id	sid	tid	token	lemma	pos
ma-10	1	1	2021	2021	NUM
ma-10	1	2	ada	ada	PROPN
ma-10	1	3	academica	academica	PROPN
ma-10	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-10	1	5	.	.	PUNCT
ma-10	2	1	j.	j.	PROPN
ma-10	2	2	math	math	PROPN
ma-10	2	3	.	.	PUNCT
ma-10	3	1	anal	anal	ADJ
ma-10	3	2	.	.	PUNCT
ma-10	4	1	1	1	NUM
ma-10	4	2	(	(	PUNCT
ma-10	4	3	2021	2021	NUM
ma-10	4	4	)	)	PUNCT
ma-10	4	5	19	19	NUM
ma-10	4	6	-	-	PUNCT
ma-10	4	7	33doi	33doi	NUM
ma-10	4	8	:	:	PUNCT
ma-10	4	9	10.28924	10.28924	NUM
ma-10	4	10	/	/	SYM
ma-10	4	11	ada	ada	PROPN
ma-10	4	12	/	/	SYM
ma-10	4	13	ma.1.19	ma.1.19	NOUN
ma-10	4	14	the	the	DET
ma-10	4	15	generalized	generalized	ADJ
ma-10	4	16	viscosity	viscosity	NOUN
ma-10	4	17	implicit	implicit	ADJ
ma-10	4	18	rules	rule	NOUN
ma-10	4	19	of	of	ADP
ma-10	4	20	asymptotically	asymptotically	ADV
ma-10	4	21	nonexpansive	nonexpansive	ADJ
ma-10	4	22	mappings	mapping	NOUN
ma-10	4	23	in	in	ADP
ma-10	4	24	hilbert	hilbert	NOUN
ma-10	4	25	spaces	space	NOUN
ma-10	4	26	sang	sing	VERB
ma-10	4	27	b	b	ADJ
ma-10	4	28	mendy	mendy	PROPN
ma-10	4	29	,	,	PUNCT
ma-10	4	30	john	john	PROPN
ma-10	4	31	t	t	PROPN
ma-10	4	32	mendy∗	mendy∗	PROPN
ma-10	4	33	,	,	PUNCT
ma-10	4	34	alieu	alieu	PROPN
ma-10	4	35	jobe	jobe	PROPN
ma-10	4	36	university	university	PROPN
ma-10	4	37	of	of	ADP
ma-10	4	38	the	the	DET
ma-10	4	39	gambia	gambia	PROPN
ma-10	4	40	,	,	PUNCT
ma-10	4	41	brikama	brikama	NOUN
ma-10	4	42	campus	campus	PROPN
ma-10	4	43	,	,	PUNCT
ma-10	4	44	gambia	gambia	PROPN
ma-10	4	45	sangbm1@gmail.com	sangbm1@gmail.com	PROPN
ma-10	4	46	,	,	PUNCT
ma-10	4	47	jt.mendy@utg.edu.gm	jt.mendy@utg.edu.gm	PROPN
ma-10	4	48	,	,	PUNCT
ma-10	4	49	alieueejobe@gmail.com	alieueejobe@gmail.com	X
ma-10	5	1	∗correspondence	∗correspondence	NOUN
ma-10	5	2	:	:	PUNCT
ma-10	5	3	jt.mendy@utg.edu.gm	jt.mendy@utg.edu.gm	PROPN
ma-10	5	4	abstract	abstract	NOUN
ma-10	5	5	.	.	PUNCT
ma-10	6	1	the	the	DET
ma-10	6	2	generalized	generalized	ADJ
ma-10	6	3	viscosity	viscosity	NOUN
ma-10	6	4	implicit	implicit	ADJ
ma-10	6	5	rules	rule	NOUN
ma-10	6	6	of	of	ADP
ma-10	6	7	nonexpansive	nonexpansive	ADJ
ma-10	6	8	asymptotically	asymptotically	ADJ
ma-10	6	9	mappings	mapping	NOUN
ma-10	6	10	in	in	ADP
ma-10	6	11	hilbertspaces	hilbertspace	NOUN
ma-10	6	12	are	be	AUX
ma-10	6	13	considered	consider	VERB
ma-10	6	14	.	.	PUNCT
ma-10	7	1	the	the	DET
ma-10	7	2	strong	strong	ADJ
ma-10	7	3	convergence	convergence	NOUN
ma-10	7	4	theorems	theorem	NOUN
ma-10	7	5	of	of	ADP
ma-10	7	6	the	the	DET
ma-10	7	7	rules	rule	NOUN
ma-10	7	8	are	be	AUX
ma-10	7	9	proved	prove	VERB
ma-10	7	10	under	under	ADP
ma-10	7	11	certain	certain	ADJ
ma-10	7	12	as	as	ADP
ma-10	7	13	-	-	PUNCT
ma-10	7	14	sumptions	sumption	NOUN
ma-10	7	15	imposed	impose	VERB
ma-10	7	16	on	on	ADP
ma-10	7	17	the	the	DET
ma-10	7	18	sequences	sequence	NOUN
ma-10	7	19	of	of	ADP
ma-10	7	20	parameters	parameter	NOUN
ma-10	7	21	.	.	PUNCT
ma-10	8	1	an	an	DET
ma-10	8	2	application	application	NOUN
ma-10	8	3	of	of	ADP
ma-10	8	4	it	it	PRON
ma-10	8	5	in	in	ADP
ma-10	8	6	the	the	DET
ma-10	8	7	convex	convex	ADJ
ma-10	8	8	minimizationproblem	minimizationproblem	NOUN
ma-10	8	9	is	be	AUX
ma-10	8	10	considered	consider	VERB
ma-10	8	11	.	.	PUNCT
ma-10	9	1	the	the	DET
ma-10	9	2	results	result	NOUN
ma-10	9	3	presented	present	VERB
ma-10	9	4	in	in	ADP
ma-10	9	5	this	this	DET
ma-10	9	6	paper	paper	NOUN
ma-10	9	7	improve	improve	VERB
ma-10	9	8	and	and	CCONJ
ma-10	9	9	extend	extend	VERB
ma-10	9	10	some	some	DET
ma-10	9	11	recent	recent	ADJ
ma-10	9	12	corre	corre	ADJ
ma-10	9	13	-	-	PUNCT
ma-10	9	14	sponding	sponde	VERB
ma-10	9	15	results	result	NOUN
ma-10	9	16	in	in	ADP
ma-10	9	17	the	the	DET
ma-10	9	18	literature	literature	NOUN
ma-10	9	19	.	.	PUNCT
ma-10	10	1	1	1	X
ma-10	10	2	.	.	X
ma-10	10	3	background	background	NOUN
ma-10	10	4	let	let	VERB
ma-10	10	5	h	h	PRON
ma-10	10	6	be	be	AUX
ma-10	10	7	a	a	DET
ma-10	10	8	real	real	ADJ
ma-10	10	9	hilbert	hilbert	NOUN
ma-10	10	10	space	space	NOUN
ma-10	10	11	and	and	CCONJ
ma-10	10	12	m	m	AUX
ma-10	10	13	be	be	AUX
ma-10	10	14	a	a	DET
ma-10	10	15	nonempty	nonempty	ADV
ma-10	10	16	closed	close	VERB
ma-10	10	17	convex	convex	NOUN
ma-10	10	18	subset	subset	NOUN
ma-10	10	19	of	of	ADP
ma-10	10	20	h	h	PROPN
ma-10	10	21	,	,	PUNCT
ma-10	10	22	t	t	PROPN
ma-10	10	23	:	:	PUNCT
ma-10	10	24	m→mbe	m→mbe	NUM
ma-10	10	25	a	a	DET
ma-10	10	26	nonexpansive	nonexpansive	ADJ
ma-10	10	27	mapping	mapping	NOUN
ma-10	10	28	with	with	ADP
ma-10	10	29	a	a	DET
ma-10	10	30	nonempty	nonempty	ADV
ma-10	10	31	fixed	fix	VERB
ma-10	10	32	point	point	NOUN
ma-10	10	33	set	set	VERB
ma-10	10	34	f(t	f(t	PROPN
ma-10	10	35	)	)	PUNCT
ma-10	10	36	the	the	DET
ma-10	10	37	following	follow	VERB
ma-10	10	38	iteration	iteration	NOUN
ma-10	10	39	method	method	NOUN
ma-10	10	40	is	be	AUX
ma-10	10	41	known	know	VERB
ma-10	10	42	as	as	ADP
ma-10	10	43	the	the	DET
ma-10	10	44	viscosity	viscosity	NOUN
ma-10	10	45	approximation	approximation	NOUN
ma-10	10	46	method	method	NOUN
ma-10	10	47	:	:	PUNCT
ma-10	10	48	for	for	ADP
ma-10	10	49	arbitrarilychosen	arbitrarilychosen	PROPN
ma-10	10	50	u0	u0	PROPN
ma-10	10	51	∈m	∈m	NOUN
ma-10	10	52	un+1	un+1	NOUN
ma-10	10	53	=	=	SYM
ma-10	10	54	αnψ(un	αnψ(un	NOUN
ma-10	10	55	)	)	PUNCT
ma-10	11	1	+	+	CCONJ
ma-10	11	2	(	(	PUNCT
ma-10	11	3	1−	1−	NUM
ma-10	11	4	αn)t	αn)t	NUM
ma-10	11	5	un	un	PROPN
ma-10	11	6	,	,	PUNCT
ma-10	11	7	n	n	PRON
ma-10	11	8	≥	≥	NOUN
ma-10	11	9	0	0	NUM
ma-10	11	10	,	,	PUNCT
ma-10	11	11	(	(	PUNCT
ma-10	11	12	1.1)where	1.1)where	NUM
ma-10	11	13	ψ	ψ	X
ma-10	11	14	:	:	PUNCT
ma-10	11	15	m	m	VERB
ma-10	11	16	→	→	NOUN
ma-10	11	17	m	m	VERB
ma-10	11	18	is	be	AUX
ma-10	11	19	a	a	DET
ma-10	11	20	contraction	contraction	NOUN
ma-10	11	21	and	and	CCONJ
ma-10	11	22	{	{	PUNCT
ma-10	11	23	αn	αn	NOUN
ma-10	11	24	}	}	PUNCT
ma-10	11	25	is	be	AUX
ma-10	11	26	a	a	DET
ma-10	11	27	sequence	sequence	NOUN
ma-10	11	28	in	in	ADP
ma-10	11	29	(	(	PUNCT
ma-10	11	30	0	0	NUM
ma-10	11	31	,	,	PUNCT
ma-10	11	32	1	1	NUM
ma-10	11	33	)	)	PUNCT
ma-10	11	34	.	.	PUNCT
ma-10	12	1	under	under	ADP
ma-10	12	2	some	some	DET
ma-10	12	3	certainconditions	certaincondition	NOUN
ma-10	12	4	,	,	PUNCT
ma-10	12	5	the	the	DET
ma-10	12	6	sequence	sequence	NOUN
ma-10	12	7	{	{	PUNCT
ma-10	12	8	un	un	PROPN
ma-10	12	9	}	}	PUNCT
ma-10	12	10	converges	converge	VERB
ma-10	12	11	strongly	strongly	ADV
ma-10	12	12	to	to	ADP
ma-10	12	13	a	a	DET
ma-10	12	14	point	point	NOUN
ma-10	12	15	z	z	NOUN
ma-10	12	16	∈	∈	PROPN
ma-10	12	17	f	f	X
ma-10	12	18	(	(	PUNCT
ma-10	12	19	t	t	PROPN
ma-10	12	20	)	)	PUNCT
ma-10	12	21	which	which	PRON
ma-10	12	22	solves	solve	VERB
ma-10	12	23	the	the	DET
ma-10	12	24	variationalinequality	variationalinequality	NOUN
ma-10	12	25	(	(	PUNCT
ma-10	12	26	v	v	NOUN
ma-10	12	27	i	i	NOUN
ma-10	12	28	)	)	PUNCT
ma-10	13	1	〈	〈	PROPN
ma-10	13	2	(	(	PUNCT
ma-10	13	3	i	i	PRON
ma-10	13	4	−	−	PROPN
ma-10	13	5	ψ)z	ψ)z	ADJ
ma-10	13	6	,	,	PUNCT
ma-10	13	7	u	u	NOUN
ma-10	13	8	−	−	PROPN
ma-10	13	9	z	z	PROPN
ma-10	13	10	〉	〉	PROPN
ma-10	13	11	≥	≥	NUM
ma-10	13	12	0	0	NUM
ma-10	13	13	,	,	PUNCT
ma-10	13	14	u	u	PROPN
ma-10	13	15	∈	∈	PROPN
ma-10	13	16	f	f	X
ma-10	13	17	(	(	PUNCT
ma-10	13	18	t	t	PROPN
ma-10	13	19	)	)	PUNCT
ma-10	13	20	,	,	PUNCT
ma-10	13	21	(	(	PUNCT
ma-10	13	22	1.2)where	1.2)where	NUM
ma-10	13	23	i	i	PRON
ma-10	13	24	is	be	AUX
ma-10	13	25	the	the	DET
ma-10	13	26	identity	identity	NOUN
ma-10	13	27	of	of	ADP
ma-10	13	28	h.	h.	NOUN
ma-10	13	29	many	many	ADJ
ma-10	13	30	authors	author	NOUN
ma-10	13	31	studied	study	VERB
ma-10	13	32	iterative	iterative	NOUN
ma-10	13	33	sequence	sequence	NOUN
ma-10	13	34	for	for	ADP
ma-10	13	35	the	the	DET
ma-10	13	36	implicit	implicit	ADJ
ma-10	13	37	midpointrule	midpointrule	NOUN
ma-10	13	38	because	because	SCONJ
ma-10	13	39	of	of	ADP
ma-10	13	40	it	it	PRON
ma-10	13	41	’s	’	VERB
ma-10	13	42	significant	significant	ADJ
ma-10	13	43	for	for	ADP
ma-10	13	44	solving	solve	VERB
ma-10	13	45	ordinary	ordinary	ADJ
ma-10	13	46	differential	differential	ADJ
ma-10	13	47	equations	equation	NOUN
ma-10	13	48	;	;	PUNCT
ma-10	13	49	see	see	VERB
ma-10	13	50	[	[	X
ma-10	13	51	?	?	PUNCT
ma-10	13	52	]	]	X
ma-10	14	1	[	[	X
ma-10	14	2	12	12	NUM
ma-10	14	3	]	]	X
ma-10	14	4	,	,	PUNCT
ma-10	14	5	john	john	PROPN
ma-10	14	6	t	t	PROPN
ma-10	15	1	[	[	X
ma-10	15	2	9	9	NUM
ma-10	15	3	]	]	PUNCT
ma-10	15	4	,	,	PUNCT
ma-10	16	1	[	[	X
ma-10	16	2	7]and	7]and	NOUN
ma-10	16	3	the	the	DET
ma-10	16	4	references	reference	NOUN
ma-10	16	5	therein	therein	ADV
ma-10	16	6	.	.	PUNCT
ma-10	17	1	recently	recently	ADV
ma-10	17	2	,	,	PUNCT
ma-10	17	3	xu	xu	PROPN
ma-10	17	4	et	et	PROPN
ma-10	17	5	al	al	PROPN
ma-10	18	1	[	[	X
ma-10	18	2	3	3	NUM
ma-10	18	3	]	]	PUNCT
ma-10	18	4	proposed	propose	VERB
ma-10	18	5	the	the	DET
ma-10	18	6	following	follow	VERB
ma-10	18	7	viscosity	viscosity	NOUN
ma-10	18	8	implicit	implicit	ADJ
ma-10	18	9	midpointrule	midpointrule	NOUN
ma-10	18	10	(	(	PUNCT
ma-10	18	11	vimr	vimr	NOUN
ma-10	18	12	)	)	PUNCT
ma-10	18	13	for	for	ADP
ma-10	18	14	nonexpansive	nonexpansive	ADJ
ma-10	18	15	mappings	mapping	NOUN
ma-10	18	16	:	:	PUNCT
ma-10	18	17	un+1	un+1	NOUN
ma-10	18	18	=	=	SYM
ma-10	18	19	αnψ(un	αnψ(un	NOUN
ma-10	18	20	)	)	PUNCT
ma-10	18	21	+	+	CCONJ
ma-10	19	1	(	(	PUNCT
ma-10	19	2	1−	1−	NUM
ma-10	19	3	αn)t	αn)t	PROPN
ma-10	19	4	(	(	PUNCT
ma-10	19	5	un	un	PROPN
ma-10	19	6	+	+	CCONJ
ma-10	19	7	un+1	un+1	PROPN
ma-10	19	8	2	2	NUM
ma-10	19	9	)	)	PUNCT
ma-10	19	10	,	,	PUNCT
ma-10	19	11	n	n	X
ma-10	19	12	≥	≥	NOUN
ma-10	19	13	0	0	NUM
ma-10	19	14	,	,	PUNCT
ma-10	19	15	(	(	PUNCT
ma-10	19	16	1.3	1.3	NUM
ma-10	19	17	)	)	PUNCT
ma-10	19	18	received	receive	VERB
ma-10	19	19	:	:	PUNCT
ma-10	19	20	23	23	NUM
ma-10	19	21	aug	aug	PROPN
ma-10	19	22	2021	2021	NUM
ma-10	19	23	.	.	PUNCT
ma-10	20	1	key	key	ADJ
ma-10	20	2	words	word	NOUN
ma-10	20	3	and	and	CCONJ
ma-10	20	4	phrases	phrase	NOUN
ma-10	20	5	.	.	PUNCT
ma-10	21	1	viscosity	viscosity	NOUN
ma-10	21	2	;	;	PUNCT
ma-10	21	3	hilbert	hilbert	NOUN
ma-10	21	4	space	space	NOUN
ma-10	21	5	;	;	PUNCT
ma-10	21	6	convex	convex	NOUN
ma-10	21	7	minimization	minimization	NOUN
ma-10	21	8	;	;	PUNCT
ma-10	21	9	asymptotically	asymptotically	ADV
ma-10	21	10	nonexpansive	nonexpansive	ADJ
ma-10	21	11	mapping	mapping	NOUN
ma-10	21	12	;	;	PUNCT
ma-10	21	13	varia	varia	NOUN
ma-10	21	14	-	-	PUNCT
ma-10	21	15	tional	tional	ADJ
ma-10	21	16	inequality	inequality	NOUN
ma-10	21	17	;	;	PUNCT
ma-10	21	18	fixed	fix	VERB
ma-10	21	19	point	point	NOUN
ma-10	21	20	.	.	PUNCT
ma-10	22	1	19	19	NUM
ma-10	22	2	https://adac.ee	https://adac.ee	PROPN
ma-10	22	3	https://doi.org/10.28924/ada/ma.1.19	https://doi.org/10.28924/ada/ma.1.19	PROPN
ma-10	22	4	https://orcid.org/0000-0002-3774-0761	https://orcid.org/0000-0002-3774-0761	PROPN
ma-10	22	5	eur	eur	PROPN
ma-10	22	6	.	.	PUNCT
ma-10	23	1	j.	j.	PROPN
ma-10	23	2	math	math	PROPN
ma-10	23	3	.	.	PUNCT
ma-10	24	1	anal	anal	ADJ
ma-10	24	2	.	.	PUNCT
ma-10	25	1	1	1	NUM
ma-10	25	2	(	(	PUNCT
ma-10	25	3	2021	2021	NUM
ma-10	25	4	)	)	PUNCT
ma-10	25	5	20	20	NUM
ma-10	25	6	in	in	ADP
ma-10	25	7	2015	2015	NUM
ma-10	25	8	,	,	PUNCT
ma-10	25	9	ke	ke	NOUN
ma-10	25	10	and	and	CCONJ
ma-10	25	11	ma	ma	PROPN
ma-10	26	1	[	[	X
ma-10	26	2	4	4	X
ma-10	26	3	]	]	PUNCT
ma-10	26	4	proposed	propose	VERB
ma-10	26	5	the	the	DET
ma-10	26	6	generalized	generalized	ADJ
ma-10	26	7	viscosity	viscosity	NOUN
ma-10	26	8	implicit	implicit	ADJ
ma-10	26	9	rules	rule	NOUN
ma-10	26	10	of	of	ADP
ma-10	26	11	nonexpansive	nonexpansive	ADJ
ma-10	26	12	mappingsin	mappingsin	PROPN
ma-10	26	13	hilbert	hilbert	PROPN
ma-10	26	14	spaces	space	NOUN
ma-10	26	15	as	as	SCONJ
ma-10	26	16	follows	follow	VERB
ma-10	26	17	:	:	PUNCT
ma-10	26	18	un+1	un+1	NOUN
ma-10	26	19	=	=	SYM
ma-10	26	20	αnψ(un	αnψ(un	NOUN
ma-10	26	21	)	)	PUNCT
ma-10	27	1	+	+	CCONJ
ma-10	27	2	(	(	PUNCT
ma-10	27	3	1−	1−	NUM
ma-10	27	4	αn)t	αn)t	NUM
ma-10	27	5	(	(	PUNCT
ma-10	27	6	snun	snun	NOUN
ma-10	27	7	+	+	CCONJ
ma-10	27	8	(	(	PUNCT
ma-10	27	9	1−	1−	NUM
ma-10	27	10	sn)un+1	sn)un+1	NOUN
ma-10	27	11	)	)	PUNCT
ma-10	27	12	,	,	PUNCT
ma-10	27	13	n	n	PRON
ma-10	27	14	≥	≥	NOUN
ma-10	27	15	0	0	NUM
ma-10	27	16	,	,	PUNCT
ma-10	27	17	(	(	PUNCT
ma-10	27	18	1.4	1.4	NUM
ma-10	27	19	)	)	PUNCT
ma-10	27	20	and	and	CCONJ
ma-10	27	21	un+1	un+1	ADV
ma-10	27	22	=	=	PUNCT
ma-10	27	23	αnun	αnun	ADJ
ma-10	27	24	+	+	CCONJ
ma-10	27	25	βnψ(un	βnψ(un	NUM
ma-10	27	26	)	)	PUNCT
ma-10	28	1	+	+	CCONJ
ma-10	28	2	γnt	γnt	ADJ
ma-10	28	3	(	(	PUNCT
ma-10	28	4	snun	snun	NOUN
ma-10	28	5	+	+	CCONJ
ma-10	28	6	(	(	PUNCT
ma-10	28	7	1−	1−	NUM
ma-10	28	8	sn)un+1	sn)un+1	NOUN
ma-10	28	9	)	)	PUNCT
ma-10	28	10	,	,	PUNCT
ma-10	28	11	n	n	PRON
ma-10	28	12	≥	≥	NOUN
ma-10	28	13	0	0	NUM
ma-10	28	14	,	,	PUNCT
ma-10	28	15	(	(	PUNCT
ma-10	28	16	1.5	1.5	NUM
ma-10	28	17	)	)	PUNCT
ma-10	28	18	they	they	PRON
ma-10	28	19	proved	prove	VERB
ma-10	28	20	that	that	SCONJ
ma-10	28	21	the	the	DET
ma-10	28	22	generalized	generalized	ADJ
ma-10	28	23	viscosity	viscosity	NOUN
ma-10	28	24	implicit	implicit	ADJ
ma-10	28	25	rules	rule	NOUN
ma-10	28	26	1.4	1.4	NUM
ma-10	28	27	and	and	CCONJ
ma-10	28	28	1.5	1.5	NUM
ma-10	28	29	converge	converge	NOUN
ma-10	28	30	strongly	strongly	ADV
ma-10	28	31	to	to	ADP
ma-10	28	32	a	a	DET
ma-10	28	33	fixedpoint	fixedpoint	NOUN
ma-10	28	34	of	of	ADP
ma-10	28	35	t	t	PROPN
ma-10	28	36	under	under	ADP
ma-10	28	37	certain	certain	ADJ
ma-10	28	38	assumptions	assumption	NOUN
ma-10	28	39	,	,	PUNCT
ma-10	28	40	which	which	PRON
ma-10	28	41	also	also	ADV
ma-10	28	42	solved	solve	VERB
ma-10	28	43	the	the	DET
ma-10	28	44	v	v	NOUN
ma-10	28	45	i(1.1	i(1.1	PROPN
ma-10	28	46	)	)	PUNCT
ma-10	28	47	.	.	PUNCT
ma-10	29	1	in	in	ADP
ma-10	29	2	2016	2016	NUM
ma-10	29	3	,	,	PUNCT
ma-10	29	4	motivated	motivate	VERB
ma-10	29	5	by	by	ADP
ma-10	29	6	the	the	DET
ma-10	29	7	work	work	NOUN
ma-10	29	8	of	of	ADP
ma-10	29	9	xu	xu	PROPN
ma-10	30	1	[	[	X
ma-10	30	2	3	3	NUM
ma-10	30	3	]	]	PUNCT
ma-10	30	4	,	,	PUNCT
ma-10	30	5	zhao	zhao	PROPN
ma-10	30	6	et	et	PROPN
ma-10	30	7	al	al	PROPN
ma-10	31	1	[	[	X
ma-10	31	2	5	5	NUM
ma-10	31	3	]	]	PUNCT
ma-10	31	4	proposed	propose	VERB
ma-10	31	5	the	the	DET
ma-10	31	6	following	follow	VERB
ma-10	31	7	implicit	implicit	ADJ
ma-10	31	8	midpointrule	midpointrule	NOUN
ma-10	31	9	for	for	ADP
ma-10	31	10	asymptotically	asymptotically	ADV
ma-10	31	11	nonexpansive	nonexpansive	ADJ
ma-10	31	12	mappings	mapping	NOUN
ma-10	31	13	:	:	PUNCT
ma-10	31	14	un+1	un+1	NOUN
ma-10	31	15	=	=	SYM
ma-10	31	16	αnψ(un	αnψ(un	NOUN
ma-10	31	17	)	)	PUNCT
ma-10	31	18	+	+	CCONJ
ma-10	32	1	(	(	PUNCT
ma-10	32	2	1−	1−	NUM
ma-10	32	3	αn)t	αn)t	NUM
ma-10	32	4	n	n	PROPN
ma-10	32	5	(	(	PUNCT
ma-10	32	6	un	un	PROPN
ma-10	32	7	+	+	CCONJ
ma-10	32	8	un+1	un+1	PROPN
ma-10	32	9	2	2	NUM
ma-10	32	10	)	)	PUNCT
ma-10	32	11	,	,	PUNCT
ma-10	32	12	n	n	X
ma-10	32	13	≥	≥	NOUN
ma-10	32	14	0	0	NUM
ma-10	32	15	,	,	PUNCT
ma-10	32	16	(	(	PUNCT
ma-10	32	17	1.6	1.6	NUM
ma-10	32	18	)	)	PUNCT
ma-10	32	19	where	where	SCONJ
ma-10	32	20	t	t	PROPN
ma-10	32	21	is	be	AUX
ma-10	32	22	an	an	DET
ma-10	32	23	asymptotically	asymptotically	ADV
ma-10	32	24	nonexpansive	nonexpansive	ADJ
ma-10	32	25	mapping	mapping	NOUN
ma-10	32	26	.	.	PUNCT
ma-10	33	1	they	they	PRON
ma-10	33	2	proved	prove	VERB
ma-10	33	3	that	that	SCONJ
ma-10	33	4	the	the	DET
ma-10	33	5	sequence	sequence	NOUN
ma-10	33	6	{	{	PUNCT
ma-10	33	7	un	un	PROPN
ma-10	33	8	}	}	PUNCT
ma-10	33	9	con	con	ADJ
ma-10	33	10	-	-	PUNCT
ma-10	33	11	verges	verge	NOUN
ma-10	33	12	strongly	strongly	ADV
ma-10	33	13	to	to	ADP
ma-10	33	14	a	a	DET
ma-10	33	15	fixed	fix	VERB
ma-10	33	16	point	point	NOUN
ma-10	33	17	of	of	ADP
ma-10	33	18	t	t	PROPN
ma-10	33	19	,	,	PUNCT
ma-10	33	20	which	which	PRON
ma-10	33	21	,	,	PUNCT
ma-10	33	22	in	in	ADP
ma-10	33	23	addition	addition	NOUN
ma-10	33	24	,	,	PUNCT
ma-10	33	25	also	also	ADV
ma-10	33	26	solves	solve	VERB
ma-10	33	27	the	the	DET
ma-10	33	28	v	v	NOUN
ma-10	33	29	i(1.1	i(1.1	PROPN
ma-10	33	30	)	)	PUNCT
ma-10	33	31	.	.	PUNCT
ma-10	34	1	in	in	ADP
ma-10	34	2	2017	2017	NUM
ma-10	34	3	,	,	PUNCT
ma-10	34	4	he	he	PRON
ma-10	34	5	et	et	VERB
ma-10	34	6	la	la	PROPN
ma-10	35	1	[	[	X
ma-10	35	2	14	14	NUM
ma-10	35	3	]	]	PUNCT
ma-10	35	4	studied	study	VERB
ma-10	35	5	the	the	DET
ma-10	35	6	following	following	ADJ
ma-10	35	7	iterative	iterative	NOUN
ma-10	35	8	un+1	un+1	NOUN
ma-10	35	9	=	=	SYM
ma-10	35	10	αnψ(un	αnψ(un	NOUN
ma-10	35	11	)	)	PUNCT
ma-10	36	1	+	+	CCONJ
ma-10	36	2	(	(	PUNCT
ma-10	36	3	1−	1−	NUM
ma-10	36	4	αn)t	αn)t	NUM
ma-10	36	5	n(βnun	n(βnun	NOUN
ma-10	36	6	+	+	CCONJ
ma-10	36	7	(	(	PUNCT
ma-10	36	8	1−	1−	NUM
ma-10	36	9	βn)un+1	βn)un+1	ADJ
ma-10	36	10	)	)	PUNCT
ma-10	36	11	,	,	PUNCT
ma-10	36	12	n	n	PRON
ma-10	36	13	≥	≥	NOUN
ma-10	36	14	0	0	NUM
ma-10	36	15	(	(	PUNCT
ma-10	36	16	1.7	1.7	NUM
ma-10	36	17	)	)	PUNCT
ma-10	36	18	in	in	ADP
ma-10	36	19	the	the	DET
ma-10	36	20	setting	setting	NOUN
ma-10	36	21	of	of	ADP
ma-10	36	22	a	a	DET
ma-10	36	23	hilbert	hilbert	NOUN
ma-10	36	24	space	space	NOUN
ma-10	36	25	and	and	CCONJ
ma-10	36	26	proved	prove	VERB
ma-10	36	27	that	that	SCONJ
ma-10	36	28	the	the	DET
ma-10	36	29	sequence	sequence	NOUN
ma-10	36	30	{	{	PUNCT
ma-10	36	31	un	un	PROPN
ma-10	36	32	}	}	PUNCT
ma-10	36	33	converges	converge	VERB
ma-10	36	34	strongly	strongly	ADV
ma-10	36	35	to	to	PART
ma-10	36	36	u∗	u∗	VERB
ma-10	36	37	=	=	PUNCT
ma-10	36	38	pf	pf	X
ma-10	36	39	(	(	PUNCT
ma-10	36	40	t	t	NOUN
ma-10	36	41	)	)	PUNCT
ma-10	36	42	ψ(u∗	ψ(u∗	PUNCT
ma-10	36	43	)	)	PUNCT
ma-10	36	44	which	which	PRON
ma-10	36	45	is	be	AUX
ma-10	36	46	also	also	ADV
ma-10	36	47	the	the	DET
ma-10	36	48	unique	unique	ADJ
ma-10	36	49	solution	solution	NOUN
ma-10	36	50	of	of	ADP
ma-10	36	51	the	the	DET
ma-10	36	52	following	following	NOUN
ma-10	36	53	v	v	ADP
ma-10	36	54	i	i	PRON
ma-10	36	55	〈	〈	PROPN
ma-10	36	56	(	(	PUNCT
ma-10	36	57	i	i	NOUN
ma-10	36	58	−	−	PROPN
ma-10	36	59	ψ)u	ψ)u	NOUN
ma-10	36	60	,	,	PUNCT
ma-10	36	61	v	v	ADP
ma-10	36	62	−	−	PROPN
ma-10	36	63	u	u	NOUN
ma-10	36	64	〉	〉	PROPN
ma-10	36	65	≥	≥	NOUN
ma-10	36	66	0,∀v	0,∀v	X
ma-10	36	67	∈	∈	PROPN
ma-10	36	68	f	f	X
ma-10	36	69	(	(	PUNCT
ma-10	36	70	t	t	PROPN
ma-10	36	71	)	)	PUNCT
ma-10	36	72	(	(	PUNCT
ma-10	36	73	1.8	1.8	NUM
ma-10	36	74	)	)	PUNCT
ma-10	36	75	in	in	ADP
ma-10	36	76	this	this	DET
ma-10	36	77	paper	paper	NOUN
ma-10	36	78	,	,	PUNCT
ma-10	36	79	we	we	PRON
ma-10	36	80	introduce	introduce	VERB
ma-10	36	81	and	and	CCONJ
ma-10	36	82	study	study	VERB
ma-10	36	83	the	the	DET
ma-10	36	84	generalized	generalized	ADJ
ma-10	36	85	viscosity	viscosity	NOUN
ma-10	36	86	implicit	implicit	ADJ
ma-10	36	87	rules	rule	NOUN
ma-10	36	88	of	of	ADP
ma-10	36	89	asymptoticallynonexpansive	asymptoticallynonexpansive	ADJ
ma-10	36	90	mappings	mapping	NOUN
ma-10	36	91	in	in	ADP
ma-10	36	92	hilbert	hilbert	PROPN
ma-10	36	93	spaces	space	NOUN
ma-10	36	94	.	.	PUNCT
ma-10	37	1	more	more	ADV
ma-10	37	2	precisely	precisely	ADV
ma-10	37	3	,	,	PUNCT
ma-10	37	4	we	we	PRON
ma-10	37	5	consider	consider	VERB
ma-10	37	6	the	the	DET
ma-10	37	7	following	follow	VERB
ma-10	37	8	implicititerative	implicititerative	ADJ
ma-10	37	9	algorithm:	algorithm:	PROPN
ma-10	37	10	u1	u1	PROPN
ma-10	37	11	∈m	∈m	NOUN
ma-10	37	12	un+1	un+1	NOUN
ma-10	37	13	=	=	NOUN
ma-10	37	14	αnun	αnun	ADJ
ma-10	37	15	+	+	CCONJ
ma-10	37	16	βnψ(un	βnψ(un	NUM
ma-10	37	17	)	)	PUNCT
ma-10	37	18	+	+	CCONJ
ma-10	37	19	γnt	γnt	ADJ
ma-10	37	20	n	n	CCONJ
ma-10	37	21	(	(	PUNCT
ma-10	37	22	snun	snun	NOUN
ma-10	37	23	+	+	CCONJ
ma-10	37	24	(	(	PUNCT
ma-10	37	25	1−	1−	NUM
ma-10	37	26	sn)un+1	sn)un+1	NOUN
ma-10	37	27	)	)	PUNCT
ma-10	37	28	∀n	∀n	NUM
ma-10	38	1	∈	∈	PROPN
ma-10	38	2	n	n	CCONJ
ma-10	38	3	(	(	PUNCT
ma-10	38	4	1.9	1.9	NUM
ma-10	38	5	)	)	PUNCT
ma-10	38	6	under	under	ADP
ma-10	38	7	suitable	suitable	ADJ
ma-10	38	8	conditions	condition	NOUN
ma-10	38	9	,	,	PUNCT
ma-10	38	10	we	we	PRON
ma-10	38	11	proved	prove	VERB
ma-10	38	12	that	that	SCONJ
ma-10	38	13	the	the	DET
ma-10	38	14	sequence	sequence	NOUN
ma-10	38	15	{	{	PUNCT
ma-10	38	16	un	un	PROPN
ma-10	38	17	}	}	PUNCT
ma-10	38	18	converge	converge	VERB
ma-10	38	19	strongly	strongly	ADV
ma-10	38	20	to	to	ADP
ma-10	38	21	a	a	DET
ma-10	38	22	fixed	fix	VERB
ma-10	38	23	point	point	NOUN
ma-10	38	24	ofthe	ofthe	VERB
ma-10	38	25	asymptotically	asymptotically	ADV
ma-10	38	26	nonexpansive	nonexpansive	ADJ
ma-10	38	27	mapping	mapping	PROPN
ma-10	38	28	t	t	PROPN
ma-10	38	29	,	,	PUNCT
ma-10	38	30	which	which	PRON
ma-10	38	31	also	also	ADV
ma-10	38	32	solves	solve	VERB
ma-10	38	33	the	the	DET
ma-10	38	34	variational	variational	ADJ
ma-10	38	35	inequality	inequality	NOUN
ma-10	38	36	〈	〈	PROPN
ma-10	38	37	(	(	PUNCT
ma-10	38	38	i	i	NOUN
ma-10	38	39	−	−	PROPN
ma-10	38	40	ψ)u	ψ)u	NOUN
ma-10	38	41	,	,	PUNCT
ma-10	38	42	p	p	NOUN
ma-10	38	43	−	−	PROPN
ma-10	38	44	u	u	NOUN
ma-10	38	45	〉	〉	PROPN
ma-10	38	46	≥	≥	NOUN
ma-10	38	47	0	0	NUM
ma-10	39	1	p	p	X
ma-10	39	2	∈	∈	PROPN
ma-10	39	3	f	f	X
ma-10	39	4	(	(	PUNCT
ma-10	39	5	t	t	PROPN
ma-10	39	6	)	)	PUNCT
ma-10	39	7	.	.	PUNCT
ma-10	40	1	as	as	ADP
ma-10	40	2	applications	application	NOUN
ma-10	40	3	,	,	PUNCT
ma-10	40	4	we	we	PRON
ma-10	40	5	apply	apply	VERB
ma-10	40	6	our	our	PRON
ma-10	40	7	results	result	NOUN
ma-10	40	8	to	to	PART
ma-10	40	9	solve	solve	VERB
ma-10	40	10	convexly	convexly	ADV
ma-10	40	11	constrained	constrain	VERB
ma-10	40	12	minimization	minimization	NOUN
ma-10	40	13	problem	problem	NOUN
ma-10	40	14	.	.	PUNCT
ma-10	41	1	this	this	DET
ma-10	41	2	wayresults	wayresult	NOUN
ma-10	41	3	in	in	ADP
ma-10	41	4	1.5	1.5	NUM
ma-10	41	5	are	be	AUX
ma-10	41	6	complemented	complement	VERB
ma-10	41	7	,	,	PUNCT
ma-10	41	8	extended	extended	ADJ
ma-10	41	9	and	and	CCONJ
ma-10	41	10	generalized	generalize	VERB
ma-10	41	11	.	.	PUNCT
ma-10	42	1	eur	eur	PROPN
ma-10	42	2	.	.	PUNCT
ma-10	43	1	j.	j.	PROPN
ma-10	43	2	math	math	PROPN
ma-10	43	3	.	.	PUNCT
ma-10	44	1	anal	anal	ADJ
ma-10	44	2	.	.	PUNCT
ma-10	45	1	1	1	NUM
ma-10	45	2	(	(	PUNCT
ma-10	45	3	2021	2021	NUM
ma-10	45	4	)	)	PUNCT
ma-10	45	5	212	212	NUM
ma-10	45	6	.	.	PUNCT
ma-10	46	1	preliminaries	preliminary	NOUN
ma-10	46	2	in	in	ADP
ma-10	46	3	the	the	DET
ma-10	46	4	sequel	sequel	NOUN
ma-10	46	5	,	,	PUNCT
ma-10	46	6	we	we	PRON
ma-10	46	7	always	always	ADV
ma-10	46	8	assume	assume	VERB
ma-10	46	9	that	that	SCONJ
ma-10	46	10	h	h	NOUN
ma-10	46	11	is	be	AUX
ma-10	46	12	a	a	DET
ma-10	46	13	real	real	ADJ
ma-10	46	14	hilbert	hilbert	NOUN
ma-10	46	15	space	space	NOUN
ma-10	46	16	and	and	CCONJ
ma-10	46	17	m	m	PROPN
ma-10	46	18	is	be	AUX
ma-10	46	19	a	a	DET
ma-10	46	20	nonempty	nonempty	ADJ
ma-10	46	21	,	,	PUNCT
ma-10	46	22	closed	closed	ADJ
ma-10	46	23	,	,	PUNCT
ma-10	46	24	and	and	CCONJ
ma-10	46	25	convex	convex	PROPN
ma-10	46	26	subset	subset	NOUN
ma-10	46	27	of	of	ADP
ma-10	46	28	h.	h.	PROPN
ma-10	46	29	the	the	DET
ma-10	46	30	nearest	near	ADJ
ma-10	46	31	point	point	NOUN
ma-10	46	32	projection	projection	NOUN
ma-10	46	33	from	from	ADP
ma-10	46	34	h	h	PROPN
ma-10	46	35	onto	onto	ADP
ma-10	46	36	m	m	PROPN
ma-10	46	37	,	,	PUNCT
ma-10	46	38	pm	pm	VERB
ma-10	46	39	,	,	PUNCT
ma-10	46	40	is	be	AUX
ma-10	46	41	defined	define	VERB
ma-10	46	42	by	by	ADP
ma-10	46	43	pm(u	pm(u	NOUN
ma-10	46	44	)	)	PUNCT
ma-10	46	45	:	:	PUNCT
ma-10	47	1	=	=	PUNCT
ma-10	47	2	arg	arg	NOUN
ma-10	47	3	min	min	PROPN
ma-10	47	4	z∈m	z∈m	PROPN
ma-10	47	5	∥∥∥u	∥∥∥u	NOUN
ma-10	47	6	−	−	PROPN
ma-10	47	7	z∥∥∥2	z∥∥∥2	PROPN
ma-10	47	8	,	,	PUNCT
ma-10	47	9	u	u	PROPN
ma-10	47	10	∈	∈	PROPN
ma-10	47	11	h.	h.	PROPN
ma-10	47	12	(	(	PUNCT
ma-10	47	13	2.1	2.1	NUM
ma-10	47	14	)	)	PUNCT
ma-10	47	15	namely	namely	ADV
ma-10	47	16	,	,	PUNCT
ma-10	47	17	pm(u	pm(u	X
ma-10	47	18	)	)	PUNCT
ma-10	47	19	is	be	AUX
ma-10	47	20	the	the	DET
ma-10	47	21	only	only	ADJ
ma-10	47	22	point	point	NOUN
ma-10	47	23	in	in	ADP
ma-10	47	24	m	m	PROPN
ma-10	47	25	that	that	PRON
ma-10	47	26	minimizes	minimize	VERB
ma-10	47	27	the	the	DET
ma-10	47	28	objective	objective	ADJ
ma-10	47	29	∥∥∥u	∥∥∥u	NOUN
ma-10	47	30	−	−	PROPN
ma-10	47	31	z∥∥∥	z∥∥∥	PROPN
ma-10	47	32	over	over	ADP
ma-10	47	33	z	z	PROPN
ma-10	47	34	∈	∈	PROPN
ma-10	47	35	m.	m.	NOUN
ma-10	47	36	and	and	CCONJ
ma-10	47	37	pm(u	pm(u	NOUN
ma-10	47	38	)	)	PUNCT
ma-10	47	39	is	be	AUX
ma-10	47	40	characterized	characterize	VERB
ma-10	47	41	as	as	SCONJ
ma-10	47	42	follows	follow	VERB
ma-10	47	43	:	:	PUNCT
ma-10	47	44	pm(u	pm(u	X
ma-10	47	45	)	)	PUNCT
ma-10	47	46	∈m	∈m	NOUN
ma-10	47	47	and	and	CCONJ
ma-10	47	48	〈	〈	NOUN
ma-10	47	49	u	u	NOUN
ma-10	47	50	−	−	PROPN
ma-10	47	51	pm(u	pm(u	X
ma-10	47	52	)	)	PUNCT
ma-10	47	53	,	,	PUNCT
ma-10	48	1	z	z	NOUN
ma-10	48	2	−	−	PROPN
ma-10	48	3	pm(u	pm(u	X
ma-10	48	4	)	)	PUNCT
ma-10	48	5	〉	〉	NOUN
ma-10	48	6	≤	≤	NOUN
ma-10	48	7	0	0	NUM
ma-10	49	1	f	f	NOUN
ma-10	49	2	or	or	CCONJ
ma-10	49	3	al	al	PROPN
ma-10	49	4	l	l	NOUN
ma-10	49	5	z	z	NOUN
ma-10	49	6	∈m	∈m	NOUN
ma-10	49	7	.	.	PUNCT
ma-10	50	1	(	(	PUNCT
ma-10	50	2	2.2	2.2	NUM
ma-10	50	3	)	)	PUNCT
ma-10	50	4	definition	definition	NOUN
ma-10	50	5	2.1	2.1	NUM
ma-10	50	6	.	.	PUNCT
ma-10	50	7	.	.	PUNCT
ma-10	51	1	a	a	DET
ma-10	51	2	mapping	mapping	NOUN
ma-10	51	3	t	t	NOUN
ma-10	51	4	:	:	PUNCT
ma-10	51	5	m→m	m→m	NOUN
ma-10	51	6	is	be	AUX
ma-10	51	7	said	say	VERB
ma-10	51	8	to	to	PART
ma-10	51	9	be	be	AUX
ma-10	51	10	:	:	PUNCT
ma-10	51	11	a	a	X
ma-10	51	12	):	):	PUNCT
ma-10	51	13	α	α	NUM
ma-10	51	14	-	-	PUNCT
ma-10	51	15	inverse	inverse	NOUN
ma-10	51	16	strongly	strongly	ADV
ma-10	51	17	monotone	monotone	ADJ
ma-10	51	18	if	if	SCONJ
ma-10	51	19	there	there	PRON
ma-10	51	20	exists	exist	VERB
ma-10	51	21	α	α	PROPN
ma-10	51	22	>	>	X
ma-10	51	23	0	0	PUNCT
ma-10	52	1	satisfying	satisfy	VERB
ma-10	52	2	〈	〈	PROPN
ma-10	52	3	u	u	NOUN
ma-10	52	4	−	−	PROPN
ma-10	52	5	v	v	NOUN
ma-10	52	6	,	,	PUNCT
ma-10	52	7	t	t	PROPN
ma-10	52	8	u	u	NOUN
ma-10	52	9	−	−	PROPN
ma-10	52	10	t	t	PROPN
ma-10	52	11	v	v	PROPN
ma-10	52	12	〉	〉	PROPN
ma-10	52	13	≥	≥	NOUN
ma-10	53	1	α‖au	α‖au	NOUN
ma-10	53	2	−	−	NOUN
ma-10	53	3	av‖2	av‖2	NOUN
ma-10	53	4	∀u	∀u	NOUN
ma-10	53	5	,	,	PUNCT
ma-10	53	6	v	v	NOUN
ma-10	53	7	∈m	∈m	NOUN
ma-10	53	8	;	;	PUNCT
ma-10	53	9	(	(	PUNCT
ma-10	53	10	2.3	2.3	NUM
ma-10	53	11	)	)	PUNCT
ma-10	53	12	b	b	NOUN
ma-10	53	13	):	):	PUNCT
ma-10	53	14	l	l	ADJ
ma-10	53	15	-	-	ADJ
ma-10	53	16	lipschitz	lipschitz	ADJ
ma-10	53	17	continuous	continuous	ADJ
ma-10	53	18	if	if	SCONJ
ma-10	53	19	there	there	PRON
ma-10	53	20	exists	exist	VERB
ma-10	53	21	l	l	PROPN
ma-10	53	22	≥	≥	X
ma-10	53	23	0	0	NUM
ma-10	53	24	satisfying	satisfy	VERB
ma-10	53	25	‖t	‖t	ADJ
ma-10	53	26	u	u	NOUN
ma-10	53	27	−	−	PROPN
ma-10	53	28	t	t	PROPN
ma-10	53	29	v‖	v‖	NOUN
ma-10	53	30	≤	≤	PUNCT
ma-10	53	31	l‖u	l‖u	VERB
ma-10	53	32	−	−	PROPN
ma-10	53	33	v‖	v‖	NOUN
ma-10	53	34	∀u	∀u	NOUN
ma-10	53	35	,	,	PUNCT
ma-10	53	36	v	v	NOUN
ma-10	53	37	∈m	∈m	NOUN
ma-10	53	38	;	;	PUNCT
ma-10	53	39	(	(	PUNCT
ma-10	53	40	2.4	2.4	NUM
ma-10	53	41	)	)	PUNCT
ma-10	53	42	c	c	NOUN
ma-10	53	43	):	):	PUNCT
ma-10	53	44	nonexpansive	nonexpansive	ADJ
ma-10	53	45	if	if	SCONJ
ma-10	53	46	‖t	‖t	ADJ
ma-10	53	47	u	u	NOUN
ma-10	53	48	−	−	PROPN
ma-10	53	49	t	t	NOUN
ma-10	53	50	v‖	v‖	NOUN
ma-10	53	51	≤	≤	ADP
ma-10	53	52	‖u	‖u	NOUN
ma-10	54	1	−	−	PROPN
ma-10	54	2	v‖	v‖	NOUN
ma-10	54	3	∀u	∀u	NOUN
ma-10	54	4	,	,	PUNCT
ma-10	54	5	v	v	NOUN
ma-10	54	6	∈m	∈m	NOUN
ma-10	54	7	;	;	PUNCT
ma-10	54	8	(	(	PUNCT
ma-10	54	9	2.5	2.5	NUM
ma-10	54	10	)	)	PUNCT
ma-10	55	1	d	d	NOUN
ma-10	55	2	):	):	PUNCT
ma-10	55	3	asymptotically	asymptotically	ADV
ma-10	55	4	nonexpansive	nonexpansive	ADJ
ma-10	55	5	if	if	SCONJ
ma-10	55	6	there	there	PRON
ma-10	55	7	exists	exist	VERB
ma-10	55	8	a	a	DET
ma-10	55	9	sequence	sequence	NOUN
ma-10	55	10	{	{	PUNCT
ma-10	55	11	kn	kn	PROPN
ma-10	55	12	}	}	PUNCT
ma-10	55	13	⊂	⊂	PROPN
ma-10	56	1	[	[	X
ma-10	56	2	1,∞	1,∞	NUM
ma-10	56	3	)	)	PUNCT
ma-10	56	4	with	with	ADP
ma-10	56	5	lim	lim	PROPN
ma-10	56	6	n→∞	n→∞	PRON
ma-10	57	1	kn	kn	PROPN
ma-10	57	2	=	=	SYM
ma-10	57	3	1	1	NUM
ma-10	57	4	suchthat	suchthat	VERB
ma-10	57	5	‖t	‖t	PROPN
ma-10	57	6	nu	nu	PROPN
ma-10	57	7	−	−	PROPN
ma-10	57	8	t	t	PROPN
ma-10	57	9	nv‖	nv‖	NOUN
ma-10	57	10	≤	≤	ADV
ma-10	57	11	kn‖u	kn‖u	NOUN
ma-10	57	12	−	−	PROPN
ma-10	57	13	v‖	v‖	NOUN
ma-10	57	14	∀u	∀u	NOUN
ma-10	57	15	,	,	PUNCT
ma-10	57	16	v	v	NOUN
ma-10	57	17	∈m	∈m	NOUN
ma-10	57	18	and	and	CCONJ
ma-10	57	19	∀n	∀n	NUM
ma-10	57	20	∈	∈	PROPN
ma-10	57	21	n	n	CCONJ
ma-10	57	22	;	;	PUNCT
ma-10	57	23	(	(	PUNCT
ma-10	57	24	2.6	2.6	NUM
ma-10	57	25	)	)	PUNCT
ma-10	57	26	e	e	NOUN
ma-10	57	27	):	):	PUNCT
ma-10	57	28	contraction	contraction	NOUN
ma-10	57	29	if	if	SCONJ
ma-10	57	30	there	there	PRON
ma-10	57	31	exists	exist	VERB
ma-10	57	32	the	the	DET
ma-10	57	33	contractive	contractive	ADJ
ma-10	57	34	constant	constant	ADJ
ma-10	57	35	α	α	PRON
ma-10	57	36	∈	∈	PROPN
ma-10	58	1	[	[	X
ma-10	58	2	0	0	NUM
ma-10	58	3	,	,	PUNCT
ma-10	58	4	1	1	NUM
ma-10	58	5	)	)	PUNCT
ma-10	58	6	such	such	ADJ
ma-10	58	7	that	that	SCONJ
ma-10	58	8	‖t	‖t	ADJ
ma-10	58	9	u	u	NOUN
ma-10	58	10	−	−	PROPN
ma-10	58	11	t	t	PROPN
ma-10	58	12	v‖	v‖	NOUN
ma-10	58	13	≤	≤	NUM
ma-10	58	14	α‖u	α‖u	ADP
ma-10	58	15	−	−	PROPN
ma-10	58	16	v‖	v‖	NOUN
ma-10	58	17	∀u	∀u	NOUN
ma-10	58	18	,	,	PUNCT
ma-10	58	19	v	v	NOUN
ma-10	58	20	∈m	∈m	NOUN
ma-10	58	21	;	;	PUNCT
ma-10	58	22	(	(	PUNCT
ma-10	58	23	2.7	2.7	NUM
ma-10	58	24	)	)	PUNCT
ma-10	58	25	lemma	lemma	PROPN
ma-10	58	26	2.2	2.2	NUM
ma-10	58	27	.	.	PUNCT
ma-10	59	1	(	(	PUNCT
ma-10	59	2	the	the	DET
ma-10	59	3	demiclosedness	demiclosedness	NOUN
ma-10	59	4	principle	principle	NOUN
ma-10	59	5	[	[	X
ma-10	59	6	10	10	NUM
ma-10	59	7	]	]	PUNCT
ma-10	59	8	)	)	PUNCT
ma-10	59	9	.	.	PUNCT
ma-10	60	1	let	let	VERB
ma-10	60	2	h	h	PRON
ma-10	60	3	be	be	AUX
ma-10	60	4	a	a	DET
ma-10	60	5	hilbert	hilbert	NOUN
ma-10	60	6	space	space	NOUN
ma-10	60	7	,	,	PUNCT
ma-10	60	8	m	m	VERB
ma-10	60	9	be	be	VERB
ma-10	60	10	a	a	DET
ma-10	60	11	nonempty	nonempty	ADV
ma-10	60	12	closed	close	VERB
ma-10	60	13	convex	convex	NOUN
ma-10	60	14	subset	subset	NOUN
ma-10	60	15	of	of	ADP
ma-10	60	16	h	h	NOUN
ma-10	60	17	,	,	PUNCT
ma-10	60	18	and	and	CCONJ
ma-10	60	19	t	t	X
ma-10	60	20	:	:	PUNCT
ma-10	60	21	m	m	AUX
ma-10	60	22	→	→	PUNCT
ma-10	60	23	m	m	AUX
ma-10	60	24	be	be	AUX
ma-10	60	25	a	a	DET
ma-10	60	26	asymptotically	asymptotically	ADV
ma-10	60	27	nonexpansive	nonexpansive	ADJ
ma-10	60	28	mapping	mapping	NOUN
ma-10	60	29	with	with	ADP
ma-10	60	30	f	f	PROPN
ma-10	60	31	ix(t	ix(t	ADV
ma-10	60	32	)	)	PUNCT
ma-10	60	33	6=	6=	ADP
ma-10	60	34	∅.	∅.	ADP
ma-10	60	35	if	if	SCONJ
ma-10	60	36	{	{	PUNCT
ma-10	60	37	un	un	ADJ
ma-10	60	38	}	}	PUNCT
ma-10	60	39	is	be	AUX
ma-10	60	40	a	a	DET
ma-10	60	41	sequence	sequence	NOUN
ma-10	60	42	in	in	ADP
ma-10	60	43	m	m	PRON
ma-10	60	44	such	such	ADJ
ma-10	60	45	that	that	SCONJ
ma-10	60	46	{	{	PUNCT
ma-10	60	47	un	un	ADJ
ma-10	60	48	}	}	PUNCT
ma-10	60	49	weakly	weakly	ADJ
ma-10	60	50	converges	converge	NOUN
ma-10	60	51	to	to	ADP
ma-10	60	52	u	u	PRON
ma-10	60	53	and	and	CCONJ
ma-10	60	54	{	{	PUNCT
ma-10	60	55	(	(	PUNCT
ma-10	60	56	i	i	PRON
ma-10	60	57	−	−	PROPN
ma-10	60	58	t	t	NOUN
ma-10	60	59	)	)	PUNCT
ma-10	60	60	un	un	AUX
ma-10	60	61	}	}	PUNCT
ma-10	60	62	converges	converge	VERB
ma-10	60	63	strongly	strongly	ADV
ma-10	60	64	to	to	ADP
ma-10	60	65	0	0	NUM
ma-10	60	66	,	,	PUNCT
ma-10	60	67	then	then	ADV
ma-10	60	68	u	u	PROPN
ma-10	60	69	=	=	PROPN
ma-10	60	70	t	t	PROPN
ma-10	60	71	(	(	PUNCT
ma-10	60	72	u	u	NOUN
ma-10	60	73	)	)	PUNCT
ma-10	60	74	lemma	lemma	PROPN
ma-10	60	75	2.3	2.3	NUM
ma-10	60	76	.	.	PUNCT
ma-10	61	1	let	let	VERB
ma-10	61	2	h	h	PRON
ma-10	61	3	be	be	AUX
ma-10	61	4	a	a	DET
ma-10	61	5	hilbert	hilbert	NOUN
ma-10	61	6	space	space	NOUN
ma-10	61	7	.	.	PUNCT
ma-10	62	1	then	then	ADV
ma-10	62	2	for	for	ADP
ma-10	62	3	all	all	DET
ma-10	62	4	θ	θ	PROPN
ma-10	62	5	,	,	PUNCT
ma-10	62	6	u	u	NOUN
ma-10	62	7	,	,	PUNCT
ma-10	62	8	v	v	PROPN
ma-10	62	9	∈	∈	PROPN
ma-10	62	10	h	h	NOUN
ma-10	62	11	,	,	PUNCT
ma-10	62	12	the	the	DET
ma-10	62	13	following	follow	VERB
ma-10	62	14	inequality	inequality	NOUN
ma-10	62	15	holds	hold	VERB
ma-10	62	16	‖u	‖u	NOUN
ma-10	62	17	−	−	PROPN
ma-10	62	18	θ‖2	θ‖2	SYM
ma-10	62	19	≤	≤	PROPN
ma-10	62	20	‖v	‖v	NOUN
ma-10	62	21	−	−	PROPN
ma-10	62	22	θ‖2	θ‖2	PUNCT
ma-10	63	1	+	+	CCONJ
ma-10	63	2	2〈u	2〈u	NUM
ma-10	63	3	−	−	PROPN
ma-10	63	4	v	v	NOUN
ma-10	63	5	,	,	PUNCT
ma-10	63	6	u	u	NOUN
ma-10	63	7	−	−	PROPN
ma-10	63	8	θ	θ	PROPN
ma-10	63	9	〉	〉	PROPN
ma-10	63	10	lemma	lemma	PROPN
ma-10	63	11	2.4	2.4	NUM
ma-10	63	12	.	.	PUNCT
ma-10	64	1	[	[	X
ma-10	64	2	11	11	NUM
ma-10	64	3	]	]	NUM
ma-10	64	4	)	)	PUNCT
ma-10	64	5	.	.	PUNCT
ma-10	65	1	assume	assume	VERB
ma-10	65	2	that	that	SCONJ
ma-10	65	3	{	{	PUNCT
ma-10	65	4	αn	αn	NOUN
ma-10	65	5	}	}	PUNCT
ma-10	65	6	is	be	AUX
ma-10	65	7	a	a	DET
ma-10	65	8	sequence	sequence	NOUN
ma-10	65	9	of	of	ADP
ma-10	65	10	nonnegative	nonnegative	ADJ
ma-10	65	11	real	real	ADJ
ma-10	65	12	numbers	number	NOUN
ma-10	65	13	such	such	ADJ
ma-10	65	14	that	that	DET
ma-10	65	15	αn+1	αn+1	NUM
ma-10	65	16	≤	≤	NUM
ma-10	65	17	(	(	PUNCT
ma-10	65	18	1−	1−	NUM
ma-10	65	19	λn)αn	λn)αn	PUNCT
ma-10	66	1	+	+	NUM
ma-10	66	2	δn	δn	NOUN
ma-10	66	3	for	for	ADP
ma-10	66	4	all	all	PRON
ma-10	66	5	n	n	PRON
ma-10	66	6	∈	∈	PROPN
ma-10	66	7	n	n	CCONJ
ma-10	66	8	,	,	PUNCT
ma-10	66	9	where	where	SCONJ
ma-10	66	10	{	{	PUNCT
ma-10	66	11	λn	λn	NOUN
ma-10	66	12	}	}	PUNCT
ma-10	66	13	⊆	⊆	NUM
ma-10	66	14	(	(	PUNCT
ma-10	66	15	0	0	NUM
ma-10	66	16	,	,	PUNCT
ma-10	66	17	1	1	NUM
ma-10	66	18	)	)	PUNCT
ma-10	66	19	and	and	CCONJ
ma-10	66	20	{	{	PUNCT
ma-10	66	21	δn	δn	NOUN
ma-10	66	22	}	}	PUNCT
ma-10	66	23	⊆	⊆	NUM
ma-10	66	24	r	r	NOUN
ma-10	66	25	are	be	AUX
ma-10	66	26	two	two	NUM
ma-10	66	27	sequences	sequence	NOUN
ma-10	66	28	satisfying	satisfy	VERB
ma-10	66	29	the	the	DET
ma-10	66	30	following	follow	VERB
ma-10	66	31	conditions	condition	NOUN
ma-10	66	32	:	:	PUNCT
ma-10	67	1	eur	eur	PROPN
ma-10	67	2	.	.	PUNCT
ma-10	68	1	j.	j.	PROPN
ma-10	68	2	math	math	PROPN
ma-10	68	3	.	.	PUNCT
ma-10	69	1	anal	anal	ADJ
ma-10	69	2	.	.	PUNCT
ma-10	70	1	1	1	NUM
ma-10	70	2	(	(	PUNCT
ma-10	70	3	2021	2021	NUM
ma-10	70	4	)	)	PUNCT
ma-10	70	5	22	22	NUM
ma-10	71	1	(	(	PUNCT
ma-10	71	2	i	i	NOUN
ma-10	71	3	):	):	PUNCT
ma-10	71	4	∞∑	∞∑	NUM
ma-10	71	5	n=1	n=1	PROPN
ma-10	71	6	λn	λn	PROPN
ma-10	71	7	=	=	SYM
ma-10	71	8	∞	∞	PROPN
ma-10	71	9	(	(	PUNCT
ma-10	71	10	ii	ii	PROPN
ma-10	71	11	):	):	PUNCT
ma-10	71	12	lim	lim	PROPN
ma-10	71	13	sup	sup	VERB
ma-10	71	14	n→∞	n→∞	NUM
ma-10	71	15	δn	δn	NOUN
ma-10	71	16	λn	λn	NOUN
ma-10	71	17	≤	≤	NUM
ma-10	71	18	0	0	NUM
ma-10	71	19	or	or	CCONJ
ma-10	71	20	∞∑	∞∑	NUM
ma-10	71	21	n=1	n=1	PROPN
ma-10	72	1	|δn|	|δn|	PROPN
ma-10	72	2	<	<	X
ma-10	72	3	∞	∞	PROPN
ma-10	72	4	then	then	ADV
ma-10	72	5	lim	lim	PROPN
ma-10	72	6	n→∞	n→∞	X
ma-10	72	7	αn	αn	NOUN
ma-10	73	1	=	=	NOUN
ma-10	73	2	0	0	PUNCT
ma-10	74	1	then	then	ADV
ma-10	74	2	the	the	DET
ma-10	74	3	sequence	sequence	NOUN
ma-10	74	4	{	{	PUNCT
ma-10	74	5	αn	αn	NOUN
ma-10	74	6	}	}	PUNCT
ma-10	74	7	converges	converge	NOUN
ma-10	74	8	to	to	ADP
ma-10	74	9	0	0	NUM
ma-10	74	10	.	.	NOUN
ma-10	75	1	3	3	NUM
ma-10	75	2	.	.	X
ma-10	75	3	main	main	ADJ
ma-10	75	4	result	result	NOUN
ma-10	75	5	we	we	PRON
ma-10	75	6	now	now	ADV
ma-10	75	7	prove	prove	VERB
ma-10	75	8	the	the	DET
ma-10	75	9	following	follow	VERB
ma-10	75	10	new	new	ADJ
ma-10	75	11	result	result	NOUN
ma-10	75	12	.	.	PUNCT
ma-10	76	1	theorem	theorem	VERB
ma-10	76	2	3.1	3.1	NUM
ma-10	76	3	.	.	PUNCT
ma-10	77	1	let	let	VERB
ma-10	77	2	m	m	PRON
ma-10	77	3	be	be	AUX
ma-10	77	4	a	a	DET
ma-10	77	5	nonempty	nonempty	ADV
ma-10	77	6	closed	close	VERB
ma-10	77	7	convex	convex	NOUN
ma-10	77	8	subset	subset	VERB
ma-10	77	9	a	a	DET
ma-10	77	10	real	real	ADJ
ma-10	77	11	hilbert	hilbert	NOUN
ma-10	77	12	space	space	NOUN
ma-10	77	13	h	h	PROPN
ma-10	77	14	,	,	PUNCT
ma-10	77	15	t	t	X
ma-10	77	16	:	:	PUNCT
ma-10	77	17	m	m	VERB
ma-10	77	18	→	→	PUNCT
ma-10	77	19	m	m	AUX
ma-10	77	20	be	be	VERB
ma-10	77	21	asymptotically	asymptotically	ADV
ma-10	77	22	nonexpansive	nonexpansive	ADJ
ma-10	77	23	mappings	mapping	NOUN
ma-10	77	24	with	with	ADP
ma-10	77	25	the	the	DET
ma-10	77	26	same	same	ADJ
ma-10	77	27	sequence	sequence	NOUN
ma-10	77	28	{	{	PUNCT
ma-10	77	29	kn	kn	PROPN
ma-10	77	30	}	}	PUNCT
ma-10	77	31	⊆	⊆	NUM
ma-10	78	1	[	[	X
ma-10	78	2	1,∞	1,∞	NUM
ma-10	78	3	)	)	PUNCT
ma-10	79	1	such	such	ADJ
ma-10	79	2	that	that	SCONJ
ma-10	79	3	limn→∞	limn→∞	PROPN
ma-10	79	4	kn	kn	NOUN
ma-10	79	5	=	=	SYM
ma-10	79	6	1	1	NUM
ma-10	79	7	,	,	PUNCT
ma-10	79	8	f	f	PROPN
ma-10	79	9	ix(t	ix(t	ADJ
ma-10	79	10	)	)	PUNCT
ma-10	80	1	6=	6=	ADP
ma-10	80	2	∅	∅	NOUN
ma-10	80	3	and	and	CCONJ
ma-10	80	4	ψ	ψ	X
ma-10	80	5	:	:	PUNCT
ma-10	80	6	m	m	VERB
ma-10	80	7	→	→	NOUN
ma-10	80	8	m	m	AUX
ma-10	80	9	be	be	AUX
ma-10	80	10	a	a	DET
ma-10	80	11	contraction	contraction	NOUN
ma-10	80	12	mapping	mapping	NOUN
ma-10	80	13	with	with	ADP
ma-10	80	14	the	the	DET
ma-10	80	15	contractive	contractive	ADJ
ma-10	80	16	constant	constant	ADJ
ma-10	80	17	α	α	PRON
ma-10	80	18	∈	∈	PROPN
ma-10	81	1	[	[	X
ma-10	81	2	0	0	NUM
ma-10	81	3	,	,	PUNCT
ma-10	81	4	1	1	NUM
ma-10	81	5	)	)	PUNCT
ma-10	81	6	.	.	PUNCT
ma-10	82	1	define	define	VERB
ma-10	82	2	a	a	DET
ma-10	82	3	sequence	sequence	NOUN
ma-10	82	4	{	{	PUNCT
ma-10	82	5	un	un	PROPN
ma-10	82	6	}	}	PUNCT
ma-10	82	7	in	in	ADP
ma-10	82	8	m	m	PROPN
ma-10	82	9	as	as	ADP
ma-10	82	10	follows:	follows:	NOUN
ma-10	82	11	u1	u1	PROPN
ma-10	82	12	∈m	∈m	NOUN
ma-10	82	13	un+1	un+1	NOUN
ma-10	82	14	=	=	NOUN
ma-10	82	15	αnun	αnun	ADJ
ma-10	82	16	+	+	CCONJ
ma-10	82	17	βnψ(un	βnψ(un	NUM
ma-10	82	18	)	)	PUNCT
ma-10	83	1	+	+	CCONJ
ma-10	83	2	γnt	γnt	ADJ
ma-10	83	3	n	n	CCONJ
ma-10	83	4	(	(	PUNCT
ma-10	83	5	snun	snun	NOUN
ma-10	83	6	+	+	CCONJ
ma-10	83	7	(	(	PUNCT
ma-10	83	8	1−	1−	NUM
ma-10	83	9	sn)un+1	sn)un+1	NOUN
ma-10	83	10	)	)	PUNCT
ma-10	83	11	∀n	∀n	NUM
ma-10	84	1	∈	∈	PROPN
ma-10	84	2	n	n	CCONJ
ma-10	84	3	(	(	PUNCT
ma-10	84	4	3.1	3.1	NUM
ma-10	84	5	)	)	PUNCT
ma-10	84	6	where	where	SCONJ
ma-10	84	7	αn	αn	NOUN
ma-10	84	8	,	,	PUNCT
ma-10	84	9	βn	βn	NOUN
ma-10	84	10	,	,	PUNCT
ma-10	84	11	γn	γn	NUM
ma-10	84	12	,	,	PUNCT
ma-10	84	13	sn	sn	PROPN
ma-10	84	14	∈	∈	PROPN
ma-10	84	15	(	(	PUNCT
ma-10	84	16	0	0	NUM
ma-10	84	17	,	,	PUNCT
ma-10	84	18	1	1	X
ma-10	84	19	)	)	PUNCT
ma-10	84	20	satisfying	satisfy	VERB
ma-10	84	21	the	the	DET
ma-10	84	22	following	follow	VERB
ma-10	84	23	conditions	condition	NOUN
ma-10	84	24	,	,	PUNCT
ma-10	84	25	a1	a1	NOUN
ma-10	84	26	:	:	PUNCT
ma-10	84	27	αn	αn	NOUN
ma-10	85	1	+	+	CCONJ
ma-10	85	2	βn	βn	NOUN
ma-10	85	3	+	+	CCONJ
ma-10	85	4	γn	γn	NOUN
ma-10	85	5	=	=	SYM
ma-10	85	6	1	1	NUM
ma-10	85	7	a2	a2	NOUN
ma-10	85	8	:	:	PUNCT
ma-10	85	9	∞∑	∞∑	PRON
ma-10	85	10	n=0	n=0	NUM
ma-10	85	11	αn	αn	NOUN
ma-10	85	12	=	=	SYM
ma-10	85	13	∞	∞	NUM
ma-10	85	14	a3	a3	NOUN
ma-10	85	15	:	:	PUNCT
ma-10	85	16	0	0	NUM
ma-10	85	17	<	<	X
ma-10	85	18	ε	ε	PROPN
ma-10	85	19	≤	≤	PROPN
ma-10	85	20	sn	sn	PROPN
ma-10	85	21	≤	≤	NUM
ma-10	85	22	sn+1	sn+1	X
ma-10	85	23	<	<	X
ma-10	85	24	1	1	NUM
ma-10	85	25	for	for	ADP
ma-10	85	26	all	all	DET
ma-10	85	27	n	n	PRON
ma-10	85	28	≥	≥	NUM
ma-10	85	29	0	0	NUM
ma-10	85	30	a4	a4	NUM
ma-10	85	31	:	:	PUNCT
ma-10	85	32	lim	lim	PROPN
ma-10	85	33	n→∞	n→∞	X
ma-10	85	34	γn	γn	NOUN
ma-10	85	35	=	=	SYM
ma-10	85	36	1	1	NUM
ma-10	85	37	and	and	CCONJ
ma-10	85	38	lim	lim	PROPN
ma-10	85	39	n→∞	n→∞	PRON
ma-10	85	40	αn	αn	NOUN
ma-10	86	1	=	=	PROPN
ma-10	86	2	lim	lim	PROPN
ma-10	86	3	n→∞	n→∞	NUM
ma-10	86	4	βn	βn	PROPN
ma-10	86	5	=	=	PUNCT
ma-10	86	6	lim	lim	PROPN
ma-10	86	7	n→∞	n→∞	X
ma-10	86	8	sn	sn	PROPN
ma-10	86	9	=	=	SYM
ma-10	86	10	0	0	NUM
ma-10	87	1	lim	lim	PROPN
ma-10	87	2	n→∞	n→∞	X
ma-10	88	1	‖un	‖un	PROPN
ma-10	88	2	−	−	PROPN
ma-10	88	3	t	t	NOUN
ma-10	88	4	nun‖	nun‖	NOUN
ma-10	88	5	=	=	SYM
ma-10	88	6	0	0	NUM
ma-10	88	7	then	then	ADV
ma-10	88	8	the	the	DET
ma-10	88	9	sequence	sequence	NOUN
ma-10	88	10	{	{	PUNCT
ma-10	88	11	un	un	PROPN
ma-10	88	12	}	}	PUNCT
ma-10	88	13	strongly	strongly	ADV
ma-10	88	14	converges	converge	VERB
ma-10	88	15	to	to	ADP
ma-10	88	16	a	a	DET
ma-10	88	17	common	common	ADJ
ma-10	88	18	fixed	fix	VERB
ma-10	88	19	point	point	NOUN
ma-10	88	20	q	q	PROPN
ma-10	88	21	of	of	ADP
ma-10	88	22	t	t	PROPN
ma-10	88	23	,	,	PUNCT
ma-10	88	24	which	which	PRON
ma-10	88	25	is	be	AUX
ma-10	88	26	also	also	ADV
ma-10	88	27	the	the	DET
ma-10	88	28	unique	unique	ADJ
ma-10	88	29	solution	solution	NOUN
ma-10	88	30	of	of	ADP
ma-10	88	31	the	the	DET
ma-10	88	32	following	follow	VERB
ma-10	88	33	variational	variational	ADJ
ma-10	88	34	inequality	inequality	NOUN
ma-10	88	35	〈	〈	PROPN
ma-10	88	36	(	(	PUNCT
ma-10	88	37	i	i	NOUN
ma-10	88	38	−	−	PROPN
ma-10	88	39	ψ)u	ψ)u	NOUN
ma-10	88	40	,	,	PUNCT
ma-10	88	41	p	p	NOUN
ma-10	88	42	−	−	PROPN
ma-10	88	43	u	u	NOUN
ma-10	88	44	〉	〉	PROPN
ma-10	88	45	≥	≥	NOUN
ma-10	88	46	0	0	NUM
ma-10	89	1	p	p	X
ma-10	89	2	∈	∈	PROPN
ma-10	89	3	f	f	X
ma-10	89	4	(	(	PUNCT
ma-10	89	5	t	t	PROPN
ma-10	89	6	)	)	PUNCT
ma-10	89	7	.	.	PUNCT
ma-10	90	1	we	we	PRON
ma-10	90	2	now	now	ADV
ma-10	90	3	show	show	VERB
ma-10	90	4	that	that	SCONJ
ma-10	90	5	algorithm	algorithm	NOUN
ma-10	90	6	3.1	3.1	NUM
ma-10	90	7	is	be	AUX
ma-10	90	8	well	well	ADV
ma-10	90	9	posed	pose	VERB
ma-10	90	10	.	.	PUNCT
ma-10	91	1	letting	let	VERB
ma-10	91	2	bn(u	bn(u	NOUN
ma-10	91	3	)	)	PUNCT
ma-10	92	1	=	=	SYM
ma-10	92	2	αnun	αnun	ADJ
ma-10	92	3	+	+	CCONJ
ma-10	92	4	βnψ(un	βnψ(un	NUM
ma-10	92	5	)	)	PUNCT
ma-10	92	6	+	+	CCONJ
ma-10	92	7	γnt	γnt	ADJ
ma-10	92	8	n	n	CCONJ
ma-10	92	9	(	(	PUNCT
ma-10	92	10	snun	snun	NOUN
ma-10	92	11	+	+	CCONJ
ma-10	92	12	(	(	PUNCT
ma-10	92	13	1−	1−	NUM
ma-10	92	14	sn)un	sn)un	NUM
ma-10	92	15	)	)	PUNCT
ma-10	92	16	‖bn(u)−	‖bn(u)−	NOUN
ma-10	92	17	bn(v)‖	bn(v)‖	PROPN
ma-10	93	1	=	=	PUNCT
ma-10	94	1	‖γnt	‖γnt	PROPN
ma-10	95	1	n	n	CCONJ
ma-10	95	2	(	(	PUNCT
ma-10	95	3	snun	snun	NOUN
ma-10	95	4	+	+	CCONJ
ma-10	95	5	(	(	PUNCT
ma-10	95	6	1−	1−	NUM
ma-10	95	7	sn)u	sn)u	PROPN
ma-10	95	8	)	)	PUNCT
ma-10	96	1	−	−	PROPN
ma-10	96	2	γnt	γnt	ADJ
ma-10	96	3	n	n	CCONJ
ma-10	96	4	(	(	PUNCT
ma-10	96	5	snun	snun	NOUN
ma-10	96	6	+	+	CCONJ
ma-10	96	7	(	(	PUNCT
ma-10	96	8	1−	1−	NUM
ma-10	96	9	sn)v	sn)v	PROPN
ma-10	96	10	)	)	PUNCT
ma-10	96	11	‖	‖	PROPN
ma-10	96	12	=	=	SYM
ma-10	97	1	‖γnt	‖γnt	PROPN
ma-10	97	2	n(1−	n(1−	PROPN
ma-10	98	1	sn)u	sn)u	PROPN
ma-10	98	2	−	−	PROPN
ma-10	98	3	γnt	γnt	ADJ
ma-10	98	4	n(1−	n(1−	NOUN
ma-10	98	5	sn)v‖	sn)v‖	NOUN
ma-10	98	6	≤	≤	ADJ
ma-10	98	7	γnkn(1−	γnkn(1−	NOUN
ma-10	98	8	sn)‖u	sn)‖u	ADJ
ma-10	98	9	−	−	PROPN
ma-10	98	10	v‖	v‖	NOUN
ma-10	98	11	since	since	SCONJ
ma-10	98	12	lim	lim	PROPN
ma-10	98	13	n→∞	n→∞	X
ma-10	98	14	sn	sn	PROPN
ma-10	98	15	=	=	SYM
ma-10	98	16	0	0	PROPN
ma-10	98	17	,	,	PUNCT
ma-10	98	18	lim	lim	PROPN
ma-10	98	19	n→∞	n→∞	X
ma-10	99	1	kn	kn	PROPN
ma-10	99	2	=	=	PROPN
ma-10	99	3	1	1	PROPN
ma-10	99	4	,	,	PUNCT
ma-10	99	5	lim	lim	PROPN
ma-10	99	6	n→∞	n→∞	X
ma-10	100	1	γn	γn	NOUN
ma-10	100	2	=	=	SYM
ma-10	100	3	1	1	NUM
ma-10	100	4	and	and	CCONJ
ma-10	100	5	0	0	NUM
ma-10	100	6	<	<	X
ma-10	100	7	ε	ε	PROPN
ma-10	100	8	≤	≤	PROPN
ma-10	100	9	sn	sn	PROPN
ma-10	100	10	≤	≤	NUM
ma-10	100	11	sn+1	sn+1	X
ma-10	100	12	<	<	X
ma-10	100	13	1	1	NUM
ma-10	100	14	for	for	ADP
ma-10	100	15	all	all	PRON
ma-10	100	16	n	n	CCONJ
ma-10	100	17	>	>	X
ma-10	100	18	0	0	NUM
ma-10	100	19	,	,	PUNCT
ma-10	100	20	we	we	PRON
ma-10	100	21	mayassume	mayassume	VERB
ma-10	100	22	that	that	SCONJ
ma-10	100	23	γnkn(1	γnkn(1	PROPN
ma-10	100	24	−	−	PROPN
ma-10	100	25	sn	sn	NOUN
ma-10	100	26	)	)	PUNCT
ma-10	100	27	≤	≤	NOUN
ma-10	100	28	1	1	NUM
ma-10	100	29	−	−	NOUN
ma-10	100	30	ε	ε	PROPN
ma-10	100	31	for	for	ADP
ma-10	100	32	all	all	DET
ma-10	100	33	n	n	CCONJ
ma-10	100	34	>	>	X
ma-10	100	35	0	0	X
ma-10	100	36	.	.	PUNCT
ma-10	101	1	this	this	PRON
ma-10	101	2	implies	imply	VERB
ma-10	101	3	that	that	SCONJ
ma-10	101	4	bn	bn	PROPN
ma-10	101	5	is	be	VERB
ma-10	101	6	a	a	DET
ma-10	101	7	contraction	contraction	NOUN
ma-10	101	8	for	for	ADP
ma-10	101	9	each	each	DET
ma-10	101	10	eur	eur	NOUN
ma-10	101	11	.	.	PUNCT
ma-10	102	1	j.	j.	PROPN
ma-10	102	2	math	math	PROPN
ma-10	102	3	.	.	PUNCT
ma-10	103	1	anal	anal	ADJ
ma-10	103	2	.	.	PUNCT
ma-10	104	1	1	1	NUM
ma-10	104	2	(	(	PUNCT
ma-10	104	3	2021	2021	NUM
ma-10	104	4	)	)	PUNCT
ma-10	105	1	23	23	NUM
ma-10	105	2	n.	n.	NOUN
ma-10	105	3	therefore	therefore	ADV
ma-10	105	4	there	there	PRON
ma-10	105	5	exists	exist	VERB
ma-10	105	6	a	a	DET
ma-10	105	7	unique	unique	ADJ
ma-10	105	8	fixed	fix	VERB
ma-10	105	9	point	point	NOUN
ma-10	105	10	for	for	ADP
ma-10	105	11	bn	bn	INTJ
ma-10	105	12	by	by	ADP
ma-10	105	13	banach	banach	NOUN
ma-10	105	14	contraction	contraction	NOUN
ma-10	105	15	principle	principle	NOUN
ma-10	105	16	,	,	PUNCT
ma-10	105	17	which	which	PRON
ma-10	105	18	alsoimplies	alsoimplie	VERB
ma-10	105	19	that	that	SCONJ
ma-10	105	20	(	(	PUNCT
ma-10	105	21	3.1	3.1	NUM
ma-10	105	22	)	)	PUNCT
ma-10	105	23	is	be	AUX
ma-10	105	24	well	well	ADV
ma-10	105	25	-	-	PUNCT
ma-10	105	26	defined	define	VERB
ma-10	105	27	.	.	PUNCT
ma-10	106	1	we	we	PRON
ma-10	106	2	now	now	ADV
ma-10	106	3	show	show	VERB
ma-10	106	4	that	that	SCONJ
ma-10	106	5	the	the	DET
ma-10	106	6	sequence	sequence	NOUN
ma-10	106	7	{	{	PUNCT
ma-10	106	8	un	un	PROPN
ma-10	106	9	}	}	PUNCT
ma-10	106	10	is	be	AUX
ma-10	106	11	bounded	bound	VERB
ma-10	106	12	.	.	PUNCT
ma-10	107	1	rewriting	rewrite	VERB
ma-10	107	2	3.1	3.1	NUM
ma-10	107	3	,	,	PUNCT
ma-10	107	4	we	we	PRON
ma-10	107	5	have	have	VERB
ma-10	107	6	un+1	un+1	NOUN
ma-10	107	7	=	=	SYM
ma-10	107	8	βnψ(un	βnψ(un	NUM
ma-10	107	9	)	)	PUNCT
ma-10	108	1	+	+	CCONJ
ma-10	108	2	αnun	αnun	ADJ
ma-10	108	3	+	+	CCONJ
ma-10	108	4	(	(	PUNCT
ma-10	108	5	1−	1−	NUM
ma-10	108	6	βn)vn	βn)vn	PUNCT
ma-10	108	7	(	(	PUNCT
ma-10	108	8	3.2	3.2	NUM
ma-10	108	9	)	)	PUNCT
ma-10	108	10	where	where	SCONJ
ma-10	108	11	vn	vn	NOUN
ma-10	108	12	=	=	PUNCT
ma-10	108	13	γnt	γnt	ADJ
ma-10	108	14	n(snun	n(snun	NOUN
ma-10	108	15	+	+	CCONJ
ma-10	108	16	(	(	PUNCT
ma-10	108	17	1−	1−	NUM
ma-10	108	18	sn)un+1	sn)un+1	NOUN
ma-10	108	19	)	)	PUNCT
ma-10	108	20	1−	1−	NUM
ma-10	108	21	βn	βn	NOUN
ma-10	108	22	remark	remark	NOUN
ma-10	108	23	3.2	3.2	NUM
ma-10	108	24	.	.	PUNCT
ma-10	109	1	the	the	DET
ma-10	109	2	real	real	ADJ
ma-10	109	3	sequences	sequence	NOUN
ma-10	109	4	that	that	PRON
ma-10	109	5	satisfies	satisfy	VERB
ma-10	109	6	the	the	DET
ma-10	109	7	above	above	ADJ
ma-10	109	8	conditions	condition	NOUN
ma-10	109	9	are	be	AUX
ma-10	109	10	αn	αn	NOUN
ma-10	109	11	=	=	SYM
ma-10	109	12	1	1	NUM
ma-10	109	13	n	n	NOUN
ma-10	109	14	,	,	PUNCT
ma-10	109	15	βn	βn	X
ma-10	109	16	=	=	SYM
ma-10	109	17	1	1	NUM
ma-10	109	18	n	n	NUM
ma-10	109	19	and	and	CCONJ
ma-10	109	20	γn	γn	X
ma-10	109	21	=	=	SYM
ma-10	109	22	1−	1−	NUM
ma-10	109	23	2	2	NUM
ma-10	109	24	n	n	DET
ma-10	109	25	proof	proof	NOUN
ma-10	109	26	.	.	PUNCT
ma-10	110	1	our	our	PRON
ma-10	110	2	prove	prove	NOUN
ma-10	110	3	are	be	AUX
ma-10	110	4	in	in	ADP
ma-10	110	5	six	six	NUM
ma-10	110	6	steps	step	NOUN
ma-10	110	7	.	.	PUNCT
ma-10	111	1	first	first	ADV
ma-10	111	2	we	we	PRON
ma-10	111	3	prove	prove	VERB
ma-10	111	4	that	that	SCONJ
ma-10	111	5	the	the	DET
ma-10	111	6	sequence	sequence	NOUN
ma-10	111	7	{	{	PUNCT
ma-10	111	8	un	un	PROPN
ma-10	111	9	}	}	PUNCT
ma-10	111	10	defined	define	VERB
ma-10	111	11	by	by	ADP
ma-10	111	12	3.1	3.1	NUM
ma-10	111	13	is	be	AUX
ma-10	111	14	bounded	bound	VERB
ma-10	111	15	.	.	PUNCT
ma-10	112	1	step	step	NOUN
ma-10	112	2	1	1	NUM
ma-10	112	3	:	:	PUNCT
ma-10	112	4	letting	let	VERB
ma-10	112	5	p	p	X
ma-10	112	6	∈	∈	PROPN
ma-10	112	7	f	f	PROPN
ma-10	112	8	ix(t	ix(t	PROPN
ma-10	112	9	)	)	PUNCT
ma-10	112	10	,	,	PUNCT
ma-10	112	11	we	we	PRON
ma-10	112	12	have	have	VERB
ma-10	112	13	the	the	DET
ma-10	112	14	following	follow	VERB
ma-10	112	15	estimates	estimate	NOUN
ma-10	112	16	‖un+1	‖un+1	NUM
ma-10	112	17	−	−	NOUN
ma-10	112	18	p‖	p‖	NOUN
ma-10	112	19	=	=	SYM
ma-10	112	20	‖βnψ(un	‖βnψ(un	PROPN
ma-10	112	21	)	)	PUNCT
ma-10	113	1	+	+	CCONJ
ma-10	113	2	αnun	αnun	ADJ
ma-10	113	3	+	+	CCONJ
ma-10	113	4	(	(	PUNCT
ma-10	113	5	1−	1−	NUM
ma-10	113	6	βn)vn	βn)vn	PUNCT
ma-10	113	7	−	−	PROPN
ma-10	113	8	p‖	p‖	NOUN
ma-10	113	9	≤	≤	PUNCT
ma-10	113	10	βn‖ψ(un)−	βn‖ψ(un)−	X
ma-10	113	11	ψ(p)‖+	ψ(p)‖+	PROPN
ma-10	113	12	βn‖ψ(p)−	βn‖ψ(p)−	PROPN
ma-10	113	13	p‖+	p‖+	PROPN
ma-10	113	14	αn‖un	αn‖un	PROPN
ma-10	114	1	−	−	PROPN
ma-10	114	2	p‖+	p‖+	NOUN
ma-10	114	3	(	(	PUNCT
ma-10	114	4	1−	1−	NUM
ma-10	114	5	βn)‖vn	βn)‖vn	ADJ
ma-10	114	6	−	−	PROPN
ma-10	114	7	p‖	p‖	NOUN
ma-10	114	8	≤	≤	NOUN
ma-10	114	9	(	(	PUNCT
ma-10	114	10	αβn	αβn	NOUN
ma-10	114	11	+	+	CCONJ
ma-10	114	12	αn)‖un	αn)‖un	NOUN
ma-10	114	13	−	−	NOUN
ma-10	114	14	p‖+	p‖+	PROPN
ma-10	114	15	βn‖ψ(p)−	βn‖ψ(p)−	PROPN
ma-10	114	16	p‖+	p‖+	NOUN
ma-10	114	17	(	(	PUNCT
ma-10	114	18	1−	1−	NUM
ma-10	114	19	βn)‖vn	βn)‖vn	ADJ
ma-10	114	20	−	−	PROPN
ma-10	114	21	p‖	p‖	NOUN
ma-10	114	22	(	(	PUNCT
ma-10	114	23	3.3	3.3	NUM
ma-10	114	24	)	)	PUNCT
ma-10	115	1	‖vn	‖vn	PROPN
ma-10	115	2	−	−	PROPN
ma-10	115	3	p‖	p‖	NOUN
ma-10	115	4	=	=	PUNCT
ma-10	115	5	‖	‖	PROPN
ma-10	115	6	γnt	γnt	ADJ
ma-10	115	7	n(snun	n(snun	NOUN
ma-10	115	8	+	+	CCONJ
ma-10	115	9	(	(	PUNCT
ma-10	115	10	1−	1−	NUM
ma-10	115	11	sn)un+1	sn)un+1	NOUN
ma-10	115	12	)	)	PUNCT
ma-10	115	13	1−	1−	NUM
ma-10	115	14	βn	βn	NOUN
ma-10	116	1	−	−	PROPN
ma-10	116	2	p‖	p‖	NOUN
ma-10	116	3	=	=	NOUN
ma-10	116	4	γnt	γnt	ADJ
ma-10	116	5	nsn(un	nsn(un	NOUN
ma-10	116	6	−	−	PROPN
ma-10	116	7	p	p	X
ma-10	116	8	)	)	PUNCT
ma-10	116	9	1−	1−	NUM
ma-10	116	10	βn	βn	VERB
ma-10	116	11	+	+	CCONJ
ma-10	116	12	γnt	γnt	ADJ
ma-10	116	13	n(1−	n(1−	PROPN
ma-10	116	14	sn)(un+1	sn)(un+1	PROPN
ma-10	116	15	−	−	PROPN
ma-10	116	16	p	p	NOUN
ma-10	116	17	)	)	PUNCT
ma-10	116	18	1−	1−	NUM
ma-10	116	19	βn	βn	VERB
ma-10	116	20	‖	‖	PROPN
ma-10	116	21	≤	≤	PROPN
ma-10	116	22	γnknsn	γnknsn	NOUN
ma-10	116	23	1−	1−	NUM
ma-10	116	24	βn	βn	NOUN
ma-10	116	25	‖un	‖un	PROPN
ma-10	116	26	−	−	NOUN
ma-10	116	27	p‖+	p‖+	NOUN
ma-10	116	28	γnkn(1−	γnkn(1−	PROPN
ma-10	116	29	sn	sn	NOUN
ma-10	116	30	)	)	PUNCT
ma-10	116	31	1−	1−	NUM
ma-10	116	32	βn	βn	X
ma-10	116	33	‖un+1	‖un+1	SYM
ma-10	116	34	−	−	PROPN
ma-10	116	35	p‖	p‖	NOUN
ma-10	116	36	(	(	PUNCT
ma-10	116	37	3.4	3.4	NUM
ma-10	116	38	)	)	PUNCT
ma-10	116	39	putting	put	VERB
ma-10	116	40	3.4	3.4	NUM
ma-10	116	41	in	in	ADP
ma-10	116	42	3.3	3.3	NUM
ma-10	116	43	,	,	PUNCT
ma-10	116	44	gives	give	VERB
ma-10	116	45	the	the	DET
ma-10	116	46	following	follow	VERB
ma-10	116	47	‖un+1	‖un+1	PUNCT
ma-10	116	48	−	−	PROPN
ma-10	116	49	p‖	p‖	NOUN
ma-10	116	50	≤	≤	NOUN
ma-10	116	51	(	(	PUNCT
ma-10	116	52	αβn	αβn	NOUN
ma-10	116	53	+	+	CCONJ
ma-10	116	54	αn)‖un	αn)‖un	NOUN
ma-10	116	55	−	−	VERB
ma-10	116	56	p‖+	p‖+	PROPN
ma-10	116	57	βn‖ψ(p)−	βn‖ψ(p)−	PROPN
ma-10	116	58	p‖	p‖	NOUN
ma-10	117	1	+	+	CCONJ
ma-10	117	2	γnknsn‖un	γnknsn‖un	PROPN
ma-10	118	1	−	−	NOUN
ma-10	118	2	p‖+	p‖+	NOUN
ma-10	118	3	γnkn(1−	γnkn(1−	PROPN
ma-10	118	4	sn)‖un+1	sn)‖un+1	PROPN
ma-10	118	5	−	−	PROPN
ma-10	118	6	p‖	p‖	NOUN
ma-10	118	7	(	(	PUNCT
ma-10	118	8	1−	1−	NUM
ma-10	118	9	γnkn(1−	γnkn(1−	NOUN
ma-10	118	10	sn))‖un+1	sn))‖un+1	NOUN
ma-10	118	11	−	−	PROPN
ma-10	118	12	p‖	p‖	NOUN
ma-10	118	13	≤	≤	NOUN
ma-10	118	14	(	(	PUNCT
ma-10	118	15	αβn	αβn	NOUN
ma-10	118	16	+	+	CCONJ
ma-10	118	17	αn	αn	NOUN
ma-10	118	18	+	+	NUM
ma-10	118	19	γnknsn)‖un	γnknsn)‖un	NOUN
ma-10	118	20	−	−	NOUN
ma-10	118	21	p‖+	p‖+	NOUN
ma-10	118	22	βn‖ψ(p)−	βn‖ψ(p)−	PROPN
ma-10	118	23	p‖	p‖	NOUN
ma-10	118	24	‖un+1	‖un+1	PUNCT
ma-10	118	25	−	−	PROPN
ma-10	118	26	p‖	p‖	NOUN
ma-10	118	27	≤	≤	NOUN
ma-10	118	28	(	(	PUNCT
ma-10	118	29	αβn	αβn	NOUN
ma-10	118	30	+	+	CCONJ
ma-10	118	31	αn	αn	NOUN
ma-10	118	32	+	+	NUM
ma-10	118	33	γnknsn	γnknsn	NOUN
ma-10	118	34	)	)	PUNCT
ma-10	118	35	1−	1−	NUM
ma-10	118	36	γnkn(1−	γnkn(1−	PROPN
ma-10	118	37	sn	sn	NOUN
ma-10	118	38	)	)	PUNCT
ma-10	118	39	‖un	‖un	PROPN
ma-10	118	40	−	−	PROPN
ma-10	118	41	p‖	p‖	NOUN
ma-10	118	42	+	+	CCONJ
ma-10	118	43	βn	βn	PROPN
ma-10	118	44	1−	1−	NUM
ma-10	118	45	γnkn(1−	γnkn(1−	PROPN
ma-10	118	46	sn	sn	NOUN
ma-10	118	47	)	)	PUNCT
ma-10	118	48	‖ψ(p)−	‖ψ(p)−	PROPN
ma-10	118	49	p‖	p‖	NOUN
ma-10	118	50	eur	eur	PROPN
ma-10	118	51	.	.	PUNCT
ma-10	119	1	j.	j.	PROPN
ma-10	119	2	math	math	PROPN
ma-10	119	3	.	.	PUNCT
ma-10	120	1	anal	anal	ADJ
ma-10	120	2	.	.	PUNCT
ma-10	121	1	1	1	NUM
ma-10	121	2	(	(	PUNCT
ma-10	121	3	2021	2021	NUM
ma-10	121	4	)	)	PUNCT
ma-10	122	1	24since	24since	NOUN
ma-10	122	2	γn	γn	NUM
ma-10	122	3	,	,	PUNCT
ma-10	122	4	sn	sn	PROPN
ma-10	122	5	∈	∈	PROPN
ma-10	122	6	(	(	PUNCT
ma-10	122	7	0	0	NUM
ma-10	122	8	,	,	PUNCT
ma-10	122	9	1	1	NUM
ma-10	122	10	)	)	PUNCT
ma-10	122	11	,	,	PUNCT
ma-10	122	12	1	1	NUM
ma-10	122	13	−	−	PROPN
ma-10	122	14	γnkn(1	γnkn(1	PROPN
ma-10	122	15	−	−	PROPN
ma-10	122	16	sn	sn	PROPN
ma-10	122	17	)	)	PUNCT
ma-10	122	18	>	>	X
ma-10	122	19	0	0	PUNCT
ma-10	123	1	and	and	CCONJ
ma-10	123	2	lim	lim	PROPN
ma-10	123	3	n→∞	n→∞	PRON
ma-10	124	1	kn	kn	PROPN
ma-10	124	2	=	=	PROPN
ma-10	124	3	1	1	NUM
ma-10	124	4	.	.	PUNCT
ma-10	124	5	from	from	ADP
ma-10	124	6	the	the	DET
ma-10	124	7	condition	condition	NOUN
ma-10	124	8	(	(	PUNCT
ma-10	124	9	a1	a1	NOUN
ma-10	124	10	)	)	PUNCT
ma-10	124	11	,	,	PUNCT
ma-10	124	12	wehave	wehave	NOUN
ma-10	124	13	‖un+1	‖un+1	PUNCT
ma-10	125	1	−	−	PROPN
ma-10	125	2	p‖	p‖	NOUN
ma-10	125	3	≤	≤	PROPN
ma-10	125	4	1−	1−	NUM
ma-10	125	5	1−	1−	NUM
ma-10	125	6	αβn	αβn	NOUN
ma-10	125	7	−	−	NOUN
ma-10	125	8	αn	αn	NOUN
ma-10	125	9	−	−	PROPN
ma-10	125	10	γnkn	γnkn	NOUN
ma-10	125	11	1−	1−	NUM
ma-10	125	12	γnkn(1−	γnkn(1−	PROPN
ma-10	125	13	sn	sn	NOUN
ma-10	125	14	)	)	PUNCT
ma-10	125	15	‖un	‖un	PROPN
ma-10	125	16	−	−	PROPN
ma-10	125	17	p‖	p‖	NOUN
ma-10	125	18	+	+	CCONJ
ma-10	125	19	βn	βn	PROPN
ma-10	125	20	1−	1−	NUM
ma-10	125	21	γnkn(1−	γnkn(1−	PROPN
ma-10	125	22	sn	sn	NOUN
ma-10	125	23	)	)	PUNCT
ma-10	125	24	‖ψ(p)−	‖ψ(p)−	PROPN
ma-10	125	25	p‖	p‖	NOUN
ma-10	125	26	]	]	PUNCT
ma-10	125	27	‖un+1	‖un+1	PUNCT
ma-10	125	28	−	−	PROPN
ma-10	125	29	p‖	p‖	NOUN
ma-10	125	30	≤	≤	NOUN
ma-10	125	31	1−	1−	NUM
ma-10	126	1	βn(1−	βn(1−	ADJ
ma-10	126	2	α	α	NUM
ma-10	126	3	)	)	PUNCT
ma-10	126	4	1−	1−	NUM
ma-10	126	5	γnkn(1−	γnkn(1−	PROPN
ma-10	126	6	sn	sn	NOUN
ma-10	126	7	)	)	PUNCT
ma-10	126	8	‖un	‖un	PROPN
ma-10	126	9	−	−	PROPN
ma-10	126	10	p‖	p‖	NOUN
ma-10	126	11	+	+	CCONJ
ma-10	126	12	βn(1−	βn(1−	ADJ
ma-10	126	13	α	α	X
ma-10	126	14	)	)	PUNCT
ma-10	126	15	1−	1−	NUM
ma-10	126	16	γnkn(1−	γnkn(1−	PROPN
ma-10	126	17	sn	sn	NOUN
ma-10	126	18	)	)	PUNCT
ma-10	126	19	1	1	NUM
ma-10	126	20	(	(	PUNCT
ma-10	126	21	1−	1−	NUM
ma-10	126	22	α	α	NOUN
ma-10	126	23	)	)	PUNCT
ma-10	126	24	‖ψ(p)−	‖ψ(p)−	PROPN
ma-10	126	25	p‖	p‖	NOUN
ma-10	126	26	]	]	PUNCT
ma-10	126	27	‖un+1	‖un+1	PUNCT
ma-10	126	28	−	−	PROPN
ma-10	126	29	p‖	p‖	NOUN
ma-10	126	30	≤	≤	PROPN
ma-10	126	31	max	max	PROPN
ma-10	126	32	{	{	PUNCT
ma-10	126	33	‖un	‖un	PROPN
ma-10	126	34	−	−	PROPN
ma-10	126	35	p‖	p‖	NOUN
ma-10	126	36	,	,	PUNCT
ma-10	126	37	1	1	NUM
ma-10	126	38	(	(	PUNCT
ma-10	126	39	1−	1−	NUM
ma-10	126	40	α	α	NOUN
ma-10	126	41	)	)	PUNCT
ma-10	126	42	‖ψ(p)−	‖ψ(p)−	PROPN
ma-10	126	43	p‖	p‖	NOUN
ma-10	126	44	}	}	PUNCT
ma-10	126	45	therefore	therefore	ADV
ma-10	126	46	by	by	ADP
ma-10	126	47	mathematical	mathematical	ADJ
ma-10	126	48	induction	induction	NOUN
ma-10	126	49	,	,	PUNCT
ma-10	126	50	we	we	PRON
ma-10	126	51	have	have	VERB
ma-10	126	52	‖un+1	‖un+1	PUNCT
ma-10	127	1	−	−	PRON
ma-10	127	2	p‖	p‖	NOUN
ma-10	127	3	≤	≤	PROPN
ma-10	127	4	max	max	PROPN
ma-10	127	5	{	{	PUNCT
ma-10	127	6	‖u0	‖u0	NOUN
ma-10	128	1	−	−	PROPN
ma-10	128	2	p‖	p‖	NOUN
ma-10	128	3	,	,	PUNCT
ma-10	128	4	1	1	NUM
ma-10	128	5	(	(	PUNCT
ma-10	128	6	1−	1−	NUM
ma-10	128	7	α	α	NOUN
ma-10	128	8	)	)	PUNCT
ma-10	128	9	‖ψ(p)−	‖ψ(p)−	PROPN
ma-10	128	10	p‖	p‖	NOUN
ma-10	128	11	}	}	PUNCT
ma-10	128	12	for	for	ADP
ma-10	128	13	all	all	DET
ma-10	128	14	n	n	DET
ma-10	128	15	≥	≥	NOUN
ma-10	128	16	n	n	ADV
ma-10	128	17	.	.	PUNCT
ma-10	129	1	therefore	therefore	ADV
ma-10	129	2	{	{	PUNCT
ma-10	129	3	un	un	PROPN
ma-10	129	4	}	}	PUNCT
ma-10	129	5	is	be	AUX
ma-10	129	6	bounded	bound	VERB
ma-10	129	7	.	.	PUNCT
ma-10	130	1	consequently	consequently	ADV
ma-10	130	2	,	,	PUNCT
ma-10	130	3	{	{	PUNCT
ma-10	130	4	ψ(un	ψ(un	NOUN
ma-10	130	5	)	)	PUNCT
ma-10	130	6	}	}	PUNCT
ma-10	130	7	and	and	CCONJ
ma-10	130	8	{	{	PUNCT
ma-10	130	9	vn	vn	NOUN
ma-10	130	10	}	}	PUNCT
ma-10	130	11	are	be	AUX
ma-10	130	12	also	also	ADV
ma-10	130	13	bounded	bound	VERB
ma-10	130	14	.	.	PUNCT
ma-10	131	1	step	step	NOUN
ma-10	131	2	2	2	NUM
ma-10	131	3	:	:	PUNCT
ma-10	131	4	we	we	PRON
ma-10	131	5	now	now	ADV
ma-10	131	6	prove	prove	VERB
ma-10	131	7	that	that	SCONJ
ma-10	131	8	the	the	DET
ma-10	131	9	sequence	sequence	NOUN
ma-10	131	10	{	{	PUNCT
ma-10	131	11	un+1	un+1	NOUN
ma-10	131	12	}	}	PUNCT
ma-10	131	13	converges	converge	NOUN
ma-10	131	14	to	to	ADP
ma-10	131	15	{	{	PUNCT
ma-10	131	16	un	un	VERB
ma-10	131	17	}	}	PUNCT
ma-10	131	18	as	as	ADP
ma-10	131	19	n	n	PROPN
ma-10	131	20	→∞.	→∞.	PROPN
ma-10	131	21	that	that	PRON
ma-10	131	22	is	is	ADV
ma-10	131	23	lim	lim	PROPN
ma-10	131	24	n→∞	n→∞	X
ma-10	131	25	‖un+1−	‖un+1−	ADP
ma-10	131	26	un‖	un‖	NOUN
ma-10	131	27	=	=	SYM
ma-10	131	28	0	0	X
ma-10	131	29	‖un+1	‖un+1	SYM
ma-10	131	30	−	−	NOUN
ma-10	131	31	un‖	un‖	PROPN
ma-10	131	32	=	=	SYM
ma-10	131	33	‖un+1	‖un+1	PUNCT
ma-10	132	1	−	−	PROPN
ma-10	132	2	t	t	PROPN
ma-10	132	3	nun	nun	PROPN
ma-10	132	4	+	+	PROPN
ma-10	132	5	t	t	X
ma-10	132	6	nun	nun	NOUN
ma-10	132	7	−	−	PROPN
ma-10	132	8	un‖	un‖	PROPN
ma-10	132	9	=	=	SYM
ma-10	132	10	‖βnψ(un	‖βnψ(un	PROPN
ma-10	132	11	)	)	PUNCT
ma-10	133	1	+	+	CCONJ
ma-10	133	2	αnun	αnun	ADJ
ma-10	133	3	+	+	CCONJ
ma-10	133	4	(	(	PUNCT
ma-10	133	5	1−	1−	NUM
ma-10	133	6	βn)vn	βn)vn	PUNCT
ma-10	133	7	−	−	PROPN
ma-10	133	8	(	(	PUNCT
ma-10	133	9	βn	βn	PROPN
ma-10	133	10	+	+	CCONJ
ma-10	133	11	αn	αn	NOUN
ma-10	134	1	+	+	CCONJ
ma-10	134	2	γn)t	γn)t	PROPN
ma-10	134	3	n	n	NOUN
ma-10	134	4	+	+	NOUN
ma-10	134	5	t	t	PROPN
ma-10	134	6	nun	nun	NOUN
ma-10	134	7	−	−	PROPN
ma-10	134	8	un‖	un‖	NOUN
ma-10	134	9	≤	≤	X
ma-10	134	10	‖βnψ(un)−	‖βnψ(un)−	NOUN
ma-10	134	11	βnt	βnt	ADP
ma-10	134	12	nun‖+	nun‖+	PROPN
ma-10	134	13	‖αnun	‖αnun	SYM
ma-10	134	14	−	−	NOUN
ma-10	134	15	αnt	αnt	NOUN
ma-10	134	16	nun‖	nun‖	NOUN
ma-10	134	17	+	+	ADJ
ma-10	134	18	‖(1−	‖(1−	ADJ
ma-10	134	19	βn)vn	βn)vn	SYM
ma-10	134	20	−	−	NOUN
ma-10	134	21	γnt	γnt	ADJ
ma-10	134	22	n	n	PROPN
ma-10	134	23	+	+	SYM
ma-10	134	24	t	t	PROPN
ma-10	134	25	nun	nun	NOUN
ma-10	134	26	−	−	PROPN
ma-10	134	27	un‖	un‖	PROPN
ma-10	134	28	≤	≤	NUM
ma-10	134	29	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	134	30	t	t	PROPN
ma-10	134	31	nun‖+	nun‖+	PROPN
ma-10	134	32	αn‖un	αn‖un	PROPN
ma-10	134	33	−	−	PROPN
ma-10	134	34	t	t	PROPN
ma-10	134	35	nun‖	nun‖	NOUN
ma-10	134	36	+	+	PROPN
ma-10	134	37	(	(	PUNCT
ma-10	134	38	1−	1−	NUM
ma-10	134	39	βn)‖vn	βn)‖vn	ADJ
ma-10	134	40	−	−	NUM
ma-10	134	41	γnt	γnt	ADJ
ma-10	134	42	n‖+	n‖+	PROPN
ma-10	134	43	‖t	‖t	PROPN
ma-10	134	44	nun	nun	NOUN
ma-10	134	45	−	−	PROPN
ma-10	134	46	un‖	un‖	PROPN
ma-10	134	47	(	(	PUNCT
ma-10	134	48	3.5	3.5	NUM
ma-10	134	49	)	)	PUNCT
ma-10	135	1	‖vn	‖vn	PROPN
ma-10	135	2	−	−	ADP
ma-10	135	3	γnt	γnt	ADJ
ma-10	135	4	nun‖	nun‖	NOUN
ma-10	135	5	=	=	SYM
ma-10	135	6	‖	‖	PROPN
ma-10	135	7	γnsn	γnsn	NOUN
ma-10	135	8	1−	1−	NUM
ma-10	135	9	βn	βn	NOUN
ma-10	135	10	t	t	NOUN
ma-10	135	11	nun	nun	NOUN
ma-10	135	12	+	+	CCONJ
ma-10	135	13	γn(1−	γn(1−	PROPN
ma-10	135	14	sn	sn	PROPN
ma-10	135	15	)	)	PUNCT
ma-10	135	16	1−	1−	NUM
ma-10	135	17	βn	βn	NOUN
ma-10	135	18	t	t	PROPN
ma-10	135	19	nun+1	nun+1	PROPN
ma-10	135	20	−	−	PROPN
ma-10	135	21	γnt	γnt	ADJ
ma-10	135	22	nun‖	nun‖	NOUN
ma-10	135	23	≤	≤	ADV
ma-10	135	24	‖	‖	NUM
ma-10	135	25	γnsn	γnsn	NOUN
ma-10	135	26	1−	1−	NUM
ma-10	135	27	βn	βn	PROPN
ma-10	135	28	‖t	‖t	PROPN
ma-10	135	29	nun	nun	PROPN
ma-10	135	30	−	−	PROPN
ma-10	135	31	t	t	PROPN
ma-10	135	32	nun‖+	nun‖+	PROPN
ma-10	135	33	γn(1−	γn(1−	PROPN
ma-10	135	34	sn	sn	PROPN
ma-10	135	35	)	)	PUNCT
ma-10	135	36	1−	1−	NUM
ma-10	135	37	βn	βn	X
ma-10	135	38	‖t	‖t	PROPN
ma-10	135	39	nun+1	nun+1	VERB
ma-10	135	40	−	−	PROPN
ma-10	135	41	t	t	PROPN
ma-10	135	42	nun‖	nun‖	NOUN
ma-10	135	43	≤	≤	ADV
ma-10	135	44	γn(1−	γn(1−	ADP
ma-10	135	45	sn)kn	sn)kn	NUM
ma-10	135	46	1−	1−	NUM
ma-10	135	47	βn	βn	NOUN
ma-10	135	48	‖un+1	‖un+1	PUNCT
ma-10	135	49	−	−	PRON
ma-10	136	1	un‖	un‖	PROPN
ma-10	136	2	(	(	PUNCT
ma-10	136	3	3.6	3.6	NUM
ma-10	136	4	)	)	PUNCT
ma-10	136	5	eur	eur	PROPN
ma-10	136	6	.	.	PUNCT
ma-10	137	1	j.	j.	PROPN
ma-10	137	2	math	math	PROPN
ma-10	137	3	.	.	PUNCT
ma-10	138	1	anal	anal	ADJ
ma-10	138	2	.	.	PUNCT
ma-10	139	1	1	1	NUM
ma-10	139	2	(	(	PUNCT
ma-10	139	3	2021	2021	NUM
ma-10	139	4	)	)	PUNCT
ma-10	139	5	25now	25now	NOUN
ma-10	139	6	putting	put	VERB
ma-10	139	7	3.6	3.6	NUM
ma-10	139	8	in	in	ADP
ma-10	139	9	3.5	3.5	NUM
ma-10	139	10	,	,	PUNCT
ma-10	139	11	we	we	PRON
ma-10	139	12	have	have	VERB
ma-10	139	13	the	the	DET
ma-10	139	14	following	follow	VERB
ma-10	139	15	‖un+1	‖un+1	PUNCT
ma-10	139	16	−	−	NOUN
ma-10	139	17	un‖	un‖	PROPN
ma-10	139	18	≤	≤	NUM
ma-10	139	19	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	139	20	t	t	PROPN
ma-10	139	21	nun‖+	nun‖+	PROPN
ma-10	139	22	αn‖un	αn‖un	PROPN
ma-10	139	23	−	−	PROPN
ma-10	139	24	t	t	PROPN
ma-10	139	25	nun‖	nun‖	NOUN
ma-10	139	26	+	+	PROPN
ma-10	139	27	(	(	PUNCT
ma-10	139	28	1−	1−	NUM
ma-10	139	29	βn	βn	NOUN
ma-10	139	30	)	)	PUNCT
ma-10	140	1	[	[	X
ma-10	140	2	γn(1−	γn(1−	ADP
ma-10	140	3	sn)kn	sn)kn	NUM
ma-10	140	4	1−	1−	NUM
ma-10	140	5	βn	βn	NOUN
ma-10	140	6	‖un+1	‖un+1	PUNCT
ma-10	140	7	−	−	PRON
ma-10	140	8	un‖	un‖	NOUN
ma-10	140	9	]	]	PUNCT
ma-10	140	10	+	+	CCONJ
ma-10	140	11	‖t	‖t	ADJ
ma-10	140	12	nun	nun	NOUN
ma-10	140	13	−	−	PROPN
ma-10	140	14	un‖	un‖	PROPN
ma-10	140	15	≤	≤	NUM
ma-10	140	16	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	140	17	t	t	PROPN
ma-10	140	18	nun‖+	nun‖+	PROPN
ma-10	140	19	αn‖un	αn‖un	PROPN
ma-10	140	20	−	−	PROPN
ma-10	140	21	t	t	PROPN
ma-10	140	22	nun‖	nun‖	NOUN
ma-10	141	1	+	+	SCONJ
ma-10	141	2	γn(1−	γn(1−	NUM
ma-10	141	3	sn)kn‖un+1	sn)kn‖un+1	NOUN
ma-10	141	4	−	−	PRON
ma-10	141	5	un‖	un‖	NOUN
ma-10	141	6	]	]	PUNCT
ma-10	141	7	+	+	CCONJ
ma-10	141	8	‖t	‖t	ADJ
ma-10	141	9	nun	nun	NOUN
ma-10	141	10	−	−	PROPN
ma-10	141	11	un‖	un‖	PROPN
ma-10	141	12	≤	≤	NUM
ma-10	141	13	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	141	14	t	t	PROPN
ma-10	141	15	nun‖+	nun‖+	PROPN
ma-10	141	16	(	(	PUNCT
ma-10	141	17	αn	αn	NOUN
ma-10	142	1	+	+	NOUN
ma-10	142	2	1)‖un	1)‖un	NUM
ma-10	142	3	−	−	PROPN
ma-10	142	4	t	t	NOUN
ma-10	142	5	nun‖	nun‖	NOUN
ma-10	142	6	+	+	CCONJ
ma-10	142	7	γn(1−	γn(1−	NUM
ma-10	142	8	sn)kn‖un+1	sn)kn‖un+1	NOUN
ma-10	142	9	−	−	PROPN
ma-10	142	10	un‖	un‖	PROPN
ma-10	142	11	[	[	PUNCT
ma-10	142	12	1−	1−	NUM
ma-10	142	13	γn(1−	γn(1−	ADP
ma-10	142	14	sn)kn	sn)kn	PROPN
ma-10	142	15	]	]	PUNCT
ma-10	142	16	‖un+1	‖un+1	PUNCT
ma-10	142	17	−	−	NOUN
ma-10	143	1	un‖	un‖	PROPN
ma-10	143	2	≤	≤	NUM
ma-10	143	3	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	143	4	t	t	PROPN
ma-10	143	5	nun‖+	nun‖+	PROPN
ma-10	143	6	(	(	PUNCT
ma-10	143	7	αn	αn	NOUN
ma-10	144	1	+	+	NOUN
ma-10	144	2	1)‖un	1)‖un	NUM
ma-10	144	3	−	−	PROPN
ma-10	144	4	t	t	PROPN
ma-10	144	5	nun‖	nun‖	NOUN
ma-10	144	6	‖un+1	‖un+1	PUNCT
ma-10	144	7	−	−	NOUN
ma-10	144	8	un‖	un‖	NOUN
ma-10	144	9	≤	≤	NUM
ma-10	144	10	βn	βn	NOUN
ma-10	144	11	1−	1−	NUM
ma-10	144	12	γn(1−	γn(1−	ADP
ma-10	144	13	sn)kn	sn)kn	PROPN
ma-10	144	14	‖ψ(un)−	‖ψ(un)−	PROPN
ma-10	144	15	t	t	NOUN
ma-10	144	16	nun‖	nun‖	NOUN
ma-10	144	17	+	+	CCONJ
ma-10	144	18	(	(	PUNCT
ma-10	144	19	αn	αn	NOUN
ma-10	144	20	+	+	NOUN
ma-10	144	21	1	1	NUM
ma-10	144	22	)	)	PUNCT
ma-10	144	23	1−	1−	NUM
ma-10	145	1	γn(1−	γn(1−	ADP
ma-10	145	2	sn)kn	sn)kn	PROPN
ma-10	145	3	‖un	‖un	PROPN
ma-10	145	4	−	−	PROPN
ma-10	145	5	t	t	NOUN
ma-10	145	6	nun‖	nun‖	NOUN
ma-10	145	7	let	let	VERB
ma-10	145	8	m	m	PRON
ma-10	145	9	:>	:>	VERB
ma-10	145	10	max	max	PROPN
ma-10	145	11	{	{	PUNCT
ma-10	145	12	‖ψ(un)−	‖ψ(un)−	PROPN
ma-10	145	13	t	t	PROPN
ma-10	145	14	nun‖	nun‖	NOUN
ma-10	145	15	}	}	PUNCT
ma-10	145	16	,	,	PUNCT
ma-10	145	17	then	then	ADV
ma-10	145	18	we	we	PRON
ma-10	145	19	have	have	VERB
ma-10	145	20	‖un+1	‖un+1	PUNCT
ma-10	145	21	−	−	VERB
ma-10	145	22	un‖	un‖	NOUN
ma-10	145	23	≤	≤	PUNCT
ma-10	145	24	βnm	βnm	X
ma-10	145	25	1−	1−	NUM
ma-10	146	1	γn(1−	γn(1−	ADP
ma-10	146	2	sn)kn	sn)kn	NOUN
ma-10	146	3	+	+	CCONJ
ma-10	146	4	(	(	PUNCT
ma-10	146	5	αn	αn	NOUN
ma-10	146	6	+	+	NOUN
ma-10	146	7	1	1	NUM
ma-10	146	8	)	)	PUNCT
ma-10	146	9	1−	1−	NUM
ma-10	147	1	γn(1−	γn(1−	ADP
ma-10	147	2	sn)kn	sn)kn	PROPN
ma-10	147	3	‖un	‖un	PROPN
ma-10	147	4	−	−	PROPN
ma-10	147	5	t	t	NOUN
ma-10	147	6	nxn‖	nxn‖	NUM
ma-10	147	7	‖un+1	‖un+1	PUNCT
ma-10	147	8	−	−	NOUN
ma-10	147	9	un‖	un‖	PROPN
ma-10	147	10	≤	≤	PUNCT
ma-10	147	11	βnm	βnm	X
ma-10	147	12	1−	1−	NUM
ma-10	148	1	γn(1−	γn(1−	ADP
ma-10	148	2	sn)(1	sn)(1	ADP
ma-10	148	3	+	+	NOUN
ma-10	148	4	εαn	εαn	NOUN
ma-10	148	5	)	)	PUNCT
ma-10	149	1	+	+	CCONJ
ma-10	149	2	(	(	PUNCT
ma-10	149	3	αn	αn	NOUN
ma-10	149	4	+	+	NOUN
ma-10	149	5	1	1	NUM
ma-10	149	6	)	)	PUNCT
ma-10	149	7	1−	1−	NUM
ma-10	150	1	γn(1−	γn(1−	ADP
ma-10	150	2	sn)(1	sn)(1	ADP
ma-10	150	3	+	+	NOUN
ma-10	150	4	εαn	εαn	NOUN
ma-10	150	5	)	)	PUNCT
ma-10	151	1	‖un	‖un	PROPN
ma-10	151	2	−	−	PROPN
ma-10	151	3	t	t	NOUN
ma-10	151	4	nun‖	nun‖	NOUN
ma-10	151	5	since	since	SCONJ
ma-10	151	6	lim	lim	PROPN
ma-10	151	7	n→∞	n→∞	PRON
ma-10	151	8	αn	αn	NOUN
ma-10	152	1	=	=	PROPN
ma-10	152	2	lim	lim	PROPN
ma-10	152	3	n→∞	n→∞	NUM
ma-10	152	4	βn	βn	PROPN
ma-10	152	5	=	=	PUNCT
ma-10	152	6	lim	lim	PROPN
ma-10	152	7	n→∞	n→∞	X
ma-10	153	1	‖un	‖un	PROPN
ma-10	153	2	−	−	PROPN
ma-10	153	3	t	t	NOUN
ma-10	153	4	nun‖	nun‖	NOUN
ma-10	153	5	=	=	SYM
ma-10	153	6	0	0	NUM
ma-10	153	7	,	,	PUNCT
ma-10	153	8	we	we	PRON
ma-10	153	9	then	then	ADV
ma-10	153	10	conclude	conclude	VERB
ma-10	153	11	that	that	SCONJ
ma-10	153	12	lim	lim	PROPN
ma-10	153	13	n→∞	n→∞	X
ma-10	153	14	‖un+1	‖un+1	PUNCT
ma-10	153	15	−	−	NOUN
ma-10	153	16	un‖	un‖	PROPN
ma-10	153	17	=	=	SYM
ma-10	153	18	0	0	NUM
ma-10	153	19	step	step	NOUN
ma-10	153	20	3	3	NUM
ma-10	153	21	:	:	PUNCT
ma-10	153	22	again	again	ADV
ma-10	153	23	we	we	PRON
ma-10	153	24	then	then	ADV
ma-10	153	25	show	show	VERB
ma-10	153	26	that	that	SCONJ
ma-10	153	27	lim	lim	PROPN
ma-10	153	28	n→∞	n→∞	PRON
ma-10	153	29	∥∥∥un	∥∥∥un	PROPN
ma-10	153	30	−	−	PROPN
ma-10	153	31	t	t	PROPN
ma-10	153	32	(	(	PUNCT
ma-10	153	33	un	un	PROPN
ma-10	153	34	)	)	PUNCT
ma-10	153	35	∥∥∥	∥∥∥	PROPN
ma-10	153	36	=	=	SYM
ma-10	154	1	0	0	X
ma-10	154	2	.	.	X
ma-10	154	3	estimating	estimate	VERB
ma-10	154	4	as	as	SCONJ
ma-10	154	5	follows	follow	VERB
ma-10	154	6	we	we	PRON
ma-10	154	7	have	have	VERB
ma-10	154	8	‖un	‖un	PROPN
ma-10	154	9	−	−	PROPN
ma-10	154	10	t	t	NOUN
ma-10	154	11	nun‖	nun‖	NOUN
ma-10	154	12	=	=	PUNCT
ma-10	154	13	‖un	‖un	PROPN
ma-10	154	14	−	−	NOUN
ma-10	154	15	un+1	un+1	NOUN
ma-10	155	1	+	+	CCONJ
ma-10	155	2	un+1	un+1	ADJ
ma-10	155	3	−	−	PROPN
ma-10	155	4	t	t	PROPN
ma-10	155	5	nun‖	nun‖	NOUN
ma-10	155	6	≤	≤	NUM
ma-10	155	7	‖un	‖un	PROPN
ma-10	155	8	−	−	PROPN
ma-10	155	9	un+1‖+	un+1‖+	NOUN
ma-10	155	10	‖un+1	‖un+1	PUNCT
ma-10	155	11	−	−	PROPN
ma-10	155	12	t	t	PROPN
ma-10	155	13	nun‖	nun‖	VERB
ma-10	155	14	≤	≤	NUM
ma-10	155	15	‖un	‖un	PROPN
ma-10	155	16	−	−	PROPN
ma-10	155	17	un+1‖+	un+1‖+	NOUN
ma-10	155	18	‖βnψ(un	‖βnψ(un	PROPN
ma-10	155	19	)	)	PUNCT
ma-10	156	1	+	+	CCONJ
ma-10	156	2	αnun	αnun	ADJ
ma-10	156	3	+	+	CCONJ
ma-10	156	4	(	(	PUNCT
ma-10	156	5	1−	1−	NUM
ma-10	156	6	βn)vn	βn)vn	PUNCT
ma-10	156	7	−	−	PROPN
ma-10	156	8	t	t	NOUN
ma-10	156	9	nun	nun	PROPN
ma-10	156	10	∥∥∥	∥∥∥	PROPN
ma-10	156	11	≤	≤	PUNCT
ma-10	157	1	‖un	‖un	PROPN
ma-10	157	2	−	−	PROPN
ma-10	157	3	un+1‖+	un+1‖+	NOUN
ma-10	157	4	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	157	5	t	t	PROPN
ma-10	157	6	nun‖+	nun‖+	PROPN
ma-10	157	7	αn‖un	αn‖un	PROPN
ma-10	157	8	−	−	PROPN
ma-10	157	9	t	t	PROPN
ma-10	157	10	nun‖+	nun‖+	PROPN
ma-10	157	11	(	(	PUNCT
ma-10	157	12	1−	1−	NUM
ma-10	157	13	βn)‖vn	βn)‖vn	ADJ
ma-10	157	14	−	−	NUM
ma-10	157	15	γnt	γnt	ADJ
ma-10	157	16	nun‖(3.7	nun‖(3.7	NOUN
ma-10	157	17	)	)	PUNCT
ma-10	157	18	‖vn	‖vn	NUM
ma-10	157	19	−	−	ADP
ma-10	157	20	γnt	γnt	ADJ
ma-10	157	21	nun‖	nun‖	NOUN
ma-10	157	22	=	=	PUNCT
ma-10	157	23	‖	‖	ADJ
ma-10	157	24	γnt	γnt	ADJ
ma-10	157	25	n(snun	n(snun	NOUN
ma-10	157	26	+	+	CCONJ
ma-10	157	27	(	(	PUNCT
ma-10	157	28	1−	1−	NUM
ma-10	157	29	sn)un+1	sn)un+1	NOUN
ma-10	157	30	)	)	PUNCT
ma-10	157	31	1−	1−	NUM
ma-10	157	32	βn	βn	NOUN
ma-10	157	33	−	−	PROPN
ma-10	157	34	γnt	γnt	ADJ
ma-10	157	35	nun‖	nun‖	NOUN
ma-10	157	36	≤	≤	ADV
ma-10	157	37	‖	‖	NUM
ma-10	157	38	γnsn	γnsn	NOUN
ma-10	157	39	1−	1−	NUM
ma-10	157	40	βn	βn	PROPN
ma-10	157	41	‖t	‖t	PROPN
ma-10	157	42	nun	nun	PROPN
ma-10	157	43	−	−	PROPN
ma-10	157	44	t	t	PROPN
ma-10	157	45	nun‖+	nun‖+	PROPN
ma-10	157	46	(	(	PUNCT
ma-10	157	47	1−	1−	NUM
ma-10	157	48	sn)γn	sn)γn	ADP
ma-10	157	49	1−	1−	NUM
ma-10	157	50	βn	βn	PROPN
ma-10	157	51	‖t	‖t	NOUN
ma-10	157	52	nun+1	nun+1	NOUN
ma-10	157	53	−	−	PROPN
ma-10	157	54	t	t	PROPN
ma-10	157	55	nun‖	nun‖	NOUN
ma-10	157	56	≤	≤	NUM
ma-10	157	57	(	(	PUNCT
ma-10	157	58	1−	1−	NUM
ma-10	157	59	sn)γnkn	sn)γnkn	NOUN
ma-10	157	60	1−	1−	NUM
ma-10	157	61	βn	βn	PROPN
ma-10	157	62	‖un+1	‖un+1	PUNCT
ma-10	157	63	−	−	PRON
ma-10	157	64	un‖	un‖	PROPN
ma-10	157	65	(	(	PUNCT
ma-10	157	66	3.8	3.8	NUM
ma-10	157	67	)	)	PUNCT
ma-10	157	68	eur	eur	PROPN
ma-10	157	69	.	.	PUNCT
ma-10	158	1	j.	j.	PROPN
ma-10	158	2	math	math	PROPN
ma-10	158	3	.	.	PUNCT
ma-10	159	1	anal	anal	ADJ
ma-10	159	2	.	.	PUNCT
ma-10	160	1	1	1	NUM
ma-10	160	2	(	(	PUNCT
ma-10	160	3	2021	2021	NUM
ma-10	160	4	)	)	PUNCT
ma-10	160	5	26now	26now	NOUN
ma-10	160	6	substituting	substitute	VERB
ma-10	160	7	3.8	3.8	NUM
ma-10	160	8	into	into	ADP
ma-10	160	9	3.7	3.7	NUM
ma-10	160	10	,	,	PUNCT
ma-10	160	11	gives	give	VERB
ma-10	160	12	the	the	DET
ma-10	160	13	following	follow	VERB
ma-10	160	14	estimation	estimation	NOUN
ma-10	160	15	‖un	‖un	PROPN
ma-10	160	16	−	−	PROPN
ma-10	160	17	t	t	PROPN
ma-10	160	18	nun‖	nun‖	NOUN
ma-10	160	19	≤	≤	NUM
ma-10	160	20	‖un	‖un	PROPN
ma-10	160	21	−	−	PROPN
ma-10	160	22	un+1‖+	un+1‖+	NOUN
ma-10	160	23	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	160	24	t	t	PROPN
ma-10	160	25	nun‖+	nun‖+	PROPN
ma-10	160	26	αn‖un	αn‖un	PROPN
ma-10	160	27	−	−	PROPN
ma-10	160	28	t	t	PROPN
ma-10	160	29	nun‖	nun‖	NOUN
ma-10	160	30	+	+	CCONJ
ma-10	160	31	(	(	PUNCT
ma-10	160	32	1−	1−	NUM
ma-10	160	33	βn	βn	NOUN
ma-10	160	34	)	)	PUNCT
ma-10	160	35	(	(	PUNCT
ma-10	160	36	(	(	PUNCT
ma-10	160	37	1−	1−	NUM
ma-10	160	38	sn)γnkn	sn)γnkn	NOUN
ma-10	160	39	1−	1−	NUM
ma-10	160	40	βn	βn	PROPN
ma-10	160	41	‖un+1	‖un+1	PUNCT
ma-10	161	1	−	−	PRON
ma-10	161	2	un‖	un‖	PROPN
ma-10	161	3	)	)	PUNCT
ma-10	161	4	≤	≤	NOUN
ma-10	161	5	(	(	PUNCT
ma-10	161	6	1	1	NUM
ma-10	161	7	+	+	CCONJ
ma-10	161	8	(	(	PUNCT
ma-10	161	9	1−	1−	NUM
ma-10	161	10	sn)γnkn	sn)γnkn	NOUN
ma-10	161	11	)	)	PUNCT
ma-10	162	1	‖un	‖un	PROPN
ma-10	162	2	−	−	PROPN
ma-10	162	3	un+1‖+	un+1‖+	NOUN
ma-10	163	1	βn‖ψ(un)−	βn‖ψ(un)−	PROPN
ma-10	163	2	t	t	PROPN
ma-10	163	3	nun‖+	nun‖+	PROPN
ma-10	163	4	αn‖un	αn‖un	PROPN
ma-10	163	5	−	−	PROPN
ma-10	163	6	t	t	PROPN
ma-10	163	7	nun‖	nun‖	VERB
ma-10	163	8	≤	≤	NUM
ma-10	163	9	(	(	PUNCT
ma-10	163	10	1	1	NUM
ma-10	163	11	+	+	CCONJ
ma-10	163	12	(	(	PUNCT
ma-10	163	13	1−	1−	NUM
ma-10	163	14	sn)γnkn	sn)γnkn	NOUN
ma-10	163	15	)	)	PUNCT
ma-10	164	1	1−	1−	NUM
ma-10	164	2	αn	αn	NOUN
ma-10	165	1	‖un	‖un	PROPN
ma-10	165	2	−	−	PROPN
ma-10	165	3	un+1‖+	un+1‖+	NOUN
ma-10	166	1	βn	βn	PROPN
ma-10	166	2	1−	1−	NUM
ma-10	166	3	αn	αn	NOUN
ma-10	166	4	‖ψ(un)−	‖ψ(un)−	PROPN
ma-10	166	5	t	t	PROPN
ma-10	166	6	nun‖	nun‖	VERB
ma-10	166	7	‖un	‖un	PROPN
ma-10	166	8	−	−	PROPN
ma-10	166	9	t	t	PROPN
ma-10	166	10	nun‖	nun‖	NOUN
ma-10	166	11	≤	≤	NUM
ma-10	166	12	(	(	PUNCT
ma-10	166	13	1	1	NUM
ma-10	166	14	+	+	CCONJ
ma-10	166	15	(	(	PUNCT
ma-10	166	16	1−	1−	NUM
ma-10	166	17	sn)γnkn	sn)γnkn	NOUN
ma-10	166	18	)	)	PUNCT
ma-10	167	1	1−	1−	NUM
ma-10	167	2	αn	αn	NOUN
ma-10	167	3	‖un+1	‖un+1	PUNCT
ma-10	168	1	−	−	PROPN
ma-10	168	2	xn‖+	xn‖+	PROPN
ma-10	168	3	βnm	βnm	X
ma-10	168	4	1−	1−	NUM
ma-10	168	5	αn	αn	NOUN
ma-10	168	6	therefore	therefore	ADV
ma-10	168	7	from	from	ADP
ma-10	168	8	3.1	3.1	NUM
ma-10	168	9	condition	condition	NOUN
ma-10	168	10	a4	a4	NOUN
ma-10	168	11	,	,	PUNCT
ma-10	168	12	with	with	ADP
ma-10	168	13	lim	lim	PROPN
ma-10	168	14	n→∞	n→∞	X
ma-10	168	15	‖un+1	‖un+1	PUNCT
ma-10	168	16	−	−	NOUN
ma-10	168	17	un‖	un‖	PROPN
ma-10	168	18	=	=	SYM
ma-10	168	19	0	0	NUM
ma-10	168	20	,	,	PUNCT
ma-10	168	21	we	we	PRON
ma-10	168	22	can	can	AUX
ma-10	168	23	conclude	conclude	VERB
ma-10	168	24	that	that	SCONJ
ma-10	168	25	lim	lim	PROPN
ma-10	168	26	n→∞	n→∞	PRON
ma-10	168	27	‖un	‖un	PROPN
ma-10	168	28	−	−	PROPN
ma-10	168	29	t	t	NOUN
ma-10	168	30	nun‖	nun‖	NOUN
ma-10	168	31	=	=	SYM
ma-10	168	32	0	0	NUM
ma-10	168	33	(	(	PUNCT
ma-10	168	34	3.9	3.9	NUM
ma-10	168	35	)	)	PUNCT
ma-10	168	36	but	but	CCONJ
ma-10	168	37	we	we	PRON
ma-10	168	38	know	know	VERB
ma-10	168	39	that	that	SCONJ
ma-10	168	40	from	from	ADP
ma-10	168	41	the	the	DET
ma-10	168	42	following	follow	VERB
ma-10	168	43	fact	fact	NOUN
ma-10	168	44	lim	lim	PROPN
ma-10	168	45	n→∞	n→∞	PRON
ma-10	169	1	‖un	‖un	PROPN
ma-10	169	2	−	−	PROPN
ma-10	169	3	t	t	PROPN
ma-10	169	4	(	(	PUNCT
ma-10	169	5	un)‖	un)‖	PROPN
ma-10	169	6	≤	≤	PROPN
ma-10	169	7	lim	lim	PROPN
ma-10	169	8	n→∞	n→∞	PRON
ma-10	170	1	‖un	‖un	PROPN
ma-10	170	2	−	−	PROPN
ma-10	170	3	t	t	PROPN
ma-10	170	4	nun‖+	nun‖+	PROPN
ma-10	170	5	lim	lim	PROPN
ma-10	170	6	n→∞	n→∞	NUM
ma-10	170	7	‖t	‖t	PROPN
ma-10	170	8	nun	nun	PROPN
ma-10	170	9	−	−	PROPN
ma-10	170	10	t	t	PROPN
ma-10	170	11	xn‖	xn‖	PROPN
ma-10	170	12	≤	≤	PROPN
ma-10	170	13	lim	lim	PROPN
ma-10	170	14	n→∞	n→∞	PRON
ma-10	171	1	‖un	‖un	PROPN
ma-10	171	2	−	−	PROPN
ma-10	171	3	t	t	PROPN
ma-10	171	4	nun‖+	nun‖+	PROPN
ma-10	171	5	lim	lim	PROPN
ma-10	171	6	n→∞	n→∞	NUM
ma-10	171	7	k1‖t	k1‖t	PROPN
ma-10	171	8	n−1un	n−1un	PROPN
ma-10	171	9	−	−	PROPN
ma-10	171	10	un‖	un‖	PROPN
ma-10	171	11	(	(	PUNCT
ma-10	171	12	3.10	3.10	NUM
ma-10	171	13	)	)	PUNCT
ma-10	171	14	proving	prove	VERB
ma-10	171	15	that	that	SCONJ
ma-10	171	16	lim	lim	PROPN
ma-10	171	17	n→∞	n→∞	NUM
ma-10	171	18	‖t	‖t	PROPN
ma-10	171	19	n−1un	n−1un	NOUN
ma-10	171	20	−	−	NOUN
ma-10	171	21	un‖	un‖	PROPN
ma-10	171	22	=	=	SYM
ma-10	171	23	0	0	NUM
ma-10	171	24	,	,	PUNCT
ma-10	171	25	we	we	PRON
ma-10	171	26	have	have	VERB
ma-10	171	27	the	the	DET
ma-10	171	28	following	follow	VERB
ma-10	171	29	estimation	estimation	NOUN
ma-10	171	30	‖t	‖t	NOUN
ma-10	171	31	n−1(un)−	n−1(un)−	NOUN
ma-10	172	1	un‖	un‖	NOUN
ma-10	172	2	=	=	PUNCT
ma-10	173	1	‖un	‖un	PROPN
ma-10	173	2	−	−	PROPN
ma-10	173	3	t	t	PROPN
ma-10	173	4	n−1(un)‖	n−1(un)‖	NOUN
ma-10	173	5	=	=	SYM
ma-10	173	6	‖βn−1ψ(un−1	‖βn−1ψ(un−1	PROPN
ma-10	173	7	)	)	PUNCT
ma-10	174	1	+	+	NUM
ma-10	174	2	αn−1un−1	αn−1un−1	NUM
ma-10	174	3	+	+	CCONJ
ma-10	174	4	(	(	PUNCT
ma-10	174	5	1−	1−	NUM
ma-10	174	6	βn−1)vn−1	βn−1)vn−1	NOUN
ma-10	174	7	−(βn−1	−(βn−1	PROPN
ma-10	175	1	+	+	PUNCT
ma-10	176	1	αn−1	αn−1	ADJ
ma-10	177	1	+	+	CCONJ
ma-10	177	2	γn−1)t	γn−1)t	PUNCT
ma-10	177	3	n−1un‖	n−1un‖	NOUN
ma-10	177	4	=	=	X
ma-10	177	5	‖βn−1ψ(un−1)−	‖βn−1ψ(un−1)−	PROPN
ma-10	177	6	βn−1	βn−1	PROPN
ma-10	177	7	t	t	NOUN
ma-10	177	8	n−1un	n−1un	NOUN
ma-10	178	1	+	+	CCONJ
ma-10	178	2	αn−1un−1	αn−1un−1	NUM
ma-10	178	3	−	−	PROPN
ma-10	178	4	αn−1	αn−1	PROPN
ma-10	178	5	t	t	PROPN
ma-10	178	6	n−1un	n−1un	NOUN
ma-10	178	7	+	+	PROPN
ma-10	178	8	(	(	PUNCT
ma-10	178	9	1−	1−	NUM
ma-10	178	10	βn−1)vn−1	βn−1)vn−1	NOUN
ma-10	178	11	−	−	PROPN
ma-10	179	1	γn−1	γn−1	PROPN
ma-10	179	2	t	t	PROPN
ma-10	179	3	n−1un‖	n−1un‖	NOUN
ma-10	179	4	≤	≤	NUM
ma-10	179	5	βn−1‖ψ(un−1)−	βn−1‖ψ(un−1)−	PROPN
ma-10	180	1	t	t	PROPN
ma-10	180	2	n−1un‖+	n−1un‖+	PROPN
ma-10	180	3	αn−1‖un−1	αn−1‖un−1	PROPN
ma-10	181	1	−	−	PROPN
ma-10	181	2	t	t	NOUN
ma-10	181	3	n−1un‖	n−1un‖	X
ma-10	182	1	+	+	PROPN
ma-10	182	2	(	(	PUNCT
ma-10	182	3	1−	1−	NUM
ma-10	182	4	βn−1)‖vn−1	βn−1)‖vn−1	NUM
ma-10	182	5	−	−	PROPN
ma-10	183	1	γn−1	γn−1	PROPN
ma-10	183	2	t	t	PROPN
ma-10	183	3	n−1xn‖	n−1xn‖	NUM
ma-10	183	4	(	(	PUNCT
ma-10	183	5	3.11	3.11	NUM
ma-10	183	6	)	)	PUNCT
ma-10	183	7	‖vn−1	‖vn−1	PROPN
ma-10	183	8	−	−	PROPN
ma-10	183	9	γn−1	γn−1	PROPN
ma-10	183	10	t	t	PROPN
ma-10	183	11	n−1un‖	n−1un‖	NOUN
ma-10	183	12	=	=	SYM
ma-10	183	13	‖	‖	PROPN
ma-10	183	14	γn−1	γn−1	PROPN
ma-10	183	15	t	t	PROPN
ma-10	183	16	n−1(sn−1un−1	n−1(sn−1un−1	PROPN
ma-10	183	17	+	+	CCONJ
ma-10	183	18	(	(	PUNCT
ma-10	183	19	1−	1−	NUM
ma-10	183	20	sn−1)un	sn−1)un	NOUN
ma-10	183	21	)	)	PUNCT
ma-10	183	22	1−	1−	NUM
ma-10	184	1	βn−1	βn−1	ADJ
ma-10	184	2	−	−	PROPN
ma-10	184	3	γn−1	γn−1	PROPN
ma-10	184	4	t	t	PROPN
ma-10	184	5	n−1un‖	n−1un‖	NOUN
ma-10	184	6	≤	≤	PROPN
ma-10	184	7	γn−1kn−1sn−1	γn−1kn−1sn−1	ADP
ma-10	185	1	1−	1−	NUM
ma-10	185	2	βn−1	βn−1	PROPN
ma-10	185	3	‖|un	‖|un	ADJ
ma-10	186	1	−	−	PROPN
ma-10	186	2	un−1‖	un−1‖	PROPN
ma-10	186	3	(	(	PUNCT
ma-10	186	4	3.12	3.12	NUM
ma-10	186	5	)	)	PUNCT
ma-10	186	6	eur	eur	PROPN
ma-10	186	7	.	.	PUNCT
ma-10	187	1	j.	j.	PROPN
ma-10	187	2	math	math	PROPN
ma-10	187	3	.	.	PUNCT
ma-10	188	1	anal	anal	ADJ
ma-10	188	2	.	.	PUNCT
ma-10	189	1	1	1	NUM
ma-10	189	2	(	(	PUNCT
ma-10	189	3	2021	2021	NUM
ma-10	189	4	)	)	PUNCT
ma-10	190	1	27combining	27combine	VERB
ma-10	190	2	3.12	3.12	NUM
ma-10	190	3	and	and	CCONJ
ma-10	190	4	3.11	3.11	NUM
ma-10	190	5	we	we	PRON
ma-10	190	6	have	have	VERB
ma-10	190	7	the	the	DET
ma-10	190	8	following	follow	VERB
ma-10	190	9	‖t	‖t	NOUN
ma-10	190	10	n−1(un)−	n−1(un)−	NOUN
ma-10	191	1	un‖	un‖	VERB
ma-10	191	2	≤	≤	PROPN
ma-10	192	1	βn−1‖ψ(un−1)−	βn−1‖ψ(un−1)−	PROPN
ma-10	192	2	t	t	PROPN
ma-10	192	3	n−1un‖+	n−1un‖+	PROPN
ma-10	192	4	αn−1‖un−1	αn−1‖un−1	PROPN
ma-10	193	1	−	−	PROPN
ma-10	193	2	t	t	NOUN
ma-10	193	3	n−1un‖	n−1un‖	X
ma-10	194	1	+	+	PROPN
ma-10	194	2	(	(	PUNCT
ma-10	194	3	1−	1−	NUM
ma-10	194	4	βn−1	βn−1	ADJ
ma-10	194	5	)	)	PUNCT
ma-10	195	1	[	[	X
ma-10	195	2	γn−1kn−1sn−1	γn−1kn−1sn−1	PROPN
ma-10	195	3	1−	1−	NUM
ma-10	195	4	βn−1	βn−1	PROPN
ma-10	196	1	‖|un	‖|un	ADJ
ma-10	196	2	−	−	PROPN
ma-10	196	3	un−1‖	un−1‖	PROPN
ma-10	196	4	]	]	PUNCT
ma-10	196	5	≤	≤	NUM
ma-10	197	1	βn−1‖ψ(un−1)−	βn−1‖ψ(un−1)−	PROPN
ma-10	197	2	t	t	PROPN
ma-10	197	3	n−1un‖+	n−1un‖+	PROPN
ma-10	197	4	αn−1‖un−1	αn−1‖un−1	PROPN
ma-10	198	1	−	−	PROPN
ma-10	198	2	t	t	NOUN
ma-10	198	3	n−1un‖	n−1un‖	NOUN
ma-10	199	1	+	+	PROPN
ma-10	199	2	γn−1kn−1sn−1‖un	γn−1kn−1sn−1‖un	PROPN
ma-10	199	3	−	−	PROPN
ma-10	199	4	un−1‖	un−1‖	PROPN
ma-10	199	5	≤	≤	PROPN
ma-10	200	1	βn−1‖ψ(un−1)−	βn−1‖ψ(un−1)−	PROPN
ma-10	200	2	t	t	PROPN
ma-10	200	3	n−1un‖+	n−1un‖+	PROPN
ma-10	200	4	αn−1‖un−1	αn−1‖un−1	PROPN
ma-10	201	1	−	−	PROPN
ma-10	201	2	t	t	NOUN
ma-10	201	3	n−1un‖	n−1un‖	NOUN
ma-10	202	1	+	+	NOUN
ma-10	202	2	γn−1kn−1sn−1‖|un	γn−1kn−1sn−1‖|un	ADV
ma-10	202	3	−	−	ADP
ma-10	202	4	un−1‖	un−1‖	PROPN
ma-10	202	5	with	with	ADP
ma-10	202	6	the	the	DET
ma-10	202	7	assumption	assumption	NOUN
ma-10	202	8	of	of	ADP
ma-10	202	9	{	{	PUNCT
ma-10	202	10	αn	αn	NOUN
ma-10	202	11	}	}	PUNCT
ma-10	202	12	,	,	PUNCT
ma-10	202	13	{	{	PUNCT
ma-10	202	14	βn	βn	VERB
ma-10	202	15	}	}	PUNCT
ma-10	202	16	and	and	CCONJ
ma-10	202	17	lim	lim	PROPN
ma-10	202	18	n→∞	n→∞	X
ma-10	202	19	‖un+1	‖un+1	PUNCT
ma-10	202	20	−	−	NOUN
ma-10	202	21	un‖	un‖	PROPN
ma-10	202	22	=	=	SYM
ma-10	202	23	0	0	NUM
ma-10	202	24	,	,	PUNCT
ma-10	202	25	we	we	PRON
ma-10	202	26	can	can	AUX
ma-10	202	27	conclude	conclude	VERB
ma-10	202	28	that	that	SCONJ
ma-10	202	29	lim	lim	PROPN
ma-10	202	30	n→∞	n→∞	NUM
ma-10	202	31	‖t	‖t	PROPN
ma-10	202	32	n−1un	n−1un	NOUN
ma-10	202	33	−	−	NOUN
ma-10	202	34	un‖	un‖	PROPN
ma-10	202	35	=	=	X
ma-10	202	36	0	0	NUM
ma-10	202	37	(	(	PUNCT
ma-10	202	38	3.13	3.13	NUM
ma-10	202	39	)	)	PUNCT
ma-10	202	40	therefore	therefore	ADV
ma-10	202	41	from	from	ADP
ma-10	202	42	3.9	3.9	NUM
ma-10	202	43	and	and	CCONJ
ma-10	202	44	3.13	3.13	NUM
ma-10	202	45	,	,	PUNCT
ma-10	202	46	we	we	PRON
ma-10	202	47	can	can	AUX
ma-10	202	48	see	see	VERB
ma-10	202	49	from	from	ADP
ma-10	202	50	inequality	inequality	NOUN
ma-10	202	51	3.10	3.10	NUM
ma-10	202	52	,	,	PUNCT
ma-10	202	53	that	that	SCONJ
ma-10	202	54	lim	lim	PROPN
ma-10	202	55	n→∞	n→∞	VERB
ma-10	202	56	‖un	‖un	PROPN
ma-10	202	57	−	−	PROPN
ma-10	202	58	t	t	PROPN
ma-10	202	59	(	(	PUNCT
ma-10	202	60	un)‖	un)‖	PROPN
ma-10	202	61	=	=	SYM
ma-10	202	62	0	0	NUM
ma-10	202	63	(	(	PUNCT
ma-10	202	64	3.14	3.14	NUM
ma-10	202	65	)	)	PUNCT
ma-10	202	66	step	step	NOUN
ma-10	202	67	4	4	NUM
ma-10	202	68	:	:	PUNCT
ma-10	202	69	in	in	ADP
ma-10	202	70	this	this	DET
ma-10	202	71	step	step	NOUN
ma-10	202	72	,	,	PUNCT
ma-10	202	73	we	we	PRON
ma-10	202	74	will	will	AUX
ma-10	202	75	show	show	VERB
ma-10	202	76	that	that	SCONJ
ma-10	202	77	wω(xn	wω(xn	NOUN
ma-10	202	78	)	)	PUNCT
ma-10	202	79	⊆	⊆	NUM
ma-10	202	80	f	f	NOUN
ma-10	202	81	ix(t	ix(t	ADJ
ma-10	202	82	)	)	PUNCT
ma-10	202	83	,	,	PUNCT
ma-10	202	84	where	where	SCONJ
ma-10	202	85	wω(un	wω(un	NOUN
ma-10	202	86	)	)	PUNCT
ma-10	202	87	:	:	PUNCT
ma-10	203	1	=	=	SYM
ma-10	203	2	{	{	PUNCT
ma-10	203	3	u	u	NOUN
ma-10	203	4	∈	∈	PROPN
ma-10	203	5	h	h	NOUN
ma-10	203	6	:	:	PUNCT
ma-10	203	7	there	there	PRON
ma-10	203	8	exist	exist	VERB
ma-10	203	9	a	a	DET
ma-10	203	10	subsequence	subsequence	NOUN
ma-10	203	11	of	of	ADP
ma-10	203	12	{	{	PUNCT
ma-10	203	13	un	un	PROPN
ma-10	203	14	}	}	PUNCT
ma-10	203	15	converges	converge	VERB
ma-10	203	16	weakly	weakly	ADV
ma-10	203	17	to	to	ADP
ma-10	203	18	u}.suppose	u}.suppose	PRON
ma-10	203	19	that	that	DET
ma-10	203	20	u	u	PROPN
ma-10	203	21	∈	∈	PROPN
ma-10	203	22	wω(un	wω(un	PROPN
ma-10	203	23	)	)	PUNCT
ma-10	203	24	.	.	PUNCT
ma-10	204	1	then	then	ADV
ma-10	204	2	there	there	PRON
ma-10	204	3	exists	exist	VERB
ma-10	204	4	a	a	DET
ma-10	204	5	subsequence	subsequence	NOUN
ma-10	204	6	{	{	PUNCT
ma-10	204	7	uni	uni	PROPN
ma-10	204	8	}	}	PUNCT
ma-10	204	9	of	of	ADP
ma-10	204	10	{	{	PUNCT
ma-10	204	11	un	un	PROPN
ma-10	204	12	}	}	PUNCT
ma-10	204	13	such	such	ADJ
ma-10	204	14	that	that	SCONJ
ma-10	204	15	uni	uni	INTJ
ma-10	205	1	⇀	⇀	NUM
ma-10	205	2	xas	xas	NOUN
ma-10	206	1	i	i	PRON
ma-10	206	2	→∞	→∞	PROPN
ma-10	206	3	.	.	PUNCT
ma-10	207	1	from	from	ADP
ma-10	207	2	3.14	3.14	NUM
ma-10	207	3	,	,	PUNCT
ma-10	207	4	we	we	PRON
ma-10	207	5	have	have	VERB
ma-10	207	6	lim	lim	PROPN
ma-10	207	7	i→∞	i→∞	PROPN
ma-10	207	8	∥∥∥(i	∥∥∥(i	PUNCT
ma-10	207	9	−	−	PROPN
ma-10	207	10	t	t	PROPN
ma-10	207	11	)	)	PUNCT
ma-10	208	1	xni	xni	PROPN
ma-10	208	2	∥∥∥	∥∥∥	PROPN
ma-10	209	1	=	=	PRON
ma-10	209	2	lim	lim	PROPN
ma-10	209	3	n→∞	n→∞	X
ma-10	209	4	∥∥∥uni	∥∥∥uni	X
ma-10	209	5	−	−	X
ma-10	209	6	t	t	NOUN
ma-10	209	7	uni∥∥∥	uni∥∥∥	NOUN
ma-10	209	8	=	=	NOUN
ma-10	209	9	0	0	NUM
ma-10	209	10	.	.	PUNCT
ma-10	210	1	this	this	PRON
ma-10	210	2	implies	imply	VERB
ma-10	210	3	that	that	SCONJ
ma-10	210	4	{	{	PUNCT
ma-10	210	5	(	(	PUNCT
ma-10	210	6	i	i	PRON
ma-10	210	7	−	−	PROPN
ma-10	210	8	t	t	NOUN
ma-10	210	9	)	)	PUNCT
ma-10	210	10	uni	uni	ADJ
ma-10	210	11	}	}	PUNCT
ma-10	210	12	converges	converge	VERB
ma-10	210	13	strongly	strongly	ADV
ma-10	210	14	to	to	ADP
ma-10	210	15	0	0	NUM
ma-10	210	16	.	.	PUNCT
ma-10	210	17	by	by	ADP
ma-10	210	18	using	use	VERB
ma-10	210	19	lemma	lemma	PROPN
ma-10	210	20	2.2	2.2	NUM
ma-10	210	21	,	,	PUNCT
ma-10	210	22	we	we	PRON
ma-10	210	23	have	have	VERB
ma-10	210	24	t	t	NOUN
ma-10	210	25	u	u	NOUN
ma-10	210	26	=	=	PROPN
ma-10	210	27	u	u	PROPN
ma-10	210	28	,	,	PUNCT
ma-10	210	29	and	and	CCONJ
ma-10	210	30	so	so	ADV
ma-10	210	31	u	u	PROPN
ma-10	210	32	∈	∈	PROPN
ma-10	210	33	f	f	PROPN
ma-10	210	34	ix(t	ix(t	PROPN
ma-10	210	35	)	)	PUNCT
ma-10	210	36	.	.	PUNCT
ma-10	211	1	step	step	NOUN
ma-10	211	2	5	5	NUM
ma-10	211	3	:	:	PUNCT
ma-10	211	4	in	in	ADP
ma-10	211	5	this	this	DET
ma-10	211	6	step	step	NOUN
ma-10	211	7	,	,	PUNCT
ma-10	211	8	we	we	PRON
ma-10	211	9	will	will	AUX
ma-10	211	10	show	show	VERB
ma-10	211	11	that	that	SCONJ
ma-10	211	12	lim	lim	PROPN
ma-10	211	13	sup	sup	VERB
ma-10	211	14	n→∞	n→∞	NUM
ma-10	211	15	〈	〈	PROPN
ma-10	211	16	q	q	X
ma-10	211	17	−	−	PROPN
ma-10	211	18	ψ(q	ψ(q	PROPN
ma-10	211	19	)	)	PUNCT
ma-10	211	20	,	,	PUNCT
ma-10	211	21	q	q	PROPN
ma-10	211	22	−	−	PROPN
ma-10	211	23	un	un	PROPN
ma-10	211	24	〉	〉	PROPN
ma-10	211	25	≤	≤	NUM
ma-10	211	26	0	0	NUM
ma-10	211	27	,	,	PUNCT
ma-10	211	28	(	(	PUNCT
ma-10	211	29	3.15	3.15	NUM
ma-10	211	30	)	)	PUNCT
ma-10	211	31	where	where	SCONJ
ma-10	211	32	q	q	PROPN
ma-10	211	33	∈	∈	PROPN
ma-10	211	34	f	f	X
ma-10	211	35	(	(	PUNCT
ma-10	211	36	t	t	PROPN
ma-10	211	37	)	)	PUNCT
ma-10	211	38	is	be	AUX
ma-10	211	39	the	the	DET
ma-10	211	40	unique	unique	ADJ
ma-10	211	41	fixed	fix	VERB
ma-10	211	42	point	point	NOUN
ma-10	211	43	of	of	ADP
ma-10	211	44	pf	pf	PROPN
ma-10	211	45	(	(	PUNCT
ma-10	211	46	t	t	PROPN
ma-10	211	47	)	)	PUNCT
ma-10	211	48	◦	◦	NOUN
ma-10	211	49	ψ	ψ	SYM
ma-10	211	50	,	,	PUNCT
ma-10	211	51	that	that	ADV
ma-10	211	52	is	is	ADV
ma-10	211	53	,	,	PUNCT
ma-10	211	54	q	q	X
ma-10	211	55	=	=	PRON
ma-10	211	56	pf	pf	X
ma-10	211	57	(	(	PUNCT
ma-10	211	58	t	t	PROPN
ma-10	211	59	)	)	PUNCT
ma-10	211	60	(	(	PUNCT
ma-10	211	61	ψ(z	ψ(z	PROPN
ma-10	211	62	)	)	PUNCT
ma-10	211	63	)	)	PUNCT
ma-10	211	64	.	.	PUNCT
ma-10	212	1	since	since	SCONJ
ma-10	212	2	{	{	PUNCT
ma-10	212	3	un	un	VERB
ma-10	212	4	}	}	PUNCT
ma-10	212	5	is	be	AUX
ma-10	212	6	bounded	bound	VERB
ma-10	212	7	,	,	PUNCT
ma-10	212	8	there	there	PRON
ma-10	212	9	exists	exist	VERB
ma-10	212	10	a	a	DET
ma-10	212	11	subsequence	subsequence	NOUN
ma-10	212	12	{	{	PUNCT
ma-10	212	13	uni	uni	PROPN
ma-10	212	14	}	}	PUNCT
ma-10	212	15	of	of	ADP
ma-10	212	16	{	{	PUNCT
ma-10	212	17	un	un	PROPN
ma-10	212	18	}	}	PUNCT
ma-10	212	19	such	such	ADJ
ma-10	212	20	that	that	SCONJ
ma-10	212	21	uni	uni	INTJ
ma-10	212	22	⇀	⇀	NUM
ma-10	212	23	u	u	NOUN
ma-10	212	24	as	as	ADP
ma-10	212	25	i	i	PRON
ma-10	212	26	→∞	→∞	PROPN
ma-10	212	27	forsome	forsome	NOUN
ma-10	212	28	u	u	PROPN
ma-10	212	29	∈	∈	PROPN
ma-10	212	30	h	h	NOUN
ma-10	212	31	and	and	CCONJ
ma-10	212	32	lim	lim	PROPN
ma-10	212	33	sup	sup	PROPN
ma-10	212	34	n→∞	n→∞	NUM
ma-10	213	1	〈	〈	PROPN
ma-10	213	2	q	q	X
ma-10	213	3	−	−	PROPN
ma-10	213	4	ψ(q	ψ(q	PROPN
ma-10	213	5	)	)	PUNCT
ma-10	213	6	,	,	PUNCT
ma-10	213	7	q	q	PROPN
ma-10	213	8	−	−	PROPN
ma-10	213	9	un	un	PROPN
ma-10	213	10	〉	〉	PROPN
ma-10	213	11	=	=	PROPN
ma-10	213	12	lim	lim	PROPN
ma-10	213	13	i→∞	i→∞	VERB
ma-10	213	14	〈	〈	PROPN
ma-10	213	15	q	q	X
ma-10	213	16	−	−	PROPN
ma-10	213	17	ψ(q	ψ(q	PROPN
ma-10	213	18	)	)	PUNCT
ma-10	213	19	,	,	PUNCT
ma-10	213	20	q	q	PUNCT
ma-10	213	21	−	−	PROPN
ma-10	213	22	uni	uni	INTJ
ma-10	213	23	〉	〉	PROPN
ma-10	213	24	(	(	PUNCT
ma-10	213	25	3.16	3.16	NUM
ma-10	213	26	)	)	PUNCT
ma-10	213	27	from	from	ADP
ma-10	213	28	step	step	NOUN
ma-10	213	29	4	4	NUM
ma-10	213	30	,	,	PUNCT
ma-10	213	31	we	we	PRON
ma-10	213	32	get	get	VERB
ma-10	213	33	x	x	PUNCT
ma-10	213	34	∈	∈	PROPN
ma-10	213	35	f	f	X
ma-10	213	36	(	(	PUNCT
ma-10	213	37	t	t	PROPN
ma-10	213	38	)	)	PUNCT
ma-10	213	39	.	.	PUNCT
ma-10	214	1	by	by	ADP
ma-10	214	2	using	use	VERB
ma-10	214	3	inequality	inequality	NOUN
ma-10	214	4	2.2	2.2	NUM
ma-10	214	5	,	,	PUNCT
ma-10	214	6	we	we	PRON
ma-10	214	7	obtain	obtain	VERB
ma-10	214	8	lim	lim	PROPN
ma-10	214	9	sup	sup	X
ma-10	214	10	n→∞	n→∞	NUM
ma-10	215	1	〈	〈	PROPN
ma-10	215	2	q	q	X
ma-10	215	3	−	−	PROPN
ma-10	215	4	ψ(q	ψ(q	PROPN
ma-10	215	5	)	)	PUNCT
ma-10	215	6	,	,	PUNCT
ma-10	215	7	q	q	PROPN
ma-10	215	8	−	−	PROPN
ma-10	215	9	un	un	PROPN
ma-10	215	10	〉	〉	PROPN
ma-10	215	11	=	=	PROPN
ma-10	215	12	lim	lim	PROPN
ma-10	215	13	i→∞	i→∞	VERB
ma-10	215	14	〈	〈	PROPN
ma-10	215	15	q	q	X
ma-10	215	16	−	−	PROPN
ma-10	215	17	ψ(q	ψ(q	PROPN
ma-10	215	18	)	)	PUNCT
ma-10	215	19	,	,	PUNCT
ma-10	215	20	q	q	PUNCT
ma-10	215	21	−	−	PROPN
ma-10	215	22	uni	uni	INTJ
ma-10	216	1	〉	〉	PROPN
ma-10	216	2	=	=	SYM
ma-10	216	3	〈	〈	PROPN
ma-10	216	4	q	q	X
ma-10	216	5	−	−	PROPN
ma-10	216	6	ψ(q	ψ(q	PROPN
ma-10	216	7	)	)	PUNCT
ma-10	216	8	,	,	PUNCT
ma-10	216	9	q	q	NOUN
ma-10	216	10	−	−	PUNCT
ma-10	216	11	u	u	NOUN
ma-10	216	12	〉	〉	NOUN
ma-10	216	13	≤	≤	NUM
ma-10	216	14	0	0	NUM
ma-10	216	15	eur	eur	NOUN
ma-10	216	16	.	.	PUNCT
ma-10	217	1	j.	j.	PROPN
ma-10	217	2	math	math	PROPN
ma-10	217	3	.	.	PUNCT
ma-10	218	1	anal	anal	ADJ
ma-10	218	2	.	.	PUNCT
ma-10	219	1	1	1	NUM
ma-10	219	2	(	(	PUNCT
ma-10	219	3	2021	2021	NUM
ma-10	219	4	)	)	PUNCT
ma-10	219	5	28	28	NUM
ma-10	219	6	step	step	NOUN
ma-10	219	7	6	6	NUM
ma-10	219	8	:	:	PUNCT
ma-10	219	9	finally	finally	ADV
ma-10	219	10	,	,	PUNCT
ma-10	219	11	setting	set	VERB
ma-10	219	12	ϕn	ϕn	ADP
ma-10	219	13	=	=	NOUN
ma-10	219	14	βnq	βnq	NOUN
ma-10	220	1	+	+	CCONJ
ma-10	220	2	αnq	αnq	X
ma-10	220	3	+	+	CCONJ
ma-10	220	4	(	(	PUNCT
ma-10	220	5	1	1	NUM
ma-10	220	6	−	−	NOUN
ma-10	220	7	βn)vn	βn)vn	PUNCT
ma-10	220	8	we	we	PRON
ma-10	220	9	show	show	VERB
ma-10	220	10	that	that	SCONJ
ma-10	220	11	un	un	PROPN
ma-10	220	12	→	→	X
ma-10	220	13	q	q	X
ma-10	220	14	as	as	ADP
ma-10	220	15	n	n	PROPN
ma-10	220	16	→	→	SYM
ma-10	220	17	∞.	∞.	PROPN
ma-10	220	18	again	again	ADV
ma-10	220	19	,	,	PUNCT
ma-10	220	20	take	take	VERB
ma-10	220	21	q	q	NOUN
ma-10	220	22	∈	∈	PROPN
ma-10	220	23	f	f	X
ma-10	220	24	(	(	PUNCT
ma-10	220	25	t	t	PROPN
ma-10	220	26	)	)	PUNCT
ma-10	220	27	to	to	PART
ma-10	220	28	be	be	AUX
ma-10	220	29	the	the	DET
ma-10	220	30	unique	unique	ADJ
ma-10	220	31	fixed	fix	VERB
ma-10	220	32	point	point	NOUN
ma-10	220	33	of	of	ADP
ma-10	220	34	the	the	DET
ma-10	220	35	contraction	contraction	NOUN
ma-10	220	36	pf	pf	PROPN
ma-10	220	37	(	(	PUNCT
ma-10	220	38	t	t	PROPN
ma-10	220	39	)	)	PUNCT
ma-10	220	40	◦	◦	NOUN
ma-10	220	41	ψ	ψ	X
ma-10	220	42	.	.	PUNCT
ma-10	221	1	for	for	ADP
ma-10	221	2	each	each	DET
ma-10	221	3	n	n	PRON
ma-10	221	4	∈	∈	PROPN
ma-10	221	5	n	n	CCONJ
ma-10	221	6	,	,	PUNCT
ma-10	221	7	consider	consider	VERB
ma-10	221	8	‖un+1	‖un+1	PUNCT
ma-10	221	9	−	−	PRON
ma-10	221	10	q‖2	q‖2	VERB
ma-10	221	11	≤	≤	NUM
ma-10	221	12	‖ϕn	‖ϕn	NUM
ma-10	222	1	−	−	NOUN
ma-10	222	2	q‖2	q‖2	PROPN
ma-10	222	3	+	+	CCONJ
ma-10	222	4	2〈un+1	2〈un+1	PROPN
ma-10	222	5	−	−	PROPN
ma-10	222	6	ϕn	ϕn	INTJ
ma-10	222	7	,	,	PUNCT
ma-10	222	8	un+1	un+1	ADV
ma-10	222	9	−	−	PROPN
ma-10	222	10	q	q	NOUN
ma-10	222	11	〉	〉	NOUN
ma-10	222	12	=	=	SYM
ma-10	222	13	(	(	PUNCT
ma-10	222	14	1−	1−	NUM
ma-10	222	15	βn)2‖vn	βn)2‖vn	NUM
ma-10	222	16	−	−	PROPN
ma-10	222	17	q‖2	q‖2	PROPN
ma-10	222	18	+	+	CCONJ
ma-10	222	19	2〈βn(ψ(un)−	2〈βn(ψ(un)−	NUM
ma-10	222	20	q	q	NOUN
ma-10	222	21	)	)	PUNCT
ma-10	223	1	+	+	CCONJ
ma-10	224	1	αn(un	αn(un	ADJ
ma-10	224	2	−	−	PROPN
ma-10	224	3	q	q	NOUN
ma-10	224	4	)	)	PUNCT
ma-10	224	5	,	,	PUNCT
ma-10	224	6	un+1	un+1	ADV
ma-10	224	7	−	−	PROPN
ma-10	224	8	q	q	NOUN
ma-10	224	9	〉	〉	NOUN
ma-10	224	10	≤	≤	NOUN
ma-10	224	11	(	(	PUNCT
ma-10	224	12	1−	1−	NUM
ma-10	224	13	βn)‖vn	βn)‖vn	ADJ
ma-10	224	14	−	−	NOUN
ma-10	224	15	q‖2	q‖2	NOUN
ma-10	224	16	+	+	CCONJ
ma-10	224	17	2〈βn(ψ(un)−	2〈βn(ψ(un)−	NUM
ma-10	224	18	ψ(q	ψ(q	NOUN
ma-10	224	19	)	)	PUNCT
ma-10	224	20	)	)	PUNCT
ma-10	225	1	+	+	CCONJ
ma-10	225	2	βn(ψ(q)−	βn(ψ(q)−	NUM
ma-10	225	3	q	q	X
ma-10	225	4	)	)	PUNCT
ma-10	225	5	+	+	CCONJ
ma-10	225	6	αn(un	αn(un	ADJ
ma-10	225	7	−	−	PROPN
ma-10	225	8	q	q	NOUN
ma-10	225	9	)	)	PUNCT
ma-10	225	10	,	,	PUNCT
ma-10	225	11	un+1	un+1	ADV
ma-10	225	12	−	−	PROPN
ma-10	225	13	q	q	NOUN
ma-10	225	14	〉	〉	NOUN
ma-10	225	15	≤	≤	NOUN
ma-10	225	16	(	(	PUNCT
ma-10	225	17	1−	1−	NUM
ma-10	225	18	βn)2‖vn	βn)2‖vn	NUM
ma-10	225	19	−	−	PROPN
ma-10	225	20	q‖2	q‖2	PROPN
ma-10	225	21	+	+	CCONJ
ma-10	225	22	2βn‖ψ(xn)−	2βn‖ψ(xn)−	NUM
ma-10	225	23	ψ(q)‖‖un+1	ψ(q)‖‖un+1	NUM
ma-10	225	24	−	−	NOUN
ma-10	225	25	q‖+	q‖+	ADJ
ma-10	225	26	2αn‖un	2αn‖un	NUM
ma-10	225	27	−	−	PROPN
ma-10	225	28	q‖‖un+1	q‖‖un+1	NOUN
ma-10	225	29	−	−	NOUN
ma-10	225	30	q‖	q‖	NOUN
ma-10	225	31	+2βn〈ψ(q)−	+2βn〈ψ(q)−	PROPN
ma-10	225	32	q	q	NOUN
ma-10	225	33	,	,	PUNCT
ma-10	225	34	un+1	un+1	ADV
ma-10	225	35	−	−	PROPN
ma-10	225	36	q	q	NOUN
ma-10	225	37	〉	〉	NOUN
ma-10	225	38	≤	≤	NOUN
ma-10	225	39	(	(	PUNCT
ma-10	225	40	1−	1−	NUM
ma-10	225	41	βn)2‖vn	βn)2‖vn	NUM
ma-10	226	1	−	−	NOUN
ma-10	226	2	q‖2	q‖2	PROPN
ma-10	226	3	+	+	CCONJ
ma-10	226	4	2βnα‖un	2βnα‖un	NUM
ma-10	226	5	−	−	NOUN
ma-10	226	6	q‖‖un+1	q‖‖un+1	NOUN
ma-10	226	7	−	−	NOUN
ma-10	226	8	q‖+	q‖+	ADJ
ma-10	226	9	2αn‖un	2αn‖un	NUM
ma-10	226	10	−	−	PROPN
ma-10	226	11	q‖‖un+1	q‖‖un+1	NOUN
ma-10	226	12	−	−	NOUN
ma-10	226	13	q‖	q‖	NOUN
ma-10	226	14	+2βn〈ψ(q)−	+2βn〈ψ(q)−	PROPN
ma-10	226	15	q	q	NOUN
ma-10	226	16	,	,	PUNCT
ma-10	226	17	un+1	un+1	ADV
ma-10	226	18	−	−	PROPN
ma-10	226	19	q	q	NOUN
ma-10	226	20	〉	〉	NOUN
ma-10	226	21	≤	≤	NOUN
ma-10	226	22	(	(	PUNCT
ma-10	226	23	1−	1−	NUM
ma-10	226	24	βn)2‖vn	βn)2‖vn	NUM
ma-10	226	25	−	−	NOUN
ma-10	226	26	q‖2	q‖2	PROPN
ma-10	226	27	+	+	CCONJ
ma-10	226	28	(	(	PUNCT
ma-10	226	29	2βnα+	2βnα+	NUM
ma-10	226	30	2αn)‖un	2αn)‖un	NUM
ma-10	226	31	−	−	PROPN
ma-10	226	32	q‖‖un+1	q‖‖un+1	NOUN
ma-10	226	33	−	−	PROPN
ma-10	226	34	q‖	q‖	NOUN
ma-10	226	35	+2βn〈ψ(q)−	+2βn〈ψ(q)−	PROPN
ma-10	226	36	q	q	NOUN
ma-10	226	37	,	,	PUNCT
ma-10	226	38	un+1	un+1	ADV
ma-10	226	39	−	−	PROPN
ma-10	226	40	q	q	NOUN
ma-10	226	41	〉	〉	NOUN
ma-10	226	42	(	(	PUNCT
ma-10	226	43	3.17	3.17	NUM
ma-10	226	44	)	)	PUNCT
ma-10	226	45	for	for	ADP
ma-10	226	46	the	the	DET
ma-10	226	47	fact	fact	NOUN
ma-10	226	48	that	that	SCONJ
ma-10	226	49	‖vn	‖vn	PROPN
ma-10	226	50	−	−	NOUN
ma-10	226	51	q‖2	q‖2	PROPN
ma-10	227	1	=	=	SYM
ma-10	227	2	∥∥∥γnt	∥∥∥γnt	NOUN
ma-10	227	3	n(snun	n(snun	NOUN
ma-10	227	4	+	+	CCONJ
ma-10	227	5	(	(	PUNCT
ma-10	227	6	1−	1−	NUM
ma-10	227	7	sn)un+1	sn)un+1	NOUN
ma-10	227	8	)	)	PUNCT
ma-10	227	9	(	(	PUNCT
ma-10	227	10	1−	1−	NUM
ma-10	227	11	βn	βn	NOUN
ma-10	227	12	)	)	PUNCT
ma-10	227	13	−	−	PROPN
ma-10	227	14	q	q	NOUN
ma-10	227	15	∥∥∥2	∥∥∥2	NOUN
ma-10	227	16	≤	≤	NUM
ma-10	227	17	γ2ns	γ2ns	SYM
ma-10	227	18	2	2	NUM
ma-10	227	19	nk	nk	PROPN
ma-10	227	20	2	2	NUM
ma-10	227	21	n	n	NOUN
ma-10	227	22	(	(	PUNCT
ma-10	227	23	1−	1−	NUM
ma-10	227	24	βn)2	βn)2	PROPN
ma-10	227	25	‖un	‖un	PROPN
ma-10	227	26	−	−	PROPN
ma-10	228	1	q‖2	q‖2	PROPN
ma-10	228	2	+	+	CCONJ
ma-10	228	3	γ2n(1−	γ2n(1−	ADJ
ma-10	228	4	sn)2k2n	sn)2k2n	NOUN
ma-10	228	5	(	(	PUNCT
ma-10	228	6	1−	1−	NUM
ma-10	228	7	βn)2	βn)2	PROPN
ma-10	228	8	‖un+1	‖un+1	PUNCT
ma-10	228	9	−	−	PROPN
ma-10	229	1	q‖2	q‖2	VERB
ma-10	229	2	+	+	CCONJ
ma-10	229	3	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	229	4	sn)k2n	sn)k2n	SYM
ma-10	229	5	(	(	PUNCT
ma-10	229	6	1−	1−	NUM
ma-10	229	7	βn)2	βn)2	PROPN
ma-10	229	8	〈	〈	PROPN
ma-10	229	9	un	un	PROPN
ma-10	229	10	−	−	PROPN
ma-10	229	11	q	q	PROPN
ma-10	229	12	,	,	PUNCT
ma-10	229	13	un+1	un+1	ADV
ma-10	229	14	−	−	PROPN
ma-10	230	1	q	q	NOUN
ma-10	230	2	〉	〉	NOUN
ma-10	230	3	≤	≤	NOUN
ma-10	230	4	γ2ns	γ2ns	SYM
ma-10	230	5	2	2	NUM
ma-10	230	6	nk	nk	PROPN
ma-10	230	7	2	2	NUM
ma-10	230	8	n	n	NOUN
ma-10	230	9	(	(	PUNCT
ma-10	230	10	1−	1−	NUM
ma-10	230	11	βn)2	βn)2	PROPN
ma-10	230	12	‖un	‖un	PROPN
ma-10	230	13	−	−	PROPN
ma-10	230	14	q‖2	q‖2	PROPN
ma-10	230	15	+	+	CCONJ
ma-10	230	16	γ2n(1−	γ2n(1−	ADJ
ma-10	230	17	sn)2k2n	sn)2k2n	NOUN
ma-10	230	18	(	(	PUNCT
ma-10	230	19	1−	1−	NUM
ma-10	230	20	βn)2	βn)2	PROPN
ma-10	230	21	‖un+1	‖un+1	PUNCT
ma-10	230	22	−	−	PROPN
ma-10	231	1	q‖2	q‖2	VERB
ma-10	231	2	+	+	CCONJ
ma-10	231	3	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	231	4	sn)k2n	sn)k2n	SYM
ma-10	231	5	(	(	PUNCT
ma-10	231	6	1−	1−	NUM
ma-10	231	7	βn)2	βn)2	PROPN
ma-10	231	8	‖un	‖un	PROPN
ma-10	232	1	−	−	PROPN
ma-10	232	2	q‖‖un+1	q‖‖un+1	NOUN
ma-10	232	3	−	−	PROPN
ma-10	233	1	q‖	q‖	NOUN
ma-10	233	2	+2αnβn	+2αnβn	PROPN
ma-10	233	3	〈	〈	PROPN
ma-10	233	4	ψ(un)−	ψ(un)−	PRON
ma-10	233	5	ψ(q	ψ(q	PROPN
ma-10	233	6	)	)	PUNCT
ma-10	233	7	,	,	PUNCT
ma-10	233	8	t	t	PROPN
ma-10	233	9	n	n	PROPN
ma-10	233	10	(	(	PUNCT
ma-10	233	11	un	un	PROPN
ma-10	233	12	+	+	CCONJ
ma-10	233	13	un+1	un+1	PROPN
ma-10	233	14	2	2	X
ma-10	233	15	)	)	PUNCT
ma-10	233	16	−	−	PRON
ma-10	233	17	q	q	SYM
ma-10	233	18	〉	〉	NOUN
ma-10	233	19	(	(	PUNCT
ma-10	233	20	3.18	3.18	NUM
ma-10	233	21	)	)	PUNCT
ma-10	233	22	now	now	ADV
ma-10	233	23	substituting	substitute	VERB
ma-10	233	24	3.18	3.18	NUM
ma-10	233	25	into	into	ADP
ma-10	233	26	3.17	3.17	NUM
ma-10	233	27	,	,	PUNCT
ma-10	233	28	we	we	PRON
ma-10	233	29	have	have	VERB
ma-10	233	30	the	the	DET
ma-10	233	31	following	follow	VERB
ma-10	233	32	estimation	estimation	NOUN
ma-10	233	33	‖un+1	‖un+1	PUNCT
ma-10	233	34	−	−	PROPN
ma-10	233	35	q‖2	q‖2	VERB
ma-10	233	36	≤	≤	NUM
ma-10	234	1	γ2ns	γ2ns	SYM
ma-10	234	2	2	2	NUM
ma-10	234	3	nk	nk	PROPN
ma-10	234	4	2	2	NUM
ma-10	234	5	n‖un	n‖un	PROPN
ma-10	234	6	−	−	NOUN
ma-10	234	7	q‖2	q‖2	NOUN
ma-10	234	8	+	+	CCONJ
ma-10	234	9	γ2n(1−	γ2n(1−	NOUN
ma-10	234	10	sn)2k2n‖un+1	sn)2k2n‖un+1	NOUN
ma-10	234	11	−	−	PROPN
ma-10	234	12	q‖2	q‖2	VERB
ma-10	234	13	+	+	NOUN
ma-10	234	14	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	234	15	sn)k2n‖un	sn)k2n‖un	NOUN
ma-10	234	16	−	−	PROPN
ma-10	234	17	q‖‖un+1	q‖‖un+1	NOUN
ma-10	234	18	−	−	NOUN
ma-10	234	19	q‖	q‖	NOUN
ma-10	234	20	+2(βnα+	+2(βnα+	PROPN
ma-10	234	21	αn)‖un	αn)‖un	NOUN
ma-10	234	22	−	−	PROPN
ma-10	235	1	q‖‖un+1	q‖‖un+1	NOUN
ma-10	235	2	−	−	NOUN
ma-10	235	3	q‖+	q‖+	ADJ
ma-10	235	4	2βn〈ψ(q)−	2βn〈ψ(q)−	NUM
ma-10	235	5	q	q	NOUN
ma-10	235	6	,	,	PUNCT
ma-10	235	7	un+1	un+1	ADV
ma-10	235	8	−	−	PROPN
ma-10	235	9	q	q	NOUN
ma-10	235	10	〉	〉	NOUN
ma-10	235	11	≤	≤	NOUN
ma-10	235	12	γ2ns	γ2ns	SYM
ma-10	235	13	2	2	NUM
ma-10	235	14	nk	nk	PROPN
ma-10	235	15	2	2	NUM
ma-10	235	16	n‖un	n‖un	PROPN
ma-10	235	17	−	−	NOUN
ma-10	235	18	q‖2	q‖2	NOUN
ma-10	235	19	+	+	CCONJ
ma-10	235	20	γ2n(1−	γ2n(1−	NOUN
ma-10	235	21	sn)2k2n‖un+1	sn)2k2n‖un+1	NOUN
ma-10	235	22	−	−	PROPN
ma-10	235	23	q‖2	q‖2	VERB
ma-10	235	24	+	+	CCONJ
ma-10	235	25	[	[	PUNCT
ma-10	235	26	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	235	27	sn)k2n	sn)k2n	PUNCT
ma-10	236	1	+	+	CCONJ
ma-10	236	2	2(βnα+	2(βnα+	NUM
ma-10	236	3	αn	αn	NOUN
ma-10	236	4	)	)	PUNCT
ma-10	236	5	]	]	PUNCT
ma-10	237	1	‖un	‖un	PROPN
ma-10	237	2	−	−	PROPN
ma-10	237	3	q‖‖un+1	q‖‖un+1	NOUN
ma-10	237	4	−	−	PROPN
ma-10	237	5	q‖	q‖	NOUN
ma-10	237	6	+2βn〈ψ(q)−	+2βn〈ψ(q)−	PROPN
ma-10	237	7	q	q	NOUN
ma-10	237	8	,	,	PUNCT
ma-10	237	9	un+1	un+1	ADV
ma-10	237	10	−	−	PROPN
ma-10	237	11	q	q	NOUN
ma-10	237	12	〉	〉	NOUN
ma-10	237	13	(	(	PUNCT
ma-10	237	14	3.19	3.19	NUM
ma-10	237	15	)	)	PUNCT
ma-10	237	16	eur	eur	PROPN
ma-10	237	17	.	.	PUNCT
ma-10	238	1	j.	j.	PROPN
ma-10	238	2	math	math	PROPN
ma-10	238	3	.	.	PUNCT
ma-10	239	1	anal	anal	ADJ
ma-10	239	2	.	.	PUNCT
ma-10	240	1	1	1	NUM
ma-10	240	2	(	(	PUNCT
ma-10	240	3	2021	2021	NUM
ma-10	240	4	)	)	PUNCT
ma-10	241	1	29again	29again	PUNCT
ma-10	242	1	using	use	VERB
ma-10	242	2	the	the	DET
ma-10	242	3	fact	fact	NOUN
ma-10	242	4	that	that	SCONJ
ma-10	242	5	(	(	PUNCT
ma-10	242	6	‖un	‖un	PROPN
ma-10	242	7	−	−	PROPN
ma-10	242	8	q‖	q‖	NOUN
ma-10	242	9	−	−	PROPN
ma-10	242	10	‖un+1	‖un+1	SYM
ma-10	242	11	−	−	PROPN
ma-10	242	12	q‖	q‖	NOUN
ma-10	242	13	)	)	PUNCT
ma-10	242	14	2	2	NUM
ma-10	242	15	≤	≤	NUM
ma-10	242	16	‖un	‖un	PROPN
ma-10	242	17	−	−	PROPN
ma-10	242	18	q‖2	q‖2	PROPN
ma-10	242	19	−	−	PROPN
ma-10	242	20	2‖un	2‖un	NOUN
ma-10	242	21	−	−	PROPN
ma-10	242	22	q‖‖un+1	q‖‖un+1	NOUN
ma-10	242	23	−	−	PROPN
ma-10	242	24	q‖	q‖	PROPN
ma-10	242	25	+	+	PROPN
ma-10	242	26	‖un+1	‖un+1	X
ma-10	242	27	−	−	PROPN
ma-10	242	28	q‖2	q‖2	NOUN
ma-10	242	29	setting	set	VERB
ma-10	242	30	the	the	DET
ma-10	242	31	left	left	ADJ
ma-10	242	32	hand	hand	NOUN
ma-10	242	33	to	to	ADP
ma-10	242	34	zero	zero	NUM
ma-10	242	35	,	,	PUNCT
ma-10	242	36	we	we	PRON
ma-10	242	37	have	have	VERB
ma-10	242	38	the	the	DET
ma-10	242	39	following	follow	VERB
ma-10	242	40	estimate	estimate	NOUN
ma-10	242	41	2‖un	2‖un	NOUN
ma-10	242	42	−	−	PROPN
ma-10	242	43	q‖‖un+1	q‖‖un+1	NOUN
ma-10	242	44	−	−	PROPN
ma-10	242	45	q‖	q‖	NOUN
ma-10	242	46	≤	≤	SCONJ
ma-10	242	47	‖un	‖un	PROPN
ma-10	242	48	−	−	PROPN
ma-10	242	49	q‖2	q‖2	PROPN
ma-10	242	50	+	+	CCONJ
ma-10	242	51	‖un+1	‖un+1	SYM
ma-10	242	52	−	−	NOUN
ma-10	242	53	q‖2	q‖2	VERB
ma-10	242	54	‖un	‖un	PROPN
ma-10	242	55	−	−	PROPN
ma-10	242	56	q‖‖un+1	q‖‖un+1	NOUN
ma-10	242	57	−	−	NOUN
ma-10	243	1	q‖	q‖	NOUN
ma-10	243	2	≤	≤	ADV
ma-10	243	3	1	1	NUM
ma-10	243	4	2	2	NUM
ma-10	243	5	‖un	‖un	PROPN
ma-10	243	6	−	−	NOUN
ma-10	243	7	q‖2	q‖2	PROPN
ma-10	243	8	+	+	CCONJ
ma-10	243	9	1	1	NUM
ma-10	243	10	2	2	NUM
ma-10	243	11	‖un+1	‖un+1	NUM
ma-10	243	12	−	−	NOUN
ma-10	243	13	q‖2	q‖2	PROPN
ma-10	243	14	(	(	PUNCT
ma-10	243	15	3.20	3.20	NUM
ma-10	243	16	)	)	PUNCT
ma-10	243	17	putting	put	VERB
ma-10	243	18	inequality	inequality	NOUN
ma-10	243	19	3.20	3.20	NUM
ma-10	243	20	in	in	ADP
ma-10	243	21	inequality	inequality	NOUN
ma-10	243	22	3.19	3.19	NUM
ma-10	243	23	,	,	PUNCT
ma-10	243	24	gives	give	VERB
ma-10	243	25	the	the	DET
ma-10	243	26	following	follow	VERB
ma-10	243	27	‖un+1	‖un+1	PUNCT
ma-10	243	28	−	−	NOUN
ma-10	243	29	q‖2	q‖2	VERB
ma-10	243	30	≤	≤	NUM
ma-10	243	31	γ2ns	γ2ns	SYM
ma-10	243	32	2	2	NUM
ma-10	243	33	nk	nk	PROPN
ma-10	243	34	2	2	NUM
ma-10	243	35	n‖un	n‖un	PROPN
ma-10	243	36	−	−	NOUN
ma-10	243	37	q‖2	q‖2	NOUN
ma-10	243	38	+	+	CCONJ
ma-10	243	39	γ2n(1−	γ2n(1−	NOUN
ma-10	243	40	sn)2k2n‖un+1	sn)2k2n‖un+1	NOUN
ma-10	243	41	−	−	NOUN
ma-10	243	42	q‖2	q‖2	PROPN
ma-10	244	1	+	+	CCONJ
ma-10	244	2	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	244	3	sn)k2n	sn)k2n	SYM
ma-10	244	4	2	2	NUM
ma-10	244	5	‖un	‖un	PROPN
ma-10	244	6	−	−	PROPN
ma-10	244	7	q‖2	q‖2	PROPN
ma-10	244	8	+	+	CCONJ
ma-10	244	9	(	(	PUNCT
ma-10	244	10	βnα+	βnα+	ADJ
ma-10	244	11	αn)‖un	αn)‖un	NOUN
ma-10	244	12	−	−	PROPN
ma-10	244	13	q‖2	q‖2	VERB
ma-10	244	14	+	+	CCONJ
ma-10	244	15	γ2nsn(1−	γ2nsn(1−	NUM
ma-10	244	16	sn)k2n	sn)k2n	SYM
ma-10	244	17	2	2	NUM
ma-10	244	18	‖un+1	‖un+1	NUM
ma-10	244	19	−	−	NOUN
ma-10	244	20	q‖2	q‖2	PROPN
ma-10	245	1	+	+	CCONJ
ma-10	245	2	(	(	PUNCT
ma-10	245	3	βnα+	βnα+	PROPN
ma-10	245	4	αn)‖un+1	αn)‖un+1	PROPN
ma-10	245	5	−	−	NOUN
ma-10	245	6	q‖2	q‖2	VERB
ma-10	245	7	+2βn〈ψ(q)−	+2βn〈ψ(q)−	NUM
ma-10	245	8	q	q	NOUN
ma-10	245	9	,	,	PUNCT
ma-10	245	10	un+1	un+1	ADV
ma-10	245	11	−	−	PROPN
ma-10	245	12	q	q	PROPN
ma-10	245	13	〉	〉	PROPN
ma-10	245	14	‖un+1	‖un+1	SYM
ma-10	245	15	−	−	PROPN
ma-10	245	16	q‖2	q‖2	VERB
ma-10	245	17	≤	≤	NOUN
ma-10	246	1	[	[	X
ma-10	246	2	γ2nsnk2n	γ2nsnk2n	PROPN
ma-10	246	3	(	(	PUNCT
ma-10	246	4	sn	sn	PROPN
ma-10	246	5	+	+	PROPN
ma-10	246	6	1	1	X
ma-10	246	7	)	)	PUNCT
ma-10	246	8	+	+	CCONJ
ma-10	246	9	2(βnα+	2(βnα+	NUM
ma-10	246	10	αn	αn	NOUN
ma-10	246	11	)	)	PUNCT
ma-10	246	12	2	2	NUM
ma-10	246	13	]	]	PUNCT
ma-10	246	14	‖un	‖un	PROPN
ma-10	246	15	−	−	PROPN
ma-10	246	16	q‖2	q‖2	PROPN
ma-10	246	17	+	+	CCONJ
ma-10	247	1	[	[	X
ma-10	247	2	γ2n(1−	γ2n(1−	X
ma-10	247	3	sn)2k2n	sn)2k2n	NOUN
ma-10	247	4	(	(	PUNCT
ma-10	247	5	2−	2−	NUM
ma-10	247	6	sn	sn	NOUN
ma-10	247	7	)	)	PUNCT
ma-10	248	1	+	+	CCONJ
ma-10	248	2	2(βnα+	2(βnα+	NUM
ma-10	248	3	αn	αn	NOUN
ma-10	248	4	)	)	PUNCT
ma-10	248	5	2	2	NUM
ma-10	248	6	]	]	PUNCT
ma-10	248	7	‖un+1	‖un+1	PUNCT
ma-10	248	8	−	−	PROPN
ma-10	248	9	q‖2	q‖2	VERB
ma-10	248	10	+2βn〈ψ(q)−	+2βn〈ψ(q)−	NUM
ma-10	248	11	q	q	NOUN
ma-10	248	12	,	,	PUNCT
ma-10	248	13	un+1	un+1	ADV
ma-10	248	14	−	−	PROPN
ma-10	249	1	q	q	NOUN
ma-10	249	2	〉	〉	NOUN
ma-10	249	3	thus	thus	ADV
ma-10	249	4	we	we	PRON
ma-10	249	5	have	have	VERB
ma-10	249	6	(	(	PUNCT
ma-10	249	7	1−	1−	NUM
ma-10	250	1	[	[	X
ma-10	250	2	γ2n(1−	γ2n(1−	X
ma-10	250	3	sn)2k2n	sn)2k2n	NOUN
ma-10	250	4	(	(	PUNCT
ma-10	250	5	2−	2−	NUM
ma-10	250	6	sn	sn	NOUN
ma-10	250	7	)	)	PUNCT
ma-10	251	1	+	+	CCONJ
ma-10	251	2	2(βnα+	2(βnα+	NUM
ma-10	251	3	αn	αn	NOUN
ma-10	251	4	)	)	PUNCT
ma-10	251	5	2	2	NUM
ma-10	251	6	]	]	PUNCT
ma-10	251	7	)	)	PUNCT
ma-10	251	8	‖un+1	‖un+1	PUNCT
ma-10	252	1	−	−	PROPN
ma-10	252	2	q‖2	q‖2	VERB
ma-10	252	3	≤	≤	NOUN
ma-10	253	1	[	[	X
ma-10	253	2	γ2nsnk2n	γ2nsnk2n	PROPN
ma-10	253	3	(	(	PUNCT
ma-10	253	4	sn	sn	PROPN
ma-10	253	5	+	+	PROPN
ma-10	253	6	1	1	X
ma-10	253	7	)	)	PUNCT
ma-10	253	8	+	+	CCONJ
ma-10	253	9	2(βnα+	2(βnα+	NUM
ma-10	253	10	αn	αn	NOUN
ma-10	253	11	)	)	PUNCT
ma-10	253	12	2	2	NUM
ma-10	253	13	]	]	PUNCT
ma-10	253	14	‖un	‖un	PROPN
ma-10	253	15	−	−	PROPN
ma-10	253	16	q‖2	q‖2	PROPN
ma-10	253	17	+	+	CCONJ
ma-10	253	18	2βn〈ψ(q)−	2βn〈ψ(q)−	NUM
ma-10	253	19	q	q	ADJ
ma-10	253	20	,	,	PUNCT
ma-10	253	21	un+1	un+1	ADV
ma-10	253	22	−	−	PROPN
ma-10	253	23	q	q	PROPN
ma-10	253	24	〉	〉	PROPN
ma-10	253	25	‖un+1	‖un+1	SYM
ma-10	253	26	−	−	PROPN
ma-10	253	27	q‖2	q‖2	VERB
ma-10	253	28	≤	≤	NUM
ma-10	253	29	γ2nsnk	γ2nsnk	VERB
ma-10	253	30	2	2	NUM
ma-10	253	31	n	n	NOUN
ma-10	253	32	(	(	PUNCT
ma-10	253	33	sn	sn	PROPN
ma-10	253	34	+	+	NOUN
ma-10	253	35	1	1	X
ma-10	253	36	)	)	PUNCT
ma-10	253	37	+	+	CCONJ
ma-10	253	38	2(βnα+	2(βnα+	NUM
ma-10	253	39	αn	αn	NOUN
ma-10	253	40	)	)	PUNCT
ma-10	253	41	2−	2−	NUM
ma-10	253	42	[	[	PUNCT
ma-10	253	43	γ2n(1−	γ2n(1−	X
ma-10	253	44	sn)2k2n	sn)2k2n	NOUN
ma-10	253	45	(	(	PUNCT
ma-10	253	46	2−	2−	NUM
ma-10	253	47	sn	sn	NOUN
ma-10	253	48	)	)	PUNCT
ma-10	254	1	+	+	CCONJ
ma-10	254	2	2(βnα+	2(βnα+	NUM
ma-10	254	3	αn	αn	NOUN
ma-10	254	4	)	)	PUNCT
ma-10	254	5	]	]	PUNCT
ma-10	254	6	‖un	‖un	PROPN
ma-10	254	7	−	−	PROPN
ma-10	254	8	q‖2	q‖2	PROPN
ma-10	254	9	+	+	CCONJ
ma-10	254	10	4βn	4βn	ADJ
ma-10	254	11	2−	2−	NUM
ma-10	254	12	[	[	PUNCT
ma-10	254	13	γ2n(1−	γ2n(1−	X
ma-10	254	14	sn)2k2n	sn)2k2n	NOUN
ma-10	254	15	(	(	PUNCT
ma-10	254	16	2−	2−	NUM
ma-10	254	17	sn	sn	NOUN
ma-10	254	18	)	)	PUNCT
ma-10	255	1	+	+	CCONJ
ma-10	255	2	2(βnα+	2(βnα+	NUM
ma-10	255	3	αn	αn	NOUN
ma-10	255	4	)	)	PUNCT
ma-10	255	5	]	]	PUNCT
ma-10	255	6	〈	〈	X
ma-10	255	7	ψ(q)−	ψ(q)−	NOUN
ma-10	255	8	q	q	NOUN
ma-10	255	9	,	,	PUNCT
ma-10	255	10	un+1	un+1	ADV
ma-10	255	11	−	−	PROPN
ma-10	255	12	q	q	PROPN
ma-10	255	13	〉	〉	PROPN
ma-10	255	14	‖un+1	‖un+1	SYM
ma-10	255	15	−	−	PROPN
ma-10	255	16	q‖2	q‖2	VERB
ma-10	255	17	≤	≤	NUM
ma-10	255	18	(	(	PUNCT
ma-10	255	19	1−	1−	NUM
ma-10	255	20	2−	2−	NUM
ma-10	255	21	γ2n(1−	γ2n(1−	NOUN
ma-10	255	22	sn)2k2n	sn)2k2n	NOUN
ma-10	255	23	(	(	PUNCT
ma-10	255	24	2−	2−	NUM
ma-10	255	25	sn)−	sn)−	NOUN
ma-10	255	26	γ2nsnk2n	γ2nsnk2n	PROPN
ma-10	255	27	(	(	PUNCT
ma-10	255	28	sn	sn	PROPN
ma-10	256	1	+	+	PROPN
ma-10	256	2	1	1	NUM
ma-10	256	3	)	)	PUNCT
ma-10	256	4	2−	2−	NUM
ma-10	256	5	[	[	PUNCT
ma-10	256	6	γ2n(1−	γ2n(1−	X
ma-10	256	7	sn)2k2n	sn)2k2n	NOUN
ma-10	256	8	(	(	PUNCT
ma-10	256	9	2−	2−	NUM
ma-10	256	10	sn	sn	NOUN
ma-10	256	11	)	)	PUNCT
ma-10	257	1	+	+	CCONJ
ma-10	257	2	2(βnα+	2(βnα+	NUM
ma-10	257	3	αn	αn	NOUN
ma-10	257	4	)	)	PUNCT
ma-10	257	5	]	]	PUNCT
ma-10	257	6	)	)	PUNCT
ma-10	258	1	‖un	‖un	PROPN
ma-10	258	2	−	−	PROPN
ma-10	258	3	q‖2	q‖2	PROPN
ma-10	258	4	+	+	CCONJ
ma-10	258	5	4βn	4βn	ADJ
ma-10	258	6	2−	2−	NUM
ma-10	258	7	[	[	PUNCT
ma-10	258	8	γ2n(1−	γ2n(1−	X
ma-10	258	9	sn)2k2n	sn)2k2n	NOUN
ma-10	258	10	(	(	PUNCT
ma-10	258	11	2−	2−	NUM
ma-10	258	12	sn	sn	NOUN
ma-10	258	13	)	)	PUNCT
ma-10	258	14	+	+	CCONJ
ma-10	258	15	2(βnα+	2(βnα+	NUM
ma-10	258	16	αn	αn	NOUN
ma-10	258	17	)	)	PUNCT
ma-10	258	18	]	]	PUNCT
ma-10	258	19	〈	〈	X
ma-10	258	20	ψ(q)−	ψ(q)−	NOUN
ma-10	258	21	q	q	NOUN
ma-10	258	22	,	,	PUNCT
ma-10	258	23	un+1	un+1	ADV
ma-10	258	24	−	−	PROPN
ma-10	258	25	q	q	NOUN
ma-10	258	26	〉	〉	PROPN
ma-10	258	27	eur	eur	NOUN
ma-10	258	28	.	.	PUNCT
ma-10	259	1	j.	j.	PROPN
ma-10	259	2	math	math	PROPN
ma-10	259	3	.	.	PUNCT
ma-10	260	1	anal	anal	ADJ
ma-10	260	2	.	.	PUNCT
ma-10	261	1	1	1	NUM
ma-10	261	2	(	(	PUNCT
ma-10	261	3	2021	2021	NUM
ma-10	261	4	)	)	PUNCT
ma-10	262	1	30therefore	30therefore	NUM
ma-10	262	2	from	from	ADP
ma-10	262	3	condition	condition	NOUN
ma-10	262	4	lim	lim	PROPN
ma-10	262	5	n→∞	n→∞	NUM
ma-10	262	6	αn	αn	NOUN
ma-10	263	1	=	=	PROPN
ma-10	263	2	lim	lim	PROPN
ma-10	263	3	n→∞	n→∞	NUM
ma-10	263	4	βn	βn	PROPN
ma-10	263	5	=	=	PUNCT
ma-10	263	6	lim	lim	PROPN
ma-10	263	7	n→∞	n→∞	X
ma-10	263	8	sn	sn	PROPN
ma-10	263	9	=	=	NOUN
ma-10	263	10	0	0	NUM
ma-10	263	11	in	in	ADP
ma-10	263	12	3.1	3.1	NUM
ma-10	263	13	,	,	PUNCT
ma-10	263	14	we	we	PRON
ma-10	263	15	concludes	conclude	VERB
ma-10	263	16	that	that	PRON
ma-10	263	17	‖un+1	‖un+1	PUNCT
ma-10	263	18	−	−	PROPN
ma-10	263	19	q‖2	q‖2	VERB
ma-10	263	20	≤	≤	NUM
ma-10	263	21	(	(	PUNCT
ma-10	263	22	1−	1−	NUM
ma-10	263	23	2−	2−	NUM
ma-10	263	24	2γ2nk	2γ2nk	NUM
ma-10	263	25	2	2	NUM
ma-10	263	26	n	n	NUM
ma-10	263	27	2−	2−	NUM
ma-10	263	28	2γ2nk	2γ2nk	NUM
ma-10	263	29	2	2	NUM
ma-10	263	30	n	n	NOUN
ma-10	263	31	)	)	PUNCT
ma-10	264	1	‖un	‖un	PROPN
ma-10	264	2	−	−	PROPN
ma-10	264	3	q‖2	q‖2	PROPN
ma-10	264	4	lim	lim	PROPN
ma-10	264	5	n→∞	n→∞	X
ma-10	264	6	‖un+1	‖un+1	SYM
ma-10	264	7	−	−	PROPN
ma-10	264	8	q‖2	q‖2	PROPN
ma-10	264	9	=	=	SYM
ma-10	264	10	0	0	NUM
ma-10	265	1	this	this	PRON
ma-10	265	2	complete	complete	ADJ
ma-10	265	3	the	the	DET
ma-10	265	4	proof	proof	NOUN
ma-10	265	5	.	.	PUNCT
ma-10	266	1	�	�	PROPN
ma-10	266	2	theorem	theorem	VERB
ma-10	266	3	3.3	3.3	NUM
ma-10	266	4	.	.	PUNCT
ma-10	267	1	let	let	VERB
ma-10	267	2	m	m	PRON
ma-10	267	3	be	be	AUX
ma-10	267	4	a	a	DET
ma-10	267	5	nonempty	nonempty	ADV
ma-10	267	6	closed	close	VERB
ma-10	267	7	convex	convex	NOUN
ma-10	267	8	subset	subset	VERB
ma-10	267	9	a	a	DET
ma-10	267	10	real	real	ADJ
ma-10	267	11	hilbert	hilbert	NOUN
ma-10	267	12	space	space	NOUN
ma-10	267	13	h	h	PROPN
ma-10	267	14	,	,	PUNCT
ma-10	267	15	t	t	X
ma-10	267	16	:	:	PUNCT
ma-10	267	17	m	m	VERB
ma-10	267	18	→	→	PUNCT
ma-10	267	19	m	m	AUX
ma-10	267	20	be	be	VERB
ma-10	267	21	asymptotically	asymptotically	ADV
ma-10	267	22	nonexpansive	nonexpansive	ADJ
ma-10	267	23	mappings	mapping	NOUN
ma-10	267	24	with	with	ADP
ma-10	267	25	the	the	DET
ma-10	267	26	same	same	ADJ
ma-10	267	27	sequence	sequence	NOUN
ma-10	267	28	{	{	PUNCT
ma-10	267	29	kn	kn	PROPN
ma-10	267	30	}	}	PUNCT
ma-10	267	31	⊆	⊆	NUM
ma-10	267	32	[	[	X
ma-10	267	33	1,∞	1,∞	NUM
ma-10	267	34	)	)	PUNCT
ma-10	267	35	such	such	ADJ
ma-10	267	36	that	that	SCONJ
ma-10	267	37	limn→∞	limn→∞	PROPN
ma-10	267	38	kn	kn	NOUN
ma-10	267	39	=	=	SYM
ma-10	267	40	1	1	NUM
ma-10	267	41	,	,	PUNCT
ma-10	267	42	f	f	PROPN
ma-10	267	43	ix(t	ix(t	ADJ
ma-10	267	44	)	)	PUNCT
ma-10	267	45	6=	6=	ADP
ma-10	267	46	∅	∅	NOUN
ma-10	267	47	and	and	CCONJ
ma-10	267	48	ω	ω	NUM
ma-10	267	49	be	be	AUX
ma-10	267	50	a	a	DET
ma-10	267	51	constant	constant	ADJ
ma-10	267	52	.	.	PUNCT
ma-10	268	1	define	define	VERB
ma-10	268	2	a	a	DET
ma-10	268	3	sequence	sequence	NOUN
ma-10	268	4	{	{	PUNCT
ma-10	268	5	un	un	PROPN
ma-10	268	6	}	}	PUNCT
ma-10	268	7	in	in	ADP
ma-10	268	8	m	m	PROPN
ma-10	268	9	as	as	ADP
ma-10	268	10	follows:	follows:	NOUN
ma-10	268	11	u1	u1	PROPN
ma-10	268	12	∈m	∈m	NOUN
ma-10	268	13	un+1	un+1	NOUN
ma-10	268	14	=	=	NOUN
ma-10	268	15	αnun	αnun	PROPN
ma-10	268	16	+	+	CCONJ
ma-10	268	17	βnω	βnω	NOUN
ma-10	269	1	+	+	CCONJ
ma-10	269	2	γnt	γnt	ADJ
ma-10	269	3	n	n	CCONJ
ma-10	269	4	(	(	PUNCT
ma-10	269	5	snun	snun	NOUN
ma-10	269	6	+	+	CCONJ
ma-10	269	7	(	(	PUNCT
ma-10	269	8	1−	1−	NUM
ma-10	269	9	sn)un+1	sn)un+1	NOUN
ma-10	269	10	)	)	PUNCT
ma-10	270	1	∀n	∀n	NUM
ma-10	270	2	∈	∈	PROPN
ma-10	270	3	n	n	CCONJ
ma-10	270	4	(	(	PUNCT
ma-10	270	5	3.21	3.21	NUM
ma-10	270	6	)	)	PUNCT
ma-10	270	7	where	where	SCONJ
ma-10	270	8	αn	αn	NOUN
ma-10	270	9	,	,	PUNCT
ma-10	270	10	βn	βn	NOUN
ma-10	270	11	,	,	PUNCT
ma-10	270	12	γn	γn	NUM
ma-10	270	13	,	,	PUNCT
ma-10	270	14	sn	sn	PROPN
ma-10	270	15	∈	∈	PROPN
ma-10	270	16	(	(	PUNCT
ma-10	270	17	0	0	NUM
ma-10	270	18	,	,	PUNCT
ma-10	270	19	1	1	X
ma-10	270	20	)	)	PUNCT
ma-10	270	21	satisfying	satisfy	VERB
ma-10	270	22	conditions	condition	NOUN
ma-10	270	23	a1−	a1−	NOUN
ma-10	270	24	a4	a4	NOUN
ma-10	270	25	and	and	CCONJ
ma-10	270	26	ψ(un	ψ(un	PROPN
ma-10	270	27	)	)	PUNCT
ma-10	270	28	=	=	PUNCT
ma-10	270	29	ω	ω	PROPN
ma-10	270	30	lim	lim	PROPN
ma-10	270	31	n→∞	n→∞	NUM
ma-10	270	32	‖t	‖t	PROPN
ma-10	270	33	nun	nun	NOUN
ma-10	270	34	−	−	NOUN
ma-10	270	35	un‖	un‖	X
ma-10	270	36	=	=	PUNCT
ma-10	270	37	0	0	NUM
ma-10	270	38	then	then	ADV
ma-10	270	39	the	the	DET
ma-10	270	40	sequence	sequence	NOUN
ma-10	270	41	{	{	PUNCT
ma-10	270	42	un	un	PROPN
ma-10	270	43	}	}	PUNCT
ma-10	270	44	strongly	strongly	ADV
ma-10	270	45	converges	converge	VERB
ma-10	270	46	to	to	ADP
ma-10	270	47	a	a	DET
ma-10	270	48	common	common	ADJ
ma-10	270	49	fixed	fix	VERB
ma-10	270	50	point	point	NOUN
ma-10	270	51	q	q	PROPN
ma-10	270	52	of	of	ADP
ma-10	270	53	t	t	PROPN
ma-10	270	54	,	,	PUNCT
ma-10	270	55	which	which	PRON
ma-10	270	56	is	be	AUX
ma-10	270	57	also	also	ADV
ma-10	270	58	the	the	DET
ma-10	270	59	unique	unique	ADJ
ma-10	270	60	solution	solution	NOUN
ma-10	270	61	of	of	ADP
ma-10	270	62	the	the	DET
ma-10	270	63	following	follow	VERB
ma-10	270	64	variational	variational	ADJ
ma-10	270	65	inequality	inequality	NOUN
ma-10	270	66	〈	〈	PROPN
ma-10	270	67	(	(	PUNCT
ma-10	270	68	i	i	NOUN
ma-10	270	69	−	−	PROPN
ma-10	270	70	ψ)u	ψ)u	NOUN
ma-10	270	71	,	,	PUNCT
ma-10	270	72	p	p	NOUN
ma-10	270	73	−	−	PROPN
ma-10	270	74	u	u	NOUN
ma-10	270	75	〉	〉	PROPN
ma-10	270	76	≥	≥	NOUN
ma-10	270	77	0	0	NUM
ma-10	271	1	p	p	X
ma-10	271	2	∈	∈	PROPN
ma-10	271	3	f	f	X
ma-10	271	4	(	(	PUNCT
ma-10	271	5	t	t	PROPN
ma-10	271	6	)	)	PUNCT
ma-10	271	7	.	.	PUNCT
ma-10	272	1	taking	take	VERB
ma-10	272	2	sn	sn	PROPN
ma-10	272	3	=	=	SYM
ma-10	272	4	0the	0the	NUM
ma-10	272	5	following	follow	VERB
ma-10	272	6	corollaries	corollary	NOUN
ma-10	272	7	holds	hold	VERB
ma-10	272	8	:	:	PUNCT
ma-10	272	9	corollary	corollary	ADJ
ma-10	272	10	3.4	3.4	NUM
ma-10	272	11	.	.	PUNCT
ma-10	273	1	let	let	VERB
ma-10	273	2	m	m	PRON
ma-10	273	3	be	be	AUX
ma-10	273	4	a	a	DET
ma-10	273	5	nonempty	nonempty	ADV
ma-10	273	6	closed	close	VERB
ma-10	273	7	convex	convex	NOUN
ma-10	273	8	subset	subset	VERB
ma-10	273	9	a	a	DET
ma-10	273	10	real	real	ADJ
ma-10	273	11	hilbert	hilbert	NOUN
ma-10	273	12	space	space	NOUN
ma-10	273	13	h	h	PROPN
ma-10	273	14	,	,	PUNCT
ma-10	273	15	t	t	X
ma-10	273	16	:	:	PUNCT
ma-10	273	17	m	m	VERB
ma-10	273	18	→	→	PUNCT
ma-10	273	19	m	m	AUX
ma-10	273	20	be	be	VERB
ma-10	273	21	asymptotically	asymptotically	ADV
ma-10	273	22	nonexpansive	nonexpansive	ADJ
ma-10	273	23	mappings	mapping	NOUN
ma-10	273	24	with	with	ADP
ma-10	273	25	the	the	DET
ma-10	273	26	same	same	ADJ
ma-10	273	27	sequence	sequence	NOUN
ma-10	273	28	{	{	PUNCT
ma-10	273	29	kn	kn	PROPN
ma-10	273	30	}	}	PUNCT
ma-10	273	31	⊆	⊆	NUM
ma-10	273	32	[	[	X
ma-10	273	33	1,∞	1,∞	NUM
ma-10	273	34	)	)	PUNCT
ma-10	273	35	such	such	ADJ
ma-10	273	36	that	that	SCONJ
ma-10	273	37	limn→∞	limn→∞	PROPN
ma-10	273	38	kn	kn	NOUN
ma-10	273	39	=	=	SYM
ma-10	273	40	1	1	NUM
ma-10	273	41	,	,	PUNCT
ma-10	273	42	f	f	PROPN
ma-10	273	43	ix(t	ix(t	ADJ
ma-10	273	44	)	)	PUNCT
ma-10	273	45	6=	6=	ADP
ma-10	273	46	∅	∅	NOUN
ma-10	273	47	and	and	CCONJ
ma-10	273	48	ψ	ψ	X
ma-10	273	49	:	:	PUNCT
ma-10	273	50	m	m	VERB
ma-10	273	51	→	→	NOUN
ma-10	273	52	m	m	AUX
ma-10	273	53	be	be	AUX
ma-10	273	54	a	a	DET
ma-10	273	55	contraction	contraction	NOUN
ma-10	273	56	mapping	mapping	NOUN
ma-10	273	57	with	with	ADP
ma-10	273	58	the	the	DET
ma-10	273	59	contractive	contractive	ADJ
ma-10	273	60	constant	constant	ADJ
ma-10	273	61	α	α	PRON
ma-10	273	62	∈	∈	PROPN
ma-10	274	1	[	[	X
ma-10	274	2	0	0	NUM
ma-10	274	3	,	,	PUNCT
ma-10	274	4	1	1	NUM
ma-10	274	5	)	)	PUNCT
ma-10	274	6	.	.	PUNCT
ma-10	275	1	define	define	VERB
ma-10	275	2	a	a	DET
ma-10	275	3	sequence	sequence	NOUN
ma-10	275	4	{	{	PUNCT
ma-10	275	5	un	un	PROPN
ma-10	275	6	}	}	PUNCT
ma-10	275	7	in	in	ADP
ma-10	275	8	m	m	NOUN
ma-10	275	9	as	as	SCONJ
ma-10	275	10	follows	follow	VERB
ma-10	275	11	:	:	PUNCT
ma-10	275	12	{	{	PUNCT
ma-10	275	13	u1	u1	NOUN
ma-10	275	14	∈m	∈m	NOUN
ma-10	275	15	un+1	un+1	NOUN
ma-10	275	16	=	=	NOUN
ma-10	275	17	αnun	αnun	ADJ
ma-10	275	18	+	+	CCONJ
ma-10	275	19	βnψ(un	βnψ(un	NUM
ma-10	275	20	)	)	PUNCT
ma-10	276	1	+	+	CCONJ
ma-10	276	2	γnt	γnt	ADJ
ma-10	276	3	n(un+1	n(un+1	NUM
ma-10	276	4	)	)	PUNCT
ma-10	276	5	∀n	∀n	NUM
ma-10	277	1	∈	∈	PROPN
ma-10	277	2	n	n	CCONJ
ma-10	277	3	(	(	PUNCT
ma-10	277	4	3.22	3.22	NUM
ma-10	277	5	)	)	PUNCT
ma-10	277	6	where	where	SCONJ
ma-10	277	7	αn	αn	NOUN
ma-10	277	8	,	,	PUNCT
ma-10	277	9	βn	βn	ADJ
ma-10	277	10	,	,	PUNCT
ma-10	277	11	γn	γn	ADP
ma-10	277	12	∈	∈	PROPN
ma-10	277	13	(	(	PUNCT
ma-10	277	14	0	0	NUM
ma-10	277	15	,	,	PUNCT
ma-10	277	16	1	1	X
ma-10	277	17	)	)	PUNCT
ma-10	277	18	satisfying	satisfy	VERB
ma-10	277	19	conditions	condition	NOUN
ma-10	277	20	a1−	a1−	ADP
ma-10	277	21	a4	a4	NOUN
ma-10	277	22	without	without	ADP
ma-10	277	23	lim	lim	PROPN
ma-10	277	24	n→∞	n→∞	X
ma-10	277	25	sn	sn	PROPN
ma-10	277	26	=	=	SYM
ma-10	277	27	0	0	NUM
ma-10	278	1	lim	lim	PROPN
ma-10	278	2	n→∞	n→∞	NUM
ma-10	278	3	‖t	‖t	PROPN
ma-10	278	4	nun	nun	NOUN
ma-10	278	5	−	−	NOUN
ma-10	278	6	un‖	un‖	X
ma-10	278	7	=	=	PUNCT
ma-10	278	8	0	0	NUM
ma-10	278	9	then	then	ADV
ma-10	278	10	the	the	DET
ma-10	278	11	sequence	sequence	NOUN
ma-10	278	12	{	{	PUNCT
ma-10	278	13	un	un	PROPN
ma-10	278	14	}	}	PUNCT
ma-10	278	15	strongly	strongly	ADV
ma-10	278	16	converges	converge	VERB
ma-10	278	17	to	to	ADP
ma-10	278	18	a	a	DET
ma-10	278	19	common	common	ADJ
ma-10	278	20	fixed	fix	VERB
ma-10	278	21	point	point	NOUN
ma-10	278	22	q	q	PROPN
ma-10	278	23	of	of	ADP
ma-10	278	24	t	t	PROPN
ma-10	278	25	,	,	PUNCT
ma-10	278	26	which	which	PRON
ma-10	278	27	is	be	AUX
ma-10	278	28	also	also	ADV
ma-10	278	29	the	the	DET
ma-10	278	30	unique	unique	ADJ
ma-10	278	31	solution	solution	NOUN
ma-10	278	32	of	of	ADP
ma-10	278	33	the	the	DET
ma-10	278	34	following	follow	VERB
ma-10	278	35	variational	variational	ADJ
ma-10	278	36	inequality	inequality	NOUN
ma-10	278	37	〈	〈	PROPN
ma-10	278	38	(	(	PUNCT
ma-10	278	39	i	i	NOUN
ma-10	278	40	−	−	PROPN
ma-10	278	41	ψ)u	ψ)u	NOUN
ma-10	278	42	,	,	PUNCT
ma-10	278	43	p	p	NOUN
ma-10	278	44	−	−	PROPN
ma-10	278	45	u	u	NOUN
ma-10	278	46	〉	〉	PROPN
ma-10	278	47	≥	≥	NOUN
ma-10	278	48	0	0	NUM
ma-10	279	1	p	p	X
ma-10	279	2	∈	∈	PROPN
ma-10	279	3	f	f	X
ma-10	279	4	(	(	PUNCT
ma-10	279	5	t	t	PROPN
ma-10	279	6	)	)	PUNCT
ma-10	279	7	.	.	PUNCT
ma-10	280	1	eur	eur	PROPN
ma-10	280	2	.	.	PUNCT
ma-10	281	1	j.	j.	PROPN
ma-10	281	2	math	math	PROPN
ma-10	281	3	.	.	PUNCT
ma-10	282	1	anal	anal	ADJ
ma-10	282	2	.	.	PUNCT
ma-10	283	1	1	1	NUM
ma-10	283	2	(	(	PUNCT
ma-10	283	3	2021	2021	NUM
ma-10	283	4	)	)	PUNCT
ma-10	283	5	31	31	NUM
ma-10	284	1	corollary	corollary	NOUN
ma-10	284	2	3.5	3.5	NUM
ma-10	284	3	.	.	PUNCT
ma-10	285	1	let	let	VERB
ma-10	285	2	m	m	PRON
ma-10	285	3	be	be	AUX
ma-10	285	4	a	a	DET
ma-10	285	5	nonempty	nonempty	ADV
ma-10	285	6	closed	close	VERB
ma-10	285	7	convex	convex	NOUN
ma-10	285	8	subset	subset	VERB
ma-10	285	9	a	a	DET
ma-10	285	10	real	real	ADJ
ma-10	285	11	hilbert	hilbert	NOUN
ma-10	285	12	space	space	NOUN
ma-10	285	13	h	h	PROPN
ma-10	285	14	,	,	PUNCT
ma-10	285	15	t	t	X
ma-10	285	16	:	:	PUNCT
ma-10	285	17	m	m	VERB
ma-10	285	18	→	→	PUNCT
ma-10	285	19	m	m	AUX
ma-10	285	20	be	be	VERB
ma-10	285	21	asymptotically	asymptotically	ADV
ma-10	285	22	nonexpansive	nonexpansive	ADJ
ma-10	285	23	mappings	mapping	NOUN
ma-10	285	24	with	with	ADP
ma-10	285	25	the	the	DET
ma-10	285	26	same	same	ADJ
ma-10	285	27	sequence	sequence	NOUN
ma-10	285	28	{	{	PUNCT
ma-10	285	29	kn	kn	PROPN
ma-10	285	30	}	}	PUNCT
ma-10	285	31	⊆	⊆	NUM
ma-10	285	32	[	[	X
ma-10	285	33	1,∞	1,∞	NUM
ma-10	285	34	)	)	PUNCT
ma-10	285	35	such	such	ADJ
ma-10	285	36	that	that	SCONJ
ma-10	285	37	limn→∞	limn→∞	PROPN
ma-10	285	38	kn	kn	NOUN
ma-10	285	39	=	=	SYM
ma-10	285	40	1	1	NUM
ma-10	285	41	,	,	PUNCT
ma-10	285	42	f	f	PROPN
ma-10	285	43	ix(t	ix(t	ADJ
ma-10	285	44	)	)	PUNCT
ma-10	285	45	6=	6=	SCONJ
ma-10	285	46	∅	∅	NOUN
ma-10	285	47	and	and	CCONJ
ma-10	285	48	u	u	NOUN
ma-10	285	49	∈m	∈m	NOUN
ma-10	285	50	be	be	AUX
ma-10	285	51	a	a	DET
ma-10	285	52	constant	constant	ADJ
ma-10	285	53	.	.	PUNCT
ma-10	286	1	define	define	VERB
ma-10	286	2	a	a	DET
ma-10	286	3	sequence	sequence	NOUN
ma-10	286	4	{	{	PUNCT
ma-10	286	5	un	un	PROPN
ma-10	286	6	}	}	PUNCT
ma-10	286	7	in	in	ADP
ma-10	286	8	m	m	NOUN
ma-10	286	9	as	as	SCONJ
ma-10	286	10	follows	follow	VERB
ma-10	286	11	:	:	PUNCT
ma-10	286	12	{	{	PUNCT
ma-10	286	13	u1	u1	NOUN
ma-10	286	14	∈m	∈m	NOUN
ma-10	286	15	un+1	un+1	NOUN
ma-10	286	16	=	=	NOUN
ma-10	286	17	αnun	αnun	PROPN
ma-10	286	18	+	+	CCONJ
ma-10	286	19	βnω	βnω	X
ma-10	287	1	+	+	CCONJ
ma-10	287	2	γnt	γnt	ADJ
ma-10	287	3	n(un+1	n(un+1	NOUN
ma-10	287	4	)	)	PUNCT
ma-10	287	5	∀n	∀n	NUM
ma-10	288	1	∈	∈	PROPN
ma-10	288	2	n	n	CCONJ
ma-10	288	3	(	(	PUNCT
ma-10	288	4	3.23	3.23	NUM
ma-10	288	5	)	)	PUNCT
ma-10	288	6	where	where	SCONJ
ma-10	288	7	αn	αn	NOUN
ma-10	288	8	,	,	PUNCT
ma-10	288	9	βn	βn	ADJ
ma-10	288	10	,	,	PUNCT
ma-10	288	11	γn	γn	ADP
ma-10	288	12	∈	∈	PROPN
ma-10	288	13	(	(	PUNCT
ma-10	288	14	0	0	NUM
ma-10	288	15	,	,	PUNCT
ma-10	288	16	1	1	X
ma-10	288	17	)	)	PUNCT
ma-10	288	18	satisfying	satisfy	VERB
ma-10	288	19	conditions	condition	NOUN
ma-10	288	20	a1−	a1−	ADP
ma-10	288	21	a4	a4	NOUN
ma-10	288	22	without	without	ADP
ma-10	288	23	lim	lim	PROPN
ma-10	288	24	n→∞	n→∞	X
ma-10	288	25	sn	sn	PROPN
ma-10	288	26	=	=	SYM
ma-10	288	27	0	0	NUM
ma-10	289	1	lim	lim	PROPN
ma-10	289	2	n→∞	n→∞	NUM
ma-10	289	3	‖t	‖t	PROPN
ma-10	289	4	nun	nun	NOUN
ma-10	289	5	−	−	NOUN
ma-10	289	6	un‖	un‖	X
ma-10	289	7	=	=	PUNCT
ma-10	289	8	0	0	NUM
ma-10	289	9	then	then	ADV
ma-10	289	10	the	the	DET
ma-10	289	11	sequence	sequence	NOUN
ma-10	289	12	{	{	PUNCT
ma-10	289	13	un	un	PROPN
ma-10	289	14	}	}	PUNCT
ma-10	289	15	strongly	strongly	ADV
ma-10	289	16	converges	converge	VERB
ma-10	289	17	to	to	ADP
ma-10	289	18	a	a	DET
ma-10	289	19	common	common	ADJ
ma-10	289	20	fixed	fix	VERB
ma-10	289	21	point	point	NOUN
ma-10	289	22	q	q	PROPN
ma-10	289	23	of	of	ADP
ma-10	289	24	t	t	PROPN
ma-10	289	25	,	,	PUNCT
ma-10	289	26	which	which	PRON
ma-10	289	27	is	be	AUX
ma-10	289	28	also	also	ADV
ma-10	289	29	the	the	DET
ma-10	289	30	unique	unique	ADJ
ma-10	289	31	solution	solution	NOUN
ma-10	289	32	of	of	ADP
ma-10	289	33	the	the	DET
ma-10	289	34	following	follow	VERB
ma-10	289	35	variational	variational	ADJ
ma-10	289	36	inequality	inequality	NOUN
ma-10	289	37	〈	〈	PROPN
ma-10	289	38	(	(	PUNCT
ma-10	289	39	i	i	NOUN
ma-10	289	40	−	−	PROPN
ma-10	289	41	ψ)u	ψ)u	NOUN
ma-10	289	42	,	,	PUNCT
ma-10	289	43	p	p	NOUN
ma-10	289	44	−	−	PROPN
ma-10	289	45	u	u	NOUN
ma-10	289	46	〉	〉	PROPN
ma-10	289	47	≥	≥	NOUN
ma-10	289	48	0	0	NUM
ma-10	290	1	p	p	X
ma-10	290	2	∈	∈	PROPN
ma-10	290	3	f	f	X
ma-10	290	4	(	(	PUNCT
ma-10	290	5	t	t	PROPN
ma-10	290	6	)	)	PUNCT
ma-10	290	7	.	.	PUNCT
ma-10	291	1	4	4	X
ma-10	291	2	.	.	X
ma-10	291	3	application	application	NOUN
ma-10	291	4	to	to	PART
ma-10	291	5	convex	convex	VERB
ma-10	291	6	minimization	minimization	NOUN
ma-10	291	7	problems	problem	NOUN
ma-10	291	8	in	in	ADP
ma-10	291	9	this	this	DET
ma-10	291	10	section	section	NOUN
ma-10	291	11	,	,	PUNCT
ma-10	291	12	we	we	PRON
ma-10	291	13	study	study	VERB
ma-10	291	14	the	the	DET
ma-10	291	15	problem	problem	NOUN
ma-10	291	16	of	of	ADP
ma-10	291	17	finding	find	VERB
ma-10	291	18	a	a	DET
ma-10	291	19	minimizer	minimizer	NOUN
ma-10	291	20	of	of	ADP
ma-10	291	21	a	a	DET
ma-10	291	22	convex	convex	NOUN
ma-10	291	23	function	function	NOUN
ma-10	291	24	φ	φ	PROPN
ma-10	291	25	defined	define	VERB
ma-10	291	26	from	from	ADP
ma-10	291	27	areal	areal	PROPN
ma-10	291	28	hilbert	hilbert	PROPN
ma-10	291	29	space	space	NOUN
ma-10	291	30	m	m	VERB
ma-10	291	31	to	to	PART
ma-10	291	32	r.consider	r.consider	VERB
ma-10	291	33	the	the	DET
ma-10	291	34	optimization	optimization	NOUN
ma-10	291	35	problem	problem	NOUN
ma-10	291	36	min	min	PROPN
ma-10	291	37	x∈c	x∈c	PROPN
ma-10	291	38	φ(x	φ(x	PROPN
ma-10	291	39	)	)	PUNCT
ma-10	291	40	(	(	PUNCT
ma-10	291	41	4.1)where	4.1)where	NUM
ma-10	291	42	φ	φ	NOUN
ma-10	291	43	:	:	PUNCT
ma-10	291	44	m	m	VERB
ma-10	291	45	→	→	SYM
ma-10	291	46	r	r	NOUN
ma-10	291	47	is	be	AUX
ma-10	291	48	a	a	DET
ma-10	291	49	convex	convex	ADJ
ma-10	291	50	and	and	CCONJ
ma-10	291	51	differentiable	differentiable	ADJ
ma-10	291	52	function	function	NOUN
ma-10	291	53	.	.	PUNCT
ma-10	292	1	assume	assume	VERB
ma-10	292	2	4.1	4.1	NUM
ma-10	292	3	is	be	AUX
ma-10	292	4	consistent	consistent	ADJ
ma-10	292	5	,	,	PUNCT
ma-10	292	6	and	and	CCONJ
ma-10	292	7	let	let	VERB
ma-10	292	8	ω	ω	PROPN
ma-10	292	9	6=	6=	NOUN
ma-10	292	10	∅	∅	NOUN
ma-10	292	11	be	be	AUX
ma-10	292	12	its	its	PRON
ma-10	292	13	set	set	NOUN
ma-10	292	14	of	of	ADP
ma-10	292	15	solutions	solution	NOUN
ma-10	292	16	.	.	PUNCT
ma-10	293	1	the	the	DET
ma-10	293	2	gradient	gradient	PROPN
ma-10	293	3	projection	projection	NOUN
ma-10	293	4	algorithm	algorithm	NOUN
ma-10	293	5	generates	generate	VERB
ma-10	293	6	a	a	DET
ma-10	293	7	sequence	sequence	NOUN
ma-10	293	8	{	{	PUNCT
ma-10	293	9	un	un	PROPN
ma-10	293	10	}	}	PUNCT
ma-10	293	11	via	via	ADP
ma-10	293	12	theiterative	theiterative	ADJ
ma-10	293	13	procedure	procedure	NOUN
ma-10	293	14	:	:	PUNCT
ma-10	293	15	un+1	un+1	PROPN
ma-10	293	16	=	=	SYM
ma-10	293	17	pm(un	pm(un	PROPN
ma-10	293	18	−	−	PROPN
ma-10	293	19	δ∇φ(u	δ∇φ(u	PROPN
ma-10	293	20	)	)	PUNCT
ma-10	293	21	)	)	PUNCT
ma-10	293	22	(	(	PUNCT
ma-10	293	23	4.2)if	4.2)if	NOUN
ma-10	293	24	∇φ	∇φ	ADV
ma-10	293	25	is	be	AUX
ma-10	293	26	θ−inverse	θ−inverse	ADV
ma-10	293	27	strongly	strongly	ADV
ma-10	293	28	monotone	monotone	ADJ
ma-10	293	29	mapping	mapping	NOUN
ma-10	293	30	and	and	CCONJ
ma-10	293	31	δ(0	δ(0	PROPN
ma-10	293	32	,	,	PUNCT
ma-10	293	33	2θ	2θ	NUM
ma-10	293	34	)	)	PUNCT
ma-10	293	35	.	.	PUNCT
ma-10	294	1	the	the	DET
ma-10	294	2	following	following	ADJ
ma-10	294	3	basic	basic	ADJ
ma-10	294	4	results	result	NOUN
ma-10	294	5	are	be	AUX
ma-10	294	6	wellknown	wellknown	ADJ
ma-10	294	7	.	.	PUNCT
ma-10	295	1	remark	remark	PROPN
ma-10	295	2	4.1	4.1	NUM
ma-10	295	3	.	.	PUNCT
ma-10	296	1	it	it	PRON
ma-10	296	2	is	be	AUX
ma-10	296	3	well	well	ADV
ma-10	296	4	known	know	VERB
ma-10	296	5	that	that	SCONJ
ma-10	296	6	if	if	SCONJ
ma-10	296	7	φ	φ	PROPN
ma-10	296	8	:	:	PUNCT
ma-10	296	9	m	m	AUX
ma-10	296	10	→	→	SYM
ma-10	296	11	r	r	NOUN
ma-10	296	12	be	be	AUX
ma-10	296	13	a	a	DET
ma-10	296	14	real	real	ADV
ma-10	296	15	-	-	PUNCT
ma-10	296	16	valued	value	VERB
ma-10	296	17	differentiable	differentiable	ADJ
ma-10	296	18	convex	convex	NOUN
ma-10	296	19	functionand	functionand	NOUN
ma-10	296	20	u∗	u∗	PROPN
ma-10	296	21	∈m	∈m	NOUN
ma-10	296	22	,	,	PUNCT
ma-10	296	23	then	then	ADV
ma-10	296	24	the	the	DET
ma-10	296	25	point	point	NOUN
ma-10	296	26	u∗	u∗	ADV
ma-10	296	27	is	be	AUX
ma-10	296	28	a	a	DET
ma-10	296	29	minimizer	minimizer	NOUN
ma-10	296	30	of	of	ADP
ma-10	296	31	φ	φ	PROPN
ma-10	296	32	on	on	ADP
ma-10	296	33	m	m	PROPN
ma-10	296	34	if	if	SCONJ
ma-10	296	35	and	and	CCONJ
ma-10	296	36	only	only	ADV
ma-10	296	37	if	if	SCONJ
ma-10	296	38	dφ(u∗	dφ(u∗	NOUN
ma-10	296	39	)	)	PUNCT
ma-10	297	1	=	=	SYM
ma-10	297	2	0	0	X
ma-10	297	3	.	.	PUNCT
ma-10	298	1	definition	definition	NOUN
ma-10	298	2	4.2	4.2	NUM
ma-10	298	3	.	.	PUNCT
ma-10	299	1	a	a	DET
ma-10	299	2	function	function	NOUN
ma-10	299	3	φ	φ	NOUN
ma-10	299	4	:	:	PUNCT
ma-10	299	5	m→	m→	NOUN
ma-10	299	6	r	r	NOUN
ma-10	299	7	is	be	AUX
ma-10	299	8	said	say	VERB
ma-10	299	9	to	to	PART
ma-10	299	10	be	be	AUX
ma-10	299	11	strongly	strongly	ADV
ma-10	299	12	convex	convex	ADJ
ma-10	299	13	if	if	SCONJ
ma-10	299	14	there	there	PRON
ma-10	299	15	exists	exist	VERB
ma-10	299	16	α	α	PROPN
ma-10	299	17	>	>	X
ma-10	299	18	0	0	NUM
ma-10	300	1	such	such	ADJ
ma-10	300	2	thatfor	thatfor	NOUN
ma-10	300	3	every	every	DET
ma-10	300	4	u	u	NOUN
ma-10	300	5	,	,	PUNCT
ma-10	300	6	v	v	NOUN
ma-10	300	7	∈m	∈m	NOUN
ma-10	300	8	and	and	CCONJ
ma-10	300	9	λ	λ	X
ma-10	300	10	∈	∈	PROPN
ma-10	300	11	(	(	PUNCT
ma-10	300	12	0	0	NUM
ma-10	300	13	,	,	PUNCT
ma-10	300	14	1	1	NUM
ma-10	300	15	)	)	PUNCT
ma-10	301	1	,	,	PUNCT
ma-10	301	2	the	the	DET
ma-10	301	3	following	follow	VERB
ma-10	301	4	inequality	inequality	NOUN
ma-10	301	5	holds	hold	VERB
ma-10	301	6	:	:	PUNCT
ma-10	301	7	φ(λu	φ(λu	NUM
ma-10	301	8	+	+	CCONJ
ma-10	301	9	(	(	PUNCT
ma-10	301	10	1−	1−	NUM
ma-10	301	11	λ)v	λ)v	NOUN
ma-10	301	12	)	)	PUNCT
ma-10	301	13	≤	≤	NOUN
ma-10	301	14	λφ(u	λφ(u	X
ma-10	301	15	)	)	PUNCT
ma-10	302	1	+	+	CCONJ
ma-10	302	2	(	(	PUNCT
ma-10	302	3	1−	1−	NUM
ma-10	302	4	λ)φ(v)−	λ)φ(v)−	NUM
ma-10	302	5	α‖u	α‖u	NOUN
ma-10	302	6	−	−	PRON
ma-10	302	7	v‖2	v‖2	PROPN
ma-10	302	8	.	.	PUNCT
ma-10	303	1	(	(	PUNCT
ma-10	303	2	4.3	4.3	NUM
ma-10	303	3	)	)	PUNCT
ma-10	303	4	lemma	lemma	PROPN
ma-10	303	5	4.3	4.3	NUM
ma-10	303	6	.	.	PUNCT
ma-10	304	1	let	let	VERB
ma-10	304	2	e	e	PRON
ma-10	304	3	be	be	AUX
ma-10	304	4	normed	norme	VERB
ma-10	304	5	linear	linear	ADJ
ma-10	304	6	space	space	NOUN
ma-10	304	7	and	and	CCONJ
ma-10	304	8	φ	φ	NOUN
ma-10	304	9	:	:	PUNCT
ma-10	304	10	m	m	VERB
ma-10	304	11	→	→	SYM
ma-10	304	12	r	r	VERB
ma-10	304	13	a	a	DET
ma-10	304	14	real	real	ADV
ma-10	304	15	-	-	PUNCT
ma-10	304	16	valued	value	VERB
ma-10	304	17	differentiable	differentiable	ADJ
ma-10	304	18	convex	convex	NOUN
ma-10	304	19	function	function	NOUN
ma-10	304	20	.	.	PUNCT
ma-10	305	1	assume	assume	VERB
ma-10	305	2	that	that	SCONJ
ma-10	305	3	φ	φ	PROPN
ma-10	305	4	is	be	AUX
ma-10	305	5	strongly	strongly	ADV
ma-10	305	6	convex	convex	ADJ
ma-10	305	7	.	.	PUNCT
ma-10	306	1	then	then	ADV
ma-10	306	2	the	the	DET
ma-10	306	3	differential	differential	ADJ
ma-10	306	4	map	map	NOUN
ma-10	306	5	dψ	dψ	X
ma-10	306	6	:	:	PUNCT
ma-10	306	7	m→m	m→m	NOUN
ma-10	306	8	is	be	AUX
ma-10	306	9	strongly	strongly	ADV
ma-10	306	10	monotone	monotone	ADJ
ma-10	306	11	,	,	PUNCT
ma-10	306	12	i.e.	i.e.	X
ma-10	306	13	,	,	PUNCT
ma-10	306	14	there	there	PRON
ma-10	306	15	exists	exist	VERB
ma-10	306	16	a	a	DET
ma-10	306	17	positive	positive	ADJ
ma-10	306	18	constant	constant	ADJ
ma-10	306	19	k	k	NOUN
ma-10	306	20	such	such	ADJ
ma-10	306	21	that	that	SCONJ
ma-10	306	22	〈	〈	PROPN
ma-10	306	23	dφ(u)−	dφ(u)−	PROPN
ma-10	306	24	dφ(v	dφ(v	NOUN
ma-10	306	25	)	)	PUNCT
ma-10	306	26	,	,	PUNCT
ma-10	306	27	u	u	NOUN
ma-10	306	28	−	−	PROPN
ma-10	306	29	v	v	PROPN
ma-10	306	30	〉	〉	PROPN
ma-10	306	31	≥	≥	NOUN
ma-10	306	32	k‖u	k‖u	NOUN
ma-10	306	33	−	−	NOUN
ma-10	306	34	v‖2	v‖2	PROPN
ma-10	306	35	∀	∀	X
ma-10	306	36	u	u	NOUN
ma-10	306	37	,	,	PUNCT
ma-10	306	38	v	v	NOUN
ma-10	306	39	∈m	∈m	NOUN
ma-10	306	40	.	.	PUNCT
ma-10	307	1	(	(	PUNCT
ma-10	307	2	4.4	4.4	NUM
ma-10	307	3	)	)	PUNCT
ma-10	307	4	the	the	DET
ma-10	307	5	prove	prove	NOUN
ma-10	307	6	of	of	ADP
ma-10	307	7	the	the	DET
ma-10	307	8	following	follow	VERB
ma-10	307	9	theorem	theorem	NOUN
ma-10	307	10	follows	follow	VERB
ma-10	307	11	from	from	ADP
ma-10	307	12	3.1	3.1	NUM
ma-10	307	13	eur	eur	NOUN
ma-10	307	14	.	.	PUNCT
ma-10	308	1	j.	j.	PROPN
ma-10	308	2	math	math	PROPN
ma-10	308	3	.	.	PUNCT
ma-10	309	1	anal	anal	ADJ
ma-10	309	2	.	.	PUNCT
ma-10	310	1	1	1	NUM
ma-10	310	2	(	(	PUNCT
ma-10	310	3	2021	2021	NUM
ma-10	310	4	)	)	PUNCT
ma-10	310	5	32	32	NUM
ma-10	310	6	theorem	theorem	VERB
ma-10	310	7	4.4	4.4	NUM
ma-10	310	8	.	.	PUNCT
ma-10	311	1	let	let	VERB
ma-10	311	2	m	m	PRON
ma-10	311	3	be	be	AUX
ma-10	311	4	a	a	DET
ma-10	311	5	nonempty	nonempty	ADV
ma-10	311	6	closed	close	VERB
ma-10	311	7	convex	convex	NOUN
ma-10	311	8	subset	subset	VERB
ma-10	311	9	a	a	DET
ma-10	311	10	real	real	ADJ
ma-10	311	11	hilbert	hilbert	NOUN
ma-10	311	12	space	space	PROPN
ma-10	311	13	h.	h.	PROPN
ma-10	311	14	for	for	ADP
ma-10	311	15	the	the	DET
ma-10	311	16	minimization	minimization	NOUN
ma-10	311	17	problem	problem	NOUN
ma-10	311	18	4.1	4.1	NUM
ma-10	311	19	,	,	PUNCT
ma-10	311	20	assume	assume	VERB
ma-10	311	21	that	that	SCONJ
ma-10	311	22	φ	φ	PROPN
ma-10	311	23	is	be	AUX
ma-10	311	24	(	(	PUNCT
ma-10	311	25	gateaux	gateaux	ADV
ma-10	311	26	)	)	PUNCT
ma-10	311	27	differentiable	differentiable	ADJ
ma-10	311	28	and	and	CCONJ
ma-10	311	29	the	the	DET
ma-10	311	30	gradient	gradient	NOUN
ma-10	311	31	∇φ	∇φ	PROPN
ma-10	311	32	is	be	AUX
ma-10	311	33	a	a	DET
ma-10	311	34	θ−inverse	θ−inverse	ADV
ma-10	311	35	-	-	PUNCT
ma-10	311	36	strongly	strongly	ADV
ma-10	311	37	monotone	monotone	ADJ
ma-10	311	38	mapping	mapping	NOUN
ma-10	311	39	for	for	ADP
ma-10	311	40	some	some	DET
ma-10	311	41	positive	positive	ADJ
ma-10	311	42	real	real	ADJ
ma-10	311	43	number	number	NOUN
ma-10	311	44	θ	θ	NOUN
ma-10	311	45	.	.	PUNCT
ma-10	312	1	let	let	VERB
ma-10	312	2	ψ	ψ	X
ma-10	312	3	:	:	PUNCT
ma-10	312	4	m	m	VERB
ma-10	312	5	→	→	NOUN
ma-10	312	6	m	m	AUX
ma-10	312	7	be	be	AUX
ma-10	312	8	a	a	DET
ma-10	312	9	contraction	contraction	NOUN
ma-10	312	10	with	with	ADP
ma-10	312	11	coefficient	coefficient	NOUN
ma-10	312	12	α	α	PROPN
ma-10	312	13	∈	∈	PROPN
ma-10	313	1	[	[	X
ma-10	313	2	0	0	NUM
ma-10	313	3	,	,	PUNCT
ma-10	313	4	1	1	NUM
ma-10	313	5	)	)	PUNCT
ma-10	313	6	.	.	PUNCT
ma-10	314	1	for	for	ADP
ma-10	314	2	a	a	DET
ma-10	314	3	given	give	VERB
ma-10	314	4	u1	u1	NOUN
ma-10	314	5	∈m	∈m	NOUN
ma-10	314	6	,	,	PUNCT
ma-10	314	7	let	let	VERB
ma-10	314	8	{	{	PUNCT
ma-10	314	9	un	un	AUX
ma-10	314	10	}	}	PUNCT
ma-10	314	11	be	be	AUX
ma-10	314	12	a	a	DET
ma-10	314	13	sequence	sequence	NOUN
ma-10	314	14	generated	generate	VERB
ma-10	314	15	by	by	ADP
ma-10	314	16	:	:	PUNCT
ma-10	314	17	{	{	PUNCT
ma-10	314	18	u1	u1	PROPN
ma-10	314	19	∈m	∈m	NOUN
ma-10	314	20	un+1	un+1	NOUN
ma-10	314	21	=	=	NOUN
ma-10	314	22	αnun	αnun	ADJ
ma-10	314	23	+	+	CCONJ
ma-10	314	24	βnψ(un	βnψ(un	NUM
ma-10	314	25	)	)	PUNCT
ma-10	314	26	+	+	NUM
ma-10	314	27	γnpm(1−	γnpm(1−	DET
ma-10	314	28	δ∇φ)(snun	δ∇φ)(snun	NOUN
ma-10	314	29	+	+	CCONJ
ma-10	314	30	(	(	PUNCT
ma-10	314	31	1−	1−	NUM
ma-10	314	32	sn)(un+1	sn)(un+1	PROPN
ma-10	314	33	)	)	PUNCT
ma-10	314	34	)	)	PUNCT
ma-10	315	1	∀n	∀n	NUM
ma-10	315	2	∈	∈	PROPN
ma-10	315	3	n	n	CCONJ
ma-10	315	4	(	(	PUNCT
ma-10	315	5	4.5	4.5	NUM
ma-10	315	6	)	)	PUNCT
ma-10	315	7	where	where	SCONJ
ma-10	315	8	αn	αn	NOUN
ma-10	315	9	,	,	PUNCT
ma-10	315	10	βn	βn	NOUN
ma-10	315	11	,	,	PUNCT
ma-10	315	12	γn	γn	NUM
ma-10	315	13	,	,	PUNCT
ma-10	315	14	sn	sn	PROPN
ma-10	315	15	∈	∈	PROPN
ma-10	315	16	(	(	PUNCT
ma-10	315	17	0	0	NUM
ma-10	315	18	,	,	PUNCT
ma-10	315	19	1	1	X
ma-10	315	20	)	)	PUNCT
ma-10	315	21	satisfying	satisfy	VERB
ma-10	315	22	the	the	DET
ma-10	315	23	following	follow	VERB
ma-10	315	24	conditions	condition	NOUN
ma-10	315	25	a1	a1	NOUN
ma-10	315	26	:	:	PUNCT
ma-10	315	27	αn	αn	NOUN
ma-10	316	1	+	+	CCONJ
ma-10	316	2	βn	βn	NOUN
ma-10	316	3	+	+	CCONJ
ma-10	316	4	γn	γn	NOUN
ma-10	316	5	=	=	SYM
ma-10	316	6	1	1	NUM
ma-10	316	7	a2	a2	PROPN
ma-10	316	8	:	:	PUNCT
ma-10	316	9	lim	lim	PROPN
ma-10	316	10	n→∞	n→∞	NUM
ma-10	316	11	k2n	k2n	PROPN
ma-10	316	12	−	−	PROPN
ma-10	316	13	1	1	NUM
ma-10	316	14	αn	αn	NOUN
ma-10	316	15	=	=	SYM
ma-10	316	16	0	0	NUM
ma-10	316	17	a3	a3	NOUN
ma-10	316	18	:	:	PUNCT
ma-10	316	19	∞∑	∞∑	PRON
ma-10	316	20	n=0	n=0	NUM
ma-10	316	21	αn	αn	NOUN
ma-10	316	22	=	=	NUM
ma-10	316	23	∞	∞	NUM
ma-10	316	24	a4	a4	NUM
ma-10	316	25	:	:	PUNCT
ma-10	316	26	lim	lim	PROPN
ma-10	316	27	n→∞	n→∞	X
ma-10	316	28	γn	γn	NOUN
ma-10	316	29	=	=	SYM
ma-10	316	30	1	1	NUM
ma-10	316	31	and	and	CCONJ
ma-10	316	32	lim	lim	PROPN
ma-10	316	33	n→∞	n→∞	PRON
ma-10	316	34	αn	αn	NOUN
ma-10	317	1	=	=	PROPN
ma-10	317	2	lim	lim	PROPN
ma-10	317	3	n→∞	n→∞	NUM
ma-10	317	4	βn	βn	PROPN
ma-10	317	5	=	=	PUNCT
ma-10	317	6	lim	lim	PROPN
ma-10	317	7	n→∞	n→∞	X
ma-10	318	1	sn	sn	PROPN
ma-10	318	2	=	=	NOUN
ma-10	318	3	0	0	PUNCT
ma-10	318	4	then	then	ADV
ma-10	318	5	{	{	PUNCT
ma-10	318	6	un	un	PROPN
ma-10	318	7	}	}	PUNCT
ma-10	318	8	converges	converge	VERB
ma-10	318	9	strongly	strongly	ADV
ma-10	318	10	to	to	ADP
ma-10	318	11	a	a	DET
ma-10	318	12	solution	solution	NOUN
ma-10	318	13	(	(	PUNCT
ma-10	318	14	u∗	u∗	PROPN
ma-10	318	15	)	)	PUNCT
ma-10	318	16	of	of	ADP
ma-10	318	17	the	the	DET
ma-10	318	18	minimization	minimization	NOUN
ma-10	318	19	problem	problem	NOUN
ma-10	318	20	4.1	4.1	NUM
ma-10	318	21	,	,	PUNCT
ma-10	318	22	which	which	PRON
ma-10	318	23	is	be	AUX
ma-10	318	24	also	also	ADV
ma-10	318	25	the	the	DET
ma-10	318	26	unique	unique	ADJ
ma-10	318	27	solution	solution	NOUN
ma-10	318	28	of	of	ADP
ma-10	318	29	the	the	DET
ma-10	318	30	variational	variational	ADJ
ma-10	318	31	inequality	inequality	NOUN
ma-10	318	32	〈	〈	PROPN
ma-10	318	33	(	(	PUNCT
ma-10	318	34	i	i	NOUN
ma-10	318	35	−	−	PROPN
ma-10	318	36	ψ)u	ψ)u	NOUN
ma-10	318	37	,	,	PUNCT
ma-10	318	38	p	p	NOUN
ma-10	318	39	−	−	PROPN
ma-10	318	40	u	u	NOUN
ma-10	318	41	〉	〉	PROPN
ma-10	318	42	≥	≥	NOUN
ma-10	318	43	0	0	NUM
ma-10	319	1	p	p	X
ma-10	319	2	∈	∈	PROPN
ma-10	319	3	f	f	X
ma-10	319	4	(	(	PUNCT
ma-10	319	5	t	t	PROPN
ma-10	319	6	)	)	PUNCT
ma-10	319	7	.	.	PUNCT
ma-10	320	1	conflict	conflict	NOUN
ma-10	320	2	of	of	ADP
ma-10	320	3	interest	interest	NOUN
ma-10	320	4	:	:	PUNCT
ma-10	320	5	the	the	DET
ma-10	320	6	authors	author	NOUN
ma-10	320	7	declare	declare	VERB
ma-10	320	8	that	that	SCONJ
ma-10	320	9	they	they	PRON
ma-10	320	10	have	have	VERB
ma-10	320	11	no	no	DET
ma-10	320	12	competing	compete	VERB
ma-10	320	13	interests	interest	NOUN
ma-10	320	14	.	.	PUNCT
ma-10	321	1	availability	availability	NOUN
ma-10	321	2	of	of	ADP
ma-10	321	3	data	datum	NOUN
ma-10	321	4	and	and	CCONJ
ma-10	321	5	materials	material	NOUN
ma-10	321	6	:	:	PUNCT
ma-10	321	7	no	no	DET
ma-10	321	8	data	datum	NOUN
ma-10	321	9	were	be	AUX
ma-10	321	10	used	use	VERB
ma-10	321	11	to	to	PART
ma-10	321	12	support	support	VERB
ma-10	321	13	this	this	DET
ma-10	321	14	study	study	NOUN
ma-10	321	15	.	.	PUNCT
ma-10	322	1	funding	funding	NOUN
ma-10	322	2	:	:	PUNCT
ma-10	322	3	no	no	DET
ma-10	322	4	funding	funding	NOUN
ma-10	322	5	was	be	AUX
ma-10	322	6	given	give	VERB
ma-10	322	7	towards	towards	ADP
ma-10	322	8	this	this	DET
ma-10	322	9	manuscript	manuscript	NOUN
ma-10	322	10	.	.	PUNCT
ma-10	323	1	authors	author	NOUN
ma-10	323	2	contributions	contribution	VERB
ma-10	323	3	:	:	PUNCT
ma-10	323	4	all	all	DET
ma-10	323	5	authors	author	NOUN
ma-10	323	6	have	have	AUX
ma-10	323	7	contributed	contribute	VERB
ma-10	323	8	equally	equally	ADV
ma-10	323	9	and	and	CCONJ
ma-10	323	10	significantly	significantly	ADV
ma-10	323	11	in	in	ADP
ma-10	323	12	writing	write	VERB
ma-10	323	13	this	this	DET
ma-10	323	14	paper	paper	NOUN
ma-10	323	15	and	and	CCONJ
ma-10	323	16	also	also	ADV
ma-10	323	17	readand	readand	PROPN
ma-10	323	18	approved	approve	VERB
ma-10	323	19	the	the	DET
ma-10	323	20	final	final	ADJ
ma-10	323	21	manuscript	manuscript	NOUN
ma-10	323	22	.	.	PUNCT
ma-10	324	1	acknowledgement	acknowledgement	NOUN
ma-10	324	2	:	:	PUNCT
ma-10	324	3	the	the	DET
ma-10	324	4	authors	author	NOUN
ma-10	324	5	are	be	AUX
ma-10	324	6	very	very	ADV
ma-10	324	7	grateful	grateful	ADJ
ma-10	324	8	to	to	ADP
ma-10	324	9	the	the	DET
ma-10	324	10	editor	editor	NOUN
ma-10	324	11	and	and	CCONJ
ma-10	324	12	anonymous	anonymous	ADJ
ma-10	324	13	referees	referee	NOUN
ma-10	324	14	for	for	ADP
ma-10	324	15	their	their	PRON
ma-10	324	16	helpfulcomments	helpfulcomment	NOUN
ma-10	324	17	.	.	PUNCT
ma-10	325	1	references	reference	NOUN
ma-10	325	2	[	[	X
ma-10	325	3	1	1	NUM
ma-10	325	4	]	]	X
ma-10	325	5	h.	h.	PROPN
ma-10	325	6	attouch	attouch	PROPN
ma-10	325	7	,	,	PUNCT
ma-10	325	8	viscosity	viscosity	NOUN
ma-10	325	9	approximation	approximation	NOUN
ma-10	325	10	methods	method	NOUN
ma-10	325	11	for	for	ADP
ma-10	325	12	minimization	minimization	NOUN
ma-10	325	13	problems	problem	NOUN
ma-10	325	14	,	,	PUNCT
ma-10	325	15	siam	siam	PROPN
ma-10	325	16	j.	j.	PROPN
ma-10	325	17	optim	optim	PROPN
ma-10	325	18	.	.	PROPN
ma-10	326	1	6	6	NUM
ma-10	326	2	(	(	PUNCT
ma-10	326	3	3	3	NUM
ma-10	326	4	)	)	PUNCT
ma-10	326	5	(	(	PUNCT
ma-10	326	6	1996	1996	NUM
ma-10	326	7	)	)	PUNCT
ma-10	326	8	769	769	NUM
ma-10	326	9	-	-	SYM
ma-10	326	10	806	806	NUM
ma-10	326	11	.	.	PUNCT
ma-10	327	1	https://doi.org/10.1137/s1052623493259616.[2	https://doi.org/10.1137/s1052623493259616.[2	ADP
ma-10	327	2	]	]	X
ma-10	327	3	a.	a.	NOUN
ma-10	327	4	moudafi	moudafi	PROPN
ma-10	327	5	,	,	PUNCT
ma-10	327	6	viscosity	viscosity	NOUN
ma-10	327	7	approximation	approximation	NOUN
ma-10	327	8	methods	method	NOUN
ma-10	327	9	for	for	ADP
ma-10	327	10	fixed	fix	VERB
ma-10	327	11	-	-	PUNCT
ma-10	327	12	points	point	NOUN
ma-10	327	13	problems	problem	NOUN
ma-10	327	14	,	,	PUNCT
ma-10	327	15	j.	j.	PROPN
ma-10	327	16	math	math	PROPN
ma-10	327	17	.	.	PUNCT
ma-10	328	1	anal	anal	PROPN
ma-10	328	2	.	.	PUNCT
ma-10	328	3	appl	appl	PROPN
ma-10	328	4	.	.	PUNCT
ma-10	329	1	241	241	NUM
ma-10	329	2	(	(	PUNCT
ma-10	329	3	1	1	NUM
ma-10	329	4	)	)	PUNCT
ma-10	329	5	(	(	PUNCT
ma-10	329	6	2000	2000	NUM
ma-10	329	7	)	)	PUNCT
ma-10	329	8	46	46	NUM
ma-10	329	9	-	-	SYM
ma-10	329	10	55	55	NUM
ma-10	329	11	.	.	PUNCT
ma-10	330	1	https://doi.org/10.1006/jmaa.1999.6615.[3	https://doi.org/10.1006/jmaa.1999.6615.[3	NOUN
ma-10	330	2	]	]	X
ma-10	330	3	h.k	h.k	PROPN
ma-10	330	4	.	.	PROPN
ma-10	330	5	xu	xu	PROPN
ma-10	330	6	,	,	PUNCT
ma-10	330	7	m.a	m.a	PROPN
ma-10	330	8	.	.	PROPN
ma-10	330	9	alghamdi	alghamdi	PROPN
ma-10	330	10	,	,	PUNCT
ma-10	330	11	n.	n.	PROPN
ma-10	330	12	shahzad	shahzad	PROPN
ma-10	330	13	,	,	PUNCT
ma-10	330	14	the	the	DET
ma-10	330	15	viscosity	viscosity	NOUN
ma-10	330	16	technique	technique	NOUN
ma-10	330	17	for	for	ADP
ma-10	330	18	the	the	DET
ma-10	330	19	implicit	implicit	ADJ
ma-10	330	20	midpoint	midpoint	NOUN
ma-10	330	21	rule	rule	NOUN
ma-10	330	22	of	of	ADP
ma-10	330	23	nonexpansive	nonexpansive	ADJ
ma-10	330	24	mappingsin	mappingsin	PROPN
ma-10	330	25	hilbert	hilbert	PROPN
ma-10	330	26	spaces	space	NOUN
ma-10	330	27	,	,	PUNCT
ma-10	330	28	fixed	fix	VERB
ma-10	330	29	point	point	NOUN
ma-10	330	30	theory	theory	NOUN
ma-10	330	31	appl	appl	NOUN
ma-10	330	32	.	.	PROPN
ma-10	331	1	2015	2015	NUM
ma-10	331	2	(	(	PUNCT
ma-10	331	3	2015	2015	NUM
ma-10	331	4	)	)	PUNCT
ma-10	331	5	41	41	NUM
ma-10	331	6	.	.	PUNCT
ma-10	332	1	https://doi.org/10.1186/s13663-015-0282-9	https://doi.org/10.1186/s13663-015-0282-9	NOUN
ma-10	332	2	.	.	PUNCT
ma-10	333	1	https://doi.org/10.1137/s1052623493259616	https://doi.org/10.1137/s1052623493259616	NUM
ma-10	333	2	https://doi.org/10.1006/jmaa.1999.6615	https://doi.org/10.1006/jmaa.1999.6615	NOUN
ma-10	333	3	https://doi.org/10.1186/s13663-015-0282-9	https://doi.org/10.1186/s13663-015-0282-9	NUM
ma-10	333	4	eur	eur	NOUN
ma-10	333	5	.	.	PUNCT
ma-10	334	1	j.	j.	PROPN
ma-10	334	2	math	math	PROPN
ma-10	334	3	.	.	PUNCT
ma-10	335	1	anal	anal	ADJ
ma-10	335	2	.	.	PUNCT
ma-10	336	1	1	1	NUM
ma-10	336	2	(	(	PUNCT
ma-10	336	3	2021	2021	NUM
ma-10	336	4	)	)	PUNCT
ma-10	337	1	33	33	NUM
ma-10	338	1	[	[	SYM
ma-10	338	2	4	4	NUM
ma-10	338	3	]	]	X
ma-10	338	4	y.	y.	PROPN
ma-10	338	5	ke	ke	PROPN
ma-10	338	6	,	,	PUNCT
ma-10	338	7	c.	c.	PROPN
ma-10	338	8	ma	ma	PROPN
ma-10	338	9	,	,	PUNCT
ma-10	338	10	the	the	DET
ma-10	338	11	generalized	generalized	ADJ
ma-10	338	12	viscosity	viscosity	NOUN
ma-10	338	13	implicit	implicit	ADJ
ma-10	338	14	rules	rule	NOUN
ma-10	338	15	of	of	ADP
ma-10	338	16	nonexpansive	nonexpansive	ADJ
ma-10	338	17	mappings	mapping	NOUN
ma-10	338	18	in	in	ADP
ma-10	338	19	hilbert	hilbert	NOUN
ma-10	338	20	spaces	space	NOUN
ma-10	338	21	,	,	PUNCT
ma-10	338	22	fixed	fix	VERB
ma-10	338	23	pointtheory	pointtheory	NOUN
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ma-10	338	25	appl	appl	NOUN
ma-10	338	26	.	.	PROPN
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ma-10	339	2	(	(	PUNCT
ma-10	339	3	2015	2015	NUM
ma-10	339	4	)	)	PUNCT
ma-10	339	5	,	,	PUNCT
ma-10	339	6	190	190	NUM
ma-10	339	7	.	.	PUNCT
ma-10	340	1	https://doi.org/10.1186/s13663-015-0439-6.[5	https://doi.org/10.1186/s13663-015-0439-6.[5	PRON
ma-10	340	2	]	]	X
ma-10	340	3	l.c	l.c	PROPN
ma-10	340	4	.	.	PROPN
ma-10	340	5	zhao	zhao	PROPN
ma-10	340	6	,	,	PUNCT
ma-10	340	7	s.s	s.s	PROPN
ma-10	340	8	.	.	PROPN
ma-10	340	9	chang	chang	PROPN
ma-10	340	10	,	,	PUNCT
ma-10	340	11	c.f	c.f	PROPN
ma-10	340	12	.	.	PROPN
ma-10	340	13	wen	wen	PROPN
ma-10	340	14	,	,	PUNCT
ma-10	340	15	viscosity	viscosity	NOUN
ma-10	340	16	approximation	approximation	NOUN
ma-10	340	17	methods	method	NOUN
ma-10	340	18	for	for	ADP
ma-10	340	19	the	the	DET
ma-10	340	20	implicit	implicit	ADJ
ma-10	340	21	midpoint	midpoint	NOUN
ma-10	340	22	rule	rule	NOUN
ma-10	340	23	of	of	ADP
ma-10	340	24	asymptoticallynonexpansive	asymptoticallynonexpansive	ADJ
ma-10	340	25	mappings	mapping	NOUN
ma-10	340	26	in	in	ADP
ma-10	340	27	hilbert	hilbert	PROPN
ma-10	340	28	spaces	space	NOUN
ma-10	340	29	,	,	PUNCT
ma-10	340	30	j.	j.	PROPN
ma-10	340	31	nonlinear	nonlinear	PROPN
ma-10	340	32	sci	sci	PROPN
ma-10	340	33	.	.	PUNCT
ma-10	340	34	appl	appl	PROPN
ma-10	340	35	.	.	PROPN
ma-10	341	1	9	9	NUM
ma-10	341	2	(	(	PUNCT
ma-10	341	3	2016	2016	NUM
ma-10	341	4	)	)	PUNCT
ma-10	341	5	4478	4478	NUM
ma-10	341	6	-	-	SYM
ma-10	341	7	4488	4488	NUM
ma-10	341	8	.	.	PUNCT
ma-10	342	1	http://doi.org/10.22436/	http://doi.org/10.22436/	PROPN
ma-10	342	2	jnsa.009.06.86.[6	jnsa.009.06.86.[6	PROPN
ma-10	342	3	]	]	PUNCT
ma-10	343	1	s.	s.	PROPN
ma-10	343	2	he	he	PRON
ma-10	343	3	,	,	PUNCT
ma-10	343	4	y.	y.	PROPN
ma-10	343	5	mao	mao	PROPN
ma-10	343	6	,	,	PUNCT
ma-10	343	7	z.	z.	PROPN
ma-10	343	8	zhou	zhou	PROPN
ma-10	343	9	,	,	PUNCT
ma-10	343	10	j.q	j.q	PROPN
ma-10	343	11	.	.	PROPN
ma-10	343	12	zhang	zhang	PROPN
ma-10	343	13	,	,	PUNCT
ma-10	343	14	the	the	DET
ma-10	343	15	generalized	generalized	ADJ
ma-10	343	16	viscosity	viscosity	NOUN
ma-10	343	17	implicit	implicit	ADJ
ma-10	343	18	rules	rule	NOUN
ma-10	343	19	of	of	ADP
ma-10	343	20	asymptotically	asymptotically	ADV
ma-10	343	21	nonexpansive	nonexpansive	ADJ
ma-10	343	22	mappingsin	mappingsin	PROPN
ma-10	343	23	hilbert	hilbert	PROPN
ma-10	343	24	spaces	space	NOUN
ma-10	343	25	,	,	PUNCT
ma-10	343	26	appl	appl	PROPN
ma-10	343	27	.	.	PROPN
ma-10	343	28	math	math	PROPN
ma-10	343	29	.	.	PUNCT
ma-10	344	1	sci	sci	PROPN
ma-10	344	2	.	.	PROPN
ma-10	344	3	11	11	NUM
ma-10	344	4	(	(	PUNCT
ma-10	344	5	12	12	NUM
ma-10	344	6	)	)	PUNCT
ma-10	344	7	(	(	PUNCT
ma-10	344	8	2017	2017	NUM
ma-10	344	9	)	)	PUNCT
ma-10	344	10	549	549	NUM
ma-10	344	11	-	-	SYM
ma-10	344	12	560	560	NUM
ma-10	344	13	.	.	PUNCT
ma-10	345	1	https://doi.org/10.12988/ams.2017.718.[7	https://doi.org/10.12988/ams.2017.718.[7	PROPN
ma-10	345	2	]	]	X
ma-10	345	3	j.t	j.t	PROPN
ma-10	345	4	.	.	PROPN
ma-10	345	5	mendy	mendy	PROPN
ma-10	345	6	,	,	PUNCT
ma-10	345	7	s.	s.	PROPN
ma-10	345	8	rahule	rahule	PROPN
ma-10	345	9	,	,	PUNCT
ma-10	345	10	viscosity	viscosity	NOUN
ma-10	345	11	like	like	ADP
ma-10	345	12	implicit	implicit	ADJ
ma-10	345	13	methods	method	NOUN
ma-10	345	14	for	for	ADP
ma-10	345	15	zeros	zero	NOUN
ma-10	345	16	of	of	ADP
ma-10	345	17	monotone	monotone	ADJ
ma-10	345	18	operators	operator	NOUN
ma-10	345	19	in	in	ADP
ma-10	345	20	banach	banach	NOUN
ma-10	345	21	spaces	space	NOUN
ma-10	345	22	,	,	PUNCT
ma-10	345	23	khayyamj	khayyamj	PROPN
ma-10	345	24	.	.	PUNCT
ma-10	346	1	math	math	NOUN
ma-10	346	2	.	.	PUNCT
ma-10	347	1	2021.[8	2021.[8	NUM
ma-10	347	2	]	]	X
ma-10	347	3	s.f.a	s.f.a	PROPN
ma-10	347	4	.	.	PUNCT
ma-10	347	5	naqvi	naqvi	PROPN
ma-10	347	6	,	,	PUNCT
ma-10	347	7	m.s	m.s	PROPN
ma-10	347	8	.	.	PROPN
ma-10	347	9	khan	khan	PROPN
ma-10	347	10	,	,	PUNCT
ma-10	347	11	on	on	ADP
ma-10	347	12	the	the	DET
ma-10	347	13	viscosity	viscosity	NOUN
ma-10	347	14	rule	rule	NOUN
ma-10	347	15	for	for	ADP
ma-10	347	16	common	common	ADJ
ma-10	347	17	fixed	fix	VERB
ma-10	347	18	points	point	NOUN
ma-10	347	19	of	of	ADP
ma-10	347	20	two	two	NUM
ma-10	347	21	nonexpansive	nonexpansive	ADJ
ma-10	347	22	mappings	mapping	NOUN
ma-10	347	23	in	in	ADP
ma-10	347	24	hilbertspaces	hilbertspace	NOUN
ma-10	347	25	,	,	PUNCT
ma-10	347	26	open	open	ADJ
ma-10	347	27	j.	j.	PROPN
ma-10	347	28	math	math	PROPN
ma-10	347	29	.	.	PUNCT
ma-10	348	1	sci	sci	PROPN
ma-10	348	2	.	.	PROPN
ma-10	348	3	1	1	NUM
ma-10	348	4	(	(	PUNCT
ma-10	348	5	1	1	NUM
ma-10	348	6	)	)	PUNCT
ma-10	348	7	(	(	PUNCT
ma-10	348	8	2017	2017	NUM
ma-10	348	9	)	)	PUNCT
ma-10	348	10	111	111	NUM
ma-10	348	11	-	-	SYM
ma-10	348	12	125	125	NUM
ma-10	348	13	.	.	PUNCT
ma-10	349	1	http://doi.org/10.30538/oms2017.0011.[9	http://doi.org/10.30538/oms2017.0011.[9	PROPN
ma-10	349	2	]	]	X
ma-10	349	3	j.t	j.t	PROPN
ma-10	349	4	.	.	PROPN
ma-10	349	5	mendy	mendy	PROPN
ma-10	349	6	,	,	PUNCT
ma-10	349	7	the	the	DET
ma-10	349	8	viscosity	viscosity	NOUN
ma-10	349	9	iterative	iterative	NOUN
ma-10	349	10	algorithms	algorithm	NOUN
ma-10	349	11	for	for	ADP
ma-10	349	12	the	the	DET
ma-10	349	13	implicit	implicit	ADJ
ma-10	349	14	double	double	ADJ
ma-10	349	15	midpoint	midpoint	NOUN
ma-10	349	16	rule	rule	NOUN
ma-10	349	17	of	of	ADP
ma-10	349	18	nonexpansive	nonexpansive	ADJ
ma-10	349	19	mappings	mapping	NOUN
ma-10	349	20	inhilbert	inhilbert	PROPN
ma-10	349	21	spaces	space	NOUN
ma-10	349	22	,	,	PUNCT
ma-10	349	23	amer	amer	PROPN
ma-10	349	24	.	.	PUNCT
ma-10	350	1	j.	j.	PROPN
ma-10	350	2	math	math	PROPN
ma-10	350	3	.	.	PUNCT
ma-10	351	1	anal	anal	PROPN
ma-10	351	2	.	.	PUNCT
ma-10	352	1	8	8	NUM
ma-10	352	2	(	(	PUNCT
ma-10	352	3	2020	2020	NUM
ma-10	352	4	)	)	PUNCT
ma-10	352	5	,	,	PUNCT
ma-10	352	6	1	1	NUM
ma-10	352	7	-	-	SYM
ma-10	352	8	8.[10	8.[10	NUM
ma-10	352	9	]	]	PUNCT
ma-10	352	10	k.	k.	PROPN
ma-10	352	11	go	go	VERB
ma-10	352	12	eb	eb	PROPN
ma-10	352	13	el	el	PROPN
ma-10	352	14	,	,	PUNCT
ma-10	352	15	w.a	w.a	PROPN
ma-10	352	16	.	.	PROPN
ma-10	352	17	kirk	kirk	PROPN
ma-10	352	18	,	,	PUNCT
ma-10	352	19	topics	topic	NOUN
ma-10	352	20	in	in	ADP
ma-10	352	21	me	i	PRON
ma-10	352	22	tric	tric	ADV
ma-10	352	23	fixed	fix	VERB
ma-10	352	24	point	point	NOUN
ma-10	352	25	theory	theory	NOUN
ma-10	352	26	,	,	PUNCT
ma-10	352	27	cambridge	cambridge	PROPN
ma-10	352	28	studies	study	NOUN
ma-10	352	29	in	in	ADP
ma-10	352	30	advanced	advanced	ADJ
ma-10	352	31	mathematics	mathematic	NOUN
ma-10	352	32	,	,	PUNCT
ma-10	352	33	vol	vol	NOUN
ma-10	352	34	.	.	PUNCT
ma-10	353	1	28.cambridge	28.cambridge	NUM
ma-10	353	2	university	university	NOUN
ma-10	353	3	press	press	NOUN
ma-10	353	4	,	,	PUNCT
ma-10	353	5	cambridge	cambridge	PROPN
ma-10	353	6	(	(	PUNCT
ma-10	353	7	1990).[11	1990).[11	NUM
ma-10	353	8	]	]	X
ma-10	353	9	h.k	h.k	PROPN
ma-10	353	10	.	.	PROPN
ma-10	353	11	xu	xu	PROPN
ma-10	353	12	,	,	PUNCT
ma-10	353	13	iterative	iterative	NOUN
ma-10	353	14	algorithms	algorithm	NOUN
ma-10	353	15	for	for	ADP
ma-10	353	16	nonlinear	nonlinear	ADJ
ma-10	353	17	operators	operator	NOUN
ma-10	353	18	,	,	PUNCT
ma-10	353	19	j.	j.	PROPN
ma-10	353	20	lond	lond	PROPN
ma-10	353	21	.	.	PUNCT
ma-10	354	1	math	math	PROPN
ma-10	354	2	.	.	PUNCT
ma-10	355	1	soc	soc	PROPN
ma-10	355	2	.	.	PUNCT
ma-10	356	1	66	66	NUM
ma-10	356	2	(	(	PUNCT
ma-10	356	3	2	2	NUM
ma-10	356	4	)	)	PUNCT
ma-10	356	5	(	(	PUNCT
ma-10	356	6	2002	2002	NUM
ma-10	356	7	)	)	PUNCT
ma-10	356	8	240	240	NUM
ma-10	356	9	-	-	SYM
ma-10	356	10	256	256	NUM
ma-10	356	11	.	.	PUNCT
ma-10	357	1	https://doi	https://doi	NOUN
ma-10	357	2	.	.	PUNCT
ma-10	357	3	org/10.1112	org/10.1112	PROPN
ma-10	357	4	/	/	SYM
ma-10	357	5	s0024610702003332.[12	s0024610702003332.[12	PROPN
ma-10	357	6	]	]	X
ma-10	357	7	f.e	f.e	PROPN
ma-10	357	8	.	.	PROPN
ma-10	357	9	browder	browder	PROPN
ma-10	357	10	,	,	PUNCT
ma-10	357	11	existence	existence	NOUN
ma-10	357	12	of	of	ADP
ma-10	357	13	periodic	periodic	ADJ
ma-10	357	14	solutions	solution	NOUN
ma-10	357	15	for	for	ADP
ma-10	357	16	nonlinear	nonlinear	ADJ
ma-10	357	17	equations	equation	NOUN
ma-10	357	18	of	of	ADP
ma-10	357	19	evolution	evolution	NOUN
ma-10	357	20	,	,	PUNCT
ma-10	357	21	proc	proc	PROPN
ma-10	357	22	.	.	PUNCT
ma-10	358	1	natl	natl	PROPN
ma-10	358	2	.	.	PUNCT
ma-10	359	1	acad	acad	PROPN
ma-10	359	2	.	.	PUNCT
ma-10	360	1	sci	sci	PROPN
ma-10	360	2	.	.	PROPN
ma-10	360	3	usa	usa	PROPN
ma-10	360	4	53(5	53(5	PROPN
ma-10	360	5	)	)	PUNCT
ma-10	360	6	(	(	PUNCT
ma-10	360	7	1965	1965	NUM
ma-10	360	8	)	)	PUNCT
ma-10	360	9	,	,	PUNCT
ma-10	360	10	1100	1100	NUM
ma-10	360	11	-	-	SYM
ma-10	360	12	1103	1103	NUM
ma-10	360	13	.	.	PUNCT
ma-10	361	1	https://dx.doi.org/10.1073/pnas.53.5.1100.[13	https://dx.doi.org/10.1073/pnas.53.5.1100.[13	NOUN
ma-10	361	2	]	]	PUNCT
ma-10	361	3	s.	s.	PROPN
ma-10	361	4	dhakal	dhakal	PROPN
ma-10	361	5	,	,	PUNCT
ma-10	361	6	w.	w.	PROPN
ma-10	361	7	sintunavarat	sintunavarat	PROPN
ma-10	361	8	,	,	PUNCT
ma-10	361	9	the	the	DET
ma-10	361	10	viscosity	viscosity	NOUN
ma-10	361	11	implicit	implicit	ADJ
ma-10	361	12	midpoint	midpoint	NOUN
ma-10	361	13	rule	rule	NOUN
ma-10	361	14	for	for	ADP
ma-10	361	15	finding	find	VERB
ma-10	361	16	common	common	ADJ
ma-10	361	17	fixed	fix	VERB
ma-10	361	18	points	point	NOUN
ma-10	361	19	of	of	ADP
ma-10	361	20	two	two	NUM
ma-10	361	21	asymptoticallynonexpansive	asymptoticallynonexpansive	ADJ
ma-10	361	22	mappings	mapping	NOUN
ma-10	361	23	with	with	ADP
ma-10	361	24	applications	application	NOUN
ma-10	361	25	,	,	PUNCT
ma-10	361	26	thai	thai	PROPN
ma-10	361	27	j.	j.	PROPN
ma-10	361	28	math	math	PROPN
ma-10	361	29	.	.	PUNCT
ma-10	362	1	17	17	NUM
ma-10	362	2	(	(	PUNCT
ma-10	362	3	2019	2019	NUM
ma-10	362	4	)	)	PUNCT
ma-10	362	5	495	495	NUM
ma-10	362	6	-	-	SYM
ma-10	362	7	514.[14	514.[14	PROPN
ma-10	362	8	]	]	PUNCT
ma-10	362	9	s.	s.	PROPN
ma-10	362	10	he	he	PRON
ma-10	362	11	,	,	PUNCT
ma-10	362	12	y.	y.	PROPN
ma-10	362	13	mao	mao	PROPN
ma-10	362	14	,	,	PUNCT
ma-10	362	15	z.	z.	PROPN
ma-10	362	16	zhou	zhou	PROPN
ma-10	362	17	,	,	PUNCT
ma-10	362	18	j.q	j.q	PROPN
ma-10	362	19	.	.	PROPN
ma-10	362	20	zhang	zhang	PROPN
ma-10	362	21	,	,	PUNCT
ma-10	362	22	the	the	DET
ma-10	362	23	generalized	generalized	ADJ
ma-10	362	24	viscosity	viscosity	NOUN
ma-10	362	25	implicit	implicit	ADJ
ma-10	362	26	rules	rule	NOUN
ma-10	362	27	of	of	ADP
ma-10	362	28	asymptotically	asymptotically	ADV
ma-10	362	29	nonexpansivemappings	nonexpansivemapping	NOUN
ma-10	362	30	in	in	ADP
ma-10	362	31	hilbert	hilbert	PROPN
ma-10	362	32	spaces	space	NOUN
ma-10	362	33	,	,	PUNCT
ma-10	362	34	appl	appl	PROPN
ma-10	362	35	.	.	PROPN
ma-10	362	36	math	math	PROPN
ma-10	362	37	.	.	PUNCT
ma-10	363	1	sci	sci	PROPN
ma-10	363	2	.	.	PROPN
ma-10	363	3	11	11	NUM
ma-10	363	4	(	(	PUNCT
ma-10	363	5	2017	2017	NUM
ma-10	363	6	)	)	PUNCT
ma-10	363	7	,	,	PUNCT
ma-10	363	8	549	549	NUM
ma-10	363	9	-	-	SYM
ma-10	363	10	560	560	NUM
ma-10	363	11	.	.	PUNCT
ma-10	364	1	https://doi.org/10.12988/ams.2017.718	https://doi.org/10.12988/ams.2017.718	PROPN
ma-10	364	2	.	.	PUNCT
ma-10	365	1	https://doi.org/10.1186/s13663-015-0439-6	https://doi.org/10.1186/s13663-015-0439-6	NUM
ma-10	365	2	http://doi.org/10.22436/jnsa.009.06.86	http://doi.org/10.22436/jnsa.009.06.86	NUM
ma-10	365	3	http://doi.org/10.22436/jnsa.009.06.86	http://doi.org/10.22436/jnsa.009.06.86	PROPN
ma-10	365	4	https://doi.org/10.12988/ams.2017.718	https://doi.org/10.12988/ams.2017.718	PROPN
ma-10	365	5	http://doi.org/10.30538/oms2017.0011	http://doi.org/10.30538/oms2017.0011	NUM
ma-10	365	6	https://doi.org/10.1112/s0024610702003332	https://doi.org/10.1112/s0024610702003332	PROPN
ma-10	365	7	https://doi.org/10.1112/s0024610702003332	https://doi.org/10.1112/s0024610702003332	PROPN
ma-10	365	8	https://dx.doi.org/10.1073/pnas.53.5.1100	https://dx.doi.org/10.1073/pnas.53.5.1100	PROPN
ma-10	365	9	https://doi.org/10.12988/ams.2017.718	https://doi.org/10.12988/ams.2017.718	PROPN
ma-10	365	10	1	1	NUM
ma-10	365	11	.	.	PUNCT
ma-10	365	12	background	background	NOUN
ma-10	365	13	2	2	NUM
ma-10	365	14	.	.	PUNCT
ma-10	365	15	preliminaries	preliminary	NOUN
ma-10	365	16	3	3	NUM
ma-10	365	17	.	.	X
ma-10	365	18	main	main	ADJ
ma-10	365	19	result	result	NOUN
ma-10	365	20	4	4	NUM
ma-10	365	21	.	.	X
ma-10	365	22	application	application	NOUN
ma-10	365	23	to	to	PART
ma-10	365	24	convex	convex	VERB
ma-10	365	25	minimization	minimization	NOUN
ma-10	365	26	problems	problem	NOUN
ma-10	365	27	references	reference	NOUN