id	sid	tid	token	lemma	pos
ejpam-6837	1	1	european	european	PROPN
ejpam-6837	1	2	journal	journal	PROPN
ejpam-6837	1	3	of	of	ADP
ejpam-6837	1	4	pure	pure	ADJ
ejpam-6837	1	5	and	and	CCONJ
ejpam-6837	1	6	applied	applied	ADJ
ejpam-6837	1	7	mathematics	mathematic	NOUN
ejpam-6837	1	8	2025	2025	NUM
ejpam-6837	1	9	,	,	PUNCT
ejpam-6837	1	10	vol	vol	NOUN
ejpam-6837	1	11	.	.	PROPN
ejpam-6837	1	12	18	18	NUM
ejpam-6837	1	13	,	,	PUNCT
ejpam-6837	1	14	issue	issue	NOUN
ejpam-6837	1	15	4	4	NUM
ejpam-6837	1	16	,	,	PUNCT
ejpam-6837	1	17	article	article	NOUN
ejpam-6837	1	18	number	number	NOUN
ejpam-6837	1	19	6837	6837	NUM
ejpam-6837	1	20	issn	issn	VERB
ejpam-6837	1	21	1307	1307	NUM
ejpam-6837	1	22	-	-	SYM
ejpam-6837	1	23	5543	5543	NUM
ejpam-6837	1	24	–	–	PUNCT
ejpam-6837	1	25	ejpam.com	ejpam.com	X
ejpam-6837	1	26	published	publish	VERB
ejpam-6837	1	27	by	by	ADP
ejpam-6837	1	28	new	new	PROPN
ejpam-6837	1	29	york	york	PROPN
ejpam-6837	1	30	business	business	PROPN
ejpam-6837	1	31	global	global	ADJ
ejpam-6837	1	32	further	further	ADJ
ejpam-6837	1	33	study	study	NOUN
ejpam-6837	1	34	on	on	ADP
ejpam-6837	1	35	r	r	NOUN
ejpam-6837	1	36	-	-	PUNCT
ejpam-6837	1	37	sets	set	NOUN
ejpam-6837	1	38	operator	operator	NOUN
ejpam-6837	1	39	in	in	ADP
ejpam-6837	1	40	acyclic	acyclic	ADJ
ejpam-6837	1	41	fashion	fashion	NOUN
ejpam-6837	1	42	salihah	salihah	ADJ
ejpam-6837	1	43	thabet	thabet	NOUN
ejpam-6837	1	44	alwadani1	alwadani1	PROPN
ejpam-6837	1	45	,	,	PUNCT
ejpam-6837	1	46	*	*	SYM
ejpam-6837	1	47	1	1	NUM
ejpam-6837	1	48	mathematics	mathematic	NOUN
ejpam-6837	1	49	,	,	PUNCT
ejpam-6837	1	50	yanbu	yanbu	PROPN
ejpam-6837	1	51	industrial	industrial	PROPN
ejpam-6837	1	52	college	college	PROPN
ejpam-6837	1	53	,	,	PUNCT
ejpam-6837	1	54	the	the	DET
ejpam-6837	1	55	royal	royal	ADJ
ejpam-6837	1	56	commission	commission	NOUN
ejpam-6837	1	57	for	for	ADP
ejpam-6837	1	58	jubail	jubail	PROPN
ejpam-6837	1	59	and	and	CCONJ
ejpam-6837	1	60	yanbu	yanbu	ADJ
ejpam-6837	1	61	,	,	PUNCT
ejpam-6837	1	62	yanbu	yanbu	ADJ
ejpam-6837	1	63	,	,	PUNCT
ejpam-6837	1	64	saudi	saudi	PROPN
ejpam-6837	1	65	arabia	arabia	PROPN
ejpam-6837	1	66	abstract	abstract	NOUN
ejpam-6837	1	67	.	.	PUNCT
ejpam-6837	2	1	we	we	PRON
ejpam-6837	2	2	provide	provide	VERB
ejpam-6837	2	3	a	a	DET
ejpam-6837	2	4	distinct	distinct	ADJ
ejpam-6837	2	5	and	and	CCONJ
ejpam-6837	2	6	detailed	detailed	ADJ
ejpam-6837	2	7	proof	proof	NOUN
ejpam-6837	2	8	of	of	ADP
ejpam-6837	2	9	the	the	DET
ejpam-6837	2	10	weak	weak	ADJ
ejpam-6837	2	11	convergence	convergence	NOUN
ejpam-6837	2	12	of	of	ADP
ejpam-6837	2	13	the	the	DET
ejpam-6837	2	14	acyclic	acyclic	ADJ
ejpam-6837	2	15	douglas	douglas	PROPN
ejpam-6837	2	16	–	–	PUNCT
ejpam-6837	2	17	rachford	rachford	ADJ
ejpam-6837	2	18	iteration	iteration	NOUN
ejpam-6837	2	19	to	to	ADP
ejpam-6837	2	20	a	a	DET
ejpam-6837	2	21	point	point	NOUN
ejpam-6837	2	22	whose	whose	DET
ejpam-6837	2	23	nearest	near	ADJ
ejpam-6837	2	24	-	-	PUNCT
ejpam-6837	2	25	point	point	NOUN
ejpam-6837	2	26	projections	projection	NOUN
ejpam-6837	2	27	onto	onto	ADP
ejpam-6837	2	28	each	each	PRON
ejpam-6837	2	29	of	of	ADP
ejpam-6837	2	30	the	the	DET
ejpam-6837	2	31	n	n	NUM
ejpam-6837	2	32	convex	convex	NOUN
ejpam-6837	2	33	sets	set	NOUN
ejpam-6837	2	34	coincide	coincide	NOUN
ejpam-6837	2	35	.	.	PUNCT
ejpam-6837	3	1	our	our	PRON
ejpam-6837	3	2	analysis	analysis	NOUN
ejpam-6837	3	3	shows	show	VERB
ejpam-6837	3	4	that	that	SCONJ
ejpam-6837	3	5	the	the	DET
ejpam-6837	3	6	cyclic	cyclic	ADJ
ejpam-6837	3	7	douglas	douglas	PROPN
ejpam-6837	3	8	–	–	PUNCT
ejpam-6837	3	9	rachford	rachford	ADJ
ejpam-6837	3	10	operator	operator	NOUN
ejpam-6837	3	11	is	be	AUX
ejpam-6837	3	12	asymptotically	asymptotically	ADV
ejpam-6837	3	13	regular	regular	ADJ
ejpam-6837	3	14	,	,	PUNCT
ejpam-6837	3	15	that	that	SCONJ
ejpam-6837	3	16	its	its	PRON
ejpam-6837	3	17	fixed	fix	VERB
ejpam-6837	3	18	-	-	PUNCT
ejpam-6837	3	19	point	point	NOUN
ejpam-6837	3	20	set	set	NOUN
ejpam-6837	3	21	coincides	coincide	VERB
ejpam-6837	3	22	with	with	ADP
ejpam-6837	3	23	the	the	DET
ejpam-6837	3	24	intersection	intersection	NOUN
ejpam-6837	3	25	of	of	ADP
ejpam-6837	3	26	the	the	DET
ejpam-6837	3	27	individual	individual	ADJ
ejpam-6837	3	28	fixed	fix	VERB
ejpam-6837	3	29	-	-	PUNCT
ejpam-6837	3	30	point	point	NOUN
ejpam-6837	3	31	sets	set	NOUN
ejpam-6837	3	32	when	when	SCONJ
ejpam-6837	3	33	this	this	DET
ejpam-6837	3	34	intersection	intersection	NOUN
ejpam-6837	3	35	is	be	AUX
ejpam-6837	3	36	nonempty	nonempty	ADJ
ejpam-6837	3	37	,	,	PUNCT
ejpam-6837	3	38	and	and	CCONJ
ejpam-6837	3	39	that	that	SCONJ
ejpam-6837	3	40	the	the	DET
ejpam-6837	3	41	iteration	iteration	NOUN
ejpam-6837	3	42	converges	converge	VERB
ejpam-6837	3	43	weakly	weakly	ADV
ejpam-6837	3	44	to	to	ADP
ejpam-6837	3	45	such	such	DET
ejpam-6837	3	46	a	a	DET
ejpam-6837	3	47	point	point	NOUN
ejpam-6837	3	48	.	.	PUNCT
ejpam-6837	4	1	special	special	ADJ
ejpam-6837	4	2	cases	case	NOUN
ejpam-6837	4	3	highlight	highlight	VERB
ejpam-6837	4	4	when	when	SCONJ
ejpam-6837	4	5	the	the	DET
ejpam-6837	4	6	method	method	NOUN
ejpam-6837	4	7	coincides	coincide	VERB
ejpam-6837	4	8	with	with	ADP
ejpam-6837	4	9	alternating	alternate	VERB
ejpam-6837	4	10	projections	projection	NOUN
ejpam-6837	4	11	and	and	CCONJ
ejpam-6837	4	12	when	when	SCONJ
ejpam-6837	4	13	it	it	PRON
ejpam-6837	4	14	diverges	diverge	VERB
ejpam-6837	4	15	from	from	ADP
ejpam-6837	4	16	von	von	PROPN
ejpam-6837	4	17	neumann	neumann	PROPN
ejpam-6837	4	18	’s	’s	PART
ejpam-6837	4	19	scheme	scheme	NOUN
ejpam-6837	4	20	.	.	PUNCT
ejpam-6837	5	1	2020	2020	NUM
ejpam-6837	5	2	mathematics	mathematic	NOUN
ejpam-6837	5	3	subject	subject	NOUN
ejpam-6837	5	4	classifications	classification	NOUN
ejpam-6837	5	5	:	:	PUNCT
ejpam-6837	5	6	47h09	47h09	NUM
ejpam-6837	5	7	,	,	PUNCT
ejpam-6837	5	8	47h05	47h05	NUM
ejpam-6837	5	9	,	,	PUNCT
ejpam-6837	5	10	47a06	47a06	NUM
ejpam-6837	5	11	,	,	PUNCT
ejpam-6837	5	12	90c25	90c25	NUM
ejpam-6837	5	13	key	key	ADJ
ejpam-6837	5	14	words	word	NOUN
ejpam-6837	5	15	and	and	CCONJ
ejpam-6837	5	16	phrases	phrase	NOUN
ejpam-6837	5	17	:	:	PUNCT
ejpam-6837	5	18	nonexpansive	nonexpansive	ADJ
ejpam-6837	5	19	mapping	mapping	NOUN
ejpam-6837	5	20	,	,	PUNCT
ejpam-6837	5	21	acyclic	acyclic	ADJ
ejpam-6837	5	22	douglas	douglas	PROPN
ejpam-6837	5	23	–	–	PUNCT
ejpam-6837	5	24	rachford	rachford	ADJ
ejpam-6837	5	25	method	method	NOUN
ejpam-6837	5	26	,	,	PUNCT
ejpam-6837	5	27	cyclic	cyclic	PROPN
ejpam-6837	5	28	douglas	douglas	PROPN
ejpam-6837	5	29	–	–	PUNCT
ejpam-6837	5	30	rachford	rachford	NOUN
ejpam-6837	5	31	operator	operator	NOUN
ejpam-6837	5	32	,	,	PUNCT
ejpam-6837	5	33	fixed	fix	VERB
ejpam-6837	5	34	point	point	NOUN
ejpam-6837	5	35	theory	theory	NOUN
ejpam-6837	5	36	,	,	PUNCT
ejpam-6837	5	37	convex	convex	VERB
ejpam-6837	5	38	analysis	analysis	NOUN
ejpam-6837	5	39	,	,	PUNCT
ejpam-6837	5	40	projection	projection	NOUN
ejpam-6837	5	41	algorithms	algorithm	NOUN
ejpam-6837	5	42	,	,	PUNCT
ejpam-6837	5	43	alternating	alternate	VERB
ejpam-6837	5	44	projections	projection	NOUN
ejpam-6837	5	45	,	,	PUNCT
ejpam-6837	5	46	weak	weak	ADJ
ejpam-6837	5	47	convergence	convergence	NOUN
ejpam-6837	5	48	,	,	PUNCT
ejpam-6837	5	49	asymptotic	asymptotic	ADJ
ejpam-6837	5	50	regularity	regularity	NOUN
ejpam-6837	5	51	1	1	NUM
ejpam-6837	5	52	.	.	PUNCT
ejpam-6837	5	53	introduction	introduction	NOUN
ejpam-6837	5	54	the	the	DET
ejpam-6837	5	55	douglas	douglas	PROPN
ejpam-6837	5	56	rachford	rachford	PROPN
ejpam-6837	5	57	algorithm	algorithm	PROPN
ejpam-6837	5	58	is	be	AUX
ejpam-6837	5	59	a	a	DET
ejpam-6837	5	60	very	very	ADV
ejpam-6837	5	61	popular	popular	ADJ
ejpam-6837	5	62	splitting	splitting	NOUN
ejpam-6837	5	63	technique	technique	NOUN
ejpam-6837	5	64	for	for	ADP
ejpam-6837	5	65	finding	find	VERB
ejpam-6837	5	66	a	a	DET
ejpam-6837	5	67	zero	zero	NUM
ejpam-6837	5	68	of	of	ADP
ejpam-6837	5	69	the	the	DET
ejpam-6837	5	70	sum	sum	NOUN
ejpam-6837	5	71	of	of	ADP
ejpam-6837	5	72	two	two	NUM
ejpam-6837	5	73	maximally	maximally	ADV
ejpam-6837	5	74	monotone	monotone	ADJ
ejpam-6837	5	75	operators	operator	NOUN
ejpam-6837	5	76	.	.	PUNCT
ejpam-6837	6	1	it	it	PRON
ejpam-6837	6	2	is	be	AUX
ejpam-6837	6	3	also	also	ADV
ejpam-6837	6	4	used	use	VERB
ejpam-6837	6	5	to	to	PART
ejpam-6837	6	6	solve	solve	VERB
ejpam-6837	6	7	the	the	DET
ejpam-6837	6	8	convex	convex	NOUN
ejpam-6837	6	9	feasibility	feasibility	NOUN
ejpam-6837	6	10	problem	problem	NOUN
ejpam-6837	6	11	.	.	PUNCT
ejpam-6837	7	1	that	that	PRON
ejpam-6837	7	2	is	is	AUX
ejpam-6837	7	3	,	,	PUNCT
ejpam-6837	7	4	given	give	VERB
ejpam-6837	7	5	convex	convex	PROPN
ejpam-6837	7	6	subsets	subset	NOUN
ejpam-6837	7	7	c1	c1	PROPN
ejpam-6837	7	8	,	,	PUNCT
ejpam-6837	7	9	c2	c2	PROPN
ejpam-6837	7	10	,	,	PUNCT
ejpam-6837	7	11	.	.	PUNCT
ejpam-6837	7	12	.	.	PUNCT
ejpam-6837	7	13	.	.	PUNCT
ejpam-6837	8	1	,	,	PUNCT
ejpam-6837	8	2	cm	cm	NOUN
ejpam-6837	8	3	and	and	CCONJ
ejpam-6837	8	4	c	c	NOUN
ejpam-6837	8	5	=	=	SYM
ejpam-6837	8	6	∩ci	∩ci	PROPN
ejpam-6837	8	7	̸=	̸=	PROPN
ejpam-6837	8	8	∅	∅	NOUN
ejpam-6837	8	9	,	,	PUNCT
ejpam-6837	8	10	fid	fid	NOUN
ejpam-6837	8	11	x	x	SYM
ejpam-6837	8	12	∈	∈	PROPN
ejpam-6837	8	13	c	c	X
ejpam-6837	8	14	(	(	PUNCT
ejpam-6837	8	15	1	1	NUM
ejpam-6837	8	16	)	)	PUNCT
ejpam-6837	8	17	for	for	ADP
ejpam-6837	8	18	more	more	ADJ
ejpam-6837	8	19	information	information	NOUN
ejpam-6837	8	20	about	about	ADP
ejpam-6837	8	21	feasibility	feasibility	NOUN
ejpam-6837	8	22	problems	problem	NOUN
ejpam-6837	8	23	,	,	PUNCT
ejpam-6837	8	24	we	we	PRON
ejpam-6837	8	25	refer	refer	VERB
ejpam-6837	8	26	the	the	DET
ejpam-6837	8	27	reader	reader	NOUN
ejpam-6837	8	28	to	to	ADP
ejpam-6837	8	29	[	[	X
ejpam-6837	8	30	1	1	NUM
ejpam-6837	8	31	]	]	PUNCT
ejpam-6837	8	32	which	which	PRON
ejpam-6837	8	33	provides	provide	VERB
ejpam-6837	8	34	a	a	DET
ejpam-6837	8	35	thorough	thorough	ADJ
ejpam-6837	8	36	treatment	treatment	NOUN
ejpam-6837	8	37	of	of	ADP
ejpam-6837	8	38	feasibility	feasibility	NOUN
ejpam-6837	8	39	problems	problem	NOUN
ejpam-6837	8	40	,	,	PUNCT
ejpam-6837	8	41	especially	especially	ADV
ejpam-6837	8	42	in	in	ADP
ejpam-6837	8	43	hilbert	hilbert	PROPN
ejpam-6837	8	44	spaces	space	NOUN
ejpam-6837	8	45	,	,	PUNCT
ejpam-6837	8	46	which	which	PRON
ejpam-6837	8	47	are	be	AUX
ejpam-6837	8	48	common	common	ADJ
ejpam-6837	8	49	in	in	ADP
ejpam-6837	8	50	signal	signal	ADJ
ejpam-6837	8	51	processing	processing	NOUN
ejpam-6837	8	52	,	,	PUNCT
ejpam-6837	8	53	image	image	NOUN
ejpam-6837	8	54	recovery	recovery	NOUN
ejpam-6837	8	55	,	,	PUNCT
ejpam-6837	8	56	and	and	CCONJ
ejpam-6837	8	57	optimization	optimization	NOUN
ejpam-6837	8	58	.	.	PUNCT
ejpam-6837	9	1	it	it	PRON
ejpam-6837	9	2	dicusses	dicusse	VERB
ejpam-6837	9	3	projection	projection	NOUN
ejpam-6837	9	4	methods	method	NOUN
ejpam-6837	9	5	,	,	PUNCT
ejpam-6837	9	6	such	such	ADJ
ejpam-6837	9	7	as	as	ADP
ejpam-6837	9	8	douglas	douglas	PROPN
ejpam-6837	9	9	-rachford	-rachford	PROPN
ejpam-6837	9	10	algorithm	algorithm	NOUN
ejpam-6837	9	11	and	and	CCONJ
ejpam-6837	9	12	alternating	alternate	VERB
ejpam-6837	9	13	projections	projection	NOUN
ejpam-6837	9	14	,	,	PUNCT
ejpam-6837	9	15	which	which	PRON
ejpam-6837	9	16	are	be	AUX
ejpam-6837	9	17	standard	standard	ADJ
ejpam-6837	9	18	techniques	technique	NOUN
ejpam-6837	9	19	used	use	VERB
ejpam-6837	9	20	to	to	PART
ejpam-6837	9	21	solve	solve	VERB
ejpam-6837	9	22	feasibility	feasibility	NOUN
ejpam-6837	9	23	problems	problem	NOUN
ejpam-6837	9	24	involving	involve	VERB
ejpam-6837	9	25	convex	convex	NOUN
ejpam-6837	9	26	sets	set	NOUN
ejpam-6837	9	27	.	.	PUNCT
ejpam-6837	10	1	see	see	VERB
ejpam-6837	10	2	also	also	ADV
ejpam-6837	10	3	[	[	X
ejpam-6837	10	4	2–4	2–4	X
ejpam-6837	10	5	]	]	X
ejpam-6837	10	6	for	for	ADP
ejpam-6837	10	7	more	more	ADJ
ejpam-6837	10	8	details	detail	NOUN
ejpam-6837	10	9	,	,	PUNCT
ejpam-6837	10	10	where	where	SCONJ
ejpam-6837	10	11	[	[	X
ejpam-6837	10	12	2	2	NUM
ejpam-6837	10	13	]	]	PUNCT
ejpam-6837	10	14	presents	present	VERB
ejpam-6837	10	15	projection	projection	NOUN
ejpam-6837	10	16	methods	method	NOUN
ejpam-6837	10	17	and	and	CCONJ
ejpam-6837	10	18	their	their	PRON
ejpam-6837	10	19	use	use	NOUN
ejpam-6837	10	20	in	in	ADP
ejpam-6837	10	21	solving	solve	VERB
ejpam-6837	10	22	large	large	ADJ
ejpam-6837	10	23	-	-	PUNCT
ejpam-6837	10	24	scale	scale	NOUN
ejpam-6837	10	25	feasibility	feasibility	NOUN
ejpam-6837	10	26	problems	problem	NOUN
ejpam-6837	10	27	,	,	PUNCT
ejpam-6837	10	28	particulary	particulary	ADJ
ejpam-6837	10	29	in	in	ADP
ejpam-6837	10	30	applications	application	NOUN
ejpam-6837	10	31	such	such	ADJ
ejpam-6837	10	32	as	as	ADP
ejpam-6837	10	33	image	image	NOUN
ejpam-6837	10	34	reconstruction	reconstruction	NOUN
ejpam-6837	10	35	and	and	CCONJ
ejpam-6837	10	36	medical	medical	ADJ
ejpam-6837	10	37	imaging	imaging	NOUN
ejpam-6837	10	38	.	.	PUNCT
ejpam-6837	11	1	[	[	X
ejpam-6837	11	2	3	3	X
ejpam-6837	11	3	]	]	PUNCT
ejpam-6837	11	4	provides	provide	VERB
ejpam-6837	11	5	a	a	DET
ejpam-6837	11	6	unified	unified	ADJ
ejpam-6837	11	7	treatment	treatment	NOUN
ejpam-6837	11	8	of	of	ADP
ejpam-6837	11	9	algorithms	algorithm	NOUN
ejpam-6837	11	10	for	for	ADP
ejpam-6837	11	11	feasibility	feasibility	NOUN
ejpam-6837	11	12	and	and	CCONJ
ejpam-6837	11	13	∗corresponding	∗corresponde	VERB
ejpam-6837	11	14	author	author	NOUN
ejpam-6837	11	15	.	.	PUNCT
ejpam-6837	12	1	doi	doi	NOUN
ejpam-6837	12	2	:	:	PUNCT
ejpam-6837	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6837	https://doi.org/10.29020/nybg.ejpam.v18i4.6837	PRON
ejpam-6837	12	4	email	email	NOUN
ejpam-6837	12	5	addresses	address	NOUN
ejpam-6837	12	6	:	:	PUNCT
ejpam-6837	13	1	salihah.s.alwadani@gmail.com	salihah.s.alwadani@gmail.com	PROPN
ejpam-6837	13	2	(	(	PUNCT
ejpam-6837	13	3	s.	s.	PROPN
ejpam-6837	13	4	th	th	PROPN
ejpam-6837	13	5	.	.	PUNCT
ejpam-6837	13	6	alwadani	alwadani	PROPN
ejpam-6837	13	7	)	)	PUNCT
ejpam-6837	13	8	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6837	13	9	1	1	NUM
ejpam-6837	13	10	copyright	copyright	NOUN
ejpam-6837	13	11	:	:	PUNCT
ejpam-6837	13	12	©	©	PROPN
ejpam-6837	13	13	2025	2025	NUM
ejpam-6837	13	14	the	the	DET
ejpam-6837	13	15	author(s	author(s	NOUN
ejpam-6837	13	16	)	)	PUNCT
ejpam-6837	13	17	.	.	PUNCT
ejpam-6837	14	1	(	(	PUNCT
ejpam-6837	14	2	cc	cc	NOUN
ejpam-6837	14	3	by	by	ADP
ejpam-6837	14	4	-	-	PUNCT
ejpam-6837	14	5	nc	nc	PROPN
ejpam-6837	14	6	4.0	4.0	NUM
ejpam-6837	14	7	)	)	PUNCT
ejpam-6837	14	8	s.	s.	PROPN
ejpam-6837	14	9	th	th	PROPN
ejpam-6837	14	10	.	.	PUNCT
ejpam-6837	15	1	alwadani	alwadani	PROPN
ejpam-6837	15	2	/	/	SYM
ejpam-6837	15	3	eur	eur	PROPN
ejpam-6837	15	4	.	.	PUNCT
ejpam-6837	16	1	j.	j.	PROPN
ejpam-6837	16	2	pure	pure	PROPN
ejpam-6837	16	3	appl	appl	PROPN
ejpam-6837	16	4	.	.	PROPN
ejpam-6837	16	5	math	math	PROPN
ejpam-6837	16	6	,	,	PUNCT
ejpam-6837	16	7	18	18	NUM
ejpam-6837	16	8	(	(	PUNCT
ejpam-6837	16	9	4	4	NUM
ejpam-6837	16	10	)	)	PUNCT
ejpam-6837	16	11	(	(	PUNCT
ejpam-6837	16	12	2025	2025	NUM
ejpam-6837	16	13	)	)	PUNCT
ejpam-6837	16	14	,	,	PUNCT
ejpam-6837	16	15	6837	6837	NUM
ejpam-6837	16	16	2	2	NUM
ejpam-6837	16	17	of	of	ADP
ejpam-6837	16	18	15	15	NUM
ejpam-6837	16	19	inverse	inverse	NOUN
ejpam-6837	16	20	problems	problem	NOUN
ejpam-6837	16	21	where	where	SCONJ
ejpam-6837	16	22	[	[	X
ejpam-6837	16	23	4	4	NUM
ejpam-6837	16	24	]	]	PUNCT
ejpam-6837	16	25	focuses	focus	VERB
ejpam-6837	16	26	on	on	ADP
ejpam-6837	16	27	feasibility	feasibility	NOUN
ejpam-6837	16	28	problems	problem	NOUN
ejpam-6837	16	29	in	in	ADP
ejpam-6837	16	30	signal	signal	NOUN
ejpam-6837	16	31	processing	processing	NOUN
ejpam-6837	16	32	.	.	PUNCT
ejpam-6837	17	1	it	it	PRON
ejpam-6837	17	2	explores	explore	VERB
ejpam-6837	17	3	how	how	SCONJ
ejpam-6837	17	4	projection	projection	NOUN
ejpam-6837	17	5	-	-	PUNCT
ejpam-6837	17	6	based	base	VERB
ejpam-6837	17	7	algrithms	algrithm	NOUN
ejpam-6837	17	8	can	can	AUX
ejpam-6837	17	9	be	be	AUX
ejpam-6837	17	10	used	use	VERB
ejpam-6837	17	11	to	to	PART
ejpam-6837	17	12	recover	recover	VERB
ejpam-6837	17	13	signal	signal	NOUN
ejpam-6837	17	14	that	that	PRON
ejpam-6837	17	15	satisfy	satisfy	VERB
ejpam-6837	17	16	multiple	multiple	ADJ
ejpam-6837	17	17	constraints	constraint	NOUN
ejpam-6837	17	18	represented	represent	VERB
ejpam-6837	17	19	as	as	ADP
ejpam-6837	17	20	convex	convex	NOUN
ejpam-6837	17	21	sets	set	NOUN
ejpam-6837	17	22	.	.	PUNCT
ejpam-6837	18	1	throughout	throughout	ADP
ejpam-6837	18	2	this	this	DET
ejpam-6837	18	3	paper	paper	NOUN
ejpam-6837	18	4	,	,	PUNCT
ejpam-6837	18	5	we	we	PRON
ejpam-6837	18	6	shall	shall	AUX
ejpam-6837	18	7	assume	assume	VERB
ejpam-6837	18	8	that	that	SCONJ
ejpam-6837	18	9	x	x	NOUN
ejpam-6837	18	10	=	=	PRON
ejpam-6837	18	11	h	h	NOUN
ejpam-6837	18	12	is	be	AUX
ejpam-6837	18	13	a	a	DET
ejpam-6837	18	14	real	real	ADJ
ejpam-6837	18	15	hilbert	hilbert	NOUN
ejpam-6837	18	16	space	space	NOUN
ejpam-6837	18	17	with	with	ADP
ejpam-6837	18	18	the	the	DET
ejpam-6837	18	19	product	product	NOUN
ejpam-6837	18	20	⟨	⟨	VERB
ejpam-6837	18	21	·	·	PUNCT
ejpam-6837	18	22	,	,	PUNCT
ejpam-6837	18	23	·	·	PUNCT
ejpam-6837	18	24	⟩	⟩	NOUN
ejpam-6837	18	25	and	and	CCONJ
ejpam-6837	18	26	induced	induce	VERB
ejpam-6837	18	27	norm	norm	NOUN
ejpam-6837	18	28	∥	∥	X
ejpam-6837	18	29	·	·	PUNCT
ejpam-6837	18	30	∥	∥	X
ejpam-6837	18	31	(	(	PUNCT
ejpam-6837	18	32	2	2	NUM
ejpam-6837	18	33	)	)	PUNCT
ejpam-6837	18	34	in	in	ADP
ejpam-6837	18	35	this	this	DET
ejpam-6837	18	36	paper	paper	NOUN
ejpam-6837	18	37	,	,	PUNCT
ejpam-6837	18	38	we	we	PRON
ejpam-6837	18	39	provide	provide	VERB
ejpam-6837	18	40	a	a	DET
ejpam-6837	18	41	different	different	ADJ
ejpam-6837	18	42	,	,	PUNCT
ejpam-6837	18	43	detailed	detailed	ADJ
ejpam-6837	18	44	proof	proof	NOUN
ejpam-6837	18	45	to	to	ADP
ejpam-6837	18	46	the	the	DET
ejpam-6837	18	47	weak	weak	ADJ
ejpam-6837	18	48	convergence	convergence	NOUN
ejpam-6837	18	49	of	of	ADP
ejpam-6837	18	50	acyclic	acyclic	ADJ
ejpam-6837	18	51	douglas	douglas	PROPN
ejpam-6837	18	52	-	-	PUNCT
ejpam-6837	18	53	rachford	rachford	ADJ
ejpam-6837	18	54	iteration	iteration	NOUN
ejpam-6837	18	55	schema	schema	NOUN
ejpam-6837	18	56	to	to	ADP
ejpam-6837	18	57	a	a	DET
ejpam-6837	18	58	point	point	NOUN
ejpam-6837	18	59	whose	whose	DET
ejpam-6837	18	60	nearest	near	ADJ
ejpam-6837	18	61	point	point	NOUN
ejpam-6837	18	62	projections	projection	NOUN
ejpam-6837	18	63	onto	onto	ADP
ejpam-6837	18	64	each	each	PRON
ejpam-6837	18	65	of	of	ADP
ejpam-6837	18	66	the	the	DET
ejpam-6837	18	67	n	n	NOUN
ejpam-6837	18	68	sets	set	VERB
ejpam-6837	18	69	coincide	coincide	NOUN
ejpam-6837	18	70	using	use	VERB
ejpam-6837	18	71	the	the	DET
ejpam-6837	18	72	assumption	assumption	NOUN
ejpam-6837	18	73	in	in	ADP
ejpam-6837	18	74	(	(	PUNCT
ejpam-6837	18	75	2	2	NUM
ejpam-6837	18	76	)	)	PUNCT
ejpam-6837	18	77	and	and	CCONJ
ejpam-6837	18	78	convex	convex	VERB
ejpam-6837	18	79	analysis	analysis	NOUN
ejpam-6837	18	80	.	.	PUNCT
ejpam-6837	19	1	this	this	DET
ejpam-6837	19	2	paper	paper	NOUN
ejpam-6837	19	3	is	be	AUX
ejpam-6837	19	4	distributed	distribute	VERB
ejpam-6837	19	5	as	as	SCONJ
ejpam-6837	19	6	follows	follow	VERB
ejpam-6837	19	7	:	:	PUNCT
ejpam-6837	19	8	section	section	NOUN
ejpam-6837	19	9	2	2	NUM
ejpam-6837	19	10	presents	present	VERB
ejpam-6837	19	11	standard	standard	ADJ
ejpam-6837	19	12	material	material	NOUN
ejpam-6837	19	13	and	and	CCONJ
ejpam-6837	19	14	basic	basic	ADJ
ejpam-6837	19	15	facts	fact	NOUN
ejpam-6837	19	16	and	and	CCONJ
ejpam-6837	19	17	collects	collect	VERB
ejpam-6837	19	18	some	some	DET
ejpam-6837	19	19	useful	useful	ADJ
ejpam-6837	19	20	properties	property	NOUN
ejpam-6837	19	21	from	from	ADP
ejpam-6837	19	22	convex	convex	ADJ
ejpam-6837	19	23	analysis	analysis	NOUN
ejpam-6837	19	24	and	and	CCONJ
ejpam-6837	19	25	algebra	algebra	NOUN
ejpam-6837	19	26	,	,	PUNCT
ejpam-6837	19	27	which	which	PRON
ejpam-6837	19	28	are	be	AUX
ejpam-6837	19	29	useful	useful	ADJ
ejpam-6837	19	30	in	in	ADP
ejpam-6837	19	31	our	our	PRON
ejpam-6837	19	32	later	later	ADJ
ejpam-6837	19	33	proofs	proof	NOUN
ejpam-6837	19	34	.	.	PUNCT
ejpam-6837	20	1	we	we	PRON
ejpam-6837	20	2	designate	designate	VERB
ejpam-6837	20	3	all	all	PRON
ejpam-6837	20	4	of	of	ADP
ejpam-6837	20	5	the	the	DET
ejpam-6837	20	6	known	know	VERB
ejpam-6837	20	7	results	result	NOUN
ejpam-6837	20	8	as	as	ADP
ejpam-6837	20	9	facts	fact	NOUN
ejpam-6837	20	10	with	with	ADP
ejpam-6837	20	11	explicit	explicit	ADJ
ejpam-6837	20	12	references	reference	NOUN
ejpam-6837	20	13	.	.	PUNCT
ejpam-6837	21	1	in	in	ADP
ejpam-6837	21	2	section	section	NOUN
ejpam-6837	21	3	3	3	NUM
ejpam-6837	21	4	,	,	PUNCT
ejpam-6837	21	5	we	we	PRON
ejpam-6837	21	6	visit	visit	VERB
ejpam-6837	21	7	the	the	DET
ejpam-6837	21	8	cyclic	cyclic	ADJ
ejpam-6837	21	9	douglas	douglas	PROPN
ejpam-6837	21	10	–	–	PUNCT
ejpam-6837	21	11	rachford	rachford	ADJ
ejpam-6837	21	12	iteration	iteration	NOUN
ejpam-6837	21	13	scheme	scheme	NOUN
ejpam-6837	21	14	that	that	PRON
ejpam-6837	21	15	is	be	AUX
ejpam-6837	21	16	defined	define	VERB
ejpam-6837	21	17	in	in	ADP
ejpam-6837	21	18	[	[	X
ejpam-6837	21	19	5	5	NUM
ejpam-6837	21	20	]	]	PUNCT
ejpam-6837	21	21	and	and	CCONJ
ejpam-6837	21	22	show	show	VERB
ejpam-6837	21	23	that	that	SCONJ
ejpam-6837	21	24	even	even	ADV
ejpam-6837	21	25	with	with	ADP
ejpam-6837	21	26	the	the	DET
ejpam-6837	21	27	case	case	NOUN
ejpam-6837	21	28	n	n	NOUN
ejpam-6837	21	29	=	=	SYM
ejpam-6837	21	30	2	2	NUM
ejpam-6837	21	31	the	the	DET
ejpam-6837	21	32	the	the	DET
ejpam-6837	21	33	cyclic	cyclic	ADJ
ejpam-6837	21	34	douglas	douglas	PROPN
ejpam-6837	21	35	–	–	PUNCT
ejpam-6837	21	36	rachford	rachford	ADJ
ejpam-6837	21	37	iteration	iteration	NOUN
ejpam-6837	21	38	is	be	AUX
ejpam-6837	21	39	different	different	ADJ
ejpam-6837	21	40	from	from	ADP
ejpam-6837	21	41	the	the	DET
ejpam-6837	21	42	douglas	douglas	PROPN
ejpam-6837	21	43	–	–	PUNCT
ejpam-6837	21	44	rachford	rachford	ADJ
ejpam-6837	21	45	iteration	iteration	NOUN
ejpam-6837	21	46	see	see	VERB
ejpam-6837	21	47	proposition	proposition	NOUN
ejpam-6837	21	48	2	2	NUM
ejpam-6837	21	49	,	,	PUNCT
ejpam-6837	21	50	example	example	NOUN
ejpam-6837	21	51	1	1	NUM
ejpam-6837	21	52	,	,	PUNCT
ejpam-6837	21	53	and	and	CCONJ
ejpam-6837	21	54	example	example	NOUN
ejpam-6837	22	1	2	2	NUM
ejpam-6837	22	2	.	.	PUNCT
ejpam-6837	23	1	the	the	DET
ejpam-6837	23	2	main	main	ADJ
ejpam-6837	23	3	results	result	NOUN
ejpam-6837	23	4	are	be	AUX
ejpam-6837	23	5	in	in	ADP
ejpam-6837	23	6	section	section	NOUN
ejpam-6837	23	7	4	4	NUM
ejpam-6837	23	8	,	,	PUNCT
ejpam-6837	23	9	where	where	SCONJ
ejpam-6837	23	10	can	can	AUX
ejpam-6837	23	11	be	be	AUX
ejpam-6837	23	12	summarized	summarize	VERB
ejpam-6837	23	13	as	as	SCONJ
ejpam-6837	23	14	follows	follow	VERB
ejpam-6837	23	15	:	:	PUNCT
ejpam-6837	23	16	•	•	NUM
ejpam-6837	23	17	we	we	PRON
ejpam-6837	23	18	show	show	VERB
ejpam-6837	23	19	that	that	SCONJ
ejpam-6837	23	20	the	the	DET
ejpam-6837	23	21	cyclic	cyclic	ADJ
ejpam-6837	23	22	douglas	douglas	PROPN
ejpam-6837	23	23	–	–	PUNCT
ejpam-6837	23	24	rachford	rachford	ADJ
ejpam-6837	23	25	operator	operator	NOUN
ejpam-6837	23	26	t[c1c2	t[c1c2	PROPN
ejpam-6837	23	27	...	...	PUNCT
ejpam-6837	24	1	cn	cn	PROPN
ejpam-6837	24	2	]	]	X
ejpam-6837	24	3	is	be	AUX
ejpam-6837	24	4	asymptotically	asymptotically	ADV
ejpam-6837	24	5	regular	regular	ADJ
ejpam-6837	24	6	,	,	PUNCT
ejpam-6837	24	7	see	see	VERB
ejpam-6837	24	8	section	section	NOUN
ejpam-6837	24	9	4	4	NUM
ejpam-6837	24	10	.	.	NOUN
ejpam-6837	25	1	•	•	NUM
ejpam-6837	25	2	section	section	NOUN
ejpam-6837	25	3	4	4	NUM
ejpam-6837	25	4	shows	show	VERB
ejpam-6837	25	5	that	that	SCONJ
ejpam-6837	25	6	the	the	DET
ejpam-6837	25	7	fixed	fix	VERB
ejpam-6837	25	8	point	point	NOUN
ejpam-6837	25	9	sets	set	NOUN
ejpam-6837	25	10	of	of	ADP
ejpam-6837	25	11	the	the	DET
ejpam-6837	25	12	cyclic	cyclic	ADJ
ejpam-6837	25	13	douglas	douglas	PROPN
ejpam-6837	25	14	–	–	PUNCT
ejpam-6837	25	15	rachford	rachford	ADJ
ejpam-6837	25	16	operator	operator	NOUN
ejpam-6837	25	17	are	be	AUX
ejpam-6837	25	18	equal	equal	ADJ
ejpam-6837	25	19	to	to	ADP
ejpam-6837	25	20	the	the	DET
ejpam-6837	25	21	intersection	intersection	NOUN
ejpam-6837	25	22	of	of	ADP
ejpam-6837	25	23	the	the	DET
ejpam-6837	25	24	individual	individual	ADJ
ejpam-6837	25	25	fixed	fix	VERB
ejpam-6837	25	26	point	point	NOUN
ejpam-6837	25	27	sets	set	NOUN
ejpam-6837	25	28	of	of	ADP
ejpam-6837	25	29	the	the	DET
ejpam-6837	25	30	individual	individual	ADJ
ejpam-6837	25	31	operators	operator	NOUN
ejpam-6837	25	32	under	under	ADP
ejpam-6837	25	33	the	the	DET
ejpam-6837	25	34	assumption	assumption	NOUN
ejpam-6837	25	35	that	that	SCONJ
ejpam-6837	25	36	the	the	DET
ejpam-6837	25	37	intersection	intersection	NOUN
ejpam-6837	25	38	is	be	AUX
ejpam-6837	25	39	not	not	PART
ejpam-6837	25	40	empty	empty	ADJ
ejpam-6837	25	41	.	.	PUNCT
ejpam-6837	26	1	•	•	NUM
ejpam-6837	26	2	the	the	DET
ejpam-6837	26	3	cyclic	cyclic	ADJ
ejpam-6837	26	4	douglas	douglas	PROPN
ejpam-6837	26	5	–	–	PUNCT
ejpam-6837	26	6	rachford	rachford	ADJ
ejpam-6837	26	7	iteration	iteration	NOUN
ejpam-6837	26	8	converges	converge	VERB
ejpam-6837	26	9	weakly	weakly	ADV
ejpam-6837	26	10	to	to	ADP
ejpam-6837	26	11	a	a	DET
ejpam-6837	26	12	point	point	NOUN
ejpam-6837	26	13	in	in	ADP
ejpam-6837	26	14	the	the	DET
ejpam-6837	26	15	fixed	fix	VERB
ejpam-6837	26	16	point	point	NOUN
ejpam-6837	26	17	sets	set	NOUN
ejpam-6837	26	18	of	of	ADP
ejpam-6837	26	19	the	the	DET
ejpam-6837	26	20	cyclic	cyclic	ADJ
ejpam-6837	26	21	douglas	douglas	PROPN
ejpam-6837	26	22	–	–	PUNCT
ejpam-6837	26	23	rachford	rachford	ADJ
ejpam-6837	26	24	operator	operator	NOUN
ejpam-6837	26	25	,	,	PUNCT
ejpam-6837	26	26	see	see	VERB
ejpam-6837	26	27	theorem	theorem	NOUN
ejpam-6837	26	28	1	1	NUM
ejpam-6837	26	29	for	for	ADP
ejpam-6837	26	30	more	more	ADJ
ejpam-6837	26	31	details	detail	NOUN
ejpam-6837	26	32	.	.	PUNCT
ejpam-6837	27	1	•	•	NUM
ejpam-6837	27	2	proposition	proposition	NOUN
ejpam-6837	27	3	4	4	NUM
ejpam-6837	27	4	illustrates	illustrate	VERB
ejpam-6837	27	5	that	that	SCONJ
ejpam-6837	27	6	if	if	SCONJ
ejpam-6837	27	7	the	the	DET
ejpam-6837	27	8	initial	initial	ADJ
ejpam-6837	27	9	point	point	NOUN
ejpam-6837	27	10	belongs	belong	VERB
ejpam-6837	27	11	to	to	ADP
ejpam-6837	27	12	the	the	DET
ejpam-6837	27	13	first	first	ADJ
ejpam-6837	27	14	set	set	NOUN
ejpam-6837	27	15	,	,	PUNCT
ejpam-6837	27	16	then	then	ADV
ejpam-6837	27	17	the	the	DET
ejpam-6837	27	18	cyclic	cyclic	ADJ
ejpam-6837	27	19	douglas	douglas	PROPN
ejpam-6837	27	20	-	-	PUNCT
ejpam-6837	27	21	rachford	rachford	ADJ
ejpam-6837	27	22	method	method	NOUN
ejpam-6837	27	23	coincides	coincide	VERB
ejpam-6837	27	24	with	with	ADP
ejpam-6837	27	25	the	the	DET
ejpam-6837	27	26	alternating	alternate	VERB
ejpam-6837	27	27	projection	projection	NOUN
ejpam-6837	27	28	method	method	NOUN
ejpam-6837	27	29	.	.	PUNCT
ejpam-6837	28	1	additionally	additionally	ADV
ejpam-6837	28	2	,	,	PUNCT
ejpam-6837	28	3	if	if	SCONJ
ejpam-6837	28	4	the	the	DET
ejpam-6837	28	5	cyclic	cyclic	ADJ
ejpam-6837	28	6	douglas	douglas	PROPN
ejpam-6837	28	7	–	–	PUNCT
ejpam-6837	28	8	rachford	rachford	ADJ
ejpam-6837	28	9	schema	schema	NOUN
ejpam-6837	28	10	defined	define	VERB
ejpam-6837	28	11	on	on	ADP
ejpam-6837	28	12	to	to	ADP
ejpam-6837	28	13	two	two	NUM
ejpam-6837	28	14	closed	closed	ADJ
ejpam-6837	28	15	affine	affine	NOUN
ejpam-6837	28	16	subspaces	subspace	NOUN
ejpam-6837	28	17	c2	c2	PROPN
ejpam-6837	28	18	and	and	CCONJ
ejpam-6837	28	19	c2	c2	PROPN
ejpam-6837	28	20	is	be	AUX
ejpam-6837	28	21	equal	equal	ADJ
ejpam-6837	28	22	to	to	ADP
ejpam-6837	28	23	the	the	DET
ejpam-6837	28	24	averaged	average	VERB
ejpam-6837	28	25	of	of	ADP
ejpam-6837	28	26	tc1,c2	tc1,c2	NOUN
ejpam-6837	28	27	and	and	CCONJ
ejpam-6837	28	28	tc2,c1	tc2,c1	NOUN
ejpam-6837	28	29	,	,	PUNCT
ejpam-6837	28	30	see	see	VERB
ejpam-6837	28	31	lemma	lemma	PROPN
ejpam-6837	28	32	1	1	NUM
ejpam-6837	28	33	for	for	ADP
ejpam-6837	28	34	more	more	ADJ
ejpam-6837	28	35	details	detail	NOUN
ejpam-6837	28	36	.	.	PUNCT
ejpam-6837	29	1	•	•	NUM
ejpam-6837	29	2	example	example	NOUN
ejpam-6837	29	3	3	3	NUM
ejpam-6837	29	4	indicates	indicate	VERB
ejpam-6837	29	5	that	that	SCONJ
ejpam-6837	29	6	if	if	SCONJ
ejpam-6837	29	7	x0	x0	PROPN
ejpam-6837	29	8	/∈	/∈	PUNCT
ejpam-6837	29	9	c1	c1	PROPN
ejpam-6837	29	10	,	,	PUNCT
ejpam-6837	29	11	then	then	ADV
ejpam-6837	29	12	the	the	DET
ejpam-6837	29	13	cyclic	cyclic	ADJ
ejpam-6837	29	14	douglas	douglas	PROPN
ejpam-6837	29	15	–	–	PUNCT
ejpam-6837	29	16	rachford	rachford	ADJ
ejpam-6837	29	17	iteration	iteration	NOUN
ejpam-6837	29	18	need	need	AUX
ejpam-6837	29	19	not	not	PART
ejpam-6837	29	20	coincide	coincide	VERB
ejpam-6837	29	21	with	with	ADP
ejpam-6837	29	22	von	von	PROPN
ejpam-6837	29	23	neumann	neumann	PROPN
ejpam-6837	29	24	’s	’s	PART
ejpam-6837	29	25	alternating	alternate	VERB
ejpam-6837	29	26	projection	projection	NOUN
ejpam-6837	29	27	method	method	NOUN
ejpam-6837	29	28	.	.	PUNCT
ejpam-6837	30	1	2	2	X
ejpam-6837	30	2	.	.	X
ejpam-6837	30	3	background	background	NOUN
ejpam-6837	30	4	recall	recall	NOUN
ejpam-6837	30	5	x	x	PUNCT
ejpam-6837	31	1	=	=	NOUN
ejpam-6837	31	2	h	h	NOUN
ejpam-6837	31	3	is	be	AUX
ejpam-6837	31	4	a	a	DET
ejpam-6837	31	5	real	real	ADJ
ejpam-6837	31	6	hilbert	hilbert	NOUN
ejpam-6837	31	7	space	space	NOUN
ejpam-6837	31	8	with	with	ADP
ejpam-6837	31	9	the	the	DET
ejpam-6837	31	10	product	product	NOUN
ejpam-6837	31	11	⟨	⟨	VERB
ejpam-6837	31	12	·	·	PUNCT
ejpam-6837	31	13	,	,	PUNCT
ejpam-6837	31	14	·	·	PUNCT
ejpam-6837	31	15	⟩	⟩	NOUN
ejpam-6837	31	16	and	and	CCONJ
ejpam-6837	31	17	induced	induce	VERB
ejpam-6837	31	18	norm	norm	NOUN
ejpam-6837	31	19	∥	∥	X
ejpam-6837	31	20	·	·	PUNCT
ejpam-6837	31	21	∥.	∥.	NUM
ejpam-6837	32	1	the	the	DET
ejpam-6837	32	2	identity	identity	NOUN
ejpam-6837	32	3	operator	operator	NOUN
ejpam-6837	32	4	on	on	ADP
ejpam-6837	32	5	h	h	NOUN
ejpam-6837	32	6	is	be	AUX
ejpam-6837	32	7	denoted	denote	VERB
ejpam-6837	32	8	by	by	ADP
ejpam-6837	32	9	i	i	PROPN
ejpam-6837	32	10	d.	d.	PROPN
ejpam-6837	32	11	let	let	VERB
ejpam-6837	32	12	c	c	PROPN
ejpam-6837	32	13	⊂	⊂	PROPN
ejpam-6837	32	14	h	h	PROPN
ejpam-6837	32	15	is	be	AUX
ejpam-6837	32	16	closed	closed	ADJ
ejpam-6837	32	17	and	and	CCONJ
ejpam-6837	32	18	convex	convex	NOUN
ejpam-6837	32	19	set	set	NOUN
ejpam-6837	32	20	,	,	PUNCT
ejpam-6837	32	21	the	the	DET
ejpam-6837	32	22	projector	projector	NOUN
ejpam-6837	32	23	onto	onto	ADP
ejpam-6837	32	24	the	the	DET
ejpam-6837	32	25	set	set	NOUN
ejpam-6837	33	1	c	c	NOUN
ejpam-6837	33	2	is	be	AUX
ejpam-6837	33	3	the	the	DET
ejpam-6837	33	4	mapping	mapping	NOUN
ejpam-6837	33	5	pc	pc	NOUN
ejpam-6837	33	6	:	:	PUNCT
ejpam-6837	33	7	h	h	NOUN
ejpam-6837	33	8	→	→	SYM
ejpam-6837	33	9	c	c	NOUN
ejpam-6837	33	10	defined	define	VERB
ejpam-6837	33	11	as	as	ADP
ejpam-6837	33	12	,	,	PUNCT
ejpam-6837	33	13	pc	pc	NOUN
ejpam-6837	33	14	:	:	PUNCT
ejpam-6837	33	15	=	=	SYM
ejpam-6837	33	16	argmin	argmin	NOUN
ejpam-6837	33	17	c∈c	c∈c	NOUN
ejpam-6837	34	1	∥x	∥x	PROPN
ejpam-6837	34	2	−	−	PROPN
ejpam-6837	34	3	c∥	c∥	PROPN
ejpam-6837	35	1	=	=	PUNCT
ejpam-6837	35	2	{	{	PUNCT
ejpam-6837	35	3	z	z	NOUN
ejpam-6837	35	4	∈	∈	PROPN
ejpam-6837	35	5	c	c	NOUN
ejpam-6837	35	6	:	:	PUNCT
ejpam-6837	35	7	∥x	∥x	PROPN
ejpam-6837	35	8	−	−	PROPN
ejpam-6837	35	9	z∥	z∥	NOUN
ejpam-6837	35	10	=	=	PUNCT
ejpam-6837	35	11	inf	inf	PROPN
ejpam-6837	35	12	c∈c	c∈c	NOUN
ejpam-6837	35	13	∥x	∥x	PROPN
ejpam-6837	35	14	−	−	PROPN
ejpam-6837	35	15	c∥	c∥	PROPN
ejpam-6837	35	16	}	}	PUNCT
ejpam-6837	35	17	,	,	PUNCT
ejpam-6837	35	18	for	for	ADP
ejpam-6837	35	19	all	all	DET
ejpam-6837	35	20	x	x	SYM
ejpam-6837	35	21	∈	∈	PROPN
ejpam-6837	35	22	h	h	NOUN
ejpam-6837	35	23	(	(	PUNCT
ejpam-6837	35	24	3	3	X
ejpam-6837	35	25	)	)	PUNCT
ejpam-6837	35	26	s.	s.	PROPN
ejpam-6837	35	27	th	th	PROPN
ejpam-6837	35	28	.	.	PUNCT
ejpam-6837	36	1	alwadani	alwadani	PROPN
ejpam-6837	36	2	/	/	SYM
ejpam-6837	36	3	eur	eur	PROPN
ejpam-6837	36	4	.	.	PUNCT
ejpam-6837	37	1	j.	j.	PROPN
ejpam-6837	37	2	pure	pure	PROPN
ejpam-6837	37	3	appl	appl	PROPN
ejpam-6837	37	4	.	.	PROPN
ejpam-6837	37	5	math	math	PROPN
ejpam-6837	37	6	,	,	PUNCT
ejpam-6837	37	7	18	18	NUM
ejpam-6837	37	8	(	(	PUNCT
ejpam-6837	37	9	4	4	NUM
ejpam-6837	37	10	)	)	PUNCT
ejpam-6837	37	11	(	(	PUNCT
ejpam-6837	37	12	2025	2025	NUM
ejpam-6837	37	13	)	)	PUNCT
ejpam-6837	37	14	,	,	PUNCT
ejpam-6837	37	15	6837	6837	NUM
ejpam-6837	37	16	3	3	NUM
ejpam-6837	37	17	of	of	ADP
ejpam-6837	37	18	15	15	NUM
ejpam-6837	37	19	the	the	DET
ejpam-6837	37	20	reflector	reflector	NOUN
ejpam-6837	37	21	with	with	ADP
ejpam-6837	37	22	respect	respect	NOUN
ejpam-6837	37	23	to	to	ADP
ejpam-6837	37	24	the	the	DET
ejpam-6837	37	25	set	set	NOUN
ejpam-6837	37	26	c	c	NOUN
ejpam-6837	37	27	is	be	AUX
ejpam-6837	37	28	a	a	DET
ejpam-6837	37	29	set	set	NOUN
ejpam-6837	37	30	valued	value	VERB
ejpam-6837	37	31	mapping	mapping	NOUN
ejpam-6837	37	32	pc	pc	NOUN
ejpam-6837	37	33	:	:	PUNCT
ejpam-6837	38	1	h	h	NOUN
ejpam-6837	38	2	→	→	SYM
ejpam-6837	38	3	h	h	PRON
ejpam-6837	38	4	defined	define	VERB
ejpam-6837	38	5	as	as	ADP
ejpam-6837	38	6	,	,	PUNCT
ejpam-6837	38	7	rc	rc	PROPN
ejpam-6837	38	8	:	:	PUNCT
ejpam-6837	38	9	=	=	SYM
ejpam-6837	38	10	pc	pc	NOUN
ejpam-6837	38	11	+	+	NOUN
ejpam-6837	38	12	(	(	PUNCT
ejpam-6837	38	13	pc	pc	NOUN
ejpam-6837	38	14	−	−	NOUN
ejpam-6837	38	15	i	i	NOUN
ejpam-6837	38	16	d	d	PROPN
ejpam-6837	38	17	)	)	PUNCT
ejpam-6837	39	1	=	=	SYM
ejpam-6837	39	2	2	2	NUM
ejpam-6837	39	3	pc	pc	NOUN
ejpam-6837	39	4	−	−	NOUN
ejpam-6837	40	1	i	i	PROPN
ejpam-6837	40	2	d	d	PROPN
ejpam-6837	40	3	,	,	PUNCT
ejpam-6837	40	4	for	for	ADP
ejpam-6837	40	5	all	all	DET
ejpam-6837	40	6	x	x	SYM
ejpam-6837	40	7	∈	∈	PROPN
ejpam-6837	40	8	h	h	NOUN
ejpam-6837	40	9	(	(	PUNCT
ejpam-6837	40	10	4	4	X
ejpam-6837	40	11	)	)	PUNCT
ejpam-6837	40	12	let	let	VERB
ejpam-6837	40	13	t	t	NOUN
ejpam-6837	40	14	:	:	PUNCT
ejpam-6837	40	15	h	h	PROPN
ejpam-6837	40	16	→	→	PUNCT
ejpam-6837	40	17	h	h	NOUN
ejpam-6837	40	18	be	be	AUX
ejpam-6837	40	19	an	an	DET
ejpam-6837	40	20	operator	operator	NOUN
ejpam-6837	40	21	.	.	PUNCT
ejpam-6837	41	1	then	then	ADV
ejpam-6837	41	2	a	a	DET
ejpam-6837	41	3	fixed	fix	VERB
ejpam-6837	41	4	point	point	NOUN
ejpam-6837	41	5	of	of	ADP
ejpam-6837	41	6	t	t	PROPN
ejpam-6837	41	7	is	be	AUX
ejpam-6837	41	8	a	a	DET
ejpam-6837	41	9	point	point	NOUN
ejpam-6837	41	10	x	x	SYM
ejpam-6837	41	11	∈	∈	NOUN
ejpam-6837	41	12	h	h	NOUN
ejpam-6837	41	13	that	that	PRON
ejpam-6837	41	14	map	map	VERB
ejpam-6837	41	15	a	a	DET
ejpam-6837	41	16	point	point	NOUN
ejpam-6837	41	17	to	to	ADP
ejpam-6837	41	18	itself	itself	PRON
ejpam-6837	41	19	.	.	PUNCT
ejpam-6837	42	1	that	that	PRON
ejpam-6837	42	2	is	be	AUX
ejpam-6837	42	3	,	,	PUNCT
ejpam-6837	42	4	tx	tx	PROPN
ejpam-6837	42	5	=	=	PUNCT
ejpam-6837	42	6	x.	x.	NOUN
ejpam-6837	42	7	the	the	DET
ejpam-6837	42	8	set	set	NOUN
ejpam-6837	42	9	of	of	ADP
ejpam-6837	42	10	fixed	fix	VERB
ejpam-6837	42	11	points	point	NOUN
ejpam-6837	42	12	of	of	ADP
ejpam-6837	42	13	the	the	DET
ejpam-6837	42	14	operator	operator	NOUN
ejpam-6837	42	15	t	t	NOUN
ejpam-6837	42	16	is	be	AUX
ejpam-6837	42	17	denoted	denote	VERB
ejpam-6837	42	18	by	by	ADP
ejpam-6837	42	19	fix	fix	PROPN
ejpam-6837	42	20	t	t	PROPN
ejpam-6837	42	21	,	,	PUNCT
ejpam-6837	42	22	i.e.	i.e.	X
ejpam-6837	42	23	,	,	PUNCT
ejpam-6837	42	24	fix	fix	NOUN
ejpam-6837	42	25	t	t	X
ejpam-6837	42	26	:	:	PUNCT
ejpam-6837	42	27	=	=	SYM
ejpam-6837	42	28	{	{	PUNCT
ejpam-6837	42	29	x	x	PUNCT
ejpam-6837	42	30	∈	∈	PROPN
ejpam-6837	42	31	h	h	NOUN
ejpam-6837	42	32	:	:	PUNCT
ejpam-6837	42	33	t(x	t(x	PROPN
ejpam-6837	42	34	)	)	PUNCT
ejpam-6837	42	35	=	=	PUNCT
ejpam-6837	43	1	x	x	X
ejpam-6837	43	2	}	}	PUNCT
ejpam-6837	43	3	̸=	̸=	PROPN
ejpam-6837	43	4	∅	∅	NOUN
ejpam-6837	43	5	,	,	PUNCT
ejpam-6837	43	6	for	for	ADP
ejpam-6837	43	7	all	all	DET
ejpam-6837	43	8	x	x	SYM
ejpam-6837	43	9	∈	∈	PROPN
ejpam-6837	43	10	h	h	NOUN
ejpam-6837	43	11	(	(	PUNCT
ejpam-6837	43	12	5	5	NUM
ejpam-6837	43	13	)	)	PUNCT
ejpam-6837	43	14	definition	definition	NOUN
ejpam-6837	43	15	1	1	NUM
ejpam-6837	43	16	.	.	PUNCT
ejpam-6837	44	1	[	[	X
ejpam-6837	44	2	1	1	NUM
ejpam-6837	44	3	,	,	PUNCT
ejpam-6837	44	4	definition	definition	NOUN
ejpam-6837	44	5	4.1	4.1	NUM
ejpam-6837	44	6	]	]	PUNCT
ejpam-6837	44	7	let	let	VERB
ejpam-6837	44	8	c	c	PRON
ejpam-6837	44	9	be	be	AUX
ejpam-6837	44	10	a	a	DET
ejpam-6837	44	11	nonempty	nonempty	ADJ
ejpam-6837	44	12	,	,	PUNCT
ejpam-6837	44	13	closed	closed	ADJ
ejpam-6837	44	14	and	and	CCONJ
ejpam-6837	44	15	convex	convex	PROPN
ejpam-6837	44	16	subset	subset	NOUN
ejpam-6837	44	17	of	of	ADP
ejpam-6837	44	18	h.	h.	PROPN
ejpam-6837	44	19	let	let	VERB
ejpam-6837	44	20	t	t	NOUN
ejpam-6837	44	21	:	:	PUNCT
ejpam-6837	44	22	c	c	X
ejpam-6837	44	23	→	→	SYM
ejpam-6837	44	24	h	h	NOUN
ejpam-6837	44	25	then	then	ADV
ejpam-6837	44	26	t	t	PROPN
ejpam-6837	44	27	is	be	AUX
ejpam-6837	44	28	;	;	PUNCT
ejpam-6837	44	29	(	(	PUNCT
ejpam-6837	44	30	i	i	NOUN
ejpam-6837	44	31	)	)	PUNCT
ejpam-6837	44	32	nonexpansive	nonexpansive	ADJ
ejpam-6837	44	33	on	on	ADP
ejpam-6837	44	34	c	c	PROPN
ejpam-6837	44	35	if	if	SCONJ
ejpam-6837	44	36	it	it	PRON
ejpam-6837	44	37	is	be	AUX
ejpam-6837	44	38	lipschitz	lipschitz	NOUN
ejpam-6837	44	39	continuous	continuous	ADJ
ejpam-6837	44	40	with	with	ADP
ejpam-6837	44	41	constant	constant	ADJ
ejpam-6837	44	42	1	1	NUM
ejpam-6837	44	43	,	,	PUNCT
ejpam-6837	44	44	i.e.	i.e.	X
ejpam-6837	44	45	,	,	PUNCT
ejpam-6837	44	46	(	(	PUNCT
ejpam-6837	44	47	∀x	∀x	X
ejpam-6837	44	48	∈	∈	PROPN
ejpam-6837	44	49	c)(∀y	c)(∀y	ADP
ejpam-6837	44	50	∈	∈	PROPN
ejpam-6837	44	51	c	c	NOUN
ejpam-6837	44	52	)	)	PUNCT
ejpam-6837	45	1	∥tx	∥tx	ADP
ejpam-6837	46	1	−	−	PROPN
ejpam-6837	47	1	ty∥	ty∥	NOUN
ejpam-6837	47	2	≤	≤	ADV
ejpam-6837	48	1	∥x	∥x	PROPN
ejpam-6837	48	2	−	−	PROPN
ejpam-6837	48	3	y∥	y∥	NOUN
ejpam-6837	48	4	;	;	PUNCT
ejpam-6837	48	5	(	(	PUNCT
ejpam-6837	48	6	6	6	NUM
ejpam-6837	48	7	)	)	PUNCT
ejpam-6837	48	8	(	(	PUNCT
ejpam-6837	48	9	ii	ii	NOUN
ejpam-6837	48	10	)	)	PUNCT
ejpam-6837	48	11	firmly	firmly	ADV
ejpam-6837	48	12	nonexpansive	nonexpansive	ADJ
ejpam-6837	48	13	if	if	SCONJ
ejpam-6837	48	14	(	(	PUNCT
ejpam-6837	48	15	∀x	∀x	X
ejpam-6837	48	16	∈	∈	PROPN
ejpam-6837	48	17	c)(∀y	c)(∀y	ADP
ejpam-6837	48	18	∈	∈	PROPN
ejpam-6837	48	19	c	c	NOUN
ejpam-6837	48	20	)	)	PUNCT
ejpam-6837	48	21	∥tx	∥tx	PRON
ejpam-6837	48	22	−	−	NOUN
ejpam-6837	49	1	ty∥2	ty∥2	NOUN
ejpam-6837	49	2	+	+	CCONJ
ejpam-6837	49	3	∥	∥	PRON
ejpam-6837	49	4	(	(	PUNCT
ejpam-6837	49	5	id−t	id−t	PROPN
ejpam-6837	49	6	)	)	PUNCT
ejpam-6837	50	1	x	x	X
ejpam-6837	50	2	−	−	PROPN
ejpam-6837	50	3	(	(	PUNCT
ejpam-6837	50	4	id−t	id−t	PROPN
ejpam-6837	50	5	)	)	PUNCT
ejpam-6837	50	6	y∥	y∥	VERB
ejpam-6837	50	7	≤	≤	PUNCT
ejpam-6837	50	8	∥x	∥x	PROPN
ejpam-6837	50	9	−	−	PROPN
ejpam-6837	50	10	y∥2	y∥2	NOUN
ejpam-6837	50	11	;	;	PUNCT
ejpam-6837	50	12	(	(	PUNCT
ejpam-6837	50	13	7	7	X
ejpam-6837	50	14	)	)	PUNCT
ejpam-6837	50	15	(	(	PUNCT
ejpam-6837	50	16	iii	iii	NOUN
ejpam-6837	50	17	)	)	PUNCT
ejpam-6837	50	18	quasinonexpansive	quasinonexpansive	NOUN
ejpam-6837	50	19	if	if	SCONJ
ejpam-6837	50	20	t	t	PROPN
ejpam-6837	50	21	is	be	AUX
ejpam-6837	50	22	fejér	fejér	NOUN
ejpam-6837	50	23	montone	montone	NOUN
ejpam-6837	50	24	with	with	ADP
ejpam-6837	50	25	respect	respect	NOUN
ejpam-6837	50	26	to	to	AUX
ejpam-6837	50	27	fix	fix	VERB
ejpam-6837	50	28	t	t	PROPN
ejpam-6837	50	29	,	,	PUNCT
ejpam-6837	50	30	i.e.	i.e.	X
ejpam-6837	50	31	,	,	PUNCT
ejpam-6837	50	32	(	(	PUNCT
ejpam-6837	50	33	∀x	∀x	X
ejpam-6837	50	34	∈	∈	NOUN
ejpam-6837	50	35	c)(∀y	c)(∀y	ADP
ejpam-6837	50	36	∈	∈	PROPN
ejpam-6837	50	37	fix	fix	NOUN
ejpam-6837	50	38	t	t	PROPN
ejpam-6837	50	39	)	)	PUNCT
ejpam-6837	51	1	∥tx	∥tx	ADP
ejpam-6837	51	2	−	−	NOUN
ejpam-6837	52	1	y∥	y∥	VERB
ejpam-6837	52	2	≤	≤	NUM
ejpam-6837	53	1	∥x	∥x	PROPN
ejpam-6837	53	2	−	−	PROPN
ejpam-6837	53	3	y∥	y∥	NOUN
ejpam-6837	53	4	;	;	PUNCT
ejpam-6837	53	5	(	(	PUNCT
ejpam-6837	53	6	8)	8)	NUM
ejpam-6837	53	7	(	(	PUNCT
ejpam-6837	53	8	iv	iv	NOUN
ejpam-6837	53	9	)	)	PUNCT
ejpam-6837	53	10	strictly	strictly	ADV
ejpam-6837	53	11	quasinonexpansive	quasinonexpansive	ADJ
ejpam-6837	53	12	if	if	SCONJ
ejpam-6837	53	13	(	(	PUNCT
ejpam-6837	53	14	∀x	∀x	X
ejpam-6837	53	15	/∈	/∈	PUNCT
ejpam-6837	53	16	fix	fix	VERB
ejpam-6837	53	17	t)(∀y	t)(∀y	NOUN
ejpam-6837	53	18	∈	∈	PROPN
ejpam-6837	53	19	fix	fix	NOUN
ejpam-6837	53	20	t	t	PROPN
ejpam-6837	53	21	)	)	PUNCT
ejpam-6837	54	1	∥tx	∥tx	ADP
ejpam-6837	54	2	−	−	NOUN
ejpam-6837	54	3	y∥	y∥	VERB
ejpam-6837	54	4	<	<	X
ejpam-6837	54	5	∥x	∥x	PROPN
ejpam-6837	54	6	−	−	PROPN
ejpam-6837	54	7	y∥	y∥	NOUN
ejpam-6837	54	8	;	;	PUNCT
ejpam-6837	54	9	(	(	PUNCT
ejpam-6837	54	10	9	9	NUM
ejpam-6837	54	11	)	)	PUNCT
ejpam-6837	54	12	(	(	PUNCT
ejpam-6837	54	13	v	v	NOUN
ejpam-6837	54	14	)	)	PUNCT
ejpam-6837	54	15	αavaraged	αavarage	VERB
ejpam-6837	54	16	for	for	ADP
ejpam-6837	54	17	α	α	PROPN
ejpam-6837	54	18	∈	∈	PROPN
ejpam-6837	54	19	(	(	PUNCT
ejpam-6837	54	20	0	0	NUM
ejpam-6837	54	21	,	,	PUNCT
ejpam-6837	54	22	1	1	NUM
ejpam-6837	54	23	)	)	PUNCT
ejpam-6837	54	24	,	,	PUNCT
ejpam-6837	54	25	if	if	SCONJ
ejpam-6837	54	26	there	there	PRON
ejpam-6837	54	27	exisits	exisit	VERB
ejpam-6837	54	28	anonexpansive	anonexpansive	ADJ
ejpam-6837	54	29	operator	operator	NOUN
ejpam-6837	54	30	n	n	NOUN
ejpam-6837	55	1	:	:	PUNCT
ejpam-6837	55	2	c	c	X
ejpam-6837	55	3	→	→	PUNCT
ejpam-6837	55	4	h	h	NOUN
ejpam-6837	55	5	such	such	ADJ
ejpam-6837	55	6	that	that	DET
ejpam-6837	55	7	t	t	NOUN
ejpam-6837	55	8	=	=	PUNCT
ejpam-6837	55	9	(	(	PUNCT
ejpam-6837	55	10	1	1	NUM
ejpam-6837	55	11	−	−	PROPN
ejpam-6837	55	12	α	α	NUM
ejpam-6837	55	13	)	)	PUNCT
ejpam-6837	55	14	id+αn	id+αn	NOUN
ejpam-6837	55	15	(	(	PUNCT
ejpam-6837	55	16	10	10	NUM
ejpam-6837	55	17	)	)	PUNCT
ejpam-6837	55	18	definition	definition	NOUN
ejpam-6837	55	19	2	2	NUM
ejpam-6837	55	20	.	.	PUNCT
ejpam-6837	56	1	[	[	X
ejpam-6837	56	2	6	6	NUM
ejpam-6837	56	3	,	,	PUNCT
ejpam-6837	56	4	definition	definition	NOUN
ejpam-6837	56	5	4.8	4.8	NUM
ejpam-6837	56	6	-	-	SYM
ejpam-6837	56	7	1	1	NUM
ejpam-6837	56	8	]	]	PUNCT
ejpam-6837	56	9	a	a	DET
ejpam-6837	56	10	sequence	sequence	NOUN
ejpam-6837	56	11	(	(	PUNCT
ejpam-6837	56	12	xn)n∈n	xn)n∈n	NUM
ejpam-6837	56	13	in	in	ADP
ejpam-6837	56	14	a	a	DET
ejpam-6837	56	15	normed	normed	ADJ
ejpam-6837	56	16	space	space	NOUN
ejpam-6837	56	17	is	be	AUX
ejpam-6837	56	18	said	say	VERB
ejpam-6837	56	19	to	to	PART
ejpam-6837	56	20	be	be	AUX
ejpam-6837	56	21	convergent	convergent	ADJ
ejpam-6837	56	22	(	(	PUNCT
ejpam-6837	56	23	strongly	strongly	ADV
ejpam-6837	56	24	convergent	convergent	ADJ
ejpam-6837	56	25	or	or	CCONJ
ejpam-6837	56	26	convergent	convergent	NOUN
ejpam-6837	56	27	in	in	ADP
ejpam-6837	56	28	the	the	DET
ejpam-6837	56	29	norm	norm	NOUN
ejpam-6837	56	30	)	)	PUNCT
ejpam-6837	56	31	if	if	SCONJ
ejpam-6837	56	32	there	there	PRON
ejpam-6837	56	33	is	be	VERB
ejpam-6837	56	34	an	an	DET
ejpam-6837	56	35	x∗	x∗	PROPN
ejpam-6837	56	36	∈	∈	PROPN
ejpam-6837	56	37	h	h	NOUN
ejpam-6837	57	1	such	such	ADJ
ejpam-6837	57	2	that	that	SCONJ
ejpam-6837	57	3	lim	lim	PROPN
ejpam-6837	57	4	n→∞	n→∞	PRON
ejpam-6837	57	5	∥xn	∥xn	PROPN
ejpam-6837	57	6	−	−	PROPN
ejpam-6837	57	7	x∗∥	x∗∥	PROPN
ejpam-6837	58	1	=	=	PUNCT
ejpam-6837	58	2	0	0	PROPN
ejpam-6837	59	1	this	this	PRON
ejpam-6837	59	2	is	be	AUX
ejpam-6837	59	3	written	write	VERB
ejpam-6837	59	4	lim	lim	PROPN
ejpam-6837	59	5	n→∞	n→∞	X
ejpam-6837	59	6	xn	xn	PROPN
ejpam-6837	59	7	=	=	SYM
ejpam-6837	59	8	x∗	x∗	PROPN
ejpam-6837	59	9	,	,	PUNCT
ejpam-6837	59	10	or	or	CCONJ
ejpam-6837	59	11	simply	simply	ADV
ejpam-6837	59	12	as	as	ADP
ejpam-6837	59	13	xn	xn	PROPN
ejpam-6837	59	14	→	→	SYM
ejpam-6837	59	15	x∗.	x∗.	SYM
ejpam-6837	60	1	definition	definition	NOUN
ejpam-6837	60	2	3	3	NUM
ejpam-6837	60	3	.	.	PUNCT
ejpam-6837	61	1	[	[	X
ejpam-6837	61	2	6	6	NUM
ejpam-6837	61	3	,	,	PUNCT
ejpam-6837	61	4	definition	definition	NOUN
ejpam-6837	61	5	4.8	4.8	NUM
ejpam-6837	61	6	-	-	SYM
ejpam-6837	61	7	2	2	NUM
ejpam-6837	61	8	]	]	PUNCT
ejpam-6837	61	9	a	a	DET
ejpam-6837	61	10	sequence	sequence	NOUN
ejpam-6837	61	11	(	(	PUNCT
ejpam-6837	61	12	xn)n∈n	xn)n∈n	NUM
ejpam-6837	61	13	in	in	ADP
ejpam-6837	61	14	a	a	DET
ejpam-6837	61	15	normed	normed	ADJ
ejpam-6837	61	16	space	space	NOUN
ejpam-6837	61	17	is	be	AUX
ejpam-6837	61	18	said	say	VERB
ejpam-6837	61	19	to	to	PART
ejpam-6837	61	20	be	be	AUX
ejpam-6837	61	21	weakly	weakly	ADV
ejpam-6837	61	22	convergent	convergent	ADJ
ejpam-6837	61	23	if	if	SCONJ
ejpam-6837	61	24	there	there	PRON
ejpam-6837	61	25	is	be	VERB
ejpam-6837	61	26	an	an	DET
ejpam-6837	61	27	x∗	x∗	PROPN
ejpam-6837	61	28	∈	∈	PROPN
ejpam-6837	61	29	h	h	NOUN
ejpam-6837	61	30	such	such	ADJ
ejpam-6837	61	31	that	that	PRON
ejpam-6837	61	32	for	for	ADP
ejpam-6837	61	33	every	every	DET
ejpam-6837	61	34	bounded	bound	VERB
ejpam-6837	61	35	linear	linear	PROPN
ejpam-6837	61	36	functional	functional	ADJ
ejpam-6837	61	37	f	f	PROPN
ejpam-6837	61	38	on	on	ADP
ejpam-6837	61	39	h	h	PROPN
ejpam-6837	61	40	,	,	PUNCT
ejpam-6837	61	41	lim	lim	PROPN
ejpam-6837	61	42	n→∞	n→∞	X
ejpam-6837	62	1	f	f	X
ejpam-6837	62	2	(	(	PUNCT
ejpam-6837	62	3	xn	xn	PROPN
ejpam-6837	62	4	)	)	PUNCT
ejpam-6837	62	5	=	=	SYM
ejpam-6837	62	6	f	f	PROPN
ejpam-6837	62	7	(	(	PUNCT
ejpam-6837	62	8	x∗	x∗	PROPN
ejpam-6837	62	9	)	)	PUNCT
ejpam-6837	62	10	.	.	PUNCT
ejpam-6837	63	1	this	this	PRON
ejpam-6837	63	2	is	be	AUX
ejpam-6837	63	3	written	write	VERB
ejpam-6837	63	4	xn	xn	PUNCT
ejpam-6837	64	1	⇀	⇀	PUNCT
ejpam-6837	64	2	x∗.	x∗.	PUNCT
ejpam-6837	65	1	s.	s.	PROPN
ejpam-6837	65	2	th	th	PROPN
ejpam-6837	65	3	.	.	PUNCT
ejpam-6837	66	1	alwadani	alwadani	PROPN
ejpam-6837	66	2	/	/	SYM
ejpam-6837	66	3	eur	eur	PROPN
ejpam-6837	66	4	.	.	PUNCT
ejpam-6837	67	1	j.	j.	PROPN
ejpam-6837	67	2	pure	pure	PROPN
ejpam-6837	67	3	appl	appl	PROPN
ejpam-6837	67	4	.	.	PROPN
ejpam-6837	67	5	math	math	PROPN
ejpam-6837	67	6	,	,	PUNCT
ejpam-6837	67	7	18	18	NUM
ejpam-6837	67	8	(	(	PUNCT
ejpam-6837	67	9	4	4	NUM
ejpam-6837	67	10	)	)	PUNCT
ejpam-6837	67	11	(	(	PUNCT
ejpam-6837	67	12	2025	2025	NUM
ejpam-6837	67	13	)	)	PUNCT
ejpam-6837	67	14	,	,	PUNCT
ejpam-6837	67	15	6837	6837	NUM
ejpam-6837	67	16	4	4	NUM
ejpam-6837	67	17	of	of	ADP
ejpam-6837	67	18	15	15	NUM
ejpam-6837	67	19	definition	definition	NOUN
ejpam-6837	67	20	4	4	NUM
ejpam-6837	67	21	.	.	PUNCT
ejpam-6837	68	1	let	let	VERB
ejpam-6837	68	2	t	t	NOUN
ejpam-6837	68	3	:	:	PUNCT
ejpam-6837	68	4	h	h	PROPN
ejpam-6837	68	5	→	→	SYM
ejpam-6837	68	6	h.	h.	PROPN
ejpam-6837	68	7	we	we	PRON
ejpam-6837	68	8	recall	recall	VERB
ejpam-6837	68	9	that	that	SCONJ
ejpam-6837	68	10	t	t	PROPN
ejpam-6837	68	11	is	be	AUX
ejpam-6837	68	12	asymptotically	asymptotically	ADV
ejpam-6837	68	13	regular	regular	ADJ
ejpam-6837	68	14	if	if	SCONJ
ejpam-6837	68	15	tnx−	tnx−	PROPN
ejpam-6837	68	16	tn+1x	tn+1x	NOUN
ejpam-6837	68	17	→	→	SYM
ejpam-6837	68	18	0	0	NUM
ejpam-6837	68	19	,	,	PUNCT
ejpam-6837	68	20	in	in	ADP
ejpam-6837	68	21	norm	norm	NOUN
ejpam-6837	68	22	,	,	PUNCT
ejpam-6837	68	23	for	for	ADP
ejpam-6837	68	24	all	all	DET
ejpam-6837	68	25	x	x	SYM
ejpam-6837	68	26	∈	∈	PROPN
ejpam-6837	68	27	h.	h.	NOUN
ejpam-6837	68	28	definition	definition	NOUN
ejpam-6837	68	29	5	5	NUM
ejpam-6837	68	30	.	.	PUNCT
ejpam-6837	69	1	[	[	X
ejpam-6837	69	2	7	7	NUM
ejpam-6837	69	3	,	,	PUNCT
ejpam-6837	69	4	fact	fact	NOUN
ejpam-6837	69	5	3.52	3.52	NUM
ejpam-6837	69	6	]	]	PUNCT
ejpam-6837	69	7	let	let	VERB
ejpam-6837	69	8	c1	c1	PROPN
ejpam-6837	69	9	,	,	PUNCT
ejpam-6837	69	10	c2	c2	PROPN
ejpam-6837	69	11	,	,	PUNCT
ejpam-6837	69	12	.	.	PUNCT
ejpam-6837	69	13	.	.	PUNCT
ejpam-6837	69	14	.	.	PUNCT
ejpam-6837	70	1	,	,	PUNCT
ejpam-6837	70	2	cn	cn	PROPN
ejpam-6837	70	3	be	be	AUX
ejpam-6837	70	4	closed	close	VERB
ejpam-6837	70	5	and	and	CCONJ
ejpam-6837	70	6	convex	convex	PROPN
ejpam-6837	70	7	subset	subset	NOUN
ejpam-6837	70	8	of	of	ADP
ejpam-6837	70	9	h	h	PROPN
ejpam-6837	70	10	with	with	ADP
ejpam-6837	70	11	n⋂	n⋂	PROPN
ejpam-6837	70	12	i=1	i=1	PROPN
ejpam-6837	70	13	ci	ci	PROPN
ejpam-6837	70	14	̸=	̸=	PROPN
ejpam-6837	70	15	∅.	∅.	ADP
ejpam-6837	70	16	the	the	DET
ejpam-6837	70	17	douglas	douglas	PROPN
ejpam-6837	70	18	-	-	PUNCT
ejpam-6837	70	19	rachford	rachford	ADJ
ejpam-6837	70	20	operator	operator	NOUN
ejpam-6837	70	21	associated	associate	VERB
ejpam-6837	70	22	with	with	ADP
ejpam-6837	70	23	the	the	DET
ejpam-6837	70	24	ordered	order	VERB
ejpam-6837	70	25	tuple	tuple	NOUN
ejpam-6837	70	26	(	(	PUNCT
ejpam-6837	70	27	c1	c1	PROPN
ejpam-6837	70	28	,	,	PUNCT
ejpam-6837	70	29	c2	c2	PROPN
ejpam-6837	70	30	,	,	PUNCT
ejpam-6837	70	31	.	.	PUNCT
ejpam-6837	70	32	.	.	PUNCT
ejpam-6837	71	1	.	.	PUNCT
ejpam-6837	72	1	,	,	PUNCT
ejpam-6837	72	2	cn	cn	PROPN
ejpam-6837	72	3	)	)	PUNCT
ejpam-6837	72	4	is	be	AUX
ejpam-6837	72	5	tc1,c2,	tc1,c2,	ADJ
ejpam-6837	72	6	...	...	PUNCT
ejpam-6837	72	7	,cn	,cn	PUNCT
ejpam-6837	72	8	:	:	PUNCT
ejpam-6837	72	9	=	=	SYM
ejpam-6837	72	10	1	1	NUM
ejpam-6837	72	11	2	2	NUM
ejpam-6837	72	12	(	(	PUNCT
ejpam-6837	72	13	id+rcn	id+rcn	X
ejpam-6837	72	14	rcn−1	rcn−1	PROPN
ejpam-6837	72	15	.	.	PUNCT
ejpam-6837	72	16	.	.	PUNCT
ejpam-6837	72	17	.	.	PUNCT
ejpam-6837	73	1	rc2	rc2	PROPN
ejpam-6837	73	2	rc1	rc1	PROPN
ejpam-6837	73	3	)	)	PUNCT
ejpam-6837	73	4	.	.	PUNCT
ejpam-6837	74	1	for	for	ADP
ejpam-6837	74	2	n	n	NOUN
ejpam-6837	74	3	=	=	SYM
ejpam-6837	74	4	2	2	NUM
ejpam-6837	74	5	,	,	PUNCT
ejpam-6837	74	6	let	let	VERB
ejpam-6837	74	7	c1	c1	PROPN
ejpam-6837	74	8	and	and	CCONJ
ejpam-6837	74	9	c2	c2	PROPN
ejpam-6837	74	10	closed	close	VERB
ejpam-6837	74	11	and	and	CCONJ
ejpam-6837	74	12	convex	convex	PROPN
ejpam-6837	74	13	subset	subset	NOUN
ejpam-6837	74	14	of	of	ADP
ejpam-6837	74	15	h	h	PROPN
ejpam-6837	74	16	with	with	ADP
ejpam-6837	74	17	c1	c1	PROPN
ejpam-6837	74	18	∩	∩	PROPN
ejpam-6837	74	19	c2	c2	PROPN
ejpam-6837	74	20	̸=	̸=	PROPN
ejpam-6837	74	21	∅.	∅.	ADP
ejpam-6837	74	22	the	the	DET
ejpam-6837	74	23	douglas	douglas	PROPN
ejpam-6837	74	24	-	-	PUNCT
ejpam-6837	74	25	rachford	rachford	ADJ
ejpam-6837	74	26	operator	operator	NOUN
ejpam-6837	74	27	associated	associate	VERB
ejpam-6837	74	28	with	with	ADP
ejpam-6837	74	29	the	the	DET
ejpam-6837	74	30	ordered	order	VERB
ejpam-6837	74	31	pair	pair	NOUN
ejpam-6837	74	32	(	(	PUNCT
ejpam-6837	74	33	c1	c1	PROPN
ejpam-6837	74	34	,	,	PUNCT
ejpam-6837	74	35	c2	c2	PROPN
ejpam-6837	74	36	)	)	PUNCT
ejpam-6837	74	37	is	be	AUX
ejpam-6837	74	38	:	:	PUNCT
ejpam-6837	74	39	tc1,c2	tc1,c2	NOUN
ejpam-6837	74	40	:	:	PUNCT
ejpam-6837	74	41	=	=	SYM
ejpam-6837	74	42	1	1	NUM
ejpam-6837	74	43	2	2	NUM
ejpam-6837	74	44	(	(	PUNCT
ejpam-6837	74	45	id+rc2	id+rc2	NOUN
ejpam-6837	74	46	rc1	rc1	NOUN
ejpam-6837	74	47	)	)	PUNCT
ejpam-6837	74	48	,	,	PUNCT
ejpam-6837	74	49	(	(	PUNCT
ejpam-6837	74	50	11	11	NUM
ejpam-6837	74	51	)	)	PUNCT
ejpam-6837	74	52	and	and	CCONJ
ejpam-6837	74	53	the	the	DET
ejpam-6837	74	54	generated	generate	VERB
ejpam-6837	74	55	sequence	sequence	NOUN
ejpam-6837	74	56	(	(	PUNCT
ejpam-6837	74	57	xn	xn	PROPN
ejpam-6837	74	58	)	)	PUNCT
ejpam-6837	74	59	n∈n	n∈n	NOUN
ejpam-6837	74	60	is	be	AUX
ejpam-6837	74	61	(	(	PUNCT
ejpam-6837	74	62	∀n	∀n	X
ejpam-6837	74	63	∈	∈	PROPN
ejpam-6837	74	64	n	n	NOUN
ejpam-6837	74	65	)	)	PUNCT
ejpam-6837	74	66	xn+1	xn+1	PROPN
ejpam-6837	75	1	=	=	SYM
ejpam-6837	75	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	75	3	xn	xn	X
ejpam-6837	75	4	where	where	SCONJ
ejpam-6837	75	5	x0	x0	PROPN
ejpam-6837	75	6	∈	∈	PROPN
ejpam-6837	75	7	h	h	NOUN
ejpam-6837	75	8	,	,	PUNCT
ejpam-6837	75	9	also	also	ADV
ejpam-6837	75	10	called	call	VERB
ejpam-6837	75	11	the	the	DET
ejpam-6837	75	12	(	(	PUNCT
ejpam-6837	75	13	dra	dra	PROPN
ejpam-6837	75	14	)	)	PUNCT
ejpam-6837	75	15	sequence	sequence	NOUN
ejpam-6837	75	16	.	.	PUNCT
ejpam-6837	76	1	for	for	ADP
ejpam-6837	76	2	more	more	ADJ
ejpam-6837	76	3	information	information	NOUN
ejpam-6837	76	4	about	about	ADP
ejpam-6837	76	5	douglas	douglas	PROPN
ejpam-6837	76	6	rachford	rachford	PROPN
ejpam-6837	76	7	algorithm	algorithm	NOUN
ejpam-6837	76	8	you	you	PRON
ejpam-6837	76	9	can	can	AUX
ejpam-6837	76	10	see	see	VERB
ejpam-6837	76	11	[	[	X
ejpam-6837	76	12	8	8	NUM
ejpam-6837	76	13	]	]	PUNCT
ejpam-6837	76	14	where	where	SCONJ
ejpam-6837	76	15	the	the	DET
ejpam-6837	76	16	original	original	ADJ
ejpam-6837	76	17	theoretical	theoretical	ADJ
ejpam-6837	76	18	foundation	foundation	NOUN
ejpam-6837	76	19	of	of	ADP
ejpam-6837	76	20	the	the	DET
ejpam-6837	76	21	dougalsrachford	dougalsrachford	PROPN
ejpam-6837	76	22	algorithm	algorithm	NOUN
ejpam-6837	76	23	for	for	ADP
ejpam-6837	76	24	monotone	monotone	ADJ
ejpam-6837	76	25	operator	operator	NOUN
ejpam-6837	76	26	splitting	splitting	NOUN
ejpam-6837	76	27	.	.	PUNCT
ejpam-6837	77	1	a	a	DET
ejpam-6837	77	2	comprehensive	comprehensive	ADJ
ejpam-6837	77	3	analysis	analysis	NOUN
ejpam-6837	77	4	linking	link	VERB
ejpam-6837	77	5	the	the	DET
ejpam-6837	77	6	dougalsrachford	dougalsrachford	PROPN
ejpam-6837	77	7	method	method	NOUN
ejpam-6837	77	8	to	to	ADP
ejpam-6837	77	9	the	the	DET
ejpam-6837	77	10	proximal	proximal	ADJ
ejpam-6837	77	11	point	point	NOUN
ejpam-6837	77	12	algorithm	algorithm	NOUN
ejpam-6837	77	13	is	be	AUX
ejpam-6837	77	14	provided	provide	VERB
ejpam-6837	77	15	in	in	ADP
ejpam-6837	77	16	[	[	NOUN
ejpam-6837	77	17	9	9	NUM
ejpam-6837	77	18	]	]	PUNCT
ejpam-6837	77	19	.	.	PUNCT
ejpam-6837	78	1	in	in	ADP
ejpam-6837	78	2	2004	2004	NUM
ejpam-6837	78	3	,	,	PUNCT
ejpam-6837	78	4	bauschke	bauschke	ADJ
ejpam-6837	78	5	,	,	PUNCT
ejpam-6837	78	6	combettes	combette	NOUN
ejpam-6837	78	7	,	,	PUNCT
ejpam-6837	78	8	and	and	CCONJ
ejpam-6837	78	9	luke	luke	PROPN
ejpam-6837	78	10	analyze	analyze	VERB
ejpam-6837	78	11	the	the	DET
ejpam-6837	78	12	application	application	NOUN
ejpam-6837	78	13	of	of	ADP
ejpam-6837	78	14	douglas	douglas	PROPN
ejpam-6837	78	15	-	-	PUNCT
ejpam-6837	78	16	rachford	rachford	PROPN
ejpam-6837	78	17	to	to	PART
ejpam-6837	78	18	convex	convex	VERB
ejpam-6837	78	19	feasibility	feasibility	NOUN
ejpam-6837	78	20	and	and	CCONJ
ejpam-6837	78	21	best	good	ADJ
ejpam-6837	78	22	approximation	approximation	NOUN
ejpam-6837	78	23	problems	problem	NOUN
ejpam-6837	78	24	.	.	PUNCT
ejpam-6837	79	1	see	see	VERB
ejpam-6837	79	2	[	[	X
ejpam-6837	79	3	10	10	NUM
ejpam-6837	79	4	]	]	PUNCT
ejpam-6837	79	5	in	in	ADP
ejpam-6837	79	6	2005	2005	NUM
ejpam-6837	79	7	combettes	combette	NOUN
ejpam-6837	79	8	and	and	CCONJ
ejpam-6837	79	9	wajs	wajs	NOUN
ejpam-6837	79	10	introduce	introduce	VERB
ejpam-6837	79	11	proximal	proximal	ADJ
ejpam-6837	79	12	splitting	splitting	NOUN
ejpam-6837	79	13	methods	method	NOUN
ejpam-6837	79	14	that	that	PRON
ejpam-6837	79	15	are	be	AUX
ejpam-6837	79	16	closely	closely	ADV
ejpam-6837	79	17	related	relate	VERB
ejpam-6837	79	18	to	to	ADP
ejpam-6837	79	19	and	and	CCONJ
ejpam-6837	79	20	extend	extend	VERB
ejpam-6837	79	21	the	the	DET
ejpam-6837	79	22	douglas	douglas	PROPN
ejpam-6837	79	23	-	-	PUNCT
ejpam-6837	79	24	rachford	rachford	ADJ
ejpam-6837	79	25	algorithm	algorithm	NOUN
ejpam-6837	79	26	,	,	PUNCT
ejpam-6837	79	27	see	see	VERB
ejpam-6837	79	28	[	[	X
ejpam-6837	79	29	11	11	NUM
ejpam-6837	79	30	]	]	SYM
ejpam-6837	79	31	.	.	PUNCT
ejpam-6837	80	1	6	6	NUM
ejpam-6837	80	2	years	year	NOUN
ejpam-6837	80	3	later	later	ADV
ejpam-6837	80	4	combettes	combette	NOUN
ejpam-6837	80	5	and	and	CCONJ
ejpam-6837	80	6	pesquet	pesquet	NOUN
ejpam-6837	80	7	applies	apply	VERB
ejpam-6837	80	8	douglas	douglas	PROPN
ejpam-6837	80	9	-	-	PUNCT
ejpam-6837	80	10	rachford	rachford	ADJ
ejpam-6837	80	11	and	and	CCONJ
ejpam-6837	80	12	related	related	ADJ
ejpam-6837	80	13	algorithms	algorithm	NOUN
ejpam-6837	80	14	to	to	PART
ejpam-6837	80	15	signal	signal	VERB
ejpam-6837	80	16	processing	processing	NOUN
ejpam-6837	80	17	and	and	CCONJ
ejpam-6837	80	18	inverse	inverse	NOUN
ejpam-6837	80	19	problems	problem	NOUN
ejpam-6837	80	20	,	,	PUNCT
ejpam-6837	80	21	see	see	VERB
ejpam-6837	80	22	[	[	X
ejpam-6837	80	23	12	12	NUM
ejpam-6837	80	24	]	]	PUNCT
ejpam-6837	80	25	.	.	PUNCT
ejpam-6837	81	1	in	in	ADP
ejpam-6837	81	2	2017	2017	NUM
ejpam-6837	81	3	,	,	PUNCT
ejpam-6837	81	4	bauschke	bauschke	ADJ
ejpam-6837	81	5	and	and	CCONJ
ejpam-6837	81	6	combettes	combette	NOUN
ejpam-6837	81	7	comes	come	VERB
ejpam-6837	81	8	up	up	ADP
ejpam-6837	81	9	with	with	ADP
ejpam-6837	81	10	a	a	DET
ejpam-6837	81	11	textbook	textbook	NOUN
ejpam-6837	81	12	-	-	PUNCT
ejpam-6837	81	13	level	level	NOUN
ejpam-6837	81	14	comprehensive	comprehensive	ADJ
ejpam-6837	81	15	treatment	treatment	NOUN
ejpam-6837	81	16	of	of	ADP
ejpam-6837	81	17	the	the	DET
ejpam-6837	81	18	douglasrachford	douglasrachford	PROPN
ejpam-6837	81	19	method	method	NOUN
ejpam-6837	81	20	and	and	CCONJ
ejpam-6837	81	21	its	its	PRON
ejpam-6837	81	22	role	role	NOUN
ejpam-6837	81	23	in	in	ADP
ejpam-6837	81	24	convex	convex	NOUN
ejpam-6837	81	25	feasibility	feasibility	NOUN
ejpam-6837	81	26	and	and	CCONJ
ejpam-6837	81	27	optimization	optimization	NOUN
ejpam-6837	81	28	,	,	PUNCT
ejpam-6837	81	29	see	see	VERB
ejpam-6837	81	30	[	[	X
ejpam-6837	81	31	1	1	NUM
ejpam-6837	81	32	]	]	PUNCT
ejpam-6837	81	33	.	.	PUNCT
ejpam-6837	82	1	proposition	proposition	NOUN
ejpam-6837	82	2	1	1	NUM
ejpam-6837	82	3	.	.	PUNCT
ejpam-6837	83	1	let	let	VERB
ejpam-6837	83	2	c1	c1	PROPN
ejpam-6837	83	3	and	and	CCONJ
ejpam-6837	83	4	c2	c2	PROPN
ejpam-6837	83	5	be	be	VERB
ejpam-6837	83	6	a	a	DET
ejpam-6837	83	7	nonempty	nonempty	ADV
ejpam-6837	83	8	closed	close	VERB
ejpam-6837	83	9	convex	convex	ADJ
ejpam-6837	83	10	subsets	subset	NOUN
ejpam-6837	83	11	of	of	ADP
ejpam-6837	83	12	h.	h.	PROPN
ejpam-6837	83	13	then	then	ADV
ejpam-6837	83	14	pc1	pc1	PROPN
ejpam-6837	83	15	is	be	AUX
ejpam-6837	83	16	firmly	firmly	ADV
ejpam-6837	83	17	nonexpansive	nonexpansive	ADJ
ejpam-6837	83	18	,	,	PUNCT
ejpam-6837	83	19	rc1	rc1	NOUN
ejpam-6837	83	20	is	be	AUX
ejpam-6837	83	21	nonexpansive	nonexpansive	ADJ
ejpam-6837	83	22	,	,	PUNCT
ejpam-6837	83	23	n	n	PROPN
ejpam-6837	83	24	=	=	SYM
ejpam-6837	83	25	rc2	rc2	PROPN
ejpam-6837	83	26	rc1	rc1	NOUN
ejpam-6837	83	27	is	be	AUX
ejpam-6837	83	28	nonexpansive	nonexpansive	ADJ
ejpam-6837	83	29	and	and	CCONJ
ejpam-6837	83	30	tc1,c2	tc1,c2	NOUN
ejpam-6837	83	31	:	:	PUNCT
ejpam-6837	83	32	=	=	SYM
ejpam-6837	83	33	1	1	NUM
ejpam-6837	83	34	2	2	NUM
ejpam-6837	83	35	(	(	PUNCT
ejpam-6837	83	36	id+rc2	id+rc2	NOUN
ejpam-6837	83	37	rc1	rc1	NOUN
ejpam-6837	83	38	)	)	PUNCT
ejpam-6837	83	39	is	be	AUX
ejpam-6837	83	40	firmly	firmly	ADV
ejpam-6837	83	41	nonexpansive	nonexpansive	ADJ
ejpam-6837	83	42	.	.	PUNCT
ejpam-6837	84	1	proof	proof	NOUN
ejpam-6837	84	2	.	.	PUNCT
ejpam-6837	85	1	see	see	VERB
ejpam-6837	85	2	[	[	X
ejpam-6837	85	3	1	1	NUM
ejpam-6837	85	4	,	,	PUNCT
ejpam-6837	85	5	lemma	lemma	PROPN
ejpam-6837	85	6	222	222	NUM
ejpam-6837	85	7	]	]	PUNCT
ejpam-6837	85	8	.	.	PUNCT
ejpam-6837	86	1	■	■	PUNCT
ejpam-6837	86	2	definition	definition	NOUN
ejpam-6837	86	3	6	6	NUM
ejpam-6837	86	4	.	.	PUNCT
ejpam-6837	87	1	[	[	X
ejpam-6837	87	2	1	1	NUM
ejpam-6837	87	3	,	,	PUNCT
ejpam-6837	87	4	definition	definition	NOUN
ejpam-6837	87	5	5.1	5.1	NUM
ejpam-6837	87	6	]	]	PUNCT
ejpam-6837	87	7	let	let	VERB
ejpam-6837	87	8	c	c	PRON
ejpam-6837	87	9	be	be	AUX
ejpam-6837	87	10	a	a	DET
ejpam-6837	87	11	nonempty	nonempty	ADJ
ejpam-6837	87	12	subset	subset	NOUN
ejpam-6837	87	13	of	of	ADP
ejpam-6837	87	14	h	h	NOUN
ejpam-6837	87	15	and	and	CCONJ
ejpam-6837	87	16	let	let	VERB
ejpam-6837	87	17	(	(	PUNCT
ejpam-6837	87	18	xn)n∈n	xn)n∈n	NUM
ejpam-6837	87	19	be	be	AUX
ejpam-6837	87	20	a	a	DET
ejpam-6837	87	21	sequence	sequence	NOUN
ejpam-6837	87	22	in	in	ADP
ejpam-6837	87	23	h.	h.	PROPN
ejpam-6837	87	24	then	then	ADV
ejpam-6837	87	25	(	(	PUNCT
ejpam-6837	87	26	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	87	27	is	be	AUX
ejpam-6837	87	28	fejér	fejér	NOUN
ejpam-6837	87	29	monotone	monotone	ADJ
ejpam-6837	87	30	with	with	ADP
ejpam-6837	87	31	respect	respect	NOUN
ejpam-6837	87	32	to	to	ADP
ejpam-6837	87	33	c	c	NOUN
ejpam-6837	87	34	if	if	SCONJ
ejpam-6837	87	35	(	(	PUNCT
ejpam-6837	87	36	∀x	∀x	X
ejpam-6837	87	37	∈	∈	PROPN
ejpam-6837	87	38	c	c	NOUN
ejpam-6837	87	39	)	)	PUNCT
ejpam-6837	87	40	(	(	PUNCT
ejpam-6837	87	41	∀n	∀n	NUM
ejpam-6837	87	42	∈	∈	AUX
ejpam-6837	87	43	n	n	CCONJ
ejpam-6837	87	44	)	)	PUNCT
ejpam-6837	87	45	∥xn+1	∥xn+1	NOUN
ejpam-6837	87	46	−	−	PROPN
ejpam-6837	88	1	x∥	x∥	PROPN
ejpam-6837	89	1	≤	≤	PROPN
ejpam-6837	89	2	∥xn	∥xn	PROPN
ejpam-6837	89	3	−	−	PROPN
ejpam-6837	89	4	x∥.	x∥.	PROPN
ejpam-6837	90	1	[	[	X
ejpam-6837	90	2	1	1	NUM
ejpam-6837	90	3	,	,	PUNCT
ejpam-6837	90	4	proposition	proposition	NOUN
ejpam-6837	90	5	5.7	5.7	NUM
ejpam-6837	90	6	]	]	PUNCT
ejpam-6837	91	1	let	let	VERB
ejpam-6837	91	2	(	(	PUNCT
ejpam-6837	91	3	xn)n	xn)n	PROPN
ejpam-6837	91	4	∈	∈	PROPN
ejpam-6837	92	1	n	n	PRON
ejpam-6837	92	2	be	be	AUX
ejpam-6837	92	3	a	a	DET
ejpam-6837	92	4	sequence	sequence	NOUN
ejpam-6837	92	5	in	in	ADP
ejpam-6837	92	6	h	h	NOUN
ejpam-6837	92	7	and	and	CCONJ
ejpam-6837	92	8	let	let	VERB
ejpam-6837	92	9	c	c	PRON
ejpam-6837	92	10	be	be	AUX
ejpam-6837	92	11	a	a	DET
ejpam-6837	92	12	nonempty	nonempty	ADV
ejpam-6837	92	13	closed	close	VERB
ejpam-6837	92	14	convex	convex	NOUN
ejpam-6837	92	15	subset	subset	NOUN
ejpam-6837	92	16	of	of	ADP
ejpam-6837	92	17	h.	h.	PROPN
ejpam-6837	92	18	suppose	suppose	VERB
ejpam-6837	92	19	that	that	SCONJ
ejpam-6837	92	20	(	(	PUNCT
ejpam-6837	92	21	xn)n	xn)n	PROPN
ejpam-6837	92	22	∈	∈	PROPN
ejpam-6837	92	23	n	n	PRON
ejpam-6837	92	24	is	be	AUX
ejpam-6837	92	25	fejér	fejér	NOUN
ejpam-6837	92	26	monotone	monotone	ADJ
ejpam-6837	92	27	with	with	ADP
ejpam-6837	92	28	respect	respect	NOUN
ejpam-6837	92	29	to	to	ADP
ejpam-6837	92	30	c.	c.	NOUN
ejpam-6837	92	31	then	then	ADV
ejpam-6837	92	32	the	the	DET
ejpam-6837	92	33	shadow	shadow	NOUN
ejpam-6837	92	34	sequence	sequence	NOUN
ejpam-6837	92	35	(	(	PUNCT
ejpam-6837	92	36	p	p	X
ejpam-6837	92	37	xn)n	xn)n	PROPN
ejpam-6837	92	38	∈	∈	PROPN
ejpam-6837	92	39	n	n	PRON
ejpam-6837	92	40	converges	converge	VERB
ejpam-6837	92	41	strongly	strongly	ADV
ejpam-6837	92	42	to	to	ADP
ejpam-6837	92	43	a	a	DET
ejpam-6837	92	44	point	point	NOUN
ejpam-6837	92	45	in	in	ADP
ejpam-6837	92	46	c.	c.	PROPN
ejpam-6837	93	1	[	[	X
ejpam-6837	93	2	1	1	NUM
ejpam-6837	93	3	,	,	PUNCT
ejpam-6837	93	4	corollary	corollary	ADJ
ejpam-6837	93	5	5.8	5.8	NUM
ejpam-6837	93	6	]	]	PUNCT
ejpam-6837	94	1	let	let	VERB
ejpam-6837	94	2	(	(	PUNCT
ejpam-6837	94	3	xn)n	xn)n	PROPN
ejpam-6837	94	4	∈	∈	PROPN
ejpam-6837	94	5	n	n	PRON
ejpam-6837	94	6	be	be	AUX
ejpam-6837	94	7	a	a	DET
ejpam-6837	94	8	sequence	sequence	NOUN
ejpam-6837	94	9	in	in	ADP
ejpam-6837	94	10	h	h	NOUN
ejpam-6837	94	11	,	,	PUNCT
ejpam-6837	94	12	let	let	VERB
ejpam-6837	94	13	c	c	PRON
ejpam-6837	94	14	be	be	AUX
ejpam-6837	94	15	a	a	DET
ejpam-6837	94	16	nonempty	nonempty	ADV
ejpam-6837	94	17	closed	close	VERB
ejpam-6837	94	18	convex	convex	NOUN
ejpam-6837	94	19	subset	subset	NOUN
ejpam-6837	94	20	of	of	ADP
ejpam-6837	94	21	h	h	NOUN
ejpam-6837	94	22	,	,	PUNCT
ejpam-6837	94	23	and	and	CCONJ
ejpam-6837	94	24	let	let	VERB
ejpam-6837	94	25	x	x	SYM
ejpam-6837	94	26	∈	∈	PROPN
ejpam-6837	94	27	c.	c.	NOUN
ejpam-6837	94	28	suppose	suppose	VERB
ejpam-6837	94	29	that	that	SCONJ
ejpam-6837	94	30	(	(	PUNCT
ejpam-6837	94	31	xn)n	xn)n	PROPN
ejpam-6837	94	32	∈	∈	PROPN
ejpam-6837	94	33	n	n	PRON
ejpam-6837	94	34	is	be	AUX
ejpam-6837	94	35	fejér	fejér	NOUN
ejpam-6837	94	36	monotone	monotone	ADJ
ejpam-6837	94	37	with	with	ADP
ejpam-6837	94	38	respect	respect	NOUN
ejpam-6837	94	39	to	to	ADP
ejpam-6837	94	40	c	c	NOUN
ejpam-6837	94	41	and	and	CCONJ
ejpam-6837	94	42	that	that	PRON
ejpam-6837	94	43	xn	xn	PROPN
ejpam-6837	95	1	⇀	⇀	PROPN
ejpam-6837	95	2	x.	x.	NOUN
ejpam-6837	96	1	then	then	ADV
ejpam-6837	96	2	pc	pc	VERB
ejpam-6837	96	3	xn	xn	PROPN
ejpam-6837	97	1	→	→	PUNCT
ejpam-6837	97	2	x.	x.	PROPN
ejpam-6837	97	3	s.	s.	PROPN
ejpam-6837	97	4	th	th	PROPN
ejpam-6837	97	5	.	.	PUNCT
ejpam-6837	98	1	alwadani	alwadani	PROPN
ejpam-6837	98	2	/	/	SYM
ejpam-6837	98	3	eur	eur	PROPN
ejpam-6837	98	4	.	.	PUNCT
ejpam-6837	99	1	j.	j.	PROPN
ejpam-6837	99	2	pure	pure	PROPN
ejpam-6837	99	3	appl	appl	PROPN
ejpam-6837	99	4	.	.	PROPN
ejpam-6837	99	5	math	math	PROPN
ejpam-6837	99	6	,	,	PUNCT
ejpam-6837	99	7	18	18	NUM
ejpam-6837	99	8	(	(	PUNCT
ejpam-6837	99	9	4	4	NUM
ejpam-6837	99	10	)	)	PUNCT
ejpam-6837	99	11	(	(	PUNCT
ejpam-6837	99	12	2025	2025	NUM
ejpam-6837	99	13	)	)	PUNCT
ejpam-6837	99	14	,	,	PUNCT
ejpam-6837	99	15	6837	6837	NUM
ejpam-6837	99	16	5	5	NUM
ejpam-6837	99	17	of	of	ADP
ejpam-6837	99	18	15	15	NUM
ejpam-6837	99	19	3	3	NUM
ejpam-6837	99	20	.	.	PUNCT
ejpam-6837	100	1	the	the	DET
ejpam-6837	100	2	cyclic	cyclic	PROPN
ejpam-6837	100	3	douglasrachford	douglasrachford	PROPN
ejpam-6837	100	4	method	method	NOUN
ejpam-6837	100	5	in	in	ADP
ejpam-6837	100	6	order	order	NOUN
ejpam-6837	100	7	to	to	PART
ejpam-6837	100	8	solve	solve	VERB
ejpam-6837	100	9	the	the	DET
ejpam-6837	100	10	feasibility	feasibility	NOUN
ejpam-6837	100	11	problem	problem	NOUN
ejpam-6837	100	12	(	(	PUNCT
ejpam-6837	100	13	1	1	NUM
ejpam-6837	100	14	)	)	PUNCT
ejpam-6837	100	15	,	,	PUNCT
ejpam-6837	100	16	where	where	SCONJ
ejpam-6837	100	17	ci	ci	PROPN
ejpam-6837	100	18	are	be	AUX
ejpam-6837	100	19	closed	closed	ADJ
ejpam-6837	100	20	and	and	CCONJ
ejpam-6837	100	21	convex	convex	ADJ
ejpam-6837	100	22	subsets	subset	NOUN
ejpam-6837	100	23	of	of	ADP
ejpam-6837	100	24	h	h	NOUN
ejpam-6837	100	25	with	with	ADP
ejpam-6837	100	26	nonempty	nonempty	ADJ
ejpam-6837	100	27	intersection	intersection	NOUN
ejpam-6837	100	28	,	,	PUNCT
ejpam-6837	100	29	we	we	PRON
ejpam-6837	100	30	employ	employ	VERB
ejpam-6837	100	31	the	the	DET
ejpam-6837	100	32	cyclic	cyclic	ADJ
ejpam-6837	100	33	douglas	douglas	PROPN
ejpam-6837	100	34	–	–	PUNCT
ejpam-6837	100	35	rachford	rachford	ADJ
ejpam-6837	100	36	iteration	iteration	NOUN
ejpam-6837	100	37	scheme	scheme	NOUN
ejpam-6837	100	38	that	that	PRON
ejpam-6837	100	39	generates	generate	VERB
ejpam-6837	100	40	a	a	DET
ejpam-6837	100	41	sequence	sequence	NOUN
ejpam-6837	100	42	(	(	PUNCT
ejpam-6837	100	43	xn)n∈n	xn)n∈n	NUM
ejpam-6837	100	44	by	by	ADP
ejpam-6837	100	45	(	(	PUNCT
ejpam-6837	100	46	∀n	∀n	NUM
ejpam-6837	100	47	∈	∈	PROPN
ejpam-6837	100	48	n	n	CCONJ
ejpam-6837	100	49	)	)	PUNCT
ejpam-6837	100	50	xn+1	xn+1	PROPN
ejpam-6837	101	1	=	=	SYM
ejpam-6837	101	2	t[c1c2···cn]xn	t[c1c2···cn]xn	X
ejpam-6837	101	3	(	(	PUNCT
ejpam-6837	101	4	12	12	NUM
ejpam-6837	101	5	)	)	PUNCT
ejpam-6837	101	6	and	and	CCONJ
ejpam-6837	101	7	where	where	SCONJ
ejpam-6837	101	8	t[c1c2	t[c1c2	NOUN
ejpam-6837	101	9	...	...	PUNCT
ejpam-6837	101	10	cn	cn	X
ejpam-6837	101	11	]	]	X
ejpam-6837	101	12	:	:	PUNCT
ejpam-6837	101	13	=	=	SYM
ejpam-6837	101	14	tcn	tcn	PROPN
ejpam-6837	101	15	,	,	PUNCT
ejpam-6837	101	16	c1	c1	PROPN
ejpam-6837	101	17	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	101	18	.	.	PUNCT
ejpam-6837	101	19	.	.	PUNCT
ejpam-6837	101	20	.	.	PUNCT
ejpam-6837	102	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	102	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	102	3	.	.	PUNCT
ejpam-6837	103	1	(	(	PUNCT
ejpam-6837	103	2	13	13	NUM
ejpam-6837	103	3	)	)	PUNCT
ejpam-6837	103	4	proposition	proposition	NOUN
ejpam-6837	103	5	2	2	NUM
ejpam-6837	103	6	.	.	X
ejpam-6837	103	7	assume	assume	VERB
ejpam-6837	103	8	n	n	NOUN
ejpam-6837	103	9	=	=	SYM
ejpam-6837	103	10	2	2	NUM
ejpam-6837	103	11	,	,	PUNCT
ejpam-6837	103	12	let	let	VERB
ejpam-6837	103	13	c1	c1	PROPN
ejpam-6837	103	14	and	and	CCONJ
ejpam-6837	103	15	c2	c2	PROPN
ejpam-6837	103	16	closed	close	VERB
ejpam-6837	103	17	and	and	CCONJ
ejpam-6837	103	18	convex	convex	PROPN
ejpam-6837	103	19	subset	subset	NOUN
ejpam-6837	103	20	of	of	ADP
ejpam-6837	103	21	h	h	PROPN
ejpam-6837	103	22	with	with	ADP
ejpam-6837	103	23	c1	c1	PROPN
ejpam-6837	103	24	∩	∩	PROPN
ejpam-6837	103	25	c2	c2	PROPN
ejpam-6837	103	26	̸=	̸=	PROPN
ejpam-6837	103	27	∅.	∅.	PRON
ejpam-6837	103	28	recall	recall	NOUN
ejpam-6837	103	29	(	(	PUNCT
ejpam-6837	103	30	12	12	NUM
ejpam-6837	103	31	)	)	PUNCT
ejpam-6837	103	32	,	,	PUNCT
ejpam-6837	103	33	(	(	PUNCT
ejpam-6837	103	34	13	13	NUM
ejpam-6837	103	35	)	)	PUNCT
ejpam-6837	103	36	,	,	PUNCT
ejpam-6837	103	37	and	and	CCONJ
ejpam-6837	103	38	(	(	PUNCT
ejpam-6837	103	39	11	11	NUM
ejpam-6837	103	40	)	)	PUNCT
ejpam-6837	103	41	.	.	PUNCT
ejpam-6837	104	1	then	then	ADV
ejpam-6837	104	2	t[c1c2	t[c1c2	PROPN
ejpam-6837	104	3	]	]	PUNCT
ejpam-6837	104	4	̸=	̸=	PROPN
ejpam-6837	104	5	tc1,c2	tc1,c2	NOUN
ejpam-6837	104	6	.	.	PUNCT
ejpam-6837	105	1	proof	proof	NOUN
ejpam-6837	105	2	.	.	PUNCT
ejpam-6837	106	1	let	let	VERB
ejpam-6837	106	2	n	n	NOUN
ejpam-6837	106	3	=	=	SYM
ejpam-6837	106	4	2	2	NUM
ejpam-6837	106	5	,	,	PUNCT
ejpam-6837	106	6	c1	c1	PROPN
ejpam-6837	106	7	and	and	CCONJ
ejpam-6837	106	8	c2	c2	PROPN
ejpam-6837	106	9	closed	close	VERB
ejpam-6837	106	10	and	and	CCONJ
ejpam-6837	106	11	convex	convex	PROPN
ejpam-6837	106	12	subset	subset	NOUN
ejpam-6837	106	13	of	of	ADP
ejpam-6837	106	14	h	h	PROPN
ejpam-6837	106	15	with	with	ADP
ejpam-6837	106	16	c1	c1	PROPN
ejpam-6837	106	17	∩	∩	PROPN
ejpam-6837	106	18	c2	c2	PROPN
ejpam-6837	106	19	̸=	̸=	PROPN
ejpam-6837	106	20	∅.	∅.	NOUN
ejpam-6837	106	21	using	use	VERB
ejpam-6837	106	22	(	(	PUNCT
ejpam-6837	106	23	12	12	NUM
ejpam-6837	106	24	)	)	PUNCT
ejpam-6837	106	25	,	,	PUNCT
ejpam-6837	106	26	(	(	PUNCT
ejpam-6837	106	27	13	13	NUM
ejpam-6837	106	28	)	)	PUNCT
ejpam-6837	106	29	,	,	PUNCT
ejpam-6837	106	30	and	and	CCONJ
ejpam-6837	106	31	(	(	PUNCT
ejpam-6837	106	32	11	11	NUM
ejpam-6837	106	33	)	)	PUNCT
ejpam-6837	106	34	gives	give	VERB
ejpam-6837	106	35	t[c1c2	t[c1c2	NOUN
ejpam-6837	106	36	]	]	X
ejpam-6837	106	37	:	:	PUNCT
ejpam-6837	106	38	=	=	SYM
ejpam-6837	106	39	tc2,c1	tc2,c1	NOUN
ejpam-6837	106	40	tc1,c2	tc1,c2	NOUN
ejpam-6837	106	41	(	(	PUNCT
ejpam-6837	106	42	14	14	NUM
ejpam-6837	106	43	)	)	PUNCT
ejpam-6837	106	44	=	=	NOUN
ejpam-6837	107	1	(	(	PUNCT
ejpam-6837	107	2	id+rc1	id+rc1	X
ejpam-6837	107	3	rc2	rc2	PROPN
ejpam-6837	107	4	2	2	NUM
ejpam-6837	107	5	)	)	PUNCT
ejpam-6837	107	6	(	(	PUNCT
ejpam-6837	107	7	id+rc2	id+rc2	NOUN
ejpam-6837	107	8	rc1	rc1	NOUN
ejpam-6837	107	9	2	2	NUM
ejpam-6837	107	10	)	)	PUNCT
ejpam-6837	107	11	(	(	PUNCT
ejpam-6837	107	12	15	15	X
ejpam-6837	107	13	)	)	PUNCT
ejpam-6837	107	14	observe	observe	VERB
ejpam-6837	107	15	that	that	SCONJ
ejpam-6837	107	16	t[c1c2	t[c1c2	NOUN
ejpam-6837	107	17	]	]	X
ejpam-6837	107	18	̸=	̸=	PROPN
ejpam-6837	107	19	tc1,c2	tc1,c2	NOUN
ejpam-6837	107	20	.	.	PUNCT
ejpam-6837	108	1	■	■	PUNCT
ejpam-6837	108	2	example	example	NOUN
ejpam-6837	108	3	1	1	X
ejpam-6837	108	4	.	.	PUNCT
ejpam-6837	108	5	suppose	suppose	VERB
ejpam-6837	108	6	that	that	SCONJ
ejpam-6837	108	7	x	x	NOUN
ejpam-6837	108	8	=	=	SYM
ejpam-6837	108	9	r2	r2	PROPN
ejpam-6837	108	10	,	,	PUNCT
ejpam-6837	108	11	c1	c1	NOUN
ejpam-6837	108	12	=	=	PUNCT
ejpam-6837	108	13	r	r	NOUN
ejpam-6837	108	14	×	×	NOUN
ejpam-6837	108	15	{	{	PUNCT
ejpam-6837	108	16	0	0	NUM
ejpam-6837	108	17	}	}	PUNCT
ejpam-6837	108	18	and	and	CCONJ
ejpam-6837	108	19	c2	c2	PROPN
ejpam-6837	108	20	=	=	SYM
ejpam-6837	108	21	{	{	PUNCT
ejpam-6837	108	22	x	x	SYM
ejpam-6837	108	23	∈	∈	PROPN
ejpam-6837	108	24	r2	r2	NOUN
ejpam-6837	109	1	|	|	NOUN
ejpam-6837	109	2	∥x	∥x	PROPN
ejpam-6837	109	3	−	−	PROPN
ejpam-6837	110	1	3∥	3∥	NUM
ejpam-6837	110	2	≤	≤	NUM
ejpam-6837	110	3	3	3	NUM
ejpam-6837	110	4	}	}	PUNCT
ejpam-6837	110	5	.	.	PUNCT
ejpam-6837	111	1	then	then	ADV
ejpam-6837	111	2	2	2	NUM
ejpam-6837	111	3	∩	∩	NOUN
ejpam-6837	111	4	i=1	i=1	PROPN
ejpam-6837	111	5	ci	ci	PROPN
ejpam-6837	111	6	̸=	̸=	PROPN
ejpam-6837	111	7	∅	∅	NOUN
ejpam-6837	111	8	,	,	PUNCT
ejpam-6837	111	9	and	and	CCONJ
ejpam-6837	111	10	for	for	ADP
ejpam-6837	111	11	starting	start	VERB
ejpam-6837	111	12	point	point	NOUN
ejpam-6837	111	13	x0	x0	PROPN
ejpam-6837	111	14	∈	∈	PROPN
ejpam-6837	111	15	]	]	PUNCT
ejpam-6837	111	16	−∞	−∞	NOUN
ejpam-6837	111	17	,	,	PUNCT
ejpam-6837	111	18	1	1	NUM
ejpam-6837	111	19	[	[	PUNCT
ejpam-6837	111	20	×	×	NOUN
ejpam-6837	111	21	{	{	PUNCT
ejpam-6837	111	22	1	1	NUM
ejpam-6837	111	23	}	}	PUNCT
ejpam-6837	111	24	,	,	PUNCT
ejpam-6837	111	25	the	the	DET
ejpam-6837	111	26	dra	dra	PROPN
ejpam-6837	111	27	sequence	sequence	NOUN
ejpam-6837	111	28	(	(	PUNCT
ejpam-6837	111	29	xn)n∈n	xn)n∈n	NUM
ejpam-6837	111	30	with	with	ADP
ejpam-6837	111	31	respect	respect	NOUN
ejpam-6837	111	32	to	to	ADP
ejpam-6837	111	33	(	(	PUNCT
ejpam-6837	111	34	c1	c1	PROPN
ejpam-6837	111	35	,	,	PUNCT
ejpam-6837	111	36	c2	c2	PROPN
ejpam-6837	111	37	)	)	PUNCT
ejpam-6837	111	38	satisfies	satisfie	NOUN
ejpam-6837	111	39	(	(	PUNCT
ejpam-6837	111	40	∀n	∀n	X
ejpam-6837	111	41	∈	∈	PROPN
ejpam-6837	111	42	{	{	PUNCT
ejpam-6837	111	43	2	2	NUM
ejpam-6837	111	44	,	,	PUNCT
ejpam-6837	111	45	3	3	NUM
ejpam-6837	111	46	,	,	PUNCT
ejpam-6837	111	47	·	·	PUNCT
ejpam-6837	111	48	·	·	PUNCT
ejpam-6837	111	49	·	·	PUNCT
ejpam-6837	111	50	}	}	PUNCT
ejpam-6837	111	51	)	)	PUNCT
ejpam-6837	111	52	xn	xn	PUNCT
ejpam-6837	112	1	=	=	PUNCT
ejpam-6837	112	2	(	(	PUNCT
ejpam-6837	112	3	0	0	NUM
ejpam-6837	112	4	,	,	PUNCT
ejpam-6837	112	5	n	n	CCONJ
ejpam-6837	112	6	)	)	PUNCT
ejpam-6837	112	7	and	and	CCONJ
ejpam-6837	112	8	pc1	pc1	PROPN
ejpam-6837	112	9	xn	xn	PUNCT
ejpam-6837	113	1	=	=	PUNCT
ejpam-6837	113	2	(	(	PUNCT
ejpam-6837	113	3	0	0	NUM
ejpam-6837	113	4	,	,	PUNCT
ejpam-6837	113	5	0	0	NUM
ejpam-6837	113	6	)	)	PUNCT
ejpam-6837	113	7	∈	∈	NOUN
ejpam-6837	113	8	2	2	NUM
ejpam-6837	113	9	∩	∩	X
ejpam-6837	113	10	i=1	i=1	PROPN
ejpam-6837	113	11	ci	ci	PROPN
ejpam-6837	113	12	.	.	PUNCT
ejpam-6837	114	1	the	the	DET
ejpam-6837	114	2	cdra	cdra	PROPN
ejpam-6837	114	3	sequence	sequence	NOUN
ejpam-6837	114	4	(	(	PUNCT
ejpam-6837	114	5	xn)n∈n	xn)n∈n	NUM
ejpam-6837	114	6	with	with	ADP
ejpam-6837	114	7	respect	respect	NOUN
ejpam-6837	114	8	to	to	ADP
ejpam-6837	114	9	(	(	PUNCT
ejpam-6837	114	10	c1	c1	PROPN
ejpam-6837	114	11	,	,	PUNCT
ejpam-6837	114	12	c2	c2	PROPN
ejpam-6837	114	13	)	)	PUNCT
ejpam-6837	114	14	will	will	AUX
ejpam-6837	114	15	converge	converge	VERB
ejpam-6837	114	16	to	to	ADP
ejpam-6837	114	17	(	(	PUNCT
ejpam-6837	114	18	0	0	NUM
ejpam-6837	114	19	,	,	PUNCT
ejpam-6837	114	20	0	0	NUM
ejpam-6837	114	21	)	)	PUNCT
ejpam-6837	114	22	.	.	PUNCT
ejpam-6837	115	1	see	see	VERB
ejpam-6837	115	2	fig	fig	NOUN
ejpam-6837	115	3	.	.	PUNCT
ejpam-6837	116	1	1	1	NUM
ejpam-6837	116	2	for	for	ADP
ejpam-6837	116	3	an	an	DET
ejpam-6837	116	4	illustration	illustration	NOUN
ejpam-6837	116	5	,	,	PUNCT
ejpam-6837	116	6	created	create	VERB
ejpam-6837	116	7	with	with	ADP
ejpam-6837	116	8	geogebra	geogebra	NOUN
ejpam-6837	116	9	[	[	X
ejpam-6837	116	10	13	13	NUM
ejpam-6837	116	11	]	]	PUNCT
ejpam-6837	116	12	.	.	PUNCT
ejpam-6837	117	1	example	example	NOUN
ejpam-6837	118	1	2	2	NUM
ejpam-6837	118	2	.	.	PUNCT
ejpam-6837	118	3	suppose	suppose	VERB
ejpam-6837	118	4	that	that	SCONJ
ejpam-6837	118	5	x	x	NOUN
ejpam-6837	118	6	=	=	SYM
ejpam-6837	118	7	r2	r2	PROPN
ejpam-6837	118	8	,	,	PUNCT
ejpam-6837	118	9	c1	c1	NOUN
ejpam-6837	118	10	=	=	PUNCT
ejpam-6837	118	11	r	r	NOUN
ejpam-6837	118	12	·	·	PUNCT
ejpam-6837	118	13	(	(	PUNCT
ejpam-6837	118	14	1	1	NUM
ejpam-6837	118	15	,	,	PUNCT
ejpam-6837	118	16	1	1	NUM
ejpam-6837	118	17	)	)	PUNCT
ejpam-6837	118	18	,	,	PUNCT
ejpam-6837	118	19	c2	c2	PROPN
ejpam-6837	118	20	=	=	SYM
ejpam-6837	118	21	{	{	PUNCT
ejpam-6837	118	22	0	0	NUM
ejpam-6837	118	23	}	}	PUNCT
ejpam-6837	118	24	×	×	NOUN
ejpam-6837	118	25	r	r	NOUN
ejpam-6837	118	26	and	and	CCONJ
ejpam-6837	118	27	c3	c3	NOUN
ejpam-6837	118	28	=	=	PROPN
ejpam-6837	118	29	r	r	NOUN
ejpam-6837	118	30	·	·	PUNCT
ejpam-6837	118	31	(	(	PUNCT
ejpam-6837	118	32	1,−1	1,−1	NUM
ejpam-6837	118	33	)	)	PUNCT
ejpam-6837	118	34	.	.	PUNCT
ejpam-6837	119	1	then	then	ADV
ejpam-6837	119	2	the	the	DET
ejpam-6837	119	3	3	3	NUM
ejpam-6837	119	4	-	-	PUNCT
ejpam-6837	119	5	set	set	VERB
ejpam-6837	119	6	douglas	douglas	PROPN
ejpam-6837	119	7	-	-	PUNCT
ejpam-6837	119	8	rachford	rachford	ADJ
ejpam-6837	119	9	sequence	sequence	NOUN
ejpam-6837	119	10	(	(	PUNCT
ejpam-6837	119	11	xn)n∈n	xn)n∈n	NUM
ejpam-6837	119	12	with	with	ADP
ejpam-6837	119	13	respect	respect	NOUN
ejpam-6837	119	14	to	to	ADP
ejpam-6837	119	15	(	(	PUNCT
ejpam-6837	119	16	c1	c1	PROPN
ejpam-6837	119	17	,	,	PUNCT
ejpam-6837	119	18	c2	c2	PROPN
ejpam-6837	119	19	,	,	PUNCT
ejpam-6837	119	20	c3	c3	PROPN
ejpam-6837	119	21	)	)	PUNCT
ejpam-6837	119	22	will	will	AUX
ejpam-6837	119	23	fail	fail	VERB
ejpam-6837	119	24	to	to	PART
ejpam-6837	119	25	converge	converge	VERB
ejpam-6837	119	26	to	to	ADP
ejpam-6837	119	27	a	a	DET
ejpam-6837	119	28	point	point	NOUN
ejpam-6837	119	29	(	(	PUNCT
ejpam-6837	119	30	0	0	NUM
ejpam-6837	119	31	,	,	PUNCT
ejpam-6837	119	32	0	0	NUM
ejpam-6837	119	33	)	)	PUNCT
ejpam-6837	119	34	∈	∈	NOUN
ejpam-6837	119	35	3	3	NUM
ejpam-6837	119	36	∩	∩	PROPN
ejpam-6837	119	37	i=1	i=1	PROPN
ejpam-6837	119	38	ci	ci	PROPN
ejpam-6837	119	39	.	.	PUNCT
ejpam-6837	120	1	the	the	DET
ejpam-6837	120	2	cdra	cdra	PROPN
ejpam-6837	120	3	sequence	sequence	NOUN
ejpam-6837	120	4	(	(	PUNCT
ejpam-6837	120	5	xn)n∈n	xn)n∈n	NUM
ejpam-6837	120	6	with	with	ADP
ejpam-6837	120	7	respect	respect	NOUN
ejpam-6837	120	8	to	to	ADP
ejpam-6837	120	9	(	(	PUNCT
ejpam-6837	120	10	c1	c1	PROPN
ejpam-6837	120	11	,	,	PUNCT
ejpam-6837	120	12	c2	c2	PROPN
ejpam-6837	120	13	,	,	PUNCT
ejpam-6837	120	14	c3	c3	PROPN
ejpam-6837	120	15	)	)	PUNCT
ejpam-6837	120	16	will	will	AUX
ejpam-6837	120	17	converge	converge	VERB
ejpam-6837	120	18	to	to	ADP
ejpam-6837	120	19	x∗	x∗	PROPN
ejpam-6837	120	20	=	=	SYM
ejpam-6837	120	21	(	(	PUNCT
ejpam-6837	120	22	0	0	NUM
ejpam-6837	120	23	,	,	PUNCT
ejpam-6837	120	24	0	0	NUM
ejpam-6837	120	25	)	)	PUNCT
ejpam-6837	120	26	∈	∈	NOUN
ejpam-6837	120	27	3	3	NUM
ejpam-6837	120	28	∩	∩	PROPN
ejpam-6837	120	29	i=1	i=1	PROPN
ejpam-6837	120	30	ci	ci	PROPN
ejpam-6837	120	31	.	.	PUNCT
ejpam-6837	120	32	see	see	VERB
ejpam-6837	120	33	fig	fig	NOUN
ejpam-6837	120	34	.	.	PUNCT
ejpam-6837	120	35	2	2	NUM
ejpam-6837	120	36	for	for	ADP
ejpam-6837	120	37	an	an	DET
ejpam-6837	120	38	illustration	illustration	NOUN
ejpam-6837	120	39	,	,	PUNCT
ejpam-6837	120	40	created	create	VERB
ejpam-6837	120	41	with	with	ADP
ejpam-6837	120	42	geogebra	geogebra	NOUN
ejpam-6837	120	43	[	[	X
ejpam-6837	120	44	13	13	NUM
ejpam-6837	120	45	]	]	PUNCT
ejpam-6837	120	46	.	.	PUNCT
ejpam-6837	121	1	the	the	DET
ejpam-6837	121	2	notation	notation	NOUN
ejpam-6837	121	3	employed	employ	VERB
ejpam-6837	121	4	in	in	ADP
ejpam-6837	121	5	this	this	DET
ejpam-6837	121	6	paper	paper	NOUN
ejpam-6837	121	7	is	be	AUX
ejpam-6837	121	8	standard	standard	ADJ
ejpam-6837	121	9	and	and	CCONJ
ejpam-6837	121	10	closely	closely	ADV
ejpam-6837	121	11	aligned	aligned	ADJ
ejpam-6837	121	12	with	with	ADP
ejpam-6837	121	13	that	that	PRON
ejpam-6837	121	14	in	in	ADP
ejpam-6837	121	15	[	[	X
ejpam-6837	121	16	14	14	NUM
ejpam-6837	121	17	]	]	PUNCT
ejpam-6837	121	18	,	,	PUNCT
ejpam-6837	121	19	[	[	X
ejpam-6837	121	20	7	7	NUM
ejpam-6837	121	21	]	]	PUNCT
ejpam-6837	121	22	,	,	PUNCT
ejpam-6837	121	23	[	[	X
ejpam-6837	121	24	15	15	NUM
ejpam-6837	121	25	]	]	PUNCT
ejpam-6837	121	26	,	,	PUNCT
ejpam-6837	121	27	and	and	CCONJ
ejpam-6837	121	28	[	[	X
ejpam-6837	121	29	16	16	NUM
ejpam-6837	121	30	]	]	PUNCT
ejpam-6837	121	31	.	.	PUNCT
ejpam-6837	122	1	s.	s.	PROPN
ejpam-6837	122	2	th	th	PROPN
ejpam-6837	122	3	.	.	PUNCT
ejpam-6837	123	1	alwadani	alwadani	PROPN
ejpam-6837	123	2	/	/	SYM
ejpam-6837	123	3	eur	eur	PROPN
ejpam-6837	123	4	.	.	PUNCT
ejpam-6837	124	1	j.	j.	PROPN
ejpam-6837	124	2	pure	pure	PROPN
ejpam-6837	124	3	appl	appl	PROPN
ejpam-6837	124	4	.	.	PROPN
ejpam-6837	124	5	math	math	PROPN
ejpam-6837	124	6	,	,	PUNCT
ejpam-6837	124	7	18	18	NUM
ejpam-6837	124	8	(	(	PUNCT
ejpam-6837	124	9	4	4	NUM
ejpam-6837	124	10	)	)	PUNCT
ejpam-6837	124	11	(	(	PUNCT
ejpam-6837	124	12	2025	2025	NUM
ejpam-6837	124	13	)	)	PUNCT
ejpam-6837	124	14	,	,	PUNCT
ejpam-6837	124	15	6837	6837	NUM
ejpam-6837	124	16	6	6	NUM
ejpam-6837	124	17	of	of	ADP
ejpam-6837	124	18	15	15	NUM
ejpam-6837	124	19	figure	figure	NOUN
ejpam-6837	124	20	1	1	NUM
ejpam-6837	124	21	:	:	PUNCT
ejpam-6837	124	22	an	an	DET
ejpam-6837	124	23	illustration	illustration	NOUN
ejpam-6837	124	24	for	for	ADP
ejpam-6837	124	25	example	example	NOUN
ejpam-6837	124	26	1	1	NUM
ejpam-6837	124	27	with	with	ADP
ejpam-6837	124	28	the	the	DET
ejpam-6837	124	29	starting	starting	NOUN
ejpam-6837	124	30	point	point	NOUN
ejpam-6837	124	31	x0	x0	PROPN
ejpam-6837	124	32	=	=	PUNCT
ejpam-6837	124	33	(	(	PUNCT
ejpam-6837	124	34	−4	−4	X
ejpam-6837	124	35	,	,	PUNCT
ejpam-6837	124	36	1	1	NUM
ejpam-6837	124	37	)	)	PUNCT
ejpam-6837	124	38	.	.	PUNCT
ejpam-6837	125	1	in	in	ADP
ejpam-6837	125	2	the	the	DET
ejpam-6837	125	3	left	left	NOUN
ejpam-6837	125	4	,	,	PUNCT
ejpam-6837	125	5	the	the	DET
ejpam-6837	125	6	dra	dra	PROPN
ejpam-6837	125	7	sequence	sequence	NOUN
ejpam-6837	125	8	(	(	PUNCT
ejpam-6837	125	9	xn)n∈n	xn)n∈n	NUM
ejpam-6837	125	10	converges	converge	VERB
ejpam-6837	125	11	to	to	ADP
ejpam-6837	125	12	x	x	SYM
ejpam-6837	125	13	=	=	SYM
ejpam-6837	125	14	(	(	PUNCT
ejpam-6837	125	15	0	0	NUM
ejpam-6837	125	16	,	,	PUNCT
ejpam-6837	125	17	2.4	2.4	NUM
ejpam-6837	125	18	)	)	PUNCT
ejpam-6837	125	19	/∈	/∈	PUNCT
ejpam-6837	126	1	2	2	NUM
ejpam-6837	126	2	∩	∩	X
ejpam-6837	126	3	i=1	i=1	PROPN
ejpam-6837	126	4	ci	ci	PROPN
ejpam-6837	126	5	.	.	PUNCT
ejpam-6837	127	1	however	however	ADV
ejpam-6837	127	2	,	,	PUNCT
ejpam-6837	127	3	the	the	DET
ejpam-6837	127	4	shadew	shadew	NOUN
ejpam-6837	127	5	sequence	sequence	NOUN
ejpam-6837	127	6	pc1	pc1	PROPN
ejpam-6837	127	7	(	(	PUNCT
ejpam-6837	127	8	xn	xn	X
ejpam-6837	127	9	)	)	PUNCT
ejpam-6837	127	10	converges	converge	VERB
ejpam-6837	127	11	to	to	ADP
ejpam-6837	127	12	(	(	PUNCT
ejpam-6837	127	13	0	0	NUM
ejpam-6837	127	14	,	,	PUNCT
ejpam-6837	127	15	0	0	NUM
ejpam-6837	127	16	)	)	PUNCT
ejpam-6837	127	17	=	=	SYM
ejpam-6837	127	18	2	2	NUM
ejpam-6837	127	19	∩	∩	X
ejpam-6837	127	20	i=1	i=1	PROPN
ejpam-6837	127	21	ci	ci	PROPN
ejpam-6837	127	22	.	.	PROPN
ejpam-6837	128	1	in	in	ADP
ejpam-6837	128	2	the	the	DET
ejpam-6837	128	3	right	right	NOUN
ejpam-6837	128	4	,	,	PUNCT
ejpam-6837	128	5	the	the	DET
ejpam-6837	128	6	cdra	cdra	PROPN
ejpam-6837	128	7	sequece	sequece	PROPN
ejpam-6837	128	8	(	(	PUNCT
ejpam-6837	128	9	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	128	10	converges	converge	VERB
ejpam-6837	128	11	to	to	ADP
ejpam-6837	128	12	(	(	PUNCT
ejpam-6837	128	13	0	0	NUM
ejpam-6837	128	14	,	,	PUNCT
ejpam-6837	128	15	0	0	NUM
ejpam-6837	128	16	)	)	PUNCT
ejpam-6837	128	17	=	=	SYM
ejpam-6837	128	18	2	2	NUM
ejpam-6837	128	19	∩	∩	X
ejpam-6837	128	20	i=1	i=1	PROPN
ejpam-6837	128	21	ci	ci	PROPN
ejpam-6837	128	22	.	.	PROPN
ejpam-6837	128	23	4	4	NUM
ejpam-6837	128	24	.	.	X
ejpam-6837	128	25	main	main	ADJ
ejpam-6837	128	26	results	result	NOUN
ejpam-6837	128	27	let	let	VERB
ejpam-6837	128	28	ti	ti	NOUN
ejpam-6837	128	29	:	:	PUNCT
ejpam-6837	128	30	h	h	PROPN
ejpam-6837	128	31	→	→	PUNCT
ejpam-6837	128	32	h	h	NOUN
ejpam-6837	128	33	be	be	VERB
ejpam-6837	128	34	firmly	firmly	ADV
ejpam-6837	128	35	nonexpansive	nonexpansive	ADJ
ejpam-6837	128	36	,	,	PUNCT
ejpam-6837	128	37	for	for	ADP
ejpam-6837	128	38	each	each	DET
ejpam-6837	128	39	i.	i.	NOUN
ejpam-6837	128	40	recall	recall	PROPN
ejpam-6837	128	41	from	from	ADP
ejpam-6837	128	42	(	(	PUNCT
ejpam-6837	128	43	13	13	NUM
ejpam-6837	128	44	)	)	PUNCT
ejpam-6837	128	45	that	that	DET
ejpam-6837	128	46	t[c1c2	t[c1c2	PROPN
ejpam-6837	129	1	...	...	PUNCT
ejpam-6837	129	2	cn	cn	X
ejpam-6837	130	1	]	]	X
ejpam-6837	130	2	:	:	PUNCT
ejpam-6837	130	3	=	=	SYM
ejpam-6837	130	4	tcn	tcn	NOUN
ejpam-6837	130	5	,	,	PUNCT
ejpam-6837	130	6	c1	c1	PROPN
ejpam-6837	130	7	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	130	8	.	.	PUNCT
ejpam-6837	130	9	.	.	PUNCT
ejpam-6837	130	10	.	.	PUNCT
ejpam-6837	131	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	131	2	tc1,c2	tc1,c2	PROPN
ejpam-6837	131	3	with	with	ADP
ejpam-6837	131	4	fix	fix	PROPN
ejpam-6837	131	5	t[c1c2	t[c1c2	PROPN
ejpam-6837	131	6	...	...	PUNCT
ejpam-6837	132	1	cn	cn	X
ejpam-6837	132	2	]	]	PUNCT
ejpam-6837	133	1	̸=	̸=	PROPN
ejpam-6837	133	2	∅.	∅.	VERB
ejpam-6837	133	3	then	then	ADV
ejpam-6837	133	4	t[c1c2	t[c1c2	PROPN
ejpam-6837	133	5	...	...	PUNCT
ejpam-6837	134	1	cn	cn	PROPN
ejpam-6837	134	2	]	]	X
ejpam-6837	134	3	is	be	AUX
ejpam-6837	134	4	asymptotically	asymptotically	ADV
ejpam-6837	134	5	regular	regular	ADJ
ejpam-6837	134	6	.	.	PUNCT
ejpam-6837	135	1	proof	proof	NOUN
ejpam-6837	135	2	.	.	PUNCT
ejpam-6837	136	1	from	from	ADP
ejpam-6837	136	2	(	(	PUNCT
ejpam-6837	136	3	13	13	NUM
ejpam-6837	136	4	)	)	PUNCT
ejpam-6837	136	5	and	and	CCONJ
ejpam-6837	136	6	proposition	proposition	NOUN
ejpam-6837	136	7	1	1	NUM
ejpam-6837	136	8	we	we	PRON
ejpam-6837	136	9	have	have	VERB
ejpam-6837	136	10	tci	tci	NOUN
ejpam-6837	136	11	,	,	PUNCT
ejpam-6837	136	12	ci+1	ci+1	PROPN
ejpam-6837	136	13	is	be	AUX
ejpam-6837	136	14	firmly	firmly	ADV
ejpam-6837	136	15	nonexpansive	nonexpansive	ADJ
ejpam-6837	136	16	for	for	ADP
ejpam-6837	136	17	all	all	DET
ejpam-6837	136	18	i.	i.	NOUN
ejpam-6837	136	19	we	we	PRON
ejpam-6837	136	20	also	also	ADV
ejpam-6837	136	21	have	have	VERB
ejpam-6837	136	22	,	,	PUNCT
ejpam-6837	136	23	∅	∅	NOUN
ejpam-6837	136	24	̸=	̸=	PROPN
ejpam-6837	136	25	fix	fix	VERB
ejpam-6837	136	26	t[c1c2	t[c1c2	NOUN
ejpam-6837	136	27	...	...	PUNCT
ejpam-6837	136	28	cn	cn	X
ejpam-6837	136	29	]	]	X
ejpam-6837	136	30	.	.	PUNCT
ejpam-6837	137	1	let	let	VERB
ejpam-6837	137	2	y	y	PROPN
ejpam-6837	137	3	∈	∈	PROPN
ejpam-6837	137	4	fix	fix	VERB
ejpam-6837	137	5	t[c1c2	t[c1c2	PROPN
ejpam-6837	137	6	...	...	PUNCT
ejpam-6837	138	1	cn	cn	X
ejpam-6837	138	2	]	]	PUNCT
ejpam-6837	139	1	then	then	ADV
ejpam-6837	139	2	;	;	PUNCT
ejpam-6837	139	3	∥txn	∥txn	PRON
ejpam-6837	139	4	−	−	NUM
ejpam-6837	139	5	ty∥2	ty∥2	NOUN
ejpam-6837	139	6	†	†	PROPN
ejpam-6837	139	7	≤	≤	PROPN
ejpam-6837	139	8	∥tcn−1,cn	∥tcn−1,cn	PUNCT
ejpam-6837	139	9	·	·	PUNCT
ejpam-6837	139	10	·	·	PUNCT
ejpam-6837	139	11	·	·	PUNCT
ejpam-6837	139	12	tc2,c3	tc2,c3	PROPN
ejpam-6837	139	13	tc1,c2	tc1,c2	NOUN
ejpam-6837	139	14	xn	xn	PROPN
ejpam-6837	140	1	−	−	PROPN
ejpam-6837	140	2	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	140	3	·	·	PUNCT
ejpam-6837	140	4	·	·	PUNCT
ejpam-6837	140	5	·	·	PUNCT
ejpam-6837	140	6	tc2,c3	tc2,c3	PROPN
ejpam-6837	140	7	tc1,c2	tc1,c2	PROPN
ejpam-6837	140	8	y∥2	y∥2	NOUN
ejpam-6837	141	1	−	−	PROPN
ejpam-6837	141	2	∥(id−tcn	∥(id−tcn	PROPN
ejpam-6837	141	3	,	,	PUNCT
ejpam-6837	141	4	c1)xn	c1)xn	PROPN
ejpam-6837	141	5	−	−	PROPN
ejpam-6837	141	6	(	(	PUNCT
ejpam-6837	141	7	id−tcn	id−tcn	PUNCT
ejpam-6837	141	8	,	,	PUNCT
ejpam-6837	141	9	c1)y∥	c1)y∥	NOUN
ejpam-6837	141	10	2	2	NUM
ejpam-6837	141	11	†by	†by	NOUN
ejpam-6837	141	12	using	use	VERB
ejpam-6837	141	13	the	the	DET
ejpam-6837	141	14	definition	definition	NOUN
ejpam-6837	141	15	of	of	ADP
ejpam-6837	141	16	t[c1c2···cn	t[c1c2···cn	PROPN
ejpam-6837	141	17	]	]	PUNCT
ejpam-6837	141	18	and	and	CCONJ
ejpam-6837	141	19	the	the	DET
ejpam-6837	141	20	fact	fact	NOUN
ejpam-6837	141	21	that	that	SCONJ
ejpam-6837	141	22	(	(	PUNCT
ejpam-6837	141	23	∀i	∀i	NOUN
ejpam-6837	141	24	)	)	PUNCT
ejpam-6837	141	25	tci	tci	NOUN
ejpam-6837	141	26	,	,	PUNCT
ejpam-6837	141	27	ci+1	ci+1	PROPN
ejpam-6837	141	28	is	be	AUX
ejpam-6837	141	29	firmly	firmly	ADV
ejpam-6837	141	30	nonexpansive	nonexpansive	ADJ
ejpam-6837	141	31	.	.	PUNCT
ejpam-6837	142	1	s.	s.	PROPN
ejpam-6837	142	2	th	th	PROPN
ejpam-6837	142	3	.	.	PUNCT
ejpam-6837	143	1	alwadani	alwadani	PROPN
ejpam-6837	143	2	/	/	SYM
ejpam-6837	143	3	eur	eur	PROPN
ejpam-6837	143	4	.	.	PUNCT
ejpam-6837	144	1	j.	j.	PROPN
ejpam-6837	144	2	pure	pure	PROPN
ejpam-6837	144	3	appl	appl	PROPN
ejpam-6837	144	4	.	.	PROPN
ejpam-6837	144	5	math	math	PROPN
ejpam-6837	144	6	,	,	PUNCT
ejpam-6837	144	7	18	18	NUM
ejpam-6837	144	8	(	(	PUNCT
ejpam-6837	144	9	4	4	NUM
ejpam-6837	144	10	)	)	PUNCT
ejpam-6837	144	11	(	(	PUNCT
ejpam-6837	144	12	2025	2025	NUM
ejpam-6837	144	13	)	)	PUNCT
ejpam-6837	144	14	,	,	PUNCT
ejpam-6837	144	15	6837	6837	NUM
ejpam-6837	144	16	7	7	NUM
ejpam-6837	144	17	of	of	ADP
ejpam-6837	144	18	15	15	NUM
ejpam-6837	144	19	figure	figure	NOUN
ejpam-6837	144	20	2	2	NUM
ejpam-6837	144	21	:	:	PUNCT
ejpam-6837	144	22	an	an	DET
ejpam-6837	144	23	illustration	illustration	NOUN
ejpam-6837	144	24	for	for	ADP
ejpam-6837	144	25	example	example	NOUN
ejpam-6837	144	26	2	2	NUM
ejpam-6837	144	27	with	with	ADP
ejpam-6837	144	28	the	the	DET
ejpam-6837	144	29	starting	starting	NOUN
ejpam-6837	144	30	point	point	NOUN
ejpam-6837	144	31	x0	x0	PROPN
ejpam-6837	144	32	=	=	PUNCT
ejpam-6837	144	33	(	(	PUNCT
ejpam-6837	144	34	0	0	NUM
ejpam-6837	144	35	,	,	PUNCT
ejpam-6837	144	36	2	2	NUM
ejpam-6837	144	37	)	)	PUNCT
ejpam-6837	144	38	.	.	PUNCT
ejpam-6837	145	1	the	the	DET
ejpam-6837	145	2	graph	graph	NOUN
ejpam-6837	145	3	in	in	ADP
ejpam-6837	145	4	the	the	DET
ejpam-6837	145	5	left	left	ADJ
ejpam-6837	145	6	side	side	NOUN
ejpam-6837	145	7	describes	describe	VERB
ejpam-6837	145	8	the	the	DET
ejpam-6837	145	9	3sets	3sets	NUM
ejpam-6837	145	10	dra	dra	PROPN
ejpam-6837	145	11	iterations	iteration	NOUN
ejpam-6837	145	12	which	which	PRON
ejpam-6837	145	13	faill	faill	NOUN
ejpam-6837	145	14	to	to	PART
ejpam-6837	145	15	converge	converge	VERB
ejpam-6837	145	16	to	to	ADP
ejpam-6837	145	17	(	(	PUNCT
ejpam-6837	145	18	0	0	NUM
ejpam-6837	145	19	,	,	PUNCT
ejpam-6837	145	20	0	0	NUM
ejpam-6837	145	21	)	)	PUNCT
ejpam-6837	145	22	.	.	PUNCT
ejpam-6837	146	1	however	however	ADV
ejpam-6837	146	2	,	,	PUNCT
ejpam-6837	146	3	the	the	DET
ejpam-6837	146	4	graph	graph	NOUN
ejpam-6837	146	5	in	in	ADP
ejpam-6837	146	6	the	the	DET
ejpam-6837	146	7	right	right	ADJ
ejpam-6837	146	8	side	side	NOUN
ejpam-6837	146	9	describes	describe	VERB
ejpam-6837	146	10	the	the	DET
ejpam-6837	146	11	3sets	3sets	NUM
ejpam-6837	146	12	cdra	cdra	NOUN
ejpam-6837	146	13	iteration	iteration	NOUN
ejpam-6837	146	14	which	which	PRON
ejpam-6837	146	15	converges	converge	VERB
ejpam-6837	146	16	to	to	ADP
ejpam-6837	146	17	(	(	PUNCT
ejpam-6837	146	18	0	0	NUM
ejpam-6837	146	19	,	,	PUNCT
ejpam-6837	146	20	0	0	NUM
ejpam-6837	146	21	)	)	PUNCT
ejpam-6837	146	22	.	.	PUNCT
ejpam-6837	147	1	≤	≤	NUM
ejpam-6837	147	2	∥tcn−2,cn−1	∥tcn−2,cn−1	PROPN
ejpam-6837	147	3	·	·	PUNCT
ejpam-6837	147	4	·	·	PUNCT
ejpam-6837	147	5	·	·	PUNCT
ejpam-6837	148	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	148	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	148	3	xn	xn	PROPN
ejpam-6837	149	1	−	−	PUNCT
ejpam-6837	149	2	tcn−2,cn−1	tcn−2,cn−1	PROPN
ejpam-6837	149	3	·	·	PUNCT
ejpam-6837	149	4	·	·	PUNCT
ejpam-6837	149	5	·	·	PUNCT
ejpam-6837	149	6	tc2,c3	tc2,c3	PROPN
ejpam-6837	149	7	tc1,c2	tc1,c2	PROPN
ejpam-6837	149	8	y∥2	y∥2	NOUN
ejpam-6837	150	1	−	−	PROPN
ejpam-6837	150	2	∥(id−tcn−1,cn	∥(id−tcn−1,cn	NOUN
ejpam-6837	150	3	)	)	PUNCT
ejpam-6837	150	4	tcn	tcn	PROPN
ejpam-6837	150	5	,	,	PUNCT
ejpam-6837	150	6	c1	c1	PROPN
ejpam-6837	150	7	xn	xn	PROPN
ejpam-6837	151	1	−	−	PROPN
ejpam-6837	151	2	(	(	PUNCT
ejpam-6837	151	3	id−tcn−1,cn	id−tcn−1,cn	NUM
ejpam-6837	151	4	)	)	PUNCT
ejpam-6837	151	5	tcn	tcn	NOUN
ejpam-6837	151	6	,	,	PUNCT
ejpam-6837	151	7	c1	c1	PROPN
ejpam-6837	151	8	y∥2	y∥2	PROPN
ejpam-6837	152	1	−	−	PROPN
ejpam-6837	152	2	∥(id−tcn	∥(id−tcn	PROPN
ejpam-6837	152	3	,	,	PUNCT
ejpam-6837	152	4	c1)xn	c1)xn	PROPN
ejpam-6837	152	5	−	−	PROPN
ejpam-6837	152	6	(	(	PUNCT
ejpam-6837	152	7	id−tcn	id−tcn	PUNCT
ejpam-6837	152	8	,	,	PUNCT
ejpam-6837	152	9	c1)y∥	c1)y∥	NOUN
ejpam-6837	152	10	2	2	NUM
ejpam-6837	152	11	≤	≤	NUM
ejpam-6837	152	12	...	...	PUNCT
ejpam-6837	153	1	≤	≤	NUM
ejpam-6837	153	2	∥tc1,c2	∥tc1,c2	NUM
ejpam-6837	153	3	xn	xn	NUM
ejpam-6837	153	4	−	−	PROPN
ejpam-6837	153	5	tc1,c2	tc1,c2	NOUN
ejpam-6837	153	6	y∥2	y∥2	NOUN
ejpam-6837	153	7	−	−	PROPN
ejpam-6837	153	8	∥(id−tc1,c2)tc2,c3	∥(id−tc1,c2)tc2,c3	NOUN
ejpam-6837	153	9	·	·	PUNCT
ejpam-6837	153	10	·	·	PUNCT
ejpam-6837	153	11	·	·	PUNCT
ejpam-6837	154	1	tcn	tcn	NOUN
ejpam-6837	154	2	,	,	PUNCT
ejpam-6837	154	3	c1	c1	PROPN
ejpam-6837	154	4	xn	xn	PROPN
ejpam-6837	155	1	−	−	PROPN
ejpam-6837	155	2	(	(	PUNCT
ejpam-6837	155	3	id−tc1,c2)tc2,c3	id−tc1,c2)tc2,c3	NOUN
ejpam-6837	155	4	·	·	PUNCT
ejpam-6837	155	5	·	·	PUNCT
ejpam-6837	155	6	·	·	PUNCT
ejpam-6837	156	1	tcn	tcn	NOUN
ejpam-6837	156	2	,	,	PUNCT
ejpam-6837	156	3	c1	c1	PROPN
ejpam-6837	156	4	y∥2	y∥2	NOUN
ejpam-6837	156	5	−	−	PROPN
ejpam-6837	156	6	·	·	PUNCT
ejpam-6837	156	7	·	·	PUNCT
ejpam-6837	156	8	·	·	PUNCT
ejpam-6837	157	1	−	−	ADP
ejpam-6837	157	2	∥(id−tcn−1,cn	∥(id−tcn−1,cn	NOUN
ejpam-6837	157	3	)	)	PUNCT
ejpam-6837	157	4	tcn	tcn	PROPN
ejpam-6837	157	5	,	,	PUNCT
ejpam-6837	157	6	c1	c1	PROPN
ejpam-6837	157	7	xn	xn	PROPN
ejpam-6837	158	1	−	−	PROPN
ejpam-6837	158	2	(	(	PUNCT
ejpam-6837	158	3	id−tcn−1,cn	id−tcn−1,cn	NUM
ejpam-6837	158	4	)	)	PUNCT
ejpam-6837	158	5	tcn	tcn	NOUN
ejpam-6837	158	6	,	,	PUNCT
ejpam-6837	158	7	c1	c1	PROPN
ejpam-6837	158	8	y∥2	y∥2	PROPN
ejpam-6837	159	1	−	−	PROPN
ejpam-6837	159	2	∥(id−tcn	∥(id−tcn	PROPN
ejpam-6837	159	3	,	,	PUNCT
ejpam-6837	159	4	c1)xn	c1)xn	PROPN
ejpam-6837	159	5	−	−	PROPN
ejpam-6837	159	6	(	(	PUNCT
ejpam-6837	159	7	id−tcn	id−tcn	PUNCT
ejpam-6837	159	8	,	,	PUNCT
ejpam-6837	159	9	c1)y∥	c1)y∥	NUM
ejpam-6837	159	10	2	2	NUM
ejpam-6837	159	11	‡	‡	NOUN
ejpam-6837	159	12	≤	≤	NOUN
ejpam-6837	159	13	∥xn	∥xn	PROPN
ejpam-6837	159	14	−	−	PROPN
ejpam-6837	159	15	y∥2	y∥2	NOUN
ejpam-6837	160	1	−	−	PROPN
ejpam-6837	161	1	∥(id−tcn	∥(id−tcn	PROPN
ejpam-6837	161	2	,	,	PUNCT
ejpam-6837	161	3	c1)xn	c1)xn	PROPN
ejpam-6837	161	4	−	−	PROPN
ejpam-6837	161	5	(	(	PUNCT
ejpam-6837	161	6	id−tcn	id−tcn	PUNCT
ejpam-6837	161	7	,	,	PUNCT
ejpam-6837	161	8	c1)y∥	c1)y∥	NOUN
ejpam-6837	161	9	2	2	NUM
ejpam-6837	161	10	−	−	NOUN
ejpam-6837	161	11	∥(id−tcn−1,cn	∥(id−tcn−1,cn	NOUN
ejpam-6837	161	12	)	)	PUNCT
ejpam-6837	161	13	tcn	tcn	PROPN
ejpam-6837	161	14	,	,	PUNCT
ejpam-6837	161	15	c1	c1	PROPN
ejpam-6837	161	16	xn	xn	PROPN
ejpam-6837	162	1	−	−	PROPN
ejpam-6837	162	2	(	(	PUNCT
ejpam-6837	162	3	id−tcn−1,cn	id−tcn−1,cn	NUM
ejpam-6837	162	4	)	)	PUNCT
ejpam-6837	162	5	tcn	tcn	NOUN
ejpam-6837	162	6	,	,	PUNCT
ejpam-6837	162	7	c1	c1	PROPN
ejpam-6837	162	8	y∥2	y∥2	NOUN
ejpam-6837	162	9	−	−	PROPN
ejpam-6837	162	10	·	·	PUNCT
ejpam-6837	162	11	·	·	PUNCT
ejpam-6837	162	12	·	·	PUNCT
ejpam-6837	163	1	−	−	NOUN
ejpam-6837	163	2	∥(id−tc2,c3)tc3,c4	∥(id−tc2,c3)tc3,c4	PROPN
ejpam-6837	163	3	·	·	PUNCT
ejpam-6837	163	4	·	·	PUNCT
ejpam-6837	163	5	·	·	PUNCT
ejpam-6837	163	6	tcn	tcn	NOUN
ejpam-6837	163	7	,	,	PUNCT
ejpam-6837	163	8	c1	c1	PROPN
ejpam-6837	163	9	xn	xn	PROPN
ejpam-6837	164	1	−	−	PROPN
ejpam-6837	164	2	(	(	PUNCT
ejpam-6837	164	3	id−tc2,c3)tc3,c4	id−tc2,c3)tc3,c4	X
ejpam-6837	164	4	·	·	PUNCT
ejpam-6837	164	5	·	·	PUNCT
ejpam-6837	164	6	·	·	PUNCT
ejpam-6837	164	7	tcn	tcn	NOUN
ejpam-6837	164	8	,	,	PUNCT
ejpam-6837	164	9	c1	c1	PROPN
ejpam-6837	164	10	y∥2	y∥2	PROPN
ejpam-6837	164	11	−	−	PROPN
ejpam-6837	164	12	∥(id−tc1,c2)tc2,c3	∥(id−tc1,c2)tc2,c3	NOUN
ejpam-6837	164	13	·	·	PUNCT
ejpam-6837	164	14	·	·	PUNCT
ejpam-6837	164	15	·	·	PUNCT
ejpam-6837	165	1	tcn	tcn	NOUN
ejpam-6837	165	2	,	,	PUNCT
ejpam-6837	165	3	c1	c1	PROPN
ejpam-6837	165	4	xn	xn	PROPN
ejpam-6837	166	1	−	−	PROPN
ejpam-6837	166	2	(	(	PUNCT
ejpam-6837	166	3	id−tc1,c2)tc2,c3	id−tc1,c2)tc2,c3	NOUN
ejpam-6837	166	4	·	·	PUNCT
ejpam-6837	166	5	·	·	PUNCT
ejpam-6837	166	6	·	·	PUNCT
ejpam-6837	167	1	tcn	tcn	NOUN
ejpam-6837	167	2	,	,	PUNCT
ejpam-6837	167	3	c1	c1	PROPN
ejpam-6837	167	4	y∥2	y∥2	NOUN
ejpam-6837	167	5	(	(	PUNCT
ejpam-6837	167	6	16	16	NUM
ejpam-6837	167	7	)	)	PUNCT
ejpam-6837	167	8	therefore	therefore	ADV
ejpam-6837	167	9	,	,	PUNCT
ejpam-6837	167	10	(	(	PUNCT
ejpam-6837	167	11	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	167	12	is	be	AUX
ejpam-6837	167	13	fejér	fejér	ADJ
ejpam-6837	167	14	montone	montone	NOUN
ejpam-6837	167	15	with	with	ADP
ejpam-6837	167	16	respect	respect	NOUN
ejpam-6837	167	17	to	to	ADP
ejpam-6837	167	18	fixt[c1c2	fixt[c1c2	NUM
ejpam-6837	167	19	...	...	PUNCT
ejpam-6837	168	1	cn	cn	X
ejpam-6837	168	2	]	]	PUNCT
ejpam-6837	168	3	and	and	CCONJ
ejpam-6837	168	4	,	,	PUNCT
ejpam-6837	168	5	(	(	PUNCT
ejpam-6837	168	6	id−tcn	id−tcn	X
ejpam-6837	168	7	,	,	PUNCT
ejpam-6837	168	8	c1)xn	c1)xn	NOUN
ejpam-6837	168	9	−	−	PROPN
ejpam-6837	168	10	(	(	PUNCT
ejpam-6837	168	11	id−tcn	id−tcn	PROPN
ejpam-6837	168	12	,	,	PUNCT
ejpam-6837	168	13	c1)y	c1)y	PROPN
ejpam-6837	168	14	→	→	SYM
ejpam-6837	168	15	0	0	NUM
ejpam-6837	168	16	(	(	PUNCT
ejpam-6837	168	17	17	17	NUM
ejpam-6837	168	18	)	)	PUNCT
ejpam-6837	168	19	(	(	PUNCT
ejpam-6837	168	20	id−tcn−1,cn	id−tcn−1,cn	X
ejpam-6837	168	21	)	)	PUNCT
ejpam-6837	168	22	tcn	tcn	NOUN
ejpam-6837	168	23	,	,	PUNCT
ejpam-6837	168	24	c1	c1	PROPN
ejpam-6837	168	25	xn	xn	PROPN
ejpam-6837	169	1	−	−	PROPN
ejpam-6837	169	2	(	(	PUNCT
ejpam-6837	169	3	id−tcn−1,cn	id−tcn−1,cn	NUM
ejpam-6837	169	4	)	)	PUNCT
ejpam-6837	169	5	tcn	tcn	NOUN
ejpam-6837	169	6	,	,	PUNCT
ejpam-6837	169	7	c1	c1	PROPN
ejpam-6837	169	8	y	y	PROPN
ejpam-6837	169	9	→	→	SYM
ejpam-6837	169	10	0	0	NUM
ejpam-6837	169	11	(	(	PUNCT
ejpam-6837	169	12	18	18	NUM
ejpam-6837	169	13	)	)	PUNCT
ejpam-6837	169	14	...	...	PUNCT
ejpam-6837	169	15	(	(	PUNCT
ejpam-6837	169	16	19	19	NUM
ejpam-6837	169	17	)	)	PUNCT
ejpam-6837	169	18	(	(	PUNCT
ejpam-6837	169	19	id−tc1,c2)tc2,c3	id−tc1,c2)tc2,c3	X
ejpam-6837	169	20	·	·	PUNCT
ejpam-6837	169	21	·	·	PUNCT
ejpam-6837	169	22	·	·	PUNCT
ejpam-6837	170	1	tcn	tcn	NOUN
ejpam-6837	170	2	,	,	PUNCT
ejpam-6837	170	3	c1	c1	PROPN
ejpam-6837	170	4	xn	xn	PROPN
ejpam-6837	171	1	−	−	PROPN
ejpam-6837	171	2	(	(	PUNCT
ejpam-6837	171	3	id−tc1,c2)tc2,c3	id−tc1,c2)tc2,c3	NOUN
ejpam-6837	171	4	.	.	PUNCT
ejpam-6837	171	5	.	.	PUNCT
ejpam-6837	171	6	.	.	PUNCT
ejpam-6837	172	1	tcn	tcn	PROPN
ejpam-6837	172	2	,	,	PUNCT
ejpam-6837	172	3	c1	c1	PROPN
ejpam-6837	172	4	y	y	PROPN
ejpam-6837	172	5	→	→	SYM
ejpam-6837	172	6	0	0	NUM
ejpam-6837	172	7	(	(	PUNCT
ejpam-6837	172	8	20	20	NUM
ejpam-6837	172	9	)	)	PUNCT
ejpam-6837	172	10	adding	add	VERB
ejpam-6837	172	11	(	(	PUNCT
ejpam-6837	172	12	17	17	NUM
ejpam-6837	172	13	)	)	PUNCT
ejpam-6837	172	14	(	(	PUNCT
ejpam-6837	172	15	20	20	NUM
ejpam-6837	172	16	)	)	PUNCT
ejpam-6837	172	17	,	,	PUNCT
ejpam-6837	172	18	we	we	PRON
ejpam-6837	172	19	obtain	obtain	VERB
ejpam-6837	172	20	xn	xn	X
ejpam-6837	173	1	−	−	PROPN
ejpam-6837	173	2	tcn	tcn	NOUN
ejpam-6837	173	3	,	,	PUNCT
ejpam-6837	173	4	c1	c1	PROPN
ejpam-6837	173	5	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	173	6	.	.	PUNCT
ejpam-6837	173	7	.	.	PUNCT
ejpam-6837	173	8	.	.	PUNCT
ejpam-6837	174	1	tc1,c2	tc1,c2	NOUN
ejpam-6837	174	2	xn	xn	PROPN
ejpam-6837	174	3	→	→	SYM
ejpam-6837	174	4	0	0	NUM
ejpam-6837	174	5	■	■	PUNCT
ejpam-6837	174	6	‡because	‡because	NOUN
ejpam-6837	174	7	tc1,c2	tc1,c2	NOUN
ejpam-6837	174	8	is	be	AUX
ejpam-6837	174	9	firmly	firmly	ADV
ejpam-6837	174	10	nonexpansive	nonexpansive	ADJ
ejpam-6837	174	11	which	which	PRON
ejpam-6837	174	12	means	mean	VERB
ejpam-6837	174	13	it	it	PRON
ejpam-6837	174	14	is	be	AUX
ejpam-6837	174	15	nonexpansive	nonexpansive	ADJ
ejpam-6837	174	16	.	.	PUNCT
ejpam-6837	175	1	s.	s.	PROPN
ejpam-6837	175	2	th	th	PROPN
ejpam-6837	175	3	.	.	PUNCT
ejpam-6837	176	1	alwadani	alwadani	PROPN
ejpam-6837	176	2	/	/	SYM
ejpam-6837	176	3	eur	eur	PROPN
ejpam-6837	176	4	.	.	PUNCT
ejpam-6837	177	1	j.	j.	PROPN
ejpam-6837	177	2	pure	pure	PROPN
ejpam-6837	177	3	appl	appl	PROPN
ejpam-6837	177	4	.	.	PROPN
ejpam-6837	177	5	math	math	PROPN
ejpam-6837	177	6	,	,	PUNCT
ejpam-6837	177	7	18	18	NUM
ejpam-6837	177	8	(	(	PUNCT
ejpam-6837	177	9	4	4	NUM
ejpam-6837	177	10	)	)	PUNCT
ejpam-6837	177	11	(	(	PUNCT
ejpam-6837	177	12	2025	2025	NUM
ejpam-6837	177	13	)	)	PUNCT
ejpam-6837	177	14	,	,	PUNCT
ejpam-6837	177	15	6837	6837	NUM
ejpam-6837	177	16	8	8	NUM
ejpam-6837	177	17	of	of	ADP
ejpam-6837	177	18	15	15	NUM
ejpam-6837	177	19	let	let	VERB
ejpam-6837	177	20	tci	tci	NOUN
ejpam-6837	177	21	,	,	PUNCT
ejpam-6837	177	22	ci+1	ci+1	PUNCT
ejpam-6837	177	23	:	:	PUNCT
ejpam-6837	177	24	h→h	h→h	NOUN
ejpam-6837	177	25	be	be	VERB
ejpam-6837	177	26	firmly	firmly	ADV
ejpam-6837	177	27	nonexpansive	nonexpansive	ADJ
ejpam-6837	177	28	for	for	ADP
ejpam-6837	177	29	each	each	DET
ejpam-6837	177	30	i	i	PRON
ejpam-6837	177	31	and	and	CCONJ
ejpam-6837	177	32	recall	recall	VERB
ejpam-6837	177	33	from	from	ADP
ejpam-6837	177	34	(	(	PUNCT
ejpam-6837	177	35	13	13	NUM
ejpam-6837	177	36	)	)	PUNCT
ejpam-6837	177	37	that	that	PRON
ejpam-6837	177	38	t[c1c2	t[c1c2	PROPN
ejpam-6837	177	39	...	...	PUNCT
ejpam-6837	177	40	cn	cn	X
ejpam-6837	177	41	]	]	PUNCT
ejpam-6837	178	1	=	=	PUNCT
ejpam-6837	178	2	tcn	tcn	PROPN
ejpam-6837	178	3	,	,	PUNCT
ejpam-6837	178	4	c1	c1	PROPN
ejpam-6837	178	5	.	.	PUNCT
ejpam-6837	178	6	.	.	PUNCT
ejpam-6837	178	7	.	.	PUNCT
ejpam-6837	179	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	179	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	179	3	.	.	PUNCT
ejpam-6837	180	1	if	if	SCONJ
ejpam-6837	180	2	n+1	n+1	PROPN
ejpam-6837	180	3	∩	∩	NOUN
ejpam-6837	180	4	i=1	i=1	PRON
ejpam-6837	180	5	fix	fix	NOUN
ejpam-6837	180	6	tci	tci	PROPN
ejpam-6837	180	7	,	,	PUNCT
ejpam-6837	180	8	ci+1	ci+1	PROPN
ejpam-6837	180	9	̸=∅	̸=∅	PROPN
ejpam-6837	180	10	,	,	PUNCT
ejpam-6837	180	11	then	then	ADV
ejpam-6837	180	12	fix	fix	VERB
ejpam-6837	180	13	t[c1c2···cn	t[c1c2···cn	X
ejpam-6837	180	14	]	]	PUNCT
ejpam-6837	180	15	=	=	SYM
ejpam-6837	180	16	n+1	n+1	PROPN
ejpam-6837	180	17	∩	∩	NOUN
ejpam-6837	180	18	i=1	i=1	PRON
ejpam-6837	180	19	fix	fix	NOUN
ejpam-6837	180	20	tci	tci	NOUN
ejpam-6837	180	21	,	,	PUNCT
ejpam-6837	180	22	ci+1	ci+1	PROPN
ejpam-6837	180	23	.	.	PUNCT
ejpam-6837	181	1	proof	proof	NOUN
ejpam-6837	181	2	.	.	PUNCT
ejpam-6837	182	1	since	since	SCONJ
ejpam-6837	182	2	tci	tci	PROPN
ejpam-6837	182	3	,	,	PUNCT
ejpam-6837	182	4	ci+1	ci+1	PROPN
ejpam-6837	182	5	is	be	AUX
ejpam-6837	182	6	firmly	firmly	ADV
ejpam-6837	182	7	nonexpansive	nonexpansive	ADJ
ejpam-6837	182	8	for	for	SCONJ
ejpam-6837	182	9	each	each	DET
ejpam-6837	182	10	i	i	PRON
ejpam-6837	182	11	,	,	PUNCT
ejpam-6837	182	12	then	then	ADV
ejpam-6837	182	13	tci	tci	PROPN
ejpam-6837	182	14	,	,	PUNCT
ejpam-6837	182	15	ci+1	ci+1	PROPN
ejpam-6837	182	16	is	be	AUX
ejpam-6837	182	17	αavaraged	αavarage	VERB
ejpam-6837	182	18	with	with	ADP
ejpam-6837	182	19	α	α	NOUN
ejpam-6837	182	20	=	=	SYM
ejpam-6837	182	21	1	1	NUM
ejpam-6837	182	22	2	2	NUM
ejpam-6837	182	23	for	for	ADP
ejpam-6837	182	24	each	each	DET
ejpam-6837	182	25	i.	i.	NOUN
ejpam-6837	182	26	moreover	moreover	ADV
ejpam-6837	182	27	,	,	PUNCT
ejpam-6837	183	1	∅	∅	NOUN
ejpam-6837	183	2	̸=	̸=	PROPN
ejpam-6837	183	3	n	n	PART
ejpam-6837	183	4	∩	∩	NOUN
ejpam-6837	183	5	i=1	i=1	PROPN
ejpam-6837	183	6	ci	ci	PROPN
ejpam-6837	183	7	⊆	⊆	NUM
ejpam-6837	183	8	n+1	n+1	PROPN
ejpam-6837	183	9	∩	∩	NOUN
ejpam-6837	183	10	i=1	i=1	PRON
ejpam-6837	183	11	fix	fix	NOUN
ejpam-6837	183	12	tci	tci	PROPN
ejpam-6837	183	13	,	,	PUNCT
ejpam-6837	183	14	ci+1	ci+1	VERB
ejpam-6837	183	15	the	the	DET
ejpam-6837	183	16	inclusion	inclusion	NOUN
ejpam-6837	183	17	n+1	n+1	PROPN
ejpam-6837	183	18	∩	∩	PROPN
ejpam-6837	183	19	i=1	i=1	PROPN
ejpam-6837	183	20	fix	fix	NOUN
ejpam-6837	183	21	tci	tci	NOUN
ejpam-6837	183	22	,	,	PUNCT
ejpam-6837	183	23	ci+1	ci+1	PROPN
ejpam-6837	183	24	⊆	⊆	NUM
ejpam-6837	183	25	fix	fix	NOUN
ejpam-6837	183	26	t[c1c2	t[c1c2	PROPN
ejpam-6837	183	27	...	...	PUNCT
ejpam-6837	183	28	cn	cn	X
ejpam-6837	183	29	]	]	X
ejpam-6837	183	30	is	be	AUX
ejpam-6837	183	31	obvious	obvious	ADJ
ejpam-6837	183	32	.	.	PUNCT
ejpam-6837	184	1	now	now	ADV
ejpam-6837	184	2	we	we	PRON
ejpam-6837	184	3	show	show	VERB
ejpam-6837	184	4	that	that	SCONJ
ejpam-6837	184	5	the	the	DET
ejpam-6837	184	6	converse	converse	NOUN
ejpam-6837	184	7	inclusion	inclusion	NOUN
ejpam-6837	184	8	also	also	ADV
ejpam-6837	184	9	holds	hold	VERB
ejpam-6837	184	10	.	.	PUNCT
ejpam-6837	185	1	when	when	SCONJ
ejpam-6837	185	2	n	n	PROPN
ejpam-6837	185	3	=	=	SYM
ejpam-6837	185	4	1	1	NUM
ejpam-6837	185	5	let	let	VERB
ejpam-6837	185	6	y	y	PROPN
ejpam-6837	185	7	∈	∈	PROPN
ejpam-6837	185	8	fix	fix	NOUN
ejpam-6837	185	9	tc1,c2	tc1,c2	NOUN
ejpam-6837	185	10	and	and	CCONJ
ejpam-6837	185	11	let	let	VERB
ejpam-6837	185	12	x	x	PUNCT
ejpam-6837	185	13	∈	∈	PROPN
ejpam-6837	185	14	fix	fix	NOUN
ejpam-6837	185	15	t[c1c2	t[c1c2	NOUN
ejpam-6837	185	16	]	]	X
ejpam-6837	185	17	:	:	PUNCT
ejpam-6837	185	18	=	=	PUNCT
ejpam-6837	185	19	fix	fix	NOUN
ejpam-6837	185	20	tc2,c1	tc2,c1	NOUN
ejpam-6837	185	21	tc1,c2	tc1,c2	NOUN
ejpam-6837	185	22	.	.	PUNCT
ejpam-6837	186	1	then	then	ADV
ejpam-6837	186	2	;	;	PUNCT
ejpam-6837	186	3	◦	◦	VERB
ejpam-6837	186	4	if	if	SCONJ
ejpam-6837	186	5	x	x	SYM
ejpam-6837	186	6	∈	∈	PROPN
ejpam-6837	186	7	fix	fix	NOUN
ejpam-6837	186	8	tc1,c2	tc1,c2	ADJ
ejpam-6837	186	9	⇒	⇒	NOUN
ejpam-6837	186	10	tc1,c2	tc1,c2	NOUN
ejpam-6837	186	11	x	x	PUNCT
ejpam-6837	186	12	=	=	PUNCT
ejpam-6837	186	13	x.	x.	NOUN
ejpam-6837	186	14	therefore	therefore	ADV
ejpam-6837	186	15	,	,	PUNCT
ejpam-6837	186	16	tc2,c1	tc2,c1	NOUN
ejpam-6837	186	17	x	x	SYM
ejpam-6837	186	18	=	=	SYM
ejpam-6837	186	19	tc2,c1	tc2,c1	NOUN
ejpam-6837	186	20	tc1,c2	tc1,c2	NOUN
ejpam-6837	186	21	x	x	X
ejpam-6837	186	22	=	=	PUNCT
ejpam-6837	186	23	x	x	SYM
ejpam-6837	186	24	∈	∈	PROPN
ejpam-6837	186	25	fix	fix	NOUN
ejpam-6837	186	26	tc1,c2	tc1,c2	NOUN
ejpam-6837	186	27	.	.	PUNCT
ejpam-6837	187	1	therefore	therefore	ADV
ejpam-6837	187	2	,	,	PUNCT
ejpam-6837	187	3	under	under	ADP
ejpam-6837	187	4	this	this	DET
ejpam-6837	187	5	case	case	NOUN
ejpam-6837	187	6	we	we	PRON
ejpam-6837	187	7	have	have	AUX
ejpam-6837	187	8	fix	fix	NOUN
ejpam-6837	187	9	t[c1c2	t[c1c2	NOUN
ejpam-6837	187	10	]	]	PUNCT
ejpam-6837	187	11	⊆	⊆	NUM
ejpam-6837	187	12	fix	fix	NOUN
ejpam-6837	187	13	tc1,c2	tc1,c2	NOUN
ejpam-6837	187	14	.	.	PUNCT
ejpam-6837	188	1	◦	◦	VERB
ejpam-6837	188	2	if	if	SCONJ
ejpam-6837	188	3	tc1,c2	tc1,c2	NOUN
ejpam-6837	188	4	x	x	SYM
ejpam-6837	188	5	∈	∈	PROPN
ejpam-6837	188	6	fix	fix	NOUN
ejpam-6837	188	7	tc2,c1	tc2,c1	NOUN
ejpam-6837	188	8	⇒	⇒	NOUN
ejpam-6837	188	9	tc1,c2	tc1,c2	NOUN
ejpam-6837	188	10	x	x	X
ejpam-6837	188	11	=	=	SYM
ejpam-6837	188	12	tc2,c1	tc2,c1	NOUN
ejpam-6837	188	13	tc1,c2	tc1,c2	NOUN
ejpam-6837	188	14	x	x	X
ejpam-6837	188	15	=	=	PUNCT
ejpam-6837	188	16	x	x	SYM
ejpam-6837	188	17	∈	∈	PROPN
ejpam-6837	188	18	fix	fix	NOUN
ejpam-6837	188	19	tc1,c2	tc1,c2	NOUN
ejpam-6837	188	20	⇒	⇒	NOUN
ejpam-6837	188	21	fix	fix	VERB
ejpam-6837	188	22	t[c1c2	t[c1c2	NOUN
ejpam-6837	188	23	]	]	PUNCT
ejpam-6837	188	24	⊆	⊆	NUM
ejpam-6837	188	25	fix	fix	NOUN
ejpam-6837	188	26	tc1,c2	tc1,c2	NOUN
ejpam-6837	188	27	.	.	PUNCT
ejpam-6837	189	1	◦	◦	NOUN
ejpam-6837	189	2	let	let	VERB
ejpam-6837	189	3	x	x	PRON
ejpam-6837	189	4	/∈	/∈	PUNCT
ejpam-6837	189	5	fix	fix	NOUN
ejpam-6837	189	6	tc2,c1	tc2,c1	NOUN
ejpam-6837	189	7	and	and	CCONJ
ejpam-6837	189	8	tc2,c1	tc2,c1	NOUN
ejpam-6837	189	9	x	x	SYM
ejpam-6837	189	10	/∈	/∈	PUNCT
ejpam-6837	190	1	fix	fix	NOUN
ejpam-6837	190	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	190	3	.	.	PUNCT
ejpam-6837	191	1	since	since	SCONJ
ejpam-6837	191	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	191	3	and	and	CCONJ
ejpam-6837	191	4	tc2,c1	tc2,c1	NOUN
ejpam-6837	191	5	are	be	AUX
ejpam-6837	191	6	firmly	firmly	ADV
ejpam-6837	191	7	nonexpansive	nonexpansive	ADJ
ejpam-6837	191	8	and	and	CCONJ
ejpam-6837	191	9	by	by	ADP
ejpam-6837	191	10	[	[	X
ejpam-6837	191	11	1	1	NUM
ejpam-6837	191	12	,	,	PUNCT
ejpam-6837	191	13	corollary	corollary	NOUN
ejpam-6837	191	14	2.15	2.15	NUM
ejpam-6837	191	15	]	]	X
ejpam-6837	191	16	they	they	PRON
ejpam-6837	191	17	are	be	AUX
ejpam-6837	191	18	strictly	strictly	ADV
ejpam-6837	191	19	quasinonexpansive	quasinonexpansive	ADJ
ejpam-6837	191	20	.	.	PUNCT
ejpam-6837	192	1	therefore	therefore	ADV
ejpam-6837	192	2	,	,	PUNCT
ejpam-6837	192	3	∥x	∥x	PROPN
ejpam-6837	192	4	−	−	PROPN
ejpam-6837	192	5	y∥	y∥	NOUN
ejpam-6837	192	6	=	=	PUNCT
ejpam-6837	192	7	∥tc2,c1	∥tc2,c1	PROPN
ejpam-6837	192	8	tc1,c2	tc1,c2	NOUN
ejpam-6837	192	9	x	x	PUNCT
ejpam-6837	192	10	−	−	PROPN
ejpam-6837	192	11	y∥	y∥	VERB
ejpam-6837	192	12	<	<	X
ejpam-6837	192	13	∥tc1,c2	∥tc1,c2	NUM
ejpam-6837	192	14	x	x	SYM
ejpam-6837	192	15	−	−	PROPN
ejpam-6837	192	16	y∥	y∥	NOUN
ejpam-6837	192	17	<	<	X
ejpam-6837	192	18	∥x	∥x	PROPN
ejpam-6837	192	19	−	−	PROPN
ejpam-6837	192	20	y∥	y∥	NOUN
ejpam-6837	192	21	which	which	PRON
ejpam-6837	192	22	is	be	AUX
ejpam-6837	192	23	not	not	PART
ejpam-6837	192	24	true	true	ADJ
ejpam-6837	192	25	.	.	PUNCT
ejpam-6837	193	1	therefore	therefore	ADV
ejpam-6837	193	2	,	,	PUNCT
ejpam-6837	193	3	fix	fix	NOUN
ejpam-6837	193	4	tc2,c1	tc2,c1	NOUN
ejpam-6837	193	5	tc1,c2	tc1,c2	NOUN
ejpam-6837	193	6	=	=	PUNCT
ejpam-6837	193	7	fix	fix	NOUN
ejpam-6837	193	8	tc1,c2	tc1,c2	NOUN
ejpam-6837	193	9	.	.	PUNCT
ejpam-6837	194	1	hypothesis	hypothesis	NOUN
ejpam-6837	194	2	induction	induction	NOUN
ejpam-6837	194	3	assumption	assumption	NOUN
ejpam-6837	194	4	:	:	PUNCT
ejpam-6837	194	5	for	for	ADP
ejpam-6837	194	6	n	n	PRON
ejpam-6837	194	7	≥	≥	NUM
ejpam-6837	194	8	2	2	NUM
ejpam-6837	194	9	the	the	DET
ejpam-6837	194	10	result	result	NOUN
ejpam-6837	194	11	holds	hold	VERB
ejpam-6837	194	12	up	up	ADP
ejpam-6837	194	13	to	to	ADP
ejpam-6837	194	14	n	n	NOUN
ejpam-6837	194	15	operators	operator	NOUN
ejpam-6837	194	16	.	.	PUNCT
ejpam-6837	195	1	we	we	PRON
ejpam-6837	195	2	have	have	AUX
ejpam-6837	195	3	fix	fix	VERB
ejpam-6837	195	4	t[c1c2···cn−1	t[c1c2···cn−1	NUM
ejpam-6837	195	5	]	]	X
ejpam-6837	195	6	=	=	SYM
ejpam-6837	195	7	n	n	NOUN
ejpam-6837	195	8	∩	∩	NOUN
ejpam-6837	195	9	i=1	i=1	PRON
ejpam-6837	195	10	fix	fix	NOUN
ejpam-6837	195	11	tci	tci	NOUN
ejpam-6837	195	12	,	,	PUNCT
ejpam-6837	195	13	ci+1	ci+1	PROPN
ejpam-6837	195	14	.	.	PUNCT
ejpam-6837	196	1	then	then	ADV
ejpam-6837	196	2	show	show	VERB
ejpam-6837	196	3	the	the	DET
ejpam-6837	196	4	results	result	NOUN
ejpam-6837	196	5	hold	hold	VERB
ejpam-6837	196	6	for	for	ADP
ejpam-6837	196	7	n	n	PROPN
ejpam-6837	196	8	+	+	CCONJ
ejpam-6837	196	9	1	1	NUM
ejpam-6837	196	10	operators	operator	NOUN
ejpam-6837	196	11	.	.	PUNCT
ejpam-6837	197	1	let	let	VERB
ejpam-6837	197	2	s1	s1	NOUN
ejpam-6837	197	3	=	=	PUNCT
ejpam-6837	197	4	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	197	5	.	.	PUNCT
ejpam-6837	197	6	.	.	PUNCT
ejpam-6837	197	7	.	.	PUNCT
ejpam-6837	198	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	198	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	198	3	and	and	CCONJ
ejpam-6837	198	4	let	let	VERB
ejpam-6837	198	5	s2	s2	VERB
ejpam-6837	198	6	=	=	PUNCT
ejpam-6837	198	7	tcn	tcn	PROPN
ejpam-6837	198	8	,	,	PUNCT
ejpam-6837	198	9	c1	c1	PROPN
ejpam-6837	198	10	because	because	SCONJ
ejpam-6837	198	11	s2	s2	PROPN
ejpam-6837	198	12	is	be	AUX
ejpam-6837	198	13	quasinonexpansive	quasinonexpansive	ADJ
ejpam-6837	198	14	with	with	ADP
ejpam-6837	198	15	fix	fix	NOUN
ejpam-6837	198	16	s2	s2	NOUN
ejpam-6837	198	17	=	=	PUNCT
ejpam-6837	198	18	fix	fix	NOUN
ejpam-6837	198	19	tcn	tcn	NOUN
ejpam-6837	198	20	,	,	PUNCT
ejpam-6837	198	21	c1	c1	PROPN
ejpam-6837	198	22	and	and	CCONJ
ejpam-6837	198	23	by	by	ADP
ejpam-6837	198	24	the	the	DET
ejpam-6837	198	25	induction	induction	NOUN
ejpam-6837	198	26	hypothesis	hypothesis	NOUN
ejpam-6837	198	27	we	we	PRON
ejpam-6837	198	28	have	have	VERB
ejpam-6837	198	29	,	,	PUNCT
ejpam-6837	198	30	fix	fix	VERB
ejpam-6837	198	31	s1	s1	NOUN
ejpam-6837	198	32	=	=	SYM
ejpam-6837	198	33	n	n	NOUN
ejpam-6837	198	34	∩	∩	NOUN
ejpam-6837	198	35	i=1	i=1	PRON
ejpam-6837	198	36	fix	fix	NOUN
ejpam-6837	198	37	tci	tci	NOUN
ejpam-6837	198	38	,	,	PUNCT
ejpam-6837	198	39	ci+1	ci+1	PROPN
ejpam-6837	198	40	.	.	PUNCT
ejpam-6837	199	1	therefore	therefore	ADV
ejpam-6837	199	2	,	,	PUNCT
ejpam-6837	199	3	by	by	ADP
ejpam-6837	199	4	the	the	DET
ejpam-6837	199	5	fact	fact	NOUN
ejpam-6837	199	6	that	that	SCONJ
ejpam-6837	199	7	s1s2	s1s2	PROPN
ejpam-6837	199	8	=	=	SYM
ejpam-6837	199	9	tcn	tcn	NOUN
ejpam-6837	199	10	,	,	PUNCT
ejpam-6837	199	11	c1	c1	PROPN
ejpam-6837	199	12	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	199	13	·	·	PUNCT
ejpam-6837	199	14	·	·	PUNCT
ejpam-6837	199	15	·	·	PUNCT
ejpam-6837	199	16	tc2,c3	tc2,c3	PROPN
ejpam-6837	199	17	tc1,c2	tc1,c2	NOUN
ejpam-6837	199	18	is	be	AUX
ejpam-6837	199	19	strictly	strictly	ADV
ejpam-6837	199	20	quasinonexpansive	quasinonexpansive	ADJ
ejpam-6837	199	21	then	then	ADV
ejpam-6837	199	22	,	,	PUNCT
ejpam-6837	199	23	fix	fix	NOUN
ejpam-6837	199	24	tcn	tcn	NOUN
ejpam-6837	199	25	,	,	PUNCT
ejpam-6837	199	26	c1	c1	PROPN
ejpam-6837	199	27	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	199	28	.	.	PUNCT
ejpam-6837	199	29	.	.	PUNCT
ejpam-6837	199	30	.	.	PUNCT
ejpam-6837	200	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	200	2	tc1,c2	tc1,c2	NOUN
ejpam-6837	200	3	=	=	PUNCT
ejpam-6837	200	4	fix	fix	NOUN
ejpam-6837	200	5	s1s2	s1s2	PROPN
ejpam-6837	200	6	=	=	PUNCT
ejpam-6837	200	7	fix	fix	NOUN
ejpam-6837	200	8	s1	s1	NOUN
ejpam-6837	200	9	∩	∩	ADJ
ejpam-6837	200	10	s2	s2	NOUN
ejpam-6837	200	11	=	=	SYM
ejpam-6837	200	12	n+1	n+1	PROPN
ejpam-6837	200	13	∩	∩	NOUN
ejpam-6837	200	14	i=1	i=1	PRON
ejpam-6837	200	15	fix	fix	NOUN
ejpam-6837	200	16	tci	tci	NOUN
ejpam-6837	200	17	,	,	PUNCT
ejpam-6837	200	18	ci+1	ci+1	PROPN
ejpam-6837	200	19	■	■	PUNCT
ejpam-6837	200	20	theorem	theorem	ADJ
ejpam-6837	200	21	1	1	NUM
ejpam-6837	200	22	.	.	PUNCT
ejpam-6837	201	1	let	let	VERB
ejpam-6837	201	2	tci	tci	VERB
ejpam-6837	201	3	,	,	PUNCT
ejpam-6837	201	4	ci+1	ci+1	PUNCT
ejpam-6837	201	5	:	:	PUNCT
ejpam-6837	201	6	h→h	h→h	NOUN
ejpam-6837	201	7	be	be	VERB
ejpam-6837	201	8	firmly	firmly	ADV
ejpam-6837	201	9	nonexpansive	nonexpansive	ADJ
ejpam-6837	201	10	for	for	ADP
ejpam-6837	201	11	each	each	DET
ejpam-6837	201	12	i	i	NOUN
ejpam-6837	201	13	,	,	PUNCT
ejpam-6837	201	14	with	with	ADP
ejpam-6837	201	15	n+1	n+1	PROPN
ejpam-6837	201	16	∩	∩	NOUN
ejpam-6837	202	1	i=1	i=1	PRON
ejpam-6837	202	2	fix	fix	NOUN
ejpam-6837	202	3	tci	tci	NOUN
ejpam-6837	202	4	,	,	PUNCT
ejpam-6837	202	5	ci+1	ci+1	PROPN
ejpam-6837	202	6	̸=∅.	̸=∅.	NOUN
ejpam-6837	202	7	then	then	ADV
ejpam-6837	202	8	,	,	PUNCT
ejpam-6837	202	9	for	for	ADP
ejpam-6837	202	10	any	any	DET
ejpam-6837	202	11	x0	x0	PROPN
ejpam-6837	202	12	∈	∈	PROPN
ejpam-6837	202	13	h	h	NOUN
ejpam-6837	202	14	,	,	PUNCT
ejpam-6837	202	15	the	the	DET
ejpam-6837	202	16	sequence	sequence	NOUN
ejpam-6837	202	17	tn	tn	PROPN
ejpam-6837	203	1	[	[	X
ejpam-6837	203	2	c1c2	c1c2	NOUN
ejpam-6837	203	3	...	...	PUNCT
ejpam-6837	203	4	cn	cn	X
ejpam-6837	203	5	]	]	X
ejpam-6837	204	1	x0	x0	PUNCT
ejpam-6837	204	2	⇀	⇀	PUNCT
ejpam-6837	204	3	x	x	PUNCT
ejpam-6837	204	4	∈	∈	PROPN
ejpam-6837	204	5	n+1	n+1	PROPN
ejpam-6837	204	6	∩	∩	X
ejpam-6837	204	7	i=1	i=1	PROPN
ejpam-6837	204	8	fix	fix	NOUN
ejpam-6837	204	9	tci	tci	NOUN
ejpam-6837	204	10	,	,	PUNCT
ejpam-6837	204	11	ci+1	ci+1	PROPN
ejpam-6837	204	12	.	.	PUNCT
ejpam-6837	205	1	s.	s.	PROPN
ejpam-6837	205	2	th	th	PROPN
ejpam-6837	205	3	.	.	PUNCT
ejpam-6837	206	1	alwadani	alwadani	PROPN
ejpam-6837	206	2	/	/	SYM
ejpam-6837	206	3	eur	eur	PROPN
ejpam-6837	206	4	.	.	PUNCT
ejpam-6837	207	1	j.	j.	PROPN
ejpam-6837	207	2	pure	pure	PROPN
ejpam-6837	207	3	appl	appl	PROPN
ejpam-6837	207	4	.	.	PROPN
ejpam-6837	207	5	math	math	PROPN
ejpam-6837	207	6	,	,	PUNCT
ejpam-6837	207	7	18	18	NUM
ejpam-6837	207	8	(	(	PUNCT
ejpam-6837	207	9	4	4	NUM
ejpam-6837	207	10	)	)	PUNCT
ejpam-6837	207	11	(	(	PUNCT
ejpam-6837	207	12	2025	2025	NUM
ejpam-6837	207	13	)	)	PUNCT
ejpam-6837	207	14	,	,	PUNCT
ejpam-6837	207	15	6837	6837	NUM
ejpam-6837	207	16	9	9	NUM
ejpam-6837	207	17	of	of	ADP
ejpam-6837	207	18	15	15	NUM
ejpam-6837	207	19	proof	proof	NOUN
ejpam-6837	207	20	.	.	PUNCT
ejpam-6837	208	1	first	first	ADV
ejpam-6837	208	2	,	,	PUNCT
ejpam-6837	208	3	show	show	VERB
ejpam-6837	208	4	that	that	SCONJ
ejpam-6837	208	5	every	every	DET
ejpam-6837	208	6	weak	weak	ADJ
ejpam-6837	208	7	cluster	cluster	NOUN
ejpam-6837	208	8	point	point	NOUN
ejpam-6837	208	9	x	x	PUNCT
ejpam-6837	208	10	of	of	ADP
ejpam-6837	208	11	(	(	PUNCT
ejpam-6837	208	12	xn)∈n	xn)∈n	PROPN
ejpam-6837	208	13	lies	lie	VERB
ejpam-6837	208	14	in	in	ADP
ejpam-6837	208	15	fix	fix	NOUN
ejpam-6837	208	16	t[c1c2	t[c1c2	PROPN
ejpam-6837	208	17	...	...	PUNCT
ejpam-6837	208	18	cn	cn	X
ejpam-6837	208	19	]	]	X
ejpam-6837	208	20	.	.	PUNCT
ejpam-6837	209	1	by	by	ADP
ejpam-6837	209	2	section	section	NOUN
ejpam-6837	209	3	4	4	NUM
ejpam-6837	209	4	(	(	PUNCT
ejpam-6837	209	5	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	209	6	is	be	AUX
ejpam-6837	209	7	fejér	fejér	VERB
ejpam-6837	209	8	montone	montone	NOUN
ejpam-6837	209	9	with	with	ADP
ejpam-6837	209	10	respect	respect	NOUN
ejpam-6837	209	11	to	to	PART
ejpam-6837	209	12	fix	fix	VERB
ejpam-6837	209	13	t[c1c2	t[c1c2	PROPN
ejpam-6837	209	14	...	...	PUNCT
ejpam-6837	210	1	cn	cn	X
ejpam-6837	210	2	]	]	X
ejpam-6837	210	3	,	,	PUNCT
ejpam-6837	210	4	it	it	PRON
ejpam-6837	210	5	is	be	AUX
ejpam-6837	210	6	bounded	bound	VERB
ejpam-6837	210	7	.	.	PUNCT
ejpam-6837	211	1	let	let	VERB
ejpam-6837	211	2	x	x	PRON
ejpam-6837	211	3	be	be	AUX
ejpam-6837	211	4	a	a	DET
ejpam-6837	211	5	weak	weak	ADJ
ejpam-6837	211	6	sequential	sequential	ADJ
ejpam-6837	211	7	cluster	cluster	NOUN
ejpam-6837	211	8	point	point	NOUN
ejpam-6837	211	9	of	of	ADP
ejpam-6837	211	10	(	(	PUNCT
ejpam-6837	211	11	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	211	12	.	.	PUNCT
ejpam-6837	212	1	then	then	ADV
ejpam-6837	212	2	,	,	PUNCT
ejpam-6837	212	3	there	there	PRON
ejpam-6837	212	4	exists	exist	VERB
ejpam-6837	212	5	a	a	DET
ejpam-6837	212	6	subsequence	subsequence	NOUN
ejpam-6837	212	7	xnk	xnk	NOUN
ejpam-6837	212	8	of	of	ADP
ejpam-6837	212	9	xn	xn	PROPN
ejpam-6837	213	1	such	such	ADJ
ejpam-6837	213	2	that	that	SCONJ
ejpam-6837	213	3	xnk	xnk	PROPN
ejpam-6837	213	4	⇀	⇀	INTJ
ejpam-6837	213	5	x.∥∥∥x	x.∥∥∥x	PUNCT
ejpam-6837	214	1	−	−	NOUN
ejpam-6837	214	2	t[c1	t[c1	ADP
ejpam-6837	214	3	...	...	PUNCT
ejpam-6837	214	4	cn	cn	X
ejpam-6837	215	1	]	]	X
ejpam-6837	215	2	x	x	SYM
ejpam-6837	215	3	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	215	4	=	=	NOUN
ejpam-6837	216	1	∥∥∥xnk	∥∥∥xnk	INTJ
ejpam-6837	217	1	−	−	PROPN
ejpam-6837	217	2	t[c1	t[c1	NUM
ejpam-6837	217	3	...	...	PUNCT
ejpam-6837	217	4	cn	cn	X
ejpam-6837	218	1	]	]	X
ejpam-6837	218	2	x	x	SYM
ejpam-6837	218	3	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	218	4	−	−	PROPN
ejpam-6837	218	5	∥xnk	∥xnk	PROPN
ejpam-6837	218	6	−	−	PROPN
ejpam-6837	218	7	x∥2	x∥2	NOUN
ejpam-6837	218	8	−	−	PROPN
ejpam-6837	218	9	2	2	NUM
ejpam-6837	218	10	〈	〈	NOUN
ejpam-6837	218	11	xnk	xnk	NOUN
ejpam-6837	218	12	−	−	NOUN
ejpam-6837	218	13	x	x	SYM
ejpam-6837	218	14	,	,	PUNCT
ejpam-6837	218	15	x	x	INTJ
ejpam-6837	218	16	−	−	NOUN
ejpam-6837	218	17	t[c1	t[c1	X
ejpam-6837	218	18	...	...	PUNCT
ejpam-6837	218	19	cn	cn	X
ejpam-6837	218	20	]	]	X
ejpam-6837	218	21	x	x	SYM
ejpam-6837	218	22	〉	〉	NOUN
ejpam-6837	218	23	=	=	PUNCT
ejpam-6837	218	24	∥∥∥xnk	∥∥∥xnk	NOUN
ejpam-6837	218	25	−	−	PROPN
ejpam-6837	219	1	t[c1	t[c1	NUM
ejpam-6837	219	2	...	...	PUNCT
ejpam-6837	219	3	cn	cn	X
ejpam-6837	219	4	]	]	X
ejpam-6837	219	5	x	x	X
ejpam-6837	220	1	+	+	CCONJ
ejpam-6837	220	2	t[c1	t[c1	PRON
ejpam-6837	220	3	...	...	PUNCT
ejpam-6837	220	4	cn	cn	X
ejpam-6837	220	5	]	]	X
ejpam-6837	220	6	xnk	xnk	PROPN
ejpam-6837	220	7	−	−	PROPN
ejpam-6837	220	8	t[c1	t[c1	ADP
ejpam-6837	220	9	...	...	PUNCT
ejpam-6837	221	1	cn	cn	X
ejpam-6837	222	1	]	]	X
ejpam-6837	222	2	xnk	xnk	PROPN
ejpam-6837	222	3	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	222	4	−	−	PROPN
ejpam-6837	222	5	∥xnk	∥xnk	PROPN
ejpam-6837	223	1	−	−	PROPN
ejpam-6837	223	2	x∥2	x∥2	NOUN
ejpam-6837	223	3	−	−	PROPN
ejpam-6837	223	4	2	2	NUM
ejpam-6837	223	5	〈	〈	NOUN
ejpam-6837	223	6	xnk	xnk	NOUN
ejpam-6837	223	7	−	−	NOUN
ejpam-6837	224	1	x	x	SYM
ejpam-6837	224	2	,	,	PUNCT
ejpam-6837	224	3	x	x	INTJ
ejpam-6837	224	4	−	−	NOUN
ejpam-6837	224	5	t[c1	t[c1	X
ejpam-6837	224	6	...	...	PUNCT
ejpam-6837	224	7	cn	cn	X
ejpam-6837	224	8	]	]	X
ejpam-6837	224	9	x	x	SYM
ejpam-6837	224	10	〉	〉	NOUN
ejpam-6837	224	11	=	=	PUNCT
ejpam-6837	224	12	∥∥∥xnk	∥∥∥xnk	NOUN
ejpam-6837	224	13	−	−	PROPN
ejpam-6837	225	1	t[c1	t[c1	NUM
ejpam-6837	225	2	...	...	PUNCT
ejpam-6837	226	1	cn	cn	X
ejpam-6837	226	2	]	]	X
ejpam-6837	227	1	xnk	xnk	PROPN
ejpam-6837	227	2	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	228	1	+	+	CCONJ
ejpam-6837	228	2	2	2	NUM
ejpam-6837	228	3	〈	〈	NOUN
ejpam-6837	228	4	xnk	xnk	NOUN
ejpam-6837	228	5	−	−	PROPN
ejpam-6837	228	6	t[c1	t[c1	PRON
ejpam-6837	228	7	...	...	PUNCT
ejpam-6837	229	1	cn	cn	X
ejpam-6837	229	2	]	]	X
ejpam-6837	229	3	xnk	xnk	PROPN
ejpam-6837	229	4	,	,	PUNCT
ejpam-6837	229	5	t[c1	t[c1	ADV
ejpam-6837	229	6	...	...	PUNCT
ejpam-6837	230	1	cn	cn	X
ejpam-6837	231	1	]	]	X
ejpam-6837	231	2	xnk	xnk	PROPN
ejpam-6837	232	1	−	−	PROPN
ejpam-6837	232	2	t[c1···cn	t[c1···cn	PROPN
ejpam-6837	232	3	]	]	X
ejpam-6837	232	4	x	x	SYM
ejpam-6837	232	5	〉	〉	NOUN
ejpam-6837	232	6	+	+	CCONJ
ejpam-6837	232	7	∥∥∥t[c1	∥∥∥t[c1	NOUN
ejpam-6837	232	8	...	...	PUNCT
ejpam-6837	232	9	cn	cn	X
ejpam-6837	233	1	]	]	X
ejpam-6837	233	2	xnk	xnk	PROPN
ejpam-6837	234	1	−	−	PROPN
ejpam-6837	234	2	t[c1	t[c1	PRON
ejpam-6837	234	3	...	...	PUNCT
ejpam-6837	235	1	cn	cn	X
ejpam-6837	236	1	]	]	X
ejpam-6837	236	2	x	x	SYM
ejpam-6837	236	3	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	236	4	−	−	PROPN
ejpam-6837	236	5	∥xnk	∥xnk	PROPN
ejpam-6837	236	6	−	−	PROPN
ejpam-6837	236	7	x∥2	x∥2	NOUN
ejpam-6837	236	8	−	−	PROPN
ejpam-6837	236	9	2	2	NUM
ejpam-6837	236	10	〈	〈	NOUN
ejpam-6837	236	11	xnk	xnk	NOUN
ejpam-6837	236	12	−	−	NOUN
ejpam-6837	236	13	x	x	SYM
ejpam-6837	236	14	,	,	PUNCT
ejpam-6837	236	15	x	x	INTJ
ejpam-6837	236	16	−	−	NOUN
ejpam-6837	236	17	t[c1	t[c1	NUM
ejpam-6837	236	18	...	...	PUNCT
ejpam-6837	236	19	cn	cn	X
ejpam-6837	236	20	]	]	X
ejpam-6837	236	21	x	x	SYM
ejpam-6837	236	22	〉	〉	NOUN
ejpam-6837	236	23	§	§	NOUN
ejpam-6837	236	24	≤	≤	NOUN
ejpam-6837	236	25	∥∥∥xnk	∥∥∥xnk	X
ejpam-6837	237	1	−	−	PROPN
ejpam-6837	237	2	t[c1	t[c1	ADP
ejpam-6837	237	3	...	...	PUNCT
ejpam-6837	237	4	cn	cn	X
ejpam-6837	237	5	]	]	X
ejpam-6837	238	1	xnk	xnk	PROPN
ejpam-6837	238	2	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	239	1	+	+	CCONJ
ejpam-6837	239	2	2	2	NUM
ejpam-6837	239	3	〈	〈	NOUN
ejpam-6837	239	4	xnk	xnk	NOUN
ejpam-6837	239	5	−	−	PROPN
ejpam-6837	239	6	t[c1	t[c1	PRON
ejpam-6837	239	7	...	...	PUNCT
ejpam-6837	240	1	cn	cn	X
ejpam-6837	240	2	]	]	X
ejpam-6837	240	3	xnk	xnk	PROPN
ejpam-6837	240	4	,	,	PUNCT
ejpam-6837	240	5	t[c1	t[c1	ADV
ejpam-6837	240	6	...	...	PUNCT
ejpam-6837	241	1	cn	cn	X
ejpam-6837	242	1	]	]	X
ejpam-6837	242	2	xnk	xnk	PROPN
ejpam-6837	243	1	−	−	PROPN
ejpam-6837	243	2	t[c1	t[c1	PRON
ejpam-6837	243	3	...	...	PUNCT
ejpam-6837	244	1	cn	cn	X
ejpam-6837	244	2	]	]	X
ejpam-6837	244	3	x	x	SYM
ejpam-6837	244	4	〉	〉	NOUN
ejpam-6837	244	5	+	+	CCONJ
ejpam-6837	244	6	∥xnk	∥xnk	PROPN
ejpam-6837	244	7	−	−	VERB
ejpam-6837	244	8	x∥2	x∥2	NOUN
ejpam-6837	244	9	−	−	PROPN
ejpam-6837	244	10	∥xnk	∥xnk	PROPN
ejpam-6837	244	11	−	−	PROPN
ejpam-6837	244	12	x∥2	x∥2	NOUN
ejpam-6837	244	13	−	−	PROPN
ejpam-6837	244	14	2	2	NUM
ejpam-6837	244	15	〈	〈	NOUN
ejpam-6837	244	16	xnk	xnk	NOUN
ejpam-6837	244	17	−	−	NOUN
ejpam-6837	245	1	x	x	SYM
ejpam-6837	245	2	,	,	PUNCT
ejpam-6837	245	3	x	x	INTJ
ejpam-6837	245	4	−	−	NOUN
ejpam-6837	245	5	t[c1	t[c1	X
ejpam-6837	245	6	...	...	PUNCT
ejpam-6837	245	7	cn	cn	X
ejpam-6837	245	8	]	]	X
ejpam-6837	245	9	x	x	SYM
ejpam-6837	245	10	〉	〉	NOUN
ejpam-6837	245	11	=	=	PUNCT
ejpam-6837	245	12	∥∥∥xnk	∥∥∥xnk	NOUN
ejpam-6837	245	13	−	−	PROPN
ejpam-6837	246	1	t[c1	t[c1	NUM
ejpam-6837	246	2	...	...	PUNCT
ejpam-6837	247	1	cn	cn	X
ejpam-6837	247	2	]	]	X
ejpam-6837	248	1	xnk	xnk	PROPN
ejpam-6837	248	2	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	249	1	+	+	CCONJ
ejpam-6837	249	2	2	2	NUM
ejpam-6837	249	3	〈	〈	NOUN
ejpam-6837	249	4	xnk	xnk	NOUN
ejpam-6837	249	5	−	−	PROPN
ejpam-6837	249	6	t[c1	t[c1	PRON
ejpam-6837	249	7	...	...	PUNCT
ejpam-6837	250	1	cn	cn	X
ejpam-6837	250	2	]	]	X
ejpam-6837	250	3	xnk	xnk	PROPN
ejpam-6837	250	4	,	,	PUNCT
ejpam-6837	250	5	t[c1	t[c1	ADV
ejpam-6837	250	6	...	...	PUNCT
ejpam-6837	251	1	cn	cn	X
ejpam-6837	252	1	]	]	X
ejpam-6837	252	2	xnk	xnk	PROPN
ejpam-6837	253	1	−	−	PROPN
ejpam-6837	253	2	t[c1	t[c1	PRON
ejpam-6837	253	3	...	...	PUNCT
ejpam-6837	254	1	cn	cn	X
ejpam-6837	254	2	]	]	X
ejpam-6837	254	3	x	x	SYM
ejpam-6837	254	4	〉	〉	NOUN
ejpam-6837	254	5	−	−	PROPN
ejpam-6837	254	6	2	2	NUM
ejpam-6837	254	7	〈	〈	NOUN
ejpam-6837	254	8	xnk	xnk	NOUN
ejpam-6837	255	1	−	−	NOUN
ejpam-6837	255	2	x	x	SYM
ejpam-6837	255	3	,	,	PUNCT
ejpam-6837	255	4	x	x	INTJ
ejpam-6837	255	5	−	−	NOUN
ejpam-6837	255	6	t[c1	t[c1	NUM
ejpam-6837	255	7	...	...	PUNCT
ejpam-6837	255	8	cn	cn	X
ejpam-6837	255	9	]	]	X
ejpam-6837	255	10	x	x	SYM
ejpam-6837	255	11	〉	〉	NOUN
ejpam-6837	255	12	note	note	VERB
ejpam-6837	255	13	that	that	SCONJ
ejpam-6837	255	14	;	;	PUNCT
ejpam-6837	255	15	∥∥∥〈xnk	∥∥∥〈xnk	PROPN
ejpam-6837	255	16	−	−	PROPN
ejpam-6837	255	17	t[c1	t[c1	ADP
ejpam-6837	255	18	...	...	PUNCT
ejpam-6837	255	19	cn	cn	X
ejpam-6837	256	1	]	]	X
ejpam-6837	256	2	xnk	xnk	PROPN
ejpam-6837	256	3	,	,	PUNCT
ejpam-6837	256	4	t[c1	t[c1	ADV
ejpam-6837	256	5	...	...	PUNCT
ejpam-6837	256	6	cn	cn	X
ejpam-6837	257	1	]	]	X
ejpam-6837	257	2	xnk	xnk	PROPN
ejpam-6837	258	1	−	−	PROPN
ejpam-6837	258	2	t[c1	t[c1	PRON
ejpam-6837	258	3	...	...	PUNCT
ejpam-6837	259	1	cn	cn	X
ejpam-6837	259	2	]	]	X
ejpam-6837	259	3	x	x	SYM
ejpam-6837	259	4	〉	〉	PROPN
ejpam-6837	259	5	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	259	6	¶	¶	NOUN
ejpam-6837	259	7	≤	≤	NUM
ejpam-6837	260	1	∥∥∥xnk	∥∥∥xnk	X
ejpam-6837	261	1	−	−	PROPN
ejpam-6837	262	1	t[c1	t[c1	PRON
ejpam-6837	262	2	...	...	PUNCT
ejpam-6837	263	1	cn	cn	X
ejpam-6837	263	2	]	]	X
ejpam-6837	263	3	xnk	xnk	PROPN
ejpam-6837	263	4	∥∥∥2	∥∥∥2	PROPN
ejpam-6837	263	5	∥∥∥t[c1	∥∥∥t[c1	PUNCT
ejpam-6837	263	6	...	...	PUNCT
ejpam-6837	264	1	cn	cn	X
ejpam-6837	264	2	]	]	X
ejpam-6837	264	3	xnk	xnk	PROPN
ejpam-6837	264	4	−	−	PROPN
ejpam-6837	264	5	t[c1	t[c1	ADP
ejpam-6837	264	6	...	...	PUNCT
ejpam-6837	265	1	cn	cn	X
ejpam-6837	266	1	]	]	X
ejpam-6837	266	2	x	x	SYM
ejpam-6837	266	3	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	266	4	||	||	NOUN
ejpam-6837	267	1	≤	≤	NUM
ejpam-6837	268	1	∥∥∥xnk	∥∥∥xnk	X
ejpam-6837	269	1	−	−	NOUN
ejpam-6837	270	1	t[c1	t[c1	PRON
ejpam-6837	270	2	...	...	PUNCT
ejpam-6837	271	1	cn	cn	X
ejpam-6837	271	2	]	]	X
ejpam-6837	272	1	xnk	xnk	PROPN
ejpam-6837	272	2	∥∥∥2	∥∥∥2	X
ejpam-6837	272	3	∥xnk	∥xnk	PROPN
ejpam-6837	272	4	−	−	VERB
ejpam-6837	273	1	x∥2	x∥2	NOUN
ejpam-6837	274	1	=	=	PUNCT
ejpam-6837	275	1	∥∥∥xnk	∥∥∥xnk	INTJ
ejpam-6837	276	1	−	−	NOUN
ejpam-6837	277	1	t[c1	t[c1	PRON
ejpam-6837	277	2	...	...	PUNCT
ejpam-6837	278	1	cn	cn	X
ejpam-6837	278	2	]	]	X
ejpam-6837	279	1	xnk	xnk	PROPN
ejpam-6837	279	2	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	279	3	(	(	PUNCT
ejpam-6837	279	4	∥xnk∥2	∥xnk∥2	ADV
ejpam-6837	279	5	−	−	NUM
ejpam-6837	279	6	2	2	NUM
ejpam-6837	279	7	⟨xnk	⟨xnk	NOUN
ejpam-6837	279	8	,	,	PUNCT
ejpam-6837	279	9	x⟩	x⟩	PUNCT
ejpam-6837	279	10	+	+	CCONJ
ejpam-6837	279	11	∥x∥2	∥x∥2	NOUN
ejpam-6837	279	12	)	)	PUNCT
ejpam-6837	279	13	≤	≤	NUM
ejpam-6837	280	1	∥∥∥xnk	∥∥∥xnk	X
ejpam-6837	281	1	−	−	NOUN
ejpam-6837	282	1	t[c1	t[c1	PRON
ejpam-6837	282	2	...	...	PUNCT
ejpam-6837	283	1	cn	cn	X
ejpam-6837	283	2	]	]	X
ejpam-6837	284	1	xnk	xnk	PROPN
ejpam-6837	284	2	∥∥∥2	∥∥∥2	NOUN
ejpam-6837	284	3	(	(	PUNCT
ejpam-6837	284	4	∥xnk∥2	∥xnk∥2	ADV
ejpam-6837	284	5	−	−	NUM
ejpam-6837	284	6	2∥xnk∥∥x∥	2∥xnk∥∥x∥	NUM
ejpam-6837	284	7	+	+	CCONJ
ejpam-6837	284	8	∥x∥2	∥x∥2	NOUN
ejpam-6837	284	9	)	)	PUNCT
ejpam-6837	284	10	therefore	therefore	ADV
ejpam-6837	284	11	,	,	PUNCT
ejpam-6837	284	12	sup∥xnk∥	sup∥xnk∥	NOUN
ejpam-6837	284	13	=	=	PUNCT
ejpam-6837	284	14	m	m	VERB
ejpam-6837	284	15	<	<	X
ejpam-6837	284	16	∞.	∞.	PROPN
ejpam-6837	284	17	also	also	ADV
ejpam-6837	284	18	,	,	PUNCT
ejpam-6837	284	19	xnk	xnk	PROPN
ejpam-6837	284	20	⇀	⇀	VERB
ejpam-6837	284	21	x.	x.	NOUN
ejpam-6837	284	22	then	then	ADV
ejpam-6837	284	23	∥x∥	∥x∥	NOUN
ejpam-6837	285	1	=	=	PROPN
ejpam-6837	285	2	lim	lim	PROPN
ejpam-6837	285	3	|	|	ADV
ejpam-6837	285	4	⟨xnk	⟨xnk	PROPN
ejpam-6837	285	5	,	,	PUNCT
ejpam-6837	285	6	x⟩	x⟩	PUNCT
ejpam-6837	286	1	|	|	ADV
ejpam-6837	286	2	≤	≤	NUM
ejpam-6837	286	3	lim	lim	PROPN
ejpam-6837	286	4	∥xnk∥<∞.	∥xnk∥<∞.	NUM
ejpam-6837	286	5	§	§	PROPN
ejpam-6837	286	6	follows	follow	VERB
ejpam-6837	286	7	from	from	ADP
ejpam-6837	286	8	the	the	DET
ejpam-6837	286	9	nonexpansiveness	nonexpansiveness	NOUN
ejpam-6837	286	10	of	of	ADP
ejpam-6837	286	11	t[c1	t[c1	PRON
ejpam-6837	286	12	...	...	PUNCT
ejpam-6837	287	1	cn	cn	X
ejpam-6837	287	2	]	]	X
ejpam-6837	287	3	.	.	PUNCT
ejpam-6837	288	1	¶follows	¶follow	NOUN
ejpam-6837	288	2	from	from	ADP
ejpam-6837	288	3	cauchy	cauchy	NOUN
ejpam-6837	288	4	-	-	PUNCT
ejpam-6837	288	5	schwarz	schwarz	PROPN
ejpam-6837	288	6	inequality	inequality	NOUN
ejpam-6837	288	7	|	|	ADV
ejpam-6837	288	8	⟨x	⟨x	VERB
ejpam-6837	288	9	,	,	PUNCT
ejpam-6837	288	10	y⟩	y⟩	NOUN
ejpam-6837	288	11	|≤	|≤	PROPN
ejpam-6837	288	12	∥x∥∥y∥.	∥x∥∥y∥.	PROPN
ejpam-6837	288	13	∥follows	∥follow	VERB
ejpam-6837	288	14	from	from	ADP
ejpam-6837	288	15	the	the	DET
ejpam-6837	288	16	nonexpansiveness	nonexpansiveness	NOUN
ejpam-6837	288	17	of	of	ADP
ejpam-6837	288	18	t[c1	t[c1	PRON
ejpam-6837	288	19	...	...	PUNCT
ejpam-6837	289	1	cn	cn	X
ejpam-6837	289	2	]	]	X
ejpam-6837	289	3	.	.	PUNCT
ejpam-6837	290	1	s.	s.	PROPN
ejpam-6837	290	2	th	th	PROPN
ejpam-6837	290	3	.	.	PUNCT
ejpam-6837	291	1	alwadani	alwadani	PROPN
ejpam-6837	291	2	/	/	SYM
ejpam-6837	291	3	eur	eur	PROPN
ejpam-6837	291	4	.	.	PUNCT
ejpam-6837	292	1	j.	j.	PROPN
ejpam-6837	292	2	pure	pure	PROPN
ejpam-6837	292	3	appl	appl	PROPN
ejpam-6837	292	4	.	.	PROPN
ejpam-6837	292	5	math	math	PROPN
ejpam-6837	292	6	,	,	PUNCT
ejpam-6837	292	7	18	18	NUM
ejpam-6837	292	8	(	(	PUNCT
ejpam-6837	292	9	4	4	NUM
ejpam-6837	292	10	)	)	PUNCT
ejpam-6837	292	11	(	(	PUNCT
ejpam-6837	292	12	2025	2025	NUM
ejpam-6837	292	13	)	)	PUNCT
ejpam-6837	292	14	,	,	PUNCT
ejpam-6837	292	15	6837	6837	NUM
ejpam-6837	292	16	10	10	NUM
ejpam-6837	292	17	of	of	ADP
ejpam-6837	292	18	15	15	NUM
ejpam-6837	292	19	therefore	therefore	ADV
ejpam-6837	292	20	,	,	PUNCT
ejpam-6837	292	21	(	(	PUNCT
ejpam-6837	292	22	∥xnk∥2	∥xnk∥2	ADV
ejpam-6837	292	23	−	−	NUM
ejpam-6837	292	24	2∥xnk∥∥x∥	2∥xnk∥∥x∥	NUM
ejpam-6837	292	25	+	+	CCONJ
ejpam-6837	292	26	∥x∥2	∥x∥2	NOUN
ejpam-6837	292	27	)	)	PUNCT
ejpam-6837	293	1	<	<	X
ejpam-6837	293	2	∞.	∞.	PROPN
ejpam-6837	293	3	hence	hence	ADV
ejpam-6837	293	4	,	,	PUNCT
ejpam-6837	293	5	taking	take	VERB
ejpam-6837	293	6	the	the	DET
ejpam-6837	293	7	limit	limit	NOUN
ejpam-6837	293	8	as	as	ADP
ejpam-6837	293	9	n	n	PROPN
ejpam-6837	293	10	→	→	SYM
ejpam-6837	293	11	∞	∞	PROPN
ejpam-6837	293	12	,	,	PUNCT
ejpam-6837	293	13	we	we	PRON
ejpam-6837	293	14	have	have	VERB
ejpam-6837	293	15	∥xnk	∥xnk	PROPN
ejpam-6837	293	16	−	−	PROPN
ejpam-6837	293	17	t[c1	t[c1	ADV
ejpam-6837	293	18	...	...	PUNCT
ejpam-6837	294	1	cn	cn	X
ejpam-6837	295	1	]	]	X
ejpam-6837	295	2	xnk∥2	xnk∥2	PROPN
ejpam-6837	295	3	(	(	PUNCT
ejpam-6837	295	4	∥xnk∥2	∥xnk∥2	ADV
ejpam-6837	295	5	−	−	PROPN
ejpam-6837	295	6	2∥xnk∥∥x∥+	2∥xnk∥∥x∥+	NUM
ejpam-6837	295	7	∥x∥2	∥x∥2	NOUN
ejpam-6837	295	8	)	)	PUNCT
ejpam-6837	295	9	→	→	SYM
ejpam-6837	295	10	0	0	NUM
ejpam-6837	296	1	moreover	moreover	ADV
ejpam-6837	296	2	,	,	PUNCT
ejpam-6837	296	3	xnk	xnk	PROPN
ejpam-6837	296	4	−	−	PROPN
ejpam-6837	296	5	t[c1	t[c1	ADP
ejpam-6837	296	6	...	...	PUNCT
ejpam-6837	296	7	cn	cn	X
ejpam-6837	297	1	]	]	X
ejpam-6837	297	2	xnk	xnk	PROPN
ejpam-6837	297	3	→	→	SYM
ejpam-6837	297	4	0	0	NUM
ejpam-6837	297	5	because	because	SCONJ
ejpam-6837	297	6	t[c1	t[c1	NOUN
ejpam-6837	297	7	...	...	PUNCT
ejpam-6837	298	1	cn	cn	PROPN
ejpam-6837	298	2	is	be	AUX
ejpam-6837	298	3	asympotically	asympotically	ADV
ejpam-6837	298	4	regular	regular	ADJ
ejpam-6837	298	5	by	by	ADP
ejpam-6837	298	6	section	section	NOUN
ejpam-6837	298	7	4	4	NUM
ejpam-6837	298	8	.	.	PUNCT
ejpam-6837	299	1	also	also	ADV
ejpam-6837	299	2	,	,	PUNCT
ejpam-6837	299	3	by	by	ADP
ejpam-6837	299	4	definition	definition	NOUN
ejpam-6837	299	5	3	3	NUM
ejpam-6837	299	6	,	,	PUNCT
ejpam-6837	299	7	〈	〈	PROPN
ejpam-6837	299	8	xnk	xnk	NOUN
ejpam-6837	299	9	−	−	PROPN
ejpam-6837	299	10	x	x	SYM
ejpam-6837	299	11	,	,	PUNCT
ejpam-6837	299	12	x	x	INTJ
ejpam-6837	299	13	−	−	NOUN
ejpam-6837	299	14	t[c1	t[c1	X
ejpam-6837	299	15	...	...	PUNCT
ejpam-6837	299	16	cn	cn	X
ejpam-6837	300	1	]	]	X
ejpam-6837	300	2	x	x	SYM
ejpam-6837	300	3	〉	〉	NOUN
ejpam-6837	300	4	=	=	SYM
ejpam-6837	300	5	〈	〈	NOUN
ejpam-6837	300	6	xnk	xnk	NOUN
ejpam-6837	300	7	,	,	PUNCT
ejpam-6837	300	8	x	x	X
ejpam-6837	300	9	−	−	NOUN
ejpam-6837	300	10	t[c1	t[c1	X
ejpam-6837	300	11	...	...	PUNCT
ejpam-6837	301	1	cn	cn	X
ejpam-6837	301	2	]	]	X
ejpam-6837	301	3	x	x	SYM
ejpam-6837	301	4	〉	〉	NOUN
ejpam-6837	301	5	−	−	NOUN
ejpam-6837	301	6	〈	〈	PROPN
ejpam-6837	301	7	x	x	NOUN
ejpam-6837	301	8	,	,	PUNCT
ejpam-6837	301	9	x	x	INTJ
ejpam-6837	301	10	−	−	NOUN
ejpam-6837	301	11	t[c1	t[c1	NUM
ejpam-6837	301	12	...	...	PUNCT
ejpam-6837	301	13	cn	cn	X
ejpam-6837	302	1	]	]	X
ejpam-6837	302	2	x	x	SYM
ejpam-6837	302	3	〉	〉	NOUN
ejpam-6837	302	4	=	=	SYM
ejpam-6837	302	5	0	0	X
ejpam-6837	302	6	.	.	PUNCT
ejpam-6837	303	1	therefore	therefore	ADV
ejpam-6837	303	2	,	,	PUNCT
ejpam-6837	303	3	x	x	PUNCT
ejpam-6837	303	4	−	−	NOUN
ejpam-6837	303	5	t[c1	t[c1	X
ejpam-6837	303	6	...	...	PUNCT
ejpam-6837	303	7	cn	cn	X
ejpam-6837	303	8	]	]	X
ejpam-6837	303	9	x	x	X
ejpam-6837	303	10	=	=	SYM
ejpam-6837	303	11	0	0	NUM
ejpam-6837	303	12	next	next	ADV
ejpam-6837	303	13	,	,	PUNCT
ejpam-6837	303	14	show	show	VERB
ejpam-6837	303	15	that	that	SCONJ
ejpam-6837	303	16	(	(	PUNCT
ejpam-6837	303	17	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	303	18	can	can	AUX
ejpam-6837	303	19	not	not	PART
ejpam-6837	303	20	have	have	VERB
ejpam-6837	303	21	two	two	NUM
ejpam-6837	303	22	distinct	distinct	ADJ
ejpam-6837	303	23	weak	weak	ADJ
ejpam-6837	303	24	sequential	sequential	ADJ
ejpam-6837	303	25	cluster	cluster	NOUN
ejpam-6837	303	26	points	point	NOUN
ejpam-6837	303	27	in	in	ADP
ejpam-6837	303	28	fix	fix	NOUN
ejpam-6837	303	29	t[c1	t[c1	X
ejpam-6837	303	30	...	...	PUNCT
ejpam-6837	304	1	cn	cn	X
ejpam-6837	304	2	]	]	X
ejpam-6837	304	3	.	.	PUNCT
ejpam-6837	305	1	let	let	VERB
ejpam-6837	305	2	x	x	PRON
ejpam-6837	305	3	and	and	CCONJ
ejpam-6837	305	4	y	y	PROPN
ejpam-6837	305	5	be	be	AUX
ejpam-6837	305	6	weak	weak	ADJ
ejpam-6837	305	7	sequential	sequential	ADJ
ejpam-6837	305	8	cluster	cluster	NOUN
ejpam-6837	305	9	points	point	NOUN
ejpam-6837	305	10	of	of	ADP
ejpam-6837	305	11	(	(	PUNCT
ejpam-6837	305	12	xn)n∈n	xn)n∈n	PROPN
ejpam-6837	305	13	∈	∈	PROPN
ejpam-6837	305	14	fix	fix	NOUN
ejpam-6837	305	15	t[c1	t[c1	NUM
ejpam-6837	305	16	...	...	PUNCT
ejpam-6837	306	1	cn	cn	X
ejpam-6837	306	2	]	]	PUNCT
ejpam-6837	306	3	,	,	PUNCT
ejpam-6837	306	4	say	say	VERB
ejpam-6837	306	5	xnk	xnk	PROPN
ejpam-6837	306	6	⇀	⇀	PUNCT
ejpam-6837	307	1	x	x	PUNCT
ejpam-6837	308	1	and	and	CCONJ
ejpam-6837	308	2	xnl	xnl	PROPN
ejpam-6837	309	1	⇀	⇀	INTJ
ejpam-6837	310	1	y	y	NOUN
ejpam-6837	310	2	then	then	ADV
ejpam-6837	310	3	,	,	PUNCT
ejpam-6837	310	4	by	by	ADP
ejpam-6837	310	5	monotonicity	monotonicity	NOUN
ejpam-6837	310	6	the	the	DET
ejpam-6837	310	7	sequences	sequence	NOUN
ejpam-6837	310	8	(	(	PUNCT
ejpam-6837	310	9	∥xn	∥xn	PRON
ejpam-6837	310	10	−	−	PROPN
ejpam-6837	310	11	x∥2)n∈n	x∥2)n∈n	PROPN
ejpam-6837	310	12	and	and	CCONJ
ejpam-6837	310	13	(	(	PUNCT
ejpam-6837	310	14	∥xn	∥xn	NUM
ejpam-6837	310	15	−	−	PROPN
ejpam-6837	310	16	y∥2)n∈n	y∥2)n∈n	PROPN
ejpam-6837	310	17	converge	converge	VERB
ejpam-6837	310	18	.	.	PUNCT
ejpam-6837	311	1	since	since	SCONJ
ejpam-6837	311	2	∥x	∥x	PROPN
ejpam-6837	311	3	−	−	PROPN
ejpam-6837	311	4	y∥2	y∥2	NOUN
ejpam-6837	311	5	=	=	SYM
ejpam-6837	311	6	∥xn	∥xn	PROPN
ejpam-6837	311	7	−	−	PROPN
ejpam-6837	311	8	y∥2	y∥2	NOUN
ejpam-6837	311	9	−	−	PROPN
ejpam-6837	311	10	∥xn	∥xn	PROPN
ejpam-6837	311	11	−	−	PROPN
ejpam-6837	311	12	x∥2	x∥2	NOUN
ejpam-6837	311	13	−	−	NOUN
ejpam-6837	311	14	2	2	NUM
ejpam-6837	311	15	⟨xn	⟨xn	NOUN
ejpam-6837	311	16	−	−	NOUN
ejpam-6837	311	17	x	x	SYM
ejpam-6837	311	18	,	,	PUNCT
ejpam-6837	311	19	x	x	PROPN
ejpam-6837	311	20	−	−	NOUN
ejpam-6837	311	21	y⟩	y⟩	NOUN
ejpam-6837	311	22	⇒	⇒	VERB
ejpam-6837	311	23	∥x	∥x	PROPN
ejpam-6837	311	24	−	−	PROPN
ejpam-6837	311	25	y∥2	y∥2	ADJ
ejpam-6837	311	26	+	+	CCONJ
ejpam-6837	311	27	2	2	NUM
ejpam-6837	311	28	⟨xn	⟨xn	NOUN
ejpam-6837	311	29	,	,	PUNCT
ejpam-6837	311	30	x	x	NOUN
ejpam-6837	311	31	−	−	NOUN
ejpam-6837	311	32	y⟩	y⟩	NOUN
ejpam-6837	311	33	=	=	SYM
ejpam-6837	311	34	∥xn	∥xn	PROPN
ejpam-6837	311	35	−	−	PROPN
ejpam-6837	311	36	y∥2	y∥2	NOUN
ejpam-6837	311	37	−	−	PROPN
ejpam-6837	311	38	∥xn	∥xn	PROPN
ejpam-6837	311	39	−	−	PROPN
ejpam-6837	311	40	x∥2	x∥2	NOUN
ejpam-6837	312	1	+	+	CCONJ
ejpam-6837	312	2	2	2	NUM
ejpam-6837	312	3	⟨xn	⟨xn	NOUN
ejpam-6837	312	4	,	,	PUNCT
ejpam-6837	312	5	x	x	NOUN
ejpam-6837	312	6	−	−	NOUN
ejpam-6837	312	7	y⟩	y⟩	NOUN
ejpam-6837	312	8	−	−	PROPN
ejpam-6837	312	9	2	2	NUM
ejpam-6837	312	10	⟨xn	⟨xn	NOUN
ejpam-6837	312	11	−	−	NOUN
ejpam-6837	312	12	x	x	SYM
ejpam-6837	312	13	,	,	PUNCT
ejpam-6837	312	14	x	x	NOUN
ejpam-6837	312	15	−	−	NOUN
ejpam-6837	312	16	y⟩	y⟩	NOUN
ejpam-6837	312	17	=	=	SYM
ejpam-6837	312	18	∥xn	∥xn	PROPN
ejpam-6837	312	19	−	−	PROPN
ejpam-6837	312	20	y∥2	y∥2	NOUN
ejpam-6837	312	21	−	−	PROPN
ejpam-6837	312	22	∥xn	∥xn	PROPN
ejpam-6837	312	23	−	−	PROPN
ejpam-6837	312	24	x∥2	x∥2	NOUN
ejpam-6837	312	25	+	+	CCONJ
ejpam-6837	312	26	2	2	NUM
ejpam-6837	312	27	⟨x	⟨x	NUM
ejpam-6837	312	28	,	,	PUNCT
ejpam-6837	312	29	x	x	PUNCT
ejpam-6837	312	30	−	−	NOUN
ejpam-6837	312	31	y⟩	y⟩	NOUN
ejpam-6837	312	32	2	2	NUM
ejpam-6837	312	33	⟨xn	⟨xn	NOUN
ejpam-6837	312	34	,	,	PUNCT
ejpam-6837	312	35	x	x	NOUN
ejpam-6837	312	36	−	−	NOUN
ejpam-6837	312	37	y⟩	y⟩	NOUN
ejpam-6837	312	38	=	=	SYM
ejpam-6837	312	39	∥xn	∥xn	PROPN
ejpam-6837	312	40	−	−	PROPN
ejpam-6837	312	41	y∥2	y∥2	NOUN
ejpam-6837	312	42	−	−	PROPN
ejpam-6837	312	43	∥xn	∥xn	PROPN
ejpam-6837	312	44	−	−	PROPN
ejpam-6837	312	45	x∥2	x∥2	NOUN
ejpam-6837	312	46	+	+	CCONJ
ejpam-6837	312	47	2	2	NUM
ejpam-6837	312	48	⟨x	⟨x	NUM
ejpam-6837	312	49	,	,	PUNCT
ejpam-6837	312	50	x	x	PUNCT
ejpam-6837	312	51	−	−	NOUN
ejpam-6837	312	52	y⟩	y⟩	NOUN
ejpam-6837	312	53	−	−	PROPN
ejpam-6837	313	1	∥x	∥x	PROPN
ejpam-6837	313	2	−	−	PROPN
ejpam-6837	313	3	y∥2	y∥2	NOUN
ejpam-6837	313	4	=	=	SYM
ejpam-6837	313	5	∥xn	∥xn	PROPN
ejpam-6837	313	6	−	−	PROPN
ejpam-6837	313	7	y∥2	y∥2	NOUN
ejpam-6837	313	8	−	−	PROPN
ejpam-6837	313	9	∥xn	∥xn	PROPN
ejpam-6837	313	10	−	−	PROPN
ejpam-6837	313	11	x∥2	x∥2	NOUN
ejpam-6837	313	12	+	+	CCONJ
ejpam-6837	313	13	2	2	NUM
ejpam-6837	313	14	⟨x	⟨x	NUM
ejpam-6837	313	15	,	,	PUNCT
ejpam-6837	313	16	x	x	PUNCT
ejpam-6837	313	17	−	−	NOUN
ejpam-6837	313	18	y⟩	y⟩	NOUN
ejpam-6837	313	19	−	−	PROPN
ejpam-6837	313	20	⟨x	⟨x	VERB
ejpam-6837	313	21	−	−	PROPN
ejpam-6837	313	22	y	y	PROPN
ejpam-6837	313	23	,	,	PUNCT
ejpam-6837	313	24	x	x	NOUN
ejpam-6837	313	25	−	−	NOUN
ejpam-6837	313	26	y⟩	y⟩	NOUN
ejpam-6837	313	27	=	=	SYM
ejpam-6837	313	28	∥xn	∥xn	PROPN
ejpam-6837	313	29	−	−	PROPN
ejpam-6837	313	30	y∥2	y∥2	NOUN
ejpam-6837	314	1	−	−	PROPN
ejpam-6837	314	2	∥xn	∥xn	PROPN
ejpam-6837	314	3	−	−	PROPN
ejpam-6837	314	4	x∥2	x∥2	NOUN
ejpam-6837	314	5	+	+	CCONJ
ejpam-6837	314	6	∥x∥2	∥x∥2	NOUN
ejpam-6837	314	7	−	−	NOUN
ejpam-6837	314	8	∥y∥2	∥y∥2	NOUN
ejpam-6837	314	9	(	(	PUNCT
ejpam-6837	314	10	∀n	∀n	NUM
ejpam-6837	314	11	∈	∈	PROPN
ejpam-6837	314	12	n	n	CCONJ
ejpam-6837	314	13	)	)	PUNCT
ejpam-6837	314	14	2	2	NUM
ejpam-6837	314	15	⟨xn	⟨xn	NOUN
ejpam-6837	314	16	,	,	PUNCT
ejpam-6837	314	17	x	x	NOUN
ejpam-6837	314	18	−	−	NOUN
ejpam-6837	314	19	y⟩	y⟩	NOUN
ejpam-6837	314	20	=	=	SYM
ejpam-6837	314	21	∥xn	∥xn	PROPN
ejpam-6837	314	22	−	−	PROPN
ejpam-6837	314	23	y∥2	y∥2	NOUN
ejpam-6837	314	24	−	−	PROPN
ejpam-6837	314	25	∥xn	∥xn	PROPN
ejpam-6837	314	26	−	−	PROPN
ejpam-6837	314	27	x∥2	x∥2	NOUN
ejpam-6837	314	28	+	+	CCONJ
ejpam-6837	314	29	∥x∥2	∥x∥2	NOUN
ejpam-6837	314	30	−	−	NOUN
ejpam-6837	314	31	∥y∥2	∥y∥2	NOUN
ejpam-6837	314	32	(	(	PUNCT
ejpam-6837	314	33	21	21	NUM
ejpam-6837	314	34	)	)	PUNCT
ejpam-6837	314	35	(	(	PUNCT
ejpam-6837	314	36	⟨xn	⟨xn	NOUN
ejpam-6837	314	37	,	,	PUNCT
ejpam-6837	314	38	x	x	NOUN
ejpam-6837	314	39	−	−	NOUN
ejpam-6837	314	40	y⟩)n∈n	y⟩)n∈n	NOUN
ejpam-6837	314	41	converges	converge	NOUN
ejpam-6837	314	42	as	as	ADV
ejpam-6837	314	43	well	well	ADV
ejpam-6837	314	44	.	.	PUNCT
ejpam-6837	315	1	let	let	VERB
ejpam-6837	315	2	⟨xn	⟨xn	NOUN
ejpam-6837	315	3	,	,	PUNCT
ejpam-6837	315	4	x	x	NOUN
ejpam-6837	315	5	−	−	NOUN
ejpam-6837	315	6	y⟩	y⟩	NOUN
ejpam-6837	315	7	→	→	SYM
ejpam-6837	315	8	m.	m.	NOUN
ejpam-6837	315	9	taking	take	VERB
ejpam-6837	315	10	the	the	DET
ejpam-6837	315	11	limit	limit	NOUN
ejpam-6837	315	12	along	along	ADP
ejpam-6837	315	13	(	(	PUNCT
ejpam-6837	315	14	xnk	xnk	PROPN
ejpam-6837	315	15	)	)	PUNCT
ejpam-6837	315	16	and	and	CCONJ
ejpam-6837	315	17	(	(	PUNCT
ejpam-6837	315	18	xnl	xnl	PROPN
ejpam-6837	315	19	)	)	PUNCT
ejpam-6837	315	20	repectively	repectively	ADV
ejpam-6837	315	21	,	,	PUNCT
ejpam-6837	315	22	we	we	PRON
ejpam-6837	315	23	have	have	VERB
ejpam-6837	315	24	m	m	VERB
ejpam-6837	315	25	=	=	PUNCT
ejpam-6837	315	26	⟨x	⟨x	VERB
ejpam-6837	315	27	,	,	PUNCT
ejpam-6837	315	28	x	x	PUNCT
ejpam-6837	315	29	−	−	NOUN
ejpam-6837	315	30	y⟩	y⟩	NOUN
ejpam-6837	315	31	=	=	PUNCT
ejpam-6837	316	1	⟨y	⟨y	NOUN
ejpam-6837	316	2	,	,	PUNCT
ejpam-6837	316	3	x	x	PUNCT
ejpam-6837	316	4	−	−	NOUN
ejpam-6837	316	5	y⟩	y⟩	NOUN
ejpam-6837	316	6	therefore	therefore	ADV
ejpam-6837	316	7	,	,	PUNCT
ejpam-6837	316	8	∥x	∥x	PROPN
ejpam-6837	316	9	−	−	PROPN
ejpam-6837	316	10	y∥2	y∥2	NOUN
ejpam-6837	316	11	=	=	NOUN
ejpam-6837	316	12	0	0	X
ejpam-6837	316	13	.	.	PUNCT
ejpam-6837	317	1	hence	hence	ADV
ejpam-6837	317	2	,	,	PUNCT
ejpam-6837	317	3	tn	tn	PROPN
ejpam-6837	318	1	[	[	X
ejpam-6837	318	2	c1c2	c1c2	NOUN
ejpam-6837	318	3	...	...	PUNCT
ejpam-6837	318	4	cn	cn	X
ejpam-6837	318	5	]	]	X
ejpam-6837	319	1	x0	x0	PUNCT
ejpam-6837	319	2	⇀	⇀	PUNCT
ejpam-6837	319	3	x	x	PUNCT
ejpam-6837	319	4	∈	∈	PROPN
ejpam-6837	319	5	fix	fix	NOUN
ejpam-6837	319	6	t[c1	t[c1	PRON
ejpam-6837	319	7	...	...	PUNCT
ejpam-6837	319	8	cn	cn	X
ejpam-6837	319	9	]	]	PUNCT
ejpam-6837	319	10	and	and	CCONJ
ejpam-6837	319	11	from	from	ADP
ejpam-6837	319	12	section	section	NOUN
ejpam-6837	319	13	4	4	NUM
ejpam-6837	319	14	tn	tn	NOUN
ejpam-6837	320	1	[	[	X
ejpam-6837	320	2	c1c2	c1c2	NOUN
ejpam-6837	320	3	...	...	PUNCT
ejpam-6837	320	4	cn	cn	X
ejpam-6837	320	5	]	]	X
ejpam-6837	321	1	x0	x0	PUNCT
ejpam-6837	321	2	⇀	⇀	PUNCT
ejpam-6837	321	3	x	x	PUNCT
ejpam-6837	321	4	∈	∈	PROPN
ejpam-6837	321	5	n+1	n+1	PROPN
ejpam-6837	321	6	∩	∩	X
ejpam-6837	321	7	i=1	i=1	PROPN
ejpam-6837	321	8	fix	fix	NOUN
ejpam-6837	321	9	tci	tci	NOUN
ejpam-6837	321	10	,	,	PUNCT
ejpam-6837	321	11	ci+1	ci+1	PROPN
ejpam-6837	321	12	.	.	PUNCT
ejpam-6837	322	1	finally	finally	ADV
ejpam-6837	322	2	,	,	PUNCT
ejpam-6837	322	3	by	by	ADP
ejpam-6837	322	4	using	use	VERB
ejpam-6837	322	5	section	section	NOUN
ejpam-6837	322	6	2	2	NUM
ejpam-6837	322	7	and	and	CCONJ
ejpam-6837	322	8	section	section	NOUN
ejpam-6837	322	9	2	2	NUM
ejpam-6837	322	10	,	,	PUNCT
ejpam-6837	322	11	we	we	PRON
ejpam-6837	322	12	get	get	VERB
ejpam-6837	322	13	that	that	DET
ejpam-6837	322	14	shadow	shadow	NOUN
ejpam-6837	322	15	sequence	sequence	NOUN
ejpam-6837	322	16	(	(	PUNCT
ejpam-6837	322	17	pfix	pfix	ADJ
ejpam-6837	322	18	t[c1	t[c1	NUM
ejpam-6837	322	19	...	...	PUNCT
ejpam-6837	322	20	cn	cn	X
ejpam-6837	322	21	]	]	PUNCT
ejpam-6837	322	22	)	)	PUNCT
ejpam-6837	322	23	n∈n	n∈n	NOUN
ejpam-6837	322	24	converges	converge	VERB
ejpam-6837	322	25	strongly	strongly	ADV
ejpam-6837	322	26	to	to	ADP
ejpam-6837	322	27	a	a	DET
ejpam-6837	322	28	point	point	NOUN
ejpam-6837	322	29	in	in	ADP
ejpam-6837	322	30	x	x	PART
ejpam-6837	322	31	∈	∈	PROPN
ejpam-6837	322	32	fix	fix	NOUN
ejpam-6837	322	33	t[c1	t[c1	PRON
ejpam-6837	322	34	...	...	PUNCT
ejpam-6837	322	35	cn	cn	X
ejpam-6837	322	36	]	]	X
ejpam-6837	323	1	=	=	SYM
ejpam-6837	323	2	n+1	n+1	PROPN
ejpam-6837	323	3	∩	∩	NOUN
ejpam-6837	323	4	i=1	i=1	PRON
ejpam-6837	323	5	fix	fix	NOUN
ejpam-6837	323	6	tci	tci	NOUN
ejpam-6837	323	7	,	,	PUNCT
ejpam-6837	323	8	ci+1	ci+1	PROPN
ejpam-6837	323	9	.	.	PUNCT
ejpam-6837	324	1	■	■	PUNCT
ejpam-6837	324	2	s.	s.	PROPN
ejpam-6837	324	3	th	th	PROPN
ejpam-6837	324	4	.	.	PUNCT
ejpam-6837	324	5	alwadani	alwadani	PROPN
ejpam-6837	324	6	/	/	SYM
ejpam-6837	324	7	eur	eur	PROPN
ejpam-6837	324	8	.	.	PUNCT
ejpam-6837	325	1	j.	j.	PROPN
ejpam-6837	325	2	pure	pure	PROPN
ejpam-6837	325	3	appl	appl	PROPN
ejpam-6837	325	4	.	.	PROPN
ejpam-6837	325	5	math	math	PROPN
ejpam-6837	325	6	,	,	PUNCT
ejpam-6837	325	7	18	18	NUM
ejpam-6837	325	8	(	(	PUNCT
ejpam-6837	325	9	4	4	NUM
ejpam-6837	325	10	)	)	PUNCT
ejpam-6837	325	11	(	(	PUNCT
ejpam-6837	325	12	2025	2025	NUM
ejpam-6837	325	13	)	)	PUNCT
ejpam-6837	325	14	,	,	PUNCT
ejpam-6837	325	15	6837	6837	NUM
ejpam-6837	325	16	11	11	NUM
ejpam-6837	325	17	of	of	ADP
ejpam-6837	325	18	15	15	NUM
ejpam-6837	325	19	proposition	proposition	NOUN
ejpam-6837	325	20	3	3	NUM
ejpam-6837	325	21	.	.	PUNCT
ejpam-6837	326	1	let	let	VERB
ejpam-6837	326	2	c1	c1	PROPN
ejpam-6837	326	3	,	,	PUNCT
ejpam-6837	326	4	c2	c2	PROPN
ejpam-6837	326	5	·	·	PUNCT
ejpam-6837	326	6	·	·	PUNCT
ejpam-6837	326	7	·	·	PUNCT
ejpam-6837	326	8	cn	cn	PROPN
ejpam-6837	326	9	⊆	⊆	NUM
ejpam-6837	326	10	h	h	NOUN
ejpam-6837	326	11	be	be	AUX
ejpam-6837	326	12	closed	close	VERB
ejpam-6837	326	13	and	and	CCONJ
ejpam-6837	326	14	convex	convex	NOUN
ejpam-6837	326	15	set	set	VERB
ejpam-6837	326	16	with	with	ADP
ejpam-6837	326	17	non	non	ADJ
ejpam-6837	326	18	empty	empty	ADJ
ejpam-6837	326	19	intersection	intersection	NOUN
ejpam-6837	326	20	.	.	PUNCT
ejpam-6837	327	1	recall	recall	NOUN
ejpam-6837	327	2	from	from	ADP
ejpam-6837	327	3	definition	definition	NOUN
ejpam-6837	327	4	5	5	NUM
ejpam-6837	327	5	that	that	DET
ejpam-6837	327	6	tc1,c2,	tc1,c2,	NOUN
ejpam-6837	327	7	...	...	PUNCT
ejpam-6837	327	8	,cn	,cn	PUNCT
ejpam-6837	327	9	:	:	PUNCT
ejpam-6837	327	10	=	=	SYM
ejpam-6837	327	11	1	1	NUM
ejpam-6837	327	12	2	2	NUM
ejpam-6837	327	13	(	(	PUNCT
ejpam-6837	327	14	id+rcn	id+rcn	X
ejpam-6837	327	15	rcn−1	rcn−1	PROPN
ejpam-6837	327	16	.	.	PUNCT
ejpam-6837	327	17	.	.	PUNCT
ejpam-6837	327	18	.	.	PUNCT
ejpam-6837	328	1	rc2	rc2	PROPN
ejpam-6837	328	2	rc1	rc1	PROPN
ejpam-6837	328	3	)	)	PUNCT
ejpam-6837	328	4	.	.	PUNCT
ejpam-6837	329	1	if	if	SCONJ
ejpam-6837	329	2	x	x	PROPN
ejpam-6837	329	3	∈	∈	PROPN
ejpam-6837	329	4	ci	ci	PROPN
ejpam-6837	329	5	,	,	PUNCT
ejpam-6837	329	6	then	then	ADV
ejpam-6837	329	7	tci	tci	PROPN
ejpam-6837	329	8	,	,	PUNCT
ejpam-6837	329	9	ci+1	ci+1	PROPN
ejpam-6837	329	10	x	x	NOUN
ejpam-6837	329	11	=	=	PUNCT
ejpam-6837	329	12	pci+1	pci+1	NOUN
ejpam-6837	329	13	x.	x.	NOUN
ejpam-6837	329	14	(	(	PUNCT
ejpam-6837	329	15	22	22	NUM
ejpam-6837	329	16	)	)	PUNCT
ejpam-6837	329	17	proof	proof	NOUN
ejpam-6837	329	18	.	.	PUNCT
ejpam-6837	330	1	let	let	VERB
ejpam-6837	330	2	x	x	SYM
ejpam-6837	330	3	∈	∈	PROPN
ejpam-6837	330	4	ci	ci	PROPN
ejpam-6837	330	5	,	,	PUNCT
ejpam-6837	330	6	then	then	ADV
ejpam-6837	330	7	tci	tci	PROPN
ejpam-6837	330	8	,	,	PUNCT
ejpam-6837	330	9	ci+1	ci+1	PROPN
ejpam-6837	330	10	x	x	PUNCT
ejpam-6837	331	1	=	=	SYM
ejpam-6837	331	2	2−1(x	2−1(x	NUM
ejpam-6837	331	3	+	+	CCONJ
ejpam-6837	331	4	rci+1	rci+1	PROPN
ejpam-6837	331	5	rci	rci	NOUN
ejpam-6837	331	6	x	x	NOUN
ejpam-6837	331	7	)	)	PUNCT
ejpam-6837	332	1	*	*	PUNCT
ejpam-6837	333	1	*	*	PUNCT
ejpam-6837	333	2	=	=	PUNCT
ejpam-6837	333	3	2−1(x	2−1(x	NUM
ejpam-6837	333	4	+	+	NUM
ejpam-6837	333	5	rci+1	rci+1	NOUN
ejpam-6837	333	6	x	x	X
ejpam-6837	333	7	)	)	PUNCT
ejpam-6837	334	1	=	=	PUNCT
ejpam-6837	335	1	2−1(x	2−1(x	NUM
ejpam-6837	335	2	+	+	NUM
ejpam-6837	335	3	2	2	NUM
ejpam-6837	335	4	pci+1	pci+1	NOUN
ejpam-6837	335	5	x	x	NOUN
ejpam-6837	335	6	−	−	NOUN
ejpam-6837	335	7	x	x	SYM
ejpam-6837	335	8	)	)	PUNCT
ejpam-6837	335	9	by	by	ADP
ejpam-6837	335	10	(	(	PUNCT
ejpam-6837	335	11	4	4	NUM
ejpam-6837	335	12	)	)	PUNCT
ejpam-6837	335	13	=	=	SYM
ejpam-6837	335	14	pci+1	pci+1	NOUN
ejpam-6837	335	15	x	x	NOUN
ejpam-6837	335	16	,	,	PUNCT
ejpam-6837	335	17	as	as	SCONJ
ejpam-6837	335	18	required	require	VERB
ejpam-6837	335	19	.	.	PUNCT
ejpam-6837	336	1	■	■	PUNCT
ejpam-6837	336	2	lemma	lemma	PROPN
ejpam-6837	336	3	1	1	X
ejpam-6837	336	4	.	.	PUNCT
ejpam-6837	337	1	let	let	VERB
ejpam-6837	337	2	c1	c1	PROPN
ejpam-6837	337	3	and	and	CCONJ
ejpam-6837	337	4	c2	c2	PROPN
ejpam-6837	337	5	be	be	VERB
ejpam-6837	337	6	two	two	NUM
ejpam-6837	337	7	closed	closed	ADJ
ejpam-6837	337	8	affine	affine	NOUN
ejpam-6837	337	9	subspaces	subspace	NOUN
ejpam-6837	337	10	.	.	PUNCT
ejpam-6837	338	1	recall	recall	NOUN
ejpam-6837	338	2	from	from	ADP
ejpam-6837	338	3	(	(	PUNCT
ejpam-6837	338	4	13	13	NUM
ejpam-6837	338	5	)	)	PUNCT
ejpam-6837	338	6	that	that	DET
ejpam-6837	338	7	t[c1c2	t[c1c2	NOUN
ejpam-6837	338	8	...	...	PUNCT
ejpam-6837	338	9	cn	cn	X
ejpam-6837	338	10	]	]	X
ejpam-6837	339	1	:	:	PUNCT
ejpam-6837	339	2	=	=	SYM
ejpam-6837	339	3	tcn	tcn	PROPN
ejpam-6837	339	4	,	,	PUNCT
ejpam-6837	339	5	c1	c1	PROPN
ejpam-6837	339	6	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	339	7	.	.	PUNCT
ejpam-6837	339	8	.	.	PUNCT
ejpam-6837	339	9	.	.	PUNCT
ejpam-6837	340	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	340	2	tc1,c2	tc1,c2	PROPN
ejpam-6837	340	3	.	.	PUNCT
ejpam-6837	341	1	then	then	ADV
ejpam-6837	341	2	t[c1c2	t[c1c2	NOUN
ejpam-6837	341	3	]	]	X
ejpam-6837	341	4	=	=	PUNCT
ejpam-6837	341	5	2−1(tc1,c2	2−1(tc1,c2	NUM
ejpam-6837	341	6	+	+	CCONJ
ejpam-6837	341	7	tc2,c1	tc2,c1	NOUN
ejpam-6837	341	8	)	)	PUNCT
ejpam-6837	341	9	.	.	PUNCT
ejpam-6837	342	1	proof	proof	NOUN
ejpam-6837	342	2	.	.	PUNCT
ejpam-6837	343	1	using	use	VERB
ejpam-6837	343	2	(	(	PUNCT
ejpam-6837	343	3	13	13	NUM
ejpam-6837	343	4	)	)	PUNCT
ejpam-6837	343	5	with	with	ADP
ejpam-6837	343	6	n	n	NOUN
ejpam-6837	343	7	=	=	SYM
ejpam-6837	343	8	2	2	NUM
ejpam-6837	343	9	and	and	CCONJ
ejpam-6837	343	10	(	(	PUNCT
ejpam-6837	343	11	11	11	NUM
ejpam-6837	343	12	)	)	PUNCT
ejpam-6837	343	13	give	give	VERB
ejpam-6837	343	14	t[c1c2	t[c1c2	NOUN
ejpam-6837	343	15	]	]	X
ejpam-6837	343	16	=	=	SYM
ejpam-6837	343	17	tc2,c1	tc2,c1	NOUN
ejpam-6837	343	18	tc1,c2	tc1,c2	NOUN
ejpam-6837	343	19	=	=	SYM
ejpam-6837	343	20	2−1	2−1	NUM
ejpam-6837	343	21	(	(	PUNCT
ejpam-6837	343	22	id+rc1	id+rc1	PROPN
ejpam-6837	343	23	rc2	rc2	PROPN
ejpam-6837	343	24	)	)	PUNCT
ejpam-6837	343	25	tc1,c2	tc1,c2	NOUN
ejpam-6837	344	1	=	=	PUNCT
ejpam-6837	344	2	2−1(tc1,c2	2−1(tc1,c2	NUM
ejpam-6837	344	3	+	+	CCONJ
ejpam-6837	344	4	rc1	rc1	PROPN
ejpam-6837	344	5	rc2	rc2	PROPN
ejpam-6837	344	6	tc1,c2	tc1,c2	NOUN
ejpam-6837	344	7	)	)	PUNCT
ejpam-6837	344	8	=	=	PUNCT
ejpam-6837	345	1	2−1	2−1	NUM
ejpam-6837	345	2	(	(	PUNCT
ejpam-6837	345	3	tc1,c2	tc1,c2	NOUN
ejpam-6837	345	4	+	+	CCONJ
ejpam-6837	345	5	rc1	rc1	NOUN
ejpam-6837	345	6	rc2	rc2	PROPN
ejpam-6837	345	7	(	(	PUNCT
ejpam-6837	345	8	2−1	2−1	NUM
ejpam-6837	345	9	(	(	PUNCT
ejpam-6837	345	10	id+rc2	id+rc2	PROPN
ejpam-6837	345	11	rc1	rc1	NOUN
ejpam-6837	345	12	)	)	PUNCT
ejpam-6837	345	13	)	)	PUNCT
ejpam-6837	345	14	)	)	PUNCT
ejpam-6837	346	1	=	=	PUNCT
ejpam-6837	347	1	2−1	2−1	NUM
ejpam-6837	347	2	(	(	PUNCT
ejpam-6837	347	3	tc1,c2	tc1,c2	NOUN
ejpam-6837	347	4	+	+	CCONJ
ejpam-6837	347	5	rc1	rc1	NOUN
ejpam-6837	347	6	(	(	PUNCT
ejpam-6837	347	7	2−1(rc2	2−1(rc2	NUM
ejpam-6837	347	8	+	+	NUM
ejpam-6837	347	9	rc2	rc2	PROPN
ejpam-6837	347	10	rc2	rc2	PROPN
ejpam-6837	347	11	rc1	rc1	PROPN
ejpam-6837	347	12	)	)	PUNCT
ejpam-6837	347	13	)	)	PUNCT
ejpam-6837	347	14	)	)	PUNCT
ejpam-6837	347	15	††	††	X
ejpam-6837	348	1	=	=	SYM
ejpam-6837	348	2	2−1	2−1	NUM
ejpam-6837	348	3	(	(	PUNCT
ejpam-6837	348	4	tc1,c2	tc1,c2	NOUN
ejpam-6837	348	5	+	+	CCONJ
ejpam-6837	348	6	2−1(rc1	2−1(rc1	NUM
ejpam-6837	348	7	rc2	rc2	NOUN
ejpam-6837	349	1	+	+	CCONJ
ejpam-6837	349	2	rc1	rc1	NOUN
ejpam-6837	349	3	rc1	rc1	NOUN
ejpam-6837	349	4	)	)	PUNCT
ejpam-6837	349	5	)	)	PUNCT
ejpam-6837	350	1	=	=	PUNCT
ejpam-6837	351	1	2−1	2−1	NUM
ejpam-6837	351	2	(	(	PUNCT
ejpam-6837	351	3	tc1,c2	tc1,c2	NOUN
ejpam-6837	351	4	+	+	CCONJ
ejpam-6837	351	5	2−1(rc1	2−1(rc1	NUM
ejpam-6837	351	6	rc2	rc2	NOUN
ejpam-6837	351	7	+	+	CCONJ
ejpam-6837	351	8	i	i	PROPN
ejpam-6837	351	9	d	d	PROPN
ejpam-6837	351	10	)	)	PUNCT
ejpam-6837	351	11	)	)	PUNCT
ejpam-6837	352	1	=	=	PUNCT
ejpam-6837	352	2	2−1(tc1,c2	2−1(tc1,c2	NUM
ejpam-6837	352	3	+	+	CCONJ
ejpam-6837	352	4	tc2,c1	tc2,c1	NOUN
ejpam-6837	352	5	)	)	PUNCT
ejpam-6837	352	6	.	.	PUNCT
ejpam-6837	353	1	■	■	PUNCT
ejpam-6837	353	2	proposition	proposition	NOUN
ejpam-6837	353	3	4	4	NUM
ejpam-6837	353	4	.	.	PUNCT
ejpam-6837	353	5	when	when	SCONJ
ejpam-6837	353	6	x0	x0	PROPN
ejpam-6837	353	7	∈	∈	PROPN
ejpam-6837	353	8	c1	c1	PROPN
ejpam-6837	353	9	,	,	PUNCT
ejpam-6837	353	10	the	the	DET
ejpam-6837	353	11	cyclic	cyclic	PROPN
ejpam-6837	353	12	douglasrachford	douglasrachford	PROPN
ejpam-6837	353	13	method	method	NOUN
ejpam-6837	353	14	coincides	coincide	VERB
ejpam-6837	353	15	with	with	ADP
ejpam-6837	353	16	alternating	alternate	VERB
ejpam-6837	353	17	projection	projection	NOUN
ejpam-6837	353	18	method	method	NOUN
ejpam-6837	353	19	.	.	PUNCT
ejpam-6837	354	1	∗∗by	∗∗by	ADP
ejpam-6837	354	2	assumption	assumption	NOUN
ejpam-6837	354	3	that	that	SCONJ
ejpam-6837	354	4	x	x	SYM
ejpam-6837	354	5	∈	∈	PROPN
ejpam-6837	354	6	ci	ci	NOUN
ejpam-6837	354	7	††by	††by	ADV
ejpam-6837	354	8	using	use	VERB
ejpam-6837	354	9	the	the	DET
ejpam-6837	354	10	fact	fact	NOUN
ejpam-6837	354	11	that	that	SCONJ
ejpam-6837	354	12	c2	c2	PROPN
ejpam-6837	354	13	is	be	AUX
ejpam-6837	354	14	closed	close	VERB
ejpam-6837	354	15	an	an	DET
ejpam-6837	354	16	affine	affine	NOUN
ejpam-6837	354	17	therefore	therefore	ADV
ejpam-6837	354	18	r2	r2	PROPN
ejpam-6837	354	19	c2	c2	PROPN
ejpam-6837	354	20	=	=	PUNCT
ejpam-6837	355	1	i	i	PROPN
ejpam-6837	355	2	d.	d.	PROPN
ejpam-6837	355	3	similarly	similarly	ADV
ejpam-6837	355	4	for	for	ADP
ejpam-6837	355	5	c1	c1	PROPN
ejpam-6837	355	6	.	.	PUNCT
ejpam-6837	356	1	s.	s.	PROPN
ejpam-6837	356	2	th	th	PROPN
ejpam-6837	356	3	.	.	PUNCT
ejpam-6837	357	1	alwadani	alwadani	PROPN
ejpam-6837	357	2	/	/	SYM
ejpam-6837	357	3	eur	eur	PROPN
ejpam-6837	357	4	.	.	PUNCT
ejpam-6837	358	1	j.	j.	PROPN
ejpam-6837	358	2	pure	pure	PROPN
ejpam-6837	358	3	appl	appl	PROPN
ejpam-6837	358	4	.	.	PROPN
ejpam-6837	358	5	math	math	PROPN
ejpam-6837	358	6	,	,	PUNCT
ejpam-6837	358	7	18	18	NUM
ejpam-6837	358	8	(	(	PUNCT
ejpam-6837	358	9	4	4	NUM
ejpam-6837	358	10	)	)	PUNCT
ejpam-6837	358	11	(	(	PUNCT
ejpam-6837	358	12	2025	2025	NUM
ejpam-6837	358	13	)	)	PUNCT
ejpam-6837	358	14	,	,	PUNCT
ejpam-6837	358	15	6837	6837	NUM
ejpam-6837	358	16	12	12	NUM
ejpam-6837	358	17	of	of	ADP
ejpam-6837	358	18	15	15	NUM
ejpam-6837	358	19	proof	proof	NOUN
ejpam-6837	358	20	.	.	PUNCT
ejpam-6837	359	1	let	let	VERB
ejpam-6837	359	2	x0	x0	PROPN
ejpam-6837	359	3	∈	∈	PROPN
ejpam-6837	359	4	c1	c1	PROPN
ejpam-6837	359	5	,	,	PUNCT
ejpam-6837	359	6	then	then	ADV
ejpam-6837	359	7	by	by	ADP
ejpam-6837	359	8	(	(	PUNCT
ejpam-6837	359	9	13	13	NUM
ejpam-6837	359	10	)	)	PUNCT
ejpam-6837	359	11	we	we	PRON
ejpam-6837	359	12	have	have	VERB
ejpam-6837	359	13	,	,	PUNCT
ejpam-6837	359	14	t[c1c2	t[c1c2	NOUN
ejpam-6837	359	15	...	...	PUNCT
ejpam-6837	360	1	cn−1cn	cn−1cn	PROPN
ejpam-6837	360	2	]	]	PUNCT
ejpam-6837	360	3	x0	x0	PROPN
ejpam-6837	360	4	=	=	PUNCT
ejpam-6837	360	5	tcn	tcn	PROPN
ejpam-6837	360	6	,	,	PUNCT
ejpam-6837	360	7	c1	c1	PROPN
ejpam-6837	360	8	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	360	9	.	.	PUNCT
ejpam-6837	360	10	.	.	PUNCT
ejpam-6837	360	11	.	.	PUNCT
ejpam-6837	361	1	tc1,c2	tc1,c2	NOUN
ejpam-6837	361	2	x0	x0	PROPN
ejpam-6837	361	3	note	note	NOUN
ejpam-6837	361	4	:	:	PUNCT
ejpam-6837	361	5	tc1,c2	tc1,c2	NOUN
ejpam-6837	361	6	x0	x0	PROPN
ejpam-6837	361	7	=	=	PUNCT
ejpam-6837	362	1	2−1	2−1	NUM
ejpam-6837	362	2	(	(	PUNCT
ejpam-6837	362	3	x0	x0	PROPN
ejpam-6837	362	4	+	+	CCONJ
ejpam-6837	362	5	rc2(rc1	rc2(rc1	ADJ
ejpam-6837	362	6	x0	x0	NUM
ejpam-6837	362	7	)	)	PUNCT
ejpam-6837	362	8	)	)	PUNCT
ejpam-6837	363	1	=	=	PUNCT
ejpam-6837	364	1	2−1	2−1	NUM
ejpam-6837	364	2	(	(	PUNCT
ejpam-6837	364	3	x0	x0	PROPN
ejpam-6837	364	4	+	+	PROPN
ejpam-6837	364	5	rc2	rc2	PROPN
ejpam-6837	364	6	x0	x0	PROPN
ejpam-6837	364	7	)	)	PUNCT
ejpam-6837	365	1	=	=	PUNCT
ejpam-6837	366	1	2−1	2−1	NUM
ejpam-6837	366	2	(	(	PUNCT
ejpam-6837	366	3	x0	x0	PROPN
ejpam-6837	366	4	+	+	CCONJ
ejpam-6837	366	5	2pc2	2pc2	NUM
ejpam-6837	366	6	x0	x0	NUM
ejpam-6837	366	7	−	−	PROPN
ejpam-6837	366	8	x0	x0	PROPN
ejpam-6837	366	9	)	)	PUNCT
ejpam-6837	367	1	=	=	PUNCT
ejpam-6837	367	2	pc2	pc2	VERB
ejpam-6837	367	3	x0	x0	PROPN
ejpam-6837	367	4	∈	∈	PROPN
ejpam-6837	367	5	c2	c2	PROPN
ejpam-6837	367	6	tc2,c3(pc2	tc2,c3(pc2	VERB
ejpam-6837	367	7	x0	x0	PROPN
ejpam-6837	367	8	)	)	PUNCT
ejpam-6837	367	9	=	=	SYM
ejpam-6837	367	10	1	1	NUM
ejpam-6837	367	11	2	2	NUM
ejpam-6837	367	12	(	(	PUNCT
ejpam-6837	367	13	pc2	pc2	VERB
ejpam-6837	367	14	x0	x0	PROPN
ejpam-6837	367	15	+	+	CCONJ
ejpam-6837	367	16	rc3(rc2(pc2	rc3(rc2(pc2	VERB
ejpam-6837	367	17	x0	x0	PROPN
ejpam-6837	367	18	)	)	PUNCT
ejpam-6837	367	19	)	)	PUNCT
ejpam-6837	367	20	)	)	PUNCT
ejpam-6837	368	1	=	=	SYM
ejpam-6837	368	2	1	1	NUM
ejpam-6837	368	3	2	2	NUM
ejpam-6837	368	4	(	(	PUNCT
ejpam-6837	368	5	pc2	pc2	VERB
ejpam-6837	368	6	x0	x0	PROPN
ejpam-6837	368	7	+	+	CCONJ
ejpam-6837	368	8	rc3(pc2	rc3(pc2	VERB
ejpam-6837	368	9	x0	x0	NUM
ejpam-6837	368	10	)	)	PUNCT
ejpam-6837	368	11	)	)	PUNCT
ejpam-6837	369	1	=	=	SYM
ejpam-6837	369	2	1	1	NUM
ejpam-6837	369	3	2	2	NUM
ejpam-6837	369	4	(	(	PUNCT
ejpam-6837	369	5	pc2	pc2	VERB
ejpam-6837	369	6	x0	x0	PROPN
ejpam-6837	369	7	+	+	NUM
ejpam-6837	369	8	2pc3(pc2	2pc3(pc2	NUM
ejpam-6837	369	9	x0)−	x0)−	X
ejpam-6837	369	10	pc2	pc2	NOUN
ejpam-6837	369	11	x0	x0	PROPN
ejpam-6837	369	12	)	)	PUNCT
ejpam-6837	370	1	=	=	PUNCT
ejpam-6837	370	2	pc3	pc3	PROPN
ejpam-6837	370	3	pc2	pc2	PROPN
ejpam-6837	370	4	x0	x0	PROPN
ejpam-6837	370	5	∈	∈	PROPN
ejpam-6837	370	6	c3	c3	NOUN
ejpam-6837	370	7	keep	keep	VERB
ejpam-6837	370	8	doing	do	VERB
ejpam-6837	370	9	that	that	SCONJ
ejpam-6837	370	10	we	we	PRON
ejpam-6837	370	11	have	have	VERB
ejpam-6837	370	12	tcn	tcn	NOUN
ejpam-6837	370	13	,	,	PUNCT
ejpam-6837	370	14	c1	c1	PROPN
ejpam-6837	370	15	tcn−1,cn	tcn−1,cn	ADP
ejpam-6837	370	16	.	.	PUNCT
ejpam-6837	370	17	.	.	PUNCT
ejpam-6837	370	18	.	.	PUNCT
ejpam-6837	371	1	tc2,c3	tc2,c3	PROPN
ejpam-6837	371	2	pc2	pc2	PROPN
ejpam-6837	371	3	x0	x0	PROPN
ejpam-6837	371	4	(	(	PUNCT
ejpam-6837	371	5	22	22	NUM
ejpam-6837	371	6	)	)	PUNCT
ejpam-6837	371	7	=	=	VERB
ejpam-6837	372	1	pc1	pc1	PROPN
ejpam-6837	372	2	pn	pn	INTJ
ejpam-6837	372	3	.	.	PUNCT
ejpam-6837	372	4	.	.	PUNCT
ejpam-6837	372	5	.	.	PUNCT
ejpam-6837	373	1	pc3	pc3	PROPN
ejpam-6837	373	2	p2	p2	PROPN
ejpam-6837	373	3	x0	x0	PROPN
ejpam-6837	373	4	∈	∈	PROPN
ejpam-6837	373	5	c1	c1	PROPN
ejpam-6837	373	6	■	■	PUNCT
ejpam-6837	373	7	the	the	DET
ejpam-6837	373	8	next	next	ADJ
ejpam-6837	373	9	example	example	NOUN
ejpam-6837	373	10	indicates	indicate	VERB
ejpam-6837	373	11	that	that	SCONJ
ejpam-6837	373	12	if	if	SCONJ
ejpam-6837	373	13	x0	x0	PROPN
ejpam-6837	373	14	/∈	/∈	PUNCT
ejpam-6837	373	15	c1	c1	PROPN
ejpam-6837	373	16	,	,	PUNCT
ejpam-6837	373	17	then	then	ADV
ejpam-6837	373	18	the	the	DET
ejpam-6837	373	19	cyclic	cyclic	ADJ
ejpam-6837	373	20	douglas	douglas	PROPN
ejpam-6837	373	21	–	–	PUNCT
ejpam-6837	373	22	rachford	rachford	ADJ
ejpam-6837	373	23	iteration	iteration	NOUN
ejpam-6837	373	24	need	need	AUX
ejpam-6837	373	25	not	not	PART
ejpam-6837	373	26	coincide	coincide	VERB
ejpam-6837	373	27	with	with	ADP
ejpam-6837	373	28	von	von	PROPN
ejpam-6837	373	29	neumann	neumann	PROPN
ejpam-6837	373	30	’s	’s	PART
ejpam-6837	373	31	alternating	alternate	VERB
ejpam-6837	373	32	projection	projection	NOUN
ejpam-6837	373	33	method	method	NOUN
ejpam-6837	373	34	.	.	PUNCT
ejpam-6837	374	1	example	example	NOUN
ejpam-6837	375	1	3	3	X
ejpam-6837	375	2	.	.	PUNCT
ejpam-6837	375	3	let	let	VERB
ejpam-6837	375	4	c1	c1	PROPN
ejpam-6837	375	5	=	=	PUNCT
ejpam-6837	375	6	{	{	PUNCT
ejpam-6837	375	7	x	x	PUNCT
ejpam-6837	375	8	∈	∈	PROPN
ejpam-6837	375	9	h	h	NOUN
ejpam-6837	375	10	|	|	ADV
ejpam-6837	375	11	⟨a	⟨a	PROPN
ejpam-6837	375	12	,	,	PUNCT
ejpam-6837	375	13	x⟩	x⟩	PUNCT
ejpam-6837	375	14	≤	≤	ADV
ejpam-6837	375	15	0	0	NUM
ejpam-6837	375	16	}	}	PUNCT
ejpam-6837	375	17	,	,	PUNCT
ejpam-6837	375	18	and	and	CCONJ
ejpam-6837	375	19	c2	c2	PROPN
ejpam-6837	375	20	=	=	SYM
ejpam-6837	375	21	{	{	PUNCT
ejpam-6837	375	22	x	x	PUNCT
ejpam-6837	375	23	∈	∈	PROPN
ejpam-6837	375	24	h	h	NOUN
ejpam-6837	375	25	|	|	ADV
ejpam-6837	375	26	⟨a	⟨a	PROPN
ejpam-6837	375	27	,	,	PUNCT
ejpam-6837	375	28	x⟩	x⟩	PUNCT
ejpam-6837	376	1	=	=	PUNCT
ejpam-6837	376	2	0	0	NUM
ejpam-6837	376	3	}	}	PUNCT
ejpam-6837	376	4	,	,	PUNCT
ejpam-6837	376	5	where	where	SCONJ
ejpam-6837	376	6	a	a	DET
ejpam-6837	376	7	∈	∈	PROPN
ejpam-6837	376	8	h	h	NOUN
ejpam-6837	376	9	and	and	CCONJ
ejpam-6837	376	10	∥a∥	∥a∥	VERB
ejpam-6837	376	11	=	=	SYM
ejpam-6837	376	12	1	1	X
ejpam-6837	376	13	.	.	PUNCT
ejpam-6837	377	1	if	if	SCONJ
ejpam-6837	377	2	x0	x0	PROPN
ejpam-6837	377	3	/∈	/∈	PROPN
ejpam-6837	377	4	c1	c1	PROPN
ejpam-6837	377	5	∪	∪	PROPN
ejpam-6837	377	6	c2	c2	PROPN
ejpam-6837	377	7	,	,	PUNCT
ejpam-6837	377	8	then	then	ADV
ejpam-6837	377	9	〈	〈	PROPN
ejpam-6837	377	10	a	a	PRON
ejpam-6837	377	11	,	,	PUNCT
ejpam-6837	377	12	t[c1c2]x	t[c1c2]x	VERB
ejpam-6837	377	13	〉	〉	NOUN
ejpam-6837	377	14	̸=	̸=	PROPN
ejpam-6837	377	15	0	0	NUM
ejpam-6837	377	16	.	.	PUNCT
ejpam-6837	378	1	proof	proof	NOUN
ejpam-6837	378	2	.	.	PUNCT
ejpam-6837	379	1	the	the	DET
ejpam-6837	379	2	projection	projection	NOUN
ejpam-6837	379	3	to	to	ADP
ejpam-6837	379	4	c1	c1	PROPN
ejpam-6837	379	5	and	and	CCONJ
ejpam-6837	379	6	c2	c2	PROPN
ejpam-6837	379	7	,	,	PUNCT
ejpam-6837	379	8	see	see	VERB
ejpam-6837	379	9	[	[	X
ejpam-6837	379	10	1	1	NUM
ejpam-6837	379	11	,	,	PUNCT
ejpam-6837	379	12	example	example	NOUN
ejpam-6837	379	13	28.15	28.15	NUM
ejpam-6837	379	14	and	and	CCONJ
ejpam-6837	379	15	example	example	NOUN
ejpam-6837	379	16	28.16	28.16	NUM
ejpam-6837	379	17	]	]	PUNCT
ejpam-6837	379	18	,	,	PUNCT
ejpam-6837	379	19	are	be	AUX
ejpam-6837	379	20	pc1	pc1	ADJ
ejpam-6837	379	21	x	x	X
ejpam-6837	379	22	=	=	PUNCT
ejpam-6837	379	23	{	{	PUNCT
ejpam-6837	379	24	x	x	NOUN
ejpam-6837	379	25	−	−	PROPN
ejpam-6837	379	26	⟨a	⟨a	NOUN
ejpam-6837	379	27	,	,	PUNCT
ejpam-6837	379	28	x⟩	x⟩	PUNCT
ejpam-6837	379	29	a	a	DET
ejpam-6837	379	30	if	if	SCONJ
ejpam-6837	379	31	⟨a	⟨a	NOUN
ejpam-6837	379	32	,	,	PUNCT
ejpam-6837	379	33	x⟩	x⟩	PUNCT
ejpam-6837	379	34	>	>	X
ejpam-6837	379	35	0	0	PUNCT
ejpam-6837	380	1	x	x	SYM
ejpam-6837	380	2	if	if	SCONJ
ejpam-6837	380	3	⟨a	⟨a	NOUN
ejpam-6837	380	4	,	,	PUNCT
ejpam-6837	380	5	x⟩	x⟩	PUNCT
ejpam-6837	380	6	≤	≤	NUM
ejpam-6837	380	7	0	0	PUNCT
ejpam-6837	381	1	and	and	CCONJ
ejpam-6837	381	2	,	,	PUNCT
ejpam-6837	381	3	pc2	pc2	NOUN
ejpam-6837	381	4	x	x	SYM
ejpam-6837	381	5	=	=	PUNCT
ejpam-6837	381	6	x	x	SYM
ejpam-6837	382	1	−	−	PROPN
ejpam-6837	382	2	⟨a	⟨a	NOUN
ejpam-6837	382	3	,	,	PUNCT
ejpam-6837	382	4	x⟩	x⟩	PUNCT
ejpam-6837	382	5	a	a	DET
ejpam-6837	382	6	tc1,c2	tc1,c2	NOUN
ejpam-6837	382	7	=	=	SYM
ejpam-6837	382	8	2−1(x	2−1(x	PROPN
ejpam-6837	382	9	+	+	CCONJ
ejpam-6837	382	10	rc2	rc2	PROPN
ejpam-6837	382	11	rc1	rc1	NOUN
ejpam-6837	382	12	x	x	PUNCT
ejpam-6837	382	13	)	)	PUNCT
ejpam-6837	382	14	.	.	PUNCT
ejpam-6837	383	1	(	(	PUNCT
ejpam-6837	383	2	23	23	NUM
ejpam-6837	383	3	)	)	PUNCT
ejpam-6837	383	4	rc1	rc1	NOUN
ejpam-6837	383	5	x	x	SYM
ejpam-6837	384	1	=	=	PRON
ejpam-6837	384	2	{	{	PUNCT
ejpam-6837	384	3	x	x	SYM
ejpam-6837	384	4	−	−	PROPN
ejpam-6837	384	5	2	2	NUM
ejpam-6837	384	6	⟨a	⟨a	NOUN
ejpam-6837	384	7	,	,	PUNCT
ejpam-6837	384	8	x⟩	x⟩	PUNCT
ejpam-6837	385	1	a	a	DET
ejpam-6837	385	2	if	if	SCONJ
ejpam-6837	385	3	⟨a	⟨a	NOUN
ejpam-6837	385	4	,	,	PUNCT
ejpam-6837	385	5	x⟩	x⟩	PUNCT
ejpam-6837	385	6	>	>	X
ejpam-6837	385	7	0	0	PUNCT
ejpam-6837	386	1	x	x	SYM
ejpam-6837	386	2	if	if	SCONJ
ejpam-6837	386	3	⟨a	⟨a	NOUN
ejpam-6837	386	4	,	,	PUNCT
ejpam-6837	386	5	x⟩	x⟩	PUNCT
ejpam-6837	386	6	≤	≤	NUM
ejpam-6837	386	7	0	0	NUM
ejpam-6837	386	8	s.	s.	PROPN
ejpam-6837	386	9	th	th	PROPN
ejpam-6837	386	10	.	.	PUNCT
ejpam-6837	387	1	alwadani	alwadani	PROPN
ejpam-6837	387	2	/	/	SYM
ejpam-6837	387	3	eur	eur	PROPN
ejpam-6837	387	4	.	.	PUNCT
ejpam-6837	388	1	j.	j.	PROPN
ejpam-6837	388	2	pure	pure	PROPN
ejpam-6837	388	3	appl	appl	PROPN
ejpam-6837	388	4	.	.	PROPN
ejpam-6837	388	5	math	math	PROPN
ejpam-6837	388	6	,	,	PUNCT
ejpam-6837	388	7	18	18	NUM
ejpam-6837	388	8	(	(	PUNCT
ejpam-6837	388	9	4	4	NUM
ejpam-6837	388	10	)	)	PUNCT
ejpam-6837	388	11	(	(	PUNCT
ejpam-6837	388	12	2025	2025	NUM
ejpam-6837	388	13	)	)	PUNCT
ejpam-6837	388	14	,	,	PUNCT
ejpam-6837	388	15	6837	6837	NUM
ejpam-6837	388	16	13	13	NUM
ejpam-6837	388	17	of	of	ADP
ejpam-6837	388	18	15	15	NUM
ejpam-6837	388	19	and	and	CCONJ
ejpam-6837	388	20	,	,	PUNCT
ejpam-6837	388	21	rc2(rc1	rc2(rc1	ADJ
ejpam-6837	388	22	x	x	NOUN
ejpam-6837	388	23	)	)	PUNCT
ejpam-6837	388	24	=	=	PRON
ejpam-6837	388	25	{	{	PUNCT
ejpam-6837	389	1	x	x	X
ejpam-6837	389	2	if	if	SCONJ
ejpam-6837	389	3	⟨a	⟨a	NOUN
ejpam-6837	389	4	,	,	PUNCT
ejpam-6837	389	5	x⟩	x⟩	PUNCT
ejpam-6837	389	6	>	>	X
ejpam-6837	389	7	0	0	PUNCT
ejpam-6837	390	1	x	x	SYM
ejpam-6837	390	2	−	−	PROPN
ejpam-6837	390	3	2	2	NUM
ejpam-6837	390	4	⟨a	⟨a	NOUN
ejpam-6837	390	5	,	,	PUNCT
ejpam-6837	390	6	x⟩	x⟩	PUNCT
ejpam-6837	391	1	a	a	DET
ejpam-6837	391	2	if	if	SCONJ
ejpam-6837	391	3	⟨a	⟨a	NOUN
ejpam-6837	391	4	,	,	PUNCT
ejpam-6837	391	5	x⟩	x⟩	PUNCT
ejpam-6837	392	1	≤	≤	NUM
ejpam-6837	392	2	0	0	NUM
ejpam-6837	392	3	then	then	ADV
ejpam-6837	392	4	plugging	plug	VERB
ejpam-6837	392	5	this	this	DET
ejpam-6837	392	6	result	result	NOUN
ejpam-6837	392	7	in	in	ADP
ejpam-6837	392	8	(	(	PUNCT
ejpam-6837	392	9	23	23	NUM
ejpam-6837	392	10	)	)	PUNCT
ejpam-6837	392	11	we	we	PRON
ejpam-6837	392	12	get	get	VERB
ejpam-6837	392	13	that	that	DET
ejpam-6837	392	14	tc1,c2	tc1,c2	NOUN
ejpam-6837	392	15	x	x	PUNCT
ejpam-6837	392	16	=	=	PRON
ejpam-6837	392	17	{	{	PUNCT
ejpam-6837	392	18	x	x	X
ejpam-6837	392	19	if	if	SCONJ
ejpam-6837	392	20	⟨a	⟨a	NOUN
ejpam-6837	392	21	,	,	PUNCT
ejpam-6837	392	22	x⟩	x⟩	PUNCT
ejpam-6837	392	23	>	>	X
ejpam-6837	392	24	0	0	PUNCT
ejpam-6837	393	1	x	x	SYM
ejpam-6837	393	2	−	−	PROPN
ejpam-6837	393	3	⟨a	⟨a	NOUN
ejpam-6837	393	4	,	,	PUNCT
ejpam-6837	393	5	x⟩	x⟩	PUNCT
ejpam-6837	393	6	a	a	DET
ejpam-6837	393	7	if	if	SCONJ
ejpam-6837	393	8	⟨a	⟨a	NOUN
ejpam-6837	393	9	,	,	PUNCT
ejpam-6837	393	10	x⟩	x⟩	PUNCT
ejpam-6837	393	11	≤	≤	NUM
ejpam-6837	393	12	0	0	NUM
ejpam-6837	393	13	similarly	similarly	ADV
ejpam-6837	393	14	,	,	PUNCT
ejpam-6837	393	15	tc2,c1	tc2,c1	NOUN
ejpam-6837	393	16	x	x	X
ejpam-6837	393	17	=	=	PRON
ejpam-6837	393	18	{	{	PUNCT
ejpam-6837	393	19	x	x	X
ejpam-6837	393	20	if	if	SCONJ
ejpam-6837	393	21	⟨a	⟨a	NOUN
ejpam-6837	393	22	,	,	PUNCT
ejpam-6837	393	23	x⟩	x⟩	PUNCT
ejpam-6837	393	24	>	>	X
ejpam-6837	393	25	0	0	PUNCT
ejpam-6837	394	1	x	x	SYM
ejpam-6837	394	2	−	−	PROPN
ejpam-6837	394	3	⟨a	⟨a	NOUN
ejpam-6837	394	4	,	,	PUNCT
ejpam-6837	394	5	x⟩	x⟩	PUNCT
ejpam-6837	394	6	a	a	DET
ejpam-6837	394	7	if	if	SCONJ
ejpam-6837	394	8	⟨a	⟨a	NOUN
ejpam-6837	394	9	,	,	PUNCT
ejpam-6837	394	10	x⟩	x⟩	PUNCT
ejpam-6837	394	11	≤	≤	NUM
ejpam-6837	394	12	0	0	PUNCT
ejpam-6837	395	1	then	then	ADV
ejpam-6837	395	2	,	,	PUNCT
ejpam-6837	395	3	by	by	ADP
ejpam-6837	395	4	lemma	lemma	PROPN
ejpam-6837	395	5	1	1	NUM
ejpam-6837	395	6	we	we	PRON
ejpam-6837	395	7	have	have	VERB
ejpam-6837	395	8	,	,	PUNCT
ejpam-6837	395	9	2	2	NUM
ejpam-6837	395	10	〈	〈	PROPN
ejpam-6837	395	11	a	a	PRON
ejpam-6837	395	12	,	,	PUNCT
ejpam-6837	395	13	t[c1c2]x	t[c1c2]x	VERB
ejpam-6837	395	14	〉	〉	NOUN
ejpam-6837	395	15	=	=	SYM
ejpam-6837	395	16	2	2	NUM
ejpam-6837	395	17	〈	〈	PROPN
ejpam-6837	395	18	a	a	PRON
ejpam-6837	395	19	,	,	PUNCT
ejpam-6837	395	20	2−1(tc1,c2	2−1(tc1,c2	NUM
ejpam-6837	395	21	+	+	NUM
ejpam-6837	395	22	tc2,c1)x	tc2,c1)x	NUM
ejpam-6837	395	23	〉	〉	NOUN
ejpam-6837	395	24	=	=	SYM
ejpam-6837	395	25	⟨a	⟨a	PROPN
ejpam-6837	395	26	,	,	PUNCT
ejpam-6837	395	27	tc1,c2	tc1,c2	NOUN
ejpam-6837	395	28	x⟩+	x⟩+	PROPN
ejpam-6837	395	29	⟨a	⟨a	PROPN
ejpam-6837	395	30	,	,	PUNCT
ejpam-6837	395	31	tc2,c1	tc2,c1	NOUN
ejpam-6837	395	32	x⟩	x⟩	PUNCT
ejpam-6837	395	33	(	(	PUNCT
ejpam-6837	395	34	24	24	NUM
ejpam-6837	395	35	)	)	PUNCT
ejpam-6837	395	36	when	when	SCONJ
ejpam-6837	395	37	⟨a	⟨a	NOUN
ejpam-6837	395	38	,	,	PUNCT
ejpam-6837	395	39	x⟩	x⟩	PUNCT
ejpam-6837	395	40	>	>	X
ejpam-6837	395	41	0	0	NUM
ejpam-6837	395	42	;	;	PUNCT
ejpam-6837	395	43	〈	〈	PROPN
ejpam-6837	395	44	a	a	PRON
ejpam-6837	395	45	,	,	PUNCT
ejpam-6837	395	46	t[c1c2	t[c1c2	NOUN
ejpam-6837	395	47	]	]	X
ejpam-6837	395	48	〉	〉	X
ejpam-6837	395	49	(	(	PUNCT
ejpam-6837	395	50	24	24	NUM
ejpam-6837	395	51	)	)	PUNCT
ejpam-6837	395	52	=	=	SYM
ejpam-6837	395	53	⟨a	⟨a	PROPN
ejpam-6837	395	54	,	,	PUNCT
ejpam-6837	395	55	x⟩+	x⟩+	PROPN
ejpam-6837	395	56	⟨a	⟨a	PROPN
ejpam-6837	395	57	,	,	PUNCT
ejpam-6837	395	58	x⟩	x⟩	PUNCT
ejpam-6837	396	1	=	=	SYM
ejpam-6837	396	2	2	2	NUM
ejpam-6837	396	3	⟨a	⟨a	NOUN
ejpam-6837	396	4	,	,	PUNCT
ejpam-6837	396	5	x⟩	x⟩	X
ejpam-6837	396	6	.	.	PUNCT
ejpam-6837	397	1	(	(	PUNCT
ejpam-6837	397	2	25	25	NUM
ejpam-6837	397	3	)	)	PUNCT
ejpam-6837	397	4	when	when	SCONJ
ejpam-6837	397	5	⟨a	⟨a	NOUN
ejpam-6837	397	6	,	,	PUNCT
ejpam-6837	397	7	x⟩	x⟩	PUNCT
ejpam-6837	397	8	≤	≤	NOUN
ejpam-6837	397	9	0	0	NUM
ejpam-6837	397	10	;	;	PUNCT
ejpam-6837	397	11	〈	〈	PROPN
ejpam-6837	397	12	a	a	PRON
ejpam-6837	397	13	,	,	PUNCT
ejpam-6837	397	14	t[c1c2	t[c1c2	NOUN
ejpam-6837	397	15	]	]	X
ejpam-6837	397	16	〉	〉	X
ejpam-6837	397	17	(	(	PUNCT
ejpam-6837	397	18	24	24	NUM
ejpam-6837	397	19	)	)	PUNCT
ejpam-6837	397	20	=	=	SYM
ejpam-6837	397	21	⟨a	⟨a	NOUN
ejpam-6837	397	22	,	,	PUNCT
ejpam-6837	397	23	x⟩	x⟩	PUNCT
ejpam-6837	397	24	−	−	PROPN
ejpam-6837	398	1	⟨a	⟨a	PROPN
ejpam-6837	398	2	,	,	PUNCT
ejpam-6837	398	3	x⟩	x⟩	X
ejpam-6837	398	4	∥a∥2	∥a∥2	PROPN
ejpam-6837	398	5	+	+	CCONJ
ejpam-6837	398	6	⟨a	⟨a	PROPN
ejpam-6837	398	7	,	,	PUNCT
ejpam-6837	398	8	x⟩	x⟩	PUNCT
ejpam-6837	399	1	−	−	PROPN
ejpam-6837	399	2	⟨a	⟨a	PROPN
ejpam-6837	399	3	,	,	PUNCT
ejpam-6837	399	4	x⟩	x⟩	X
ejpam-6837	399	5	∥a∥2	∥a∥2	PROPN
ejpam-6837	399	6	=	=	SYM
ejpam-6837	399	7	0	0	PROPN
ejpam-6837	399	8	.	.	PUNCT
ejpam-6837	400	1	(	(	PUNCT
ejpam-6837	400	2	26	26	NUM
ejpam-6837	400	3	)	)	PUNCT
ejpam-6837	400	4	therefore	therefore	ADV
ejpam-6837	400	5	(	(	PUNCT
ejpam-6837	400	6	25	25	NUM
ejpam-6837	400	7	)	)	PUNCT
ejpam-6837	400	8	and	and	CCONJ
ejpam-6837	400	9	(	(	PUNCT
ejpam-6837	400	10	26	26	NUM
ejpam-6837	400	11	)	)	PUNCT
ejpam-6837	400	12	show	show	VERB
ejpam-6837	400	13	that	that	SCONJ
ejpam-6837	400	14	if	if	SCONJ
ejpam-6837	400	15	x0	x0	PROPN
ejpam-6837	400	16	/∈	/∈	PROPN
ejpam-6837	400	17	c1	c1	PROPN
ejpam-6837	400	18	∪	∪	PROPN
ejpam-6837	400	19	c2	c2	PROPN
ejpam-6837	400	20	then	then	ADV
ejpam-6837	400	21	the	the	DET
ejpam-6837	400	22	douglasrachford	douglasrachford	PROPN
ejpam-6837	400	23	iterates	iterate	VERB
ejpam-6837	400	24	will	will	AUX
ejpam-6837	400	25	not	not	PART
ejpam-6837	400	26	lie	lie	VERB
ejpam-6837	400	27	in	in	ADP
ejpam-6837	400	28	c1	c1	PROPN
ejpam-6837	400	29	or	or	CCONJ
ejpam-6837	400	30	c2	c2	PROPN
ejpam-6837	400	31	.	.	PUNCT
ejpam-6837	401	1	hence	hence	ADV
ejpam-6837	401	2	,	,	PUNCT
ejpam-6837	401	3	if	if	SCONJ
ejpam-6837	401	4	⟨a	⟨a	NOUN
ejpam-6837	401	5	,	,	PUNCT
ejpam-6837	401	6	x⟩	x⟩	PUNCT
ejpam-6837	401	7	̸≤	̸≤	PROPN
ejpam-6837	401	8	0	0	NUM
ejpam-6837	401	9	,	,	PUNCT
ejpam-6837	401	10	then	then	ADV
ejpam-6837	401	11	〈	〈	PROPN
ejpam-6837	401	12	a	a	PRON
ejpam-6837	401	13	,	,	PUNCT
ejpam-6837	401	14	t[c1c2	t[c1c2	NOUN
ejpam-6837	401	15	]	]	PUNCT
ejpam-6837	401	16	〉	〉	NOUN
ejpam-6837	401	17	̸=	̸=	PROPN
ejpam-6837	401	18	0	0	NUM
ejpam-6837	401	19	.	.	PUNCT
ejpam-6837	402	1	■	■	PUNCT
ejpam-6837	402	2	4.1	4.1	NUM
ejpam-6837	402	3	.	.	PUNCT
ejpam-6837	403	1	a	a	DET
ejpam-6837	403	2	product	product	NOUN
ejpam-6837	403	3	version	version	NOUN
ejpam-6837	403	4	of	of	ADP
ejpam-6837	403	5	the	the	DET
ejpam-6837	403	6	cyclic	cyclic	ADJ
ejpam-6837	403	7	douglas	douglas	PROPN
ejpam-6837	403	8	–	–	PUNCT
ejpam-6837	403	9	rachford	rachford	ADJ
ejpam-6837	403	10	method	method	NOUN
ejpam-6837	403	11	consider	consider	VERB
ejpam-6837	403	12	the	the	DET
ejpam-6837	403	13	hilbert	hilbert	NOUN
ejpam-6837	403	14	space	space	NOUN
ejpam-6837	403	15	hn	hn	PROPN
ejpam-6837	403	16	=	=	PUNCT
ejpam-6837	403	17	h×h×	h×h×	PROPN
ejpam-6837	403	18	·	·	PUNCT
ejpam-6837	403	19	·	·	PUNCT
ejpam-6837	403	20	·	·	PUNCT
ejpam-6837	404	1	×	×	NOUN
ejpam-6837	404	2	h.	h.	NOUN
ejpam-6837	404	3	define	define	VERB
ejpam-6837	404	4	two	two	NUM
ejpam-6837	404	5	closed	closed	ADJ
ejpam-6837	404	6	and	and	CCONJ
ejpam-6837	404	7	convex	convex	ADJ
ejpam-6837	404	8	subsets	subset	NOUN
ejpam-6837	404	9	c	c	PROPN
ejpam-6837	404	10	and	and	CCONJ
ejpam-6837	404	11	d	d	PROPN
ejpam-6837	404	12	of	of	ADP
ejpam-6837	404	13	hn	hn	PROPN
ejpam-6837	404	14	,	,	PUNCT
ejpam-6837	404	15	where	where	SCONJ
ejpam-6837	404	16	c	c	NOUN
ejpam-6837	404	17	∩	∩	PROPN
ejpam-6837	404	18	d	d	PROPN
ejpam-6837	404	19	̸=	̸=	PROPN
ejpam-6837	404	20	∅	∅	NOUN
ejpam-6837	404	21	,	,	PUNCT
ejpam-6837	404	22	by	by	ADP
ejpam-6837	404	23	c	c	NOUN
ejpam-6837	404	24	:	:	PUNCT
ejpam-6837	404	25	=	=	SYM
ejpam-6837	404	26	{	{	PUNCT
ejpam-6837	404	27	(	(	PUNCT
ejpam-6837	404	28	x1	x1	PROPN
ejpam-6837	404	29	,	,	PUNCT
ejpam-6837	404	30	x2	x2	PROPN
ejpam-6837	404	31	,	,	PUNCT
ejpam-6837	404	32	.	.	PUNCT
ejpam-6837	404	33	.	.	PUNCT
ejpam-6837	404	34	.	.	PUNCT
ejpam-6837	405	1	,	,	PUNCT
ejpam-6837	405	2	xn	xn	X
ejpam-6837	405	3	)	)	PUNCT
ejpam-6837	405	4	∈	∈	NOUN
ejpam-6837	406	1	hn	hn	INTJ
ejpam-6837	406	2	|	|	ADV
ejpam-6837	406	3	xi	xi	PROPN
ejpam-6837	406	4	∈	∈	PROPN
ejpam-6837	406	5	ci	ci	PROPN
ejpam-6837	406	6	}	}	PUNCT
ejpam-6837	406	7	,	,	PUNCT
ejpam-6837	406	8	and	and	CCONJ
ejpam-6837	406	9	d	d	NOUN
ejpam-6837	406	10	:	:	PUNCT
ejpam-6837	406	11	=	=	SYM
ejpam-6837	406	12	{	{	PUNCT
ejpam-6837	406	13	(	(	PUNCT
ejpam-6837	406	14	x	x	X
ejpam-6837	406	15	,	,	PUNCT
ejpam-6837	406	16	x	x	X
ejpam-6837	406	17	,	,	PUNCT
ejpam-6837	406	18	.	.	PUNCT
ejpam-6837	406	19	.	.	PUNCT
ejpam-6837	406	20	.	.	PUNCT
ejpam-6837	407	1	,	,	PUNCT
ejpam-6837	407	2	x	x	X
ejpam-6837	407	3	)	)	PUNCT
ejpam-6837	407	4	∈	∈	NOUN
ejpam-6837	408	1	hn	hn	INTJ
ejpam-6837	409	1	|	|	ADV
ejpam-6837	409	2	x	x	SYM
ejpam-6837	409	3	∈	∈	PROPN
ejpam-6837	409	4	h	h	NOUN
ejpam-6837	409	5	}	}	PUNCT
ejpam-6837	409	6	.	.	PUNCT
ejpam-6837	410	1	(	(	PUNCT
ejpam-6837	410	2	1	1	X
ejpam-6837	410	3	)	)	PUNCT
ejpam-6837	410	4	will	will	AUX
ejpam-6837	410	5	be	be	AUX
ejpam-6837	410	6	solved	solve	VERB
ejpam-6837	410	7	by	by	ADP
ejpam-6837	410	8	find	find	NOUN
ejpam-6837	410	9	x	x	X
ejpam-6837	410	10	∈	∈	PROPN
ejpam-6837	410	11	(	(	PUNCT
ejpam-6837	410	12	c	c	NOUN
ejpam-6837	410	13	∩	∩	X
ejpam-6837	410	14	d	d	NOUN
ejpam-6837	410	15	)	)	PUNCT
ejpam-6837	410	16	⊆	⊆	NUM
ejpam-6837	410	17	hn	hn	PROPN
ejpam-6837	410	18	.	.	PUNCT
ejpam-6837	411	1	the	the	DET
ejpam-6837	411	2	projection	projection	NOUN
ejpam-6837	411	3	on	on	ADP
ejpam-6837	411	4	c	c	PROPN
ejpam-6837	411	5	and	and	CCONJ
ejpam-6837	411	6	d	d	PROPN
ejpam-6837	411	7	will	will	AUX
ejpam-6837	411	8	be	be	AUX
ejpam-6837	411	9	pc	pc	NOUN
ejpam-6837	411	10	=	=	PUNCT
ejpam-6837	411	11	(	(	PUNCT
ejpam-6837	411	12	pc1	pc1	PROPN
ejpam-6837	411	13	x1	x1	PROPN
ejpam-6837	411	14	,	,	PUNCT
ejpam-6837	411	15	pc2	pc2	NOUN
ejpam-6837	411	16	x2	x2	PROPN
ejpam-6837	411	17	,	,	PUNCT
ejpam-6837	411	18	.	.	PUNCT
ejpam-6837	411	19	.	.	PUNCT
ejpam-6837	412	1	.	.	PUNCT
ejpam-6837	413	1	,	,	PUNCT
ejpam-6837	413	2	pcn	pcn	PROPN
ejpam-6837	413	3	xn	xn	PROPN
ejpam-6837	413	4	)	)	PUNCT
ejpam-6837	413	5	,	,	PUNCT
ejpam-6837	413	6	and	and	CCONJ
ejpam-6837	413	7	pd	pd	X
ejpam-6837	413	8	=	=	PUNCT
ejpam-6837	413	9	(	(	PUNCT
ejpam-6837	413	10	1	1	NUM
ejpam-6837	413	11	n	n	CCONJ
ejpam-6837	413	12	n	n	NOUN
ejpam-6837	413	13	∑	∑	ADV
ejpam-6837	413	14	i=1	i=1	PROPN
ejpam-6837	413	15	xi	xi	PROPN
ejpam-6837	413	16	,	,	PUNCT
ejpam-6837	413	17	1	1	NUM
ejpam-6837	413	18	n	n	ADP
ejpam-6837	413	19	n	n	ADV
ejpam-6837	413	20	∑	∑	ADV
ejpam-6837	413	21	i=1	i=1	PROPN
ejpam-6837	413	22	xi	xi	PROPN
ejpam-6837	413	23	,	,	PUNCT
ejpam-6837	413	24	.	.	PUNCT
ejpam-6837	413	25	.	.	PUNCT
ejpam-6837	413	26	.	.	PUNCT
ejpam-6837	414	1	,	,	PUNCT
ejpam-6837	414	2	1	1	NUM
ejpam-6837	414	3	n	n	CCONJ
ejpam-6837	414	4	n	n	ADV
ejpam-6837	414	5	∑	∑	ADV
ejpam-6837	414	6	i=1	i=1	PROPN
ejpam-6837	414	7	xi	xi	PROPN
ejpam-6837	414	8	)	)	PUNCT
ejpam-6837	414	9	.	.	PUNCT
ejpam-6837	415	1	see	see	VERB
ejpam-6837	415	2	[	[	X
ejpam-6837	415	3	1	1	NUM
ejpam-6837	415	4	,	,	PUNCT
ejpam-6837	415	5	proposition	proposition	NOUN
ejpam-6837	415	6	25.4(iii	25.4(iii	NUM
ejpam-6837	415	7	)	)	PUNCT
ejpam-6837	415	8	and	and	CCONJ
ejpam-6837	415	9	(	(	PUNCT
ejpam-6837	415	10	iv	iv	X
ejpam-6837	415	11	)	)	PUNCT
ejpam-6837	415	12	]	]	PUNCT
ejpam-6837	415	13	for	for	ADP
ejpam-6837	415	14	more	more	ADJ
ejpam-6837	415	15	details	detail	NOUN
ejpam-6837	415	16	.	.	PUNCT
ejpam-6837	416	1	s.	s.	PROPN
ejpam-6837	416	2	th	th	PROPN
ejpam-6837	416	3	.	.	PUNCT
ejpam-6837	417	1	alwadani	alwadani	PROPN
ejpam-6837	417	2	/	/	SYM
ejpam-6837	417	3	eur	eur	PROPN
ejpam-6837	417	4	.	.	PUNCT
ejpam-6837	418	1	j.	j.	PROPN
ejpam-6837	418	2	pure	pure	PROPN
ejpam-6837	418	3	appl	appl	PROPN
ejpam-6837	418	4	.	.	PROPN
ejpam-6837	418	5	math	math	PROPN
ejpam-6837	418	6	,	,	PUNCT
ejpam-6837	418	7	18	18	NUM
ejpam-6837	418	8	(	(	PUNCT
ejpam-6837	418	9	4	4	NUM
ejpam-6837	418	10	)	)	PUNCT
ejpam-6837	418	11	(	(	PUNCT
ejpam-6837	418	12	2025	2025	NUM
ejpam-6837	418	13	)	)	PUNCT
ejpam-6837	418	14	,	,	PUNCT
ejpam-6837	418	15	6837	6837	NUM
ejpam-6837	418	16	14	14	NUM
ejpam-6837	418	17	of	of	ADP
ejpam-6837	418	18	15	15	NUM
ejpam-6837	418	19	lemma	lemma	PROPN
ejpam-6837	418	20	2	2	NUM
ejpam-6837	418	21	.	.	PUNCT
ejpam-6837	419	1	the	the	DET
ejpam-6837	419	2	iteration	iteration	NOUN
ejpam-6837	419	3	for	for	ADP
ejpam-6837	419	4	the	the	DET
ejpam-6837	419	5	product	product	NOUN
ejpam-6837	419	6	version	version	NOUN
ejpam-6837	419	7	of	of	ADP
ejpam-6837	419	8	the	the	DET
ejpam-6837	419	9	cyclic	cyclic	ADJ
ejpam-6837	419	10	douglas	douglas	PROPN
ejpam-6837	419	11	-	-	PUNCT
ejpam-6837	419	12	rachford	rachford	ADJ
ejpam-6837	419	13	method	method	NOUN
ejpam-6837	419	14	will	will	AUX
ejpam-6837	419	15	be	be	AUX
ejpam-6837	419	16	define	define	VERB
ejpam-6837	419	17	as	as	ADP
ejpam-6837	419	18	t[d	t[d	NOUN
ejpam-6837	419	19	c]x	c]x	NOUN
ejpam-6837	420	1	=	=	SYM
ejpam-6837	420	2	x	x	SYM
ejpam-6837	420	3	−	−	PROPN
ejpam-6837	420	4	pd	pd	X
ejpam-6837	420	5	x	x	SYM
ejpam-6837	420	6	+	+	NUM
ejpam-6837	420	7	2	2	NUM
ejpam-6837	420	8	pd	pd	NOUN
ejpam-6837	420	9	pc	pc	NOUN
ejpam-6837	420	10	td	td	NOUN
ejpam-6837	420	11	,	,	PUNCT
ejpam-6837	420	12	cx	cx	NOUN
ejpam-6837	420	13	−	−	PROPN
ejpam-6837	420	14	pc	pc	NOUN
ejpam-6837	420	15	td	td	NOUN
ejpam-6837	420	16	,	,	PUNCT
ejpam-6837	420	17	cx	cx	PROPN
ejpam-6837	420	18	+	+	CCONJ
ejpam-6837	420	19	pc	pc	NOUN
ejpam-6837	420	20	rdx	rdx	NOUN
ejpam-6837	420	21	−	−	PROPN
ejpam-6837	420	22	pd	pd	PROPN
ejpam-6837	420	23	pc	pc	PROPN
ejpam-6837	420	24	rdx	rdx	PROPN
ejpam-6837	420	25	.	.	PUNCT
ejpam-6837	421	1	(	(	PUNCT
ejpam-6837	421	2	27	27	NUM
ejpam-6837	421	3	)	)	PUNCT
ejpam-6837	421	4	proof	proof	NOUN
ejpam-6837	421	5	.	.	PUNCT
ejpam-6837	422	1	then	then	ADV
ejpam-6837	422	2	rdrctdcx	rdrctdcx	VERB
ejpam-6837	422	3	=	=	SYM
ejpam-6837	422	4	(	(	PUNCT
ejpam-6837	422	5	2	2	NUM
ejpam-6837	422	6	pd	pd	NOUN
ejpam-6837	422	7	−	−	PROPN
ejpam-6837	422	8	id)rctdcx	id)rctdcx	ADV
ejpam-6837	422	9	=	=	SYM
ejpam-6837	422	10	2	2	NUM
ejpam-6837	422	11	pd	pd	NOUN
ejpam-6837	422	12	rctdcx	rctdcx	NOUN
ejpam-6837	422	13	−	−	PROPN
ejpam-6837	422	14	rctd	rctd	NOUN
ejpam-6837	422	15	,	,	PUNCT
ejpam-6837	422	16	cx	cx	PROPN
ejpam-6837	422	17	=	=	SYM
ejpam-6837	422	18	2	2	NUM
ejpam-6837	422	19	pd(2	pd(2	NOUN
ejpam-6837	422	20	pc	pc	NOUN
ejpam-6837	422	21	−	−	NOUN
ejpam-6837	422	22	id)tdcx	id)tdcx	NOUN
ejpam-6837	422	23	−	−	ADV
ejpam-6837	422	24	rctdcx	rctdcx	ADV
ejpam-6837	422	25	=	=	SYM
ejpam-6837	422	26	4	4	NUM
ejpam-6837	422	27	pd	pd	NOUN
ejpam-6837	422	28	pc	pc	NOUN
ejpam-6837	422	29	tdcx	tdcx	ADV
ejpam-6837	422	30	−	−	PROPN
ejpam-6837	422	31	2	2	NUM
ejpam-6837	422	32	pd	pd	NOUN
ejpam-6837	422	33	tdcx	tdcx	ADV
ejpam-6837	422	34	−	−	PROPN
ejpam-6837	422	35	rctdcx	rctdcx	ADV
ejpam-6837	422	36	=	=	SYM
ejpam-6837	422	37	4	4	NUM
ejpam-6837	422	38	pd	pd	NOUN
ejpam-6837	422	39	pc	pc	NOUN
ejpam-6837	422	40	tdcx	tdcx	ADV
ejpam-6837	422	41	−	−	PROPN
ejpam-6837	422	42	2	2	NUM
ejpam-6837	422	43	pd	pd	NOUN
ejpam-6837	422	44	tdcx	tdcx	ADV
ejpam-6837	422	45	−	−	PROPN
ejpam-6837	423	1	(	(	PUNCT
ejpam-6837	423	2	2	2	NUM
ejpam-6837	423	3	pc	pc	NOUN
ejpam-6837	423	4	−	−	NOUN
ejpam-6837	423	5	id)tdcx	id)tdcx	NOUN
ejpam-6837	423	6	=	=	SYM
ejpam-6837	423	7	4	4	NUM
ejpam-6837	423	8	pd	pd	NOUN
ejpam-6837	423	9	pc	pc	NOUN
ejpam-6837	423	10	tdcx	tdcx	ADV
ejpam-6837	423	11	−	−	PROPN
ejpam-6837	423	12	2	2	NUM
ejpam-6837	423	13	pd	pd	NOUN
ejpam-6837	423	14	tdcx	tdcx	ADV
ejpam-6837	423	15	−	−	PROPN
ejpam-6837	423	16	2	2	NUM
ejpam-6837	423	17	pc	pc	NOUN
ejpam-6837	423	18	tdcx	tdcx	ADV
ejpam-6837	423	19	+	+	CCONJ
ejpam-6837	423	20	tdcx	tdcx	PROPN
ejpam-6837	423	21	(	(	PUNCT
ejpam-6837	423	22	28	28	NUM
ejpam-6837	423	23	)	)	PUNCT
ejpam-6837	423	24	using	use	VERB
ejpam-6837	423	25	the	the	DET
ejpam-6837	423	26	result	result	NOUN
ejpam-6837	423	27	from	from	ADP
ejpam-6837	423	28	(	(	PUNCT
ejpam-6837	423	29	28	28	NUM
ejpam-6837	423	30	)	)	PUNCT
ejpam-6837	423	31	in	in	ADP
ejpam-6837	423	32	(	(	PUNCT
ejpam-6837	423	33	?	?	PUNCT
ejpam-6837	423	34	?	?	PUNCT
ejpam-6837	423	35	)	)	PUNCT
ejpam-6837	423	36	,	,	PUNCT
ejpam-6837	423	37	we	we	PRON
ejpam-6837	423	38	have	have	VERB
ejpam-6837	423	39	t[d	t[d	NOUN
ejpam-6837	424	1	c]x	c]x	NOUN
ejpam-6837	424	2	=	=	SYM
ejpam-6837	424	3	td	td	NOUN
ejpam-6837	424	4	,	,	PUNCT
ejpam-6837	424	5	cx	cx	PROPN
ejpam-6837	424	6	+	+	CCONJ
ejpam-6837	424	7	2	2	NUM
ejpam-6837	424	8	pd	pd	NOUN
ejpam-6837	424	9	pc	pc	NOUN
ejpam-6837	424	10	td	td	NOUN
ejpam-6837	424	11	,	,	PUNCT
ejpam-6837	424	12	cx	cx	PROPN
ejpam-6837	424	13	−	−	PROPN
ejpam-6837	424	14	pd	pd	PROPN
ejpam-6837	424	15	td	td	PROPN
ejpam-6837	424	16	,	,	PUNCT
ejpam-6837	424	17	cx	cx	NOUN
ejpam-6837	424	18	−	−	PROPN
ejpam-6837	424	19	pc	pc	NOUN
ejpam-6837	424	20	td	td	NOUN
ejpam-6837	424	21	,	,	PUNCT
ejpam-6837	424	22	cx	cx	PROPN
ejpam-6837	424	23	(	(	PUNCT
ejpam-6837	424	24	29	29	NUM
ejpam-6837	424	25	)	)	PUNCT
ejpam-6837	424	26	however	however	ADV
ejpam-6837	424	27	,	,	PUNCT
ejpam-6837	424	28	tdcx	tdcx	PROPN
ejpam-6837	424	29	=	=	SYM
ejpam-6837	424	30	2−1(x	2−1(x	PROPN
ejpam-6837	424	31	+	+	NUM
ejpam-6837	424	32	rcrdx	rcrdx	NOUN
ejpam-6837	424	33	)	)	PUNCT
ejpam-6837	424	34	(	(	PUNCT
ejpam-6837	424	35	30	30	NUM
ejpam-6837	424	36	)	)	PUNCT
ejpam-6837	424	37	=	=	SYM
ejpam-6837	425	1	2−1(x	2−1(x	NUM
ejpam-6837	425	2	+	+	CCONJ
ejpam-6837	425	3	(	(	PUNCT
ejpam-6837	425	4	2	2	NUM
ejpam-6837	425	5	pc	pc	NOUN
ejpam-6837	425	6	−	−	NOUN
ejpam-6837	425	7	id)rdx	id)rdx	NOUN
ejpam-6837	425	8	)	)	PUNCT
ejpam-6837	425	9	(	(	PUNCT
ejpam-6837	425	10	31	31	NUM
ejpam-6837	425	11	)	)	PUNCT
ejpam-6837	425	12	=	=	SYM
ejpam-6837	426	1	2−1(x	2−1(x	NUM
ejpam-6837	426	2	+	+	SYM
ejpam-6837	426	3	2	2	NUM
ejpam-6837	426	4	pc	pc	NOUN
ejpam-6837	426	5	rdx	rdx	NOUN
ejpam-6837	426	6	−	−	PROPN
ejpam-6837	426	7	rdx	rdx	PROPN
ejpam-6837	426	8	)	)	PUNCT
ejpam-6837	426	9	(	(	PUNCT
ejpam-6837	426	10	32	32	NUM
ejpam-6837	426	11	)	)	PUNCT
ejpam-6837	426	12	=	=	SYM
ejpam-6837	427	1	x	x	PUNCT
ejpam-6837	427	2	−	−	PROPN
ejpam-6837	427	3	pd	pd	NOUN
ejpam-6837	427	4	x	x	SYM
ejpam-6837	427	5	−	−	PROPN
ejpam-6837	427	6	pc	pc	NOUN
ejpam-6837	427	7	rdx	rdx	NOUN
ejpam-6837	427	8	.	.	PUNCT
ejpam-6837	428	1	(	(	PUNCT
ejpam-6837	428	2	33	33	NUM
ejpam-6837	428	3	)	)	PUNCT
ejpam-6837	428	4	moreover	moreover	ADV
ejpam-6837	428	5	,	,	PUNCT
ejpam-6837	428	6	−pd	−pd	PROPN
ejpam-6837	428	7	tdcx	tdcx	PROPN
ejpam-6837	428	8	=	=	SYM
ejpam-6837	429	1	−2−1	−2−1	NOUN
ejpam-6837	429	2	pd	pd	X
ejpam-6837	429	3	x	x	X
ejpam-6837	429	4	−	−	PROPN
ejpam-6837	429	5	2−1	2−1	NUM
ejpam-6837	429	6	pd(rcrdx	pd(rcrdx	PROPN
ejpam-6837	429	7	)	)	PUNCT
ejpam-6837	429	8	=	=	SYM
ejpam-6837	430	1	−2−1	−2−1	PRON
ejpam-6837	430	2	pd	pd	X
ejpam-6837	430	3	x	x	X
ejpam-6837	430	4	−	−	PROPN
ejpam-6837	430	5	2−1	2−1	NUM
ejpam-6837	430	6	pd	pd	X
ejpam-6837	430	7	(	(	PUNCT
ejpam-6837	430	8	(	(	PUNCT
ejpam-6837	430	9	2	2	NUM
ejpam-6837	430	10	pc	pc	NOUN
ejpam-6837	430	11	−	−	NOUN
ejpam-6837	430	12	id)rdx	id)rdx	NOUN
ejpam-6837	430	13	)	)	PUNCT
ejpam-6837	430	14	=	=	PUNCT
ejpam-6837	431	1	−2−1	−2−1	PRON
ejpam-6837	431	2	pd	pd	X
ejpam-6837	431	3	x	x	SYM
ejpam-6837	431	4	−	−	PROPN
ejpam-6837	431	5	pd	pd	PROPN
ejpam-6837	431	6	pc	pc	NOUN
ejpam-6837	431	7	rdx	rdx	NOUN
ejpam-6837	431	8	+	+	CCONJ
ejpam-6837	431	9	2−1	2−1	NUM
ejpam-6837	431	10	pd	pd	PROPN
ejpam-6837	431	11	rdx	rdx	PROPN
ejpam-6837	431	12	=	=	PROPN
ejpam-6837	431	13	−2−1	−2−1	PROPN
ejpam-6837	431	14	pd	pd	X
ejpam-6837	431	15	x	x	SYM
ejpam-6837	431	16	−	−	PROPN
ejpam-6837	431	17	pd	pd	PROPN
ejpam-6837	431	18	pc	pc	NOUN
ejpam-6837	431	19	rdx	rdx	NOUN
ejpam-6837	431	20	+	+	CCONJ
ejpam-6837	431	21	2−1	2−1	NUM
ejpam-6837	431	22	pd(2	pd(2	NOUN
ejpam-6837	431	23	pd	pd	PROPN
ejpam-6837	431	24	−	−	PROPN
ejpam-6837	431	25	i	i	PROPN
ejpam-6837	431	26	d	d	PROPN
ejpam-6837	431	27	)	)	PUNCT
ejpam-6837	432	1	=	=	PUNCT
ejpam-6837	432	2	−2−1	−2−1	PRON
ejpam-6837	432	3	pd	pd	X
ejpam-6837	432	4	x	x	SYM
ejpam-6837	432	5	−	−	PROPN
ejpam-6837	432	6	pd	pd	PROPN
ejpam-6837	432	7	pc	pc	NOUN
ejpam-6837	432	8	rdx	rdx	NOUN
ejpam-6837	432	9	+	+	CCONJ
ejpam-6837	432	10	pd	pd	X
ejpam-6837	432	11	x	x	X
ejpam-6837	432	12	−	−	PROPN
ejpam-6837	432	13	2−1	2−1	NUM
ejpam-6837	432	14	pd	pd	X
ejpam-6837	432	15	x	x	PUNCT
ejpam-6837	432	16	=	=	SYM
ejpam-6837	432	17	−pd	−pd	PROPN
ejpam-6837	432	18	pc	pc	NOUN
ejpam-6837	432	19	rdx	rdx	NOUN
ejpam-6837	432	20	(	(	PUNCT
ejpam-6837	432	21	34	34	NUM
ejpam-6837	432	22	)	)	PUNCT
ejpam-6837	432	23	by	by	ADP
ejpam-6837	432	24	(	(	PUNCT
ejpam-6837	432	25	33	33	NUM
ejpam-6837	432	26	)	)	PUNCT
ejpam-6837	432	27	and	and	CCONJ
ejpam-6837	432	28	(	(	PUNCT
ejpam-6837	432	29	34	34	NUM
ejpam-6837	432	30	)	)	PUNCT
ejpam-6837	432	31	,	,	PUNCT
ejpam-6837	432	32	the	the	DET
ejpam-6837	432	33	updated	update	VERB
ejpam-6837	432	34	formula	formula	NOUN
ejpam-6837	432	35	for	for	ADP
ejpam-6837	432	36	equation	equation	NOUN
ejpam-6837	432	37	(	(	PUNCT
ejpam-6837	432	38	29	29	NUM
ejpam-6837	432	39	)	)	PUNCT
ejpam-6837	432	40	will	will	AUX
ejpam-6837	432	41	be	be	AUX
ejpam-6837	432	42	t[d	t[d	NOUN
ejpam-6837	432	43	c]x	c]x	NOUN
ejpam-6837	433	1	=	=	SYM
ejpam-6837	433	2	x	x	SYM
ejpam-6837	433	3	−	−	PROPN
ejpam-6837	433	4	pd	pd	X
ejpam-6837	433	5	x	x	SYM
ejpam-6837	433	6	+	+	NUM
ejpam-6837	433	7	2	2	NUM
ejpam-6837	433	8	pd	pd	NOUN
ejpam-6837	433	9	pc	pc	NOUN
ejpam-6837	433	10	td	td	NOUN
ejpam-6837	433	11	,	,	PUNCT
ejpam-6837	433	12	cx	cx	NOUN
ejpam-6837	433	13	−	−	PROPN
ejpam-6837	433	14	pc	pc	NOUN
ejpam-6837	433	15	td	td	NOUN
ejpam-6837	433	16	,	,	PUNCT
ejpam-6837	433	17	cx	cx	PROPN
ejpam-6837	433	18	+	+	CCONJ
ejpam-6837	433	19	pc	pc	NOUN
ejpam-6837	433	20	rdx	rdx	NOUN
ejpam-6837	433	21	−	−	PROPN
ejpam-6837	433	22	pd	pd	PROPN
ejpam-6837	433	23	pc	pc	PROPN
ejpam-6837	433	24	rdx	rdx	PROPN
ejpam-6837	433	25	.	.	PUNCT
ejpam-6837	434	1	■	■	PUNCT
ejpam-6837	434	2	5	5	X
ejpam-6837	434	3	.	.	X
ejpam-6837	434	4	clarification	clarification	NOUN
ejpam-6837	434	5	there	there	PRON
ejpam-6837	434	6	is	be	VERB
ejpam-6837	434	7	no	no	DET
ejpam-6837	434	8	conflict	conflict	NOUN
ejpam-6837	434	9	of	of	ADP
ejpam-6837	434	10	interest	interest	NOUN
ejpam-6837	434	11	and	and	CCONJ
ejpam-6837	434	12	there	there	PRON
ejpam-6837	434	13	is	be	VERB
ejpam-6837	434	14	no	no	DET
ejpam-6837	434	15	data	datum	NOUN
ejpam-6837	434	16	were	be	AUX
ejpam-6837	434	17	used	use	VERB
ejpam-6837	434	18	to	to	PART
ejpam-6837	434	19	support	support	VERB
ejpam-6837	434	20	this	this	DET
ejpam-6837	434	21	study	study	NOUN
ejpam-6837	434	22	.	.	PUNCT
ejpam-6837	435	1	moreover	moreover	ADV
ejpam-6837	435	2	,	,	PUNCT
ejpam-6837	435	3	i	i	PRON
ejpam-6837	435	4	would	would	AUX
ejpam-6837	435	5	like	like	VERB
ejpam-6837	435	6	to	to	PART
ejpam-6837	435	7	bring	bring	VERB
ejpam-6837	435	8	to	to	ADP
ejpam-6837	435	9	your	your	PRON
ejpam-6837	435	10	attention	attention	NOUN
ejpam-6837	435	11	that	that	SCONJ
ejpam-6837	435	12	the	the	DET
ejpam-6837	435	13	work	work	NOUN
ejpam-6837	435	14	i	i	PRON
ejpam-6837	435	15	am	be	AUX
ejpam-6837	435	16	submitting	submit	VERB
ejpam-6837	435	17	is	be	AUX
ejpam-6837	435	18	authored	author	VERB
ejpam-6837	435	19	solely	solely	ADV
ejpam-6837	435	20	by	by	ADP
ejpam-6837	435	21	myself	myself	PRON
ejpam-6837	435	22	.	.	PUNCT
ejpam-6837	436	1	s.	s.	PROPN
ejpam-6837	436	2	th	th	PROPN
ejpam-6837	436	3	.	.	PUNCT
ejpam-6837	437	1	alwadani	alwadani	PROPN
ejpam-6837	437	2	/	/	SYM
ejpam-6837	437	3	eur	eur	PROPN
ejpam-6837	437	4	.	.	PUNCT
ejpam-6837	438	1	j.	j.	PROPN
ejpam-6837	438	2	pure	pure	PROPN
ejpam-6837	438	3	appl	appl	PROPN
ejpam-6837	438	4	.	.	PROPN
ejpam-6837	438	5	math	math	PROPN
ejpam-6837	438	6	,	,	PUNCT
ejpam-6837	438	7	18	18	NUM
ejpam-6837	438	8	(	(	PUNCT
ejpam-6837	438	9	4	4	NUM
ejpam-6837	438	10	)	)	PUNCT
ejpam-6837	438	11	(	(	PUNCT
ejpam-6837	438	12	2025	2025	NUM
ejpam-6837	438	13	)	)	PUNCT
ejpam-6837	438	14	,	,	PUNCT
ejpam-6837	438	15	6837	6837	NUM
ejpam-6837	438	16	15	15	NUM
ejpam-6837	438	17	of	of	ADP
ejpam-6837	438	18	15	15	NUM
ejpam-6837	438	19	references	reference	NOUN
ejpam-6837	438	20	[	[	X
ejpam-6837	438	21	1	1	NUM
ejpam-6837	438	22	]	]	PUNCT
ejpam-6837	438	23	heinz	heinz	ADJ
ejpam-6837	438	24	h	h	PROPN
ejpam-6837	438	25	bauschke	bauschke	PROPN
ejpam-6837	438	26	,	,	PUNCT
ejpam-6837	438	27	patrick	patrick	PROPN
ejpam-6837	438	28	l	l	PROPN
ejpam-6837	438	29	combettes	combettes	PROPN
ejpam-6837	438	30	,	,	PUNCT
ejpam-6837	438	31	heinz	heinz	ADJ
ejpam-6837	438	32	h	h	NOUN
ejpam-6837	438	33	bauschke	bauschke	NOUN
ejpam-6837	438	34	,	,	PUNCT
ejpam-6837	438	35	and	and	CCONJ
ejpam-6837	438	36	patrick	patrick	PROPN
ejpam-6837	438	37	l	l	PROPN
ejpam-6837	438	38	combettes	combettes	PROPN
ejpam-6837	438	39	.	.	PUNCT
ejpam-6837	439	1	correction	correction	NOUN
ejpam-6837	439	2	to	to	PART
ejpam-6837	439	3	:	:	PUNCT
ejpam-6837	439	4	convex	convex	VERB
ejpam-6837	439	5	analysis	analysis	NOUN
ejpam-6837	439	6	and	and	CCONJ
ejpam-6837	439	7	monotone	monotone	ADJ
ejpam-6837	439	8	operator	operator	NOUN
ejpam-6837	439	9	theory	theory	NOUN
ejpam-6837	439	10	in	in	ADP
ejpam-6837	439	11	hilbert	hilbert	PROPN
ejpam-6837	439	12	spaces	space	NOUN
ejpam-6837	439	13	.	.	PUNCT
ejpam-6837	440	1	springer	springer	NOUN
ejpam-6837	440	2	,	,	PUNCT
ejpam-6837	440	3	2017	2017	NUM
ejpam-6837	440	4	.	.	PUNCT
ejpam-6837	441	1	[	[	X
ejpam-6837	441	2	2	2	X
ejpam-6837	441	3	]	]	X
ejpam-6837	441	4	patrick	patrick	PROPN
ejpam-6837	441	5	l	l	PROPN
ejpam-6837	441	6	combettes	combettes	PROPN
ejpam-6837	441	7	.	.	PUNCT
ejpam-6837	442	1	the	the	DET
ejpam-6837	442	2	convex	convex	PROPN
ejpam-6837	442	3	feasibility	feasibility	NOUN
ejpam-6837	442	4	problem	problem	NOUN
ejpam-6837	442	5	in	in	ADP
ejpam-6837	442	6	image	image	NOUN
ejpam-6837	442	7	recovery	recovery	NOUN
ejpam-6837	442	8	.	.	PUNCT
ejpam-6837	443	1	in	in	ADP
ejpam-6837	443	2	advances	advance	NOUN
ejpam-6837	443	3	in	in	ADP
ejpam-6837	443	4	imaging	imaging	NOUN
ejpam-6837	443	5	and	and	CCONJ
ejpam-6837	443	6	electron	electron	NOUN
ejpam-6837	443	7	physics	physics	PROPN
ejpam-6837	443	8	,	,	PUNCT
ejpam-6837	443	9	volume	volume	NOUN
ejpam-6837	443	10	95	95	NUM
ejpam-6837	443	11	,	,	PUNCT
ejpam-6837	443	12	pages	page	NOUN
ejpam-6837	443	13	155–270	155–270	NUM
ejpam-6837	443	14	.	.	PUNCT
ejpam-6837	443	15	elsevier	elsevier	NOUN
ejpam-6837	443	16	,	,	PUNCT
ejpam-6837	443	17	1996	1996	NUM
ejpam-6837	443	18	.	.	PUNCT
ejpam-6837	444	1	[	[	X
ejpam-6837	444	2	3	3	NUM
ejpam-6837	444	3	]	]	X
ejpam-6837	444	4	charles	charles	PROPN
ejpam-6837	444	5	byrne	byrne	PROPN
ejpam-6837	444	6	.	.	PUNCT
ejpam-6837	445	1	a	a	DET
ejpam-6837	445	2	unified	unified	ADJ
ejpam-6837	445	3	treatment	treatment	NOUN
ejpam-6837	445	4	of	of	ADP
ejpam-6837	445	5	some	some	DET
ejpam-6837	445	6	iterative	iterative	ADJ
ejpam-6837	445	7	algorithms	algorithm	NOUN
ejpam-6837	445	8	in	in	ADP
ejpam-6837	445	9	signal	signal	NOUN
ejpam-6837	445	10	processing	processing	NOUN
ejpam-6837	445	11	and	and	CCONJ
ejpam-6837	445	12	imagereconstruction	imagereconstruction	NOUN
ejpam-6837	445	13	.	.	PUNCT
ejpam-6837	446	1	inverse	inverse	NOUN
ejpam-6837	446	2	problems	problem	NOUN
ejpam-6837	446	3	,	,	PUNCT
ejpam-6837	446	4	20(1):103	20(1):103	NUM
ejpam-6837	446	5	,	,	PUNCT
ejpam-6837	446	6	2003	2003	NUM
ejpam-6837	446	7	.	.	PUNCT
ejpam-6837	447	1	[	[	X
ejpam-6837	447	2	4	4	NUM
ejpam-6837	447	3	]	]	X
ejpam-6837	447	4	avishy	avishy	PROPN
ejpam-6837	447	5	carmi	carmi	PROPN
ejpam-6837	447	6	,	,	PUNCT
ejpam-6837	447	7	yair	yair	PROPN
ejpam-6837	447	8	censor	censor	NOUN
ejpam-6837	447	9	,	,	PUNCT
ejpam-6837	447	10	and	and	CCONJ
ejpam-6837	447	11	pini	pini	PROPN
ejpam-6837	447	12	gurfil	gurfil	PROPN
ejpam-6837	447	13	.	.	PUNCT
ejpam-6837	448	1	convex	convex	VERB
ejpam-6837	448	2	feasibility	feasibility	NOUN
ejpam-6837	448	3	modeling	modeling	NOUN
ejpam-6837	448	4	and	and	CCONJ
ejpam-6837	448	5	projection	projection	NOUN
ejpam-6837	448	6	methods	method	NOUN
ejpam-6837	448	7	for	for	ADP
ejpam-6837	448	8	sparse	sparse	ADJ
ejpam-6837	448	9	signal	signal	NOUN
ejpam-6837	448	10	recovery	recovery	NOUN
ejpam-6837	448	11	.	.	PUNCT
ejpam-6837	449	1	journal	journal	NOUN
ejpam-6837	449	2	of	of	ADP
ejpam-6837	449	3	computational	computational	ADJ
ejpam-6837	449	4	and	and	CCONJ
ejpam-6837	449	5	applied	applied	ADJ
ejpam-6837	449	6	mathematics	mathematic	NOUN
ejpam-6837	449	7	,	,	PUNCT
ejpam-6837	449	8	236(17):4318–4335	236(17):4318–4335	NUM
ejpam-6837	449	9	,	,	PUNCT
ejpam-6837	449	10	2012	2012	NUM
ejpam-6837	449	11	.	.	PUNCT
ejpam-6837	450	1	[	[	X
ejpam-6837	450	2	5	5	X
ejpam-6837	450	3	]	]	X
ejpam-6837	450	4	jonathan	jonathan	PROPN
ejpam-6837	450	5	m	m	PROPN
ejpam-6837	450	6	borwein	borwein	NOUN
ejpam-6837	450	7	and	and	CCONJ
ejpam-6837	450	8	matthew	matthew	PROPN
ejpam-6837	450	9	k	k	PROPN
ejpam-6837	450	10	tam	tam	PROPN
ejpam-6837	450	11	.	.	PUNCT
ejpam-6837	451	1	a	a	DET
ejpam-6837	451	2	cyclic	cyclic	ADJ
ejpam-6837	451	3	douglas	douglas	PROPN
ejpam-6837	451	4	–	–	PUNCT
ejpam-6837	451	5	rachford	rachford	ADJ
ejpam-6837	451	6	iteration	iteration	NOUN
ejpam-6837	451	7	scheme	scheme	NOUN
ejpam-6837	451	8	.	.	PUNCT
ejpam-6837	452	1	journal	journal	NOUN
ejpam-6837	452	2	of	of	ADP
ejpam-6837	452	3	optimization	optimization	NOUN
ejpam-6837	452	4	theory	theory	NOUN
ejpam-6837	452	5	and	and	CCONJ
ejpam-6837	452	6	applications	application	NOUN
ejpam-6837	452	7	,	,	PUNCT
ejpam-6837	452	8	160(1):1–29	160(1):1–29	NUM
ejpam-6837	452	9	,	,	PUNCT
ejpam-6837	452	10	2014	2014	NUM
ejpam-6837	452	11	.	.	PUNCT
ejpam-6837	453	1	[	[	X
ejpam-6837	453	2	6	6	NUM
ejpam-6837	453	3	]	]	X
ejpam-6837	453	4	erwin	erwin	PROPN
ejpam-6837	453	5	kreyszig	kreyszig	PROPN
ejpam-6837	453	6	.	.	PUNCT
ejpam-6837	454	1	introductory	introductory	ADJ
ejpam-6837	454	2	functional	functional	ADJ
ejpam-6837	454	3	analysis	analysis	NOUN
ejpam-6837	454	4	with	with	ADP
ejpam-6837	454	5	applications	application	NOUN
ejpam-6837	454	6	.	.	PUNCT
ejpam-6837	455	1	john	john	PROPN
ejpam-6837	455	2	wiley	wiley	PROPN
ejpam-6837	455	3	&	&	CCONJ
ejpam-6837	455	4	sons	son	NOUN
ejpam-6837	455	5	,	,	PUNCT
ejpam-6837	455	6	1991	1991	NUM
ejpam-6837	455	7	.	.	PUNCT
ejpam-6837	456	1	[	[	X
ejpam-6837	456	2	7	7	X
ejpam-6837	456	3	]	]	X
ejpam-6837	456	4	salihah	salihah	ADJ
ejpam-6837	456	5	thabet	thabet	ADJ
ejpam-6837	456	6	alwadani	alwadani	ADJ
ejpam-6837	456	7	.	.	PUNCT
ejpam-6837	457	1	on	on	ADP
ejpam-6837	457	2	the	the	DET
ejpam-6837	457	3	behaviour	behaviour	NOUN
ejpam-6837	457	4	of	of	ADP
ejpam-6837	457	5	algorithms	algorithm	NOUN
ejpam-6837	457	6	featuring	feature	VERB
ejpam-6837	457	7	compositions	composition	NOUN
ejpam-6837	457	8	of	of	ADP
ejpam-6837	457	9	projectors	projector	NOUN
ejpam-6837	457	10	and	and	CCONJ
ejpam-6837	457	11	proximal	proximal	ADJ
ejpam-6837	457	12	mappings	mapping	NOUN
ejpam-6837	457	13	with	with	ADP
ejpam-6837	457	14	no	no	DET
ejpam-6837	457	15	solutions	solution	NOUN
ejpam-6837	457	16	.	.	PUNCT
ejpam-6837	458	1	phd	phd	NOUN
ejpam-6837	458	2	thesis	thesis	PROPN
ejpam-6837	458	3	,	,	PUNCT
ejpam-6837	458	4	university	university	PROPN
ejpam-6837	458	5	of	of	ADP
ejpam-6837	458	6	british	british	PROPN
ejpam-6837	458	7	columbia	columbia	PROPN
ejpam-6837	458	8	,	,	PUNCT
ejpam-6837	458	9	2021	2021	NUM
ejpam-6837	458	10	.	.	PUNCT
ejpam-6837	459	1	[	[	X
ejpam-6837	459	2	8	8	NUM
ejpam-6837	459	3	]	]	X
ejpam-6837	459	4	pierre	pierre	NOUN
ejpam-6837	459	5	-	-	PUNCT
ejpam-6837	459	6	louis	louis	NOUN
ejpam-6837	459	7	lions	lion	NOUN
ejpam-6837	459	8	and	and	CCONJ
ejpam-6837	459	9	bertrand	bertrand	PROPN
ejpam-6837	459	10	mercier	mercier	PROPN
ejpam-6837	459	11	.	.	PUNCT
ejpam-6837	460	1	splitting	split	VERB
ejpam-6837	460	2	algorithms	algorithm	NOUN
ejpam-6837	460	3	for	for	ADP
ejpam-6837	460	4	the	the	DET
ejpam-6837	460	5	sum	sum	NOUN
ejpam-6837	460	6	of	of	ADP
ejpam-6837	460	7	two	two	NUM
ejpam-6837	460	8	nonlinear	nonlinear	ADJ
ejpam-6837	460	9	operators	operator	NOUN
ejpam-6837	460	10	.	.	PUNCT
ejpam-6837	461	1	siam	siam	PROPN
ejpam-6837	461	2	journal	journal	PROPN
ejpam-6837	461	3	on	on	ADP
ejpam-6837	461	4	numerical	numerical	ADJ
ejpam-6837	461	5	analysis	analysis	NOUN
ejpam-6837	461	6	,	,	PUNCT
ejpam-6837	461	7	16(6):964–979	16(6):964–979	NUM
ejpam-6837	461	8	,	,	PUNCT
ejpam-6837	461	9	1979	1979	NUM
ejpam-6837	461	10	.	.	PUNCT
ejpam-6837	462	1	[	[	X
ejpam-6837	462	2	9	9	NUM
ejpam-6837	462	3	]	]	X
ejpam-6837	462	4	jonathan	jonathan	PROPN
ejpam-6837	462	5	eckstein	eckstein	PROPN
ejpam-6837	462	6	and	and	CCONJ
ejpam-6837	462	7	dimitri	dimitri	PROPN
ejpam-6837	462	8	p	p	PROPN
ejpam-6837	462	9	bertsekas	bertsekas	PROPN
ejpam-6837	462	10	.	.	PUNCT
ejpam-6837	463	1	on	on	ADP
ejpam-6837	463	2	the	the	DET
ejpam-6837	463	3	douglas	douglas	PROPN
ejpam-6837	463	4	—	—	PUNCT
ejpam-6837	463	5	rachford	rachford	ADJ
ejpam-6837	463	6	splitting	splitting	NOUN
ejpam-6837	463	7	method	method	NOUN
ejpam-6837	463	8	and	and	CCONJ
ejpam-6837	463	9	the	the	DET
ejpam-6837	463	10	proximal	proximal	ADJ
ejpam-6837	463	11	point	point	NOUN
ejpam-6837	463	12	algorithm	algorithm	NOUN
ejpam-6837	463	13	for	for	ADP
ejpam-6837	463	14	maximal	maximal	ADJ
ejpam-6837	463	15	monotone	monotone	ADJ
ejpam-6837	463	16	operators	operator	NOUN
ejpam-6837	463	17	.	.	PUNCT
ejpam-6837	464	1	mathematical	mathematical	ADJ
ejpam-6837	464	2	programming	programming	NOUN
ejpam-6837	464	3	,	,	PUNCT
ejpam-6837	464	4	55(1):293–318	55(1):293–318	PROPN
ejpam-6837	464	5	,	,	PUNCT
ejpam-6837	464	6	1992	1992	NUM
ejpam-6837	464	7	.	.	PUNCT
ejpam-6837	465	1	[	[	X
ejpam-6837	465	2	10	10	NUM
ejpam-6837	465	3	]	]	X
ejpam-6837	465	4	heinz	heinz	PROPN
ejpam-6837	465	5	h	h	PROPN
ejpam-6837	465	6	bauschke	bauschke	PROPN
ejpam-6837	465	7	,	,	PUNCT
ejpam-6837	465	8	patrick	patrick	PROPN
ejpam-6837	465	9	l	l	PROPN
ejpam-6837	465	10	combettes	combette	NOUN
ejpam-6837	465	11	,	,	PUNCT
ejpam-6837	465	12	and	and	CCONJ
ejpam-6837	465	13	d	d	PROPN
ejpam-6837	465	14	russell	russell	PROPN
ejpam-6837	465	15	luke	luke	PROPN
ejpam-6837	465	16	.	.	PUNCT
ejpam-6837	466	1	finding	find	VERB
ejpam-6837	466	2	best	good	ADJ
ejpam-6837	466	3	approximation	approximation	NOUN
ejpam-6837	466	4	pairs	pair	NOUN
ejpam-6837	466	5	relative	relative	ADJ
ejpam-6837	466	6	to	to	ADP
ejpam-6837	466	7	two	two	NUM
ejpam-6837	466	8	closed	closed	ADJ
ejpam-6837	466	9	convex	convex	NOUN
ejpam-6837	466	10	sets	set	NOUN
ejpam-6837	466	11	in	in	ADP
ejpam-6837	466	12	hilbert	hilbert	PROPN
ejpam-6837	466	13	spaces	space	NOUN
ejpam-6837	466	14	.	.	PUNCT
ejpam-6837	467	1	journal	journal	NOUN
ejpam-6837	467	2	of	of	ADP
ejpam-6837	467	3	approximation	approximation	NOUN
ejpam-6837	467	4	theory	theory	NOUN
ejpam-6837	467	5	,	,	PUNCT
ejpam-6837	467	6	127(2):178–192	127(2):178–192	NUM
ejpam-6837	467	7	,	,	PUNCT
ejpam-6837	467	8	2004	2004	NUM
ejpam-6837	467	9	.	.	PUNCT
ejpam-6837	468	1	[	[	X
ejpam-6837	468	2	11	11	NUM
ejpam-6837	468	3	]	]	X
ejpam-6837	468	4	patrick	patrick	PROPN
ejpam-6837	468	5	l	l	PROPN
ejpam-6837	468	6	combettes	combette	NOUN
ejpam-6837	468	7	and	and	CCONJ
ejpam-6837	468	8	valérie	valérie	ADJ
ejpam-6837	468	9	r	r	NOUN
ejpam-6837	468	10	wajs	wajs	NOUN
ejpam-6837	468	11	.	.	PUNCT
ejpam-6837	469	1	signal	signal	PROPN
ejpam-6837	469	2	recovery	recovery	NOUN
ejpam-6837	469	3	by	by	ADP
ejpam-6837	469	4	proximal	proximal	ADJ
ejpam-6837	469	5	forwardbackward	forwardbackward	ADJ
ejpam-6837	469	6	splitting	splitting	NOUN
ejpam-6837	469	7	.	.	PUNCT
ejpam-6837	470	1	multiscale	multiscale	ADJ
ejpam-6837	470	2	modeling	modeling	PROPN
ejpam-6837	470	3	&	&	CCONJ
ejpam-6837	470	4	simulation	simulation	PROPN
ejpam-6837	470	5	,	,	PUNCT
ejpam-6837	470	6	4(4):1168–1200	4(4):1168–1200	PROPN
ejpam-6837	470	7	,	,	PUNCT
ejpam-6837	470	8	2005	2005	NUM
ejpam-6837	470	9	.	.	PUNCT
ejpam-6837	471	1	[	[	X
ejpam-6837	471	2	12	12	NUM
ejpam-6837	471	3	]	]	X
ejpam-6837	471	4	patrick	patrick	PROPN
ejpam-6837	471	5	l	l	PROPN
ejpam-6837	471	6	combettes	combettes	PROPN
ejpam-6837	471	7	and	and	CCONJ
ejpam-6837	471	8	jean	jean	PROPN
ejpam-6837	471	9	-	-	PUNCT
ejpam-6837	471	10	christophe	christophe	PROPN
ejpam-6837	471	11	pesquet	pesquet	NOUN
ejpam-6837	471	12	.	.	PUNCT
ejpam-6837	472	1	a	a	DET
ejpam-6837	472	2	douglas	douglas	PROPN
ejpam-6837	472	3	–	–	PUNCT
ejpam-6837	472	4	rachford	rachford	ADJ
ejpam-6837	472	5	splitting	splitting	NOUN
ejpam-6837	472	6	approach	approach	NOUN
ejpam-6837	472	7	to	to	PART
ejpam-6837	472	8	nonsmooth	nonsmooth	VERB
ejpam-6837	472	9	convex	convex	PROPN
ejpam-6837	472	10	variational	variational	ADJ
ejpam-6837	472	11	signal	signal	NOUN
ejpam-6837	472	12	recovery	recovery	NOUN
ejpam-6837	472	13	.	.	PUNCT
ejpam-6837	473	1	ieee	ieee	PROPN
ejpam-6837	473	2	journal	journal	PROPN
ejpam-6837	473	3	of	of	ADP
ejpam-6837	473	4	selected	select	VERB
ejpam-6837	473	5	topics	topic	NOUN
ejpam-6837	473	6	in	in	ADP
ejpam-6837	473	7	signal	signal	ADJ
ejpam-6837	473	8	processing	processing	NOUN
ejpam-6837	473	9	,	,	PUNCT
ejpam-6837	473	10	1(4):564–574	1(4):564–574	NUM
ejpam-6837	473	11	,	,	PUNCT
ejpam-6837	473	12	2008	2008	NUM
ejpam-6837	473	13	.	.	PUNCT
ejpam-6837	474	1	[	[	X
ejpam-6837	474	2	13	13	NUM
ejpam-6837	474	3	]	]	PUNCT
ejpam-6837	474	4	geogebra	geogebra	NOUN
ejpam-6837	474	5	.	.	PUNCT
ejpam-6837	475	1	[	[	X
ejpam-6837	475	2	14	14	NUM
ejpam-6837	475	3	]	]	X
ejpam-6837	475	4	salihah	salihah	ADJ
ejpam-6837	475	5	alwadani	alwadani	ADJ
ejpam-6837	475	6	,	,	PUNCT
ejpam-6837	475	7	heinz	heinz	PROPN
ejpam-6837	475	8	h	h	PROPN
ejpam-6837	475	9	bauschke	bauschke	PROPN
ejpam-6837	475	10	,	,	PUNCT
ejpam-6837	475	11	julian	julian	PROPN
ejpam-6837	475	12	p	p	PROPN
ejpam-6837	475	13	revalski	revalski	PROPN
ejpam-6837	475	14	,	,	PUNCT
ejpam-6837	475	15	and	and	CCONJ
ejpam-6837	475	16	xianfu	xianfu	PROPN
ejpam-6837	475	17	wang	wang	PROPN
ejpam-6837	475	18	.	.	PUNCT
ejpam-6837	476	1	resolvents	resolvent	NOUN
ejpam-6837	476	2	and	and	CCONJ
ejpam-6837	476	3	yosida	yosida	PROPN
ejpam-6837	476	4	approximations	approximation	NOUN
ejpam-6837	476	5	of	of	ADP
ejpam-6837	476	6	displacement	displacement	ADJ
ejpam-6837	476	7	mappings	mapping	NOUN
ejpam-6837	476	8	of	of	ADP
ejpam-6837	476	9	isometries	isometry	NOUN
ejpam-6837	476	10	.	.	PUNCT
ejpam-6837	477	1	setvalued	setvalued	ADJ
ejpam-6837	477	2	and	and	CCONJ
ejpam-6837	477	3	variational	variational	ADJ
ejpam-6837	477	4	analysis	analysis	NOUN
ejpam-6837	477	5	,	,	PUNCT
ejpam-6837	477	6	29(3):721–733	29(3):721–733	NUM
ejpam-6837	477	7	,	,	PUNCT
ejpam-6837	477	8	2021	2021	NUM
ejpam-6837	477	9	.	.	PUNCT
ejpam-6837	478	1	[	[	X
ejpam-6837	478	2	15	15	NUM
ejpam-6837	478	3	]	]	X
ejpam-6837	478	4	salihah	salihah	ADJ
ejpam-6837	478	5	thabet	thabet	ADJ
ejpam-6837	478	6	alwadani	alwadani	ADJ
ejpam-6837	478	7	.	.	PUNCT
ejpam-6837	479	1	additional	additional	ADJ
ejpam-6837	479	2	studies	study	NOUN
ejpam-6837	479	3	on	on	ADP
ejpam-6837	479	4	displacement	displacement	ADJ
ejpam-6837	479	5	mapping	mapping	NOUN
ejpam-6837	479	6	with	with	ADP
ejpam-6837	479	7	restrictions	restriction	NOUN
ejpam-6837	479	8	.	.	PUNCT
ejpam-6837	480	1	arxiv	arxiv	PROPN
ejpam-6837	480	2	preprint	preprint	NOUN
ejpam-6837	480	3	arxiv:2405.13510	arxiv:2405.13510	NOUN
ejpam-6837	480	4	,	,	PUNCT
ejpam-6837	480	5	2024	2024	NUM
ejpam-6837	480	6	.	.	PUNCT
ejpam-6837	481	1	[	[	X
ejpam-6837	481	2	16	16	NUM
ejpam-6837	481	3	]	]	PUNCT
ejpam-6837	481	4	salihah	salihah	ADJ
ejpam-6837	481	5	alwadani	alwadani	ADJ
ejpam-6837	481	6	,	,	PUNCT
ejpam-6837	481	7	heinz	heinz	PROPN
ejpam-6837	481	8	h	h	PROPN
ejpam-6837	481	9	bauschke	bauschke	PROPN
ejpam-6837	481	10	,	,	PUNCT
ejpam-6837	481	11	walaa	walaa	PROPN
ejpam-6837	481	12	m	m	VERB
ejpam-6837	481	13	moursi	moursi	ADJ
ejpam-6837	481	14	,	,	PUNCT
ejpam-6837	481	15	and	and	CCONJ
ejpam-6837	481	16	xianfu	xianfu	PROPN
ejpam-6837	481	17	wang	wang	PROPN
ejpam-6837	481	18	.	.	PUNCT
ejpam-6837	482	1	on	on	ADP
ejpam-6837	482	2	the	the	DET
ejpam-6837	482	3	asymptotic	asymptotic	ADJ
ejpam-6837	482	4	behaviour	behaviour	NOUN
ejpam-6837	482	5	of	of	ADP
ejpam-6837	482	6	the	the	DET
ejpam-6837	482	7	aragón	aragón	PROPN
ejpam-6837	482	8	artacho	artacho	ADJ
ejpam-6837	482	9	–	–	PUNCT
ejpam-6837	482	10	campoy	campoy	ADJ
ejpam-6837	482	11	algorithm	algorithm	NOUN
ejpam-6837	482	12	.	.	PUNCT
ejpam-6837	483	1	operations	operation	NOUN
ejpam-6837	483	2	research	research	NOUN
ejpam-6837	483	3	letters	letter	NOUN
ejpam-6837	483	4	,	,	PUNCT
ejpam-6837	483	5	46(6):585–587	46(6):585–587	PROPN
ejpam-6837	483	6	,	,	PUNCT
ejpam-6837	483	7	2018	2018	NUM
ejpam-6837	483	8	.	.	PUNCT
ejpam-6837	484	1	introduction	introduction	NOUN
ejpam-6837	484	2	background	background	NOUN
ejpam-6837	484	3	the	the	DET
ejpam-6837	484	4	cyclic	cyclic	PROPN
ejpam-6837	484	5	douglasrachford	douglasrachford	PROPN
ejpam-6837	484	6	method	method	NOUN
ejpam-6837	484	7	main	main	ADJ
ejpam-6837	484	8	results	result	NOUN
ejpam-6837	484	9	a	a	DET
ejpam-6837	484	10	product	product	NOUN
ejpam-6837	484	11	version	version	NOUN
ejpam-6837	484	12	of	of	ADP
ejpam-6837	484	13	the	the	DET
ejpam-6837	484	14	cyclic	cyclic	ADJ
ejpam-6837	484	15	douglas	douglas	PROPN
ejpam-6837	484	16	–	–	PUNCT
ejpam-6837	484	17	rachford	rachford	ADJ
ejpam-6837	484	18	method	method	NOUN
ejpam-6837	484	19	clarification	clarification	NOUN