpam-6154	315	15	=	=	SYM
ejpam-6154	316	1	0	0	NUM
ejpam-6154	316	2	couple	couple	NOUN
ejpam-6154	316	3	with	with	ADP
ejpam-6154	316	4	the	the	DET
ejpam-6154	316	5	demiclosedness	demiclosedness	NOUN
ejpam-6154	316	6	of	of	ADP
ejpam-6154	316	7	(	(	PUNCT
ejpam-6154	316	8	t1−	t1−	NOUN
ejpam-6154	316	9	i	i	NOUN
ejpam-6154	316	10	)	)	PUNCT
ejpam-6154	316	11	at	at	ADP
ejpam-6154	316	12	origin	origin	NOUN
ejpam-6154	316	13	,	,	PUNCT
ejpam-6154	316	14	we	we	PRON
ejpam-6154	316	15	have	have	VERB
ejpam-6154	316	16	y	y	PROPN
ejpam-6154	316	17	∈	∈	PROPN
ejpam-6154	316	18	fix(t1	fix(t1	NOUN
ejpam-6154	316	19	)	)	PUNCT
ejpam-6154	316	20	.	.	PUNCT
ejpam-6154	317	1	similarly	similarly	ADV
ejpam-6154	317	2	,	,	PUNCT
ejpam-6154	317	3	zn	zn	PROPN
ejpam-6154	317	4	→	→	SYM
ejpam-6154	317	5	z	z	PROPN
ejpam-6154	317	6	and	and	CCONJ
ejpam-6154	317	7	lim	lim	PROPN
ejpam-6154	317	8	n→∞	n→∞	PROPN
ejpam-6154	317	9	∥t2zn	∥t2zn	ADP
ejpam-6154	318	1	−	−	PROPN
ejpam-6154	318	2	zn∥	zn∥	NOUN
ejpam-6154	318	3	=	=	SYM
ejpam-6154	318	4	0	0	PUNCT
ejpam-6154	318	5	together	together	ADV
ejpam-6154	318	6	with	with	ADP
ejpam-6154	318	7	the	the	DET
ejpam-6154	318	8	demiclosedness	demiclosedness	NOUN
ejpam-6154	318	9	of	of	ADP
ejpam-6154	318	10	(	(	PUNCT
ejpam-6154	318	11	t2−i	t2−i	PROPN
ejpam-6154	318	12	)	)	PUNCT
ejpam-6154	318	13	at	at	ADP
ejpam-6154	318	14	origin	origin	NOUN
ejpam-6154	318	15	,	,	PUNCT
ejpam-6154	318	16	we	we	PRON
ejpam-6154	318	17	see	see	VERB
ejpam-6154	318	18	that	that	SCONJ
ejpam-6154	318	19	z	z	PROPN
ejpam-6154	318	20	∈	∈	PROPN
ejpam-6154	318	21	fix(t2	fix(t2	NOUN
ejpam-6154	318	22	)	)	PUNCT
ejpam-6154	318	23	.	.	PUNCT
ejpam-6154	319	1	on	on	ADP
ejpam-6154	319	2	the	the	DET
ejpam-6154	319	3	other	other	ADJ
ejpam-6154	319	4	hand	hand	NOUN
ejpam-6154	319	5	,	,	PUNCT
ejpam-6154	319	6	since	since	SCONJ
ejpam-6154	319	7	yn	yn	PROPN
ejpam-6154	319	8	→	→	SYM
ejpam-6154	319	9	y	y	PROPN
ejpam-6154	319	10	,	,	PUNCT
ejpam-6154	319	11	it	it	PRON
ejpam-6154	319	12	is	be	AUX
ejpam-6154	319	13	not	not	PART
ejpam-6154	319	14	difficult	difficult	ADJ
ejpam-6154	319	15	to	to	PART
ejpam-6154	319	16	see	see	VERB
ejpam-6154	319	17	that	that	DET
ejpam-6154	319	18	vn	vn	PROPN
ejpam-6154	319	19	=	=	SYM
ejpam-6154	319	20	(	(	PUNCT
ejpam-6154	319	21	1−	1−	NUM
ejpam-6154	319	22	τn)yn	τn)yn	PUNCT
ejpam-6154	320	1	+	+	CCONJ
ejpam-6154	320	2	τnu1yn	τnu1yn	PUNCT
ejpam-6154	320	3	+	+	NUM
ejpam-6154	320	4	τna∗	τna∗	NOUN
ejpam-6154	320	5	1(a1yn	1(a1yn	NUM
ejpam-6154	320	6	−a2zn	−a2zn	NUM
ejpam-6154	320	7	)	)	PUNCT
ejpam-6154	320	8	→	→	SYM
ejpam-6154	320	9	0	0	X
ejpam-6154	320	10	.	.	PUNCT
ejpam-6154	321	1	similarly	similarly	ADV
ejpam-6154	321	2	,	,	PUNCT
ejpam-6154	321	3	wn	wn	PROPN
ejpam-6154	321	4	→	→	SYM
ejpam-6154	321	5	z.	z.	PROPN
ejpam-6154	321	6	since	since	SCONJ
ejpam-6154	321	7	a1	a1	NOUN
ejpam-6154	321	8	and	and	CCONJ
ejpam-6154	321	9	a2	a2	PROPN
ejpam-6154	321	10	are	be	AUX
ejpam-6154	321	11	continuous	continuous	ADJ
ejpam-6154	321	12	mappings	mapping	NOUN
ejpam-6154	321	13	,	,	PUNCT
ejpam-6154	321	14	we	we	PRON
ejpam-6154	321	15	have	have	VERB
ejpam-6154	321	16	a1vn	a1vn	NOUN
ejpam-6154	321	17	→	→	SYM
ejpam-6154	321	18	a1y	a1y	PROPN
ejpam-6154	321	19	,	,	PUNCT
ejpam-6154	321	20	and	and	CCONJ
ejpam-6154	321	21	a2wn	a2wn	PUNCT
ejpam-6154	321	22	→	→	SYM
ejpam-6154	321	23	a2z	a2z	PROPN
ejpam-6154	321	24	.	.	PUNCT
ejpam-6154	322	1	this	this	PRON
ejpam-6154	322	2	implies	imply	VERB
ejpam-6154	322	3	that	that	SCONJ
ejpam-6154	322	4	a1vn	a1vn	PUNCT
ejpam-6154	322	5	−a2wn	−a2wn	NUM
ejpam-6154	322	6	→	→	SYM
ejpam-6154	322	7	a1y	a1y	PROPN
ejpam-6154	322	8	−a2z	−a2z	PROPN
ejpam-6154	322	9	,	,	PUNCT
ejpam-6154	322	10	l.	l.	PROPN
ejpam-6154	322	11	b.	b.	PROPN
ejpam-6154	322	12	mohammed	mohammed	PROPN
ejpam-6154	322	13	,	,	PUNCT
ejpam-6154	322	14	a.	a.	PROPN
ejpam-6154	322	15	kılıçman	kılıçman	PROPN
ejpam-6154	322	16	,	,	PUNCT
ejpam-6154	322	17	d.	d.	PROPN
ejpam-6154	322	18	bamanga	bamanga	PROPN
ejpam-6154	322	19	/	/	SYM
ejpam-6154	322	20	eur	eur	PROPN
ejpam-6154	322	21	.	.	PUNCT
ejpam-6154	323	1	j.	j.	PROPN
ejpam-6154	323	2	pure	pure	PROPN
ejpam-6154	323	3	appl	appl	PROPN
ejpam-6154	323	4	.	.	PROPN
ejpam-6154	323	5	math	math	PROPN
ejpam-6154	323	6	,	,	PUNCT
ejpam-6154	323	7	18	18	NUM
ejpam-6154	323	8	(	(	PUNCT
ejpam-6154	323	9	4	4	NUM
ejpam-6154	323	10	)	)	PUNCT
ejpam-6154	323	11	(	(	PUNCT
ejpam-6154	323	12	2025	2025	NUM
ejpam-6154	323	13	)	)	PUNCT
ejpam-6154	323	14	,	,	PUNCT
ejpam-6154	323	15	6154	6154	NUM
ejpam-6154	323	16	13	13	NUM
ejpam-6154	323	17	of	of	ADP
ejpam-6154	323	18	18	18	NUM
ejpam-6154	323	19	which	which	PRON
ejpam-6154	323	20	further	far	ADV
ejpam-6154	323	21	implies	imply	VERB
ejpam-6154	323	22	that	that	SCONJ
ejpam-6154	323	23	∥a1y	∥a1y	PROPN
ejpam-6154	323	24	−a2z∥	−a2z∥	PROPN
ejpam-6154	323	25	≤	≤	PROPN
ejpam-6154	323	26	lim	lim	PROPN
ejpam-6154	323	27	inf	inf	PROPN
ejpam-6154	323	28	n→∞	n→∞	X
ejpam-6154	323	29	∥a1vn	∥a1vn	PUNCT
ejpam-6154	323	30	−a2wn∥	−a2wn∥	PROPN
ejpam-6154	323	31	=	=	PUNCT
ejpam-6154	323	32	0	0	NUM
ejpam-6154	323	33	.	.	PUNCT
ejpam-6154	324	1	thus	thus	ADV
ejpam-6154	324	2	,	,	PUNCT
ejpam-6154	324	3	a1y	a1y	PROPN
ejpam-6154	324	4	=	=	PUNCT
ejpam-6154	324	5	a2z	a2z	PROPN
ejpam-6154	324	6	,	,	PUNCT
ejpam-6154	324	7	and	and	CCONJ
ejpam-6154	324	8	noticing	notice	VERB
ejpam-6154	324	9	that	that	DET
ejpam-6154	324	10	(	(	PUNCT
ejpam-6154	324	11	y	y	NOUN
ejpam-6154	324	12	,	,	PUNCT
ejpam-6154	324	13	z	z	NOUN
ejpam-6154	324	14	)	)	PUNCT
ejpam-6154	324	15	∈	∈	PROPN
ejpam-6154	324	16	fix(t1	fix(t1	PROPN
ejpam-6154	324	17	)	)	PUNCT
ejpam-6154	324	18	×	×	PROPN
ejpam-6154	324	19	fix(t2	fix(t2	NOUN
ejpam-6154	324	20	)	)	PUNCT
ejpam-6154	324	21	,	,	PUNCT
ejpam-6154	324	22	we	we	PRON
ejpam-6154	324	23	conclude	conclude	VERB
ejpam-6154	324	24	that	that	SCONJ
ejpam-6154	324	25	(	(	PUNCT
ejpam-6154	324	26	y	y	NOUN
ejpam-6154	324	27	,	,	PUNCT
ejpam-6154	324	28	z	z	NOUN
ejpam-6154	324	29	)	)	PUNCT
ejpam-6154	324	30	∈	∈	PROPN
ejpam-6154	324	31	s	s	NOUN
ejpam-6154	324	32	,	,	PUNCT
ejpam-6154	324	33	which	which	PRON
ejpam-6154	324	34	completes	complete	VERB
ejpam-6154	324	35	the	the	DET
ejpam-6154	324	36	proof	proof	NOUN
ejpam-6154	324	37	.	.	PUNCT
ejpam-6154	325	1	corollary	corollary	ADJ
ejpam-6154	325	2	2	2	NUM
ejpam-6154	325	3	.	.	PUNCT
ejpam-6154	325	4	suppose	suppose	VERB
ejpam-6154	325	5	conditions	condition	NOUN
ejpam-6154	325	6	(	(	PUNCT
ejpam-6154	325	7	k1	k1	NOUN
ejpam-6154	325	8	)	)	PUNCT
ejpam-6154	325	9	−	−	PROPN
ejpam-6154	325	10	(	(	PUNCT
ejpam-6154	325	11	k4	k4	PROPN
ejpam-6154	325	12	)	)	PUNCT
ejpam-6154	325	13	are	be	AUX
ejpam-6154	325	14	satisfied	satisfied	ADJ
ejpam-6154	325	15	,	,	PUNCT
ejpam-6154	325	16	and	and	CCONJ
ejpam-6154	325	17	that	that	PRON
ejpam-6154	325	18	s	s	VERB
ejpam-6154	325	19	=	=	NOUN
ejpam-6154	325	20	̸	̸	ADV
ejpam-6154	325	21	∅.	∅.	ADV
ejpam-6154	325	22	then	then	ADV
ejpam-6154	325	23	the	the	DET
ejpam-6154	325	24	sequence	sequence	NOUN
ejpam-6154	325	25	{	{	PUNCT
ejpam-6154	325	26	(	(	PUNCT
ejpam-6154	325	27	yn	yn	PROPN
ejpam-6154	325	28	,	,	PUNCT
ejpam-6154	325	29	zn	zn	PROPN
ejpam-6154	325	30	)	)	PUNCT
ejpam-6154	325	31	}	}	PUNCT
ejpam-6154	325	32	generated	generate	VERB
ejpam-6154	325	33	by	by	PROPN
ejpam-6154	325	34	yn+1	yn+1	PUNCT
ejpam-6154	326	1	=	=	NOUN
ejpam-6154	326	2	αnvn	αnvn	NOUN
ejpam-6154	327	1	+	+	CCONJ
ejpam-6154	328	1	(	(	PUNCT
ejpam-6154	328	2	1−	1−	NUM
ejpam-6154	328	3	αn)u1vn	αn)u1vn	NOUN
ejpam-6154	328	4	;	;	PUNCT
ejpam-6154	328	5	vn	vn	PROPN
ejpam-6154	328	6	=	=	SYM
ejpam-6154	328	7	(	(	PUNCT
ejpam-6154	328	8	1−	1−	NUM
ejpam-6154	328	9	τn)yn	τn)yn	PUNCT
ejpam-6154	329	1	+	+	CCONJ
ejpam-6154	329	2	τnu1yn	τnu1yn	PUNCT
ejpam-6154	329	3	+	+	NUM
ejpam-6154	329	4	τna∗	τna∗	NOUN
ejpam-6154	329	5	1(a1yn	1(a1yn	PROPN
ejpam-6154	329	6	−a2zn	−a2zn	NUM
ejpam-6154	329	7	)	)	PUNCT
ejpam-6154	329	8	;	;	PUNCT
ejpam-6154	329	9	zn+1	zn+1	X
ejpam-6154	329	10	=	=	PRON
ejpam-6154	329	11	αnwn	αnwn	VERB
ejpam-6154	329	12	+	+	X
ejpam-6154	330	1	(	(	PUNCT
ejpam-6154	330	2	1−	1−	NUM
ejpam-6154	330	3	αn)u2wn	αn)u2wn	NUM
ejpam-6154	330	4	;	;	PUNCT
ejpam-6154	330	5	wn	wn	PROPN
ejpam-6154	330	6	=	=	PUNCT
ejpam-6154	330	7	(	(	PUNCT
ejpam-6154	330	8	1−	1−	NUM
ejpam-6154	330	9	τn)zn	τn)zn	NUM
ejpam-6154	330	10	+	+	CCONJ
ejpam-6154	330	11	τnu2zn	τnu2zn	PUNCT
ejpam-6154	331	1	+	+	CCONJ
ejpam-6154	331	2	τna∗	τna∗	NOUN
ejpam-6154	331	3	2(a2zn	2(a2zn	PROPN
ejpam-6154	331	4	−a1yn	−a1yn	NUM
ejpam-6154	331	5	)	)	PUNCT
ejpam-6154	331	6	,	,	PUNCT
ejpam-6154	331	7	∀n	∀n	NUM
ejpam-6154	331	8	≥	≥	NOUN
ejpam-6154	331	9	0	0	NUM
ejpam-6154	331	10	;	;	PUNCT
ejpam-6154	331	11	(	(	PUNCT
ejpam-6154	331	12	36	36	NUM
ejpam-6154	331	13	)	)	PUNCT
ejpam-6154	331	14	where	where	SCONJ
ejpam-6154	331	15	uj	uj	PROPN
ejpam-6154	331	16	=	=	SYM
ejpam-6154	331	17	(	(	PUNCT
ejpam-6154	331	18	1−η)i+ηtj((1−ζ)i+ζtj	1−η)i+ηtj((1−ζ)i+ζtj	NUM
ejpam-6154	331	19	)	)	PUNCT
ejpam-6154	331	20	,	,	PUNCT
ejpam-6154	331	21	j	j	PROPN
ejpam-6154	331	22	=	=	SYM
ejpam-6154	331	23	1	1	NUM
ejpam-6154	331	24	,	,	PUNCT
ejpam-6154	331	25	2	2	NUM
ejpam-6154	331	26	,	,	PUNCT
ejpam-6154	331	27	(	(	PUNCT
ejpam-6154	331	28	y0	y0	NOUN
ejpam-6154	331	29	,	,	PUNCT
ejpam-6154	331	30	z0	z0	PROPN
ejpam-6154	331	31	)	)	PUNCT
ejpam-6154	331	32	∈	∈	PROPN
ejpam-6154	331	33	h1×h2	h1×h2	PROPN
ejpam-6154	331	34	are	be	AUX
ejpam-6154	331	35	chosen	choose	VERB
ejpam-6154	331	36	arbitrary	arbitrary	ADJ
ejpam-6154	331	37	,	,	PUNCT
ejpam-6154	331	38	0	0	NUM
ejpam-6154	331	39	<	<	X
ejpam-6154	331	40	αn	αn	NOUN
ejpam-6154	331	41	<	<	X
ejpam-6154	331	42	1	1	NUM
ejpam-6154	331	43	such	such	ADJ
ejpam-6154	331	44	that	that	SCONJ
ejpam-6154	331	45	∑	∑	PUNCT
ejpam-6154	331	46	n≥1	n≥1	VERB
ejpam-6154	331	47	αn	αn	NOUN
ejpam-6154	331	48	=	=	SYM
ejpam-6154	331	49	∞	∞	PROPN
ejpam-6154	331	50	,	,	PUNCT
ejpam-6154	331	51	∑	∑	ADP
ejpam-6154	331	52	n≥1	n≥1	NOUN
ejpam-6154	331	53	(	(	PUNCT
ejpam-6154	331	54	1−	1−	NUM
ejpam-6154	331	55	αn)αn	αn)αn	NUM
ejpam-6154	331	56	<	<	X
ejpam-6154	331	57	∞	∞	PROPN
ejpam-6154	331	58	,	,	PUNCT
ejpam-6154	331	59	and	and	CCONJ
ejpam-6154	331	60	lim	lim	PROPN
ejpam-6154	331	61	n→∞	n→∞	PRON
ejpam-6154	331	62	αn	αn	NOUN
ejpam-6154	331	63	=	=	SYM
ejpam-6154	331	64	0	0	NUM
ejpam-6154	331	65	,	,	PUNCT
ejpam-6154	331	66	0	0	PUNCT
ejpam-6154	331	67	<	<	X
ejpam-6154	331	68	τn	τn	X
ejpam-6154	331	69	<	<	X
ejpam-6154	331	70	1	1	NUM
ejpam-6154	331	71	such	such	ADJ
ejpam-6154	331	72	that	that	DET
ejpam-6154	331	73	inf	inf	ADJ
ejpam-6154	331	74	n≥1	n≥1	NOUN
ejpam-6154	331	75	τn	τn	ADP
ejpam-6154	331	76	(	(	PUNCT
ejpam-6154	331	77	(	(	PUNCT
ejpam-6154	331	78	1−	1−	NUM
ejpam-6154	331	79	αn(1−	αn(1−	NUM
ejpam-6154	331	80	2ρ2))λ−	2ρ2))λ−	NUM
ejpam-6154	331	81	τn	τn	NOUN
ejpam-6154	331	82	)	)	PUNCT
ejpam-6154	331	83	≥	≥	PROPN
ejpam-6154	331	84	β	β	X
ejpam-6154	331	85	>	>	X
ejpam-6154	331	86	0	0	PROPN
ejpam-6154	331	87	,	,	PUNCT
ejpam-6154	331	88	where	where	SCONJ
ejpam-6154	331	89	λ	λ	X
ejpam-6154	331	90	=	=	VERB
ejpam-6154	331	91	1	1	NUM
ejpam-6154	331	92	2max{1,∥a1∥2,∥a2∥2	2max{1,∥a1∥2,∥a2∥2	NUM
ejpam-6154	331	93	}	}	PUNCT
ejpam-6154	331	94	,	,	PUNCT
ejpam-6154	331	95	and	and	CCONJ
ejpam-6154	331	96	0	0	NUM
ejpam-6154	331	97	<	<	X
ejpam-6154	331	98	η	η	X
ejpam-6154	331	99	<	<	X
ejpam-6154	331	100	ζ	ζ	X
ejpam-6154	331	101	<	<	X
ejpam-6154	331	102	1	1	NUM
ejpam-6154	331	103	1	1	NUM
ejpam-6154	331	104	+	+	NUM
ejpam-6154	331	105	√	√	PROPN
ejpam-6154	331	106	1+l2	1+l2	NUM
ejpam-6154	331	107	.	.	PUNCT
ejpam-6154	332	1	then	then	ADV
ejpam-6154	332	2	the	the	DET
ejpam-6154	332	3	sequence	sequence	NOUN
ejpam-6154	332	4	{	{	PUNCT
ejpam-6154	332	5	(	(	PUNCT
ejpam-6154	332	6	yn	yn	PROPN
ejpam-6154	332	7	,	,	PUNCT
ejpam-6154	332	8	zn	zn	NOUN
ejpam-6154	332	9	)	)	PUNCT
ejpam-6154	332	10	}	}	PUNCT
ejpam-6154	332	11	converges	converge	VERB
ejpam-6154	332	12	to	to	ADP
ejpam-6154	332	13	(	(	PUNCT
ejpam-6154	332	14	y	y	PROPN
ejpam-6154	332	15	,	,	PUNCT
ejpam-6154	332	16	z	z	NOUN
ejpam-6154	332	17	)	)	PUNCT
ejpam-6154	332	18	∈	∈	PROPN
ejpam-6154	332	19	s.	s.	PROPN
ejpam-6154	332	20	proof	proof	PROPN
ejpam-6154	332	21	.	.	PUNCT
ejpam-6154	333	1	this	this	DET
ejpam-6154	333	2	proof	proof	NOUN
ejpam-6154	333	3	is	be	AUX
ejpam-6154	333	4	a	a	DET
ejpam-6154	333	5	direct	direct	ADJ
ejpam-6154	333	6	consequence	consequence	NOUN
ejpam-6154	333	7	of	of	ADP
ejpam-6154	333	8	theorem	theorem	NOUN
ejpam-6154	333	9	1	1	NUM
ejpam-6154	333	10	by	by	ADP
ejpam-6154	333	11	setting	set	VERB
ejpam-6154	333	12	f	f	X
ejpam-6154	333	13	=	=	PUNCT
ejpam-6154	333	14	i.	i.	PROPN
ejpam-6154	333	15	algorithm	algorithm	PROPN
ejpam-6154	333	16	36	36	NUM
ejpam-6154	333	17	was	be	AUX
ejpam-6154	333	18	studied	study	VERB
ejpam-6154	333	19	by	by	ADP
ejpam-6154	333	20	mohammed	mohammed	PROPN
ejpam-6154	333	21	and	and	CCONJ
ejpam-6154	333	22	kilicman	kilicman	NOUN
ejpam-6154	333	23	[	[	X
ejpam-6154	333	24	10	10	NUM
ejpam-6154	333	25	]	]	PUNCT
ejpam-6154	333	26	in	in	ADP
ejpam-6154	333	27	their	their	PRON
ejpam-6154	333	28	work	work	NOUN
ejpam-6154	333	29	.	.	PUNCT
ejpam-6154	334	1	corollary	corollary	ADJ
ejpam-6154	334	2	3	3	NUM
ejpam-6154	334	3	.	.	PUNCT
ejpam-6154	334	4	suppose	suppose	VERB
ejpam-6154	334	5	conditions	condition	NOUN
ejpam-6154	334	6	(	(	PUNCT
ejpam-6154	334	7	k1	k1	NOUN
ejpam-6154	334	8	)	)	PUNCT
ejpam-6154	334	9	−	−	PROPN
ejpam-6154	334	10	(	(	PUNCT
ejpam-6154	334	11	k4	k4	PROPN
ejpam-6154	334	12	)	)	PUNCT
ejpam-6154	334	13	are	be	AUX
ejpam-6154	334	14	satisfied	satisfied	ADJ
ejpam-6154	334	15	,	,	PUNCT
ejpam-6154	334	16	and	and	CCONJ
ejpam-6154	334	17	that	that	PRON
ejpam-6154	334	18	s	s	VERB
ejpam-6154	334	19	=	=	NOUN
ejpam-6154	334	20	̸	̸	ADV
ejpam-6154	334	21	∅.	∅.	ADV
ejpam-6154	334	22	then	then	ADV
ejpam-6154	334	23	the	the	DET
ejpam-6154	334	24	sequence	sequence	NOUN
ejpam-6154	334	25	{	{	PUNCT
ejpam-6154	334	26	(	(	PUNCT
ejpam-6154	334	27	yn	yn	PROPN
ejpam-6154	334	28	,	,	PUNCT
ejpam-6154	334	29	zn	zn	PROPN
ejpam-6154	334	30	)	)	PUNCT
ejpam-6154	334	31	}	}	PUNCT
ejpam-6154	334	32	generated	generate	VERB
ejpam-6154	334	33	by	by	PROPN
ejpam-6154	334	34	yn+1	yn+1	PUNCT
ejpam-6154	335	1	=	=	NOUN
ejpam-6154	335	2	αnvn	αnvn	NOUN
ejpam-6154	336	1	+	+	CCONJ
ejpam-6154	337	1	(	(	PUNCT
ejpam-6154	337	2	1−	1−	NUM
ejpam-6154	337	3	αn)u1vn	αn)u1vn	NUM
ejpam-6154	337	4	;	;	PUNCT
ejpam-6154	337	5	vn	vn	PROPN
ejpam-6154	337	6	=	=	SYM
ejpam-6154	337	7	yn	yn	PROPN
ejpam-6154	338	1	+	+	CCONJ
ejpam-6154	338	2	λna∗	λna∗	PROPN
ejpam-6154	338	3	1(a1yn	1(a1yn	PROPN
ejpam-6154	338	4	−a2zn	−a2zn	NUM
ejpam-6154	338	5	)	)	PUNCT
ejpam-6154	338	6	;	;	PUNCT
ejpam-6154	338	7	zn+1	zn+1	X
ejpam-6154	338	8	=	=	PRON
ejpam-6154	338	9	αnwn	αnwn	VERB
ejpam-6154	338	10	+	+	X
ejpam-6154	339	1	(	(	PUNCT
ejpam-6154	339	2	1−	1−	NUM
ejpam-6154	339	3	αn)u2wn	αn)u2wn	NUM
ejpam-6154	339	4	;	;	PUNCT
ejpam-6154	339	5	wn	wn	PROPN
ejpam-6154	339	6	=	=	SYM
ejpam-6154	339	7	zn	zn	PROPN
ejpam-6154	340	1	+	+	NUM
ejpam-6154	340	2	λna∗	λna∗	PROPN
ejpam-6154	340	3	2(a2zn	2(a2zn	PROPN
ejpam-6154	340	4	−a1yn),∀n	−a1yn),∀n	NOUN
ejpam-6154	340	5	≥	≥	NOUN
ejpam-6154	340	6	0	0	NUM
ejpam-6154	340	7	;	;	PUNCT
ejpam-6154	340	8	(	(	PUNCT
ejpam-6154	340	9	37	37	NUM
ejpam-6154	340	10	)	)	PUNCT
ejpam-6154	340	11	where	where	SCONJ
ejpam-6154	340	12	uj	uj	PROPN
ejpam-6154	340	13	=	=	SYM
ejpam-6154	340	14	(	(	PUNCT
ejpam-6154	340	15	1−η)i+ηtj((1−ζ)i+ζtj	1−η)i+ηtj((1−ζ)i+ζtj	NUM
ejpam-6154	340	16	)	)	PUNCT
ejpam-6154	340	17	,	,	PUNCT
ejpam-6154	340	18	j	j	PROPN
ejpam-6154	340	19	=	=	SYM
ejpam-6154	340	20	1	1	NUM
ejpam-6154	340	21	,	,	PUNCT
ejpam-6154	340	22	2	2	NUM
ejpam-6154	340	23	,	,	PUNCT
ejpam-6154	340	24	(	(	PUNCT
ejpam-6154	340	25	y0	y0	NOUN
ejpam-6154	340	26	,	,	PUNCT
ejpam-6154	340	27	z0	z0	PROPN
ejpam-6154	340	28	)	)	PUNCT
ejpam-6154	340	29	∈	∈	PROPN
ejpam-6154	340	30	h1×h2	h1×h2	PROPN
ejpam-6154	340	31	are	be	AUX
ejpam-6154	340	32	chosen	choose	VERB
ejpam-6154	340	33	arbitrary	arbitrary	ADJ
ejpam-6154	340	34	,	,	PUNCT
ejpam-6154	340	35	0	0	NUM
ejpam-6154	340	36	<	<	X
ejpam-6154	340	37	αn	αn	X
ejpam-6154	340	38	<	<	X
ejpam-6154	340	39	1	1	NUM
ejpam-6154	340	40	,	,	PUNCT
ejpam-6154	340	41	such	such	ADJ
ejpam-6154	340	42	that	that	SCONJ
ejpam-6154	340	43	∑	∑	PUNCT
ejpam-6154	340	44	n≥1	n≥1	VERB
ejpam-6154	340	45	αn	αn	NOUN
ejpam-6154	340	46	=	=	SYM
ejpam-6154	340	47	∞	∞	PROPN
ejpam-6154	340	48	,	,	PUNCT
ejpam-6154	340	49	∑	∑	ADP
ejpam-6154	340	50	n≥1	n≥1	NOUN
ejpam-6154	340	51	(	(	PUNCT
ejpam-6154	340	52	1−	1−	NUM
ejpam-6154	340	53	αn)αn	αn)αn	NUM
ejpam-6154	340	54	<	<	X
ejpam-6154	340	55	∞	∞	PROPN
ejpam-6154	340	56	,	,	PUNCT
ejpam-6154	340	57	and	and	CCONJ
ejpam-6154	340	58	lim	lim	PROPN
ejpam-6154	340	59	n→∞	n→∞	PRON
ejpam-6154	340	60	αn	αn	NOUN
ejpam-6154	340	61	=	=	SYM
ejpam-6154	340	62	0	0	NUM
ejpam-6154	340	63	,	,	PUNCT
ejpam-6154	340	64	0	0	PUNCT
ejpam-6154	340	65	<	<	X
ejpam-6154	340	66	λn	λn	X
ejpam-6154	340	67	<	<	X
ejpam-6154	340	68	1	1	NUM
ejpam-6154	340	69	,	,	PUNCT
ejpam-6154	340	70	and	and	CCONJ
ejpam-6154	340	71	0	0	NUM
ejpam-6154	340	72	<	<	X
ejpam-6154	340	73	η	η	X
ejpam-6154	340	74	<	<	X
ejpam-6154	340	75	ζ	ζ	X
ejpam-6154	340	76	<	<	X
ejpam-6154	340	77	1	1	NUM
ejpam-6154	340	78	1	1	NUM
ejpam-6154	340	79	+	+	NUM
ejpam-6154	340	80	√	√	PROPN
ejpam-6154	340	81	1+l2	1+l2	NUM
ejpam-6154	340	82	.	.	PUNCT
ejpam-6154	341	1	then	then	ADV
ejpam-6154	341	2	the	the	DET
ejpam-6154	341	3	sequence	sequence	NOUN
ejpam-6154	341	4	{	{	PUNCT
ejpam-6154	341	5	(	(	PUNCT
ejpam-6154	341	6	yn	yn	PROPN
ejpam-6154	341	7	,	,	PUNCT
ejpam-6154	341	8	zn	zn	NOUN
ejpam-6154	341	9	)	)	PUNCT
ejpam-6154	341	10	}	}	PUNCT
ejpam-6154	341	11	converges	converge	VERB
ejpam-6154	341	12	to	to	ADP
ejpam-6154	341	13	(	(	PUNCT
ejpam-6154	341	14	y	y	PROPN
ejpam-6154	341	15	,	,	PUNCT
ejpam-6154	341	16	z	z	NOUN
ejpam-6154	341	17	)	)	PUNCT
ejpam-6154	341	18	∈	∈	PROPN
ejpam-6154	341	19	s.	s.	PROPN
ejpam-6154	341	20	proof	proof	PROPN
ejpam-6154	341	21	.	.	PUNCT
ejpam-6154	342	1	this	this	DET
ejpam-6154	342	2	proof	proof	NOUN
ejpam-6154	342	3	follows	follow	VERB
ejpam-6154	342	4	directly	directly	ADV
ejpam-6154	342	5	from	from	ADP
ejpam-6154	342	6	theorem	theorem	NOUN
ejpam-6154	342	7	1	1	NUM
ejpam-6154	342	8	by	by	ADP
ejpam-6154	342	9	taking	take	VERB
ejpam-6154	342	10	f	f	PROPN
ejpam-6154	342	11	=	=	PUNCT
ejpam-6154	342	12	i	i	PROPN
ejpam-6154	342	13	,	,	PUNCT
ejpam-6154	342	14	and	and	CCONJ
ejpam-6154	342	15	τn	τn	ADP
ejpam-6154	342	16	=	=	NOUN
ejpam-6154	342	17	0	0	X
ejpam-6154	342	18	.	.	PUNCT
ejpam-6154	343	1	algorithm	algorithm	PROPN
ejpam-6154	343	2	37	37	NUM
ejpam-6154	343	3	was	be	AUX
ejpam-6154	343	4	proposed	propose	VERB
ejpam-6154	343	5	by	by	ADP
ejpam-6154	343	6	(	(	PUNCT
ejpam-6154	343	7	chang	chang	PROPN
ejpam-6154	343	8	et	et	PROPN
ejpam-6154	343	9	al	al	PROPN
ejpam-6154	343	10	.	.	PROPN
ejpam-6154	343	11	,	,	PUNCT
ejpam-6154	344	1	[	[	X
ejpam-6154	344	2	9	9	NUM
ejpam-6154	344	3	]	]	SYM
ejpam-6154	344	4	)	)	PUNCT
ejpam-6154	344	5	.	.	PUNCT
ejpam-6154	345	1	corollary	corollary	ADJ
ejpam-6154	345	2	4	4	NUM
ejpam-6154	345	3	.	.	PUNCT
ejpam-6154	345	4	suppose	suppose	VERB
ejpam-6154	345	5	conditions	condition	NOUN
ejpam-6154	345	6	(	(	PUNCT
ejpam-6154	345	7	k1	k1	NOUN
ejpam-6154	345	8	)	)	PUNCT
ejpam-6154	345	9	−	−	PROPN
ejpam-6154	345	10	(	(	PUNCT
ejpam-6154	345	11	k4	k4	PROPN
ejpam-6154	345	12	)	)	PUNCT
ejpam-6154	345	13	are	be	AUX
ejpam-6154	345	14	satisfied	satisfied	ADJ
ejpam-6154	345	15	,	,	PUNCT
ejpam-6154	345	16	and	and	CCONJ
ejpam-6154	345	17	that	that	PRON
ejpam-6154	345	18	s	s	VERB
ejpam-6154	345	19	=	=	NOUN
ejpam-6154	345	20	̸	̸	ADV
ejpam-6154	345	21	∅.	∅.	ADV
ejpam-6154	345	22	then	then	ADV
ejpam-6154	345	23	the	the	DET
ejpam-6154	345	24	sequence	sequence	NOUN
ejpam-6154	345	25	{	{	PUNCT
ejpam-6154	345	26	(	(	PUNCT
ejpam-6154	345	27	yn	yn	PROPN
ejpam-6154	345	28	,	,	PUNCT
ejpam-6154	345	29	zn	zn	PROPN
ejpam-6154	345	30	)	)	PUNCT
ejpam-6154	345	31	}	}	PUNCT
ejpam-6154	345	32	generated	generate	VERB
ejpam-6154	345	33	by	by	ADP
ejpam-6154	345	34	l.	l.	PROPN
ejpam-6154	345	35	b.	b.	PROPN
ejpam-6154	345	36	mohammed	mohammed	PROPN
ejpam-6154	345	37	,	,	PUNCT
ejpam-6154	345	38	a.	a.	PROPN
ejpam-6154	345	39	kılıçman	kılıçman	PROPN
ejpam-6154	345	40	,	,	PUNCT
ejpam-6154	345	41	d.	d.	PROPN
ejpam-6154	345	42	bamanga	bamanga	PROPN
ejpam-6154	345	43	/	/	SYM
ejpam-6154	345	44	eur	eur	PROPN
ejpam-6154	345	45	.	.	PUNCT
ejpam-6154	346	1	j.	j.	PROPN
ejpam-6154	346	2	pure	pure	PROPN
ejpam-6154	346	3	appl	appl	PROPN
ejpam-6154	346	4	.	.	PROPN
ejpam-6154	346	5	math	math	PROPN
ejpam-6154	346	6	,	,	PUNCT
ejpam-6154	346	7	18	18	NUM
ejpam-6154	346	8	(	(	PUNCT
ejpam-6154	346	9	4	4	NUM
ejpam-6154	346	10	)	)	PUNCT
ejpam-6154	346	11	(	(	PUNCT
ejpam-6154	346	12	2025	2025	NUM
ejpam-6154	346	13	)	)	PUNCT
ejpam-6154	346	14	,	,	PUNCT
ejpam-6154	346	15	6154	6154	NUM
ejpam-6154	346	16	14	14	NUM
ejpam-6154	346	17	of	of	ADP
ejpam-6154	346	18	18	18	NUM
ejpam-6154	346	19			NUM
ejpam-6154	346	20	yn+1	yn+1	X
ejpam-6154	346	21	=	=	PUNCT
ejpam-6154	346	22	u1vn	u1vn	PROPN
ejpam-6154	346	23	;	;	PUNCT
ejpam-6154	346	24	vn	vn	PROPN
ejpam-6154	346	25	=	=	SYM
ejpam-6154	346	26	yn	yn	PROPN
ejpam-6154	347	1	+	+	CCONJ
ejpam-6154	347	2	λna∗	λna∗	PROPN
ejpam-6154	347	3	1(a1yn	1(a1yn	PROPN
ejpam-6154	347	4	−a2zn	−a2zn	NUM
ejpam-6154	347	5	)	)	PUNCT
ejpam-6154	347	6	;	;	PUNCT
ejpam-6154	347	7	zn+1	zn+1	X
ejpam-6154	347	8	=	=	PUNCT
ejpam-6154	347	9	u2wn	u2wn	PRON
ejpam-6154	347	10	;	;	PUNCT
ejpam-6154	347	11	wn	wn	PROPN
ejpam-6154	347	12	=	=	SYM
ejpam-6154	347	13	zn	zn	PROPN
ejpam-6154	348	1	+	+	NUM
ejpam-6154	348	2	λna∗	λna∗	PROPN
ejpam-6154	348	3	2(a2zn	2(a2zn	PROPN
ejpam-6154	348	4	−a1yn),∀n	−a1yn),∀n	NOUN
ejpam-6154	348	5	≥	≥	NOUN
ejpam-6154	348	6	0	0	NUM
ejpam-6154	348	7	;	;	PUNCT
ejpam-6154	348	8	(	(	PUNCT
ejpam-6154	348	9	38	38	NUM
ejpam-6154	348	10	)	)	PUNCT
ejpam-6154	348	11	where	where	SCONJ
ejpam-6154	348	12	uj	uj	PROPN
ejpam-6154	348	13	=	=	PRON
ejpam-6154	348	14	(	(	PUNCT
ejpam-6154	348	15	1−η)i+ηtj((1−	1−η)i+ηtj((1−	PROPN
ejpam-6154	348	16	ζ)i+	ζ)i+	NOUN
ejpam-6154	348	17	ζtj	ζtj	NOUN
ejpam-6154	348	18	)	)	PUNCT
ejpam-6154	348	19	,	,	PUNCT
ejpam-6154	348	20	j	j	PROPN
ejpam-6154	348	21	=	=	SYM
ejpam-6154	348	22	1	1	NUM
ejpam-6154	348	23	,	,	PUNCT
ejpam-6154	348	24	2	2	NUM
ejpam-6154	348	25	(	(	PUNCT
ejpam-6154	348	26	y0	y0	NOUN
ejpam-6154	348	27	,	,	PUNCT
ejpam-6154	348	28	z0	z0	PROPN
ejpam-6154	348	29	)	)	PUNCT
ejpam-6154	348	30	∈	∈	PROPN
ejpam-6154	348	31	h1×h2	h1×h2	PROPN
ejpam-6154	348	32	are	be	AUX
ejpam-6154	348	33	chosen	choose	VERB
ejpam-6154	348	34	arbitrary	arbitrary	ADJ
ejpam-6154	348	35	,	,	PUNCT
ejpam-6154	348	36	0	0	NUM
ejpam-6154	348	37	<	<	X
ejpam-6154	348	38	αn	αn	X
ejpam-6154	348	39	<	<	X
ejpam-6154	348	40	1	1	NUM
ejpam-6154	348	41	,	,	PUNCT
ejpam-6154	348	42	such	such	ADJ
ejpam-6154	348	43	that	that	SCONJ
ejpam-6154	348	44	∑	∑	PUNCT
ejpam-6154	348	45	n≥1	n≥1	VERB
ejpam-6154	348	46	αn	αn	NOUN
ejpam-6154	348	47	=	=	SYM
ejpam-6154	348	48	∞	∞	PROPN
ejpam-6154	348	49	,	,	PUNCT
ejpam-6154	348	50	∑	∑	ADP
ejpam-6154	348	51	n≥1	n≥1	NOUN
ejpam-6154	348	52	(	(	PUNCT
ejpam-6154	348	53	1−	1−	NUM
ejpam-6154	348	54	αn)αn	αn)αn	NUM
ejpam-6154	348	55	<	<	X
ejpam-6154	348	56	∞	∞	PROPN
ejpam-6154	348	57	,	,	PUNCT
ejpam-6154	348	58	and	and	CCONJ
ejpam-6154	348	59	lim	lim	PROPN
ejpam-6154	348	60	n→∞	n→∞	PRON
ejpam-6154	348	61	αn	αn	NOUN
ejpam-6154	348	62	=	=	SYM
ejpam-6154	348	63	0	0	NUM
ejpam-6154	348	64	,	,	PUNCT
ejpam-6154	348	65	and	and	CCONJ
ejpam-6154	348	66	0	0	NUM
ejpam-6154	348	67	<	<	X
ejpam-6154	348	68	λn	λn	X
ejpam-6154	348	69	<	<	X
ejpam-6154	348	70	1	1	NUM
ejpam-6154	348	71	,	,	PUNCT
ejpam-6154	348	72	and	and	CCONJ
ejpam-6154	348	73	0	0	NUM
ejpam-6154	348	74	<	<	X
ejpam-6154	348	75	η	η	X
ejpam-6154	348	76	<	<	X
ejpam-6154	348	77	ζ	ζ	X
ejpam-6154	348	78	<	<	X
ejpam-6154	348	79	1	1	NUM
ejpam-6154	348	80	1	1	NUM
ejpam-6154	348	81	+	+	NUM
ejpam-6154	348	82	√	√	PROPN
ejpam-6154	348	83	1+l2	1+l2	NUM
ejpam-6154	348	84	.	.	PUNCT
ejpam-6154	349	1	then	then	ADV
ejpam-6154	349	2	the	the	DET
ejpam-6154	349	3	sequence	sequence	NOUN
ejpam-6154	349	4	{	{	PUNCT
ejpam-6154	349	5	(	(	PUNCT
ejpam-6154	349	6	yn	yn	PROPN
ejpam-6154	349	7	,	,	PUNCT
ejpam-6154	349	8	zn	zn	NOUN
ejpam-6154	349	9	)	)	PUNCT
ejpam-6154	349	10	}	}	PUNCT
ejpam-6154	349	11	converges	converge	VERB
ejpam-6154	349	12	to	to	ADP
ejpam-6154	349	13	(	(	PUNCT
ejpam-6154	349	14	y	y	PROPN
ejpam-6154	349	15	,	,	PUNCT
ejpam-6154	349	16	z	z	NOUN
ejpam-6154	349	17	)	)	PUNCT
ejpam-6154	349	18	∈	∈	PROPN
ejpam-6154	349	19	s.	s.	PROPN
ejpam-6154	349	20	proof	proof	PROPN
ejpam-6154	349	21	.	.	PUNCT
ejpam-6154	350	1	this	this	DET
ejpam-6154	350	2	proof	proof	NOUN
ejpam-6154	350	3	follows	follow	VERB
ejpam-6154	350	4	directly	directly	ADV
ejpam-6154	350	5	from	from	ADP
ejpam-6154	350	6	theorem	theorem	NOUN
ejpam-6154	350	7	1	1	NUM
ejpam-6154	350	8	by	by	ADP
ejpam-6154	350	9	taking	take	VERB
ejpam-6154	350	10	f	f	PROPN
ejpam-6154	350	11	=	=	PUNCT
ejpam-6154	350	12	i	i	PROPN
ejpam-6154	350	13	,	,	PUNCT
ejpam-6154	350	14	and	and	CCONJ
ejpam-6154	350	15	τn	τn	ADP
ejpam-6154	350	16	=	=	VERB
ejpam-6154	350	17	αn	αn	NOUN
ejpam-6154	350	18	=	=	SYM
ejpam-6154	350	19	0	0	PROPN
ejpam-6154	350	20	.	.	PUNCT
ejpam-6154	350	21	algorithm	algorithm	PROPN
ejpam-6154	350	22	38	38	NUM
ejpam-6154	350	23	was	be	AUX
ejpam-6154	350	24	proposed	propose	VERB
ejpam-6154	350	25	and	and	CCONJ
ejpam-6154	350	26	studied	study	VERB
ejpam-6154	350	27	by	by	ADP
ejpam-6154	350	28	(	(	PUNCT
ejpam-6154	350	29	moudafi	moudafi	PROPN
ejpam-6154	350	30	and	and	CCONJ
ejpam-6154	350	31	al	al	PROPN
ejpam-6154	350	32	-	-	PUNCT
ejpam-6154	350	33	shemas	shemas	PROPN
ejpam-6154	351	1	[	[	X
ejpam-6154	351	2	8	8	NUM
ejpam-6154	351	3	]	]	NUM
ejpam-6154	351	4	)	)	PUNCT
ejpam-6154	351	5	.	.	PUNCT
ejpam-6154	352	1	corollary	corollary	ADJ
ejpam-6154	352	2	5	5	NUM
ejpam-6154	352	3	.	.	PUNCT
ejpam-6154	352	4	suppose	suppose	VERB
ejpam-6154	352	5	conditions	condition	NOUN
ejpam-6154	352	6	(	(	PUNCT
ejpam-6154	352	7	k1	k1	NOUN
ejpam-6154	352	8	)	)	PUNCT
ejpam-6154	352	9	−	−	PROPN
ejpam-6154	352	10	(	(	PUNCT
ejpam-6154	352	11	k4	k4	PROPN
ejpam-6154	352	12	)	)	PUNCT
ejpam-6154	352	13	are	be	AUX
ejpam-6154	352	14	satisfied	satisfied	ADJ
ejpam-6154	352	15	,	,	PUNCT
ejpam-6154	352	16	and	and	CCONJ
ejpam-6154	352	17	that	that	PRON
ejpam-6154	352	18	s	s	VERB
ejpam-6154	352	19	=	=	NOUN
ejpam-6154	352	20	̸	̸	ADV
ejpam-6154	352	21	∅.	∅.	ADV
ejpam-6154	352	22	then	then	ADV
ejpam-6154	352	23	the	the	DET
ejpam-6154	352	24	sequence	sequence	NOUN
ejpam-6154	352	25	{	{	PUNCT
ejpam-6154	352	26	(	(	PUNCT
ejpam-6154	352	27	yn	yn	PROPN
ejpam-6154	352	28	,	,	PUNCT
ejpam-6154	352	29	zn	zn	PROPN
ejpam-6154	352	30	)	)	PUNCT
ejpam-6154	352	31	}	}	PUNCT
ejpam-6154	352	32	generated	generate	VERB
ejpam-6154	352	33	by	by	PROPN
ejpam-6154	352	34	yn+1	yn+1	PROPN
ejpam-6154	353	1	=	=	PUNCT
ejpam-6154	353	2	βnf1(yn	βnf1(yn	PROPN
ejpam-6154	353	3	)	)	PUNCT
ejpam-6154	354	1	+	+	CCONJ
ejpam-6154	354	2	(	(	PUNCT
ejpam-6154	354	3	1−	1−	NUM
ejpam-6154	354	4	βn)vn	βn)vn	NUM
ejpam-6154	354	5	,	,	PUNCT
ejpam-6154	354	6	vn	vn	PROPN
ejpam-6154	354	7	=	=	PROPN
ejpam-6154	354	8	yn	yn	PROPN
ejpam-6154	355	1	−	−	PROPN
ejpam-6154	355	2	λn	λn	PROPN
ejpam-6154	355	3	(	(	PUNCT
ejpam-6154	355	4	yn	yn	PROPN
ejpam-6154	355	5	−	−	PROPN
ejpam-6154	355	6	t1yn	t1yn	PUNCT
ejpam-6154	356	1	+	+	ADJ
ejpam-6154	356	2	a∗	a∗	ADJ
ejpam-6154	356	3	1	1	NUM
ejpam-6154	356	4	(	(	PUNCT
ejpam-6154	356	5	a1yn	a1yn	X
ejpam-6154	356	6	−a2zn	−a2zn	NUM
ejpam-6154	356	7	)	)	PUNCT
ejpam-6154	356	8	)	)	PUNCT
ejpam-6154	356	9	,	,	PUNCT
ejpam-6154	356	10	zn+1	zn+1	X
ejpam-6154	356	11	=	=	PUNCT
ejpam-6154	356	12	βnf2(yn	βnf2(yn	PROPN
ejpam-6154	356	13	)	)	PUNCT
ejpam-6154	357	1	+	+	CCONJ
ejpam-6154	357	2	(	(	PUNCT
ejpam-6154	357	3	1−	1−	NUM
ejpam-6154	357	4	βn)wn	βn)wn	PROPN
ejpam-6154	357	5	,	,	PUNCT
ejpam-6154	357	6	wn	wn	PROPN
ejpam-6154	357	7	=	=	SYM
ejpam-6154	357	8	zn	zn	PROPN
ejpam-6154	357	9	−	−	PROPN
ejpam-6154	358	1	λn	λn	PROPN
ejpam-6154	358	2	(	(	PUNCT
ejpam-6154	358	3	zn	zn	PROPN
ejpam-6154	358	4	−	−	PROPN
ejpam-6154	358	5	t2zn	t2zn	X
ejpam-6154	359	1	+	+	ADJ
ejpam-6154	359	2	a∗	a∗	ADJ
ejpam-6154	359	3	2	2	NUM
ejpam-6154	359	4	(	(	PUNCT
ejpam-6154	359	5	a2zn	a2zn	ADP
ejpam-6154	359	6	−a1yn	−a1yn	NUM
ejpam-6154	359	7	)	)	PUNCT
ejpam-6154	359	8	)	)	PUNCT
ejpam-6154	359	9	,	,	PUNCT
ejpam-6154	359	10	n	n	X
ejpam-6154	359	11	≥	≥	NOUN
ejpam-6154	359	12	0	0	NUM
ejpam-6154	359	13	;	;	PUNCT
ejpam-6154	359	14	(	(	PUNCT
ejpam-6154	359	15	39	39	NUM
ejpam-6154	359	16	)	)	PUNCT
ejpam-6154	359	17	where	where	SCONJ
ejpam-6154	359	18	(	(	PUNCT
ejpam-6154	359	19	y0	y0	NOUN
ejpam-6154	359	20	,	,	PUNCT
ejpam-6154	359	21	z0	z0	PROPN
ejpam-6154	359	22	)	)	PUNCT
ejpam-6154	359	23	∈	∈	PROPN
ejpam-6154	359	24	h1	h1	PROPN
ejpam-6154	359	25	×	×	PROPN
ejpam-6154	359	26	h2	h2	NOUN
ejpam-6154	359	27	are	be	AUX
ejpam-6154	359	28	chosen	choose	VERB
ejpam-6154	359	29	arbitrary	arbitrary	ADJ
ejpam-6154	359	30	,	,	PUNCT
ejpam-6154	359	31	0	0	PUNCT
ejpam-6154	359	32	<	<	X
ejpam-6154	359	33	βn	βn	X
ejpam-6154	359	34	<	<	X
ejpam-6154	359	35	1	1	NUM
ejpam-6154	359	36	,	,	PUNCT
ejpam-6154	359	37	such	such	ADJ
ejpam-6154	359	38	that	that	SCONJ
ejpam-6154	359	39	∑	∑	PUNCT
ejpam-6154	359	40	n≥1	n≥1	VERB
ejpam-6154	359	41	βn	βn	NOUN
ejpam-6154	359	42	=	=	SYM
ejpam-6154	359	43	∞,∑	∞,∑	ADP
ejpam-6154	359	44	n≥1	n≥1	NOUN
ejpam-6154	359	45	(	(	PUNCT
ejpam-6154	359	46	1−	1−	NUM
ejpam-6154	359	47	βn)βn	βn)βn	PUNCT
ejpam-6154	359	48	<	<	X
ejpam-6154	359	49	∞	∞	PROPN
ejpam-6154	359	50	,	,	PUNCT
ejpam-6154	359	51	and	and	CCONJ
ejpam-6154	359	52	lim	lim	PROPN
ejpam-6154	359	53	n→∞	n→∞	NUM
ejpam-6154	359	54	βn	βn	NOUN
ejpam-6154	359	55	=	=	SYM
ejpam-6154	359	56	0	0	NUM
ejpam-6154	359	57	,	,	PUNCT
ejpam-6154	359	58	0	0	PUNCT
ejpam-6154	359	59	<	<	X
ejpam-6154	359	60	λn	λn	X
ejpam-6154	359	61	<	<	X
ejpam-6154	359	62	1	1	NUM
ejpam-6154	359	63	such	such	ADJ
ejpam-6154	359	64	that	that	DET
ejpam-6154	359	65	inf	inf	ADJ
ejpam-6154	359	66	n≥1	n≥1	NOUN
ejpam-6154	359	67	λn	λn	PROPN
ejpam-6154	359	68	(	(	PUNCT
ejpam-6154	359	69	λ−	λ−	PROPN
ejpam-6154	359	70	λn	λn	NOUN
ejpam-6154	359	71	)	)	PUNCT
ejpam-6154	359	72	≥	≥	PROPN
ejpam-6154	359	73	β	β	X
ejpam-6154	359	74	>	>	X
ejpam-6154	359	75	0	0	PROPN
ejpam-6154	359	76	,	,	PUNCT
ejpam-6154	359	77	where	where	SCONJ
ejpam-6154	359	78	λ	λ	X
ejpam-6154	359	79	=	=	VERB
ejpam-6154	359	80	1	1	NUM
ejpam-6154	359	81	2max{1,∥a1∥2,∥a2∥2	2max{1,∥a1∥2,∥a2∥2	NUM
ejpam-6154	359	82	}	}	PUNCT
ejpam-6154	359	83	.	.	PUNCT
ejpam-6154	360	1	then	then	ADV
ejpam-6154	360	2	the	the	DET
ejpam-6154	360	3	sequence	sequence	NOUN
ejpam-6154	360	4	{	{	PUNCT
ejpam-6154	360	5	(	(	PUNCT
ejpam-6154	360	6	yn	yn	PROPN
ejpam-6154	360	7	,	,	PUNCT
ejpam-6154	360	8	zn	zn	NOUN
ejpam-6154	360	9	)	)	PUNCT
ejpam-6154	360	10	}	}	PUNCT
ejpam-6154	360	11	converges	converge	VERB
ejpam-6154	360	12	to	to	ADP
ejpam-6154	360	13	(	(	PUNCT
ejpam-6154	360	14	y	y	PROPN
ejpam-6154	360	15	,	,	PUNCT
ejpam-6154	360	16	z	z	NOUN
ejpam-6154	360	17	)	)	PUNCT
ejpam-6154	360	18	∈	∈	PROPN
ejpam-6154	360	19	s.	s.	PROPN
ejpam-6154	360	20	proof	proof	PROPN
ejpam-6154	360	21	.	.	PUNCT
ejpam-6154	361	1	this	this	DET
ejpam-6154	361	2	proof	proof	NOUN
ejpam-6154	361	3	is	be	AUX
ejpam-6154	361	4	a	a	DET
ejpam-6154	361	5	direct	direct	ADJ
ejpam-6154	361	6	consequence	consequence	NOUN
ejpam-6154	361	7	of	of	ADP
ejpam-6154	361	8	theorem	theorem	NOUN
ejpam-6154	361	9	1	1	NUM
ejpam-6154	361	10	by	by	ADP
ejpam-6154	361	11	setting	set	VERB
ejpam-6154	361	12	uj	uj	PROPN
ejpam-6154	361	13	=	=	SYM
ejpam-6154	361	14	(	(	PUNCT
ejpam-6154	361	15	1	1	NUM
ejpam-6154	361	16	−	−	NOUN
ejpam-6154	361	17	η)i	η)i	ADJ
ejpam-6154	361	18	+	+	CCONJ
ejpam-6154	361	19	ηtj((1−	ηtj((1−	ADJ
ejpam-6154	361	20	ζ)i	ζ)i	NOUN
ejpam-6154	361	21	+	+	CCONJ
ejpam-6154	361	22	ζtj	ζtj	NOUN
ejpam-6154	361	23	)	)	PUNCT
ejpam-6154	361	24	=	=	SYM
ejpam-6154	361	25	i.	i.	NOUN
ejpam-6154	361	26	algorithm	algorithm	PROPN
ejpam-6154	361	27	39	39	NUM
ejpam-6154	361	28	was	be	AUX
ejpam-6154	361	29	studies	study	NOUN
ejpam-6154	361	30	by	by	ADP
ejpam-6154	361	31	wang	wang	PROPN
ejpam-6154	361	32	et	et	PROPN
ejpam-6154	361	33	al	al	PROPN
ejpam-6154	361	34	.	.	PROPN
ejpam-6154	361	35	,	,	PUNCT
ejpam-6154	362	1	[	[	X
ejpam-6154	362	2	11	11	NUM
ejpam-6154	362	3	]	]	PUNCT
ejpam-6154	362	4	in	in	ADP
ejpam-6154	362	5	their	their	PRON
ejpam-6154	362	6	work	work	NOUN
ejpam-6154	362	7	.	.	PUNCT
ejpam-6154	363	1	4	4	X
ejpam-6154	363	2	.	.	X
ejpam-6154	363	3	numerical	numerical	ADJ
ejpam-6154	363	4	examples	example	NOUN
ejpam-6154	363	5	this	this	DET
ejpam-6154	363	6	section	section	NOUN
ejpam-6154	363	7	presents	present	VERB
ejpam-6154	363	8	numerical	numerical	ADJ
ejpam-6154	363	9	results	result	NOUN
ejpam-6154	363	10	that	that	PRON
ejpam-6154	363	11	demonstrate	demonstrate	VERB
ejpam-6154	363	12	our	our	PRON
ejpam-6154	363	13	theoretical	theoretical	ADJ
ejpam-6154	363	14	findings	finding	NOUN
ejpam-6154	363	15	and	and	CCONJ
ejpam-6154	363	16	compares	compare	VERB
ejpam-6154	363	17	them	they	PRON
ejpam-6154	363	18	with	with	ADP
ejpam-6154	363	19	some	some	DET
ejpam-6154	363	20	existing	exist	VERB
ejpam-6154	363	21	results	result	NOUN
ejpam-6154	363	22	from	from	ADP
ejpam-6154	363	23	the	the	DET
ejpam-6154	363	24	literature	literature	NOUN
ejpam-6154	363	25	.	.	PUNCT
ejpam-6154	364	1	the	the	DET
ejpam-6154	364	2	following	following	ADJ
ejpam-6154	364	3	example	example	NOUN
ejpam-6154	364	4	is	be	AUX
ejpam-6154	364	5	an	an	DET
ejpam-6154	364	6	example	example	NOUN
ejpam-6154	364	7	of	of	ADP
ejpam-6154	364	8	a	a	DET
ejpam-6154	364	9	nonlinear	nonlinear	ADJ
ejpam-6154	364	10	mapping	mapping	NOUN
ejpam-6154	364	11	that	that	PRON
ejpam-6154	364	12	is	be	AUX
ejpam-6154	364	13	not	not	PART
ejpam-6154	364	14	semi	semi	ADJ
ejpam-6154	364	15	-	-	ADJ
ejpam-6154	364	16	compact	compact	ADJ
ejpam-6154	364	17	example	example	NOUN
ejpam-6154	364	18	1	1	X
ejpam-6154	364	19	.	.	PUNCT
ejpam-6154	365	1	let	let	VERB
ejpam-6154	365	2	h1	h1	VERB
ejpam-6154	365	3	=	=	SYM
ejpam-6154	365	4	ℓ2(n	ℓ2(n	PROPN
ejpam-6154	365	5	)	)	PUNCT
ejpam-6154	365	6	,	,	PUNCT
ejpam-6154	365	7	and	and	CCONJ
ejpam-6154	365	8	define	define	VERB
ejpam-6154	365	9	a	a	DET
ejpam-6154	365	10	mapping	mapping	NOUN
ejpam-6154	365	11	t	t	NOUN
ejpam-6154	365	12	:	:	PUNCT
ejpam-6154	365	13	ℓ2	ℓ2	PROPN
ejpam-6154	365	14	→	→	SYM
ejpam-6154	365	15	ℓ2	ℓ2	PROPN
ejpam-6154	365	16	by	by	ADP
ejpam-6154	365	17	t	t	PROPN
ejpam-6154	365	18	(	(	PUNCT
ejpam-6154	365	19	x	x	NOUN
ejpam-6154	365	20	)	)	PUNCT
ejpam-6154	365	21	=	=	SYM
ejpam-6154	365	22	{	{	PUNCT
ejpam-6154	365	23	(	(	PUNCT
ejpam-6154	365	24	1−	1−	NUM
ejpam-6154	365	25	1	1	NUM
ejpam-6154	365	26	n	n	NOUN
ejpam-6154	365	27	)	)	PUNCT
ejpam-6154	365	28	en	en	ADP
ejpam-6154	365	29	,	,	PUNCT
ejpam-6154	365	30	if	if	SCONJ
ejpam-6154	365	31	x	x	X
ejpam-6154	365	32	=	=	SYM
ejpam-6154	365	33	en	en	X
ejpam-6154	365	34	for	for	ADP
ejpam-6154	365	35	some	some	DET
ejpam-6154	365	36	n	n	CCONJ
ejpam-6154	365	37	,	,	PUNCT
ejpam-6154	365	38	0	0	NUM
ejpam-6154	365	39	,	,	PUNCT
ejpam-6154	365	40	otherwise	otherwise	ADV
ejpam-6154	365	41	.	.	PUNCT
ejpam-6154	366	1	then	then	ADV
ejpam-6154	366	2	t	t	PROPN
ejpam-6154	366	3	is	be	AUX
ejpam-6154	366	4	not	not	PART
ejpam-6154	366	5	semi	semi	ADJ
ejpam-6154	366	6	-	-	ADJ
ejpam-6154	366	7	compact	compact	ADJ
ejpam-6154	366	8	.	.	PUNCT
ejpam-6154	367	1	l.	l.	PROPN
ejpam-6154	367	2	b.	b.	PROPN
ejpam-6154	367	3	mohammed	mohammed	PROPN
ejpam-6154	367	4	,	,	PUNCT
ejpam-6154	367	5	a.	a.	PROPN
ejpam-6154	367	6	kılıçman	kılıçman	PROPN
ejpam-6154	367	7	,	,	PUNCT
ejpam-6154	367	8	d.	d.	PROPN
ejpam-6154	367	9	bamanga	bamanga	PROPN
ejpam-6154	367	10	/	/	SYM
ejpam-6154	367	11	eur	eur	PROPN
ejpam-6154	367	12	.	.	PUNCT
ejpam-6154	368	1	j.	j.	PROPN
ejpam-6154	368	2	pure	pure	PROPN
ejpam-6154	368	3	appl	appl	PROPN
ejpam-6154	368	4	.	.	PROPN
ejpam-6154	368	5	math	math	PROPN
ejpam-6154	368	6	,	,	PUNCT
ejpam-6154	368	7	18	18	NUM
ejpam-6154	368	8	(	(	PUNCT
ejpam-6154	368	9	4	4	NUM
ejpam-6154	368	10	)	)	PUNCT
ejpam-6154	368	11	(	(	PUNCT
ejpam-6154	368	12	2025	2025	NUM
ejpam-6154	368	13	)	)	PUNCT
ejpam-6154	368	14	,	,	PUNCT
ejpam-6154	368	15	6154	6154	NUM
ejpam-6154	368	16	15	15	NUM
ejpam-6154	368	17	of	of	ADP
ejpam-6154	368	18	18	18	NUM
ejpam-6154	368	19	proof	proof	NOUN
ejpam-6154	368	20	.	.	PUNCT
ejpam-6154	369	1	clearly	clearly	ADV
ejpam-6154	369	2	,	,	PUNCT
ejpam-6154	369	3	t	t	PROPN
ejpam-6154	369	4	is	be	AUX
ejpam-6154	369	5	not	not	PART
ejpam-6154	369	6	linear	linear	ADJ
ejpam-6154	369	7	.	.	PUNCT
ejpam-6154	370	1	l	l	NOUN
ejpam-6154	370	2	et	et	NOUN
ejpam-6154	370	3	{	{	PUNCT
ejpam-6154	370	4	xn	xn	PROPN
ejpam-6154	370	5	}	}	PUNCT
ejpam-6154	370	6	⊆	⊆	NUM
ejpam-6154	370	7	ℓ2	ℓ2	NOUN
ejpam-6154	370	8	defined	define	VERB
ejpam-6154	370	9	by	by	ADP
ejpam-6154	370	10	xn	xn	PROPN
ejpam-6154	370	11	=	=	SYM
ejpam-6154	370	12	en	en	PROPN
ejpam-6154	370	13	,	,	PUNCT
ejpam-6154	370	14	where	where	SCONJ
ejpam-6154	370	15	en	en	X
ejpam-6154	370	16	is	be	AUX
ejpam-6154	370	17	the	the	DET
ejpam-6154	370	18	standard	standard	ADJ
ejpam-6154	370	19	basis	basis	NOUN
ejpam-6154	370	20	vector	vector	NOUN
ejpam-6154	370	21	with	with	ADP
ejpam-6154	370	22	1	1	NUM
ejpam-6154	370	23	in	in	ADP
ejpam-6154	370	24	the	the	DET
ejpam-6154	370	25	n	n	CCONJ
ejpam-6154	370	26	-	-	PUNCT
ejpam-6154	370	27	th	th	VERB
ejpam-6154	370	28	position	position	NOUN
ejpam-6154	370	29	and	and	CCONJ
ejpam-6154	370	30	0	0	NUM
ejpam-6154	370	31	elsewhere	elsewhere	ADV
ejpam-6154	370	32	.	.	PUNCT
ejpam-6154	371	1	this	this	DET
ejpam-6154	371	2	sequence	sequence	NOUN
ejpam-6154	371	3	is	be	AUX
ejpam-6154	371	4	bounded	bound	VERB
ejpam-6154	371	5	since	since	SCONJ
ejpam-6154	371	6	∥en∥	∥en∥	VERB
ejpam-6154	371	7	=	=	SYM
ejpam-6154	371	8	1	1	NUM
ejpam-6154	371	9	for	for	ADP
ejpam-6154	371	10	all	all	DET
ejpam-6154	371	11	n.	n.	NOUN
ejpam-6154	371	12	on	on	ADP
ejpam-6154	371	13	the	the	DET
ejpam-6154	371	14	other	other	ADJ
ejpam-6154	371	15	hand	hand	NOUN
ejpam-6154	371	16	,	,	PUNCT
ejpam-6154	371	17	∥xn	∥xn	PROPN
ejpam-6154	371	18	−	−	PROPN
ejpam-6154	371	19	t	t	PROPN
ejpam-6154	371	20	(	(	PUNCT
ejpam-6154	371	21	xn)∥	xn)∥	PUNCT
ejpam-6154	371	22	=	=	SYM
ejpam-6154	371	23	1	1	NUM
ejpam-6154	371	24	n	n	PROPN
ejpam-6154	371	25	→	→	SYM
ejpam-6154	371	26	0	0	NUM
ejpam-6154	371	27	however	however	ADV
ejpam-6154	371	28	,	,	PUNCT
ejpam-6154	371	29	no	no	DET
ejpam-6154	371	30	subsequence	subsequence	NOUN
ejpam-6154	371	31	of	of	ADP
ejpam-6154	371	32	{	{	PUNCT
ejpam-6154	371	33	xn	xn	PROPN
ejpam-6154	371	34	}	}	PUNCT
ejpam-6154	371	35	converges	converge	VERB
ejpam-6154	371	36	strongly	strongly	ADV
ejpam-6154	371	37	in	in	ADP
ejpam-6154	371	38	ℓ2	ℓ2	NOUN
ejpam-6154	371	39	since	since	SCONJ
ejpam-6154	371	40	∥xn	∥xn	PRON
ejpam-6154	371	41	−	−	PROPN
ejpam-6154	371	42	xm∥	xm∥	PROPN
ejpam-6154	371	43	=	=	SYM
ejpam-6154	372	1	∥en	∥en	PROPN
ejpam-6154	373	1	−	−	PROPN
ejpam-6154	373	2	em∥	em∥	NOUN
ejpam-6154	373	3	=	=	NOUN
ejpam-6154	373	4	√	√	PROPN
ejpam-6154	373	5	2	2	NUM
ejpam-6154	373	6	does	do	AUX
ejpam-6154	373	7	not	not	PART
ejpam-6154	373	8	converge	converge	VERB
ejpam-6154	373	9	to	to	ADP
ejpam-6154	373	10	0	0	NUM
ejpam-6154	373	11	.	.	PUNCT
ejpam-6154	374	1	thus	thus	ADV
ejpam-6154	374	2	,	,	PUNCT
ejpam-6154	374	3	t	t	PROPN
ejpam-6154	374	4	is	be	AUX
ejpam-6154	374	5	not	not	PART
ejpam-6154	374	6	semi	semi	ADJ
ejpam-6154	374	7	-	-	ADJ
ejpam-6154	374	8	compact	compact	ADJ
ejpam-6154	374	9	.	.	PUNCT
ejpam-6154	375	1	example	example	NOUN
ejpam-6154	376	1	2	2	NUM
ejpam-6154	376	2	.	.	PUNCT
ejpam-6154	377	1	the	the	DET
ejpam-6154	377	2	mapping	mapping	NOUN
ejpam-6154	377	3	f	f	X
ejpam-6154	377	4	:	:	PUNCT
ejpam-6154	377	5	r	r	NOUN
ejpam-6154	377	6	→	→	SYM
ejpam-6154	377	7	r	r	NOUN
ejpam-6154	377	8	define	define	NOUN
ejpam-6154	377	9	by	by	ADP
ejpam-6154	377	10	f(z	f(z	PROPN
ejpam-6154	377	11	)	)	PUNCT
ejpam-6154	377	12	=	=	SYM
ejpam-6154	377	13	1	1	NUM
ejpam-6154	377	14	2	2	NUM
ejpam-6154	377	15	sin(z	sin(z	PROPN
ejpam-6154	377	16	)	)	PUNCT
ejpam-6154	377	17	,	,	PUNCT
ejpam-6154	377	18	for	for	ADP
ejpam-6154	377	19	all	all	DET
ejpam-6154	377	20	z	z	NOUN
ejpam-6154	377	21	∈	∈	NOUN
ejpam-6154	377	22	r	r	NOUN
ejpam-6154	377	23	is	be	AUX
ejpam-6154	377	24	a	a	DET
ejpam-6154	377	25	contraction	contraction	NOUN
ejpam-6154	377	26	mapping	mapping	NOUN
ejpam-6154	377	27	.	.	PUNCT
ejpam-6154	378	1	proof	proof	NOUN
ejpam-6154	378	2	.	.	PUNCT
ejpam-6154	379	1	clearly	clearly	ADV
ejpam-6154	379	2	,	,	PUNCT
ejpam-6154	379	3	the	the	DET
ejpam-6154	379	4	function	function	NOUN
ejpam-6154	379	5	is	be	AUX
ejpam-6154	379	6	continuous	continuous	ADJ
ejpam-6154	379	7	for	for	ADP
ejpam-6154	379	8	all	all	DET
ejpam-6154	379	9	z	z	NOUN
ejpam-6154	379	10	∈	∈	PROPN
ejpam-6154	379	11	r.	r.	NOUN
ejpam-6154	379	12	by	by	ADP
ejpam-6154	379	13	the	the	DET
ejpam-6154	379	14	mean	mean	ADJ
ejpam-6154	379	15	value	value	NOUN
ejpam-6154	379	16	theorem	theorem	NOUN
ejpam-6154	379	17	(	(	PUNCT
ejpam-6154	379	18	mvt	mvt	PROPN
ejpam-6154	379	19	)	)	PUNCT
ejpam-6154	379	20	,	,	PUNCT
ejpam-6154	379	21	there	there	PRON
ejpam-6154	379	22	exists	exist	VERB
ejpam-6154	379	23	c	c	NOUN
ejpam-6154	379	24	∈	∈	PROPN
ejpam-6154	379	25	r	r	NOUN
ejpam-6154	379	26	such	such	ADJ
ejpam-6154	379	27	that	that	SCONJ
ejpam-6154	379	28	|f(y)−f(z)|	|f(y)−f(z)|	PROPN
ejpam-6154	379	29	=	=	NOUN
ejpam-6154	379	30	1	1	NUM
ejpam-6154	379	31	2	2	NUM
ejpam-6154	379	32	|	|	NOUN
ejpam-6154	379	33	sin(y)−	sin(y)−	VERB
ejpam-6154	379	34	sin(z)|	sin(z)|	PROPN
ejpam-6154	379	35	≤	≤	PRON
ejpam-6154	379	36	cos(c)|y	cos(c)|y	NOUN
ejpam-6154	379	37	−	−	PROPN
ejpam-6154	379	38	z|	z|	NOUN
ejpam-6154	379	39	≤	≤	NOUN
ejpam-6154	379	40	|y	|y	NOUN
ejpam-6154	379	41	−	−	PROPN
ejpam-6154	379	42	z|	z|	PROPN
ejpam-6154	379	43	.	.	PUNCT
ejpam-6154	380	1	thus	thus	ADV
ejpam-6154	380	2	we	we	PRON
ejpam-6154	380	3	see	see	VERB
ejpam-6154	380	4	that	that	SCONJ
ejpam-6154	380	5	f	f	PROPN
ejpam-6154	380	6	is	be	AUX
ejpam-6154	380	7	a	a	DET
ejpam-6154	380	8	contraction	contraction	NOUN
ejpam-6154	380	9	mapping	mapping	NOUN
ejpam-6154	380	10	with	with	ADP
ejpam-6154	380	11	a	a	DET
ejpam-6154	380	12	contraction	contraction	NOUN
ejpam-6154	380	13	constant	constant	ADJ
ejpam-6154	380	14	cos(c	cos(c	PROPN
ejpam-6154	380	15	)	)	PUNCT
ejpam-6154	380	16	.	.	PUNCT
ejpam-6154	381	1	the	the	DET
ejpam-6154	381	2	following	follow	VERB
ejpam-6154	381	3	are	be	AUX
ejpam-6154	381	4	examples	example	NOUN
ejpam-6154	381	5	of	of	ADP
ejpam-6154	381	6	quasi	quasi	ADJ
ejpam-6154	381	7	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	381	8	mapping	mapping	NOUN
ejpam-6154	381	9	.	.	PUNCT
ejpam-6154	382	1	example	example	NOUN
ejpam-6154	383	1	3	3	NUM
ejpam-6154	383	2	.	.	PUNCT
ejpam-6154	384	1	the	the	DET
ejpam-6154	384	2	mapping	mapping	NOUN
ejpam-6154	384	3	f	f	X
ejpam-6154	384	4	:	:	PUNCT
ejpam-6154	384	5	r	r	NOUN
ejpam-6154	384	6	→	→	SYM
ejpam-6154	384	7	r	r	NOUN
ejpam-6154	384	8	define	define	NOUN
ejpam-6154	384	9	by	by	ADP
ejpam-6154	384	10	f(z	f(z	PROPN
ejpam-6154	384	11	)	)	PUNCT
ejpam-6154	384	12	=	=	PUNCT
ejpam-6154	385	1	z	z	NOUN
ejpam-6154	385	2	2	2	NUM
ejpam-6154	385	3	for	for	ADP
ejpam-6154	385	4	all	all	DET
ejpam-6154	385	5	z	z	NOUN
ejpam-6154	385	6	∈	∈	NOUN
ejpam-6154	385	7	r	r	NOUN
ejpam-6154	386	1	then	then	ADV
ejpam-6154	386	2	f	f	PROPN
ejpam-6154	386	3	is	be	AUX
ejpam-6154	386	4	quasi	quasi	ADJ
ejpam-6154	386	5	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	386	6	with	with	ADP
ejpam-6154	386	7	fix(f	fix(f	NOUN
ejpam-6154	386	8	)	)	PUNCT
ejpam-6154	386	9	=	=	SYM
ejpam-6154	386	10	0	0	X
ejpam-6154	386	11	.	.	NOUN
ejpam-6154	386	12	example	example	NOUN
ejpam-6154	387	1	4	4	NUM
ejpam-6154	387	2	.	.	PUNCT
ejpam-6154	388	1	the	the	DET
ejpam-6154	388	2	mapping	mapping	NOUN
ejpam-6154	388	3	f	f	X
ejpam-6154	388	4	:	:	PUNCT
ejpam-6154	388	5	r	r	NOUN
ejpam-6154	388	6	→	→	SYM
ejpam-6154	388	7	r	r	NOUN
ejpam-6154	388	8	define	define	NOUN
ejpam-6154	388	9	by	by	ADP
ejpam-6154	388	10	f(x	f(x	PROPN
ejpam-6154	388	11	)	)	PUNCT
ejpam-6154	389	1	=	=	PUNCT
ejpam-6154	390	1	x+	x+	PUNCT
ejpam-6154	390	2	sin(x	sin(x	PROPN
ejpam-6154	390	3	)	)	PUNCT
ejpam-6154	390	4	for	for	ADP
ejpam-6154	390	5	all	all	PRON
ejpam-6154	390	6	x	x	SYM
ejpam-6154	390	7	∈	∈	NOUN
ejpam-6154	391	1	r	r	NOUN
ejpam-6154	391	2	then	then	ADV
ejpam-6154	391	3	f	f	PROPN
ejpam-6154	391	4	is	be	AUX
ejpam-6154	391	5	quasi	quasi	ADJ
ejpam-6154	391	6	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	391	7	.	.	PUNCT
ejpam-6154	392	1	proof	proof	NOUN
ejpam-6154	392	2	.	.	PUNCT
ejpam-6154	393	1	it	it	PRON
ejpam-6154	393	2	is	be	AUX
ejpam-6154	393	3	not	not	PART
ejpam-6154	393	4	difficult	difficult	ADJ
ejpam-6154	393	5	to	to	PART
ejpam-6154	393	6	see	see	VERB
ejpam-6154	393	7	that	that	PRON
ejpam-6154	393	8	with	with	ADP
ejpam-6154	393	9	fix(f	fix(f	NOUN
ejpam-6154	393	10	)	)	PUNCT
ejpam-6154	393	11	=	=	SYM
ejpam-6154	393	12	0	0	NUM
ejpam-6154	393	13	,	,	PUNCT
ejpam-6154	393	14	f	f	PROPN
ejpam-6154	393	15	is	be	AUX
ejpam-6154	393	16	quasi	quasi	ADJ
ejpam-6154	393	17	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	393	18	mapping	mapping	NOUN
ejpam-6154	393	19	.	.	PUNCT
ejpam-6154	394	1	corollary	corollary	ADJ
ejpam-6154	394	2	6	6	NUM
ejpam-6154	394	3	.	.	PUNCT
ejpam-6154	395	1	in	in	ADP
ejpam-6154	395	2	theorem	theorem	NOUN
ejpam-6154	395	3	(	(	PUNCT
ejpam-6154	395	4	9	9	NUM
ejpam-6154	395	5	)	)	PUNCT
ejpam-6154	395	6	,	,	PUNCT
ejpam-6154	395	7	let	let	VERB
ejpam-6154	395	8	h1	h1	VERB
ejpam-6154	395	9	=	=	SYM
ejpam-6154	395	10	r	r	NOUN
ejpam-6154	395	11	,	,	PUNCT
ejpam-6154	395	12	c	c	NOUN
ejpam-6154	395	13	,	,	PUNCT
ejpam-6154	395	14	q	q	NOUN
ejpam-6154	395	15	⊆	⊆	NUM
ejpam-6154	395	16	(	(	PUNCT
ejpam-6154	395	17	0,∞	0,∞	NOUN
ejpam-6154	395	18	)	)	PUNCT
ejpam-6154	395	19	,	,	PUNCT
ejpam-6154	395	20	and	and	CCONJ
ejpam-6154	395	21	define	define	VERB
ejpam-6154	395	22	the	the	DET
ejpam-6154	395	23	operators	operator	NOUN
ejpam-6154	395	24	a1y	a1y	NOUN
ejpam-6154	395	25	=	=	PUNCT
ejpam-6154	395	26	y	y	PROPN
ejpam-6154	395	27	and	and	CCONJ
ejpam-6154	395	28	a2y	a2y	PROPN
ejpam-6154	395	29	=	=	PUNCT
ejpam-6154	396	1	z	z	PROPN
ejpam-6154	396	2	5	5	NUM
ejpam-6154	396	3	.	.	PUNCT
ejpam-6154	397	1	it	it	PRON
ejpam-6154	397	2	follows	follow	VERB
ejpam-6154	397	3	that	that	DET
ejpam-6154	397	4	a1	a1	NOUN
ejpam-6154	397	5	=	=	SYM
ejpam-6154	397	6	a∗	a∗	NOUN
ejpam-6154	397	7	1	1	NUM
ejpam-6154	397	8	=	=	SYM
ejpam-6154	397	9	1	1	NUM
ejpam-6154	397	10	and	and	CCONJ
ejpam-6154	397	11	a2	a2	PROPN
ejpam-6154	397	12	=	=	SYM
ejpam-6154	397	13	a∗	a∗	PROPN
ejpam-6154	397	14	2	2	NUM
ejpam-6154	397	15	=	=	SYM
ejpam-6154	397	16	1	1	NUM
ejpam-6154	397	17	5	5	NUM
ejpam-6154	397	18	,	,	PUNCT
ejpam-6154	397	19	respectively	respectively	ADV
ejpam-6154	397	20	.	.	PUNCT
ejpam-6154	398	1	let	let	VERB
ejpam-6154	398	2	f	f	NOUN
ejpam-6154	398	3	:	:	PUNCT
ejpam-6154	398	4	r	r	NOUN
ejpam-6154	398	5	→	→	SYM
ejpam-6154	398	6	r	r	NOUN
ejpam-6154	398	7	be	be	AUX
ejpam-6154	398	8	defined	define	VERB
ejpam-6154	398	9	by	by	ADP
ejpam-6154	398	10	f(z	f(z	PROPN
ejpam-6154	398	11	)	)	PUNCT
ejpam-6154	398	12	=	=	SYM
ejpam-6154	398	13	1	1	NUM
ejpam-6154	398	14	2	2	NUM
ejpam-6154	398	15	sin(z	sin(z	PROPN
ejpam-6154	398	16	)	)	PUNCT
ejpam-6154	398	17	,	,	PUNCT
ejpam-6154	398	18	for	for	ADP
ejpam-6154	398	19	all	all	DET
ejpam-6154	398	20	z	z	NOUN
ejpam-6154	398	21	∈	∈	PROPN
ejpam-6154	398	22	r	r	NOUN
ejpam-6154	398	23	,	,	PUNCT
ejpam-6154	398	24	which	which	PRON
ejpam-6154	398	25	is	be	AUX
ejpam-6154	398	26	a	a	DET
ejpam-6154	398	27	contraction	contraction	NOUN
ejpam-6154	398	28	mapping	mapping	NOUN
ejpam-6154	398	29	.	.	PUNCT
ejpam-6154	399	1	define	define	VERB
ejpam-6154	399	2	the	the	DET
ejpam-6154	399	3	mappings	mapping	NOUN
ejpam-6154	399	4	t1	t1	NOUN
ejpam-6154	399	5	:	:	PUNCT
ejpam-6154	400	1	c	c	X
ejpam-6154	400	2	→	→	SYM
ejpam-6154	400	3	r	r	NOUN
ejpam-6154	400	4	and	and	CCONJ
ejpam-6154	400	5	t2	t2	PROPN
ejpam-6154	400	6	:	:	PUNCT
ejpam-6154	400	7	q	q	X
ejpam-6154	400	8	→	→	PUNCT
ejpam-6154	400	9	r	r	NOUN
ejpam-6154	400	10	as	as	ADP
ejpam-6154	400	11	t1y	t1y	PROPN
ejpam-6154	400	12	=	=	SYM
ejpam-6154	400	13	y	y	PROPN
ejpam-6154	400	14	2	2	NUM
ejpam-6154	400	15	,	,	PUNCT
ejpam-6154	400	16	∀y	∀y	NUM
ejpam-6154	400	17	∈	∈	PROPN
ejpam-6154	400	18	c	c	NOUN
ejpam-6154	400	19	,	,	PUNCT
ejpam-6154	400	20	and	and	CCONJ
ejpam-6154	400	21	t2z	t2z	NOUN
ejpam-6154	400	22	=	=	SYM
ejpam-6154	400	23	z	z	PROPN
ejpam-6154	400	24	+	+	NUM
ejpam-6154	400	25	sin(z	sin(z	PROPN
ejpam-6154	400	26	)	)	PUNCT
ejpam-6154	400	27	,	,	PUNCT
ejpam-6154	400	28	∀z	∀z	PROPN
ejpam-6154	400	29	∈	∈	PROPN
ejpam-6154	400	30	q.	q.	NOUN
ejpam-6154	400	31	clearly	clearly	ADV
ejpam-6154	400	32	,	,	PUNCT
ejpam-6154	400	33	t1	t1	NOUN
ejpam-6154	400	34	and	and	CCONJ
ejpam-6154	400	35	t2	t2	NOUN
ejpam-6154	400	36	are	be	AUX
ejpam-6154	400	37	quasi	quasi	ADJ
ejpam-6154	400	38	-	-	ADJ
ejpam-6154	400	39	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	400	40	mappings	mapping	NOUN
ejpam-6154	400	41	with	with	ADP
ejpam-6154	400	42	fixed	fix	VERB
ejpam-6154	400	43	points	point	NOUN
ejpam-6154	400	44	fix(t1	fix(t1	X
ejpam-6154	400	45	)	)	PUNCT
ejpam-6154	401	1	=	=	SYM
ejpam-6154	401	2	0	0	NUM
ejpam-6154	401	3	and	and	CCONJ
ejpam-6154	401	4	fix(t2	fix(t2	NOUN
ejpam-6154	401	5	)	)	PUNCT
ejpam-6154	401	6	=	=	SYM
ejpam-6154	401	7	0	0	X
ejpam-6154	401	8	.	.	PUNCT
ejpam-6154	401	9	let	let	VERB
ejpam-6154	401	10	η	η	PROPN
ejpam-6154	401	11	=	=	PROPN
ejpam-6154	401	12	1	1	NUM
ejpam-6154	401	13	5	5	NUM
ejpam-6154	401	14	,	,	PUNCT
ejpam-6154	401	15	ξ	ξ	X
ejpam-6154	401	16	=	=	SYM
ejpam-6154	401	17	1	1	NUM
ejpam-6154	401	18	7	7	NUM
ejpam-6154	401	19	,	,	PUNCT
ejpam-6154	401	20	τn	τn	ADP
ejpam-6154	401	21	=	=	SYM
ejpam-6154	401	22	1	1	NUM
ejpam-6154	401	23	9	9	NUM
ejpam-6154	401	24	,	,	PUNCT
ejpam-6154	401	25	and	and	CCONJ
ejpam-6154	401	26	αn	αn	NOUN
ejpam-6154	401	27	=	=	SYM
ejpam-6154	401	28	1	1	NUM
ejpam-6154	401	29	11	11	NUM
ejpam-6154	401	30	.	.	PUNCT
ejpam-6154	402	1	these	these	DET
ejpam-6154	402	2	parameters	parameter	NOUN
ejpam-6154	402	3	satisfy	satisfy	VERB
ejpam-6154	402	4	the	the	DET
ejpam-6154	402	5	hypotheses	hypothesis	NOUN
ejpam-6154	402	6	of	of	ADP
ejpam-6154	402	7	theorem	theorem	NOUN
ejpam-6154	402	8	9	9	NUM
ejpam-6154	402	9	.	.	PUNCT
ejpam-6154	402	10	by	by	ADP
ejpam-6154	402	11	setting	set	VERB
ejpam-6154	402	12	the	the	DET
ejpam-6154	402	13	number	number	NOUN
ejpam-6154	402	14	of	of	ADP
ejpam-6154	402	15	iterations	iteration	NOUN
ejpam-6154	402	16	to	to	ADP
ejpam-6154	402	17	150	150	NUM
ejpam-6154	402	18	and	and	CCONJ
ejpam-6154	402	19	using	use	VERB
ejpam-6154	402	20	maple	maple	NOUN
ejpam-6154	402	21	,	,	PUNCT
ejpam-6154	402	22	we	we	PRON
ejpam-6154	402	23	obtain	obtain	VERB
ejpam-6154	402	24	the	the	DET
ejpam-6154	402	25	following	follow	VERB
ejpam-6154	402	26	results	result	NOUN
ejpam-6154	402	27	:	:	PUNCT
ejpam-6154	402	28	l.	l.	PROPN
ejpam-6154	402	29	b.	b.	PROPN
ejpam-6154	402	30	mohammed	mohammed	PROPN
ejpam-6154	402	31	,	,	PUNCT
ejpam-6154	402	32	a.	a.	PROPN
ejpam-6154	402	33	kılıçman	kılıçman	PROPN
ejpam-6154	402	34	,	,	PUNCT
ejpam-6154	402	35	d.	d.	PROPN
ejpam-6154	402	36	bamanga	bamanga	PROPN
ejpam-6154	402	37	/	/	SYM
ejpam-6154	402	38	eur	eur	PROPN
ejpam-6154	402	39	.	.	PUNCT
ejpam-6154	403	1	j.	j.	PROPN
ejpam-6154	403	2	pure	pure	PROPN
ejpam-6154	403	3	appl	appl	PROPN
ejpam-6154	403	4	.	.	PROPN
ejpam-6154	403	5	math	math	PROPN
ejpam-6154	403	6	,	,	PUNCT
ejpam-6154	403	7	18	18	NUM
ejpam-6154	403	8	(	(	PUNCT
ejpam-6154	403	9	4	4	NUM
ejpam-6154	403	10	)	)	PUNCT
ejpam-6154	403	11	(	(	PUNCT
ejpam-6154	403	12	2025	2025	NUM
ejpam-6154	403	13	)	)	PUNCT
ejpam-6154	403	14	,	,	PUNCT
ejpam-6154	403	15	6154	6154	NUM
ejpam-6154	403	16	16	16	NUM
ejpam-6154	403	17	of	of	ADP
ejpam-6154	403	18	18	18	NUM
ejpam-6154	403	19	n	n	NUM
ejpam-6154	403	20	algorithm	algorithm	NOUN
ejpam-6154	403	21	10	10	NUM
ejpam-6154	403	22	{	{	PUNCT
ejpam-6154	403	23	yn	yn	PROPN
ejpam-6154	403	24	}	}	PUNCT
ejpam-6154	403	25	{	{	PUNCT
ejpam-6154	403	26	zn	zn	NOUN
ejpam-6154	403	27	}	}	PUNCT
ejpam-6154	403	28	1	1	NUM
ejpam-6154	403	29	1.0000000000	1.0000000000	NUM
ejpam-6154	403	30	1.0000000000	1.0000000000	NUM
ejpam-6154	403	31	2	2	NUM
ejpam-6154	403	32	0.8958712178	0.8958712178	NUM
ejpam-6154	403	33	0.9167912023	0.9167912023	NUM
ejpam-6154	403	34	3	3	NUM
ejpam-6154	403	35	0.8037675809	0.8037675809	NUM
ejpam-6154	403	36	0.8418283630	0.8418283630	NUM
ejpam-6154	403	37	4	4	NUM
ejpam-6154	403	38	0.7219891992	0.7219891992	NUM
ejpam-6154	403	39	0.7740135339	0.7740135339	NUM
ejpam-6154	403	40	.	.	PUNCT
ejpam-6154	403	41	.	.	PUNCT
ejpam-6154	403	42	.	.	PUNCT
ejpam-6154	403	43	.	.	PUNCT
ejpam-6154	403	44	.	.	PUNCT
ejpam-6154	403	45	.	.	PUNCT
ejpam-6154	403	46	.	.	PUNCT
ejpam-6154	403	47	.	.	PUNCT
ejpam-6154	404	1	.	.	PUNCT
ejpam-6154	405	1	148	148	NUM
ejpam-6154	405	2	0.0000000258	0.0000000258	NUM
ejpam-6154	405	3	0.0000110780	0.0000110780	NUM
ejpam-6154	405	4	149	149	NUM
ejpam-6154	405	5	0.0000000233	0.0000000233	NUM
ejpam-6154	405	6	0.0000102608	0.0000102608	NUM
ejpam-6154	405	7	150	150	NUM
ejpam-6154	405	8	0.0000000210	0.0000000210	NUM
ejpam-6154	405	9	0.0000095038	0.0000095038	NUM
ejpam-6154	405	10	table	table	NOUN
ejpam-6154	405	11	1	1	NUM
ejpam-6154	405	12	:	:	PUNCT
ejpam-6154	405	13	the	the	DET
ejpam-6154	405	14	numerical	numerical	ADJ
ejpam-6154	405	15	results	result	NOUN
ejpam-6154	405	16	of	of	ADP
ejpam-6154	405	17	algorithm	algorithm	NOUN
ejpam-6154	405	18	(	(	PUNCT
ejpam-6154	405	19	10	10	NUM
ejpam-6154	405	20	)	)	PUNCT
ejpam-6154	405	21	,	,	PUNCT
ejpam-6154	405	22	starting	start	VERB
ejpam-6154	405	23	with	with	ADP
ejpam-6154	405	24	the	the	DET
ejpam-6154	405	25	initial	initial	ADJ
ejpam-6154	405	26	values	value	NOUN
ejpam-6154	405	27	y1	y1	NOUN
ejpam-6154	405	28	=	=	SYM
ejpam-6154	405	29	1	1	NUM
ejpam-6154	405	30	and	and	CCONJ
ejpam-6154	405	31	z1	z1	VERB
ejpam-6154	405	32	=	=	SYM
ejpam-6154	405	33	1	1	NUM
ejpam-6154	405	34	,	,	PUNCT
ejpam-6154	405	35	showed	show	VERB
ejpam-6154	405	36	how	how	SCONJ
ejpam-6154	405	37	the	the	DET
ejpam-6154	405	38	sequence	sequence	NOUN
ejpam-6154	405	39	(	(	PUNCT
ejpam-6154	405	40	yn	yn	PROPN
ejpam-6154	405	41	,	,	PUNCT
ejpam-6154	405	42	zn	zn	PROPN
ejpam-6154	405	43	)	)	PUNCT
ejpam-6154	405	44	converges	converge	VERB
ejpam-6154	405	45	to	to	ADP
ejpam-6154	405	46	(	(	PUNCT
ejpam-6154	405	47	0	0	NUM
ejpam-6154	405	48	,	,	PUNCT
ejpam-6154	405	49	0	0	NUM
ejpam-6154	405	50	)	)	PUNCT
ejpam-6154	405	51	.	.	PUNCT
ejpam-6154	406	1	figure	figure	VERB
ejpam-6154	406	2	1	1	NUM
ejpam-6154	406	3	:	:	PUNCT
ejpam-6154	406	4	graphical	graphical	ADJ
ejpam-6154	406	5	results	result	NOUN
ejpam-6154	406	6	presentation	presentation	NOUN
ejpam-6154	406	7	of	of	ADP
ejpam-6154	406	8	algorithm	algorithm	NOUN
ejpam-6154	406	9	(	(	PUNCT
ejpam-6154	406	10	10	10	NUM
ejpam-6154	406	11	)	)	PUNCT
ejpam-6154	406	12	,	,	PUNCT
ejpam-6154	406	13	starting	start	VERB
ejpam-6154	406	14	with	with	ADP
ejpam-6154	406	15	the	the	DET
ejpam-6154	406	16	initial	initial	ADJ
ejpam-6154	406	17	values	value	NOUN
ejpam-6154	406	18	y1	y1	NOUN
ejpam-6154	406	19	=	=	SYM
ejpam-6154	406	20	1	1	NUM
ejpam-6154	406	21	and	and	CCONJ
ejpam-6154	406	22	z1	z1	VERB
ejpam-6154	406	23	=	=	SYM
ejpam-6154	406	24	1	1	NUM
ejpam-6154	406	25	,	,	PUNCT
ejpam-6154	406	26	demonstrated	demonstrate	VERB
ejpam-6154	406	27	how	how	SCONJ
ejpam-6154	406	28	the	the	DET
ejpam-6154	406	29	sequence	sequence	NOUN
ejpam-6154	406	30	(	(	PUNCT
ejpam-6154	406	31	yn	yn	PROPN
ejpam-6154	406	32	,	,	PUNCT
ejpam-6154	406	33	zn	zn	PROPN
ejpam-6154	406	34	)	)	PUNCT
ejpam-6154	406	35	converges	converge	VERB
ejpam-6154	406	36	to	to	ADP
ejpam-6154	406	37	(	(	PUNCT
ejpam-6154	406	38	0	0	NUM
ejpam-6154	406	39	,	,	PUNCT
ejpam-6154	406	40	0	0	NUM
ejpam-6154	406	41	)	)	PUNCT
ejpam-6154	406	42	.	.	PUNCT
ejpam-6154	407	1	the	the	DET
ejpam-6154	407	2	following	follow	VERB
ejpam-6154	407	3	table	table	NOUN
ejpam-6154	407	4	provides	provide	VERB
ejpam-6154	407	5	a	a	DET
ejpam-6154	407	6	comparison	comparison	NOUN
ejpam-6154	407	7	of	of	ADP
ejpam-6154	407	8	algorithm	algorithm	NOUN
ejpam-6154	407	9	(	(	PUNCT
ejpam-6154	407	10	10	10	NUM
ejpam-6154	407	11	)	)	PUNCT
ejpam-6154	407	12	as	as	SCONJ
ejpam-6154	407	13	presented	present	VERB
ejpam-6154	407	14	in	in	ADP
ejpam-6154	407	15	table	table	NOUN
ejpam-6154	407	16	1	1	NUM
ejpam-6154	407	17	with	with	ADP
ejpam-6154	407	18	some	some	PRON
ejpam-6154	407	19	of	of	ADP
ejpam-6154	407	20	the	the	DET
ejpam-6154	407	21	recent	recent	ADJ
ejpam-6154	407	22	results	result	NOUN
ejpam-6154	407	23	published	publish	VERB
ejpam-6154	407	24	in	in	ADP
ejpam-6154	407	25	the	the	DET
ejpam-6154	407	26	literature	literature	NOUN
ejpam-6154	407	27	.	.	PUNCT
ejpam-6154	408	1	l.	l.	PROPN
ejpam-6154	408	2	b.	b.	PROPN
ejpam-6154	408	3	mohammed	mohammed	PROPN
ejpam-6154	408	4	,	,	PUNCT
ejpam-6154	408	5	a.	a.	PROPN
ejpam-6154	408	6	kılıçman	kılıçman	PROPN
ejpam-6154	408	7	,	,	PUNCT
ejpam-6154	408	8	d.	d.	PROPN
ejpam-6154	408	9	bamanga	bamanga	PROPN
ejpam-6154	408	10	/	/	SYM
ejpam-6154	408	11	eur	eur	PROPN
ejpam-6154	408	12	.	.	PUNCT
ejpam-6154	409	1	j.	j.	PROPN
ejpam-6154	409	2	pure	pure	PROPN
ejpam-6154	409	3	appl	appl	PROPN
ejpam-6154	409	4	.	.	PROPN
ejpam-6154	409	5	math	math	PROPN
ejpam-6154	409	6	,	,	PUNCT
ejpam-6154	409	7	18	18	NUM
ejpam-6154	409	8	(	(	PUNCT
ejpam-6154	409	9	4	4	NUM
ejpam-6154	409	10	)	)	PUNCT
ejpam-6154	409	11	(	(	PUNCT
ejpam-6154	409	12	2025	2025	NUM
ejpam-6154	409	13	)	)	PUNCT
ejpam-6154	409	14	,	,	PUNCT
ejpam-6154	409	15	6154	6154	NUM
ejpam-6154	409	16	17	17	NUM
ejpam-6154	409	17	of	of	ADP
ejpam-6154	409	18	18	18	NUM
ejpam-6154	409	19	n	n	NUM
ejpam-6154	409	20	algorithm	algorithm	NOUN
ejpam-6154	409	21	36	36	NUM
ejpam-6154	409	22	algorithm	algorithm	NOUN
ejpam-6154	409	23	37	37	NUM
ejpam-6154	409	24	algorithm	algorithm	NOUN
ejpam-6154	409	25	39	39	NUM
ejpam-6154	409	26	{	{	PUNCT
ejpam-6154	409	27	yn	yn	NOUN
ejpam-6154	409	28	}	}	PUNCT
ejpam-6154	409	29	{	{	PUNCT
ejpam-6154	409	30	zn	zn	NOUN
ejpam-6154	409	31	}	}	PUNCT
ejpam-6154	409	32	{	{	PUNCT
ejpam-6154	409	33	yn	yn	NOUN
ejpam-6154	409	34	}	}	PUNCT
ejpam-6154	409	35	{	{	PUNCT
ejpam-6154	409	36	zn	zn	NOUN
ejpam-6154	409	37	}	}	PUNCT
ejpam-6154	409	38	{	{	PUNCT
ejpam-6154	409	39	yn	yn	NOUN
ejpam-6154	409	40	}	}	PUNCT
ejpam-6154	409	41	{	{	PUNCT
ejpam-6154	409	42	zn	zn	NOUN
ejpam-6154	409	43	}	}	PUNCT
ejpam-6154	409	44	1	1	NUM
ejpam-6154	409	45	1.00000	1.00000	NUM
ejpam-6154	409	46	1.00000	1.00000	NUM
ejpam-6154	409	47	1.00000	1.00000	NUM
ejpam-6154	409	48	1.00000	1.00000	NUM
ejpam-6154	409	49	1.00000	1.00000	NUM
ejpam-6154	409	50	1.0000	1.0000	NUM
ejpam-6154	409	51	2	2	NUM
ejpam-6154	409	52	0.94774	0.94774	NUM
ejpam-6154	409	53	0.96880	0.96880	NUM
ejpam-6154	409	54	0.95916	0.95916	NUM
ejpam-6154	409	55	0.97832	0.97832	NUM
ejpam-6154	409	56	1.07480	1.07480	NUM
ejpam-6154	409	57	1.0935	1.0935	NUM
ejpam-6154	409	58	3	3	NUM
ejpam-6154	409	59	0.89822	0.89822	NUM
ejpam-6154	409	60	0.93872	0.93872	NUM
ejpam-6154	409	61	0.91999	0.91999	NUM
ejpam-6154	409	62	0.95721	0.95721	NUM
ejpam-6154	409	63	1.14970	1.14970	NUM
ejpam-6154	409	64	1.1725	1.1725	NUM
ejpam-6154	409	65	.	.	PUNCT
ejpam-6154	409	66	.	.	PUNCT
ejpam-6154	409	67	.	.	PUNCT
ejpam-6154	409	68	.	.	PUNCT
ejpam-6154	409	69	.	.	PUNCT
ejpam-6154	409	70	.	.	PUNCT
ejpam-6154	409	71	.	.	PUNCT
ejpam-6154	409	72	.	.	PUNCT
ejpam-6154	409	73	.	.	PUNCT
ejpam-6154	409	74	.	.	PUNCT
ejpam-6154	409	75	.	.	PUNCT
ejpam-6154	409	76	.	.	PUNCT
ejpam-6154	409	77	.	.	PUNCT
ejpam-6154	409	78	.	.	PUNCT
ejpam-6154	409	79	.	.	PUNCT
ejpam-6154	409	80	.	.	PUNCT
ejpam-6154	409	81	.	.	PUNCT
ejpam-6154	409	82	.	.	PUNCT
ejpam-6154	409	83	.	.	PUNCT
ejpam-6154	409	84	.	.	PUNCT
ejpam-6154	410	1	.	.	PUNCT
ejpam-6154	411	1	148	148	NUM
ejpam-6154	411	2	0.00036	0.00036	NUM
ejpam-6154	411	3	0.01277	0.01277	NUM
ejpam-6154	411	4	0.00209	0.00209	NUM
ejpam-6154	411	5	0.05188	0.05188	NUM
ejpam-6154	411	6	1.93210	1.93210	NUM
ejpam-6154	411	7	2.0360	2.0360	NUM
ejpam-6154	411	8	149	149	NUM
ejpam-6154	411	9	0.00034	0.00034	NUM
ejpam-6154	411	10	0.01240	0.01240	NUM
ejpam-6154	411	11	0.00200	0.00200	NUM
ejpam-6154	411	12	0.05088	0.05088	NUM
ejpam-6154	411	13	1.93210	1.93210	NUM
ejpam-6154	412	1	2.0360	2.0360	NUM
ejpam-6154	412	2	150	150	NUM
ejpam-6154	412	3	0.00032	0.00032	NUM
ejpam-6154	412	4	0.012046	0.012046	NUM
ejpam-6154	412	5	0.00192	0.00192	NUM
ejpam-6154	412	6	0.04989	0.04989	NUM
ejpam-6154	412	7	1.93210	1.93210	NUM
ejpam-6154	412	8	2.0360	2.0360	NUM
ejpam-6154	412	9	table	table	NOUN
ejpam-6154	412	10	2	2	NUM
ejpam-6154	412	11	:	:	PUNCT
ejpam-6154	412	12	this	this	DET
ejpam-6154	412	13	table	table	NOUN
ejpam-6154	412	14	presents	present	VERB
ejpam-6154	412	15	the	the	DET
ejpam-6154	412	16	convergence	convergence	NOUN
ejpam-6154	412	17	rates	rate	NOUN
ejpam-6154	412	18	of	of	ADP
ejpam-6154	412	19	algorithms	algorithm	NOUN
ejpam-6154	412	20	36	36	NUM
ejpam-6154	412	21	,	,	PUNCT
ejpam-6154	412	22	37	37	NUM
ejpam-6154	412	23	,	,	PUNCT
ejpam-6154	412	24	and	and	CCONJ
ejpam-6154	412	25	39	39	NUM
ejpam-6154	412	26	,	,	PUNCT
ejpam-6154	412	27	as	as	SCONJ
ejpam-6154	412	28	studied	study	VERB
ejpam-6154	412	29	by	by	ADP
ejpam-6154	412	30	mohammed	mohammed	PROPN
ejpam-6154	412	31	and	and	CCONJ
ejpam-6154	412	32	kilicman	kilicman	NOUN
ejpam-6154	412	33	[	[	X
ejpam-6154	412	34	10	10	NUM
ejpam-6154	412	35	]	]	PUNCT
ejpam-6154	412	36	,	,	PUNCT
ejpam-6154	412	37	chang	chang	PROPN
ejpam-6154	412	38	et	et	PROPN
ejpam-6154	412	39	al	al	PROPN
ejpam-6154	412	40	.	.	PUNCT
ejpam-6154	413	1	[	[	X
ejpam-6154	413	2	9	9	NUM
ejpam-6154	413	3	]	]	PUNCT
ejpam-6154	413	4	,	,	PUNCT
ejpam-6154	413	5	and	and	CCONJ
ejpam-6154	413	6	wang	wang	PROPN
ejpam-6154	413	7	et	et	PROPN
ejpam-6154	413	8	al	al	PROPN
ejpam-6154	413	9	.	.	PUNCT
ejpam-6154	414	1	[	[	X
ejpam-6154	414	2	11	11	NUM
ejpam-6154	414	3	]	]	PUNCT
ejpam-6154	414	4	,	,	PUNCT
ejpam-6154	414	5	respectively	respectively	ADV
ejpam-6154	414	6	.	.	PUNCT
ejpam-6154	415	1	by	by	ADP
ejpam-6154	415	2	comparing	compare	VERB
ejpam-6154	415	3	algorithm	algorithm	NOUN
ejpam-6154	415	4	10	10	NUM
ejpam-6154	415	5	with	with	ADP
ejpam-6154	415	6	these	these	DET
ejpam-6154	415	7	algorithms	algorithm	NOUN
ejpam-6154	415	8	,	,	PUNCT
ejpam-6154	415	9	it	it	PRON
ejpam-6154	415	10	is	be	AUX
ejpam-6154	415	11	clear	clear	ADJ
ejpam-6154	415	12	that	that	SCONJ
ejpam-6154	415	13	the	the	DET
ejpam-6154	415	14	proposed	propose	VERB
ejpam-6154	415	15	in	in	ADP
ejpam-6154	415	16	this	this	DET
ejpam-6154	415	17	paper	paper	NOUN
ejpam-6154	415	18	converges	converge	VERB
ejpam-6154	415	19	more	more	ADV
ejpam-6154	415	20	rapidly	rapidly	ADV
ejpam-6154	415	21	.	.	PUNCT
ejpam-6154	416	1	this	this	PRON
ejpam-6154	416	2	demonstrates	demonstrate	VERB
ejpam-6154	416	3	that	that	SCONJ
ejpam-6154	416	4	the	the	DET
ejpam-6154	416	5	method	method	NOUN
ejpam-6154	416	6	proposed	propose	VERB
ejpam-6154	416	7	in	in	ADP
ejpam-6154	416	8	this	this	DET
ejpam-6154	416	9	paper	paper	NOUN
ejpam-6154	416	10	is	be	AUX
ejpam-6154	416	11	more	more	ADV
ejpam-6154	416	12	efficient	efficient	ADJ
ejpam-6154	416	13	in	in	ADP
ejpam-6154	416	14	terms	term	NOUN
ejpam-6154	416	15	of	of	ADP
ejpam-6154	416	16	convergence	convergence	NOUN
ejpam-6154	416	17	speed	speed	NOUN
ejpam-6154	416	18	compared	compare	VERB
ejpam-6154	416	19	to	to	ADP
ejpam-6154	416	20	the	the	DET
ejpam-6154	416	21	existing	exist	VERB
ejpam-6154	416	22	methods	method	NOUN
ejpam-6154	416	23	.	.	PUNCT
ejpam-6154	417	1	figure	figure	NOUN
ejpam-6154	417	2	2	2	NUM
ejpam-6154	417	3	:	:	PUNCT
ejpam-6154	417	4	graphical	graphical	ADJ
ejpam-6154	417	5	results	result	NOUN
ejpam-6154	417	6	presentation	presentation	NOUN
ejpam-6154	417	7	of	of	ADP
ejpam-6154	417	8	algorithms	algorithm	NOUN
ejpam-6154	417	9	(	(	PUNCT
ejpam-6154	417	10	10	10	NUM
ejpam-6154	417	11	)	)	PUNCT
ejpam-6154	417	12	,	,	PUNCT
ejpam-6154	417	13	(	(	PUNCT
ejpam-6154	417	14	36	36	NUM
ejpam-6154	417	15	)	)	PUNCT
ejpam-6154	417	16	,	,	PUNCT
ejpam-6154	417	17	(	(	PUNCT
ejpam-6154	417	18	37	37	NUM
ejpam-6154	417	19	)	)	PUNCT
ejpam-6154	417	20	and	and	CCONJ
ejpam-6154	417	21	(	(	PUNCT
ejpam-6154	417	22	39	39	NUM
ejpam-6154	417	23	)	)	PUNCT
ejpam-6154	417	24	starting	start	VERB
ejpam-6154	417	25	with	with	ADP
ejpam-6154	417	26	the	the	DET
ejpam-6154	417	27	initial	initial	ADJ
ejpam-6154	417	28	values	value	NOUN
ejpam-6154	417	29	y1	y1	NOUN
ejpam-6154	417	30	=	=	SYM
ejpam-6154	417	31	1	1	NUM
ejpam-6154	417	32	and	and	CCONJ
ejpam-6154	417	33	z1	z1	VERB
ejpam-6154	417	34	=	=	SYM
ejpam-6154	417	35	1	1	NUM
ejpam-6154	417	36	,	,	PUNCT
ejpam-6154	417	37	demonstrated	demonstrate	VERB
ejpam-6154	417	38	how	how	SCONJ
ejpam-6154	417	39	the	the	DET
ejpam-6154	417	40	sequence	sequence	NOUN
ejpam-6154	417	41	(	(	PUNCT
ejpam-6154	417	42	yn	yn	PROPN
ejpam-6154	417	43	,	,	PUNCT
ejpam-6154	417	44	zn	zn	PROPN
ejpam-6154	417	45	)	)	PUNCT
ejpam-6154	417	46	converges	converge	VERB
ejpam-6154	417	47	to	to	ADP
ejpam-6154	417	48	(	(	PUNCT
ejpam-6154	417	49	0	0	NUM
ejpam-6154	417	50	,	,	PUNCT
ejpam-6154	417	51	0	0	NUM
ejpam-6154	417	52	)	)	PUNCT
ejpam-6154	417	53	.	.	PUNCT
ejpam-6154	418	1	5	5	X
ejpam-6154	418	2	.	.	X
ejpam-6154	418	3	conclusion	conclusion	NOUN
ejpam-6154	418	4	this	this	DET
ejpam-6154	418	5	study	study	NOUN
ejpam-6154	418	6	focused	focus	VERB
ejpam-6154	418	7	on	on	ADP
ejpam-6154	418	8	the	the	DET
ejpam-6154	418	9	split	split	ADJ
ejpam-6154	418	10	equality	equality	NOUN
ejpam-6154	418	11	fixed	fix	VERB
ejpam-6154	418	12	-	-	PUNCT
ejpam-6154	418	13	point	point	NOUN
ejpam-6154	418	14	problem	problem	NOUN
ejpam-6154	418	15	(	(	PUNCT
ejpam-6154	418	16	sefpp	sefpp	NOUN
ejpam-6154	418	17	)	)	PUNCT
ejpam-6154	418	18	within	within	ADP
ejpam-6154	418	19	the	the	DET
ejpam-6154	418	20	context	context	NOUN
ejpam-6154	418	21	of	of	ADP
ejpam-6154	418	22	quasi	quasi	ADJ
ejpam-6154	418	23	-	-	ADJ
ejpam-6154	418	24	pseudocontractive	pseudocontractive	ADJ
ejpam-6154	418	25	mappings	mapping	NOUN
ejpam-6154	418	26	in	in	ADP
ejpam-6154	418	27	hilbert	hilbert	PROPN
ejpam-6154	418	28	spaces	space	NOUN
ejpam-6154	418	29	.	.	PUNCT
ejpam-6154	419	1	we	we	PRON
ejpam-6154	419	2	introduced	introduce	VERB
ejpam-6154	419	3	new	new	ADJ
ejpam-6154	419	4	viscosity	viscosity	NOUN
ejpam-6154	419	5	algorithms	algorithm	NOUN
ejpam-6154	419	6	for	for	ADP
ejpam-6154	419	7	solving	solve	VERB
ejpam-6154	419	8	this	this	DET
ejpam-6154	419	9	problem	problem	NOUN
ejpam-6154	419	10	,	,	PUNCT
ejpam-6154	419	11	which	which	PRON
ejpam-6154	419	12	indicated	indicate	VERB
ejpam-6154	419	13	that	that	SCONJ
ejpam-6154	419	14	the	the	DET
ejpam-6154	419	15	proposed	propose	VERB
ejpam-6154	419	16	algorithms	algorithm	NOUN
ejpam-6154	419	17	converged	converge	VERB
ejpam-6154	419	18	strongly	strongly	ADV
ejpam-6154	419	19	in	in	ADP
ejpam-6154	419	20	an	an	DET
ejpam-6154	419	21	infinite	infinite	ADJ
ejpam-6154	419	22	-	-	PUNCT
ejpam-6154	419	23	dimensional	dimensional	ADJ
ejpam-6154	419	24	hilbert	hilbert	NOUN
ejpam-6154	419	25	space	space	NOUN
ejpam-6154	419	26	.	.	PUNCT
ejpam-6154	420	1	our	our	PRON
ejpam-6154	420	2	findings	finding	NOUN
ejpam-6154	420	3	not	not	PART
ejpam-6154	420	4	only	only	ADV
ejpam-6154	420	5	broadened	broaden	VERB
ejpam-6154	420	6	several	several	ADJ
ejpam-6154	420	7	key	key	ADJ
ejpam-6154	420	8	results	result	NOUN
ejpam-6154	420	9	from	from	ADP
ejpam-6154	420	10	the	the	DET
ejpam-6154	420	11	existing	exist	VERB
ejpam-6154	420	12	literature	literature	NOUN
ejpam-6154	420	13	but	but	CCONJ
ejpam-6154	420	14	also	also	ADV
ejpam-6154	420	15	addressed	address	VERB
ejpam-6154	420	16	the	the	DET
ejpam-6154	420	17	computational	computational	ADJ
ejpam-6154	420	18	challenges	challenge	NOUN
ejpam-6154	420	19	associated	associate	VERB
ejpam-6154	420	20	with	with	ADP
ejpam-6154	420	21	calculating	calculate	VERB
ejpam-6154	420	22	operator	operator	NOUN
ejpam-6154	420	23	norms	norm	NOUN
ejpam-6154	420	24	.	.	PUNCT
ejpam-6154	421	1	to	to	PART
ejpam-6154	421	2	support	support	VERB
ejpam-6154	421	3	our	our	PRON
ejpam-6154	421	4	theoretical	theoretical	ADJ
ejpam-6154	421	5	results	result	NOUN
ejpam-6154	421	6	,	,	PUNCT
ejpam-6154	421	7	numerical	numerical	ADJ
ejpam-6154	421	8	experiments	experiment	NOUN
ejpam-6154	421	9	were	be	AUX
ejpam-6154	421	10	performed	perform	VERB
ejpam-6154	421	11	,	,	PUNCT
ejpam-6154	421	12	and	and	CCONJ
ejpam-6154	421	13	a	a	DET
ejpam-6154	421	14	comparison	comparison	NOUN
ejpam-6154	421	15	with	with	ADP
ejpam-6154	421	16	existing	exist	VERB
ejpam-6154	421	17	methods	method	NOUN
ejpam-6154	421	18	confirmed	confirm	VERB
ejpam-6154	421	19	the	the	DET
ejpam-6154	421	20	superior	superior	ADJ
ejpam-6154	421	21	efficiency	efficiency	NOUN
ejpam-6154	421	22	and	and	CCONJ
ejpam-6154	421	23	effectiveness	effectiveness	NOUN
ejpam-6154	421	24	of	of	ADP
ejpam-6154	421	25	our	our	PRON
ejpam-6154	421	26	proposed	propose	VERB
ejpam-6154	421	27	algorithms	algorithm	NOUN
ejpam-6154	421	28	.	.	PUNCT
ejpam-6154	422	1	in	in	ADP
ejpam-6154	422	2	summary	summary	NOUN
ejpam-6154	422	3	,	,	PUNCT
ejpam-6154	422	4	the	the	DET
ejpam-6154	422	5	algorithms	algorithm	NOUN
ejpam-6154	422	6	developed	develop	VERB
ejpam-6154	422	7	in	in	ADP
ejpam-6154	422	8	this	this	DET
ejpam-6154	422	9	paper	paper	NOUN
ejpam-6154	422	10	provide	provide	VERB
ejpam-6154	422	11	a	a	DET
ejpam-6154	422	12	reliable	reliable	ADJ
ejpam-6154	422	13	solution	solution	NOUN
ejpam-6154	422	14	to	to	ADP
ejpam-6154	422	15	the	the	DET
ejpam-6154	422	16	sefpp	sefpp	NOUN
ejpam-6154	422	17	,	,	PUNCT
ejpam-6154	422	18	achieving	achieve	VERB
ejpam-6154	422	19	strong	strong	ADJ
ejpam-6154	422	20	convergence	convergence	NOUN
ejpam-6154	422	21	without	without	ADP
ejpam-6154	422	22	the	the	DET
ejpam-6154	422	23	need	need	NOUN
ejpam-6154	422	24	for	for	ADP
ejpam-6154	422	25	the	the	DET
ejpam-6154	422	26	compactness	compactness	NOUN
ejpam-6154	422	27	assumption	assumption	NOUN
ejpam-6154	422	28	on	on	ADP
ejpam-6154	422	29	l.	l.	PROPN
ejpam-6154	422	30	b.	b.	PROPN
ejpam-6154	422	31	mohammed	mohammed	PROPN
ejpam-6154	422	32	,	,	PUNCT
ejpam-6154	422	33	a.	a.	PROPN
ejpam-6154	422	34	kılıçman	kılıçman	PROPN
ejpam-6154	422	35	,	,	PUNCT
ejpam-6154	422	36	d.	d.	PROPN
ejpam-6154	422	37	bamanga	bamanga	PROPN
ejpam-6154	422	38	/	/	SYM
ejpam-6154	422	39	eur	eur	PROPN
ejpam-6154	422	40	.	.	PUNCT
ejpam-6154	423	1	j.	j.	PROPN
ejpam-6154	423	2	pure	pure	PROPN
ejpam-6154	423	3	appl	appl	PROPN
ejpam-6154	423	4	.	.	PROPN
ejpam-6154	423	5	math	math	PROPN
ejpam-6154	423	6	,	,	PUNCT
ejpam-6154	423	7	18	18	NUM
ejpam-6154	423	8	(	(	PUNCT
ejpam-6154	423	9	4	4	NUM
ejpam-6154	423	10	)	)	PUNCT
ejpam-6154	423	11	(	(	PUNCT
ejpam-6154	423	12	2025	2025	NUM
ejpam-6154	423	13	)	)	PUNCT
ejpam-6154	423	14	,	,	PUNCT
ejpam-6154	423	15	6154	6154	NUM
ejpam-6154	423	16	18	18	NUM
ejpam-6154	423	17	of	of	ADP
ejpam-6154	423	18	18	18	NUM
ejpam-6154	423	19	the	the	DET
ejpam-6154	423	20	operators	operator	NOUN
ejpam-6154	423	21	involved	involve	VERB
ejpam-6154	423	22	.	.	PUNCT
ejpam-6154	424	1	our	our	PRON
ejpam-6154	424	2	research	research	NOUN
ejpam-6154	424	3	advances	advance	VERB
ejpam-6154	424	4	the	the	DET
ejpam-6154	424	5	field	field	NOUN
ejpam-6154	424	6	of	of	ADP
ejpam-6154	424	7	fixed	fix	VERB
ejpam-6154	424	8	-	-	PUNCT
ejpam-6154	424	9	point	point	NOUN
ejpam-6154	424	10	theory	theory	NOUN
ejpam-6154	424	11	by	by	ADP
ejpam-6154	424	12	extending	extend	VERB
ejpam-6154	424	13	prior	prior	ADJ
ejpam-6154	424	14	results	result	NOUN
ejpam-6154	424	15	and	and	CCONJ
ejpam-6154	424	16	offering	offer	VERB
ejpam-6154	424	17	more	more	ADV
ejpam-6154	424	18	practical	practical	ADJ
ejpam-6154	424	19	solutions	solution	NOUN
ejpam-6154	424	20	to	to	ADP
ejpam-6154	424	21	the	the	DET
ejpam-6154	424	22	sefpp	sefpp	NOUN
ejpam-6154	424	23	,	,	PUNCT
ejpam-6154	424	24	especially	especially	ADV
ejpam-6154	424	25	in	in	ADP
ejpam-6154	424	26	scenarios	scenario	NOUN
ejpam-6154	424	27	where	where	SCONJ
ejpam-6154	424	28	computing	computing	NOUN
ejpam-6154	424	29	operator	operator	NOUN
ejpam-6154	424	30	norms	norm	NOUN
ejpam-6154	424	31	is	be	AUX
ejpam-6154	424	32	challenging	challenge	VERB
ejpam-6154	424	33	.	.	PUNCT
ejpam-6154	425	1	the	the	DET
ejpam-6154	425	2	algorithms	algorithm	NOUN
ejpam-6154	425	3	’	'	PUNCT
ejpam-6154	425	4	strong	strong	ADJ
ejpam-6154	425	5	convergence	convergence	NOUN
ejpam-6154	425	6	makes	make	VERB
ejpam-6154	425	7	them	they	PRON
ejpam-6154	425	8	well	well	ADV
ejpam-6154	425	9	-	-	PUNCT
ejpam-6154	425	10	suited	suit	VERB
ejpam-6154	425	11	for	for	ADP
ejpam-6154	425	12	practical	practical	ADJ
ejpam-6154	425	13	applications	application	NOUN
ejpam-6154	425	14	.	.	PUNCT
ejpam-6154	426	1	acknowledgements	acknowledgement	NOUN
ejpam-6154	426	2	the	the	DET
ejpam-6154	426	3	authors	author	NOUN
ejpam-6154	426	4	wish	wish	VERB
ejpam-6154	426	5	to	to	PART
ejpam-6154	426	6	express	express	VERB
ejpam-6154	426	7	their	their	PRON
ejpam-6154	426	8	gratitude	gratitude	NOUN
ejpam-6154	426	9	to	to	ADP
ejpam-6154	426	10	the	the	DET
ejpam-6154	426	11	tertiary	tertiary	ADJ
ejpam-6154	426	12	education	education	PROPN
ejpam-6154	426	13	trust	trust	NOUN
ejpam-6154	426	14	fund	fund	PROPN
ejpam-6154	426	15	(	(	PUNCT
ejpam-6154	426	16	tetfund	tetfund	PROPN
ejpam-6154	426	17	)	)	PUNCT
ejpam-6154	426	18	for	for	ADP
ejpam-6154	426	19	the	the	DET
ejpam-6154	426	20	financial	financial	ADJ
ejpam-6154	426	21	support	support	NOUN
ejpam-6154	426	22	provided	provide	VERB
ejpam-6154	426	23	for	for	ADP
ejpam-6154	426	24	the	the	DET
ejpam-6154	426	25	conduct	conduct	NOUN
ejpam-6154	426	26	of	of	ADP
ejpam-6154	426	27	this	this	DET
ejpam-6154	426	28	research	research	NOUN
ejpam-6154	426	29	under	under	ADP
ejpam-6154	426	30	its	its	PRON
ejpam-6154	426	31	institutional	institutional	ADJ
ejpam-6154	426	32	-	-	PUNCT
ejpam-6154	426	33	based	base	VERB
ejpam-6154	426	34	research	research	NOUN
ejpam-6154	426	35	(	(	PUNCT
ejpam-6154	426	36	ibr	ibr	PROPN
ejpam-6154	426	37	)	)	PUNCT
ejpam-6154	426	38	scheme	scheme	NOUN
ejpam-6154	426	39	references	reference	NOUN
ejpam-6154	426	40	[	[	X
ejpam-6154	426	41	1	1	NUM
ejpam-6154	426	42	]	]	PUNCT
ejpam-6154	426	43	yair	yair	PROPN
ejpam-6154	426	44	censor	censor	PROPN
ejpam-6154	426	45	and	and	CCONJ
ejpam-6154	426	46	tommy	tommy	NOUN
ejpam-6154	426	47	elfving	elfving	NOUN
ejpam-6154	426	48	.	.	PUNCT
ejpam-6154	427	1	a	a	DET
ejpam-6154	427	2	multiprojection	multiprojection	NOUN
ejpam-6154	427	3	algorithm	algorithm	NOUN
ejpam-6154	427	4	using	use	VERB
ejpam-6154	427	5	bregman	bregman	NOUN
ejpam-6154	427	6	projections	projection	NOUN
ejpam-6154	427	7	in	in	ADP
ejpam-6154	427	8	a	a	DET
ejpam-6154	427	9	product	product	NOUN
ejpam-6154	427	10	space	space	NOUN
ejpam-6154	427	11	.	.	PUNCT
ejpam-6154	428	1	numerical	numerical	ADJ
ejpam-6154	428	2	algorithms	algorithms	PROPN
ejpam-6154	428	3	,	,	PUNCT
ejpam-6154	428	4	8(2):221–239	8(2):221–239	NUM
ejpam-6154	428	5	,	,	PUNCT
ejpam-6154	428	6	1994	1994	NUM
ejpam-6154	428	7	.	.	PUNCT
ejpam-6154	429	1	[	[	X
ejpam-6154	429	2	2	2	NUM
ejpam-6154	429	3	]	]	PUNCT
ejpam-6154	429	4	charles	charles	PROPN
ejpam-6154	429	5	byrne	byrne	PROPN
ejpam-6154	429	6	.	.	PUNCT
ejpam-6154	430	1	iterative	iterative	NOUN
ejpam-6154	430	2	oblique	oblique	ADJ
ejpam-6154	430	3	projection	projection	NOUN
ejpam-6154	430	4	onto	onto	ADP
ejpam-6154	430	5	convex	convex	NOUN
ejpam-6154	430	6	sets	set	NOUN
ejpam-6154	430	7	and	and	CCONJ
ejpam-6154	430	8	the	the	DET
ejpam-6154	430	9	split	split	ADJ
ejpam-6154	430	10	feasibility	feasibility	NOUN
ejpam-6154	430	11	problem	problem	NOUN
ejpam-6154	430	12	.	.	PUNCT
ejpam-6154	431	1	inverse	inverse	NOUN
ejpam-6154	431	2	problems	problem	NOUN
ejpam-6154	431	3	,	,	PUNCT
ejpam-6154	431	4	18(2):441	18(2):441	NUM
ejpam-6154	431	5	,	,	PUNCT
ejpam-6154	431	6	2002	2002	NUM
ejpam-6154	431	7	.	.	PUNCT
ejpam-6154	432	1	[	[	X
ejpam-6154	432	2	3	3	NUM
ejpam-6154	432	3	]	]	X
ejpam-6154	432	4	yair	yair	NOUN
ejpam-6154	432	5	censor	censor	PROPN
ejpam-6154	432	6	,	,	PUNCT
ejpam-6154	432	7	tommy	tommy	NOUN
ejpam-6154	432	8	elfving	elfving	NOUN
ejpam-6154	432	9	,	,	PUNCT
ejpam-6154	432	10	nirit	nirit	PROPN
ejpam-6154	432	11	kopf	kopf	PROPN
ejpam-6154	432	12	,	,	PUNCT
ejpam-6154	432	13	and	and	CCONJ
ejpam-6154	432	14	thomas	thomas	PROPN
ejpam-6154	432	15	bortfeld	bortfeld	PROPN
ejpam-6154	432	16	.	.	PUNCT
ejpam-6154	433	1	the	the	DET
ejpam-6154	433	2	multiple	multiple	ADJ
ejpam-6154	433	3	-	-	PUNCT
ejpam-6154	433	4	sets	set	NOUN
ejpam-6154	433	5	split	split	VERB
ejpam-6154	433	6	feasibility	feasibility	NOUN
ejpam-6154	433	7	problem	problem	NOUN
ejpam-6154	433	8	and	and	CCONJ
ejpam-6154	433	9	its	its	PRON
ejpam-6154	433	10	applications	application	NOUN
ejpam-6154	433	11	for	for	ADP
ejpam-6154	433	12	inverse	inverse	NOUN
ejpam-6154	433	13	problems	problem	NOUN
ejpam-6154	433	14	.	.	PUNCT
ejpam-6154	434	1	inverse	inverse	NOUN
ejpam-6154	434	2	problems	problem	NOUN
ejpam-6154	434	3	,	,	PUNCT
ejpam-6154	434	4	21(6):2071	21(6):2071	NUM
ejpam-6154	434	5	,	,	PUNCT
ejpam-6154	434	6	2005	2005	NUM
ejpam-6154	434	7	.	.	PUNCT
ejpam-6154	435	1	[	[	X
ejpam-6154	435	2	4	4	NUM
ejpam-6154	435	3	]	]	PUNCT
ejpam-6154	435	4	yair	yair	NOUN
ejpam-6154	435	5	censor	censor	NOUN
ejpam-6154	435	6	,	,	PUNCT
ejpam-6154	435	7	avi	avi	VERB
ejpam-6154	435	8	motova	motova	NOUN
ejpam-6154	435	9	,	,	PUNCT
ejpam-6154	435	10	and	and	CCONJ
ejpam-6154	435	11	alexander	alexander	PROPN
ejpam-6154	435	12	segal	segal	PROPN
ejpam-6154	435	13	.	.	PUNCT
ejpam-6154	436	1	perturbed	perturb	VERB
ejpam-6154	436	2	projections	projection	NOUN
ejpam-6154	436	3	and	and	CCONJ
ejpam-6154	436	4	subgradient	subgradient	NOUN
ejpam-6154	436	5	projections	projection	NOUN
ejpam-6154	436	6	for	for	ADP
ejpam-6154	436	7	the	the	DET
ejpam-6154	436	8	multiple	multiple	ADJ
ejpam-6154	436	9	-	-	PUNCT
ejpam-6154	436	10	sets	set	NOUN
ejpam-6154	436	11	split	split	VERB
ejpam-6154	436	12	feasibility	feasibility	NOUN
ejpam-6154	436	13	problem	problem	NOUN
ejpam-6154	436	14	.	.	PUNCT
ejpam-6154	437	1	journal	journal	NOUN
ejpam-6154	437	2	of	of	ADP
ejpam-6154	437	3	mathematical	mathematical	ADJ
ejpam-6154	437	4	analysis	analysis	NOUN
ejpam-6154	437	5	and	and	CCONJ
ejpam-6154	437	6	applications	application	NOUN
ejpam-6154	437	7	,	,	PUNCT
ejpam-6154	437	8	327(2):1244–1256	327(2):1244–1256	NUM
ejpam-6154	437	9	,	,	PUNCT
ejpam-6154	437	10	2007	2007	NUM
ejpam-6154	437	11	.	.	PUNCT
ejpam-6154	438	1	[	[	X
ejpam-6154	438	2	5	5	X
ejpam-6154	438	3	]	]	X
ejpam-6154	438	4	abdellatif	abdellatif	NOUN
ejpam-6154	438	5	moudafi	moudafi	NOUN
ejpam-6154	438	6	.	.	PUNCT
ejpam-6154	439	1	alternating	alternate	VERB
ejpam-6154	439	2	cq	cq	NOUN
ejpam-6154	439	3	-	-	NOUN
ejpam-6154	439	4	algorithm	algorithm	NOUN
ejpam-6154	439	5	for	for	ADP
ejpam-6154	439	6	convex	convex	NOUN
ejpam-6154	439	7	feasibility	feasibility	NOUN
ejpam-6154	439	8	and	and	CCONJ
ejpam-6154	439	9	split	split	ADJ
ejpam-6154	439	10	fixedpoint	fixedpoint	NOUN
ejpam-6154	439	11	problems	problem	NOUN
ejpam-6154	439	12	.	.	PUNCT
ejpam-6154	440	1	j.	j.	PROPN
ejpam-6154	440	2	nonlinear	nonlinear	PROPN
ejpam-6154	440	3	convex	convex	PROPN
ejpam-6154	440	4	anal	anal	NOUN
ejpam-6154	440	5	,	,	PUNCT
ejpam-6154	440	6	15(4):809–818	15(4):809–818	NUM
ejpam-6154	440	7	,	,	PUNCT
ejpam-6154	440	8	2014	2014	NUM
ejpam-6154	440	9	.	.	PUNCT
ejpam-6154	441	1	[	[	X
ejpam-6154	441	2	6	6	NUM
ejpam-6154	441	3	]	]	PUNCT
ejpam-6154	441	4	a	a	DET
ejpam-6154	441	5	kılıçman	kılıçman	NOUN
ejpam-6154	441	6	and	and	CCONJ
ejpam-6154	441	7	lbmohammed	lbmohammed	PROPN
ejpam-6154	441	8	.	.	PUNCT
ejpam-6154	442	1	iterative	iterative	NOUN
ejpam-6154	442	2	methods	method	NOUN
ejpam-6154	442	3	for	for	ADP
ejpam-6154	442	4	solving	solve	VERB
ejpam-6154	442	5	split	split	VERB
ejpam-6154	442	6	feasibility	feasibility	NOUN
ejpam-6154	442	7	problem	problem	NOUN
ejpam-6154	442	8	in	in	ADP
ejpam-6154	442	9	hilbert	hilbert	NOUN
ejpam-6154	442	10	space	space	NOUN
ejpam-6154	442	11	.	.	PUNCT
ejpam-6154	443	1	malaysian	malaysian	ADJ
ejpam-6154	443	2	journal	journal	PROPN
ejpam-6154	443	3	of	of	ADP
ejpam-6154	443	4	mathematical	mathematical	ADJ
ejpam-6154	443	5	sciences	science	NOUN
ejpam-6154	443	6	,	,	PUNCT
ejpam-6154	443	7	10:127–143	10:127–143	NUM
ejpam-6154	443	8	,	,	PUNCT
ejpam-6154	443	9	2016	2016	NUM
ejpam-6154	443	10	.	.	PUNCT
ejpam-6154	444	1	[	[	X
ejpam-6154	444	2	7	7	NUM
ejpam-6154	444	3	]	]	SYM
ejpam-6154	444	4	lb	lb	DET
ejpam-6154	444	5	mohammed	mohammed	PROPN
ejpam-6154	444	6	,	,	PUNCT
ejpam-6154	444	7	a	a	DET
ejpam-6154	444	8	kılıçman	kılıçman	NOUN
ejpam-6154	444	9	,	,	PUNCT
ejpam-6154	444	10	and	and	CCONJ
ejpam-6154	444	11	au	au	PROPN
ejpam-6154	444	12	saje	saje	NOUN
ejpam-6154	444	13	.	.	PUNCT
ejpam-6154	445	1	on	on	ADP
ejpam-6154	445	2	split	split	ADJ
ejpam-6154	445	3	equality	equality	NOUN
ejpam-6154	445	4	fixed	fix	VERB
ejpam-6154	445	5	-	-	PUNCT
ejpam-6154	445	6	point	point	NOUN
ejpam-6154	445	7	problems	problem	NOUN
ejpam-6154	445	8	.	.	PUNCT
ejpam-6154	446	1	alexandria	alexandria	PROPN
ejpam-6154	446	2	engineering	engineering	PROPN
ejpam-6154	446	3	journal	journal	PROPN
ejpam-6154	446	4	,	,	PUNCT
ejpam-6154	446	5	66:43–51	66:43–51	PROPN
ejpam-6154	446	6	,	,	PUNCT
ejpam-6154	446	7	2023	2023	NUM
ejpam-6154	446	8	.	.	PUNCT
ejpam-6154	447	1	[	[	X
ejpam-6154	447	2	8	8	NUM
ejpam-6154	447	3	]	]	X
ejpam-6154	447	4	a	a	DET
ejpam-6154	447	5	moudafi	moudafi	NOUN
ejpam-6154	447	6	and	and	CCONJ
ejpam-6154	447	7	eman	eman	PROPN
ejpam-6154	447	8	al	al	PROPN
ejpam-6154	447	9	-	-	PUNCT
ejpam-6154	447	10	shemas	shemas	PROPN
ejpam-6154	447	11	.	.	PUNCT
ejpam-6154	448	1	simultaneous	simultaneous	ADJ
ejpam-6154	448	2	iterative	iterative	NOUN
ejpam-6154	448	3	methods	method	NOUN
ejpam-6154	448	4	for	for	ADP
ejpam-6154	448	5	split	split	ADJ
ejpam-6154	448	6	equality	equality	NOUN
ejpam-6154	448	7	problem	problem	NOUN
ejpam-6154	448	8	.	.	PUNCT
ejpam-6154	449	1	trans	trans	PROPN
ejpam-6154	449	2	.	.	PUNCT
ejpam-6154	450	1	math	math	PROPN
ejpam-6154	450	2	.	.	PUNCT
ejpam-6154	451	1	program	program	NOUN
ejpam-6154	451	2	.	.	PUNCT
ejpam-6154	452	1	appl	appl	PROPN
ejpam-6154	452	2	,	,	PUNCT
ejpam-6154	452	3	1(2):1–11	1(2):1–11	PROPN
ejpam-6154	452	4	,	,	PUNCT
ejpam-6154	452	5	2013	2013	NUM
ejpam-6154	452	6	.	.	PUNCT
ejpam-6154	453	1	[	[	X
ejpam-6154	453	2	9	9	NUM
ejpam-6154	453	3	]	]	X
ejpam-6154	453	4	shih	shih	PROPN
ejpam-6154	453	5	-	-	PUNCT
ejpam-6154	453	6	sen	sen	PROPN
ejpam-6154	453	7	chang	chang	PROPN
ejpam-6154	453	8	,	,	PUNCT
ejpam-6154	453	9	lin	lin	PROPN
ejpam-6154	453	10	wang	wang	PROPN
ejpam-6154	453	11	,	,	PUNCT
ejpam-6154	453	12	and	and	CCONJ
ejpam-6154	453	13	li	li	PROPN
ejpam-6154	453	14	-	-	PROPN
ejpam-6154	453	15	juan	juan	PROPN
ejpam-6154	453	16	qin	qin	PROPN
ejpam-6154	453	17	.	.	PROPN
ejpam-6154	453	18	split	split	ADJ
ejpam-6154	453	19	equality	equality	NOUN
ejpam-6154	453	20	fixed	fix	VERB
ejpam-6154	453	21	point	point	NOUN
ejpam-6154	453	22	problem	problem	NOUN
ejpam-6154	453	23	for	for	ADP
ejpam-6154	453	24	quasi	quasi	ADJ
ejpam-6154	453	25	-	-	ADJ
ejpam-6154	453	26	pseudo	pseudo	ADJ
ejpam-6154	453	27	-	-	ADJ
ejpam-6154	453	28	contractive	contractive	ADJ
ejpam-6154	453	29	mappings	mapping	NOUN
ejpam-6154	453	30	with	with	ADP
ejpam-6154	453	31	applications	application	NOUN
ejpam-6154	453	32	.	.	PUNCT
ejpam-6154	454	1	fixed	fix	VERB
ejpam-6154	454	2	point	point	NOUN
ejpam-6154	454	3	theory	theory	NOUN
ejpam-6154	454	4	and	and	CCONJ
ejpam-6154	454	5	applications	application	NOUN
ejpam-6154	454	6	,	,	PUNCT
ejpam-6154	454	7	2015(1):208	2015(1):208	NUM
ejpam-6154	454	8	,	,	PUNCT
ejpam-6154	454	9	2015	2015	NUM
ejpam-6154	454	10	.	.	PUNCT
ejpam-6154	455	1	[	[	X
ejpam-6154	455	2	10	10	NUM
ejpam-6154	455	3	]	]	X
ejpam-6154	455	4	lawan	lawan	PROPN
ejpam-6154	455	5	bulama	bulama	PROPN
ejpam-6154	455	6	mohammed	mohammed	PROPN
ejpam-6154	455	7	and	and	CCONJ
ejpam-6154	455	8	adem	adem	PROPN
ejpam-6154	455	9	kılıçman	kılıçman	PROPN
ejpam-6154	455	10	.	.	PUNCT
ejpam-6154	456	1	the	the	DET
ejpam-6154	456	2	split	split	ADJ
ejpam-6154	456	3	equality	equality	NOUN
ejpam-6154	456	4	fixed	fix	VERB
ejpam-6154	456	5	-	-	PUNCT
ejpam-6154	456	6	point	point	NOUN
ejpam-6154	456	7	problem	problem	NOUN
ejpam-6154	456	8	and	and	CCONJ
ejpam-6154	456	9	its	its	PRON
ejpam-6154	456	10	applications	application	NOUN
ejpam-6154	456	11	.	.	PUNCT
ejpam-6154	457	1	axioms	axiom	NOUN
ejpam-6154	457	2	,	,	PUNCT
ejpam-6154	457	3	13(7):460	13(7):460	NUM
ejpam-6154	457	4	,	,	PUNCT
ejpam-6154	457	5	2024	2024	NUM
ejpam-6154	457	6	.	.	PUNCT
ejpam-6154	458	1	[	[	X
ejpam-6154	458	2	11	11	NUM
ejpam-6154	458	3	]	]	X
ejpam-6154	458	4	yaqin	yaqin	NOUN
ejpam-6154	458	5	wang	wang	PROPN
ejpam-6154	458	6	,	,	PUNCT
ejpam-6154	458	7	jinzuo	jinzuo	PROPN
ejpam-6154	458	8	chen	chen	PROPN
ejpam-6154	458	9	,	,	PUNCT
ejpam-6154	458	10	and	and	CCONJ
ejpam-6154	458	11	ariana	ariana	PROPN
ejpam-6154	458	12	pitea	pitea	NOUN
ejpam-6154	458	13	.	.	PUNCT
ejpam-6154	459	1	the	the	DET
ejpam-6154	459	2	split	split	ADJ
ejpam-6154	459	3	equality	equality	NOUN
ejpam-6154	459	4	fixed	fix	VERB
ejpam-6154	459	5	point	point	NOUN
ejpam-6154	459	6	problem	problem	NOUN
ejpam-6154	459	7	of	of	ADP
ejpam-6154	459	8	demicontractive	demicontractive	ADJ
ejpam-6154	459	9	operators	operator	NOUN
ejpam-6154	459	10	with	with	ADP
ejpam-6154	459	11	numerical	numerical	ADJ
ejpam-6154	459	12	example	example	NOUN
ejpam-6154	459	13	and	and	CCONJ
ejpam-6154	459	14	application	application	NOUN
ejpam-6154	459	15	.	.	PUNCT
ejpam-6154	460	1	symmetry	symmetry	PROPN
ejpam-6154	460	2	,	,	PUNCT
ejpam-6154	460	3	12(6):902	12(6):902	NUM
ejpam-6154	460	4	,	,	PUNCT
ejpam-6154	460	5	2020	2020	NUM
ejpam-6154	460	6	.	.	PUNCT
ejpam-6154	461	1	[	[	X
ejpam-6154	461	2	12	12	NUM
ejpam-6154	461	3	]	]	X
ejpam-6154	461	4	hong	hong	PROPN
ejpam-6154	461	5	-	-	PUNCT
ejpam-6154	461	6	kun	kun	PROPN
ejpam-6154	461	7	xu	xu	PROPN
ejpam-6154	461	8	.	.	PUNCT
ejpam-6154	462	1	iterative	iterative	NOUN
ejpam-6154	462	2	algorithms	algorithm	NOUN
ejpam-6154	462	3	for	for	ADP
ejpam-6154	462	4	nonlinear	nonlinear	ADJ
ejpam-6154	462	5	operators	operator	NOUN
ejpam-6154	462	6	.	.	PUNCT
ejpam-6154	463	1	journal	journal	NOUN
ejpam-6154	463	2	of	of	ADP
ejpam-6154	463	3	the	the	DET
ejpam-6154	463	4	london	london	PROPN
ejpam-6154	463	5	mathematical	mathematical	ADJ
ejpam-6154	463	6	society	society	NOUN
ejpam-6154	463	7	,	,	PUNCT
ejpam-6154	463	8	66(1):240–256	66(1):240–256	PROPN
ejpam-6154	463	9	,	,	PUNCT
ejpam-6154	463	10	2002	2002	NUM
ejpam-6154	463	11	.	.	PUNCT